LMFDB - Embedded newform 4830.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.a (trivial)

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:	yes
Analytic conductor:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} -4.74456 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.74456 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.74456 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.74456 q^{29} +1.00000 q^{30} -6.74456 q^{31} -1.00000 q^{32} +4.00000 q^{33} -1.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +6.74456 q^{38} +4.74456 q^{39} -1.00000 q^{40} +2.74456 q^{41} -1.00000 q^{42} -4.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} -1.25544 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.74456 q^{52} +1.25544 q^{53} +1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +6.74456 q^{57} +6.74456 q^{58} +4.00000 q^{59} -1.00000 q^{60} +11.4891 q^{61} +6.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.74456 q^{65} -4.00000 q^{66} +8.00000 q^{67} +1.00000 q^{69} +1.00000 q^{70} -8.00000 q^{71} -1.00000 q^{72} +10.7446 q^{73} -2.00000 q^{74} -1.00000 q^{75} -6.74456 q^{76} +4.00000 q^{77} -4.74456 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.74456 q^{82} +5.25544 q^{83} +1.00000 q^{84} +6.74456 q^{87} +4.00000 q^{88} -3.25544 q^{89} -1.00000 q^{90} +4.74456 q^{91} -1.00000 q^{92} +6.74456 q^{93} +1.25544 q^{94} -6.74456 q^{95} +1.00000 q^{96} +12.7446 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 2 q^{20} + 2 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} + 8 q^{33} - 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 6 q^{41} - 2 q^{42} - 8 q^{44} + 2 q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{52} + 14 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} + 2 q^{57} + 2 q^{58} + 8 q^{59} - 2 q^{60} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 8 q^{66} + 16 q^{67} + 2 q^{69} + 2 q^{70} - 16 q^{71} - 2 q^{72} + 10 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 8 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 6 q^{82} + 22 q^{83} + 2 q^{84} + 2 q^{87} + 8 q^{88} - 18 q^{89} - 2 q^{90} - 2 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 2 q^{95} + 2 q^{96} + 14 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 2 * q^20 + 2 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 + 8 * q^33 - 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 6 * q^41 - 2 * q^42 - 8 * q^44 + 2 * q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^52 + 14 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 + 2 * q^57 + 2 * q^58 + 8 * q^59 - 2 * q^60 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 8 * q^66 + 16 * q^67 + 2 * q^69 + 2 * q^70 - 16 * q^71 - 2 * q^72 + 10 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 8 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 6 * q^82 + 22 * q^83 + 2 * q^84 + 2 * q^87 + 8 * q^88 - 18 * q^89 - 2 * q^90 - 2 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 2 * q^95 + 2 * q^96 + 14 * q^97 - 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

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	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	−4.74456	−1.31590	−0.657952	−	0.753059i	$-0.728577\pi$
$13$	−4.74456	−1.31590	−0.657952	+	0.753059i	$0.728577\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−1.00000	−0.235702
$19$	−6.74456	−1.54731	−0.773654	−	0.633608i	$-0.781573\pi$
$19$	−6.74456	−1.54731	−0.773654	+	0.633608i	$0.781573\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	4.00000	0.852803
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.74456	0.930485
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−6.74456	−1.25243	−0.626217	−	0.779649i	$-0.715398\pi$
$29$	−6.74456	−1.25243	−0.626217	+	0.779649i	$0.715398\pi$
$30$	1.00000	0.182574
$31$	−6.74456	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	0	0
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	6.74456	1.09411
$39$	4.74456	0.759738
$40$	−1.00000	−0.158114
$41$	2.74456	0.428629	0.214314	−	0.976765i	$-0.431248\pi$
$41$	2.74456	0.428629	0.214314	+	0.976765i	$0.431248\pi$
$42$	−1.00000	−0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−4.00000	−0.603023
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	−1.25544	−0.183124	−0.0915622	−	0.995799i	$-0.529186\pi$
$47$	−1.25544	−0.183124	−0.0915622	+	0.995799i	$0.529186\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−4.74456	−0.657952
$53$	1.25544	0.172448	0.0862238	−	0.996276i	$-0.472520\pi$
$53$	1.25544	0.172448	0.0862238	+	0.996276i	$0.472520\pi$
$54$	1.00000	0.136083
$55$	−4.00000	−0.539360
$56$	1.00000	0.133631
$57$	6.74456	0.893339
$58$	6.74456	0.885604
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−0.129099
$61$	11.4891	1.47103	0.735516	−	0.677507i	$-0.236940\pi$
$61$	11.4891	1.47103	0.735516	+	0.677507i	$0.236940\pi$
$62$	6.74456	0.856560
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.74456	−0.588491
$66$	−4.00000	−0.492366
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0	0
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.00000	−0.117851
$73$	10.7446	1.25756	0.628778	−	0.777585i	$-0.283555\pi$
$73$	10.7446	1.25756	0.628778	+	0.777585i	$0.283555\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−6.74456	−0.773654
