LMFDB - Embedded newform 6014.2.a.k.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.81353 q^{3} +1.00000 q^{4} +0.592127 q^{5} -1.81353 q^{6} +0.674162 q^{7} +1.00000 q^{8} +0.288888 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.81353 q^{3} +1.00000 q^{4} +0.592127 q^{5} -1.81353 q^{6} +0.674162 q^{7} +1.00000 q^{8} +0.288888 q^{9} +0.592127 q^{10} -0.442381 q^{11} -1.81353 q^{12} +2.82970 q^{13} +0.674162 q^{14} -1.07384 q^{15} +1.00000 q^{16} +7.69704 q^{17} +0.288888 q^{18} -0.604683 q^{19} +0.592127 q^{20} -1.22261 q^{21} -0.442381 q^{22} +4.36648 q^{23} -1.81353 q^{24} -4.64939 q^{25} +2.82970 q^{26} +4.91668 q^{27} +0.674162 q^{28} +0.146897 q^{29} -1.07384 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.802271 q^{33} +7.69704 q^{34} +0.399190 q^{35} +0.288888 q^{36} -1.61773 q^{37} -0.604683 q^{38} -5.13175 q^{39} +0.592127 q^{40} +0.453700 q^{41} -1.22261 q^{42} -2.15706 q^{43} -0.442381 q^{44} +0.171058 q^{45} +4.36648 q^{46} -1.68459 q^{47} -1.81353 q^{48} -6.54551 q^{49} -4.64939 q^{50} -13.9588 q^{51} +2.82970 q^{52} +9.09605 q^{53} +4.91668 q^{54} -0.261946 q^{55} +0.674162 q^{56} +1.09661 q^{57} +0.146897 q^{58} -8.65905 q^{59} -1.07384 q^{60} -11.0927 q^{61} +1.00000 q^{62} +0.194757 q^{63} +1.00000 q^{64} +1.67555 q^{65} +0.802271 q^{66} +3.55752 q^{67} +7.69704 q^{68} -7.91874 q^{69} +0.399190 q^{70} +8.85937 q^{71} +0.288888 q^{72} -9.81044 q^{73} -1.61773 q^{74} +8.43179 q^{75} -0.604683 q^{76} -0.298237 q^{77} -5.13175 q^{78} +8.42911 q^{79} +0.592127 q^{80} -9.78321 q^{81} +0.453700 q^{82} +8.98736 q^{83} -1.22261 q^{84} +4.55763 q^{85} -2.15706 q^{86} -0.266401 q^{87} -0.442381 q^{88} -1.86445 q^{89} +0.171058 q^{90} +1.90768 q^{91} +4.36648 q^{92} -1.81353 q^{93} -1.68459 q^{94} -0.358049 q^{95} -1.81353 q^{96} +1.00000 q^{97} -6.54551 q^{98} -0.127798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.81353	−1.04704	−0.523521	−	0.852013i	$-0.675382\pi$
$3$	−1.81353	−1.04704	−0.523521	+	0.852013i	$0.675382\pi$
$4$	1.00000	0.500000
$5$	0.592127	0.264807	0.132404	−	0.991196i	$-0.457730\pi$
$5$	0.592127	0.264807	0.132404	+	0.991196i	$0.457730\pi$
$6$	−1.81353	−0.740370
$7$	0.674162	0.254809	0.127405	−	0.991851i	$-0.459335\pi$
$7$	0.674162	0.254809	0.127405	+	0.991851i	$0.459335\pi$
$8$	1.00000	0.353553
$9$	0.288888	0.0962959
$10$	0.592127	0.187247
$11$	−0.442381	−0.133383	−0.0666915	−	0.997774i	$-0.521244\pi$
$11$	−0.442381	−0.133383	−0.0666915	+	0.997774i	$0.521244\pi$
$12$	−1.81353	−0.523521
$13$	2.82970	0.784819	0.392409	−	0.919791i	$-0.371642\pi$
$13$	2.82970	0.784819	0.392409	+	0.919791i	$0.371642\pi$
$14$	0.674162	0.180177
$15$	−1.07384	−0.277264
$16$	1.00000	0.250000
$17$	7.69704	1.86681	0.933404	−	0.358828i	$-0.116824\pi$
$17$	7.69704	1.86681	0.933404	+	0.358828i	$0.116824\pi$
$18$	0.288888	0.0680915
$19$	−0.604683	−0.138724	−0.0693618	−	0.997592i	$-0.522096\pi$
$19$	−0.604683	−0.138724	−0.0693618	+	0.997592i	$0.522096\pi$
$20$	0.592127	0.132404
$21$	−1.22261	−0.266796
$22$	−0.442381	−0.0943160
$23$	4.36648	0.910474	0.455237	−	0.890370i	$-0.349555\pi$
$23$	4.36648	0.910474	0.455237	+	0.890370i	$0.349555\pi$
$24$	−1.81353	−0.370185
$25$	−4.64939	−0.929877
$26$	2.82970	0.554951
$27$	4.91668	0.946216
$28$	0.674162	0.127405
$29$	0.146897	0.0272780	0.0136390	−	0.999907i	$-0.495658\pi$
$29$	0.146897	0.0272780	0.0136390	+	0.999907i	$0.495658\pi$
$30$	−1.07384	−0.196056
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	0.802271	0.139658
$34$	7.69704	1.32003
$35$	0.399190	0.0674754
$36$	0.288888	0.0481479
$37$	−1.61773	−0.265954	−0.132977	−	0.991119i	$-0.542454\pi$
$37$	−1.61773	−0.265954	−0.132977	+	0.991119i	$0.542454\pi$
$38$	−0.604683	−0.0980925
$39$	−5.13175	−0.821738
$40$	0.592127	0.0936236
$41$	0.453700	0.0708560	0.0354280	−	0.999372i	$-0.488721\pi$
$41$	0.453700	0.0708560	0.0354280	+	0.999372i	$0.488721\pi$
$42$	−1.22261	−0.188653
$43$	−2.15706	−0.328949	−0.164474	−	0.986381i	$-0.552593\pi$
$43$	−2.15706	−0.328949	−0.164474	+	0.986381i	$0.552593\pi$
$44$	−0.442381	−0.0666915
$45$	0.171058	0.0254999
$46$	4.36648	0.643802
$47$	−1.68459	−0.245722	−0.122861	−	0.992424i	$-0.539207\pi$
$47$	−1.68459	−0.245722	−0.122861	+	0.992424i	$0.539207\pi$
$48$	−1.81353	−0.261760
$49$	−6.54551	−0.935072
$50$	−4.64939	−0.657522
$51$	−13.9588	−1.95462
$52$	2.82970	0.392409
$53$	9.09605	1.24944	0.624719	−	0.780849i	$-0.285213\pi$
$53$	9.09605	1.24944	0.624719	+	0.780849i	$0.285213\pi$
$54$	4.91668	0.669076
$55$	−0.261946	−0.0353208
$56$	0.674162	0.0900887
$57$	1.09661	0.145249
$58$	0.146897	0.0192885
$59$	−8.65905	−1.12731	−0.563656	−	0.826010i	$-0.690606\pi$
$59$	−8.65905	−1.12731	−0.563656	+	0.826010i	$0.690606\pi$
$60$	−1.07384	−0.138632
$61$	−11.0927	−1.42028	−0.710140	−	0.704061i	$-0.751368\pi$
$61$	−11.0927	−1.42028	−0.710140	+	0.704061i	$0.751368\pi$
$62$	1.00000	0.127000
$63$	0.194757	0.0245371
$64$	1.00000	0.125000
$65$	1.67555	0.207826
$66$	0.802271	0.0987528
$67$	3.55752	0.434620	0.217310	−	0.976103i	$-0.430272\pi$
$67$	3.55752	0.434620	0.217310	+	0.976103i	$0.430272\pi$
$68$	7.69704	0.933404
$69$	−7.91874	−0.953304
$70$	0.399190	0.0477123
$71$	8.85937	1.05141	0.525707	−	0.850666i	$-0.323801\pi$
$71$	8.85937	1.05141	0.525707	+	0.850666i	$0.323801\pi$
$72$	0.288888	0.0340457
$73$	−9.81044	−1.14822	−0.574112	−	0.818776i	$-0.694653\pi$
$73$	−9.81044	−1.14822	−0.574112	+	0.818776i	$0.694653\pi$
$74$	−1.61773	−0.188058
$75$	8.43179	0.973620
$76$	−0.604683	−0.0693618
$77$	−0.298237	−0.0339872
$78$	−5.13175	−0.581056
$79$	8.42911	0.948349	0.474175	−	0.880431i	$-0.342747\pi$
