LMFDB - Embedded newform 2001.4.a.h.1.6

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:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.70747 q^{2} +3.00000 q^{3} +14.1603 q^{4} -20.4476 q^{5} -14.1224 q^{6} -29.3817 q^{7} -28.9995 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.70747 q^{2} +3.00000 q^{3} +14.1603 q^{4} -20.4476 q^{5} -14.1224 q^{6} -29.3817 q^{7} -28.9995 q^{8} +9.00000 q^{9} +96.2567 q^{10} -9.03393 q^{11} +42.4809 q^{12} +84.4253 q^{13} +138.314 q^{14} -61.3429 q^{15} +23.2319 q^{16} -60.8734 q^{17} -42.3673 q^{18} -112.816 q^{19} -289.545 q^{20} -88.1452 q^{21} +42.5270 q^{22} +23.0000 q^{23} -86.9985 q^{24} +293.106 q^{25} -397.430 q^{26} +27.0000 q^{27} -416.055 q^{28} -29.0000 q^{29} +288.770 q^{30} -183.371 q^{31} +122.632 q^{32} -27.1018 q^{33} +286.560 q^{34} +600.787 q^{35} +127.443 q^{36} -166.978 q^{37} +531.079 q^{38} +253.276 q^{39} +592.971 q^{40} -263.043 q^{41} +414.941 q^{42} +256.099 q^{43} -127.923 q^{44} -184.029 q^{45} -108.272 q^{46} -217.987 q^{47} +69.6958 q^{48} +520.287 q^{49} -1379.79 q^{50} -182.620 q^{51} +1195.49 q^{52} -290.828 q^{53} -127.102 q^{54} +184.722 q^{55} +852.056 q^{56} -338.448 q^{57} +136.517 q^{58} -831.252 q^{59} -868.635 q^{60} -358.884 q^{61} +863.213 q^{62} -264.436 q^{63} -763.144 q^{64} -1726.30 q^{65} +127.581 q^{66} -456.178 q^{67} -861.986 q^{68} +69.0000 q^{69} -2828.19 q^{70} -837.253 q^{71} -260.996 q^{72} +678.276 q^{73} +786.043 q^{74} +879.317 q^{75} -1597.51 q^{76} +265.433 q^{77} -1192.29 q^{78} +63.6718 q^{79} -475.038 q^{80} +81.0000 q^{81} +1238.27 q^{82} -1109.41 q^{83} -1248.16 q^{84} +1244.72 q^{85} -1205.58 q^{86} -87.0000 q^{87} +261.980 q^{88} -1146.32 q^{89} +866.310 q^{90} -2480.56 q^{91} +325.687 q^{92} -550.112 q^{93} +1026.17 q^{94} +2306.82 q^{95} +367.897 q^{96} +391.274 q^{97} -2449.24 q^{98} -81.3054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * 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 $

$2$	−4.70747	−1.66434	−0.832172	−	0.554518i	$-0.812903\pi$
$2$	−4.70747	−1.66434	−0.832172	+	0.554518i	$0.812903\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.1603	1.77004
$5$	−20.4476	−1.82889	−0.914446	−	0.404708i	$-0.867373\pi$
$5$	−20.4476	−1.82889	−0.914446	+	0.404708i	$0.867373\pi$
$6$	−14.1224	−0.960909
$7$	−29.3817	−1.58647	−0.793233	−	0.608919i	$-0.791604\pi$
$7$	−29.3817	−1.58647	−0.793233	+	0.608919i	$0.791604\pi$
$8$	−28.9995	−1.28161
$9$	9.00000	0.333333
$10$	96.2567	3.04390
$11$	−9.03393	−0.247621	−0.123811	−	0.992306i	$-0.539512\pi$
$11$	−9.03393	−0.247621	−0.123811	+	0.992306i	$0.539512\pi$
$12$	42.4809	1.02193
$13$	84.4253	1.80118	0.900591	−	0.434668i	$-0.143134\pi$
$13$	84.4253	1.80118	0.900591	+	0.434668i	$0.143134\pi$
$14$	138.314	2.64042
$15$	−61.3429	−1.05591
$16$	23.2319	0.362999
$17$	−60.8734	−0.868469	−0.434234	−	0.900800i	$-0.642981\pi$
$17$	−60.8734	−0.868469	−0.434234	+	0.900800i	$0.642981\pi$
$18$	−42.3673	−0.554781
$19$	−112.816	−1.36220	−0.681100	−	0.732191i	$-0.738498\pi$
$19$	−112.816	−1.36220	−0.681100	+	0.732191i	$0.738498\pi$
$20$	−289.545	−3.23721
$21$	−88.1452	−0.915946
$22$	42.5270	0.412127
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−86.9985	−0.739938
$25$	293.106	2.34484
$26$	−397.430	−2.99778
$27$	27.0000	0.192450
$28$	−416.055	−2.80811
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	288.770	1.75740
$31$	−183.371	−1.06240	−0.531199	−	0.847247i	$-0.678258\pi$
$31$	−183.371	−1.06240	−0.531199	+	0.847247i	$0.678258\pi$
$32$	122.632	0.677454
$33$	−27.1018	−0.142964
$34$	286.560	1.44543
$35$	600.787	2.90147
$36$	127.443	0.590013
$37$	−166.978	−0.741918	−0.370959	−	0.928649i	$-0.620971\pi$
$37$	−166.978	−0.741918	−0.370959	+	0.928649i	$0.620971\pi$
$38$	531.079	2.26717
$39$	253.276	1.03991
$40$	592.971	2.34392
$41$	−263.043	−1.00196	−0.500982	−	0.865458i	$-0.667028\pi$
$41$	−263.043	−1.00196	−0.500982	+	0.865458i	$0.667028\pi$
$42$	414.941	1.52445
$43$	256.099	0.908249	0.454125	−	0.890938i	$-0.349952\pi$
$43$	256.099	0.908249	0.454125	+	0.890938i	$0.349952\pi$
$44$	−127.923	−0.438299
$45$	−184.029	−0.609631
$46$	−108.272	−0.347040
$47$	−217.987	−0.676524	−0.338262	−	0.941052i	$-0.609839\pi$
$47$	−217.987	−0.676524	−0.338262	+	0.941052i	$0.609839\pi$
$48$	69.6958	0.209578
$49$	520.287	1.51687
$50$	−1379.79	−3.90263
$51$	−182.620	−0.501411
$52$	1195.49	3.18816
$53$	−290.828	−0.753740	−0.376870	−	0.926266i	$-0.623000\pi$
$53$	−290.828	−0.753740	−0.376870	+	0.926266i	$0.623000\pi$
$54$	−127.102	−0.320303
$55$	184.722	0.452872
$56$	852.056	2.03323
$57$	−338.448	−0.786466
$58$	136.517	0.309061
$59$	−831.252	−1.83423	−0.917117	−	0.398618i	$-0.869490\pi$
$59$	−831.252	−1.83423	−0.917117	+	0.398618i	$0.869490\pi$
$60$	−868.635	−1.86900
$61$	−358.884	−0.753286	−0.376643	−	0.926359i	$-0.622922\pi$
$61$	−358.884	−0.753286	−0.376643	+	0.926359i	$0.622922\pi$
$62$	863.213	1.76820
$63$	−264.436	−0.528822
$64$	−763.144	−1.49052
$65$	−1726.30	−3.29417
$66$	127.581	0.237941
$67$	−456.178	−0.831807	−0.415903	−	0.909409i	$-0.636535\pi$
$67$	−456.178	−0.831807	−0.415903	+	0.909409i	$0.636535\pi$
$68$	−861.986	−1.53722
$69$	69.0000	0.120386
$70$	−2828.19	−4.82905
$71$	−837.253	−1.39949	−0.699744	−	0.714394i	$-0.746702\pi$
$71$	−837.253	−1.39949	−0.699744	+	0.714394i	$0.746702\pi$
$72$	−260.996	−0.427203
$73$	678.276	1.08748	0.543741	−	0.839253i	$-0.317007\pi$
$73$	678.276	1.08748	0.543741	+	0.839253i	$0.317007\pi$
$74$	786.043	1.23481
$75$	879.317	1.35380
