LMFDB - Embedded newform 6017.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32398 q^{2} -3.12042 q^{3} +3.40089 q^{4} +3.91464 q^{5} +7.25180 q^{6} -0.989043 q^{7} -3.25564 q^{8} +6.73703 q^{9} +O(q^{10})$	\(q-2.32398 q^{2} -3.12042 q^{3} +3.40089 q^{4} +3.91464 q^{5} +7.25180 q^{6} -0.989043 q^{7} -3.25564 q^{8} +6.73703 q^{9} -9.09756 q^{10} +1.00000 q^{11} -10.6122 q^{12} -5.46513 q^{13} +2.29852 q^{14} -12.2153 q^{15} +0.764273 q^{16} +2.88434 q^{17} -15.6567 q^{18} -4.30630 q^{19} +13.3133 q^{20} +3.08623 q^{21} -2.32398 q^{22} -7.74043 q^{23} +10.1590 q^{24} +10.3244 q^{25} +12.7009 q^{26} -11.6611 q^{27} -3.36363 q^{28} +0.271701 q^{29} +28.3882 q^{30} +10.4398 q^{31} +4.73513 q^{32} -3.12042 q^{33} -6.70315 q^{34} -3.87175 q^{35} +22.9119 q^{36} +7.72811 q^{37} +10.0078 q^{38} +17.0535 q^{39} -12.7447 q^{40} -0.0770176 q^{41} -7.17235 q^{42} -0.563563 q^{43} +3.40089 q^{44} +26.3731 q^{45} +17.9886 q^{46} -8.68749 q^{47} -2.38486 q^{48} -6.02179 q^{49} -23.9938 q^{50} -9.00035 q^{51} -18.5863 q^{52} +1.79037 q^{53} +27.1002 q^{54} +3.91464 q^{55} +3.21997 q^{56} +13.4375 q^{57} -0.631429 q^{58} +1.90517 q^{59} -41.5430 q^{60} -2.52628 q^{61} -24.2620 q^{62} -6.66322 q^{63} -12.5329 q^{64} -21.3940 q^{65} +7.25180 q^{66} +13.7996 q^{67} +9.80932 q^{68} +24.1534 q^{69} +8.99788 q^{70} -4.88488 q^{71} -21.9334 q^{72} +2.95790 q^{73} -17.9600 q^{74} -32.2166 q^{75} -14.6452 q^{76} -0.989043 q^{77} -39.6320 q^{78} +4.88730 q^{79} +2.99186 q^{80} +16.1765 q^{81} +0.178987 q^{82} -10.2679 q^{83} +10.4959 q^{84} +11.2912 q^{85} +1.30971 q^{86} -0.847823 q^{87} -3.25564 q^{88} +3.31687 q^{89} -61.2905 q^{90} +5.40525 q^{91} -26.3244 q^{92} -32.5767 q^{93} +20.1896 q^{94} -16.8576 q^{95} -14.7756 q^{96} -7.85906 q^{97} +13.9945 q^{98} +6.73703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.32398	−1.64330	−0.821652	−	0.569990i	$-0.806947\pi$
$2$	−2.32398	−1.64330	−0.821652	+	0.569990i	$0.806947\pi$
$3$	−3.12042	−1.80158	−0.900788	−	0.434259i	$-0.857010\pi$
$3$	−3.12042	−1.80158	−0.900788	+	0.434259i	$0.857010\pi$
$4$	3.40089	1.70045
$5$	3.91464	1.75068	0.875341	−	0.483507i	$-0.160637\pi$
$5$	3.91464	1.75068	0.875341	+	0.483507i	$0.160637\pi$
$6$	7.25180	2.96054
$7$	−0.989043	−0.373823	−0.186912	−	0.982377i	$-0.559848\pi$
$7$	−0.989043	−0.373823	−0.186912	+	0.982377i	$0.559848\pi$
$8$	−3.25564	−1.15104
$9$	6.73703	2.24568
$10$	−9.09756	−2.87690
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−10.6122	−3.06348
$13$	−5.46513	−1.51575	−0.757877	−	0.652397i	$-0.773763\pi$
$13$	−5.46513	−1.51575	−0.757877	+	0.652397i	$0.773763\pi$
$14$	2.29852	0.614305
$15$	−12.2153	−3.15399
$16$	0.764273	0.191068
$17$	2.88434	0.699555	0.349777	−	0.936833i	$-0.386257\pi$
$17$	2.88434	0.699555	0.349777	+	0.936833i	$0.386257\pi$
$18$	−15.6567	−3.69033
$19$	−4.30630	−0.987932	−0.493966	−	0.869481i	$-0.664453\pi$
$19$	−4.30630	−0.987932	−0.493966	+	0.869481i	$0.664453\pi$
$20$	13.3133	2.97694
$21$	3.08623	0.673471
$22$	−2.32398	−0.495475
$23$	−7.74043	−1.61399	−0.806996	−	0.590557i	$-0.798908\pi$
$23$	−7.74043	−1.61399	−0.806996	+	0.590557i	$0.798908\pi$
$24$	10.1590	2.07369
$25$	10.3244	2.06489
$26$	12.7009	2.49084
$27$	−11.6611	−2.24418
$28$	−3.36363	−0.635666
$29$	0.271701	0.0504537	0.0252268	−	0.999682i	$-0.491969\pi$
$29$	0.271701	0.0504537	0.0252268	+	0.999682i	$0.491969\pi$
$30$	28.3882	5.18295
$31$	10.4398	1.87505	0.937525	−	0.347918i	$-0.113111\pi$
$31$	10.4398	1.87505	0.937525	+	0.347918i	$0.113111\pi$
$32$	4.73513	0.837060
$33$	−3.12042	−0.543196
$34$	−6.70315	−1.14958
$35$	−3.87175	−0.654445
$36$	22.9119	3.81865
$37$	7.72811	1.27049	0.635247	−	0.772309i	$-0.280898\pi$
$37$	7.72811	1.27049	0.635247	+	0.772309i	$0.280898\pi$
$38$	10.0078	1.62347
$39$	17.0535	2.73075
$40$	−12.7447	−2.01511
$41$	−0.0770176	−0.0120281	−0.00601406	−	0.999982i	$-0.501914\pi$
$41$	−0.0770176	−0.0120281	−0.00601406	+	0.999982i	$0.501914\pi$
$42$	−7.17235	−1.10672
$43$	−0.563563	−0.0859425	−0.0429712	−	0.999076i	$-0.513682\pi$
$43$	−0.563563	−0.0859425	−0.0429712	+	0.999076i	$0.513682\pi$
$44$	3.40089	0.512703
$45$	26.3731	3.93147
$46$	17.9886	2.65228
$47$	−8.68749	−1.26720	−0.633601	−	0.773660i	$-0.718424\pi$
$47$	−8.68749	−1.26720	−0.633601	+	0.773660i	$0.718424\pi$
$48$	−2.38486	−0.344224
$49$	−6.02179	−0.860256
$50$	−23.9938	−3.39323
$51$	−9.00035	−1.26030
$52$	−18.5863	−2.57746
$53$	1.79037	0.245926	0.122963	−	0.992411i	$-0.460760\pi$
$53$	1.79037	0.245926	0.122963	+	0.992411i	$0.460760\pi$
$54$	27.1002	3.68787
$55$	3.91464	0.527850
$56$	3.21997	0.430287
$57$	13.4375	1.77984
$58$	−0.631429	−0.0829107
$59$	1.90517	0.248032	0.124016	−	0.992280i	$-0.460423\pi$
$59$	1.90517	0.248032	0.124016	+	0.992280i	$0.460423\pi$
$60$	−41.5430	−5.36318
$61$	−2.52628	−0.323458	−0.161729	−	0.986835i	$-0.551707\pi$
$61$	−2.52628	−0.323458	−0.161729	+	0.986835i	$0.551707\pi$
$62$	−24.2620	−3.08128
$63$	−6.66322	−0.839486
$64$	−12.5329	−1.56661
$65$	−21.3940	−2.65360
$66$	7.25180	0.892635
$67$	13.7996	1.68589	0.842945	−	0.538000i	$-0.180820\pi$
$67$	13.7996	1.68589	0.842945	+	0.538000i	$0.180820\pi$
$68$	9.80932	1.18955
$69$	24.1534	2.90773
$70$	8.99788	1.07545
$71$	−4.88488	−0.579729	−0.289864	−	0.957068i	$-0.593610\pi$
$71$	−4.88488	−0.579729	−0.289864	+	0.957068i	$0.593610\pi$
$72$	−21.9334	−2.58487
$73$	2.95790	0.346196	0.173098	−	0.984905i	$-0.444622\pi$
$73$	2.95790	0.346196	0.173098	+	0.984905i	$0.444622\pi$
$74$	−17.9600	−2.08781
