LMFDB - Embedded newform 6041.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.61803 q^{3} -1.00000 q^{4} -0.618034 q^{5} -2.61803 q^{6} -1.00000 q^{7} +3.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.61803 q^{3} -1.00000 q^{4} -0.618034 q^{5} -2.61803 q^{6} -1.00000 q^{7} +3.00000 q^{8} +3.85410 q^{9} +0.618034 q^{10} -2.61803 q^{11} -2.61803 q^{12} +5.61803 q^{13} +1.00000 q^{14} -1.61803 q^{15} -1.00000 q^{16} -3.23607 q^{17} -3.85410 q^{18} -4.09017 q^{19} +0.618034 q^{20} -2.61803 q^{21} +2.61803 q^{22} +5.09017 q^{23} +7.85410 q^{24} -4.61803 q^{25} -5.61803 q^{26} +2.23607 q^{27} +1.00000 q^{28} -4.47214 q^{29} +1.61803 q^{30} +2.47214 q^{31} -5.00000 q^{32} -6.85410 q^{33} +3.23607 q^{34} +0.618034 q^{35} -3.85410 q^{36} -2.14590 q^{37} +4.09017 q^{38} +14.7082 q^{39} -1.85410 q^{40} +8.94427 q^{41} +2.61803 q^{42} -5.70820 q^{43} +2.61803 q^{44} -2.38197 q^{45} -5.09017 q^{46} +1.23607 q^{47} -2.61803 q^{48} +1.00000 q^{49} +4.61803 q^{50} -8.47214 q^{51} -5.61803 q^{52} -4.32624 q^{53} -2.23607 q^{54} +1.61803 q^{55} -3.00000 q^{56} -10.7082 q^{57} +4.47214 q^{58} -10.6180 q^{59} +1.61803 q^{60} +13.7082 q^{61} -2.47214 q^{62} -3.85410 q^{63} +7.00000 q^{64} -3.47214 q^{65} +6.85410 q^{66} -7.14590 q^{67} +3.23607 q^{68} +13.3262 q^{69} -0.618034 q^{70} -2.47214 q^{71} +11.5623 q^{72} -1.85410 q^{73} +2.14590 q^{74} -12.0902 q^{75} +4.09017 q^{76} +2.61803 q^{77} -14.7082 q^{78} -13.6180 q^{79} +0.618034 q^{80} -5.70820 q^{81} -8.94427 q^{82} +8.76393 q^{83} +2.61803 q^{84} +2.00000 q^{85} +5.70820 q^{86} -11.7082 q^{87} -7.85410 q^{88} -6.94427 q^{89} +2.38197 q^{90} -5.61803 q^{91} -5.09017 q^{92} +6.47214 q^{93} -1.23607 q^{94} +2.52786 q^{95} -13.0902 q^{96} -4.85410 q^{97} -1.00000 q^{98} -10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9	$ 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9} - q^{10} - 3 q^{11} - 3 q^{12} + 9 q^{13} + 2 q^{14} - q^{15} - 2 q^{16} - 2 q^{17} - q^{18} + 3 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} - q^{23} + 9 q^{24} - 7 q^{25} - 9 q^{26} + 2 q^{28} + q^{30} - 4 q^{31} - 10 q^{32} - 7 q^{33} + 2 q^{34} - q^{35} - q^{36} - 11 q^{37} - 3 q^{38} + 16 q^{39} + 3 q^{40} + 3 q^{42} + 2 q^{43} + 3 q^{44} - 7 q^{45} + q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} + 7 q^{50} - 8 q^{51} - 9 q^{52} + 7 q^{53} + q^{55} - 6 q^{56} - 8 q^{57} - 19 q^{59} + q^{60} + 14 q^{61} + 4 q^{62} - q^{63} + 14 q^{64} + 2 q^{65} + 7 q^{66} - 21 q^{67} + 2 q^{68} + 11 q^{69} + q^{70} + 4 q^{71} + 3 q^{72} + 3 q^{73} + 11 q^{74} - 13 q^{75} - 3 q^{76} + 3 q^{77} - 16 q^{78} - 25 q^{79} - q^{80} + 2 q^{81} + 22 q^{83} + 3 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} - 9 q^{88} + 4 q^{89} + 7 q^{90} - 9 q^{91} + q^{92} + 4 q^{93} + 2 q^{94} + 14 q^{95} - 15 q^{96} - 3 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9 - q^10 - 3 * q^11 - 3 * q^12 + 9 * q^13 + 2 * q^14 - q^15 - 2 * q^16 - 2 * q^17 - q^18 + 3 * q^19 - q^20 - 3 * q^21 + 3 * q^22 - q^23 + 9 * q^24 - 7 * q^25 - 9 * q^26 + 2 * q^28 + q^30 - 4 * q^31 - 10 * q^32 - 7 * q^33 + 2 * q^34 - q^35 - q^36 - 11 * q^37 - 3 * q^38 + 16 * q^39 + 3 * q^40 + 3 * q^42 + 2 * q^43 + 3 * q^44 - 7 * q^45 + q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 + 7 * q^50 - 8 * q^51 - 9 * q^52 + 7 * q^53 + q^55 - 6 * q^56 - 8 * q^57 - 19 * q^59 + q^60 + 14 * q^61 + 4 * q^62 - q^63 + 14 * q^64 + 2 * q^65 + 7 * q^66 - 21 * q^67 + 2 * q^68 + 11 * q^69 + q^70 + 4 * q^71 + 3 * q^72 + 3 * q^73 + 11 * q^74 - 13 * q^75 - 3 * q^76 + 3 * q^77 - 16 * q^78 - 25 * q^79 - q^80 + 2 * q^81 + 22 * q^83 + 3 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 - 9 * q^88 + 4 * q^89 + 7 * q^90 - 9 * q^91 + q^92 + 4 * q^93 + 2 * q^94 + 14 * q^95 - 15 * q^96 - 3 * q^97 - 2 * q^98 - 9 * 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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	−1.00000	−0.500000
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	−2.61803	−1.06881
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.00000	1.06066
$9$	3.85410	1.28470
$10$	0.618034	0.195440
$11$	−2.61803	−0.789367	−0.394683	−	0.918817i	$-0.629146\pi$
$11$	−2.61803	−0.789367	−0.394683	+	0.918817i	$0.629146\pi$
$12$	−2.61803	−0.755761
$13$	5.61803	1.55816	0.779081	−	0.626923i	$-0.215686\pi$
$13$	5.61803	1.55816	0.779081	+	0.626923i	$0.215686\pi$
$14$	1.00000	0.267261
$15$	−1.61803	−0.417775
$16$	−1.00000	−0.250000
$17$	−3.23607	−0.784862	−0.392431	−	0.919781i	$-0.628366\pi$
$17$	−3.23607	−0.784862	−0.392431	+	0.919781i	$0.628366\pi$
$18$	−3.85410	−0.908421
$19$	−4.09017	−0.938349	−0.469175	−	0.883105i	$-0.655449\pi$
$19$	−4.09017	−0.938349	−0.469175	+	0.883105i	$0.655449\pi$
$20$	0.618034	0.138197
$21$	−2.61803	−0.571302
$22$	2.61803	0.558167
$23$	5.09017	1.06137	0.530687	−	0.847568i	$-0.321934\pi$
$23$	5.09017	1.06137	0.530687	+	0.847568i	$0.321934\pi$
$24$	7.85410	1.60321
$25$	−4.61803	−0.923607
$26$	−5.61803	−1.10179
$27$	2.23607	0.430331
$28$	1.00000	0.188982
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	1.61803	0.295411
$31$	2.47214	0.444009	0.222004	−	0.975046i	$-0.428740\pi$
$31$	2.47214	0.444009	0.222004	+	0.975046i	$0.428740\pi$
$32$	−5.00000	−0.883883
$33$	−6.85410	−1.19315
$34$	3.23607	0.554981
$35$	0.618034	0.104467
$36$	−3.85410	−0.642350
$37$	−2.14590	−0.352783	−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590	−0.352783	−0.176392	+	0.984320i	$0.556443\pi$
$38$	4.09017	0.663513
$39$	14.7082	2.35520
$40$	−1.85410	−0.293159
$41$	8.94427	1.39686	0.698430	−	0.715678i	$-0.253882\pi$
$41$	8.94427	1.39686	0.698430	+	0.715678i	$0.253882\pi$
$42$	2.61803	0.403971
$43$	−5.70820	−0.870493	−0.435246	−	0.900311i	$-0.643339\pi$
$43$	−5.70820	−0.870493	−0.435246	+	0.900311i	$0.643339\pi$
$44$	2.61803	0.394683
$45$	−2.38197	−0.355083
$46$	−5.09017	−0.750505
