LMFDB - Embedded newform 143.4.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.71870$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.71870 q^{2} +7.61710 q^{3} +5.82875 q^{4} +15.9808 q^{5} +28.3257 q^{6} -21.9580 q^{7} -8.07423 q^{8} +31.0202 q^{9} +O(q^{10})$	\(q+3.71870 q^{2} +7.61710 q^{3} +5.82875 q^{4} +15.9808 q^{5} +28.3257 q^{6} -21.9580 q^{7} -8.07423 q^{8} +31.0202 q^{9} +59.4279 q^{10} -11.0000 q^{11} +44.3982 q^{12} -13.0000 q^{13} -81.6552 q^{14} +121.727 q^{15} -76.6557 q^{16} -94.2436 q^{17} +115.355 q^{18} +13.8658 q^{19} +93.1482 q^{20} -167.256 q^{21} -40.9057 q^{22} +77.7248 q^{23} -61.5022 q^{24} +130.386 q^{25} -48.3431 q^{26} +30.6225 q^{27} -127.988 q^{28} +295.256 q^{29} +452.668 q^{30} +136.346 q^{31} -220.466 q^{32} -83.7881 q^{33} -350.464 q^{34} -350.906 q^{35} +180.809 q^{36} -145.717 q^{37} +51.5626 q^{38} -99.0223 q^{39} -129.033 q^{40} +324.335 q^{41} -621.976 q^{42} -287.434 q^{43} -64.1163 q^{44} +495.728 q^{45} +289.035 q^{46} +413.107 q^{47} -583.894 q^{48} +139.152 q^{49} +484.868 q^{50} -717.863 q^{51} -75.7738 q^{52} +522.747 q^{53} +113.876 q^{54} -175.789 q^{55} +177.294 q^{56} +105.617 q^{57} +1097.97 q^{58} -215.425 q^{59} +709.519 q^{60} -862.881 q^{61} +507.029 q^{62} -681.141 q^{63} -206.602 q^{64} -207.751 q^{65} -311.583 q^{66} -282.000 q^{67} -549.323 q^{68} +592.038 q^{69} -1304.92 q^{70} -768.489 q^{71} -250.464 q^{72} +767.477 q^{73} -541.877 q^{74} +993.165 q^{75} +80.8200 q^{76} +241.538 q^{77} -368.235 q^{78} -641.682 q^{79} -1225.02 q^{80} -604.292 q^{81} +1206.11 q^{82} -193.350 q^{83} -974.894 q^{84} -1506.09 q^{85} -1068.88 q^{86} +2248.99 q^{87} +88.8165 q^{88} +758.862 q^{89} +1843.47 q^{90} +285.454 q^{91} +453.039 q^{92} +1038.56 q^{93} +1536.22 q^{94} +221.586 q^{95} -1679.31 q^{96} +994.465 q^{97} +517.467 q^{98} -341.223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * 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 $

$2$	3.71870	1.31476	0.657380	−	0.753559i	$-0.271665\pi$
$2$	3.71870	1.31476	0.657380	+	0.753559i	$0.271665\pi$
$3$	7.61710	1.46591	0.732956	−	0.680276i	$-0.238140\pi$
$3$	7.61710	1.46591	0.732956	+	0.680276i	$0.238140\pi$
$4$	5.82875	0.728594
$5$	15.9808	1.42937	0.714684	−	0.699448i	$-0.246571\pi$
$5$	15.9808	1.42937	0.714684	+	0.699448i	$0.246571\pi$
$6$	28.3257	1.92732
$7$	−21.9580	−1.18562	−0.592809	−	0.805343i	$-0.701981\pi$
$7$	−21.9580	−1.18562	−0.592809	+	0.805343i	$0.701981\pi$
$8$	−8.07423	−0.356834
$9$	31.0202	1.14890
$10$	59.4279	1.87927
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	44.3982	1.06805
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−81.6552	−1.55880
$15$	121.727	2.09533
$16$	−76.6557	−1.19774
$17$	−94.2436	−1.34455	−0.672277	−	0.740299i	$-0.734684\pi$
$17$	−94.2436	−1.34455	−0.672277	+	0.740299i	$0.734684\pi$
$18$	115.355	1.51052
$19$	13.8658	0.167422	0.0837111	−	0.996490i	$-0.473323\pi$
$19$	13.8658	0.167422	0.0837111	+	0.996490i	$0.473323\pi$
$20$	93.1482	1.04143
$21$	−167.256	−1.73801
$22$	−40.9057	−0.396415
$23$	77.7248	0.704641	0.352320	−	0.935879i	$-0.385393\pi$
$23$	77.7248	0.704641	0.352320	+	0.935879i	$0.385393\pi$
$24$	−61.5022	−0.523087
$25$	130.386	1.04309
$26$	−48.3431	−0.364649
$27$	30.6225	0.218270
$28$	−127.988	−0.863835
$29$	295.256	1.89061	0.945304	−	0.326191i	$-0.105765\pi$
$29$	295.256	1.89061	0.945304	+	0.326191i	$0.105765\pi$
$30$	452.668	2.75485
$31$	136.346	0.789949	0.394975	−	0.918692i	$-0.370753\pi$
$31$	136.346	0.789949	0.394975	+	0.918692i	$0.370753\pi$
$32$	−220.466	−1.21791
$33$	−83.7881	−0.441989
$34$	−350.464	−1.76777
$35$	−350.906	−1.69468
$36$	180.809	0.837080
$37$	−145.717	−0.647451	−0.323725	−	0.946151i	$-0.604935\pi$
$37$	−145.717	−0.647451	−0.323725	+	0.946151i	$0.604935\pi$
$38$	51.5626	0.220120
$39$	−99.0223	−0.406571
$40$	−129.033	−0.510046
$41$	324.335	1.23543	0.617715	−	0.786402i	$-0.288058\pi$
$41$	324.335	1.23543	0.617715	+	0.786402i	$0.288058\pi$
$42$	−621.976	−2.28507
$43$	−287.434	−1.01938	−0.509689	−	0.860359i	$-0.670239\pi$
$43$	−287.434	−1.01938	−0.509689	+	0.860359i	$0.670239\pi$
$44$	−64.1163	−0.219679
$45$	495.728	1.64220
$46$	289.035	0.926434
$47$	413.107	1.28208	0.641041	−	0.767507i	$-0.278503\pi$
$47$	413.107	1.28208	0.641041	+	0.767507i	$0.278503\pi$
$48$	−583.894	−1.75579
$49$	139.152	0.405692
$50$	484.868	1.37141
$51$	−717.863	−1.97100
$52$	−75.7738	−0.202076
$53$	522.747	1.35481	0.677403	−	0.735612i	$-0.263105\pi$
$53$	522.747	1.35481	0.677403	+	0.735612i	$0.263105\pi$
$54$	113.876	0.286973
$55$	−175.789	−0.430970
$56$	177.294	0.423069
$57$	105.617	0.245426
$58$	1097.97	2.48570
$59$	−215.425	−0.475355	−0.237678	−	0.971344i	$-0.576386\pi$
$59$	−215.425	−0.475355	−0.237678	+	0.971344i	$0.576386\pi$
$60$	709.519	1.52664
$61$	−862.881	−1.81116	−0.905579	−	0.424178i	$-0.860563\pi$
$61$	−862.881	−1.81116	−0.905579	+	0.424178i	$0.860563\pi$
$62$	507.029	1.03859
$63$	−681.141	−1.36215
$64$	−206.602	−0.403519
$65$	−207.751	−0.396435
$66$	−311.583	−0.581110
$67$	−282.000	−0.514205	−0.257103	−	0.966384i	$-0.582768\pi$
$67$	−282.000	−0.514205	−0.257103	+	0.966384i	$0.582768\pi$
$68$	−549.323	−0.979634
$69$	592.038	1.03294
$70$	−1304.92	−2.22810
$71$	−768.489	−1.28455	−0.642274	−	0.766475i	$-0.722009\pi$
$71$	−768.489	−1.28455	−0.642274	+	0.766475i	$0.722009\pi$
$72$	−250.464	−0.409965
$73$	767.477	1.23050	0.615249	−	0.788333i	$-0.289055\pi$
$73$	767.477	1.23050	0.615249	+	0.788333i	$0.289055\pi$
$74$	−541.877	−0.851242
$75$	993.165	1.52908
$76$	80.8200	0.121983
