LMFDB - Embedded newform 6022.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.13476 q^{3} +1.00000 q^{4} +3.93476 q^{5} +1.13476 q^{6} +4.57427 q^{7} -1.00000 q^{8} -1.71231 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.13476 q^{3} +1.00000 q^{4} +3.93476 q^{5} +1.13476 q^{6} +4.57427 q^{7} -1.00000 q^{8} -1.71231 q^{9} -3.93476 q^{10} +0.0153971 q^{11} -1.13476 q^{12} +3.92451 q^{13} -4.57427 q^{14} -4.46502 q^{15} +1.00000 q^{16} +5.90653 q^{17} +1.71231 q^{18} +7.86873 q^{19} +3.93476 q^{20} -5.19071 q^{21} -0.0153971 q^{22} -1.42378 q^{23} +1.13476 q^{24} +10.4823 q^{25} -3.92451 q^{26} +5.34736 q^{27} +4.57427 q^{28} +3.86000 q^{29} +4.46502 q^{30} -8.70807 q^{31} -1.00000 q^{32} -0.0174721 q^{33} -5.90653 q^{34} +17.9986 q^{35} -1.71231 q^{36} -1.84306 q^{37} -7.86873 q^{38} -4.45339 q^{39} -3.93476 q^{40} +1.78213 q^{41} +5.19071 q^{42} +1.71782 q^{43} +0.0153971 q^{44} -6.73753 q^{45} +1.42378 q^{46} +4.03816 q^{47} -1.13476 q^{48} +13.9239 q^{49} -10.4823 q^{50} -6.70252 q^{51} +3.92451 q^{52} -8.24660 q^{53} -5.34736 q^{54} +0.0605840 q^{55} -4.57427 q^{56} -8.92916 q^{57} -3.86000 q^{58} +2.88671 q^{59} -4.46502 q^{60} -7.58440 q^{61} +8.70807 q^{62} -7.83257 q^{63} +1.00000 q^{64} +15.4420 q^{65} +0.0174721 q^{66} -7.27185 q^{67} +5.90653 q^{68} +1.61566 q^{69} -17.9986 q^{70} +0.785801 q^{71} +1.71231 q^{72} +5.91895 q^{73} +1.84306 q^{74} -11.8950 q^{75} +7.86873 q^{76} +0.0704305 q^{77} +4.45339 q^{78} -4.17465 q^{79} +3.93476 q^{80} -0.931057 q^{81} -1.78213 q^{82} +5.21858 q^{83} -5.19071 q^{84} +23.2408 q^{85} -1.71782 q^{86} -4.38019 q^{87} -0.0153971 q^{88} +11.0328 q^{89} +6.73753 q^{90} +17.9517 q^{91} -1.42378 q^{92} +9.88160 q^{93} -4.03816 q^{94} +30.9616 q^{95} +1.13476 q^{96} -3.27956 q^{97} -13.9239 q^{98} -0.0263647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.13476	−0.655156	−0.327578	−	0.944824i	$-0.606232\pi$
$3$	−1.13476	−0.655156	−0.327578	+	0.944824i	$0.606232\pi$
$4$	1.00000	0.500000
$5$	3.93476	1.75968	0.879839	−	0.475272i	$-0.157650\pi$
$5$	3.93476	1.75968	0.879839	+	0.475272i	$0.157650\pi$
$6$	1.13476	0.463265
$7$	4.57427	1.72891	0.864455	−	0.502710i	$-0.167664\pi$
$7$	4.57427	1.72891	0.864455	+	0.502710i	$0.167664\pi$
$8$	−1.00000	−0.353553
$9$	−1.71231	−0.570770
$10$	−3.93476	−1.24428
$11$	0.0153971	0.00464241	0.00232120	−	0.999997i	$-0.499261\pi$
$11$	0.0153971	0.00464241	0.00232120	+	0.999997i	$0.499261\pi$
$12$	−1.13476	−0.327578
$13$	3.92451	1.08846	0.544231	−	0.838935i	$-0.316821\pi$
$13$	3.92451	1.08846	0.544231	+	0.838935i	$0.316821\pi$
$14$	−4.57427	−1.22252
$15$	−4.46502	−1.15286
$16$	1.00000	0.250000
$17$	5.90653	1.43254	0.716272	−	0.697821i	$-0.245847\pi$
$17$	5.90653	1.43254	0.716272	+	0.697821i	$0.245847\pi$
$18$	1.71231	0.403596
$19$	7.86873	1.80521	0.902606	−	0.430468i	$-0.141652\pi$
$19$	7.86873	1.80521	0.902606	+	0.430468i	$0.141652\pi$
$20$	3.93476	0.879839
$21$	−5.19071	−1.13271
$22$	−0.0153971	−0.00328268
$23$	−1.42378	−0.296880	−0.148440	−	0.988921i	$-0.547425\pi$
$23$	−1.42378	−0.296880	−0.148440	+	0.988921i	$0.547425\pi$
$24$	1.13476	0.231633
$25$	10.4823	2.09647
$26$	−3.92451	−0.769659
$27$	5.34736	1.02910
$28$	4.57427	0.864455
$29$	3.86000	0.716784	0.358392	−	0.933571i	$-0.383325\pi$
$29$	3.86000	0.716784	0.358392	+	0.933571i	$0.383325\pi$
$30$	4.46502	0.815198
$31$	−8.70807	−1.56402	−0.782008	−	0.623269i	$-0.785804\pi$
$31$	−8.70807	−1.56402	−0.782008	+	0.623269i	$0.785804\pi$
$32$	−1.00000	−0.176777
$33$	−0.0174721	−0.00304150
$34$	−5.90653	−1.01296
$35$	17.9986	3.04232
$36$	−1.71231	−0.285385
$37$	−1.84306	−0.302997	−0.151498	−	0.988458i	$-0.548410\pi$
$37$	−1.84306	−0.302997	−0.151498	+	0.988458i	$0.548410\pi$
$38$	−7.86873	−1.27648
$39$	−4.45339	−0.713113
$40$	−3.93476	−0.622140
$41$	1.78213	0.278321	0.139161	−	0.990270i	$-0.455560\pi$
$41$	1.78213	0.278321	0.139161	+	0.990270i	$0.455560\pi$
$42$	5.19071	0.800944
$43$	1.71782	0.261965	0.130982	−	0.991385i	$-0.458187\pi$
$43$	1.71782	0.261965	0.130982	+	0.991385i	$0.458187\pi$
$44$	0.0153971	0.00232120
$45$	−6.73753	−1.00437
$46$	1.42378	0.209926
$47$	4.03816	0.589026	0.294513	−	0.955647i	$-0.404843\pi$
$47$	4.03816	0.589026	0.294513	+	0.955647i	$0.404843\pi$
$48$	−1.13476	−0.163789
$49$	13.9239	1.98913
$50$	−10.4823	−1.48243
$51$	−6.70252	−0.938541
$52$	3.92451	0.544231
$53$	−8.24660	−1.13276	−0.566379	−	0.824145i	$-0.691656\pi$
$53$	−8.24660	−1.13276	−0.566379	+	0.824145i	$0.691656\pi$
$54$	−5.34736	−0.727684
$55$	0.0605840	0.00816914
$56$	−4.57427	−0.611262
$57$	−8.92916	−1.18270
$58$	−3.86000	−0.506843
$59$	2.88671	0.375818	0.187909	−	0.982186i	$-0.439829\pi$
$59$	2.88671	0.375818	0.187909	+	0.982186i	$0.439829\pi$
$60$	−4.46502	−0.576432
$61$	−7.58440	−0.971083	−0.485542	−	0.874213i	$-0.661378\pi$
$61$	−7.58440	−0.971083	−0.485542	+	0.874213i	$0.661378\pi$
$62$	8.70807	1.10593
$63$	−7.83257	−0.986811
$64$	1.00000	0.125000
$65$	15.4420	1.91534
$66$	0.0174721	0.00215067
$67$	−7.27185	−0.888398	−0.444199	−	0.895928i	$-0.646512\pi$
$67$	−7.27185	−0.888398	−0.444199	+	0.895928i	$0.646512\pi$
$68$	5.90653	0.716272
$69$	1.61566	0.194502
$70$	−17.9986	−2.15125
$71$	0.785801	0.0932574	0.0466287	−	0.998912i	$-0.485152\pi$
$71$	0.785801	0.0932574	0.0466287	+	0.998912i	$0.485152\pi$
$72$	1.71231	0.201798
$73$	5.91895	0.692761	0.346380	−	0.938094i	$-0.387411\pi$
$73$	5.91895	0.692761	0.346380	+	0.938094i	$0.387411\pi$
$74$	1.84306	0.214251
$75$	−11.8950	−1.37351
$76$	7.86873	0.902606
$77$	0.0704305	0.00802631
$78$	4.45339	0.504247