$47$	1.23607	0.180299	0.0901495	−	0.995928i	$-0.471266\pi$
$47$	1.23607	0.180299	0.0901495	+	0.995928i	$0.471266\pi$
$48$	−2.61803	−0.377881
$49$	1.00000	0.142857
$50$	4.61803	0.653089
$51$	−8.47214	−1.18634
$52$	−5.61803	−0.779081
$53$	−4.32624	−0.594254	−0.297127	−	0.954838i	$-0.596029\pi$
$53$	−4.32624	−0.594254	−0.297127	+	0.954838i	$0.596029\pi$
$54$	−2.23607	−0.304290
$55$	1.61803	0.218176
$56$	−3.00000	−0.400892
$57$	−10.7082	−1.41834
$58$	4.47214	0.587220
$59$	−10.6180	−1.38235	−0.691175	−	0.722687i	$-0.742907\pi$
$59$	−10.6180	−1.38235	−0.691175	+	0.722687i	$0.742907\pi$
$60$	1.61803	0.208887
$61$	13.7082	1.75516	0.877578	−	0.479434i	$-0.159158\pi$
$61$	13.7082	1.75516	0.877578	+	0.479434i	$0.159158\pi$
$62$	−2.47214	−0.313962
$63$	−3.85410	−0.485571
$64$	7.00000	0.875000
$65$	−3.47214	−0.430665
$66$	6.85410	0.843682
$67$	−7.14590	−0.873010	−0.436505	−	0.899702i	$-0.643784\pi$
$67$	−7.14590	−0.873010	−0.436505	+	0.899702i	$0.643784\pi$
$68$	3.23607	0.392431
$69$	13.3262	1.60429
$70$	−0.618034	−0.0738692
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	11.5623	1.36263
$73$	−1.85410	−0.217006	−0.108503	−	0.994096i	$-0.534606\pi$
$73$	−1.85410	−0.217006	−0.108503	+	0.994096i	$0.534606\pi$
$74$	2.14590	0.249456
$75$	−12.0902	−1.39605
$76$	4.09017	0.469175
$77$	2.61803	0.298353
$78$	−14.7082	−1.66538
$79$	−13.6180	−1.53215	−0.766074	−	0.642752i	$-0.777793\pi$
$79$	−13.6180	−1.53215	−0.766074	+	0.642752i	$0.777793\pi$
$80$	0.618034	0.0690983
$81$	−5.70820	−0.634245
$82$	−8.94427	−0.987730
$83$	8.76393	0.961967	0.480983	−	0.876730i	$-0.340280\pi$
$83$	8.76393	0.961967	0.480983	+	0.876730i	$0.340280\pi$
$84$	2.61803	0.285651
$85$	2.00000	0.216930
$86$	5.70820	0.615531
$87$	−11.7082	−1.25525
$88$	−7.85410	−0.837250
$89$	−6.94427	−0.736091	−0.368046	−	0.929808i	$-0.619973\pi$
$89$	−6.94427	−0.736091	−0.368046	+	0.929808i	$0.619973\pi$
$90$	2.38197	0.251081
$91$	−5.61803	−0.588930
$92$	−5.09017	−0.530687
$93$	6.47214	0.671129
$94$	−1.23607	−0.127491
$95$	2.52786	0.259353
$96$	−13.0902	−1.33601
$97$	−4.85410	−0.492859	−0.246430	−	0.969161i	$-0.579257\pi$
$97$	−4.85410	−0.492859	−0.246430	+	0.969161i	$0.579257\pi$
$98$	−1.00000	−0.101015
$99$	−10.0902	−1.01410
$100$	4.61803	0.461803
$101$	−4.47214	−0.444994	−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214	−0.444994	−0.222497	+	0.974933i	$0.571421\pi$
$102$	8.47214	0.838866
$103$	17.0902	1.68394	0.841972	−	0.539521i	$-0.181395\pi$
$103$	17.0902	1.68394	0.841972	+	0.539521i	$0.181395\pi$
$104$	16.8541	1.65268
$105$	1.61803	0.157904
$106$	4.32624	0.420201
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−2.23607	−0.215166
$109$	−9.85410	−0.943852	−0.471926	−	0.881638i	$-0.656441\pi$
$109$	−9.85410	−0.943852	−0.471926	+	0.881638i	$0.656441\pi$
$110$	−1.61803	−0.154273
$111$	−5.61803	−0.533240
$112$	1.00000	0.0944911
$113$	−14.3820	−1.35294	−0.676471	−	0.736469i	$-0.736491\pi$
$113$	−14.3820	−1.35294	−0.676471	+	0.736469i	$0.736491\pi$
$114$	10.7082	1.00292
$115$	−3.14590	−0.293357
$116$	4.47214	0.415227
$117$	21.6525	2.00177
$118$	10.6180	0.977469
$119$	3.23607	0.296650
$120$	−4.85410	−0.443117
$121$	−4.14590	−0.376900
$122$	−13.7082	−1.24108
$123$	23.4164	2.11139
$124$	−2.47214	−0.222004
$125$	5.94427	0.531672
$126$	3.85410	0.343351
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	3.00000	0.265165
$129$	−14.9443	−1.31577
$130$	3.47214	0.304526
$131$	−6.29180	−0.549717	−0.274858	−	0.961485i	$-0.588631\pi$
$131$	−6.29180	−0.549717	−0.274858	+	0.961485i	$0.588631\pi$
$132$	6.85410	0.596573
$133$	4.09017	0.354663
$134$	7.14590	0.617312
$135$	−1.38197	−0.118941
$136$	−9.70820	−0.832472
$137$	12.4721	1.06557	0.532783	−	0.846252i	$-0.321146\pi$
$137$	12.4721	1.06557	0.532783	+	0.846252i	$0.321146\pi$
$138$	−13.3262	−1.13440
$139$	−11.4164	−0.968327	−0.484164	−	0.874978i	$-0.660876\pi$
$139$	−11.4164	−0.968327	−0.484164	+	0.874978i	$0.660876\pi$
$140$	−0.618034	−0.0522334
$141$	3.23607	0.272526
$142$	2.47214	0.207457
$143$	−14.7082	−1.22996
$144$	−3.85410	−0.321175
$145$	2.76393	0.229532
$146$	1.85410	0.153447
$147$	2.61803	0.215932
$148$	2.14590	0.176392
$149$	−5.41641	−0.443729	−0.221865	−	0.975077i	$-0.571214\pi$
$149$	−5.41641	−0.443729	−0.221865	+	0.975077i	$0.571214\pi$
$150$	12.0902	0.987158
$151$	−6.76393	−0.550441	−0.275220	−	0.961381i	$-0.588751\pi$
$151$	−6.76393	−0.550441	−0.275220	+	0.961381i	$0.588751\pi$
$152$	−12.2705	−0.995270
$153$	−12.4721	−1.00831
$154$	−2.61803	−0.210967
$155$	−1.52786	−0.122721
$156$	−14.7082	−1.17760
$157$	3.14590	0.251070	0.125535	−	0.992089i	$-0.459935\pi$
$157$	3.14590	0.251070	0.125535	+	0.992089i	$0.459935\pi$
$158$	13.6180	1.08339
$159$	−11.3262	−0.898229
$160$	3.09017	0.244299
$161$	−5.09017	−0.401162
$162$	5.70820	0.448479
$163$	−6.47214	−0.506937	−0.253468	−	0.967344i	$-0.581571\pi$
$163$	−6.47214	−0.506937	−0.253468	+	0.967344i	$0.581571\pi$
$164$	−8.94427	−0.698430
$165$	4.23607	0.329777
$166$	−8.76393	−0.680213
$167$	12.1803	0.942543	0.471271	−	0.881988i	$-0.343795\pi$
$167$	12.1803	0.942543	0.471271	+	0.881988i	$0.343795\pi$
$168$	−7.85410	−0.605957
$169$	18.5623	1.42787
$170$	−2.00000	−0.153393
$171$	−15.7639	−1.20550
$172$	5.70820	0.435246
$173$	1.56231	0.118780	0.0593900	−	0.998235i	$-0.481084\pi$
$173$	1.56231	0.118780	0.0593900	+	0.998235i	$0.481084\pi$
$174$	11.7082	0.887597
$175$	4.61803	0.349091
$176$	2.61803	0.197342
$177$	−27.7984	−2.08945
$178$	6.94427	0.520495
$179$	3.32624	0.248615	0.124307	−	0.992244i	$-0.460329\pi$
$179$	3.32624	0.248615	0.124307	+	0.992244i	$0.460329\pi$
$180$	2.38197	0.177541
$181$	−2.94427	−0.218846	−0.109423	−	0.993995i	$-0.534900\pi$
$181$	−2.94427	−0.218846	−0.109423	+	0.993995i	$0.534900\pi$
$182$	5.61803	0.416436
$183$	35.8885	2.65296
$184$	15.2705	1.12576
$185$	1.32624	0.0975070
$186$	−6.47214	−0.474560
$187$	8.47214	0.619544
$188$	−1.23607	−0.0901495
