LMFDB - Embedded newform 4830.2.a.bv.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:	$\Z[a_1, \ldots, a_{29}]$
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{21} -2.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} -2.74456 q^{29} -1.00000 q^{30} -2.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} +2.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +8.74456 q^{37} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +8.74456 q^{43} -2.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} +13.4891 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +4.74456 q^{53} +1.00000 q^{54} +2.00000 q^{55} -1.00000 q^{56} -2.74456 q^{58} +14.7446 q^{59} -1.00000 q^{60} -2.00000 q^{61} -2.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -4.74456 q^{67} +2.00000 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.25544 q^{71} +1.00000 q^{72} +12.7446 q^{73} +8.74456 q^{74} +1.00000 q^{75} +2.00000 q^{77} -6.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -13.4891 q^{83} -1.00000 q^{84} -2.00000 q^{85} +8.74456 q^{86} -2.74456 q^{87} -2.00000 q^{88} -10.7446 q^{89} -1.00000 q^{90} +1.00000 q^{92} -2.74456 q^{93} +13.4891 q^{94} +1.00000 q^{96} -6.74456 q^{97} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 4 q^{11} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{20} - 2 q^{21} - 4 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 2 q^{36} + 6 q^{37} - 2 q^{40} + 12 q^{41} - 2 q^{42} + 6 q^{43} - 4 q^{44} - 2 q^{45} + 2 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{50} + 4 q^{51} - 2 q^{53} + 2 q^{54} + 4 q^{55} - 2 q^{56} + 6 q^{58} + 18 q^{59} - 2 q^{60} - 4 q^{61} + 6 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} + 2 q^{70} + 18 q^{71} + 2 q^{72} + 14 q^{73} + 6 q^{74} + 2 q^{75} + 4 q^{77} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 4 q^{83} - 2 q^{84} - 4 q^{85} + 6 q^{86} + 6 q^{87} - 4 q^{88} - 10 q^{89} - 2 q^{90} + 2 q^{92} + 6 q^{93} + 4 q^{94} + 2 q^{96} - 2 q^{97} + 2 q^{98} - 4 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 - 4 * q^11 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^20 - 2 * q^21 - 4 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 2 * q^36 + 6 * q^37 - 2 * q^40 + 12 * q^41 - 2 * q^42 + 6 * q^43 - 4 * q^44 - 2 * q^45 + 2 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^50 + 4 * q^51 - 2 * q^53 + 2 * q^54 + 4 * q^55 - 2 * q^56 + 6 * q^58 + 18 * q^59 - 2 * q^60 - 4 * q^61 + 6 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 4 * q^68 + 2 * q^69 + 2 * q^70 + 18 * q^71 + 2 * q^72 + 14 * q^73 + 6 * q^74 + 2 * q^75 + 4 * q^77 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 4 * q^83 - 2 * q^84 - 4 * q^85 + 6 * q^86 + 6 * q^87 - 4 * q^88 - 10 * q^89 - 2 * q^90 + 2 * q^92 + 6 * q^93 + 4 * q^94 + 2 * q^96 - 2 * q^97 + 2 * q^98 - 4 * 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
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	−2.00000	−0.426401
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.74456	−0.509652	−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456	−0.509652	−0.254826	+	0.966987i	$0.582018\pi$
$30$	−1.00000	−0.182574
$31$	−2.74456	−0.492938	−0.246469	−	0.969151i	$-0.579270\pi$
$31$	−2.74456	−0.492938	−0.246469	+	0.969151i	$0.579270\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	2.00000	0.342997
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	8.74456	1.43760	0.718799	−	0.695218i	$-0.244692\pi$
$37$	8.74456	1.43760	0.718799	+	0.695218i	$0.244692\pi$
$38$	0	0
$39$	0	0
$40$	−1.00000	−0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	8.74456	1.33353	0.666767	−	0.745267i	$-0.267678\pi$
$43$	8.74456	1.33353	0.666767	+	0.745267i	$0.267678\pi$
$44$	−2.00000	−0.301511
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	13.4891	1.96759	0.983796	−	0.179294i	$-0.0573813\pi$
$47$	13.4891	1.96759	0.983796	+	0.179294i	$0.0573813\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	0	0
$53$	4.74456	0.651716	0.325858	−	0.945419i	$-0.394347\pi$
$53$	4.74456	0.651716	0.325858	+	0.945419i	$0.394347\pi$
$54$	1.00000	0.136083
$55$	2.00000	0.269680
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−2.74456	−0.360379
$59$	14.7446	1.91958	0.959789	−	0.280721i	$-0.0905737\pi$
$59$	14.7446	1.91958	0.959789	+	0.280721i	$0.0905737\pi$
$60$	−1.00000	−0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−2.74456	−0.348560
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−4.74456	−0.579641	−0.289820	−	0.957081i	$-0.593596\pi$
$67$	−4.74456	−0.579641	−0.289820	+	0.957081i	$0.593596\pi$
$68$	2.00000	0.242536
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	3.25544	0.386349	0.193175	−	0.981164i	$-0.438122\pi$
$71$	3.25544	0.386349	0.193175	+	0.981164i	$0.438122\pi$
$72$	1.00000	0.117851
$73$	12.7446	1.49164	0.745819	−	0.666149i	$-0.232058\pi$
$73$	12.7446	1.49164	0.745819	+	0.666149i	$0.232058\pi$
$74$	8.74456	1.01653
$75$	1.00000	0.115470
$76$	0	0
$77$	2.00000	0.227921
$78$	0	0
$79$	−6.74456	−0.758823	−0.379411	−	0.925228i	$-0.623873\pi$
$79$	−6.74456	−0.758823	−0.379411	+	0.925228i	$0.623873\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−13.4891	−1.48062	−0.740312	−	0.672264i	$-0.765322\pi$