$79$	8.42911	0.948349	0.474175	+	0.880431i	$0.342747\pi$
$80$	0.592127	0.0662019
$81$	−9.78321	−1.08702
$82$	0.453700	0.0501028
$83$	8.98736	0.986491	0.493245	−	0.869890i	$-0.335811\pi$
$83$	8.98736	0.986491	0.493245	+	0.869890i	$0.335811\pi$
$84$	−1.22261	−0.133398
$85$	4.55763	0.494344
$86$	−2.15706	−0.232602
$87$	−0.266401	−0.0285612
$88$	−0.442381	−0.0471580
$89$	−1.86445	−0.197632	−0.0988159	−	0.995106i	$-0.531505\pi$
$89$	−1.86445	−0.197632	−0.0988159	+	0.995106i	$0.531505\pi$
$90$	0.171058	0.0180311
$91$	1.90768	0.199979
$92$	4.36648	0.455237
$93$	−1.81353	−0.188054
$94$	−1.68459	−0.173752
$95$	−0.358049	−0.0367351
$96$	−1.81353	−0.185093
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−6.54551	−0.661196
$99$	−0.127798	−0.0128442
$100$	−4.64939	−0.464939
$101$	11.1112	1.10561	0.552803	−	0.833312i	$-0.313558\pi$
$101$	11.1112	1.10561	0.552803	+	0.833312i	$0.313558\pi$
$102$	−13.9588	−1.38213
$103$	9.64908	0.950752	0.475376	−	0.879783i	$-0.342312\pi$
$103$	9.64908	0.950752	0.475376	+	0.879783i	$0.342312\pi$
$104$	2.82970	0.277475
$105$	−0.723942	−0.0706496
$106$	9.09605	0.883486
$107$	20.1361	1.94663	0.973317	−	0.229464i	$-0.0736973\pi$
$107$	20.1361	1.94663	0.973317	+	0.229464i	$0.0736973\pi$
$108$	4.91668	0.473108
$109$	−5.40298	−0.517511	−0.258756	−	0.965943i	$-0.583312\pi$
$109$	−5.40298	−0.517511	−0.258756	+	0.965943i	$0.583312\pi$
$110$	−0.261946	−0.0249756
$111$	2.93381	0.278465
$112$	0.674162	0.0637023
$113$	16.6022	1.56181	0.780904	−	0.624652i	$-0.214759\pi$
$113$	16.6022	1.56181	0.780904	+	0.624652i	$0.214759\pi$
$114$	1.09661	0.102707
$115$	2.58551	0.241100
$116$	0.146897	0.0136390
$117$	0.817466	0.0755748
$118$	−8.65905	−0.797130
$119$	5.18906	0.475680
$120$	−1.07384	−0.0980278
$121$	−10.8043	−0.982209
$122$	−11.0927	−1.00429
$123$	−0.822798	−0.0741892
$124$	1.00000	0.0898027
$125$	−5.71367	−0.511046
$126$	0.194757	0.0173503
$127$	2.31954	0.205826	0.102913	−	0.994690i	$-0.467184\pi$
$127$	2.31954	0.205826	0.102913	+	0.994690i	$0.467184\pi$
$128$	1.00000	0.0883883
$129$	3.91189	0.344423
$130$	1.67555	0.146955
$131$	2.29586	0.200590	0.100295	−	0.994958i	$-0.468021\pi$
$131$	2.29586	0.200590	0.100295	+	0.994958i	$0.468021\pi$
$132$	0.802271	0.0698288
$133$	−0.407654	−0.0353481
$134$	3.55752	0.307323
$135$	2.91130	0.250565
$136$	7.69704	0.660016
$137$	−3.14691	−0.268858	−0.134429	−	0.990923i	$-0.542920\pi$
$137$	−3.14691	−0.268858	−0.134429	+	0.990923i	$0.542920\pi$
$138$	−7.91874	−0.674088
$139$	13.3522	1.13252	0.566258	−	0.824228i	$-0.308391\pi$
$139$	13.3522	1.13252	0.566258	+	0.824228i	$0.308391\pi$
$140$	0.399190	0.0337377
$141$	3.05505	0.257282
$142$	8.85937	0.743462
$143$	−1.25181	−0.104681
$144$	0.288888	0.0240740
$145$	0.0869815	0.00722342
$146$	−9.81044	−0.811918
$147$	11.8705	0.979059
$148$	−1.61773	−0.132977
$149$	−16.9934	−1.39215	−0.696076	−	0.717968i	$-0.745072\pi$
$149$	−16.9934	−1.39215	−0.696076	+	0.717968i	$0.745072\pi$
$150$	8.43179	0.688453
$151$	23.3337	1.89887	0.949433	−	0.313970i	$-0.101659\pi$
$151$	23.3337	1.89887	0.949433	+	0.313970i	$0.101659\pi$
$152$	−0.604683	−0.0490462
$153$	2.22358	0.179766
$154$	−0.298237	−0.0240326
$155$	0.592127	0.0475608
$156$	−5.13175	−0.410869
$157$	5.74938	0.458850	0.229425	−	0.973326i	$-0.426315\pi$
$157$	5.74938	0.458850	0.229425	+	0.973326i	$0.426315\pi$
$158$	8.42911	0.670584
$159$	−16.4959	−1.30821
$160$	0.592127	0.0468118
$161$	2.94372	0.231997
$162$	−9.78321	−0.768641
$163$	−1.75879	−0.137759	−0.0688796	−	0.997625i	$-0.521942\pi$
$163$	−1.75879	−0.137759	−0.0688796	+	0.997625i	$0.521942\pi$
$164$	0.453700	0.0354280
$165$	0.475047	0.0369823
$166$	8.98736	0.697554
$167$	−16.4218	−1.27076	−0.635380	−	0.772200i	$-0.719156\pi$
$167$	−16.4218	−1.27076	−0.635380	+	0.772200i	$0.719156\pi$
$168$	−1.22261	−0.0943266
$169$	−4.99277	−0.384060
$170$	4.55763	0.349554
$171$	−0.174685	−0.0133585
$172$	−2.15706	−0.164474
$173$	7.54614	0.573722	0.286861	−	0.957972i	$-0.407388\pi$
$173$	7.54614	0.573722	0.286861	+	0.957972i	$0.407388\pi$
$174$	−0.266401	−0.0201958
$175$	−3.13444	−0.236941
$176$	−0.442381	−0.0333457
$177$	15.7034	1.18034
$178$	−1.86445	−0.139747
$179$	9.82020	0.733996	0.366998	−	0.930222i	$-0.380386\pi$
$179$	9.82020	0.733996	0.366998	+	0.930222i	$0.380386\pi$
$180$	0.171058	0.0127499
$181$	−1.11775	−0.0830814	−0.0415407	−	0.999137i	$-0.513227\pi$
$181$	−1.11775	−0.0830814	−0.0415407	+	0.999137i	$0.513227\pi$
$182$	1.90768	0.141407
$183$	20.1170	1.48709
$184$	4.36648	0.321901
$185$	−0.957905	−0.0704266
$186$	−1.81353	−0.132974
$187$	−3.40503	−0.249000
$188$	−1.68459	−0.122861
$189$	3.31464	0.241105
$190$	−0.358049	−0.0259756
$191$	−26.5038	−1.91775	−0.958873	−	0.283837i	$-0.908393\pi$
$191$	−26.5038	−1.91775	−0.958873	+	0.283837i	$0.908393\pi$
$192$	−1.81353	−0.130880
$193$	15.5999	1.12290	0.561451	−	0.827510i	$-0.310243\pi$
$193$	15.5999	1.12290	0.561451	+	0.827510i	$0.310243\pi$
$194$	1.00000	0.0717958
$195$	−3.03865	−0.217602
$196$	−6.54551	−0.467536
$197$	−2.53285	−0.180458	−0.0902289	−	0.995921i	$-0.528760\pi$
$197$	−2.53285	−0.180458	−0.0902289	+	0.995921i	$0.528760\pi$
$198$	−0.127798	−0.00908224
$199$	−18.0791	−1.28160	−0.640798	−	0.767709i	$-0.721397\pi$
$199$	−18.0791	−1.28160	−0.640798	+	0.767709i	$0.721397\pi$
$200$	−4.64939	−0.328761
$201$	−6.45167	−0.455066
$202$	11.1112	0.781782
$203$	0.0990322	0.00695070
$204$	−13.9588	−0.977312
$205$	0.268648	0.0187632
$206$	9.64908	0.672283
$207$	1.26142	0.0876749
$208$	2.82970	0.196205
$209$	0.267500	0.0185034
$210$	−0.723942	−0.0499568
