LMFDB - Embedded newform 2001.4.a.e.1.21

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:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q+0.532246 q^{2} -3.00000 q^{3} -7.71671 q^{4} -20.3716 q^{5} -1.59674 q^{6} +24.4902 q^{7} -8.36516 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.532246 q^{2} -3.00000 q^{3} -7.71671 q^{4} -20.3716 q^{5} -1.59674 q^{6} +24.4902 q^{7} -8.36516 q^{8} +9.00000 q^{9} -10.8427 q^{10} -54.1038 q^{11} +23.1501 q^{12} -45.5217 q^{13} +13.0348 q^{14} +61.1147 q^{15} +57.2814 q^{16} -56.1860 q^{17} +4.79022 q^{18} +69.2121 q^{19} +157.202 q^{20} -73.4705 q^{21} -28.7965 q^{22} -23.0000 q^{23} +25.0955 q^{24} +290.001 q^{25} -24.2287 q^{26} -27.0000 q^{27} -188.984 q^{28} +29.0000 q^{29} +32.5281 q^{30} -336.148 q^{31} +97.4091 q^{32} +162.311 q^{33} -29.9048 q^{34} -498.903 q^{35} -69.4504 q^{36} +393.256 q^{37} +36.8379 q^{38} +136.565 q^{39} +170.411 q^{40} -95.1886 q^{41} -39.1044 q^{42} +415.804 q^{43} +417.503 q^{44} -183.344 q^{45} -12.2417 q^{46} +7.59200 q^{47} -171.844 q^{48} +256.768 q^{49} +154.352 q^{50} +168.558 q^{51} +351.278 q^{52} +228.186 q^{53} -14.3706 q^{54} +1102.18 q^{55} -204.864 q^{56} -207.636 q^{57} +15.4351 q^{58} +543.935 q^{59} -471.605 q^{60} +901.170 q^{61} -178.914 q^{62} +220.411 q^{63} -406.405 q^{64} +927.347 q^{65} +86.3896 q^{66} -1054.51 q^{67} +433.571 q^{68} +69.0000 q^{69} -265.539 q^{70} +612.210 q^{71} -75.2864 q^{72} +313.312 q^{73} +209.309 q^{74} -870.002 q^{75} -534.090 q^{76} -1325.01 q^{77} +72.6862 q^{78} -792.894 q^{79} -1166.91 q^{80} +81.0000 q^{81} -50.6638 q^{82} -513.300 q^{83} +566.951 q^{84} +1144.60 q^{85} +221.310 q^{86} -87.0000 q^{87} +452.587 q^{88} +1019.89 q^{89} -97.5842 q^{90} -1114.83 q^{91} +177.484 q^{92} +1008.45 q^{93} +4.04081 q^{94} -1409.96 q^{95} -292.227 q^{96} +826.700 q^{97} +136.664 q^{98} -486.934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 114 q^{3} + 138 q^{4} - 25 q^{5} - 34 q^{7} + 18 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 114 * q^3 + 138 * q^4 - 25 * q^5 - 34 * q^7 + 18 * q^8 + 342 * q^9	\( 38 q - 114 q^{3} + 138 q^{4} - 25 q^{5} - 34 q^{7} + 18 q^{8} + 342 q^{9} - 156 q^{10} - 111 q^{11} - 414 q^{12} + 179 q^{13} - 142 q^{14} + 75 q^{15} + 470 q^{16} + 58 q^{17} + 25 q^{19} - 193 q^{20} + 102 q^{21} - 171 q^{22} - 874 q^{23} - 54 q^{24} + 749 q^{25} + 116 q^{26} - 1026 q^{27} - 576 q^{28} + 1102 q^{29} + 468 q^{30} - 846 q^{31} + 174 q^{32} + 333 q^{33} - 277 q^{34} - 943 q^{35} + 1242 q^{36} + 183 q^{37} + 27 q^{38} - 537 q^{39} - 1517 q^{40} - 115 q^{41} + 426 q^{42} - 585 q^{43} - 273 q^{44} - 225 q^{45} - 746 q^{47} - 1410 q^{48} + 1494 q^{49} + 833 q^{50} - 174 q^{51} + 1547 q^{52} - 470 q^{53} + 152 q^{55} - 1629 q^{56} - 75 q^{57} - 2409 q^{59} + 579 q^{60} + 812 q^{61} - 2390 q^{62} - 306 q^{63} + 966 q^{64} - 1410 q^{65} + 513 q^{66} - 549 q^{67} - 818 q^{68} + 2622 q^{69} + 745 q^{70} - 5612 q^{71} + 162 q^{72} + 2592 q^{73} - 1427 q^{74} - 2247 q^{75} + 1241 q^{76} - 431 q^{77} - 348 q^{78} - 3514 q^{79} - 1835 q^{80} + 3078 q^{81} + 2701 q^{82} - 1526 q^{83} + 1728 q^{84} + 3659 q^{85} - 4267 q^{86} - 3306 q^{87} + 451 q^{88} - 359 q^{89} - 1404 q^{90} - 5169 q^{91} - 3174 q^{92} + 2538 q^{93} + 33 q^{94} - 3929 q^{95} - 522 q^{96} + 3554 q^{97} + 1876 q^{98} - 999 q^{99}+O(q^{100}) \) 38 * q - 114 * q^3 + 138 * q^4 - 25 * q^5 - 34 * q^7 + 18 * q^8 + 342 * q^9 - 156 * q^10 - 111 * q^11 - 414 * q^12 + 179 * q^13 - 142 * q^14 + 75 * q^15 + 470 * q^16 + 58 * q^17 + 25 * q^19 - 193 * q^20 + 102 * q^21 - 171 * q^22 - 874 * q^23 - 54 * q^24 + 749 * q^25 + 116 * q^26 - 1026 * q^27 - 576 * q^28 + 1102 * q^29 + 468 * q^30 - 846 * q^31 + 174 * q^32 + 333 * q^33 - 277 * q^34 - 943 * q^35 + 1242 * q^36 + 183 * q^37 + 27 * q^38 - 537 * q^39 - 1517 * q^40 - 115 * q^41 + 426 * q^42 - 585 * q^43 - 273 * q^44 - 225 * q^45 - 746 * q^47 - 1410 * q^48 + 1494 * q^49 + 833 * q^50 - 174 * q^51 + 1547 * q^52 - 470 * q^53 + 152 * q^55 - 1629 * q^56 - 75 * q^57 - 2409 * q^59 + 579 * q^60 + 812 * q^61 - 2390 * q^62 - 306 * q^63 + 966 * q^64 - 1410 * q^65 + 513 * q^66 - 549 * q^67 - 818 * q^68 + 2622 * q^69 + 745 * q^70 - 5612 * q^71 + 162 * q^72 + 2592 * q^73 - 1427 * q^74 - 2247 * q^75 + 1241 * q^76 - 431 * q^77 - 348 * q^78 - 3514 * q^79 - 1835 * q^80 + 3078 * q^81 + 2701 * q^82 - 1526 * q^83 + 1728 * q^84 + 3659 * q^85 - 4267 * q^86 - 3306 * q^87 + 451 * q^88 - 359 * q^89 - 1404 * q^90 - 5169 * q^91 - 3174 * q^92 + 2538 * q^93 + 33 * q^94 - 3929 * q^95 - 522 * q^96 + 3554 * q^97 + 1876 * q^98 - 999 * 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 $

$2$	0.532246	0.188177	0.0940887	−	0.995564i	$-0.470006\pi$
$2$	0.532246	0.188177	0.0940887	+	0.995564i	$0.470006\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.71671	−0.964589
$5$	−20.3716	−1.82209	−0.911044	−	0.412309i	$-0.864722\pi$
$5$	−20.3716	−1.82209	−0.911044	+	0.412309i	$0.864722\pi$
$6$	−1.59674	−0.108644
$7$	24.4902	1.32234	0.661172	−	0.750234i	$-0.270059\pi$
$7$	24.4902	1.32234	0.661172	+	0.750234i	$0.270059\pi$
$8$	−8.36516	−0.369691
$9$	9.00000	0.333333
$10$	−10.8427	−0.342876
$11$	−54.1038	−1.48299	−0.741495	−	0.670958i	$-0.765883\pi$
$11$	−54.1038	−1.48299	−0.741495	+	0.670958i	$0.765883\pi$
$12$	23.1501	0.556906
$13$	−45.5217	−0.971188	−0.485594	−	0.874185i	$-0.661397\pi$
$13$	−45.5217	−0.971188	−0.485594	+	0.874185i	$0.661397\pi$
$14$	13.0348	0.248835
$15$	61.1147	1.05198
$16$	57.2814	0.895022
$17$	−56.1860	−0.801595	−0.400797	−	0.916167i	$-0.631267\pi$
$17$	−56.1860	−0.801595	−0.400797	+	0.916167i	$0.631267\pi$
$18$	4.79022	0.0627258
$19$	69.2121	0.835702	0.417851	−	0.908516i	$-0.362783\pi$
$19$	69.2121	0.835702	0.417851	+	0.908516i	$0.362783\pi$
$20$	157.202	1.75757
$21$	−73.4705	−0.763456
$22$	−28.7965	−0.279065
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	25.0955	0.213441
$25$	290.001	2.32000
$26$	−24.2287	−0.182756
$27$	−27.0000	−0.192450
$28$	−188.984	−1.27552
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	32.5281	0.197959
$31$	−336.148	−1.94755	−0.973775	−	0.227514i	$-0.926940\pi$
$31$	−336.148	−1.94755	−0.973775	+	0.227514i	$0.926940\pi$
$32$	97.4091	0.538114
