LMFDB - Embedded newform 1849.4.a.k.1.13

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:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-3.57276 q^{2} +1.25498 q^{3} +4.76459 q^{4} -8.29511 q^{5} -4.48372 q^{6} -13.8938 q^{7} +11.5593 q^{8} -25.4250 q^{9} +O(q^{10})$	\(q-3.57276 q^{2} +1.25498 q^{3} +4.76459 q^{4} -8.29511 q^{5} -4.48372 q^{6} -13.8938 q^{7} +11.5593 q^{8} -25.4250 q^{9} +29.6364 q^{10} +34.6545 q^{11} +5.97945 q^{12} +27.6929 q^{13} +49.6391 q^{14} -10.4102 q^{15} -79.4154 q^{16} +43.3957 q^{17} +90.8375 q^{18} -19.1508 q^{19} -39.5228 q^{20} -17.4363 q^{21} -123.812 q^{22} +56.6562 q^{23} +14.5067 q^{24} -56.1912 q^{25} -98.9399 q^{26} -65.7922 q^{27} -66.1982 q^{28} -193.431 q^{29} +37.1930 q^{30} -204.576 q^{31} +191.257 q^{32} +43.4905 q^{33} -155.042 q^{34} +115.250 q^{35} -121.140 q^{36} -10.9857 q^{37} +68.4211 q^{38} +34.7539 q^{39} -95.8858 q^{40} +231.294 q^{41} +62.2958 q^{42} +165.114 q^{44} +210.903 q^{45} -202.419 q^{46} +385.334 q^{47} -99.6644 q^{48} -149.963 q^{49} +200.757 q^{50} +54.4606 q^{51} +131.945 q^{52} +10.6104 q^{53} +235.059 q^{54} -287.462 q^{55} -160.603 q^{56} -24.0338 q^{57} +691.081 q^{58} +608.588 q^{59} -49.6002 q^{60} +358.926 q^{61} +730.899 q^{62} +353.250 q^{63} -47.9929 q^{64} -229.715 q^{65} -155.381 q^{66} +280.010 q^{67} +206.763 q^{68} +71.1021 q^{69} -411.761 q^{70} +553.163 q^{71} -293.896 q^{72} -1002.35 q^{73} +39.2492 q^{74} -70.5186 q^{75} -91.2457 q^{76} -481.481 q^{77} -124.167 q^{78} +861.551 q^{79} +658.759 q^{80} +603.908 q^{81} -826.359 q^{82} -243.285 q^{83} -83.0771 q^{84} -359.972 q^{85} -242.751 q^{87} +400.582 q^{88} +1284.29 q^{89} -753.507 q^{90} -384.758 q^{91} +269.944 q^{92} -256.737 q^{93} -1376.70 q^{94} +158.858 q^{95} +240.023 q^{96} +1700.53 q^{97} +535.782 q^{98} -881.091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * 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 $

$2$	−3.57276	−1.26316	−0.631580	−	0.775311i	$-0.717593\pi$
$2$	−3.57276	−1.26316	−0.631580	+	0.775311i	$0.717593\pi$
$3$	1.25498	0.241520	0.120760	−	0.992682i	$-0.461467\pi$
$3$	1.25498	0.241520	0.120760	+	0.992682i	$0.461467\pi$
$4$	4.76459	0.595574
$5$	−8.29511	−0.741937	−0.370969	−	0.928645i	$-0.620974\pi$
$5$	−8.29511	−0.741937	−0.370969	+	0.928645i	$0.620974\pi$
$6$	−4.48372	−0.305079
$7$	−13.8938	−0.750193	−0.375097	−	0.926986i	$-0.622390\pi$
$7$	−13.8938	−0.750193	−0.375097	+	0.926986i	$0.622390\pi$
$8$	11.5593	0.510855
$9$	−25.4250	−0.941668
$10$	29.6364	0.937185
$11$	34.6545	0.949883	0.474941	−	0.880017i	$-0.342469\pi$
$11$	34.6545	0.949883	0.474941	+	0.880017i	$0.342469\pi$
$12$	5.97945	0.143843
$13$	27.6929	0.590817	0.295408	−	0.955371i	$-0.404544\pi$
$13$	27.6929	0.590817	0.295408	+	0.955371i	$0.404544\pi$
$14$	49.6391	0.947614
$15$	−10.4102	−0.179193
$16$	−79.4154	−1.24087
$17$	43.3957	0.619118	0.309559	−	0.950880i	$-0.399819\pi$
$17$	43.3957	0.619118	0.309559	+	0.950880i	$0.399819\pi$
$18$	90.8375	1.18948
$19$	−19.1508	−0.231236	−0.115618	−	0.993294i	$-0.536885\pi$
$19$	−19.1508	−0.231236	−0.115618	+	0.993294i	$0.536885\pi$
$20$	−39.5228	−0.441879
$21$	−17.4363	−0.181187
$22$	−123.812	−1.19985
$23$	56.6562	0.513636	0.256818	−	0.966460i	$-0.417326\pi$
$23$	56.6562	0.513636	0.256818	+	0.966460i	$0.417326\pi$
$24$	14.5067	0.123382
$25$	−56.1912	−0.449529
$26$	−98.9399	−0.746296
$27$	−65.7922	−0.468952
$28$	−66.1982	−0.446796
$29$	−193.431	−1.23859	−0.619296	−	0.785158i	$-0.712582\pi$
$29$	−193.431	−1.23859	−0.619296	+	0.785158i	$0.712582\pi$
$30$	37.1930	0.226349
$31$	−204.576	−1.18525	−0.592627	−	0.805477i	$-0.701909\pi$
$31$	−204.576	−1.18525	−0.592627	+	0.805477i	$0.701909\pi$
$32$	191.257	1.05656
$33$	43.4905	0.229416
$34$	−155.042	−0.782045
$35$	115.250	0.556596
$36$	−121.140	−0.560833
$37$	−10.9857	−0.0488118	−0.0244059	−	0.999702i	$-0.507769\pi$
$37$	−10.9857	−0.0488118	−0.0244059	+	0.999702i	$0.507769\pi$
$38$	68.4211	0.292088
$39$	34.7539	0.142694
$40$	−95.8858	−0.379022
$41$	231.294	0.881028	0.440514	−	0.897746i	$-0.354796\pi$
$41$	231.294	0.881028	0.440514	+	0.897746i	$0.354796\pi$
$42$	62.2958	0.228868
$43$	0	0
$43$	0	0
$44$	165.114	0.565726
$45$	210.903	0.698658
$46$	−202.419	−0.648804
$47$	385.334	1.19589	0.597944	−	0.801538i	$-0.295985\pi$
$47$	385.334	1.19589	0.597944	+	0.801538i	$0.295985\pi$
$48$	−99.6644	−0.299694
$49$	−149.963	−0.437210
$50$	200.757	0.567828
$51$	54.4606	0.149530
$52$	131.945	0.351875
$53$	10.6104	0.0274991	0.0137496	−	0.999905i	$-0.495623\pi$
$53$	10.6104	0.0274991	0.0137496	+	0.999905i	$0.495623\pi$
$54$	235.059	0.592362
$55$	−287.462	−0.704753
$56$	−160.603	−0.383240
$57$	−24.0338	−0.0558482
$58$	691.081	1.56454
$59$	608.588	1.34290	0.671452	−	0.741048i	$-0.265671\pi$
$59$	608.588	1.34290	0.671452	+	0.741048i	$0.265671\pi$
$60$	−49.6002	−0.106723
$61$	358.926	0.753373	0.376687	−	0.926341i	$-0.377063\pi$
$61$	358.926	0.753373	0.376687	+	0.926341i	$0.377063\pi$
$62$	730.899	1.49716
$63$	353.250	0.706433
$64$	−47.9929	−0.0937361
$65$	−229.715	−0.438349
$66$	−155.381	−0.289789
$67$	280.010	0.510577	0.255288	−	0.966865i	$-0.417830\pi$
$67$	280.010	0.510577	0.255288	+	0.966865i	$0.417830\pi$
$68$	206.763	0.368731
$69$	71.1021	0.124053
$70$	−411.761	−0.703070
$71$	553.163	0.924624	0.462312	−	0.886717i	$-0.347020\pi$
$71$	553.163	0.924624	0.462312	+	0.886717i	$0.347020\pi$
$72$	−293.896	−0.481055
$73$	−1002.35	−1.60707	−0.803534	−	0.595260i	$-0.797049\pi$
$73$	−1002.35	−1.60707	−0.803534	+	0.595260i	$0.797049\pi$
$74$	39.2492	0.0616572
