LMFDB - Embedded newform 1849.4.a.i.1.9

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			1.9
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)

$f(q)$	$=$	$q-3.90499 q^{2} +3.52020 q^{3} +7.24897 q^{4} -10.7056 q^{5} -13.7464 q^{6} +28.1424 q^{7} +2.93275 q^{8} -14.6082 q^{9} +O(q^{10})$	\(q-3.90499 q^{2} +3.52020 q^{3} +7.24897 q^{4} -10.7056 q^{5} -13.7464 q^{6} +28.1424 q^{7} +2.93275 q^{8} -14.6082 q^{9} +41.8054 q^{10} +63.0835 q^{11} +25.5179 q^{12} -23.3564 q^{13} -109.896 q^{14} -37.6860 q^{15} -69.4442 q^{16} +49.0078 q^{17} +57.0448 q^{18} -57.3067 q^{19} -77.6048 q^{20} +99.0669 q^{21} -246.341 q^{22} +137.960 q^{23} +10.3239 q^{24} -10.3896 q^{25} +91.2066 q^{26} -146.469 q^{27} +204.003 q^{28} -129.150 q^{29} +147.164 q^{30} -69.2254 q^{31} +247.717 q^{32} +222.067 q^{33} -191.375 q^{34} -301.282 q^{35} -105.894 q^{36} +51.1938 q^{37} +223.782 q^{38} -82.2194 q^{39} -31.3969 q^{40} -179.964 q^{41} -386.856 q^{42} +457.291 q^{44} +156.389 q^{45} -538.732 q^{46} -432.101 q^{47} -244.458 q^{48} +448.993 q^{49} +40.5715 q^{50} +172.517 q^{51} -169.310 q^{52} -753.298 q^{53} +571.961 q^{54} -675.348 q^{55} +82.5346 q^{56} -201.731 q^{57} +504.330 q^{58} -845.732 q^{59} -273.185 q^{60} +156.589 q^{61} +270.325 q^{62} -411.108 q^{63} -411.780 q^{64} +250.045 q^{65} -867.170 q^{66} +618.378 q^{67} +355.256 q^{68} +485.647 q^{69} +1176.50 q^{70} +723.463 q^{71} -42.8421 q^{72} +315.462 q^{73} -199.912 q^{74} -36.5737 q^{75} -415.415 q^{76} +1775.32 q^{77} +321.066 q^{78} -1029.04 q^{79} +743.443 q^{80} -121.181 q^{81} +702.757 q^{82} -587.747 q^{83} +718.134 q^{84} -524.659 q^{85} -454.635 q^{87} +185.008 q^{88} +1076.10 q^{89} -610.700 q^{90} -657.305 q^{91} +1000.07 q^{92} -243.688 q^{93} +1687.35 q^{94} +613.504 q^{95} +872.015 q^{96} -402.331 q^{97} -1753.32 q^{98} -921.534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.90499	−1.38062	−0.690312	−	0.723512i	$-0.742527\pi$
$2$	−3.90499	−1.38062	−0.690312	+	0.723512i	$0.742527\pi$
$3$	3.52020	0.677464	0.338732	−	0.940883i	$-0.390002\pi$
$3$	3.52020	0.677464	0.338732	+	0.940883i	$0.390002\pi$
$4$	7.24897	0.906122
$5$	−10.7056	−0.957540	−0.478770	−	0.877940i	$-0.658917\pi$
$5$	−10.7056	−0.957540	−0.478770	+	0.877940i	$0.658917\pi$
$6$	−13.7464	−0.935322
$7$	28.1424	1.51955	0.759773	−	0.650189i	$-0.225310\pi$
$7$	28.1424	1.51955	0.759773	+	0.650189i	$0.225310\pi$
$8$	2.93275	0.129611
$9$	−14.6082	−0.541043
$10$	41.8054	1.32200
$11$	63.0835	1.72913	0.864563	−	0.502524i	$-0.167595\pi$
$11$	63.0835	1.72913	0.864563	+	0.502524i	$0.167595\pi$
$12$	25.5179	0.613865
$13$	−23.3564	−0.498300	−0.249150	−	0.968465i	$-0.580151\pi$
$13$	−23.3564	−0.498300	−0.249150	+	0.968465i	$0.580151\pi$
$14$	−109.896	−2.09792
$15$	−37.6860	−0.648699
$16$	−69.4442	−1.08507
$17$	49.0078	0.699184	0.349592	−	0.936902i	$-0.386320\pi$
$17$	49.0078	0.699184	0.349592	+	0.936902i	$0.386320\pi$
$18$	57.0448	0.746977
$19$	−57.3067	−0.691950	−0.345975	−	0.938244i	$-0.612452\pi$
$19$	−57.3067	−0.691950	−0.345975	+	0.938244i	$0.612452\pi$
$20$	−77.6048	−0.867648
$21$	99.0669	1.02944
$22$	−246.341	−2.38727
$23$	137.960	1.25072	0.625361	−	0.780336i	$-0.284952\pi$
$23$	137.960	1.25072	0.625361	+	0.780336i	$0.284952\pi$
$24$	10.3239	0.0878064
$25$	−10.3896	−0.0831171
$26$	91.2066	0.687965
$27$	−146.469	−1.04400
$28$	204.003	1.37689
$29$	−129.150	−0.826985	−0.413493	−	0.910508i	$-0.635691\pi$
$29$	−129.150	−0.826985	−0.413493	+	0.910508i	$0.635691\pi$
$30$	147.164	0.895609
$31$	−69.2254	−0.401072	−0.200536	−	0.979686i	$-0.564268\pi$
$31$	−69.2254	−0.401072	−0.200536	+	0.979686i	$0.564268\pi$
$32$	247.717	1.36846
$33$	222.067	1.17142
$34$	−191.375	−0.965310
$35$	−301.282	−1.45503
$36$	−105.894	−0.490251
$37$	51.1938	0.227465	0.113733	−	0.993511i	$-0.463719\pi$
$37$	51.1938	0.227465	0.113733	+	0.993511i	$0.463719\pi$
$38$	223.782	0.955323
$39$	−82.2194	−0.337580
$40$	−31.3969	−0.124107
$41$	−179.964	−0.685503	−0.342751	−	0.939426i	$-0.611359\pi$
$41$	−179.964	−0.685503	−0.342751	+	0.939426i	$0.611359\pi$
$42$	−386.856	−1.42127
$43$	0	0
$43$	0	0
$44$	457.291	1.56680
$45$	156.389	0.518070
$46$	−538.732	−1.72678
$47$	−432.101	−1.34103	−0.670515	−	0.741896i	$-0.733927\pi$
$47$	−432.101	−1.34103	−0.670515	+	0.741896i	$0.733927\pi$
$48$	−244.458	−0.735092
$49$	448.993	1.30902
$50$	40.5715	0.114753
$51$	172.517	0.473672
$52$	−169.310	−0.451521
$53$	−753.298	−1.95233	−0.976164	−	0.217033i	$-0.930362\pi$
$53$	−753.298	−1.95233	−0.976164	+	0.217033i	$0.930362\pi$
$54$	571.961	1.44137
$55$	−675.348	−1.65571
$56$	82.5346	0.196949
$57$	−201.731	−0.468771
$58$	504.330	1.14176
$59$	−845.732	−1.86619	−0.933093	−	0.359635i	$-0.882901\pi$
$59$	−845.732	−1.86619	−0.933093	+	0.359635i	$0.882901\pi$
$60$	−273.185	−0.587800
$61$	156.589	0.328676	0.164338	−	0.986404i	$-0.447451\pi$
$61$	156.589	0.328676	0.164338	+	0.986404i	$0.447451\pi$
$62$	270.325	0.553730
$63$	−411.108	−0.822139
$64$	−411.780	−0.804258
$65$	250.045	0.477142
$66$	−867.170	−1.61729
$67$	618.378	1.12757	0.563783	−	0.825923i	$-0.309345\pi$
$67$	618.378	1.12757	0.563783	+	0.825923i	$0.309345\pi$
$68$	355.256	0.633546
$69$	485.647	0.847318
$70$	1176.50	2.00884
$71$	723.463	1.20928	0.604642	−	0.796497i	$-0.293316\pi$
$71$	723.463	1.20928	0.604642	+	0.796497i	$0.293316\pi$
$72$	−42.8421	−0.0701249
$73$	315.462	0.505781	0.252890	−	0.967495i	$-0.418619\pi$
$73$	315.462	0.505781	0.252890	+	0.967495i	$0.418619\pi$
$74$	−199.912	−0.314044