$189$	−2.23607	−0.162650
$190$	−2.52786	−0.183391
$191$	17.8885	1.29437	0.647185	−	0.762333i	$-0.275946\pi$
$191$	17.8885	1.29437	0.647185	+	0.762333i	$0.275946\pi$
$192$	18.3262	1.32258
$193$	−18.7639	−1.35066	−0.675329	−	0.737517i	$-0.735998\pi$
$193$	−18.7639	−1.35066	−0.675329	+	0.737517i	$0.735998\pi$
$194$	4.85410	0.348504
$195$	−9.09017	−0.650961
$196$	−1.00000	−0.0714286
$197$	−3.05573	−0.217712	−0.108856	−	0.994058i	$-0.534719\pi$
$197$	−3.05573	−0.217712	−0.108856	+	0.994058i	$0.534719\pi$
$198$	10.0902	0.717077
$199$	0.854102	0.0605457	0.0302728	−	0.999542i	$-0.490362\pi$
$199$	0.854102	0.0605457	0.0302728	+	0.999542i	$0.490362\pi$
$200$	−13.8541	−0.979633
$201$	−18.7082	−1.31957
$202$	4.47214	0.314658
$203$	4.47214	0.313882
$204$	8.47214	0.593168
$205$	−5.52786	−0.386083
$206$	−17.0902	−1.19073
$207$	19.6180	1.36355
$208$	−5.61803	−0.389541
$209$	10.7082	0.740702
$210$	−1.61803	−0.111655
$211$	−26.5623	−1.82862	−0.914312	−	0.405010i	$-0.867268\pi$
$211$	−26.5623	−1.82862	−0.914312	+	0.405010i	$0.867268\pi$
$212$	4.32624	0.297127
$213$	−6.47214	−0.443463
$214$	−6.00000	−0.410152
$215$	3.52786	0.240598
$216$	6.70820	0.456435
$217$	−2.47214	−0.167820
$218$	9.85410	0.667404
$219$	−4.85410	−0.328010
$220$	−1.61803	−0.109088
$221$	−18.1803	−1.22294
$222$	5.61803	0.377058
$223$	0.437694	0.0293102	0.0146551	−	0.999893i	$-0.495335\pi$
$223$	0.437694	0.0293102	0.0146551	+	0.999893i	$0.495335\pi$
$224$	5.00000	0.334077
$225$	−17.7984	−1.18656
$226$	14.3820	0.956674
$227$	18.9443	1.25738	0.628688	−	0.777658i	$-0.283592\pi$
$227$	18.9443	1.25738	0.628688	+	0.777658i	$0.283592\pi$
$228$	10.7082	0.709168
$229$	22.1803	1.46572	0.732859	−	0.680380i	$-0.238185\pi$
$229$	22.1803	1.46572	0.732859	+	0.680380i	$0.238185\pi$
$230$	3.14590	0.207434
$231$	6.85410	0.450967
$232$	−13.4164	−0.880830
$233$	−1.81966	−0.119210	−0.0596049	−	0.998222i	$-0.518984\pi$
$233$	−1.81966	−0.119210	−0.0596049	+	0.998222i	$0.518984\pi$
$234$	−21.6525	−1.41547
$235$	−0.763932	−0.0498334
$236$	10.6180	0.691175
$237$	−35.6525	−2.31588
$238$	−3.23607	−0.209763
$239$	−24.7639	−1.60185	−0.800923	−	0.598768i	$-0.795657\pi$
$239$	−24.7639	−1.60185	−0.800923	+	0.598768i	$0.795657\pi$
$240$	1.61803	0.104444
$241$	10.3820	0.668761	0.334381	−	0.942438i	$-0.391473\pi$
$241$	10.3820	0.668761	0.334381	+	0.942438i	$0.391473\pi$
$242$	4.14590	0.266508
$243$	−21.6525	−1.38901
$244$	−13.7082	−0.877578
$245$	−0.618034	−0.0394847
$246$	−23.4164	−1.49298
$247$	−22.9787	−1.46210
$248$	7.41641	0.470942
$249$	22.9443	1.45403
$250$	−5.94427	−0.375949
$251$	−10.6525	−0.672378	−0.336189	−	0.941794i	$-0.609138\pi$
$251$	−10.6525	−0.672378	−0.336189	+	0.941794i	$0.609138\pi$
$252$	3.85410	0.242786
$253$	−13.3262	−0.837813
$254$	4.00000	0.250982
$255$	5.23607	0.327895
$256$	−17.0000	−1.06250
$257$	−16.9443	−1.05695	−0.528477	−	0.848947i	$-0.677237\pi$
$257$	−16.9443	−1.05695	−0.528477	+	0.848947i	$0.677237\pi$
$258$	14.9443	0.930390
$259$	2.14590	0.133340
$260$	3.47214	0.215333
$261$	−17.2361	−1.06689
$262$	6.29180	0.388708
$263$	22.7426	1.40237	0.701186	−	0.712979i	$-0.252654\pi$
$263$	22.7426	1.40237	0.701186	+	0.712979i	$0.252654\pi$
$264$	−20.5623	−1.26552
$265$	2.67376	0.164248
$266$	−4.09017	−0.250784
$267$	−18.1803	−1.11262
$268$	7.14590	0.436505
$269$	−7.70820	−0.469977	−0.234989	−	0.971998i	$-0.575505\pi$
$269$	−7.70820	−0.469977	−0.234989	+	0.971998i	$0.575505\pi$
$270$	1.38197	0.0841038
$271$	−25.1246	−1.52621	−0.763106	−	0.646274i	$-0.776326\pi$
$271$	−25.1246	−1.52621	−0.763106	+	0.646274i	$0.776326\pi$
$272$	3.23607	0.196215
$273$	−14.7082	−0.890181
$274$	−12.4721	−0.753469
$275$	12.0902	0.729065
$276$	−13.3262	−0.802145
$277$	−5.52786	−0.332137	−0.166069	−	0.986114i	$-0.553107\pi$
$277$	−5.52786	−0.332137	−0.166069	+	0.986114i	$0.553107\pi$
$278$	11.4164	0.684711
$279$	9.52786	0.570418
$280$	1.85410	0.110804
$281$	−25.2705	−1.50751	−0.753756	−	0.657154i	$-0.771760\pi$
$281$	−25.2705	−1.50751	−0.753756	+	0.657154i	$0.771760\pi$
$282$	−3.23607	−0.192705
$283$	0.673762	0.0400510	0.0200255	−	0.999799i	$-0.493625\pi$
$283$	0.673762	0.0400510	0.0200255	+	0.999799i	$0.493625\pi$
$284$	2.47214	0.146694
$285$	6.61803	0.392019
$286$	14.7082	0.869714
$287$	−8.94427	−0.527964
$288$	−19.2705	−1.13553
$289$	−6.52786	−0.383992
$290$	−2.76393	−0.162304
$291$	−12.7082	−0.744968
$292$	1.85410	0.108503
$293$	−16.4721	−0.962312	−0.481156	−	0.876635i	$-0.659783\pi$
$293$	−16.4721	−0.962312	−0.481156	+	0.876635i	$0.659783\pi$
$294$	−2.61803	−0.152687
$295$	6.56231	0.382072
$296$	−6.43769	−0.374183
$297$	−5.85410	−0.339689
$298$	5.41641	0.313764
$299$	28.5967	1.65379
$300$	12.0902	0.698026
$301$	5.70820	0.329015
$302$	6.76393	0.389221
$303$	−11.7082	−0.672619
$304$	4.09017	0.234587
$305$	−8.47214	−0.485113
$306$	12.4721	0.712985
$307$	−29.7984	−1.70068	−0.850342	−	0.526231i	$-0.823605\pi$
$307$	−29.7984	−1.70068	−0.850342	+	0.526231i	$0.823605\pi$
$308$	−2.61803	−0.149176
$309$	44.7426	2.54532
$310$	1.52786	0.0867768
$311$	8.94427	0.507183	0.253592	−	0.967311i	$-0.418388\pi$
$311$	8.94427	0.507183	0.253592	+	0.967311i	$0.418388\pi$
$312$	44.1246	2.49806
$313$	22.1803	1.25371	0.626853	−	0.779137i	$-0.284342\pi$
$313$	22.1803	1.25371	0.626853	+	0.779137i	$0.284342\pi$
$314$	−3.14590	−0.177533
$315$	2.38197	0.134209
$316$	13.6180	0.766074
$317$	−28.6525	−1.60928	−0.804642	−	0.593761i	$-0.797643\pi$
$317$	−28.6525	−1.60928	−0.804642	+	0.593761i	$0.797643\pi$
$318$	11.3262	0.635144
$319$	11.7082	0.655534
$320$	−4.32624	−0.241844
$321$	15.7082	0.876746
$322$	5.09017	0.283664
$323$	13.2361	0.736475
$324$	5.70820	0.317122
$325$	−25.9443	−1.43913
$326$	6.47214	0.358458
$327$	−25.7984	−1.42665
$328$	26.8328	1.48159
$329$	−1.23607	−0.0681466
$330$	−4.23607	−0.233188
$331$	−22.4721	−1.23518	−0.617590	−	0.786500i	$-0.711891\pi$
