LMFDB - Embedded newform 1849.4.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} +O(q^{10})$	\(q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} -90.3106 q^{10} -21.9318 q^{11} -83.2181 q^{12} +90.1443 q^{13} -2.70592 q^{14} -103.994 q^{15} +42.1470 q^{16} -68.5734 q^{17} -17.1239 q^{18} +29.2074 q^{19} +283.125 q^{20} -3.11590 q^{21} +105.300 q^{22} -171.303 q^{23} +187.194 q^{24} +228.809 q^{25} -432.806 q^{26} +129.557 q^{27} +8.48310 q^{28} +9.36853 q^{29} +499.300 q^{30} +244.427 q^{31} +68.5095 q^{32} +121.255 q^{33} +329.238 q^{34} +10.6009 q^{35} +53.6839 q^{36} +213.593 q^{37} -140.232 q^{38} -498.381 q^{39} -636.872 q^{40} -191.608 q^{41} +14.9602 q^{42} -330.118 q^{44} +67.0863 q^{45} +822.469 q^{46} -341.454 q^{47} -233.018 q^{48} -342.682 q^{49} -1098.57 q^{50} +379.122 q^{51} +1356.85 q^{52} -488.826 q^{53} -622.034 q^{54} -412.533 q^{55} -19.0822 q^{56} -161.479 q^{57} -44.9807 q^{58} +319.938 q^{59} -1565.32 q^{60} -51.1903 q^{61} -1173.56 q^{62} +2.01006 q^{63} -666.107 q^{64} +1695.60 q^{65} -582.173 q^{66} -733.622 q^{67} -1032.17 q^{68} +947.083 q^{69} -50.8978 q^{70} -417.297 q^{71} -120.758 q^{72} +35.6291 q^{73} -1025.51 q^{74} -1265.01 q^{75} +439.630 q^{76} -12.3605 q^{77} +2392.85 q^{78} +32.5557 q^{79} +792.777 q^{80} -812.577 q^{81} +919.957 q^{82} -73.6881 q^{83} -46.9006 q^{84} -1289.85 q^{85} -51.7958 q^{87} +742.578 q^{88} -1128.32 q^{89} -322.098 q^{90} +50.8041 q^{91} -2578.45 q^{92} -1351.37 q^{93} +1639.41 q^{94} +549.385 q^{95} -378.768 q^{96} -309.477 q^{97} +1645.30 q^{98} -78.2211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * 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 $

$2$	−4.80125	−1.69750	−0.848749	−	0.528795i	$-0.822644\pi$
$2$	−4.80125	−1.69750	−0.848749	+	0.528795i	$0.822644\pi$
$3$	−5.52870	−1.06400	−0.532000	−	0.846745i	$-0.678559\pi$
$3$	−5.52870	−1.06400	−0.532000	+	0.846745i	$0.678559\pi$
$4$	15.0520	1.88150
$5$	18.8098	1.68240	0.841200	−	0.540724i	$-0.181850\pi$
$5$	18.8098	1.68240	0.841200	+	0.540724i	$0.181850\pi$
$6$	26.5447	1.80614
$7$	0.563586	0.0304308	0.0152154	−	0.999884i	$-0.495157\pi$
$7$	0.563586	0.0304308	0.0152154	+	0.999884i	$0.495157\pi$
$8$	−33.8585	−1.49635
$9$	3.56656	0.132095
$10$	−90.3106	−2.85587
$11$	−21.9318	−0.601154	−0.300577	−	0.953758i	$-0.597179\pi$
$11$	−21.9318	−0.601154	−0.300577	+	0.953758i	$0.597179\pi$
$12$	−83.2181	−2.00192
$13$	90.1443	1.92320	0.961598	−	0.274463i	$-0.0885001\pi$
$13$	90.1443	1.92320	0.961598	+	0.274463i	$0.0885001\pi$
$14$	−2.70592	−0.0516562
$15$	−103.994	−1.79007
$16$	42.1470	0.658547
$17$	−68.5734	−0.978323	−0.489161	−	0.872193i	$-0.662697\pi$
$17$	−68.5734	−0.978323	−0.489161	+	0.872193i	$0.662697\pi$
$18$	−17.1239	−0.224231
$19$	29.2074	0.352665	0.176332	−	0.984331i	$-0.443577\pi$
$19$	29.2074	0.352665	0.176332	+	0.984331i	$0.443577\pi$
$20$	283.125	3.16544
$21$	−3.11590	−0.0323783
$22$	105.300	1.02046
$23$	−171.303	−1.55301	−0.776503	−	0.630114i	$-0.783008\pi$
$23$	−171.303	−1.55301	−0.776503	+	0.630114i	$0.783008\pi$
$24$	187.194	1.59211
$25$	228.809	1.83047
$26$	−432.806	−3.26462
$27$	129.557	0.923451
$28$	8.48310	0.0572556
$29$	9.36853	0.0599894	0.0299947	−	0.999550i	$-0.490451\pi$
$29$	9.36853	0.0599894	0.0299947	+	0.999550i	$0.490451\pi$
$30$	499.300	3.03865
$31$	244.427	1.41614	0.708071	−	0.706141i	$-0.249565\pi$
$31$	244.427	1.41614	0.708071	+	0.706141i	$0.249565\pi$
$32$	68.5095	0.378465
$33$	121.255	0.639627
$34$	329.238	1.66070
$35$	10.6009	0.0511967
$36$	53.6839	0.248537
$37$	213.593	0.949041	0.474520	−	0.880245i	$-0.342622\pi$
$37$	213.593	0.949041	0.474520	+	0.880245i	$0.342622\pi$
$38$	−140.232	−0.598648
$39$	−498.381	−2.04628
$40$	−636.872	−2.51746
$41$	−191.608	−0.729856	−0.364928	−	0.931036i	$-0.618906\pi$
$41$	−191.608	−0.729856	−0.364928	+	0.931036i	$0.618906\pi$
$42$	14.9602	0.0549622
$43$	0	0
$43$	0	0
$44$	−330.118	−1.13107
$45$	67.0863	0.222236
$46$	822.469	2.63623
$47$	−341.454	−1.05971	−0.529853	−	0.848089i	$-0.677753\pi$
$47$	−341.454	−1.05971	−0.529853	+	0.848089i	$0.677753\pi$
$48$	−233.018	−0.700694
$49$	−342.682	−0.999074
$50$	−1098.57	−3.10722
$51$	379.122	1.04093
$52$	1356.85	3.61850
$53$	−488.826	−1.26690	−0.633448	−	0.773785i	$-0.718361\pi$
$53$	−488.826	−1.26690	−0.633448	+	0.773785i	$0.718361\pi$
$54$	−622.034	−1.56756
$55$	−412.533	−1.01138
$56$	−19.0822	−0.0455350
$57$	−161.479	−0.375235
$58$	−44.9807	−0.101832
$59$	319.938	0.705972	0.352986	−	0.935629i	$-0.385166\pi$
$59$	319.938	0.705972	0.352986	+	0.935629i	$0.385166\pi$
$60$	−1565.32	−3.36802
$61$	−51.1903	−0.107447	−0.0537234	−	0.998556i	$-0.517109\pi$
$61$	−51.1903	−0.107447	−0.0537234	+	0.998556i	$0.517109\pi$
$62$	−1173.56	−2.40390
$63$	2.01006	0.00401975
$64$	−666.107	−1.30099
$65$	1695.60	3.23558
$66$	−582.173	−1.08577
$67$	−733.622	−1.33771	−0.668853	−	0.743395i	$-0.733214\pi$
$67$	−733.622	−1.33771	−0.668853	+	0.743395i	$0.733214\pi$
$68$	−1032.17	−1.84072
$69$	947.083	1.65240
$70$	−50.8978	−0.0869064
$71$	−417.297	−0.697522	−0.348761	−	0.937212i	$-0.613398\pi$
$71$	−417.297	−0.697522	−0.348761	+	0.937212i	$0.613398\pi$
$72$	−120.758	−0.197660
$73$	35.6291	0.0571243	0.0285621	−	0.999592i	$-0.490907\pi$
$73$	35.6291	0.0571243	0.0285621	+	0.999592i	$0.490907\pi$
$74$	−1025.51	−1.61100
$75$	−1265.01	−1.94762
$76$	439.630	0.663539
$77$	−12.3605	−0.0182936
$78$	2392.85	3.47356
$79$	32.5557	0.0463645	0.0231823	−	0.999731i	$-0.492620\pi$