$83$	−13.4891	−1.48062	−0.740312	+	0.672264i	$0.765322\pi$
$84$	−1.00000	−0.109109
$85$	−2.00000	−0.216930
$86$	8.74456	0.942950
$87$	−2.74456	−0.294248
$88$	−2.00000	−0.213201
$89$	−10.7446	−1.13892	−0.569461	−	0.822019i	$-0.692848\pi$
$89$	−10.7446	−1.13892	−0.569461	+	0.822019i	$0.692848\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	1.00000	0.104257
$93$	−2.74456	−0.284598
$94$	13.4891	1.39130
$95$	0	0
$96$	1.00000	0.102062
$97$	−6.74456	−0.684807	−0.342403	−	0.939553i	$-0.611241\pi$
$97$	−6.74456	−0.684807	−0.342403	+	0.939553i	$0.611241\pi$
$98$	1.00000	0.101015
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	1.25544	0.124921	0.0624603	−	0.998047i	$-0.480105\pi$
$101$	1.25544	0.124921	0.0624603	+	0.998047i	$0.480105\pi$
$102$	2.00000	0.198030
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	0	0
$105$	1.00000	0.0975900
$106$	4.74456	0.460833
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000	0.0962250
$109$	−11.4891	−1.10046	−0.550229	−	0.835014i	$-0.685460\pi$
$109$	−11.4891	−1.10046	−0.550229	+	0.835014i	$0.685460\pi$
$110$	2.00000	0.190693
$111$	8.74456	0.829997
$112$	−1.00000	−0.0944911
$113$	8.74456	0.822619	0.411310	−	0.911496i	$-0.365071\pi$
$113$	8.74456	0.822619	0.411310	+	0.911496i	$0.365071\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	−2.74456	−0.254826
$117$	0	0
$118$	14.7446	1.35735
$119$	−2.00000	−0.183340
$120$	−1.00000	−0.0912871
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	6.00000	0.541002
$124$	−2.74456	−0.246469
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−4.74456	−0.421012	−0.210506	−	0.977593i	$-0.567511\pi$
$127$	−4.74456	−0.421012	−0.210506	+	0.977593i	$0.567511\pi$
$128$	1.00000	0.0883883
$129$	8.74456	0.769916
$130$	0	0
$131$	−2.74456	−0.239794	−0.119897	−	0.992786i	$-0.538256\pi$
$131$	−2.74456	−0.239794	−0.119897	+	0.992786i	$0.538256\pi$
$132$	−2.00000	−0.174078
$133$	0	0
$134$	−4.74456	−0.409868
$135$	−1.00000	−0.0860663
$136$	2.00000	0.171499
$137$	−20.7446	−1.77233	−0.886164	−	0.463372i	$-0.846639\pi$
$137$	−20.7446	−1.77233	−0.886164	+	0.463372i	$0.846639\pi$
$138$	1.00000	0.0851257
$139$	2.74456	0.232791	0.116395	−	0.993203i	$-0.462866\pi$
$139$	2.74456	0.232791	0.116395	+	0.993203i	$0.462866\pi$
$140$	1.00000	0.0845154
$141$	13.4891	1.13599
$142$	3.25544	0.273190
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.74456	0.227924
$146$	12.7446	1.05475
$147$	1.00000	0.0824786
$148$	8.74456	0.718799
$149$	15.4891	1.26892	0.634459	−	0.772956i	$-0.281223\pi$
$149$	15.4891	1.26892	0.634459	+	0.772956i	$0.281223\pi$
$150$	1.00000	0.0816497
$151$	22.9783	1.86994	0.934972	−	0.354722i	$-0.115425\pi$
$151$	22.9783	1.86994	0.934972	+	0.354722i	$0.115425\pi$
$152$	0	0
$153$	2.00000	0.161690
$154$	2.00000	0.161165
$155$	2.74456	0.220449
$156$	0	0
$157$	15.4891	1.23617	0.618083	−	0.786113i	$-0.287909\pi$
$157$	15.4891	1.23617	0.618083	+	0.786113i	$0.287909\pi$
$158$	−6.74456	−0.536569
$159$	4.74456	0.376268
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	−13.4891	−1.05655	−0.528275	−	0.849073i	$-0.677161\pi$
$163$	−13.4891	−1.05655	−0.528275	+	0.849073i	$0.677161\pi$
$164$	6.00000	0.468521
$165$	2.00000	0.155700
$166$	−13.4891	−1.04696
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	−1.00000	−0.0771517
$169$	−13.0000	−1.00000
$170$	−2.00000	−0.153393
$171$	0	0
$172$	8.74456	0.666767
$173$	3.25544	0.247506	0.123753	−	0.992313i	$-0.460507\pi$
$173$	3.25544	0.247506	0.123753	+	0.992313i	$0.460507\pi$
$174$	−2.74456	−0.208065
$175$	−1.00000	−0.0755929
$176$	−2.00000	−0.150756
$177$	14.7446	1.10827
$178$	−10.7446	−0.805339
$179$	21.4891	1.60617	0.803086	−	0.595863i	$-0.203190\pi$
$179$	21.4891	1.60617	0.803086	+	0.595863i	$0.203190\pi$
$180$	−1.00000	−0.0745356
$181$	3.48913	0.259345	0.129672	−	0.991557i	$-0.458607\pi$
$181$	3.48913	0.259345	0.129672	+	0.991557i	$0.458607\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	1.00000	0.0737210
$185$	−8.74456	−0.642913
$186$	−2.74456	−0.201241
$187$	−4.00000	−0.292509
$188$	13.4891	0.983796
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	14.7446	1.06688	0.533440	−	0.845838i	$-0.320899\pi$
$191$	14.7446	1.06688	0.533440	+	0.845838i	$0.320899\pi$
$192$	1.00000	0.0721688
$193$	−19.4891	−1.40286	−0.701429	−	0.712739i	$-0.747454\pi$
$193$	−19.4891	−1.40286	−0.701429	+	0.712739i	$0.747454\pi$
$194$	−6.74456	−0.484231
$195$	0	0
$196$	1.00000	0.0714286
$197$	−7.48913	−0.533578	−0.266789	−	0.963755i	$-0.585963\pi$
$197$	−7.48913	−0.533578	−0.266789	+	0.963755i	$0.585963\pi$
$198$	−2.00000	−0.142134
$199$	−13.4891	−0.956219	−0.478109	−	0.878300i	$-0.658678\pi$
$199$	−13.4891	−0.956219	−0.478109	+	0.878300i	$0.658678\pi$
$200$	1.00000	0.0707107
$201$	−4.74456	−0.334656
$202$	1.25544	0.0883323
$203$	2.74456	0.192631
$204$	2.00000	0.140028
$205$	−6.00000	−0.419058
$206$	8.00000	0.557386
$207$	1.00000	0.0695048
$208$	0	0
$209$	0	0
$210$	1.00000	0.0690066
$211$	−17.4891	−1.20400	−0.602001	−	0.798496i	$-0.705629\pi$
$211$	−17.4891	−1.20400	−0.602001	+	0.798496i	$0.705629\pi$
$212$	4.74456	0.325858
$213$	3.25544	0.223059
$214$	8.00000	0.546869
$215$	−8.74456	−0.596374
$216$	1.00000	0.0680414
