LMFDB - Embedded newform 201.4.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 3 x^{10} - 74 x^{9} + 208 x^{8} + 1913 x^{7} - 4831 x^{6} - 20432 x^{5} + 42994 x^{4} + \cdots + 3072 $ x^11 - 3x^10 - 74x^9 + 208x^8 + 1913x^7 - 4831x^6 - 20432x^5 + 42994x^4 + 79648x^3 - 112288x^2 - 85440x + 3072
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$4.59496$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.59496 q^{2} +3.00000 q^{3} +13.1136 q^{4} +11.7140 q^{5} +13.7849 q^{6} +4.20913 q^{7} +23.4970 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.59496 q^{2} +3.00000 q^{3} +13.1136 q^{4} +11.7140 q^{5} +13.7849 q^{6} +4.20913 q^{7} +23.4970 q^{8} +9.00000 q^{9} +53.8252 q^{10} -65.7556 q^{11} +39.3409 q^{12} +41.4029 q^{13} +19.3408 q^{14} +35.1419 q^{15} +3.05858 q^{16} -33.7977 q^{17} +41.3546 q^{18} -31.8147 q^{19} +153.613 q^{20} +12.6274 q^{21} -302.144 q^{22} +46.7383 q^{23} +70.4910 q^{24} +12.2171 q^{25} +190.245 q^{26} +27.0000 q^{27} +55.1970 q^{28} -58.6320 q^{29} +161.476 q^{30} +233.534 q^{31} -173.922 q^{32} -197.267 q^{33} -155.299 q^{34} +49.3056 q^{35} +118.023 q^{36} -271.466 q^{37} -146.187 q^{38} +124.209 q^{39} +275.243 q^{40} +234.725 q^{41} +58.0223 q^{42} +342.187 q^{43} -862.296 q^{44} +105.426 q^{45} +214.761 q^{46} +280.259 q^{47} +9.17575 q^{48} -325.283 q^{49} +56.1369 q^{50} -101.393 q^{51} +542.943 q^{52} -607.347 q^{53} +124.064 q^{54} -770.260 q^{55} +98.9018 q^{56} -95.4441 q^{57} -269.411 q^{58} +298.421 q^{59} +460.839 q^{60} -541.678 q^{61} +1073.08 q^{62} +37.8821 q^{63} -823.633 q^{64} +484.992 q^{65} -906.433 q^{66} +67.0000 q^{67} -443.211 q^{68} +140.215 q^{69} +226.557 q^{70} -533.451 q^{71} +211.473 q^{72} +114.983 q^{73} -1247.37 q^{74} +36.6512 q^{75} -417.207 q^{76} -276.774 q^{77} +570.734 q^{78} +164.085 q^{79} +35.8281 q^{80} +81.0000 q^{81} +1078.55 q^{82} +177.313 q^{83} +165.591 q^{84} -395.905 q^{85} +1572.33 q^{86} -175.896 q^{87} -1545.06 q^{88} -190.697 q^{89} +484.427 q^{90} +174.270 q^{91} +612.910 q^{92} +700.602 q^{93} +1287.78 q^{94} -372.676 q^{95} -521.766 q^{96} +1608.03 q^{97} -1494.66 q^{98} -591.801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) $ 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * 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 $

$2$	4.59496	1.62456	0.812282	−	0.583265i	$-0.198225\pi$
$2$	4.59496	1.62456	0.812282	+	0.583265i	$0.198225\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	13.1136	1.63921
$5$	11.7140	1.04773	0.523865	−	0.851802i	$-0.324490\pi$
$5$	11.7140	1.04773	0.523865	+	0.851802i	$0.324490\pi$
$6$	13.7849	0.937942
$7$	4.20913	0.227271	0.113636	−	0.993522i	$-0.463750\pi$
$7$	4.20913	0.227271	0.113636	+	0.993522i	$0.463750\pi$
$8$	23.4970	1.03843
$9$	9.00000	0.333333
$10$	53.8252	1.70210
$11$	−65.7556	−1.80237	−0.901185	−	0.433435i	$-0.857302\pi$
$11$	−65.7556	−1.80237	−0.901185	+	0.433435i	$0.857302\pi$
$12$	39.3409	0.946396
$13$	41.4029	0.883315	0.441657	−	0.897184i	$-0.354391\pi$
$13$	41.4029	0.883315	0.441657	+	0.897184i	$0.354391\pi$
$14$	19.3408	0.369217
$15$	35.1419	0.604907
$16$	3.05858	0.0477903
$17$	−33.7977	−0.482185	−0.241093	−	0.970502i	$-0.577506\pi$
$17$	−33.7977	−0.482185	−0.241093	+	0.970502i	$0.577506\pi$
$18$	41.3546	0.541521
$19$	−31.8147	−0.384147	−0.192073	−	0.981381i	$-0.561521\pi$
$19$	−31.8147	−0.384147	−0.192073	+	0.981381i	$0.561521\pi$
$20$	153.613	1.71744
$21$	12.6274	0.131215
$22$	−302.144	−2.92806
$23$	46.7383	0.423723	0.211861	−	0.977300i	$-0.432047\pi$
$23$	46.7383	0.423723	0.211861	+	0.977300i	$0.432047\pi$
$24$	70.4910	0.599538
$25$	12.2171	0.0977366
$26$	190.245	1.43500
$27$	27.0000	0.192450
$28$	55.1970	0.372545
$29$	−58.6320	−0.375437	−0.187719	−	0.982223i	$-0.560109\pi$
$29$	−58.6320	−0.375437	−0.187719	+	0.982223i	$0.560109\pi$
$30$	161.476	0.982709
$31$	233.534	1.35303	0.676515	−	0.736428i	$-0.263489\pi$
$31$	233.534	1.35303	0.676515	+	0.736428i	$0.263489\pi$
$32$	−173.922	−0.960792
$33$	−197.267	−1.04060
$34$	−155.299	−0.783340
$35$	49.3056	0.238119
$36$	118.023	0.546402
$37$	−271.466	−1.20618	−0.603090	−	0.797673i	$-0.706064\pi$
$37$	−271.466	−1.20618	−0.603090	+	0.797673i	$0.706064\pi$
$38$	−146.187	−0.624071
$39$	124.209	0.509982
$40$	275.243	1.08799
$41$	234.725	0.894095	0.447048	−	0.894510i	$-0.352475\pi$
$41$	234.725	0.894095	0.447048	+	0.894510i	$0.352475\pi$
$42$	58.0223	0.213167
$43$	342.187	1.21356	0.606779	−	0.794870i	$-0.292461\pi$
$43$	342.187	1.21356	0.606779	+	0.794870i	$0.292461\pi$
$44$	−862.296	−2.95446
$45$	105.426	0.349243
$46$	214.761	0.688364
$47$	280.259	0.869787	0.434894	−	0.900482i	$-0.356786\pi$
$47$	280.259	0.869787	0.434894	+	0.900482i	$0.356786\pi$
$48$	9.17575	0.0275918
$49$	−325.283	−0.948348
$50$	56.1369	0.158779
$51$	−101.393	−0.278390
$52$	542.943	1.44794
$53$	−607.347	−1.57407	−0.787033	−	0.616911i	$-0.788384\pi$
$53$	−607.347	−1.57407	−0.787033	+	0.616911i	$0.788384\pi$
$54$	124.064	0.312647
$55$	−770.260	−1.88840
$56$	98.9018	0.236006
$57$	−95.4441	−0.221787
$58$	−269.411	−0.609922
$59$	298.421	0.658493	0.329246	−	0.944244i	$-0.393205\pi$
$59$	298.421	0.658493	0.329246	+	0.944244i	$0.393205\pi$
$60$	460.839	0.991567
$61$	−541.678	−1.13696	−0.568482	−	0.822696i	$-0.692469\pi$
$61$	−541.678	−1.13696	−0.568482	+	0.822696i	$0.692469\pi$
$62$	1073.08	2.19808
$63$	37.8821	0.0757571
$64$	−823.633	−1.60866
$65$	484.992	0.925475
$66$	−906.433	−1.69052
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	−443.211	−0.790401
$69$	140.215	0.244636
$70$	226.557	0.386839