$79$	32.5557	0.0463645	0.0231823	+	0.999731i	$0.492620\pi$
$80$	792.777	1.10794
$81$	−812.577	−1.11465
$82$	919.957	1.23893
$83$	−73.6881	−0.0974497	−0.0487248	−	0.998812i	$-0.515516\pi$
$83$	−73.6881	−0.0974497	−0.0487248	+	0.998812i	$0.515516\pi$
$84$	−46.9006	−0.0609199
$85$	−1289.85	−1.64593
$86$	0	0
$87$	−51.7958	−0.0638287
$88$	742.578	0.899536
$89$	−1128.32	−1.34384	−0.671918	−	0.740626i	$-0.734529\pi$
$89$	−1128.32	−1.34384	−0.671918	+	0.740626i	$0.734529\pi$
$90$	−322.098	−0.377246
$91$	50.8041	0.0585243
$92$	−2578.45	−2.92198
$93$	−1351.37	−1.50678
$94$	1639.41	1.79885
$95$	549.385	0.593323
$96$	−378.768	−0.402686
$97$	−309.477	−0.323944	−0.161972	−	0.986795i	$-0.551785\pi$
$97$	−309.477	−0.323944	−0.161972	+	0.986795i	$0.551785\pi$
$98$	1645.30	1.69593
$99$	−78.2211	−0.0794093
$100$	3444.03	3.44403
$101$	331.449	0.326538	0.163269	−	0.986582i	$-0.447796\pi$
$101$	331.449	0.326538	0.163269	+	0.986582i	$0.447796\pi$
$102$	−1820.26	−1.76699
$103$	132.978	0.127211	0.0636053	−	0.997975i	$-0.479740\pi$
$103$	132.978	0.127211	0.0636053	+	0.997975i	$0.479740\pi$
$104$	−3052.15	−2.87777
$105$	−58.6094	−0.0544733
$106$	2346.98	2.15055
$107$	−273.667	−0.247256	−0.123628	−	0.992329i	$-0.539453\pi$
$107$	−273.667	−0.247256	−0.123628	+	0.992329i	$0.539453\pi$
$108$	1950.09	1.73747
$109$	1590.63	1.39775	0.698874	−	0.715245i	$-0.253685\pi$
$109$	1590.63	1.39775	0.698874	+	0.715245i	$0.253685\pi$
$110$	1980.68	1.71682
$111$	−1180.89	−1.00978
$112$	23.7535	0.0200401
$113$	484.817	0.403608	0.201804	−	0.979426i	$-0.435320\pi$
$113$	484.817	0.403608	0.201804	+	0.979426i	$0.435320\pi$
$114$	775.300	0.636961
$115$	−3222.17	−2.61278
$116$	141.015	0.112870
$117$	321.505	0.254044
$118$	−1536.10	−1.19839
$119$	−38.6470	−0.0297711
$120$	3521.07	2.67857
$121$	−849.995	−0.638614
$122$	245.778	0.182391
$123$	1059.34	0.776566
$124$	3679.12	2.66448
$125$	1952.62	1.39718
$126$	−9.65081	−0.00682351
$127$	401.864	0.280785	0.140392	−	0.990096i	$-0.455164\pi$
$127$	401.864	0.280785	0.140392	+	0.990096i	$0.455164\pi$
$128$	2650.07	1.82997
$129$	0	0
$130$	−8140.99	−5.49240
$131$	−2186.29	−1.45815	−0.729073	−	0.684436i	$-0.760049\pi$
$131$	−2186.29	−1.45815	−0.729073	+	0.684436i	$0.760049\pi$
$132$	1825.12	1.20346
$133$	16.4609	0.0107319
$134$	3522.31	2.27075
$135$	2436.93	1.55361
$136$	2321.79	1.46391
$137$	830.062	0.517642	0.258821	−	0.965925i	$-0.416666\pi$
$137$	830.062	0.517642	0.258821	+	0.965925i	$0.416666\pi$
$138$	−4547.18	−2.80494
$139$	−1919.05	−1.17102	−0.585511	−	0.810664i	$-0.699106\pi$
$139$	−1919.05	−1.17102	−0.585511	+	0.810664i	$0.699106\pi$
$140$	159.565	0.0963267
$141$	1887.80	1.12753
$142$	2003.55	1.18404
$143$	−1977.03	−1.15614
$144$	150.320	0.0869907
$145$	176.220	0.100926
$146$	−171.064	−0.0969684
$147$	1894.59	1.06301
$148$	3215.01	1.78562
$149$	1690.89	0.929686	0.464843	−	0.885393i	$-0.346111\pi$
$149$	1690.89	0.929686	0.464843	+	0.885393i	$0.346111\pi$
$150$	6073.65	3.30608
$151$	1011.84	0.545311	0.272656	−	0.962112i	$-0.412098\pi$
$151$	1011.84	0.545311	0.272656	+	0.962112i	$0.412098\pi$
$152$	−988.917	−0.527709
$153$	−244.571	−0.129231
$154$	59.3457	0.0310533
$155$	4597.63	2.38252
$156$	−7501.64	−3.85008
$157$	−1236.95	−0.628786	−0.314393	−	0.949293i	$-0.601801\pi$
$157$	−1236.95	−0.628786	−0.314393	+	0.949293i	$0.601801\pi$
$158$	−156.308	−0.0787037
$159$	2702.58	1.34798
$160$	1288.65	0.636729
$161$	−96.5439	−0.0472592
$162$	3901.39	1.89211
$163$	1060.28	0.509495	0.254747	−	0.967008i	$-0.418008\pi$
$163$	1060.28	0.509495	0.254747	+	0.967008i	$0.418008\pi$
$164$	−2884.08	−1.37323
$165$	2280.77	1.07611
$166$	353.795	0.165421
$167$	−1645.91	−0.762660	−0.381330	−	0.924439i	$-0.624534\pi$
$167$	−1645.91	−0.762660	−0.381330	+	0.924439i	$0.624534\pi$
$168$	105.500	0.0484493
$169$	5929.00	2.69868
$170$	6192.90	2.79396
$171$	104.170	0.0465852
$172$	0	0
$173$	2977.10	1.30835	0.654176	−	0.756342i	$-0.273015\pi$
$173$	2977.10	1.30835	0.654176	+	0.756342i	$0.273015\pi$
$174$	248.685	0.108349
$175$	128.953	0.0557026
$176$	−924.361	−0.395888
$177$	−1768.84	−0.751154
$178$	5417.33	2.28116
$179$	4.36944	0.00182451	0.000912256	−	1.00000i	$-0.499710\pi$
$179$	4.36944	0.00182451	0.000912256		1.00000i	$0.499710\pi$
$180$	1009.78	0.418138
$181$	1585.58	0.651134	0.325567	−	0.945519i	$-0.394445\pi$
$181$	1585.58	0.651134	0.325567	+	0.945519i	$0.394445\pi$
$182$	−243.923	−0.0993450
$183$	283.016	0.114323
$184$	5800.06	2.32384
$185$	4017.65	1.59667
$186$	6488.25	2.55775
$187$	1503.94	0.588122
$188$	−5139.57	−1.99384
$189$	73.0162	0.0281013
$190$	−2637.73	−1.00716
$191$	632.532	0.239625	0.119813	−	0.992797i	$-0.461771\pi$
$191$	632.532	0.239625	0.119813	+	0.992797i	$0.461771\pi$
$192$	3682.71	1.38425
$193$	2150.82	0.802174	0.401087	−	0.916040i	$-0.368633\pi$
$193$	2150.82	0.802174	0.401087	+	0.916040i	$0.368633\pi$
$194$	1485.88	0.549895
$195$	−9374.45	−3.44266
$196$	−5158.06	−1.87976
$197$	−865.753	−0.313109	−0.156554	−	0.987669i	$-0.550039\pi$
$197$	−865.753	−0.313109	−0.156554	+	0.987669i	$0.550039\pi$
$198$	375.559	0.134797
$199$	−4687.11	−1.66965	−0.834825	−	0.550516i	$-0.814431\pi$
$199$	−4687.11	−1.66965	−0.834825	+	0.550516i	$0.814431\pi$
$200$	−7747.11	−2.73902
$201$	4055.98	1.42332
$202$	−1591.37	−0.554298
$203$	5.27997	0.00182552
$204$	5706.55	1.95852
$205$	−3604.10	−1.22791
$206$	−638.460	−0.215940
$207$	−610.962	−0.205144
$208$	3799.32	1.26652