$211$	8.12334	0.559234	0.279617	−	0.960112i	$-0.409793\pi$
$211$	8.12334	0.559234	0.279617	+	0.960112i	$0.409793\pi$
$212$	9.09605	0.624719
$213$	−16.0667	−1.10087
$214$	20.1361	1.37648
$215$	−1.27726	−0.0871081
$216$	4.91668	0.334538
$217$	0.674162	0.0457651
$218$	−5.40298	−0.365936
$219$	17.7915	1.20224
$220$	−0.261946	−0.0176604
$221$	21.7804	1.46511
$222$	2.93381	0.196904
$223$	12.6215	0.845195	0.422597	−	0.906317i	$-0.361118\pi$
$223$	12.6215	0.845195	0.422597	+	0.906317i	$0.361118\pi$
$224$	0.674162	0.0450444
$225$	−1.34315	−0.0895433
$226$	16.6022	1.10436
$227$	20.4829	1.35950	0.679749	−	0.733445i	$-0.262089\pi$
$227$	20.4829	1.35950	0.679749	+	0.733445i	$0.262089\pi$
$228$	1.09661	0.0726247
$229$	5.90706	0.390350	0.195175	−	0.980768i	$-0.437473\pi$
$229$	5.90706	0.390350	0.195175	+	0.980768i	$0.437473\pi$
$230$	2.58551	0.170484
$231$	0.540861	0.0355860
$232$	0.146897	0.00964424
$233$	10.2844	0.673751	0.336875	−	0.941549i	$-0.390630\pi$
$233$	10.2844	0.673751	0.336875	+	0.941549i	$0.390630\pi$
$234$	0.817466	0.0534394
$235$	−0.997491	−0.0650691
$236$	−8.65905	−0.563656
$237$	−15.2864	−0.992961
$238$	5.18906	0.336357
$239$	−4.80807	−0.311008	−0.155504	−	0.987835i	$-0.549700\pi$
$239$	−4.80807	−0.311008	−0.155504	+	0.987835i	$0.549700\pi$
$240$	−1.07384	−0.0693161
$241$	−24.5739	−1.58295	−0.791473	−	0.611204i	$-0.790686\pi$
$241$	−24.5739	−1.58295	−0.791473	+	0.611204i	$0.790686\pi$
$242$	−10.8043	−0.694527
$243$	2.99209	0.191942
$244$	−11.0927	−0.710140
$245$	−3.87577	−0.247614
$246$	−0.822798	−0.0524597
$247$	−1.71107	−0.108873
$248$	1.00000	0.0635001
$249$	−16.2988	−1.03290
$250$	−5.71367	−0.361364
$251$	12.3349	0.778570	0.389285	−	0.921117i	$-0.372722\pi$
$251$	12.3349	0.778570	0.389285	+	0.921117i	$0.372722\pi$
$252$	0.194757	0.0122685
$253$	−1.93165	−0.121442
$254$	2.31954	0.145541
$255$	−8.26539	−0.517599
$256$	1.00000	0.0625000
$257$	9.85933	0.615008	0.307504	−	0.951547i	$-0.400506\pi$
$257$	9.85933	0.615008	0.307504	+	0.951547i	$0.400506\pi$
$258$	3.91189	0.243544
$259$	−1.09062	−0.0677675
$260$	1.67555	0.103913
$261$	0.0424366	0.00262676
$262$	2.29586	0.141838
$263$	5.31497	0.327735	0.163867	−	0.986482i	$-0.447603\pi$
$263$	5.31497	0.327735	0.163867	+	0.986482i	$0.447603\pi$
$264$	0.802271	0.0493764
$265$	5.38602	0.330861
$266$	−0.407654	−0.0249949
$267$	3.38124	0.206929
$268$	3.55752	0.217310
$269$	8.43185	0.514099	0.257050	−	0.966398i	$-0.417250\pi$
$269$	8.43185	0.514099	0.257050	+	0.966398i	$0.417250\pi$
$270$	2.91130	0.177176
$271$	4.24266	0.257723	0.128862	−	0.991663i	$-0.458868\pi$
$271$	4.24266	0.257723	0.128862	+	0.991663i	$0.458868\pi$
$272$	7.69704	0.466702
$273$	−3.45963	−0.209386
$274$	−3.14691	−0.190112
$275$	2.05680	0.124030
$276$	−7.91874	−0.476652
$277$	−3.74947	−0.225284	−0.112642	−	0.993636i	$-0.535931\pi$
$277$	−3.74947	−0.225284	−0.112642	+	0.993636i	$0.535931\pi$
$278$	13.3522	0.800810
$279$	0.288888	0.0172952
$280$	0.399190	0.0238562
$281$	12.5329	0.747649	0.373824	−	0.927500i	$-0.378046\pi$
$281$	12.5329	0.747649	0.373824	+	0.927500i	$0.378046\pi$
$282$	3.05505	0.181926
$283$	26.9836	1.60401	0.802003	−	0.597320i	$-0.203768\pi$
$283$	26.9836	1.60401	0.802003	+	0.597320i	$0.203768\pi$
$284$	8.85937	0.525707
$285$	0.649332	0.0384631
$286$	−1.25181	−0.0740210
$287$	0.305867	0.0180548
$288$	0.288888	0.0170229
$289$	42.2445	2.48497
$290$	0.0869815	0.00510773
$291$	−1.81353	−0.106311
$292$	−9.81044	−0.574112
$293$	27.6592	1.61587	0.807935	−	0.589272i	$-0.200585\pi$
$293$	27.6592	1.61587	0.807935	+	0.589272i	$0.200585\pi$
$294$	11.8705	0.692300
$295$	−5.12726	−0.298521
$296$	−1.61773	−0.0940289
$297$	−2.17505	−0.126209
$298$	−16.9934	−0.984401
$299$	12.3558	0.714557
$300$	8.43179	0.486810
$301$	−1.45421	−0.0838192
$302$	23.3337	1.34270
$303$	−20.1505	−1.15762
$304$	−0.604683	−0.0346809
$305$	−6.56832	−0.376101
$306$	2.22358	0.127114
$307$	0.342286	0.0195353	0.00976766	−	0.999952i	$-0.496891\pi$
$307$	0.342286	0.0195353	0.00976766	+	0.999952i	$0.496891\pi$
$308$	−0.298237	−0.0169936
$309$	−17.4989	−0.995476
$310$	0.592127	0.0336306
$311$	−18.9135	−1.07248	−0.536242	−	0.844064i	$-0.680156\pi$
$311$	−18.9135	−1.07248	−0.536242	+	0.844064i	$0.680156\pi$
$312$	−5.13175	−0.290528
$313$	20.5936	1.16402	0.582009	−	0.813183i	$-0.302267\pi$
$313$	20.5936	1.16402	0.582009	+	0.813183i	$0.302267\pi$
$314$	5.74938	0.324456
$315$	0.115321	0.00649760
$316$	8.42911	0.474175
$317$	13.0711	0.734147	0.367073	−	0.930192i	$-0.380360\pi$
$317$	13.0711	0.734147	0.367073	+	0.930192i	$0.380360\pi$
$318$	−16.4959	−0.925047
$319$	−0.0649843	−0.00363842
$320$	0.592127	0.0331009
$321$	−36.5175	−2.03821
$322$	2.94372	0.164047
$323$	−4.65427	−0.258970
$324$	−9.78321	−0.543511
$325$	−13.1564	−0.729785
$326$	−1.75879	−0.0974104
$327$	9.79846	0.541856
$328$	0.453700	0.0250514
$329$	−1.13569	−0.0626124
$330$	0.475047	0.0261505
$331$	−18.1123	−0.995544	−0.497772	−	0.867308i	$-0.665848\pi$
$331$	−18.1123	−0.995544	−0.497772	+	0.867308i	$0.665848\pi$
$332$	8.98736	0.493245
$333$	−0.467343	−0.0256103
$334$	−16.4218	−0.898562
$335$	2.10651	0.115091
$336$	−1.22261	−0.0666990
$337$	−6.48620	−0.353326	−0.176663	−	0.984271i	$-0.556530\pi$
$337$	−6.48620	−0.353326	−0.176663	+	0.984271i	$0.556530\pi$
$338$	−4.99277	−0.271571
$339$	−30.1086	−1.63528
$340$	4.55763	0.247172
$341$	−0.442381	−0.0239563
$342$	−0.174685	−0.00944590
$343$	−9.13187	−0.493075
$344$	−2.15706	−0.116301
$345$	−4.68890	−0.252442
$346$	7.54614	0.405683
$347$	−26.7324	−1.43507	−0.717535	−	0.696522i	$-0.754730\pi$