$33$	162.311	0.856205
$34$	−29.9048	−0.150842
$35$	−498.903	−2.40943
$36$	−69.4504	−0.321530
$37$	393.256	1.74732	0.873660	−	0.486538i	$-0.161740\pi$
$37$	393.256	1.74732	0.873660	+	0.486538i	$0.161740\pi$
$38$	36.8379	0.157260
$39$	136.565	0.560715
$40$	170.411	0.673610
$41$	−95.1886	−0.362585	−0.181292	−	0.983429i	$-0.558028\pi$
$41$	−95.1886	−0.362585	−0.181292	+	0.983429i	$0.558028\pi$
$42$	−39.1044	−0.143665
$43$	415.804	1.47464	0.737319	−	0.675545i	$-0.236091\pi$
$43$	415.804	1.47464	0.737319	+	0.675545i	$0.236091\pi$
$44$	417.503	1.43048
$45$	−183.344	−0.607363
$46$	−12.2417	−0.0392377
$47$	7.59200	0.0235619	0.0117809	−	0.999931i	$-0.496250\pi$
$47$	7.59200	0.0235619	0.0117809	+	0.999931i	$0.496250\pi$
$48$	−171.844	−0.516741
$49$	256.768	0.748594
$50$	154.352	0.436572
$51$	168.558	0.462801
$52$	351.278	0.936797
$53$	228.186	0.591392	0.295696	−	0.955282i	$-0.404448\pi$
$53$	228.186	0.591392	0.295696	+	0.955282i	$0.404448\pi$
$54$	−14.3706	−0.0362148
$55$	1102.18	2.70214
$56$	−204.864	−0.488859
$57$	−207.636	−0.482493
$58$	15.4351	0.0349437
$59$	543.935	1.20024	0.600121	−	0.799909i	$-0.295119\pi$
$59$	543.935	1.20024	0.600121	+	0.799909i	$0.295119\pi$
$60$	−471.605	−1.01473
$61$	901.170	1.89152	0.945762	−	0.324860i	$-0.105317\pi$
$61$	901.170	1.89152	0.945762	+	0.324860i	$0.105317\pi$
$62$	−178.914	−0.366485
$63$	220.411	0.440781
$64$	−406.405	−0.793761
$65$	927.347	1.76959
$66$	86.3896	0.161118
$67$	−1054.51	−1.92282	−0.961412	−	0.275111i	$-0.911285\pi$
$67$	−1054.51	−1.92282	−0.961412	+	0.275111i	$0.911285\pi$
$68$	433.571	0.773210
$69$	69.0000	0.120386
$70$	−265.539	−0.453400
$71$	612.210	1.02332	0.511662	−	0.859187i	$-0.329030\pi$
$71$	612.210	1.02332	0.511662	+	0.859187i	$0.329030\pi$
$72$	−75.2864	−0.123230
$73$	313.312	0.502334	0.251167	−	0.967944i	$-0.419186\pi$
$73$	313.312	0.502334	0.251167	+	0.967944i	$0.419186\pi$
$74$	209.309	0.328806
$75$	−870.002	−1.33946
$76$	−534.090	−0.806109
$77$	−1325.01	−1.96102
$78$	72.6862	0.105514
$79$	−792.894	−1.12921	−0.564605	−	0.825362i	$-0.690971\pi$
$79$	−792.894	−1.12921	−0.564605	+	0.825362i	$0.690971\pi$
$80$	−1166.91	−1.63081
$81$	81.0000	0.111111
$82$	−50.6638	−0.0682302
$83$	−513.300	−0.678819	−0.339409	−	0.940639i	$-0.610227\pi$
$83$	−513.300	−0.678819	−0.339409	+	0.940639i	$0.610227\pi$
$84$	566.951	0.736421
$85$	1144.60	1.46058
$86$	221.310	0.277494
$87$	−87.0000	−0.107211
$88$	452.587	0.548249
$89$	1019.89	1.21470	0.607349	−	0.794435i	$-0.292233\pi$
$89$	1019.89	1.21470	0.607349	+	0.794435i	$0.292233\pi$
$90$	−97.5842	−0.114292
$91$	−1114.83	−1.28424
$92$	177.484	0.201131
$93$	1008.45	1.12442
$94$	4.04081	0.00443381
$95$	−1409.96	−1.52272
$96$	−292.227	−0.310680
$97$	826.700	0.865347	0.432674	−	0.901551i	$-0.357570\pi$
$97$	826.700	0.865347	0.432674	+	0.901551i	$0.357570\pi$
$98$	136.664	0.140869
$99$	−486.934	−0.494330
$100$	−2237.85	−2.23785
$101$	−1523.39	−1.50082	−0.750408	−	0.660974i	$-0.770143\pi$
$101$	−1523.39	−1.50082	−0.750408	+	0.660974i	$0.770143\pi$
$102$	89.7144	0.0870887
$103$	1878.23	1.79677	0.898387	−	0.439206i	$-0.144740\pi$
$103$	1878.23	1.79677	0.898387	+	0.439206i	$0.144740\pi$
$104$	380.796	0.359040
$105$	1496.71	1.39108
$106$	121.451	0.111287
$107$	528.291	0.477307	0.238653	−	0.971105i	$-0.423294\pi$
$107$	528.291	0.477307	0.238653	+	0.971105i	$0.423294\pi$
$108$	208.351	0.185635
$109$	1679.05	1.47545	0.737725	−	0.675101i	$-0.235900\pi$
$109$	1679.05	1.47545	0.737725	+	0.675101i	$0.235900\pi$
$110$	586.630	0.508482
$111$	−1179.77	−1.00882
$112$	1402.83	1.18353
$113$	−1997.99	−1.66332	−0.831658	−	0.555288i	$-0.812608\pi$
$113$	−1997.99	−1.66332	−0.831658	+	0.555288i	$0.812608\pi$
$114$	−110.514	−0.0907943
$115$	468.546	0.379932
$116$	−223.785	−0.179120
$117$	−409.695	−0.323729
$118$	289.507	0.225858
$119$	−1376.00	−1.05998
$120$	−511.234	−0.388909
$121$	1596.22	1.19926
$122$	479.644	0.355942
$123$	285.566	0.209338
$124$	2593.96	1.87859
$125$	−3361.32	−2.40516
$126$	117.313	0.0829451
$127$	−675.249	−0.471800	−0.235900	−	0.971777i	$-0.575804\pi$
$127$	−675.249	−0.471800	−0.235900	+	0.971777i	$0.575804\pi$
$128$	−995.580	−0.687482
$129$	−1247.41	−0.851383
$130$	493.577	0.332997
$131$	−815.681	−0.544018	−0.272009	−	0.962295i	$-0.587688\pi$
$131$	−815.681	−0.544018	−0.272009	+	0.962295i	$0.587688\pi$
$132$	−1252.51	−0.825886
$133$	1695.02	1.10509
$134$	−561.260	−0.361832
$135$	550.032	0.350661
$136$	470.005	0.296343
$137$	−889.508	−0.554714	−0.277357	−	0.960767i	$-0.589458\pi$
$137$	−889.508	−0.554714	−0.277357	+	0.960767i	$0.589458\pi$
$138$	36.7250	0.0226539
$139$	1536.45	0.937551	0.468776	−	0.883317i	$-0.344695\pi$
$139$	1536.45	0.937551	0.468776	+	0.883317i	$0.344695\pi$
$140$	3849.89	2.32411
$141$	−22.7760	−0.0136034
$142$	325.846	0.192566
$143$	2462.89	1.44026
$144$	515.532	0.298341
$145$	−590.775	−0.338353
$146$	166.759	0.0945279
$147$	−770.304	−0.432201
$148$	−3034.64	−1.68545
$149$	1578.83	0.868071	0.434036	−	0.900896i	$-0.357089\pi$
$149$	1578.83	0.868071	0.434036	+	0.900896i	$0.357089\pi$
$150$	−463.055	−0.252055
$151$	−2006.38	−1.08130	−0.540651	−	0.841247i	$-0.681822\pi$
$151$	−2006.38	−1.08130	−0.540651	+	0.841247i	$0.681822\pi$
$152$	−578.970	−0.308952
$153$	−505.674	−0.267198
$154$	−705.231	−0.369021
$155$	6847.87	3.54861
$156$	−1053.83	−0.540860
$157$	1464.03	0.744217	0.372108	−	0.928189i	$-0.378635\pi$
$157$	1464.03	0.744217	0.372108	+	0.928189i	$0.378635\pi$
$158$	−422.015	−0.212492
$159$	−684.558	−0.341440
$160$	−1984.38	−0.980491
$161$	−563.274	−0.275728
$162$	43.1119	0.0209086
$163$	−3386.65	−1.62738	−0.813691	−	0.581298i	$-0.802545\pi$
$163$	−3386.65	−1.62738	−0.813691	+	0.581298i	$0.802545\pi$
$164$	734.543	0.349745
$165$	−3306.53	−1.56008
$166$	−273.202	−0.127738
$167$	−237.197	−0.109909	−0.0549546	−	0.998489i	$-0.517501\pi$
$167$	−237.197	−0.109909	−0.0549546	+	0.998489i	$0.517501\pi$
$168$	614.592	0.282243
$169$	−124.778	−0.0567946
$170$	609.207	0.274847
$171$	622.909	0.278567
$172$	−3208.64	−1.42242
$173$	757.249	0.332789	0.166395	−	0.986059i	$-0.446787\pi$
$173$	757.249	0.332789	0.166395	+	0.986059i	$0.446787\pi$
$174$	−46.3054	−0.0201747
$175$	7102.16	3.06784
$176$	−3099.14	−1.32731
