LMFDB - Embedded newform 5054.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} -5.00000 q^{11} -1.61803 q^{12} +1.85410 q^{13} +1.00000 q^{14} -1.61803 q^{15} +1.00000 q^{16} +0.145898 q^{17} +0.381966 q^{18} +1.00000 q^{20} +1.61803 q^{21} +5.00000 q^{22} -8.23607 q^{23} +1.61803 q^{24} -4.00000 q^{25} -1.85410 q^{26} +5.47214 q^{27} -1.00000 q^{28} +3.76393 q^{29} +1.61803 q^{30} -6.70820 q^{31} -1.00000 q^{32} +8.09017 q^{33} -0.145898 q^{34} -1.00000 q^{35} -0.381966 q^{36} +11.9443 q^{37} -3.00000 q^{39} -1.00000 q^{40} -10.0902 q^{41} -1.61803 q^{42} -0.145898 q^{43} -5.00000 q^{44} -0.381966 q^{45} +8.23607 q^{46} -9.94427 q^{47} -1.61803 q^{48} +1.00000 q^{49} +4.00000 q^{50} -0.236068 q^{51} +1.85410 q^{52} -0.708204 q^{53} -5.47214 q^{54} -5.00000 q^{55} +1.00000 q^{56} -3.76393 q^{58} -11.0000 q^{59} -1.61803 q^{60} -1.47214 q^{61} +6.70820 q^{62} +0.381966 q^{63} +1.00000 q^{64} +1.85410 q^{65} -8.09017 q^{66} -1.14590 q^{67} +0.145898 q^{68} +13.3262 q^{69} +1.00000 q^{70} +10.0000 q^{71} +0.381966 q^{72} +5.56231 q^{73} -11.9443 q^{74} +6.47214 q^{75} +5.00000 q^{77} +3.00000 q^{78} +2.14590 q^{79} +1.00000 q^{80} -7.70820 q^{81} +10.0902 q^{82} +11.4164 q^{83} +1.61803 q^{84} +0.145898 q^{85} +0.145898 q^{86} -6.09017 q^{87} +5.00000 q^{88} +1.85410 q^{89} +0.381966 q^{90} -1.85410 q^{91} -8.23607 q^{92} +10.8541 q^{93} +9.94427 q^{94} +1.61803 q^{96} +0.527864 q^{97} -1.00000 q^{98} +1.90983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} - 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} + 3 q^{18} + 2 q^{20} + q^{21} + 10 q^{22} - 12 q^{23} + q^{24} - 8 q^{25} + 3 q^{26} + 2 q^{27} - 2 q^{28} + 12 q^{29} + q^{30} - 2 q^{32} + 5 q^{33} - 7 q^{34} - 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 2 q^{40} - 9 q^{41} - q^{42} - 7 q^{43} - 10 q^{44} - 3 q^{45} + 12 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} + 8 q^{50} + 4 q^{51} - 3 q^{52} + 12 q^{53} - 2 q^{54} - 10 q^{55} + 2 q^{56} - 12 q^{58} - 22 q^{59} - q^{60} + 6 q^{61} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 5 q^{66} - 9 q^{67} + 7 q^{68} + 11 q^{69} + 2 q^{70} + 20 q^{71} + 3 q^{72} - 9 q^{73} - 6 q^{74} + 4 q^{75} + 10 q^{77} + 6 q^{78} + 11 q^{79} + 2 q^{80} - 2 q^{81} + 9 q^{82} - 4 q^{83} + q^{84} + 7 q^{85} + 7 q^{86} - q^{87} + 10 q^{88} - 3 q^{89} + 3 q^{90} + 3 q^{91} - 12 q^{92} + 15 q^{93} + 2 q^{94} + q^{96} + 10 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9 - 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 7 * q^17 + 3 * q^18 + 2 * q^20 + q^21 + 10 * q^22 - 12 * q^23 + q^24 - 8 * q^25 + 3 * q^26 + 2 * q^27 - 2 * q^28 + 12 * q^29 + q^30 - 2 * q^32 + 5 * q^33 - 7 * q^34 - 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 2 * q^40 - 9 * q^41 - q^42 - 7 * q^43 - 10 * q^44 - 3 * q^45 + 12 * q^46 - 2 * q^47 - q^48 + 2 * q^49 + 8 * q^50 + 4 * q^51 - 3 * q^52 + 12 * q^53 - 2 * q^54 - 10 * q^55 + 2 * q^56 - 12 * q^58 - 22 * q^59 - q^60 + 6 * q^61 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 5 * q^66 - 9 * q^67 + 7 * q^68 + 11 * q^69 + 2 * q^70 + 20 * q^71 + 3 * q^72 - 9 * q^73 - 6 * q^74 + 4 * q^75 + 10 * q^77 + 6 * q^78 + 11 * q^79 + 2 * q^80 - 2 * q^81 + 9 * q^82 - 4 * q^83 + q^84 + 7 * q^85 + 7 * q^86 - q^87 + 10 * q^88 - 3 * q^89 + 3 * q^90 + 3 * q^91 - 12 * q^92 + 15 * q^93 + 2 * q^94 + q^96 + 10 * q^97 - 2 * q^98 + 15 * 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	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.61803	0.660560
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.381966	−0.127322
$10$	−1.00000	−0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−1.61803	−0.467086
$13$	1.85410	0.514235	0.257118	−	0.966380i	$-0.417227\pi$
$13$	1.85410	0.514235	0.257118	+	0.966380i	$0.417227\pi$
$14$	1.00000	0.267261
$15$	−1.61803	−0.417775
$16$	1.00000	0.250000
$17$	0.145898	0.0353855	0.0176927	−	0.999843i	$-0.494368\pi$
$17$	0.145898	0.0353855	0.0176927	+	0.999843i	$0.494368\pi$
$18$	0.381966	0.0900303
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	1.61803	0.353084
$22$	5.00000	1.06600
$23$	−8.23607	−1.71734	−0.858669	−	0.512530i	$-0.828708\pi$
$23$	−8.23607	−1.71734	−0.858669	+	0.512530i	$0.828708\pi$
$24$	1.61803	0.330280
$25$	−4.00000	−0.800000
$26$	−1.85410	−0.363619
$27$	5.47214	1.05311
$28$	−1.00000	−0.188982
$29$	3.76393	0.698945	0.349472	−	0.936947i	$-0.386361\pi$
$29$	3.76393	0.698945	0.349472	+	0.936947i	$0.386361\pi$
$30$	1.61803	0.295411
$31$	−6.70820	−1.20483	−0.602414	−	0.798183i	$-0.705795\pi$
$31$	−6.70820	−1.20483	−0.602414	+	0.798183i	$0.705795\pi$
$32$	−1.00000	−0.176777
$33$	8.09017	1.40832
$34$	−0.145898	−0.0250213
$35$	−1.00000	−0.169031
$36$	−0.381966	−0.0636610
$37$	11.9443	1.96363	0.981813	−	0.189850i	$-0.0608002\pi$
$37$	11.9443	1.96363	0.981813	+	0.189850i	$0.0608002\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	−1.00000	−0.158114
$41$	−10.0902	−1.57582	−0.787910	−	0.615791i	$-0.788837\pi$
$41$	−10.0902	−1.57582	−0.787910	+	0.615791i	$0.788837\pi$
$42$	−1.61803	−0.249668
$43$	−0.145898	−0.0222492	−0.0111246	−	0.999938i	$-0.503541\pi$
$43$	−0.145898	−0.0222492	−0.0111246	+	0.999938i	$0.503541\pi$
$44$	−5.00000	−0.753778
$45$	−0.381966	−0.0569401
$46$	8.23607	1.21434
$47$	−9.94427	−1.45052	−0.725261	−	0.688474i	$-0.758281\pi$
$47$	−9.94427	−1.45052	−0.725261	+	0.688474i	$0.758281\pi$
$48$	−1.61803	−0.233543
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	−0.236068	−0.0330561
$52$	1.85410	0.257118
$53$	−0.708204	−0.0972793	−0.0486396	−	0.998816i	$-0.515489\pi$
$53$	−0.708204	−0.0972793	−0.0486396	+	0.998816i	$0.515489\pi$
$54$	−5.47214	−0.744663
$55$	−5.00000	−0.674200
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.76393	−0.494228
$59$	−11.0000	−1.43208	−0.716039	−	0.698060i	$-0.754047\pi$
