LMFDB - Embedded newform 2001.4.a.d.1.11

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:	$37$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.64188 q^{2} -3.00000 q^{3} -1.02048 q^{4} +4.63395 q^{5} +7.92563 q^{6} +7.87352 q^{7} +23.8310 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.64188 q^{2} -3.00000 q^{3} -1.02048 q^{4} +4.63395 q^{5} +7.92563 q^{6} +7.87352 q^{7} +23.8310 q^{8} +9.00000 q^{9} -12.2423 q^{10} -51.2333 q^{11} +3.06144 q^{12} -1.10730 q^{13} -20.8009 q^{14} -13.9018 q^{15} -54.7948 q^{16} -38.2929 q^{17} -23.7769 q^{18} -62.0319 q^{19} -4.72885 q^{20} -23.6206 q^{21} +135.352 q^{22} -23.0000 q^{23} -71.4930 q^{24} -103.527 q^{25} +2.92535 q^{26} -27.0000 q^{27} -8.03477 q^{28} -29.0000 q^{29} +36.7270 q^{30} +61.5365 q^{31} -45.8870 q^{32} +153.700 q^{33} +101.165 q^{34} +36.4855 q^{35} -9.18432 q^{36} -297.201 q^{37} +163.881 q^{38} +3.32189 q^{39} +110.432 q^{40} +435.660 q^{41} +62.4026 q^{42} +496.793 q^{43} +52.2826 q^{44} +41.7055 q^{45} +60.7632 q^{46} -192.498 q^{47} +164.384 q^{48} -281.008 q^{49} +273.505 q^{50} +114.879 q^{51} +1.12998 q^{52} +4.53932 q^{53} +71.3307 q^{54} -237.413 q^{55} +187.634 q^{56} +186.096 q^{57} +76.6145 q^{58} -664.623 q^{59} +14.1866 q^{60} -125.325 q^{61} -162.572 q^{62} +70.8617 q^{63} +559.586 q^{64} -5.13116 q^{65} -406.057 q^{66} +206.108 q^{67} +39.0772 q^{68} +69.0000 q^{69} -96.3901 q^{70} +443.667 q^{71} +214.479 q^{72} +130.124 q^{73} +785.168 q^{74} +310.580 q^{75} +63.3024 q^{76} -403.387 q^{77} -8.77604 q^{78} -437.089 q^{79} -253.916 q^{80} +81.0000 q^{81} -1150.96 q^{82} -337.244 q^{83} +24.1043 q^{84} -177.447 q^{85} -1312.47 q^{86} +87.0000 q^{87} -1220.94 q^{88} +382.521 q^{89} -110.181 q^{90} -8.71833 q^{91} +23.4711 q^{92} -184.609 q^{93} +508.557 q^{94} -287.453 q^{95} +137.661 q^{96} +520.010 q^{97} +742.388 q^{98} -461.100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.64188	−0.934045	−0.467022	−	0.884245i	$-0.654673\pi$
$2$	−2.64188	−0.934045	−0.467022	+	0.884245i	$0.654673\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−1.02048	−0.127560
$5$	4.63395	0.414473	0.207236	−	0.978291i	$-0.433553\pi$
$5$	4.63395	0.414473	0.207236	+	0.978291i	$0.433553\pi$
$6$	7.92563	0.539271
$7$	7.87352	0.425130	0.212565	−	0.977147i	$-0.431818\pi$
$7$	7.87352	0.425130	0.212565	+	0.977147i	$0.431818\pi$
$8$	23.8310	1.05319
$9$	9.00000	0.333333
$10$	−12.2423	−0.387136
$11$	−51.2333	−1.40431	−0.702156	−	0.712023i	$-0.747779\pi$
$11$	−51.2333	−1.40431	−0.702156	+	0.712023i	$0.747779\pi$
$12$	3.06144	0.0736468
$13$	−1.10730	−0.0236238	−0.0118119	−	0.999930i	$-0.503760\pi$
$13$	−1.10730	−0.0236238	−0.0118119	+	0.999930i	$0.503760\pi$
$14$	−20.8009	−0.397091
$15$	−13.9018	−0.239296
$16$	−54.7948	−0.856168
$17$	−38.2929	−0.546317	−0.273159	−	0.961969i	$-0.588068\pi$
$17$	−38.2929	−0.546317	−0.273159	+	0.961969i	$0.588068\pi$
$18$	−23.7769	−0.311348
$19$	−62.0319	−0.749005	−0.374503	−	0.927226i	$-0.622187\pi$
$19$	−62.0319	−0.749005	−0.374503	+	0.927226i	$0.622187\pi$
$20$	−4.72885	−0.0528702
$21$	−23.6206	−0.245449
$22$	135.352	1.31169
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−71.4930	−0.608061
$25$	−103.527	−0.828212
$26$	2.92535	0.0220657
$27$	−27.0000	−0.192450
$28$	−8.03477	−0.0542296
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	36.7270	0.223513
$31$	61.5365	0.356525	0.178262	−	0.983983i	$-0.442952\pi$
$31$	61.5365	0.356525	0.178262	+	0.983983i	$0.442952\pi$
$32$	−45.8870	−0.253492
$33$	153.700	0.810780
$34$	101.165	0.510285
$35$	36.4855	0.176205
$36$	−9.18432	−0.0425200
$37$	−297.201	−1.32053	−0.660264	−	0.751034i	$-0.729556\pi$
$37$	−297.201	−1.32053	−0.660264	+	0.751034i	$0.729556\pi$
$38$	163.881	0.699605
$39$	3.32189	0.0136392
$40$	110.432	0.436519
$41$	435.660	1.65948	0.829739	−	0.558151i	$-0.188489\pi$
$41$	435.660	1.65948	0.829739	+	0.558151i	$0.188489\pi$
$42$	62.4026	0.229260
$43$	496.793	1.76187	0.880933	−	0.473241i	$-0.156916\pi$
$43$	496.793	1.76187	0.880933	+	0.473241i	$0.156916\pi$
$44$	52.2826	0.179134
$45$	41.7055	0.138158
$46$	60.7632	0.194762
$47$	−192.498	−0.597421	−0.298710	−	0.954344i	$-0.596556\pi$
$47$	−192.498	−0.597421	−0.298710	+	0.954344i	$0.596556\pi$
$48$	164.384	0.494309
$49$	−281.008	−0.819264
$50$	273.505	0.773588
$51$	114.879	0.315416
$52$	1.12998	0.00301345
$53$	4.53932	0.0117646	0.00588230	−	0.999983i	$-0.498128\pi$
$53$	4.53932	0.0117646	0.00588230	+	0.999983i	$0.498128\pi$
$54$	71.3307	0.179757
$55$	−237.413	−0.582049
$56$	187.634	0.447744
$57$	186.096	0.432438
$58$	76.6145	0.173448
$59$	−664.623	−1.46655	−0.733276	−	0.679931i	$-0.762010\pi$
$59$	−664.623	−1.46655	−0.733276	+	0.679931i	$0.762010\pi$
$60$	14.1866	0.0305246
$61$	−125.325	−0.263053	−0.131526	−	0.991313i	$-0.541988\pi$
$61$	−125.325	−0.263053	−0.131526	+	0.991313i	$0.541988\pi$
$62$	−162.572	−0.333010
$63$	70.8617	0.141710
$64$	559.586	1.09294
$65$	−5.13116	−0.00979142
$66$	−406.057	−0.757305
$67$	206.108	0.375823	0.187911	−	0.982186i	$-0.439828\pi$
$67$	206.108	0.375823	0.187911	+	0.982186i	$0.439828\pi$
$68$	39.0772	0.0696882
$69$	69.0000	0.120386
$70$	−96.3901	−0.164583
$71$	443.667	0.741600	0.370800	−	0.928713i	$-0.379084\pi$
$71$	443.667	0.741600	0.370800	+	0.928713i	$0.379084\pi$
$72$	214.479	0.351064
$73$	130.124	0.208628	0.104314	−	0.994544i	$-0.466735\pi$
$73$	130.124	0.208628	0.104314	+	0.994544i	$0.466735\pi$
$74$	785.168	1.23343
$75$	310.580	0.478169
$76$	63.3024	0.0955432
$77$	−403.387	−0.597015
$78$	−8.77604	−0.0127396
$79$	−437.089	−0.622486	−0.311243	−	0.950330i	$-0.600745\pi$
