LMFDB - Embedded newform 1045.4.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.62064 q^{2} -7.41696 q^{3} +5.10901 q^{4} +5.00000 q^{5} +26.8541 q^{6} -14.1058 q^{7} +10.4672 q^{8} +28.0113 q^{9} +O(q^{10})$	\(q-3.62064 q^{2} -7.41696 q^{3} +5.10901 q^{4} +5.00000 q^{5} +26.8541 q^{6} -14.1058 q^{7} +10.4672 q^{8} +28.0113 q^{9} -18.1032 q^{10} -11.0000 q^{11} -37.8933 q^{12} +26.6865 q^{13} +51.0720 q^{14} -37.0848 q^{15} -78.7701 q^{16} +9.72805 q^{17} -101.419 q^{18} +19.0000 q^{19} +25.5450 q^{20} +104.622 q^{21} +39.8270 q^{22} +183.071 q^{23} -77.6351 q^{24} +25.0000 q^{25} -96.6221 q^{26} -7.50044 q^{27} -72.0666 q^{28} -85.6328 q^{29} +134.271 q^{30} +219.798 q^{31} +201.460 q^{32} +81.5865 q^{33} -35.2217 q^{34} -70.5290 q^{35} +143.110 q^{36} +260.168 q^{37} -68.7921 q^{38} -197.933 q^{39} +52.3362 q^{40} -107.308 q^{41} -378.799 q^{42} -238.820 q^{43} -56.1991 q^{44} +140.056 q^{45} -662.835 q^{46} +107.727 q^{47} +584.235 q^{48} -144.026 q^{49} -90.5159 q^{50} -72.1525 q^{51} +136.342 q^{52} -700.312 q^{53} +27.1564 q^{54} -55.0000 q^{55} -147.649 q^{56} -140.922 q^{57} +310.045 q^{58} -224.209 q^{59} -189.466 q^{60} +284.984 q^{61} -795.809 q^{62} -395.121 q^{63} -99.2524 q^{64} +133.433 q^{65} -295.395 q^{66} +240.010 q^{67} +49.7006 q^{68} -1357.83 q^{69} +255.360 q^{70} +193.200 q^{71} +293.201 q^{72} +222.580 q^{73} -941.972 q^{74} -185.424 q^{75} +97.0711 q^{76} +155.164 q^{77} +716.642 q^{78} -983.246 q^{79} -393.851 q^{80} -700.673 q^{81} +388.524 q^{82} +392.922 q^{83} +534.515 q^{84} +48.6402 q^{85} +864.680 q^{86} +635.135 q^{87} -115.140 q^{88} -1620.55 q^{89} -507.093 q^{90} -376.435 q^{91} +935.313 q^{92} -1630.23 q^{93} -390.041 q^{94} +95.0000 q^{95} -1494.22 q^{96} -519.624 q^{97} +521.467 q^{98} -308.124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	−3.62064	−1.28009	−0.640044	−	0.768338i	$-0.721084\pi$
$2$	−3.62064	−1.28009	−0.640044	+	0.768338i	$0.721084\pi$
$3$	−7.41696	−1.42739	−0.713697	−	0.700455i	$-0.752981\pi$
$3$	−7.41696	−1.42739	−0.713697	+	0.700455i	$0.752981\pi$
$4$	5.10901	0.638626
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	26.8541	1.82719
$7$	−14.1058	−0.761642	−0.380821	−	0.924649i	$-0.624359\pi$
$7$	−14.1058	−0.761642	−0.380821	+	0.924649i	$0.624359\pi$
$8$	10.4672	0.462591
$9$	28.0113	1.03745
$10$	−18.1032	−0.572473
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−37.8933	−0.911571
$13$	26.6865	0.569347	0.284673	−	0.958625i	$-0.408115\pi$
$13$	26.6865	0.569347	0.284673	+	0.958625i	$0.408115\pi$
$14$	51.0720	0.974968
$15$	−37.0848	−0.638350
$16$	−78.7701	−1.23078
$17$	9.72805	0.138788	0.0693941	−	0.997589i	$-0.477893\pi$
$17$	9.72805	0.138788	0.0693941	+	0.997589i	$0.477893\pi$
$18$	−101.419	−1.32803
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	25.5450	0.285602
$21$	104.622	1.08716
$22$	39.8270	0.385961
$23$	183.071	1.65970	0.829849	−	0.557989i	$-0.188427\pi$
$23$	183.071	1.65970	0.829849	+	0.557989i	$0.188427\pi$
$24$	−77.6351	−0.660300
$25$	25.0000	0.200000
$26$	−96.6221	−0.728814
$27$	−7.50044	−0.0534615
$28$	−72.0666	−0.486404
$29$	−85.6328	−0.548331	−0.274166	−	0.961683i	$-0.588402\pi$
$29$	−85.6328	−0.548331	−0.274166	+	0.961683i	$0.588402\pi$
$30$	134.271	0.817144
$31$	219.798	1.27345	0.636725	−	0.771091i	$-0.280289\pi$
$31$	219.798	1.27345	0.636725	+	0.771091i	$0.280289\pi$
$32$	201.460	1.11292
$33$	81.5865	0.430376
$34$	−35.2217	−0.177661
$35$	−70.5290	−0.340616
$36$	143.110	0.662545
$37$	260.168	1.15598	0.577991	−	0.816043i	$-0.303837\pi$
$37$	260.168	1.15598	0.577991	+	0.816043i	$0.303837\pi$
$38$	−68.7921	−0.293672
$39$	−197.933	−0.812682
$40$	52.3362	0.206877
$41$	−107.308	−0.408750	−0.204375	−	0.978893i	$-0.565516\pi$
$41$	−107.308	−0.408750	−0.204375	+	0.978893i	$0.565516\pi$
$42$	−378.799	−1.39166
$43$	−238.820	−0.846969	−0.423485	−	0.905903i	$-0.639193\pi$
$43$	−238.820	−0.846969	−0.423485	+	0.905903i	$0.639193\pi$
$44$	−56.1991	−0.192553
$45$	140.056	0.463963
$46$	−662.835	−2.12456
$47$	107.727	0.334333	0.167166	−	0.985929i	$-0.446538\pi$
$47$	107.727	0.334333	0.167166	+	0.985929i	$0.446538\pi$
$48$	584.235	1.75681
$49$	−144.026	−0.419902
$50$	−90.5159	−0.256018
$51$	−72.1525	−0.198105
$52$	136.342	0.363599
$53$	−700.312	−1.81500	−0.907502	−	0.420048i	$-0.862013\pi$
$53$	−700.312	−1.81500	−0.907502	+	0.420048i	$0.862013\pi$
$54$	27.1564	0.0684354
$55$	−55.0000	−0.134840
$56$	−147.649	−0.352329
$57$	−140.922	−0.327467
$58$	310.045	0.701912
$59$	−224.209	−0.494738	−0.247369	−	0.968921i	$-0.579566\pi$
$59$	−224.209	−0.494738	−0.247369	+	0.968921i	$0.579566\pi$
$60$	−189.466	−0.407667
$61$	284.984	0.598172	0.299086	−	0.954226i	$-0.403318\pi$
$61$	284.984	0.598172	0.299086	+	0.954226i	$0.403318\pi$
$62$	−795.809	−1.63013
$63$	−395.121	−0.790168
$64$	−99.2524	−0.193852
$65$	133.433	0.254620
$66$	−295.395	−0.550919
$67$	240.010	0.437641	0.218820	−	0.975765i	$-0.429779\pi$
$67$	240.010	0.437641	0.218820	+	0.975765i	$0.429779\pi$
$68$	49.7006	0.0886336
$69$	−1357.83	−2.36904
$70$	255.360	0.436019
$71$	193.200	0.322938	0.161469	−	0.986878i	$-0.448377\pi$
$71$	193.200	0.322938	0.161469	+	0.986878i	$0.448377\pi$
$72$	293.201	0.479917
$73$	222.580	0.356863	0.178432	−	0.983952i	$-0.442898\pi$
$73$	222.580	0.356863	0.178432	+	0.983952i	$0.442898\pi$
$74$	−941.972	−1.47976
$75$	−185.424	−0.285479
$76$	97.0711	0.146511
$77$	155.164	0.229644
$78$	716.642	1.04030
$79$	−983.246	−1.40030	−0.700151	−	0.713995i	$-0.746884\pi$
