LMFDB - Embedded newform 1849.4.a.j.1.11

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			1.11
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)

$f(q)$	$=$	$q-3.61756 q^{2} -2.47684 q^{3} +5.08677 q^{4} -17.9947 q^{5} +8.96012 q^{6} +10.9253 q^{7} +10.5388 q^{8} -20.8653 q^{9} +O(q^{10})$	\(q-3.61756 q^{2} -2.47684 q^{3} +5.08677 q^{4} -17.9947 q^{5} +8.96012 q^{6} +10.9253 q^{7} +10.5388 q^{8} -20.8653 q^{9} +65.0971 q^{10} -60.2496 q^{11} -12.5991 q^{12} +83.3256 q^{13} -39.5231 q^{14} +44.5701 q^{15} -78.8189 q^{16} -55.2843 q^{17} +75.4815 q^{18} -24.4261 q^{19} -91.5351 q^{20} -27.0603 q^{21} +217.957 q^{22} -128.082 q^{23} -26.1029 q^{24} +198.811 q^{25} -301.436 q^{26} +118.555 q^{27} +55.5746 q^{28} +119.404 q^{29} -161.235 q^{30} -124.927 q^{31} +200.822 q^{32} +149.229 q^{33} +199.994 q^{34} -196.598 q^{35} -106.137 q^{36} -279.623 q^{37} +88.3631 q^{38} -206.384 q^{39} -189.643 q^{40} +88.4105 q^{41} +97.8923 q^{42} -306.476 q^{44} +375.465 q^{45} +463.344 q^{46} +102.372 q^{47} +195.222 q^{48} -223.637 q^{49} -719.210 q^{50} +136.930 q^{51} +423.858 q^{52} +184.241 q^{53} -428.879 q^{54} +1084.18 q^{55} +115.140 q^{56} +60.4996 q^{57} -431.951 q^{58} -539.091 q^{59} +226.718 q^{60} +709.639 q^{61} +451.931 q^{62} -227.960 q^{63} -95.9353 q^{64} -1499.42 q^{65} -539.844 q^{66} +74.0370 q^{67} -281.218 q^{68} +317.238 q^{69} +711.207 q^{70} +555.772 q^{71} -219.895 q^{72} +659.489 q^{73} +1011.56 q^{74} -492.422 q^{75} -124.250 q^{76} -658.247 q^{77} +746.607 q^{78} -531.541 q^{79} +1418.33 q^{80} +269.722 q^{81} -319.831 q^{82} -731.654 q^{83} -137.649 q^{84} +994.826 q^{85} -295.744 q^{87} -634.959 q^{88} +927.680 q^{89} -1358.27 q^{90} +910.360 q^{91} -651.522 q^{92} +309.424 q^{93} -370.337 q^{94} +439.542 q^{95} -497.404 q^{96} +1297.66 q^{97} +809.022 q^{98} +1257.12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} + 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} + 386 q^{18} - 12 q^{19} - 108 q^{20} - 408 q^{21} - 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} - 1493 q^{26} - 10 q^{27} + 242 q^{28} - 208 q^{29} + 48 q^{30} - 932 q^{31} + 1124 q^{32} - 254 q^{33} - 765 q^{34} - 1452 q^{35} + 747 q^{36} + 90 q^{37} - 1213 q^{38} + 1610 q^{39} - 1693 q^{40} - 1354 q^{41} + 16 q^{42} - 2704 q^{44} - 4508 q^{45} - 233 q^{46} - 3484 q^{47} + 376 q^{48} + 1324 q^{49} + 408 q^{50} - 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} + 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} - 1172 q^{61} + 1546 q^{62} + 3686 q^{63} + 606 q^{64} - 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} - 136 q^{69} + 1310 q^{70} - 162 q^{71} + 5814 q^{72} - 746 q^{73} - 4332 q^{74} - 236 q^{75} - 1338 q^{76} - 2024 q^{77} - 2782 q^{78} - 2656 q^{79} + 5713 q^{80} - 86 q^{81} + 4168 q^{82} - 3514 q^{83} - 4269 q^{84} + 7558 q^{85} - 10278 q^{87} - 11692 q^{88} - 2640 q^{89} - 8286 q^{90} + 5946 q^{91} - 4271 q^{92} + 2 q^{93} - 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} + 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 + 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 + 386 * q^18 - 12 * q^19 - 108 * q^20 - 408 * q^21 - 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 - 1493 * q^26 - 10 * q^27 + 242 * q^28 - 208 * q^29 + 48 * q^30 - 932 * q^31 + 1124 * q^32 - 254 * q^33 - 765 * q^34 - 1452 * q^35 + 747 * q^36 + 90 * q^37 - 1213 * q^38 + 1610 * q^39 - 1693 * q^40 - 1354 * q^41 + 16 * q^42 - 2704 * q^44 - 4508 * q^45 - 233 * q^46 - 3484 * q^47 + 376 * q^48 + 1324 * q^49 + 408 * q^50 - 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 + 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 - 1172 * q^61 + 1546 * q^62 + 3686 * q^63 + 606 * q^64 - 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 - 136 * q^69 + 1310 * q^70 - 162 * q^71 + 5814 * q^72 - 746 * q^73 - 4332 * q^74 - 236 * q^75 - 1338 * q^76 - 2024 * q^77 - 2782 * q^78 - 2656 * q^79 + 5713 * q^80 - 86 * q^81 + 4168 * q^82 - 3514 * q^83 - 4269 * q^84 + 7558 * q^85 - 10278 * q^87 - 11692 * q^88 - 2640 * q^89 - 8286 * q^90 + 5946 * q^91 - 4271 * q^92 + 2 * q^93 - 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 + 2826 * q^98 - 8174 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.61756	−1.27900	−0.639501	−	0.768790i	$-0.720859\pi$
$2$	−3.61756	−1.27900	−0.639501	+	0.768790i	$0.720859\pi$
$3$	−2.47684	−0.476668	−0.238334	−	0.971183i	$-0.576601\pi$
$3$	−2.47684	−0.476668	−0.238334	+	0.971183i	$0.576601\pi$
$4$	5.08677	0.635846
$5$	−17.9947	−1.60950	−0.804749	−	0.593615i	$-0.797700\pi$
$5$	−17.9947	−1.60950	−0.804749	+	0.593615i	$0.797700\pi$
$6$	8.96012	0.609659
$7$	10.9253	0.589912	0.294956	−	0.955511i	$-0.404695\pi$
$7$	10.9253	0.589912	0.294956	+	0.955511i	$0.404695\pi$
$8$	10.5388	0.465754
$9$	−20.8653	−0.772788
$10$	65.0971	2.05855
$11$	−60.2496	−1.65145	−0.825725	−	0.564073i	$-0.809234\pi$
$11$	−60.2496	−1.65145	−0.825725	+	0.564073i	$0.809234\pi$
$12$	−12.5991	−0.303087
$13$	83.3256	1.77772	0.888860	−	0.458179i	$-0.151498\pi$
$13$	83.3256	1.77772	0.888860	+	0.458179i	$0.151498\pi$
$14$	−39.5231	−0.754499
$15$	44.5701	0.767196
$16$	−78.8189	−1.23155
$17$	−55.2843	−0.788729	−0.394365	−	0.918954i	$-0.629035\pi$
$17$	−55.2843	−0.788729	−0.394365	+	0.918954i	$0.629035\pi$
$18$	75.4815	0.988397
$19$	−24.4261	−0.294934	−0.147467	−	0.989067i	$-0.547112\pi$
$19$	−24.4261	−0.294934	−0.147467	+	0.989067i	$0.547112\pi$
$20$	−91.5351	−1.02339
$21$	−27.0603	−0.281192
$22$	217.957	2.11221
$23$	−128.082	−1.16117	−0.580584	−	0.814200i	$-0.697176\pi$
$23$	−128.082	−1.16117	−0.580584	+	0.814200i	$0.697176\pi$
$24$	−26.1029	−0.222010
$25$	198.811	1.59048
$26$	−301.436	−2.27371
$27$	118.555	0.845031
$28$	55.5746	0.375093
$29$	119.404	0.764577	0.382288	−	0.924043i	$-0.375136\pi$
