LMFDB - Embedded newform 4830.2.a.bs.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:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.47214 q^{11} +1.00000 q^{12} -5.23607 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.23607 q^{17} -1.00000 q^{18} -1.23607 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.47214 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +5.23607 q^{26} +1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{30} +7.70820 q^{31} -1.00000 q^{32} -4.47214 q^{33} -7.23607 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.94427 q^{37} +1.23607 q^{38} -5.23607 q^{39} -1.00000 q^{40} +2.00000 q^{41} -1.00000 q^{42} +6.00000 q^{43} -4.47214 q^{44} +1.00000 q^{45} +1.00000 q^{46} +3.70820 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.23607 q^{51} -5.23607 q^{52} -4.47214 q^{53} -1.00000 q^{54} -4.47214 q^{55} -1.00000 q^{56} -1.23607 q^{57} -2.47214 q^{59} +1.00000 q^{60} +2.94427 q^{61} -7.70820 q^{62} +1.00000 q^{63} +1.00000 q^{64} -5.23607 q^{65} +4.47214 q^{66} +6.00000 q^{67} +7.23607 q^{68} -1.00000 q^{69} -1.00000 q^{70} +12.4721 q^{71} -1.00000 q^{72} +6.00000 q^{73} +6.94427 q^{74} +1.00000 q^{75} -1.23607 q^{76} -4.47214 q^{77} +5.23607 q^{78} -12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +11.7082 q^{83} +1.00000 q^{84} +7.23607 q^{85} -6.00000 q^{86} +4.47214 q^{88} +16.6525 q^{89} -1.00000 q^{90} -5.23607 q^{91} -1.00000 q^{92} +7.70820 q^{93} -3.70820 q^{94} -1.23607 q^{95} -1.00000 q^{96} +2.76393 q^{97} -1.00000 q^{98} -4.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} + 10 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 2 q^{21} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{30} + 2 q^{31} - 2 q^{32} - 10 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} + 4 q^{41} - 2 q^{42} + 12 q^{43} + 2 q^{45} + 2 q^{46} - 6 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 10 q^{51} - 6 q^{52} - 2 q^{54} - 2 q^{56} + 2 q^{57} + 4 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{67} + 10 q^{68} - 2 q^{69} - 2 q^{70} + 16 q^{71} - 2 q^{72} + 12 q^{73} - 4 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{78} - 24 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 10 q^{83} + 2 q^{84} + 10 q^{85} - 12 q^{86} + 2 q^{89} - 2 q^{90} - 6 q^{91} - 2 q^{92} + 2 q^{93} + 6 q^{94} + 2 q^{95} - 2 q^{96} + 10 q^{97} - 2 q^{98}+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 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 + 10 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 2 * q^21 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 - 2 * q^30 + 2 * q^31 - 2 * q^32 - 10 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 + 4 * q^41 - 2 * q^42 + 12 * q^43 + 2 * q^45 + 2 * q^46 - 6 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 10 * q^51 - 6 * q^52 - 2 * q^54 - 2 * q^56 + 2 * q^57 + 4 * q^59 + 2 * q^60 - 12 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^67 + 10 * q^68 - 2 * q^69 - 2 * q^70 + 16 * q^71 - 2 * q^72 + 12 * q^73 - 4 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^78 - 24 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 10 * q^83 + 2 * q^84 + 10 * q^85 - 12 * q^86 + 2 * q^89 - 2 * q^90 - 6 * q^91 - 2 * q^92 + 2 * q^93 + 6 * q^94 + 2 * q^95 - 2 * q^96 + 10 * q^97 - 2 * q^98

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
$11$	−4.47214	−1.34840	−0.674200	−	0.738549i	$-0.735511\pi$
$11$	−4.47214	−1.34840	−0.674200	+	0.738549i	$0.735511\pi$
$12$	1.00000	0.288675
$13$	−5.23607	−1.45222	−0.726112	−	0.687576i	$-0.758675\pi$
$13$	−5.23607	−1.45222	−0.726112	+	0.687576i	$0.758675\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	7.23607	1.75500	0.877502	−	0.479573i	$-0.159208\pi$
$17$	7.23607	1.75500	0.877502	+	0.479573i	$0.159208\pi$
$18$	−1.00000	−0.235702
$19$	−1.23607	−0.283573	−0.141787	−	0.989897i	$-0.545285\pi$
$19$	−1.23607	−0.283573	−0.141787	+	0.989897i	$0.545285\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	4.47214	0.953463
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	5.23607	1.02688
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−1.00000	−0.182574
$31$	7.70820	1.38443	0.692217	−	0.721689i	$-0.256634\pi$
$31$	7.70820	1.38443	0.692217	+	0.721689i	$0.256634\pi$
$32$	−1.00000	−0.176777
$33$	−4.47214	−0.778499
$34$	−7.23607	−1.24098
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−6.94427	−1.14163	−0.570816	−	0.821078i	$-0.693373\pi$
$37$	−6.94427	−1.14163	−0.570816	+	0.821078i	$0.693373\pi$
$38$	1.23607	0.200517
$39$	−5.23607	−0.838442
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−1.00000	−0.154303
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−4.47214	−0.674200
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	3.70820	0.540897	0.270449	−	0.962734i	$-0.412828\pi$
$47$	3.70820	0.540897	0.270449	+	0.962734i	$0.412828\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	7.23607	1.01325
$52$	−5.23607	−0.726112
$53$	−4.47214	−0.614295	−0.307148	−	0.951662i	$-0.599375\pi$
$53$	−4.47214	−0.614295	−0.307148	+	0.951662i	$0.599375\pi$
$54$	−1.00000	−0.136083
$55$	−4.47214	−0.603023
$56$	−1.00000	−0.133631
$57$	−1.23607	−0.163721
$58$	0	0
$59$	−2.47214	−0.321845	−0.160922	−	0.986967i	$-0.551447\pi$
$59$	−2.47214	−0.321845	−0.160922	+	0.986967i	$0.551447\pi$
$60$	1.00000	0.129099
$61$	2.94427	0.376975	0.188488	−	0.982076i	$-0.439641\pi$
$61$	2.94427	0.376975	0.188488	+	0.982076i	$0.439641\pi$
$62$	−7.70820	−0.978943
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−5.23607	−0.649454
$66$	4.47214	0.550482
