LMFDB - Embedded newform 1339.4.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,4,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1339.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1339.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:	$79.0035574977$
Analytic rank:	$1$
Dimension:	$72$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.59728 q^{2} +2.67027 q^{3} +4.94044 q^{4} +4.14791 q^{5} -9.60572 q^{6} +19.2068 q^{7} +11.0061 q^{8} -19.8697 q^{9} +O(q^{10})$	\(q-3.59728 q^{2} +2.67027 q^{3} +4.94044 q^{4} +4.14791 q^{5} -9.60572 q^{6} +19.2068 q^{7} +11.0061 q^{8} -19.8697 q^{9} -14.9212 q^{10} +54.9936 q^{11} +13.1923 q^{12} -13.0000 q^{13} -69.0924 q^{14} +11.0760 q^{15} -79.1156 q^{16} +85.9624 q^{17} +71.4768 q^{18} -130.777 q^{19} +20.4925 q^{20} +51.2875 q^{21} -197.828 q^{22} +33.8378 q^{23} +29.3893 q^{24} -107.795 q^{25} +46.7647 q^{26} -125.155 q^{27} +94.8903 q^{28} -35.5772 q^{29} -39.8437 q^{30} -42.5919 q^{31} +196.552 q^{32} +146.848 q^{33} -309.231 q^{34} +79.6682 q^{35} -98.1649 q^{36} -420.069 q^{37} +470.441 q^{38} -34.7135 q^{39} +45.6523 q^{40} -286.436 q^{41} -184.495 q^{42} -272.807 q^{43} +271.693 q^{44} -82.4175 q^{45} -121.724 q^{46} +322.260 q^{47} -211.260 q^{48} +25.9025 q^{49} +387.769 q^{50} +229.543 q^{51} -64.2258 q^{52} -52.8511 q^{53} +450.217 q^{54} +228.109 q^{55} +211.392 q^{56} -349.210 q^{57} +127.981 q^{58} -749.958 q^{59} +54.7206 q^{60} -284.987 q^{61} +153.215 q^{62} -381.633 q^{63} -74.1298 q^{64} -53.9228 q^{65} -528.253 q^{66} -114.439 q^{67} +424.692 q^{68} +90.3561 q^{69} -286.589 q^{70} +772.501 q^{71} -218.687 q^{72} -154.203 q^{73} +1511.11 q^{74} -287.841 q^{75} -646.096 q^{76} +1056.25 q^{77} +124.874 q^{78} -212.132 q^{79} -328.164 q^{80} +202.284 q^{81} +1030.39 q^{82} -897.559 q^{83} +253.383 q^{84} +356.564 q^{85} +981.363 q^{86} -95.0007 q^{87} +605.265 q^{88} -730.413 q^{89} +296.479 q^{90} -249.689 q^{91} +167.174 q^{92} -113.732 q^{93} -1159.26 q^{94} -542.451 q^{95} +524.848 q^{96} -1431.84 q^{97} -93.1784 q^{98} -1092.70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{2} - 19 q^{3} + 261 q^{4} - 73 q^{5} - 52 q^{6} + 3 q^{7} - 18 q^{8} + 517 q^{9}+O(q^{10}) $ 72 * q - q^2 - 19 * q^3 + 261 * q^4 - 73 * q^5 - 52 * q^6 + 3 * q^7 - 18 * q^8 + 517 * q^9	\( 72 q - q^{2} - 19 q^{3} + 261 q^{4} - 73 q^{5} - 52 q^{6} + 3 q^{7} - 18 q^{8} + 517 q^{9} - 100 q^{10} - 104 q^{11} - 228 q^{12} - 936 q^{13} - 337 q^{14} + 63 q^{15} + 833 q^{16} - 307 q^{17} - 110 q^{18} - 182 q^{19} - 428 q^{20} - 177 q^{21} - 74 q^{22} - 516 q^{23} - 901 q^{24} + 1285 q^{25} + 13 q^{26} - 817 q^{27} + 187 q^{28} - 1458 q^{29} - 178 q^{30} - 620 q^{31} - 35 q^{32} - 196 q^{33} - 1619 q^{34} - 1155 q^{35} - 615 q^{36} - 1031 q^{37} - 1614 q^{38} + 247 q^{39} - 3300 q^{40} - 1124 q^{41} - 2190 q^{42} - 383 q^{43} - 1902 q^{44} - 1828 q^{45} - 1109 q^{46} - 1531 q^{47} - 4464 q^{48} + 1191 q^{49} - 352 q^{50} - 1267 q^{51} - 3393 q^{52} - 3092 q^{53} - 1581 q^{54} - 2264 q^{55} - 1470 q^{56} - 502 q^{57} - 2003 q^{58} - 2452 q^{59} - 1909 q^{60} - 1764 q^{61} - 2232 q^{62} - 1086 q^{63} + 2272 q^{64} + 949 q^{65} - 2539 q^{66} + 832 q^{67} - 1796 q^{68} - 4738 q^{69} - 3251 q^{70} - 2995 q^{71} - 2534 q^{72} + 16 q^{73} - 3408 q^{74} - 3060 q^{75} - 3729 q^{76} - 5454 q^{77} + 676 q^{78} - 3594 q^{79} - 1631 q^{80} + 16 q^{81} - 1293 q^{82} - 2832 q^{83} - 4565 q^{84} - 887 q^{85} - 3982 q^{86} - 1530 q^{87} - 1757 q^{88} - 8104 q^{89} - 5932 q^{90} - 39 q^{91} - 5371 q^{92} - 3042 q^{93} - 3464 q^{94} - 4582 q^{95} - 3991 q^{96} - 2514 q^{97} - 2886 q^{98} - 2752 q^{99}+O(q^{100}) \) 72 * q - q^2 - 19 * q^3 + 261 * q^4 - 73 * q^5 - 52 * q^6 + 3 * q^7 - 18 * q^8 + 517 * q^9 - 100 * q^10 - 104 * q^11 - 228 * q^12 - 936 * q^13 - 337 * q^14 + 63 * q^15 + 833 * q^16 - 307 * q^17 - 110 * q^18 - 182 * q^19 - 428 * q^20 - 177 * q^21 - 74 * q^22 - 516 * q^23 - 901 * q^24 + 1285 * q^25 + 13 * q^26 - 817 * q^27 + 187 * q^28 - 1458 * q^29 - 178 * q^30 - 620 * q^31 - 35 * q^32 - 196 * q^33 - 1619 * q^34 - 1155 * q^35 - 615 * q^36 - 1031 * q^37 - 1614 * q^38 + 247 * q^39 - 3300 * q^40 - 1124 * q^41 - 2190 * q^42 - 383 * q^43 - 1902 * q^44 - 1828 * q^45 - 1109 * q^46 - 1531 * q^47 - 4464 * q^48 + 1191 * q^49 - 352 * q^50 - 1267 * q^51 - 3393 * q^52 - 3092 * q^53 - 1581 * q^54 - 2264 * q^55 - 1470 * q^56 - 502 * q^57 - 2003 * q^58 - 2452 * q^59 - 1909 * q^60 - 1764 * q^61 - 2232 * q^62 - 1086 * q^63 + 2272 * q^64 + 949 * q^65 - 2539 * q^66 + 832 * q^67 - 1796 * q^68 - 4738 * q^69 - 3251 * q^70 - 2995 * q^71 - 2534 * q^72 + 16 * q^73 - 3408 * q^74 - 3060 * q^75 - 3729 * q^76 - 5454 * q^77 + 676 * q^78 - 3594 * q^79 - 1631 * q^80 + 16 * q^81 - 1293 * q^82 - 2832 * q^83 - 4565 * q^84 - 887 * q^85 - 3982 * q^86 - 1530 * q^87 - 1757 * q^88 - 8104 * q^89 - 5932 * q^90 - 39 * q^91 - 5371 * q^92 - 3042 * q^93 - 3464 * q^94 - 4582 * q^95 - 3991 * q^96 - 2514 * q^97 - 2886 * q^98 - 2752 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.59728	−1.27183	−0.635916	−	0.771758i	$-0.719377\pi$
$2$	−3.59728	−1.27183	−0.635916	+	0.771758i	$0.719377\pi$
$3$	2.67027	0.513894	0.256947	−	0.966426i	$-0.417283\pi$
$3$	2.67027	0.513894	0.256947	+	0.966426i	$0.417283\pi$
$4$	4.94044	0.617555
$5$	4.14791	0.371000	0.185500	−	0.982644i	$-0.440609\pi$
$5$	4.14791	0.371000	0.185500	+	0.982644i	$0.440609\pi$
$6$	−9.60572	−0.653587
$7$	19.2068	1.03707	0.518536	−	0.855056i	$-0.326477\pi$
$7$	19.2068	1.03707	0.518536	+	0.855056i	$0.326477\pi$
$8$	11.0061	0.486405
$9$	−19.8697	−0.735913
$10$	−14.9212	−0.471850
$11$	54.9936	1.50738	0.753691	−	0.657229i	$-0.228272\pi$
$11$	54.9936	1.50738	0.753691	+	0.657229i	$0.228272\pi$
$12$	13.1923	0.317358
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−69.0924	−1.31898
$15$	11.0760	0.190655
$16$	−79.1156	−1.23618
$17$	85.9624	1.22641	0.613204	−	0.789924i	$-0.289880\pi$
$17$	85.9624	1.22641	0.613204	+	0.789924i	$0.289880\pi$
$18$	71.4768	0.935957
$19$	−130.777	−1.57907	−0.789534	−	0.613707i	$-0.789678\pi$
$19$	−130.777	−1.57907	−0.789534	+	0.613707i	$0.789678\pi$
$20$	20.4925	0.229113
$21$	51.2875	0.532945
$22$	−197.828	−1.91714
$23$	33.8378	0.306768	0.153384	−	0.988167i	$-0.450983\pi$