$29$	119.404	0.764577	0.382288	+	0.924043i	$0.375136\pi$
$30$	−161.235	−0.981245
$31$	−124.927	−0.723791	−0.361895	−	0.932219i	$-0.617870\pi$
$31$	−124.927	−0.723791	−0.361895	+	0.932219i	$0.617870\pi$
$32$	200.822	1.10940
$33$	149.229	0.787193
$34$	199.994	1.00879
$35$	−196.598	−0.949463
$36$	−106.137	−0.491374
$37$	−279.623	−1.24243	−0.621214	−	0.783641i	$-0.713360\pi$
$37$	−279.623	−1.24243	−0.621214	+	0.783641i	$0.713360\pi$
$38$	88.3631	0.377221
$39$	−206.384	−0.847382
$40$	−189.643	−0.749630
$41$	88.4105	0.336766	0.168383	−	0.985722i	$-0.446145\pi$
$41$	88.4105	0.336766	0.168383	+	0.985722i	$0.446145\pi$
$42$	97.8923	0.359645
$43$	0	0
$43$	0	0
$44$	−306.476	−1.05007
$45$	375.465	1.24380
$46$	463.344	1.48514
$47$	102.372	0.317713	0.158856	−	0.987302i	$-0.449219\pi$
$47$	102.372	0.317713	0.158856	+	0.987302i	$0.449219\pi$
$48$	195.222	0.587038
$49$	−223.637	−0.652003
$50$	−719.210	−2.03423
$51$	136.930	0.375962
$52$	423.858	1.13036
$53$	184.241	0.477498	0.238749	−	0.971081i	$-0.423263\pi$
$53$	184.241	0.477498	0.238749	+	0.971081i	$0.423263\pi$
$54$	−428.879	−1.08080
$55$	1084.18	2.65800
$56$	115.140	0.274754
$57$	60.4996	0.140585
$58$	−431.951	−0.977895
$59$	−539.091	−1.18955	−0.594776	−	0.803891i	$-0.702759\pi$
$59$	−539.091	−1.18955	−0.594776	+	0.803891i	$0.702759\pi$
$60$	226.718	0.487818
$61$	709.639	1.48951	0.744754	−	0.667339i	$-0.232567\pi$
$61$	709.639	1.48951	0.744754	+	0.667339i	$0.232567\pi$
$62$	451.931	0.925730
$63$	−227.960	−0.455877
$64$	−95.9353	−0.187374
$65$	−1499.42	−2.86124
$66$	−539.844	−1.00682
$67$	74.0370	0.135001	0.0675005	−	0.997719i	$-0.478498\pi$
$67$	74.0370	0.135001	0.0675005	+	0.997719i	$0.478498\pi$
$68$	−281.218	−0.501511
$69$	317.238	0.553492
$70$	711.207	1.21436
$71$	555.772	0.928986	0.464493	−	0.885577i	$-0.346237\pi$
$71$	555.772	0.928986	0.464493	+	0.885577i	$0.346237\pi$
$72$	−219.895	−0.359929
$73$	659.489	1.05736	0.528681	−	0.848821i	$-0.322687\pi$
$73$	659.489	1.05736	0.528681	+	0.848821i	$0.322687\pi$
$74$	1011.56	1.58907
$75$	−492.422	−0.758133
$76$	−124.250	−0.187532
$77$	−658.247	−0.974211
$78$	746.607	1.08380
$79$	−531.541	−0.757001	−0.378501	−	0.925601i	$-0.623560\pi$
$79$	−531.541	−0.757001	−0.378501	+	0.925601i	$0.623560\pi$
$80$	1418.33	1.98217
$81$	269.722	0.369989
$82$	−319.831	−0.430724
$83$	−731.654	−0.967584	−0.483792	−	0.875183i	$-0.660741\pi$
$83$	−731.654	−0.967584	−0.483792	+	0.875183i	$0.660741\pi$
$84$	−137.649	−0.178795
$85$	994.826	1.26946
$86$	0	0
$87$	−295.744	−0.364449
$88$	−634.959	−0.769169
$89$	927.680	1.10488	0.552438	−	0.833554i	$-0.313698\pi$
$89$	927.680	1.10488	0.552438	+	0.833554i	$0.313698\pi$
$90$	−1358.27	−1.59082
$91$	910.360	1.04870
$92$	−651.522	−0.738324
$93$	309.424	0.345008
$94$	−370.337	−0.406355
$95$	439.542	0.474695
$96$	−497.404	−0.528813
$97$	1297.66	1.35833	0.679164	−	0.733987i	$-0.262343\pi$
$97$	1297.66	1.35833	0.679164	+	0.733987i	$0.262343\pi$
$98$	809.022	0.833914
$99$	1257.12	1.27622
$100$	1011.30	1.01130
$101$	315.009	0.310342	0.155171	−	0.987888i	$-0.450407\pi$
$101$	315.009	0.310342	0.155171	+	0.987888i	$0.450407\pi$
$102$	−495.354	−0.480856
$103$	1434.80	1.37258	0.686288	−	0.727330i	$-0.259239\pi$
$103$	1434.80	1.37258	0.686288	+	0.727330i	$0.259239\pi$
$104$	878.152	0.827980
$105$	486.943	0.452578
$106$	−666.502	−0.610721
$107$	−719.465	−0.650031	−0.325015	−	0.945709i	$-0.605369\pi$
$107$	−719.465	−0.650031	−0.325015	+	0.945709i	$0.605369\pi$
$108$	603.059	0.537309
$109$	1089.84	0.957688	0.478844	−	0.877900i	$-0.341056\pi$
$109$	1089.84	0.957688	0.478844	+	0.877900i	$0.341056\pi$
$110$	−3922.08	−3.39959
$111$	692.582	0.592225
$112$	−861.123	−0.726504
$113$	281.293	0.234176	0.117088	−	0.993122i	$-0.462644\pi$
$113$	281.293	0.234176	0.117088	+	0.993122i	$0.462644\pi$
$114$	−218.861	−0.179809
$115$	2304.80	1.86890
$116$	607.379	0.486153
$117$	−1738.61	−1.37380
$118$	1950.19	1.52144
$119$	−603.999	−0.465281
$120$	469.715	0.357324
$121$	2299.02	1.72729
$122$	−2567.17	−1.90508
$123$	−218.979	−0.160525
$124$	−635.474	−0.460220
$125$	−1328.20	−0.950384
$126$	824.660	0.583068
$127$	−687.188	−0.480142	−0.240071	−	0.970755i	$-0.577171\pi$
$127$	−687.188	−0.480142	−0.240071	+	0.970755i	$0.577171\pi$
$128$	−1259.52	−0.869745
$129$	0	0
$130$	5424.26	3.65953
$131$	−551.794	−0.368019	−0.184009	−	0.982924i	$-0.558908\pi$
$131$	−551.794	−0.368019	−0.184009	+	0.982924i	$0.558908\pi$
$132$	759.091	0.500533
$133$	−266.864	−0.173985
$134$	−267.834	−0.172666
$135$	−2133.36	−1.36008
$136$	−582.630	−0.367354
$137$	1879.78	1.17227	0.586134	−	0.810214i	$-0.300649\pi$
$137$	1879.78	1.17227	0.586134	+	0.810214i	$0.300649\pi$
$138$	−1147.63	−0.707917
$139$	1766.14	1.07771	0.538855	−	0.842399i	$-0.318857\pi$
$139$	1766.14	1.07771	0.538855	+	0.842399i	$0.318857\pi$
$140$	−1000.05	−0.603712
$141$	−253.559	−0.151443
$142$	−2010.54	−1.18817
$143$	−5020.34	−2.93582
$144$	1644.58	0.951724
$145$	−2148.64	−1.23059
$146$	−2385.74	−1.35237
$147$	553.913	0.310789
$148$	−1422.38	−0.789992
$149$	1233.08	0.677974	0.338987	−	0.940791i	$-0.389916\pi$
$149$	1233.08	0.677974	0.338987	+	0.940791i	$0.389916\pi$
$150$	1781.37	0.969653
$151$	1127.73	0.607771	0.303885	−	0.952709i	$-0.401716\pi$
$151$	1127.73	0.607771	0.303885	+	0.952709i	$0.401716\pi$
$152$	−257.422	−0.137366
$153$	1153.52	0.609521
$154$	2381.25	1.24602
$155$	2248.03	1.16494
$156$	−1049.83	−0.538804
$157$	−605.410	−0.307751	−0.153876	−	0.988090i	$-0.549176\pi$
$157$	−605.410	−0.307751	−0.153876	+	0.988090i	$0.549176\pi$
$158$	1922.89	0.968206
$159$	−456.334	−0.227608
$160$	−3613.74	−1.78557
$161$	−1399.33	−0.684988
$162$	−975.736	−0.473217
$163$	−2491.95	−1.19745	−0.598725	−	0.800955i	$-0.704326\pi$
$163$	−2491.95	−1.19745	−0.598725	+	0.800955i	$0.704326\pi$