$59$	−11.0000	−1.43208	−0.716039	+	0.698060i	$0.754047\pi$
$60$	−1.61803	−0.208887
$61$	−1.47214	−0.188488	−0.0942438	−	0.995549i	$-0.530043\pi$
$61$	−1.47214	−0.188488	−0.0942438	+	0.995549i	$0.530043\pi$
$62$	6.70820	0.851943
$63$	0.381966	0.0481232
$64$	1.00000	0.125000
$65$	1.85410	0.229973
$66$	−8.09017	−0.995831
$67$	−1.14590	−0.139994	−0.0699969	−	0.997547i	$-0.522299\pi$
$67$	−1.14590	−0.139994	−0.0699969	+	0.997547i	$0.522299\pi$
$68$	0.145898	0.0176927
$69$	13.3262	1.60429
$70$	1.00000	0.119523
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	0.381966	0.0450151
$73$	5.56231	0.651019	0.325509	−	0.945539i	$-0.394464\pi$
$73$	5.56231	0.651019	0.325509	+	0.945539i	$0.394464\pi$
$74$	−11.9443	−1.38849
$75$	6.47214	0.747338
$76$	0	0
$77$	5.00000	0.569803
$78$	3.00000	0.339683
$79$	2.14590	0.241432	0.120716	−	0.992687i	$-0.461481\pi$
$79$	2.14590	0.241432	0.120716	+	0.992687i	$0.461481\pi$
$80$	1.00000	0.111803
$81$	−7.70820	−0.856467
$82$	10.0902	1.11427
$83$	11.4164	1.25311	0.626557	−	0.779376i	$-0.284464\pi$
$83$	11.4164	1.25311	0.626557	+	0.779376i	$0.284464\pi$
$84$	1.61803	0.176542
$85$	0.145898	0.0158249
$86$	0.145898	0.0157326
$87$	−6.09017	−0.652935
$88$	5.00000	0.533002
$89$	1.85410	0.196534	0.0982672	−	0.995160i	$-0.468670\pi$
$89$	1.85410	0.196534	0.0982672	+	0.995160i	$0.468670\pi$
$90$	0.381966	0.0402628
$91$	−1.85410	−0.194363
$92$	−8.23607	−0.858669
$93$	10.8541	1.12552
$94$	9.94427	1.02567
$95$	0	0
$96$	1.61803	0.165140
$97$	0.527864	0.0535965	0.0267982	−	0.999641i	$-0.491469\pi$
$97$	0.527864	0.0535965	0.0267982	+	0.999641i	$0.491469\pi$
$98$	−1.00000	−0.101015
$99$	1.90983	0.191945
$100$	−4.00000	−0.400000
$101$	10.8541	1.08002	0.540012	−	0.841657i	$-0.318420\pi$
$101$	10.8541	1.08002	0.540012	+	0.841657i	$0.318420\pi$
$102$	0.236068	0.0233742
$103$	3.90983	0.385247	0.192624	−	0.981273i	$-0.438300\pi$
$103$	3.90983	0.385247	0.192624	+	0.981273i	$0.438300\pi$
$104$	−1.85410	−0.181810
$105$	1.61803	0.157904
$106$	0.708204	0.0687868
$107$	−3.94427	−0.381307	−0.190654	−	0.981657i	$-0.561061\pi$
$107$	−3.94427	−0.381307	−0.190654	+	0.981657i	$0.561061\pi$
$108$	5.47214	0.526557
$109$	−6.56231	−0.628555	−0.314277	−	0.949331i	$-0.601762\pi$
$109$	−6.56231	−0.628555	−0.314277	+	0.949331i	$0.601762\pi$
$110$	5.00000	0.476731
$111$	−19.3262	−1.83437
$112$	−1.00000	−0.0944911
$113$	2.85410	0.268491	0.134246	−	0.990948i	$-0.457139\pi$
$113$	2.85410	0.268491	0.134246	+	0.990948i	$0.457139\pi$
$114$	0	0
$115$	−8.23607	−0.768017
$116$	3.76393	0.349472
$117$	−0.708204	−0.0654735
$118$	11.0000	1.01263
$119$	−0.145898	−0.0133745
$120$	1.61803	0.147706
$121$	14.0000	1.27273
$122$	1.47214	0.133281
$123$	16.3262	1.47209
$124$	−6.70820	−0.602414
$125$	−9.00000	−0.804984
$126$	−0.381966	−0.0340282
$127$	−8.32624	−0.738834	−0.369417	−	0.929264i	$-0.620443\pi$
$127$	−8.32624	−0.738834	−0.369417	+	0.929264i	$0.620443\pi$
$128$	−1.00000	−0.0883883
$129$	0.236068	0.0207846
$130$	−1.85410	−0.162615
$131$	−6.61803	−0.578220	−0.289110	−	0.957296i	$-0.593359\pi$
$131$	−6.61803	−0.578220	−0.289110	+	0.957296i	$0.593359\pi$
$132$	8.09017	0.704159
$133$	0	0
$134$	1.14590	0.0989905
$135$	5.47214	0.470966
$136$	−0.145898	−0.0125107
$137$	−19.1246	−1.63393	−0.816963	−	0.576690i	$-0.804344\pi$
$137$	−19.1246	−1.63393	−0.816963	+	0.576690i	$0.804344\pi$
$138$	−13.3262	−1.13440
$139$	4.23607	0.359299	0.179649	−	0.983731i	$-0.442504\pi$
$139$	4.23607	0.359299	0.179649	+	0.983731i	$0.442504\pi$
$140$	−1.00000	−0.0845154
$141$	16.0902	1.35504
$142$	−10.0000	−0.839181
$143$	−9.27051	−0.775239
$144$	−0.381966	−0.0318305
$145$	3.76393	0.312578
$146$	−5.56231	−0.460340
$147$	−1.61803	−0.133453
$148$	11.9443	0.981813
$149$	3.61803	0.296401	0.148200	−	0.988957i	$-0.452652\pi$
$149$	3.61803	0.296401	0.148200	+	0.988957i	$0.452652\pi$
$150$	−6.47214	−0.528448
$151$	9.76393	0.794578	0.397289	−	0.917694i	$-0.369951\pi$
$151$	9.76393	0.794578	0.397289	+	0.917694i	$0.369951\pi$
$152$	0	0
$153$	−0.0557281	−0.00450535
$154$	−5.00000	−0.402911
$155$	−6.70820	−0.538816
$156$	−3.00000	−0.240192
$157$	6.67376	0.532624	0.266312	−	0.963887i	$-0.414195\pi$
$157$	6.67376	0.532624	0.266312	+	0.963887i	$0.414195\pi$
$158$	−2.14590	−0.170718
$159$	1.14590	0.0908756
$160$	−1.00000	−0.0790569
$161$	8.23607	0.649093
$162$	7.70820	0.605614
$163$	−8.47214	−0.663589	−0.331794	−	0.943352i	$-0.607654\pi$
$163$	−8.47214	−0.663589	−0.331794	+	0.943352i	$0.607654\pi$
$164$	−10.0902	−0.787910
$165$	8.09017	0.629819
$166$	−11.4164	−0.886085
$167$	−24.1803	−1.87113	−0.935565	−	0.353153i	$-0.885109\pi$
$167$	−24.1803	−1.87113	−0.935565	+	0.353153i	$0.885109\pi$
$168$	−1.61803	−0.124834
$169$	−9.56231	−0.735562
$170$	−0.145898	−0.0111899
$171$	0	0
$172$	−0.145898	−0.0111246
$173$	−6.23607	−0.474119	−0.237060	−	0.971495i	$-0.576184\pi$
$173$	−6.23607	−0.474119	−0.237060	+	0.971495i	$0.576184\pi$
$174$	6.09017	0.461695
$175$	4.00000	0.302372
$176$	−5.00000	−0.376889
$177$	17.7984	1.33781
$178$	−1.85410	−0.138971
$179$	20.0344	1.49744	0.748722	−	0.662884i	$-0.230668\pi$
$179$	20.0344	1.49744	0.748722	+	0.662884i	$0.230668\pi$
$180$	−0.381966	−0.0284701
$181$	20.2361	1.50414	0.752068	−	0.659086i	$-0.229057\pi$
$181$	20.2361	1.50414	0.752068	+	0.659086i	$0.229057\pi$
$182$	1.85410	0.137435
$183$	2.38197	0.176080
$184$	8.23607	0.607171
$185$	11.9443	0.878160
$186$	−10.8541	−0.795861
$187$	−0.729490	−0.0533456
$188$	−9.94427	−0.725261
$189$	−5.47214	−0.398039
$190$	0	0
$191$	25.1803	1.82199	0.910993	−	0.412422i	$-0.135317\pi$
$191$	25.1803	1.82199	0.910993	+	0.412422i	$0.135317\pi$
$192$	−1.61803	−0.116772
$193$	−12.1803	−0.876760	−0.438380	−	0.898790i	$-0.644448\pi$
$193$	−12.1803	−0.876760	−0.438380	+	0.898790i	$0.644448\pi$
$194$	−0.527864	−0.0378984
$195$	−3.00000	−0.214834