$79$	−983.246	−1.40030	−0.700151	+	0.713995i	$0.746884\pi$
$80$	−393.851	−0.550423
$81$	−700.673	−0.961143
$82$	388.524	0.523236
$83$	392.922	0.519624	0.259812	−	0.965659i	$-0.416339\pi$
$83$	392.922	0.519624	0.259812	+	0.965659i	$0.416339\pi$
$84$	534.515	0.694290
$85$	48.6402	0.0620679
$86$	864.680	1.08420
$87$	635.135	0.782685
$88$	−115.140	−0.139476
$89$	−1620.55	−1.93009	−0.965044	−	0.262086i	$-0.915589\pi$
$89$	−1620.55	−1.93009	−0.965044	+	0.262086i	$0.915589\pi$
$90$	−507.093	−0.593914
$91$	−376.435	−0.433638
$92$	935.313	1.05993
$93$	−1630.23	−1.81771
$94$	−390.041	−0.427975
$95$	95.0000	0.102598
$96$	−1494.22	−1.58857
$97$	−519.624	−0.543915	−0.271958	−	0.962309i	$-0.587671\pi$
$97$	−519.624	−0.543915	−0.271958	+	0.962309i	$0.587671\pi$
$98$	521.467	0.537512
$99$	−308.124	−0.312804
$100$	127.725	0.127725
$101$	−1078.85	−1.06287	−0.531433	−	0.847100i	$-0.678346\pi$
$101$	−1078.85	−1.06287	−0.531433	+	0.847100i	$0.678346\pi$
$102$	261.238	0.253592
$103$	1035.58	0.990669	0.495335	−	0.868702i	$-0.335045\pi$
$103$	1035.58	0.990669	0.495335	+	0.868702i	$0.335045\pi$
$104$	279.334	0.263375
$105$	523.111	0.486194
$106$	2535.57	2.32336
$107$	826.379	0.746626	0.373313	−	0.927705i	$-0.378222\pi$
$107$	826.379	0.746626	0.373313	+	0.927705i	$0.378222\pi$
$108$	−38.3198	−0.0341419
$109$	−283.728	−0.249323	−0.124662	−	0.992199i	$-0.539785\pi$
$109$	−283.728	−0.249323	−0.124662	+	0.992199i	$0.539785\pi$
$110$	199.135	0.172607
$111$	−1929.65	−1.65004
$112$	1111.12	0.937415
$113$	1285.75	1.07038	0.535192	−	0.844730i	$-0.320239\pi$
$113$	1285.75	1.07038	0.535192	+	0.844730i	$0.320239\pi$
$114$	510.228	0.419186
$115$	915.357	0.742239
$116$	−437.498	−0.350178
$117$	747.523	0.590671
$118$	811.779	0.633308
$119$	−137.222	−0.105707
$120$	−388.175	−0.295295
$121$	121.000	0.0909091
$122$	−1031.82	−0.765713
$123$	795.901	0.583447
$124$	1122.95	0.813257
$125$	125.000	0.0894427
$126$	1430.59	1.01148
$127$	−564.150	−0.394175	−0.197087	−	0.980386i	$-0.563148\pi$
$127$	−564.150	−0.394175	−0.197087	+	0.980386i	$0.563148\pi$
$128$	−1252.32	−0.864772
$129$	1771.32	1.20896
$130$	−483.111	−0.325935
$131$	385.421	0.257057	0.128528	−	0.991706i	$-0.458975\pi$
$131$	385.421	0.257057	0.128528	+	0.991706i	$0.458975\pi$
$132$	416.826	0.274849
$133$	−268.010	−0.174733
$134$	−868.990	−0.560218
$135$	−37.5022	−0.0239087
$136$	101.826	0.0642021
$137$	−1438.38	−0.897001	−0.448500	−	0.893783i	$-0.648042\pi$
$137$	−1438.38	−0.897001	−0.448500	+	0.893783i	$0.648042\pi$
$138$	4916.22	3.03258
$139$	−1085.88	−0.662611	−0.331305	−	0.943524i	$-0.607489\pi$
$139$	−1085.88	−0.662611	−0.331305	+	0.943524i	$0.607489\pi$
$140$	−360.333	−0.217526
$141$	−799.008	−0.477224
$142$	−699.506	−0.413389
$143$	−293.552	−0.171664
$144$	−2206.45	−1.27688
$145$	−428.164	−0.245221
$146$	−805.881	−0.456817
$147$	1068.24	0.599366
$148$	1329.20	0.738239
$149$	3593.80	1.97594	0.987972	−	0.154632i	$-0.0494192\pi$
$149$	3593.80	1.97594	0.987972	+	0.154632i	$0.0494192\pi$
$150$	671.353	0.365438
$151$	−2072.44	−1.11691	−0.558453	−	0.829536i	$-0.688605\pi$
$151$	−2072.44	−1.11691	−0.558453	+	0.829536i	$0.688605\pi$
$152$	198.878	0.106126
$153$	272.495	0.143986
$154$	−561.792	−0.293964
$155$	1098.99	0.569504
$156$	−1011.24	−0.519000
$157$	−2537.68	−1.28999	−0.644997	−	0.764185i	$-0.723141\pi$
$157$	−2537.68	−1.28999	−0.644997	+	0.764185i	$0.723141\pi$
$158$	3559.98	1.79251
$159$	5194.18	2.59073
$160$	1007.30	0.497713
$161$	−2582.37	−1.26409
$162$	2536.88	1.23035
$163$	3762.84	1.80815	0.904075	−	0.427374i	$-0.140561\pi$
$163$	3762.84	1.80815	0.904075	+	0.427374i	$0.140561\pi$
$164$	−548.239	−0.261038
$165$	407.933	0.192470
$166$	−1422.63	−0.665164
$167$	1204.06	0.557922	0.278961	−	0.960302i	$-0.410010\pi$
$167$	1204.06	0.557922	0.278961	+	0.960302i	$0.410010\pi$
$168$	1095.10	0.502912
$169$	−1484.83	−0.675845
$170$	−176.109	−0.0794524
$171$	532.214	0.238008
$172$	−1220.13	−0.540896
$173$	1927.96	0.847284	0.423642	−	0.905830i	$-0.360751\pi$
$173$	1927.96	0.847284	0.423642	+	0.905830i	$0.360751\pi$
$174$	−2299.59	−1.00191
$175$	−352.645	−0.152328
$176$	866.471	0.371095
$177$	1662.95	0.706186
$178$	5867.42	2.47068
$179$	1047.49	0.437391	0.218696	−	0.975793i	$-0.429820\pi$
$179$	1047.49	0.437391	0.218696	+	0.975793i	$0.429820\pi$
$180$	715.548	0.296299
$181$	2019.71	0.829416	0.414708	−	0.909955i	$-0.363884\pi$
$181$	2019.71	0.829416	0.414708	+	0.909955i	$0.363884\pi$
$182$	1362.93	0.555095
$183$	−2113.71	−0.853827
$184$	1916.25	0.767761
$185$	1300.84	0.516970
$186$	5902.48	2.32683
$187$	−107.009	−0.0418462
$188$	550.379	0.213513
$189$	105.800	0.0407185
$190$	−343.960	−0.131334
$191$	486.884	0.184449	0.0922243	−	0.995738i	$-0.470602\pi$
$191$	486.884	0.184449	0.0922243	+	0.995738i	$0.470602\pi$
$192$	736.151	0.276704
$193$	2813.82	1.04945	0.524723	−	0.851273i	$-0.324169\pi$
$193$	2813.82	1.04945	0.524723	+	0.851273i	$0.324169\pi$
$194$	1881.37	0.696260
$195$	−989.663	−0.363442
$196$	−735.832	−0.268160
$197$	4309.80	1.55868	0.779341	−	0.626600i	$-0.215554\pi$
$197$	4309.80	1.55868	0.779341	+	0.626600i	$0.215554\pi$
$198$	1115.60	0.400417
$199$	4437.68	1.58080	0.790400	−	0.612592i	$-0.209873\pi$
$199$	4437.68	1.58080	0.790400	+	0.612592i	$0.209873\pi$
$200$	261.681	0.0925182
$201$	−1780.15	−0.624686
$202$	3906.12	1.36056
$203$	1207.92	0.417632
$204$	−368.628	−0.126515
$205$	−536.541	−0.182798
$206$	−3749.47	−1.26814
$207$	5128.06	1.72186
$208$	−2102.10	−0.700742
$209$	−209.000	−0.0691714
