LMFDB - Embedded newform 1441.4.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.91972 q^{2} -6.88382 q^{3} +7.36419 q^{4} +10.4958 q^{5} +26.9826 q^{6} +12.1414 q^{7} +2.49219 q^{8} +20.3870 q^{9} +O(q^{10})$	\(q-3.91972 q^{2} -6.88382 q^{3} +7.36419 q^{4} +10.4958 q^{5} +26.9826 q^{6} +12.1414 q^{7} +2.49219 q^{8} +20.3870 q^{9} -41.1406 q^{10} -11.0000 q^{11} -50.6938 q^{12} +79.4191 q^{13} -47.5908 q^{14} -72.2512 q^{15} -68.6822 q^{16} -26.3141 q^{17} -79.9113 q^{18} +102.919 q^{19} +77.2931 q^{20} -83.5791 q^{21} +43.1169 q^{22} +119.768 q^{23} -17.1558 q^{24} -14.8382 q^{25} -311.300 q^{26} +45.5227 q^{27} +89.4115 q^{28} +139.827 q^{29} +283.204 q^{30} +159.703 q^{31} +249.277 q^{32} +75.7220 q^{33} +103.144 q^{34} +127.434 q^{35} +150.134 q^{36} +9.86011 q^{37} -403.414 q^{38} -546.707 q^{39} +26.1575 q^{40} +388.049 q^{41} +327.607 q^{42} +411.467 q^{43} -81.0061 q^{44} +213.978 q^{45} -469.457 q^{46} +331.709 q^{47} +472.796 q^{48} -195.587 q^{49} +58.1615 q^{50} +181.142 q^{51} +584.857 q^{52} +602.923 q^{53} -178.436 q^{54} -115.454 q^{55} +30.2586 q^{56} -708.476 q^{57} -548.083 q^{58} -287.637 q^{59} -532.072 q^{60} +443.733 q^{61} -625.989 q^{62} +247.526 q^{63} -427.639 q^{64} +833.567 q^{65} -296.809 q^{66} -312.151 q^{67} -193.782 q^{68} -824.462 q^{69} -499.504 q^{70} +390.452 q^{71} +50.8083 q^{72} +706.874 q^{73} -38.6489 q^{74} +102.143 q^{75} +757.916 q^{76} -133.555 q^{77} +2142.94 q^{78} -1219.95 q^{79} -720.875 q^{80} -863.819 q^{81} -1521.04 q^{82} +317.029 q^{83} -615.493 q^{84} -276.188 q^{85} -1612.84 q^{86} -962.546 q^{87} -27.4141 q^{88} -756.439 q^{89} -838.733 q^{90} +964.258 q^{91} +881.995 q^{92} -1099.36 q^{93} -1300.21 q^{94} +1080.22 q^{95} -1715.98 q^{96} -898.441 q^{97} +766.645 q^{98} -224.257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−3.91972	−1.38583	−0.692915	−	0.721019i	$-0.743674\pi$
$2$	−3.91972	−1.38583	−0.692915	+	0.721019i	$0.743674\pi$
$3$	−6.88382	−1.32479	−0.662396	−	0.749154i	$-0.730460\pi$
$3$	−6.88382	−1.32479	−0.662396	+	0.749154i	$0.730460\pi$
$4$	7.36419	0.920524
$5$	10.4958	0.938773	0.469386	−	0.882993i	$-0.344475\pi$
$5$	10.4958	0.938773	0.469386	+	0.882993i	$0.344475\pi$
$6$	26.9826	1.83594
$7$	12.1414	0.655573	0.327787	−	0.944752i	$-0.393697\pi$
$7$	12.1414	0.655573	0.327787	+	0.944752i	$0.393697\pi$
$8$	2.49219	0.110140
$9$	20.3870	0.755074
$10$	−41.1406	−1.30098
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−50.6938	−1.21950
$13$	79.4191	1.69438	0.847188	−	0.531293i	$-0.178294\pi$
$13$	79.4191	1.69438	0.847188	+	0.531293i	$0.178294\pi$
$14$	−47.5908	−0.908513
$15$	−72.2512	−1.24368
$16$	−68.6822	−1.07316
$17$	−26.3141	−0.375418	−0.187709	−	0.982225i	$-0.560106\pi$
$17$	−26.3141	−0.375418	−0.187709	+	0.982225i	$0.560106\pi$
$18$	−79.9113	−1.04640
$19$	102.919	1.24270	0.621349	−	0.783534i	$-0.286585\pi$
$19$	102.919	1.24270	0.621349	+	0.783534i	$0.286585\pi$
$20$	77.2931	0.864163
$21$	−83.5791	−0.868498
$22$	43.1169	0.417843
$23$	119.768	1.08580	0.542899	−	0.839798i	$-0.317326\pi$
$23$	119.768	1.08580	0.542899	+	0.839798i	$0.317326\pi$
$24$	−17.1558	−0.145913
$25$	−14.8382	−0.118705
$26$	−311.300	−2.34812
$27$	45.5227	0.324476
$28$	89.4115	0.603471
$29$	139.827	0.895354	0.447677	−	0.894195i	$-0.352251\pi$
$29$	139.827	0.895354	0.447677	+	0.894195i	$0.352251\pi$
$30$	283.204	1.72353
$31$	159.703	0.925272	0.462636	−	0.886548i	$-0.346904\pi$
$31$	159.703	0.925272	0.462636	+	0.886548i	$0.346904\pi$
$32$	249.277	1.37708
$33$	75.7220	0.399440
$34$	103.144	0.520266
$35$	127.434	0.615434
$36$	150.134	0.695064
$37$	9.86011	0.0438106	0.0219053	−	0.999760i	$-0.493027\pi$
$37$	9.86011	0.0438106	0.0219053	+	0.999760i	$0.493027\pi$
$38$	−403.414	−1.72217
$39$	−546.707	−2.24470
$40$	26.1575	0.103397
$41$	388.049	1.47812	0.739061	−	0.673638i	$-0.235269\pi$
$41$	388.049	1.47812	0.739061	+	0.673638i	$0.235269\pi$
$42$	327.607	1.20359
$43$	411.467	1.45926	0.729630	−	0.683842i	$-0.239692\pi$
$43$	411.467	1.45926	0.729630	+	0.683842i	$0.239692\pi$
$44$	−81.0061	−0.277548
$45$	213.978	0.708843
$46$	−469.457	−1.50473
$47$	331.709	1.02946	0.514732	−	0.857351i	$-0.327892\pi$
$47$	331.709	1.02946	0.514732	+	0.857351i	$0.327892\pi$
$48$	472.796	1.42171
$49$	−195.587	−0.570224
$50$	58.1615	0.164506
$51$	181.142	0.497351
$52$	584.857	1.55971
$53$	602.923	1.56260	0.781300	−	0.624155i	$-0.214557\pi$
$53$	602.923	1.56260	0.781300	+	0.624155i	$0.214557\pi$
$54$	−178.436	−0.449668
$55$	−115.454	−0.283051
$56$	30.2586	0.0722050
$57$	−708.476	−1.64632
$58$	−548.083	−1.24081
$59$	−287.637	−0.634697	−0.317349	−	0.948309i	$-0.602793\pi$
$59$	−287.637	−0.634697	−0.317349	+	0.948309i	$0.602793\pi$
$60$	−532.072	−1.14484
$61$	443.733	0.931380	0.465690	−	0.884948i	$-0.345806\pi$
$61$	443.733	0.931380	0.465690	+	0.884948i	$0.345806\pi$
$62$	−625.989	−1.28227
$63$	247.526	0.495006
$64$	−427.639	−0.835233
$65$	833.567	1.59063
$66$	−296.809	−0.553556
$67$	−312.151	−0.569184	−0.284592	−	0.958649i	$-0.591858\pi$
$67$	−312.151	−0.569184	−0.284592	+	0.958649i	$0.591858\pi$
$68$	−193.782	−0.345581
$69$	−824.462	−1.43846
$70$	−499.504	−0.852887
$71$	390.452	0.652650	0.326325	−	0.945258i	$-0.394190\pi$
$71$	390.452	0.652650	0.326325	+	0.945258i	$0.394190\pi$
$72$	50.8083	0.0831641
$73$	706.874	1.13333	0.566666	−	0.823947i	$-0.308233\pi$
$73$	706.874	1.13333	0.566666	+	0.823947i	$0.308233\pi$
$74$	−38.6489	−0.0607140
$75$	102.143	0.157260
$76$	757.916	1.14393
$77$	−133.555	−0.197663
