LMFDB - Embedded newform 93.2.e.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(25,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("93.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	93.25
Dual form			93.2.e.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(0.500000 + 0.866025i) q^{3} +(0.292893 - 0.507306i) q^{5} +(0.707107 + 1.22474i) q^{6} +(-0.414214 - 0.717439i) q^{7} -2.82843 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(0.500000 + 0.866025i) q^{3} +(0.292893 - 0.507306i) q^{5} +(0.707107 + 1.22474i) q^{6} +(-0.414214 - 0.717439i) q^{7} -2.82843 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{10} +(0.707107 - 1.22474i) q^{11} +(-0.914214 + 1.58346i) q^{13} +(-0.585786 - 1.01461i) q^{14} +0.585786 q^{15} -4.00000 q^{16} +(-3.41421 - 5.91359i) q^{17} +(-0.707107 + 1.22474i) q^{18} +(1.91421 + 3.31552i) q^{19} +(0.414214 - 0.717439i) q^{21} +(1.00000 - 1.73205i) q^{22} +3.65685 q^{23} +(-1.41421 - 2.44949i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-1.29289 + 2.23936i) q^{26} -1.00000 q^{27} -3.41421 q^{29} +0.828427 q^{30} +(2.00000 + 5.19615i) q^{31} +1.41421 q^{33} +(-4.82843 - 8.36308i) q^{34} -0.485281 q^{35} +(-0.500000 - 0.866025i) q^{37} +(2.70711 + 4.68885i) q^{38} -1.82843 q^{39} +(-0.828427 + 1.43488i) q^{40} +(2.12132 - 3.67423i) q^{41} +(0.585786 - 1.01461i) q^{42} +(2.74264 + 4.75039i) q^{43} +(0.292893 + 0.507306i) q^{45} +5.17157 q^{46} +0.585786 q^{47} +(-2.00000 - 3.46410i) q^{48} +(3.15685 - 5.46783i) q^{49} +(3.29289 + 5.70346i) q^{50} +(3.41421 - 5.91359i) q^{51} +(0.707107 - 1.22474i) q^{53} -1.41421 q^{54} +(-0.414214 - 0.717439i) q^{55} +(1.17157 + 2.02922i) q^{56} +(-1.91421 + 3.31552i) q^{57} -4.82843 q^{58} +(4.24264 + 7.34847i) q^{59} -12.4853 q^{61} +(2.82843 + 7.34847i) q^{62} +0.828427 q^{63} +8.00000 q^{64} +(0.535534 + 0.927572i) q^{65} +2.00000 q^{66} +(7.24264 - 12.5446i) q^{67} +(1.82843 + 3.16693i) q^{69} -0.686292 q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.41421 - 2.44949i) q^{72} +(-1.91421 + 3.31552i) q^{73} +(-0.707107 - 1.22474i) q^{74} +(-2.32843 + 4.03295i) q^{75} -1.17157 q^{77} -2.58579 q^{78} +(-7.82843 - 13.5592i) q^{79} +(-1.17157 + 2.02922i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(3.87868 + 6.71807i) q^{86} +(-1.70711 - 2.95680i) q^{87} +(-2.00000 + 3.46410i) q^{88} -17.8995 q^{89} +(0.414214 + 0.717439i) q^{90} +1.51472 q^{91} +(-3.50000 + 4.33013i) q^{93} +0.828427 q^{94} +2.24264 q^{95} -11.4853 q^{97} +(4.46447 - 7.73268i) q^{98} +(0.707107 + 1.22474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 + 4 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} - 2 q^{9} - 4 q^{10} + 2 q^{13} - 8 q^{14} + 8 q^{15} - 16 q^{16} - 8 q^{17} + 2 q^{19} - 4 q^{21} + 4 q^{22} - 8 q^{23} - 2 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} - 8 q^{30} + 8 q^{31} - 8 q^{34} + 32 q^{35} - 2 q^{37} + 8 q^{38} + 4 q^{39} + 8 q^{40} + 8 q^{42} - 6 q^{43} + 4 q^{45} + 32 q^{46} + 8 q^{47} - 8 q^{48} - 10 q^{49} + 16 q^{50} + 8 q^{51} + 4 q^{55} + 16 q^{56} - 2 q^{57} - 8 q^{58} - 16 q^{61} - 8 q^{63} + 32 q^{64} - 12 q^{65} + 8 q^{66} + 12 q^{67} - 4 q^{69} - 48 q^{70} - 12 q^{71} - 2 q^{73} + 2 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} - 16 q^{80} - 2 q^{81} + 12 q^{82} + 12 q^{83} - 16 q^{85} + 24 q^{86} - 4 q^{87} - 8 q^{88} - 32 q^{89} - 4 q^{90} + 40 q^{91} - 14 q^{93} - 8 q^{94} - 8 q^{95} - 12 q^{97} + 32 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 + 4 * q^7 - 2 * q^9 - 4 * q^10 + 2 * q^13 - 8 * q^14 + 8 * q^15 - 16 * q^16 - 8 * q^17 + 2 * q^19 - 4 * q^21 + 4 * q^22 - 8 * q^23 - 2 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 - 8 * q^30 + 8 * q^31 - 8 * q^34 + 32 * q^35 - 2 * q^37 + 8 * q^38 + 4 * q^39 + 8 * q^40 + 8 * q^42 - 6 * q^43 + 4 * q^45 + 32 * q^46 + 8 * q^47 - 8 * q^48 - 10 * q^49 + 16 * q^50 + 8 * q^51 + 4 * q^55 + 16 * q^56 - 2 * q^57 - 8 * q^58 - 16 * q^61 - 8 * q^63 + 32 * q^64 - 12 * q^65 + 8 * q^66 + 12 * q^67 - 4 * q^69 - 48 * q^70 - 12 * q^71 - 2 * q^73 + 2 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 - 16 * q^80 - 2 * q^81 + 12 * q^82 + 12 * q^83 - 16 * q^85 + 24 * q^86 - 4 * q^87 - 8 * q^88 - 32 * q^89 - 4 * q^90 + 40 * q^91 - 14 * q^93 - 8 * q^94 - 8 * q^95 - 12 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.41421			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.41421			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	−0.793071	−	0.609129i	$-0.791519\pi$
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	0.924057	+	0.382255i	$0.124852\pi$
$6$	0.707107	+	1.22474i	0.288675	+	0.500000i
$7$	−0.414214	−	0.717439i	−0.156558	−	0.271166i	0.777067	−	0.629418i	$-0.216706\pi$
$7$	−0.414214	−	0.717439i	−0.156558	−	0.271166i	−0.933625	+	0.358251i	$0.883373\pi$
$8$	−2.82843			−1.00000
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.414214	−	0.717439i	0.130986	−	0.226874i
$11$	0.707107	−	1.22474i	0.213201	−	0.369274i	−0.739514	−	0.673141i	$-0.764945\pi$
$11$	0.707107	−	1.22474i	0.213201	−	0.369274i	0.952714	+	0.303867i	$0.0982778\pi$
$12$		0			0
$13$	−0.914214	+	1.58346i	−0.253557	+	0.439174i	−0.964503	−	0.264073i	$-0.914934\pi$
$13$	−0.914214	+	1.58346i	−0.253557	+	0.439174i	0.710945	+	0.703247i	$0.248267\pi$
$14$	−0.585786	−	1.01461i	−0.156558	−	0.271166i
$15$	0.585786			0.151249
$16$	−4.00000			−1.00000
$17$	−3.41421	−	5.91359i	−0.828068	−	1.43426i	−0.899551	−	0.436815i	$-0.856107\pi$
$17$	−3.41421	−	5.91359i	−0.828068	−	1.43426i	0.0714831	−	0.997442i	$-0.477227\pi$
$18$	−0.707107	+	1.22474i	−0.166667	+	0.288675i
$19$	1.91421	+	3.31552i	0.439151	+	0.760631i	0.997624	−	0.0688910i	$-0.0219461\pi$
$19$	1.91421	+	3.31552i	0.439151	+	0.760631i	−0.558473	+	0.829522i	$0.688613\pi$
$20$		0			0
$21$	0.414214	−	0.717439i	0.0903888	−	0.156558i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	3.65685			0.762507			0.381253	−	0.924471i	$-0.375493\pi$
$23$	3.65685			0.762507			0.381253	+	0.924471i	$0.375493\pi$
$24$	−1.41421	−	2.44949i	−0.288675	−	0.500000i
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$	−1.29289	+	2.23936i	−0.253557	+	0.439174i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.41421			−0.634004			−0.317002	−	0.948425i	$-0.602676\pi$
$29$	−3.41421			−0.634004			−0.317002	+	0.948425i	$0.602676\pi$
$30$	0.828427			0.151249
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$32$		0			0
$33$	1.41421			0.246183
$34$	−4.82843	−	8.36308i	−0.828068	−	1.43426i
$35$	−0.485281			−0.0820275
$36$		0			0
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	2.70711	+	4.68885i	0.439151	+	0.760631i
$39$	−1.82843			−0.292783
$40$	−0.828427	+	1.43488i	−0.130986	+	0.226874i
$41$	2.12132	−	3.67423i	0.331295	−	0.573819i	−0.651471	−	0.758673i	$-0.725848\pi$
$41$	2.12132	−	3.67423i	0.331295	−	0.573819i	0.982766	+	0.184854i	$0.0591813\pi$
$42$	0.585786	−	1.01461i	0.0903888	−	0.156558i
$43$	2.74264	+	4.75039i	0.418249	+	0.724428i	0.995763	−	0.0919522i	$-0.0293107\pi$
$43$	2.74264	+	4.75039i	0.418249	+	0.724428i	−0.577515	+	0.816380i	$0.695977\pi$
$44$		0			0
$45$	0.292893	+	0.507306i	0.0436619	+	0.0756247i
$46$	5.17157			0.762507
$47$	0.585786			0.0854457			0.0427229	−	0.999087i	$-0.486397\pi$
$47$	0.585786			0.0854457			0.0427229	+	0.999087i	$0.486397\pi$
$48$	−2.00000	−	3.46410i	−0.288675	−	0.500000i
$49$	3.15685	−	5.46783i	0.450979	−	0.781119i
$50$	3.29289	+	5.70346i	0.465685	+	0.806591i
$51$	3.41421	−	5.91359i	0.478086	−	0.828068i
$52$		0			0
$53$	0.707107	−	1.22474i	0.0971286	−	0.168232i	−0.813366	−	0.581752i	$-0.802368\pi$
$53$	0.707107	−	1.22474i	0.0971286	−	0.168232i	0.910495	+	0.413520i	$0.135701\pi$
$54$	−1.41421			−0.192450
$55$	−0.414214	−	0.717439i	−0.0558525	−	0.0967394i
$56$	1.17157	+	2.02922i	0.156558	+	0.271166i
$57$	−1.91421	+	3.31552i	−0.253544	+	0.439151i
$58$	−4.82843			−0.634004
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	0.998105	+	0.0615367i	$0.0196001\pi$
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	−0.445760	+	0.895152i	$0.647067\pi$
