LMFDB - Embedded newform 6019.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22409 q^{2} -1.49293 q^{3} +2.94657 q^{4} -0.404702 q^{5} +3.32042 q^{6} -4.24821 q^{7} -2.10525 q^{8} -0.771146 q^{9} +O(q^{10})$	\(q-2.22409 q^{2} -1.49293 q^{3} +2.94657 q^{4} -0.404702 q^{5} +3.32042 q^{6} -4.24821 q^{7} -2.10525 q^{8} -0.771146 q^{9} +0.900094 q^{10} -6.36641 q^{11} -4.39903 q^{12} +1.00000 q^{13} +9.44839 q^{14} +0.604194 q^{15} -1.21088 q^{16} +0.592065 q^{17} +1.71510 q^{18} -0.753420 q^{19} -1.19248 q^{20} +6.34230 q^{21} +14.1595 q^{22} -4.06363 q^{23} +3.14300 q^{24} -4.83622 q^{25} -2.22409 q^{26} +5.63007 q^{27} -12.5176 q^{28} -6.15728 q^{29} -1.34378 q^{30} +9.15205 q^{31} +6.90359 q^{32} +9.50463 q^{33} -1.31680 q^{34} +1.71926 q^{35} -2.27223 q^{36} -10.6897 q^{37} +1.67567 q^{38} -1.49293 q^{39} +0.851999 q^{40} +5.63411 q^{41} -14.1058 q^{42} +7.64228 q^{43} -18.7590 q^{44} +0.312085 q^{45} +9.03787 q^{46} +4.47909 q^{47} +1.80776 q^{48} +11.0473 q^{49} +10.7562 q^{50} -0.883914 q^{51} +2.94657 q^{52} -3.94209 q^{53} -12.5218 q^{54} +2.57650 q^{55} +8.94354 q^{56} +1.12481 q^{57} +13.6943 q^{58} +7.80382 q^{59} +1.78030 q^{60} -5.87806 q^{61} -20.3550 q^{62} +3.27599 q^{63} -12.9324 q^{64} -0.404702 q^{65} -21.1391 q^{66} +4.62948 q^{67} +1.74456 q^{68} +6.06674 q^{69} -3.82379 q^{70} +0.822478 q^{71} +1.62345 q^{72} +9.34079 q^{73} +23.7748 q^{74} +7.22015 q^{75} -2.22000 q^{76} +27.0458 q^{77} +3.32042 q^{78} +14.0183 q^{79} +0.490045 q^{80} -6.09189 q^{81} -12.5308 q^{82} -11.1594 q^{83} +18.6880 q^{84} -0.239610 q^{85} -16.9971 q^{86} +9.19242 q^{87} +13.4029 q^{88} +8.34703 q^{89} -0.694104 q^{90} -4.24821 q^{91} -11.9738 q^{92} -13.6634 q^{93} -9.96188 q^{94} +0.304911 q^{95} -10.3066 q^{96} +13.5359 q^{97} -24.5701 q^{98} +4.90943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.22409	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$2$	−2.22409	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$3$	−1.49293	−0.861946	−0.430973	−	0.902365i	$-0.641830\pi$
$3$	−1.49293	−0.861946	−0.430973	+	0.902365i	$0.641830\pi$
$4$	2.94657	1.47328
$5$	−0.404702	−0.180988	−0.0904942	−	0.995897i	$-0.528845\pi$
$5$	−0.404702	−0.180988	−0.0904942	+	0.995897i	$0.528845\pi$
$6$	3.32042	1.35555
$7$	−4.24821	−1.60567	−0.802836	−	0.596199i	$-0.796677\pi$
$7$	−4.24821	−1.60567	−0.802836	+	0.596199i	$0.796677\pi$
$8$	−2.10525	−0.744318
$9$	−0.771146	−0.257049
$10$	0.900094	0.284635
$11$	−6.36641	−1.91954	−0.959772	−	0.280780i	$-0.909407\pi$
$11$	−6.36641	−1.91954	−0.959772	+	0.280780i	$0.909407\pi$
$12$	−4.39903	−1.26989
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	9.44839	2.52519
$15$	0.604194	0.156002
$16$	−1.21088	−0.302719
$17$	0.592065	0.143597	0.0717984	−	0.997419i	$-0.477126\pi$
$17$	0.592065	0.143597	0.0717984	+	0.997419i	$0.477126\pi$
$18$	1.71510	0.404252
$19$	−0.753420	−0.172846	−0.0864232	−	0.996259i	$-0.527544\pi$
$19$	−0.753420	−0.172846	−0.0864232	+	0.996259i	$0.527544\pi$
$20$	−1.19248	−0.266647
$21$	6.34230	1.38400
$22$	14.1595	3.01880
$23$	−4.06363	−0.847326	−0.423663	−	0.905820i	$-0.639256\pi$
$23$	−4.06363	−0.847326	−0.423663	+	0.905820i	$0.639256\pi$
$24$	3.14300	0.641562
$25$	−4.83622	−0.967243
$26$	−2.22409	−0.436180
$27$	5.63007	1.08351
$28$	−12.5176	−2.36561
$29$	−6.15728	−1.14338	−0.571689	−	0.820470i	$-0.693712\pi$
$29$	−6.15728	−1.14338	−0.571689	+	0.820470i	$0.693712\pi$
$30$	−1.34378	−0.245340
$31$	9.15205	1.64376	0.821879	−	0.569662i	$-0.192926\pi$
$31$	9.15205	1.64376	0.821879	+	0.569662i	$0.192926\pi$
$32$	6.90359	1.22039
$33$	9.50463	1.65454
$34$	−1.31680	−0.225830
$35$	1.71926	0.290608
$36$	−2.27223	−0.378706
$37$	−10.6897	−1.75737	−0.878686	−	0.477401i	$-0.841579\pi$
$37$	−10.6897	−1.75737	−0.878686	+	0.477401i	$0.841579\pi$
$38$	1.67567	0.271830
$39$	−1.49293	−0.239061
$40$	0.851999	0.134713
$41$	5.63411	0.879900	0.439950	−	0.898022i	$-0.354996\pi$
$41$	5.63411	0.879900	0.439950	+	0.898022i	$0.354996\pi$
$42$	−14.1058	−2.17658
$43$	7.64228	1.16544	0.582718	−	0.812674i	$-0.301989\pi$
$43$	7.64228	1.16544	0.582718	+	0.812674i	$0.301989\pi$
$44$	−18.7590	−2.82803
$45$	0.312085	0.0465229
$46$	9.03787	1.33256
$47$	4.47909	0.653342	0.326671	−	0.945138i	$-0.394073\pi$
$47$	4.47909	0.653342	0.326671	+	0.945138i	$0.394073\pi$
$48$	1.80776	0.260928
$49$	11.0473	1.57818
$50$	10.7562	1.52115
$51$	−0.883914	−0.123773
$52$	2.94657	0.408615
$53$	−3.94209	−0.541487	−0.270744	−	0.962651i	$-0.587270\pi$
$53$	−3.94209	−0.541487	−0.270744	+	0.962651i	$0.587270\pi$
$54$	−12.5218	−1.70400
$55$	2.57650	0.347415
$56$	8.94354	1.19513
$57$	1.12481	0.148984
$58$	13.6943	1.79816
$59$	7.80382	1.01597	0.507985	−	0.861366i	$-0.330390\pi$
$59$	7.80382	1.01597	0.507985	+	0.861366i	$0.330390\pi$
$60$	1.78030	0.229836
$61$	−5.87806	−0.752608	−0.376304	−	0.926496i	$-0.622805\pi$
$61$	−5.87806	−0.752608	−0.376304	+	0.926496i	$0.622805\pi$
$62$	−20.3550	−2.58508
$63$	3.27599	0.412736
$64$	−12.9324	−1.61656
$65$	−0.404702	−0.0501972
$66$	−21.1391	−2.60205
$67$	4.62948	0.565581	0.282791	−	0.959182i	$-0.408740\pi$
$67$	4.62948	0.565581	0.282791	+	0.959182i	$0.408740\pi$
$68$	1.74456	0.211559
$69$	6.06674	0.730349
$70$	−3.82379	−0.457030
$71$	0.822478	0.0976102	0.0488051	−	0.998808i	$-0.484459\pi$
$71$	0.822478	0.0976102	0.0488051	+	0.998808i	$0.484459\pi$
$72$	1.62345	0.191326
$73$	9.34079	1.09326	0.546628	−	0.837375i	$-0.315911\pi$
$73$	9.34079	1.09326	0.546628	+	0.837375i	$0.315911\pi$
$74$	23.7748	2.76376
$75$	7.22015	0.833712
