LMFDB - Embedded newform 1849.4.a.i.1.8

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			1.8
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)

$f(q)$	$=$	$q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +O(q^{10})$	\(q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +58.9799 q^{10} -55.2516 q^{11} -21.7771 q^{12} -37.7658 q^{13} -19.5627 q^{14} +22.8493 q^{15} -8.85170 q^{16} -24.9093 q^{17} +108.189 q^{18} +39.7201 q^{19} -162.241 q^{20} -7.57876 q^{21} +249.765 q^{22} -2.55110 q^{23} +35.1100 q^{24} +45.2293 q^{25} +170.720 q^{26} +89.1980 q^{27} +53.8129 q^{28} -238.086 q^{29} -103.290 q^{30} +263.063 q^{31} +200.400 q^{32} +96.7611 q^{33} +112.603 q^{34} -56.4624 q^{35} -297.606 q^{36} +353.428 q^{37} -179.555 q^{38} +66.1386 q^{39} +261.573 q^{40} +254.188 q^{41} +34.2598 q^{42} -687.051 q^{44} +312.259 q^{45} +11.5323 q^{46} -386.866 q^{47} +15.5018 q^{48} -324.272 q^{49} -204.459 q^{50} +43.6232 q^{51} -469.616 q^{52} -35.7551 q^{53} -403.220 q^{54} +720.878 q^{55} -86.7595 q^{56} -69.5611 q^{57} +1076.27 q^{58} -87.4154 q^{59} +284.130 q^{60} +890.643 q^{61} -1189.18 q^{62} -103.571 q^{63} -835.093 q^{64} +492.738 q^{65} -437.409 q^{66} -998.120 q^{67} -309.746 q^{68} +4.46769 q^{69} +255.238 q^{70} +443.994 q^{71} +479.813 q^{72} -70.5226 q^{73} -1597.67 q^{74} -79.2092 q^{75} +493.917 q^{76} -239.104 q^{77} -298.980 q^{78} +975.256 q^{79} +115.490 q^{80} +489.980 q^{81} -1149.06 q^{82} +836.712 q^{83} -94.2415 q^{84} +324.997 q^{85} +416.956 q^{87} +1107.69 q^{88} -1086.38 q^{89} -1411.57 q^{90} -163.434 q^{91} -31.7228 q^{92} -460.697 q^{93} +1748.83 q^{94} -518.236 q^{95} -350.956 q^{96} -1132.50 q^{97} +1465.87 q^{98} +1322.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.52050	−1.59824	−0.799120	−	0.601172i	$-0.794701\pi$
$2$	−4.52050	−1.59824	−0.799120	+	0.601172i	$0.794701\pi$
$3$	−1.75128	−0.337034	−0.168517	−	0.985699i	$-0.553898\pi$
$3$	−1.75128	−0.337034	−0.168517	+	0.985699i	$0.553898\pi$
$4$	12.4349	1.55437
$5$	−13.0472	−1.16698	−0.583488	−	0.812122i	$-0.698313\pi$
$5$	−13.0472	−1.16698	−0.583488	+	0.812122i	$0.698313\pi$
$6$	7.91667	0.538661
$7$	4.32755	0.233666	0.116833	−	0.993152i	$-0.462726\pi$
$7$	4.32755	0.233666	0.116833	+	0.993152i	$0.462726\pi$
$8$	−20.0482	−0.886013
$9$	−23.9330	−0.886408
$10$	58.9799	1.86511
$11$	−55.2516	−1.51445	−0.757227	−	0.653152i	$-0.773446\pi$
$11$	−55.2516	−1.51445	−0.757227	+	0.653152i	$0.773446\pi$
$12$	−21.7771	−0.523875
$13$	−37.7658	−0.805719	−0.402860	−	0.915262i	$-0.631984\pi$
$13$	−37.7658	−0.805719	−0.402860	+	0.915262i	$0.631984\pi$
$14$	−19.5627	−0.373454
$15$	22.8493	0.393311
$16$	−8.85170	−0.138308
$17$	−24.9093	−0.355376	−0.177688	−	0.984087i	$-0.556862\pi$
$17$	−24.9093	−0.355376	−0.177688	+	0.984087i	$0.556862\pi$
$18$	108.189	1.41669
$19$	39.7201	0.479601	0.239800	−	0.970822i	$-0.422918\pi$
$19$	39.7201	0.479601	0.239800	+	0.970822i	$0.422918\pi$
$20$	−162.241	−1.81391
$21$	−7.57876	−0.0787534
$22$	249.765	2.42046
$23$	−2.55110	−0.0231279	−0.0115639	−	0.999933i	$-0.503681\pi$
$23$	−2.55110	−0.0231279	−0.0115639	+	0.999933i	$0.503681\pi$
$24$	35.1100	0.298617
$25$	45.2293	0.361834
$26$	170.720	1.28773
$27$	89.1980	0.635784
$28$	53.8129	0.363203
$29$	−238.086	−1.52454	−0.762268	−	0.647262i	$-0.775914\pi$
$29$	−238.086	−1.52454	−0.762268	+	0.647262i	$0.775914\pi$
$30$	−103.290	−0.628605
$31$	263.063	1.52411	0.762056	−	0.647512i	$-0.224190\pi$
$31$	263.063	1.52411	0.762056	+	0.647512i	$0.224190\pi$
$32$	200.400	1.10706
$33$	96.7611	0.510423
$34$	112.603	0.567977
$35$	−56.4624	−0.272682
$36$	−297.606	−1.37780
$37$	353.428	1.57036	0.785178	−	0.619270i	$-0.212571\pi$
$37$	353.428	1.57036	0.785178	+	0.619270i	$0.212571\pi$
$38$	−179.555	−0.766517
$39$	66.1386	0.271555
$40$	261.573	1.03396
$41$	254.188	0.968233	0.484117	−	0.875004i	$-0.339141\pi$
$41$	254.188	0.968233	0.484117	+	0.875004i	$0.339141\pi$
$42$	34.2598	0.125867
$43$	0	0
$43$	0	0
$44$	−687.051	−2.35402
$45$	312.259	1.03442
$46$	11.5323	0.0369639
$47$	−386.866	−1.20064	−0.600321	−	0.799759i	$-0.704961\pi$
$47$	−386.866	−1.20064	−0.600321	+	0.799759i	$0.704961\pi$
$48$	15.5018	0.0466145
$49$	−324.272	−0.945400
$50$	−204.459	−0.578297