$60$		0			0
$61$	−12.4853			−1.59858			−0.799288	−	0.600948i	$-0.794790\pi$
$61$	−12.4853			−1.59858			−0.799288	+	0.600948i	$0.794790\pi$
$62$	2.82843	+	7.34847i	0.359211	+	0.933257i
$63$	0.828427			0.104372
$64$	8.00000			1.00000
$65$	0.535534	+	0.927572i	0.0664248	+	0.115051i
$66$	2.00000			0.246183
$67$	7.24264	−	12.5446i	0.884829	−	1.53257i	0.0389203	−	0.999242i	$-0.487608\pi$
$67$	7.24264	−	12.5446i	0.884829	−	1.53257i	0.845909	−	0.533327i	$-0.179059\pi$
$68$		0			0
$69$	1.82843	+	3.16693i	0.220117	+	0.381253i
$70$	−0.686292			−0.0820275
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	1.41421	−	2.44949i	0.166667	−	0.288675i
$73$	−1.91421	+	3.31552i	−0.224042	+	0.388052i	−0.956032	−	0.293264i	$-0.905259\pi$
$73$	−1.91421	+	3.31552i	−0.224042	+	0.388052i	0.731990	+	0.681316i	$0.238592\pi$
$74$	−0.707107	−	1.22474i	−0.0821995	−	0.142374i
$75$	−2.32843	+	4.03295i	−0.268864	+	0.465685i
$76$		0			0
$77$	−1.17157			−0.133513
$78$	−2.58579			−0.292783
$79$	−7.82843	−	13.5592i	−0.880767	−	1.52553i	−0.850490	−	0.525991i	$-0.823694\pi$
$79$	−7.82843	−	13.5592i	−0.880767	−	1.52553i	−0.0302770	−	0.999542i	$-0.509639\pi$
$80$	−1.17157	+	2.02922i	−0.130986	+	0.226874i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	3.70711	−	6.42090i	0.406908	−	0.704785i	−0.587634	−	0.809127i	$-0.699940\pi$
$83$	3.70711	−	6.42090i	0.406908	−	0.704785i	0.994541	+	0.104342i	$0.0332737\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	3.87868	+	6.71807i	0.418249	+	0.724428i
$87$	−1.70711	−	2.95680i	−0.183021	−	0.317002i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−17.8995			−1.89734			−0.948671	−	0.316264i	$-0.897572\pi$
$89$	−17.8995			−1.89734			−0.948671	+	0.316264i	$0.897572\pi$
$90$	0.414214	+	0.717439i	0.0436619	+	0.0756247i
$91$	1.51472			0.158786
$92$		0			0
$93$	−3.50000	+	4.33013i	−0.362933	+	0.449013i
$94$	0.828427			0.0854457
$95$	2.24264			0.230090
$96$		0			0
$97$	−11.4853			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$97$	−11.4853			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$98$	4.46447	−	7.73268i	0.450979	−	0.781119i
$99$	0.707107	+	1.22474i	0.0710669	+	0.123091i
$100$		0			0
$101$	−15.4142			−1.53377			−0.766886	−	0.641784i	$-0.778195\pi$
$101$	−15.4142			−1.53377			−0.766886	+	0.641784i	$0.778195\pi$
$102$	4.82843	−	8.36308i	0.478086	−	0.828068i
$103$	−8.15685	+	14.1281i	−0.803719	+	1.39208i	0.113434	+	0.993546i	$0.463815\pi$
$103$	−8.15685	+	14.1281i	−0.803719	+	1.39208i	−0.917153	+	0.398536i	$0.869518\pi$
$104$	2.58579	−	4.47871i	0.253557	−	0.439174i
$105$	−0.242641	−	0.420266i	−0.0236793	−	0.0410138i
$106$	1.00000	−	1.73205i	0.0971286	−	0.168232i
$107$	−1.94975	−	3.37706i	−0.188489	−	0.326473i	0.756258	−	0.654274i	$-0.227026\pi$
$107$	−1.94975	−	3.37706i	−0.188489	−	0.326473i	−0.944747	+	0.327801i	$0.893692\pi$
$108$		0			0
$109$	9.48528			0.908525			0.454263	−	0.890868i	$-0.349903\pi$
$109$	9.48528			0.908525			0.454263	+	0.890868i	$0.349903\pi$
$110$	−0.585786	−	1.01461i	−0.0558525	−	0.0967394i
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$	1.65685	+	2.86976i	0.156558	+	0.271166i
$113$	7.82843	−	13.5592i	0.736436	−	1.27555i	−0.217654	−	0.976026i	$-0.569840\pi$
$113$	7.82843	−	13.5592i	0.736436	−	1.27555i	0.954090	−	0.299519i	$-0.0968263\pi$
$114$	−2.70711	+	4.68885i	−0.253544	+	0.439151i
$115$	1.07107	−	1.85514i	0.0998776	−	0.172993i
$116$		0			0
$117$	−0.914214	−	1.58346i	−0.0845191	−	0.146391i
$118$	6.00000	+	10.3923i	0.552345	+	0.956689i
$119$	−2.82843	+	4.89898i	−0.259281	+	0.449089i
$120$	−1.65685			−0.151249
$121$	4.50000	+	7.79423i	0.409091	+	0.708566i
$122$	−17.6569			−1.59858
$123$	4.24264			0.382546
$124$		0			0
$125$	5.65685			0.505964
$126$	1.17157			0.104372
$127$	−2.67157	−	4.62730i	−0.237064	−	0.410606i	0.722807	−	0.691050i	$-0.242852\pi$
$127$	−2.67157	−	4.62730i	−0.237064	−	0.410606i	−0.959870	+	0.280444i	$0.909518\pi$
$128$	11.3137			1.00000
$129$	−2.74264	+	4.75039i	−0.241476	+	0.418249i
$130$	0.757359	+	1.31178i	0.0664248	+	0.115051i
$131$	8.12132	+	14.0665i	0.709563	+	1.22900i	0.965019	+	0.262179i	$0.0844410\pi$
$131$	8.12132	+	14.0665i	0.709563	+	1.22900i	−0.255456	+	0.966821i	$0.582226\pi$
$132$		0			0
$133$	1.58579	−	2.74666i	0.137505	−	0.238166i
$134$	10.2426	−	17.7408i	0.884829	−	1.53257i
$135$	−0.292893	+	0.507306i	−0.0252082	+	0.0436619i
$136$	9.65685	+	16.7262i	0.828068	+	1.43426i
$137$	7.70711	−	13.3491i	0.658463	−	1.14049i	−0.322551	−	0.946552i	$-0.604540\pi$
$137$	7.70711	−	13.3491i	0.658463	−	1.14049i	0.981014	−	0.193939i	$-0.0621262\pi$
$138$	2.58579	+	4.47871i	0.220117	+	0.381253i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	0.292893	+	0.507306i	0.0246661	+	0.0427229i
$142$	−4.24264	+	7.34847i	−0.356034	+	0.616670i
$143$	1.29289	+	2.23936i	0.108117	+	0.187264i
$144$	2.00000	−	3.46410i	0.166667	−	0.288675i
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$	−2.70711	+	4.68885i	−0.224042	+	0.388052i
$147$	6.31371			0.520746
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	−3.29289	+	5.70346i	−0.268864	+	0.465685i
$151$	6.31371			0.513802			0.256901	−	0.966438i	$-0.417299\pi$
$151$	6.31371			0.513802			0.256901	+	0.966438i	$0.417299\pi$
$152$	−5.41421	−	9.37769i	−0.439151	−	0.760631i
$153$	6.82843			0.552046
$154$	−1.65685			−0.133513
$155$	3.22183	+	0.507306i	0.258783	+	0.0407478i
$156$		0			0
$157$	7.82843			0.624777			0.312388	−	0.949955i	$-0.398871\pi$
$157$	7.82843			0.624777			0.312388	+	0.949955i	$0.398871\pi$
$158$	−11.0711	−	19.1757i	−0.880767	−	1.52553i
$159$	1.41421			0.112154
$160$		0			0
$161$	−1.51472	−	2.62357i	−0.119377	−	0.206766i
$162$	−0.707107	−	1.22474i	−0.0555556	−	0.0962250i
$163$	−4.65685			−0.364753			−0.182376	−	0.983229i	$-0.558379\pi$
$163$	−4.65685			−0.364753			−0.182376	+	0.983229i	$0.558379\pi$
$164$		0			0
$165$	0.414214	−	0.717439i	0.0322465	−	0.0558525i
$166$	5.24264	−	9.08052i	0.406908	−	0.704785i
$167$	−5.94975	−	10.3053i	−0.460405	−	0.797445i	0.538576	−	0.842577i	$-0.318963\pi$
$167$	−5.94975	−	10.3053i	−0.460405	−	0.797445i	−0.998981	+	0.0451317i	$0.985629\pi$
$168$	−1.17157	+	2.02922i	−0.0903888	+	0.156558i
$169$	4.82843	+	8.36308i	0.371417	+	0.643314i
$170$	−5.65685			−0.433861
$171$	−3.82843			−0.292767
$172$		0			0
$173$	−4.65685	+	8.06591i	−0.354054	+	0.613240i	−0.986956	−	0.160993i	$-0.948530\pi$
$173$	−4.65685	+	8.06591i	−0.354054	+	0.613240i	0.632902	+	0.774232i	$0.281864\pi$
$174$	−2.41421	−	4.18154i	−0.183021	−	0.317002i
$175$	1.92893	−	3.34101i	0.145814	−	0.252557i
$176$	−2.82843	+	4.89898i	−0.213201	+	0.369274i
$177$	−4.24264	+	7.34847i	−0.318896	+	0.552345i
$178$	−25.3137			−1.89734
$179$	6.87868	+	11.9142i	0.514137	+	0.890511i	0.999865	+	0.0164013i	$0.00522092\pi$
$179$	6.87868	+	11.9142i	0.514137	+	0.890511i	−0.485729	+	0.874110i	$0.661446\pi$
$180$		0			0
$181$	−0.257359	+	0.445759i	−0.0191294	+	0.0331330i	−0.875432	−	0.483342i	$-0.839423\pi$
$181$	−0.257359	+	0.445759i	−0.0191294	+	0.0331330i	0.856302	+	0.516475i	$0.172756\pi$
$182$	2.14214			0.158786
$183$	−6.24264	−	10.8126i	−0.461469	−	0.799288i
$184$	−10.3431			−0.762507
$185$	−0.585786			−0.0430679
$186$	−4.94975	+	6.12372i	−0.362933	+	0.449013i
$187$	−9.65685			−0.706179
$188$		0			0
$189$	0.414214	+	0.717439i	0.0301296	+	0.0521860i
$190$	3.17157			0.230090
$191$	1.53553	−	2.65962i	0.111107	−	0.192444i	−0.805110	−	0.593126i	$-0.797894\pi$
$191$	1.53553	−	2.65962i	0.111107	−	0.192444i	0.916217	+	0.400682i	$0.131227\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	−6.98528	−	12.0989i	−0.502812	−	0.870895i	−0.999995	−	0.00324955i	$-0.998966\pi$
$193$	−6.98528	−	12.0989i	−0.502812	−	0.870895i	0.497183	−	0.867646i	$-0.334368\pi$
$194$	−16.2426			−1.16615
$195$	−0.535534	+	0.927572i	−0.0383504	+	0.0664248i
$196$		0			0
$197$	−1.41421	+	2.44949i	−0.100759	+	0.174519i	−0.911997	−	0.410196i	$-0.865460\pi$
$197$	−1.41421	+	2.44949i	−0.100759	+	0.174519i	0.811239	+	0.584715i	$0.198794\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	6.07107	−	10.5154i	0.430367	−	0.745417i	−0.566538	−	0.824035i	$-0.691718\pi$