$76$	−2.22000	−0.254652
$77$	27.0458	3.08216
$78$	3.32042	0.375963
$79$	14.0183	1.57718	0.788591	−	0.614918i	$-0.210811\pi$
$79$	14.0183	1.57718	0.788591	+	0.614918i	$0.210811\pi$
$80$	0.490045	0.0547887
$81$	−6.09189	−0.676877
$82$	−12.5308	−1.38379
$83$	−11.1594	−1.22491	−0.612454	−	0.790507i	$-0.709817\pi$
$83$	−11.1594	−1.22491	−0.612454	+	0.790507i	$0.709817\pi$
$84$	18.6880	2.03903
$85$	−0.239610	−0.0259894
$86$	−16.9971	−1.83284
$87$	9.19242	0.985531
$88$	13.4029	1.42875
$89$	8.34703	0.884783	0.442392	−	0.896822i	$-0.354130\pi$
$89$	8.34703	0.884783	0.442392	+	0.896822i	$0.354130\pi$
$90$	−0.694104	−0.0731650
$91$	−4.24821	−0.445333
$92$	−11.9738	−1.24835
$93$	−13.6634	−1.41683
$94$	−9.96188	−1.02749
$95$	0.304911	0.0312832
$96$	−10.3066	−1.05191
$97$	13.5359	1.37436	0.687180	−	0.726487i	$-0.258848\pi$
$97$	13.5359	1.37436	0.687180	+	0.726487i	$0.258848\pi$
$98$	−24.5701	−2.48196
$99$	4.90943	0.493416
$100$	−14.2502	−1.42502
$101$	−13.2709	−1.32051	−0.660254	−	0.751042i	$-0.729551\pi$
$101$	−13.2709	−1.32051	−0.660254	+	0.751042i	$0.729551\pi$
$102$	1.96590	0.194653
$103$	−13.7213	−1.35200	−0.676000	−	0.736902i	$-0.736288\pi$
$103$	−13.7213	−1.35200	−0.676000	+	0.736902i	$0.736288\pi$
$104$	−2.10525	−0.206437
$105$	−2.56674	−0.250489
$106$	8.76755	0.851579
$107$	5.27645	0.510094	0.255047	−	0.966929i	$-0.417909\pi$
$107$	5.27645	0.510094	0.255047	+	0.966929i	$0.417909\pi$
$108$	16.5894	1.59632
$109$	−16.1228	−1.54429	−0.772144	−	0.635447i	$-0.780816\pi$
$109$	−16.1228	−1.54429	−0.772144	+	0.635447i	$0.780816\pi$
$110$	−5.73036	−0.546369
$111$	15.9590	1.51476
$112$	5.14406	0.486068
$113$	18.6582	1.75522	0.877610	−	0.479376i	$-0.159137\pi$
$113$	18.6582	1.75522	0.877610	+	0.479376i	$0.159137\pi$
$114$	−2.50167	−0.234303
$115$	1.64456	0.153356
$116$	−18.1429	−1.68452
$117$	−0.771146	−0.0712925
$118$	−17.3564	−1.59778
$119$	−2.51522	−0.230570
$120$	−1.27198	−0.116115
$121$	29.5311	2.68465
$122$	13.0733	1.18360
$123$	−8.41136	−0.758427
$124$	26.9671	2.42172
$125$	3.98074	0.356048
$126$	−7.28609	−0.649097
$127$	−5.07343	−0.450194	−0.225097	−	0.974336i	$-0.572270\pi$
$127$	−5.07343	−0.450194	−0.225097	+	0.974336i	$0.572270\pi$
$128$	14.9557	1.32191
$129$	−11.4094	−1.00454
$130$	0.900094	0.0789434
$131$	−17.5186	−1.53061	−0.765303	−	0.643670i	$-0.777411\pi$
$131$	−17.5186	−1.53061	−0.765303	+	0.643670i	$0.777411\pi$
$132$	28.0060	2.43761
$133$	3.20069	0.277535
$134$	−10.2964	−0.889471
$135$	−2.27850	−0.196102
$136$	−1.24644	−0.106882
$137$	−11.5154	−0.983830	−0.491915	−	0.870643i	$-0.663703\pi$
$137$	−11.5154	−0.983830	−0.491915	+	0.870643i	$0.663703\pi$
$138$	−13.4930	−1.14860
$139$	9.02568	0.765548	0.382774	−	0.923842i	$-0.374969\pi$
$139$	9.02568	0.765548	0.382774	+	0.923842i	$0.374969\pi$
$140$	5.06592	0.428148
$141$	−6.68698	−0.563146
$142$	−1.82926	−0.153508
$143$	−6.36641	−0.532386
$144$	0.933763	0.0778136
$145$	2.49187	0.206938
$146$	−20.7747	−1.71933
$147$	−16.4929	−1.36031
$148$	−31.4978	−2.58911
$149$	−12.0918	−0.990602	−0.495301	−	0.868721i	$-0.664942\pi$
$149$	−12.0918	−0.990602	−0.495301	+	0.868721i	$0.664942\pi$
$150$	−16.0583	−1.31115
$151$	22.8482	1.85936	0.929679	−	0.368370i	$-0.120084\pi$
$151$	22.8482	1.85936	0.929679	+	0.368370i	$0.120084\pi$
$152$	1.58614	0.128653
$153$	−0.456569	−0.0369114
$154$	−60.1523	−4.84721
$155$	−3.70386	−0.297501
$156$	−4.39903	−0.352204
$157$	−6.11197	−0.487789	−0.243894	−	0.969802i	$-0.578425\pi$
$157$	−6.11197	−0.487789	−0.243894	+	0.969802i	$0.578425\pi$
$158$	−31.1779	−2.48038
$159$	5.88528	0.466733
$160$	−2.79390	−0.220877
$161$	17.2632	1.36053
$162$	13.5489	1.06450
$163$	5.76209	0.451322	0.225661	−	0.974206i	$-0.427546\pi$
$163$	5.76209	0.451322	0.225661	+	0.974206i	$0.427546\pi$
$164$	16.6013	1.29634
$165$	−3.84655	−0.299453
$166$	24.8196	1.92637
$167$	−0.261943	−0.0202698	−0.0101349	−	0.999949i	$-0.503226\pi$
$167$	−0.261943	−0.0202698	−0.0101349	+	0.999949i	$0.503226\pi$
$168$	−13.3521	−1.03014
$169$	1.00000	0.0769231
$170$	0.532914	0.0408726
$171$	0.580997	0.0444300
$172$	22.5185	1.71702
$173$	−8.60546	−0.654261	−0.327131	−	0.944979i	$-0.606082\pi$
$173$	−8.60546	−0.654261	−0.327131	+	0.944979i	$0.606082\pi$
$174$	−20.4448	−1.54991
$175$	20.5453	1.55308
$176$	7.70894	0.581083
$177$	−11.6506	−0.875712
$178$	−18.5645	−1.39147
$179$	20.5236	1.53400	0.767002	−	0.641645i	$-0.221748\pi$
$179$	20.5236	1.53400	0.767002	+	0.641645i	$0.221748\pi$
$180$	0.919579	0.0685413
$181$	−26.0854	−1.93892	−0.969458	−	0.245259i	$-0.921127\pi$
$181$	−26.0854	−1.93892	−0.969458	+	0.245259i	$0.921127\pi$
$182$	9.44839	0.700362
$183$	8.77556	0.648708
$184$	8.55495	0.630679
$185$	4.32614	0.318064
$186$	30.3886	2.22820
$187$	−3.76933	−0.275641
$188$	13.1979	0.962558
$189$	−23.9177	−1.73976
$190$	−0.678149	−0.0491981
$191$	−4.75601	−0.344133	−0.172066	−	0.985085i	$-0.555044\pi$
$191$	−4.75601	−0.344133	−0.172066	+	0.985085i	$0.555044\pi$
$192$	19.3073	1.39338
$193$	4.98140	0.358569	0.179284	−	0.983797i	$-0.442622\pi$
$193$	4.98140	0.358569	0.179284	+	0.983797i	$0.442622\pi$
$194$	−30.1050	−2.16141
$195$	0.604194	0.0432672
$196$	32.5516	2.32511
$197$	22.7347	1.61978	0.809888	−	0.586584i	$-0.199528\pi$
$197$	22.7347	1.61978	0.809888	+	0.586584i	$0.199528\pi$
$198$	−10.9190	−0.775980
$199$	1.84859	0.131043	0.0655215	−	0.997851i	$-0.479129\pi$
$199$	1.84859	0.131043	0.0655215	+	0.997851i	$0.479129\pi$
$200$	10.1814	0.719936
$201$	−6.91151	−0.487500
$202$	29.5158	2.07672
$203$	26.1574	1.83589