$79$	−437.089	−0.622486	−0.311243	+	0.950330i	$0.600745\pi$
$80$	−253.916	−0.354858
$81$	81.0000	0.111111
$82$	−1150.96	−1.55003
$83$	−337.244	−0.445992	−0.222996	−	0.974819i	$-0.571584\pi$
$83$	−337.244	−0.445992	−0.222996	+	0.974819i	$0.571584\pi$
$84$	24.1043	0.0313095
$85$	−177.447	−0.226434
$86$	−1312.47	−1.64566
$87$	87.0000	0.107211
$88$	−1220.94	−1.47901
$89$	382.521	0.455586	0.227793	−	0.973710i	$-0.426849\pi$
$89$	382.521	0.455586	0.227793	+	0.973710i	$0.426849\pi$
$90$	−110.181	−0.129045
$91$	−8.71833	−0.0100432
$92$	23.4711	0.0265981
$93$	−184.609	−0.205840
$94$	508.557	0.558018
$95$	−287.453	−0.310442
$96$	137.661	0.146354
$97$	520.010	0.544320	0.272160	−	0.962252i	$-0.412262\pi$
$97$	520.010	0.544320	0.272160	+	0.962252i	$0.412262\pi$
$98$	742.388	0.765230
$99$	−461.100	−0.468104
$100$	105.647	0.105647
$101$	−445.774	−0.439170	−0.219585	−	0.975593i	$-0.570470\pi$
$101$	−445.774	−0.439170	−0.219585	+	0.975593i	$0.570470\pi$
$102$	−303.495	−0.294613
$103$	−288.180	−0.275681	−0.137841	−	0.990454i	$-0.544016\pi$
$103$	−288.180	−0.275681	−0.137841	+	0.990454i	$0.544016\pi$
$104$	−26.3880	−0.0248804
$105$	−109.456	−0.101732
$106$	−11.9923	−0.0109887
$107$	817.410	0.738524	0.369262	−	0.929325i	$-0.379611\pi$
$107$	817.410	0.738524	0.369262	+	0.929325i	$0.379611\pi$
$108$	27.5530	0.0245489
$109$	−520.155	−0.457081	−0.228541	−	0.973534i	$-0.573395\pi$
$109$	−520.155	−0.457081	−0.228541	+	0.973534i	$0.573395\pi$
$110$	627.215	0.543660
$111$	891.603	0.762407
$112$	−431.428	−0.363983
$113$	−552.084	−0.459608	−0.229804	−	0.973237i	$-0.573808\pi$
$113$	−552.084	−0.459608	−0.229804	+	0.973237i	$0.573808\pi$
$114$	−491.642	−0.403917
$115$	−106.581	−0.0864235
$116$	29.5939	0.0236873
$117$	−9.96568	−0.00787460
$118$	1755.85	1.36983
$119$	−301.500	−0.232256
$120$	−331.295	−0.252025
$121$	1293.85	0.972092
$122$	331.094	0.245703
$123$	−1306.98	−0.958100
$124$	−62.7968	−0.0454783
$125$	−1058.98	−0.757744
$126$	−187.208	−0.132364
$127$	−2302.67	−1.60889	−0.804444	−	0.594029i	$-0.797537\pi$
$127$	−2302.67	−1.60889	−0.804444	+	0.594029i	$0.797537\pi$
$128$	−1111.26	−0.767364
$129$	−1490.38	−1.01721
$130$	13.5559	0.00914562
$131$	−1491.54	−0.994784	−0.497392	−	0.867526i	$-0.665709\pi$
$131$	−1491.54	−0.994784	−0.497392	+	0.867526i	$0.665709\pi$
$132$	−156.848	−0.103423
$133$	−488.410	−0.318425
$134$	−544.512	−0.351035
$135$	−125.117	−0.0797653
$136$	−912.558	−0.575377
$137$	−2041.47	−1.27310	−0.636550	−	0.771235i	$-0.719639\pi$
$137$	−2041.47	−1.27310	−0.636550	+	0.771235i	$0.719639\pi$
$138$	−182.290	−0.112446
$139$	−986.258	−0.601823	−0.300911	−	0.953652i	$-0.597291\pi$
$139$	−986.258	−0.601823	−0.300911	+	0.953652i	$0.597291\pi$
$140$	−37.2327	−0.0224767
$141$	577.495	0.344921
$142$	−1172.11	−0.692688
$143$	56.7306	0.0331752
$144$	−493.153	−0.285389
$145$	−134.384	−0.0769657
$146$	−343.772	−0.194868
$147$	843.023	0.473003
$148$	303.288	0.168447
$149$	−1022.82	−0.562367	−0.281183	−	0.959654i	$-0.590727\pi$
$149$	−1022.82	−0.562367	−0.281183	+	0.959654i	$0.590727\pi$
$150$	−820.514	−0.446631
$151$	1617.49	0.871720	0.435860	−	0.900015i	$-0.356444\pi$
$151$	1617.49	0.871720	0.435860	+	0.900015i	$0.356444\pi$
$152$	−1478.28	−0.788846
$153$	−344.636	−0.182106
$154$	1065.70	0.557639
$155$	285.157	0.147770
$156$	−3.38993	−0.00173982
$157$	1062.80	0.540260	0.270130	−	0.962824i	$-0.412933\pi$
$157$	1062.80	0.540260	0.270130	+	0.962824i	$0.412933\pi$
$158$	1154.74	0.581429
$159$	−13.6180	−0.00679230
$160$	−212.638	−0.105066
$161$	−181.091	−0.0886458
$162$	−213.992	−0.103783
$163$	954.044	0.458445	0.229222	−	0.973374i	$-0.426382\pi$
$163$	954.044	0.458445	0.229222	+	0.973374i	$0.426382\pi$
$164$	−444.582	−0.211683
$165$	712.238	0.336046
$166$	890.958	0.416577
$167$	3683.81	1.70696	0.853478	−	0.521128i	$-0.174489\pi$
$167$	3683.81	1.70696	0.853478	+	0.521128i	$0.174489\pi$
$168$	−562.902	−0.258505
$169$	−2195.77	−0.999442
$170$	468.794	0.211499
$171$	−558.287	−0.249668
$172$	−506.968	−0.224744
$173$	2703.02	1.18790	0.593950	−	0.804502i	$-0.297568\pi$
$173$	2703.02	1.18790	0.593950	+	0.804502i	$0.297568\pi$
$174$	−229.843	−0.100140
$175$	−815.118	−0.352098
$176$	2807.32	1.20233
$177$	1993.87	0.846714
$178$	−1010.58	−0.425538
$179$	−2209.23	−0.922491	−0.461246	−	0.887273i	$-0.652597\pi$
$179$	−2209.23	−0.922491	−0.461246	+	0.887273i	$0.652597\pi$
$180$	−42.5597	−0.0176234
$181$	−1837.33	−0.754517	−0.377258	−	0.926108i	$-0.623133\pi$
$181$	−1837.33	−0.754517	−0.377258	+	0.926108i	$0.623133\pi$
$182$	23.0328	0.00938078
$183$	375.975	0.151874
$184$	−548.113	−0.219606
$185$	−1377.21	−0.547323
$186$	487.715	0.192264
$187$	1961.87	0.767200
$188$	196.441	0.0762070
$189$	−212.585	−0.0818163
$190$	759.415	0.289967
$191$	2880.57	1.09126	0.545631	−	0.838026i	$-0.316290\pi$
$191$	2880.57	1.09126	0.545631	+	0.838026i	$0.316290\pi$
$192$	−1678.76	−0.631010
$193$	3484.53	1.29960	0.649798	−	0.760107i	$-0.274853\pi$
$193$	3484.53	1.29960	0.649798	+	0.760107i	$0.274853\pi$
$194$	−1373.80	−0.508419
$195$	15.3935	0.00565308
$196$	286.763	0.104505
$197$	1523.80	0.551099	0.275549	−	0.961287i	$-0.411140\pi$
$197$	1523.80	0.551099	0.275549	+	0.961287i	$0.411140\pi$
$198$	1218.17	0.437230
$199$	−1126.38	−0.401241	−0.200621	−	0.979669i	$-0.564296\pi$
$199$	−1126.38	−0.401241	−0.200621	+	0.979669i	$0.564296\pi$
$200$	−2467.14	−0.872266
$201$	−618.324	−0.216981
$202$	1177.68	0.410205
$203$	−228.332	−0.0789447
$204$	−117.231	−0.0402345
$205$	2018.82	0.687809
$206$	761.335	0.257499
$207$	−207.000	−0.0695048