$75$	−70.5186	−0.108570
$76$	−91.2457	−0.137718
$77$	−481.481	−0.712595
$78$	−124.167	−0.180246
$79$	861.551	1.22699	0.613494	−	0.789699i	$-0.289763\pi$
$79$	861.551	1.22699	0.613494	+	0.789699i	$0.289763\pi$
$80$	658.759	0.920644
$81$	603.908	0.828407
$82$	−826.359	−1.11288
$83$	−243.285	−0.321735	−0.160867	−	0.986976i	$-0.551429\pi$
$83$	−243.285	−0.321735	−0.160867	+	0.986976i	$0.551429\pi$
$84$	−83.0771	−0.107910
$85$	−359.972	−0.459347
$86$	0	0
$87$	−242.751	−0.299145
$88$	400.582	0.485252
$89$	1284.29	1.52960	0.764798	−	0.644271i	$-0.222839\pi$
$89$	1284.29	1.52960	0.764798	+	0.644271i	$0.222839\pi$
$90$	−753.507	−0.882518
$91$	−384.758	−0.443227
$92$	269.944	0.305908
$93$	−256.737	−0.286263
$94$	−1376.70	−1.51060
$95$	158.858	0.171563
$96$	240.023	0.255180
$97$	1700.53	1.78003	0.890015	−	0.455930i	$-0.150693\pi$
$97$	1700.53	1.78003	0.890015	+	0.455930i	$0.150693\pi$
$98$	535.782	0.552267
$99$	−881.091	−0.894474
$100$	−267.728	−0.267728
$101$	689.750	0.679531	0.339766	−	0.940510i	$-0.389652\pi$
$101$	689.750	0.679531	0.339766	+	0.940510i	$0.389652\pi$
$102$	−194.574	−0.188880
$103$	262.712	0.251318	0.125659	−	0.992073i	$-0.459895\pi$
$103$	262.712	0.251318	0.125659	+	0.992073i	$0.459895\pi$
$104$	320.111	0.301822
$105$	144.636	0.134429
$106$	−37.9085	−0.0347358
$107$	−1760.15	−1.59028	−0.795140	−	0.606426i	$-0.792603\pi$
$107$	−1760.15	−1.59028	−0.795140	+	0.606426i	$0.792603\pi$
$108$	−313.473	−0.279296
$109$	−974.424	−0.856265	−0.428132	−	0.903716i	$-0.640828\pi$
$109$	−974.424	−0.856265	−0.428132	+	0.903716i	$0.640828\pi$
$110$	1027.03	0.890216
$111$	−13.7868	−0.0117890
$112$	1103.38	0.930889
$113$	−2220.33	−1.84841	−0.924207	−	0.381892i	$-0.875273\pi$
$113$	−2220.33	−1.84841	−0.924207	+	0.381892i	$0.875273\pi$
$114$	85.8668	0.0705453
$115$	−469.969	−0.381085
$116$	−921.619	−0.737674
$117$	−704.092	−0.556353
$118$	−2174.34	−1.69630
$119$	−602.930	−0.464458
$120$	−120.334	−0.0915415
$121$	−130.069	−0.0977226
$122$	−1282.36	−0.951631
$123$	290.269	0.212786
$124$	−974.719	−0.705906
$125$	1503.00	1.07546
$126$	−1262.07	−0.892338
$127$	2528.14	1.76643	0.883213	−	0.468972i	$-0.155375\pi$
$127$	2528.14	1.76643	0.883213	+	0.468972i	$0.155375\pi$
$128$	−1358.59	−0.938154
$129$	0	0
$130$	820.717	0.553705
$131$	1318.74	0.879535	0.439768	−	0.898112i	$-0.355061\pi$
$131$	1318.74	0.879535	0.439768	+	0.898112i	$0.355061\pi$
$132$	207.215	0.136634
$133$	266.076	0.173472
$134$	−1000.41	−0.644940
$135$	545.753	0.347933
$136$	501.625	0.316279
$137$	−1537.45	−0.958780	−0.479390	−	0.877602i	$-0.659142\pi$
$137$	−1537.45	−0.958780	−0.479390	+	0.877602i	$0.659142\pi$
$138$	−254.031	−0.156699
$139$	1322.27	0.806861	0.403431	−	0.915010i	$-0.367818\pi$
$139$	1322.27	0.806861	0.403431	+	0.915010i	$0.367818\pi$
$140$	549.121	0.331494
$141$	483.585	0.288831
$142$	−1976.32	−1.16795
$143$	959.681	0.561207
$144$	2019.14	1.16848
$145$	1604.53	0.918957
$146$	3581.14	2.02998
$147$	−188.200	−0.105595
$148$	−52.3424	−0.0290711
$149$	−820.521	−0.451139	−0.225570	−	0.974227i	$-0.572424\pi$
$149$	−820.521	−0.451139	−0.225570	+	0.974227i	$0.572424\pi$
$150$	251.946	0.137142
$151$	−2341.41	−1.26186	−0.630932	−	0.775838i	$-0.717327\pi$
$151$	−2341.41	−1.26186	−0.630932	+	0.775838i	$0.717327\pi$
$152$	−221.370	−0.118128
$153$	−1103.34	−0.583004
$154$	1720.21	0.900122
$155$	1696.98	0.879383
$156$	165.588	0.0849850
$157$	−181.763	−0.0923965	−0.0461982	−	0.998932i	$-0.514711\pi$
$157$	−181.763	−0.0923965	−0.0461982	+	0.998932i	$0.514711\pi$
$158$	−3078.11	−1.54988
$159$	13.3158	0.00664160
$160$	−1586.50	−0.783899
$161$	−787.168	−0.385326
$162$	−2157.62	−1.04641
$163$	−2773.65	−1.33281	−0.666407	−	0.745588i	$-0.732169\pi$
$163$	−2773.65	−1.33281	−0.666407	+	0.745588i	$0.732169\pi$
$164$	1102.02	0.524717
$165$	−360.758	−0.170212
$166$	869.198	0.406403
$167$	−3707.84	−1.71809	−0.859046	−	0.511898i	$-0.828942\pi$
$167$	−3707.84	−1.71809	−0.859046	+	0.511898i	$0.828942\pi$
$168$	−201.552	−0.0925601
$169$	−1430.11	−0.650935
$170$	1286.09	0.580228
$171$	486.909	0.217748
$172$	0	0
$173$	3335.00	1.46564	0.732820	−	0.680423i	$-0.238204\pi$
$173$	3335.00	1.46564	0.732820	+	0.680423i	$0.238204\pi$
$174$	867.290	0.377868
$175$	780.707	0.337234
$176$	−2752.10	−1.17868
$177$	763.763	0.324339
$178$	−4588.44	−1.93212
$179$	506.719	0.211586	0.105793	−	0.994388i	$-0.466262\pi$
$179$	506.719	0.211586	0.105793	+	0.994388i	$0.466262\pi$
$180$	1004.87	0.416103
$181$	3641.67	1.49549	0.747744	−	0.663987i	$-0.231137\pi$
$181$	3641.67	1.49549	0.747744	+	0.663987i	$0.231137\pi$
$182$	1374.65	0.559866
$183$	450.443	0.181955
$184$	654.907	0.262393
$185$	91.1275	0.0362153
$186$	917.260	0.361596
$187$	1503.85	0.588090
$188$	1835.96	0.712240
$189$	914.101	0.351805
$190$	−567.560	−0.216711
$191$	2212.62	0.838216	0.419108	−	0.907936i	$-0.362343\pi$
$191$	2212.62	0.838216	0.419108	+	0.907936i	$0.362343\pi$
$192$	−60.2299	−0.0226392
$193$	−3168.63	−1.18178	−0.590888	−	0.806753i	$-0.701223\pi$
$193$	−3168.63	−1.18178	−0.590888	+	0.806753i	$0.701223\pi$
$194$	−6075.59	−2.24846
$195$	−288.287	−0.105870
$196$	−714.514	−0.260391
$197$	−1476.99	−0.534168	−0.267084	−	0.963673i	$-0.586060\pi$
$197$	−1476.99	−0.534168	−0.267084	+	0.963673i	$0.586060\pi$
$198$	3147.92	1.12986
$199$	−881.839	−0.314130	−0.157065	−	0.987588i	$-0.550203\pi$
$199$	−881.839	−0.314130	−0.157065	+	0.987588i	$0.550203\pi$
$200$	−649.532	−0.229644
$201$	351.406	0.123315
$202$	−2464.31	−0.858357
$203$	2687.48	0.929183
$204$	259.483	0.0890559