$78$	2142.94	3.11077
$79$	−1219.95	−1.73741	−0.868705	−	0.495330i	$-0.835047\pi$
$79$	−1219.95	−1.73741	−0.868705	+	0.495330i	$0.835047\pi$
$80$	−720.875	−1.00745
$81$	−863.819	−1.18494
$82$	−1521.04	−2.04843
$83$	317.029	0.419258	0.209629	−	0.977781i	$-0.432774\pi$
$83$	317.029	0.419258	0.209629	+	0.977781i	$0.432774\pi$
$84$	−615.493	−0.799473
$85$	−276.188	−0.352432
$86$	−1612.84	−2.02228
$87$	−962.546	−1.18616
$88$	−27.4141	−0.0332086
$89$	−756.439	−0.900925	−0.450463	−	0.892795i	$-0.648741\pi$
$89$	−756.439	−0.900925	−0.450463	+	0.892795i	$0.648741\pi$
$90$	−838.733	−0.982336
$91$	964.258	1.11079
$92$	881.995	0.999504
$93$	−1099.36	−1.22579
$94$	−1300.21	−1.42666
$95$	1080.22	1.16661
$96$	−1715.98	−1.82434
$97$	−898.441	−0.940442	−0.470221	−	0.882549i	$-0.655826\pi$
$97$	−898.441	−0.940442	−0.470221	+	0.882549i	$0.655826\pi$
$98$	766.645	0.790233
$99$	−224.257	−0.227663
$100$	−109.271	−0.109271
$101$	1222.12	1.20401	0.602005	−	0.798492i	$-0.294369\pi$
$101$	1222.12	1.20401	0.602005	+	0.798492i	$0.294369\pi$
$102$	−710.024	−0.689244
$103$	−755.634	−0.722863	−0.361431	−	0.932399i	$-0.617712\pi$
$103$	−755.634	−0.722863	−0.361431	+	0.932399i	$0.617712\pi$
$104$	197.927	0.186619
$105$	−877.230	−0.815323
$106$	−2363.29	−2.16550
$107$	777.433	0.702405	0.351202	−	0.936300i	$-0.385773\pi$
$107$	777.433	0.702405	0.351202	+	0.936300i	$0.385773\pi$
$108$	335.238	0.298688
$109$	861.586	0.757109	0.378555	−	0.925579i	$-0.376421\pi$
$109$	861.586	0.757109	0.378555	+	0.925579i	$0.376421\pi$
$110$	452.546	0.392260
$111$	−67.8752	−0.0580399
$112$	−833.897	−0.703535
$113$	−2261.09	−1.88235	−0.941173	−	0.337924i	$-0.890275\pi$
$113$	−2261.09	−1.88235	−0.941173	+	0.337924i	$0.890275\pi$
$114$	2777.03	2.28151
$115$	1257.06	1.01932
$116$	1029.71	0.824195
$117$	1619.12	1.27938
$118$	1127.46	0.879582
$119$	−319.490	−0.246114
$120$	−180.064	−0.136979
$121$	121.000	0.0909091
$122$	−1739.31	−1.29073
$123$	−2671.26	−1.95821
$124$	1176.08	0.851735
$125$	−1467.71	−1.05021
$126$	−970.234	−0.685994
$127$	688.575	0.481111	0.240556	−	0.970635i	$-0.422670\pi$
$127$	688.575	0.481111	0.240556	+	0.970635i	$0.422670\pi$
$128$	−317.993	−0.219585
$129$	−2832.47	−1.93322
$130$	−3267.35	−2.20435
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	557.632	0.367694
$133$	1249.58	0.814679
$134$	1223.55	0.788793
$135$	477.797	0.304609
$136$	−65.5798	−0.0413487
$137$	−2103.04	−1.31149	−0.655747	−	0.754981i	$-0.727646\pi$
$137$	−2103.04	−1.31149	−0.655747	+	0.754981i	$0.727646\pi$
$138$	3231.66	1.99346
$139$	385.094	0.234987	0.117494	−	0.993074i	$-0.462514\pi$
$139$	385.094	0.234987	0.117494	+	0.993074i	$0.462514\pi$
$140$	938.445	0.566522
$141$	−2283.43	−1.36383
$142$	−1530.46	−0.904461
$143$	−873.610	−0.510874
$144$	−1400.22	−0.810315
$145$	1467.60	0.840534
$146$	−2770.75	−1.57061
$147$	1346.38	0.755428
$148$	72.6117	0.0403287
$149$	−895.897	−0.492582	−0.246291	−	0.969196i	$-0.579212\pi$
$149$	−895.897	−0.492582	−0.246291	+	0.969196i	$0.579212\pi$
$150$	−400.373	−0.217936
$151$	−3072.29	−1.65576	−0.827880	−	0.560905i	$-0.810453\pi$
$151$	−3072.29	−1.65576	−0.827880	+	0.560905i	$0.810453\pi$
$152$	256.494	0.136871
$153$	−536.466	−0.283469
$154$	523.499	0.273927
$155$	1676.21	0.868620
$156$	−4026.05	−2.06630
$157$	−694.055	−0.352813	−0.176406	−	0.984317i	$-0.556447\pi$
$157$	−694.055	−0.352813	−0.176406	+	0.984317i	$0.556447\pi$
$158$	4781.87	2.40775
$159$	−4150.41	−2.07012
$160$	2616.37	1.29276
$161$	1454.15	0.711821
$162$	3385.93	1.64212
$163$	1354.44	0.650847	0.325424	−	0.945568i	$-0.394493\pi$
$163$	1354.44	0.650847	0.325424	+	0.945568i	$0.394493\pi$
$164$	2857.67	1.36065
$165$	794.763	0.374983
$166$	−1242.66	−0.581020
$167$	3781.59	1.75227	0.876133	−	0.482069i	$-0.160115\pi$
$167$	3781.59	1.75227	0.876133	+	0.482069i	$0.160115\pi$
$168$	−208.295	−0.0956567
$169$	4110.39	1.87091
$170$	1082.58	0.488411
$171$	2098.21	0.938328
$172$	3030.12	1.34328
$173$	−1022.12	−0.449191	−0.224596	−	0.974452i	$-0.572106\pi$
$173$	−1022.12	−0.449191	−0.224596	+	0.974452i	$0.572106\pi$
$174$	3772.91	1.64381
$175$	−180.156	−0.0778201
$176$	755.504	0.323570
$177$	1980.04	0.840842
$178$	2965.03	1.24853
$179$	−3481.07	−1.45356	−0.726780	−	0.686870i	$-0.758984\pi$
$179$	−3481.07	−1.45356	−0.726780	+	0.686870i	$0.758984\pi$
$180$	1575.77	0.652507
$181$	3890.19	1.59754	0.798772	−	0.601634i	$-0.205483\pi$
$181$	3890.19	1.59754	0.798772	+	0.601634i	$0.205483\pi$
$182$	−3779.62	−1.53936
$183$	−3054.58	−1.23389
$184$	298.485	0.119590
$185$	103.490	0.0411282
$186$	4309.20	1.69874
$187$	289.455	0.113193
$188$	2442.77	0.947646
$189$	552.709	0.212718
$190$	−4234.15	−1.61672
$191$	−1092.73	−0.413965	−0.206983	−	0.978345i	$-0.566364\pi$
$191$	−1092.73	−0.413965	−0.206983	+	0.978345i	$0.566364\pi$
$192$	2943.79	1.10651
$193$	−912.711	−0.340406	−0.170203	−	0.985409i	$-0.554442\pi$
$193$	−912.711	−0.340406	−0.170203	+	0.985409i	$0.554442\pi$
$194$	3521.64	1.30329
$195$	−5738.12	−2.10726
$196$	−1440.34	−0.524905
$197$	3398.76	1.22919	0.614597	−	0.788841i	$-0.289319\pi$
$197$	3398.76	1.22919	0.614597	+	0.788841i	$0.289319\pi$
$198$	879.024	0.315503
$199$	−2412.82	−0.859499	−0.429750	−	0.902948i	$-0.641398\pi$
$199$	−2412.82	−0.859499	−0.429750	+	0.902948i	$0.641398\pi$
$200$	−36.9796	−0.0130743
$201$	2148.79	0.754051
$202$	−4790.35	−1.66855
$203$	1697.70	0.586970
$204$	1333.96	0.457824
$205$	4072.88	1.38762
$206$	2961.87	1.00176
$207$	2441.71	0.819859
$208$	−5454.68	−1.81834