$217$	2.74456	0.186313
$218$	−11.4891	−0.778142
$219$	12.7446	0.861198
$220$	2.00000	0.134840
$221$	0	0
$222$	8.74456	0.586897
$223$	24.7446	1.65702	0.828509	−	0.559975i	$-0.189189\pi$
$223$	24.7446	1.65702	0.828509	+	0.559975i	$0.189189\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	8.74456	0.581680
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	23.4891	1.55221	0.776103	−	0.630607i	$-0.217194\pi$
$229$	23.4891	1.55221	0.776103	+	0.630607i	$0.217194\pi$
$230$	−1.00000	−0.0659380
$231$	2.00000	0.131590
$232$	−2.74456	−0.180189
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	−13.4891	−0.879934
$236$	14.7446	0.959789
$237$	−6.74456	−0.438106
$238$	−2.00000	−0.129641
$239$	14.2337	0.920701	0.460350	−	0.887737i	$-0.347724\pi$
$239$	14.2337	0.920701	0.460350	+	0.887737i	$0.347724\pi$
$240$	−1.00000	−0.0645497
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	−1.00000	−0.0638877
$246$	6.00000	0.382546
$247$	0	0
$248$	−2.74456	−0.174280
$249$	−13.4891	−0.854839
$250$	−1.00000	−0.0632456
$251$	−22.2337	−1.40338	−0.701689	−	0.712483i	$-0.747570\pi$
$251$	−22.2337	−1.40338	−0.701689	+	0.712483i	$0.747570\pi$
$252$	−1.00000	−0.0629941
$253$	−2.00000	−0.125739
$254$	−4.74456	−0.297700
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	−11.2554	−0.702095	−0.351047	−	0.936358i	$-0.614174\pi$
$257$	−11.2554	−0.702095	−0.351047	+	0.936358i	$0.614174\pi$
$258$	8.74456	0.544413
$259$	−8.74456	−0.543361
$260$	0	0
$261$	−2.74456	−0.169884
$262$	−2.74456	−0.169560
$263$	5.48913	0.338474	0.169237	−	0.985575i	$-0.445870\pi$
$263$	5.48913	0.338474	0.169237	+	0.985575i	$0.445870\pi$
$264$	−2.00000	−0.123091
$265$	−4.74456	−0.291456
$266$	0	0
$267$	−10.7446	−0.657557
$268$	−4.74456	−0.289820
$269$	−8.23369	−0.502017	−0.251008	−	0.967985i	$-0.580762\pi$
$269$	−8.23369	−0.502017	−0.251008	+	0.967985i	$0.580762\pi$
$270$	−1.00000	−0.0608581
$271$	−18.7446	−1.13865	−0.569326	−	0.822112i	$-0.692796\pi$
$271$	−18.7446	−1.13865	−0.569326	+	0.822112i	$0.692796\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−20.7446	−1.25322
$275$	−2.00000	−0.120605
$276$	1.00000	0.0601929
$277$	−18.7446	−1.12625	−0.563126	−	0.826371i	$-0.690401\pi$
$277$	−18.7446	−1.12625	−0.563126	+	0.826371i	$0.690401\pi$
$278$	2.74456	0.164608
$279$	−2.74456	−0.164313
$280$	1.00000	0.0597614
$281$	28.2337	1.68428	0.842140	−	0.539258i	$-0.181295\pi$
$281$	28.2337	1.68428	0.842140	+	0.539258i	$0.181295\pi$
$282$	13.4891	0.803266
$283$	8.74456	0.519810	0.259905	−	0.965634i	$-0.416309\pi$
$283$	8.74456	0.519810	0.259905	+	0.965634i	$0.416309\pi$
$284$	3.25544	0.193175
$285$	0	0
$286$	0	0
$287$	−6.00000	−0.354169
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	2.74456	0.161166
$291$	−6.74456	−0.395373
$292$	12.7446	0.745819
$293$	11.4891	0.671202	0.335601	−	0.942004i	$-0.391061\pi$
$293$	11.4891	0.671202	0.335601	+	0.942004i	$0.391061\pi$
$294$	1.00000	0.0583212
$295$	−14.7446	−0.858462
$296$	8.74456	0.508267
$297$	−2.00000	−0.116052
$298$	15.4891	0.897261
$299$	0	0
$300$	1.00000	0.0577350
$301$	−8.74456	−0.504028
$302$	22.9783	1.32225
$303$	1.25544	0.0721230
$304$	0	0
$305$	2.00000	0.114520
$306$	2.00000	0.114332
$307$	22.9783	1.31144	0.655719	−	0.755005i	$-0.272366\pi$
$307$	22.9783	1.31144	0.655719	+	0.755005i	$0.272366\pi$
$308$	2.00000	0.113961
$309$	8.00000	0.455104
$310$	2.74456	0.155881
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	0	0
$313$	−10.7446	−0.607319	−0.303659	−	0.952781i	$-0.598208\pi$
$313$	−10.7446	−0.607319	−0.303659	+	0.952781i	$0.598208\pi$
$314$	15.4891	0.874102
$315$	1.00000	0.0563436
$316$	−6.74456	−0.379411
$317$	−32.9783	−1.85224	−0.926122	−	0.377225i	$-0.876878\pi$
$317$	−32.9783	−1.85224	−0.926122	+	0.377225i	$0.876878\pi$
$318$	4.74456	0.266062
$319$	5.48913	0.307332
$320$	−1.00000	−0.0559017
$321$	8.00000	0.446516
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	1.00000	0.0555556
$325$	0	0
$326$	−13.4891	−0.747094
$327$	−11.4891	−0.635350
$328$	6.00000	0.331295
$329$	−13.4891	−0.743680
$330$	2.00000	0.110096
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−13.4891	−0.740312
$333$	8.74456	0.479199
$334$	4.00000	0.218870
$335$	4.74456	0.259223
$336$	−1.00000	−0.0545545
$337$	5.48913	0.299012	0.149506	−	0.988761i	$-0.452232\pi$
$337$	5.48913	0.299012	0.149506	+	0.988761i	$0.452232\pi$
$338$	−13.0000	−0.707107
$339$	8.74456	0.474939
$340$	−2.00000	−0.108465
$341$	5.48913	0.297253
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	8.74456	0.471475
$345$	−1.00000	−0.0538382
$346$	3.25544	0.175013
$347$	30.9783	1.66300	0.831500	−	0.555525i	$-0.187483\pi$
$347$	30.9783	1.66300	0.831500	+	0.555525i	$0.187483\pi$
$348$	−2.74456	−0.147124
$349$	27.4891	1.47146	0.735730	−	0.677275i	$-0.236839\pi$
$349$	27.4891	1.47146	0.735730	+	0.677275i	$0.236839\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	−2.00000	−0.106600
$353$	24.7446	1.31702	0.658510	−	0.752572i	$-0.271187\pi$
$353$	24.7446	1.31702	0.658510	+	0.752572i	$0.271187\pi$
$354$	14.7446	0.783665
$355$	−3.25544	−0.172781
$356$	−10.7446	−0.569461
$357$	−2.00000	−0.105851
$358$	21.4891	1.13574
$359$	−6.74456	−0.355964	−0.177982	−	0.984034i	$-0.556957\pi$
