LMFDB - Embedded newform 1045.4.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.12095 q^{2} -6.27512 q^{3} +8.98226 q^{4} +5.00000 q^{5} -25.8595 q^{6} -21.3904 q^{7} +4.04785 q^{8} +12.3772 q^{9} +O(q^{10})$	\(q+4.12095 q^{2} -6.27512 q^{3} +8.98226 q^{4} +5.00000 q^{5} -25.8595 q^{6} -21.3904 q^{7} +4.04785 q^{8} +12.3772 q^{9} +20.6048 q^{10} +11.0000 q^{11} -56.3648 q^{12} -33.2266 q^{13} -88.1490 q^{14} -31.3756 q^{15} -55.1771 q^{16} +29.7879 q^{17} +51.0058 q^{18} -19.0000 q^{19} +44.9113 q^{20} +134.228 q^{21} +45.3305 q^{22} +163.548 q^{23} -25.4007 q^{24} +25.0000 q^{25} -136.925 q^{26} +91.7600 q^{27} -192.134 q^{28} -12.1113 q^{29} -129.297 q^{30} -111.585 q^{31} -259.765 q^{32} -69.0264 q^{33} +122.755 q^{34} -106.952 q^{35} +111.175 q^{36} +22.3558 q^{37} -78.2981 q^{38} +208.501 q^{39} +20.2392 q^{40} +374.260 q^{41} +553.146 q^{42} +233.047 q^{43} +98.8049 q^{44} +61.8859 q^{45} +673.974 q^{46} +137.712 q^{47} +346.243 q^{48} +114.550 q^{49} +103.024 q^{50} -186.923 q^{51} -298.450 q^{52} -26.5800 q^{53} +378.139 q^{54} +55.0000 q^{55} -86.5851 q^{56} +119.227 q^{57} -49.9101 q^{58} +143.308 q^{59} -281.824 q^{60} +547.037 q^{61} -459.836 q^{62} -264.753 q^{63} -629.063 q^{64} -166.133 q^{65} -284.454 q^{66} -70.0120 q^{67} +267.563 q^{68} -1026.28 q^{69} -440.745 q^{70} +649.386 q^{71} +50.1009 q^{72} -160.329 q^{73} +92.1272 q^{74} -156.878 q^{75} -170.663 q^{76} -235.295 q^{77} +859.223 q^{78} +75.2460 q^{79} -275.885 q^{80} -909.989 q^{81} +1542.31 q^{82} -149.088 q^{83} +1205.67 q^{84} +148.940 q^{85} +960.376 q^{86} +75.9999 q^{87} +44.5263 q^{88} -416.755 q^{89} +255.029 q^{90} +710.731 q^{91} +1469.03 q^{92} +700.209 q^{93} +567.504 q^{94} -95.0000 q^{95} +1630.06 q^{96} +1529.53 q^{97} +472.057 q^{98} +136.149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * 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 $

$2$	4.12095	1.45698	0.728489	−	0.685058i	$-0.240223\pi$
$2$	4.12095	1.45698	0.728489	+	0.685058i	$0.240223\pi$
$3$	−6.27512	−1.20765	−0.603824	−	0.797118i	$-0.706357\pi$
$3$	−6.27512	−1.20765	−0.603824	+	0.797118i	$0.706357\pi$
$4$	8.98226	1.12278
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−25.8595	−1.75952
$7$	−21.3904	−1.15497	−0.577487	−	0.816400i	$-0.695967\pi$
$7$	−21.3904	−1.15497	−0.577487	+	0.816400i	$0.695967\pi$
$8$	4.04785	0.178891
$9$	12.3772	0.458414
$10$	20.6048	0.651580
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−56.3648	−1.35593
$13$	−33.2266	−0.708877	−0.354438	−	0.935079i	$-0.615328\pi$
$13$	−33.2266	−0.708877	−0.354438	+	0.935079i	$0.615328\pi$
$14$	−88.1490	−1.68277
$15$	−31.3756	−0.540077
$16$	−55.1771	−0.862142
$17$	29.7879	0.424978	0.212489	−	0.977163i	$-0.431843\pi$
$17$	29.7879	0.424978	0.212489	+	0.977163i	$0.431843\pi$
$18$	51.0058	0.667899
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	44.9113	0.502124
$21$	134.228	1.39480
$22$	45.3305	0.439295
$23$	163.548	1.48270	0.741350	−	0.671118i	$-0.234186\pi$
$23$	163.548	1.48270	0.741350	+	0.671118i	$0.234186\pi$
$24$	−25.4007	−0.216038
$25$	25.0000	0.200000
$26$	−136.925	−1.03282
$27$	91.7600	0.654045
$28$	−192.134	−1.29679
$29$	−12.1113	−0.0775521	−0.0387760	−	0.999248i	$-0.512346\pi$
$29$	−12.1113	−0.0775521	−0.0387760	+	0.999248i	$0.512346\pi$
$30$	−129.297	−0.786879
$31$	−111.585	−0.646491	−0.323246	−	0.946315i	$-0.604774\pi$
$31$	−111.585	−0.646491	−0.323246	+	0.946315i	$0.604774\pi$
$32$	−259.765	−1.43501
$33$	−69.0264	−0.364120
$34$	122.755	0.619184
$35$	−106.952	−0.516520
$36$	111.175	0.514699
$37$	22.3558	0.0993317	0.0496658	−	0.998766i	$-0.484184\pi$
$37$	22.3558	0.0993317	0.0496658	+	0.998766i	$0.484184\pi$
$38$	−78.2981	−0.334253
$39$	208.501	0.856074
$40$	20.2392	0.0800026
$41$	374.260	1.42560	0.712800	−	0.701368i	$-0.247427\pi$
$41$	374.260	1.42560	0.712800	+	0.701368i	$0.247427\pi$
$42$	553.146	2.03220
$43$	233.047	0.826497	0.413248	−	0.910618i	$-0.364394\pi$
$43$	233.047	0.826497	0.413248	+	0.910618i	$0.364394\pi$
$44$	98.8049	0.338532
$45$	61.8859	0.205009
$46$	673.974	2.16026
$47$	137.712	0.427390	0.213695	−	0.976900i	$-0.431450\pi$
$47$	137.712	0.427390	0.213695	+	0.976900i	$0.431450\pi$
$48$	346.243	1.04116
$49$	114.550	0.333966
$50$	103.024	0.291395
$51$	−186.923	−0.513224
$52$	−298.450	−0.795915
$53$	−26.5800	−0.0688876	−0.0344438	−	0.999407i	$-0.510966\pi$
$53$	−26.5800	−0.0688876	−0.0344438	+	0.999407i	$0.510966\pi$
$54$	378.139	0.952929
$55$	55.0000	0.134840
$56$	−86.5851	−0.206615
$57$	119.227	0.277053
$58$	−49.9101	−0.112992
$59$	143.308	0.316222	0.158111	−	0.987421i	$-0.449460\pi$
$59$	143.308	0.316222	0.158111	+	0.987421i	$0.449460\pi$
$60$	−281.824	−0.606389
$61$	547.037	1.14821	0.574105	−	0.818781i	$-0.305350\pi$
$61$	547.037	1.14821	0.574105	+	0.818781i	$0.305350\pi$
$62$	−459.836	−0.941923
$63$	−264.753	−0.529457
$64$	−629.063	−1.22864
$65$	−166.133	−0.317019
$66$	−284.454	−0.530514
$67$	−70.0120	−0.127662	−0.0638308	−	0.997961i	$-0.520332\pi$
$67$	−70.0120	−0.127662	−0.0638308	+	0.997961i	$0.520332\pi$
$68$	267.563	0.477158
$69$	−1026.28	−1.79058
$70$	−440.745	−0.752558
$71$	649.386	1.08546	0.542732	−	0.839906i	$-0.317390\pi$
$71$	649.386	1.08546	0.542732	+	0.839906i	$0.317390\pi$
$72$	50.1009	0.0820062
$73$	−160.329	−0.257056	−0.128528	−	0.991706i	$-0.541025\pi$
$73$	−160.329	−0.257056	−0.128528	+	0.991706i	$0.541025\pi$
$74$	92.1272	0.144724
$75$	−156.878	−0.241530
$76$	−170.663	−0.257584
$77$	−235.295	−0.348238
$78$	859.223	1.24728
$79$	75.2460	0.107162	0.0535812	−	0.998563i	$-0.482936\pi$