$208$	60.6741	0.0202259
$209$	3178.10	1.05184
$210$	289.170	0.0950222
$211$	−1786.56	−0.582898	−0.291449	−	0.956586i	$-0.594137\pi$
$211$	−1786.56	−0.582898	−0.291449	+	0.956586i	$0.594137\pi$
$212$	−4.63229	−0.00150069
$213$	−1331.00	−0.428163
$214$	−2159.50	−0.689814
$215$	2302.11	0.730245
$216$	−643.437	−0.202687
$217$	484.508	0.151569
$218$	1374.19	0.426934
$219$	−390.372	−0.120452
$220$	242.275	0.0742462
$221$	42.4016	0.0129061
$222$	−2355.51	−0.712122
$223$	354.225	0.106371	0.0531854	−	0.998585i	$-0.483063\pi$
$223$	354.225	0.106371	0.0531854	+	0.998585i	$0.483063\pi$
$224$	−361.292	−0.107767
$225$	−931.739	−0.276071
$226$	1458.54	0.429294
$227$	−2183.37	−0.638395	−0.319197	−	0.947688i	$-0.603413\pi$
$227$	−2183.37	−0.638395	−0.319197	+	0.947688i	$0.603413\pi$
$228$	−189.907	−0.0551619
$229$	4158.89	1.20012	0.600060	−	0.799955i	$-0.295143\pi$
$229$	4158.89	1.20012	0.600060	+	0.799955i	$0.295143\pi$
$230$	281.573	0.0807235
$231$	1210.16	0.344687
$232$	−691.099	−0.195573
$233$	5587.94	1.57115	0.785575	−	0.618766i	$-0.212367\pi$
$233$	5587.94	1.57115	0.785575	+	0.618766i	$0.212367\pi$
$234$	26.3281	0.00735523
$235$	−892.027	−0.247615
$236$	678.235	0.187073
$237$	1311.27	0.359392
$238$	796.526	0.216937
$239$	4134.66	1.11903	0.559516	−	0.828819i	$-0.310987\pi$
$239$	4134.66	1.11903	0.559516	+	0.828819i	$0.310987\pi$
$240$	761.748	0.204878
$241$	−1510.43	−0.403715	−0.201857	−	0.979415i	$-0.564698\pi$
$241$	−1510.43	−0.403715	−0.201857	+	0.979415i	$0.564698\pi$
$242$	−3418.21	−0.907978
$243$	−243.000	−0.0641500
$244$	127.892	0.0335550
$245$	−1302.17	−0.339563
$246$	3452.88	0.894909
$247$	68.6878	0.0176943
$248$	1466.48	0.375489
$249$	1011.73	0.257494
$250$	2797.70	0.707767
$251$	2301.44	0.578748	0.289374	−	0.957216i	$-0.406553\pi$
$251$	2301.44	0.578748	0.289374	+	0.957216i	$0.406553\pi$
$252$	−72.3130	−0.0180765
$253$	1178.37	0.292819
$254$	6083.37	1.50277
$255$	532.342	0.130731
$256$	−1540.87	−0.376189
$257$	−2472.77	−0.600183	−0.300091	−	0.953910i	$-0.597017\pi$
$257$	−2472.77	−0.600183	−0.300091	+	0.953910i	$0.597017\pi$
$258$	3937.40	0.950123
$259$	−2340.02	−0.561396
$260$	5.23625	0.00124899
$261$	−261.000	−0.0618984
$262$	3940.47	0.929173
$263$	4477.03	1.04968	0.524840	−	0.851201i	$-0.324125\pi$
$263$	4477.03	1.04968	0.524840	+	0.851201i	$0.324125\pi$
$264$	3662.83	0.853907
$265$	21.0350	0.00487611
$266$	1290.32	0.297423
$267$	−1147.56	−0.263033
$268$	−210.329	−0.0479400
$269$	−7340.51	−1.66379	−0.831893	−	0.554935i	$-0.812743\pi$
$269$	−7340.51	−1.66379	−0.831893	+	0.554935i	$0.812743\pi$
$270$	330.543	0.0745044
$271$	−2113.04	−0.473646	−0.236823	−	0.971553i	$-0.576106\pi$
$271$	−2113.04	−0.473646	−0.236823	+	0.971553i	$0.576106\pi$
$272$	2098.25	0.467739
$273$	26.1550	0.00579843
$274$	5393.32	1.18913
$275$	5304.01	1.16307
$276$	−70.4132	−0.0153564
$277$	−142.619	−0.0309355	−0.0154678	−	0.999880i	$-0.504924\pi$
$277$	−142.619	−0.0309355	−0.0154678	+	0.999880i	$0.504924\pi$
$278$	2605.57	0.562129
$279$	553.828	0.118842
$280$	869.485	0.185577
$281$	−6859.15	−1.45617	−0.728083	−	0.685489i	$-0.759588\pi$
$281$	−6859.15	−1.45617	−0.728083	+	0.685489i	$0.759588\pi$
$282$	−1525.67	−0.322172
$283$	−121.966	−0.0256188	−0.0128094	−	0.999918i	$-0.504077\pi$
$283$	−121.966	−0.0256188	−0.0128094	+	0.999918i	$0.504077\pi$
$284$	−452.754	−0.0945985
$285$	862.358	0.179234
$286$	−149.875	−0.0309871
$287$	3430.18	0.705494
$288$	−412.983	−0.0844973
$289$	−3446.65	−0.701538
$290$	355.027	0.0718894
$291$	−1560.03	−0.314263
$292$	−132.789	−0.0266126
$293$	7109.65	1.41758	0.708788	−	0.705421i	$-0.249242\pi$
$293$	7109.65	1.41758	0.708788	+	0.705421i	$0.249242\pi$
$294$	−2227.16	−0.441806
$295$	−3079.83	−0.607846
$296$	−7082.60	−1.39077
$297$	1383.30	0.270260
$298$	2702.16	0.525276
$299$	25.4679	0.00492590
$300$	−316.940	−0.0609952
$301$	3911.51	0.749022
$302$	−4273.22	−0.814225
$303$	1337.32	0.253555
$304$	3399.03	0.641275
$305$	−580.750	−0.109028
$306$	910.486	0.170095
$307$	3973.53	0.738702	0.369351	−	0.929290i	$-0.379580\pi$
$307$	3973.53	0.738702	0.369351	+	0.929290i	$0.379580\pi$
$308$	411.648	0.0761553
$309$	864.539	0.159165
$310$	−753.349	−0.138024
$311$	9510.42	1.73404	0.867020	−	0.498274i	$-0.166033\pi$
$311$	9510.42	1.73404	0.867020	+	0.498274i	$0.166033\pi$
$312$	79.1641	0.0143647
$313$	−5039.61	−0.910081	−0.455041	−	0.890471i	$-0.650375\pi$
$313$	−5039.61	−0.910081	−0.455041	+	0.890471i	$0.650375\pi$
$314$	−2807.79	−0.504627
$315$	328.369	0.0587349
$316$	446.041	0.0794043
$317$	5932.68	1.05114	0.525572	−	0.850749i	$-0.323851\pi$
$317$	5932.68	1.05114	0.525572	+	0.850749i	$0.323851\pi$
$318$	35.9770	0.00634431
$319$	1485.77	0.260774
$320$	2593.09	0.452994
$321$	−2452.23	−0.426387
$322$	478.420	0.0827991
$323$	2375.38	0.409194
$324$	−82.6589	−0.0141733
$325$	114.635	0.0195655
$326$	−2520.47	−0.428208
$327$	1560.47	0.263896
$328$	10382.2	1.74775
$329$	−1515.64	−0.253982
$330$	−1881.64	−0.313882
$331$	7442.49	1.23588	0.617940	−	0.786225i	$-0.287967\pi$
$331$	7442.49	1.23588	0.617940	+	0.786225i	$0.287967\pi$
$332$	344.151	0.0568908
$333$	−2674.81	−0.440176
$334$	−9732.18	−1.59437
$335$	955.094	0.155768
$336$	1294.28	0.210146
$337$	8253.03	1.33404	0.667020	−	0.745040i	$-0.267570\pi$
$337$	8253.03	1.33404	0.667020	+	0.745040i	$0.267570\pi$
$338$	5800.97	0.933524
$339$	1656.25	0.265355
$340$	181.081	0.0288839
$341$	−3152.72	−0.500672
$342$	1474.93	0.233202
$343$	−4913.14	−0.773424
$344$	11839.1	1.85558
$345$	319.742	0.0498967
$346$	−7141.04	−1.10955
$347$	5808.36	0.898586	0.449293	−	0.893385i	$-0.351676\pi$