$204$	−2.60451	−0.182352
$205$	−2.28014	−0.159252
$206$	30.5174	2.12625
$207$	3.13365	0.217804
$208$	−1.21088	−0.0839592
$209$	4.79658	0.331786
$210$	5.70866	0.393935
$211$	−18.4431	−1.26967	−0.634837	−	0.772646i	$-0.718933\pi$
$211$	−18.4431	−1.26967	−0.634837	+	0.772646i	$0.718933\pi$
$212$	−11.6156	−0.797764
$213$	−1.22791	−0.0841347
$214$	−11.7353	−0.802208
$215$	−3.09285	−0.210931
$216$	−11.8527	−0.806474
$217$	−38.8799	−2.63934
$218$	35.8586	2.42865
$219$	−13.9452	−0.942329
$220$	7.59183	0.511841
$221$	0.592065	0.0398266
$222$	−35.4942	−2.38221
$223$	8.66509	0.580258	0.290129	−	0.956988i	$-0.406302\pi$
$223$	8.66509	0.580258	0.290129	+	0.956988i	$0.406302\pi$
$224$	−29.3279	−1.95955
$225$	3.72943	0.248629
$226$	−41.4976	−2.76038
$227$	−1.79851	−0.119371	−0.0596857	−	0.998217i	$-0.519010\pi$
$227$	−1.79851	−0.119371	−0.0596857	+	0.998217i	$0.519010\pi$
$228$	3.31432	0.219496
$229$	6.79533	0.449048	0.224524	−	0.974469i	$-0.427917\pi$
$229$	6.79533	0.449048	0.224524	+	0.974469i	$0.427917\pi$
$230$	−3.65765	−0.241178
$231$	−40.3777	−2.65666
$232$	12.9626	0.851037
$233$	7.41400	0.485707	0.242854	−	0.970063i	$-0.421917\pi$
$233$	7.41400	0.485707	0.242854	+	0.970063i	$0.421917\pi$
$234$	1.71510	0.112119
$235$	−1.81270	−0.118247
$236$	22.9945	1.49681
$237$	−20.9284	−1.35945
$238$	5.59406	0.362609
$239$	−23.2892	−1.50645	−0.753225	−	0.657763i	$-0.771503\pi$
$239$	−23.2892	−1.50645	−0.753225	+	0.657763i	$0.771503\pi$
$240$	−0.731605	−0.0472249
$241$	20.1372	1.29715	0.648574	−	0.761152i	$-0.275366\pi$
$241$	20.1372	1.29715	0.648574	+	0.761152i	$0.275366\pi$
$242$	−65.6799	−4.22206
$243$	−7.79542	−0.500077
$244$	−17.3201	−1.10881
$245$	−4.47087	−0.285633
$246$	18.7076	1.19275
$247$	−0.753420	−0.0479390
$248$	−19.2673	−1.22348
$249$	16.6603	1.05580
$250$	−8.85352	−0.559946
$251$	4.08385	0.257770	0.128885	−	0.991660i	$-0.458860\pi$
$251$	4.08385	0.257770	0.128885	+	0.991660i	$0.458860\pi$
$252$	9.65293	0.608077
$253$	25.8707	1.62648
$254$	11.2838	0.708006
$255$	0.357722	0.0224014
$256$	−7.39792	−0.462370
$257$	0.591059	0.0368693	0.0184346	−	0.999830i	$-0.494132\pi$
$257$	0.591059	0.0368693	0.0184346	+	0.999830i	$0.494132\pi$
$258$	25.3756	1.57981
$259$	45.4120	2.82176
$260$	−1.19248	−0.0739546
$261$	4.74817	0.293904
$262$	38.9629	2.40713
$263$	−3.68813	−0.227420	−0.113710	−	0.993514i	$-0.536273\pi$
$263$	−3.68813	−0.227420	−0.113710	+	0.993514i	$0.536273\pi$
$264$	−20.0096	−1.23151
$265$	1.59537	0.0980029
$266$	−7.11861	−0.436470
$267$	−12.4616	−0.762635
$268$	13.6411	0.833261
$269$	−26.0450	−1.58799	−0.793994	−	0.607925i	$-0.792002\pi$
$269$	−26.0450	−1.58799	−0.793994	+	0.607925i	$0.792002\pi$
$270$	5.06759	0.308404
$271$	16.1503	0.981059	0.490529	−	0.871425i	$-0.336803\pi$
$271$	16.1503	0.981059	0.490529	+	0.871425i	$0.336803\pi$
$272$	−0.716918	−0.0434695
$273$	6.34230	0.383853
$274$	25.6113	1.54724
$275$	30.7893	1.85667
$276$	17.8760	1.07601
$277$	13.5353	0.813259	0.406629	−	0.913593i	$-0.366704\pi$
$277$	13.5353	0.813259	0.406629	+	0.913593i	$0.366704\pi$
$278$	−20.0739	−1.20395
$279$	−7.05757	−0.422526
$280$	−3.61947	−0.216305
$281$	27.5658	1.64444	0.822218	−	0.569173i	$-0.192737\pi$
$281$	27.5658	1.64444	0.822218	+	0.569173i	$0.192737\pi$
$282$	14.8724	0.885641
$283$	31.7782	1.88902	0.944510	−	0.328483i	$-0.106537\pi$
$283$	31.7782	1.88902	0.944510	+	0.328483i	$0.106537\pi$
$284$	2.42349	0.143807
$285$	−0.455212	−0.0269644
$286$	14.1595	0.837266
$287$	−23.9349	−1.41283
$288$	−5.32368	−0.313701
$289$	−16.6495	−0.979380
$290$	−5.54213	−0.325445
$291$	−20.2082	−1.18462
$292$	27.5233	1.61068
$293$	9.29062	0.542764	0.271382	−	0.962472i	$-0.412519\pi$
$293$	9.29062	0.542764	0.271382	+	0.962472i	$0.412519\pi$
$294$	36.6816	2.13932
$295$	−3.15822	−0.183879
$296$	22.5044	1.30804
$297$	−35.8434	−2.07984
$298$	26.8933	1.55789
$299$	−4.06363	−0.235006
$300$	21.2747	1.22829
$301$	−32.4660	−1.87131
$302$	−50.8164	−2.92415
$303$	19.8127	1.13821
$304$	0.912299	0.0523239
$305$	2.37886	0.136213
$306$	1.01545	0.0580494
$307$	31.0650	1.77297	0.886486	−	0.462755i	$-0.153139\pi$
$307$	31.0650	1.77297	0.886486	+	0.462755i	$0.153139\pi$
$308$	79.6924	4.54089
$309$	20.4850	1.16535
$310$	8.23771	0.467870
$311$	4.73653	0.268584	0.134292	−	0.990942i	$-0.457124\pi$
$311$	4.73653	0.268584	0.134292	+	0.990942i	$0.457124\pi$
$312$	3.14300	0.177937
$313$	6.60976	0.373606	0.186803	−	0.982397i	$-0.440187\pi$
$313$	6.60976	0.373606	0.186803	+	0.982397i	$0.440187\pi$
$314$	13.5936	0.767129
$315$	−1.32580	−0.0747005
$316$	41.3059	2.32364
$317$	18.8469	1.05855	0.529274	−	0.848451i	$-0.322464\pi$
$317$	18.8469	1.05855	0.529274	+	0.848451i	$0.322464\pi$
$318$	−13.0894	−0.734016
$319$	39.1998	2.19477
$320$	5.23379	0.292578
$321$	−7.87739	−0.439673
$322$	−38.3948	−2.13966
$323$	−0.446074	−0.0248202
$324$	−17.9502	−0.997232
$325$	−4.83622	−0.268265
$326$	−12.8154	−0.709779
$327$	24.0704	1.33109
$328$	−11.8612	−0.654925
$329$	−19.0281	−1.04905
$330$	8.55506	0.470940
$331$	−21.8754	−1.20238	−0.601190	−	0.799106i	$-0.705307\pi$
$331$	−21.8754	−1.20238	−0.601190	+	0.799106i	$0.705307\pi$
$332$	−32.8820	−1.80464
$333$	8.24330	0.451730
$334$	0.582585	0.0318777
$335$	−1.87356	−0.102364
$336$	−7.67975	−0.418965
$337$	10.8026	0.588453	0.294226	−	0.955736i	$-0.404938\pi$
$337$	10.8026	0.588453	0.294226	+	0.955736i	$0.404938\pi$
$338$	−2.22409	−0.120974
$339$	−27.8555	−1.51290
$340$	−0.706027	−0.0382897
$341$	−58.2657	−3.15527
$342$	−1.29219	−0.0698735
$343$	−17.1938	−0.928375
$344$	−16.0889	−0.867455