$177$	−1631.80	−0.692960
$178$	542.832	0.228579
$179$	−3313.01	−1.38339	−0.691694	−	0.722191i	$-0.743135\pi$
$179$	−3313.01	−1.38339	−0.691694	+	0.722191i	$0.743135\pi$
$180$	1414.81	0.585855
$181$	−1016.11	−0.417277	−0.208639	−	0.977993i	$-0.566903\pi$
$181$	−1016.11	−0.417277	−0.208639	+	0.977993i	$0.566903\pi$
$182$	−593.365	−0.241666
$183$	−2703.51	−1.09207
$184$	192.399	0.0770860
$185$	−8011.23	−3.18377
$186$	536.741	0.211590
$187$	3039.87	1.18876
$188$	−58.5853	−0.0227275
$189$	−661.234	−0.254485
$190$	−750.445	−0.286542
$191$	−1018.40	−0.385805	−0.192902	−	0.981218i	$-0.561790\pi$
$191$	−1018.40	−0.385805	−0.192902	+	0.981218i	$0.561790\pi$
$192$	1219.22	0.458278
$193$	1369.13	0.510634	0.255317	−	0.966857i	$-0.417820\pi$
$193$	1369.13	0.510634	0.255317	+	0.966857i	$0.417820\pi$
$194$	440.008	0.162839
$195$	−2782.04	−1.02167
$196$	−1981.40	−0.722086
$197$	−1202.19	−0.434785	−0.217393	−	0.976084i	$-0.569755\pi$
$197$	−1202.19	−0.434785	−0.217393	+	0.976084i	$0.569755\pi$
$198$	−259.169	−0.0930218
$199$	−2513.65	−0.895415	−0.447707	−	0.894180i	$-0.647759\pi$
$199$	−2513.65	−0.895415	−0.447707	+	0.894180i	$0.647759\pi$
$200$	−2425.90	−0.857686
$201$	3163.54	1.11014
$202$	−810.816	−0.282420
$203$	710.215	0.245553
$204$	−1300.71	−0.446413
$205$	1939.14	0.660661
$206$	999.681	0.338112
$207$	−207.000	−0.0695048
$208$	−2607.54	−0.869234
$209$	−3744.63	−1.23934
$210$	796.617	0.261771
$211$	872.901	0.284801	0.142400	−	0.989809i	$-0.454518\pi$
$211$	872.901	0.284801	0.142400	+	0.989809i	$0.454518\pi$
$212$	−1760.85	−0.570450
$213$	−1836.63	−0.590816
$214$	281.181	0.0898184
$215$	−8470.57	−2.68692
$216$	225.859	0.0711471
$217$	−8232.33	−2.57533
$218$	893.669	0.277646
$219$	−939.935	−0.290023
$220$	−8505.19	−2.60645
$221$	2557.68	0.778499
$222$	−627.926	−0.189836
$223$	−3139.96	−0.942901	−0.471451	−	0.881892i	$-0.656269\pi$
$223$	−3139.96	−0.942901	−0.471451	+	0.881892i	$0.656269\pi$
$224$	2385.56	0.711572
$225$	2610.00	0.773335
$226$	−1063.42	−0.312999
$227$	4004.79	1.17096	0.585478	−	0.810688i	$-0.300907\pi$
$227$	4004.79	1.17096	0.585478	+	0.810688i	$0.300907\pi$
$228$	1602.27	0.465408
$229$	2981.49	0.860360	0.430180	−	0.902743i	$-0.358450\pi$
$229$	2981.49	0.860360	0.430180	+	0.902743i	$0.358450\pi$
$230$	249.382	0.0714946
$231$	3975.03	1.13220
$232$	−242.590	−0.0686500
$233$	6194.97	1.74183	0.870914	−	0.491435i	$-0.163528\pi$
$233$	6194.97	1.74183	0.870914	+	0.491435i	$0.163528\pi$
$234$	−218.059	−0.0609185
$235$	−154.661	−0.0429318
$236$	−4197.39	−1.15774
$237$	2378.68	0.651949
$238$	−732.373	−0.199465
$239$	−4785.08	−1.29507	−0.647533	−	0.762037i	$-0.724199\pi$
$239$	−4785.08	−1.29507	−0.647533	+	0.762037i	$0.724199\pi$
$240$	3500.73	0.941548
$241$	−3384.66	−0.904669	−0.452335	−	0.891848i	$-0.649409\pi$
$241$	−3384.66	−0.904669	−0.452335	+	0.891848i	$0.649409\pi$
$242$	849.580	0.225674
$243$	−243.000	−0.0641500
$244$	−6954.07	−1.82454
$245$	−5230.76	−1.36400
$246$	151.991	0.0393927
$247$	−3150.65	−0.811624
$248$	2811.94	0.719992
$249$	1539.90	0.391916
$250$	−1789.05	−0.452598
$251$	5355.28	1.34670	0.673351	−	0.739323i	$-0.264854\pi$
$251$	5355.28	1.34670	0.673351	+	0.739323i	$0.264854\pi$
$252$	−1700.85	−0.425173
$253$	1244.39	0.309225
$254$	−359.399	−0.0887822
$255$	−3433.79	−0.843264
$256$	2721.35	0.664392
$257$	−4852.22	−1.17772	−0.588859	−	0.808236i	$-0.700423\pi$
$257$	−4852.22	−1.17772	−0.588859	+	0.808236i	$0.700423\pi$
$258$	−663.930	−0.160211
$259$	9630.89	2.31056
$260$	−7156.08	−1.70693
$261$	261.000	0.0618984
$262$	−434.143	−0.102372
$263$	1460.20	0.342356	0.171178	−	0.985240i	$-0.445243\pi$
$263$	1460.20	0.342356	0.171178	+	0.985240i	$0.445243\pi$
$264$	−1357.76	−0.316532
$265$	−4648.51	−1.07757
$266$	902.165	0.207952
$267$	−3059.67	−0.701306
$268$	8137.38	1.85474
$269$	−682.331	−0.154656	−0.0773280	−	0.997006i	$-0.524639\pi$
$269$	−682.331	−0.154656	−0.0773280	+	0.997006i	$0.524639\pi$
$270$	292.753	0.0659865
$271$	−4658.30	−1.04418	−0.522088	−	0.852892i	$-0.674847\pi$
$271$	−4658.30	−1.04418	−0.522088	+	0.852892i	$0.674847\pi$
$272$	−3218.41	−0.717445
$273$	3344.50	0.741459
$274$	−473.437	−0.104385
$275$	−15690.1	−3.44055
$276$	−532.453	−0.116123
$277$	−5737.71	−1.24457	−0.622284	−	0.782791i	$-0.713795\pi$
$277$	−5737.71	−1.24457	−0.622284	+	0.782791i	$0.713795\pi$
$278$	817.767	0.176426
$279$	−3025.34	−0.649183
$280$	4173.40	0.890745
$281$	−3983.52	−0.845684	−0.422842	−	0.906204i	$-0.638967\pi$
$281$	−3983.52	−0.845684	−0.422842	+	0.906204i	$0.638967\pi$
$282$	−12.1224	−0.00255986
$283$	−1424.60	−0.299236	−0.149618	−	0.988744i	$-0.547804\pi$
$283$	−1424.60	−0.299236	−0.149618	+	0.988744i	$0.547804\pi$
$284$	−4724.25	−0.987086
$285$	4229.88	0.879145
$286$	1310.87	0.271025
$287$	−2331.18	−0.479462
$288$	876.682	0.179371
$289$	−1756.13	−0.357446
$290$	−314.438	−0.0636704
$291$	−2480.10	−0.499608
$292$	−2417.74	−0.484546
$293$	112.546	0.0224402	0.0112201	−	0.999937i	$-0.496428\pi$
$293$	112.546	0.0224402	0.0112201	+	0.999937i	$0.496428\pi$
$294$	−409.991	−0.0813305
$295$	−11080.8	−2.18695
$296$	−3289.65	−0.645969
$297$	1460.80	0.285402
$298$	840.325	0.163351
$299$	1047.00	0.202507
$300$	6713.55	1.29202
$301$	10183.1	1.94998
$302$	−1067.89	−0.203477
$303$	4570.16	0.866497
$304$	3964.56	0.747972
$305$	−18358.2	−3.44652
$306$	−269.143	−0.0502807
$307$	−473.722	−0.0880676	−0.0440338	−	0.999030i	$-0.514021\pi$
$307$	−473.722	−0.0880676	−0.0440338	+	0.999030i	$0.514021\pi$
$308$	10224.7	1.89158
$309$	−5634.69	−1.03737
$310$	3644.75	0.667768
$311$	2333.26	0.425424	0.212712	−	0.977115i	$-0.431770\pi$
$311$	2333.26	0.425424	0.212712	+	0.977115i	$0.431770\pi$
$312$	−1142.39	−0.207292
$313$	316.946	0.0572359	0.0286180	−	0.999590i	$-0.490889\pi$
$313$	316.946	0.0572359	0.0286180	+	0.999590i	$0.490889\pi$
$314$	779.222	0.140045
$315$	−4490.13	−0.803142
$316$	6118.54	1.08922
$317$	8696.75	1.54088	0.770438	−	0.637514i	$-0.220037\pi$
$317$	8696.75	1.54088	0.770438	+	0.637514i	$0.220037\pi$
$318$	−364.353	−0.0642513
$319$	−1569.01	−0.275384
$320$	8279.11	1.44630
$321$	−1584.87	−0.275573
$322$	−299.800	−0.0518858
$323$	−3888.75	−0.669895
$324$	−625.054	−0.107177
$325$	−13201.3	−2.25316