$209$	−640.571	−0.212006
$210$	281.399	0.0924683
$211$	−1447.08	−0.472138	−0.236069	−	0.971736i	$-0.575859\pi$
$211$	−1447.08	−0.472138	−0.236069	+	0.971736i	$0.575859\pi$
$212$	−7357.82	−2.38367
$213$	2307.11	0.742163
$214$	1313.94	0.419717
$215$	0	0
$216$	−4386.59	−1.38180
$217$	137.756	0.0430943
$218$	−7637.00	−2.37267
$219$	−196.983	−0.0607802
$220$	−6209.45	−1.90292
$221$	−6181.50	−1.88151
$222$	5669.77	1.71410
$223$	−5483.79	−1.64673	−0.823367	−	0.567510i	$-0.807907\pi$
$223$	−5483.79	−1.64673	−0.823367	+	0.567510i	$0.807907\pi$
$224$	38.6110	0.0115170
$225$	816.059	0.241795
$226$	−2327.73	−0.685125
$227$	6340.18	1.85380	0.926900	−	0.375309i	$-0.122463\pi$
$227$	6340.18	1.85380	0.926900	+	0.375309i	$0.122463\pi$
$228$	−2430.58	−0.706005
$229$	−5138.02	−1.48266	−0.741332	−	0.671139i	$-0.765805\pi$
$229$	−5138.02	−1.48266	−0.741332	+	0.671139i	$0.765805\pi$
$230$	15470.5	4.43518
$231$	68.3373	0.0194644
$232$	−317.204	−0.0897650
$233$	−3941.80	−1.10831	−0.554154	−	0.832414i	$-0.686958\pi$
$233$	−3941.80	−1.10831	−0.554154	+	0.832414i	$0.686958\pi$
$234$	−1543.63	−0.431239
$235$	−6422.68	−1.78285
$236$	4815.71	1.32829
$237$	−179.991	−0.0493318
$238$	185.554	0.0505364
$239$	−367.931	−0.0995794	−0.0497897	−	0.998760i	$-0.515855\pi$
$239$	−367.931	−0.0995794	−0.0497897	+	0.998760i	$0.515855\pi$
$240$	−4383.03	−1.17885
$241$	812.124	0.217068	0.108534	−	0.994093i	$-0.465384\pi$
$241$	812.124	0.217068	0.108534	+	0.994093i	$0.465384\pi$
$242$	4081.04	1.08405
$243$	994.469	0.262532
$244$	−770.518	−0.202161
$245$	−6445.79	−1.68084
$246$	−5086.17	−1.31822
$247$	2632.88	0.678243
$248$	−8275.94	−2.11904
$249$	407.400	0.103686
$250$	−9375.01	−2.37171
$251$	−3984.26	−1.00193	−0.500964	−	0.865468i	$-0.667021\pi$
$251$	−3984.26	−1.00193	−0.500964	+	0.865468i	$0.667021\pi$
$252$	30.2555	0.00756316
$253$	3756.99	0.933595
$254$	−1929.45	−0.476631
$255$	7131.20	1.75127
$256$	−7394.81	−1.80537
$257$	2945.96	0.715034	0.357517	−	0.933907i	$-0.383623\pi$
$257$	2945.96	0.715034	0.357517	+	0.933907i	$0.383623\pi$
$258$	0	0
$259$	120.378	0.0288800
$260$	25522.1	6.08776
$261$	33.4134	0.00792429
$262$	10496.9	2.47520
$263$	−1825.81	−0.428076	−0.214038	−	0.976825i	$-0.568662\pi$
$263$	−1825.81	−0.428076	−0.214038	+	0.976825i	$0.568662\pi$
$264$	−4105.50	−0.957105
$265$	−9194.72	−2.13142
$266$	−79.0327	−0.0182173
$267$	6238.13	1.42984
$268$	−11042.5	−2.51689
$269$	3509.27	0.795404	0.397702	−	0.917515i	$-0.369808\pi$
$269$	3509.27	0.795404	0.397702	+	0.917515i	$0.369808\pi$
$270$	−11700.3	−2.63726
$271$	−8225.07	−1.84368	−0.921840	−	0.387571i	$-0.873314\pi$
$271$	−8225.07	−1.84368	−0.921840	+	0.387571i	$0.873314\pi$
$272$	−2890.16	−0.644272
$273$	−280.881	−0.0622698
$274$	−3985.34	−0.878697
$275$	−5018.19	−1.10039
$276$	14255.5	3.10899
$277$	−1286.60	−0.279076	−0.139538	−	0.990217i	$-0.544562\pi$
$277$	−1286.60	−0.279076	−0.139538	+	0.990217i	$0.544562\pi$
$278$	9213.87	1.98781
$279$	871.764	0.187065
$280$	−358.932	−0.0766081
$281$	4799.08	1.01882	0.509411	−	0.860523i	$-0.329863\pi$
$281$	4799.08	1.01882	0.509411	+	0.860523i	$0.329863\pi$
$282$	−9063.80	−1.91398
$283$	792.682	0.166502	0.0832510	−	0.996529i	$-0.473470\pi$
$283$	792.682	0.166502	0.0832510	+	0.996529i	$0.473470\pi$
$284$	−6281.17	−1.31239
$285$	−3037.38	−0.631295
$286$	9492.21	1.96254
$287$	−107.987	−0.0222101
$288$	244.343	0.0499932
$289$	−210.694	−0.0428850
$290$	−846.077	−0.171322
$291$	1711.01	0.344677
$292$	536.290	0.107479
$293$	5226.15	1.04203	0.521015	−	0.853547i	$-0.325553\pi$
$293$	5226.15	1.04203	0.521015	+	0.853547i	$0.325553\pi$
$294$	−9096.40	−1.80447
$295$	6017.97	1.18773
$296$	−7231.95	−1.42010
$297$	−2841.41	−0.555136
$298$	−8118.39	−1.57814
$299$	−15442.0	−2.98673
$300$	−19041.0	−3.66445
$301$	0	0
$302$	−4858.08	−0.925665
$303$	−1832.48	−0.347437
$304$	1231.00	0.232246
$305$	−962.880	−0.180768
$306$	1174.25	0.219370
$307$	5434.88	1.01037	0.505187	−	0.863010i	$-0.331423\pi$
$307$	5434.88	1.01037	0.505187	+	0.863010i	$0.331423\pi$
$308$	−186.050	−0.0344194
$309$	−735.195	−0.135352
$310$	−22074.4	−4.04432
$311$	434.161	0.0791608	0.0395804	−	0.999216i	$-0.487398\pi$
$311$	434.161	0.0791608	0.0395804	+	0.999216i	$0.487398\pi$
$312$	16874.4	3.06195
$313$	7130.42	1.28765	0.643826	−	0.765172i	$-0.277346\pi$
$313$	7130.42	1.28765	0.643826	+	0.765172i	$0.277346\pi$
$314$	5938.91	1.06736
$315$	37.8089	0.00676282
$316$	490.028	0.0872350
$317$	−3967.42	−0.702942	−0.351471	−	0.936199i	$-0.614318\pi$
$317$	−3967.42	−0.702942	−0.351471	+	0.936199i	$0.614318\pi$
$318$	−12975.7	−2.28819
$319$	−205.469	−0.0360629
$320$	−12529.3	−2.18879
$321$	1513.02	0.263080
$322$	463.532	0.0802224
$323$	−2002.85	−0.345020
$324$	−12230.9	−2.09721
$325$	20625.8	3.52035
$326$	−5090.68	−0.864867
$327$	−8794.11	−1.48720
$328$	6487.55	1.09212
$329$	−192.439	−0.0322477
$330$	−10950.6	−1.82669
$331$	−2977.86	−0.494495	−0.247248	−	0.968952i	$-0.579526\pi$
$331$	−2977.86	−0.494495	−0.247248	+	0.968952i	$0.579526\pi$
$332$	−1109.15	−0.183352
$333$	761.793	0.125363
$334$	7902.43	1.29462
$335$	−13799.3	−2.25055
$336$	−131.326	−0.0213227
$337$	3415.37	0.552069	0.276035	−	0.961148i	$-0.410980\pi$
$337$	3415.37	0.552069	0.276035	+	0.961148i	$0.410980\pi$
$338$	−28466.6	−4.58101
$339$	−2680.41	−0.429439
$340$	−19414.9	−3.09682
$341$	−5360.73	−0.851320
$342$	−500.145	−0.0790782
$343$	−386.441	−0.0608334
$344$	0	0
$345$	17814.4	2.77999
$346$	−14293.8	−2.22093