$76$	−1597.51	−2.41115
$77$	265.433	0.392842
$78$	−1192.29	−1.73077
$79$	63.6718	0.0906790	0.0453395	−	0.998972i	$-0.485563\pi$
$79$	63.6718	0.0906790	0.0453395	+	0.998972i	$0.485563\pi$
$80$	−475.038	−0.663886
$81$	81.0000	0.111111
$82$	1238.27	1.66761
$83$	−1109.41	−1.46716	−0.733579	−	0.679605i	$-0.762151\pi$
$83$	−1109.41	−1.46716	−0.733579	+	0.679605i	$0.762151\pi$
$84$	−1248.16	−1.62126
$85$	1244.72	1.58834
$86$	−1205.58	−1.51164
$87$	−87.0000	−0.107211
$88$	261.980	0.317354
$89$	−1146.32	−1.36528	−0.682638	−	0.730756i	$-0.739168\pi$
$89$	−1146.32	−1.36528	−0.682638	+	0.730756i	$0.739168\pi$
$90$	866.310	1.01463
$91$	−2480.56	−2.85751
$92$	325.687	0.369079
$93$	−550.112	−0.613376
$94$	1026.17	1.12597
$95$	2306.82	2.49132
$96$	367.897	0.391128
$97$	391.274	0.409565	0.204783	−	0.978807i	$-0.434351\pi$
$97$	391.274	0.409565	0.204783	+	0.978807i	$0.434351\pi$
$98$	−2449.24	−2.52460
$99$	−81.3054	−0.0825404
$100$	4150.47	4.15047
$101$	−159.465	−0.157103	−0.0785515	−	0.996910i	$-0.525030\pi$
$101$	−159.465	−0.157103	−0.0785515	+	0.996910i	$0.525030\pi$
$102$	859.680	0.834520
$103$	−748.187	−0.715739	−0.357869	−	0.933772i	$-0.616497\pi$
$103$	−748.187	−0.715739	−0.357869	+	0.933772i	$0.616497\pi$
$104$	−2448.29	−2.30841
$105$	1802.36	1.67517
$106$	1369.06	1.25448
$107$	−317.958	−0.287272	−0.143636	−	0.989631i	$-0.545879\pi$
$107$	−317.958	−0.287272	−0.143636	+	0.989631i	$0.545879\pi$
$108$	382.328	0.340644
$109$	1746.56	1.53477	0.767386	−	0.641185i	$-0.221557\pi$
$109$	1746.56	1.53477	0.767386	+	0.641185i	$0.221557\pi$
$110$	−869.576	−0.753735
$111$	−500.933	−0.428346
$112$	−682.595	−0.575886
$113$	−1859.57	−1.54809	−0.774043	−	0.633133i	$-0.781769\pi$
$113$	−1859.57	−1.54809	−0.774043	+	0.633133i	$0.781769\pi$
$114$	1593.24	1.30895
$115$	−470.296	−0.381350
$116$	−410.649	−0.328688
$117$	759.828	0.600394
$118$	3913.10	3.05280
$119$	1788.57	1.37780
$120$	1778.91	1.35327
$121$	−1249.39	−0.938684
$122$	1689.44	1.25373
$123$	−789.130	−0.578484
$124$	−2596.59	−1.88049
$125$	−3437.36	−2.45958
$126$	1244.82	0.880141
$127$	−256.288	−0.179070	−0.0895349	−	0.995984i	$-0.528538\pi$
$127$	−256.288	−0.179070	−0.0895349	+	0.995984i	$0.528538\pi$
$128$	2611.42	1.80328
$129$	768.297	0.524378
$130$	8126.50	5.48262
$131$	2677.68	1.78588	0.892940	−	0.450175i	$-0.148639\pi$
$131$	2677.68	1.78588	0.892940	+	0.450175i	$0.148639\pi$
$132$	−383.770	−0.253052
$133$	3314.73	2.16108
$134$	2147.45	1.38441
$135$	−552.086	−0.351970
$136$	1765.30	1.11304
$137$	−1946.05	−1.21359	−0.606797	−	0.794857i	$-0.707546\pi$
$137$	−1946.05	−1.21359	−0.606797	+	0.794857i	$0.707546\pi$
$138$	−324.816	−0.200363
$139$	−2145.61	−1.30927	−0.654634	−	0.755946i	$-0.727177\pi$
$139$	−2145.61	−1.30927	−0.654634	+	0.755946i	$0.727177\pi$
$140$	8507.33	5.13572
$141$	−653.960	−0.390591
$142$	3941.35	2.32923
$143$	−762.692	−0.446011
$144$	209.088	0.121000
$145$	592.981	0.339617
$146$	−3192.97	−1.80994
$147$	1560.86	0.875766
$148$	−2364.46	−1.31322
$149$	−1520.60	−0.836058	−0.418029	−	0.908434i	$-0.637279\pi$
$149$	−1520.60	−0.836058	−0.418029	+	0.908434i	$0.637279\pi$
$150$	−4139.36	−2.25318
$151$	−1563.14	−0.842428	−0.421214	−	0.906961i	$-0.638396\pi$
$151$	−1563.14	−0.842428	−0.421214	+	0.906961i	$0.638396\pi$
$152$	3271.61	1.74581
$153$	−547.861	−0.289490
$154$	−1249.52	−0.653824
$155$	3749.50	1.94301
$156$	3586.47	1.84069
$157$	−1877.35	−0.954325	−0.477163	−	0.878815i	$-0.658335\pi$
$157$	−1877.35	−0.954325	−0.477163	+	0.878815i	$0.658335\pi$
$158$	−299.733	−0.150921
$159$	−872.483	−0.435172
$160$	−2507.54	−1.23899
$161$	−675.780	−0.330801
$162$	−381.305	−0.184927
$163$	−256.307	−0.123163	−0.0615813	−	0.998102i	$-0.519614\pi$
$163$	−256.307	−0.123163	−0.0615813	+	0.998102i	$0.519614\pi$
$164$	−3724.78	−1.77351
$165$	554.167	0.261466
$166$	5222.54	2.44185
$167$	938.580	0.434907	0.217454	−	0.976071i	$-0.430225\pi$
$167$	938.580	0.434907	0.217454	+	0.976071i	$0.430225\pi$
$168$	2556.17	1.17389
$169$	4930.63	2.24426
$170$	−5859.47	−2.64354
$171$	−1015.34	−0.454066
$172$	3626.44	1.60764
$173$	264.031	0.116034	0.0580171	−	0.998316i	$-0.481522\pi$
$173$	264.031	0.116034	0.0580171	+	0.998316i	$0.481522\pi$
$174$	409.550	0.178436
$175$	−8611.95	−3.72001
$176$	−209.876	−0.0898863
$177$	−2493.76	−1.05900
$178$	5396.27	2.27229
$179$	4030.22	1.68286	0.841432	−	0.540363i	$-0.181713\pi$
$179$	4030.22	1.68286	0.841432	+	0.540363i	$0.181713\pi$
$180$	−2605.90	−1.07907
$181$	−4580.11	−1.88087	−0.940434	−	0.339975i	$-0.889581\pi$
$181$	−4580.11	−1.88087	−0.940434	+	0.339975i	$0.889581\pi$
$182$	11677.2	4.75588
$183$	−1076.65	−0.434910
$184$	−666.989	−0.267234
$185$	3414.30	1.35689
$186$	2589.64	1.02087
$187$	549.926	0.215051
$188$	−3086.76	−1.19747
$189$	−793.307	−0.305315
$190$	−10859.3	−4.14640
$191$	2295.81	0.869731	0.434866	−	0.900495i	$-0.356796\pi$
$191$	2295.81	0.869731	0.434866	+	0.900495i	$0.356796\pi$
$192$	−2289.43	−0.860550
$193$	−4701.86	−1.75361	−0.876807	−	0.480842i	$-0.840331\pi$
$193$	−4701.86	−1.75361	−0.876807	+	0.480842i	$0.840331\pi$
$194$	−1841.91	−0.681657
$195$	−5178.89	−1.90189
$196$	7367.43	2.68492
$197$	3153.76	1.14059	0.570294	−	0.821441i	$-0.306829\pi$
$197$	3153.76	1.14059	0.570294	+	0.821441i	$0.306829\pi$
$198$	382.743	0.137376
$199$	4332.72	1.54341	0.771704	−	0.635982i	$-0.219405\pi$
$199$	4332.72	1.54341	0.771704	+	0.635982i	$0.219405\pi$
$200$	−8499.92	−3.00518
$201$	−1368.53	−0.480244
$202$	750.680	0.261473
$203$	852.071	0.294599
$204$	−2585.96	−0.887517