$347$	−26.7324	−1.43507	−0.717535	+	0.696522i	$0.754730\pi$
$348$	−0.266401	−0.0142806
$349$	−0.457625	−0.0244961	−0.0122481	−	0.999925i	$-0.503899\pi$
$349$	−0.457625	−0.0244961	−0.0122481	+	0.999925i	$0.503899\pi$
$350$	−3.13444	−0.167543
$351$	13.9128	0.742608
$352$	−0.442381	−0.0235790
$353$	24.2481	1.29060	0.645298	−	0.763931i	$-0.276733\pi$
$353$	24.2481	1.29060	0.645298	+	0.763931i	$0.276733\pi$
$354$	15.7034	0.834628
$355$	5.24588	0.278422
$356$	−1.86445	−0.0988159
$357$	−9.41050	−0.498057
$358$	9.82020	0.519014
$359$	3.53304	0.186467	0.0932335	−	0.995644i	$-0.470280\pi$
$359$	3.53304	0.186467	0.0932335	+	0.995644i	$0.470280\pi$
$360$	0.171058	0.00901556
$361$	−18.6344	−0.980756
$362$	−1.11775	−0.0587474
$363$	19.5939	1.02841
$364$	1.90768	0.0999896
$365$	−5.80903	−0.304058
$366$	20.1170	1.05153
$367$	18.4077	0.960873	0.480437	−	0.877029i	$-0.340478\pi$
$367$	18.4077	0.960873	0.480437	+	0.877029i	$0.340478\pi$
$368$	4.36648	0.227619
$369$	0.131068	0.00682314
$370$	−0.957905	−0.0497991
$371$	6.13221	0.318369
$372$	−1.81353	−0.0940271
$373$	14.3586	0.743463	0.371731	−	0.928340i	$-0.378764\pi$
$373$	14.3586	0.743463	0.371731	+	0.928340i	$0.378764\pi$
$374$	−3.40503	−0.176070
$375$	10.3619	0.535086
$376$	−1.68459	−0.0868760
$377$	0.415674	0.0214083
$378$	3.31464	0.170487
$379$	18.0750	0.928452	0.464226	−	0.885717i	$-0.346333\pi$
$379$	18.0750	0.928452	0.464226	+	0.885717i	$0.346333\pi$
$380$	−0.358049	−0.0183675
$381$	−4.20655	−0.215508
$382$	−26.5038	−1.35605
$383$	5.76679	0.294669	0.147335	−	0.989087i	$-0.452931\pi$
$383$	5.76679	0.294669	0.147335	+	0.989087i	$0.452931\pi$
$384$	−1.81353	−0.0925463
$385$	−0.176594	−0.00900007
$386$	15.5999	0.794012
$387$	−0.623148	−0.0316764
$388$	1.00000	0.0507673
$389$	−17.9862	−0.911938	−0.455969	−	0.889996i	$-0.650707\pi$
$389$	−17.9862	−0.911938	−0.455969	+	0.889996i	$0.650707\pi$
$390$	−3.03865	−0.153868
$391$	33.6090	1.69968
$392$	−6.54551	−0.330598
$393$	−4.16360	−0.210026
$394$	−2.53285	−0.127603
$395$	4.99111	0.251130
$396$	−0.127798	−0.00642211
$397$	4.07717	0.204627	0.102314	−	0.994752i	$-0.467375\pi$
$397$	4.07717	0.204627	0.102314	+	0.994752i	$0.467375\pi$
$398$	−18.0791	−0.906226
$399$	0.739293	0.0370109
$400$	−4.64939	−0.232469
$401$	−4.52991	−0.226213	−0.113106	−	0.993583i	$-0.536080\pi$
$401$	−4.52991	−0.226213	−0.113106	+	0.993583i	$0.536080\pi$
$402$	−6.45167	−0.321780
$403$	2.82970	0.140958
$404$	11.1112	0.552803
$405$	−5.79290	−0.287852
$406$	0.0990322	0.00491488
$407$	0.715655	0.0354737
$408$	−13.9588	−0.691064
$409$	−25.8820	−1.27978	−0.639892	−	0.768465i	$-0.721021\pi$
$409$	−25.8820	−1.27978	−0.639892	+	0.768465i	$0.721021\pi$
$410$	0.268648	0.0132676
$411$	5.70701	0.281506
$412$	9.64908	0.475376
$413$	−5.83760	−0.287250
$414$	1.26142	0.0619955
$415$	5.32166	0.261230
$416$	2.82970	0.138738
$417$	−24.2145	−1.18579
$418$	0.267500	0.0130839
$419$	−19.1182	−0.933987	−0.466993	−	0.884261i	$-0.654663\pi$
$419$	−19.1182	−0.933987	−0.466993	+	0.884261i	$0.654663\pi$
$420$	−0.723942	−0.0353248
$421$	30.3434	1.47885	0.739423	−	0.673241i	$-0.235098\pi$
$421$	30.3434	1.47885	0.739423	+	0.673241i	$0.235098\pi$
$422$	8.12334	0.395438
$423$	−0.486657	−0.0236621
$424$	9.09605	0.441743
$425$	−35.7865	−1.73590
$426$	−16.0667	−0.778436
$427$	−7.47831	−0.361901
$428$	20.1361	0.973317
$429$	2.27019	0.109606
$430$	−1.27726	−0.0615947
$431$	−8.54513	−0.411604	−0.205802	−	0.978594i	$-0.565980\pi$
$431$	−8.54513	−0.411604	−0.205802	+	0.978594i	$0.565980\pi$
$432$	4.91668	0.236554
$433$	−16.2785	−0.782297	−0.391148	−	0.920328i	$-0.627922\pi$
$433$	−16.2785	−0.782297	−0.391148	+	0.920328i	$0.627922\pi$
$434$	0.674162	0.0323608
$435$	−0.157744	−0.00756322
$436$	−5.40298	−0.258756
$437$	−2.64033	−0.126304
$438$	17.7915	0.850111
$439$	22.3894	1.06859	0.534294	−	0.845299i	$-0.320578\pi$
$439$	22.3894	1.06859	0.534294	+	0.845299i	$0.320578\pi$
$440$	−0.261946	−0.0124878
$441$	−1.89092	−0.0900436
$442$	21.7804	1.03599
$443$	−4.54099	−0.215749	−0.107875	−	0.994165i	$-0.534404\pi$
$443$	−4.54099	−0.215749	−0.107875	+	0.994165i	$0.534404\pi$
$444$	2.93381	0.139232
$445$	−1.10399	−0.0523344
$446$	12.6215	0.597643
$447$	30.8180	1.45764
$448$	0.674162	0.0318512
$449$	−12.7726	−0.602778	−0.301389	−	0.953501i	$-0.597450\pi$
$449$	−12.7726	−0.602778	−0.301389	+	0.953501i	$0.597450\pi$
$450$	−1.34315	−0.0633167
$451$	−0.200708	−0.00945099
$452$	16.6022	0.780904
$453$	−42.3163	−1.98819
$454$	20.4829	0.961310
$455$	1.12959	0.0529560
$456$	1.09661	0.0513534
$457$	14.9328	0.698527	0.349264	−	0.937025i	$-0.386432\pi$
$457$	14.9328	0.698527	0.349264	+	0.937025i	$0.386432\pi$
$458$	5.90706	0.276019
$459$	37.8439	1.76640
$460$	2.58551	0.120550
$461$	14.2531	0.663834	0.331917	−	0.943309i	$-0.392305\pi$
$461$	14.2531	0.663834	0.331917	+	0.943309i	$0.392305\pi$
$462$	0.540861	0.0251631
$463$	−5.39155	−0.250566	−0.125283	−	0.992121i	$-0.539984\pi$
$463$	−5.39155	−0.250566	−0.125283	+	0.992121i	$0.539984\pi$
$464$	0.146897	0.00681951
$465$	−1.07384	−0.0497981
$466$	10.2844	0.476414
$467$	−25.0520	−1.15927	−0.579635	−	0.814876i	$-0.696805\pi$
$467$	−25.0520	−1.15927	−0.579635	+	0.814876i	$0.696805\pi$
$468$	0.817466	0.0377874
$469$	2.39835	0.110745
$470$	−0.997491	−0.0460108
$471$	−10.4267	−0.480435
$472$	−8.65905	−0.398565
$473$	0.954244	0.0438762
$474$	−15.2864	−0.702129
$475$	2.81140	0.128996
$476$	5.18906	0.237840
$477$	2.62774	0.120316
$478$	−4.80807	−0.219916
$479$	7.93891	0.362738	0.181369	−	0.983415i	$-0.441947\pi$
$479$	7.93891	0.362738	0.181369	+	0.983415i	$0.441947\pi$