$71$	−533.451	−0.891676	−0.445838	−	0.895114i	$-0.647094\pi$
$71$	−533.451	−0.891676	−0.445838	+	0.895114i	$0.647094\pi$
$72$	211.473	0.346144
$73$	114.983	0.184352	0.0921762	−	0.995743i	$-0.470618\pi$
$73$	114.983	0.184352	0.0921762	+	0.995743i	$0.470618\pi$
$74$	−1247.37	−1.95952
$75$	36.6512	0.0564282
$76$	−417.207	−0.629696
$77$	−276.774	−0.409627
$78$	570.734	0.828498
$79$	164.085	0.233684	0.116842	−	0.993151i	$-0.462723\pi$
$79$	164.085	0.233684	0.116842	+	0.993151i	$0.462723\pi$
$80$	35.8281	0.0500713
$81$	81.0000	0.111111
$82$	1078.55	1.45251
$83$	177.313	0.234490	0.117245	−	0.993103i	$-0.462594\pi$
$83$	177.313	0.234490	0.117245	+	0.993103i	$0.462594\pi$
$84$	165.591	0.215089
$85$	−395.905	−0.505199
$86$	1572.33	1.97150
$87$	−175.896	−0.216759
$88$	−1545.06	−1.87164
$89$	−190.697	−0.227122	−0.113561	−	0.993531i	$-0.536226\pi$
$89$	−190.697	−0.227122	−0.113561	+	0.993531i	$0.536226\pi$
$90$	484.427	0.567368
$91$	174.270	0.200752
$92$	612.910	0.694569
$93$	700.602	0.781173
$94$	1287.78	1.41302
$95$	−372.676	−0.402482
$96$	−521.766	−0.554714
$97$	1608.03	1.68320	0.841600	−	0.540101i	$-0.181614\pi$
$97$	1608.03	1.68320	0.841600	+	0.540101i	$0.181614\pi$
$98$	−1494.66	−1.54065
$99$	−591.801	−0.600790
$100$	160.210	0.160210
$101$	−273.261	−0.269213	−0.134606	−	0.990899i	$-0.542977\pi$
$101$	−273.261	−0.269213	−0.134606	+	0.990899i	$0.542977\pi$
$102$	−465.897	−0.452262
$103$	1656.25	1.58442	0.792209	−	0.610249i	$-0.208931\pi$
$103$	1656.25	1.58442	0.792209	+	0.610249i	$0.208931\pi$
$104$	972.844	0.917261
$105$	147.917	0.137478
$106$	−2790.73	−2.55717
$107$	525.740	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$107$	525.740	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$108$	354.068	0.315465
$109$	−1583.91	−1.39184	−0.695922	−	0.718118i	$-0.745004\pi$
$109$	−1583.91	−1.39184	−0.695922	+	0.718118i	$0.745004\pi$
$110$	−3539.31	−3.06782
$111$	−814.397	−0.696388
$112$	12.8740	0.0108614
$113$	212.091	0.176565	0.0882824	−	0.996095i	$-0.471862\pi$
$113$	212.091	0.176565	0.0882824	+	0.996095i	$0.471862\pi$
$114$	−438.562	−0.360308
$115$	547.492	0.443947
$116$	−768.879	−0.615419
$117$	372.626	0.294438
$118$	1371.23	1.06976
$119$	−142.259	−0.109587
$120$	825.730	0.628154
$121$	2992.80	2.24854
$122$	−2488.99	−1.84707
$123$	704.175	0.516206
$124$	3062.48	2.21790
$125$	−1321.14	−0.945328
$126$	174.067	0.123072
$127$	−338.637	−0.236608	−0.118304	−	0.992977i	$-0.537746\pi$
$127$	−338.637	−0.236608	−0.118304	+	0.992977i	$0.537746\pi$
$128$	−2393.18	−1.65257
$129$	1026.56	0.700648
$130$	2228.52	1.50349
$131$	−674.823	−0.450073	−0.225037	−	0.974350i	$-0.572250\pi$
$131$	−674.823	−0.450073	−0.225037	+	0.974350i	$0.572250\pi$
$132$	−2586.89	−1.70576
$133$	−133.912	−0.0873056
$134$	307.862	0.198472
$135$	316.277	0.201636
$136$	−794.145	−0.500716
$137$	−274.010	−0.170878	−0.0854389	−	0.996343i	$-0.527229\pi$
$137$	−274.010	−0.170878	−0.0854389	+	0.996343i	$0.527229\pi$
$138$	644.282	0.397427
$139$	1633.95	0.997051	0.498525	−	0.866875i	$-0.333875\pi$
$139$	1633.95	0.997051	0.498525	+	0.866875i	$0.333875\pi$
$140$	646.576	0.390326
$141$	840.777	0.502172
$142$	−2451.18	−1.44858
$143$	−2722.47	−1.59206
$144$	27.5272	0.0159301
$145$	−686.813	−0.393357
$146$	528.342	0.299492
$147$	−975.850	−0.547529
$148$	−3559.90	−1.97718
$149$	−1704.94	−0.937412	−0.468706	−	0.883354i	$-0.655280\pi$
$149$	−1704.94	−0.937412	−0.468706	+	0.883354i	$0.655280\pi$
$150$	168.411	0.0916713
$151$	2473.01	1.33278	0.666392	−	0.745602i	$-0.267838\pi$
$151$	2473.01	1.33278	0.666392	+	0.745602i	$0.267838\pi$
$152$	−747.550	−0.398910
$153$	−304.179	−0.160728
$154$	−1271.76	−0.665465
$155$	2735.61	1.41761
$156$	1628.83	0.835966
$157$	3105.52	1.57865	0.789323	−	0.613979i	$-0.210432\pi$
$157$	3105.52	1.57865	0.789323	+	0.613979i	$0.210432\pi$
$158$	753.965	0.379634
$159$	−1822.04	−0.908788
$160$	−2037.32	−1.00665
$161$	196.728	0.0963000
$162$	372.192	0.180507
$163$	90.0916	0.0432915	0.0216458	−	0.999766i	$-0.493109\pi$
$163$	90.0916	0.0432915	0.0216458	+	0.999766i	$0.493109\pi$
$164$	3078.10	1.46561
$165$	−2310.78	−1.09027
$166$	814.746	0.380943
$167$	−1458.11	−0.675641	−0.337821	−	0.941211i	$-0.609690\pi$
$167$	−1458.11	−0.675641	−0.337821	+	0.941211i	$0.609690\pi$
$168$	296.706	0.136258
$169$	−482.801	−0.219755
$170$	−1819.17	−0.820728
$171$	−286.332	−0.128049
$172$	4487.32	1.98927
$173$	3427.13	1.50613	0.753063	−	0.657949i	$-0.228576\pi$
$173$	3427.13	1.50613	0.753063	+	0.657949i	$0.228576\pi$
$174$	−808.234	−0.352138
$175$	51.4232	0.0222127
$176$	−201.119	−0.0861359
$177$	895.263	0.380181
$178$	−876.247	−0.368975
$179$	−195.986	−0.0818362	−0.0409181	−	0.999163i	$-0.513028\pi$
$179$	−195.986	−0.0818362	−0.0409181	+	0.999163i	$0.513028\pi$
$180$	1382.52	0.572481
$181$	−1772.48	−0.727888	−0.363944	−	0.931421i	$-0.618570\pi$
$181$	−1772.48	−0.727888	−0.363944	+	0.931421i	$0.618570\pi$
$182$	800.763	0.326135
$183$	−1625.03	−0.656426
$184$	1098.21	0.440007
$185$	−3179.94	−1.26375
$186$	3219.24	1.26906
$187$	2222.39	0.869076
$188$	3675.22	1.42576
$189$	113.646	0.0437384
$190$	−1712.43	−0.653858
$191$	−484.239	−0.183447	−0.0917234	−	0.995785i	$-0.529238\pi$
$191$	−484.239	−0.183447	−0.0917234	+	0.995785i	$0.529238\pi$
$192$	−2470.90	−0.928759
$193$	3088.49	1.15189	0.575945	−	0.817489i	$-0.304634\pi$
$193$	3088.49	1.15189	0.575945	+	0.817489i	$0.304634\pi$
$194$	7388.82	2.73447
$195$	1454.98	0.534323
$196$	−4265.65	−1.55454
$197$	5156.87	1.86504	0.932518	−	0.361125i	$-0.117607\pi$
$197$	5156.87	1.86504	0.932518	+	0.361125i	$0.117607\pi$
$198$	−2719.30	−0.976021
