LMFDB - Embedded newform 1849.4.a.j.1.34

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			1.34
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)

$f(q)$	$=$	$q+2.53235 q^{2} -8.01322 q^{3} -1.58719 q^{4} -20.7136 q^{5} -20.2923 q^{6} -3.06093 q^{7} -24.2781 q^{8} +37.2117 q^{9} +O(q^{10})$	\(q+2.53235 q^{2} -8.01322 q^{3} -1.58719 q^{4} -20.7136 q^{5} -20.2923 q^{6} -3.06093 q^{7} -24.2781 q^{8} +37.2117 q^{9} -52.4541 q^{10} -50.3240 q^{11} +12.7185 q^{12} -26.3471 q^{13} -7.75136 q^{14} +165.983 q^{15} -48.7833 q^{16} -23.1013 q^{17} +94.2331 q^{18} +135.885 q^{19} +32.8765 q^{20} +24.5279 q^{21} -127.438 q^{22} -91.8712 q^{23} +194.546 q^{24} +304.053 q^{25} -66.7201 q^{26} -81.8285 q^{27} +4.85830 q^{28} +15.5009 q^{29} +420.326 q^{30} -34.9791 q^{31} +70.6888 q^{32} +403.257 q^{33} -58.5007 q^{34} +63.4029 q^{35} -59.0622 q^{36} +221.246 q^{37} +344.110 q^{38} +211.125 q^{39} +502.888 q^{40} +206.730 q^{41} +62.1133 q^{42} +79.8739 q^{44} -770.788 q^{45} -232.650 q^{46} -600.224 q^{47} +390.911 q^{48} -333.631 q^{49} +769.970 q^{50} +185.116 q^{51} +41.8180 q^{52} +408.162 q^{53} -207.218 q^{54} +1042.39 q^{55} +74.3138 q^{56} -1088.88 q^{57} +39.2539 q^{58} -740.433 q^{59} -263.447 q^{60} -51.7496 q^{61} -88.5794 q^{62} -113.902 q^{63} +569.275 q^{64} +545.743 q^{65} +1021.19 q^{66} +334.159 q^{67} +36.6663 q^{68} +736.184 q^{69} +160.559 q^{70} +487.740 q^{71} -903.431 q^{72} +722.667 q^{73} +560.272 q^{74} -2436.45 q^{75} -215.677 q^{76} +154.038 q^{77} +534.643 q^{78} -171.428 q^{79} +1010.48 q^{80} -349.006 q^{81} +523.513 q^{82} -241.764 q^{83} -38.9306 q^{84} +478.511 q^{85} -124.213 q^{87} +1221.77 q^{88} +333.067 q^{89} -1951.91 q^{90} +80.6467 q^{91} +145.817 q^{92} +280.295 q^{93} -1519.98 q^{94} -2814.68 q^{95} -566.445 q^{96} +687.004 q^{97} -844.870 q^{98} -1872.64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.53235	0.895322	0.447661	−	0.894203i	$-0.352257\pi$
$2$	2.53235	0.895322	0.447661	+	0.894203i	$0.352257\pi$
$3$	−8.01322	−1.54214	−0.771072	−	0.636747i	$-0.780279\pi$
$3$	−8.01322	−1.54214	−0.771072	+	0.636747i	$0.780279\pi$
$4$	−1.58719	−0.198399
$5$	−20.7136	−1.85268	−0.926340	−	0.376687i	$-0.877063\pi$
$5$	−20.7136	−1.85268	−0.926340	+	0.376687i	$0.877063\pi$
$6$	−20.2923	−1.38072
$7$	−3.06093	−0.165275	−0.0826374	−	0.996580i	$-0.526334\pi$
$7$	−3.06093	−0.165275	−0.0826374	+	0.996580i	$0.526334\pi$
$8$	−24.2781	−1.07295
$9$	37.2117	1.37821
$10$	−52.4541	−1.65875
$11$	−50.3240	−1.37939	−0.689693	−	0.724102i	$-0.742255\pi$
$11$	−50.3240	−1.37939	−0.689693	+	0.724102i	$0.742255\pi$
$12$	12.7185	0.305961
$13$	−26.3471	−0.562105	−0.281053	−	0.959692i	$-0.590684\pi$
$13$	−26.3471	−0.562105	−0.281053	+	0.959692i	$0.590684\pi$
$14$	−7.75136	−0.147974
$15$	165.983	2.85710
$16$	−48.7833	−0.762238
$17$	−23.1013	−0.329582	−0.164791	−	0.986329i	$-0.552695\pi$
$17$	−23.1013	−0.329582	−0.164791	+	0.986329i	$0.552695\pi$
$18$	94.2331	1.23394
$19$	135.885	1.64075	0.820375	−	0.571826i	$-0.193765\pi$
$19$	135.885	1.64075	0.820375	+	0.571826i	$0.193765\pi$
$20$	32.8765	0.367571
$21$	24.5279	0.254878
$22$	−127.438	−1.23499
$23$	−91.8712	−0.832890	−0.416445	−	0.909161i	$-0.636724\pi$
$23$	−91.8712	−0.832890	−0.416445	+	0.909161i	$0.636724\pi$
$24$	194.546	1.65465
$25$	304.053	2.43243
$26$	−66.7201	−0.503265
$27$	−81.8285	−0.583255
$28$	4.85830	0.0327904
$29$	15.5009	0.0992570	0.0496285	−	0.998768i	$-0.484196\pi$
$29$	15.5009	0.0992570	0.0496285	+	0.998768i	$0.484196\pi$
$30$	420.326	2.55802
$31$	−34.9791	−0.202659	−0.101330	−	0.994853i	$-0.532310\pi$
$31$	−34.9791	−0.202659	−0.101330	+	0.994853i	$0.532310\pi$
$32$	70.6888	0.390504
$33$	403.257	2.12721
$34$	−58.5007	−0.295082
$35$	63.4029	0.306201
$36$	−59.0622	−0.273436
$37$	221.246	0.983043	0.491522	−	0.870865i	$-0.336441\pi$
$37$	221.246	0.983043	0.491522	+	0.870865i	$0.336441\pi$
$38$	344.110	1.46900
$39$	211.125	0.866848
$40$	502.888	1.98784
$41$	206.730	0.787459	0.393729	−	0.919226i	$-0.371185\pi$
$41$	206.730	0.787459	0.393729	+	0.919226i	$0.371185\pi$
$42$	62.1133	0.228197
$43$	0	0
$43$	0	0
$44$	79.8739	0.273669
$45$	−770.788	−2.55338
$46$	−232.650	−0.745704
$47$	−600.224	−1.86280	−0.931400	−	0.363997i	$-0.881412\pi$
$47$	−600.224	−1.86280	−0.931400	+	0.363997i	$0.881412\pi$
$48$	390.911	1.17548
$49$	−333.631	−0.972684
$50$	769.970	2.17780
$51$	185.116	0.508263
$52$	41.8180	0.111521
$53$	408.162	1.05784	0.528919	−	0.848672i	$-0.322598\pi$
$53$	408.162	1.05784	0.528919	+	0.848672i	$0.322598\pi$
$54$	−207.218	−0.522201
$55$	1042.39	2.55556
$56$	74.3138	0.177332
$57$	−1088.88	−2.53027
$58$	39.2539	0.0888670
$59$	−740.433	−1.63383	−0.816916	−	0.576756i	$-0.804318\pi$
$59$	−740.433	−1.63383	−0.816916	+	0.576756i	$0.804318\pi$
$60$	−263.447	−0.566847
$61$	−51.7496	−0.108621	−0.0543103	−	0.998524i	$-0.517296\pi$
$61$	−51.7496	−0.108621	−0.0543103	+	0.998524i	$0.517296\pi$
$62$	−88.5794	−0.181445
$63$	−113.902	−0.227783
$64$	569.275	1.11187
$65$	545.743	1.04140
$66$	1021.19	1.90454
$67$	334.159	0.609314	0.304657	−	0.952462i	$-0.401458\pi$
$67$	334.159	0.609314	0.304657	+	0.952462i	$0.401458\pi$
$68$	36.6663	0.0653888
$69$	736.184	1.28444
$70$	160.559	0.274149
$71$	487.740	0.815269	0.407634	−	0.913145i	$-0.366354\pi$
$71$	487.740	0.815269	0.407634	+	0.913145i	$0.366354\pi$
$72$	−903.431	−1.47875
$73$	722.667	1.15865	0.579327	−	0.815095i	$-0.303315\pi$
$73$	722.667	1.15865	0.579327	+	0.815095i	$0.303315\pi$
$74$	560.272	0.880140