$75$	−32.2166	−3.72005
$76$	−14.6452	−1.67992
$77$	−0.989043	−0.112712
$78$	−39.6320	−4.48744
$79$	4.88730	0.549864	0.274932	−	0.961464i	$-0.411345\pi$
$79$	4.88730	0.549864	0.274932	+	0.961464i	$0.411345\pi$
$80$	2.99186	0.334500
$81$	16.1765	1.79739
$82$	0.178987	0.0197659
$83$	−10.2679	−1.12705	−0.563525	−	0.826099i	$-0.690555\pi$
$83$	−10.2679	−1.12705	−0.563525	+	0.826099i	$0.690555\pi$
$84$	10.4959	1.14520
$85$	11.2912	1.22470
$86$	1.30971	0.141230
$87$	−0.847823	−0.0908962
$88$	−3.25564	−0.347053
$89$	3.31687	0.351587	0.175794	−	0.984427i	$-0.443751\pi$
$89$	3.31687	0.351587	0.175794	+	0.984427i	$0.443751\pi$
$90$	−61.2905	−6.46059
$91$	5.40525	0.566624
$92$	−26.3244	−2.74450
$93$	−32.5767	−3.37805
$94$	20.1896	2.08240
$95$	−16.8576	−1.72955
$96$	−14.7756	−1.50803
$97$	−7.85906	−0.797966	−0.398983	−	0.916958i	$-0.630637\pi$
$97$	−7.85906	−0.797966	−0.398983	+	0.916958i	$0.630637\pi$
$98$	13.9945	1.41366
$99$	6.73703	0.677097
$100$	35.1122	3.51122
$101$	−9.28820	−0.924210	−0.462105	−	0.886825i	$-0.652906\pi$
$101$	−9.28820	−0.924210	−0.462105	+	0.886825i	$0.652906\pi$
$102$	20.9167	2.07106
$103$	−13.3614	−1.31654	−0.658270	−	0.752782i	$-0.728711\pi$
$103$	−13.3614	−1.31654	−0.658270	+	0.752782i	$0.728711\pi$
$104$	17.7925	1.74470
$105$	12.0815	1.17903
$106$	−4.16078	−0.404130
$107$	−5.85554	−0.566076	−0.283038	−	0.959109i	$-0.591342\pi$
$107$	−5.85554	−0.566076	−0.283038	+	0.959109i	$0.591342\pi$
$108$	−39.6582	−3.81611
$109$	18.7078	1.79189	0.895943	−	0.444168i	$-0.146501\pi$
$109$	18.7078	1.79189	0.895943	+	0.444168i	$0.146501\pi$
$110$	−9.09756	−0.867418
$111$	−24.1150	−2.28889
$112$	−0.755899	−0.0714258
$113$	18.5240	1.74259	0.871295	−	0.490759i	$-0.163281\pi$
$113$	18.5240	1.74259	0.871295	+	0.490759i	$0.163281\pi$
$114$	−31.2284	−2.92481
$115$	−30.3010	−2.82559
$116$	0.924027	0.0857937
$117$	−36.8187	−3.40389
$118$	−4.42759	−0.407592
$119$	−2.85274	−0.261510
$120$	39.7688	3.63038
$121$	1.00000	0.0909091
$122$	5.87104	0.531539
$123$	0.240327	0.0216696
$124$	35.5047	3.18842
$125$	20.8432	1.86427
$126$	15.4852	1.37953
$127$	−12.5205	−1.11101	−0.555506	−	0.831512i	$-0.687476\pi$
$127$	−12.5205	−1.11101	−0.555506	+	0.831512i	$0.687476\pi$
$128$	19.6560	1.73736
$129$	1.75855	0.154832
$130$	49.7193	4.36067
$131$	16.4051	1.43332	0.716661	−	0.697422i	$-0.245669\pi$
$131$	16.4051	1.43332	0.716661	+	0.697422i	$0.245669\pi$
$132$	−10.6122	−0.923674
$133$	4.25911	0.369312
$134$	−32.0700	−2.77043
$135$	−45.6491	−3.92885
$136$	−9.39037	−0.805218
$137$	6.54882	0.559503	0.279752	−	0.960072i	$-0.409748\pi$
$137$	6.54882	0.559503	0.279752	+	0.960072i	$0.409748\pi$
$138$	−56.1321	−4.77828
$139$	−14.7493	−1.25102	−0.625509	−	0.780217i	$-0.715109\pi$
$139$	−14.7493	−1.25102	−0.625509	+	0.780217i	$0.715109\pi$
$140$	−13.1674	−1.11285
$141$	27.1086	2.28296
$142$	11.3524	0.952670
$143$	−5.46513	−0.457017
$144$	5.14893	0.429078
$145$	1.06361	0.0883283
$146$	−6.87411	−0.568905
$147$	18.7905	1.54982
$148$	26.2825	2.16040
$149$	−20.8605	−1.70896	−0.854478	−	0.519487i	$-0.826123\pi$
$149$	−20.8605	−1.70896	−0.854478	+	0.519487i	$0.826123\pi$
$150$	74.8707	6.11317
$151$	8.79515	0.715739	0.357870	−	0.933772i	$-0.383503\pi$
$151$	8.79515	0.715739	0.357870	+	0.933772i	$0.383503\pi$
$152$	14.0198	1.13715
$153$	19.4319	1.57097
$154$	2.29852	0.185220
$155$	40.8682	3.28261
$156$	57.9971	4.64348
$157$	0.853945	0.0681522	0.0340761	−	0.999419i	$-0.489151\pi$
$157$	0.853945	0.0681522	0.0340761	+	0.999419i	$0.489151\pi$
$158$	−11.3580	−0.903594
$159$	−5.58669	−0.443054
$160$	18.5363	1.46543
$161$	7.65562	0.603348
$162$	−37.5939	−2.95365
$163$	−16.8640	−1.32089	−0.660445	−	0.750875i	$-0.729632\pi$
$163$	−16.8640	−1.32089	−0.660445	+	0.750875i	$0.729632\pi$
$164$	−0.261928	−0.0204532
$165$	−12.2153	−0.950963
$166$	23.8624	1.85208
$167$	−5.35048	−0.414032	−0.207016	−	0.978338i	$-0.566375\pi$
$167$	−5.35048	−0.414032	−0.207016	+	0.978338i	$0.566375\pi$
$168$	−10.0477	−0.775195
$169$	16.8676	1.29751
$170$	−26.2404	−2.01255
$171$	−29.0117	−2.21858
$172$	−1.91661	−0.146140
$173$	−17.5815	−1.33670	−0.668350	−	0.743847i	$-0.732999\pi$
$173$	−17.5815	−1.33670	−0.668350	+	0.743847i	$0.732999\pi$
$174$	1.97033	0.149370
$175$	−10.2113	−0.771902
$176$	0.764273	0.0576093
$177$	−5.94494	−0.446849
$178$	−7.70834	−0.577764
$179$	8.33719	0.623151	0.311576	−	0.950221i	$-0.399143\pi$
$179$	8.33719	0.623151	0.311576	+	0.950221i	$0.399143\pi$
$180$	89.6919	6.68524
$181$	−10.0813	−0.749340	−0.374670	−	0.927158i	$-0.622244\pi$
$181$	−10.0813	−0.749340	−0.374670	+	0.927158i	$0.622244\pi$
$182$	−12.5617	−0.931135
$183$	7.88307	0.582734
$184$	25.2001	1.85777
$185$	30.2528	2.22423
$186$	75.7076	5.55115
$187$	2.88434	0.210924
$188$	−29.5452	−2.15481
$189$	11.5333	0.838928
$190$	39.1768	2.84218
$191$	3.91318	0.283148	0.141574	−	0.989928i	$-0.454784\pi$
$191$	3.91318	0.283148	0.141574	+	0.989928i	$0.454784\pi$
$192$	39.1079	2.82237
$193$	−13.2973	−0.957162	−0.478581	−	0.878043i	$-0.658849\pi$
$193$	−13.2973	−0.957162	−0.478581	+	0.878043i	$0.658849\pi$
$194$	18.2643	1.31130
$195$	66.7584	4.78067
$196$	−20.4795	−1.46282
$197$	−8.35699	−0.595411	−0.297705	−	0.954658i	$-0.596221\pi$
$197$	−8.35699	−0.595411	−0.297705	+	0.954658i	$0.596221\pi$
$198$	−15.6567	−1.11268
$199$	18.0808	1.28171	0.640855	−	0.767662i	$-0.278580\pi$
$199$	18.0808	1.28171	0.640855	+	0.767662i	$0.278580\pi$
$200$	−33.6126	−2.37677
$201$	−43.0606	−3.03726
$202$	21.5856	1.51876
$203$	−0.268725	−0.0188608