$199$	5361.03	1.90972	0.954858	−	0.297063i	$-0.0960071\pi$
$199$	5361.03	1.90972	0.954858	+	0.297063i	$0.0960071\pi$
$200$	287.065	0.101493
$201$	201.000	0.0705346
$202$	−1255.62	−0.437353
$203$	−246.789	−0.0853262
$204$	−1329.63	−0.456338
$205$	2749.56	0.936770
$206$	7610.40	2.57399
$207$	420.645	0.141241
$208$	126.634	0.0422139
$209$	2092.00	0.692375
$210$	679.671	0.223342
$211$	2300.05	0.750435	0.375217	−	0.926937i	$-0.377568\pi$
$211$	2300.05	0.750435	0.375217	+	0.926937i	$0.377568\pi$
$212$	−7964.53	−2.58022
$213$	−1600.35	−0.514809
$214$	2415.75	0.771671
$215$	4008.37	1.27148
$216$	634.419	0.199846
$217$	982.974	0.307505
$218$	−7278.00	−2.26114
$219$	344.949	0.106436
$220$	−10100.9	−3.09547
$221$	−1399.32	−0.425921
$222$	−3742.12	−1.13133
$223$	4101.58	1.23167	0.615834	−	0.787876i	$-0.288819\pi$
$223$	4101.58	1.23167	0.615834	+	0.787876i	$0.288819\pi$
$224$	−732.059	−0.218361
$225$	109.954	0.0325789
$226$	974.549	0.286841
$227$	−5391.55	−1.57643	−0.788215	−	0.615399i	$-0.788995\pi$
$227$	−5391.55	−1.57643	−0.788215	+	0.615399i	$0.788995\pi$
$228$	−1251.62	−0.363555
$229$	−557.513	−0.160880	−0.0804399	−	0.996759i	$-0.525633\pi$
$229$	−557.513	−0.160880	−0.0804399	+	0.996759i	$0.525633\pi$
$230$	2515.70	0.721219
$231$	−830.321	−0.236498
$232$	−1377.68	−0.389866
$233$	6736.44	1.89407	0.947037	−	0.321125i	$-0.104061\pi$
$233$	6736.44	1.89407	0.947037	+	0.321125i	$0.104061\pi$
$234$	1712.20	0.478334
$235$	3282.95	0.911301
$236$	3913.39	1.07941
$237$	492.256	0.134917
$238$	−653.673	−0.178031
$239$	1811.34	0.490234	0.245117	−	0.969493i	$-0.421174\pi$
$239$	1811.34	0.490234	0.245117	+	0.969493i	$0.421174\pi$
$240$	107.484	0.0289087
$241$	−4903.87	−1.31073	−0.655365	−	0.755313i	$-0.727485\pi$
$241$	−4903.87	−1.31073	−0.655365	+	0.755313i	$0.727485\pi$
$242$	13751.8	3.65289
$243$	243.000	0.0641500
$244$	−7103.38	−1.86372
$245$	−3810.36	−0.993612
$246$	3235.66	0.838609
$247$	−1317.22	−0.339323
$248$	5487.35	1.40503
$249$	531.939	0.135383
$250$	−6070.56	−1.53574
$251$	−600.385	−0.150980	−0.0754900	−	0.997147i	$-0.524052\pi$
$251$	−600.385	−0.150980	−0.0754900	+	0.997147i	$0.524052\pi$
$252$	496.773	0.124182
$253$	−3073.31	−0.763705
$254$	−1556.02	−0.384384
$255$	−1187.72	−0.291677
$256$	−4407.52	−1.07605
$257$	−2979.65	−0.723212	−0.361606	−	0.932331i	$-0.617772\pi$
$257$	−2979.65	−0.723212	−0.361606	+	0.932331i	$0.617772\pi$
$258$	4717.00	1.13825
$259$	−1142.63	−0.274130
$260$	6360.02	1.51704
$261$	−527.688	−0.125146
$262$	−3100.79	−0.731172
$263$	−5704.61	−1.33750	−0.668748	−	0.743489i	$-0.733169\pi$
$263$	−5704.61	−1.33750	−0.668748	+	0.743489i	$0.733169\pi$
$264$	−4635.18	−1.08059
$265$	−7114.44	−1.64920
$266$	−615.320	−0.141834
$267$	−572.092	−0.131129
$268$	878.614	0.200261
$269$	210.034	0.0476060	0.0238030	−	0.999717i	$-0.492423\pi$
$269$	210.034	0.0476060	0.0238030	+	0.999717i	$0.492423\pi$
$270$	1453.28	0.327570
$271$	−6376.52	−1.42932	−0.714661	−	0.699471i	$-0.753419\pi$
$271$	−6376.52	−1.42932	−0.714661	+	0.699471i	$0.753419\pi$
$272$	−103.373	−0.0230438
$273$	522.810	0.115904
$274$	−1259.06	−0.277602
$275$	−803.341	−0.176157
$276$	1838.73	0.401009
$277$	−7386.94	−1.60230	−0.801152	−	0.598462i	$-0.795779\pi$
$277$	−7386.94	−1.60230	−0.801152	+	0.598462i	$0.795779\pi$
$278$	7507.95	1.61977
$279$	2101.81	0.451010
$280$	1158.53	0.247270
$281$	−2024.03	−0.429692	−0.214846	−	0.976648i	$-0.568925\pi$
$281$	−2024.03	−0.429692	−0.214846	+	0.976648i	$0.568925\pi$
$282$	3863.34	0.815810
$283$	−1011.82	−0.212531	−0.106266	−	0.994338i	$-0.533889\pi$
$283$	−1011.82	−0.212531	−0.106266	+	0.994338i	$0.533889\pi$
$284$	−6995.49	−1.46164
$285$	−1118.03	−0.232373
$286$	−12509.7	−2.58640
$287$	987.987	0.203202
$288$	−1565.30	−0.320264
$289$	−3770.72	−0.767498
$290$	−3155.88	−0.639033
$291$	4824.08	0.971796
$292$	1507.85	0.302192
$293$	−6676.47	−1.33121	−0.665603	−	0.746306i	$-0.731826\pi$
$293$	−6676.47	−1.33121	−0.665603	+	0.746306i	$0.731826\pi$
$294$	−4483.99	−0.889495
$295$	3495.69	0.689922
$296$	−6378.63	−1.25253
$297$	−1775.40	−0.346866
$298$	−7834.15	−1.52289
$299$	1935.10	0.374281
$300$	480.631	0.0924975
$301$	1440.31	0.275807
$302$	11363.4	2.16519
$303$	−819.783	−0.155430
$304$	−97.3079	−0.0183585
$305$	−6345.20	−1.19123
$306$	−1397.69	−0.261113
$307$	7855.50	1.46038	0.730191	−	0.683243i	$-0.239431\pi$
$307$	7855.50	1.46038	0.730191	+	0.683243i	$0.239431\pi$
$308$	−3629.51	−0.671463
$309$	4968.75	0.914765
$310$	12570.0	2.30300
$311$	−3038.49	−0.554009	−0.277005	−	0.960869i	$-0.589342\pi$
$311$	−3038.49	−0.554009	−0.277005	+	0.960869i	$0.589342\pi$
$312$	2918.53	0.529581
$313$	−3673.04	−0.663299	−0.331649	−	0.943403i	$-0.607605\pi$
$313$	−3673.04	−0.663299	−0.331649	+	0.943403i	$0.607605\pi$
$314$	14269.7	2.56461
$315$	443.750	0.0793730
$316$	2151.76	0.383056
$317$	2732.23	0.484092	0.242046	−	0.970265i	$-0.422181\pi$
$317$	2732.23	0.484092	0.242046	+	0.970265i	$0.422181\pi$
$318$	−8372.20	−1.47638
$319$	3855.38	0.676677
$320$	−9648.01	−1.68544
$321$	1577.22	0.274243
$322$	903.955	0.156446
$323$	1075.26	0.185230
$324$	1062.21	0.182134
$325$	505.822	0.0863322
$326$	413.967	0.0703298
$327$	−4751.73	−0.803581
$328$	5515.34	0.928456
$329$	1179.65	0.197678
$330$	−10617.9	−1.77121
$331$	−9546.74	−1.58531	−0.792653	−	0.609673i	$-0.791301\pi$
$331$	−9546.74	−1.58531	−0.792653	+	0.609673i	$0.791301\pi$
$332$	2325.22	0.384377
$333$	−2443.19	−0.402060
$334$	−6699.96	−1.09762
$335$	784.836	0.128001
$336$	38.6219	0.00627082
$337$	11369.8	1.83785	0.918924	−	0.394434i	$-0.129059\pi$