$67$	6.00000	0.733017	0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000	0.733017	0.366508	+	0.930415i	$0.380553\pi$
$68$	7.23607	0.877502
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	12.4721	1.48017	0.740085	−	0.672513i	$-0.234785\pi$
$71$	12.4721	1.48017	0.740085	+	0.672513i	$0.234785\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	6.94427	0.807255
$75$	1.00000	0.115470
$76$	−1.23607	−0.141787
$77$	−4.47214	−0.509647
$78$	5.23607	0.592868
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	11.7082	1.28514	0.642571	−	0.766226i	$-0.277868\pi$
$83$	11.7082	1.28514	0.642571	+	0.766226i	$0.277868\pi$
$84$	1.00000	0.109109
$85$	7.23607	0.784862
$86$	−6.00000	−0.646997
$87$	0	0
$88$	4.47214	0.476731
$89$	16.6525	1.76516	0.882579	−	0.470163i	$-0.155805\pi$
$89$	16.6525	1.76516	0.882579	+	0.470163i	$0.155805\pi$
$90$	−1.00000	−0.105409
$91$	−5.23607	−0.548889
$92$	−1.00000	−0.104257
$93$	7.70820	0.799304
$94$	−3.70820	−0.382472
$95$	−1.23607	−0.126818
$96$	−1.00000	−0.102062
$97$	2.76393	0.280635	0.140317	−	0.990107i	$-0.455188\pi$
$97$	2.76393	0.280635	0.140317	+	0.990107i	$0.455188\pi$
$98$	−1.00000	−0.101015
$99$	−4.47214	−0.449467
$100$	1.00000	0.100000
$101$	13.2361	1.31704	0.658519	−	0.752564i	$-0.271183\pi$
$101$	13.2361	1.31704	0.658519	+	0.752564i	$0.271183\pi$
$102$	−7.23607	−0.716477
$103$	4.94427	0.487174	0.243587	−	0.969879i	$-0.421676\pi$
$103$	4.94427	0.487174	0.243587	+	0.969879i	$0.421676\pi$
$104$	5.23607	0.513439
$105$	1.00000	0.0975900
$106$	4.47214	0.434372
$107$	10.4721	1.01238	0.506190	−	0.862422i	$-0.331054\pi$
$107$	10.4721	1.01238	0.506190	+	0.862422i	$0.331054\pi$
$108$	1.00000	0.0962250
$109$	6.94427	0.665141	0.332570	−	0.943078i	$-0.392084\pi$
$109$	6.94427	0.665141	0.332570	+	0.943078i	$0.392084\pi$
$110$	4.47214	0.426401
$111$	−6.94427	−0.659121
$112$	1.00000	0.0944911
$113$	3.52786	0.331874	0.165937	−	0.986136i	$-0.446935\pi$
$113$	3.52786	0.331874	0.165937	+	0.986136i	$0.446935\pi$
$114$	1.23607	0.115768
$115$	−1.00000	−0.0932505
$116$	0	0
$117$	−5.23607	−0.484075
$118$	2.47214	0.227579
$119$	7.23607	0.663329
$120$	−1.00000	−0.0912871
$121$	9.00000	0.818182
$122$	−2.94427	−0.266562
$123$	2.00000	0.180334
$124$	7.70820	0.692217
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−4.47214	−0.396838	−0.198419	−	0.980117i	$-0.563581\pi$
$127$	−4.47214	−0.396838	−0.198419	+	0.980117i	$0.563581\pi$
$128$	−1.00000	−0.0883883
$129$	6.00000	0.528271
$130$	5.23607	0.459234
$131$	−0.944272	−0.0825014	−0.0412507	−	0.999149i	$-0.513134\pi$
$131$	−0.944272	−0.0825014	−0.0412507	+	0.999149i	$0.513134\pi$
$132$	−4.47214	−0.389249
$133$	−1.23607	−0.107181
$134$	−6.00000	−0.518321
$135$	1.00000	0.0860663
$136$	−7.23607	−0.620488
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	1.00000	0.0851257
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	1.00000	0.0845154
$141$	3.70820	0.312287
$142$	−12.4721	−1.04664
$143$	23.4164	1.95818
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.00000	−0.496564
$147$	1.00000	0.0824786
$148$	−6.94427	−0.570816
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−1.00000	−0.0816497
$151$	−1.52786	−0.124336	−0.0621679	−	0.998066i	$-0.519801\pi$
$151$	−1.52786	−0.124336	−0.0621679	+	0.998066i	$0.519801\pi$
$152$	1.23607	0.100258
$153$	7.23607	0.585001
$154$	4.47214	0.360375
$155$	7.70820	0.619138
$156$	−5.23607	−0.419221
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	12.0000	0.954669
$159$	−4.47214	−0.354663
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	−19.4164	−1.52081	−0.760405	−	0.649449i	$-0.775000\pi$
$163$	−19.4164	−1.52081	−0.760405	+	0.649449i	$0.775000\pi$
$164$	2.00000	0.156174
$165$	−4.47214	−0.348155
$166$	−11.7082	−0.908733
$167$	13.2361	1.02424	0.512119	−	0.858915i	$-0.328861\pi$
$167$	13.2361	1.02424	0.512119	+	0.858915i	$0.328861\pi$
$168$	−1.00000	−0.0771517
$169$	14.4164	1.10895
$170$	−7.23607	−0.554981
$171$	−1.23607	−0.0945245
$172$	6.00000	0.457496
$173$	−5.70820	−0.433987	−0.216993	−	0.976173i	$-0.569625\pi$
$173$	−5.70820	−0.433987	−0.216993	+	0.976173i	$0.569625\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	−4.47214	−0.337100
$177$	−2.47214	−0.185817
$178$	−16.6525	−1.24816
$179$	−4.94427	−0.369552	−0.184776	−	0.982781i	$-0.559156\pi$
$179$	−4.94427	−0.369552	−0.184776	+	0.982781i	$0.559156\pi$
$180$	1.00000	0.0745356
$181$	15.8885	1.18099	0.590493	−	0.807043i	$-0.298933\pi$
$181$	15.8885	1.18099	0.590493	+	0.807043i	$0.298933\pi$
$182$	5.23607	0.388123
$183$	2.94427	0.217647
$184$	1.00000	0.0737210
$185$	−6.94427	−0.510553
$186$	−7.70820	−0.565193
$187$	−32.3607	−2.36645
$188$	3.70820	0.270449
$189$	1.00000	0.0727393
$190$	1.23607	0.0896738
$191$	−14.4721	−1.04717	−0.523584	−	0.851974i	$-0.675405\pi$
$191$	−14.4721	−1.04717	−0.523584	+	0.851974i	$0.675405\pi$
$192$	1.00000	0.0721688
$193$	2.94427	0.211933	0.105967	−	0.994370i	$-0.466206\pi$
$193$	2.94427	0.211933	0.105967	+	0.994370i	$0.466206\pi$
$194$	−2.76393	−0.198439
$195$	−5.23607	−0.374963
$196$	1.00000	0.0714286
$197$	17.4164	1.24087	0.620434	−	0.784259i	$-0.286957\pi$
$197$	17.4164	1.24087	0.620434	+	0.784259i	$0.286957\pi$
$198$	4.47214	0.317821
$199$	−4.94427	−0.350490	−0.175245	−	0.984525i	$-0.556072\pi$
$199$	−4.94427	−0.350490	−0.175245	+	0.984525i	$0.556072\pi$
$200$	−1.00000	−0.0707107
$201$	6.00000	0.423207
$202$	−13.2361	−0.931286
$203$	0	0
$204$	7.23607	0.506626
$205$	2.00000	0.139686
$206$	−4.94427	−0.344484
$207$	−1.00000	−0.0695048
$208$	−5.23607	−0.363056
$209$	5.52786	0.382370
$210$	−1.00000	−0.0690066