$326$	−1802.53	−0.306236
$327$	−5037.16	−0.851852
$328$	796.268	0.134044
$329$	185.929	0.0311569
$330$	−1759.89	−0.293572
$331$	9796.75	1.62682	0.813411	−	0.581690i	$-0.197608\pi$
$331$	9796.75	1.62682	0.813411	+	0.581690i	$0.197608\pi$
$332$	3960.99	0.654781
$333$	3539.30	0.582440
$334$	−126.247	−0.0206824
$335$	21482.1	3.50356
$336$	−4208.49	−0.683310
$337$	−7652.54	−1.23697	−0.618487	−	0.785795i	$-0.712254\pi$
$337$	−7652.54	−1.23697	−0.618487	+	0.785795i	$0.712254\pi$
$338$	−66.4125	−0.0106875
$339$	5993.96	0.960316
$340$	−8832.53	−1.40886
$341$	18186.9	2.88820
$342$	331.541	0.0524201
$343$	−2111.84	−0.332445
$344$	−3478.26	−0.545161
$345$	−1405.64	−0.219354
$346$	403.043	0.0626235
$347$	−3727.83	−0.576716	−0.288358	−	0.957523i	$-0.593109\pi$
$347$	−3727.83	−0.576716	−0.288358	+	0.957523i	$0.593109\pi$
$348$	671.354	0.103415
$349$	1829.50	0.280605	0.140302	−	0.990109i	$-0.455193\pi$
$349$	1829.50	0.280605	0.140302	+	0.990109i	$0.455193\pi$
$350$	3780.10	0.577299
$351$	1229.09	0.186905
$352$	−5270.20	−0.798018
$353$	8286.40	1.24941	0.624704	−	0.780862i	$-0.285220\pi$
$353$	8286.40	1.24941	0.624704	+	0.780862i	$0.285220\pi$
$354$	−868.521	−0.130399
$355$	−12471.7	−1.86458
$356$	−7870.19	−1.17168
$357$	4128.01	0.611982
$358$	−1763.34	−0.260322
$359$	−6027.39	−0.886110	−0.443055	−	0.896495i	$-0.646105\pi$
$359$	−6027.39	−0.886110	−0.443055	+	0.896495i	$0.646105\pi$
$360$	1533.70	0.224537
$361$	−2068.69	−0.301602
$362$	−540.823	−0.0785222
$363$	−4788.65	−0.692394
$364$	8602.85	1.23877
$365$	−6382.65	−0.915296
$366$	−1438.93	−0.205503
$367$	8883.59	1.26354	0.631770	−	0.775156i	$-0.282329\pi$
$367$	8883.59	1.26354	0.631770	+	0.775156i	$0.282329\pi$
$368$	−1317.47	−0.186625
$369$	−856.698	−0.120862
$370$	−4263.95	−0.599113
$371$	5588.31	0.782024
$372$	−7781.88	−1.08460
$373$	−6930.47	−0.962055	−0.481027	−	0.876706i	$-0.659736\pi$
$373$	−6930.47	−0.962055	−0.481027	+	0.876706i	$0.659736\pi$
$374$	1617.96	0.223697
$375$	10084.0	1.38862
$376$	−63.5083	−0.00871062
$377$	−1320.13	−0.180345
$378$	−351.939	−0.0478884
$379$	5115.22	0.693276	0.346638	−	0.937999i	$-0.387323\pi$
$379$	5115.22	0.693276	0.346638	+	0.937999i	$0.387323\pi$
$380$	10880.2	1.46880
$381$	2025.75	0.272394
$382$	−542.038	−0.0725997
$383$	12401.4	1.65453	0.827264	−	0.561814i	$-0.189896\pi$
$383$	12401.4	1.65453	0.827264	+	0.561814i	$0.189896\pi$
$384$	2986.74	0.396918
$385$	26992.5	3.57316
$386$	728.715	0.0960897
$387$	3742.23	0.491546
$388$	−6379.41	−0.834704
$389$	3409.74	0.444424	0.222212	−	0.974998i	$-0.428672\pi$
$389$	3409.74	0.444424	0.222212	+	0.974998i	$0.428672\pi$
$390$	−1480.73	−0.192256
$391$	1292.28	0.167144
$392$	−2147.90	−0.276749
$393$	2447.04	0.314089
$394$	−639.862	−0.0818168
$395$	16152.5	2.05752
$396$	3757.53	0.476826
$397$	927.400	0.117242	0.0586208	−	0.998280i	$-0.481330\pi$
$397$	927.400	0.117242	0.0586208	+	0.998280i	$0.481330\pi$
$398$	−1337.88	−0.168497
$399$	−5085.05	−0.638022
$400$	16611.6	2.07645
$401$	1228.02	0.152929	0.0764644	−	0.997072i	$-0.475637\pi$
$401$	1228.02	0.152929	0.0764644	+	0.997072i	$0.475637\pi$
$402$	1683.78	0.208904
$403$	15302.0	1.89144
$404$	11755.5	1.44767
$405$	−1650.10	−0.202454
$406$	378.009	0.0462076
$407$	−21276.6	−2.59126
$408$	−1410.02	−0.171093
$409$	4610.61	0.557408	0.278704	−	0.960377i	$-0.410095\pi$
$409$	4610.61	0.557408	0.278704	+	0.960377i	$0.410095\pi$
$410$	1032.10	0.124321
$411$	2668.52	0.320264
$412$	−14493.8	−1.73315
$413$	13321.0	1.58713
$414$	−110.175	−0.0130792
$415$	10456.7	1.23687
$416$	−4434.22	−0.522610
$417$	−4609.34	−0.541296
$418$	−1993.07	−0.233216
$419$	7140.94	0.832597	0.416298	−	0.909228i	$-0.363327\pi$
$419$	7140.94	0.832597	0.416298	+	0.909228i	$0.363327\pi$
$420$	−11549.7	−1.34182
$421$	−3544.78	−0.410362	−0.205181	−	0.978724i	$-0.565778\pi$
$421$	−3544.78	−0.410362	−0.205181	+	0.978724i	$0.565778\pi$
$422$	464.598	0.0535931
$423$	68.3280	0.00785395
$424$	−1908.81	−0.218632
$425$	−16294.0	−1.85970
$426$	−977.539	−0.111178
$427$	22069.8	2.50125
$428$	−4076.67	−0.460405
$429$	−7388.68	−0.831536
$430$	−4508.43	−0.505618
$431$	−532.707	−0.0595350	−0.0297675	−	0.999557i	$-0.509477\pi$
$431$	−532.707	−0.0595350	−0.0297675	+	0.999557i	$0.509477\pi$
$432$	−1546.60	−0.172247
$433$	−450.385	−0.0499864	−0.0249932	−	0.999688i	$-0.507956\pi$
$433$	−450.385	−0.0499864	−0.0249932	+	0.999688i	$0.507956\pi$
$434$	−4381.62	−0.484619
$435$	1772.33	0.195348
$436$	−12956.8	−1.42320
$437$	−1591.88	−0.174256
$438$	−500.277	−0.0545757
$439$	13175.6	1.43243	0.716214	−	0.697881i	$-0.245874\pi$
$439$	13175.6	1.43243	0.716214	+	0.697881i	$0.245874\pi$
$440$	−9219.90	−0.998958
$441$	2310.91	0.249531
$442$	1361.32	0.146496
$443$	5048.13	0.541408	0.270704	−	0.962663i	$-0.412743\pi$
$443$	5048.13	0.541408	0.270704	+	0.962663i	$0.412743\pi$
$444$	9103.92	0.973092
$445$	−20776.7	−2.21329
$446$	−1671.23	−0.177433
$447$	−4736.48	−0.501181
$448$	−9952.93	−1.04962
$449$	−14602.8	−1.53486	−0.767428	−	0.641136i	$-0.778464\pi$
$449$	−14602.8	−1.53486	−0.767428	+	0.641136i	$0.778464\pi$
$450$	1389.17	0.145524
$451$	5150.06	0.537710
$452$	15417.9	1.60442
$453$	6019.13	0.624290
$454$	2131.53	0.220348
$455$	22710.9	2.34001
$456$	1736.91	0.178373
$457$	−13261.8	−1.35746	−0.678731	−	0.734387i	$-0.737470\pi$
$457$	−13261.8	−1.35746	−0.678731	+	0.734387i	$0.737470\pi$
$458$	1586.89	0.161900
$459$	1517.02	0.154267
$460$	−3615.63	−0.366478
$461$	12240.4	1.23664	0.618321	−	0.785926i	$-0.287813\pi$
$461$	12240.4	1.23664	0.618321	+	0.785926i	$0.287813\pi$
$462$	2115.69	0.213054
$463$	3886.09	0.390069	0.195035	−	0.980796i	$-0.437518\pi$
$463$	3886.09	0.390069	0.195035	+	0.980796i	$0.437518\pi$
$464$	1661.16	0.166201
$465$	−20543.6	−2.04879
$466$	3297.25	0.327773
$467$	−15553.3	−1.54116	−0.770578	−	0.637345i	$-0.780033\pi$
$467$	−15553.3	−1.54116	−0.770578	+	0.637345i	$0.780033\pi$
$468$	3161.50	0.312266
$469$	−25825.2	−2.54264
$470$	−82.3177	−0.00807879
$471$	−4392.08	−0.429674
$472$	−4550.10	−0.443719
$473$	−22496.5	−2.18688
$474$	1266.04	0.122682
$475$	20071.5	1.93883
$476$	10618.2	1.02245
$477$	2053.67	0.197131
$478$	−2546.84	−0.243702
$479$	−8063.49	−0.769166	−0.384583	−	0.923090i	$-0.625655\pi$
