LMFDB - Embedded newform 2013.4.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.89062 q^{2} -3.00000 q^{3} +15.9181 q^{4} +15.5621 q^{5} +14.6718 q^{6} +16.9638 q^{7} -38.7245 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.89062 q^{2} -3.00000 q^{3} +15.9181 q^{4} +15.5621 q^{5} +14.6718 q^{6} +16.9638 q^{7} -38.7245 q^{8} +9.00000 q^{9} -76.1085 q^{10} -11.0000 q^{11} -47.7544 q^{12} -53.6054 q^{13} -82.9632 q^{14} -46.6864 q^{15} +62.0417 q^{16} -69.8904 q^{17} -44.0155 q^{18} +56.3860 q^{19} +247.720 q^{20} -50.8913 q^{21} +53.7968 q^{22} -33.8893 q^{23} +116.174 q^{24} +117.180 q^{25} +262.163 q^{26} -27.0000 q^{27} +270.031 q^{28} +174.351 q^{29} +228.325 q^{30} +121.214 q^{31} +6.37393 q^{32} +33.0000 q^{33} +341.807 q^{34} +263.992 q^{35} +143.263 q^{36} -324.698 q^{37} -275.762 q^{38} +160.816 q^{39} -602.637 q^{40} +208.037 q^{41} +248.890 q^{42} -245.398 q^{43} -175.099 q^{44} +140.059 q^{45} +165.739 q^{46} +328.411 q^{47} -186.125 q^{48} -55.2310 q^{49} -573.085 q^{50} +209.671 q^{51} -853.297 q^{52} -268.489 q^{53} +132.047 q^{54} -171.184 q^{55} -656.913 q^{56} -169.158 q^{57} -852.686 q^{58} -707.553 q^{59} -743.161 q^{60} +61.0000 q^{61} -592.810 q^{62} +152.674 q^{63} -527.506 q^{64} -834.215 q^{65} -161.390 q^{66} +618.129 q^{67} -1112.52 q^{68} +101.668 q^{69} -1291.09 q^{70} +156.953 q^{71} -348.521 q^{72} -454.492 q^{73} +1587.97 q^{74} -351.541 q^{75} +897.559 q^{76} -186.601 q^{77} -786.490 q^{78} +1214.77 q^{79} +965.502 q^{80} +81.0000 q^{81} -1017.43 q^{82} +254.049 q^{83} -810.093 q^{84} -1087.64 q^{85} +1200.15 q^{86} -523.054 q^{87} +425.970 q^{88} +60.0919 q^{89} -684.976 q^{90} -909.348 q^{91} -539.454 q^{92} -363.641 q^{93} -1606.13 q^{94} +877.487 q^{95} -19.1218 q^{96} -1549.02 q^{97} +270.114 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.89062	−1.72909	−0.864547	−	0.502552i	$-0.832395\pi$
$2$	−4.89062	−1.72909	−0.864547	+	0.502552i	$0.832395\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.9181	1.98977
$5$	15.5621	1.39192	0.695960	−	0.718080i	$-0.254979\pi$
$5$	15.5621	1.39192	0.695960	+	0.718080i	$0.254979\pi$
$6$	14.6718	0.998293
$7$	16.9638	0.915957	0.457978	−	0.888963i	$-0.348574\pi$
$7$	16.9638	0.915957	0.457978	+	0.888963i	$0.348574\pi$
$8$	−38.7245	−1.71140
$9$	9.00000	0.333333
$10$	−76.1085	−2.40676
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−47.7544	−1.14879
$13$	−53.6054	−1.14365	−0.571825	−	0.820376i	$-0.693764\pi$
$13$	−53.6054	−1.14365	−0.571825	+	0.820376i	$0.693764\pi$
$14$	−82.9632	−1.58377
$15$	−46.6864	−0.803626
$16$	62.0417	0.969402
$17$	−69.8904	−0.997112	−0.498556	−	0.866857i	$-0.666136\pi$
$17$	−69.8904	−0.997112	−0.498556	+	0.866857i	$0.666136\pi$
$18$	−44.0155	−0.576365
$19$	56.3860	0.680833	0.340417	−	0.940275i	$-0.389432\pi$
$19$	56.3860	0.680833	0.340417	+	0.940275i	$0.389432\pi$
$20$	247.720	2.76960
$21$	−50.8913	−0.528828
$22$	53.7968	0.521341
$23$	−33.8893	−0.307235	−0.153617	−	0.988130i	$-0.549092\pi$
$23$	−33.8893	−0.307235	−0.153617	+	0.988130i	$0.549092\pi$
$24$	116.174	0.988076
$25$	117.180	0.937444
$26$	262.163	1.97748
$27$	−27.0000	−0.192450
$28$	270.031	1.82254
$29$	174.351	1.11642	0.558211	−	0.829699i	$-0.311488\pi$
$29$	174.351	1.11642	0.558211	+	0.829699i	$0.311488\pi$
$30$	228.325	1.38954
$31$	121.214	0.702279	0.351139	−	0.936323i	$-0.385794\pi$
$31$	121.214	0.702279	0.351139	+	0.936323i	$0.385794\pi$
$32$	6.37393	0.0352113
$33$	33.0000	0.174078
$34$	341.807	1.72410
$35$	263.992	1.27494
$36$	143.263	0.663255
$37$	−324.698	−1.44270	−0.721351	−	0.692570i	$-0.756479\pi$
$37$	−324.698	−1.44270	−0.721351	+	0.692570i	$0.756479\pi$
$38$	−275.762	−1.17722
$39$	160.816	0.660287
$40$	−602.637	−2.38213
$41$	208.037	0.792435	0.396218	−	0.918157i	$-0.370323\pi$
$41$	208.037	0.792435	0.396218	+	0.918157i	$0.370323\pi$
$42$	248.890	0.914393
$43$	−245.398	−0.870299	−0.435149	−	0.900358i	$-0.643304\pi$
$43$	−245.398	−0.870299	−0.435149	+	0.900358i	$0.643304\pi$
$44$	−175.099	−0.599937
$45$	140.059	0.463974
$46$	165.739	0.531238
$47$	328.411	1.01923	0.509614	−	0.860403i	$-0.329788\pi$
$47$	328.411	1.01923	0.509614	+	0.860403i	$0.329788\pi$
$48$	−186.125	−0.559684
$49$	−55.2310	−0.161023
$50$	−573.085	−1.62093
$51$	209.671	0.575683
$52$	−853.297	−2.27560
$53$	−268.489	−0.695846	−0.347923	−	0.937523i	$-0.613113\pi$
$53$	−268.489	−0.695846	−0.347923	+	0.937523i	$0.613113\pi$
$54$	132.047	0.332764
$55$	−171.184	−0.419680
$56$	−656.913	−1.56757
$57$	−169.158	−0.393079
$58$	−852.686	−1.93040
$59$	−707.553	−1.56128	−0.780641	−	0.624980i	$-0.785107\pi$
$59$	−707.553	−1.56128	−0.780641	+	0.624980i	$0.785107\pi$
$60$	−743.161	−1.59903
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−592.810	−1.21431
$63$	152.674	0.305319
$64$	−527.506	−1.03029
$65$	−834.215	−1.59187
$66$	−161.390	−0.300997
$67$	618.129	1.12711	0.563556	−	0.826078i	$-0.309433\pi$
$67$	618.129	1.12711	0.563556	+	0.826078i	$0.309433\pi$
$68$	−1112.52	−1.98402
$69$	101.668	0.177382
$70$	−1291.09	−2.20449
$71$	156.953	0.262351	0.131175	−	0.991359i	$-0.458125\pi$
$71$	156.953	0.262351	0.131175	+	0.991359i	$0.458125\pi$
$72$	−348.521	−0.570466
$73$	−454.492	−0.728688	−0.364344	−	0.931264i	$-0.618707\pi$
$73$	−454.492	−0.728688	−0.364344	+	0.931264i	$0.618707\pi$
$74$	1587.97	2.49457
$75$	−351.541	−0.541234
$76$	897.559	1.35470
$77$	−186.601	−0.276171
$78$	−786.490	−1.14170
$79$	1214.77	1.73003	0.865013	−	0.501750i	$-0.167310\pi$
$79$	1214.77	1.73003	0.865013	+	0.501750i	$0.167310\pi$