$196$	1.00000	0.0714286
$197$	12.5623	0.895027	0.447514	−	0.894277i	$-0.352310\pi$
$197$	12.5623	0.895027	0.447514	+	0.894277i	$0.352310\pi$
$198$	−1.90983	−0.135726
$199$	−16.0902	−1.14060	−0.570301	−	0.821436i	$-0.693173\pi$
$199$	−16.0902	−1.14060	−0.570301	+	0.821436i	$0.693173\pi$
$200$	4.00000	0.282843
$201$	1.85410	0.130778
$202$	−10.8541	−0.763692
$203$	−3.76393	−0.264176
$204$	−0.236068	−0.0165281
$205$	−10.0902	−0.704728
$206$	−3.90983	−0.272411
$207$	3.14590	0.218655
$208$	1.85410	0.128559
$209$	0	0
$210$	−1.61803	−0.111655
$211$	21.9443	1.51071	0.755353	−	0.655318i	$-0.227465\pi$
$211$	21.9443	1.51071	0.755353	+	0.655318i	$0.227465\pi$
$212$	−0.708204	−0.0486396
$213$	−16.1803	−1.10866
$214$	3.94427	0.269625
$215$	−0.145898	−0.00995016
$216$	−5.47214	−0.372332
$217$	6.70820	0.455383
$218$	6.56231	0.444455
$219$	−9.00000	−0.608164
$220$	−5.00000	−0.337100
$221$	0.270510	0.0181965
$222$	19.3262	1.29709
$223$	25.6525	1.71782	0.858908	−	0.512129i	$-0.171143\pi$
$223$	25.6525	1.71782	0.858908	+	0.512129i	$0.171143\pi$
$224$	1.00000	0.0668153
$225$	1.52786	0.101858
$226$	−2.85410	−0.189852
$227$	9.76393	0.648055	0.324027	−	0.946048i	$-0.394963\pi$
$227$	9.76393	0.648055	0.324027	+	0.946048i	$0.394963\pi$
$228$	0	0
$229$	1.09017	0.0720405	0.0360202	−	0.999351i	$-0.488532\pi$
$229$	1.09017	0.0720405	0.0360202	+	0.999351i	$0.488532\pi$
$230$	8.23607	0.543070
$231$	−8.09017	−0.532294
$232$	−3.76393	−0.247114
$233$	18.0344	1.18148	0.590738	−	0.806864i	$-0.298837\pi$
$233$	18.0344	1.18148	0.590738	+	0.806864i	$0.298837\pi$
$234$	0.708204	0.0462967
$235$	−9.94427	−0.648693
$236$	−11.0000	−0.716039
$237$	−3.47214	−0.225539
$238$	0.145898	0.00945716
$239$	−17.8541	−1.15489	−0.577443	−	0.816431i	$-0.695949\pi$
$239$	−17.8541	−1.15489	−0.577443	+	0.816431i	$0.695949\pi$
$240$	−1.61803	−0.104444
$241$	−19.0902	−1.22971	−0.614853	−	0.788642i	$-0.710785\pi$
$241$	−19.0902	−1.22971	−0.614853	+	0.788642i	$0.710785\pi$
$242$	−14.0000	−0.899954
$243$	−3.94427	−0.253025
$244$	−1.47214	−0.0942438
$245$	1.00000	0.0638877
$246$	−16.3262	−1.04092
$247$	0	0
$248$	6.70820	0.425971
$249$	−18.4721	−1.17062
$250$	9.00000	0.569210
$251$	−2.47214	−0.156040	−0.0780199	−	0.996952i	$-0.524860\pi$
$251$	−2.47214	−0.156040	−0.0780199	+	0.996952i	$0.524860\pi$
$252$	0.381966	0.0240616
$253$	41.1803	2.58899
$254$	8.32624	0.522435
$255$	−0.236068	−0.0147832
$256$	1.00000	0.0625000
$257$	−25.9443	−1.61836	−0.809180	−	0.587561i	$-0.800088\pi$
$257$	−25.9443	−1.61836	−0.809180	+	0.587561i	$0.800088\pi$
$258$	−0.236068	−0.0146970
$259$	−11.9443	−0.742181
$260$	1.85410	0.114987
$261$	−1.43769	−0.0889910
$262$	6.61803	0.408864
$263$	−2.81966	−0.173868	−0.0869338	−	0.996214i	$-0.527707\pi$
$263$	−2.81966	−0.173868	−0.0869338	+	0.996214i	$0.527707\pi$
$264$	−8.09017	−0.497916
$265$	−0.708204	−0.0435046
$266$	0	0
$267$	−3.00000	−0.183597
$268$	−1.14590	−0.0699969
$269$	13.1803	0.803620	0.401810	−	0.915723i	$-0.368381\pi$
$269$	13.1803	0.803620	0.401810	+	0.915723i	$0.368381\pi$
$270$	−5.47214	−0.333024
$271$	−29.6525	−1.80126	−0.900630	−	0.434587i	$-0.856894\pi$
$271$	−29.6525	−1.80126	−0.900630	+	0.434587i	$0.856894\pi$
$272$	0.145898	0.00884637
$273$	3.00000	0.181568
$274$	19.1246	1.15536
$275$	20.0000	1.20605
$276$	13.3262	0.802145
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−4.23607	−0.254062
$279$	2.56231	0.153401
$280$	1.00000	0.0597614
$281$	7.76393	0.463157	0.231579	−	0.972816i	$-0.425611\pi$
$281$	7.76393	0.463157	0.231579	+	0.972816i	$0.425611\pi$
$282$	−16.0902	−0.958156
$283$	26.5623	1.57897	0.789483	−	0.613773i	$-0.210349\pi$
$283$	26.5623	1.57897	0.789483	+	0.613773i	$0.210349\pi$
$284$	10.0000	0.593391
$285$	0	0
$286$	9.27051	0.548177
$287$	10.0902	0.595604
$288$	0.381966	0.0225076
$289$	−16.9787	−0.998748
$290$	−3.76393	−0.221026
$291$	−0.854102	−0.0500683
$292$	5.56231	0.325509
$293$	−11.7639	−0.687256	−0.343628	−	0.939106i	$-0.611656\pi$
$293$	−11.7639	−0.687256	−0.343628	+	0.939106i	$0.611656\pi$
$294$	1.61803	0.0943657
$295$	−11.0000	−0.640445
$296$	−11.9443	−0.694247
$297$	−27.3607	−1.58763
$298$	−3.61803	−0.209587
$299$	−15.2705	−0.883116
$300$	6.47214	0.373669
$301$	0.145898	0.00840942
$302$	−9.76393	−0.561851
$303$	−17.5623	−1.00893
$304$	0	0
$305$	−1.47214	−0.0842943
$306$	0.0557281	0.00318576
$307$	12.9443	0.738769	0.369384	−	0.929277i	$-0.379569\pi$
$307$	12.9443	0.738769	0.369384	+	0.929277i	$0.379569\pi$
$308$	5.00000	0.284901
$309$	−6.32624	−0.359887
$310$	6.70820	0.381000
$311$	24.2361	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$311$	24.2361	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$312$	3.00000	0.169842
$313$	30.0902	1.70080	0.850398	−	0.526139i	$-0.176361\pi$
$313$	30.0902	1.70080	0.850398	+	0.526139i	$0.176361\pi$
$314$	−6.67376	−0.376622
$315$	0.381966	0.0215213
$316$	2.14590	0.120716
$317$	18.4164	1.03437	0.517184	−	0.855874i	$-0.326980\pi$
$317$	18.4164	1.03437	0.517184	+	0.855874i	$0.326980\pi$
$318$	−1.14590	−0.0642588
$319$	−18.8197	−1.05370
$320$	1.00000	0.0559017
$321$	6.38197	0.356207
$322$	−8.23607	−0.458978
$323$	0	0
$324$	−7.70820	−0.428234
$325$	−7.41641	−0.411388
$326$	8.47214	0.469228
$327$	10.6180	0.587179
$328$	10.0902	0.557136
$329$	9.94427	0.548245
$330$	−8.09017	−0.445349
$331$	−3.52786	−0.193909	−0.0969545	−	0.995289i	$-0.530910\pi$
$331$	−3.52786	−0.193909	−0.0969545	+	0.995289i	$0.530910\pi$
$332$	11.4164	0.626557
$333$	−4.56231	−0.250013
$334$	24.1803	1.32309
$335$	−1.14590	−0.0626071
$336$	1.61803	0.0882710
$337$	−22.4508	−1.22298	−0.611488	−	0.791254i	$-0.709429\pi$
$337$	−22.4508	−1.22298	−0.611488	+	0.791254i	$0.709429\pi$
$338$	9.56231	0.520121
$339$	−4.61803	−0.250817
$340$	0.145898	0.00791243
$341$	33.5410	1.81635
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0.145898	0.00786629