$211$	−4.94427	−0.340378	−0.170189	−	0.985411i	$-0.554438\pi$
$211$	−4.94427	−0.340378	−0.170189	+	0.985411i	$0.554438\pi$
$212$	−4.47214	−0.307148
$213$	12.4721	0.854577
$214$	−10.4721	−0.715860
$215$	6.00000	0.409197
$216$	−1.00000	−0.0680414
$217$	7.70820	0.523267
$218$	−6.94427	−0.470325
$219$	6.00000	0.405442
$220$	−4.47214	−0.301511
$221$	−37.8885	−2.54866
$222$	6.94427	0.466069
$223$	−16.7639	−1.12260	−0.561298	−	0.827614i	$-0.689698\pi$
$223$	−16.7639	−1.12260	−0.561298	+	0.827614i	$0.689698\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−3.52786	−0.234670
$227$	29.2361	1.94047	0.970233	−	0.242173i	$-0.0778603\pi$
$227$	29.2361	1.94047	0.970233	+	0.242173i	$0.0778603\pi$
$228$	−1.23607	−0.0818606
$229$	−5.41641	−0.357926	−0.178963	−	0.983856i	$-0.557274\pi$
$229$	−5.41641	−0.357926	−0.178963	+	0.983856i	$0.557274\pi$
$230$	1.00000	0.0659380
$231$	−4.47214	−0.294245
$232$	0	0
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	5.23607	0.342292
$235$	3.70820	0.241897
$236$	−2.47214	−0.160922
$237$	−12.0000	−0.779484
$238$	−7.23607	−0.469045
$239$	−21.4164	−1.38531	−0.692656	−	0.721268i	$-0.743560\pi$
$239$	−21.4164	−1.38531	−0.692656	+	0.721268i	$0.743560\pi$
$240$	1.00000	0.0645497
$241$	−3.81966	−0.246046	−0.123023	−	0.992404i	$-0.539259\pi$
$241$	−3.81966	−0.246046	−0.123023	+	0.992404i	$0.539259\pi$
$242$	−9.00000	−0.578542
$243$	1.00000	0.0641500
$244$	2.94427	0.188488
$245$	1.00000	0.0638877
$246$	−2.00000	−0.127515
$247$	6.47214	0.411812
$248$	−7.70820	−0.489471
$249$	11.7082	0.741977
$250$	−1.00000	−0.0632456
$251$	−6.29180	−0.397135	−0.198567	−	0.980087i	$-0.563629\pi$
$251$	−6.29180	−0.397135	−0.198567	+	0.980087i	$0.563629\pi$
$252$	1.00000	0.0629941
$253$	4.47214	0.281161
$254$	4.47214	0.280607
$255$	7.23607	0.453140
$256$	1.00000	0.0625000
$257$	17.4164	1.08641	0.543203	−	0.839601i	$-0.317211\pi$
$257$	17.4164	1.08641	0.543203	+	0.839601i	$0.317211\pi$
$258$	−6.00000	−0.373544
$259$	−6.94427	−0.431496
$260$	−5.23607	−0.324727
$261$	0	0
$262$	0.944272	0.0583373
$263$	−17.8885	−1.10305	−0.551527	−	0.834157i	$-0.685955\pi$
$263$	−17.8885	−1.10305	−0.551527	+	0.834157i	$0.685955\pi$
$264$	4.47214	0.275241
$265$	−4.47214	−0.274721
$266$	1.23607	0.0757882
$267$	16.6525	1.01911
$268$	6.00000	0.366508
$269$	−21.5967	−1.31678	−0.658388	−	0.752678i	$-0.728762\pi$
$269$	−21.5967	−1.31678	−0.658388	+	0.752678i	$0.728762\pi$
$270$	−1.00000	−0.0608581
$271$	−21.2361	−1.29000	−0.645000	−	0.764183i	$-0.723142\pi$
$271$	−21.2361	−1.29000	−0.645000	+	0.764183i	$0.723142\pi$
$272$	7.23607	0.438751
$273$	−5.23607	−0.316901
$274$	2.00000	0.120824
$275$	−4.47214	−0.269680
$276$	−1.00000	−0.0601929
$277$	3.05573	0.183601	0.0918005	−	0.995777i	$-0.470738\pi$
$277$	3.05573	0.183601	0.0918005	+	0.995777i	$0.470738\pi$
$278$	4.00000	0.239904
$279$	7.70820	0.461478
$280$	−1.00000	−0.0597614
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	−3.70820	−0.220820
$283$	6.65248	0.395449	0.197724	−	0.980258i	$-0.436645\pi$
$283$	6.65248	0.395449	0.197724	+	0.980258i	$0.436645\pi$
$284$	12.4721	0.740085
$285$	−1.23607	−0.0732183
$286$	−23.4164	−1.38464
$287$	2.00000	0.118056
$288$	−1.00000	−0.0589256
$289$	35.3607	2.08004
$290$	0	0
$291$	2.76393	0.162025
$292$	6.00000	0.351123
$293$	9.41641	0.550112	0.275056	−	0.961428i	$-0.411304\pi$
$293$	9.41641	0.550112	0.275056	+	0.961428i	$0.411304\pi$
$294$	−1.00000	−0.0583212
$295$	−2.47214	−0.143933
$296$	6.94427	0.403628
$297$	−4.47214	−0.259500
$298$	−6.00000	−0.347571
$299$	5.23607	0.302810
$300$	1.00000	0.0577350
$301$	6.00000	0.345834
$302$	1.52786	0.0879187
$303$	13.2361	0.760392
$304$	−1.23607	−0.0708934
$305$	2.94427	0.168589
$306$	−7.23607	−0.413658
$307$	−13.8885	−0.792661	−0.396331	−	0.918108i	$-0.629717\pi$
$307$	−13.8885	−0.792661	−0.396331	+	0.918108i	$0.629717\pi$
$308$	−4.47214	−0.254824
$309$	4.94427	0.281270
$310$	−7.70820	−0.437797
$311$	25.7082	1.45778	0.728889	−	0.684632i	$-0.240037\pi$
$311$	25.7082	1.45778	0.728889	+	0.684632i	$0.240037\pi$
$312$	5.23607	0.296434
$313$	14.1803	0.801520	0.400760	−	0.916183i	$-0.368746\pi$
$313$	14.1803	0.801520	0.400760	+	0.916183i	$0.368746\pi$
$314$	6.00000	0.338600
$315$	1.00000	0.0563436
$316$	−12.0000	−0.675053
$317$	29.4164	1.65219	0.826095	−	0.563531i	$-0.190557\pi$
$317$	29.4164	1.65219	0.826095	+	0.563531i	$0.190557\pi$
$318$	4.47214	0.250785
$319$	0	0
$320$	1.00000	0.0559017
$321$	10.4721	0.584498
$322$	1.00000	0.0557278
$323$	−8.94427	−0.497673
$324$	1.00000	0.0555556
$325$	−5.23607	−0.290445
$326$	19.4164	1.07538
$327$	6.94427	0.384019
$328$	−2.00000	−0.110432
$329$	3.70820	0.204440
$330$	4.47214	0.246183
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	11.7082	0.642571
$333$	−6.94427	−0.380544
$334$	−13.2361	−0.724245
$335$	6.00000	0.327815
$336$	1.00000	0.0545545
$337$	27.4164	1.49347	0.746733	−	0.665123i	$-0.231621\pi$
$337$	27.4164	1.49347	0.746733	+	0.665123i	$0.231621\pi$
$338$	−14.4164	−0.784149
$339$	3.52786	0.191607
$340$	7.23607	0.392431
$341$	−34.4721	−1.86677
$342$	1.23607	0.0668389
$343$	1.00000	0.0539949
$344$	−6.00000	−0.323498
$345$	−1.00000	−0.0538382
$346$	5.70820	0.306875
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	−18.6525	−0.998444	−0.499222	−	0.866474i	$-0.666381\pi$
$349$	−18.6525	−0.998444	−0.499222	+	0.866474i	$0.666381\pi$
$350$	−1.00000	−0.0534522
$351$	−5.23607	−0.279481
$352$	4.47214	0.238366
$353$	−7.52786	−0.400668	−0.200334	−	0.979728i	$-0.564203\pi$
$353$	−7.52786	−0.400668	−0.200334	+	0.979728i	$0.564203\pi$
$354$	2.47214	0.131393
$355$	12.4721	0.661952