$205$	5378.62	1.83248
$206$	3522.07	1.19123
$207$	207.000	0.0695048
$208$	1961.36	0.653827
$209$	1019.17	0.337309
$210$	−8484.57	−2.78805
$211$	−2180.03	−0.711277	−0.355639	−	0.934624i	$-0.615737\pi$
$211$	−2180.03	−0.711277	−0.355639	+	0.934624i	$0.615737\pi$
$212$	−4118.21	−1.33415
$213$	−2511.76	−0.807994
$214$	1496.78	0.478119
$215$	−5236.61	−1.66109
$216$	−782.987	−0.246646
$217$	5387.75	1.68546
$218$	−8221.89	−2.55439
$219$	2034.83	0.627858
$220$	2615.73	0.801602
$221$	−5139.25	−1.56427
$222$	2358.13	0.712915
$223$	5474.37	1.64390	0.821952	−	0.569557i	$-0.192885\pi$
$223$	5474.37	1.64390	0.821952	+	0.569557i	$0.192885\pi$
$224$	−3603.15	−1.07476
$225$	2637.95	0.781615
$226$	8753.88	2.57655
$227$	−777.482	−0.227327	−0.113664	−	0.993519i	$-0.536259\pi$
$227$	−777.482	−0.227327	−0.113664	+	0.993519i	$0.536259\pi$
$228$	−4792.53	−1.39208
$229$	706.754	0.203946	0.101973	−	0.994787i	$-0.467484\pi$
$229$	706.754	0.203946	0.101973	+	0.994787i	$0.467484\pi$
$230$	2213.90	0.634698
$231$	796.298	0.226808
$232$	840.986	0.237989
$233$	−978.306	−0.275068	−0.137534	−	0.990497i	$-0.543918\pi$
$233$	−978.306	−0.275068	−0.137534	+	0.990497i	$0.543918\pi$
$234$	−3576.87	−0.999262
$235$	4457.31	1.23729
$236$	−11770.8	−3.24667
$237$	191.015	0.0523535
$238$	−8419.63	−2.29312
$239$	−3269.91	−0.884992	−0.442496	−	0.896770i	$-0.645907\pi$
$239$	−3269.91	−0.884992	−0.442496	+	0.896770i	$0.645907\pi$
$240$	−1425.11	−0.383295
$241$	2010.66	0.537420	0.268710	−	0.963221i	$-0.413403\pi$
$241$	2010.66	0.537420	0.268710	+	0.963221i	$0.413403\pi$
$242$	5881.46	1.56229
$243$	243.000	0.0641500
$244$	−5081.92	−1.33335
$245$	−10638.6	−2.77419
$246$	3714.81	0.962796
$247$	−9524.53	−2.45357
$248$	5317.66	1.36158
$249$	−3328.24	−0.847064
$250$	16181.3	4.09358
$251$	−3434.57	−0.863698	−0.431849	−	0.901946i	$-0.642139\pi$
$251$	−3434.57	−0.863698	−0.431849	+	0.901946i	$0.642139\pi$
$252$	−3744.49	−0.936035
$253$	−207.780	−0.0516326
$254$	1206.47	0.298034
$255$	3734.15	0.917026
$256$	−6188.05	−1.51075
$257$	−6288.12	−1.52623	−0.763117	−	0.646261i	$-0.776332\pi$
$257$	−6288.12	−1.52623	−0.763117	+	0.646261i	$0.776332\pi$
$258$	−3616.74	−0.872745
$259$	4906.09	1.17703
$260$	−24444.9	−5.83080
$261$	−261.000	−0.0618984
$262$	−12605.1	−2.97232
$263$	−1395.16	−0.327107	−0.163554	−	0.986534i	$-0.552296\pi$
$263$	−1395.16	−0.327107	−0.163554	+	0.986534i	$0.552296\pi$
$264$	785.939	0.183224
$265$	5946.73	1.37851
$266$	−15604.0	−3.59678
$267$	−3438.96	−0.788243
$268$	−6459.63	−1.47233
$269$	−3501.76	−0.793703	−0.396852	−	0.917883i	$-0.629897\pi$
$269$	−3501.76	−0.793703	−0.396852	+	0.917883i	$0.629897\pi$
$270$	2598.93	0.585800
$271$	4654.23	1.04326	0.521631	−	0.853171i	$-0.325324\pi$
$271$	4654.23	1.04326	0.521631	+	0.853171i	$0.325324\pi$
$272$	−1414.21	−0.315253
$273$	−7441.69	−1.64979
$274$	9160.99	2.01984
$275$	−2647.90	−0.580633
$276$	977.062	0.213088
$277$	−8753.44	−1.89871	−0.949356	−	0.314203i	$-0.898263\pi$
$277$	−8753.44	−1.89871	−0.949356	+	0.314203i	$0.898263\pi$
$278$	10100.4	2.17907
$279$	−1650.34	−0.354133
$280$	−17422.5	−3.71855
$281$	966.530	0.205190	0.102595	−	0.994723i	$-0.467285\pi$
$281$	966.530	0.205190	0.102595	+	0.994723i	$0.467285\pi$
$282$	3078.50	0.650078
$283$	4767.41	1.00139	0.500695	−	0.865624i	$-0.333078\pi$
$283$	4767.41	1.00139	0.500695	+	0.865624i	$0.333078\pi$
$284$	−11855.8	−2.47715
$285$	6920.47	1.43836
$286$	3590.35	0.742315
$287$	7728.68	1.58958
$288$	1103.69	0.225818
$289$	−1207.43	−0.245762
$290$	−2791.44	−0.565239
$291$	1173.82	0.236463
$292$	9604.60	1.92489
$293$	3919.03	0.781407	0.390703	−	0.920517i	$-0.372232\pi$
$293$	3919.03	0.781407	0.390703	+	0.920517i	$0.372232\pi$
$294$	−7347.71	−1.45758
$295$	16997.1	3.35462
$296$	4842.27	0.950849
$297$	−243.916	−0.0476547
$298$	7158.20	1.39149
$299$	1941.78	0.375572
$300$	12451.4	2.39627
$301$	−7524.63	−1.44091
$302$	7358.45	1.40209
$303$	−478.396	−0.0907035
$304$	−2620.94	−0.494477
$305$	7338.34	1.37768
$306$	2579.04	0.481810
$307$	4510.42	0.838513	0.419256	−	0.907868i	$-0.362291\pi$
$307$	4510.42	0.838513	0.419256	+	0.907868i	$0.362291\pi$
$308$	3758.61	0.695346
$309$	−2244.56	−0.413232
$310$	−17650.7	−3.23384
$311$	6452.53	1.17649	0.588246	−	0.808682i	$-0.299819\pi$
$311$	6452.53	1.17649	0.588246	+	0.808682i	$0.299819\pi$
$312$	−7344.88	−1.33276
$313$	−5096.44	−0.920345	−0.460172	−	0.887830i	$-0.652212\pi$
$313$	−5096.44	−0.920345	−0.460172	+	0.887830i	$0.652212\pi$
$314$	8837.59	1.58833
$315$	5407.08	0.967158
$316$	901.613	0.160505
$317$	−1960.10	−0.347288	−0.173644	−	0.984808i	$-0.555554\pi$
$317$	−1960.10	−0.347288	−0.173644	+	0.984808i	$0.555554\pi$
$318$	4107.19	0.724276
$319$	261.984	0.0459821
$320$	15604.5	2.72599
$321$	−953.873	−0.165857
$322$	3181.22	0.550566
$323$	6867.50	1.18303
$324$	1146.99	0.196671
$325$	24745.5	4.22349
$326$	1206.56	0.204985
$327$	5239.68	0.886102
$328$	7628.13	1.28413
$329$	6404.83	1.07328
$330$	−2608.73	−0.435169
$331$	7789.46	1.29350	0.646748	−	0.762703i	$-0.276128\pi$
$331$	7789.46	1.29350	0.646748	+	0.762703i	$0.276128\pi$
$332$	−15709.7	−2.59693
$333$	−1502.80	−0.247306
$334$	−4418.34	−0.723835
$335$	9327.77	1.52128
$336$	−2047.79	−0.332488
$337$	−2907.31	−0.469945	−0.234972	−	0.972002i	$-0.575500\pi$
$337$	−2907.31	−0.469945	−0.234972	+	0.972002i	$0.575500\pi$
$338$	−23210.8	−3.73521
$339$	−5578.71	−0.893788
$340$	17625.6	2.81142
$341$	1656.56	0.263072
$342$	4779.71	0.755723
$343$	−5209.00	−0.819999
$344$	−7426.74	−1.16402