$75$	−2436.45	−3.75115
$76$	−215.677	−0.325524
$77$	154.038	0.227978
$78$	534.643	0.776107
$79$	−171.428	−0.244141	−0.122071	−	0.992521i	$-0.538953\pi$
$79$	−171.428	−0.244141	−0.122071	+	0.992521i	$0.538953\pi$
$80$	1010.48	1.41218
$81$	−349.006	−0.478746
$82$	523.513	0.705029
$83$	−241.764	−0.319724	−0.159862	−	0.987139i	$-0.551105\pi$
$83$	−241.764	−0.319724	−0.159862	+	0.987139i	$0.551105\pi$
$84$	−38.9306	−0.0505676
$85$	478.511	0.610610
$86$	0	0
$87$	−124.213	−0.153069
$88$	1221.77	1.48002
$89$	333.067	0.396686	0.198343	−	0.980133i	$-0.436444\pi$
$89$	333.067	0.396686	0.198343	+	0.980133i	$0.436444\pi$
$90$	−1951.91	−2.28610
$91$	80.6467	0.0929019
$92$	145.817	0.165245
$93$	280.295	0.312530
$94$	−1519.98	−1.66781
$95$	−2814.68	−3.03979
$96$	−566.445	−0.602214
$97$	687.004	0.719120	0.359560	−	0.933122i	$-0.382927\pi$
$97$	687.004	0.719120	0.359560	+	0.933122i	$0.382927\pi$
$98$	−844.870	−0.870865
$99$	−1872.64	−1.90108
$100$	−482.592	−0.482592
$101$	918.164	0.904561	0.452281	−	0.891876i	$-0.350611\pi$
$101$	918.164	0.904561	0.452281	+	0.891876i	$0.350611\pi$
$102$	468.779	0.455059
$103$	−348.289	−0.333184	−0.166592	−	0.986026i	$-0.553276\pi$
$103$	−348.289	−0.333184	−0.166592	+	0.986026i	$0.553276\pi$
$104$	639.659	0.603112
$105$	−508.062	−0.472207
$106$	1033.61	0.947105
$107$	830.251	0.750125	0.375063	−	0.927000i	$-0.377621\pi$
$107$	830.251	0.750125	0.375063	+	0.927000i	$0.377621\pi$
$108$	129.878	0.115717
$109$	−295.829	−0.259957	−0.129979	−	0.991517i	$-0.541491\pi$
$109$	−295.829	−0.259957	−0.129979	+	0.991517i	$0.541491\pi$
$110$	2639.70	2.28805
$111$	−1772.89	−1.51599
$112$	149.322	0.125979
$113$	−1631.99	−1.35862	−0.679311	−	0.733850i	$-0.737721\pi$
$113$	−1631.99	−1.35862	−0.679311	+	0.733850i	$0.737721\pi$
$114$	−2757.43	−2.26541
$115$	1902.98	1.54308
$116$	−24.6030	−0.0196925
$117$	−980.420	−0.774699
$118$	−1875.04	−1.46281
$119$	70.7116	0.0544716
$120$	−4029.75	−3.06554
$121$	1201.50	0.902706
$122$	−131.048	−0.0972503
$123$	−1656.57	−1.21438
$124$	55.5186	0.0402074
$125$	−3708.84	−2.65383
$126$	−288.441	−0.203939
$127$	243.422	0.170080	0.0850401	−	0.996378i	$-0.472898\pi$
$127$	243.422	0.170080	0.0850401	+	0.996378i	$0.472898\pi$
$128$	876.094	0.604973
$129$	0	0
$130$	1382.01	0.932389
$131$	2342.26	1.56217	0.781083	−	0.624427i	$-0.214667\pi$
$131$	2342.26	1.56217	0.781083	+	0.624427i	$0.214667\pi$
$132$	−640.047	−0.422038
$133$	−415.936	−0.271175
$134$	846.208	0.545532
$135$	1694.96	1.08059
$136$	560.857	0.353626
$137$	−1232.79	−0.768788	−0.384394	−	0.923169i	$-0.625590\pi$
$137$	−1232.79	−0.768788	−0.384394	+	0.923169i	$0.625590\pi$
$138$	1864.28	1.14998
$139$	−310.063	−0.189203	−0.0946014	−	0.995515i	$-0.530158\pi$
$139$	−310.063	−0.189203	−0.0946014	+	0.995515i	$0.530158\pi$
$140$	−100.633	−0.0607502
$141$	4809.72	2.87271
$142$	1235.13	0.729928
$143$	1325.89	0.775360
$144$	−1815.31	−1.05052
$145$	−321.080	−0.183892
$146$	1830.05	1.03737
$147$	2673.46	1.50002
$148$	−351.160	−0.195035
$149$	−2522.04	−1.38667	−0.693334	−	0.720616i	$-0.743859\pi$
$149$	−2522.04	−1.38667	−0.693334	+	0.720616i	$0.743859\pi$
$150$	−6169.94	−3.35849
$151$	999.113	0.538455	0.269227	−	0.963077i	$-0.413232\pi$
$151$	999.113	0.538455	0.269227	+	0.963077i	$0.413232\pi$
$152$	−3299.05	−1.76045
$153$	−859.639	−0.454233
$154$	390.079	0.204113
$155$	724.543	0.375462
$156$	−335.097	−0.171982
$157$	1192.13	0.606002	0.303001	−	0.952990i	$-0.402011\pi$
$157$	1192.13	0.606002	0.303001	+	0.952990i	$0.402011\pi$
$158$	−434.116	−0.218585
$159$	−3270.69	−1.63134
$160$	−1464.22	−0.723480
$161$	281.212	0.137656
$162$	−883.806	−0.428632
$163$	114.218	0.0548847	0.0274424	−	0.999623i	$-0.491264\pi$
$163$	114.218	0.0548847	0.0274424	+	0.999623i	$0.491264\pi$
$164$	−328.121	−0.156231
$165$	−8352.91	−3.94105
$166$	−612.232	−0.286256
$167$	3106.64	1.43952	0.719758	−	0.694225i	$-0.244253\pi$
$167$	3106.64	1.43952	0.719758	+	0.694225i	$0.244253\pi$
$168$	−595.493	−0.273472
$169$	−1502.83	−0.684038
$170$	1211.76	0.546692
$171$	5056.53	2.26130
$172$	0	0
$173$	−2342.86	−1.02962	−0.514810	−	0.857304i	$-0.672138\pi$
$173$	−2342.86	−1.02962	−0.514810	+	0.857304i	$0.672138\pi$
$174$	−314.550	−0.137046
$175$	−930.687	−0.402019
$176$	2454.97	1.05142
$177$	5933.25	2.51961
$178$	843.442	0.355161
$179$	−1671.04	−0.697762	−0.348881	−	0.937167i	$-0.613438\pi$
$179$	−1671.04	−0.697762	−0.348881	+	0.937167i	$0.613438\pi$
$180$	1223.39	0.506590
$181$	2195.16	0.901465	0.450732	−	0.892659i	$-0.351163\pi$
$181$	2195.16	0.901465	0.450732	+	0.892659i	$0.351163\pi$
$182$	204.226	0.0831770
$183$	414.681	0.167509
$184$	2230.46	0.893652
$185$	−4582.80	−1.82127
$186$	709.806	0.279814
$187$	1162.55	0.454621
$188$	952.672	0.369578
$189$	250.471	0.0963974
$190$	−7127.75	−2.72159
$191$	−79.6602	−0.0301781	−0.0150890	−	0.999886i	$-0.504803\pi$
$191$	−79.6602	−0.0301781	−0.0150890	+	0.999886i	$0.504803\pi$
$192$	−4561.73	−1.71466
$193$	1109.31	0.413730	0.206865	−	0.978369i	$-0.433674\pi$
$193$	1109.31	0.413730	0.206865	+	0.978369i	$0.433674\pi$
$194$	1739.73	0.643844
$195$	−4373.16	−1.60599
$196$	529.537	0.192980
$197$	2392.69	0.865340	0.432670	−	0.901552i	$-0.357572\pi$
$197$	2392.69	0.865340	0.432670	+	0.901552i	$0.357572\pi$
$198$	−4742.18	−1.70208
$199$	210.234	0.0748899	0.0374450	−	0.999299i	$-0.488078\pi$
$199$	210.234	0.0748899	0.0374450	+	0.999299i	$0.488078\pi$
$200$	−7381.85	−2.60988
$201$	−2677.69	−0.939650
$202$	2325.11	0.809873
$203$	−47.4474	−0.0164047