$79$	75.2460	0.107162	0.0535812	+	0.998563i	$0.482936\pi$
$80$	−275.885	−0.385562
$81$	−909.989	−1.24827
$82$	1542.31	2.07707
$83$	−149.088	−0.197163	−0.0985817	−	0.995129i	$-0.531431\pi$
$83$	−149.088	−0.197163	−0.0985817	+	0.995129i	$0.531431\pi$
$84$	1205.67	1.56606
$85$	148.940	0.190056
$86$	960.376	1.20419
$87$	75.9999	0.0936556
$88$	44.5263	0.0539377
$89$	−416.755	−0.496359	−0.248179	−	0.968714i	$-0.579832\pi$
$89$	−416.755	−0.496359	−0.248179	+	0.968714i	$0.579832\pi$
$90$	255.029	0.298693
$91$	710.731	0.818735
$92$	1469.03	1.66475
$93$	700.209	0.780734
$94$	567.504	0.622698
$95$	−95.0000	−0.102598
$96$	1630.06	1.73299
$97$	1529.53	1.60104	0.800519	−	0.599307i	$-0.204557\pi$
$97$	1529.53	1.60104	0.800519	+	0.599307i	$0.204557\pi$
$98$	472.057	0.486581
$99$	136.149	0.138217
$100$	224.556	0.224556
$101$	−707.746	−0.697261	−0.348630	−	0.937260i	$-0.613353\pi$
$101$	−707.746	−0.697261	−0.348630	+	0.937260i	$0.613353\pi$
$102$	−770.301	−0.747756
$103$	1393.03	1.33262	0.666309	−	0.745676i	$-0.267873\pi$
$103$	1393.03	1.33262	0.666309	+	0.745676i	$0.267873\pi$
$104$	−134.496	−0.126812
$105$	671.138	0.623775
$106$	−109.535	−0.100368
$107$	2083.63	1.88254	0.941270	−	0.337654i	$-0.109633\pi$
$107$	2083.63	1.88254	0.941270	+	0.337654i	$0.109633\pi$
$108$	824.212	0.734350
$109$	232.826	0.204594	0.102297	−	0.994754i	$-0.467381\pi$
$109$	232.826	0.204594	0.102297	+	0.994754i	$0.467381\pi$
$110$	226.652	0.196459
$111$	−140.285	−0.119958
$112$	1180.26	0.995752
$113$	−1704.67	−1.41913	−0.709565	−	0.704640i	$-0.751109\pi$
$113$	−1704.67	−1.41913	−0.709565	+	0.704640i	$0.751109\pi$
$114$	491.330	0.403661
$115$	817.740	0.663084
$116$	−108.787	−0.0870741
$117$	−411.252	−0.324959
$118$	590.566	0.460729
$119$	−637.176	−0.490839
$120$	−127.004	−0.0966150
$121$	121.000	0.0909091
$122$	2254.31	1.67292
$123$	−2348.53	−1.72162
$124$	−1002.28	−0.725869
$125$	125.000	0.0894427
$126$	−1091.04	−0.771406
$127$	−916.745	−0.640535	−0.320267	−	0.947327i	$-0.603773\pi$
$127$	−916.745	−0.640535	−0.320267	+	0.947327i	$0.603773\pi$
$128$	−514.219	−0.355085
$129$	−1462.40	−0.998117
$130$	−684.626	−0.461890
$131$	55.0190	0.0366949	0.0183474	−	0.999832i	$-0.494160\pi$
$131$	55.0190	0.0366949	0.0183474	+	0.999832i	$0.494160\pi$
$132$	−620.013	−0.408827
$133$	406.418	0.264969
$134$	−288.516	−0.186000
$135$	458.800	0.292498
$136$	120.577	0.0760249
$137$	2266.78	1.41360	0.706802	−	0.707411i	$-0.250137\pi$
$137$	2266.78	1.41360	0.706802	+	0.707411i	$0.250137\pi$
$138$	−4229.27	−2.60884
$139$	685.685	0.418411	0.209205	−	0.977872i	$-0.432912\pi$
$139$	685.685	0.418411	0.209205	+	0.977872i	$0.432912\pi$
$140$	−960.672	−0.579940
$141$	−864.159	−0.516137
$142$	2676.09	1.58150
$143$	−365.493	−0.213734
$144$	−682.937	−0.395218
$145$	−60.5565	−0.0346823
$146$	−660.709	−0.374525
$147$	−718.818	−0.403314
$148$	200.806	0.111528
$149$	−43.4062	−0.0238656	−0.0119328	−	0.999929i	$-0.503798\pi$
$149$	−43.4062	−0.0238656	−0.0119328	+	0.999929i	$0.503798\pi$
$150$	−646.487	−0.351903
$151$	−391.726	−0.211114	−0.105557	−	0.994413i	$-0.533663\pi$
$151$	−391.726	−0.211114	−0.105557	+	0.994413i	$0.533663\pi$
$152$	−76.9091	−0.0410405
$153$	368.690	0.194816
$154$	−969.639	−0.507375
$155$	−557.924	−0.289120
$156$	1872.81	0.961185
$157$	2202.89	1.11981	0.559905	−	0.828557i	$-0.310838\pi$
$157$	2202.89	1.11981	0.559905	+	0.828557i	$0.310838\pi$
$158$	310.085	0.156133
$159$	166.793	0.0831920
$160$	−1298.83	−0.641757
$161$	−3498.36	−1.71248
$162$	−3750.02	−1.81870
$163$	634.108	0.304707	0.152353	−	0.988326i	$-0.451315\pi$
$163$	634.108	0.304707	0.152353	+	0.988326i	$0.451315\pi$
$164$	3361.70	1.60064
$165$	−345.132	−0.162839
$166$	−614.386	−0.287263
$167$	2379.41	1.10254	0.551271	−	0.834326i	$-0.314143\pi$
$167$	2379.41	1.10254	0.551271	+	0.834326i	$0.314143\pi$
$168$	543.333	0.249518
$169$	−1092.99	−0.497493
$170$	613.773	0.276907
$171$	−235.166	−0.105167
$172$	2093.29	0.927976
$173$	−1823.44	−0.801350	−0.400675	−	0.916220i	$-0.631224\pi$
$173$	−1823.44	−0.801350	−0.400675	+	0.916220i	$0.631224\pi$
$174$	313.192	0.136454
$175$	−534.761	−0.230995
$176$	−606.948	−0.259946
$177$	−899.275	−0.381885
$178$	−1717.43	−0.723183
$179$	177.361	0.0740592	0.0370296	−	0.999314i	$-0.488210\pi$
$179$	177.361	0.0740592	0.0370296	+	0.999314i	$0.488210\pi$
$180$	555.875	0.230181
$181$	3587.68	1.47332	0.736659	−	0.676265i	$-0.236402\pi$
$181$	3587.68	1.47332	0.736659	+	0.676265i	$0.236402\pi$
$182$	2928.89	1.19288
$183$	−3432.72	−1.38663
$184$	662.017	0.265242
$185$	111.779	0.0444225
$186$	2885.53	1.13751
$187$	327.667	0.128136
$188$	1236.96	0.479866
$189$	−1962.79	−0.755406
$190$	−391.491	−0.149483
$191$	−3157.56	−1.19619	−0.598097	−	0.801424i	$-0.704076\pi$
$191$	−3157.56	−1.19619	−0.598097	+	0.801424i	$0.704076\pi$
$192$	3947.45	1.48376
$193$	−354.764	−0.132313	−0.0661567	−	0.997809i	$-0.521074\pi$
$193$	−354.764	−0.132313	−0.0661567	+	0.997809i	$0.521074\pi$
$194$	6303.14	2.33268
$195$	1042.51	0.382848
$196$	1028.92	0.374971
$197$	−409.846	−0.148225	−0.0741125	−	0.997250i	$-0.523612\pi$
$197$	−409.846	−0.148225	−0.0741125	+	0.997250i	$0.523612\pi$
$198$	561.064	0.201379
$199$	−3382.43	−1.20490	−0.602448	−	0.798158i	$-0.705808\pi$
$199$	−3382.43	−1.20490	−0.602448	+	0.798158i	$0.705808\pi$
$200$	101.196	0.0357782
$201$	439.334	0.154170
$202$	−2916.59	−1.01589
$203$	259.066	0.0895707
$204$	−1678.99	−0.576239
$205$	1871.30	0.637548
$206$	5740.63	1.94159
$207$	2024.26	0.679691
$208$	1833.35	0.611153