$51$	43.6232	0.119774
$52$	−469.616	−1.25238
$53$	−35.7551	−0.0926668	−0.0463334	−	0.998926i	$-0.514754\pi$
$53$	−35.7551	−0.0926668	−0.0463334	+	0.998926i	$0.514754\pi$
$54$	−403.220	−1.01614
$55$	720.878	1.76733
$56$	−86.7595	−0.207031
$57$	−69.5611	−0.161642
$58$	1076.27	2.43657
$59$	−87.4154	−0.192890	−0.0964451	−	0.995338i	$-0.530747\pi$
$59$	−87.4154	−0.192890	−0.0964451	+	0.995338i	$0.530747\pi$
$60$	284.130	0.611350
$61$	890.643	1.86943	0.934714	−	0.355400i	$-0.115655\pi$
$61$	890.643	1.86943	0.934714	+	0.355400i	$0.115655\pi$
$62$	−1189.18	−2.43589
$63$	−103.571	−0.207123
$64$	−835.093	−1.63104
$65$	492.738	0.940256
$66$	−437.409	−0.815777
$67$	−998.120	−1.82000	−0.909998	−	0.414612i	$-0.863917\pi$
$67$	−998.120	−1.82000	−0.909998	+	0.414612i	$0.863917\pi$
$68$	−309.746	−0.552386
$69$	4.46769	0.00779489
$70$	255.238	0.435812
$71$	443.994	0.742146	0.371073	−	0.928604i	$-0.378990\pi$
$71$	443.994	0.742146	0.371073	+	0.928604i	$0.378990\pi$
$72$	479.813	0.785369
$73$	−70.5226	−0.113069	−0.0565346	−	0.998401i	$-0.518005\pi$
$73$	−70.5226	−0.113069	−0.0565346	+	0.998401i	$0.518005\pi$
$74$	−1597.67	−2.50980
$75$	−79.2092	−0.121951
$76$	493.917	0.745476
$77$	−239.104	−0.353876
$78$	−298.980	−0.434010
$79$	975.256	1.38892	0.694461	−	0.719530i	$-0.255643\pi$
$79$	975.256	1.38892	0.694461	+	0.719530i	$0.255643\pi$
$80$	115.490	0.161402
$81$	489.980	0.672127
$82$	−1149.06	−1.54747
$83$	836.712	1.10652	0.553260	−	0.833009i	$-0.313384\pi$
$83$	836.712	1.10652	0.553260	+	0.833009i	$0.313384\pi$
$84$	−94.2415	−0.122412
$85$	324.997	0.414716
$86$	0	0
$87$	416.956	0.513821
$88$	1107.69	1.34182
$89$	−1086.38	−1.29389	−0.646944	−	0.762537i	$-0.723953\pi$
$89$	−1086.38	−1.29389	−0.646944	+	0.762537i	$0.723953\pi$
$90$	−1411.57	−1.65325
$91$	−163.434	−0.188269
$92$	−31.7228	−0.0359492
$93$	−460.697	−0.513678
$94$	1748.83	1.91891
$95$	−518.236	−0.559683
$96$	−350.956	−0.373118
$97$	−1132.50	−1.18544	−0.592720	−	0.805408i	$-0.701946\pi$
$97$	−1132.50	−1.18544	−0.592720	+	0.805408i	$0.701946\pi$
$98$	1465.87	1.51098
$99$	1322.34	1.34242
$100$	562.423	0.562423
$101$	1437.96	1.41665	0.708326	−	0.705885i	$-0.249450\pi$
$101$	1437.96	1.41665	0.708326	+	0.705885i	$0.249450\pi$
$102$	−197.199	−0.191428
$103$	1763.53	1.68704	0.843521	−	0.537096i	$-0.180479\pi$
$103$	1763.53	1.68704	0.843521	+	0.537096i	$0.180479\pi$
$104$	757.136	0.713878
$105$	98.8816	0.0919033
$106$	161.631	0.148104
$107$	166.103	0.150073	0.0750365	−	0.997181i	$-0.476093\pi$
$107$	166.103	0.150073	0.0750365	+	0.997181i	$0.476093\pi$
$108$	1109.17	0.988243
$109$	−441.796	−0.388224	−0.194112	−	0.980979i	$-0.562182\pi$
$109$	−441.796	−0.388224	−0.194112	+	0.980979i	$0.562182\pi$
$110$	−3258.73	−2.82462
$111$	−618.951	−0.529264
$112$	−38.3062	−0.0323178
$113$	−971.442	−0.808722	−0.404361	−	0.914599i	$-0.632506\pi$
$113$	−971.442	−0.808722	−0.404361	+	0.914599i	$0.632506\pi$
$114$	314.451	0.258342
$115$	33.2847	0.0269897
$116$	−2960.59	−2.36969
$117$	903.850	0.714196
$118$	395.162	0.308285
$119$	−107.796	−0.0830393
$120$	−458.087	−0.348479
$121$	1721.74	1.29357
$122$	−4026.15	−2.98779
$123$	−445.155	−0.326328
$124$	3271.17	2.36903
$125$	1040.78	0.744725
$126$	468.195	0.331032
$127$	−1595.77	−1.11498	−0.557489	−	0.830185i	$-0.688235\pi$
$127$	−1595.77	−1.11498	−0.557489	+	0.830185i	$0.688235\pi$
$128$	2171.84	1.49973
$129$	0	0
$130$	−2227.42	−1.50275
$131$	55.8044	0.0372187	0.0186094	−	0.999827i	$-0.494076\pi$
$131$	55.8044	0.0372187	0.0186094	+	0.999827i	$0.494076\pi$
$132$	1203.22	0.793385
$133$	171.891	0.112066
$134$	4512.00	2.90879
$135$	−1163.78	−0.741945
$136$	499.387	0.314868
$137$	137.795	0.0859316	0.0429658	−	0.999077i	$-0.486319\pi$
$137$	137.795	0.0859316	0.0429658	+	0.999077i	$0.486319\pi$
$138$	−20.1962	−0.0124581
$139$	1016.38	0.620206	0.310103	−	0.950703i	$-0.399637\pi$
$139$	1016.38	0.620206	0.310103	+	0.950703i	$0.399637\pi$
$140$	−702.107	−0.423849
$141$	677.511	0.404658
$142$	−2007.08	−1.18613
$143$	2086.62	1.22022
$144$	211.848	0.122597
$145$	3106.36	1.77910
$146$	318.798	0.180712
$147$	567.892	0.318632
$148$	4394.85	2.44091
$149$	−2725.90	−1.49876	−0.749378	−	0.662142i	$-0.769648\pi$
$149$	−2725.90	−1.49876	−0.749378	+	0.662142i	$0.769648\pi$