$204$	−293.815	−0.100839
$205$	−4282.12	−1.45891
$206$	−881.991	−0.298307
$207$	−3418.68	−1.14790
$208$	1285.30	0.428458
$209$	−6838.29	−2.26323
$210$	−1286.59	−0.422777
$211$	857.579	0.279802	0.139901	−	0.990166i	$-0.455322\pi$
$211$	857.579	0.279802	0.139901	+	0.990166i	$0.455322\pi$
$212$	−647.833	−0.209874
$213$	−3908.37	−1.25726
$214$	2102.49	0.671603
$215$	0	0
$216$	1986.64	0.625805
$217$	107.069	0.0334944
$218$	−749.144	−0.232745
$219$	−5790.89	−1.78681
$220$	−1654.48	−0.507022
$221$	608.652	0.185260
$222$	−4489.58	−1.35730
$223$	−3532.28	−1.06071	−0.530356	−	0.847775i	$-0.677942\pi$
$223$	−3532.28	−1.06071	−0.530356	+	0.847775i	$0.677942\pi$
$224$	−216.374	−0.0645405
$225$	11314.3	3.35240
$226$	−4132.76	−1.21640
$227$	−5188.68	−1.51711	−0.758557	−	0.651607i	$-0.774095\pi$
$227$	−5188.68	−1.51711	−0.758557	+	0.651607i	$0.774095\pi$
$228$	1728.26	0.502005
$229$	3482.36	1.00490	0.502448	−	0.864607i	$-0.332433\pi$
$229$	3482.36	1.00490	0.502448	+	0.864607i	$0.332433\pi$
$230$	4819.02	1.38155
$231$	−1234.34	−0.351575
$232$	−376.334	−0.106498
$233$	1545.34	0.434500	0.217250	−	0.976116i	$-0.430291\pi$
$233$	1545.34	0.434500	0.217250	+	0.976116i	$0.430291\pi$
$234$	−2482.77	−0.693605
$235$	12432.8	3.45117
$236$	1175.21	0.324151
$237$	1373.69	0.376501
$238$	179.067	0.0487696
$239$	−2562.59	−0.693558	−0.346779	−	0.937947i	$-0.612725\pi$
$239$	−2562.59	−0.693558	−0.346779	+	0.937947i	$0.612725\pi$
$240$	−8097.17	−2.17779
$241$	−4941.93	−1.32090	−0.660452	−	0.750868i	$-0.729635\pi$
$241$	−4941.93	−1.32090	−0.660452	+	0.750868i	$0.729635\pi$
$242$	3042.63	0.808212
$243$	5006.03	1.32155
$244$	82.1366	0.0215502
$245$	6910.69	1.80207
$246$	−4195.03	−1.08726
$247$	−3580.19	−0.922274
$248$	849.228	0.217444
$249$	1937.31	0.493060
$250$	−9392.08	−2.37603
$251$	4464.77	1.12276	0.561382	−	0.827557i	$-0.310270\pi$
$251$	4464.77	1.12276	0.561382	+	0.827557i	$0.310270\pi$
$252$	180.785	0.0451921
$253$	4623.32	1.14888
$254$	616.430	0.152277
$255$	−3834.42	−0.941649
$256$	−2335.62	−0.570220
$257$	−5954.45	−1.44525	−0.722624	−	0.691242i	$-0.757064\pi$
$257$	−5954.45	−1.44525	−0.722624	+	0.691242i	$0.757064\pi$
$258$	0	0
$259$	−677.219	−0.162472
$260$	−866.201	−0.206613
$261$	576.816	0.136797
$262$	5931.41	1.39864
$263$	46.0385	0.0107941	0.00539706	−	0.999985i	$-0.498282\pi$
$263$	46.0385	0.0107941	0.00539706	+	0.999985i	$0.498282\pi$
$264$	−9790.33	−2.28240
$265$	−8454.51	−1.95984
$266$	−1053.30	−0.242789
$267$	−2668.94	−0.611747
$268$	−530.375	−0.120887
$269$	924.553	0.209558	0.104779	−	0.994496i	$-0.466587\pi$
$269$	924.553	0.209558	0.104779	+	0.994496i	$0.466587\pi$
$270$	4292.24	0.967472
$271$	−5175.61	−1.16013	−0.580067	−	0.814569i	$-0.696974\pi$
$271$	−5175.61	−1.16013	−0.580067	+	0.814569i	$0.696974\pi$
$272$	1126.96	0.251220
$273$	−646.239	−0.143268
$274$	−3121.85	−0.688313
$275$	−15301.2	−3.35526
$276$	−1168.47	−0.254831
$277$	6775.52	1.46968	0.734840	−	0.678240i	$-0.237257\pi$
$277$	6775.52	1.46968	0.734840	+	0.678240i	$0.237257\pi$
$278$	−785.189	−0.169397
$279$	−1301.63	−0.279307
$280$	−1539.31	−0.328540
$281$	2921.27	0.620172	0.310086	−	0.950709i	$-0.399642\pi$
$281$	2921.27	0.620172	0.310086	+	0.950709i	$0.399642\pi$
$282$	12179.9	2.57200
$283$	−5154.70	−1.08274	−0.541369	−	0.840785i	$-0.682094\pi$
$283$	−5154.70	−1.08274	−0.541369	+	0.840785i	$0.682094\pi$
$284$	−774.138	−0.161749
$285$	22554.6	4.68779
$286$	3357.62	0.694197
$287$	−632.787	−0.130147
$288$	2630.45	0.538197
$289$	−4379.33	−0.891376
$290$	−813.089	−0.164642
$291$	−5505.11	−1.10899
$292$	−1147.01	−0.229876
$293$	−5833.97	−1.16322	−0.581611	−	0.813467i	$-0.697578\pi$
$293$	−5833.97	−1.16322	−0.581611	+	0.813467i	$0.697578\pi$
$294$	6770.13	1.34300
$295$	15337.0	3.02697
$296$	−5371.44	−1.05476
$297$	4117.93	0.804534
$298$	−6386.69	−1.24151
$299$	2420.54	0.468172
$300$	3867.11	0.744226
$301$	0	0
$302$	2530.11	0.482090
$303$	−7357.45	−1.39496
$304$	−6628.93	−1.25064
$305$	1071.92	0.201239
$306$	−2176.91	−0.406685
$307$	6732.61	1.25163	0.625815	−	0.779971i	$-0.284766\pi$
$307$	6732.61	1.25163	0.625815	+	0.779971i	$0.284766\pi$
$308$	−244.489	−0.0452306
$309$	2790.92	0.513818
$310$	1834.80	0.336160
$311$	8757.73	1.59680	0.798401	−	0.602127i	$-0.205680\pi$
$311$	8757.73	1.59680	0.798401	+	0.602127i	$0.205680\pi$
$312$	−5125.73	−0.930087
$313$	6736.28	1.21648	0.608238	−	0.793754i	$-0.291876\pi$
$313$	6736.28	1.21648	0.608238	+	0.793754i	$0.291876\pi$
$314$	3018.89	0.542567
$315$	2359.33	0.422010
$316$	272.090	0.0484374
$317$	8651.72	1.53290	0.766450	−	0.642304i	$-0.222021\pi$
$317$	8651.72	1.53290	0.766450	+	0.642304i	$0.222021\pi$
$318$	−8282.55	−1.46057
$319$	−780.069	−0.136914
$320$	−11791.7	−2.05993
$321$	−6652.98	−1.15680
$322$	712.127	0.123246
$323$	−3139.13	−0.540762
$324$	553.941	0.0949830
$325$	−8010.92	−1.36728
$326$	289.239	0.0491395
$327$	2370.55	0.400891
$328$	−5019.02	−0.844906
$329$	1837.24	0.307874
$330$	−21152.5	−3.52850
$331$	5530.88	0.918444	0.459222	−	0.888322i	$-0.348128\pi$
$331$	5530.88	0.918444	0.459222	+	0.888322i	$0.348128\pi$
$332$	383.727	0.0634330
$333$	8232.93	1.35484
$334$	7867.11	1.28883
$335$	−6921.63	−1.12886
$336$	−1196.55	−0.194278
$337$	2734.73	0.442049	0.221024	−	0.975268i	$-0.429060\pi$
$337$	2734.73	0.442049	0.221024	+	0.975268i	$0.429060\pi$
$338$	−3805.70	−0.612434
$339$	13077.5	2.09519
$340$	−759.491	−0.121145
$341$	1760.29	0.279545
$342$	12804.9	2.02459
$343$	2071.12	0.326035
$344$	0	0