$345$	13.3262	0.717461
$346$	6.23607	0.335253
$347$	−22.9443	−1.23171	−0.615857	−	0.787858i	$-0.711190\pi$
$347$	−22.9443	−1.23171	−0.615857	+	0.787858i	$0.711190\pi$
$348$	−6.09017	−0.326467
$349$	6.70820	0.359082	0.179541	−	0.983750i	$-0.442539\pi$
$349$	6.70820	0.359082	0.179541	+	0.983750i	$0.442539\pi$
$350$	−4.00000	−0.213809
$351$	10.1459	0.541548
$352$	5.00000	0.266501
$353$	1.90983	0.101650	0.0508250	−	0.998708i	$-0.483815\pi$
$353$	1.90983	0.101650	0.0508250	+	0.998708i	$0.483815\pi$
$354$	−17.7984	−0.945973
$355$	10.0000	0.530745
$356$	1.85410	0.0982672
$357$	0.236068	0.0124940
$358$	−20.0344	−1.05885
$359$	10.0557	0.530721	0.265361	−	0.964149i	$-0.414509\pi$
$359$	10.0557	0.530721	0.265361	+	0.964149i	$0.414509\pi$
$360$	0.381966	0.0201314
$361$	0	0
$362$	−20.2361	−1.06358
$363$	−22.6525	−1.18895
$364$	−1.85410	−0.0971813
$365$	5.56231	0.291144
$366$	−2.38197	−0.124507
$367$	25.3262	1.32202	0.661009	−	0.750378i	$-0.270128\pi$
$367$	25.3262	1.32202	0.661009	+	0.750378i	$0.270128\pi$
$368$	−8.23607	−0.429335
$369$	3.85410	0.200637
$370$	−11.9443	−0.620953
$371$	0.708204	0.0367681
$372$	10.8541	0.562759
$373$	0.145898	0.00755431	0.00377716	−	0.999993i	$-0.498798\pi$
$373$	0.145898	0.00755431	0.00377716	+	0.999993i	$0.498798\pi$
$374$	0.729490	0.0377210
$375$	14.5623	0.751994
$376$	9.94427	0.512837
$377$	6.97871	0.359422
$378$	5.47214	0.281456
$379$	17.0344	0.875001	0.437500	−	0.899218i	$-0.355864\pi$
$379$	17.0344	0.875001	0.437500	+	0.899218i	$0.355864\pi$
$380$	0	0
$381$	13.4721	0.690198
$382$	−25.1803	−1.28834
$383$	11.9443	0.610324	0.305162	−	0.952300i	$-0.401289\pi$
$383$	11.9443	0.610324	0.305162	+	0.952300i	$0.401289\pi$
$384$	1.61803	0.0825700
$385$	5.00000	0.254824
$386$	12.1803	0.619963
$387$	0.0557281	0.00283282
$388$	0.527864	0.0267982
$389$	13.6180	0.690462	0.345231	−	0.938518i	$-0.387801\pi$
$389$	13.6180	0.690462	0.345231	+	0.938518i	$0.387801\pi$
$390$	3.00000	0.151911
$391$	−1.20163	−0.0607688
$392$	−1.00000	−0.0505076
$393$	10.7082	0.540157
$394$	−12.5623	−0.632880
$395$	2.14590	0.107972
$396$	1.90983	0.0959726
$397$	1.27051	0.0637651	0.0318825	−	0.999492i	$-0.489850\pi$
$397$	1.27051	0.0637651	0.0318825	+	0.999492i	$0.489850\pi$
$398$	16.0902	0.806527
$399$	0	0
$400$	−4.00000	−0.200000
$401$	33.4164	1.66874	0.834368	−	0.551208i	$-0.185833\pi$
$401$	33.4164	1.66874	0.834368	+	0.551208i	$0.185833\pi$
$402$	−1.85410	−0.0924742
$403$	−12.4377	−0.619566
$404$	10.8541	0.540012
$405$	−7.70820	−0.383024
$406$	3.76393	0.186801
$407$	−59.7214	−2.96028
$408$	0.236068	0.0116871
$409$	34.2148	1.69181	0.845906	−	0.533332i	$-0.179060\pi$
$409$	34.2148	1.69181	0.845906	+	0.533332i	$0.179060\pi$
$410$	10.0902	0.498318
$411$	30.9443	1.52637
$412$	3.90983	0.192624
$413$	11.0000	0.541275
$414$	−3.14590	−0.154612
$415$	11.4164	0.560409
$416$	−1.85410	−0.0909048
$417$	−6.85410	−0.335647
$418$	0	0
$419$	16.7426	0.817932	0.408966	−	0.912550i	$-0.365890\pi$
$419$	16.7426	0.817932	0.408966	+	0.912550i	$0.365890\pi$
$420$	1.61803	0.0789520
$421$	25.9443	1.26445	0.632223	−	0.774786i	$-0.282143\pi$
$421$	25.9443	1.26445	0.632223	+	0.774786i	$0.282143\pi$
$422$	−21.9443	−1.06823
$423$	3.79837	0.184683
$424$	0.708204	0.0343934
$425$	−0.583592	−0.0283084
$426$	16.1803	0.783940
$427$	1.47214	0.0712417
$428$	−3.94427	−0.190654
$429$	15.0000	0.724207
$430$	0.145898	0.00703583
$431$	14.9443	0.719840	0.359920	−	0.932983i	$-0.382804\pi$
$431$	14.9443	0.719840	0.359920	+	0.932983i	$0.382804\pi$
$432$	5.47214	0.263278
$433$	25.3820	1.21978	0.609890	−	0.792486i	$-0.291214\pi$
$433$	25.3820	1.21978	0.609890	+	0.792486i	$0.291214\pi$
$434$	−6.70820	−0.322004
$435$	−6.09017	−0.292001
$436$	−6.56231	−0.314277
$437$	0	0
$438$	9.00000	0.430037
$439$	39.9443	1.90644	0.953218	−	0.302284i	$-0.0977490\pi$
$439$	39.9443	1.90644	0.953218	+	0.302284i	$0.0977490\pi$
$440$	5.00000	0.238366
$441$	−0.381966	−0.0181889
$442$	−0.270510	−0.0128668
$443$	−34.2148	−1.62559	−0.812797	−	0.582547i	$-0.802056\pi$
$443$	−34.2148	−1.62559	−0.812797	+	0.582547i	$0.802056\pi$
$444$	−19.3262	−0.917183
$445$	1.85410	0.0878929
$446$	−25.6525	−1.21468
$447$	−5.85410	−0.276890
$448$	−1.00000	−0.0472456
$449$	−0.180340	−0.00851077	−0.00425538	−	0.999991i	$-0.501355\pi$
$449$	−0.180340	−0.00851077	−0.00425538	+	0.999991i	$0.501355\pi$
$450$	−1.52786	−0.0720242
$451$	50.4508	2.37564
$452$	2.85410	0.134246
$453$	−15.7984	−0.742272
$454$	−9.76393	−0.458244
$455$	−1.85410	−0.0869216
$456$	0	0
$457$	−5.88854	−0.275454	−0.137727	−	0.990470i	$-0.543980\pi$
$457$	−5.88854	−0.275454	−0.137727	+	0.990470i	$0.543980\pi$
$458$	−1.09017	−0.0509403
$459$	0.798374	0.0372649
$460$	−8.23607	−0.384009
$461$	−24.5410	−1.14299	−0.571495	−	0.820606i	$-0.693636\pi$
$461$	−24.5410	−1.14299	−0.571495	+	0.820606i	$0.693636\pi$
$462$	8.09017	0.376389
$463$	6.56231	0.304976	0.152488	−	0.988305i	$-0.451271\pi$
$463$	6.56231	0.304976	0.152488	+	0.988305i	$0.451271\pi$
$464$	3.76393	0.174736
$465$	10.8541	0.503347
$466$	−18.0344	−0.835429
$467$	24.5279	1.13501	0.567507	−	0.823369i	$-0.307908\pi$
$467$	24.5279	1.13501	0.567507	+	0.823369i	$0.307908\pi$
$468$	−0.708204	−0.0327367
$469$	1.14590	0.0529127
$470$	9.94427	0.458695
$471$	−10.7984	−0.497563
$472$	11.0000	0.506316
$473$	0.729490	0.0335420
$474$	3.47214	0.159480
$475$	0	0
$476$	−0.145898	−0.00668723
$477$	0.270510	0.0123858
$478$	17.8541	0.816628
$479$	22.1803	1.01345	0.506723	−	0.862109i	$-0.330857\pi$
$479$	22.1803	1.01345	0.506723	+	0.862109i	$0.330857\pi$
$480$	1.61803	0.0738528
$481$	22.1459	1.00977
$482$	19.0902	0.869533
$483$	−13.3262	−0.606365
$484$	14.0000	0.636364
$485$	0.527864	0.0239691
$486$	3.94427	0.178916
$487$	11.1803	0.506630	0.253315	−	0.967384i	$-0.418479\pi$
$487$	11.1803	0.506630	0.253315	+	0.967384i	$0.418479\pi$