$479$	−8063.49	−0.769166	−0.384583	+	0.923090i	$0.625655\pi$
$480$	5953.13	0.566087
$481$	−17901.6	−1.69697
$482$	−1801.47	−0.170238
$483$	1689.82	0.159192
$484$	−12317.6	−1.15679
$485$	−16841.2	−1.57674
$486$	−129.336	−0.0120716
$487$	1058.65	0.0985053	0.0492527	−	0.998786i	$-0.484316\pi$
$487$	1058.65	0.0985053	0.0492527	+	0.998786i	$0.484316\pi$
$488$	−7538.43	−0.699280
$489$	10160.0	0.939569
$490$	−2784.05	−0.256675
$491$	−4005.74	−0.368180	−0.184090	−	0.982909i	$-0.558934\pi$
$491$	−4005.74	−0.368180	−0.184090	+	0.982909i	$0.558934\pi$
$492$	−2203.63	−0.201925
$493$	−1629.39	−0.148852
$494$	−1676.92	−0.152729
$495$	9919.60	0.900713
$496$	−19255.0	−1.74310
$497$	14993.1	1.35319
$498$	819.605	0.0737498
$499$	8513.51	0.763762	0.381881	−	0.924212i	$-0.375277\pi$
$499$	8513.51	0.763762	0.381881	+	0.924212i	$0.375277\pi$
$500$	25938.3	2.32000
$501$	711.590	0.0634561
$502$	2850.33	0.253419
$503$	10961.5	0.971665	0.485833	−	0.874052i	$-0.338516\pi$
$503$	10961.5	0.971665	0.485833	+	0.874052i	$0.338516\pi$
$504$	−1843.78	−0.162953
$505$	31033.7	2.73462
$506$	662.320	0.0581892
$507$	374.334	0.0327904
$508$	5210.70	0.455093
$509$	9113.16	0.793583	0.396792	−	0.917909i	$-0.370124\pi$
$509$	9113.16	0.793583	0.396792	+	0.917909i	$0.370124\pi$
$510$	−1827.62	−0.158683
$511$	7673.05	0.664258
$512$	9413.07	0.812506
$513$	−1868.73	−0.160831
$514$	−2582.58	−0.221620
$515$	−38262.5	−3.27388
$516$	9625.91	0.821235
$517$	−410.756	−0.0349420
$518$	5126.00	0.434795
$519$	−2271.75	−0.192136
$520$	−7757.41	−0.654202
$521$	13996.1	1.17693	0.588465	−	0.808523i	$-0.299732\pi$
$521$	13996.1	1.17693	0.588465	+	0.808523i	$0.299732\pi$
$522$	138.916	0.0116479
$523$	−5107.90	−0.427061	−0.213531	−	0.976936i	$-0.568496\pi$
$523$	−5107.90	−0.427061	−0.213531	+	0.976936i	$0.568496\pi$
$524$	6294.38	0.524754
$525$	−21306.5	−1.77122
$526$	777.185	0.0644237
$527$	18886.8	1.56115
$528$	9297.42	0.766322
$529$	529.000	0.0434783
$530$	−2474.15	−0.202774
$531$	4895.41	0.400081
$532$	−13079.9	−1.06595
$533$	4333.15	0.352138
$534$	−1628.50	−0.131970
$535$	−10762.1	−0.869695
$536$	8821.17	0.710852
$537$	9939.04	0.798699
$538$	−363.168	−0.0291028
$539$	−13892.1	−1.11016
$540$	−4244.44	−0.338244
$541$	2691.36	0.213883	0.106941	−	0.994265i	$-0.465894\pi$
$541$	2691.36	0.213883	0.106941	+	0.994265i	$0.465894\pi$
$542$	−2479.36	−0.196490
$543$	3048.34	0.240915
$544$	−5473.03	−0.431350
$545$	−34204.9	−2.68840
$546$	1780.10	0.139526
$547$	11167.0	0.872882	0.436441	−	0.899733i	$-0.356239\pi$
$547$	11167.0	0.872882	0.436441	+	0.899733i	$0.356239\pi$
$548$	6864.08	0.535071
$549$	8110.53	0.630508
$550$	−8351.01	−0.647433
$551$	2007.15	0.155186
$552$	−577.196	−0.0445056
$553$	−19418.1	−1.49320
$554$	−3053.87	−0.234200
$555$	24033.7	1.83815
$556$	−11856.3	−0.904352
$557$	−24395.9	−1.85581	−0.927907	−	0.372811i	$-0.878394\pi$
$557$	−24395.9	−1.85581	−0.927907	+	0.372811i	$0.878394\pi$
$558$	−1610.22	−0.122162
$559$	−18928.1	−1.43215
$560$	−28577.8	−2.15649
$561$	−9119.62	−0.686329
$562$	−2120.21	−0.159139
$563$	5574.22	0.417274	0.208637	−	0.977993i	$-0.433097\pi$
$563$	5574.22	0.417274	0.208637	+	0.977993i	$0.433097\pi$
$564$	175.756	0.0131217
$565$	40702.1	3.03071
$566$	−758.238	−0.0563094
$567$	1983.70	0.146927
$568$	−5121.23	−0.378314
$569$	−13378.6	−0.985693	−0.492846	−	0.870116i	$-0.664044\pi$
$569$	−13378.6	−0.985693	−0.492846	+	0.870116i	$0.664044\pi$
$570$	2251.33	0.165435
$571$	−13862.4	−1.01598	−0.507990	−	0.861363i	$-0.669611\pi$
$571$	−13862.4	−1.01598	−0.507990	+	0.861363i	$0.669611\pi$
$572$	−19005.4	−1.38926
$573$	3055.19	0.222744
$574$	−1240.76	−0.0902239
$575$	−6670.01	−0.483754
$576$	−3657.65	−0.264587
$577$	−13202.9	−0.952591	−0.476295	−	0.879285i	$-0.658021\pi$
$577$	−13202.9	−0.952591	−0.476295	+	0.879285i	$0.658021\pi$
$578$	−934.694	−0.0672633
$579$	−4107.40	−0.294814
$580$	4558.84	0.326372
$581$	−12570.8	−0.897632
$582$	−1320.02	−0.0940150
$583$	−12345.7	−0.877029
$584$	−2620.90	−0.185708
$585$	8346.13	0.589863
$586$	59.9020	0.00422275
$587$	20336.2	1.42992	0.714962	−	0.699164i	$-0.246444\pi$
$587$	20336.2	1.42992	0.714962	+	0.699164i	$0.246444\pi$
$588$	5944.21	0.416897
$589$	−23265.5	−1.62757
$590$	−5897.71	−0.411534
$591$	3606.58	0.251023
$592$	22526.2	1.56389
$593$	−4408.43	−0.305283	−0.152641	−	0.988282i	$-0.548778\pi$
$593$	−4408.43	−0.305283	−0.152641	+	0.988282i	$0.548778\pi$
$594$	777.506	0.0537062
$595$	28031.4	1.93138
$596$	−12183.4	−0.837332
$597$	7540.94	0.516968
$598$	557.261	0.0381072
$599$	18153.6	1.23829	0.619144	−	0.785277i	$-0.287480\pi$
$599$	18153.6	1.23829	0.619144	+	0.785277i	$0.287480\pi$
$600$	7277.70	0.495185
$601$	25018.7	1.69806	0.849030	−	0.528344i	$-0.177187\pi$
$601$	25018.7	1.69806	0.849030	+	0.528344i	$0.177187\pi$
$602$	5419.91	0.366942
$603$	−9490.62	−0.640942
$604$	15482.6	1.04301
$605$	−32517.4	−2.18516
$606$	2432.45	0.163055
$607$	7367.35	0.492638	0.246319	−	0.969189i	$-0.420779\pi$
$607$	7367.35	0.492638	0.246319	+	0.969189i	$0.420779\pi$
$608$	6741.89	0.449703
$609$	−2130.64	−0.141770
$610$	−9771.10	−0.648558
$611$	−345.601	−0.0228830
$612$	3902.14	0.257737
$613$	−18128.2	−1.19444	−0.597219	−	0.802078i	$-0.703728\pi$
$613$	−18128.2	−1.19444	−0.597219	+	0.802078i	$0.703728\pi$
$614$	−252.137	−0.0165723
$615$	−5817.42	−0.381433
$616$	11083.9	0.724974
$617$	−1612.77	−0.105231	−0.0526156	−	0.998615i	$-0.516756\pi$
$617$	−1612.77	−0.105231	−0.0526156	+	0.998615i	$0.516756\pi$
$618$	−2999.04	−0.195209
$619$	−9993.10	−0.648880	−0.324440	−	0.945906i	$-0.605176\pi$
$619$	−9993.10	−0.648880	−0.324440	+	0.945906i	$0.605176\pi$
$620$	−52843.0	−3.42295
$621$	621.000	0.0401286
$622$	1241.87	0.0800552
$623$	24977.3	1.60625
$624$	7822.63	0.501852
$625$	32225.2	2.06242
$626$	168.693	0.0107705
$627$	11233.9	0.715533
$628$	−11297.5	−0.717863
$629$	−22095.5	−1.40064
$630$	−2389.85	−0.151133
$631$	−6242.10	−0.393810	−0.196905	−	0.980423i	$-0.563089\pi$
$631$	−6242.10	−0.393810	−0.196905	+	0.980423i	$0.563089\pi$
$632$	6632.68	0.417459
$633$	−2618.70	−0.164430
$634$	4628.81	0.289958
$635$	13755.9	0.859662
$636$	5282.54	0.329350
$637$	−11688.5	−0.727026
$638$	−835.099	−0.0518211
$639$	5509.89	0.341108
$640$	20281.5	1.25265
