LMFDB - Embedded newform 8018.2.a.b.1.2

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			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +2.23607 q^{5} -1.61803 q^{6} +2.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +2.23607 q^{5} -1.61803 q^{6} +2.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} -2.23607 q^{10} +0.618034 q^{11} +1.61803 q^{12} -3.00000 q^{13} -2.00000 q^{14} +3.61803 q^{15} +1.00000 q^{16} -3.00000 q^{17} +0.381966 q^{18} -1.00000 q^{19} +2.23607 q^{20} +3.23607 q^{21} -0.618034 q^{22} +3.00000 q^{23} -1.61803 q^{24} +3.00000 q^{26} -5.47214 q^{27} +2.00000 q^{28} -6.85410 q^{29} -3.61803 q^{30} +2.61803 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.00000 q^{34} +4.47214 q^{35} -0.381966 q^{36} -7.70820 q^{37} +1.00000 q^{38} -4.85410 q^{39} -2.23607 q^{40} -4.70820 q^{41} -3.23607 q^{42} -9.32624 q^{43} +0.618034 q^{44} -0.854102 q^{45} -3.00000 q^{46} -9.18034 q^{47} +1.61803 q^{48} -3.00000 q^{49} -4.85410 q^{51} -3.00000 q^{52} -8.94427 q^{53} +5.47214 q^{54} +1.38197 q^{55} -2.00000 q^{56} -1.61803 q^{57} +6.85410 q^{58} +7.61803 q^{59} +3.61803 q^{60} -12.2361 q^{61} -2.61803 q^{62} -0.763932 q^{63} +1.00000 q^{64} -6.70820 q^{65} -1.00000 q^{66} +7.47214 q^{67} -3.00000 q^{68} +4.85410 q^{69} -4.47214 q^{70} -4.85410 q^{71} +0.381966 q^{72} +10.7082 q^{73} +7.70820 q^{74} -1.00000 q^{76} +1.23607 q^{77} +4.85410 q^{78} -0.291796 q^{79} +2.23607 q^{80} -7.70820 q^{81} +4.70820 q^{82} +4.85410 q^{83} +3.23607 q^{84} -6.70820 q^{85} +9.32624 q^{86} -11.0902 q^{87} -0.618034 q^{88} +13.9443 q^{89} +0.854102 q^{90} -6.00000 q^{91} +3.00000 q^{92} +4.23607 q^{93} +9.18034 q^{94} -2.23607 q^{95} -1.61803 q^{96} +0.236068 q^{97} +3.00000 q^{98} -0.236068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	2.23607	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	−1.61803	−0.660560
$7$	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
$9$	−0.381966	−0.127322
$10$	−2.23607	−0.707107
$11$	0.618034	0.186344	0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034	0.186344	0.0931721	+	0.995650i	$0.470299\pi$
$12$	1.61803	0.467086
$13$	−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
$15$	3.61803	0.934172
$16$	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	$0.618522\pi$
$18$	0.381966	0.0900303
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.23607	0.500000
$21$	3.23607	0.706168
$22$	−0.618034	−0.131765
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	−1.61803	−0.330280
$25$	0	0
$26$	3.00000	0.588348
$27$	−5.47214	−1.05311
$28$	2.00000	0.377964
$29$	−6.85410	−1.27277	−0.636387	−	0.771370i	$-0.719572\pi$
$29$	−6.85410	−1.27277	−0.636387	+	0.771370i	$0.719572\pi$
$30$	−3.61803	−0.660560
$31$	2.61803	0.470213	0.235106	−	0.971970i	$-0.424456\pi$
$31$	2.61803	0.470213	0.235106	+	0.971970i	$0.424456\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	3.00000	0.514496
$35$	4.47214	0.755929
$36$	−0.381966	−0.0636610
$37$	−7.70820	−1.26722	−0.633610	−	0.773652i	$-0.718428\pi$
$37$	−7.70820	−1.26722	−0.633610	+	0.773652i	$0.718428\pi$
$38$	1.00000	0.162221
$39$	−4.85410	−0.777278
$40$	−2.23607	−0.353553
$41$	−4.70820	−0.735298	−0.367649	−	0.929965i	$-0.619837\pi$
$41$	−4.70820	−0.735298	−0.367649	+	0.929965i	$0.619837\pi$
$42$	−3.23607	−0.499336
$43$	−9.32624	−1.42224	−0.711119	−	0.703072i	$-0.751811\pi$
$43$	−9.32624	−1.42224	−0.711119	+	0.703072i	$0.751811\pi$
$44$	0.618034	0.0931721
$45$	−0.854102	−0.127322
$46$	−3.00000	−0.442326
$47$	−9.18034	−1.33909	−0.669545	−	0.742771i	$-0.733511\pi$
$47$	−9.18034	−1.33909	−0.669545	+	0.742771i	$0.733511\pi$
$48$	1.61803	0.233543
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−4.85410	−0.679710
$52$	−3.00000	−0.416025
$53$	−8.94427	−1.22859	−0.614295	−	0.789076i	$-0.710560\pi$
$53$	−8.94427	−1.22859	−0.614295	+	0.789076i	$0.710560\pi$
$54$	5.47214	0.744663
$55$	1.38197	0.186344
$56$	−2.00000	−0.267261
$57$	−1.61803	−0.214314
$58$	6.85410	0.899988
$59$	7.61803	0.991784	0.495892	−	0.868384i	$-0.334841\pi$
$59$	7.61803	0.991784	0.495892	+	0.868384i	$0.334841\pi$
$60$	3.61803	0.467086
$61$	−12.2361	−1.56667	−0.783334	−	0.621601i	$-0.786483\pi$
$61$	−12.2361	−1.56667	−0.783334	+	0.621601i	$0.786483\pi$
$62$	−2.61803	−0.332491
$63$	−0.763932	−0.0962464
$64$	1.00000	0.125000
$65$	−6.70820	−0.832050
$66$	−1.00000	−0.123091
$67$	7.47214	0.912867	0.456433	−	0.889758i	$-0.349127\pi$
$67$	7.47214	0.912867	0.456433	+	0.889758i	$0.349127\pi$
$68$	−3.00000	−0.363803
$69$	4.85410	0.584365
$70$	−4.47214	−0.534522
$71$	−4.85410	−0.576076	−0.288038	−	0.957619i	$-0.593003\pi$
$71$	−4.85410	−0.576076	−0.288038	+	0.957619i	$0.593003\pi$
$72$	0.381966	0.0450151
$73$	10.7082	1.25330	0.626650	−	0.779301i	$-0.284425\pi$
$73$	10.7082	1.25330	0.626650	+	0.779301i	$0.284425\pi$
$74$	7.70820	0.896061
$75$	0	0
$76$	−1.00000	−0.114708
$77$	1.23607	0.140863
$78$	4.85410	0.549619
$79$	−0.291796	−0.0328296	−0.0164148	−	0.999865i	$-0.505225\pi$
$79$	−0.291796	−0.0328296	−0.0164148	+	0.999865i	$0.505225\pi$
$80$	2.23607	0.250000
$81$	−7.70820	−0.856467
$82$	4.70820	0.519934
$83$	4.85410	0.532807	0.266403	−	0.963862i	$-0.414165\pi$
$83$	4.85410	0.532807	0.266403	+	0.963862i	$0.414165\pi$
$84$	3.23607	0.353084
$85$	−6.70820	−0.727607
$86$	9.32624	1.00567
$87$	−11.0902	−1.18899
$88$	−0.618034	−0.0658826