$347$	5808.36	0.898586	0.449293	+	0.893385i	$0.351676\pi$
$348$	−88.7818	−0.0136759
$349$	−3427.34	−0.525678	−0.262839	−	0.964840i	$-0.584659\pi$
$349$	−3427.34	−0.525678	−0.262839	+	0.964840i	$0.584659\pi$
$350$	2153.44	0.328875
$351$	29.8970	0.00454640
$352$	2350.94	0.355982
$353$	−2852.55	−0.430102	−0.215051	−	0.976603i	$-0.568992\pi$
$353$	−2852.55	−0.430102	−0.215051	+	0.976603i	$0.568992\pi$
$354$	−5267.56	−0.790869
$355$	2055.93	0.307373
$356$	−390.356	−0.0581146
$357$	904.500	0.134093
$358$	5836.53	0.861648
$359$	6881.36	1.01165	0.505827	−	0.862635i	$-0.331187\pi$
$359$	6881.36	1.01165	0.505827	+	0.862635i	$0.331187\pi$
$360$	993.884	0.145506
$361$	−3011.04	−0.438991
$362$	4854.00	0.704753
$363$	−3881.56	−0.561238
$364$	8.89689	0.00128111
$365$	602.988	0.0864707
$366$	−993.281	−0.141857
$367$	−6717.31	−0.955425	−0.477713	−	0.878516i	$-0.658534\pi$
$367$	−6717.31	−0.955425	−0.477713	+	0.878516i	$0.658534\pi$
$368$	1260.28	0.178523
$369$	3920.94	0.553159
$370$	3638.43	0.511224
$371$	35.7405	0.00500149
$372$	188.390	0.0262569
$373$	−5545.48	−0.769797	−0.384898	−	0.922959i	$-0.625763\pi$
$373$	−5545.48	−0.769797	−0.384898	+	0.922959i	$0.625763\pi$
$374$	−5183.03	−0.716599
$375$	3176.94	0.437484
$376$	−4587.43	−0.629199
$377$	32.1116	0.00438683
$378$	561.624	0.0764201
$379$	−12909.0	−1.74958	−0.874789	−	0.484504i	$-0.839000\pi$
$379$	−12909.0	−1.74958	−0.874789	+	0.484504i	$0.839000\pi$
$380$	293.340	0.0396000
$381$	6908.00	0.928892
$382$	−7610.12	−1.01929
$383$	1882.65	0.251173	0.125586	−	0.992083i	$-0.459919\pi$
$383$	1882.65	0.251173	0.125586	+	0.992083i	$0.459919\pi$
$384$	3333.79	0.443038
$385$	−1869.27	−0.247447
$386$	−9205.71	−1.21388
$387$	4471.14	0.587289
$388$	−530.660	−0.0694335
$389$	5024.53	0.654894	0.327447	−	0.944870i	$-0.393812\pi$
$389$	5024.53	0.654894	0.327447	+	0.944870i	$0.393812\pi$
$390$	−40.6677	−0.00528023
$391$	880.737	0.113915
$392$	−6696.70	−0.862842
$393$	4474.63	0.574339
$394$	−4025.70	−0.514751
$395$	−2025.45	−0.258003
$396$	470.544	0.0597114
$397$	−4461.97	−0.564081	−0.282040	−	0.959403i	$-0.591011\pi$
$397$	−4461.97	−0.564081	−0.282040	+	0.959403i	$0.591011\pi$
$398$	2975.76	0.374777
$399$	1465.23	0.183843
$400$	5672.71	0.709089
$401$	4944.55	0.615759	0.307879	−	0.951425i	$-0.400381\pi$
$401$	4944.55	0.615759	0.307879	+	0.951425i	$0.400381\pi$
$402$	1633.54	0.202670
$403$	−68.1392	−0.00842247
$404$	454.904	0.0560206
$405$	375.350	0.0460525
$406$	603.226	0.0737379
$407$	15226.6	1.85443
$408$	2737.67	0.332194
$409$	5347.07	0.646444	0.323222	−	0.946323i	$-0.395234\pi$
$409$	5347.07	0.646444	0.323222	+	0.946323i	$0.395234\pi$
$410$	−5333.49	−0.642444
$411$	6124.42	0.735025
$412$	294.082	0.0351659
$413$	−5232.92	−0.623475
$414$	546.869	0.0649206
$415$	−1562.77	−0.184852
$416$	50.8105	0.00598844
$417$	2958.78	0.347462
$418$	−8396.16	−0.982463
$419$	1886.49	0.219955	0.109978	−	0.993934i	$-0.464922\pi$
$419$	1886.49	0.219955	0.109978	+	0.993934i	$0.464922\pi$
$420$	111.698	0.0129769
$421$	10461.0	1.21102	0.605508	−	0.795840i	$-0.292970\pi$
$421$	10461.0	1.21102	0.605508	+	0.795840i	$0.292970\pi$
$422$	4719.86	0.544453
$423$	−1732.49	−0.199140
$424$	108.177	0.0123904
$425$	3964.33	0.452467
$426$	3516.34	0.399923
$427$	−986.749	−0.111832
$428$	−834.151	−0.0942061
$429$	−170.192	−0.0191537
$430$	−6081.90	−0.682082
$431$	15499.5	1.73221	0.866107	−	0.499858i	$-0.166615\pi$
$431$	15499.5	1.73221	0.866107	+	0.499858i	$0.166615\pi$
$432$	1479.46	0.164770
$433$	−881.584	−0.0978434	−0.0489217	−	0.998803i	$-0.515578\pi$
$433$	−881.584	−0.0978434	−0.0489217	+	0.998803i	$0.515578\pi$
$434$	−1280.01	−0.141573
$435$	403.153	0.0444361
$436$	530.808	0.0583053
$437$	1426.73	0.156178
$438$	1031.32	0.112507
$439$	5839.70	0.634883	0.317441	−	0.948278i	$-0.397176\pi$
$439$	5839.70	0.634883	0.317441	+	0.948278i	$0.397176\pi$
$440$	−5657.78	−0.613009
$441$	−2529.07	−0.273088
$442$	−112.020	−0.0120549
$443$	−4149.11	−0.444989	−0.222494	−	0.974934i	$-0.571420\pi$
$443$	−4149.11	−0.444989	−0.222494	+	0.974934i	$0.571420\pi$
$444$	−909.863	−0.0972527
$445$	1772.58	0.188828
$446$	−935.820	−0.0993551
$447$	3068.46	0.324683
$448$	4405.91	0.464642
$449$	−555.048	−0.0583393	−0.0291696	−	0.999574i	$-0.509286\pi$
$449$	−555.048	−0.0583393	−0.0291696	+	0.999574i	$0.509286\pi$
$450$	2461.54	0.257863
$451$	−22320.3	−2.33043
$452$	563.391	0.0586276
$453$	−4852.48	−0.503288
$454$	5768.21	0.596289
$455$	−40.4003	−0.00416263
$456$	4434.85	0.455441
$457$	−2384.35	−0.244059	−0.122030	−	0.992526i	$-0.538940\pi$
$457$	−2384.35	−0.244059	−0.122030	+	0.992526i	$0.538940\pi$
$458$	−10987.3	−1.12097
$459$	1033.91	0.105139
$460$	108.764	0.0110242
$461$	14737.5	1.48892	0.744461	−	0.667666i	$-0.232706\pi$
$461$	14737.5	1.48892	0.744461	+	0.667666i	$0.232706\pi$
$462$	−3197.10	−0.321953
$463$	−10972.4	−1.10136	−0.550680	−	0.834716i	$-0.685632\pi$
$463$	−10972.4	−1.10136	−0.550680	+	0.834716i	$0.685632\pi$
$464$	1589.05	0.158986
$465$	−855.470	−0.0853150
$466$	−14762.7	−1.46753
$467$	8452.71	0.837569	0.418784	−	0.908086i	$-0.362456\pi$
$467$	8452.71	0.837569	0.418784	+	0.908086i	$0.362456\pi$
$468$	10.1698	0.00100448
$469$	1622.80	0.159774
$470$	2356.63	0.231283
$471$	−3188.40	−0.311919
$472$	−15838.6	−1.54456
$473$	−25452.4	−2.47421
$474$	−3464.21	−0.335688
$475$	6421.95	0.620336
$476$	307.675	0.0296266
$477$	40.8539	0.00392153
$478$	−10923.3	−1.04523
$479$	6528.33	0.622729	0.311364	−	0.950291i	$-0.399214\pi$
$479$	6528.33	0.622729	0.311364	+	0.950291i	$0.399214\pi$
$480$	637.913	0.0606596