$209$	−209.000	−0.0691714
$210$	2765.73	0.908826
$211$	−869.072	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$211$	−869.072	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$212$	−238.748	−0.0773458
$213$	−4074.98	−1.31086
$214$	8586.53	2.74282
$215$	1165.24	0.369621
$216$	371.430	0.117003
$217$	2386.85	0.746681
$218$	959.467	0.298088
$219$	1006.09	0.310434
$220$	494.024	0.151396
$221$	−989.751	−0.301257
$222$	−578.110	−0.174776
$223$	3203.60	0.962014	0.481007	−	0.876717i	$-0.340271\pi$
$223$	3203.60	0.962014	0.481007	+	0.876717i	$0.340271\pi$
$224$	5556.48	1.65740
$225$	309.430	0.0916828
$226$	−7024.86	−2.06764
$227$	2650.47	0.774970	0.387485	−	0.921876i	$-0.373344\pi$
$227$	2650.47	0.774970	0.387485	+	0.921876i	$0.373344\pi$
$228$	1070.93	0.311071
$229$	−2621.88	−0.756587	−0.378293	−	0.925686i	$-0.623489\pi$
$229$	−2621.88	−0.756587	−0.378293	+	0.925686i	$0.623489\pi$
$230$	3369.87	0.966098
$231$	1476.50	0.420549
$232$	−49.0246	−0.0138734
$233$	−5170.06	−1.45366	−0.726828	−	0.686820i	$-0.759006\pi$
$233$	−5170.06	−1.45366	−0.726828	+	0.686820i	$0.759006\pi$
$234$	−1694.75	−0.473458
$235$	688.559	0.191135
$236$	1287.23	0.355049
$237$	−472.178	−0.129415
$238$	−2625.77	−0.715141
$239$	6069.57	1.64271	0.821355	−	0.570417i	$-0.193218\pi$
$239$	6069.57	1.64271	0.821355	+	0.570417i	$0.193218\pi$
$240$	1731.22	0.465623
$241$	−490.444	−0.131088	−0.0655441	−	0.997850i	$-0.520878\pi$
$241$	−490.444	−0.131088	−0.0655441	+	0.997850i	$0.520878\pi$
$242$	498.635	0.132452
$243$	3232.78	0.853427
$244$	4913.62	1.28919
$245$	572.752	0.149354
$246$	−9678.17	−2.50836
$247$	631.305	0.162628
$248$	−451.678	−0.115652
$249$	935.547	0.238104
$250$	515.119	0.130316
$251$	−5155.11	−1.29637	−0.648183	−	0.761484i	$-0.724471\pi$
$251$	−5155.11	−1.29637	−0.648183	+	0.761484i	$0.724471\pi$
$252$	−2378.08	−0.594465
$253$	1799.03	0.447051
$254$	−3777.86	−0.933245
$255$	−934.614	−0.229521
$256$	2913.43	0.711287
$257$	−5333.76	−1.29459	−0.647297	−	0.762238i	$-0.724101\pi$
$257$	−5333.76	−1.29459	−0.647297	+	0.762238i	$0.724101\pi$
$258$	−6026.48	−1.45423
$259$	−478.200	−0.114726
$260$	−1492.25	−0.355944
$261$	−149.904	−0.0355510
$262$	226.731	0.0534636
$263$	2294.39	0.537939	0.268969	−	0.963149i	$-0.413317\pi$
$263$	2294.39	0.537939	0.268969	+	0.963149i	$0.413317\pi$
$264$	−279.408	−0.0651378
$265$	−132.900	−0.0308075
$266$	1674.83	0.386054
$267$	2615.19	0.599426
$268$	−628.866	−0.143336
$269$	4249.11	0.963096	0.481548	−	0.876420i	$-0.340075\pi$
$269$	4249.11	0.963096	0.481548	+	0.876420i	$0.340075\pi$
$270$	1890.69	0.426163
$271$	−632.742	−0.141832	−0.0709158	−	0.997482i	$-0.522592\pi$
$271$	−632.742	−0.141832	−0.0709158	+	0.997482i	$0.522592\pi$
$272$	−1643.61	−0.366392
$273$	−4459.93	−0.988744
$274$	9341.28	2.05959
$275$	275.000	0.0603023
$276$	−9218.35	−2.01043
$277$	2404.17	0.521490	0.260745	−	0.965408i	$-0.416032\pi$
$277$	2404.17	0.521490	0.260745	+	0.965408i	$0.416032\pi$
$278$	2825.68	0.609615
$279$	−1381.11	−0.296361
$280$	−432.926	−0.0924009
$281$	3720.63	0.789873	0.394937	−	0.918708i	$-0.370767\pi$
$281$	3720.63	0.789873	0.394937	+	0.918708i	$0.370767\pi$
$282$	−3561.16	−0.752000
$283$	4361.20	0.916065	0.458033	−	0.888935i	$-0.348554\pi$
$283$	4361.20	0.916065	0.458033	+	0.888935i	$0.348554\pi$
$284$	5832.96	1.21874
$285$	596.137	0.123902
$286$	−1506.18	−0.311406
$287$	−8005.58	−1.64653
$288$	−3215.16	−0.657830
$289$	−4025.68	−0.819393
$290$	−249.550	−0.0505314
$291$	−9598.02	−1.93349
$292$	−1440.12	−0.288618
$293$	−7952.97	−1.58572	−0.792862	−	0.609401i	$-0.791410\pi$
$293$	−7952.97	−1.58572	−0.792862	+	0.609401i	$0.791410\pi$
$294$	−2962.22	−0.587619
$295$	716.540	0.141419
$296$	90.4928	0.0177696
$297$	1009.36	0.197202
$298$	−178.875	−0.0347716
$299$	−5434.14	−1.05105
$300$	−1409.12	−0.271185
$301$	−4984.98	−0.954583
$302$	−1614.29	−0.307589
$303$	4441.19	0.842046
$304$	1048.36	0.197789
$305$	2735.18	0.513495
$306$	1519.36	0.283843
$307$	6684.04	1.24260	0.621300	−	0.783573i	$-0.286605\pi$
$307$	6684.04	1.24260	0.621300	+	0.783573i	$0.286605\pi$
$308$	−2113.48	−0.390995
$309$	−8741.46	−1.60933
$310$	−2299.18	−0.421241
$311$	−8900.35	−1.62281	−0.811403	−	0.584488i	$-0.801296\pi$
$311$	−8900.35	−1.62281	−0.811403	+	0.584488i	$0.801296\pi$
$312$	843.980	0.153144
$313$	14.5204	0.00262217	0.00131109	−	0.999999i	$-0.499583\pi$
$313$	14.5204	0.00262217	0.00131109	+	0.999999i	$0.499583\pi$
$314$	9078.02	1.63154
$315$	−1323.77	−0.236780
$316$	675.879	0.120320
$317$	−6827.28	−1.20965	−0.604824	−	0.796359i	$-0.706756\pi$
$317$	−6827.28	−1.20965	−0.604824	+	0.796359i	$0.706756\pi$
$318$	687.345	0.121209
$319$	−133.224	−0.0233828
$320$	−3145.31	−0.549464
$321$	−13075.0	−2.27345
$322$	−14416.6	−2.49505
$323$	−565.970	−0.0974967
$324$	−8173.76	−1.40154
$325$	−830.665	−0.141775
$326$	2613.13	0.443951
$327$	−1461.01	−0.247077
$328$	1514.95	0.255027
$329$	−2945.72	−0.493625
$330$	−1422.27	−0.237253
$331$	−8747.88	−1.45265	−0.726325	−	0.687351i	$-0.758773\pi$
$331$	−8747.88	−1.45265	−0.726325	+	0.687351i	$0.758773\pi$
$332$	−1339.15	−0.221372
$333$	276.702	0.0455350
$334$	9805.44	1.60638
$335$	−350.060	−0.0570920
$336$	−7406.29	−1.20252
$337$	1759.66	0.284436	0.142218	−	0.989835i	$-0.454577\pi$
$337$	1759.66	0.284436	0.142218	+	0.989835i	$0.454577\pi$
$338$	−4504.17	−0.724837
$339$	10697.0	1.71381
$340$	1337.81	0.213392
$341$	−1227.43	−0.194924
$342$	−969.110	−0.153227
$343$	4886.63	0.769252
$344$	943.339	0.147853
$345$	−5131.42	−0.800772
$346$	−7514.31	−1.16755