$347$	−4500.31	−0.696222	−0.348111	−	0.937453i	$-0.613177\pi$
$347$	−4500.31	−0.696222	−0.348111	+	0.937453i	$0.613177\pi$
$348$	−779.632	−0.120094
$349$	−746.598	−0.114511	−0.0572557	−	0.998360i	$-0.518235\pi$
$349$	−746.598	−0.114511	−0.0572557	+	0.998360i	$0.518235\pi$
$350$	−619.137	−0.0945550
$351$	11678.8	1.77598
$352$	−1502.54	−0.227516
$353$	8674.41	1.30791	0.653955	−	0.756533i	$-0.273108\pi$
$353$	8674.41	1.30791	0.653955	+	0.756533i	$0.273108\pi$
$354$	8492.65	1.27508
$355$	−7849.28	−1.17351
$356$	−16983.4	−2.52843
$357$	213.668	0.0316764
$358$	−20.9788	−0.00309711
$359$	−6602.33	−0.970634	−0.485317	−	0.874338i	$-0.661296\pi$
$359$	−6602.33	−0.970634	−0.485317	+	0.874338i	$0.661296\pi$
$360$	−2271.44	−0.332543
$361$	−6005.93	−0.875628
$362$	−7612.77	−1.10530
$363$	4699.37	0.679485
$364$	764.704	0.110114
$365$	670.177	0.0961059
$366$	−1358.83	−0.194064
$367$	6165.86	0.876990	0.438495	−	0.898734i	$-0.355512\pi$
$367$	6165.86	0.876990	0.438495	+	0.898734i	$0.355512\pi$
$368$	−7219.91	−1.02273
$369$	−683.380	−0.0964102
$370$	−19289.7	−2.71034
$371$	−275.496	−0.0385526
$372$	−20340.8	−2.83500
$373$	−13214.6	−1.83438	−0.917191	−	0.398447i	$-0.869549\pi$
$373$	−13214.6	−1.83438	−0.917191	+	0.398447i	$0.869549\pi$
$374$	−7220.79	−0.998337
$375$	−10795.4	−1.48660
$376$	11561.1	1.58569
$377$	844.520	0.115371
$378$	−350.569	−0.0477020
$379$	−3031.81	−0.410907	−0.205453	−	0.978667i	$-0.565867\pi$
$379$	−3031.81	−0.410907	−0.205453	+	0.978667i	$0.565867\pi$
$380$	8269.35	1.11634
$381$	−2221.78	−0.298755
$382$	−3036.94	−0.406763
$383$	−345.297	−0.0460675	−0.0230337	−	0.999735i	$-0.507333\pi$
$383$	−345.297	−0.0460675	−0.0230337	+	0.999735i	$0.507333\pi$
$384$	−14651.5	−1.94708
$385$	−232.498	−0.0307771
$386$	−10326.6	−1.36169
$387$	0	0
$388$	−4658.25	−0.609502
$389$	1815.47	0.236628	0.118314	−	0.992976i	$-0.462251\pi$
$389$	1815.47	0.236628	0.118314	+	0.992976i	$0.462251\pi$
$390$	45009.1	5.84391
$391$	11746.8	1.51934
$392$	11602.7	1.49496
$393$	12087.4	1.55147
$394$	4156.70	0.531501
$395$	612.365	0.0780037
$396$	−1177.39	−0.149409
$397$	13316.0	1.68341	0.841704	−	0.539939i	$-0.181553\pi$
$397$	13316.0	1.68341	0.841704	+	0.539939i	$0.181553\pi$
$398$	22504.0	2.83423
$399$	−91.0072	−0.0114187
$400$	9643.60	1.20545
$401$	3895.31	0.485094	0.242547	−	0.970140i	$-0.422017\pi$
$401$	3895.31	0.485094	0.242547	+	0.970140i	$0.422017\pi$
$402$	−19473.8	−2.41608
$403$	22033.7	2.72352
$404$	4988.97	0.614383
$405$	−15284.4	−1.87528
$406$	−25.3505	−0.00309882
$407$	−4684.49	−0.570520
$408$	−12836.5	−1.55760
$409$	7160.50	0.865682	0.432841	−	0.901470i	$-0.357511\pi$
$409$	7160.50	0.865682	0.432841	+	0.901470i	$0.357511\pi$
$410$	17304.2	2.08437
$411$	−4589.17	−0.550771
$412$	2001.58	0.239347
$413$	180.312	0.0214833
$414$	2933.38	0.348232
$415$	−1386.06	−0.163949
$416$	6175.74	0.727862
$417$	10609.9	1.24597
$418$	3075.54	0.359879
$419$	−8139.57	−0.949032	−0.474516	−	0.880247i	$-0.657377\pi$
$419$	−8139.57	−0.949032	−0.474516	+	0.880247i	$0.657377\pi$
$420$	−882.190	−0.102492
$421$	4012.83	0.464545	0.232272	−	0.972651i	$-0.425384\pi$
$421$	4012.83	0.464545	0.232272	+	0.972651i	$0.425384\pi$
$422$	6947.80	0.801454
$423$	−1217.82	−0.139982
$424$	16550.9	1.89572
$425$	−15690.2	−1.79079
$426$	−11077.0	−1.25982
$427$	−28.8501	−0.00326969
$428$	−4119.24	−0.465212
$429$	10930.4	1.23013
$430$	0	0
$431$	4194.35	0.468758	0.234379	−	0.972145i	$-0.424694\pi$
$431$	4194.35	0.468758	0.234379	+	0.972145i	$0.424694\pi$
$432$	5460.42	0.608136
$433$	7807.78	0.866555	0.433277	−	0.901261i	$-0.357357\pi$
$433$	7807.78	0.866555	0.433277	+	0.901261i	$0.357357\pi$
$434$	−661.400	−0.0731526
$435$	−974.269	−0.107385
$436$	23942.2	2.62986
$437$	−5003.31	−0.547690
$438$	945.764	0.103174
$439$	−16558.6	−1.80022	−0.900112	−	0.435660i	$-0.856515\pi$
$439$	−16558.6	−1.80022	−0.900112	+	0.435660i	$0.856515\pi$
$440$	13967.8	1.51338
$441$	−1222.20	−0.131972
$442$	29678.9	3.19385
$443$	−13329.5	−1.42958	−0.714788	−	0.699341i	$-0.753477\pi$
$443$	−13329.5	−1.42958	−0.714788	+	0.699341i	$0.753477\pi$
$444$	−17774.8	−1.89990
$445$	−21223.4	−2.26087
$446$	26329.0	2.79533
$447$	−9348.44	−0.989185
$448$	−375.409	−0.0395902
$449$	−2475.47	−0.260189	−0.130094	−	0.991502i	$-0.541528\pi$
$449$	−2475.47	−0.260189	−0.130094	+	0.991502i	$0.541528\pi$
$450$	−3918.10	−0.410447
$451$	4202.31	0.438756
$452$	7297.47	0.759390
$453$	−5594.14	−0.580211
$454$	−30440.8	−3.14682
$455$	955.614	0.0984613
$456$	5467.43	0.561482
$457$	11342.0	1.16095	0.580477	−	0.814276i	$-0.302866\pi$
$457$	11342.0	1.16095	0.580477	+	0.814276i	$0.302866\pi$
$458$	24668.9	2.51682
$459$	−8884.13	−0.903433
$460$	−48500.2	−4.91594
$461$	−5072.43	−0.512465	−0.256233	−	0.966615i	$-0.582481\pi$
$461$	−5072.43	−0.512465	−0.256233	+	0.966615i	$0.582481\pi$
$462$	−328.105	−0.0330407
$463$	−13775.2	−1.38269	−0.691346	−	0.722524i	$-0.742982\pi$
$463$	−13775.2	−1.38269	−0.691346	+	0.722524i	$0.742982\pi$
$464$	394.856	0.0395059
$465$	−25418.9	−2.53500
$466$	18925.6	1.88135
$467$	11957.0	1.18481	0.592403	−	0.805642i	$-0.298179\pi$
$467$	11957.0	1.18481	0.592403	+	0.805642i	$0.298179\pi$
$468$	4839.30	0.477984
$469$	−413.459	−0.0407074
$470$	30836.9	3.02639
$471$	6838.73	0.669028
$472$	−10832.6	−1.05638
$473$	0	0
$474$	864.180	0.0837407
$475$	6682.89	0.645541
$476$	−581.715	−0.0560144
$477$	−1743.43	−0.167350
$478$	1766.53	0.169036
$479$	−15782.6	−1.50548	−0.752739	−	0.658319i	$-0.771268\pi$