$204$	−30.6092	−2.14307
$205$	−0.301496	−0.0210574
$206$	31.0517	2.16347
$207$	−52.1475	−3.62450
$208$	−4.17685	−0.289613
$209$	−4.30630	−0.297873
$210$	−28.0772	−1.93751
$211$	4.83386	0.332776	0.166388	−	0.986060i	$-0.446790\pi$
$211$	4.83386	0.332776	0.166388	+	0.986060i	$0.446790\pi$
$212$	6.08884	0.418183
$213$	15.2429	1.04443
$214$	13.6082	0.930235
$215$	−2.20615	−0.150458
$216$	37.9644	2.58315
$217$	−10.3255	−0.700937
$218$	−43.4767	−2.94461
$219$	−9.22990	−0.623699
$220$	13.3133	0.897580
$221$	−15.7633	−1.06035
$222$	56.0427	3.76134
$223$	−3.64940	−0.244382	−0.122191	−	0.992507i	$-0.538992\pi$
$223$	−3.64940	−0.244382	−0.122191	+	0.992507i	$0.538992\pi$
$224$	−4.68325	−0.312913
$225$	69.5560	4.63707
$226$	−43.0494	−2.86360
$227$	11.3474	0.753156	0.376578	−	0.926385i	$-0.377101\pi$
$227$	11.3474	0.753156	0.376578	+	0.926385i	$0.377101\pi$
$228$	45.6993	3.02651
$229$	10.0950	0.667095	0.333548	−	0.942733i	$-0.391754\pi$
$229$	10.0950	0.667095	0.333548	+	0.942733i	$0.391754\pi$
$230$	70.4190	4.64329
$231$	3.08623	0.203059
$232$	−0.884563	−0.0580744
$233$	3.27832	0.214770	0.107385	−	0.994218i	$-0.465752\pi$
$233$	3.27832	0.214770	0.107385	+	0.994218i	$0.465752\pi$
$234$	85.5661	5.59363
$235$	−34.0084	−2.21847
$236$	6.47928	0.421765
$237$	−15.2504	−0.990623
$238$	6.62971	0.429740
$239$	30.5312	1.97490	0.987449	−	0.157940i	$-0.0504852\pi$
$239$	30.5312	1.97490	0.987449	+	0.157940i	$0.0504852\pi$
$240$	−9.33585	−0.602627
$241$	−0.511349	−0.0329389	−0.0164694	−	0.999864i	$-0.505243\pi$
$241$	−0.511349	−0.0329389	−0.0164694	+	0.999864i	$0.505243\pi$
$242$	−2.32398	−0.149391
$243$	−15.4942	−0.993951
$244$	−8.59162	−0.550022
$245$	−23.5732	−1.50603
$246$	−0.558516	−0.0356097
$247$	23.5345	1.49746
$248$	−33.9884	−2.15826
$249$	32.0402	2.03047
$250$	−48.4393	−3.06357
$251$	−7.72835	−0.487809	−0.243905	−	0.969799i	$-0.578428\pi$
$251$	−7.72835	−0.487809	−0.243905	+	0.969799i	$0.578428\pi$
$252$	−22.6609	−1.42750
$253$	−7.74043	−0.486637
$254$	29.0974	1.82573
$255$	−35.2332	−2.20639
$256$	−20.6143	−1.28839
$257$	−0.877666	−0.0547473	−0.0273737	−	0.999625i	$-0.508714\pi$
$257$	−0.877666	−0.0547473	−0.0273737	+	0.999625i	$0.508714\pi$
$258$	−4.08684	−0.254436
$259$	−7.64344	−0.474940
$260$	−72.7587	−4.51231
$261$	1.83046	0.113303
$262$	−38.1252	−2.35538
$263$	0.120138	0.00740801	0.00370400	−	0.999993i	$-0.498821\pi$
$263$	0.120138	0.00740801	0.00370400	+	0.999993i	$0.498821\pi$
$264$	10.1590	0.625242
$265$	7.00864	0.430537
$266$	−9.89810	−0.606892
$267$	−10.3500	−0.633411
$268$	46.9309	2.86676
$269$	10.7429	0.655005	0.327503	−	0.944850i	$-0.393793\pi$
$269$	10.7429	0.655005	0.327503	+	0.944850i	$0.393793\pi$
$270$	106.088	6.45629
$271$	−21.3912	−1.29942	−0.649711	−	0.760182i	$-0.725110\pi$
$271$	−21.3912	−1.29942	−0.649711	+	0.760182i	$0.725110\pi$
$272$	2.20442	0.133663
$273$	−16.8667	−1.02082
$274$	−15.2193	−0.919434
$275$	10.3244	0.622586
$276$	82.1431	4.94443
$277$	31.0245	1.86408	0.932042	−	0.362351i	$-0.118026\pi$
$277$	31.0245	1.86408	0.932042	+	0.362351i	$0.118026\pi$
$278$	34.2771	2.05580
$279$	70.3335	4.21076
$280$	12.6050	0.753295
$281$	−7.99646	−0.477029	−0.238514	−	0.971139i	$-0.576660\pi$
$281$	−7.99646	−0.477029	−0.238514	+	0.971139i	$0.576660\pi$
$282$	−63.0000	−3.75159
$283$	−22.0007	−1.30781	−0.653903	−	0.756578i	$-0.726870\pi$
$283$	−22.0007	−1.30781	−0.653903	+	0.756578i	$0.726870\pi$
$284$	−16.6129	−0.985797
$285$	52.6029	3.11592
$286$	12.7009	0.751018
$287$	0.0761737	0.00449639
$288$	31.9007	1.87977
$289$	−8.68059	−0.510623
$290$	−2.47182	−0.145150
$291$	24.5236	1.43760
$292$	10.0595	0.588688
$293$	−21.7929	−1.27315	−0.636577	−	0.771214i	$-0.719650\pi$
$293$	−21.7929	−1.27315	−0.636577	+	0.771214i	$0.719650\pi$
$294$	−43.6689	−2.54682
$295$	7.45807	0.434226
$296$	−25.1600	−1.46239
$297$	−11.6611	−0.676646
$298$	48.4794	2.80833
$299$	42.3025	2.44641
$300$	−109.565	−6.32574
$301$	0.557388	0.0321273
$302$	−20.4398	−1.17618
$303$	28.9831	1.66504
$304$	−3.29119	−0.188763
$305$	−9.88950	−0.566271
$306$	−45.1593	−2.58159
$307$	12.4051	0.707998	0.353999	−	0.935246i	$-0.384822\pi$
$307$	12.4051	0.707998	0.353999	+	0.935246i	$0.384822\pi$
$308$	−3.36363	−0.191660
$309$	41.6933	2.37185
$310$	−94.9770	−5.39433
$311$	−24.0234	−1.36224	−0.681121	−	0.732171i	$-0.738507\pi$
$311$	−24.0234	−1.36224	−0.681121	+	0.732171i	$0.738507\pi$
$312$	−55.5201	−3.14321
$313$	−34.6386	−1.95789	−0.978944	−	0.204129i	$-0.934564\pi$
$313$	−34.6386	−1.95789	−0.978944	+	0.204129i	$0.934564\pi$
$314$	−1.98455	−0.111995
$315$	−26.0841	−1.46967
$316$	16.6212	0.935014
$317$	26.3736	1.48129	0.740645	−	0.671897i	$-0.234520\pi$
$317$	26.3736	1.48129	0.740645	+	0.671897i	$0.234520\pi$
$318$	12.9834	0.728071
$319$	0.271701	0.0152124
$320$	−49.0618	−2.74264
$321$	18.2718	1.01983
$322$	−17.7915	−0.991483
$323$	−12.4208	−0.691113
$324$	55.0145	3.05636
$325$	−56.4243	−3.12986
$326$	39.1916	2.17062
$327$	−58.3764	−3.22822
$328$	0.250742	0.0138449
$329$	8.59231	0.473709
$330$	28.3882	1.56272
$331$	2.15727	0.118574	0.0592872	−	0.998241i	$-0.481117\pi$
$331$	2.15727	0.118574	0.0592872	+	0.998241i	$0.481117\pi$
$332$	−34.9200	−1.91649
$333$	52.0645	2.85312
$334$	12.4344	0.680381
$335$	54.0205	2.95146
$336$	2.35873	0.128679
$337$	−30.3746	−1.65461	−0.827304	−	0.561755i	$-0.810126\pi$
$337$	−30.3746	−1.65461	−0.827304	+	0.561755i	$0.810126\pi$
$338$	−39.2001	−2.13220
$339$	−57.8027	−3.13941
$340$	38.4000	2.08253
$341$	10.4398	0.565349
$342$	67.4225	3.64579