$210$	−1893.99	−0.622371
$211$	1863.07	0.607862	0.303931	−	0.952694i	$-0.401701\pi$
$211$	1863.07	0.607862	0.303931	+	0.952694i	$0.401701\pi$
$212$	−3577.90	−1.15911
$213$	−1432.95	−0.460960
$214$	−2992.02	−0.955748
$215$	−1194.10	−0.378776
$216$	−78.5089	−0.0247308
$217$	−3100.43	−0.969912
$218$	1027.28	0.319156
$219$	−1650.87	−0.509385
$220$	−280.995	−0.0861123
$221$	259.608	0.0790185
$222$	6986.57	2.11220
$223$	−1626.70	−0.488484	−0.244242	−	0.969714i	$-0.578539\pi$
$223$	−1626.70	−0.488484	−0.244242	+	0.969714i	$0.578539\pi$
$224$	−2841.75	−0.847646
$225$	700.281	0.207491
$226$	−4655.24	−1.37019
$227$	−6041.15	−1.76637	−0.883183	−	0.469028i	$-0.844604\pi$
$227$	−6041.15	−1.76637	−0.883183	+	0.469028i	$0.844604\pi$
$228$	−719.972	−0.209129
$229$	2319.88	0.669441	0.334721	−	0.942317i	$-0.391358\pi$
$229$	2319.88	0.669441	0.334721	+	0.942317i	$0.391358\pi$
$230$	−3314.18	−0.950132
$231$	−1150.84	−0.327792
$232$	−896.339	−0.253653
$233$	−2847.18	−0.800536	−0.400268	−	0.916398i	$-0.631083\pi$
$233$	−2847.18	−0.800536	−0.400268	+	0.916398i	$0.631083\pi$
$234$	−2706.51	−0.756111
$235$	538.636	0.149518
$236$	−1145.49	−0.315952
$237$	7292.70	1.99878
$238$	496.830	0.135314
$239$	4452.00	1.20492	0.602460	−	0.798149i	$-0.294187\pi$
$239$	4452.00	1.20492	0.602460	+	0.798149i	$0.294187\pi$
$240$	2921.17	0.785670
$241$	−2022.09	−0.540474	−0.270237	−	0.962794i	$-0.587102\pi$
$241$	−2022.09	−0.540474	−0.270237	+	0.962794i	$0.587102\pi$
$242$	−438.097	−0.116372
$243$	5399.38	1.42539
$244$	1455.99	0.382008
$245$	−720.132	−0.187786
$246$	−2881.67	−0.746863
$247$	507.044	0.130617
$248$	2300.68	0.589086
$249$	−2914.28	−0.741708
$250$	−452.580	−0.114495
$251$	4131.35	1.03892	0.519460	−	0.854495i	$-0.326133\pi$
$251$	4131.35	1.03892	0.519460	+	0.854495i	$0.326133\pi$
$252$	−2018.68	−0.504622
$253$	−2013.79	−0.500418
$254$	2042.58	0.504578
$255$	−360.763	−0.0885954
$256$	5328.22	1.30084
$257$	−5679.20	−1.37844	−0.689220	−	0.724552i	$-0.742046\pi$
$257$	−5679.20	−1.37844	−0.689220	+	0.724552i	$0.742046\pi$
$258$	−6413.29	−1.54757
$259$	−3669.87	−0.880443
$260$	681.708	0.162607
$261$	−2398.68	−0.568868
$262$	−1395.47	−0.329055
$263$	7061.58	1.65565	0.827824	−	0.560988i	$-0.189579\pi$
$263$	7061.58	1.65565	0.827824	+	0.560988i	$0.189579\pi$
$264$	853.986	0.199088
$265$	−3501.56	−0.811694
$266$	970.367	0.223673
$267$	12019.5	2.75500
$268$	1226.21	0.279488
$269$	−3153.04	−0.714662	−0.357331	−	0.933978i	$-0.616313\pi$
$269$	−3153.04	−0.714662	−0.357331	+	0.933978i	$0.616313\pi$
$270$	135.782	0.0306053
$271$	−5761.62	−1.29149	−0.645745	−	0.763553i	$-0.723453\pi$
$271$	−5761.62	−1.29149	−0.645745	+	0.763553i	$0.723453\pi$
$272$	−766.279	−0.170818
$273$	2792.00	0.618972
$274$	5207.85	1.14824
$275$	−275.000	−0.0603023
$276$	−6937.18	−1.51293
$277$	692.471	0.150204	0.0751021	−	0.997176i	$-0.476072\pi$
$277$	692.471	0.150204	0.0751021	+	0.997176i	$0.476072\pi$
$278$	3931.57	0.848200
$279$	6156.82	1.32115
$280$	−738.244	−0.157566
$281$	684.132	0.145238	0.0726190	−	0.997360i	$-0.476864\pi$
$281$	684.132	0.145238	0.0726190	+	0.997360i	$0.476864\pi$
$282$	2892.92	0.610889
$283$	−3392.77	−0.712647	−0.356323	−	0.934363i	$-0.615970\pi$
$283$	−3392.77	−0.712647	−0.356323	+	0.934363i	$0.615970\pi$
$284$	987.059	0.206237
$285$	−704.611	−0.146448
$286$	1062.84	0.219746
$287$	1513.67	0.311321
$288$	5643.15	1.15460
$289$	−4818.37	−0.980738
$290$	1550.23	0.313905
$291$	3854.03	0.776382
$292$	1137.16	0.227902
$293$	−3683.94	−0.734532	−0.367266	−	0.930116i	$-0.619706\pi$
$293$	−3683.94	−0.734532	−0.367266	+	0.930116i	$0.619706\pi$
$294$	−3867.70	−0.767241
$295$	−1121.05	−0.221253
$296$	2723.24	0.534746
$297$	82.5048	0.0161192
$298$	−13011.8	−2.52938
$299$	4885.54	0.944943
$300$	−947.332	−0.182314
$301$	3368.74	0.645087
$302$	7503.56	1.42974
$303$	8001.77	1.51713
$304$	−1496.63	−0.282361
$305$	1424.92	0.267511
$306$	−986.604	−0.184315
$307$	−4552.78	−0.846388	−0.423194	−	0.906039i	$-0.639091\pi$
$307$	−4552.78	−0.846388	−0.423194	+	0.906039i	$0.639091\pi$
$308$	792.733	0.146656
$309$	−7680.87	−1.41408
$310$	−3979.05	−0.729015
$311$	7844.12	1.43022	0.715112	−	0.699010i	$-0.246376\pi$
$311$	7844.12	1.43022	0.715112	+	0.699010i	$0.246376\pi$
$312$	−2071.81	−0.375939
$313$	7789.48	1.40667	0.703335	−	0.710859i	$-0.251694\pi$
$313$	7789.48	1.40667	0.703335	+	0.710859i	$0.251694\pi$
$314$	9188.02	1.65131
$315$	−1975.61	−0.353374
$316$	−5023.41	−0.894269
$317$	−3588.45	−0.635796	−0.317898	−	0.948125i	$-0.602977\pi$
$317$	−3588.45	−0.635796	−0.317898	+	0.948125i	$0.602977\pi$
$318$	−18806.2	−3.31636
$319$	941.960	0.165328
$320$	−496.262	−0.0866934
$321$	−6129.21	−1.06573
$322$	9349.82	1.61815
$323$	184.833	0.0318402
$324$	−3579.74	−0.613811
$325$	667.163	0.113869
$326$	−13623.9	−2.31459
$327$	2104.40	0.355883
$328$	−1123.22	−0.189084
$329$	−1519.58	−0.254642
$330$	−1476.98	−0.246378
$331$	−6049.37	−1.00454	−0.502271	−	0.864710i	$-0.667502\pi$
$331$	−6049.37	−1.00454	−0.502271	+	0.864710i	$0.667502\pi$
$332$	2007.44	0.331845
$333$	7287.62	1.19928
$334$	−4359.46	−0.714189
$335$	1200.05	0.195719
$336$	−8241.10	−1.33806
$337$	−6417.48	−1.03734	−0.518668	−	0.854976i	$-0.673572\pi$
$337$	−6417.48	−1.03734	−0.518668	+	0.854976i	$0.673572\pi$
$338$	5376.03	0.865141
$339$	−9536.37	−1.52786
$340$	248.503	0.0396382
$341$	−2417.78	−0.383959
$342$	−1926.95	−0.304672
$343$	6869.90	1.08146
$344$	−2499.78	−0.391800
$345$	−6789.17	−1.05947
$346$	−6980.45	−1.08460