$205$	−1918.61	−0.653667
$206$	−938.605	−0.317455
$207$	−1440.48	−0.483674
$208$	−2199.24	−0.733124
$209$	−663.660	−0.219647
$210$	−516.751	−0.169806
$211$	2483.23	0.810201	0.405100	−	0.914272i	$-0.367237\pi$
$211$	2483.23	0.810201	0.405100	+	0.914272i	$0.367237\pi$
$212$	50.5544	0.0163778
$213$	694.206	0.223315
$214$	6288.58	2.00878
$215$	0	0
$216$	−760.513	−0.239566
$217$	2842.33	0.889169
$218$	3481.38	1.08160
$219$	−1257.92	−0.388139
$220$	−1369.64	−0.419733
$221$	1201.75	0.365785
$222$	49.2568	0.0148915
$223$	−1978.75	−0.594201	−0.297100	−	0.954846i	$-0.596020\pi$
$223$	−1978.75	−0.594201	−0.297100	+	0.954846i	$0.596020\pi$
$224$	−2657.29	−0.792622
$225$	1428.66	0.423308
$226$	7932.69	2.33484
$227$	2844.52	0.831707	0.415854	−	0.909432i	$-0.363483\pi$
$227$	2844.52	0.831707	0.415854	+	0.909432i	$0.363483\pi$
$228$	−114.511	−0.0332618
$229$	−1362.27	−0.393107	−0.196553	−	0.980493i	$-0.562975\pi$
$229$	−1362.27	−0.393107	−0.196553	+	0.980493i	$0.562975\pi$
$230$	1679.08	0.481372
$231$	−604.247	−0.172106
$232$	−2235.93	−0.632741
$233$	−1566.77	−0.440526	−0.220263	−	0.975440i	$-0.570692\pi$
$233$	−1566.77	−0.440526	−0.220263	+	0.975440i	$0.570692\pi$
$234$	2515.55	0.702763
$235$	−3196.39	−0.887273
$236$	2899.67	0.799799
$237$	1081.23	0.296343
$238$	2154.12	0.586685
$239$	1575.99	0.426536	0.213268	−	0.976994i	$-0.431589\pi$
$239$	1575.99	0.426536	0.213268	+	0.976994i	$0.431589\pi$
$240$	826.727	0.222354
$241$	−58.2482	−0.0155689	−0.00778443	−	0.999970i	$-0.502478\pi$
$241$	−58.2482	−0.0155689	−0.00778443	+	0.999970i	$0.502478\pi$
$242$	464.704	0.123439
$243$	2534.28	0.669029
$244$	1710.14	0.448690
$245$	1243.96	0.324383
$246$	−1037.06	−0.268783
$247$	−530.340	−0.136618
$248$	−2364.75	−0.605492
$249$	−305.317	−0.0777055
$250$	−5369.86	−1.35848
$251$	−6276.96	−1.57848	−0.789239	−	0.614086i	$-0.789525\pi$
$251$	−6276.96	−1.57848	−0.789239	+	0.614086i	$0.789525\pi$
$252$	1683.09	0.420733
$253$	1963.39	0.487894
$254$	−9032.43	−2.23128
$255$	−451.756	−0.110941
$256$	5237.86	1.27877
$257$	3958.37	0.960763	0.480382	−	0.877060i	$-0.340498\pi$
$257$	3958.37	0.960763	0.480382	+	0.877060i	$0.340498\pi$
$258$	0	0
$259$	152.633	0.0366183
$260$	−1094.50	−0.261069
$261$	4917.98	1.16634
$262$	−4711.55	−1.11099
$263$	−4707.40	−1.10369	−0.551846	−	0.833946i	$-0.686076\pi$
$263$	−4707.40	−1.10369	−0.551846	+	0.833946i	$0.686076\pi$
$264$	502.721	0.117198
$265$	−88.0147	−0.0204026
$266$	−950.626	−0.219123
$267$	1611.75	0.369428
$268$	1334.13	0.304086
$269$	−1943.59	−0.440532	−0.220266	−	0.975440i	$-0.570692\pi$
$269$	−1943.59	−0.440532	−0.220266	+	0.975440i	$0.570692\pi$
$270$	−1949.84	−0.439495
$271$	991.173	0.222175	0.111088	−	0.993811i	$-0.464567\pi$
$271$	991.173	0.222175	0.111088	+	0.993811i	$0.464567\pi$
$272$	−3446.29	−0.768242
$273$	−482.862	−0.107048
$274$	5492.92	1.21109
$275$	−1947.27	−0.427000
$276$	338.773	0.0738830
$277$	159.130	0.0345169	0.0172584	−	0.999851i	$-0.494506\pi$
$277$	159.130	0.0345169	0.0172584	+	0.999851i	$0.494506\pi$
$278$	−4724.16	−1.01919
$279$	5201.34	1.11612
$280$	1332.22	0.284340
$281$	4474.51	0.949917	0.474959	−	0.880008i	$-0.342463\pi$
$281$	4474.51	0.949917	0.474959	+	0.880008i	$0.342463\pi$
$282$	−1727.73	−0.364840
$283$	1795.31	0.377104	0.188552	−	0.982063i	$-0.439621\pi$
$283$	1795.31	0.377104	0.188552	+	0.982063i	$0.439621\pi$
$284$	2635.60	0.550682
$285$	199.363	0.0414359
$286$	−3428.71	−0.708894
$287$	−3213.55	−0.660941
$288$	−4862.72	−0.994926
$289$	−3029.81	−0.616693
$290$	−5732.59	−1.16079
$291$	2134.13	0.429913
$292$	−4775.78	−0.957128
$293$	2894.29	0.577087	0.288543	−	0.957467i	$-0.406829\pi$
$293$	2894.29	0.577087	0.288543	+	0.957467i	$0.406829\pi$
$294$	672.393	0.133384
$295$	−5048.30	−0.996351
$296$	−126.987	−0.0249357
$297$	−2279.99	−0.445450
$298$	2931.52	0.569861
$299$	1568.97	0.303465
$300$	−335.992	−0.0646618
$301$	0	0
$302$	8365.30	1.59394
$303$	865.619	0.164121
$304$	1520.87	0.286933
$305$	−2977.33	−0.558955
$306$	3941.96	0.736427
$307$	7314.00	1.35971	0.679856	−	0.733345i	$-0.262042\pi$
$307$	7314.00	1.35971	0.679856	+	0.733345i	$0.262042\pi$
$308$	−2294.06	−0.424403
$309$	329.697	0.0606984
$310$	−6062.88	−1.11080
$311$	−6927.61	−1.26312	−0.631558	−	0.775329i	$-0.717584\pi$
$311$	−6927.61	−1.26312	−0.631558	+	0.775329i	$0.717584\pi$
$312$	401.731	0.0728960
$313$	−5667.98	−1.02356	−0.511778	−	0.859118i	$-0.671013\pi$
$313$	−5667.98	−1.02356	−0.511778	+	0.859118i	$0.671013\pi$
$314$	649.394	0.116712
$315$	−2930.24	−0.524129
$316$	4104.94	0.730763
$317$	−3740.18	−0.662680	−0.331340	−	0.943511i	$-0.607501\pi$
$317$	−3740.18	−0.662680	−0.331340	+	0.943511i	$0.607501\pi$
$318$	−47.5742	−0.00838941
$319$	−6703.23	−1.17652
$320$	398.106	0.0695463
$321$	−2208.94	−0.384085
$322$	2812.36	0.486729
$323$	−831.062	−0.143163
$324$	2877.38	0.493378
$325$	−1556.09	−0.265590
$326$	9909.57	1.68356
$327$	−1222.88	−0.206805
$328$	2673.61	0.450077
$329$	−5353.74	−0.897146
$330$	1288.90	0.215005
$331$	−5030.92	−0.835421	−0.417711	−	0.908580i	$-0.637167\pi$
$331$	−5030.92	−0.835421	−0.417711	+	0.908580i	$0.637167\pi$
$332$	−1159.15	−0.191617
$333$	279.312	0.0459645
$334$	13247.2	2.17023
$335$	−2322.71	−0.378816
$336$	1384.71	0.224828
$337$	−4466.73	−0.722012	−0.361006	−	0.932563i	$-0.617567\pi$
$337$	−4466.73	−0.722012	−0.361006	+	0.932563i	$0.617567\pi$
$338$	5109.42	0.822236
$339$	−2786.46	−0.446429
$340$	−1715.12	−0.273575
$341$	−7089.45	−1.12585
$342$	−1739.61	−0.275050
$343$	6849.12	1.07819
$344$	0	0
$345$	−589.800	−0.0920398
