LMFDB - Embedded newform 299.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(1,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, 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("299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.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:	$2.38752702044$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +0.618034 q^{3} -1.61803 q^{4} -0.381966 q^{5} -0.381966 q^{6} -1.00000 q^{7} +2.23607 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +0.618034 q^{3} -1.61803 q^{4} -0.381966 q^{5} -0.381966 q^{6} -1.00000 q^{7} +2.23607 q^{8} -2.61803 q^{9} +0.236068 q^{10} -2.61803 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.618034 q^{14} -0.236068 q^{15} +1.85410 q^{16} -3.85410 q^{17} +1.61803 q^{18} -4.23607 q^{19} +0.618034 q^{20} -0.618034 q^{21} +1.61803 q^{22} -1.00000 q^{23} +1.38197 q^{24} -4.85410 q^{25} +0.618034 q^{26} -3.47214 q^{27} +1.61803 q^{28} +3.85410 q^{29} +0.145898 q^{30} +3.85410 q^{31} -5.61803 q^{32} -1.61803 q^{33} +2.38197 q^{34} +0.381966 q^{35} +4.23607 q^{36} -0.763932 q^{37} +2.61803 q^{38} -0.618034 q^{39} -0.854102 q^{40} +3.76393 q^{41} +0.381966 q^{42} -0.145898 q^{43} +4.23607 q^{44} +1.00000 q^{45} +0.618034 q^{46} +1.14590 q^{47} +1.14590 q^{48} -6.00000 q^{49} +3.00000 q^{50} -2.38197 q^{51} +1.61803 q^{52} +1.47214 q^{53} +2.14590 q^{54} +1.00000 q^{55} -2.23607 q^{56} -2.61803 q^{57} -2.38197 q^{58} +5.00000 q^{59} +0.381966 q^{60} -0.527864 q^{61} -2.38197 q^{62} +2.61803 q^{63} -0.236068 q^{64} +0.381966 q^{65} +1.00000 q^{66} -3.47214 q^{67} +6.23607 q^{68} -0.618034 q^{69} -0.236068 q^{70} +6.70820 q^{71} -5.85410 q^{72} +4.38197 q^{73} +0.472136 q^{74} -3.00000 q^{75} +6.85410 q^{76} +2.61803 q^{77} +0.381966 q^{78} -0.381966 q^{79} -0.708204 q^{80} +5.70820 q^{81} -2.32624 q^{82} +14.5623 q^{83} +1.00000 q^{84} +1.47214 q^{85} +0.0901699 q^{86} +2.38197 q^{87} -5.85410 q^{88} +5.70820 q^{89} -0.618034 q^{90} +1.00000 q^{91} +1.61803 q^{92} +2.38197 q^{93} -0.708204 q^{94} +1.61803 q^{95} -3.47214 q^{96} -5.29180 q^{97} +3.70820 q^{98} +6.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{9} - 4 q^{10} - 3 q^{11} - 2 q^{12} - 2 q^{13} - q^{14} + 4 q^{15} - 3 q^{16} - q^{17} + q^{18} - 4 q^{19} - q^{20} + q^{21} + q^{22} - 2 q^{23} + 5 q^{24} - 3 q^{25} - q^{26} + 2 q^{27} + q^{28} + q^{29} + 7 q^{30} + q^{31} - 9 q^{32} - q^{33} + 7 q^{34} + 3 q^{35} + 4 q^{36} - 6 q^{37} + 3 q^{38} + q^{39} + 5 q^{40} + 12 q^{41} + 3 q^{42} - 7 q^{43} + 4 q^{44} + 2 q^{45} - q^{46} + 9 q^{47} + 9 q^{48} - 12 q^{49} + 6 q^{50} - 7 q^{51} + q^{52} - 6 q^{53} + 11 q^{54} + 2 q^{55} - 3 q^{57} - 7 q^{58} + 10 q^{59} + 3 q^{60} - 10 q^{61} - 7 q^{62} + 3 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 2 q^{67} + 8 q^{68} + q^{69} + 4 q^{70} - 5 q^{72} + 11 q^{73} - 8 q^{74} - 6 q^{75} + 7 q^{76} + 3 q^{77} + 3 q^{78} - 3 q^{79} + 12 q^{80} - 2 q^{81} + 11 q^{82} + 9 q^{83} + 2 q^{84} - 6 q^{85} - 11 q^{86} + 7 q^{87} - 5 q^{88} - 2 q^{89} + q^{90} + 2 q^{91} + q^{92} + 7 q^{93} + 12 q^{94} + q^{95} + 2 q^{96} - 24 q^{97} - 6 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^9 - 4 * q^10 - 3 * q^11 - 2 * q^12 - 2 * q^13 - q^14 + 4 * q^15 - 3 * q^16 - q^17 + q^18 - 4 * q^19 - q^20 + q^21 + q^22 - 2 * q^23 + 5 * q^24 - 3 * q^25 - q^26 + 2 * q^27 + q^28 + q^29 + 7 * q^30 + q^31 - 9 * q^32 - q^33 + 7 * q^34 + 3 * q^35 + 4 * q^36 - 6 * q^37 + 3 * q^38 + q^39 + 5 * q^40 + 12 * q^41 + 3 * q^42 - 7 * q^43 + 4 * q^44 + 2 * q^45 - q^46 + 9 * q^47 + 9 * q^48 - 12 * q^49 + 6 * q^50 - 7 * q^51 + q^52 - 6 * q^53 + 11 * q^54 + 2 * q^55 - 3 * q^57 - 7 * q^58 + 10 * q^59 + 3 * q^60 - 10 * q^61 - 7 * q^62 + 3 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 2 * q^67 + 8 * q^68 + q^69 + 4 * q^70 - 5 * q^72 + 11 * q^73 - 8 * q^74 - 6 * q^75 + 7 * q^76 + 3 * q^77 + 3 * q^78 - 3 * q^79 + 12 * q^80 - 2 * q^81 + 11 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 - 11 * q^86 + 7 * q^87 - 5 * q^88 - 2 * q^89 + q^90 + 2 * q^91 + q^92 + 7 * q^93 + 12 * q^94 + q^95 + 2 * q^96 - 24 * q^97 - 6 * q^98 + 7 * 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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	−1.61803	−0.809017
$5$	−0.381966	−0.170820	−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966	−0.170820	−0.0854102	+	0.996346i	$0.527220\pi$
$6$	−0.381966	−0.155937
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	2.23607	0.790569
$9$	−2.61803	−0.872678
$10$	0.236068	0.0746512
$11$	−2.61803	−0.789367	−0.394683	−	0.918817i	$-0.629146\pi$
$11$	−2.61803	−0.789367	−0.394683	+	0.918817i	$0.629146\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.618034	0.165177
$15$	−0.236068	−0.0609525
$16$	1.85410	0.463525
$17$	−3.85410	−0.934757	−0.467379	−	0.884057i	$-0.654801\pi$
$17$	−3.85410	−0.934757	−0.467379	+	0.884057i	$0.654801\pi$
$18$	1.61803	0.381374
$19$	−4.23607	−0.971821	−0.485910	−	0.874009i	$-0.661512\pi$
$19$	−4.23607	−0.971821	−0.485910	+	0.874009i	$0.661512\pi$
$20$	0.618034	0.138197
$21$	−0.618034	−0.134866
$22$	1.61803	0.344966
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.38197	0.282093
$25$	−4.85410	−0.970820
$26$	0.618034	0.121206
$27$	−3.47214	−0.668213
$28$	1.61803	0.305780
$29$	3.85410	0.715689	0.357844	−	0.933781i	$-0.383512\pi$
$29$	3.85410	0.715689	0.357844	+	0.933781i	$0.383512\pi$
$30$	0.145898	0.0266372
$31$	3.85410	0.692217	0.346109	−	0.938194i	$-0.387503\pi$
$31$	3.85410	0.692217	0.346109	+	0.938194i	$0.387503\pi$
$32$	−5.61803	−0.993137
$33$	−1.61803	−0.281664
$34$	2.38197	0.408504
$35$	0.381966	0.0645640
$36$	4.23607	0.706011
$37$	−0.763932	−0.125590	−0.0627948	−	0.998026i	$-0.520001\pi$
$37$	−0.763932	−0.125590	−0.0627948	+	0.998026i	$0.520001\pi$
$38$	2.61803	0.424701
$39$	−0.618034	−0.0989646
$40$	−0.854102	−0.135045
$41$	3.76393	0.587827	0.293914	−	0.955832i	$-0.405042\pi$
$41$	3.76393	0.587827	0.293914	+	0.955832i	$0.405042\pi$
$42$	0.381966	0.0589386
$43$	−0.145898	−0.0222492	−0.0111246	−	0.999938i	$-0.503541\pi$
$43$	−0.145898	−0.0222492	−0.0111246	+	0.999938i	$0.503541\pi$