$89$	13.9443	1.47809	0.739045	−	0.673656i	$-0.235277\pi$
$89$	13.9443	1.47809	0.739045	+	0.673656i	$0.235277\pi$
$90$	0.854102	0.0900303
$91$	−6.00000	−0.628971
$92$	3.00000	0.312772
$93$	4.23607	0.439260
$94$	9.18034	0.946880
$95$	−2.23607	−0.229416
$96$	−1.61803	−0.165140
$97$	0.236068	0.0239691	0.0119845	−	0.999928i	$-0.496185\pi$
$97$	0.236068	0.0239691	0.0119845	+	0.999928i	$0.496185\pi$
$98$	3.00000	0.303046
$99$	−0.236068	−0.0237257
$100$	0	0
$101$	1.00000	0.0995037	0.0497519	−	0.998762i	$-0.484157\pi$
$101$	1.00000	0.0995037	0.0497519	+	0.998762i	$0.484157\pi$
$102$	4.85410	0.480628
$103$	−1.09017	−0.107418	−0.0537088	−	0.998557i	$-0.517104\pi$
$103$	−1.09017	−0.107418	−0.0537088	+	0.998557i	$0.517104\pi$
$104$	3.00000	0.294174
$105$	7.23607	0.706168
$106$	8.94427	0.868744
$107$	−6.09017	−0.588759	−0.294379	−	0.955689i	$-0.595113\pi$
$107$	−6.09017	−0.588759	−0.294379	+	0.955689i	$0.595113\pi$
$108$	−5.47214	−0.526557
$109$	−3.23607	−0.309959	−0.154980	−	0.987918i	$-0.549531\pi$
$109$	−3.23607	−0.309959	−0.154980	+	0.987918i	$0.549531\pi$
$110$	−1.38197	−0.131765
$111$	−12.4721	−1.18380
$112$	2.00000	0.188982
$113$	−19.4721	−1.83178	−0.915892	−	0.401424i	$-0.868515\pi$
$113$	−19.4721	−1.83178	−0.915892	+	0.401424i	$0.868515\pi$
$114$	1.61803	0.151543
$115$	6.70820	0.625543
$116$	−6.85410	−0.636387
$117$	1.14590	0.105938
$118$	−7.61803	−0.701297
$119$	−6.00000	−0.550019
$120$	−3.61803	−0.330280
$121$	−10.6180	−0.965276
$122$	12.2361	1.10780
$123$	−7.61803	−0.686895
$124$	2.61803	0.235106
$125$	−11.1803	−1.00000
$126$	0.763932	0.0680565
$127$	18.3262	1.62619	0.813095	−	0.582131i	$-0.197781\pi$
$127$	18.3262	1.62619	0.813095	+	0.582131i	$0.197781\pi$
$128$	−1.00000	−0.0883883
$129$	−15.0902	−1.32862
$130$	6.70820	0.588348
$131$	15.3820	1.34393	0.671964	−	0.740584i	$-0.265451\pi$
$131$	15.3820	1.34393	0.671964	+	0.740584i	$0.265451\pi$
$132$	1.00000	0.0870388
$133$	−2.00000	−0.173422
$134$	−7.47214	−0.645494
$135$	−12.2361	−1.05311
$136$	3.00000	0.257248
$137$	6.41641	0.548191	0.274095	−	0.961703i	$-0.411622\pi$
$137$	6.41641	0.548191	0.274095	+	0.961703i	$0.411622\pi$
$138$	−4.85410	−0.413209
$139$	17.8885	1.51729	0.758643	−	0.651506i	$-0.225863\pi$
$139$	17.8885	1.51729	0.758643	+	0.651506i	$0.225863\pi$
$140$	4.47214	0.377964
$141$	−14.8541	−1.25094
$142$	4.85410	0.407347
$143$	−1.85410	−0.155048
$144$	−0.381966	−0.0318305
$145$	−15.3262	−1.27277
$146$	−10.7082	−0.886217
$147$	−4.85410	−0.400360
$148$	−7.70820	−0.633610
$149$	−17.8541	−1.46267	−0.731333	−	0.682021i	$-0.761101\pi$
$149$	−17.8541	−1.46267	−0.731333	+	0.682021i	$0.761101\pi$
$150$	0	0
$151$	−3.85410	−0.313642	−0.156821	−	0.987627i	$-0.550125\pi$
$151$	−3.85410	−0.313642	−0.156821	+	0.987627i	$0.550125\pi$
$152$	1.00000	0.0811107
$153$	1.14590	0.0926404
$154$	−1.23607	−0.0996052
$155$	5.85410	0.470213
$156$	−4.85410	−0.388639
$157$	−13.7639	−1.09848	−0.549241	−	0.835664i	$-0.685083\pi$
$157$	−13.7639	−1.09848	−0.549241	+	0.835664i	$0.685083\pi$
$158$	0.291796	0.0232140
$159$	−14.4721	−1.14772
$160$	−2.23607	−0.176777
$161$	6.00000	0.472866
$162$	7.70820	0.605614
$163$	−10.8885	−0.852857	−0.426428	−	0.904521i	$-0.640228\pi$
$163$	−10.8885	−0.852857	−0.426428	+	0.904521i	$0.640228\pi$
$164$	−4.70820	−0.367649
$165$	2.23607	0.174078
$166$	−4.85410	−0.376751
$167$	0.291796	0.0225799	0.0112899	−	0.999936i	$-0.496406\pi$
$167$	0.291796	0.0225799	0.0112899	+	0.999936i	$0.496406\pi$
$168$	−3.23607	−0.249668
$169$	−4.00000	−0.307692
$170$	6.70820	0.514496
$171$	0.381966	0.0292097
$172$	−9.32624	−0.711119
$173$	−2.61803	−0.199045	−0.0995227	−	0.995035i	$-0.531732\pi$
$173$	−2.61803	−0.199045	−0.0995227	+	0.995035i	$0.531732\pi$
$174$	11.0902	0.840744
$175$	0	0
$176$	0.618034	0.0465861
$177$	12.3262	0.926497
$178$	−13.9443	−1.04517
$179$	15.2361	1.13880	0.569399	−	0.822062i	$-0.307176\pi$
$179$	15.2361	1.13880	0.569399	+	0.822062i	$0.307176\pi$
$180$	−0.854102	−0.0636610
$181$	18.4164	1.36888	0.684440	−	0.729069i	$-0.260047\pi$
$181$	18.4164	1.36888	0.684440	+	0.729069i	$0.260047\pi$
$182$	6.00000	0.444750
$183$	−19.7984	−1.46354
$184$	−3.00000	−0.221163
$185$	−17.2361	−1.26722
$186$	−4.23607	−0.310604
$187$	−1.85410	−0.135585
$188$	−9.18034	−0.669545
$189$	−10.9443	−0.796079
$190$	2.23607	0.162221
$191$	−3.94427	−0.285397	−0.142699	−	0.989766i	$-0.545578\pi$
$191$	−3.94427	−0.285397	−0.142699	+	0.989766i	$0.545578\pi$
$192$	1.61803	0.116772
$193$	−1.52786	−0.109978	−0.0549890	−	0.998487i	$-0.517512\pi$
$193$	−1.52786	−0.109978	−0.0549890	+	0.998487i	$0.517512\pi$
$194$	−0.236068	−0.0169487
$195$	−10.8541	−0.777278
$196$	−3.00000	−0.214286
$197$	23.8885	1.70199	0.850994	−	0.525175i	$-0.176000\pi$
$197$	23.8885	1.70199	0.850994	+	0.525175i	$0.176000\pi$
$198$	0.236068	0.0167766
$199$	26.4164	1.87261	0.936305	−	0.351189i	$-0.114222\pi$
$199$	26.4164	1.87261	0.936305	+	0.351189i	$0.114222\pi$
$200$	0	0
$201$	12.0902	0.852775
$202$	−1.00000	−0.0703598
$203$	−13.7082	−0.962127
$204$	−4.85410	−0.339855
$205$	−10.5279	−0.735298
$206$	1.09017	0.0759557
$207$	−1.14590	−0.0796454
$208$	−3.00000	−0.208013
$209$	−0.618034	−0.0427503
$210$	−7.23607	−0.499336
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−8.94427	−0.614295
$213$	−7.85410	−0.538154
$214$	6.09017	0.416315
$215$	−20.8541	−1.42224
$216$	5.47214	0.372332
$217$	5.23607	0.355447
$218$	3.23607	0.219174