$345$	−2.45522	−0.132185
$346$	19.1393	1.02894
$347$	12.3327	0.662055	0.331028	−	0.943621i	$-0.392605\pi$
$347$	12.3327	0.662055	0.331028	+	0.943621i	$0.392605\pi$
$348$	27.0861	1.45197
$349$	−2.49127	−0.133354	−0.0666772	−	0.997775i	$-0.521240\pi$
$349$	−2.49127	−0.133354	−0.0666772	+	0.997775i	$0.521240\pi$
$350$	−45.6945	−2.44247
$351$	5.63007	0.300511
$352$	−43.9511	−2.34260
$353$	19.8479	1.05640	0.528199	−	0.849121i	$-0.322867\pi$
$353$	19.8479	1.05640	0.528199	+	0.849121i	$0.322867\pi$
$354$	25.9119	1.37720
$355$	−0.332859	−0.0176663
$356$	24.5951	1.30354
$357$	3.75505	0.198739
$358$	−45.6462	−2.41248
$359$	−13.7859	−0.727593	−0.363796	−	0.931479i	$-0.618520\pi$
$359$	−13.7859	−0.727593	−0.363796	+	0.931479i	$0.618520\pi$
$360$	−0.657016	−0.0346278
$361$	−18.4324	−0.970124
$362$	58.0163	3.04927
$363$	−44.0881	−2.31402
$364$	−12.5176	−0.656102
$365$	−3.78024	−0.197867
$366$	−19.5176	−1.02020
$367$	11.7589	0.613811	0.306905	−	0.951740i	$-0.400706\pi$
$367$	11.7589	0.613811	0.306905	+	0.951740i	$0.400706\pi$
$368$	4.92056	0.256502
$369$	−4.34472	−0.226177
$370$	−9.62171	−0.500209
$371$	16.7468	0.869451
$372$	−40.2602	−2.08739
$373$	15.7240	0.814156	0.407078	−	0.913393i	$-0.366548\pi$
$373$	15.7240	0.814156	0.407078	+	0.913393i	$0.366548\pi$
$374$	8.38332	0.433491
$375$	−5.94298	−0.306894
$376$	−9.42959	−0.486294
$377$	−6.15728	−0.317116
$378$	53.1952	2.73606
$379$	−0.542684	−0.0278758	−0.0139379	−	0.999903i	$-0.504437\pi$
$379$	−0.542684	−0.0278758	−0.0139379	+	0.999903i	$0.504437\pi$
$380$	0.898440	0.0460890
$381$	7.57430	0.388043
$382$	10.5778	0.541206
$383$	−2.72239	−0.139108	−0.0695539	−	0.997578i	$-0.522158\pi$
$383$	−2.72239	−0.139108	−0.0695539	+	0.997578i	$0.522158\pi$
$384$	−22.3279	−1.13942
$385$	−10.9455	−0.557835
$386$	−11.0791	−0.563909
$387$	−5.89332	−0.299574
$388$	39.8844	2.02482
$389$	−29.4047	−1.49088	−0.745440	−	0.666573i	$-0.767761\pi$
$389$	−29.4047	−1.49088	−0.745440	+	0.666573i	$0.767761\pi$
$390$	−1.34378	−0.0680450
$391$	−2.40593	−0.121673
$392$	−23.2573	−1.17467
$393$	26.1541	1.31930
$394$	−50.5639	−2.54737
$395$	−5.67324	−0.285452
$396$	14.4660	0.726942
$397$	−10.8240	−0.543239	−0.271619	−	0.962405i	$-0.587559\pi$
$397$	−10.8240	−0.543239	−0.271619	+	0.962405i	$0.587559\pi$
$398$	−4.11142	−0.206087
$399$	−4.77842	−0.239220
$400$	5.85606	0.292803
$401$	−12.8972	−0.644054	−0.322027	−	0.946731i	$-0.604364\pi$
$401$	−12.8972	−0.644054	−0.322027	+	0.946731i	$0.604364\pi$
$402$	15.3718	0.766676
$403$	9.15205	0.455896
$404$	−39.1037	−1.94548
$405$	2.46540	0.122507
$406$	−58.1764	−2.88725
$407$	68.0548	3.37335
$408$	1.86086	0.0921262
$409$	−1.27635	−0.0631115	−0.0315557	−	0.999502i	$-0.510046\pi$
$409$	−1.27635	−0.0631115	−0.0315557	+	0.999502i	$0.510046\pi$
$410$	5.07123	0.250450
$411$	17.1918	0.848008
$412$	−40.4307	−1.99188
$413$	−33.1523	−1.63132
$414$	−6.96952	−0.342533
$415$	4.51625	0.221694
$416$	6.90359	0.338477
$417$	−13.4748	−0.659861
$418$	−10.6680	−0.521790
$419$	−7.30755	−0.356997	−0.178499	−	0.983940i	$-0.557124\pi$
$419$	−7.30755	−0.356997	−0.178499	+	0.983940i	$0.557124\pi$
$420$	−7.56308	−0.369041
$421$	6.81919	0.332347	0.166173	−	0.986097i	$-0.446859\pi$
$421$	6.81919	0.332347	0.166173	+	0.986097i	$0.446859\pi$
$422$	41.0190	1.99678
$423$	−3.45403	−0.167941
$424$	8.29907	0.403038
$425$	−2.86335	−0.138893
$426$	2.73097	0.132316
$427$	24.9712	1.20844
$428$	15.5474	0.751513
$429$	9.50463	0.458888
$430$	6.87877	0.331724
$431$	−8.33789	−0.401622	−0.200811	−	0.979630i	$-0.564358\pi$
$431$	−8.33789	−0.401622	−0.200811	+	0.979630i	$0.564358\pi$
$432$	−6.81733	−0.327999
$433$	−15.6929	−0.754154	−0.377077	−	0.926182i	$-0.623071\pi$
$433$	−15.6929	−0.754154	−0.377077	+	0.926182i	$0.623071\pi$
$434$	86.4722	4.15080
$435$	−3.72020	−0.178370
$436$	−47.5071	−2.27518
$437$	3.06162	0.146457
$438$	31.0153	1.48197
$439$	−17.1020	−0.816232	−0.408116	−	0.912930i	$-0.633814\pi$
$439$	−17.1020	−0.816232	−0.408116	+	0.912930i	$0.633814\pi$
$440$	−5.42417	−0.258587
$441$	−8.51908	−0.405670
$442$	−1.31680	−0.0626340
$443$	−22.9063	−1.08831	−0.544154	−	0.838985i	$-0.683149\pi$
$443$	−22.9063	−1.08831	−0.544154	+	0.838985i	$0.683149\pi$
$444$	47.0242	2.23167
$445$	−3.37806	−0.160135
$446$	−19.2719	−0.912552
$447$	18.0523	0.853846
$448$	54.9397	2.59566
$449$	−7.04553	−0.332499	−0.166250	−	0.986084i	$-0.553166\pi$
$449$	−7.04553	−0.332499	−0.166250	+	0.986084i	$0.553166\pi$
$450$	−8.29458	−0.391010
$451$	−35.8690	−1.68901
$452$	54.9777	2.58594
$453$	−34.1108	−1.60267
$454$	4.00004	0.187731
$455$	1.71926	0.0806002
$456$	−2.36800	−0.110892
$457$	−24.3015	−1.13678	−0.568389	−	0.822760i	$-0.692433\pi$
$457$	−24.3015	−1.13678	−0.568389	+	0.822760i	$0.692433\pi$
$458$	−15.1134	−0.706204
$459$	3.33337	0.155588
$460$	4.84581	0.225937
$461$	−36.9100	−1.71907	−0.859534	−	0.511078i	$-0.829246\pi$
$461$	−36.9100	−1.71907	−0.859534	+	0.511078i	$0.829246\pi$
$462$	89.8035	4.17804
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	7.45572	0.346123
$465$	5.52962	0.256430
$466$	−16.4894	−0.763856
$467$	35.3985	1.63805	0.819023	−	0.573761i	$-0.194516\pi$
$467$	35.3985	1.63805	0.819023	+	0.573761i	$0.194516\pi$
$468$	−2.27223	−0.105034
$469$	−19.6670	−0.908138
$470$	4.03160	0.185964
$471$	9.12478	0.420448
$472$	−16.4290	−0.756205
$473$	−48.6539	−2.23711
$474$	46.5466	2.13796
$475$	3.64370	0.167184
$476$	−7.41126	−0.339694
$477$	3.03993	0.139189
$478$	51.7971	2.36915
$479$	−21.6316	−0.988374	−0.494187	−	0.869356i	$-0.664534\pi$