$356$	16.6525	0.882579
$357$	7.23607	0.382973
$358$	4.94427	0.261313
$359$	16.3607	0.863484	0.431742	−	0.901997i	$-0.357899\pi$
$359$	16.3607	0.863484	0.431742	+	0.901997i	$0.357899\pi$
$360$	−1.00000	−0.0527046
$361$	−17.4721	−0.919586
$362$	−15.8885	−0.835083
$363$	9.00000	0.472377
$364$	−5.23607	−0.274445
$365$	6.00000	0.314054
$366$	−2.94427	−0.153900
$367$	−3.05573	−0.159508	−0.0797539	−	0.996815i	$-0.525413\pi$
$367$	−3.05573	−0.159508	−0.0797539	+	0.996815i	$0.525413\pi$
$368$	−1.00000	−0.0521286
$369$	2.00000	0.104116
$370$	6.94427	0.361016
$371$	−4.47214	−0.232182
$372$	7.70820	0.399652
$373$	−19.8885	−1.02979	−0.514895	−	0.857253i	$-0.672169\pi$
$373$	−19.8885	−1.02979	−0.514895	+	0.857253i	$0.672169\pi$
$374$	32.3607	1.67333
$375$	1.00000	0.0516398
$376$	−3.70820	−0.191236
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−7.41641	−0.380955	−0.190478	−	0.981692i	$-0.561004\pi$
$379$	−7.41641	−0.380955	−0.190478	+	0.981692i	$0.561004\pi$
$380$	−1.23607	−0.0634089
$381$	−4.47214	−0.229114
$382$	14.4721	0.740459
$383$	−2.47214	−0.126320	−0.0631601	−	0.998003i	$-0.520118\pi$
$383$	−2.47214	−0.126320	−0.0631601	+	0.998003i	$0.520118\pi$
$384$	−1.00000	−0.0510310
$385$	−4.47214	−0.227921
$386$	−2.94427	−0.149859
$387$	6.00000	0.304997
$388$	2.76393	0.140317
$389$	−14.9443	−0.757705	−0.378852	−	0.925457i	$-0.623681\pi$
$389$	−14.9443	−0.757705	−0.378852	+	0.925457i	$0.623681\pi$
$390$	5.23607	0.265139
$391$	−7.23607	−0.365944
$392$	−1.00000	−0.0505076
$393$	−0.944272	−0.0476322
$394$	−17.4164	−0.877426
$395$	−12.0000	−0.603786
$396$	−4.47214	−0.224733
$397$	−5.23607	−0.262791	−0.131395	−	0.991330i	$-0.541946\pi$
$397$	−5.23607	−0.262791	−0.131395	+	0.991330i	$0.541946\pi$
$398$	4.94427	0.247834
$399$	−1.23607	−0.0618808
$400$	1.00000	0.0500000
$401$	−14.8328	−0.740715	−0.370358	−	0.928889i	$-0.620765\pi$
$401$	−14.8328	−0.740715	−0.370358	+	0.928889i	$0.620765\pi$
$402$	−6.00000	−0.299253
$403$	−40.3607	−2.01051
$404$	13.2361	0.658519
$405$	1.00000	0.0496904
$406$	0	0
$407$	31.0557	1.53938
$408$	−7.23607	−0.358239
$409$	11.5279	0.570016	0.285008	−	0.958525i	$-0.408004\pi$
$409$	11.5279	0.570016	0.285008	+	0.958525i	$0.408004\pi$
$410$	−2.00000	−0.0987730
$411$	−2.00000	−0.0986527
$412$	4.94427	0.243587
$413$	−2.47214	−0.121646
$414$	1.00000	0.0491473
$415$	11.7082	0.574733
$416$	5.23607	0.256719
$417$	−4.00000	−0.195881
$418$	−5.52786	−0.270377
$419$	2.65248	0.129582	0.0647910	−	0.997899i	$-0.479362\pi$
$419$	2.65248	0.129582	0.0647910	+	0.997899i	$0.479362\pi$
$420$	1.00000	0.0487950
$421$	−35.8885	−1.74910	−0.874550	−	0.484935i	$-0.838843\pi$
$421$	−35.8885	−1.74910	−0.874550	+	0.484935i	$0.838843\pi$
$422$	4.94427	0.240683
$423$	3.70820	0.180299
$424$	4.47214	0.217186
$425$	7.23607	0.351001
$426$	−12.4721	−0.604277
$427$	2.94427	0.142483
$428$	10.4721	0.506190
$429$	23.4164	1.13055
$430$	−6.00000	−0.289346
$431$	22.8328	1.09982	0.549909	−	0.835225i	$-0.314662\pi$
$431$	22.8328	1.09982	0.549909	+	0.835225i	$0.314662\pi$
$432$	1.00000	0.0481125
$433$	36.6525	1.76141	0.880703	−	0.473669i	$-0.157071\pi$
$433$	36.6525	1.76141	0.880703	+	0.473669i	$0.157071\pi$
$434$	−7.70820	−0.370006
$435$	0	0
$436$	6.94427	0.332570
$437$	1.23607	0.0591292
$438$	−6.00000	−0.286691
$439$	17.2361	0.822633	0.411316	−	0.911493i	$-0.365069\pi$
$439$	17.2361	0.822633	0.411316	+	0.911493i	$0.365069\pi$
$440$	4.47214	0.213201
$441$	1.00000	0.0476190
$442$	37.8885	1.80217
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−6.94427	−0.329561
$445$	16.6525	0.789403
$446$	16.7639	0.793795
$447$	6.00000	0.283790
$448$	1.00000	0.0472456
$449$	−20.8328	−0.983161	−0.491581	−	0.870832i	$-0.663581\pi$
$449$	−20.8328	−0.983161	−0.491581	+	0.870832i	$0.663581\pi$
$450$	−1.00000	−0.0471405
$451$	−8.94427	−0.421169
$452$	3.52786	0.165937
$453$	−1.52786	−0.0717853
$454$	−29.2361	−1.37212
$455$	−5.23607	−0.245471
$456$	1.23607	0.0578842
$457$	−38.8328	−1.81652	−0.908261	−	0.418404i	$-0.862590\pi$
$457$	−38.8328	−1.81652	−0.908261	+	0.418404i	$0.862590\pi$
$458$	5.41641	0.253092
$459$	7.23607	0.337751
$460$	−1.00000	−0.0466252
$461$	−2.76393	−0.128729	−0.0643646	−	0.997926i	$-0.520502\pi$
$461$	−2.76393	−0.128729	−0.0643646	+	0.997926i	$0.520502\pi$
$462$	4.47214	0.208063
$463$	3.88854	0.180716	0.0903580	−	0.995909i	$-0.471199\pi$
$463$	3.88854	0.180716	0.0903580	+	0.995909i	$0.471199\pi$
$464$	0	0
$465$	7.70820	0.357459
$466$	−10.0000	−0.463241
$467$	−6.76393	−0.312997	−0.156499	−	0.987678i	$-0.550021\pi$
$467$	−6.76393	−0.312997	−0.156499	+	0.987678i	$0.550021\pi$
$468$	−5.23607	−0.242037
$469$	6.00000	0.277054
$470$	−3.70820	−0.171047
$471$	−6.00000	−0.276465
$472$	2.47214	0.113789
$473$	−26.8328	−1.23377
$474$	12.0000	0.551178
$475$	−1.23607	−0.0567147
$476$	7.23607	0.331665
$477$	−4.47214	−0.204765
$478$	21.4164	0.979564
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	−1.00000	−0.0456435
$481$	36.3607	1.65790
$482$	3.81966	0.173981
$483$	−1.00000	−0.0455016
$484$	9.00000	0.409091
$485$	2.76393	0.125504
$486$	−1.00000	−0.0453609
$487$	40.8328	1.85031	0.925156	−	0.379588i	$-0.123934\pi$
$487$	40.8328	1.85031	0.925156	+	0.379588i	$0.123934\pi$
$488$	−2.94427	−0.133281
$489$	−19.4164	−0.878040
$490$	−1.00000	−0.0451754
$491$	−29.5279	−1.33257	−0.666287	−	0.745695i	$-0.732117\pi$
$491$	−29.5279	−1.33257	−0.666287	+	0.745695i	$0.732117\pi$
$492$	2.00000	0.0901670
$493$	0	0
$494$	−6.47214	−0.291195
$495$	−4.47214	−0.201008
$496$	7.70820	0.346109
$497$	12.4721	0.559452
$498$	−11.7082	−0.524657
$499$	41.8885	1.87519	0.937594	−	0.347731i	$-0.113048\pi$