$337$	11369.8	1.83785	0.918924	+	0.394434i	$0.129059\pi$
$338$	−2218.45	−0.357005
$339$	636.273	0.101940
$340$	−5191.76	−0.828126
$341$	−15356.2	−2.43866
$342$	−1315.69	−0.208024
$343$	−2812.89	−0.442804
$344$	8040.37	1.26020
$345$	1642.47	0.256313
$346$	15747.5	2.44680
$347$	−7425.36	−1.14874	−0.574372	−	0.818595i	$-0.694754\pi$
$347$	−7425.36	−1.14874	−0.574372	+	0.818595i	$0.694754\pi$
$348$	−2306.64	−0.355312
$349$	3554.51	0.545183	0.272591	−	0.962130i	$-0.412119\pi$
$349$	3554.51	0.545183	0.272591	+	0.962130i	$0.412119\pi$
$350$	236.287	0.0360860
$351$	1117.88	0.169994
$352$	11436.4	1.73170
$353$	−1390.33	−0.209631	−0.104816	−	0.994492i	$-0.533425\pi$
$353$	−1390.33	−0.209631	−0.104816	+	0.994492i	$0.533425\pi$
$354$	4113.69	0.617628
$355$	−6248.83	−0.934235
$356$	−2500.74	−0.372300
$357$	−426.776	−0.0632700
$358$	−900.548	−0.132948
$359$	1269.87	0.186688	0.0933442	−	0.995634i	$-0.470244\pi$
$359$	1269.87	0.186688	0.0933442	+	0.995634i	$0.470244\pi$
$360$	2477.19	0.362665
$361$	−5846.83	−0.852431
$362$	−8144.49	−1.18250
$363$	8978.41	1.29819
$364$	2285.31	0.329074
$365$	1346.91	0.193151
$366$	−7466.97	−1.06641
$367$	2937.27	0.417778	0.208889	−	0.977939i	$-0.433015\pi$
$367$	2937.27	0.417778	0.208889	+	0.977939i	$0.433015\pi$
$368$	142.953	0.0202498
$369$	2112.53	0.298032
$370$	−14611.7	−2.05304
$371$	−2556.40	−0.357740
$372$	9187.45	1.28050
$373$	9574.53	1.32909	0.664545	−	0.747249i	$-0.268626\pi$
$373$	9574.53	1.32909	0.664545	+	0.747249i	$0.268626\pi$
$374$	10211.8	1.41187
$375$	−3963.41	−0.545785
$376$	6585.25	0.903214
$377$	−2427.53	−0.331629
$378$	522.201	0.0710558
$379$	−9848.40	−1.33477	−0.667386	−	0.744712i	$-0.732587\pi$
$379$	−9848.40	−1.33477	−0.667386	+	0.744712i	$0.732587\pi$
$380$	−4887.15	−0.659751
$381$	−1015.91	−0.136605
$382$	−2225.06	−0.298021
$383$	−9894.39	−1.32005	−0.660026	−	0.751243i	$-0.729455\pi$
$383$	−9894.39	−1.32005	−0.660026	+	0.751243i	$0.729455\pi$
$384$	−7179.55	−0.954115
$385$	−3242.12	−0.429178
$386$	14191.5	1.87132
$387$	3079.68	0.404519
$388$	21087.1	2.75911
$389$	969.739	0.126395	0.0631976	−	0.998001i	$-0.479870\pi$
$389$	969.739	0.126395	0.0631976	+	0.998001i	$0.479870\pi$
$390$	6685.56	0.868042
$391$	−1579.65	−0.204313
$392$	−7643.18	−0.984793
$393$	−2024.47	−0.259850
$394$	23695.6	3.02987
$395$	1922.09	0.244837
$396$	−7760.67	−0.984819
$397$	9424.75	1.19147	0.595736	−	0.803180i	$-0.296860\pi$
$397$	9424.75	1.19147	0.595736	+	0.803180i	$0.296860\pi$
$398$	24633.7	3.10245
$399$	−401.736	−0.0504059
$400$	37.3669	0.00467087
$401$	−11657.2	−1.45171	−0.725853	−	0.687850i	$-0.758555\pi$
$401$	−11657.2	−1.45171	−0.725853	+	0.687850i	$0.758555\pi$
$402$	923.587	0.114588
$403$	9668.98	1.19515
$404$	−3583.45	−0.441295
$405$	948.831	0.116414
$406$	−1133.99	−0.138618
$407$	17850.4	2.17398
$408$	−2382.43	−0.289088
$409$	−3910.89	−0.472815	−0.236407	−	0.971654i	$-0.575970\pi$
$409$	−3910.89	−0.472815	−0.236407	+	0.971654i	$0.575970\pi$
$410$	12634.1	1.52184
$411$	−822.030	−0.0986563
$412$	21719.5	2.59719
$413$	1256.09	0.149657
$414$	1932.85	0.229455
$415$	2077.04	0.245682
$416$	−7200.87	−0.848682
$417$	4901.86	0.575648
$418$	9612.63	1.12481
$419$	7874.51	0.918127	0.459063	−	0.888404i	$-0.348185\pi$
$419$	7874.51	0.918127	0.459063	+	0.888404i	$0.348185\pi$
$420$	1939.73	0.225355
$421$	7011.11	0.811640	0.405820	−	0.913953i	$-0.366986\pi$
$421$	7011.11	0.811640	0.405820	+	0.913953i	$0.366986\pi$
$422$	10568.6	1.21913
$423$	2522.33	0.289929
$424$	−14270.8	−1.63456
$425$	−412.909	−0.0471271
$426$	−7353.55	−0.836340
$427$	−2279.99	−0.258399
$428$	6894.37	0.778626
$429$	−8167.42	−0.919177
$430$	18418.3	2.06560
$431$	4210.40	0.470552	0.235276	−	0.971929i	$-0.424401\pi$
$431$	4210.40	0.470552	0.235276	+	0.971929i	$0.424401\pi$
$432$	82.5817	0.00919726
$433$	−1861.18	−0.206565	−0.103282	−	0.994652i	$-0.532935\pi$
$433$	−1861.18	−0.206565	−0.103282	+	0.994652i	$0.532935\pi$
$434$	4516.73	0.499562
$435$	−2060.44	−0.227105
$436$	−20770.8	−2.28152
$437$	−1486.97	−0.162772
$438$	1585.03	0.172912
$439$	−13318.2	−1.44794	−0.723968	−	0.689833i	$-0.757684\pi$
$439$	−13318.2	−1.44794	−0.723968	+	0.689833i	$0.757684\pi$
$440$	−18098.8	−1.96097
$441$	−2927.55	−0.316116
$442$	−6429.83	−0.691936
$443$	−12494.3	−1.34001	−0.670003	−	0.742358i	$-0.733707\pi$
$443$	−12494.3	−1.34001	−0.670003	+	0.742358i	$0.733707\pi$
$444$	−10679.7	−1.14152
$445$	−2233.82	−0.237963
$446$	18846.6	2.00092
$447$	−5114.83	−0.541215
$448$	−3466.77	−0.365602
$449$	5026.82	0.528353	0.264176	−	0.964474i	$-0.414900\pi$
$449$	5026.82	0.528353	0.264176	+	0.964474i	$0.414900\pi$
$450$	505.233	0.0529264
$451$	−15434.5	−1.61149
$452$	2781.28	0.289426
$453$	7419.02	0.769483
$454$	−24774.0	−2.56101
$455$	2041.39	0.210334
$456$	−2242.65	−0.230311
$457$	−13463.3	−1.37809	−0.689045	−	0.724719i	$-0.741970\pi$
$457$	−13463.3	−1.37809	−0.689045	+	0.724719i	$0.741970\pi$
$458$	−2561.75	−0.261359
$459$	−912.538	−0.0927966
$460$	7179.61	0.727720
$461$	−11154.0	−1.12688	−0.563441	−	0.826156i	$-0.690523\pi$
$461$	−11154.0	−1.12688	−0.563441	+	0.826156i	$0.690523\pi$
$462$	−3815.29	−0.384207
$463$	8547.32	0.857943	0.428971	−	0.903318i	$-0.358876\pi$
$463$	8547.32	0.857943	0.428971	+	0.903318i	$0.358876\pi$
$464$	−179.331	−0.0179423
$465$	8206.83	0.818457
$466$	30953.7	3.07704
$467$	4408.15	0.436798	0.218399	−	0.975860i	$-0.429917\pi$
$467$	4408.15	0.436798	0.218399	+	0.975860i	$0.429917\pi$
$468$	4886.49	0.482645
$469$	282.011	0.0277656
$470$	15085.0	1.48047
$471$	9316.55	0.911431
$472$	7012.00	0.683799
$473$	−22500.7	−2.18728
$474$	2261.89	0.219182
