LMFDB - Embedded newform 4830.2.a.bq.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:	$\Z[a_1, \ldots, a_{11}]$
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.23607 q^{11} +1.00000 q^{12} +3.23607 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} -1.00000 q^{18} -4.47214 q^{19} +1.00000 q^{20} -1.00000 q^{21} +3.23607 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23607 q^{26} +1.00000 q^{27} -1.00000 q^{28} +7.70820 q^{29} -1.00000 q^{30} -4.47214 q^{31} -1.00000 q^{32} -3.23607 q^{33} +2.47214 q^{34} -1.00000 q^{35} +1.00000 q^{36} -0.472136 q^{37} +4.47214 q^{38} +3.23607 q^{39} -1.00000 q^{40} +8.47214 q^{41} +1.00000 q^{42} -0.763932 q^{43} -3.23607 q^{44} +1.00000 q^{45} -1.00000 q^{46} -2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.47214 q^{51} +3.23607 q^{52} +10.0000 q^{53} -1.00000 q^{54} -3.23607 q^{55} +1.00000 q^{56} -4.47214 q^{57} -7.70820 q^{58} +8.94427 q^{59} +1.00000 q^{60} -2.00000 q^{61} +4.47214 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.23607 q^{65} +3.23607 q^{66} -8.76393 q^{67} -2.47214 q^{68} +1.00000 q^{69} +1.00000 q^{70} +9.70820 q^{71} -1.00000 q^{72} +14.9443 q^{73} +0.472136 q^{74} +1.00000 q^{75} -4.47214 q^{76} +3.23607 q^{77} -3.23607 q^{78} -4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.47214 q^{82} -0.472136 q^{83} -1.00000 q^{84} -2.47214 q^{85} +0.763932 q^{86} +7.70820 q^{87} +3.23607 q^{88} +7.23607 q^{89} -1.00000 q^{90} -3.23607 q^{91} +1.00000 q^{92} -4.47214 q^{93} +2.00000 q^{94} -4.47214 q^{95} -1.00000 q^{96} +5.70820 q^{97} -1.00000 q^{98} -3.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} - 2 q^{32} - 2 q^{33} - 4 q^{34} - 2 q^{35} + 2 q^{36} + 8 q^{37} + 2 q^{39} - 2 q^{40} + 8 q^{41} + 2 q^{42} - 6 q^{43} - 2 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^{52} + 20 q^{53} - 2 q^{54} - 2 q^{55} + 2 q^{56} - 2 q^{58} + 2 q^{60} - 4 q^{61} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 2 q^{66} - 22 q^{67} + 4 q^{68} + 2 q^{69} + 2 q^{70} + 6 q^{71} - 2 q^{72} + 12 q^{73} - 8 q^{74} + 2 q^{75} + 2 q^{77} - 2 q^{78} - 8 q^{79} + 2 q^{80} + 2 q^{81} - 8 q^{82} + 8 q^{83} - 2 q^{84} + 4 q^{85} + 6 q^{86} + 2 q^{87} + 2 q^{88} + 10 q^{89} - 2 q^{90} - 2 q^{91} + 2 q^{92} + 4 q^{94} - 2 q^{96} - 2 q^{97} - 2 q^{98} - 2 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 - 2 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 - 2 * q^32 - 2 * q^33 - 4 * q^34 - 2 * q^35 + 2 * q^36 + 8 * q^37 + 2 * q^39 - 2 * q^40 + 8 * q^41 + 2 * q^42 - 6 * q^43 - 2 * 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^52 + 20 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 - 2 * q^58 + 2 * q^60 - 4 * q^61 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 2 * q^66 - 22 * q^67 + 4 * q^68 + 2 * q^69 + 2 * q^70 + 6 * q^71 - 2 * q^72 + 12 * q^73 - 8 * q^74 + 2 * q^75 + 2 * q^77 - 2 * q^78 - 8 * q^79 + 2 * q^80 + 2 * q^81 - 8 * q^82 + 8 * q^83 - 2 * q^84 + 4 * q^85 + 6 * q^86 + 2 * q^87 + 2 * q^88 + 10 * q^89 - 2 * q^90 - 2 * q^91 + 2 * q^92 + 4 * q^94 - 2 * q^96 - 2 * q^97 - 2 * q^98 - 2 * 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
$11$	−3.23607	−0.975711	−0.487856	−	0.872924i	$-0.662221\pi$
$11$	−3.23607	−0.975711	−0.487856	+	0.872924i	$0.662221\pi$
$12$	1.00000	0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.47214	−0.599581	−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214	−0.599581	−0.299791	+	0.954005i	$0.596917\pi$
$18$	−1.00000	−0.235702
$19$	−4.47214	−1.02598	−0.512989	−	0.858395i	$-0.671462\pi$
$19$	−4.47214	−1.02598	−0.512989	+	0.858395i	$0.671462\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	3.23607	0.689932
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.23607	−0.634645
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	7.70820	1.43138	0.715689	−	0.698419i	$-0.246113\pi$
$29$	7.70820	1.43138	0.715689	+	0.698419i	$0.246113\pi$
$30$	−1.00000	−0.182574
$31$	−4.47214	−0.803219	−0.401610	−	0.915811i	$-0.631549\pi$
$31$	−4.47214	−0.803219	−0.401610	+	0.915811i	$0.631549\pi$
$32$	−1.00000	−0.176777
$33$	−3.23607	−0.563327
$34$	2.47214	0.423968
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−0.472136	−0.0776187	−0.0388093	−	0.999247i	$-0.512356\pi$
$37$	−0.472136	−0.0776187	−0.0388093	+	0.999247i	$0.512356\pi$
$38$	4.47214	0.725476
$39$	3.23607	0.518186
$40$	−1.00000	−0.158114
$41$	8.47214	1.32313	0.661563	−	0.749890i	$-0.269894\pi$
$41$	8.47214	1.32313	0.661563	+	0.749890i	$0.269894\pi$
$42$	1.00000	0.154303
$43$	−0.763932	−0.116499	−0.0582493	−	0.998302i	$-0.518552\pi$
$43$	−0.763932	−0.116499	−0.0582493	+	0.998302i	$0.518552\pi$
$44$	−3.23607	−0.487856
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−2.47214	−0.346168
$52$	3.23607	0.448762
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	−3.23607	−0.436351
$56$	1.00000	0.133631
$57$	−4.47214	−0.592349
$58$	−7.70820	−1.01214
$59$	8.94427	1.16445	0.582223	−	0.813029i	$-0.302183\pi$
$59$	8.94427	1.16445	0.582223	+	0.813029i	$0.302183\pi$
$60$	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	$0.540868\pi$
$62$	4.47214	0.567962
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.23607	0.401385
$66$	3.23607	0.398332
$67$	−8.76393	−1.07068	−0.535342	−	0.844635i	$-0.679817\pi$
$67$	−8.76393	−1.07068	−0.535342	+	0.844635i	$0.679817\pi$
$68$	−2.47214	−0.299791
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	9.70820	1.15215	0.576076	−	0.817396i	$-0.304583\pi$
$71$	9.70820	1.15215	0.576076	+	0.817396i	$0.304583\pi$
$72$	−1.00000	−0.117851
$73$	14.9443	1.74909	0.874547	−	0.484940i	$-0.161159\pi$