$488$	1.47214	0.0666405
$489$	13.7082	0.619906
$490$	−1.00000	−0.0451754
$491$	29.5967	1.33568	0.667841	−	0.744304i	$-0.267218\pi$
$491$	29.5967	1.33568	0.667841	+	0.744304i	$0.267218\pi$
$492$	16.3262	0.736044
$493$	0.549150	0.0247325
$494$	0	0
$495$	1.90983	0.0858405
$496$	−6.70820	−0.301207
$497$	−10.0000	−0.448561
$498$	18.4721	0.827756
$499$	−10.4164	−0.466302	−0.233151	−	0.972440i	$-0.574904\pi$
$499$	−10.4164	−0.466302	−0.233151	+	0.972440i	$0.574904\pi$
$500$	−9.00000	−0.402492
$501$	39.1246	1.74796
$502$	2.47214	0.110337
$503$	−39.7771	−1.77357	−0.886786	−	0.462180i	$-0.847068\pi$
$503$	−39.7771	−1.77357	−0.886786	+	0.462180i	$0.847068\pi$
$504$	−0.381966	−0.0170141
$505$	10.8541	0.483001
$506$	−41.1803	−1.83069
$507$	15.4721	0.687142
$508$	−8.32624	−0.369417
$509$	25.4164	1.12656	0.563281	−	0.826265i	$-0.309539\pi$
$509$	25.4164	1.12656	0.563281	+	0.826265i	$0.309539\pi$
$510$	0.236068	0.0104533
$511$	−5.56231	−0.246062
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	25.9443	1.14435
$515$	3.90983	0.172288
$516$	0.236068	0.0103923
$517$	49.7214	2.18674
$518$	11.9443	0.524801
$519$	10.0902	0.442909
$520$	−1.85410	−0.0813077
$521$	5.65248	0.247639	0.123820	−	0.992305i	$-0.460486\pi$
$521$	5.65248	0.247639	0.123820	+	0.992305i	$0.460486\pi$
$522$	1.43769	0.0629262
$523$	−34.1591	−1.49367	−0.746836	−	0.665009i	$-0.768428\pi$
$523$	−34.1591	−1.49367	−0.746836	+	0.665009i	$0.768428\pi$
$524$	−6.61803	−0.289110
$525$	−6.47214	−0.282467
$526$	2.81966	0.122943
$527$	−0.978714	−0.0426334
$528$	8.09017	0.352079
$529$	44.8328	1.94925
$530$	0.708204	0.0307624
$531$	4.20163	0.182335
$532$	0	0
$533$	−18.7082	−0.810342
$534$	3.00000	0.129823
$535$	−3.94427	−0.170526
$536$	1.14590	0.0494953
$537$	−32.4164	−1.39887
$538$	−13.1803	−0.568245
$539$	−5.00000	−0.215365
$540$	5.47214	0.235483
$541$	32.3050	1.38890	0.694449	−	0.719542i	$-0.255648\pi$
$541$	32.3050	1.38890	0.694449	+	0.719542i	$0.255648\pi$
$542$	29.6525	1.27368
$543$	−32.7426	−1.40512
$544$	−0.145898	−0.00625533
$545$	−6.56231	−0.281098
$546$	−3.00000	−0.128388
$547$	13.1803	0.563551	0.281775	−	0.959480i	$-0.409077\pi$
$547$	13.1803	0.563551	0.281775	+	0.959480i	$0.409077\pi$
$548$	−19.1246	−0.816963
$549$	0.562306	0.0239986
$550$	−20.0000	−0.852803
$551$	0	0
$552$	−13.3262	−0.567202
$553$	−2.14590	−0.0912529
$554$	8.00000	0.339887
$555$	−19.3262	−0.820353
$556$	4.23607	0.179649
$557$	−32.2361	−1.36589	−0.682943	−	0.730472i	$-0.739300\pi$
$557$	−32.2361	−1.36589	−0.682943	+	0.730472i	$0.739300\pi$
$558$	−2.56231	−0.108471
$559$	−0.270510	−0.0114413
$560$	−1.00000	−0.0422577
$561$	1.18034	0.0498340
$562$	−7.76393	−0.327502
$563$	22.0689	0.930093	0.465046	−	0.885286i	$-0.346038\pi$
$563$	22.0689	0.930093	0.465046	+	0.885286i	$0.346038\pi$
$564$	16.0902	0.677518
$565$	2.85410	0.120073
$566$	−26.5623	−1.11650
$567$	7.70820	0.323714
$568$	−10.0000	−0.419591
$569$	−3.27051	−0.137107	−0.0685535	−	0.997647i	$-0.521838\pi$
$569$	−3.27051	−0.137107	−0.0685535	+	0.997647i	$0.521838\pi$
$570$	0	0
$571$	−45.0132	−1.88374	−0.941871	−	0.335975i	$-0.890934\pi$
$571$	−45.0132	−1.88374	−0.941871	+	0.335975i	$0.890934\pi$
$572$	−9.27051	−0.387619
$573$	−40.7426	−1.70205
$574$	−10.0902	−0.421156
$575$	32.9443	1.37387
$576$	−0.381966	−0.0159153
$577$	−16.7082	−0.695572	−0.347786	−	0.937574i	$-0.613066\pi$
$577$	−16.7082	−0.695572	−0.347786	+	0.937574i	$0.613066\pi$
$578$	16.9787	0.706221
$579$	19.7082	0.819045
$580$	3.76393	0.156289
$581$	−11.4164	−0.473632
$582$	0.854102	0.0354037
$583$	3.54102	0.146654
$584$	−5.56231	−0.230170
$585$	−0.708204	−0.0292806
$586$	11.7639	0.485964
$587$	−24.0557	−0.992886	−0.496443	−	0.868069i	$-0.665361\pi$
$587$	−24.0557	−0.992886	−0.496443	+	0.868069i	$0.665361\pi$
$588$	−1.61803	−0.0667266
$589$	0	0
$590$	11.0000	0.452863
$591$	−20.3262	−0.836110
$592$	11.9443	0.490907
$593$	25.5623	1.04972	0.524859	−	0.851189i	$-0.324118\pi$
$593$	25.5623	1.04972	0.524859	+	0.851189i	$0.324118\pi$
$594$	27.3607	1.12262
$595$	−0.145898	−0.00598124
$596$	3.61803	0.148200
$597$	26.0344	1.06552
$598$	15.2705	0.624458
$599$	−17.0000	−0.694601	−0.347301	−	0.937754i	$-0.612902\pi$
$599$	−17.0000	−0.694601	−0.347301	+	0.937754i	$0.612902\pi$
$600$	−6.47214	−0.264224
$601$	26.1246	1.06565	0.532823	−	0.846227i	$-0.321131\pi$
$601$	26.1246	1.06565	0.532823	+	0.846227i	$0.321131\pi$
$602$	−0.145898	−0.00594636
$603$	0.437694	0.0178243
$604$	9.76393	0.397289
$605$	14.0000	0.569181
$606$	17.5623	0.713420
$607$	0.944272	0.0383268	0.0191634	−	0.999816i	$-0.493900\pi$
$607$	0.944272	0.0383268	0.0191634	+	0.999816i	$0.493900\pi$
$608$	0	0
$609$	6.09017	0.246786
$610$	1.47214	0.0596050
$611$	−18.4377	−0.745909
$612$	−0.0557281	−0.00225267
$613$	20.6525	0.834146	0.417073	−	0.908873i	$-0.363056\pi$
$613$	20.6525	0.834146	0.417073	+	0.908873i	$0.363056\pi$
$614$	−12.9443	−0.522388
$615$	16.3262	0.658337
$616$	−5.00000	−0.201456
$617$	−8.67376	−0.349193	−0.174596	−	0.984640i	$-0.555862\pi$
$617$	−8.67376	−0.349193	−0.174596	+	0.984640i	$0.555862\pi$
$618$	6.32624	0.254479
$619$	−10.2016	−0.410038	−0.205019	−	0.978758i	$-0.565726\pi$
$619$	−10.2016	−0.410038	−0.205019	+	0.978758i	$0.565726\pi$
$620$	−6.70820	−0.269408
$621$	−45.0689	−1.80855
$622$	−24.2361	−0.971778
$623$	−1.85410	−0.0742830
$624$	−3.00000	−0.120096
$625$	11.0000	0.440000
$626$	−30.0902	−1.20265
$627$	0	0
$628$	6.67376	0.266312
$629$	1.74265	0.0694838
$630$	−0.381966	−0.0152179
$631$	−4.94427	−0.196828	−0.0984142	−	0.995146i	$-0.531377\pi$
$631$	−4.94427	−0.196828	−0.0984142	+	0.995146i	$0.531377\pi$
$632$	−2.14590	−0.0853592
$633$	−35.5066	−1.41126
$634$	−18.4164	−0.731409
$635$	−8.32624	−0.330417
$636$	1.14590	0.0454378
$637$	1.85410	0.0734622
$638$	18.8197	0.745077
$639$	−3.81966	−0.151103