$79$	−4.17465	−0.469685	−0.234842	−	0.972033i	$-0.575457\pi$
$79$	−4.17465	−0.469685	−0.234842	+	0.972033i	$0.575457\pi$
$80$	3.93476	0.439920
$81$	−0.931057	−0.103451
$82$	−1.78213	−0.196803
$83$	5.21858	0.572814	0.286407	−	0.958108i	$-0.407539\pi$
$83$	5.21858	0.572814	0.286407	+	0.958108i	$0.407539\pi$
$84$	−5.19071	−0.566353
$85$	23.2408	2.52082
$86$	−1.71782	−0.185237
$87$	−4.38019	−0.469605
$88$	−0.0153971	−0.00164134
$89$	11.0328	1.16948	0.584738	−	0.811222i	$-0.301197\pi$
$89$	11.0328	1.16948	0.584738	+	0.811222i	$0.301197\pi$
$90$	6.73753	0.710198
$91$	17.9517	1.88185
$92$	−1.42378	−0.148440
$93$	9.88160	1.02467
$94$	−4.03816	−0.416504
$95$	30.9616	3.17659
$96$	1.13476	0.115816
$97$	−3.27956	−0.332989	−0.166495	−	0.986042i	$-0.553245\pi$
$97$	−3.27956	−0.332989	−0.166495	+	0.986042i	$0.553245\pi$
$98$	−13.9239	−1.40653
$99$	−0.0263647	−0.00264975
$100$	10.4823	1.04823
$101$	1.40859	0.140160	0.0700799	−	0.997541i	$-0.477675\pi$
$101$	1.40859	0.140160	0.0700799	+	0.997541i	$0.477675\pi$
$102$	6.70252	0.663648
$103$	−3.38461	−0.333496	−0.166748	−	0.986000i	$-0.553327\pi$
$103$	−3.38461	−0.333496	−0.166748	+	0.986000i	$0.553327\pi$
$104$	−3.92451	−0.384830
$105$	−20.4242	−1.99320
$106$	8.24660	0.800981
$107$	−14.3324	−1.38557	−0.692785	−	0.721145i	$-0.743616\pi$
$107$	−14.3324	−1.38557	−0.692785	+	0.721145i	$0.743616\pi$
$108$	5.34736	0.514550
$109$	−5.03433	−0.482202	−0.241101	−	0.970500i	$-0.577508\pi$
$109$	−5.03433	−0.482202	−0.241101	+	0.970500i	$0.577508\pi$
$110$	−0.0605840	−0.00577646
$111$	2.09143	0.198510
$112$	4.57427	0.432227
$113$	−14.3578	−1.35067	−0.675333	−	0.737513i	$-0.736000\pi$
$113$	−14.3578	−1.35067	−0.675333	+	0.737513i	$0.736000\pi$
$114$	8.92916	0.836292
$115$	−5.60225	−0.522412
$116$	3.86000	0.358392
$117$	−6.71998	−0.621262
$118$	−2.88671	−0.265743
$119$	27.0181	2.47674
$120$	4.46502	0.407599
$121$	−10.9998	−0.999978
$122$	7.58440	0.686660
$123$	−2.02229	−0.182344
$124$	−8.70807	−0.782008
$125$	21.5717	1.92943
$126$	7.83257	0.697780
$127$	−19.4224	−1.72346	−0.861732	−	0.507364i	$-0.830620\pi$
$127$	−19.4224	−1.72346	−0.861732	+	0.507364i	$0.830620\pi$
$128$	−1.00000	−0.0883883
$129$	−1.94932	−0.171628
$130$	−15.4420	−1.35435
$131$	14.4036	1.25845	0.629224	−	0.777224i	$-0.283373\pi$
$131$	14.4036	1.25845	0.629224	+	0.777224i	$0.283373\pi$
$132$	−0.0174721	−0.00152075
$133$	35.9937	3.12105
$134$	7.27185	0.628192
$135$	21.0406	1.81088
$136$	−5.90653	−0.506481
$137$	9.57782	0.818288	0.409144	−	0.912470i	$-0.365827\pi$
$137$	9.57782	0.818288	0.409144	+	0.912470i	$0.365827\pi$
$138$	−1.61566	−0.137534
$139$	−4.53977	−0.385059	−0.192529	−	0.981291i	$-0.561669\pi$
$139$	−4.53977	−0.385059	−0.192529	+	0.981291i	$0.561669\pi$
$140$	17.9986	1.52116
$141$	−4.58236	−0.385904
$142$	−0.785801	−0.0659429
$143$	0.0604261	0.00505309
$144$	−1.71231	−0.142693
$145$	15.1882	1.26131
$146$	−5.91895	−0.489856
$147$	−15.8003	−1.30319
$148$	−1.84306	−0.151498
$149$	−9.69003	−0.793838	−0.396919	−	0.917854i	$-0.629921\pi$
$149$	−9.69003	−0.793838	−0.396919	+	0.917854i	$0.629921\pi$
$150$	11.8950	0.971220
$151$	4.27467	0.347868	0.173934	−	0.984757i	$-0.444352\pi$
$151$	4.27467	0.347868	0.173934	+	0.984757i	$0.444352\pi$
$152$	−7.86873	−0.638239
$153$	−10.1138	−0.817654
$154$	−0.0704305	−0.00567546
$155$	−34.2642	−2.75216
$156$	−4.45339	−0.356557
$157$	−11.7306	−0.936206	−0.468103	−	0.883674i	$-0.655062\pi$
$157$	−11.7306	−0.936206	−0.468103	+	0.883674i	$0.655062\pi$
$158$	4.17465	0.332117
$159$	9.35795	0.742133
$160$	−3.93476	−0.311070
$161$	−6.51277	−0.513278
$162$	0.931057	0.0731507
$163$	−23.4773	−1.83889	−0.919443	−	0.393223i	$-0.871360\pi$
$163$	−23.4773	−1.83889	−0.919443	+	0.393223i	$0.871360\pi$
$164$	1.78213	0.139161
$165$	−0.0687485	−0.00535206
$166$	−5.21858	−0.405041
$167$	−13.1562	−1.01806	−0.509028	−	0.860750i	$-0.669995\pi$
$167$	−13.1562	−1.01806	−0.509028	+	0.860750i	$0.669995\pi$
$168$	5.19071	0.400472
$169$	2.40176	0.184751
$170$	−23.2408	−1.78249
$171$	−13.4737	−1.03036
$172$	1.71782	0.130982
$173$	4.68002	0.355815	0.177908	−	0.984047i	$-0.443067\pi$
$173$	4.68002	0.355815	0.177908	+	0.984047i	$0.443067\pi$
$174$	4.38019	0.332061
$175$	47.9490	3.62460
$176$	0.0153971	0.00116060
$177$	−3.27573	−0.246219
$178$	−11.0328	−0.826944
$179$	10.9632	0.819430	0.409715	−	0.912213i	$-0.365628\pi$
$179$	10.9632	0.819430	0.409715	+	0.912213i	$0.365628\pi$
$180$	−6.73753	−0.502186
$181$	−4.64220	−0.345052	−0.172526	−	0.985005i	$-0.555193\pi$
$181$	−4.64220	−0.345052	−0.172526	+	0.985005i	$0.555193\pi$
$182$	−17.9517	−1.33067
$183$	8.60651	0.636211
$184$	1.42378	0.104963
$185$	−7.25198	−0.533177
$186$	−9.88160	−0.724554
$187$	0.0909437	0.00665046
$188$	4.03816	0.294513
$189$	24.4602	1.77922
$190$	−30.9616	−2.24619
$191$	−6.21455	−0.449669	−0.224834	−	0.974397i	$-0.572184\pi$
$191$	−6.21455	−0.449669	−0.224834	+	0.974397i	$0.572184\pi$
$192$	−1.13476	−0.0818945
$193$	18.3019	1.31740	0.658699	−	0.752407i	$-0.271107\pi$
$193$	18.3019	1.31740	0.658699	+	0.752407i	$0.271107\pi$
$194$	3.27956	0.235459
$195$	−17.5230	−1.25485
$196$	13.9239	0.994565
$197$	15.7263	1.12045	0.560224	−	0.828341i	$-0.310715\pi$
$197$	15.7263	1.12045	0.560224	+	0.828341i	$0.310715\pi$
$198$	0.0263647	0.00187366
$199$	−23.4087	−1.65940	−0.829701	−	0.558208i	$-0.811489\pi$
$199$	−23.4087	−1.65940	−0.829701	+	0.558208i	$0.811489\pi$
$200$	−10.4823	−0.741213
$201$	8.25183	0.582039
$202$	−1.40859	−0.0991080
$203$	17.6567	1.23925
$204$	−6.70252	−0.469270
$205$	7.01223	0.489756
$206$	3.38461	0.235817
$207$	2.43796	0.169450