$331$	−22.4721	−1.23518	−0.617590	+	0.786500i	$0.711891\pi$
$332$	−8.76393	−0.480983
$333$	−8.27051	−0.453221
$334$	−12.1803	−0.666479
$335$	4.41641	0.241294
$336$	2.61803	0.142825
$337$	16.0902	0.876487	0.438244	−	0.898856i	$-0.355601\pi$
$337$	16.0902	0.876487	0.438244	+	0.898856i	$0.355601\pi$
$338$	−18.5623	−1.00966
$339$	−37.6525	−2.04500
$340$	−2.00000	−0.108465
$341$	−6.47214	−0.350486
$342$	15.7639	0.852416
$343$	−1.00000	−0.0539949
$344$	−17.1246	−0.923297
$345$	−8.23607	−0.443415
$346$	−1.56231	−0.0839901
$347$	−32.4508	−1.74205	−0.871026	−	0.491236i	$-0.836545\pi$
$347$	−32.4508	−1.74205	−0.871026	+	0.491236i	$0.836545\pi$
$348$	11.7082	0.627626
$349$	31.8885	1.70695	0.853477	−	0.521130i	$-0.174489\pi$
$349$	31.8885	1.70695	0.853477	+	0.521130i	$0.174489\pi$
$350$	−4.61803	−0.246844
$351$	12.5623	0.670526
$352$	13.0902	0.697708
$353$	−13.7082	−0.729614	−0.364807	−	0.931083i	$-0.618865\pi$
$353$	−13.7082	−0.729614	−0.364807	+	0.931083i	$0.618865\pi$
$354$	27.7984	1.47747
$355$	1.52786	0.0810906
$356$	6.94427	0.368046
$357$	8.47214	0.448393
$358$	−3.32624	−0.175797
$359$	32.1803	1.69841	0.849207	−	0.528061i	$-0.177081\pi$
$359$	32.1803	1.69841	0.849207	+	0.528061i	$0.177081\pi$
$360$	−7.14590	−0.376622
$361$	−2.27051	−0.119501
$362$	2.94427	0.154747
$363$	−10.8541	−0.569693
$364$	5.61803	0.294465
$365$	1.14590	0.0599790
$366$	−35.8885	−1.87592
$367$	−30.0000	−1.56599	−0.782994	−	0.622030i	$-0.786308\pi$
$367$	−30.0000	−1.56599	−0.782994	+	0.622030i	$0.786308\pi$
$368$	−5.09017	−0.265343
$369$	34.4721	1.79455
$370$	−1.32624	−0.0689478
$371$	4.32624	0.224607
$372$	−6.47214	−0.335565
$373$	−19.3262	−1.00067	−0.500337	−	0.865831i	$-0.666791\pi$
$373$	−19.3262	−1.00067	−0.500337	+	0.865831i	$0.666791\pi$
$374$	−8.47214	−0.438084
$375$	15.5623	0.803634
$376$	3.70820	0.191236
$377$	−25.1246	−1.29398
$378$	2.23607	0.115011
$379$	13.0344	0.669534	0.334767	−	0.942301i	$-0.391342\pi$
$379$	13.0344	0.669534	0.334767	+	0.942301i	$0.391342\pi$
$380$	−2.52786	−0.129677
$381$	−10.4721	−0.536504
$382$	−17.8885	−0.915258
$383$	−12.8541	−0.656814	−0.328407	−	0.944536i	$-0.606512\pi$
$383$	−12.8541	−0.656814	−0.328407	+	0.944536i	$0.606512\pi$
$384$	7.85410	0.400803
$385$	−1.61803	−0.0824626
$386$	18.7639	0.955059
$387$	−22.0000	−1.11832
$388$	4.85410	0.246430
$389$	21.9787	1.11437	0.557183	−	0.830390i	$-0.311882\pi$
$389$	21.9787	1.11437	0.557183	+	0.830390i	$0.311882\pi$
$390$	9.09017	0.460299
$391$	−16.4721	−0.833032
$392$	3.00000	0.151523
$393$	−16.4721	−0.830909
$394$	3.05573	0.153945
$395$	8.41641	0.423475
$396$	10.0902	0.507050
$397$	7.88854	0.395915	0.197957	−	0.980211i	$-0.436569\pi$
$397$	7.88854	0.395915	0.197957	+	0.980211i	$0.436569\pi$
$398$	−0.854102	−0.0428123
$399$	10.7082	0.536081
$400$	4.61803	0.230902
$401$	−1.05573	−0.0527205	−0.0263603	−	0.999653i	$-0.508392\pi$
$401$	−1.05573	−0.0527205	−0.0263603	+	0.999653i	$0.508392\pi$
$402$	18.7082	0.933080
$403$	13.8885	0.691838
$404$	4.47214	0.222497
$405$	3.52786	0.175301
$406$	−4.47214	−0.221948
$407$	5.61803	0.278476
$408$	−25.4164	−1.25830
$409$	−20.6525	−1.02120	−0.510600	−	0.859819i	$-0.670577\pi$
$409$	−20.6525	−1.02120	−0.510600	+	0.859819i	$0.670577\pi$
$410$	5.52786	0.273002
$411$	32.6525	1.61063
$412$	−17.0902	−0.841972
$413$	10.6180	0.522479
$414$	−19.6180	−0.964174
$415$	−5.41641	−0.265881
$416$	−28.0902	−1.37723
$417$	−29.8885	−1.46365
$418$	−10.7082	−0.523755
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	−1.61803	−0.0789520
$421$	2.20163	0.107301	0.0536503	−	0.998560i	$-0.482914\pi$
$421$	2.20163	0.107301	0.0536503	+	0.998560i	$0.482914\pi$
$422$	26.5623	1.29303
$423$	4.76393	0.231630
$424$	−12.9787	−0.630302
$425$	14.9443	0.724904
$426$	6.47214	0.313576
$427$	−13.7082	−0.663386
$428$	−6.00000	−0.290021
$429$	−38.5066	−1.85912
$430$	−3.52786	−0.170129
$431$	−36.9443	−1.77954	−0.889771	−	0.456406i	$-0.849136\pi$
$431$	−36.9443	−1.77954	−0.889771	+	0.456406i	$0.849136\pi$
$432$	−2.23607	−0.107583
$433$	−18.3607	−0.882358	−0.441179	−	0.897419i	$-0.645440\pi$
$433$	−18.3607	−0.882358	−0.441179	+	0.897419i	$0.645440\pi$
$434$	2.47214	0.118666
$435$	7.23607	0.346943
$436$	9.85410	0.471926
$437$	−20.8197	−0.995939
$438$	4.85410	0.231938
$439$	17.1246	0.817313	0.408657	−	0.912688i	$-0.365997\pi$
$439$	17.1246	0.817313	0.408657	+	0.912688i	$0.365997\pi$
$440$	4.85410	0.231410
$441$	3.85410	0.183529
$442$	18.1803	0.864751
$443$	−13.7984	−0.655581	−0.327790	−	0.944751i	$-0.606304\pi$
$443$	−13.7984	−0.655581	−0.327790	+	0.944751i	$0.606304\pi$
$444$	5.61803	0.266620
$445$	4.29180	0.203451
$446$	−0.437694	−0.0207254
$447$	−14.1803	−0.670707
$448$	−7.00000	−0.330719
$449$	39.6869	1.87294	0.936471	−	0.350746i	$-0.114072\pi$
$449$	39.6869	1.87294	0.936471	+	0.350746i	$0.114072\pi$
$450$	17.7984	0.839023
$451$	−23.4164	−1.10264
$452$	14.3820	0.676471
$453$	−17.7082	−0.832004
$454$	−18.9443	−0.889099
$455$	3.47214	0.162776
$456$	−32.1246	−1.50437
$457$	20.6869	0.967693	0.483847	−	0.875153i	$-0.339239\pi$
$457$	20.6869	0.967693	0.483847	+	0.875153i	$0.339239\pi$
$458$	−22.1803	−1.03642
$459$	−7.23607	−0.337751
$460$	3.14590	0.146678
$461$	27.5967	1.28531	0.642654	−	0.766156i	$-0.277833\pi$
$461$	27.5967	1.28531	0.642654	+	0.766156i	$0.277833\pi$
$462$	−6.85410	−0.318882
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	4.47214	0.207614
$465$	−4.00000	−0.185496
$466$	1.81966	0.0842941
$467$	−21.0344	−0.973358	−0.486679	−	0.873581i	$-0.661792\pi$
$467$	−21.0344	−0.973358	−0.486679	+	0.873581i	$0.661792\pi$
$468$	−21.6525	−1.00089
$469$	7.14590	0.329967
$470$	0.763932	0.0352376
$471$	8.23607	0.379498
$472$	−31.8541	−1.46620
$473$	14.9443	0.687138
$474$	35.6525	1.63757
$475$	18.8885	0.866666
$476$	−3.23607	−0.148325
$477$	−16.6738	−0.763439
$478$	24.7639	1.13268
$479$	−6.65248	−0.303959	−0.151980	−	0.988384i	$-0.548565\pi$