$640$	−1.00000	−0.0395285
$641$	−30.0902	−1.18849	−0.594245	−	0.804284i	$-0.702549\pi$
$641$	−30.0902	−1.18849	−0.594245	+	0.804284i	$0.702549\pi$
$642$	−6.38197	−0.251876
$643$	−8.65248	−0.341220	−0.170610	−	0.985339i	$-0.554574\pi$
$643$	−8.65248	−0.341220	−0.170610	+	0.985339i	$0.554574\pi$
$644$	8.23607	0.324547
$645$	0.236068	0.00929517
$646$	0	0
$647$	46.1033	1.81251	0.906254	−	0.422733i	$-0.138929\pi$
$647$	46.1033	1.81251	0.906254	+	0.422733i	$0.138929\pi$
$648$	7.70820	0.302807
$649$	55.0000	2.15894
$650$	7.41641	0.290895
$651$	−10.8541	−0.425406
$652$	−8.47214	−0.331794
$653$	−36.6869	−1.43567	−0.717835	−	0.696213i	$-0.754867\pi$
$653$	−36.6869	−1.43567	−0.717835	+	0.696213i	$0.754867\pi$
$654$	−10.6180	−0.415198
$655$	−6.61803	−0.258588
$656$	−10.0902	−0.393955
$657$	−2.12461	−0.0828890
$658$	−9.94427	−0.387668
$659$	33.5410	1.30657	0.653286	−	0.757111i	$-0.273390\pi$
$659$	33.5410	1.30657	0.653286	+	0.757111i	$0.273390\pi$
$660$	8.09017	0.314909
$661$	−41.8328	−1.62711	−0.813554	−	0.581489i	$-0.802470\pi$
$661$	−41.8328	−1.62711	−0.813554	+	0.581489i	$0.802470\pi$
$662$	3.52786	0.137114
$663$	−0.437694	−0.0169986
$664$	−11.4164	−0.443043
$665$	0	0
$666$	4.56231	0.176786
$667$	−31.0000	−1.20032
$668$	−24.1803	−0.935565
$669$	−41.5066	−1.60474
$670$	1.14590	0.0442699
$671$	7.36068	0.284156
$672$	−1.61803	−0.0624170
$673$	−32.0902	−1.23699	−0.618493	−	0.785791i	$-0.712256\pi$
$673$	−32.0902	−1.23699	−0.618493	+	0.785791i	$0.712256\pi$
$674$	22.4508	0.864774
$675$	−21.8885	−0.842490
$676$	−9.56231	−0.367781
$677$	9.70820	0.373117	0.186558	−	0.982444i	$-0.440267\pi$
$677$	9.70820	0.373117	0.186558	+	0.982444i	$0.440267\pi$
$678$	4.61803	0.177355
$679$	−0.527864	−0.0202576
$680$	−0.145898	−0.00559493
$681$	−15.7984	−0.605395
$682$	−33.5410	−1.28435
$683$	−13.2705	−0.507782	−0.253891	−	0.967233i	$-0.581710\pi$
$683$	−13.2705	−0.507782	−0.253891	+	0.967233i	$0.581710\pi$
$684$	0	0
$685$	−19.1246	−0.730714
$686$	1.00000	0.0381802
$687$	−1.76393	−0.0672982
$688$	−0.145898	−0.00556231
$689$	−1.31308	−0.0500245
$690$	−13.3262	−0.507321
$691$	0.527864	0.0200809	0.0100404	−	0.999950i	$-0.496804\pi$
$691$	0.527864	0.0200809	0.0100404	+	0.999950i	$0.496804\pi$
$692$	−6.23607	−0.237060
$693$	−1.90983	−0.0725484
$694$	22.9443	0.870953
$695$	4.23607	0.160683
$696$	6.09017	0.230847
$697$	−1.47214	−0.0557611
$698$	−6.70820	−0.253909
$699$	−29.1803	−1.10370
$700$	4.00000	0.151186
$701$	35.2705	1.33215	0.666074	−	0.745885i	$-0.267973\pi$
$701$	35.2705	1.33215	0.666074	+	0.745885i	$0.267973\pi$
$702$	−10.1459	−0.382932
$703$	0	0
$704$	−5.00000	−0.188445
$705$	16.0902	0.605991
$706$	−1.90983	−0.0718774
$707$	−10.8541	−0.408211
$708$	17.7984	0.668904
$709$	8.34752	0.313498	0.156749	−	0.987638i	$-0.449899\pi$
$709$	8.34752	0.313498	0.156749	+	0.987638i	$0.449899\pi$
$710$	−10.0000	−0.375293
$711$	−0.819660	−0.0307397
$712$	−1.85410	−0.0694854
$713$	55.2492	2.06910
$714$	−0.236068	−0.00883462
$715$	−9.27051	−0.346697
$716$	20.0344	0.748722
$717$	28.8885	1.07886
$718$	−10.0557	−0.375276
$719$	−13.8328	−0.515877	−0.257938	−	0.966161i	$-0.583043\pi$
$719$	−13.8328	−0.515877	−0.257938	+	0.966161i	$0.583043\pi$
$720$	−0.381966	−0.0142350
$721$	−3.90983	−0.145610
$722$	0	0
$723$	30.8885	1.14876
$724$	20.2361	0.752068
$725$	−15.0557	−0.559156
$726$	22.6525	0.840712
$727$	48.1246	1.78484	0.892422	−	0.451203i	$-0.149005\pi$
$727$	48.1246	1.78484	0.892422	+	0.451203i	$0.149005\pi$
$728$	1.85410	0.0687176
$729$	29.5066	1.09284
$730$	−5.56231	−0.205870
$731$	−0.0212862	−0.000787300 0
$732$	2.38197	0.0880400
$733$	43.6525	1.61234	0.806170	−	0.591683i	$-0.201536\pi$
$733$	43.6525	1.61234	0.806170	+	0.591683i	$0.201536\pi$
$734$	−25.3262	−0.934808
$735$	−1.61803	−0.0596821
$736$	8.23607	0.303585
$737$	5.72949	0.211048
$738$	−3.85410	−0.141871
$739$	−15.4164	−0.567102	−0.283551	−	0.958957i	$-0.591512\pi$
$739$	−15.4164	−0.567102	−0.283551	+	0.958957i	$0.591512\pi$
$740$	11.9443	0.439080
$741$	0	0
$742$	−0.708204	−0.0259990
$743$	12.4934	0.458339	0.229170	−	0.973387i	$-0.426399\pi$
$743$	12.4934	0.458339	0.229170	+	0.973387i	$0.426399\pi$
$744$	−10.8541	−0.397931
$745$	3.61803	0.132555
$746$	−0.145898	−0.00534171
$747$	−4.36068	−0.159549
$748$	−0.729490	−0.0266728
$749$	3.94427	0.144121
$750$	−14.5623	−0.531740
$751$	10.1803	0.371486	0.185743	−	0.982598i	$-0.440531\pi$
$751$	10.1803	0.371486	0.185743	+	0.982598i	$0.440531\pi$
$752$	−9.94427	−0.362630
$753$	4.00000	0.145768
$754$	−6.97871	−0.254150
$755$	9.76393	0.355346
$756$	−5.47214	−0.199020
$757$	29.8885	1.08632	0.543159	−	0.839630i	$-0.317228\pi$
$757$	29.8885	1.08632	0.543159	+	0.839630i	$0.317228\pi$
$758$	−17.0344	−0.618719
$759$	−66.6312	−2.41856
$760$	0	0
$761$	−39.8328	−1.44394	−0.721969	−	0.691925i	$-0.756763\pi$
$761$	−39.8328	−1.44394	−0.721969	+	0.691925i	$0.756763\pi$
$762$	−13.4721	−0.488044
$763$	6.56231	0.237571
$764$	25.1803	0.910993
$765$	−0.0557281	−0.00201485
$766$	−11.9443	−0.431564
$767$	−20.3951	−0.736425
$768$	−1.61803	−0.0583858
$769$	12.5836	0.453776	0.226888	−	0.973921i	$-0.427145\pi$
$769$	12.5836	0.453776	0.226888	+	0.973921i	$0.427145\pi$
$770$	−5.00000	−0.180187
$771$	41.9787	1.51183
$772$	−12.1803	−0.438380
$773$	−20.5623	−0.739575	−0.369787	−	0.929116i	$-0.620569\pi$
$773$	−20.5623	−0.739575	−0.369787	+	0.929116i	$0.620569\pi$
$774$	−0.0557281	−0.00200310
$775$	26.8328	0.963863
$776$	−0.527864	−0.0189492
$777$	19.3262	0.693325
$778$	−13.6180	−0.488230
$779$	0	0
$780$	−3.00000	−0.107417
$781$	−50.0000	−1.78914
$782$	1.20163	0.0429701
$783$	20.5967	0.736068
$784$	1.00000	0.0357143
$785$	6.67376	0.238197
$786$	−10.7082	−0.381949
$787$	34.3262	1.22360	0.611799	−	0.791013i	$-0.290446\pi$
$787$	34.3262	1.22360	0.611799	+	0.791013i	$0.290446\pi$
$788$	12.5623	0.447514