$208$	3.92451	0.272116
$209$	0.121156	0.00838053
$210$	20.4242	1.40940
$211$	−19.2508	−1.32528	−0.662639	−	0.748939i	$-0.730564\pi$
$211$	−19.2508	−1.32528	−0.662639	+	0.748939i	$0.730564\pi$
$212$	−8.24660	−0.566379
$213$	−0.891698	−0.0610982
$214$	14.3324	0.979745
$215$	6.75920	0.460973
$216$	−5.34736	−0.363842
$217$	−39.8330	−2.70404
$218$	5.03433	0.340968
$219$	−6.71661	−0.453866
$220$	0.0605840	0.00408457
$221$	23.1802	1.55927
$222$	−2.09143	−0.140368
$223$	−12.4118	−0.831157	−0.415578	−	0.909557i	$-0.636421\pi$
$223$	−12.4118	−0.831157	−0.415578	+	0.909557i	$0.636421\pi$
$224$	−4.57427	−0.305631
$225$	−17.9490	−1.19660
$226$	14.3578	0.955065
$227$	11.2467	0.746468	0.373234	−	0.927737i	$-0.378249\pi$
$227$	11.2467	0.746468	0.373234	+	0.927737i	$0.378249\pi$
$228$	−8.92916	−0.591348
$229$	8.89434	0.587754	0.293877	−	0.955843i	$-0.405054\pi$
$229$	8.89434	0.587754	0.293877	+	0.955843i	$0.405054\pi$
$230$	5.60225	0.369401
$231$	−0.0799220	−0.00525848
$232$	−3.86000	−0.253421
$233$	−23.7665	−1.55699	−0.778496	−	0.627649i	$-0.784017\pi$
$233$	−23.7665	−1.55699	−0.778496	+	0.627649i	$0.784017\pi$
$234$	6.71998	0.439299
$235$	15.8892	1.03650
$236$	2.88671	0.187909
$237$	4.73724	0.307717
$238$	−27.0181	−1.75132
$239$	−2.63371	−0.170361	−0.0851804	−	0.996366i	$-0.527147\pi$
$239$	−2.63371	−0.170361	−0.0851804	+	0.996366i	$0.527147\pi$
$240$	−4.46502	−0.288216
$241$	−26.1494	−1.68443	−0.842215	−	0.539142i	$-0.818748\pi$
$241$	−26.1494	−1.68443	−0.842215	+	0.539142i	$0.818748\pi$
$242$	10.9998	0.707092
$243$	−14.9856	−0.961324
$244$	−7.58440	−0.485542
$245$	54.7872	3.50023
$246$	2.02229	0.128937
$247$	30.8809	1.96491
$248$	8.70807	0.552963
$249$	−5.92186	−0.375282
$250$	−21.5717	−1.36431
$251$	−13.8676	−0.875315	−0.437657	−	0.899142i	$-0.644192\pi$
$251$	−13.8676	−0.875315	−0.437657	+	0.899142i	$0.644192\pi$
$252$	−7.83257	−0.493405
$253$	−0.0219222	−0.00137824
$254$	19.4224	1.21867
$255$	−26.3728	−1.65153
$256$	1.00000	0.0625000
$257$	−16.6328	−1.03753	−0.518763	−	0.854918i	$-0.673607\pi$
$257$	−16.6328	−1.03753	−0.518763	+	0.854918i	$0.673607\pi$
$258$	1.94932	0.121359
$259$	−8.43063	−0.523854
$260$	15.4420	0.957672
$261$	−6.60952	−0.409119
$262$	−14.4036	−0.889857
$263$	1.92911	0.118954	0.0594771	−	0.998230i	$-0.481057\pi$
$263$	1.92911	0.118954	0.0594771	+	0.998230i	$0.481057\pi$
$264$	0.0174721	0.00107533
$265$	−32.4484	−1.99329
$266$	−35.9937	−2.20691
$267$	−12.5196	−0.766189
$268$	−7.27185	−0.444199
$269$	16.3692	0.998047	0.499023	−	0.866588i	$-0.333692\pi$
$269$	16.3692	0.998047	0.499023	+	0.866588i	$0.333692\pi$
$270$	−21.0406	−1.28049
$271$	0.0530257	0.00322108	0.00161054	−	0.999999i	$-0.499487\pi$
$271$	0.0530257	0.00322108	0.00161054	+	0.999999i	$0.499487\pi$
$272$	5.90653	0.358136
$273$	−20.3710	−1.23291
$274$	−9.57782	−0.578617
$275$	0.161398	0.00973265
$276$	1.61566	0.0972512
$277$	−6.36466	−0.382415	−0.191208	−	0.981550i	$-0.561240\pi$
$277$	−6.36466	−0.382415	−0.191208	+	0.981550i	$0.561240\pi$
$278$	4.53977	0.272278
$279$	14.9109	0.892694
$280$	−17.9986	−1.07562
$281$	−14.0335	−0.837169	−0.418585	−	0.908178i	$-0.637474\pi$
$281$	−14.0335	−0.837169	−0.418585	+	0.908178i	$0.637474\pi$
$282$	4.58236	0.272875
$283$	−10.4681	−0.622262	−0.311131	−	0.950367i	$-0.600708\pi$
$283$	−10.4681	−0.622262	−0.311131	+	0.950367i	$0.600708\pi$
$284$	0.785801	0.0466287
$285$	−35.1341	−2.08116
$286$	−0.0604261	−0.00357307
$287$	8.15191	0.481192
$288$	1.71231	0.100899
$289$	17.8871	1.05219
$290$	−15.1882	−0.891880
$291$	3.72153	0.218160
$292$	5.91895	0.346380
$293$	−23.4894	−1.37226	−0.686131	−	0.727478i	$-0.740693\pi$
$293$	−23.4894	−1.37226	−0.686131	+	0.727478i	$0.740693\pi$
$294$	15.8003	0.921495
$295$	11.3585	0.661318
$296$	1.84306	0.107125
$297$	0.0823340	0.00477750
$298$	9.69003	0.561329
$299$	−5.58765	−0.323142
$300$	−11.8950	−0.686757
$301$	7.85775	0.452913
$302$	−4.27467	−0.245980
$303$	−1.59842	−0.0918266
$304$	7.86873	0.451303
$305$	−29.8428	−1.70879
$306$	10.1138	0.578169
$307$	−32.0967	−1.83186	−0.915928	−	0.401342i	$-0.868544\pi$
$307$	−32.0967	−1.83186	−0.915928	+	0.401342i	$0.868544\pi$
$308$	0.0704305	0.00401315
$309$	3.84073	0.218492
$310$	34.2642	1.94607
$311$	−26.5241	−1.50404	−0.752022	−	0.659138i	$-0.770921\pi$
$311$	−26.5241	−1.50404	−0.752022	+	0.659138i	$0.770921\pi$
$312$	4.45339	0.252124
$313$	28.6176	1.61756	0.808782	−	0.588108i	$-0.200127\pi$
$313$	28.6176	1.61756	0.808782	+	0.588108i	$0.200127\pi$
$314$	11.7306	0.661997
$315$	−30.8193	−1.73647
$316$	−4.17465	−0.234842
$317$	−26.1274	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$317$	−26.1274	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$318$	−9.35795	−0.524768
$319$	0.0594329	0.00332760
$320$	3.93476	0.219960
$321$	16.2639	0.907764
$322$	6.51277	0.362942
$323$	46.4770	2.58605
$324$	−0.931057	−0.0517254
$325$	41.1380	2.28193
$326$	23.4773	1.30029
$327$	5.71278	0.315917
$328$	−1.78213	−0.0984014
$329$	18.4716	1.01837
$330$	0.0687485	0.00378448
$331$	−18.5023	−1.01698	−0.508488	−	0.861069i	$-0.669795\pi$
$331$	−18.5023	−1.01698	−0.508488	+	0.861069i	$0.669795\pi$
$332$	5.21858	0.286407
$333$	3.15589	0.172942
$334$	13.1562	0.719875
$335$	−28.6130	−1.56329
$336$	−5.19071	−0.283176
$337$	33.6511	1.83309	0.916547	−	0.399927i	$-0.130965\pi$
$337$	33.6511	1.83309	0.916547	+	0.399927i	$0.130965\pi$
$338$	−2.40176	−0.130639
$339$	16.2927	0.884897
$340$	23.2408	1.26041
$341$	−0.134079	−0.00726080
$342$	13.4737	0.728575
$343$	31.6718	1.71012
$344$	−1.71782	−0.0926185
$345$	6.35723	0.342262