$23$	33.8378	0.306768	0.153384	+	0.988167i	$0.450983\pi$
$24$	29.3893	0.249961
$25$	−107.795	−0.862359
$26$	46.7647	0.352743
$27$	−125.155	−0.892075
$28$	94.8903	0.640449
$29$	−35.5772	−0.227811	−0.113905	−	0.993492i	$-0.536336\pi$
$29$	−35.5772	−0.227811	−0.113905	+	0.993492i	$0.536336\pi$
$30$	−39.8437	−0.242481
$31$	−42.5919	−0.246765	−0.123383	−	0.992359i	$-0.539374\pi$
$31$	−42.5919	−0.246765	−0.123383	+	0.992359i	$0.539374\pi$
$32$	196.552	1.08581
$33$	146.848	0.774634
$34$	−309.231	−1.55978
$35$	79.6682	0.384754
$36$	−98.1649	−0.454467
$37$	−420.069	−1.86646	−0.933230	−	0.359281i	$-0.883022\pi$
$37$	−420.069	−1.86646	−0.933230	+	0.359281i	$0.883022\pi$
$38$	470.441	2.00831
$39$	−34.7135	−0.142529
$40$	45.6523	0.180456
$41$	−286.436	−1.09107	−0.545534	−	0.838088i	$-0.683673\pi$
$41$	−286.436	−1.09107	−0.545534	+	0.838088i	$0.683673\pi$
$42$	−184.495	−0.677816
$43$	−272.807	−0.967503	−0.483752	−	0.875205i	$-0.660726\pi$
$43$	−272.807	−0.967503	−0.483752	+	0.875205i	$0.660726\pi$
$44$	271.693	0.930892
$45$	−82.4175	−0.273024
$46$	−121.724	−0.390157
$47$	322.260	1.00014	0.500068	−	0.865986i	$-0.333308\pi$
$47$	322.260	1.00014	0.500068	+	0.865986i	$0.333308\pi$
$48$	−211.260	−0.635266
$49$	25.9025	0.0755174
$50$	387.769	1.09678
$51$	229.543	0.630244
$52$	−64.2258	−0.171279
$53$	−52.8511	−0.136975	−0.0684873	−	0.997652i	$-0.521817\pi$
$53$	−52.8511	−0.136975	−0.0684873	+	0.997652i	$0.521817\pi$
$54$	450.217	1.13457
$55$	228.109	0.559239
$56$	211.392	0.504437
$57$	−349.210	−0.811473
$58$	127.981	0.289737
$59$	−749.958	−1.65485	−0.827426	−	0.561575i	$-0.810196\pi$
$59$	−749.958	−1.65485	−0.827426	+	0.561575i	$0.810196\pi$
$60$	54.7206	0.117740
$61$	−284.987	−0.598177	−0.299089	−	0.954225i	$-0.596683\pi$
$61$	−284.987	−0.598177	−0.299089	+	0.954225i	$0.596683\pi$
$62$	153.215	0.313844
$63$	−381.633	−0.763194
$64$	−74.1298	−0.144785
$65$	−53.9228	−0.102897
$66$	−528.253	−0.985204
$67$	−114.439	−0.208671	−0.104336	−	0.994542i	$-0.533272\pi$
$67$	−114.439	−0.208671	−0.104336	+	0.994542i	$0.533272\pi$
$68$	424.692	0.757375
$69$	90.3561	0.157646
$70$	−286.589	−0.489342
$71$	772.501	1.29125	0.645626	−	0.763653i	$-0.276596\pi$
$71$	772.501	1.29125	0.645626	+	0.763653i	$0.276596\pi$
$72$	−218.687	−0.357952
$73$	−154.203	−0.247235	−0.123617	−	0.992330i	$-0.539450\pi$
$73$	−154.203	−0.247235	−0.123617	+	0.992330i	$0.539450\pi$
$74$	1511.11	2.37382
$75$	−287.841	−0.443161
$76$	−646.096	−0.975161
$77$	1056.25	1.56326
$78$	124.874	0.181272
$79$	−212.132	−0.302111	−0.151055	−	0.988525i	$-0.548267\pi$
$79$	−212.132	−0.302111	−0.151055	+	0.988525i	$0.548267\pi$
$80$	−328.164	−0.458623
$81$	202.284	0.277481
$82$	1030.39	1.38766
$83$	−897.559	−1.18699	−0.593493	−	0.804839i	$-0.702252\pi$
$83$	−897.559	−1.18699	−0.593493	+	0.804839i	$0.702252\pi$
$84$	253.383	0.329123
$85$	356.564	0.454998
$86$	981.363	1.23050
$87$	−95.0007	−0.117071
$88$	605.265	0.733198
$89$	−730.413	−0.869929	−0.434964	−	0.900448i	$-0.643239\pi$
$89$	−730.413	−0.869929	−0.434964	+	0.900448i	$0.643239\pi$
$90$	296.479	0.347241
$91$	−249.689	−0.287632
$92$	167.174	0.189446
$93$	−113.732	−0.126811
$94$	−1159.26	−1.27201
$95$	−542.451	−0.585835
$96$	524.848	0.557990
$97$	−1431.84	−1.49878	−0.749388	−	0.662131i	$-0.769652\pi$
$97$	−1431.84	−1.49878	−0.749388	+	0.662131i	$0.769652\pi$
$98$	−93.1784	−0.0960454
$99$	−1092.70	−1.10930
$100$	−532.554	−0.532554
$101$	1843.39	1.81608	0.908041	−	0.418881i	$-0.137578\pi$
$101$	1843.39	1.81608	0.908041	+	0.418881i	$0.137578\pi$
$102$	−825.731	−0.801564
$103$	103.000	0.0985329
$103$	103.000	0.0985329
$104$	−143.079	−0.134905
$105$	212.736	0.197723
$106$	190.120	0.174209
$107$	−1237.59	−1.11816	−0.559078	−	0.829115i	$-0.688845\pi$
$107$	−1237.59	−1.11816	−0.559078	+	0.829115i	$0.688845\pi$
$108$	−618.320	−0.550906
$109$	962.349	0.845654	0.422827	−	0.906210i	$-0.361038\pi$
$109$	962.349	0.845654	0.422827	+	0.906210i	$0.361038\pi$
$110$	−820.571	−0.711258
$111$	−1121.70	−0.959162
$112$	−1519.56	−1.28201
$113$	1635.95	1.36192	0.680959	−	0.732321i	$-0.261563\pi$
$113$	1635.95	1.36192	0.680959	+	0.732321i	$0.261563\pi$
$114$	1256.21	1.03206
$115$	140.356	0.113811
$116$	−175.767	−0.140686
$117$	258.305	0.204106
$118$	2697.81	2.10469
$119$	1651.07	1.27187
$120$	121.904	0.0927355
$121$	1693.30	1.27220
$122$	1025.18	0.760781
$123$	−764.862	−0.560694
$124$	−210.423	−0.152391
$125$	−965.612	−0.690936
$126$	1372.84	0.970655
$127$	1835.95	1.28279	0.641394	−	0.767212i	$-0.278356\pi$
$127$	1835.95	1.28279	0.641394	+	0.767212i	$0.278356\pi$
$128$	−1305.75	−0.901667
$129$	−728.468	−0.497194
$130$	193.976	0.130868
$131$	−82.8956	−0.0552872	−0.0276436	−	0.999618i	$-0.508800\pi$
$131$	−82.8956	−0.0552872	−0.0276436	+	0.999618i	$0.508800\pi$
$132$	725.494	0.478380
$133$	−2511.81	−1.63761
$134$	411.670	0.265395
$135$	−519.130	−0.330960
$136$	946.110	0.596531
$137$	−965.840	−0.602316	−0.301158	−	0.953574i	$-0.597373\pi$
$137$	−965.840	−0.602316	−0.301158	+	0.953574i	$0.597373\pi$
$138$	−325.036	−0.200499
$139$	−543.054	−0.331376	−0.165688	−	0.986178i	$-0.552984\pi$
$139$	−543.054	−0.331376	−0.165688	+	0.986178i	$0.552984\pi$
$140$	393.596	0.237607
$141$	860.521	0.513964
$142$	−2778.90	−1.64226
$143$	−714.917	−0.418072
$144$	1572.00	0.909721
$145$	−147.571	−0.0845179
$146$	554.713	0.314441
$147$	69.1666	0.0388079
$148$	−2075.33	−1.15264
$149$	2359.91	1.29753	0.648764	−	0.760990i	$-0.275286\pi$
$149$	2359.91	1.29753	0.648764	+	0.760990i	$0.275286\pi$
$150$	1035.45	0.563626
$151$	2431.95	1.31066	0.655328	−	0.755345i	$-0.272531\pi$
$151$	2431.95	1.31066	0.655328	+	0.755345i	$0.272531\pi$
$152$	−1439.34	−0.768066
$153$	−1708.04	−0.902530
$154$	−3799.64	−1.98821
$155$	−176.667	−0.0915501
$156$	−171.500	−0.0880193
$157$	−2120.59	−1.07797	−0.538986	−	0.842315i	$-0.681192\pi$
$157$	−2120.59	−1.07797	−0.538986	+	0.842315i	$0.681192\pi$
$158$	763.100	0.384234
$159$	−141.127	−0.0703905
$160$	815.281	0.402835
$161$	649.917	0.318140
$162$	−727.671	−0.352909
$163$	1419.31	0.682019	0.341009	−	0.940060i	$-0.389231\pi$
$163$	1419.31	0.682019	0.341009	+	0.940060i	$0.389231\pi$
$164$	−1415.12	−0.673795
$165$	609.112	0.287390
$166$	3228.77	1.50965
$167$	−2138.19	−0.990769	−0.495385	−	0.868674i	$-0.664973\pi$
$167$	−2138.19	−0.990769	−0.495385	+	0.868674i	$0.664973\pi$