$164$	449.724	0.214131
$165$	−2685.33	−1.26699
$166$	2646.81	1.23754
$167$	−2713.05	−1.25714	−0.628569	−	0.777754i	$-0.716359\pi$
$167$	−2713.05	−1.25714	−0.628569	+	0.777754i	$0.716359\pi$
$168$	−285.183	−0.130966
$169$	4746.15	2.16029
$170$	−3598.85	−1.62364
$171$	509.658	0.227921
$172$	0	0
$173$	1135.63	0.499077	0.249538	−	0.968365i	$-0.419721\pi$
$173$	1135.63	0.499077	0.249538	+	0.968365i	$0.419721\pi$
$174$	1069.87	0.466131
$175$	2172.07	0.938246
$176$	4748.81	2.03384
$177$	1335.24	0.567022
$178$	−3355.94	−1.41314
$179$	−3005.54	−1.25500	−0.627500	−	0.778617i	$-0.715922\pi$
$179$	−3005.54	−1.25500	−0.627500	+	0.778617i	$0.715922\pi$
$180$	1909.90	0.790866
$181$	1380.70	0.566997	0.283499	−	0.958973i	$-0.408505\pi$
$181$	1380.70	0.566997	0.283499	+	0.958973i	$0.408505\pi$
$182$	−3293.28	−1.34129
$183$	−1757.66	−0.710001
$184$	−1349.83	−0.540818
$185$	5031.75	1.99968
$186$	−1119.36	−0.441266
$187$	3330.86	1.30255
$188$	520.743	0.202016
$189$	1295.25	0.498494
$190$	−1590.07	−0.607136
$191$	−197.941	−0.0749870	−0.0374935	−	0.999297i	$-0.511937\pi$
$191$	−197.941	−0.0749870	−0.0374935	+	0.999297i	$0.511937\pi$
$192$	237.616	0.0893150
$193$	731.734	0.272909	0.136454	−	0.990646i	$-0.456429\pi$
$193$	731.734	0.272909	0.136454	+	0.990646i	$0.456429\pi$
$194$	−4694.38	−1.73730
$195$	3713.83	1.36386
$196$	−1137.59	−0.414574
$197$	2219.55	0.802723	0.401362	−	0.915920i	$-0.368537\pi$
$197$	2219.55	0.802723	0.401362	+	0.915920i	$0.368537\pi$
$198$	−4547.73	−1.63229
$199$	2457.75	0.875505	0.437753	−	0.899095i	$-0.355775\pi$
$199$	2457.75	0.875505	0.437753	+	0.899095i	$0.355775\pi$
$200$	2095.23	0.740774
$201$	−183.378	−0.0643506
$202$	−1139.56	−0.396928
$203$	1304.53	0.451033
$204$	696.532	0.239054
$205$	−1590.92	−0.542024
$206$	−5190.49	−1.75553
$207$	2672.46	0.897337
$208$	−6567.63	−2.18934
$209$	1471.67	0.487068
$210$	−1761.55	−0.578849
$211$	152.246	0.0496731	0.0248366	−	0.999692i	$-0.492093\pi$
$211$	152.246	0.0496731	0.0248366	+	0.999692i	$0.492093\pi$
$212$	937.189	0.303615
$213$	−1376.56	−0.442817
$214$	2602.71	0.831390
$215$	0	0
$216$	1249.42	0.393576
$217$	−1364.87	−0.426973
$218$	−3942.58	−1.22488
$219$	−1633.45	−0.504010
$220$	5514.95	1.69008
$221$	−4606.59	−1.40214
$222$	−2505.46	−0.757457
$223$	−4272.05	−1.28286	−0.641429	−	0.767182i	$-0.721658\pi$
$223$	−4272.05	−1.28286	−0.641429	+	0.767182i	$0.721658\pi$
$224$	2194.05	0.654446
$225$	−4148.24	−1.22911
$226$	−1017.60	−0.299511
$227$	2146.82	0.627706	0.313853	−	0.949472i	$-0.398380\pi$
$227$	2146.82	0.627706	0.313853	+	0.949472i	$0.398380\pi$
$228$	307.747	0.0893906
$229$	5101.80	1.47221	0.736106	−	0.676867i	$-0.236663\pi$
$229$	5101.80	1.47221	0.736106	+	0.676867i	$0.236663\pi$
$230$	−8337.75	−2.39033
$231$	1630.37	0.464375
$232$	1258.37	0.356104
$233$	−5124.12	−1.44074	−0.720369	−	0.693591i	$-0.756028\pi$
$233$	−5124.12	−1.44074	−0.720369	+	0.693591i	$0.756028\pi$
$234$	6289.54	1.75709
$235$	−1842.16	−0.511358
$236$	−2742.23	−0.756373
$237$	1316.54	0.360838
$238$	2185.00	0.595096
$239$	−5810.98	−1.57273	−0.786363	−	0.617765i	$-0.788038\pi$
$239$	−5810.98	−1.57273	−0.786363	+	0.617765i	$0.788038\pi$
$240$	−3512.96	−0.944837
$241$	2897.00	0.774325	0.387163	−	0.922011i	$-0.373455\pi$
$241$	2897.00	0.774325	0.387163	+	0.922011i	$0.373455\pi$
$242$	−8316.84	−2.20920
$243$	−3869.03	−1.02139
$244$	3609.77	0.947098
$245$	4024.29	1.04940
$246$	792.169	0.205312
$247$	−2035.32	−0.524309
$248$	−1316.58	−0.337108
$249$	1812.19	0.461216
$250$	4804.85	1.21554
$251$	5952.10	1.49679	0.748393	−	0.663255i	$-0.230826\pi$
$251$	5952.10	1.49679	0.748393	+	0.663255i	$0.230826\pi$
$252$	−1159.58	−0.289868
$253$	7716.87	1.91761
$254$	2485.95	0.614103
$255$	−2464.02	−0.605110
$256$	5323.89	1.29978
$257$	1636.32	0.397162	0.198581	−	0.980084i	$-0.436367\pi$
$257$	1636.32	0.397162	0.198581	+	0.980084i	$0.436367\pi$
$258$	0	0
$259$	−3054.98	−0.732923
$260$	−7627.21	−1.81931
$261$	−2491.39	−0.590856
$262$	1996.15	0.470697
$263$	5471.20	1.28277	0.641385	−	0.767219i	$-0.278360\pi$
$263$	5471.20	1.28277	0.641385	+	0.767219i	$0.278360\pi$
$264$	1572.69	0.366638
$265$	−3315.36	−0.768532
$266$	965.396	0.222527
$267$	−2297.71	−0.526659
$268$	376.609	0.0858398
$269$	−5056.33	−1.14606	−0.573030	−	0.819535i	$-0.694232\pi$
$269$	−5056.33	−1.14606	−0.573030	+	0.819535i	$0.694232\pi$
$270$	7717.56	1.73954
$271$	2645.05	0.592899	0.296449	−	0.955049i	$-0.404197\pi$
$271$	2645.05	0.592899	0.296449	+	0.955049i	$0.404197\pi$
$272$	4357.45	0.971357
$273$	−2254.81	−0.499881
$274$	−6800.23	−1.49933
$275$	−11978.3	−2.62660
$276$	1613.71	0.351935
$277$	1722.07	0.373535	0.186768	−	0.982404i	$-0.440199\pi$
$277$	1722.07	0.373535	0.186768	+	0.982404i	$0.440199\pi$
$278$	−6389.11	−1.37839
$279$	2606.63	0.559337
$280$	−2071.91	−0.442216
$281$	−8409.61	−1.78532	−0.892661	−	0.450729i	$-0.851164\pi$
$281$	−8409.61	−1.78532	−0.892661	+	0.450729i	$0.851164\pi$
$282$	917.265	0.193696
$283$	−7474.29	−1.56997	−0.784983	−	0.619518i	$-0.787328\pi$
$283$	−7474.29	−1.56997	−0.784983	+	0.619518i	$0.787328\pi$
$284$	2827.08	0.590692
$285$	−1088.67	−0.226272
$286$	18161.4	3.75491
$287$	965.914	0.198662
$288$	−4190.21	−0.857328
$289$	−1856.65	−0.377906
$290$	7772.84	1.57392
$291$	−3214.10	−0.647471
$292$	3354.67	0.672319
$293$	2830.74	0.564415	0.282207	−	0.959353i	$-0.408933\pi$
$293$	2830.74	0.564415	0.282207	+	0.959353i	$0.408933\pi$
$294$	−2003.82	−0.397500
$295$	9700.79	1.91458
$296$	−2946.90	−0.578665
$297$	−7142.87	−1.39553
$298$	−4460.76	−0.867130
$299$	−10672.5	−2.06423
$300$	−2504.83	−0.482056
$301$	0	0
$302$	−4079.64	−0.777340
$303$	−780.225	−0.147930
$304$	1925.24	0.363224
$305$	−12769.8	−2.39736
$306$	−4172.94	−0.779578
$307$	1054.02	0.195948	0.0979739	−	0.995189i	$-0.468764\pi$