$209$	−1132.11	−0.374687
$210$	3438.49	1.12990
$211$	1017.95	0.332126	0.166063	−	0.986115i	$-0.446895\pi$
$211$	1017.95	0.332126	0.166063	+	0.986115i	$0.446895\pi$
$212$	4440.04	1.43841
$213$	−2687.80	−0.864625
$214$	−3047.32	−0.973413
$215$	4318.68	1.36991
$216$	113.451	0.0357379
$217$	1939.01	0.606583
$218$	−3377.17	−1.04922
$219$	−4865.99	−1.50143
$220$	−850.224	−0.260555
$221$	−2089.84	−0.636100
$222$	266.052	0.0804335
$223$	−4494.79	−1.34974	−0.674872	−	0.737934i	$-0.735801\pi$
$223$	−4494.79	−1.34974	−0.674872	+	0.737934i	$0.735801\pi$
$224$	3026.57	0.902774
$225$	−302.506	−0.0896314
$226$	8862.82	2.60861
$227$	4436.21	1.29710	0.648550	−	0.761172i	$-0.275376\pi$
$227$	4436.21	1.29710	0.648550	+	0.761172i	$0.275376\pi$
$228$	−5217.36	−1.51547
$229$	−201.219	−0.0580652	−0.0290326	−	0.999578i	$-0.509243\pi$
$229$	−201.219	−0.0580652	−0.0290326	+	0.999578i	$0.509243\pi$
$230$	−4927.33	−1.41260
$231$	919.370	0.261862
$232$	348.476	0.0986146
$233$	−3907.80	−1.09875	−0.549374	−	0.835576i	$-0.685134\pi$
$233$	−3907.80	−1.09875	−0.549374	+	0.835576i	$0.685134\pi$
$234$	−6346.48	−1.77300
$235$	3481.56	0.966432
$236$	−2118.21	−0.584254
$237$	8397.93	2.30171
$238$	1252.31	0.341072
$239$	6411.13	1.73515	0.867577	−	0.497303i	$-0.165676\pi$
$239$	6411.13	1.73515	0.867577	+	0.497303i	$0.165676\pi$
$240$	4962.37	1.33467
$241$	−4165.43	−1.11336	−0.556678	−	0.830728i	$-0.687924\pi$
$241$	−4165.43	−1.11336	−0.556678	+	0.830728i	$0.687924\pi$
$242$	−474.286	−0.125985
$243$	4717.26	1.24532
$244$	3267.73	0.857358
$245$	−2052.84	−0.535311
$246$	10470.6	2.71374
$247$	8173.73	2.10560
$248$	398.009	0.101910
$249$	−2182.37	−0.555430
$250$	5753.02	1.45541
$251$	−208.454	−0.0524203	−0.0262101	−	0.999656i	$-0.508344\pi$
$251$	−208.454	−0.0524203	−0.0262101	+	0.999656i	$0.508344\pi$
$252$	1822.83	0.455665
$253$	−1317.45	−0.327381
$254$	−2699.02	−0.666738
$255$	1901.23	0.466900
$256$	4667.56	1.13954
$257$	−2914.00	−0.707278	−0.353639	−	0.935382i	$-0.615056\pi$
$257$	−2914.00	−0.707278	−0.353639	+	0.935382i	$0.615056\pi$
$258$	11102.5	2.67911
$259$	119.715	0.0287211
$260$	6138.54	1.46422
$261$	2850.66	0.676058
$262$	513.483	0.121081
$263$	−4546.09	−1.06587	−0.532936	−	0.846156i	$-0.678911\pi$
$263$	−4546.09	−1.06587	−0.532936	+	0.846156i	$0.678911\pi$
$264$	188.714	0.0439944
$265$	6328.16	1.46693
$266$	−4898.00	−1.12901
$267$	5207.19	1.19354
$268$	−2298.74	−0.523948
$269$	−1169.76	−0.265135	−0.132567	−	0.991174i	$-0.542322\pi$
$269$	−1169.76	−0.265135	−0.132567	+	0.991174i	$0.542322\pi$
$270$	−1872.83	−0.422137
$271$	7414.04	1.66189	0.830943	−	0.556358i	$-0.187802\pi$
$271$	7414.04	1.66189	0.830943	+	0.556358i	$0.187802\pi$
$272$	1807.31	0.402884
$273$	−6637.78	−1.47156
$274$	8243.31	1.81751
$275$	163.220	0.0357910
$276$	−6071.50	−1.32413
$277$	−7443.69	−1.61461	−0.807307	−	0.590132i	$-0.799076\pi$
$277$	−7443.69	−1.61461	−0.807307	+	0.590132i	$0.799076\pi$
$278$	−1509.46	−0.325652
$279$	3255.86	0.698649
$280$	317.589	0.0677841
$281$	1577.87	0.334973	0.167487	−	0.985874i	$-0.446435\pi$
$281$	1577.87	0.334973	0.167487	+	0.985874i	$0.446435\pi$
$282$	8950.39	1.89003
$283$	−324.585	−0.0681786	−0.0340893	−	0.999419i	$-0.510853\pi$
$283$	−324.585	−0.0681786	−0.0340893	+	0.999419i	$0.510853\pi$
$284$	2875.36	0.600780
$285$	−7436.03	−1.54552
$286$	3424.30	0.707984
$287$	4711.45	0.969018
$288$	5082.02	1.03979
$289$	−4220.57	−0.859061
$290$	−5752.57	−1.16484
$291$	6184.71	1.24589
$292$	5205.55	1.04326
$293$	855.141	0.170505	0.0852523	−	0.996359i	$-0.472830\pi$
$293$	855.141	0.170505	0.0852523	+	0.996359i	$0.472830\pi$
$294$	−5277.45	−1.04689
$295$	−3018.98	−0.595837
$296$	24.5733	0.00482531
$297$	−500.750	−0.0978332
$298$	3511.66	0.682635
$299$	9511.87	1.83975
$300$	752.203	0.144762
$301$	4995.78	0.956651
$302$	12042.5	2.29460
$303$	−8412.83	−1.59506
$304$	−7068.71	−1.33361
$305$	4657.33	0.874355
$306$	2102.79	0.392839
$307$	−8203.06	−1.52499	−0.762497	−	0.646992i	$-0.776027\pi$
$307$	−8203.06	−1.52499	−0.762497	+	0.646992i	$0.776027\pi$
$308$	−983.526	−0.181953
$309$	5201.65	0.957643
$310$	−6570.26	−1.20376
$311$	7643.62	1.39367	0.696833	−	0.717233i	$-0.254592\pi$
$311$	7643.62	1.39367	0.696833	+	0.717233i	$0.254592\pi$
$312$	−1362.50	−0.247231
$313$	4262.88	0.769816	0.384908	−	0.922955i	$-0.374233\pi$
$313$	4262.88	0.769816	0.384908	+	0.922955i	$0.374233\pi$
$314$	2720.50	0.488938
$315$	2597.99	0.464698
$316$	−8983.96	−1.59933
$317$	367.819	0.0651696	0.0325848	−	0.999469i	$-0.489626\pi$
$317$	367.819	0.0651696	0.0325848	+	0.999469i	$0.489626\pi$
$318$	16268.5	2.86884
$319$	−1538.10	−0.269959
$320$	−4488.42	−0.784094
$321$	−5351.71	−0.930540
$322$	−5699.86	−0.986462
$323$	−2708.22	−0.466531
$324$	−6361.33	−1.09076
$325$	−1178.43	−0.201132
$326$	−5309.03	−0.901963
$327$	−5931.00	−1.00301
$328$	967.092	0.162801
$329$	4027.41	0.674889
$330$	−3115.25	−0.519663
$331$	−8498.96	−1.41131	−0.705657	−	0.708553i	$-0.749348\pi$
$331$	−8498.96	−1.41131	−0.705657	+	0.708553i	$0.749348\pi$
$332$	2334.66	0.385937
$333$	201.018	0.0330802
$334$	−14822.8	−2.42834
$335$	−3276.28	−0.534335
$336$	5740.40	0.932037
$337$	−5272.50	−0.852259	−0.426130	−	0.904662i	$-0.640123\pi$
$337$	−5272.50	−0.852259	−0.426130	+	0.904662i	$0.640123\pi$
$338$	−16111.6	−2.59276
$339$	15564.9	2.49372
$340$	−2033.90	−0.324422
$341$	−1756.73	−0.278980
$342$	−8224.39	−1.30036
$343$	−6539.19	−1.02940
$344$	1025.45	0.160723
$345$	−8653.39	−1.35039
$346$	4006.41	0.622503