$73$	14.9443	1.74909	0.874547	+	0.484940i	$0.161159\pi$
$74$	0.472136	0.0548847
$75$	1.00000	0.115470
$76$	−4.47214	−0.512989
$77$	3.23607	0.368784
$78$	−3.23607	−0.366413
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−8.47214	−0.935591
$83$	−0.472136	−0.0518237	−0.0259118	−	0.999664i	$-0.508249\pi$
$83$	−0.472136	−0.0518237	−0.0259118	+	0.999664i	$0.508249\pi$
$84$	−1.00000	−0.109109
$85$	−2.47214	−0.268141
$86$	0.763932	0.0823769
$87$	7.70820	0.826406
$88$	3.23607	0.344966
$89$	7.23607	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$89$	7.23607	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$90$	−1.00000	−0.105409
$91$	−3.23607	−0.339232
$92$	1.00000	0.104257
$93$	−4.47214	−0.463739
$94$	2.00000	0.206284
$95$	−4.47214	−0.458831
$96$	−1.00000	−0.102062
$97$	5.70820	0.579580	0.289790	−	0.957090i	$-0.406414\pi$
$97$	5.70820	0.579580	0.289790	+	0.957090i	$0.406414\pi$
$98$	−1.00000	−0.101015
$99$	−3.23607	−0.325237
$100$	1.00000	0.100000
$101$	4.18034	0.415959	0.207980	−	0.978133i	$-0.433311\pi$
$101$	4.18034	0.415959	0.207980	+	0.978133i	$0.433311\pi$
$102$	2.47214	0.244778
$103$	18.4721	1.82011	0.910057	−	0.414484i	$-0.136038\pi$
$103$	18.4721	1.82011	0.910057	+	0.414484i	$0.136038\pi$
$104$	−3.23607	−0.317323
$105$	−1.00000	−0.0975900
$106$	−10.0000	−0.971286
$107$	−7.41641	−0.716971	−0.358486	−	0.933535i	$-0.616707\pi$
$107$	−7.41641	−0.716971	−0.358486	+	0.933535i	$0.616707\pi$
$108$	1.00000	0.0962250
$109$	7.52786	0.721039	0.360519	−	0.932752i	$-0.382599\pi$
$109$	7.52786	0.721039	0.360519	+	0.932752i	$0.382599\pi$
$110$	3.23607	0.308547
$111$	−0.472136	−0.0448132
$112$	−1.00000	−0.0944911
$113$	−10.9443	−1.02955	−0.514775	−	0.857325i	$-0.672125\pi$
$113$	−10.9443	−1.02955	−0.514775	+	0.857325i	$0.672125\pi$
$114$	4.47214	0.418854
$115$	1.00000	0.0932505
$116$	7.70820	0.715689
$117$	3.23607	0.299175
$118$	−8.94427	−0.823387
$119$	2.47214	0.226620
$120$	−1.00000	−0.0912871
$121$	−0.527864	−0.0479876
$122$	2.00000	0.181071
$123$	8.47214	0.763907
$124$	−4.47214	−0.401610
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	4.76393	0.422731	0.211365	−	0.977407i	$-0.432209\pi$
$127$	4.76393	0.422731	0.211365	+	0.977407i	$0.432209\pi$
$128$	−1.00000	−0.0883883
$129$	−0.763932	−0.0672605
$130$	−3.23607	−0.283822
$131$	−8.94427	−0.781465	−0.390732	−	0.920504i	$-0.627778\pi$
$131$	−8.94427	−0.781465	−0.390732	+	0.920504i	$0.627778\pi$
$132$	−3.23607	−0.281664
$133$	4.47214	0.387783
$134$	8.76393	0.757088
$135$	1.00000	0.0860663
$136$	2.47214	0.211984
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	−1.00000	−0.0851257
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	−1.00000	−0.0845154
$141$	−2.00000	−0.168430
$142$	−9.70820	−0.814694
$143$	−10.4721	−0.875724
$144$	1.00000	0.0833333
$145$	7.70820	0.640131
$146$	−14.9443	−1.23680
$147$	1.00000	0.0824786
$148$	−0.472136	−0.0388093
$149$	7.52786	0.616707	0.308353	−	0.951272i	$-0.400222\pi$
$149$	7.52786	0.616707	0.308353	+	0.951272i	$0.400222\pi$
$150$	−1.00000	−0.0816497
$151$	5.52786	0.449851	0.224926	−	0.974376i	$-0.427786\pi$
$151$	5.52786	0.449851	0.224926	+	0.974376i	$0.427786\pi$
$152$	4.47214	0.362738
$153$	−2.47214	−0.199860
$154$	−3.23607	−0.260770
$155$	−4.47214	−0.359211
$156$	3.23607	0.259093
$157$	−13.4164	−1.07075	−0.535373	−	0.844616i	$-0.679829\pi$
$157$	−13.4164	−1.07075	−0.535373	+	0.844616i	$0.679829\pi$
$158$	4.00000	0.318223
$159$	10.0000	0.793052
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	7.41641	0.580898	0.290449	−	0.956890i	$-0.406195\pi$
$163$	7.41641	0.580898	0.290449	+	0.956890i	$0.406195\pi$
$164$	8.47214	0.661563
$165$	−3.23607	−0.251928
$166$	0.472136	0.0366449
$167$	16.4721	1.27465	0.637326	−	0.770594i	$-0.280040\pi$
$167$	16.4721	1.27465	0.637326	+	0.770594i	$0.280040\pi$
$168$	1.00000	0.0771517
$169$	−2.52786	−0.194451
$170$	2.47214	0.189604
$171$	−4.47214	−0.341993
$172$	−0.763932	−0.0582493
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	−7.70820	−0.584357
$175$	−1.00000	−0.0755929
$176$	−3.23607	−0.243928
$177$	8.94427	0.672293
$178$	−7.23607	−0.542366
$179$	−7.41641	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$179$	−7.41641	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$180$	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	$0.298933\pi$
$182$	3.23607	0.239873
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	−0.472136	−0.0347121
$186$	4.47214	0.327913
$187$	8.00000	0.585018
$188$	−2.00000	−0.145865
$189$	−1.00000	−0.0727393
$190$	4.47214	0.324443
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	−13.4164	−0.965734	−0.482867	−	0.875694i	$-0.660405\pi$
$193$	−13.4164	−0.965734	−0.482867	+	0.875694i	$0.660405\pi$
$194$	−5.70820	−0.409825
$195$	3.23607	0.231740
$196$	1.00000	0.0714286
$197$	18.9443	1.34972	0.674862	−	0.737944i	$-0.264203\pi$
$197$	18.9443	1.34972	0.674862	+	0.737944i	$0.264203\pi$
$198$	3.23607	0.229977
$199$	−14.4721	−1.02590	−0.512951	−	0.858418i	$-0.671448\pi$
$199$	−14.4721	−1.02590	−0.512951	+	0.858418i	$0.671448\pi$
$200$	−1.00000	−0.0707107
$201$	−8.76393	−0.618160
$202$	−4.18034	−0.294128
$203$	−7.70820	−0.541010
$204$	−2.47214	−0.173084
$205$	8.47214	0.591720
$206$	−18.4721	−1.28701
$207$	1.00000	0.0695048
$208$	3.23607	0.224381
$209$	14.4721	1.00106
$210$	1.00000	0.0690066
$211$	−3.05573	−0.210365	−0.105182	−	0.994453i	$-0.533543\pi$
$211$	−3.05573	−0.210365	−0.105182	+	0.994453i	$0.533543\pi$
$212$	10.0000	0.686803
$213$	9.70820	0.665195
$214$	7.41641	0.506975
$215$	−0.763932	−0.0520997
$216$	−1.00000	−0.0680414
$217$	4.47214	0.303588
$218$	−7.52786	−0.509851