$347$	9704.07	1.50127	0.750636	−	0.660715i	$-0.229747\pi$
$347$	9704.07	1.50127	0.750636	+	0.660715i	$0.229747\pi$
$348$	682.650	0.105155
$349$	−5570.62	−0.854409	−0.427204	−	0.904155i	$-0.640502\pi$
$349$	−5570.62	−0.854409	−0.427204	+	0.904155i	$0.640502\pi$
$350$	−2203.72	−0.336554
$351$	−3048.87	−0.463638
$352$	−2857.42	−0.432673
$353$	−7544.01	−1.13747	−0.568735	−	0.822521i	$-0.692567\pi$
$353$	−7544.01	−1.13747	−0.568735	+	0.822521i	$0.692567\pi$
$354$	−3705.87	−0.556398
$355$	3246.93	0.485435
$356$	−3743.40	−0.557303
$357$	3998.36	0.592761
$358$	730.898	0.107903
$359$	−4096.09	−0.602182	−0.301091	−	0.953595i	$-0.597351\pi$
$359$	−4096.09	−0.602182	−0.301091	+	0.953595i	$0.597351\pi$
$360$	250.505	0.0366743
$361$	361.000	0.0526316
$362$	14784.7	2.14659
$363$	−759.290	−0.109786
$364$	6383.97	0.919261
$365$	−801.646	−0.114959
$366$	−14146.1	−2.02030
$367$	1527.90	0.217318	0.108659	−	0.994079i	$-0.465344\pi$
$367$	1527.90	0.217318	0.108659	+	0.994079i	$0.465344\pi$
$368$	−9024.10	−1.27830
$369$	4632.28	0.653515
$370$	460.636	0.0647225
$371$	568.557	0.0795634
$372$	6289.46	0.876595
$373$	4587.48	0.636811	0.318406	−	0.947955i	$-0.396853\pi$
$373$	4587.48	0.636811	0.318406	+	0.947955i	$0.396853\pi$
$374$	1350.30	0.186691
$375$	−784.391	−0.108015
$376$	557.436	0.0764564
$377$	402.417	0.0549749
$378$	−8088.55	−1.10061
$379$	−7319.07	−0.991967	−0.495983	−	0.868332i	$-0.665192\pi$
$379$	−7319.07	−0.991967	−0.495983	+	0.868332i	$0.665192\pi$
$380$	−853.315	−0.115195
$381$	5752.69	0.773541
$382$	−13012.2	−1.74283
$383$	11875.5	1.58436	0.792180	−	0.610288i	$-0.208946\pi$
$383$	11875.5	1.58436	0.792180	+	0.610288i	$0.208946\pi$
$384$	3226.79	0.428818
$385$	−1176.47	−0.155737
$386$	−1461.97	−0.192777
$387$	2884.47	0.378878
$388$	13738.7	1.79762
$389$	2121.38	0.276500	0.138250	−	0.990397i	$-0.455852\pi$
$389$	2121.38	0.276500	0.138250	+	0.990397i	$0.455852\pi$
$390$	4296.12	0.557801
$391$	4871.76	0.630116
$392$	463.682	0.0597436
$393$	−345.251	−0.0443145
$394$	−1688.96	−0.215960
$395$	376.230	0.0479245
$396$	1222.93	0.155188
$397$	−4892.76	−0.618541	−0.309270	−	0.950974i	$-0.600085\pi$
$397$	−4892.76	−0.618541	−0.309270	+	0.950974i	$0.600085\pi$
$398$	−13938.9	−1.75551
$399$	−2550.32	−0.319990
$400$	−1379.43	−0.172428
$401$	2710.54	0.337550	0.168775	−	0.985655i	$-0.446019\pi$
$401$	2710.54	0.337550	0.168775	+	0.985655i	$0.446019\pi$
$402$	1810.47	0.224623
$403$	3707.59	0.458283
$404$	−6357.16	−0.782872
$405$	−4549.95	−0.558244
$406$	1067.60	0.130502
$407$	245.914	0.0299496
$408$	−756.635	−0.0918113
$409$	3303.73	0.399411	0.199705	−	0.979856i	$-0.436002\pi$
$409$	3303.73	0.399411	0.199705	+	0.979856i	$0.436002\pi$
$410$	7711.54	0.928892
$411$	−14224.3	−1.70714
$412$	12512.6	1.49624
$413$	−3065.42	−0.365229
$414$	8341.90	0.990294
$415$	−745.441	−0.0881742
$416$	8631.11	1.01725
$417$	−4302.76	−0.505293
$418$	−861.279	−0.100781
$419$	5743.61	0.669675	0.334837	−	0.942276i	$-0.391319\pi$
$419$	5743.61	0.669675	0.334837	+	0.942276i	$0.391319\pi$
$420$	6028.34	0.700363
$421$	121.887	0.0141103	0.00705514	−	0.999975i	$-0.497754\pi$
$421$	121.887	0.0141103	0.00705514	+	0.999975i	$0.497754\pi$
$422$	−3581.40	−0.413128
$423$	1704.49	0.195922
$424$	−107.592	−0.0123234
$425$	744.698	0.0849957
$426$	−16792.8	−1.90989
$427$	−11701.3	−1.32615
$428$	18715.7	2.11368
$429$	2293.51	0.258116
$430$	4801.88	0.538529
$431$	−1071.18	−0.119715	−0.0598575	−	0.998207i	$-0.519065\pi$
$431$	−1071.18	−0.119715	−0.0598575	+	0.998207i	$0.519065\pi$
$432$	−5063.05	−0.563880
$433$	2115.24	0.234762	0.117381	−	0.993087i	$-0.462550\pi$
$433$	2115.24	0.234762	0.117381	+	0.993087i	$0.462550\pi$
$434$	9836.09	1.08790
$435$	379.999	0.0418841
$436$	2091.31	0.229714
$437$	−3107.41	−0.340155
$438$	4146.03	0.452295
$439$	14960.0	1.62643	0.813216	−	0.581962i	$-0.197715\pi$
$439$	14960.0	1.62643	0.813216	+	0.581962i	$0.197715\pi$
$440$	222.631	0.0241217
$441$	1417.81	0.153095
$442$	−4078.72	−0.438925
$443$	−4759.72	−0.510476	−0.255238	−	0.966878i	$-0.582154\pi$
$443$	−4759.72	−0.510476	−0.255238	+	0.966878i	$0.582154\pi$
$444$	−1260.08	−0.134686
$445$	−2083.77	−0.221978
$446$	13201.9	1.40163
$447$	272.379	0.0288213
$448$	13455.9	1.41905
$449$	7748.13	0.814380	0.407190	−	0.913343i	$-0.366509\pi$
$449$	7748.13	0.814380	0.407190	+	0.913343i	$0.366509\pi$
$450$	1275.14	0.133580
$451$	4116.86	0.429834
$452$	−15311.8	−1.59337
$453$	2458.13	0.254952
$454$	10922.5	1.12911
$455$	3553.66	0.366149
$456$	482.614	0.0495624
$457$	7806.08	0.799022	0.399511	−	0.916728i	$-0.369180\pi$
$457$	7806.08	0.799022	0.399511	+	0.916728i	$0.369180\pi$
$458$	−10804.6	−1.10233
$459$	2733.34	0.277955
$460$	7345.15	0.744499
$461$	−1865.45	−0.188466	−0.0942329	−	0.995550i	$-0.530040\pi$
$461$	−1865.45	−0.188466	−0.0942329	+	0.995550i	$0.530040\pi$
$462$	6084.60	0.612730
$463$	−485.085	−0.0486908	−0.0243454	−	0.999704i	$-0.507750\pi$
$463$	−485.085	−0.0486908	−0.0243454	+	0.999704i	$0.507750\pi$
$464$	668.266	0.0668609
$465$	3501.04	0.349155
$466$	−21305.6	−2.11794
$467$	4108.95	0.407151	0.203576	−	0.979059i	$-0.434744\pi$
$467$	4108.95	0.407151	0.203576	+	0.979059i	$0.434744\pi$
$468$	−3693.97	−0.364858
$469$	1497.59	0.147446
$470$	2837.52	0.278479
$471$	−13823.4	−1.35234
$472$	580.089	0.0565694
$473$	2563.52	0.249198
$474$	−1945.82	−0.188554
$475$	−475.000	−0.0458831
$476$	−5723.28	−0.551106
$477$	−328.985	−0.0315790
$478$	25012.4	2.39339
$479$	87.6685	0.00836258	0.00418129	−	0.999991i	$-0.498669\pi$
$479$	87.6685	0.00836258	0.00418129	+	0.999991i	$0.498669\pi$
