LMFDB - Embedded newform 1441.4.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-3.52442 q^{2} -4.70924 q^{3} +4.42151 q^{4} +7.44138 q^{5} +16.5973 q^{6} +32.1322 q^{7} +12.6121 q^{8} -4.82309 q^{9} +O(q^{10})$	\(q-3.52442 q^{2} -4.70924 q^{3} +4.42151 q^{4} +7.44138 q^{5} +16.5973 q^{6} +32.1322 q^{7} +12.6121 q^{8} -4.82309 q^{9} -26.2265 q^{10} -11.0000 q^{11} -20.8219 q^{12} -75.2374 q^{13} -113.247 q^{14} -35.0432 q^{15} -79.8223 q^{16} +21.3313 q^{17} +16.9986 q^{18} +20.3049 q^{19} +32.9022 q^{20} -151.318 q^{21} +38.7686 q^{22} -59.6721 q^{23} -59.3933 q^{24} -69.6258 q^{25} +265.168 q^{26} +149.862 q^{27} +142.073 q^{28} +66.1481 q^{29} +123.507 q^{30} -115.353 q^{31} +180.430 q^{32} +51.8016 q^{33} -75.1805 q^{34} +239.108 q^{35} -21.3254 q^{36} +182.374 q^{37} -71.5629 q^{38} +354.311 q^{39} +93.8513 q^{40} +130.714 q^{41} +533.309 q^{42} +171.039 q^{43} -48.6366 q^{44} -35.8905 q^{45} +210.309 q^{46} -286.858 q^{47} +375.902 q^{48} +689.480 q^{49} +245.390 q^{50} -100.454 q^{51} -332.663 q^{52} -337.644 q^{53} -528.178 q^{54} -81.8552 q^{55} +405.254 q^{56} -95.6205 q^{57} -233.133 q^{58} -651.892 q^{59} -154.944 q^{60} +480.256 q^{61} +406.553 q^{62} -154.977 q^{63} +2.66657 q^{64} -559.870 q^{65} -182.570 q^{66} +620.437 q^{67} +94.3168 q^{68} +281.010 q^{69} -842.717 q^{70} -230.487 q^{71} -60.8293 q^{72} +693.337 q^{73} -642.763 q^{74} +327.885 q^{75} +89.7783 q^{76} -353.455 q^{77} -1248.74 q^{78} -108.273 q^{79} -593.988 q^{80} -575.514 q^{81} -460.692 q^{82} +546.329 q^{83} -669.055 q^{84} +158.735 q^{85} -602.812 q^{86} -311.507 q^{87} -138.733 q^{88} +281.463 q^{89} +126.493 q^{90} -2417.55 q^{91} -263.841 q^{92} +543.225 q^{93} +1011.01 q^{94} +151.096 q^{95} -849.690 q^{96} -1555.88 q^{97} -2430.02 q^{98} +53.0540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.52442	−1.24607	−0.623035	−	0.782194i	$-0.714100\pi$
$2$	−3.52442	−1.24607	−0.623035	+	0.782194i	$0.714100\pi$
$3$	−4.70924	−0.906293	−0.453146	−	0.891436i	$-0.649699\pi$
$3$	−4.70924	−0.906293	−0.453146	+	0.891436i	$0.649699\pi$
$4$	4.42151	0.552689
$5$	7.44138	0.665577	0.332789	−	0.943001i	$-0.392010\pi$
$5$	7.44138	0.665577	0.332789	+	0.943001i	$0.392010\pi$
$6$	16.5973	1.12930
$7$	32.1322	1.73498	0.867489	−	0.497457i	$-0.165733\pi$
$7$	32.1322	1.73498	0.867489	+	0.497457i	$0.165733\pi$
$8$	12.6121	0.557381
$9$	−4.82309	−0.178633
$10$	−26.2265	−0.829356
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−20.8219	−0.500898
$13$	−75.2374	−1.60516	−0.802581	−	0.596543i	$-0.796540\pi$
$13$	−75.2374	−1.60516	−0.802581	+	0.596543i	$0.796540\pi$
$14$	−113.247	−2.16190
$15$	−35.0432	−0.603208
$16$	−79.8223	−1.24722
$17$	21.3313	0.304330	0.152165	−	0.988355i	$-0.451375\pi$
$17$	21.3313	0.304330	0.152165	+	0.988355i	$0.451375\pi$
$18$	16.9986	0.222589
$19$	20.3049	0.245172	0.122586	−	0.992458i	$-0.460881\pi$
$19$	20.3049	0.245172	0.122586	+	0.992458i	$0.460881\pi$
$20$	32.9022	0.367857
$21$	−151.318	−1.57240
$22$	38.7686	0.375704
$23$	−59.6721	−0.540978	−0.270489	−	0.962723i	$-0.587185\pi$
$23$	−59.6721	−0.540978	−0.270489	+	0.962723i	$0.587185\pi$
$24$	−59.3933	−0.505150
$25$	−69.6258	−0.557007
$26$	265.168	2.00014
$27$	149.862	1.06819
$28$	142.073	0.958903
$29$	66.1481	0.423565	0.211783	−	0.977317i	$-0.432073\pi$
$29$	66.1481	0.423565	0.211783	+	0.977317i	$0.432073\pi$
$30$	123.507	0.751639
$31$	−115.353	−0.668324	−0.334162	−	0.942516i	$-0.608453\pi$
$31$	−115.353	−0.668324	−0.334162	+	0.942516i	$0.608453\pi$
$32$	180.430	0.996747
$33$	51.8016	0.273258
$34$	−75.1805	−0.379216
$35$	239.108	1.15476
$36$	−21.3254	−0.0987285
$37$	182.374	0.810328	0.405164	−	0.914244i	$-0.367214\pi$
$37$	182.374	0.810328	0.405164	+	0.914244i	$0.367214\pi$
$38$	−71.5629	−0.305501
$39$	354.311	1.45475
$40$	93.8513	0.370980
$41$	130.714	0.497906	0.248953	−	0.968516i	$-0.419914\pi$
$41$	130.714	0.497906	0.248953	+	0.968516i	$0.419914\pi$
$42$	533.309	1.95932
$43$	171.039	0.606585	0.303293	−	0.952897i	$-0.401914\pi$
$43$	171.039	0.606585	0.303293	+	0.952897i	$0.401914\pi$
$44$	−48.6366	−0.166642
$45$	−35.8905	−0.118894
$46$	210.309	0.674096
$47$	−286.858	−0.890267	−0.445134	−	0.895464i	$-0.646844\pi$
$47$	−286.858	−0.890267	−0.445134	+	0.895464i	$0.646844\pi$
$48$	375.902	1.13035
$49$	689.480	2.01015
$50$	245.390	0.694069
$51$	−100.454	−0.275812
$52$	−332.663	−0.887155
$53$	−337.644	−0.875076	−0.437538	−	0.899200i	$-0.644149\pi$
$53$	−337.644	−0.875076	−0.437538	+	0.899200i	$0.644149\pi$
$54$	−528.178	−1.33103
$55$	−81.8552	−0.200679
$56$	405.254	0.967043
$57$	−95.6205	−0.222197
$58$	−233.133	−0.527792
$59$	−651.892	−1.43846	−0.719230	−	0.694772i	$-0.755505\pi$
$59$	−651.892	−1.43846	−0.719230	+	0.694772i	$0.755505\pi$
$60$	−154.944	−0.333386
$61$	480.256	1.00804	0.504021	−	0.863692i	$-0.331854\pi$
$61$	480.256	1.00804	0.504021	+	0.863692i	$0.331854\pi$
$62$	406.553	0.832778
$63$	−154.977	−0.309924
$64$	2.66657	0.00520815
$65$	−559.870	−1.06836
$66$	−182.570	−0.340498
$67$	620.437	1.13132	0.565660	−	0.824639i	$-0.308621\pi$
$67$	620.437	1.13132	0.565660	+	0.824639i	$0.308621\pi$
$68$	94.3168	0.168200
$69$	281.010	0.490285
$70$	−842.717	−1.43891
$71$	−230.487	−0.385265	−0.192633	−	0.981271i	$-0.561703\pi$
$71$	−230.487	−0.385265	−0.192633	+	0.981271i	$0.561703\pi$
$72$	−60.8293	−0.0995666
$73$	693.337	1.11163	0.555815	−	0.831306i	$-0.312406\pi$
$73$	693.337	1.11163	0.555815	+	0.831306i	$0.312406\pi$
$74$	−642.763	−1.00972
$75$	327.885	0.504811