$479$	−21.6316	−0.988374	−0.494187	+	0.869356i	$0.664534\pi$
$480$	4.17111	0.190384
$481$	−10.6897	−0.487407
$482$	−44.7868	−2.03998
$483$	−25.7728	−1.17270
$484$	87.0155	3.95525
$485$	−5.47800	−0.248743
$486$	17.3377	0.786454
$487$	10.2207	0.463142	0.231571	−	0.972818i	$-0.425613\pi$
$487$	10.2207	0.463142	0.231571	+	0.972818i	$0.425613\pi$
$488$	12.3748	0.560180
$489$	−8.60242	−0.389015
$490$	9.94360	0.449206
$491$	−5.56832	−0.251295	−0.125647	−	0.992075i	$-0.540101\pi$
$491$	−5.56832	−0.251295	−0.125647	+	0.992075i	$0.540101\pi$
$492$	−24.7846	−1.11738
$493$	−3.64551	−0.164186
$494$	1.67567	0.0753921
$495$	−1.98686	−0.0893027
$496$	−11.0820	−0.497597
$497$	−3.49406	−0.156730
$498$	−37.0540	−1.66043
$499$	20.5419	0.919583	0.459791	−	0.888027i	$-0.347924\pi$
$499$	20.5419	0.919583	0.459791	+	0.888027i	$0.347924\pi$
$500$	11.7295	0.524560
$501$	0.391064	0.0174715
$502$	−9.08283	−0.405387
$503$	17.8947	0.797884	0.398942	−	0.916976i	$-0.369377\pi$
$503$	17.8947	0.797884	0.398942	+	0.916976i	$0.369377\pi$
$504$	−6.89678	−0.307207
$505$	5.37078	0.238997
$506$	−57.5388	−2.55791
$507$	−1.49293	−0.0663036
$508$	−14.9492	−0.663264
$509$	−1.90821	−0.0845800	−0.0422900	−	0.999105i	$-0.513465\pi$
$509$	−1.90821	−0.0845800	−0.0422900	+	0.999105i	$0.513465\pi$
$510$	−0.795606	−0.0352300
$511$	−39.6816	−1.75541
$512$	−13.4578	−0.594756
$513$	−4.24181	−0.187281
$514$	−1.31457	−0.0579831
$515$	5.55304	0.244696
$516$	−33.6186	−1.47998
$517$	−28.5157	−1.25412
$518$	−101.000	−4.43770
$519$	12.8474	0.563938
$520$	0.851999	0.0373626
$521$	5.09827	0.223359	0.111680	−	0.993744i	$-0.464377\pi$
$521$	5.09827	0.223359	0.111680	+	0.993744i	$0.464377\pi$
$522$	−10.5603	−0.462214
$523$	−10.1237	−0.442677	−0.221338	−	0.975197i	$-0.571043\pi$
$523$	−10.1237	−0.442677	−0.221338	+	0.975197i	$0.571043\pi$
$524$	−51.6197	−2.25502
$525$	−30.6727	−1.33867
$526$	8.20272	0.357656
$527$	5.41861	0.236038
$528$	−11.5089	−0.500862
$529$	−6.48690	−0.282039
$530$	−3.54825	−0.154126
$531$	−6.01788	−0.261154
$532$	9.43104	0.408887
$533$	5.63411	0.244040
$534$	27.7156	1.19937
$535$	−2.13539	−0.0923210
$536$	−9.74621	−0.420972
$537$	−30.6403	−1.32223
$538$	57.9263	2.49738
$539$	−70.3316	−3.02940
$540$	−6.71377	−0.288915
$541$	−17.3008	−0.743819	−0.371909	−	0.928269i	$-0.621297\pi$
$541$	−17.3008	−0.743819	−0.371909	+	0.928269i	$0.621297\pi$
$542$	−35.9196	−1.54288
$543$	38.9438	1.67124
$544$	4.08738	0.175245
$545$	6.52496	0.279498
$546$	−14.1058	−0.603674
$547$	23.6763	1.01233	0.506163	−	0.862438i	$-0.331064\pi$
$547$	23.6763	1.01233	0.506163	+	0.862438i	$0.331064\pi$
$548$	−33.9310	−1.44946
$549$	4.53284	0.193457
$550$	−68.4782	−2.91992
$551$	4.63902	0.197629
$552$	−12.7720	−0.543612
$553$	−59.5527	−2.53244
$554$	−30.1037	−1.27899
$555$	−6.45864	−0.274154
$556$	26.5948	1.12787
$557$	5.01757	0.212601	0.106301	−	0.994334i	$-0.466099\pi$
$557$	5.01757	0.212601	0.106301	+	0.994334i	$0.466099\pi$
$558$	15.6967	0.664493
$559$	7.64228	0.323234
$560$	−2.08181	−0.0879727
$561$	5.62736	0.237587
$562$	−61.3087	−2.58615
$563$	−22.5421	−0.950035	−0.475018	−	0.879976i	$-0.657558\pi$
$563$	−22.5421	−0.950035	−0.475018	+	0.879976i	$0.657558\pi$
$564$	−19.7036	−0.829673
$565$	−7.55103	−0.317674
$566$	−70.6776	−2.97080
$567$	25.8796	1.08684
$568$	−1.73152	−0.0726530
$569$	−41.6749	−1.74710	−0.873551	−	0.486733i	$-0.838188\pi$
$569$	−41.6749	−1.74710	−0.873551	+	0.486733i	$0.838188\pi$
$570$	1.01243	0.0424061
$571$	36.0374	1.50812	0.754059	−	0.656806i	$-0.228093\pi$
$571$	36.0374	1.50812	0.754059	+	0.656806i	$0.228093\pi$
$572$	−18.7590	−0.784355
$573$	7.10041	0.296624
$574$	53.2333	2.22191
$575$	19.6526	0.819570
$576$	9.97281	0.415534
$577$	−8.63281	−0.359388	−0.179694	−	0.983723i	$-0.557511\pi$
$577$	−8.63281	−0.359388	−0.179694	+	0.983723i	$0.557511\pi$
$578$	37.0299	1.54024
$579$	−7.43690	−0.309067
$580$	7.34246	0.304879
$581$	47.4076	1.96680
$582$	44.9448	1.86302
$583$	25.0969	1.03941
$584$	−19.6647	−0.813730
$585$	0.312085	0.0129031
$586$	−20.6632	−0.853587
$587$	8.53482	0.352270	0.176135	−	0.984366i	$-0.443641\pi$
$587$	8.53482	0.352270	0.176135	+	0.984366i	$0.443641\pi$
$588$	−48.5974	−2.00412
$589$	−6.89534	−0.284118
$590$	7.02417	0.289180
$591$	−33.9413	−1.39616
$592$	12.9439	0.531990
$593$	11.0799	0.454997	0.227499	−	0.973778i	$-0.426945\pi$
$593$	11.0799	0.454997	0.227499	+	0.973778i	$0.426945\pi$
$594$	79.7188	3.27090
$595$	1.01791	0.0417304
$596$	−35.6294	−1.45944
$597$	−2.75982	−0.112952
$598$	9.03787	0.369586
$599$	−27.4614	−1.12204	−0.561022	−	0.827801i	$-0.689592\pi$
$599$	−27.4614	−1.12204	−0.561022	+	0.827801i	$0.689592\pi$
$600$	−15.2002	−0.620546
$601$	−1.00381	−0.0409463	−0.0204731	−	0.999790i	$-0.506517\pi$
$601$	−1.00381	−0.0409463	−0.0204731	+	0.999790i	$0.506517\pi$
$602$	72.2073	2.94295
$603$	−3.57001	−0.145382
$604$	67.3237	2.73936
$605$	−11.9513	−0.485890
$606$	−44.0651	−1.79002
$607$	−30.8270	−1.25123	−0.625616	−	0.780131i	$-0.715152\pi$
$607$	−30.8270	−1.25123	−0.625616	+	0.780131i	$0.715152\pi$
$608$	−5.20130	−0.210941
$609$	−39.0513	−1.58244
$610$	−5.29080	−0.214218
$611$	4.47909	0.181204
$612$	−1.34531	−0.0543810
$613$	−29.1051	−1.17554	−0.587772	−	0.809026i	$-0.699995\pi$
$613$	−29.1051	−1.17554	−0.587772	+	0.809026i	$0.699995\pi$
$614$	−69.0912	−2.78830
$615$	3.40410	0.137266
$616$	−56.9382	−2.29411
$617$	−18.7075	−0.753135	−0.376567	−	0.926389i	$-0.622896\pi$
$617$	−18.7075	−0.753135	−0.376567	+	0.926389i	$0.622896\pi$
$618$	−45.5604	−1.83271