$345$	−15249.0	−2.37965
$346$	−5932.95	−0.921842
$347$	8367.34	1.29447	0.647237	−	0.762289i	$-0.275924\pi$
$347$	8367.34	1.29447	0.647237	+	0.762289i	$0.275924\pi$
$348$	197.149	0.0303687
$349$	−2243.31	−0.344074	−0.172037	−	0.985090i	$-0.555035\pi$
$349$	−2243.31	−0.344074	−0.172037	+	0.985090i	$0.555035\pi$
$350$	−2356.83	−0.359936
$351$	2155.94	0.327851
$352$	−3557.34	−0.538656
$353$	1573.11	0.237190	0.118595	−	0.992943i	$-0.462161\pi$
$353$	1573.11	0.237190	0.118595	+	0.992943i	$0.462161\pi$
$354$	15025.1	2.25586
$355$	−10102.8	−1.51043
$356$	−528.642	−0.0787022
$357$	−566.627	−0.0840031
$358$	−4231.66	−0.624722
$359$	5107.31	0.750846	0.375423	−	0.926854i	$-0.377497\pi$
$359$	5107.31	0.750846	0.375423	+	0.926854i	$0.377497\pi$
$360$	18713.3	2.73966
$361$	11605.8	1.69206
$362$	5558.92	0.807101
$363$	−9627.90	−1.39210
$364$	−128.002	−0.0184317
$365$	−14969.0	−2.14662
$366$	1050.12	0.149974
$367$	3195.77	0.454545	0.227273	−	0.973831i	$-0.427019\pi$
$367$	3195.77	0.454545	0.227273	+	0.973831i	$0.427019\pi$
$368$	4481.78	0.634861
$369$	7692.77	1.08528
$370$	−11605.3	−1.63062
$371$	−1249.36	−0.174834
$372$	−444.883	−0.0620057
$373$	12608.7	1.75027	0.875136	−	0.483876i	$-0.160772\pi$
$373$	12608.7	1.75027	0.875136	+	0.483876i	$0.160772\pi$
$374$	2943.99	0.407032
$375$	29719.7	4.09259
$376$	14572.3	1.99870
$377$	−408.405	−0.0557929
$378$	634.282	0.0863067
$379$	1660.61	0.225065	0.112532	−	0.993648i	$-0.464104\pi$
$379$	1660.61	0.225065	0.112532	+	0.993648i	$0.464104\pi$
$380$	4467.44	0.603092
$381$	−1950.59	−0.262288
$382$	−201.728	−0.0270191
$383$	10824.1	1.44409	0.722043	−	0.691849i	$-0.243203\pi$
$383$	10824.1	1.44409	0.722043	+	0.691849i	$0.243203\pi$
$384$	−7020.33	−0.932955
$385$	−3190.69	−0.422370
$386$	2809.17	0.370422
$387$	0	0
$388$	−1090.41	−0.142673
$389$	6272.78	0.817590	0.408795	−	0.912626i	$-0.365949\pi$
$389$	6272.78	0.817590	0.408795	+	0.912626i	$0.365949\pi$
$390$	−11074.4	−1.43788
$391$	2122.35	0.274505
$392$	8099.94	1.04364
$393$	−18769.0	−2.40909
$394$	6059.13	0.774758
$395$	3550.89	0.452316
$396$	2972.24	0.377174
$397$	−2427.36	−0.306866	−0.153433	−	0.988159i	$-0.549033\pi$
$397$	−2427.36	−0.306866	−0.153433	+	0.988159i	$0.549033\pi$
$398$	532.387	0.0670506
$399$	3332.99	0.418191
$400$	−14832.7	−1.85409
$401$	5002.47	0.622971	0.311486	−	0.950251i	$-0.399173\pi$
$401$	5002.47	0.622971	0.311486	+	0.950251i	$0.399173\pi$
$402$	−6780.85	−0.841289
$403$	921.597	0.113916
$404$	−1457.30	−0.179464
$405$	7229.17	0.886964
$406$	−120.153	−0.0146875
$407$	−11134.0	−1.35600
$408$	−4494.27	−0.545342
$409$	−8971.14	−1.08458	−0.542292	−	0.840190i	$-0.682443\pi$
$409$	−8971.14	−1.08458	−0.542292	+	0.840190i	$0.682443\pi$
$410$	−10843.8	−1.30619
$411$	9878.58	1.18558
$412$	552.803	0.0661035
$413$	2266.41	0.270031
$414$	−8657.31	−1.02774
$415$	5007.81	0.592346
$416$	−1862.45	−0.219505
$417$	2484.60	0.291778
$418$	−17317.0	−2.02632
$419$	−11112.1	−1.29561	−0.647806	−	0.761805i	$-0.724313\pi$
$419$	−11112.1	−1.29561	−0.647806	+	0.761805i	$0.724313\pi$
$420$	806.393	0.0936856
$421$	1138.09	0.131751	0.0658754	−	0.997828i	$-0.479016\pi$
$421$	1138.09	0.131751	0.0658754	+	0.997828i	$0.479016\pi$
$422$	2171.69	0.250513
$423$	−22335.3	−2.56733
$424$	−9909.42	−1.13501
$425$	−7024.03	−0.801684
$426$	−9897.36	−1.12565
$427$	158.402	0.0179522
$428$	−1317.77	−0.148824
$429$	−10624.7	−1.19572
$430$	0	0
$431$	−7440.65	−0.831563	−0.415781	−	0.909465i	$-0.636492\pi$
$431$	−7440.65	−0.831563	−0.415781	+	0.909465i	$0.636492\pi$
$432$	3991.86	0.444580
$433$	8252.84	0.915949	0.457975	−	0.888965i	$-0.348575\pi$
$433$	8252.84	0.915949	0.457975	+	0.888965i	$0.348575\pi$
$434$	271.135	0.0299883
$435$	2572.89	0.283587
$436$	469.539	0.0515753
$437$	−12484.0	−1.36656
$438$	−14664.6	−1.59977
$439$	−11729.5	−1.27521	−0.637605	−	0.770364i	$-0.720075\pi$
$439$	−11729.5	−1.27521	−0.637605	+	0.770364i	$0.720075\pi$
$440$	−25307.3	−2.74200
$441$	−12415.0	−1.34056
$442$	1541.32	0.165867
$443$	1411.13	0.151343	0.0756714	−	0.997133i	$-0.475890\pi$
$443$	1411.13	0.151343	0.0756714	+	0.997133i	$0.475890\pi$
$444$	2813.92	0.300772
$445$	−6899.01	−0.734932
$446$	−8944.97	−0.949679
$447$	20209.7	2.13844
$448$	−1742.51	−0.183763
$449$	9517.45	1.00035	0.500174	−	0.865925i	$-0.333269\pi$
$449$	9517.45	1.00035	0.500174	+	0.865925i	$0.333269\pi$
$450$	28651.9	3.00147
$451$	−10403.5	−1.08621
$452$	2590.28	0.269550
$453$	−8006.11	−0.830375
$454$	−13139.6	−1.35830
$455$	−1670.48	−0.172117
$456$	26436.0	2.71486
$457$	11178.2	1.14419	0.572093	−	0.820189i	$-0.306132\pi$
$457$	11178.2	1.14419	0.572093	+	0.820189i	$0.306132\pi$
$458$	8818.57	0.899705
$459$	1890.34	0.192230
$460$	−3020.41	−0.306146
$461$	−15694.1	−1.58557	−0.792786	−	0.609500i	$-0.791370\pi$
$461$	−15694.1	−1.58557	−0.792786	+	0.609500i	$0.791370\pi$
$462$	−3125.79	−0.314772
$463$	2547.36	0.255693	0.127847	−	0.991794i	$-0.459193\pi$
$463$	2547.36	0.255693	0.127847	+	0.991794i	$0.459193\pi$
$464$	−756.187	−0.0756575
$465$	−5805.92	−0.579017
$466$	3913.34	0.389017
$467$	7822.43	0.775115	0.387558	−	0.921845i	$-0.373319\pi$
$467$	7822.43	0.775115	0.387558	+	0.921845i	$0.373319\pi$
$468$	1556.12	0.153700
$469$	−1022.84	−0.100704
$470$	31484.2	3.08991
$471$	−9552.80	−0.934543
$472$	17976.3	1.75302
$473$	0	0
$474$	3478.67	0.337089
$475$	41316.4	3.99100
$476$	−112.233	−0.0108071
$477$	15188.4	1.45792
$478$	−6489.39	−0.620957
$479$	−14772.7	−1.40915	−0.704573	−	0.709632i	$-0.748861\pi$
