LMFDB - Embedded newform 2001.4.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.75649 q^{2} +3.00000 q^{3} +14.6242 q^{4} -4.17105 q^{5} -14.2695 q^{6} -30.3756 q^{7} -31.5078 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.75649 q^{2} +3.00000 q^{3} +14.6242 q^{4} -4.17105 q^{5} -14.2695 q^{6} -30.3756 q^{7} -31.5078 q^{8} +9.00000 q^{9} +19.8395 q^{10} -34.2306 q^{11} +43.8725 q^{12} -14.7793 q^{13} +144.481 q^{14} -12.5131 q^{15} +32.8730 q^{16} -2.37953 q^{17} -42.8084 q^{18} +92.5411 q^{19} -60.9981 q^{20} -91.1267 q^{21} +162.818 q^{22} +23.0000 q^{23} -94.5234 q^{24} -107.602 q^{25} +70.2976 q^{26} +27.0000 q^{27} -444.218 q^{28} +29.0000 q^{29} +59.5186 q^{30} -8.32753 q^{31} +95.7021 q^{32} -102.692 q^{33} +11.3182 q^{34} +126.698 q^{35} +131.618 q^{36} +61.5499 q^{37} -440.171 q^{38} -44.3380 q^{39} +131.420 q^{40} -29.9942 q^{41} +433.443 q^{42} +474.242 q^{43} -500.595 q^{44} -37.5394 q^{45} -109.399 q^{46} +58.8321 q^{47} +98.6191 q^{48} +579.676 q^{49} +511.809 q^{50} -7.13860 q^{51} -216.135 q^{52} +97.0803 q^{53} -128.425 q^{54} +142.777 q^{55} +957.067 q^{56} +277.623 q^{57} -137.938 q^{58} +483.143 q^{59} -182.994 q^{60} -20.5984 q^{61} +39.6098 q^{62} -273.380 q^{63} -718.190 q^{64} +61.6452 q^{65} +488.453 q^{66} +88.4255 q^{67} -34.7987 q^{68} +69.0000 q^{69} -602.637 q^{70} +1141.25 q^{71} -283.570 q^{72} +89.5015 q^{73} -292.761 q^{74} -322.807 q^{75} +1353.34 q^{76} +1039.77 q^{77} +210.893 q^{78} -602.408 q^{79} -137.115 q^{80} +81.0000 q^{81} +142.667 q^{82} +145.329 q^{83} -1332.65 q^{84} +9.92514 q^{85} -2255.73 q^{86} +87.0000 q^{87} +1078.53 q^{88} -730.976 q^{89} +178.556 q^{90} +448.930 q^{91} +336.356 q^{92} -24.9826 q^{93} -279.834 q^{94} -385.993 q^{95} +287.106 q^{96} -500.651 q^{97} -2757.22 q^{98} -308.076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9}+O(q^{10}) $ 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9} - 6 q^{10} - 109 q^{11} + 222 q^{12} - 317 q^{13} - 159 q^{14} - 75 q^{15} + 54 q^{16} - 180 q^{17} - 90 q^{18} - 217 q^{19} - 193 q^{20} - 228 q^{21} - 160 q^{22} + 713 q^{23} - 351 q^{24} + 208 q^{25} + 211 q^{26} + 837 q^{27} + 5 q^{28} + 899 q^{29} - 18 q^{30} - 622 q^{31} - 696 q^{32} - 327 q^{33} + 126 q^{34} - 627 q^{35} + 666 q^{36} - 539 q^{37} + 35 q^{38} - 951 q^{39} + 371 q^{40} - 459 q^{41} - 477 q^{42} - 719 q^{43} - 876 q^{44} - 225 q^{45} - 230 q^{46} - 1384 q^{47} + 162 q^{48} - 747 q^{49} - 2005 q^{50} - 540 q^{51} - 2190 q^{52} - 730 q^{53} - 270 q^{54} - 1408 q^{55} - 1107 q^{56} - 651 q^{57} - 290 q^{58} - 3765 q^{59} - 579 q^{60} - 1300 q^{61} - 70 q^{62} - 684 q^{63} - 813 q^{64} - 2490 q^{65} - 480 q^{66} - 2735 q^{67} - 2031 q^{68} + 2139 q^{69} - 2581 q^{70} - 4800 q^{71} - 1053 q^{72} - 1858 q^{73} - 801 q^{74} + 624 q^{75} - 2699 q^{76} - 1661 q^{77} + 633 q^{78} - 4466 q^{79} + 3587 q^{80} + 2511 q^{81} - 5615 q^{82} - 1234 q^{83} + 15 q^{84} - 3623 q^{85} - 1873 q^{86} + 2697 q^{87} - 6893 q^{88} - 455 q^{89} - 54 q^{90} - 2425 q^{91} + 1702 q^{92} - 1866 q^{93} - 3912 q^{94} - 1851 q^{95} - 2088 q^{96} - 2114 q^{97} + 1769 q^{98} - 981 q^{99}+O(q^{100}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9 - 6 * q^10 - 109 * q^11 + 222 * q^12 - 317 * q^13 - 159 * q^14 - 75 * q^15 + 54 * q^16 - 180 * q^17 - 90 * q^18 - 217 * q^19 - 193 * q^20 - 228 * q^21 - 160 * q^22 + 713 * q^23 - 351 * q^24 + 208 * q^25 + 211 * q^26 + 837 * q^27 + 5 * q^28 + 899 * q^29 - 18 * q^30 - 622 * q^31 - 696 * q^32 - 327 * q^33 + 126 * q^34 - 627 * q^35 + 666 * q^36 - 539 * q^37 + 35 * q^38 - 951 * q^39 + 371 * q^40 - 459 * q^41 - 477 * q^42 - 719 * q^43 - 876 * q^44 - 225 * q^45 - 230 * q^46 - 1384 * q^47 + 162 * q^48 - 747 * q^49 - 2005 * q^50 - 540 * q^51 - 2190 * q^52 - 730 * q^53 - 270 * q^54 - 1408 * q^55 - 1107 * q^56 - 651 * q^57 - 290 * q^58 - 3765 * q^59 - 579 * q^60 - 1300 * q^61 - 70 * q^62 - 684 * q^63 - 813 * q^64 - 2490 * q^65 - 480 * q^66 - 2735 * q^67 - 2031 * q^68 + 2139 * q^69 - 2581 * q^70 - 4800 * q^71 - 1053 * q^72 - 1858 * q^73 - 801 * q^74 + 624 * q^75 - 2699 * q^76 - 1661 * q^77 + 633 * q^78 - 4466 * q^79 + 3587 * q^80 + 2511 * q^81 - 5615 * q^82 - 1234 * q^83 + 15 * q^84 - 3623 * q^85 - 1873 * q^86 + 2697 * q^87 - 6893 * q^88 - 455 * q^89 - 54 * q^90 - 2425 * q^91 + 1702 * q^92 - 1866 * q^93 - 3912 * q^94 - 1851 * q^95 - 2088 * q^96 - 2114 * q^97 + 1769 * q^98 - 981 * 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 $

$2$	−4.75649	−1.68167	−0.840836	−	0.541290i	$-0.817936\pi$
$2$	−4.75649	−1.68167	−0.840836	+	0.541290i	$0.817936\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.6242	1.82802
$5$	−4.17105	−0.373070	−0.186535	−	0.982448i	$-0.559726\pi$
$5$	−4.17105	−0.373070	−0.186535	+	0.982448i	$0.559726\pi$
$6$	−14.2695	−0.970914
$7$	−30.3756	−1.64013	−0.820063	−	0.572273i	$-0.806062\pi$
$7$	−30.3756	−1.64013	−0.820063	+	0.572273i	$0.806062\pi$
$8$	−31.5078	−1.39246
$9$	9.00000	0.333333
$10$	19.8395	0.627381
$11$	−34.2306	−0.938266	−0.469133	−	0.883128i	$-0.655433\pi$
$11$	−34.2306	−0.938266	−0.469133	+	0.883128i	$0.655433\pi$
$12$	43.8725	1.05541
$13$	−14.7793	−0.315311	−0.157656	−	0.987494i	$-0.550394\pi$
$13$	−14.7793	−0.315311	−0.157656	+	0.987494i	$0.550394\pi$
$14$	144.481	2.75816
$15$	−12.5131	−0.215392
$16$	32.8730	0.513641
$17$	−2.37953	−0.0339483	−0.0169742	−	0.999856i	$-0.505403\pi$
$17$	−2.37953	−0.0339483	−0.0169742	+	0.999856i	$0.505403\pi$
$18$	−42.8084	−0.560557
$19$	92.5411	1.11739	0.558695	−	0.829373i	$-0.311302\pi$
$19$	92.5411	1.11739	0.558695	+	0.829373i	$0.311302\pi$
$20$	−60.9981	−0.681979
$21$	−91.1267	−0.946928
$22$	162.818	1.57786
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−94.5234	−0.803938
$25$	−107.602	−0.860819
$26$	70.2976	0.530250
$27$	27.0000	0.192450
$28$	−444.218	−2.99819
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	59.5186	0.362218
$31$	−8.32753	−0.0482474	−0.0241237	−	0.999709i	$-0.507680\pi$
$31$	−8.32753	−0.0482474	−0.0241237	+	0.999709i	$0.507680\pi$
$32$	95.7021	0.528685
$33$	−102.692	−0.541708
$34$	11.3182	0.0570900
$35$	126.698	0.611882
$36$	131.618	0.609341
$37$	61.5499	0.273480	0.136740	−	0.990607i	$-0.456338\pi$