$219$	17.3262	1.17080
$220$	1.38197	0.0931721
$221$	9.00000	0.605406
$222$	12.4721	0.837075
$223$	−20.2361	−1.35511	−0.677554	−	0.735473i	$-0.736960\pi$
$223$	−20.2361	−1.35511	−0.677554	+	0.735473i	$0.736960\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	19.4721	1.29527
$227$	−10.2361	−0.679392	−0.339696	−	0.940535i	$-0.610324\pi$
$227$	−10.2361	−0.679392	−0.339696	+	0.940535i	$0.610324\pi$
$228$	−1.61803	−0.107157
$229$	−23.3262	−1.54144	−0.770721	−	0.637173i	$-0.780104\pi$
$229$	−23.3262	−1.54144	−0.770721	+	0.637173i	$0.780104\pi$
$230$	−6.70820	−0.442326
$231$	2.00000	0.131590
$232$	6.85410	0.449994
$233$	20.4164	1.33752	0.668762	−	0.743477i	$-0.266825\pi$
$233$	20.4164	1.33752	0.668762	+	0.743477i	$0.266825\pi$
$234$	−1.14590	−0.0749097
$235$	−20.5279	−1.33909
$236$	7.61803	0.495892
$237$	−0.472136	−0.0306685
$238$	6.00000	0.388922
$239$	23.2361	1.50302	0.751508	−	0.659724i	$-0.229327\pi$
$239$	23.2361	1.50302	0.751508	+	0.659724i	$0.229327\pi$
$240$	3.61803	0.233543
$241$	11.2705	0.725997	0.362999	−	0.931790i	$-0.381753\pi$
$241$	11.2705	0.725997	0.362999	+	0.931790i	$0.381753\pi$
$242$	10.6180	0.682553
$243$	3.94427	0.253025
$244$	−12.2361	−0.783334
$245$	−6.70820	−0.428571
$246$	7.61803	0.485708
$247$	3.00000	0.190885
$248$	−2.61803	−0.166245
$249$	7.85410	0.497733
$250$	11.1803	0.707107
$251$	1.09017	0.0688109	0.0344055	−	0.999408i	$-0.489046\pi$
$251$	1.09017	0.0688109	0.0344055	+	0.999408i	$0.489046\pi$
$252$	−0.763932	−0.0481232
$253$	1.85410	0.116566
$254$	−18.3262	−1.14989
$255$	−10.8541	−0.679710
$256$	1.00000	0.0625000
$257$	−14.1803	−0.884545	−0.442273	−	0.896881i	$-0.645828\pi$
$257$	−14.1803	−0.884545	−0.442273	+	0.896881i	$0.645828\pi$
$258$	15.0902	0.939473
$259$	−15.4164	−0.957929
$260$	−6.70820	−0.416025
$261$	2.61803	0.162052
$262$	−15.3820	−0.950301
$263$	25.9443	1.59979	0.799896	−	0.600138i	$-0.204888\pi$
$263$	25.9443	1.59979	0.799896	+	0.600138i	$0.204888\pi$
$264$	−1.00000	−0.0615457
$265$	−20.0000	−1.22859
$266$	2.00000	0.122628
$267$	22.5623	1.38079
$268$	7.47214	0.456433
$269$	−11.3262	−0.690573	−0.345286	−	0.938497i	$-0.612218\pi$
$269$	−11.3262	−0.690573	−0.345286	+	0.938497i	$0.612218\pi$
$270$	12.2361	0.744663
$271$	5.29180	0.321454	0.160727	−	0.986999i	$-0.448616\pi$
$271$	5.29180	0.321454	0.160727	+	0.986999i	$0.448616\pi$
$272$	−3.00000	−0.181902
$273$	−9.70820	−0.587567
$274$	−6.41641	−0.387629
$275$	0	0
$276$	4.85410	0.292183
$277$	20.8885	1.25507	0.627535	−	0.778588i	$-0.284064\pi$
$277$	20.8885	1.25507	0.627535	+	0.778588i	$0.284064\pi$
$278$	−17.8885	−1.07288
$279$	−1.00000	−0.0598684
$280$	−4.47214	−0.267261
$281$	−7.76393	−0.463157	−0.231579	−	0.972816i	$-0.574389\pi$
$281$	−7.76393	−0.463157	−0.231579	+	0.972816i	$0.574389\pi$
$282$	14.8541	0.884549
$283$	7.43769	0.442125	0.221063	−	0.975260i	$-0.429048\pi$
$283$	7.43769	0.442125	0.221063	+	0.975260i	$0.429048\pi$
$284$	−4.85410	−0.288038
$285$	−3.61803	−0.214314
$286$	1.85410	0.109635
$287$	−9.41641	−0.555833
$288$	0.381966	0.0225076
$289$	−8.00000	−0.470588
$290$	15.3262	0.899988
$291$	0.381966	0.0223912
$292$	10.7082	0.626650
$293$	−2.38197	−0.139156	−0.0695780	−	0.997577i	$-0.522165\pi$
$293$	−2.38197	−0.139156	−0.0695780	+	0.997577i	$0.522165\pi$
$294$	4.85410	0.283097
$295$	17.0344	0.991784
$296$	7.70820	0.448030
$297$	−3.38197	−0.196242
$298$	17.8541	1.03426
$299$	−9.00000	−0.520483
$300$	0	0
$301$	−18.6525	−1.07511
$302$	3.85410	0.221779
$303$	1.61803	0.0929536
$304$	−1.00000	−0.0573539
$305$	−27.3607	−1.56667
$306$	−1.14590	−0.0655066
$307$	−0.819660	−0.0467805	−0.0233902	−	0.999726i	$-0.507446\pi$
$307$	−0.819660	−0.0467805	−0.0233902	+	0.999726i	$0.507446\pi$
$308$	1.23607	0.0704315
$309$	−1.76393	−0.100347
$310$	−5.85410	−0.332491
$311$	33.0344	1.87321	0.936606	−	0.350385i	$-0.113949\pi$
$311$	33.0344	1.87321	0.936606	+	0.350385i	$0.113949\pi$
$312$	4.85410	0.274809
$313$	−5.09017	−0.287713	−0.143857	−	0.989599i	$-0.545950\pi$
$313$	−5.09017	−0.287713	−0.143857	+	0.989599i	$0.545950\pi$
$314$	13.7639	0.776744
$315$	−1.70820	−0.0962464
$316$	−0.291796	−0.0164148
$317$	0.819660	0.0460367	0.0230183	−	0.999735i	$-0.492672\pi$
$317$	0.819660	0.0460367	0.0230183	+	0.999735i	$0.492672\pi$
$318$	14.4721	0.811557
$319$	−4.23607	−0.237174
$320$	2.23607	0.125000
$321$	−9.85410	−0.550002
$322$	−6.00000	−0.334367
$323$	3.00000	0.166924
$324$	−7.70820	−0.428234
$325$	0	0
$326$	10.8885	0.603061
$327$	−5.23607	−0.289555
$328$	4.70820	0.259967
$329$	−18.3607	−1.01226
$330$	−2.23607	−0.123091
$331$	14.1803	0.779422	0.389711	−	0.920937i	$-0.372575\pi$
$331$	14.1803	0.779422	0.389711	+	0.920937i	$0.372575\pi$
$332$	4.85410	0.266403
$333$	2.94427	0.161345
$334$	−0.291796	−0.0159664
$335$	16.7082	0.912867
$336$	3.23607	0.176542
$337$	8.94427	0.487226	0.243613	−	0.969873i	$-0.421667\pi$
$337$	8.94427	0.487226	0.243613	+	0.969873i	$0.421667\pi$
$338$	4.00000	0.217571
$339$	−31.5066	−1.71120
$340$	−6.70820	−0.363803
$341$	1.61803	0.0876215
$342$	−0.381966	−0.0206544
$343$	−20.0000	−1.07990
$344$	9.32624	0.502837
$345$	10.8541	0.584365
$346$	2.61803	0.140746
$347$	18.4721	0.991636	0.495818	−	0.868426i	$-0.334868\pi$
$347$	18.4721	0.991636	0.495818	+	0.868426i	$0.334868\pi$
$348$	−11.0902	−0.594496
$349$	15.9098	0.851634	0.425817	−	0.904809i	$-0.359987\pi$
$349$	15.9098	0.851634	0.425817	+	0.904809i	$0.359987\pi$
$350$	0	0