$168$	564.474	0.259227
$169$	169.000	0.0769231
$170$	−1282.66	−0.578681
$171$	2598.49	1.16206
$172$	−1347.79	−0.597487
$173$	−1043.16	−0.458438	−0.229219	−	0.973375i	$-0.573617\pi$
$173$	−1043.16	−0.458438	−0.229219	+	0.973375i	$0.573617\pi$
$174$	341.744	0.148894
$175$	−2070.40	−0.894328
$176$	−4350.85	−1.86340
$177$	−2002.59	−0.850418
$178$	2627.50	1.10640
$179$	−1851.08	−0.772938	−0.386469	−	0.922302i	$-0.626305\pi$
$179$	−1851.08	−0.772938	−0.386469	+	0.922302i	$0.626305\pi$
$180$	−407.179	−0.168607
$181$	−1175.68	−0.482803	−0.241402	−	0.970425i	$-0.577607\pi$
$181$	−1175.68	−0.482803	−0.241402	+	0.970425i	$0.577607\pi$
$182$	898.201	0.365819
$183$	−760.992	−0.307400
$184$	372.422	0.149214
$185$	−1742.41	−0.692457
$186$	409.126	0.161283
$187$	4727.38	1.84867
$188$	1592.11	0.617640
$189$	−2403.83	−0.925146
$190$	1951.35	0.745083
$191$	3688.60	1.39737	0.698685	−	0.715430i	$-0.253769\pi$
$191$	3688.60	1.39737	0.698685	+	0.715430i	$0.253769\pi$
$192$	−197.947	−0.0744040
$193$	2695.76	1.00541	0.502707	−	0.864457i	$-0.332338\pi$
$193$	2695.76	1.00541	0.502707	+	0.864457i	$0.332338\pi$
$194$	5150.73	1.90619
$195$	−143.989	−0.0528781
$196$	127.970	0.0466361
$197$	1069.03	0.386624	0.193312	−	0.981137i	$-0.438077\pi$
$197$	1069.03	0.386624	0.193312	+	0.981137i	$0.438077\pi$
$198$	3930.77	1.41085
$199$	1892.78	0.674251	0.337126	−	0.941460i	$-0.390545\pi$
$199$	1892.78	0.674251	0.337126	+	0.941460i	$0.390545\pi$
$200$	−1186.40	−0.419456
$201$	−305.584	−0.107235
$202$	−6631.20	−2.30975
$203$	−683.325	−0.236256
$204$	1134.04	0.389211
$205$	−1188.11	−0.404787
$206$	−370.520	−0.125317
$207$	−672.345	−0.225755
$208$	1028.50	0.342855
$209$	−7191.89	−2.38026
$210$	−765.271	−0.251470
$211$	−5629.06	−1.83659	−0.918295	−	0.395896i	$-0.870434\pi$
$211$	−5629.06	−1.83659	−0.918295	+	0.395896i	$0.870434\pi$
$212$	−261.108	−0.0845894
$213$	2062.79	0.663567
$214$	4451.98	1.42211
$215$	−1131.58	−0.358944
$216$	−1377.46	−0.433910
$217$	−818.055	−0.255913
$218$	−3461.84	−1.07553
$219$	−411.765	−0.127052
$220$	1126.96	0.345361
$221$	−1117.51	−0.340145
$222$	4035.07	1.21989
$223$	5724.05	1.71888	0.859440	−	0.511236i	$-0.170812\pi$
$223$	5724.05	1.71888	0.859440	+	0.511236i	$0.170812\pi$
$224$	3775.15	1.12606
$225$	2141.85	0.634621
$226$	−5884.96	−1.73213
$227$	−5913.07	−1.72892	−0.864459	−	0.502703i	$-0.832339\pi$
$227$	−5913.07	−1.72892	−0.864459	+	0.502703i	$0.832339\pi$
$228$	−1725.25	−0.501130
$229$	−2781.15	−0.802548	−0.401274	−	0.915958i	$-0.631432\pi$
$229$	−2781.15	−0.802548	−0.401274	+	0.915958i	$0.631432\pi$
$230$	−504.900	−0.144748
$231$	2820.48	0.803351
$232$	−391.566	−0.110808
$233$	2260.53	0.635590	0.317795	−	0.948159i	$-0.397058\pi$
$233$	2260.53	0.635590	0.317795	+	0.948159i	$0.397058\pi$
$234$	−929.198	−0.259588
$235$	1336.70	0.371051
$236$	−3705.13	−1.02196
$237$	−566.451	−0.155253
$238$	−5939.35	−1.61761
$239$	−2495.87	−0.675499	−0.337749	−	0.941236i	$-0.609666\pi$
$239$	−2495.87	−0.675499	−0.337749	+	0.941236i	$0.609666\pi$
$240$	−876.288	−0.235684
$241$	−1387.45	−0.370845	−0.185422	−	0.982659i	$-0.559365\pi$
$241$	−1387.45	−0.370845	−0.185422	+	0.982659i	$0.559365\pi$
$242$	−6091.27	−1.61802
$243$	3919.33	1.03467
$244$	−1407.96	−0.369408
$245$	107.441	0.0280170
$246$	2751.43	0.713108
$247$	1700.10	0.437954
$248$	−468.770	−0.120028
$249$	−2396.73	−0.609985
$250$	3473.58	0.878754
$251$	−3829.49	−0.963009	−0.481504	−	0.876444i	$-0.659909\pi$
$251$	−3829.49	−0.963009	−0.481504	+	0.876444i	$0.659909\pi$
$252$	−1885.44	−0.471315
$253$	1860.86	0.462417
$254$	−6604.43	−1.63149
$255$	952.123	0.233821
$256$	5290.20	1.29155
$257$	2441.85	0.592679	0.296340	−	0.955083i	$-0.404234\pi$
$257$	2441.85	0.592679	0.296340	+	0.955083i	$0.404234\pi$
$258$	2620.51	0.632347
$259$	−8068.20	−1.93565
$260$	−266.403	−0.0635446
$261$	706.906	0.167649
$262$	298.199	0.0703160
$263$	−3845.67	−0.901651	−0.450826	−	0.892612i	$-0.648870\pi$
$263$	−3845.67	−0.901651	−0.450826	+	0.892612i	$0.648870\pi$
$264$	1616.22	0.376786
$265$	−219.222	−0.0508177
$266$	9035.69	2.08276
$267$	−1950.40	−0.447051
$268$	−565.380	−0.128866
$269$	−1364.00	−0.309161	−0.154581	−	0.987980i	$-0.549403\pi$
$269$	−1364.00	−0.309161	−0.154581	+	0.987980i	$0.549403\pi$
$270$	1867.46	0.420926
$271$	−5282.55	−1.18410	−0.592052	−	0.805900i	$-0.701682\pi$
$271$	−5282.55	−1.18410	−0.592052	+	0.805900i	$0.701682\pi$
$272$	−6800.96	−1.51606
$273$	−666.737	−0.147812
$274$	3474.40	0.766045
$275$	−5928.03	−1.29990
$276$	446.399	0.0973553
$277$	−1905.56	−0.413337	−0.206668	−	0.978411i	$-0.566262\pi$
$277$	−1905.56	−0.413337	−0.206668	+	0.978411i	$0.566262\pi$
$278$	1953.52	0.421454
$279$	846.286	0.181598
$280$	876.836	0.187146
$281$	2298.49	0.487959	0.243979	−	0.969780i	$-0.421547\pi$
$281$	2298.49	0.487959	0.243979	+	0.969780i	$0.421547\pi$
$282$	−3095.54	−0.653676
$283$	−6002.56	−1.26083	−0.630415	−	0.776258i	$-0.717115\pi$
$283$	−6002.56	−1.26083	−0.630415	+	0.776258i	$0.717115\pi$
$284$	3816.49	0.797420
$285$	−1448.49	−0.301057
$286$	2571.76	0.531718
$287$	−5501.53	−1.13152
$288$	−3905.43	−0.799061
$289$	2476.53	0.504078
$290$	530.854	0.107493
$291$	−3823.40	−0.770212
$292$	−761.832	−0.152681
$293$	−1846.84	−0.368238	−0.184119	−	0.982904i	$-0.558943\pi$
$293$	−1846.84	−0.368238	−0.184119	+	0.982904i	$0.558943\pi$
$294$	−248.812	−0.0493571
$295$	−3110.76	−0.613951
$296$	−4623.32	−0.907855
$297$	−6882.71	−1.34470
$298$	−8489.27	−1.65024
$299$	−439.891	−0.0850821
$300$	−1422.06	−0.273676
$301$	−5239.75	−1.00337
$302$	−8748.40	−1.66693
$303$	4922.36	0.933274
$304$	10346.5	1.95201
$305$	−1182.10	−0.221924
$306$	6144.31	1.14787
$307$	1527.10	0.283896	0.141948	−	0.989874i	$-0.454663\pi$
$307$	1527.10	0.283896	0.141948	+	0.989874i	$0.454663\pi$
$308$	5218.36	0.965401
$309$	275.038	0.0506355
$310$	635.522	0.116436
$311$	5129.97	0.935350	0.467675	−	0.883900i	$-0.345092\pi$
$311$	5129.97	0.935350	0.467675	+	0.883900i	$0.345092\pi$
$312$	−382.060	−0.0693266
$313$	−1302.50	−0.235212	−0.117606	−	0.993060i	$-0.537522\pi$
$313$	−1302.50	−0.235212	−0.117606	+	0.993060i	$0.537522\pi$
$314$	7628.36	1.37100
$315$	−1582.98	−0.283145
$316$	−1048.03	−0.186570
$317$	2044.86	0.362305	0.181153	−	0.983455i	$-0.442017\pi$