$499$	41.8885	1.87519	0.937594	+	0.347731i	$0.113048\pi$
$500$	1.00000	0.0447214
$501$	13.2361	0.591344
$502$	6.29180	0.280817
$503$	−1.88854	−0.0842060	−0.0421030	−	0.999113i	$-0.513406\pi$
$503$	−1.88854	−0.0842060	−0.0421030	+	0.999113i	$0.513406\pi$
$504$	−1.00000	−0.0445435
$505$	13.2361	0.588997
$506$	−4.47214	−0.198811
$507$	14.4164	0.640255
$508$	−4.47214	−0.198419
$509$	3.34752	0.148376	0.0741882	−	0.997244i	$-0.476363\pi$
$509$	3.34752	0.148376	0.0741882	+	0.997244i	$0.476363\pi$
$510$	−7.23607	−0.320418
$511$	6.00000	0.265424
$512$	−1.00000	−0.0441942
$513$	−1.23607	−0.0545737
$514$	−17.4164	−0.768205
$515$	4.94427	0.217871
$516$	6.00000	0.264135
$517$	−16.5836	−0.729346
$518$	6.94427	0.305114
$519$	−5.70820	−0.250562
$520$	5.23607	0.229617
$521$	1.81966	0.0797208	0.0398604	−	0.999205i	$-0.487309\pi$
$521$	1.81966	0.0797208	0.0398604	+	0.999205i	$0.487309\pi$
$522$	0	0
$523$	−11.2361	−0.491319	−0.245659	−	0.969356i	$-0.579004\pi$
$523$	−11.2361	−0.491319	−0.245659	+	0.969356i	$0.579004\pi$
$524$	−0.944272	−0.0412507
$525$	1.00000	0.0436436
$526$	17.8885	0.779978
$527$	55.7771	2.42969
$528$	−4.47214	−0.194625
$529$	1.00000	0.0434783
$530$	4.47214	0.194257
$531$	−2.47214	−0.107282
$532$	−1.23607	−0.0535903
$533$	−10.4721	−0.453599
$534$	−16.6525	−0.720623
$535$	10.4721	0.452750
$536$	−6.00000	−0.259161
$537$	−4.94427	−0.213361
$538$	21.5967	0.931102
$539$	−4.47214	−0.192629
$540$	1.00000	0.0430331
$541$	24.8328	1.06765	0.533823	−	0.845596i	$-0.320755\pi$
$541$	24.8328	1.06765	0.533823	+	0.845596i	$0.320755\pi$
$542$	21.2361	0.912167
$543$	15.8885	0.681843
$544$	−7.23607	−0.310244
$545$	6.94427	0.297460
$546$	5.23607	0.224083
$547$	−21.8885	−0.935887	−0.467943	−	0.883759i	$-0.655005\pi$
$547$	−21.8885	−0.935887	−0.467943	+	0.883759i	$0.655005\pi$
$548$	−2.00000	−0.0854358
$549$	2.94427	0.125658
$550$	4.47214	0.190693
$551$	0	0
$552$	1.00000	0.0425628
$553$	−12.0000	−0.510292
$554$	−3.05573	−0.129825
$555$	−6.94427	−0.294768
$556$	−4.00000	−0.169638
$557$	9.05573	0.383704	0.191852	−	0.981424i	$-0.438551\pi$
$557$	9.05573	0.383704	0.191852	+	0.981424i	$0.438551\pi$
$558$	−7.70820	−0.326314
$559$	−31.4164	−1.32877
$560$	1.00000	0.0422577
$561$	−32.3607	−1.36627
$562$	12.0000	0.506189
$563$	−11.1246	−0.468846	−0.234423	−	0.972135i	$-0.575320\pi$
$563$	−11.1246	−0.468846	−0.234423	+	0.972135i	$0.575320\pi$
$564$	3.70820	0.156144
$565$	3.52786	0.148418
$566$	−6.65248	−0.279624
$567$	1.00000	0.0419961
$568$	−12.4721	−0.523319
$569$	33.8885	1.42068	0.710341	−	0.703858i	$-0.248541\pi$
$569$	33.8885	1.42068	0.710341	+	0.703858i	$0.248541\pi$
$570$	1.23607	0.0517732
$571$	−44.9443	−1.88086	−0.940430	−	0.339988i	$-0.889577\pi$
$571$	−44.9443	−1.88086	−0.940430	+	0.339988i	$0.889577\pi$
$572$	23.4164	0.979089
$573$	−14.4721	−0.604582
$574$	−2.00000	−0.0834784
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	27.5279	1.14600	0.573000	−	0.819555i	$-0.305779\pi$
$577$	27.5279	1.14600	0.573000	+	0.819555i	$0.305779\pi$
$578$	−35.3607	−1.47081
$579$	2.94427	0.122360
$580$	0	0
$581$	11.7082	0.485738
$582$	−2.76393	−0.114569
$583$	20.0000	0.828315
$584$	−6.00000	−0.248282
$585$	−5.23607	−0.216485
$586$	−9.41641	−0.388988
$587$	0.944272	0.0389743	0.0194871	−	0.999810i	$-0.493797\pi$
$587$	0.944272	0.0389743	0.0194871	+	0.999810i	$0.493797\pi$
$588$	1.00000	0.0412393
$589$	−9.52786	−0.392589
$590$	2.47214	0.101776
$591$	17.4164	0.716415
$592$	−6.94427	−0.285408
$593$	30.3607	1.24676	0.623382	−	0.781918i	$-0.285758\pi$
$593$	30.3607	1.24676	0.623382	+	0.781918i	$0.285758\pi$
$594$	4.47214	0.183494
$595$	7.23607	0.296650
$596$	6.00000	0.245770
$597$	−4.94427	−0.202356
$598$	−5.23607	−0.214119
$599$	−42.0000	−1.71607	−0.858037	−	0.513588i	$-0.828316\pi$
$599$	−42.0000	−1.71607	−0.858037	+	0.513588i	$0.828316\pi$
$600$	−1.00000	−0.0408248
$601$	−14.9443	−0.609590	−0.304795	−	0.952418i	$-0.598588\pi$
$601$	−14.9443	−0.609590	−0.304795	+	0.952418i	$0.598588\pi$
$602$	−6.00000	−0.244542
$603$	6.00000	0.244339
$604$	−1.52786	−0.0621679
$605$	9.00000	0.365902
$606$	−13.2361	−0.537679
$607$	−3.23607	−0.131348	−0.0656740	−	0.997841i	$-0.520920\pi$
$607$	−3.23607	−0.131348	−0.0656740	+	0.997841i	$0.520920\pi$
$608$	1.23607	0.0501292
$609$	0	0
$610$	−2.94427	−0.119210
$611$	−19.4164	−0.785504
$612$	7.23607	0.292501
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	13.8885	0.560496
$615$	2.00000	0.0806478
$616$	4.47214	0.180187
$617$	−36.8328	−1.48283	−0.741417	−	0.671045i	$-0.765846\pi$
$617$	−36.8328	−1.48283	−0.741417	+	0.671045i	$0.765846\pi$
$618$	−4.94427	−0.198888
$619$	−6.76393	−0.271865	−0.135933	−	0.990718i	$-0.543403\pi$
$619$	−6.76393	−0.271865	−0.135933	+	0.990718i	$0.543403\pi$
$620$	7.70820	0.309569
$621$	−1.00000	−0.0401286
$622$	−25.7082	−1.03081
$623$	16.6525	0.667167
$624$	−5.23607	−0.209610
$625$	1.00000	0.0400000
$626$	−14.1803	−0.566760
$627$	5.52786	0.220762
$628$	−6.00000	−0.239426
$629$	−50.2492	−2.00357
$630$	−1.00000	−0.0398410
$631$	−29.8885	−1.18984	−0.594922	−	0.803783i	$-0.702817\pi$
$631$	−29.8885	−1.18984	−0.594922	+	0.803783i	$0.702817\pi$
$632$	12.0000	0.477334
$633$	−4.94427	−0.196517
$634$	−29.4164	−1.16827
$635$	−4.47214	−0.177471
$636$	−4.47214	−0.177332
$637$	−5.23607	−0.207461
$638$	0	0
$639$	12.4721	0.493390
$640$	−1.00000	−0.0395285
$641$	26.8328	1.05983	0.529916	−	0.848050i	$-0.322223\pi$
$641$	26.8328	1.05983	0.529916	+	0.848050i	$0.322223\pi$
$642$	−10.4721	−0.413302
$643$	−41.4853	−1.63602	−0.818010	−	0.575204i	$-0.804923\pi$
$643$	−41.4853	−1.63602	−0.818010	+	0.575204i	$0.804923\pi$