$219$	14.9443	1.00984
$220$	−3.23607	−0.218176
$221$	−8.00000	−0.538138
$222$	0.472136	0.0316877
$223$	2.18034	0.146006	0.0730032	−	0.997332i	$-0.476742\pi$
$223$	2.18034	0.146006	0.0730032	+	0.997332i	$0.476742\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.9443	0.728002
$227$	14.9443	0.991886	0.495943	−	0.868355i	$-0.334822\pi$
$227$	14.9443	0.991886	0.495943	+	0.868355i	$0.334822\pi$
$228$	−4.47214	−0.296174
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−1.00000	−0.0659380
$231$	3.23607	0.212918
$232$	−7.70820	−0.506068
$233$	24.4721	1.60322	0.801611	−	0.597845i	$-0.203976\pi$
$233$	24.4721	1.60322	0.801611	+	0.597845i	$0.203976\pi$
$234$	−3.23607	−0.211548
$235$	−2.00000	−0.130466
$236$	8.94427	0.582223
$237$	−4.00000	−0.259828
$238$	−2.47214	−0.160245
$239$	4.76393	0.308153	0.154077	−	0.988059i	$-0.450760\pi$
$239$	4.76393	0.308153	0.154077	+	0.988059i	$0.450760\pi$
$240$	1.00000	0.0645497
$241$	−21.8885	−1.40997	−0.704983	−	0.709225i	$-0.749045\pi$
$241$	−21.8885	−1.40997	−0.704983	+	0.709225i	$0.749045\pi$
$242$	0.527864	0.0339324
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	1.00000	0.0638877
$246$	−8.47214	−0.540164
$247$	−14.4721	−0.920840
$248$	4.47214	0.283981
$249$	−0.472136	−0.0299204
$250$	−1.00000	−0.0632456
$251$	−20.6525	−1.30357	−0.651786	−	0.758403i	$-0.725980\pi$
$251$	−20.6525	−1.30357	−0.651786	+	0.758403i	$0.725980\pi$
$252$	−1.00000	−0.0629941
$253$	−3.23607	−0.203450
$254$	−4.76393	−0.298916
$255$	−2.47214	−0.154811
$256$	1.00000	0.0625000
$257$	−24.8328	−1.54903	−0.774514	−	0.632556i	$-0.782006\pi$
$257$	−24.8328	−1.54903	−0.774514	+	0.632556i	$0.782006\pi$
$258$	0.763932	0.0475603
$259$	0.472136	0.0293371
$260$	3.23607	0.200692
$261$	7.70820	0.477126
$262$	8.94427	0.552579
$263$	24.9443	1.53813	0.769065	−	0.639171i	$-0.220722\pi$
$263$	24.9443	1.53813	0.769065	+	0.639171i	$0.220722\pi$
$264$	3.23607	0.199166
$265$	10.0000	0.614295
$266$	−4.47214	−0.274204
$267$	7.23607	0.442840
$268$	−8.76393	−0.535342
$269$	−2.29180	−0.139733	−0.0698666	−	0.997556i	$-0.522257\pi$
$269$	−2.29180	−0.139733	−0.0698666	+	0.997556i	$0.522257\pi$
$270$	−1.00000	−0.0608581
$271$	−25.4164	−1.54394	−0.771968	−	0.635661i	$-0.780728\pi$
$271$	−25.4164	−1.54394	−0.771968	+	0.635661i	$0.780728\pi$
$272$	−2.47214	−0.149895
$273$	−3.23607	−0.195856
$274$	−14.0000	−0.845771
$275$	−3.23607	−0.195142
$276$	1.00000	0.0601929
$277$	24.6525	1.48122	0.740612	−	0.671933i	$-0.234536\pi$
$277$	24.6525	1.48122	0.740612	+	0.671933i	$0.234536\pi$
$278$	−8.00000	−0.479808
$279$	−4.47214	−0.267740
$280$	1.00000	0.0597614
$281$	1.81966	0.108552	0.0542759	−	0.998526i	$-0.482715\pi$
$281$	1.81966	0.108552	0.0542759	+	0.998526i	$0.482715\pi$
$282$	2.00000	0.119098
$283$	−0.291796	−0.0173455	−0.00867274	−	0.999962i	$-0.502761\pi$
$283$	−0.291796	−0.0173455	−0.00867274	+	0.999962i	$0.502761\pi$
$284$	9.70820	0.576076
$285$	−4.47214	−0.264906
$286$	10.4721	0.619230
$287$	−8.47214	−0.500094
$288$	−1.00000	−0.0589256
$289$	−10.8885	−0.640503
$290$	−7.70820	−0.452641
$291$	5.70820	0.334621
$292$	14.9443	0.874547
$293$	−18.9443	−1.10674	−0.553368	−	0.832937i	$-0.686658\pi$
$293$	−18.9443	−1.10674	−0.553368	+	0.832937i	$0.686658\pi$
$294$	−1.00000	−0.0583212
$295$	8.94427	0.520756
$296$	0.472136	0.0274423
$297$	−3.23607	−0.187776
$298$	−7.52786	−0.436077
$299$	3.23607	0.187147
$300$	1.00000	0.0577350
$301$	0.763932	0.0440323
$302$	−5.52786	−0.318093
$303$	4.18034	0.240154
$304$	−4.47214	−0.256495
$305$	−2.00000	−0.114520
$306$	2.47214	0.141323
$307$	17.5279	1.00037	0.500184	−	0.865919i	$-0.333266\pi$
$307$	17.5279	1.00037	0.500184	+	0.865919i	$0.333266\pi$
$308$	3.23607	0.184392
$309$	18.4721	1.05084
$310$	4.47214	0.254000
$311$	−25.2361	−1.43101	−0.715503	−	0.698610i	$-0.753802\pi$
$311$	−25.2361	−1.43101	−0.715503	+	0.698610i	$0.753802\pi$
$312$	−3.23607	−0.183206
$313$	24.1803	1.36675	0.683377	−	0.730066i	$-0.260511\pi$
$313$	24.1803	1.36675	0.683377	+	0.730066i	$0.260511\pi$
$314$	13.4164	0.757132
$315$	−1.00000	−0.0563436
$316$	−4.00000	−0.225018
$317$	9.41641	0.528878	0.264439	−	0.964402i	$-0.414813\pi$
$317$	9.41641	0.528878	0.264439	+	0.964402i	$0.414813\pi$
$318$	−10.0000	−0.560772
$319$	−24.9443	−1.39661
$320$	1.00000	0.0559017
$321$	−7.41641	−0.413944
$322$	1.00000	0.0557278
$323$	11.0557	0.615157
$324$	1.00000	0.0555556
$325$	3.23607	0.179505
$326$	−7.41641	−0.410757
$327$	7.52786	0.416292
$328$	−8.47214	−0.467795
$329$	2.00000	0.110264
$330$	3.23607	0.178140
$331$	−11.0557	−0.607678	−0.303839	−	0.952723i	$-0.598268\pi$
$331$	−11.0557	−0.607678	−0.303839	+	0.952723i	$0.598268\pi$
$332$	−0.472136	−0.0259118
$333$	−0.472136	−0.0258729
$334$	−16.4721	−0.901315
$335$	−8.76393	−0.478825
$336$	−1.00000	−0.0545545
$337$	−25.2361	−1.37470	−0.687348	−	0.726328i	$-0.741225\pi$
$337$	−25.2361	−1.37470	−0.687348	+	0.726328i	$0.741225\pi$
$338$	2.52786	0.137498
$339$	−10.9443	−0.594411
$340$	−2.47214	−0.134070
$341$	14.4721	0.783710
$342$	4.47214	0.241825
$343$	−1.00000	−0.0539949
$344$	0.763932	0.0411885
$345$	1.00000	0.0538382
$346$	−8.00000	−0.430083
$347$	13.8885	0.745576	0.372788	−	0.927917i	$-0.378402\pi$
$347$	13.8885	0.745576	0.372788	+	0.927917i	$0.378402\pi$
$348$	7.70820	0.413203
$349$	22.4721	1.20291	0.601453	−	0.798908i	$-0.294589\pi$
$349$	22.4721	1.20291	0.601453	+	0.798908i	$0.294589\pi$
$350$	1.00000	0.0534522
$351$	3.23607	0.172729
$352$	3.23607	0.172483
$353$	−3.88854	−0.206966	−0.103483	−	0.994631i	$-0.532999\pi$
$353$	−3.88854	−0.206966	−0.103483	+	0.994631i	$0.532999\pi$
$354$	−8.94427	−0.475383