$479$	−15782.6	−1.50548	−0.752739	+	0.658319i	$0.771268\pi$
$480$	−7124.56	−0.677479
$481$	19254.2	1.82519
$482$	−3899.21	−0.368473
$483$	533.763	0.0502837
$484$	−12794.1	−1.20155
$485$	−5821.20	−0.545004
$486$	−4774.70	−0.445647
$487$	2228.11	0.207321	0.103661	−	0.994613i	$-0.466944\pi$
$487$	2228.11	0.207321	0.103661	+	0.994613i	$0.466944\pi$
$488$	1733.23	0.160778
$489$	−5861.98	−0.542102
$490$	30947.8	2.85323
$491$	−8782.43	−0.807221	−0.403611	−	0.914931i	$-0.632245\pi$
$491$	−8782.43	−0.807221	−0.403611	+	0.914931i	$0.632245\pi$
$492$	15945.2	1.46111
$493$	−642.432	−0.0586890
$494$	−12641.1	−1.15132
$495$	−1471.32	−0.133598
$496$	10301.9	0.932597
$497$	−235.183	−0.0212261
$498$	−1956.03	−0.176008
$499$	680.761	0.0610722	0.0305361	−	0.999534i	$-0.490279\pi$
$499$	680.761	0.0610722	0.0305361	+	0.999534i	$0.490279\pi$
$500$	29390.8	2.62880
$501$	9099.74	0.811470
$502$	19129.4	1.70077
$503$	5406.14	0.479220	0.239610	−	0.970869i	$-0.422980\pi$
$503$	5406.14	0.479220	0.239610	+	0.970869i	$0.422980\pi$
$504$	−68.0577	−0.00601494
$505$	6234.48	0.549368
$506$	−18038.2	−1.58478
$507$	−32779.7	−2.87139
$508$	6048.86	0.528297
$509$	−21162.7	−1.84286	−0.921432	−	0.388539i	$-0.872980\pi$
$509$	−21162.7	−1.84286	−0.921432	+	0.388539i	$0.872980\pi$
$510$	−34238.7	−2.97278
$511$	20.0801	0.00173834
$512$	14303.8	1.23465
$513$	3784.00	0.325668
$514$	−14144.3	−1.21377
$515$	2501.29	0.214019
$516$	0	0
$517$	7488.71	0.637047
$518$	−577.966	−0.0490238
$519$	−16459.5	−1.39209
$520$	−57410.4	−4.84156
$521$	172.007	0.0144641	0.00723203	−	0.999974i	$-0.497698\pi$
$521$	172.007	0.0144641	0.00723203	+	0.999974i	$0.497698\pi$
$522$	−160.426	−0.0134515
$523$	6460.04	0.540111	0.270055	−	0.962845i	$-0.412958\pi$
$523$	6460.04	0.540111	0.270055	+	0.962845i	$0.412958\pi$
$524$	−32908.1	−2.74351
$525$	−712.944	−0.0592675
$526$	8766.15	0.726658
$527$	−16761.2	−1.38544
$528$	5110.52	0.421225
$529$	17177.7	1.41183
$530$	44146.2	3.61809
$531$	1141.08	0.0932552
$532$	247.769	0.0201920
$533$	−17272.3	−1.40366
$534$	−29950.8	−2.42715
$535$	−5147.62	−0.415983
$536$	24839.4	2.00167
$537$	−24.1574	−0.00194128
$538$	−16848.9	−1.35020
$539$	7515.65	0.600597
$540$	36680.7	2.92313
$541$	−8894.36	−0.706837	−0.353418	−	0.935465i	$-0.614981\pi$
$541$	−8894.36	−0.706837	−0.353418	+	0.935465i	$0.614981\pi$
$542$	39490.6	3.12964
$543$	−8766.21	−0.692806
$544$	−4697.92	−0.370261
$545$	29919.4	2.35157
$546$	1348.58	0.105703
$547$	7309.10	0.571325	0.285662	−	0.958330i	$-0.407786\pi$
$547$	7309.10	0.571325	0.285662	+	0.958330i	$0.407786\pi$
$548$	12494.1	0.973945
$549$	−182.573	−0.0141932
$550$	24093.6	1.86792
$551$	273.630	0.0211561
$552$	−32066.8	−2.47256
$553$	18.3479	0.00141091
$554$	6177.27	0.473731
$555$	−22212.4	−1.69885
$556$	−28885.6	−2.20328
$557$	−20239.8	−1.53965	−0.769826	−	0.638254i	$-0.779657\pi$
$557$	−20239.8	−1.53965	−0.769826	+	0.638254i	$0.779657\pi$
$558$	−4185.56	−0.317543
$559$	0	0
$560$	446.798	0.0337155
$561$	−8314.83	−0.625762
$562$	−23041.6	−1.72945
$563$	4935.99	0.369498	0.184749	−	0.982786i	$-0.440853\pi$
$563$	4935.99	0.369498	0.184749	+	0.982786i	$0.440853\pi$
$564$	28415.2	2.12144
$565$	9119.31	0.679031
$566$	−3805.87	−0.282637
$567$	−457.957	−0.0339195
$568$	14129.1	1.04374
$569$	10385.0	0.765132	0.382566	−	0.923928i	$-0.375040\pi$
$569$	10385.0	0.765132	0.382566	+	0.923928i	$0.375040\pi$
$570$	14583.2	1.07162
$571$	−8599.14	−0.630232	−0.315116	−	0.949053i	$-0.602043\pi$
$571$	−8599.14	−0.630232	−0.315116	+	0.949053i	$0.602043\pi$
$572$	−29758.3	−2.17527
$573$	−3497.08	−0.254961
$574$	518.475	0.0377016
$575$	−39195.6	−2.84273
$576$	−2375.71	−0.171854
$577$	14110.2	1.01805	0.509026	−	0.860751i	$-0.330006\pi$
$577$	14110.2	1.01805	0.509026	+	0.860751i	$0.330006\pi$
$578$	1011.59	0.0727972
$579$	−11891.3	−0.853513
$580$	2652.47	0.189893
$581$	−41.5296	−0.00296547
$582$	−8214.97	−0.585088
$583$	10720.9	0.761599
$584$	−1206.35	−0.0854778
$585$	6047.45	0.427404
$586$	−25092.1	−1.76885
$587$	5528.80	0.388753	0.194376	−	0.980927i	$-0.437732\pi$
$587$	5528.80	0.388753	0.194376	+	0.980927i	$0.437732\pi$
$588$	28517.4	2.00006
$589$	7139.07	0.499423
$590$	−28893.8	−2.01617
$591$	4786.49	0.333147
$592$	9002.32	0.624988
$593$	−14338.2	−0.992918	−0.496459	−	0.868060i	$-0.665367\pi$
$593$	−14338.2	−0.992918	−0.496459	+	0.868060i	$0.665367\pi$
$594$	13642.3	0.942343
$595$	−726.942	−0.0500869
$596$	25451.3	1.74921
$597$	25913.6	1.77651
$598$	74140.9	5.06998
$599$	17319.7	1.18141	0.590705	−	0.806888i	$-0.298850\pi$
$599$	17319.7	1.18141	0.590705	+	0.806888i	$0.298850\pi$
$600$	42831.5	2.91431
$601$	28433.6	1.92984	0.964918	−	0.262550i	$-0.0845633\pi$
$601$	28433.6	1.92984	0.964918	+	0.262550i	$0.0845633\pi$
$602$	0	0
$603$	−2616.51	−0.176704
$604$	15230.2	1.02600
$605$	−15988.2	−1.07440
$606$	8798.20	0.589773
$607$	6746.30	0.451110	0.225555	−	0.974230i	$-0.427580\pi$
$607$	6746.30	0.451110	0.225555	+	0.974230i	$0.427580\pi$
$608$	2000.98	0.133471
$609$	−29.1914	−0.00194236
$610$	4623.03	0.306854
$611$	−30780.2	−2.03802
$612$	−3681.29	−0.243149
$613$	−4756.54	−0.313401	−0.156701	−	0.987646i	$-0.550086\pi$
$613$	−4756.54	−0.313401	−0.156701	+	0.987646i	$0.550086\pi$
$614$	−26094.2	−1.71511
$615$	19926.0	1.30649
$616$	418.507	0.0273736
$617$	−13947.4	−0.910051	−0.455026	−	0.890478i	$-0.650370\pi$
$617$	−13947.4	−0.910051	−0.455026	+	0.890478i	$0.650370\pi$
$618$	3529.86	0.229760