$307$	1054.02	0.195948	0.0979739	+	0.995189i	$0.468764\pi$
$308$	−3348.35	−0.619448
$309$	−3553.77	−0.654263
$310$	−8132.38	−1.48996
$311$	9646.08	1.75877	0.879387	−	0.476107i	$-0.157953\pi$
$311$	9646.08	1.75877	0.879387	+	0.476107i	$0.157953\pi$
$312$	−2175.04	−0.394671
$313$	−1750.95	−0.316197	−0.158098	−	0.987423i	$-0.550536\pi$
$313$	−1750.95	−0.316197	−0.158098	+	0.987423i	$0.550536\pi$
$314$	2190.11	0.393615
$315$	4102.08	0.733733
$316$	−2703.83	−0.481336
$317$	704.472	0.124817	0.0624086	−	0.998051i	$-0.480122\pi$
$317$	704.472	0.124817	0.0624086	+	0.998051i	$0.480122\pi$
$318$	1650.82	0.291111
$319$	−7194.03	−1.26266
$320$	1726.33	0.301578
$321$	1782.00	0.309849
$322$	5062.18	0.876101
$323$	1350.38	0.232623
$324$	1372.01	0.235256
$325$	16566.0	2.82744
$326$	9014.77	1.53154
$327$	−2699.36	−0.456499
$328$	931.741	0.156850
$329$	1118.45	0.187423
$330$	9714.35	1.62048
$331$	−5792.53	−0.961892	−0.480946	−	0.876750i	$-0.659707\pi$
$331$	−5792.53	−0.961892	−0.480946	+	0.876750i	$0.659707\pi$
$332$	−3721.76	−0.615235
$333$	5834.42	0.960133
$334$	9814.63	1.60788
$335$	−1332.28	−0.217284
$336$	2132.86	0.346301
$337$	−5869.09	−0.948694	−0.474347	−	0.880338i	$-0.657316\pi$
$337$	−5869.09	−0.948694	−0.474347	+	0.880338i	$0.657316\pi$
$338$	−17169.5	−2.76301
$339$	−696.718	−0.111624
$340$	5060.45	0.807180
$341$	7526.79	1.19530
$342$	−1843.72	−0.291512
$343$	−6190.70	−0.974537
$344$	0	0
$345$	−5708.61	−0.890844
$346$	−4108.21	−0.638320
$347$	7730.08	1.19589	0.597943	−	0.801538i	$-0.295985\pi$
$347$	7730.08	1.19589	0.597943	+	0.801538i	$0.295985\pi$
$348$	−1504.38	−0.231734
$349$	−406.164	−0.0622965	−0.0311482	−	0.999515i	$-0.509916\pi$
$349$	−406.164	−0.0622965	−0.0311482	+	0.999515i	$0.509916\pi$
$350$	−7857.61	−1.20002
$351$	9878.63	1.50223
$352$	−12099.5	−1.83211
$353$	−5126.15	−0.772911	−0.386456	−	0.922308i	$-0.626301\pi$
$353$	−5126.15	−0.772911	−0.386456	+	0.922308i	$0.626301\pi$
$354$	−4830.32	−0.725222
$355$	−10001.0	−1.49520
$356$	4718.89	0.702531
$357$	1496.01	0.221785
$358$	10872.7	1.60515
$359$	−1617.42	−0.237783	−0.118892	−	0.992907i	$-0.537934\pi$
$359$	−1617.42	−0.237783	−0.118892	+	0.992907i	$0.537934\pi$
$360$	3956.95	0.579305
$361$	−6262.36	−0.913014
$362$	−4994.76	−0.725190
$363$	−5694.29	−0.823341
$364$	4630.79	0.666811
$365$	−11867.3	−1.70182
$366$	6358.45	0.908092
$367$	−10719.8	−1.52471	−0.762354	−	0.647161i	$-0.775956\pi$
$367$	−10719.8	−1.52471	−0.762354	+	0.647161i	$0.775956\pi$
$368$	10095.3	1.43003
$369$	−1844.71	−0.260249
$370$	−18202.7	−2.55760
$371$	2012.89	0.281682
$372$	1573.97	0.219372
$373$	−8000.84	−1.11064	−0.555319	−	0.831637i	$-0.687404\pi$
$373$	−8000.84	−1.11064	−0.555319	+	0.831637i	$0.687404\pi$
$374$	−12049.6	−1.66596
$375$	3289.74	0.453017
$376$	1078.88	0.147976
$377$	9949.39	1.35920
$378$	−4685.64	−0.637575
$379$	−10844.9	−1.46982	−0.734911	−	0.678163i	$-0.762776\pi$
$379$	−10844.9	−1.46982	−0.734911	+	0.678163i	$0.762776\pi$
$380$	2235.85	0.301833
$381$	1702.05	0.228868
$382$	716.065	0.0959085
$383$	12651.9	1.68794	0.843972	−	0.536388i	$-0.180212\pi$
$383$	12651.9	1.68794	0.843972	+	0.536388i	$0.180212\pi$
$384$	3119.64	0.414579
$385$	11845.0	1.56799
$386$	−2647.09	−0.349051
$387$	0	0
$388$	6600.91	0.863687
$389$	2845.89	0.370931	0.185466	−	0.982651i	$-0.440621\pi$
$389$	2845.89	0.370931	0.185466	+	0.982651i	$0.440621\pi$
$390$	−13435.0	−1.74438
$391$	7080.90	0.915848
$392$	−2356.87	−0.303673
$393$	1366.71	0.175423
$394$	−8029.37	−1.02668
$395$	9564.95	1.21839
$396$	6394.70	0.811479
$397$	5007.64	0.633063	0.316532	−	0.948582i	$-0.397482\pi$
$397$	5007.64	0.633063	0.316532	+	0.948582i	$0.397482\pi$
$398$	−8891.08	−1.11977
$399$	660.978	0.0829330
$400$	−15670.0	−1.95875
$401$	−1390.02	−0.173103	−0.0865513	−	0.996247i	$-0.527585\pi$
$401$	−1390.02	−0.173103	−0.0865513	+	0.996247i	$0.527585\pi$
$402$	663.381	0.0823045
$403$	−10409.6	−1.28670
$404$	1602.38	0.197330
$405$	−4853.57	−0.595496
$406$	−4719.21	−0.576873
$407$	16847.2	2.05181
$408$	1443.08	0.175106
$409$	−402.096	−0.0486121	−0.0243060	−	0.999705i	$-0.507738\pi$
$409$	−402.096	−0.0486121	−0.0243060	+	0.999705i	$0.507738\pi$
$410$	5755.27	0.693250
$411$	−4655.92	−0.558782
$412$	7298.51	0.872747
$413$	−5889.74	−0.701732
$414$	−9667.79	−1.14770
$415$	13165.9	1.55732
$416$	16733.6	1.97220
$417$	−4374.43	−0.513710
$418$	−5323.84	−0.622961
$419$	−4606.62	−0.537107	−0.268554	−	0.963265i	$-0.586546\pi$
$419$	−4606.62	−0.537107	−0.268554	+	0.963265i	$0.586546\pi$
$420$	2476.96	0.287770
$421$	−5395.50	−0.624609	−0.312305	−	0.949982i	$-0.601101\pi$
$421$	−5395.50	−0.624609	−0.312305	+	0.949982i	$0.601101\pi$
$422$	−550.759	−0.0635320
$423$	−2136.02	−0.245524
$424$	1941.67	0.222396
$425$	−10991.1	−1.25446
$426$	4979.78	0.566364
$427$	7753.04	0.878679
$428$	−3659.75	−0.413319
$429$	12434.6	1.39941
$430$	0	0
$431$	−934.590	−0.104449	−0.0522246	−	0.998635i	$-0.516631\pi$
$431$	−934.590	−0.104449	−0.0522246	+	0.998635i	$0.516631\pi$
$432$	−9344.34	−1.04069
$433$	−6512.81	−0.722831	−0.361415	−	0.932405i	$-0.617706\pi$
$433$	−6512.81	−0.722831	−0.361415	+	0.932405i	$0.617706\pi$
$434$	4937.49	0.546100
$435$	5321.83	0.586580
$436$	5543.78	0.608942
$437$	3128.54	0.342468
$438$	5909.10	0.644630
$439$	−4162.25	−0.452513	−0.226257	−	0.974068i	$-0.572649\pi$
$439$	−4162.25	−0.452513	−0.226257	+	0.974068i	$0.572649\pi$
$440$	11425.9	1.23798
$441$	4666.25	0.503860
$442$	16664.6	1.79334
$443$	−5508.69	−0.590803	−0.295402	−	0.955373i	$-0.595453\pi$
$443$	−5508.69	−0.590803	−0.295402	+	0.955373i	$0.595453\pi$
$444$	3523.00	0.376564
$445$	−16693.4	−1.77830
$446$	15454.4	1.64078
$447$	−3054.15	−0.323168
$448$	−1048.13	−0.110534
$449$	−11101.7	−1.16686	−0.583430	−	0.812163i	$-0.698290\pi$