$359$	−6.74456	−0.355964	−0.177982	+	0.984034i	$0.556957\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	3.48913	0.183384
$363$	−7.00000	−0.367405
$364$	0	0
$365$	−12.7446	−0.667081
$366$	−2.00000	−0.104542
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	1.00000	0.0521286
$369$	6.00000	0.312348
$370$	−8.74456	−0.454608
$371$	−4.74456	−0.246325
$372$	−2.74456	−0.142299
$373$	35.7228	1.84966	0.924829	−	0.380384i	$-0.124208\pi$
$373$	35.7228	1.84966	0.924829	+	0.380384i	$0.124208\pi$
$374$	−4.00000	−0.206835
$375$	−1.00000	−0.0516398
$376$	13.4891	0.695649
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−12.2337	−0.628402	−0.314201	−	0.949356i	$-0.601737\pi$
$379$	−12.2337	−0.628402	−0.314201	+	0.949356i	$0.601737\pi$
$380$	0	0
$381$	−4.74456	−0.243071
$382$	14.7446	0.754397
$383$	−34.9783	−1.78731	−0.893653	−	0.448760i	$-0.851866\pi$
$383$	−34.9783	−1.78731	−0.893653	+	0.448760i	$0.851866\pi$
$384$	1.00000	0.0510310
$385$	−2.00000	−0.101929
$386$	−19.4891	−0.991970
$387$	8.74456	0.444511
$388$	−6.74456	−0.342403
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	1.00000	0.0505076
$393$	−2.74456	−0.138445
$394$	−7.48913	−0.377297
$395$	6.74456	0.339356
$396$	−2.00000	−0.100504
$397$	−37.4891	−1.88153	−0.940763	−	0.339066i	$-0.889889\pi$
$397$	−37.4891	−1.88153	−0.940763	+	0.339066i	$0.889889\pi$
$398$	−13.4891	−0.676149
$399$	0	0
$400$	1.00000	0.0500000
$401$	−18.7446	−0.936059	−0.468029	−	0.883713i	$-0.655036\pi$
$401$	−18.7446	−0.936059	−0.468029	+	0.883713i	$0.655036\pi$
$402$	−4.74456	−0.236637
$403$	0	0
$404$	1.25544	0.0624603
$405$	−1.00000	−0.0496904
$406$	2.74456	0.136210
$407$	−17.4891	−0.866904
$408$	2.00000	0.0990148
$409$	27.4891	1.35925	0.679625	−	0.733560i	$-0.262143\pi$
$409$	27.4891	1.35925	0.679625	+	0.733560i	$0.262143\pi$
$410$	−6.00000	−0.296319
$411$	−20.7446	−1.02325
$412$	8.00000	0.394132
$413$	−14.7446	−0.725532
$414$	1.00000	0.0491473
$415$	13.4891	0.662155
$416$	0	0
$417$	2.74456	0.134402
$418$	0	0
$419$	−18.2337	−0.890774	−0.445387	−	0.895338i	$-0.646934\pi$
$419$	−18.2337	−0.890774	−0.445387	+	0.895338i	$0.646934\pi$
$420$	1.00000	0.0487950
$421$	−23.4891	−1.14479	−0.572395	−	0.819978i	$-0.693986\pi$
$421$	−23.4891	−1.14479	−0.572395	+	0.819978i	$0.693986\pi$
$422$	−17.4891	−0.851357
$423$	13.4891	0.655864
$424$	4.74456	0.230416
$425$	2.00000	0.0970143
$426$	3.25544	0.157726
$427$	2.00000	0.0967868
$428$	8.00000	0.386695
$429$	0	0
$430$	−8.74456	−0.421700
$431$	−14.7446	−0.710221	−0.355110	−	0.934824i	$-0.615557\pi$
$431$	−14.7446	−0.710221	−0.355110	+	0.934824i	$0.615557\pi$
$432$	1.00000	0.0481125
$433$	−17.7228	−0.851704	−0.425852	−	0.904793i	$-0.640026\pi$
$433$	−17.7228	−0.851704	−0.425852	+	0.904793i	$0.640026\pi$
$434$	2.74456	0.131743
$435$	2.74456	0.131592
$436$	−11.4891	−0.550229
$437$	0	0
$438$	12.7446	0.608959
$439$	4.23369	0.202063	0.101031	−	0.994883i	$-0.467786\pi$
$439$	4.23369	0.202063	0.101031	+	0.994883i	$0.467786\pi$
$440$	2.00000	0.0953463
$441$	1.00000	0.0476190
$442$	0	0
$443$	−20.0000	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$444$	8.74456	0.414999
$445$	10.7446	0.509341
$446$	24.7446	1.17169
$447$	15.4891	0.732610
$448$	−1.00000	−0.0472456
$449$	40.9783	1.93388	0.966942	−	0.254998i	$-0.0820748\pi$
$449$	40.9783	1.93388	0.966942	+	0.254998i	$0.0820748\pi$
$450$	1.00000	0.0471405
$451$	−12.0000	−0.565058
$452$	8.74456	0.411310
$453$	22.9783	1.07961
$454$	−4.00000	−0.187729
$455$	0	0
$456$	0	0
$457$	−41.4891	−1.94078	−0.970390	−	0.241545i	$-0.922346\pi$
$457$	−41.4891	−1.94078	−0.970390	+	0.241545i	$0.922346\pi$
$458$	23.4891	1.09757
$459$	2.00000	0.0933520
$460$	−1.00000	−0.0466252
$461$	28.2337	1.31497	0.657487	−	0.753466i	$-0.271619\pi$
$461$	28.2337	1.31497	0.657487	+	0.753466i	$0.271619\pi$
$462$	2.00000	0.0930484
$463$	−22.2337	−1.03329	−0.516644	−	0.856201i	$-0.672819\pi$
$463$	−22.2337	−1.03329	−0.516644	+	0.856201i	$0.672819\pi$
$464$	−2.74456	−0.127413
$465$	2.74456	0.127276
$466$	−10.0000	−0.463241
$467$	10.5109	0.486385	0.243193	−	0.969978i	$-0.421805\pi$
$467$	10.5109	0.486385	0.243193	+	0.969978i	$0.421805\pi$
$468$	0	0
$469$	4.74456	0.219084
$470$	−13.4891	−0.622207
$471$	15.4891	0.713701
$472$	14.7446	0.678674
$473$	−17.4891	−0.804151
$474$	−6.74456	−0.309788
$475$	0	0
$476$	−2.00000	−0.0916698
$477$	4.74456	0.217239
$478$	14.2337	0.651034
$479$	29.4891	1.34739	0.673696	−	0.739008i	$-0.264706\pi$
$479$	29.4891	1.34739	0.673696	+	0.739008i	$0.264706\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	−2.00000	−0.0910975
$483$	−1.00000	−0.0455016
$484$	−7.00000	−0.318182
$485$	6.74456	0.306255
$486$	1.00000	0.0453609
$487$	−22.2337	−1.00750	−0.503752	−	0.863848i	$-0.668048\pi$
$487$	−22.2337	−1.00750	−0.503752	+	0.863848i	$0.668048\pi$
$488$	−2.00000	−0.0905357
$489$	−13.4891	−0.609999
$490$	−1.00000	−0.0451754
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	6.00000	0.270501
$493$	−5.48913	−0.247218
$494$	0	0
$495$	2.00000	0.0898933
$496$	−2.74456	−0.123235
$497$	−3.25544	−0.146026
$498$	−13.4891	−0.604462
$499$	−1.48913	−0.0666624	−0.0333312	−	0.999444i	$-0.510612\pi$
$499$	−1.48913	−0.0666624	−0.0333312	+	0.999444i	$0.510612\pi$
$500$	−1.00000	−0.0447214