$479$	−6.65248	−0.303959	−0.151980	+	0.988384i	$0.548565\pi$
$480$	8.09017	0.369264
$481$	−12.0557	−0.549694
$482$	−10.3820	−0.472886
$483$	−13.3262	−0.606365
$484$	4.14590	0.188450
$485$	3.00000	0.136223
$486$	21.6525	0.982176
$487$	−25.4164	−1.15173	−0.575864	−	0.817546i	$-0.695334\pi$
$487$	−25.4164	−1.15173	−0.575864	+	0.817546i	$0.695334\pi$
$488$	41.1246	1.86162
$489$	−16.9443	−0.766246
$490$	0.618034	0.0279199
$491$	21.7426	0.981232	0.490616	−	0.871376i	$-0.336772\pi$
$491$	21.7426	0.981232	0.490616	+	0.871376i	$0.336772\pi$
$492$	−23.4164	−1.05569
$493$	14.4721	0.651792
$494$	22.9787	1.03386
$495$	6.23607	0.280290
$496$	−2.47214	−0.111002
$497$	2.47214	0.110890
$498$	−22.9443	−1.02816
$499$	21.8885	0.979866	0.489933	−	0.871760i	$-0.337021\pi$
$499$	21.8885	0.979866	0.489933	+	0.871760i	$0.337021\pi$
$500$	−5.94427	−0.265836
$501$	31.8885	1.42468
$502$	10.6525	0.475443
$503$	−28.0902	−1.25248	−0.626239	−	0.779631i	$-0.715407\pi$
$503$	−28.0902	−1.25248	−0.626239	+	0.779631i	$0.715407\pi$
$504$	−11.5623	−0.515026
$505$	2.76393	0.122993
$506$	13.3262	0.592424
$507$	48.5967	2.15826
$508$	4.00000	0.177471
$509$	32.8541	1.45623	0.728116	−	0.685454i	$-0.240396\pi$
$509$	32.8541	1.45623	0.728116	+	0.685454i	$0.240396\pi$
$510$	−5.23607	−0.231857
$511$	1.85410	0.0820206
$512$	11.0000	0.486136
$513$	−9.14590	−0.403801
$514$	16.9443	0.747380
$515$	−10.5623	−0.465431
$516$	14.9443	0.657885
$517$	−3.23607	−0.142322
$518$	−2.14590	−0.0942853
$519$	4.09017	0.179539
$520$	−10.4164	−0.456790
$521$	4.90983	0.215104	0.107552	−	0.994199i	$-0.465699\pi$
$521$	4.90983	0.215104	0.107552	+	0.994199i	$0.465699\pi$
$522$	17.2361	0.754402
$523$	30.7426	1.34428	0.672141	−	0.740423i	$-0.265375\pi$
$523$	30.7426	1.34428	0.672141	+	0.740423i	$0.265375\pi$
$524$	6.29180	0.274858
$525$	12.0902	0.527658
$526$	−22.7426	−0.991626
$527$	−8.00000	−0.348485
$528$	6.85410	0.298287
$529$	2.90983	0.126514
$530$	−2.67376	−0.116141
$531$	−40.9230	−1.77591
$532$	−4.09017	−0.177331
$533$	50.2492	2.17654
$534$	18.1803	0.786740
$535$	−3.70820	−0.160320
$536$	−21.4377	−0.925967
$537$	8.70820	0.375787
$538$	7.70820	0.332324
$539$	−2.61803	−0.112767
$540$	1.38197	0.0594703
$541$	38.5410	1.65701	0.828504	−	0.559983i	$-0.189192\pi$
$541$	38.5410	1.65701	0.828504	+	0.559983i	$0.189192\pi$
$542$	25.1246	1.07919
$543$	−7.70820	−0.330791
$544$	16.1803	0.693726
$545$	6.09017	0.260874
$546$	14.7082	0.629453
$547$	−44.0689	−1.88425	−0.942125	−	0.335263i	$-0.891175\pi$
$547$	−44.0689	−1.88425	−0.942125	+	0.335263i	$0.891175\pi$
$548$	−12.4721	−0.532783
$549$	52.8328	2.25485
$550$	−12.0902	−0.515527
$551$	18.2918	0.779257
$552$	39.9787	1.70161
$553$	13.6180	0.579098
$554$	5.52786	0.234856
$555$	3.47214	0.147384
$556$	11.4164	0.484164
$557$	−7.12461	−0.301879	−0.150940	−	0.988543i	$-0.548230\pi$
$557$	−7.12461	−0.301879	−0.150940	+	0.988543i	$0.548230\pi$
$558$	−9.52786	−0.403347
$559$	−32.0689	−1.35637
$560$	−0.618034	−0.0261167
$561$	22.1803	0.936455
$562$	25.2705	1.06597
$563$	30.0689	1.26725	0.633626	−	0.773639i	$-0.281566\pi$
$563$	30.0689	1.26725	0.633626	+	0.773639i	$0.281566\pi$
$564$	−3.23607	−0.136263
$565$	8.88854	0.373944
$566$	−0.673762	−0.0283203
$567$	5.70820	0.239722
$568$	−7.41641	−0.311186
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	−6.61803	−0.277199
$571$	22.0689	0.923554	0.461777	−	0.886996i	$-0.347212\pi$
$571$	22.0689	0.923554	0.461777	+	0.886996i	$0.347212\pi$
$572$	14.7082	0.614981
$573$	46.8328	1.95647
$574$	8.94427	0.373327
$575$	−23.5066	−0.980292
$576$	26.9787	1.12411
$577$	−17.4377	−0.725941	−0.362970	−	0.931801i	$-0.618237\pi$
$577$	−17.4377	−0.725941	−0.362970	+	0.931801i	$0.618237\pi$
$578$	6.52786	0.271523
$579$	−49.1246	−2.04155
$580$	−2.76393	−0.114766
$581$	−8.76393	−0.363589
$582$	12.7082	0.526772
$583$	11.3262	0.469085
$584$	−5.56231	−0.230170
$585$	−13.3820	−0.553276
$586$	16.4721	0.680458
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−2.61803	−0.107966
$589$	−10.1115	−0.416635
$590$	−6.56231	−0.270166
$591$	−8.00000	−0.329076
$592$	2.14590	0.0881959
$593$	24.2918	0.997545	0.498772	−	0.866733i	$-0.333784\pi$
$593$	24.2918	0.997545	0.498772	+	0.866733i	$0.333784\pi$
$594$	5.85410	0.240197
$595$	−2.00000	−0.0819920
$596$	5.41641	0.221865
$597$	2.23607	0.0915162
$598$	−28.5967	−1.16941
$599$	12.6525	0.516966	0.258483	−	0.966016i	$-0.416777\pi$
$599$	12.6525	0.516966	0.258483	+	0.966016i	$0.416777\pi$
$600$	−36.2705	−1.48074
$601$	−1.34752	−0.0549667	−0.0274833	−	0.999622i	$-0.508749\pi$
$601$	−1.34752	−0.0549667	−0.0274833	+	0.999622i	$0.508749\pi$
$602$	−5.70820	−0.232649
$603$	−27.5410	−1.12156
$604$	6.76393	0.275220
$605$	2.56231	0.104173
$606$	11.7082	0.475613
$607$	32.9443	1.33717	0.668583	−	0.743637i	$-0.266901\pi$
$607$	32.9443	1.33717	0.668583	+	0.743637i	$0.266901\pi$
$608$	20.4508	0.829391
$609$	11.7082	0.474440
$610$	8.47214	0.343027
$611$	6.94427	0.280935
$612$	12.4721	0.504156
$613$	23.4508	0.947171	0.473585	−	0.880748i	$-0.342960\pi$
$613$	23.4508	0.947171	0.473585	+	0.880748i	$0.342960\pi$
$614$	29.7984	1.20256
$615$	−14.4721	−0.583573
$616$	7.85410	0.316451
$617$	−10.3607	−0.417105	−0.208553	−	0.978011i	$-0.566875\pi$
$617$	−10.3607	−0.417105	−0.208553	+	0.978011i	$0.566875\pi$
$618$	−44.7426	−1.79981
$619$	5.70820	0.229432	0.114716	−	0.993398i	$-0.463404\pi$
$619$	5.70820	0.229432	0.114716	+	0.993398i	$0.463404\pi$
$620$	1.52786	0.0613605
$621$	11.3820	0.456743
$622$	−8.94427	−0.358633
$623$	6.94427	0.278216
$624$	−14.7082	−0.588799
$625$	19.4164	0.776656
$626$	−22.1803	−0.886505
$627$	28.0344	1.11959
$628$	−3.14590	−0.125535
$629$	6.94427	0.276886
$630$	−2.38197	−0.0948998
$631$	−37.7426	−1.50251	−0.751256	−	0.660011i	$-0.770551\pi$
$631$	−37.7426	−1.50251	−0.751256	+	0.660011i	$0.770551\pi$
$632$	−40.8541	−1.62509
$633$	−69.5410	−2.76401
$634$	28.6525	1.13794
$635$	2.47214	0.0981037