$480$	−1.07384	−0.0490139
$481$	−4.57771	−0.208726
$482$	−24.5739	−1.11931
$483$	−5.33851	−0.242911
$484$	−10.8043	−0.491104
$485$	0.592127	0.0268871
$486$	2.99209	0.135724
$487$	36.3983	1.64936	0.824681	−	0.565598i	$-0.191355\pi$
$487$	36.3983	1.64936	0.824681	+	0.565598i	$0.191355\pi$
$488$	−11.0927	−0.502145
$489$	3.18962	0.144240
$490$	−3.87577	−0.175090
$491$	31.0908	1.40311	0.701554	−	0.712616i	$-0.252490\pi$
$491$	31.0908	1.40311	0.701554	+	0.712616i	$0.252490\pi$
$492$	−0.822798	−0.0370946
$493$	1.13067	0.0509228
$494$	−1.71107	−0.0769848
$495$	−0.0756730	−0.00340125
$496$	1.00000	0.0449013
$497$	5.97266	0.267910
$498$	−16.2988	−0.730368
$499$	−7.89425	−0.353395	−0.176698	−	0.984265i	$-0.556541\pi$
$499$	−7.89425	−0.353395	−0.176698	+	0.984265i	$0.556541\pi$
$500$	−5.71367	−0.255523
$501$	29.7815	1.33054
$502$	12.3349	0.550532
$503$	12.4081	0.553249	0.276625	−	0.960978i	$-0.410784\pi$
$503$	12.4081	0.553249	0.276625	+	0.960978i	$0.410784\pi$
$504$	0.194757	0.00867517
$505$	6.57925	0.292773
$506$	−1.93165	−0.0858723
$507$	9.05454	0.402126
$508$	2.31954	0.102913
$509$	−36.2510	−1.60680	−0.803399	−	0.595441i	$-0.796977\pi$
$509$	−36.2510	−1.60680	−0.803399	+	0.595441i	$0.796977\pi$
$510$	−8.26539	−0.365998
$511$	−6.61383	−0.292578
$512$	1.00000	0.0441942
$513$	−2.97303	−0.131263
$514$	9.85933	0.434877
$515$	5.71348	0.251766
$516$	3.91189	0.172212
$517$	0.745230	0.0327752
$518$	−1.09062	−0.0479189
$519$	−13.6851	−0.600711
$520$	1.67555	0.0734775
$521$	−41.7271	−1.82810	−0.914048	−	0.405605i	$-0.867061\pi$
$521$	−41.7271	−1.82810	−0.914048	+	0.405605i	$0.867061\pi$
$522$	0.0424366	0.00185740
$523$	−30.1677	−1.31914	−0.659571	−	0.751642i	$-0.729262\pi$
$523$	−30.1677	−1.31914	−0.659571	+	0.751642i	$0.729262\pi$
$524$	2.29586	0.100295
$525$	5.68440	0.248087
$526$	5.31497	0.231744
$527$	7.69704	0.335288
$528$	0.802271	0.0349144
$529$	−3.93385	−0.171037
$530$	5.38602	0.233954
$531$	−2.50149	−0.108555
$532$	−0.407654	−0.0176740
$533$	1.28384	0.0556091
$534$	3.38124	0.146321
$535$	11.9232	0.515483
$536$	3.55752	0.153662
$537$	−17.8092	−0.768524
$538$	8.43185	0.363523
$539$	2.89561	0.124723
$540$	2.91130	0.125282
$541$	−6.06734	−0.260855	−0.130428	−	0.991458i	$-0.541635\pi$
$541$	−6.06734	−0.260855	−0.130428	+	0.991458i	$0.541635\pi$
$542$	4.24266	0.182238
$543$	2.02706	0.0869896
$544$	7.69704	0.330008
$545$	−3.19925	−0.137041
$546$	−3.45963	−0.148059
$547$	−10.1274	−0.433014	−0.216507	−	0.976281i	$-0.569466\pi$
$547$	−10.1274	−0.433014	−0.216507	+	0.976281i	$0.569466\pi$
$548$	−3.14691	−0.134429
$549$	−3.20455	−0.136767
$550$	2.05680	0.0877023
$551$	−0.0888259	−0.00378411
$552$	−7.91874	−0.337044
$553$	5.68259	0.241648
$554$	−3.74947	−0.159300
$555$	1.73719	0.0737395
$556$	13.3522	0.566258
$557$	−32.3435	−1.37044	−0.685219	−	0.728337i	$-0.740294\pi$
$557$	−32.3435	−1.37044	−0.685219	+	0.728337i	$0.740294\pi$
$558$	0.288888	0.0122296
$559$	−6.10385	−0.258165
$560$	0.399190	0.0168689
$561$	6.17512	0.260714
$562$	12.5329	0.528667
$563$	11.0958	0.467634	0.233817	−	0.972281i	$-0.424878\pi$
$563$	11.0958	0.467634	0.233817	+	0.972281i	$0.424878\pi$
$564$	3.05505	0.128641
$565$	9.83064	0.413578
$566$	26.9836	1.13420
$567$	−6.59547	−0.276984
$568$	8.85937	0.371731
$569$	31.5023	1.32065	0.660323	−	0.750982i	$-0.270419\pi$
$569$	31.5023	1.32065	0.660323	+	0.750982i	$0.270419\pi$
$570$	0.649332	0.0271975
$571$	8.88074	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$571$	8.88074	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$572$	−1.25181	−0.0523407
$573$	48.0653	2.00796
$574$	0.305867	0.0127667
$575$	−20.3014	−0.846629
$576$	0.288888	0.0120370
$577$	−23.4797	−0.977472	−0.488736	−	0.872432i	$-0.662542\pi$
$577$	−23.4797	−0.977472	−0.488736	+	0.872432i	$0.662542\pi$
$578$	42.2445	1.75714
$579$	−28.2908	−1.17573
$580$	0.0869815	0.00361171
$581$	6.05894	0.251367
$582$	−1.81353	−0.0751732
$583$	−4.02392	−0.166654
$584$	−9.81044	−0.405959
$585$	0.484044	0.0200128
$586$	27.6592	1.14259
$587$	10.4101	0.429672	0.214836	−	0.976650i	$-0.431078\pi$
$587$	10.4101	0.429672	0.214836	+	0.976650i	$0.431078\pi$
$588$	11.8705	0.489530
$589$	−0.604683	−0.0249155
$590$	−5.12726	−0.211086
$591$	4.59339	0.188947
$592$	−1.61773	−0.0664885
$593$	−15.9403	−0.654591	−0.327296	−	0.944922i	$-0.606137\pi$
$593$	−15.9403	−0.654591	−0.327296	+	0.944922i	$0.606137\pi$
$594$	−2.17505	−0.0892433
$595$	3.07258	0.125964
$596$	−16.9934	−0.696076
$597$	32.7871	1.34189
$598$	12.3558	0.505268
$599$	−2.30417	−0.0941457	−0.0470729	−	0.998891i	$-0.514989\pi$
$599$	−2.30417	−0.0941457	−0.0470729	+	0.998891i	$0.514989\pi$
$600$	8.43179	0.344227
$601$	−6.47266	−0.264025	−0.132013	−	0.991248i	$-0.542144\pi$
$601$	−6.47266	−0.264025	−0.132013	+	0.991248i	$0.542144\pi$
$602$	−1.45421	−0.0592691
$603$	1.02772	0.0418521
$604$	23.3337	0.949433
$605$	−6.39752	−0.260096
$606$	−20.1505	−0.818558
$607$	18.2316	0.739999	0.369999	−	0.929032i	$-0.379358\pi$
$607$	18.2316	0.739999	0.369999	+	0.929032i	$0.379358\pi$
$608$	−0.604683	−0.0245231
$609$	−0.179598	−0.00727767
$610$	−6.56832	−0.265943
$611$	−4.76689	−0.192848
$612$	2.22358	0.0898829
$613$	0.596170	0.0240791	0.0120395	−	0.999928i	$-0.496168\pi$
$613$	0.596170	0.0240791	0.0120395	+	0.999928i	$0.496168\pi$
$614$	0.342286	0.0138136
$615$	−0.487201	−0.0196459
$616$	−0.298237	−0.0120163
$617$	24.9677	1.00516	0.502581	−	0.864530i	$-0.332384\pi$
$617$	24.9677	1.00516	0.502581	+	0.864530i	$0.332384\pi$
$618$	−17.4989	−0.703908
$619$	39.9422	1.60541	0.802707	−	0.596374i	$-0.203392\pi$