$475$	−388.682	−0.0375452
$476$	−1865.53	−0.179635
$477$	−5466.12	−0.524689
$478$	8323.05	0.796417
$479$	2685.80	0.256195	0.128097	−	0.991762i	$-0.459113\pi$
$479$	2685.80	0.256195	0.128097	+	0.991762i	$0.459113\pi$
$480$	−6111.95	−0.581190
$481$	−11239.5	−1.06544
$482$	−22533.1	−2.12936
$483$	590.183	0.0555989
$484$	39246.6	3.68582
$485$	18836.4	1.76354
$486$	1116.58	0.104216
$487$	−3040.07	−0.282872	−0.141436	−	0.989947i	$-0.545172\pi$
$487$	−3040.07	−0.282872	−0.141436	+	0.989947i	$0.545172\pi$
$488$	−12727.8	−1.18066
$489$	270.275	0.0249944
$490$	−17508.4	−1.61419
$491$	−4079.81	−0.374988	−0.187494	−	0.982266i	$-0.560037\pi$
$491$	−4079.81	−0.374988	−0.187494	+	0.982266i	$0.560037\pi$
$492$	9234.31	0.846168
$493$	1981.63	0.181030
$494$	−6052.57	−0.551251
$495$	−6932.34	−0.629465
$496$	714.283	0.0646618
$497$	−2245.36	−0.202652
$498$	2444.24	0.219938
$499$	14668.5	1.31594	0.657969	−	0.753045i	$-0.271416\pi$
$499$	14668.5	1.31594	0.657969	+	0.753045i	$0.271416\pi$
$500$	−17324.9	−1.54959
$501$	−4374.33	−0.390082
$502$	−2758.75	−0.245277
$503$	−1926.55	−0.170777	−0.0853884	−	0.996348i	$-0.527213\pi$
$503$	−1926.55	−0.170777	−0.0853884	+	0.996348i	$0.527213\pi$
$504$	890.117	0.0786685
$505$	−3200.97	−0.282062
$506$	−14121.7	−1.24069
$507$	−1448.40	−0.126875
$508$	−4440.76	−0.387849
$509$	−8672.34	−0.755196	−0.377598	−	0.925970i	$-0.623250\pi$
$509$	−8672.34	−0.755196	−0.377598	+	0.925970i	$0.623250\pi$
$510$	−5457.50	−0.473848
$511$	483.977	0.0418980
$512$	−1106.89	−0.0955436
$513$	−858.997	−0.0739291
$514$	−13691.4	−1.17490
$515$	19401.3	1.66004
$516$	13462.0	1.14851
$517$	−18428.6	−1.56768
$518$	−5250.35	−0.445342
$519$	10281.4	0.869562
$520$	11395.9	0.961042
$521$	−6520.30	−0.548291	−0.274146	−	0.961688i	$-0.588395\pi$
$521$	−6520.30	−0.548291	−0.274146	+	0.961688i	$0.588395\pi$
$522$	−2424.70	−0.203307
$523$	7834.26	0.655006	0.327503	−	0.944850i	$-0.393793\pi$
$523$	7834.26	0.655006	0.327503	+	0.944850i	$0.393793\pi$
$524$	−8849.40	−0.737763
$525$	154.270	0.0128245
$526$	−26212.4	−2.17285
$527$	−7892.91	−0.652411
$528$	−603.357	−0.0497306
$529$	−9982.53	−0.820459
$530$	−32690.6	−2.67922
$531$	2685.79	0.219498
$532$	−1756.08	−0.143112
$533$	9718.30	0.789768
$534$	−2628.74	−0.213028
$535$	6158.50	0.497674
$536$	1574.30	0.126864
$537$	−587.958	−0.0472482
$538$	965.098	0.0773389
$539$	21389.2	1.70927
$540$	4147.55	0.330522
$541$	−3985.10	−0.316697	−0.158348	−	0.987383i	$-0.550617\pi$
$541$	−3985.10	−0.316697	−0.158348	+	0.987383i	$0.550617\pi$
$542$	−29299.9	−2.32202
$543$	−5317.45	−0.420246
$544$	5878.16	0.463280
$545$	−18553.9	−1.45828
$546$	2402.29	0.188294
$547$	1404.85	0.109811	0.0549057	−	0.998492i	$-0.482514\pi$
$547$	1404.85	0.109811	0.0549057	+	0.998492i	$0.482514\pi$
$548$	−3593.27	−0.280104
$549$	−4875.10	−0.378988
$550$	−3691.32	−0.286179
$551$	1865.36	0.144223
$552$	3294.63	0.254038
$553$	690.655	0.0531097
$554$	−33942.7	−2.60304
$555$	−9539.82	−0.729626
$556$	21427.1	1.63437
$557$	4922.14	0.374430	0.187215	−	0.982319i	$-0.440054\pi$
$557$	4922.14	0.374430	0.187215	+	0.982319i	$0.440054\pi$
$558$	9657.71	0.732695
$559$	14167.5	1.07195
$560$	150.805	0.0113798
$561$	6667.17	0.501761
$562$	−9300.32	−0.698061
$563$	20417.4	1.52840	0.764202	−	0.644978i	$-0.223133\pi$
$563$	20417.4	1.52840	0.764202	+	0.644978i	$0.223133\pi$
$564$	11025.7	0.823163
$565$	2484.43	0.184992
$566$	−4649.27	−0.345271
$567$	340.939	0.0252524
$568$	−12534.5	−0.925943
$569$	10506.6	0.774092	0.387046	−	0.922060i	$-0.373495\pi$
$569$	10506.6	0.774092	0.387046	+	0.922060i	$0.373495\pi$
$570$	−5137.30	−0.377505
$571$	7722.22	0.565963	0.282981	−	0.959125i	$-0.408677\pi$
$571$	7722.22	0.565963	0.282981	+	0.959125i	$0.408677\pi$
$572$	−35701.6	−2.60972
$573$	−1452.72	−0.105913
$574$	4539.76	0.330115
$575$	571.006	0.0414132
$576$	−7412.70	−0.536219
$577$	2518.40	0.181703	0.0908514	−	0.995864i	$-0.471041\pi$
$577$	2518.40	0.181703	0.0908514	+	0.995864i	$0.471041\pi$
$578$	−17326.3	−1.24685
$579$	9265.48	0.665044
$580$	−9006.62	−0.644793
$581$	746.333	0.0532928
$582$	22166.5	1.57874
$583$	39936.5	2.83705
$584$	2701.75	0.191437
$585$	4364.93	0.308492
$586$	−30678.1	−2.16263
$587$	12197.2	0.857633	0.428817	−	0.903392i	$-0.358931\pi$
$587$	12197.2	0.857633	0.428817	+	0.903392i	$0.358931\pi$
$588$	−12797.0	−0.897513
$589$	−7429.82	−0.519763
$590$	16062.6	1.12082
$591$	15470.6	1.07678
$592$	−830.300	−0.0576438
$593$	−21975.2	−1.52177	−0.760887	−	0.648884i	$-0.775236\pi$
$593$	−21975.2	−1.52177	−0.760887	+	0.648884i	$0.775236\pi$
$594$	−8157.90	−0.563506
$595$	−1666.41	−0.114817
$596$	−22358.0	−1.53661
$597$	16083.1	1.10257
$598$	8891.72	0.608042
$599$	13742.0	0.937366	0.468683	−	0.883366i	$-0.344729\pi$
$599$	13742.0	0.937366	0.468683	+	0.883366i	$0.344729\pi$
$600$	861.194	0.0585968
$601$	21246.6	1.44204	0.721021	−	0.692913i	$-0.243673\pi$
$601$	21246.6	1.44204	0.721021	+	0.692913i	$0.243673\pi$
$602$	6618.15	0.448066
$603$	603.000	0.0407231
$604$	32430.1	2.18471
$605$	35057.6	2.35586
$606$	−3766.87	−0.252506
$607$	−26498.9	−1.77193	−0.885963	−	0.463756i	$-0.846501\pi$
$607$	−26498.9	−1.77193	−0.885963	+	0.463756i	$0.846501\pi$
$608$	5533.27	0.369085
$609$	−740.368	−0.0492631
$610$	−29155.9	−1.93523
$611$	11603.5	0.768296
$612$	−3988.90	−0.263467
$613$	21618.6	1.42442	0.712209	−	0.701968i	$-0.247695\pi$
$613$	21618.6	1.42442	0.712209	+	0.701968i	$0.247695\pi$
$614$	36095.7	2.37248
$615$	8248.69	0.540844
$616$	−6503.35	−0.425369
$617$	13717.2	0.895031	0.447516	−	0.894276i	$-0.352309\pi$