$75$	−36.5737	−0.0563088
$76$	−415.415	−0.626991
$77$	1775.32	2.62749
$78$	321.066	0.466071
$79$	−1029.04	−1.46552	−0.732760	−	0.680487i	$-0.761768\pi$
$79$	−1029.04	−1.46552	−0.732760	+	0.680487i	$0.761768\pi$
$80$	743.443	1.03899
$81$	−121.181	−0.166230
$82$	702.757	0.946421
$83$	−587.747	−0.777272	−0.388636	−	0.921391i	$-0.627054\pi$
$83$	−587.747	−0.777272	−0.388636	+	0.921391i	$0.627054\pi$
$84$	718.134	0.932795
$85$	−524.659	−0.669497
$86$	0	0
$87$	−454.635	−0.560252
$88$	185.008	0.224113
$89$	1076.10	1.28165	0.640823	−	0.767689i	$-0.278593\pi$
$89$	1076.10	1.28165	0.640823	+	0.767689i	$0.278593\pi$
$90$	−610.700	−0.715260
$91$	−657.305	−0.757190
$92$	1000.07	1.13331
$93$	−243.688	−0.271712
$94$	1687.35	1.85146
$95$	613.504	0.662570
$96$	872.015	0.927079
$97$	−402.331	−0.421139	−0.210570	−	0.977579i	$-0.567532\pi$
$97$	−402.331	−0.421139	−0.210570	+	0.977579i	$0.567532\pi$
$98$	−1753.32	−1.80726
$99$	−921.534	−0.935532
$100$	−75.3142	−0.0753142
$101$	−67.5492	−0.0665485	−0.0332743	−	0.999446i	$-0.510593\pi$
$101$	−67.5492	−0.0665485	−0.0332743	+	0.999446i	$0.510593\pi$
$102$	−673.679	−0.653962
$103$	−352.283	−0.337005	−0.168502	−	0.985701i	$-0.553893\pi$
$103$	−352.283	−0.337005	−0.168502	+	0.985701i	$0.553893\pi$
$104$	−68.4986	−0.0645850
$105$	−1060.57	−0.985727
$106$	2941.62	2.69543
$107$	1370.03	1.23781	0.618907	−	0.785464i	$-0.287576\pi$
$107$	1370.03	1.23781	0.618907	+	0.785464i	$0.287576\pi$
$108$	−1061.75	−0.945992
$109$	−430.759	−0.378525	−0.189262	−	0.981927i	$-0.560610\pi$
$109$	−430.759	−0.378525	−0.189262	+	0.981927i	$0.560610\pi$
$110$	2637.23	2.28591
$111$	180.213	0.154100
$112$	−1954.32	−1.64881
$113$	−670.846	−0.558477	−0.279238	−	0.960222i	$-0.590082\pi$
$113$	−670.846	−0.558477	−0.279238	+	0.960222i	$0.590082\pi$
$114$	787.759	0.647197
$115$	−1476.94	−1.19762
$116$	−936.206	−0.749349
$117$	341.194	0.269602
$118$	3302.58	2.57650
$119$	1379.19	1.06244
$120$	−110.524	−0.0840782
$121$	2648.53	1.98988
$122$	−611.480	−0.453777
$123$	−633.509	−0.464403
$124$	−501.813	−0.363420
$125$	1449.43	1.03713
$126$	1605.38	1.13507
$127$	−2571.14	−1.79647	−0.898237	−	0.439512i	$-0.855151\pi$
$127$	−2571.14	−1.79647	−0.898237	+	0.439512i	$0.855151\pi$
$128$	−373.738	−0.258079
$129$	0	0
$130$	−976.424	−0.658754
$131$	−1438.60	−0.959476	−0.479738	−	0.877412i	$-0.659268\pi$
$131$	−1438.60	−0.959476	−0.479738	+	0.877412i	$0.659268\pi$
$132$	1609.76	1.06145
$133$	−1612.75	−1.05145
$134$	−2414.76	−1.55674
$135$	1568.04	0.999672
$136$	143.728	0.0906216
$137$	−1790.29	−1.11646	−0.558230	−	0.829686i	$-0.688519\pi$
$137$	−1790.29	−1.11646	−0.558230	+	0.829686i	$0.688519\pi$
$138$	−1896.45	−1.16983
$139$	2724.94	1.66278	0.831390	−	0.555689i	$-0.187546\pi$
$139$	2724.94	1.66278	0.831390	+	0.555689i	$0.187546\pi$
$140$	−2183.98	−1.31843
$141$	−1521.08	−0.908499
$142$	−2825.12	−1.66957
$143$	−1473.40	−0.861624
$144$	1014.45	0.587067
$145$	1382.63	0.791871
$146$	−1231.88	−0.698293
$147$	1580.55	0.886813
$148$	371.103	0.206111
$149$	−1234.42	−0.678711	−0.339355	−	0.940658i	$-0.610209\pi$
$149$	−1234.42	−0.678711	−0.339355	+	0.940658i	$0.610209\pi$
$150$	142.820	0.0777413
$151$	863.120	0.465164	0.232582	−	0.972577i	$-0.425283\pi$
$151$	863.120	0.465164	0.232582	+	0.972577i	$0.425283\pi$
$152$	−168.066	−0.0896840
$153$	−715.913	−0.378288
$154$	−6932.61	−3.62757
$155$	741.101	0.384043
$156$	−596.006	−0.305889
$157$	−33.1386	−0.0168455	−0.00842276	−	0.999965i	$-0.502681\pi$
$157$	−33.1386	−0.0168455	−0.00842276	+	0.999965i	$0.502681\pi$
$158$	4018.40	2.02333
$159$	−2651.76	−1.32263
$160$	−2651.96	−1.31035
$161$	3882.52	1.90053
$162$	473.213	0.229501
$163$	3113.81	1.49627	0.748136	−	0.663545i	$-0.230949\pi$
$163$	3113.81	1.49627	0.748136	+	0.663545i	$0.230949\pi$
$164$	−1304.55	−0.621149
$165$	−2377.36	−1.12168
$166$	2295.15	1.07312
$167$	−602.453	−0.279157	−0.139578	−	0.990211i	$-0.544575\pi$
$167$	−602.453	−0.279157	−0.139578	+	0.990211i	$0.544575\pi$
$168$	290.539	0.133426
$169$	−1651.48	−0.751697
$170$	2048.79	0.924323
$171$	837.145	0.374375
$172$	0	0
$173$	2194.51	0.964423	0.482211	−	0.876055i	$-0.339834\pi$
$173$	2194.51	0.964423	0.482211	+	0.876055i	$0.339834\pi$
$174$	1775.35	0.773498
$175$	−292.389	−0.126300
$176$	−4380.78	−1.87621
$177$	−2977.15	−1.26427
$178$	−4202.17	−1.76947
$179$	−2282.67	−0.953153	−0.476577	−	0.879133i	$-0.658123\pi$
$179$	−2282.67	−0.953153	−0.476577	+	0.879133i	$0.658123\pi$
$180$	1133.66	0.469435
$181$	−3042.27	−1.24934	−0.624669	−	0.780890i	$-0.714766\pi$
$181$	−3042.27	−1.24934	−0.624669	+	0.780890i	$0.714766\pi$
$182$	2566.77	1.04539
$183$	551.227	0.222666
$184$	404.602	0.162107
$185$	−548.062	−0.217807
$186$	951.598	0.375132
$187$	3091.58	1.20898
$188$	−3132.29	−1.21514
$189$	−4121.99	−1.58641
$190$	−2395.73	−0.914760
$191$	1473.13	0.558074	0.279037	−	0.960280i	$-0.409985\pi$
$191$	1473.13	0.558074	0.279037	+	0.960280i	$0.409985\pi$
$192$	−1449.55	−0.544855
$193$	535.690	0.199792	0.0998959	−	0.994998i	$-0.468149\pi$
$193$	535.690	0.199792	0.0998959	+	0.994998i	$0.468149\pi$
$194$	1571.10	0.581435
$195$	880.209	0.323247
$196$	3254.74	1.18613
$197$	1305.23	0.472051	0.236025	−	0.971747i	$-0.424155\pi$
$197$	1305.23	0.472051	0.236025	+	0.971747i	$0.424155\pi$
$198$	3598.58	1.29162
$199$	3474.39	1.23765	0.618827	−	0.785527i	$-0.287608\pi$
$199$	3474.39	1.23765	0.618827	+	0.785527i	$0.287608\pi$
$200$	−30.4702	−0.0107729
$201$	2176.82	0.763885
$202$	263.779	0.0918785
$203$	−3634.59	−1.25664