$449$	−11101.7	−1.16686	−0.583430	+	0.812163i	$0.698290\pi$
$450$	15006.5	1.57203
$451$	−5326.70	−0.556152
$452$	1430.87	0.148900
$453$	−2793.21	−0.289705
$454$	−7766.25	−0.802837
$455$	−16381.7	−1.68788
$456$	637.593	0.0654781
$457$	−11637.9	−1.19124	−0.595621	−	0.803265i	$-0.703094\pi$
$457$	−11637.9	−1.19124	−0.595621	+	0.803265i	$0.703094\pi$
$458$	−18456.1	−1.88296
$459$	−6554.20	−0.666501
$460$	11724.0	1.18833
$461$	3771.32	0.381015	0.190507	−	0.981686i	$-0.438987\pi$
$461$	3771.32	0.381015	0.190507	+	0.981686i	$0.438987\pi$
$462$	−5897.97	−0.593936
$463$	−11682.2	−1.17261	−0.586306	−	0.810090i	$-0.699418\pi$
$463$	−11682.2	−1.17261	−0.586306	+	0.810090i	$0.699418\pi$
$464$	−9411.28	−0.941611
$465$	−5568.00	−0.555289
$466$	18536.8	1.84271
$467$	2086.46	0.206745	0.103372	−	0.994643i	$-0.467037\pi$
$467$	2086.46	0.206745	0.103372	+	0.994643i	$0.467037\pi$
$468$	−8843.91	−0.873526
$469$	808.879	0.0796387
$470$	6664.12	0.654028
$471$	1499.50	0.146695
$472$	−5681.37	−0.554039
$473$	0	0
$474$	−4762.68	−0.461513
$475$	−4856.17	−0.469087
$476$	−3072.40	−0.295847
$477$	−3844.23	−0.369005
$478$	21021.6	2.01152
$479$	15342.3	1.46348	0.731742	−	0.681582i	$-0.238708\pi$
$479$	15342.3	1.46348	0.731742	+	0.681582i	$0.238708\pi$
$480$	8950.65	0.851124
$481$	−23299.8	−2.20869
$482$	−10480.1	−0.990364
$483$	3465.93	0.326512
$484$	11694.6	1.09829
$485$	−23351.1	−2.18623
$486$	13996.5	1.30636
$487$	−1046.75	−0.0973977	−0.0486989	−	0.998814i	$-0.515507\pi$
$487$	−1046.75	−0.0973977	−0.0486989	+	0.998814i	$0.515507\pi$
$488$	7478.75	0.693744
$489$	6172.15	0.570785
$490$	−14558.1	−1.34218
$491$	−7721.24	−0.709684	−0.354842	−	0.934926i	$-0.615465\pi$
$491$	−7721.24	−0.709684	−0.354842	+	0.934926i	$0.615465\pi$
$492$	−1113.89	−0.102069
$493$	−6601.15	−0.603044
$494$	7362.91	0.670593
$495$	−22621.6	−2.05407
$496$	9846.60	0.891382
$497$	6071.99	0.548020
$498$	−6555.71	−0.589896
$499$	17819.9	1.59865	0.799326	−	0.600897i	$-0.205190\pi$
$499$	17819.9	1.59865	0.799326	+	0.600897i	$0.205190\pi$
$500$	−6756.25	−0.604298
$501$	6719.79	0.599238
$502$	−21532.1	−1.91439
$503$	−10784.0	−0.955938	−0.477969	−	0.878377i	$-0.658627\pi$
$503$	−10784.0	−0.955938	−0.477969	+	0.878377i	$0.658627\pi$
$504$	−2402.43	−0.212326
$505$	−5668.50	−0.499495
$506$	−27916.3	−2.45263
$507$	−11755.5	−1.02974
$508$	−3495.57	−0.305297
$509$	−15169.1	−1.32094	−0.660472	−	0.750851i	$-0.729644\pi$
$509$	−15169.1	−1.32094	−0.660472	+	0.750851i	$0.729644\pi$
$510$	8913.76	0.773937
$511$	7205.14	0.623750
$512$	−9183.33	−0.792675
$513$	−2895.83	−0.249228
$514$	−5919.48	−0.507971
$515$	−25818.9	−2.20916
$516$	0	0
$517$	−6167.87	−0.524686
$518$	11051.6	0.937410
$519$	−2812.77	−0.237894
$520$	−15802.1	−1.33263
$521$	−2765.08	−0.232515	−0.116257	−	0.993219i	$-0.537090\pi$
$521$	−2765.08	−0.232515	−0.116257	+	0.993219i	$0.537090\pi$
$522$	9012.77	0.755706
$523$	2271.48	0.189914	0.0949568	−	0.995481i	$-0.469729\pi$
$523$	2271.48	0.189914	0.0949568	+	0.995481i	$0.469729\pi$
$524$	−2806.85	−0.234003
$525$	−5379.87	−0.447232
$526$	−19792.4	−1.64067
$527$	6906.49	0.570875
$528$	−11762.0	−0.969464
$529$	4237.92	0.348312
$530$	11993.5	0.982954
$531$	11248.3	0.919272
$532$	−1357.47	−0.110628
$533$	7366.86	0.598675
$534$	8312.13	0.673597
$535$	12946.6	1.04622
$536$	780.261	0.0628772
$537$	7444.25	0.598218
$538$	18291.6	1.46581
$539$	13474.1	1.07675
$540$	−10851.9	−0.864799
$541$	−4266.25	−0.339040	−0.169520	−	0.985527i	$-0.554222\pi$
$541$	−4266.25	−0.339040	−0.169520	+	0.985527i	$0.554222\pi$
$542$	−9568.65	−0.758319
$543$	−3419.77	−0.270269
$544$	−11102.3	−0.875013
$545$	−19611.4	−1.54140
$546$	8156.93	0.639349
$547$	23063.3	1.80277	0.901386	−	0.433017i	$-0.142551\pi$
$547$	23063.3	1.80277	0.901386	+	0.433017i	$0.142551\pi$
$548$	9562.02	0.745381
$549$	−14806.8	−1.15107
$550$	43332.1	3.35943
$551$	−2916.57	−0.225499
$552$	3343.30	0.257791
$553$	−5807.27	−0.446564
$554$	−6229.71	−0.477752
$555$	−12462.8	−0.953185
$556$	8983.92	0.685258
$557$	−3638.87	−0.276811	−0.138406	−	0.990376i	$-0.544198\pi$
$557$	−3638.87	−0.276811	−0.138406	+	0.990376i	$0.544198\pi$
$558$	−9429.66	−0.715393
$559$	0	0
$560$	15495.7	1.16931
$561$	−8249.99	−0.620882
$562$	30422.3	2.28343
$563$	−6527.20	−0.488612	−0.244306	−	0.969698i	$-0.578560\pi$
$563$	−6527.20	−0.488612	−0.244306	+	0.969698i	$0.578560\pi$
$564$	−1289.80	−0.0962946
$565$	−5061.80	−0.376905
$566$	27038.7	2.00799
$567$	2946.80	0.218261
$568$	5857.17	0.432678
$569$	−20981.2	−1.54583	−0.772917	−	0.634507i	$-0.781203\pi$
$569$	−20981.2	−1.54583	−0.772917	+	0.634507i	$0.781203\pi$
$570$	3938.35	0.289402
$571$	15555.5	1.14006	0.570032	−	0.821622i	$-0.306931\pi$
$571$	15555.5	1.14006	0.570032	+	0.821622i	$0.306931\pi$
$572$	−25537.3	−1.86673
$573$	490.268	0.0357439
$574$	−3494.26	−0.254090
$575$	−25464.0	−1.84682
$576$	2001.72	0.144800
$577$	−5345.98	−0.385713	−0.192856	−	0.981227i	$-0.561775\pi$
$577$	−5345.98	−0.385713	−0.192856	+	0.981227i	$0.561775\pi$
$578$	6716.55	0.483342
$579$	−1812.39	−0.130087
$580$	−10929.6	−0.782463
$581$	−7993.56	−0.570790
$582$	11627.2	0.828117
$583$	−11100.4	−0.788564
$584$	6950.22	0.492470
$585$	31285.9	2.21113
$586$	−10240.4	−0.721887
$587$	1744.52	0.122665	0.0613324	−	0.998117i	$-0.480465\pi$
$587$	1744.52	0.122665	0.0613324	+	0.998117i	$0.480465\pi$
$588$	2817.63	0.197614
$589$	3051.48	0.213470
$590$	−35093.2	−2.44876
$591$	−5497.47	−0.382632
$592$	22039.6	1.53011
$593$	−9301.56	−0.644130	−0.322065	−	0.946718i	$-0.604377\pi$
$593$	−9301.56	−0.644130	−0.322065	+	0.946718i	$0.604377\pi$
$594$	25839.8	1.78488
$595$	10868.8	0.748869
$596$	6272.41	0.431087
$597$	−6087.46	−0.417325
$598$	38608.4	2.64016
$599$	1942.24	0.132484	0.0662420	−	0.997804i	$-0.478899\pi$