$44$	4.23607	0.638611
$45$	1.00000	0.149071
$46$	0.618034	0.0911241
$47$	1.14590	0.167146	0.0835732	−	0.996502i	$-0.473367\pi$
$47$	1.14590	0.167146	0.0835732	+	0.996502i	$0.473367\pi$
$48$	1.14590	0.165396
$49$	−6.00000	−0.857143
$50$	3.00000	0.424264
$51$	−2.38197	−0.333542
$52$	1.61803	0.224381
$53$	1.47214	0.202213	0.101107	−	0.994876i	$-0.467762\pi$
$53$	1.47214	0.202213	0.101107	+	0.994876i	$0.467762\pi$
$54$	2.14590	0.292020
$55$	1.00000	0.134840
$56$	−2.23607	−0.298807
$57$	−2.61803	−0.346767
$58$	−2.38197	−0.312767
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0.381966	0.0493116
$61$	−0.527864	−0.0675861	−0.0337930	−	0.999429i	$-0.510759\pi$
$61$	−0.527864	−0.0675861	−0.0337930	+	0.999429i	$0.510759\pi$
$62$	−2.38197	−0.302510
$63$	2.61803	0.329841
$64$	−0.236068	−0.0295085
$65$	0.381966	0.0473771
$66$	1.00000	0.123091
$67$	−3.47214	−0.424189	−0.212094	−	0.977249i	$-0.568028\pi$
$67$	−3.47214	−0.424189	−0.212094	+	0.977249i	$0.568028\pi$
$68$	6.23607	0.756234
$69$	−0.618034	−0.0744025
$70$	−0.236068	−0.0282155
$71$	6.70820	0.796117	0.398059	−	0.917360i	$-0.369684\pi$
$71$	6.70820	0.796117	0.398059	+	0.917360i	$0.369684\pi$
$72$	−5.85410	−0.689913
$73$	4.38197	0.512870	0.256435	−	0.966561i	$-0.417452\pi$
$73$	4.38197	0.512870	0.256435	+	0.966561i	$0.417452\pi$
$74$	0.472136	0.0548847
$75$	−3.00000	−0.346410
$76$	6.85410	0.786219
$77$	2.61803	0.298353
$78$	0.381966	0.0432491
$79$	−0.381966	−0.0429745	−0.0214873	−	0.999769i	$-0.506840\pi$
$79$	−0.381966	−0.0429745	−0.0214873	+	0.999769i	$0.506840\pi$
$80$	−0.708204	−0.0791796
$81$	5.70820	0.634245
$82$	−2.32624	−0.256890
$83$	14.5623	1.59842	0.799210	−	0.601051i	$-0.205251\pi$
$83$	14.5623	1.59842	0.799210	+	0.601051i	$0.205251\pi$
$84$	1.00000	0.109109
$85$	1.47214	0.159676
$86$	0.0901699	0.00972328
$87$	2.38197	0.255374
$88$	−5.85410	−0.624049
$89$	5.70820	0.605068	0.302534	−	0.953139i	$-0.402167\pi$
$89$	5.70820	0.605068	0.302534	+	0.953139i	$0.402167\pi$
$90$	−0.618034	−0.0651465
$91$	1.00000	0.104828
$92$	1.61803	0.168692
$93$	2.38197	0.246998
$94$	−0.708204	−0.0730457
$95$	1.61803	0.166007
$96$	−3.47214	−0.354373
$97$	−5.29180	−0.537300	−0.268650	−	0.963238i	$-0.586578\pi$
$97$	−5.29180	−0.537300	−0.268650	+	0.963238i	$0.586578\pi$
$98$	3.70820	0.374585
$99$	6.85410	0.688863
$100$	7.85410	0.785410
$101$	−16.7082	−1.66253	−0.831264	−	0.555878i	$-0.812382\pi$
$101$	−16.7082	−1.66253	−0.831264	+	0.555878i	$0.812382\pi$
$102$	1.47214	0.145763
$103$	−17.4164	−1.71609	−0.858045	−	0.513575i	$-0.828321\pi$
$103$	−17.4164	−1.71609	−0.858045	+	0.513575i	$0.828321\pi$
$104$	−2.23607	−0.219265
$105$	0.236068	0.0230379
$106$	−0.909830	−0.0883705
$107$	13.0902	1.26547	0.632737	−	0.774367i	$-0.281931\pi$
$107$	13.0902	1.26547	0.632737	+	0.774367i	$0.281931\pi$
$108$	5.61803	0.540596
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	−0.618034	−0.0589272
$111$	−0.472136	−0.0448132
$112$	−1.85410	−0.175196
$113$	2.23607	0.210352	0.105176	−	0.994454i	$-0.466459\pi$
$113$	2.23607	0.210352	0.105176	+	0.994454i	$0.466459\pi$
$114$	1.61803	0.151543
$115$	0.381966	0.0356185
$116$	−6.23607	−0.579004
$117$	2.61803	0.242037
$118$	−3.09017	−0.284473
$119$	3.85410	0.353305
$120$	−0.527864	−0.0481872
$121$	−4.14590	−0.376900
$122$	0.326238	0.0295362
$123$	2.32624	0.209750
$124$	−6.23607	−0.560015
$125$	3.76393	0.336656
$126$	−1.61803	−0.144146
$127$	−8.32624	−0.738834	−0.369417	−	0.929264i	$-0.620443\pi$
$127$	−8.32624	−0.738834	−0.369417	+	0.929264i	$0.620443\pi$
$128$	11.3820	1.00603
$129$	−0.0901699	−0.00793902
$130$	−0.236068	−0.0207045
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	2.61803	0.227871
$133$	4.23607	0.367314
$134$	2.14590	0.185377
$135$	1.32624	0.114144
$136$	−8.61803	−0.738990
$137$	−10.4164	−0.889934	−0.444967	−	0.895547i	$-0.646785\pi$
$137$	−10.4164	−0.889934	−0.444967	+	0.895547i	$0.646785\pi$
$138$	0.381966	0.0325151
$139$	−21.4164	−1.81652	−0.908258	−	0.418411i	$-0.862587\pi$
$139$	−21.4164	−1.81652	−0.908258	+	0.418411i	$0.862587\pi$
$140$	−0.618034	−0.0522334
$141$	0.708204	0.0596415
$142$	−4.14590	−0.347916
$143$	2.61803	0.218931
$144$	−4.85410	−0.404508
$145$	−1.47214	−0.122254
$146$	−2.70820	−0.224133
$147$	−3.70820	−0.305848
$148$	1.23607	0.101604
$149$	−18.0902	−1.48200	−0.741002	−	0.671503i	$-0.765649\pi$
$149$	−18.0902	−1.48200	−0.741002	+	0.671503i	$0.765649\pi$
$150$	1.85410	0.151387
$151$	2.52786	0.205715	0.102857	−	0.994696i	$-0.467201\pi$
$151$	2.52786	0.205715	0.102857	+	0.994696i	$0.467201\pi$
$152$	−9.47214	−0.768292
$153$	10.0902	0.815742
$154$	−1.61803	−0.130385
$155$	−1.47214	−0.118245
$156$	1.00000	0.0800641
$157$	−15.7984	−1.26085	−0.630424	−	0.776251i	$-0.717119\pi$
$157$	−15.7984	−1.26085	−0.630424	+	0.776251i	$0.717119\pi$
$158$	0.236068	0.0187806
$159$	0.909830	0.0721542
$160$	2.14590	0.169648
$161$	1.00000	0.0788110
$162$	−3.52786	−0.277175
$163$	18.4164	1.44248	0.721242	−	0.692683i	$-0.243571\pi$
$163$	18.4164	1.44248	0.721242	+	0.692683i	$0.243571\pi$
$164$	−6.09017	−0.475562
$165$	0.618034	0.0481139
$166$	−9.00000	−0.698535
$167$	−4.94427	−0.382599	−0.191300	−	0.981532i	$-0.561270\pi$
$167$	−4.94427	−0.382599	−0.191300	+	0.981532i	$0.561270\pi$
$168$	−1.38197	−0.106621
$169$	1.00000	0.0769231
$170$	−0.909830	−0.0697808
$171$	11.0902	0.848086
$172$	0.236068	0.0180000
$173$	−4.52786	−0.344247	−0.172124	−	0.985075i	$-0.555063\pi$
$173$	−4.52786	−0.344247	−0.172124	+	0.985075i	$0.555063\pi$
$174$	−1.47214	−0.111602
$175$	4.85410	0.366936
$176$	−4.85410	−0.365892
$177$	3.09017	0.232271
$178$	−3.52786	−0.264425
$179$	−2.41641	−0.180611	−0.0903054	−	0.995914i	$-0.528784\pi$
$179$	−2.41641	−0.180611	−0.0903054	+	0.995914i	$0.528784\pi$
$180$	−1.61803	−0.120601
$181$	−24.2361	−1.80145	−0.900726	−	0.434387i	$-0.856965\pi$
$181$	−24.2361	−1.80145	−0.900726	+	0.434387i	$0.856965\pi$
$182$	−0.618034	−0.0458117
$183$	−0.326238	−0.0241162
$184$	−2.23607	−0.164845
$185$	0.291796	0.0214533
$186$	−1.47214	−0.107942
$187$	10.0902	0.737866
$188$	−1.85410	−0.135224
$189$	3.47214	0.252561