$204$	1250.57	0.429204
$205$	1926.62	0.656396
$206$	1375.66	0.465277
$207$	−2015.34	−0.676694
$208$	1621.97	0.540688
$209$	−3615.11	−1.19647
$210$	4141.53	1.36092
$211$	−597.942	−0.195090	−0.0975450	−	0.995231i	$-0.531099\pi$
$211$	−597.942	−0.195090	−0.0975450	+	0.995231i	$0.531099\pi$
$212$	−5460.64	−1.76905
$213$	2546.74	0.819247
$214$	−5349.97	−1.70896
$215$	0	0
$216$	−429.558	−0.135313
$217$	−1948.17	−0.609448
$218$	1682.11	0.522600
$219$	1110.49	0.342648
$220$	−4895.58	−1.50027
$221$	−1144.65	−0.348403
$222$	−703.730	−0.212753
$223$	−3216.08	−0.965761	−0.482881	−	0.875686i	$-0.660409\pi$
$223$	−3216.08	−0.965761	−0.482881	+	0.875686i	$0.660409\pi$
$224$	6971.35	2.07943
$225$	151.773	0.0449699
$226$	2619.65	0.771046
$227$	−4588.34	−1.34158	−0.670790	−	0.741647i	$-0.734045\pi$
$227$	−4588.34	−1.34158	−0.670790	+	0.741647i	$0.734045\pi$
$228$	−1462.34	−0.424764
$229$	4872.42	1.40602	0.703009	−	0.711181i	$-0.251839\pi$
$229$	4872.42	1.40602	0.703009	+	0.711181i	$0.251839\pi$
$230$	5767.46	1.65346
$231$	6249.49	1.78003
$232$	−378.765	−0.107186
$233$	−1175.26	−0.330447	−0.165224	−	0.986256i	$-0.552835\pi$
$233$	−1175.26	−0.330447	−0.165224	+	0.986256i	$0.552835\pi$
$234$	−1332.36	−0.372219
$235$	4625.91	1.28409
$236$	−6130.69	−1.69099
$237$	−3622.43	−0.992837
$238$	−5385.75	−1.46683
$239$	−3114.29	−0.842874	−0.421437	−	0.906858i	$-0.638474\pi$
$239$	−3114.29	−0.842874	−0.421437	+	0.906858i	$0.638474\pi$
$240$	2617.07	0.703880
$241$	3808.63	1.01799	0.508994	−	0.860770i	$-0.330017\pi$
$241$	3808.63	1.01799	0.508994	+	0.860770i	$0.330017\pi$
$242$	−10342.5	−2.74727
$243$	3528.09	0.931386
$244$	1135.11	0.297820
$245$	−4806.75	−1.25344
$246$	2473.85	0.641166
$247$	1338.48	0.344799
$248$	−203.021	−0.0519832
$249$	−2068.99	−0.526574
$250$	−5660.02	−1.43188
$251$	670.351	0.168574	0.0842872	−	0.996442i	$-0.473139\pi$
$251$	670.351	0.168574	0.0842872	+	0.996442i	$0.473139\pi$
$252$	−2980.11	−0.744958
$253$	8702.98	2.16266
$254$	10040.3	2.48025
$255$	−1846.91	−0.453560
$256$	4753.68	1.16057
$257$	−5924.21	−1.43791	−0.718953	−	0.695058i	$-0.755379\pi$
$257$	−5924.21	−1.43791	−0.718953	+	0.695058i	$0.755379\pi$
$258$	0	0
$259$	1440.72	0.345644
$260$	1812.57	0.432349
$261$	1886.64	0.447434
$262$	5617.73	1.32467
$263$	4838.94	1.13453	0.567266	−	0.823535i	$-0.308001\pi$
$263$	4838.94	1.13453	0.567266	+	0.823535i	$0.308001\pi$
$264$	651.267	0.151828
$265$	8064.52	1.86943
$266$	6297.76	1.45166
$267$	3788.10	0.868269
$268$	4482.61	1.02171
$269$	−3925.10	−0.889657	−0.444828	−	0.895616i	$-0.646735\pi$
$269$	−3925.10	−0.889657	−0.444828	+	0.895616i	$0.646735\pi$
$270$	−6123.20	−1.38017
$271$	−3220.97	−0.721992	−0.360996	−	0.932567i	$-0.617563\pi$
$271$	−3220.97	−0.721992	−0.360996	+	0.932567i	$0.617563\pi$
$272$	−3403.30	−0.758660
$273$	−2313.85	−0.512969
$274$	6991.08	1.54141
$275$	−655.415	−0.143720
$276$	3520.44	0.767774
$277$	500.239	0.108507	0.0542535	−	0.998527i	$-0.482722\pi$
$277$	500.239	0.108507	0.0542535	+	0.998527i	$0.482722\pi$
$278$	−10640.9	−2.29567
$279$	1011.26	0.216997
$280$	−883.584	−0.188587
$281$	2081.73	0.441942	0.220971	−	0.975280i	$-0.429077\pi$
$281$	2081.73	0.441942	0.220971	+	0.975280i	$0.429077\pi$
$282$	5939.82	1.25430
$283$	4247.16	0.892111	0.446055	−	0.895005i	$-0.352828\pi$
$283$	4247.16	0.892111	0.446055	+	0.895005i	$0.352828\pi$
$284$	5244.36	1.09576
$285$	2159.66	0.448867
$286$	5753.63	1.18958
$287$	−5064.61	−1.04165
$288$	−3618.69	−0.740393
$289$	−2511.24	−0.511142
$290$	−5399.17	−1.09328
$291$	−1416.29	−0.285306
$292$	2286.77	0.458299
$293$	−3078.85	−0.613885	−0.306943	−	0.951728i	$-0.599306\pi$
$293$	−3078.85	−0.613885	−0.306943	+	0.951728i	$0.599306\pi$
$294$	−6172.03	−1.22435
$295$	9054.09	1.78695
$296$	150.139	0.0294819
$297$	−9239.79	−1.80521
$298$	4820.42	0.937044
$299$	−3222.24	−0.623235
$300$	−265.121	−0.0510227
$301$	0	0
$302$	−3370.48	−0.642216
$303$	−237.787	−0.0450842
$304$	3979.61	0.750811
$305$	−1676.39	−0.314720
$306$	2795.64	0.522274
$307$	−2386.54	−0.443671	−0.221835	−	0.975084i	$-0.571205\pi$
$307$	−2386.54	−0.443671	−0.221835	+	0.975084i	$0.571205\pi$
$308$	12869.2	2.38082
$309$	−1240.11	−0.228308
$310$	−2893.99	−0.530219
$311$	5088.76	0.927836	0.463918	−	0.885878i	$-0.346443\pi$
$311$	5088.76	0.927836	0.463918	+	0.885878i	$0.346443\pi$
$312$	−241.129	−0.0437540
$313$	2442.28	0.441041	0.220520	−	0.975382i	$-0.429224\pi$
$313$	2442.28	0.441041	0.220520	+	0.975382i	$0.429224\pi$
$314$	129.406	0.0232573
$315$	4401.17	0.787231
$316$	−7459.49	−1.32794
$317$	−7346.87	−1.30171	−0.650854	−	0.759203i	$-0.725589\pi$
$317$	−7346.87	−1.30171	−0.650854	+	0.759203i	$0.725589\pi$
$318$	10355.1	1.82606
$319$	−8147.24	−1.42996
$320$	4408.36	0.770109
$321$	4822.80	0.838575
$322$	−15161.2	−2.62391
$323$	−2808.47	−0.483800
$324$	−878.441	−0.150624
$325$	242.665	0.0414173
$326$	−12159.4	−2.06579
$327$	−1516.36	−0.256437
$328$	−527.789	−0.0888484
$329$	−12160.4	−2.03776
$330$	9283.59	1.54862
$331$	6905.46	1.14670	0.573351	−	0.819310i	$-0.305643\pi$
$331$	6905.46	1.14670	0.573351	+	0.819310i	$0.305643\pi$
$332$	−4260.56	−0.704303
$333$	−747.848	−0.123068
$334$	2352.57	0.385411
$335$	−6620.12	−1.07969
$336$	−6879.62	−1.11701
$337$	−1575.18	−0.254616	−0.127308	−	0.991863i	$-0.540634\pi$
$337$	−1575.18	−0.254616	−0.127308	+	0.991863i	$0.540634\pi$
$338$	6449.01	1.03781
$339$	−2361.51	−0.378348
$340$	−3803.24	−0.606645
$341$	−4366.98	−0.693505
$342$	−3269.05	−0.516871
$343$	2982.91	0.469568