$80$	965.502	1.34933
$81$	81.0000	0.111111
$82$	−1017.43	−1.37019
$83$	254.049	0.335970	0.167985	−	0.985790i	$-0.446274\pi$
$83$	254.049	0.335970	0.167985	+	0.985790i	$0.446274\pi$
$84$	−810.093	−1.05224
$85$	−1087.64	−1.38790
$86$	1200.15	1.50483
$87$	−523.054	−0.644567
$88$	425.970	0.516006
$89$	60.0919	0.0715700	0.0357850	−	0.999360i	$-0.488607\pi$
$89$	60.0919	0.0715700	0.0357850	+	0.999360i	$0.488607\pi$
$90$	−684.976	−0.802254
$91$	−909.348	−1.04753
$92$	−539.454	−0.611326
$93$	−363.641	−0.405461
$94$	−1606.13	−1.76234
$95$	877.487	0.947666
$96$	−19.1218	−0.0203293
$97$	−1549.02	−1.62144	−0.810719	−	0.585436i	$-0.800923\pi$
$97$	−1549.02	−1.62144	−0.810719	+	0.585436i	$0.800923\pi$
$98$	270.114	0.278425
$99$	−99.0000	−0.100504
$100$	1865.29	1.86529
$101$	−640.024	−0.630542	−0.315271	−	0.949002i	$-0.602095\pi$
$101$	−640.024	−0.630542	−0.315271	+	0.949002i	$0.602095\pi$
$102$	−1025.42	−0.995410
$103$	−1546.20	−1.47914	−0.739569	−	0.673081i	$-0.764971\pi$
$103$	−1546.20	−1.47914	−0.739569	+	0.673081i	$0.764971\pi$
$104$	2075.84	1.95724
$105$	−791.977	−0.736087
$106$	1313.08	1.20318
$107$	−630.838	−0.569958	−0.284979	−	0.958534i	$-0.591987\pi$
$107$	−630.838	−0.569958	−0.284979	+	0.958534i	$0.591987\pi$
$108$	−429.789	−0.382931
$109$	−286.943	−0.252148	−0.126074	−	0.992021i	$-0.540238\pi$
$109$	−286.943	−0.252148	−0.126074	+	0.992021i	$0.540238\pi$
$110$	837.193	0.725666
$111$	974.093	0.832944
$112$	1052.46	0.887930
$113$	859.415	0.715460	0.357730	−	0.933825i	$-0.383551\pi$
$113$	859.415	0.715460	0.357730	+	0.933825i	$0.383551\pi$
$114$	827.287	0.679671
$115$	−527.390	−0.427647
$116$	2775.35	2.22142
$117$	−482.448	−0.381217
$118$	3460.37	2.69960
$119$	−1185.60	−0.913311
$120$	1807.91	1.37532
$121$	121.000	0.0909091
$122$	−298.328	−0.221388
$123$	−624.110	−0.457513
$124$	1929.50	1.39737
$125$	−121.688	−0.0870731
$126$	−746.669	−0.527925
$127$	−104.936	−0.0733197	−0.0366599	−	0.999328i	$-0.511672\pi$
$127$	−104.936	−0.0733197	−0.0366599	+	0.999328i	$0.511672\pi$
$128$	2528.84	1.74625
$129$	736.194	0.502467
$130$	4079.82	2.75249
$131$	−244.802	−0.163271	−0.0816353	−	0.996662i	$-0.526014\pi$
$131$	−244.802	−0.163271	−0.0816353	+	0.996662i	$0.526014\pi$
$132$	525.298	0.346374
$133$	956.518	0.623614
$134$	−3023.03	−1.94888
$135$	−420.178	−0.267875
$136$	2706.47	1.70646
$137$	478.631	0.298483	0.149241	−	0.988801i	$-0.452317\pi$
$137$	478.631	0.298483	0.149241	+	0.988801i	$0.452317\pi$
$138$	−497.218	−0.306710
$139$	11.4488	0.00698615	0.00349308	−	0.999994i	$-0.498888\pi$
$139$	11.4488	0.00698615	0.00349308	+	0.999994i	$0.498888\pi$
$140$	4202.27	2.53683
$141$	−985.233	−0.588451
$142$	−767.597	−0.453629
$143$	589.659	0.344823
$144$	558.375	0.323134
$145$	2713.28	1.55397
$146$	2222.74	1.25997
$147$	165.693	0.0929669
$148$	−5168.58	−2.87064
$149$	−441.125	−0.242539	−0.121270	−	0.992620i	$-0.538697\pi$
$149$	−441.125	−0.242539	−0.121270	+	0.992620i	$0.538697\pi$
$150$	1719.25	0.935844
$151$	1028.74	0.554420	0.277210	−	0.960809i	$-0.410590\pi$
$151$	1028.74	0.554420	0.277210	+	0.960809i	$0.410590\pi$
$152$	−2183.52	−1.16518
$153$	−629.013	−0.332371
$154$	912.595	0.477526
$155$	1886.35	0.977516
$156$	2559.89	1.31382
$157$	−1196.76	−0.608354	−0.304177	−	0.952615i	$-0.598382\pi$
$157$	−1196.76	−0.608354	−0.304177	+	0.952615i	$0.598382\pi$
$158$	−5940.96	−2.99138
$159$	805.468	0.401747
$160$	99.1920	0.0490114
$161$	−574.890	−0.281414
$162$	−396.140	−0.192122
$163$	−1779.40	−0.855052	−0.427526	−	0.904003i	$-0.640615\pi$
$163$	−1779.40	−0.855052	−0.427526	+	0.904003i	$0.640615\pi$
$164$	3311.55	1.57676
$165$	513.551	0.242302
$166$	−1242.46	−0.580924
$167$	−1710.93	−0.792790	−0.396395	−	0.918080i	$-0.629739\pi$
$167$	−1710.93	−0.792790	−0.396395	+	0.918080i	$0.629739\pi$
$168$	1970.74	0.905035
$169$	676.534	0.307935
$170$	5319.25	2.39981
$171$	507.474	0.226944
$172$	−3906.28	−1.73169
$173$	373.137	0.163983	0.0819915	−	0.996633i	$-0.473872\pi$
$173$	373.137	0.163983	0.0819915	+	0.996633i	$0.473872\pi$
$174$	2558.06	1.11452
$175$	1987.82	0.858658
$176$	−682.459	−0.292286
$177$	2122.66	0.901406
$178$	−293.886	−0.123751
$179$	1226.86	0.512291	0.256146	−	0.966638i	$-0.417547\pi$
$179$	1226.86	0.512291	0.256146	+	0.966638i	$0.417547\pi$
$180$	2229.48	0.923199
$181$	−648.207	−0.266193	−0.133096	−	0.991103i	$-0.542492\pi$
$181$	−648.207	−0.266193	−0.133096	+	0.991103i	$0.542492\pi$
$182$	4447.27	1.81128
$183$	−183.000	−0.0739221
$184$	1312.35	0.525801
$185$	−5052.99	−2.00813
$186$	1778.43	0.701080
$187$	768.794	0.300641
$188$	5227.69	2.02802
$189$	−458.021	−0.176276
$190$	−4291.45	−1.63860
$191$	−711.163	−0.269413	−0.134707	−	0.990886i	$-0.543009\pi$
$191$	−711.163	−0.269413	−0.134707	+	0.990886i	$0.543009\pi$
$192$	1582.52	0.594835
$193$	1321.26	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$193$	1321.26	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$194$	7575.67	2.80362
$195$	2502.64	0.919067
$196$	−879.175	−0.320399
$197$	4645.22	1.67999	0.839996	−	0.542592i	$-0.182557\pi$
$197$	4645.22	1.67999	0.839996	+	0.542592i	$0.182557\pi$
$198$	484.171	0.173780
$199$	−4112.68	−1.46503	−0.732513	−	0.680753i	$-0.761653\pi$
$199$	−4112.68	−1.46503	−0.732513	+	0.680753i	$0.761653\pi$
$200$	−4537.76	−1.60434
$201$	−1854.39	−0.650738
$202$	3130.11	1.09027
$203$	2957.65	1.02259
$204$	3337.57	1.14547
$205$	3237.50	1.10301
$206$	7561.85	2.55757
$207$	−305.004	−0.102412
$208$	−3325.77	−1.10866
