LMFDB - Embedded newform 8018.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -2.23607 q^{5} +0.618034 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -2.23607 q^{5} +0.618034 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +2.23607 q^{10} -1.61803 q^{11} -0.618034 q^{12} -3.00000 q^{13} -2.00000 q^{14} +1.38197 q^{15} +1.00000 q^{16} -3.00000 q^{17} +2.61803 q^{18} -1.00000 q^{19} -2.23607 q^{20} -1.23607 q^{21} +1.61803 q^{22} +3.00000 q^{23} +0.618034 q^{24} +3.00000 q^{26} +3.47214 q^{27} +2.00000 q^{28} -0.145898 q^{29} -1.38197 q^{30} +0.381966 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.00000 q^{34} -4.47214 q^{35} -2.61803 q^{36} +5.70820 q^{37} +1.00000 q^{38} +1.85410 q^{39} +2.23607 q^{40} +8.70820 q^{41} +1.23607 q^{42} +6.32624 q^{43} -1.61803 q^{44} +5.85410 q^{45} -3.00000 q^{46} +13.1803 q^{47} -0.618034 q^{48} -3.00000 q^{49} +1.85410 q^{51} -3.00000 q^{52} +8.94427 q^{53} -3.47214 q^{54} +3.61803 q^{55} -2.00000 q^{56} +0.618034 q^{57} +0.145898 q^{58} +5.38197 q^{59} +1.38197 q^{60} -7.76393 q^{61} -0.381966 q^{62} -5.23607 q^{63} +1.00000 q^{64} +6.70820 q^{65} -1.00000 q^{66} -1.47214 q^{67} -3.00000 q^{68} -1.85410 q^{69} +4.47214 q^{70} +1.85410 q^{71} +2.61803 q^{72} -2.70820 q^{73} -5.70820 q^{74} -1.00000 q^{76} -3.23607 q^{77} -1.85410 q^{78} -13.7082 q^{79} -2.23607 q^{80} +5.70820 q^{81} -8.70820 q^{82} -1.85410 q^{83} -1.23607 q^{84} +6.70820 q^{85} -6.32624 q^{86} +0.0901699 q^{87} +1.61803 q^{88} -3.94427 q^{89} -5.85410 q^{90} -6.00000 q^{91} +3.00000 q^{92} -0.236068 q^{93} -13.1803 q^{94} +2.23607 q^{95} +0.618034 q^{96} -4.23607 q^{97} +3.00000 q^{98} +4.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 4 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 4 * q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 4 q^{7} - 2 q^{8} - 3 q^{9} - q^{11} + q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{15} + 2 q^{16} - 6 q^{17} + 3 q^{18} - 2 q^{19} + 2 q^{21} + q^{22} + 6 q^{23} - q^{24} + 6 q^{26} - 2 q^{27} + 4 q^{28} - 7 q^{29} - 5 q^{30} + 3 q^{31} - 2 q^{32} + 2 q^{33} + 6 q^{34} - 3 q^{36} - 2 q^{37} + 2 q^{38} - 3 q^{39} + 4 q^{41} - 2 q^{42} - 3 q^{43} - q^{44} + 5 q^{45} - 6 q^{46} + 4 q^{47} + q^{48} - 6 q^{49} - 3 q^{51} - 6 q^{52} + 2 q^{54} + 5 q^{55} - 4 q^{56} - q^{57} + 7 q^{58} + 13 q^{59} + 5 q^{60} - 20 q^{61} - 3 q^{62} - 6 q^{63} + 2 q^{64} - 2 q^{66} + 6 q^{67} - 6 q^{68} + 3 q^{69} - 3 q^{71} + 3 q^{72} + 8 q^{73} + 2 q^{74} - 2 q^{76} - 2 q^{77} + 3 q^{78} - 14 q^{79} - 2 q^{81} - 4 q^{82} + 3 q^{83} + 2 q^{84} + 3 q^{86} - 11 q^{87} + q^{88} + 10 q^{89} - 5 q^{90} - 12 q^{91} + 6 q^{92} + 4 q^{93} - 4 q^{94} - q^{96} - 4 q^{97} + 6 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 4 * q^7 - 2 * q^8 - 3 * q^9 - q^11 + q^12 - 6 * q^13 - 4 * q^14 + 5 * q^15 + 2 * q^16 - 6 * q^17 + 3 * q^18 - 2 * q^19 + 2 * q^21 + q^22 + 6 * q^23 - q^24 + 6 * q^26 - 2 * q^27 + 4 * q^28 - 7 * q^29 - 5 * q^30 + 3 * q^31 - 2 * q^32 + 2 * q^33 + 6 * q^34 - 3 * q^36 - 2 * q^37 + 2 * q^38 - 3 * q^39 + 4 * q^41 - 2 * q^42 - 3 * q^43 - q^44 + 5 * q^45 - 6 * q^46 + 4 * q^47 + q^48 - 6 * q^49 - 3 * q^51 - 6 * q^52 + 2 * q^54 + 5 * q^55 - 4 * q^56 - q^57 + 7 * q^58 + 13 * q^59 + 5 * q^60 - 20 * q^61 - 3 * q^62 - 6 * q^63 + 2 * q^64 - 2 * q^66 + 6 * q^67 - 6 * q^68 + 3 * q^69 - 3 * q^71 + 3 * q^72 + 8 * q^73 + 2 * q^74 - 2 * q^76 - 2 * q^77 + 3 * q^78 - 14 * q^79 - 2 * q^81 - 4 * q^82 + 3 * q^83 + 2 * q^84 + 3 * q^86 - 11 * q^87 + q^88 + 10 * q^89 - 5 * q^90 - 12 * q^91 + 6 * q^92 + 4 * q^93 - 4 * q^94 - q^96 - 4 * q^97 + 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	−2.23607	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	0.618034	0.252311
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	−2.61803	−0.872678
$10$	2.23607	0.707107
$11$	−1.61803	−0.487856	−0.243928	−	0.969793i	$-0.578436\pi$
$11$	−1.61803	−0.487856	−0.243928	+	0.969793i	$0.578436\pi$
$12$	−0.618034	−0.178411
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−2.00000	−0.534522
$15$	1.38197	0.356822
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	2.61803	0.617077
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.23607	−0.500000
$21$	−1.23607	−0.269732
$22$	1.61803	0.344966
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0.618034	0.126156
$25$	0	0
$26$	3.00000	0.588348
$27$	3.47214	0.668213
$28$	2.00000	0.377964
$29$	−0.145898	−0.0270926	−0.0135463	−	0.999908i	$-0.504312\pi$
$29$	−0.145898	−0.0270926	−0.0135463	+	0.999908i	$0.504312\pi$
$30$	−1.38197	−0.252311
$31$	0.381966	0.0686031	0.0343016	−	0.999412i	$-0.489079\pi$
$31$	0.381966	0.0686031	0.0343016	+	0.999412i	$0.489079\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	3.00000	0.514496
$35$	−4.47214	−0.755929
$36$	−2.61803	−0.436339
$37$	5.70820	0.938423	0.469211	−	0.883086i	$-0.344538\pi$
$37$	5.70820	0.938423	0.469211	+	0.883086i	$0.344538\pi$
$38$	1.00000	0.162221
$39$	1.85410	0.296894
$40$	2.23607	0.353553
$41$	8.70820	1.35999	0.679996	−	0.733215i	$-0.261981\pi$
$41$	8.70820	1.35999	0.679996	+	0.733215i	$0.261981\pi$
$42$	1.23607	0.190729
$43$	6.32624	0.964742	0.482371	−	0.875967i	$-0.339776\pi$
$43$	6.32624	0.964742	0.482371	+	0.875967i	$0.339776\pi$
$44$	−1.61803	−0.243928
$45$	5.85410	0.872678
$46$	−3.00000	−0.442326
$47$	13.1803	1.92255	0.961275	−	0.275591i	$-0.0888734\pi$
$47$	13.1803	1.92255	0.961275	+	0.275591i	$0.0888734\pi$
$48$	−0.618034	−0.0892055
$49$	−3.00000	−0.428571
$50$	0	0
$51$	1.85410	0.259626
$52$	−3.00000	−0.416025
$53$	8.94427	1.22859	0.614295	−	0.789076i	$-0.289440\pi$
$53$	8.94427	1.22859	0.614295	+	0.789076i	$0.289440\pi$
$54$	−3.47214	−0.472498
$55$	3.61803	0.487856
$56$	−2.00000	−0.267261
$57$	0.618034	0.0818606
$58$	0.145898	0.0191574
$59$	5.38197	0.700672	0.350336	−	0.936624i	$-0.386067\pi$
$59$	5.38197	0.700672	0.350336	+	0.936624i	$0.386067\pi$