$77$	4.00000	0.455842
$78$	−4.74456	−0.537216
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−2.74456	−0.303086
$83$	5.25544	0.576859	0.288430	−	0.957501i	$-0.406867\pi$
$83$	5.25544	0.576859	0.288430	+	0.957501i	$0.406867\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	0	0
$87$	6.74456	0.723093
$88$	4.00000	0.426401
$89$	−3.25544	−0.345076	−0.172538	−	0.985003i	$-0.555197\pi$
$89$	−3.25544	−0.345076	−0.172538	+	0.985003i	$0.555197\pi$
$90$	−1.00000	−0.105409
$91$	4.74456	0.497365
$92$	−1.00000	−0.104257
$93$	6.74456	0.699379
$94$	1.25544	0.129488
$95$	−6.74456	−0.691978
$96$	1.00000	0.102062
$97$	12.7446	1.29401	0.647007	−	0.762484i	$-0.276020\pi$
$97$	12.7446	1.29401	0.647007	+	0.762484i	$0.276020\pi$
$98$	−1.00000	−0.101015
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	7.25544	0.721943	0.360971	−	0.932577i	$-0.382445\pi$
$101$	7.25544	0.721943	0.360971	+	0.932577i	$0.382445\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	4.74456	0.465243
$105$	1.00000	0.0975900
$106$	−1.25544	−0.121939
$107$	4.74456	0.458674	0.229337	−	0.973347i	$-0.426344\pi$
$107$	4.74456	0.458674	0.229337	+	0.973347i	$0.426344\pi$
$108$	−1.00000	−0.0962250
$109$	1.25544	0.120249	0.0601245	−	0.998191i	$-0.480850\pi$
$109$	1.25544	0.120249	0.0601245	+	0.998191i	$0.480850\pi$
$110$	4.00000	0.381385
$111$	−2.00000	−0.189832
$112$	−1.00000	−0.0944911
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	−6.74456	−0.631686
$115$	−1.00000	−0.0932505
$116$	−6.74456	−0.626217
$117$	−4.74456	−0.438635
$118$	−4.00000	−0.368230
$119$	0	0
$120$	1.00000	0.0912871
$121$	5.00000	0.454545
$122$	−11.4891	−1.04018
$123$	−2.74456	−0.247469
$124$	−6.74456	−0.605680
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	4.74456	0.416126
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	4.00000	0.348155
$133$	6.74456	0.584828
$134$	−8.00000	−0.691095
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−11.4891	−0.981582	−0.490791	−	0.871277i	$-0.663292\pi$
$137$	−11.4891	−0.981582	−0.490791	+	0.871277i	$0.663292\pi$
$138$	−1.00000	−0.0851257
$139$	9.48913	0.804857	0.402429	−	0.915451i	$-0.368166\pi$
$139$	9.48913	0.804857	0.402429	+	0.915451i	$0.368166\pi$
$140$	−1.00000	−0.0845154
$141$	1.25544	0.105727
$142$	8.00000	0.671345
$143$	18.9783	1.58704
$144$	1.00000	0.0833333
$145$	−6.74456	−0.560105
$146$	−10.7446	−0.889226
$147$	−1.00000	−0.0824786
$148$	2.00000	0.164399
$149$	−15.4891	−1.26892	−0.634459	−	0.772956i	$-0.718777\pi$
$149$	−15.4891	−1.26892	−0.634459	+	0.772956i	$0.718777\pi$
$150$	1.00000	0.0816497
$151$	13.4891	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$151$	13.4891	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$152$	6.74456	0.547056
$153$	0	0
$154$	−4.00000	−0.322329
$155$	−6.74456	−0.541736
$156$	4.74456	0.379869
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	8.00000	0.636446
$159$	−1.25544	−0.0995627
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	0.744563	0.0583186	0.0291593	−	0.999575i	$-0.490717\pi$
$163$	0.744563	0.0583186	0.0291593	+	0.999575i	$0.490717\pi$
$164$	2.74456	0.214314
$165$	4.00000	0.311400
$166$	−5.25544	−0.407901
$167$	−5.25544	−0.406678	−0.203339	−	0.979108i	$-0.565179\pi$
$167$	−5.25544	−0.406678	−0.203339	+	0.979108i	$0.565179\pi$
$168$	−1.00000	−0.0771517
$169$	9.51087	0.731606
$170$	0	0
$171$	−6.74456	−0.515770
$172$	0	0
$173$	−4.74456	−0.360722	−0.180361	−	0.983600i	$-0.557727\pi$
$173$	−4.74456	−0.360722	−0.180361	+	0.983600i	$0.557727\pi$
$174$	−6.74456	−0.511304
$175$	−1.00000	−0.0755929
$176$	−4.00000	−0.301511
$177$	−4.00000	−0.300658
$178$	3.25544	0.244005
$179$	−0.744563	−0.0556512	−0.0278256	−	0.999613i	$-0.508858\pi$
$179$	−0.744563	−0.0556512	−0.0278256	+	0.999613i	$0.508858\pi$
$180$	1.00000	0.0745356
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	−4.74456	−0.351690
$183$	−11.4891	−0.849301
$184$	1.00000	0.0737210
$185$	2.00000	0.147043
$186$	−6.74456	−0.494535
$187$	0	0
$188$	−1.25544	−0.0915622
$189$	1.00000	0.0727393
$190$	6.74456	0.489302
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−12.7446	−0.915006
$195$	4.74456	0.339765
$196$	1.00000	0.0714286
$197$	−3.48913	−0.248590	−0.124295	−	0.992245i	$-0.539667\pi$
$197$	−3.48913	−0.248590	−0.124295	+	0.992245i	$0.539667\pi$
$198$	4.00000	0.284268
$199$	−10.2337	−0.725447	−0.362723	−	0.931897i	$-0.618153\pi$
$199$	−10.2337	−0.725447	−0.362723	+	0.931897i	$0.618153\pi$
$200$	−1.00000	−0.0707107
$201$	−8.00000	−0.564276
$202$	−7.25544	−0.510491
$203$	6.74456	0.473375
$204$	0	0
$205$	2.74456	0.191689
$206$	−4.00000	−0.278693
$207$	−1.00000	−0.0695048
$208$	−4.74456	−0.328976
$209$	26.9783	1.86612
$210$	−1.00000	−0.0690066
$211$	−13.4891	−0.928630	−0.464315	−	0.885670i	$-0.653699\pi$
$211$	−13.4891	−0.928630	−0.464315	+	0.885670i	$0.653699\pi$
$212$	1.25544	0.0862238
$213$	8.00000	0.548151
$214$	−4.74456	−0.324332
$215$	0	0
$216$	1.00000	0.0680414
$217$	6.74456	0.457851
$218$	−1.25544	−0.0850289
$219$	−10.7446	−0.726050
$220$	−4.00000	−0.269680
$221$	0	0
$222$	2.00000	0.134231
$223$	−3.48913	−0.233649	−0.116825	−	0.993153i	$-0.537272\pi$
$223$	−3.48913	−0.233649	−0.116825	+	0.993153i	$0.537272\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−2.00000	−0.133038
$227$	−6.74456	−0.447652	−0.223826	−	0.974629i	$-0.571855\pi$