$644$	−1.00000	−0.0394055
$645$	6.00000	0.236250
$646$	8.94427	0.351908
$647$	14.1803	0.557487	0.278743	−	0.960366i	$-0.410082\pi$
$647$	14.1803	0.557487	0.278743	+	0.960366i	$0.410082\pi$
$648$	−1.00000	−0.0392837
$649$	11.0557	0.433975
$650$	5.23607	0.205375
$651$	7.70820	0.302108
$652$	−19.4164	−0.760405
$653$	18.9443	0.741347	0.370673	−	0.928763i	$-0.379127\pi$
$653$	18.9443	0.741347	0.370673	+	0.928763i	$0.379127\pi$
$654$	−6.94427	−0.271543
$655$	−0.944272	−0.0368958
$656$	2.00000	0.0780869
$657$	6.00000	0.234082
$658$	−3.70820	−0.144561
$659$	−32.8328	−1.27898	−0.639492	−	0.768797i	$-0.720855\pi$
$659$	−32.8328	−1.27898	−0.639492	+	0.768797i	$0.720855\pi$
$660$	−4.47214	−0.174078
$661$	15.5279	0.603964	0.301982	−	0.953314i	$-0.402352\pi$
$661$	15.5279	0.603964	0.301982	+	0.953314i	$0.402352\pi$
$662$	−12.0000	−0.466393
$663$	−37.8885	−1.47147
$664$	−11.7082	−0.454366
$665$	−1.23607	−0.0479327
$666$	6.94427	0.269085
$667$	0	0
$668$	13.2361	0.512119
$669$	−16.7639	−0.648131
$670$	−6.00000	−0.231800
$671$	−13.1672	−0.508314
$672$	−1.00000	−0.0385758
$673$	22.9443	0.884437	0.442218	−	0.896907i	$-0.354192\pi$
$673$	22.9443	0.884437	0.442218	+	0.896907i	$0.354192\pi$
$674$	−27.4164	−1.05604
$675$	1.00000	0.0384900
$676$	14.4164	0.554477
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	−3.52786	−0.135487
$679$	2.76393	0.106070
$680$	−7.23607	−0.277491
$681$	29.2361	1.12033
$682$	34.4721	1.32001
$683$	1.88854	0.0722631	0.0361316	−	0.999347i	$-0.488496\pi$
$683$	1.88854	0.0722631	0.0361316	+	0.999347i	$0.488496\pi$
$684$	−1.23607	−0.0472622
$685$	−2.00000	−0.0764161
$686$	−1.00000	−0.0381802
$687$	−5.41641	−0.206649
$688$	6.00000	0.228748
$689$	23.4164	0.892094
$690$	1.00000	0.0380693
$691$	−33.5279	−1.27546	−0.637730	−	0.770260i	$-0.720126\pi$
$691$	−33.5279	−1.27546	−0.637730	+	0.770260i	$0.720126\pi$
$692$	−5.70820	−0.216993
$693$	−4.47214	−0.169882
$694$	−32.0000	−1.21470
$695$	−4.00000	−0.151729
$696$	0	0
$697$	14.4721	0.548171
$698$	18.6525	0.706007
$699$	10.0000	0.378235
$700$	1.00000	0.0377964
$701$	−18.9443	−0.715515	−0.357758	−	0.933814i	$-0.616459\pi$
$701$	−18.9443	−0.715515	−0.357758	+	0.933814i	$0.616459\pi$
$702$	5.23607	0.197623
$703$	8.58359	0.323736
$704$	−4.47214	−0.168550
$705$	3.70820	0.139659
$706$	7.52786	0.283315
$707$	13.2361	0.497794
$708$	−2.47214	−0.0929086
$709$	−30.3607	−1.14022	−0.570110	−	0.821569i	$-0.693099\pi$
$709$	−30.3607	−1.14022	−0.570110	+	0.821569i	$0.693099\pi$
$710$	−12.4721	−0.468071
$711$	−12.0000	−0.450035
$712$	−16.6525	−0.624078
$713$	−7.70820	−0.288675
$714$	−7.23607	−0.270803
$715$	23.4164	0.875724
$716$	−4.94427	−0.184776
$717$	−21.4164	−0.799810
$718$	−16.3607	−0.610575
$719$	9.34752	0.348604	0.174302	−	0.984692i	$-0.444233\pi$
$719$	9.34752	0.348604	0.174302	+	0.984692i	$0.444233\pi$
$720$	1.00000	0.0372678
$721$	4.94427	0.184134
$722$	17.4721	0.650246
$723$	−3.81966	−0.142055
$724$	15.8885	0.590493
$725$	0	0
$726$	−9.00000	−0.334021
$727$	−35.4164	−1.31352	−0.656761	−	0.754099i	$-0.728074\pi$
$727$	−35.4164	−1.31352	−0.656761	+	0.754099i	$0.728074\pi$
$728$	5.23607	0.194062
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	43.4164	1.60581
$732$	2.94427	0.108823
$733$	−5.41641	−0.200060	−0.100030	−	0.994984i	$-0.531894\pi$
$733$	−5.41641	−0.200060	−0.100030	+	0.994984i	$0.531894\pi$
$734$	3.05573	0.112789
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	−26.8328	−0.988399
$738$	−2.00000	−0.0736210
$739$	48.7214	1.79224	0.896122	−	0.443808i	$-0.146373\pi$
$739$	48.7214	1.79224	0.896122	+	0.443808i	$0.146373\pi$
$740$	−6.94427	−0.255277
$741$	6.47214	0.237760
$742$	4.47214	0.164177
$743$	31.7771	1.16579	0.582894	−	0.812548i	$-0.301920\pi$
$743$	31.7771	1.16579	0.582894	+	0.812548i	$0.301920\pi$
$744$	−7.70820	−0.282596
$745$	6.00000	0.219823
$746$	19.8885	0.728171
$747$	11.7082	0.428381
$748$	−32.3607	−1.18322
$749$	10.4721	0.382644
$750$	−1.00000	−0.0365148
$751$	46.8328	1.70895	0.854477	−	0.519489i	$-0.173878\pi$
$751$	46.8328	1.70895	0.854477	+	0.519489i	$0.173878\pi$
$752$	3.70820	0.135224
$753$	−6.29180	−0.229286
$754$	0	0
$755$	−1.52786	−0.0556047
$756$	1.00000	0.0363696
$757$	−6.94427	−0.252394	−0.126197	−	0.992005i	$-0.540277\pi$
$757$	−6.94427	−0.252394	−0.126197	+	0.992005i	$0.540277\pi$
$758$	7.41641	0.269376
$759$	4.47214	0.162328
$760$	1.23607	0.0448369
$761$	39.8885	1.44596	0.722979	−	0.690870i	$-0.242772\pi$
$761$	39.8885	1.44596	0.722979	+	0.690870i	$0.242772\pi$
$762$	4.47214	0.162008
$763$	6.94427	0.251400
$764$	−14.4721	−0.523584
$765$	7.23607	0.261621
$766$	2.47214	0.0893219
$767$	12.9443	0.467391
$768$	1.00000	0.0360844
$769$	5.12461	0.184798	0.0923991	−	0.995722i	$-0.470546\pi$
$769$	5.12461	0.184798	0.0923991	+	0.995722i	$0.470546\pi$
$770$	4.47214	0.161165
$771$	17.4164	0.627237
$772$	2.94427	0.105967
$773$	32.8328	1.18091	0.590457	−	0.807069i	$-0.298947\pi$
$773$	32.8328	1.18091	0.590457	+	0.807069i	$0.298947\pi$
$774$	−6.00000	−0.215666
$775$	7.70820	0.276887
$776$	−2.76393	−0.0992194
$777$	−6.94427	−0.249124
$778$	14.9443	0.535778
$779$	−2.47214	−0.0885735
$780$	−5.23607	−0.187481
$781$	−55.7771	−1.99586
$782$	7.23607	0.258761
$783$	0	0
$784$	1.00000	0.0357143
$785$	−6.00000	−0.214149
$786$	0.944272	0.0336811
$787$	5.34752	0.190619	0.0953093	−	0.995448i	$-0.469616\pi$
$787$	5.34752	0.190619	0.0953093	+	0.995448i	$0.469616\pi$
$788$	17.4164	0.620434
$789$	−17.8885	−0.636849
$790$	12.0000	0.426941
$791$	3.52786	0.125436
$792$	4.47214	0.158910
$793$	−15.4164	−0.547453
$794$	5.23607	0.185821