$345$	−1410.89	−0.220173
$346$	−1242.92	−0.193121
$347$	7220.69	1.11708	0.558540	−	0.829477i	$-0.311362\pi$
$347$	7220.69	1.11708	0.558540	+	0.829477i	$0.311362\pi$
$348$	−1231.95	−0.189768
$349$	−5782.09	−0.886843	−0.443421	−	0.896313i	$-0.646236\pi$
$349$	−5782.09	−0.886843	−0.443421	+	0.896313i	$0.646236\pi$
$350$	40540.5	6.19138
$351$	2279.48	0.346638
$352$	−1107.85	−0.167752
$353$	−4449.21	−0.670843	−0.335421	−	0.942068i	$-0.608879\pi$
$353$	−4449.21	−0.670843	−0.335421	+	0.942068i	$0.608879\pi$
$354$	11739.3	1.76253
$355$	17119.8	2.55951
$356$	−16232.2	−2.41659
$357$	5365.70	0.795471
$358$	−18972.1	−2.80086
$359$	−10080.5	−1.48197	−0.740984	−	0.671523i	$-0.765641\pi$
$359$	−10080.5	−1.48197	−0.740984	+	0.671523i	$0.765641\pi$
$360$	5336.74	0.781308
$361$	5868.47	0.855587
$362$	21560.8	3.13041
$363$	−3748.16	−0.541949
$364$	−35125.5	−5.05791
$365$	−13869.1	−1.98889
$366$	5068.32	0.723839
$367$	8451.12	1.20203	0.601015	−	0.799238i	$-0.294763\pi$
$367$	8451.12	1.20203	0.601015	+	0.799238i	$0.294763\pi$
$368$	534.335	0.0756906
$369$	−2367.39	−0.333988
$370$	−16072.7	−2.25833
$371$	8545.02	1.19578
$372$	−7789.76	−1.08570
$373$	−4053.15	−0.562639	−0.281319	−	0.959614i	$-0.590772\pi$
$373$	−4053.15	−0.562639	−0.281319	+	0.959614i	$0.590772\pi$
$374$	−2588.76	−0.357919
$375$	−10312.1	−1.42004
$376$	6321.51	0.867039
$377$	−2448.33	−0.334471
$378$	3734.47	0.508150
$379$	9903.52	1.34224	0.671121	−	0.741348i	$-0.265813\pi$
$379$	9903.52	1.34224	0.671121	+	0.741348i	$0.265813\pi$
$380$	32665.3	4.40973
$381$	−768.864	−0.103386
$382$	−10807.4	−1.44753
$383$	796.536	0.106269	0.0531345	−	0.998587i	$-0.483079\pi$
$383$	796.536	0.106269	0.0531345	+	0.998587i	$0.483079\pi$
$384$	7834.27	1.04112
$385$	−5427.47	−0.718466
$386$	22133.9	2.91862
$387$	2304.89	0.302750
$388$	5540.56	0.724946
$389$	325.962	0.0424857	0.0212428	−	0.999774i	$-0.493238\pi$
$389$	325.962	0.0424857	0.0212428	+	0.999774i	$0.493238\pi$
$390$	24379.5	3.16539
$391$	−1400.09	−0.181088
$392$	−15088.1	−1.94404
$393$	8033.05	1.03108
$394$	−14846.2	−1.89833
$395$	−1301.94	−0.165842
$396$	−1151.31	−0.146100
$397$	−6442.70	−0.814483	−0.407242	−	0.913320i	$-0.633509\pi$
$397$	−6442.70	−0.814483	−0.407242	+	0.913320i	$0.633509\pi$
$398$	−20396.1	−2.56876
$399$	9944.20	1.24770
$400$	6809.41	0.851177
$401$	−11224.1	−1.39777	−0.698885	−	0.715234i	$-0.746320\pi$
$401$	−11224.1	−1.39777	−0.698885	+	0.715234i	$0.746320\pi$
$402$	6442.34	0.799291
$403$	−15481.1	−1.91357
$404$	−2258.08	−0.278079
$405$	−1656.26	−0.203210
$406$	−4011.10	−0.490314
$407$	1508.46	0.183714
$408$	5295.90	0.642613
$409$	8882.06	1.07381	0.536906	−	0.843642i	$-0.319593\pi$
$409$	8882.06	1.07381	0.536906	+	0.843642i	$0.319593\pi$
$410$	−25319.7	−3.04988
$411$	−5838.16	−0.700669
$412$	−10594.6	−1.26689
$413$	24423.6	2.90995
$414$	−974.447	−0.115680
$415$	22684.9	2.68327
$416$	10353.3	1.22022
$417$	−6436.83	−0.755907
$418$	−4797.73	−0.561399
$419$	7569.01	0.882507	0.441253	−	0.897383i	$-0.354534\pi$
$419$	7569.01	0.882507	0.441253	+	0.897383i	$0.354534\pi$
$420$	25522.0	2.96511
$421$	5717.08	0.661838	0.330919	−	0.943659i	$-0.392641\pi$
$421$	5717.08	0.661838	0.330919	+	0.943659i	$0.392641\pi$
$422$	10262.4	1.18381
$423$	−1961.88	−0.225508
$424$	8433.86	0.966001
$425$	−17842.3	−2.03642
$426$	11824.0	1.34478
$427$	10544.7	1.19506
$428$	−4502.38	−0.508483
$429$	−2288.08	−0.257504
$430$	24651.2	2.76462
$431$	4708.12	0.526177	0.263089	−	0.964772i	$-0.415259\pi$
$431$	4708.12	0.526177	0.263089	+	0.964772i	$0.415259\pi$
$432$	627.263	0.0698592
$433$	−11745.9	−1.30363	−0.651813	−	0.758379i	$-0.725991\pi$
$433$	−11745.9	−1.30363	−0.651813	+	0.758379i	$0.725991\pi$
$434$	−25362.7	−2.80518
$435$	1778.94	0.196078
$436$	24731.9	2.71661
$437$	−2594.77	−0.284038
$438$	−9578.90	−1.04497
$439$	−9950.85	−1.08184	−0.540921	−	0.841074i	$-0.681924\pi$
$439$	−9950.85	−1.08184	−0.540921	+	0.841074i	$0.681924\pi$
$440$	−5356.86	−0.580405
$441$	4682.58	0.505624
$442$	24192.9	2.60348
$443$	−10602.7	−1.13713	−0.568564	−	0.822639i	$-0.692501\pi$
$443$	−10602.7	−1.13713	−0.568564	+	0.822639i	$0.692501\pi$
$444$	−7093.37	−0.758190
$445$	23439.5	2.49694
$446$	−25770.4	−2.73602
$447$	−4561.81	−0.482698
$448$	22422.5	2.36465
$449$	15522.7	1.63154	0.815771	−	0.578375i	$-0.196313\pi$
$449$	15522.7	1.63154	0.815771	+	0.578375i	$0.196313\pi$
$450$	−12418.1	−1.30088
$451$	2376.32	0.248107
$452$	−26332.1	−2.74017
$453$	−4689.42	−0.486376
$454$	3659.98	0.378351
$455$	50721.6	5.22608
$456$	9814.84	1.00794
$457$	11237.9	1.15029	0.575147	−	0.818050i	$-0.304945\pi$
$457$	11237.9	1.15029	0.575147	+	0.818050i	$0.304945\pi$
$458$	−3327.02	−0.339436
$459$	−1643.58	−0.167137
$460$	−6659.53	−0.675005
$461$	−4488.62	−0.453484	−0.226742	−	0.973955i	$-0.572807\pi$
$461$	−4488.62	−0.453484	−0.226742	+	0.973955i	$0.572807\pi$
$462$	−3748.55	−0.377486
$463$	−7311.98	−0.733945	−0.366972	−	0.930232i	$-0.619606\pi$
$463$	−7311.98	−0.733945	−0.366972	+	0.930232i	$0.619606\pi$
$464$	−673.726	−0.0674073
$465$	11248.5	1.12180
$466$	4605.35	0.457808
$467$	147.682	0.0146336	0.00731680	−	0.999973i	$-0.497671\pi$
$467$	147.682	0.0146336	0.00731680	+	0.999973i	$0.497671\pi$
$468$	10759.4	1.06272
$469$	13403.3	1.31963
$470$	−20982.7	−2.05927
$471$	−5632.06	−0.550980
$472$	24105.9	2.35077
$473$	−2313.58	−0.224902
$474$	−899.200	−0.0871343
$475$	−33067.0	−3.19415
$476$	25326.7	2.43875
$477$	−2617.45	−0.251247
$478$	15393.0	1.47293
$479$	−3375.15	−0.321951	−0.160976	−	0.986958i	$-0.551464\pi$