$346$	−4.68002	−0.251599
$347$	−34.4206	−1.84779	−0.923897	−	0.382641i	$-0.875015\pi$
$347$	−34.4206	−1.84779	−0.923897	+	0.382641i	$0.875015\pi$
$348$	−4.38019	−0.234803
$349$	−0.751923	−0.0402495	−0.0201248	−	0.999797i	$-0.506406\pi$
$349$	−0.751923	−0.0402495	−0.0201248	+	0.999797i	$0.506406\pi$
$350$	−47.9490	−2.56298
$351$	20.9858	1.12014
$352$	−0.0153971	−0.000820670 0
$353$	1.93776	0.103137	0.0515684	−	0.998669i	$-0.483578\pi$
$353$	1.93776	0.103137	0.0515684	+	0.998669i	$0.483578\pi$
$354$	3.27573	0.174103
$355$	3.09194	0.164103
$356$	11.0328	0.584738
$357$	−30.6591	−1.62265
$358$	−10.9632	−0.579425
$359$	34.5060	1.82116	0.910578	−	0.413336i	$-0.135637\pi$
$359$	34.5060	1.82116	0.910578	+	0.413336i	$0.135637\pi$
$360$	6.73753	0.355099
$361$	42.9170	2.25879
$362$	4.64220	0.243988
$363$	12.4821	0.655142
$364$	17.9517	0.940927
$365$	23.2896	1.21904
$366$	−8.60651	−0.449869
$367$	−11.9224	−0.622345	−0.311173	−	0.950353i	$-0.600722\pi$
$367$	−11.9224	−0.622345	−0.311173	+	0.950353i	$0.600722\pi$
$368$	−1.42378	−0.0742199
$369$	−3.05155	−0.158857
$370$	7.25198	0.377013
$371$	−37.7221	−1.95844
$372$	9.88160	0.512337
$373$	−18.2778	−0.946390	−0.473195	−	0.880958i	$-0.656899\pi$
$373$	−18.2778	−0.946390	−0.473195	+	0.880958i	$0.656899\pi$
$374$	−0.0909437	−0.00470258
$375$	−24.4787	−1.26408
$376$	−4.03816	−0.208252
$377$	15.1486	0.780192
$378$	−24.4602	−1.25810
$379$	−5.50543	−0.282795	−0.141398	−	0.989953i	$-0.545160\pi$
$379$	−5.50543	−0.282795	−0.141398	+	0.989953i	$0.545160\pi$
$380$	30.9616	1.58830
$381$	22.0399	1.12914
$382$	6.21455	0.317964
$383$	26.0096	1.32903	0.664515	−	0.747274i	$-0.268638\pi$
$383$	26.0096	1.32903	0.664515	+	0.747274i	$0.268638\pi$
$384$	1.13476	0.0579082
$385$	0.277127	0.0141237
$386$	−18.3019	−0.931541
$387$	−2.94144	−0.149522
$388$	−3.27956	−0.166495
$389$	−1.85343	−0.0939726	−0.0469863	−	0.998896i	$-0.514962\pi$
$389$	−1.85343	−0.0939726	−0.0469863	+	0.998896i	$0.514962\pi$
$390$	17.5230	0.887312
$391$	−8.40963	−0.425293
$392$	−13.9239	−0.703263
$393$	−16.3447	−0.824480
$394$	−15.7263	−0.792277
$395$	−16.4262	−0.826494
$396$	−0.0263647	−0.00132487
$397$	19.7166	0.989549	0.494774	−	0.869022i	$-0.335251\pi$
$397$	19.7166	0.989549	0.494774	+	0.869022i	$0.335251\pi$
$398$	23.4087	1.17337
$399$	−40.8443	−2.04477
$400$	10.4823	0.524117
$401$	33.8736	1.69157	0.845783	−	0.533527i	$-0.179134\pi$
$401$	33.8736	1.69157	0.845783	+	0.533527i	$0.179134\pi$
$402$	−8.25183	−0.411564
$403$	−34.1749	−1.70237
$404$	1.40859	0.0700799
$405$	−3.66348	−0.182040
$406$	−17.6567	−0.876285
$407$	−0.0283778	−0.00140663
$408$	6.70252	0.331824
$409$	−18.3199	−0.905861	−0.452931	−	0.891546i	$-0.649621\pi$
$409$	−18.3199	−0.905861	−0.452931	+	0.891546i	$0.649621\pi$
$410$	−7.01223	−0.346310
$411$	−10.8686	−0.536107
$412$	−3.38461	−0.166748
$413$	13.2046	0.649755
$414$	−2.43796	−0.119819
$415$	20.5339	1.00797
$416$	−3.92451	−0.192415
$417$	5.15157	0.252274
$418$	−0.121156	−0.00592593
$419$	6.86468	0.335362	0.167681	−	0.985841i	$-0.446372\pi$
$419$	6.86468	0.335362	0.167681	+	0.985841i	$0.446372\pi$
$420$	−20.4242	−0.996599
$421$	36.7808	1.79259	0.896293	−	0.443463i	$-0.146250\pi$
$421$	36.7808	1.79259	0.896293	+	0.443463i	$0.146250\pi$
$422$	19.2508	0.937113
$423$	−6.91458	−0.336199
$424$	8.24660	0.400490
$425$	61.9143	3.00328
$426$	0.891698	0.0432029
$427$	−34.6931	−1.67892
$428$	−14.3324	−0.692785
$429$	−0.0685694	−0.00331056
$430$	−6.75920	−0.325957
$431$	25.5159	1.22906	0.614528	−	0.788895i	$-0.289346\pi$
$431$	25.5159	1.22906	0.614528	+	0.788895i	$0.289346\pi$
$432$	5.34736	0.257275
$433$	5.51689	0.265125	0.132562	−	0.991175i	$-0.457680\pi$
$433$	5.51689	0.265125	0.132562	+	0.991175i	$0.457680\pi$
$434$	39.8330	1.91205
$435$	−17.2350	−0.826354
$436$	−5.03433	−0.241101
$437$	−11.2034	−0.535930
$438$	6.71661	0.320932
$439$	35.0980	1.67514	0.837568	−	0.546333i	$-0.183977\pi$
$439$	35.0980	1.67514	0.837568	+	0.546333i	$0.183977\pi$
$440$	−0.0605840	−0.00288823
$441$	−23.8421	−1.13534
$442$	−23.1802	−1.10257
$443$	27.3957	1.30161	0.650805	−	0.759245i	$-0.274432\pi$
$443$	27.3957	1.30161	0.650805	+	0.759245i	$0.274432\pi$
$444$	2.09143	0.0992551
$445$	43.4115	2.05790
$446$	12.4118	0.587717
$447$	10.9959	0.520088
$448$	4.57427	0.216114
$449$	−9.48377	−0.447567	−0.223783	−	0.974639i	$-0.571841\pi$
$449$	−9.48377	−0.447567	−0.223783	+	0.974639i	$0.571841\pi$
$450$	17.9490	0.846125
$451$	0.0274396	0.00129208
$452$	−14.3578	−0.675333
$453$	−4.85074	−0.227908
$454$	−11.2467	−0.527832
$455$	70.6358	3.31146
$456$	8.92916	0.418146
$457$	9.36207	0.437939	0.218969	−	0.975732i	$-0.429730\pi$
$457$	9.36207	0.437939	0.218969	+	0.975732i	$0.429730\pi$
$458$	−8.89434	−0.415605
$459$	31.5844	1.47423
$460$	−5.60225	−0.261206
$461$	−23.8236	−1.10958	−0.554788	−	0.831992i	$-0.687201\pi$
$461$	−23.8236	−1.10958	−0.554788	+	0.831992i	$0.687201\pi$
$462$	0.0799220	0.00371831
$463$	−26.9978	−1.25470	−0.627348	−	0.778739i	$-0.715860\pi$
$463$	−26.9978	−1.25470	−0.627348	+	0.778739i	$0.715860\pi$
$464$	3.86000	0.179196
$465$	38.8817	1.80310
$466$	23.7665	1.10096
$467$	18.3814	0.850590	0.425295	−	0.905055i	$-0.360170\pi$
$467$	18.3814	0.850590	0.425295	+	0.905055i	$0.360170\pi$
$468$	−6.71998	−0.310631
$469$	−33.2634	−1.53596
$470$	−15.8892	−0.732913
$471$	13.3115	0.613361
$472$	−2.88671	−0.132872
$473$	0.0264494	0.00121615
$474$	−4.73724	−0.217589
$475$	82.4827	3.78457
$476$	27.0181	1.23837
$477$	14.1207	0.646545
$478$	2.63371	0.120463
$479$	−6.54219	−0.298920	−0.149460	−	0.988768i	$-0.547754\pi$