$199$	6.07107	−	10.5154i	0.430367	−	0.745417i	0.996905	+	0.0786187i	$0.0250510\pi$
$200$	−6.58579	−	11.4069i	−0.465685	−	0.806591i
$201$	14.4853			1.02171
$202$	−21.7990			−1.53377
$203$	1.41421	+	2.44949i	0.0992583	+	0.171920i
$204$		0			0
$205$	−1.24264	−	2.15232i	−0.0867898	−	0.150324i
$206$	−11.5355	+	19.9801i	−0.803719	+	1.39208i
$207$	−1.82843	+	3.16693i	−0.127084	+	0.220117i
$208$	3.65685	−	6.33386i	0.253557	−	0.439174i
$209$	5.41421			0.374509
$210$	−0.343146	−	0.594346i	−0.0236793	−	0.0410138i
$211$	2.74264	+	4.75039i	0.188811	+	0.327031i	0.944854	−	0.327491i	$-0.106203\pi$
$211$	2.74264	+	4.75039i	0.188811	+	0.327031i	−0.756043	+	0.654522i	$0.772870\pi$
$212$		0			0
$213$	−6.00000			−0.411113
$214$	−2.75736	−	4.77589i	−0.188489	−	0.326473i
$215$	3.21320			0.219139
$216$	2.82843			0.192450
$217$	2.89949	−	3.58719i	0.196831	−	0.243515i
$218$	13.4142			0.908525
$219$	−3.82843			−0.258701
$220$		0			0
$221$	12.4853			0.839851
$222$	0.707107	−	1.22474i	0.0474579	−	0.0821995i
$223$	−8.32843	−	14.4253i	−0.557713	−	0.965987i	−0.997687	−	0.0679764i	$-0.978346\pi$
$223$	−8.32843	−	14.4253i	−0.557713	−	0.965987i	0.439974	−	0.898010i	$-0.354988\pi$
$224$		0			0
$225$	−4.65685			−0.310457
$226$	11.0711	−	19.1757i	0.736436	−	1.27555i
$227$	−5.41421	+	9.37769i	−0.359354	+	0.622419i	−0.987853	−	0.155391i	$-0.950336\pi$
$227$	−5.41421	+	9.37769i	−0.359354	+	0.622419i	0.628499	+	0.777810i	$0.283670\pi$
$228$		0			0
$229$	5.74264	+	9.94655i	0.379484	+	0.657286i	0.990987	−	0.133956i	$-0.0427681\pi$
$229$	5.74264	+	9.94655i	0.379484	+	0.657286i	−0.611503	+	0.791242i	$0.709435\pi$
$230$	1.51472	−	2.62357i	0.0998776	−	0.172993i
$231$	−0.585786	−	1.01461i	−0.0385419	−	0.0667566i
$232$	9.65685			0.634004
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−1.29289	−	2.23936i	−0.0845191	−	0.146391i
$235$	0.171573	−	0.297173i	0.0111922	−	0.0193854i
$236$		0			0
$237$	7.82843	−	13.5592i	0.508511	−	0.880767i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$	−12.8995	+	22.3426i	−0.834399	+	1.44522i	0.0601199	+	0.998191i	$0.480852\pi$
$239$	−12.8995	+	22.3426i	−0.834399	+	1.44522i	−0.894519	+	0.447030i	$0.852482\pi$
$240$	−2.34315			−0.151249
$241$	2.98528	+	5.17066i	0.192299	+	0.333071i	0.946012	−	0.324132i	$-0.105072\pi$
$241$	2.98528	+	5.17066i	0.192299	+	0.333071i	−0.753713	+	0.657204i	$0.771739\pi$
$242$	6.36396	+	11.0227i	0.409091	+	0.708566i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.84924	−	3.20298i	−0.118144	−	0.204631i
$246$	6.00000			0.382546
$247$	−7.00000			−0.445399
$248$	−5.65685	−	14.6969i	−0.359211	−	0.933257i
$249$	7.41421			0.469857
$250$	8.00000			0.505964
$251$	12.5355	+	21.7122i	0.791236	+	1.37046i	0.925202	+	0.379475i	$0.123895\pi$
$251$	12.5355	+	21.7122i	0.791236	+	1.37046i	−0.133966	+	0.990986i	$0.542771\pi$
$252$		0			0
$253$	2.58579	−	4.47871i	0.162567	−	0.281574i
$254$	−3.77817	−	6.54399i	−0.237064	−	0.410606i
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$		0			0
$257$	−5.12132	+	8.87039i	−0.319459	+	0.553320i	−0.980375	−	0.197140i	$-0.936835\pi$
$257$	−5.12132	+	8.87039i	−0.319459	+	0.553320i	0.660916	+	0.750460i	$0.270168\pi$
$258$	−3.87868	+	6.71807i	−0.241476	+	0.418249i
$259$	−0.414214	+	0.717439i	−0.0257380	+	0.0445795i
$260$		0			0
$261$	1.70711	−	2.95680i	0.105667	−	0.183021i
$262$	11.4853	+	19.8931i	0.709563	+	1.22900i
$263$	−12.8284			−0.791035			−0.395517	−	0.918459i	$-0.629435\pi$
$263$	−12.8284			−0.791035			−0.395517	+	0.918459i	$0.629435\pi$
$264$	−4.00000			−0.246183
$265$	−0.414214	−	0.717439i	−0.0254449	−	0.0440719i
$266$	2.24264	−	3.88437i	0.137505	−	0.238166i
$267$	−8.94975	−	15.5014i	−0.547716	−	0.948671i
$268$		0			0
$269$	9.89949	−	17.1464i	0.603583	−	1.04544i	−0.388691	−	0.921368i	$-0.627073\pi$
$269$	9.89949	−	17.1464i	0.603583	−	1.04544i	0.992274	−	0.124068i	$-0.0395941\pi$
$270$	−0.414214	+	0.717439i	−0.0252082	+	0.0436619i
$271$	−28.4558			−1.72857			−0.864285	−	0.503003i	$-0.832228\pi$
$271$	−28.4558			−1.72857			−0.864285	+	0.503003i	$0.832228\pi$
$272$	13.6569	+	23.6544i	0.828068	+	1.43426i
$273$	0.757359	+	1.31178i	0.0458375	+	0.0793928i
$274$	10.8995	−	18.8785i	0.658463	−	1.14049i
$275$	6.58579			0.397138
$276$		0			0
$277$	11.3431			0.681544			0.340772	−	0.940146i	$-0.389312\pi$
$277$	11.3431			0.681544			0.340772	+	0.940146i	$0.389312\pi$
$278$	19.7990			1.18746
$279$	−5.50000	−	0.866025i	−0.329276	−	0.0518476i
$280$	1.37258			0.0820275
$281$	−20.0416			−1.19558			−0.597792	−	0.801651i	$-0.703955\pi$
$281$	−20.0416			−1.19558			−0.597792	+	0.801651i	$0.703955\pi$
$282$	0.414214	+	0.717439i	0.0246661	+	0.0427229i
$283$	15.4853			0.920504			0.460252	−	0.887788i	$-0.347759\pi$
$283$	15.4853			0.920504			0.460252	+	0.887788i	$0.347759\pi$
$284$		0			0
$285$	1.12132	+	1.94218i	0.0664213	+	0.115045i
$286$	1.82843	+	3.16693i	0.108117	+	0.187264i
$287$	−3.51472			−0.207467
$288$		0			0
$289$	−14.8137	+	25.6581i	−0.871395	+	1.50930i
$290$	−1.41421	+	2.44949i	−0.0830455	+	0.143839i
$291$	−5.74264	−	9.94655i	−0.336640	−	0.583077i
$292$		0			0
$293$	−6.41421	−	11.1097i	−0.374722	−	0.649038i	0.615563	−	0.788088i	$-0.288929\pi$
$293$	−6.41421	−	11.1097i	−0.374722	−	0.649038i	−0.990285	+	0.139049i	$0.955595\pi$
$294$	8.92893			0.520746
$295$	4.97056			0.289397
$296$	1.41421	+	2.44949i	0.0821995	+	0.142374i
$297$	−0.707107	+	1.22474i	−0.0410305	+	0.0710669i
$298$	4.24264	+	7.34847i	0.245770	+	0.425685i
$299$	−3.34315	+	5.79050i	−0.193339	+	0.334873i
$300$		0			0
$301$	2.27208	−	3.93535i	0.130960	−	0.226830i
$302$	8.92893			0.513802
$303$	−7.70711	−	13.3491i	−0.442762	−	0.766886i
$304$	−7.65685	−	13.2621i	−0.439151	−	0.760631i
$305$	−3.65685	+	6.33386i	−0.209391	+	0.362676i
$306$	9.65685			0.552046
$307$	−3.84315	−	6.65652i	−0.219340	−	0.379908i	0.735266	−	0.677778i	$-0.237057\pi$
$307$	−3.84315	−	6.65652i	−0.219340	−	0.379908i	−0.954606	+	0.297870i	$0.903724\pi$
$308$		0			0
$309$	−16.3137			−0.928054
$310$	4.55635	+	0.717439i	0.258783	+	0.0407478i
$311$	−19.8995			−1.12840			−0.564198	−	0.825639i	$-0.690815\pi$
$311$	−19.8995			−1.12840			−0.564198	+	0.825639i	$0.690815\pi$
$312$	5.17157			0.292783
$313$	2.84315	+	4.92447i	0.160704	+	0.278348i	0.935121	−	0.354327i	$-0.115290\pi$
$313$	2.84315	+	4.92447i	0.160704	+	0.278348i	−0.774417	+	0.632675i	$0.781957\pi$
$314$	11.0711			0.624777
$315$	0.242641	−	0.420266i	0.0136713	−	0.0236793i
$316$		0			0
$317$	11.1213	+	19.2627i	0.624636	+	1.08190i	0.988611	+	0.150492i	$0.0480858\pi$
$317$	11.1213	+	19.2627i	0.624636	+	1.08190i	−0.363976	+	0.931408i	$0.618581\pi$
$318$	2.00000			0.112154
$319$	−2.41421	+	4.18154i	−0.135170	+	0.234121i
$320$	2.34315	−	4.05845i	0.130986	−	0.226874i
$321$	1.94975	−	3.37706i	0.108824	−	0.188489i
$322$	−2.14214	−	3.71029i	−0.119377	−	0.206766i
$323$	13.0711	−	22.6398i	0.727294	−	1.25971i
$324$		0			0
$325$	−8.51472			−0.472312
$326$	−6.58579			−0.364753
$327$	4.74264	+	8.21449i	0.262269	+	0.454263i
$328$	−6.00000	+	10.3923i	−0.331295	+	0.573819i
$329$	−0.242641	−	0.420266i	−0.0133772	−	0.0231700i
$330$	0.585786	−	1.01461i	0.0322465	−	0.0558525i
$331$	−1.50000	+	2.59808i	−0.0824475	+	0.142803i	−0.904301	−	0.426896i	$-0.859607\pi$
$331$	−1.50000	+	2.59808i	−0.0824475	+	0.142803i	0.821853	+	0.569699i	$0.192940\pi$
$332$		0			0
$333$	1.00000			0.0547997
$334$	−8.41421	−	14.5738i	−0.460405	−	0.797445i
$335$	−4.24264	−	7.34847i	−0.231800	−	0.401490i
$336$	−1.65685	+	2.86976i	−0.0903888	+	0.156558i
$337$	18.6274			1.01470			0.507350	−	0.861740i	$-0.330625\pi$
$337$	18.6274			1.01470			0.507350	+	0.861740i	$0.330625\pi$
$338$	6.82843	+	11.8272i	0.371417	+	0.643314i
$339$	15.6569			0.850364
$340$		0			0
$341$	7.77817	+	1.22474i	0.421212	+	0.0663237i
$342$	−5.41421			−0.292767
$343$	−11.0294			−0.595534
$344$	−7.75736	−	13.4361i	−0.418249	−	0.724428i
$345$	2.14214			0.115329
$346$	−6.58579	+	11.4069i	−0.354054	+	0.613240i
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	0.531885	−	0.846816i	$-0.321484\pi$