$190$	−1.00000	−0.0725476
$191$	−19.4721	−1.40895	−0.704477	−	0.709727i	$-0.748818\pi$
$191$	−19.4721	−1.40895	−0.704477	+	0.709727i	$0.748818\pi$
$192$	−0.145898	−0.0105293
$193$	−15.6525	−1.12669	−0.563345	−	0.826222i	$-0.690486\pi$
$193$	−15.6525	−1.12669	−0.563345	+	0.826222i	$0.690486\pi$
$194$	3.27051	0.234809
$195$	0.236068	0.0169052
$196$	9.70820	0.693443
$197$	23.1246	1.64756	0.823780	−	0.566909i	$-0.191861\pi$
$197$	23.1246	1.64756	0.823780	+	0.566909i	$0.191861\pi$
$198$	−4.23607	−0.301044
$199$	25.2705	1.79138	0.895689	−	0.444680i	$-0.146683\pi$
$199$	25.2705	1.79138	0.895689	+	0.444680i	$0.146683\pi$
$200$	−10.8541	−0.767501
$201$	−2.14590	−0.151360
$202$	10.3262	0.726552
$203$	−3.85410	−0.270505
$204$	3.85410	0.269841
$205$	−1.43769	−0.100413
$206$	10.7639	0.749959
$207$	2.61803	0.181966
$208$	−1.85410	−0.128559
$209$	11.0902	0.767123
$210$	−0.145898	−0.0100679
$211$	14.7984	1.01876	0.509381	−	0.860541i	$-0.329874\pi$
$211$	14.7984	1.01876	0.509381	+	0.860541i	$0.329874\pi$
$212$	−2.38197	−0.163594
$213$	4.14590	0.284072
$214$	−8.09017	−0.553033
$215$	0.0557281	0.00380062
$216$	−7.76393	−0.528269
$217$	−3.85410	−0.261633
$218$	6.79837	0.460444
$219$	2.70820	0.183003
$220$	−1.61803	−0.109088
$221$	3.85410	0.259255
$222$	0.291796	0.0195841
$223$	11.0344	0.738921	0.369460	−	0.929246i	$-0.379543\pi$
$223$	11.0344	0.738921	0.369460	+	0.929246i	$0.379543\pi$
$224$	5.61803	0.375371
$225$	12.7082	0.847214
$226$	−1.38197	−0.0919270
$227$	−9.47214	−0.628688	−0.314344	−	0.949309i	$-0.601784\pi$
$227$	−9.47214	−0.628688	−0.314344	+	0.949309i	$0.601784\pi$
$228$	4.23607	0.280540
$229$	−7.79837	−0.515331	−0.257666	−	0.966234i	$-0.582953\pi$
$229$	−7.79837	−0.515331	−0.257666	+	0.966234i	$0.582953\pi$
$230$	−0.236068	−0.0155659
$231$	1.61803	0.106459
$232$	8.61803	0.565802
$233$	18.4721	1.21015	0.605075	−	0.796169i	$-0.293143\pi$
$233$	18.4721	1.21015	0.605075	+	0.796169i	$0.293143\pi$
$234$	−1.61803	−0.105774
$235$	−0.437694	−0.0285520
$236$	−8.09017	−0.526625
$237$	−0.236068	−0.0153343
$238$	−2.38197	−0.154400
$239$	2.05573	0.132974	0.0664870	−	0.997787i	$-0.478821\pi$
$239$	2.05573	0.132974	0.0664870	+	0.997787i	$0.478821\pi$
$240$	−0.437694	−0.0282530
$241$	4.03444	0.259881	0.129941	−	0.991522i	$-0.458521\pi$
$241$	4.03444	0.259881	0.129941	+	0.991522i	$0.458521\pi$
$242$	2.56231	0.164711
$243$	13.9443	0.894525
$244$	0.854102	0.0546783
$245$	2.29180	0.146417
$246$	−1.43769	−0.0916640
$247$	4.23607	0.269535
$248$	8.61803	0.547246
$249$	9.00000	0.570352
$250$	−2.32624	−0.147124
$251$	16.0344	1.01208	0.506042	−	0.862509i	$-0.331108\pi$
$251$	16.0344	1.01208	0.506042	+	0.862509i	$0.331108\pi$
$252$	−4.23607	−0.266847
$253$	2.61803	0.164594
$254$	5.14590	0.322882
$255$	0.909830	0.0569758
$256$	−6.56231	−0.410144
$257$	−4.70820	−0.293690	−0.146845	−	0.989160i	$-0.546912\pi$
$257$	−4.70820	−0.293690	−0.146845	+	0.989160i	$0.546912\pi$
$258$	0.0557281	0.00346948
$259$	0.763932	0.0474684
$260$	−0.618034	−0.0383288
$261$	−10.0902	−0.624566
$262$	3.70820	0.229094
$263$	0.819660	0.0505424	0.0252712	−	0.999681i	$-0.491955\pi$
$263$	0.819660	0.0505424	0.0252712	+	0.999681i	$0.491955\pi$
$264$	−3.61803	−0.222675
$265$	−0.562306	−0.0345422
$266$	−2.61803	−0.160522
$267$	3.52786	0.215902
$268$	5.61803	0.343176
$269$	−5.32624	−0.324746	−0.162373	−	0.986729i	$-0.551915\pi$
$269$	−5.32624	−0.324746	−0.162373	+	0.986729i	$0.551915\pi$
$270$	−0.819660	−0.0498829
$271$	−2.47214	−0.150172	−0.0750858	−	0.997177i	$-0.523923\pi$
$271$	−2.47214	−0.150172	−0.0750858	+	0.997177i	$0.523923\pi$
$272$	−7.14590	−0.433284
$273$	0.618034	0.0374051
$274$	6.43769	0.388915
$275$	12.7082	0.766334
$276$	1.00000	0.0601929
$277$	−6.81966	−0.409754	−0.204877	−	0.978788i	$-0.565679\pi$
$277$	−6.81966	−0.409754	−0.204877	+	0.978788i	$0.565679\pi$
$278$	13.2361	0.793847
$279$	−10.0902	−0.604083
$280$	0.854102	0.0510424
$281$	−23.7426	−1.41637	−0.708184	−	0.706028i	$-0.750485\pi$
$281$	−23.7426	−1.41637	−0.708184	+	0.706028i	$0.750485\pi$
$282$	−0.437694	−0.0260643
$283$	−2.41641	−0.143641	−0.0718203	−	0.997418i	$-0.522881\pi$
$283$	−2.41641	−0.143641	−0.0718203	+	0.997418i	$0.522881\pi$
$284$	−10.8541	−0.644072
$285$	1.00000	0.0592349
$286$	−1.61803	−0.0956764
$287$	−3.76393	−0.222178
$288$	14.7082	0.866689
$289$	−2.14590	−0.126229
$290$	0.909830	0.0534271
$291$	−3.27051	−0.191721
$292$	−7.09017	−0.414921
$293$	−13.4164	−0.783795	−0.391897	−	0.920009i	$-0.628181\pi$
$293$	−13.4164	−0.783795	−0.391897	+	0.920009i	$0.628181\pi$
$294$	2.29180	0.133660
$295$	−1.90983	−0.111195
$296$	−1.70820	−0.0992873
$297$	9.09017	0.527465
$298$	11.1803	0.647660
$299$	1.00000	0.0578315
$300$	4.85410	0.280252
$301$	0.145898	0.00840942
$302$	−1.56231	−0.0899006
$303$	−10.3262	−0.593227
$304$	−7.85410	−0.450464
$305$	0.201626	0.0115451
$306$	−6.23607	−0.356492
$307$	30.3820	1.73399	0.866995	−	0.498316i	$-0.166048\pi$
$307$	30.3820	1.73399	0.866995	+	0.498316i	$0.166048\pi$
$308$	−4.23607	−0.241372
$309$	−10.7639	−0.612339
$310$	0.909830	0.0516749
$311$	4.05573	0.229979	0.114990	−	0.993367i	$-0.463317\pi$
$311$	4.05573	0.229979	0.114990	+	0.993367i	$0.463317\pi$
$312$	−1.38197	−0.0782384
$313$	5.00000	0.282617	0.141308	−	0.989966i	$-0.454869\pi$
$313$	5.00000	0.282617	0.141308	+	0.989966i	$0.454869\pi$
$314$	9.76393	0.551011
$315$	−1.00000	−0.0563436
$316$	0.618034	0.0347671
$317$	−0.0901699	−0.00506445	−0.00253222	−	0.999997i	$-0.500806\pi$
$317$	−0.0901699	−0.00506445	−0.00253222	+	0.999997i	$0.500806\pi$
$318$	−0.562306	−0.0315325
$319$	−10.0902	−0.564941
$320$	0.0901699	0.00504065
$321$	8.09017	0.451549
$322$	−0.618034	−0.0344417
$323$	16.3262	0.908416
$324$	−9.23607	−0.513115
$325$	4.85410	0.269257
$326$	−11.3820	−0.630389
$327$	−6.79837	−0.375951
$328$	8.41641	0.464718
$329$	−1.14590	−0.0631754
$330$	−0.381966	−0.0210265
$331$	13.1803	0.724457	0.362228	−	0.932089i	$-0.382016\pi$
$331$	13.1803	0.724457	0.362228	+	0.932089i	$0.382016\pi$
$332$	−23.5623	−1.29315
$333$	2.00000	0.109599
$334$	3.05573	0.167202
$335$	1.32624	0.0724601
$336$	−1.14590	−0.0625139