$150$	358.065	0.194906
$151$	1350.49	0.727822	0.363911	−	0.931434i	$-0.381441\pi$
$151$	1350.49	0.727822	0.363911	+	0.931434i	$0.381441\pi$
$152$	−796.315	−0.424932
$153$	596.155	0.315008
$154$	1080.87	0.565578
$155$	−3432.23	−1.77860
$156$	822.430	0.422097
$157$	2623.54	1.33364	0.666818	−	0.745220i	$-0.267656\pi$
$157$	2623.54	1.33364	0.666818	+	0.745220i	$0.267656\pi$
$158$	−4408.65	−2.21983
$159$	62.6172	0.0312319
$160$	−2614.65	−1.29192
$161$	−11.0400	−0.00540419
$162$	−2214.96	−1.07422
$163$	407.303	0.195721	0.0978603	−	0.995200i	$-0.468800\pi$
$163$	407.303	0.195721	0.0978603	+	0.995200i	$0.468800\pi$
$164$	3160.82	1.50499
$165$	−1262.46	−0.595651
$166$	−3782.36	−1.76848
$167$	1743.79	0.808015	0.404008	−	0.914756i	$-0.367617\pi$
$167$	1743.79	0.808015	0.404008	+	0.914756i	$0.367617\pi$
$168$	151.940	0.0697765
$169$	−770.743	−0.350816
$170$	−1469.15	−0.662815
$171$	−950.621	−0.425122
$172$	0	0
$173$	1182.29	0.519584	0.259792	−	0.965665i	$-0.416346\pi$
$173$	1182.29	0.519584	0.259792	+	0.965665i	$0.416346\pi$
$174$	−1884.85	−0.821208
$175$	195.732	0.0845483
$176$	489.071	0.209461
$177$	153.089	0.0650106
$178$	4910.99	2.06794
$179$	4505.20	1.88120	0.940600	−	0.339517i	$-0.110263\pi$
$179$	4505.20	1.88120	0.940600	+	0.339517i	$0.110263\pi$
$180$	3882.92	1.60787
$181$	−2610.79	−1.07215	−0.536073	−	0.844172i	$-0.680093\pi$
$181$	−2610.79	−1.07215	−0.536073	+	0.844172i	$0.680093\pi$
$182$	738.802	0.300899
$183$	−1559.77	−0.630061
$184$	51.1449	0.0204916
$185$	−4611.24	−1.83257
$186$	2082.58	0.820980
$187$	1376.28	0.538201
$188$	−4810.66	−1.86624
$189$	386.009	0.148561
$190$	2342.69	0.894507
$191$	2992.98	1.13384	0.566922	−	0.823771i	$-0.308134\pi$
$191$	2992.98	1.13384	0.566922	+	0.823771i	$0.308134\pi$
$192$	1462.48	0.549717
$193$	−842.048	−0.314051	−0.157026	−	0.987595i	$-0.550191\pi$
$193$	−842.048	−0.314051	−0.157026	+	0.987595i	$0.550191\pi$
$194$	5119.46	1.89462
$195$	−862.923	−0.316898
$196$	−4032.31	−1.46950
$197$	1391.04	0.503082	0.251541	−	0.967847i	$-0.419063\pi$
$197$	1391.04	0.503082	0.251541	+	0.967847i	$0.419063\pi$
$198$	−5977.63	−2.14551
$199$	989.587	0.352512	0.176256	−	0.984344i	$-0.443601\pi$
$199$	989.587	0.352512	0.176256	+	0.984344i	$0.443601\pi$
$200$	−906.764	−0.320590
$201$	1747.99	0.613401
$202$	−6500.28	−2.26415
$203$	−1030.33	−0.356232
$204$	542.453	0.186173
$205$	−3316.45	−1.12991
$206$	−7972.02	−2.69630
$207$	61.0555	0.0205007
$208$	334.292	0.111437
$209$	−2194.60	−0.726333
$210$	−446.994	−0.146884
$211$	−943.172	−0.307728	−0.153864	−	0.988092i	$-0.549172\pi$
$211$	−943.172	−0.307728	−0.153864	+	0.988092i	$0.549172\pi$
$212$	−444.612	−0.144038
$213$	−777.558	−0.250129
$214$	−750.871	−0.239853
$215$	0	0
$216$	−1788.26	−0.563313
$217$	1138.42	0.356133
$218$	1997.14	0.620474
$219$	123.505	0.0381082
$220$	8964.08	2.74708
$221$	940.721	0.286334
$222$	2797.97	0.845890
$223$	4371.74	1.31280	0.656398	−	0.754415i	$-0.272079\pi$
$223$	4371.74	1.31280	0.656398	+	0.754415i	$0.272079\pi$
$224$	867.240	0.258682
$225$	−1082.47	−0.320733
$226$	4391.41	1.29253
$227$	−1293.65	−0.378249	−0.189124	−	0.981953i	$-0.560565\pi$
$227$	−1293.65	−0.378249	−0.189124	+	0.981953i	$0.560565\pi$
$228$	−864.988	−0.251251
$229$	2720.83	0.785141	0.392570	−	0.919722i	$-0.371586\pi$
$229$	2720.83	0.785141	0.392570	+	0.919722i	$0.371586\pi$
$230$	−150.464	−0.0431360
$231$	418.739	0.119268
$232$	4773.20	1.35076
$233$	−1824.91	−0.513108	−0.256554	−	0.966530i	$-0.582587\pi$
$233$	−1824.91	−0.513108	−0.256554	+	0.966530i	$0.582587\pi$
$234$	−4085.86	−1.14146
$235$	5047.52	1.40112
$236$	−1087.01	−0.299822
$237$	−1707.95	−0.468114
$238$	487.294	0.132717
$239$	2517.89	0.681460	0.340730	−	0.940161i	$-0.389326\pi$
$239$	2517.89	0.681460	0.340730	+	0.940161i	$0.389326\pi$
$240$	−202.255	−0.0543980
$241$	−2023.30	−0.540797	−0.270398	−	0.962749i	$-0.587155\pi$
$241$	−2023.30	−0.540797	−0.270398	+	0.962749i	$0.587155\pi$
$242$	−7783.13	−2.06743
$243$	−3266.44	−0.862314
$244$	11075.1	2.90578
$245$	4230.84	1.10326
$246$	2012.33	0.521550
$247$	−1500.06	−0.386424
$248$	−5273.93	−1.35038
$249$	−1465.32	−0.372935
$250$	−4704.87	−1.19025
$251$	−2200.46	−0.553355	−0.276677	−	0.960963i	$-0.589233\pi$