$479$	−14772.7	−1.40915	−0.704573	+	0.709632i	$0.748861\pi$
$480$	11733.1	1.11571
$481$	−5829.19	−0.552574
$482$	−12514.7	−1.18263
$483$	−2253.41	−0.212285
$484$	−1907.02	−0.179096
$485$	−14230.3	−1.33230
$486$	12677.0	1.18321
$487$	5286.95	0.491939	0.245970	−	0.969278i	$-0.420894\pi$
$487$	5286.95	0.491939	0.245970	+	0.969278i	$0.420894\pi$
$488$	1256.38	0.116545
$489$	−915.251	−0.0846402
$490$	17500.3	1.61344
$491$	17508.4	1.60925	0.804624	−	0.593784i	$-0.202367\pi$
$491$	17508.4	1.60925	0.804624	+	0.593784i	$0.202367\pi$
$492$	2629.30	0.240931
$493$	−358.092	−0.0327133
$494$	−9066.29	−0.825732
$495$	38789.1	3.52210
$496$	1706.39	0.154474
$497$	−1492.94	−0.134743
$498$	4905.95	0.441447
$499$	1560.31	0.139978	0.0699888	−	0.997548i	$-0.477704\pi$
$499$	1560.31	0.139978	0.0699888	+	0.997548i	$0.477704\pi$
$500$	5886.65	0.526518
$501$	−24894.2	−2.21994
$502$	11306.4	1.00523
$503$	−7420.52	−0.657783	−0.328891	−	0.944368i	$-0.606675\pi$
$503$	−7420.52	−0.657783	−0.328891	+	0.944368i	$0.606675\pi$
$504$	2765.34	0.244401
$505$	−19018.5	−1.67586
$506$	11707.9	1.02861
$507$	12042.5	1.05489
$508$	−386.358	−0.0337438
$509$	661.902	0.0576390	0.0288195	−	0.999585i	$-0.490825\pi$
$509$	661.902	0.0576390	0.0288195	+	0.999585i	$0.490825\pi$
$510$	−9710.09	−0.843079
$511$	−2212.03	−0.191496
$512$	−12923.4	−1.11550
$513$	−11119.3	−0.956976
$514$	−15078.8	−1.29396
$515$	7214.33	0.617284
$516$	0	0
$517$	30205.6	2.56952
$518$	−1714.96	−0.145465
$519$	18773.9	1.58782
$520$	−13249.6	−1.11737
$521$	−13039.0	−1.09645	−0.548225	−	0.836331i	$-0.684696\pi$
$521$	−13039.0	−1.09645	−0.548225	+	0.836331i	$0.684696\pi$
$522$	1460.70	0.122477
$523$	18176.0	1.51966	0.759829	−	0.650123i	$-0.225283\pi$
$523$	18176.0	1.51966	0.759829	+	0.650123i	$0.225283\pi$
$524$	−3717.62	−0.309933
$525$	7457.80	0.619971
$526$	116.586	0.00966421
$527$	808.063	0.0667927
$528$	−19672.2	−1.62144
$529$	−3726.68	−0.306294
$530$	−21409.8	−1.75468
$531$	−27552.7	−2.25176
$532$	660.172	0.0538009
$533$	−5446.74	−0.442635
$534$	−6758.69	−0.547710
$535$	−17197.5	−1.38974
$536$	−8112.76	−0.653765
$537$	13390.4	1.07605
$538$	2341.29	0.187622
$539$	16789.6	1.34171
$540$	−2690.23	−0.214388
$541$	3752.56	0.298216	0.149108	−	0.988821i	$-0.452360\pi$
$541$	3752.56	0.298216	0.149108	+	0.988821i	$0.452360\pi$
$542$	−13106.5	−1.03869
$543$	−17590.3	−1.39019
$544$	−1633.00	−0.128703
$545$	6127.69	0.481617
$546$	−1636.51	−0.128271
$547$	7414.69	0.579578	0.289789	−	0.957090i	$-0.406415\pi$
$547$	7414.69	0.579578	0.289789	+	0.957090i	$0.406415\pi$
$548$	1956.67	0.152527
$549$	−1925.69	−0.149702
$550$	−38747.9	−3.00403
$551$	2106.35	0.162856
$552$	−17873.2	−1.37814
$553$	524.729	0.0403504
$554$	17158.0	1.31584
$555$	36723.0	2.80865
$556$	492.130	0.0375377
$557$	−14232.7	−1.08269	−0.541345	−	0.840801i	$-0.682085\pi$
$557$	−14232.7	−1.08269	−0.541345	+	0.840801i	$0.682085\pi$
$558$	−3296.19	−0.250069
$559$	0	0
$560$	−3093.00	−0.233399
$561$	−9315.77	−0.701091
$562$	7397.68	0.555253
$563$	−20932.3	−1.56695	−0.783475	−	0.621423i	$-0.786555\pi$
$563$	−20932.3	−1.56695	−0.783475	+	0.621423i	$0.786555\pi$
$564$	−7633.97	−0.569943
$565$	33804.3	2.51709
$566$	−13053.5	−0.969399
$567$	1068.28	0.0791247
$568$	−11841.4	−0.874745
$569$	−3328.84	−0.245259	−0.122629	−	0.992453i	$-0.539133\pi$
$569$	−3328.84	−0.245259	−0.122629	+	0.992453i	$0.539133\pi$
$570$	57116.2	4.19708
$571$	2268.00	0.166222	0.0831110	−	0.996540i	$-0.473514\pi$
$571$	2268.00	0.166222	0.0831110	+	0.996540i	$0.473514\pi$
$572$	−2104.45	−0.153831
$573$	638.335	0.0465389
$574$	−1602.44	−0.116524
$575$	−27933.7	−2.02594
$576$	21183.7	1.53238
$577$	−11714.3	−0.845190	−0.422595	−	0.906319i	$-0.638881\pi$
$577$	−11714.3	−0.845190	−0.422595	+	0.906319i	$0.638881\pi$
$578$	−11090.0	−0.798068
$579$	−8889.16	−0.638032
$580$	509.617	0.0364840
$581$	740.024	0.0528423
$582$	−13940.9	−0.992900
$583$	−20540.3	−1.45917
$584$	−17545.0	−1.24318
$585$	20308.0	1.43527
$586$	−14773.7	−1.04146
$587$	13734.5	0.965730	0.482865	−	0.875695i	$-0.339596\pi$
$587$	13734.5	0.965730	0.482865	+	0.875695i	$0.339596\pi$
$588$	−4243.30	−0.297603
$589$	−4753.15	−0.332513
$590$	38838.7	2.71011
$591$	−19173.1	−1.33448
$592$	−10793.1	−0.749313
$593$	26981.9	1.86849	0.934244	−	0.356634i	$-0.116076\pi$
$593$	26981.9	1.86849	0.934244	+	0.356634i	$0.116076\pi$
$594$	10428.1	0.720317
$595$	−1464.69	−0.100918
$596$	4002.97	0.275114
$597$	−1684.65	−0.115491
$598$	6129.66	0.419164
$599$	2470.79	0.168537	0.0842685	−	0.996443i	$-0.473145\pi$
$599$	2470.79	0.168537	0.0842685	+	0.996443i	$0.473145\pi$
$600$	59152.4	4.02481
$601$	20621.9	1.39964	0.699820	−	0.714319i	$-0.253263\pi$
$601$	20621.9	1.39964	0.699820	+	0.714319i	$0.253263\pi$
$602$	0	0
$603$	12434.6	0.839762
$604$	−1585.79	−0.106829
$605$	−24887.4	−1.67243
$606$	−18631.6	−1.24894
$607$	4220.90	0.282242	0.141121	−	0.989992i	$-0.454929\pi$
$607$	4220.90	0.282242	0.141121	+	0.989992i	$0.454929\pi$
$608$	9605.58	0.640720
$609$	380.206	0.0252984
$610$	2714.48	0.180174
$611$	15814.1	1.04709
$612$	1364.41	0.0901196
$613$	12018.1	0.791852	0.395926	−	0.918282i	$-0.370424\pi$
$613$	12018.1	0.791852	0.395926	+	0.918282i	$0.370424\pi$
$614$	17049.3	1.12061
$615$	34313.6	2.24985
$616$	−3739.76	−0.244609
$617$	−5171.02	−0.337403	−0.168701	−	0.985667i	$-0.553957\pi$
$617$	−5171.02	−0.337403	−0.168701	+	0.985667i	$0.553957\pi$
$618$	7067.59	0.460033
$619$	5055.56	0.328272	0.164136	−	0.986438i	$-0.447516\pi$