$60$	1.38197	0.178411
$61$	−7.76393	−0.994070	−0.497035	−	0.867731i	$-0.665578\pi$
$61$	−7.76393	−0.994070	−0.497035	+	0.867731i	$0.665578\pi$
$62$	−0.381966	−0.0485097
$63$	−5.23607	−0.659683
$64$	1.00000	0.125000
$65$	6.70820	0.832050
$66$	−1.00000	−0.123091
$67$	−1.47214	−0.179850	−0.0899250	−	0.995949i	$-0.528663\pi$
$67$	−1.47214	−0.179850	−0.0899250	+	0.995949i	$0.528663\pi$
$68$	−3.00000	−0.363803
$69$	−1.85410	−0.223208
$70$	4.47214	0.534522
$71$	1.85410	0.220041	0.110021	−	0.993929i	$-0.464908\pi$
$71$	1.85410	0.220041	0.110021	+	0.993929i	$0.464908\pi$
$72$	2.61803	0.308538
$73$	−2.70820	−0.316971	−0.158486	−	0.987361i	$-0.550661\pi$
$73$	−2.70820	−0.316971	−0.158486	+	0.987361i	$0.550661\pi$
$74$	−5.70820	−0.663565
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−3.23607	−0.368784
$78$	−1.85410	−0.209936
$79$	−13.7082	−1.54229	−0.771147	−	0.636657i	$-0.780317\pi$
$79$	−13.7082	−1.54229	−0.771147	+	0.636657i	$0.780317\pi$
$80$	−2.23607	−0.250000
$81$	5.70820	0.634245
$82$	−8.70820	−0.961660
$83$	−1.85410	−0.203514	−0.101757	−	0.994809i	$-0.532446\pi$
$83$	−1.85410	−0.203514	−0.101757	+	0.994809i	$0.532446\pi$
$84$	−1.23607	−0.134866
$85$	6.70820	0.727607
$86$	−6.32624	−0.682176
$87$	0.0901699	0.00966723
$88$	1.61803	0.172483
$89$	−3.94427	−0.418092	−0.209046	−	0.977906i	$-0.567036\pi$
$89$	−3.94427	−0.418092	−0.209046	+	0.977906i	$0.567036\pi$
$90$	−5.85410	−0.617077
$91$	−6.00000	−0.628971
$92$	3.00000	0.312772
$93$	−0.236068	−0.0244791
$94$	−13.1803	−1.35945
$95$	2.23607	0.229416
$96$	0.618034	0.0630778
$97$	−4.23607	−0.430108	−0.215054	−	0.976602i	$-0.568993\pi$
$97$	−4.23607	−0.430108	−0.215054	+	0.976602i	$0.568993\pi$
$98$	3.00000	0.303046
$99$	4.23607	0.425741
$100$	0	0
$101$	1.00000	0.0995037	0.0497519	−	0.998762i	$-0.484157\pi$
$101$	1.00000	0.0995037	0.0497519	+	0.998762i	$0.484157\pi$
$102$	−1.85410	−0.183583
$103$	10.0902	0.994214	0.497107	−	0.867689i	$-0.334396\pi$
$103$	10.0902	0.994214	0.497107	+	0.867689i	$0.334396\pi$
$104$	3.00000	0.294174
$105$	2.76393	0.269732
$106$	−8.94427	−0.868744
$107$	5.09017	0.492085	0.246043	−	0.969259i	$-0.420870\pi$
$107$	5.09017	0.492085	0.246043	+	0.969259i	$0.420870\pi$
$108$	3.47214	0.334106
$109$	1.23607	0.118394	0.0591969	−	0.998246i	$-0.481146\pi$
$109$	1.23607	0.118394	0.0591969	+	0.998246i	$0.481146\pi$
$110$	−3.61803	−0.344966
$111$	−3.52786	−0.334850
$112$	2.00000	0.188982
$113$	−10.5279	−0.990378	−0.495189	−	0.868785i	$-0.664901\pi$
$113$	−10.5279	−0.990378	−0.495189	+	0.868785i	$0.664901\pi$
$114$	−0.618034	−0.0578842
$115$	−6.70820	−0.625543
$116$	−0.145898	−0.0135463
$117$	7.85410	0.726112
$118$	−5.38197	−0.495450
$119$	−6.00000	−0.550019
$120$	−1.38197	−0.126156
$121$	−8.38197	−0.761997
$122$	7.76393	0.702913
$123$	−5.38197	−0.485276
$124$	0.381966	0.0343016
$125$	11.1803	1.00000
$126$	5.23607	0.466466
$127$	2.67376	0.237258	0.118629	−	0.992939i	$-0.462150\pi$
$127$	2.67376	0.237258	0.118629	+	0.992939i	$0.462150\pi$
$128$	−1.00000	−0.0883883
$129$	−3.90983	−0.344241
$130$	−6.70820	−0.588348
$131$	17.6180	1.53929	0.769647	−	0.638469i	$-0.220432\pi$
$131$	17.6180	1.53929	0.769647	+	0.638469i	$0.220432\pi$
$132$	1.00000	0.0870388
$133$	−2.00000	−0.173422
$134$	1.47214	0.127173
$135$	−7.76393	−0.668213
$136$	3.00000	0.257248
$137$	−20.4164	−1.74429	−0.872146	−	0.489246i	$-0.837272\pi$
$137$	−20.4164	−1.74429	−0.872146	+	0.489246i	$0.837272\pi$
$138$	1.85410	0.157832
$139$	−17.8885	−1.51729	−0.758643	−	0.651506i	$-0.774137\pi$
$139$	−17.8885	−1.51729	−0.758643	+	0.651506i	$0.774137\pi$
$140$	−4.47214	−0.377964
$141$	−8.14590	−0.686008
$142$	−1.85410	−0.155593
$143$	4.85410	0.405920
$144$	−2.61803	−0.218169
$145$	0.326238	0.0270926
$146$	2.70820	0.224133
$147$	1.85410	0.152924
$148$	5.70820	0.469211
$149$	−11.1459	−0.913108	−0.456554	−	0.889696i	$-0.650916\pi$
$149$	−11.1459	−0.913108	−0.456554	+	0.889696i	$0.650916\pi$
$150$	0	0
$151$	2.85410	0.232264	0.116132	−	0.993234i	$-0.462951\pi$
$151$	2.85410	0.232264	0.116132	+	0.993234i	$0.462951\pi$
$152$	1.00000	0.0811107
$153$	7.85410	0.634967
$154$	3.23607	0.260770
$155$	−0.854102	−0.0686031
$156$	1.85410	0.148447
$157$	−18.2361	−1.45540	−0.727698	−	0.685897i	$-0.759410\pi$
$157$	−18.2361	−1.45540	−0.727698	+	0.685897i	$0.759410\pi$
$158$	13.7082	1.09057
$159$	−5.52786	−0.438388
$160$	2.23607	0.176777
$161$	6.00000	0.472866
$162$	−5.70820	−0.448479
$163$	24.8885	1.94942	0.974711	−	0.223471i	$-0.0717388\pi$
$163$	24.8885	1.94942	0.974711	+	0.223471i	$0.0717388\pi$
$164$	8.70820	0.679996
$165$	−2.23607	−0.174078
$166$	1.85410	0.143906
$167$	13.7082	1.06077	0.530386	−	0.847756i	$-0.322047\pi$
$167$	13.7082	1.06077	0.530386	+	0.847756i	$0.322047\pi$
$168$	1.23607	0.0953647
$169$	−4.00000	−0.307692
$170$	−6.70820	−0.514496
$171$	2.61803	0.200206
$172$	6.32624	0.482371
$173$	−0.381966	−0.0290403	−0.0145202	−	0.999895i	$-0.504622\pi$
$173$	−0.381966	−0.0290403	−0.0145202	+	0.999895i	$0.504622\pi$
$174$	−0.0901699	−0.00683577
$175$	0	0
$176$	−1.61803	−0.121964
$177$	−3.32624	−0.250015
$178$	3.94427	0.295636
$179$	10.7639	0.804534	0.402267	−	0.915522i	$-0.368222\pi$
$179$	10.7639	0.804534	0.402267	+	0.915522i	$0.368222\pi$
$180$	5.85410	0.436339
$181$	−8.41641	−0.625587	−0.312793	−	0.949821i	$-0.601265\pi$
$181$	−8.41641	−0.625587	−0.312793	+	0.949821i	$0.601265\pi$
$182$	6.00000	0.444750
$183$	4.79837	0.354706
$184$	−3.00000	−0.221163
$185$	−12.7639	−0.938423
$186$	0.236068	0.0173093
$187$	4.85410	0.354967
$188$	13.1803	0.961275
$189$	6.94427	0.505121
$190$	−2.23607	−0.162221
$191$	13.9443	1.00897	0.504486	−	0.863420i	$-0.331682\pi$
$191$	13.9443	1.00897	0.504486	+	0.863420i	$0.331682\pi$
$192$	−0.618034	−0.0446028
$193$	−10.4721	−0.753801	−0.376900	−	0.926254i	$-0.623010\pi$
$193$	−10.4721	−0.753801	−0.376900	+	0.926254i	$0.623010\pi$
$194$	4.23607	0.304132