$619$	10744.9	0.697699	0.348849	−	0.937179i	$-0.386572\pi$
$619$	10744.9	0.697699	0.348849	+	0.937179i	$0.386572\pi$
$620$	69203.5	4.48271
$621$	−22193.4	−1.43412
$622$	−2084.52	−0.134375
$623$	−635.903	−0.0408939
$624$	−21005.3	−1.34757
$625$	8127.28	0.520146
$626$	−34234.9	−2.18579
$627$	3541.52	0.225574
$628$	−18618.6	−1.18306
$629$	−14646.8	−0.928468
$630$	−181.530	−0.0114799
$631$	−8390.63	−0.529360	−0.264680	−	0.964336i	$-0.585266\pi$
$631$	−8390.63	−0.529360	−0.264680	+	0.964336i	$0.585266\pi$
$632$	−1102.29	−0.0693775
$633$	8000.48	0.502355
$634$	19048.6	1.19324
$635$	7558.97	0.472392
$636$	40679.2	2.53622
$637$	−30890.9	−1.92141
$638$	986.508	0.0612167
$639$	−1488.32	−0.0921390
$640$	49847.3	3.07873
$641$	−6432.67	−0.396373	−0.198187	−	0.980164i	$-0.563505\pi$
$641$	−6432.67	−0.396373	−0.198187	+	0.980164i	$0.563505\pi$
$642$	−7264.41	−0.446578
$643$	6600.52	0.404820	0.202410	−	0.979301i	$-0.435123\pi$
$643$	6600.52	0.404820	0.202410	+	0.979301i	$0.435123\pi$
$644$	−1453.18	−0.0889182
$645$	0	0
$646$	9616.17	0.585671
$647$	16454.6	0.999839	0.499920	−	0.866072i	$-0.333363\pi$
$647$	16454.6	0.999839	0.499920	+	0.866072i	$0.333363\pi$
$648$	27512.6	1.66790
$649$	−7016.82	−0.424398
$650$	−99029.6	−5.97579
$651$	−761.610	−0.0458523
$652$	15959.4	0.958615
$653$	22219.0	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$653$	22219.0	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$654$	42222.7	2.52452
$655$	−41123.7	−2.45318
$656$	−8075.70	−0.480645
$657$	127.073	0.00754582
$658$	923.947	0.0547404
$659$	−29368.5	−1.73601	−0.868007	−	0.496551i	$-0.834599\pi$
$659$	−29368.5	−1.73601	−0.868007	+	0.496551i	$0.834599\pi$
$660$	34330.2	2.02470
$661$	−16178.2	−0.951981	−0.475990	−	0.879451i	$-0.657910\pi$
$661$	−16178.2	−0.951981	−0.475990	+	0.879451i	$0.657910\pi$
$662$	14297.4	0.839405
$663$	34175.7	2.00192
$664$	2494.97	0.145819
$665$	309.625	0.0180553
$666$	−3657.56	−0.212804
$667$	−1604.86	−0.0931639
$668$	−24774.3	−1.43495
$669$	30318.2	1.75212
$670$	66253.9	3.82031
$671$	1122.70	0.0645920
$672$	−213.469	−0.0122541
$673$	−30064.0	−1.72197	−0.860983	−	0.508634i	$-0.830151\pi$
$673$	−30064.0	−1.72197	−0.860983	+	0.508634i	$0.830151\pi$
$674$	−16398.1	−0.937136
$675$	29643.6	1.69035
$676$	89243.4	5.07757
$677$	−27396.2	−1.55528	−0.777638	−	0.628713i	$-0.783582\pi$
$677$	−27396.2	−1.55528	−0.777638	+	0.628713i	$0.783582\pi$
$678$	12869.3	0.728972
$679$	−174.417	−0.00985788
$680$	43672.4	2.46288
$681$	−35053.0	−1.97244
$682$	25738.2	1.44511
$683$	−27000.7	−1.51267	−0.756335	−	0.654185i	$-0.773012\pi$
$683$	−27000.7	−1.51267	−0.756335	+	0.654185i	$0.773012\pi$
$684$	1567.97	0.0876501
$685$	15613.3	0.870881
$686$	1855.40	0.103265
$687$	28406.6	1.57755
$688$	0	0
$689$	−44064.9	−2.43649
$690$	−85531.6	−4.71903
$691$	−20353.7	−1.12054	−0.560270	−	0.828310i	$-0.689303\pi$
$691$	−20353.7	−1.12054	−0.560270	+	0.828310i	$0.689303\pi$
$692$	44811.4	2.46167
$693$	−44.0843	−0.00241649
$694$	21607.1	1.18184
$695$	−36097.0	−1.97013
$696$	1753.73	0.0955100
$697$	13139.2	0.714035
$698$	3584.61	0.194383
$699$	21793.0	1.17924
$700$	1941.01	0.104804
$701$	−12725.1	−0.685622	−0.342811	−	0.939404i	$-0.611379\pi$
$701$	−12725.1	−0.685622	−0.342811	+	0.939404i	$0.611379\pi$
$702$	−56072.8	−3.01472
$703$	6238.49	0.334693
$704$	14608.9	0.782096
$705$	35509.1	1.89695
$706$	−41648.0	−2.22018
$707$	186.800	0.00993681
$708$	−26624.6	−1.41330
$709$	−29784.5	−1.57769	−0.788843	−	0.614595i	$-0.789320\pi$
$709$	−29784.5	−1.57769	−0.788843	+	0.614595i	$0.789320\pi$
$710$	37686.4	1.99203
$711$	116.112	0.00612451
$712$	38203.1	2.01085
$713$	−41871.1	−2.19928
$714$	−1025.87	−0.0537707
$715$	−37187.5	−1.94508
$716$	65.7689	0.00343282
$717$	2034.18	0.105952
$718$	31699.4	1.64765
$719$	−26156.8	−1.35673	−0.678363	−	0.734727i	$-0.737310\pi$
$719$	−26156.8	−1.35673	−0.678363	+	0.734727i	$0.737310\pi$
$720$	2827.49	0.146353
$721$	74.9444	0.00387112
$722$	28836.0	1.48638
$723$	−4489.99	−0.230961
$724$	23866.2	1.22511
$725$	2143.60	0.109809
$726$	−22562.9	−1.15342
$727$	−13708.6	−0.699346	−0.349673	−	0.936872i	$-0.613707\pi$
$727$	−13708.6	−0.699346	−0.349673	+	0.936872i	$0.613707\pi$
$728$	−1720.15	−0.0875728
$729$	16441.4	0.835312
$730$	−3217.69	−0.163140
$731$	0	0
$732$	4259.96	0.215099
$733$	−19482.8	−0.981736	−0.490868	−	0.871234i	$-0.663320\pi$
$733$	−19482.8	−0.981736	−0.490868	+	0.871234i	$0.663320\pi$
$734$	−29603.8	−1.48869
$735$	35636.8	1.78841
$736$	−11735.9	−0.587758
$737$	16089.7	0.804167
$738$	3281.08	0.163656
$739$	9397.10	0.467764	0.233882	−	0.972265i	$-0.424857\pi$
$739$	9397.10	0.467764	0.233882	+	0.972265i	$0.424857\pi$
$740$	60473.7	3.00413
$741$	−14556.4	−0.721650
$742$	1322.72	0.0654430
$743$	21996.2	1.08609	0.543044	−	0.839705i	$-0.317272\pi$
$743$	21996.2	1.08609	0.543044	+	0.839705i	$0.317272\pi$
$744$	45755.2	2.25466
$745$	31805.3	1.56410
$746$	63446.5	3.11386
$747$	−262.813	−0.0128726
$748$	22637.3	1.10655
$749$	−154.235	−0.00752419
$750$	51831.6	2.52350
$751$	26869.9	1.30559	0.652795	−	0.757534i	$-0.273596\pi$
$751$	26869.9	1.30559	0.652795	+	0.757534i	$0.273596\pi$
$752$	−14391.3	−0.697867
$753$	22027.8	1.06605
$754$	−4054.75	−0.195843
$755$	19032.4	0.917431
$756$	1099.04	0.0528727
$757$	−1187.31	−0.0570058	−0.0285029	−	0.999594i	$-0.509074\pi$
$757$	−1187.31	−0.0570058	−0.0285029	+	0.999594i	$0.509074\pi$
$758$	14556.5	0.697514
$759$	−20771.3	−0.993345
$760$	−18601.3	−0.887818