$351$	16.4164	0.876243
$352$	−0.618034	−0.0329413
$353$	−25.5623	−1.36054	−0.680272	−	0.732960i	$-0.738138\pi$
$353$	−25.5623	−1.36054	−0.680272	+	0.732960i	$0.738138\pi$
$354$	−12.3262	−0.655132
$355$	−10.8541	−0.576076
$356$	13.9443	0.739045
$357$	−9.70820	−0.513813
$358$	−15.2361	−0.805251
$359$	21.3607	1.12737	0.563687	−	0.825989i	$-0.309383\pi$
$359$	21.3607	1.12737	0.563687	+	0.825989i	$0.309383\pi$
$360$	0.854102	0.0450151
$361$	1.00000	0.0526316
$362$	−18.4164	−0.967945
$363$	−17.1803	−0.901734
$364$	−6.00000	−0.314485
$365$	23.9443	1.25330
$366$	19.7984	1.03488
$367$	−16.5066	−0.861636	−0.430818	−	0.902439i	$-0.641775\pi$
$367$	−16.5066	−0.861636	−0.430818	+	0.902439i	$0.641775\pi$
$368$	3.00000	0.156386
$369$	1.79837	0.0936196
$370$	17.2361	0.896061
$371$	−17.8885	−0.928727
$372$	4.23607	0.219630
$373$	10.3820	0.537558	0.268779	−	0.963202i	$-0.413380\pi$
$373$	10.3820	0.537558	0.268779	+	0.963202i	$0.413380\pi$
$374$	1.85410	0.0958733
$375$	−18.0902	−0.934172
$376$	9.18034	0.473440
$377$	20.5623	1.05901
$378$	10.9443	0.562913
$379$	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
$381$	29.6525	1.51914
$382$	3.94427	0.201807
$383$	−23.5279	−1.20222	−0.601109	−	0.799167i	$-0.705274\pi$
$383$	−23.5279	−1.20222	−0.601109	+	0.799167i	$0.705274\pi$
$384$	−1.61803	−0.0825700
$385$	2.76393	0.140863
$386$	1.52786	0.0777662
$387$	3.56231	0.181082
$388$	0.236068	0.0119845
$389$	21.2361	1.07671	0.538356	−	0.842718i	$-0.319046\pi$
$389$	21.2361	1.07671	0.538356	+	0.842718i	$0.319046\pi$
$390$	10.8541	0.549619
$391$	−9.00000	−0.455150
$392$	3.00000	0.151523
$393$	24.8885	1.25546
$394$	−23.8885	−1.20349
$395$	−0.652476	−0.0328296
$396$	−0.236068	−0.0118629
$397$	−7.14590	−0.358642	−0.179321	−	0.983791i	$-0.557390\pi$
$397$	−7.14590	−0.358642	−0.179321	+	0.983791i	$0.557390\pi$
$398$	−26.4164	−1.32413
$399$	−3.23607	−0.162006
$400$	0	0
$401$	−34.1803	−1.70688	−0.853442	−	0.521187i	$-0.825489\pi$
$401$	−34.1803	−1.70688	−0.853442	+	0.521187i	$0.825489\pi$
$402$	−12.0902	−0.603003
$403$	−7.85410	−0.391241
$404$	1.00000	0.0497519
$405$	−17.2361	−0.856467
$406$	13.7082	0.680327
$407$	−4.76393	−0.236139
$408$	4.85410	0.240314
$409$	−13.0902	−0.647267	−0.323634	−	0.946182i	$-0.604905\pi$
$409$	−13.0902	−0.647267	−0.323634	+	0.946182i	$0.604905\pi$
$410$	10.5279	0.519934
$411$	10.3820	0.512105
$412$	−1.09017	−0.0537088
$413$	15.2361	0.749718
$414$	1.14590	0.0563178
$415$	10.8541	0.532807
$416$	3.00000	0.147087
$417$	28.9443	1.41741
$418$	0.618034	0.0302290
$419$	23.8885	1.16703	0.583516	−	0.812102i	$-0.301677\pi$
$419$	23.8885	1.16703	0.583516	+	0.812102i	$0.301677\pi$
$420$	7.23607	0.353084
$421$	1.56231	0.0761421	0.0380711	−	0.999275i	$-0.487879\pi$
$421$	1.56231	0.0761421	0.0380711	+	0.999275i	$0.487879\pi$
$422$	1.00000	0.0486792
$423$	3.50658	0.170496
$424$	8.94427	0.434372
$425$	0	0
$426$	7.85410	0.380532
$427$	−24.4721	−1.18429
$428$	−6.09017	−0.294379
$429$	−3.00000	−0.144841
$430$	20.8541	1.00567
$431$	9.23607	0.444886	0.222443	−	0.974946i	$-0.428597\pi$
$431$	9.23607	0.444886	0.222443	+	0.974946i	$0.428597\pi$
$432$	−5.47214	−0.263278
$433$	−15.4721	−0.743543	−0.371772	−	0.928324i	$-0.621250\pi$
$433$	−15.4721	−0.743543	−0.371772	+	0.928324i	$0.621250\pi$
$434$	−5.23607	−0.251339
$435$	−24.7984	−1.18899
$436$	−3.23607	−0.154980
$437$	−3.00000	−0.143509
$438$	−17.3262	−0.827880
$439$	−40.3951	−1.92795	−0.963977	−	0.265986i	$-0.914303\pi$
$439$	−40.3951	−1.92795	−0.963977	+	0.265986i	$0.914303\pi$
$440$	−1.38197	−0.0658826
$441$	1.14590	0.0545666
$442$	−9.00000	−0.428086
$443$	15.2361	0.723887	0.361944	−	0.932200i	$-0.382113\pi$
$443$	15.2361	0.723887	0.361944	+	0.932200i	$0.382113\pi$
$444$	−12.4721	−0.591901
$445$	31.1803	1.47809
$446$	20.2361	0.958206
$447$	−28.8885	−1.36638
$448$	2.00000	0.0944911
$449$	−19.2918	−0.910436	−0.455218	−	0.890380i	$-0.650439\pi$
$449$	−19.2918	−0.910436	−0.455218	+	0.890380i	$0.650439\pi$
$450$	0	0
$451$	−2.90983	−0.137019
$452$	−19.4721	−0.915892
$453$	−6.23607	−0.292996
$454$	10.2361	0.480402
$455$	−13.4164	−0.628971
$456$	1.61803	0.0757714
$457$	−11.3262	−0.529819	−0.264910	−	0.964273i	$-0.585342\pi$
$457$	−11.3262	−0.529819	−0.264910	+	0.964273i	$0.585342\pi$
$458$	23.3262	1.08996
$459$	16.4164	0.766252
$460$	6.70820	0.312772
$461$	24.7426	1.15238	0.576190	−	0.817316i	$-0.304539\pi$
$461$	24.7426	1.15238	0.576190	+	0.817316i	$0.304539\pi$
$462$	−2.00000	−0.0930484
$463$	18.7639	0.872034	0.436017	−	0.899938i	$-0.356389\pi$
$463$	18.7639	0.872034	0.436017	+	0.899938i	$0.356389\pi$
$464$	−6.85410	−0.318194
$465$	9.47214	0.439260
$466$	−20.4164	−0.945772
$467$	6.88854	0.318764	0.159382	−	0.987217i	$-0.449050\pi$
$467$	6.88854	0.318764	0.159382	+	0.987217i	$0.449050\pi$
$468$	1.14590	0.0529692
$469$	14.9443	0.690062
$470$	20.5279	0.946880
$471$	−22.2705	−1.02617
$472$	−7.61803	−0.350648
$473$	−5.76393	−0.265026
$474$	0.472136	0.0216859
$475$	0	0
$476$	−6.00000	−0.275010
$477$	3.41641	0.156427
$478$	−23.2361	−1.06279
$479$	−6.34752	−0.290026	−0.145013	−	0.989430i	$-0.546322\pi$
$479$	−6.34752	−0.290026	−0.145013	+	0.989430i	$0.546322\pi$
$480$	−3.61803	−0.165140
$481$	23.1246	1.05439
$482$	−11.2705	−0.513358
$483$	9.70820	0.441739
$484$	−10.6180	−0.482638
$485$	0.527864	0.0239691
$486$	−3.94427	−0.178916
$487$	12.7984	0.579950	0.289975	−	0.957034i	$-0.406353\pi$