$227$	−6.74456	−0.447652	−0.223826	+	0.974629i	$0.571855\pi$
$228$	6.74456	0.446670
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	1.00000	0.0659380
$231$	−4.00000	−0.263181
$232$	6.74456	0.442802
$233$	−0.510875	−0.0334685	−0.0167343	−	0.999860i	$-0.505327\pi$
$233$	−0.510875	−0.0334685	−0.0167343	+	0.999860i	$0.505327\pi$
$234$	4.74456	0.310162
$235$	−1.25544	−0.0818957
$236$	4.00000	0.260378
$237$	8.00000	0.519656
$238$	0	0
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−1.00000	−0.0645497
$241$	9.48913	0.611248	0.305624	−	0.952152i	$-0.401135\pi$
$241$	9.48913	0.611248	0.305624	+	0.952152i	$0.401135\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	11.4891	0.735516
$245$	1.00000	0.0638877
$246$	2.74456	0.174987
$247$	32.0000	2.03611
$248$	6.74456	0.428280
$249$	−5.25544	−0.333050
$250$	−1.00000	−0.0632456
$251$	−16.2337	−1.02466	−0.512331	−	0.858788i	$-0.671218\pi$
$251$	−16.2337	−1.02466	−0.512331	+	0.858788i	$0.671218\pi$
$252$	−1.00000	−0.0629941
$253$	4.00000	0.251478
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	−4.74456	−0.294245
$261$	−6.74456	−0.417478
$262$	−4.00000	−0.247121
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	−4.00000	−0.246183
$265$	1.25544	0.0771209
$266$	−6.74456	−0.413536
$267$	3.25544	0.199230
$268$	8.00000	0.488678
$269$	−15.2554	−0.930140	−0.465070	−	0.885274i	$-0.653971\pi$
$269$	−15.2554	−0.930140	−0.465070	+	0.885274i	$0.653971\pi$
$270$	1.00000	0.0608581
$271$	1.25544	0.0762624	0.0381312	−	0.999273i	$-0.487860\pi$
$271$	1.25544	0.0762624	0.0381312	+	0.999273i	$0.487860\pi$
$272$	0	0
$273$	−4.74456	−0.287154
$274$	11.4891	0.694083
$275$	−4.00000	−0.241209
$276$	1.00000	0.0601929
$277$	21.2554	1.27712	0.638558	−	0.769574i	$-0.279531\pi$
$277$	21.2554	1.27712	0.638558	+	0.769574i	$0.279531\pi$
$278$	−9.48913	−0.569120
$279$	−6.74456	−0.403786
$280$	1.00000	0.0597614
$281$	19.4891	1.16262	0.581312	−	0.813681i	$-0.302540\pi$
$281$	19.4891	1.16262	0.581312	+	0.813681i	$0.302540\pi$
$282$	−1.25544	−0.0747602
$283$	−18.7446	−1.11425	−0.557124	−	0.830429i	$-0.688095\pi$
$283$	−18.7446	−1.11425	−0.557124	+	0.830429i	$0.688095\pi$
$284$	−8.00000	−0.474713
$285$	6.74456	0.399513
$286$	−18.9783	−1.12221
$287$	−2.74456	−0.162006
$288$	−1.00000	−0.0589256
$289$	−17.0000	−1.00000
$290$	6.74456	0.396054
$291$	−12.7446	−0.747099
$292$	10.7446	0.628778
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	1.00000	0.0583212
$295$	4.00000	0.232889
$296$	−2.00000	−0.116248
$297$	4.00000	0.232104
$298$	15.4891	0.897261
$299$	4.74456	0.274385
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−13.4891	−0.776212
$303$	−7.25544	−0.416814
$304$	−6.74456	−0.386827
$305$	11.4891	0.657865
$306$	0	0
$307$	26.9783	1.53973	0.769865	−	0.638207i	$-0.220323\pi$
$307$	26.9783	1.53973	0.769865	+	0.638207i	$0.220323\pi$
$308$	4.00000	0.227921
$309$	−4.00000	−0.227552
$310$	6.74456	0.383065
$311$	−19.4891	−1.10513	−0.552563	−	0.833471i	$-0.686350\pi$
$311$	−19.4891	−1.10513	−0.552563	+	0.833471i	$0.686350\pi$
$312$	−4.74456	−0.268608
$313$	16.7446	0.946459	0.473229	−	0.880939i	$-0.343088\pi$
$313$	16.7446	0.946459	0.473229	+	0.880939i	$0.343088\pi$
$314$	2.00000	0.112867
$315$	−1.00000	−0.0563436
$316$	−8.00000	−0.450035
$317$	−28.9783	−1.62758	−0.813790	−	0.581159i	$-0.802600\pi$
$317$	−28.9783	−1.62758	−0.813790	+	0.581159i	$0.802600\pi$
$318$	1.25544	0.0704014
$319$	26.9783	1.51049
$320$	1.00000	0.0559017
$321$	−4.74456	−0.264816
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	1.00000	0.0555556
$325$	−4.74456	−0.263181
$326$	−0.744563	−0.0412375
$327$	−1.25544	−0.0694258
$328$	−2.74456	−0.151543
$329$	1.25544	0.0692145
$330$	−4.00000	−0.220193
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	5.25544	0.288430
$333$	2.00000	0.109599
$334$	5.25544	0.287565
$335$	8.00000	0.437087
$336$	1.00000	0.0545545
$337$	10.0000	0.544735	0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000	0.544735	0.272367	+	0.962193i	$0.412193\pi$
$338$	−9.51087	−0.517323
$339$	−2.00000	−0.108625
$340$	0	0
$341$	26.9783	1.46095
$342$	6.74456	0.364704
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	1.00000	0.0538382
$346$	4.74456	0.255069
$347$	22.9783	1.23354	0.616769	−	0.787145i	$-0.288441\pi$
$347$	22.9783	1.23354	0.616769	+	0.787145i	$0.288441\pi$
$348$	6.74456	0.361547
$349$	20.7446	1.11043	0.555215	−	0.831707i	$-0.312636\pi$
$349$	20.7446	1.11043	0.555215	+	0.831707i	$0.312636\pi$
$350$	1.00000	0.0534522
$351$	4.74456	0.253246
$352$	4.00000	0.213201
$353$	−3.48913	−0.185707	−0.0928537	−	0.995680i	$-0.529599\pi$
$353$	−3.48913	−0.185707	−0.0928537	+	0.995680i	$0.529599\pi$
$354$	4.00000	0.212598
$355$	−8.00000	−0.424596
$356$	−3.25544	−0.172538
$357$	0	0
$358$	0.744563	0.0393514
$359$	18.9783	1.00163	0.500817	−	0.865553i	$-0.333033\pi$
$359$	18.9783	1.00163	0.500817	+	0.865553i	$0.333033\pi$
$360$	−1.00000	−0.0527046
$361$	26.4891	1.39416
$362$	14.0000	0.735824
$363$	−5.00000	−0.262432
$364$	4.74456	0.248683
$365$	10.7446	0.562396
$366$	11.4891	0.600546
$367$	29.4891	1.53932	0.769660	−	0.638454i	$-0.220426\pi$
$367$	29.4891	1.53932	0.769660	+	0.638454i	$0.220426\pi$
$368$	−1.00000	−0.0521286
$369$	2.74456	0.142876
$370$	−2.00000	−0.103975
$371$	−1.25544	−0.0651791
$372$	6.74456	0.349689