$77$	241.538	0.357478
$78$	−368.235	−0.534543
$79$	−641.682	−0.913859	−0.456930	−	0.889503i	$-0.651051\pi$
$79$	−641.682	−0.913859	−0.456930	+	0.889503i	$0.651051\pi$
$80$	−1225.02	−1.71202
$81$	−604.292	−0.828932
$82$	1206.11	1.62429
$83$	−193.350	−0.255697	−0.127849	−	0.991794i	$-0.540807\pi$
$83$	−193.350	−0.255697	−0.127849	+	0.991794i	$0.540807\pi$
$84$	−974.894	−1.26631
$85$	−1506.09	−1.92186
$86$	−1068.88	−1.34024
$87$	2248.99	2.77146
$88$	88.8165	0.107589
$89$	758.862	0.903811	0.451906	−	0.892066i	$-0.350744\pi$
$89$	758.862	0.903811	0.451906	+	0.892066i	$0.350744\pi$
$90$	1843.47	2.15909
$91$	285.454	0.328832
$92$	453.039	0.513397
$93$	1038.56	1.15800
$94$	1536.22	1.68563
$95$	221.586	0.239308
$96$	−1679.31	−1.78535
$97$	994.465	1.04096	0.520478	−	0.853875i	$-0.325754\pi$
$97$	994.465	1.04096	0.520478	+	0.853875i	$0.325754\pi$
$98$	517.467	0.533388
$99$	−341.223	−0.346406
$100$	759.989	0.759989
$101$	−577.765	−0.569206	−0.284603	−	0.958645i	$-0.591862\pi$
$101$	−577.765	−0.569206	−0.284603	+	0.958645i	$0.591862\pi$
$102$	−2669.52	−2.59139
$103$	−124.959	−0.119539	−0.0597697	−	0.998212i	$-0.519037\pi$
$103$	−124.959	−0.119539	−0.0597697	+	0.998212i	$0.519037\pi$
$104$	104.965	0.0989679
$105$	−2672.89	−2.48426
$106$	1943.94	1.78125
$107$	1038.47	0.938250	0.469125	−	0.883132i	$-0.344569\pi$
$107$	1038.47	0.938250	0.469125	+	0.883132i	$0.344569\pi$
$108$	178.491	0.159030
$109$	−1472.49	−1.29393	−0.646966	−	0.762518i	$-0.723963\pi$
$109$	−1472.49	−1.29393	−0.646966	+	0.762518i	$0.723963\pi$
$110$	−653.707	−0.566623
$111$	−1109.94	−0.949105
$112$	1683.20	1.42007
$113$	450.818	0.375304	0.187652	−	0.982236i	$-0.439912\pi$
$113$	450.818	0.375304	0.187652	+	0.982236i	$0.439912\pi$
$114$	392.758	0.322677
$115$	1242.11	1.00719
$116$	1720.97	1.37749
$117$	−403.263	−0.318647
$118$	−801.102	−0.624978
$119$	2069.40	1.59413
$120$	−982.855	−0.747683
$121$	121.000	0.0909091
$122$	−3208.80	−2.38124
$123$	2470.49	1.81103
$124$	794.726	0.575552
$125$	86.0768	0.0615916
$126$	−2532.96	−1.79091
$127$	−626.309	−0.437606	−0.218803	−	0.975769i	$-0.570215\pi$
$127$	−626.309	−0.437606	−0.218803	+	0.975769i	$0.570215\pi$
$128$	995.437	0.687383
$129$	−2189.41	−1.49432
$130$	−772.562	−0.521217
$131$	1392.91	0.929001	0.464500	−	0.885573i	$-0.346234\pi$
$131$	1392.91	0.929001	0.464500	+	0.885573i	$0.346234\pi$
$132$	−488.380	−0.322031
$133$	−304.464	−0.198499
$134$	−1048.67	−0.676057
$135$	489.372	0.311988
$136$	760.944	0.479783
$137$	1426.92	0.889855	0.444927	−	0.895567i	$-0.353229\pi$
$137$	1426.92	0.889855	0.444927	+	0.895567i	$0.353229\pi$
$138$	2201.61	1.35807
$139$	2504.42	1.52822	0.764110	−	0.645086i	$-0.223179\pi$
$139$	2504.42	1.52822	0.764110	+	0.645086i	$0.223179\pi$
$140$	−2045.34	−1.23474
$141$	3146.68	1.87942
$142$	−2857.78	−1.68887
$143$	143.000	0.0836242
$144$	−2377.88	−1.37609
$145$	4718.43	2.70237
$146$	2854.02	1.61781
$147$	1059.94	0.594709
$148$	−849.346	−0.471729
$149$	−253.565	−0.139415	−0.0697076	−	0.997567i	$-0.522207\pi$
$149$	−253.565	−0.139415	−0.0697076	+	0.997567i	$0.522207\pi$
$150$	3693.29	2.01037
$151$	1107.30	0.596763	0.298381	−	0.954447i	$-0.403553\pi$
$151$	1107.30	0.596763	0.298381	+	0.954447i	$0.403553\pi$
$152$	−111.955	−0.0597419
$153$	−2923.46	−1.54476
$154$	898.207	0.469997
$155$	2178.92	1.12913
$156$	−577.176	−0.296225
$157$	300.304	0.152655	0.0763275	−	0.997083i	$-0.475681\pi$
$157$	300.304	0.152655	0.0763275	+	0.997083i	$0.475681\pi$
$158$	−2386.22	−1.20151
$159$	3981.81	1.98603
$160$	−3523.22	−1.74084
$161$	−1706.68	−0.835436
$162$	−2247.18	−1.08985
$163$	−2397.73	−1.15218	−0.576088	−	0.817388i	$-0.695422\pi$
$163$	−2397.73	−1.15218	−0.576088	+	0.817388i	$0.695422\pi$
$164$	1890.47	0.900127
$165$	−1339.00	−0.631765
$166$	−719.010	−0.336181
$167$	−409.645	−0.189816	−0.0949081	−	0.995486i	$-0.530256\pi$
$167$	−409.645	−0.189816	−0.0949081	+	0.995486i	$0.530256\pi$
$168$	1350.46	0.620182
$169$	169.000	0.0769231
$170$	−5600.70	−2.52679
$171$	430.119	0.192351
$172$	−1675.38	−0.742712
$173$	4156.37	1.82661	0.913304	−	0.407279i	$-0.133522\pi$
$173$	4156.37	1.82661	0.913304	+	0.407279i	$0.133522\pi$
$174$	8363.34	3.64381
$175$	−2863.02	−1.23671
$176$	843.212	0.361134
$177$	−1640.91	−0.696829
$178$	2821.98	1.18829
$179$	−3264.66	−1.36320	−0.681599	−	0.731726i	$-0.738715\pi$
$179$	−3264.66	−1.36320	−0.681599	+	0.731726i	$0.738715\pi$
$180$	2889.48	1.19649
$181$	−4281.02	−1.75804	−0.879021	−	0.476783i	$-0.841803\pi$
$181$	−4281.02	−1.75804	−0.879021	+	0.476783i	$0.841803\pi$
$182$	1061.52	0.432335
$183$	−6572.65	−2.65500
$184$	−627.568	−0.251440
$185$	−2328.67	−0.925444
$186$	3862.09	1.52249
$187$	1036.68	0.405399
$188$	2407.90	0.934117
$189$	−672.408	−0.258785
$190$	824.012	0.314632
$191$	500.149	0.189474	0.0947370	−	0.995502i	$-0.469799\pi$
$191$	500.149	0.189474	0.0947370	+	0.995502i	$0.469799\pi$
$192$	−1573.71	−0.591523
$193$	4747.58	1.77067	0.885333	−	0.464958i	$-0.153931\pi$
$193$	4747.58	1.77067	0.885333	+	0.464958i	$0.153931\pi$
$194$	3698.12	1.36861
$195$	−1582.46	−0.581139
$196$	811.085	0.295585
$197$	949.462	0.343382	0.171691	−	0.985151i	$-0.445077\pi$
$197$	949.462	0.343382	0.171691	+	0.985151i	$0.445077\pi$
$198$	−1268.91	−0.455440
$199$	−2842.58	−1.01259	−0.506294	−	0.862361i	$-0.668985\pi$
$199$	−2842.58	−1.01259	−0.506294	+	0.862361i	$0.668985\pi$
$200$	−1052.77	−0.372210
$201$	−2148.02	−0.753780
$202$	−2148.54	−0.748369
$203$	−6483.22	−2.24154
$204$	−4184.25	−1.43606
$205$	5183.14	1.76588
$206$	−464.685	−0.157166
$207$	2411.04	0.809560