$343$	12.8791	0.695407
$344$	1.83476	0.0989236
$345$	94.5520	5.09051
$346$	40.8592	2.19660
$347$	−13.2719	−0.712472	−0.356236	−	0.934396i	$-0.615940\pi$
$347$	−13.2719	−0.712472	−0.356236	+	0.934396i	$0.615940\pi$
$348$	−2.88335	−0.154564
$349$	25.8817	1.38542	0.692708	−	0.721218i	$-0.256417\pi$
$349$	25.8817	1.38542	0.692708	+	0.721218i	$0.256417\pi$
$350$	23.7309	1.26847
$351$	63.7295	3.40163
$352$	4.73513	0.252383
$353$	−7.14649	−0.380369	−0.190185	−	0.981748i	$-0.560909\pi$
$353$	−7.14649	−0.380369	−0.190185	+	0.981748i	$0.560909\pi$
$354$	13.8159	0.734309
$355$	−19.1226	−1.01492
$356$	11.2803	0.597855
$357$	8.90174	0.471130
$358$	−19.3755	−1.02403
$359$	−22.8912	−1.20815	−0.604075	−	0.796928i	$-0.706457\pi$
$359$	−22.8912	−1.20815	−0.604075	+	0.796928i	$0.706457\pi$
$360$	−85.8613	−4.52529
$361$	−0.455812	−0.0239901
$362$	23.4289	1.23139
$363$	−3.12042	−0.163780
$364$	18.3827	0.963513
$365$	11.5791	0.606079
$366$	−18.3201	−0.957608
$367$	−31.5802	−1.64847	−0.824236	−	0.566246i	$-0.808395\pi$
$367$	−31.5802	−1.64847	−0.824236	+	0.566246i	$0.808395\pi$
$368$	−5.91581	−0.308383
$369$	−0.518870	−0.0270113
$370$	−70.3069	−3.65508
$371$	−1.77075	−0.0919327
$372$	−110.790	−5.74418
$373$	8.13353	0.421138	0.210569	−	0.977579i	$-0.432468\pi$
$373$	8.13353	0.421138	0.210569	+	0.977579i	$0.432468\pi$
$374$	−6.70315	−0.346612
$375$	−65.0396	−3.35863
$376$	28.2834	1.45860
$377$	−1.48488	−0.0764754
$378$	−26.8033	−1.37861
$379$	9.60766	0.493512	0.246756	−	0.969078i	$-0.420635\pi$
$379$	9.60766	0.493512	0.246756	+	0.969078i	$0.420635\pi$
$380$	−57.3309	−2.94101
$381$	39.0692	2.00157
$382$	−9.09416	−0.465298
$383$	26.9494	1.37705	0.688525	−	0.725212i	$-0.258258\pi$
$383$	26.9494	1.37705	0.688525	+	0.725212i	$0.258258\pi$
$384$	−61.3349	−3.12998
$385$	−3.87175	−0.197323
$386$	30.9027	1.57291
$387$	−3.79674	−0.192999
$388$	−26.7278	−1.35690
$389$	1.85321	0.0939616	0.0469808	−	0.998896i	$-0.485040\pi$
$389$	1.85321	0.0939616	0.0469808	+	0.998896i	$0.485040\pi$
$390$	−155.145	−7.85609
$391$	−22.3260	−1.12908
$392$	19.6048	0.990192
$393$	−51.1909	−2.58224
$394$	19.4215	0.978441
$395$	19.1320	0.962637
$396$	22.9119	1.15137
$397$	29.8357	1.49741	0.748706	−	0.662902i	$-0.230675\pi$
$397$	29.8357	1.49741	0.748706	+	0.662902i	$0.230675\pi$
$398$	−42.0193	−2.10624
$399$	−13.2902	−0.665344
$400$	7.89068	0.394534
$401$	7.20686	0.359894	0.179947	−	0.983676i	$-0.442407\pi$
$401$	7.20686	0.359894	0.179947	+	0.983676i	$0.442407\pi$
$402$	100.072	4.99114
$403$	−57.0551	−2.84211
$404$	−31.5881	−1.57157
$405$	63.3252	3.14666
$406$	0.624511	0.0309940
$407$	7.72811	0.383068
$408$	29.3019	1.45066
$409$	−29.8441	−1.47569	−0.737847	−	0.674968i	$-0.764157\pi$
$409$	−29.8441	−1.47569	−0.737847	+	0.674968i	$0.764157\pi$
$410$	0.700672	0.0346037
$411$	−20.4351	−1.00799
$412$	−45.4407	−2.23870
$413$	−1.88430	−0.0927203
$414$	121.190	5.95616
$415$	−40.1952	−1.97311
$416$	−25.8781	−1.26878
$417$	46.0240	2.25380
$418$	10.0078	0.489495
$419$	−27.4342	−1.34025	−0.670125	−	0.742248i	$-0.733760\pi$
$419$	−27.4342	−1.34025	−0.670125	+	0.742248i	$0.733760\pi$
$420$	41.0878	2.00488
$421$	−19.1594	−0.933770	−0.466885	−	0.884318i	$-0.654624\pi$
$421$	−19.1594	−0.933770	−0.466885	+	0.884318i	$0.654624\pi$
$422$	−11.2338	−0.546853
$423$	−58.5279	−2.84572
$424$	−5.82879	−0.283071
$425$	29.7791	1.44450
$426$	−35.4242	−1.71631
$427$	2.49861	0.120916
$428$	−19.9140	−0.962582
$429$	17.0535	0.823351
$430$	5.12704	0.247248
$431$	5.18554	0.249779	0.124889	−	0.992171i	$-0.460142\pi$
$431$	5.18554	0.249779	0.124889	+	0.992171i	$0.460142\pi$
$432$	−8.91228	−0.428792
$433$	−9.97758	−0.479492	−0.239746	−	0.970836i	$-0.577064\pi$
$433$	−9.97758	−0.479492	−0.239746	+	0.970836i	$0.577064\pi$
$434$	23.9962	1.15185
$435$	−3.31892	−0.159130
$436$	63.6233	3.04700
$437$	33.3326	1.59451
$438$	21.4501	1.02493
$439$	−6.52581	−0.311460	−0.155730	−	0.987800i	$-0.549773\pi$
$439$	−6.52581	−0.311460	−0.155730	+	0.987800i	$0.549773\pi$
$440$	−12.7447	−0.607579
$441$	−40.5690	−1.93186
$442$	36.6336	1.74248
$443$	2.91342	0.138421	0.0692104	−	0.997602i	$-0.477952\pi$
$443$	2.91342	0.138421	0.0692104	+	0.997602i	$0.477952\pi$
$444$	−82.0123	−3.89213
$445$	12.9843	0.615517
$446$	8.48113	0.401593
$447$	65.0935	3.07882
$448$	12.3956	0.585636
$449$	39.0106	1.84102	0.920512	−	0.390715i	$-0.127772\pi$
$449$	39.0106	1.84102	0.920512	+	0.390715i	$0.127772\pi$
$450$	−161.647	−7.62010
$451$	−0.0770176	−0.00362662
$452$	62.9981	2.96318
$453$	−27.4446	−1.28946
$454$	−26.3712	−1.23766
$455$	21.1596	0.991978
$456$	−43.7476	−2.04867
$457$	−12.5891	−0.588891	−0.294446	−	0.955668i	$-0.595135\pi$
$457$	−12.5891	−0.588891	−0.294446	+	0.955668i	$0.595135\pi$
$458$	−23.4606	−1.09624
$459$	−33.6346	−1.56993
$460$	−103.050	−4.80475
$461$	6.64598	0.309534	0.154767	−	0.987951i	$-0.450537\pi$
$461$	6.64598	0.309534	0.154767	+	0.987951i	$0.450537\pi$
$462$	−7.17235	−0.333688
$463$	−13.7760	−0.640225	−0.320113	−	0.947379i	$-0.603721\pi$
$463$	−13.7760	−0.640225	−0.320113	+	0.947379i	$0.603721\pi$
$464$	0.207654	0.00964010
$465$	−127.526	−5.91388
$466$	−7.61876	−0.352932
$467$	29.5667	1.36818	0.684092	−	0.729396i	$-0.260199\pi$
$467$	29.5667	1.36818	0.684092	+	0.729396i	$0.260199\pi$
$468$	−125.217	−5.78814
$469$	−13.6484	−0.630225
$470$	79.0350	3.64561
$471$	−2.66467	−0.122781
$472$	−6.20256	−0.285496
$473$	−0.563563	−0.0259126
$474$	35.4417	1.62789
$475$	−44.4600	−2.03997
$476$	−9.70184	−0.444683