$209$	−620.246	−0.205279
$210$	3873.26	1.27276
$211$	−5730.92	−1.86982	−0.934911	−	0.354881i	$-0.884521\pi$
$211$	−5730.92	−1.86982	−0.934911	+	0.354881i	$0.884521\pi$
$212$	−4273.85	−1.38457
$213$	−470.859	−0.151468
$214$	3085.19	0.985510
$215$	−3818.92	−1.21139
$216$	1045.56	0.329359
$217$	2056.24	0.643257
$218$	1403.33	0.435988
$219$	1363.48	0.420708
$220$	−2724.92	−0.835065
$221$	3746.50	1.14035
$222$	−4763.92	−1.44024
$223$	−2208.04	−0.663056	−0.331528	−	0.943445i	$-0.607564\pi$
$223$	−2208.04	−0.663056	−0.331528	+	0.943445i	$0.607564\pi$
$224$	108.126	0.0322520
$225$	1054.62	0.312481
$226$	−4203.07	−1.23710
$227$	−595.041	−0.173983	−0.0869917	−	0.996209i	$-0.527725\pi$
$227$	−595.041	−0.173983	−0.0869917	+	0.996209i	$0.527725\pi$
$228$	−2692.68	−0.782136
$229$	−6456.68	−1.86319	−0.931593	−	0.363503i	$-0.881581\pi$
$229$	−6456.68	−1.86319	−0.931593	+	0.363503i	$0.881581\pi$
$230$	2579.26	0.739441
$231$	559.804	0.159448
$232$	−6751.67	−1.91064
$233$	3344.29	0.940307	0.470154	−	0.882585i	$-0.344199\pi$
$233$	3344.29	0.940307	0.470154	+	0.882585i	$0.344199\pi$
$234$	2359.47	0.659159
$235$	5110.78	1.41868
$236$	−11262.9	−3.10658
$237$	−3644.30	−0.998831
$238$	5798.33	1.57920
$239$	4071.09	1.10183	0.550914	−	0.834562i	$-0.314279\pi$
$239$	4071.09	1.10183	0.550914	+	0.834562i	$0.314279\pi$
$240$	−2896.51	−0.779036
$241$	−649.186	−0.173518	−0.0867588	−	0.996229i	$-0.527651\pi$
$241$	−649.186	−0.173518	−0.0867588	+	0.996229i	$0.527651\pi$
$242$	−591.765	−0.157190
$243$	−243.000	−0.0641500
$244$	971.006	0.254763
$245$	−859.514	−0.224132
$246$	3052.28	0.791082
$247$	−3022.59	−0.778635
$248$	−4693.94	−1.20188
$249$	−762.148	−0.193972
$250$	595.131	0.150558
$251$	−1059.42	−0.266415	−0.133208	−	0.991088i	$-0.542528\pi$
$251$	−1059.42	−0.266415	−0.133208	+	0.991088i	$0.542528\pi$
$252$	2430.28	0.607513
$253$	372.782	0.0926348
$254$	513.204	0.126777
$255$	3262.93	0.801305
$256$	−8147.53	−1.98914
$257$	5569.05	1.35170	0.675852	−	0.737037i	$-0.263776\pi$
$257$	5569.05	1.35170	0.675852	+	0.737037i	$0.263776\pi$
$258$	−3600.44	−0.868813
$259$	−5508.09	−1.32145
$260$	−13279.1	−3.16745
$261$	1569.16	0.372141
$262$	1197.23	0.282310
$263$	2262.94	0.530565	0.265283	−	0.964171i	$-0.414535\pi$
$263$	2262.94	0.530565	0.265283	+	0.964171i	$0.414535\pi$
$264$	−1277.91	−0.297916
$265$	−4178.27	−0.968563
$266$	−4677.96	−1.07829
$267$	−180.276	−0.0413209
$268$	9839.46	2.24269
$269$	−1507.63	−0.341717	−0.170858	−	0.985296i	$-0.554654\pi$
$269$	−1507.63	−0.341717	−0.170858	+	0.985296i	$0.554654\pi$
$270$	2054.93	0.463182
$271$	1880.87	0.421604	0.210802	−	0.977529i	$-0.432392\pi$
$271$	1880.87	0.421604	0.210802	+	0.977529i	$0.432392\pi$
$272$	−4336.12	−0.966602
$273$	2728.04	0.604794
$274$	−2340.80	−0.516105
$275$	−1288.99	−0.282650
$276$	1618.36	0.352949
$277$	957.721	0.207740	0.103870	−	0.994591i	$-0.466877\pi$
$277$	957.721	0.207740	0.103870	+	0.994591i	$0.466877\pi$
$278$	−55.9917	−0.0120797
$279$	1090.92	0.234093
$280$	−10223.0	−2.18193
$281$	7826.89	1.66161	0.830807	−	0.556561i	$-0.187879\pi$
$281$	7826.89	1.66161	0.830807	+	0.556561i	$0.187879\pi$
$282$	4818.40	1.01749
$283$	−7059.85	−1.48291	−0.741457	−	0.671000i	$-0.765865\pi$
$283$	−7059.85	−1.48291	−0.741457	+	0.671000i	$0.765865\pi$
$284$	2498.40	0.522017
$285$	−2632.46	−0.547135
$286$	−2883.80	−0.596232
$287$	3529.08	0.725836
$288$	57.3654	0.0117371
$289$	−28.3353	−0.00576741
$290$	−13269.6	−2.68696
$291$	4647.07	0.936137
$292$	−7234.66	−1.44992
$293$	−4363.64	−0.870056	−0.435028	−	0.900417i	$-0.643262\pi$
$293$	−4363.64	−0.870056	−0.435028	+	0.900417i	$0.643262\pi$
$294$	−810.342	−0.160749
$295$	−11011.1	−2.17318
$296$	12573.8	2.46904
$297$	297.000	0.0580259
$298$	2157.37	0.419373
$299$	1816.65	0.351369
$300$	−5595.88	−1.07693
$301$	−4162.87	−0.797156
$302$	−5031.16	−0.958645
$303$	1920.07	0.364044
$304$	3498.28	0.660001
$305$	949.291	0.178217
$306$	3076.26	0.574700
$307$	−1829.44	−0.340103	−0.170052	−	0.985435i	$-0.554393\pi$
$307$	−1829.44	−0.340103	−0.170052	+	0.985435i	$0.554393\pi$
$308$	−2970.34	−0.549516
$309$	4638.59	0.853981
$310$	−9225.40	−1.69022
$311$	223.044	0.0406677	0.0203339	−	0.999793i	$-0.493527\pi$
$311$	223.044	0.0406677	0.0203339	+	0.999793i	$0.493527\pi$
$312$	−6227.52	−1.13001
$313$	3503.18	0.632624	0.316312	−	0.948655i	$-0.397555\pi$
$313$	3503.18	0.632624	0.316312	+	0.948655i	$0.397555\pi$
$314$	5852.88	1.05190
$315$	2375.93	0.424980
$316$	19336.8	3.44235
$317$	−8111.60	−1.43720	−0.718601	−	0.695423i	$-0.755217\pi$
$317$	−8111.60	−1.43720	−0.718601	+	0.695423i	$0.755217\pi$
$318$	−3939.23	−0.694658
$319$	−1917.87	−0.336614
$320$	−8209.13	−1.43408
$321$	1892.52	0.329065
$322$	2811.56	0.486591
$323$	−3940.84	−0.678867
$324$	1289.37	0.221085
$325$	−6281.50	−1.07211
$326$	8702.37	1.47847
$327$	860.828	0.145578
$328$	−8056.11	−1.35617
$329$	5571.08	0.933568
$330$	−2511.58	−0.418963
$331$	8785.78	1.45894	0.729472	−	0.684011i	$-0.239766\pi$
$331$	8785.78	1.45894	0.729472	+	0.684011i	$0.239766\pi$
$332$	4043.99	0.668502
$333$	−2922.28	−0.480901
$334$	8367.51	1.37081
$335$	9619.42	1.56885
$336$	−3157.38	−0.512647
$337$	−11850.0	−1.91547	−0.957734	−	0.287654i	$-0.907125\pi$
$337$	−11850.0	−1.91547	−0.957734	+	0.287654i	$0.907125\pi$
$338$	−3308.67	−0.532449
$339$	−2578.24	−0.413071
$340$	−17313.3	−2.76160
$341$	−1333.35	−0.211745
$342$	−2481.86	−0.392408
$343$	−6755.49	−1.06345
$344$	9502.92	1.48943
$345$	1582.17	0.246902
$346$	−1824.87	−0.283542