$481$	329.090	0.0311959
$482$	3990.37	0.377088
$483$	543.273	0.0511797
$484$	−1320.35	−0.124000
$485$	2409.70	0.225606
$486$	641.976	0.0599190
$487$	9226.15	0.858474	0.429237	−	0.903192i	$-0.358782\pi$
$487$	9226.15	0.858474	0.429237	+	0.903192i	$0.358782\pi$
$488$	−2986.62	−0.277045
$489$	−2862.13	−0.264683
$490$	3440.19	0.317167
$491$	7432.73	0.683166	0.341583	−	0.939852i	$-0.389037\pi$
$491$	7432.73	0.683166	0.341583	+	0.939852i	$0.389037\pi$
$492$	1333.75	0.122215
$493$	1110.49	0.101449
$494$	−181.465	−0.0165273
$495$	−2136.71	−0.194016
$496$	−3371.88	−0.305245
$497$	3493.22	0.315276
$498$	−2672.87	−0.240511
$499$	−1552.50	−0.139278	−0.0696388	−	0.997572i	$-0.522185\pi$
$499$	−1552.50	−0.139278	−0.0696388	+	0.997572i	$0.522185\pi$
$500$	1080.67	0.0966579
$501$	−11051.4	−0.985512
$502$	−6080.13	−0.540576
$503$	18150.0	1.60888	0.804441	−	0.594033i	$-0.202465\pi$
$503$	18150.0	1.60888	0.804441	+	0.594033i	$0.202465\pi$
$504$	1688.71	0.149248
$505$	−2065.69	−0.182024
$506$	−3113.10	−0.273506
$507$	6587.32	0.577028
$508$	2349.83	0.205230
$509$	−16006.8	−1.39389	−0.696943	−	0.717127i	$-0.745457\pi$
$509$	−16006.8	−1.39389	−0.696943	+	0.717127i	$0.745457\pi$
$510$	−1406.38	−0.122109
$511$	1024.53	0.0886942
$512$	12960.9	1.11874
$513$	1674.86	0.144146
$514$	6532.75	0.560598
$515$	−1335.41	−0.114262
$516$	1520.90	0.129756
$517$	9862.34	0.838965
$518$	6182.04	0.524369
$519$	−8109.05	−0.685834
$520$	−122.281	−0.0103122
$521$	21322.2	1.79298	0.896492	−	0.443060i	$-0.146107\pi$
$521$	21322.2	1.79298	0.896492	+	0.443060i	$0.146107\pi$
$522$	689.530	0.0578159
$523$	5691.67	0.475868	0.237934	−	0.971281i	$-0.423530\pi$
$523$	5691.67	0.475868	0.237934	+	0.971281i	$0.423530\pi$
$524$	1522.09	0.126895
$525$	2445.36	0.203284
$526$	−11827.8	−0.980447
$527$	−2356.41	−0.194776
$528$	−8421.96	−0.694164
$529$	529.000	0.0434783
$530$	−55.5718	−0.00455450
$531$	−5981.61	−0.488851
$532$	498.413	0.0406183
$533$	−482.405	−0.0392032
$534$	3031.73	0.245685
$535$	3787.84	0.306098
$536$	4911.76	0.395813
$537$	6627.70	0.532600
$538$	19392.7	1.55405
$539$	14397.0	1.15050
$540$	127.679	0.0101749
$541$	−10024.6	−0.796658	−0.398329	−	0.917243i	$-0.630410\pi$
$541$	−10024.6	−0.796658	−0.398329	+	0.917243i	$0.630410\pi$
$542$	5582.39	0.442406
$543$	5511.99	0.435621
$544$	1757.14	0.138487
$545$	−2410.37	−0.189448
$546$	−69.0983	−0.00541600
$547$	15616.0	1.22065	0.610323	−	0.792153i	$-0.291040\pi$
$547$	15616.0	1.22065	0.610323	+	0.792153i	$0.291040\pi$
$548$	2083.28	0.162397
$549$	−1127.93	−0.0876843
$550$	−14012.5	−1.08636
$551$	1798.93	0.139087
$552$	1644.34	0.126789
$553$	−3441.43	−0.264637
$554$	376.782	0.0288952
$555$	4131.64	0.315997
$556$	1006.46	0.0767685
$557$	9677.64	0.736184	0.368092	−	0.929789i	$-0.380011\pi$
$557$	9677.64	0.736184	0.368092	+	0.929789i	$0.380011\pi$
$558$	−1463.15	−0.111003
$559$	−550.098	−0.0416219
$560$	−1999.21	−0.150861
$561$	−5885.62	−0.442943
$562$	18121.0	1.36012
$563$	2476.25	0.185367	0.0926835	−	0.995696i	$-0.470456\pi$
$563$	2476.25	0.185367	0.0926835	+	0.995696i	$0.470456\pi$
$564$	−589.323	−0.0439982
$565$	−2558.33	−0.190495
$566$	322.219	0.0239291
$567$	637.755	0.0472367
$568$	10573.0	0.781047
$569$	16648.4	1.22660	0.613301	−	0.789849i	$-0.289841\pi$
$569$	16648.4	1.22660	0.613301	+	0.789849i	$0.289841\pi$
$570$	−2278.24	−0.167413
$571$	3895.87	0.285529	0.142764	−	0.989757i	$-0.454401\pi$
$571$	3895.87	0.285529	0.142764	+	0.989757i	$0.454401\pi$
$572$	−57.8924	−0.00423183
$573$	−8641.72	−0.630040
$574$	−9062.11	−0.658963
$575$	2381.11	0.172694
$576$	5036.27	0.364314
$577$	−1542.34	−0.111280	−0.0556400	−	0.998451i	$-0.517720\pi$
$577$	−1542.34	−0.111280	−0.0556400	+	0.998451i	$0.517720\pi$
$578$	9105.64	0.655268
$579$	−10453.6	−0.750322
$580$	137.137	0.00981774
$581$	−2655.30	−0.189605
$582$	4121.41	0.293536
$583$	−232.565	−0.0165212
$584$	3100.99	0.219726
$585$	−46.1804	−0.00326381
$586$	−18782.8	−1.32408
$587$	26568.5	1.86814	0.934071	−	0.357086i	$-0.116230\pi$
$587$	26568.5	1.86814	0.934071	+	0.357086i	$0.116230\pi$
$588$	−860.289	−0.0603362
$589$	−3817.23	−0.267039
$590$	8136.53	0.567755
$591$	−4571.41	−0.318177
$592$	16285.1	1.13059
$593$	1644.37	0.113872	0.0569359	−	0.998378i	$-0.481867\pi$
$593$	1644.37	0.113872	0.0569359	+	0.998378i	$0.481867\pi$
$594$	−3654.51	−0.252435
$595$	−1397.13	−0.0962637
$596$	1043.77	0.0717355
$597$	3379.14	0.231657
$598$	−67.2830	−0.00460101
$599$	−810.589	−0.0552917	−0.0276459	−	0.999618i	$-0.508801\pi$
$599$	−810.589	−0.0552917	−0.0276459	+	0.999618i	$0.508801\pi$
$600$	7401.43	0.503603
$601$	−20157.6	−1.36813	−0.684065	−	0.729422i	$-0.739789\pi$
$601$	−20157.6	−1.36813	−0.684065	+	0.729422i	$0.739789\pi$
$602$	−10333.7	−0.699620
$603$	1854.97	0.125274
$604$	−1650.62	−0.111197
$605$	5995.65	0.402906
$606$	−3533.04	−0.236832
$607$	22223.3	1.48603	0.743013	−	0.669277i	$-0.233396\pi$
$607$	22223.3	1.48603	0.743013	+	0.669277i	$0.233396\pi$
$608$	2846.46	0.189867
$609$	684.996	0.0455787
$610$	1534.27	0.101837
$611$	213.153	0.0141133
$612$	351.694	0.0232294
$613$	−3335.26	−0.219755	−0.109877	−	0.993945i	$-0.535046\pi$
$613$	−3335.26	−0.219755	−0.109877	+	0.993945i	$0.535046\pi$
$614$	−10497.6	−0.689981
$615$	−6056.47	−0.397106
$616$	−9613.11	−0.628772
$617$	−4329.06	−0.282466	−0.141233	−	0.989976i	$-0.545107\pi$
$617$	−4329.06	−0.282466	−0.141233	+	0.989976i	$0.545107\pi$
$618$	−2284.01	−0.148667
$619$	1324.30	0.0859904	0.0429952	−	0.999075i	$-0.486310\pi$
$619$	1324.30	0.0859904	0.0429952	+	0.999075i	$0.486310\pi$
$620$	−290.997	−0.0188495