$195$	−4.14590	−0.296894
$196$	−3.00000	−0.214286
$197$	−11.8885	−0.847024	−0.423512	−	0.905891i	$-0.639203\pi$
$197$	−11.8885	−0.847024	−0.423512	+	0.905891i	$0.639203\pi$
$198$	−4.23607	−0.301044
$199$	−0.416408	−0.0295184	−0.0147592	−	0.999891i	$-0.504698\pi$
$199$	−0.416408	−0.0295184	−0.0147592	+	0.999891i	$0.504698\pi$
$200$	0	0
$201$	0.909830	0.0641745
$202$	−1.00000	−0.0703598
$203$	−0.291796	−0.0204801
$204$	1.85410	0.129813
$205$	−19.4721	−1.35999
$206$	−10.0902	−0.703015
$207$	−7.85410	−0.545898
$208$	−3.00000	−0.208013
$209$	1.61803	0.111922
$210$	−2.76393	−0.190729
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	8.94427	0.614295
$213$	−1.14590	−0.0785156
$214$	−5.09017	−0.347957
$215$	−14.1459	−0.964742
$216$	−3.47214	−0.236249
$217$	0.763932	0.0518591
$218$	−1.23607	−0.0837171
$219$	1.67376	0.113102
$220$	3.61803	0.243928
$221$	9.00000	0.605406
$222$	3.52786	0.236775
$223$	−15.7639	−1.05563	−0.527815	−	0.849359i	$-0.676989\pi$
$223$	−15.7639	−1.05563	−0.527815	+	0.849359i	$0.676989\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	10.5279	0.700303
$227$	−5.76393	−0.382566	−0.191283	−	0.981535i	$-0.561265\pi$
$227$	−5.76393	−0.382566	−0.191283	+	0.981535i	$0.561265\pi$
$228$	0.618034	0.0409303
$229$	−7.67376	−0.507096	−0.253548	−	0.967323i	$-0.581598\pi$
$229$	−7.67376	−0.507096	−0.253548	+	0.967323i	$0.581598\pi$
$230$	6.70820	0.442326
$231$	2.00000	0.131590
$232$	0.145898	0.00957868
$233$	−6.41641	−0.420353	−0.210176	−	0.977663i	$-0.567404\pi$
$233$	−6.41641	−0.420353	−0.210176	+	0.977663i	$0.567404\pi$
$234$	−7.85410	−0.513439
$235$	−29.4721	−1.92255
$236$	5.38197	0.350336
$237$	8.47214	0.550324
$238$	6.00000	0.388922
$239$	18.7639	1.21374	0.606869	−	0.794802i	$-0.292425\pi$
$239$	18.7639	1.21374	0.606869	+	0.794802i	$0.292425\pi$
$240$	1.38197	0.0892055
$241$	−22.2705	−1.43457	−0.717285	−	0.696780i	$-0.754615\pi$
$241$	−22.2705	−1.43457	−0.717285	+	0.696780i	$0.754615\pi$
$242$	8.38197	0.538813
$243$	−13.9443	−0.894525
$244$	−7.76393	−0.497035
$245$	6.70820	0.428571
$246$	5.38197	0.343142
$247$	3.00000	0.190885
$248$	−0.381966	−0.0242549
$249$	1.14590	0.0726183
$250$	−11.1803	−0.707107
$251$	−10.0902	−0.636886	−0.318443	−	0.947942i	$-0.603160\pi$
$251$	−10.0902	−0.636886	−0.318443	+	0.947942i	$0.603160\pi$
$252$	−5.23607	−0.329841
$253$	−4.85410	−0.305175
$254$	−2.67376	−0.167767
$255$	−4.14590	−0.259626
$256$	1.00000	0.0625000
$257$	8.18034	0.510276	0.255138	−	0.966905i	$-0.417879\pi$
$257$	8.18034	0.510276	0.255138	+	0.966905i	$0.417879\pi$
$258$	3.90983	0.243415
$259$	11.4164	0.709381
$260$	6.70820	0.416025
$261$	0.381966	0.0236431
$262$	−17.6180	−1.08845
$263$	8.05573	0.496737	0.248369	−	0.968666i	$-0.420106\pi$
$263$	8.05573	0.496737	0.248369	+	0.968666i	$0.420106\pi$
$264$	−1.00000	−0.0615457
$265$	−20.0000	−1.22859
$266$	2.00000	0.122628
$267$	2.43769	0.149184
$268$	−1.47214	−0.0899250
$269$	4.32624	0.263775	0.131888	−	0.991265i	$-0.457896\pi$
$269$	4.32624	0.263775	0.131888	+	0.991265i	$0.457896\pi$
$270$	7.76393	0.472498
$271$	18.7082	1.13644	0.568221	−	0.822876i	$-0.307632\pi$
$271$	18.7082	1.13644	0.568221	+	0.822876i	$0.307632\pi$
$272$	−3.00000	−0.181902
$273$	3.70820	0.224431
$274$	20.4164	1.23340
$275$	0	0
$276$	−1.85410	−0.111604
$277$	−14.8885	−0.894566	−0.447283	−	0.894393i	$-0.647608\pi$
$277$	−14.8885	−0.894566	−0.447283	+	0.894393i	$0.647608\pi$
$278$	17.8885	1.07288
$279$	−1.00000	−0.0598684
$280$	4.47214	0.267261
$281$	−12.2361	−0.729943	−0.364971	−	0.931019i	$-0.618921\pi$
$281$	−12.2361	−0.729943	−0.364971	+	0.931019i	$0.618921\pi$
$282$	8.14590	0.485081
$283$	27.5623	1.63841	0.819205	−	0.573501i	$-0.194415\pi$
$283$	27.5623	1.63841	0.819205	+	0.573501i	$0.194415\pi$
$284$	1.85410	0.110021
$285$	−1.38197	−0.0818606
$286$	−4.85410	−0.287029
$287$	17.4164	1.02806
$288$	2.61803	0.154269
$289$	−8.00000	−0.470588
$290$	−0.326238	−0.0191574
$291$	2.61803	0.153472
$292$	−2.70820	−0.158486
$293$	−4.61803	−0.269788	−0.134894	−	0.990860i	$-0.543069\pi$
$293$	−4.61803	−0.269788	−0.134894	+	0.990860i	$0.543069\pi$
$294$	−1.85410	−0.108133
$295$	−12.0344	−0.700672
$296$	−5.70820	−0.331783
$297$	−5.61803	−0.325991
$298$	11.1459	0.645665
$299$	−9.00000	−0.520483
$300$	0	0
$301$	12.6525	0.729277
$302$	−2.85410	−0.164235
$303$	−0.618034	−0.0355051
$304$	−1.00000	−0.0573539
$305$	17.3607	0.994070
$306$	−7.85410	−0.448989
$307$	−23.1803	−1.32297	−0.661486	−	0.749958i	$-0.730074\pi$
$307$	−23.1803	−1.32297	−0.661486	+	0.749958i	$0.730074\pi$
$308$	−3.23607	−0.184392
$309$	−6.23607	−0.354758
$310$	0.854102	0.0485097
$311$	3.96556	0.224866	0.112433	−	0.993659i	$-0.464136\pi$
$311$	3.96556	0.224866	0.112433	+	0.993659i	$0.464136\pi$
$312$	−1.85410	−0.104968
$313$	6.09017	0.344237	0.172118	−	0.985076i	$-0.444939\pi$
$313$	6.09017	0.344237	0.172118	+	0.985076i	$0.444939\pi$
$314$	18.2361	1.02912
$315$	11.7082	0.659683
$316$	−13.7082	−0.771147
$317$	23.1803	1.30194	0.650969	−	0.759104i	$-0.274363\pi$
$317$	23.1803	1.30194	0.650969	+	0.759104i	$0.274363\pi$
$318$	5.52786	0.309987
$319$	0.236068	0.0132173
$320$	−2.23607	−0.125000
$321$	−3.14590	−0.175587
$322$	−6.00000	−0.334367
$323$	3.00000	0.166924
$324$	5.70820	0.317122
$325$	0	0
$326$	−24.8885	−1.37845
$327$	−0.763932	−0.0422455
$328$	−8.70820	−0.480830
$329$	26.3607	1.45331
$330$	2.23607	0.123091
$331$	−8.18034	−0.449632	−0.224816	−	0.974401i	$-0.572178\pi$
$331$	−8.18034	−0.449632	−0.224816	+	0.974401i	$0.572178\pi$
$332$	−1.85410	−0.101757
$333$	−14.9443	−0.818941
$334$	−13.7082	−0.750080
$335$	3.29180	0.179850
$336$	−1.23607	−0.0674330
$337$	−8.94427	−0.487226	−0.243613	−	0.969873i	$-0.578333\pi$
$337$	−8.94427	−0.487226	−0.243613	+	0.969873i	$0.578333\pi$
$338$	4.00000	0.217571
$339$	6.50658	0.353389
$340$	6.70820	0.363803
$341$	−0.618034	−0.0334684
$342$	−2.61803	−0.141567
$343$	−20.0000	−1.07990
$344$	−6.32624	−0.341088