$346$	−11915.2	−1.85134
$347$	−4714.85	−0.729413	−0.364706	−	0.931123i	$-0.618831\pi$
$347$	−4714.85	−0.729413	−0.364706	+	0.931123i	$0.618831\pi$
$348$	−1156.61	−0.178163
$349$	−12419.6	−1.90489	−0.952444	−	0.304714i	$-0.901439\pi$
$349$	−12419.6	−1.90489	−0.952444	+	0.304714i	$0.901439\pi$
$350$	−2789.28	−0.425980
$351$	−1821.97	−0.277065
$352$	6627.92	1.00361
$353$	−10528.6	−1.58748	−0.793741	−	0.608256i	$-0.791870\pi$
$353$	−10528.6	−1.58748	−0.793741	+	0.608256i	$0.791870\pi$
$354$	−2728.74	−0.409692
$355$	−4588.54	−0.686013
$356$	6119.10	0.910987
$357$	−756.663	−0.112176
$358$	−1810.38	−0.267267
$359$	−4566.89	−0.671396	−0.335698	−	0.941970i	$-0.608972\pi$
$359$	−4566.89	−0.671396	−0.335698	+	0.941970i	$0.608972\pi$
$360$	2437.90	0.356913
$361$	−6492.25	−0.946530
$362$	−13010.8	−1.88904
$363$	−163.233	−0.0236020
$364$	−1833.22	−0.263974
$365$	8314.58	1.19234
$366$	−1609.33	−0.229838
$367$	3824.04	0.543905	0.271953	−	0.962311i	$-0.412331\pi$
$367$	3824.04	0.543905	0.271953	+	0.962311i	$0.412331\pi$
$368$	−4499.37	−0.637353
$369$	−5880.67	−0.829635
$370$	−325.577	−0.0457457
$371$	−147.419	−0.0206297
$372$	−1223.25	−0.170491
$373$	−12569.3	−1.74480	−0.872402	−	0.488790i	$-0.837439\pi$
$373$	−12569.3	−1.74480	−0.872402	+	0.488790i	$0.837439\pi$
$374$	−5372.91	−0.742852
$375$	1886.23	0.259745
$376$	4454.20	0.610925
$377$	−5356.65	−0.731781
$378$	−3265.86	−0.444386
$379$	−5707.58	−0.773559	−0.386779	−	0.922172i	$-0.626413\pi$
$379$	−5707.58	−0.773559	−0.386779	+	0.922172i	$0.626413\pi$
$380$	756.893	0.102178
$381$	3172.75	0.426628
$382$	−7905.14	−1.05880
$383$	5274.62	0.703709	0.351855	−	0.936055i	$-0.385551\pi$
$383$	5274.62	0.703709	0.351855	+	0.936055i	$0.385551\pi$
$384$	−1705.00	−0.226583
$385$	3993.94	0.528701
$386$	11320.7	1.49277
$387$	0	0
$388$	8102.35	1.06014
$389$	−10222.4	−1.33238	−0.666191	−	0.745781i	$-0.732076\pi$
$389$	−10222.4	−1.33238	−0.666191	+	0.745781i	$0.732076\pi$
$390$	1029.98	0.133731
$391$	2458.63	0.318001
$392$	−1733.47	−0.223351
$393$	1654.99	0.212426
$394$	5276.92	0.674740
$395$	−7146.66	−0.910348
$396$	−4198.04	−0.532726
$397$	−6740.16	−0.852088	−0.426044	−	0.904702i	$-0.640093\pi$
$397$	−6740.16	−0.852088	−0.426044	+	0.904702i	$0.640093\pi$
$398$	3150.60	0.396797
$399$	333.920	0.0418970
$400$	4462.45	0.557806
$401$	12726.2	1.58482	0.792411	−	0.609987i	$-0.208825\pi$
$401$	12726.2	1.58482	0.792411	+	0.609987i	$0.208825\pi$
$402$	−1255.49	−0.155766
$403$	−5665.28	−0.700268
$404$	3286.38	0.404711
$405$	−5009.49	−0.614625
$406$	−9601.72	−1.17371
$407$	−380.703	−0.0463655
$408$	629.527	0.0763879
$409$	11745.4	1.41998	0.709992	−	0.704210i	$-0.248699\pi$
$409$	11745.4	1.41998	0.709992	+	0.704210i	$0.248699\pi$
$410$	6854.74	0.825686
$411$	−1929.46	−0.231565
$412$	1251.71	0.149678
$413$	−8455.58	−1.00744
$414$	5146.50	0.610958
$415$	2018.07	0.238707
$416$	5296.46	0.624232
$417$	1659.42	0.194873
$418$	2371.09	0.277450
$419$	11910.6	1.38871	0.694355	−	0.719633i	$-0.255690\pi$
$419$	11910.6	1.38871	0.694355	+	0.719633i	$0.255690\pi$
$420$	689.133	0.0800626
$421$	3361.34	0.389125	0.194563	−	0.980890i	$-0.437671\pi$
$421$	3361.34	0.389125	0.194563	+	0.980890i	$0.437671\pi$
$422$	−8871.96	−1.02341
$423$	−9797.13	−1.12613
$424$	122.649	0.0140481
$425$	−2438.46	−0.278312
$426$	−2480.23	−0.282083
$427$	−4986.84	−0.565175
$428$	−8386.39	−0.947129
$429$	1204.38	0.135543
$430$	0	0
$431$	−12995.6	−1.45238	−0.726189	−	0.687495i	$-0.758710\pi$
$431$	−12995.6	−1.45238	−0.726189	+	0.687495i	$0.758710\pi$
$432$	5224.91	0.581906
$433$	7744.49	0.859530	0.429765	−	0.902941i	$-0.358596\pi$
$433$	7744.49	0.859530	0.429765	+	0.902941i	$0.358596\pi$
$434$	−10154.9	−1.12316
$435$	2013.64	0.221947
$436$	−4642.73	−0.509969
$437$	−1085.01	−0.118771
$438$	4494.25	0.490282
$439$	−6347.63	−0.690105	−0.345052	−	0.938583i	$-0.612139\pi$
$439$	−6347.63	−0.690105	−0.345052	+	0.938583i	$0.612139\pi$
$440$	−3322.87	−0.360026
$441$	3812.82	0.411707
$442$	−4293.57	−0.462046
$443$	8114.19	0.870242	0.435121	−	0.900372i	$-0.356706\pi$
$443$	8114.19	0.870242	0.435121	+	0.900372i	$0.356706\pi$
$444$	−65.6884	−0.00702125
$445$	−10653.3	−1.13486
$446$	7069.58	0.750571
$447$	−1029.73	−0.108959
$448$	666.802	0.0703202
$449$	−14407.5	−1.51432	−0.757162	−	0.653227i	$-0.773415\pi$
$449$	−14407.5	−1.51432	−0.757162	+	0.653227i	$0.773415\pi$
$450$	−5104.27	−0.534705
$451$	8015.38	0.836873
$452$	−10579.0	−1.10087
$453$	−2938.42	−0.304766
$454$	−10162.8	−1.05058
$455$	3191.61	0.328846
$456$	−277.814	−0.0285303
$457$	−790.592	−0.0809242	−0.0404621	−	0.999181i	$-0.512883\pi$
$457$	−790.592	−0.0809242	−0.0404621	+	0.999181i	$0.512883\pi$
$458$	4867.06	0.496557
$459$	−2855.10	−0.290337
$460$	−2239.21	−0.226965
$461$	−10108.5	−1.02126	−0.510630	−	0.859801i	$-0.670588\pi$
$461$	−10108.5	−1.02126	−0.510630	+	0.859801i	$0.670588\pi$
$462$	2158.83	0.217398
$463$	14434.8	1.44890	0.724449	−	0.689328i	$-0.242094\pi$
$463$	14434.8	1.44890	0.724449	+	0.689328i	$0.242094\pi$
$464$	15361.4	1.53693
$465$	2129.66	0.212389
$466$	5597.69	0.556455
$467$	−2805.85	−0.278028	−0.139014	−	0.990290i	$-0.544393\pi$
$467$	−2805.85	−0.278028	−0.139014	+	0.990290i	$0.544393\pi$
$468$	−3354.71	−0.331350
$469$	−3890.39	−0.383031
$470$	11419.9	1.12077
$471$	−228.108	−0.0223156
$472$	7034.86	0.686029
$473$	0	0
$474$	−3862.96	−0.374328
$475$	1076.10	0.103948
$476$	−2872.72	−0.276619
$477$	−269.771	−0.0258951
$478$	−5630.61	−0.538783
$479$	−7069.57	−0.674357	−0.337178	−	0.941441i	$-0.609473\pi$
$479$	−7069.57	−0.674357	−0.337178	+	0.941441i	$0.609473\pi$