$479$	−6.54219	−0.298920	−0.149460	+	0.988768i	$0.547754\pi$
$480$	4.46502	0.203799
$481$	−7.23309	−0.329801
$482$	26.1494	1.19107
$483$	7.39045	0.336277
$484$	−10.9998	−0.499989
$485$	−12.9043	−0.585954
$486$	14.9856	0.679758
$487$	15.0683	0.682808	0.341404	−	0.939917i	$-0.389098\pi$
$487$	15.0683	0.682808	0.341404	+	0.939917i	$0.389098\pi$
$488$	7.58440	0.343330
$489$	26.6412	1.20476
$490$	−54.7872	−2.47503
$491$	−11.2325	−0.506918	−0.253459	−	0.967346i	$-0.581568\pi$
$491$	−11.2325	−0.506918	−0.253459	+	0.967346i	$0.581568\pi$
$492$	−2.02229	−0.0911719
$493$	22.7992	1.02682
$494$	−30.8809	−1.38940
$495$	−0.103739	−0.00466271
$496$	−8.70807	−0.391004
$497$	3.59446	0.161234
$498$	5.92186	0.265365
$499$	−30.2317	−1.35336	−0.676678	−	0.736279i	$-0.736581\pi$
$499$	−30.2317	−1.35336	−0.676678	+	0.736279i	$0.736581\pi$
$500$	21.5717	0.964714
$501$	14.9292	0.666986
$502$	13.8676	0.618941
$503$	30.7138	1.36946	0.684730	−	0.728797i	$-0.259920\pi$
$503$	30.7138	1.36946	0.684730	+	0.728797i	$0.259920\pi$
$504$	7.83257	0.348890
$505$	5.54246	0.246636
$506$	0.0219222	0.000974560 0
$507$	−2.72543	−0.121041
$508$	−19.4224	−0.861732
$509$	11.8801	0.526574	0.263287	−	0.964717i	$-0.415193\pi$
$509$	11.8801	0.526574	0.263287	+	0.964717i	$0.415193\pi$
$510$	26.3728	1.16781
$511$	27.0748	1.19772
$512$	−1.00000	−0.0441942
$513$	42.0770	1.85774
$514$	16.6328	0.733642
$515$	−13.3176	−0.586845
$516$	−1.94932	−0.0858139
$517$	0.0621760	0.00273450
$518$	8.43063	0.370421
$519$	−5.31071	−0.233114
$520$	−15.4420	−0.677176
$521$	−13.0180	−0.570327	−0.285164	−	0.958479i	$-0.592048\pi$
$521$	−13.0180	−0.570327	−0.285164	+	0.958479i	$0.592048\pi$
$522$	6.60952	0.289291
$523$	−22.9101	−1.00179	−0.500894	−	0.865508i	$-0.666996\pi$
$523$	−22.9101	−1.00179	−0.500894	+	0.865508i	$0.666996\pi$
$524$	14.4036	0.629224
$525$	−54.4108	−2.37468
$526$	−1.92911	−0.0841134
$527$	−51.4345	−2.24052
$528$	−0.0174721	−0.000760376 0
$529$	−20.9728	−0.911863
$530$	32.4484	1.40947
$531$	−4.94294	−0.214506
$532$	35.9937	1.56052
$533$	6.99396	0.302942
$534$	12.5196	0.541777
$535$	−56.3947	−2.43816
$536$	7.27185	0.314096
$537$	−12.4407	−0.536855
$538$	−16.3692	−0.705726
$539$	0.214388	0.00923435
$540$	21.0406	0.905442
$541$	33.4048	1.43619	0.718093	−	0.695947i	$-0.245015\pi$
$541$	33.4048	1.43619	0.718093	+	0.695947i	$0.245015\pi$
$542$	−0.0530257	−0.00227765
$543$	5.26780	0.226063
$544$	−5.90653	−0.253241
$545$	−19.8089	−0.848519
$546$	20.3710	0.871798
$547$	31.6261	1.35223	0.676116	−	0.736795i	$-0.263662\pi$
$547$	31.6261	1.35223	0.676116	+	0.736795i	$0.263662\pi$
$548$	9.57782	0.409144
$549$	12.9869	0.554266
$550$	−0.161398	−0.00688203
$551$	30.3733	1.29395
$552$	−1.61566	−0.0687670
$553$	−19.0960	−0.812043
$554$	6.36466	0.270408
$555$	8.22929	0.349314
$556$	−4.53977	−0.192529
$557$	−16.2622	−0.689052	−0.344526	−	0.938777i	$-0.611960\pi$
$557$	−16.2622	−0.689052	−0.344526	+	0.938777i	$0.611960\pi$
$558$	−14.9109	−0.631230
$559$	6.74159	0.285139
$560$	17.9986	0.760581
$561$	−0.103200	−0.00435709
$562$	14.0335	0.591968
$563$	13.3378	0.562123	0.281062	−	0.959690i	$-0.409313\pi$
$563$	13.3378	0.562123	0.281062	+	0.959690i	$0.409313\pi$
$564$	−4.58236	−0.192952
$565$	−56.4944	−2.37674
$566$	10.4681	0.440006
$567$	−4.25890	−0.178857
$568$	−0.785801	−0.0329715
$569$	10.7055	0.448798	0.224399	−	0.974497i	$-0.427958\pi$
$569$	10.7055	0.448798	0.224399	+	0.974497i	$0.427958\pi$
$570$	35.1341	1.47160
$571$	−16.5837	−0.694004	−0.347002	−	0.937864i	$-0.612800\pi$
$571$	−16.5837	−0.694004	−0.347002	+	0.937864i	$0.612800\pi$
$572$	0.0604261	0.00252654
$573$	7.05204	0.294603
$574$	−8.15191	−0.340254
$575$	−14.9246	−0.622398
$576$	−1.71231	−0.0713463
$577$	37.1052	1.54471	0.772354	−	0.635192i	$-0.219079\pi$
$577$	37.1052	1.54471	0.772354	+	0.635192i	$0.219079\pi$
$578$	−17.8871	−0.744007
$579$	−20.7683	−0.863101
$580$	15.1882	0.630654
$581$	23.8712	0.990343
$582$	−3.72153	−0.154262
$583$	−0.126974	−0.00525872
$584$	−5.91895	−0.244928
$585$	−26.4415	−1.09322
$586$	23.4894	0.970336
$587$	19.3061	0.796849	0.398425	−	0.917201i	$-0.369557\pi$
$587$	19.3061	0.796849	0.398425	+	0.917201i	$0.369557\pi$
$588$	−15.8003	−0.651595
$589$	−68.5215	−2.82338
$590$	−11.3585	−0.467622
$591$	−17.8456	−0.734069
$592$	−1.84306	−0.0757492
$593$	5.11908	0.210216	0.105108	−	0.994461i	$-0.466481\pi$
$593$	5.11908	0.210216	0.105108	+	0.994461i	$0.466481\pi$
$594$	−0.0823340	−0.00337820
$595$	106.310	4.35827
$596$	−9.69003	−0.396919
$597$	26.5634	1.08717
$598$	5.58765	0.228496
$599$	−0.421438	−0.0172195	−0.00860974	−	0.999963i	$-0.502741\pi$
$599$	−0.421438	−0.0172195	−0.00860974	+	0.999963i	$0.502741\pi$
$600$	11.8950	0.485610
$601$	−2.73482	−0.111556	−0.0557779	−	0.998443i	$-0.517764\pi$
$601$	−2.73482	−0.111556	−0.0557779	+	0.998443i	$0.517764\pi$
$602$	−7.85775	−0.320258
$603$	12.4517	0.507071
$604$	4.27467	0.173934
$605$	−43.2814	−1.75964
$606$	1.59842	0.0649312
$607$	−7.14117	−0.289851	−0.144925	−	0.989443i	$-0.546294\pi$
$607$	−7.14117	−0.289851	−0.144925	+	0.989443i	$0.546294\pi$
$608$	−7.86873	−0.319119
$609$	−20.0361	−0.811905
$610$	29.8428	1.20830
$611$	15.8478	0.641133
$612$	−10.1138	−0.408827
$613$	35.9204	1.45081	0.725405	−	0.688323i	$-0.241653\pi$
$613$	35.9204	1.45081	0.725405	+	0.688323i	$0.241653\pi$
$614$	32.0967	1.29532
$615$	−7.95723	−0.320866
$616$	−0.0704305	−0.00283773
$617$	−1.35429	−0.0545218	−0.0272609	−	0.999628i	$-0.508678\pi$
$617$	−1.35429	−0.0545218	−0.0272609	+	0.999628i	$0.508678\pi$
$618$	−3.84073	−0.154497
$619$	40.1091	1.61212	0.806061	−	0.591833i	$-0.201595\pi$