$789$	4.56231	0.162422
$790$	−2.14590	−0.0763476
$791$	−2.85410	−0.101480
$792$	−1.90983	−0.0678629
$793$	−2.72949	−0.0969270
$794$	−1.27051	−0.0450887
$795$	1.14590	0.0406408
$796$	−16.0902	−0.570301
$797$	11.7984	0.417920	0.208960	−	0.977924i	$-0.432992\pi$
$797$	11.7984	0.417920	0.208960	+	0.977924i	$0.432992\pi$
$798$	0	0
$799$	−1.45085	−0.0513274
$800$	4.00000	0.141421
$801$	−0.708204	−0.0250232
$802$	−33.4164	−1.17997
$803$	−27.8115	−0.981448
$804$	1.85410	0.0653891
$805$	8.23607	0.290283
$806$	12.4377	0.438099
$807$	−21.3262	−0.750719
$808$	−10.8541	−0.381846
$809$	−32.8541	−1.15509	−0.577544	−	0.816359i	$-0.695989\pi$
$809$	−32.8541	−1.15509	−0.577544	+	0.816359i	$0.695989\pi$
$810$	7.70820	0.270839
$811$	−26.5410	−0.931981	−0.465991	−	0.884790i	$-0.654302\pi$
$811$	−26.5410	−0.931981	−0.465991	+	0.884790i	$0.654302\pi$
$812$	−3.76393	−0.132088
$813$	47.9787	1.68269
$814$	59.7214	2.09323
$815$	−8.47214	−0.296766
$816$	−0.236068	−0.00826403
$817$	0	0
$818$	−34.2148	−1.19629
$819$	0.708204	0.0247466
$820$	−10.0902	−0.352364
$821$	14.2361	0.496842	0.248421	−	0.968652i	$-0.420088\pi$
$821$	14.2361	0.496842	0.248421	+	0.968652i	$0.420088\pi$
$822$	−30.9443	−1.07931
$823$	−38.2361	−1.33283	−0.666413	−	0.745583i	$-0.732171\pi$
$823$	−38.2361	−1.33283	−0.666413	+	0.745583i	$0.732171\pi$
$824$	−3.90983	−0.136205
$825$	−32.3607	−1.12665
$826$	−11.0000	−0.382739
$827$	−15.6180	−0.543092	−0.271546	−	0.962425i	$-0.587535\pi$
$827$	−15.6180	−0.543092	−0.271546	+	0.962425i	$0.587535\pi$
$828$	3.14590	0.109328
$829$	28.8885	1.00334	0.501670	−	0.865059i	$-0.332719\pi$
$829$	28.8885	1.00334	0.501670	+	0.865059i	$0.332719\pi$
$830$	−11.4164	−0.396269
$831$	12.9443	0.449032
$832$	1.85410	0.0642794
$833$	0.145898	0.00505507
$834$	6.85410	0.237338
$835$	−24.1803	−0.836795
$836$	0	0
$837$	−36.7082	−1.26882
$838$	−16.7426	−0.578365
$839$	−18.8197	−0.649727	−0.324863	−	0.945761i	$-0.605318\pi$
$839$	−18.8197	−0.649727	−0.324863	+	0.945761i	$0.605318\pi$
$840$	−1.61803	−0.0558275
$841$	−14.8328	−0.511476
$842$	−25.9443	−0.894099
$843$	−12.5623	−0.432669
$844$	21.9443	0.755353
$845$	−9.56231	−0.328953
$846$	−3.79837	−0.130591
$847$	−14.0000	−0.481046
$848$	−0.708204	−0.0243198
$849$	−42.9787	−1.47503
$850$	0.583592	0.0200170
$851$	−98.3738	−3.37221
$852$	−16.1803	−0.554329
$853$	−54.9574	−1.88171	−0.940853	−	0.338814i	$-0.889974\pi$
$853$	−54.9574	−1.88171	−0.940853	+	0.338814i	$0.889974\pi$
$854$	−1.47214	−0.0503755
$855$	0	0
$856$	3.94427	0.134812
$857$	24.7426	0.845193	0.422596	−	0.906318i	$-0.361119\pi$
$857$	24.7426	0.845193	0.422596	+	0.906318i	$0.361119\pi$
$858$	−15.0000	−0.512092
$859$	53.0689	1.81069	0.905343	−	0.424680i	$-0.139613\pi$
$859$	53.0689	1.81069	0.905343	+	0.424680i	$0.139613\pi$
$860$	−0.145898	−0.00497508
$861$	−16.3262	−0.556397
$862$	−14.9443	−0.509004
$863$	20.7082	0.704915	0.352458	−	0.935828i	$-0.385346\pi$
$863$	20.7082	0.704915	0.352458	+	0.935828i	$0.385346\pi$
$864$	−5.47214	−0.186166
$865$	−6.23607	−0.212033
$866$	−25.3820	−0.862514
$867$	27.4721	0.933003
$868$	6.70820	0.227691
$869$	−10.7295	−0.363973
$870$	6.09017	0.206476
$871$	−2.12461	−0.0719897
$872$	6.56231	0.222228
$873$	−0.201626	−0.00682401
$874$	0	0
$875$	9.00000	0.304256
$876$	−9.00000	−0.304082
$877$	10.3262	0.348692	0.174346	−	0.984684i	$-0.444219\pi$
$877$	10.3262	0.348692	0.174346	+	0.984684i	$0.444219\pi$
$878$	−39.9443	−1.34805
$879$	19.0344	0.642016
$880$	−5.00000	−0.168550
$881$	20.8541	0.702593	0.351296	−	0.936264i	$-0.385741\pi$
$881$	20.8541	0.702593	0.351296	+	0.936264i	$0.385741\pi$
$882$	0.381966	0.0128615
$883$	−57.9787	−1.95114	−0.975570	−	0.219691i	$-0.929495\pi$
$883$	−57.9787	−1.95114	−0.975570	+	0.219691i	$0.929495\pi$
$884$	0.270510	0.00909823
$885$	17.7984	0.598286
$886$	34.2148	1.14947
$887$	32.8328	1.10242	0.551209	−	0.834367i	$-0.314167\pi$
$887$	32.8328	1.10242	0.551209	+	0.834367i	$0.314167\pi$
$888$	19.3262	0.648546
$889$	8.32624	0.279253
$890$	−1.85410	−0.0621496
$891$	38.5410	1.29117
$892$	25.6525	0.858908
$893$	0	0
$894$	5.85410	0.195790
$895$	20.0344	0.669678
$896$	1.00000	0.0334077
$897$	24.7082	0.824983
$898$	0.180340	0.00601802
$899$	−25.2492	−0.842109
$900$	1.52786	0.0509288
$901$	−0.103326	−0.00344227
$902$	−50.4508	−1.67983
$903$	−0.236068	−0.00785585
$904$	−2.85410	−0.0949260
$905$	20.2361	0.672670
$906$	15.7984	0.524866
$907$	−32.3262	−1.07338	−0.536688	−	0.843781i	$-0.680325\pi$
$907$	−32.3262	−1.07338	−0.536688	+	0.843781i	$0.680325\pi$
$908$	9.76393	0.324027
$909$	−4.14590	−0.137511
$910$	1.85410	0.0614629
$911$	23.1591	0.767294	0.383647	−	0.923480i	$-0.374668\pi$
$911$	23.1591	0.767294	0.383647	+	0.923480i	$0.374668\pi$
$912$	0	0
$913$	−57.0820	−1.88914
$914$	5.88854	0.194776
$915$	2.38197	0.0787454
$916$	1.09017	0.0360202
$917$	6.61803	0.218547
$918$	−0.798374	−0.0263503
$919$	−19.0344	−0.627888	−0.313944	−	0.949441i	$-0.601650\pi$
$919$	−19.0344	−0.627888	−0.313944	+	0.949441i	$0.601650\pi$
$920$	8.23607	0.271535
$921$	−20.9443	−0.690137
$922$	24.5410	0.808215
$923$	18.5410	0.610285
$924$	−8.09017	−0.266147
$925$	−47.7771	−1.57090
$926$	−6.56231	−0.215651
$927$	−1.49342	−0.0490504
$928$	−3.76393	−0.123557
$929$	8.88854	0.291624	0.145812	−	0.989312i	$-0.453421\pi$
$929$	8.88854	0.291624	0.145812	+	0.989312i	$0.453421\pi$
$930$	−10.8541	−0.355920
$931$	0	0
$932$	18.0344	0.590738
$933$	−39.2148	−1.28383
$934$	−24.5279	−0.802576
$935$	−0.729490	−0.0238569
$936$	0.708204	0.0231484
$937$	−33.3951	−1.09097	−0.545486	−	0.838120i	$-0.683655\pi$
$937$	−33.3951	−1.09097	−0.545486	+	0.838120i	$0.683655\pi$
$938$	−1.14590	−0.0374149
$939$	−48.6869	−1.58884
$940$	−9.94427	−0.324346
$941$	24.2148	0.789379	0.394690	−	0.918814i	$-0.370852\pi$
$941$	24.2148	0.789379	0.394690	+	0.918814i	$0.370852\pi$
$942$	10.7984	0.351830