$317$	2044.86	0.362305	0.181153	+	0.983455i	$0.442017\pi$
$318$	507.673	0.0895248
$319$	−1956.52	−0.343398
$320$	−307.484	−0.0537152
$321$	−3304.71	−0.574614
$322$	−2337.93	−0.404621
$323$	−11241.9	−1.93658
$324$	999.371	0.171360
$325$	1401.33	0.239175
$326$	−5105.66	−0.867413
$327$	2569.73	0.434577
$328$	−3152.54	−0.530701
$329$	6189.59	1.03721
$330$	−2191.15	−0.365511
$331$	−4365.84	−0.724979	−0.362490	−	0.931988i	$-0.618073\pi$
$331$	−4365.84	−0.724979	−0.362490	+	0.931988i	$0.618073\pi$
$332$	−4434.34	−0.733030
$333$	8346.63	1.37355
$334$	7691.69	1.26009
$335$	−474.683	−0.0774171
$336$	−4057.64	−0.658816
$337$	−6958.70	−1.12482	−0.562410	−	0.826858i	$-0.690126\pi$
$337$	−6958.70	−1.12482	−0.562410	+	0.826858i	$0.690126\pi$
$338$	−607.941	−0.0978332
$339$	4368.42	0.699882
$340$	1761.59	0.280986
$341$	−2342.28	−0.371970
$342$	−9347.51	−1.47794
$343$	−6090.44	−0.958755
$344$	−3002.54	−0.470599
$345$	374.789	0.0584868
$346$	3752.53	0.583055
$347$	−5276.70	−0.816335	−0.408167	−	0.912907i	$-0.633832\pi$
$347$	−5276.70	−0.816335	−0.408167	+	0.912907i	$0.633832\pi$
$348$	−469.345	−0.0722976
$349$	−10900.9	−1.67195	−0.835977	−	0.548764i	$-0.815099\pi$
$349$	−10900.9	−1.67195	−0.835977	+	0.548764i	$0.815099\pi$
$350$	7447.81	1.13743
$351$	1627.01	0.247417
$352$	10809.1	1.63673
$353$	6360.55	0.959030	0.479515	−	0.877534i	$-0.340813\pi$
$353$	6360.55	0.959030	0.479515	+	0.877534i	$0.340813\pi$
$354$	7203.89	1.08159
$355$	3204.26	0.479055
$356$	−3608.56	−0.537229
$357$	4408.79	0.653608
$358$	6658.85	0.983047
$359$	8780.74	1.29089	0.645445	−	0.763806i	$-0.276672\pi$
$359$	8780.74	1.29089	0.645445	+	0.763806i	$0.276672\pi$
$360$	−907.095	−0.132800
$361$	10243.6	1.49345
$362$	4229.24	0.614044
$363$	4521.56	0.653776
$364$	−1233.57	−0.177629
$365$	−639.621	−0.0917241
$366$	2737.50	0.390961
$367$	−7193.18	−1.02311	−0.511554	−	0.859251i	$-0.670930\pi$
$367$	−7193.18	−1.02311	−0.511554	+	0.859251i	$0.670930\pi$
$368$	−2677.10	−0.379221
$369$	5691.39	0.802932
$370$	6267.94	0.880689
$371$	−1015.10	−0.142053
$372$	−561.886	−0.0783130
$373$	764.546	0.106131	0.0530653	−	0.998591i	$-0.483101\pi$
$373$	764.546	0.106131	0.0530653	+	0.998591i	$0.483101\pi$
$374$	−17005.7	−2.35119
$375$	−2578.45	−0.355068
$376$	3546.82	0.486472
$377$	462.503	0.0631834
$378$	8647.24	1.17663
$379$	−14054.0	−1.90476	−0.952380	−	0.304915i	$-0.901372\pi$
$379$	−14054.0	−1.90476	−0.952380	+	0.304915i	$0.901372\pi$
$380$	−2679.95	−0.361785
$381$	4902.48	0.659217
$382$	−13268.9	−1.77722
$383$	−13537.0	−1.80603	−0.903014	−	0.429610i	$-0.858651\pi$
$383$	−13537.0	−1.80603	−0.903014	+	0.429610i	$0.858651\pi$
$384$	−3486.71	−0.463361
$385$	4381.24	0.579971
$386$	−9697.40	−1.27872
$387$	5420.57	0.711998
$388$	−7073.92	−0.925577
$389$	−3403.13	−0.443562	−0.221781	−	0.975097i	$-0.571187\pi$
$389$	−3403.13	−0.443562	−0.221781	+	0.975097i	$0.571187\pi$
$390$	517.968	0.0672521
$391$	2908.78	0.376223
$392$	285.085	0.0367320
$393$	−221.354	−0.0284118
$394$	−3845.59	−0.491720
$395$	−879.906	−0.112083
$396$	−5398.44	−0.685055
$397$	2399.84	0.303387	0.151693	−	0.988428i	$-0.451527\pi$
$397$	2399.84	0.303387	0.151693	+	0.988428i	$0.451527\pi$
$398$	−6808.88	−0.857534
$399$	−6707.21	−0.841556
$400$	8528.25	1.06603
$401$	5604.85	0.697987	0.348994	−	0.937125i	$-0.386523\pi$
$401$	5604.85	0.697987	0.348994	+	0.937125i	$0.386523\pi$
$402$	1099.27	0.136385
$403$	553.695	0.0684404
$404$	9107.17	1.12153
$405$	839.054	0.102946
$406$	2458.11	0.300478
$407$	−23101.1	−2.81347
$408$	2526.37	0.306554
$409$	10417.5	1.25944	0.629720	−	0.776823i	$-0.283170\pi$
$409$	10417.5	1.25944	0.629720	+	0.776823i	$0.283170\pi$
$410$	4273.97	0.514821
$411$	−2579.06	−0.309527
$412$	508.866	0.0608495
$413$	−14404.3	−1.71620
$414$	2418.61	0.287122
$415$	−3722.99	−0.440373
$416$	−2555.18	−0.301149
$417$	−1450.10	−0.170292
$418$	25871.3	3.02729
$419$	15585.1	1.81715	0.908573	−	0.417726i	$-0.137173\pi$
$419$	15585.1	1.81715	0.908573	+	0.417726i	$0.137173\pi$
$420$	1051.01	0.122105
$421$	15203.6	1.76004	0.880020	−	0.474938i	$-0.157529\pi$
$421$	15203.6	1.76004	0.880020	+	0.474938i	$0.157529\pi$
$422$	20249.3	2.33583
$423$	−6403.19	−0.736013
$424$	−581.684	−0.0666252
$425$	−9266.30	−1.05760
$426$	−7420.42	−0.843945
$427$	−5473.69	−0.620353
$428$	−6114.26	−0.690523
$429$	−1909.02	−0.214845
$430$	4070.61	0.456516
$431$	−11342.5	−1.26763	−0.633817	−	0.773483i	$-0.718513\pi$
$431$	−11342.5	−1.26763	−0.633817	+	0.773483i	$0.718513\pi$
$432$	9901.68	1.10277
$433$	−15778.6	−1.75121	−0.875604	−	0.483030i	$-0.839536\pi$
$433$	−15778.6	−1.75121	−0.875604	+	0.483030i	$0.839536\pi$
$434$	2942.78	0.325479
$435$	−394.054	−0.0434332
$436$	4754.43	0.522238
$437$	−4425.20	−0.484407
$438$	1481.23	0.161589
$439$	478.445	0.0520158	0.0260079	−	0.999662i	$-0.491720\pi$
$439$	478.445	0.0520158	0.0260079	+	0.999662i	$0.491720\pi$
$440$	2510.58	0.272017
$441$	−514.673	−0.0555742
$442$	4020.00	0.432607
$443$	−9388.34	−1.00689	−0.503447	−	0.864026i	$-0.667935\pi$
$443$	−9388.34	−1.00689	−0.503447	+	0.864026i	$0.667935\pi$
$444$	−5541.69	−0.592336
$445$	−3029.69	−0.322744
$446$	−20591.0	−2.18613
$447$	6301.61	0.666792
$448$	−1423.80	−0.150152
$449$	17203.0	1.80815	0.904074	−	0.427377i	$-0.140562\pi$
$449$	17203.0	1.80815	0.904074	+	0.427377i	$0.140562\pi$
$450$	−7704.83	−0.807131
$451$	−15752.2	−1.64466
$452$	8082.30	0.841060
$453$	6493.96	0.673538
$454$	21271.0	2.19889
$455$	−1035.69	−0.106712
$456$	−3843.44	−0.394705
$457$	12788.4	1.30901	0.654506	−	0.756057i	$-0.272877\pi$
$457$	12788.4	1.30901	0.654506	+	0.756057i	$0.272877\pi$
$458$	10004.6	1.02071
$459$	−10758.6	−1.09405
$460$	693.421	0.0702846
$461$	−19027.1	−1.92230	−0.961150	−	0.276027i	$-0.910982\pi$
$461$	−19027.1	−1.92230	−0.961150	+	0.276027i	$0.910982\pi$
$462$	−10146.1	−1.02173
$463$	1203.98	0.120851	0.0604253	−	0.998173i	$-0.480754\pi$
$463$	1203.98	0.120851	0.0604253	+	0.998173i	$0.480754\pi$
$464$	2814.71	0.281615
$465$	−471.750	−0.0470470
$466$	−8131.78	−0.808363
$467$	16267.0	1.61188	0.805940	−	0.591998i	$-0.201661\pi$
$467$	16267.0	1.61188	0.805940	+	0.591998i	$0.201661\pi$
$468$	1276.14	0.126046
$469$	−2198.01	−0.216407
$470$	−4808.50	−0.471914
$471$	−5662.55	−0.553963
$472$	−8254.11	−0.804928
$473$	−15002.6	−1.45840
$474$	2037.69	0.197456