$337$	21.6525	1.17949	0.589743	−	0.807591i	$-0.299229\pi$
$337$	21.6525	1.17949	0.589743	+	0.807591i	$0.299229\pi$
$338$	−0.618034	−0.0336166
$339$	1.38197	0.0750581
$340$	−2.38197	−0.129180
$341$	−10.0902	−0.546413
$342$	−6.85410	−0.370627
$343$	13.0000	0.701934
$344$	−0.326238	−0.0175896
$345$	0.236068	0.0127095
$346$	2.79837	0.150442
$347$	−2.29180	−0.123030	−0.0615150	−	0.998106i	$-0.519593\pi$
$347$	−2.29180	−0.123030	−0.0615150	+	0.998106i	$0.519593\pi$
$348$	−3.85410	−0.206602
$349$	−16.8541	−0.902179	−0.451090	−	0.892479i	$-0.648965\pi$
$349$	−16.8541	−0.902179	−0.451090	+	0.892479i	$0.648965\pi$
$350$	−3.00000	−0.160357
$351$	3.47214	0.185329
$352$	14.7082	0.783950
$353$	22.0000	1.17094	0.585471	−	0.810693i	$-0.300910\pi$
$353$	22.0000	1.17094	0.585471	+	0.810693i	$0.300910\pi$
$354$	−1.90983	−0.101506
$355$	−2.56231	−0.135993
$356$	−9.23607	−0.489511
$357$	2.38197	0.126067
$358$	1.49342	0.0789298
$359$	29.6869	1.56682	0.783408	−	0.621508i	$-0.213480\pi$
$359$	29.6869	1.56682	0.783408	+	0.621508i	$0.213480\pi$
$360$	2.23607	0.117851
$361$	−1.05573	−0.0555646
$362$	14.9787	0.787264
$363$	−2.56231	−0.134486
$364$	−1.61803	−0.0848080
$365$	−1.67376	−0.0876087
$366$	0.201626	0.0105392
$367$	8.94427	0.466887	0.233444	−	0.972370i	$-0.425001\pi$
$367$	8.94427	0.466887	0.233444	+	0.972370i	$0.425001\pi$
$368$	−1.85410	−0.0966517
$369$	−9.85410	−0.512984
$370$	−0.180340	−0.00937542
$371$	−1.47214	−0.0764295
$372$	−3.85410	−0.199826
$373$	−11.8197	−0.611999	−0.305999	−	0.952032i	$-0.598991\pi$
$373$	−11.8197	−0.611999	−0.305999	+	0.952032i	$0.598991\pi$
$374$	−6.23607	−0.322459
$375$	2.32624	0.120126
$376$	2.56231	0.132141
$377$	−3.85410	−0.198496
$378$	−2.14590	−0.110373
$379$	−34.2361	−1.75859	−0.879294	−	0.476279i	$-0.841985\pi$
$379$	−34.2361	−1.75859	−0.879294	+	0.476279i	$0.841985\pi$
$380$	−2.61803	−0.134302
$381$	−5.14590	−0.263632
$382$	12.0344	0.615736
$383$	−10.4721	−0.535101	−0.267551	−	0.963544i	$-0.586214\pi$
$383$	−10.4721	−0.535101	−0.267551	+	0.963544i	$0.586214\pi$
$384$	7.03444	0.358975
$385$	−1.00000	−0.0509647
$386$	9.67376	0.492382
$387$	0.381966	0.0194164
$388$	8.56231	0.434685
$389$	1.85410	0.0940067	0.0470034	−	0.998895i	$-0.485033\pi$
$389$	1.85410	0.0940067	0.0470034	+	0.998895i	$0.485033\pi$
$390$	−0.145898	−0.00738783
$391$	3.85410	0.194910
$392$	−13.4164	−0.677631
$393$	−3.70820	−0.187054
$394$	−14.2918	−0.720010
$395$	0.145898	0.00734093
$396$	−11.0902	−0.557302
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−15.6180	−0.782861
$399$	2.61803	0.131066
$400$	−9.00000	−0.450000
$401$	−10.3262	−0.515668	−0.257834	−	0.966189i	$-0.583009\pi$
$401$	−10.3262	−0.515668	−0.257834	+	0.966189i	$0.583009\pi$
$402$	1.32624	0.0661467
$403$	−3.85410	−0.191986
$404$	27.0344	1.34501
$405$	−2.18034	−0.108342
$406$	2.38197	0.118215
$407$	2.00000	0.0991363
$408$	−5.32624	−0.263688
$409$	1.96556	0.0971906	0.0485953	−	0.998819i	$-0.484526\pi$
$409$	1.96556	0.0971906	0.0485953	+	0.998819i	$0.484526\pi$
$410$	0.888544	0.0438821
$411$	−6.43769	−0.317548
$412$	28.1803	1.38835
$413$	−5.00000	−0.246034
$414$	−1.61803	−0.0795220
$415$	−5.56231	−0.273043
$416$	5.61803	0.275447
$417$	−13.2361	−0.648173
$418$	−6.85410	−0.335245
$419$	−18.1803	−0.888168	−0.444084	−	0.895985i	$-0.646471\pi$
$419$	−18.1803	−0.888168	−0.444084	+	0.895985i	$0.646471\pi$
$420$	−0.381966	−0.0186380
$421$	−30.5066	−1.48680	−0.743400	−	0.668847i	$-0.766788\pi$
$421$	−30.5066	−1.48680	−0.743400	+	0.668847i	$0.766788\pi$
$422$	−9.14590	−0.445215
$423$	−3.00000	−0.145865
$424$	3.29180	0.159864
$425$	18.7082	0.907481
$426$	−2.56231	−0.124144
$427$	0.527864	0.0255451
$428$	−21.1803	−1.02379
$429$	1.61803	0.0781194
$430$	−0.0344419	−0.00166093
$431$	7.12461	0.343180	0.171590	−	0.985168i	$-0.445109\pi$
$431$	7.12461	0.343180	0.171590	+	0.985168i	$0.445109\pi$
$432$	−6.43769	−0.309734
$433$	23.3607	1.12264	0.561321	−	0.827598i	$-0.310293\pi$
$433$	23.3607	1.12264	0.561321	+	0.827598i	$0.310293\pi$
$434$	2.38197	0.114338
$435$	−0.909830	−0.0436230
$436$	17.7984	0.852388
$437$	4.23607	0.202639
$438$	−1.67376	−0.0799754
$439$	15.8328	0.755659	0.377830	−	0.925875i	$-0.376671\pi$
$439$	15.8328	0.755659	0.377830	+	0.925875i	$0.376671\pi$
$440$	2.23607	0.106600
$441$	15.7082	0.748010
$442$	−2.38197	−0.113299
$443$	−33.2361	−1.57909	−0.789547	−	0.613691i	$-0.789684\pi$
$443$	−33.2361	−1.57909	−0.789547	+	0.613691i	$0.789684\pi$
$444$	0.763932	0.0362546
$445$	−2.18034	−0.103358
$446$	−6.81966	−0.322920
$447$	−11.1803	−0.528812
$448$	0.236068	0.0111532
$449$	−27.6525	−1.30500	−0.652501	−	0.757788i	$-0.726280\pi$
$449$	−27.6525	−1.30500	−0.652501	+	0.757788i	$0.726280\pi$
$450$	−7.85410	−0.370246
$451$	−9.85410	−0.464012
$452$	−3.61803	−0.170178
$453$	1.56231	0.0734035
$454$	5.85410	0.274747
$455$	−0.381966	−0.0179068
$456$	−5.85410	−0.274143
$457$	−40.3050	−1.88539	−0.942693	−	0.333661i	$-0.891716\pi$
$457$	−40.3050	−1.88539	−0.942693	+	0.333661i	$0.891716\pi$
$458$	4.81966	0.225208
$459$	13.3820	0.624617
$460$	−0.618034	−0.0288160
$461$	32.1591	1.49780	0.748898	−	0.662685i	$-0.230583\pi$
$461$	32.1591	1.49780	0.748898	+	0.662685i	$0.230583\pi$
$462$	−1.00000	−0.0465242
$463$	33.6525	1.56396	0.781982	−	0.623302i	$-0.214209\pi$
$463$	33.6525	1.56396	0.781982	+	0.623302i	$0.214209\pi$
$464$	7.14590	0.331740
$465$	−0.909830	−0.0421924
$466$	−11.4164	−0.528855
$467$	4.12461	0.190864	0.0954321	−	0.995436i	$-0.469577\pi$
$467$	4.12461	0.190864	0.0954321	+	0.995436i	$0.469577\pi$
$468$	−4.23607	−0.195812
$469$	3.47214	0.160328
$470$	0.270510	0.0124777
$471$	−9.76393	−0.449898
$472$	11.1803	0.514617
$473$	0.381966	0.0175628
$474$	0.145898	0.00670132
$475$	20.5623	0.943463
$476$	−6.23607	−0.285830
$477$	−3.85410	−0.176467
$478$	−1.27051	−0.0581118
$479$	−30.8541	−1.40976	−0.704880	−	0.709327i	$-0.748999\pi$
$479$	−30.8541	−1.40976	−0.704880	+	0.709327i	$0.748999\pi$
$480$	1.32624	0.0605342
$481$	0.763932	0.0348323
$482$	−2.49342	−0.113572
$483$	0.618034	0.0281215
$484$	6.70820	0.304918
$485$	2.02129	0.0917819
$486$	−8.61803	−0.390922