$619$	39.9422	1.60541	0.802707	+	0.596374i	$0.203392\pi$
$620$	0.592127	0.0237804
$621$	21.4686	0.861505
$622$	−18.9135	−0.758360
$623$	−1.25694	−0.0503584
$624$	−5.13175	−0.205434
$625$	19.8637	0.794548
$626$	20.5936	0.823085
$627$	−0.485119	−0.0193738
$628$	5.74938	0.229425
$629$	−12.4518	−0.496485
$630$	0.115321	0.00459450
$631$	−8.96183	−0.356765	−0.178382	−	0.983961i	$-0.557086\pi$
$631$	−8.96183	−0.356765	−0.178382	+	0.983961i	$0.557086\pi$
$632$	8.42911	0.335292
$633$	−14.7319	−0.585541
$634$	13.0711	0.519120
$635$	1.37346	0.0545042
$636$	−16.4959	−0.654107
$637$	−18.5218	−0.733862
$638$	−0.0649843	−0.00257275
$639$	2.55936	0.101247
$640$	0.592127	0.0234059
$641$	4.16169	0.164377	0.0821884	−	0.996617i	$-0.473809\pi$
$641$	4.16169	0.164377	0.0821884	+	0.996617i	$0.473809\pi$
$642$	−36.5175	−1.44123
$643$	21.4731	0.846816	0.423408	−	0.905939i	$-0.360834\pi$
$643$	21.4731	0.846816	0.423408	+	0.905939i	$0.360834\pi$
$644$	2.94372	0.115999
$645$	2.31634	0.0912058
$646$	−4.65427	−0.183120
$647$	−24.2231	−0.952308	−0.476154	−	0.879362i	$-0.657970\pi$
$647$	−24.2231	−0.952308	−0.476154	+	0.879362i	$0.657970\pi$
$648$	−9.78321	−0.384321
$649$	3.83060	0.150364
$650$	−13.1564	−0.516036
$651$	−1.22261	−0.0479180
$652$	−1.75879	−0.0688796
$653$	−29.2458	−1.14448	−0.572239	−	0.820087i	$-0.693925\pi$
$653$	−29.2458	−1.14448	−0.572239	+	0.820087i	$0.693925\pi$
$654$	9.79846	0.383150
$655$	1.35944	0.0531177
$656$	0.453700	0.0177140
$657$	−2.83411	−0.110569
$658$	−1.13569	−0.0442736
$659$	−27.6365	−1.07657	−0.538283	−	0.842764i	$-0.680927\pi$
$659$	−27.6365	−1.07657	−0.538283	+	0.842764i	$0.680927\pi$
$660$	0.475047	0.0184912
$661$	−15.7618	−0.613062	−0.306531	−	0.951861i	$-0.599168\pi$
$661$	−15.7618	−0.613062	−0.306531	+	0.951861i	$0.599168\pi$
$662$	−18.1123	−0.703956
$663$	−39.4993	−1.53403
$664$	8.98736	0.348777
$665$	−0.241383	−0.00936044
$666$	−0.467343	−0.0181092
$667$	0.641421	0.0248359
$668$	−16.4218	−0.635380
$669$	−22.8894	−0.884954
$670$	2.10651	0.0813814
$671$	4.90722	0.189441
$672$	−1.22261	−0.0471633
$673$	−21.3324	−0.822304	−0.411152	−	0.911567i	$-0.634873\pi$
$673$	−21.3324	−0.822304	−0.411152	+	0.911567i	$0.634873\pi$
$674$	−6.48620	−0.249839
$675$	−22.8595	−0.879864
$676$	−4.99277	−0.192030
$677$	−20.0622	−0.771054	−0.385527	−	0.922697i	$-0.625980\pi$
$677$	−20.0622	−0.771054	−0.385527	+	0.922697i	$0.625980\pi$
$678$	−30.1086	−1.15632
$679$	0.674162	0.0258720
$680$	4.55763	0.174777
$681$	−37.1463	−1.42345
$682$	−0.442381	−0.0169397
$683$	2.61175	0.0999358	0.0499679	−	0.998751i	$-0.484088\pi$
$683$	2.61175	0.0999358	0.0499679	+	0.998751i	$0.484088\pi$
$684$	−0.174685	−0.00667926
$685$	−1.86337	−0.0711957
$686$	−9.13187	−0.348656
$687$	−10.7126	−0.408712
$688$	−2.15706	−0.0822372
$689$	25.7391	0.980583
$690$	−4.68890	−0.178503
$691$	8.28906	0.315331	0.157665	−	0.987493i	$-0.449603\pi$
$691$	8.28906	0.315331	0.157665	+	0.987493i	$0.449603\pi$
$692$	7.54614	0.286861
$693$	−0.0861569	−0.00327283
$694$	−26.7324	−1.01475
$695$	7.90618	0.299899
$696$	−0.266401	−0.0100979
$697$	3.49215	0.132275
$698$	−0.457625	−0.0173214
$699$	−18.6510	−0.705445
$700$	−3.13444	−0.118471
$701$	−37.9850	−1.43467	−0.717336	−	0.696727i	$-0.754639\pi$
$701$	−37.9850	−1.43467	−0.717336	+	0.696727i	$0.754639\pi$
$702$	13.9128	0.525103
$703$	0.978216	0.0368941
$704$	−0.442381	−0.0166729
$705$	1.80898	0.0681301
$706$	24.2481	0.912590
$707$	7.49076	0.281719
$708$	15.7034	0.590171
$709$	−22.1780	−0.832913	−0.416456	−	0.909156i	$-0.636728\pi$
$709$	−22.1780	−0.832913	−0.416456	+	0.909156i	$0.636728\pi$
$710$	5.24588	0.196874
$711$	2.43507	0.0913221
$712$	−1.86445	−0.0698734
$713$	4.36648	0.163526
$714$	−9.41050	−0.352179
$715$	−0.741230	−0.0277204
$716$	9.82020	0.366998
$717$	8.71958	0.325639
$718$	3.53304	0.131852
$719$	−2.57930	−0.0961917	−0.0480958	−	0.998843i	$-0.515315\pi$
$719$	−2.57930	−0.0961917	−0.0480958	+	0.998843i	$0.515315\pi$
$720$	0.171058	0.00637496
$721$	6.50504	0.242260
$722$	−18.6344	−0.693499
$723$	44.5655	1.65741
$724$	−1.11775	−0.0415407
$725$	−0.682979	−0.0253652
$726$	19.5939	0.727198
$727$	−36.8647	−1.36723	−0.683617	−	0.729841i	$-0.739594\pi$
$727$	−36.8647	−1.36723	−0.683617	+	0.729841i	$0.739594\pi$
$728$	1.90768	0.0707033
$729$	23.9234	0.886051
$730$	−5.80903	−0.215002
$731$	−16.6030	−0.614084
$732$	20.1170	0.743546
$733$	−4.61503	−0.170460	−0.0852301	−	0.996361i	$-0.527163\pi$
$733$	−4.61503	−0.170460	−0.0852301	+	0.996361i	$0.527163\pi$
$734$	18.4077	0.679440
$735$	7.02883	0.259262
$736$	4.36648	0.160951
$737$	−1.57378	−0.0579710
$738$	0.131068	0.00482469
$739$	17.1592	0.631211	0.315605	−	0.948891i	$-0.397792\pi$
$739$	17.1592	0.631211	0.315605	+	0.948891i	$0.397792\pi$
$740$	−0.957905	−0.0352133
$741$	3.10308	0.113994
$742$	6.13221	0.225121
$743$	10.3788	0.380763	0.190381	−	0.981710i	$-0.439028\pi$
$743$	10.3788	0.380763	0.190381	+	0.981710i	$0.439028\pi$
$744$	−1.81353	−0.0664872
$745$	−10.0623	−0.368652
$746$	14.3586	0.525707
$747$	2.59634	0.0949949
$748$	−3.40503	−0.124500
$749$	13.5750	0.496021
$750$	10.3619	0.378363
$751$	8.91370	0.325265	0.162633	−	0.986687i	$-0.448001\pi$
$751$	8.91370	0.325265	0.162633	+	0.986687i	$0.448001\pi$
$752$	−1.68459	−0.0614306
$753$	−22.3696	−0.815195
$754$	0.415674	0.0151380
$755$	13.8165	0.502834
$756$	3.31464	0.120552
$757$	−54.6167	−1.98508	−0.992539	−	0.121927i	$-0.961092\pi$
$757$	−54.6167	−1.98508	−0.992539	+	0.121927i	$0.961092\pi$
$758$	18.0750	0.656515
$759$	3.50310	0.127155
$760$	−0.358049	−0.0129878
$761$	−48.0582	−1.74211	−0.871055	−	0.491186i	$-0.836563\pi$