$487$	12.7984	0.579950	0.289975	+	0.957034i	$0.406353\pi$
$488$	12.2361	0.553901
$489$	−17.6180	−0.796715
$490$	6.70820	0.303046
$491$	−3.94427	−0.178002	−0.0890012	−	0.996032i	$-0.528368\pi$
$491$	−3.94427	−0.178002	−0.0890012	+	0.996032i	$0.528368\pi$
$492$	−7.61803	−0.343447
$493$	20.5623	0.926080
$494$	−3.00000	−0.134976
$495$	−0.527864	−0.0237257
$496$	2.61803	0.117553
$497$	−9.70820	−0.435472
$498$	−7.85410	−0.351951
$499$	−34.5279	−1.54568	−0.772840	−	0.634601i	$-0.781164\pi$
$499$	−34.5279	−1.54568	−0.772840	+	0.634601i	$0.781164\pi$
$500$	−11.1803	−0.500000
$501$	0.472136	0.0210935
$502$	−1.09017	−0.0486567
$503$	14.8328	0.661363	0.330681	−	0.943742i	$-0.392721\pi$
$503$	14.8328	0.661363	0.330681	+	0.943742i	$0.392721\pi$
$504$	0.763932	0.0340282
$505$	2.23607	0.0995037
$506$	−1.85410	−0.0824249
$507$	−6.47214	−0.287438
$508$	18.3262	0.813095
$509$	24.7082	1.09517	0.547586	−	0.836749i	$-0.315547\pi$
$509$	24.7082	1.09517	0.547586	+	0.836749i	$0.315547\pi$
$510$	10.8541	0.480628
$511$	21.4164	0.947406
$512$	−1.00000	−0.0441942
$513$	5.47214	0.241601
$514$	14.1803	0.625468
$515$	−2.43769	−0.107418
$516$	−15.0902	−0.664308
$517$	−5.67376	−0.249532
$518$	15.4164	0.677358
$519$	−4.23607	−0.185943
$520$	6.70820	0.294174
$521$	14.6738	0.642869	0.321435	−	0.946932i	$-0.395835\pi$
$521$	14.6738	0.642869	0.321435	+	0.946932i	$0.395835\pi$
$522$	−2.61803	−0.114588
$523$	37.4721	1.63854	0.819271	−	0.573406i	$-0.194378\pi$
$523$	37.4721	1.63854	0.819271	+	0.573406i	$0.194378\pi$
$524$	15.3820	0.671964
$525$	0	0
$526$	−25.9443	−1.13122
$527$	−7.85410	−0.342130
$528$	1.00000	0.0435194
$529$	−14.0000	−0.608696
$530$	20.0000	0.868744
$531$	−2.90983	−0.126276
$532$	−2.00000	−0.0867110
$533$	14.1246	0.611805
$534$	−22.5623	−0.976366
$535$	−13.6180	−0.588759
$536$	−7.47214	−0.322747
$537$	24.6525	1.06383
$538$	11.3262	0.488309
$539$	−1.85410	−0.0798618
$540$	−12.2361	−0.526557
$541$	36.7984	1.58209	0.791043	−	0.611761i	$-0.209538\pi$
$541$	36.7984	1.58209	0.791043	+	0.611761i	$0.209538\pi$
$542$	−5.29180	−0.227302
$543$	29.7984	1.27877
$544$	3.00000	0.128624
$545$	−7.23607	−0.309959
$546$	9.70820	0.415473
$547$	29.4508	1.25923	0.629614	−	0.776908i	$-0.283213\pi$
$547$	29.4508	1.25923	0.629614	+	0.776908i	$0.283213\pi$
$548$	6.41641	0.274095
$549$	4.67376	0.199471
$550$	0	0
$551$	6.85410	0.291995
$552$	−4.85410	−0.206604
$553$	−0.583592	−0.0248169
$554$	−20.8885	−0.887469
$555$	−27.8885	−1.18380
$556$	17.8885	0.758643
$557$	15.9443	0.675580	0.337790	−	0.941221i	$-0.390321\pi$
$557$	15.9443	0.675580	0.337790	+	0.941221i	$0.390321\pi$
$558$	1.00000	0.0423334
$559$	27.9787	1.18337
$560$	4.47214	0.188982
$561$	−3.00000	−0.126660
$562$	7.76393	0.327502
$563$	−40.2492	−1.69630	−0.848151	−	0.529754i	$-0.822284\pi$
$563$	−40.2492	−1.69630	−0.848151	+	0.529754i	$0.822284\pi$
$564$	−14.8541	−0.625471
$565$	−43.5410	−1.83178
$566$	−7.43769	−0.312630
$567$	−15.4164	−0.647428
$568$	4.85410	0.203674
$569$	21.0344	0.881810	0.440905	−	0.897554i	$-0.354658\pi$
$569$	21.0344	0.881810	0.440905	+	0.897554i	$0.354658\pi$
$570$	3.61803	0.151543
$571$	33.8541	1.41675	0.708375	−	0.705836i	$-0.249429\pi$
$571$	33.8541	1.41675	0.708375	+	0.705836i	$0.249429\pi$
$572$	−1.85410	−0.0775239
$573$	−6.38197	−0.266610
$574$	9.41641	0.393033
$575$	0	0
$576$	−0.381966	−0.0159153
$577$	−26.0902	−1.08615	−0.543074	−	0.839685i	$-0.682740\pi$
$577$	−26.0902	−1.08615	−0.543074	+	0.839685i	$0.682740\pi$
$578$	8.00000	0.332756
$579$	−2.47214	−0.102738
$580$	−15.3262	−0.636387
$581$	9.70820	0.402764
$582$	−0.381966	−0.0158330
$583$	−5.52786	−0.228941
$584$	−10.7082	−0.443109
$585$	2.56231	0.105938
$586$	2.38197	0.0983981
$587$	−22.2361	−0.917781	−0.458890	−	0.888493i	$-0.651753\pi$
$587$	−22.2361	−0.917781	−0.458890	+	0.888493i	$0.651753\pi$
$588$	−4.85410	−0.200180
$589$	−2.61803	−0.107874
$590$	−17.0344	−0.701297
$591$	38.6525	1.58995
$592$	−7.70820	−0.316805
$593$	−29.0000	−1.19089	−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000	−1.19089	−0.595444	+	0.803397i	$0.703024\pi$
$594$	3.38197	0.138764
$595$	−13.4164	−0.550019
$596$	−17.8541	−0.731333
$597$	42.7426	1.74934
$598$	9.00000	0.368037
$599$	−48.7426	−1.99157	−0.995785	−	0.0917154i	$-0.970765\pi$
$599$	−48.7426	−1.99157	−0.995785	+	0.0917154i	$0.970765\pi$
$600$	0	0
$601$	−16.5967	−0.676995	−0.338498	−	0.940967i	$-0.609919\pi$
$601$	−16.5967	−0.676995	−0.338498	+	0.940967i	$0.609919\pi$
$602$	18.6525	0.760218
$603$	−2.85410	−0.116228
$604$	−3.85410	−0.156821
$605$	−23.7426	−0.965276
$606$	−1.61803	−0.0657281
$607$	−11.7639	−0.477483	−0.238742	−	0.971083i	$-0.576735\pi$
$607$	−11.7639	−0.477483	−0.238742	+	0.971083i	$0.576735\pi$
$608$	1.00000	0.0405554
$609$	−22.1803	−0.898793
$610$	27.3607	1.10780
$611$	27.5410	1.11419
$612$	1.14590	0.0463202
$613$	−32.7426	−1.32246	−0.661232	−	0.750182i	$-0.729966\pi$
$613$	−32.7426	−1.32246	−0.661232	+	0.750182i	$0.729966\pi$
$614$	0.819660	0.0330788
$615$	−17.0344	−0.686895
$616$	−1.23607	−0.0498026
$617$	3.36068	0.135296	0.0676479	−	0.997709i	$-0.478451\pi$
$617$	3.36068	0.135296	0.0676479	+	0.997709i	$0.478451\pi$
$618$	1.76393	0.0709558
$619$	−18.9443	−0.761435	−0.380717	−	0.924691i	$-0.624323\pi$
$619$	−18.9443	−0.761435	−0.380717	+	0.924691i	$0.624323\pi$
$620$	5.85410	0.235106
$621$	−16.4164	−0.658768
$622$	−33.0344	−1.32456
$623$	27.8885	1.11733