$251$	−2200.46	−0.553355	−0.276677	+	0.960963i	$0.589233\pi$
$252$	−1287.90	−0.321946
$253$	140.952	0.0350261
$254$	7213.71	1.78200
$255$	−569.161	−0.139773
$256$	−3137.08	−0.765890
$257$	869.760	0.211106	0.105553	−	0.994414i	$-0.466339\pi$
$257$	869.760	0.211106	0.105553	+	0.994414i	$0.466339\pi$
$258$	0	0
$259$	1529.48	0.366938
$260$	6127.17	1.46150
$261$	5698.12	1.35136
$262$	−252.264	−0.0594844
$263$	−4849.52	−1.13701	−0.568506	−	0.822679i	$-0.692478\pi$
$263$	−4849.52	−1.13701	−0.568506	+	0.822679i	$0.692478\pi$
$264$	−1939.88	−0.452241
$265$	466.503	0.108140
$266$	−777.032	−0.179109
$267$	1902.56	0.436085
$268$	−12411.6	−2.82894
$269$	432.453	0.0980191	0.0490096	−	0.998798i	$-0.484394\pi$
$269$	432.453	0.0980191	0.0490096	+	0.998798i	$0.484394\pi$
$270$	5260.89	1.18581
$271$	861.175	0.193036	0.0965179	−	0.995331i	$-0.469230\pi$
$271$	861.175	0.193036	0.0965179	+	0.995331i	$0.469230\pi$
$272$	220.490	0.0491514
$273$	286.218	0.0634531
$274$	−622.903	−0.137339
$275$	−2498.99	−0.547981
$276$	55.5555	0.0121161
$277$	−2228.63	−0.483412	−0.241706	−	0.970350i	$-0.577707\pi$
$277$	−2228.63	−0.483412	−0.241706	+	0.970350i	$0.577707\pi$
$278$	−4594.57	−0.991237
$279$	−6295.88	−1.35098
$280$	1131.97	0.241600
$281$	−5991.67	−1.27200	−0.636002	−	0.771688i	$-0.719413\pi$
$281$	−5991.67	−1.27200	−0.636002	+	0.771688i	$0.719413\pi$
$282$	−3062.69	−0.646740
$283$	1125.62	0.236434	0.118217	−	0.992988i	$-0.462282\pi$
$283$	1125.62	0.236434	0.118217	+	0.992988i	$0.462282\pi$
$284$	5521.04	1.15357
$285$	907.577	0.188632
$286$	−9432.58	−1.95021
$287$	1100.01	0.226243
$288$	−4796.17	−0.981308
$289$	−4292.53	−0.873708
$290$	−14042.3	−2.84342
$291$	1983.32	0.399534
$292$	−876.945	−0.175751
$293$	6457.05	1.28746	0.643729	−	0.765254i	$-0.277387\pi$
$293$	6457.05	1.28746	0.643729	+	0.765254i	$0.277387\pi$
$294$	−2567.16	−0.509251
$295$	1140.53	0.225098
$296$	−7085.58	−1.39136
$297$	−4928.33	−0.962865
$298$	12322.5	2.39537
$299$	96.3444	0.0186346
$300$	−984.962	−0.189556
$301$	0	0
$302$	−6104.88	−1.16323
$303$	−2518.27	−0.477461
$304$	−351.590	−0.0663325
$305$	−11620.4	−2.18158
$306$	−2694.92	−0.503459
$307$	7900.21	1.46869	0.734347	−	0.678775i	$-0.237489\pi$
$307$	7900.21	1.46869	0.734347	+	0.678775i	$0.237489\pi$
$308$	−2973.25	−0.550053
$309$	−3088.43	−0.568591
$310$	15515.4	2.84263
$311$	3923.50	0.715374	0.357687	−	0.933841i	$-0.383565\pi$
$311$	3923.50	0.715374	0.357687	+	0.933841i	$0.383565\pi$
$312$	−1325.96	−0.240601
$313$	−7259.87	−1.31103	−0.655515	−	0.755182i	$-0.727548\pi$
$313$	−7259.87	−1.31103	−0.655515	+	0.755182i	$0.727548\pi$
$314$	−11859.7	−2.13147
$315$	1351.32	0.241708
$316$	12127.3	2.15890
$317$	−5967.29	−1.05728	−0.528638	−	0.848847i	$-0.677297\pi$
$317$	−5967.29	−1.05728	−0.528638	+	0.848847i	$0.677297\pi$
$318$	−283.061	−0.0499160
$319$	13154.7	2.30884
$320$	10895.6	1.90339
$321$	−290.894	−0.0505798
$322$	49.9064	0.00863719
$323$	−989.401	−0.170439
$324$	6092.88	1.04473
$325$	−1708.12	−0.291537
$326$	−1841.22	−0.312808
$327$	773.709	0.130845
$328$	−5096.01	−0.857867
$329$	−1674.18	−0.280549
$330$	5706.96	0.951993
$331$	7412.74	1.23094	0.615470	−	0.788161i	$-0.288966\pi$
$331$	7412.74	1.23094	0.615470	+	0.788161i	$0.288966\pi$
$332$	10404.5	1.71994
$333$	−8458.59	−1.39198
$334$	−7882.81	−1.29140
$335$	13022.7	2.12389
$336$	67.0849	0.0108922
$337$	12010.9	1.94147	0.970733	−	0.240160i	$-0.0771998\pi$
$337$	12010.9	1.94147	0.970733	+	0.240160i	$0.0771998\pi$
$338$	3484.15	0.560688
$339$	1701.27	0.272567
$340$	4041.32	0.644621
$341$	−14534.6	−2.30819
$342$	4297.29	0.679446
$343$	−2887.66	−0.454574
$344$	0	0
$345$	−58.2909	−0.00909645
$346$	−5344.56	−0.830419
$347$	−2376.88	−0.367716	−0.183858	−	0.982953i	$-0.558859\pi$
$347$	−2376.88	−0.367716	−0.183858	+	0.982953i	$0.558859\pi$
$348$	5184.83	0.798666
$349$	−2443.29	−0.374747	−0.187373	−	0.982289i	$-0.559997\pi$
$349$	−2443.29	−0.374747	−0.187373	+	0.982289i	$0.559997\pi$
$350$	−884.807	−0.135128
$351$	−3368.64	−0.512264
$352$	−11072.4	−1.67659
$353$	−6845.61	−1.03217	−0.516084	−	0.856538i	$-0.672611\pi$
$353$	−6845.61	−1.03217	−0.516084	+	0.856538i	$0.672611\pi$
$354$	−692.039	−0.103902
$355$	−5792.88	−0.866067
$356$	−13509.1	−2.01118