$475$	14097.1	1.36172
$476$	8156.99	0.785452
$477$	1050.13	0.100801
$478$	8978.34	0.859121
$479$	14191.8	1.35374	0.676870	−	0.736102i	$-0.263336\pi$
$479$	14191.8	1.35374	0.676870	+	0.736102i	$0.263336\pi$
$480$	2177.02	0.207015
$481$	5460.90	0.517663
$482$	4991.05	0.471652
$483$	1735.45	0.163490
$484$	8365.64	0.785654
$485$	−5939.14	−0.556047
$486$	−14098.9	−1.31593
$487$	−1071.80	−0.0997292	−0.0498646	−	0.998756i	$-0.515879\pi$
$487$	−1071.80	−0.0997292	−0.0498646	+	0.998756i	$0.515879\pi$
$488$	−3136.59	−0.290957
$489$	3789.95	0.350485
$490$	−386.496	−0.0356329
$491$	1731.49	0.159147	0.0795735	−	0.996829i	$-0.474644\pi$
$491$	1731.49	0.159147	0.0795735	+	0.996829i	$0.474644\pi$
$492$	−3778.76	−0.346259
$493$	−3058.30	−0.279389
$494$	−6115.74	−0.557004
$495$	−4532.44	−0.411551
$496$	3369.68	0.305047
$497$	14837.3	1.33912
$498$	8621.70	0.775799
$499$	11166.7	1.00179	0.500893	−	0.865509i	$-0.333005\pi$
$499$	11166.7	1.00179	0.500893	+	0.865509i	$0.333005\pi$
$500$	−4770.55	−0.426691
$501$	−5709.56	−0.509150
$502$	13775.8	1.22479
$503$	16175.3	1.43384	0.716921	−	0.697154i	$-0.245551\pi$
$503$	16175.3	1.43384	0.716921	+	0.697154i	$0.245551\pi$
$504$	−4200.29	−0.371222
$505$	7646.22	0.673767
$506$	−6694.05	−0.588116
$507$	451.276	0.0395303
$508$	9070.40	0.792193
$509$	7630.25	0.664450	0.332225	−	0.943200i	$-0.392201\pi$
$509$	7630.25	0.664450	0.332225	+	0.943200i	$0.392201\pi$
$510$	−3425.06	−0.297381
$511$	−2961.76	−0.256400
$512$	−8584.32	−0.740971
$513$	16367.3	1.40865
$514$	−8784.04	−0.753788
$515$	427.235	0.0365558
$516$	−3598.95	−0.307045
$517$	17722.2	1.50759
$518$	29023.6	2.46182
$519$	−2785.51	−0.235588
$520$	−593.480	−0.0500496
$521$	17260.3	1.45141	0.725707	−	0.688004i	$-0.241513\pi$
$521$	17260.3	1.45141	0.725707	+	0.688004i	$0.241513\pi$
$522$	−2542.94	−0.213221
$523$	954.027	0.0797643	0.0398821	−	0.999204i	$-0.487302\pi$
$523$	954.027	0.0797643	0.0398821	+	0.999204i	$0.487302\pi$
$524$	−409.541	−0.0341429
$525$	−5528.52	−0.459590
$526$	13834.0	1.14675
$527$	−3661.30	−0.302635
$528$	−11618.0	−0.957588
$529$	−11022.0	−0.905893
$530$	788.602	0.0646315
$531$	14901.4	1.21783
$532$	−12409.5	−1.01131
$533$	3723.67	0.302608
$534$	7016.15	0.568574
$535$	−5133.43	−0.414836
$536$	−1259.53	−0.101499
$537$	−4942.88	−0.397208
$538$	4906.68	0.393201
$539$	1424.47	0.113833
$540$	−2564.73	−0.204386
$541$	17921.4	1.42422	0.712108	−	0.702070i	$-0.247741\pi$
$541$	17921.4	1.42422	0.712108	+	0.702070i	$0.247741\pi$
$542$	19002.8	1.50598
$543$	−3139.38	−0.248110
$544$	16896.1	1.33164
$545$	3991.74	0.313738
$546$	2398.44	0.187992
$547$	−10539.4	−0.823823	−0.411911	−	0.911224i	$-0.635139\pi$
$547$	−10539.4	−0.823823	−0.411911	+	0.911224i	$0.635139\pi$
$548$	−4771.68	−0.371964
$549$	5662.59	0.440207
$550$	21324.8	1.65326
$551$	4652.67	0.359729
$552$	994.467	0.0766799
$553$	−4074.39	−0.313311
$554$	6854.85	0.525694
$555$	−4652.71	−0.355849
$556$	−2682.93	−0.204643
$557$	12048.1	0.916505	0.458253	−	0.888822i	$-0.348475\pi$
$557$	12048.1	0.916505	0.458253	+	0.888822i	$0.348475\pi$
$558$	−3044.33	−0.230962
$559$	3546.49	0.268337
$560$	−6303.00	−0.475625
$561$	12623.4	0.950018
$562$	−8268.31	−0.620601
$563$	−14002.9	−1.04822	−0.524112	−	0.851649i	$-0.675603\pi$
$563$	−14002.9	−1.04822	−0.524112	+	0.851649i	$0.675603\pi$
$564$	4251.35	0.317401
$565$	6785.75	0.505272
$566$	21592.9	1.60356
$567$	3885.23	0.287768
$568$	8502.21	0.628072
$569$	3040.97	0.224049	0.112025	−	0.993705i	$-0.464266\pi$
$569$	3040.97	0.224049	0.112025	+	0.993705i	$0.464266\pi$
$570$	5210.63	0.382894
$571$	−3251.09	−0.238273	−0.119137	−	0.992878i	$-0.538013\pi$
$571$	−3251.09	−0.238273	−0.119137	+	0.992878i	$0.538013\pi$
$572$	−3532.01	−0.258183
$573$	9849.56	0.718100
$574$	19790.6	1.43910
$575$	−3647.54	−0.264544
$576$	1472.93	0.106549
$577$	−8158.52	−0.588637	−0.294319	−	0.955707i	$-0.595093\pi$
$577$	−8158.52	−0.588637	−0.294319	+	0.955707i	$0.595093\pi$
$578$	−8908.79	−0.641102
$579$	7198.40	0.516676
$580$	−729.066	−0.0521945
$581$	−17239.3	−1.23099
$582$	13753.9	0.979580
$583$	−2906.47	−0.206473
$584$	−1697.18	−0.120256
$585$	1071.43	0.0757232
$586$	6643.62	0.468337
$587$	−3520.82	−0.247563	−0.123782	−	0.992309i	$-0.539502\pi$
$587$	−3520.82	−0.247563	−0.123782	+	0.992309i	$0.539502\pi$
$588$	341.714	0.0239660
$589$	5570.04	0.389659
$590$	11190.3	0.780842
$591$	2854.59	0.198684
$592$	33234.0	2.30728
$593$	20591.4	1.42595	0.712974	−	0.701191i	$-0.247348\pi$
$593$	20591.4	1.42595	0.712974	+	0.701191i	$0.247348\pi$
$594$	24759.0	1.71023
$595$	6848.47	0.471865
$596$	11659.0	0.801295
$597$	5054.25	0.346494
$598$	1582.41	0.108210
$599$	17164.2	1.17080	0.585400	−	0.810745i	$-0.300937\pi$
$599$	17164.2	1.17080	0.585400	+	0.810745i	$0.300937\pi$
$600$	−3168.01	−0.215556
$601$	−7455.06	−0.505987	−0.252994	−	0.967468i	$-0.581415\pi$
$601$	−7455.06	−0.505987	−0.252994	+	0.967468i	$0.581415\pi$
$602$	18848.9	1.27612
$603$	2273.87	0.153564
$604$	12014.9	0.809402
$605$	7023.65	0.471987
$606$	−17707.1	−1.18697
$607$	23519.1	1.57267	0.786335	−	0.617801i	$-0.211976\pi$
$607$	23519.1	1.57267	0.786335	+	0.617801i	$0.211976\pi$
$608$	−25704.5	−1.71456
$609$	−1824.66	−0.121411
$610$	4252.35	0.282250
$611$	−4189.38	−0.277388
$612$	−8438.49	−0.557362
$613$	12717.9	0.837965	0.418983	−	0.907994i	$-0.362387\pi$
$613$	12717.9	0.837965	0.418983	+	0.907994i	$0.362387\pi$
$614$	−5493.40	−0.361068
$615$	−3172.58	−0.208018
$616$	11625.2	0.760379
$617$	6783.92	0.442642	0.221321	−	0.975201i	$-0.428963\pi$
$617$	6783.92	0.442642	0.221321	+	0.975201i	$0.428963\pi$
$618$	−989.389	−0.0643998
$619$	−10966.5	−0.712085	−0.356042	−	0.934470i	$-0.615874\pi$
$619$	−10966.5	−0.712085	−0.356042	+	0.934470i	$0.615874\pi$
$620$	−872.815	−0.0565372
$621$	−4234.96	−0.273660
$622$	−18454.0	−1.18961
$623$	−14028.9	−0.902178
$624$	2746.38	0.176191
$625$	9469.08	0.606021
$626$	4685.45	0.299150
$627$	−19204.3	−1.22320
$628$	−10476.7	−0.665707
$629$	−36110.2	−2.28904
$630$	5694.43	0.360113
$631$	23939.9	1.51035	0.755176	−	0.655523i	$-0.227552\pi$
$631$	23939.9	1.51035	0.755176	+	0.655523i	$0.227552\pi$
$632$	−2334.75	−0.146948
$633$	−15031.1	−0.943813
$634$	−7355.94	−0.460791
$635$	7615.35	0.475915
$636$	−697.229	−0.0434700
$637$	−336.732	−0.0209447
$638$	7038.14	0.436744