$373$	0.510875	0.0264521	0.0132260	−	0.999913i	$-0.495790\pi$
$373$	0.510875	0.0264521	0.0132260	+	0.999913i	$0.495790\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	1.25544	0.0647442
$377$	32.0000	1.64808
$378$	−1.00000	−0.0514344
$379$	4.74456	0.243712	0.121856	−	0.992548i	$-0.461115\pi$
$379$	4.74456	0.243712	0.121856	+	0.992548i	$0.461115\pi$
$380$	−6.74456	−0.345989
$381$	−8.00000	−0.409852
$382$	16.0000	0.818631
$383$	27.2554	1.39269	0.696344	−	0.717708i	$-0.254809\pi$
$383$	27.2554	1.39269	0.696344	+	0.717708i	$0.254809\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	−14.0000	−0.712581
$387$	0	0
$388$	12.7446	0.647007
$389$	−19.4891	−0.988138	−0.494069	−	0.869423i	$-0.664491\pi$
$389$	−19.4891	−0.988138	−0.494069	+	0.869423i	$0.664491\pi$
$390$	−4.74456	−0.240250
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	−4.00000	−0.201773
$394$	3.48913	0.175780
$395$	−8.00000	−0.402524
$396$	−4.00000	−0.201008
$397$	−23.7228	−1.19061	−0.595307	−	0.803498i	$-0.702970\pi$
$397$	−23.7228	−1.19061	−0.595307	+	0.803498i	$0.702970\pi$
$398$	10.2337	0.512968
$399$	−6.74456	−0.337650
$400$	1.00000	0.0500000
$401$	−8.97825	−0.448352	−0.224176	−	0.974549i	$-0.571969\pi$
$401$	−8.97825	−0.448352	−0.224176	+	0.974549i	$0.571969\pi$
$402$	8.00000	0.399004
$403$	32.0000	1.59403
$404$	7.25544	0.360971
$405$	1.00000	0.0496904
$406$	−6.74456	−0.334727
$407$	−8.00000	−0.396545
$408$	0	0
$409$	36.9783	1.82846	0.914228	−	0.405199i	$-0.132798\pi$
$409$	36.9783	1.82846	0.914228	+	0.405199i	$0.132798\pi$
$410$	−2.74456	−0.135544
$411$	11.4891	0.566717
$412$	4.00000	0.197066
$413$	−4.00000	−0.196827
$414$	1.00000	0.0491473
$415$	5.25544	0.257979
$416$	4.74456	0.232621
$417$	−9.48913	−0.464684
$418$	−26.9783	−1.31955
$419$	−8.23369	−0.402242	−0.201121	−	0.979566i	$-0.564458\pi$
$419$	−8.23369	−0.402242	−0.201121	+	0.979566i	$0.564458\pi$
$420$	1.00000	0.0487950
$421$	26.7446	1.30345	0.651725	−	0.758455i	$-0.274046\pi$
$421$	26.7446	1.30345	0.651725	+	0.758455i	$0.274046\pi$
$422$	13.4891	0.656640
$423$	−1.25544	−0.0610415
$424$	−1.25544	−0.0609694
$425$	0	0
$426$	−8.00000	−0.387601
$427$	−11.4891	−0.555998
$428$	4.74456	0.229337
$429$	−18.9783	−0.916279
$430$	0	0
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	−1.00000	−0.0481125
$433$	−30.2337	−1.45294	−0.726469	−	0.687199i	$-0.758840\pi$
$433$	−30.2337	−1.45294	−0.726469	+	0.687199i	$0.758840\pi$
$434$	−6.74456	−0.323749
$435$	6.74456	0.323377
$436$	1.25544	0.0601245
$437$	6.74456	0.322636
$438$	10.7446	0.513395
$439$	30.7446	1.46736	0.733679	−	0.679496i	$-0.237802\pi$
$439$	30.7446	1.46736	0.733679	+	0.679496i	$0.237802\pi$
$440$	4.00000	0.190693
$441$	1.00000	0.0476190
$442$	0	0
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	−2.00000	−0.0949158
$445$	−3.25544	−0.154323
$446$	3.48913	0.165215
$447$	15.4891	0.732610
$448$	−1.00000	−0.0472456
$449$	16.9783	0.801253	0.400627	−	0.916241i	$-0.368792\pi$
$449$	16.9783	0.801253	0.400627	+	0.916241i	$0.368792\pi$
$450$	−1.00000	−0.0471405
$451$	−10.9783	−0.516946
$452$	2.00000	0.0940721
$453$	−13.4891	−0.633774
$454$	6.74456	0.316538
$455$	4.74456	0.222429
$456$	−6.74456	−0.315843
$457$	4.51087	0.211010	0.105505	−	0.994419i	$-0.466354\pi$
$457$	4.51087	0.211010	0.105505	+	0.994419i	$0.466354\pi$
$458$	−2.00000	−0.0934539
$459$	0	0
$460$	−1.00000	−0.0466252
$461$	−2.23369	−0.104033	−0.0520166	−	0.998646i	$-0.516565\pi$
$461$	−2.23369	−0.104033	−0.0520166	+	0.998646i	$0.516565\pi$
$462$	4.00000	0.186097
$463$	−32.4674	−1.50889	−0.754443	−	0.656365i	$-0.772093\pi$
$463$	−32.4674	−1.50889	−0.754443	+	0.656365i	$0.772093\pi$
$464$	−6.74456	−0.313108
$465$	6.74456	0.312772
$466$	0.510875	0.0236658
$467$	−25.7228	−1.19031	−0.595155	−	0.803611i	$-0.702909\pi$
$467$	−25.7228	−1.19031	−0.595155	+	0.803611i	$0.702909\pi$
$468$	−4.74456	−0.219317
$469$	−8.00000	−0.369406
$470$	1.25544	0.0579090
$471$	2.00000	0.0921551
$472$	−4.00000	−0.184115
$473$	0	0
$474$	−8.00000	−0.367452
$475$	−6.74456	−0.309462
$476$	0	0
$477$	1.25544	0.0574825
$478$	−8.00000	−0.365911
$479$	−29.4891	−1.34739	−0.673696	−	0.739008i	$-0.735294\pi$
$479$	−29.4891	−1.34739	−0.673696	+	0.739008i	$0.735294\pi$
$480$	1.00000	0.0456435
$481$	−9.48913	−0.432667
$482$	−9.48913	−0.432218
$483$	−1.00000	−0.0455016
$484$	5.00000	0.227273
$485$	12.7446	0.578701
$486$	1.00000	0.0453609
$487$	30.9783	1.40376	0.701879	−	0.712296i	$-0.252345\pi$
$487$	30.9783	1.40376	0.701879	+	0.712296i	$0.252345\pi$
$488$	−11.4891	−0.520088
$489$	−0.744563	−0.0336703
$490$	−1.00000	−0.0451754
$491$	43.7228	1.97318	0.986591	−	0.163209i	$-0.0521846\pi$
$491$	43.7228	1.97318	0.986591	+	0.163209i	$0.0521846\pi$
$492$	−2.74456	−0.123734
$493$	0	0
$494$	−32.0000	−1.43975
$495$	−4.00000	−0.179787
$496$	−6.74456	−0.302840
$497$	8.00000	0.358849
$498$	5.25544	0.235502
$499$	−32.4674	−1.45344	−0.726720	−	0.686934i	$-0.758956\pi$
$499$	−32.4674	−1.45344	−0.726720	+	0.686934i	$0.758956\pi$
$500$	1.00000	0.0447214
$501$	5.25544	0.234796
$502$	16.2337	0.724545
$503$	−31.7228	−1.41445	−0.707225	−	0.706988i	$-0.750053\pi$
$503$	−31.7228	−1.41445	−0.707225	+	0.706988i	$0.750053\pi$
$504$	1.00000	0.0445435
$505$	7.25544	0.322863
$506$	−4.00000	−0.177822
$507$	−9.51087	−0.422393
$508$	8.00000	0.354943
$509$	19.7228	0.874198	0.437099	−	0.899413i	$-0.356006\pi$