$621$	621.000	0.0401286
$622$	−25125.4	−1.61967
$623$	3011.79	0.193684
$624$	−182.022	−0.0116775
$625$	8033.56	0.514148
$626$	13314.0	0.850057
$627$	−9534.31	−0.607279
$628$	−1084.57	−0.0689155
$629$	11380.7	0.721427
$630$	−867.511	−0.0548611
$631$	−21579.1	−1.36141	−0.680706	−	0.732556i	$-0.738327\pi$
$631$	−21579.1	−1.36141	−0.680706	+	0.732556i	$0.738327\pi$
$632$	−10416.3	−0.655597
$633$	5359.67	0.336537
$634$	−15673.4	−0.981816
$635$	−10670.4	−0.666840
$636$	13.8969	0.000866426 0
$637$	311.159	0.0193541
$638$	−3925.21	−0.243575
$639$	3993.00	0.247200
$640$	−5149.53	−0.318052
$641$	−3505.12	−0.215981	−0.107991	−	0.994152i	$-0.534442\pi$
$641$	−3505.12	−0.215981	−0.107991	+	0.994152i	$0.534442\pi$
$642$	6478.49	0.398264
$643$	−15407.9	−0.944992	−0.472496	−	0.881333i	$-0.656647\pi$
$643$	−15407.9	−0.944992	−0.472496	+	0.881333i	$0.656647\pi$
$644$	184.800	0.0113077
$645$	−6906.34	−0.421607
$646$	−6275.47	−0.382206
$647$	8194.14	0.497905	0.248953	−	0.968516i	$-0.419914\pi$
$647$	8194.14	0.497905	0.248953	+	0.968516i	$0.419914\pi$
$648$	1930.31	0.117021
$649$	34050.9	2.05950
$650$	−302.851	−0.0182751
$651$	−1453.53	−0.0875087
$652$	−973.584	−0.0584793
$653$	−33016.7	−1.97863	−0.989314	−	0.145802i	$-0.953424\pi$
$653$	−33016.7	−1.97863	−0.989314	+	0.145802i	$0.953424\pi$
$654$	−4122.56	−0.246491
$655$	−6911.73	−0.412311
$656$	−23871.9	−1.42079
$657$	1171.12	0.0695428
$658$	4004.14	0.237230
$659$	11194.7	0.661738	0.330869	−	0.943677i	$-0.392658\pi$
$659$	11194.7	0.661738	0.330869	+	0.943677i	$0.392658\pi$
$660$	−726.825	−0.0428661
$661$	−19916.7	−1.17197	−0.585984	−	0.810322i	$-0.699292\pi$
$661$	−19916.7	−1.17197	−0.585984	+	0.810322i	$0.699292\pi$
$662$	−19662.2	−1.15437
$663$	−127.205	−0.00745133
$664$	−8036.87	−0.469715
$665$	−2263.26	−0.131978
$666$	7066.52	0.411144
$667$	667.000	0.0387202
$668$	−3759.26	−0.217740
$669$	−1062.68	−0.0614132
$670$	−2523.24	−0.145495
$671$	6420.82	0.369408
$672$	1083.88	0.0622194
$673$	−5249.11	−0.300651	−0.150326	−	0.988637i	$-0.548032\pi$
$673$	−5249.11	−0.300651	−0.150326	+	0.988637i	$0.548032\pi$
$674$	−21803.5	−1.24605
$675$	2795.22	0.159390
$676$	2240.74	0.127489
$677$	−23698.4	−1.34536	−0.672678	−	0.739936i	$-0.734856\pi$
$677$	−23698.4	−1.34536	−0.672678	+	0.739936i	$0.734856\pi$
$678$	−4375.61	−0.247853
$679$	4094.31	0.231407
$680$	−4228.75	−0.238478
$681$	6550.12	0.368577
$682$	8329.10	0.467650
$683$	−16541.9	−0.926733	−0.463367	−	0.886167i	$-0.653359\pi$
$683$	−16541.9	−0.926733	−0.463367	+	0.886167i	$0.653359\pi$
$684$	569.721	0.0318477
$685$	−9460.07	−0.527665
$686$	12979.9	0.722413
$687$	−12476.7	−0.692890
$688$	−27221.7	−1.50845
$689$	−5.02638	−0.000277924 0
$690$	−844.720	−0.0466057
$691$	33921.2	1.86747	0.933735	−	0.357965i	$-0.116529\pi$
$691$	33921.2	1.86747	0.933735	+	0.357965i	$0.116529\pi$
$692$	−2758.38	−0.151529
$693$	−3630.48	−0.199005
$694$	−15345.0	−0.839319
$695$	−4570.27	−0.249439
$696$	2073.30	0.112914
$697$	−16682.7	−0.906601
$698$	9054.62	0.491007
$699$	−16763.8	−0.907104
$700$	831.812	0.0449136
$701$	−3338.97	−0.179902	−0.0899508	−	0.995946i	$-0.528671\pi$
$701$	−3338.97	−0.179902	−0.0899508	+	0.995946i	$0.528671\pi$
$702$	−78.9844	−0.00424654
$703$	18435.9	0.989082
$704$	−28669.5	−1.53483
$705$	2676.08	0.142960
$706$	7536.10	0.401735
$707$	−3509.81	−0.186704
$708$	−2034.71	−0.108007
$709$	9889.31	0.523837	0.261919	−	0.965090i	$-0.415645\pi$
$709$	9889.31	0.523837	0.261919	+	0.965090i	$0.415645\pi$
$710$	−5431.51	−0.287100
$711$	−3933.80	−0.207495
$712$	9115.87	0.479820
$713$	−1415.34	−0.0743406
$714$	−2389.58	−0.125249
$715$	262.886	0.0137502
$716$	2254.48	0.117673
$717$	−12404.0	−0.646074
$718$	−18179.7	−0.944931
$719$	−17903.0	−0.928606	−0.464303	−	0.885676i	$-0.653695\pi$
$719$	−17903.0	−0.928606	−0.464303	+	0.885676i	$0.653695\pi$
$720$	−2285.24	−0.118286
$721$	−2268.99	−0.117200
$722$	7954.80	0.410037
$723$	4531.29	0.233085
$724$	1874.96	0.0962462
$725$	3002.27	0.153795
$726$	10254.6	0.524221
$727$	6848.21	0.349362	0.174681	−	0.984625i	$-0.444111\pi$
$727$	6848.21	0.349362	0.174681	+	0.984625i	$0.444111\pi$
$728$	−207.767	−0.0105774
$729$	729.000	0.0370370
$730$	−1593.02	−0.0807675
$731$	−19023.6	−0.962537
$732$	−383.675	−0.0193730
$733$	14410.7	0.726156	0.363078	−	0.931759i	$-0.381726\pi$
$733$	14410.7	0.726156	0.363078	+	0.931759i	$0.381726\pi$
$734$	17746.3	0.892410
$735$	3906.52	0.196047
$736$	1055.40	0.0528567
$737$	−10559.6	−0.527772
$738$	−10358.6	−0.516676
$739$	−25030.7	−1.24596	−0.622982	−	0.782236i	$-0.714079\pi$
$739$	−25030.7	−1.24596	−0.622982	+	0.782236i	$0.714079\pi$
$740$	1405.42	0.0698165
$741$	−206.064	−0.0102158
$742$	−94.4219	−0.00467161
$743$	−10263.5	−0.506771	−0.253386	−	0.967365i	$-0.581544\pi$
$743$	−10263.5	−0.506771	−0.253386	+	0.967365i	$0.581544\pi$
$744$	−4399.43	−0.216789
$745$	−4739.69	−0.233086
$746$	14650.5	0.719025
$747$	−3035.20	−0.148664
$748$	−2002.05	−0.0978640
$749$	6435.90	0.313969
$750$	−8393.09	−0.408630
$751$	−33584.5	−1.63185	−0.815924	−	0.578160i	$-0.803771\pi$
$751$	−33584.5	−1.63185	−0.815924	+	0.578160i	$0.803771\pi$
$752$	10547.9	0.511493
$753$	−6904.32	−0.334140
$754$	−84.8350	−0.00409749
$755$	7495.37	0.361304
$756$	216.939	0.0104365
$757$	16031.3	0.769704	0.384852	−	0.922978i	$-0.374253\pi$
$757$	16031.3	0.769704	0.384852	+	0.922978i	$0.374253\pi$
$758$	34104.0	1.63418
$759$	−3535.10	−0.169059
$760$	−6850.29	−0.326955
$761$	25893.7	1.23344	0.616719	−	0.787184i	$-0.288462\pi$
$761$	25893.7	1.23344	0.616719	+	0.787184i	$0.288462\pi$