$479$	−3375.15	−0.321951	−0.160976	+	0.986958i	$0.551464\pi$
$480$	−7522.62	−0.715331
$481$	−14097.1	−1.33633
$482$	−9465.15	−0.894451
$483$	−2027.34	−0.190988
$484$	−17691.7	−1.66151
$485$	−8000.62	−0.749050
$486$	−1143.92	−0.106768
$487$	−9.49226	−0.000883234 0	−0.000441617	−	1.00000i	$-0.500141\pi$
$487$	−9.49226	−0.000883234 0	−0.000441617		1.00000i	$0.500141\pi$
$488$	10407.5	0.965418
$489$	−768.920	−0.0711079
$490$	50081.1	4.61721
$491$	−1491.92	−0.137127	−0.0685636	−	0.997647i	$-0.521842\pi$
$491$	−1491.92	−0.137127	−0.0685636	+	0.997647i	$0.521842\pi$
$492$	−11174.3	−1.02394
$493$	1765.33	0.161271
$494$	44836.5	4.08358
$495$	1662.50	0.150957
$496$	−4260.06	−0.385650
$497$	24599.9	2.22024
$498$	15667.6	1.40980
$499$	4572.06	0.410167	0.205084	−	0.978744i	$-0.434253\pi$
$499$	4572.06	0.410167	0.205084	+	0.978744i	$0.434253\pi$
$500$	−48674.1	−4.35354
$501$	2815.74	0.251094
$502$	16168.1	1.43749
$503$	5525.30	0.489783	0.244892	−	0.969550i	$-0.421248\pi$
$503$	5525.30	0.489783	0.244892	+	0.969550i	$0.421248\pi$
$504$	7668.51	0.677743
$505$	3260.69	0.287324
$506$	978.121	0.0859343
$507$	14791.9	1.29572
$508$	−3629.12	−0.316961
$509$	−1787.05	−0.155618	−0.0778089	−	0.996968i	$-0.524792\pi$
$509$	−1787.05	−0.155618	−0.0778089	+	0.996968i	$0.524792\pi$
$510$	−17578.4	−1.52625
$511$	−19928.9	−1.72525
$512$	8238.71	0.711138
$513$	−3046.03	−0.262155
$514$	29601.2	2.54018
$515$	15298.7	1.30901
$516$	10879.3	0.928169
$517$	1969.28	0.167522
$518$	−23095.3	−1.95898
$519$	792.094	0.0669924
$520$	50061.8	4.22183
$521$	14985.2	1.26010	0.630049	−	0.776555i	$-0.283035\pi$
$521$	14985.2	1.26010	0.630049	+	0.776555i	$0.283035\pi$
$522$	1228.65	0.103020
$523$	−23877.8	−1.99637	−0.998186	−	0.0602036i	$-0.980825\pi$
$523$	−23877.8	−1.99637	−0.998186	+	0.0602036i	$0.980825\pi$
$524$	37916.8	3.16108
$525$	−25835.9	−2.14775
$526$	6567.68	0.544419
$527$	11162.4	0.922660
$528$	−629.627	−0.0518959
$529$	529.000	0.0434783
$530$	−27994.1	−2.29431
$531$	−7481.27	−0.611411
$532$	46937.7	3.82520
$533$	−22207.5	−1.80472
$534$	16188.8	1.31191
$535$	6501.48	0.525390
$536$	13228.9	1.06605
$537$	12090.7	0.971602
$538$	16484.4	1.32099
$539$	−4700.24	−0.375609
$540$	−7817.71	−0.623001
$541$	4019.80	0.319454	0.159727	−	0.987161i	$-0.448939\pi$
$541$	4019.80	0.319454	0.159727	+	0.987161i	$0.448939\pi$
$542$	−21909.6	−1.73635
$543$	−13740.3	−1.08592
$544$	−7465.05	−0.588348
$545$	−35713.0	−2.80693
$546$	35031.5	2.74581
$547$	−17788.8	−1.39049	−0.695243	−	0.718775i	$-0.744703\pi$
$547$	−17788.8	−1.39049	−0.695243	+	0.718775i	$0.744703\pi$
$548$	−27556.7	−2.14811
$549$	−3229.96	−0.251095
$550$	12464.9	0.966373
$551$	3271.67	0.252954
$552$	−2000.97	−0.154288
$553$	−1870.79	−0.143859
$554$	41206.6	3.16011
$555$	10242.9	0.783399
$556$	−30382.5	−2.31746
$557$	−4905.51	−0.373165	−0.186583	−	0.982439i	$-0.559741\pi$
$557$	−4905.51	−0.373165	−0.186583	+	0.982439i	$0.559741\pi$
$558$	7768.92	0.589399
$559$	21621.2	1.63592
$560$	13957.5	1.05323
$561$	1649.78	0.124160
$562$	−4549.91	−0.341506
$563$	−1438.36	−0.107673	−0.0538364	−	0.998550i	$-0.517145\pi$
$563$	−1438.36	−0.107673	−0.0538364	+	0.998550i	$0.517145\pi$
$564$	−9260.28	−0.691362
$565$	38023.8	2.83128
$566$	−22442.5	−1.66666
$567$	−2379.92	−0.176274
$568$	24279.9	1.79360
$569$	6723.27	0.495350	0.247675	−	0.968843i	$-0.420333\pi$
$569$	6723.27	0.495350	0.247675	+	0.968843i	$0.420333\pi$
$570$	−32577.9	−2.39393
$571$	25924.0	1.89998	0.949989	−	0.312283i	$-0.101094\pi$
$571$	25924.0	1.89998	0.949989	+	0.312283i	$0.101094\pi$
$572$	−10800.0	−0.789456
$573$	6887.42	0.502140
$574$	−36382.5	−2.64561
$575$	6741.43	0.488934
$576$	−6868.30	−0.496839
$577$	−12714.8	−0.917369	−0.458685	−	0.888599i	$-0.651679\pi$
$577$	−12714.8	−0.917369	−0.458685	+	0.888599i	$0.651679\pi$
$578$	5683.94	0.409032
$579$	−14105.6	−1.01245
$580$	8396.80	0.601135
$581$	32596.5	2.32759
$582$	−5525.73	−0.393555
$583$	2627.32	0.186642
$584$	−19669.7	−1.39373
$585$	−15536.7	−1.09806
$586$	−18448.7	−1.30053
$587$	−6463.75	−0.454493	−0.227247	−	0.973837i	$-0.572972\pi$
$587$	−6463.75	−0.454493	−0.227247	+	0.973837i	$0.572972\pi$
$588$	22102.3	1.55014
$589$	20687.2	1.44720
$590$	−80013.6	−5.58323
$591$	9461.27	0.658519
$592$	−3879.22	−0.269316
$593$	11089.0	0.767913	0.383957	−	0.923351i	$-0.374561\pi$
$593$	11089.0	0.767913	0.383957	+	0.923351i	$0.374561\pi$
$594$	1148.23	0.0793138
$595$	−36572.0	−2.51984
$596$	−21532.2	−1.47986
$597$	12998.1	0.891087
$598$	−9140.89	−0.625081
$599$	12956.7	0.883803	0.441902	−	0.897064i	$-0.354304\pi$
$599$	12956.7	0.883803	0.441902	+	0.897064i	$0.354304\pi$
$600$	−25499.8	−1.73504
$601$	−26926.7	−1.82756	−0.913779	−	0.406212i	$-0.866850\pi$
$601$	−26926.7	−1.82756	−0.913779	+	0.406212i	$0.866850\pi$
$602$	35422.0	2.39816
$603$	−4105.60	−0.277269
$604$	−22134.6	−1.49113
$605$	25547.0	1.71675
$606$	2252.04	0.150962
$607$	15867.5	1.06102	0.530511	−	0.847678i	$-0.322000\pi$
$607$	15867.5	1.06102	0.530511	+	0.847678i	$0.322000\pi$
$608$	−13834.9	−0.922828
$609$	2556.21	0.170087
$610$	−34545.0	−2.29293
$611$	−18403.6	−1.21854
$612$	−7757.88	−0.512408
$613$	−270.576	−0.0178278	−0.00891391	−	0.999960i	$-0.502837\pi$
$613$	−270.576	−0.0178278	−0.00891391	+	0.999960i	$0.502837\pi$
$614$	−21232.7	−1.39557
$615$	16135.8	1.05798
$616$	−7697.42	−0.503470
$617$	2438.58	0.159114	0.0795571	−	0.996830i	$-0.474649\pi$
$617$	2438.58	0.159114	0.0795571	+	0.996830i	$0.474649\pi$
$618$	10566.2	0.687760