$617$	13717.2	0.895031	0.447516	+	0.894276i	$0.352309\pi$
$618$	22831.2	1.48609
$619$	−9151.74	−0.594248	−0.297124	−	0.954839i	$-0.596027\pi$
$619$	−9151.74	−0.594248	−0.297124	+	0.954839i	$0.596027\pi$
$620$	35873.8	2.32375
$621$	1261.94	0.0815454
$622$	−13961.7	−0.900023
$623$	−802.669	−0.0516184
$624$	379.902	0.0243722
$625$	−17002.9	−1.08818
$626$	−16877.5	−1.07757
$627$	6275.99	0.399743
$628$	40724.7	2.58772
$629$	9174.91	0.581602
$630$	2039.01	0.128946
$631$	18479.0	1.16583	0.582913	−	0.812534i	$-0.301913\pi$
$631$	18479.0	1.16583	0.582913	+	0.812534i	$0.301913\pi$
$632$	3855.51	0.242665
$633$	6900.14	0.433264
$634$	12554.5	0.786439
$635$	−3966.78	−0.247901
$636$	−23893.6	−1.48969
$637$	−13467.7	−0.837690
$638$	17715.3	1.09930
$639$	−4801.06	−0.297225
$640$	−28033.7	−1.73145
$641$	−29026.3	−1.78856	−0.894282	−	0.447505i	$-0.852313\pi$
$641$	−29026.3	−1.78856	−0.894282	+	0.447505i	$0.852313\pi$
$642$	7247.26	0.445524
$643$	5177.26	0.317529	0.158765	−	0.987316i	$-0.449249\pi$
$643$	5177.26	0.317529	0.158765	+	0.987316i	$0.449249\pi$
$644$	2579.82	0.157856
$645$	12025.1	0.734090
$646$	4940.79	0.300918
$647$	−18812.3	−1.14310	−0.571552	−	0.820566i	$-0.693658\pi$
$647$	−18812.3	−1.14310	−0.571552	+	0.820566i	$0.693658\pi$
$648$	1903.26	0.115381
$649$	−19622.9	−1.18685
$650$	2324.23	0.140252
$651$	2948.92	0.177538
$652$	1181.43	0.0709637
$653$	−31166.8	−1.86777	−0.933884	−	0.357576i	$-0.883603\pi$
$653$	−31166.8	−1.86777	−0.933884	+	0.357576i	$0.883603\pi$
$654$	−21834.0	−1.30547
$655$	−7904.86	−0.471555
$656$	717.926	0.0427291
$657$	1034.85	0.0614508
$658$	5420.42	0.321140
$659$	21129.6	1.24900	0.624501	−	0.781024i	$-0.285302\pi$
$659$	21129.6	1.24900	0.624501	+	0.781024i	$0.285302\pi$
$660$	−30302.7	−1.78717
$661$	−20437.8	−1.20263	−0.601316	−	0.799011i	$-0.705357\pi$
$661$	−20437.8	−1.20263	−0.601316	+	0.799011i	$0.705357\pi$
$662$	−43866.9	−2.57543
$663$	−4197.97	−0.245906
$664$	4166.33	0.243501
$665$	−1568.64	−0.0914727
$666$	−11226.4	−0.653172
$667$	−2740.36	−0.159081
$668$	−19121.2	−1.10751
$669$	12304.7	0.711103
$670$	3606.29	0.207945
$671$	35618.4	2.04923
$672$	−2196.18	−0.126071
$673$	24370.1	1.39584	0.697919	−	0.716177i	$-0.254110\pi$
$673$	24370.1	1.39584	0.697919	+	0.716177i	$0.254110\pi$
$674$	52244.0	2.98570
$675$	329.861	0.0188094
$676$	−6331.28	−0.360223
$677$	−16927.3	−0.960960	−0.480480	−	0.877006i	$-0.659538\pi$
$677$	−16927.3	−0.960960	−0.480480	+	0.877006i	$0.659538\pi$
$678$	2923.65	0.165608
$679$	6768.39	0.382543
$680$	−9302.59	−0.524614
$681$	−16174.7	−0.910153
$682$	−70561.0	−3.96176
$683$	20529.2	1.15011	0.575056	−	0.818114i	$-0.304980\pi$
$683$	20529.2	1.15011	0.575056	+	0.818114i	$0.304980\pi$
$684$	−3754.86	−0.209899
$685$	−3209.75	−0.179034
$686$	−12925.1	−0.719363
$687$	−1672.54	−0.0928840
$688$	1046.61	0.0579964
$689$	−25145.9	−1.39040
$690$	7547.10	0.416396
$691$	−28708.8	−1.58051	−0.790257	−	0.612776i	$-0.790053\pi$
$691$	−28708.8	−1.58051	−0.790257	+	0.612776i	$0.790053\pi$
$692$	44942.1	2.46885
$693$	−2490.96	−0.136542
$694$	−34119.2	−1.86621
$695$	19140.1	1.04464
$696$	−4133.03	−0.225089
$697$	−7933.17	−0.431119
$698$	16332.8	0.885684
$699$	20209.3	1.09354
$700$	674.346	0.0364112
$701$	−32285.3	−1.73952	−0.869758	−	0.493479i	$-0.835725\pi$
$701$	−32285.3	−1.73952	−0.869758	+	0.493479i	$0.835725\pi$
$702$	5136.60	0.276166
$703$	8636.59	0.463350
$704$	54158.5	2.89940
$705$	9848.84	0.526140
$706$	−6388.51	−0.340559
$707$	−1150.19	−0.0611843
$708$	11740.2	0.623195
$709$	23839.2	1.26277	0.631383	−	0.775471i	$-0.282488\pi$
$709$	23839.2	1.26277	0.631383	+	0.775471i	$0.282488\pi$
$710$	−28713.1	−1.51772
$711$	1476.77	0.0778946
$712$	−4480.82	−0.235851
$713$	10915.0	0.573310
$714$	−1961.02	−0.102786
$715$	−31891.0	−1.66805
$716$	−2570.09	−0.134146
$717$	5434.03	0.283037
$718$	5835.00	0.303287
$719$	−22272.6	−1.15525	−0.577627	−	0.816301i	$-0.696021\pi$
$719$	−22272.6	−1.15525	−0.577627	+	0.816301i	$0.696021\pi$
$720$	322.453	0.0166904
$721$	6971.36	0.360093
$722$	−26865.9	−1.38483
$723$	−14711.6	−0.756750
$724$	−23243.7	−1.19316
$725$	−716.311	−0.0366940
$726$	41255.4	2.10900
$727$	28060.5	1.43151	0.715755	−	0.698352i	$-0.246083\pi$
$727$	28060.5	1.43151	0.715755	+	0.698352i	$0.246083\pi$
$728$	4094.82	0.208467
$729$	729.000	0.0370370
$730$	6188.98	0.313787
$731$	−11565.1	−0.585160
$732$	−21310.1	−1.07602
$733$	19143.1	0.964619	0.482309	−	0.876001i	$-0.339798\pi$
$733$	19143.1	0.964619	0.482309	+	0.876001i	$0.339798\pi$
$734$	13496.7	0.678707
$735$	−11431.1	−0.573662
$736$	−8128.83	−0.407109
$737$	−4405.63	−0.220195
$738$	9706.97	0.484171
$739$	−19379.2	−0.964648	−0.482324	−	0.875993i	$-0.660207\pi$
$739$	−19379.2	−0.964648	−0.482324	+	0.875993i	$0.660207\pi$
$740$	−41700.6	−2.07155
$741$	−3951.66	−0.195908
$742$	−11746.6	−0.581172
$743$	−22166.0	−1.09447	−0.547234	−	0.836979i	$-0.684319\pi$
$743$	−22166.0	−1.09447	−0.547234	+	0.836979i	$0.684319\pi$
$744$	16462.1	0.811194
$745$	−19971.7	−0.982154
$746$	43994.6	2.15919
$747$	1595.82	0.0781632
$748$	29143.6	1.42459
$749$	2212.91	0.107954
$750$	−18211.7	−0.886663
$751$	−8409.91	−0.408631	−0.204315	−	0.978905i	$-0.565497\pi$
$751$	−8409.91	−0.408631	−0.204315	+	0.978905i	$0.565497\pi$
$752$	857.195	0.0415674
$753$	−1801.16	−0.0871684
$754$	−11154.4	−0.538753
$755$	28968.7	1.39640
$756$	1490.32	0.0716963
$757$	−6000.03	−0.288078	−0.144039	−	0.989572i	$-0.546009\pi$
$757$	−6000.03	−0.288078	−0.144039	+	0.989572i	$0.546009\pi$
$758$	−45253.0	−2.16842
$759$	−9219.93	−0.440925
$760$	−8756.78	−0.417950
$761$	35558.0	1.69379	0.846897	−	0.531756i	$-0.178468\pi$