$345$	4.14590	0.223208
$346$	0.381966	0.0205346
$347$	9.52786	0.511483	0.255741	−	0.966745i	$-0.417680\pi$
$347$	9.52786	0.511483	0.255741	+	0.966745i	$0.417680\pi$
$348$	0.0901699	0.00483362
$349$	27.0902	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$349$	27.0902	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$350$	0	0
$351$	−10.4164	−0.555987
$352$	1.61803	0.0862415
$353$	−5.43769	−0.289419	−0.144710	−	0.989474i	$-0.546225\pi$
$353$	−5.43769	−0.289419	−0.144710	+	0.989474i	$0.546225\pi$
$354$	3.32624	0.176788
$355$	−4.14590	−0.220041
$356$	−3.94427	−0.209046
$357$	3.70820	0.196259
$358$	−10.7639	−0.568891
$359$	−23.3607	−1.23293	−0.616465	−	0.787382i	$-0.711436\pi$
$359$	−23.3607	−1.23293	−0.616465	+	0.787382i	$0.711436\pi$
$360$	−5.85410	−0.308538
$361$	1.00000	0.0526316
$362$	8.41641	0.442357
$363$	5.18034	0.271897
$364$	−6.00000	−0.314485
$365$	6.05573	0.316971
$366$	−4.79837	−0.250815
$367$	21.5066	1.12263	0.561317	−	0.827601i	$-0.310295\pi$
$367$	21.5066	1.12263	0.561317	+	0.827601i	$0.310295\pi$
$368$	3.00000	0.156386
$369$	−22.7984	−1.18684
$370$	12.7639	0.663565
$371$	17.8885	0.928727
$372$	−0.236068	−0.0122396
$373$	12.6180	0.653337	0.326669	−	0.945139i	$-0.394074\pi$
$373$	12.6180	0.653337	0.326669	+	0.945139i	$0.394074\pi$
$374$	−4.85410	−0.251000
$375$	−6.90983	−0.356822
$376$	−13.1803	−0.679724
$377$	0.437694	0.0225424
$378$	−6.94427	−0.357175
$379$	6.00000	0.308199	0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000	0.308199	0.154100	+	0.988055i	$0.450752\pi$
$380$	2.23607	0.114708
$381$	−1.65248	−0.0846589
$382$	−13.9443	−0.713451
$383$	−32.4721	−1.65925	−0.829624	−	0.558322i	$-0.811445\pi$
$383$	−32.4721	−1.65925	−0.829624	+	0.558322i	$0.811445\pi$
$384$	0.618034	0.0315389
$385$	7.23607	0.368784
$386$	10.4721	0.533018
$387$	−16.5623	−0.841909
$388$	−4.23607	−0.215054
$389$	16.7639	0.849965	0.424983	−	0.905202i	$-0.360280\pi$
$389$	16.7639	0.849965	0.424983	+	0.905202i	$0.360280\pi$
$390$	4.14590	0.209936
$391$	−9.00000	−0.455150
$392$	3.00000	0.151523
$393$	−10.8885	−0.549254
$394$	11.8885	0.598936
$395$	30.6525	1.54229
$396$	4.23607	0.212870
$397$	−13.8541	−0.695317	−0.347659	−	0.937621i	$-0.613023\pi$
$397$	−13.8541	−0.695317	−0.347659	+	0.937621i	$0.613023\pi$
$398$	0.416408	0.0208726
$399$	1.23607	0.0618808
$400$	0	0
$401$	−11.8197	−0.590246	−0.295123	−	0.955459i	$-0.595361\pi$
$401$	−11.8197	−0.590246	−0.295123	+	0.955459i	$0.595361\pi$
$402$	−0.909830	−0.0453782
$403$	−1.14590	−0.0570812
$404$	1.00000	0.0497519
$405$	−12.7639	−0.634245
$406$	0.291796	0.0144816
$407$	−9.23607	−0.457815
$408$	−1.85410	−0.0917917
$409$	−1.90983	−0.0944350	−0.0472175	−	0.998885i	$-0.515035\pi$
$409$	−1.90983	−0.0944350	−0.0472175	+	0.998885i	$0.515035\pi$
$410$	19.4721	0.961660
$411$	12.6180	0.622402
$412$	10.0902	0.497107
$413$	10.7639	0.529658
$414$	7.85410	0.386008
$415$	4.14590	0.203514
$416$	3.00000	0.147087
$417$	11.0557	0.541401
$418$	−1.61803	−0.0791406
$419$	−11.8885	−0.580793	−0.290397	−	0.956906i	$-0.593787\pi$
$419$	−11.8885	−0.580793	−0.290397	+	0.956906i	$0.593787\pi$
$420$	2.76393	0.134866
$421$	−18.5623	−0.904671	−0.452336	−	0.891848i	$-0.649409\pi$
$421$	−18.5623	−0.904671	−0.452336	+	0.891848i	$0.649409\pi$
$422$	1.00000	0.0486792
$423$	−34.5066	−1.67777
$424$	−8.94427	−0.434372
$425$	0	0
$426$	1.14590	0.0555189
$427$	−15.5279	−0.751446
$428$	5.09017	0.246043
$429$	−3.00000	−0.144841
$430$	14.1459	0.682176
$431$	4.76393	0.229471	0.114735	−	0.993396i	$-0.463398\pi$
$431$	4.76393	0.229471	0.114735	+	0.993396i	$0.463398\pi$
$432$	3.47214	0.167053
$433$	−6.52786	−0.313709	−0.156855	−	0.987622i	$-0.550135\pi$
$433$	−6.52786	−0.313709	−0.156855	+	0.987622i	$0.550135\pi$
$434$	−0.763932	−0.0366699
$435$	−0.201626	−0.00966723
$436$	1.23607	0.0591969
$437$	−3.00000	−0.143509
$438$	−1.67376	−0.0799754
$439$	33.3951	1.59386	0.796931	−	0.604070i	$-0.206455\pi$
$439$	33.3951	1.59386	0.796931	+	0.604070i	$0.206455\pi$
$440$	−3.61803	−0.172483
$441$	7.85410	0.374005
$442$	−9.00000	−0.428086
$443$	10.7639	0.511410	0.255705	−	0.966755i	$-0.417692\pi$
$443$	10.7639	0.511410	0.255705	+	0.966755i	$0.417692\pi$
$444$	−3.52786	−0.167425
$445$	8.81966	0.418092
$446$	15.7639	0.746444
$447$	6.88854	0.325817
$448$	2.00000	0.0944911
$449$	−32.7082	−1.54360	−0.771798	−	0.635868i	$-0.780642\pi$
$449$	−32.7082	−1.54360	−0.771798	+	0.635868i	$0.780642\pi$
$450$	0	0
$451$	−14.0902	−0.663480
$452$	−10.5279	−0.495189
$453$	−1.76393	−0.0828768
$454$	5.76393	0.270515
$455$	13.4164	0.628971
$456$	−0.618034	−0.0289421
$457$	4.32624	0.202373	0.101186	−	0.994867i	$-0.467736\pi$
$457$	4.32624	0.202373	0.101186	+	0.994867i	$0.467736\pi$
$458$	7.67376	0.358571
$459$	−10.4164	−0.486196
$460$	−6.70820	−0.312772
$461$	−17.7426	−0.826357	−0.413179	−	0.910650i	$-0.635582\pi$
$461$	−17.7426	−0.826357	−0.413179	+	0.910650i	$0.635582\pi$
$462$	−2.00000	−0.0930484
$463$	23.2361	1.07987	0.539936	−	0.841706i	$-0.318448\pi$
$463$	23.2361	1.07987	0.539936	+	0.841706i	$0.318448\pi$
$464$	−0.145898	−0.00677315
$465$	0.527864	0.0244791
$466$	6.41641	0.297234
$467$	−28.8885	−1.33680	−0.668401	−	0.743801i	$-0.733021\pi$
$467$	−28.8885	−1.33680	−0.668401	+	0.743801i	$0.733021\pi$
$468$	7.85410	0.363056
$469$	−2.94427	−0.135954
$470$	29.4721	1.35945
$471$	11.2705	0.519318
$472$	−5.38197	−0.247725
$473$	−10.2361	−0.470655
$474$	−8.47214	−0.389138
$475$	0	0
$476$	−6.00000	−0.275010
$477$	−23.4164	−1.07216
$478$	−18.7639	−0.858242
$479$	−37.6525	−1.72039	−0.860193	−	0.509969i	$-0.829657\pi$
$479$	−37.6525	−1.72039	−0.860193	+	0.509969i	$0.829657\pi$
$480$	−1.38197	−0.0630778
$481$	−17.1246	−0.780815
$482$	22.2705	1.01439
$483$	−3.70820	−0.168729
$484$	−8.38197	−0.380998
$485$	9.47214	0.430108
$486$	13.9443	0.632525
$487$	−11.7984	−0.534635	−0.267318	−	0.963608i	$-0.586137\pi$
$487$	−11.7984	−0.534635	−0.267318	+	0.963608i	$0.586137\pi$