$480$	8150.29	0.775017
$481$	−742.807	−0.0704139
$482$	−2021.10	−0.190993
$483$	21952.7	2.06808
$484$	1086.85	0.102071
$485$	7647.67	0.716006
$486$	13322.1	1.24342
$487$	−2206.11	−0.205274	−0.102637	−	0.994719i	$-0.532728\pi$
$487$	−2206.11	−0.205274	−0.102637	+	0.994719i	$0.532728\pi$
$488$	2214.32	0.205405
$489$	−3979.11	−0.367978
$490$	2360.28	0.217606
$491$	−13258.5	−1.21863	−0.609313	−	0.792930i	$-0.708555\pi$
$491$	−13258.5	−1.21863	−0.609313	+	0.792930i	$0.708555\pi$
$492$	−21095.1	−1.93301
$493$	−360.770	−0.0329580
$494$	2601.58	0.236945
$495$	680.745	0.0618125
$496$	6156.93	0.557367
$497$	−13890.7	−1.25368
$498$	3855.35	0.346912
$499$	12585.2	1.12904	0.564518	−	0.825421i	$-0.309062\pi$
$499$	12585.2	1.12904	0.564518	+	0.825421i	$0.309062\pi$
$500$	1122.78	0.100425
$501$	−14931.1	−1.33148
$502$	−21244.0	−1.88878
$503$	20093.0	1.78112	0.890560	−	0.454865i	$-0.150312\pi$
$503$	20093.0	1.78112	0.890560	+	0.454865i	$0.150312\pi$
$504$	−1071.68	−0.0947151
$505$	−3538.73	−0.311825
$506$	7413.71	0.651343
$507$	6858.67	0.600797
$508$	−8234.44	−0.719181
$509$	−4342.07	−0.378112	−0.189056	−	0.981966i	$-0.560543\pi$
$509$	−4342.07	−0.378112	−0.189056	+	0.981966i	$0.560543\pi$
$510$	−3851.50	−0.334407
$511$	3429.51	0.296894
$512$	16119.9	1.39141
$513$	−1743.44	−0.150048
$514$	−21980.2	−1.88619
$515$	6965.17	0.595965
$516$	−13135.7	−1.12067
$517$	1514.83	0.128863
$518$	−1970.64	−0.167152
$519$	11442.3	0.967749
$520$	−672.481	−0.0567120
$521$	17232.8	1.44910	0.724550	−	0.689222i	$-0.242048\pi$
$521$	17232.8	1.44910	0.724550	+	0.689222i	$0.242048\pi$
$522$	−617.746	−0.0517970
$523$	4289.27	0.358617	0.179308	−	0.983793i	$-0.442614\pi$
$523$	4289.27	0.358617	0.179308	+	0.983793i	$0.442614\pi$
$524$	494.195	0.0412004
$525$	3355.69	0.278961
$526$	9455.06	0.783764
$527$	−3323.88	−0.274745
$528$	3808.67	0.313923
$529$	14581.0	1.19840
$530$	−547.674	−0.0448858
$531$	1773.75	0.144961
$532$	3650.55	0.297503
$533$	−12435.4	−1.01057
$534$	10777.1	0.873351
$535$	10418.1	0.841898
$536$	−283.398	−0.0228375
$537$	−1112.96	−0.0894375
$538$	17510.4	1.40321
$539$	1260.05	0.100695
$540$	4121.06	0.328412
$541$	−13660.4	−1.08560	−0.542799	−	0.839863i	$-0.682635\pi$
$541$	−13660.4	−1.08560	−0.542799	+	0.839863i	$0.682635\pi$
$542$	−2607.50	−0.206645
$543$	−22513.2	−1.77925
$544$	−7737.86	−0.609849
$545$	1164.13	0.0914971
$546$	−18379.1	−1.44058
$547$	12539.5	0.980162	0.490081	−	0.871677i	$-0.336967\pi$
$547$	12539.5	0.980162	0.490081	+	0.871677i	$0.336967\pi$
$548$	20360.8	1.58717
$549$	6770.77	0.526356
$550$	1133.26	0.0878590
$551$	230.115	0.0177917
$552$	−4154.24	−0.320319
$553$	−1609.54	−0.123770
$554$	9907.48	0.759799
$555$	−701.427	−0.0536467
$556$	6159.00	0.469784
$557$	9646.26	0.733798	0.366899	−	0.930261i	$-0.380420\pi$
$557$	9646.26	0.733798	0.366899	+	0.930261i	$0.380420\pi$
$558$	−5691.47	−0.431791
$559$	−7743.36	−0.585884
$560$	5901.31	0.445314
$561$	−2056.15	−0.154743
$562$	15332.6	1.15083
$563$	−14876.9	−1.11366	−0.556828	−	0.830628i	$-0.687982\pi$
$563$	−14876.9	−1.11366	−0.556828	+	0.830628i	$0.687982\pi$
$564$	−7762.10	−0.579510
$565$	−8523.34	−0.634654
$566$	17972.3	1.33469
$567$	19465.1	1.44172
$568$	2628.62	0.194180
$569$	−18657.4	−1.37462	−0.687309	−	0.726365i	$-0.741208\pi$
$569$	−18657.4	−1.37462	−0.687309	+	0.726365i	$0.741208\pi$
$570$	2456.65	0.180523
$571$	23157.2	1.69720	0.848599	−	0.529037i	$-0.177447\pi$
$571$	23157.2	1.69720	0.848599	+	0.529037i	$0.177447\pi$
$572$	−3282.95	−0.239977
$573$	19814.1	1.44458
$574$	−32990.6	−2.39896
$575$	4088.70	0.296540
$576$	−7786.02	−0.563225
$577$	−12971.2	−0.935869	−0.467935	−	0.883763i	$-0.655002\pi$
$577$	−12971.2	−0.935869	−0.467935	+	0.883763i	$0.655002\pi$
$578$	−16589.6	−1.19384
$579$	2226.19	0.159788
$580$	−543.934	−0.0389407
$581$	3189.06	0.227719
$582$	−39553.0	−2.81705
$583$	−292.380	−0.0207704
$584$	−648.988	−0.0459851
$585$	−2056.26	−0.145326
$586$	−32773.8	−2.31036
$587$	18588.9	1.30706	0.653532	−	0.756898i	$-0.273286\pi$
$587$	18588.9	1.30706	0.653532	+	0.756898i	$0.273286\pi$
$588$	−6456.61	−0.452834
$589$	2120.11	0.148315
$590$	2952.83	0.206044
$591$	2571.83	0.179004
$592$	−1233.53	−0.0856380
$593$	8773.48	0.607561	0.303780	−	0.952742i	$-0.401751\pi$
$593$	8773.48	0.607561	0.303780	+	0.952742i	$0.401751\pi$
$594$	4159.53	0.287319
$595$	−3185.88	−0.219510
$596$	−389.886	−0.0267959
$597$	21225.2	1.45509
$598$	−22393.9	−1.53136
$599$	−2688.85	−0.183411	−0.0917057	−	0.995786i	$-0.529232\pi$
$599$	−2688.85	−0.183411	−0.0917057	+	0.995786i	$0.529232\pi$
$600$	−635.018	−0.0432075
$601$	18850.9	1.27944	0.639719	−	0.768608i	$-0.279051\pi$
$601$	18850.9	1.27944	0.639719	+	0.768608i	$0.279051\pi$
$602$	−20542.9	−1.39080
$603$	−866.551	−0.0585219
$604$	−3518.59	−0.237035
$605$	605.000	0.0406558
$606$	18302.0	1.22684
$607$	8442.18	0.564510	0.282255	−	0.959339i	$-0.408918\pi$
$607$	8442.18	0.564510	0.282255	+	0.959339i	$0.408918\pi$
$608$	4935.54	0.329214
$609$	−1625.67	−0.108170
$610$	11271.6	0.748151
$611$	−4575.70	−0.302967
$612$	3311.67	0.218736
$613$	1723.24	0.113542	0.0567709	−	0.998387i	$-0.481920\pi$
$613$	1723.24	0.113542	0.0567709	+	0.998387i	$0.481920\pi$
$614$	27544.6	1.81044
$615$	−11742.6	−0.769933
$616$	−952.437	−0.0622967
$617$	10206.4	0.665955	0.332978	−	0.942935i	$-0.391947\pi$
$617$	10206.4	0.665955	0.332978	+	0.942935i	$0.391947\pi$
$618$	−36023.1	−2.34476
$619$	6720.62	0.436389	0.218194	−	0.975905i	$-0.429983\pi$
$619$	6720.62	0.436389	0.218194	+	0.975905i	$0.429983\pi$