$624$	−4.85410	−0.194320
$625$	−25.0000	−1.00000
$626$	5.09017	0.203444
$627$	−1.00000	−0.0399362
$628$	−13.7639	−0.549241
$629$	23.1246	0.922039
$630$	1.70820	0.0680565
$631$	−25.9443	−1.03283	−0.516413	−	0.856340i	$-0.672733\pi$
$631$	−25.9443	−1.03283	−0.516413	+	0.856340i	$0.672733\pi$
$632$	0.291796	0.0116070
$633$	−1.61803	−0.0643111
$634$	−0.819660	−0.0325529
$635$	40.9787	1.62619
$636$	−14.4721	−0.573858
$637$	9.00000	0.356593
$638$	4.23607	0.167708
$639$	1.85410	0.0733471
$640$	−2.23607	−0.0883883
$641$	−10.0902	−0.398538	−0.199269	−	0.979945i	$-0.563857\pi$
$641$	−10.0902	−0.398538	−0.199269	+	0.979945i	$0.563857\pi$
$642$	9.85410	0.388910
$643$	35.6525	1.40600	0.702998	−	0.711192i	$-0.251844\pi$
$643$	35.6525	1.40600	0.702998	+	0.711192i	$0.251844\pi$
$644$	6.00000	0.236433
$645$	−33.7426	−1.32862
$646$	−3.00000	−0.118033
$647$	−20.4508	−0.804006	−0.402003	−	0.915638i	$-0.631686\pi$
$647$	−20.4508	−0.804006	−0.402003	+	0.915638i	$0.631686\pi$
$648$	7.70820	0.302807
$649$	4.70820	0.184813
$650$	0	0
$651$	8.47214	0.332049
$652$	−10.8885	−0.426428
$653$	−18.3607	−0.718509	−0.359254	−	0.933240i	$-0.616969\pi$
$653$	−18.3607	−0.718509	−0.359254	+	0.933240i	$0.616969\pi$
$654$	5.23607	0.204746
$655$	34.3951	1.34393
$656$	−4.70820	−0.183824
$657$	−4.09017	−0.159573
$658$	18.3607	0.715774
$659$	−5.65248	−0.220189	−0.110095	−	0.993921i	$-0.535115\pi$
$659$	−5.65248	−0.220189	−0.110095	+	0.993921i	$0.535115\pi$
$660$	2.23607	0.0870388
$661$	−31.2361	−1.21494	−0.607471	−	0.794342i	$-0.707816\pi$
$661$	−31.2361	−1.21494	−0.607471	+	0.794342i	$0.707816\pi$
$662$	−14.1803	−0.551135
$663$	14.5623	0.565553
$664$	−4.85410	−0.188376
$665$	−4.47214	−0.173422
$666$	−2.94427	−0.114088
$667$	−20.5623	−0.796176
$668$	0.291796	0.0112899
$669$	−32.7426	−1.26590
$670$	−16.7082	−0.645494
$671$	−7.56231	−0.291940
$672$	−3.23607	−0.124834
$673$	−36.6180	−1.41152	−0.705761	−	0.708450i	$-0.749395\pi$
$673$	−36.6180	−1.41152	−0.705761	+	0.708450i	$0.749395\pi$
$674$	−8.94427	−0.344520
$675$	0	0
$676$	−4.00000	−0.153846
$677$	−35.4721	−1.36330	−0.681652	−	0.731676i	$-0.738738\pi$
$677$	−35.4721	−1.36330	−0.681652	+	0.731676i	$0.738738\pi$
$678$	31.5066	1.21000
$679$	0.472136	0.0181189
$680$	6.70820	0.257248
$681$	−16.5623	−0.634669
$682$	−1.61803	−0.0619577
$683$	−29.0000	−1.10965	−0.554827	−	0.831966i	$-0.687216\pi$
$683$	−29.0000	−1.10965	−0.554827	+	0.831966i	$0.687216\pi$
$684$	0.381966	0.0146048
$685$	14.3475	0.548191
$686$	20.0000	0.763604
$687$	−37.7426	−1.43997
$688$	−9.32624	−0.355559
$689$	26.8328	1.02225
$690$	−10.8541	−0.413209
$691$	23.8541	0.907453	0.453726	−	0.891141i	$-0.350094\pi$
$691$	23.8541	0.907453	0.453726	+	0.891141i	$0.350094\pi$
$692$	−2.61803	−0.0995227
$693$	−0.472136	−0.0179350
$694$	−18.4721	−0.701193
$695$	40.0000	1.51729
$696$	11.0902	0.420372
$697$	14.1246	0.535008
$698$	−15.9098	−0.602196
$699$	33.0344	1.24948
$700$	0	0
$701$	−14.1246	−0.533479	−0.266740	−	0.963769i	$-0.585946\pi$
$701$	−14.1246	−0.533479	−0.266740	+	0.963769i	$0.585946\pi$
$702$	−16.4164	−0.619597
$703$	7.70820	0.290720
$704$	0.618034	0.0232930
$705$	−33.2148	−1.25094
$706$	25.5623	0.962050
$707$	2.00000	0.0752177
$708$	12.3262	0.463248
$709$	−8.38197	−0.314791	−0.157396	−	0.987536i	$-0.550310\pi$
$709$	−8.38197	−0.314791	−0.157396	+	0.987536i	$0.550310\pi$
$710$	10.8541	0.407347
$711$	0.111456	0.00417993
$712$	−13.9443	−0.522584
$713$	7.85410	0.294138
$714$	9.70820	0.363320
$715$	−4.14590	−0.155048
$716$	15.2361	0.569399
$717$	37.5967	1.40408
$718$	−21.3607	−0.797173
$719$	26.5967	0.991891	0.495946	−	0.868354i	$-0.334822\pi$
$719$	26.5967	0.991891	0.495946	+	0.868354i	$0.334822\pi$
$720$	−0.854102	−0.0318305
$721$	−2.18034	−0.0812001
$722$	−1.00000	−0.0372161
$723$	18.2361	0.678207
$724$	18.4164	0.684440
$725$	0	0
$726$	17.1803	0.637622
$727$	9.23607	0.342547	0.171273	−	0.985224i	$-0.445212\pi$
$727$	9.23607	0.342547	0.171273	+	0.985224i	$0.445212\pi$
$728$	6.00000	0.222375
$729$	29.5066	1.09284
$730$	−23.9443	−0.886217
$731$	27.9787	1.03483
$732$	−19.7984	−0.731769
$733$	−13.0344	−0.481438	−0.240719	−	0.970595i	$-0.577383\pi$
$733$	−13.0344	−0.481438	−0.240719	+	0.970595i	$0.577383\pi$
$734$	16.5066	0.609269
$735$	−10.8541	−0.400360
$736$	−3.00000	−0.110581
$737$	4.61803	0.170107
$738$	−1.79837	−0.0661991
$739$	−14.0000	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$739$	−14.0000	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$740$	−17.2361	−0.633610
$741$	4.85410	0.178320
$742$	17.8885	0.656709
$743$	4.49342	0.164848	0.0824238	−	0.996597i	$-0.473734\pi$
$743$	4.49342	0.164848	0.0824238	+	0.996597i	$0.473734\pi$
$744$	−4.23607	−0.155302
$745$	−39.9230	−1.46267
$746$	−10.3820	−0.380111
$747$	−1.85410	−0.0678380
$748$	−1.85410	−0.0677927
$749$	−12.1803	−0.445060
$750$	18.0902	0.660560
$751$	−32.1803	−1.17428	−0.587139	−	0.809486i	$-0.699746\pi$
$751$	−32.1803	−1.17428	−0.587139	+	0.809486i	$0.699746\pi$
$752$	−9.18034	−0.334773
$753$	1.76393	0.0642813
$754$	−20.5623	−0.748835
$755$	−8.61803	−0.313642
$756$	−10.9443	−0.398039
$757$	10.6738	0.387944	0.193972	−	0.981007i	$-0.437863\pi$
$757$	10.6738	0.387944	0.193972	+	0.981007i	$0.437863\pi$
$758$	−6.00000	−0.217930
$759$	3.00000	0.108893
$760$	2.23607	0.0811107
$761$	−30.7426	−1.11442	−0.557210	−	0.830372i	$-0.688128\pi$
$761$	−30.7426	−1.11442	−0.557210	+	0.830372i	$0.688128\pi$