$208$	996.524	0.332195
$209$	−152.523	−0.0504797
$210$	−9939.67	−3.26620
$211$	−5461.11	−1.78179	−0.890897	−	0.454205i	$-0.849923\pi$
$211$	−5461.11	−1.78179	−0.890897	+	0.454205i	$0.849923\pi$
$212$	3046.96	0.987104
$213$	−5853.66	−1.88303
$214$	3861.77	1.23357
$215$	−4593.42	−1.45706
$216$	−247.253	−0.0778862
$217$	−2993.88	−0.936579
$218$	−5475.74	−1.70121
$219$	5845.95	1.80380
$220$	−1024.63	−0.314002
$221$	1225.17	0.372912
$222$	−4127.53	−1.24785
$223$	−619.715	−0.186095	−0.0930475	−	0.995662i	$-0.529661\pi$
$223$	−619.715	−0.186095	−0.0930475	+	0.995662i	$0.529661\pi$
$224$	4840.98	1.44398
$225$	4044.61	1.19840
$226$	1676.46	0.493435
$227$	385.194	0.112627	0.0563133	−	0.998413i	$-0.482065\pi$
$227$	385.194	0.112627	0.0563133	+	0.998413i	$0.482065\pi$
$228$	615.614	0.178816
$229$	3469.19	1.00109	0.500546	−	0.865710i	$-0.333132\pi$
$229$	3469.19	1.00109	0.500546	+	0.865710i	$0.333132\pi$
$230$	4619.02	1.32421
$231$	1839.82	0.524031
$232$	−2383.96	−0.674633
$233$	−4810.92	−1.35268	−0.676339	−	0.736591i	$-0.736434\pi$
$233$	−4810.92	−1.35268	−0.676339	+	0.736591i	$0.736434\pi$
$234$	−1499.62	−0.418944
$235$	6601.78	1.83257
$236$	−1255.66	−0.346341
$237$	−4887.76	−1.33964
$238$	7695.48	2.09590
$239$	−1958.13	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$239$	−1958.13	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$240$	−9331.10	−2.50967
$241$	−598.534	−0.159979	−0.0799896	−	0.996796i	$-0.525489\pi$
$241$	−598.534	−0.159979	−0.0799896	+	0.996796i	$0.525489\pi$
$242$	449.963	0.119524
$243$	−5429.76	−1.43341
$244$	−5029.52	−1.31960
$245$	2223.77	0.579883
$246$	9187.03	2.38107
$247$	−180.255	−0.0464346
$248$	−1100.89	−0.281881
$249$	−1472.76	−0.374830
$250$	320.094	0.0809781
$251$	4796.24	1.20612	0.603060	−	0.797696i	$-0.293948\pi$
$251$	4796.24	1.20612	0.603060	+	0.797696i	$0.293948\pi$
$252$	−3970.20	−0.992458
$253$	−854.973	−0.212457
$254$	−2329.06	−0.575346
$255$	−11472.0	−2.81728
$256$	5354.55	1.30726
$257$	−1653.19	−0.401259	−0.200629	−	0.979667i	$-0.564299\pi$
$257$	−1653.19	−0.401259	−0.200629	+	0.979667i	$0.564299\pi$
$258$	−8141.77	−1.96467
$259$	3199.64	0.767630
$260$	−1210.93	−0.288840
$261$	9158.90	2.17211
$262$	5179.82	1.22141
$263$	−6804.82	−1.59545	−0.797725	−	0.603022i	$-0.793963\pi$
$263$	−6804.82	−1.59545	−0.797725	+	0.603022i	$0.793963\pi$
$264$	676.524	0.157717
$265$	8353.91	1.93652
$266$	−1132.21	−0.260979
$267$	5780.33	1.32491
$268$	−1643.71	−0.374647
$269$	−6668.90	−1.51156	−0.755781	−	0.654824i	$-0.772743\pi$
$269$	−6668.90	−1.51156	−0.755781	+	0.654824i	$0.772743\pi$
$270$	1819.83	0.410190
$271$	−3452.63	−0.773920	−0.386960	−	0.922097i	$-0.626475\pi$
$271$	−3452.63	−0.773920	−0.386960	+	0.922097i	$0.626475\pi$
$272$	7224.31	1.61043
$273$	2174.33	0.482038
$274$	5306.30	1.16995
$275$	−1434.25	−0.314503
$276$	3450.84	0.752595
$277$	7688.28	1.66767	0.833834	−	0.552016i	$-0.186141\pi$
$277$	7688.28	1.66767	0.833834	+	0.552016i	$0.186141\pi$
$278$	9313.21	2.00924
$279$	4229.48	0.907570
$280$	2833.30	0.604721
$281$	2718.52	0.577129	0.288564	−	0.957461i	$-0.406822\pi$
$281$	2718.52	0.577129	0.288564	+	0.957461i	$0.406822\pi$
$282$	11701.6	2.47098
$283$	−1760.48	−0.369786	−0.184893	−	0.982759i	$-0.559194\pi$
$283$	−1760.48	−0.369786	−0.184893	+	0.982759i	$0.559194\pi$
$284$	−4479.33	−0.935914
$285$	1687.84	0.350804
$286$	531.775	0.109946
$287$	−7121.74	−1.46475
$288$	−6838.90	−1.39926
$289$	3968.86	0.807827
$290$	17546.4	3.55297
$291$	7574.94	1.52595
$292$	4473.43	0.896534
$293$	−3812.17	−0.760100	−0.380050	−	0.924966i	$-0.624093\pi$
$293$	−3812.17	−0.760100	−0.380050	+	0.924966i	$0.624093\pi$
$294$	3941.60	0.781900
$295$	−3442.67	−0.679457
$296$	1176.55	0.231032
$297$	−336.847	−0.0658110
$298$	−942.934	−0.183298
$299$	−1010.42	−0.195432
$300$	5788.91	1.11408
$301$	6311.46	1.20859
$302$	4117.74	0.784600
$303$	−4400.90	−0.834406
$304$	−1062.89	−0.200529
$305$	−13789.5	−2.58881
$306$	−10871.5	−2.03098
$307$	5461.19	1.01527	0.507633	−	0.861573i	$-0.330521\pi$
$307$	5461.19	1.01527	0.507633	+	0.861573i	$0.330521\pi$
$308$	1407.86	0.260456
$309$	−951.824	−0.175234
$310$	8102.74	1.48453
$311$	−10343.7	−1.88598	−0.942990	−	0.332822i	$-0.891999\pi$
$311$	−10343.7	−1.88598	−0.942990	+	0.332822i	$0.891999\pi$
$312$	799.529	0.145078
$313$	2140.94	0.386624	0.193312	−	0.981137i	$-0.438077\pi$
$313$	2140.94	0.386624	0.193312	+	0.981137i	$0.438077\pi$
$314$	1116.74	0.200705
$315$	−10885.2	−1.94702
$316$	−3740.21	−0.665832
$317$	3706.97	0.656796	0.328398	−	0.944539i	$-0.393491\pi$
$317$	3706.97	0.656796	0.328398	+	0.944539i	$0.393491\pi$
$318$	14807.2	2.61115
$319$	−3247.81	−0.570040
$320$	−3301.66	−0.576777
$321$	7910.14	1.37539
$322$	−6346.63	−1.09840
$323$	−1306.76	−0.225108
$324$	−3522.27	−0.603955
$325$	−1695.02	−0.289301
$326$	−8916.45	−1.51484
$327$	−11216.1	−1.89679
$328$	−2618.76	−0.440843
$329$	−9070.99	−1.52006
$330$	−4979.35	−0.830619
$331$	8767.20	1.45586	0.727928	−	0.685653i	$-0.240483\pi$
$331$	8767.20	1.45586	0.727928	+	0.685653i	$0.240483\pi$
$332$	−1126.99	−0.186300
$333$	−4520.16	−0.743854
$334$	−1523.35	−0.249563
$335$	−4506.58	−0.734988
$336$	12821.1	2.08170
$337$	106.728	0.0172518	0.00862588	−	0.999963i	$-0.497254\pi$
$337$	106.728	0.0172518	0.00862588	+	0.999963i	$0.497254\pi$
$338$	628.461	0.101135
$339$	3433.93	0.550163
$340$	−8778.62	−1.40026
$341$	−1499.80	−0.238179
$342$	1599.48	0.252895
$343$	4476.08	0.704623
$344$	2320.81	0.363748
$345$	9461.24	1.47645
$346$	15456.3	2.40155