$347$	8430.87	1.30430	0.652151	−	0.758089i	$-0.273867\pi$
$347$	8430.87	1.30430	0.652151	+	0.758089i	$0.273867\pi$
$348$	3244.91	0.499843
$349$	−6382.24	−0.978892	−0.489446	−	0.872034i	$-0.662801\pi$
$349$	−6382.24	−0.978892	−0.489446	+	0.872034i	$0.662801\pi$
$350$	1276.80	0.194994
$351$	−200.161	−0.0304381
$352$	−2216.06	−0.335558
$353$	1169.62	0.176353	0.0881766	−	0.996105i	$-0.471896\pi$
$353$	1169.62	0.176353	0.0881766	+	0.996105i	$0.471896\pi$
$354$	−6020.93	−0.903980
$355$	965.999	0.144422
$356$	−8279.40	−1.23260
$357$	1017.77	0.150885
$358$	−3792.58	−0.559899
$359$	4560.04	0.670389	0.335194	−	0.942149i	$-0.391198\pi$
$359$	4560.04	0.670389	0.335194	+	0.942149i	$0.391198\pi$
$360$	1466.00	0.214625
$361$	361.000	0.0526316
$362$	−7312.65	−1.06173
$363$	−897.452	−0.129763
$364$	−1923.21	−0.276932
$365$	1112.90	0.159594
$366$	7652.99	1.09297
$367$	6818.37	0.969798	0.484899	−	0.874570i	$-0.338856\pi$
$367$	6818.37	0.969798	0.484899	+	0.874570i	$0.338856\pi$
$368$	−14420.6	−2.04273
$369$	−3005.84	−0.424059
$370$	−4709.86	−0.661768
$371$	9878.45	1.38238
$372$	−8328.88	−1.16084
$373$	1630.59	0.226350	0.113175	−	0.993575i	$-0.463898\pi$
$373$	1630.59	0.226350	0.113175	+	0.993575i	$0.463898\pi$
$374$	387.439	0.0535668
$375$	−927.120	−0.127670
$376$	1127.61	0.154659
$377$	−2285.24	−0.312190
$378$	−383.062	−0.0521233
$379$	−6415.24	−0.869469	−0.434735	−	0.900559i	$-0.643158\pi$
$379$	−6415.24	−0.869469	−0.434735	+	0.900559i	$0.643158\pi$
$380$	485.356	0.0655216
$381$	4184.27	0.562643
$382$	−1762.83	−0.236111
$383$	−7897.88	−1.05369	−0.526844	−	0.849962i	$-0.676625\pi$
$383$	−7897.88	−1.05369	−0.526844	+	0.849962i	$0.676625\pi$
$384$	9288.43	1.23437
$385$	775.819	0.102700
$386$	−10187.8	−1.34338
$387$	−6689.64	−0.878692
$388$	−2654.76	−0.347358
$389$	748.949	0.0976175	0.0488088	−	0.998808i	$-0.484458\pi$
$389$	748.949	0.0976175	0.0488088	+	0.998808i	$0.484458\pi$
$390$	3583.21	0.465238
$391$	1780.93	0.230346
$392$	−1507.56	−0.194243
$393$	−2858.65	−0.366921
$394$	−15604.2	−1.99525
$395$	−4916.23	−0.626234
$396$	−1574.21	−0.199765
$397$	6481.59	0.819400	0.409700	−	0.912220i	$-0.365633\pi$
$397$	6481.59	0.819400	0.409700	+	0.912220i	$0.365633\pi$
$398$	−16067.2	−2.02356
$399$	1987.82	0.249412
$400$	−1969.25	−0.246157
$401$	9198.25	1.14548	0.572741	−	0.819736i	$-0.305880\pi$
$401$	9198.25	1.14548	0.572741	+	0.819736i	$0.305880\pi$
$402$	6445.26	0.799653
$403$	5865.65	0.725034
$404$	−5511.84	−0.678773
$405$	−3503.37	−0.429836
$406$	−4373.43	−0.534606
$407$	−2861.84	−0.348541
$408$	−755.238	−0.0916417
$409$	9053.44	1.09453	0.547266	−	0.836959i	$-0.315669\pi$
$409$	9053.44	1.09453	0.547266	+	0.836959i	$0.315669\pi$
$410$	1942.62	0.233998
$411$	10668.4	1.28037
$412$	5290.80	0.632667
$413$	3162.65	0.376813
$414$	−18566.8	−2.20413
$415$	1964.61	0.232383
$416$	5376.26	0.633637
$417$	8053.91	0.945807
$418$	756.713	0.0885455
$419$	10525.4	1.22721	0.613603	−	0.789615i	$-0.289719\pi$
$419$	10525.4	1.22721	0.613603	+	0.789615i	$0.289719\pi$
$420$	2672.57	0.310496
$421$	13466.4	1.55893	0.779467	−	0.626444i	$-0.215490\pi$
$421$	13466.4	1.55893	0.779467	+	0.626444i	$0.215490\pi$
$422$	−6745.49	−0.778116
$423$	3017.57	0.346855
$424$	−7330.33	−0.839604
$425$	243.201	0.0277576
$426$	5188.21	0.590069
$427$	−4019.93	−0.455592
$428$	4221.97	0.476815
$429$	2177.26	0.245033
$430$	4323.40	0.484867
$431$	7567.44	0.845733	0.422866	−	0.906192i	$-0.361024\pi$
$431$	7567.44	0.845733	0.422866	+	0.906192i	$0.361024\pi$
$432$	590.810	0.0657995
$433$	6811.49	0.755979	0.377990	−	0.925810i	$-0.376615\pi$
$433$	6811.49	0.755979	0.377990	+	0.925810i	$0.376615\pi$
$434$	11225.5	1.24157
$435$	3175.67	0.350027
$436$	−1449.57	−0.159224
$437$	3478.36	0.380761
$438$	5977.19	0.652057
$439$	−1394.41	−0.151598	−0.0757991	−	0.997123i	$-0.524151\pi$
$439$	−1394.41	−0.151598	−0.0757991	+	0.997123i	$0.524151\pi$
$440$	−575.698	−0.0623758
$441$	−4034.36	−0.435629
$442$	−939.945	−0.101151
$443$	8760.62	0.939571	0.469785	−	0.882781i	$-0.344331\pi$
$443$	8760.62	0.939571	0.469785	+	0.882781i	$0.344331\pi$
$444$	−9858.61	−1.05376
$445$	−8102.75	−0.863162
$446$	5889.69	0.625302
$447$	−26655.1	−2.82045
$448$	1400.03	0.147646
$449$	−12756.8	−1.34083	−0.670414	−	0.741987i	$-0.733884\pi$
$449$	−12756.8	−1.34083	−0.670414	+	0.741987i	$0.733884\pi$
$450$	−2535.46	−0.265606
$451$	1180.39	0.123243
$452$	6568.92	0.683575
$453$	15371.2	1.59427
$454$	21872.8	2.26110
$455$	−1882.17	−0.193929
$456$	−1475.07	−0.151483
$457$	−13344.8	−1.36596	−0.682981	−	0.730437i	$-0.739317\pi$
$457$	−13344.8	−1.36596	−0.682981	+	0.730437i	$0.739317\pi$
$458$	−8399.44	−0.856944
$459$	−72.9646	−0.00741982
$460$	4676.56	0.474013
$461$	−7155.61	−0.722929	−0.361464	−	0.932386i	$-0.617723\pi$
$461$	−7155.61	−0.722929	−0.361464	+	0.932386i	$0.617723\pi$
$462$	4166.78	0.419603
$463$	−9196.93	−0.923148	−0.461574	−	0.887102i	$-0.652715\pi$
$463$	−9196.93	−0.923148	−0.461574	+	0.887102i	$0.652715\pi$
$464$	6745.30	0.674877
$465$	−8151.17	−0.812906
$466$	10308.6	1.02476
$467$	118.874	0.0117791	0.00588956	−	0.999983i	$-0.498125\pi$
$467$	118.874	0.0117791	0.00588956	+	0.999983i	$0.498125\pi$
$468$	3819.10	0.377218
$469$	−3385.54	−0.333325
$470$	−1950.21	−0.191396
$471$	18821.9	1.84133
$472$	−2346.85	−0.228861
$473$	2627.02	0.255371
$474$	−26404.2	−2.55862
$475$	475.000	0.0458831
$476$	−701.067	−0.0675071
$477$	−19616.6	−1.88298
$478$	−16119.1	−1.54240
$479$	12479.4	1.19040	0.595198	−	0.803579i	$-0.297074\pi$