$639$	−15349.3	−0.950250
$640$	−5416.15	−0.334519
$641$	29231.7	1.80122	0.900611	−	0.434626i	$-0.143119\pi$
$641$	29231.7	1.80122	0.900611	+	0.434626i	$0.143119\pi$
$642$	11888.0	0.730812
$643$	−22545.2	−1.38273	−0.691367	−	0.722504i	$-0.742991\pi$
$643$	−22545.2	−1.38273	−0.691367	+	0.722504i	$0.742991\pi$
$644$	3210.88	0.196469
$645$	−3021.62	−0.184459
$646$	40440.3	2.46301
$647$	17342.8	1.05381	0.526905	−	0.849924i	$-0.323352\pi$
$647$	17342.8	1.05381	0.526905	+	0.849924i	$0.323352\pi$
$648$	2226.35	0.134968
$649$	−41242.9	−2.49449
$650$	−5040.99	−0.304191
$651$	−2184.43	−0.131512
$652$	7012.03	0.421184
$653$	866.173	0.0519081	0.0259540	−	0.999663i	$-0.491738\pi$
$653$	866.173	0.0519081	0.0259540	+	0.999663i	$0.491738\pi$
$654$	−9244.06	−0.552708
$655$	−343.844	−0.0205116
$656$	22661.6	1.34876
$657$	3063.96	0.181943
$658$	−22265.7	−1.31916
$659$	−18288.6	−1.08107	−0.540534	−	0.841322i	$-0.681778\pi$
$659$	−18288.6	−1.08107	−0.540534	+	0.841322i	$0.681778\pi$
$660$	3009.28	0.177479
$661$	−21133.4	−1.24356	−0.621780	−	0.783192i	$-0.713590\pi$
$661$	−21133.4	−1.24356	−0.621780	+	0.783192i	$0.713590\pi$
$662$	15705.1	0.922051
$663$	−2984.06	−0.174798
$664$	−9878.62	−0.577356
$665$	−10418.8	−0.607552
$666$	−30025.2	−1.74693
$667$	−1203.85	−0.0698851
$668$	−10563.6	−0.611855
$669$	15284.8	0.883323
$670$	1707.57	0.0984615
$671$	−15672.5	−0.901682
$672$	10080.7	0.578676
$673$	−91.1046	−0.00521816	−0.00260908	−	0.999997i	$-0.500830\pi$
$673$	−91.1046	−0.00521816	−0.00260908	+	0.999997i	$0.500830\pi$
$674$	25032.4	1.43058
$675$	13491.0	0.769289
$676$	834.935	0.0475043
$677$	−7348.94	−0.417197	−0.208599	−	0.978001i	$-0.566890\pi$
$677$	−7348.94	−0.417197	−0.208599	+	0.978001i	$0.566890\pi$
$678$	−15714.4	−0.890132
$679$	−27501.1	−1.55434
$680$	3924.38	0.221313
$681$	−15789.5	−0.888481
$682$	8425.85	0.473083
$683$	−30385.4	−1.70229	−0.851145	−	0.524930i	$-0.824091\pi$
$683$	−30385.4	−1.70229	−0.851145	+	0.524930i	$0.824091\pi$
$684$	12837.7	0.717634
$685$	−4006.22	−0.223459
$686$	21909.0	1.21937
$687$	−7426.42	−0.412425
$688$	21583.3	1.19601
$689$	687.064	0.0379899
$690$	−1348.22	−0.0743854
$691$	9243.24	0.508870	0.254435	−	0.967090i	$-0.418110\pi$
$691$	9243.24	0.508870	0.254435	+	0.967090i	$0.418110\pi$
$692$	−5153.65	−0.283111
$693$	−20987.4	−1.15043
$694$	18981.8	1.03824
$695$	−2252.54	−0.122941
$696$	−1045.59	−0.0569437
$697$	−24622.7	−1.33810
$698$	39213.7	2.12645
$699$	6036.24	0.326626
$700$	−10228.7	−0.552297
$701$	6382.44	0.343882	0.171941	−	0.985107i	$-0.444996\pi$
$701$	6382.44	0.343882	0.171941	+	0.985107i	$0.444996\pi$
$702$	−5852.82	−0.314673
$703$	54935.4	2.94726
$704$	−4076.66	−0.218246
$705$	3569.36	0.190681
$706$	−22880.7	−1.21973
$707$	35405.7	1.88341
$708$	−9893.69	−0.525180
$709$	−24005.5	−1.27157	−0.635787	−	0.771865i	$-0.719324\pi$
$709$	−24005.5	−1.27157	−0.635787	+	0.771865i	$0.719324\pi$
$710$	−11526.6	−0.609278
$711$	4215.00	0.222327
$712$	−8038.99	−0.423138
$713$	−1441.22	−0.0756998
$714$	−15859.7	−0.831279
$715$	−2965.41	−0.155105
$716$	−9145.14	−0.477332
$717$	−6664.64	−0.347135
$718$	−31586.8	−1.64180
$719$	−32689.3	−1.69556	−0.847778	−	0.530351i	$-0.822060\pi$
$719$	−32689.3	−1.69556	−0.847778	+	0.530351i	$0.822060\pi$
$720$	6520.51	0.337507
$721$	1978.30	0.102186
$722$	−36849.1	−1.89942
$723$	−3704.87	−0.190575
$724$	−5808.36	−0.298158
$725$	3835.03	0.196455
$726$	−16265.3	−0.831493
$727$	−13571.2	−0.692336	−0.346168	−	0.938173i	$-0.612517\pi$
$727$	−13571.2	−0.692336	−0.346168	+	0.938173i	$0.612517\pi$
$728$	−2748.10	−0.139906
$729$	5004.01	0.254230
$730$	2300.90	0.116658
$731$	−23451.1	−1.18655
$732$	−3759.64	−0.189836
$733$	15160.6	0.763941	0.381970	−	0.924175i	$-0.375246\pi$
$733$	15160.6	0.763941	0.381970	+	0.924175i	$0.375246\pi$
$734$	25875.9	1.30122
$735$	286.897	0.0143978
$736$	6650.89	0.333091
$737$	−6293.42	−0.314547
$738$	−20473.5	−1.02119
$739$	11387.6	0.566846	0.283423	−	0.958995i	$-0.408530\pi$
$739$	11387.6	0.566846	0.283423	+	0.958995i	$0.408530\pi$
$740$	−8608.28	−0.427631
$741$	4539.73	0.225062
$742$	3651.61	0.180667
$743$	27428.8	1.35433	0.677163	−	0.735833i	$-0.263209\pi$
$743$	27428.8	1.35433	0.677163	+	0.735833i	$0.263209\pi$
$744$	−1251.74	−0.0616817
$745$	9788.71	0.481383
$746$	−2750.29	−0.134980
$747$	17834.2	0.873519
$748$	23355.4	1.14165
$749$	−23770.3	−1.15961
$750$	9275.40	0.451586
$751$	−31516.5	−1.53136	−0.765682	−	0.643219i	$-0.777598\pi$
$751$	−31516.5	−1.53136	−0.765682	+	0.643219i	$0.777598\pi$
$752$	−25495.8	−1.23635
$753$	−10225.8	−0.494884
$754$	−1663.75	−0.0803586
$755$	10087.5	0.486254
$756$	−11876.0	−0.571329
$757$	9766.47	0.468915	0.234457	−	0.972126i	$-0.424669\pi$
$757$	9766.47	0.468915	0.234457	+	0.972126i	$0.424669\pi$
$758$	50556.1	2.42253
$759$	4969.01	0.237633
$760$	−5970.26	−0.284953
$761$	−7670.23	−0.365369	−0.182684	−	0.983172i	$-0.558479\pi$
$761$	−7670.23	−0.365369	−0.182684	+	0.983172i	$0.558479\pi$
$762$	−17635.6	−0.838413
$763$	18483.7	0.877004
$764$	18223.3	0.862953
$765$	−7084.81	−0.334839
$766$	48696.5	2.29696
$767$	9749.46	0.458973
$768$	14126.3	0.663721
$769$	−2160.25	−0.101301	−0.0506507	−	0.998716i	$-0.516130\pi$
$769$	−2160.25	−0.101301	−0.0506507	+	0.998716i	$0.516130\pi$
$770$	−15760.6	−0.737625
$771$	6520.41	0.304574
$772$	13318.2	0.620899
$773$	22646.7	1.05374	0.526872	−	0.849945i	$-0.323365\pi$
$773$	22646.7	1.05374	0.526872	+	0.849945i	$0.323365\pi$
$774$	−19499.3	−0.905542
$775$	4591.19	0.212800
$776$	−15759.0	−0.729012
$777$	−21544.3	−0.994720
$778$	12242.0	0.564136
$779$	37459.2	1.72287
$780$	−711.367	−0.0326552
$781$	42482.6	1.94641
$782$	−10463.7	−0.478492
$783$	4452.65	0.203224
$784$	−2049.29	−0.0933531
$785$	−8796.02	−0.399928
$786$	796.272	0.0361350
$787$	−43739.0	−1.98110	−0.990550	−	0.137153i	$-0.956205\pi$
$787$	−43739.0	−1.98110	−0.990550	+	0.137153i	$0.956205\pi$
$788$	5281.46	0.238762
$789$	−10269.0	−0.463353
$790$	3165.27	0.142551
$791$	31421.3	1.41241
$792$	−12026.4	−0.539570
$793$	3704.83	0.165905
$794$	−8632.90	−0.385857
$795$	−585.381	−0.0261149
$796$	9351.20	0.416387
$797$	−22721.0	−1.00981	−0.504906	−	0.863175i	$-0.668473\pi$
$797$	−22721.0	−1.00981	−0.504906	+	0.863175i	$0.668473\pi$
$798$	24127.7	1.07032
$799$	27702.2	1.22658
$800$	−21187.3	−0.936356