$761$	−48.0582	−1.74211	−0.871055	+	0.491186i	$0.836563\pi$
$762$	−4.20655	−0.152387
$763$	−3.64248	−0.131867
$764$	−26.5038	−0.958873
$765$	1.31664	0.0476033
$766$	5.76679	0.208362
$767$	−24.5025	−0.884736
$768$	−1.81353	−0.0654401
$769$	34.4839	1.24352	0.621761	−	0.783207i	$-0.286418\pi$
$769$	34.4839	1.24352	0.621761	+	0.783207i	$0.286418\pi$
$770$	−0.176594	−0.00636401
$771$	−17.8802	−0.643939
$772$	15.5999	0.561451
$773$	39.6046	1.42448	0.712240	−	0.701936i	$-0.247681\pi$
$773$	39.6046	1.42448	0.712240	+	0.701936i	$0.247681\pi$
$774$	−0.623148	−0.0223986
$775$	−4.64939	−0.167011
$776$	1.00000	0.0358979
$777$	1.97786	0.0709554
$778$	−17.9862	−0.644838
$779$	−0.274344	−0.00982941
$780$	−3.03865	−0.108801
$781$	−3.91922	−0.140241
$782$	33.6090	1.20186
$783$	0.722244	0.0258109
$784$	−6.54551	−0.233768
$785$	3.40436	0.121507
$786$	−4.16360	−0.148511
$787$	11.5790	0.412745	0.206373	−	0.978473i	$-0.433834\pi$
$787$	11.5790	0.412745	0.206373	+	0.978473i	$0.433834\pi$
$788$	−2.53285	−0.0902289
$789$	−9.63884	−0.343152
$790$	4.99111	0.177576
$791$	11.1926	0.397963
$792$	−0.127798	−0.00454112
$793$	−31.3892	−1.11466
$794$	4.07717	0.144693
$795$	−9.76770	−0.346425
$796$	−18.0791	−0.640798
$797$	7.42283	0.262930	0.131465	−	0.991321i	$-0.458032\pi$
$797$	7.42283	0.262930	0.131465	+	0.991321i	$0.458032\pi$
$798$	0.739293	0.0261707
$799$	−12.9664	−0.458717
$800$	−4.64939	−0.164381
$801$	−0.538618	−0.0190311
$802$	−4.52991	−0.159957
$803$	4.33995	0.153154
$804$	−6.45167	−0.227533
$805$	1.74305	0.0614346
$806$	2.82970	0.0996721
$807$	−15.2914	−0.538283
$808$	11.1112	0.390891
$809$	−55.9231	−1.96615	−0.983076	−	0.183196i	$-0.941356\pi$
$809$	−55.9231	−1.96615	−0.983076	+	0.183196i	$0.941356\pi$
$810$	−5.79290	−0.203542
$811$	−18.2340	−0.640284	−0.320142	−	0.947370i	$-0.603731\pi$
$811$	−18.2340	−0.640284	−0.320142	+	0.947370i	$0.603731\pi$
$812$	0.0990322	0.00347535
$813$	−7.69419	−0.269847
$814$	0.715655	0.0250837
$815$	−1.04143	−0.0364796
$816$	−13.9588	−0.488656
$817$	1.30434	0.0456330
$818$	−25.8820	−0.904944
$819$	0.551105	0.0192572
$820$	0.268648	0.00938160
$821$	18.0815	0.631050	0.315525	−	0.948917i	$-0.397819\pi$
$821$	18.0815	0.631050	0.315525	+	0.948917i	$0.397819\pi$
$822$	5.70701	0.199055
$823$	42.0518	1.46583	0.732917	−	0.680318i	$-0.238158\pi$
$823$	42.0518	1.46583	0.732917	+	0.680318i	$0.238158\pi$
$824$	9.64908	0.336141
$825$	−3.73007	−0.129864
$826$	−5.83760	−0.203116
$827$	−29.3356	−1.02010	−0.510049	−	0.860145i	$-0.670373\pi$
$827$	−29.3356	−1.02010	−0.510049	+	0.860145i	$0.670373\pi$
$828$	1.26142	0.0438374
$829$	26.1766	0.909153	0.454576	−	0.890708i	$-0.349791\pi$
$829$	26.1766	0.909153	0.454576	+	0.890708i	$0.349791\pi$
$830$	5.32166	0.184718
$831$	6.79978	0.235882
$832$	2.82970	0.0981023
$833$	−50.3810	−1.74560
$834$	−24.2145	−0.838481
$835$	−9.72381	−0.336506
$836$	0.267500	0.00925169
$837$	4.91668	0.169945
$838$	−19.1182	−0.660428
$839$	−22.8172	−0.787738	−0.393869	−	0.919167i	$-0.628864\pi$
$839$	−22.8172	−0.787738	−0.393869	+	0.919167i	$0.628864\pi$
$840$	−0.723942	−0.0249784
$841$	−28.9784	−0.999256
$842$	30.3434	1.04570
$843$	−22.7287	−0.782819
$844$	8.12334	0.279617
$845$	−2.95636	−0.101702
$846$	−0.486657	−0.0167316
$847$	−7.28385	−0.250276
$848$	9.09605	0.312360
$849$	−48.9355	−1.67946
$850$	−35.7865	−1.22747
$851$	−7.06380	−0.242144
$852$	−16.0667	−0.550437
$853$	6.76309	0.231564	0.115782	−	0.993275i	$-0.463063\pi$
$853$	6.76309	0.231564	0.115782	+	0.993275i	$0.463063\pi$
$854$	−7.47831	−0.255902
$855$	−0.103436	−0.00353743
$856$	20.1361	0.688239
$857$	51.0118	1.74253	0.871264	−	0.490814i	$-0.163301\pi$
$857$	51.0118	1.74253	0.871264	+	0.490814i	$0.163301\pi$
$858$	2.27019	0.0775030
$859$	41.5255	1.41683	0.708415	−	0.705796i	$-0.249410\pi$
$859$	41.5255	1.41683	0.708415	+	0.705796i	$0.249410\pi$
$860$	−1.27726	−0.0435540
$861$	−0.554699	−0.0189041
$862$	−8.54513	−0.291048
$863$	10.9776	0.373683	0.186841	−	0.982390i	$-0.440175\pi$
$863$	10.9776	0.373683	0.186841	+	0.982390i	$0.440175\pi$
$864$	4.91668	0.167269
$865$	4.46827	0.151926
$866$	−16.2785	−0.553167
$867$	−76.6116	−2.60187
$868$	0.674162	0.0228826
$869$	−3.72888	−0.126494
$870$	−0.157744	−0.00534801
$871$	10.0667	0.341098
$872$	−5.40298	−0.182968
$873$	0.288888	0.00977736
$874$	−2.64033	−0.0893106
$875$	−3.85194	−0.130219
$876$	17.7915	0.601120
$877$	−3.35091	−0.113152	−0.0565762	−	0.998398i	$-0.518018\pi$
$877$	−3.35091	−0.113152	−0.0565762	+	0.998398i	$0.518018\pi$
$878$	22.3894	0.755606
$879$	−50.1608	−1.69188
$880$	−0.261946	−0.00883020
$881$	31.7716	1.07041	0.535207	−	0.844721i	$-0.320234\pi$
$881$	31.7716	1.07041	0.535207	+	0.844721i	$0.320234\pi$
$882$	−1.89092	−0.0636704
$883$	9.12965	0.307237	0.153619	−	0.988130i	$-0.450907\pi$
$883$	9.12965	0.307237	0.153619	+	0.988130i	$0.450907\pi$
$884$	21.7804	0.732553
$885$	9.29843	0.312563
$886$	−4.54099	−0.152558
$887$	−48.5148	−1.62897	−0.814484	−	0.580186i	$-0.802980\pi$
$887$	−48.5148	−1.62897	−0.814484	+	0.580186i	$0.802980\pi$
$888$	2.93381	0.0984521
$889$	1.56374	0.0524463
$890$	−1.10399	−0.0370060
$891$	4.32791	0.144990
$892$	12.6215	0.422597
$893$	1.01864	0.0340875
$894$	30.8180	1.03071
$895$	5.81481	0.194368
$896$	0.674162	0.0225222
$897$	−22.4077	−0.748171
$898$	−12.7726	−0.426229
$899$	0.146897	0.00489928
$900$	−1.34315	−0.0447717
$901$	70.0127	2.33246
$902$	−0.200708	−0.00668286
$903$	2.63725	0.0877622
$904$	16.6022	0.552182
$905$	−0.661848	−0.0220006
$906$	−42.3163	−1.40586
$907$	11.5224	0.382596	0.191298	−	0.981532i	$-0.438730\pi$