$355$	9.70820	0.515258
$356$	7.23607	0.383511
$357$	2.47214	0.130839
$358$	7.41641	0.391969
$359$	3.05573	0.161275	0.0806376	−	0.996743i	$-0.474304\pi$
$359$	3.05573	0.161275	0.0806376	+	0.996743i	$0.474304\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	−15.8885	−0.835083
$363$	−0.527864	−0.0277057
$364$	−3.23607	−0.169616
$365$	14.9443	0.782219
$366$	2.00000	0.104542
$367$	−31.4164	−1.63992	−0.819962	−	0.572419i	$-0.806005\pi$
$367$	−31.4164	−1.63992	−0.819962	+	0.572419i	$0.806005\pi$
$368$	1.00000	0.0521286
$369$	8.47214	0.441042
$370$	0.472136	0.0245452
$371$	−10.0000	−0.519174
$372$	−4.47214	−0.231869
$373$	−19.5279	−1.01111	−0.505557	−	0.862793i	$-0.668713\pi$
$373$	−19.5279	−1.01111	−0.505557	+	0.862793i	$0.668713\pi$
$374$	−8.00000	−0.413670
$375$	1.00000	0.0516398
$376$	2.00000	0.103142
$377$	24.9443	1.28470
$378$	1.00000	0.0514344
$379$	18.4721	0.948850	0.474425	−	0.880296i	$-0.342656\pi$
$379$	18.4721	0.948850	0.474425	+	0.880296i	$0.342656\pi$
$380$	−4.47214	−0.229416
$381$	4.76393	0.244064
$382$	0	0
$383$	17.8885	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$384$	−1.00000	−0.0510310
$385$	3.23607	0.164925
$386$	13.4164	0.682877
$387$	−0.763932	−0.0388328
$388$	5.70820	0.289790
$389$	0.472136	0.0239382	0.0119691	−	0.999928i	$-0.496190\pi$
$389$	0.472136	0.0239382	0.0119691	+	0.999928i	$0.496190\pi$
$390$	−3.23607	−0.163865
$391$	−2.47214	−0.125021
$392$	−1.00000	−0.0505076
$393$	−8.94427	−0.451179
$394$	−18.9443	−0.954399
$395$	−4.00000	−0.201262
$396$	−3.23607	−0.162619
$397$	6.29180	0.315776	0.157888	−	0.987457i	$-0.449531\pi$
$397$	6.29180	0.315776	0.157888	+	0.987457i	$0.449531\pi$
$398$	14.4721	0.725423
$399$	4.47214	0.223887
$400$	1.00000	0.0500000
$401$	7.12461	0.355786	0.177893	−	0.984050i	$-0.443072\pi$
$401$	7.12461	0.355786	0.177893	+	0.984050i	$0.443072\pi$
$402$	8.76393	0.437105
$403$	−14.4721	−0.720908
$404$	4.18034	0.207980
$405$	1.00000	0.0496904
$406$	7.70820	0.382552
$407$	1.52786	0.0757334
$408$	2.47214	0.122389
$409$	−27.8885	−1.37900	−0.689500	−	0.724286i	$-0.742170\pi$
$409$	−27.8885	−1.37900	−0.689500	+	0.724286i	$0.742170\pi$
$410$	−8.47214	−0.418409
$411$	14.0000	0.690569
$412$	18.4721	0.910057
$413$	−8.94427	−0.440119
$414$	−1.00000	−0.0491473
$415$	−0.472136	−0.0231762
$416$	−3.23607	−0.158661
$417$	8.00000	0.391762
$418$	−14.4721	−0.707855
$419$	−6.18034	−0.301929	−0.150965	−	0.988539i	$-0.548238\pi$
$419$	−6.18034	−0.301929	−0.150965	+	0.988539i	$0.548238\pi$
$420$	−1.00000	−0.0487950
$421$	−15.8885	−0.774360	−0.387180	−	0.922004i	$-0.626551\pi$
$421$	−15.8885	−0.774360	−0.387180	+	0.922004i	$0.626551\pi$
$422$	3.05573	0.148751
$423$	−2.00000	−0.0972433
$424$	−10.0000	−0.485643
$425$	−2.47214	−0.119916
$426$	−9.70820	−0.470364
$427$	2.00000	0.0967868
$428$	−7.41641	−0.358486
$429$	−10.4721	−0.505599
$430$	0.763932	0.0368401
$431$	32.3607	1.55876	0.779380	−	0.626552i	$-0.215534\pi$
$431$	32.3607	1.55876	0.779380	+	0.626552i	$0.215534\pi$
$432$	1.00000	0.0481125
$433$	−1.12461	−0.0540454	−0.0270227	−	0.999635i	$-0.508603\pi$
$433$	−1.12461	−0.0540454	−0.0270227	+	0.999635i	$0.508603\pi$
$434$	−4.47214	−0.214669
$435$	7.70820	0.369580
$436$	7.52786	0.360519
$437$	−4.47214	−0.213931
$438$	−14.9443	−0.714065
$439$	2.94427	0.140522	0.0702612	−	0.997529i	$-0.477617\pi$
$439$	2.94427	0.140522	0.0702612	+	0.997529i	$0.477617\pi$
$440$	3.23607	0.154273
$441$	1.00000	0.0476190
$442$	8.00000	0.380521
$443$	−7.05573	−0.335228	−0.167614	−	0.985853i	$-0.553606\pi$
$443$	−7.05573	−0.335228	−0.167614	+	0.985853i	$0.553606\pi$
$444$	−0.472136	−0.0224066
$445$	7.23607	0.343023
$446$	−2.18034	−0.103242
$447$	7.52786	0.356056
$448$	−1.00000	−0.0472456
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	−1.00000	−0.0471405
$451$	−27.4164	−1.29099
$452$	−10.9443	−0.514775
$453$	5.52786	0.259722
$454$	−14.9443	−0.701369
$455$	−3.23607	−0.151709
$456$	4.47214	0.209427
$457$	7.34752	0.343703	0.171851	−	0.985123i	$-0.445025\pi$
$457$	7.34752	0.343703	0.171851	+	0.985123i	$0.445025\pi$
$458$	14.0000	0.654177
$459$	−2.47214	−0.115389
$460$	1.00000	0.0466252
$461$	−13.7082	−0.638455	−0.319227	−	0.947678i	$-0.603423\pi$
$461$	−13.7082	−0.638455	−0.319227	+	0.947678i	$0.603423\pi$
$462$	−3.23607	−0.150556
$463$	30.0689	1.39742	0.698710	−	0.715405i	$-0.253758\pi$
$463$	30.0689	1.39742	0.698710	+	0.715405i	$0.253758\pi$
$464$	7.70820	0.357844
$465$	−4.47214	−0.207390
$466$	−24.4721	−1.13365
$467$	6.58359	0.304652	0.152326	−	0.988330i	$-0.451324\pi$
$467$	6.58359	0.304652	0.152326	+	0.988330i	$0.451324\pi$
$468$	3.23607	0.149587
$469$	8.76393	0.404681
$470$	2.00000	0.0922531
$471$	−13.4164	−0.618195
$472$	−8.94427	−0.411693
$473$	2.47214	0.113669
$474$	4.00000	0.183726
$475$	−4.47214	−0.205196
$476$	2.47214	0.113310
$477$	10.0000	0.457869
$478$	−4.76393	−0.217897
$479$	39.4164	1.80098	0.900491	−	0.434875i	$-0.143207\pi$
$479$	39.4164	1.80098	0.900491	+	0.434875i	$0.143207\pi$
$480$	−1.00000	−0.0456435
$481$	−1.52786	−0.0696646
$482$	21.8885	0.996996
$483$	−1.00000	−0.0455016
$484$	−0.527864	−0.0239938
$485$	5.70820	0.259196
$486$	−1.00000	−0.0453609
$487$	25.1246	1.13850	0.569252	−	0.822163i	$-0.307233\pi$
$487$	25.1246	1.13850	0.569252	+	0.822163i	$0.307233\pi$
$488$	2.00000	0.0905357
$489$	7.41641	0.335382
$490$	−1.00000	−0.0451754
$491$	−10.4721	−0.472601	−0.236300	−	0.971680i	$-0.575935\pi$
$491$	−10.4721	−0.472601	−0.236300	+	0.971680i	$0.575935\pi$
$492$	8.47214	0.381953
$493$	−19.0557	−0.858227
$494$	14.4721	0.651132
$495$	−3.23607	−0.145450
$496$	−4.47214	−0.200805
$497$	−9.70820	−0.435472