$344$	0	0
$345$	−5199.15	−0.811341
$346$	−8569.53	−1.33151
$347$	−9101.68	−1.40808	−0.704040	−	0.710160i	$-0.748623\pi$
$347$	−9101.68	−1.40808	−0.704040	+	0.710160i	$0.748623\pi$
$348$	−3295.64	−0.507657
$349$	1577.99	0.242028	0.121014	−	0.992651i	$-0.461385\pi$
$349$	1577.99	0.242028	0.121014	+	0.992651i	$0.461385\pi$
$350$	1141.78	0.174373
$351$	3421.00	0.520226
$352$	15626.9	2.36623
$353$	−9222.14	−1.39050	−0.695248	−	0.718770i	$-0.744705\pi$
$353$	−9222.14	−1.39050	−0.695248	+	0.718770i	$0.744705\pi$
$354$	11625.8	1.74549
$355$	−7745.12	−1.15794
$356$	7800.63	1.16133
$357$	4855.05	0.719766
$358$	8913.80	1.31595
$359$	−3662.12	−0.538382	−0.269191	−	0.963087i	$-0.586756\pi$
$359$	−3662.12	−0.538382	−0.269191	+	0.963087i	$0.586756\pi$
$360$	458.651	0.0671474
$361$	−3574.94	−0.521205
$362$	11880.0	1.72486
$363$	9323.36	1.34807
$364$	−4764.79	−0.686106
$365$	−3377.21	−0.484305
$366$	−2152.54	−0.307418
$367$	−8159.43	−1.16054	−0.580271	−	0.814423i	$-0.697053\pi$
$367$	−8159.43	−1.16054	−0.580271	+	0.814423i	$0.697053\pi$
$368$	−9580.50	−1.35711
$369$	2628.94	0.370886
$370$	2140.18	0.300710
$371$	−21199.6	−2.96665
$372$	−1766.48	−0.246204
$373$	5635.31	0.782267	0.391133	−	0.920334i	$-0.372083\pi$
$373$	5635.31	0.782267	0.391133	+	0.920334i	$0.372083\pi$
$374$	−12072.6	−1.66914
$375$	5102.29	0.702617
$376$	−1267.24	−0.173812
$377$	3016.48	0.412087
$378$	16096.4	2.19023
$379$	−9744.43	−1.32068	−0.660340	−	0.750967i	$-0.729588\pi$
$379$	−9744.43	−1.32068	−0.660340	+	0.750967i	$0.729588\pi$
$380$	4447.27	0.600369
$381$	−9050.95	−1.21705
$382$	−5752.57	−0.770490
$383$	−10689.7	−1.42616	−0.713078	−	0.701084i	$-0.752700\pi$
$383$	−10689.7	−1.42616	−0.713078	+	0.701084i	$0.752700\pi$
$384$	−1315.63	−0.174839
$385$	−19005.9	−2.51592
$386$	−2091.87	−0.275837
$387$	0	0
$388$	−2916.48	−0.381603
$389$	−8888.68	−1.15854	−0.579272	−	0.815134i	$-0.696663\pi$
$389$	−8888.68	−1.15854	−0.579272	+	0.815134i	$0.696663\pi$
$390$	−3437.21	−0.446282
$391$	6761.10	0.874484
$392$	1316.79	0.169663
$393$	−5064.18	−0.650010
$394$	−5096.93	−0.651724
$395$	11016.5	1.40329
$396$	−6680.17	−0.847705
$397$	−14090.4	−1.78130	−0.890649	−	0.454692i	$-0.849749\pi$
$397$	−14090.4	−1.78130	−0.890649	+	0.454692i	$0.849749\pi$
$398$	−13567.5	−1.70873
$399$	−5677.20	−0.712319
$400$	721.500	0.0901875
$401$	−1953.93	−0.243328	−0.121664	−	0.992571i	$-0.538823\pi$
$401$	−1953.93	−0.243328	−0.121664	+	0.992571i	$0.538823\pi$
$402$	−8500.46	−1.05464
$403$	1616.86	0.199854
$404$	−489.663	−0.0603011
$405$	1297.32	0.159172
$406$	14193.1	1.73495
$407$	3229.49	0.393316
$408$	505.950	0.0613928
$409$	−8069.26	−0.975548	−0.487774	−	0.872970i	$-0.662191\pi$
$409$	−8069.26	−0.975548	−0.487774	+	0.872970i	$0.662191\pi$
$410$	−7523.45	−0.906236
$411$	−6302.20	−0.756361
$412$	−2553.69	−0.305367
$413$	−23800.9	−2.83575
$414$	7869.88	0.934260
$415$	6292.20	0.744269
$416$	−5785.78	−0.681902
$417$	9592.35	1.12647
$418$	14117.0	1.65187
$419$	8731.19	1.01801	0.509006	−	0.860763i	$-0.330013\pi$
$419$	8731.19	1.01801	0.509006	+	0.860763i	$0.330013\pi$
$420$	−7688.07	−0.893189
$421$	−3707.32	−0.429177	−0.214589	−	0.976705i	$-0.568841\pi$
$421$	−3707.32	−0.429177	−0.214589	+	0.976705i	$0.568841\pi$
$422$	2334.96	0.269346
$423$	6312.20	0.725555
$424$	−2209.24	−0.253042
$425$	−509.173	−0.0581141
$426$	−9944.99	−1.13107
$427$	4406.80	0.499438
$428$	9931.34	1.12161
$429$	−5186.68	−0.583719
$430$	0	0
$431$	−4090.48	−0.457149	−0.228575	−	0.973526i	$-0.573406\pi$
$431$	−4090.48	−0.457149	−0.228575	+	0.973526i	$0.573406\pi$
$432$	10171.4	1.13281
$433$	−10181.0	−1.12995	−0.564973	−	0.825110i	$-0.691113\pi$
$433$	−10181.0	−1.12995	−0.564973	+	0.825110i	$0.691113\pi$
$434$	7607.58	0.841418
$435$	4867.15	0.536464
$436$	−3122.56	−0.342990
$437$	−7906.01	−0.865437
$438$	−4336.45	−0.473068
$439$	10981.6	1.19390	0.596952	−	0.802277i	$-0.296378\pi$
$439$	10981.6	1.19390	0.596952	+	0.802277i	$0.296378\pi$
$440$	−1980.63	−0.214597
$441$	−6558.97	−0.708235
$442$	4469.83	0.481014
$443$	−2325.24	−0.249380	−0.124690	−	0.992196i	$-0.539794\pi$
$443$	−2325.24	−0.249380	−0.124690	+	0.992196i	$0.539794\pi$
$444$	1306.36	0.139633
$445$	−11520.3	−1.22723
$446$	12558.8	1.33335
$447$	−4345.42	−0.459802
$448$	−11588.5	−1.22211
$449$	3298.40	0.346684	0.173342	−	0.984862i	$-0.444543\pi$
$449$	3298.40	0.346684	0.173342	+	0.984862i	$0.444543\pi$
$450$	−592.674	−0.0620865
$451$	−11352.7	−1.18532
$452$	−4862.94	−0.506048
$453$	3038.36	0.315132
$454$	17917.4	1.85222
$455$	7036.86	0.725040
$456$	−591.628	−0.0607577
$457$	−10638.0	−1.08890	−0.544448	−	0.838795i	$-0.683261\pi$
$457$	−10638.0	−1.08890	−0.544448	+	0.838795i	$0.683261\pi$
$458$	−19026.8	−1.94118
$459$	−7178.13	−0.729948
$460$	−10706.3	−1.08519
$461$	8689.61	0.877908	0.438954	−	0.898510i	$-0.355349\pi$
$461$	8689.61	0.877908	0.438954	+	0.898510i	$0.355349\pi$
$462$	−24404.2	−2.45755
$463$	10497.9	1.05373	0.526866	−	0.849948i	$-0.323367\pi$
$463$	10497.9	1.05373	0.526866	+	0.849948i	$0.323367\pi$
$464$	8968.72	0.897333
$465$	2608.83	0.260175
$466$	4589.40	0.456223
$467$	8248.45	0.817330	0.408665	−	0.912685i	$-0.365995\pi$
$467$	8248.45	0.817330	0.408665	+	0.912685i	$0.365995\pi$
$468$	2473.31	0.244292
$469$	17402.6	1.71339
$470$	−18064.2	−1.77284
$471$	−116.655	−0.0114122
$472$	−2480.32	−0.241877
$473$	0	0
$474$	14145.6	1.37073
$475$	595.396	0.0575129
$476$	9997.75	0.962702
$477$	11004.3	1.05629
$478$	12161.3	1.16369
$479$	−14009.0	−1.33630	−0.668150	−	0.744027i	$-0.732914\pi$
