LMFDB - Embedded newform 1849.4.a.i.1.40

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			1.40
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	$-0.279141\pi$
$2$	3.61756	1.27900	0.639501	+	0.768790i	$0.279141\pi$
$3$	2.47684	0.476668	0.238334	−	0.971183i	$-0.423399\pi$
$3$	2.47684	0.476668	0.238334	+	0.971183i	$0.423399\pi$
$4$	5.08677	0.635846
$5$	17.9947	1.60950	0.804749	−	0.593615i	$-0.202300\pi$
$5$	17.9947	1.60950	0.804749	+	0.593615i	$0.202300\pi$
$6$	8.96012	0.609659
$7$	−10.9253	−0.589912	−0.294956	−	0.955511i	$-0.595305\pi$
$7$	−10.9253	−0.589912	−0.294956	+	0.955511i	$0.595305\pi$
$8$	−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	$-0.452888\pi$
$19$	24.4261	0.294934	0.147467	+	0.989067i	$0.452888\pi$
$20$	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	$-0.624864\pi$
$29$	−119.404	−0.764577	−0.382288	+	0.924043i	$0.624864\pi$
$30$	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	$-0.286640\pi$
$37$	279.623	1.24243	0.621214	+	0.783641i	$0.286640\pi$
$38$	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	$-0.767433\pi$
$61$	−709.639	−1.48951	−0.744754	+	0.667339i	$0.767433\pi$
$62$	−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	$-0.653763\pi$
$71$	−555.772	−0.928986	−0.464493	+	0.885577i	$0.653763\pi$
$72$	219.895	0.359929
$73$	−659.489	−1.05736	−0.528681	−	0.848821i	$-0.677313\pi$
$73$	−659.489	−1.05736	−0.528681	+	0.848821i	$0.677313\pi$
$74$	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	$-0.686302\pi$
$89$	−927.680	−1.10488	−0.552438	+	0.833554i	$0.686302\pi$
$90$	−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	$-0.537356\pi$
$113$	−281.293	−0.234176	−0.117088	+	0.993122i	$0.537356\pi$
$114$	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	$-0.441092\pi$
$131$	551.794	0.368019	0.184009	+	0.982924i	$0.441092\pi$
$132$	−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	$-0.699351\pi$
$137$	−1879.78	−1.17227	−0.586134	+	0.810214i	$0.699351\pi$
$138$	−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	$-0.610084\pi$
$149$	−1233.08	−0.677974	−0.338987	+	0.940791i	$0.610084\pi$
$150$	1781.37	0.969653
$151$	−1127.73	−0.607771	−0.303885	−	0.952709i	$-0.598284\pi$
$151$	−1127.73	−0.607771	−0.303885	+	0.952709i	$0.598284\pi$
$152$	−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	$-0.450824\pi$
$157$	605.410	0.307751	0.153876	+	0.988090i	$0.450824\pi$
$158$	−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	$-0.295674\pi$
$163$	2491.95	1.19745	0.598725	+	0.800955i	$0.295674\pi$
$164$	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	$-0.284078\pi$
$179$	3005.54	1.25500	0.627500	+	0.778617i	$0.284078\pi$
$180$	−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	$-0.488063\pi$
$191$	197.941	0.0749870	0.0374935	+	0.999297i	$0.488063\pi$
$192$	−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	$-0.644225\pi$
$199$	−2457.75	−0.875505	−0.437753	+	0.899095i	$0.644225\pi$
$200$	−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	$-0.507907\pi$
$211$	−152.246	−0.0496731	−0.0248366	+	0.999692i	$0.507907\pi$
$212$	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	$-0.278342\pi$
$223$	4272.05	1.28286	0.641429	+	0.767182i	$0.278342\pi$
$224$	2194.05	0.654446
$225$	−4148.24	−1.22911
$226$	−1017.60	−0.299511
$227$	−2146.82	−0.627706	−0.313853	−	0.949472i	$-0.601620\pi$
$227$	−2146.82	−0.627706	−0.313853	+	0.949472i	$0.601620\pi$
$228$	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	$-0.243972\pi$
$233$	5124.12	1.44074	0.720369	+	0.693591i	$0.243972\pi$
$234$	−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	$-0.626545\pi$
$241$	−2897.00	−0.774325	−0.387163	+	0.922011i	$0.626545\pi$
$242$	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	$-0.563633\pi$
$257$	−1636.32	−0.397162	−0.198581	+	0.980084i	$0.563633\pi$
$258$	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	$-0.721640\pi$
$263$	−5471.20	−1.28277	−0.641385	+	0.767219i	$0.721640\pi$
$264$	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	$-0.559801\pi$