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	−0.999307	+	0.0372179i	$0.988150\pi$
$348$		0			0
$349$	33.1421			1.77406			0.887029	−	0.461714i	$-0.152765\pi$
$349$	33.1421			1.77406			0.887029	+	0.461714i	$0.152765\pi$
$350$	2.72792	−	4.72490i	0.145814	−	0.252557i
$351$	0.914214	−	1.58346i	0.0487971	−	0.0845191i
$352$		0			0
$353$	−13.5858	−	23.5313i	−0.723098	−	1.25244i	−0.959752	−	0.280849i	$-0.909384\pi$
$353$	−13.5858	−	23.5313i	−0.723098	−	1.25244i	0.236653	−	0.971594i	$-0.423949\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	1.75736	+	3.04384i	0.0932709	+	0.161550i
$356$		0			0
$357$	−5.65685			−0.299392
$358$	9.72792	+	16.8493i	0.514137	+	0.890511i
$359$	−9.02082	+	15.6245i	−0.476100	+	0.824630i	−0.999625	−	0.0273804i	$-0.991283\pi$
$359$	−9.02082	+	15.6245i	−0.476100	+	0.824630i	0.523525	+	0.852011i	$0.324617\pi$
$360$	−0.828427	−	1.43488i	−0.0436619	−	0.0756247i
$361$	2.17157	−	3.76127i	0.114293	−	0.197962i
$362$	−0.363961	+	0.630399i	−0.0191294	+	0.0331330i
$363$	−4.50000	+	7.79423i	−0.236189	+	0.409091i
$364$		0			0
$365$	1.12132	+	1.94218i	0.0586926	+	0.101659i
$366$	−8.82843	−	15.2913i	−0.461469	−	0.799288i
$367$	−9.57107	+	16.5776i	−0.499606	+	0.865342i	−1.00000		0.000455270i	$-0.999855\pi$
$367$	−9.57107	+	16.5776i	−0.499606	+	0.865342i	0.500394	+	0.865798i	$0.333188\pi$
$368$	−14.6274			−0.762507
$369$	2.12132	+	3.67423i	0.110432	+	0.191273i
$370$	−0.828427			−0.0430679
$371$	−1.17157			−0.0608250
$372$		0			0
$373$	−29.4853			−1.52669			−0.763345	−	0.645991i	$-0.776444\pi$
$373$	−29.4853			−1.52669			−0.763345	+	0.645991i	$0.776444\pi$
$374$	−13.6569			−0.706179
$375$	2.82843	+	4.89898i	0.146059	+	0.252982i
$376$	−1.65685			−0.0854457
$377$	3.12132	−	5.40629i	0.160756	−	0.278438i
$378$	0.585786	+	1.01461i	0.0301296	+	0.0521860i
$379$	−4.91421	−	8.51167i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$379$	−4.91421	−	8.51167i	−0.252426	−	0.437215i	−0.964193	+	0.265201i	$0.914562\pi$
$380$		0			0
$381$	2.67157	−	4.62730i	0.136869	−	0.237064i
$382$	2.17157	−	3.76127i	0.111107	−	0.192444i
$383$	3.19239	−	5.52938i	0.163123	−	0.282538i	−0.772864	−	0.634572i	$-0.781176\pi$
$383$	3.19239	−	5.52938i	0.163123	−	0.282538i	0.935987	+	0.352034i	$0.114510\pi$
$384$	5.65685	+	9.79796i	0.288675	+	0.500000i
$385$	−0.343146	+	0.594346i	−0.0174883	+	0.0302907i
$386$	−9.87868	−	17.1104i	−0.502812	−	0.870895i
$387$	−5.48528			−0.278833
$388$		0			0
$389$	8.65685	+	14.9941i	0.438920	+	0.760232i	0.997606	−	0.0691473i	$-0.0220278\pi$
$389$	8.65685	+	14.9941i	0.438920	+	0.760232i	−0.558687	+	0.829379i	$0.688695\pi$
$390$	−0.757359	+	1.31178i	−0.0383504	+	0.0664248i
$391$	−12.4853	−	21.6251i	−0.631408	−	1.09363i
$392$	−8.92893	+	15.4654i	−0.450979	+	0.781119i
$393$	−8.12132	+	14.0665i	−0.409666	+	0.709563i
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$	−9.17157			−0.461472
$396$		0			0
$397$	−4.48528	−	7.76874i	−0.225110	−	0.389902i	0.731243	−	0.682118i	$-0.238941\pi$
$397$	−4.48528	−	7.76874i	−0.225110	−	0.389902i	−0.956352	+	0.292216i	$0.905607\pi$
$398$	8.58579	−	14.8710i	0.430367	−	0.745417i
$399$	3.17157			0.158777
$400$	−9.31371	−	16.1318i	−0.465685	−	0.806591i
$401$	−14.8284			−0.740496			−0.370248	−	0.928933i	$-0.620727\pi$
$401$	−14.8284			−0.740496			−0.370248	+	0.928933i	$0.620727\pi$
$402$	20.4853			1.02171
$403$	−10.0563	−	1.58346i	−0.500942	−	0.0788780i
$404$		0			0
$405$	−0.585786			−0.0291080
$406$	2.00000	+	3.46410i	0.0992583	+	0.171920i
$407$	−1.41421			−0.0701000
$408$	−9.65685	+	16.7262i	−0.478086	+	0.828068i
$409$	3.25736	+	5.64191i	0.161066	+	0.278975i	0.935251	−	0.353985i	$-0.115173\pi$
$409$	3.25736	+	5.64191i	0.161066	+	0.278975i	−0.774185	+	0.632959i	$0.781840\pi$
$410$	−1.75736	−	3.04384i	−0.0867898	−	0.150324i
$411$	15.4142			0.760327
$412$		0			0
$413$	3.51472	−	6.08767i	0.172948	−	0.299555i
$414$	−2.58579	+	4.47871i	−0.127084	+	0.220117i
$415$	−2.17157	−	3.76127i	−0.106598	−	0.184634i
$416$		0			0
$417$	7.00000	+	12.1244i	0.342791	+	0.593732i
$418$	7.65685			0.374509
$419$	22.9706			1.12219			0.561093	−	0.827753i	$-0.310381\pi$
$419$	22.9706			1.12219			0.561093	+	0.827753i	$0.310381\pi$
$420$		0			0
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$	3.87868	+	6.71807i	0.188811	+	0.327031i
$423$	−0.292893	+	0.507306i	−0.0142410	+	0.0246661i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	15.8995	−	27.5387i	0.771239	−	1.33582i
$426$	−8.48528			−0.411113
$427$	5.17157	+	8.95743i	0.250270	+	0.433480i
$428$		0			0
$429$	−1.29289	+	2.23936i	−0.0624215	+	0.108117i
$430$	4.54416			0.219139
$431$	−2.17157	−	3.76127i	−0.104601	−	0.181174i	0.808974	−	0.587844i	$-0.200023\pi$
$431$	−2.17157	−	3.76127i	−0.104601	−	0.181174i	−0.913575	+	0.406670i	$0.866690\pi$
$432$	4.00000			0.192450
$433$	−3.82843			−0.183982			−0.0919912	−	0.995760i	$-0.529323\pi$
$433$	−3.82843			−0.183982			−0.0919912	+	0.995760i	$0.529323\pi$
$434$	4.10051	−	5.07306i	0.196831	−	0.243515i
$435$	−2.00000			−0.0958927
$436$		0			0
$437$	7.00000	+	12.1244i	0.334855	+	0.579987i
$438$	−5.41421			−0.258701
$439$	1.74264	−	3.01834i	0.0831717	−	0.144058i	−0.821439	−	0.570296i	$-0.806828\pi$
$439$	1.74264	−	3.01834i	0.0831717	−	0.144058i	0.904611	+	0.426239i	$0.140162\pi$
$440$	1.17157	+	2.02922i	0.0558525	+	0.0967394i
$441$	3.15685	+	5.46783i	0.150326	+	0.260373i
$442$	17.6569			0.839851
$443$	−4.07107	+	7.05130i	−0.193422	+	0.335017i	−0.946382	−	0.323049i	$-0.895292\pi$
$443$	−4.07107	+	7.05130i	−0.193422	+	0.335017i	0.752960	+	0.658066i	$0.228625\pi$
$444$		0			0
$445$	−5.24264	+	9.08052i	−0.248525	+	0.430458i
$446$	−11.7782	−	20.4004i	−0.557713	−	0.965987i
$447$	−3.00000	+	5.19615i	−0.141895	+	0.245770i
$448$	−3.31371	−	5.73951i	−0.156558	−	0.271166i
$449$	−18.3431			−0.865667			−0.432833	−	0.901474i	$-0.642486\pi$
$449$	−18.3431			−0.865667			−0.432833	+	0.901474i	$0.642486\pi$
$450$	−6.58579			−0.310457
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$		0			0
$453$	3.15685	+	5.46783i	0.148322	+	0.256901i
$454$	−7.65685	+	13.2621i	−0.359354	+	0.622419i
$455$	0.443651	−	0.768426i	0.0207987	−	0.0360244i
$456$	5.41421	−	9.37769i	0.253544	−	0.439151i
$457$	35.4853			1.65993			0.829966	−	0.557814i	$-0.188360\pi$
$457$	35.4853			1.65993			0.829966	+	0.557814i	$0.188360\pi$
$458$	8.12132	+	14.0665i	0.379484	+	0.657286i
$459$	3.41421	+	5.91359i	0.159362	+	0.276023i
$460$		0			0
$461$	3.55635			0.165636			0.0828178	−	0.996565i	$-0.473608\pi$
$461$	3.55635			0.165636			0.0828178	+	0.996565i	$0.473608\pi$
$462$	−0.828427	−	1.43488i	−0.0385419	−	0.0667566i
$463$	36.4558			1.69425			0.847123	−	0.531396i	$-0.178332\pi$
$463$	36.4558			1.69425			0.847123	+	0.531396i	$0.178332\pi$
$464$	13.6569			0.634004
$465$	1.17157	+	3.04384i	0.0543304	+	0.141154i
$466$	33.9411			1.57229
$467$	−9.31371			−0.430987			−0.215494	−	0.976505i	$-0.569136\pi$
$467$	−9.31371			−0.430987			−0.215494	+	0.976505i	$0.569136\pi$
$468$		0			0
$469$	−12.0000			−0.554109
$470$	0.242641	−	0.420266i	0.0111922	−	0.0193854i
$471$	3.91421	+	6.77962i	0.180357	+	0.312388i
$472$	−12.0000	−	20.7846i	−0.552345	−	0.956689i
$473$	7.75736			0.356684
$474$	11.0711	−	19.1757i	0.508511	−	0.880767i
$475$	−8.91421	+	15.4399i	−0.409012	+	0.708430i
$476$		0			0
$477$	0.707107	+	1.22474i	0.0323762	+	0.0560772i
$478$	−18.2426	+	31.5972i	−0.834399	+	1.44522i
$479$	5.82843	+	10.0951i	0.266308	+	0.461258i	0.967905	−	0.251315i	$-0.0808630\pi$
$479$	5.82843	+	10.0951i	0.266308	+	0.461258i	−0.701598	+	0.712573i	$0.747530\pi$
$480$		0			0
$481$	1.82843			0.0833691
$482$	4.22183	+	7.31242i	0.192299	+	0.333071i
$483$	1.51472	−	2.62357i	0.0689221	−	0.119377i
$484$		0			0
$485$	−3.36396	+	5.82655i	−0.152750	+	0.264570i
$486$	0.707107	−	1.22474i	0.0320750	−	0.0555556i
$487$	−3.25736	+	5.64191i	−0.147605	+	0.255659i	−0.930342	−	0.366693i	$-0.880490\pi$
$487$	−3.25736	+	5.64191i	−0.147605	+	0.255659i	0.782737	+	0.622353i	$0.213823\pi$
$488$	35.3137			1.59858
$489$	−2.32843	−	4.03295i	−0.105295	−	0.182376i
$490$	−2.61522	−	4.52970i	−0.118144	−	0.204631i