$620$	−5011.42	−0.324619
$621$	15007.2	0.969753
$622$	−36677.9	−2.36439
$623$	8914.56	0.573281
$624$	−11504.5	−0.738057
$625$	625.000	0.0400000
$626$	59.8378	0.00382045
$627$	1311.50	0.0835348
$628$	19787.0	1.25730
$629$	665.933	0.0422138
$630$	−5455.18	−0.344983
$631$	13123.8	0.827972	0.413986	−	0.910283i	$-0.364136\pi$
$631$	13123.8	0.827972	0.413986	+	0.910283i	$0.364136\pi$
$632$	304.584	0.0191704
$633$	5453.53	0.342430
$634$	−28134.9	−1.76243
$635$	−4583.72	−0.286456
$636$	1498.18	0.0934065
$637$	−3806.12	−0.236741
$638$	−549.011	−0.0340683
$639$	8037.57	0.497592
$640$	−2571.09	−0.158799
$641$	−1151.04	−0.0709254	−0.0354627	−	0.999371i	$-0.511290\pi$
$641$	−1151.04	−0.0709254	−0.0354627	+	0.999371i	$0.511290\pi$
$642$	−53881.6	−3.31236
$643$	1236.23	0.0758198	0.0379099	−	0.999281i	$-0.487930\pi$
$643$	1236.23	0.0758198	0.0379099	+	0.999281i	$0.487930\pi$
$644$	−31423.2	−1.92274
$645$	−7312.00	−0.446372
$646$	−2332.34	−0.142050
$647$	9440.58	0.573644	0.286822	−	0.957984i	$-0.407401\pi$
$647$	9440.58	0.573644	0.286822	+	0.957984i	$0.407401\pi$
$648$	−3683.50	−0.223305
$649$	1576.39	0.0953446
$650$	−3423.13	−0.206564
$651$	−14977.8	−0.901728
$652$	5695.72	0.342119
$653$	−17717.0	−1.06175	−0.530873	−	0.847452i	$-0.678136\pi$
$653$	−17717.0	−1.06175	−0.530873	+	0.847452i	$0.678136\pi$
$654$	−6020.77	−0.359986
$655$	275.095	0.0164104
$656$	−20650.6	−1.22907
$657$	−1984.42	−0.117838
$658$	−12139.2	−0.719200
$659$	8592.81	0.507934	0.253967	−	0.967213i	$-0.418265\pi$
$659$	8592.81	0.507934	0.253967	+	0.967213i	$0.418265\pi$
$660$	−3100.06	−0.182833
$661$	27904.3	1.64199	0.820993	−	0.570938i	$-0.193420\pi$
$661$	27904.3	1.64199	0.820993	+	0.570938i	$0.193420\pi$
$662$	−36049.6	−2.11648
$663$	6210.81	0.363813
$664$	−603.486	−0.0352708
$665$	2032.09	0.118498
$666$	1140.28	0.0663435
$667$	−1980.78	−0.114987
$668$	21372.5	1.23791
$669$	−20103.0	−1.16177
$670$	−1442.58	−0.0831817
$671$	6017.40	0.346199
$672$	−34867.6	−2.00156
$673$	−16907.0	−0.968375	−0.484188	−	0.874964i	$-0.660885\pi$
$673$	−16907.0	−0.968375	−0.484188	+	0.874964i	$0.660885\pi$
$674$	7251.50	0.414417
$675$	2294.00	0.130809
$676$	−9817.55	−0.558577
$677$	−6274.92	−0.356226	−0.178113	−	0.984010i	$-0.556999\pi$
$677$	−6274.92	−0.356226	−0.178113	+	0.984010i	$0.556999\pi$
$678$	44081.9	2.49698
$679$	−32717.4	−1.84916
$680$	602.884	0.0339994
$681$	−16632.1	−0.935891
$682$	−5058.20	−0.284001
$683$	−9947.57	−0.557296	−0.278648	−	0.960393i	$-0.589886\pi$
$683$	−9947.57	−0.557296	−0.278648	+	0.960393i	$0.589886\pi$
$684$	−2112.33	−0.118080
$685$	11333.9	0.632183
$686$	20137.6	1.12078
$687$	16452.6	0.913691
$688$	−12858.9	−0.712557
$689$	883.163	0.0488328
$690$	−21146.3	−1.16671
$691$	−3928.37	−0.216270	−0.108135	−	0.994136i	$-0.534488\pi$
$691$	−3928.37	−0.216270	−0.108135	+	0.994136i	$0.534488\pi$
$692$	−16378.6	−0.899742
$693$	−2912.29	−0.159637
$694$	39990.0	2.18732
$695$	3428.43	0.187119
$696$	307.636	0.0167542
$697$	11148.4	0.605849
$698$	−22956.3	−1.24485
$699$	32442.8	1.75550
$700$	−4803.36	−0.259357
$701$	5928.55	0.319427	0.159713	−	0.987163i	$-0.448943\pi$
$701$	5928.55	0.319427	0.159713	+	0.987163i	$0.448943\pi$
$702$	−12564.3	−0.675509
$703$	−424.760	−0.0227882
$704$	−6919.69	−0.370448
$705$	−4320.80	−0.230824
$706$	−31088.5	−1.65727
$707$	15139.0	0.805319
$708$	−8077.52	−0.428774
$709$	−12497.4	−0.661991	−0.330995	−	0.943632i	$-0.607384\pi$
$709$	−12497.4	−0.661991	−0.330995	+	0.943632i	$0.607384\pi$
$710$	13380.5	0.707267
$711$	931.333	0.0491248
$712$	−1686.96	−0.0887942
$713$	−18249.5	−0.958553
$714$	16477.1	0.863639
$715$	−1827.46	−0.0955849
$716$	1593.11	0.0831524
$717$	−38087.3	−1.98382
$718$	−16879.8	−0.877366
$719$	36867.9	1.91230	0.956148	−	0.292883i	$-0.0946148\pi$
$719$	36867.9	1.91230	0.956148	+	0.292883i	$0.0946148\pi$
$720$	−3414.68	−0.176747
$721$	−29797.6	−1.53914
$722$	1487.66	0.0766830
$723$	3077.60	0.158308
$724$	32225.5	1.65422
$725$	−302.782	−0.0155104
$726$	−3129.00	−0.159956
$727$	32673.4	1.66684	0.833418	−	0.552643i	$-0.186381\pi$
$727$	32673.4	1.66684	0.833418	+	0.552643i	$0.186381\pi$
$728$	2876.93	0.146464
$729$	4283.64	0.217632
$730$	−3303.55	−0.167493
$731$	6941.99	0.351243
$732$	−30833.6	−1.55689
$733$	−9549.12	−0.481180	−0.240590	−	0.970627i	$-0.577341\pi$
$733$	−9549.12	−0.481180	−0.240590	+	0.970627i	$0.577341\pi$
$734$	6296.40	0.316627
$735$	−3594.09	−0.180367
$736$	−42484.1	−2.12769
$737$	−770.132	−0.0384914
$738$	19089.4	0.952156
$739$	−9006.13	−0.448303	−0.224151	−	0.974554i	$-0.571961\pi$
$739$	−9006.13	−0.448303	−0.224151	+	0.974554i	$0.571961\pi$
$740$	1004.03	0.0498768
$741$	−3961.52	−0.196397
$742$	2343.00	0.115922
$743$	8176.35	0.403716	0.201858	−	0.979415i	$-0.435302\pi$
$743$	8176.35	0.403716	0.201858	+	0.979415i	$0.435302\pi$
$744$	2834.34	0.139666
$745$	−217.031	−0.0106730
$746$	18904.8	0.927819
$747$	−1845.29	−0.0903825
$748$	2943.19	0.143869
$749$	−44569.7	−2.17429
$750$	−3232.44	−0.157376
$751$	−10861.2	−0.527739	−0.263869	−	0.964558i	$-0.584999\pi$
$751$	−10861.2	−0.527739	−0.263869	+	0.964558i	$0.584999\pi$
$752$	−7598.54	−0.368471
$753$	32349.0	1.56555
$754$	1658.34	0.0800972
$755$	−1958.63	−0.0944131
$756$	−17630.3	−0.848156
$757$	−20789.1	−0.998142	−0.499071	−	0.866561i	$-0.666325\pi$
$757$	−20789.1	−0.998142	−0.499071	+	0.866561i	$0.666325\pi$
$758$	−30161.5	−1.44527
$759$	−11289.1	−0.539881
$760$	−384.545	−0.0183538
$761$	31773.6	1.51352	0.756761	−	0.653692i	$-0.226781\pi$
$761$	31773.6	1.51352	0.756761	+	0.653692i	$0.226781\pi$