$477$	12.0617	0.552269
$478$	−70.9539	−3.24536
$479$	−17.0721	−0.780046	−0.390023	−	0.920805i	$-0.627533\pi$
$479$	−17.0721	−0.780046	−0.390023	+	0.920805i	$0.627533\pi$
$480$	−57.8412	−2.64008
$481$	−42.2351	−1.92576
$482$	1.18836	0.0541285
$483$	−23.8888	−1.08698
$484$	3.40089	0.154586
$485$	−30.7654	−1.39698
$486$	36.0081	1.63336
$487$	31.4032	1.42301	0.711507	−	0.702679i	$-0.248013\pi$
$487$	31.4032	1.42301	0.711507	+	0.702679i	$0.248013\pi$
$488$	8.22468	0.372314
$489$	52.6227	2.37968
$490$	54.7836	2.47487
$491$	−27.5209	−1.24200	−0.621000	−	0.783810i	$-0.713273\pi$
$491$	−27.5209	−1.24200	−0.621000	+	0.783810i	$0.713273\pi$
$492$	0.817327	0.0368479
$493$	0.783679	0.0352951
$494$	−54.6937	−2.46078
$495$	26.3731	1.18538
$496$	7.97889	0.358263
$497$	4.83136	0.216716
$498$	−74.4609	−3.33667
$499$	5.11144	0.228819	0.114410	−	0.993434i	$-0.463502\pi$
$499$	5.11144	0.228819	0.114410	+	0.993434i	$0.463502\pi$
$500$	70.8855	3.17010
$501$	16.6957	0.745911
$502$	17.9606	0.801619
$503$	−4.40334	−0.196335	−0.0981676	−	0.995170i	$-0.531298\pi$
$503$	−4.40334	−0.196335	−0.0981676	+	0.995170i	$0.531298\pi$
$504$	21.6931	0.966285
$505$	−36.3600	−1.61800
$506$	17.9886	0.799692
$507$	−52.6341	−2.33756
$508$	−42.5808	−1.88922
$509$	−5.18003	−0.229601	−0.114800	−	0.993389i	$-0.536623\pi$
$509$	−5.18003	−0.229601	−0.114800	+	0.993389i	$0.536623\pi$
$510$	81.8812	3.62576
$511$	−2.92549	−0.129416
$512$	8.59533	0.379864
$513$	50.2162	2.21710
$514$	2.03968	0.0899665
$515$	−52.3052	−2.30484
$516$	5.98065	0.263283
$517$	−8.68749	−0.382076
$518$	17.7632	0.780471
$519$	54.8618	2.40817
$520$	69.6513	3.05441
$521$	37.4812	1.64208	0.821041	−	0.570869i	$-0.193394\pi$
$521$	37.4812	1.64208	0.821041	+	0.570869i	$0.193394\pi$
$522$	−4.25396	−0.186191
$523$	15.4728	0.676578	0.338289	−	0.941042i	$-0.390152\pi$
$523$	15.4728	0.676578	0.338289	+	0.941042i	$0.390152\pi$
$524$	55.7920	2.43729
$525$	31.8636	1.39064
$526$	−0.279198	−0.0121736
$527$	30.1120	1.31170
$528$	−2.38486	−0.103787
$529$	36.9143	1.60497
$530$	−16.2879	−0.707503
$531$	12.8352	0.557001
$532$	14.4848	0.627995
$533$	0.420911	0.0182317
$534$	24.0533	1.04089
$535$	−22.9223	−0.991019
$536$	−44.9266	−1.94053
$537$	−26.0156	−1.12265
$538$	−24.9663	−1.07637
$539$	−6.02179	−0.259377
$540$	−155.248	−6.68079
$541$	−33.1585	−1.42560	−0.712799	−	0.701369i	$-0.752573\pi$
$541$	−33.1585	−1.42560	−0.712799	+	0.701369i	$0.752573\pi$
$542$	49.7127	2.13534
$543$	31.4580	1.34999
$544$	13.6577	0.585570
$545$	73.2345	3.13702
$546$	39.1978	1.67751
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	22.2718	0.951405
$549$	−17.0197	−0.726381
$550$	−23.9938	−1.02310
$551$	−1.17003	−0.0498448
$552$	−78.6349	−3.34692
$553$	−4.83375	−0.205552
$554$	−72.1004	−3.06325
$555$	−94.4015	−4.00712
$556$	−50.1607	−2.12729
$557$	10.1001	0.427954	0.213977	−	0.976839i	$-0.431358\pi$
$557$	10.1001	0.427954	0.213977	+	0.976839i	$0.431358\pi$
$558$	−163.454	−6.91955
$559$	3.07994	0.130268
$560$	−2.95908	−0.125044
$561$	−9.00035	−0.379995
$562$	18.5836	0.783903
$563$	13.2203	0.557168	0.278584	−	0.960412i	$-0.410135\pi$
$563$	13.2203	0.557168	0.278584	+	0.960412i	$0.410135\pi$
$564$	92.1935	3.88205
$565$	72.5148	3.05072
$566$	51.1293	2.14912
$567$	−15.9993	−0.671906
$568$	15.9034	0.667293
$569$	−33.1591	−1.39010	−0.695050	−	0.718961i	$-0.744618\pi$
$569$	−33.1591	−1.39010	−0.695050	+	0.718961i	$0.744618\pi$
$570$	−122.248	−5.12041
$571$	−4.12183	−0.172493	−0.0862466	−	0.996274i	$-0.527487\pi$
$571$	−4.12183	−0.172493	−0.0862466	+	0.996274i	$0.527487\pi$
$572$	−18.5863	−0.777132
$573$	−12.2108	−0.510112
$574$	−0.177026	−0.00738894
$575$	−79.9155	−3.33271
$576$	−84.4345	−3.51811
$577$	12.9288	0.538232	0.269116	−	0.963108i	$-0.413268\pi$
$577$	12.9288	0.538232	0.269116	+	0.963108i	$0.413268\pi$
$578$	20.1735	0.839109
$579$	41.4932	1.72440
$580$	3.61723	0.150197
$581$	10.1554	0.421317
$582$	−56.9923	−2.36241
$583$	1.79037	0.0741493
$584$	−9.62987	−0.398487
$585$	−144.132	−5.95913
$586$	50.6462	2.09218
$587$	2.70196	0.111522	0.0557609	−	0.998444i	$-0.482242\pi$
$587$	2.70196	0.111522	0.0557609	+	0.998444i	$0.482242\pi$
$588$	63.9045	2.63538
$589$	−44.9570	−1.85242
$590$	−17.3324	−0.713564
$591$	26.0773	1.07268
$592$	5.90639	0.242751
$593$	2.24776	0.0923043	0.0461521	−	0.998934i	$-0.485304\pi$
$593$	2.24776	0.0923043	0.0461521	+	0.998934i	$0.485304\pi$
$594$	27.1002	1.11194
$595$	−11.1674	−0.457820
$596$	−70.9442	−2.90599
$597$	−56.4196	−2.30910
$598$	−98.3101	−4.02020
$599$	−39.3969	−1.60971	−0.804856	−	0.593470i	$-0.797758\pi$
$599$	−39.3969	−1.60971	−0.804856	+	0.593470i	$0.797758\pi$
$600$	104.886	4.28194
$601$	−46.1784	−1.88366	−0.941828	−	0.336095i	$-0.890894\pi$
$601$	−46.1784	−1.88366	−0.941828	+	0.336095i	$0.890894\pi$
$602$	−1.29536	−0.0527949
$603$	92.9684	3.78596
$604$	29.9113	1.21708
$605$	3.91464	0.159153
$606$	−67.3562	−2.73616
$607$	−35.5472	−1.44282	−0.721408	−	0.692510i	$-0.756505\pi$
$607$	−35.5472	−1.44282	−0.721408	+	0.692510i	$0.756505\pi$
$608$	−20.3909	−0.826959
$609$	0.838534	0.0339791
$610$	22.9830	0.930555
$611$	47.4783	1.92077
$612$	66.0857	2.67136
$613$	29.3972	1.18734	0.593672	−	0.804707i	$-0.297678\pi$
$613$	29.3972	1.18734	0.593672	+	0.804707i	$0.297678\pi$
$614$	−28.8293	−1.16346
$615$	0.940796	0.0379365
$616$	3.21997	0.129736
$617$	−26.7220	−1.07579	−0.537894	−	0.843012i	$-0.680780\pi$
$617$	−26.7220	−1.07579	−0.537894	+	0.843012i	$0.680780\pi$
$618$	−96.8944	−3.89766