$76$	89.7783	0.135504
$77$	−353.455	−0.523115
$78$	−1248.74	−1.81272
$79$	−108.273	−0.154198	−0.0770990	−	0.997023i	$-0.524566\pi$
$79$	−108.273	−0.154198	−0.0770990	+	0.997023i	$0.524566\pi$
$80$	−593.988	−0.830124
$81$	−575.514	−0.789457
$82$	−460.692	−0.620426
$83$	546.329	0.722499	0.361250	−	0.932469i	$-0.382350\pi$
$83$	546.329	0.722499	0.361250	+	0.932469i	$0.382350\pi$
$84$	−669.055	−0.869047
$85$	158.735	0.202555
$86$	−602.812	−0.755847
$87$	−311.507	−0.383874
$88$	−138.733	−0.168057
$89$	281.463	0.335225	0.167612	−	0.985853i	$-0.446394\pi$
$89$	281.463	0.335225	0.167612	+	0.985853i	$0.446394\pi$
$90$	126.493	0.148150
$91$	−2417.55	−2.78492
$92$	−263.841	−0.298993
$93$	543.225	0.605697
$94$	1011.01	1.10933
$95$	151.096	0.163181
$96$	−849.690	−0.903345
$97$	−1555.88	−1.62861	−0.814305	−	0.580437i	$-0.802882\pi$
$97$	−1555.88	−1.62861	−0.814305	+	0.580437i	$0.802882\pi$
$98$	−2430.02	−2.50478
$99$	53.0540	0.0538599
$100$	−307.851	−0.307851
$101$	−2002.39	−1.97273	−0.986365	−	0.164575i	$-0.947375\pi$
$101$	−2002.39	−1.97273	−0.986365	+	0.164575i	$0.947375\pi$
$102$	354.043	0.343681
$103$	−564.778	−0.540284	−0.270142	−	0.962820i	$-0.587071\pi$
$103$	−564.778	−0.540284	−0.270142	+	0.962820i	$0.587071\pi$
$104$	−948.901	−0.894686
$105$	−1126.02	−1.04655
$106$	1190.00	1.09041
$107$	1045.12	0.944259	0.472129	−	0.881529i	$-0.343485\pi$
$107$	1045.12	0.944259	0.472129	+	0.881529i	$0.343485\pi$
$108$	662.619	0.590375
$109$	−650.496	−0.571617	−0.285808	−	0.958287i	$-0.592262\pi$
$109$	−650.496	−0.571617	−0.285808	+	0.958287i	$0.592262\pi$
$110$	288.492	0.250060
$111$	−858.843	−0.734394
$112$	−2564.87	−2.16391
$113$	2244.21	1.86830	0.934149	−	0.356884i	$-0.116161\pi$
$113$	2244.21	1.86830	0.934149	+	0.356884i	$0.116161\pi$
$114$	337.007	0.276873
$115$	−444.043	−0.360063
$116$	292.475	0.234100
$117$	362.877	0.286735
$118$	2297.54	1.79242
$119$	685.424	0.528006
$120$	−441.968	−0.336217
$121$	121.000	0.0909091
$122$	−1692.62	−1.25609
$123$	−615.565	−0.451249
$124$	−510.035	−0.369375
$125$	−1448.29	−1.03631
$126$	546.203	0.386187
$127$	1032.08	0.721120	0.360560	−	0.932736i	$-0.382586\pi$
$127$	1032.08	0.721120	0.360560	+	0.932736i	$0.382586\pi$
$128$	−1452.84	−1.00324
$129$	−805.462	−0.549744
$130$	1973.22	1.33125
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	229.041	0.151026
$133$	652.442	0.425367
$134$	−2186.68	−1.40970
$135$	1115.18	0.710961
$136$	269.033	0.169628
$137$	2114.99	1.31895	0.659475	−	0.751726i	$-0.270779\pi$
$137$	2114.99	1.31895	0.659475	+	0.751726i	$0.270779\pi$
$138$	−990.396	−0.610929
$139$	577.833	0.352598	0.176299	−	0.984337i	$-0.443587\pi$
$139$	577.833	0.352598	0.176299	+	0.984337i	$0.443587\pi$
$140$	1057.22	0.638224
$141$	1350.88	0.806843
$142$	812.333	0.480067
$143$	827.612	0.483975
$144$	384.990	0.222795
$145$	492.233	0.281915
$146$	−2443.61	−1.38517
$147$	−3246.93	−1.82178
$148$	806.369	0.447859
$149$	2690.93	1.47953	0.739765	−	0.672866i	$-0.234937\pi$
$149$	2690.93	1.47953	0.739765	+	0.672866i	$0.234937\pi$
$150$	−1155.60	−0.629030
$151$	944.417	0.508977	0.254489	−	0.967076i	$-0.418093\pi$
$151$	944.417	0.508977	0.254489	+	0.967076i	$0.418093\pi$
$152$	256.087	0.136654
$153$	−102.883	−0.0543634
$154$	1245.72	0.651838
$155$	−858.387	−0.444821
$156$	1566.59	0.804023
$157$	−1527.18	−0.776319	−0.388159	−	0.921592i	$-0.626889\pi$
$157$	−1527.18	−0.776319	−0.388159	+	0.921592i	$0.626889\pi$
$158$	381.598	0.192141
$159$	1590.05	0.793075
$160$	1342.65	0.663412
$161$	−1917.40	−0.938585
$162$	2028.35	0.983718
$163$	−2679.90	−1.28777	−0.643883	−	0.765124i	$-0.722677\pi$
$163$	−2679.90	−1.28777	−0.643883	+	0.765124i	$0.722677\pi$
$164$	577.955	0.275187
$165$	385.475	0.181874
$166$	−1925.49	−0.900284
$167$	2793.66	1.29449	0.647245	−	0.762282i	$-0.275921\pi$
$167$	2793.66	1.29449	0.647245	+	0.762282i	$0.275921\pi$
$168$	−1908.44	−0.876424
$169$	3463.67	1.57655
$170$	−559.447	−0.252398
$171$	−97.9324	−0.0437958
$172$	756.250	0.335253
$173$	4272.70	1.87773	0.938866	−	0.344283i	$-0.111878\pi$
$173$	4272.70	1.87773	0.938866	+	0.344283i	$0.111878\pi$
$174$	1097.88	0.478334
$175$	−2237.23	−0.966394
$176$	878.046	0.376052
$177$	3069.91	1.30367
$178$	−991.992	−0.417713
$179$	487.691	0.203641	0.101821	−	0.994803i	$-0.467533\pi$
$179$	487.691	0.203641	0.101821	+	0.994803i	$0.467533\pi$
$180$	−158.690	−0.0657115
$181$	−2271.37	−0.932760	−0.466380	−	0.884584i	$-0.654442\pi$
$181$	−2271.37	−0.932760	−0.466380	+	0.884584i	$0.654442\pi$
$182$	8520.44	3.47020
$183$	−2261.64	−0.913581
$184$	−752.590	−0.301531
$185$	1357.12	0.539336
$186$	−1914.55	−0.754741
$187$	−234.645	−0.0917589
$188$	−1268.35	−0.492041
$189$	4815.42	1.85328
$190$	−532.527	−0.203335
$191$	−174.827	−0.0662307	−0.0331153	−	0.999452i	$-0.510543\pi$
$191$	−174.827	−0.0662307	−0.0331153	+	0.999452i	$0.510543\pi$
$192$	−12.5575	−0.00472011
$193$	3918.59	1.46148	0.730742	−	0.682654i	$-0.239174\pi$
$193$	3918.59	1.46148	0.730742	+	0.682654i	$0.239174\pi$
$194$	5483.55	2.02936
$195$	2636.56	0.968247
$196$	3048.55	1.11099
$197$	1944.00	0.703066	0.351533	−	0.936175i	$-0.385660\pi$
$197$	1944.00	0.703066	0.351533	+	0.936175i	$0.385660\pi$
$198$	−186.984	−0.0671132
$199$	−3795.62	−1.35208	−0.676040	−	0.736865i	$-0.736305\pi$
$199$	−3795.62	−1.35208	−0.676040	+	0.736865i	$0.736305\pi$
$200$	−878.127	−0.310465
$201$	−2921.78	−1.02531
$202$	7057.27	2.45816
$203$	2125.49	0.734876
$204$	−444.160	−0.152438
$205$	972.695	0.331395
$206$	1990.51	0.673232
$207$	287.804	0.0966366