$479$	12479.4	1.19040	0.595198	+	0.803579i	$0.297074\pi$
$480$	−7471.10	−0.710432
$481$	6942.97	0.658154
$482$	7321.25	0.691855
$483$	19153.3	1.80436
$484$	618.190	0.0580569
$485$	−2598.12	−0.243246
$486$	−19549.2	−1.82463
$487$	12264.7	1.14120	0.570602	−	0.821227i	$-0.306710\pi$
$487$	12264.7	1.14120	0.570602	+	0.821227i	$0.306710\pi$
$488$	2983.00	0.276709
$489$	−27908.8	−2.58094
$490$	2607.34	0.240383
$491$	−8965.63	−0.824059	−0.412030	−	0.911170i	$-0.635180\pi$
$491$	−8965.63	−0.824059	−0.412030	+	0.911170i	$0.635180\pi$
$492$	4066.26	0.372604
$493$	−833.039	−0.0761018
$494$	−1835.82	−0.167201
$495$	−1540.62	−0.139890
$496$	−17313.5	−1.56734
$497$	−2725.24	−0.245963
$498$	10551.6	0.949451
$499$	−11591.8	−1.03992	−0.519960	−	0.854191i	$-0.674053\pi$
$499$	−11591.8	−1.03992	−0.519960	+	0.854191i	$0.674053\pi$
$500$	638.626	0.0571204
$501$	−8930.46	−0.796375
$502$	−14958.1	−1.32991
$503$	11214.8	0.994121	0.497060	−	0.867716i	$-0.334413\pi$
$503$	11214.8	0.994121	0.497060	+	0.867716i	$0.334413\pi$
$504$	−4135.83	−0.365525
$505$	−5394.24	−0.475328
$506$	7291.19	0.640579
$507$	11012.9	0.964696
$508$	−2882.24	−0.251730
$509$	−982.189	−0.0855300	−0.0427650	−	0.999085i	$-0.513617\pi$
$509$	−982.189	−0.0855300	−0.0427650	+	0.999085i	$0.513617\pi$
$510$	1306.19	0.113410
$511$	−3139.67	−0.271802
$512$	−9272.98	−0.800413
$513$	−142.508	−0.0122649
$514$	20562.3	1.76452
$515$	5177.91	0.443041
$516$	9049.67	0.772072
$517$	−1185.00	−0.100805
$518$	13287.3	1.12705
$519$	−14299.6	−1.20941
$520$	1396.67	0.117785
$521$	6439.68	0.541511	0.270756	−	0.962648i	$-0.412726\pi$
$521$	6439.68	0.541511	0.270756	+	0.962648i	$0.412726\pi$
$522$	8684.75	0.728202
$523$	2813.54	0.235234	0.117617	−	0.993059i	$-0.462474\pi$
$523$	2813.54	0.235234	0.117617	+	0.993059i	$0.462474\pi$
$524$	1969.12	0.164163
$525$	2615.55	0.217433
$526$	−25567.4	−2.11938
$527$	2138.21	0.176740
$528$	−6426.58	−0.529699
$529$	21348.2	1.75459
$530$	12677.9	1.03904
$531$	−6280.38	−0.513268
$532$	−1369.27	−0.111589
$533$	−2863.68	−0.232720
$534$	−43518.4	−3.52664
$535$	4131.89	0.333902
$536$	2512.24	0.202449
$537$	−7769.18	−0.624330
$538$	11416.0	0.914830
$539$	1584.29	0.126605
$540$	−191.599	−0.0152687
$541$	−6011.03	−0.477698	−0.238849	−	0.971057i	$-0.576770\pi$
$541$	−6011.03	−0.477698	−0.238849	+	0.971057i	$0.576770\pi$
$542$	20860.7	1.65322
$543$	−14980.1	−1.18390
$544$	1959.81	0.154460
$545$	−1418.64	−0.111501
$546$	−10108.8	−0.792339
$547$	−5337.54	−0.417215	−0.208608	−	0.977999i	$-0.566893\pi$
$547$	−5337.54	−0.417215	−0.208608	+	0.977999i	$0.566893\pi$
$548$	−7348.69	−0.572848
$549$	7982.76	0.620576
$550$	995.675	0.0771922
$551$	−1627.02	−0.125796
$552$	−14212.8	−1.09590
$553$	13869.5	1.06653
$554$	−2507.19	−0.192275
$555$	−9648.26	−0.737921
$556$	−5547.75	−0.423160
$557$	−14478.5	−1.10139	−0.550695	−	0.834707i	$-0.685637\pi$
$557$	−14478.5	−1.10139	−0.550695	+	0.834707i	$0.685637\pi$
$558$	−22291.6	−1.69118
$559$	−6373.27	−0.482219
$560$	5555.58	0.419225
$561$	793.678	0.0597310
$562$	−2476.99	−0.185917
$563$	21041.0	1.57509	0.787544	−	0.616259i	$-0.211352\pi$
$563$	21041.0	1.57509	0.787544	+	0.616259i	$0.211352\pi$
$564$	−4082.14	−0.304768
$565$	6428.76	0.478691
$566$	12284.0	0.912251
$567$	9883.56	0.732047
$568$	2022.27	0.149388
$569$	17522.2	1.29098	0.645490	−	0.763769i	$-0.276653\pi$
$569$	17522.2	1.29098	0.645490	+	0.763769i	$0.276653\pi$
$570$	2551.14	0.187466
$571$	−13289.1	−0.973961	−0.486981	−	0.873413i	$-0.661902\pi$
$571$	−13289.1	−0.973961	−0.486981	+	0.873413i	$0.661902\pi$
$572$	−1499.76	−0.109629
$573$	−3611.20	−0.263281
$574$	−5480.44	−0.398518
$575$	4576.79	0.331939
$576$	−2780.18	−0.201113
$577$	−1436.72	−0.103660	−0.0518298	−	0.998656i	$-0.516505\pi$
$577$	−1436.72	−0.103660	−0.0518298	+	0.998656i	$0.516505\pi$
$578$	17445.5	1.25543
$579$	−20870.0	−1.49797
$580$	−2187.49	−0.156605
$581$	−5542.48	−0.395767
$582$	−13954.0	−0.993837
$583$	7703.43	0.547244
$584$	2329.80	0.165082
$585$	3737.61	0.264156
$586$	13338.2	0.940266
$587$	−4746.95	−0.333778	−0.166889	−	0.985976i	$-0.553372\pi$
$587$	−4746.95	−0.333778	−0.166889	+	0.985976i	$0.553372\pi$
$588$	5457.63	0.382770
$589$	4176.17	0.292149
$590$	4058.90	0.283224
$591$	−31965.6	−2.22485
$592$	−20493.4	−1.42276
$593$	−170.876	−0.0118331	−0.00591656	−	0.999982i	$-0.501883\pi$
$593$	−170.876	−0.0118331	−0.00591656	+	0.999982i	$0.501883\pi$
$594$	−298.720	−0.0206341
$595$	−686.109	−0.0472735
$596$	18360.8	1.26189
$597$	−32914.1	−2.25642
$598$	−17688.8	−1.20961
$599$	5245.23	0.357787	0.178893	−	0.983868i	$-0.442748\pi$
$599$	5245.23	0.357787	0.178893	+	0.983868i	$0.442748\pi$
$600$	−1940.88	−0.132060
$601$	−21584.1	−1.46495	−0.732473	−	0.680796i	$-0.761634\pi$
$601$	−21584.1	−1.46495	−0.732473	+	0.680796i	$0.761634\pi$
$602$	−12197.0	−0.825768
$603$	6722.99	0.454032
$604$	−10588.1	−0.713285
$605$	605.000	0.0406558
$606$	−28971.5	−1.94206
$607$	−4.00350	−0.000267705 0	−0.000133852	−	1.00000i	$-0.500043\pi$
$607$	−4.00350	−0.000267705 0	−0.000133852		1.00000i	$0.500043\pi$
$608$	3827.74	0.255321
$609$	−8959.08	−0.596125
$610$	−5159.12	−0.342437
$611$	2874.86	0.190351
$612$	1392.18	0.0919533
$613$	19393.2	1.27779	0.638893	−	0.769296i	$-0.279393\pi$
$613$	19393.2	1.27779	0.638893	+	0.769296i	$0.279393\pi$
$614$	16484.0	1.08345
$615$	3979.50	0.260925
$616$	1624.14	0.106231
$617$	27484.2	1.79331	0.896656	−	0.442728i	$-0.145989\pi$
$617$	27484.2	1.79331	0.896656	+	0.442728i	$0.145989\pi$
$618$	27809.6	1.81014