$619$	−37.3098	−1.49961	−0.749803	−	0.661661i	$-0.769852\pi$
$619$	−37.3098	−1.49961	−0.749803	+	0.661661i	$0.769852\pi$
$620$	138.988	5.58191
$621$	90.2621	3.62209
$622$	55.8300	2.23858
$623$	−3.28052	−0.131431
$624$	13.0335	0.521759
$625$	29.9716	1.19887
$626$	80.4994	3.21740
$627$	13.4375	0.536640
$628$	2.90417	0.115889
$629$	22.2905	0.888780
$630$	60.6190	2.41512
$631$	17.8482	0.710526	0.355263	−	0.934766i	$-0.384391\pi$
$631$	17.8482	0.710526	0.355263	+	0.934766i	$0.384391\pi$
$632$	−15.9113	−0.632918
$633$	−15.0837	−0.599522
$634$	−61.2918	−2.43421
$635$	−49.0132	−1.94503
$636$	−18.9997	−0.753388
$637$	32.9099	1.30394
$638$	−0.631429	−0.0249985
$639$	−32.9096	−1.30188
$640$	76.9461	3.04156
$641$	−1.39722	−0.0551867	−0.0275934	−	0.999619i	$-0.508784\pi$
$641$	−1.39722	−0.0551867	−0.0275934	+	0.999619i	$0.508784\pi$
$642$	−42.4632	−1.67589
$643$	20.7995	0.820251	0.410126	−	0.912029i	$-0.365485\pi$
$643$	20.7995	0.820251	0.410126	+	0.912029i	$0.365485\pi$
$644$	26.0359	1.02596
$645$	6.88411	0.271061
$646$	28.8657	1.13571
$647$	−22.4543	−0.882770	−0.441385	−	0.897318i	$-0.645513\pi$
$647$	−22.4543	−0.882770	−0.441385	+	0.897318i	$0.645513\pi$
$648$	−52.6649	−2.06887
$649$	1.90517	0.0747846
$650$	131.129	5.14331
$651$	32.2198	1.26279
$652$	−57.3526	−2.24610
$653$	16.1770	0.633056	0.316528	−	0.948583i	$-0.397483\pi$
$653$	16.1770	0.633056	0.316528	+	0.948583i	$0.397483\pi$
$654$	135.666	5.30494
$655$	64.2202	2.50929
$656$	−0.0588625	−0.00229819
$657$	19.9275	0.777445
$658$	−19.9684	−0.778448
$659$	−18.0432	−0.702862	−0.351431	−	0.936214i	$-0.614305\pi$
$659$	−18.0432	−0.702862	−0.351431	+	0.936214i	$0.614305\pi$
$660$	−41.5430	−1.61706
$661$	−24.3431	−0.946839	−0.473419	−	0.880837i	$-0.656980\pi$
$661$	−24.3431	−0.946839	−0.473419	+	0.880837i	$0.656980\pi$
$662$	−5.01346	−0.194854
$663$	49.1881	1.91031
$664$	33.4287	1.29728
$665$	16.6729	0.646548
$666$	−120.997	−4.68854
$667$	−2.10309	−0.0814318
$668$	−18.1964	−0.704039
$669$	11.3877	0.440272
$670$	−125.543	−4.85014
$671$	−2.52628	−0.0975261
$672$	14.6137	0.563736
$673$	−23.5376	−0.907307	−0.453653	−	0.891178i	$-0.649880\pi$
$673$	−23.5376	−0.907307	−0.453653	+	0.891178i	$0.649880\pi$
$674$	70.5899	2.71902
$675$	−120.394	−4.63398
$676$	57.3650	2.20635
$677$	23.1229	0.888687	0.444343	−	0.895857i	$-0.353437\pi$
$677$	23.1229	0.888687	0.444343	+	0.895857i	$0.353437\pi$
$678$	134.332	5.15900
$679$	7.77295	0.298298
$680$	−36.7600	−1.40968
$681$	−35.4088	−1.35687
$682$	−24.2620	−0.929039
$683$	−20.5893	−0.787828	−0.393914	−	0.919147i	$-0.628879\pi$
$683$	−20.5893	−0.787828	−0.393914	+	0.919147i	$0.628879\pi$
$684$	−98.6654	−3.77257
$685$	25.6363	0.979512
$686$	−29.9308	−1.14276
$687$	−31.5006	−1.20182
$688$	−0.430716	−0.0164209
$689$	−9.78458	−0.372763
$690$	−219.737	−8.36525
$691$	18.2539	0.694412	0.347206	−	0.937789i	$-0.387130\pi$
$691$	18.2539	0.694412	0.347206	+	0.937789i	$0.387130\pi$
$692$	−59.7929	−2.27299
$693$	−6.66322	−0.253115
$694$	30.8436	1.17081
$695$	−57.7382	−2.19013
$696$	2.76021	0.104625
$697$	−0.222145	−0.00841433
$698$	−60.1486	−2.27666
$699$	−10.2298	−0.386925
$700$	−34.7275	−1.31258
$701$	10.1841	0.384650	0.192325	−	0.981331i	$-0.438397\pi$
$701$	10.1841	0.384650	0.192325	+	0.981331i	$0.438397\pi$
$702$	−148.106	−5.58991
$703$	−33.2795	−1.25516
$704$	−12.5329	−0.472351
$705$	106.121	3.99673
$706$	16.6083	0.625062
$707$	9.18643	0.345491
$708$	−20.2181	−0.759843
$709$	−36.9445	−1.38748	−0.693739	−	0.720226i	$-0.744038\pi$
$709$	−36.9445	−1.38748	−0.693739	+	0.720226i	$0.744038\pi$
$710$	44.4405	1.66782
$711$	32.9259	1.23482
$712$	−10.7985	−0.404692
$713$	−80.8089	−3.02632
$714$	−20.6875	−0.774209
$715$	−21.3940	−0.800091
$716$	28.3539	1.05963
$717$	−95.2701	−3.55793
$718$	53.1986	1.98536
$719$	−13.1988	−0.492232	−0.246116	−	0.969240i	$-0.579154\pi$
$719$	−13.1988	−0.492232	−0.246116	+	0.969240i	$0.579154\pi$
$720$	20.1562	0.751178
$721$	13.2150	0.492153
$722$	1.05930	0.0394230
$723$	1.59562	0.0593419
$724$	−34.2855	−1.27421
$725$	2.80516	0.104181
$726$	7.25180	0.269140
$727$	−3.14236	−0.116544	−0.0582718	−	0.998301i	$-0.518559\pi$
$727$	−3.14236	−0.116544	−0.0582718	+	0.998301i	$0.518559\pi$
$728$	−17.5976	−0.652209
$729$	−0.181194	−0.00671090
$730$	−26.9097	−0.995972
$731$	−1.62551	−0.0601215
$732$	26.8095	0.990906
$733$	−9.07674	−0.335257	−0.167628	−	0.985850i	$-0.553611\pi$
$733$	−9.07674	−0.335257	−0.167628	+	0.985850i	$0.553611\pi$
$734$	73.3918	2.70894
$735$	73.5582	2.71324
$736$	−36.6519	−1.35101
$737$	13.7996	0.508315
$738$	1.20584	0.0443877
$739$	35.5021	1.30597	0.652983	−	0.757373i	$-0.273517\pi$
$739$	35.5021	1.30597	0.652983	+	0.757373i	$0.273517\pi$
$740$	102.886	3.78218
$741$	−73.4375	−2.69779
$742$	4.11519	0.151073
$743$	−25.9303	−0.951290	−0.475645	−	0.879637i	$-0.657785\pi$
$743$	−25.9303	−0.951290	−0.475645	+	0.879637i	$0.657785\pi$
$744$	106.058	3.88828
$745$	−81.6613	−2.99184
$746$	−18.9022	−0.692058
$747$	−69.1753	−2.53099
$748$	9.80932	0.358664
$749$	5.79138	0.211613
$750$	151.151	5.51925
$751$	−0.803820	−0.0293318	−0.0146659	−	0.999892i	$-0.504668\pi$
$751$	−0.803820	−0.0293318	−0.0146659	+	0.999892i	$0.504668\pi$
$752$	−6.63962	−0.242122
$753$	24.1157	0.878826
$754$	3.45084	0.125672
$755$	34.4299	1.25303
$756$	39.2237	1.42655
$757$	−20.6466	−0.750414	−0.375207	−	0.926941i	$-0.622428\pi$
$757$	−20.6466	−0.750414	−0.375207	+	0.926941i	$0.622428\pi$
$758$	−22.3280	−0.810990
$759$	24.1534	0.876713
$760$	54.8824	1.99079