$357$	188.782	0.0279871
$358$	−20365.8	−3.00661
$359$	−8886.04	−1.30637	−0.653185	−	0.757198i	$-0.726568\pi$
$359$	−8886.04	−1.30637	−0.653185	+	0.757198i	$0.726568\pi$
$360$	−6260.22	−0.916507
$361$	−5281.31	−0.769983
$362$	11802.1	1.71354
$363$	−3015.25	−0.435977
$364$	−2032.29	−0.292639
$365$	920.122	0.131949
$366$	7050.93	1.00699
$367$	1772.16	0.252060	0.126030	−	0.992026i	$-0.459776\pi$
$367$	1772.16	0.252060	0.126030	+	0.992026i	$0.459776\pi$
$368$	22.5816	0.00319877
$369$	−6083.49	−0.858249
$370$	20845.1	2.92888
$371$	−154.732	−0.0216531
$372$	−5728.74	−0.798444
$373$	2089.79	0.290095	0.145047	−	0.989425i	$-0.453667\pi$
$373$	2089.79	0.290095	0.145047	+	0.989425i	$0.453667\pi$
$374$	−6221.48	−0.860174
$375$	−1822.71	−0.250998
$376$	7755.96	1.06378
$377$	8991.53	1.22835
$378$	−1744.96	−0.237436
$379$	−12958.0	−1.75622	−0.878108	−	0.478462i	$-0.841194\pi$
$379$	−12958.0	−1.75622	−0.878108	+	0.478462i	$0.841194\pi$
$380$	−6444.23	−0.869953
$381$	2794.65	0.375786
$382$	−13529.8	−1.81215
$383$	−2891.35	−0.385747	−0.192874	−	0.981224i	$-0.561781\pi$
$383$	−2891.35	−0.385747	−0.192874	+	0.981224i	$0.561781\pi$
$384$	−3803.51	−0.505461
$385$	3119.64	0.412965
$386$	3806.48	0.501929
$387$	0	0
$388$	−14082.5	−1.84261
$389$	−8007.52	−1.04370	−0.521848	−	0.853039i	$-0.674757\pi$
$389$	−8007.52	−1.04370	−0.521848	+	0.853039i	$0.674757\pi$
$390$	3900.84	0.506479
$391$	63.5462	0.00821910
$392$	6501.07	0.837637
$393$	−97.7292	−0.0125440
$394$	−6288.18	−0.804046
$395$	−12724.4	−1.62084
$396$	16443.2	2.08662
$397$	−5407.44	−0.683606	−0.341803	−	0.939772i	$-0.611038\pi$
$397$	−5407.44	−0.683606	−0.341803	+	0.939772i	$0.611038\pi$
$398$	−4473.43	−0.563399
$399$	−301.029	−0.0377702
$400$	−400.356	−0.0500445
$401$	−11696.4	−1.45658	−0.728290	−	0.685269i	$-0.759684\pi$
$401$	−11696.4	−1.45658	−0.728290	+	0.685269i	$0.759684\pi$
$402$	−7901.79	−0.980362
$403$	−9934.78	−1.22801
$404$	17880.9	2.20200
$405$	−6392.87	−0.784356
$406$	4657.61	0.569344
$407$	−19527.4	−2.37823
$408$	−874.567	−0.106121
$409$	−4629.41	−0.559681	−0.279840	−	0.960047i	$-0.590282\pi$
$409$	−4629.41	−0.559681	−0.279840	+	0.960047i	$0.590282\pi$
$410$	14992.0	1.80586
$411$	−241.318	−0.0289619
$412$	21929.4	2.62229
$413$	−378.295	−0.0450718
$414$	−276.002	−0.0327651
$415$	−10916.7	−1.29128
$416$	−7568.25	−0.891981
$417$	−1779.97	−0.209031
$418$	9920.69	1.16085
$419$	3307.85	0.385678	0.192839	−	0.981230i	$-0.438230\pi$
$419$	3307.85	0.385678	0.192839	+	0.981230i	$0.438230\pi$
$420$	1229.59	0.142852
$421$	−242.081	−0.0280245	−0.0140122	−	0.999902i	$-0.504460\pi$
$421$	−242.081	−0.0280245	−0.0140122	+	0.999902i	$0.504460\pi$
$422$	4263.61	0.491823
$423$	9258.87	1.06426
$424$	716.824	0.0821039
$425$	−1126.63	−0.128587
$426$	3514.95	0.399766
$427$	3854.30	0.436821
$428$	2065.49	0.233269
$429$	−3654.26	−0.411257
$430$	0	0
$431$	−16410.0	−1.83398	−0.916989	−	0.398913i	$-0.869387\pi$
$431$	−16410.0	−1.83398	−0.916989	+	0.398913i	$0.869387\pi$
$432$	−789.555	−0.0879339
$433$	6230.06	0.691450	0.345725	−	0.938336i	$-0.387633\pi$
$433$	6230.06	0.691450	0.345725	+	0.938336i	$0.387633\pi$
$434$	−5146.22	−0.569185
$435$	−5440.11	−0.599617
$436$	−5493.71	−0.603442
$437$	−101.330	−0.0110921
$438$	−558.305	−0.0609060
$439$	−4436.43	−0.482322	−0.241161	−	0.970485i	$-0.577528\pi$
$439$	−4436.43	−0.482322	−0.241161	+	0.970485i	$0.577528\pi$
$440$	−14452.3	−1.56588
$441$	7760.81	0.838010
$442$	−4252.53	−0.457630
$443$	−13607.7	−1.45941	−0.729707	−	0.683760i	$-0.760343\pi$
$443$	−13607.7	−1.45941	−0.729707	+	0.683760i	$0.760343\pi$
$444$	−7696.63	−0.822671
$445$	14174.2	1.50994
$446$	−19762.5	−2.09816
$447$	4773.82	0.505132
$448$	−3613.91	−0.381119
$449$	−3677.16	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$449$	−3677.16	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$450$	4893.32	0.512607
$451$	−14044.3	−1.46634
$452$	−12079.8	−1.25705
$453$	−2365.08	−0.245301
$454$	5847.94	0.604532
$455$	2132.35	0.219706
$456$	1394.57	0.143217
$457$	9654.94	0.988270	0.494135	−	0.869385i	$-0.335485\pi$
$457$	9654.94	0.988270	0.494135	+	0.869385i	$0.335485\pi$
$458$	−12299.5	−1.25484
$459$	−2221.86	−0.225943
$460$	413.893	0.0419519
$461$	6387.32	0.645308	0.322654	−	0.946517i	$-0.395425\pi$