$277$	−1722.07	−0.373535	−0.186768	+	0.982404i	$0.559801\pi$
$278$	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	$-0.449464\pi$
$313$	1750.95	0.316197	0.158098	+	0.987423i	$0.449464\pi$
$314$	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	$-0.340293\pi$
$331$	5792.53	0.961892	0.480946	+	0.876750i	$0.340293\pi$
$332$	−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	$-0.704015\pi$
$347$	−7730.08	−1.19589	−0.597943	+	0.801538i	$0.704015\pi$
$348$	−1504.38	−0.231734
$349$	406.164	0.0622965	0.0311482	−	0.999515i	$-0.490084\pi$
$349$	406.164	0.0622965	0.0311482	+	0.999515i	$0.490084\pi$
$350$	−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	$-0.312596\pi$
$373$	8000.84	1.11064	0.555319	+	0.831637i	$0.312596\pi$
$374$	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	$-0.819788\pi$
$383$	−12651.9	−1.68794	−0.843972	+	0.536388i	$0.819788\pi$
$384$	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	$-0.559379\pi$
$389$	−2845.89	−0.370931	−0.185466	+	0.982651i	$0.559379\pi$
$390$	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	$-0.492262\pi$
$409$	402.096	0.0486121	0.0243060	+	0.999705i	$0.492262\pi$
$410$	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	$-0.413454\pi$
$419$	4606.62	0.537107	0.268554	+	0.963265i	$0.413454\pi$
$420$	−2476.96	−0.287770
$421$	5395.50	0.624609	0.312305	−	0.949982i	$-0.398899\pi$
$421$	5395.50	0.624609	0.312305	+	0.949982i	$0.398899\pi$
$422$	−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	$-0.382294\pi$
$433$	6512.81	0.722831	0.361415	+	0.932405i	$0.382294\pi$
$434$	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	$-0.301710\pi$
$449$	11101.7	1.16686	0.583430	+	0.812163i	$0.301710\pi$
$450$	−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	$-0.296906\pi$
$457$	11637.9	1.19124	0.595621	+	0.803265i	$0.296906\pi$
$458$	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	$-0.300582\pi$
$463$	11682.2	1.17261	0.586306	+	0.810090i	$0.300582\pi$
$464$	9411.28	0.941611
$465$	−5568.00	−0.555289
$466$	18536.8	1.84271
$467$	−2086.46	−0.206745	−0.103372	−	0.994643i	$-0.532963\pi$
$467$	−2086.46	−0.206745	−0.103372	+	0.994643i	$0.532963\pi$
$468$	−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	$-0.384535\pi$
$491$	7721.24	0.709684	0.354842	+	0.934926i	$0.384535\pi$
$492$	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	$-0.794810\pi$
$499$	−17819.9	−1.59865	−0.799326	+	0.600897i	$0.794810\pi$
$500$	6756.25	0.604298
$501$	−6719.79	−0.599238
$502$	21532.1	1.91439
$503$	10784.0	0.955938	0.477969	−	0.878377i	$-0.341373\pi$
$503$	10784.0	0.955938	0.477969	+	0.878377i	$0.341373\pi$
$504$	−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	$-0.462910\pi$
$521$	2765.08	0.232515	0.116257	+	0.993219i	$0.462910\pi$
$522$	9012.77	0.755706
$523$	−2271.48	−0.189914	−0.0949568	−	0.995481i	$-0.530271\pi$
$523$	−2271.48	−0.189914	−0.0949568	+	0.995481i	$0.530271\pi$
$524$	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	$-0.693069\pi$
$571$	−15555.5	−1.14006	−0.570032	+	0.821622i	$0.693069\pi$
$572$	−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	$-0.438225\pi$
$577$	5345.98	0.385713	0.192856	+	0.981227i	$0.438225\pi$
$578$	−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	$-0.519535\pi$
$587$	−1744.52	−0.122665	−0.0613324	+	0.998117i	$0.519535\pi$
$588$	−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	$-0.395623\pi$
$593$	9301.56	0.644130	0.322065	+	0.946718i	$0.395623\pi$
$594$	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	$-0.766840\pi$
$601$	−21909.3	−1.48702	−0.743509	+	0.668725i	$0.766840\pi$
$602$	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	$-0.510388\pi$
$607$	−975.955	−0.0652599	−0.0326300	+	0.999468i	$0.510388\pi$
$608$	−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	$-0.473095\pi$
$631$	2676.32	0.168847	0.0844235	+	0.996430i	$0.473095\pi$
$632$	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	$-0.274112\pi$
$641$	21148.3	1.30313	0.651566	+	0.758592i	$0.274112\pi$