$37$	61.5499	0.273480	0.136740	+	0.990607i	$0.456338\pi$
$38$	−440.171	−1.87908
$39$	−44.3380	−0.182045
$40$	131.420	0.519485
$41$	−29.9942	−0.114252	−0.0571258	−	0.998367i	$-0.518194\pi$
$41$	−29.9942	−0.114252	−0.0571258	+	0.998367i	$0.518194\pi$
$42$	433.443	1.59242
$43$	474.242	1.68189	0.840945	−	0.541121i	$-0.182000\pi$
$43$	474.242	1.68189	0.840945	+	0.541121i	$0.182000\pi$
$44$	−500.595	−1.71517
$45$	−37.5394	−0.124357
$46$	−109.399	−0.350653
$47$	58.8321	0.182586	0.0912931	−	0.995824i	$-0.470900\pi$
$47$	58.8321	0.182586	0.0912931	+	0.995824i	$0.470900\pi$
$48$	98.6191	0.296551
$49$	579.676	1.69002
$50$	511.809	1.44762
$51$	−7.13860	−0.0196001
$52$	−216.135	−0.576396
$53$	97.0803	0.251604	0.125802	−	0.992055i	$-0.459850\pi$
$53$	97.0803	0.251604	0.125802	+	0.992055i	$0.459850\pi$
$54$	−128.425	−0.323638
$55$	142.777	0.350038
$56$	957.067	2.28381
$57$	277.623	0.645125
$58$	−137.938	−0.312279
$59$	483.143	1.06610	0.533050	−	0.846084i	$-0.321046\pi$
$59$	483.143	1.06610	0.533050	+	0.846084i	$0.321046\pi$
$60$	−182.994	−0.393741
$61$	−20.5984	−0.0432353	−0.0216176	−	0.999766i	$-0.506882\pi$
$61$	−20.5984	−0.0432353	−0.0216176	+	0.999766i	$0.506882\pi$
$62$	39.6098	0.0811362
$63$	−273.380	−0.546709
$64$	−718.190	−1.40272
$65$	61.6452	0.117633
$66$	488.453	0.910975
$67$	88.4255	0.161237	0.0806186	−	0.996745i	$-0.474310\pi$
$67$	88.4255	0.161237	0.0806186	+	0.996745i	$0.474310\pi$
$68$	−34.7987	−0.0620583
$69$	69.0000	0.120386
$70$	−602.637	−1.02898
$71$	1141.25	1.90762	0.953811	−	0.300407i	$-0.0971224\pi$
$71$	1141.25	1.90762	0.953811	+	0.300407i	$0.0971224\pi$
$72$	−283.570	−0.464154
$73$	89.5015	0.143498	0.0717490	−	0.997423i	$-0.477142\pi$
$73$	89.5015	0.143498	0.0717490	+	0.997423i	$0.477142\pi$
$74$	−292.761	−0.459903
$75$	−322.807	−0.496994
$76$	1353.34	2.04261
$77$	1039.77	1.53887
$78$	210.893	0.306140
$79$	−602.408	−0.857926	−0.428963	−	0.903322i	$-0.641121\pi$
$79$	−602.408	−0.857926	−0.428963	+	0.903322i	$0.641121\pi$
$80$	−137.115	−0.191624
$81$	81.0000	0.111111
$82$	142.667	0.192134
$83$	145.329	0.192191	0.0960957	−	0.995372i	$-0.469365\pi$
$83$	145.329	0.192191	0.0960957	+	0.995372i	$0.469365\pi$
$84$	−1332.65	−1.73100
$85$	9.92514	0.0126651
$86$	−2255.73	−2.82839
$87$	87.0000	0.107211
$88$	1078.53	1.30650
$89$	−730.976	−0.870599	−0.435300	−	0.900286i	$-0.643358\pi$
$89$	−730.976	−0.870599	−0.435300	+	0.900286i	$0.643358\pi$
$90$	178.556	0.209127
$91$	448.930	0.517150
$92$	336.356	0.381169
$93$	−24.9826	−0.0278556
$94$	−279.834	−0.307050
$95$	−385.993	−0.416864
$96$	287.106	0.305236
$97$	−500.651	−0.524056	−0.262028	−	0.965060i	$-0.584391\pi$
$97$	−500.651	−0.524056	−0.262028	+	0.965060i	$0.584391\pi$
$98$	−2757.22	−2.84205
$99$	−308.076	−0.312755
$100$	−1573.60	−1.57360
$101$	−235.097	−0.231614	−0.115807	−	0.993272i	$-0.536945\pi$
$101$	−235.097	−0.231614	−0.115807	+	0.993272i	$0.536945\pi$
$102$	33.9547	0.0329609
$103$	114.274	0.109318	0.0546592	−	0.998505i	$-0.482593\pi$
$103$	114.274	0.109318	0.0546592	+	0.998505i	$0.482593\pi$
$104$	465.664	0.439058
$105$	380.094	0.353270
$106$	−461.761	−0.423115
$107$	1244.46	1.12436	0.562181	−	0.827015i	$-0.309963\pi$
$107$	1244.46	1.12436	0.562181	+	0.827015i	$0.309963\pi$
$108$	394.853	0.351803
$109$	−1892.27	−1.66281	−0.831405	−	0.555667i	$-0.812463\pi$
$109$	−1892.27	−1.66281	−0.831405	+	0.555667i	$0.812463\pi$
$110$	−679.119	−0.588650
$111$	184.650	0.157894
$112$	−998.538	−0.842437
$113$	262.197	0.218278	0.109139	−	0.994027i	$-0.465191\pi$
$113$	262.197	0.218278	0.109139	+	0.994027i	$0.465191\pi$
$114$	−1320.51	−1.08489
$115$	−95.9340	−0.0777904
$116$	424.101	0.339455
$117$	−133.014	−0.105104
$118$	−2298.06	−1.79283
$119$	72.2797	0.0556796
$120$	394.261	0.299925
$121$	−159.265	−0.119658
$122$	97.9759	0.0727075
$123$	−89.9827	−0.0659632
$124$	−121.783	−0.0881972
$125$	970.195	0.694215
$126$	1300.33	0.919385
$127$	−2094.86	−1.46369	−0.731844	−	0.681472i	$-0.761340\pi$
$127$	−2094.86	−1.46369	−0.731844	+	0.681472i	$0.761340\pi$
$128$	2650.45	1.83022
$129$	1422.73	0.971039
$130$	−293.215	−0.197820
$131$	−115.778	−0.0772182	−0.0386091	−	0.999254i	$-0.512293\pi$
$131$	−115.778	−0.0772182	−0.0386091	+	0.999254i	$0.512293\pi$
$132$	−1501.78	−0.990254
$133$	−2810.99	−1.83266
$134$	−420.595	−0.271148
$135$	−112.618	−0.0717973
$136$	74.9738	0.0472717
$137$	−520.689	−0.324712	−0.162356	−	0.986732i	$-0.551909\pi$
$137$	−520.689	−0.324712	−0.162356	+	0.986732i	$0.551909\pi$
$138$	−328.198	−0.202450
$139$	−1648.93	−1.00619	−0.503094	−	0.864232i	$-0.667805\pi$
$139$	−1648.93	−1.00619	−0.503094	+	0.864232i	$0.667805\pi$
$140$	1852.85	1.11853
$141$	176.496	0.105416
$142$	−5428.33	−3.20800
$143$	505.905	0.295846
$144$	295.857	0.171214
$145$	−120.960	−0.0692773
$146$	−425.713	−0.241317
$147$	1739.03	0.975732
$148$	900.117	0.499927
$149$	827.014	0.454709	0.227354	−	0.973812i	$-0.426992\pi$
$149$	827.014	0.454709	0.227354	+	0.973812i	$0.426992\pi$
$150$	1535.43	0.835781
$151$	1625.26	0.875904	0.437952	−	0.898998i	$-0.355704\pi$
$151$	1625.26	0.875904	0.437952	+	0.898998i	$0.355704\pi$
$152$	−2915.77	−1.55592
$153$	−21.4158	−0.0113161
$154$	−4945.68	−2.58788
$155$	34.7345	0.0179996
$156$	−648.406	−0.332782
$157$	604.461	0.307269	0.153634	−	0.988128i	$-0.450902\pi$
$157$	604.461	0.307269	0.153634	+	0.988128i	$0.450902\pi$
$158$	2865.35	1.44275
$159$	291.241	0.145264
$160$	−399.178	−0.197236
$161$	−698.638	−0.341990
$162$	−385.275	−0.186852
$163$	5.82846	0.00280074	0.00140037	−	0.999999i	$-0.499554\pi$
$163$	5.82846	0.00280074	0.00140037	+	0.999999i	$0.499554\pi$
$164$	−438.641	−0.208854
$165$	428.332	0.202095
$166$	−691.253	−0.323203
$167$	626.393	0.290250	0.145125	−	0.989413i	$-0.453642\pi$
$167$	626.393	0.290250	0.145125	+	0.989413i	$0.453642\pi$
$168$	2871.20	1.31856
$169$	−1978.57	−0.900579
$170$	−47.2088	−0.0212985
$171$	832.870	0.372463
$172$	6935.40	3.07453
$173$	−1430.16	−0.628514	−0.314257	−	0.949338i	$-0.601755\pi$
$173$	−1430.16	−0.628514	−0.314257	+	0.949338i	$0.601755\pi$
$174$	−413.814	−0.180294
$175$	3268.48	1.41185
$176$	−1125.26	−0.481932
$177$	1449.43	0.615513
$178$	3476.88	1.46406