$619$	40.1091	1.61212	0.806061	+	0.591833i	$0.201595\pi$
$620$	−34.2642	−1.37608
$621$	−7.61349	−0.305519
$622$	26.5241	1.06352
$623$	50.4670	2.02192
$624$	−4.45339	−0.178278
$625$	32.4677	1.29871
$626$	−28.6176	−1.14379
$627$	−0.137483	−0.00549056
$628$	−11.7306	−0.468103
$629$	−10.8861	−0.434056
$630$	30.8193	1.22787
$631$	−10.7738	−0.428898	−0.214449	−	0.976735i	$-0.568796\pi$
$631$	−10.7738	−0.428898	−0.214449	+	0.976735i	$0.568796\pi$
$632$	4.17465	0.166059
$633$	21.8451	0.868264
$634$	26.1274	1.03765
$635$	−76.4227	−3.03274
$636$	9.35795	0.371067
$637$	54.6445	2.16509
$638$	−0.0594329	−0.00235297
$639$	−1.34554	−0.0532286
$640$	−3.93476	−0.155535
$641$	33.3826	1.31853	0.659266	−	0.751909i	$-0.270867\pi$
$641$	33.3826	1.31853	0.659266	+	0.751909i	$0.270867\pi$
$642$	−16.2639	−0.641886
$643$	16.0681	0.633662	0.316831	−	0.948482i	$-0.397381\pi$
$643$	16.0681	0.633662	0.316831	+	0.948482i	$0.397381\pi$
$644$	−6.51277	−0.256639
$645$	−7.67009	−0.302010
$646$	−46.4770	−1.82861
$647$	29.8593	1.17389	0.586944	−	0.809627i	$-0.300331\pi$
$647$	29.8593	1.17389	0.586944	+	0.809627i	$0.300331\pi$
$648$	0.931057	0.0365754
$649$	0.0444470	0.00174470
$650$	−41.1380	−1.61357
$651$	45.2011	1.77157
$652$	−23.4773	−0.919443
$653$	−16.6227	−0.650497	−0.325248	−	0.945629i	$-0.605448\pi$
$653$	−16.6227	−0.650497	−0.325248	+	0.945629i	$0.605448\pi$
$654$	−5.71278	−0.223387
$655$	56.6747	2.21446
$656$	1.78213	0.0695803
$657$	−10.1351	−0.395407
$658$	−18.4716	−0.720098
$659$	3.72529	0.145117	0.0725584	−	0.997364i	$-0.476884\pi$
$659$	3.72529	0.145117	0.0725584	+	0.997364i	$0.476884\pi$
$660$	−0.0687485	−0.00267603
$661$	18.0109	0.700542	0.350271	−	0.936648i	$-0.386089\pi$
$661$	18.0109	0.700542	0.350271	+	0.936648i	$0.386089\pi$
$662$	18.5023	0.719111
$663$	−26.3041	−1.02157
$664$	−5.21858	−0.202520
$665$	141.626	5.49204
$666$	−3.15589	−0.122288
$667$	−5.49581	−0.212798
$668$	−13.1562	−0.509028
$669$	14.0845	0.544538
$670$	28.6130	1.10542
$671$	−0.116778	−0.00450817
$672$	5.19071	0.200236
$673$	22.8335	0.880167	0.440084	−	0.897957i	$-0.354949\pi$
$673$	22.8335	0.880167	0.440084	+	0.897957i	$0.354949\pi$
$674$	−33.6511	−1.29619
$675$	56.0528	2.15747
$676$	2.40176	0.0923755
$677$	−36.1136	−1.38796	−0.693980	−	0.719995i	$-0.744144\pi$
$677$	−36.1136	−1.38796	−0.693980	+	0.719995i	$0.744144\pi$
$678$	−16.2927	−0.625717
$679$	−15.0016	−0.575708
$680$	−23.2408	−0.891244
$681$	−12.7623	−0.489053
$682$	0.134079	0.00513416
$683$	−30.2375	−1.15701	−0.578503	−	0.815681i	$-0.696363\pi$
$683$	−30.2375	−1.15701	−0.578503	+	0.815681i	$0.696363\pi$
$684$	−13.4737	−0.515181
$685$	37.6864	1.43992
$686$	−31.6718	−1.20923
$687$	−10.0930	−0.385071
$688$	1.71782	0.0654912
$689$	−32.3639	−1.23296
$690$	−6.35723	−0.242016
$691$	4.28207	0.162898	0.0814488	−	0.996678i	$-0.474045\pi$
$691$	4.28207	0.162898	0.0814488	+	0.996678i	$0.474045\pi$
$692$	4.68002	0.177908
$693$	−0.120599	−0.00458118
$694$	34.4206	1.30659
$695$	−17.8629	−0.677579
$696$	4.38019	0.166031
$697$	10.5262	0.398708
$698$	0.751923	0.0284607
$699$	26.9693	1.02007
$700$	47.9490	1.81230
$701$	13.2695	0.501182	0.250591	−	0.968093i	$-0.419375\pi$
$701$	13.2695	0.501182	0.250591	+	0.968093i	$0.419375\pi$
$702$	−20.9858	−0.792056
$703$	−14.5025	−0.546973
$704$	0.0153971	0.000580301 0
$705$	−18.0305	−0.679067
$706$	−1.93776	−0.0729287
$707$	6.44326	0.242324
$708$	−3.27573	−0.123110
$709$	−33.0471	−1.24111	−0.620554	−	0.784163i	$-0.713092\pi$
$709$	−33.0471	−1.24111	−0.620554	+	0.784163i	$0.713092\pi$
$710$	−3.09194	−0.116038
$711$	7.14830	0.268082
$712$	−11.0328	−0.413472
$713$	12.3984	0.464324
$714$	30.6591	1.14739
$715$	0.237762	0.00889181
$716$	10.9632	0.409715
$717$	2.98864	0.111613
$718$	−34.5060	−1.28775
$719$	20.1907	0.752985	0.376493	−	0.926420i	$-0.377130\pi$
$719$	20.1907	0.752985	0.376493	+	0.926420i	$0.377130\pi$
$720$	−6.73753	−0.251093
$721$	−15.4821	−0.576584
$722$	−42.9170	−1.59720
$723$	29.6734	1.10356
$724$	−4.64220	−0.172526
$725$	40.4618	1.50271
$726$	−12.4821	−0.463255
$727$	−15.0651	−0.558733	−0.279366	−	0.960185i	$-0.590124\pi$
$727$	−15.0651	−0.558733	−0.279366	+	0.960185i	$0.590124\pi$
$728$	−17.9517	−0.665336
$729$	19.7982	0.733268
$730$	−23.2896	−0.861988
$731$	10.1463	0.375276
$732$	8.60651	0.318106
$733$	53.2618	1.96727	0.983635	−	0.180174i	$-0.0576660\pi$
$733$	53.2618	1.96727	0.983635	+	0.180174i	$0.0576660\pi$
$734$	11.9224	0.440064
$735$	−62.1706	−2.29320
$736$	1.42378	0.0524814
$737$	−0.111966	−0.00412430
$738$	3.05155	0.112329
$739$	−51.5016	−1.89452	−0.947259	−	0.320470i	$-0.896159\pi$
$739$	−51.5016	−1.89452	−0.947259	+	0.320470i	$0.896159\pi$
$740$	−7.25198	−0.266588
$741$	−35.0425	−1.28732
$742$	37.7221	1.38482
$743$	−6.83169	−0.250630	−0.125315	−	0.992117i	$-0.539994\pi$
$743$	−6.83169	−0.250630	−0.125315	+	0.992117i	$0.539994\pi$
$744$	−9.88160	−0.362277
$745$	−38.1280	−1.39690
$746$	18.2778	0.669199
$747$	−8.93584	−0.326945
$748$	0.0909437	0.00332523
$749$	−65.5604	−2.39552
$750$	24.4787	0.893837
$751$	50.2187	1.83250	0.916252	−	0.400601i	$-0.131199\pi$
$751$	50.2187	1.83250	0.916252	+	0.400601i	$0.131199\pi$
$752$	4.03816	0.147257
$753$	15.7364	0.573468
$754$	−15.1486	−0.551679
$755$	16.8198	0.612135
$756$	24.4602	0.889611
$757$	0.465410	0.0169156	0.00845780	−	0.999964i	$-0.497308\pi$
$757$	0.465410	0.0169156	0.00845780	+	0.999964i	$0.497308\pi$
$758$	5.50543	0.199966
$759$	0.0248765	0.000902960 0
$760$	−30.9616	−1.12309
$761$	−31.2635	−1.13330	−0.566650	−	0.823959i	$-0.691761\pi$