$762$	−29.6525	−1.07420
$763$	−6.47214	−0.234307
$764$	−3.94427	−0.142699
$765$	2.56231	0.0926404
$766$	23.5279	0.850096
$767$	−22.8541	−0.825214
$768$	1.61803	0.0583858
$769$	10.3820	0.374383	0.187192	−	0.982323i	$-0.440061\pi$
$769$	10.3820	0.374383	0.187192	+	0.982323i	$0.440061\pi$
$770$	−2.76393	−0.0996052
$771$	−22.9443	−0.826318
$772$	−1.52786	−0.0549890
$773$	53.3951	1.92049	0.960245	−	0.279160i	$-0.0900561\pi$
$773$	53.3951	1.92049	0.960245	+	0.279160i	$0.0900561\pi$
$774$	−3.56231	−0.128044
$775$	0	0
$776$	−0.236068	−0.00847435
$777$	−24.9443	−0.894871
$778$	−21.2361	−0.761350
$779$	4.70820	0.168689
$780$	−10.8541	−0.388639
$781$	−3.00000	−0.107348
$782$	9.00000	0.321839
$783$	37.5066	1.34038
$784$	−3.00000	−0.107143
$785$	−30.7771	−1.09848
$786$	−24.8885	−0.887745
$787$	−27.1246	−0.966888	−0.483444	−	0.875375i	$-0.660614\pi$
$787$	−27.1246	−0.966888	−0.483444	+	0.875375i	$0.660614\pi$
$788$	23.8885	0.850994
$789$	41.9787	1.49448
$790$	0.652476	0.0232140
$791$	−38.9443	−1.38470
$792$	0.236068	0.00838831
$793$	36.7082	1.30355
$794$	7.14590	0.253598
$795$	−32.3607	−1.14772
$796$	26.4164	0.936305
$797$	15.8328	0.560827	0.280414	−	0.959879i	$-0.409528\pi$
$797$	15.8328	0.560827	0.280414	+	0.959879i	$0.409528\pi$
$798$	3.23607	0.114556
$799$	27.5410	0.974331
$800$	0	0
$801$	−5.32624	−0.188193
$802$	34.1803	1.20695
$803$	6.61803	0.233545
$804$	12.0902	0.426387
$805$	13.4164	0.472866
$806$	7.85410	0.276649
$807$	−18.3262	−0.645114
$808$	−1.00000	−0.0351799
$809$	−27.0902	−0.952440	−0.476220	−	0.879326i	$-0.657993\pi$
$809$	−27.0902	−0.952440	−0.476220	+	0.879326i	$0.657993\pi$
$810$	17.2361	0.605614
$811$	−31.2361	−1.09685	−0.548423	−	0.836201i	$-0.684772\pi$
$811$	−31.2361	−1.09685	−0.548423	+	0.836201i	$0.684772\pi$
$812$	−13.7082	−0.481064
$813$	8.56231	0.300293
$814$	4.76393	0.166976
$815$	−24.3475	−0.852857
$816$	−4.85410	−0.169928
$817$	9.32624	0.326284
$818$	13.0902	0.457687
$819$	2.29180	0.0800818
$820$	−10.5279	−0.367649
$821$	38.7984	1.35407	0.677036	−	0.735950i	$-0.263264\pi$
$821$	38.7984	1.35407	0.677036	+	0.735950i	$0.263264\pi$
$822$	−10.3820	−0.362113
$823$	7.09017	0.247148	0.123574	−	0.992335i	$-0.460564\pi$
$823$	7.09017	0.247148	0.123574	+	0.992335i	$0.460564\pi$
$824$	1.09017	0.0379779
$825$	0	0
$826$	−15.2361	−0.530131
$827$	57.0689	1.98448	0.992240	−	0.124339i	$-0.0396811\pi$
$827$	57.0689	1.98448	0.992240	+	0.124339i	$0.0396811\pi$
$828$	−1.14590	−0.0398227
$829$	−48.7771	−1.69410	−0.847049	−	0.531515i	$-0.821623\pi$
$829$	−48.7771	−1.69410	−0.847049	+	0.531515i	$0.821623\pi$
$830$	−10.8541	−0.376751
$831$	33.7984	1.17245
$832$	−3.00000	−0.104006
$833$	9.00000	0.311832
$834$	−28.9443	−1.00226
$835$	0.652476	0.0225799
$836$	−0.618034	−0.0213752
$837$	−14.3262	−0.495187
$838$	−23.8885	−0.825216
$839$	−30.1246	−1.04002	−0.520009	−	0.854161i	$-0.674071\pi$
$839$	−30.1246	−1.04002	−0.520009	+	0.854161i	$0.674071\pi$
$840$	−7.23607	−0.249668
$841$	17.9787	0.619956
$842$	−1.56231	−0.0538406
$843$	−12.5623	−0.432669
$844$	−1.00000	−0.0344214
$845$	−8.94427	−0.307692
$846$	−3.50658	−0.120559
$847$	−21.2361	−0.729680
$848$	−8.94427	−0.307148
$849$	12.0344	0.413021
$850$	0	0
$851$	−23.1246	−0.792701
$852$	−7.85410	−0.269077
$853$	−13.1803	−0.451286	−0.225643	−	0.974210i	$-0.572448\pi$
$853$	−13.1803	−0.451286	−0.225643	+	0.974210i	$0.572448\pi$
$854$	24.4721	0.837419
$855$	0.854102	0.0292097
$856$	6.09017	0.208158
$857$	32.5967	1.11348	0.556742	−	0.830686i	$-0.312051\pi$
$857$	32.5967	1.11348	0.556742	+	0.830686i	$0.312051\pi$
$858$	3.00000	0.102418
$859$	−43.5410	−1.48560	−0.742800	−	0.669513i	$-0.766503\pi$
$859$	−43.5410	−1.48560	−0.742800	+	0.669513i	$0.766503\pi$
$860$	−20.8541	−0.711119
$861$	−15.2361	−0.519244
$862$	−9.23607	−0.314582
$863$	−37.1803	−1.26563	−0.632817	−	0.774302i	$-0.718101\pi$
$863$	−37.1803	−1.26563	−0.632817	+	0.774302i	$0.718101\pi$
$864$	5.47214	0.186166
$865$	−5.85410	−0.199045
$866$	15.4721	0.525765
$867$	−12.9443	−0.439611
$868$	5.23607	0.177724
$869$	−0.180340	−0.00611761
$870$	24.7984	0.840744
$871$	−22.4164	−0.759551
$872$	3.23607	0.109587
$873$	−0.0901699	−0.00305179
$874$	3.00000	0.101477
$875$	−22.3607	−0.755929
$876$	17.3262	0.585399
$877$	−54.0689	−1.82578	−0.912888	−	0.408210i	$-0.866153\pi$
$877$	−54.0689	−1.82578	−0.912888	+	0.408210i	$0.866153\pi$
$878$	40.3951	1.36327
$879$	−3.85410	−0.129996
$880$	1.38197	0.0465861
$881$	43.7082	1.47257	0.736283	−	0.676673i	$-0.236579\pi$
$881$	43.7082	1.47257	0.736283	+	0.676673i	$0.236579\pi$
$882$	−1.14590	−0.0385844
$883$	8.06888	0.271540	0.135770	−	0.990740i	$-0.456649\pi$
$883$	8.06888	0.271540	0.135770	+	0.990740i	$0.456649\pi$
$884$	9.00000	0.302703
$885$	27.5623	0.926497
$886$	−15.2361	−0.511866
$887$	29.4853	0.990019	0.495010	−	0.868888i	$-0.335165\pi$
$887$	29.4853	0.990019	0.495010	+	0.868888i	$0.335165\pi$
$888$	12.4721	0.418537
$889$	36.6525	1.22928
$890$	−31.1803	−1.04517
$891$	−4.76393	−0.159598
$892$	−20.2361	−0.677554
$893$	9.18034	0.307208
$894$	28.8885	0.966177
$895$	34.0689	1.13880
$896$	−2.00000	−0.0668153
$897$	−14.5623	−0.486221
$898$	19.2918	0.643776
$899$	−17.9443	−0.598475
$900$	0	0
$901$	26.8328	0.893931
$902$	2.90983	0.0968867
$903$	−30.1803	−1.00434
$904$	19.4721	0.647634
$905$	41.1803	1.36888
$906$	6.23607	0.207179
$907$	28.8885	0.959228	0.479614	−	0.877479i	$-0.340777\pi$