$208$	6005.63	2.00200
$209$	−223.354	−0.0739220
$210$	3968.55	1.30408
$211$	−4074.58	−1.32941	−0.664706	−	0.747105i	$-0.731443\pi$
$211$	−4074.58	−1.32941	−0.664706	+	0.747105i	$0.731443\pi$
$212$	−1492.90	−0.483645
$213$	1085.42	0.349163
$214$	−3683.44	−1.17661
$215$	1272.76	0.403729
$216$	1890.08	0.595387
$217$	−3706.55	−1.15953
$218$	2292.62	0.712274
$219$	−3265.09	−1.00746
$220$	−361.924	−0.110913
$221$	−1604.92	−0.488499
$222$	3026.92	0.915106
$223$	−3436.56	−1.03197	−0.515984	−	0.856598i	$-0.672574\pi$
$223$	−3436.56	−1.03197	−0.515984	+	0.856598i	$0.672574\pi$
$224$	5797.63	1.72933
$225$	335.812	0.0994998
$226$	−7909.53	−2.32803
$227$	−1222.50	−0.357447	−0.178723	−	0.983899i	$-0.557197\pi$
$227$	−1222.50	−0.357447	−0.178723	+	0.983899i	$0.557197\pi$
$228$	−422.787	−0.122806
$229$	−1544.63	−0.445729	−0.222865	−	0.974849i	$-0.571541\pi$
$229$	−1544.63	−0.445729	−0.222865	+	0.974849i	$0.571541\pi$
$230$	1564.99	0.448663
$231$	1664.50	0.474096
$232$	834.265	0.236087
$233$	−4610.29	−1.29627	−0.648133	−	0.761527i	$-0.724450\pi$
$233$	−4610.29	−1.29627	−0.648133	+	0.761527i	$0.724450\pi$
$234$	−1278.93	−0.357292
$235$	−2134.62	−0.592542
$236$	−2882.35	−0.795021
$237$	509.882	0.139749
$238$	−2415.72	−0.657932
$239$	−626.454	−0.169548	−0.0847739	−	0.996400i	$-0.527017\pi$
$239$	−626.454	−0.169548	−0.0847739	+	0.996400i	$0.527017\pi$
$240$	2797.23	0.752336
$241$	3242.33	0.866626	0.433313	−	0.901243i	$-0.357344\pi$
$241$	3242.33	0.866626	0.433313	+	0.901243i	$0.357344\pi$
$242$	−426.454	−0.113279
$243$	−1336.05	−0.352707
$244$	2123.46	0.557133
$245$	5130.69	1.33791
$246$	2169.51	0.562287
$247$	−1527.69	−0.393540
$248$	−1454.84	−0.372511
$249$	−2572.79	−0.654796
$250$	5104.36	1.29131
$251$	4719.38	1.18679	0.593396	−	0.804911i	$-0.297787\pi$
$251$	4719.38	1.18679	0.593396	+	0.804911i	$0.297787\pi$
$252$	−685.231	−0.171292
$253$	656.393	0.163111
$254$	−3637.48	−0.898565
$255$	−747.519	−0.183574
$256$	5099.09	1.24489
$257$	−5161.92	−1.25289	−0.626443	−	0.779467i	$-0.715490\pi$
$257$	−5161.92	−1.25289	−0.626443	+	0.779467i	$0.715490\pi$
$258$	2838.78	0.685019
$259$	5860.09	1.40590
$260$	−2475.47	−0.590471
$261$	−319.038	−0.0756628
$262$	461.699	0.108870
$263$	4622.82	1.08386	0.541930	−	0.840423i	$-0.317694\pi$
$263$	4622.82	1.08386	0.541930	+	0.840423i	$0.317694\pi$
$264$	653.326	0.152309
$265$	−2512.54	−0.582431
$266$	−2299.48	−0.530037
$267$	−1325.48	−0.303812
$268$	2743.27	0.625268
$269$	5570.69	1.26264	0.631321	−	0.775522i	$-0.282513\pi$
$269$	5570.69	1.26264	0.631321	+	0.775522i	$0.282513\pi$
$270$	−3930.37	−0.885907
$271$	3904.50	0.875209	0.437605	−	0.899168i	$-0.355827\pi$
$271$	3904.50	0.875209	0.437605	+	0.899168i	$0.355827\pi$
$272$	−1702.72	−0.379568
$273$	11384.8	2.52395
$274$	−7454.12	−1.64350
$275$	765.884	0.167944
$276$	1242.49	0.270975
$277$	−2534.86	−0.549838	−0.274919	−	0.961467i	$-0.588651\pi$
$277$	−2534.86	−0.549838	−0.274919	+	0.961467i	$0.588651\pi$
$278$	−2036.52	−0.439362
$279$	556.359	0.119385
$280$	3015.65	0.643642
$281$	−3991.06	−0.847284	−0.423642	−	0.905830i	$-0.639249\pi$
$281$	−3991.06	−0.847284	−0.423642	+	0.905830i	$0.639249\pi$
$282$	−4761.07	−1.00538
$283$	1895.02	0.398047	0.199023	−	0.979995i	$-0.436223\pi$
$283$	1895.02	0.398047	0.199023	+	0.979995i	$0.436223\pi$
$284$	−1019.10	−0.212932
$285$	−711.549	−0.147890
$286$	−2916.85	−0.603066
$287$	4200.14	0.863856
$288$	−870.233	−0.178052
$289$	−4457.97	−0.907383
$290$	−1734.83	−0.351286
$291$	7326.98	1.47600
$292$	3065.60	0.614385
$293$	3417.06	0.681321	0.340660	−	0.940186i	$-0.389349\pi$
$293$	3417.06	0.681321	0.340660	+	0.940186i	$0.389349\pi$
$294$	11443.5	2.27007
$295$	−4850.98	−0.957406
$296$	2300.12	0.451661
$297$	−1648.49	−0.322070
$298$	−9483.97	−1.84360
$299$	4489.58	0.868357
$300$	1449.75	0.279004
$301$	5495.86	1.05241
$302$	−3328.52	−0.634221
$303$	9429.75	1.78787
$304$	−1620.78	−0.305784
$305$	3573.77	0.670929
$306$	362.603	0.0677406
$307$	2505.12	0.465715	0.232858	−	0.972511i	$-0.425192\pi$
$307$	2505.12	0.465715	0.232858	+	0.972511i	$0.425192\pi$
$308$	−1562.80	−0.289120
$309$	2659.67	0.489656
$310$	3025.31	0.554278
$311$	−6196.25	−1.12977	−0.564883	−	0.825171i	$-0.691079\pi$
$311$	−6196.25	−1.12977	−0.564883	+	0.825171i	$0.691079\pi$
$312$	4468.60	0.810848
$313$	8155.95	1.47285	0.736424	−	0.676520i	$-0.236513\pi$
$313$	8155.95	1.47285	0.736424	+	0.676520i	$0.236513\pi$
$314$	5382.41	0.967347
$315$	−1153.24	−0.206279
$316$	−478.729	−0.0852235
$317$	6369.52	1.12854	0.564271	−	0.825589i	$-0.309157\pi$
$317$	6369.52	1.12854	0.564271	+	0.825589i	$0.309157\pi$
$318$	−5603.99	−0.988227
$319$	−727.629	−0.127710
$320$	19.8430	0.00346643
$321$	−4921.72	−0.855775
$322$	6757.71	1.16954
$323$	433.131	0.0746131
$324$	−2544.64	−0.436324
$325$	5238.47	0.894086
$326$	9445.07	1.60464
$327$	3063.34	0.518052
$328$	1648.58	0.277523
$329$	−9217.39	−1.54459
$330$	−1358.58	−0.226628
$331$	1968.03	0.326805	0.163403	−	0.986559i	$-0.447753\pi$
$331$	1968.03	0.326805	0.163403	+	0.986559i	$0.447753\pi$
$332$	2415.60	0.399317
$333$	−879.608	−0.144751
$334$	−9846.01	−1.61302
$335$	4616.91	0.752981
$336$	12078.6	1.96113
$337$	9417.50	1.52227	0.761133	−	0.648595i	$-0.224643\pi$
$337$	9417.50	1.52227	0.761133	+	0.648595i	$0.224643\pi$
$338$	−12207.4	−1.96449
$339$	−10568.5	−1.69322
$340$	701.847	0.111950
$341$	1268.88	0.201507
$342$	345.155	0.0545726
$343$	11133.2	1.75258
$344$	2157.16	0.338099
$345$	2091.10	0.326322
$346$	−15058.8	−2.33978