$599$	1942.24	0.132484	0.0662420	+	0.997804i	$0.478899\pi$
$600$	−5189.53	−0.353103
$601$	21909.3	1.48702	0.743509	−	0.668725i	$-0.233160\pi$
$601$	21909.3	1.48702	0.743509	+	0.668725i	$0.233160\pi$
$602$	0	0
$603$	−1544.80	−0.104327
$604$	5736.50	0.386449
$605$	−41370.2	−2.78006
$606$	2822.52	0.189203
$607$	975.955	0.0652599	0.0326300	−	0.999468i	$-0.489612\pi$
$607$	975.955	0.0652599	0.0326300	+	0.999468i	$0.489612\pi$
$608$	−4905.31	−0.327198
$609$	−3231.10	−0.214993
$610$	46195.5	3.06623
$611$	8530.21	0.564804
$612$	5867.69	0.387561
$613$	5980.96	0.394076	0.197038	−	0.980396i	$-0.436868\pi$
$613$	5980.96	0.394076	0.197038	+	0.980396i	$0.436868\pi$
$614$	−3812.98	−0.250618
$615$	3940.46	0.258365
$616$	−6937.14	−0.453742
$617$	27743.2	1.81021	0.905105	−	0.425188i	$-0.139792\pi$
$617$	27743.2	1.81021	0.905105	+	0.425188i	$0.139792\pi$
$618$	12856.0	0.836803
$619$	5498.82	0.357053	0.178527	−	0.983935i	$-0.442867\pi$
$619$	5498.82	0.357053	0.178527	+	0.983935i	$0.442867\pi$
$620$	11435.2	0.740723
$621$	−15184.7	−0.981223
$622$	−34895.3	−2.24948
$623$	10135.2	0.651780
$624$	16267.0	1.04359
$625$	−950.684	−0.0608438
$626$	6334.18	0.404416
$627$	−3645.08	−0.232170
$628$	−3079.58	−0.195682
$629$	15458.8	0.979939
$630$	−14839.5	−0.938446
$631$	−2676.32	−0.168847	−0.0844235	−	0.996430i	$-0.526905\pi$
$631$	−2676.32	−0.168847	−0.0844235	+	0.996430i	$0.526905\pi$
$632$	−5601.81	−0.352576
$633$	−377.088	−0.0236776
$634$	−2548.47	−0.159642
$635$	12365.8	0.772788
$636$	−2321.27	−0.144724
$637$	−18634.7	−1.15908
$638$	26024.9	1.61494
$639$	−11596.3	−0.717909
$640$	22664.8	1.39985
$641$	−21148.3	−1.30313	−0.651566	−	0.758592i	$-0.725888\pi$
$641$	−21148.3	−1.30313	−0.651566	+	0.758592i	$0.725888\pi$
$642$	−6446.49	−0.396297
$643$	−246.770	−0.0151348	−0.00756739	−	0.999971i	$-0.502409\pi$
$643$	−246.770	−0.0151348	−0.00756739	+	0.999971i	$0.502409\pi$
$644$	−7118.09	−0.435547
$645$	0	0
$646$	−4885.09	−0.297525
$647$	32803.7	1.99327	0.996634	−	0.0819754i	$-0.0261229\pi$
$647$	32803.7	1.99327	0.996634	+	0.0819754i	$0.0261229\pi$
$648$	2842.55	0.172324
$649$	32480.0	1.96449
$650$	−59928.6	−3.61630
$651$	3380.55	0.203524
$652$	−12675.9	−0.761393
$653$	8579.88	0.514176	0.257088	−	0.966388i	$-0.417237\pi$
$653$	8579.88	0.514176	0.257088	+	0.966388i	$0.417237\pi$
$654$	9765.12	0.583863
$655$	9929.39	0.592326
$656$	−6968.42	−0.414743
$657$	−13760.4	−0.817116
$658$	−4046.06	−0.239714
$659$	−22596.8	−1.33573	−0.667866	−	0.744281i	$-0.732792\pi$
$659$	−22596.8	−1.33573	−0.667866	+	0.744281i	$0.732792\pi$
$660$	−13659.6	−0.805608
$661$	8017.05	0.471750	0.235875	−	0.971783i	$-0.424204\pi$
$661$	8017.05	0.471750	0.235875	+	0.971783i	$0.424204\pi$
$662$	20954.8	1.23026
$663$	11409.8	0.668355
$664$	−7710.76	−0.450656
$665$	4802.14	0.280029
$666$	−21106.4	−1.22801
$667$	−15293.4	−0.887803
$668$	−13800.7	−0.799347
$669$	10581.2	0.611497
$670$	4819.60	0.277906
$671$	−42755.5	−2.45985
$672$	−5434.30	−0.311954
$673$	25565.1	1.46428	0.732140	−	0.681154i	$-0.238522\pi$
$673$	25565.1	1.46428	0.732140	+	0.681154i	$0.238522\pi$
$674$	21231.8	1.21338
$675$	23569.9	1.34401
$676$	24142.6	1.37361
$677$	−103.167	−0.00585674	−0.00292837	−	0.999996i	$-0.500932\pi$
$677$	−103.167	−0.00585674	−0.00292837	+	0.999996i	$0.500932\pi$
$678$	2520.42	0.142767
$679$	14177.4	0.801294
$680$	10484.3	0.591255
$681$	−5317.32	−0.299207
$682$	−27228.7	−1.52880
$683$	−18832.6	−1.05507	−0.527533	−	0.849534i	$-0.676883\pi$
$683$	−18832.6	−1.05507	−0.527533	+	0.849534i	$0.676883\pi$
$684$	2592.51	0.144923
$685$	−33826.2	−1.88676
$686$	22395.2	1.24644
$687$	−12636.3	−0.701756
$688$	0	0
$689$	15352.0	0.848858
$690$	20651.3	1.13939
$691$	26.0919	0.00143644	0.000718222	−	1.00000i	$-0.499771\pi$
$691$	26.0919	0.00143644	0.000718222		1.00000i	$0.499771\pi$
$692$	5776.68	0.317336
$693$	13734.5	0.752858
$694$	−27964.1	−1.52954
$695$	−31781.1	−1.73457
$696$	−3116.79	−0.169744
$697$	−4887.71	−0.265617
$698$	1469.33	0.0796773
$699$	12691.6	0.686754
$700$	11048.8	0.596580
$701$	30741.8	1.65635	0.828176	−	0.560468i	$-0.189379\pi$
$701$	30741.8	1.65635	0.828176	+	0.560468i	$0.189379\pi$
$702$	−35736.6	−1.92135
$703$	6830.12	0.366434
$704$	5780.07	0.309438
$705$	4562.73	0.243748
$706$	18544.2	0.988555
$707$	3441.57	0.183075
$708$	6792.06	0.360538
$709$	32760.2	1.73531	0.867656	−	0.497165i	$-0.165626\pi$
$709$	32760.2	1.73531	0.867656	+	0.497165i	$0.165626\pi$
$710$	36179.1	1.91236
$711$	11090.8	0.585001
$712$	9776.64	0.514600
$713$	16000.8	0.840443
$714$	−5411.90	−0.283663
$715$	90339.6	4.72519
$716$	−15288.5	−0.797986
$717$	14392.9	0.749667
$718$	5851.13	0.304126
$719$	27352.4	1.41874	0.709370	−	0.704837i	$-0.248980\pi$
$719$	27352.4	1.41874	0.709370	+	0.704837i	$0.248980\pi$
$720$	−29593.8	−1.53180
$721$	15675.7	0.809700
$722$	22654.5	1.16775
$723$	−7175.41	−0.369096
$724$	7023.29	0.360523
$725$	23738.7	1.21605
$726$	20599.5	1.05306
$727$	6560.47	0.334683	0.167342	−	0.985899i	$-0.446482\pi$
$727$	6560.47	0.334683	0.167342	+	0.985899i	$0.446482\pi$
$728$	9594.10	0.488435
$729$	2300.47	0.116876
$730$	42930.8	2.17663
$731$	0	0
$732$	−8940.82	−0.451451
$733$	−4640.51	−0.233835	−0.116918	−	0.993142i	$-0.537301\pi$
$733$	−4640.51	−0.233835	−0.116918	+	0.993142i	$0.537301\pi$
$734$	38779.5	1.95010
$735$	−9967.52	−0.500214
$736$	−25721.6	−1.28820
$737$	−4460.70	−0.222947
$738$	6673.35	0.332858
$739$	−25462.4	−1.26745	−0.633727	−	0.773557i	$-0.718476\pi$
$739$	−25462.4	−1.26745	−0.633727	+	0.773557i	$0.718476\pi$
$740$	25595.3	1.27149
$741$	5041.16	0.249921
$742$	−7281.75	−0.360272
$743$	−31591.6	−1.55987	−0.779935	−	0.625861i	$-0.784748\pi$
$743$	−31591.6	−1.55987	−0.779935	+	0.625861i	$0.784748\pi$
$744$	3260.95	0.160689
$745$	−22189.0	−1.09120
$746$	28943.6	1.42051
$747$	15266.2	0.747737