$619$	13935.4	0.904867	0.452433	−	0.891798i	$-0.350556\pi$
$619$	13935.4	0.904867	0.452433	+	0.891798i	$0.350556\pi$
$620$	53094.0	3.43921
$621$	621.000	0.0401286
$622$	−30375.1	−1.95809
$623$	33680.9	2.16596
$624$	5884.09	0.377487
$625$	33647.7	2.15345
$626$	23991.4	1.53177
$627$	3057.52	0.194746
$628$	−26583.9	−1.68919
$629$	10164.5	0.644332
$630$	−25453.7	−1.60968
$631$	19663.3	1.24055	0.620273	−	0.784386i	$-0.287022\pi$
$631$	19663.3	1.24055	0.620273	+	0.784386i	$0.287022\pi$
$632$	−1846.45	−0.116215
$633$	−6540.09	−0.410656
$634$	9227.13	0.578006
$635$	5240.48	0.327499
$636$	−12354.6	−0.770272
$637$	43925.4	2.73216
$638$	−1233.28	−0.0765300
$639$	−7535.27	−0.466496
$640$	−53397.4	−3.29800
$641$	−8569.56	−0.528045	−0.264023	−	0.964516i	$-0.585049\pi$
$641$	−8569.56	−0.528045	−0.264023	+	0.964516i	$0.585049\pi$
$642$	4490.33	0.276042
$643$	3089.80	0.189502	0.0947510	−	0.995501i	$-0.469795\pi$
$643$	3089.80	0.189502	0.0947510	+	0.995501i	$0.469795\pi$
$644$	−9569.26	−0.585530
$645$	−15709.8	−0.959030
$646$	−32328.6	−1.96896
$647$	15174.0	0.922026	0.461013	−	0.887393i	$-0.347486\pi$
$647$	15174.0	0.922026	0.461013	+	0.887393i	$0.347486\pi$
$648$	−2348.96	−0.142401
$649$	7509.47	0.454195
$650$	−116489.	−7.02934
$651$	16163.3	0.973100
$652$	−3629.38	−0.218003
$653$	17173.0	1.02915	0.514573	−	0.857447i	$-0.327951\pi$
$653$	17173.0	1.02915	0.514573	+	0.857447i	$0.327951\pi$
$654$	−24665.7	−1.47478
$655$	−54752.3	−3.26618
$656$	−6111.01	−0.363712
$657$	6104.49	0.362494
$658$	−30150.6	−1.78631
$659$	−1228.14	−0.0725970	−0.0362985	−	0.999341i	$-0.511557\pi$
$659$	−1228.14	−0.0725970	−0.0362985	+	0.999341i	$0.511557\pi$
$660$	7847.18	0.462805
$661$	2528.16	0.148766	0.0743828	−	0.997230i	$-0.476301\pi$
$661$	2528.16	0.148766	0.0743828	+	0.997230i	$0.476301\pi$
$662$	−36668.7	−2.15282
$663$	−15417.8	−0.903132
$664$	32172.5	1.88032
$665$	−67778.5	−3.95238
$666$	7074.39	0.411602
$667$	−667.000	−0.0387202
$668$	13290.6	0.769803
$669$	16423.1	0.949109
$670$	−43910.2	−2.53194
$671$	3242.14	0.186529
$672$	−10809.5	−0.620511
$673$	−20612.1	−1.18059	−0.590297	−	0.807186i	$-0.700989\pi$
$673$	−20612.1	−1.18059	−0.590297	+	0.807186i	$0.700989\pi$
$674$	13686.1	0.782149
$675$	7913.85	0.451266
$676$	69819.2	3.97242
$677$	−1899.84	−0.107854	−0.0539268	−	0.998545i	$-0.517174\pi$
$677$	−1899.84	−0.107854	−0.0539268	+	0.998545i	$0.517174\pi$
$678$	26261.6	1.48757
$679$	−11496.3	−0.649761
$680$	−36096.2	−2.03563
$681$	−2332.45	−0.131247
$682$	−7798.20	−0.437843
$683$	13241.1	0.741809	0.370904	−	0.928671i	$-0.379048\pi$
$683$	13241.1	0.741809	0.370904	+	0.928671i	$0.379048\pi$
$684$	−14377.6	−0.803715
$685$	39792.2	2.21953
$686$	24521.2	1.36476
$687$	2120.26	0.117748
$688$	5949.67	0.329694
$689$	−24553.2	−1.35762
$690$	6641.71	0.366443
$691$	−34154.7	−1.88033	−0.940163	−	0.340724i	$-0.889328\pi$
$691$	−34154.7	−1.88033	−0.940163	+	0.340724i	$0.889328\pi$
$692$	3738.76	0.205385
$693$	2388.89	0.130947
$694$	−33991.2	−1.85921
$695$	43872.7	2.39451
$696$	2522.96	0.137403
$697$	16012.4	0.870174
$698$	27219.0	1.47601
$699$	−2934.92	−0.158811
$700$	−121948.	−6.58457
$701$	7574.11	0.408089	0.204044	−	0.978962i	$-0.434591\pi$
$701$	7574.11	0.408089	0.204044	+	0.978962i	$0.434591\pi$
$702$	−10730.6	−0.576924
$703$	18837.8	1.01064
$704$	6894.19	0.369083
$705$	13371.9	0.714349
$706$	20944.5	1.11651
$707$	4685.37	0.249239
$708$	−35312.4	−1.87446
$709$	32322.6	1.71213	0.856066	−	0.516866i	$-0.172902\pi$
$709$	32322.6	1.71213	0.856066	+	0.516866i	$0.172902\pi$
$710$	−80591.2	−4.25991
$711$	573.046	0.0302263
$712$	33242.7	1.74975
$713$	−4217.53	−0.221525
$714$	−25258.9	−1.32394
$715$	15595.2	0.815705
$716$	57069.1	2.97873
$717$	−9809.74	−0.510950
$718$	47453.5	2.46650
$719$	−14208.3	−0.736969	−0.368484	−	0.929634i	$-0.620123\pi$
$719$	−14208.3	−0.736969	−0.368484	+	0.929634i	$0.620123\pi$
$720$	−4275.34	−0.221295
$721$	21983.0	1.13549
$722$	−27625.7	−1.42399
$723$	6031.99	0.310280
$724$	−64855.9	−3.32921
$725$	−8500.06	−0.435427
$726$	17644.4	0.901990
$727$	2740.52	0.139808	0.0699039	−	0.997554i	$-0.477731\pi$
$727$	2740.52	0.139808	0.0699039	+	0.997554i	$0.477731\pi$
$728$	71935.1	3.66221
$729$	729.000	0.0370370
$730$	65288.6	3.31019
$731$	−15589.6	−0.788786
$732$	−15245.7	−0.769807
$733$	−1896.29	−0.0955540	−0.0477770	−	0.998858i	$-0.515214\pi$
$733$	−1896.29	−0.0955540	−0.0477770	+	0.998858i	$0.515214\pi$
$734$	−39783.4	−2.00059
$735$	−31915.9	−1.60168
$736$	2820.54	0.141259
$737$	4121.08	0.205973
$738$	11144.4	0.555870
$739$	14593.0	0.726402	0.363201	−	0.931711i	$-0.381684\pi$
$739$	14593.0	0.726402	0.363201	+	0.931711i	$0.381684\pi$
$740$	48347.5	2.40174
$741$	−28573.6	−1.41657
$742$	−40225.5	−1.99019
$743$	29.3469	0.00144904	0.000724519	−	1.00000i	$-0.499769\pi$
$743$	29.3469	0.00144904	0.000724519		1.00000i	$0.499769\pi$
$744$	15953.0	0.786108
$745$	31092.7	1.52906
$746$	19080.1	0.936424
$747$	−9984.73	−0.489052
$748$	7787.13	0.380649
$749$	9342.15	0.455747
$750$	48543.9	2.36343
$751$	2896.30	0.140729	0.0703646	−	0.997521i	$-0.477584\pi$
$751$	2896.30	0.140729	0.0703646	+	0.997521i	$0.477584\pi$
$752$	−5064.25	−0.245578
$753$	−10303.7	−0.498656
$754$	11525.5	0.556675
$755$	31962.5	1.54071
$756$	−11233.5	−0.540420
$757$	30560.8	1.46731	0.733655	−	0.679523i	$-0.237813\pi$
$757$	30560.8	1.46731	0.733655	+	0.679523i	$0.237813\pi$
$758$	−46620.6	−2.23395
$759$	−623.341	−0.0298101
$760$	−66896.7	−3.19289
$761$	11346.0	0.540461	0.270230	−	0.962796i	$-0.412900\pi$