$347$	−5910.60	−0.914402	−0.457201	−	0.889363i	$-0.651148\pi$
$347$	−5910.60	−0.914402	−0.457201	+	0.889363i	$0.651148\pi$
$348$	−8326.04	−1.28254
$349$	−5348.52	−0.820342	−0.410171	−	0.912009i	$-0.634531\pi$
$349$	−5348.52	−0.820342	−0.410171	+	0.912009i	$0.634531\pi$
$350$	−9721.67	−1.48470
$351$	1447.34	0.220096
$352$	−70.1132	−0.0106166
$353$	3695.27	0.557166	0.278583	−	0.960412i	$-0.410135\pi$
$353$	3695.27	0.557166	0.278583	+	0.960412i	$0.410135\pi$
$354$	−10381.1	−1.55862
$355$	2442.53	0.365172
$356$	956.550	0.142407
$357$	3556.81	0.527301
$358$	−6000.12	−0.885800
$359$	568.000	0.0835039	0.0417519	−	0.999128i	$-0.486706\pi$
$359$	568.000	0.0835039	0.0417519	+	0.999128i	$0.486706\pi$
$360$	−5423.73	−0.794043
$361$	−3679.62	−0.536466
$362$	3170.13	0.460272
$363$	−363.000	−0.0524864
$364$	−14475.1	−2.08435
$365$	−7072.87	−1.01428
$366$	894.983	0.127818
$367$	445.721	0.0633964	0.0316982	−	0.999497i	$-0.489908\pi$
$367$	445.721	0.0633964	0.0316982	+	0.999497i	$0.489908\pi$
$368$	−2102.55	−0.297834
$369$	1872.33	0.264145
$370$	24712.3	3.47224
$371$	−4554.59	−0.637365
$372$	−5788.49	−0.806772
$373$	8870.72	1.23139	0.615695	−	0.787984i	$-0.288875\pi$
$373$	8870.72	1.23139	0.615695	+	0.787984i	$0.288875\pi$
$374$	−3759.88	−0.519836
$375$	365.065	0.0502717
$376$	−12717.6	−1.74430
$377$	−9346.17	−1.27680
$378$	2240.01	0.304798
$379$	−8525.86	−1.15553	−0.577763	−	0.816205i	$-0.696074\pi$
$379$	−8525.86	−1.15553	−0.577763	+	0.816205i	$0.696074\pi$
$380$	13968.0	1.88563
$381$	314.809	0.0423312
$382$	3478.02	0.465841
$383$	2737.56	0.365230	0.182615	−	0.983185i	$-0.441544\pi$
$383$	2737.56	0.365230	0.182615	+	0.983185i	$0.441544\pi$
$384$	−7586.51	−1.00820
$385$	−2903.92	−0.384409
$386$	−6461.80	−0.852065
$387$	−2208.58	−0.290100
$388$	−24657.5	−3.22628
$389$	−3774.52	−0.491968	−0.245984	−	0.969274i	$-0.579111\pi$
$389$	−3774.52	−0.491968	−0.245984	+	0.969274i	$0.579111\pi$
$390$	−12239.5	−1.58915
$391$	2368.53	0.306348
$392$	2138.80	0.275575
$393$	734.406	0.0942643
$394$	−22718.0	−2.90486
$395$	18904.4	2.40806
$396$	−1575.89	−0.199979
$397$	1452.02	0.183564	0.0917820	−	0.995779i	$-0.470744\pi$
$397$	1452.02	0.183564	0.0917820	+	0.995779i	$0.470744\pi$
$398$	20113.5	2.53317
$399$	−2869.55	−0.360044
$400$	7270.08	0.908760
$401$	−6263.20	−0.779973	−0.389987	−	0.920821i	$-0.627520\pi$
$401$	−6263.20	−0.779973	−0.389987	+	0.920821i	$0.627520\pi$
$402$	9069.10	1.12519
$403$	−6497.71	−0.803161
$404$	−10188.0	−1.25463
$405$	1260.53	0.154658
$406$	−14464.8	−1.76816
$407$	3571.67	0.434991
$408$	−8119.41	−0.985222
$409$	−8956.93	−1.08286	−0.541432	−	0.840744i	$-0.682118\pi$
$409$	−8956.93	−1.08286	−0.541432	+	0.840744i	$0.682118\pi$
$410$	−15833.3	−1.90720
$411$	−1435.89	−0.172329
$412$	−24612.5	−2.94314
$413$	−12002.8	−1.43007
$414$	1491.66	0.177079
$415$	3953.55	0.467644
$416$	−341.677	−0.0402694
$417$	−34.3464	−0.00403346
$418$	3033.38	0.354947
$419$	−9134.03	−1.06498	−0.532490	−	0.846436i	$-0.678744\pi$
$419$	−9134.03	−1.06498	−0.532490	+	0.846436i	$0.678744\pi$
$420$	−12606.8	−1.46464
$421$	7023.35	0.813057	0.406529	−	0.913638i	$-0.366739\pi$
$421$	7023.35	0.813057	0.406529	+	0.913638i	$0.366739\pi$
$422$	28027.7	3.23310
$423$	2955.70	0.339742
$424$	10397.1	1.19087
$425$	−8189.79	−0.934737
$426$	2302.79	0.261903
$427$	1034.79	0.117276
$428$	−10041.8	−1.13408
$429$	−1768.98	−0.199084
$430$	18676.9	2.09460
$431$	1336.02	0.149313	0.0746564	−	0.997209i	$-0.476214\pi$
$431$	1336.02	0.149313	0.0746564	+	0.997209i	$0.476214\pi$
$432$	−1675.13	−0.186561
$433$	11368.4	1.26173	0.630866	−	0.775892i	$-0.282700\pi$
$433$	11368.4	1.26173	0.630866	+	0.775892i	$0.282700\pi$
$434$	−10056.3	−1.11225
$435$	−8139.85	−0.897186
$436$	−4567.59	−0.501715
$437$	−1910.88	−0.209176
$438$	−6668.23	−0.727444
$439$	582.039	0.0632784	0.0316392	−	0.999499i	$-0.489927\pi$
$439$	582.039	0.0632784	0.0316392	+	0.999499i	$0.489927\pi$
$440$	6629.00	0.718239
$441$	−497.079	−0.0536745
$442$	−18322.7	−1.97177
$443$	−8735.93	−0.936923	−0.468461	−	0.883484i	$-0.655191\pi$
$443$	−8735.93	−0.936923	−0.468461	+	0.883484i	$0.655191\pi$
$444$	15505.7	1.65736
$445$	935.159	0.0996197
$446$	10798.7	1.14649
$447$	1323.37	0.140030
$448$	−8948.48	−0.943697
$449$	14720.0	1.54717	0.773584	−	0.633694i	$-0.218462\pi$
$449$	14720.0	1.54717	0.773584	+	0.633694i	$0.218462\pi$
$450$	−5157.76	−0.540310
$451$	−2288.40	−0.238928
$452$	13680.3	1.42360
$453$	−3086.21	−0.320095
$454$	2910.12	0.300834
$455$	−14151.4	−1.45808
$456$	6550.56	0.672715
$457$	−13005.4	−1.33122	−0.665608	−	0.746301i	$-0.731828\pi$
$457$	−13005.4	−1.33122	−0.665608	+	0.746301i	$0.731828\pi$
$458$	31577.2	3.22162
$459$	1887.04	0.191894
$460$	−8395.06	−0.850917
$461$	11620.7	1.17404	0.587018	−	0.809574i	$-0.300302\pi$
$461$	11620.7	1.17404	0.587018	+	0.809574i	$0.300302\pi$
$462$	−2737.79	−0.275700
$463$	664.427	0.0666923	0.0333462	−	0.999444i	$-0.489384\pi$
$463$	664.427	0.0666923	0.0333462	+	0.999444i	$0.489384\pi$
$464$	10817.1	1.08226
$465$	−5659.04	−0.564369
$466$	−16355.6	−1.62588
$467$	−908.953	−0.0900671	−0.0450336	−	0.998985i	$-0.514339\pi$
$467$	−908.953	−0.0900671	−0.0450336	+	0.998985i	$0.514339\pi$
$468$	−7679.67	−0.758532
$469$	10485.8	1.03239
$470$	−24994.9	−2.45304
$471$	3590.27	0.351234
$472$	27399.7	2.67197
$473$	2699.38	0.262405
$474$	17822.9	1.72707
$475$	6607.34	0.638243
$476$	−18872.6	−1.81728
$477$	−2416.40	−0.231949
$478$	−19910.1	−1.90516
$479$	−11803.4	−1.12591	−0.562955	−	0.826488i	$-0.690336\pi$