$498$	0.472136	0.0211569
$499$	−17.8885	−0.800801	−0.400401	−	0.916340i	$-0.631129\pi$
$499$	−17.8885	−0.800801	−0.400401	+	0.916340i	$0.631129\pi$
$500$	1.00000	0.0447214
$501$	16.4721	0.735921
$502$	20.6525	0.921765
$503$	25.3050	1.12829	0.564146	−	0.825675i	$-0.309205\pi$
$503$	25.3050	1.12829	0.564146	+	0.825675i	$0.309205\pi$
$504$	1.00000	0.0445435
$505$	4.18034	0.186023
$506$	3.23607	0.143861
$507$	−2.52786	−0.112266
$508$	4.76393	0.211365
$509$	20.1803	0.894478	0.447239	−	0.894415i	$-0.352407\pi$
$509$	20.1803	0.894478	0.447239	+	0.894415i	$0.352407\pi$
$510$	2.47214	0.109468
$511$	−14.9443	−0.661096
$512$	−1.00000	−0.0441942
$513$	−4.47214	−0.197450
$514$	24.8328	1.09533
$515$	18.4721	0.813980
$516$	−0.763932	−0.0336302
$517$	6.47214	0.284644
$518$	−0.472136	−0.0207445
$519$	8.00000	0.351161
$520$	−3.23607	−0.141911
$521$	9.12461	0.399757	0.199878	−	0.979821i	$-0.435945\pi$
$521$	9.12461	0.399757	0.199878	+	0.979821i	$0.435945\pi$
$522$	−7.70820	−0.337379
$523$	−10.1803	−0.445155	−0.222578	−	0.974915i	$-0.571447\pi$
$523$	−10.1803	−0.445155	−0.222578	+	0.974915i	$0.571447\pi$
$524$	−8.94427	−0.390732
$525$	−1.00000	−0.0436436
$526$	−24.9443	−1.08762
$527$	11.0557	0.481595
$528$	−3.23607	−0.140832
$529$	1.00000	0.0434783
$530$	−10.0000	−0.434372
$531$	8.94427	0.388148
$532$	4.47214	0.193892
$533$	27.4164	1.18754
$534$	−7.23607	−0.313135
$535$	−7.41641	−0.320639
$536$	8.76393	0.378544
$537$	−7.41641	−0.320042
$538$	2.29180	0.0988063
$539$	−3.23607	−0.139387
$540$	1.00000	0.0430331
$541$	27.3050	1.17393	0.586966	−	0.809612i	$-0.300322\pi$
$541$	27.3050	1.17393	0.586966	+	0.809612i	$0.300322\pi$
$542$	25.4164	1.09173
$543$	15.8885	0.681843
$544$	2.47214	0.105992
$545$	7.52786	0.322458
$546$	3.23607	0.138491
$547$	−28.3607	−1.21262	−0.606308	−	0.795230i	$-0.707350\pi$
$547$	−28.3607	−1.21262	−0.606308	+	0.795230i	$0.707350\pi$
$548$	14.0000	0.598050
$549$	−2.00000	−0.0853579
$550$	3.23607	0.137986
$551$	−34.4721	−1.46856
$552$	−1.00000	−0.0425628
$553$	4.00000	0.170097
$554$	−24.6525	−1.04738
$555$	−0.472136	−0.0200411
$556$	8.00000	0.339276
$557$	42.3607	1.79488	0.897440	−	0.441137i	$-0.145425\pi$
$557$	42.3607	1.79488	0.897440	+	0.441137i	$0.145425\pi$
$558$	4.47214	0.189321
$559$	−2.47214	−0.104560
$560$	−1.00000	−0.0422577
$561$	8.00000	0.337760
$562$	−1.81966	−0.0767577
$563$	−8.47214	−0.357058	−0.178529	−	0.983935i	$-0.557134\pi$
$563$	−8.47214	−0.357058	−0.178529	+	0.983935i	$0.557134\pi$
$564$	−2.00000	−0.0842152
$565$	−10.9443	−0.460429
$566$	0.291796	0.0122651
$567$	−1.00000	−0.0419961
$568$	−9.70820	−0.407347
$569$	2.18034	0.0914046	0.0457023	−	0.998955i	$-0.485447\pi$
$569$	2.18034	0.0914046	0.0457023	+	0.998955i	$0.485447\pi$
$570$	4.47214	0.187317
$571$	30.4721	1.27522	0.637610	−	0.770360i	$-0.279923\pi$
$571$	30.4721	1.27522	0.637610	+	0.770360i	$0.279923\pi$
$572$	−10.4721	−0.437862
$573$	0	0
$574$	8.47214	0.353620
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−25.4164	−1.05810	−0.529049	−	0.848591i	$-0.677451\pi$
$577$	−25.4164	−1.05810	−0.529049	+	0.848591i	$0.677451\pi$
$578$	10.8885	0.452904
$579$	−13.4164	−0.557567
$580$	7.70820	0.320066
$581$	0.472136	0.0195875
$582$	−5.70820	−0.236613
$583$	−32.3607	−1.34024
$584$	−14.9443	−0.618398
$585$	3.23607	0.133795
$586$	18.9443	0.782581
$587$	44.3607	1.83096	0.915481	−	0.402362i	$-0.131811\pi$
$587$	44.3607	1.83096	0.915481	+	0.402362i	$0.131811\pi$
$588$	1.00000	0.0412393
$589$	20.0000	0.824086
$590$	−8.94427	−0.368230
$591$	18.9443	0.779263
$592$	−0.472136	−0.0194047
$593$	36.8328	1.51254	0.756271	−	0.654258i	$-0.227019\pi$
$593$	36.8328	1.51254	0.756271	+	0.654258i	$0.227019\pi$
$594$	3.23607	0.132777
$595$	2.47214	0.101348
$596$	7.52786	0.308353
$597$	−14.4721	−0.592305
$598$	−3.23607	−0.132333
$599$	−7.59675	−0.310395	−0.155197	−	0.987883i	$-0.549601\pi$
$599$	−7.59675	−0.310395	−0.155197	+	0.987883i	$0.549601\pi$
$600$	−1.00000	−0.0408248
$601$	32.8328	1.33928	0.669639	−	0.742687i	$-0.266449\pi$
$601$	32.8328	1.33928	0.669639	+	0.742687i	$0.266449\pi$
$602$	−0.763932	−0.0311355
$603$	−8.76393	−0.356895
$604$	5.52786	0.224926
$605$	−0.527864	−0.0214607
$606$	−4.18034	−0.169815
$607$	29.0132	1.17761	0.588804	−	0.808276i	$-0.299599\pi$
$607$	29.0132	1.17761	0.588804	+	0.808276i	$0.299599\pi$
$608$	4.47214	0.181369
$609$	−7.70820	−0.312352
$610$	2.00000	0.0809776
$611$	−6.47214	−0.261835
$612$	−2.47214	−0.0999302
$613$	−46.3607	−1.87249	−0.936245	−	0.351348i	$-0.885724\pi$
$613$	−46.3607	−1.87249	−0.936245	+	0.351348i	$0.885724\pi$
$614$	−17.5279	−0.707367
$615$	8.47214	0.341629
$616$	−3.23607	−0.130385
$617$	25.4164	1.02323	0.511613	−	0.859216i	$-0.329048\pi$
$617$	25.4164	1.02323	0.511613	+	0.859216i	$0.329048\pi$
$618$	−18.4721	−0.743058
$619$	22.3607	0.898752	0.449376	−	0.893343i	$-0.351646\pi$
$619$	22.3607	0.898752	0.449376	+	0.893343i	$0.351646\pi$
$620$	−4.47214	−0.179605
$621$	1.00000	0.0401286
$622$	25.2361	1.01187
$623$	−7.23607	−0.289907
$624$	3.23607	0.129546
$625$	1.00000	0.0400000
$626$	−24.1803	−0.966441
$627$	14.4721	0.577961
$628$	−13.4164	−0.535373
$629$	1.16718	0.0465387
$630$	1.00000	0.0398410
$631$	24.9443	0.993016	0.496508	−	0.868032i	$-0.334615\pi$
$631$	24.9443	0.993016	0.496508	+	0.868032i	$0.334615\pi$
$632$	4.00000	0.159111
$633$	−3.05573	−0.121454
$634$	−9.41641	−0.373973
$635$	4.76393	0.189051
$636$	10.0000	0.396526
$637$	3.23607	0.128218
$638$	24.9443	0.987553
$639$	9.70820	0.384051
$640$	−1.00000	−0.0395285
$641$	−16.0689	−0.634683	−0.317341	−	0.948311i	$-0.602790\pi$
$641$	−16.0689	−0.634683	−0.317341	+	0.948311i	$0.602790\pi$