$619$	34.3173	1.37933	0.689665	−	0.724129i	$-0.257758\pi$
$619$	34.3173	1.37933	0.689665	+	0.724129i	$0.257758\pi$
$620$	−10.9137	−0.438303
$621$	−22.8785	−0.918084
$622$	−10.5345	−0.422393
$623$	−35.4599	−1.42067
$624$	1.80776	0.0723683
$625$	22.5701	0.902803
$626$	−14.7007	−0.587557
$627$	−7.16098	−0.285982
$628$	−18.0093	−0.718651
$629$	−6.32898	−0.252353
$630$	2.94870	0.117479
$631$	9.42582	0.375236	0.187618	−	0.982242i	$-0.439923\pi$
$631$	9.42582	0.375236	0.187618	+	0.982242i	$0.439923\pi$
$632$	−29.5120	−1.17392
$633$	27.5343	1.09439
$634$	−41.9172	−1.66474
$635$	2.05323	0.0814800
$636$	17.3414	0.687630
$637$	11.0473	0.437710
$638$	−87.1838	−3.45164
$639$	−0.634251	−0.0250906
$640$	−6.05261	−0.239250
$641$	4.98461	0.196880	0.0984401	−	0.995143i	$-0.468615\pi$
$641$	4.98461	0.196880	0.0984401	+	0.995143i	$0.468615\pi$
$642$	17.5200	0.691460
$643$	1.65964	0.0654497	0.0327249	−	0.999464i	$-0.489581\pi$
$643$	1.65964	0.0654497	0.0327249	+	0.999464i	$0.489581\pi$
$644$	50.8671	2.00444
$645$	4.61742	0.181811
$646$	0.992107	0.0390339
$647$	7.33083	0.288204	0.144102	−	0.989563i	$-0.453971\pi$
$647$	7.33083	0.288204	0.144102	+	0.989563i	$0.453971\pi$
$648$	12.8249	0.503812
$649$	−49.6823	−1.95020
$650$	10.7562	0.421892
$651$	58.0451	2.27497
$652$	16.9784	0.664925
$653$	−0.684418	−0.0267833	−0.0133917	−	0.999910i	$-0.504263\pi$
$653$	−0.684418	−0.0267833	−0.0133917	+	0.999910i	$0.504263\pi$
$654$	−53.5346	−2.09337
$655$	7.08981	0.277022
$656$	−6.82222	−0.266363
$657$	−7.20312	−0.281020
$658$	42.3202	1.64981
$659$	−29.3553	−1.14352	−0.571760	−	0.820421i	$-0.693739\pi$
$659$	−29.3553	−1.14352	−0.571760	+	0.820421i	$0.693739\pi$
$660$	−11.3341	−0.441180
$661$	−4.51949	−0.175788	−0.0878939	−	0.996130i	$-0.528014\pi$
$661$	−4.51949	−0.175788	−0.0878939	+	0.996130i	$0.528014\pi$
$662$	48.6528	1.89094
$663$	−0.883914	−0.0343284
$664$	23.4934	0.911720
$665$	−1.29533	−0.0502306
$666$	−18.3338	−0.710421
$667$	25.0209	0.968814
$668$	−0.771834	−0.0298632
$669$	−12.9364	−0.500151
$670$	4.16697	0.160984
$671$	37.4221	1.44467
$672$	43.7847	1.68903
$673$	11.8917	0.458392	0.229196	−	0.973380i	$-0.426390\pi$
$673$	11.8917	0.458392	0.229196	+	0.973380i	$0.426390\pi$
$674$	−24.0258	−0.925441
$675$	−27.2283	−1.04802
$676$	2.94657	0.113329
$677$	−13.0227	−0.500505	−0.250252	−	0.968181i	$-0.580514\pi$
$677$	−13.0227	−0.500505	−0.250252	+	0.968181i	$0.580514\pi$
$678$	61.9531	2.37930
$679$	−57.5033	−2.20677
$680$	0.504439	0.0193443
$681$	2.68506	0.102892
$682$	129.588	4.96218
$683$	18.3578	0.702443	0.351222	−	0.936292i	$-0.385766\pi$
$683$	18.3578	0.702443	0.351222	+	0.936292i	$0.385766\pi$
$684$	1.71195	0.0654579
$685$	4.66032	0.178062
$686$	38.2404	1.46003
$687$	−10.1450	−0.387055
$688$	−9.25386	−0.352800
$689$	−3.94209	−0.150182
$690$	5.46063	0.207883
$691$	11.9928	0.456229	0.228115	−	0.973634i	$-0.426744\pi$
$691$	11.9928	0.456229	0.228115	+	0.973634i	$0.426744\pi$
$692$	−25.3566	−0.963912
$693$	−20.8563	−0.792265
$694$	−27.4291	−1.04119
$695$	−3.65272	−0.138555
$696$	−19.3523	−0.733548
$697$	3.33576	0.126351
$698$	5.54080	0.209722
$699$	−11.0686	−0.418654
$700$	60.5380	2.28812
$701$	−24.3749	−0.920629	−0.460314	−	0.887756i	$-0.652263\pi$
$701$	−24.3749	−0.920629	−0.460314	+	0.887756i	$0.652263\pi$
$702$	−12.5218	−0.472604
$703$	8.05381	0.303755
$704$	82.3332	3.10305
$705$	2.70624	0.101923
$706$	−44.1435	−1.66136
$707$	56.3778	2.12030
$708$	−34.3292	−1.29017
$709$	33.0521	1.24130	0.620649	−	0.784088i	$-0.286869\pi$
$709$	33.0521	1.24130	0.620649	+	0.784088i	$0.286869\pi$
$710$	0.740307	0.0277832
$711$	−10.8102	−0.405413
$712$	−17.5726	−0.658560
$713$	−37.1906	−1.39280
$714$	−8.35157	−0.312550
$715$	2.57650	0.0963557
$716$	60.4741	2.26002
$717$	34.7692	1.29848
$718$	30.6611	1.14426
$719$	−19.5970	−0.730844	−0.365422	−	0.930842i	$-0.619075\pi$
$719$	−19.5970	−0.730844	−0.365422	+	0.930842i	$0.619075\pi$
$720$	−0.377896	−0.0140834
$721$	58.2910	2.17087
$722$	40.9952	1.52568
$723$	−30.0635	−1.11807
$724$	−76.8625	−2.85657
$725$	29.7780	1.10593
$726$	98.0557	3.63919
$727$	20.7843	0.770848	0.385424	−	0.922740i	$-0.374055\pi$
$727$	20.7843	0.770848	0.385424	+	0.922740i	$0.374055\pi$
$728$	8.94354	0.331470
$729$	29.9137	1.10792
$730$	8.40759	0.311179
$731$	4.52473	0.167353
$732$	25.8578	0.955731
$733$	−40.0988	−1.48108	−0.740542	−	0.672010i	$-0.765431\pi$
$733$	−40.0988	−1.48108	−0.740542	+	0.672010i	$0.765431\pi$
$734$	−26.1529	−0.965321
$735$	6.67471	0.246200
$736$	−28.0537	−1.03407
$737$	−29.4732	−1.08566
$738$	9.66305	0.355702
$739$	30.5706	1.12456	0.562278	−	0.826948i	$-0.309925\pi$
$739$	30.5706	1.12456	0.562278	+	0.826948i	$0.309925\pi$
$740$	12.7472	0.468598
$741$	1.12481	0.0413208
$742$	−37.2464	−1.36736
$743$	−34.3786	−1.26123	−0.630615	−	0.776096i	$-0.717197\pi$
$743$	−34.3786	−1.26123	−0.630615	+	0.776096i	$0.717197\pi$
$744$	28.7649	1.05457
$745$	4.89360	0.179288
$746$	−34.9715	−1.28040
$747$	8.60556	0.314861
$748$	−11.1066	−0.406097
$749$	−22.4155	−0.819043
$750$	13.2177	0.482643
$751$	−9.06991	−0.330966	−0.165483	−	0.986213i	$-0.552918\pi$
$751$	−9.06991	−0.330966	−0.165483	+	0.986213i	$0.552918\pi$
$752$	−5.42362	−0.197779
$753$	−6.09692	−0.222184
$754$	13.6943	0.498719
$755$	−9.24671	−0.336522
$756$	−70.4752	−2.56316
$757$	7.02806	0.255439	0.127720	−	0.991810i	$-0.459234\pi$
$757$	7.02806	0.255439	0.127720	+	0.991810i	$0.459234\pi$
$758$	1.20698	0.0438394
$759$	−38.6233	−1.40194
$760$	−0.641913	−0.0232846
$761$	−2.74794	−0.0996126	−0.0498063	−	0.998759i	$-0.515860\pi$