$479$	−14009.0	−1.33630	−0.668150	+	0.744027i	$0.732914\pi$
$480$	−9335.46	−0.887716
$481$	−1195.70	−0.113346
$482$	−14872.7	−1.40546
$483$	13667.2	1.28754
$484$	19199.1	1.80307
$485$	4307.20	0.403258
$486$	−13777.2	−1.28589
$487$	−3912.41	−0.364041	−0.182021	−	0.983295i	$-0.558264\pi$
$487$	−3912.41	−0.364041	−0.182021	+	0.983295i	$0.558264\pi$
$488$	459.238	0.0425998
$489$	10961.2	1.01367
$490$	18770.3	1.73053
$491$	−7916.93	−0.727670	−0.363835	−	0.931463i	$-0.618533\pi$
$491$	−7916.93	−0.727670	−0.363835	+	0.931463i	$0.618533\pi$
$492$	−4592.29	−0.420806
$493$	−6329.36	−0.578215
$494$	−5226.75	−0.476038
$495$	9865.59	0.895809
$496$	4807.30	0.435190
$497$	20360.0	1.83756
$498$	8079.39	0.727000
$499$	4207.97	0.377504	0.188752	−	0.982025i	$-0.439556\pi$
$499$	4207.97	0.377504	0.188752	+	0.982025i	$0.439556\pi$
$500$	10506.9	0.939764
$501$	−2120.76	−0.189119
$502$	−2617.72	−0.232738
$503$	−5613.91	−0.497638	−0.248819	−	0.968550i	$-0.580042\pi$
$503$	−5613.91	−0.497638	−0.248819	+	0.968550i	$0.580042\pi$
$504$	−1205.68	−0.106558
$505$	723.157	0.0637229
$506$	−33985.1	−2.98581
$507$	−5813.54	−0.509247
$508$	−18638.2	−1.62782
$509$	−1936.88	−0.168665	−0.0843325	−	0.996438i	$-0.526876\pi$
$509$	−1936.88	−0.168665	−0.0843325	+	0.996438i	$0.526876\pi$
$510$	7212.15	0.626195
$511$	8877.84	0.768557
$512$	−15573.2	−1.34423
$513$	8393.67	0.722396
$514$	23134.0	1.98521
$515$	3771.41	0.322695
$516$	0	0
$517$	−27258.4	−2.31881
$518$	−5625.99	−0.477204
$519$	7725.11	0.653362
$520$	733.320	0.0618427
$521$	−3402.75	−0.286137	−0.143068	−	0.989713i	$-0.545697\pi$
$521$	−3402.75	−0.286137	−0.143068	+	0.989713i	$0.545697\pi$
$522$	−7367.34	−0.617739
$523$	13408.0	1.12101	0.560506	−	0.828150i	$-0.310607\pi$
$523$	13408.0	1.12101	0.560506	+	0.828150i	$0.310607\pi$
$524$	−10428.4	−0.869402
$525$	−1029.27	−0.0855638
$526$	−18896.0	−1.56636
$527$	−3392.58	−0.280423
$528$	−15421.2	−1.27107
$529$	6865.89	0.564304
$530$	−31491.9	−2.58098
$531$	12354.6	1.00969
$532$	−11690.8	−0.952742
$533$	4203.31	0.341586
$534$	−14792.5	−1.19875
$535$	−14667.1	−1.18526
$536$	1813.55	0.146144
$537$	−8035.45	−0.645727
$538$	15327.5	1.22828
$539$	28324.1	2.26346
$540$	11366.7	0.905825
$541$	11248.0	0.893881	0.446940	−	0.894564i	$-0.352514\pi$
$541$	11248.0	0.893881	0.446940	+	0.894564i	$0.352514\pi$
$542$	12577.9	0.996800
$543$	−10709.4	−0.846381
$544$	12140.1	0.956802
$545$	4611.54	0.362453
$546$	9035.56	0.708217
$547$	21075.0	1.64736	0.823678	−	0.567058i	$-0.191918\pi$
$547$	21075.0	1.64736	0.823678	+	0.567058i	$0.191918\pi$
$548$	−12977.8	−1.01165
$549$	−2287.48	−0.177828
$550$	2559.39	0.198423
$551$	7401.16	0.572232
$552$	1424.28	0.109821
$553$	−28959.6	−2.22692
$554$	−1953.43	−0.149807
$555$	−1929.29	−0.147556
$556$	19753.0	1.50668
$557$	−6250.35	−0.475468	−0.237734	−	0.971330i	$-0.576405\pi$
$557$	−6250.35	−0.475468	−0.237734	+	0.971330i	$0.576405\pi$
$558$	−3948.95	−0.299592
$559$	0	0
$560$	20922.3	1.57880
$561$	10883.0	0.819038
$562$	−8129.16	−0.610156
$563$	−7955.02	−0.595496	−0.297748	−	0.954644i	$-0.596236\pi$
$563$	−7955.02	−0.595496	−0.297748	+	0.954644i	$0.596236\pi$
$564$	−11026.3	−0.823211
$565$	7181.82	0.534764
$566$	−16585.1	−1.23167
$567$	−3410.34	−0.252594
$568$	2121.74	0.156736
$569$	−13925.5	−1.02599	−0.512995	−	0.858391i	$-0.671464\pi$
$569$	−13925.5	−1.02599	−0.512995	+	0.858391i	$0.671464\pi$
$570$	−8433.45	−0.619717
$571$	11857.0	0.869005	0.434502	−	0.900671i	$-0.356924\pi$
$571$	11857.0	0.869005	0.434502	+	0.900671i	$0.356924\pi$
$572$	−10680.7	−0.780736
$573$	5185.73	0.378075
$574$	19777.3	1.43813
$575$	−1433.35	−0.103956
$576$	6015.35	0.435138
$577$	−2884.39	−0.208109	−0.104054	−	0.994572i	$-0.533182\pi$
$577$	−2884.39	−0.208109	−0.104054	+	0.994572i	$0.533182\pi$
$578$	9806.38	0.705695
$579$	1885.74	0.135352
$580$	10022.7	0.717532
$581$	−16540.6	−1.18110
$582$	5530.59	0.393901
$583$	−47520.7	−3.37582
$584$	925.171	0.0655545
$585$	−3652.70	−0.258154
$586$	12022.9	0.847545
$587$	12049.5	0.847254	0.423627	−	0.905837i	$-0.360757\pi$
$587$	12049.5	0.847254	0.423627	+	0.905837i	$0.360757\pi$
$588$	11457.4	0.803560
$589$	3967.08	0.277522
$590$	−35356.2	−2.46710
$591$	4594.69	0.319797
$592$	−3555.11	−0.246815
$593$	−20939.8	−1.45008	−0.725038	−	0.688709i	$-0.758178\pi$
$593$	−20939.8	−1.45008	−0.725038	+	0.688709i	$0.758178\pi$
$594$	36081.3	2.49231
$595$	−14765.1	−1.01733
$596$	−8948.30	−0.614995
$597$	12230.6	0.838466
$598$	12582.8	0.860453
$599$	18862.1	1.28662	0.643308	−	0.765607i	$-0.277561\pi$
$599$	18862.1	1.28662	0.643308	+	0.765607i	$0.277561\pi$
$600$	−107.261	−0.00729822
$601$	−6381.91	−0.433151	−0.216575	−	0.976266i	$-0.569489\pi$
$601$	−6381.91	−0.433151	−0.216575	+	0.976266i	$0.569489\pi$
$602$	0	0
$603$	−9033.36	−0.610061
$604$	6256.74	0.421495
$605$	−28354.1	−1.90539
$606$	928.557	0.0622443
$607$	3055.87	0.204339	0.102170	−	0.994767i	$-0.467422\pi$
$607$	3055.87	0.204339	0.102170	+	0.994767i	$0.467422\pi$
$608$	−14195.8	−0.946903
$609$	−12794.5	−0.851329
$610$	6546.28	0.434510
$611$	10092.3	0.668236
$612$	−5189.63	−0.342775
$613$	339.125	0.0223444	0.0111722	−	0.999938i	$-0.496444\pi$
$613$	339.125	0.0223444	0.0111722	+	0.999938i	$0.496444\pi$
$614$	9319.42	0.612543
$615$	6782.11	0.444685
$616$	5206.57	0.340550
$617$	5525.71	0.360546	0.180273	−	0.983617i	$-0.442302\pi$
$617$	5525.71	0.360546	0.180273	+	0.983617i	$0.442302\pi$
$618$	4842.62	0.315208
$619$	−9145.73	−0.593858	−0.296929	−	0.954900i	$-0.595962\pi$