$179$	121.525	0.0507441	0.0253720	−	0.999678i	$-0.491923\pi$
$179$	121.525	0.0507441	0.0253720	+	0.999678i	$0.491923\pi$
$180$	−548.983	−0.227326
$181$	−2870.35	−1.17874	−0.589369	−	0.807864i	$-0.700623\pi$
$181$	−2870.35	−1.17874	−0.589369	+	0.807864i	$0.700623\pi$
$182$	−2135.33	−0.869677
$183$	−61.7951	−0.0249619
$184$	−724.679	−0.290348
$185$	−256.728	−0.102027
$186$	118.829	0.0468440
$187$	81.4529	0.0318525
$188$	860.371	0.333771
$189$	−820.141	−0.315643
$190$	1835.97	0.701029
$191$	−28.4527	−0.0107789	−0.00538944	−	0.999985i	$-0.501716\pi$
$191$	−28.4527	−0.0107789	−0.00538944	+	0.999985i	$0.501716\pi$
$192$	−2154.57	−0.809858
$193$	1560.94	0.582170	0.291085	−	0.956697i	$-0.405984\pi$
$193$	1560.94	0.582170	0.291085	+	0.956697i	$0.405984\pi$
$194$	2381.34	0.881290
$195$	184.936	0.0679155
$196$	8477.28	3.08939
$197$	2641.10	0.955180	0.477590	−	0.878583i	$-0.341510\pi$
$197$	2641.10	0.955180	0.477590	+	0.878583i	$0.341510\pi$
$198$	1465.36	0.525952
$199$	200.290	0.0713478	0.0356739	−	0.999363i	$-0.488642\pi$
$199$	200.290	0.0713478	0.0356739	+	0.999363i	$0.488642\pi$
$200$	3390.31	1.19866
$201$	265.277	0.0930904
$202$	1118.24	0.389499
$203$	−880.892	−0.304564
$204$	−104.396	−0.0358294
$205$	125.107	0.0426238
$206$	−543.545	−0.183838
$207$	207.000	0.0695048
$208$	−485.841	−0.161957
$209$	−3167.74	−1.04841
$210$	−1807.91	−0.594084
$211$	630.294	0.205646	0.102823	−	0.994700i	$-0.467213\pi$
$211$	630.294	0.205646	0.102823	+	0.994700i	$0.467213\pi$
$212$	1419.72	0.459937
$213$	3423.74	1.10137
$214$	−5919.27	−1.89081
$215$	−1978.09	−0.627462
$216$	−850.710	−0.267979
$217$	252.953	0.0791318
$218$	9000.54	2.79630
$219$	268.504	0.0828486
$220$	2088.00	0.639878
$221$	35.1679	0.0107043
$222$	−878.284	−0.265525
$223$	−2655.31	−0.797368	−0.398684	−	0.917088i	$-0.630533\pi$
$223$	−2655.31	−0.797368	−0.398684	+	0.917088i	$0.630533\pi$
$224$	−2907.01	−0.867110
$225$	−968.421	−0.286940
$226$	−1247.14	−0.367072
$227$	2035.31	0.595102	0.297551	−	0.954706i	$-0.403830\pi$
$227$	2035.31	0.595102	0.297551	+	0.954706i	$0.403830\pi$
$228$	4060.01	1.17930
$229$	430.447	0.124213	0.0621063	−	0.998070i	$-0.480218\pi$
$229$	430.447	0.124213	0.0621063	+	0.998070i	$0.480218\pi$
$230$	456.309	0.130818
$231$	3119.32	0.888470
$232$	−913.726	−0.258574
$233$	−666.832	−0.187492	−0.0937459	−	0.995596i	$-0.529884\pi$
$233$	−666.832	−0.187492	−0.0937459	+	0.995596i	$0.529884\pi$
$234$	632.679	0.176750
$235$	−245.391	−0.0681173
$236$	7065.56	1.94885
$237$	−1807.22	−0.495324
$238$	−343.797	−0.0936348
$239$	2290.76	0.619987	0.309993	−	0.950739i	$-0.399673\pi$
$239$	2290.76	0.619987	0.309993	+	0.950739i	$0.399673\pi$
$240$	−411.345	−0.110634
$241$	6763.00	1.80765	0.903824	−	0.427904i	$-0.140748\pi$
$241$	6763.00	1.80765	0.903824	+	0.427904i	$0.140748\pi$
$242$	757.540	0.201225
$243$	243.000	0.0641500
$244$	−301.234	−0.0790350
$245$	−2417.85	−0.630494
$246$	428.002	0.110928
$247$	−1367.69	−0.352325
$248$	262.382	0.0671826
$249$	435.986	0.110962
$250$	−4614.72	−1.16744
$251$	−1338.24	−0.336530	−0.168265	−	0.985742i	$-0.553816\pi$
$251$	−1338.24	−0.336530	−0.168265	+	0.985742i	$0.553816\pi$
$252$	−3997.96	−0.999396
$253$	−787.304	−0.195642
$254$	9964.15	2.46144
$255$	29.7754	0.00731219
$256$	−6861.29	−1.67512
$257$	1117.77	0.271302	0.135651	−	0.990757i	$-0.456687\pi$
$257$	1117.77	0.271302	0.135651	+	0.990757i	$0.456687\pi$
$258$	−6767.18	−1.63297
$259$	−1869.61	−0.448541
$260$	901.510	0.215036
$261$	261.000	0.0618984
$262$	550.698	0.129856
$263$	4382.25	1.02746	0.513728	−	0.857953i	$-0.328264\pi$
$263$	4382.25	1.02746	0.513728	+	0.857953i	$0.328264\pi$
$264$	3235.59	0.754307
$265$	−404.926	−0.0938658
$266$	13370.4	3.08193
$267$	−2192.93	−0.502641
$268$	1293.15	0.294745
$269$	−2316.75	−0.525111	−0.262556	−	0.964917i	$-0.584565\pi$
$269$	−2316.75	−0.525111	−0.262556	+	0.964917i	$0.584565\pi$
$270$	535.667	0.120739
$271$	2355.32	0.527954	0.263977	−	0.964529i	$-0.414966\pi$
$271$	2355.32	0.527954	0.263977	+	0.964529i	$0.414966\pi$
$272$	−78.2225	−0.0174373
$273$	1346.79	0.298577
$274$	2476.65	0.546058
$275$	3683.30	0.807677
$276$	1009.07	0.220068
$277$	−2844.52	−0.617007	−0.308503	−	0.951223i	$-0.599828\pi$
$277$	−2844.52	−0.617007	−0.308503	+	0.951223i	$0.599828\pi$
$278$	7843.10	1.69208
$279$	−74.9477	−0.0160825
$280$	−3991.97	−0.852021
$281$	2718.98	0.577227	0.288613	−	0.957446i	$-0.406806\pi$
$281$	2718.98	0.577227	0.288613	+	0.957446i	$0.406806\pi$
$282$	−839.503	−0.177275
$283$	3930.48	0.825592	0.412796	−	0.910823i	$-0.364552\pi$
$283$	3930.48	0.825592	0.412796	+	0.910823i	$0.364552\pi$
$284$	16689.8	3.48717
$285$	−1157.98	−0.240677
$286$	−2406.33	−0.497515
$287$	911.092	0.187387
$288$	861.319	0.176228
$289$	−4907.34	−0.998848
$290$	575.346	0.116502
$291$	−1501.95	−0.302564
$292$	1308.89	0.262318
$293$	5997.30	1.19579	0.597894	−	0.801575i	$-0.296004\pi$
$293$	5997.30	1.19579	0.597894	+	0.801575i	$0.296004\pi$
$294$	−8271.66	−1.64086
$295$	−2015.21	−0.397729
$296$	−1939.30	−0.380810
$297$	−924.227	−0.180569
$298$	−3933.68	−0.764671
$299$	−339.924	−0.0657469
$300$	−4720.79	−0.908516
$301$	−14405.4	−2.75851
$302$	−7730.51	−1.47298
$303$	−705.291	−0.133722
$304$	3042.11	0.573937
$305$	85.9167	0.0161298
$306$	101.864	0.0190300
$307$	−8219.88	−1.52812	−0.764060	−	0.645145i	$-0.776797\pi$
$307$	−8219.88	−1.52812	−0.764060	+	0.645145i	$0.776797\pi$
$308$	15205.8	2.81310
$309$	342.823	0.0631150
$310$	−165.214	−0.0302695
$311$	−9415.76	−1.71678	−0.858391	−	0.512997i	$-0.828535\pi$
$311$	−9415.76	−1.71678	−0.858391	+	0.512997i	$0.828535\pi$
$312$	1396.99	0.253491
$313$	1807.98	0.326496	0.163248	−	0.986585i	$-0.447803\pi$
$313$	1807.98	0.326496	0.163248	+	0.986585i	$0.447803\pi$
$314$	−2875.11	−0.516726
$315$	1140.28	0.203961
$316$	−8809.72	−1.56831
$317$	−5819.06	−1.03101	−0.515506	−	0.856886i	$-0.672396\pi$
$317$	−5819.06	−1.03101	−0.515506	+	0.856886i	$0.672396\pi$
$318$	−1385.28	−0.244286
$319$	−992.688	−0.174232
$320$	2995.60	0.523311
$321$	3733.38	0.649150
$322$	3323.06	0.575115
$323$	−220.205	−0.0379335
$324$	1184.56	0.203114
$325$	1590.29	0.271426
$326$	−27.7230	−0.00470992
$327$	−5676.80	−0.960024
$328$	945.052	0.159091
$329$	−1787.06	−0.299464