$347$	−2036.28	−0.315024	−0.157512	−	0.987517i	$-0.550347\pi$
$347$	−2036.28	−0.315024	−0.157512	+	0.987517i	$0.550347\pi$
$348$	−1377.33	−0.212163
$349$	4329.72	0.664082	0.332041	−	0.943265i	$-0.392263\pi$
$349$	4329.72	0.664082	0.332041	+	0.943265i	$0.392263\pi$
$350$	7884.94	1.20419
$351$	−11275.3	−1.71461
$352$	−1984.73	−0.300530
$353$	935.834	0.141103	0.0705516	−	0.997508i	$-0.477524\pi$
$353$	935.834	0.141103	0.0705516	+	0.997508i	$0.477524\pi$
$354$	−10819.7	−1.62446
$355$	−1715.14	−0.256424
$356$	1244.49	0.185275
$357$	−3227.82	−0.478528
$358$	−1718.83	−0.253751
$359$	6734.04	0.989997	0.494999	−	0.868894i	$-0.335169\pi$
$359$	6734.04	0.989997	0.494999	+	0.868894i	$0.335169\pi$
$360$	−452.654	−0.0662693
$361$	−6446.71	−0.939891
$362$	8005.25	1.16228
$363$	−569.818	−0.0823903
$364$	−10689.2	−1.53919
$365$	5159.38	0.739875
$366$	7970.96	1.13838
$367$	−4033.33	−0.573673	−0.286836	−	0.957980i	$-0.592604\pi$
$367$	−4033.33	−0.573673	−0.286836	+	0.957980i	$0.592604\pi$
$368$	4763.17	0.674721
$369$	−630.447	−0.0889425
$370$	−4783.04	−0.672050
$371$	−10849.3	−1.51824
$372$	2401.88	0.334762
$373$	1696.41	0.235487	0.117744	−	0.993044i	$-0.462434\pi$
$373$	1696.41	0.235487	0.117744	+	0.993044i	$0.462434\pi$
$374$	826.986	0.114338
$375$	6820.32	0.939199
$376$	−3617.88	−0.496218
$377$	−4976.81	−0.679891
$378$	−16971.5	−2.30932
$379$	10279.1	1.39314	0.696569	−	0.717490i	$-0.254709\pi$
$379$	10279.1	1.39314	0.696569	+	0.717490i	$0.254709\pi$
$380$	668.075	0.0901882
$381$	−4860.30	−0.653546
$382$	616.164	0.0825280
$383$	−38.3261	−0.00511324	−0.00255662	−	0.999997i	$-0.500814\pi$
$383$	−38.3261	−0.00511324	−0.00255662	+	0.999997i	$0.500814\pi$
$384$	6841.78	0.909226
$385$	−2630.19	−0.348174
$386$	−13810.7	−1.82111
$387$	−824.936	−0.108356
$388$	−6879.32	−0.900115
$389$	9426.95	1.22870	0.614351	−	0.789033i	$-0.289418\pi$
$389$	9426.95	1.22870	0.614351	+	0.789033i	$0.289418\pi$
$390$	−9292.34	−1.20650
$391$	−1272.89	−0.164636
$392$	8695.78	1.12042
$393$	616.910	0.0791832
$394$	−6851.45	−0.876069
$395$	−805.699	−0.102631
$396$	234.579	0.0297678
$397$	−2596.37	−0.328231	−0.164116	−	0.986441i	$-0.552477\pi$
$397$	−2596.37	−0.328231	−0.164116	+	0.986441i	$0.552477\pi$
$398$	13377.3	1.68479
$399$	−3072.50	−0.385507
$400$	5557.70	0.694712
$401$	−6408.16	−0.798026	−0.399013	−	0.916945i	$-0.630647\pi$
$401$	−6408.16	−0.798026	−0.399013	+	0.916945i	$0.630647\pi$
$402$	10297.6	1.27760
$403$	8678.88	1.07277
$404$	−8853.61	−1.09031
$405$	−4282.62	−0.525445
$406$	−7491.10	−0.915707
$407$	−2006.12	−0.244323
$408$	−1266.94	−0.153732
$409$	6515.21	0.787669	0.393834	−	0.919181i	$-0.371148\pi$
$409$	6515.21	0.787669	0.393834	+	0.919181i	$0.371148\pi$
$410$	−3428.18	−0.412941
$411$	−9960.01	−1.19536
$412$	−2497.17	−0.298609
$413$	−20946.7	−2.49569
$414$	−1014.34	−0.120416
$415$	4065.45	0.480879
$416$	−13575.1	−1.59994
$417$	−2721.15	−0.319557
$418$	787.192	0.0921120
$419$	299.151	0.0348794	0.0174397	−	0.999848i	$-0.494448\pi$
$419$	299.151	0.0348794	0.0174397	+	0.999848i	$0.494448\pi$
$420$	−4978.70	−0.578418
$421$	13014.3	1.50660	0.753299	−	0.657678i	$-0.228461\pi$
$421$	13014.3	1.50660	0.753299	+	0.657678i	$0.228461\pi$
$422$	14360.5	1.65654
$423$	1383.54	0.159031
$424$	−4258.40	−0.487750
$425$	−1485.21	−0.169514
$426$	−3825.47	−0.435081
$427$	15431.7	1.74893
$428$	4621.02	0.521881
$429$	−3897.42	−0.438623
$430$	−4485.75	−0.503075
$431$	10181.7	1.13790	0.568952	−	0.822371i	$-0.307349\pi$
$431$	10181.7	1.13790	0.568952	+	0.822371i	$0.307349\pi$
$432$	−11962.4	−1.33227
$433$	−10023.4	−1.11246	−0.556230	−	0.831028i	$-0.687753\pi$
$433$	−10023.4	−1.11246	−0.556230	+	0.831028i	$0.687753\pi$
$434$	13063.4	1.44485
$435$	−2318.04	−0.255498
$436$	−2876.18	−0.315926
$437$	−1211.64	−0.132632
$438$	11507.5	1.25537
$439$	2496.61	0.271428	0.135714	−	0.990748i	$-0.456667\pi$
$439$	2496.61	0.271428	0.135714	+	0.990748i	$0.456667\pi$
$440$	−1032.36	−0.111855
$441$	−3325.43	−0.359079
$442$	5656.39	0.608704
$443$	−1383.79	−0.148411	−0.0742053	−	0.997243i	$-0.523642\pi$
$443$	−1383.79	−0.148411	−0.0742053	+	0.997243i	$0.523642\pi$
$444$	−3797.38	−0.405892
$445$	2094.47	0.223118
$446$	12111.9	1.28590
$447$	−12672.2	−1.34089
$448$	85.6830	0.00903603
$449$	14721.0	1.54727	0.773637	−	0.633629i	$-0.218435\pi$
$449$	14721.0	1.54727	0.773637	+	0.633629i	$0.218435\pi$
$450$	−1183.54	−0.123984
$451$	−1437.86	−0.150124
$452$	9922.80	1.03259
$453$	−4447.48	−0.461283
$454$	4308.61	0.445404
$455$	−17989.9	−1.85358
$456$	−1205.97	−0.123849
$457$	12076.2	1.23610	0.618052	−	0.786137i	$-0.287922\pi$
$457$	12076.2	1.23610	0.618052	+	0.786137i	$0.287922\pi$
$458$	5443.92	0.555409
$459$	3196.77	0.325081
$460$	−1963.34	−0.199003
$461$	5035.38	0.508723	0.254361	−	0.967109i	$-0.418135\pi$
$461$	5035.38	0.508723	0.254361	+	0.967109i	$0.418135\pi$
$462$	−5866.39	−0.590756
$463$	−1659.67	−0.166591	−0.0832953	−	0.996525i	$-0.526544\pi$
$463$	−1659.67	−0.166591	−0.0832953	+	0.996525i	$0.526544\pi$
$464$	−5280.09	−0.528281
$465$	4042.35	0.403138
$466$	16248.6	1.61524
$467$	1008.84	0.0999644	0.0499822	−	0.998750i	$-0.484084\pi$
$467$	1008.84	0.0999644	0.0499822	+	0.998750i	$0.484084\pi$
$468$	1604.47	0.158475
$469$	19936.0	1.96282
$470$	7523.29	0.738348
$471$	7191.84	0.703572
$472$	−8221.72	−0.801769
$473$	−1881.43	−0.182892
$474$	−1797.04	−0.174136
$475$	−1413.75	−0.136562
$476$	3030.61	0.291823
$477$	1628.49	0.156317
$478$	2207.89	0.211268
$479$	18520.3	1.76663	0.883314	−	0.468781i	$-0.155307\pi$