$501$	4.00000	0.178707
$502$	−22.2337	−0.992338
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	−1.00000	−0.0445435
$505$	−1.25544	−0.0558662
$506$	−2.00000	−0.0889108
$507$	−13.0000	−0.577350
$508$	−4.74456	−0.210506
$509$	−12.2337	−0.542249	−0.271124	−	0.962544i	$-0.587395\pi$
$509$	−12.2337	−0.542249	−0.271124	+	0.962544i	$0.587395\pi$
$510$	−2.00000	−0.0885615
$511$	−12.7446	−0.563786
$512$	1.00000	0.0441942
$513$	0	0
$514$	−11.2554	−0.496456
$515$	−8.00000	−0.352522
$516$	8.74456	0.384958
$517$	−26.9783	−1.18650
$518$	−8.74456	−0.384214
$519$	3.25544	0.142898
$520$	0	0
$521$	43.2119	1.89315	0.946575	−	0.322485i	$-0.104518\pi$
$521$	43.2119	1.89315	0.946575	+	0.322485i	$0.104518\pi$
$522$	−2.74456	−0.120126
$523$	−15.2554	−0.667074	−0.333537	−	0.942737i	$-0.608242\pi$
$523$	−15.2554	−0.667074	−0.333537	+	0.942737i	$0.608242\pi$
$524$	−2.74456	−0.119897
$525$	−1.00000	−0.0436436
$526$	5.48913	0.239337
$527$	−5.48913	−0.239110
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	−4.74456	−0.206091
$531$	14.7446	0.639860
$532$	0	0
$533$	0	0
$534$	−10.7446	−0.464963
$535$	−8.00000	−0.345870
$536$	−4.74456	−0.204934
$537$	21.4891	0.927324
$538$	−8.23369	−0.354979
$539$	−2.00000	−0.0861461
$540$	−1.00000	−0.0430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−18.7446	−0.805148
$543$	3.48913	0.149733
$544$	2.00000	0.0857493
$545$	11.4891	0.492140
$546$	0	0
$547$	14.9783	0.640424	0.320212	−	0.947346i	$-0.396246\pi$
$547$	14.9783	0.640424	0.320212	+	0.947346i	$0.396246\pi$
$548$	−20.7446	−0.886164
$549$	−2.00000	−0.0853579
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	1.00000	0.0425628
$553$	6.74456	0.286808
$554$	−18.7446	−0.796380
$555$	−8.74456	−0.371186
$556$	2.74456	0.116395
$557$	−20.7446	−0.878975	−0.439488	−	0.898249i	$-0.644840\pi$
$557$	−20.7446	−0.878975	−0.439488	+	0.898249i	$0.644840\pi$
$558$	−2.74456	−0.116187
$559$	0	0
$560$	1.00000	0.0422577
$561$	−4.00000	−0.168880
$562$	28.2337	1.19097
$563$	−5.48913	−0.231339	−0.115670	−	0.993288i	$-0.536901\pi$
$563$	−5.48913	−0.231339	−0.115670	+	0.993288i	$0.536901\pi$
$564$	13.4891	0.567995
$565$	−8.74456	−0.367887
$566$	8.74456	0.367561
$567$	−1.00000	−0.0419961
$568$	3.25544	0.136595
$569$	−18.7446	−0.785813	−0.392906	−	0.919578i	$-0.628530\pi$
$569$	−18.7446	−0.785813	−0.392906	+	0.919578i	$0.628530\pi$
$570$	0	0
$571$	−17.2554	−0.722118	−0.361059	−	0.932543i	$-0.617585\pi$
$571$	−17.2554	−0.722118	−0.361059	+	0.932543i	$0.617585\pi$
$572$	0	0
$573$	14.7446	0.615963
$574$	−6.00000	−0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−3.25544	−0.135526	−0.0677628	−	0.997701i	$-0.521586\pi$
$577$	−3.25544	−0.135526	−0.0677628	+	0.997701i	$0.521586\pi$
$578$	−13.0000	−0.540729
$579$	−19.4891	−0.809940
$580$	2.74456	0.113962
$581$	13.4891	0.559623
$582$	−6.74456	−0.279571
$583$	−9.48913	−0.392999
$584$	12.7446	0.527374
$585$	0	0
$586$	11.4891	0.474611
$587$	22.9783	0.948414	0.474207	−	0.880413i	$-0.342735\pi$
$587$	22.9783	0.948414	0.474207	+	0.880413i	$0.342735\pi$
$588$	1.00000	0.0412393
$589$	0	0
$590$	−14.7446	−0.607024
$591$	−7.48913	−0.308061
$592$	8.74456	0.359399
$593$	45.2119	1.85663	0.928316	−	0.371792i	$-0.121257\pi$
$593$	45.2119	1.85663	0.928316	+	0.371792i	$0.121257\pi$
$594$	−2.00000	−0.0820610
$595$	2.00000	0.0819920
$596$	15.4891	0.634459
$597$	−13.4891	−0.552073
$598$	0	0
$599$	−35.7228	−1.45959	−0.729797	−	0.683664i	$-0.760386\pi$
$599$	−35.7228	−1.45959	−0.729797	+	0.683664i	$0.760386\pi$
$600$	1.00000	0.0408248
$601$	−20.9783	−0.855721	−0.427860	−	0.903845i	$-0.640732\pi$
$601$	−20.9783	−0.855721	−0.427860	+	0.903845i	$0.640732\pi$
$602$	−8.74456	−0.356402
$603$	−4.74456	−0.193214
$604$	22.9783	0.934972
$605$	7.00000	0.284590
$606$	1.25544	0.0509987
$607$	−20.7446	−0.841996	−0.420998	−	0.907062i	$-0.638320\pi$
$607$	−20.7446	−0.841996	−0.420998	+	0.907062i	$0.638320\pi$
$608$	0	0
$609$	2.74456	0.111215
$610$	2.00000	0.0809776
$611$	0	0
$612$	2.00000	0.0808452
$613$	−11.2554	−0.454603	−0.227301	−	0.973824i	$-0.572990\pi$
$613$	−11.2554	−0.454603	−0.227301	+	0.973824i	$0.572990\pi$
$614$	22.9783	0.927327
$615$	−6.00000	−0.241943
$616$	2.00000	0.0805823
$617$	−8.74456	−0.352043	−0.176021	−	0.984386i	$-0.556323\pi$
$617$	−8.74456	−0.352043	−0.176021	+	0.984386i	$0.556323\pi$
$618$	8.00000	0.321807
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	2.74456	0.110224
$621$	1.00000	0.0401286
$622$	14.0000	0.561349
$623$	10.7446	0.430472
$624$	0	0
$625$	1.00000	0.0400000
$626$	−10.7446	−0.429439
$627$	0	0
$628$	15.4891	0.618083
$629$	17.4891	0.697337
$630$	1.00000	0.0398410
$631$	−11.7663	−0.468409	−0.234205	−	0.972187i	$-0.575249\pi$
$631$	−11.7663	−0.468409	−0.234205	+	0.972187i	$0.575249\pi$
$632$	−6.74456	−0.268284
$633$	−17.4891	−0.695130
$634$	−32.9783	−1.30973
$635$	4.74456	0.188282
$636$	4.74456	0.188134
$637$	0	0
$638$	5.48913	0.217317
$639$	3.25544	0.128783
$640$	−1.00000	−0.0395285
$641$	−49.7228	−1.96393	−0.981967	−	0.189055i	$-0.939458\pi$
$641$	−49.7228	−1.96393	−0.981967	+	0.189055i	$0.939458\pi$
$642$	8.00000	0.315735
$643$	24.7446	0.975830	0.487915	−	0.872891i	$-0.337758\pi$
$643$	24.7446	0.975830	0.487915	+	0.872891i	$0.337758\pi$