$347$	−11612.3	−1.79648	−0.898240	−	0.439506i	$-0.855154\pi$
$347$	−11612.3	−1.79648	−0.898240	+	0.439506i	$0.855154\pi$
$348$	−7088.37	−1.09189
$349$	2122.79	0.325589	0.162794	−	0.986660i	$-0.447949\pi$
$349$	2122.79	0.325589	0.162794	+	0.986660i	$0.447949\pi$
$350$	706.161	0.107845
$351$	3615.37	0.549784
$352$	−2742.05	−0.415204
$353$	−5163.11	−0.778483	−0.389242	−	0.921136i	$-0.627263\pi$
$353$	−5163.11	−0.778483	−0.389242	+	0.921136i	$0.627263\pi$
$354$	−7761.21	−1.16526
$355$	4098.11	0.612690
$356$	−5570.56	−0.829323
$357$	2199.31	0.326050
$358$	13644.8	2.01439
$359$	−1767.22	−0.259806	−0.129903	−	0.991527i	$-0.541467\pi$
$359$	−1767.22	−0.259806	−0.129903	+	0.991527i	$0.541467\pi$
$360$	533.274	0.0780722
$361$	3733.33	0.544296
$362$	−15248.4	−2.21392
$363$	−832.942	−0.120436
$364$	7100.98	1.02251
$365$	7419.20	1.06394
$366$	11973.1	1.70995
$367$	11071.4	1.57472	0.787361	−	0.616492i	$-0.211447\pi$
$367$	11071.4	1.57472	0.787361	+	0.616492i	$0.211447\pi$
$368$	−8225.94	−1.16524
$369$	7911.15	1.11609
$370$	−405.651	−0.0569967
$371$	7320.32	1.02440
$372$	−8095.93	−1.12837
$373$	−9996.42	−1.38765	−0.693827	−	0.720142i	$-0.744077\pi$
$373$	−9996.42	−1.38765	−0.693827	+	0.720142i	$0.744077\pi$
$374$	−1134.58	−0.156866
$375$	10103.5	1.39131
$376$	826.683	0.113385
$377$	11104.9	1.51707
$378$	−2166.46	−0.294791
$379$	2098.55	0.284421	0.142210	−	0.989836i	$-0.454579\pi$
$379$	2098.55	0.284421	0.142210	+	0.989836i	$0.454579\pi$
$380$	7954.93	1.07389
$381$	−4740.03	−0.637372
$382$	4283.21	0.573686
$383$	3217.01	0.429194	0.214597	−	0.976703i	$-0.431156\pi$
$383$	3217.01	0.429194	0.214597	+	0.976703i	$0.431156\pi$
$384$	2189.01	0.290904
$385$	−1401.77	−0.185560
$386$	3577.57	0.471745
$387$	8388.58	1.10185
$388$	−6616.29	−0.865699
$389$	503.966	0.0656866	0.0328433	−	0.999461i	$-0.489544\pi$
$389$	503.966	0.0656866	0.0328433	+	0.999461i	$0.489544\pi$
$390$	22491.8	2.92030
$391$	−3151.59	−0.407629
$392$	−487.440	−0.0628046
$393$	901.781	0.115748
$394$	−13322.2	−1.70345
$395$	−12804.4	−1.63103
$396$	−1651.47	−0.209570
$397$	−5250.55	−0.663772	−0.331886	−	0.943319i	$-0.607685\pi$
$397$	−5250.55	−0.663772	−0.331886	+	0.943319i	$0.607685\pi$
$398$	9457.58	1.19112
$399$	−8601.88	−1.07928
$400$	1019.12	0.127390
$401$	12479.9	1.55416	0.777078	−	0.629404i	$-0.216701\pi$
$401$	12479.9	1.55416	0.777078	+	0.629404i	$0.216701\pi$
$402$	−8422.67	−1.04499
$403$	12683.4	1.56776
$404$	8999.90	1.10832
$405$	−9066.47	−1.11239
$406$	−6654.49	−0.813440
$407$	−108.461	−0.0132094
$408$	451.440	0.0547784
$409$	−881.458	−0.106566	−0.0532828	−	0.998579i	$-0.516968\pi$
$409$	−881.458	−0.106566	−0.0532828	+	0.998579i	$0.516968\pi$
$410$	−15964.6	−1.92301
$411$	14476.9	1.73746
$412$	−5564.64	−0.665412
$413$	−3492.31	−0.416091
$414$	−9570.82	−1.13618
$415$	3327.47	0.393588
$416$	19797.4	2.33328
$417$	−2650.92	−0.311309
$418$	4437.55	0.519253
$419$	8303.83	0.968183	0.484092	−	0.875017i	$-0.339150\pi$
$419$	8303.83	0.968183	0.484092	+	0.875017i	$0.339150\pi$
$420$	−6460.09	−0.750524
$421$	−12095.8	−1.40027	−0.700136	−	0.714010i	$-0.746877\pi$
$421$	−12095.8	−1.40027	−0.700136	+	0.714010i	$0.746877\pi$
$422$	−3990.08	−0.460270
$423$	6762.56	0.777321
$424$	1502.60	0.172105
$425$	390.453	0.0445642
$426$	10535.4	1.19822
$427$	5387.53	0.610588
$428$	5725.17	0.646580
$429$	6013.77	0.676801
$430$	−16928.0	−1.89847
$431$	11095.5	1.24002	0.620011	−	0.784593i	$-0.287128\pi$
$431$	11095.5	1.24002	0.620011	+	0.784593i	$0.287128\pi$
$432$	−3126.60	−0.348215
$433$	−6455.00	−0.716414	−0.358207	−	0.933642i	$-0.616612\pi$
$433$	−6455.00	−0.716414	−0.358207	+	0.933642i	$0.616612\pi$
$434$	−7600.37	−0.840621
$435$	−10102.7	−1.11353
$436$	6344.88	0.696937
$437$	12326.4	1.34932
$438$	19073.3	2.08073
$439$	2109.32	0.229322	0.114661	−	0.993405i	$-0.463422\pi$
$439$	2109.32	0.229322	0.114661	+	0.993405i	$0.463422\pi$
$440$	−287.733	−0.0311753
$441$	−3987.43	−0.430561
$442$	8191.59	0.881526
$443$	6323.22	0.678161	0.339081	−	0.940757i	$-0.389884\pi$
$443$	6323.22	0.678161	0.339081	+	0.940757i	$0.389884\pi$
$444$	−499.846	−0.0534271
$445$	−7939.43	−0.845764
$446$	17618.3	1.87052
$447$	6167.20	0.652569
$448$	−5192.14	−0.547557
$449$	−13930.8	−1.46422	−0.732111	−	0.681185i	$-0.761465\pi$
$449$	−13930.8	−1.46422	−0.732111	+	0.681185i	$0.761465\pi$
$450$	1185.74	0.124214
$451$	−4268.54	−0.445671
$452$	−16651.1	−1.73275
$453$	21149.1	2.19354
$454$	−17388.7	−1.79756
$455$	10120.7	1.04278
$456$	−1765.66	−0.181326
$457$	−11666.4	−1.19416	−0.597081	−	0.802181i	$-0.703673\pi$
$457$	−11666.4	−1.19416	−0.597081	+	0.802181i	$0.703673\pi$
$458$	788.722	0.0804684
$459$	−1197.89	−0.121814
$460$	9257.24	0.938307
$461$	−6081.99	−0.614461	−0.307231	−	0.951635i	$-0.599402\pi$
$461$	−6081.99	−0.614461	−0.307231	+	0.951635i	$0.599402\pi$
$462$	−3603.67	−0.362896
$463$	2894.28	0.290515	0.145258	−	0.989394i	$-0.453599\pi$
$463$	2894.28	0.290515	0.145258	+	0.989394i	$0.453599\pi$
$464$	−9603.64	−0.960858
$465$	−11538.7	−1.15074
$466$	15317.5	1.52268
$467$	−6034.33	−0.597935	−0.298967	−	0.954263i	$-0.596642\pi$
$467$	−6034.33	−0.597935	−0.298967	+	0.954263i	$0.596642\pi$
$468$	11923.5	1.17770
$469$	−3789.95	−0.373142
$470$	−13646.7	−1.33931
$471$	4777.75	0.467404
$472$	−716.846	−0.0699058
$473$	−4526.14	−0.439983
$474$	−32917.5	−3.18977
$475$	−1527.13	−0.147515
$476$	−2352.78	−0.226554
$477$	12291.8	1.17988
$478$	−25129.8	−2.40463
$479$	11163.7	1.06489	0.532445	−	0.846464i	$-0.321273\pi$