$509$	19.7228	0.874198	0.437099	+	0.899413i	$0.356006\pi$
$510$	0	0
$511$	−10.7446	−0.475311
$512$	−1.00000	−0.0441942
$513$	6.74456	0.297780
$514$	−18.0000	−0.793946
$515$	4.00000	0.176261
$516$	0	0
$517$	5.02175	0.220856
$518$	2.00000	0.0878750
$519$	4.74456	0.208263
$520$	4.74456	0.208063
$521$	14.2337	0.623589	0.311795	−	0.950150i	$-0.399070\pi$
$521$	14.2337	0.623589	0.311795	+	0.950150i	$0.399070\pi$
$522$	6.74456	0.295201
$523$	24.2337	1.05967	0.529833	−	0.848102i	$-0.322255\pi$
$523$	24.2337	1.05967	0.529833	+	0.848102i	$0.322255\pi$
$524$	4.00000	0.174741
$525$	1.00000	0.0436436
$526$	8.00000	0.348817
$527$	0	0
$528$	4.00000	0.174078
$529$	1.00000	0.0434783
$530$	−1.25544	−0.0545327
$531$	4.00000	0.173585
$532$	6.74456	0.292414
$533$	−13.0217	−0.564035
$534$	−3.25544	−0.140877
$535$	4.74456	0.205125
$536$	−8.00000	−0.345547
$537$	0.744563	0.0321302
$538$	15.2554	0.657709
$539$	−4.00000	−0.172292
$540$	−1.00000	−0.0430331
$541$	−36.9783	−1.58982	−0.794910	−	0.606728i	$-0.792482\pi$
$541$	−36.9783	−1.58982	−0.794910	+	0.606728i	$0.792482\pi$
$542$	−1.25544	−0.0539257
$543$	14.0000	0.600798
$544$	0	0
$545$	1.25544	0.0537770
$546$	4.74456	0.203049
$547$	18.2337	0.779616	0.389808	−	0.920896i	$-0.372541\pi$
$547$	18.2337	0.779616	0.389808	+	0.920896i	$0.372541\pi$
$548$	−11.4891	−0.490791
$549$	11.4891	0.490344
$550$	4.00000	0.170561
$551$	45.4891	1.93790
$552$	−1.00000	−0.0425628
$553$	8.00000	0.340195
$554$	−21.2554	−0.903057
$555$	−2.00000	−0.0848953
$556$	9.48913	0.402429
$557$	0.233688	0.00990168	0.00495084	−	0.999988i	$-0.498424\pi$
$557$	0.233688	0.00990168	0.00495084	+	0.999988i	$0.498424\pi$
$558$	6.74456	0.285520
$559$	0	0
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−19.4891	−0.822099
$563$	−44.2337	−1.86423	−0.932114	−	0.362165i	$-0.882038\pi$
$563$	−44.2337	−1.86423	−0.932114	+	0.362165i	$0.882038\pi$
$564$	1.25544	0.0528634
$565$	2.00000	0.0841406
$566$	18.7446	0.787893
$567$	−1.00000	−0.0419961
$568$	8.00000	0.335673
$569$	20.9783	0.879454	0.439727	−	0.898131i	$-0.355075\pi$
$569$	20.9783	0.879454	0.439727	+	0.898131i	$0.355075\pi$
$570$	−6.74456	−0.282499
$571$	−43.7228	−1.82974	−0.914871	−	0.403745i	$-0.867708\pi$
$571$	−43.7228	−1.82974	−0.914871	+	0.403745i	$0.867708\pi$
$572$	18.9783	0.793521
$573$	16.0000	0.668410
$574$	2.74456	0.114556
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	17.2554	0.718353	0.359177	−	0.933270i	$-0.383058\pi$
$577$	17.2554	0.718353	0.359177	+	0.933270i	$0.383058\pi$
$578$	17.0000	0.707107
$579$	−14.0000	−0.581820
$580$	−6.74456	−0.280053
$581$	−5.25544	−0.218032
$582$	12.7446	0.528279
$583$	−5.02175	−0.207980
$584$	−10.7446	−0.444613
$585$	−4.74456	−0.196164
$586$	−14.0000	−0.578335
$587$	6.51087	0.268733	0.134366	−	0.990932i	$-0.457100\pi$
$587$	6.51087	0.268733	0.134366	+	0.990932i	$0.457100\pi$
$588$	−1.00000	−0.0412393
$589$	45.4891	1.87435
$590$	−4.00000	−0.164677
$591$	3.48913	0.143523
$592$	2.00000	0.0821995
$593$	−16.9783	−0.697213	−0.348607	−	0.937269i	$-0.613345\pi$
$593$	−16.9783	−0.697213	−0.348607	+	0.937269i	$0.613345\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−15.4891	−0.634459
$597$	10.2337	0.418837
$598$	−4.74456	−0.194020
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	1.00000	0.0408248
$601$	26.4674	1.07963	0.539813	−	0.841785i	$-0.318495\pi$
$601$	26.4674	1.07963	0.539813	+	0.841785i	$0.318495\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	13.4891	0.548865
$605$	5.00000	0.203279
$606$	7.25544	0.294732
$607$	24.5109	0.994866	0.497433	−	0.867502i	$-0.334276\pi$
$607$	24.5109	0.994866	0.497433	+	0.867502i	$0.334276\pi$
$608$	6.74456	0.273528
$609$	−6.74456	−0.273303
$610$	−11.4891	−0.465181
$611$	5.95650	0.240974
$612$	0	0
$613$	22.0000	0.888572	0.444286	−	0.895885i	$-0.353457\pi$
$613$	22.0000	0.888572	0.444286	+	0.895885i	$0.353457\pi$
$614$	−26.9783	−1.08875
$615$	−2.74456	−0.110671
$616$	−4.00000	−0.161165
$617$	16.9783	0.683519	0.341759	−	0.939788i	$-0.388977\pi$
$617$	16.9783	0.683519	0.341759	+	0.939788i	$0.388977\pi$
$618$	4.00000	0.160904
$619$	−28.2337	−1.13481	−0.567404	−	0.823440i	$-0.692052\pi$
$619$	−28.2337	−1.13481	−0.567404	+	0.823440i	$0.692052\pi$
$620$	−6.74456	−0.270868
$621$	1.00000	0.0401286
$622$	19.4891	0.781443
$623$	3.25544	0.130426
$624$	4.74456	0.189935
$625$	1.00000	0.0400000
$626$	−16.7446	−0.669247
$627$	−26.9783	−1.07741
$628$	−2.00000	−0.0798087
$629$	0	0
$630$	1.00000	0.0398410
$631$	26.9783	1.07399	0.536994	−	0.843586i	$-0.319560\pi$
$631$	26.9783	1.07399	0.536994	+	0.843586i	$0.319560\pi$
$632$	8.00000	0.318223
$633$	13.4891	0.536145
$634$	28.9783	1.15087
$635$	8.00000	0.317470
$636$	−1.25544	−0.0497813
$637$	−4.74456	−0.187986
$638$	−26.9783	−1.06808
$639$	−8.00000	−0.316475
$640$	−1.00000	−0.0395285
$641$	35.4891	1.40174	0.700868	−	0.713291i	$-0.252796\pi$
$641$	35.4891	1.40174	0.700868	+	0.713291i	$0.252796\pi$
$642$	4.74456	0.187253
$643$	29.7228	1.17215	0.586077	−	0.810256i	$-0.300672\pi$
$643$	29.7228	1.17215	0.586077	+	0.810256i	$0.300672\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	0	0
$647$	10.7446	0.422412	0.211206	−	0.977442i	$-0.432261\pi$
$647$	10.7446	0.422412	0.211206	+	0.977442i	$0.432261\pi$
$648$	−1.00000	−0.0392837
$649$	−16.0000	−0.628055
$650$	4.74456	0.186097
$651$	−6.74456	−0.264340