$619$	5055.56	0.328272	0.164136	+	0.986438i	$0.447516\pi$
$620$	−1149.99	−0.0744915
$621$	7517.68	0.485788
$622$	22177.6	1.42965
$623$	−1019.50	−0.0655621
$624$	−10299.4	−0.660745
$625$	38816.7	2.48427
$626$	17058.6	1.08914
$627$	54796.8	3.49023
$628$	−1892.14	−0.120230
$629$	−5111.07	−0.323993
$630$	5974.65	0.377835
$631$	−20865.9	−1.31642	−0.658209	−	0.752835i	$-0.728686\pi$
$631$	−20865.9	−1.31642	−0.658209	+	0.752835i	$0.728686\pi$
$632$	4161.95	0.261952
$633$	−6871.97	−0.431495
$634$	21909.2	1.37244
$635$	−5042.14	−0.315105
$636$	5191.23	0.323657
$637$	8790.20	0.546751
$638$	−1975.41	−0.122582
$639$	18149.6	1.12361
$640$	−18147.1	−1.12082
$641$	−20942.5	−1.29045	−0.645226	−	0.763992i	$-0.723237\pi$
$641$	−20942.5	−1.29045	−0.645226	+	0.763992i	$0.723237\pi$
$642$	−16847.7	−1.03571
$643$	−1235.94	−0.0758020	−0.0379010	−	0.999281i	$-0.512067\pi$
$643$	−1235.94	−0.0758020	−0.0379010	+	0.999281i	$0.512067\pi$
$644$	−446.337	−0.0273108
$645$	0	0
$646$	−7949.39	−0.484155
$647$	−16372.8	−0.994873	−0.497437	−	0.867500i	$-0.665725\pi$
$647$	−16372.8	−0.994873	−0.497437	+	0.867500i	$0.665725\pi$
$648$	8473.22	0.513672
$649$	37261.5	2.25369
$650$	−20286.5	−1.22415
$651$	−857.964	−0.0516533
$652$	−181.286	−0.0108891
$653$	3699.21	0.221686	0.110843	−	0.993838i	$-0.464645\pi$
$653$	3699.21	0.221686	0.110843	+	0.993838i	$0.464645\pi$
$654$	6003.06	0.358927
$655$	−48516.5	−2.89420
$656$	−10085.0	−0.600231
$657$	26891.6	1.59687
$658$	4652.55	0.275646
$659$	−27786.0	−1.64247	−0.821237	−	0.570588i	$-0.806715\pi$
$659$	−27786.0	−1.64247	−0.821237	+	0.570588i	$0.806715\pi$
$660$	13257.7	0.781901
$661$	5798.03	0.341176	0.170588	−	0.985342i	$-0.445433\pi$
$661$	5798.03	0.341176	0.170588	+	0.985342i	$0.445433\pi$
$662$	14006.1	0.822302
$663$	−4877.27	−0.285697
$664$	5869.59	0.343048
$665$	8615.53	0.502400
$666$	20848.7	1.21302
$667$	−1424.09	−0.0826702
$668$	−4930.85	−0.285599
$669$	28304.9	1.63577
$670$	−17528.0	−1.01070
$671$	2604.24	0.149830
$672$	1733.85	0.0995308
$673$	−4577.82	−0.262202	−0.131101	−	0.991369i	$-0.541851\pi$
$673$	−4577.82	−0.262202	−0.131101	+	0.991369i	$0.541851\pi$
$674$	6925.30	0.395776
$675$	−24880.2	−1.41873
$676$	2385.28	0.135713
$677$	−12344.6	−0.700801	−0.350401	−	0.936600i	$-0.613955\pi$
$677$	−12344.6	−0.700801	−0.350401	+	0.936600i	$0.613955\pi$
$678$	33116.7	1.87587
$679$	−2102.87	−0.118852
$680$	−11617.4	−0.655156
$681$	41578.0	2.33961
$682$	4457.66	0.250283
$683$	16504.5	0.924635	0.462318	−	0.886714i	$-0.347018\pi$
$683$	16504.5	0.924635	0.462318	+	0.886714i	$0.347018\pi$
$684$	−8025.69	−0.448640
$685$	25535.4	1.42432
$686$	5244.81	0.291906
$687$	−27905.0	−1.54969
$688$	0	0
$689$	−10753.9	−0.594616
$690$	−38615.9	−2.13055
$691$	−11094.6	−0.610791	−0.305396	−	0.952226i	$-0.598789\pi$
$691$	−11094.6	−0.610791	−0.305396	+	0.952226i	$0.598789\pi$
$692$	3718.58	0.204276
$693$	5732.02	0.314201
$694$	21189.1	1.15897
$695$	6422.52	0.350533
$696$	3015.65	0.164236
$697$	−4775.74	−0.259532
$698$	−5680.86	−0.308057
$699$	−12383.1	−0.670061
$700$	1477.18	0.0797603
$701$	3488.71	0.187970	0.0939850	−	0.995574i	$-0.470039\pi$
$701$	3488.71	0.187970	0.0939850	+	0.995574i	$0.470039\pi$
$702$	5459.60	0.293532
$703$	30064.1	1.61293
$704$	−28648.2	−1.53369
$705$	−99626.7	−5.32221
$706$	3983.66	0.212361
$707$	−2810.44	−0.149501
$708$	−9417.22	−0.499888
$709$	11358.7	0.601669	0.300835	−	0.953676i	$-0.402735\pi$
$709$	11358.7	0.601669	0.300835	+	0.953676i	$0.402735\pi$
$710$	−25584.0	−1.35232
$711$	−6379.12	−0.336478
$712$	−8086.25	−0.425625
$713$	3213.57	0.168793
$714$	−1434.90	−0.0752098
$715$	−27464.0	−1.43650
$716$	2652.27	0.138436
$717$	20534.6	1.06957
$718$	12933.5	0.672249
$719$	−34524.2	−1.79073	−0.895364	−	0.445335i	$-0.853085\pi$
$719$	−34524.2	−1.79073	−0.895364	+	0.445335i	$0.853085\pi$
$720$	37601.5	1.94629
$721$	1066.09	0.0550670
$722$	29390.1	1.51494
$723$	39600.8	2.03703
$724$	−3484.15	−0.178850
$725$	4713.11	0.241435
$726$	−24381.2	−1.24638
$727$	−16846.5	−0.859426	−0.429713	−	0.902966i	$-0.641385\pi$
$727$	−16846.5	−0.859426	−0.429713	+	0.902966i	$0.641385\pi$
$728$	−1957.95	−0.0996793
$729$	−30691.3	−1.55928
$730$	−37906.9	−1.92191
$731$	0	0
$732$	−658.179	−0.0332336
$733$	13917.8	0.701317	0.350658	−	0.936503i	$-0.385958\pi$
$733$	13917.8	0.701317	0.350658	+	0.936503i	$0.385958\pi$
$734$	8092.82	0.406964
$735$	−55376.9	−2.77906
$736$	−6494.27	−0.325247
$737$	−16816.2	−0.840479
$738$	19480.8	0.971678
$739$	−10001.0	−0.497825	−0.248912	−	0.968526i	$-0.580073\pi$
$739$	−10001.0	−0.497825	−0.248912	+	0.968526i	$0.580073\pi$
$740$	7273.79	0.361338
$741$	28688.8	1.42228
$742$	−3163.81	−0.156533
$743$	5356.46	0.264481	0.132240	−	0.991218i	$-0.457783\pi$
$743$	5356.46	0.264481	0.132240	+	0.991218i	$0.457783\pi$
$744$	−6805.05	−0.335329
$745$	52240.5	2.56905
$746$	31929.6	1.56706
$747$	−8996.45	−0.440647
$748$	−1845.19	−0.0901964
$749$	−2541.34	−0.123977
$750$	75260.8	3.66418
$751$	−30162.2	−1.46556	−0.732779	−	0.680467i	$-0.761777\pi$
$751$	−30162.2	−1.46556	−0.732779	+	0.680467i	$0.761777\pi$
$752$	29280.9	1.41990
$753$	−35777.2	−1.73146
$754$	−1034.22	−0.0499526
$755$	−20695.2	−0.997585
$756$	−397.547	−0.0191252
$757$	−35857.4	−1.72161	−0.860805	−	0.508935i	$-0.830039\pi$
$757$	−35857.4	−1.72161	−0.860805	+	0.508935i	$0.830039\pi$
$758$	4205.24	0.201505
$759$	−37047.7	−1.77173
$760$	68335.1	3.26155
$761$	−3433.69	−0.163563	−0.0817814	−	0.996650i	$-0.526061\pi$
$761$	−3433.69	−0.163563	−0.0817814	+	0.996650i	$0.526061\pi$