$488$	7.76393	0.351457
$489$	−15.3820	−0.695597
$490$	−6.70820	−0.303046
$491$	13.9443	0.629296	0.314648	−	0.949208i	$-0.398113\pi$
$491$	13.9443	0.629296	0.314648	+	0.949208i	$0.398113\pi$
$492$	−5.38197	−0.242638
$493$	0.437694	0.0197128
$494$	−3.00000	−0.134976
$495$	−9.47214	−0.425741
$496$	0.381966	0.0171508
$497$	3.70820	0.166336
$498$	−1.14590	−0.0513489
$499$	−43.4721	−1.94608	−0.973040	−	0.230636i	$-0.925919\pi$
$499$	−43.4721	−1.94608	−0.973040	+	0.230636i	$0.925919\pi$
$500$	11.1803	0.500000
$501$	−8.47214	−0.378507
$502$	10.0902	0.450346
$503$	−38.8328	−1.73147	−0.865735	−	0.500503i	$-0.833148\pi$
$503$	−38.8328	−1.73147	−0.865735	+	0.500503i	$0.833148\pi$
$504$	5.23607	0.233233
$505$	−2.23607	−0.0995037
$506$	4.85410	0.215791
$507$	2.47214	0.109791
$508$	2.67376	0.118629
$509$	11.2918	0.500500	0.250250	−	0.968181i	$-0.419487\pi$
$509$	11.2918	0.500500	0.250250	+	0.968181i	$0.419487\pi$
$510$	4.14590	0.183583
$511$	−5.41641	−0.239608
$512$	−1.00000	−0.0441942
$513$	−3.47214	−0.153299
$514$	−8.18034	−0.360819
$515$	−22.5623	−0.994214
$516$	−3.90983	−0.172121
$517$	−21.3262	−0.937927
$518$	−11.4164	−0.501608
$519$	0.236068	0.0103622
$520$	−6.70820	−0.294174
$521$	30.3262	1.32862	0.664308	−	0.747459i	$-0.268726\pi$
$521$	30.3262	1.32862	0.664308	+	0.747459i	$0.268726\pi$
$522$	−0.381966	−0.0167182
$523$	28.5279	1.24744	0.623718	−	0.781649i	$-0.285621\pi$
$523$	28.5279	1.24744	0.623718	+	0.781649i	$0.285621\pi$
$524$	17.6180	0.769647
$525$	0	0
$526$	−8.05573	−0.351246
$527$	−1.14590	−0.0499161
$528$	1.00000	0.0435194
$529$	−14.0000	−0.608696
$530$	20.0000	0.868744
$531$	−14.0902	−0.611461
$532$	−2.00000	−0.0867110
$533$	−26.1246	−1.13158
$534$	−2.43769	−0.105489
$535$	−11.3820	−0.492085
$536$	1.47214	0.0635866
$537$	−6.65248	−0.287076
$538$	−4.32624	−0.186517
$539$	4.85410	0.209081
$540$	−7.76393	−0.334106
$541$	12.2016	0.524589	0.262294	−	0.964988i	$-0.415521\pi$
$541$	12.2016	0.524589	0.262294	+	0.964988i	$0.415521\pi$
$542$	−18.7082	−0.803586
$543$	5.20163	0.223223
$544$	3.00000	0.128624
$545$	−2.76393	−0.118394
$546$	−3.70820	−0.158696
$547$	−26.4508	−1.13096	−0.565478	−	0.824763i	$-0.691308\pi$
$547$	−26.4508	−1.13096	−0.565478	+	0.824763i	$0.691308\pi$
$548$	−20.4164	−0.872146
$549$	20.3262	0.867503
$550$	0	0
$551$	0.145898	0.00621547
$552$	1.85410	0.0789158
$553$	−27.4164	−1.16586
$554$	14.8885	0.632554
$555$	7.88854	0.334850
$556$	−17.8885	−0.758643
$557$	−1.94427	−0.0823814	−0.0411907	−	0.999151i	$-0.513115\pi$
$557$	−1.94427	−0.0823814	−0.0411907	+	0.999151i	$0.513115\pi$
$558$	1.00000	0.0423334
$559$	−18.9787	−0.802714
$560$	−4.47214	−0.188982
$561$	−3.00000	−0.126660
$562$	12.2361	0.516147
$563$	40.2492	1.69630	0.848151	−	0.529754i	$-0.177716\pi$
$563$	40.2492	1.69630	0.848151	+	0.529754i	$0.177716\pi$
$564$	−8.14590	−0.343004
$565$	23.5410	0.990378
$566$	−27.5623	−1.15853
$567$	11.4164	0.479444
$568$	−1.85410	−0.0777964
$569$	−8.03444	−0.336821	−0.168411	−	0.985717i	$-0.553863\pi$
$569$	−8.03444	−0.336821	−0.168411	+	0.985717i	$0.553863\pi$
$570$	1.38197	0.0578842
$571$	27.1459	1.13602	0.568010	−	0.823021i	$-0.307713\pi$
$571$	27.1459	1.13602	0.568010	+	0.823021i	$0.307713\pi$
$572$	4.85410	0.202960
$573$	−8.61803	−0.360024
$574$	−17.4164	−0.726947
$575$	0	0
$576$	−2.61803	−0.109085
$577$	−14.9098	−0.620704	−0.310352	−	0.950622i	$-0.600447\pi$
$577$	−14.9098	−0.620704	−0.310352	+	0.950622i	$0.600447\pi$
$578$	8.00000	0.332756
$579$	6.47214	0.268973
$580$	0.326238	0.0135463
$581$	−3.70820	−0.153842
$582$	−2.61803	−0.108521
$583$	−14.4721	−0.599375
$584$	2.70820	0.112066
$585$	−17.5623	−0.726112
$586$	4.61803	0.190769
$587$	−17.7639	−0.733196	−0.366598	−	0.930379i	$-0.619478\pi$
$587$	−17.7639	−0.733196	−0.366598	+	0.930379i	$0.619478\pi$
$588$	1.85410	0.0764619
$589$	−0.381966	−0.0157386
$590$	12.0344	0.495450
$591$	7.34752	0.302237
$592$	5.70820	0.234606
$593$	−29.0000	−1.19089	−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000	−1.19089	−0.595444	+	0.803397i	$0.703024\pi$
$594$	5.61803	0.230511
$595$	13.4164	0.550019
$596$	−11.1459	−0.456554
$597$	0.257354	0.0105328
$598$	9.00000	0.368037
$599$	−6.25735	−0.255669	−0.127834	−	0.991796i	$-0.540803\pi$
$599$	−6.25735	−0.255669	−0.127834	+	0.991796i	$0.540803\pi$
$600$	0	0
$601$	32.5967	1.32965	0.664825	−	0.747000i	$-0.268506\pi$
$601$	32.5967	1.32965	0.664825	+	0.747000i	$0.268506\pi$
$602$	−12.6525	−0.515676
$603$	3.85410	0.156951
$604$	2.85410	0.116132
$605$	18.7426	0.761997
$606$	0.618034	0.0251059
$607$	−16.2361	−0.659002	−0.329501	−	0.944155i	$-0.606880\pi$
$607$	−16.2361	−0.659002	−0.329501	+	0.944155i	$0.606880\pi$
$608$	1.00000	0.0405554
$609$	0.180340	0.00730774
$610$	−17.3607	−0.702913
$611$	−39.5410	−1.59966
$612$	7.85410	0.317483
$613$	9.74265	0.393502	0.196751	−	0.980454i	$-0.436961\pi$
$613$	9.74265	0.393502	0.196751	+	0.980454i	$0.436961\pi$
$614$	23.1803	0.935482
$615$	12.0344	0.485276
$616$	3.23607	0.130385
$617$	−41.3607	−1.66512	−0.832559	−	0.553936i	$-0.813125\pi$
$617$	−41.3607	−1.66512	−0.832559	+	0.553936i	$0.813125\pi$
$618$	6.23607	0.250851
$619$	−1.05573	−0.0424333	−0.0212166	−	0.999775i	$-0.506754\pi$
$619$	−1.05573	−0.0424333	−0.0212166	+	0.999775i	$0.506754\pi$
$620$	−0.854102	−0.0343016
$621$	10.4164	0.417996
$622$	−3.96556	−0.159004
$623$	−7.88854	−0.316048
$624$	1.85410	0.0742235
$625$	−25.0000	−1.00000
$626$	−6.09017	−0.243412
$627$	−1.00000	−0.0399362
$628$	−18.2361	−0.727698
$629$	−17.1246	−0.682803
$630$	−11.7082	−0.466466
$631$	−8.05573	−0.320693	−0.160347	−	0.987061i	$-0.551261\pi$
$631$	−8.05573	−0.320693	−0.160347	+	0.987061i	$0.551261\pi$
$632$	13.7082	0.545283
$633$	0.618034	0.0245646
$634$	−23.1803	−0.920609
$635$	−5.97871	−0.237258
$636$	−5.52786	−0.219194
$637$	9.00000	0.356593
$638$	−0.236068	−0.00934602
$639$	−4.85410	−0.192025
$640$	2.23607	0.0883883