$479$	−11803.4	−1.12591	−0.562955	+	0.826488i	$0.690336\pi$
$480$	−297.576	−0.0282967
$481$	17405.5	1.64995
$482$	3174.92	0.300028
$483$	1724.67	0.162474
$484$	1926.09	0.180888
$485$	−24106.1	−2.25691
$486$	1188.42	0.110921
$487$	6614.64	0.615478	0.307739	−	0.951471i	$-0.400428\pi$
$487$	6614.64	0.615478	0.307739	+	0.951471i	$0.400428\pi$
$488$	−2362.20	−0.219122
$489$	5338.21	0.493665
$490$	4203.55	0.387545
$491$	13784.0	1.26693	0.633464	−	0.773773i	$-0.281633\pi$
$491$	13784.0	1.26693	0.633464	+	0.773773i	$0.281633\pi$
$492$	−9934.65	−0.910343
$493$	−12185.5	−1.11320
$494$	14782.3	1.34633
$495$	−1540.65	−0.139893
$496$	7520.31	0.680790
$497$	2662.51	0.240302
$498$	3727.37	0.335397
$499$	−1500.13	−0.134579	−0.0672896	−	0.997733i	$-0.521435\pi$
$499$	−1500.13	−0.134579	−0.0672896	+	0.997733i	$0.521435\pi$
$500$	−1937.05	−0.173255
$501$	5132.80	0.457717
$502$	5181.23	0.460657
$503$	−21192.9	−1.87862	−0.939309	−	0.343073i	$-0.888532\pi$
$503$	−21192.9	−1.87862	−0.939309	+	0.343073i	$0.888532\pi$
$504$	−5912.22	−0.522522
$505$	−9960.14	−0.877665
$506$	−1823.13	−0.160174
$507$	−2029.60	−0.177787
$508$	−1670.39	−0.145889
$509$	18394.5	1.60181	0.800905	−	0.598792i	$-0.204352\pi$
$509$	18394.5	1.60181	0.800905	+	0.598792i	$0.204352\pi$
$510$	−15957.8	−1.38553
$511$	−7709.89	−0.667447
$512$	19615.7	1.69317
$513$	−1522.42	−0.131026
$514$	−27236.1	−2.33722
$515$	−24062.1	−2.05884
$516$	11718.8	0.999792
$517$	−3612.52	−0.307309
$518$	26938.0	2.28492
$519$	−1119.41	−0.0946756
$520$	32304.5	2.72432
$521$	−15584.3	−1.31048	−0.655240	−	0.755421i	$-0.727432\pi$
$521$	−15584.3	−1.31048	−0.655240	+	0.755421i	$0.727432\pi$
$522$	−7674.17	−0.643466
$523$	18976.6	1.58660	0.793298	−	0.608833i	$-0.208362\pi$
$523$	18976.6	1.58660	0.793298	+	0.608833i	$0.208362\pi$
$524$	−3896.79	−0.324870
$525$	−5963.46	−0.495746
$526$	−11067.2	−0.917397
$527$	−8471.68	−0.700251
$528$	2047.38	0.168751
$529$	−11018.5	−0.905607
$530$	20434.3	1.67474
$531$	−6367.98	−0.520427
$532$	15226.0	1.24085
$533$	−11151.9	−0.906269
$534$	881.659	0.0714478
$535$	−9817.20	−0.793336
$536$	−23936.8	−1.92894
$537$	−3680.59	−0.295772
$538$	7373.24	0.590860
$539$	607.542	0.0485504
$540$	−6688.45	−0.533009
$541$	15636.7	1.24265	0.621326	−	0.783552i	$-0.286594\pi$
$541$	15636.7	1.24265	0.621326	+	0.783552i	$0.286594\pi$
$542$	−9198.62	−0.728994
$543$	1944.62	0.153686
$544$	−445.476	−0.0351096
$545$	−4465.45	−0.350970
$546$	−13341.8	−1.04575
$547$	16727.5	1.30753	0.653764	−	0.756699i	$-0.273189\pi$
$547$	16727.5	1.30753	0.653764	+	0.756699i	$0.273189\pi$
$548$	7618.90	0.593911
$549$	549.000	0.0426790
$550$	6303.93	0.488728
$551$	9830.98	0.760098
$552$	−3937.04	−0.303571
$553$	20607.0	1.58463
$554$	−4683.84	−0.359201
$555$	15159.0	1.15939
$556$	182.243	0.0139008
$557$	6907.91	0.525490	0.262745	−	0.964865i	$-0.415372\pi$
$557$	6907.91	0.525490	0.262745	+	0.964865i	$0.415372\pi$
$558$	−5335.29	−0.404769
$559$	13154.6	0.995317
$560$	16378.5	1.23593
$561$	−2306.38	−0.173575
$562$	−38278.3	−2.87309
$563$	−5866.44	−0.439149	−0.219574	−	0.975596i	$-0.570467\pi$
$563$	−5866.44	−0.439149	−0.219574	+	0.975596i	$0.570467\pi$
$564$	−15683.1	−1.17088
$565$	13374.3	0.995863
$566$	34527.0	2.56410
$567$	1374.06	0.101773
$568$	−6077.93	−0.448986
$569$	8876.88	0.654021	0.327011	−	0.945021i	$-0.393959\pi$
$569$	8876.88	0.654021	0.327011	+	0.945021i	$0.393959\pi$
$570$	12874.4	0.946048
$571$	−20718.2	−1.51844	−0.759219	−	0.650835i	$-0.774419\pi$
$571$	−20718.2	−1.51844	−0.759219	+	0.650835i	$0.774419\pi$
$572$	9386.26	0.686118
$573$	2133.49	0.155546
$574$	−17259.4	−1.25504
$575$	−3971.16	−0.288016
$576$	−4747.55	−0.343428
$577$	−10064.2	−0.726131	−0.363065	−	0.931764i	$-0.618270\pi$
$577$	−10064.2	−0.726131	−0.363065	+	0.931764i	$0.618270\pi$
$578$	138.577	0.00997239
$579$	−3963.79	−0.284507
$580$	43190.4	3.09204
$581$	4309.63	0.307734
$582$	−22727.0	−1.61867
$583$	2953.38	0.209805
$584$	17600.0	1.24708
$585$	−7507.93	−0.530624
$586$	21340.9	1.50441
$587$	−20691.5	−1.45490	−0.727451	−	0.686159i	$-0.759295\pi$
$587$	−20691.5	−1.45490	−0.727451	+	0.686159i	$0.759295\pi$
$588$	2637.52	0.184982
$589$	6834.76	0.478135
$590$	53850.8	3.75763
$591$	−13935.7	−0.969944
$592$	−20144.8	−1.39856
$593$	−19150.8	−1.32619	−0.663093	−	0.748537i	$-0.730757\pi$
$593$	−19150.8	−1.32619	−0.663093	+	0.748537i	$0.730757\pi$
$594$	−1452.51	−0.100332
$595$	−18450.5	−1.27126
$596$	−7021.88	−0.482596
$597$	12338.0	0.845833
$598$	−8884.52	−0.607551
$599$	18684.2	1.27449	0.637243	−	0.770663i	$-0.280075\pi$
$599$	18684.2	1.27449	0.637243	+	0.770663i	$0.280075\pi$
$600$	13613.3	0.926266
$601$	25042.9	1.69970	0.849852	−	0.527021i	$-0.176691\pi$
$601$	25042.9	1.69970	0.849852	+	0.527021i	$0.176691\pi$
$602$	20359.0	1.37836
$603$	5563.16	0.375704
$604$	16375.6	1.10317
$605$	1883.02	0.126538
$606$	−9390.33	−0.629465
$607$	−16582.2	−1.10881	−0.554407	−	0.832246i	$-0.687055\pi$
$607$	−16582.2	−1.10881	−0.554407	+	0.832246i	$0.687055\pi$
$608$	359.400	0.0239730
$609$	−8872.96	−0.590395
$610$	−4642.62	−0.308154
$611$	−17604.6	−1.16564
$612$	−10012.7	−0.661340
$613$	2602.92	0.171502	0.0857512	−	0.996317i	$-0.472671\pi$
$613$	2602.92	0.171502	0.0857512	+	0.996317i	$0.472671\pi$
$614$	8947.09	0.588070
$615$	−9712.49	−0.636822
$616$	7226.04	0.472639
$617$	466.769	0.0304561	0.0152280	−	0.999884i	$-0.495153\pi$
$617$	466.769	0.0304561	0.0152280	+	0.999884i	$0.495153\pi$
$618$	−22685.6	−1.47661
$619$	9737.57	0.632288	0.316144	−	0.948711i	$-0.397612\pi$