$652$	0.744563	0.0291593
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	1.25544	0.0490915
$655$	4.00000	0.156293
$656$	2.74456	0.107157
$657$	10.7446	0.419185
$658$	−1.25544	−0.0489420
$659$	−10.9783	−0.427652	−0.213826	−	0.976872i	$-0.568593\pi$
$659$	−10.9783	−0.427652	−0.213826	+	0.976872i	$0.568593\pi$
$660$	4.00000	0.155700
$661$	8.51087	0.331035	0.165517	−	0.986207i	$-0.447071\pi$
$661$	8.51087	0.331035	0.165517	+	0.986207i	$0.447071\pi$
$662$	12.0000	0.466393
$663$	0	0
$664$	−5.25544	−0.203951
$665$	6.74456	0.261543
$666$	−2.00000	−0.0774984
$667$	6.74456	0.261151
$668$	−5.25544	−0.203339
$669$	3.48913	0.134897
$670$	−8.00000	−0.309067
$671$	−45.9565	−1.77413
$672$	−1.00000	−0.0385758
$673$	−27.4891	−1.05963	−0.529814	−	0.848114i	$-0.677738\pi$
$673$	−27.4891	−1.05963	−0.529814	+	0.848114i	$0.677738\pi$
$674$	−10.0000	−0.385186
$675$	−1.00000	−0.0384900
$676$	9.51087	0.365803
$677$	15.4891	0.595295	0.297648	−	0.954676i	$-0.403798\pi$
$677$	15.4891	0.595295	0.297648	+	0.954676i	$0.403798\pi$
$678$	2.00000	0.0768095
$679$	−12.7446	−0.489091
$680$	0	0
$681$	6.74456	0.258452
$682$	−26.9783	−1.03305
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−6.74456	−0.257885
$685$	−11.4891	−0.438977
$686$	1.00000	0.0381802
$687$	−2.00000	−0.0763048
$688$	0	0
$689$	−5.95650	−0.226925
$690$	−1.00000	−0.0380693
$691$	36.4674	1.38728	0.693642	−	0.720320i	$-0.256005\pi$
$691$	36.4674	1.38728	0.693642	+	0.720320i	$0.256005\pi$
$692$	−4.74456	−0.180361
$693$	4.00000	0.151947
$694$	−22.9783	−0.872242
$695$	9.48913	0.359943
$696$	−6.74456	−0.255652
$697$	0	0
$698$	−20.7446	−0.785193
$699$	0.510875	0.0193231
$700$	−1.00000	−0.0377964
$701$	4.97825	0.188026	0.0940130	−	0.995571i	$-0.470030\pi$
$701$	4.97825	0.188026	0.0940130	+	0.995571i	$0.470030\pi$
$702$	−4.74456	−0.179072
$703$	−13.4891	−0.508752
$704$	−4.00000	−0.150756
$705$	1.25544	0.0472825
$706$	3.48913	0.131315
$707$	−7.25544	−0.272869
$708$	−4.00000	−0.150329
$709$	−52.2337	−1.96168	−0.980839	−	0.194822i	$-0.937587\pi$
$709$	−52.2337	−1.96168	−0.980839	+	0.194822i	$0.937587\pi$
$710$	8.00000	0.300235
$711$	−8.00000	−0.300023
$712$	3.25544	0.122003
$713$	6.74456	0.252586
$714$	0	0
$715$	18.9783	0.709746
$716$	−0.744563	−0.0278256
$717$	−8.00000	−0.298765
$718$	−18.9783	−0.708262
$719$	−14.0000	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$719$	−14.0000	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$720$	1.00000	0.0372678
$721$	−4.00000	−0.148968
$722$	−26.4891	−0.985823
$723$	−9.48913	−0.352904
$724$	−14.0000	−0.520306
$725$	−6.74456	−0.250487
$726$	5.00000	0.185567
$727$	44.0000	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$728$	−4.74456	−0.175845
$729$	1.00000	0.0370370
$730$	−10.7446	−0.397674
$731$	0	0
$732$	−11.4891	−0.424650
$733$	7.48913	0.276617	0.138309	−	0.990389i	$-0.455833\pi$
$733$	7.48913	0.276617	0.138309	+	0.990389i	$0.455833\pi$
$734$	−29.4891	−1.08846
$735$	−1.00000	−0.0368856
$736$	1.00000	0.0368605
$737$	−32.0000	−1.17874
$738$	−2.74456	−0.101029
$739$	−32.4674	−1.19433	−0.597166	−	0.802118i	$-0.703707\pi$
$739$	−32.4674	−1.19433	−0.597166	+	0.802118i	$0.703707\pi$
$740$	2.00000	0.0735215
$741$	−32.0000	−1.17555
$742$	1.25544	0.0460886
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	−6.74456	−0.247268
$745$	−15.4891	−0.567478
$746$	−0.510875	−0.0187045
$747$	5.25544	0.192286
$748$	0	0
$749$	−4.74456	−0.173363
$750$	1.00000	0.0365148
$751$	−33.4891	−1.22204	−0.611018	−	0.791617i	$-0.709240\pi$
$751$	−33.4891	−1.22204	−0.611018	+	0.791617i	$0.709240\pi$
$752$	−1.25544	−0.0457811
$753$	16.2337	0.591588
$754$	−32.0000	−1.16537
$755$	13.4891	0.490920
$756$	1.00000	0.0363696
$757$	15.4891	0.562962	0.281481	−	0.959567i	$-0.409174\pi$
$757$	15.4891	0.562962	0.281481	+	0.959567i	$0.409174\pi$
$758$	−4.74456	−0.172330
$759$	−4.00000	−0.145191
$760$	6.74456	0.244651
$761$	−37.7228	−1.36745	−0.683725	−	0.729739i	$-0.739641\pi$
$761$	−37.7228	−1.36745	−0.683725	+	0.729739i	$0.739641\pi$
$762$	8.00000	0.289809
$763$	−1.25544	−0.0454499
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−27.2554	−0.984779
$767$	−18.9783	−0.685265
$768$	−1.00000	−0.0360844
$769$	32.0000	1.15395	0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000	1.15395	0.576975	+	0.816762i	$0.304233\pi$
$770$	−4.00000	−0.144150
$771$	−18.0000	−0.648254
$772$	14.0000	0.503871
$773$	−12.5109	−0.449985	−0.224992	−	0.974361i	$-0.572236\pi$
$773$	−12.5109	−0.449985	−0.224992	+	0.974361i	$0.572236\pi$
$774$	0	0
$775$	−6.74456	−0.242272
$776$	−12.7446	−0.457503
$777$	2.00000	0.0717496
$778$	19.4891	0.698719
$779$	−18.5109	−0.663221
$780$	4.74456	0.169883
$781$	32.0000	1.14505
$782$	0	0
$783$	6.74456	0.241031
$784$	1.00000	0.0357143
$785$	−2.00000	−0.0713831
$786$	4.00000	0.142675
$787$	45.7228	1.62984	0.814921	−	0.579572i	$-0.196780\pi$
$787$	45.7228	1.62984	0.814921	+	0.579572i	$0.196780\pi$
$788$	−3.48913	−0.124295
$789$	8.00000	0.284808
$790$	8.00000	0.284627
$791$	−2.00000	−0.0711118
$792$	4.00000	0.142134
$793$	−54.5109	−1.93574
$794$	23.7228	0.841891
$795$	−1.25544	−0.0445258
$796$	−10.2337	−0.362723
$797$	7.02175	0.248723	0.124362	−	0.992237i	$-0.460312\pi$
$797$	7.02175	0.248723	0.124362	+	0.992237i	$0.460312\pi$
$798$	6.74456	0.238755
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−3.25544	−0.115025