$761$	50.6273	1.83524	0.917618	−	0.397462i	$-0.130109\pi$
$761$	50.6273	1.83524	0.917618	+	0.397462i	$0.130109\pi$
$762$	−90.7960	−3.28919
$763$	−18.5029	−0.669849
$764$	13.3083	0.481477
$765$	76.0689	2.75028
$766$	−62.6299	−2.26291
$767$	−10.4120	−0.375956
$768$	64.3253	2.32114
$769$	18.1721	0.655303	0.327651	−	0.944799i	$-0.393743\pi$
$769$	18.1721	0.655303	0.327651	+	0.944799i	$0.393743\pi$
$770$	8.99788	0.324261
$771$	2.73869	0.0986315
$772$	−45.2227	−1.62760
$773$	34.1281	1.22750	0.613750	−	0.789500i	$-0.289660\pi$
$773$	34.1281	1.22750	0.613750	+	0.789500i	$0.289660\pi$
$774$	8.82355	0.317156
$775$	107.785	3.87176
$776$	25.5863	0.918494
$777$	23.8507	0.855641
$778$	−4.30683	−0.154407
$779$	0.331661	0.0118830
$780$	227.038	8.12926
$781$	−4.88488	−0.174795
$782$	51.8853	1.85541
$783$	−3.16834	−0.113227
$784$	−4.60230	−0.164368
$785$	3.34289	0.119313
$786$	118.967	4.24340
$787$	36.8236	1.31262	0.656309	−	0.754492i	$-0.272117\pi$
$787$	36.8236	1.31262	0.656309	+	0.754492i	$0.272117\pi$
$788$	−28.4212	−1.01246
$789$	−0.374880	−0.0133461
$790$	−44.4625	−1.58191
$791$	−18.3210	−0.651421
$792$	−21.9334	−0.779368
$793$	13.8065	0.490282
$794$	−69.3377	−2.46070
$795$	−21.8699	−0.775646
$796$	61.4906	2.17948
$797$	−45.3960	−1.60801	−0.804005	−	0.594622i	$-0.797302\pi$
$797$	−45.3960	−1.60801	−0.804005	+	0.594622i	$0.797302\pi$
$798$	30.8863	1.09336
$799$	−25.0577	−0.886477
$800$	48.8875	1.72843
$801$	22.3458	0.789551
$802$	−16.7486	−0.591414
$803$	2.95790	0.104382
$804$	−146.444	−5.16469
$805$	29.9690	1.05627
$806$	132.595	4.67046
$807$	−33.5223	−1.18004
$808$	30.2391	1.06381
$809$	−34.4760	−1.21211	−0.606055	−	0.795423i	$-0.707249\pi$
$809$	−34.4760	−1.21211	−0.606055	+	0.795423i	$0.707249\pi$
$810$	−147.167	−5.17091
$811$	19.1727	0.673246	0.336623	−	0.941640i	$-0.390715\pi$
$811$	19.1727	0.673246	0.336623	+	0.941640i	$0.390715\pi$
$812$	−0.913903	−0.0320717
$813$	66.7495	2.34101
$814$	−17.9600	−0.629497
$815$	−66.0165	−2.31246
$816$	−6.87873	−0.240804
$817$	2.42687	0.0849054
$818$	69.3571	2.42501
$819$	36.4153	1.27245
$820$	−1.02536	−0.0358070
$821$	−35.3962	−1.23534	−0.617668	−	0.786439i	$-0.711922\pi$
$821$	−35.3962	−1.23534	−0.617668	+	0.786439i	$0.711922\pi$
$822$	47.4907	1.65643
$823$	14.9994	0.522846	0.261423	−	0.965224i	$-0.415808\pi$
$823$	14.9994	0.522846	0.261423	+	0.965224i	$0.415808\pi$
$824$	43.5000	1.51539
$825$	−32.2166	−1.12164
$826$	4.37907	0.152367
$827$	17.1114	0.595023	0.297511	−	0.954718i	$-0.403843\pi$
$827$	17.1114	0.595023	0.297511	+	0.954718i	$0.403843\pi$
$828$	−177.348	−6.16327
$829$	−32.2151	−1.11888	−0.559438	−	0.828872i	$-0.688983\pi$
$829$	−32.2151	−1.11888	−0.559438	+	0.828872i	$0.688983\pi$
$830$	93.4129	3.24241
$831$	−96.8096	−3.35829
$832$	68.4939	2.37460
$833$	−17.3689	−0.601796
$834$	−106.959	−3.70368
$835$	−20.9452	−0.724839
$836$	−14.6452	−0.506516
$837$	−121.740	−4.20795
$838$	63.7567	2.20244
$839$	−57.2147	−1.97527	−0.987635	−	0.156773i	$-0.949891\pi$
$839$	−57.2147	−1.97527	−0.987635	+	0.156773i	$0.949891\pi$
$840$	−39.3330	−1.35712
$841$	−28.9262	−0.997454
$842$	44.5260	1.53447
$843$	24.9523	0.859404
$844$	16.4394	0.565868
$845$	66.0308	2.27153
$846$	136.018	4.67639
$847$	−0.989043	−0.0339839
$848$	1.36833	0.0469886
$849$	68.6515	2.35611
$850$	−69.2062	−2.37375
$851$	−59.8189	−2.05057
$852$	51.8394	1.77599
$853$	26.3255	0.901370	0.450685	−	0.892683i	$-0.351180\pi$
$853$	26.3255	0.901370	0.450685	+	0.892683i	$0.351180\pi$
$854$	−5.80671	−0.198702
$855$	−113.570	−3.88402
$856$	19.0635	0.651579
$857$	−9.70733	−0.331596	−0.165798	−	0.986160i	$-0.553020\pi$
$857$	−9.70733	−0.331596	−0.165798	+	0.986160i	$0.553020\pi$
$858$	−39.6320	−1.35302
$859$	−22.4855	−0.767197	−0.383598	−	0.923500i	$-0.625315\pi$
$859$	−22.4855	−0.767197	−0.383598	+	0.923500i	$0.625315\pi$
$860$	−7.50286	−0.255845
$861$	−0.237694	−0.00810060
$862$	−12.0511	−0.410462
$863$	−40.7277	−1.38639	−0.693193	−	0.720752i	$-0.743797\pi$
$863$	−40.7277	−1.38639	−0.693193	+	0.720752i	$0.743797\pi$
$864$	−55.2169	−1.87852
$865$	−68.8255	−2.34014
$866$	23.1877	0.787951
$867$	27.0871	0.919927
$868$	−35.1157	−1.19191
$869$	4.88730	0.165790
$870$	7.71312	0.261499
$871$	−75.4166	−2.55539
$872$	−60.9061	−2.06254
$873$	−52.9467	−1.79197
$874$	−77.4643	−2.62027
$875$	−20.6149	−0.696909
$876$	−31.3899	−1.06057
$877$	−34.6196	−1.16902	−0.584510	−	0.811387i	$-0.698713\pi$
$877$	−34.6196	−1.16902	−0.584510	+	0.811387i	$0.698713\pi$
$878$	15.1659	0.511823
$879$	68.0029	2.29368
$880$	2.99186	0.100855
$881$	4.22540	0.142357	0.0711787	−	0.997464i	$-0.477324\pi$
$881$	4.22540	0.142357	0.0711787	+	0.997464i	$0.477324\pi$
$882$	94.2816	3.17463
$883$	12.4434	0.418755	0.209378	−	0.977835i	$-0.432856\pi$
$883$	12.4434	0.418755	0.209378	+	0.977835i	$0.432856\pi$
$884$	−53.6092	−1.80307
$885$	−23.2723	−0.782291
$886$	−6.77074	−0.227467
$887$	48.0810	1.61440	0.807201	−	0.590276i	$-0.200981\pi$
$887$	48.0810	1.61440	0.807201	+	0.590276i	$0.200981\pi$
$888$	78.5097	2.63461
$889$	12.3833	0.415322
$890$	−30.1754	−1.01148
$891$	16.1765	0.541933
$892$	−12.4112	−0.415558
$893$	37.4109	1.25191
$894$	−151.276	−5.05943
$895$	32.6371	1.09094
$896$	−19.4406	−0.649465
$897$	−132.002	−4.40740
$898$	−90.6599	−3.02536
$899$	2.83652	0.0946032
$900$	236.552	7.88507
$901$	5.16402	0.172038
$902$	0.178987	0.00595963
$903$	−1.73929	−0.0578798
$904$	−60.3075	−2.00580
$905$	−39.4648	−1.31186
$906$	63.7807	2.11897
$907$	−29.8929	−0.992578	−0.496289	−	0.868157i	$-0.665304\pi$