$761$	−31.2635	−1.13330	−0.566650	+	0.823959i	$0.691761\pi$
$762$	−22.0399	−0.798421
$763$	−23.0284	−0.833683
$764$	−6.21455	−0.224834
$765$	−39.7955	−1.43881
$766$	−26.0096	−0.939767
$767$	11.3289	0.409063
$768$	−1.13476	−0.0409473
$769$	−32.3655	−1.16713	−0.583566	−	0.812066i	$-0.698343\pi$
$769$	−32.3655	−1.16713	−0.583566	+	0.812066i	$0.698343\pi$
$770$	−0.277127	−0.00998697
$771$	18.8743	0.679742
$772$	18.3019	0.658699
$773$	12.5276	0.450586	0.225293	−	0.974291i	$-0.427666\pi$
$773$	12.5276	0.450586	0.225293	+	0.974291i	$0.427666\pi$
$774$	2.94144	0.105728
$775$	−91.2809	−3.27891
$776$	3.27956	0.117729
$777$	9.56677	0.343206
$778$	1.85343	0.0664487
$779$	14.0231	0.502429
$780$	−17.5230	−0.627425
$781$	0.0120991	0.000432939 0
$782$	8.40963	0.300728
$783$	20.6408	0.737642
$784$	13.9239	0.497282
$785$	−46.1572	−1.64742
$786$	16.3447	0.582996
$787$	8.07383	0.287801	0.143901	−	0.989592i	$-0.454035\pi$
$787$	8.07383	0.287801	0.143901	+	0.989592i	$0.454035\pi$
$788$	15.7263	0.560224
$789$	−2.18909	−0.0779336
$790$	16.4262	0.584419
$791$	−65.6763	−2.33518
$792$	0.0263647	0.000936828 0
$793$	−29.7651	−1.05699
$794$	−19.7166	−0.699716
$795$	36.8213	1.30592
$796$	−23.4087	−0.829701
$797$	−13.3274	−0.472080	−0.236040	−	0.971743i	$-0.575850\pi$
$797$	−13.3274	−0.472080	−0.236040	+	0.971743i	$0.575850\pi$
$798$	40.8443	1.44587
$799$	23.8515	0.843806
$800$	−10.4823	−0.370606
$801$	−18.8916	−0.667502
$802$	−33.8736	−1.19612
$803$	0.0911348	0.00321608
$804$	8.25183	0.291020
$805$	−25.6262	−0.903204
$806$	34.1749	1.20376
$807$	−18.5752	−0.653877
$808$	−1.40859	−0.0495540
$809$	−23.1318	−0.813272	−0.406636	−	0.913590i	$-0.633298\pi$
$809$	−23.1318	−0.813272	−0.406636	+	0.913590i	$0.633298\pi$
$810$	3.66348	0.128722
$811$	2.19604	0.0771136	0.0385568	−	0.999256i	$-0.487724\pi$
$811$	2.19604	0.0771136	0.0385568	+	0.999256i	$0.487724\pi$
$812$	17.6567	0.619627
$813$	−0.0601716	−0.00211031
$814$	0.0283778	0.000994640 0
$815$	−92.3777	−3.23585
$816$	−6.70252	−0.234635
$817$	13.5170	0.472902
$818$	18.3199	0.640541
$819$	−30.7390	−1.07411
$820$	7.01223	0.244878
$821$	45.8469	1.60007	0.800034	−	0.599955i	$-0.204815\pi$
$821$	45.8469	1.60007	0.800034	+	0.599955i	$0.204815\pi$
$822$	10.8686	0.379085
$823$	49.4167	1.72256	0.861279	−	0.508133i	$-0.169664\pi$
$823$	49.4167	1.72256	0.861279	+	0.508133i	$0.169664\pi$
$824$	3.38461	0.117909
$825$	−0.183148	−0.00637641
$826$	−13.2046	−0.459446
$827$	4.04297	0.140588	0.0702940	−	0.997526i	$-0.477606\pi$
$827$	4.04297	0.140588	0.0702940	+	0.997526i	$0.477606\pi$
$828$	2.43796	0.0847250
$829$	−25.8554	−0.897997	−0.448998	−	0.893533i	$-0.648219\pi$
$829$	−25.8554	−0.897997	−0.448998	+	0.893533i	$0.648219\pi$
$830$	−20.5339	−0.712741
$831$	7.22238	0.250542
$832$	3.92451	0.136058
$833$	82.2420	2.84952
$834$	−5.15157	−0.178384
$835$	−51.7664	−1.79145
$836$	0.121156	0.00419026
$837$	−46.5652	−1.60953
$838$	−6.86468	−0.237136
$839$	−2.60424	−0.0899082	−0.0449541	−	0.998989i	$-0.514314\pi$
$839$	−2.60424	−0.0899082	−0.0449541	+	0.998989i	$0.514314\pi$
$840$	20.4242	0.704702
$841$	−14.1004	−0.486221
$842$	−36.7808	−1.26755
$843$	15.9247	0.548476
$844$	−19.2508	−0.662639
$845$	9.45036	0.325102
$846$	6.91458	0.237728
$847$	−50.3158	−1.72887
$848$	−8.24660	−0.283189
$849$	11.8788	0.407679
$850$	−61.9143	−2.12364
$851$	2.62412	0.0899535
$852$	−0.891698	−0.0305491
$853$	−2.10284	−0.0719999	−0.0360000	−	0.999352i	$-0.511462\pi$
$853$	−2.10284	−0.0719999	−0.0360000	+	0.999352i	$0.511462\pi$
$854$	34.6931	1.18717
$855$	−53.0159	−1.81310
$856$	14.3324	0.489873
$857$	12.1540	0.415172	0.207586	−	0.978217i	$-0.433439\pi$
$857$	12.1540	0.415172	0.207586	+	0.978217i	$0.433439\pi$
$858$	0.0685694	0.00234092
$859$	−55.1342	−1.88116	−0.940578	−	0.339579i	$-0.889716\pi$
$859$	−55.1342	−1.88116	−0.940578	+	0.339579i	$0.889716\pi$
$860$	6.75920	0.230487
$861$	−9.25050	−0.315256
$862$	−25.5159	−0.869075
$863$	−35.8069	−1.21888	−0.609441	−	0.792832i	$-0.708606\pi$
$863$	−35.8069	−1.21888	−0.609441	+	0.792832i	$0.708606\pi$
$864$	−5.34736	−0.181921
$865$	18.4147	0.626120
$866$	−5.51689	−0.187471
$867$	−20.2977	−0.689346
$868$	−39.8330	−1.35202
$869$	−0.0642776	−0.00218047
$870$	17.2350	0.584321
$871$	−28.5384	−0.966988
$872$	5.03433	0.170484
$873$	5.61563	0.190060
$874$	11.2034	0.378960
$875$	98.6745	3.33581
$876$	−6.71661	−0.226933
$877$	37.3172	1.26011	0.630055	−	0.776550i	$-0.283032\pi$
$877$	37.3172	1.26011	0.630055	+	0.776550i	$0.283032\pi$
$878$	−35.0980	−1.18450
$879$	26.6549	0.899046
$880$	0.0605840	0.00204229
$881$	23.1784	0.780900	0.390450	−	0.920624i	$-0.372319\pi$
$881$	23.1784	0.780900	0.390450	+	0.920624i	$0.372319\pi$
$882$	23.8421	0.802804
$883$	−9.88240	−0.332569	−0.166285	−	0.986078i	$-0.553177\pi$
$883$	−9.88240	−0.332569	−0.166285	+	0.986078i	$0.553177\pi$
$884$	23.1802	0.779636
$885$	−12.8892	−0.433266
$886$	−27.3957	−0.920377
$887$	−37.9263	−1.27344	−0.636721	−	0.771095i	$-0.719710\pi$
$887$	−37.9263	−1.27344	−0.636721	+	0.771095i	$0.719710\pi$
$888$	−2.09143	−0.0701839
$889$	−88.8434	−2.97971
$890$	−43.4115	−1.45516
$891$	−0.0143356	−0.000480261 0
$892$	−12.4118	−0.415578
$893$	31.7752	1.06332
$894$	−10.9959	−0.367758
$895$	43.1377	1.44193
$896$	−4.57427	−0.152815
$897$	6.34067	0.211709
$898$	9.48377	0.316477
$899$	−33.6131	−1.12106
$900$	−17.9490	−0.598301
$901$	−48.7088	−1.62273
$902$	−0.0274396	−0.000913639 0
$903$	−8.91669	−0.296729
$904$	14.3578	0.477532
$905$	−18.2659	−0.607180
$906$	4.85074	0.161155
$907$	−17.3341	−0.575569	−0.287785	−	0.957695i	$-0.592919\pi$