$619$	−9145.73	−0.593858	−0.296929	+	0.954900i	$0.595962\pi$
$620$	5372.22	0.347990
$621$	−20206.9	−1.30575
$622$	−19871.6	−1.28099
$623$	30284.0	1.94752
$624$	5709.65	0.366297
$625$	−14218.4	−0.909974
$626$	−9537.08	−0.608911
$627$	−12725.9	−0.810565
$628$	−240.221	−0.0152641
$629$	2508.90	0.159040
$630$	−17186.5	−1.08687
$631$	−13263.0	−0.836753	−0.418376	−	0.908274i	$-0.637401\pi$
$631$	−13263.0	−0.836753	−0.418376	+	0.908274i	$0.637401\pi$
$632$	−3017.92	−0.189947
$633$	−2104.88	−0.132166
$634$	28689.5	1.79717
$635$	27525.7	1.72020
$636$	−19222.6	−1.19847
$637$	−10486.9	−0.652284
$638$	31814.9	1.97424
$639$	−10568.5	−0.654275
$640$	4001.10	0.247121
$641$	−19417.2	−1.19647	−0.598233	−	0.801322i	$-0.704130\pi$
$641$	−19417.2	−1.19647	−0.598233	+	0.801322i	$0.704130\pi$
$642$	−18833.0	−1.15776
$643$	265.029	0.0162546	0.00812732	−	0.999967i	$-0.497413\pi$
$643$	265.029	0.0162546	0.00812732	+	0.999967i	$0.497413\pi$
$644$	28144.3	1.72211
$645$	0	0
$646$	10967.1	0.667946
$647$	−16950.6	−1.02998	−0.514989	−	0.857197i	$-0.672204\pi$
$647$	−16950.6	−1.02998	−0.514989	+	0.857197i	$0.672204\pi$
$648$	−355.395	−0.0215451
$649$	−53351.8	−3.22687
$650$	−947.604	−0.0571817
$651$	−6857.95	−0.412879
$652$	22571.9	1.35580
$653$	−14811.0	−0.887596	−0.443798	−	0.896127i	$-0.646369\pi$
$653$	−14811.0	−0.887596	−0.443798	+	0.896127i	$0.646369\pi$
$654$	5921.37	0.354043
$655$	15401.1	0.918736
$656$	12497.4	0.743815
$657$	−4608.31	−0.273649
$658$	47486.1	2.81337
$659$	12313.7	0.727882	0.363941	−	0.931422i	$-0.381431\pi$
$659$	12313.7	0.727882	0.363941	+	0.931422i	$0.381431\pi$
$660$	−17233.4	−1.01638
$661$	−12928.7	−0.760769	−0.380385	−	0.924828i	$-0.624208\pi$
$661$	−12928.7	−0.760769	−0.380385	+	0.924828i	$0.624208\pi$
$662$	−26965.8	−1.58316
$663$	−4029.39	−0.236031
$664$	−1723.72	−0.100743
$665$	17265.5	1.00681
$666$	2920.34	0.169911
$667$	−17817.5	−1.03433
$668$	−4367.17	−0.252950
$669$	−11321.3	−0.654268
$670$	25851.5	1.49064
$671$	9878.21	0.568322
$672$	24540.6	1.40874
$673$	1829.04	0.104761	0.0523806	−	0.998627i	$-0.483319\pi$
$673$	1829.04	0.104761	0.0523806	+	0.998627i	$0.483319\pi$
$674$	6151.07	0.351529
$675$	1521.76	0.0867743
$676$	−11971.5	−0.681129
$677$	31239.7	1.77347	0.886734	−	0.462281i	$-0.152969\pi$
$677$	31239.7	1.77347	0.886734	+	0.462281i	$0.152969\pi$
$678$	9221.70	0.522356
$679$	−11322.5	−0.639940
$680$	−1538.69	−0.0867738
$681$	−16151.9	−0.908872
$682$	17053.0	0.957469
$683$	−13225.0	−0.740908	−0.370454	−	0.928851i	$-0.620798\pi$
$683$	−13225.0	−0.740908	−0.370454	+	0.928851i	$0.620798\pi$
$684$	6068.44	0.339229
$685$	19166.2	1.06906
$686$	−11648.2	−0.648297
$687$	17151.9	0.952527
$688$	0	0
$689$	17594.3	0.972846
$690$	20302.6	1.12016
$691$	32827.9	1.80728	0.903641	−	0.428290i	$-0.140884\pi$
$691$	32827.9	1.80728	0.903641	+	0.428290i	$0.140884\pi$
$692$	15907.9	0.873885
$693$	−25934.2	−1.42158
$694$	35542.0	1.94403
$695$	−29172.2	−1.59218
$696$	−1333.33	−0.0726146
$697$	−8819.62	−0.479292
$698$	−6162.03	−0.334150
$699$	−4137.17	−0.223866
$700$	−2119.52	−0.114443
$701$	−2531.25	−0.136382	−0.0681911	−	0.997672i	$-0.521723\pi$
$701$	−2531.25	−0.136382	−0.0681911	+	0.997672i	$0.521723\pi$
$702$	−13359.0	−0.718236
$703$	−2933.75	−0.157395
$704$	−25976.5	−1.39066
$705$	16284.2	0.869924
$706$	36012.4	1.91975
$707$	−1901.00	−0.101124
$708$	−21581.3	−1.14559
$709$	22917.0	1.21392	0.606958	−	0.794734i	$-0.292389\pi$
$709$	22917.0	1.21392	0.606958	+	0.794734i	$0.292389\pi$
$710$	30244.6	1.59868
$711$	15032.4	0.792909
$712$	3155.94	0.166115
$713$	−9550.32	−0.501630
$714$	−18958.9	−0.993726
$715$	15773.7	0.825040
$716$	−16547.0	−0.863673
$717$	−10963.0	−0.571017
$718$	14300.5	0.743303
$719$	−16579.6	−0.859967	−0.429983	−	0.902837i	$-0.641481\pi$
$719$	−16579.6	−0.859967	−0.429983	+	0.902837i	$0.641481\pi$
$720$	−10860.3	−0.562140
$721$	−9914.08	−0.512094
$722$	13960.1	0.719588
$723$	13407.1	0.689650
$724$	−22053.3	−1.13205
$725$	1341.82	0.0687366
$726$	−36407.7	−1.86118
$727$	13124.1	0.669528	0.334764	−	0.942302i	$-0.391343\pi$
$727$	13124.1	0.669528	0.334764	+	0.942302i	$0.391343\pi$
$728$	−1927.71	−0.0981398
$729$	15691.5	0.797210
$730$	13188.0	0.668643
$731$	0	0
$732$	3995.83	0.201762
$733$	−19053.7	−0.960115	−0.480057	−	0.877237i	$-0.659384\pi$
$733$	−19053.7	−0.960115	−0.480057	+	0.877237i	$0.659384\pi$
$734$	31862.5	1.60227
$735$	−16920.8	−0.849159
$736$	34175.0	1.71156
$737$	39009.5	1.94970
$738$	−10266.0	−0.512054
$739$	−14039.8	−0.698867	−0.349434	−	0.936961i	$-0.613626\pi$
$739$	−14039.8	−0.698867	−0.349434	+	0.936961i	$0.613626\pi$
$740$	−3972.89	−0.197360
$741$	4711.72	0.233589
$742$	82784.3	4.09583
$743$	19227.3	0.949368	0.474684	−	0.880156i	$-0.342562\pi$
$743$	19227.3	0.949368	0.474684	+	0.880156i	$0.342562\pi$
$744$	−714.675	−0.0352167
$745$	13215.3	0.649893
$746$	−22005.9	−1.08002
$747$	8585.90	0.420538
$748$	22410.8	1.09548
$749$	38556.0	1.88092
$750$	−19924.4	−0.970049
$751$	12740.9	0.619071	0.309536	−	0.950888i	$-0.399826\pi$
$751$	12740.9	0.619071	0.309536	+	0.950888i	$0.399826\pi$
$752$	30006.9	1.45510
$753$	2359.77	0.114203
$754$	−11779.3	−0.568937
$755$	−9240.24	−0.445413
$756$	−29880.2	−1.43748
$757$	−8644.05	−0.415024	−0.207512	−	0.978232i	$-0.566537\pi$
$757$	−8644.05	−0.415024	−0.207512	+	0.978232i	$0.566537\pi$
$758$	38051.9	1.82336
$759$	30636.3	1.46512
$760$	1799.25	0.0858761
$761$	−26953.2	−1.28391	−0.641954	−	0.766743i	$-0.721876\pi$