$347$	708.265	0.109572	0.0547862	−	0.998498i	$-0.482552\pi$
$347$	708.265	0.109572	0.0547862	+	0.998498i	$0.482552\pi$
$348$	13108.8	2.01927
$349$	−1463.34	−0.224443	−0.112222	−	0.993683i	$-0.535797\pi$
$349$	−1463.34	−0.224443	−0.112222	+	0.993683i	$0.535797\pi$
$350$	−10646.7	−1.62597
$351$	−398.092	−0.0605373
$352$	2425.12	0.367215
$353$	−3520.97	−0.530885	−0.265443	−	0.964127i	$-0.585518\pi$
$353$	−3520.97	−0.530885	−0.265443	+	0.964127i	$0.585518\pi$
$354$	−6102.07	−0.916163
$355$	−12281.1	−1.83609
$356$	4423.22	0.658511
$357$	15762.8	2.33685
$358$	−12140.3	−1.79228
$359$	3643.08	0.535583	0.267791	−	0.963477i	$-0.413706\pi$
$359$	3643.08	0.535583	0.267791	+	0.963477i	$0.413706\pi$
$360$	−4002.62	−0.585991
$361$	−6666.74	−0.971970
$362$	−15919.8	−2.31140
$363$	921.669	0.133265
$364$	1663.84	0.239585
$365$	12264.9	1.75883
$366$	−24441.7	−3.49068
$367$	−2441.67	−0.347286	−0.173643	−	0.984809i	$-0.555554\pi$
$367$	−2441.67	−0.347286	−0.173643	+	0.984809i	$0.555554\pi$
$368$	−5958.05	−0.843980
$369$	10061.0	1.41938
$370$	−8659.63	−1.21674
$371$	−11478.5	−1.60628
$372$	6053.50	0.843709
$373$	−12672.7	−1.75917	−0.879584	−	0.475743i	$-0.842179\pi$
$373$	−12672.7	−1.75917	−0.879584	+	0.475743i	$0.842179\pi$
$374$	3855.10	0.533002
$375$	655.656	0.0902878
$376$	−3335.52	−0.457490
$377$	−3838.33	−0.524360
$378$	−2500.48	−0.340241
$379$	−3687.51	−0.499775	−0.249887	−	0.968275i	$-0.580394\pi$
$379$	−3687.51	−0.499775	−0.249887	+	0.968275i	$0.580394\pi$
$380$	1291.57	0.174358
$381$	−4770.66	−0.641491
$382$	1859.91	0.249113
$383$	10948.6	1.46070	0.730349	−	0.683074i	$-0.239357\pi$
$383$	10948.6	1.46070	0.730349	+	0.683074i	$0.239357\pi$
$384$	7582.34	1.00764
$385$	3859.97	0.510967
$386$	17654.8	2.32800
$387$	−8916.26	−1.17116
$388$	5796.49	0.758434
$389$	13215.2	1.72245	0.861227	−	0.508220i	$-0.169696\pi$
$389$	13215.2	1.72245	0.861227	+	0.508220i	$0.169696\pi$
$390$	−5884.69	−0.764058
$391$	−7325.06	−0.947428
$392$	−1123.55	−0.144765
$393$	10609.9	1.36183
$394$	3530.77	0.451465
$395$	−10254.6	−1.30624
$396$	−1988.90	−0.252389
$397$	13313.7	1.68312	0.841559	−	0.540166i	$-0.181639\pi$
$397$	13313.7	1.68312	0.841559	+	0.540166i	$0.181639\pi$
$398$	−10570.7	−1.33131
$399$	−2319.13	−0.290982
$400$	−9994.85	−1.24936
$401$	9739.87	1.21293	0.606466	−	0.795109i	$-0.292587\pi$
$401$	9739.87	1.21293	0.606466	+	0.795109i	$0.292587\pi$
$402$	−7987.85	−0.991039
$403$	−1772.49	−0.219092
$404$	−3367.65	−0.414720
$405$	−9657.07	−1.18485
$406$	−24109.2	−2.94709
$407$	1602.88	0.195214
$408$	5796.19	0.703319
$409$	−1456.71	−0.176112	−0.0880558	−	0.996116i	$-0.528065\pi$
$409$	−1456.71	−0.176112	−0.0880558	+	0.996116i	$0.528065\pi$
$410$	19274.6	2.32171
$411$	10869.0	1.30445
$412$	−728.354	−0.0870957
$413$	4730.30	0.563590
$414$	8965.95	1.06438
$415$	−3089.89	−0.365486
$416$	2866.06	0.337788
$417$	19076.5	2.24023
$418$	−567.189	−0.0663687
$419$	3735.44	0.435532	0.217766	−	0.976001i	$-0.430123\pi$
$419$	3735.44	0.435532	0.217766	+	0.976001i	$0.430123\pi$
$420$	−15579.6	−1.81002
$421$	−1058.82	−0.122574	−0.0612869	−	0.998120i	$-0.519520\pi$
$421$	−1058.82	−0.122574	−0.0612869	+	0.998120i	$0.519520\pi$
$422$	−20308.3	−2.34263
$423$	12814.7	1.47298
$424$	−4220.77	−0.483441
$425$	−12288.1	−1.40249
$426$	−21768.0	−2.47574
$427$	18947.1	2.14734
$428$	6052.99	0.683603
$429$	1089.25	0.122586
$430$	−17081.6	−1.91569
$431$	−900.238	−0.100610	−0.0503050	−	0.998734i	$-0.516019\pi$
$431$	−900.238	−0.100610	−0.0503050	+	0.998734i	$0.516019\pi$
$432$	−2347.39	−0.261432
$433$	−4473.75	−0.496523	−0.248262	−	0.968693i	$-0.579859\pi$
$433$	−4473.75	−0.496523	−0.248262	+	0.968693i	$0.579859\pi$
$434$	−11133.3	−1.23138
$435$	35940.7	3.96144
$436$	−8582.76	−0.942752
$437$	1077.71	0.117973
$438$	21739.3	2.37157
$439$	5968.25	0.648859	0.324430	−	0.945910i	$-0.394828\pi$
$439$	5968.25	0.648859	0.324430	+	0.945910i	$0.394828\pi$
$440$	1419.36	0.153785
$441$	4316.54	0.466099
$442$	4556.03	0.490290
$443$	−7593.30	−0.814376	−0.407188	−	0.913344i	$-0.633491\pi$
$443$	−7593.30	−0.814376	−0.407188	+	0.913344i	$0.633491\pi$
$444$	−6469.56	−0.691512
$445$	12127.2	1.29188
$446$	−2304.53	−0.244670
$447$	−1931.43	−0.204370
$448$	4536.55	0.478420
$449$	−4889.43	−0.513912	−0.256956	−	0.966423i	$-0.582719\pi$
$449$	−4889.43	−0.513912	−0.256956	+	0.966423i	$0.582719\pi$
$450$	15040.7	1.57561
$451$	−3567.69	−0.372496
$452$	2627.71	0.273444
$453$	8434.45	0.874802
$454$	1432.42	0.148077
$455$	4561.78	0.470021
$456$	−852.774	−0.0875764
$457$	9449.05	0.967195	0.483598	−	0.875290i	$-0.339330\pi$
$457$	9449.05	0.967195	0.483598	+	0.875290i	$0.339330\pi$
$458$	12900.9	1.31620
$459$	−2885.97	−0.293476
$460$	7239.92	0.733833
$461$	−5529.77	−0.558670	−0.279335	−	0.960194i	$-0.590114\pi$
$461$	−5529.77	−0.558670	−0.279335	+	0.960194i	$0.590114\pi$
$462$	6841.73	0.688974
$463$	−13352.6	−1.34027	−0.670136	−	0.742238i	$-0.733764\pi$
$463$	−13352.6	−1.34027	−0.670136	+	0.742238i	$0.733764\pi$
$464$	−22633.0	−2.26447
$465$	16597.0	1.65520
$466$	−17890.4	−1.77845
$467$	−1189.20	−0.117837	−0.0589184	−	0.998263i	$-0.518765\pi$
$467$	−1189.20	−0.117837	−0.0589184	+	0.998263i	$0.518765\pi$
$468$	−2350.52	−0.232164
$469$	6192.14	0.609652
$470$	24550.1	2.40938
$471$	2287.44	0.223779
$472$	1739.39	0.169623
$473$	3161.77	0.307354
$474$	−18176.1	−1.76130
$475$	1807.90	0.174636
$476$	12062.0	1.16147
$477$	16215.7	1.55653
$478$	−7281.72	−0.696775
$479$	−12097.0	−1.15392	−0.576960	−	0.816773i	$-0.695761\pi$
$479$	−12097.0	−1.15392	−0.576960	+	0.816773i	$0.695761\pi$
$480$	−26836.7	−2.55193