$487$	−20.2705	−0.918544	−0.459272	−	0.888296i	$-0.651890\pi$
$487$	−20.2705	−0.918544	−0.459272	+	0.888296i	$0.651890\pi$
$488$	−1.18034	−0.0534315
$489$	11.3820	0.514710
$490$	−1.41641	−0.0639868
$491$	−4.41641	−0.199310	−0.0996548	−	0.995022i	$-0.531774\pi$
$491$	−4.41641	−0.199310	−0.0996548	+	0.995022i	$0.531774\pi$
$492$	−3.76393	−0.169691
$493$	−14.8541	−0.668995
$494$	−2.61803	−0.117791
$495$	−2.61803	−0.117672
$496$	7.14590	0.320860
$497$	−6.70820	−0.300904
$498$	−5.56231	−0.249253
$499$	6.00000	0.268597	0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000	0.268597	0.134298	+	0.990941i	$0.457122\pi$
$500$	−6.09017	−0.272361
$501$	−3.05573	−0.136520
$502$	−9.90983	−0.442297
$503$	16.0902	0.717425	0.358713	−	0.933448i	$-0.383216\pi$
$503$	16.0902	0.717425	0.358713	+	0.933448i	$0.383216\pi$
$504$	5.85410	0.260762
$505$	6.38197	0.283994
$506$	−1.61803	−0.0719304
$507$	0.618034	0.0274479
$508$	13.4721	0.597729
$509$	−15.6738	−0.694727	−0.347364	−	0.937731i	$-0.612923\pi$
$509$	−15.6738	−0.694727	−0.347364	+	0.937731i	$0.612923\pi$
$510$	−0.562306	−0.0248993
$511$	−4.38197	−0.193847
$512$	−18.7082	−0.826794
$513$	14.7082	0.649383
$514$	2.90983	0.128347
$515$	6.65248	0.293143
$516$	0.145898	0.00642280
$517$	−3.00000	−0.131940
$518$	−0.472136	−0.0207445
$519$	−2.79837	−0.122835
$520$	0.854102	0.0374548
$521$	−34.0689	−1.49258	−0.746292	−	0.665618i	$-0.768168\pi$
$521$	−34.0689	−1.49258	−0.746292	+	0.665618i	$0.768168\pi$
$522$	6.23607	0.272945
$523$	−24.9443	−1.09074	−0.545368	−	0.838196i	$-0.683610\pi$
$523$	−24.9443	−1.09074	−0.545368	+	0.838196i	$0.683610\pi$
$524$	9.70820	0.424105
$525$	3.00000	0.130931
$526$	−0.506578	−0.0220878
$527$	−14.8541	−0.647055
$528$	−3.00000	−0.130558
$529$	1.00000	0.0434783
$530$	0.347524	0.0150955
$531$	−13.0902	−0.568065
$532$	−6.85410	−0.297163
$533$	−3.76393	−0.163034
$534$	−2.18034	−0.0943525
$535$	−5.00000	−0.216169
$536$	−7.76393	−0.335351
$537$	−1.49342	−0.0644459
$538$	3.29180	0.141919
$539$	15.7082	0.676600
$540$	−2.14590	−0.0923447
$541$	−4.90983	−0.211090	−0.105545	−	0.994415i	$-0.533659\pi$
$541$	−4.90983	−0.211090	−0.105545	+	0.994415i	$0.533659\pi$
$542$	1.52786	0.0656274
$543$	−14.9787	−0.642798
$544$	21.6525	0.928342
$545$	4.20163	0.179978
$546$	−0.381966	−0.0163466
$547$	32.7426	1.39997	0.699987	−	0.714155i	$-0.253189\pi$
$547$	32.7426	1.39997	0.699987	+	0.714155i	$0.253189\pi$
$548$	16.8541	0.719972
$549$	1.38197	0.0589809
$550$	−7.85410	−0.334900
$551$	−16.3262	−0.695521
$552$	−1.38197	−0.0588204
$553$	0.381966	0.0162428
$554$	4.21478	0.179069
$555$	0.180340	0.00765500
$556$	34.6525	1.46959
$557$	−27.8328	−1.17931	−0.589657	−	0.807654i	$-0.700737\pi$
$557$	−27.8328	−1.17931	−0.589657	+	0.807654i	$0.700737\pi$
$558$	6.23607	0.263994
$559$	0.145898	0.00617083
$560$	0.708204	0.0299271
$561$	6.23607	0.263287
$562$	14.6738	0.618975
$563$	−3.90983	−0.164780	−0.0823898	−	0.996600i	$-0.526255\pi$
$563$	−3.90983	−0.164780	−0.0823898	+	0.996600i	$0.526255\pi$
$564$	−1.14590	−0.0482510
$565$	−0.854102	−0.0359323
$566$	1.49342	0.0627732
$567$	−5.70820	−0.239722
$568$	15.0000	0.629386
$569$	21.9230	0.919059	0.459530	−	0.888162i	$-0.348018\pi$
$569$	21.9230	0.919059	0.459530	+	0.888162i	$0.348018\pi$
$570$	−0.618034	−0.0258866
$571$	16.2148	0.678567	0.339284	−	0.940684i	$-0.389815\pi$
$571$	16.2148	0.678567	0.339284	+	0.940684i	$0.389815\pi$
$572$	−4.23607	−0.177119
$573$	−12.0344	−0.502746
$574$	2.32624	0.0970953
$575$	4.85410	0.202430
$576$	0.618034	0.0257514
$577$	29.8885	1.24428	0.622138	−	0.782907i	$-0.286264\pi$
$577$	29.8885	1.24428	0.622138	+	0.782907i	$0.286264\pi$
$578$	1.32624	0.0551642
$579$	−9.67376	−0.402028
$580$	2.38197	0.0989058
$581$	−14.5623	−0.604146
$582$	2.02129	0.0837850
$583$	−3.85410	−0.159621
$584$	9.79837	0.405460
$585$	−1.00000	−0.0413449
$586$	8.29180	0.342531
$587$	−0.583592	−0.0240874	−0.0120437	−	0.999927i	$-0.503834\pi$
$587$	−0.583592	−0.0240874	−0.0120437	+	0.999927i	$0.503834\pi$
$588$	6.00000	0.247436
$589$	−16.3262	−0.672711
$590$	1.18034	0.0485938
$591$	14.2918	0.587886
$592$	−1.41641	−0.0582140
$593$	31.3607	1.28783	0.643914	−	0.765098i	$-0.277309\pi$
$593$	31.3607	1.28783	0.643914	+	0.765098i	$0.277309\pi$
$594$	−5.61803	−0.230511
$595$	−1.47214	−0.0603517
$596$	29.2705	1.19897
$597$	15.6180	0.639204
$598$	−0.618034	−0.0252733
$599$	25.7771	1.05322	0.526612	−	0.850106i	$-0.323462\pi$
$599$	25.7771	1.05322	0.526612	+	0.850106i	$0.323462\pi$
$600$	−6.70820	−0.273861
$601$	16.0344	0.654059	0.327029	−	0.945014i	$-0.393952\pi$
$601$	16.0344	0.654059	0.327029	+	0.945014i	$0.393952\pi$
$602$	−0.0901699	−0.00367505
$603$	9.09017	0.370180
$604$	−4.09017	−0.166427
$605$	1.58359	0.0643822
$606$	6.38197	0.259250
$607$	−11.7984	−0.478881	−0.239441	−	0.970911i	$-0.576964\pi$
$607$	−11.7984	−0.478881	−0.239441	+	0.970911i	$0.576964\pi$
$608$	23.7984	0.965152
$609$	−2.38197	−0.0965221
$610$	−0.124612	−0.00504538
$611$	−1.14590	−0.0463581
$612$	−16.3262	−0.659949
$613$	−16.6525	−0.672587	−0.336294	−	0.941757i	$-0.609173\pi$
$613$	−16.6525	−0.672587	−0.336294	+	0.941757i	$0.609173\pi$
$614$	−18.7771	−0.757782
$615$	−0.888544	−0.0358295
$616$	5.85410	0.235868
$617$	25.7082	1.03497	0.517487	−	0.855691i	$-0.326868\pi$
$617$	25.7082	1.03497	0.517487	+	0.855691i	$0.326868\pi$
$618$	6.65248	0.267602
$619$	−15.5836	−0.626357	−0.313179	−	0.949694i	$-0.601394\pi$
$619$	−15.5836	−0.626357	−0.313179	+	0.949694i	$0.601394\pi$
$620$	2.38197	0.0956621
$621$	3.47214	0.139332
$622$	−2.50658	−0.100505
$623$	−5.70820	−0.228694
$624$	−1.14590	−0.0458726
$625$	22.8328	0.913313
$626$	−3.09017	−0.123508
$627$	6.85410	0.273726
$628$	25.5623	1.02005
$629$	2.94427	0.117396
$630$	0.618034	0.0246231
$631$	−21.2705	−0.846766	−0.423383	−	0.905951i	$-0.639157\pi$
$631$	−21.2705	−0.846766	−0.423383	+	0.905951i	$0.639157\pi$
$632$	−0.854102	−0.0339744
$633$	9.14590	0.363517
$634$	0.0557281	0.00221325
$635$	3.18034	0.126208
$636$	−1.47214	−0.0583740
$637$	6.00000	0.237729
$638$	6.23607	0.246888
$639$	−17.5623	−0.694754
$640$	−4.34752	−0.171851
$641$	−28.4508	−1.12374	−0.561871	−	0.827225i	$-0.689918\pi$