$641$	1.09017	0.0430591	0.0215296	−	0.999768i	$-0.493146\pi$
$641$	1.09017	0.0430591	0.0215296	+	0.999768i	$0.493146\pi$
$642$	3.14590	0.124159
$643$	4.34752	0.171450	0.0857248	−	0.996319i	$-0.472679\pi$
$643$	4.34752	0.171450	0.0857248	+	0.996319i	$0.472679\pi$
$644$	6.00000	0.236433
$645$	8.74265	0.344241
$646$	−3.00000	−0.118033
$647$	35.4508	1.39372	0.696858	−	0.717209i	$-0.254581\pi$
$647$	35.4508	1.39372	0.696858	+	0.717209i	$0.254581\pi$
$648$	−5.70820	−0.224239
$649$	−8.70820	−0.341827
$650$	0	0
$651$	−0.472136	−0.0185045
$652$	24.8885	0.974711
$653$	26.3607	1.03157	0.515787	−	0.856717i	$-0.327500\pi$
$653$	26.3607	1.03157	0.515787	+	0.856717i	$0.327500\pi$
$654$	0.763932	0.0298721
$655$	−39.3951	−1.53929
$656$	8.70820	0.339998
$657$	7.09017	0.276614
$658$	−26.3607	−1.02765
$659$	25.6525	0.999279	0.499639	−	0.866234i	$-0.333466\pi$
$659$	25.6525	0.999279	0.499639	+	0.866234i	$0.333466\pi$
$660$	−2.23607	−0.0870388
$661$	−26.7639	−1.04100	−0.520498	−	0.853863i	$-0.674254\pi$
$661$	−26.7639	−1.04100	−0.520498	+	0.853863i	$0.674254\pi$
$662$	8.18034	0.317938
$663$	−5.56231	−0.216022
$664$	1.85410	0.0719531
$665$	4.47214	0.173422
$666$	14.9443	0.579079
$667$	−0.437694	−0.0169476
$668$	13.7082	0.530386
$669$	9.74265	0.376672
$670$	−3.29180	−0.127173
$671$	12.5623	0.484962
$672$	1.23607	0.0476824
$673$	−34.3820	−1.32533	−0.662664	−	0.748917i	$-0.730574\pi$
$673$	−34.3820	−1.32533	−0.662664	+	0.748917i	$0.730574\pi$
$674$	8.94427	0.344520
$675$	0	0
$676$	−4.00000	−0.153846
$677$	−26.5279	−1.01955	−0.509774	−	0.860308i	$-0.670271\pi$
$677$	−26.5279	−1.01955	−0.509774	+	0.860308i	$0.670271\pi$
$678$	−6.50658	−0.249884
$679$	−8.47214	−0.325131
$680$	−6.70820	−0.257248
$681$	3.56231	0.136508
$682$	0.618034	0.0236657
$683$	−29.0000	−1.10965	−0.554827	−	0.831966i	$-0.687216\pi$
$683$	−29.0000	−1.10965	−0.554827	+	0.831966i	$0.687216\pi$
$684$	2.61803	0.100103
$685$	45.6525	1.74429
$686$	20.0000	0.763604
$687$	4.74265	0.180943
$688$	6.32624	0.241186
$689$	−26.8328	−1.02225
$690$	−4.14590	−0.157832
$691$	17.1459	0.652261	0.326130	−	0.945325i	$-0.394255\pi$
$691$	17.1459	0.652261	0.326130	+	0.945325i	$0.394255\pi$
$692$	−0.381966	−0.0145202
$693$	8.47214	0.321830
$694$	−9.52786	−0.361673
$695$	40.0000	1.51729
$696$	−0.0901699	−0.00341788
$697$	−26.1246	−0.989540
$698$	−27.0902	−1.02538
$699$	3.96556	0.149991
$700$	0	0
$701$	26.1246	0.986713	0.493356	−	0.869827i	$-0.335770\pi$
$701$	26.1246	0.986713	0.493356	+	0.869827i	$0.335770\pi$
$702$	10.4164	0.393142
$703$	−5.70820	−0.215289
$704$	−1.61803	−0.0609820
$705$	18.2148	0.686008
$706$	5.43769	0.204650
$707$	2.00000	0.0752177
$708$	−3.32624	−0.125008
$709$	−10.6180	−0.398769	−0.199384	−	0.979921i	$-0.563894\pi$
$709$	−10.6180	−0.398769	−0.199384	+	0.979921i	$0.563894\pi$
$710$	4.14590	0.155593
$711$	35.8885	1.34593
$712$	3.94427	0.147818
$713$	1.14590	0.0429142
$714$	−3.70820	−0.138776
$715$	−10.8541	−0.405920
$716$	10.7639	0.402267
$717$	−11.5967	−0.433088
$718$	23.3607	0.871813
$719$	−22.5967	−0.842716	−0.421358	−	0.906894i	$-0.638446\pi$
$719$	−22.5967	−0.842716	−0.421358	+	0.906894i	$0.638446\pi$
$720$	5.85410	0.218169
$721$	20.1803	0.751555
$722$	−1.00000	−0.0372161
$723$	13.7639	0.511886
$724$	−8.41641	−0.312793
$725$	0	0
$726$	−5.18034	−0.192260
$727$	4.76393	0.176684	0.0883422	−	0.996090i	$-0.471843\pi$
$727$	4.76393	0.176684	0.0883422	+	0.996090i	$0.471843\pi$
$728$	6.00000	0.222375
$729$	−8.50658	−0.315058
$730$	−6.05573	−0.224133
$731$	−18.9787	−0.701953
$732$	4.79837	0.177353
$733$	16.0344	0.592246	0.296123	−	0.955150i	$-0.404306\pi$
$733$	16.0344	0.592246	0.296123	+	0.955150i	$0.404306\pi$
$734$	−21.5066	−0.793822
$735$	−4.14590	−0.152924
$736$	−3.00000	−0.110581
$737$	2.38197	0.0877408
$738$	22.7984	0.839220
$739$	−14.0000	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$739$	−14.0000	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$740$	−12.7639	−0.469211
$741$	−1.85410	−0.0681121
$742$	−17.8885	−0.656709
$743$	42.5066	1.55942	0.779708	−	0.626144i	$-0.215368\pi$
$743$	42.5066	1.55942	0.779708	+	0.626144i	$0.215368\pi$
$744$	0.236068	0.00865467
$745$	24.9230	0.913108
$746$	−12.6180	−0.461979
$747$	4.85410	0.177602
$748$	4.85410	0.177484
$749$	10.1803	0.371982
$750$	6.90983	0.252311
$751$	−9.81966	−0.358324	−0.179162	−	0.983820i	$-0.557339\pi$
$751$	−9.81966	−0.358324	−0.179162	+	0.983820i	$0.557339\pi$
$752$	13.1803	0.480638
$753$	6.23607	0.227255
$754$	−0.437694	−0.0159399
$755$	−6.38197	−0.232264
$756$	6.94427	0.252561
$757$	26.3262	0.956843	0.478422	−	0.878130i	$-0.341209\pi$
$757$	26.3262	0.956843	0.478422	+	0.878130i	$0.341209\pi$
$758$	−6.00000	−0.217930
$759$	3.00000	0.108893
$760$	−2.23607	−0.0811107
$761$	11.7426	0.425671	0.212835	−	0.977088i	$-0.431730\pi$
$761$	11.7426	0.425671	0.212835	+	0.977088i	$0.431730\pi$
$762$	1.65248	0.0598629
$763$	2.47214	0.0894973
$764$	13.9443	0.504486
$765$	−17.5623	−0.634967
$766$	32.4721	1.17327
$767$	−16.1459	−0.582995
$768$	−0.618034	−0.0223014
$769$	12.6180	0.455018	0.227509	−	0.973776i	$-0.426942\pi$
$769$	12.6180	0.455018	0.227509	+	0.973776i	$0.426942\pi$
$770$	−7.23607	−0.260770
$771$	−5.05573	−0.182078
$772$	−10.4721	−0.376900
$773$	−20.3951	−0.733562	−0.366781	−	0.930307i	$-0.619540\pi$
$773$	−20.3951	−0.733562	−0.366781	+	0.930307i	$0.619540\pi$
$774$	16.5623	0.595320
$775$	0	0
$776$	4.23607	0.152066
$777$	−7.05573	−0.253123
$778$	−16.7639	−0.601016
$779$	−8.70820	−0.312004
$780$	−4.14590	−0.148447
$781$	−3.00000	−0.107348
$782$	9.00000	0.321839
$783$	−0.506578	−0.0181036
$784$	−3.00000	−0.107143
$785$	40.7771	1.45540
$786$	10.8885	0.388381
$787$	13.1246	0.467842	0.233921	−	0.972256i	$-0.424844\pi$
$787$	13.1246	0.467842	0.233921	+	0.972256i	$0.424844\pi$
$788$	−11.8885	−0.423512
$789$	−4.97871	−0.177247
$790$	−30.6525	−1.09057
$791$	−21.0557	−0.748656
$792$	−4.23607	−0.150522