$801$	14513.1	0.640192
$802$	−20162.2	−0.887722
$803$	−8480.19	−0.372677
$804$	−1509.72	−0.0662235
$805$	2695.80	0.118030
$806$	−1991.80	−0.0870447
$807$	−3642.24	−0.158876
$808$	20288.5	0.883352
$809$	−44838.0	−1.94860	−0.974302	−	0.225245i	$-0.927682\pi$
$809$	−44838.0	−1.94860	−0.974302	+	0.225245i	$0.927682\pi$
$810$	−3018.32	−0.130929
$811$	−11097.9	−0.480518	−0.240259	−	0.970709i	$-0.577232\pi$
$811$	−11097.9	−0.480518	−0.240259	+	0.970709i	$0.577232\pi$
$812$	−3375.93	−0.145901
$813$	−14105.8	−0.608504
$814$	83101.3	3.57826
$815$	5887.17	0.253029
$816$	−18160.4	−0.779095
$817$	35676.8	1.52775
$818$	−37474.6	−1.60179
$819$	4961.23	0.211672
$820$	−5869.80	−0.249978
$821$	−13760.0	−0.584929	−0.292464	−	0.956276i	$-0.594475\pi$
$821$	−13760.0	−0.584929	−0.292464	+	0.956276i	$0.594475\pi$
$822$	9277.59	0.393666
$823$	26115.5	1.10611	0.553055	−	0.833145i	$-0.313462\pi$
$823$	26115.5	1.10611	0.553055	+	0.833145i	$0.313462\pi$
$824$	1133.63	0.0479269
$825$	−15829.4	−0.668013
$826$	51816.4	2.18272
$827$	3685.94	0.154985	0.0774926	−	0.996993i	$-0.475309\pi$
$827$	3685.94	0.154985	0.0774926	+	0.996993i	$0.475309\pi$
$828$	−3321.68	−0.139416
$829$	31140.3	1.30464	0.652321	−	0.757943i	$-0.273796\pi$
$829$	31140.3	1.30464	0.652321	+	0.757943i	$0.273796\pi$
$830$	13392.7	0.560080
$831$	−5088.37	−0.212411
$832$	963.687	0.0401560
$833$	2226.64	0.0926151
$834$	5216.42	0.216583
$835$	−8869.04	−0.367576
$836$	−35531.1	−1.46994
$837$	5330.58	0.220133
$838$	−56064.2	−2.31110
$839$	8910.46	0.366655	0.183327	−	0.983052i	$-0.441313\pi$
$839$	8910.46	0.366655	0.183327	+	0.983052i	$0.441313\pi$
$840$	2341.39	0.0961733
$841$	−23123.3	−0.948102
$842$	−54691.5	−2.23847
$843$	6137.59	0.250759
$844$	−27810.1	−1.13420
$845$	700.997	0.0285385
$846$	23034.1	0.936085
$847$	32522.9	1.31936
$848$	4181.35	0.169325
$849$	−16028.5	−0.647933
$850$	33333.5	1.34509
$851$	−14214.2	−0.572570
$852$	10191.1	0.409789
$853$	4060.07	0.162971	0.0814854	−	0.996675i	$-0.474034\pi$
$853$	4060.07	0.162971	0.0814854	+	0.996675i	$0.474034\pi$
$854$	19690.4	0.788984
$855$	10778.3	0.431123
$856$	−13621.1	−0.543877
$857$	−26063.8	−1.03888	−0.519441	−	0.854506i	$-0.673860\pi$
$857$	−26063.8	−1.03888	−0.519441	+	0.854506i	$0.673860\pi$
$858$	6867.29	0.273247
$859$	5472.27	0.217359	0.108680	−	0.994077i	$-0.465338\pi$
$859$	5472.27	0.217359	0.108680	+	0.994077i	$0.465338\pi$
$860$	−5590.50	−0.221668
$861$	−14690.6	−0.581479
$862$	40802.3	1.61222
$863$	−35744.3	−1.40991	−0.704954	−	0.709253i	$-0.749032\pi$
$863$	−35744.3	−1.40991	−0.704954	+	0.709253i	$0.749032\pi$
$864$	−24599.4	−0.968623
$865$	−4326.92	−0.170081
$866$	56760.2	2.22724
$867$	6613.02	0.259043
$868$	−4041.56	−0.158041
$869$	−11665.9	−0.455397
$870$	1417.52	0.0552398
$871$	1487.71	0.0578750
$872$	10591.7	0.411331
$873$	28450.2	1.10297
$874$	15918.7	0.616085
$875$	−18546.4	−0.716550
$876$	−2034.30	−0.0784619
$877$	35182.0	1.35463	0.677315	−	0.735693i	$-0.263143\pi$
$877$	35182.0	1.35463	0.677315	+	0.735693i	$0.263143\pi$
$878$	−1721.10	−0.0661554
$879$	−4931.58	−0.189235
$880$	−18046.9	−0.691321
$881$	−22201.2	−0.849009	−0.424504	−	0.905426i	$-0.639552\pi$
$881$	−22201.2	−0.849009	−0.424504	+	0.905426i	$0.639552\pi$
$882$	1851.42	0.0706810
$883$	43027.8	1.63986	0.819932	−	0.572461i	$-0.194011\pi$
$883$	43027.8	1.63986	0.819932	+	0.572461i	$0.194011\pi$
$884$	−5521.00	−0.210058
$885$	−8306.57	−0.315506
$886$	33772.5	1.28060
$887$	−43714.5	−1.65478	−0.827389	−	0.561629i	$-0.810175\pi$
$887$	−43714.5	−1.65478	−0.827389	+	0.561629i	$0.810175\pi$
$888$	−12345.5	−0.466541
$889$	35262.8	1.33034
$890$	10898.6	0.410476
$891$	11124.3	0.418270
$892$	28279.3	1.06150
$893$	−42144.1	−1.57928
$894$	−22668.7	−0.848046
$895$	−7678.10	−0.286760
$896$	−25079.4	−0.935093
$897$	−1174.63	−0.0437232
$898$	−61883.9	−2.29966
$899$	1515.30	0.0562158
$900$	10581.7	0.391914
$901$	−4543.21	−0.167987
$902$	56665.0	2.09173
$903$	−13991.6	−0.515626
$904$	18005.4	0.662444
$905$	−4876.60	−0.179120
$906$	−23360.6	−0.856627
$907$	−30425.2	−1.11384	−0.556920	−	0.830566i	$-0.688017\pi$
$907$	−30425.2	−1.11384	−0.556920	+	0.830566i	$0.688017\pi$
$908$	−29213.2	−1.06770
$909$	−36627.5	−1.33648
$910$	3725.66	0.135719
$911$	37498.1	1.36374	0.681870	−	0.731474i	$-0.261167\pi$
$911$	37498.1	1.36374	0.681870	+	0.731474i	$0.261167\pi$
$912$	27627.9	1.00313
$913$	−49360.0	−1.78924
$914$	−46003.7	−1.66484
$915$	−3156.53	−0.114045
$916$	−13740.1	−0.495618
$917$	−1592.16	−0.0573368
$918$	38701.7	1.39145
$919$	−35092.3	−1.25962	−0.629808	−	0.776751i	$-0.716867\pi$
$919$	−35092.3	−1.25962	−0.629808	+	0.776751i	$0.716867\pi$
$920$	1544.77	0.0553583
$921$	4077.77	0.145892
$922$	68445.8	2.44484
$923$	−10042.5	−0.358129
$924$	13934.4	0.496114
$925$	45281.3	1.60956
$926$	−4331.07	−0.153702
$927$	−2046.57	−0.0725117
$928$	−6992.77	−0.247359
$929$	−5491.51	−0.193940	−0.0969702	−	0.995287i	$-0.530915\pi$
$929$	−5491.51	−0.193940	−0.0969702	+	0.995287i	$0.530915\pi$
$930$	1697.02	0.0598359
$931$	−3387.44	−0.119247
$932$	11168.0	0.392512
$933$	13698.4	0.480671
$934$	−58517.0	−2.05004
$935$	19608.8	0.685856
$936$	2842.93	0.0992780
$937$	−13412.6	−0.467630	−0.233815	−	0.972281i	$-0.575121\pi$
$937$	−13412.6	−0.467630	−0.233815	+	0.972281i	$0.575121\pi$
$938$	7906.88	0.275233
$939$	−3478.02	−0.120874
$940$	6603.91	0.229145
$941$	5309.21	0.183927	0.0919634	−	0.995762i	$-0.470686\pi$
$941$	5309.21	0.183927	0.0919634	+	0.995762i	$0.470686\pi$
$942$	20369.8	0.704548
$943$	−9692.37	−0.334705
$944$	59333.4	2.04570
$945$	−9970.85	−0.343229
$946$	53968.7	1.85483
$947$	55806.9	1.91497	0.957487	−	0.288477i	$-0.0931488\pi$
$947$	55806.9	1.91497	0.957487	+	0.288477i	$0.0931488\pi$
$948$	−2798.52	−0.0958773
$949$	2004.64	0.0685705
$950$	−50711.2	−1.73188
$951$	5460.33	0.186186
$952$	18171.8	0.618646
$953$	−29347.7	−0.997551	−0.498776	−	0.866731i	$-0.666217\pi$
$953$	−29347.7	−0.997551	−0.498776	+	0.866731i	$0.666217\pi$
$954$	−3777.63	−0.128202
$955$	15300.0	0.518425
$956$	−12330.7	−0.417158
$957$	−5224.43	−0.176470
$958$	−51052.0	−1.72173
$959$	−18550.7	−0.624645
$960$	−821.065	−0.0276039
$961$	−27976.9	−0.939107
$962$	−19644.4	−0.658380
$963$	24590.6	0.822866
$964$	−6854.62	−0.229017
$965$	11181.8	0.373009
$966$	−6242.92	−0.207932