$761$	−3960.08	−0.188637	−0.0943185	−	0.995542i	$-0.530067\pi$
$761$	−3960.08	−0.188637	−0.0943185	+	0.995542i	$0.530067\pi$
$762$	10667.3	0.507135
$763$	896.455	0.0425345
$764$	9520.88	0.450855
$765$	−4600.33	−0.217419
$766$	1657.86	0.0781995
$767$	28840.6	1.35772
$768$	40883.7	1.92092
$769$	−18342.9	−0.860157	−0.430079	−	0.902791i	$-0.641514\pi$
$769$	−18342.9	−0.860157	−0.430079	+	0.902791i	$0.641514\pi$
$770$	1116.28	0.0522441
$771$	−16287.3	−0.760796
$772$	32374.2	1.50929
$773$	10523.7	0.489667	0.244834	−	0.969565i	$-0.421267\pi$
$773$	10523.7	0.489667	0.244834	+	0.969565i	$0.421267\pi$
$774$	0	0
$775$	55927.0	2.59220
$776$	10478.4	0.484734
$777$	−665.535	−0.0307284
$778$	−8716.55	−0.401675
$779$	−5596.36	−0.257394
$780$	−141104.	−6.47737
$781$	9152.09	0.419318
$782$	−56399.4	−2.57908
$783$	1213.75	0.0553973
$784$	−14443.0	−0.657938
$785$	−23266.8	−1.05787
$786$	−58034.4	−2.63361
$787$	1362.84	0.0617281	0.0308641	−	0.999524i	$-0.490174\pi$
$787$	1362.84	0.0617281	0.0308641	+	0.999524i	$0.490174\pi$
$788$	−13031.3	−0.589114
$789$	10094.3	0.455473
$790$	−2940.12	−0.132411
$791$	273.236	0.0122821
$792$	2648.45	0.118824
$793$	−4614.52	−0.206641
$794$	−63933.7	−2.85758
$795$	50834.9	2.26783
$796$	−70550.4	−3.14145
$797$	−30311.6	−1.34717	−0.673584	−	0.739111i	$-0.735246\pi$
$797$	−30311.6	−1.34717	−0.673584	+	0.739111i	$0.735246\pi$
$798$	436.948	0.0193832
$799$	23414.7	1.03673
$800$	15675.5	0.692768
$801$	−4024.21	−0.177514
$802$	−18702.4	−0.823446
$803$	−781.411	−0.0343405
$804$	61050.7	2.67797
$805$	−1815.97	−0.0795088
$806$	−105789.	−4.62317
$807$	−19401.7	−0.846309
$808$	−11222.4	−0.488615
$809$	39233.5	1.70504	0.852520	−	0.522694i	$-0.175073\pi$
$809$	39233.5	1.70504	0.852520	+	0.522694i	$0.175073\pi$
$810$	73384.3	3.18328
$811$	−43510.5	−1.88392	−0.941961	−	0.335723i	$-0.891019\pi$
$811$	−43510.5	−1.88392	−0.941961	+	0.335723i	$0.891019\pi$
$812$	79.4742	0.00343473
$813$	45473.9	1.96167
$814$	22491.4	0.968456
$815$	19943.7	0.857174
$816$	15978.9	0.685505
$817$	0	0
$818$	−34379.4	−1.46949
$819$	181.196	0.00773076
$820$	−54249.0	−2.31031
$821$	−20770.7	−0.882951	−0.441475	−	0.897273i	$-0.645545\pi$
$821$	−20770.7	−0.882951	−0.441475	+	0.897273i	$0.645545\pi$
$822$	22033.7	0.934933
$823$	−15244.0	−0.645652	−0.322826	−	0.946458i	$-0.604633\pi$
$823$	−15244.0	−0.645652	−0.322826	+	0.946458i	$0.604633\pi$
$824$	−4502.43	−0.190351
$825$	27744.1	1.17082
$826$	−865.725	−0.0364678
$827$	−32831.8	−1.38050	−0.690251	−	0.723570i	$-0.742500\pi$
$827$	−32831.8	−1.38050	−0.690251	+	0.723570i	$0.742500\pi$
$828$	−9196.21	−0.385979
$829$	20720.4	0.868092	0.434046	−	0.900891i	$-0.357086\pi$
$829$	20720.4	0.868092	0.434046	+	0.900891i	$0.357086\pi$
$830$	6654.82	0.278304
$831$	7113.21	0.296937
$832$	−60045.8	−2.50206
$833$	23498.9	0.977417
$834$	−50940.7	−2.11503
$835$	−30959.2	−1.28310
$836$	−9641.88	−0.398889
$837$	31667.1	1.30774
$838$	39080.1	1.61098
$839$	−45367.8	−1.86683	−0.933415	−	0.358799i	$-0.883186\pi$
$839$	−45367.8	−1.86683	−0.933415	+	0.358799i	$0.883186\pi$
$840$	1984.43	0.0815110
$841$	−24301.2	−0.996401
$842$	−19266.6	−0.788564
$843$	−26532.7	−1.08403
$844$	−21781.5	−0.888329
$845$	111523.	4.54026
$846$	5847.04	0.237619
$847$	−479.045	−0.0194335
$848$	−20602.6	−0.834311
$849$	−4382.50	−0.177158
$850$	75332.5	3.03986
$851$	−36589.1	−1.47387
$852$	34726.7	1.39638
$853$	9272.95	0.372216	0.186108	−	0.982529i	$-0.440413\pi$
$853$	9272.95	0.372216	0.186108	+	0.982529i	$0.440413\pi$
$854$	138.517	0.00555029
$855$	1959.41	0.0783748
$856$	9265.95	0.369981
$857$	8958.78	0.357090	0.178545	−	0.983932i	$-0.442861\pi$
$857$	8958.78	0.357090	0.178545	+	0.983932i	$0.442861\pi$
$858$	−52479.6	−2.08814
$859$	−3992.34	−0.158576	−0.0792880	−	0.996852i	$-0.525265\pi$
$859$	−3992.34	−0.158576	−0.0792880	+	0.996852i	$0.525265\pi$
$860$	0	0
$861$	597.030	0.0236315
$862$	−20138.1	−0.795717
$863$	25382.8	1.00121	0.500603	−	0.865677i	$-0.333112\pi$
$863$	25382.8	1.00121	0.500603	+	0.865677i	$0.333112\pi$
$864$	8875.85	0.349494
$865$	55998.7	2.20117
$866$	−37487.1	−1.47098
$867$	1164.86	0.0456296
$868$	2073.50	0.0810820
$869$	−714.005	−0.0278722
$870$	4677.71	0.182287
$871$	−66131.9	−2.57267
$872$	−53856.3	−2.09152
$873$	−1103.77	−0.0427914
$874$	24022.1	0.929704
$875$	1100.47	0.0425172
$876$	−2964.99	−0.114358
$877$	−34007.1	−1.30940	−0.654698	−	0.755891i	$-0.727204\pi$
$877$	−34007.1	−1.30940	−0.654698	+	0.755891i	$0.727204\pi$
$878$	79501.9	3.05588
$879$	−28893.8	−1.10872
$880$	−17387.0	−0.666042
$881$	−34430.4	−1.31667	−0.658337	−	0.752723i	$-0.728740\pi$
$881$	−34430.4	−1.31667	−0.658337	+	0.752723i	$0.728740\pi$
$882$	5868.07	0.224023
$883$	−4762.11	−0.181492	−0.0907461	−	0.995874i	$-0.528925\pi$
$883$	−4762.11	−0.181492	−0.0907461	+	0.995874i	$0.528925\pi$
$884$	−93044.0	−3.54006
$885$	−33271.6	−1.26374
$886$	63998.2	2.42670
$887$	42087.0	1.59317	0.796587	−	0.604524i	$-0.206637\pi$
$887$	42087.0	1.59317	0.796587	+	0.604524i	$0.206637\pi$
$888$	39983.3	1.51098
$889$	226.485	0.00854449
$890$	101899.	3.83782
$891$	17821.3	0.670074
$892$	−82542.1	−3.09833
$893$	−9972.97	−0.373721
$894$	44884.2	1.67914
$895$	82.1884	0.00306956
$896$	1493.54	0.0556873
$897$	85374.2	3.17788
$898$	11885.4	0.441670
$899$	2289.92	0.0849536
$900$	12283.3	0.454938
$901$	33520.5	1.23943
$902$	−20176.3	−0.744787
$903$	0	0
$904$	−16415.2	−0.603939
$905$	29824.5	1.09547
$906$	26858.9	0.984907