$793$	23.2918	0.827116
$794$	13.8541	0.491664
$795$	12.3607	0.438388
$796$	−0.416408	−0.0147592
$797$	−37.8328	−1.34011	−0.670054	−	0.742313i	$-0.733729\pi$
$797$	−37.8328	−1.34011	−0.670054	+	0.742313i	$0.733729\pi$
$798$	−1.23607	−0.0437563
$799$	−39.5410	−1.39886
$800$	0	0
$801$	10.3262	0.364860
$802$	11.8197	0.417367
$803$	4.38197	0.154636
$804$	0.909830	0.0320872
$805$	−13.4164	−0.472866
$806$	1.14590	0.0403625
$807$	−2.67376	−0.0941209
$808$	−1.00000	−0.0351799
$809$	−15.9098	−0.559360	−0.279680	−	0.960093i	$-0.590228\pi$
$809$	−15.9098	−0.559360	−0.279680	+	0.960093i	$0.590228\pi$
$810$	12.7639	0.448479
$811$	−26.7639	−0.939809	−0.469904	−	0.882717i	$-0.655712\pi$
$811$	−26.7639	−0.939809	−0.469904	+	0.882717i	$0.655712\pi$
$812$	−0.291796	−0.0102400
$813$	−11.5623	−0.405508
$814$	9.23607	0.323724
$815$	−55.6525	−1.94942
$816$	1.85410	0.0649066
$817$	−6.32624	−0.221327
$818$	1.90983	0.0667756
$819$	15.7082	0.548889
$820$	−19.4721	−0.679996
$821$	14.2016	0.495640	0.247820	−	0.968806i	$-0.420286\pi$
$821$	14.2016	0.495640	0.247820	+	0.968806i	$0.420286\pi$
$822$	−12.6180	−0.440104
$823$	−4.09017	−0.142574	−0.0712872	−	0.997456i	$-0.522711\pi$
$823$	−4.09017	−0.142574	−0.0712872	+	0.997456i	$0.522711\pi$
$824$	−10.0902	−0.351508
$825$	0	0
$826$	−10.7639	−0.374525
$827$	−1.06888	−0.0371687	−0.0185844	−	0.999827i	$-0.505916\pi$
$827$	−1.06888	−0.0371687	−0.0185844	+	0.999827i	$0.505916\pi$
$828$	−7.85410	−0.272949
$829$	22.7771	0.791081	0.395540	−	0.918449i	$-0.370557\pi$
$829$	22.7771	0.791081	0.395540	+	0.918449i	$0.370557\pi$
$830$	−4.14590	−0.143906
$831$	9.20163	0.319201
$832$	−3.00000	−0.104006
$833$	9.00000	0.311832
$834$	−11.0557	−0.382829
$835$	−30.6525	−1.06077
$836$	1.61803	0.0559609
$837$	1.32624	0.0458415
$838$	11.8885	0.410683
$839$	10.1246	0.349540	0.174770	−	0.984609i	$-0.444082\pi$
$839$	10.1246	0.349540	0.174770	+	0.984609i	$0.444082\pi$
$840$	−2.76393	−0.0953647
$841$	−28.9787	−0.999266
$842$	18.5623	0.639699
$843$	7.56231	0.260460
$844$	−1.00000	−0.0344214
$845$	8.94427	0.307692
$846$	34.5066	1.18636
$847$	−16.7639	−0.576016
$848$	8.94427	0.307148
$849$	−17.0344	−0.584621
$850$	0	0
$851$	17.1246	0.587024
$852$	−1.14590	−0.0392578
$853$	9.18034	0.314329	0.157164	−	0.987572i	$-0.449765\pi$
$853$	9.18034	0.314329	0.157164	+	0.987572i	$0.449765\pi$
$854$	15.5279	0.531353
$855$	−5.85410	−0.200206
$856$	−5.09017	−0.173978
$857$	−16.5967	−0.566934	−0.283467	−	0.958982i	$-0.591485\pi$
$857$	−16.5967	−0.566934	−0.283467	+	0.958982i	$0.591485\pi$
$858$	3.00000	0.102418
$859$	23.5410	0.803209	0.401605	−	0.915813i	$-0.368453\pi$
$859$	23.5410	0.803209	0.401605	+	0.915813i	$0.368453\pi$
$860$	−14.1459	−0.482371
$861$	−10.7639	−0.366834
$862$	−4.76393	−0.162260
$863$	−14.8197	−0.504467	−0.252234	−	0.967666i	$-0.581165\pi$
$863$	−14.8197	−0.504467	−0.252234	+	0.967666i	$0.581165\pi$
$864$	−3.47214	−0.118124
$865$	0.854102	0.0290403
$866$	6.52786	0.221826
$867$	4.94427	0.167916
$868$	0.763932	0.0259295
$869$	22.1803	0.752416
$870$	0.201626	0.00683577
$871$	4.41641	0.149644
$872$	−1.23607	−0.0418585
$873$	11.0902	0.375345
$874$	3.00000	0.101477
$875$	22.3607	0.755929
$876$	1.67376	0.0565512
$877$	4.06888	0.137396	0.0686982	−	0.997637i	$-0.478115\pi$
$877$	4.06888	0.137396	0.0686982	+	0.997637i	$0.478115\pi$
$878$	−33.3951	−1.12703
$879$	2.85410	0.0962665
$880$	3.61803	0.121964
$881$	30.2918	1.02056	0.510278	−	0.860009i	$-0.329542\pi$
$881$	30.2918	1.02056	0.510278	+	0.860009i	$0.329542\pi$
$882$	−7.85410	−0.264461
$883$	−50.0689	−1.68495	−0.842476	−	0.538734i	$-0.818903\pi$
$883$	−50.0689	−1.68495	−0.842476	+	0.538734i	$0.818903\pi$
$884$	9.00000	0.302703
$885$	7.43769	0.250015
$886$	−10.7639	−0.361621
$887$	−55.4853	−1.86301	−0.931507	−	0.363724i	$-0.881505\pi$
$887$	−55.4853	−1.86301	−0.931507	+	0.363724i	$0.881505\pi$
$888$	3.52786	0.118387
$889$	5.34752	0.179350
$890$	−8.81966	−0.295636
$891$	−9.23607	−0.309420
$892$	−15.7639	−0.527815
$893$	−13.1803	−0.441063
$894$	−6.88854	−0.230387
$895$	−24.0689	−0.804534
$896$	−2.00000	−0.0668153
$897$	5.56231	0.185720
$898$	32.7082	1.09149
$899$	−0.0557281	−0.00185864
$900$	0	0
$901$	−26.8328	−0.893931
$902$	14.0902	0.469151
$903$	−7.81966	−0.260222
$904$	10.5279	0.350152
$905$	18.8197	0.625587
$906$	1.76393	0.0586027
$907$	−6.88854	−0.228730	−0.114365	−	0.993439i	$-0.536483\pi$
$907$	−6.88854	−0.228730	−0.114365	+	0.993439i	$0.536483\pi$
$908$	−5.76393	−0.191283
$909$	−2.61803	−0.0868347
$910$	−13.4164	−0.444750
$911$	−24.1246	−0.799284	−0.399642	−	0.916671i	$-0.630866\pi$
$911$	−24.1246	−0.799284	−0.399642	+	0.916671i	$0.630866\pi$
$912$	0.618034	0.0204652
$913$	3.00000	0.0992855
$914$	−4.32624	−0.143099
$915$	−10.7295	−0.354706
$916$	−7.67376	−0.253548
$917$	35.2361	1.16360
$918$	10.4164	0.343793
$919$	−30.3820	−1.00221	−0.501104	−	0.865387i	$-0.667073\pi$
$919$	−30.3820	−1.00221	−0.501104	+	0.865387i	$0.667073\pi$
$920$	6.70820	0.221163
$921$	14.3262	0.472066
$922$	17.7426	0.584323
$923$	−5.56231	−0.183086
$924$	2.00000	0.0657952
$925$	0	0
$926$	−23.2361	−0.763585
$927$	−26.4164	−0.867629
$928$	0.145898	0.00478934
$929$	6.29180	0.206427	0.103214	−	0.994659i	$-0.467087\pi$
$929$	6.29180	0.206427	0.103214	+	0.994659i	$0.467087\pi$
$930$	−0.527864	−0.0173093
$931$	3.00000	0.0983210
$932$	−6.41641	−0.210176
$933$	−2.45085	−0.0802372
$934$	28.8885	0.945262
$935$	−10.8541	−0.354967
$936$	−7.85410	−0.256719
$937$	35.2361	1.15111	0.575556	−	0.817762i	$-0.304786\pi$
$937$	35.2361	1.15111	0.575556	+	0.817762i	$0.304786\pi$
$938$	2.94427	0.0961339
$939$	−3.76393	−0.122831
$940$	−29.4721	−0.961275
$941$	−0.618034	−0.0201473	−0.0100737	−	0.999949i	$-0.503207\pi$
$941$	−0.618034	−0.0201473	−0.0100737	+	0.999949i	$0.503207\pi$
$942$	−11.2705	−0.367213
$943$	26.1246	0.850734
$944$	5.38197	0.175168
$945$	−15.5279	−0.505121
$946$	10.2361	0.332803