$636$	11.3262	0.449115
$637$	5.61803	0.222595
$638$	−11.7082	−0.463532
$639$	−9.52786	−0.376916
$640$	−1.85410	−0.0732898
$641$	−35.0132	−1.38294	−0.691468	−	0.722407i	$-0.743036\pi$
$641$	−35.0132	−1.38294	−0.691468	+	0.722407i	$0.743036\pi$
$642$	−15.7082	−0.619953
$643$	46.3607	1.82829	0.914143	−	0.405391i	$-0.132865\pi$
$643$	46.3607	1.82829	0.914143	+	0.405391i	$0.132865\pi$
$644$	5.09017	0.200581
$645$	9.23607	0.363670
$646$	−13.2361	−0.520766
$647$	−3.70820	−0.145785	−0.0728923	−	0.997340i	$-0.523223\pi$
$647$	−3.70820	−0.145785	−0.0728923	+	0.997340i	$0.523223\pi$
$648$	−17.1246	−0.672718
$649$	27.7984	1.09118
$650$	25.9443	1.01762
$651$	−6.47214	−0.253663
$652$	6.47214	0.253468
$653$	15.0557	0.589176	0.294588	−	0.955624i	$-0.404818\pi$
$653$	15.0557	0.589176	0.294588	+	0.955624i	$0.404818\pi$
$654$	25.7984	1.00880
$655$	3.88854	0.151938
$656$	−8.94427	−0.349215
$657$	−7.14590	−0.278788
$658$	1.23607	0.0481869
$659$	9.03444	0.351932	0.175966	−	0.984396i	$-0.443695\pi$
$659$	9.03444	0.351932	0.175966	+	0.984396i	$0.443695\pi$
$660$	−4.23607	−0.164889
$661$	−17.2361	−0.670405	−0.335203	−	0.942146i	$-0.608805\pi$
$661$	−17.2361	−0.670405	−0.335203	+	0.942146i	$0.608805\pi$
$662$	22.4721	0.873404
$663$	−47.5967	−1.84850
$664$	26.2918	1.02032
$665$	−2.52786	−0.0980264
$666$	8.27051	0.320476
$667$	−22.7639	−0.881423
$668$	−12.1803	−0.471271
$669$	1.14590	0.0443030
$670$	−4.41641	−0.170621
$671$	−35.8885	−1.38546
$672$	13.0902	0.504964
$673$	−43.5066	−1.67706	−0.838528	−	0.544859i	$-0.816583\pi$
$673$	−43.5066	−1.67706	−0.838528	+	0.544859i	$0.816583\pi$
$674$	−16.0902	−0.619770
$675$	−10.3262	−0.397457
$676$	−18.5623	−0.713935
$677$	−22.1459	−0.851136	−0.425568	−	0.904926i	$-0.639926\pi$
$677$	−22.1459	−0.851136	−0.425568	+	0.904926i	$0.639926\pi$
$678$	37.6525	1.44603
$679$	4.85410	0.186283
$680$	6.00000	0.230089
$681$	49.5967	1.90055
$682$	6.47214	0.247831
$683$	−11.5279	−0.441101	−0.220551	−	0.975376i	$-0.570785\pi$
$683$	−11.5279	−0.441101	−0.220551	+	0.975376i	$0.570785\pi$
$684$	15.7639	0.602749
$685$	−7.70820	−0.294515
$686$	1.00000	0.0381802
$687$	58.0689	2.21547
$688$	5.70820	0.217623
$689$	−24.3050	−0.925945
$690$	8.23607	0.313542
$691$	33.7082	1.28232	0.641160	−	0.767407i	$-0.278453\pi$
$691$	33.7082	1.28232	0.641160	+	0.767407i	$0.278453\pi$
$692$	−1.56231	−0.0593900
$693$	10.0902	0.383294
$694$	32.4508	1.23182
$695$	7.05573	0.267639
$696$	−35.1246	−1.33139
$697$	−28.9443	−1.09634
$698$	−31.8885	−1.20700
$699$	−4.76393	−0.180188
$700$	−4.61803	−0.174545
$701$	2.11146	0.0797486	0.0398743	−	0.999205i	$-0.487304\pi$
$701$	2.11146	0.0797486	0.0398743	+	0.999205i	$0.487304\pi$
$702$	−12.5623	−0.474134
$703$	8.77709	0.331034
$704$	−18.3262	−0.690696
$705$	−2.00000	−0.0753244
$706$	13.7082	0.515915
$707$	4.47214	0.168192
$708$	27.7984	1.04473
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	−1.52786	−0.0573397
$711$	−52.4853	−1.96835
$712$	−20.8328	−0.780743
$713$	12.5836	0.471259
$714$	−8.47214	−0.317062
$715$	9.09017	0.339953
$716$	−3.32624	−0.124307
$717$	−64.8328	−2.42123
$718$	−32.1803	−1.20096
$719$	−10.3607	−0.386388	−0.193194	−	0.981161i	$-0.561885\pi$
$719$	−10.3607	−0.386388	−0.193194	+	0.981161i	$0.561885\pi$
$720$	2.38197	0.0887706
$721$	−17.0902	−0.636471
$722$	2.27051	0.0844996
$723$	27.1803	1.01085
$724$	2.94427	0.109423
$725$	20.6525	0.767014
$726$	10.8541	0.402834
$727$	30.5410	1.13270	0.566352	−	0.824164i	$-0.308354\pi$
$727$	30.5410	1.13270	0.566352	+	0.824164i	$0.308354\pi$
$728$	−16.8541	−0.624655
$729$	−39.5623	−1.46527
$730$	−1.14590	−0.0424116
$731$	18.4721	0.683217
$732$	−35.8885	−1.32648
$733$	−24.6738	−0.911346	−0.455673	−	0.890147i	$-0.650601\pi$
$733$	−24.6738	−0.911346	−0.455673	+	0.890147i	$0.650601\pi$
$734$	30.0000	1.10732
$735$	−1.61803	−0.0596821
$736$	−25.4508	−0.938131
$737$	18.7082	0.689126
$738$	−34.4721	−1.26894
$739$	22.4721	0.826651	0.413325	−	0.910583i	$-0.364367\pi$
$739$	22.4721	0.826651	0.413325	+	0.910583i	$0.364367\pi$
$740$	−1.32624	−0.0487535
$741$	−60.1591	−2.21000
$742$	−4.32624	−0.158821
$743$	−15.7082	−0.576278	−0.288139	−	0.957589i	$-0.593037\pi$
$743$	−15.7082	−0.576278	−0.288139	+	0.957589i	$0.593037\pi$
$744$	19.4164	0.711840
$745$	3.34752	0.122644
$746$	19.3262	0.707584
$747$	33.7771	1.23584
$748$	−8.47214	−0.309772
$749$	−6.00000	−0.219235
$750$	−15.5623	−0.568255
$751$	−18.2918	−0.667477	−0.333739	−	0.942666i	$-0.608310\pi$
$751$	−18.2918	−0.667477	−0.333739	+	0.942666i	$0.608310\pi$
$752$	−1.23607	−0.0450748
$753$	−27.8885	−1.01632
$754$	25.1246	0.914984
$755$	4.18034	0.152138
$756$	2.23607	0.0813250
$757$	−18.2918	−0.664827	−0.332413	−	0.943134i	$-0.607863\pi$
$757$	−18.2918	−0.664827	−0.332413	+	0.943134i	$0.607863\pi$
$758$	−13.0344	−0.473432
$759$	−34.8885	−1.26637
$760$	7.58359	0.275086
$761$	24.3262	0.881825	0.440913	−	0.897550i	$-0.354655\pi$
$761$	24.3262	0.881825	0.440913	+	0.897550i	$0.354655\pi$
$762$	10.4721	0.379365
$763$	9.85410	0.356742
$764$	−17.8885	−0.647185
$765$	7.70820	0.278691
$766$	12.8541	0.464438
$767$	−59.6525	−2.15393
$768$	−44.5066	−1.60599
$769$	3.63932	0.131237	0.0656186	−	0.997845i	$-0.479098\pi$
$769$	3.63932	0.131237	0.0656186	+	0.997845i	$0.479098\pi$
$770$	1.61803	0.0583099
$771$	−44.3607	−1.59761
$772$	18.7639	0.675329
$773$	1.88854	0.0679262	0.0339631	−	0.999423i	$-0.489187\pi$
$773$	1.88854	0.0679262	0.0339631	+	0.999423i	$0.489187\pi$
$774$	22.0000	0.790774
$775$	−11.4164	−0.410089
$776$	−14.5623	−0.522756
$777$	5.61803	0.201546
$778$	−21.9787	−0.787975
$779$	−36.5836	−1.31074
$780$	9.09017	0.325480
$781$	6.47214	0.231591
$782$	16.4721	0.589042
$783$	−10.0000	−0.357371
$784$	−1.00000	−0.0357143
$785$	−1.94427	−0.0693940
$786$	16.4721	0.587542
$787$	−27.7082	−0.987691	−0.493845	−	0.869550i	$-0.664409\pi$
$787$	−27.7082	−0.987691	−0.493845	+	0.869550i	$0.664409\pi$