$967$	−51945.5	−1.72746	−0.863731	−	0.503953i	$-0.831879\pi$
$967$	−51945.5	−1.72746	−0.863731	+	0.503953i	$0.831879\pi$
$968$	18636.6	0.618805
$969$	−30018.9	−0.995198
$970$	21364.8	0.707197
$971$	−20696.2	−0.684010	−0.342005	−	0.939698i	$-0.611106\pi$
$971$	−20696.2	−0.684010	−0.342005	+	0.939698i	$0.611106\pi$
$972$	19363.2	0.638967
$973$	−10430.3	−0.343660
$974$	3855.58	0.126839
$975$	3741.94	0.122911
$976$	22546.9	0.739455
$977$	−15342.6	−0.502410	−0.251205	−	0.967934i	$-0.580827\pi$
$977$	−15342.6	−0.502410	−0.251205	+	0.967934i	$0.580827\pi$
$978$	−13633.5	−0.445758
$979$	−40168.1	−1.31131
$980$	530.806	0.0173020
$981$	−19121.5	−0.622328
$982$	−6228.67	−0.202408
$983$	−9604.18	−0.311623	−0.155812	−	0.987787i	$-0.549799\pi$
$983$	−9604.18	−0.311623	−0.155812	+	0.987787i	$0.549799\pi$
$984$	−8418.15	−0.272724
$985$	4434.22	0.143438
$986$	11001.6	0.355336
$987$	16527.9	0.533018
$988$	8399.25	0.270461
$989$	−9231.18	−0.296799
$990$	16304.5	0.523424
$991$	27529.5	0.882446	0.441223	−	0.897397i	$-0.354545\pi$
$991$	27529.5	0.882446	0.441223	+	0.897397i	$0.354545\pi$
$992$	−8371.54	−0.267940
$993$	−11658.0	−0.372562
$994$	−53373.9	−1.70314
$995$	7851.10	0.250147
$996$	−11840.9	−0.376700
$997$	2479.91	0.0787760	0.0393880	−	0.999224i	$-0.487459\pi$
$997$	2479.91	0.0787760	0.0393880	+	0.999224i	$0.487459\pi$
$998$	−40169.9	−1.27410
$999$	52573.7	1.66502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.4.a.a.1.15	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.4.a.a.1.15	✓	72	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-3.59728 q^{2} +2.67027 q^{3} +4.94044 q^{4} +4.14791 q^{5} -9.60572 q^{6} +19.2068 q^{7} +11.0061 q^{8} -19.8697 q^{9} +O(q^{10})\)	\(q-3.59728 q^{2} +2.67027 q^{3} +4.94044 q^{4} +4.14791 q^{5} -9.60572 q^{6} +19.2068 q^{7} +11.0061 q^{8} -19.8697 q^{9} -14.9212 q^{10} +54.9936 q^{11} +13.1923 q^{12} -13.0000 q^{13} -69.0924 q^{14} +11.0760 q^{15} -79.1156 q^{16} +85.9624 q^{17} +71.4768 q^{18} -130.777 q^{19} +20.4925 q^{20} +51.2875 q^{21} -197.828 q^{22} +33.8378 q^{23} +29.3893 q^{24} -107.795 q^{25} +46.7647 q^{26} -125.155 q^{27} +94.8903 q^{28} -35.5772 q^{29} -39.8437 q^{30} -42.5919 q^{31} +196.552 q^{32} +146.848 q^{33} -309.231 q^{34} +79.6682 q^{35} -98.1649 q^{36} -420.069 q^{37} +470.441 q^{38} -34.7135 q^{39} +45.6523 q^{40} -286.436 q^{41} -184.495 q^{42} -272.807 q^{43} +271.693 q^{44} -82.4175 q^{45} -121.724 q^{46} +322.260 q^{47} -211.260 q^{48} +25.9025 q^{49} +387.769 q^{50} +229.543 q^{51} -64.2258 q^{52} -52.8511 q^{53} +450.217 q^{54} +228.109 q^{55} +211.392 q^{56} -349.210 q^{57} +127.981 q^{58} -749.958 q^{59} +54.7206 q^{60} -284.987 q^{61} +153.215 q^{62} -381.633 q^{63} -74.1298 q^{64} -53.9228 q^{65} -528.253 q^{66} -114.439 q^{67} +424.692 q^{68} +90.3561 q^{69} -286.589 q^{70} +772.501 q^{71} -218.687 q^{72} -154.203 q^{73} +1511.11 q^{74} -287.841 q^{75} -646.096 q^{76} +1056.25 q^{77} +124.874 q^{78} -212.132 q^{79} -328.164 q^{80} +202.284 q^{81} +1030.39 q^{82} -897.559 q^{83} +253.383 q^{84} +356.564 q^{85} +981.363 q^{86} -95.0007 q^{87} +605.265 q^{88} -730.413 q^{89} +296.479 q^{90} -249.689 q^{91} +167.174 q^{92} -113.732 q^{93} -1159.26 q^{94} -542.451 q^{95} +524.848 q^{96} -1431.84 q^{97} -93.1784 q^{98} -1092.70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{2} - 19 q^{3} + 261 q^{4} - 73 q^{5} - 52 q^{6} + 3 q^{7} - 18 q^{8} + 517 q^{9}+O(q^{10}) \) 72 * q - q^2 - 19 * q^3 + 261 * q^4 - 73 * q^5 - 52 * q^6 + 3 * q^7 - 18 * q^8 + 517 * q^9	\( 72 q - q^{2} - 19 q^{3} + 261 q^{4} - 73 q^{5} - 52 q^{6} + 3 q^{7} - 18 q^{8} + 517 q^{9} - 100 q^{10} - 104 q^{11} - 228 q^{12} - 936 q^{13} - 337 q^{14} + 63 q^{15} + 833 q^{16} - 307 q^{17} - 110 q^{18} - 182 q^{19} - 428 q^{20} - 177 q^{21} - 74 q^{22} - 516 q^{23} - 901 q^{24} + 1285 q^{25} + 13 q^{26} - 817 q^{27} + 187 q^{28} - 1458 q^{29} - 178 q^{30} - 620 q^{31} - 35 q^{32} - 196 q^{33} - 1619 q^{34} - 1155 q^{35} - 615 q^{36} - 1031 q^{37} - 1614 q^{38} + 247 q^{39} - 3300 q^{40} - 1124 q^{41} - 2190 q^{42} - 383 q^{43} - 1902 q^{44} - 1828 q^{45} - 1109 q^{46} - 1531 q^{47} - 4464 q^{48} + 1191 q^{49} - 352 q^{50} - 1267 q^{51} - 3393 q^{52} - 3092 q^{53} - 1581 q^{54} - 2264 q^{55} - 1470 q^{56} - 502 q^{57} - 2003 q^{58} - 2452 q^{59} - 1909 q^{60} - 1764 q^{61} - 2232 q^{62} - 1086 q^{63} + 2272 q^{64} + 949 q^{65} - 2539 q^{66} + 832 q^{67} - 1796 q^{68} - 4738 q^{69} - 3251 q^{70} - 2995 q^{71} - 2534 q^{72} + 16 q^{73} - 3408 q^{74} - 3060 q^{75} - 3729 q^{76} - 5454 q^{77} + 676 q^{78} - 3594 q^{79} - 1631 q^{80} + 16 q^{81} - 1293 q^{82} - 2832 q^{83} - 4565 q^{84} - 887 q^{85} - 3982 q^{86} - 1530 q^{87} - 1757 q^{88} - 8104 q^{89} - 5932 q^{90} - 39 q^{91} - 5371 q^{92} - 3042 q^{93} - 3464 q^{94} - 4582 q^{95} - 3991 q^{96} - 2514 q^{97} - 2886 q^{98} - 2752 q^{99}+O(q^{100}) \) 72 * q - q^2 - 19 * q^3 + 261 * q^4 - 73 * q^5 - 52 * q^6 + 3 * q^7 - 18 * q^8 + 517 * q^9 - 100 * q^10 - 104 * q^11 - 228 * q^12 - 936 * q^13 - 337 * q^14 + 63 * q^15 + 833 * q^16 - 307 * q^17 - 110 * q^18 - 182 * q^19 - 428 * q^20 - 177 * q^21 - 74 * q^22 - 516 * q^23 - 901 * q^24 + 1285 * q^25 + 13 * q^26 - 817 * q^27 + 187 * q^28 - 1458 * q^29 - 178 * q^30 - 620 * q^31 - 35 * q^32 - 196 * q^33 - 1619 * q^34 - 1155 * q^35 - 615 * q^36 - 1031 * q^37 - 1614 * q^38 + 247 * q^39 - 3300 * q^40 - 1124 * q^41 - 2190 * q^42 - 383 * q^43 - 1902 * q^44 - 1828 * q^45 - 1109 * q^46 - 1531 * q^47 - 4464 * q^48 + 1191 * q^49 - 352 * q^50 - 1267 * q^51 - 3393 * q^52 - 3092 * q^53 - 1581 * q^54 - 2264 * q^55 - 1470 * q^56 - 502 * q^57 - 2003 * q^58 - 2452 * q^59 - 1909 * q^60 - 1764 * q^61 - 2232 * q^62 - 1086 * q^63 + 2272 * q^64 + 949 * q^65 - 2539 * q^66 + 832 * q^67 - 1796 * q^68 - 4738 * q^69 - 3251 * q^70 - 2995 * q^71 - 2534 * q^72 + 16 * q^73 - 3408 * q^74 - 3060 * q^75 - 3729 * q^76 - 5454 * q^77 + 676 * q^78 - 3594 * q^79 - 1631 * q^80 + 16 * q^81 - 1293 * q^82 - 2832 * q^83 - 4565 * q^84 - 887 * q^85 - 3982 * q^86 - 1530 * q^87 - 1757 * q^88 - 8104 * q^89 - 5932 * q^90 - 39 * q^91 - 5371 * q^92 - 3042 * q^93 - 3464 * q^94 - 4582 * q^95 - 3991 * q^96 - 2514 * q^97 - 2886 * q^98 - 2752 * q^99

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