$795$	−4.47214	−0.158610
$796$	−4.94427	−0.175245
$797$	−12.4721	−0.441786	−0.220893	−	0.975298i	$-0.570897\pi$
$797$	−12.4721	−0.441786	−0.220893	+	0.975298i	$0.570897\pi$
$798$	1.23607	0.0437563
$799$	26.8328	0.949277
$800$	−1.00000	−0.0353553
$801$	16.6525	0.588386
$802$	14.8328	0.523765
$803$	−26.8328	−0.946910
$804$	6.00000	0.211604
$805$	−1.00000	−0.0352454
$806$	40.3607	1.42164
$807$	−21.5967	−0.760242
$808$	−13.2361	−0.465643
$809$	39.8885	1.40241	0.701203	−	0.712961i	$-0.252647\pi$
$809$	39.8885	1.40241	0.701203	+	0.712961i	$0.252647\pi$
$810$	−1.00000	−0.0351364
$811$	−31.0557	−1.09051	−0.545257	−	0.838269i	$-0.683568\pi$
$811$	−31.0557	−1.09051	−0.545257	+	0.838269i	$0.683568\pi$
$812$	0	0
$813$	−21.2361	−0.744781
$814$	−31.0557	−1.08850
$815$	−19.4164	−0.680127
$816$	7.23607	0.253313
$817$	−7.41641	−0.259467
$818$	−11.5279	−0.403062
$819$	−5.23607	−0.182963
$820$	2.00000	0.0698430
$821$	11.4164	0.398435	0.199218	−	0.979955i	$-0.436160\pi$
$821$	11.4164	0.398435	0.199218	+	0.979955i	$0.436160\pi$
$822$	2.00000	0.0697580
$823$	−35.3050	−1.23065	−0.615327	−	0.788272i	$-0.710976\pi$
$823$	−35.3050	−1.23065	−0.615327	+	0.788272i	$0.710976\pi$
$824$	−4.94427	−0.172242
$825$	−4.47214	−0.155700
$826$	2.47214	0.0860166
$827$	37.5279	1.30497	0.652486	−	0.757801i	$-0.273726\pi$
$827$	37.5279	1.30497	0.652486	+	0.757801i	$0.273726\pi$
$828$	−1.00000	−0.0347524
$829$	17.7082	0.615031	0.307516	−	0.951543i	$-0.400502\pi$
$829$	17.7082	0.615031	0.307516	+	0.951543i	$0.400502\pi$
$830$	−11.7082	−0.406398
$831$	3.05573	0.106002
$832$	−5.23607	−0.181528
$833$	7.23607	0.250715
$834$	4.00000	0.138509
$835$	13.2361	0.458053
$836$	5.52786	0.191185
$837$	7.70820	0.266435
$838$	−2.65248	−0.0916283
$839$	0.360680	0.0124520	0.00622602	−	0.999981i	$-0.498018\pi$
$839$	0.360680	0.0124520	0.00622602	+	0.999981i	$0.498018\pi$
$840$	−1.00000	−0.0345033
$841$	−29.0000	−1.00000
$842$	35.8885	1.23680
$843$	−12.0000	−0.413302
$844$	−4.94427	−0.170189
$845$	14.4164	0.495940
$846$	−3.70820	−0.127491
$847$	9.00000	0.309244
$848$	−4.47214	−0.153574
$849$	6.65248	0.228312
$850$	−7.23607	−0.248195
$851$	6.94427	0.238047
$852$	12.4721	0.427288
$853$	33.5967	1.15033	0.575165	−	0.818037i	$-0.304938\pi$
$853$	33.5967	1.15033	0.575165	+	0.818037i	$0.304938\pi$
$854$	−2.94427	−0.100751
$855$	−1.23607	−0.0422726
$856$	−10.4721	−0.357930
$857$	−58.1378	−1.98595	−0.992974	−	0.118331i	$-0.962245\pi$
$857$	−58.1378	−1.98595	−0.992974	+	0.118331i	$0.962245\pi$
$858$	−23.4164	−0.799423
$859$	45.3050	1.54579	0.772893	−	0.634537i	$-0.218809\pi$
$859$	45.3050	1.54579	0.772893	+	0.634537i	$0.218809\pi$
$860$	6.00000	0.204598
$861$	2.00000	0.0681598
$862$	−22.8328	−0.777689
$863$	48.3607	1.64622	0.823108	−	0.567884i	$-0.192238\pi$
$863$	48.3607	1.64622	0.823108	+	0.567884i	$0.192238\pi$
$864$	−1.00000	−0.0340207
$865$	−5.70820	−0.194085
$866$	−36.6525	−1.24550
$867$	35.3607	1.20091
$868$	7.70820	0.261633
$869$	53.6656	1.82048
$870$	0	0
$871$	−31.4164	−1.06450
$872$	−6.94427	−0.235163
$873$	2.76393	0.0935449
$874$	−1.23607	−0.0418106
$875$	1.00000	0.0338062
$876$	6.00000	0.202721
$877$	5.52786	0.186663	0.0933314	−	0.995635i	$-0.470248\pi$
$877$	5.52786	0.186663	0.0933314	+	0.995635i	$0.470248\pi$
$878$	−17.2361	−0.581689
$879$	9.41641	0.317608
$880$	−4.47214	−0.150756
$881$	−14.7639	−0.497410	−0.248705	−	0.968579i	$-0.580005\pi$
$881$	−14.7639	−0.497410	−0.248705	+	0.968579i	$0.580005\pi$
$882$	−1.00000	−0.0336718
$883$	−12.5836	−0.423472	−0.211736	−	0.977327i	$-0.567912\pi$
$883$	−12.5836	−0.423472	−0.211736	+	0.977327i	$0.567912\pi$
$884$	−37.8885	−1.27433
$885$	−2.47214	−0.0830999
$886$	24.0000	0.806296
$887$	12.2918	0.412718	0.206359	−	0.978476i	$-0.433839\pi$
$887$	12.2918	0.412718	0.206359	+	0.978476i	$0.433839\pi$
$888$	6.94427	0.233035
$889$	−4.47214	−0.149991
$890$	−16.6525	−0.558192
$891$	−4.47214	−0.149822
$892$	−16.7639	−0.561298
$893$	−4.58359	−0.153384
$894$	−6.00000	−0.200670
$895$	−4.94427	−0.165269
$896$	−1.00000	−0.0334077
$897$	5.23607	0.174827
$898$	20.8328	0.695200
$899$	0	0
$900$	1.00000	0.0333333
$901$	−32.3607	−1.07809
$902$	8.94427	0.297812
$903$	6.00000	0.199667
$904$	−3.52786	−0.117335
$905$	15.8885	0.528153
$906$	1.52786	0.0507599
$907$	19.5279	0.648412	0.324206	−	0.945986i	$-0.394903\pi$
$907$	19.5279	0.648412	0.324206	+	0.945986i	$0.394903\pi$
$908$	29.2361	0.970233
$909$	13.2361	0.439013
$910$	5.23607	0.173574
$911$	−41.3050	−1.36849	−0.684247	−	0.729250i	$-0.739869\pi$
$911$	−41.3050	−1.36849	−0.684247	+	0.729250i	$0.739869\pi$
$912$	−1.23607	−0.0409303
$913$	−52.3607	−1.73289
$914$	38.8328	1.28448
$915$	2.94427	0.0973346
$916$	−5.41641	−0.178963
$917$	−0.944272	−0.0311826
$918$	−7.23607	−0.238826
$919$	−26.8328	−0.885133	−0.442566	−	0.896736i	$-0.645932\pi$
$919$	−26.8328	−0.885133	−0.442566	+	0.896736i	$0.645932\pi$
$920$	1.00000	0.0329690
$921$	−13.8885	−0.457643
$922$	2.76393	0.0910253
$923$	−65.3050	−2.14954
$924$	−4.47214	−0.147122
$925$	−6.94427	−0.228326
$926$	−3.88854	−0.127785
$927$	4.94427	0.162391
$928$	0	0
$929$	24.2492	0.795591	0.397796	−	0.917474i	$-0.369775\pi$
$929$	24.2492	0.795591	0.397796	+	0.917474i	$0.369775\pi$
$930$	−7.70820	−0.252762
$931$	−1.23607	−0.0405105
$932$	10.0000	0.327561
$933$	25.7082	0.841649
$934$	6.76393	0.221323
$935$	−32.3607	−1.05831
$936$	5.23607	0.171146
$937$	−21.8197	−0.712817	−0.356409	−	0.934330i	$-0.615999\pi$
$937$	−21.8197	−0.712817	−0.356409	+	0.934330i	$0.615999\pi$
$938$	−6.00000	−0.195907
$939$	14.1803	0.462758
$940$	3.70820	0.120948
$941$	42.9443	1.39994	0.699972	−	0.714171i	$-0.253196\pi$