$619$	9737.57	0.632288	0.316144	+	0.948711i	$0.397612\pi$
$620$	30027.1	1.94503
$621$	915.011	0.0591274
$622$	−1090.82	−0.0703184
$623$	1019.38	0.0655550
$624$	9977.30	0.640083
$625$	−16541.3	−1.05864
$626$	−17132.7	−1.09387
$627$	1860.74	0.118518
$628$	−19050.1	−1.21048
$629$	22693.2	1.43854
$630$	−11619.8	−0.734830
$631$	10314.4	0.650731	0.325365	−	0.945588i	$-0.394513\pi$
$631$	10314.4	0.650731	0.325365	+	0.945588i	$0.394513\pi$
$632$	−47041.3	−2.96076
$633$	17192.8	1.07954
$634$	39670.7	2.48506
$635$	−1633.04	−0.102055
$636$	12821.5	0.799382
$637$	2960.68	0.184154
$638$	9379.54	0.582037
$639$	1412.58	0.0874503
$640$	39354.2	2.43064
$641$	−26845.1	−1.65416	−0.827081	−	0.562083i	$-0.810000\pi$
$641$	−26845.1	−1.65416	−0.827081	+	0.562083i	$0.810000\pi$
$642$	−9255.57	−0.568985
$643$	19070.6	1.16963	0.584815	−	0.811166i	$-0.301167\pi$
$643$	19070.6	1.16963	0.584815	+	0.811166i	$0.301167\pi$
$644$	−9151.16	−0.559948
$645$	11456.8	0.699395
$646$	19273.1	1.17383
$647$	−17160.3	−1.04272	−0.521360	−	0.853337i	$-0.674575\pi$
$647$	−17160.3	−1.04272	−0.521360	+	0.853337i	$0.674575\pi$
$648$	−3136.69	−0.190155
$649$	7783.09	0.470744
$650$	30720.4	1.85378
$651$	−6168.72	−0.371384
$652$	−28324.7	−1.70135
$653$	−17689.2	−1.06008	−0.530041	−	0.847972i	$-0.677823\pi$
$653$	−17689.2	−1.06008	−0.530041	+	0.847972i	$0.677823\pi$
$654$	−4209.98	−0.251718
$655$	−3809.64	−0.227260
$656$	12906.9	0.768188
$657$	−4090.43	−0.242896
$658$	−27246.0	−1.61423
$659$	−9944.80	−0.587852	−0.293926	−	0.955828i	$-0.594962\pi$
$659$	−9944.80	−0.587852	−0.293926	+	0.955828i	$0.594962\pi$
$660$	8174.77	0.482125
$661$	3776.60	0.222228	0.111114	−	0.993808i	$-0.464558\pi$
$661$	3776.60	0.222228	0.111114	+	0.993808i	$0.464558\pi$
$662$	−42967.9	−2.52265
$663$	−11239.5	−0.658380
$664$	−9837.93	−0.574978
$665$	14885.5	0.868021
$666$	14291.7	0.831522
$667$	−5908.64	−0.343004
$668$	−27234.8	−1.57747
$669$	6624.13	0.382816
$670$	−47044.9	−2.71269
$671$	−671.000	−0.0386046
$672$	−324.377	−0.0186207
$673$	1791.82	0.102630	0.0513148	−	0.998683i	$-0.483659\pi$
$673$	1791.82	0.102630	0.0513148	+	0.998683i	$0.483659\pi$
$674$	57954.0	3.31203
$675$	−3163.87	−0.180411
$676$	10769.2	0.612719
$677$	−25760.3	−1.46241	−0.731203	−	0.682160i	$-0.761041\pi$
$677$	−25760.3	−1.46241	−0.731203	+	0.682160i	$0.761041\pi$
$678$	12609.2	0.714238
$679$	−26277.2	−1.48517
$680$	42118.5	2.37525
$681$	1785.12	0.100449
$682$	6520.91	0.366127
$683$	33615.5	1.88325	0.941626	−	0.336662i	$-0.109298\pi$
$683$	33615.5	1.88325	0.941626	+	0.336662i	$0.109298\pi$
$684$	8078.03	0.451566
$685$	7448.52	0.415465
$686$	33038.5	1.83880
$687$	19370.1	1.07571
$688$	−15224.9	−0.843669
$689$	14392.5	0.795804
$690$	−7737.79	−0.426917
$691$	−24921.3	−1.37200	−0.685999	−	0.727603i	$-0.740634\pi$
$691$	−24921.3	−1.37200	−0.685999	+	0.727603i	$0.740634\pi$
$692$	5939.64	0.326288
$693$	−1679.41	−0.0920571
$694$	28906.5	1.58109
$695$	178.168	0.00972417
$696$	20255.0	1.10311
$697$	−14539.8	−0.790147
$698$	26157.5	1.41845
$699$	−10032.9	−0.542887
$700$	31642.4	1.70853
$701$	−16082.7	−0.866525	−0.433262	−	0.901268i	$-0.642638\pi$
$701$	−16082.7	−0.866525	−0.433262	+	0.901268i	$0.642638\pi$
$702$	−7078.41	−0.380566
$703$	−18308.4	−0.982240
$704$	5802.57	0.310643
$705$	−15332.3	−0.819077
$706$	−18072.2	−0.963392
$707$	−10857.2	−0.577549
$708$	33788.8	1.79359
$709$	−35144.5	−1.86161	−0.930803	−	0.365521i	$-0.880891\pi$
$709$	−35144.5	−1.86161	−0.930803	+	0.365521i	$0.880891\pi$
$710$	−11945.5	−0.631416
$711$	10932.9	0.576675
$712$	−2327.03	−0.122485
$713$	−4107.85	−0.215765
$714$	−17395.0	−0.911752
$715$	9176.36	0.479967
$716$	19529.4	1.01934
$717$	−12213.3	−0.636141
$718$	−2777.87	−0.144386
$719$	14566.3	0.755537	0.377769	−	0.925900i	$-0.376691\pi$
$719$	14566.3	0.755537	0.377769	+	0.925900i	$0.376691\pi$
$720$	8689.52	0.449777
$721$	−26229.3	−1.35483
$722$	17995.6	0.927600
$723$	1947.56	0.100180
$724$	−10318.2	−0.529661
$725$	20430.6	1.04658
$726$	1775.29	0.0907539
$727$	13336.3	0.680354	0.340177	−	0.940361i	$-0.389513\pi$
$727$	13336.3	0.680354	0.340177	+	0.940361i	$0.389513\pi$
$728$	35214.1	1.79275
$729$	729.000	0.0370370
$730$	34590.7	1.75378
$731$	17151.0	0.867785
$732$	−2913.02	−0.147088
$733$	11994.2	0.604385	0.302193	−	0.953247i	$-0.402281\pi$
$733$	11994.2	0.604385	0.302193	+	0.953247i	$0.402281\pi$
$734$	−2179.85	−0.109618
$735$	2578.54	0.129403
$736$	−216.008	−0.0108181
$737$	−6799.42	−0.339837
$738$	−9156.84	−0.456732
$739$	−33463.3	−1.66572	−0.832861	−	0.553482i	$-0.813299\pi$
$739$	−33463.3	−1.66572	−0.832861	+	0.553482i	$0.813299\pi$
$740$	−80434.2	−3.99570
$741$	9067.77	0.449545
$742$	22274.7	1.10206
$743$	−10896.2	−0.538014	−0.269007	−	0.963138i	$-0.586695\pi$
$743$	−10896.2	−0.538014	−0.269007	+	0.963138i	$0.586695\pi$
$744$	14081.8	0.693905
$745$	−6864.85	−0.337595
$746$	−43383.3	−2.12919
$747$	2286.44	0.111990
$748$	12237.8	0.598204
$749$	−10701.4	−0.522056
$750$	−1785.39	−0.0869244
$751$	−6219.98	−0.302224	−0.151112	−	0.988517i	$-0.548285\pi$
$751$	−6219.98	−0.302224	−0.151112	+	0.988517i	$0.548285\pi$
$752$	20375.2	0.988040
$753$	3178.27	0.153815
$754$	45708.5	2.20770
$755$	16009.4	0.771709
$756$	−7290.84	−0.350748
$757$	1760.89	0.0845451	0.0422726	−	0.999106i	$-0.486540\pi$
$757$	1760.89	0.0845451	0.0422726	+	0.999106i	$0.486540\pi$
$758$	41696.7	1.99801
$759$	−1118.35	−0.0534827
$760$	−33980.3	−1.62183
$761$	23105.8	1.10064	0.550319	−	0.834954i	$-0.314506\pi$