$762$	−4939.59	−0.234832
$763$	905.514	0.0429644
$764$	126.436	0.00598731
$765$	17806.2	0.841549
$766$	27410.4	1.29292
$767$	19508.2	0.918386
$768$	18715.9	0.879362
$769$	−2028.54	−0.0951248	−0.0475624	−	0.998868i	$-0.515145\pi$
$769$	−2028.54	−0.0951248	−0.0475624	+	0.998868i	$0.515145\pi$
$770$	−8079.94	−0.378157
$771$	47714.3	2.22878
$772$	−1760.69	−0.0820839
$773$	−39469.4	−1.83650	−0.918251	−	0.395999i	$-0.870398\pi$
$773$	−39469.4	−1.83650	−0.918251	+	0.395999i	$0.870398\pi$
$774$	0	0
$775$	−10635.5	−0.492953
$776$	−16679.2	−0.771582
$777$	5426.70	0.250556
$778$	15884.9	0.732006
$779$	28091.6	1.29202
$780$	6941.06	0.318628
$781$	−24545.0	−1.12457
$782$	5374.53	0.245771
$783$	−1268.42	−0.0578922
$784$	16275.6	0.741417
$785$	−24693.3	−1.12273
$786$	−47529.7	−2.15691
$787$	−39757.2	−1.80075	−0.900376	−	0.435113i	$-0.856708\pi$
$787$	−39757.2	−1.80075	−0.900376	+	0.435113i	$0.856708\pi$
$788$	−3797.66	−0.171683
$789$	−368.916	−0.0166461
$790$	8992.10	0.404968
$791$	4995.40	0.224546
$792$	45464.2	2.03977
$793$	1363.45	0.0610562
$794$	−6146.94	−0.274744
$795$	67747.8	3.02235
$796$	−333.682	−0.0148581
$797$	9242.68	0.410781	0.205391	−	0.978680i	$-0.434154\pi$
$797$	9242.68	0.410781	0.205391	+	0.978680i	$0.434154\pi$
$798$	8440.30	0.374415
$799$	13866.0	0.613945
$800$	21493.2	0.949873
$801$	12394.0	0.546716
$802$	12668.0	0.557760
$803$	−36367.5	−1.59823
$804$	4250.01	0.186426
$805$	−5824.90	−0.255032
$806$	2333.81	0.101991
$807$	−7408.65	−0.323168
$808$	−22291.3	−0.970552
$809$	−14493.7	−0.629877	−0.314939	−	0.949112i	$-0.601984\pi$
$809$	−14493.7	−0.629877	−0.314939	+	0.949112i	$0.601984\pi$
$810$	18306.8	0.794118
$811$	−36976.4	−1.60101	−0.800504	−	0.599328i	$-0.795435\pi$
$811$	−36976.4	−1.60101	−0.800504	+	0.599328i	$0.795435\pi$
$812$	75.3082	0.00325468
$813$	41473.3	1.78909
$814$	−28195.1	−1.21405
$815$	−2365.86	−0.101684
$816$	−9030.56	−0.387418
$817$	0	0
$818$	−22718.1	−0.971051
$819$	3001.00	0.128038
$820$	6796.57	0.289447
$821$	41436.7	1.76145	0.880724	−	0.473629i	$-0.157056\pi$
$821$	41436.7	1.76145	0.880724	+	0.473629i	$0.157056\pi$
$822$	25016.0	1.06148
$823$	−29097.3	−1.23241	−0.616203	−	0.787588i	$-0.711330\pi$
$823$	−29097.3	−1.23241	−0.616203	+	0.787588i	$0.711330\pi$
$824$	8455.82	0.357491
$825$	122612.	5.17429
$826$	5739.36	0.241765
$827$	−16157.9	−0.679402	−0.339701	−	0.940534i	$-0.610326\pi$
$827$	−16157.9	−0.679402	−0.339701	+	0.940534i	$0.610326\pi$
$828$	5426.11	0.227742
$829$	−41034.9	−1.71918	−0.859591	−	0.510983i	$-0.829282\pi$
$829$	−41034.9	−1.71918	−0.859591	+	0.510983i	$0.829282\pi$
$830$	12681.5	0.530340
$831$	−54293.7	−2.26646
$832$	−14998.7	−0.624985
$833$	7707.31	0.320579
$834$	6291.89	0.261235
$835$	−64349.7	−2.66696
$836$	10853.7	0.449023
$837$	2862.28	0.118202
$838$	−28139.7	−1.15999
$839$	−28367.1	−1.16727	−0.583636	−	0.812015i	$-0.698371\pi$
$839$	−28367.1	−1.16727	−0.583636	+	0.812015i	$0.698371\pi$
$840$	12334.8	0.506656
$841$	−24148.7	−0.990148
$842$	2882.04	0.117959
$843$	−23408.8	−0.956395
$844$	−1361.15	−0.0555125
$845$	31129.0	1.26730
$846$	−56560.9	−2.29859
$847$	−3677.72	−0.149195
$848$	−19911.5	−0.806324
$849$	41305.7	1.66974
$850$	−17787.3	−0.717765
$851$	−20326.1	−0.818767
$852$	6203.34	0.249440
$853$	−18754.4	−0.752801	−0.376400	−	0.926457i	$-0.622838\pi$
$853$	−18754.4	−0.752801	−0.376400	+	0.926457i	$0.622838\pi$
$854$	401.129	0.0160730
$855$	−104739.	−4.18947
$856$	−20157.0	−0.804849
$857$	−12782.0	−0.509481	−0.254741	−	0.967009i	$-0.581990\pi$
$857$	−12782.0	−0.509481	−0.254741	+	0.967009i	$0.581990\pi$
$858$	−26905.4	−1.07055
$859$	−2156.19	−0.0856442	−0.0428221	−	0.999083i	$-0.513635\pi$
$859$	−2156.19	−0.0856442	−0.0428221	+	0.999083i	$0.513635\pi$
$860$	0	0
$861$	5070.66	0.200706
$862$	−18842.3	−0.744516
$863$	−20877.3	−0.823489	−0.411744	−	0.911299i	$-0.635080\pi$
$863$	−20877.3	−0.823489	−0.411744	+	0.911299i	$0.635080\pi$
$864$	−5784.36	−0.227764
$865$	48529.1	1.90756
$866$	20899.1	0.820069
$867$	35092.5	1.37463
$868$	−169.939	−0.00664527
$869$	8626.93	0.336765
$870$	6515.46	0.253902
$871$	−8804.12	−0.342498
$872$	7182.19	0.278922
$873$	25564.6	0.991099
$874$	−31613.8	−1.22351
$875$	11352.5	0.438611
$876$	9191.27	0.354502
$877$	21747.0	0.837336	0.418668	−	0.908139i	$-0.362497\pi$
$877$	21747.0	0.837336	0.418668	+	0.908139i	$0.362497\pi$
$878$	−29703.1	−1.14172
$879$	46748.9	1.79386
$880$	−50851.2	−1.94795
$881$	39665.9	1.51689	0.758444	−	0.651738i	$-0.225960\pi$
$881$	39665.9	1.51689	0.758444	+	0.651738i	$0.225960\pi$
$882$	−31439.0	−1.20024
$883$	−32675.0	−1.24530	−0.622652	−	0.782499i	$-0.713945\pi$
$883$	−32675.0	−1.24530	−0.622652	+	0.782499i	$0.713945\pi$
$884$	−966.050	−0.0367554
$885$	−122899.	−4.66803
$886$	3573.48	0.135500
$887$	1318.70	0.0499183	0.0249592	−	0.999688i	$-0.492054\pi$
$887$	1318.70	0.0499183	0.0249592	+	0.999688i	$0.492054\pi$
$888$	43042.5	1.62659
$889$	−745.098	−0.0281100
$890$	−17470.7	−0.658000
$891$	17563.4	0.660376
$892$	5606.41	0.210445
$893$	−81561.6	−3.05639
$894$	51178.0	1.91459
$895$	34613.3	1.29273
$896$	−2681.66	−0.0999867
$897$	−19396.3	−0.721989
$898$	24101.5	0.895634
$899$	−542.209	−0.0201153
$900$	−17958.1	−0.665113
$901$	−9429.08	−0.348644
$902$	−26345.3	−0.972507
$903$	0	0
$904$	39621.6	1.45774
$905$	−45469.7	−1.67013
$906$	−20274.3	−0.743453
$907$	−2202.10	−0.0806170	−0.0403085	−	0.999187i	$-0.512834\pi$
$907$	−2202.10	−0.0806170	−0.0403085	+	0.999187i	$0.512834\pi$
$908$	8235.45	0.300994