$802$	8.97825	0.317033
$803$	−42.9783	−1.51667
$804$	−8.00000	−0.282138
$805$	1.00000	0.0352454
$806$	−32.0000	−1.12715
$807$	15.2554	0.537017
$808$	−7.25544	−0.255245
$809$	−7.02175	−0.246872	−0.123436	−	0.992353i	$-0.539391\pi$
$809$	−7.02175	−0.246872	−0.123436	+	0.992353i	$0.539391\pi$
$810$	−1.00000	−0.0351364
$811$	−1.02175	−0.0358785	−0.0179392	−	0.999839i	$-0.505711\pi$
$811$	−1.02175	−0.0358785	−0.0179392	+	0.999839i	$0.505711\pi$
$812$	6.74456	0.236688
$813$	−1.25544	−0.0440301
$814$	8.00000	0.280400
$815$	0.744563	0.0260809
$816$	0	0
$817$	0	0
$818$	−36.9783	−1.29291
$819$	4.74456	0.165788
$820$	2.74456	0.0958443
$821$	−31.2119	−1.08930	−0.544652	−	0.838662i	$-0.683338\pi$
$821$	−31.2119	−1.08930	−0.544652	+	0.838662i	$0.683338\pi$
$822$	−11.4891	−0.400729
$823$	45.9565	1.60194	0.800971	−	0.598703i	$-0.204317\pi$
$823$	45.9565	1.60194	0.800971	+	0.598703i	$0.204317\pi$
$824$	−4.00000	−0.139347
$825$	4.00000	0.139262
$826$	4.00000	0.139178
$827$	−31.7228	−1.10311	−0.551555	−	0.834138i	$-0.685965\pi$
$827$	−31.7228	−1.10311	−0.551555	+	0.834138i	$0.685965\pi$
$828$	−1.00000	−0.0347524
$829$	11.7228	0.407150	0.203575	−	0.979059i	$-0.434744\pi$
$829$	11.7228	0.407150	0.203575	+	0.979059i	$0.434744\pi$
$830$	−5.25544	−0.182419
$831$	−21.2554	−0.737343
$832$	−4.74456	−0.164488
$833$	0	0
$834$	9.48913	0.328582
$835$	−5.25544	−0.181872
$836$	26.9783	0.933062
$837$	6.74456	0.233126
$838$	8.23369	0.284428
$839$	41.4891	1.43236	0.716182	−	0.697914i	$-0.245888\pi$
$839$	41.4891	1.43236	0.716182	+	0.697914i	$0.245888\pi$
$840$	−1.00000	−0.0345033
$841$	16.4891	0.568591
$842$	−26.7446	−0.921678
$843$	−19.4891	−0.671241
$844$	−13.4891	−0.464315
$845$	9.51087	0.327184
$846$	1.25544	0.0431628
$847$	−5.00000	−0.171802
$848$	1.25544	0.0431119
$849$	18.7446	0.643312
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	8.00000	0.274075
$853$	−1.76631	−0.0604774	−0.0302387	−	0.999543i	$-0.509627\pi$
$853$	−1.76631	−0.0604774	−0.0302387	+	0.999543i	$0.509627\pi$
$854$	11.4891	0.393150
$855$	−6.74456	−0.230659
$856$	−4.74456	−0.162166
$857$	−7.02175	−0.239858	−0.119929	−	0.992782i	$-0.538267\pi$
$857$	−7.02175	−0.239858	−0.119929	+	0.992782i	$0.538267\pi$
$858$	18.9783	0.647907
$859$	−20.4674	−0.698338	−0.349169	−	0.937060i	$-0.613536\pi$
$859$	−20.4674	−0.698338	−0.349169	+	0.937060i	$0.613536\pi$
$860$	0	0
$861$	2.74456	0.0935344
$862$	−32.0000	−1.08992
$863$	−53.4891	−1.82079	−0.910396	−	0.413739i	$-0.864223\pi$
$863$	−53.4891	−1.82079	−0.910396	+	0.413739i	$0.864223\pi$
$864$	1.00000	0.0340207
$865$	−4.74456	−0.161320
$866$	30.2337	1.02738
$867$	17.0000	0.577350
$868$	6.74456	0.228925
$869$	32.0000	1.08553
$870$	−6.74456	−0.228662
$871$	−37.9565	−1.28611
$872$	−1.25544	−0.0425145
$873$	12.7446	0.431338
$874$	−6.74456	−0.228138
$875$	−1.00000	−0.0338062
$876$	−10.7446	−0.363025
$877$	−6.74456	−0.227748	−0.113874	−	0.993495i	$-0.536326\pi$
$877$	−6.74456	−0.227748	−0.113874	+	0.993495i	$0.536326\pi$
$878$	−30.7446	−1.03758
$879$	−14.0000	−0.472208
$880$	−4.00000	−0.134840
$881$	15.2554	0.513969	0.256984	−	0.966416i	$-0.417271\pi$
$881$	15.2554	0.513969	0.256984	+	0.966416i	$0.417271\pi$
$882$	−1.00000	−0.0336718
$883$	−31.2554	−1.05183	−0.525915	−	0.850537i	$-0.676277\pi$
$883$	−31.2554	−1.05183	−0.525915	+	0.850537i	$0.676277\pi$
$884$	0	0
$885$	−4.00000	−0.134459
$886$	28.0000	0.940678
$887$	20.2337	0.679381	0.339690	−	0.940537i	$-0.389678\pi$
$887$	20.2337	0.679381	0.339690	+	0.940537i	$0.389678\pi$
$888$	2.00000	0.0671156
$889$	−8.00000	−0.268311
$890$	3.25544	0.109123
$891$	−4.00000	−0.134005
$892$	−3.48913	−0.116825
$893$	8.46738	0.283350
$894$	−15.4891	−0.518034
$895$	−0.744563	−0.0248880
$896$	1.00000	0.0334077
$897$	−4.74456	−0.158416
$898$	−16.9783	−0.566572
$899$	45.4891	1.51715
$900$	1.00000	0.0333333
$901$	0	0
$902$	10.9783	0.365536
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	−14.0000	−0.465376
$906$	13.4891	0.448146
$907$	10.5109	0.349008	0.174504	−	0.984656i	$-0.444168\pi$
$907$	10.5109	0.349008	0.174504	+	0.984656i	$0.444168\pi$
$908$	−6.74456	−0.223826
$909$	7.25544	0.240648
$910$	−4.74456	−0.157281
$911$	−34.9783	−1.15888	−0.579441	−	0.815014i	$-0.696729\pi$
$911$	−34.9783	−1.15888	−0.579441	+	0.815014i	$0.696729\pi$
$912$	6.74456	0.223335
$913$	−21.0217	−0.695718
$914$	−4.51087	−0.149206
$915$	−11.4891	−0.379819
$916$	2.00000	0.0660819
$917$	−4.00000	−0.132092
$918$	0	0
$919$	1.48913	0.0491217	0.0245609	−	0.999698i	$-0.492181\pi$
$919$	1.48913	0.0491217	0.0245609	+	0.999698i	$0.492181\pi$
$920$	1.00000	0.0329690
$921$	−26.9783	−0.888964
$922$	2.23369	0.0735626
$923$	37.9565	1.24935
$924$	−4.00000	−0.131590
$925$	2.00000	0.0657596
$926$	32.4674	1.06694
$927$	4.00000	0.131377
$928$	6.74456	0.221401
$929$	−14.7446	−0.483753	−0.241877	−	0.970307i	$-0.577763\pi$
$929$	−14.7446	−0.483753	−0.241877	+	0.970307i	$0.577763\pi$
$930$	−6.74456	−0.221163
$931$	−6.74456	−0.221044
$932$	−0.510875	−0.0167343
$933$	19.4891	0.638045
$934$	25.7228	0.841676
$935$	0	0
$936$	4.74456	0.155081
$937$	8.74456	0.285672	0.142836	−	0.989746i	$-0.454378\pi$
$937$	8.74456	0.285672	0.142836	+	0.989746i	$0.454378\pi$
$938$	8.00000	0.261209
$939$	−16.7446	−0.546438
$940$	−1.25544	−0.0409479
$941$	7.48913	0.244139	0.122069	−	0.992522i	$-0.461047\pi$