$480$	−1991.02	−0.189328
$481$	−304.225	−0.0288388
$482$	208.107	0.0196660
$483$	−987.876	−0.0930640
$484$	−619.725	−0.0582011
$485$	−14106.1	−1.32067
$486$	−9054.36	−0.845091
$487$	−12034.6	−1.11980	−0.559898	−	0.828561i	$-0.689160\pi$
$487$	−12034.6	−1.11980	−0.559898	+	0.828561i	$0.689160\pi$
$488$	4148.94	0.384864
$489$	−3480.86	−0.321902
$490$	−4444.37	−0.409747
$491$	−12096.6	−1.11184	−0.555919	−	0.831237i	$-0.687633\pi$
$491$	−12096.6	−1.11184	−0.555919	+	0.831237i	$0.687633\pi$
$492$	1383.01	0.126730
$493$	−8394.06	−0.766835
$494$	1894.78	0.172571
$495$	7308.74	0.663644
$496$	16246.4	1.47074
$497$	−7685.51	−0.693647
$498$	1090.82	0.0981545
$499$	1015.37	0.0910910	0.0455455	−	0.998962i	$-0.485497\pi$
$499$	1015.37	0.0910910	0.0455455	+	0.998962i	$0.485497\pi$
$500$	7161.19	0.640516
$501$	−4653.25	−0.414954
$502$	22426.1	1.99387
$503$	4666.48	0.413654	0.206827	−	0.978378i	$-0.433686\pi$
$503$	4666.48	0.413654	0.206827	+	0.978378i	$0.433686\pi$
$504$	4083.33	0.360884
$505$	−5721.55	−0.504169
$506$	−7014.71	−0.616288
$507$	−1794.75	−0.157214
$508$	12045.6	1.05204
$509$	−17702.1	−1.54151	−0.770757	−	0.637129i	$-0.780122\pi$
$509$	−17702.1	−1.54151	−0.770757	+	0.637129i	$0.780122\pi$
$510$	1614.02	0.140137
$511$	13926.4	1.20561
$512$	−7844.87	−0.677144
$513$	1259.97	0.108439
$514$	−14142.3	−1.21360
$515$	−2179.22	−0.186462
$516$	0	0
$517$	13353.5	1.13595
$518$	−545.320	−0.0462548
$519$	4185.35	0.353982
$520$	−2655.35	−0.223933
$521$	7876.51	0.662334	0.331167	−	0.943572i	$-0.392558\pi$
$521$	7876.51	0.662334	0.331167	+	0.943572i	$0.392558\pi$
$522$	−17570.8	−1.47328
$523$	5922.39	0.495158	0.247579	−	0.968868i	$-0.420365\pi$
$523$	5922.39	0.495158	0.247579	+	0.968868i	$0.420365\pi$
$524$	6283.27	0.523828
$525$	979.769	0.0814488
$526$	16818.4	1.39414
$527$	−8877.70	−0.733812
$528$	−3453.82	−0.284674
$529$	−8957.08	−0.736178
$530$	314.455	0.0257718
$531$	−15473.4	−1.26457
$532$	1267.75	0.103315
$533$	6405.21	0.520526
$534$	−5758.38	−0.466647
$535$	14600.6	1.17989
$536$	3236.72	0.260831
$537$	635.920	0.0511023
$538$	6943.99	0.556462
$539$	−5196.89	−0.415299
$540$	2600.29	0.207220
$541$	−8920.82	−0.708939	−0.354469	−	0.935068i	$-0.615338\pi$
$541$	−8920.82	−0.708939	−0.354469	+	0.935068i	$0.615338\pi$
$542$	−3541.22	−0.280643
$543$	4570.21	0.361191
$544$	8299.75	0.654134
$545$	8082.95	0.635295
$546$	1725.15	0.135219
$547$	6882.32	0.537965	0.268982	−	0.963145i	$-0.413313\pi$
$547$	6882.32	0.537965	0.268982	+	0.963145i	$0.413313\pi$
$548$	−7325.31	−0.571025
$549$	−9125.71	−0.709427
$550$	6957.14	0.539370
$551$	3704.35	0.286407
$552$	821.892	0.0633733
$553$	−11970.2	−0.920478
$554$	−568.532	−0.0436004
$555$	114.363	0.00874673
$556$	6300.09	0.480546
$557$	14510.3	1.10381	0.551904	−	0.833908i	$-0.313902\pi$
$557$	14510.3	1.10381	0.551904	+	0.833908i	$0.313902\pi$
$558$	−18583.1	−1.40983
$559$	0	0
$560$	−9152.65	−0.690661
$561$	1887.30	0.142036
$562$	−15986.3	−1.19990
$563$	−836.118	−0.0625900	−0.0312950	−	0.999510i	$-0.509963\pi$
$563$	−836.118	−0.0625900	−0.0312950	+	0.999510i	$0.509963\pi$
$564$	2304.08	0.172020
$565$	18417.9	1.37141
$566$	−6414.22	−0.476342
$567$	−8390.56	−0.621465
$568$	6394.19	0.472349
$569$	−19603.1	−1.44430	−0.722148	−	0.691738i	$-0.756845\pi$
$569$	−19603.1	−1.44430	−0.722148	+	0.691738i	$0.756845\pi$
$570$	−712.274	−0.0523401
$571$	20540.5	1.50542	0.752709	−	0.658353i	$-0.228747\pi$
$571$	20540.5	1.50542	0.752709	+	0.658353i	$0.228747\pi$
$572$	4572.49	0.334240
$573$	2776.78	0.202446
$574$	11481.2	0.834874
$575$	−3183.58	−0.230894
$576$	1220.22	0.0882683
$577$	22388.6	1.61534	0.807669	−	0.589636i	$-0.200729\pi$
$577$	22388.6	1.61534	0.807669	+	0.589636i	$0.200729\pi$
$578$	10824.8	0.778982
$579$	−3976.55	−0.285423
$580$	7644.93	0.547307
$581$	3380.14	0.241363
$582$	−7624.72	−0.543050
$583$	367.699	0.0261210
$584$	−11586.5	−0.820978
$585$	5840.52	0.412779
$586$	−10340.6	−0.728953
$587$	−6974.08	−0.490376	−0.245188	−	0.969476i	$-0.578850\pi$
$587$	−6974.08	−0.490376	−0.245188	+	0.969476i	$0.578850\pi$
$588$	−896.697	−0.0628898
$589$	3917.78	0.274074
$590$	18036.4	1.25855
$591$	−1853.58	−0.129012
$592$	872.433	0.0605689
$593$	−3580.85	−0.247973	−0.123987	−	0.992284i	$-0.539568\pi$
$593$	−3580.85	−0.247973	−0.123987	+	0.992284i	$0.539568\pi$
$594$	8145.85	0.562674
$595$	5001.37	0.344599
$596$	−3909.45	−0.268687
$597$	−1106.69	−0.0758688
$598$	−5605.55	−0.383325
$599$	−15138.5	−1.03263	−0.516313	−	0.856400i	$-0.672696\pi$
$599$	−15138.5	−1.03263	−0.516313	+	0.856400i	$0.672696\pi$
$600$	−815.147	−0.0554637
$601$	1482.01	0.100587	0.0502933	−	0.998734i	$-0.483984\pi$
$601$	1482.01	0.100587	0.0502933	+	0.998734i	$0.483984\pi$
$602$	0	0
$603$	−7119.26	−0.480794
$604$	−11155.9	−0.751534
$605$	1078.93	0.0725040
$606$	−3092.65	−0.207311
$607$	13467.4	0.900536	0.450268	−	0.892893i	$-0.351328\pi$
$607$	13467.4	0.900536	0.450268	+	0.892893i	$0.351328\pi$
$608$	−3662.73	−0.244314
$609$	3372.72	0.224417
$610$	10637.3	0.706050
$611$	10671.0	0.706550
$612$	−5256.96	−0.347222
$613$	−305.652	−0.0201389	−0.0100695	−	0.999949i	$-0.503205\pi$
$613$	−305.652	−0.0201389	−0.0100695	+	0.999949i	$0.503205\pi$
$614$	−26131.1	−1.71754
$615$	−2407.81	−0.157874
$616$	−5565.59	−0.364033
$617$	−9622.99	−0.627888	−0.313944	−	0.949441i	$-0.601650\pi$
$617$	−9622.99	−0.627888	−0.313944	+	0.949441i	$0.601650\pi$
$618$	−1177.93	−0.0766718
$619$	−22066.0	−1.43280	−0.716402	−	0.697688i	$-0.754212\pi$
$619$	−22066.0	−1.43280	−0.716402	+	0.697688i	$0.754212\pi$