$491$	16.1421	−	27.9590i	0.728484	−	1.26177i	−0.229039	−	0.973417i	$-0.573558\pi$
$491$	16.1421	−	27.9590i	0.728484	−	1.26177i	0.957524	−	0.288355i	$-0.0931082\pi$
$492$		0			0
$493$	11.6569	+	20.1903i	0.524998	+	0.909324i
$494$	−9.89949			−0.445399
$495$	0.828427			0.0372350
$496$	−8.00000	−	20.7846i	−0.359211	−	0.933257i
$497$	4.97056			0.222960
$498$	10.4853			0.469857
$499$	3.92893	+	6.80511i	0.175883	+	0.304639i	0.940467	−	0.339886i	$-0.110389\pi$
$499$	3.92893	+	6.80511i	0.175883	+	0.304639i	−0.764583	+	0.644525i	$0.777055\pi$
$500$		0			0
$501$	5.94975	−	10.3053i	0.265815	−	0.460405i
$502$	17.7279	+	30.7057i	0.791236	+	1.37046i
$503$	−3.89949	−	6.75412i	−0.173870	−	0.301151i	0.765900	−	0.642960i	$-0.222294\pi$
$503$	−3.89949	−	6.75412i	−0.173870	−	0.301151i	−0.939770	+	0.341809i	$0.888961\pi$
$504$	−2.34315			−0.104372
$505$	−4.51472	+	7.81972i	−0.200902	+	0.347973i
$506$	3.65685	−	6.33386i	0.162567	−	0.281574i
$507$	−4.82843	+	8.36308i	−0.214438	+	0.371417i
$508$		0			0
$509$	−13.2426	+	22.9369i	−0.586970	+	1.01666i	0.407657	+	0.913135i	$0.366346\pi$
$509$	−13.2426	+	22.9369i	−0.586970	+	1.01666i	−0.994627	+	0.103526i	$0.966987\pi$
$510$	−2.82843	−	4.89898i	−0.125245	−	0.216930i
$511$	3.17157			0.140302
$512$	−22.6274			−1.00000
$513$	−1.91421	−	3.31552i	−0.0845146	−	0.146384i
$514$	−7.24264	+	12.5446i	−0.319459	+	0.553320i
$515$	4.77817	+	8.27604i	0.210552	+	0.364686i
$516$		0			0
$517$	0.414214	−	0.717439i	0.0182171	−	0.0315529i
$518$	−0.585786	+	1.01461i	−0.0257380	+	0.0445795i
$519$	−9.31371			−0.408826
$520$	−1.51472	−	2.62357i	−0.0664248	−	0.115051i
$521$	−9.94975	−	17.2335i	−0.435906	−	0.755012i	0.561463	−	0.827502i	$-0.310239\pi$
$521$	−9.94975	−	17.2335i	−0.435906	−	0.755012i	−0.997369	+	0.0724900i	$0.976905\pi$
$522$	2.41421	−	4.18154i	0.105667	−	0.183021i
$523$	6.00000			0.262362			0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000			0.262362			0.131181	+	0.991358i	$0.458123\pi$
$524$		0			0
$525$	3.85786			0.168371
$526$	−18.1421			−0.791035
$527$	23.8995	−	29.5680i	1.04108	−	1.28800i
$528$	−5.65685			−0.246183
$529$	−9.62742			−0.418583
$530$	−0.585786	−	1.01461i	−0.0254449	−	0.0440719i
$531$	−8.48528			−0.368230
$532$		0			0
$533$	3.87868	+	6.71807i	0.168004	+	0.290992i
$534$	−12.6569	−	21.9223i	−0.547716	−	0.948671i
$535$	−2.28427			−0.0987577
$536$	−20.4853	+	35.4815i	−0.884829	+	1.53257i
$537$	−6.87868	+	11.9142i	−0.296837	+	0.514137i
$538$	14.0000	−	24.2487i	0.603583	−	1.04544i
$539$	−4.46447	−	7.73268i	−0.192298	−	0.333070i
$540$		0			0
$541$	−18.9853	−	32.8835i	−0.816241	−	1.41377i	−0.908433	−	0.418030i	$-0.862721\pi$
$541$	−18.9853	−	32.8835i	−0.816241	−	1.41377i	0.0921924	−	0.995741i	$-0.470613\pi$
$542$	−40.2426			−1.72857
$543$	−0.514719			−0.0220887
$544$		0			0
$545$	2.77817	−	4.81194i	0.119004	−	0.206121i
$546$	1.07107	+	1.85514i	0.0458375	+	0.0793928i
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	0.876517	+	0.481371i	$0.159861\pi$
$548$		0			0
$549$	6.24264	−	10.8126i	0.266429	−	0.461469i
$550$	9.31371			0.397138
$551$	−6.53553	−	11.3199i	−0.278423	−	0.482243i
$552$	−5.17157	−	8.95743i	−0.220117	−	0.381253i
$553$	−6.48528	+	11.2328i	−0.275782	+	0.477669i
$554$	16.0416			0.681544
$555$	−0.292893	−	0.507306i	−0.0124326	−	0.0215339i
$556$		0			0
$557$	−4.62742			−0.196070			−0.0980350	−	0.995183i	$-0.531256\pi$
$557$	−4.62742			−0.196070			−0.0980350	+	0.995183i	$0.531256\pi$
$558$	−7.77817	−	1.22474i	−0.329276	−	0.0518476i
$559$	−10.0294			−0.424200
$560$	1.94113			0.0820275
$561$	−4.82843	−	8.36308i	−0.203856	−	0.353090i
$562$	−28.3431			−1.19558
$563$	−11.6777	+	20.2263i	−0.492155	+	0.852438i	−0.999959	−	0.00903495i	$-0.997124\pi$
$563$	−11.6777	+	20.2263i	−0.492155	+	0.852438i	0.507804	+	0.861473i	$0.330457\pi$
$564$		0			0
$565$	−4.58579	−	7.94282i	−0.192925	−	0.334157i
$566$	21.8995			0.920504
$567$	−0.414214	+	0.717439i	−0.0173953	+	0.0301296i
$568$	8.48528	−	14.6969i	0.356034	−	0.616670i
$569$	−4.07107	+	7.05130i	−0.170668	+	0.295606i	−0.938654	−	0.344861i	$-0.887926\pi$
$569$	−4.07107	+	7.05130i	−0.170668	+	0.295606i	0.767986	+	0.640467i	$0.221259\pi$
$570$	1.58579	+	2.74666i	0.0664213	+	0.115045i
$571$	−0.742641	+	1.28629i	−0.0310785	+	0.0538296i	−0.881146	−	0.472844i	$-0.843228\pi$
$571$	−0.742641	+	1.28629i	−0.0310785	+	0.0538296i	0.850068	+	0.526673i	$0.176561\pi$
$572$		0			0
$573$	3.07107			0.128296
$574$	−4.97056			−0.207467
$575$	8.51472	+	14.7479i	0.355088	+	0.615031i
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	−1.17157	−	2.02922i	−0.0487732	−	0.0844777i	0.840608	−	0.541644i	$-0.182198\pi$
$577$	−1.17157	−	2.02922i	−0.0487732	−	0.0844777i	−0.889381	+	0.457166i	$0.848864\pi$
$578$	−20.9497	+	36.2860i	−0.871395	+	1.50930i
$579$	6.98528	−	12.0989i	0.290298	−	0.502812i
$580$		0			0
$581$	−6.14214			−0.254819
$582$	−8.12132	−	14.0665i	−0.336640	−	0.583077i
$583$	−1.00000	−	1.73205i	−0.0414158	−	0.0717342i
$584$	5.41421	−	9.37769i	0.224042	−	0.388052i
$585$	−1.07107			−0.0442832
$586$	−9.07107	−	15.7116i	−0.374722	−	0.649038i
$587$	−16.6274			−0.686287			−0.343143	−	0.939283i	$-0.611492\pi$
$587$	−16.6274			−0.686287			−0.343143	+	0.939283i	$0.611492\pi$
$588$		0			0
$589$	−13.3995	+	16.5776i	−0.552117	+	0.683067i
$590$	7.02944			0.289397
$591$	−2.82843			−0.116346
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	1.65685	+	2.86976i	0.0679244	+	0.117649i
$596$		0			0
$597$	12.1421			0.496945
$598$	−4.72792	+	8.18900i	−0.193339	+	0.334873i
$599$	11.2635	−	19.5089i	0.460212	−	0.797111i	−0.538759	−	0.842460i	$-0.681107\pi$
$599$	11.2635	−	19.5089i	0.460212	−	0.797111i	0.998971	+	0.0453489i	$0.0144399\pi$
$600$	6.58579	−	11.4069i	0.268864	−	0.465685i
$601$	3.48528	+	6.03668i	0.142168	+	0.246241i	0.928313	−	0.371801i	$-0.121259\pi$
$601$	3.48528	+	6.03668i	0.142168	+	0.246241i	−0.786145	+	0.618042i	$0.787926\pi$
$602$	3.21320	−	5.56543i	0.130960	−	0.226830i
$603$	7.24264	+	12.5446i	0.294943	+	0.510856i
$604$		0			0
$605$	5.27208			0.214340
$606$	−10.8995	−	18.8785i	−0.442762	−	0.766886i
$607$	20.2279	−	35.0358i	0.821026	−	1.42206i	−0.0838929	−	0.996475i	$-0.526735\pi$
$607$	20.2279	−	35.0358i	0.821026	−	1.42206i	0.904919	−	0.425584i	$-0.139931\pi$
$608$		0			0
$609$	−1.41421	+	2.44949i	−0.0573068	+	0.0992583i
$610$	−5.17157	+	8.95743i	−0.209391	+	0.362676i
$611$	−0.535534	+	0.927572i	−0.0216654	+	0.0375255i
$612$		0			0
$613$	−18.7426	−	32.4632i	−0.757008	−	1.31118i	−0.944370	−	0.328886i	$-0.893327\pi$
$613$	−18.7426	−	32.4632i	−0.757008	−	1.31118i	0.187362	−	0.982291i	$-0.440006\pi$
$614$	−5.43503	−	9.41375i	−0.219340	−	0.379908i
$615$	1.24264	−	2.15232i	0.0501081	−	0.0867898i
$616$	3.31371			0.133513
$617$	16.6066	+	28.7635i	0.668557	+	1.15797i	0.978308	+	0.207156i	$0.0664209\pi$
$617$	16.6066	+	28.7635i	0.668557	+	1.15797i	−0.309751	+	0.950818i	$0.600246\pi$
$618$	−23.0711			−0.928054
$619$	29.4853			1.18511			0.592557	−	0.805529i	$-0.298119\pi$
$619$	29.4853			1.18511			0.592557	+	0.805529i	$0.298119\pi$
$620$		0			0
$621$	−3.65685			−0.146745
$622$	−28.1421			−1.12840
$623$	7.41421	+	12.8418i	0.297044	+	0.514496i
$624$	7.31371			0.292783
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	4.02082	+	6.96426i	0.160704	+	0.278348i
$627$	2.70711	+	4.68885i	0.108111	+	0.187254i
$628$		0			0
$629$	−3.41421	+	5.91359i	−0.136134	+	0.235790i
$630$	0.343146	−	0.594346i	0.0136713	−	0.0236793i
$631$	−21.4853	+	37.2136i	−0.855316	+	1.48145i	0.0210364	+	0.999779i	$0.493303\pi$
$631$	−21.4853	+	37.2136i	−0.855316	+	1.48145i	−0.876352	+	0.481671i	$0.840030\pi$
$632$	22.1421	+	38.3513i	0.880767	+	1.52553i
$633$	−2.74264	+	4.75039i	−0.109010	+	0.188811i
$634$	15.7279	+	27.2416i	0.624636	+	1.08190i
$635$	−3.12994			−0.124208
$636$		0			0
$637$	5.77208	+	9.99753i	0.228698	+	0.396117i
$638$	−3.41421	+	5.91359i	−0.135170	+	0.234121i
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	3.31371	−	5.73951i	0.130986	−	0.226874i
$641$	22.0919	−	38.2643i	0.872577	−	1.51135i	0.0132552	−	0.999912i	$-0.495781\pi$