$644$	−1.00000	−0.0394055
$645$	−8.74456	−0.344317
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	1.00000	0.0392837
$649$	−29.4891	−1.15755
$650$	0	0
$651$	2.74456	0.107568
$652$	−13.4891	−0.528275
$653$	20.9783	0.820942	0.410471	−	0.911874i	$-0.365364\pi$
$653$	20.9783	0.820942	0.410471	+	0.911874i	$0.365364\pi$
$654$	−11.4891	−0.449260
$655$	2.74456	0.107239
$656$	6.00000	0.234261
$657$	12.7446	0.497213
$658$	−13.4891	−0.525861
$659$	−34.4674	−1.34266	−0.671329	−	0.741159i	$-0.734276\pi$
$659$	−34.4674	−1.34266	−0.671329	+	0.741159i	$0.734276\pi$
$660$	2.00000	0.0778499
$661$	−24.9783	−0.971541	−0.485771	−	0.874086i	$-0.661461\pi$
$661$	−24.9783	−0.971541	−0.485771	+	0.874086i	$0.661461\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	−13.4891	−0.523480
$665$	0	0
$666$	8.74456	0.338845
$667$	−2.74456	−0.106270
$668$	4.00000	0.154765
$669$	24.7446	0.956680
$670$	4.74456	0.183298
$671$	4.00000	0.154418
$672$	−1.00000	−0.0385758
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	5.48913	0.211433
$675$	1.00000	0.0384900
$676$	−13.0000	−0.500000
$677$	−19.4891	−0.749028	−0.374514	−	0.927221i	$-0.622190\pi$
$677$	−19.4891	−0.749028	−0.374514	+	0.927221i	$0.622190\pi$
$678$	8.74456	0.335833
$679$	6.74456	0.258833
$680$	−2.00000	−0.0766965
$681$	−4.00000	−0.153280
$682$	5.48913	0.210189
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	0	0
$685$	20.7446	0.792609
$686$	−1.00000	−0.0381802
$687$	23.4891	0.896166
$688$	8.74456	0.333383
$689$	0	0
$690$	−1.00000	−0.0380693
$691$	−5.25544	−0.199926	−0.0999631	−	0.994991i	$-0.531872\pi$
$691$	−5.25544	−0.199926	−0.0999631	+	0.994991i	$0.531872\pi$
$692$	3.25544	0.123753
$693$	2.00000	0.0759737
$694$	30.9783	1.17592
$695$	−2.74456	−0.104107
$696$	−2.74456	−0.104032
$697$	12.0000	0.454532
$698$	27.4891	1.04048
$699$	−10.0000	−0.378235
$700$	−1.00000	−0.0377964
$701$	−47.4891	−1.79364	−0.896820	−	0.442396i	$-0.854129\pi$
$701$	−47.4891	−1.79364	−0.896820	+	0.442396i	$0.854129\pi$
$702$	0	0
$703$	0	0
$704$	−2.00000	−0.0753778
$705$	−13.4891	−0.508030
$706$	24.7446	0.931274
$707$	−1.25544	−0.0472156
$708$	14.7446	0.554135
$709$	36.9783	1.38875	0.694374	−	0.719615i	$-0.255682\pi$
$709$	36.9783	1.38875	0.694374	+	0.719615i	$0.255682\pi$
$710$	−3.25544	−0.122174
$711$	−6.74456	−0.252941
$712$	−10.7446	−0.402670
$713$	−2.74456	−0.102785
$714$	−2.00000	−0.0748481
$715$	0	0
$716$	21.4891	0.803086
$717$	14.2337	0.531567
$718$	−6.74456	−0.251705
$719$	47.9565	1.78848	0.894238	−	0.447592i	$-0.147718\pi$
$719$	47.9565	1.78848	0.894238	+	0.447592i	$0.147718\pi$
$720$	−1.00000	−0.0372678
$721$	−8.00000	−0.297936
$722$	−19.0000	−0.707107
$723$	−2.00000	−0.0743808
$724$	3.48913	0.129672
$725$	−2.74456	−0.101930
$726$	−7.00000	−0.259794
$727$	9.48913	0.351932	0.175966	−	0.984396i	$-0.443695\pi$
$727$	9.48913	0.351932	0.175966	+	0.984396i	$0.443695\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−12.7446	−0.471697
$731$	17.4891	0.646859
$732$	−2.00000	−0.0739221
$733$	−8.97825	−0.331619	−0.165810	−	0.986158i	$-0.553024\pi$
$733$	−8.97825	−0.331619	−0.165810	+	0.986158i	$0.553024\pi$
$734$	−8.00000	−0.295285
$735$	−1.00000	−0.0368856
$736$	1.00000	0.0368605
$737$	9.48913	0.349536
$738$	6.00000	0.220863
$739$	25.4891	0.937633	0.468816	−	0.883296i	$-0.344681\pi$
$739$	25.4891	0.937633	0.468816	+	0.883296i	$0.344681\pi$
$740$	−8.74456	−0.321457
$741$	0	0
$742$	−4.74456	−0.174178
$743$	40.0000	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$743$	40.0000	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$744$	−2.74456	−0.100621
$745$	−15.4891	−0.567478
$746$	35.7228	1.30791
$747$	−13.4891	−0.493541
$748$	−4.00000	−0.146254
$749$	−8.00000	−0.292314
$750$	−1.00000	−0.0365148
$751$	4.23369	0.154489	0.0772447	−	0.997012i	$-0.475388\pi$
$751$	4.23369	0.154489	0.0772447	+	0.997012i	$0.475388\pi$
$752$	13.4891	0.491898
$753$	−22.2337	−0.810241
$754$	0	0
$755$	−22.9783	−0.836264
$756$	−1.00000	−0.0363696
$757$	15.7228	0.571455	0.285728	−	0.958311i	$-0.407765\pi$
$757$	15.7228	0.571455	0.285728	+	0.958311i	$0.407765\pi$
$758$	−12.2337	−0.444348
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	−40.9783	−1.48546	−0.742730	−	0.669591i	$-0.766469\pi$
$761$	−40.9783	−1.48546	−0.742730	+	0.669591i	$0.766469\pi$
$762$	−4.74456	−0.171877
$763$	11.4891	0.415934
$764$	14.7446	0.533440
$765$	−2.00000	−0.0723102
$766$	−34.9783	−1.26382
$767$	0	0
$768$	1.00000	0.0360844
$769$	−14.4674	−0.521707	−0.260853	−	0.965378i	$-0.584004\pi$
$769$	−14.4674	−0.521707	−0.260853	+	0.965378i	$0.584004\pi$
$770$	−2.00000	−0.0720750
$771$	−11.2554	−0.405355
$772$	−19.4891	−0.701429
$773$	−47.9565	−1.72488	−0.862438	−	0.506163i	$-0.831063\pi$
$773$	−47.9565	−1.72488	−0.862438	+	0.506163i	$0.831063\pi$
$774$	8.74456	0.314317
$775$	−2.74456	−0.0985876
$776$	−6.74456	−0.242116
$777$	−8.74456	−0.313709
$778$	6.00000	0.215110
$779$	0	0
$780$	0	0
$781$	−6.51087	−0.232977
$782$	2.00000	0.0715199
$783$	−2.74456	−0.0980827
$784$	1.00000	0.0357143
$785$	−15.4891	−0.552831
$786$	−2.74456	−0.0978953
$787$	−7.25544	−0.258628	−0.129314	−	0.991604i	$-0.541278\pi$
$787$	−7.25544	−0.258628	−0.129314	+	0.991604i	$0.541278\pi$