$479$	18520.3	1.76663	0.883314	+	0.468781i	$0.155307\pi$
$480$	−6322.86	−0.601246
$481$	−13721.4	−1.30071
$482$	−11427.3	−1.07988
$483$	9029.48	0.850633
$484$	535.003	0.0502444
$485$	−11577.9	−1.08397
$486$	4708.81	0.439498
$487$	6228.09	0.579511	0.289755	−	0.957101i	$-0.406426\pi$
$487$	6228.09	0.579511	0.289755	+	0.957101i	$0.406426\pi$
$488$	6057.03	0.561863
$489$	12620.3	1.16709
$490$	−18082.7	−1.66713
$491$	5044.03	0.463613	0.231806	−	0.972762i	$-0.425536\pi$
$491$	5044.03	0.463613	0.231806	+	0.972762i	$0.425536\pi$
$492$	−2721.73	−0.249400
$493$	1411.03	0.128904
$494$	5384.21	0.490379
$495$	394.795	0.0358479
$496$	9207.76	0.833549
$497$	−7406.07	−0.668426
$498$	9067.60	0.815921
$499$	−17374.1	−1.55866	−0.779331	−	0.626613i	$-0.784441\pi$
$499$	−17374.1	−1.55866	−0.779331	+	0.626613i	$0.784441\pi$
$500$	−6403.61	−0.572756
$501$	−13156.0	−1.17319
$502$	−16633.1	−1.47883
$503$	11903.6	1.05518	0.527592	−	0.849498i	$-0.323095\pi$
$503$	11903.6	1.05518	0.527592	+	0.849498i	$0.323095\pi$
$504$	−1954.58	−0.172746
$505$	−14900.6	−1.31300
$506$	−2313.40	−0.203248
$507$	−16311.2	−1.42881
$508$	4563.35	0.398555
$509$	5236.18	0.455971	0.227986	−	0.973664i	$-0.426786\pi$
$509$	5236.18	0.455971	0.227986	+	0.973664i	$0.426786\pi$
$510$	2634.57	0.228746
$511$	22278.5	1.92865
$512$	−6348.57	−0.547988
$513$	3042.94	0.261889
$514$	18192.8	1.56118
$515$	−4202.73	−0.359601
$516$	−3561.36	−0.303837
$517$	3155.44	0.268426
$518$	−20653.4	−1.75185
$519$	−20121.2	−1.70178
$520$	−7061.13	−0.595483
$521$	14151.5	1.19000	0.594998	−	0.803727i	$-0.297153\pi$
$521$	14151.5	1.19000	0.594998	+	0.803727i	$0.297153\pi$
$522$	1124.42	0.0942810
$523$	−2156.78	−0.180324	−0.0901620	−	0.995927i	$-0.528738\pi$
$523$	−2156.78	−0.180324	−0.0901620	+	0.995927i	$0.528738\pi$
$524$	−579.218	−0.0482887
$525$	10535.7	0.875836
$526$	−16292.7	−1.35057
$527$	−2460.64	−0.203391
$528$	−4134.92	−0.340813
$529$	−8606.24	−0.707343
$530$	8855.24	0.725749
$531$	3144.14	0.256956
$532$	2884.78	0.235096
$533$	−9834.61	−0.799220
$534$	4671.53	0.378571
$535$	7777.15	0.628477
$536$	7825.00	0.630576
$537$	−2296.65	−0.184558
$538$	−19633.4	−1.57334
$539$	−7584.28	−0.606082
$540$	4930.80	0.392940
$541$	−23498.5	−1.86743	−0.933716	−	0.358015i	$-0.883454\pi$
$541$	−23498.5	−1.86743	−0.933716	+	0.358015i	$0.883454\pi$
$542$	−13761.1	−1.09057
$543$	10696.4	0.845354
$544$	3848.82	0.303340
$545$	−4840.59	−0.380455
$546$	−40124.8	−3.14502
$547$	−20847.8	−1.62960	−0.814798	−	0.579745i	$-0.803152\pi$
$547$	−20847.8	−1.62960	−0.814798	+	0.579745i	$0.803152\pi$
$548$	9351.47	0.728969
$549$	−2316.32	−0.180069
$550$	−2699.30	−0.209270
$551$	1343.13	0.103846
$552$	3544.12	0.273275
$553$	−3479.05	−0.267530
$554$	8933.92	0.685137
$555$	−6390.98	−0.488796
$556$	2554.89	0.194877
$557$	−17944.5	−1.36505	−0.682524	−	0.730863i	$-0.739118\pi$
$557$	−17944.5	−1.36505	−0.682524	+	0.730863i	$0.739118\pi$
$558$	−1960.84	−0.148762
$559$	−12868.5	−0.973668
$560$	−19086.2	−1.44025
$561$	1105.00	0.0831605
$562$	14066.2	1.05577
$563$	4234.19	0.316962	0.158481	−	0.987362i	$-0.449340\pi$
$563$	4234.19	0.316962	0.158481	+	0.987362i	$0.449340\pi$
$564$	5972.94	0.445933
$565$	16700.0	1.24350
$566$	−6678.84	−0.495994
$567$	−18492.6	−1.36969
$568$	−2906.93	−0.214739
$569$	18079.6	1.33205	0.666026	−	0.745928i	$-0.267994\pi$
$569$	18079.6	1.33205	0.666026	+	0.745928i	$0.267994\pi$
$570$	2507.79	0.184281
$571$	−803.923	−0.0589196	−0.0294598	−	0.999566i	$-0.509379\pi$
$571$	−803.923	−0.0589196	−0.0294598	+	0.999566i	$0.509379\pi$
$572$	3659.29	0.267487
$573$	823.303	0.0600244
$574$	−14803.1	−1.07642
$575$	4154.72	0.301328
$576$	−12.8611	−0.000930348 0
$577$	−9709.96	−0.700573	−0.350287	−	0.936643i	$-0.613916\pi$
$577$	−9709.96	−0.700573	−0.350287	+	0.936643i	$0.613916\pi$
$578$	15711.8	1.13066
$579$	−18453.6	−1.32453
$580$	2176.41	0.155812
$581$	17554.8	1.25352
$582$	−25823.3	−1.83920
$583$	3714.09	0.263845
$584$	8744.42	0.619601
$585$	2700.31	0.190844
$586$	−12043.2	−0.848973
$587$	−10347.7	−0.727593	−0.363797	−	0.931478i	$-0.618520\pi$
$587$	−10347.7	−0.727593	−0.363797	+	0.931478i	$0.618520\pi$
$588$	−14356.3	−1.00688
$589$	−2342.23	−0.163854
$590$	17096.9	1.19299
$591$	−9154.74	−0.637184
$592$	−14557.5	−1.01066
$593$	−1473.76	−0.102058	−0.0510288	−	0.998697i	$-0.516250\pi$
$593$	−1473.76	−0.102058	−0.0510288	+	0.998697i	$0.516250\pi$
$594$	5809.96	0.401322
$595$	5100.50	0.351429
$596$	11898.0	0.817719
$597$	17874.4	1.22538
$598$	−15823.1	−1.08203
$599$	28576.3	1.94924	0.974620	−	0.223864i	$-0.0718671\pi$
$599$	28576.3	1.94924	0.974620	+	0.223864i	$0.0718671\pi$
$600$	4135.31	0.281372
$601$	3288.45	0.223192	0.111596	−	0.993754i	$-0.464404\pi$
$601$	3288.45	0.223192	0.111596	+	0.993754i	$0.464404\pi$
$602$	−19369.7	−1.31138
$603$	−2992.43	−0.202091
$604$	4175.75	0.281306
$605$	900.407	0.0605070
$606$	−33234.4	−2.22781
$607$	1246.44	0.0833467	0.0416734	−	0.999131i	$-0.486731\pi$
$607$	1246.44	0.0833467	0.0416734	+	0.999131i	$0.486731\pi$
$608$	3663.62	0.244374
$609$	−10009.4	−0.666013
$610$	−12595.5	−0.836025
$611$	21582.5	1.42902
$612$	−454.898	−0.0300460
$613$	−25036.9	−1.64964	−0.824821	−	0.565394i	$-0.808724\pi$
$613$	−25036.9	−1.64964	−0.824821	+	0.565394i	$0.808724\pi$
$614$	−8829.08	−0.580314
$615$	−4580.65	−0.300341
$616$	−4457.80	−0.291574
$617$	−2509.92	−0.163769	−0.0818847	−	0.996642i	$-0.526094\pi$
$617$	−2509.92	−0.163769	−0.0818847	+	0.996642i	$0.526094\pi$
$618$	−9373.80	−0.610145