$642$	−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	$-0.973877\pi$
$647$	−32803.7	−1.99327	−0.996634	+	0.0819754i	$0.973877\pi$
$648$	−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	$-0.582763\pi$
$653$	−8579.88	−0.514176	−0.257088	+	0.966388i	$0.582763\pi$
$654$	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	$-0.761478\pi$
$673$	−25565.1	−1.46428	−0.732140	+	0.681154i	$0.761478\pi$
$674$	−21231.8	−1.21338
$675$	−23569.9	−1.34401
$676$	24142.6	1.37361
$677$	103.167	0.00585674	0.00292837	−	0.999996i	$-0.499068\pi$
$677$	103.167	0.00585674	0.00292837	+	0.999996i	$0.499068\pi$
$678$	−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	$-0.500229\pi$
$691$	−26.0919	−0.00143644	−0.000718222		1.00000i	$0.500229\pi$
$692$	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	$-0.553518\pi$
$727$	−6560.47	−0.334683	−0.167342	+	0.985899i	$0.553518\pi$
$728$	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	$-0.462699\pi$
$733$	4640.51	0.233835	0.116918	+	0.993142i	$0.462699\pi$
$734$	−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	$-0.281524\pi$
$739$	25462.4	1.26745	0.633727	+	0.773557i	$0.281524\pi$
$740$	25595.3	1.27149
$741$	5041.16	0.249921
$742$	−7281.75	−0.360272
$743$	31591.6	1.55987	0.779935	−	0.625861i	$-0.215252\pi$
$743$	31591.6	1.55987	0.779935	+	0.625861i	$0.215252\pi$
$744$	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	$-0.588134\pi$
$751$	−11251.7	−0.546712	−0.273356	+	0.961913i	$0.588134\pi$
$752$	−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	$-0.766493\pi$
$757$	−30940.9	−1.48556	−0.742779	+	0.669536i	$0.766493\pi$
$758$	−39232.0	−1.87991
$759$	19113.4	0.914063
$760$	−4632.24	−0.221091
$761$	−9097.60	−0.433361	−0.216681	−	0.976243i	$-0.569523\pi$
$761$	−9097.60	−0.433361	−0.216681	+	0.976243i	$0.569523\pi$
$762$	−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	$-0.884225\pi$
$773$	−40171.3	−1.86916	−0.934581	+	0.355750i	$0.884225\pi$
$774$	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	$-0.554302\pi$
$811$	−7841.91	−0.339540	−0.169770	+	0.985484i	$0.554302\pi$
$812$	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	$-0.514878\pi$
$829$	−2230.44	−0.0934454	−0.0467227	+	0.998908i	$0.514878\pi$
$830$	−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	$-0.494211\pi$
$839$	883.921	0.0363723	0.0181861	+	0.999835i	$0.494211\pi$
$840$	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	$-0.539642\pi$
$859$	−6254.63	−0.248435	−0.124217	+	0.992255i	$0.539642\pi$
$860$	0	0
$861$	−2392.41	−0.0946959
$862$	−3380.94	−0.133591
$863$	−34856.0	−1.37487	−0.687434	−	0.726247i	$-0.741263\pi$
$863$	−34856.0	−1.37487	−0.687434	+	0.726247i	$0.741263\pi$
$864$	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	$-0.324866\pi$
$887$	27624.7	1.04571	0.522856	+	0.852421i	$0.324866\pi$
$888$	−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	$-0.476753\pi$
$911$	4012.75	0.145937	0.0729684	+	0.997334i	$0.476753\pi$
$912$	−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	$-0.560595\pi$
$929$	−10715.5	−0.378432	−0.189216	+	0.981935i	$0.560595\pi$
$930$	−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	$-0.345648\pi$
$937$	26739.1	0.932262	0.466131	+	0.884716i	$0.345648\pi$
$938$	−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	$-0.579557\pi$
$953$	−14553.4	−0.494681	−0.247341	+	0.968929i	$0.579557\pi$
$954$	−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	$-0.757380\pi$
$983$	−44584.6	−1.44662	−0.723310	+	0.690524i	$0.757380\pi$
$984$	−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	$-0.822639\pi$
$991$	−52956.1	−1.69748	−0.848742	+	0.528808i	$0.822639\pi$
$992$	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	$-0.361618\pi$
$997$	26517.6	0.842347	0.421174	+	0.906980i	$0.361618\pi$
$998$	−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.i.1.40	✓	50
43.42	odd	2		1849.4.a.j.1.11	yes	50

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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