$761$	23105.8	1.10064	0.550319	+	0.834954i	$0.314506\pi$
$762$	−1539.61	−0.0731946
$763$	−4867.63	−0.230957
$764$	−11320.4	−0.536069
$765$	−9788.80	−0.462634
$766$	−13388.4	−0.631516
$767$	37928.6	1.78556
$768$	24442.6	1.14843
$769$	21189.5	0.993644	0.496822	−	0.867852i	$-0.334500\pi$
$769$	21189.5	0.993644	0.496822	+	0.867852i	$0.334500\pi$
$770$	14201.9	0.664679
$771$	−16707.2	−0.780407
$772$	21032.1	0.980519
$773$	−915.610	−0.0426031	−0.0213016	−	0.999773i	$-0.506781\pi$
$773$	−915.610	−0.0426031	−0.0213016	+	0.999773i	$0.506781\pi$
$774$	10801.3	0.501609
$775$	14203.9	0.658347
$776$	59985.1	2.77492
$777$	16524.3	0.762941
$778$	18459.7	0.850659
$779$	11730.3	0.539516
$780$	39837.4	1.82873
$781$	−1726.48	−0.0791017
$782$	−11583.6	−0.529704
$783$	−4707.49	−0.214856
$784$	−3426.63	−0.156096
$785$	−18624.1	−0.846781
$786$	−3591.70	−0.162992
$787$	−18020.5	−0.816214	−0.408107	−	0.912934i	$-0.633811\pi$
$787$	−18020.5	−0.816214	−0.408107	+	0.912934i	$0.633811\pi$
$788$	73943.3	3.34279
$789$	−6788.81	−0.306322
$790$	−92454.1	−4.16376
$791$	14578.9	0.655330
$792$	3833.73	0.172002
$793$	−3269.93	−0.146429
$794$	−7101.29	−0.317399
$795$	12534.8	0.559200
$796$	−65466.1	−2.91506
$797$	472.972	0.0210207	0.0105104	−	0.999945i	$-0.496654\pi$
$797$	472.972	0.0210207	0.0105104	+	0.999945i	$0.496654\pi$
$798$	14033.9	0.622549
$799$	−22952.8	−1.01628
$800$	746.900	0.0330086
$801$	540.827	0.0238567
$802$	30630.9	1.34865
$803$	4999.41	0.219708
$804$	−29518.4	−1.29482
$805$	−8946.52	−0.391706
$806$	31777.8	1.38874
$807$	4522.89	0.197290
$808$	24784.6	1.07911
$809$	−10786.4	−0.468762	−0.234381	−	0.972145i	$-0.575306\pi$
$809$	−10786.4	−0.468762	−0.234381	+	0.972145i	$0.575306\pi$
$810$	−6164.79	−0.267418
$811$	5466.11	0.236672	0.118336	−	0.992974i	$-0.462244\pi$
$811$	5466.11	0.236672	0.118336	+	0.992974i	$0.462244\pi$
$812$	47080.3	2.03472
$813$	−5642.61	−0.243413
$814$	−17467.7	−0.752140
$815$	−27691.3	−1.19017
$816$	13008.4	0.558068
$817$	−13837.0	−0.592528
$818$	43804.9	1.87237
$819$	−8184.13	−0.349178
$820$	51534.9	2.19473
$821$	14614.2	0.621240	0.310620	−	0.950534i	$-0.399463\pi$
$821$	14614.2	0.621240	0.310620	+	0.950534i	$0.399463\pi$
$822$	7022.39	0.297973
$823$	4709.07	0.199450	0.0997252	−	0.995015i	$-0.468204\pi$
$823$	4709.07	0.199450	0.0997252	+	0.995015i	$0.468204\pi$
$824$	59875.7	2.53139
$825$	3866.96	0.163188
$826$	58700.9	2.47272
$827$	−11128.0	−0.467904	−0.233952	−	0.972248i	$-0.575166\pi$
$827$	−11128.0	−0.467904	−0.233952	+	0.972248i	$0.575166\pi$
$828$	−4855.08	−0.203775
$829$	−2162.07	−0.0905811	−0.0452905	−	0.998974i	$-0.514421\pi$
$829$	−2162.07	−0.0905811	−0.0452905	+	0.998974i	$0.514421\pi$
$830$	−19335.3	−0.808600
$831$	−2873.16	−0.119938
$832$	28277.2	1.17829
$833$	3860.12	0.160558
$834$	167.975	0.00697422
$835$	−26625.8	−1.10350
$836$	−9873.15	−0.408457
$837$	−3272.77	−0.135154
$838$	44671.0	1.84145
$839$	193.984	0.00798222	0.00399111	−	0.999992i	$-0.498730\pi$
$839$	193.984	0.00798222	0.00399111	+	0.999992i	$0.498730\pi$
$840$	30668.9	1.25974
$841$	6009.42	0.246399
$842$	−34348.5	−1.40585
$843$	−23480.7	−0.959333
$844$	−91225.4	−3.72051
$845$	10528.3	0.428622
$846$	−14455.2	−0.587446
$847$	2052.61	0.0832688
$848$	−16657.5	−0.674554
$849$	21179.6	0.856161
$850$	40053.1	1.61625
$851$	11003.8	0.443249
$852$	−7495.20	−0.301386
$853$	5345.73	0.214577	0.107289	−	0.994228i	$-0.465783\pi$
$853$	5345.73	0.214577	0.107289	+	0.994228i	$0.465783\pi$
$854$	−5060.76	−0.202782
$855$	7897.39	0.315889
$856$	24428.9	0.975424
$857$	−16244.6	−0.647498	−0.323749	−	0.946143i	$-0.604943\pi$
$857$	−16244.6	−0.647498	−0.323749	+	0.946143i	$0.604943\pi$
$858$	8651.39	0.344235
$859$	17029.4	0.676409	0.338204	−	0.941073i	$-0.390180\pi$
$859$	17029.4	0.676409	0.338204	+	0.941073i	$0.390180\pi$
$860$	−60790.0	−2.41038
$861$	−10587.2	−0.419062
$862$	−6533.96	−0.258176
$863$	34173.9	1.34796	0.673982	−	0.738748i	$-0.264582\pi$
$863$	34173.9	1.34796	0.673982	+	0.738748i	$0.264582\pi$
$864$	−172.096	−0.00677642
$865$	5806.81	0.228251
$866$	−55598.4	−2.18165
$867$	85.0059	0.00332982
$868$	32731.5	1.27993
$869$	−13362.4	−0.521622
$870$	39808.9	1.55132
$871$	−33135.0	−1.28902
$872$	11111.7	0.431525
$873$	−13941.2	−0.540479
$874$	9345.39	0.361685
$875$	−2064.29	−0.0797552
$876$	21704.0	0.837111
$877$	30443.1	1.17217	0.586083	−	0.810251i	$-0.300669\pi$
$877$	30443.1	1.17217	0.586083	+	0.810251i	$0.300669\pi$
$878$	−2846.53	−0.109414
$879$	13090.9	0.502327
$880$	−10620.5	−0.406838
$881$	−20398.4	−0.780068	−0.390034	−	0.920801i	$-0.627537\pi$
$881$	−20398.4	−0.780068	−0.390034	+	0.920801i	$0.627537\pi$
$882$	2431.02	0.0928082
$883$	−49435.6	−1.88408	−0.942038	−	0.335506i	$-0.891093\pi$
$883$	−49435.6	−1.88408	−0.942038	+	0.335506i	$0.891093\pi$
$884$	59637.2	2.26902
$885$	33033.2	1.25469
$886$	42724.1	1.62003
$887$	−20528.9	−0.777105	−0.388552	−	0.921427i	$-0.627025\pi$
$887$	−20528.9	−0.777105	−0.388552	+	0.921427i	$0.627025\pi$
$888$	−37721.3	−1.42550
$889$	−1780.12	−0.0671577
$890$	−4573.50	−0.172252
$891$	−891.000	−0.0335013
$892$	−35147.9	−1.31933
$893$	18517.8	0.693924
$894$	−6472.11	−0.242125
$895$	19092.7	0.713069
$896$	42898.6	1.59949
$897$	−5449.94	−0.202863
$898$	−71989.7	−2.67520
$899$	21133.8	0.784039
$900$	16787.6	0.621765
$901$	18764.8	0.693836
$902$	11191.7	0.413129
$903$	12488.6	0.460238
$904$	−33280.4	−1.22444
$905$	−10087.5	−0.370519
$906$	15093.5	0.553474
$907$	−24475.2	−0.896017	−0.448008	−	0.894029i	$-0.647867\pi$