$762$	−18250.1	−0.867627
$763$	−4095.45	−0.194319
$764$	−2939.57	−0.139201
$765$	−1597.02	−0.0754778
$766$	−4973.74	−0.234606
$767$	735.936	0.0346455
$768$	4622.61	0.217193
$769$	2858.78	0.134058	0.0670288	−	0.997751i	$-0.478648\pi$
$769$	2858.78	0.134058	0.0670288	+	0.997751i	$0.478648\pi$
$770$	4938.39	0.231126
$771$	7418.30	0.346516
$772$	−3555.90	−0.165777
$773$	38582.1	1.79522	0.897608	−	0.440795i	$-0.145303\pi$
$773$	38582.1	1.79522	0.897608	+	0.440795i	$0.145303\pi$
$774$	−11812.2	−0.548554
$775$	−6370.66	−0.295278
$776$	12392.4	0.573273
$777$	7020.05	0.324122
$778$	−13274.2	−0.611701
$779$	−27024.8	−1.24296
$780$	−15.7087	−0.000721107 0
$781$	−22730.5	−1.04144
$782$	−2326.80	−0.106402
$783$	783.000	0.0357371
$784$	15397.8	0.701428
$785$	4924.96	0.223923
$786$	−11821.4	−0.536458
$787$	19598.1	0.887669	0.443835	−	0.896109i	$-0.353618\pi$
$787$	19598.1	0.887669	0.443835	+	0.896109i	$0.353618\pi$
$788$	−1555.01	−0.0702982
$789$	−13431.1	−0.606032
$790$	5350.98	0.240987
$791$	−4346.84	−0.195393
$792$	−10988.5	−0.493003
$793$	138.772	0.00621431
$794$	11788.0	0.526877
$795$	−63.1049	−0.00281522
$796$	1149.45	0.0511823
$797$	37140.8	1.65068	0.825341	−	0.564635i	$-0.190983\pi$
$797$	37140.8	1.65068	0.825341	+	0.564635i	$0.190983\pi$
$798$	−3870.96	−0.171717
$799$	7371.32	0.326381
$800$	4750.52	0.209945
$801$	3442.69	0.151862
$802$	−13062.9	−0.575146
$803$	−6666.69	−0.292979
$804$	630.988	0.0276781
$805$	−839.166	−0.0367412
$806$	180.015	0.00786696
$807$	22021.5	0.960588
$808$	−10623.2	−0.462530
$809$	−8093.43	−0.351730	−0.175865	−	0.984414i	$-0.556272\pi$
$809$	−8093.43	−0.351730	−0.175865	+	0.984414i	$0.556272\pi$
$810$	−991.628	−0.0430151
$811$	9521.66	0.412270	0.206135	−	0.978524i	$-0.433911\pi$
$811$	9521.66	0.412270	0.206135	+	0.978524i	$0.433911\pi$
$812$	233.008	0.0100702
$813$	6339.12	0.273459
$814$	−40226.8	−1.73212
$815$	4420.99	0.190013
$816$	−6294.75	−0.270049
$817$	−30817.0	−1.31965
$818$	−14126.3	−0.603808
$819$	−78.4650	−0.00334773
$820$	−2060.17	−0.0877369
$821$	−8206.99	−0.348875	−0.174437	−	0.984668i	$-0.555811\pi$
$821$	−8206.99	−0.348875	−0.174437	+	0.984668i	$0.555811\pi$
$822$	−16180.0	−0.686546
$823$	10666.4	0.451772	0.225886	−	0.974154i	$-0.427472\pi$
$823$	10666.4	0.451772	0.225886	+	0.974154i	$0.427472\pi$
$824$	−6867.61	−0.290345
$825$	−15912.0	−0.671498
$826$	13824.7	0.582354
$827$	−11054.3	−0.464805	−0.232403	−	0.972620i	$-0.574659\pi$
$827$	−11054.3	−0.464805	−0.232403	+	0.972620i	$0.574659\pi$
$828$	211.239	0.00886604
$829$	−22969.4	−0.962315	−0.481157	−	0.876634i	$-0.659783\pi$
$829$	−22969.4	−0.962315	−0.481157	+	0.876634i	$0.659783\pi$
$830$	4128.65	0.172660
$831$	427.857	0.0178606
$832$	−619.628	−0.0258194
$833$	10760.6	0.447578
$834$	−7816.72	−0.324546
$835$	17070.6	0.707487
$836$	−3243.19	−0.134172
$837$	−1661.48	−0.0686133
$838$	−4983.89	−0.205448
$839$	15348.6	0.631575	0.315787	−	0.948830i	$-0.397731\pi$
$839$	15348.6	0.631575	0.315787	+	0.948830i	$0.397731\pi$
$840$	−2608.46	−0.107143
$841$	841.000	0.0344828
$842$	−27636.7	−1.13114
$843$	20577.5	0.840718
$844$	1823.15	0.0743546
$845$	−10175.1	−0.414241
$846$	4577.02	0.186006
$847$	10187.2	0.413266
$848$	−248.731	−0.0100725
$849$	365.898	0.0147910
$850$	−10473.3	−0.422624
$851$	6835.62	0.275349
$852$	1358.26	0.0546165
$853$	6988.80	0.280530	0.140265	−	0.990114i	$-0.455205\pi$
$853$	6988.80	0.280530	0.140265	+	0.990114i	$0.455205\pi$
$854$	2606.87	0.104456
$855$	−2587.07	−0.103481
$856$	19479.7	0.777807
$857$	−16240.9	−0.647349	−0.323675	−	0.946168i	$-0.604918\pi$
$857$	−16240.9	−0.647349	−0.323675	+	0.946168i	$0.604918\pi$
$858$	449.626	0.0178904
$859$	12841.3	0.510059	0.255029	−	0.966933i	$-0.417915\pi$
$859$	12841.3	0.510059	0.255029	+	0.966933i	$0.417915\pi$
$860$	−2349.26	−0.0931501
$861$	−10290.5	−0.407317
$862$	−40947.8	−1.61797
$863$	−28528.7	−1.12529	−0.562647	−	0.826697i	$-0.690217\pi$
$863$	−28528.7	−1.12529	−0.562647	+	0.826697i	$0.690217\pi$
$864$	1238.95	0.0487846
$865$	12525.6	0.492352
$866$	2329.04	0.0913901
$867$	10340.0	0.405033
$868$	−494.431	−0.0193342
$869$	22393.5	0.874164
$870$	−1065.08	−0.0415054
$871$	−228.223	−0.00887835
$872$	−12395.8	−0.481394
$873$	4680.09	0.181440
$874$	−3769.26	−0.145878
$875$	−8337.90	−0.322140
$876$	398.367	0.0153648
$877$	−25433.6	−0.979282	−0.489641	−	0.871924i	$-0.662872\pi$
$877$	−25433.6	−0.979282	−0.489641	+	0.871924i	$0.662872\pi$
$878$	−15427.8	−0.593009
$879$	−21328.9	−0.818438
$880$	13009.0	0.498332
$881$	−11168.9	−0.427116	−0.213558	−	0.976930i	$-0.568505\pi$
$881$	−11168.9	−0.427116	−0.213558	+	0.976930i	$0.568505\pi$
$882$	6681.49	0.255077
$883$	5752.05	0.219221	0.109610	−	0.993975i	$-0.465040\pi$
$883$	5752.05	0.219221	0.109610	+	0.993975i	$0.465040\pi$
$884$	−43.2701	−0.00164630
$885$	9239.48	0.350940
$886$	10961.4	0.415639
$887$	−41477.0	−1.57008	−0.785040	−	0.619445i	$-0.787358\pi$
$887$	−41477.0	−1.57008	−0.785040	+	0.619445i	$0.787358\pi$
$888$	21247.8	0.802961
$889$	−18130.1	−0.683987
$890$	−4682.95	−0.176374
$891$	−4149.90	−0.156035
$892$	−361.480	−0.0135687
$893$	11941.0	0.447471
$894$	−8106.49	−0.303268
$895$	−10237.5	−0.382347
$896$	−8749.54	−0.326230
$897$	−76.4036	−0.00284397
$898$	1466.37	0.0544915
$899$	−1784.56	−0.0662050
$900$	950.821	0.0352156
$901$	−173.824	−0.00642720
$902$	58967.5	2.17672
$903$	−11734.5	−0.432448
$904$	−13156.7	−0.484055
$905$	−8514.08	−0.312727
$906$	12819.7	0.470093
$907$	−21306.9	−0.780027	−0.390013	−	0.920809i	$-0.627530\pi$
$907$	−21306.9	−0.780027	−0.390013	+	0.920809i	$0.627530\pi$
$908$	2228.09	0.0814337