$619$	9408.53	0.610922	0.305461	−	0.952205i	$-0.401189\pi$
$619$	9408.53	0.610922	0.305461	+	0.952205i	$0.401189\pi$
$620$	−3795.37	−0.245848
$621$	−8942.61	−0.577866
$622$	21838.2	1.40777
$623$	9044.03	0.581607
$624$	−28281.9	−1.81440
$625$	−2074.01	−0.132737
$626$	−28745.0	−1.83527
$627$	1051.83	0.0669950
$628$	−6752.43	−0.429063
$629$	3890.29	0.246607
$630$	4064.50	0.257037
$631$	2174.10	0.137163	0.0685813	−	0.997646i	$-0.478153\pi$
$631$	2174.10	0.137163	0.0685813	+	0.997646i	$0.478153\pi$
$632$	−1365.55	−0.0859470
$633$	19188.2	1.20484
$634$	−22448.8	−1.40624
$635$	7680.09	0.479961
$636$	7030.41	0.438324
$637$	−51874.7	−3.22661
$638$	2564.47	0.159135
$639$	1111.66	0.0688211
$640$	−10811.1	−0.667732
$641$	−1010.78	−0.0622833	−0.0311416	−	0.999515i	$-0.509914\pi$
$641$	−1010.78	−0.0622833	−0.0311416	+	0.999515i	$0.509914\pi$
$642$	17346.2	1.06636
$643$	−18240.1	−1.11869	−0.559346	−	0.828934i	$-0.688948\pi$
$643$	−18240.1	−1.11869	−0.559346	+	0.828934i	$0.688948\pi$
$644$	−8477.80	−0.518745
$645$	−5993.75	−0.365897
$646$	−1526.53	−0.0929731
$647$	17873.4	1.08606	0.543028	−	0.839715i	$-0.317278\pi$
$647$	17873.4	1.08606	0.543028	+	0.839715i	$0.317278\pi$
$648$	−7258.43	−0.440028
$649$	7170.81	0.433712
$650$	−18462.5	−1.11409
$651$	17455.0	1.05087
$652$	−11849.2	−0.711734
$653$	19584.2	1.17364	0.586822	−	0.809716i	$-0.300379\pi$
$653$	19584.2	1.17364	0.586822	+	0.809716i	$0.300379\pi$
$654$	−10796.5	−0.645529
$655$	−974.821	−0.0581518
$656$	−10433.9	−0.621000
$657$	−3344.03	−0.198574
$658$	32485.9	1.92467
$659$	18767.4	1.10937	0.554683	−	0.832062i	$-0.312839\pi$
$659$	18767.4	1.10937	0.554683	+	0.832062i	$0.312839\pi$
$660$	1704.38	0.100520
$661$	21881.6	1.28759	0.643793	−	0.765199i	$-0.277360\pi$
$661$	21881.6	1.28759	0.643793	+	0.765199i	$0.277360\pi$
$662$	−6936.14	−0.407222
$663$	7557.92	0.442723
$664$	6890.35	0.402707
$665$	4855.07	0.283115
$666$	3100.10	0.180370
$667$	−3947.20	−0.229139
$668$	12352.2	0.715450
$669$	16183.6	0.935266
$670$	−16271.9	−0.938267
$671$	−5282.82	−0.303936
$672$	−27302.4	−1.56728
$673$	13548.8	0.776027	0.388013	−	0.921654i	$-0.373161\pi$
$673$	13548.8	0.776027	0.388013	+	0.921654i	$0.373161\pi$
$674$	−33191.2	−1.89685
$675$	−10434.3	−0.594987
$676$	15314.7	0.871339
$677$	−23578.7	−1.33856	−0.669280	−	0.743011i	$-0.733397\pi$
$677$	−23578.7	−1.33856	−0.669280	+	0.743011i	$0.733397\pi$
$678$	37247.9	2.10988
$679$	−49993.7	−2.82560
$680$	2001.97	0.112900
$681$	5757.06	0.323952
$682$	−4472.08	−0.251092
$683$	15953.3	0.893759	0.446879	−	0.894594i	$-0.352535\pi$
$683$	15953.3	0.893759	0.446879	+	0.894594i	$0.352535\pi$
$684$	−433.009	−0.0242054
$685$	15738.5	0.877864
$686$	−39238.0	−2.18384
$687$	7274.02	0.403961
$688$	−13652.7	−0.756548
$689$	25403.5	1.40464
$690$	−7369.92	−0.406620
$691$	31545.5	1.73668	0.868341	−	0.495967i	$-0.165186\pi$
$691$	31545.5	1.73668	0.868341	+	0.495967i	$0.165186\pi$
$692$	18891.8	1.03780
$693$	1704.74	0.0934457
$694$	7176.70	0.392542
$695$	4299.87	0.234681
$696$	−3928.75	−0.213964
$697$	2788.31	0.151528
$698$	−15259.7	−0.827493
$699$	21710.9	1.17480
$700$	−9891.95	−0.534115
$701$	−24152.1	−1.30130	−0.650649	−	0.759378i	$-0.725503\pi$
$701$	−24152.1	−1.30130	−0.650649	+	0.759378i	$0.725503\pi$
$702$	39738.7	2.13653
$703$	3703.09	0.198669
$704$	−29.3323	−0.00157032
$705$	10052.4	0.537016
$706$	−3298.27	−0.175824
$707$	−64341.4	−3.42264
$708$	13573.7	0.720522
$709$	4697.32	0.248817	0.124409	−	0.992231i	$-0.460297\pi$
$709$	4697.32	0.248817	0.124409	+	0.992231i	$0.460297\pi$
$710$	6044.88	0.319522
$711$	522.210	0.0275449
$712$	3549.83	0.186848
$713$	6883.37	0.361549
$714$	11376.2	0.596279
$715$	6158.57	0.322123
$716$	2156.33	0.112550
$717$	2950.12	0.153660
$718$	−23733.6	−1.23360
$719$	24939.7	1.29359	0.646797	−	0.762662i	$-0.276108\pi$
$719$	24939.7	1.29359	0.646797	+	0.762662i	$0.276108\pi$
$720$	2864.86	0.148288
$721$	−18147.6	−0.937381
$722$	22720.9	1.17117
$723$	−15268.9	−0.785417
$724$	−10042.9	−0.515526
$725$	−4605.62	−0.235929
$726$	2008.27	0.102664
$727$	26224.5	1.33784	0.668922	−	0.743333i	$-0.266756\pi$
$727$	26224.5	1.33784	0.668922	+	0.743333i	$0.266756\pi$
$728$	−30490.3	−1.55226
$729$	21830.7	1.10911
$730$	−18183.8	−0.921936
$731$	3648.49	0.184602
$732$	−9999.87	−0.504926
$733$	3569.03	0.179843	0.0899216	−	0.995949i	$-0.471338\pi$
$733$	3569.03	0.179843	0.0899216	+	0.995949i	$0.471338\pi$
$734$	14215.1	0.714836
$735$	−24161.6	−1.21254
$736$	−10766.7	−0.539218
$737$	−6824.81	−0.341106
$738$	2221.96	0.110829
$739$	−10387.7	−0.517075	−0.258537	−	0.966001i	$-0.583241\pi$
$739$	−10387.7	−0.517075	−0.258537	+	0.966001i	$0.583241\pi$
$740$	6000.50	0.298085
$741$	7194.24	0.356663
$742$	38237.3	1.89183
$743$	−13804.4	−0.681606	−0.340803	−	0.940135i	$-0.610699\pi$
$743$	−13804.4	−0.681606	−0.340803	+	0.940135i	$0.610699\pi$
$744$	6851.20	0.337604
$745$	20024.3	0.984741
$746$	−5978.85	−0.293433
$747$	−2635.00	−0.129062
$748$	−1037.48	−0.0507141
$749$	33582.1	1.63827
$750$	−24037.6	−1.17031
$751$	−3618.40	−0.175815	−0.0879077	−	0.996129i	$-0.528018\pi$
$751$	−3618.40	−0.175815	−0.0879077	+	0.996129i	$0.528018\pi$
$752$	22897.7	1.11036
$753$	−22224.7	−1.07558
$754$	17540.4	0.847191
$755$	7027.77	0.338764
$756$	21291.4	1.02429
$757$	11169.2	0.536262	0.268131	−	0.963382i	$-0.413594\pi$
$757$	11169.2	0.536262	0.268131	+	0.963382i	$0.413594\pi$
$758$	−36227.7	−1.73595
$759$	−3091.11	−0.147826
$760$	1905.64	0.0909538
$761$	−4775.96	−0.227501	−0.113751	−	0.993509i	$-0.536286\pi$