$481$	1894.32	0.179570
$482$	−2225.77	−0.210334
$483$	−12999.9	−1.22467
$484$	705.279	0.0662358
$485$	15892.4	1.48791
$486$	−20191.7	−1.88459
$487$	1643.83	0.152955	0.0764775	−	0.997071i	$-0.475633\pi$
$487$	1643.83	0.152955	0.0764775	+	0.997071i	$0.475633\pi$
$488$	6967.10	0.646282
$489$	−18263.8	−1.68899
$490$	8269.54	0.762407
$491$	−14988.8	−1.37767	−0.688833	−	0.724920i	$-0.741877\pi$
$491$	−14988.8	−1.37767	−0.688833	+	0.724920i	$0.741877\pi$
$492$	14399.9	1.31951
$493$	−27826.0	−2.54203
$494$	−670.314	−0.0610503
$495$	−5453.01	−0.495141
$496$	−10451.7	−0.946157
$497$	16874.5	1.52298
$498$	−5476.77	−0.492811
$499$	−4068.12	−0.364958	−0.182479	−	0.983210i	$-0.558412\pi$
$499$	−4068.12	−0.364958	−0.182479	+	0.983210i	$0.558412\pi$
$500$	501.721	0.0448752
$501$	−3120.31	−0.278254
$502$	17835.8	1.58576
$503$	−14937.4	−1.32411	−0.662054	−	0.749456i	$-0.730315\pi$
$503$	−14937.4	−1.32411	−0.662054	+	0.749456i	$0.730315\pi$
$504$	5499.69	0.486063
$505$	−9233.16	−0.813604
$506$	−3179.39	−0.279330
$507$	1287.29	0.112762
$508$	−3650.60	−0.318837
$509$	21639.1	1.88436	0.942178	−	0.335113i	$-0.108774\pi$
$509$	21639.1	1.88436	0.942178	+	0.335113i	$0.108774\pi$
$510$	−42661.1	−3.70405
$511$	−16852.2	−1.45890
$512$	11948.5	1.03135
$513$	424.604	0.0365433
$514$	−6147.74	−0.527559
$515$	−1996.94	−0.170866
$516$	−12761.5	−1.08875
$517$	−4544.18	−0.386562
$518$	11898.5	1.00925
$519$	31659.5	2.67765
$520$	1677.42	0.141461
$521$	−4208.39	−0.353883	−0.176941	−	0.984221i	$-0.556620\pi$
$521$	−4208.39	−0.353883	−0.176941	+	0.984221i	$0.556620\pi$
$522$	34059.2	2.85581
$523$	114.908	0.00960725	0.00480362	−	0.999988i	$-0.498471\pi$
$523$	114.908	0.00960725	0.00480362	+	0.999988i	$0.498471\pi$
$524$	8118.93	0.676864
$525$	−21807.9	−1.81290
$526$	−25305.1	−2.09763
$527$	−12849.7	−1.06213
$528$	6422.83	0.529390
$529$	−6125.86	−0.503481
$530$	31065.7	2.54605
$531$	−6682.53	−0.546134
$532$	−1774.64	−0.144625
$533$	−4216.36	−0.342647
$534$	21495.3	1.74194
$535$	16595.6	1.34110
$536$	2276.93	0.183486
$537$	−24867.3	−1.99833
$538$	−24799.7	−1.98734
$539$	−1530.68	−0.122321
$540$	2852.43	0.227313
$541$	−3229.67	−0.256663	−0.128331	−	0.991731i	$-0.540962\pi$
$541$	−3229.67	−0.256663	−0.128331	+	0.991731i	$0.540962\pi$
$542$	−12839.3	−1.01752
$543$	−32608.9	−2.57713
$544$	20777.5	1.63755
$545$	−23531.5	−1.84951
$546$	8085.68	0.633764
$547$	7467.23	0.583685	0.291843	−	0.956466i	$-0.405732\pi$
$547$	7467.23	0.583685	0.291843	+	0.956466i	$0.405732\pi$
$548$	8317.17	0.648343
$549$	−26766.8	−2.08083
$550$	−5333.55	−0.413497
$551$	4093.94	0.316530
$552$	−4780.25	−0.368588
$553$	14090.0	1.08349
$554$	28590.4	2.19258
$555$	−17737.7	−1.35662
$556$	14597.7	1.11345
$557$	1031.15	0.0784400	0.0392200	−	0.999231i	$-0.487513\pi$
$557$	1031.15	0.0784400	0.0392200	+	0.999231i	$0.487513\pi$
$558$	15728.2	1.19324
$559$	3736.64	0.282724
$560$	26898.9	2.02980
$561$	7896.49	0.594278
$562$	10109.4	0.758786
$563$	18489.2	1.38406	0.692029	−	0.721869i	$-0.256717\pi$
$563$	18489.2	1.38406	0.692029	+	0.721869i	$0.256717\pi$
$564$	18341.2	1.36933
$565$	7204.44	0.536448
$566$	−6546.69	−0.486180
$567$	13269.0	0.982798
$568$	6204.96	0.458370
$569$	18482.7	1.36175	0.680876	−	0.732398i	$-0.261599\pi$
$569$	18482.7	1.36175	0.680876	+	0.732398i	$0.261599\pi$
$570$	6276.59	0.461223
$571$	−12590.0	−0.922725	−0.461362	−	0.887212i	$-0.652639\pi$
$571$	−12590.0	−0.922725	−0.461362	+	0.887212i	$0.652639\pi$
$572$	833.512	0.0609281
$573$	3809.69	0.277752
$574$	−26483.6	−1.92579
$575$	10134.2	0.735004
$576$	−6408.83	−0.463602
$577$	16214.4	1.16987	0.584933	−	0.811081i	$-0.301121\pi$
$577$	16214.4	1.16987	0.584933	+	0.811081i	$0.301121\pi$
$578$	14759.0	1.06210
$579$	36162.8	2.59564
$580$	27502.5	1.96893
$581$	4245.57	0.303160
$582$	28169.0	2.00626
$583$	−5750.21	−0.408490
$584$	−6196.78	−0.439083
$585$	−6444.47	−0.455463
$586$	−14176.3	−0.999349
$587$	−3856.14	−0.271142	−0.135571	−	0.990768i	$-0.543287\pi$
$587$	−3856.14	−0.271142	−0.135571	+	0.990768i	$0.543287\pi$
$588$	6178.12	0.433301
$589$	1890.54	0.132255
$590$	−12802.3	−0.893323
$591$	7232.14	0.503368
$592$	11170.0	0.775480
$593$	16946.5	1.17354	0.586769	−	0.809754i	$-0.300400\pi$
$593$	16946.5	1.17354	0.586769	+	0.809754i	$0.300400\pi$
$594$	−1252.64	−0.0865257
$595$	33070.7	2.27860
$596$	−1477.97	−0.101577
$597$	−21652.2	−1.48436
$598$	−3757.46	−0.256946
$599$	20632.7	1.40740	0.703698	−	0.710499i	$-0.251531\pi$
$599$	20632.7	1.40740	0.703698	+	0.710499i	$0.251531\pi$
$600$	−8019.04	−0.545627
$601$	5705.65	0.387251	0.193626	−	0.981075i	$-0.437975\pi$
$601$	5705.65	0.387251	0.193626	+	0.981075i	$0.437975\pi$
$602$	23470.5	1.58901
$603$	−8747.70	−0.590769
$604$	6454.20	0.434798
$605$	1933.68	0.129942
$606$	−16365.6	−1.09704
$607$	24873.3	1.66323	0.831613	−	0.555356i	$-0.187418\pi$
$607$	24873.3	1.66323	0.831613	+	0.555356i	$0.187418\pi$
$608$	−3056.93	−0.203906
$609$	−49383.3	−3.28590
$610$	−51279.2	−3.40366
$611$	−5370.39	−0.355585
$612$	−17040.1	−1.12550
$613$	5491.10	0.361800	0.180900	−	0.983501i	$-0.442099\pi$
$613$	5491.10	0.361800	0.180900	+	0.983501i	$0.442099\pi$
$614$	20308.6	1.33483
$615$	39480.5	2.58863
$616$	−1950.23	−0.127560
$617$	−5488.99	−0.358150	−0.179075	−	0.983835i	$-0.557310\pi$
$617$	−5488.99	−0.358150	−0.179075	+	0.983835i	$0.557310\pi$
$618$	−3539.55	−0.230391
$619$	−13880.6	−0.901309	−0.450654	−	0.892699i	$-0.648809\pi$
$619$	−13880.6	−0.901309	−0.450654	+	0.892699i	$0.648809\pi$
$620$	12700.4	0.822675
$621$	2380.13	0.153802