$941$	42.9443	1.39994	0.699972	+	0.714171i	$0.253196\pi$
$942$	6.00000	0.195491
$943$	−2.00000	−0.0651290
$944$	−2.47214	−0.0804612
$945$	1.00000	0.0325300
$946$	26.8328	0.872410
$947$	22.8328	0.741967	0.370983	−	0.928639i	$-0.379021\pi$
$947$	22.8328	0.741967	0.370983	+	0.928639i	$0.379021\pi$
$948$	−12.0000	−0.389742
$949$	−31.4164	−1.01982
$950$	1.23607	0.0401033
$951$	29.4164	0.953892
$952$	−7.23607	−0.234522
$953$	36.2492	1.17423	0.587114	−	0.809504i	$-0.300264\pi$
$953$	36.2492	1.17423	0.587114	+	0.809504i	$0.300264\pi$
$954$	4.47214	0.144791
$955$	−14.4721	−0.468307
$956$	−21.4164	−0.692656
$957$	0	0
$958$	−16.0000	−0.516937
$959$	−2.00000	−0.0645834
$960$	1.00000	0.0322749
$961$	28.4164	0.916658
$962$	−36.3607	−1.17232
$963$	10.4721	0.337460
$964$	−3.81966	−0.123023
$965$	2.94427	0.0947795
$966$	1.00000	0.0321745
$967$	16.8328	0.541307	0.270653	−	0.962677i	$-0.412760\pi$
$967$	16.8328	0.541307	0.270653	+	0.962677i	$0.412760\pi$
$968$	−9.00000	−0.289271
$969$	−8.94427	−0.287331
$970$	−2.76393	−0.0887445
$971$	−55.0132	−1.76546	−0.882728	−	0.469884i	$-0.844296\pi$
$971$	−55.0132	−1.76546	−0.882728	+	0.469884i	$0.844296\pi$
$972$	1.00000	0.0320750
$973$	−4.00000	−0.128234
$974$	−40.8328	−1.30837
$975$	−5.23607	−0.167688
$976$	2.94427	0.0942438
$977$	35.8885	1.14818	0.574088	−	0.818794i	$-0.305357\pi$
$977$	35.8885	1.14818	0.574088	+	0.818794i	$0.305357\pi$
$978$	19.4164	0.620868
$979$	−74.4721	−2.38014
$980$	1.00000	0.0319438
$981$	6.94427	0.221714
$982$	29.5279	0.942272
$983$	−16.5836	−0.528934	−0.264467	−	0.964395i	$-0.585196\pi$
$983$	−16.5836	−0.528934	−0.264467	+	0.964395i	$0.585196\pi$
$984$	−2.00000	−0.0637577
$985$	17.4164	0.554933
$986$	0	0
$987$	3.70820	0.118033
$988$	6.47214	0.205906
$989$	−6.00000	−0.190789
$990$	4.47214	0.142134
$991$	−21.3050	−0.676774	−0.338387	−	0.941007i	$-0.609881\pi$
$991$	−21.3050	−0.676774	−0.338387	+	0.941007i	$0.609881\pi$
$992$	−7.70820	−0.244736
$993$	12.0000	0.380808
$994$	−12.4721	−0.395592
$995$	−4.94427	−0.156744
$996$	11.7082	0.370989
$997$	9.59675	0.303932	0.151966	−	0.988386i	$-0.451440\pi$
$997$	9.59675	0.303932	0.151966	+	0.988386i	$0.451440\pi$
$998$	−41.8885	−1.32596
$999$	−6.94427	−0.219707

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.47214 q^{11} +1.00000 q^{12} -5.23607 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.23607 q^{17} -1.00000 q^{18} -1.23607 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.47214 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +5.23607 q^{26} +1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{30} +7.70820 q^{31} -1.00000 q^{32} -4.47214 q^{33} -7.23607 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.94427 q^{37} +1.23607 q^{38} -5.23607 q^{39} -1.00000 q^{40} +2.00000 q^{41} -1.00000 q^{42} +6.00000 q^{43} -4.47214 q^{44} +1.00000 q^{45} +1.00000 q^{46} +3.70820 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.23607 q^{51} -5.23607 q^{52} -4.47214 q^{53} -1.00000 q^{54} -4.47214 q^{55} -1.00000 q^{56} -1.23607 q^{57} -2.47214 q^{59} +1.00000 q^{60} +2.94427 q^{61} -7.70820 q^{62} +1.00000 q^{63} +1.00000 q^{64} -5.23607 q^{65} +4.47214 q^{66} +6.00000 q^{67} +7.23607 q^{68} -1.00000 q^{69} -1.00000 q^{70} +12.4721 q^{71} -1.00000 q^{72} +6.00000 q^{73} +6.94427 q^{74} +1.00000 q^{75} -1.23607 q^{76} -4.47214 q^{77} +5.23607 q^{78} -12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +11.7082 q^{83} +1.00000 q^{84} +7.23607 q^{85} -6.00000 q^{86} +4.47214 q^{88} +16.6525 q^{89} -1.00000 q^{90} -5.23607 q^{91} -1.00000 q^{92} +7.70820 q^{93} -3.70820 q^{94} -1.23607 q^{95} -1.00000 q^{96} +2.76393 q^{97} -1.00000 q^{98} -4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} + 10 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 2 q^{21} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{30} + 2 q^{31} - 2 q^{32} - 10 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} + 4 q^{41} - 2 q^{42} + 12 q^{43} + 2 q^{45} + 2 q^{46} - 6 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 10 q^{51} - 6 q^{52} - 2 q^{54} - 2 q^{56} + 2 q^{57} + 4 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{67} + 10 q^{68} - 2 q^{69} - 2 q^{70} + 16 q^{71} - 2 q^{72} + 12 q^{73} - 4 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{78} - 24 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 10 q^{83} + 2 q^{84} + 10 q^{85} - 12 q^{86} + 2 q^{89} - 2 q^{90} - 6 q^{91} - 2 q^{92} + 2 q^{93} + 6 q^{94} + 2 q^{95} - 2 q^{96} + 10 q^{97} - 2 q^{98}+O(q^{100}) \) 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 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 + 10 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 2 * q^21 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 - 2 * q^30 + 2 * q^31 - 2 * q^32 - 10 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 + 4 * q^41 - 2 * q^42 + 12 * q^43 + 2 * q^45 + 2 * q^46 - 6 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 10 * q^51 - 6 * q^52 - 2 * q^54 - 2 * q^56 + 2 * q^57 + 4 * q^59 + 2 * q^60 - 12 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^67 + 10 * q^68 - 2 * q^69 - 2 * q^70 + 16 * q^71 - 2 * q^72 + 12 * q^73 - 4 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^78 - 24 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 10 * q^83 + 2 * q^84 + 10 * q^85 - 12 * q^86 + 2 * q^89 - 2 * q^90 - 6 * q^91 - 2 * q^92 + 2 * q^93 + 6 * q^94 + 2 * q^95 - 2 * q^96 + 10 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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