$641$	6317.71	0.389290	0.194645	−	0.980874i	$-0.437645\pi$
$641$	6317.71	0.389290	0.194645	+	0.980874i	$0.437645\pi$
$642$	−843.543	−0.0518567
$643$	−12192.0	−0.747753	−0.373877	−	0.927478i	$-0.621972\pi$
$643$	−12192.0	−0.747753	−0.373877	+	0.927478i	$0.621972\pi$
$644$	4346.62	0.265964
$645$	25411.7	1.55129
$646$	−2069.77	−0.126059
$647$	−4097.88	−0.249002	−0.124501	−	0.992219i	$-0.539733\pi$
$647$	−4097.88	−0.249002	−0.124501	+	0.992219i	$0.539733\pi$
$648$	−677.578	−0.0410768
$649$	−29428.9	−1.77995
$650$	−7026.35	−0.423994
$651$	24697.0	1.48687
$652$	26133.8	1.56975
$653$	−12911.7	−0.773775	−0.386887	−	0.922127i	$-0.626450\pi$
$653$	−12911.7	−0.773775	−0.386887	+	0.922127i	$0.626450\pi$
$654$	−2681.01	−0.160299
$655$	16616.7	0.991249
$656$	−5452.54	−0.324521
$657$	2819.81	0.167445
$658$	98.9602	0.00586302
$659$	22348.5	1.32105	0.660527	−	0.750802i	$-0.270333\pi$
$659$	22348.5	1.32105	0.660527	+	0.750802i	$0.270333\pi$
$660$	25515.6	1.50484
$661$	−4920.65	−0.289548	−0.144774	−	0.989465i	$-0.546246\pi$
$661$	−4920.65	−0.289548	−0.144774	+	0.989465i	$0.546246\pi$
$662$	5214.28	0.306131
$663$	−7673.04	−0.449467
$664$	4293.83	0.250953
$665$	−34530.1	−2.01356
$666$	1883.78	0.109602
$667$	−667.000	−0.0387202
$668$	1830.38	0.106017
$669$	9419.87	0.544384
$670$	11433.8	0.659290
$671$	−48756.7	−2.80511
$672$	−7156.69	−0.410826
$673$	21778.3	1.24739	0.623693	−	0.781670i	$-0.285632\pi$
$673$	21778.3	1.24739	0.623693	+	0.781670i	$0.285632\pi$
$674$	−4073.04	−0.232771
$675$	−7830.01	−0.446485
$676$	962.875	0.0547835
$677$	19353.1	1.09867	0.549334	−	0.835603i	$-0.314881\pi$
$677$	19353.1	1.09867	0.549334	+	0.835603i	$0.314881\pi$
$678$	3190.26	0.180710
$679$	20246.0	1.14429
$680$	−9574.74	−0.539962
$681$	−12014.4	−0.676052
$682$	9679.90	0.543494
$683$	−10310.8	−0.577644	−0.288822	−	0.957383i	$-0.593264\pi$
$683$	−10310.8	−0.577644	−0.288822	+	0.957383i	$0.593264\pi$
$684$	−4806.81	−0.268703
$685$	18120.7	1.01074
$686$	−1124.02	−0.0625586
$687$	−8944.47	−0.496729
$688$	23817.8	1.31983
$689$	−10387.4	−0.574352
$690$	−748.145	−0.0412774
$691$	−8736.79	−0.480989	−0.240494	−	0.970651i	$-0.577310\pi$
$691$	−8736.79	−0.480989	−0.240494	+	0.970651i	$0.577310\pi$
$692$	−5843.47	−0.321005
$693$	−11925.1	−0.653675
$694$	−1984.12	−0.108525
$695$	−31299.8	−1.70830
$696$	727.769	0.0396351
$697$	5348.27	0.290646
$698$	973.746	0.0528035
$699$	−18584.9	−1.00564
$700$	−54805.3	−2.95921
$701$	−9159.82	−0.493526	−0.246763	−	0.969076i	$-0.579367\pi$
$701$	−9159.82	−0.493526	−0.246763	+	0.969076i	$0.579367\pi$
$702$	654.176	0.0351713
$703$	27218.0	1.46024
$704$	21988.1	1.17714
$705$	463.983	0.0247867
$706$	4410.41	0.235110
$707$	−37307.9	−1.98460
$708$	12592.2	0.668422
$709$	−9396.85	−0.497752	−0.248876	−	0.968535i	$-0.580061\pi$
$709$	−9396.85	−0.497752	−0.248876	+	0.968535i	$0.580061\pi$
$710$	−6638.00	−0.350873
$711$	−7136.04	−0.376403
$712$	−8531.54	−0.449063
$713$	7731.41	0.406092
$714$	2197.12	0.115161
$715$	−50173.0	−2.62428
$716$	25565.6	1.33440
$717$	14355.2	0.747707
$718$	−3208.05	−0.166746
$719$	−4308.33	−0.223468	−0.111734	−	0.993738i	$-0.535641\pi$
$719$	−4308.33	−0.223468	−0.111734	+	0.993738i	$0.535641\pi$
$720$	−10502.2	−0.543603
$721$	45998.2	2.37595
$722$	−1101.05	−0.0567546
$723$	10154.0	0.522311
$724$	7841.07	0.402501
$725$	8410.02	0.430814
$726$	−2548.74	−0.130293
$727$	31122.0	1.58769	0.793846	−	0.608119i	$-0.208076\pi$
$727$	31122.0	1.58769	0.793846	+	0.608119i	$0.208076\pi$
$728$	9325.76	0.474774
$729$	729.000	0.0370370
$730$	−3397.14	−0.172238
$731$	−23362.3	−1.18206
$732$	20862.2	1.05340
$733$	9846.25	0.496152	0.248076	−	0.968741i	$-0.420202\pi$
$733$	9846.25	0.496152	0.248076	+	0.968741i	$0.420202\pi$
$734$	4728.26	0.237770
$735$	15692.3	0.787508
$736$	−2240.41	−0.112205
$737$	57053.1	2.85153
$738$	−455.974	−0.0227434
$739$	−7321.89	−0.364465	−0.182233	−	0.983255i	$-0.558332\pi$
$739$	−7321.89	−0.364465	−0.182233	+	0.983255i	$0.558332\pi$
$740$	61820.4	3.07103
$741$	9451.95	0.468591
$742$	2974.36	0.147159
$743$	−7894.66	−0.389808	−0.194904	−	0.980822i	$-0.562439\pi$
$743$	−7894.66	−0.389808	−0.194904	+	0.980822i	$0.562439\pi$
$744$	−8435.81	−0.415688
$745$	−32163.2	−1.58170
$746$	−3688.72	−0.181037
$747$	−4619.70	−0.226273
$748$	−23457.8	−1.14666
$749$	12937.9	0.631164
$750$	5367.15	0.261307
$751$	−16737.3	−0.813254	−0.406627	−	0.913594i	$-0.633295\pi$
$751$	−16737.3	−0.813254	−0.406627	+	0.913594i	$0.633295\pi$
$752$	434.880	0.0210884
$753$	−16065.8	−0.777519
$754$	−702.633	−0.0339369
$755$	40873.0	1.97023
$756$	5102.56	0.245474
$757$	16087.1	0.772383	0.386191	−	0.922419i	$-0.373790\pi$
$757$	16087.1	0.772383	0.386191	+	0.922419i	$0.373790\pi$
$758$	2722.56	0.130459
$759$	−3733.16	−0.178531
$760$	11794.5	0.562938
$761$	18803.2	0.895685	0.447842	−	0.894113i	$-0.352193\pi$
$761$	18803.2	0.895685	0.447842	+	0.894113i	$0.352193\pi$
$762$	1078.20	0.0512584
$763$	41120.3	1.95105
$764$	7858.68	0.372143
$765$	10301.4	0.486859
$766$	6600.62	0.311345
$767$	−24760.8	−1.16566
$768$	−8164.05	−0.383587
$769$	33664.8	1.57865	0.789327	−	0.613973i	$-0.210430\pi$
$769$	33664.8	1.57865	0.789327	+	0.613973i	$0.210430\pi$
$770$	14366.7	0.672388
$771$	14556.7	0.679956
$772$	−10565.2	−0.492552
$773$	28086.4	1.30685	0.653426	−	0.756990i	$-0.273331\pi$
$773$	28086.4	1.30685	0.653426	+	0.756990i	$0.273331\pi$
$774$	1991.79	0.0924979
$775$	−97483.2	−4.51832
$776$	−6915.48	−0.319911
$777$	−28892.7	−1.33400
$778$	1814.82	0.0836306
$779$	−6588.20	−0.303013
$780$	21468.2	0.985495
$781$	−33122.9	−1.51758
$782$	687.810	0.0314527
$783$	−783.000	−0.0357371
$784$	14708.0	0.670008
$785$	−29824.5	−1.35603
$786$	1302.43	0.0591045
$787$	31258.2	1.41580	0.707900	−	0.706313i	$-0.249643\pi$
$787$	31258.2	1.41580	0.707900	+	0.706313i	$0.249643\pi$
$788$	9276.98	0.419389
$789$	−4380.60	−0.197660
$790$	8597.10	0.387179
$791$	−48931.0	−2.19948
$792$	4073.28	0.182750
$793$	−41022.8	−1.83702
$794$	493.605	0.0220622
$795$	13945.5	0.622134
$796$	19397.1	0.863708
$797$	−36915.5	−1.64067	−0.820335	−	0.571883i	$-0.806213\pi$
$797$	−36915.5	−1.64067	−0.820335	+	0.571883i	$0.806213\pi$
$798$	−2706.50	−0.120061
$799$	−426.564	−0.0188871