$761$	35558.0	1.69379	0.846897	+	0.531756i	$0.178468\pi$
$762$	−4668.07	−0.221924
$763$	−6666.87	−0.316326
$764$	−6350.14	−0.300707
$765$	−3563.15	−0.168400
$766$	−45464.3	−2.14451
$767$	12355.5	0.581657
$768$	−13222.6	−0.621260
$769$	18766.5	0.880021	0.440010	−	0.897993i	$-0.354975\pi$
$769$	18766.5	0.880021	0.440010	+	0.897993i	$0.354975\pi$
$770$	−14897.4	−0.697228
$771$	−8938.96	−0.417547
$772$	40501.4	1.88818
$773$	−34544.4	−1.60734	−0.803672	−	0.595073i	$-0.797123\pi$
$773$	−34544.4	−1.60734	−0.803672	+	0.595073i	$0.797123\pi$
$774$	14151.0	0.657168
$775$	2853.10	0.132241
$776$	37783.8	1.74789
$777$	−3427.90	−0.158269
$778$	4455.91	0.205337
$779$	−7467.71	−0.343464
$780$	19080.0	0.875866
$781$	35077.4	1.60713
$782$	−7258.42	−0.331919
$783$	−1583.06	−0.0722529
$784$	−994.906	−0.0453219
$785$	36377.9	1.65399
$786$	−9302.36	−0.422143
$787$	13796.6	0.624900	0.312450	−	0.949934i	$-0.398850\pi$
$787$	13796.6	0.624900	0.312450	+	0.949934i	$0.398850\pi$
$788$	67625.4	3.05718
$789$	−17113.8	−0.772203
$790$	8831.92	0.397754
$791$	892.717	0.0401281
$792$	−13905.5	−0.623879
$793$	−22427.0	−1.00430
$794$	43306.3	1.93562
$795$	−21343.3	−0.952163
$796$	70302.7	3.13042
$797$	43313.6	1.92503	0.962513	−	0.271236i	$-0.0874325\pi$
$797$	43313.6	1.92503	0.962513	+	0.271236i	$0.0874325\pi$
$798$	−1845.96	−0.0818876
$799$	−9472.11	−0.419398
$800$	−2124.82	−0.0939045
$801$	−1716.28	−0.0757074
$802$	−53564.5	−2.35839
$803$	−7560.77	−0.332271
$804$	2635.84	0.115621
$805$	2304.46	0.100896
$806$	44428.6	1.94160
$807$	630.102	0.0274853
$808$	−6420.81	−0.279559
$809$	−4989.13	−0.216821	−0.108411	−	0.994106i	$-0.534576\pi$
$809$	−4989.13	−0.216821	−0.108411	+	0.994106i	$0.534576\pi$
$810$	4359.84	0.189123
$811$	23446.0	1.01517	0.507584	−	0.861602i	$-0.330539\pi$
$811$	23446.0	1.01517	0.507584	+	0.861602i	$0.330539\pi$
$812$	−3236.31	−0.139867
$813$	−19129.6	−0.825219
$814$	82021.8	3.53177
$815$	1055.33	0.0453578
$816$	−310.119	−0.0133043
$817$	−10886.6	−0.466185
$818$	−17970.4	−0.768117
$819$	1568.43	0.0669174
$820$	36056.8	1.53556
$821$	11058.2	0.470077	0.235039	−	0.971986i	$-0.424478\pi$
$821$	11058.2	0.470077	0.235039	+	0.971986i	$0.424478\pi$
$822$	−3777.19	−0.160273
$823$	−31331.7	−1.32704	−0.663520	−	0.748159i	$-0.730938\pi$
$823$	−31331.7	−1.32704	−0.663520	+	0.748159i	$0.730938\pi$
$824$	38916.9	1.64531
$825$	−2410.02	−0.101705
$826$	5771.69	0.243127
$827$	−39446.4	−1.65863	−0.829314	−	0.558783i	$-0.811269\pi$
$827$	−39446.4	−1.65863	−0.829314	+	0.558783i	$0.811269\pi$
$828$	5516.19	0.231523
$829$	26535.7	1.11173	0.555864	−	0.831273i	$-0.312387\pi$
$829$	26535.7	1.11173	0.555864	+	0.831273i	$0.312387\pi$
$830$	9543.91	0.399125
$831$	−22160.8	−0.925090
$832$	−34100.8	−1.42095
$833$	10993.8	0.457279
$834$	22523.8	0.935176
$835$	−17080.3	−0.707889
$836$	27433.7	1.13495
$837$	6305.42	0.260391
$838$	36183.1	1.49156
$839$	−29398.6	−1.20972	−0.604859	−	0.796333i	$-0.706771\pi$
$839$	−29398.6	−1.20972	−0.604859	+	0.796333i	$0.706771\pi$
$840$	3475.60	0.142761
$841$	−20951.3	−0.859047
$842$	32215.8	1.31856
$843$	−6072.08	−0.248083
$844$	30162.0	1.23012
$845$	−5655.52	−0.230243
$846$	11590.0	0.471008
$847$	12597.1	0.511028
$848$	−1857.62	−0.0752252
$849$	−3035.46	−0.122705
$850$	−1897.30	−0.0765610
$851$	−12687.9	−0.511086
$852$	−20986.5	−0.843878
$853$	13868.9	0.556698	0.278349	−	0.960480i	$-0.410213\pi$
$853$	13868.9	0.556698	0.278349	+	0.960480i	$0.410213\pi$
$854$	−10476.5	−0.419786
$855$	−3354.09	−0.134161
$856$	12353.3	0.493257
$857$	5093.37	0.203018	0.101509	−	0.994835i	$-0.467633\pi$
$857$	5093.37	0.203018	0.101509	+	0.994835i	$0.467633\pi$
$858$	−37529.0	−1.49326
$859$	36708.8	1.45808	0.729038	−	0.684473i	$-0.239968\pi$
$859$	36708.8	1.45808	0.729038	+	0.684473i	$0.239968\pi$
$860$	52564.3	2.08422
$861$	2963.96	0.117319
$862$	19346.6	0.764442
$863$	14138.1	0.557665	0.278832	−	0.960340i	$-0.410053\pi$
$863$	14138.1	0.557665	0.278832	+	0.960340i	$0.410053\pi$
$864$	−4695.89	−0.184905
$865$	40145.3	1.57801
$866$	−8552.03	−0.335577
$867$	−11312.1	−0.443115
$868$	12890.4	0.504064
$869$	−10789.5	−0.421185
$870$	−9467.63	−0.368946
$871$	2773.99	0.107914
$872$	−37217.1	−1.44533
$873$	14472.2	0.561067
$874$	−6832.55	−0.264433
$875$	−5560.83	−0.214846
$876$	4523.54	0.174470
$877$	−25745.1	−0.991277	−0.495638	−	0.868529i	$-0.665066\pi$
$877$	−25745.1	−0.991277	−0.495638	+	0.868529i	$0.665066\pi$
$878$	−61196.7	−2.35227
$879$	−20029.4	−0.768572
$880$	−2355.90	−0.0902471
$881$	14208.4	0.543353	0.271676	−	0.962389i	$-0.412422\pi$
$881$	14208.4	0.543353	0.271676	+	0.962389i	$0.412422\pi$
$882$	−13452.0	−0.513550
$883$	−25576.5	−0.974764	−0.487382	−	0.873189i	$-0.662048\pi$
$883$	−25576.5	−0.974764	−0.487382	+	0.873189i	$0.662048\pi$
$884$	−18350.2	−0.698173
$885$	10487.1	0.398327
$886$	−57410.8	−2.17692
$887$	32855.4	1.24372	0.621859	−	0.783129i	$-0.286378\pi$
$887$	32855.4	1.24372	0.621859	+	0.783129i	$0.286378\pi$
$888$	−19135.9	−0.723151
$889$	−1425.37	−0.0537741
$890$	−10264.3	−0.386585
$891$	−5326.21	−0.200263
$892$	53786.6	2.01896
$893$	−8916.36	−0.334126
$894$	−23502.4	−0.879238
$895$	−2295.77	−0.0857422
$896$	−10073.2	−0.375583
$897$	5805.31	0.216091
$898$	23098.0	0.858342
$899$	−13692.6	−0.507978
$900$	1441.89	0.0534035
$901$	20526.9	0.758991
$902$	−70920.9	−2.61797
$903$	4320.92	0.159237
$904$	4983.50	0.183350
$905$	−20762.8	−0.762629
$906$	34090.1	1.25007
$907$	−35278.4	−1.29151	−0.645755	−	0.763545i	$-0.723457\pi$
$907$	−35278.4	−1.29151	−0.645755	+	0.763545i	$0.723457\pi$