$641$	22.0919	−	38.2643i	0.872577	−	1.51135i	0.859322	−	0.511435i	$-0.170886\pi$
$642$	2.75736	−	4.77589i	0.108824	−	0.188489i
$643$	35.7696			1.41061			0.705307	−	0.708902i	$-0.250809\pi$
$643$	35.7696			1.41061			0.705307	+	0.708902i	$0.250809\pi$
$644$		0			0
$645$	1.60660	+	2.78272i	0.0632599	+	0.109569i
$646$	18.4853	−	32.0174i	0.727294	−	1.25971i
$647$	14.4437			0.567839			0.283919	−	0.958848i	$-0.408365\pi$
$647$	14.4437			0.567839			0.283919	+	0.958848i	$0.408365\pi$
$648$	1.41421	+	2.44949i	0.0555556	+	0.0962250i
$649$	12.0000			0.471041
$650$	−12.0416			−0.472312
$651$	4.55635	+	0.717439i	0.178577	+	0.0281186i
$652$		0			0
$653$	41.0122			1.60493			0.802466	−	0.596698i	$-0.203521\pi$
$653$	41.0122			1.60493			0.802466	+	0.596698i	$0.203521\pi$
$654$	6.70711	+	11.6170i	0.262269	+	0.454263i
$655$	9.51472			0.371771
$656$	−8.48528	+	14.6969i	−0.331295	+	0.573819i
$657$	−1.91421	−	3.31552i	−0.0746806	−	0.129351i
$658$	−0.343146	−	0.594346i	−0.0133772	−	0.0231700i
$659$	1.61522			0.0629202			0.0314601	−	0.999505i	$-0.489984\pi$
$659$	1.61522			0.0629202			0.0314601	+	0.999505i	$0.489984\pi$
$660$		0			0
$661$	24.8848	−	43.1017i	0.967906	−	1.67646i	0.266309	−	0.963888i	$-0.414196\pi$
$661$	24.8848	−	43.1017i	0.967906	−	1.67646i	0.701597	−	0.712574i	$-0.252471\pi$
$662$	−2.12132	+	3.67423i	−0.0824475	+	0.142803i
$663$	6.24264	+	10.8126i	0.242444	+	0.419925i
$664$	−10.4853	+	18.1610i	−0.406908	+	0.704785i
$665$	−0.928932	−	1.60896i	−0.0360224	−	0.0623927i
$666$	1.41421			0.0547997
$667$	−12.4853			−0.483432
$668$		0			0
$669$	8.32843	−	14.4253i	0.321996	−	0.557713i
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−8.82843	+	15.2913i	−0.340818	+	0.590313i
$672$		0			0
$673$	6.24264	−	10.8126i	0.240636	−	0.416794i	−0.720260	−	0.693705i	$-0.755977\pi$
$673$	6.24264	−	10.8126i	0.240636	−	0.416794i	0.960896	+	0.276911i	$0.0893106\pi$
$674$	26.3431			1.01470
$675$	−2.32843	−	4.03295i	−0.0896212	−	0.155228i
$676$		0			0
$677$	−8.94975	+	15.5014i	−0.343967	+	0.595768i	−0.985165	−	0.171607i	$-0.945104\pi$
$677$	−8.94975	+	15.5014i	−0.343967	+	0.595768i	0.641199	+	0.767375i	$0.278437\pi$
$678$	22.1421			0.850364
$679$	4.75736	+	8.23999i	0.182571	+	0.316222i
$680$	11.3137			0.433861
$681$	−10.8284			−0.414946
$682$	11.0000	+	1.73205i	0.421212	+	0.0663237i
$683$	−23.6569			−0.905204			−0.452602	−	0.891713i	$-0.649504\pi$
$683$	−23.6569			−0.905204			−0.452602	+	0.891713i	$0.649504\pi$
$684$		0			0
$685$	−4.51472	−	7.81972i	−0.172499	−	0.298776i
$686$	−15.5980			−0.595534
$687$	−5.74264	+	9.94655i	−0.219095	+	0.379484i
$688$	−10.9706	−	19.0016i	−0.418249	−	0.724428i
$689$	1.29289	+	2.23936i	0.0492553	+	0.0853127i
$690$	3.02944			0.115329
$691$	7.48528	−	12.9649i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741422\pi$
$691$	7.48528	−	12.9649i	0.284754	−	0.493208i	0.972549	+	0.232697i	$0.0747549\pi$
$692$		0			0
$693$	0.585786	−	1.01461i	0.0222522	−	0.0385419i
$694$	−12.3137	−	21.3280i	−0.467422	−	0.809599i
$695$	4.10051	−	7.10228i	0.155541	−	0.269405i
$696$	4.82843	+	8.36308i	0.183021	+	0.317002i
$697$	−28.9706			−1.09734
$698$	46.8701			1.77406
$699$	12.0000	+	20.7846i	0.453882	+	0.786146i
$700$		0			0
$701$	18.0000	+	31.1769i	0.679851	+	1.17754i	0.975026	+	0.222093i	$0.0712887\pi$
$701$	18.0000	+	31.1769i	0.679851	+	1.17754i	−0.295175	+	0.955443i	$0.595378\pi$
$702$	1.29289	−	2.23936i	0.0487971	−	0.0845191i
$703$	1.91421	−	3.31552i	0.0721959	−	0.125047i
$704$	5.65685	−	9.79796i	0.213201	−	0.369274i
$705$	0.343146			0.0129236
$706$	−19.2132	−	33.2782i	−0.723098	−	1.25244i
$707$	6.38478	+	11.0588i	0.240124	+	0.415907i
$708$		0			0
$709$	−19.9706			−0.750010			−0.375005	−	0.927023i	$-0.622359\pi$
$709$	−19.9706			−0.750010			−0.375005	+	0.927023i	$0.622359\pi$
$710$	2.48528	+	4.30463i	0.0932709	+	0.161550i
$711$	15.6569			0.587178
$712$	50.6274			1.89734
$713$	7.31371	+	19.0016i	0.273901	+	0.711614i
$714$	−8.00000			−0.299392
$715$	1.51472			0.0566473
$716$		0			0
$717$	−25.7990			−0.963481
$718$	−12.7574	+	22.0964i	−0.476100	+	0.824630i
$719$	−12.4142	−	21.5020i	−0.462972	−	0.801891i	0.536135	−	0.844132i	$-0.319884\pi$
$719$	−12.4142	−	21.5020i	−0.462972	−	0.801891i	−0.999107	+	0.0422409i	$0.986550\pi$
$720$	−1.17157	−	2.02922i	−0.0436619	−	0.0756247i
$721$	13.5147			0.503314
$722$	3.07107	−	5.31925i	0.114293	−	0.197962i
$723$	−2.98528	+	5.17066i	−0.111024	+	0.192299i
$724$		0			0
$725$	−7.94975	−	13.7694i	−0.295246	−	0.511381i
$726$	−6.36396	+	11.0227i	−0.236189	+	0.409091i
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	0.908655	−	0.417548i	$-0.137111\pi$
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	−0.815935	+	0.578144i	$0.803777\pi$
$728$	−4.28427			−0.158786
$729$	1.00000			0.0370370
$730$	1.58579	+	2.74666i	0.0586926	+	0.101659i
$731$	18.7279	−	32.4377i	0.692677	−	1.19975i
$732$		0			0
$733$	−3.01472	+	5.22165i	−0.111351	+	0.192866i	−0.916315	−	0.400458i	$-0.868851\pi$
$733$	−3.01472	+	5.22165i	−0.111351	+	0.192866i	0.804964	+	0.593324i	$0.202185\pi$
$734$	−13.5355	+	23.4442i	−0.499606	+	0.865342i
$735$	1.84924	−	3.20298i	0.0682103	−	0.118144i
$736$		0			0
$737$	−10.2426	−	17.7408i	−0.377293	−	0.653490i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	0.843146	−	1.46037i	0.0310156	−	0.0537206i	−0.850101	−	0.526620i	$-0.823459\pi$
$739$	0.843146	−	1.46037i	0.0310156	−	0.0537206i	0.881117	+	0.472899i	$0.156793\pi$
$740$		0			0
$741$	−3.50000	−	6.06218i	−0.128576	−	0.222700i
$742$	−1.65685			−0.0608250
$743$	−17.7990			−0.652982			−0.326491	−	0.945200i	$-0.605866\pi$
$743$	−17.7990			−0.652982			−0.326491	+	0.945200i	$0.605866\pi$
$744$	9.89949	−	12.2474i	0.362933	−	0.449013i
$745$	3.51472			0.128769
$746$	−41.6985			−1.52669
$747$	3.70711	+	6.42090i	0.135636	+	0.234928i
$748$		0			0
$749$	−1.61522	+	2.79765i	−0.0590190	+	0.102224i
$750$	4.00000	+	6.92820i	0.146059	+	0.252982i
$751$	20.2279	+	35.0358i	0.738127	+	1.27847i	0.953338	+	0.301906i	$0.0976230\pi$
$751$	20.2279	+	35.0358i	0.738127	+	1.27847i	−0.215210	+	0.976568i	$0.569044\pi$
$752$	−2.34315			−0.0854457
$753$	−12.5355	+	21.7122i	−0.456820	+	0.791236i
$754$	4.41421	−	7.64564i	0.160756	−	0.278438i
$755$	1.84924	−	3.20298i	0.0673008	−	0.116568i
$756$		0			0
$757$	−25.3137	+	43.8446i	−0.920042	+	1.59356i	−0.120696	+	0.992690i	$0.538513\pi$
$757$	−25.3137	+	43.8446i	−0.920042	+	1.59356i	−0.799346	+	0.600871i	$0.794821\pi$
$758$	−6.94975	−	12.0373i	−0.252426	−	0.437215i
$759$	5.17157			0.187716
$760$	−6.34315			−0.230090
$761$	−20.5355	−	35.5686i	−0.744413	−	1.28936i	−0.950469	−	0.310820i	$-0.899396\pi$
$761$	−20.5355	−	35.5686i	−0.744413	−	1.28936i	0.206056	−	0.978540i	$-0.433937\pi$
$762$	3.77817	−	6.54399i	0.136869	−	0.237064i
$763$	−3.92893	−	6.80511i	−0.142237	−	0.246362i
$764$		0			0
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	4.51472	−	7.81972i	0.163123	−	0.282538i
$767$	−15.5147			−0.560204
$768$		0			0
$769$	−10.2426	−	17.7408i	−0.369359	−	0.639749i	0.620106	−	0.784518i	$-0.287089\pi$
$769$	−10.2426	−	17.7408i	−0.369359	−	0.639749i	−0.989465	+	0.144769i	$0.953756\pi$
$770$	−0.485281	+	0.840532i	−0.0174883	+	0.0302907i
$771$	−10.2426			−0.368880
$772$		0			0
$773$	−11.8579			−0.426498			−0.213249	−	0.976998i	$-0.568405\pi$
$773$	−11.8579			−0.426498			−0.213249	+	0.976998i	$0.568405\pi$
$774$	−7.75736			−0.278833
$775$	−16.2990	+	20.1648i	−0.585477	+	0.724340i
$776$	32.4853			1.16615
$777$	−0.828427			−0.0297197
$778$	12.2426	+	21.2049i	0.438920	+	0.760232i
$779$	16.2426			0.581953
$780$		0			0
$781$	4.24264	+	7.34847i	0.151814	+	0.262949i
$782$	−17.6569	−	30.5826i	−0.631408	−	1.09363i
$783$	3.41421			0.122014
$784$	−12.6274	+	21.8713i	−0.450979	+	0.781119i
$785$	2.29289	−	3.97141i	0.0818369	−	0.141746i
$786$	−11.4853	+	19.8931i	−0.409666	+	0.709563i
$787$	−10.7426	−	18.6068i	−0.382934	−	0.663261i	0.608546	−	0.793518i	$-0.291753\pi$
$787$	−10.7426	−	18.6068i	−0.382934	−	0.663261i	−0.991480	+	0.130258i	$0.958420\pi$
$788$		0			0
$789$	−6.41421	−	11.1097i	−0.228352	−	0.395517i
$790$	−12.9706			−0.461472