$619$	3328.00	0.216097	0.108048	−	0.994146i	$-0.465540\pi$
$619$	3328.00	0.216097	0.108048	+	0.994146i	$0.465540\pi$
$620$	5614.75	0.363700
$621$	−1373.12	−0.0887299
$622$	−28400.7	−1.83081
$623$	22859.1	1.47004
$624$	15591.2	1.00023
$625$	625.000	0.0400000
$626$	−28202.9	−1.80066
$627$	1550.14	0.0987349
$628$	−12965.0	−0.823823
$629$	2530.92	0.160436
$630$	7152.95	0.452350
$631$	6057.80	0.382183	0.191091	−	0.981572i	$-0.438797\pi$
$631$	6057.80	0.382183	0.191091	+	0.981572i	$0.438797\pi$
$632$	−10291.9	−0.647767
$633$	−13818.3	−0.867658
$634$	12992.5	0.813875
$635$	−2820.75	−0.176280
$636$	26537.1	1.65450
$637$	−3843.56	−0.239070
$638$	−3410.50	−0.211635
$639$	5411.77	0.335033
$640$	−6261.61	−0.386738
$641$	14721.8	0.907138	0.453569	−	0.891221i	$-0.350151\pi$
$641$	14721.8	0.907138	0.453569	+	0.891221i	$0.350151\pi$
$642$	22191.7	1.36423
$643$	−12863.4	−0.788932	−0.394466	−	0.918911i	$-0.629070\pi$
$643$	−12863.4	−0.788932	−0.394466	+	0.918911i	$0.629070\pi$
$644$	−13193.3	−0.807283
$645$	8856.58	0.540663
$646$	−669.213	−0.0407582
$647$	−3808.14	−0.231397	−0.115698	−	0.993284i	$-0.536911\pi$
$647$	−3808.14	−0.231397	−0.115698	+	0.993284i	$0.536911\pi$
$648$	−7334.12	−0.444616
$649$	2466.30	0.149169
$650$	−2415.55	−0.145763
$651$	22995.8	1.38445
$652$	19224.4	1.15473
$653$	10659.1	0.638777	0.319389	−	0.947624i	$-0.396522\pi$
$653$	10659.1	0.638777	0.319389	+	0.947624i	$0.396522\pi$
$654$	−7619.27	−0.455561
$655$	1927.11	0.114959
$656$	8452.68	0.503082
$657$	6234.75	0.370229
$658$	5501.84	0.325964
$659$	−12618.4	−0.745894	−0.372947	−	0.927853i	$-0.621653\pi$
$659$	−12618.4	−0.745894	−0.372947	+	0.927853i	$0.621653\pi$
$660$	2084.13	0.122916
$661$	11450.3	0.673775	0.336888	−	0.941545i	$-0.390626\pi$
$661$	11450.3	0.673775	0.336888	+	0.941545i	$0.390626\pi$
$662$	21902.6	1.28590
$663$	−1925.50	−0.112791
$664$	4112.81	0.240373
$665$	−1340.05	−0.0781428
$666$	−26385.8	−1.53518
$667$	−15676.9	−0.910064
$668$	6151.55	0.356303
$669$	12065.2	0.697259
$670$	−4344.95	−0.250537
$671$	−3134.83	−0.180356
$672$	21077.2	1.20992
$673$	−31933.5	−1.82904	−0.914522	−	0.404537i	$-0.867433\pi$
$673$	−31933.5	−1.82904	−0.914522	+	0.404537i	$0.867433\pi$
$674$	23235.4	1.32788
$675$	−187.511	−0.0106923
$676$	−7586.01	−0.431612
$677$	27294.3	1.54949	0.774747	−	0.632272i	$-0.217877\pi$
$677$	27294.3	1.54949	0.774747	+	0.632272i	$0.217877\pi$
$678$	34527.7	1.95580
$679$	7329.71	0.414269
$680$	509.129	0.0287121
$681$	44806.9	2.52130
$682$	8753.90	0.491502
$683$	−15450.2	−0.865569	−0.432784	−	0.901497i	$-0.642469\pi$
$683$	−15450.2	−0.865569	−0.432784	+	0.901497i	$0.642469\pi$
$684$	2719.08	0.151998
$685$	−7191.90	−0.401151
$686$	−24873.4	−1.38436
$687$	−17206.5	−0.955556
$688$	18811.9	1.04244
$689$	−18688.9	−1.03337
$690$	24581.1	1.35621
$691$	2983.98	0.164278	0.0821390	−	0.996621i	$-0.473825\pi$
$691$	2983.98	0.164278	0.0821390	+	0.996621i	$0.473825\pi$
$692$	9849.96	0.541097
$693$	4346.33	0.238245
$694$	−30525.1	−1.66962
$695$	−5429.39	−0.296329
$696$	6648.10	0.362063
$697$	−1043.90	−0.0567296
$698$	23107.8	1.25307
$699$	21117.4	1.14268
$700$	−1801.67	−0.0972808
$701$	13538.3	0.729434	0.364717	−	0.931118i	$-0.381166\pi$
$701$	13538.3	0.729434	0.364717	+	0.931118i	$0.381166\pi$
$702$	724.708	0.0389635
$703$	4943.19	0.265200
$704$	1091.78	0.0584487
$705$	−3995.04	−0.213421
$706$	−4234.78	−0.225748
$707$	15218.0	0.809523
$708$	8496.01	0.450988
$709$	23484.2	1.24396	0.621980	−	0.783033i	$-0.286329\pi$
$709$	23484.2	1.24396	0.621980	+	0.783033i	$0.286329\pi$
$710$	−3497.53	−0.184873
$711$	−27542.0	−1.45275
$712$	−16962.7	−0.892842
$713$	40238.8	2.11354
$714$	−3684.97	−0.193146
$715$	−1467.76	−0.0767707
$716$	5351.63	0.279329
$717$	−33020.3	−1.71989
$718$	−16510.2	−0.858157
$719$	12314.5	0.638737	0.319369	−	0.947631i	$-0.396529\pi$
$719$	12314.5	0.638737	0.319369	+	0.947631i	$0.396529\pi$
$720$	−11032.2	−0.571038
$721$	−14607.7	−0.754535
$722$	−1307.05	−0.0673731
$723$	14997.8	0.771470
$724$	10318.7	0.529686
$725$	−2140.82	−0.109666
$726$	3249.35	0.166108
$727$	−2308.96	−0.117792	−0.0588958	−	0.998264i	$-0.518758\pi$
$727$	−2308.96	−0.117792	−0.0588958	+	0.998264i	$0.518758\pi$
$728$	−3940.23	−0.200597
$729$	−21128.8	−1.07345
$730$	−4029.41	−0.204295
$731$	−2323.25	−0.117549
$732$	−10799.0	−0.545276
$733$	36343.2	1.83133	0.915667	−	0.401938i	$-0.131663\pi$
$733$	36343.2	1.83133	0.915667	+	0.401938i	$0.131663\pi$
$734$	−24686.8	−1.24143
$735$	5341.19	0.268045
$736$	36881.6	1.84711
$737$	−2640.11	−0.131954
$738$	10883.1	0.542833
$739$	2107.56	0.104909	0.0524547	−	0.998623i	$-0.483295\pi$
$739$	2107.56	0.104909	0.0524547	+	0.998623i	$0.483295\pi$
$740$	6645.99	0.330151
$741$	−3760.72	−0.186442
$742$	−35766.3	−1.76957
$743$	14978.9	0.739601	0.369800	−	0.929111i	$-0.379426\pi$
$743$	14978.9	0.739601	0.369800	+	0.929111i	$0.379426\pi$
$744$	−17064.1	−0.840858
$745$	17969.0	0.883669
$746$	−5903.77	−0.289748
$747$	11006.2	0.539086
$748$	−546.707	−0.0267241
$749$	−11656.7	−0.568662
$750$	3356.76	0.163429
$751$	−6585.41	−0.319980	−0.159990	−	0.987119i	$-0.551146\pi$
$751$	−6585.41	−0.319980	−0.159990	+	0.987119i	$0.551146\pi$
$752$	−8485.68	−0.411491
$753$	−30642.1	−1.48295
$754$	8274.02	0.399631
$755$	−10362.2	−0.499496
$756$	540.531	0.0260039
$757$	−31207.2	−1.49834	−0.749170	−	0.662377i	$-0.769548\pi$
$757$	−31207.2	−1.49834	−0.749170	+	0.662377i	$0.769548\pi$
$758$	23227.3	1.11300
$759$	14936.2	0.714293
$760$	994.388	0.0474608