$330$	−2037.36	−0.339857
$331$	−2903.63	−0.482169	−0.241085	−	0.970504i	$-0.577503\pi$
$331$	−2903.63	−0.482169	−0.241085	+	0.970504i	$0.577503\pi$
$332$	2125.31	0.351330
$333$	553.949	0.0911599
$334$	−2979.43	−0.488105
$335$	−368.827	−0.0601527
$336$	−2995.61	−0.486381
$337$	−4473.86	−0.723165	−0.361582	−	0.932340i	$-0.617763\pi$
$337$	−4473.86	−0.723165	−0.361582	+	0.932340i	$0.617763\pi$
$338$	9411.05	1.51448
$339$	786.591	0.126023
$340$	145.147	0.0231521
$341$	285.056	0.0452688
$342$	−3961.54	−0.626361
$343$	−7189.16	−1.13171
$344$	−14942.3	−2.34197
$345$	−287.802	−0.0449123
$346$	6802.53	1.05696
$347$	−5785.00	−0.894971	−0.447485	−	0.894291i	$-0.647680\pi$
$347$	−5785.00	−0.894971	−0.447485	+	0.894291i	$0.647680\pi$
$348$	1272.30	0.195984
$349$	−5033.72	−0.772060	−0.386030	−	0.922486i	$-0.626154\pi$
$349$	−5033.72	−0.772060	−0.386030	+	0.922486i	$0.626154\pi$
$350$	−15546.5	−2.37427
$351$	−399.042	−0.0606817
$352$	−3275.94	−0.496046
$353$	8943.42	1.34847	0.674236	−	0.738516i	$-0.264473\pi$
$353$	8943.42	1.34847	0.674236	+	0.738516i	$0.264473\pi$
$354$	−6894.19	−1.03509
$355$	−4760.20	−0.711676
$356$	−10689.9	−1.59147
$357$	216.839	0.0321466
$358$	−578.031	−0.0853349
$359$	−10832.1	−1.59247	−0.796235	−	0.604988i	$-0.793178\pi$
$359$	−10832.1	−1.59247	−0.796235	+	0.604988i	$0.793178\pi$
$360$	1182.78	0.173162
$361$	1704.86	0.248559
$362$	13652.8	1.98225
$363$	−477.794	−0.0690845
$364$	6565.23	0.945362
$365$	−373.315	−0.0535348
$366$	293.928	0.0419777
$367$	−8825.06	−1.25522	−0.627608	−	0.778529i	$-0.715966\pi$
$367$	−8825.06	−1.25522	−0.627608	+	0.778529i	$0.715966\pi$
$368$	756.080	0.107102
$369$	−269.948	−0.0380839
$370$	1221.12	0.171576
$371$	−2948.87	−0.412662
$372$	−365.350	−0.0509207
$373$	917.958	0.127427	0.0637133	−	0.997968i	$-0.479706\pi$
$373$	917.958	0.127427	0.0637133	+	0.997968i	$0.479706\pi$
$374$	−387.430	−0.0535655
$375$	2910.59	0.400805
$376$	−1853.67	−0.254244
$377$	−428.600	−0.0585518
$378$	3900.99	0.530807
$379$	5785.21	0.784079	0.392040	−	0.919948i	$-0.371770\pi$
$379$	5785.21	0.784079	0.392040	+	0.919948i	$0.371770\pi$
$380$	−5644.83	−0.762036
$381$	−6284.57	−0.845060
$382$	135.335	0.0181266
$383$	11569.3	1.54351	0.771753	−	0.635922i	$-0.219380\pi$
$383$	11569.3	1.54351	0.771753	+	0.635922i	$0.219380\pi$
$384$	7951.34	1.05668
$385$	−4336.95	−0.574107
$386$	−7424.59	−0.979020
$387$	4268.18	0.560630
$388$	−7321.61	−0.957985
$389$	1503.28	0.195936	0.0979681	−	0.995190i	$-0.468766\pi$
$389$	1503.28	0.195936	0.0979681	+	0.995190i	$0.468766\pi$
$390$	−879.644	−0.114212
$391$	−54.7293	−0.00707872
$392$	−18264.3	−2.35328
$393$	−347.335	−0.0445820
$394$	−12562.4	−1.60630
$395$	2512.67	0.320066
$396$	−4505.35	−0.571723
$397$	−3858.34	−0.487770	−0.243885	−	0.969804i	$-0.578422\pi$
$397$	−3858.34	−0.487770	−0.243885	+	0.969804i	$0.578422\pi$
$398$	−952.679	−0.119984
$399$	−8432.97	−1.05809
$400$	−3537.22	−0.442152
$401$	4227.38	0.526447	0.263224	−	0.964735i	$-0.415214\pi$
$401$	4227.38	0.526447	0.263224	+	0.964735i	$0.415214\pi$
$402$	−1261.78	−0.156548
$403$	123.075	0.0152129
$404$	−3438.10	−0.423396
$405$	−337.855	−0.0414522
$406$	4189.95	0.512177
$407$	−2106.89	−0.256597
$408$	224.922	0.0272923
$409$	619.844	0.0749372	0.0374686	−	0.999298i	$-0.488071\pi$
$409$	619.844	0.0749372	0.0374686	+	0.999298i	$0.488071\pi$
$410$	−595.071	−0.0716792
$411$	−1562.07	−0.187472
$412$	1671.17	0.199836
$413$	−14675.7	−1.74854
$414$	−984.593	−0.116884
$415$	−606.172	−0.0717008
$416$	−1414.41	−0.166700
$417$	−4946.78	−0.580923
$418$	15067.3	1.76308
$419$	−13430.5	−1.56593	−0.782965	−	0.622066i	$-0.786294\pi$
$419$	−13430.5	−1.56593	−0.782965	+	0.622066i	$0.786294\pi$
$420$	5558.56	0.645785
$421$	−14837.8	−1.71769	−0.858847	−	0.512233i	$-0.828819\pi$
$421$	−14837.8	−1.71769	−0.858847	+	0.512233i	$0.828819\pi$
$422$	−2997.99	−0.345829
$423$	529.489	0.0608620
$424$	−3058.79	−0.350349
$425$	256.043	0.0292234
$426$	−16285.0	−1.85214
$427$	625.687	0.0709113
$428$	18199.2	2.05536
$429$	1517.72	0.170807
$430$	9408.74	1.05519
$431$	−14087.8	−1.57445	−0.787224	−	0.616667i	$-0.788482\pi$
$431$	−14087.8	−1.57445	−0.787224	+	0.616667i	$0.788482\pi$
$432$	887.572	0.0988503
$433$	4551.22	0.505122	0.252561	−	0.967581i	$-0.418727\pi$
$433$	4551.22	0.505122	0.252561	+	0.967581i	$0.418727\pi$
$434$	−1203.17	−0.133074
$435$	−362.881	−0.0399973
$436$	−27672.8	−3.03965
$437$	2128.45	0.232992
$438$	−1277.14	−0.139324
$439$	−15148.8	−1.64695	−0.823476	−	0.567352i	$-0.807968\pi$
$439$	−15148.8	−1.64695	−0.823476	+	0.567352i	$0.807968\pi$
$440$	−4498.60	−0.487415
$441$	5217.08	0.563339
$442$	−167.276	−0.0180011
$443$	−16438.5	−1.76301	−0.881506	−	0.472172i	$-0.843470\pi$
$443$	−16438.5	−1.76301	−0.881506	+	0.472172i	$0.843470\pi$
$444$	2700.35	0.288633
$445$	3048.94	0.324794
$446$	12630.0	1.34091
$447$	2481.04	0.262526
$448$	21815.4	2.30063
$449$	−9749.87	−1.02478	−0.512388	−	0.858754i	$-0.671239\pi$
$449$	−9749.87	−1.02478	−0.512388	+	0.858754i	$0.671239\pi$
$450$	4606.28	0.482539
$451$	1026.72	0.107198
$452$	3834.41	0.399017
$453$	4875.77	0.505703
$454$	−9680.92	−1.00077
$455$	−1872.51	−0.192933
$456$	−8747.30	−0.898311
$457$	11457.8	1.17280	0.586402	−	0.810020i	$-0.300544\pi$
$457$	11457.8	1.17280	0.586402	+	0.810020i	$0.300544\pi$
$458$	−2047.41	−0.208885
$459$	−64.2474	−0.00653336
$460$	−1402.96	−0.142203
$461$	15354.8	1.55129	0.775647	−	0.631167i	$-0.217424\pi$
$461$	15354.8	1.55129	0.775647	+	0.631167i	$0.217424\pi$
$462$	−14837.0	−1.49411
$463$	4954.84	0.497345	0.248673	−	0.968588i	$-0.420006\pi$
$463$	4954.84	0.497345	0.248673	+	0.968588i	$0.420006\pi$
$464$	953.318	0.0953808
$465$	104.203	0.0103921
$466$	3171.78	0.315300
$467$	2076.75	0.205782	0.102891	−	0.994693i	$-0.467191\pi$
$467$	2076.75	0.205782	0.102891	+	0.994693i	$0.467191\pi$
$468$	−1945.22	−0.192132
$469$	−2685.98	−0.264450
$470$	1167.20	0.114551
$471$	1813.38	0.177402
$472$	−15222.8	−1.48450
$473$	−16233.6	−1.57806
$474$	8596.04	0.832973
$475$	−9957.65	−0.961870
$476$	1057.03	0.101783
$477$	873.723	0.0838680
$478$	−10896.0	−1.04261
$479$	−9149.11	−0.872721	−0.436361	−	0.899772i	$-0.643733\pi$
$479$	−9149.11	−0.872721	−0.436361	+	0.899772i	$0.643733\pi$