$791$	−12.9706			−0.461180
$792$	−2.00000	−	3.46410i	−0.0710669	−	0.123091i
$793$	11.4142	−	19.7700i	0.405331	−	0.702053i
$794$	−6.34315	−	10.9867i	−0.225110	−	0.389902i
$795$	0.414214	−	0.717439i	0.0146906	−	0.0254449i
$796$		0			0
$797$	0.343146	−	0.594346i	0.0121548	−	0.0210528i	−0.859884	−	0.510489i	$-0.829464\pi$
$797$	0.343146	−	0.594346i	0.0121548	−	0.0210528i	0.872039	+	0.489437i	$0.162798\pi$
$798$	4.48528			0.158777
$799$	−2.00000	−	3.46410i	−0.0707549	−	0.122551i
$800$		0			0
$801$	8.94975	−	15.5014i	0.316224	−	0.547716i
$802$	−20.9706			−0.740496
$803$	2.70711	+	4.68885i	0.0955317	+	0.165466i
$804$		0			0
$805$	−1.77460			−0.0625465
$806$	−14.2218	−	2.23936i	−0.500942	−	0.0788780i
$807$	19.7990			0.696957
$808$	43.5980			1.53377
$809$	8.46447	+	14.6609i	0.297595	+	0.515449i	0.975585	−	0.219621i	$-0.0704822\pi$
$809$	8.46447	+	14.6609i	0.297595	+	0.515449i	−0.677990	+	0.735071i	$0.737149\pi$
$810$	−0.828427			−0.0291080
$811$	−9.50000	+	16.4545i	−0.333590	+	0.577795i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$	−9.50000	+	16.4545i	−0.333590	+	0.577795i	0.649623	+	0.760257i	$0.274927\pi$
$812$		0			0
$813$	−14.2279	−	24.6435i	−0.498995	−	0.864285i
$814$	−2.00000			−0.0701000
$815$	−1.36396	+	2.36245i	−0.0477775	+	0.0827530i
$816$	−13.6569	+	23.6544i	−0.478086	+	0.828068i
$817$	−10.5000	+	18.1865i	−0.367348	+	0.636266i
$818$	4.60660	+	7.97887i	0.161066	+	0.278975i
$819$	−0.757359	+	1.31178i	−0.0264643	+	0.0458375i
$820$		0			0
$821$	−37.7990			−1.31919			−0.659597	−	0.751620i	$-0.729273\pi$
$821$	−37.7990			−1.31919			−0.659597	+	0.751620i	$0.729273\pi$
$822$	21.7990			0.760327
$823$	17.2426	+	29.8651i	0.601041	+	1.04103i	0.992664	+	0.120907i	$0.0385804\pi$
$823$	17.2426	+	29.8651i	0.601041	+	1.04103i	−0.391623	+	0.920126i	$0.628086\pi$
$824$	23.0711	−	39.9603i	0.803719	−	1.39208i
$825$	3.29289	+	5.70346i	0.114644	+	0.198569i
$826$	4.97056	−	8.60927i	0.172948	−	0.299555i
$827$	21.3640	−	37.0035i	0.742898	−	1.28674i	−0.208273	−	0.978071i	$-0.566784\pi$
$827$	21.3640	−	37.0035i	0.742898	−	1.28674i	0.951171	−	0.308666i	$-0.0998825\pi$
$828$		0			0
$829$	14.9411			0.518927			0.259463	−	0.965753i	$-0.416454\pi$
$829$	14.9411			0.518927			0.259463	+	0.965753i	$0.416454\pi$
$830$	−3.07107	−	5.31925i	−0.106598	−	0.184634i
$831$	5.67157	+	9.82345i	0.196745	+	0.340772i
$832$	−7.31371	+	12.6677i	−0.253557	+	0.439174i
$833$	−43.1127			−1.49377
$834$	9.89949	+	17.1464i	0.342791	+	0.593732i
$835$	−6.97056			−0.241226
$836$		0			0
$837$	−2.00000	−	5.19615i	−0.0691301	−	0.179605i
$838$	32.4853			1.12219
$839$	7.11270			0.245558			0.122779	−	0.992434i	$-0.460819\pi$
$839$	7.11270			0.245558			0.122779	+	0.992434i	$0.460819\pi$
$840$	0.686292	+	1.18869i	0.0236793	+	0.0410138i
$841$	−17.3431			−0.598040
$842$	15.5563	−	26.9444i	0.536107	−	0.928565i
$843$	−10.0208	−	17.3566i	−0.345135	−	0.597792i
$844$		0			0
$845$	5.65685			0.194602
$846$	−0.414214	+	0.717439i	−0.0142410	+	0.0246661i
$847$	3.72792	−	6.45695i	0.128093	−	0.221863i
$848$	−2.82843	+	4.89898i	−0.0971286	+	0.168232i
$849$	7.74264	+	13.4106i	0.265727	+	0.460252i
$850$	22.4853	−	38.9456i	0.771239	−	1.33582i
$851$	−1.82843	−	3.16693i	−0.0626777	−	0.108561i
$852$		0			0
$853$	9.62742			0.329636			0.164818	−	0.986324i	$-0.447296\pi$
$853$	9.62742			0.329636			0.164818	+	0.986324i	$0.447296\pi$
$854$	7.31371	+	12.6677i	0.250270	+	0.433480i
$855$	−1.12132	+	1.94218i	−0.0383483	+	0.0664213i
$856$	5.51472	+	9.55177i	0.188489	+	0.326473i
$857$	6.34315	−	10.9867i	0.216678	−	0.375297i	−0.737113	−	0.675770i	$-0.763811\pi$
$857$	6.34315	−	10.9867i	0.216678	−	0.375297i	0.953790	+	0.300473i	$0.0971446\pi$
$858$	−1.82843	+	3.16693i	−0.0624215	+	0.108117i
$859$	−22.8137	+	39.5145i	−0.778394	+	1.34822i	0.154474	+	0.987997i	$0.450632\pi$
$859$	−22.8137	+	39.5145i	−0.778394	+	1.34822i	−0.932867	+	0.360220i	$0.882701\pi$
$860$		0			0
$861$	−1.75736	−	3.04384i	−0.0598906	−	0.103734i
$862$	−3.07107	−	5.31925i	−0.104601	−	0.181174i
$863$	6.94975	−	12.0373i	0.236572	−	0.409755i	−0.723156	−	0.690684i	$-0.757309\pi$
$863$	6.94975	−	12.0373i	0.236572	−	0.409755i	0.959728	+	0.280929i	$0.0906427\pi$
$864$		0			0
$865$	2.72792	+	4.72490i	0.0927521	+	0.160651i
$866$	−5.41421			−0.183982
$867$	−29.6274			−1.00620
$868$		0			0
$869$	−22.1421			−0.751121
$870$	−2.82843			−0.0958927
$871$	13.2426	+	22.9369i	0.448710	+	0.777188i
$872$	−26.8284			−0.908525
$873$	5.74264	−	9.94655i	0.194359	−	0.336640i
$874$	9.89949	+	17.1464i	0.334855	+	0.579987i
$875$	−2.34315	−	4.05845i	−0.0792128	−	0.137201i
$876$		0			0
$877$	14.7426	−	25.5350i	0.497824	−	0.862256i	−0.502173	−	0.864767i	$-0.667466\pi$
$877$	14.7426	−	25.5350i	0.497824	−	0.862256i	0.999997	+	0.00251127i	$0.000799362\pi$
$878$	2.46447	−	4.26858i	0.0831717	−	0.144058i
$879$	6.41421	−	11.1097i	0.216346	−	0.374722i
$880$	1.65685	+	2.86976i	0.0558525	+	0.0967394i
$881$	−0.313708	+	0.543359i	−0.0105691	+	0.0183062i	−0.871262	−	0.490819i	$-0.836698\pi$
$881$	−0.313708	+	0.543359i	−0.0105691	+	0.0183062i	0.860692	+	0.509125i	$0.170031\pi$
$882$	4.46447	+	7.73268i	0.150326	+	0.260373i
$883$	−36.9411			−1.24317			−0.621584	−	0.783348i	$-0.713511\pi$
$883$	−36.9411			−1.24317			−0.621584	+	0.783348i	$0.713511\pi$
$884$		0			0
$885$	2.48528	+	4.30463i	0.0835418	+	0.144699i
$886$	−5.75736	+	9.97204i	−0.193422	+	0.335017i
$887$	−8.12132	−	14.0665i	−0.272687	−	0.472308i	0.696862	−	0.717205i	$-0.254579\pi$
$887$	−8.12132	−	14.0665i	−0.272687	−	0.472308i	−0.969549	+	0.244897i	$0.921246\pi$
$888$	−1.41421	+	2.44949i	−0.0474579	+	0.0821995i
$889$	−2.21320	+	3.83338i	−0.0742285	+	0.128567i
$890$	−7.41421	+	12.8418i	−0.248525	+	0.430458i
$891$	−1.41421			−0.0473779
$892$		0			0
$893$	1.12132	+	1.94218i	0.0375236	+	0.0649927i
$894$	−4.24264	+	7.34847i	−0.141895	+	0.245770i
$895$	8.05887			0.269378
$896$	−4.68629	−	8.11689i	−0.156558	−	0.271166i
$897$	−6.68629			−0.223249
$898$	−25.9411			−0.865667
$899$	−6.82843	−	17.7408i	−0.227741	−	0.591688i
$900$		0			0
$901$	−9.65685			−0.321716
$902$	−4.24264	−	7.34847i	−0.141264	−	0.244677i
$903$	4.54416			0.151220
$904$	−22.1421	+	38.3513i	−0.736436	+	1.27555i
$905$	0.150758	+	0.261120i	0.00501135	+	0.00867992i
$906$	4.46447	+	7.73268i	0.148322	+	0.256901i
$907$	−25.5147			−0.847202			−0.423601	−	0.905849i	$-0.639234\pi$
$907$	−25.5147			−0.847202			−0.423601	+	0.905849i	$0.639234\pi$
$908$		0			0
$909$	7.70711	−	13.3491i	0.255629	−	0.442762i
$910$	0.627417	−	1.08672i	0.0207987	−	0.0360244i
$911$	14.8284	+	25.6836i	0.491288	+	0.850935i	0.999950	−	0.0100310i	$-0.00319303\pi$
$911$	14.8284	+	25.6836i	0.491288	+	0.850935i	−0.508662	+	0.860966i	$0.669860\pi$
$912$	7.65685	−	13.2621i	0.253544	−	0.439151i
$913$	−5.24264	−	9.08052i	−0.173506	−	0.300521i
$914$	50.1838			1.65993
$915$	−7.31371			−0.241784
$916$		0			0
$917$	6.72792	−	11.6531i	0.222176	−	0.384819i
$918$	4.82843	+	8.36308i	0.159362	+	0.276023i
$919$	14.7426	−	25.5350i	0.486315	−	0.842322i	−0.513561	−	0.858053i	$-0.671674\pi$
$919$	14.7426	−	25.5350i	0.486315	−	0.842322i	0.999876	+	0.0157308i	$0.00500748\pi$
$920$	−3.02944	+	5.24714i	−0.0998776	+	0.172993i
$921$	3.84315	−	6.65652i	0.126636	−	0.219340i
$922$	5.02944			0.165636
$923$	−5.48528	−	9.50079i	−0.180550	−	0.312722i
$924$		0			0
$925$	2.32843	−	4.03295i	0.0765582	−	0.132603i
$926$	51.5563			1.69425
$927$	−8.15685	−	14.1281i	−0.267906	−	0.464027i
$928$		0			0
$929$	−0.343146			−0.0112582			−0.00562912	−	0.999984i	$-0.501792\pi$
$929$	−0.343146			−0.0112582			−0.00562912	+	0.999984i	$0.501792\pi$
$930$	1.65685	+	4.30463i	0.0543304	+	0.141154i
$931$	24.1716			0.792191
$932$		0			0
$933$	−9.94975	−	17.2335i	−0.325740	−	0.564198i
$934$	−13.1716			−0.430987
$935$	−2.82843	+	4.89898i	−0.0924995	+	0.160214i
$936$	2.58579	+	4.47871i	0.0845191	+	0.146391i
$937$	11.7426	+	20.3389i	0.383615	+	0.664441i	0.991576	−	0.129526i	$-0.0413455\pi$
$937$	11.7426	+	20.3389i	0.383615	+	0.664441i	−0.607961	+	0.793967i	$0.708012\pi$
$938$	−16.9706			−0.554109