$761$	−4775.96	−0.227501	−0.113751	+	0.993509i	$0.536286\pi$
$762$	17129.7	0.814363
$763$	−20901.9	−0.991742
$764$	−773.001	−0.0366050
$765$	−765.592	−0.0361830
$766$	135.077	0.00637145
$767$	49046.7	2.30896
$768$	−24012.8	−1.12824
$769$	−19904.5	−0.933387	−0.466694	−	0.884419i	$-0.654555\pi$
$769$	−19904.5	−0.933387	−0.466694	+	0.884419i	$0.654555\pi$
$770$	9269.89	0.433849
$771$	24308.7	1.13548
$772$	17326.1	0.807746
$773$	16536.9	0.769456	0.384728	−	0.923030i	$-0.374295\pi$
$773$	16536.9	0.769456	0.384728	+	0.923030i	$0.374295\pi$
$774$	2907.42	0.135019
$775$	8031.56	0.372261
$776$	−19622.8	−0.907756
$777$	−27596.5	−1.27416
$778$	−33224.5	−1.53105
$779$	2654.14	0.122072
$780$	11657.6	0.535139
$781$	2535.36	0.116162
$782$	4486.18	0.205148
$783$	9913.12	0.452447
$784$	−55035.9	−2.50710
$785$	−11364.3	−0.516700
$786$	−2174.25	−0.0986677
$787$	−42036.3	−1.90398	−0.951990	−	0.306128i	$-0.900967\pi$
$787$	−42036.3	−1.90398	−0.951990	+	0.306128i	$0.900967\pi$
$788$	8595.40	0.388577
$789$	−21770.0	−0.982295
$790$	2839.62	0.127885
$791$	72111.5	3.24145
$792$	669.122	0.0300205
$793$	−36133.2	−1.61807
$794$	9150.67	0.408999
$795$	11832.1	0.527853
$796$	−16782.4	−0.747280
$797$	12071.0	0.536484	0.268242	−	0.963352i	$-0.413557\pi$
$797$	12071.0	0.536484	0.268242	+	0.963352i	$0.413557\pi$
$798$	10828.8	0.480369
$799$	−6119.07	−0.270935
$800$	−12562.6	−0.555195
$801$	−1357.52	−0.0598822
$802$	22585.0	0.994396
$803$	−7626.71	−0.335169
$804$	−12918.7	−0.566676
$805$	−14268.1	−0.624701
$806$	−30588.0	−1.33674
$807$	−26233.7	−1.14432
$808$	−25254.4	−1.09956
$809$	−8355.40	−0.363115	−0.181558	−	0.983380i	$-0.558114\pi$
$809$	−8355.40	−0.363115	−0.181558	+	0.983380i	$0.558114\pi$
$810$	15093.7	0.654741
$811$	23323.0	1.00984	0.504921	−	0.863166i	$-0.331522\pi$
$811$	23323.0	1.00984	0.504921	+	0.863166i	$0.331522\pi$
$812$	9397.86	0.406158
$813$	−18387.2	−0.793196
$814$	7070.39	0.304443
$815$	−19942.1	−0.857107
$816$	8018.50	0.343999
$817$	3472.92	0.148718
$818$	−22962.3	−0.981490
$819$	11660.1	0.497479
$820$	4300.78	0.183158
$821$	26220.8	1.11463	0.557316	−	0.830300i	$-0.311831\pi$
$821$	26220.8	1.11463	0.557316	+	0.830300i	$0.311831\pi$
$822$	35103.2	1.48950
$823$	13139.5	0.556519	0.278260	−	0.960506i	$-0.410242\pi$
$823$	13139.5	0.556519	0.278260	+	0.960506i	$0.410242\pi$
$824$	−7123.03	−0.301144
$825$	−3606.73	−0.152206
$826$	73825.1	3.10981
$827$	14617.2	0.614620	0.307310	−	0.951609i	$-0.400571\pi$
$827$	14617.2	0.614620	0.307310	+	0.951609i	$0.400571\pi$
$828$	1272.53	0.0534100
$829$	−13932.3	−0.583704	−0.291852	−	0.956464i	$-0.594271\pi$
$829$	−13932.3	−0.583704	−0.291852	+	0.956464i	$0.594271\pi$
$830$	−14328.3	−0.599209
$831$	11937.3	0.498315
$832$	−200.626	−0.00835993
$833$	14707.5	0.611748
$834$	9590.47	0.398190
$835$	20788.7	0.861583
$836$	−987.562	−0.0408559
$837$	−17287.1	−0.713895
$838$	−1054.33	−0.0434622
$839$	20490.5	0.843159	0.421579	−	0.906791i	$-0.361476\pi$
$839$	20490.5	0.843159	0.421579	+	0.906791i	$0.361476\pi$
$840$	−14201.4	−0.583328
$841$	−20013.4	−0.820593
$842$	−45867.8	−1.87733
$843$	18794.9	0.767888
$844$	−18015.8	−0.734751
$845$	25774.5	1.04931
$846$	−4876.18	−0.198164
$847$	3888.00	0.157725
$848$	26951.6	1.09142
$849$	−8924.10	−0.360747
$850$	5234.51	0.211226
$851$	−10882.7	−0.438370
$852$	4799.19	0.192979
$853$	13453.1	0.540005	0.270002	−	0.962860i	$-0.412975\pi$
$853$	13453.1	0.540005	0.270002	+	0.962860i	$0.412975\pi$
$854$	−54387.8	−2.17929
$855$	−728.752	−0.0291495
$856$	13181.2	0.526312
$857$	12764.6	0.508786	0.254393	−	0.967101i	$-0.418124\pi$
$857$	12764.6	0.508786	0.254393	+	0.967101i	$0.418124\pi$
$858$	13736.1	0.546554
$859$	41973.0	1.66717	0.833585	−	0.552391i	$-0.186285\pi$
$859$	41973.0	1.66717	0.833585	+	0.552391i	$0.186285\pi$
$860$	5627.54	0.223137
$861$	−19779.5	−0.782907
$862$	−35884.7	−1.41791
$863$	7944.60	0.313369	0.156684	−	0.987649i	$-0.449919\pi$
$863$	7944.60	0.313369	0.156684	+	0.987649i	$0.449919\pi$
$864$	27039.8	1.06471
$865$	31794.8	1.24978
$866$	35326.7	1.38620
$867$	20993.7	0.822355
$868$	−16388.6	−0.640858
$869$	1191.00	0.0464924
$870$	8169.75	0.318368
$871$	−46680.1	−1.81595
$872$	−8204.11	−0.318608
$873$	7504.13	0.290924
$874$	4270.31	0.165269
$875$	−46536.6	−1.79797
$876$	−14436.6	−0.556813
$877$	21358.7	0.822385	0.411193	−	0.911548i	$-0.365112\pi$
$877$	21358.7	0.822385	0.411193	+	0.911548i	$0.365112\pi$
$878$	−8799.09	−0.338218
$879$	−16091.8	−0.617476
$880$	6533.87	0.250292
$881$	27702.5	1.05939	0.529694	−	0.848189i	$-0.322307\pi$
$881$	27702.5	1.05939	0.529694	+	0.848189i	$0.322307\pi$
$882$	11720.2	0.447437
$883$	26211.0	0.998948	0.499474	−	0.866329i	$-0.333527\pi$
$883$	26211.0	0.998948	0.499474	+	0.866329i	$0.333527\pi$
$884$	−7096.15	−0.269988
$885$	22844.4	0.867690
$886$	4877.06	0.184930
$887$	−22816.2	−0.863689	−0.431844	−	0.901948i	$-0.642137\pi$
$887$	−22816.2	−0.863689	−0.431844	+	0.901948i	$0.642137\pi$
$888$	−10831.8	−0.409337
$889$	33163.0	1.25113
$890$	−7381.79	−0.278021
$891$	6330.66	0.238030
$892$	−15194.8	−0.570357
$893$	−5824.62	−0.218268
$894$	44662.3	1.67084
$895$	3629.09	0.135539
$896$	−46683.0	−1.74059
$897$	−21142.5	−0.786986
$898$	−51882.9	−1.92801
$899$	−7630.39	−0.283079
$900$	1484.80	0.0549924
$901$	−7202.41	−0.266312
$902$	5067.61	0.187065
$903$	−25881.3	−0.953793
$904$	28304.2	1.04135
$905$	−16902.1	−0.620824
$906$	15674.8	0.574790
$907$	−5644.23	−0.206630	−0.103315	−	0.994649i	$-0.532945\pi$
$907$	−5644.23	−0.206630	−0.103315	+	0.994649i	$0.532945\pi$