$461$	6387.32	0.645308	0.322654	+	0.946517i	$0.395425\pi$
$462$	−1892.91	−0.190619
$463$	8369.16	0.840060	0.420030	−	0.907510i	$-0.362019\pi$
$463$	8369.16	0.840060	0.420030	+	0.907510i	$0.362019\pi$
$464$	2107.47	0.210855
$465$	6010.80	0.599450
$466$	8249.53	0.820069
$467$	−11897.9	−1.17895	−0.589475	−	0.807786i	$-0.700666\pi$
$467$	−11897.9	−1.17895	−0.589475	+	0.807786i	$0.700666\pi$
$468$	11239.3	1.11012
$469$	−4319.41	−0.425271
$470$	−22817.3	−2.23933
$471$	−4594.55	−0.449481
$472$	1752.52	0.170903
$473$	0	0
$474$	7720.78	0.748159
$475$	1796.51	0.173536
$476$	−1340.44	−0.129074
$477$	855.727	0.0821405
$478$	−11382.1	−1.08914
$479$	−5313.81	−0.506877	−0.253438	−	0.967352i	$-0.581562\pi$
$479$	−5313.81	−0.506877	−0.253438	+	0.967352i	$0.581562\pi$
$480$	4578.99	0.435420
$481$	−13347.5	−1.26527
$482$	9146.32	0.864322
$483$	19.3342	0.00182140
$484$	21409.7	2.01068
$485$	14775.9	1.38338
$486$	14766.0	1.37818
$487$	10792.5	1.00422	0.502110	−	0.864804i	$-0.332557\pi$
$487$	10792.5	1.00422	0.502110	+	0.864804i	$0.332557\pi$
$488$	−17855.8	−1.65634
$489$	−713.303	−0.0659645
$490$	−19125.5	−1.76327
$491$	−2458.96	−0.226011	−0.113006	−	0.993594i	$-0.536048\pi$
$491$	−2458.96	−0.226011	−0.113006	+	0.993594i	$0.536048\pi$
$492$	−5535.48	−0.507233
$493$	5930.57	0.541784
$494$	6781.03	0.617597
$495$	−17252.8	−1.56658
$496$	−2328.55	−0.210797
$497$	1921.41	0.173414
$498$	6623.98	0.596039
$499$	−8744.82	−0.784513	−0.392256	−	0.919856i	$-0.628305\pi$
$499$	−8744.82	−0.784513	−0.392256	+	0.919856i	$0.628305\pi$
$500$	12942.1	1.15758
$501$	−3053.87	−0.272329
$502$	9947.20	0.884393
$503$	12931.7	1.14631	0.573157	−	0.819446i	$-0.305719\pi$
$503$	12931.7	1.14631	0.573157	+	0.819446i	$0.305719\pi$
$504$	2076.42	0.183514
$505$	−18761.3	−1.65320
$506$	−637.175	−0.0559800
$507$	1349.79	0.118237
$508$	−19843.4	−1.73309
$509$	19155.2	1.66805	0.834026	−	0.551726i	$-0.186030\pi$
$509$	19155.2	1.66805	0.834026	+	0.551726i	$0.186030\pi$
$510$	2572.89	0.223391
$511$	−305.190	−0.0264204
$512$	−3193.56	−0.275658
$513$	3542.95	0.304923
$514$	−3931.75	−0.337397
$515$	−23009.1	−1.96874
$516$	0	0
$517$	21375.0	1.81832
$518$	−6914.00	−0.586455
$519$	−2070.53	−0.175118
$520$	−9878.50	−0.833079
$521$	−2030.86	−0.170775	−0.0853875	−	0.996348i	$-0.527213\pi$
$521$	−2030.86	−0.170775	−0.0853875	+	0.996348i	$0.527213\pi$
$522$	−25758.4	−2.15980
$523$	13361.0	1.11708	0.558542	−	0.829477i	$-0.311361\pi$
$523$	13361.0	1.11708	0.558542	+	0.829477i	$0.311361\pi$
$524$	693.925	0.0578516
$525$	−342.782	−0.0284957
$526$	21922.2	1.81722
$527$	−6552.71	−0.541633
$528$	−856.501	−0.0705955
$529$	−12160.5	−0.999465
$530$	−2108.83	−0.172833
$531$	2092.11	0.170979
$532$	2137.45	0.174192
$533$	−9599.63	−0.780124
$534$	−8600.52	−0.696968
$535$	−2167.18	−0.175132
$536$	20010.5	1.61254
$537$	−7889.88	−0.634029
$538$	−1954.91	−0.156658
$539$	17916.6	1.43176
$540$	−14471.6	−1.15326
$541$	−1543.79	−0.122685	−0.0613425	−	0.998117i	$-0.519538\pi$
$541$	−1543.79	−0.122685	−0.0613425	+	0.998117i	$0.519538\pi$
$542$	−3892.95	−0.308517
$543$	4572.22	0.361350
$544$	−4991.82	−0.393424
$545$	5764.20	0.453048
$546$	−1293.85	−0.101413
$547$	−15805.6	−1.23546	−0.617731	−	0.786390i	$-0.711948\pi$
$547$	−15805.6	−1.23546	−0.617731	+	0.786390i	$0.711948\pi$
$548$	1713.47	0.133569
$549$	−21315.8	−1.65708
$550$	11296.7	0.875804
$551$	−9456.81	−0.731168
$552$	−89.5691	−0.00690637
$553$	4220.47	0.324544
$554$	10074.5	0.772608
$555$	8075.58	0.617638
$556$	12638.7	0.964028
$557$	552.342	0.0420170	0.0210085	−	0.999779i	$-0.493312\pi$
$557$	552.342	0.0420170	0.0210085	+	0.999779i	$0.493312\pi$
$558$	28460.6	2.15920
$559$	0	0
$560$	499.788	0.0377141
$561$	−2410.25	−0.181392
$562$	27085.4	2.03297
$563$	12098.2	0.905644	0.452822	−	0.891601i	$-0.350417\pi$
$563$	12098.2	0.905644	0.452822	+	0.891601i	$0.350417\pi$
$564$	8424.81	0.628987
$565$	12674.6	0.943760
$566$	−5088.35	−0.377878
$567$	2120.42	0.157053
$568$	−8901.27	−0.657551
$569$	519.978	0.0383104	0.0191552	−	0.999817i	$-0.493902\pi$
$569$	519.978	0.0383104	0.0191552	+	0.999817i	$0.493902\pi$
$570$	−4102.70	−0.301479
$571$	13553.9	0.993365	0.496682	−	0.867932i	$-0.334551\pi$