$947$	2.03444	0.0661105	0.0330552	−	0.999454i	$-0.489476\pi$
$947$	2.03444	0.0661105	0.0330552	+	0.999454i	$0.489476\pi$
$948$	8.47214	0.275162
$949$	8.12461	0.263736
$950$	0	0
$951$	−14.3262	−0.464560
$952$	6.00000	0.194461
$953$	4.20163	0.136104	0.0680520	−	0.997682i	$-0.478322\pi$
$953$	4.20163	0.136104	0.0680520	+	0.997682i	$0.478322\pi$
$954$	23.4164	0.758134
$955$	−31.1803	−1.00897
$956$	18.7639	0.606869
$957$	−0.145898	−0.00471621
$958$	37.6525	1.21650
$959$	−40.8328	−1.31856
$960$	1.38197	0.0446028
$961$	−30.8541	−0.995294
$962$	17.1246	0.552120
$963$	−13.3262	−0.429432
$964$	−22.2705	−0.717285
$965$	23.4164	0.753801
$966$	3.70820	0.119310
$967$	6.47214	0.208130	0.104065	−	0.994571i	$-0.466815\pi$
$967$	6.47214	0.208130	0.104065	+	0.994571i	$0.466815\pi$
$968$	8.38197	0.269407
$969$	−1.85410	−0.0595623
$970$	−9.47214	−0.304132
$971$	2.41641	0.0775462	0.0387731	−	0.999248i	$-0.487655\pi$
$971$	2.41641	0.0775462	0.0387731	+	0.999248i	$0.487655\pi$
$972$	−13.9443	−0.447263
$973$	−35.7771	−1.14696
$974$	11.7984	0.378044
$975$	0	0
$976$	−7.76393	−0.248517
$977$	−57.4508	−1.83802	−0.919008	−	0.394239i	$-0.871008\pi$
$977$	−57.4508	−1.83802	−0.919008	+	0.394239i	$0.871008\pi$
$978$	15.3820	0.491861
$979$	6.38197	0.203969
$980$	6.70820	0.214286
$981$	−3.23607	−0.103320
$982$	−13.9443	−0.444980
$983$	20.7082	0.660489	0.330245	−	0.943895i	$-0.392869\pi$
$983$	20.7082	0.660489	0.330245	+	0.943895i	$0.392869\pi$
$984$	5.38197	0.171571
$985$	26.5836	0.847024
$986$	−0.437694	−0.0139390
$987$	−16.2918	−0.518574
$988$	3.00000	0.0954427
$989$	18.9787	0.603488
$990$	9.47214	0.301044
$991$	−11.5410	−0.366613	−0.183306	−	0.983056i	$-0.558680\pi$
$991$	−11.5410	−0.366613	−0.183306	+	0.983056i	$0.558680\pi$
$992$	−0.381966	−0.0121274
$993$	5.05573	0.160439
$994$	−3.70820	−0.117617
$995$	0.931116	0.0295184
$996$	1.14590	0.0363092
$997$	32.8328	1.03983	0.519913	−	0.854219i	$-0.325964\pi$
$997$	32.8328	1.03983	0.519913	+	0.854219i	$0.325964\pi$
$998$	43.4721	1.37609
$999$	19.8197	0.627066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.b.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.b.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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -2.23607 q^{5} +0.618034 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -2.23607 q^{5} +0.618034 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +2.23607 q^{10} -1.61803 q^{11} -0.618034 q^{12} -3.00000 q^{13} -2.00000 q^{14} +1.38197 q^{15} +1.00000 q^{16} -3.00000 q^{17} +2.61803 q^{18} -1.00000 q^{19} -2.23607 q^{20} -1.23607 q^{21} +1.61803 q^{22} +3.00000 q^{23} +0.618034 q^{24} +3.00000 q^{26} +3.47214 q^{27} +2.00000 q^{28} -0.145898 q^{29} -1.38197 q^{30} +0.381966 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.00000 q^{34} -4.47214 q^{35} -2.61803 q^{36} +5.70820 q^{37} +1.00000 q^{38} +1.85410 q^{39} +2.23607 q^{40} +8.70820 q^{41} +1.23607 q^{42} +6.32624 q^{43} -1.61803 q^{44} +5.85410 q^{45} -3.00000 q^{46} +13.1803 q^{47} -0.618034 q^{48} -3.00000 q^{49} +1.85410 q^{51} -3.00000 q^{52} +8.94427 q^{53} -3.47214 q^{54} +3.61803 q^{55} -2.00000 q^{56} +0.618034 q^{57} +0.145898 q^{58} +5.38197 q^{59} +1.38197 q^{60} -7.76393 q^{61} -0.381966 q^{62} -5.23607 q^{63} +1.00000 q^{64} +6.70820 q^{65} -1.00000 q^{66} -1.47214 q^{67} -3.00000 q^{68} -1.85410 q^{69} +4.47214 q^{70} +1.85410 q^{71} +2.61803 q^{72} -2.70820 q^{73} -5.70820 q^{74} -1.00000 q^{76} -3.23607 q^{77} -1.85410 q^{78} -13.7082 q^{79} -2.23607 q^{80} +5.70820 q^{81} -8.70820 q^{82} -1.85410 q^{83} -1.23607 q^{84} +6.70820 q^{85} -6.32624 q^{86} +0.0901699 q^{87} +1.61803 q^{88} -3.94427 q^{89} -5.85410 q^{90} -6.00000 q^{91} +3.00000 q^{92} -0.236068 q^{93} -13.1803 q^{94} +2.23607 q^{95} +0.618034 q^{96} -4.23607 q^{97} +3.00000 q^{98} +4.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 4 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 4 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 4 q^{7} - 2 q^{8} - 3 q^{9} - q^{11} + q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{15} + 2 q^{16} - 6 q^{17} + 3 q^{18} - 2 q^{19} + 2 q^{21} + q^{22} + 6 q^{23} - q^{24} + 6 q^{26} - 2 q^{27} + 4 q^{28} - 7 q^{29} - 5 q^{30} + 3 q^{31} - 2 q^{32} + 2 q^{33} + 6 q^{34} - 3 q^{36} - 2 q^{37} + 2 q^{38} - 3 q^{39} + 4 q^{41} - 2 q^{42} - 3 q^{43} - q^{44} + 5 q^{45} - 6 q^{46} + 4 q^{47} + q^{48} - 6 q^{49} - 3 q^{51} - 6 q^{52} + 2 q^{54} + 5 q^{55} - 4 q^{56} - q^{57} + 7 q^{58} + 13 q^{59} + 5 q^{60} - 20 q^{61} - 3 q^{62} - 6 q^{63} + 2 q^{64} - 2 q^{66} + 6 q^{67} - 6 q^{68} + 3 q^{69} - 3 q^{71} + 3 q^{72} + 8 q^{73} + 2 q^{74} - 2 q^{76} - 2 q^{77} + 3 q^{78} - 14 q^{79} - 2 q^{81} - 4 q^{82} + 3 q^{83} + 2 q^{84} + 3 q^{86} - 11 q^{87} + q^{88} + 10 q^{89} - 5 q^{90} - 12 q^{91} + 6 q^{92} + 4 q^{93} - 4 q^{94} - q^{96} - 4 q^{97} + 6 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 4 * q^7 - 2 * q^8 - 3 * q^9 - q^11 + q^12 - 6 * q^13 - 4 * q^14 + 5 * q^15 + 2 * q^16 - 6 * q^17 + 3 * q^18 - 2 * q^19 + 2 * q^21 + q^22 + 6 * q^23 - q^24 + 6 * q^26 - 2 * q^27 + 4 * q^28 - 7 * q^29 - 5 * q^30 + 3 * q^31 - 2 * q^32 + 2 * q^33 + 6 * q^34 - 3 * q^36 - 2 * q^37 + 2 * q^38 - 3 * q^39 + 4 * q^41 - 2 * q^42 - 3 * q^43 - q^44 + 5 * q^45 - 6 * q^46 + 4 * q^47 + q^48 - 6 * q^49 - 3 * q^51 - 6 * q^52 + 2 * q^54 + 5 * q^55 - 4 * q^56 - q^57 + 7 * q^58 + 13 * q^59 + 5 * q^60 - 20 * q^61 - 3 * q^62 - 6 * q^63 + 2 * q^64 - 2 * q^66 + 6 * q^67 - 6 * q^68 + 3 * q^69 - 3 * q^71 + 3 * q^72 + 8 * q^73 + 2 * q^74 - 2 * q^76 - 2 * q^77 + 3 * q^78 - 14 * q^79 - 2 * q^81 - 4 * q^82 + 3 * q^83 + 2 * q^84 + 3 * q^86 - 11 * q^87 + q^88 + 10 * q^89 - 5 * q^90 - 12 * q^91 + 6 * q^92 + 4 * q^93 - 4 * q^94 - q^96 - 4 * q^97 + 6 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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