$907$	28.8885	0.959228	0.479614	+	0.877479i	$0.340777\pi$
$908$	−10.2361	−0.339696
$909$	−0.381966	−0.0126690
$910$	13.4164	0.444750
$911$	16.1246	0.534232	0.267116	−	0.963664i	$-0.413929\pi$
$911$	16.1246	0.534232	0.267116	+	0.963664i	$0.413929\pi$
$912$	−1.61803	−0.0535785
$913$	3.00000	0.0992855
$914$	11.3262	0.374639
$915$	−44.2705	−1.46354
$916$	−23.3262	−0.770721
$917$	30.7639	1.01591
$918$	−16.4164	−0.541822
$919$	−32.6180	−1.07597	−0.537985	−	0.842955i	$-0.680814\pi$
$919$	−32.6180	−1.07597	−0.537985	+	0.842955i	$0.680814\pi$
$920$	−6.70820	−0.221163
$921$	−1.32624	−0.0437010
$922$	−24.7426	−0.814856
$923$	14.5623	0.479324
$924$	2.00000	0.0657952
$925$	0	0
$926$	−18.7639	−0.616621
$927$	0.416408	0.0136766
$928$	6.85410	0.224997
$929$	19.7082	0.646605	0.323303	−	0.946296i	$-0.395207\pi$
$929$	19.7082	0.646605	0.323303	+	0.946296i	$0.395207\pi$
$930$	−9.47214	−0.310604
$931$	3.00000	0.0983210
$932$	20.4164	0.668762
$933$	53.4508	1.74990
$934$	−6.88854	−0.225400
$935$	−4.14590	−0.135585
$936$	−1.14590	−0.0374548
$937$	30.7639	1.00501	0.502507	−	0.864573i	$-0.332411\pi$
$937$	30.7639	1.00501	0.502507	+	0.864573i	$0.332411\pi$
$938$	−14.9443	−0.487948
$939$	−8.23607	−0.268774
$940$	−20.5279	−0.669545
$941$	1.61803	0.0527464	0.0263732	−	0.999652i	$-0.491604\pi$
$941$	1.61803	0.0527464	0.0263732	+	0.999652i	$0.491604\pi$
$942$	22.2705	0.725612
$943$	−14.1246	−0.459961
$944$	7.61803	0.247946
$945$	−24.4721	−0.796079
$946$	5.76393	0.187402
$947$	−27.0344	−0.878501	−0.439251	−	0.898365i	$-0.644756\pi$
$947$	−27.0344	−0.878501	−0.439251	+	0.898365i	$0.644756\pi$
$948$	−0.472136	−0.0153343
$949$	−32.1246	−1.04281
$950$	0	0
$951$	1.32624	0.0430062
$952$	6.00000	0.194461
$953$	28.7984	0.932871	0.466435	−	0.884555i	$-0.345538\pi$
$953$	28.7984	0.932871	0.466435	+	0.884555i	$0.345538\pi$
$954$	−3.41641	−0.110610
$955$	−8.81966	−0.285397
$956$	23.2361	0.751508
$957$	−6.85410	−0.221562
$958$	6.34752	0.205079
$959$	12.8328	0.414393
$960$	3.61803	0.116772
$961$	−24.1459	−0.778900
$962$	−23.1246	−0.745567
$963$	2.32624	0.0749620
$964$	11.2705	0.362999
$965$	−3.41641	−0.109978
$966$	−9.70820	−0.312356
$967$	−2.47214	−0.0794985	−0.0397493	−	0.999210i	$-0.512656\pi$
$967$	−2.47214	−0.0794985	−0.0397493	+	0.999210i	$0.512656\pi$
$968$	10.6180	0.341277
$969$	4.85410	0.155936
$970$	−0.527864	−0.0169487
$971$	−24.4164	−0.783560	−0.391780	−	0.920059i	$-0.628141\pi$
$971$	−24.4164	−0.783560	−0.391780	+	0.920059i	$0.628141\pi$
$972$	3.94427	0.126513
$973$	35.7771	1.14696
$974$	−12.7984	−0.410086
$975$	0	0
$976$	−12.2361	−0.391667
$977$	−1.54915	−0.0495617	−0.0247809	−	0.999693i	$-0.507889\pi$
$977$	−1.54915	−0.0495617	−0.0247809	+	0.999693i	$0.507889\pi$
$978$	17.6180	0.563363
$979$	8.61803	0.275434
$980$	−6.70820	−0.214286
$981$	1.23607	0.0394646
$982$	3.94427	0.125867
$983$	7.29180	0.232572	0.116286	−	0.993216i	$-0.462901\pi$
$983$	7.29180	0.232572	0.116286	+	0.993216i	$0.462901\pi$
$984$	7.61803	0.242854
$985$	53.4164	1.70199
$986$	−20.5623	−0.654837
$987$	−29.7082	−0.945623
$988$	3.00000	0.0954427
$989$	−27.9787	−0.889671
$990$	0.527864	0.0167766
$991$	55.5410	1.76432	0.882159	−	0.470951i	$-0.156089\pi$
$991$	55.5410	1.76432	0.882159	+	0.470951i	$0.156089\pi$
$992$	−2.61803	−0.0831227
$993$	22.9443	0.728114
$994$	9.70820	0.307926
$995$	59.0689	1.87261
$996$	7.85410	0.248867
$997$	−20.8328	−0.659782	−0.329891	−	0.944019i	$-0.607012\pi$
$997$	−20.8328	−0.659782	−0.329891	+	0.944019i	$0.607012\pi$
$998$	34.5279	1.09296
$999$	42.1803	1.33453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +2.23607 q^{5} -1.61803 q^{6} +2.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +2.23607 q^{5} -1.61803 q^{6} +2.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} -2.23607 q^{10} +0.618034 q^{11} +1.61803 q^{12} -3.00000 q^{13} -2.00000 q^{14} +3.61803 q^{15} +1.00000 q^{16} -3.00000 q^{17} +0.381966 q^{18} -1.00000 q^{19} +2.23607 q^{20} +3.23607 q^{21} -0.618034 q^{22} +3.00000 q^{23} -1.61803 q^{24} +3.00000 q^{26} -5.47214 q^{27} +2.00000 q^{28} -6.85410 q^{29} -3.61803 q^{30} +2.61803 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.00000 q^{34} +4.47214 q^{35} -0.381966 q^{36} -7.70820 q^{37} +1.00000 q^{38} -4.85410 q^{39} -2.23607 q^{40} -4.70820 q^{41} -3.23607 q^{42} -9.32624 q^{43} +0.618034 q^{44} -0.854102 q^{45} -3.00000 q^{46} -9.18034 q^{47} +1.61803 q^{48} -3.00000 q^{49} -4.85410 q^{51} -3.00000 q^{52} -8.94427 q^{53} +5.47214 q^{54} +1.38197 q^{55} -2.00000 q^{56} -1.61803 q^{57} +6.85410 q^{58} +7.61803 q^{59} +3.61803 q^{60} -12.2361 q^{61} -2.61803 q^{62} -0.763932 q^{63} +1.00000 q^{64} -6.70820 q^{65} -1.00000 q^{66} +7.47214 q^{67} -3.00000 q^{68} +4.85410 q^{69} -4.47214 q^{70} -4.85410 q^{71} +0.381966 q^{72} +10.7082 q^{73} +7.70820 q^{74} -1.00000 q^{76} +1.23607 q^{77} +4.85410 q^{78} -0.291796 q^{79} +2.23607 q^{80} -7.70820 q^{81} +4.70820 q^{82} +4.85410 q^{83} +3.23607 q^{84} -6.70820 q^{85} +9.32624 q^{86} -11.0902 q^{87} -0.618034 q^{88} +13.9443 q^{89} +0.854102 q^{90} -6.00000 q^{91} +3.00000 q^{92} +4.23607 q^{93} +9.18034 q^{94} -2.23607 q^{95} -1.61803 q^{96} +0.236068 q^{97} +3.00000 q^{98} -0.236068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 4 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

Properties

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