$788$	−7.48913	−0.266789
$789$	5.48913	0.195418
$790$	6.74456	0.239961
$791$	−8.74456	−0.310921
$792$	−2.00000	−0.0710669
$793$	0	0
$794$	−37.4891	−1.33044
$795$	−4.74456	−0.168272
$796$	−13.4891	−0.478109
$797$	−8.97825	−0.318026	−0.159013	−	0.987276i	$-0.550831\pi$
$797$	−8.97825	−0.318026	−0.159013	+	0.987276i	$0.550831\pi$
$798$	0	0
$799$	26.9783	0.954422
$800$	1.00000	0.0353553
$801$	−10.7446	−0.379640
$802$	−18.7446	−0.661894
$803$	−25.4891	−0.899492
$804$	−4.74456	−0.167328
$805$	1.00000	0.0352454
$806$	0	0
$807$	−8.23369	−0.289840
$808$	1.25544	0.0441661
$809$	50.0000	1.75791	0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000	1.75791	0.878953	+	0.476908i	$0.158243\pi$
$810$	−1.00000	−0.0351364
$811$	2.74456	0.0963746	0.0481873	−	0.998838i	$-0.484656\pi$
$811$	2.74456	0.0963746	0.0481873	+	0.998838i	$0.484656\pi$
$812$	2.74456	0.0963153
$813$	−18.7446	−0.657401
$814$	−17.4891	−0.612994
$815$	13.4891	0.472503
$816$	2.00000	0.0700140
$817$	0	0
$818$	27.4891	0.961135
$819$	0	0
$820$	−6.00000	−0.209529
$821$	20.2337	0.706161	0.353080	−	0.935593i	$-0.385134\pi$
$821$	20.2337	0.706161	0.353080	+	0.935593i	$0.385134\pi$
$822$	−20.7446	−0.723550
$823$	−4.74456	−0.165385	−0.0826925	−	0.996575i	$-0.526352\pi$
$823$	−4.74456	−0.165385	−0.0826925	+	0.996575i	$0.526352\pi$
$824$	8.00000	0.278693
$825$	−2.00000	−0.0696311
$826$	−14.7446	−0.513029
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	1.00000	0.0347524
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	13.4891	0.468214
$831$	−18.7446	−0.650242
$832$	0	0
$833$	2.00000	0.0692959
$834$	2.74456	0.0950364
$835$	−4.00000	−0.138426
$836$	0	0
$837$	−2.74456	−0.0948660
$838$	−18.2337	−0.629872
$839$	22.9783	0.793297	0.396649	−	0.917971i	$-0.370173\pi$
$839$	22.9783	0.793297	0.396649	+	0.917971i	$0.370173\pi$
$840$	1.00000	0.0345033
$841$	−21.4674	−0.740254
$842$	−23.4891	−0.809489
$843$	28.2337	0.972420
$844$	−17.4891	−0.602001
$845$	13.0000	0.447214
$846$	13.4891	0.463766
$847$	7.00000	0.240523
$848$	4.74456	0.162929
$849$	8.74456	0.300113
$850$	2.00000	0.0685994
$851$	8.74456	0.299760
$852$	3.25544	0.111529
$853$	45.4891	1.55752	0.778759	−	0.627323i	$-0.215850\pi$
$853$	45.4891	1.55752	0.778759	+	0.627323i	$0.215850\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	8.00000	0.273434
$857$	−15.2554	−0.521116	−0.260558	−	0.965458i	$-0.583906\pi$
$857$	−15.2554	−0.521116	−0.260558	+	0.965458i	$0.583906\pi$
$858$	0	0
$859$	18.7446	0.639556	0.319778	−	0.947492i	$-0.396392\pi$
$859$	18.7446	0.639556	0.319778	+	0.947492i	$0.396392\pi$
$860$	−8.74456	−0.298187
$861$	−6.00000	−0.204479
$862$	−14.7446	−0.502202
$863$	33.4891	1.13998	0.569992	−	0.821651i	$-0.306946\pi$
$863$	33.4891	1.13998	0.569992	+	0.821651i	$0.306946\pi$
$864$	1.00000	0.0340207
$865$	−3.25544	−0.110688
$866$	−17.7228	−0.602246
$867$	−13.0000	−0.441503
$868$	2.74456	0.0931565
$869$	13.4891	0.457587
$870$	2.74456	0.0930494
$871$	0	0
$872$	−11.4891	−0.389071
$873$	−6.74456	−0.228269
$874$	0	0
$875$	1.00000	0.0338062
$876$	12.7446	0.430599
$877$	37.7228	1.27381	0.636904	−	0.770943i	$-0.280215\pi$
$877$	37.7228	1.27381	0.636904	+	0.770943i	$0.280215\pi$
$878$	4.23369	0.142880
$879$	11.4891	0.387519
$880$	2.00000	0.0674200
$881$	−32.2337	−1.08598	−0.542990	−	0.839739i	$-0.682708\pi$
$881$	−32.2337	−1.08598	−0.542990	+	0.839739i	$0.682708\pi$
$882$	1.00000	0.0336718
$883$	40.4674	1.36184	0.680918	−	0.732360i	$-0.261581\pi$
$883$	40.4674	1.36184	0.680918	+	0.732360i	$0.261581\pi$
$884$	0	0
$885$	−14.7446	−0.495633
$886$	−20.0000	−0.671913
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	8.74456	0.293448
$889$	4.74456	0.159128
$890$	10.7446	0.360159
$891$	−2.00000	−0.0670025
$892$	24.7446	0.828509
$893$	0	0
$894$	15.4891	0.518034
$895$	−21.4891	−0.718302
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	40.9783	1.36746
$899$	7.53262	0.251227
$900$	1.00000	0.0333333
$901$	9.48913	0.316129
$902$	−12.0000	−0.399556
$903$	−8.74456	−0.291001
$904$	8.74456	0.290840
$905$	−3.48913	−0.115982
$906$	22.9783	0.763401
$907$	−34.2337	−1.13671	−0.568355	−	0.822783i	$-0.692420\pi$
$907$	−34.2337	−1.13671	−0.568355	+	0.822783i	$0.692420\pi$
$908$	−4.00000	−0.132745
$909$	1.25544	0.0416402
$910$	0	0
$911$	−13.2554	−0.439172	−0.219586	−	0.975593i	$-0.570471\pi$
$911$	−13.2554	−0.439172	−0.219586	+	0.975593i	$0.570471\pi$
$912$	0	0
$913$	26.9783	0.892850
$914$	−41.4891	−1.37234
$915$	2.00000	0.0661180
$916$	23.4891	0.776103
$917$	2.74456	0.0906334
$918$	2.00000	0.0660098
$919$	−44.2337	−1.45913	−0.729567	−	0.683909i	$-0.760279\pi$
$919$	−44.2337	−1.45913	−0.729567	+	0.683909i	$0.760279\pi$
$920$	−1.00000	−0.0329690
$921$	22.9783	0.757159
$922$	28.2337	0.929827
$923$	0	0
$924$	2.00000	0.0657952
$925$	8.74456	0.287519
$926$	−22.2337	−0.730644
$927$	8.00000	0.262754
$928$	−2.74456	−0.0900947
$929$	−10.4674	−0.343423	−0.171712	−	0.985147i	$-0.554930\pi$
$929$	−10.4674	−0.343423	−0.171712	+	0.985147i	$0.554930\pi$
$930$	2.74456	0.0899978
$931$	0	0
$932$	−10.0000	−0.327561
$933$	14.0000	0.458339
$934$	10.5109	0.343926
$935$	4.00000	0.130814
$936$	0	0
$937$	−11.7663	−0.384389	−0.192194	−	0.981357i	$-0.561560\pi$