$641$	−28.4508	−1.12374	−0.561871	+	0.827225i	$0.689918\pi$
$642$	−5.00000	−0.197334
$643$	−1.32624	−0.0523017	−0.0261509	−	0.999658i	$-0.508325\pi$
$643$	−1.32624	−0.0523017	−0.0261509	+	0.999658i	$0.508325\pi$
$644$	−1.61803	−0.0637595
$645$	0.0344419	0.00135615
$646$	−10.0902	−0.396992
$647$	34.7082	1.36452	0.682260	−	0.731109i	$-0.260997\pi$
$647$	34.7082	1.36452	0.682260	+	0.731109i	$0.260997\pi$
$648$	12.7639	0.501415
$649$	−13.0902	−0.513834
$650$	−3.00000	−0.117670
$651$	−2.38197	−0.0933566
$652$	−29.7984	−1.16699
$653$	−20.0557	−0.784841	−0.392421	−	0.919786i	$-0.628362\pi$
$653$	−20.0557	−0.784841	−0.392421	+	0.919786i	$0.628362\pi$
$654$	4.20163	0.164297
$655$	2.29180	0.0895479
$656$	6.97871	0.272473
$657$	−11.4721	−0.447571
$658$	0.708204	0.0276087
$659$	−17.1246	−0.667080	−0.333540	−	0.942736i	$-0.608243\pi$
$659$	−17.1246	−0.667080	−0.333540	+	0.942736i	$0.608243\pi$
$660$	−1.00000	−0.0389249
$661$	−24.3951	−0.948860	−0.474430	−	0.880293i	$-0.657346\pi$
$661$	−24.3951	−0.948860	−0.474430	+	0.880293i	$0.657346\pi$
$662$	−8.14590	−0.316599
$663$	2.38197	0.0925079
$664$	32.5623	1.26366
$665$	−1.61803	−0.0627447
$666$	−1.23607	−0.0478967
$667$	−3.85410	−0.149231
$668$	8.00000	0.309529
$669$	6.81966	0.263663
$670$	−0.819660	−0.0316662
$671$	1.38197	0.0533502
$672$	3.47214	0.133941
$673$	39.9787	1.54107	0.770533	−	0.637400i	$-0.219990\pi$
$673$	39.9787	1.54107	0.770533	+	0.637400i	$0.219990\pi$
$674$	−13.3820	−0.515454
$675$	16.8541	0.648715
$676$	−1.61803	−0.0622321
$677$	5.74265	0.220708	0.110354	−	0.993892i	$-0.464802\pi$
$677$	5.74265	0.220708	0.110354	+	0.993892i	$0.464802\pi$
$678$	−0.854102	−0.0328016
$679$	5.29180	0.203080
$680$	3.29180	0.126235
$681$	−5.85410	−0.224330
$682$	6.23607	0.238791
$683$	−36.2148	−1.38572	−0.692860	−	0.721072i	$-0.743650\pi$
$683$	−36.2148	−1.38572	−0.692860	+	0.721072i	$0.743650\pi$
$684$	−17.9443	−0.686116
$685$	3.97871	0.152019
$686$	−8.03444	−0.306756
$687$	−4.81966	−0.183882
$688$	−0.270510	−0.0103131
$689$	−1.47214	−0.0560839
$690$	−0.145898	−0.00555424
$691$	−38.6312	−1.46960	−0.734800	−	0.678284i	$-0.762724\pi$
$691$	−38.6312	−1.46960	−0.734800	+	0.678284i	$0.762724\pi$
$692$	7.32624	0.278502
$693$	−6.85410	−0.260366
$694$	1.41641	0.0537661
$695$	8.18034	0.310298
$696$	5.32624	0.201891
$697$	−14.5066	−0.549476
$698$	10.4164	0.394267
$699$	11.4164	0.431808
$700$	−7.85410	−0.296857
$701$	39.7639	1.50186	0.750931	−	0.660380i	$-0.229605\pi$
$701$	39.7639	1.50186	0.750931	+	0.660380i	$0.229605\pi$
$702$	−2.14590	−0.0809917
$703$	3.23607	0.122051
$704$	0.618034	0.0232930
$705$	−0.270510	−0.0101880
$706$	−13.5967	−0.511720
$707$	16.7082	0.628377
$708$	−5.00000	−0.187912
$709$	50.5410	1.89811	0.949054	−	0.315114i	$-0.102043\pi$
$709$	50.5410	1.89811	0.949054	+	0.315114i	$0.102043\pi$
$710$	1.58359	0.0594312
$711$	1.00000	0.0375029
$712$	12.7639	0.478349
$713$	−3.85410	−0.144337
$714$	−1.47214	−0.0550933
$715$	−1.00000	−0.0373979
$716$	3.90983	0.146117
$717$	1.27051	0.0474481
$718$	−18.3475	−0.684724
$719$	−4.79837	−0.178949	−0.0894746	−	0.995989i	$-0.528519\pi$
$719$	−4.79837	−0.178949	−0.0894746	+	0.995989i	$0.528519\pi$
$720$	1.85410	0.0690983
$721$	17.4164	0.648621
$722$	0.652476	0.0242826
$723$	2.49342	0.0927314
$724$	39.2148	1.45741
$725$	−18.7082	−0.694805
$726$	1.58359	0.0587726
$727$	18.7639	0.695916	0.347958	−	0.937510i	$-0.386875\pi$
$727$	18.7639	0.695916	0.347958	+	0.937510i	$0.386875\pi$
$728$	2.23607	0.0828742
$729$	−8.50658	−0.315058
$730$	1.03444	0.0382864
$731$	0.562306	0.0207976
$732$	0.527864	0.0195104
$733$	8.83282	0.326247	0.163124	−	0.986606i	$-0.447843\pi$
$733$	8.83282	0.326247	0.163124	+	0.986606i	$0.447843\pi$
$734$	−5.52786	−0.204037
$735$	1.41641	0.0522450
$736$	5.61803	0.207083
$737$	9.09017	0.334841
$738$	6.09017	0.224182
$739$	−28.7082	−1.05605	−0.528024	−	0.849229i	$-0.677067\pi$
$739$	−28.7082	−1.05605	−0.528024	+	0.849229i	$0.677067\pi$
$740$	−0.472136	−0.0173561
$741$	2.61803	0.0961759
$742$	0.909830	0.0334009
$743$	25.0689	0.919688	0.459844	−	0.888000i	$-0.347905\pi$
$743$	25.0689	0.919688	0.459844	+	0.888000i	$0.347905\pi$
$744$	5.32624	0.195269
$745$	6.90983	0.253157
$746$	7.30495	0.267453
$747$	−38.1246	−1.39491
$748$	−16.3262	−0.596946
$749$	−13.0902	−0.478304
$750$	−1.43769	−0.0524972
$751$	4.76393	0.173838	0.0869192	−	0.996215i	$-0.472298\pi$
$751$	4.76393	0.173838	0.0869192	+	0.996215i	$0.472298\pi$
$752$	2.12461	0.0774766
$753$	9.90983	0.361134
$754$	2.38197	0.0867461
$755$	−0.965558	−0.0351403
$756$	−5.61803	−0.204326
$757$	−29.3607	−1.06713	−0.533566	−	0.845758i	$-0.679148\pi$
$757$	−29.3607	−1.06713	−0.533566	+	0.845758i	$0.679148\pi$
$758$	21.1591	0.768531
$759$	1.61803	0.0587309
$760$	3.61803	0.131240
$761$	20.2705	0.734805	0.367403	−	0.930062i	$-0.380247\pi$
$761$	20.2705	0.734805	0.367403	+	0.930062i	$0.380247\pi$
$762$	3.18034	0.115212
$763$	11.0000	0.398227
$764$	31.5066	1.13987
$765$	−3.85410	−0.139345
$766$	6.47214	0.233848
$767$	−5.00000	−0.180540
$768$	−4.05573	−0.146348
$769$	1.70820	0.0615994	0.0307997	−	0.999526i	$-0.490195\pi$
$769$	1.70820	0.0615994	0.0307997	+	0.999526i	$0.490195\pi$
$770$	0.618034	0.0222724
$771$	−2.90983	−0.104795
$772$	25.3262	0.911511
$773$	45.5623	1.63876	0.819381	−	0.573249i	$-0.194317\pi$
$773$	45.5623	1.63876	0.819381	+	0.573249i	$0.194317\pi$
$774$	−0.236068	−0.00848529
$775$	−18.7082	−0.672019
$776$	−11.8328	−0.424773
$777$	0.472136	0.0169378
$778$	−1.14590	−0.0410824
$779$	−15.9443	−0.571263
$780$	−0.381966	−0.0136766
$781$	−17.5623	−0.628429
$782$	−2.38197	−0.0851789
$783$	−13.3820	−0.478232
$784$	−11.1246	−0.397308
$785$	6.03444	0.215378
$786$	2.29180	0.0817457
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	−37.4164	−1.33290
$789$	0.506578	0.0180346
$790$	−0.0901699	−0.00320810
$791$	−2.23607	−0.0795054
$792$	15.3262	0.544594
$793$	0.527864	0.0187450
$794$	−8.65248	−0.307065
$795$	−0.347524	−0.0123254
$796$	−40.8885	−1.44926
$797$	20.7426	0.734742	0.367371	−	0.930074i	$-0.380258\pi$
$797$	20.7426	0.734742	0.367371	+	0.930074i	$0.380258\pi$