$571$	13553.9	0.993365	0.496682	+	0.867932i	$0.334551\pi$
$572$	25947.0	1.89668
$573$	−5241.55	−0.382144
$574$	−4972.61	−0.361590
$575$	−115.384	−0.00836845
$576$	19986.3	1.44577
$577$	6324.19	0.456290	0.228145	−	0.973627i	$-0.426734\pi$
$577$	6324.19	0.456290	0.228145	+	0.973627i	$0.426734\pi$
$578$	19404.4	1.39639
$579$	1474.66	0.105846
$580$	38627.4	2.76537
$581$	3620.92	0.258556
$582$	−8965.61	−0.638551
$583$	1975.53	0.140339
$584$	1413.85	0.100181
$585$	−11792.7	−0.833450
$586$	−29189.1	−2.05766
$587$	21394.9	1.50437	0.752183	−	0.658954i	$-0.229001\pi$
$587$	21394.9	1.50437	0.752183	+	0.658954i	$0.229001\pi$
$588$	7061.71	0.495272
$589$	10448.9	0.730965
$590$	−5155.75	−0.359761
$591$	−2436.10	−0.169556
$592$	−3128.44	−0.217193
$593$	−17243.2	−1.19409	−0.597043	−	0.802209i	$-0.703658\pi$
$593$	−17243.2	−1.19409	−0.597043	+	0.802209i	$0.703658\pi$
$594$	22278.5	1.53889
$595$	1406.44	0.0969049
$596$	−33896.5	−2.32962
$597$	−1733.04	−0.118809
$598$	−435.525	−0.0297825
$599$	1214.43	0.0828387	0.0414193	−	0.999142i	$-0.486812\pi$
$599$	1214.43	0.0828387	0.0414193	+	0.999142i	$0.486812\pi$
$600$	1588.00	0.108050
$601$	−3251.39	−0.220677	−0.110338	−	0.993894i	$-0.535193\pi$
$601$	−3251.39	−0.220677	−0.110338	+	0.993894i	$0.535193\pi$
$602$	0	0
$603$	23888.0	1.61326
$604$	16793.2	1.13130
$605$	−22463.9	−1.50956
$606$	11383.8	0.763096
$607$	−13945.8	−0.932526	−0.466263	−	0.884646i	$-0.654400\pi$
$607$	−13945.8	−0.932526	−0.466263	+	0.884646i	$0.654400\pi$
$608$	7959.89	0.530948
$609$	1804.40	0.120062
$610$	52530.0	3.48668
$611$	14610.3	0.967381
$612$	7413.16	0.489639
$613$	8980.34	0.591701	0.295850	−	0.955234i	$-0.404397\pi$
$613$	8980.34	0.591701	0.295850	+	0.955234i	$0.404397\pi$
$614$	−35712.9	−2.34732
$615$	5808.03	0.380817
$616$	4793.60	0.313539
$617$	−9450.64	−0.616642	−0.308321	−	0.951282i	$-0.599767\pi$
$617$	−9450.64	−0.616642	−0.308321	+	0.951282i	$0.599767\pi$
$618$	13961.3	0.908745
$619$	−9340.01	−0.606473	−0.303237	−	0.952915i	$-0.598067\pi$
$619$	−9340.01	−0.606473	−0.303237	+	0.952915i	$0.598067\pi$
$620$	−42679.6	−2.76460
$621$	−227.553	−0.0147043
$622$	−17736.2	−1.14334
$623$	−4701.37	−0.302337
$624$	−585.439	−0.0375582
$625$	−19233.0	−1.23091
$626$	32818.3	2.09534
$627$	3843.36	0.244799
$628$	32623.5	2.07296
$629$	−8803.65	−0.558067
$630$	−6108.62	−0.386307
$631$	9633.83	0.607792	0.303896	−	0.952705i	$-0.401712\pi$
$631$	9633.83	0.607792	0.303896	+	0.952705i	$0.401712\pi$
$632$	−19552.1	−1.23060
$633$	1651.76	0.103715
$634$	26975.2	1.68978
$635$	20820.4	1.30115
$636$	778.642	0.0485458
$637$	12246.4	0.761727
$638$	−59465.6	−3.69007
$639$	−10626.1	−0.657844
$640$	−28336.5	−1.75015
$641$	10806.5	0.665885	0.332943	−	0.942947i	$-0.391958\pi$
$641$	10806.5	0.665885	0.332943	+	0.942947i	$0.391958\pi$
$642$	1314.99	0.0808386
$643$	5396.16	0.330955	0.165477	−	0.986214i	$-0.447084\pi$
$643$	5396.16	0.330955	0.165477	+	0.986214i	$0.447084\pi$
$644$	−137.282	−0.00840011
$645$	0	0
$646$	4472.59	0.272402
$647$	−13276.4	−0.806722	−0.403361	−	0.915041i	$-0.632158\pi$
$647$	−13276.4	−0.806722	−0.403361	+	0.915041i	$0.632158\pi$
$648$	−9823.22	−0.595513
$649$	4829.84	0.292123
$650$	7721.56	0.465945
$651$	−1993.69	−0.120029
$652$	5064.79	0.304222
$653$	−7560.53	−0.453088	−0.226544	−	0.974001i	$-0.572743\pi$
$653$	−7560.53	−0.453088	−0.226544	+	0.974001i	$0.572743\pi$
$654$	−3497.55	−0.209121
$655$	−728.091	−0.0434334
$656$	−2250.00	−0.133914
$657$	1687.82	0.100225
$658$	7568.15	0.448385
$659$	17888.9	1.05744	0.528718	−	0.848797i	$-0.322673\pi$
$659$	17888.9	1.05744	0.528718	+	0.848797i	$0.322673\pi$
$660$	−15698.6	−0.925861
$661$	28643.1	1.68546	0.842729	−	0.538337i	$-0.180947\pi$
$661$	28643.1	1.68546	0.842729	+	0.538337i	$0.180947\pi$
$662$	−33509.3	−1.96733
$663$	−1647.47	−0.0965043
$664$	−16774.6	−0.980390
$665$	−2242.69	−0.130779
$666$	38237.1	2.22471
$667$	607.382	0.0352593
$668$	21683.9	1.25595
$669$	−7656.15	−0.442457
$670$	−58869.0	−3.39449
$671$	−49209.4	−2.83116
$672$	−1518.78	−0.0871849
$673$	26681.2	1.52821	0.764105	−	0.645091i	$-0.223181\pi$
$673$	26681.2	1.52821	0.764105	+	0.645091i	$0.223181\pi$
$674$	−54295.2	−3.10293
$675$	4034.36	0.230048
$676$	−9584.15	−0.545297
$677$	24196.9	1.37365	0.686826	−	0.726821i	$-0.259003\pi$