$622$	−38465.3	−2.47961
$623$	−16663.1	−1.07158
$624$	7590.62	0.486968
$625$	−14922.7	−0.955053
$626$	7961.53	0.508317
$627$	−1161.79	−0.0739988
$628$	1750.40	0.111224
$629$	13732.9	0.870533
$630$	−40478.8	−2.55986
$631$	5187.13	0.327253	0.163626	−	0.986522i	$-0.447681\pi$
$631$	5187.13	0.327253	0.163626	+	0.986522i	$0.447681\pi$
$632$	5181.09	0.326096
$633$	−41597.9	−2.61195
$634$	13785.1	0.863529
$635$	−10008.9	−0.625499
$636$	23209.0	1.44701
$637$	−1808.98	−0.112519
$638$	−12077.7	−0.749465
$639$	−23838.7	−1.47581
$640$	15907.9	0.982522
$641$	20625.7	1.27093	0.635464	−	0.772130i	$-0.280809\pi$
$641$	20625.7	1.27093	0.635464	+	0.772130i	$0.280809\pi$
$642$	29415.5	1.80831
$643$	−2637.03	−0.161733	−0.0808666	−	0.996725i	$-0.525769\pi$
$643$	−2637.03	−0.161733	−0.0808666	+	0.996725i	$0.525769\pi$
$644$	−9947.81	−0.608693
$645$	−34988.6	−2.13593
$646$	−4859.45	−0.295963
$647$	−27687.9	−1.68242	−0.841209	−	0.540710i	$-0.818156\pi$
$647$	−27687.9	−1.68242	−0.841209	+	0.540710i	$0.818156\pi$
$648$	4879.19	0.295791
$649$	2369.68	0.143325
$650$	−6303.28	−0.380362
$651$	−22804.7	−1.37294
$652$	−13975.8	−0.839469
$653$	−28444.2	−1.70461	−0.852304	−	0.523046i	$-0.824795\pi$
$653$	−28444.2	−1.70461	−0.852304	+	0.523046i	$0.824795\pi$
$654$	−41709.3	−2.49383
$655$	22259.8	1.32788
$656$	−24862.1	−1.47973
$657$	23807.3	1.41372
$658$	−33732.3	−1.99851
$659$	−672.802	−0.0397703	−0.0198852	−	0.999802i	$-0.506330\pi$
$659$	−672.802	−0.0397703	−0.0198852	+	0.999802i	$0.506330\pi$
$660$	−7804.71	−0.460300
$661$	−8021.48	−0.472011	−0.236006	−	0.971752i	$-0.575838\pi$
$661$	−8021.48	−0.472011	−0.236006	+	0.971752i	$0.575838\pi$
$662$	32602.6	1.91410
$663$	9332.22	0.546657
$664$	1561.15	0.0912415
$665$	−4865.58	−0.283728
$666$	−16809.1	−0.977990
$667$	22948.7	1.33220
$668$	−2387.72	−0.138299
$669$	−4720.43	−0.272799
$670$	−16758.6	−0.966333
$671$	9491.69	0.546085
$672$	36874.3	2.11675
$673$	8812.93	0.504775	0.252387	−	0.967626i	$-0.418784\pi$
$673$	8812.93	0.504775	0.252387	+	0.967626i	$0.418784\pi$
$674$	396.890	0.0226819
$675$	3992.75	0.227676
$676$	985.059	0.0560457
$677$	−26710.7	−1.51636	−0.758180	−	0.652045i	$-0.773911\pi$
$677$	−26710.7	−1.51636	−0.758180	+	0.652045i	$0.773911\pi$
$678$	12769.8	0.723332
$679$	−21836.4	−1.23418
$680$	12160.5	0.685785
$681$	2934.06	0.165101
$682$	−5577.32	−0.313148
$683$	−4813.54	−0.269671	−0.134835	−	0.990868i	$-0.543051\pi$
$683$	−4813.54	−0.269671	−0.134835	+	0.990868i	$0.543051\pi$
$684$	2507.06	0.140146
$685$	22803.4	1.27193
$686$	16645.2	0.926410
$687$	26425.1	1.46751
$688$	22033.4	1.22095
$689$	−6795.70	−0.375756
$690$	35183.5	1.94118
$691$	2812.57	0.154841	0.0774206	−	0.996999i	$-0.475332\pi$
$691$	2812.57	0.154841	0.0774206	+	0.996999i	$0.475332\pi$
$692$	24226.5	1.33086
$693$	7492.55	0.410705
$694$	2633.83	0.144062
$695$	40022.7	2.18439
$696$	−18158.9	−0.988952
$697$	−30566.5	−1.66110
$698$	−5441.72	−0.295089
$699$	−36645.3	−1.98291
$700$	−16687.8	−0.901058
$701$	17451.6	0.940284	0.470142	−	0.882591i	$-0.344203\pi$
$701$	17451.6	0.940284	0.470142	+	0.882591i	$0.344203\pi$
$702$	−1480.39	−0.0795920
$703$	−2020.47	−0.108398
$704$	2272.62	0.121666
$705$	50286.4	2.68638
$706$	−13093.5	−0.697987
$707$	12686.6	0.674861
$708$	−9564.48	−0.507705
$709$	−18296.7	−0.969178	−0.484589	−	0.874742i	$-0.661031\pi$
$709$	−18296.7	−0.969178	−0.484589	+	0.874742i	$0.661031\pi$
$710$	−45669.7	−2.41402
$711$	−19905.1	−1.04993
$712$	−6127.22	−0.322510
$713$	10597.4	0.556630
$714$	58617.2	3.07240
$715$	2285.26	0.119530
$716$	−19028.9	−0.993217
$717$	−14915.3	−0.776879
$718$	13547.5	0.704163
$719$	−6423.76	−0.333193	−0.166597	−	0.986025i	$-0.553278\pi$
$719$	−6423.76	−0.333193	−0.166597	+	0.986025i	$0.553278\pi$
$720$	−38000.4	−1.96693
$721$	2743.84	0.141728
$722$	−24791.6	−1.27791
$723$	−4559.09	−0.234515
$724$	−24953.0	−1.28090
$725$	38497.3	1.97207
$726$	3427.41	0.175211
$727$	−24996.5	−1.27520	−0.637600	−	0.770367i	$-0.720073\pi$
$727$	−24996.5	−1.27520	−0.637600	+	0.770367i	$0.720073\pi$
$728$	−2304.82	−0.117338
$729$	−25043.1	−1.27232
$730$	45609.5	2.31244
$731$	27088.8	1.37061
$732$	−38310.4	−1.93441
$733$	−16280.9	−0.820395	−0.410197	−	0.911997i	$-0.634540\pi$
$733$	−16280.9	−0.820395	−0.410197	+	0.911997i	$0.634540\pi$
$734$	−9079.83	−0.456598
$735$	16938.7	0.850058
$736$	−17135.7	−0.858191
$737$	3102.00	0.155039
$738$	37413.7	1.86615
$739$	8248.82	0.410606	0.205303	−	0.978698i	$-0.434182\pi$
$739$	8248.82	0.410606	0.205303	+	0.978698i	$0.434182\pi$
$740$	−13573.2	−0.674273
$741$	−1373.02	−0.0680690
$742$	−42685.0	−2.11188
$743$	19894.1	0.982291	0.491146	−	0.871078i	$-0.336578\pi$
$743$	19894.1	0.982291	0.491146	+	0.871078i	$0.336578\pi$
$744$	−8385.56	−0.413212
$745$	−4052.18	−0.199276
$746$	−47126.2	−2.31288
$747$	−5997.75	−0.293770
$748$	6042.55	0.295371
$749$	−22802.7	−1.11241
$750$	2438.19	0.118707
$751$	−19777.5	−0.960973	−0.480487	−	0.877002i	$-0.659540\pi$
$751$	−19777.5	−0.960973	−0.480487	+	0.877002i	$0.659540\pi$
$752$	−31667.0	−1.53561
$753$	36533.5	1.76807
$754$	−14273.6	−0.689408
$755$	17695.6	0.852993
$756$	−3919.30	−0.188550
$757$	12921.9	0.620415	0.310208	−	0.950669i	$-0.399601\pi$
$757$	12921.9	0.620415	0.310208	+	0.950669i	$0.399601\pi$
$758$	−13712.8	−0.657084
$759$	−6512.41	−0.311444
$760$	−1789.14	−0.0853931
$761$	−25236.0	−1.20211	−0.601054	−	0.799209i	$-0.705252\pi$
$761$	−25236.0	−1.20211	−0.601054	+	0.799209i	$0.705252\pi$
$762$	−17740.7	−0.843407
$763$	32332.8	1.53411
$764$	2915.24	0.138050
$765$	−46719.2	−2.20802