$479$	11163.7	1.06489	0.532445	+	0.846464i	$0.321273\pi$
$480$	−18010.6	−1.71264
$481$	783.081	0.0742316
$482$	16327.3	1.54292
$483$	−10010.1	−0.943014
$484$	891.067	0.0836840
$485$	−9429.86	−0.882862
$486$	−18490.3	−1.72580
$487$	7869.10	0.732203	0.366101	−	0.930575i	$-0.380692\pi$
$487$	7869.10	0.732203	0.366101	+	0.930575i	$0.380692\pi$
$488$	1105.87	0.102583
$489$	−9323.74	−0.862237
$490$	8046.55	0.741849
$491$	17417.6	1.60091	0.800454	−	0.599395i	$-0.204592\pi$
$491$	17417.6	1.60091	0.800454	+	0.599395i	$0.204592\pi$
$492$	−19671.7	−1.80258
$493$	−3679.43	−0.336132
$494$	−32038.7	−2.91800
$495$	−2353.76	−0.213724
$496$	−10968.7	−0.992964
$497$	4740.63	0.427860
$498$	8554.27	0.769731
$499$	14048.6	1.26033	0.630163	−	0.776463i	$-0.282988\pi$
$499$	14048.6	1.26033	0.630163	+	0.776463i	$0.282988\pi$
$500$	−10808.5	−0.966744
$501$	−26031.8	−2.32139
$502$	817.080	0.0726456
$503$	−191.770	−0.0169992	−0.00849960	−	0.999964i	$-0.502706\pi$
$503$	−191.770	−0.0169992	−0.00849960	+	0.999964i	$0.502706\pi$
$504$	616.883	0.0545201
$505$	12827.1	1.13029
$506$	5164.03	0.453694
$507$	−28295.2	−2.47857
$508$	5070.80	0.442874
$509$	9972.76	0.868438	0.434219	−	0.900807i	$-0.357024\pi$
$509$	9972.76	0.868438	0.434219	+	0.900807i	$0.357024\pi$
$510$	−7452.27	−0.647043
$511$	8582.42	0.742983
$512$	−15751.6	−1.35962
$513$	4685.15	0.403225
$514$	11422.1	0.980166
$515$	−7930.99	−0.678604
$516$	−20858.8	−1.77957
$517$	−3648.80	−0.310395
$518$	−469.251	−0.0398025
$519$	7036.07	0.595085
$520$	2077.41	0.175193
$521$	−14348.4	−1.20655	−0.603276	−	0.797533i	$-0.706138\pi$
$521$	−14348.4	−1.20655	−0.603276	+	0.797533i	$0.706138\pi$
$522$	−11173.8	−0.936902
$523$	16154.0	1.35060	0.675299	−	0.737544i	$-0.264014\pi$
$523$	16154.0	1.35060	0.675299	+	0.737544i	$0.264014\pi$
$524$	−964.709	−0.0804265
$525$	1240.16	0.103095
$526$	17819.4	1.47712
$527$	−4202.43	−0.347364
$528$	−5200.76	−0.428663
$529$	2177.39	0.178959
$530$	−24804.6	−2.03291
$531$	−5864.05	−0.479244
$532$	9202.14	0.749931
$533$	30818.5	2.50450
$534$	−20410.7	−1.65404
$535$	8159.78	0.659398
$536$	−777.941	−0.0626902
$537$	23963.1	1.92566
$538$	4585.11	0.367432
$539$	2151.45	0.171929
$540$	3518.59	0.280400
$541$	−12437.1	−0.988378	−0.494189	−	0.869355i	$-0.664535\pi$
$541$	−12437.1	−0.988378	−0.494189	+	0.869355i	$0.664535\pi$
$542$	−29061.0	−2.30309
$543$	−26779.4	−2.11641
$544$	−6559.51	−0.516979
$545$	9043.03	0.710754
$546$	26018.2	2.03933
$547$	2526.18	0.197462	0.0987308	−	0.995114i	$-0.468522\pi$
$547$	2526.18	0.197462	0.0987308	+	0.995114i	$0.468522\pi$
$548$	−15487.2	−1.20726
$549$	9046.38	0.703261
$550$	−639.776	−0.0496003
$551$	14390.9	1.11265
$552$	−2054.72	−0.158432
$553$	−14811.9	−1.13900
$554$	29177.2	2.23758
$555$	−712.405	−0.0544863
$556$	2835.90	0.216311
$557$	23353.5	1.77652	0.888259	−	0.459343i	$-0.151915\pi$
$557$	23353.5	1.77652	0.888259	+	0.459343i	$0.151915\pi$
$558$	−12762.0	−0.968208
$559$	32678.3	2.47253
$560$	−8752.42	−0.660459
$561$	−1992.56	−0.149957
$562$	−6184.79	−0.464216
$563$	10942.7	0.819150	0.409575	−	0.912276i	$-0.365677\pi$
$563$	10942.7	0.819150	0.409575	+	0.912276i	$0.365677\pi$
$564$	−16815.6	−1.25543
$565$	−23731.9	−1.76710
$566$	1272.28	0.0944840
$567$	−10488.0	−0.776813
$568$	973.081	0.0718830
$569$	−12060.8	−0.888601	−0.444301	−	0.895878i	$-0.646548\pi$
$569$	−12060.8	−0.888601	−0.444301	+	0.895878i	$0.646548\pi$
$570$	29147.1	2.14182
$571$	−2951.38	−0.216307	−0.108153	−	0.994134i	$-0.534494\pi$
$571$	−2951.38	−0.216307	−0.108153	+	0.994134i	$0.534494\pi$
$572$	−6433.43	−0.470271
$573$	7522.18	0.548418
$574$	−18467.6	−1.34289
$575$	−1777.14	−0.128890
$576$	−8718.29	−0.630663
$577$	−12914.8	−0.931800	−0.465900	−	0.884837i	$-0.654269\pi$
$577$	−12914.8	−0.931800	−0.465900	+	0.884837i	$0.654269\pi$
$578$	16543.4	1.19051
$579$	6282.94	0.450967
$580$	10807.7	0.773732
$581$	3849.17	0.274854
$582$	−24242.3	−1.72659
$583$	−6632.15	−0.471142
$584$	1761.66	0.124826
$585$	16993.9	1.20105
$586$	−3351.91	−0.236290
$587$	15732.6	1.10622	0.553111	−	0.833107i	$-0.313440\pi$
$587$	15732.6	1.10622	0.553111	+	0.833107i	$0.313440\pi$
$588$	9915.03	0.695390
$589$	16436.4	1.14983
$590$	11833.6	0.825728
$591$	−23396.4	−1.62843
$592$	−677.214	−0.0470158
$593$	−18435.2	−1.27663	−0.638315	−	0.769775i	$-0.720368\pi$
$593$	−18435.2	−1.27663	−0.638315	+	0.769775i	$0.720368\pi$
$594$	1962.80	0.135580
$595$	−3353.30	−0.231045
$596$	−6597.56	−0.453434
$597$	16609.4	1.13866
$598$	−37283.9	−2.54958
$599$	−3183.02	−0.217120	−0.108560	−	0.994090i	$-0.534624\pi$
$599$	−3183.02	−0.217120	−0.108560	+	0.994090i	$0.534624\pi$
$600$	254.561	0.0173207
$601$	−4522.01	−0.306916	−0.153458	−	0.988155i	$-0.549041\pi$
$601$	−4522.01	−0.306916	−0.153458	+	0.988155i	$0.549041\pi$
$602$	−19582.1	−1.32576
$603$	−6363.83	−0.429776
$604$	−22625.0	−1.52417
$605$	1269.99	0.0853430
$606$	32975.9	2.21049
$607$	−18090.6	−1.20968	−0.604840	−	0.796347i	$-0.706763\pi$
$607$	−18090.6	−1.20968	−0.604840	+	0.796347i	$0.706763\pi$
$608$	25655.4	1.71129
$609$	−11686.6	−0.777613
$610$	−18255.4	−1.21171
$611$	26344.0	1.74430
$612$	−3950.64	−0.260940
$613$	−9375.57	−0.617742	−0.308871	−	0.951104i	$-0.599951\pi$
$613$	−9375.57	−0.617742	−0.308871	+	0.951104i	$0.599951\pi$
$614$	32153.7	2.11338
$615$	−28037.0	−1.83831
$616$	−332.845	−0.0217706
$617$	−26406.1	−1.72297	−0.861484	−	0.507785i	$-0.830464\pi$
$617$	−26406.1	−1.72297	−0.861484	+	0.507785i	$0.830464\pi$
$618$	−20389.0	−1.32713
$619$	−18285.8	−1.18735	−0.593675	−	0.804705i	$-0.702324\pi$