$798$	−1.61803	−0.0572778
$799$	−4.41641	−0.156241
$800$	27.2705	0.964158
$801$	−14.9443	−0.528030
$802$	6.38197	0.225355
$803$	−11.4721	−0.404843
$804$	3.47214	0.122453
$805$	−0.381966	−0.0134625
$806$	2.38197	0.0839012
$807$	−3.29180	−0.115877
$808$	−37.3607	−1.31434
$809$	44.3050	1.55768	0.778840	−	0.627223i	$-0.215809\pi$
$809$	44.3050	1.55768	0.778840	+	0.627223i	$0.215809\pi$
$810$	1.34752	0.0473472
$811$	32.7984	1.15171	0.575853	−	0.817553i	$-0.304670\pi$
$811$	32.7984	1.15171	0.575853	+	0.817553i	$0.304670\pi$
$812$	6.23607	0.218843
$813$	−1.52786	−0.0535845
$814$	−1.23607	−0.0433242
$815$	−7.03444	−0.246406
$816$	−4.41641	−0.154605
$817$	0.618034	0.0216223
$818$	−1.21478	−0.0424738
$819$	−2.61803	−0.0914815
$820$	2.32624	0.0812358
$821$	−29.0344	−1.01331	−0.506655	−	0.862149i	$-0.669118\pi$
$821$	−29.0344	−1.01331	−0.506655	+	0.862149i	$0.669118\pi$
$822$	3.97871	0.138774
$823$	−39.7426	−1.38534	−0.692671	−	0.721254i	$-0.743566\pi$
$823$	−39.7426	−1.38534	−0.692671	+	0.721254i	$0.743566\pi$
$824$	−38.9443	−1.35669
$825$	7.85410	0.273445
$826$	3.09017	0.107521
$827$	−39.2148	−1.36363	−0.681816	−	0.731524i	$-0.738809\pi$
$827$	−39.2148	−1.36363	−0.681816	+	0.731524i	$0.738809\pi$
$828$	−4.23607	−0.147214
$829$	−48.5967	−1.68783	−0.843917	−	0.536473i	$-0.819756\pi$
$829$	−48.5967	−1.68783	−0.843917	+	0.536473i	$0.819756\pi$
$830$	3.43769	0.119324
$831$	−4.21478	−0.146209
$832$	0.236068	0.00818418
$833$	23.1246	0.801220
$834$	8.18034	0.283262
$835$	1.88854	0.0653558
$836$	−17.9443	−0.620616
$837$	−13.3820	−0.462548
$838$	11.2361	0.388144
$839$	−6.81966	−0.235441	−0.117720	−	0.993047i	$-0.537559\pi$
$839$	−6.81966	−0.235441	−0.117720	+	0.993047i	$0.537559\pi$
$840$	0.527864	0.0182130
$841$	−14.1459	−0.487790
$842$	18.8541	0.649755
$843$	−14.6738	−0.505391
$844$	−23.9443	−0.824196
$845$	−0.381966	−0.0131400
$846$	1.85410	0.0637453
$847$	4.14590	0.142455
$848$	2.72949	0.0937311
$849$	−1.49342	−0.0512541
$850$	−11.5623	−0.396584
$851$	0.763932	0.0261873
$852$	−6.70820	−0.229819
$853$	−46.3050	−1.58545	−0.792726	−	0.609579i	$-0.791339\pi$
$853$	−46.3050	−1.58545	−0.792726	+	0.609579i	$0.791339\pi$
$854$	−0.326238	−0.0111636
$855$	−4.23607	−0.144870
$856$	29.2705	1.00045
$857$	27.2918	0.932270	0.466135	−	0.884714i	$-0.345646\pi$
$857$	27.2918	0.932270	0.466135	+	0.884714i	$0.345646\pi$
$858$	−1.00000	−0.0341394
$859$	−17.3951	−0.593514	−0.296757	−	0.954953i	$-0.595905\pi$
$859$	−17.3951	−0.593514	−0.296757	+	0.954953i	$0.595905\pi$
$860$	−0.0901699	−0.00307477
$861$	−2.32624	−0.0792780
$862$	−4.40325	−0.149975
$863$	−31.4508	−1.07060	−0.535300	−	0.844662i	$-0.679801\pi$
$863$	−31.4508	−1.07060	−0.535300	+	0.844662i	$0.679801\pi$
$864$	19.5066	0.663627
$865$	1.72949	0.0588044
$866$	−14.4377	−0.490613
$867$	−1.32624	−0.0450414
$868$	6.23607	0.211666
$869$	1.00000	0.0339227
$870$	0.562306	0.0190640
$871$	3.47214	0.117649
$872$	−24.5967	−0.832951
$873$	13.8541	0.468890
$874$	−2.61803	−0.0885563
$875$	−3.76393	−0.127244
$876$	−4.38197	−0.148053
$877$	14.9098	0.503469	0.251735	−	0.967796i	$-0.418999\pi$
$877$	14.9098	0.503469	0.251735	+	0.967796i	$0.418999\pi$
$878$	−9.78522	−0.330235
$879$	−8.29180	−0.279675
$880$	1.85410	0.0625018
$881$	−10.8541	−0.365684	−0.182842	−	0.983142i	$-0.558530\pi$
$881$	−10.8541	−0.365684	−0.182842	+	0.983142i	$0.558530\pi$
$882$	−9.70820	−0.326892
$883$	−21.3951	−0.720003	−0.360002	−	0.932952i	$-0.617224\pi$
$883$	−21.3951	−0.720003	−0.360002	+	0.932952i	$0.617224\pi$
$884$	−6.23607	−0.209742
$885$	−1.18034	−0.0396767
$886$	20.5410	0.690089
$887$	−4.02129	−0.135022	−0.0675108	−	0.997719i	$-0.521506\pi$
$887$	−4.02129	−0.135022	−0.0675108	+	0.997719i	$0.521506\pi$
$888$	−1.05573	−0.0354279
$889$	8.32624	0.279253
$890$	1.34752	0.0451691
$891$	−14.9443	−0.500652
$892$	−17.8541	−0.597800
$893$	−4.85410	−0.162436
$894$	6.90983	0.231099
$895$	0.922986	0.0308520
$896$	−11.3820	−0.380245
$897$	0.618034	0.0206356
$898$	17.0902	0.570306
$899$	14.8541	0.495412
$900$	−20.5623	−0.685410
$901$	−5.67376	−0.189020
$902$	6.09017	0.202780
$903$	0.0901699	0.00300067
$904$	5.00000	0.166298
$905$	9.25735	0.307725
$906$	−0.965558	−0.0320785
$907$	7.20163	0.239126	0.119563	−	0.992827i	$-0.461851\pi$
$907$	7.20163	0.239126	0.119563	+	0.992827i	$0.461851\pi$
$908$	15.3262	0.508619
$909$	43.7426	1.45085
$910$	0.236068	0.00782558
$911$	−4.88854	−0.161965	−0.0809823	−	0.996716i	$-0.525806\pi$
$911$	−4.88854	−0.161965	−0.0809823	+	0.996716i	$0.525806\pi$
$912$	−4.85410	−0.160735
$913$	−38.1246	−1.26174
$914$	24.9098	0.823944
$915$	0.124612	0.00411954
$916$	12.6180	0.416912
$917$	6.00000	0.198137
$918$	−8.27051	−0.272967
$919$	−27.5623	−0.909197	−0.454598	−	0.890697i	$-0.650217\pi$
$919$	−27.5623	−0.909197	−0.454598	+	0.890697i	$0.650217\pi$
$920$	0.854102	0.0281589
$921$	18.7771	0.618726
$922$	−19.8754	−0.654561
$923$	−6.70820	−0.220803
$924$	−2.61803	−0.0861270
$925$	3.70820	0.121925
$926$	−20.7984	−0.683477
$927$	45.5967	1.49759
$928$	−21.6525	−0.710777
$929$	51.6312	1.69396	0.846982	−	0.531621i	$-0.178417\pi$
$929$	51.6312	1.69396	0.846982	+	0.531621i	$0.178417\pi$
$930$	0.562306	0.0184387
$931$	25.4164	0.832989
$932$	−29.8885	−0.979032
$933$	2.50658	0.0820617
$934$	−2.54915	−0.0834107
$935$	−3.85410	−0.126043
$936$	5.85410	0.191347
$937$	8.05573	0.263169	0.131585	−	0.991305i	$-0.457994\pi$
$937$	8.05573	0.263169	0.131585	+	0.991305i	$0.457994\pi$
$938$	−2.14590	−0.0700661
$939$	3.09017	0.100844
$940$	0.708204	0.0230991
$941$	−37.7771	−1.23150	−0.615749	−	0.787942i	$-0.711146\pi$
$941$	−37.7771	−1.23150	−0.615749	+	0.787942i	$0.711146\pi$
$942$	6.03444	0.196613
$943$	−3.76393	−0.122570
$944$	9.27051	0.301729
$945$	−1.32624	−0.0431425
$946$	−0.236068	−0.00767523
$947$	−39.9574	−1.29844	−0.649221	−	0.760600i	$-0.724905\pi$
$947$	−39.9574	−1.29844	−0.649221	+	0.760600i	$0.724905\pi$
$948$	0.381966	0.0124057
$949$	−4.38197	−0.142245
$950$	−12.7082	−0.412309
$951$	−0.0557281	−0.00180711
$952$	8.61803	0.279312
$953$	−46.1246	−1.49412	−0.747061	−	0.664755i	$-0.768536\pi$
$953$	−46.1246	−1.49412	−0.747061	+	0.664755i	$0.768536\pi$