$907$	11.5224	0.382596	0.191298	+	0.981532i	$0.438730\pi$
$908$	20.4829	0.679749
$909$	3.20989	0.106465
$910$	1.12959	0.0374455
$911$	−43.0509	−1.42634	−0.713170	−	0.700991i	$-0.752741\pi$
$911$	−43.0509	−1.42634	−0.713170	+	0.700991i	$0.752741\pi$
$912$	1.09661	0.0363124
$913$	−3.97584	−0.131581
$914$	14.9328	0.493933
$915$	11.9118	0.393793
$916$	5.90706	0.195175
$917$	1.54778	0.0511122
$918$	37.8439	1.24904
$919$	−2.10558	−0.0694568	−0.0347284	−	0.999397i	$-0.511057\pi$
$919$	−2.10558	−0.0694568	−0.0347284	+	0.999397i	$0.511057\pi$
$920$	2.58551	0.0852418
$921$	−0.620746	−0.0204543
$922$	14.2531	0.469402
$923$	25.0694	0.825170
$924$	0.540861	0.0177930
$925$	7.52147	0.247304
$926$	−5.39155	−0.177177
$927$	2.78750	0.0915534
$928$	0.146897	0.00482212
$929$	−3.11331	−0.102144	−0.0510722	−	0.998695i	$-0.516264\pi$
$929$	−3.11331	−0.102144	−0.0510722	+	0.998695i	$0.516264\pi$
$930$	−1.07384	−0.0352126
$931$	3.95795	0.129717
$932$	10.2844	0.336875
$933$	34.3001	1.12293
$934$	−25.0520	−0.819728
$935$	−2.01621	−0.0659371
$936$	0.817466	0.0267197
$937$	−23.8100	−0.777839	−0.388920	−	0.921272i	$-0.627152\pi$
$937$	−23.8100	−0.777839	−0.388920	+	0.921272i	$0.627152\pi$
$938$	2.39835	0.0783088
$939$	−37.3470	−1.21877
$940$	−0.997491	−0.0325346
$941$	1.08396	0.0353361	0.0176681	−	0.999844i	$-0.494376\pi$
$941$	1.08396	0.0353361	0.0176681	+	0.999844i	$0.494376\pi$
$942$	−10.4267	−0.339719
$943$	1.98107	0.0645126
$944$	−8.65905	−0.281828
$945$	1.96269	0.0638463
$946$	0.954244	0.0310251
$947$	−25.6064	−0.832098	−0.416049	−	0.909342i	$-0.636585\pi$
$947$	−25.6064	−0.832098	−0.416049	+	0.909342i	$0.636585\pi$
$948$	−15.2864	−0.496480
$949$	−27.7606	−0.901148
$950$	2.81140	0.0912139
$951$	−23.7048	−0.768682
$952$	5.18906	0.168178
$953$	4.65565	0.150811	0.0754056	−	0.997153i	$-0.475975\pi$
$953$	4.65565	0.150811	0.0754056	+	0.997153i	$0.475975\pi$
$954$	2.62774	0.0850761
$955$	−15.6936	−0.507833
$956$	−4.80807	−0.155504
$957$	0.117851	0.00380958
$958$	7.93891	0.256494
$959$	−2.12153	−0.0685076
$960$	−1.07384	−0.0346580
$961$	1.00000	0.0322581
$962$	−4.57771	−0.147591
$963$	5.81708	0.187453
$964$	−24.5739	−0.791473
$965$	9.23710	0.297353
$966$	−5.33851	−0.171764
$967$	−48.5535	−1.56137	−0.780687	−	0.624922i	$-0.785131\pi$
$967$	−48.5535	−1.56137	−0.780687	+	0.624922i	$0.785131\pi$
$968$	−10.8043	−0.347263
$969$	8.44065	0.271153
$970$	0.592127	0.0190121
$971$	36.2822	1.16435	0.582176	−	0.813063i	$-0.302201\pi$
$971$	36.2822	1.16435	0.582176	+	0.813063i	$0.302201\pi$
$972$	2.99209	0.0959712
$973$	9.00152	0.288576
$974$	36.3983	1.16628
$975$	23.8595	0.764115
$976$	−11.0927	−0.355070
$977$	32.5888	1.04261	0.521304	−	0.853371i	$-0.325446\pi$
$977$	32.5888	1.04261	0.521304	+	0.853371i	$0.325446\pi$
$978$	3.18962	0.101993
$979$	0.824800	0.0263607
$980$	−3.87577	−0.123807
$981$	−1.56085	−0.0498342
$982$	31.0908	0.992148
$983$	−48.9756	−1.56208	−0.781039	−	0.624483i	$-0.785310\pi$
$983$	−48.9756	−1.56208	−0.781039	+	0.624483i	$0.785310\pi$
$984$	−0.822798	−0.0262298
$985$	−1.49977	−0.0477866
$986$	1.13067	0.0360079
$987$	2.05960	0.0655578
$988$	−1.71107	−0.0544365
$989$	−9.41877	−0.299499
$990$	−0.0756730	−0.00240504
$991$	−28.2045	−0.895944	−0.447972	−	0.894048i	$-0.647854\pi$
$991$	−28.2045	−0.895944	−0.447972	+	0.894048i	$0.647854\pi$
$992$	1.00000	0.0317500
$993$	32.8472	1.04238
$994$	5.97266	0.189441
$995$	−10.7052	−0.339376
$996$	−16.2988	−0.516448
$997$	28.5349	0.903710	0.451855	−	0.892092i	$-0.350763\pi$
$997$	28.5349	0.903710	0.451855	+	0.892092i	$0.350763\pi$
$998$	−7.89425	−0.249888
$999$	−7.95388	−0.251650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.10	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.81353 q^{3} +1.00000 q^{4} +0.592127 q^{5} -1.81353 q^{6} +0.674162 q^{7} +1.00000 q^{8} +0.288888 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.81353 q^{3} +1.00000 q^{4} +0.592127 q^{5} -1.81353 q^{6} +0.674162 q^{7} +1.00000 q^{8} +0.288888 q^{9} +0.592127 q^{10} -0.442381 q^{11} -1.81353 q^{12} +2.82970 q^{13} +0.674162 q^{14} -1.07384 q^{15} +1.00000 q^{16} +7.69704 q^{17} +0.288888 q^{18} -0.604683 q^{19} +0.592127 q^{20} -1.22261 q^{21} -0.442381 q^{22} +4.36648 q^{23} -1.81353 q^{24} -4.64939 q^{25} +2.82970 q^{26} +4.91668 q^{27} +0.674162 q^{28} +0.146897 q^{29} -1.07384 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.802271 q^{33} +7.69704 q^{34} +0.399190 q^{35} +0.288888 q^{36} -1.61773 q^{37} -0.604683 q^{38} -5.13175 q^{39} +0.592127 q^{40} +0.453700 q^{41} -1.22261 q^{42} -2.15706 q^{43} -0.442381 q^{44} +0.171058 q^{45} +4.36648 q^{46} -1.68459 q^{47} -1.81353 q^{48} -6.54551 q^{49} -4.64939 q^{50} -13.9588 q^{51} +2.82970 q^{52} +9.09605 q^{53} +4.91668 q^{54} -0.261946 q^{55} +0.674162 q^{56} +1.09661 q^{57} +0.146897 q^{58} -8.65905 q^{59} -1.07384 q^{60} -11.0927 q^{61} +1.00000 q^{62} +0.194757 q^{63} +1.00000 q^{64} +1.67555 q^{65} +0.802271 q^{66} +3.55752 q^{67} +7.69704 q^{68} -7.91874 q^{69} +0.399190 q^{70} +8.85937 q^{71} +0.288888 q^{72} -9.81044 q^{73} -1.61773 q^{74} +8.43179 q^{75} -0.604683 q^{76} -0.298237 q^{77} -5.13175 q^{78} +8.42911 q^{79} +0.592127 q^{80} -9.78321 q^{81} +0.453700 q^{82} +8.98736 q^{83} -1.22261 q^{84} +4.55763 q^{85} -2.15706 q^{86} -0.266401 q^{87} -0.442381 q^{88} -1.86445 q^{89} +0.171058 q^{90} +1.90768 q^{91} +4.36648 q^{92} -1.81353 q^{93} -1.68459 q^{94} -0.358049 q^{95} -1.81353 q^{96} +1.00000 q^{97} -6.54551 q^{98} -0.127798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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