$761$	23224.0	1.10627	0.553134	−	0.833092i	$-0.313432\pi$
$761$	23224.0	1.10627	0.553134	+	0.833092i	$0.313432\pi$
$762$	−15149.7	−0.720232
$763$	4002.22	0.189895
$764$	2487.49	0.117794
$765$	1362.47	0.0643926
$766$	28595.3	1.34881
$767$	−5983.36	−0.281677
$768$	−39519.2	−1.85681
$769$	−20058.6	−0.940615	−0.470307	−	0.882503i	$-0.655857\pi$
$769$	−20058.6	−0.940615	−0.470307	+	0.882503i	$0.655857\pi$
$770$	−2808.96	−0.131465
$771$	42122.4	1.96758
$772$	14375.8	0.670203
$773$	4988.84	0.232129	0.116065	−	0.993242i	$-0.462972\pi$
$773$	4988.84	0.232129	0.116065	+	0.993242i	$0.462972\pi$
$774$	24220.8	1.12480
$775$	5494.96	0.254690
$776$	−5439.03	−0.251610
$777$	27219.3	1.25674
$778$	−2711.67	−0.124959
$779$	−2038.86	−0.0937736
$780$	−5056.20	−0.232104
$781$	−2125.20	−0.0973695
$782$	−6448.09	−0.294863
$783$	642.283	0.0293146
$784$	11345.0	0.516808
$785$	−12688.4	−0.576903
$786$	10350.1	0.469691
$787$	4122.06	0.186703	0.0933516	−	0.995633i	$-0.470242\pi$
$787$	4122.06	0.186703	0.0933516	+	0.995633i	$0.470242\pi$
$788$	22018.8	0.995414
$789$	−52375.4	−2.36326
$790$	17799.9	0.801635
$791$	−18136.6	−0.815249
$792$	−3225.21	−0.144700
$793$	7605.23	0.340567
$794$	−23467.5	−1.04890
$795$	25970.9	1.15861
$796$	22672.1	1.00954
$797$	15597.6	0.693217	0.346609	−	0.938010i	$-0.387333\pi$
$797$	15597.6	0.693217	0.346609	+	0.938010i	$0.387333\pi$
$798$	−7197.17	−0.319270
$799$	1047.98	0.0464014
$800$	5036.50	0.222584
$801$	−45393.6	−2.00238
$802$	−33303.5	−1.46632
$803$	−2448.38	−0.107598
$804$	−9094.77	−0.398940
$805$	−12911.8	−0.565320
$806$	−21237.4	−0.928107
$807$	23385.9	1.02010
$808$	−11292.6	−0.491672
$809$	10244.8	0.445225	0.222612	−	0.974907i	$-0.428542\pi$
$809$	10244.8	0.445225	0.222612	+	0.974907i	$0.428542\pi$
$810$	12684.4	0.550228
$811$	−25773.4	−1.11594	−0.557970	−	0.829861i	$-0.688420\pi$
$811$	−25773.4	−1.11594	−0.557970	+	0.829861i	$0.688420\pi$
$812$	6171.26	0.266710
$813$	42733.7	1.84346
$814$	10361.7	0.446164
$815$	18814.2	0.808629
$816$	5683.46	0.243825
$817$	−4537.58	−0.194308
$818$	−32779.2	−1.40110
$819$	−10544.4	−0.449879
$820$	−2741.19	−0.116740
$821$	32419.3	1.37812	0.689062	−	0.724702i	$-0.258023\pi$
$821$	32419.3	1.37812	0.689062	+	0.724702i	$0.258023\pi$
$822$	−38626.4	−1.63899
$823$	35513.7	1.50417	0.752083	−	0.659068i	$-0.229049\pi$
$823$	35513.7	1.50417	0.752083	+	0.659068i	$0.229049\pi$
$824$	10839.7	0.458275
$825$	2039.66	0.0860751
$826$	−11450.8	−0.482354
$827$	9000.85	0.378465	0.189232	−	0.981932i	$-0.439400\pi$
$827$	9000.85	0.378465	0.189232	+	0.981932i	$0.439400\pi$
$828$	26199.3	1.09962
$829$	−43288.5	−1.81359	−0.906797	−	0.421567i	$-0.861480\pi$
$829$	−43288.5	−1.81359	−0.906797	+	0.421567i	$0.861480\pi$
$830$	−7113.13	−0.297470
$831$	−5136.03	−0.214401
$832$	−2648.70	−0.110369
$833$	−1401.10	−0.0582774
$834$	−29160.3	−1.21072
$835$	6020.30	0.249510
$836$	−1067.78	−0.0441747
$837$	−1648.58	−0.0680805
$838$	−38108.6	−1.57093
$839$	−4905.98	−0.201875	−0.100937	−	0.994893i	$-0.532184\pi$
$839$	−4905.98	−0.201875	−0.100937	+	0.994893i	$0.532184\pi$
$840$	5475.52	0.224909
$841$	−17056.0	−0.699333
$842$	−48756.8	−1.99557
$843$	−5074.18	−0.207312
$844$	9518.42	0.388196
$845$	−7424.15	−0.302247
$846$	−10925.5	−0.444004
$847$	−1706.80	−0.0692401
$848$	55163.6	2.23388
$849$	25164.0	1.01723
$850$	−880.543	−0.0355322
$851$	47629.3	1.91858
$852$	−7320.97	−0.294381
$853$	10669.7	0.428281	0.214141	−	0.976803i	$-0.431305\pi$
$853$	10669.7	0.428281	0.214141	+	0.976803i	$0.431305\pi$
$854$	14554.7	0.583199
$855$	2661.07	0.106441
$856$	8649.90	0.345383
$857$	−16555.1	−0.659872	−0.329936	−	0.944003i	$-0.607027\pi$
$857$	−16555.1	−0.659872	−0.329936	+	0.944003i	$0.607027\pi$
$858$	−7883.06	−0.313664
$859$	7469.03	0.296671	0.148335	−	0.988937i	$-0.452609\pi$
$859$	7469.03	0.296671	0.148335	+	0.988937i	$0.452609\pi$
$860$	−6100.66	−0.241896
$861$	−11226.8	−0.444377
$862$	−27398.9	−1.08261
$863$	40683.5	1.60473	0.802364	−	0.596835i	$-0.203575\pi$
$863$	40683.5	1.60473	0.802364	+	0.596835i	$0.203575\pi$
$864$	−1511.04	−0.0594983
$865$	9639.81	0.378917
$866$	−24661.9	−0.967720
$867$	35737.6	1.39990
$868$	−15840.1	−0.619411
$869$	10815.7	0.422207
$870$	−11498.0	−0.448066
$871$	6405.03	0.249169
$872$	−2969.85	−0.115335
$873$	−14555.3	−0.564287
$874$	−12593.9	−0.487407
$875$	−1763.22	−0.0681233
$876$	−8434.29	−0.325306
$877$	−38543.7	−1.48407	−0.742035	−	0.670361i	$-0.766139\pi$
$877$	−38543.7	−1.48407	−0.742035	+	0.670361i	$0.766139\pi$
$878$	5048.65	0.194059
$879$	27323.6	1.04847
$880$	4332.36	0.165959
$881$	−2080.56	−0.0795640	−0.0397820	−	0.999208i	$-0.512666\pi$
$881$	−2080.56	−0.0795640	−0.0397820	+	0.999208i	$0.512666\pi$
$882$	14607.0	0.557644
$883$	48830.5	1.86102	0.930508	−	0.366273i	$-0.119366\pi$
$883$	48830.5	1.86102	0.930508	+	0.366273i	$0.119366\pi$
$884$	1326.34	0.0504633
$885$	8314.74	0.315816
$886$	−31719.0	−1.20273
$887$	−44934.2	−1.70095	−0.850475	−	0.526015i	$-0.823685\pi$
$887$	−44934.2	−1.70095	−0.850475	+	0.526015i	$0.823685\pi$
$888$	−20198.1	−0.763294
$889$	7957.78	0.300220
$890$	29337.1	1.10492
$891$	7707.41	0.289796
$892$	−8310.82	−0.311958
$893$	2046.82	0.0767011
$894$	96508.3	3.61043
$895$	5237.45	0.195607
$896$	17665.0	0.658646
$897$	−36235.8	−1.34881
$898$	46187.8	1.71638
$899$	−18821.9	−0.698272
$900$	3577.74	0.132509
$901$	−6812.66	−0.251901
$902$	−4273.77	−0.157761
$903$	−24985.8	−0.920794
$904$	13458.3	0.495150
$905$	10098.6	0.370926
$906$	−55653.6	−2.04080
$907$	7953.95	0.291187	0.145593	−	0.989345i	$-0.453491\pi$