$620$	8085.40	0.523738
$621$	−3727.53	−0.240871
$622$	24750.7	1.59552
$623$	−17843.6	−1.14749
$624$	−2759.99	−0.177064
$625$	−5443.65	−0.348394
$626$	20250.3	1.29292
$627$	−832.877	−0.0530493
$628$	−866.026	−0.0550290
$629$	−476.732	−0.0302203
$630$	10469.0	0.662058
$631$	−17068.5	−1.07684	−0.538421	−	0.842676i	$-0.680979\pi$
$631$	−17068.5	−1.07684	−0.538421	+	0.842676i	$0.680979\pi$
$632$	9958.95	0.626813
$633$	3116.39	0.195680
$634$	13362.8	0.837071
$635$	−20971.2	−1.31058
$636$	63.4445	0.00395557
$637$	−4152.91	−0.258311
$638$	23949.0	1.48613
$639$	−14064.2	−0.870689
$640$	11269.7	0.696051
$641$	31651.9	1.95035	0.975176	−	0.221429i	$-0.0710722\pi$
$641$	31651.9	1.95035	0.975176	+	0.221429i	$0.0710722\pi$
$642$	7892.02	0.485160
$643$	17082.4	1.04769	0.523844	−	0.851814i	$-0.324497\pi$
$643$	17082.4	1.04769	0.523844	+	0.851814i	$0.324497\pi$
$644$	−3750.53	−0.229490
$645$	0	0
$646$	2969.18	0.180837
$647$	2385.83	0.144972	0.0724858	−	0.997369i	$-0.476907\pi$
$647$	2385.83	0.144972	0.0724858	+	0.997369i	$0.476907\pi$
$648$	6980.77	0.423195
$649$	21090.3	1.27560
$650$	5559.55	0.335482
$651$	3567.05	0.214752
$652$	−13215.3	−0.793790
$653$	−12182.0	−0.730044	−0.365022	−	0.930999i	$-0.618939\pi$
$653$	−12182.0	−0.730044	−0.365022	+	0.930999i	$0.618939\pi$
$654$	4369.05	0.261228
$655$	−10939.1	−0.652560
$656$	−18368.3	−1.09324
$657$	25484.7	1.51332
$658$	19127.6	1.13324
$659$	13270.3	0.784425	0.392213	−	0.919875i	$-0.371710\pi$
$659$	13270.3	0.784425	0.392213	+	0.919875i	$0.371710\pi$
$660$	−1718.87	−0.101374
$661$	−26206.2	−1.54206	−0.771030	−	0.636799i	$-0.780258\pi$
$661$	−26206.2	−1.54206	−0.771030	+	0.636799i	$0.780258\pi$
$662$	17974.3	1.05527
$663$	1508.17	0.0883446
$664$	−2812.21	−0.164360
$665$	−2207.13	−0.128705
$666$	−997.913	−0.0580606
$667$	−10959.0	−0.636185
$668$	−17666.4	−1.02325
$669$	−2483.28	−0.143511
$670$	8298.48	0.478505
$671$	12438.4	0.715616
$672$	−3334.83	−0.191434
$673$	3880.18	0.222243	0.111122	−	0.993807i	$-0.464556\pi$
$673$	3880.18	0.222243	0.111122	+	0.993807i	$0.464556\pi$
$674$	15958.5	0.912017
$675$	3696.94	0.210808
$676$	−6813.87	−0.387680
$677$	−12772.7	−0.725103	−0.362551	−	0.931964i	$-0.618094\pi$
$677$	−12772.7	−0.725103	−0.362551	+	0.931964i	$0.618094\pi$
$678$	9955.33	0.563912
$679$	−23626.8	−1.33537
$680$	−4161.03	−0.234659
$681$	3569.81	0.200874
$682$	25328.9	1.42213
$683$	−18466.5	−1.03456	−0.517278	−	0.855817i	$-0.673055\pi$
$683$	−18466.5	−1.03456	−0.517278	+	0.855817i	$0.673055\pi$
$684$	2319.92	0.129685
$685$	12753.3	0.711355
$686$	−24470.2	−1.36192
$687$	−1709.62	−0.0949432
$688$	0	0
$689$	293.833	0.0162470
$690$	2107.21	0.116261
$691$	−18884.1	−1.03963	−0.519816	−	0.854278i	$-0.673999\pi$
$691$	−18884.1	−1.03963	−0.519816	+	0.854278i	$0.673999\pi$
$692$	15889.9	0.872897
$693$	12241.7	0.671028
$694$	16845.0	0.921365
$695$	−10968.4	−0.598640
$696$	−2806.03	−0.152820
$697$	10037.2	0.545460
$698$	44372.2	2.40618
$699$	−1966.26	−0.106396
$700$	3719.75	0.200848
$701$	1028.68	0.0554247	0.0277124	−	0.999616i	$-0.491178\pi$
$701$	1028.68	0.0554247	0.0277124	+	0.999616i	$0.491178\pi$
$702$	6509.47	0.349977
$703$	210.385	0.0112871
$704$	−1663.17	−0.0890383
$705$	−4011.39	−0.214294
$706$	37616.2	2.00525
$707$	−9583.22	−0.509780
$708$	3639.02	0.193168
$709$	−28632.8	−1.51668	−0.758342	−	0.651857i	$-0.773990\pi$
$709$	−28632.8	−1.51668	−0.758342	+	0.651857i	$0.773990\pi$
$710$	16393.8	0.866545
$711$	−21905.0	−1.15542
$712$	14845.5	0.781401
$713$	−11590.5	−0.608789
$714$	2703.37	0.141696
$715$	−7960.66	−0.416380
$716$	2414.31	0.126015
$717$	1977.82	0.103017
$718$	16316.4	0.848080
$719$	−18597.1	−0.964610	−0.482305	−	0.876003i	$-0.660200\pi$
$719$	−18597.1	−0.964610	−0.482305	+	0.876003i	$0.660200\pi$
$720$	−16749.0	−0.866941
$721$	−3650.06	−0.188537
$722$	23195.2	1.19562
$723$	−73.1001	−0.00376019
$724$	17351.1	0.890674
$725$	10869.1	0.556784
$726$	583.193	0.0298131
$727$	23634.8	1.20573	0.602865	−	0.797843i	$-0.294026\pi$
$727$	23634.8	1.20573	0.602865	+	0.797843i	$0.294026\pi$
$728$	−4447.54	−0.226424
$729$	−13125.1	−0.666823
$730$	−29706.0	−1.50612
$731$	0	0
$732$	2146.18	0.108368
$733$	19482.3	0.981713	0.490856	−	0.871241i	$-0.336684\pi$
$733$	19482.3	0.981713	0.490856	+	0.871241i	$0.336684\pi$
$734$	−13662.4	−0.687039
$735$	1561.14	0.0783450
$736$	10835.9	0.542686
$737$	9703.59	0.484988
$738$	21010.2	1.04796
$739$	24872.5	1.23809	0.619046	−	0.785354i	$-0.287519\pi$
$739$	24872.5	1.23809	0.619046	+	0.785354i	$0.287519\pi$
$740$	434.186	0.0215689
$741$	−665.564	−0.0329961
$742$	526.692	0.0260586
$743$	18338.8	0.905497	0.452748	−	0.891638i	$-0.350444\pi$
$743$	18338.8	0.905497	0.452748	+	0.891638i	$0.350444\pi$
$744$	−2967.71	−0.146239
$745$	6806.31	0.334717
$746$	44906.9	2.20397
$747$	6185.53	0.302967
$748$	7165.26	0.350251
$749$	24455.1	1.19302
$750$	−6739.04	−0.328100
$751$	22631.1	1.09963	0.549813	−	0.835288i	$-0.314699\pi$
$751$	22631.1	1.09963	0.549813	+	0.835288i	$0.314699\pi$
$752$	−30601.4	−1.48394
$753$	−7877.43	−0.381235
$754$	19138.0	0.924357
$755$	19422.3	0.936224
$756$	4355.32	0.209526
$757$	−20776.7	−0.997547	−0.498774	−	0.866732i	$-0.666216\pi$
$757$	−20776.7	−0.997547	−0.498774	+	0.866732i	$0.666216\pi$
$758$	20391.8	0.977129
$759$	2464.00	0.117836
$760$	1836.29	0.0876436
$761$	2888.31	0.137584	0.0687918	−	0.997631i	$-0.478086\pi$
$761$	2888.31	0.137584	0.0687918	+	0.997631i	$0.478086\pi$
$762$	−11335.5	−0.538899
$763$	13538.4	0.642364
$764$	10542.2	0.499220
$765$	9152.31	0.432552