$619$	−18285.8	−1.18735	−0.593675	+	0.804705i	$0.702324\pi$
$620$	12343.9	0.799586
$621$	5452.17	0.352316
$622$	−29960.9	−1.93138
$623$	−9184.21	−0.590622
$624$	37549.0	2.40892
$625$	−13550.1	−0.867204
$626$	−16709.3	−1.06683
$627$	7793.24	0.496383
$628$	−5111.15	−0.324773
$629$	−259.460	−0.0164473
$630$	−10183.4	−0.643993
$631$	20653.5	1.30302	0.651508	−	0.758641i	$-0.274137\pi$
$631$	20653.5	1.30302	0.651508	+	0.758641i	$0.274137\pi$
$632$	−3040.35	−0.191359
$633$	−7007.38	−0.439998
$634$	−1441.75	−0.0903139
$635$	7227.14	0.451654
$636$	−30564.4	−1.90560
$637$	−15533.3	−0.966173
$638$	6028.92	0.374118
$639$	7960.14	0.492799
$640$	−3337.59	−0.206140
$641$	−15170.9	−0.934809	−0.467405	−	0.884044i	$-0.654811\pi$
$641$	−15170.9	−0.934809	−0.467405	+	0.884044i	$0.654811\pi$
$642$	20977.2	1.28957
$643$	−4960.20	−0.304216	−0.152108	−	0.988364i	$-0.548606\pi$
$643$	−4960.20	−0.304216	−0.152108	+	0.988364i	$0.548606\pi$
$644$	10708.6	0.655248
$645$	−29729.0	−1.81485
$646$	10615.5	0.646533
$647$	−5337.00	−0.324295	−0.162148	−	0.986767i	$-0.551842\pi$
$647$	−5337.00	−0.324295	−0.162148	+	0.986767i	$0.551842\pi$
$648$	−2152.80	−0.130509
$649$	3164.01	0.191368
$650$	4619.13	0.278734
$651$	−13347.8	−0.803597
$652$	9974.37	0.599120
$653$	1782.87	0.106844	0.0534218	−	0.998572i	$-0.482987\pi$
$653$	1782.87	0.106844	0.0534218	+	0.998572i	$0.482987\pi$
$654$	23247.9	1.39000
$655$	−1374.95	−0.0820210
$656$	−26652.1	−1.58626
$657$	14411.0	0.855750
$658$	−15786.3	−0.935281
$659$	−8652.64	−0.511470	−0.255735	−	0.966747i	$-0.582318\pi$
$659$	−8652.64	−0.511470	−0.255735	+	0.966747i	$0.582318\pi$
$660$	5852.79	0.345181
$661$	12678.9	0.746071	0.373036	−	0.927817i	$-0.378317\pi$
$661$	12678.9	0.746071	0.373036	+	0.927817i	$0.378317\pi$
$662$	33313.5	1.95584
$663$	14386.1	0.842700
$664$	790.096	0.0461772
$665$	13115.3	0.764799
$666$	−787.934	−0.0458436
$667$	16746.8	0.972174
$668$	27848.4	1.61300
$669$	30941.3	1.78813
$670$	12842.1	0.740497
$671$	−4881.06	−0.280822
$672$	−20834.4	−1.19599
$673$	26628.9	1.52522	0.762608	−	0.646861i	$-0.223919\pi$
$673$	26628.9	1.52522	0.762608	+	0.646861i	$0.223919\pi$
$674$	20666.7	1.18109
$675$	−675.474	−0.0385171
$676$	30269.7	1.72222
$677$	13761.2	0.781219	0.390609	−	0.920557i	$-0.372264\pi$
$677$	13761.2	0.781219	0.390609	+	0.920557i	$0.372264\pi$
$678$	−61010.1	−3.45587
$679$	−10908.3	−0.616529
$680$	−688.312	−0.0388170
$681$	−30538.1	−1.71839
$682$	6885.88	0.386619
$683$	17846.5	0.999818	0.499909	−	0.866078i	$-0.333367\pi$
$683$	17846.5	0.999818	0.499909	+	0.866078i	$0.333367\pi$
$684$	15451.6	0.863754
$685$	−22073.1	−1.23119
$686$	25631.8	1.42657
$687$	1385.16	0.0769243
$688$	−28260.5	−1.56602
$689$	47883.6	2.64763
$690$	33918.9	1.87140
$691$	11032.2	0.607360	0.303680	−	0.952774i	$-0.401785\pi$
$691$	11032.2	0.607360	0.303680	+	0.952774i	$0.401785\pi$
$692$	−7527.06	−0.413491
$693$	−2722.79	−0.149250
$694$	45516.8	2.48961
$695$	4041.86	0.220600
$696$	−2398.85	−0.130644
$697$	−10211.2	−0.554914
$698$	−8320.75	−0.451211
$699$	26900.6	1.45561
$700$	−1326.70	−0.0716353
$701$	−6298.69	−0.339370	−0.169685	−	0.985498i	$-0.554275\pi$
$701$	−6298.69	−0.339370	−0.169685	+	0.985498i	$0.554275\pi$
$702$	−14171.2	−0.761907
$703$	1014.79	0.0544433
$704$	4704.03	0.251832
$705$	−23966.4	−1.28032
$706$	20237.9	1.07885
$707$	14838.2	0.789317
$708$	14581.4	0.774015
$709$	−23680.6	−1.25436	−0.627182	−	0.778873i	$-0.715792\pi$
$709$	−23680.6	−1.25436	−0.627182	+	0.778873i	$0.715792\pi$
$710$	−16063.4	−0.849084
$711$	−24871.2	−1.31187
$712$	−1885.19	−0.0992282
$713$	19127.3	1.00466
$714$	−8620.68	−0.451850
$715$	−9169.23	−0.479594
$716$	−25635.3	−1.33804
$717$	−44133.1	−2.29872
$718$	6927.00	0.360047
$719$	27936.3	1.44902	0.724511	−	0.689263i	$-0.242066\pi$
$719$	27936.3	1.44902	0.724511	+	0.689263i	$0.242066\pi$
$720$	−14696.5	−0.760702
$721$	−9174.45	−0.473889
$722$	−14633.6	−0.754302
$723$	28674.1	1.47497
$724$	28648.1	1.47058
$725$	−2074.78	−0.106283
$726$	3264.90	0.166903
$727$	−33070.6	−1.68710	−0.843549	−	0.537052i	$-0.819538\pi$
$727$	−33070.6	−1.68710	−0.843549	+	0.537052i	$0.819538\pi$
$728$	2403.11	0.122342
$729$	−9149.69	−0.464852
$730$	−29081.2	−1.47444
$731$	−10827.4	−0.547832
$732$	−22494.5	−1.13582
$733$	11112.9	0.559977	0.279988	−	0.960003i	$-0.409669\pi$
$733$	11112.9	0.559977	0.279988	+	0.960003i	$0.409669\pi$
$734$	−43396.8	−2.18230
$735$	14131.4	0.709175
$736$	29855.5	1.49523
$737$	3433.66	0.171616
$738$	−31009.5	−1.54671
$739$	−24195.1	−1.20437	−0.602186	−	0.798356i	$-0.705703\pi$
$739$	−24195.1	−1.20437	−0.602186	+	0.798356i	$0.705703\pi$
$740$	762.118	0.0378595
$741$	−56266.5	−2.78948
$742$	−28693.6	−1.41964
$743$	−10041.4	−0.495803	−0.247901	−	0.968785i	$-0.579741\pi$
$743$	−10041.4	−0.495803	−0.247901	+	0.968785i	$0.579741\pi$
$744$	−2739.82	−0.135009
$745$	−9403.16	−0.462423
$746$	39183.2	1.92305
$747$	6463.26	0.316571
$748$	2131.60	0.104197
$749$	9439.11	0.460478
$750$	−39602.8	−1.92812
$751$	29342.8	1.42575	0.712873	−	0.701293i	$-0.247393\pi$
$751$	29342.8	1.42575	0.712873	+	0.701293i	$0.247393\pi$
$752$	−22782.5	−1.10478
$753$	1434.96	0.0694460
$754$	−43528.3	−2.10240
$755$	−32246.2	−1.55438
$756$	4070.25	0.195812
$757$	21086.6	1.01243	0.506213	−	0.862409i	$-0.331045\pi$
$757$	21086.6	1.01243	0.506213	+	0.862409i	$0.331045\pi$
$758$	−8225.74	−0.394159
$759$	9069.08	0.433711
$760$	2692.11	0.128491
$761$	34133.3	1.62593	0.812964	−	0.582315i	$-0.197853\pi$