$761$	−2.74794	−0.0996126	−0.0498063	+	0.998759i	$0.515860\pi$
$762$	−16.8459	−0.610263
$763$	68.4933	2.47962
$764$	−14.0139	−0.507005
$765$	0.184774	0.00668054
$766$	6.05484	0.218770
$767$	7.80382	0.281780
$768$	11.0446	0.398538
$769$	−14.5907	−0.526155	−0.263077	−	0.964775i	$-0.584737\pi$
$769$	−14.5907	−0.526155	−0.263077	+	0.964775i	$0.584737\pi$
$770$	24.3438	0.877289
$771$	−0.882413	−0.0317793
$772$	14.6780	0.528273
$773$	−43.5463	−1.56625	−0.783126	−	0.621863i	$-0.786376\pi$
$773$	−43.5463	−1.56625	−0.783126	+	0.621863i	$0.786376\pi$
$774$	13.1073	0.471130
$775$	−44.2613	−1.58991
$776$	−28.4964	−1.02296
$777$	−67.7971	−2.43221
$778$	65.3987	2.34466
$779$	−4.24485	−0.152088
$780$	1.78030	0.0637449
$781$	−5.23623	−0.187367
$782$	5.35101	0.191352
$783$	−34.6660	−1.23886
$784$	−13.3769	−0.477747
$785$	2.47353	0.0882841
$786$	−58.1690	−2.07482
$787$	28.1836	1.00464	0.502318	−	0.864683i	$-0.332481\pi$
$787$	28.1836	1.00464	0.502318	+	0.864683i	$0.332481\pi$
$788$	66.9892	2.38639
$789$	5.50613	0.196024
$790$	12.6178	0.448921
$791$	−79.2641	−2.81831
$792$	−10.3356	−0.367259
$793$	−5.87806	−0.208736
$794$	24.0734	0.854334
$795$	−2.38179	−0.0844732
$796$	5.44699	0.193063
$797$	−12.2463	−0.433788	−0.216894	−	0.976195i	$-0.569593\pi$
$797$	−12.2463	−0.433788	−0.216894	+	0.976195i	$0.569593\pi$
$798$	10.6276	0.376214
$799$	2.65191	0.0938179
$800$	−33.3873	−1.18042
$801$	−6.43678	−0.227432
$802$	28.6844	1.01288
$803$	−59.4673	−2.09855
$804$	−20.3652	−0.718226
$805$	−6.98644	−0.246240
$806$	−20.3550	−0.716973
$807$	38.8834	1.36876
$808$	27.9386	0.982878
$809$	−15.8834	−0.558432	−0.279216	−	0.960228i	$-0.590075\pi$
$809$	−15.8834	−0.558432	−0.279216	+	0.960228i	$0.590075\pi$
$810$	−5.48328	−0.192663
$811$	−14.9568	−0.525206	−0.262603	−	0.964904i	$-0.584581\pi$
$811$	−14.9568	−0.525206	−0.262603	+	0.964904i	$0.584581\pi$
$812$	77.0746	2.70479
$813$	−24.1113	−0.845620
$814$	−151.360	−5.30516
$815$	−2.33193	−0.0816840
$816$	1.07031	0.0374684
$817$	−5.75785	−0.201442
$818$	2.83872	0.0992534
$819$	3.27599	0.114472
$820$	−6.71858	−0.234623
$821$	27.2035	0.949408	0.474704	−	0.880145i	$-0.342555\pi$
$821$	27.2035	0.949408	0.474704	+	0.880145i	$0.342555\pi$
$822$	−38.2360	−1.33363
$823$	22.2331	0.774998	0.387499	−	0.921870i	$-0.373339\pi$
$823$	22.2331	0.774998	0.387499	+	0.921870i	$0.373339\pi$
$824$	28.8867	1.00632
$825$	−45.9664	−1.60035
$826$	73.7335	2.56552
$827$	−20.1099	−0.699290	−0.349645	−	0.936882i	$-0.613698\pi$
$827$	−20.1099	−0.699290	−0.349645	+	0.936882i	$0.613698\pi$
$828$	9.23352	0.320887
$829$	35.5339	1.23414	0.617072	−	0.786907i	$-0.288319\pi$
$829$	35.5339	1.23414	0.617072	+	0.786907i	$0.288319\pi$
$830$	−10.0445	−0.348651
$831$	−20.2074	−0.700985
$832$	−12.9324	−0.448352
$833$	6.54072	0.226622
$834$	29.9690	1.03774
$835$	0.106009	0.00366860
$836$	14.1334	0.488815
$837$	51.5268	1.78103
$838$	16.2526	0.561438
$839$	−48.0395	−1.65851	−0.829254	−	0.558872i	$-0.811234\pi$
$839$	−48.0395	−1.65851	−0.829254	+	0.558872i	$0.811234\pi$
$840$	5.40363	0.186443
$841$	8.91215	0.307316
$842$	−15.1665	−0.522671
$843$	−41.1539	−1.41741
$844$	−54.3438	−1.87059
$845$	−0.404702	−0.0139222
$846$	7.68207	0.264115
$847$	−125.455	−4.31067
$848$	4.77338	0.163919
$849$	−47.4428	−1.62823
$850$	6.36835	0.218433
$851$	43.4389	1.48907
$852$	−3.61811	−0.123954
$853$	−30.3011	−1.03749	−0.518744	−	0.854930i	$-0.673600\pi$
$853$	−30.3011	−1.03749	−0.518744	+	0.854930i	$0.673600\pi$
$854$	−55.5382	−1.90048
$855$	−0.235131	−0.00804131
$856$	−11.1082	−0.379672
$857$	2.06108	0.0704052	0.0352026	−	0.999380i	$-0.488792\pi$
$857$	2.06108	0.0704052	0.0352026	+	0.999380i	$0.488792\pi$
$858$	−21.1391	−0.721678
$859$	−1.73870	−0.0593236	−0.0296618	−	0.999560i	$-0.509443\pi$
$859$	−1.73870	−0.0593236	−0.0296618	+	0.999560i	$0.509443\pi$
$860$	−9.11329	−0.310760
$861$	35.7332	1.21778
$862$	18.5442	0.631618
$863$	22.0765	0.751492	0.375746	−	0.926723i	$-0.377387\pi$
$863$	22.0765	0.751492	0.375746	+	0.926723i	$0.377387\pi$
$864$	38.8677	1.32231
$865$	3.48265	0.118414
$866$	34.9025	1.18603
$867$	24.8566	0.844173
$868$	−114.562	−3.88849
$869$	−89.2463	−3.02747
$870$	8.27404	0.280516
$871$	4.62948	0.156864
$872$	33.9426	1.14944
$873$	−10.4381	−0.353278
$874$	−6.80931	−0.230328
$875$	−16.9110	−0.571697
$876$	−41.0904	−1.38832
$877$	−5.11114	−0.172591	−0.0862954	−	0.996270i	$-0.527503\pi$
$877$	−5.11114	−0.172591	−0.0862954	+	0.996270i	$0.527503\pi$
$878$	38.0363	1.28366
$879$	−13.8703	−0.467833
$880$	−3.11983	−0.105169
$881$	34.3475	1.15720	0.578598	−	0.815613i	$-0.303600\pi$
$881$	34.3475	1.15720	0.578598	+	0.815613i	$0.303600\pi$
$882$	18.9472	0.637985
$883$	13.7571	0.462964	0.231482	−	0.972839i	$-0.425643\pi$
$883$	13.7571	0.462964	0.231482	+	0.972839i	$0.425643\pi$
$884$	1.74456	0.0586759
$885$	4.71502	0.158494
$886$	50.9455	1.71155
$887$	21.7966	0.731857	0.365928	−	0.930643i	$-0.380752\pi$
$887$	21.7966	0.731857	0.365928	+	0.930643i	$0.380752\pi$
$888$	−33.5976	−1.12746
$889$	21.5530	0.722865
$890$	7.51311	0.251840
$891$	38.7835	1.29930
$892$	25.5323	0.854884
$893$	−3.37463	−0.112928
$894$	−40.1500	−1.34282
$895$	−8.30594	−0.277637
$896$	−63.5350	−2.12255
$897$	6.06674	0.202562
$898$	15.6699	0.522911
$899$	−56.3518	−1.87944
$900$	10.9890	0.366301
$901$	−2.33397	−0.0777559
$902$	79.7759	2.65625
$903$	48.4696	1.61297
$904$	−39.2802	−1.30644
$905$	10.5568	0.350921
$906$	75.8655	2.52046
$907$	32.4876	1.07873	0.539366	−	0.842072i	$-0.318664\pi$
$907$	32.4876	1.07873	0.539366	+	0.842072i	$0.318664\pi$