$766$	40714.6	1.92047
$767$	2800.53	0.131840
$768$	40786.1	1.91633
$769$	13801.5	0.647195	0.323598	−	0.946195i	$-0.395108\pi$
$769$	13801.5	0.647195	0.323598	+	0.946195i	$0.395108\pi$
$770$	14354.1	0.671799
$771$	−12592.6	−0.588210
$772$	27672.5	1.29010
$773$	12018.9	0.559236	0.279618	−	0.960111i	$-0.409792\pi$
$773$	12018.9	0.559236	0.279618	+	0.960111i	$0.409792\pi$
$774$	−33156.9	−1.53979
$775$	17777.6	0.823988
$776$	−8029.54	−0.371448
$777$	24372.0	1.12528
$778$	49143.2	2.26461
$779$	4497.15	0.206838
$780$	−9223.75	−0.423414
$781$	8453.38	0.387306
$782$	−27239.7	−1.24564
$783$	9041.47	0.412664
$784$	−10666.8	−0.485916
$785$	4799.10	0.218200
$786$	39455.2	1.79048
$787$	22394.5	1.01433	0.507166	−	0.861849i	$-0.330693\pi$
$787$	22394.5	1.01433	0.507166	+	0.861849i	$0.330693\pi$
$788$	5534.18	0.250186
$789$	−51833.0	−2.33879
$790$	−38133.8	−1.71739
$791$	−9899.05	−0.444968
$792$	2755.11	0.123609
$793$	11217.5	0.502325
$794$	49509.8	2.21290
$795$	63632.6	2.83876
$796$	−16568.7	−0.737765
$797$	−16449.1	−0.731063	−0.365532	−	0.930799i	$-0.619113\pi$
$797$	−16449.1	−0.731063	−0.365532	+	0.930799i	$0.619113\pi$
$798$	−8624.16	−0.382571
$799$	−38932.7	−1.72383
$800$	−28745.7	−1.27039
$801$	23540.1	1.03839
$802$	36219.7	1.59472
$803$	−8442.24	−0.371009
$804$	−12520.3	−0.549199
$805$	−27274.1	−1.19414
$806$	−6591.38	−0.288054
$807$	−50797.7	−2.21582
$808$	4665.01	0.203112
$809$	8013.62	0.348262	0.174131	−	0.984723i	$-0.444288\pi$
$809$	8013.62	0.348262	0.174131	+	0.984723i	$0.444288\pi$
$810$	−35911.8	−1.55779
$811$	−16210.3	−0.701876	−0.350938	−	0.936399i	$-0.614137\pi$
$811$	−16210.3	−0.701876	−0.350938	+	0.936399i	$0.614137\pi$
$812$	−37789.1	−1.63317
$813$	−26299.0	−1.13450
$814$	5960.65	0.256659
$815$	−38317.7	−1.64688
$816$	55028.3	2.36075
$817$	−3985.49	−0.170666
$818$	−5417.07	−0.231545
$819$	8854.84	0.377794
$820$	30211.2	1.28661
$821$	−44347.1	−1.88517	−0.942585	−	0.333968i	$-0.891612\pi$
$821$	−44347.1	−1.88517	−0.942585	+	0.333968i	$0.891612\pi$
$822$	40418.6	1.71504
$823$	17902.3	0.758244	0.379122	−	0.925347i	$-0.376226\pi$
$823$	17902.3	0.758244	0.379122	+	0.925347i	$0.376226\pi$
$824$	1008.95	0.0426557
$825$	−10924.8	−0.461034
$826$	17590.6	0.740986
$827$	−36456.0	−1.53289	−0.766444	−	0.642311i	$-0.777976\pi$
$827$	−36456.0	−1.53289	−0.766444	+	0.642311i	$0.777976\pi$
$828$	14053.4	0.589841
$829$	29839.9	1.25016	0.625080	−	0.780560i	$-0.285066\pi$
$829$	29839.9	1.25016	0.625080	+	0.780560i	$0.285066\pi$
$830$	−11490.4	−0.480526
$831$	58562.4	2.44465
$832$	2685.82	0.111916
$833$	−13114.2	−0.545475
$834$	70939.7	2.94537
$835$	−6546.46	−0.271317
$836$	−889.021	−0.0367792
$837$	4175.25	0.172422
$838$	13891.0	0.572621
$839$	−33753.9	−1.38893	−0.694466	−	0.719525i	$-0.744360\pi$
$839$	−33753.9	−1.38893	−0.694466	+	0.719525i	$0.744360\pi$
$840$	21581.5	0.886467
$841$	62787.0	2.57440
$842$	−3937.43	−0.161155
$843$	20707.2	0.846020
$844$	−31831.5	−1.29820
$845$	2700.76	0.109951
$846$	47654.0	1.93662
$847$	−2656.91	−0.107784
$848$	−40071.5	−1.62271
$849$	−13409.7	−0.542074
$850$	−45695.7	−1.84394
$851$	−11325.8	−0.456220
$852$	−34119.5	−1.37197
$853$	1122.73	0.0450661	0.0225330	−	0.999746i	$-0.492827\pi$
$853$	1122.73	0.0450661	0.0225330	+	0.999746i	$0.492827\pi$
$854$	70458.7	2.82324
$855$	6873.65	0.274940
$856$	−8384.85	−0.334799
$857$	41291.0	1.64583	0.822913	−	0.568167i	$-0.192347\pi$
$857$	41291.0	1.64583	0.822913	+	0.568167i	$0.192347\pi$
$858$	4050.58	0.161171
$859$	−25321.7	−1.00578	−0.502890	−	0.864351i	$-0.667730\pi$
$859$	−25321.7	−1.00578	−0.502890	+	0.864351i	$0.667730\pi$
$860$	−26773.9	−1.06161
$861$	−54247.0	−2.14719
$862$	−3347.72	−0.132278
$863$	49281.2	1.94386	0.971930	−	0.235271i	$-0.0755978\pi$
$863$	49281.2	1.94386	0.971930	+	0.235271i	$0.0755978\pi$
$864$	−6751.21	−0.265834
$865$	66422.2	2.61089
$866$	−16636.5	−0.652809
$867$	30231.2	1.18420
$868$	−17450.6	−0.682385
$869$	7058.50	0.275539
$870$	133653.	5.20834
$871$	3666.00	0.142615
$872$	11889.2	0.461719
$873$	30848.5	1.19595
$874$	4007.69	0.155106
$875$	−1890.07	−0.0730241
$876$	34074.6	1.31424
$877$	8009.42	0.308391	0.154196	−	0.988040i	$-0.450721\pi$
$877$	8009.42	0.308391	0.154196	+	0.988040i	$0.450721\pi$
$878$	22194.2	0.853094
$879$	−29037.7	−1.11424
$880$	13475.2	0.516193
$881$	−14366.6	−0.549401	−0.274701	−	0.961530i	$-0.588579\pi$
$881$	−14366.6	−0.549401	−0.274701	+	0.961530i	$0.588579\pi$
$882$	16051.9	0.612808
$883$	20957.2	0.798716	0.399358	−	0.916795i	$-0.369233\pi$
$883$	20957.2	0.798716	0.399358	+	0.916795i	$0.369233\pi$
$884$	7141.19	0.271702
$885$	−26223.1	−0.996024
$886$	−28237.2	−1.07071
$887$	−11274.0	−0.426770	−0.213385	−	0.976968i	$-0.568449\pi$
$887$	−11274.0	−0.426770	−0.213385	+	0.976968i	$0.568449\pi$
$888$	8961.89	0.338673
$889$	13752.5	0.518834
$890$	45097.5	1.69851
$891$	6647.21	0.249932
$892$	−3612.16	−0.135588
$893$	5728.04	0.214649
$894$	−7182.42	−0.268698
$895$	−52171.9	−1.94851
$896$	−21857.8	−0.814974
$897$	−7696.49	−0.286486
$898$	−18182.3	−0.675671
$899$	40256.9	1.49348
$900$	23575.0	0.873150
$901$	−49265.5	−1.82161
$902$	−13267.2	−0.489743
$903$	48075.0	1.77169
$904$	−3640.01	−0.133921
$905$	−68414.1	−2.51289
$906$	31365.2	1.15015
$907$	−14512.2	−0.531278	−0.265639	−	0.964073i	$-0.585583\pi$
$907$	−14512.2	−0.531278	−0.265639	+	0.964073i	$0.585583\pi$
$908$	2245.20	0.0820591
$909$	−17922.4	−0.653959
$910$	16963.9	0.617965
$911$	34313.2	1.24791	0.623955	−	0.781460i	$-0.285525\pi$
$911$	34313.2	1.24791	0.623955	+	0.781460i	$0.285525\pi$
$912$	−8096.13	−0.293958