$908$	−70702.9	−2.58409
$909$	−2459.35	−0.0897375
$910$	9380.12	0.341701
$911$	−20295.5	−0.738114	−0.369057	−	0.929407i	$-0.620319\pi$
$911$	−20295.5	−0.738114	−0.369057	+	0.929407i	$0.620319\pi$
$912$	−291.924	−0.0105993
$913$	−11659.3	−0.422637
$914$	−61863.3	−2.23879
$915$	−19035.6	−0.687757
$916$	−7311.02	−0.263715
$917$	−2840.42	−0.102289
$918$	−4193.07	−0.150754
$919$	9039.55	0.324469	0.162235	−	0.986752i	$-0.448130\pi$
$919$	9039.55	0.324469	0.162235	+	0.986752i	$0.448130\pi$
$920$	12864.4	0.461008
$921$	23566.5	0.843152
$922$	−51252.1	−1.83069
$923$	−22086.4	−0.787630
$924$	−10888.5	−0.387670
$925$	−3316.51	−0.117888
$926$	39274.6	1.39378
$927$	14906.2	0.528140
$928$	10197.4	0.360717
$929$	11661.3	0.411836	0.205918	−	0.978569i	$-0.433982\pi$
$929$	11661.3	0.411836	0.205918	+	0.978569i	$0.433982\pi$
$930$	37710.1	1.32964
$931$	10348.8	0.364305
$932$	88339.4	3.10478
$933$	−9115.46	−0.319857
$934$	20255.3	0.709606
$935$	26033.0	0.910556
$936$	8755.59	0.305754
$937$	−19597.2	−0.683258	−0.341629	−	0.939835i	$-0.610979\pi$
$937$	−19597.2	−0.683258	−0.341629	+	0.939835i	$0.610979\pi$
$938$	1295.83	0.0451070
$939$	−11019.1	−0.382956
$940$	43051.4	1.49381
$941$	−55187.0	−1.91184	−0.955921	−	0.293623i	$-0.905139\pi$
$941$	−55187.0	−1.91184	−0.955921	+	0.293623i	$0.905139\pi$
$942$	42809.2	1.48068
$943$	10970.7	0.378848
$944$	912.745	0.0314696
$945$	1331.25	0.0458260
$946$	−103390.	−3.55338
$947$	−36719.0	−1.25999	−0.629994	−	0.776600i	$-0.716943\pi$
$947$	−36719.0	−1.25999	−0.629994	+	0.776600i	$0.716943\pi$
$948$	6455.27	0.221158
$949$	4760.62	0.162841
$950$	−1785.98	−0.0609946
$951$	8196.69	0.279491
$952$	−3342.65	−0.113798
$953$	−36738.7	−1.24878	−0.624388	−	0.781114i	$-0.714652\pi$
$953$	−36738.7	−1.24878	−0.624388	+	0.781114i	$0.714652\pi$
$954$	−25116.6	−0.852390
$955$	−5672.36	−0.192203
$956$	23753.3	0.803595
$957$	11566.1	0.390680
$958$	12341.1	0.416204
$959$	−1153.34	−0.0388356
$960$	−28944.0	−0.973088
$961$	24747.2	0.830692
$962$	−51644.8	−1.73087
$963$	4731.66	0.158334
$964$	−64307.6	−2.14856
$965$	36178.5	1.20687
$966$	2711.87	0.0903239
$967$	−10989.6	−0.365461	−0.182731	−	0.983163i	$-0.558494\pi$
$967$	−10989.6	−0.365461	−0.182731	+	0.983163i	$0.558494\pi$
$968$	70321.9	2.33495
$969$	3225.79	0.106943
$970$	86552.4	2.86498
$971$	27224.5	0.899768	0.449884	−	0.893087i	$-0.351465\pi$
$971$	27224.5	0.899768	0.449884	+	0.893087i	$0.351465\pi$
$972$	3186.62	0.105155
$973$	6877.51	0.226601
$974$	−13969.0	−0.459543
$975$	1517.47	0.0498439
$976$	−1656.77	−0.0543359
$977$	376.544	0.0123303	0.00616515	−	0.999981i	$-0.498038\pi$
$977$	376.544	0.0123303	0.00616515	+	0.999981i	$0.498038\pi$
$978$	1241.90	0.0406049
$979$	12539.4	0.409358
$980$	−49967.7	−1.62873
$981$	−14255.2	−0.463948
$982$	−18746.5	−0.609192
$983$	14242.4	0.462117	0.231059	−	0.972940i	$-0.425781\pi$
$983$	14242.4	0.462117	0.231059	+	0.972940i	$0.425781\pi$
$984$	16546.0	0.536044
$985$	60407.4	1.95405
$986$	9105.49	0.294095
$987$	3538.94	0.114129
$988$	−17273.6	−0.556220
$989$	15993.3	0.514212
$990$	−31853.8	−1.02261
$991$	−35321.8	−1.13222	−0.566112	−	0.824328i	$-0.691553\pi$
$991$	−35321.8	−1.13222	−0.566112	+	0.824328i	$0.691553\pi$
$992$	−40616.7	−1.29998
$993$	−28640.2	−0.915277
$994$	−10317.3	−0.329222
$995$	62799.0	2.00087
$996$	6975.66	0.221920
$997$	4248.16	0.134945	0.0674727	−	0.997721i	$-0.478506\pi$
$997$	4248.16	0.134945	0.0674727	+	0.997721i	$0.478506\pi$
$998$	67401.2	2.13782
$999$	−7329.57	−0.232129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.e.1.9	✓	11
3.2	odd	2		603.4.a.g.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.e.1.9	✓	11	1.1	even	1	trivial
603.4.a.g.1.3		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q+4.59496 q^{2} +3.00000 q^{3} +13.1136 q^{4} +11.7140 q^{5} +13.7849 q^{6} +4.20913 q^{7} +23.4970 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.59496 q^{2} +3.00000 q^{3} +13.1136 q^{4} +11.7140 q^{5} +13.7849 q^{6} +4.20913 q^{7} +23.4970 q^{8} +9.00000 q^{9} +53.8252 q^{10} -65.7556 q^{11} +39.3409 q^{12} +41.4029 q^{13} +19.3408 q^{14} +35.1419 q^{15} +3.05858 q^{16} -33.7977 q^{17} +41.3546 q^{18} -31.8147 q^{19} +153.613 q^{20} +12.6274 q^{21} -302.144 q^{22} +46.7383 q^{23} +70.4910 q^{24} +12.2171 q^{25} +190.245 q^{26} +27.0000 q^{27} +55.1970 q^{28} -58.6320 q^{29} +161.476 q^{30} +233.534 q^{31} -173.922 q^{32} -197.267 q^{33} -155.299 q^{34} +49.3056 q^{35} +118.023 q^{36} -271.466 q^{37} -146.187 q^{38} +124.209 q^{39} +275.243 q^{40} +234.725 q^{41} +58.0223 q^{42} +342.187 q^{43} -862.296 q^{44} +105.426 q^{45} +214.761 q^{46} +280.259 q^{47} +9.17575 q^{48} -325.283 q^{49} +56.1369 q^{50} -101.393 q^{51} +542.943 q^{52} -607.347 q^{53} +124.064 q^{54} -770.260 q^{55} +98.9018 q^{56} -95.4441 q^{57} -269.411 q^{58} +298.421 q^{59} +460.839 q^{60} -541.678 q^{61} +1073.08 q^{62} +37.8821 q^{63} -823.633 q^{64} +484.992 q^{65} -906.433 q^{66} +67.0000 q^{67} -443.211 q^{68} +140.215 q^{69} +226.557 q^{70} -533.451 q^{71} +211.473 q^{72} +114.983 q^{73} -1247.37 q^{74} +36.6512 q^{75} -417.207 q^{76} -276.774 q^{77} +570.734 q^{78} +164.085 q^{79} +35.8281 q^{80} +81.0000 q^{81} +1078.55 q^{82} +177.313 q^{83} +165.591 q^{84} -395.905 q^{85} +1572.33 q^{86} -175.896 q^{87} -1545.06 q^{88} -190.697 q^{89} +484.427 q^{90} +174.270 q^{91} +612.910 q^{92} +700.602 q^{93} +1287.78 q^{94} -372.676 q^{95} -521.766 q^{96} +1608.03 q^{97} -1494.66 q^{98} -591.801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * q^99

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