$766$	−18844.9	−0.888897
$767$	16853.5	0.793411
$768$	6573.39	0.308850
$769$	27242.6	1.27749	0.638747	−	0.769417i	$-0.279453\pi$
$769$	27242.6	1.27749	0.638747	+	0.769417i	$0.279453\pi$
$770$	−14269.4	−0.667834
$771$	4967.65	0.232044
$772$	−15097.2	−0.703836
$773$	−38700.3	−1.80071	−0.900357	−	0.435152i	$-0.856694\pi$
$773$	−38700.3	−1.80071	−0.900357	+	0.435152i	$0.856694\pi$
$774$	0	0
$775$	11495.3	0.532806
$776$	19657.0	0.909337
$777$	191.550	0.00884406
$778$	36522.2	1.68301
$779$	−4429.47	−0.203726
$780$	−1373.57	−0.0630535
$781$	19169.6	0.878285
$782$	−8784.10	−0.401687
$783$	12726.2	0.580840
$784$	11909.4	0.542519
$785$	1507.74	0.0685524
$786$	−5912.88	−0.268328
$787$	4612.23	0.208905	0.104452	−	0.994530i	$-0.466691\pi$
$787$	4612.23	0.208905	0.104452	+	0.994530i	$0.466691\pi$
$788$	−7037.25	−0.318137
$789$	−5907.68	−0.266564
$790$	25533.3	1.14992
$791$	30848.7	1.38667
$792$	−10184.8	−0.456946
$793$	9939.69	0.445106
$794$	24081.0	1.07632
$795$	−110.456	−0.00492765
$796$	−4201.61	−0.187088
$797$	−17700.3	−0.786672	−0.393336	−	0.919395i	$-0.628679\pi$
$797$	−17700.3	−0.786672	−0.393336	+	0.919395i	$0.628679\pi$
$798$	−1193.01	−0.0529226
$799$	16721.8	0.740396
$800$	−10747.0	−0.474954
$801$	−32653.0	−1.44037
$802$	−45467.5	−2.00189
$803$	−34735.8	−1.52653
$804$	1674.30	0.0734430
$805$	6529.64	0.285888
$806$	20240.7	0.884550
$807$	−2439.16	−0.106397
$808$	7973.04	0.347142
$809$	21577.2	0.937718	0.468859	−	0.883273i	$-0.344665\pi$
$809$	21577.2	0.937718	0.468859	+	0.883273i	$0.344665\pi$
$810$	17897.7	0.776371
$811$	−22620.0	−0.979402	−0.489701	−	0.871890i	$-0.662894\pi$
$811$	−22620.0	−0.979402	−0.489701	+	0.871890i	$0.662894\pi$
$812$	12804.8	0.553398
$813$	1243.90	0.0536598
$814$	1360.16	0.0585671
$815$	23007.7	0.988864
$816$	−4325.01	−0.185546
$817$	0	0
$818$	−41963.5	−1.79367
$819$	9782.49	0.417372
$820$	−9141.41	−0.389307
$821$	13018.6	0.553414	0.276707	−	0.960954i	$-0.410757\pi$
$821$	13018.6	0.553414	0.276707	+	0.960954i	$0.410757\pi$
$822$	6893.49	0.292504
$823$	26648.0	1.12867	0.564333	−	0.825548i	$-0.309134\pi$
$823$	26648.0	1.12867	0.564333	+	0.825548i	$0.309134\pi$
$824$	3036.77	0.128387
$825$	−2443.78	−0.103129
$826$	30209.7	1.27256
$827$	34484.0	1.44997	0.724985	−	0.688765i	$-0.241847\pi$
$827$	34484.0	1.44997	0.724985	+	0.688765i	$0.241847\pi$
$828$	−6863.32	−0.288064
$829$	1098.48	0.0460214	0.0230107	−	0.999735i	$-0.492675\pi$
$829$	1098.48	0.0460214	0.0230107	+	0.999735i	$0.492675\pi$
$830$	−7210.09	−0.301525
$831$	199.704	0.00833653
$832$	−1329.06	−0.0553809
$833$	−6507.76	−0.270685
$834$	−5928.70	−0.246156
$835$	30756.9	1.27472
$836$	−3162.07	−0.130816
$837$	13459.5	0.555827
$838$	−42553.6	−1.75416
$839$	18466.4	0.759869	0.379935	−	0.925013i	$-0.375946\pi$
$839$	18466.4	0.759869	0.379935	+	0.925013i	$0.375946\pi$
$840$	1671.90	0.0686738
$841$	13026.4	0.534111
$842$	−12009.3	−0.491528
$843$	5615.40	0.229424
$844$	11831.6	0.482535
$845$	11862.9	0.482953
$846$	35002.8	1.42248
$847$	1807.15	0.0733108
$848$	−842.632	−0.0341227
$849$	2253.08	0.0910782
$850$	8712.01	0.351552
$851$	−622.407	−0.0250715
$852$	3307.61	0.133001
$853$	18778.3	0.753758	0.376879	−	0.926262i	$-0.376997\pi$
$853$	18778.3	0.753758	0.376879	+	0.926262i	$0.376997\pi$
$854$	17816.8	0.713907
$855$	−4038.96	−0.161555
$856$	−20346.1	−0.812402
$857$	−11329.7	−0.451594	−0.225797	−	0.974174i	$-0.572499\pi$
$857$	−11329.7	−0.451594	−0.225797	+	0.974174i	$0.572499\pi$
$858$	−4302.95	−0.171212
$859$	−7802.13	−0.309901	−0.154951	−	0.987922i	$-0.549522\pi$
$859$	−7802.13	−0.309901	−0.154951	+	0.987922i	$0.549522\pi$
$860$	0	0
$861$	−4032.93	−0.159631
$862$	46430.0	1.83459
$863$	2073.23	0.0817772	0.0408886	−	0.999164i	$-0.486981\pi$
$863$	2073.23	0.0817772	0.0408886	+	0.999164i	$0.486981\pi$
$864$	−12583.2	−0.495475
$865$	−27664.2	−1.08741
$866$	−27669.2	−1.08572
$867$	−3802.34	−0.148944
$868$	13542.5	0.529566
$869$	29856.6	1.16550
$870$	−7194.26	−0.280354
$871$	7754.27	0.301657
$872$	−11263.7	−0.437427
$873$	−43236.1	−1.67620
$874$	3876.47	0.150027
$875$	−20882.3	−0.806802
$876$	−5993.49	−0.231166
$877$	−34268.5	−1.31946	−0.659730	−	0.751503i	$-0.729329\pi$
$877$	−34268.5	−1.31946	−0.659730	+	0.751503i	$0.729329\pi$
$878$	22678.5	0.871713
$879$	3632.27	0.139378
$880$	22828.9	0.874504
$881$	−1741.62	−0.0666022	−0.0333011	−	0.999445i	$-0.510602\pi$
$881$	−1741.62	−0.0666022	−0.0333011	+	0.999445i	$0.510602\pi$
$882$	−13622.3	−0.520052
$883$	−32637.7	−1.24388	−0.621940	−	0.783065i	$-0.713655\pi$
$883$	−32637.7	−1.24388	−0.621940	+	0.783065i	$0.713655\pi$
$884$	5725.86	0.217852
$885$	−6335.50	−0.240639
$886$	−28990.0	−1.09925
$887$	−8630.79	−0.326712	−0.163356	−	0.986567i	$-0.552232\pi$
$887$	−8630.79	−0.326712	−0.163356	+	0.986567i	$0.552232\pi$
$888$	−159.366	−0.00602249
$889$	−35125.4	−1.32516
$890$	38061.6	1.43351
$891$	20928.1	0.786889
$892$	−9427.93	−0.353890
$893$	−7379.44	−0.276533
$894$	3678.99	0.137633
$895$	−4203.29	−0.156984
$896$	18876.0	0.703796
$897$	1969.02	0.0732929
$898$	51474.5	1.91283
$899$	39571.2	1.46805
$900$	6807.00	0.252111
$901$	460.447	0.0170252
$902$	−28637.0	−1.05710
$903$	0	0
$904$	−25665.5	−0.944271
$905$	−30208.1	−1.10956
$906$	10498.3	0.384968
$907$	51481.3	1.88468	0.942342	−	0.334650i	$-0.108618\pi$
$907$	51481.3	1.88468	0.942342	+	0.334650i	$0.108618\pi$
$908$	13553.0	0.495343
$909$	−17536.9	−0.639893
$910$	−11402.9	−0.415386
$911$	−18219.6	−0.662616	−0.331308	−	0.943523i	$-0.607490\pi$
$911$	−18219.6	−0.662616	−0.331308	+	0.943523i	$0.607490\pi$