$761$	−26953.2	−1.28391	−0.641954	+	0.766743i	$0.721876\pi$
$762$	35343.9	1.68028
$763$	−12122.6	−0.575186
$764$	10678.7	0.505683
$765$	7664.29	0.362226
$766$	41743.2	1.96899
$767$	19753.3	0.929921
$768$	16733.9	0.786242
$769$	6330.39	0.296853	0.148426	−	0.988923i	$-0.452579\pi$
$769$	6330.39	0.296853	0.148426	+	0.988923i	$0.452579\pi$
$770$	74217.9	3.47354
$771$	−20854.4	−0.974130
$772$	3883.20	0.181036
$773$	−1515.26	−0.0705047	−0.0352523	−	0.999378i	$-0.511223\pi$
$773$	−1515.26	−0.0705047	−0.0352523	+	0.999378i	$0.511223\pi$
$774$	0	0
$775$	719.227	0.0333360
$776$	−1179.94	−0.0545841
$777$	5071.62	0.234161
$778$	34710.2	1.59951
$779$	10313.1	0.474334
$780$	6380.62	0.292901
$781$	45638.6	2.09101
$782$	−26402.0	−1.20733
$783$	18916.5	0.863373
$784$	−31180.0	−1.42037
$785$	354.769	0.0161303
$786$	19775.6	0.897419
$787$	6916.26	0.313263	0.156632	−	0.987657i	$-0.449936\pi$
$787$	6916.26	0.313263	0.156632	+	0.987657i	$0.449936\pi$
$788$	9461.60	0.427735
$789$	17034.1	0.768604
$790$	−43019.4	−1.93742
$791$	−18879.2	−0.848631
$792$	−2702.63	−0.121255
$793$	−3657.37	−0.163779
$794$	55022.8	2.45930
$795$	28388.8	1.26647
$796$	25185.8	1.12147
$797$	17973.3	0.798804	0.399402	−	0.916776i	$-0.369218\pi$
$797$	17973.3	0.798804	0.399402	+	0.916776i	$0.369218\pi$
$798$	22169.4	0.983445
$799$	−21176.3	−0.937627
$800$	−2573.69	−0.113742
$801$	−15719.9	−0.693425
$802$	7630.08	0.335944
$803$	19900.4	0.874559
$804$	15779.7	0.692173
$805$	−41564.7	−1.81983
$806$	−6313.81	−0.275924
$807$	−13817.2	−0.602710
$808$	−198.105	−0.00862539
$809$	35822.1	1.55678	0.778391	−	0.627779i	$-0.216036\pi$
$809$	35822.1	1.55678	0.778391	+	0.627779i	$0.216036\pi$
$810$	−5066.04	−0.219756
$811$	30499.7	1.32058	0.660288	−	0.751012i	$-0.270434\pi$
$811$	30499.7	1.32058	0.660288	+	0.751012i	$0.270434\pi$
$812$	−26347.1	−1.13867
$813$	−11338.5	−0.489124
$814$	−12611.1	−0.543022
$815$	−33335.3	−1.43274
$816$	−11980.3	−0.513965
$817$	0	0
$818$	31510.4	1.34687
$819$	9602.01	0.409672
$820$	13966.0	0.594775
$821$	30273.0	1.28689	0.643445	−	0.765493i	$-0.277505\pi$
$821$	30273.0	1.28689	0.643445	+	0.765493i	$0.277505\pi$
$822$	24610.0	1.04425
$823$	42243.7	1.78922	0.894608	−	0.446852i	$-0.147455\pi$
$823$	42243.7	1.78922	0.894608	+	0.446852i	$0.147455\pi$
$824$	−1033.16	−0.0436794
$825$	−2307.19	−0.0973651
$826$	92942.4	3.91511
$827$	22125.2	0.930313	0.465156	−	0.885228i	$-0.345998\pi$
$827$	22125.2	0.930313	0.465156	+	0.885228i	$0.345998\pi$
$828$	−14609.1	−0.613167
$829$	−17028.7	−0.713429	−0.356715	−	0.934213i	$-0.616103\pi$
$829$	−17028.7	−0.713429	−0.356715	+	0.934213i	$0.616103\pi$
$830$	−24571.0	−1.02756
$831$	1760.94	0.0735096
$832$	9617.70	0.400762
$833$	22004.2	0.915245
$834$	−37458.1	−1.55524
$835$	6449.63	0.267304
$836$	−26205.8	−1.08415
$837$	10139.4	0.418720
$838$	−34095.2	−1.40549
$839$	−4109.20	−0.169089	−0.0845443	−	0.996420i	$-0.526943\pi$
$839$	−4109.20	−0.169089	−0.0845443	+	0.996420i	$0.526943\pi$
$840$	−3110.40	−0.127761
$841$	−7709.26	−0.316096
$842$	14477.0	0.592532
$843$	7328.13	0.299400
$844$	−4334.46	−0.176775
$845$	17680.1	0.719780
$846$	−24649.1	−1.00172
$847$	74535.9	3.02371
$848$	52312.1	2.11840
$849$	14950.9	0.604373
$850$	1988.32	0.0802338
$851$	7062.69	0.284496
$852$	18461.2	0.742337
$853$	−9742.74	−0.391073	−0.195536	−	0.980696i	$-0.562645\pi$
$853$	−9742.74	−0.391073	−0.195536	+	0.980696i	$0.562645\pi$
$854$	−17208.5	−0.689535
$855$	−8962.16	−0.358479
$856$	4017.97	0.160434
$857$	28781.0	1.14719	0.573593	−	0.819140i	$-0.305549\pi$
$857$	28781.0	1.14719	0.573593	+	0.819140i	$0.305549\pi$
$858$	20254.0	0.805896
$859$	−28477.1	−1.13111	−0.565556	−	0.824710i	$-0.691339\pi$
$859$	−28477.1	−1.13111	−0.565556	+	0.824710i	$0.691339\pi$
$860$	0	0
$861$	−17828.5	−0.705682
$862$	15973.3	0.631151
$863$	−29789.0	−1.17501	−0.587503	−	0.809222i	$-0.699889\pi$
$863$	−29789.0	−1.17501	−0.587503	+	0.809222i	$0.699889\pi$
$864$	−36282.9	−1.42867
$865$	−23493.5	−0.923474
$866$	39756.6	1.56003
$867$	−8840.08	−0.346280
$868$	−14122.2	−0.552234
$869$	−64915.5	−2.53407
$870$	−19006.2	−0.740655
$871$	−14443.1	−0.561866
$872$	−1263.31	−0.0490608
$873$	5877.31	0.227854
$874$	30872.9	1.19484
$875$	40790.4	1.57596
$876$	8049.91	0.310481
$877$	8110.77	0.312293	0.156147	−	0.987734i	$-0.450093\pi$
$877$	8110.77	0.312293	0.156147	+	0.987734i	$0.450093\pi$
$878$	−42883.1	−1.64833
$879$	−10838.2	−0.415885
$880$	46899.0	1.79655
$881$	31359.8	1.19925	0.599624	−	0.800282i	$-0.295317\pi$
$881$	31359.8	1.19925	0.599624	+	0.800282i	$0.295317\pi$
$882$	25612.7	0.977806
$883$	−11827.4	−0.450764	−0.225382	−	0.974270i	$-0.572363\pi$
$883$	−11827.4	−0.450764	−0.225382	+	0.974270i	$0.572363\pi$
$884$	−8297.50	−0.315696
$885$	31872.3	1.21059
$886$	9080.04	0.344300
$887$	15000.4	0.567829	0.283915	−	0.958850i	$-0.408367\pi$
$887$	15000.4	0.567829	0.283915	+	0.958850i	$0.408367\pi$
$888$	528.520	0.0199729
$889$	−72358.1	−2.72982
$890$	44986.8	1.69434
$891$	−7644.55	−0.287432
$892$	−23313.3	−0.875097
$893$	24762.3	0.927926
$894$	16968.9	0.634814
$895$	24437.4	0.912683
$896$	−10517.9	−0.392163
$897$	−11343.0	−0.422219
$898$	−12880.2	−0.478640
$899$	8940.46	0.331681
$900$	1100.20	0.0407482
$901$	−36917.4	−1.36504
$902$	44332.4	1.63648
$903$	0	0
$904$	−1967.42	−0.0723845
$905$	32569.4	1.19629
$906$	−11864.8	−0.435078
$907$	7030.05	0.257364	0.128682	−	0.991686i	$-0.458925\pi$
$907$	7030.05	0.257364	0.128682	+	0.991686i	$0.458925\pi$
$908$	−33260.8	−1.21564
$909$	986.770	0.0360056
$910$	−27478.9	−1.00101