$642$	7.41641	0.292702
$643$	9.81966	0.387250	0.193625	−	0.981076i	$-0.437976\pi$
$643$	9.81966	0.387250	0.193625	+	0.981076i	$0.437976\pi$
$644$	−1.00000	−0.0394055
$645$	−0.763932	−0.0300798
$646$	−11.0557	−0.434982
$647$	2.00000	0.0786281	0.0393141	−	0.999227i	$-0.487483\pi$
$647$	2.00000	0.0786281	0.0393141	+	0.999227i	$0.487483\pi$
$648$	−1.00000	−0.0392837
$649$	−28.9443	−1.13616
$650$	−3.23607	−0.126929
$651$	4.47214	0.175277
$652$	7.41641	0.290449
$653$	−35.3050	−1.38159	−0.690795	−	0.723051i	$-0.742739\pi$
$653$	−35.3050	−1.38159	−0.690795	+	0.723051i	$0.742739\pi$
$654$	−7.52786	−0.294363
$655$	−8.94427	−0.349482
$656$	8.47214	0.330781
$657$	14.9443	0.583032
$658$	−2.00000	−0.0779681
$659$	−41.1246	−1.60199	−0.800994	−	0.598673i	$-0.795695\pi$
$659$	−41.1246	−1.60199	−0.800994	+	0.598673i	$0.795695\pi$
$660$	−3.23607	−0.125964
$661$	−9.05573	−0.352227	−0.176114	−	0.984370i	$-0.556353\pi$
$661$	−9.05573	−0.352227	−0.176114	+	0.984370i	$0.556353\pi$
$662$	11.0557	0.429693
$663$	−8.00000	−0.310694
$664$	0.472136	0.0183224
$665$	4.47214	0.173422
$666$	0.472136	0.0182949
$667$	7.70820	0.298463
$668$	16.4721	0.637326
$669$	2.18034	0.0842968
$670$	8.76393	0.338580
$671$	6.47214	0.249854
$672$	1.00000	0.0385758
$673$	−29.7771	−1.14782	−0.573911	−	0.818918i	$-0.694575\pi$
$673$	−29.7771	−1.14782	−0.573911	+	0.818918i	$0.694575\pi$
$674$	25.2361	0.972057
$675$	1.00000	0.0384900
$676$	−2.52786	−0.0972255
$677$	4.11146	0.158016	0.0790080	−	0.996874i	$-0.474825\pi$
$677$	4.11146	0.158016	0.0790080	+	0.996874i	$0.474825\pi$
$678$	10.9443	0.420312
$679$	−5.70820	−0.219061
$680$	2.47214	0.0948021
$681$	14.9443	0.572666
$682$	−14.4721	−0.554167
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−4.47214	−0.170996
$685$	14.0000	0.534913
$686$	1.00000	0.0381802
$687$	−14.0000	−0.534133
$688$	−0.763932	−0.0291246
$689$	32.3607	1.23284
$690$	−1.00000	−0.0380693
$691$	7.41641	0.282133	0.141067	−	0.990000i	$-0.454947\pi$
$691$	7.41641	0.282133	0.141067	+	0.990000i	$0.454947\pi$
$692$	8.00000	0.304114
$693$	3.23607	0.122928
$694$	−13.8885	−0.527202
$695$	8.00000	0.303457
$696$	−7.70820	−0.292179
$697$	−20.9443	−0.793321
$698$	−22.4721	−0.850583
$699$	24.4721	0.925621
$700$	−1.00000	−0.0377964
$701$	10.9443	0.413359	0.206680	−	0.978409i	$-0.433734\pi$
$701$	10.9443	0.413359	0.206680	+	0.978409i	$0.433734\pi$
$702$	−3.23607	−0.122138
$703$	2.11146	0.0796351
$704$	−3.23607	−0.121964
$705$	−2.00000	−0.0753244
$706$	3.88854	0.146347
$707$	−4.18034	−0.157218
$708$	8.94427	0.336146
$709$	−2.58359	−0.0970288	−0.0485144	−	0.998822i	$-0.515449\pi$
$709$	−2.58359	−0.0970288	−0.0485144	+	0.998822i	$0.515449\pi$
$710$	−9.70820	−0.364342
$711$	−4.00000	−0.150012
$712$	−7.23607	−0.271183
$713$	−4.47214	−0.167483
$714$	−2.47214	−0.0925174
$715$	−10.4721	−0.391636
$716$	−7.41641	−0.277164
$717$	4.76393	0.177912
$718$	−3.05573	−0.114039
$719$	−17.8197	−0.664561	−0.332281	−	0.943181i	$-0.607818\pi$
$719$	−17.8197	−0.664561	−0.332281	+	0.943181i	$0.607818\pi$
$720$	1.00000	0.0372678
$721$	−18.4721	−0.687938
$722$	−1.00000	−0.0372161
$723$	−21.8885	−0.814044
$724$	15.8885	0.590493
$725$	7.70820	0.286276
$726$	0.527864	0.0195909
$727$	26.4721	0.981797	0.490899	−	0.871217i	$-0.336669\pi$
$727$	26.4721	0.981797	0.490899	+	0.871217i	$0.336669\pi$
$728$	3.23607	0.119937
$729$	1.00000	0.0370370
$730$	−14.9443	−0.553112
$731$	1.88854	0.0698503
$732$	−2.00000	−0.0739221
$733$	−5.05573	−0.186738	−0.0933688	−	0.995632i	$-0.529764\pi$
$733$	−5.05573	−0.186738	−0.0933688	+	0.995632i	$0.529764\pi$
$734$	31.4164	1.15960
$735$	1.00000	0.0368856
$736$	−1.00000	−0.0368605
$737$	28.3607	1.04468
$738$	−8.47214	−0.311864
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	−0.472136	−0.0173561
$741$	−14.4721	−0.531647
$742$	10.0000	0.367112
$743$	−50.8328	−1.86488	−0.932438	−	0.361331i	$-0.882322\pi$
$743$	−50.8328	−1.86488	−0.932438	+	0.361331i	$0.882322\pi$
$744$	4.47214	0.163956
$745$	7.52786	0.275800
$746$	19.5279	0.714966
$747$	−0.472136	−0.0172746
$748$	8.00000	0.292509
$749$	7.41641	0.270990
$750$	−1.00000	−0.0365148
$751$	−49.8885	−1.82046	−0.910229	−	0.414104i	$-0.864095\pi$
$751$	−49.8885	−1.82046	−0.910229	+	0.414104i	$0.864095\pi$
$752$	−2.00000	−0.0729325
$753$	−20.6525	−0.752618
$754$	−24.9443	−0.908417
$755$	5.52786	0.201180
$756$	−1.00000	−0.0363696
$757$	−28.4721	−1.03484	−0.517419	−	0.855732i	$-0.673107\pi$
$757$	−28.4721	−1.03484	−0.517419	+	0.855732i	$0.673107\pi$
$758$	−18.4721	−0.670938
$759$	−3.23607	−0.117462
$760$	4.47214	0.162221
$761$	−24.4721	−0.887114	−0.443557	−	0.896246i	$-0.646284\pi$
$761$	−24.4721	−0.887114	−0.443557	+	0.896246i	$0.646284\pi$
$762$	−4.76393	−0.172579
$763$	−7.52786	−0.272527
$764$	0	0
$765$	−2.47214	−0.0893803
$766$	−17.8885	−0.646339
$767$	28.9443	1.04512
$768$	1.00000	0.0360844
$769$	8.58359	0.309532	0.154766	−	0.987951i	$-0.450538\pi$
$769$	8.58359	0.309532	0.154766	+	0.987951i	$0.450538\pi$
$770$	−3.23607	−0.116620
$771$	−24.8328	−0.894332
$772$	−13.4164	−0.482867
$773$	−35.8885	−1.29082	−0.645411	−	0.763836i	$-0.723314\pi$
$773$	−35.8885	−1.29082	−0.645411	+	0.763836i	$0.723314\pi$
$774$	0.763932	0.0274590
$775$	−4.47214	−0.160644
$776$	−5.70820	−0.204913
$777$	0.472136	0.0169378
$778$	−0.472136	−0.0169269
$779$	−37.8885	−1.35750
$780$	3.23607	0.115870
$781$	−31.4164	−1.12417
$782$	2.47214	0.0884034
$783$	7.70820	0.275469
$784$	1.00000	0.0357143
$785$	−13.4164	−0.478852
$786$	8.94427	0.319032
$787$	32.6525	1.16394	0.581968	−	0.813212i	$-0.302283\pi$
$787$	32.6525	1.16394	0.581968	+	0.813212i	$0.302283\pi$
$788$	18.9443	0.674862