$954$	2.38197	0.0771190
$955$	7.43769	0.240678
$956$	−3.32624	−0.107578
$957$	−6.23607	−0.201583
$958$	19.0689	0.616088
$959$	10.4164	0.336363
$960$	0.0557281	0.00179862
$961$	−16.1459	−0.520835
$962$	−0.472136	−0.0152223
$963$	−34.2705	−1.10435
$964$	−6.52786	−0.210248
$965$	5.97871	0.192462
$966$	−0.381966	−0.0122896
$967$	46.0344	1.48037	0.740184	−	0.672404i	$-0.234738\pi$
$967$	46.0344	1.48037	0.740184	+	0.672404i	$0.234738\pi$
$968$	−9.27051	−0.297965
$969$	10.0902	0.324143
$970$	−1.24922	−0.0401102
$971$	−22.7082	−0.728741	−0.364370	−	0.931254i	$-0.618716\pi$
$971$	−22.7082	−0.728741	−0.364370	+	0.931254i	$0.618716\pi$
$972$	−22.5623	−0.723686
$973$	21.4164	0.686579
$974$	12.5279	0.401419
$975$	3.00000	0.0960769
$976$	−0.978714	−0.0313279
$977$	−24.8328	−0.794472	−0.397236	−	0.917716i	$-0.630031\pi$
$977$	−24.8328	−0.794472	−0.397236	+	0.917716i	$0.630031\pi$
$978$	−7.03444	−0.224937
$979$	−14.9443	−0.477621
$980$	−3.70820	−0.118454
$981$	28.7984	0.919461
$982$	2.72949	0.0871015
$983$	−42.7426	−1.36328	−0.681639	−	0.731688i	$-0.738733\pi$
$983$	−42.7426	−1.36328	−0.681639	+	0.731688i	$0.738733\pi$
$984$	5.20163	0.165822
$985$	−8.83282	−0.281437
$986$	9.18034	0.292362
$987$	−0.708204	−0.0225424
$988$	−6.85410	−0.218058
$989$	0.145898	0.00463929
$990$	1.61803	0.0514245
$991$	−38.8197	−1.23315	−0.616574	−	0.787297i	$-0.711480\pi$
$991$	−38.8197	−1.23315	−0.616574	+	0.787297i	$0.711480\pi$
$992$	−21.6525	−0.687467
$993$	8.14590	0.258502
$994$	4.14590	0.131500
$995$	−9.65248	−0.306004
$996$	−14.5623	−0.461424
$997$	13.3262	0.422046	0.211023	−	0.977481i	$-0.432320\pi$
$997$	13.3262	0.422046	0.211023	+	0.977481i	$0.432320\pi$
$998$	−3.70820	−0.117381
$999$	2.65248	0.0839206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.a.d.1.1	✓	2
3.2	odd	2		2691.2.a.j.1.2		2
4.3	odd	2		4784.2.a.p.1.1		2
5.4	even	2		7475.2.a.k.1.2		2
13.12	even	2		3887.2.a.c.1.2		2
23.22	odd	2		6877.2.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.a.d.1.1	✓	2	1.1	even	1	trivial
2691.2.a.j.1.2		2	3.2	odd	2
3887.2.a.c.1.2		2	13.12	even	2
4784.2.a.p.1.1		2	4.3	odd	2
6877.2.a.f.1.1		2	23.22	odd	2
7475.2.a.k.1.2		2	5.4	even	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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +0.618034 q^{3} -1.61803 q^{4} -0.381966 q^{5} -0.381966 q^{6} -1.00000 q^{7} +2.23607 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +0.618034 q^{3} -1.61803 q^{4} -0.381966 q^{5} -0.381966 q^{6} -1.00000 q^{7} +2.23607 q^{8} -2.61803 q^{9} +0.236068 q^{10} -2.61803 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.618034 q^{14} -0.236068 q^{15} +1.85410 q^{16} -3.85410 q^{17} +1.61803 q^{18} -4.23607 q^{19} +0.618034 q^{20} -0.618034 q^{21} +1.61803 q^{22} -1.00000 q^{23} +1.38197 q^{24} -4.85410 q^{25} +0.618034 q^{26} -3.47214 q^{27} +1.61803 q^{28} +3.85410 q^{29} +0.145898 q^{30} +3.85410 q^{31} -5.61803 q^{32} -1.61803 q^{33} +2.38197 q^{34} +0.381966 q^{35} +4.23607 q^{36} -0.763932 q^{37} +2.61803 q^{38} -0.618034 q^{39} -0.854102 q^{40} +3.76393 q^{41} +0.381966 q^{42} -0.145898 q^{43} +4.23607 q^{44} +1.00000 q^{45} +0.618034 q^{46} +1.14590 q^{47} +1.14590 q^{48} -6.00000 q^{49} +3.00000 q^{50} -2.38197 q^{51} +1.61803 q^{52} +1.47214 q^{53} +2.14590 q^{54} +1.00000 q^{55} -2.23607 q^{56} -2.61803 q^{57} -2.38197 q^{58} +5.00000 q^{59} +0.381966 q^{60} -0.527864 q^{61} -2.38197 q^{62} +2.61803 q^{63} -0.236068 q^{64} +0.381966 q^{65} +1.00000 q^{66} -3.47214 q^{67} +6.23607 q^{68} -0.618034 q^{69} -0.236068 q^{70} +6.70820 q^{71} -5.85410 q^{72} +4.38197 q^{73} +0.472136 q^{74} -3.00000 q^{75} +6.85410 q^{76} +2.61803 q^{77} +0.381966 q^{78} -0.381966 q^{79} -0.708204 q^{80} +5.70820 q^{81} -2.32624 q^{82} +14.5623 q^{83} +1.00000 q^{84} +1.47214 q^{85} +0.0901699 q^{86} +2.38197 q^{87} -5.85410 q^{88} +5.70820 q^{89} -0.618034 q^{90} +1.00000 q^{91} +1.61803 q^{92} +2.38197 q^{93} -0.708204 q^{94} +1.61803 q^{95} -3.47214 q^{96} -5.29180 q^{97} +3.70820 q^{98} +6.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{9} - 4 q^{10} - 3 q^{11} - 2 q^{12} - 2 q^{13} - q^{14} + 4 q^{15} - 3 q^{16} - q^{17} + q^{18} - 4 q^{19} - q^{20} + q^{21} + q^{22} - 2 q^{23} + 5 q^{24} - 3 q^{25} - q^{26} + 2 q^{27} + q^{28} + q^{29} + 7 q^{30} + q^{31} - 9 q^{32} - q^{33} + 7 q^{34} + 3 q^{35} + 4 q^{36} - 6 q^{37} + 3 q^{38} + q^{39} + 5 q^{40} + 12 q^{41} + 3 q^{42} - 7 q^{43} + 4 q^{44} + 2 q^{45} - q^{46} + 9 q^{47} + 9 q^{48} - 12 q^{49} + 6 q^{50} - 7 q^{51} + q^{52} - 6 q^{53} + 11 q^{54} + 2 q^{55} - 3 q^{57} - 7 q^{58} + 10 q^{59} + 3 q^{60} - 10 q^{61} - 7 q^{62} + 3 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 2 q^{67} + 8 q^{68} + q^{69} + 4 q^{70} - 5 q^{72} + 11 q^{73} - 8 q^{74} - 6 q^{75} + 7 q^{76} + 3 q^{77} + 3 q^{78} - 3 q^{79} + 12 q^{80} - 2 q^{81} + 11 q^{82} + 9 q^{83} + 2 q^{84} - 6 q^{85} - 11 q^{86} + 7 q^{87} - 5 q^{88} - 2 q^{89} + q^{90} + 2 q^{91} + q^{92} + 7 q^{93} + 12 q^{94} + q^{95} + 2 q^{96} - 24 q^{97} - 6 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^9 - 4 * q^10 - 3 * q^11 - 2 * q^12 - 2 * q^13 - q^14 + 4 * q^15 - 3 * q^16 - q^17 + q^18 - 4 * q^19 - q^20 + q^21 + q^22 - 2 * q^23 + 5 * q^24 - 3 * q^25 - q^26 + 2 * q^27 + q^28 + q^29 + 7 * q^30 + q^31 - 9 * q^32 - q^33 + 7 * q^34 + 3 * q^35 + 4 * q^36 - 6 * q^37 + 3 * q^38 + q^39 + 5 * q^40 + 12 * q^41 + 3 * q^42 - 7 * q^43 + 4 * q^44 + 2 * q^45 - q^46 + 9 * q^47 + 9 * q^48 - 12 * q^49 + 6 * q^50 - 7 * q^51 + q^52 - 6 * q^53 + 11 * q^54 + 2 * q^55 - 3 * q^57 - 7 * q^58 + 10 * q^59 + 3 * q^60 - 10 * q^61 - 7 * q^62 + 3 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 2 * q^67 + 8 * q^68 + q^69 + 4 * q^70 - 5 * q^72 + 11 * q^73 - 8 * q^74 - 6 * q^75 + 7 * q^76 + 3 * q^77 + 3 * q^78 - 3 * q^79 + 12 * q^80 - 2 * q^81 + 11 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 - 11 * q^86 + 7 * q^87 - 5 * q^88 - 2 * q^89 + q^90 + 2 * q^91 + q^92 + 7 * q^93 + 12 * q^94 + q^95 + 2 * q^96 - 24 * q^97 - 6 * q^98 + 7 * q^99

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