$911$	−10526.7	−0.382838	−0.191419	−	0.981508i	$-0.561309\pi$
$911$	−10526.7	−0.382838	−0.191419	+	0.981508i	$0.561309\pi$
$912$	14009.1	0.508647
$913$	−37077.1	−1.34400
$914$	41541.4	1.50336
$915$	−5901.22	−0.213211
$916$	35320.0	1.27402
$917$	−40485.7	−1.45797
$918$	28030.5	1.00778
$919$	−23229.7	−0.833816	−0.416908	−	0.908949i	$-0.636886\pi$
$919$	−23229.7	−0.833816	−0.416908	+	0.908949i	$0.636886\pi$
$920$	−4331.51	−0.155224
$921$	−8401.11	−0.300571
$922$	−33932.9	−1.21206
$923$	−16897.5	−0.602587
$924$	45302.4	1.61292
$925$	−531.886	−0.0189063
$926$	−40994.1	−1.45481
$927$	5146.21	0.182334
$928$	−31992.7	−1.13169
$929$	−22527.4	−0.795586	−0.397793	−	0.917475i	$-0.630224\pi$
$929$	−22527.4	−0.795586	−0.397793	+	0.917475i	$0.630224\pi$
$930$	−10187.5	−0.359204
$931$	−25730.3	−0.905776
$932$	−8519.46	−0.299425
$933$	17913.5	0.628575
$934$	−32210.2	−1.12842
$935$	−33097.3	−1.15764
$936$	1000.64	0.0349432
$937$	−17122.8	−0.596987	−0.298494	−	0.954412i	$-0.596484\pi$
$937$	−17122.8	−0.596987	−0.298494	+	0.954412i	$0.596484\pi$
$938$	−67957.1	−2.36554
$939$	8597.32	0.298789
$940$	33533.1	1.16354
$941$	−21511.1	−0.745208	−0.372604	−	0.927990i	$-0.621535\pi$
$941$	−21511.1	−0.745208	−0.372604	+	0.927990i	$0.621535\pi$
$942$	455.536	0.0157560
$943$	−24827.7	−0.857373
$944$	58731.2	2.02493
$945$	44128.5	1.51905
$946$	0	0
$947$	−18487.6	−0.634387	−0.317194	−	0.948361i	$-0.602741\pi$
$947$	−18487.6	−0.634387	−0.317194	+	0.948361i	$0.602741\pi$
$948$	−26258.9	−0.899631
$949$	−7368.05	−0.252031
$950$	−2325.02	−0.0794037
$951$	−25862.5	−0.881859
$952$	4044.84	0.137704
$953$	−27815.6	−0.945471	−0.472736	−	0.881204i	$-0.656733\pi$
$953$	−27815.6	−0.945471	−0.472736	+	0.881204i	$0.656733\pi$
$954$	−42971.7	−1.45834
$955$	−15770.8	−0.534378
$956$	−22575.4	−0.763747
$957$	−28680.0	−0.968747
$958$	54705.1	1.84493
$959$	−50383.1	−1.69651
$960$	15518.3	0.521721
$961$	−24998.8	−0.839141
$962$	4669.22	0.156488
$963$	−20013.7	−0.669711
$964$	27608.6	0.922421
$965$	−5734.89	−0.191309
$966$	−53370.5	−1.77761
$967$	−1372.88	−0.0456556	−0.0228278	−	0.999739i	$-0.507267\pi$
$967$	−1372.88	−0.0456556	−0.0228278	+	0.999739i	$0.507267\pi$
$968$	7767.48	0.257909
$969$	−9886.39	−0.327757
$970$	−16819.6	−0.556747
$971$	−30280.5	−1.00077	−0.500385	−	0.865803i	$-0.666808\pi$
$971$	−30280.5	−1.00077	−0.500385	+	0.865803i	$0.666808\pi$
$972$	25575.0	0.843949
$973$	76686.3	2.52667
$974$	15277.9	0.502604
$975$	854.229	0.0280587
$976$	−10874.2	−0.356634
$977$	−31533.9	−1.03261	−0.516305	−	0.856405i	$-0.672693\pi$
$977$	−31533.9	−1.03261	−0.516305	+	0.856405i	$0.672693\pi$
$978$	−42803.6	−1.39950
$979$	67884.2	2.21613
$980$	−34844.0	−1.13577
$981$	6292.59	0.204798
$982$	30915.6	1.00464
$983$	−22289.4	−0.723217	−0.361609	−	0.932330i	$-0.617772\pi$
$983$	−22289.4	−0.723217	−0.361609	+	0.932330i	$0.617772\pi$
$984$	−1857.93	−0.0601916
$985$	−13973.3	−0.452007
$986$	24716.1	0.798297
$987$	−42806.9	−1.38051
$988$	9702.59	0.312430
$989$	0	0
$990$	−38525.1	−1.23677
$991$	2037.39	0.0653074	0.0326537	−	0.999467i	$-0.489604\pi$
$991$	2037.39	0.0653074	0.0326537	+	0.999467i	$0.489604\pi$
$992$	−17148.3	−0.548850
$993$	24308.6	0.776849
$994$	−79505.5	−2.53698
$995$	−37195.5	−1.18510
$996$	−14998.0	−0.477140
$997$	26780.4	0.850695	0.425347	−	0.905030i	$-0.360152\pi$
$997$	26780.4	0.850695	0.425347	+	0.905030i	$0.360152\pi$
$998$	−16432.1	−0.521191
$999$	−7498.32	−0.237474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.9	✓	50
43.42	odd	2		1849.4.a.j.1.42	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.9	✓	50	1.1	even	1	trivial
1849.4.a.j.1.42	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)

\(f(q)\)	\(=\)	\(q-3.90499 q^{2} +3.52020 q^{3} +7.24897 q^{4} -10.7056 q^{5} -13.7464 q^{6} +28.1424 q^{7} +2.93275 q^{8} -14.6082 q^{9} +O(q^{10})\)	\(q-3.90499 q^{2} +3.52020 q^{3} +7.24897 q^{4} -10.7056 q^{5} -13.7464 q^{6} +28.1424 q^{7} +2.93275 q^{8} -14.6082 q^{9} +41.8054 q^{10} +63.0835 q^{11} +25.5179 q^{12} -23.3564 q^{13} -109.896 q^{14} -37.6860 q^{15} -69.4442 q^{16} +49.0078 q^{17} +57.0448 q^{18} -57.3067 q^{19} -77.6048 q^{20} +99.0669 q^{21} -246.341 q^{22} +137.960 q^{23} +10.3239 q^{24} -10.3896 q^{25} +91.2066 q^{26} -146.469 q^{27} +204.003 q^{28} -129.150 q^{29} +147.164 q^{30} -69.2254 q^{31} +247.717 q^{32} +222.067 q^{33} -191.375 q^{34} -301.282 q^{35} -105.894 q^{36} +51.1938 q^{37} +223.782 q^{38} -82.2194 q^{39} -31.3969 q^{40} -179.964 q^{41} -386.856 q^{42} +457.291 q^{44} +156.389 q^{45} -538.732 q^{46} -432.101 q^{47} -244.458 q^{48} +448.993 q^{49} +40.5715 q^{50} +172.517 q^{51} -169.310 q^{52} -753.298 q^{53} +571.961 q^{54} -675.348 q^{55} +82.5346 q^{56} -201.731 q^{57} +504.330 q^{58} -845.732 q^{59} -273.185 q^{60} +156.589 q^{61} +270.325 q^{62} -411.108 q^{63} -411.780 q^{64} +250.045 q^{65} -867.170 q^{66} +618.378 q^{67} +355.256 q^{68} +485.647 q^{69} +1176.50 q^{70} +723.463 q^{71} -42.8421 q^{72} +315.462 q^{73} -199.912 q^{74} -36.5737 q^{75} -415.415 q^{76} +1775.32 q^{77} +321.066 q^{78} -1029.04 q^{79} +743.443 q^{80} -121.181 q^{81} +702.757 q^{82} -587.747 q^{83} +718.134 q^{84} -524.659 q^{85} -454.635 q^{87} +185.008 q^{88} +1076.10 q^{89} -610.700 q^{90} -657.305 q^{91} +1000.07 q^{92} -243.688 q^{93} +1687.35 q^{94} +613.504 q^{95} +872.015 q^{96} -402.331 q^{97} -1753.32 q^{98} -921.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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