$748$	16943.3	0.828219
$749$	−7860.39	−0.383461
$750$	−11900.8	−0.579410
$751$	11251.7	0.546712	0.273356	−	0.961913i	$-0.411866\pi$
$751$	11251.7	0.546712	0.273356	+	0.961913i	$0.411866\pi$
$752$	−8068.85	−0.391278
$753$	−14742.4	−0.713470
$754$	−35992.6	−1.73842
$755$	−20293.2	−0.978206
$756$	6588.62	0.316966
$757$	30940.9	1.48556	0.742779	−	0.669536i	$-0.233507\pi$
$757$	30940.9	1.48556	0.742779	+	0.669536i	$0.233507\pi$
$758$	39232.0	1.87991
$759$	−19113.4	−0.914063
$760$	4632.24	0.221091
$761$	9097.60	0.433361	0.216681	−	0.976243i	$-0.430477\pi$
$761$	9097.60	0.433361	0.216681	+	0.976243i	$0.430477\pi$
$762$	−6157.29	−0.292723
$763$	11906.9	0.564952
$764$	−1006.88	−0.0476802
$765$	−20757.3	−0.981022
$766$	−45769.1	−2.15888
$767$	−44920.1	−2.11469
$768$	−13186.4	−0.619563
$769$	27674.9	1.29777	0.648883	−	0.760888i	$-0.275236\pi$
$769$	27674.9	1.29777	0.648883	+	0.760888i	$0.275236\pi$
$770$	−42850.0	−2.00546
$771$	−4052.89	−0.189314
$772$	3722.16	0.173528
$773$	40171.3	1.86916	0.934581	−	0.355750i	$-0.115775\pi$
$773$	40171.3	1.86916	0.934581	+	0.355750i	$0.115775\pi$
$774$	0	0
$775$	−24836.8	−1.15118
$776$	13675.8	0.632646
$777$	7566.69	0.349361
$778$	−10295.2	−0.474422
$779$	−2159.53	−0.0993236
$780$	18891.4	0.867205
$781$	−33485.0	−1.53417
$782$	−25615.6	−1.17137
$783$	14155.9	0.646091
$784$	17626.8	0.802972
$785$	10894.2	0.495325
$786$	−4944.14	−0.224366
$787$	22928.4	1.03851	0.519256	−	0.854619i	$-0.326209\pi$
$787$	22928.4	1.03851	0.519256	+	0.854619i	$0.326209\pi$
$788$	11290.3	0.510408
$789$	−13551.3	−0.611455
$790$	−34601.8	−1.55833
$791$	3073.22	0.138143
$792$	13248.6	0.594404
$793$	59131.1	2.64793
$794$	−18115.4	−0.809689
$795$	8211.61	0.366334
$796$	12502.0	0.556687
$797$	−23583.5	−1.04814	−0.524072	−	0.851674i	$-0.675588\pi$
$797$	−23583.5	−1.04814	−0.524072	+	0.851674i	$0.675588\pi$
$798$	−2391.13	−0.106072
$799$	−5659.56	−0.250589
$800$	39925.6	1.76448
$801$	−19356.3	−0.853834
$802$	5028.48	0.221399
$803$	−39734.0	−1.74618
$804$	−932.800	−0.0409171
$805$	25180.7	1.10249
$806$	37657.4	1.64569
$807$	12523.7	0.546290
$808$	3319.81	0.144543
$809$	12806.6	0.556560	0.278280	−	0.960500i	$-0.410236\pi$
$809$	12806.6	0.556560	0.278280	+	0.960500i	$0.410236\pi$
$810$	17558.1	0.761641
$811$	7841.91	0.339540	0.169770	−	0.985484i	$-0.445698\pi$
$811$	7841.91	0.339540	0.169770	+	0.985484i	$0.445698\pi$
$812$	6635.82	0.286788
$813$	−6551.37	−0.282616
$814$	−60945.8	−2.62426
$815$	44841.9	1.92729
$816$	−10792.7	−0.463014
$817$	0	0
$818$	1454.61	0.0621750
$819$	−18994.9	−0.810422
$820$	−8092.66	−0.344644
$821$	29489.6	1.25358	0.626792	−	0.779186i	$-0.284367\pi$
$821$	29489.6	1.25358	0.626792	+	0.779186i	$0.284367\pi$
$822$	16843.1	0.714683
$823$	46394.4	1.96501	0.982507	−	0.186225i	$-0.0596253\pi$
$823$	46394.4	1.96501	0.982507	+	0.186225i	$0.0596253\pi$
$824$	15121.1	0.639282
$825$	29668.2	1.25202
$826$	21306.5	0.897517
$827$	−10323.6	−0.434082	−0.217041	−	0.976163i	$-0.569641\pi$
$827$	−10323.6	−0.434082	−0.217041	+	0.976163i	$0.569641\pi$
$828$	13594.2	0.570568
$829$	2230.44	0.0934454	0.0467227	−	0.998908i	$-0.485122\pi$
$829$	2230.44	0.0934454	0.0467227	+	0.998908i	$0.485122\pi$
$830$	−47628.6	−1.99182
$831$	−4265.29	−0.178052
$832$	−7993.87	−0.333098
$833$	12363.6	0.514254
$834$	15824.8	0.657036
$835$	48820.6	2.02336
$836$	7486.02	0.309700
$837$	−14810.6	−0.611626
$838$	16664.7	0.686961
$839$	−883.921	−0.0363723	−0.0181861	−	0.999835i	$-0.505789\pi$
$839$	−883.921	−0.0363723	−0.0181861	+	0.999835i	$0.505789\pi$
$840$	5131.79	0.210790
$841$	−10131.7	−0.415422
$842$	19518.6	0.798876
$843$	20829.2	0.851005
$844$	774.439	0.0315845
$845$	−85405.8	−3.47698
$846$	7727.19	0.314026
$847$	25117.5	1.01895
$848$	−14521.6	−0.588061
$849$	18512.6	0.748352
$850$	39761.0	1.60446
$851$	35814.6	1.44267
$852$	−7002.23	−0.281564
$853$	15341.3	0.615797	0.307899	−	0.951419i	$-0.400374\pi$
$853$	15341.3	0.615797	0.307899	+	0.951419i	$0.400374\pi$
$854$	−28047.1	−1.12383
$855$	−9171.16	−0.366839
$856$	−7582.30	−0.302754
$857$	−27250.3	−1.08618	−0.543088	−	0.839676i	$-0.682745\pi$
$857$	−27250.3	−1.08618	−0.543088	+	0.839676i	$0.682745\pi$
$858$	−44982.8	−1.78985
$859$	6254.63	0.248435	0.124217	−	0.992255i	$-0.460358\pi$
$859$	6254.63	0.248435	0.124217	+	0.992255i	$0.460358\pi$
$860$	0	0
$861$	−2392.41	−0.0946959
$862$	3380.94	0.133591
$863$	34856.0	1.37487	0.687434	−	0.726247i	$-0.258737\pi$
$863$	34856.0	1.37487	0.687434	+	0.726247i	$0.258737\pi$
$864$	23808.4	0.937474
$865$	−20435.3	−0.803263
$866$	23560.5	0.924502
$867$	4598.62	0.180136
$868$	−6942.76	−0.271489
$869$	32025.2	1.25015
$870$	−19252.1	−0.750237
$871$	6169.18	0.239994
$872$	11485.6	0.446047
$873$	−27076.1	−1.04970
$874$	−11317.7	−0.438017
$875$	−14511.0	−0.560643
$876$	−8308.97	−0.320473
$877$	6804.93	0.262014	0.131007	−	0.991381i	$-0.458179\pi$
$877$	6804.93	0.262014	0.131007	+	0.991381i	$0.458179\pi$
$878$	15057.2	0.578766
$879$	−7011.28	−0.269038
$880$	−85453.6	−3.27346
$881$	−47274.9	−1.80787	−0.903935	−	0.427670i	$-0.859334\pi$
$881$	−47274.9	−1.80787	−0.903935	+	0.427670i	$0.859334\pi$
$882$	−16880.5	−0.644438
$883$	−31363.8	−1.19533	−0.597665	−	0.801746i	$-0.703905\pi$
$883$	−31363.8	−1.19533	−0.597665	+	0.801746i	$0.703905\pi$
$884$	−23432.7	−0.891545
$885$	−24027.3	−0.912620
$886$	19928.0	0.755638
$887$	−27624.7	−1.04571	−0.522856	−	0.852421i	$-0.675134\pi$
$887$	−27624.7	−1.04571	−0.522856	+	0.852421i	$0.675134\pi$
$888$	7298.99	0.275831
$889$	−7507.76	−0.283242
$890$	60389.3	2.27444
$891$	−16250.6	−0.611018
$892$	−21730.9	−0.815700
$893$	−2500.55	−0.0937041
$894$	11048.6	0.413333
$895$	54084.0	2.01992
$896$	−13760.7	−0.513073
$897$	26434.0	0.983953
$898$	40161.0	1.49242
$899$	−14916.7	−0.553394
$900$	−21101.1	−0.781523