$908$	−5405.32	−0.197557
$909$	9657.73	0.352395
$910$	63403.8	2.30969
$911$	28934.2	1.05229	0.526144	−	0.850395i	$-0.323637\pi$
$911$	28934.2	1.05229	0.526144	+	0.850395i	$0.323637\pi$
$912$	7632.65	0.277130
$913$	−6009.62	−0.217842
$914$	−42561.5	−1.54027
$915$	−16829.7	−0.608059
$916$	−6829.59	−0.246350
$917$	−4209.32	−0.151586
$918$	−11266.7	−0.405074
$919$	50234.3	1.80313	0.901564	−	0.432645i	$-0.142420\pi$
$919$	50234.3	1.80313	0.901564	+	0.432645i	$0.142420\pi$
$920$	−5600.31	−0.200692
$921$	−11797.2	−0.422075
$922$	−17746.8	−0.633904
$923$	17341.3	0.618413
$924$	7359.61	0.262027
$925$	−12698.0	−0.451358
$926$	5849.37	0.207584
$927$	2723.98	0.0965126
$928$	11935.1	0.422187
$929$	−20231.1	−0.714489	−0.357244	−	0.934011i	$-0.616284\pi$
$929$	−20231.1	−0.714489	−0.357244	+	0.934011i	$0.616284\pi$
$930$	−14246.9	−0.502338
$931$	13999.8	0.492831
$932$	−20384.5	−0.716432
$933$	29179.6	1.02390
$934$	−3555.56	−0.124563
$935$	−1746.08	−0.0610727
$936$	4576.64	0.159821
$937$	−48130.7	−1.67808	−0.839040	−	0.544069i	$-0.816883\pi$
$937$	−48130.7	−1.67808	−0.839040	+	0.544069i	$0.816883\pi$
$938$	−70262.9	−2.44580
$939$	−38408.3	−1.33483
$940$	−9438.25	−0.327491
$941$	−35401.7	−1.22642	−0.613211	−	0.789919i	$-0.710123\pi$
$941$	−35401.7	−1.22642	−0.613211	+	0.789919i	$0.710123\pi$
$942$	−25347.0	−0.876700
$943$	−7800.00	−0.269356
$944$	52035.5	1.79408
$945$	35833.3	1.23350
$946$	6630.93	0.227897
$947$	−11171.4	−0.383340	−0.191670	−	0.981459i	$-0.561390\pi$
$947$	−11171.4	−0.383340	−0.191670	+	0.981459i	$0.561390\pi$
$948$	2254.45	0.0772375
$949$	−52164.9	−1.78435
$950$	4982.63	0.170166
$951$	−29995.6	−1.02279
$952$	8644.62	0.294300
$953$	−27706.6	−0.941769	−0.470884	−	0.882195i	$-0.656065\pi$
$953$	−27706.6	−0.941769	−0.470884	+	0.882195i	$0.656065\pi$
$954$	−5739.48	−0.194782
$955$	−1300.96	−0.0440816
$956$	−2769.87	−0.0937072
$957$	3426.58	0.115742
$958$	−65273.3	−2.20134
$959$	67959.5	2.28835
$960$	−93.4453	−0.00314160
$961$	−16484.6	−0.553343
$962$	48359.8	1.62077
$963$	−5040.72	−0.168676
$964$	14336.0	0.478975
$965$	29159.7	0.972730
$966$	−31823.6	−1.05995
$967$	48363.7	1.60835	0.804174	−	0.594394i	$-0.202608\pi$
$967$	48363.7	1.60835	0.804174	+	0.594394i	$0.202608\pi$
$968$	1526.06	0.0506710
$969$	−2039.71	−0.0676213
$970$	40805.2	1.35070
$971$	8061.96	0.266448	0.133224	−	0.991086i	$-0.457467\pi$
$971$	8061.96	0.266448	0.133224	+	0.991086i	$0.457467\pi$
$972$	−5907.38	−0.194937
$973$	18567.1	0.611750
$974$	−21950.4	−0.722111
$975$	−24669.2	−0.810304
$976$	−38335.2	−1.25725
$977$	7062.18	0.231258	0.115629	−	0.993292i	$-0.463112\pi$
$977$	7062.18	0.231258	0.115629	+	0.993292i	$0.463112\pi$
$978$	−44479.1	−1.45428
$979$	−3096.09	−0.101074
$980$	22685.4	0.739447
$981$	3137.40	0.102110
$982$	−17777.3	−0.577694
$983$	42633.7	1.38332	0.691660	−	0.722224i	$-0.256880\pi$
$983$	42633.7	1.38332	0.691660	+	0.722224i	$0.256880\pi$
$984$	−7763.55	−0.251517
$985$	14466.0	0.467945
$986$	−4973.05	−0.160623
$987$	43406.9	1.39985
$988$	−6754.69	−0.217505
$989$	−10206.2	−0.328149
$990$	−1391.42	−0.0446690
$991$	4673.85	0.149818	0.0749091	−	0.997190i	$-0.476133\pi$
$991$	4673.85	0.149818	0.0749091	+	0.997190i	$0.476133\pi$
$992$	−20813.2	−0.666150
$993$	−9267.90	−0.296181
$994$	26102.1	0.832905
$995$	−28244.6	−0.899914
$996$	−11375.6	−0.361899
$997$	−27021.9	−0.858368	−0.429184	−	0.903217i	$-0.641199\pi$
$997$	−27021.9	−0.858368	−0.429184	+	0.903217i	$0.641199\pi$
$998$	61233.6	1.94220
$999$	27331.0	0.865582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.19	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-3.52442 q^{2} -4.70924 q^{3} +4.42151 q^{4} +7.44138 q^{5} +16.5973 q^{6} +32.1322 q^{7} +12.6121 q^{8} -4.82309 q^{9} +O(q^{10})\)	\(q-3.52442 q^{2} -4.70924 q^{3} +4.42151 q^{4} +7.44138 q^{5} +16.5973 q^{6} +32.1322 q^{7} +12.6121 q^{8} -4.82309 q^{9} -26.2265 q^{10} -11.0000 q^{11} -20.8219 q^{12} -75.2374 q^{13} -113.247 q^{14} -35.0432 q^{15} -79.8223 q^{16} +21.3313 q^{17} +16.9986 q^{18} +20.3049 q^{19} +32.9022 q^{20} -151.318 q^{21} +38.7686 q^{22} -59.6721 q^{23} -59.3933 q^{24} -69.6258 q^{25} +265.168 q^{26} +149.862 q^{27} +142.073 q^{28} +66.1481 q^{29} +123.507 q^{30} -115.353 q^{31} +180.430 q^{32} +51.8016 q^{33} -75.1805 q^{34} +239.108 q^{35} -21.3254 q^{36} +182.374 q^{37} -71.5629 q^{38} +354.311 q^{39} +93.8513 q^{40} +130.714 q^{41} +533.309 q^{42} +171.039 q^{43} -48.6366 q^{44} -35.8905 q^{45} +210.309 q^{46} -286.858 q^{47} +375.902 q^{48} +689.480 q^{49} +245.390 q^{50} -100.454 q^{51} -332.663 q^{52} -337.644 q^{53} -528.178 q^{54} -81.8552 q^{55} +405.254 q^{56} -95.6205 q^{57} -233.133 q^{58} -651.892 q^{59} -154.944 q^{60} +480.256 q^{61} +406.553 q^{62} -154.977 q^{63} +2.66657 q^{64} -559.870 q^{65} -182.570 q^{66} +620.437 q^{67} +94.3168 q^{68} +281.010 q^{69} -842.717 q^{70} -230.487 q^{71} -60.8293 q^{72} +693.337 q^{73} -642.763 q^{74} +327.885 q^{75} +89.7783 q^{76} -353.455 q^{77} -1248.74 q^{78} -108.273 q^{79} -593.988 q^{80} -575.514 q^{81} -460.692 q^{82} +546.329 q^{83} -669.055 q^{84} +158.735 q^{85} -602.812 q^{86} -311.507 q^{87} -138.733 q^{88} +281.463 q^{89} +126.493 q^{90} -2417.55 q^{91} -263.841 q^{92} +543.225 q^{93} +1011.01 q^{94} +151.096 q^{95} -849.690 q^{96} -1555.88 q^{97} -2430.02 q^{98} +53.0540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 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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