$762$	23706.6	1.12703
$763$	−4980.26	−0.236301
$764$	−28362.0	−1.34307
$765$	1843.45	0.0871244
$766$	48938.4	2.30838
$767$	−4761.64	−0.224163
$768$	−18282.1	−0.858984
$769$	35283.9	1.65458	0.827289	−	0.561776i	$-0.189882\pi$
$769$	35283.9	1.65458	0.827289	+	0.561776i	$0.189882\pi$
$770$	−4848.19	−0.226905
$771$	33470.0	1.56341
$772$	−3186.58	−0.148559
$773$	−10691.8	−0.497489	−0.248745	−	0.968569i	$-0.580018\pi$
$773$	−10691.8	−0.497489	−0.248745	+	0.968569i	$0.580018\pi$
$774$	11886.8	0.552016
$775$	−2789.62	−0.129298
$776$	6191.32	0.286412
$777$	3000.77	0.138548
$778$	8742.12	0.402854
$779$	−7110.94	−0.327055
$780$	9364.05	0.429855
$781$	7143.25	0.327280
$782$	20076.3	0.918064
$783$	−1111.33	−0.0507226
$784$	−6320.56	−0.287926
$785$	11014.5	0.500794
$786$	−1422.76	−0.0645652
$787$	42073.7	1.90567	0.952837	−	0.303482i	$-0.0981493\pi$
$787$	42073.7	1.90567	0.952837	+	0.303482i	$0.0981493\pi$
$788$	−3681.34	−0.166424
$789$	−14397.6	−0.649641
$790$	1550.43	0.0698249
$791$	36463.6	1.63906
$792$	551.110	0.0247258
$793$	−18176.2	−0.813940
$794$	−20162.8	−0.901199
$795$	833.964	0.0372046
$796$	−30381.9	−1.35284
$797$	−16855.5	−0.749123	−0.374562	−	0.927202i	$-0.622207\pi$
$797$	−16855.5	−0.749123	−0.374562	+	0.927202i	$0.622207\pi$
$798$	−10509.8	−0.466218
$799$	4102.15	0.181632
$800$	−6494.13	−0.287002
$801$	−5158.25	−0.227538
$802$	11170.0	0.491803
$803$	−1763.62	−0.0775054
$804$	3946.21	0.173100
$805$	−17491.8	−0.765845
$806$	15278.8	0.667708
$807$	−26663.7	−1.16308
$808$	−2864.85	−0.124734
$809$	638.282	0.0277390	0.0138695	−	0.999904i	$-0.495585\pi$
$809$	638.282	0.0277390	0.0138695	+	0.999904i	$0.495585\pi$
$810$	−18750.1	−0.813348
$811$	−3849.60	−0.166680	−0.0833402	−	0.996521i	$-0.526559\pi$
$811$	−3849.60	−0.166680	−0.0833402	+	0.996521i	$0.526559\pi$
$812$	2327.00	0.100568
$813$	3970.54	0.171283
$814$	1013.40	0.0436359
$815$	3170.54	0.136269
$816$	10313.9	0.442472
$817$	−4427.90	−0.189611
$818$	13614.5	0.581932
$819$	8796.85	0.375320
$820$	16808.5	0.715827
$821$	−1279.14	−0.0543756	−0.0271878	−	0.999630i	$-0.508655\pi$
$821$	−1279.14	−0.0543756	−0.0271878	+	0.999630i	$0.508655\pi$
$822$	−58617.7	−2.48726
$823$	−18665.6	−0.790574	−0.395287	−	0.918558i	$-0.629355\pi$
$823$	−18665.6	−0.790574	−0.395287	+	0.918558i	$0.629355\pi$
$824$	5638.78	0.238394
$825$	−1725.66	−0.0728239
$826$	−12632.5	−0.532130
$827$	−12509.0	−0.525976	−0.262988	−	0.964799i	$-0.584708\pi$
$827$	−12509.0	−0.525976	−0.262988	+	0.964799i	$0.584708\pi$
$828$	18182.5	0.763145
$829$	46300.9	1.93980	0.969902	−	0.243496i	$-0.0782942\pi$
$829$	46300.9	1.93980	0.969902	+	0.243496i	$0.0782942\pi$
$830$	−3071.93	−0.128468
$831$	−15086.5	−0.629776
$832$	20901.6	0.870953
$833$	3412.22	0.141928
$834$	−17731.5	−0.736200
$835$	11897.1	0.493071
$836$	−1877.29	−0.0776645
$837$	−10239.0	−0.422835
$838$	23669.2	0.975701
$839$	−27103.4	−1.11527	−0.557637	−	0.830085i	$-0.688292\pi$
$839$	−27103.4	−1.11527	−0.557637	+	0.830085i	$0.688292\pi$
$840$	2716.66	0.111588
$841$	−24242.3	−0.993986
$842$	502.292	0.0205583
$843$	−23347.4	−0.953889
$844$	−7806.23	−0.318367
$845$	−5464.97	−0.222486
$846$	7024.10	0.285454
$847$	−2588.24	−0.104998
$848$	1466.61	0.0593909
$849$	−27367.1	−1.10628
$850$	3068.87	0.123837
$851$	3656.25	0.147279
$852$	−36602.5	−1.47181
$853$	39778.0	1.59668	0.798342	−	0.602204i	$-0.205711\pi$
$853$	39778.0	1.59668	0.798342	+	0.602204i	$0.205711\pi$
$854$	−48220.7	−1.93218
$855$	−1175.83	−0.0470323
$856$	8434.20	0.336770
$857$	3133.79	0.124911	0.0624553	−	0.998048i	$-0.480107\pi$
$857$	3133.79	0.124911	0.0624553	+	0.998048i	$0.480107\pi$
$858$	9451.45	0.376069
$859$	−1084.44	−0.0430741	−0.0215370	−	0.999768i	$-0.506856\pi$
$859$	−1084.44	−0.0430741	−0.0215370	+	0.999768i	$0.506856\pi$
$860$	10466.4	0.415003
$861$	50236.0	1.98843
$862$	−4414.30	−0.174422
$863$	−931.165	−0.0367291	−0.0183646	−	0.999831i	$-0.505846\pi$
$863$	−931.165	−0.0367291	−0.0183646	+	0.999831i	$0.505846\pi$
$864$	−23836.0	−0.938563
$865$	−9117.20	−0.358375
$866$	8716.80	0.342043
$867$	25261.6	0.989539
$868$	21439.3	0.838360
$869$	827.705	0.0323107
$870$	1565.96	0.0610241
$871$	2326.26	0.0904963
$872$	942.445	0.0366000
$873$	18931.3	0.733939
$874$	−12805.5	−0.495598
$875$	−2673.80	−0.103304
$876$	9036.92	0.348549
$877$	31613.4	1.21723	0.608615	−	0.793466i	$-0.291726\pi$
$877$	31613.4	1.21723	0.608615	+	0.793466i	$0.291726\pi$
$878$	61649.6	2.36967
$879$	49905.8	1.91500
$880$	−3034.74	−0.116251
$881$	15295.0	0.584905	0.292452	−	0.956280i	$-0.405529\pi$
$881$	15295.0	0.584905	0.292452	+	0.956280i	$0.405529\pi$
$882$	5842.73	0.223056
$883$	−12.9900	−0.000495073 0	−0.000247537	−	1.00000i	$-0.500079\pi$
$883$	−12.9900	−0.000495073 0	−0.000247537		1.00000i	$0.500079\pi$
$884$	−8890.20	−0.338246
$885$	−4496.38	−0.170784
$886$	−19614.6	−0.743752
$887$	−46709.2	−1.76814	−0.884070	−	0.467354i	$-0.845207\pi$
$887$	−46709.2	−1.76814	−0.884070	+	0.467354i	$0.845207\pi$
$888$	−567.854	−0.0214594
$889$	19609.6	0.739802
$890$	−8587.13	−0.323417
$891$	−10009.9	−0.376368
$892$	28775.6	1.08013
$893$	−2616.53	−0.0980501
$894$	1122.46	0.0419919
$895$	886.806	0.0331203
$896$	10999.4	0.410115
$897$	34099.9	1.26930
$898$	31929.7	1.18653
$899$	1351.44	0.0501368
$900$	2779.38	0.102940
$901$	−791.762	−0.0292757
$902$	16965.4	0.626259
$903$	31281.4	1.15280
$904$	−6900.24	−0.253870
$905$	17938.4	0.658888
$906$	10129.8	0.371459
$907$	18903.6	0.692042	0.346021	−	0.938227i	$-0.387533\pi$
$907$	18903.6	0.692042	0.346021	+	0.938227i	$0.387533\pi$