$480$	−1197.53	−0.113874
$481$	−909.666	−0.0862312
$482$	−32168.1	−3.03987
$483$	−2095.91	−0.197448
$484$	−2329.11	−0.218737
$485$	2088.24	0.195509
$486$	−1155.83	−0.107879
$487$	−2171.13	−0.202019	−0.101010	−	0.994885i	$-0.532207\pi$
$487$	−2171.13	−0.202019	−0.101010	+	0.994885i	$0.532207\pi$
$488$	649.009	0.0602034
$489$	17.4854	0.00161701
$490$	11500.5	1.06028
$491$	9065.76	0.833263	0.416632	−	0.909075i	$-0.363211\pi$
$491$	9065.76	0.833263	0.416632	+	0.909075i	$0.363211\pi$
$492$	−1315.92	−0.120582
$493$	−69.0065	−0.00630405
$494$	6505.42	0.592496
$495$	1285.00	0.116679
$496$	−273.751	−0.0247818
$497$	−34666.1	−3.12874
$498$	−2073.76	−0.186601
$499$	−8655.20	−0.776473	−0.388237	−	0.921560i	$-0.626916\pi$
$499$	−8655.20	−0.776473	−0.388237	+	0.921560i	$0.626916\pi$
$500$	14188.3	1.26904
$501$	1879.18	0.167576
$502$	6365.33	0.565933
$503$	11568.8	1.02550	0.512749	−	0.858539i	$-0.328627\pi$
$503$	11568.8	1.02550	0.512749	+	0.858539i	$0.328627\pi$
$504$	8613.61	0.761271
$505$	980.600	0.0864082
$506$	3744.80	0.329006
$507$	−5935.72	−0.519949
$508$	−30635.5	−2.67565
$509$	−5486.28	−0.477750	−0.238875	−	0.971050i	$-0.576779\pi$
$509$	−5486.28	−0.477750	−0.238875	+	0.971050i	$0.576779\pi$
$510$	−141.626	−0.0122967
$511$	−2718.66	−0.235355
$512$	11432.1	0.986780
$513$	2498.61	0.215042
$514$	−5316.67	−0.456242
$515$	−476.644	−0.0407834
$516$	20806.2	1.77508
$517$	−2013.86	−0.171314
$518$	8892.80	0.754299
$519$	−4290.48	−0.362873
$520$	−1942.30	−0.163799
$521$	15937.3	1.34016	0.670082	−	0.742287i	$-0.266259\pi$
$521$	15937.3	1.34016	0.670082	+	0.742287i	$0.266259\pi$
$522$	−1241.44	−0.104093
$523$	−17430.5	−1.45733	−0.728665	−	0.684870i	$-0.759859\pi$
$523$	−17430.5	−1.45733	−0.728665	+	0.684870i	$0.759859\pi$
$524$	−1693.16	−0.141157
$525$	9805.45	0.815133
$526$	−20844.1	−1.72784
$527$	19.8156	0.00163792
$528$	−3375.79	−0.278244
$529$	529.000	0.0434783
$530$	1926.03	0.157851
$531$	4348.29	0.355366
$532$	−41108.4	−3.35014
$533$	443.294	0.0360248
$534$	10430.6	0.845277
$535$	−5190.71	−0.419465
$536$	−2786.09	−0.224517
$537$	364.574	0.0292971
$538$	11019.6	0.883065
$539$	−19842.7	−1.58568
$540$	−1646.95	−0.131247
$541$	17232.0	1.36943	0.684715	−	0.728811i	$-0.259927\pi$
$541$	17232.0	1.36943	0.684715	+	0.728811i	$0.259927\pi$
$542$	−11203.1	−0.887846
$543$	−8611.05	−0.680544
$544$	−227.726	−0.0179480
$545$	7892.73	0.620344
$546$	−6405.99	−0.502108
$547$	−11565.8	−0.904053	−0.452026	−	0.892005i	$-0.649299\pi$
$547$	−11565.8	−0.904053	−0.452026	+	0.892005i	$0.649299\pi$
$548$	−7614.65	−0.593580
$549$	−185.385	−0.0144118
$550$	−17519.6	−1.35825
$551$	2683.69	0.207494
$552$	−2174.04	−0.167633
$553$	18298.5	1.40711
$554$	13529.9	1.03760
$555$	−770.183	−0.0589053
$556$	−24114.2	−1.83933
$557$	771.475	0.0586866	0.0293433	−	0.999569i	$-0.490658\pi$
$557$	771.475	0.0586866	0.0293433	+	0.999569i	$0.490658\pi$
$558$	356.488	0.0270454
$559$	−7008.97	−0.530318
$560$	4164.95	0.314288
$561$	244.359	0.0183901
$562$	−12932.8	−0.970706
$563$	3860.00	0.288951	0.144476	−	0.989508i	$-0.453851\pi$
$563$	3860.00	0.288951	0.144476	+	0.989508i	$0.453851\pi$
$564$	2581.11	0.192703
$565$	−1093.63	−0.0814329
$566$	−18695.3	−1.38838
$567$	−2460.42	−0.182236
$568$	−35958.2	−2.65629
$569$	−963.994	−0.0710241	−0.0355121	−	0.999369i	$-0.511306\pi$
$569$	−963.994	−0.0710241	−0.0355121	+	0.999369i	$0.511306\pi$
$570$	5507.92	0.404739
$571$	−13470.5	−0.987255	−0.493628	−	0.869673i	$-0.664329\pi$
$571$	−13470.5	−0.987255	−0.493628	+	0.869673i	$0.664329\pi$
$572$	7398.45	0.540812
$573$	−85.3582	−0.00622319
$574$	−4333.60	−0.315124
$575$	−2474.85	−0.179493
$576$	−6463.71	−0.467572
$577$	6991.31	0.504423	0.252212	−	0.967672i	$-0.418842\pi$
$577$	6991.31	0.504423	0.252212	+	0.967672i	$0.418842\pi$
$578$	23341.7	1.67973
$579$	4682.82	0.336116
$580$	−1768.94	−0.126640
$581$	−4414.44	−0.315218
$582$	7144.02	0.508813
$583$	−3323.12	−0.236071
$584$	−2819.99	−0.199815
$585$	554.807	0.0392110
$586$	−28526.1	−2.01092
$587$	7823.38	0.550095	0.275047	−	0.961431i	$-0.411306\pi$
$587$	7823.38	0.550095	0.275047	+	0.961431i	$0.411306\pi$
$588$	25431.8	1.78366
$589$	−770.639	−0.0539111
$590$	9585.32	0.668850
$591$	7923.30	0.551474
$592$	2023.33	0.140470
$593$	−1772.08	−0.122716	−0.0613579	−	0.998116i	$-0.519543\pi$
$593$	−1772.08	−0.122716	−0.0613579	+	0.998116i	$0.519543\pi$
$594$	4396.07	0.303658
$595$	−301.482	−0.0207724
$596$	12094.4	0.831217
$597$	600.871	0.0411927
$598$	1616.85	0.110565
$599$	−401.560	−0.0273911	−0.0136956	−	0.999906i	$-0.504360\pi$
$599$	−401.560	−0.0273911	−0.0136956	+	0.999906i	$0.504360\pi$
$600$	10170.9	0.692045
$601$	23192.4	1.57410	0.787052	−	0.616887i	$-0.211606\pi$
$601$	23192.4	1.57410	0.787052	+	0.616887i	$0.211606\pi$
$602$	68519.0	4.63891
$603$	795.830	0.0537458
$604$	23768.0	1.60117
$605$	664.300	0.0446407
$606$	3354.71	0.224877
$607$	−12291.1	−0.821876	−0.410938	−	0.911663i	$-0.634799\pi$
$607$	−12291.1	−0.821876	−0.410938	+	0.911663i	$0.634799\pi$
$608$	8856.38	0.590746
$609$	−2642.68	−0.175840
$610$	−408.662	−0.0271250
$611$	−869.499	−0.0575714
$612$	−313.188	−0.0206861
$613$	−9296.16	−0.612510	−0.306255	−	0.951950i	$-0.599076\pi$
$613$	−9296.16	−0.612510	−0.306255	+	0.951950i	$0.599076\pi$
$614$	39097.7	2.56980
$615$	375.322	0.0246089
$616$	−32761.0	−2.14282
$617$	17475.3	1.14024	0.570122	−	0.821560i	$-0.306896\pi$
$617$	17475.3	1.14024	0.570122	+	0.821560i	$0.306896\pi$
$618$	−1630.63	−0.106139
$619$	−6020.30	−0.390915	−0.195457	−	0.980712i	$-0.562619\pi$
$619$	−6020.30	−0.390915	−0.195457	+	0.980712i	$0.562619\pi$
$620$	507.963	0.0329037
$621$	621.000	0.0401286
$622$	44786.0	2.88706
$623$	22203.8	1.42789
$624$	−1457.52	−0.0935058
$625$	9403.57	0.601829
$626$	−8599.64	−0.549059
$627$	−9503.22	−0.605299
$628$	8839.74	0.561694
$629$	−146.460	−0.00928418
$630$	−5423.73	−0.342995
$631$	6007.81	0.379029	0.189514	−	0.981878i	$-0.439309\pi$
$631$	6007.81	0.379029	0.189514	+	0.981878i	$0.439309\pi$
$632$	18980.5	1.19463
$633$	1890.88	0.118730
$634$	27678.3	1.73382
$635$	8737.74	0.546057
$636$	4259.16	0.265545
$637$	−8567.21	−0.532881
$638$	4721.71	0.293000
$639$	10271.2	0.635874