$909$	34166.4	1.24668
$910$	−4230.25	−0.154100
$911$	10427.7	0.379237	0.189618	−	0.981858i	$-0.439275\pi$
$911$	10427.7	0.379237	0.189618	+	0.981858i	$0.439275\pi$
$912$	53119.1	1.92867
$913$	12166.5	0.441022
$914$	28307.1	1.02441
$915$	−8589.53	−0.310340
$916$	−5527.19	−0.199371
$917$	−7169.49	−0.258187
$918$	4787.02	0.172108
$919$	−4793.05	−0.172044	−0.0860218	−	0.996293i	$-0.527415\pi$
$919$	−4793.05	−0.172044	−0.0860218	+	0.996293i	$0.527415\pi$
$920$	−46200.9	−1.65565
$921$	−53949.9	−1.93020
$922$	−39743.1	−1.41960
$923$	−12850.5	−0.458267
$924$	1959.14	0.0697522
$925$	67270.5	2.39118
$926$	6450.82	0.228928
$927$	−12960.4	−0.459198
$928$	1095.74	0.0387603
$929$	42938.0	1.51641	0.758207	−	0.652014i	$-0.226076\pi$
$929$	42938.0	1.51641	0.758207	+	0.652014i	$0.226076\pi$
$930$	−14702.6	−0.518407
$931$	−45335.5	−1.59593
$932$	−2452.75	−0.0862044
$933$	−70177.6	−2.46250
$934$	19809.1	0.693977
$935$	−24080.6	−0.842267
$936$	23802.8	0.831216
$937$	17961.4	0.626224	0.313112	−	0.949716i	$-0.398628\pi$
$937$	17961.4	0.626224	0.313112	+	0.949716i	$0.398628\pi$
$938$	−2590.19	−0.0901626
$939$	−53979.3	−1.87598
$940$	−19733.3	−0.684711
$941$	1417.03	0.0490902	0.0245451	−	0.999699i	$-0.492186\pi$
$941$	1417.03	0.0490902	0.0245451	+	0.999699i	$0.492186\pi$
$942$	−24191.0	−0.836716
$943$	−18992.5	−0.655867
$944$	36120.7	1.24537
$945$	−5188.16	−0.178594
$946$	0	0
$947$	−1240.24	−0.0425579	−0.0212789	−	0.999774i	$-0.506774\pi$
$947$	−1240.24	−0.0425579	−0.0212789	+	0.999774i	$0.506774\pi$
$948$	−2180.31	−0.0746975
$949$	−19040.2	−0.651286
$950$	104628.	3.57323
$951$	−69328.2	−2.36395
$952$	−1716.75	−0.0584454
$953$	39421.9	1.33998	0.669989	−	0.742371i	$-0.266299\pi$
$953$	39421.9	1.33998	0.669989	+	0.742371i	$0.266299\pi$
$954$	38462.4	1.30531
$955$	1650.05	0.0559103
$956$	4067.33	0.137601
$957$	6250.87	0.211141
$958$	−37409.6	−1.26164
$959$	3773.47	0.127061
$960$	94489.8	3.17671
$961$	−28567.5	−0.958929
$962$	−14761.5	−0.494731
$963$	30895.0	1.03383
$964$	7843.81	0.262067
$965$	−22977.8	−0.766511
$966$	−5706.43	−0.190063
$967$	13213.8	0.439428	0.219714	−	0.975564i	$-0.429488\pi$
$967$	13213.8	0.439428	0.219714	+	0.975564i	$0.429488\pi$
$968$	−29170.2	−0.968561
$969$	25154.6	0.833933
$970$	−36036.2	−1.19284
$971$	16647.1	0.550186	0.275093	−	0.961418i	$-0.411291\pi$
$971$	16647.1	0.550186	0.275093	+	0.961418i	$0.411291\pi$
$972$	−7945.55	−0.262195
$973$	949.082	0.0312705
$974$	13388.4	0.440444
$975$	64193.3	2.10854
$976$	2524.51	0.0827948
$977$	−3092.02	−0.101251	−0.0506256	−	0.998718i	$-0.516122\pi$
$977$	−3092.02	−0.101251	−0.0506256	+	0.998718i	$0.516122\pi$
$978$	−2317.74	−0.0757802
$979$	−16761.2	−0.547183
$980$	−10968.6	−0.357530
$981$	−11008.3	−0.358276
$982$	44337.3	1.44079
$983$	14697.7	0.476890	0.238445	−	0.971156i	$-0.423362\pi$
$983$	14697.7	0.476890	0.238445	+	0.971156i	$0.423362\pi$
$984$	40218.5	1.30297
$985$	−49561.2	−1.60320
$986$	−906.816	−0.0292889
$987$	−14722.2	−0.474786
$988$	5682.45	0.182979
$989$	0	0
$990$	98227.7	3.15341
$991$	43483.8	1.39385	0.696927	−	0.717143i	$-0.254550\pi$
$991$	43483.8	1.39385	0.696927	+	0.717143i	$0.254550\pi$
$992$	−2472.63	−0.0791392
$993$	−44320.2	−1.41637
$994$	−3780.65	−0.120639
$995$	−4354.70	−0.138747
$996$	−3074.89	−0.0978228
$997$	35710.8	1.13437	0.567187	−	0.823589i	$-0.308032\pi$
$997$	35710.8	1.13437	0.567187	+	0.823589i	$0.308032\pi$
$998$	3951.24	0.125325
$999$	−18104.2	−0.573365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.34	yes	50
43.42	odd	2		1849.4.a.i.1.17	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.17	✓	50	43.42	odd	2
1849.4.a.j.1.34	yes	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.53235 q^{2} -8.01322 q^{3} -1.58719 q^{4} -20.7136 q^{5} -20.2923 q^{6} -3.06093 q^{7} -24.2781 q^{8} +37.2117 q^{9} +O(q^{10})\)	\(q+2.53235 q^{2} -8.01322 q^{3} -1.58719 q^{4} -20.7136 q^{5} -20.2923 q^{6} -3.06093 q^{7} -24.2781 q^{8} +37.2117 q^{9} -52.4541 q^{10} -50.3240 q^{11} +12.7185 q^{12} -26.3471 q^{13} -7.75136 q^{14} +165.983 q^{15} -48.7833 q^{16} -23.1013 q^{17} +94.2331 q^{18} +135.885 q^{19} +32.8765 q^{20} +24.5279 q^{21} -127.438 q^{22} -91.8712 q^{23} +194.546 q^{24} +304.053 q^{25} -66.7201 q^{26} -81.8285 q^{27} +4.85830 q^{28} +15.5009 q^{29} +420.326 q^{30} -34.9791 q^{31} +70.6888 q^{32} +403.257 q^{33} -58.5007 q^{34} +63.4029 q^{35} -59.0622 q^{36} +221.246 q^{37} +344.110 q^{38} +211.125 q^{39} +502.888 q^{40} +206.730 q^{41} +62.1133 q^{42} +79.8739 q^{44} -770.788 q^{45} -232.650 q^{46} -600.224 q^{47} +390.911 q^{48} -333.631 q^{49} +769.970 q^{50} +185.116 q^{51} +41.8180 q^{52} +408.162 q^{53} -207.218 q^{54} +1042.39 q^{55} +74.3138 q^{56} -1088.88 q^{57} +39.2539 q^{58} -740.433 q^{59} -263.447 q^{60} -51.7496 q^{61} -88.5794 q^{62} -113.902 q^{63} +569.275 q^{64} +545.743 q^{65} +1021.19 q^{66} +334.159 q^{67} +36.6663 q^{68} +736.184 q^{69} +160.559 q^{70} +487.740 q^{71} -903.431 q^{72} +722.667 q^{73} +560.272 q^{74} -2436.45 q^{75} -215.677 q^{76} +154.038 q^{77} +534.643 q^{78} -171.428 q^{79} +1010.48 q^{80} -349.006 q^{81} +523.513 q^{82} -241.764 q^{83} -38.9306 q^{84} +478.511 q^{85} -124.213 q^{87} +1221.77 q^{88} +333.067 q^{89} -1951.91 q^{90} +80.6467 q^{91} +145.817 q^{92} +280.295 q^{93} -1519.98 q^{94} -2814.68 q^{95} -566.445 q^{96} +687.004 q^{97} -844.870 q^{98} -1872.64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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