$908$	23807.2	0.870122
$909$	−8759.90	−0.319634
$910$	14644.5	0.533471
$911$	46809.0	1.70236	0.851180	−	0.524874i	$-0.175887\pi$
$911$	46809.0	1.70236	0.851180	+	0.524874i	$0.175887\pi$
$912$	−6578.62	−0.238859
$913$	−1639.97	−0.0594470
$914$	32168.5	1.16416
$915$	−17163.6	−0.620122
$916$	−23550.4	−0.849483
$917$	−1176.88	−0.0423817
$918$	11264.0	0.404974
$919$	−20921.1	−0.750950	−0.375475	−	0.926833i	$-0.622520\pi$
$919$	−20921.1	−0.750950	−0.375475	+	0.926833i	$0.622520\pi$
$920$	3310.09	0.118620
$921$	−41943.1	−1.50062
$922$	−7687.44	−0.274590
$923$	−21576.9	−0.769461
$924$	13262.3	0.472185
$925$	558.895	0.0198663
$926$	−1999.01	−0.0709414
$927$	17241.8	0.610891
$928$	3146.09	0.111288
$929$	−29980.3	−1.05880	−0.529398	−	0.848373i	$-0.677582\pi$
$929$	−29980.3	−1.05880	−0.529398	+	0.848373i	$0.677582\pi$
$930$	14427.6	0.508711
$931$	−2176.46	−0.0766171
$932$	−46438.8	−1.63214
$933$	55850.8	1.95978
$934$	16932.8	0.593210
$935$	1638.34	0.0573041
$936$	−1664.68	−0.0581323
$937$	36397.0	1.26899	0.634493	−	0.772929i	$-0.281209\pi$
$937$	36397.0	1.26899	0.634493	+	0.772929i	$0.281209\pi$
$938$	6171.48	0.214825
$939$	−91.1172	−0.00316666
$940$	6184.82	0.214603
$941$	−52766.3	−1.82798	−0.913991	−	0.405734i	$-0.867016\pi$
$941$	−52766.3	−1.82798	−0.913991	+	0.405734i	$0.867016\pi$
$942$	−56965.7	−1.97032
$943$	61209.5	2.11374
$944$	−7907.32	−0.272628
$945$	−9813.93	−0.337828
$946$	10564.1	0.363076
$947$	41629.2	1.42848	0.714239	−	0.699902i	$-0.246773\pi$
$947$	41629.2	1.42848	0.714239	+	0.699902i	$0.246773\pi$
$948$	−4241.22	−0.145304
$949$	5327.19	0.182221
$950$	−1957.45	−0.0668507
$951$	42842.0	1.46083
$952$	−2579.19	−0.0878068
$953$	21709.1	0.737908	0.368954	−	0.929448i	$-0.379716\pi$
$953$	21709.1	0.737908	0.368954	+	0.929448i	$0.379716\pi$
$954$	−1355.73	−0.0460099
$955$	−15787.8	−0.534954
$956$	54518.5	1.84441
$957$	835.998	0.0282382
$958$	361.278	0.0121841
$959$	−48487.3	−1.63268
$960$	19737.2	0.663559
$961$	−17339.8	−0.582049
$962$	−3061.07	−0.102591
$963$	25789.4	0.862983
$964$	−4405.29	−0.147184
$965$	−1773.82	−0.0591723
$966$	90465.9	3.01314
$967$	17943.1	0.596704	0.298352	−	0.954456i	$-0.403563\pi$
$967$	17943.1	0.596704	0.298352	+	0.954456i	$0.403563\pi$
$968$	489.789	0.0162628
$969$	3551.53	0.117742
$970$	31515.7	1.04320
$971$	−13241.5	−0.437630	−0.218815	−	0.975766i	$-0.570219\pi$
$971$	−13241.5	−0.437630	−0.218815	+	0.975766i	$0.570219\pi$
$972$	29037.6	0.958212
$973$	−14667.1	−0.483254
$974$	−9091.27	−0.299079
$975$	5212.53	0.171215
$976$	−30183.9	−0.989921
$977$	15917.0	0.521218	0.260609	−	0.965444i	$-0.416077\pi$
$977$	15917.0	0.521218	0.260609	+	0.965444i	$0.416077\pi$
$978$	−16397.7	−0.536136
$979$	−4584.30	−0.149658
$980$	5144.61	0.167692
$981$	2881.73	0.0937887
$982$	−54637.5	−1.77551
$983$	−2610.46	−0.0847005	−0.0423503	−	0.999103i	$-0.513485\pi$
$983$	−2610.46	−0.0847005	−0.0423503	+	0.999103i	$0.513485\pi$
$984$	−9506.48	−0.307983
$985$	−2049.23	−0.0662882
$986$	−1486.72	−0.0480190
$987$	18484.7	0.596125
$988$	5670.55	0.182595
$989$	38114.4	1.22545
$990$	2805.32	0.0900595
$991$	−46274.4	−1.48331	−0.741653	−	0.670784i	$-0.765958\pi$
$991$	−46274.4	−1.48331	−0.741653	+	0.670784i	$0.765958\pi$
$992$	28985.8	0.927723
$993$	54894.1	1.75429
$994$	−57242.7	−1.82659
$995$	−16912.2	−0.538846
$996$	8403.33	0.267339
$997$	−4587.86	−0.145736	−0.0728681	−	0.997342i	$-0.523215\pi$
$997$	−4587.86	−0.145736	−0.0728681	+	0.997342i	$0.523215\pi$
$998$	51862.8	1.64498
$999$	2051.37	0.0649674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.17	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.17	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+4.12095 q^{2} -6.27512 q^{3} +8.98226 q^{4} +5.00000 q^{5} -25.8595 q^{6} -21.3904 q^{7} +4.04785 q^{8} +12.3772 q^{9} +O(q^{10})\)	\(q+4.12095 q^{2} -6.27512 q^{3} +8.98226 q^{4} +5.00000 q^{5} -25.8595 q^{6} -21.3904 q^{7} +4.04785 q^{8} +12.3772 q^{9} +20.6048 q^{10} +11.0000 q^{11} -56.3648 q^{12} -33.2266 q^{13} -88.1490 q^{14} -31.3756 q^{15} -55.1771 q^{16} +29.7879 q^{17} +51.0058 q^{18} -19.0000 q^{19} +44.9113 q^{20} +134.228 q^{21} +45.3305 q^{22} +163.548 q^{23} -25.4007 q^{24} +25.0000 q^{25} -136.925 q^{26} +91.7600 q^{27} -192.134 q^{28} -12.1113 q^{29} -129.297 q^{30} -111.585 q^{31} -259.765 q^{32} -69.0264 q^{33} +122.755 q^{34} -106.952 q^{35} +111.175 q^{36} +22.3558 q^{37} -78.2981 q^{38} +208.501 q^{39} +20.2392 q^{40} +374.260 q^{41} +553.146 q^{42} +233.047 q^{43} +98.8049 q^{44} +61.8859 q^{45} +673.974 q^{46} +137.712 q^{47} +346.243 q^{48} +114.550 q^{49} +103.024 q^{50} -186.923 q^{51} -298.450 q^{52} -26.5800 q^{53} +378.139 q^{54} +55.0000 q^{55} -86.5851 q^{56} +119.227 q^{57} -49.9101 q^{58} +143.308 q^{59} -281.824 q^{60} +547.037 q^{61} -459.836 q^{62} -264.753 q^{63} -629.063 q^{64} -166.133 q^{65} -284.454 q^{66} -70.0120 q^{67} +267.563 q^{68} -1026.28 q^{69} -440.745 q^{70} +649.386 q^{71} +50.1009 q^{72} -160.329 q^{73} +92.1272 q^{74} -156.878 q^{75} -170.663 q^{76} -235.295 q^{77} +859.223 q^{78} +75.2460 q^{79} -275.885 q^{80} -909.989 q^{81} +1542.31 q^{82} -149.088 q^{83} +1205.67 q^{84} +148.940 q^{85} +960.376 q^{86} +75.9999 q^{87} +44.5263 q^{88} -416.755 q^{89} +255.029 q^{90} +710.731 q^{91} +1469.03 q^{92} +700.209 q^{93} +567.504 q^{94} -95.0000 q^{95} +1630.06 q^{96} +1529.53 q^{97} +472.057 q^{98} +136.149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * q^99

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