$640$	−11055.1	−0.682801
$641$	−16642.4	−1.02549	−0.512743	−	0.858542i	$-0.671371\pi$
$641$	−16642.4	−1.02549	−0.512743	+	0.858542i	$0.671371\pi$
$642$	−17757.8	−1.09166
$643$	1672.86	0.102599	0.0512994	−	0.998683i	$-0.483664\pi$
$643$	1672.86	0.102599	0.0512994	+	0.998683i	$0.483664\pi$
$644$	−10217.0	−0.625165
$645$	−5934.26	−0.362265
$646$	1047.40	0.0637917
$647$	−27544.7	−1.67372	−0.836858	−	0.547421i	$-0.815610\pi$
$647$	−27544.7	−1.67372	−0.836858	+	0.547421i	$0.815610\pi$
$648$	−2552.13	−0.154718
$649$	−16538.3	−1.00028
$650$	−7564.19	−0.456449
$651$	758.860	0.0456868
$652$	85.2363	0.00511980
$653$	4529.19	0.271425	0.135713	−	0.990748i	$-0.456668\pi$
$653$	4529.19	0.271425	0.135713	+	0.990748i	$0.456668\pi$
$654$	27001.6	1.61445
$655$	482.916	0.0288078
$656$	−986.002	−0.0586843
$657$	805.513	0.0478327
$658$	8500.13	0.503601
$659$	−99.5571	−0.00588497	−0.00294248	−	0.999996i	$-0.500937\pi$
$659$	−99.5571	−0.00588497	−0.00294248	+	0.999996i	$0.500937\pi$
$660$	6264.01	0.369434
$661$	−1868.55	−0.109952	−0.0549759	−	0.998488i	$-0.517508\pi$
$661$	−1868.55	−0.109952	−0.0549759	+	0.998488i	$0.517508\pi$
$662$	13811.1	0.810851
$663$	105.504	0.00618012
$664$	−4578.98	−0.267619
$665$	11724.8	0.683710
$666$	−2634.85	−0.153301
$667$	667.000	0.0387202
$668$	9160.48	0.530583
$669$	−7965.94	−0.460361
$670$	1754.32	0.101157
$671$	705.095	0.0405662
$672$	−8721.02	−0.500626
$673$	19549.3	1.11972	0.559858	−	0.828589i	$-0.310856\pi$
$673$	19549.3	1.11972	0.559858	+	0.828589i	$0.310856\pi$
$674$	21279.8	1.21613
$675$	−2905.26	−0.165665
$676$	−28935.0	−1.64628
$677$	−659.254	−0.0374257	−0.0187129	−	0.999825i	$-0.505957\pi$
$677$	−659.254	−0.0374257	−0.0187129	+	0.999825i	$0.505957\pi$
$678$	−3741.41	−0.211929
$679$	15207.6	0.859518
$680$	−312.719	−0.0176356
$681$	6105.92	0.343582
$682$	−1355.87	−0.0761273
$683$	−33338.5	−1.86774	−0.933868	−	0.357618i	$-0.883589\pi$
$683$	−33338.5	−1.86774	−0.933868	+	0.357618i	$0.883589\pi$
$684$	12180.0	0.680871
$685$	2171.82	0.121140
$686$	34195.2	1.90317
$687$	1291.34	0.0717142
$688$	15589.8	0.863888
$689$	−1434.78	−0.0793335
$690$	1368.93	0.0755278
$691$	28307.7	1.55843	0.779215	−	0.626756i	$-0.215618\pi$
$691$	28307.7	1.55843	0.779215	+	0.626756i	$0.215618\pi$
$692$	−20914.9	−1.14894
$693$	9357.97	0.512958
$694$	27516.3	1.50505
$695$	6877.75	0.375378
$696$	−2741.18	−0.149287
$697$	71.3723	0.00387865
$698$	23942.8	1.29835
$699$	−2000.49	−0.108248
$700$	47798.9	2.58090
$701$	−20500.6	−1.10456	−0.552280	−	0.833659i	$-0.686242\pi$
$701$	−20500.6	−1.10456	−0.552280	+	0.833659i	$0.686242\pi$
$702$	1898.04	0.102047
$703$	5695.90	0.305583
$704$	24584.1	1.31612
$705$	−736.174	−0.0393276
$706$	−42539.3	−2.26769
$707$	7141.21	0.379877
$708$	21196.7	1.12517
$709$	−2675.39	−0.141716	−0.0708578	−	0.997486i	$-0.522574\pi$
$709$	−2675.39	−0.141716	−0.0708578	+	0.997486i	$0.522574\pi$
$710$	22641.8	1.19681
$711$	−5421.67	−0.285975
$712$	23031.5	1.21228
$713$	−191.533	−0.0100603
$714$	−1031.39	−0.0540601
$715$	−2110.15	−0.110371
$716$	1777.20	0.0927612
$717$	6872.28	0.357950
$718$	51522.8	2.67801
$719$	4110.71	0.213218	0.106609	−	0.994301i	$-0.466001\pi$
$719$	4110.71	0.213218	0.106609	+	0.994301i	$0.466001\pi$
$720$	−1234.03	−0.0638747
$721$	−3471.15	−0.179296
$722$	−8109.16	−0.417994
$723$	20289.0	1.04365
$724$	−41976.5	−2.15476
$725$	−3120.47	−0.159850
$726$	2272.62	0.116177
$727$	−16687.3	−0.851305	−0.425652	−	0.904887i	$-0.639955\pi$
$727$	−16687.3	−0.851305	−0.425652	+	0.904887i	$0.639955\pi$
$728$	−14144.8	−0.720112
$729$	729.000	0.0370370
$730$	1775.67	0.0900279
$731$	−1128.47	−0.0570973
$732$	−903.702	−0.0456309
$733$	37662.0	1.89779	0.948894	−	0.315595i	$-0.102204\pi$
$733$	37662.0	1.89779	0.948894	+	0.315595i	$0.102204\pi$
$734$	41976.3	2.11086
$735$	−7253.56	−0.364016
$736$	2201.15	0.110238
$737$	−3026.86	−0.151283
$738$	1284.01	0.0640446
$739$	11060.2	0.550549	0.275275	−	0.961366i	$-0.411231\pi$
$739$	11060.2	0.550549	0.275275	+	0.961366i	$0.411231\pi$
$740$	−3754.43	−0.186507
$741$	−4103.08	−0.203415
$742$	14026.3	0.693963
$743$	−19691.3	−0.972279	−0.486140	−	0.873881i	$-0.661595\pi$
$743$	−19691.3	−0.972279	−0.486140	+	0.873881i	$0.661595\pi$
$744$	787.146	0.0387879
$745$	−3449.51	−0.169638
$746$	−4366.26	−0.214290
$747$	1307.96	0.0640638
$748$	1191.18	0.0582271
$749$	−37801.2	−1.84409
$750$	−13844.2	−0.674023
$751$	−6613.33	−0.321336	−0.160668	−	0.987008i	$-0.551365\pi$
$751$	−6613.33	−0.321336	−0.160668	+	0.987008i	$0.551365\pi$
$752$	1933.99	0.0937838
$753$	−4014.72	−0.194296
$754$	2038.63	0.0984650
$755$	−6779.02	−0.326773
$756$	−11993.9	−0.577001
$757$	20560.0	0.987143	0.493571	−	0.869705i	$-0.335691\pi$
$757$	20560.0	0.987143	0.493571	+	0.869705i	$0.335691\pi$
$758$	−27517.3	−1.31856
$759$	−2361.91	−0.112954
$760$	12161.8	0.580467
$761$	−9022.00	−0.429760	−0.214880	−	0.976640i	$-0.568936\pi$
$761$	−9022.00	−0.429760	−0.214880	+	0.976640i	$0.568936\pi$
$762$	29892.5	1.42111
$763$	57478.7	2.72722
$764$	−416.098	−0.0197040
$765$	89.3263	0.00422170
$766$	−55029.2	−2.59567
$767$	−7140.52	−0.336153
$768$	−20583.9	−0.967131
$769$	1032.40	0.0484127	0.0242064	−	0.999707i	$-0.492294\pi$
$769$	1032.40	0.0484127	0.0242064	+	0.999707i	$0.492294\pi$
$770$	20628.6	0.965460
$771$	3353.32	0.156637
$772$	22827.4	1.06422
$773$	−19233.4	−0.894924	−0.447462	−	0.894303i	$-0.647672\pi$
$773$	−19233.4	−0.894924	−0.447462	+	0.894303i	$0.647672\pi$
$774$	−20301.5	−0.942796
$775$	896.062	0.0415322
$776$	15774.4	0.729727
$777$	−5608.84	−0.258965
$778$	−7150.32	−0.329500
$779$	−2775.70	−0.127663
$780$	2704.53	0.124151
$781$	−39065.6	−1.78986
$782$	260.319	0.0119041
$783$	783.000	0.0357371
$784$	19055.7	0.868062
$785$	−2521.23	−0.114633
$786$	1652.09	0.0749723
$787$	−3748.08	−0.169765	−0.0848823	−	0.996391i	$-0.527051\pi$
$787$	−3748.08	−0.169765	−0.0848823	+	0.996391i	$0.527051\pi$
$788$	38623.9	1.74609
$789$	13146.7	0.593202
$790$	−11951.5	−0.538247
$791$	−7964.38	−0.358003
$792$	9706.78	0.435499
$793$	304.430	0.0136326
$794$	18352.1	0.820269
$795$	−1214.78	−0.0541934
$796$	2929.08	0.130425
$797$	17441.1	0.775149	0.387575	−	0.921838i	$-0.373313\pi$
$797$	17441.1	0.775149	0.387575	+	0.921838i	$0.373313\pi$