$941$	7.48913	0.244139	0.122069	+	0.992522i	$0.461047\pi$
$942$	−2.00000	−0.0651635
$943$	−2.74456	−0.0893753
$944$	4.00000	0.130189
$945$	1.00000	0.0325300
$946$	0	0
$947$	−13.4891	−0.438338	−0.219169	−	0.975687i	$-0.570335\pi$
$947$	−13.4891	−0.438338	−0.219169	+	0.975687i	$0.570335\pi$
$948$	8.00000	0.259828
$949$	−50.9783	−1.65482
$950$	6.74456	0.218823
$951$	28.9783	0.939684
$952$	0	0
$953$	−4.51087	−0.146122	−0.0730608	−	0.997327i	$-0.523277\pi$
$953$	−4.51087	−0.146122	−0.0730608	+	0.997327i	$0.523277\pi$
$954$	−1.25544	−0.0406463
$955$	−16.0000	−0.517748
$956$	8.00000	0.258738
$957$	−26.9783	−0.872083
$958$	29.4891	0.952750
$959$	11.4891	0.371003
$960$	−1.00000	−0.0322749
$961$	14.4891	0.467391
$962$	9.48913	0.305942
$963$	4.74456	0.152891
$964$	9.48913	0.305624
$965$	14.0000	0.450676
$966$	1.00000	0.0321745
$967$	−54.9783	−1.76798	−0.883991	−	0.467505i	$-0.845153\pi$
$967$	−54.9783	−1.76798	−0.883991	+	0.467505i	$0.845153\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	−12.7446	−0.409203
$971$	−56.2337	−1.80462	−0.902312	−	0.431083i	$-0.858132\pi$
$971$	−56.2337	−1.80462	−0.902312	+	0.431083i	$0.858132\pi$
$972$	−1.00000	−0.0320750
$973$	−9.48913	−0.304207
$974$	−30.9783	−0.992607
$975$	4.74456	0.151948
$976$	11.4891	0.367758
$977$	15.4891	0.495541	0.247771	−	0.968819i	$-0.420302\pi$
$977$	15.4891	0.495541	0.247771	+	0.968819i	$0.420302\pi$
$978$	0.744563	0.0238085
$979$	13.0217	0.416177
$980$	1.00000	0.0319438
$981$	1.25544	0.0400830
$982$	−43.7228	−1.39525
$983$	49.2119	1.56962	0.784809	−	0.619738i	$-0.212761\pi$
$983$	49.2119	1.56962	0.784809	+	0.619738i	$0.212761\pi$
$984$	2.74456	0.0874935
$985$	−3.48913	−0.111173
$986$	0	0
$987$	−1.25544	−0.0399610
$988$	32.0000	1.01806
$989$	0	0
$990$	4.00000	0.127128
$991$	−48.4674	−1.53962	−0.769808	−	0.638275i	$-0.779648\pi$
$991$	−48.4674	−1.53962	−0.769808	+	0.638275i	$0.779648\pi$
$992$	6.74456	0.214140
$993$	12.0000	0.380808
$994$	−8.00000	−0.253745
$995$	−10.2337	−0.324430
$996$	−5.25544	−0.166525
$997$	47.7228	1.51140	0.755698	−	0.654920i	$-0.227298\pi$
$997$	47.7228	1.51140	0.755698	+	0.654920i	$0.227298\pi$
$998$	32.4674	1.02774
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.bm.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bm.1.1	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} -4.74456 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.74456 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.74456 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.74456 q^{29} +1.00000 q^{30} -6.74456 q^{31} -1.00000 q^{32} +4.00000 q^{33} -1.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +6.74456 q^{38} +4.74456 q^{39} -1.00000 q^{40} +2.74456 q^{41} -1.00000 q^{42} -4.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} -1.25544 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.74456 q^{52} +1.25544 q^{53} +1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +6.74456 q^{57} +6.74456 q^{58} +4.00000 q^{59} -1.00000 q^{60} +11.4891 q^{61} +6.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.74456 q^{65} -4.00000 q^{66} +8.00000 q^{67} +1.00000 q^{69} +1.00000 q^{70} -8.00000 q^{71} -1.00000 q^{72} +10.7446 q^{73} -2.00000 q^{74} -1.00000 q^{75} -6.74456 q^{76} +4.00000 q^{77} -4.74456 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.74456 q^{82} +5.25544 q^{83} +1.00000 q^{84} +6.74456 q^{87} +4.00000 q^{88} -3.25544 q^{89} -1.00000 q^{90} +4.74456 q^{91} -1.00000 q^{92} +6.74456 q^{93} +1.25544 q^{94} -6.74456 q^{95} +1.00000 q^{96} +12.7446 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 2 q^{20} + 2 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} + 8 q^{33} - 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 6 q^{41} - 2 q^{42} - 8 q^{44} + 2 q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{52} + 14 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} + 2 q^{57} + 2 q^{58} + 8 q^{59} - 2 q^{60} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 8 q^{66} + 16 q^{67} + 2 q^{69} + 2 q^{70} - 16 q^{71} - 2 q^{72} + 10 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 8 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 6 q^{82} + 22 q^{83} + 2 q^{84} + 2 q^{87} + 8 q^{88} - 18 q^{89} - 2 q^{90} - 2 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 2 q^{95} + 2 q^{96} + 14 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 2 * q^20 + 2 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 + 8 * q^33 - 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 6 * q^41 - 2 * q^42 - 8 * q^44 + 2 * q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^52 + 14 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 + 2 * q^57 + 2 * q^58 + 8 * q^59 - 2 * q^60 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 8 * q^66 + 16 * q^67 + 2 * q^69 + 2 * q^70 - 16 * q^71 - 2 * q^72 + 10 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 8 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 6 * q^82 + 22 * q^83 + 2 * q^84 + 2 * q^87 + 8 * q^88 - 18 * q^89 - 2 * q^90 - 2 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 2 * q^95 + 2 * q^96 + 14 * q^97 - 2 * q^98 - 8 * q^99

Introduction

L-functions

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Database

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