$901$	−10185.6	−0.376617
$902$	19269.7	0.711319
$903$	0	0
$904$	2964.49	0.109068
$905$	−24845.3	−0.912581
$906$	10104.6	0.370533
$907$	−30861.9	−1.12983	−0.564914	−	0.825150i	$-0.691091\pi$
$907$	−30861.9	−1.12983	−0.564914	+	0.825150i	$0.691091\pi$
$908$	10920.4	0.399124
$909$	−6572.74	−0.239828
$910$	59261.8	2.15880
$911$	−4012.75	−0.145937	−0.0729684	−	0.997334i	$-0.523247\pi$
$911$	−4012.75	−0.145937	−0.0729684	+	0.997334i	$0.523247\pi$
$912$	−4768.51	−0.173137
$913$	44081.9	1.59792
$914$	42100.8	1.52360
$915$	31628.7	1.14274
$916$	25951.7	0.936100
$917$	−6028.53	−0.217099
$918$	23710.2	0.852456
$919$	−20261.8	−0.727285	−0.363643	−	0.931539i	$-0.618467\pi$
$919$	−20261.8	−0.727285	−0.363643	+	0.931539i	$0.618467\pi$
$920$	24289.8	0.870446
$921$	−2610.63	−0.0934020
$922$	−13643.0	−0.487318
$923$	46310.0	1.65148
$924$	8293.32	0.295271
$925$	−55592.1	−1.97606
$926$	42261.2	1.49977
$927$	−29937.5	−1.06071
$928$	23978.9	0.848218
$929$	10715.5	0.378432	0.189216	−	0.981935i	$-0.439405\pi$
$929$	10715.5	0.378432	0.189216	+	0.981935i	$0.439405\pi$
$930$	20142.6	0.710216
$931$	5462.59	0.192298
$932$	−26065.2	−0.916088
$933$	−23891.8	−0.838351
$934$	−7547.90	−0.264427
$935$	−59937.9	−2.09645
$936$	−18322.9	−0.639853
$937$	−26739.1	−0.932262	−0.466131	−	0.884716i	$-0.654352\pi$
$937$	−26739.1	−0.932262	−0.466131	+	0.884716i	$0.654352\pi$
$938$	−2926.17	−0.101858
$939$	4336.82	0.150721
$940$	−9370.63	−0.325145
$941$	40264.8	1.39489	0.697446	−	0.716637i	$-0.254320\pi$
$941$	40264.8	1.39489	0.697446	+	0.716637i	$0.254320\pi$
$942$	−5424.54	−0.187623
$943$	−11323.8	−0.391042
$944$	42490.6	1.46499
$945$	−23307.6	−0.802325
$946$	0	0
$947$	12014.0	0.412253	0.206126	−	0.978525i	$-0.433914\pi$
$947$	12014.0	0.412253	0.206126	+	0.978525i	$0.433914\pi$
$948$	6696.94	0.229437
$949$	54952.3	1.87969
$950$	17567.5	0.599964
$951$	−1744.86	−0.0594964
$952$	−6365.42	−0.216706
$953$	14553.4	0.494681	0.247341	−	0.968929i	$-0.420443\pi$
$953$	14553.4	0.494681	0.247341	+	0.968929i	$0.420443\pi$
$954$	13906.7	0.471958
$955$	3561.90	0.120691
$956$	−29559.1	−1.00001
$957$	17818.5	0.601869
$958$	−55501.8	−1.87180
$959$	20537.2	0.691535
$960$	−4275.84	−0.143752
$961$	−14184.3	−0.476127
$962$	84288.5	2.82492
$963$	15011.8	0.502336
$964$	14736.4	0.492352
$965$	−13167.4	−0.439246
$966$	−12538.2	−0.417609
$967$	−39923.2	−1.32766	−0.663828	−	0.747885i	$-0.731069\pi$
$967$	−39923.2	−1.32766	−0.663828	+	0.747885i	$0.731069\pi$
$968$	24228.9	0.804490
$969$	−3344.67	−0.110884
$970$	84474.2	2.79619
$971$	−12312.2	−0.406919	−0.203460	−	0.979083i	$-0.565219\pi$
$971$	−12312.2	−0.406919	−0.203460	+	0.979083i	$0.565219\pi$
$972$	−19680.9	−0.649448
$973$	19295.6	0.635754
$974$	3786.68	0.124572
$975$	−41031.3	−1.34775
$976$	−55933.0	−1.83440
$977$	−11000.6	−0.360225	−0.180112	−	0.983646i	$-0.557646\pi$
$977$	−11000.6	−0.360225	−0.180112	+	0.983646i	$0.557646\pi$
$978$	−22328.1	−0.730036
$979$	−55892.4	−1.82465
$980$	20470.6	0.667256
$981$	−22739.9	−0.740090
$982$	27932.1	0.907687
$983$	44584.6	1.44662	0.723310	−	0.690524i	$-0.242620\pi$
$983$	44584.6	1.44662	0.723310	+	0.690524i	$0.242620\pi$
$984$	−2307.77	−0.0747653
$985$	−39940.2	−1.29198
$986$	23880.1	0.771295
$987$	−2770.21	−0.0893383
$988$	−10353.2	−0.333380
$989$	0	0
$990$	81835.2	2.62716
$991$	52956.1	1.69748	0.848742	−	0.528808i	$-0.177361\pi$
$991$	52956.1	1.69748	0.848742	+	0.528808i	$0.177361\pi$
$992$	−25088.1	−0.802971
$993$	14347.2	0.458503
$994$	−21965.8	−0.700919
$995$	−44226.6	−1.40912
$996$	9218.19	0.293262
$997$	−26517.6	−0.842347	−0.421174	−	0.906980i	$-0.638382\pi$
$997$	−26517.6	−0.842347	−0.421174	+	0.906980i	$0.638382\pi$
$998$	−64464.6	−2.04468
$999$	−33150.6	−1.04989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.11	yes	50
43.42	odd	2		1849.4.a.i.1.40	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.40	✓	50	43.42	odd	2
1849.4.a.j.1.11	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)

\(f(q)\)	\(=\)	\(q-3.61756 q^{2} -2.47684 q^{3} +5.08677 q^{4} -17.9947 q^{5} +8.96012 q^{6} +10.9253 q^{7} +10.5388 q^{8} -20.8653 q^{9} +O(q^{10})\)	\(q-3.61756 q^{2} -2.47684 q^{3} +5.08677 q^{4} -17.9947 q^{5} +8.96012 q^{6} +10.9253 q^{7} +10.5388 q^{8} -20.8653 q^{9} +65.0971 q^{10} -60.2496 q^{11} -12.5991 q^{12} +83.3256 q^{13} -39.5231 q^{14} +44.5701 q^{15} -78.8189 q^{16} -55.2843 q^{17} +75.4815 q^{18} -24.4261 q^{19} -91.5351 q^{20} -27.0603 q^{21} +217.957 q^{22} -128.082 q^{23} -26.1029 q^{24} +198.811 q^{25} -301.436 q^{26} +118.555 q^{27} +55.5746 q^{28} +119.404 q^{29} -161.235 q^{30} -124.927 q^{31} +200.822 q^{32} +149.229 q^{33} +199.994 q^{34} -196.598 q^{35} -106.137 q^{36} -279.623 q^{37} +88.3631 q^{38} -206.384 q^{39} -189.643 q^{40} +88.4105 q^{41} +97.8923 q^{42} -306.476 q^{44} +375.465 q^{45} +463.344 q^{46} +102.372 q^{47} +195.222 q^{48} -223.637 q^{49} -719.210 q^{50} +136.930 q^{51} +423.858 q^{52} +184.241 q^{53} -428.879 q^{54} +1084.18 q^{55} +115.140 q^{56} +60.4996 q^{57} -431.951 q^{58} -539.091 q^{59} +226.718 q^{60} +709.639 q^{61} +451.931 q^{62} -227.960 q^{63} -95.9353 q^{64} -1499.42 q^{65} -539.844 q^{66} +74.0370 q^{67} -281.218 q^{68} +317.238 q^{69} +711.207 q^{70} +555.772 q^{71} -219.895 q^{72} +659.489 q^{73} +1011.56 q^{74} -492.422 q^{75} -124.250 q^{76} -658.247 q^{77} +746.607 q^{78} -531.541 q^{79} +1418.33 q^{80} +269.722 q^{81} -319.831 q^{82} -731.654 q^{83} -137.649 q^{84} +994.826 q^{85} -295.744 q^{87} -634.959 q^{88} +927.680 q^{89} -1358.27 q^{90} +910.360 q^{91} -651.522 q^{92} +309.424 q^{93} -370.337 q^{94} +439.542 q^{95} -497.404 q^{96} +1297.66 q^{97} +809.022 q^{98} +1257.12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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