$761$	11346.0	0.540461	0.270230	+	0.962796i	$0.412900\pi$
$762$	3619.41	0.172070
$763$	−51317.0	−2.43486
$764$	32509.3	1.53946
$765$	11202.5	0.529445
$766$	−3749.67	−0.176868
$767$	−70178.7	−3.30379
$768$	−18564.1	−0.872234
$769$	−22570.1	−1.05839	−0.529193	−	0.848501i	$-0.677505\pi$
$769$	−22570.1	−1.05839	−0.529193	+	0.848501i	$0.677505\pi$
$770$	25549.7	1.19577
$771$	−18864.4	−0.881171
$772$	−66579.9	−3.10397
$773$	17492.4	0.813917	0.406959	−	0.913447i	$-0.366589\pi$
$773$	17492.4	0.813917	0.406959	+	0.913447i	$0.366589\pi$
$774$	−10850.2	−0.503879
$775$	−53747.0	−2.49116
$776$	−11346.7	−0.524903
$777$	14718.3	0.679557
$778$	−1534.46	−0.0707108
$779$	29675.5	1.36487
$780$	−73334.7	−3.36642
$781$	7563.68	0.346543
$782$	6590.88	0.301393
$783$	−783.000	−0.0357371
$784$	12087.3	0.550623
$785$	38387.4	1.74536
$786$	−37815.4	−1.71607
$787$	−20528.3	−0.929802	−0.464901	−	0.885363i	$-0.653910\pi$
$787$	−20528.3	−0.929802	−0.464901	+	0.885363i	$0.653910\pi$
$788$	44658.2	2.01889
$789$	−4185.48	−0.188855
$790$	6128.84	0.276018
$791$	54637.4	2.45598
$792$	2357.82	0.105785
$793$	−30298.9	−1.35680
$794$	30328.8	1.35558
$795$	17840.2	0.795883
$796$	61352.6	2.73189
$797$	−5657.94	−0.251461	−0.125731	−	0.992064i	$-0.540128\pi$
$797$	−5657.94	−0.251461	−0.125731	+	0.992064i	$0.540128\pi$
$798$	−46812.1	−2.07660
$799$	13269.6	0.587540
$800$	35944.2	1.58852
$801$	−10316.9	−0.455092
$802$	52837.3	2.32637
$803$	−6127.50	−0.269284
$804$	−19378.9	−0.850050
$805$	13818.1	0.604999
$806$	72877.0	3.18484
$807$	−10505.3	−0.458245
$808$	4624.42	0.201345
$809$	−13203.8	−0.573821	−0.286910	−	0.957957i	$-0.592628\pi$
$809$	−13203.8	−0.573821	−0.286910	+	0.957957i	$0.592628\pi$
$810$	7796.79	0.338212
$811$	−14869.8	−0.643836	−0.321918	−	0.946768i	$-0.604327\pi$
$811$	−14869.8	−0.643836	−0.321918	+	0.946768i	$0.604327\pi$
$812$	12065.6	0.521452
$813$	13962.7	0.602328
$814$	−7101.06	−0.305764
$815$	5240.87	0.225251
$816$	−4242.62	−0.182012
$817$	−28892.1	−1.23722
$818$	−41812.0	−1.78719
$819$	−22325.1	−0.952504
$820$	76162.9	3.24356
$821$	9570.52	0.406837	0.203419	−	0.979092i	$-0.434795\pi$
$821$	9570.52	0.406837	0.203419	+	0.979092i	$0.434795\pi$
$822$	27483.0	1.16615
$823$	19542.4	0.827708	0.413854	−	0.910343i	$-0.364182\pi$
$823$	19542.4	0.827708	0.413854	+	0.910343i	$0.364182\pi$
$824$	21697.1	0.917297
$825$	−7943.69	−0.335229
$826$	−114974.	−4.84315
$827$	15938.9	0.670194	0.335097	−	0.942184i	$-0.391231\pi$
$827$	15938.9	0.670194	0.335097	+	0.942184i	$0.391231\pi$
$828$	2931.18	0.123026
$829$	−21038.1	−0.881403	−0.440702	−	0.897654i	$-0.645270\pi$
$829$	−21038.1	−0.881403	−0.440702	+	0.897654i	$0.645270\pi$
$830$	−106789.	−4.46589
$831$	−26260.3	−1.09622
$832$	−64428.6	−2.68469
$833$	−31671.6	−1.31736
$834$	30301.2	1.25809
$835$	−19191.7	−0.795398
$836$	14431.8	0.597051
$837$	−4951.01	−0.204459
$838$	−35630.9	−1.46879
$839$	15084.3	0.620702	0.310351	−	0.950622i	$-0.399553\pi$
$839$	15084.3	0.620702	0.310351	+	0.950622i	$0.399553\pi$
$840$	−52267.6	−2.14691
$841$	841.000	0.0344828
$842$	−26913.0	−1.10153
$843$	2899.59	0.118466
$844$	−30869.9	−1.25899
$845$	−100820.	−4.10450
$846$	9235.50	0.375323
$847$	36709.2	1.48919
$848$	−6756.49	−0.273607
$849$	14302.2	0.578153
$850$	83992.3	3.38931
$851$	−3840.49	−0.154701
$852$	−35567.3	−1.43018
$853$	−34908.3	−1.40122	−0.700609	−	0.713546i	$-0.747088\pi$
$853$	−34908.3	−1.40122	−0.700609	+	0.713546i	$0.747088\pi$
$854$	−49638.7	−1.98899
$855$	20761.4	0.830438
$856$	9220.61	0.368171
$857$	−9519.38	−0.379435	−0.189717	−	0.981839i	$-0.560757\pi$
$857$	−9519.38	−0.379435	−0.189717	+	0.981839i	$0.560757\pi$
$858$	10771.1	0.428576
$859$	−25962.9	−1.03125	−0.515624	−	0.856815i	$-0.672440\pi$
$859$	−25962.9	−1.03125	−0.515624	+	0.856815i	$0.672440\pi$
$860$	−74152.1	−2.94019
$861$	23186.0	0.917744
$862$	−22163.4	−0.875740
$863$	−11132.8	−0.439124	−0.219562	−	0.975599i	$-0.570463\pi$
$863$	−11132.8	−0.439124	−0.219562	+	0.975599i	$0.570463\pi$
$864$	3311.07	0.130376
$865$	−5398.81	−0.212214
$866$	55293.4	2.16968
$867$	−3622.28	−0.141891
$868$	76292.2	2.98333
$869$	−575.207	−0.0224540
$870$	−8374.33	−0.326341
$871$	−38513.0	−1.49823
$872$	−50649.4	−1.96698
$873$	3521.46	0.136522
$874$	12214.8	0.472737
$875$	100996.	3.90203
$876$	28813.8	1.11133
$877$	31090.3	1.19709	0.598543	−	0.801090i	$-0.295746\pi$
$877$	31090.3	1.19709	0.598543	+	0.801090i	$0.295746\pi$
$878$	46843.4	1.80056
$879$	11757.1	0.451145
$880$	4291.46	0.164392
$881$	−24944.9	−0.953934	−0.476967	−	0.878921i	$-0.658264\pi$
$881$	−24944.9	−0.953934	−0.476967	+	0.878921i	$0.658264\pi$
$882$	−22043.1	−0.841532
$883$	−38218.5	−1.45657	−0.728287	−	0.685272i	$-0.759683\pi$
$883$	−38218.5	−1.45657	−0.728287	+	0.685272i	$0.759683\pi$
$884$	−72773.5	−2.76882
$885$	50991.4	1.93679
$886$	49911.8	1.89257
$887$	−43715.7	−1.65483	−0.827413	−	0.561594i	$-0.810188\pi$
$887$	−43715.7	−1.65483	−0.827413	+	0.561594i	$0.810188\pi$
$888$	14526.8	0.548973
$889$	7530.19	0.284088
$890$	−110341.	−4.15577
$891$	−731.748	−0.0275135
$892$	77518.7	2.90977
$893$	24592.4	0.921560
$894$	21474.6	0.803376
$895$	−82408.4	−3.07778
$896$	−76728.1	−2.86083
$897$	5825.34	0.216837
$898$	−73072.8	−2.71545
$899$	5317.75	0.197282
$900$	37354.2	1.38349
$901$	17703.7	0.654600
$902$	−11186.4	−0.412936
$903$	−22573.9	−0.831907
$904$	53926.6	1.98404
$905$	93652.5	3.43991
$906$	22075.3	0.809497
$907$	44385.1	1.62490	0.812450	−	0.583031i	$-0.198133\pi$
$907$	44385.1	1.62490	0.812450	+	0.583031i	$0.198133\pi$