$789$	24.9443	0.888040
$790$	4.00000	0.142314
$791$	10.9443	0.389134
$792$	3.23607	0.114989
$793$	−6.47214	−0.229832
$794$	−6.29180	−0.223287
$795$	10.0000	0.354663
$796$	−14.4721	−0.512951
$797$	10.0000	0.354218	0.177109	−	0.984191i	$-0.443325\pi$
$797$	10.0000	0.354218	0.177109	+	0.984191i	$0.443325\pi$
$798$	−4.47214	−0.158312
$799$	4.94427	0.174916
$800$	−1.00000	−0.0353553
$801$	7.23607	0.255674
$802$	−7.12461	−0.251579
$803$	−48.3607	−1.70661
$804$	−8.76393	−0.309080
$805$	−1.00000	−0.0352454
$806$	14.4721	0.509759
$807$	−2.29180	−0.0806750
$808$	−4.18034	−0.147064
$809$	−49.1935	−1.72955	−0.864776	−	0.502159i	$-0.832539\pi$
$809$	−49.1935	−1.72955	−0.864776	+	0.502159i	$0.832539\pi$
$810$	−1.00000	−0.0351364
$811$	1.52786	0.0536506	0.0268253	−	0.999640i	$-0.491460\pi$
$811$	1.52786	0.0536506	0.0268253	+	0.999640i	$0.491460\pi$
$812$	−7.70820	−0.270505
$813$	−25.4164	−0.891392
$814$	−1.52786	−0.0535516
$815$	7.41641	0.259785
$816$	−2.47214	−0.0865421
$817$	3.41641	0.119525
$818$	27.8885	0.975100
$819$	−3.23607	−0.113077
$820$	8.47214	0.295860
$821$	0.291796	0.0101838	0.00509188	−	0.999987i	$-0.498379\pi$
$821$	0.291796	0.0101838	0.00509188	+	0.999987i	$0.498379\pi$
$822$	−14.0000	−0.488306
$823$	−14.2918	−0.498181	−0.249090	−	0.968480i	$-0.580132\pi$
$823$	−14.2918	−0.498181	−0.249090	+	0.968480i	$0.580132\pi$
$824$	−18.4721	−0.643507
$825$	−3.23607	−0.112665
$826$	8.94427	0.311211
$827$	15.4164	0.536081	0.268041	−	0.963408i	$-0.413624\pi$
$827$	15.4164	0.536081	0.268041	+	0.963408i	$0.413624\pi$
$828$	1.00000	0.0347524
$829$	17.3050	0.601026	0.300513	−	0.953778i	$-0.402842\pi$
$829$	17.3050	0.601026	0.300513	+	0.953778i	$0.402842\pi$
$830$	0.472136	0.0163881
$831$	24.6525	0.855185
$832$	3.23607	0.112190
$833$	−2.47214	−0.0856544
$834$	−8.00000	−0.277017
$835$	16.4721	0.570042
$836$	14.4721	0.500529
$837$	−4.47214	−0.154580
$838$	6.18034	0.213496
$839$	−6.11146	−0.210991	−0.105495	−	0.994420i	$-0.533643\pi$
$839$	−6.11146	−0.210991	−0.105495	+	0.994420i	$0.533643\pi$
$840$	1.00000	0.0345033
$841$	30.4164	1.04884
$842$	15.8885	0.547555
$843$	1.81966	0.0626724
$844$	−3.05573	−0.105182
$845$	−2.52786	−0.0869612
$846$	2.00000	0.0687614
$847$	0.527864	0.0181376
$848$	10.0000	0.343401
$849$	−0.291796	−0.0100144
$850$	2.47214	0.0847936
$851$	−0.472136	−0.0161846
$852$	9.70820	0.332598
$853$	−6.65248	−0.227776	−0.113888	−	0.993494i	$-0.536331\pi$
$853$	−6.65248	−0.227776	−0.113888	+	0.993494i	$0.536331\pi$
$854$	−2.00000	−0.0684386
$855$	−4.47214	−0.152944
$856$	7.41641	0.253488
$857$	−37.7771	−1.29044	−0.645220	−	0.763997i	$-0.723234\pi$
$857$	−37.7771	−1.29044	−0.645220	+	0.763997i	$0.723234\pi$
$858$	10.4721	0.357513
$859$	−16.5836	−0.565825	−0.282912	−	0.959146i	$-0.591301\pi$
$859$	−16.5836	−0.565825	−0.282912	+	0.959146i	$0.591301\pi$
$860$	−0.763932	−0.0260499
$861$	−8.47214	−0.288730
$862$	−32.3607	−1.10221
$863$	−44.3607	−1.51006	−0.755028	−	0.655693i	$-0.772377\pi$
$863$	−44.3607	−1.51006	−0.755028	+	0.655693i	$0.772377\pi$
$864$	−1.00000	−0.0340207
$865$	8.00000	0.272008
$866$	1.12461	0.0382159
$867$	−10.8885	−0.369794
$868$	4.47214	0.151794
$869$	12.9443	0.439104
$870$	−7.70820	−0.261333
$871$	−28.3607	−0.960965
$872$	−7.52786	−0.254926
$873$	5.70820	0.193193
$874$	4.47214	0.151272
$875$	−1.00000	−0.0338062
$876$	14.9443	0.504920
$877$	−26.1803	−0.884047	−0.442024	−	0.897003i	$-0.645739\pi$
$877$	−26.1803	−0.884047	−0.442024	+	0.897003i	$0.645739\pi$
$878$	−2.94427	−0.0993644
$879$	−18.9443	−0.638974
$880$	−3.23607	−0.109088
$881$	−11.5967	−0.390704	−0.195352	−	0.980733i	$-0.562585\pi$
$881$	−11.5967	−0.390704	−0.195352	+	0.980733i	$0.562585\pi$
$882$	−1.00000	−0.0336718
$883$	13.5279	0.455249	0.227624	−	0.973749i	$-0.426904\pi$
$883$	13.5279	0.455249	0.227624	+	0.973749i	$0.426904\pi$
$884$	−8.00000	−0.269069
$885$	8.94427	0.300658
$886$	7.05573	0.237042
$887$	43.8885	1.47363	0.736817	−	0.676093i	$-0.236328\pi$
$887$	43.8885	1.47363	0.736817	+	0.676093i	$0.236328\pi$
$888$	0.472136	0.0158438
$889$	−4.76393	−0.159777
$890$	−7.23607	−0.242554
$891$	−3.23607	−0.108412
$892$	2.18034	0.0730032
$893$	8.94427	0.299309
$894$	−7.52786	−0.251769
$895$	−7.41641	−0.247903
$896$	1.00000	0.0334077
$897$	3.23607	0.108049
$898$	2.00000	0.0667409
$899$	−34.4721	−1.14971
$900$	1.00000	0.0333333
$901$	−24.7214	−0.823588
$902$	27.4164	0.912867
$903$	0.763932	0.0254221
$904$	10.9443	0.364001
$905$	15.8885	0.528153
$906$	−5.52786	−0.183651
$907$	−27.5967	−0.916335	−0.458167	−	0.888866i	$-0.651494\pi$
$907$	−27.5967	−0.916335	−0.458167	+	0.888866i	$0.651494\pi$
$908$	14.9443	0.495943
$909$	4.18034	0.138653
$910$	3.23607	0.107275
$911$	−7.63932	−0.253102	−0.126551	−	0.991960i	$-0.540391\pi$
$911$	−7.63932	−0.253102	−0.126551	+	0.991960i	$0.540391\pi$
$912$	−4.47214	−0.148087
$913$	1.52786	0.0505649
$914$	−7.34752	−0.243034
$915$	−2.00000	−0.0661180
$916$	−14.0000	−0.462573
$917$	8.94427	0.295366
$918$	2.47214	0.0815926
$919$	19.7771	0.652386	0.326193	−	0.945303i	$-0.394234\pi$
$919$	19.7771	0.652386	0.326193	+	0.945303i	$0.394234\pi$
$920$	−1.00000	−0.0329690
$921$	17.5279	0.577563
$922$	13.7082	0.451456
$923$	31.4164	1.03408
$924$	3.23607	0.106459
$925$	−0.472136	−0.0155237
$926$	−30.0689	−0.988125
$927$	18.4721	0.606705
$928$	−7.70820	−0.253034
$929$	−38.7214	−1.27041	−0.635203	−	0.772345i	$-0.719084\pi$
$929$	−38.7214	−1.27041	−0.635203	+	0.772345i	$0.719084\pi$
$930$	4.47214	0.146647
$931$	−4.47214	−0.146568
$932$	24.4721	0.801611
$933$	−25.2361	−0.826192
$934$	−6.58359	−0.215422
$935$	8.00000	0.261628
$936$	−3.23607	−0.105774