$913$	2126.85	0.0770957
$914$	35138.2	1.27163
$915$	−105036.	−3.79497
$916$	20221.0	0.729390
$917$	−30585.5	−1.10144
$918$	−10732.1	−0.385851
$919$	7415.57	0.266177	0.133089	−	0.991104i	$-0.457510\pi$
$919$	7415.57	0.266177	0.133089	+	0.991104i	$0.457510\pi$
$920$	−10029.0	−0.359400
$921$	41598.5	1.48829
$922$	−20563.6	−0.734517
$923$	9990.36	0.356269
$924$	10723.8	0.381806
$925$	−18999.4	−0.675349
$926$	−49654.2	−1.76214
$927$	−3876.25	−0.137339
$928$	−65093.8	−2.30260
$929$	−22152.6	−0.782351	−0.391176	−	0.920316i	$-0.627931\pi$
$929$	−22152.6	−0.782351	−0.391176	+	0.920316i	$0.627931\pi$
$930$	61719.4	2.17619
$931$	1929.45	0.0679219
$932$	−28041.7	−0.985553
$933$	−78789.3	−2.76468
$934$	−4422.30	−0.154927
$935$	16567.0	0.579463
$936$	3256.04	0.113704
$937$	53812.7	1.87618	0.938091	−	0.346388i	$-0.112592\pi$
$937$	53812.7	1.87618	0.938091	+	0.346388i	$0.112592\pi$
$938$	23026.7	0.801545
$939$	16307.8	0.566756
$940$	38480.2	1.33520
$941$	−16220.0	−0.561909	−0.280955	−	0.959721i	$-0.590651\pi$
$941$	−16220.0	−0.561909	−0.280955	+	0.959721i	$0.590651\pi$
$942$	8506.32	0.294216
$943$	25208.9	0.870535
$944$	16513.6	0.569354
$945$	−10745.6	−0.369899
$946$	11757.7	0.404097
$947$	28435.1	0.975731	0.487866	−	0.872919i	$-0.337776\pi$
$947$	28435.1	0.975731	0.487866	+	0.872919i	$0.337776\pi$
$948$	−28489.5	−0.976051
$949$	−9977.20	−0.341279
$950$	6723.06	0.229605
$951$	28236.4	0.962805
$952$	−16708.8	−0.568839
$953$	28277.0	0.961157	0.480579	−	0.876952i	$-0.340427\pi$
$953$	28277.0	0.961157	0.480579	+	0.876952i	$0.340427\pi$
$954$	60301.4	2.04647
$955$	7992.79	0.270828
$956$	−11413.5	−0.386128
$957$	−24738.9	−0.835628
$958$	−44985.3	−1.51713
$959$	−31332.3	−1.05503
$960$	−25149.1	−0.845503
$961$	−11200.8	−0.375981
$962$	7044.40	0.236092
$963$	32213.6	1.07795
$964$	−3488.71	−0.116560
$965$	75870.2	2.53093
$966$	−48342.9	−1.61015
$967$	−6860.98	−0.228164	−0.114082	−	0.993471i	$-0.536393\pi$
$967$	−6860.98	−0.228164	−0.114082	+	0.993471i	$0.536393\pi$
$968$	−976.981	−0.0324394
$969$	−9953.71	−0.329989
$970$	59099.0	1.95624
$971$	25844.9	0.854172	0.427086	−	0.904211i	$-0.359540\pi$
$971$	25844.9	0.854172	0.427086	+	0.904211i	$0.359540\pi$
$972$	−31648.7	−1.04438
$973$	−54992.1	−1.81189
$974$	6112.92	0.201099
$975$	−12911.1	−0.424090
$976$	66144.7	2.16930
$977$	47778.7	1.56456	0.782281	−	0.622926i	$-0.214056\pi$
$977$	47778.7	1.56456	0.782281	+	0.622926i	$0.214056\pi$
$978$	−67917.5	−2.22062
$979$	−8347.48	−0.272509
$980$	12961.8	0.422499
$981$	−45676.9	−1.48660
$982$	−55738.8	−1.81130
$983$	−9415.03	−0.305486	−0.152743	−	0.988266i	$-0.548811\pi$
$983$	−9415.03	−0.305486	−0.152743	+	0.988266i	$0.548811\pi$
$984$	−19947.3	−0.646237
$985$	15173.2	0.490819
$986$	−103477.	−3.34215
$987$	−69094.6	−2.22827
$988$	−1050.66	−0.0338319
$989$	−22340.7	−0.718295
$990$	−20278.1	−0.650991
$991$	−11761.7	−0.377015	−0.188508	−	0.982072i	$-0.560365\pi$
$991$	−11761.7	−0.377015	−0.188508	+	0.982072i	$0.560365\pi$
$992$	−30059.6	−0.962089
$993$	66780.6	2.13416
$994$	62751.1	2.00236
$995$	−45426.7	−1.44736
$996$	−8584.38	−0.273099
$997$	19319.9	0.613708	0.306854	−	0.951757i	$-0.400724\pi$
$997$	19319.9	0.613708	0.306854	+	0.951757i	$0.400724\pi$
$998$	−15128.1	−0.479832
$999$	−4462.21	−0.141319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.7	✓	9
3.2	odd	2		1287.4.a.k.1.3		9
4.3	odd	2		2288.4.a.r.1.2		9
11.10	odd	2		1573.4.a.e.1.3		9
13.12	even	2		1859.4.a.d.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.7	✓	9	1.1	even	1	trivial
1287.4.a.k.1.3		9	3.2	odd	2
1573.4.a.e.1.3		9	11.10	odd	2
1859.4.a.d.1.3		9	13.12	even	2
2288.4.a.r.1.2		9	4.3	odd	2

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q+3.71870 q^{2} +7.61710 q^{3} +5.82875 q^{4} +15.9808 q^{5} +28.3257 q^{6} -21.9580 q^{7} -8.07423 q^{8} +31.0202 q^{9} +O(q^{10})\)	\(q+3.71870 q^{2} +7.61710 q^{3} +5.82875 q^{4} +15.9808 q^{5} +28.3257 q^{6} -21.9580 q^{7} -8.07423 q^{8} +31.0202 q^{9} +59.4279 q^{10} -11.0000 q^{11} +44.3982 q^{12} -13.0000 q^{13} -81.6552 q^{14} +121.727 q^{15} -76.6557 q^{16} -94.2436 q^{17} +115.355 q^{18} +13.8658 q^{19} +93.1482 q^{20} -167.256 q^{21} -40.9057 q^{22} +77.7248 q^{23} -61.5022 q^{24} +130.386 q^{25} -48.3431 q^{26} +30.6225 q^{27} -127.988 q^{28} +295.256 q^{29} +452.668 q^{30} +136.346 q^{31} -220.466 q^{32} -83.7881 q^{33} -350.464 q^{34} -350.906 q^{35} +180.809 q^{36} -145.717 q^{37} +51.5626 q^{38} -99.0223 q^{39} -129.033 q^{40} +324.335 q^{41} -621.976 q^{42} -287.434 q^{43} -64.1163 q^{44} +495.728 q^{45} +289.035 q^{46} +413.107 q^{47} -583.894 q^{48} +139.152 q^{49} +484.868 q^{50} -717.863 q^{51} -75.7738 q^{52} +522.747 q^{53} +113.876 q^{54} -175.789 q^{55} +177.294 q^{56} +105.617 q^{57} +1097.97 q^{58} -215.425 q^{59} +709.519 q^{60} -862.881 q^{61} +507.029 q^{62} -681.141 q^{63} -206.602 q^{64} -207.751 q^{65} -311.583 q^{66} -282.000 q^{67} -549.323 q^{68} +592.038 q^{69} -1304.92 q^{70} -768.489 q^{71} -250.464 q^{72} +767.477 q^{73} -541.877 q^{74} +993.165 q^{75} +80.8200 q^{76} +241.538 q^{77} -368.235 q^{78} -641.682 q^{79} -1225.02 q^{80} -604.292 q^{81} +1206.11 q^{82} -193.350 q^{83} -974.894 q^{84} -1506.09 q^{85} -1068.88 q^{86} +2248.99 q^{87} +88.8165 q^{88} +758.862 q^{89} +1843.47 q^{90} +285.454 q^{91} +453.039 q^{92} +1038.56 q^{93} +1536.22 q^{94} +221.586 q^{95} -1679.31 q^{96} +994.465 q^{97} +517.467 q^{98} -341.223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * q^99

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