$907$	−24475.2	−0.896017	−0.448008	+	0.894029i	$0.647867\pi$
$908$	−9471.93	−0.346186
$909$	−5760.21	−0.210181
$910$	69209.1	2.52116
$911$	−47581.8	−1.73047	−0.865234	−	0.501369i	$-0.832830\pi$
$911$	−47581.8	−1.73047	−0.865234	+	0.501369i	$0.832830\pi$
$912$	−10494.8	−0.381052
$913$	−2794.54	−0.101299
$914$	63604.3	2.30180
$915$	−2847.87	−0.102894
$916$	−102778.	−3.70730
$917$	−4152.76	−0.149549
$918$	−9228.79	−0.331803
$919$	17220.8	0.618131	0.309065	−	0.951041i	$-0.399984\pi$
$919$	17220.8	0.618131	0.309065	+	0.951041i	$0.399984\pi$
$920$	20422.9	0.731874
$921$	5488.32	0.196359
$922$	−56832.5	−2.03002
$923$	−8413.53	−0.300037
$924$	8911.03	0.317263
$925$	−38048.2	−1.35245
$926$	−3249.46	−0.115317
$927$	−13915.8	−0.493046
$928$	1111.30	0.0393107
$929$	20309.5	0.717257	0.358629	−	0.933480i	$-0.383244\pi$
$929$	20309.5	0.717257	0.358629	+	0.933480i	$0.383244\pi$
$930$	27676.2	0.975848
$931$	−3114.26	−0.109630
$932$	53234.8	1.87099
$933$	−669.132	−0.0234795
$934$	4445.34	0.155735
$935$	11964.1	0.418468
$936$	18682.6	0.652413
$937$	12238.7	0.426704	0.213352	−	0.976975i	$-0.431562\pi$
$937$	12238.7	0.426704	0.213352	+	0.976975i	$0.431562\pi$
$938$	−51282.0	−1.78509
$939$	−10509.5	−0.365245
$940$	81354.1	2.82285
$941$	−12120.1	−0.419876	−0.209938	−	0.977715i	$-0.567326\pi$
$941$	−12120.1	−0.419876	−0.209938	+	0.977715i	$0.567326\pi$
$942$	−17558.6	−0.607316
$943$	−7050.21	−0.243464
$944$	−43897.8	−1.51351
$945$	−7127.80	−0.245362
$946$	−13201.6	−0.453723
$947$	−45993.8	−1.57825	−0.789123	−	0.614236i	$-0.789464\pi$
$947$	−45993.8	−1.57825	−0.789123	+	0.614236i	$0.789464\pi$
$948$	−58010.5	−1.98744
$949$	24363.2	0.833364
$950$	−32314.0	−1.10358
$951$	24334.8	0.829769
$952$	45911.9	1.56304
$953$	6229.06	0.211730	0.105865	−	0.994380i	$-0.466239\pi$
$953$	6229.06	0.211730	0.105865	+	0.994380i	$0.466239\pi$
$954$	11817.7	0.401061
$955$	−11067.2	−0.375002
$956$	64804.1	2.19238
$957$	5753.60	0.194344
$958$	57725.9	1.94680
$959$	8119.37	0.273397
$960$	24627.4	0.827964
$961$	−15098.2	−0.506805
$962$	−85123.8	−2.85291
$963$	−5677.55	−0.189986
$964$	−10333.8	−0.345259
$965$	20561.7	0.685912
$966$	−8434.69	−0.280933
$967$	3406.85	0.113296	0.0566478	−	0.998394i	$-0.481959\pi$
$967$	3406.85	0.113296	0.0566478	+	0.998394i	$0.481959\pi$
$968$	−4685.67	−0.155582
$969$	11822.5	0.391944
$970$	117894.	3.90241
$971$	−20038.4	−0.662268	−0.331134	−	0.943584i	$-0.607431\pi$
$971$	−20038.4	−0.662268	−0.331134	+	0.943584i	$0.607431\pi$
$972$	−3868.10	−0.127644
$973$	194.215	0.00639901
$974$	−32349.6	−1.06422
$975$	18844.5	0.618982
$976$	3784.54	0.124119
$977$	−16200.6	−0.530505	−0.265253	−	0.964179i	$-0.585455\pi$
$977$	−16200.6	−0.530505	−0.265253	+	0.964179i	$0.585455\pi$
$978$	−26107.1	−0.853592
$979$	−661.011	−0.0215792
$980$	−13681.8	−0.445970
$981$	−2582.48	−0.0840493
$982$	−67412.0	−2.19064
$983$	2690.26	0.0872898	0.0436449	−	0.999047i	$-0.486103\pi$
$983$	2690.26	0.0872898	0.0436449	+	0.999047i	$0.486103\pi$
$984$	24168.3	0.782986
$985$	72289.7	2.33842
$986$	59594.5	1.92482
$987$	−16713.3	−0.538996
$988$	−48114.0	−1.54930
$989$	8316.36	0.267386
$990$	7534.74	0.241889
$991$	−35285.8	−1.13107	−0.565536	−	0.824724i	$-0.691330\pi$
$991$	−35285.8	−1.13107	−0.565536	+	0.824724i	$0.691330\pi$
$992$	772.608	0.0247282
$993$	−26357.4	−0.842322
$994$	−13021.3	−0.415505
$995$	−64002.1	−2.03920
$996$	−12132.0	−0.385960
$997$	6023.86	0.191352	0.0956758	−	0.995413i	$-0.469499\pi$
$997$	6023.86	0.191352	0.0956758	+	0.995413i	$0.469499\pi$
$998$	7336.55	0.232700
$999$	8766.84	0.277648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.b.1.3	✓	36	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-4.89062 q^{2} -3.00000 q^{3} +15.9181 q^{4} +15.5621 q^{5} +14.6718 q^{6} +16.9638 q^{7} -38.7245 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.89062 q^{2} -3.00000 q^{3} +15.9181 q^{4} +15.5621 q^{5} +14.6718 q^{6} +16.9638 q^{7} -38.7245 q^{8} +9.00000 q^{9} -76.1085 q^{10} -11.0000 q^{11} -47.7544 q^{12} -53.6054 q^{13} -82.9632 q^{14} -46.6864 q^{15} +62.0417 q^{16} -69.8904 q^{17} -44.0155 q^{18} +56.3860 q^{19} +247.720 q^{20} -50.8913 q^{21} +53.7968 q^{22} -33.8893 q^{23} +116.174 q^{24} +117.180 q^{25} +262.163 q^{26} -27.0000 q^{27} +270.031 q^{28} +174.351 q^{29} +228.325 q^{30} +121.214 q^{31} +6.37393 q^{32} +33.0000 q^{33} +341.807 q^{34} +263.992 q^{35} +143.263 q^{36} -324.698 q^{37} -275.762 q^{38} +160.816 q^{39} -602.637 q^{40} +208.037 q^{41} +248.890 q^{42} -245.398 q^{43} -175.099 q^{44} +140.059 q^{45} +165.739 q^{46} +328.411 q^{47} -186.125 q^{48} -55.2310 q^{49} -573.085 q^{50} +209.671 q^{51} -853.297 q^{52} -268.489 q^{53} +132.047 q^{54} -171.184 q^{55} -656.913 q^{56} -169.158 q^{57} -852.686 q^{58} -707.553 q^{59} -743.161 q^{60} +61.0000 q^{61} -592.810 q^{62} +152.674 q^{63} -527.506 q^{64} -834.215 q^{65} -161.390 q^{66} +618.129 q^{67} -1112.52 q^{68} +101.668 q^{69} -1291.09 q^{70} +156.953 q^{71} -348.521 q^{72} -454.492 q^{73} +1587.97 q^{74} -351.541 q^{75} +897.559 q^{76} -186.601 q^{77} -786.490 q^{78} +1214.77 q^{79} +965.502 q^{80} +81.0000 q^{81} -1017.43 q^{82} +254.049 q^{83} -810.093 q^{84} -1087.64 q^{85} +1200.15 q^{86} -523.054 q^{87} +425.970 q^{88} +60.0919 q^{89} -684.976 q^{90} -909.348 q^{91} -539.454 q^{92} -363.641 q^{93} -1606.13 q^{94} +877.487 q^{95} -19.1218 q^{96} -1549.02 q^{97} +270.114 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

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