$908$	−11009.4	−0.402378
$909$	−1435.19	−0.0523677
$910$	−238771.	−8.69799
$911$	30838.3	1.12153	0.560767	−	0.827974i	$-0.310506\pi$
$911$	30838.3	1.12153	0.560767	+	0.827974i	$0.310506\pi$
$912$	−7862.81	−0.285487
$913$	10022.4	0.363299
$914$	−52901.9	−1.91449
$915$	22015.0	0.795403
$916$	10007.9	0.360992
$917$	−78675.0	−2.83324
$918$	7737.12	0.278173
$919$	−17277.1	−0.620151	−0.310075	−	0.950712i	$-0.600354\pi$
$919$	−17277.1	−0.620151	−0.310075	+	0.950712i	$0.600354\pi$
$920$	13638.3	0.488742
$921$	13531.3	0.484116
$922$	21130.1	0.754753
$923$	−70685.3	−2.52073
$924$	11275.8	0.401458
$925$	−48942.1	−1.73968
$926$	34420.9	1.22154
$927$	−6733.68	−0.238580
$928$	−3556.34	−0.125800
$929$	−12308.5	−0.434693	−0.217347	−	0.976094i	$-0.569740\pi$
$929$	−12308.5	−0.434693	−0.217347	+	0.976094i	$0.569740\pi$
$930$	−52952.0	−1.86706
$931$	−58696.7	−2.06628
$932$	−13853.1	−0.486882
$933$	19357.6	0.679248
$934$	−695.207	−0.0243553
$935$	−11244.7	−0.393305
$936$	−22034.6	−0.769470
$937$	−43813.3	−1.52755	−0.763777	−	0.645480i	$-0.776657\pi$
$937$	−43813.3	−1.52755	−0.763777	+	0.645480i	$0.776657\pi$
$938$	−63095.8	−2.19632
$939$	−15289.3	−0.531361
$940$	63116.9	2.19005
$941$	12653.0	0.438338	0.219169	−	0.975687i	$-0.429665\pi$
$941$	12653.0	0.438338	0.219169	+	0.975687i	$0.429665\pi$
$942$	26512.8	0.917020
$943$	−6050.00	−0.208924
$944$	−19311.6	−0.665826
$945$	16221.3	0.558389
$946$	10891.1	0.374314
$947$	−14846.3	−0.509439	−0.254720	−	0.967015i	$-0.581983\pi$
$947$	−14846.3	−0.509439	−0.254720	+	0.967015i	$0.581983\pi$
$948$	2704.84	0.0926678
$949$	57263.7	1.95875
$950$	155662.	5.31616
$951$	−5880.30	−0.200507
$952$	−51867.6	−1.76580
$953$	41419.2	1.40787	0.703935	−	0.710264i	$-0.251424\pi$
$953$	41419.2	1.40787	0.703935	+	0.710264i	$0.251424\pi$
$954$	12321.6	0.418161
$955$	−46943.8	−1.59064
$956$	−46303.0	−1.56647
$957$	785.952	0.0265478
$958$	15888.4	0.535837
$959$	57178.4	1.92533
$960$	46813.5	1.57385
$961$	3833.82	0.128690
$962$	66361.9	2.22411
$963$	−2861.62	−0.0957574
$964$	28471.6	0.951254
$965$	96142.0	3.20717
$966$	9543.65	0.317870
$967$	−26230.2	−0.872293	−0.436146	−	0.899876i	$-0.643657\pi$
$967$	−26230.2	−0.872293	−0.436146	+	0.899876i	$0.643657\pi$
$968$	36231.6	1.20303
$969$	20602.5	0.683021
$970$	37662.7	1.24668
$971$	7155.43	0.236487	0.118243	−	0.992985i	$-0.462274\pi$
$971$	7155.43	0.236487	0.118243	+	0.992985i	$0.462274\pi$
$972$	3440.96	0.113548
$973$	63041.8	2.07711
$974$	44.6845	0.00147001
$975$	74236.6	2.43843
$976$	−8337.58	−0.273442
$977$	−5367.42	−0.175761	−0.0878807	−	0.996131i	$-0.528009\pi$
$977$	−5367.42	−0.175761	−0.0878807	+	0.996131i	$0.528009\pi$
$978$	3619.67	0.118348
$979$	10355.8	0.338071
$980$	−150646.	−4.91043
$981$	15719.1	0.511591
$982$	7023.18	0.228227
$983$	2746.55	0.0891162	0.0445581	−	0.999007i	$-0.485812\pi$
$983$	2746.55	0.0891162	0.0445581	+	0.999007i	$0.485812\pi$
$984$	22884.4	0.741390
$985$	−64486.9	−2.08601
$986$	−8310.24	−0.268410
$987$	19214.5	0.619659
$988$	−134870.	−4.34291
$989$	5890.27	0.189383
$990$	−7826.19	−0.251245
$991$	49289.2	1.57994	0.789971	−	0.613144i	$-0.210096\pi$
$991$	49289.2	1.57994	0.789971	+	0.613144i	$0.210096\pi$
$992$	−22487.2	−0.719726
$993$	23368.4	0.746801
$994$	−115804.	−3.69524
$995$	−88593.8	−2.82273
$996$	−47129.0	−1.49934
$997$	5057.99	0.160670	0.0803351	−	0.996768i	$-0.474401\pi$
$997$	5057.99	0.160670	0.0803351	+	0.996768i	$0.474401\pi$
$998$	−21522.8	−0.682659
$999$	−4508.40	−0.142782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.6	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.6	✓	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-4.70747 q^{2} +3.00000 q^{3} +14.1603 q^{4} -20.4476 q^{5} -14.1224 q^{6} -29.3817 q^{7} -28.9995 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.70747 q^{2} +3.00000 q^{3} +14.1603 q^{4} -20.4476 q^{5} -14.1224 q^{6} -29.3817 q^{7} -28.9995 q^{8} +9.00000 q^{9} +96.2567 q^{10} -9.03393 q^{11} +42.4809 q^{12} +84.4253 q^{13} +138.314 q^{14} -61.3429 q^{15} +23.2319 q^{16} -60.8734 q^{17} -42.3673 q^{18} -112.816 q^{19} -289.545 q^{20} -88.1452 q^{21} +42.5270 q^{22} +23.0000 q^{23} -86.9985 q^{24} +293.106 q^{25} -397.430 q^{26} +27.0000 q^{27} -416.055 q^{28} -29.0000 q^{29} +288.770 q^{30} -183.371 q^{31} +122.632 q^{32} -27.1018 q^{33} +286.560 q^{34} +600.787 q^{35} +127.443 q^{36} -166.978 q^{37} +531.079 q^{38} +253.276 q^{39} +592.971 q^{40} -263.043 q^{41} +414.941 q^{42} +256.099 q^{43} -127.923 q^{44} -184.029 q^{45} -108.272 q^{46} -217.987 q^{47} +69.6958 q^{48} +520.287 q^{49} -1379.79 q^{50} -182.620 q^{51} +1195.49 q^{52} -290.828 q^{53} -127.102 q^{54} +184.722 q^{55} +852.056 q^{56} -338.448 q^{57} +136.517 q^{58} -831.252 q^{59} -868.635 q^{60} -358.884 q^{61} +863.213 q^{62} -264.436 q^{63} -763.144 q^{64} -1726.30 q^{65} +127.581 q^{66} -456.178 q^{67} -861.986 q^{68} +69.0000 q^{69} -2828.19 q^{70} -837.253 q^{71} -260.996 q^{72} +678.276 q^{73} +786.043 q^{74} +879.317 q^{75} -1597.51 q^{76} +265.433 q^{77} -1192.29 q^{78} +63.6718 q^{79} -475.038 q^{80} +81.0000 q^{81} +1238.27 q^{82} -1109.41 q^{83} -1248.16 q^{84} +1244.72 q^{85} -1205.58 q^{86} -87.0000 q^{87} +261.980 q^{88} -1146.32 q^{89} +866.310 q^{90} -2480.56 q^{91} +325.687 q^{92} -550.112 q^{93} +1026.17 q^{94} +2306.82 q^{95} +367.897 q^{96} +391.274 q^{97} -2449.24 q^{98} -81.3054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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