$908$	−5.29943	−0.175868
$909$	10.2338	0.339435
$910$	−3.82379	−0.126757
$911$	42.1179	1.39543	0.697715	−	0.716376i	$-0.254200\pi$
$911$	42.1179	1.39543	0.697715	+	0.716376i	$0.254200\pi$
$912$	−1.36200	−0.0451004
$913$	71.0455	2.35126
$914$	54.0488	1.78777
$915$	−3.55149	−0.117409
$916$	20.0229	0.661575
$917$	74.4226	2.45765
$918$	−7.41371	−0.244689
$919$	34.2754	1.13064	0.565320	−	0.824872i	$-0.308753\pi$
$919$	34.2754	1.13064	0.565320	+	0.824872i	$0.308753\pi$
$920$	−3.46221	−0.114146
$921$	−46.3780	−1.52821
$922$	82.0910	2.70352
$923$	0.822478	0.0270722
$924$	−118.976	−3.91401
$925$	51.6976	1.69981
$926$	−2.22409	−0.0730881
$927$	10.5811	0.347530
$928$	−42.5074	−1.39537
$929$	−23.0641	−0.756707	−0.378354	−	0.925661i	$-0.623510\pi$
$929$	−23.0641	−0.756707	−0.378354	+	0.925661i	$0.623510\pi$
$930$	−12.2984	−0.403279
$931$	−8.32325	−0.272784
$932$	21.8458	0.715585
$933$	−7.07132	−0.231505
$934$	−78.7293	−2.57610
$935$	1.52546	0.0498877
$936$	1.62345	0.0530643
$937$	14.4272	0.471317	0.235658	−	0.971836i	$-0.424275\pi$
$937$	14.4272	0.471317	0.235658	+	0.971836i	$0.424275\pi$
$938$	43.7412	1.42820
$939$	−9.86794	−0.322028
$940$	−5.34123	−0.174212
$941$	41.8998	1.36589	0.682947	−	0.730467i	$-0.260698\pi$
$941$	41.8998	1.36589	0.682947	+	0.730467i	$0.260698\pi$
$942$	−20.2943	−0.661224
$943$	−22.8949	−0.745562
$944$	−9.44946	−0.307554
$945$	9.67957	0.314876
$946$	108.210	3.51823
$947$	2.09884	0.0682032	0.0341016	−	0.999418i	$-0.489143\pi$
$947$	2.09884	0.0682032	0.0341016	+	0.999418i	$0.489143\pi$
$948$	−61.6670	−2.00285
$949$	9.34079	0.303215
$950$	−8.10391	−0.262926
$951$	−28.1372	−0.912412
$952$	5.29516	0.171617
$953$	−56.4653	−1.82909	−0.914546	−	0.404483i	$-0.867452\pi$
$953$	−56.4653	−1.82909	−0.914546	+	0.404483i	$0.867452\pi$
$954$	−6.76106	−0.218897
$955$	1.92477	0.0622840
$956$	−68.6231	−2.21943
$957$	−58.5227	−1.89177
$958$	48.1106	1.55438
$959$	48.9200	1.57971
$960$	−7.81371	−0.252186
$961$	52.7601	1.70194
$962$	23.7748	0.766529
$963$	−4.06891	−0.131119
$964$	59.3355	1.91107
$965$	−2.01598	−0.0648968
$966$	57.3209	1.84427
$967$	50.4360	1.62191	0.810956	−	0.585107i	$-0.198947\pi$
$967$	50.4360	1.62191	0.810956	+	0.585107i	$0.198947\pi$
$968$	−62.1704	−1.99823
$969$	0.665959	0.0213937
$970$	12.1836	0.391190
$971$	17.0709	0.547833	0.273916	−	0.961754i	$-0.411681\pi$
$971$	17.0709	0.547833	0.273916	+	0.961754i	$0.411681\pi$
$972$	−22.9697	−0.736755
$973$	−38.3430	−1.22922
$974$	−22.7316	−0.728369
$975$	7.22015	0.231230
$976$	7.11761	0.227829
$977$	−15.0657	−0.481994	−0.240997	−	0.970526i	$-0.577474\pi$
$977$	−15.0657	−0.481994	−0.240997	+	0.970526i	$0.577474\pi$
$978$	19.1325	0.611791
$979$	−53.1406	−1.69838
$980$	−13.1737	−0.420819
$981$	12.4331	0.396958
$982$	12.3844	0.395203
$983$	−14.9776	−0.477711	−0.238855	−	0.971055i	$-0.576772\pi$
$983$	−14.9776	−0.477711	−0.238855	+	0.971055i	$0.576772\pi$
$984$	17.7080	0.564510
$985$	−9.20077	−0.293161
$986$	8.10794	0.258209
$987$	28.4077	0.904228
$988$	−2.22000	−0.0706277
$989$	−31.0554	−0.987504
$990$	4.41895	0.140443
$991$	3.25196	0.103302	0.0516510	−	0.998665i	$-0.483552\pi$
$991$	3.25196	0.103302	0.0516510	+	0.998665i	$0.483552\pi$
$992$	63.1821	2.00603
$993$	32.6585	1.03639
$994$	7.77110	0.246484
$995$	−0.748128	−0.0237173
$996$	49.0907	1.55550
$997$	−3.61380	−0.114450	−0.0572250	−	0.998361i	$-0.518225\pi$
$997$	−3.61380	−0.114450	−0.0572250	+	0.998361i	$0.518225\pi$
$998$	−45.6870	−1.44620
$999$	−60.1837	−1.90413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.14	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.14	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22409 q^{2} -1.49293 q^{3} +2.94657 q^{4} -0.404702 q^{5} +3.32042 q^{6} -4.24821 q^{7} -2.10525 q^{8} -0.771146 q^{9} +O(q^{10})\)	\(q-2.22409 q^{2} -1.49293 q^{3} +2.94657 q^{4} -0.404702 q^{5} +3.32042 q^{6} -4.24821 q^{7} -2.10525 q^{8} -0.771146 q^{9} +0.900094 q^{10} -6.36641 q^{11} -4.39903 q^{12} +1.00000 q^{13} +9.44839 q^{14} +0.604194 q^{15} -1.21088 q^{16} +0.592065 q^{17} +1.71510 q^{18} -0.753420 q^{19} -1.19248 q^{20} +6.34230 q^{21} +14.1595 q^{22} -4.06363 q^{23} +3.14300 q^{24} -4.83622 q^{25} -2.22409 q^{26} +5.63007 q^{27} -12.5176 q^{28} -6.15728 q^{29} -1.34378 q^{30} +9.15205 q^{31} +6.90359 q^{32} +9.50463 q^{33} -1.31680 q^{34} +1.71926 q^{35} -2.27223 q^{36} -10.6897 q^{37} +1.67567 q^{38} -1.49293 q^{39} +0.851999 q^{40} +5.63411 q^{41} -14.1058 q^{42} +7.64228 q^{43} -18.7590 q^{44} +0.312085 q^{45} +9.03787 q^{46} +4.47909 q^{47} +1.80776 q^{48} +11.0473 q^{49} +10.7562 q^{50} -0.883914 q^{51} +2.94657 q^{52} -3.94209 q^{53} -12.5218 q^{54} +2.57650 q^{55} +8.94354 q^{56} +1.12481 q^{57} +13.6943 q^{58} +7.80382 q^{59} +1.78030 q^{60} -5.87806 q^{61} -20.3550 q^{62} +3.27599 q^{63} -12.9324 q^{64} -0.404702 q^{65} -21.1391 q^{66} +4.62948 q^{67} +1.74456 q^{68} +6.06674 q^{69} -3.82379 q^{70} +0.822478 q^{71} +1.62345 q^{72} +9.34079 q^{73} +23.7748 q^{74} +7.22015 q^{75} -2.22000 q^{76} +27.0458 q^{77} +3.32042 q^{78} +14.0183 q^{79} +0.490045 q^{80} -6.09189 q^{81} -12.5308 q^{82} -11.1594 q^{83} +18.6880 q^{84} -0.239610 q^{85} -16.9971 q^{86} +9.19242 q^{87} +13.4029 q^{88} +8.34703 q^{89} -0.694104 q^{90} -4.24821 q^{91} -11.9738 q^{92} -13.6634 q^{93} -9.96188 q^{94} +0.304911 q^{95} -10.3066 q^{96} +13.5359 q^{97} -24.5701 q^{98} +4.90943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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