$943$	83.1033	2.70622
$944$	−11.0000	−0.358020
$945$	−5.47214	−0.178009
$946$	−0.729490	−0.0237178
$947$	14.1115	0.458561	0.229280	−	0.973360i	$-0.426363\pi$
$947$	14.1115	0.458561	0.229280	+	0.973360i	$0.426363\pi$
$948$	−3.47214	−0.112770
$949$	10.3131	0.334777
$950$	0	0
$951$	−29.7984	−0.966278
$952$	0.145898	0.00472858
$953$	−40.7771	−1.32090	−0.660450	−	0.750870i	$-0.729634\pi$
$953$	−40.7771	−1.32090	−0.660450	+	0.750870i	$0.729634\pi$
$954$	−0.270510	−0.00875808
$955$	25.1803	0.814817
$956$	−17.8541	−0.577443
$957$	30.4508	0.984336
$958$	−22.1803	−0.716614
$959$	19.1246	0.617566
$960$	−1.61803	−0.0522218
$961$	14.0000	0.451613
$962$	−22.1459	−0.714012
$963$	1.50658	0.0485488
$964$	−19.0902	−0.614853
$965$	−12.1803	−0.392099
$966$	13.3262	0.428765
$967$	−21.7295	−0.698773	−0.349387	−	0.936979i	$-0.613610\pi$
$967$	−21.7295	−0.698773	−0.349387	+	0.936979i	$0.613610\pi$
$968$	−14.0000	−0.449977
$969$	0	0
$970$	−0.527864	−0.0169487
$971$	7.58359	0.243369	0.121685	−	0.992569i	$-0.461170\pi$
$971$	7.58359	0.243369	0.121685	+	0.992569i	$0.461170\pi$
$972$	−3.94427	−0.126513
$973$	−4.23607	−0.135802
$974$	−11.1803	−0.358241
$975$	12.0000	0.384308
$976$	−1.47214	−0.0471219
$977$	−22.7771	−0.728704	−0.364352	−	0.931261i	$-0.618709\pi$
$977$	−22.7771	−0.728704	−0.364352	+	0.931261i	$0.618709\pi$
$978$	−13.7082	−0.438340
$979$	−9.27051	−0.296287
$980$	1.00000	0.0319438
$981$	2.50658	0.0800289
$982$	−29.5967	−0.944470
$983$	−47.5066	−1.51522	−0.757612	−	0.652705i	$-0.773634\pi$
$983$	−47.5066	−1.51522	−0.757612	+	0.652705i	$0.773634\pi$
$984$	−16.3262	−0.520461
$985$	12.5623	0.400268
$986$	−0.549150	−0.0174885
$987$	−16.0902	−0.512156
$988$	0	0
$989$	1.20163	0.0382095
$990$	−1.90983	−0.0606984
$991$	−1.41641	−0.0449937	−0.0224968	−	0.999747i	$-0.507162\pi$
$991$	−1.41641	−0.0449937	−0.0224968	+	0.999747i	$0.507162\pi$
$992$	6.70820	0.212986
$993$	5.70820	0.181144
$994$	10.0000	0.317181
$995$	−16.0902	−0.510093
$996$	−18.4721	−0.585312
$997$	1.96556	0.0622499	0.0311249	−	0.999516i	$-0.490091\pi$
$997$	1.96556	0.0622499	0.0311249	+	0.999516i	$0.490091\pi$
$998$	10.4164	0.329726
$999$	65.3607	2.06792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.f.1.1	✓	2
19.18	odd	2		5054.2.a.p.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.f.1.1	✓	2	1.1	even	1	trivial
5054.2.a.p.1.2	yes	2	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} -5.00000 q^{11} -1.61803 q^{12} +1.85410 q^{13} +1.00000 q^{14} -1.61803 q^{15} +1.00000 q^{16} +0.145898 q^{17} +0.381966 q^{18} +1.00000 q^{20} +1.61803 q^{21} +5.00000 q^{22} -8.23607 q^{23} +1.61803 q^{24} -4.00000 q^{25} -1.85410 q^{26} +5.47214 q^{27} -1.00000 q^{28} +3.76393 q^{29} +1.61803 q^{30} -6.70820 q^{31} -1.00000 q^{32} +8.09017 q^{33} -0.145898 q^{34} -1.00000 q^{35} -0.381966 q^{36} +11.9443 q^{37} -3.00000 q^{39} -1.00000 q^{40} -10.0902 q^{41} -1.61803 q^{42} -0.145898 q^{43} -5.00000 q^{44} -0.381966 q^{45} +8.23607 q^{46} -9.94427 q^{47} -1.61803 q^{48} +1.00000 q^{49} +4.00000 q^{50} -0.236068 q^{51} +1.85410 q^{52} -0.708204 q^{53} -5.47214 q^{54} -5.00000 q^{55} +1.00000 q^{56} -3.76393 q^{58} -11.0000 q^{59} -1.61803 q^{60} -1.47214 q^{61} +6.70820 q^{62} +0.381966 q^{63} +1.00000 q^{64} +1.85410 q^{65} -8.09017 q^{66} -1.14590 q^{67} +0.145898 q^{68} +13.3262 q^{69} +1.00000 q^{70} +10.0000 q^{71} +0.381966 q^{72} +5.56231 q^{73} -11.9443 q^{74} +6.47214 q^{75} +5.00000 q^{77} +3.00000 q^{78} +2.14590 q^{79} +1.00000 q^{80} -7.70820 q^{81} +10.0902 q^{82} +11.4164 q^{83} +1.61803 q^{84} +0.145898 q^{85} +0.145898 q^{86} -6.09017 q^{87} +5.00000 q^{88} +1.85410 q^{89} +0.381966 q^{90} -1.85410 q^{91} -8.23607 q^{92} +10.8541 q^{93} +9.94427 q^{94} +1.61803 q^{96} +0.527864 q^{97} -1.00000 q^{98} +1.90983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} - 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} + 3 q^{18} + 2 q^{20} + q^{21} + 10 q^{22} - 12 q^{23} + q^{24} - 8 q^{25} + 3 q^{26} + 2 q^{27} - 2 q^{28} + 12 q^{29} + q^{30} - 2 q^{32} + 5 q^{33} - 7 q^{34} - 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 2 q^{40} - 9 q^{41} - q^{42} - 7 q^{43} - 10 q^{44} - 3 q^{45} + 12 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} + 8 q^{50} + 4 q^{51} - 3 q^{52} + 12 q^{53} - 2 q^{54} - 10 q^{55} + 2 q^{56} - 12 q^{58} - 22 q^{59} - q^{60} + 6 q^{61} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 5 q^{66} - 9 q^{67} + 7 q^{68} + 11 q^{69} + 2 q^{70} + 20 q^{71} + 3 q^{72} - 9 q^{73} - 6 q^{74} + 4 q^{75} + 10 q^{77} + 6 q^{78} + 11 q^{79} + 2 q^{80} - 2 q^{81} + 9 q^{82} - 4 q^{83} + q^{84} + 7 q^{85} + 7 q^{86} - q^{87} + 10 q^{88} - 3 q^{89} + 3 q^{90} + 3 q^{91} - 12 q^{92} + 15 q^{93} + 2 q^{94} + q^{96} + 10 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9 - 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 7 * q^17 + 3 * q^18 + 2 * q^20 + q^21 + 10 * q^22 - 12 * q^23 + q^24 - 8 * q^25 + 3 * q^26 + 2 * q^27 - 2 * q^28 + 12 * q^29 + q^30 - 2 * q^32 + 5 * q^33 - 7 * q^34 - 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 2 * q^40 - 9 * q^41 - q^42 - 7 * q^43 - 10 * q^44 - 3 * q^45 + 12 * q^46 - 2 * q^47 - q^48 + 2 * q^49 + 8 * q^50 + 4 * q^51 - 3 * q^52 + 12 * q^53 - 2 * q^54 - 10 * q^55 + 2 * q^56 - 12 * q^58 - 22 * q^59 - q^60 + 6 * q^61 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 5 * q^66 - 9 * q^67 + 7 * q^68 + 11 * q^69 + 2 * q^70 + 20 * q^71 + 3 * q^72 - 9 * q^73 - 6 * q^74 + 4 * q^75 + 10 * q^77 + 6 * q^78 + 11 * q^79 + 2 * q^80 - 2 * q^81 + 9 * q^82 - 4 * q^83 + q^84 + 7 * q^85 + 7 * q^86 - q^87 + 10 * q^88 - 3 * q^89 + 3 * q^90 + 3 * q^91 - 12 * q^92 + 15 * q^93 + 2 * q^94 + q^96 + 10 * q^97 - 2 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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