$800$	28248.7	1.24843
$801$	9179.00	0.404899
$802$	653.609	0.0287777
$803$	−16951.3	−0.744956
$804$	−24412.1	−1.07083
$805$	11474.8	0.502400
$806$	8144.45	0.355926
$807$	2046.99	0.0892907
$808$	12743.4	0.554839
$809$	−7581.19	−0.329469	−0.164735	−	0.986338i	$-0.552677\pi$
$809$	−7581.19	−0.329469	−0.164735	+	0.986338i	$0.552677\pi$
$810$	−878.258	−0.0380973
$811$	8632.35	0.373764	0.186882	−	0.982382i	$-0.440162\pi$
$811$	8632.35	0.373764	0.186882	+	0.982382i	$0.440162\pi$
$812$	−5480.52	−0.236858
$813$	13974.9	0.602855
$814$	−11324.4	−0.487616
$815$	68991.4	2.96523
$816$	9655.24	0.414217
$817$	28778.6	1.23236
$818$	2453.98	0.104892
$819$	−10033.5	−0.428081
$820$	−14963.8	−0.637266
$821$	−10273.7	−0.436731	−0.218365	−	0.975867i	$-0.570072\pi$
$821$	−10273.7	−0.436731	−0.218365	+	0.975867i	$0.570072\pi$
$822$	1420.31	0.0602665
$823$	−33370.9	−1.41341	−0.706705	−	0.707509i	$-0.749819\pi$
$823$	−33370.9	−1.41341	−0.706705	+	0.707509i	$0.749819\pi$
$824$	−15711.7	−0.664251
$825$	47070.4	1.98640
$826$	7090.07	0.298663
$827$	3470.98	0.145947	0.0729734	−	0.997334i	$-0.476751\pi$
$827$	3470.98	0.145947	0.0729734	+	0.997334i	$0.476751\pi$
$828$	1597.36	0.0670436
$829$	6715.35	0.281343	0.140672	−	0.990056i	$-0.455074\pi$
$829$	6715.35	0.281343	0.140672	+	0.990056i	$0.455074\pi$
$830$	5565.55	0.232750
$831$	17213.1	0.718552
$832$	18500.3	0.770891
$833$	−14426.8	−0.600069
$834$	−2453.30	−0.101860
$835$	4832.07	0.200264
$836$	28896.3	1.19545
$837$	9076.01	0.374806
$838$	3800.74	0.156676
$839$	−47293.3	−1.94606	−0.973032	−	0.230670i	$-0.925908\pi$
$839$	−47293.3	−1.94606	−0.973032	+	0.230670i	$0.925908\pi$
$840$	−12520.2	−0.514272
$841$	841.000	0.0344828
$842$	−1886.70	−0.0772208
$843$	11950.6	0.488256
$844$	−6735.93	−0.274716
$845$	2541.92	0.103485
$846$	36.3673	0.00147794
$847$	39091.6	1.58584
$848$	13070.8	0.529308
$849$	4273.80	0.172764
$850$	−8672.41	−0.349954
$851$	−9044.88	−0.364341
$852$	14172.7	0.569895
$853$	433.215	0.0173892	0.00869460	−	0.999962i	$-0.497232\pi$
$853$	433.215	0.0173892	0.00869460	+	0.999962i	$0.497232\pi$
$854$	11746.6	0.470678
$855$	−12689.6	−0.507574
$856$	−4419.24	−0.176456
$857$	−43747.2	−1.74373	−0.871865	−	0.489746i	$-0.837089\pi$
$857$	−43747.2	−1.74373	−0.871865	+	0.489746i	$0.837089\pi$
$858$	−3932.60	−0.156476
$859$	−9195.45	−0.365244	−0.182622	−	0.983183i	$-0.558458\pi$
$859$	−9195.45	−0.365244	−0.182622	+	0.983183i	$0.558458\pi$
$860$	65365.0	2.59177
$861$	6993.55	0.276817
$862$	−283.531	−0.0112031
$863$	1001.74	0.0395129	0.0197564	−	0.999805i	$-0.493711\pi$
$863$	1001.74	0.0395129	0.0197564	+	0.999805i	$0.493711\pi$
$864$	−2630.05	−0.103560
$865$	−15426.3	−0.606372
$866$	−239.716	−0.00940632
$867$	5268.40	0.206372
$868$	63526.5	2.48414
$869$	42898.5	1.67461
$870$	943.314	0.0367601
$871$	48003.2	1.86742
$872$	−14045.5	−0.545461
$873$	7440.30	0.288449
$874$	−847.271	−0.0327910
$875$	−82319.2	−3.18045
$876$	7253.21	0.279753
$877$	16271.6	0.626516	0.313258	−	0.949668i	$-0.398580\pi$
$877$	16271.6	0.626516	0.313258	+	0.949668i	$0.398580\pi$
$878$	7012.65	0.269551
$879$	−337.637	−0.0129559
$880$	63134.3	2.41847
$881$	38190.4	1.46046	0.730231	−	0.683200i	$-0.239412\pi$
$881$	38190.4	1.46046	0.730231	+	0.683200i	$0.239412\pi$
$882$	1229.97	0.0469562
$883$	−26794.6	−1.02119	−0.510595	−	0.859821i	$-0.670575\pi$
$883$	−26794.6	−1.02119	−0.510595	+	0.859821i	$0.670575\pi$
$884$	−19736.9	−0.750932
$885$	33242.4	1.26263
$886$	2686.85	0.101881
$887$	−34490.6	−1.30562	−0.652808	−	0.757523i	$-0.726409\pi$
$887$	−34490.6	−1.30562	−0.652808	+	0.757523i	$0.726409\pi$
$888$	9868.94	0.372950
$889$	−16536.9	−0.623882
$890$	−11058.3	−0.416490
$891$	−4382.40	−0.164777
$892$	24230.1	0.909512
$893$	525.458	0.0196907
$894$	−2520.98	−0.0943110
$895$	67491.3	2.52065
$896$	−24381.9	−0.909088
$897$	−3141.00	−0.116917
$898$	−7772.30	−0.288825
$899$	−9748.30	−0.361651
$900$	−20140.7	−0.745950
$901$	−12820.9	−0.474057
$902$	2741.10	0.101185
$903$	−30549.3	−1.12582
$904$	16713.5	0.614914
$905$	20699.8	0.760316
$906$	3203.66	0.117477
$907$	−36754.8	−1.34556	−0.672780	−	0.739843i	$-0.734900\pi$
$907$	−36754.8	−1.34556	−0.672780	+	0.739843i	$0.734900\pi$
$908$	−30903.8	−1.12949
$909$	−13710.5	−0.500272
$910$	12087.8	0.440336
$911$	−6032.46	−0.219390	−0.109695	−	0.993965i	$-0.534987\pi$
$911$	−6032.46	−0.219390	−0.109695	+	0.993965i	$0.534987\pi$
$912$	−11893.7	−0.431842
$913$	27771.4	1.00668
$914$	−7058.53	−0.255444
$915$	55074.7	1.98985
$916$	−23007.3	−0.829894
$917$	−19976.2	−0.719379
$918$	807.429	0.0290296
$919$	−22799.1	−0.818359	−0.409179	−	0.912454i	$-0.634185\pi$
$919$	−22799.1	−0.818359	−0.409179	+	0.912454i	$0.634185\pi$
$920$	−3919.46	−0.140457
$921$	1421.17	0.0508459
$922$	6514.90	0.232708
$923$	−27868.8	−0.993839
$924$	−30674.2	−1.09211
$925$	114044.	4.05379
$926$	2068.36	0.0734022
$927$	16904.1	0.598924
$928$	2824.86	0.0999253
$929$	−13646.3	−0.481937	−0.240968	−	0.970533i	$-0.577465\pi$
$929$	−13646.3	−0.481937	−0.240968	+	0.970533i	$0.577465\pi$
$930$	−10934.3	−0.385536
$931$	17771.4	0.625602
$932$	−47804.8	−1.68015
$933$	−6999.77	−0.245619
$934$	−8278.18	−0.290011
$935$	−61927.0	−2.16602
$936$	3427.16	0.119680
$937$	−42092.2	−1.46755	−0.733774	−	0.679394i	$-0.762243\pi$
$937$	−42092.2	−1.46755	−0.733774	+	0.679394i	$0.762243\pi$
$938$	−13745.4	−0.478467
$939$	−950.838	−0.0330452
$940$	1193.47	0.0414115
$941$	10812.1	0.374564	0.187282	−	0.982306i	$-0.440032\pi$
$941$	10812.1	0.374564	0.187282	+	0.982306i	$0.440032\pi$
$942$	−2337.67	−0.0808549
$943$	2189.34	0.0756041
$944$	31157.3	1.07424
$945$	13470.4	0.463695
$946$	−11973.7	−0.411521
$947$	−33638.5	−1.15428	−0.577140	−	0.816645i	$-0.695831\pi$
$947$	−33638.5	−1.15428	−0.577140	+	0.816645i	$0.695831\pi$
$948$	−18355.6	−0.628863
$949$	−14262.5	−0.487860
$950$	10683.0	0.364845
$951$	−26090.2	−0.889626
$952$	11510.5	0.391867
$953$	−19113.9	−0.649697	−0.324849	−	0.945766i	$-0.605313\pi$
$953$	−19113.9	−0.649697	−0.324849	+	0.945766i	$0.605313\pi$
$954$	1093.06	0.0370955
$955$	20746.4	0.702970
$956$	36925.1	1.24921
$957$	4707.03	0.158993
$958$	−4291.76	−0.144740
$959$	−21784.2	−0.733522
$960$	−24837.3	−0.835023
$961$	83204.8	2.79295
$962$	−9528.08	−0.319332