$798$	40111.3	1.77936
$799$	−139.993	−0.00619849
$800$	−10297.8	−0.455102
$801$	−6578.79	−0.290200
$802$	−20107.5	−0.885312
$803$	−3063.69	−0.134639
$804$	3879.45	0.170171
$805$	2914.05	0.127586
$806$	−585.405	−0.0255832
$807$	−6950.26	−0.303173
$808$	7407.39	0.322514
$809$	−17455.6	−0.758598	−0.379299	−	0.925274i	$-0.623835\pi$
$809$	−17455.6	−0.758598	−0.379299	+	0.925274i	$0.623835\pi$
$810$	1607.00	0.0697090
$811$	−34626.8	−1.49927	−0.749636	−	0.661850i	$-0.769772\pi$
$811$	−34626.8	−1.49927	−0.749636	+	0.661850i	$0.769772\pi$
$812$	−12882.3	−0.556749
$813$	7065.96	0.304814
$814$	10021.4	0.431511
$815$	−24.3108	−0.00104487
$816$	−234.668	−0.0100674
$817$	43886.9	1.87932
$818$	−2948.28	−0.126020
$819$	4040.37	0.172383
$820$	1829.59	0.0779172
$821$	−14743.2	−0.626724	−0.313362	−	0.949634i	$-0.601455\pi$
$821$	−14743.2	−0.626724	−0.313362	+	0.949634i	$0.601455\pi$
$822$	7429.96	0.315267
$823$	−21559.4	−0.913137	−0.456569	−	0.889688i	$-0.650922\pi$
$823$	−21559.4	−0.913137	−0.456569	+	0.889688i	$0.650922\pi$
$824$	−3600.54	−0.152222
$825$	11049.9	0.466312
$826$	69805.0	2.94047
$827$	−24031.0	−1.01045	−0.505224	−	0.862988i	$-0.668590\pi$
$827$	−24031.0	−1.01045	−0.505224	+	0.862988i	$0.668590\pi$
$828$	3027.20	0.127056
$829$	−10916.9	−0.457372	−0.228686	−	0.973500i	$-0.573443\pi$
$829$	−10916.9	−0.457372	−0.228686	+	0.973500i	$0.573443\pi$
$830$	2883.25	0.120577
$831$	−8533.57	−0.356229
$832$	10614.4	0.442292
$833$	−1379.36	−0.0573732
$834$	23529.3	0.976922
$835$	−2612.71	−0.108283
$836$	−46325.6	−1.91651
$837$	−224.843	−0.00928521
$838$	63882.2	2.63338
$839$	−31649.7	−1.30235	−0.651173	−	0.758930i	$-0.725723\pi$
$839$	−31649.7	−1.30235	−0.651173	+	0.758930i	$0.725723\pi$
$840$	−11975.9	−0.491915
$841$	841.000	0.0344828
$842$	70575.7	2.88860
$843$	8156.94	0.333262
$844$	9217.53	0.375925
$845$	8252.71	0.335979
$846$	−2518.51	−0.102350
$847$	4837.75	0.196254
$848$	3191.33	0.129234
$849$	11791.4	0.476656
$850$	−1217.87	−0.0491441
$851$	1415.65	0.0570244
$852$	50069.4	2.01332
$853$	−29436.2	−1.18157	−0.590783	−	0.806830i	$-0.701181\pi$
$853$	−29436.2	−1.18157	−0.590783	+	0.806830i	$0.701181\pi$
$854$	−2976.07	−0.119250
$855$	−3473.94	−0.138955
$856$	−39210.2	−1.56563
$857$	3739.04	0.149035	0.0745175	−	0.997220i	$-0.476258\pi$
$857$	3739.04	0.149035	0.0745175	+	0.997220i	$0.476258\pi$
$858$	−7219.00	−0.287241
$859$	−1212.42	−0.0481575	−0.0240787	−	0.999710i	$-0.507665\pi$
$859$	−1212.42	−0.0481575	−0.0240787	+	0.999710i	$0.507665\pi$
$860$	−28927.9	−1.14701
$861$	2733.28	0.108188
$862$	67008.6	2.64770
$863$	15305.5	0.603714	0.301857	−	0.953353i	$-0.402394\pi$
$863$	15305.5	0.603714	0.301857	+	0.953353i	$0.402394\pi$
$864$	2583.96	0.101745
$865$	5965.26	0.234480
$866$	−21647.8	−0.849449
$867$	−14722.0	−0.576685
$868$	3699.23	0.144655
$869$	20620.8	0.804963
$870$	1726.04	0.0672623
$871$	−1306.87	−0.0508399
$872$	59621.1	2.31540
$873$	−4505.86	−0.174685
$874$	−10123.9	−0.391816
$875$	−29470.2	−1.13860
$876$	3926.66	0.151449
$877$	10534.3	0.405607	0.202803	−	0.979219i	$-0.434995\pi$
$877$	10534.3	0.405607	0.202803	+	0.979219i	$0.434995\pi$
$878$	72055.0	2.76963
$879$	17991.9	0.690389
$880$	4693.53	0.179794
$881$	−15858.8	−0.606465	−0.303232	−	0.952917i	$-0.598066\pi$
$881$	−15858.8	−0.606465	−0.303232	+	0.952917i	$0.598066\pi$
$882$	−24815.0	−0.947351
$883$	−22525.3	−0.858480	−0.429240	−	0.903191i	$-0.641219\pi$
$883$	−22525.3	−0.858480	−0.429240	+	0.903191i	$0.641219\pi$
$884$	514.301	0.0195677
$885$	−6045.63	−0.229629
$886$	78189.3	2.96481
$887$	3439.15	0.130186	0.0650932	−	0.997879i	$-0.479266\pi$
$887$	3439.15	0.130186	0.0650932	+	0.997879i	$0.479266\pi$
$888$	−5817.91	−0.219861
$889$	63632.4	2.40063
$890$	−14502.2	−0.546197
$891$	−2772.68	−0.104252
$892$	−38831.8	−1.45761
$893$	5444.39	0.204020
$894$	−11801.0	−0.441483
$895$	−506.885	−0.0189311
$896$	−80508.8	−3.00180
$897$	−1019.77	−0.0379590
$898$	46375.1	1.72334
$899$	−241.498	−0.00895931
$900$	−14162.4	−0.524532
$901$	−231.006	−0.00854153
$902$	−4883.59	−0.180272
$903$	−43216.1	−1.59263
$904$	−8261.24	−0.303943
$905$	11972.4	0.439751
$906$	−23191.5	−0.850427
$907$	−35.0271	−0.00128231	−0.000641155	−	1.00000i	$-0.500204\pi$
$907$	−35.0271	−0.00128231	−0.000641155		1.00000i	$0.500204\pi$
$908$	29764.7	1.08786
$909$	−2115.87	−0.0772047
$910$	8906.56	0.324450
$911$	−6909.82	−0.251298	−0.125649	−	0.992075i	$-0.540101\pi$
$911$	−6909.82	−0.251298	−0.125649	+	0.992075i	$0.540101\pi$
$912$	9126.33	0.331363
$913$	−4974.69	−0.180327
$914$	−54498.7	−1.97227
$915$	257.750	0.00931252
$916$	6294.92	0.227063
$917$	3516.83	0.126648
$918$	305.592	0.0109870
$919$	−31680.9	−1.13717	−0.568583	−	0.822626i	$-0.692508\pi$
$919$	−31680.9	−1.13717	−0.568583	+	0.822626i	$0.692508\pi$
$920$	3022.67	0.108320
$921$	−24659.6	−0.882261
$922$	−73035.1	−2.60877
$923$	−16866.9	−0.601495
$924$	45617.5	1.62414
$925$	−6622.92	−0.235416
$926$	−23567.6	−0.836372
$927$	1028.47	0.0364395
$928$	2775.36	0.0981742
$929$	−37305.6	−1.31750	−0.658750	−	0.752362i	$-0.728914\pi$
$929$	−37305.6	−1.31750	−0.658750	+	0.752362i	$0.728914\pi$
$930$	−495.642	−0.0174761
$931$	53643.9	1.88841
$932$	−9751.86	−0.342739
$933$	−28247.3	−0.991184
$934$	−9878.02	−0.346058
$935$	−339.744	−0.0118832
$936$	4190.97	0.146353
$937$	42882.4	1.49510	0.747549	−	0.664207i	$-0.231231\pi$
$937$	42882.4	1.49510	0.747549	+	0.664207i	$0.231231\pi$
$938$	12775.8	0.444718
$939$	5423.95	0.188502
$940$	−3588.65	−0.124520
$941$	18361.2	0.636088	0.318044	−	0.948076i	$-0.396974\pi$
$941$	18361.2	0.636088	0.318044	+	0.948076i	$0.396974\pi$
$942$	−8625.33	−0.298332
$943$	−689.868	−0.0238231
$944$	15882.4	0.547593
$945$	3420.84	0.117757
$946$	77214.9	2.65378
$947$	16273.1	0.558401	0.279200	−	0.960233i	$-0.409931\pi$
$947$	16273.1	0.558401	0.279200	+	0.960233i	$0.409931\pi$
$948$	−26429.2	−0.905463
$949$	−1322.77	−0.0452465
$950$	47363.4	1.61755
$951$	−17457.2	−0.595255
$952$	−2277.37	−0.0775316
$953$	12470.8	0.423892	0.211946	−	0.977281i	$-0.432020\pi$
$953$	12470.8	0.423892	0.211946	+	0.977281i	$0.432020\pi$
$954$	−4155.85	−0.141038
$955$	118.678	0.00402128
$956$	33500.5	1.13335
$957$	−2978.06	−0.100593