$907$	−25450.7	−0.931726	−0.465863	−	0.884857i	$-0.654256\pi$
$907$	−25450.7	−0.931726	−0.465863	+	0.884857i	$0.654256\pi$
$908$	95432.5	3.48793
$909$	1182.13	0.0431340
$910$	−4588.14	−0.167138
$911$	19434.6	0.706804	0.353402	−	0.935472i	$-0.385025\pi$
$911$	19434.6	0.706804	0.353402	+	0.935472i	$0.385025\pi$
$912$	−6805.85	−0.247110
$913$	1616.11	0.0585822
$914$	−54455.8	−1.97072
$915$	5323.48	0.192337
$916$	−77337.6	−2.78963
$917$	−1232.16	−0.0443725
$918$	42654.9	1.53358
$919$	479.135	0.0171983	0.00859913	−	0.999963i	$-0.497263\pi$
$919$	479.135	0.0171983	0.00859913	+	0.999963i	$0.497263\pi$
$920$	109098.	3.90962
$921$	−30047.8	−1.07504
$922$	24354.0	0.869909
$923$	−37617.0	−1.34147
$924$	1028.61	0.0366222
$925$	48872.0	1.73719
$926$	66138.0	2.34712
$927$	474.273	0.0168039
$928$	641.833	0.0227039
$929$	−8375.21	−0.295782	−0.147891	−	0.989004i	$-0.547249\pi$
$929$	−8375.21	−0.295782	−0.147891	+	0.989004i	$0.547249\pi$
$930$	122043.	4.30316
$931$	−10008.8	−0.352338
$932$	−59332.1	−2.08529
$933$	−2400.35	−0.0842271
$934$	−57408.6	−2.01121
$935$	28288.8	0.989457
$936$	−10885.7	−0.380138
$937$	−15853.9	−0.552746	−0.276373	−	0.961050i	$-0.589133\pi$
$937$	−15853.9	−0.552746	−0.276373	+	0.961050i	$0.589133\pi$
$938$	1985.12	0.0691008
$939$	−39422.0	−1.37006
$940$	−96674.3	−3.35444
$941$	−2647.73	−0.0917253	−0.0458626	−	0.998948i	$-0.514604\pi$
$941$	−2647.73	−0.0917253	−0.0458626	+	0.998948i	$0.514604\pi$
$942$	−32834.5	−1.13567
$943$	32823.0	1.13347
$944$	13484.4	0.464916
$945$	1373.42	0.0472776
$946$	0	0
$947$	−27521.2	−0.944369	−0.472185	−	0.881500i	$-0.656534\pi$
$947$	−27521.2	−0.944369	−0.472185	+	0.881500i	$0.656534\pi$
$948$	−2709.22	−0.0928179
$949$	3211.76	0.109861
$950$	−32086.3	−1.09581
$951$	21934.7	0.747930
$952$	1308.53	0.0445480
$953$	−49753.8	−1.69117	−0.845585	−	0.533842i	$-0.820748\pi$
$953$	−49753.8	−1.69117	−0.845585	+	0.533842i	$0.820748\pi$
$954$	8370.64	0.284077
$955$	11897.8	0.403145
$956$	−5538.11	−0.187359
$957$	1135.98	0.0383709
$958$	75776.1	2.55555
$959$	467.811	0.0157523
$960$	69271.0	2.32887
$961$	29953.7	1.00546
$962$	−92444.3	−3.09826
$963$	−976.049	−0.0326612
$964$	12224.1	0.408415
$965$	40456.5	1.34958
$966$	−2562.73	−0.0853566
$967$	52924.4	1.76002	0.880008	−	0.474960i	$-0.157537\pi$
$967$	52924.4	1.76002	0.880008	+	0.474960i	$0.157537\pi$
$968$	28779.6	0.955589
$969$	11073.1	0.367101
$970$	27949.0	0.925144
$971$	40927.9	1.35267	0.676333	−	0.736596i	$-0.263568\pi$
$971$	40927.9	1.35267	0.676333	+	0.736596i	$0.263568\pi$
$972$	14968.8	0.493954
$973$	−1081.55	−0.0356351
$974$	−10697.7	−0.351928
$975$	−114034.	−3.74565
$976$	−2157.52	−0.0707588
$977$	43543.0	1.42586	0.712930	−	0.701236i	$-0.247368\pi$
$977$	43543.0	1.42586	0.712930	+	0.701236i	$0.247368\pi$
$978$	28144.8	0.920218
$979$	24746.0	0.807852
$980$	−97022.1	−3.16251
$981$	5673.07	0.184635
$982$	42166.7	1.37026
$983$	−46016.6	−1.49309	−0.746543	−	0.665337i	$-0.768288\pi$
$983$	−46016.6	−1.49309	−0.746543	+	0.665337i	$0.768288\pi$
$984$	−35867.7	−1.16201
$985$	−16284.6	−0.526774
$986$	3084.48	0.0996245
$987$	1063.94	0.0343115
$988$	39630.1	1.27612
$989$	0	0
$990$	7064.19	0.226783
$991$	−42967.2	−1.37729	−0.688646	−	0.725098i	$-0.741795\pi$
$991$	−42967.2	−1.37729	−0.688646	+	0.725098i	$0.741795\pi$
$992$	16745.6	0.535960
$993$	16463.7	0.526143
$994$	1129.17	0.0360313
$995$	−88163.5	−2.80902
$996$	6132.19	0.195086
$997$	−43345.3	−1.37689	−0.688445	−	0.725288i	$-0.741706\pi$
$997$	−43345.3	−1.37689	−0.688445	+	0.725288i	$0.741706\pi$
$998$	−3268.50	−0.103670
$999$	27672.4	0.876392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.6	✓	50
43.42	odd	2		1849.4.a.j.1.45	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.6	✓	50	1.1	even	1	trivial
1849.4.a.j.1.45	yes	50	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} +O(q^{10})\)	\(q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} -90.3106 q^{10} -21.9318 q^{11} -83.2181 q^{12} +90.1443 q^{13} -2.70592 q^{14} -103.994 q^{15} +42.1470 q^{16} -68.5734 q^{17} -17.1239 q^{18} +29.2074 q^{19} +283.125 q^{20} -3.11590 q^{21} +105.300 q^{22} -171.303 q^{23} +187.194 q^{24} +228.809 q^{25} -432.806 q^{26} +129.557 q^{27} +8.48310 q^{28} +9.36853 q^{29} +499.300 q^{30} +244.427 q^{31} +68.5095 q^{32} +121.255 q^{33} +329.238 q^{34} +10.6009 q^{35} +53.6839 q^{36} +213.593 q^{37} -140.232 q^{38} -498.381 q^{39} -636.872 q^{40} -191.608 q^{41} +14.9602 q^{42} -330.118 q^{44} +67.0863 q^{45} +822.469 q^{46} -341.454 q^{47} -233.018 q^{48} -342.682 q^{49} -1098.57 q^{50} +379.122 q^{51} +1356.85 q^{52} -488.826 q^{53} -622.034 q^{54} -412.533 q^{55} -19.0822 q^{56} -161.479 q^{57} -44.9807 q^{58} +319.938 q^{59} -1565.32 q^{60} -51.1903 q^{61} -1173.56 q^{62} +2.01006 q^{63} -666.107 q^{64} +1695.60 q^{65} -582.173 q^{66} -733.622 q^{67} -1032.17 q^{68} +947.083 q^{69} -50.8978 q^{70} -417.297 q^{71} -120.758 q^{72} +35.6291 q^{73} -1025.51 q^{74} -1265.01 q^{75} +439.630 q^{76} -12.3605 q^{77} +2392.85 q^{78} +32.5557 q^{79} +792.777 q^{80} -812.577 q^{81} +919.957 q^{82} -73.6881 q^{83} -46.9006 q^{84} -1289.85 q^{85} -51.7958 q^{87} +742.578 q^{88} -1128.32 q^{89} -322.098 q^{90} +50.8041 q^{91} -2578.45 q^{92} -1351.37 q^{93} +1639.41 q^{94} +549.385 q^{95} -378.768 q^{96} -309.477 q^{97} +1645.30 q^{98} -78.2211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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