$939$	−2.84315	+	4.92447i	−0.0927826	+	0.160704i
$940$		0			0
$941$	−13.0711	+	22.6398i	−0.426105	+	0.738035i	−0.996523	−	0.0833195i	$-0.973448\pi$
$941$	−13.0711	+	22.6398i	−0.426105	+	0.738035i	0.570418	+	0.821354i	$0.306781\pi$
$942$	5.53553	+	9.58783i	0.180357	+	0.312388i
$943$	7.75736	−	13.4361i	0.252614	−	0.437541i
$944$	−16.9706	−	29.3939i	−0.552345	−	0.956689i
$945$	0.485281			0.0157862
$946$	10.9706			0.356684
$947$	17.3848	+	30.1113i	0.564929	+	0.978486i	0.997056	+	0.0766735i	$0.0244299\pi$
$947$	17.3848	+	30.1113i	0.564929	+	0.978486i	−0.432127	+	0.901813i	$0.642237\pi$
$948$		0			0
$949$	−3.50000	−	6.06218i	−0.113615	−	0.196787i
$950$	−12.6066	+	21.8353i	−0.409012	+	0.708430i
$951$	−11.1213	+	19.2627i	−0.360634	+	0.624636i
$952$	8.00000	−	13.8564i	0.259281	−	0.449089i
$953$	11.8995			0.385462			0.192731	−	0.981252i	$-0.438265\pi$
$953$	11.8995			0.385462			0.192731	+	0.981252i	$0.438265\pi$
$954$	1.00000	+	1.73205i	0.0323762	+	0.0560772i
$955$	−0.899495	−	1.55797i	−0.0291070	−	0.0504148i
$956$		0			0
$957$	−4.82843			−0.156081
$958$	8.24264	+	14.2767i	0.266308	+	0.461258i
$959$	−12.7696			−0.412350
$960$	4.68629			0.151249
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$	2.58579			0.0833691
$963$	3.89949			0.125659
$964$		0			0
$965$	−8.18377			−0.263445
$966$	2.14214	−	3.71029i	0.0689221	−	0.119377i
$967$	5.97056	+	10.3413i	0.192000	+	0.332554i	0.945913	−	0.324420i	$-0.105169\pi$
$967$	5.97056	+	10.3413i	0.192000	+	0.332554i	−0.753913	+	0.656975i	$0.771836\pi$
$968$	−12.7279	−	22.0454i	−0.409091	−	0.708566i
$969$	26.1421			0.839806
$970$	−4.75736	+	8.23999i	−0.152750	+	0.264570i
$971$	−19.9706	+	34.5900i	−0.640886	+	1.11005i	0.344350	+	0.938842i	$0.388099\pi$
$971$	−19.9706	+	34.5900i	−0.640886	+	1.11005i	−0.985235	+	0.171205i	$0.945234\pi$
$972$		0			0
$973$	−5.79899	−	10.0441i	−0.185907	−	0.322001i
$974$	−4.60660	+	7.97887i	−0.147605	+	0.255659i
$975$	−4.25736	−	7.37396i	−0.136345	−	0.236156i
$976$	49.9411			1.59858
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$	−3.29289	−	5.70346i	−0.105295	−	0.182376i
$979$	−12.6569	+	21.9223i	−0.404515	+	0.700640i
$980$		0			0
$981$	−4.74264	+	8.21449i	−0.151421	+	0.262269i
$982$	22.8284	−	39.5400i	0.728484	−	1.26177i
$983$	29.0416	−	50.3016i	0.926284	−	1.60437i	0.136801	−	0.990598i	$-0.456318\pi$
$983$	29.0416	−	50.3016i	0.926284	−	1.60437i	0.789483	−	0.613773i	$-0.210349\pi$
$984$	−12.0000			−0.382546
$985$	0.828427	+	1.43488i	0.0263959	+	0.0457190i
$986$	16.4853	+	28.5533i	0.524998	+	0.909324i
$987$	0.242641	−	0.420266i	0.00772334	−	0.0133772i
$988$		0			0
$989$	10.0294	+	17.3715i	0.318918	+	0.552381i
$990$	1.17157			0.0372350
$991$	45.1421			1.43399			0.716994	−	0.697080i	$-0.245518\pi$
$991$	45.1421			1.43399			0.716994	+	0.697080i	$0.245518\pi$
$992$		0			0
$993$	−3.00000			−0.0952021
$994$	7.02944			0.222960
$995$	−3.55635	−	6.15978i	−0.112744	−	0.195278i
$996$		0			0
$997$	9.51472	−	16.4800i	0.301334	−	0.521926i	−0.675104	−	0.737722i	$-0.735901\pi$
$997$	9.51472	−	16.4800i	0.301334	−	0.521926i	0.976438	+	0.215796i	$0.0692347\pi$
$998$	5.55635	+	9.62388i	0.175883	+	0.304639i
$999$	0.500000	+	0.866025i	0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.e.a.25.2	✓	4
3.2	odd	2		279.2.h.b.118.1		4
4.3	odd	2		1488.2.q.g.769.1		4
31.5	even	3	inner	93.2.e.a.67.2	yes	4
31.6	odd	6		2883.2.a.c.1.2		2
31.25	even	3		2883.2.a.b.1.2		2
93.5	odd	6		279.2.h.b.253.1		4
93.56	odd	6		8649.2.a.h.1.1		2
93.68	even	6		8649.2.a.i.1.1		2
124.67	odd	6		1488.2.q.g.625.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.e.a.25.2	✓	4	1.1	even	1	trivial
93.2.e.a.67.2	yes	4	31.5	even	3	inner
279.2.h.b.118.1		4	3.2	odd	2
279.2.h.b.253.1		4	93.5	odd	6
1488.2.q.g.625.1		4	124.67	odd	6
1488.2.q.g.769.1		4	4.3	odd	2
2883.2.a.b.1.2		2	31.25	even	3
2883.2.a.c.1.2		2	31.6	odd	6
8649.2.a.h.1.1		2	93.56	odd	6
8649.2.a.i.1.1		2	93.68	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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(0.500000 + 0.866025i) q^{3} +(0.292893 - 0.507306i) q^{5} +(0.707107 + 1.22474i) q^{6} +(-0.414214 - 0.717439i) q^{7} -2.82843 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(0.500000 + 0.866025i) q^{3} +(0.292893 - 0.507306i) q^{5} +(0.707107 + 1.22474i) q^{6} +(-0.414214 - 0.717439i) q^{7} -2.82843 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{10} +(0.707107 - 1.22474i) q^{11} +(-0.914214 + 1.58346i) q^{13} +(-0.585786 - 1.01461i) q^{14} +0.585786 q^{15} -4.00000 q^{16} +(-3.41421 - 5.91359i) q^{17} +(-0.707107 + 1.22474i) q^{18} +(1.91421 + 3.31552i) q^{19} +(0.414214 - 0.717439i) q^{21} +(1.00000 - 1.73205i) q^{22} +3.65685 q^{23} +(-1.41421 - 2.44949i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-1.29289 + 2.23936i) q^{26} -1.00000 q^{27} -3.41421 q^{29} +0.828427 q^{30} +(2.00000 + 5.19615i) q^{31} +1.41421 q^{33} +(-4.82843 - 8.36308i) q^{34} -0.485281 q^{35} +(-0.500000 - 0.866025i) q^{37} +(2.70711 + 4.68885i) q^{38} -1.82843 q^{39} +(-0.828427 + 1.43488i) q^{40} +(2.12132 - 3.67423i) q^{41} +(0.585786 - 1.01461i) q^{42} +(2.74264 + 4.75039i) q^{43} +(0.292893 + 0.507306i) q^{45} +5.17157 q^{46} +0.585786 q^{47} +(-2.00000 - 3.46410i) q^{48} +(3.15685 - 5.46783i) q^{49} +(3.29289 + 5.70346i) q^{50} +(3.41421 - 5.91359i) q^{51} +(0.707107 - 1.22474i) q^{53} -1.41421 q^{54} +(-0.414214 - 0.717439i) q^{55} +(1.17157 + 2.02922i) q^{56} +(-1.91421 + 3.31552i) q^{57} -4.82843 q^{58} +(4.24264 + 7.34847i) q^{59} -12.4853 q^{61} +(2.82843 + 7.34847i) q^{62} +0.828427 q^{63} +8.00000 q^{64} +(0.535534 + 0.927572i) q^{65} +2.00000 q^{66} +(7.24264 - 12.5446i) q^{67} +(1.82843 + 3.16693i) q^{69} -0.686292 q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.41421 - 2.44949i) q^{72} +(-1.91421 + 3.31552i) q^{73} +(-0.707107 - 1.22474i) q^{74} +(-2.32843 + 4.03295i) q^{75} -1.17157 q^{77} -2.58579 q^{78} +(-7.82843 - 13.5592i) q^{79} +(-1.17157 + 2.02922i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(3.87868 + 6.71807i) q^{86} +(-1.70711 - 2.95680i) q^{87} +(-2.00000 + 3.46410i) q^{88} -17.8995 q^{89} +(0.414214 + 0.717439i) q^{90} +1.51472 q^{91} +(-3.50000 + 4.33013i) q^{93} +0.828427 q^{94} +2.24264 q^{95} -11.4853 q^{97} +(4.46447 - 7.73268i) q^{98} +(0.707107 + 1.22474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 + 4 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} - 2 q^{9} - 4 q^{10} + 2 q^{13} - 8 q^{14} + 8 q^{15} - 16 q^{16} - 8 q^{17} + 2 q^{19} - 4 q^{21} + 4 q^{22} - 8 q^{23} - 2 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} - 8 q^{30} + 8 q^{31} - 8 q^{34} + 32 q^{35} - 2 q^{37} + 8 q^{38} + 4 q^{39} + 8 q^{40} + 8 q^{42} - 6 q^{43} + 4 q^{45} + 32 q^{46} + 8 q^{47} - 8 q^{48} - 10 q^{49} + 16 q^{50} + 8 q^{51} + 4 q^{55} + 16 q^{56} - 2 q^{57} - 8 q^{58} - 16 q^{61} - 8 q^{63} + 32 q^{64} - 12 q^{65} + 8 q^{66} + 12 q^{67} - 4 q^{69} - 48 q^{70} - 12 q^{71} - 2 q^{73} + 2 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} - 16 q^{80} - 2 q^{81} + 12 q^{82} + 12 q^{83} - 16 q^{85} + 24 q^{86} - 4 q^{87} - 8 q^{88} - 32 q^{89} - 4 q^{90} + 40 q^{91} - 14 q^{93} - 8 q^{94} - 8 q^{95} - 12 q^{97} + 32 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 + 4 * q^7 - 2 * q^9 - 4 * q^10 + 2 * q^13 - 8 * q^14 + 8 * q^15 - 16 * q^16 - 8 * q^17 + 2 * q^19 - 4 * q^21 + 4 * q^22 - 8 * q^23 - 2 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 - 8 * q^30 + 8 * q^31 - 8 * q^34 + 32 * q^35 - 2 * q^37 + 8 * q^38 + 4 * q^39 + 8 * q^40 + 8 * q^42 - 6 * q^43 + 4 * q^45 + 32 * q^46 + 8 * q^47 - 8 * q^48 - 10 * q^49 + 16 * q^50 + 8 * q^51 + 4 * q^55 + 16 * q^56 - 2 * q^57 - 8 * q^58 - 16 * q^61 - 8 * q^63 + 32 * q^64 - 12 * q^65 + 8 * q^66 + 12 * q^67 - 4 * q^69 - 48 * q^70 - 12 * q^71 - 2 * q^73 + 2 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 - 16 * q^80 - 2 * q^81 + 12 * q^82 + 12 * q^83 - 16 * q^85 + 24 * q^86 - 4 * q^87 - 8 * q^88 - 32 * q^89 - 4 * q^90 + 40 * q^91 - 14 * q^93 - 8 * q^94 - 8 * q^95 - 12 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more