$912$	1908.65	0.0693001
$913$	−8430.91	−0.305610
$914$	2824.59	0.102220
$915$	−3736.48	−0.134999
$916$	−6490.67	−0.234124
$917$	−18322.3	−0.659821
$918$	10200.6	0.366742
$919$	−4478.58	−0.160756	−0.0803781	−	0.996764i	$-0.525613\pi$
$919$	−4478.58	−0.160756	−0.0803781	+	0.996764i	$0.525613\pi$
$920$	−5432.52	−0.194679
$921$	9178.89	0.328398
$922$	36115.3	1.29001
$923$	15318.7	0.546284
$924$	−2878.99	−0.102502
$925$	617.299	0.0219424
$926$	−51571.9	−1.83019
$927$	−6679.45	−0.236658
$928$	−36995.0	−1.30864
$929$	5624.27	0.198629	0.0993145	−	0.995056i	$-0.468335\pi$
$929$	5624.27	0.198629	0.0993145	+	0.995056i	$0.468335\pi$
$930$	−7608.77	−0.268281
$931$	2871.91	0.101099
$932$	−7465.03	−0.262366
$933$	−8693.98	−0.305068
$934$	10024.6	0.351194
$935$	−12474.6	−0.436325
$936$	−8138.83	−0.284216
$937$	−10478.7	−0.365339	−0.182669	−	0.983174i	$-0.558474\pi$
$937$	−10478.7	−0.365339	−0.182669	+	0.983174i	$0.558474\pi$
$938$	13899.4	0.483830
$939$	−7113.18	−0.247210
$940$	−15229.5	−0.528437
$941$	−271.432	−0.00940323	−0.00470161	−	0.999989i	$-0.501497\pi$
$941$	−271.432	−0.00940323	−0.00470161	+	0.999989i	$0.501497\pi$
$942$	814.974	0.0281882
$943$	13104.3	0.452527
$944$	−48331.2	−1.66636
$945$	−7582.57	−0.261017
$946$	0	0
$947$	−20691.2	−0.710002	−0.355001	−	0.934866i	$-0.615520\pi$
$947$	−20691.2	−0.710002	−0.355001	+	0.934866i	$0.615520\pi$
$948$	5151.60	0.176494
$949$	−27757.9	−0.949482
$950$	−3844.66	−0.131302
$951$	−4693.84	−0.160051
$952$	−6969.46	−0.237271
$953$	4609.77	0.156690	0.0783448	−	0.996926i	$-0.475037\pi$
$953$	4609.77	0.156690	0.0783448	+	0.996926i	$0.475037\pi$
$954$	963.825	0.0327096
$955$	−18353.9	−0.621903
$956$	7508.93	0.254034
$957$	−8412.40	−0.284153
$958$	25257.8	0.851821
$959$	21360.9	0.719270
$960$	499.614	0.0167968
$961$	12060.2	0.404825
$962$	1086.92	0.0364281
$963$	44751.8	1.49752
$964$	−277.529	−0.00927241
$965$	26284.1	0.876804
$966$	3529.44	0.117555
$967$	33538.4	1.11533	0.557664	−	0.830067i	$-0.311698\pi$
$967$	33538.4	1.11533	0.557664	+	0.830067i	$0.311698\pi$
$968$	−1503.51	−0.0499221
$969$	−1042.96	−0.0345766
$970$	50397.7	1.66822
$971$	−2705.71	−0.0894238	−0.0447119	−	0.999000i	$-0.514237\pi$
$971$	−2705.71	−0.0894238	−0.0447119	+	0.999000i	$0.514237\pi$
$972$	12074.8	0.398456
$973$	−18371.3	−0.605302
$974$	42996.8	1.41448
$975$	−1952.86	−0.0641453
$976$	−28504.3	−0.934835
$977$	−12223.7	−0.400278	−0.200139	−	0.979767i	$-0.564139\pi$
$977$	−12223.7	−0.400278	−0.200139	+	0.979767i	$0.564139\pi$
$978$	12436.3	0.406613
$979$	44506.2	1.45294
$980$	5926.97	0.193194
$981$	24774.8	0.806317
$982$	43218.2	1.40443
$983$	−32799.7	−1.06424	−0.532119	−	0.846669i	$-0.678604\pi$
$983$	−32799.7	−1.06424	−0.532119	+	0.846669i	$0.678604\pi$
$984$	3355.31	0.108703
$985$	12251.8	0.396319
$986$	29989.9	0.968635
$987$	−6718.81	−0.216679
$988$	−2526.85	−0.0813663
$989$	0	0
$990$	−26112.4	−0.838288
$991$	−458.373	−0.0146929	−0.00734647	−	0.999973i	$-0.502338\pi$
$991$	−458.373	−0.0146929	−0.00734647	+	0.999973i	$0.502338\pi$
$992$	−39126.6	−1.25229
$993$	−6313.68	−0.201771
$994$	27458.5	0.876187
$995$	7314.95	0.233065
$996$	−1454.71	−0.0462794
$997$	−30483.0	−0.968312	−0.484156	−	0.874982i	$-0.660873\pi$
$997$	−30483.0	−0.968312	−0.484156	+	0.874982i	$0.660873\pi$
$998$	−3627.68	−0.115062
$999$	722.773	0.0228904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.k.1.13		60
43.3	odd	42		43.4.g.a.9.8	✓	120
43.29	odd	42		43.4.g.a.24.8	yes	120
43.42	odd	2		1849.4.a.l.1.48		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.9.8	✓	120	43.3	odd	42
43.4.g.a.24.8	yes	120	43.29	odd	42
1849.4.a.k.1.13		60	1.1	even	1	trivial
1849.4.a.l.1.48		60	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)

\(f(q)\)	\(=\)	\(q-3.57276 q^{2} +1.25498 q^{3} +4.76459 q^{4} -8.29511 q^{5} -4.48372 q^{6} -13.8938 q^{7} +11.5593 q^{8} -25.4250 q^{9} +O(q^{10})\)	\(q-3.57276 q^{2} +1.25498 q^{3} +4.76459 q^{4} -8.29511 q^{5} -4.48372 q^{6} -13.8938 q^{7} +11.5593 q^{8} -25.4250 q^{9} +29.6364 q^{10} +34.6545 q^{11} +5.97945 q^{12} +27.6929 q^{13} +49.6391 q^{14} -10.4102 q^{15} -79.4154 q^{16} +43.3957 q^{17} +90.8375 q^{18} -19.1508 q^{19} -39.5228 q^{20} -17.4363 q^{21} -123.812 q^{22} +56.6562 q^{23} +14.5067 q^{24} -56.1912 q^{25} -98.9399 q^{26} -65.7922 q^{27} -66.1982 q^{28} -193.431 q^{29} +37.1930 q^{30} -204.576 q^{31} +191.257 q^{32} +43.4905 q^{33} -155.042 q^{34} +115.250 q^{35} -121.140 q^{36} -10.9857 q^{37} +68.4211 q^{38} +34.7539 q^{39} -95.8858 q^{40} +231.294 q^{41} +62.2958 q^{42} +165.114 q^{44} +210.903 q^{45} -202.419 q^{46} +385.334 q^{47} -99.6644 q^{48} -149.963 q^{49} +200.757 q^{50} +54.4606 q^{51} +131.945 q^{52} +10.6104 q^{53} +235.059 q^{54} -287.462 q^{55} -160.603 q^{56} -24.0338 q^{57} +691.081 q^{58} +608.588 q^{59} -49.6002 q^{60} +358.926 q^{61} +730.899 q^{62} +353.250 q^{63} -47.9929 q^{64} -229.715 q^{65} -155.381 q^{66} +280.010 q^{67} +206.763 q^{68} +71.1021 q^{69} -411.761 q^{70} +553.163 q^{71} -293.896 q^{72} -1002.35 q^{73} +39.2492 q^{74} -70.5186 q^{75} -91.2457 q^{76} -481.481 q^{77} -124.167 q^{78} +861.551 q^{79} +658.759 q^{80} +603.908 q^{81} -826.359 q^{82} -243.285 q^{83} -83.0771 q^{84} -359.972 q^{85} -242.751 q^{87} +400.582 q^{88} +1284.29 q^{89} -753.507 q^{90} -384.758 q^{91} +269.944 q^{92} -256.737 q^{93} -1376.70 q^{94} +158.858 q^{95} +240.023 q^{96} +1700.53 q^{97} +535.782 q^{98} -881.091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * q^99

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