$937$	−11.7663	−0.384389	−0.192194	+	0.981357i	$0.561560\pi$
$938$	4.74456	0.154915
$939$	−10.7446	−0.350636
$940$	−13.4891	−0.439967
$941$	23.4891	0.765724	0.382862	−	0.923806i	$-0.374939\pi$
$941$	23.4891	0.765724	0.382862	+	0.923806i	$0.374939\pi$
$942$	15.4891	0.504663
$943$	6.00000	0.195387
$944$	14.7446	0.479895
$945$	1.00000	0.0325300
$946$	−17.4891	−0.568621
$947$	30.9783	1.00666	0.503329	−	0.864095i	$-0.332108\pi$
$947$	30.9783	1.00666	0.503329	+	0.864095i	$0.332108\pi$
$948$	−6.74456	−0.219053
$949$	0	0
$950$	0	0
$951$	−32.9783	−1.06939
$952$	−2.00000	−0.0648204
$953$	−4.74456	−0.153691	−0.0768457	−	0.997043i	$-0.524485\pi$
$953$	−4.74456	−0.153691	−0.0768457	+	0.997043i	$0.524485\pi$
$954$	4.74456	0.153611
$955$	−14.7446	−0.477123
$956$	14.2337	0.460350
$957$	5.48913	0.177438
$958$	29.4891	0.952750
$959$	20.7446	0.669877
$960$	−1.00000	−0.0322749
$961$	−23.4674	−0.757012
$962$	0	0
$963$	8.00000	0.257796
$964$	−2.00000	−0.0644157
$965$	19.4891	0.627377
$966$	−1.00000	−0.0321745
$967$	−57.2119	−1.83981	−0.919906	−	0.392139i	$-0.871735\pi$
$967$	−57.2119	−1.83981	−0.919906	+	0.392139i	$0.871735\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	6.74456	0.216555
$971$	7.72281	0.247837	0.123918	−	0.992292i	$-0.460454\pi$
$971$	7.72281	0.247837	0.123918	+	0.992292i	$0.460454\pi$
$972$	1.00000	0.0320750
$973$	−2.74456	−0.0879866
$974$	−22.2337	−0.712413
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	29.2119	0.934573	0.467286	−	0.884106i	$-0.345232\pi$
$977$	29.2119	0.934573	0.467286	+	0.884106i	$0.345232\pi$
$978$	−13.4891	−0.431335
$979$	21.4891	0.686795
$980$	−1.00000	−0.0319438
$981$	−11.4891	−0.366820
$982$	12.0000	0.382935
$983$	−48.0000	−1.53096	−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000	−1.53096	−0.765481	+	0.643458i	$0.777499\pi$
$984$	6.00000	0.191273
$985$	7.48913	0.238623
$986$	−5.48913	−0.174809
$987$	−13.4891	−0.429364
$988$	0	0
$989$	8.74456	0.278061
$990$	2.00000	0.0635642
$991$	−36.0000	−1.14358	−0.571789	−	0.820401i	$-0.693750\pi$
$991$	−36.0000	−1.14358	−0.571789	+	0.820401i	$0.693750\pi$
$992$	−2.74456	−0.0871400
$993$	−4.00000	−0.126936
$994$	−3.25544	−0.103256
$995$	13.4891	0.427634
$996$	−13.4891	−0.427419
$997$	−26.9783	−0.854410	−0.427205	−	0.904155i	$-0.640502\pi$
$997$	−26.9783	−0.854410	−0.427205	+	0.904155i	$0.640502\pi$
$998$	−1.48913	−0.0471374
$999$	8.74456	0.276666

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bv.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{21} -2.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} -2.74456 q^{29} -1.00000 q^{30} -2.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} +2.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +8.74456 q^{37} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +8.74456 q^{43} -2.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} +13.4891 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +4.74456 q^{53} +1.00000 q^{54} +2.00000 q^{55} -1.00000 q^{56} -2.74456 q^{58} +14.7446 q^{59} -1.00000 q^{60} -2.00000 q^{61} -2.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -4.74456 q^{67} +2.00000 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.25544 q^{71} +1.00000 q^{72} +12.7446 q^{73} +8.74456 q^{74} +1.00000 q^{75} +2.00000 q^{77} -6.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -13.4891 q^{83} -1.00000 q^{84} -2.00000 q^{85} +8.74456 q^{86} -2.74456 q^{87} -2.00000 q^{88} -10.7446 q^{89} -1.00000 q^{90} +1.00000 q^{92} -2.74456 q^{93} +13.4891 q^{94} +1.00000 q^{96} -6.74456 q^{97} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{20} - 2 q^{21} - 4 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 2 q^{36} + 6 q^{37} - 2 q^{40} + 12 q^{41} - 2 q^{42} + 6 q^{43} - 4 q^{44} - 2 q^{45} + 2 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{50} + 4 q^{51} - 2 q^{53} + 2 q^{54} + 4 q^{55} - 2 q^{56} + 6 q^{58} + 18 q^{59} - 2 q^{60} - 4 q^{61} + 6 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} + 2 q^{70} + 18 q^{71} + 2 q^{72} + 14 q^{73} + 6 q^{74} + 2 q^{75} + 4 q^{77} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 4 q^{83} - 2 q^{84} - 4 q^{85} + 6 q^{86} + 6 q^{87} - 4 q^{88} - 10 q^{89} - 2 q^{90} + 2 q^{92} + 6 q^{93} + 4 q^{94} + 2 q^{96} - 2 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 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 - 4 * q^11 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^20 - 2 * q^21 - 4 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 2 * q^36 + 6 * q^37 - 2 * q^40 + 12 * q^41 - 2 * q^42 + 6 * q^43 - 4 * q^44 - 2 * q^45 + 2 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^50 + 4 * q^51 - 2 * q^53 + 2 * q^54 + 4 * q^55 - 2 * q^56 + 6 * q^58 + 18 * q^59 - 2 * q^60 - 4 * q^61 + 6 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 4 * q^68 + 2 * q^69 + 2 * q^70 + 18 * q^71 + 2 * q^72 + 14 * q^73 + 6 * q^74 + 2 * q^75 + 4 * q^77 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 4 * q^83 - 2 * q^84 - 4 * q^85 + 6 * q^86 + 6 * q^87 - 4 * q^88 - 10 * q^89 - 2 * q^90 + 2 * q^92 + 6 * q^93 + 4 * q^94 + 2 * q^96 - 2 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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