$907$	7953.95	0.291187	0.145593	+	0.989345i	$0.453491\pi$
$908$	−30864.3	−1.12805
$909$	−30219.9	−1.10267
$910$	6814.66	0.248246
$911$	15486.5	0.563218	0.281609	−	0.959529i	$-0.409132\pi$
$911$	15486.5	0.563218	0.281609	+	0.959529i	$0.409132\pi$
$912$	11100.5	0.403040
$913$	−4322.14	−0.156672
$914$	48316.7	1.74855
$915$	−10568.6	−0.381843
$916$	11852.3	0.427522
$917$	−5436.68	−0.195785
$918$	264.178	0.00949802
$919$	−4871.90	−0.174874	−0.0874370	−	0.996170i	$-0.527868\pi$
$919$	−4871.90	−0.174874	−0.0874370	+	0.996170i	$0.527868\pi$
$920$	9581.26	0.343353
$921$	33767.8	1.20813
$922$	25907.9	0.925413
$923$	5155.83	0.183864
$924$	−5879.66	−0.209336
$925$	6504.19	0.231196
$926$	33298.7	1.18171
$927$	29008.0	1.02777
$928$	−17251.6	−0.610249
$929$	33408.4	1.17987	0.589933	−	0.807452i	$-0.299154\pi$
$929$	33408.4	1.17987	0.589933	+	0.807452i	$0.299154\pi$
$930$	29512.4	1.04059
$931$	−2736.50	−0.0963321
$932$	−14546.2	−0.511243
$933$	−58179.5	−2.04149
$934$	−430.401	−0.0150783
$935$	−535.043	−0.0187142
$936$	7824.50	0.273239
$937$	15977.2	0.557046	0.278523	−	0.960430i	$-0.410155\pi$
$937$	15977.2	0.557046	0.278523	+	0.960430i	$0.410155\pi$
$938$	12257.8	0.426686
$939$	−57774.2	−2.00787
$940$	2751.89	0.0954861
$941$	−36903.0	−1.27843	−0.639216	−	0.769027i	$-0.720741\pi$
$941$	−36903.0	−1.27843	−0.639216	+	0.769027i	$0.720741\pi$
$942$	−68147.2	−2.35706
$943$	−19645.1	−0.678401
$944$	17661.0	0.608915
$945$	528.999	0.0182099
$946$	−9511.48	−0.326897
$947$	−44536.5	−1.52824	−0.764119	−	0.645075i	$-0.776826\pi$
$947$	−44536.5	−1.52824	−0.764119	+	0.645075i	$0.776826\pi$
$948$	37258.4	1.27647
$949$	5939.88	0.203179
$950$	−1719.80	−0.0587345
$951$	26615.4	0.907532
$952$	−1436.33	−0.0488990
$953$	−42778.5	−1.45407	−0.727037	−	0.686598i	$-0.759103\pi$
$953$	−42778.5	−1.45407	−0.727037	+	0.686598i	$0.759103\pi$
$954$	71024.6	2.41038
$955$	2434.42	0.0824880
$956$	22745.3	0.769492
$957$	−6986.48	−0.235988
$958$	−45183.5	−1.52381
$959$	20289.5	0.683193
$960$	3680.75	0.123746
$961$	18520.3	0.621673
$962$	−25138.0	−0.842495
$963$	23147.9	0.774591
$964$	−10330.9	−0.345161
$965$	14069.1	0.469326
$966$	−69347.2	−2.30974
$967$	−43672.7	−1.45235	−0.726173	−	0.687512i	$-0.758703\pi$
$967$	−43672.7	−1.45235	−0.726173	+	0.687512i	$0.758703\pi$
$968$	1266.54	0.0420537
$969$	−1370.90	−0.0454485
$970$	9406.84	0.311377
$971$	47607.4	1.57342	0.786711	−	0.617321i	$-0.211782\pi$
$971$	47607.4	1.57342	0.786711	+	0.617321i	$0.211782\pi$
$972$	27585.4	0.910292
$973$	15317.2	0.504672
$974$	−44406.0	−1.46084
$975$	−4948.32	−0.162536
$976$	−22448.2	−0.736220
$977$	43626.4	1.42859	0.714295	−	0.699844i	$-0.246747\pi$
$977$	43626.4	1.42859	0.714295	+	0.699844i	$0.246747\pi$
$978$	101048.	3.30383
$979$	17826.0	0.581944
$980$	−3679.16	−0.119925
$981$	−7947.59	−0.258662
$982$	32461.3	1.05487
$983$	48019.7	1.55808	0.779040	−	0.626975i	$-0.215707\pi$
$983$	48019.7	1.55808	0.779040	+	0.626975i	$0.215707\pi$
$984$	8330.88	0.269897
$985$	21549.0	0.697063
$986$	3016.13	0.0974171
$987$	11270.6	0.363474
$988$	2590.49	0.0834154
$989$	−43721.1	−1.40571
$990$	5578.02	0.179072
$991$	−9776.69	−0.313387	−0.156694	−	0.987647i	$-0.550084\pi$
$991$	−9776.69	−0.313387	−0.156694	+	0.987647i	$0.550084\pi$
$992$	44280.5	1.41725
$993$	44867.9	1.43388
$994$	9867.10	0.314854
$995$	22188.4	0.706955
$996$	−14889.1	−0.473674
$997$	36714.2	1.16625	0.583124	−	0.812383i	$-0.301830\pi$
$997$	36714.2	1.16625	0.583124	+	0.812383i	$0.301830\pi$
$998$	41969.7	1.33119
$999$	−1951.37	−0.0618005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.6	✓	24	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-3.62064 q^{2} -7.41696 q^{3} +5.10901 q^{4} +5.00000 q^{5} +26.8541 q^{6} -14.1058 q^{7} +10.4672 q^{8} +28.0113 q^{9} +O(q^{10})\)	\(q-3.62064 q^{2} -7.41696 q^{3} +5.10901 q^{4} +5.00000 q^{5} +26.8541 q^{6} -14.1058 q^{7} +10.4672 q^{8} +28.0113 q^{9} -18.1032 q^{10} -11.0000 q^{11} -37.8933 q^{12} +26.6865 q^{13} +51.0720 q^{14} -37.0848 q^{15} -78.7701 q^{16} +9.72805 q^{17} -101.419 q^{18} +19.0000 q^{19} +25.5450 q^{20} +104.622 q^{21} +39.8270 q^{22} +183.071 q^{23} -77.6351 q^{24} +25.0000 q^{25} -96.6221 q^{26} -7.50044 q^{27} -72.0666 q^{28} -85.6328 q^{29} +134.271 q^{30} +219.798 q^{31} +201.460 q^{32} +81.5865 q^{33} -35.2217 q^{34} -70.5290 q^{35} +143.110 q^{36} +260.168 q^{37} -68.7921 q^{38} -197.933 q^{39} +52.3362 q^{40} -107.308 q^{41} -378.799 q^{42} -238.820 q^{43} -56.1991 q^{44} +140.056 q^{45} -662.835 q^{46} +107.727 q^{47} +584.235 q^{48} -144.026 q^{49} -90.5159 q^{50} -72.1525 q^{51} +136.342 q^{52} -700.312 q^{53} +27.1564 q^{54} -55.0000 q^{55} -147.649 q^{56} -140.922 q^{57} +310.045 q^{58} -224.209 q^{59} -189.466 q^{60} +284.984 q^{61} -795.809 q^{62} -395.121 q^{63} -99.2524 q^{64} +133.433 q^{65} -295.395 q^{66} +240.010 q^{67} +49.7006 q^{68} -1357.83 q^{69} +255.360 q^{70} +193.200 q^{71} +293.201 q^{72} +222.580 q^{73} -941.972 q^{74} -185.424 q^{75} +97.0711 q^{76} +155.164 q^{77} +716.642 q^{78} -983.246 q^{79} -393.851 q^{80} -700.673 q^{81} +388.524 q^{82} +392.922 q^{83} +534.515 q^{84} +48.6402 q^{85} +864.680 q^{86} +635.135 q^{87} -115.140 q^{88} -1620.55 q^{89} -507.093 q^{90} -376.435 q^{91} +935.313 q^{92} -1630.23 q^{93} -390.041 q^{94} +95.0000 q^{95} -1494.22 q^{96} -519.624 q^{97} +521.467 q^{98} -308.124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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