$909$	−4011.97	−0.146390
$910$	106.733	0.00388808
$911$	22161.5	0.805976	0.402988	−	0.915205i	$-0.367972\pi$
$911$	22161.5	0.805976	0.402988	+	0.915205i	$0.367972\pi$
$912$	−10197.1	−0.370240
$913$	17278.1	0.626312
$914$	6299.16	0.227963
$915$	1742.25	0.0629475
$916$	−4244.07	−0.153087
$917$	−11743.7	−0.422913
$918$	−2731.46	−0.0982043
$919$	39713.1	1.42548	0.712738	−	0.701430i	$-0.247455\pi$
$919$	39713.1	1.42548	0.712738	+	0.701430i	$0.247455\pi$
$920$	−2539.93	−0.0910206
$921$	−11920.6	−0.426490
$922$	−38934.7	−1.39072
$923$	−491.272	−0.0175194
$924$	−1234.94	−0.0439683
$925$	30768.2	1.09368
$926$	28987.7	1.02872
$927$	−2593.62	−0.0918938
$928$	1330.72	0.0470723
$929$	40094.2	1.41598	0.707991	−	0.706221i	$-0.249602\pi$
$929$	40094.2	1.41598	0.707991	+	0.706221i	$0.249602\pi$
$930$	2260.05	0.0796880
$931$	17431.5	0.613633
$932$	−5702.38	−0.200416
$933$	−28531.3	−1.00115
$934$	−22331.0	−0.782327
$935$	9091.21	0.317983
$936$	−237.492	−0.00829346
$937$	23796.7	0.829673	0.414837	−	0.909896i	$-0.363839\pi$
$937$	23796.7	0.829673	0.414837	+	0.909896i	$0.363839\pi$
$938$	−4287.23	−0.149236
$939$	15118.8	0.525436
$940$	910.296	0.0315857
$941$	−22775.7	−0.789020	−0.394510	−	0.918892i	$-0.629086\pi$
$941$	−22775.7	−0.789020	−0.394510	+	0.918892i	$0.629086\pi$
$942$	8423.37	0.291346
$943$	−10020.2	−0.346025
$944$	36417.9	1.25562
$945$	−985.108	−0.0339106
$946$	67242.0	2.31102
$947$	30471.5	1.04561	0.522804	−	0.852453i	$-0.324886\pi$
$947$	30471.5	1.04561	0.522804	+	0.852453i	$0.324886\pi$
$948$	−1338.12	−0.0458441
$949$	−144.086	−0.00492859
$950$	−16966.0	−0.579421
$951$	−17798.1	−0.606878
$952$	−7185.05	−0.244610
$953$	9248.97	0.314379	0.157190	−	0.987568i	$-0.449757\pi$
$953$	9248.97	0.314379	0.157190	+	0.987568i	$0.449757\pi$
$954$	−107.931	−0.00366289
$955$	13348.4	0.452298
$956$	−4219.34	−0.142744
$957$	−4457.30	−0.150558
$958$	−17247.0	−0.581656
$959$	−16073.6	−0.541233
$960$	−7779.27	−0.261536
$961$	−26004.3	−0.872890
$962$	−869.416	−0.0291383
$963$	7356.69	0.246175
$964$	1541.36	0.0514979
$965$	16147.1	0.538647
$966$	−1435.26	−0.0478041
$967$	−5444.95	−0.181073	−0.0905366	−	0.995893i	$-0.528858\pi$
$967$	−5444.95	−0.181073	−0.0905366	+	0.995893i	$0.528858\pi$
$968$	30833.9	1.02380
$969$	−7126.15	−0.236249
$970$	−6366.13	−0.210726
$971$	−16449.4	−0.543653	−0.271826	−	0.962346i	$-0.587628\pi$
$971$	−16449.4	−0.543653	−0.271826	+	0.962346i	$0.587628\pi$
$972$	247.977	0.00818298
$973$	−7765.33	−0.255853
$974$	−24374.4	−0.801853
$975$	−343.904	−0.0112962
$976$	6867.16	0.225218
$977$	14447.4	0.473095	0.236548	−	0.971620i	$-0.423984\pi$
$977$	14447.4	0.473095	0.236548	+	0.971620i	$0.423984\pi$
$978$	7561.41	0.247226
$979$	−19597.9	−0.639786
$980$	1328.84	0.0433146
$981$	−4681.40	−0.152360
$982$	−19636.4	−0.638108
$983$	14310.3	0.464321	0.232161	−	0.972677i	$-0.425420\pi$
$983$	14310.3	0.464321	0.232161	+	0.972677i	$0.425420\pi$
$984$	−31146.6	−1.00906
$985$	7061.22	0.228415
$986$	−2933.79	−0.0947575
$987$	4546.92	0.146636
$988$	−70.0946	−0.00225709
$989$	−11426.2	−0.367374
$990$	5644.93	0.181220
$991$	−25381.6	−0.813596	−0.406798	−	0.913518i	$-0.633355\pi$
$991$	−25381.6	−0.813596	−0.406798	+	0.913518i	$0.633355\pi$
$992$	−2823.72	−0.0903762
$993$	−22327.5	−0.713536
$994$	−9228.67	−0.294482
$995$	−5219.58	−0.166303
$996$	−1032.45	−0.0328459
$997$	34318.0	1.09013	0.545066	−	0.838393i	$-0.316505\pi$
$997$	34318.0	1.09013	0.545066	+	0.838393i	$0.316505\pi$
$998$	4101.52	0.130091
$999$	8024.42	0.254136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.d.1.11	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.d.1.11	✓	37	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)

\(f(q)\)	\(=\)	\(q-2.64188 q^{2} -3.00000 q^{3} -1.02048 q^{4} +4.63395 q^{5} +7.92563 q^{6} +7.87352 q^{7} +23.8310 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.64188 q^{2} -3.00000 q^{3} -1.02048 q^{4} +4.63395 q^{5} +7.92563 q^{6} +7.87352 q^{7} +23.8310 q^{8} +9.00000 q^{9} -12.2423 q^{10} -51.2333 q^{11} +3.06144 q^{12} -1.10730 q^{13} -20.8009 q^{14} -13.9018 q^{15} -54.7948 q^{16} -38.2929 q^{17} -23.7769 q^{18} -62.0319 q^{19} -4.72885 q^{20} -23.6206 q^{21} +135.352 q^{22} -23.0000 q^{23} -71.4930 q^{24} -103.527 q^{25} +2.92535 q^{26} -27.0000 q^{27} -8.03477 q^{28} -29.0000 q^{29} +36.7270 q^{30} +61.5365 q^{31} -45.8870 q^{32} +153.700 q^{33} +101.165 q^{34} +36.4855 q^{35} -9.18432 q^{36} -297.201 q^{37} +163.881 q^{38} +3.32189 q^{39} +110.432 q^{40} +435.660 q^{41} +62.4026 q^{42} +496.793 q^{43} +52.2826 q^{44} +41.7055 q^{45} +60.7632 q^{46} -192.498 q^{47} +164.384 q^{48} -281.008 q^{49} +273.505 q^{50} +114.879 q^{51} +1.12998 q^{52} +4.53932 q^{53} +71.3307 q^{54} -237.413 q^{55} +187.634 q^{56} +186.096 q^{57} +76.6145 q^{58} -664.623 q^{59} +14.1866 q^{60} -125.325 q^{61} -162.572 q^{62} +70.8617 q^{63} +559.586 q^{64} -5.13116 q^{65} -406.057 q^{66} +206.108 q^{67} +39.0772 q^{68} +69.0000 q^{69} -96.3901 q^{70} +443.667 q^{71} +214.479 q^{72} +130.124 q^{73} +785.168 q^{74} +310.580 q^{75} +63.3024 q^{76} -403.387 q^{77} -8.77604 q^{78} -437.089 q^{79} -253.916 q^{80} +81.0000 q^{81} -1150.96 q^{82} -337.244 q^{83} +24.1043 q^{84} -177.447 q^{85} -1312.47 q^{86} +87.0000 q^{87} -1220.94 q^{88} +382.521 q^{89} -110.181 q^{90} -8.71833 q^{91} +23.4711 q^{92} -184.609 q^{93} +508.557 q^{94} -287.453 q^{95} +137.661 q^{96} +520.010 q^{97} +742.388 q^{98} -461.100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * q^99

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