$958$	43517.6	1.46763
$959$	15816.2	0.532568
$960$	8986.81	0.302133
$961$	−29721.7	−0.997672
$962$	4326.81	0.145013
$963$	11200.2	0.374787
$964$	98903.3	3.30442
$965$	−6510.75	−0.217190
$966$	9969.19	0.332043
$967$	−56323.0	−1.87303	−0.936517	−	0.350622i	$-0.885970\pi$
$967$	−56323.0	−1.87303	−0.936517	+	0.350622i	$0.885970\pi$
$968$	5018.07	0.166619
$969$	−660.614	−0.0219009
$970$	−9932.68	−0.328783
$971$	−19522.9	−0.645233	−0.322616	−	0.946530i	$-0.604562\pi$
$971$	−19522.9	−0.645233	−0.322616	+	0.946530i	$0.604562\pi$
$972$	3553.67	0.117268
$973$	50087.1	1.65028
$974$	10327.0	0.339730
$975$	4770.87	0.156708
$976$	−677.131	−0.0222074
$977$	25586.7	0.837862	0.418931	−	0.908018i	$-0.362405\pi$
$977$	25586.7	0.837862	0.418931	+	0.908018i	$0.362405\pi$
$978$	−83.1689	−0.00271927
$979$	25021.8	0.816853
$980$	−35359.1	−1.15256
$981$	−17030.4	−0.554270
$982$	−43121.2	−1.40128
$983$	13431.3	0.435802	0.217901	−	0.975971i	$-0.430079\pi$
$983$	13431.3	0.435802	0.217901	+	0.975971i	$0.430079\pi$
$984$	2835.16	0.0918511
$985$	−11016.1	−0.356349
$986$	328.228	0.0106013
$987$	−5361.18	−0.172896
$988$	−20001.4	−0.644058
$989$	10907.6	0.350698
$990$	−6112.07	−0.196217
$991$	32649.4	1.04656	0.523281	−	0.852160i	$-0.324708\pi$
$991$	32649.4	1.04656	0.523281	+	0.852160i	$0.324708\pi$
$992$	−796.962	−0.0255076
$993$	−8710.89	−0.278381
$994$	164889.	5.26152
$995$	−835.420	−0.0266177
$996$	6375.93	0.202840
$997$	−24331.7	−0.772912	−0.386456	−	0.922308i	$-0.626301\pi$
$997$	−24331.7	−0.772912	−0.386456	+	0.922308i	$0.626301\pi$
$998$	41168.4	1.30577
$999$	1661.85	0.0526312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.a.1.4	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.a.1.4	✓	31	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-4.75649 q^{2} +3.00000 q^{3} +14.6242 q^{4} -4.17105 q^{5} -14.2695 q^{6} -30.3756 q^{7} -31.5078 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.75649 q^{2} +3.00000 q^{3} +14.6242 q^{4} -4.17105 q^{5} -14.2695 q^{6} -30.3756 q^{7} -31.5078 q^{8} +9.00000 q^{9} +19.8395 q^{10} -34.2306 q^{11} +43.8725 q^{12} -14.7793 q^{13} +144.481 q^{14} -12.5131 q^{15} +32.8730 q^{16} -2.37953 q^{17} -42.8084 q^{18} +92.5411 q^{19} -60.9981 q^{20} -91.1267 q^{21} +162.818 q^{22} +23.0000 q^{23} -94.5234 q^{24} -107.602 q^{25} +70.2976 q^{26} +27.0000 q^{27} -444.218 q^{28} +29.0000 q^{29} +59.5186 q^{30} -8.32753 q^{31} +95.7021 q^{32} -102.692 q^{33} +11.3182 q^{34} +126.698 q^{35} +131.618 q^{36} +61.5499 q^{37} -440.171 q^{38} -44.3380 q^{39} +131.420 q^{40} -29.9942 q^{41} +433.443 q^{42} +474.242 q^{43} -500.595 q^{44} -37.5394 q^{45} -109.399 q^{46} +58.8321 q^{47} +98.6191 q^{48} +579.676 q^{49} +511.809 q^{50} -7.13860 q^{51} -216.135 q^{52} +97.0803 q^{53} -128.425 q^{54} +142.777 q^{55} +957.067 q^{56} +277.623 q^{57} -137.938 q^{58} +483.143 q^{59} -182.994 q^{60} -20.5984 q^{61} +39.6098 q^{62} -273.380 q^{63} -718.190 q^{64} +61.6452 q^{65} +488.453 q^{66} +88.4255 q^{67} -34.7987 q^{68} +69.0000 q^{69} -602.637 q^{70} +1141.25 q^{71} -283.570 q^{72} +89.5015 q^{73} -292.761 q^{74} -322.807 q^{75} +1353.34 q^{76} +1039.77 q^{77} +210.893 q^{78} -602.408 q^{79} -137.115 q^{80} +81.0000 q^{81} +142.667 q^{82} +145.329 q^{83} -1332.65 q^{84} +9.92514 q^{85} -2255.73 q^{86} +87.0000 q^{87} +1078.53 q^{88} -730.976 q^{89} +178.556 q^{90} +448.930 q^{91} +336.356 q^{92} -24.9826 q^{93} -279.834 q^{94} -385.993 q^{95} +287.106 q^{96} -500.651 q^{97} -2757.22 q^{98} -308.076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9}+O(q^{10}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9} - 6 q^{10} - 109 q^{11} + 222 q^{12} - 317 q^{13} - 159 q^{14} - 75 q^{15} + 54 q^{16} - 180 q^{17} - 90 q^{18} - 217 q^{19} - 193 q^{20} - 228 q^{21} - 160 q^{22} + 713 q^{23} - 351 q^{24} + 208 q^{25} + 211 q^{26} + 837 q^{27} + 5 q^{28} + 899 q^{29} - 18 q^{30} - 622 q^{31} - 696 q^{32} - 327 q^{33} + 126 q^{34} - 627 q^{35} + 666 q^{36} - 539 q^{37} + 35 q^{38} - 951 q^{39} + 371 q^{40} - 459 q^{41} - 477 q^{42} - 719 q^{43} - 876 q^{44} - 225 q^{45} - 230 q^{46} - 1384 q^{47} + 162 q^{48} - 747 q^{49} - 2005 q^{50} - 540 q^{51} - 2190 q^{52} - 730 q^{53} - 270 q^{54} - 1408 q^{55} - 1107 q^{56} - 651 q^{57} - 290 q^{58} - 3765 q^{59} - 579 q^{60} - 1300 q^{61} - 70 q^{62} - 684 q^{63} - 813 q^{64} - 2490 q^{65} - 480 q^{66} - 2735 q^{67} - 2031 q^{68} + 2139 q^{69} - 2581 q^{70} - 4800 q^{71} - 1053 q^{72} - 1858 q^{73} - 801 q^{74} + 624 q^{75} - 2699 q^{76} - 1661 q^{77} + 633 q^{78} - 4466 q^{79} + 3587 q^{80} + 2511 q^{81} - 5615 q^{82} - 1234 q^{83} + 15 q^{84} - 3623 q^{85} - 1873 q^{86} + 2697 q^{87} - 6893 q^{88} - 455 q^{89} - 54 q^{90} - 2425 q^{91} + 1702 q^{92} - 1866 q^{93} - 3912 q^{94} - 1851 q^{95} - 2088 q^{96} - 2114 q^{97} + 1769 q^{98} - 981 q^{99}+O(q^{100}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9 - 6 * q^10 - 109 * q^11 + 222 * q^12 - 317 * q^13 - 159 * q^14 - 75 * q^15 + 54 * q^16 - 180 * q^17 - 90 * q^18 - 217 * q^19 - 193 * q^20 - 228 * q^21 - 160 * q^22 + 713 * q^23 - 351 * q^24 + 208 * q^25 + 211 * q^26 + 837 * q^27 + 5 * q^28 + 899 * q^29 - 18 * q^30 - 622 * q^31 - 696 * q^32 - 327 * q^33 + 126 * q^34 - 627 * q^35 + 666 * q^36 - 539 * q^37 + 35 * q^38 - 951 * q^39 + 371 * q^40 - 459 * q^41 - 477 * q^42 - 719 * q^43 - 876 * q^44 - 225 * q^45 - 230 * q^46 - 1384 * q^47 + 162 * q^48 - 747 * q^49 - 2005 * q^50 - 540 * q^51 - 2190 * q^52 - 730 * q^53 - 270 * q^54 - 1408 * q^55 - 1107 * q^56 - 651 * q^57 - 290 * q^58 - 3765 * q^59 - 579 * q^60 - 1300 * q^61 - 70 * q^62 - 684 * q^63 - 813 * q^64 - 2490 * q^65 - 480 * q^66 - 2735 * q^67 - 2031 * q^68 + 2139 * q^69 - 2581 * q^70 - 4800 * q^71 - 1053 * q^72 - 1858 * q^73 - 801 * q^74 + 624 * q^75 - 2699 * q^76 - 1661 * q^77 + 633 * q^78 - 4466 * q^79 + 3587 * q^80 + 2511 * q^81 - 5615 * q^82 - 1234 * q^83 + 15 * q^84 - 3623 * q^85 - 1873 * q^86 + 2697 * q^87 - 6893 * q^88 - 455 * q^89 - 54 * q^90 - 2425 * q^91 + 1702 * q^92 - 1866 * q^93 - 3912 * q^94 - 1851 * q^95 - 2088 * q^96 - 2114 * q^97 + 1769 * q^98 - 981 * q^99

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