$788$	3.05573	0.108856
$789$	59.5410	2.11972
$790$	−8.41641	−0.299442
$791$	14.3820	0.511364
$792$	−30.2705	−1.07562
$793$	77.0132	2.73482
$794$	−7.88854	−0.279954
$795$	7.00000	0.248264
$796$	−0.854102	−0.0302728
$797$	53.4164	1.89211	0.946053	−	0.324012i	$-0.105032\pi$
$797$	53.4164	1.89211	0.946053	+	0.324012i	$0.105032\pi$
$798$	−10.7082	−0.379066
$799$	−4.00000	−0.141510
$800$	23.0902	0.816361
$801$	−26.7639	−0.945657
$802$	1.05573	0.0372791
$803$	4.85410	0.171298
$804$	18.7082	0.659787
$805$	3.14590	0.110878
$806$	−13.8885	−0.489203
$807$	−20.1803	−0.710382
$808$	−13.4164	−0.471988
$809$	23.8885	0.839876	0.419938	−	0.907553i	$-0.362052\pi$
$809$	23.8885	0.839876	0.419938	+	0.907553i	$0.362052\pi$
$810$	−3.52786	−0.123957
$811$	36.1459	1.26925	0.634627	−	0.772819i	$-0.281154\pi$
$811$	36.1459	1.26925	0.634627	+	0.772819i	$0.281154\pi$
$812$	−4.47214	−0.156941
$813$	−65.7771	−2.30690
$814$	−5.61803	−0.196912
$815$	4.00000	0.140114
$816$	8.47214	0.296584
$817$	23.3475	0.816826
$818$	20.6525	0.722097
$819$	−21.6525	−0.756599
$820$	5.52786	0.193041
$821$	19.6738	0.686619	0.343310	−	0.939222i	$-0.388452\pi$
$821$	19.6738	0.686619	0.343310	+	0.939222i	$0.388452\pi$
$822$	−32.6525	−1.13889
$823$	−49.8885	−1.73901	−0.869503	−	0.493928i	$-0.835561\pi$
$823$	−49.8885	−1.73901	−0.869503	+	0.493928i	$0.835561\pi$
$824$	51.2705	1.78609
$825$	31.6525	1.10200
$826$	−10.6180	−0.369449
$827$	15.6869	0.545488	0.272744	−	0.962087i	$-0.412069\pi$
$827$	15.6869	0.545488	0.272744	+	0.962087i	$0.412069\pi$
$828$	−19.6180	−0.681774
$829$	48.8541	1.69677	0.848387	−	0.529377i	$-0.177574\pi$
$829$	48.8541	1.69677	0.848387	+	0.529377i	$0.177574\pi$
$830$	5.41641	0.188006
$831$	−14.4721	−0.502033
$832$	39.3262	1.36339
$833$	−3.23607	−0.112123
$834$	29.8885	1.03496
$835$	−7.52786	−0.260512
$836$	−10.7082	−0.370351
$837$	5.52786	0.191071
$838$	20.0000	0.690889
$839$	−26.7639	−0.923994	−0.461997	−	0.886882i	$-0.652867\pi$
$839$	−26.7639	−0.923994	−0.461997	+	0.886882i	$0.652867\pi$
$840$	4.85410	0.167482
$841$	−9.00000	−0.310345
$842$	−2.20163	−0.0758730
$843$	−66.1591	−2.27864
$844$	26.5623	0.914312
$845$	−11.4721	−0.394653
$846$	−4.76393	−0.163787
$847$	4.14590	0.142455
$848$	4.32624	0.148564
$849$	1.76393	0.0605380
$850$	−14.9443	−0.512584
$851$	−10.9230	−0.374435
$852$	6.47214	0.221732
$853$	−4.18034	−0.143132	−0.0715661	−	0.997436i	$-0.522800\pi$
$853$	−4.18034	−0.143132	−0.0715661	+	0.997436i	$0.522800\pi$
$854$	13.7082	0.469085
$855$	9.74265	0.333191
$856$	18.0000	0.615227
$857$	7.52786	0.257147	0.128573	−	0.991700i	$-0.458960\pi$
$857$	7.52786	0.257147	0.128573	+	0.991700i	$0.458960\pi$
$858$	38.5066	1.31459
$859$	−26.4721	−0.903218	−0.451609	−	0.892216i	$-0.649150\pi$
$859$	−26.4721	−0.903218	−0.451609	+	0.892216i	$0.649150\pi$
$860$	−3.52786	−0.120299
$861$	−23.4164	−0.798029
$862$	36.9443	1.25833
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−11.1803	−0.380363
$865$	−0.965558	−0.0328300
$866$	18.3607	0.623921
$867$	−17.0902	−0.580413
$868$	2.47214	0.0839098
$869$	35.6525	1.20943
$870$	−7.23607	−0.245326
$871$	−40.1459	−1.36029
$872$	−29.5623	−1.00111
$873$	−18.7082	−0.633177
$874$	20.8197	0.704236
$875$	−5.94427	−0.200953
$876$	4.85410	0.164005
$877$	−22.9443	−0.774773	−0.387387	−	0.921917i	$-0.626622\pi$
$877$	−22.9443	−0.774773	−0.387387	+	0.921917i	$0.626622\pi$
$878$	−17.1246	−0.577928
$879$	−43.1246	−1.45456
$880$	−1.61803	−0.0545439
$881$	10.7639	0.362646	0.181323	−	0.983424i	$-0.441962\pi$
$881$	10.7639	0.362646	0.181323	+	0.983424i	$0.441962\pi$
$882$	−3.85410	−0.129774
$883$	−35.0557	−1.17972	−0.589860	−	0.807506i	$-0.700817\pi$
$883$	−35.0557	−1.17972	−0.589860	+	0.807506i	$0.700817\pi$
$884$	18.1803	0.611471
$885$	17.1803	0.577511
$886$	13.7984	0.463565
$887$	−47.1935	−1.58460	−0.792301	−	0.610130i	$-0.791117\pi$
$887$	−47.1935	−1.58460	−0.792301	+	0.610130i	$0.791117\pi$
$888$	−16.8541	−0.565587
$889$	4.00000	0.134156
$890$	−4.29180	−0.143861
$891$	14.9443	0.500652
$892$	−0.437694	−0.0146551
$893$	−5.05573	−0.169183
$894$	14.1803	0.474262
$895$	−2.05573	−0.0687154
$896$	−3.00000	−0.100223
$897$	74.8673	2.49974
$898$	−39.6869	−1.32437
$899$	−11.0557	−0.368729
$900$	17.7984	0.593279
$901$	14.0000	0.466408
$902$	23.4164	0.779681
$903$	14.9443	0.497314
$904$	−43.1459	−1.43501
$905$	1.81966	0.0604875
$906$	17.7082	0.588316
$907$	−6.74265	−0.223886	−0.111943	−	0.993715i	$-0.535707\pi$
$907$	−6.74265	−0.223886	−0.111943	+	0.993715i	$0.535707\pi$
$908$	−18.9443	−0.628688
$909$	−17.2361	−0.571684
$910$	−3.47214	−0.115100
$911$	−14.8328	−0.491433	−0.245717	−	0.969342i	$-0.579023\pi$
$911$	−14.8328	−0.491433	−0.245717	+	0.969342i	$0.579023\pi$
$912$	10.7082	0.354584
$913$	−22.9443	−0.759345
$914$	−20.6869	−0.684262
$915$	−22.1803	−0.733259
$916$	−22.1803	−0.732859
$917$	6.29180	0.207773
$918$	7.23607	0.238826
$919$	−29.6180	−0.977009	−0.488504	−	0.872561i	$-0.662457\pi$
$919$	−29.6180	−0.977009	−0.488504	+	0.872561i	$0.662457\pi$
$920$	−9.43769	−0.311152
$921$	−78.0132	−2.57062
$922$	−27.5967	−0.908850
$923$	−13.8885	−0.457147
$924$	−6.85410	−0.225483
$925$	9.90983	0.325833
$926$	8.00000	0.262896
$927$	65.8673	2.16336
$928$	22.3607	0.734025
$929$	−7.45085	−0.244454	−0.122227	−	0.992502i	$-0.539004\pi$
$929$	−7.45085	−0.244454	−0.122227	+	0.992502i	$0.539004\pi$
$930$	4.00000	0.131165
$931$	−4.09017	−0.134050
$932$	1.81966	0.0596049
$933$	23.4164	0.766619
$934$	21.0344	0.688268
$935$	−5.23607	−0.171238
$936$	64.9574	2.12320
$937$	22.6525	0.740024	0.370012	−	0.929027i	$-0.379354\pi$
$937$	22.6525	0.740024	0.370012	+	0.929027i	$0.379354\pi$
$938$	−7.14590	−0.233322
$939$	58.0689	1.89501
$940$	0.763932	0.0249167
$941$	10.9443	0.356773	0.178387	−	0.983960i	$-0.442912\pi$
$941$	10.9443	0.356773	0.178387	+	0.983960i	$0.442912\pi$
$942$	−8.23607	−0.268346
$943$	45.5279	1.48259