$761$	34133.3	1.62593	0.812964	+	0.582315i	$0.197853\pi$
$762$	18579.6	0.883289
$763$	10460.8	0.496341
$764$	−8047.10	−0.381065
$765$	−5630.64	−0.266113
$766$	−12609.8	−0.594790
$767$	−22843.9	−1.07542
$768$	−32130.6	−1.50965
$769$	34715.2	1.62791	0.813954	−	0.580929i	$-0.197310\pi$
$769$	34715.2	1.62791	0.813954	+	0.580929i	$0.197310\pi$
$770$	5494.54	0.257155
$771$	20059.5	0.936996
$772$	−6721.38	−0.313352
$773$	21353.6	0.993576	0.496788	−	0.867872i	$-0.334513\pi$
$773$	21353.6	0.993576	0.496788	+	0.867872i	$0.334513\pi$
$774$	−32880.9	−1.52697
$775$	−2369.70	−0.109835
$776$	−2239.09	−0.103581
$777$	−824.099	−0.0380494
$778$	−1975.40	−0.0910304
$779$	39937.6	1.83686
$780$	−42256.6	−1.93978
$781$	−4294.97	−0.196781
$782$	12353.3	0.564904
$783$	6365.31	0.290521
$784$	13433.3	0.611941
$785$	−7284.66	−0.331211
$786$	−3534.73	−0.160406
$787$	19975.5	0.904764	0.452382	−	0.891824i	$-0.350574\pi$
$787$	19975.5	0.904764	0.452382	+	0.891824i	$0.350574\pi$
$788$	25029.1	1.13150
$789$	31294.5	1.41206
$790$	50189.5	2.26033
$791$	−27452.7	−1.23402
$792$	−558.891	−0.0250749
$793$	35240.9	1.57811
$794$	20580.7	0.919876
$795$	−43561.9	−1.94337
$796$	−17768.5	−0.791190
$797$	20405.2	0.906886	0.453443	−	0.891285i	$-0.350196\pi$
$797$	20405.2	0.906886	0.453443	+	0.891285i	$0.350196\pi$
$798$	33717.0	1.49570
$799$	−8728.64	−0.386479
$800$	−3698.82	−0.163466
$801$	−15421.5	−0.680265
$802$	−48917.7	−2.15380
$803$	−7775.61	−0.341713
$804$	15824.1	0.694122
$805$	15262.5	0.668238
$806$	−49715.5	−2.17265
$807$	8052.39	0.351248
$808$	3045.75	0.132610
$809$	−42027.2	−1.82645	−0.913225	−	0.407455i	$-0.866416\pi$
$809$	−42027.2	−1.82645	−0.913225	+	0.407455i	$0.866416\pi$
$810$	35538.0	1.54158
$811$	−32191.4	−1.39383	−0.696913	−	0.717156i	$-0.745444\pi$
$811$	−32191.4	−1.39383	−0.696913	+	0.717156i	$0.745444\pi$
$812$	12502.2	0.540320
$813$	−51036.9	−2.20165
$814$	425.137	0.0183060
$815$	14216.0	0.610998
$816$	−12441.2	−0.533737
$817$	42347.8	1.81342
$818$	3455.07	0.147682
$819$	19658.3	0.838727
$820$	29993.5	1.27734
$821$	32767.2	1.39291	0.696456	−	0.717599i	$-0.254759\pi$
$821$	32767.2	1.39291	0.696456	+	0.717599i	$0.254759\pi$
$822$	−56745.5	−2.40782
$823$	−36892.3	−1.56256	−0.781278	−	0.624183i	$-0.785432\pi$
$823$	−36892.3	−1.56256	−0.781278	+	0.624183i	$0.785432\pi$
$824$	−1883.18	−0.0796163
$825$	−1123.58	−0.0474157
$826$	13688.9	0.576631
$827$	15835.1	0.665827	0.332913	−	0.942957i	$-0.391968\pi$
$827$	15835.1	0.665827	0.332913	+	0.942957i	$0.391968\pi$
$828$	17981.2	0.754699
$829$	−17694.6	−0.741324	−0.370662	−	0.928768i	$-0.620869\pi$
$829$	−17694.6	−0.741324	−0.370662	+	0.928768i	$0.620869\pi$
$830$	−13042.7	−0.545446
$831$	51241.0	2.13903
$832$	−33962.7	−1.41520
$833$	5146.69	0.214072
$834$	10390.8	0.431421
$835$	39690.8	1.64498
$836$	−8337.07	−0.344909
$837$	7270.09	0.300228
$838$	−32548.7	−1.34174
$839$	5539.85	0.227958	0.113979	−	0.993483i	$-0.463640\pi$
$839$	5539.85	0.227958	0.113979	+	0.993483i	$0.463640\pi$
$840$	−2186.22	−0.0897999
$841$	−4837.35	−0.198341
$842$	47412.2	1.94054
$843$	−10861.7	−0.443770
$844$	7496.38	0.305730
$845$	43141.8	1.75636
$846$	−26507.3	−1.07723
$847$	1469.11	0.0595976
$848$	−41410.1	−1.67692
$849$	2234.38	0.0903225
$850$	−1530.47	−0.0617584
$851$	1180.93	0.0475695
$852$	−19793.5	−0.795908
$853$	−12461.9	−0.500218	−0.250109	−	0.968218i	$-0.580466\pi$
$853$	−12461.9	−0.500218	−0.250109	+	0.968218i	$0.580466\pi$
$854$	−21117.6	−0.846171
$855$	22022.4	0.880877
$856$	1937.51	0.0773631
$857$	10029.0	0.399749	0.199875	−	0.979821i	$-0.435947\pi$
$857$	10029.0	0.399749	0.199875	+	0.979821i	$0.435947\pi$
$858$	−23572.3	−0.937931
$859$	5425.47	0.215500	0.107750	−	0.994178i	$-0.465635\pi$
$859$	5425.47	0.215500	0.107750	+	0.994178i	$0.465635\pi$
$860$	31803.6	1.26104
$861$	−32432.8	−1.28375
$862$	−43491.1	−1.71846
$863$	−48559.7	−1.91540	−0.957702	−	0.287763i	$-0.907088\pi$
$863$	−48559.7	−1.91540	−0.957702	+	0.287763i	$0.907088\pi$
$864$	11347.8	0.446828
$865$	−10727.9	−0.421689
$866$	25301.8	0.992828
$867$	29053.6	1.13808
$868$	14279.2	0.558374
$869$	13419.5	0.523849
$870$	39599.7	1.54317
$871$	−24790.8	−0.964412
$872$	2147.24	0.0833883
$873$	−18316.5	−0.710103
$874$	−48316.1	−1.86993
$875$	−17820.1	−0.688490
$876$	−35834.1	−1.38210
$877$	−34017.5	−1.30979	−0.654897	−	0.755718i	$-0.727288\pi$
$877$	−34017.5	−1.30979	−0.654897	+	0.755718i	$0.727288\pi$
$878$	−8267.94	−0.317801
$879$	−5886.64	−0.225883
$880$	7929.62	0.303759
$881$	45627.3	1.74486	0.872430	−	0.488739i	$-0.162543\pi$
$881$	45627.3	1.74486	0.872430	+	0.488739i	$0.162543\pi$
$882$	15629.6	0.596684
$883$	−6443.71	−0.245581	−0.122791	−	0.992433i	$-0.539184\pi$
$883$	−6443.71	−0.245581	−0.122791	+	0.992433i	$0.539184\pi$
$884$	−15390.0	−0.585545
$885$	20782.1	0.789360
$886$	−24785.3	−0.939816
$887$	39229.0	1.48498	0.742492	−	0.669855i	$-0.233644\pi$
$887$	39229.0	1.48498	0.742492	+	0.669855i	$0.233644\pi$
$888$	−169.158	−0.00639254
$889$	8360.25	0.315404
$890$	31120.3	1.17209
$891$	9502.01	0.357272
$892$	−33100.5	−1.24247
$893$	34139.2	1.27931
$894$	−24173.7	−0.904349
$895$	−36536.6	−1.36456
$896$	−3860.87	−0.143954
$897$	−65478.0	−2.43729
$898$	54604.9	2.02916
$899$	22330.8	0.828446
$900$	−2227.71	−0.0825078
$901$	−15865.4	−0.586629
$902$	16731.5	0.617624
$903$	−34390.1	−1.26736
$904$	−5635.06	−0.207322
$905$	40830.6	1.49973
$906$	−82898.6	−3.03987
$907$	17248.7	0.631459	0.315730	−	0.948849i	$-0.397751\pi$
$907$	17248.7	0.631459	0.315730	+	0.948849i	$0.397751\pi$