$907$	−29.8929	−0.992578	−0.496289	+	0.868157i	$0.665304\pi$
$908$	38.5914	1.28070
$909$	−62.5749	−2.07548
$910$	−49.1746	−1.63012
$911$	22.9212	0.759413	0.379707	−	0.925107i	$-0.376025\pi$
$911$	22.9212	0.759413	0.379707	+	0.925107i	$0.376025\pi$
$912$	10.2699	0.340070
$913$	−10.2679	−0.339818
$914$	29.2567	0.967727
$915$	30.8594	1.02018
$916$	34.3319	1.13436
$917$	−16.2254	−0.535809
$918$	78.1662	2.57987
$919$	51.0750	1.68481	0.842404	−	0.538847i	$-0.181140\pi$
$919$	51.0750	1.68481	0.842404	+	0.538847i	$0.181140\pi$
$920$	98.6493	3.25237
$921$	−38.7092	−1.27551
$922$	−15.4451	−0.508659
$923$	26.6965	0.878726
$924$	10.4959	0.345291
$925$	79.7883	2.62342
$926$	32.0152	1.05208
$927$	−90.0163	−2.95652
$928$	1.28654	0.0422328
$929$	47.8929	1.57132	0.785658	−	0.618661i	$-0.212325\pi$
$929$	47.8929	1.57132	0.785658	+	0.618661i	$0.212325\pi$
$930$	296.368	9.71830
$931$	25.9316	0.849875
$932$	11.1492	0.365205
$933$	74.9632	2.45418
$934$	−68.7124	−2.24834
$935$	11.2912	0.369260
$936$	119.869	3.91803
$937$	32.8592	1.07346	0.536731	−	0.843754i	$-0.319659\pi$
$937$	32.8592	1.07346	0.536731	+	0.843754i	$0.319659\pi$
$938$	31.7187	1.03565
$939$	108.087	3.52728
$940$	−115.659	−3.77238
$941$	−32.8230	−1.07000	−0.535000	−	0.844852i	$-0.679689\pi$
$941$	−32.8230	−1.07000	−0.535000	+	0.844852i	$0.679689\pi$
$942$	6.19264	0.201767
$943$	0.596149	0.0194133
$944$	1.45607	0.0473911
$945$	45.1489	1.46869
$946$	1.30971	0.0425823
$947$	−4.42335	−0.143740	−0.0718698	−	0.997414i	$-0.522897\pi$
$947$	−4.42335	−0.143740	−0.0718698	+	0.997414i	$0.522897\pi$
$948$	−51.8651	−1.68450
$949$	−16.1653	−0.524748
$950$	103.324	3.35228
$951$	−82.2968	−2.66866
$952$	9.28749	0.301009
$953$	−32.7593	−1.06118	−0.530589	−	0.847629i	$-0.678029\pi$
$953$	−32.7593	−1.06118	−0.530589	+	0.847629i	$0.678029\pi$
$954$	−28.0313	−0.907546
$955$	15.3187	0.495702
$956$	103.833	3.35820
$957$	−0.847823	−0.0274062
$958$	39.6753	1.28185
$959$	−6.47707	−0.209155
$960$	153.094	4.94107
$961$	77.9902	2.51581
$962$	98.1536	3.16460
$963$	−39.4490	−1.27123
$964$	−1.73904	−0.0560107
$965$	−52.0542	−1.67569
$966$	55.5171	1.78623
$967$	34.9707	1.12458	0.562290	−	0.826940i	$-0.309920\pi$
$967$	34.9707	1.12458	0.562290	+	0.826940i	$0.309920\pi$
$968$	−3.25564	−0.104640
$969$	38.7582	1.24509
$970$	71.4982	2.29567
$971$	27.1071	0.869908	0.434954	−	0.900453i	$-0.356765\pi$
$971$	27.1071	0.869908	0.434954	+	0.900453i	$0.356765\pi$
$972$	−52.6939	−1.69016
$973$	14.5877	0.467660
$974$	−72.9804	−2.33844
$975$	176.068	5.63868
$976$	−1.93077	−0.0618025
$977$	55.0874	1.76240	0.881200	−	0.472743i	$-0.156736\pi$
$977$	55.0874	1.76240	0.881200	+	0.472743i	$0.156736\pi$
$978$	−122.294	−3.91054
$979$	3.31687	0.106008
$980$	−80.1697	−2.56093
$981$	126.035	4.02400
$982$	63.9580	2.04098
$983$	10.5168	0.335433	0.167716	−	0.985835i	$-0.446361\pi$
$983$	10.5168	0.335433	0.167716	+	0.985835i	$0.446361\pi$
$984$	−0.782420	−0.0249426
$985$	−32.7146	−1.04237
$986$	−1.82126	−0.0580006
$987$	−26.8116	−0.853423
$988$	80.0381	2.54635
$989$	4.36222	0.138710
$990$	−61.2905	−1.94794
$991$	−37.3445	−1.18629	−0.593143	−	0.805097i	$-0.702113\pi$
$991$	−37.3445	−1.18629	−0.593143	+	0.805097i	$0.702113\pi$
$992$	49.4340	1.56953
$993$	−6.73160	−0.213621
$994$	−11.2280	−0.356130
$995$	70.7797	2.24387
$996$	108.965	3.45270
$997$	−33.7762	−1.06970	−0.534852	−	0.844946i	$-0.679633\pi$
$997$	−33.7762	−1.06970	−0.534852	+	0.844946i	$0.679633\pi$
$998$	−11.8789	−0.376020
$999$	−90.1184	−2.85122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.15	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.15	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32398 q^{2} -3.12042 q^{3} +3.40089 q^{4} +3.91464 q^{5} +7.25180 q^{6} -0.989043 q^{7} -3.25564 q^{8} +6.73703 q^{9} +O(q^{10})\)	\(q-2.32398 q^{2} -3.12042 q^{3} +3.40089 q^{4} +3.91464 q^{5} +7.25180 q^{6} -0.989043 q^{7} -3.25564 q^{8} +6.73703 q^{9} -9.09756 q^{10} +1.00000 q^{11} -10.6122 q^{12} -5.46513 q^{13} +2.29852 q^{14} -12.2153 q^{15} +0.764273 q^{16} +2.88434 q^{17} -15.6567 q^{18} -4.30630 q^{19} +13.3133 q^{20} +3.08623 q^{21} -2.32398 q^{22} -7.74043 q^{23} +10.1590 q^{24} +10.3244 q^{25} +12.7009 q^{26} -11.6611 q^{27} -3.36363 q^{28} +0.271701 q^{29} +28.3882 q^{30} +10.4398 q^{31} +4.73513 q^{32} -3.12042 q^{33} -6.70315 q^{34} -3.87175 q^{35} +22.9119 q^{36} +7.72811 q^{37} +10.0078 q^{38} +17.0535 q^{39} -12.7447 q^{40} -0.0770176 q^{41} -7.17235 q^{42} -0.563563 q^{43} +3.40089 q^{44} +26.3731 q^{45} +17.9886 q^{46} -8.68749 q^{47} -2.38486 q^{48} -6.02179 q^{49} -23.9938 q^{50} -9.00035 q^{51} -18.5863 q^{52} +1.79037 q^{53} +27.1002 q^{54} +3.91464 q^{55} +3.21997 q^{56} +13.4375 q^{57} -0.631429 q^{58} +1.90517 q^{59} -41.5430 q^{60} -2.52628 q^{61} -24.2620 q^{62} -6.66322 q^{63} -12.5329 q^{64} -21.3940 q^{65} +7.25180 q^{66} +13.7996 q^{67} +9.80932 q^{68} +24.1534 q^{69} +8.99788 q^{70} -4.88488 q^{71} -21.9334 q^{72} +2.95790 q^{73} -17.9600 q^{74} -32.2166 q^{75} -14.6452 q^{76} -0.989043 q^{77} -39.6320 q^{78} +4.88730 q^{79} +2.99186 q^{80} +16.1765 q^{81} +0.178987 q^{82} -10.2679 q^{83} +10.4959 q^{84} +11.2912 q^{85} +1.30971 q^{86} -0.847823 q^{87} -3.25564 q^{88} +3.31687 q^{89} -61.2905 q^{90} +5.40525 q^{91} -26.3244 q^{92} -32.5767 q^{93} +20.1896 q^{94} -16.8576 q^{95} -14.7756 q^{96} -7.85906 q^{97} +13.9945 q^{98} +6.73703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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