$944$	10.6180	0.345588
$945$	1.38197	0.0449554
$946$	−14.9443	−0.485880
$947$	42.9787	1.39662	0.698310	−	0.715795i	$-0.253936\pi$
$947$	42.9787	1.39662	0.698310	+	0.715795i	$0.253936\pi$
$948$	35.6525	1.15794
$949$	−10.4164	−0.338131
$950$	−18.8885	−0.612825
$951$	−75.0132	−2.43247
$952$	9.70820	0.314645
$953$	17.8885	0.579467	0.289733	−	0.957107i	$-0.406433\pi$
$953$	17.8885	0.579467	0.289733	+	0.957107i	$0.406433\pi$
$954$	16.6738	0.539833
$955$	−11.0557	−0.357755
$956$	24.7639	0.800923
$957$	30.6525	0.990854
$958$	6.65248	0.214932
$959$	−12.4721	−0.402746
$960$	−11.3262	−0.365553
$961$	−24.8885	−0.802856
$962$	12.0557	0.388692
$963$	23.1246	0.745180
$964$	−10.3820	−0.334381
$965$	11.5967	0.373313
$966$	13.3262	0.428765
$967$	14.0213	0.450894	0.225447	−	0.974255i	$-0.427616\pi$
$967$	14.0213	0.450894	0.225447	+	0.974255i	$0.427616\pi$
$968$	−12.4377	−0.399763
$969$	34.6525	1.11320
$970$	−3.00000	−0.0963242
$971$	40.7214	1.30681	0.653405	−	0.757008i	$-0.273340\pi$
$971$	40.7214	1.30681	0.653405	+	0.757008i	$0.273340\pi$
$972$	21.6525	0.694503
$973$	11.4164	0.365993
$974$	25.4164	0.814394
$975$	−67.9230	−2.17528
$976$	−13.7082	−0.438789
$977$	−1.41641	−0.0453149	−0.0226575	−	0.999743i	$-0.507213\pi$
$977$	−1.41641	−0.0453149	−0.0226575	+	0.999743i	$0.507213\pi$
$978$	16.9443	0.541818
$979$	18.1803	0.581046
$980$	0.618034	0.0197424
$981$	−37.9787	−1.21257
$982$	−21.7426	−0.693836
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	70.2492	2.23946
$985$	1.88854	0.0601740
$986$	−14.4721	−0.460887
$987$	−3.23607	−0.103005
$988$	22.9787	0.731050
$989$	−29.0557	−0.923918
$990$	−6.23607	−0.198195
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	−12.3607	−0.392452
$993$	−58.8328	−1.86700
$994$	−2.47214	−0.0784114
$995$	−0.527864	−0.0167344
$996$	−22.9443	−0.727017
$997$	29.9787	0.949435	0.474718	−	0.880138i	$-0.342550\pi$
$997$	29.9787	0.949435	0.474718	+	0.880138i	$0.342550\pi$
$998$	−21.8885	−0.692870
$999$	−4.79837	−0.151814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.b.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.61803 q^{3} -1.00000 q^{4} -0.618034 q^{5} -2.61803 q^{6} -1.00000 q^{7} +3.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.61803 q^{3} -1.00000 q^{4} -0.618034 q^{5} -2.61803 q^{6} -1.00000 q^{7} +3.00000 q^{8} +3.85410 q^{9} +0.618034 q^{10} -2.61803 q^{11} -2.61803 q^{12} +5.61803 q^{13} +1.00000 q^{14} -1.61803 q^{15} -1.00000 q^{16} -3.23607 q^{17} -3.85410 q^{18} -4.09017 q^{19} +0.618034 q^{20} -2.61803 q^{21} +2.61803 q^{22} +5.09017 q^{23} +7.85410 q^{24} -4.61803 q^{25} -5.61803 q^{26} +2.23607 q^{27} +1.00000 q^{28} -4.47214 q^{29} +1.61803 q^{30} +2.47214 q^{31} -5.00000 q^{32} -6.85410 q^{33} +3.23607 q^{34} +0.618034 q^{35} -3.85410 q^{36} -2.14590 q^{37} +4.09017 q^{38} +14.7082 q^{39} -1.85410 q^{40} +8.94427 q^{41} +2.61803 q^{42} -5.70820 q^{43} +2.61803 q^{44} -2.38197 q^{45} -5.09017 q^{46} +1.23607 q^{47} -2.61803 q^{48} +1.00000 q^{49} +4.61803 q^{50} -8.47214 q^{51} -5.61803 q^{52} -4.32624 q^{53} -2.23607 q^{54} +1.61803 q^{55} -3.00000 q^{56} -10.7082 q^{57} +4.47214 q^{58} -10.6180 q^{59} +1.61803 q^{60} +13.7082 q^{61} -2.47214 q^{62} -3.85410 q^{63} +7.00000 q^{64} -3.47214 q^{65} +6.85410 q^{66} -7.14590 q^{67} +3.23607 q^{68} +13.3262 q^{69} -0.618034 q^{70} -2.47214 q^{71} +11.5623 q^{72} -1.85410 q^{73} +2.14590 q^{74} -12.0902 q^{75} +4.09017 q^{76} +2.61803 q^{77} -14.7082 q^{78} -13.6180 q^{79} +0.618034 q^{80} -5.70820 q^{81} -8.94427 q^{82} +8.76393 q^{83} +2.61803 q^{84} +2.00000 q^{85} +5.70820 q^{86} -11.7082 q^{87} -7.85410 q^{88} -6.94427 q^{89} +2.38197 q^{90} -5.61803 q^{91} -5.09017 q^{92} +6.47214 q^{93} -1.23607 q^{94} +2.52786 q^{95} -13.0902 q^{96} -4.85410 q^{97} -1.00000 q^{98} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9	\( 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9} - q^{10} - 3 q^{11} - 3 q^{12} + 9 q^{13} + 2 q^{14} - q^{15} - 2 q^{16} - 2 q^{17} - q^{18} + 3 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} - q^{23} + 9 q^{24} - 7 q^{25} - 9 q^{26} + 2 q^{28} + q^{30} - 4 q^{31} - 10 q^{32} - 7 q^{33} + 2 q^{34} - q^{35} - q^{36} - 11 q^{37} - 3 q^{38} + 16 q^{39} + 3 q^{40} + 3 q^{42} + 2 q^{43} + 3 q^{44} - 7 q^{45} + q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} + 7 q^{50} - 8 q^{51} - 9 q^{52} + 7 q^{53} + q^{55} - 6 q^{56} - 8 q^{57} - 19 q^{59} + q^{60} + 14 q^{61} + 4 q^{62} - q^{63} + 14 q^{64} + 2 q^{65} + 7 q^{66} - 21 q^{67} + 2 q^{68} + 11 q^{69} + q^{70} + 4 q^{71} + 3 q^{72} + 3 q^{73} + 11 q^{74} - 13 q^{75} - 3 q^{76} + 3 q^{77} - 16 q^{78} - 25 q^{79} - q^{80} + 2 q^{81} + 22 q^{83} + 3 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} - 9 q^{88} + 4 q^{89} + 7 q^{90} - 9 q^{91} + q^{92} + 4 q^{93} + 2 q^{94} + 14 q^{95} - 15 q^{96} - 3 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9 - q^10 - 3 * q^11 - 3 * q^12 + 9 * q^13 + 2 * q^14 - q^15 - 2 * q^16 - 2 * q^17 - q^18 + 3 * q^19 - q^20 - 3 * q^21 + 3 * q^22 - q^23 + 9 * q^24 - 7 * q^25 - 9 * q^26 + 2 * q^28 + q^30 - 4 * q^31 - 10 * q^32 - 7 * q^33 + 2 * q^34 - q^35 - q^36 - 11 * q^37 - 3 * q^38 + 16 * q^39 + 3 * q^40 + 3 * q^42 + 2 * q^43 + 3 * q^44 - 7 * q^45 + q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 + 7 * q^50 - 8 * q^51 - 9 * q^52 + 7 * q^53 + q^55 - 6 * q^56 - 8 * q^57 - 19 * q^59 + q^60 + 14 * q^61 + 4 * q^62 - q^63 + 14 * q^64 + 2 * q^65 + 7 * q^66 - 21 * q^67 + 2 * q^68 + 11 * q^69 + q^70 + 4 * q^71 + 3 * q^72 + 3 * q^73 + 11 * q^74 - 13 * q^75 - 3 * q^76 + 3 * q^77 - 16 * q^78 - 25 * q^79 - q^80 + 2 * q^81 + 22 * q^83 + 3 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 - 9 * q^88 + 4 * q^89 + 7 * q^90 - 9 * q^91 + q^92 + 4 * q^93 + 2 * q^94 + 14 * q^95 - 15 * q^96 - 3 * q^97 - 2 * q^98 - 9 * q^99

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