$963$	4754.62	0.159102
$964$	26118.5	0.872634
$965$	−27891.4	−0.930419
$966$	899.401	0.0299563
$967$	−55895.6	−1.85882	−0.929410	−	0.369048i	$-0.879684\pi$
$967$	−55895.6	−1.85882	−0.929410	+	0.369048i	$0.879684\pi$
$968$	−13352.6	−0.443357
$969$	11666.3	0.386764
$970$	−8963.65	−0.296707
$971$	15820.7	0.522874	0.261437	−	0.965221i	$-0.415804\pi$
$971$	15820.7	0.522874	0.261437	+	0.965221i	$0.415804\pi$
$972$	1875.16	0.0618784
$973$	37627.8	1.23977
$974$	563.463	0.0185365
$975$	39603.9	1.30086
$976$	51620.3	1.69296
$977$	−16582.5	−0.543009	−0.271504	−	0.962437i	$-0.587521\pi$
$977$	−16582.5	−0.543009	−0.271504	+	0.962437i	$0.587521\pi$
$978$	5407.60	0.176806
$979$	−55179.9	−1.80138
$980$	40364.3	1.31570
$981$	15111.5	0.491817
$982$	−2132.04	−0.0692831
$983$	−25753.3	−0.835608	−0.417804	−	0.908537i	$-0.637200\pi$
$983$	−25753.3	−0.835608	−0.417804	+	0.908537i	$0.637200\pi$
$984$	−2388.80	−0.0773906
$985$	24490.5	0.792217
$986$	−867.239	−0.0280107
$987$	−557.788	−0.0179884
$988$	24312.7	0.782883
$989$	−9563.48	−0.307483
$990$	5279.67	0.169494
$991$	55667.1	1.78438	0.892192	−	0.451656i	$-0.149167\pi$
$991$	55667.1	1.78438	0.892192	+	0.451656i	$0.149167\pi$
$992$	−32743.9	−1.04800
$993$	−29390.2	−0.939246
$994$	7980.03	0.254639
$995$	51206.9	1.63152
$996$	−11883.0	−0.378038
$997$	−10440.6	−0.331653	−0.165826	−	0.986155i	$-0.553029\pi$
$997$	−10440.6	−0.331653	−0.165826	+	0.986155i	$0.553029\pi$
$998$	4531.28	0.143723
$999$	−10617.9	−0.336272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.e.1.21	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.e.1.21	✓	38	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)

\(f(q)\)	\(=\)	\(q+0.532246 q^{2} -3.00000 q^{3} -7.71671 q^{4} -20.3716 q^{5} -1.59674 q^{6} +24.4902 q^{7} -8.36516 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.532246 q^{2} -3.00000 q^{3} -7.71671 q^{4} -20.3716 q^{5} -1.59674 q^{6} +24.4902 q^{7} -8.36516 q^{8} +9.00000 q^{9} -10.8427 q^{10} -54.1038 q^{11} +23.1501 q^{12} -45.5217 q^{13} +13.0348 q^{14} +61.1147 q^{15} +57.2814 q^{16} -56.1860 q^{17} +4.79022 q^{18} +69.2121 q^{19} +157.202 q^{20} -73.4705 q^{21} -28.7965 q^{22} -23.0000 q^{23} +25.0955 q^{24} +290.001 q^{25} -24.2287 q^{26} -27.0000 q^{27} -188.984 q^{28} +29.0000 q^{29} +32.5281 q^{30} -336.148 q^{31} +97.4091 q^{32} +162.311 q^{33} -29.9048 q^{34} -498.903 q^{35} -69.4504 q^{36} +393.256 q^{37} +36.8379 q^{38} +136.565 q^{39} +170.411 q^{40} -95.1886 q^{41} -39.1044 q^{42} +415.804 q^{43} +417.503 q^{44} -183.344 q^{45} -12.2417 q^{46} +7.59200 q^{47} -171.844 q^{48} +256.768 q^{49} +154.352 q^{50} +168.558 q^{51} +351.278 q^{52} +228.186 q^{53} -14.3706 q^{54} +1102.18 q^{55} -204.864 q^{56} -207.636 q^{57} +15.4351 q^{58} +543.935 q^{59} -471.605 q^{60} +901.170 q^{61} -178.914 q^{62} +220.411 q^{63} -406.405 q^{64} +927.347 q^{65} +86.3896 q^{66} -1054.51 q^{67} +433.571 q^{68} +69.0000 q^{69} -265.539 q^{70} +612.210 q^{71} -75.2864 q^{72} +313.312 q^{73} +209.309 q^{74} -870.002 q^{75} -534.090 q^{76} -1325.01 q^{77} +72.6862 q^{78} -792.894 q^{79} -1166.91 q^{80} +81.0000 q^{81} -50.6638 q^{82} -513.300 q^{83} +566.951 q^{84} +1144.60 q^{85} +221.310 q^{86} -87.0000 q^{87} +452.587 q^{88} +1019.89 q^{89} -97.5842 q^{90} -1114.83 q^{91} +177.484 q^{92} +1008.45 q^{93} +4.04081 q^{94} -1409.96 q^{95} -292.227 q^{96} +826.700 q^{97} +136.664 q^{98} -486.934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 114 q^{3} + 138 q^{4} - 25 q^{5} - 34 q^{7} + 18 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 114 * q^3 + 138 * q^4 - 25 * q^5 - 34 * q^7 + 18 * q^8 + 342 * q^9	\( 38 q - 114 q^{3} + 138 q^{4} - 25 q^{5} - 34 q^{7} + 18 q^{8} + 342 q^{9} - 156 q^{10} - 111 q^{11} - 414 q^{12} + 179 q^{13} - 142 q^{14} + 75 q^{15} + 470 q^{16} + 58 q^{17} + 25 q^{19} - 193 q^{20} + 102 q^{21} - 171 q^{22} - 874 q^{23} - 54 q^{24} + 749 q^{25} + 116 q^{26} - 1026 q^{27} - 576 q^{28} + 1102 q^{29} + 468 q^{30} - 846 q^{31} + 174 q^{32} + 333 q^{33} - 277 q^{34} - 943 q^{35} + 1242 q^{36} + 183 q^{37} + 27 q^{38} - 537 q^{39} - 1517 q^{40} - 115 q^{41} + 426 q^{42} - 585 q^{43} - 273 q^{44} - 225 q^{45} - 746 q^{47} - 1410 q^{48} + 1494 q^{49} + 833 q^{50} - 174 q^{51} + 1547 q^{52} - 470 q^{53} + 152 q^{55} - 1629 q^{56} - 75 q^{57} - 2409 q^{59} + 579 q^{60} + 812 q^{61} - 2390 q^{62} - 306 q^{63} + 966 q^{64} - 1410 q^{65} + 513 q^{66} - 549 q^{67} - 818 q^{68} + 2622 q^{69} + 745 q^{70} - 5612 q^{71} + 162 q^{72} + 2592 q^{73} - 1427 q^{74} - 2247 q^{75} + 1241 q^{76} - 431 q^{77} - 348 q^{78} - 3514 q^{79} - 1835 q^{80} + 3078 q^{81} + 2701 q^{82} - 1526 q^{83} + 1728 q^{84} + 3659 q^{85} - 4267 q^{86} - 3306 q^{87} + 451 q^{88} - 359 q^{89} - 1404 q^{90} - 5169 q^{91} - 3174 q^{92} + 2538 q^{93} + 33 q^{94} - 3929 q^{95} - 522 q^{96} + 3554 q^{97} + 1876 q^{98} - 999 q^{99}+O(q^{100}) \) 38 * q - 114 * q^3 + 138 * q^4 - 25 * q^5 - 34 * q^7 + 18 * q^8 + 342 * q^9 - 156 * q^10 - 111 * q^11 - 414 * q^12 + 179 * q^13 - 142 * q^14 + 75 * q^15 + 470 * q^16 + 58 * q^17 + 25 * q^19 - 193 * q^20 + 102 * q^21 - 171 * q^22 - 874 * q^23 - 54 * q^24 + 749 * q^25 + 116 * q^26 - 1026 * q^27 - 576 * q^28 + 1102 * q^29 + 468 * q^30 - 846 * q^31 + 174 * q^32 + 333 * q^33 - 277 * q^34 - 943 * q^35 + 1242 * q^36 + 183 * q^37 + 27 * q^38 - 537 * q^39 - 1517 * q^40 - 115 * q^41 + 426 * q^42 - 585 * q^43 - 273 * q^44 - 225 * q^45 - 746 * q^47 - 1410 * q^48 + 1494 * q^49 + 833 * q^50 - 174 * q^51 + 1547 * q^52 - 470 * q^53 + 152 * q^55 - 1629 * q^56 - 75 * q^57 - 2409 * q^59 + 579 * q^60 + 812 * q^61 - 2390 * q^62 - 306 * q^63 + 966 * q^64 - 1410 * q^65 + 513 * q^66 - 549 * q^67 - 818 * q^68 + 2622 * q^69 + 745 * q^70 - 5612 * q^71 + 162 * q^72 + 2592 * q^73 - 1427 * q^74 - 2247 * q^75 + 1241 * q^76 - 431 * q^77 - 348 * q^78 - 3514 * q^79 - 1835 * q^80 + 3078 * q^81 + 2701 * q^82 - 1526 * q^83 + 1728 * q^84 + 3659 * q^85 - 4267 * q^86 - 3306 * q^87 + 451 * q^88 - 359 * q^89 - 1404 * q^90 - 5169 * q^91 - 3174 * q^92 + 2538 * q^93 + 33 * q^94 - 3929 * q^95 - 522 * q^96 + 3554 * q^97 + 1876 * q^98 - 999 * q^99

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