$907$	−17.3341	−0.575569	−0.287785	+	0.957695i	$0.592919\pi$
$908$	11.2467	0.373234
$909$	−2.41194	−0.0799991
$910$	−70.6358	−2.34155
$911$	−25.7278	−0.852401	−0.426201	−	0.904629i	$-0.640148\pi$
$911$	−25.7278	−0.852401	−0.426201	+	0.904629i	$0.640148\pi$
$912$	−8.92916	−0.295674
$913$	0.0803512	0.00265924
$914$	−9.36207	−0.309670
$915$	33.8645	1.11953
$916$	8.89434	0.293877
$917$	65.8859	2.17574
$918$	−31.5844	−1.04244
$919$	40.5308	1.33699	0.668495	−	0.743717i	$-0.266939\pi$
$919$	40.5308	1.33699	0.668495	+	0.743717i	$0.266939\pi$
$920$	5.60225	0.184701
$921$	36.4222	1.20015
$922$	23.8236	0.784589
$923$	3.08388	0.101507
$924$	−0.0799220	−0.00262924
$925$	−19.3195	−0.635222
$926$	26.9978	0.887204
$927$	5.79551	0.190349
$928$	−3.86000	−0.126711
$929$	41.3151	1.35550	0.677752	−	0.735290i	$-0.262954\pi$
$929$	41.3151	1.35550	0.677752	+	0.735290i	$0.262954\pi$
$930$	−38.8817	−1.27498
$931$	109.564	3.59080
$932$	−23.7665	−0.778496
$933$	30.0986	0.985383
$934$	−18.3814	−0.601458
$935$	0.357841	0.0117027
$936$	6.71998	0.219649
$937$	38.7579	1.26617	0.633083	−	0.774084i	$-0.281789\pi$
$937$	38.7579	1.26617	0.633083	+	0.774084i	$0.281789\pi$
$938$	33.2634	1.08609
$939$	−32.4743	−1.05976
$940$	15.8892	0.518248
$941$	−9.13597	−0.297824	−0.148912	−	0.988850i	$-0.547577\pi$
$941$	−9.13597	−0.297824	−0.148912	+	0.988850i	$0.547577\pi$
$942$	−13.3115	−0.433712
$943$	−2.53736	−0.0826279
$944$	2.88671	0.0939544
$945$	96.2452	3.13086
$946$	−0.0264494	−0.000859946 0
$947$	22.1900	0.721079	0.360540	−	0.932744i	$-0.382593\pi$
$947$	22.1900	0.721079	0.360540	+	0.932744i	$0.382593\pi$
$948$	4.73724	0.153858
$949$	23.2290	0.754044
$950$	−82.4827	−2.67609
$951$	29.6484	0.961414
$952$	−27.0181	−0.875660
$953$	3.75124	0.121515	0.0607573	−	0.998153i	$-0.480648\pi$
$953$	3.75124	0.121515	0.0607573	+	0.998153i	$0.480648\pi$
$954$	−14.1207	−0.457176
$955$	−24.4527	−0.791272
$956$	−2.63371	−0.0851804
$957$	−0.0674423	−0.00218010
$958$	6.54219	0.211369
$959$	43.8115	1.41475
$960$	−4.46502	−0.144108
$961$	44.8304	1.44614
$962$	7.23309	0.233204
$963$	24.5416	0.790842
$964$	−26.1494	−0.842215
$965$	72.0135	2.31820
$966$	−7.39045	−0.237784
$967$	−18.6184	−0.598728	−0.299364	−	0.954139i	$-0.596774\pi$
$967$	−18.6184	−0.598728	−0.299364	+	0.954139i	$0.596774\pi$
$968$	10.9998	0.353546
$969$	−52.7404	−1.69426
$970$	12.9043	0.414332
$971$	−4.07975	−0.130926	−0.0654628	−	0.997855i	$-0.520852\pi$
$971$	−4.07975	−0.130926	−0.0654628	+	0.997855i	$0.520852\pi$
$972$	−14.9856	−0.480662
$973$	−20.7661	−0.665732
$974$	−15.0683	−0.482818
$975$	−46.6819	−1.49502
$976$	−7.58440	−0.242771
$977$	34.5710	1.10603	0.553013	−	0.833173i	$-0.313478\pi$
$977$	34.5710	1.10603	0.553013	+	0.833173i	$0.313478\pi$
$978$	−26.6412	−0.851892
$979$	0.169874	0.00542918
$980$	54.7872	1.75011
$981$	8.62034	0.275226
$982$	11.2325	0.358445
$983$	−21.6223	−0.689643	−0.344821	−	0.938668i	$-0.612061\pi$
$983$	−21.6223	−0.689643	−0.344821	+	0.938668i	$0.612061\pi$
$984$	2.02229	0.0644683
$985$	61.8790	1.97163
$986$	−22.7992	−0.726075
$987$	−20.9609	−0.667193
$988$	30.8809	0.982453
$989$	−2.44580	−0.0777719
$990$	0.103739	0.00329703
$991$	−32.2418	−1.02420	−0.512098	−	0.858927i	$-0.671132\pi$
$991$	−32.2418	−1.02420	−0.512098	+	0.858927i	$0.671132\pi$
$992$	8.70807	0.276481
$993$	20.9957	0.666278
$994$	−3.59446	−0.114009
$995$	−92.1078	−2.92001
$996$	−5.92186	−0.187641
$997$	−28.6048	−0.905922	−0.452961	−	0.891530i	$-0.649632\pi$
$997$	−28.6048	−0.905922	−0.452961	+	0.891530i	$0.649632\pi$
$998$	30.2317	0.956968
$999$	−9.85549	−0.311814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.20	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.20	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.13476 q^{3} +1.00000 q^{4} +3.93476 q^{5} +1.13476 q^{6} +4.57427 q^{7} -1.00000 q^{8} -1.71231 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.13476 q^{3} +1.00000 q^{4} +3.93476 q^{5} +1.13476 q^{6} +4.57427 q^{7} -1.00000 q^{8} -1.71231 q^{9} -3.93476 q^{10} +0.0153971 q^{11} -1.13476 q^{12} +3.92451 q^{13} -4.57427 q^{14} -4.46502 q^{15} +1.00000 q^{16} +5.90653 q^{17} +1.71231 q^{18} +7.86873 q^{19} +3.93476 q^{20} -5.19071 q^{21} -0.0153971 q^{22} -1.42378 q^{23} +1.13476 q^{24} +10.4823 q^{25} -3.92451 q^{26} +5.34736 q^{27} +4.57427 q^{28} +3.86000 q^{29} +4.46502 q^{30} -8.70807 q^{31} -1.00000 q^{32} -0.0174721 q^{33} -5.90653 q^{34} +17.9986 q^{35} -1.71231 q^{36} -1.84306 q^{37} -7.86873 q^{38} -4.45339 q^{39} -3.93476 q^{40} +1.78213 q^{41} +5.19071 q^{42} +1.71782 q^{43} +0.0153971 q^{44} -6.73753 q^{45} +1.42378 q^{46} +4.03816 q^{47} -1.13476 q^{48} +13.9239 q^{49} -10.4823 q^{50} -6.70252 q^{51} +3.92451 q^{52} -8.24660 q^{53} -5.34736 q^{54} +0.0605840 q^{55} -4.57427 q^{56} -8.92916 q^{57} -3.86000 q^{58} +2.88671 q^{59} -4.46502 q^{60} -7.58440 q^{61} +8.70807 q^{62} -7.83257 q^{63} +1.00000 q^{64} +15.4420 q^{65} +0.0174721 q^{66} -7.27185 q^{67} +5.90653 q^{68} +1.61566 q^{69} -17.9986 q^{70} +0.785801 q^{71} +1.71231 q^{72} +5.91895 q^{73} +1.84306 q^{74} -11.8950 q^{75} +7.86873 q^{76} +0.0704305 q^{77} +4.45339 q^{78} -4.17465 q^{79} +3.93476 q^{80} -0.931057 q^{81} -1.78213 q^{82} +5.21858 q^{83} -5.19071 q^{84} +23.2408 q^{85} -1.71782 q^{86} -4.38019 q^{87} -0.0153971 q^{88} +11.0328 q^{89} +6.73753 q^{90} +17.9517 q^{91} -1.42378 q^{92} +9.88160 q^{93} -4.03816 q^{94} +30.9616 q^{95} +1.13476 q^{96} -3.27956 q^{97} -13.9239 q^{98} -0.0263647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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