$908$	32669.1	1.19401
$909$	24915.3	0.909117
$910$	−39670.1	−1.44511
$911$	−3045.57	−0.110762	−0.0553810	−	0.998465i	$-0.517637\pi$
$911$	−3045.57	−0.110762	−0.0553810	+	0.998465i	$0.517637\pi$
$912$	48659.7	1.76676
$913$	−3487.31	−0.126411
$914$	45729.0	1.65490
$915$	−32060.3	−1.15834
$916$	−1481.81	−0.0534504
$917$	−1590.52	−0.0572777
$918$	4695.39	0.168814
$919$	−39035.0	−1.40114	−0.700568	−	0.713585i	$-0.747070\pi$
$919$	−39035.0	−1.40114	−0.700568	+	0.713585i	$0.747070\pi$
$920$	3132.84	0.112268
$921$	56468.4	2.02030
$922$	23839.7	0.851539
$923$	31009.3	1.10583
$924$	6770.42	0.241050
$925$	−146.306	−0.00520056
$926$	−11344.8	−0.402605
$927$	−15405.1	−0.545815
$928$	34855.8	1.23297
$929$	−9111.15	−0.321773	−0.160886	−	0.986973i	$-0.551435\pi$
$929$	−9111.15	−0.321773	−0.160886	+	0.986973i	$0.551435\pi$
$930$	45228.5	1.59473
$931$	−20129.6	−0.708616
$932$	−28777.8	−1.01142
$933$	−52617.3	−1.84632
$934$	23652.9	0.828636
$935$	3038.06	0.106262
$936$	4035.15	0.140911
$937$	−33133.7	−1.15521	−0.577604	−	0.816317i	$-0.696012\pi$
$937$	−33133.7	−1.15521	−0.577604	+	0.816317i	$0.696012\pi$
$938$	14855.5	0.517111
$939$	−29344.9	−1.01985
$940$	25638.8	0.889624
$941$	−1061.07	−0.0367588	−0.0183794	−	0.999831i	$-0.505851\pi$
$941$	−1061.07	−0.0367588	−0.0183794	+	0.999831i	$0.505851\pi$
$942$	−18727.4	−0.647742
$943$	46475.9	1.60494
$944$	19755.5	0.681132
$945$	5801.12	0.199694
$946$	17741.2	0.609742
$947$	−43573.6	−1.49520	−0.747599	−	0.664151i	$-0.768793\pi$
$947$	−43573.6	−1.49520	−0.747599	+	0.664151i	$0.768793\pi$
$948$	61844.0	2.11878
$949$	56139.2	1.92029
$950$	5985.92	0.204431
$951$	−2532.00	−0.0863361
$952$	−796.229	−0.0271071
$953$	36768.4	1.24978	0.624892	−	0.780711i	$-0.285143\pi$
$953$	36768.4	1.24978	0.624892	+	0.780711i	$0.285143\pi$
$954$	−48180.4	−1.63511
$955$	−11469.1	−0.388620
$956$	47212.8	1.59725
$957$	10588.0	0.357640
$958$	−43758.6	−1.47576
$959$	−25533.8	−0.859780
$960$	30897.5	1.03876
$961$	−4286.09	−0.143872
$962$	−3069.46	−0.102872
$963$	15849.5	0.530367
$964$	−30675.0	−1.02487
$965$	−9579.63	−0.319564
$966$	39236.8	1.30686
$967$	−10110.5	−0.336227	−0.168113	−	0.985768i	$-0.553767\pi$
$967$	−10110.5	−0.336227	−0.168113	+	0.985768i	$0.553767\pi$
$968$	301.555	0.0100128
$969$	18642.9	0.618057
$970$	36962.4	1.22350
$971$	19005.0	0.628116	0.314058	−	0.949404i	$-0.398311\pi$
$971$	19005.0	0.628116	0.314058	+	0.949404i	$0.398311\pi$
$972$	34738.8	1.14635
$973$	4675.57	0.154051
$974$	−30844.6	−1.01471
$975$	8112.13	0.266458
$976$	−30476.6	−0.999520
$977$	−10803.0	−0.353755	−0.176878	−	0.984233i	$-0.556600\pi$
$977$	−10803.0	−0.353755	−0.176878	+	0.984233i	$0.556600\pi$
$978$	36546.4	1.19491
$979$	8320.83	0.271639
$980$	−15117.5	−0.492766
$981$	17565.1	0.571674
$982$	−68272.1	−2.21858
$983$	39908.2	1.29489	0.647444	−	0.762113i	$-0.275838\pi$
$983$	39908.2	1.29489	0.647444	+	0.762113i	$0.275838\pi$
$984$	−6657.29	−0.215677
$985$	35672.7	1.15393
$986$	14422.3	0.465822
$987$	−27724.0	−0.894087
$988$	60192.9	1.93825
$989$	49280.6	1.58446
$990$	9226.06	0.296185
$991$	14162.9	0.453986	0.226993	−	0.973896i	$-0.427111\pi$
$991$	14162.9	0.453986	0.226993	+	0.973896i	$0.427111\pi$
$992$	39810.2	1.27417
$993$	58505.3	1.86970
$994$	−18581.9	−0.592941
$995$	−25324.5	−0.806875
$996$	−16071.4	−0.511286
$997$	12939.5	0.411030	0.205515	−	0.978654i	$-0.434113\pi$
$997$	12939.5	0.411030	0.205515	+	0.978654i	$0.434113\pi$
$998$	−55066.6	−1.74660
$999$	448.859	0.0142155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.15	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.15	✓	84	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-3.91972 q^{2} -6.88382 q^{3} +7.36419 q^{4} +10.4958 q^{5} +26.9826 q^{6} +12.1414 q^{7} +2.49219 q^{8} +20.3870 q^{9} +O(q^{10})\)	\(q-3.91972 q^{2} -6.88382 q^{3} +7.36419 q^{4} +10.4958 q^{5} +26.9826 q^{6} +12.1414 q^{7} +2.49219 q^{8} +20.3870 q^{9} -41.1406 q^{10} -11.0000 q^{11} -50.6938 q^{12} +79.4191 q^{13} -47.5908 q^{14} -72.2512 q^{15} -68.6822 q^{16} -26.3141 q^{17} -79.9113 q^{18} +102.919 q^{19} +77.2931 q^{20} -83.5791 q^{21} +43.1169 q^{22} +119.768 q^{23} -17.1558 q^{24} -14.8382 q^{25} -311.300 q^{26} +45.5227 q^{27} +89.4115 q^{28} +139.827 q^{29} +283.204 q^{30} +159.703 q^{31} +249.277 q^{32} +75.7220 q^{33} +103.144 q^{34} +127.434 q^{35} +150.134 q^{36} +9.86011 q^{37} -403.414 q^{38} -546.707 q^{39} +26.1575 q^{40} +388.049 q^{41} +327.607 q^{42} +411.467 q^{43} -81.0061 q^{44} +213.978 q^{45} -469.457 q^{46} +331.709 q^{47} +472.796 q^{48} -195.587 q^{49} +58.1615 q^{50} +181.142 q^{51} +584.857 q^{52} +602.923 q^{53} -178.436 q^{54} -115.454 q^{55} +30.2586 q^{56} -708.476 q^{57} -548.083 q^{58} -287.637 q^{59} -532.072 q^{60} +443.733 q^{61} -625.989 q^{62} +247.526 q^{63} -427.639 q^{64} +833.567 q^{65} -296.809 q^{66} -312.151 q^{67} -193.782 q^{68} -824.462 q^{69} -499.504 q^{70} +390.452 q^{71} +50.8083 q^{72} +706.874 q^{73} -38.6489 q^{74} +102.143 q^{75} +757.916 q^{76} -133.555 q^{77} +2142.94 q^{78} -1219.95 q^{79} -720.875 q^{80} -863.819 q^{81} -1521.04 q^{82} +317.029 q^{83} -615.493 q^{84} -276.188 q^{85} -1612.84 q^{86} -962.546 q^{87} -27.4141 q^{88} -756.439 q^{89} -838.733 q^{90} +964.258 q^{91} +881.995 q^{92} -1099.36 q^{93} -1300.21 q^{94} +1080.22 q^{95} -1715.98 q^{96} -898.441 q^{97} +766.645 q^{98} -224.257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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