$937$	56.5410	1.84711	0.923557	−	0.383460i	$-0.125268\pi$
$937$	56.5410	1.84711	0.923557	+	0.383460i	$0.125268\pi$
$938$	−8.76393	−0.286153
$939$	24.1803	0.789096
$940$	−2.00000	−0.0652328
$941$	−0.111456	−0.00363337	−0.00181668	−	0.999998i	$-0.500578\pi$
$941$	−0.111456	−0.00363337	−0.00181668	+	0.999998i	$0.500578\pi$
$942$	13.4164	0.437130
$943$	8.47214	0.275891
$944$	8.94427	0.291111
$945$	−1.00000	−0.0325300
$946$	−2.47214	−0.0803761
$947$	44.9443	1.46049	0.730246	−	0.683184i	$-0.239405\pi$
$947$	44.9443	1.46049	0.730246	+	0.683184i	$0.239405\pi$
$948$	−4.00000	−0.129914
$949$	48.3607	1.56985
$950$	4.47214	0.145095
$951$	9.41641	0.305348
$952$	−2.47214	−0.0801224
$953$	0.832816	0.0269775	0.0134888	−	0.999909i	$-0.495706\pi$
$953$	0.832816	0.0269775	0.0134888	+	0.999909i	$0.495706\pi$
$954$	−10.0000	−0.323762
$955$	0	0
$956$	4.76393	0.154077
$957$	−24.9443	−0.806334
$958$	−39.4164	−1.27349
$959$	−14.0000	−0.452084
$960$	1.00000	0.0322749
$961$	−11.0000	−0.354839
$962$	1.52786	0.0492603
$963$	−7.41641	−0.238990
$964$	−21.8885	−0.704983
$965$	−13.4164	−0.431889
$966$	1.00000	0.0321745
$967$	57.1246	1.83700	0.918502	−	0.395417i	$-0.129400\pi$
$967$	57.1246	1.83700	0.918502	+	0.395417i	$0.129400\pi$
$968$	0.527864	0.0169662
$969$	11.0557	0.355161
$970$	−5.70820	−0.183279
$971$	21.2361	0.681498	0.340749	−	0.940154i	$-0.389319\pi$
$971$	21.2361	0.681498	0.340749	+	0.940154i	$0.389319\pi$
$972$	1.00000	0.0320750
$973$	−8.00000	−0.256468
$974$	−25.1246	−0.805044
$975$	3.23607	0.103637
$976$	−2.00000	−0.0640184
$977$	9.41641	0.301258	0.150629	−	0.988590i	$-0.451870\pi$
$977$	9.41641	0.301258	0.150629	+	0.988590i	$0.451870\pi$
$978$	−7.41641	−0.237151
$979$	−23.4164	−0.748392
$980$	1.00000	0.0319438
$981$	7.52786	0.240346
$982$	10.4721	0.334179
$983$	−28.9443	−0.923179	−0.461589	−	0.887094i	$-0.652721\pi$
$983$	−28.9443	−0.923179	−0.461589	+	0.887094i	$0.652721\pi$
$984$	−8.47214	−0.270082
$985$	18.9443	0.603615
$986$	19.0557	0.606858
$987$	2.00000	0.0636607
$988$	−14.4721	−0.460420
$989$	−0.763932	−0.0242916
$990$	3.23607	0.102849
$991$	22.2492	0.706770	0.353385	−	0.935478i	$-0.385031\pi$
$991$	22.2492	0.706770	0.353385	+	0.935478i	$0.385031\pi$
$992$	4.47214	0.141990
$993$	−11.0557	−0.350843
$994$	9.70820	0.307926
$995$	−14.4721	−0.458798
$996$	−0.472136	−0.0149602
$997$	−10.8754	−0.344427	−0.172214	−	0.985060i	$-0.555092\pi$
$997$	−10.8754	−0.344427	−0.172214	+	0.985060i	$0.555092\pi$
$998$	17.8885	0.566252
$999$	−0.472136	−0.0149377

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.23607 q^{11} +1.00000 q^{12} +3.23607 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} -1.00000 q^{18} -4.47214 q^{19} +1.00000 q^{20} -1.00000 q^{21} +3.23607 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23607 q^{26} +1.00000 q^{27} -1.00000 q^{28} +7.70820 q^{29} -1.00000 q^{30} -4.47214 q^{31} -1.00000 q^{32} -3.23607 q^{33} +2.47214 q^{34} -1.00000 q^{35} +1.00000 q^{36} -0.472136 q^{37} +4.47214 q^{38} +3.23607 q^{39} -1.00000 q^{40} +8.47214 q^{41} +1.00000 q^{42} -0.763932 q^{43} -3.23607 q^{44} +1.00000 q^{45} -1.00000 q^{46} -2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.47214 q^{51} +3.23607 q^{52} +10.0000 q^{53} -1.00000 q^{54} -3.23607 q^{55} +1.00000 q^{56} -4.47214 q^{57} -7.70820 q^{58} +8.94427 q^{59} +1.00000 q^{60} -2.00000 q^{61} +4.47214 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.23607 q^{65} +3.23607 q^{66} -8.76393 q^{67} -2.47214 q^{68} +1.00000 q^{69} +1.00000 q^{70} +9.70820 q^{71} -1.00000 q^{72} +14.9443 q^{73} +0.472136 q^{74} +1.00000 q^{75} -4.47214 q^{76} +3.23607 q^{77} -3.23607 q^{78} -4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.47214 q^{82} -0.472136 q^{83} -1.00000 q^{84} -2.47214 q^{85} +0.763932 q^{86} +7.70820 q^{87} +3.23607 q^{88} +7.23607 q^{89} -1.00000 q^{90} -3.23607 q^{91} +1.00000 q^{92} -4.47214 q^{93} +2.00000 q^{94} -4.47214 q^{95} -1.00000 q^{96} +5.70820 q^{97} -1.00000 q^{98} -3.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} - 2 q^{32} - 2 q^{33} - 4 q^{34} - 2 q^{35} + 2 q^{36} + 8 q^{37} + 2 q^{39} - 2 q^{40} + 8 q^{41} + 2 q^{42} - 6 q^{43} - 2 q^{44} + 2 q^{45} - 2 q^{46} - 4 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 4 q^{51} + 2 q^{52} + 20 q^{53} - 2 q^{54} - 2 q^{55} + 2 q^{56} - 2 q^{58} + 2 q^{60} - 4 q^{61} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 2 q^{66} - 22 q^{67} + 4 q^{68} + 2 q^{69} + 2 q^{70} + 6 q^{71} - 2 q^{72} + 12 q^{73} - 8 q^{74} + 2 q^{75} + 2 q^{77} - 2 q^{78} - 8 q^{79} + 2 q^{80} + 2 q^{81} - 8 q^{82} + 8 q^{83} - 2 q^{84} + 4 q^{85} + 6 q^{86} + 2 q^{87} + 2 q^{88} + 10 q^{89} - 2 q^{90} - 2 q^{91} + 2 q^{92} + 4 q^{94} - 2 q^{96} - 2 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 2 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 - 2 * q^32 - 2 * q^33 - 4 * q^34 - 2 * q^35 + 2 * q^36 + 8 * q^37 + 2 * q^39 - 2 * q^40 + 8 * q^41 + 2 * q^42 - 6 * q^43 - 2 * 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^52 + 20 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 - 2 * q^58 + 2 * q^60 - 4 * q^61 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 2 * q^66 - 22 * q^67 + 4 * q^68 + 2 * q^69 + 2 * q^70 + 6 * q^71 - 2 * q^72 + 12 * q^73 - 8 * q^74 + 2 * q^75 + 2 * q^77 - 2 * q^78 - 8 * q^79 + 2 * q^80 + 2 * q^81 - 8 * q^82 + 8 * q^83 - 2 * q^84 + 4 * q^85 + 6 * q^86 + 2 * q^87 + 2 * q^88 + 10 * q^89 - 2 * q^90 - 2 * q^91 + 2 * q^92 + 4 * q^94 - 2 * q^96 - 2 * q^97 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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