$677$	24196.9	1.37365	0.686826	+	0.726821i	$0.259003\pi$
$678$	−7690.59	−0.435627
$679$	−4900.94	−0.276997
$680$	−6515.60	−0.367444
$681$	2265.54	0.127483
$682$	65703.8	3.68905
$683$	33758.8	1.89128	0.945641	−	0.325213i	$-0.105436\pi$
$683$	33758.8	1.89128	0.945641	+	0.325213i	$0.105436\pi$
$684$	−11820.9	−0.660796
$685$	−1797.84	−0.100280
$686$	13053.7	0.726517
$687$	−4764.93	−0.264619
$688$	0	0
$689$	1350.32	0.0746634
$690$	263.504	0.0145383
$691$	−18145.5	−0.998970	−0.499485	−	0.866322i	$-0.666477\pi$
$691$	−18145.5	−0.998970	−0.499485	+	0.866322i	$0.666477\pi$
$692$	14701.7	0.807625
$693$	5722.48	0.313678
$694$	10744.7	0.587698
$695$	−13261.0	−0.723765
$696$	−8359.21	−0.455252
$697$	−6331.66	−0.344087
$698$	11044.9	0.598935
$699$	3195.94	0.172935
$700$	2433.92	0.131419
$701$	−21944.9	−1.18238	−0.591189	−	0.806533i	$-0.701341\pi$
$701$	−21944.9	−1.18238	−0.591189	+	0.806533i	$0.701341\pi$
$702$	15227.9	0.818720
$703$	14038.2	0.753144
$704$	46140.2	2.47014
$705$	−8839.62	−0.472226
$706$	30945.6	1.64965
$707$	6222.83	0.331023
$708$	1903.65	0.101050
$709$	−36958.0	−1.95767	−0.978834	−	0.204656i	$-0.934392\pi$
$709$	−36958.0	−1.95767	−0.978834	+	0.204656i	$0.934392\pi$
$710$	26186.7	1.38418
$711$	−23340.8	−1.23115
$712$	21779.9	1.14640
$713$	−671.099	−0.0352494
$714$	−853.389	−0.0447301
$715$	−27224.6	−1.42397
$716$	56022.0	2.92408
$717$	−4409.54	−0.229675
$718$	40169.4	2.08789
$719$	5395.23	0.279845	0.139922	−	0.990162i	$-0.455315\pi$
$719$	5395.23	0.279845	0.139922	+	0.990162i	$0.455315\pi$
$720$	−2764.02	−0.143068
$721$	7631.75	0.394204
$722$	23874.2	1.23062
$723$	3543.36	0.182267
$724$	−32465.0	−1.66651
$725$	−10768.5	−0.551629
$726$	13630.4	0.696795
$727$	9561.59	0.487785	0.243892	−	0.969802i	$-0.421576\pi$
$727$	9561.59	0.487785	0.243892	+	0.969802i	$0.421576\pi$
$728$	3276.54	0.166809
$729$	−7509.02	−0.381497
$730$	−4159.42	−0.210886
$731$	0	0
$732$	−19395.6	−0.979347
$733$	−13308.7	−0.670623	−0.335312	−	0.942107i	$-0.608842\pi$
$733$	−13308.7	−0.670623	−0.335312	+	0.942107i	$0.608842\pi$
$734$	−8011.05	−0.402852
$735$	−7409.40	−0.371836
$736$	−511.239	−0.0256040
$737$	55147.7	2.75630
$738$	27500.5	1.37169
$739$	16167.3	0.804768	0.402384	−	0.915471i	$-0.368182\pi$
$739$	16167.3	0.804768	0.402384	+	0.915471i	$0.368182\pi$
$740$	−57340.5	−2.84849
$741$	2627.03	0.130238
$742$	699.466	0.0346068
$743$	25680.2	1.26799	0.633994	−	0.773338i	$-0.281415\pi$
$743$	25680.2	1.26799	0.633994	+	0.773338i	$0.281415\pi$
$744$	9236.13	0.455125
$745$	35565.4	1.74901
$746$	−9446.91	−0.463641
$747$	−20025.0	−0.980828
$748$	17114.0	0.836562
$749$	718.821	0.0350669
$750$	8239.55	0.401154
$751$	12689.2	0.616559	0.308279	−	0.951296i	$-0.400247\pi$
$751$	12689.2	0.616559	0.308279	+	0.951296i	$0.400247\pi$
$752$	3424.42	0.166058
$753$	3853.63	0.186500
$754$	−40646.2	−1.96319
$755$	−17620.1	−0.849351
$756$	4800.00	0.230918
$757$	−17431.3	−0.836926	−0.418463	−	0.908234i	$-0.637431\pi$
$757$	−17431.3	−0.836926	−0.418463	+	0.908234i	$0.637431\pi$
$758$	58576.5	2.80685
$759$	−246.847	−0.0118050
$760$	10389.7	0.495886
$761$	−16997.5	−0.809670	−0.404835	−	0.914390i	$-0.632671\pi$
$761$	−16997.5	−0.809670	−0.404835	+	0.914390i	$0.632671\pi$
$762$	−12633.2	−0.600595
$763$	−1911.89	−0.0907146
$764$	37217.5	1.76241
$765$	−7778.15	−0.367607
$766$	13070.4	0.616516
$767$	3301.31	0.155415
$768$	5493.92	0.258131
$769$	−29896.1	−1.40193	−0.700963	−	0.713198i	$-0.747246\pi$
$769$	−29896.1	−1.40193	−0.700963	+	0.713198i	$0.747246\pi$
$770$	−14102.3	−0.660017
$771$	−1523.19	−0.0711498
$772$	−10470.8	−0.488152
$773$	−18464.3	−0.859138	−0.429569	−	0.903034i	$-0.641335\pi$
$773$	−18464.3	−0.859138	−0.429569	+	0.903034i	$0.641335\pi$
$774$	0	0
$775$	11898.1	0.551475
$776$	22704.5	1.05032
$777$	−2678.54	−0.123671
$778$	36198.0	1.66807
$779$	10096.4	0.464365
$780$	−10730.4	−0.492577
$781$	−24531.4	−1.12395
$782$	−287.261	−0.0131361
$783$	−21236.8	−0.969275
$784$	2870.36	0.130756
$785$	−34229.8	−1.55632
$786$	441.785	0.0200483
$787$	−7383.94	−0.334446	−0.167223	−	0.985919i	$-0.553480\pi$
$787$	−7383.94	−0.334446	−0.167223	+	0.985919i	$0.553480\pi$
$788$	17297.5	0.781975
$789$	8492.87	0.383212
$790$	57520.5	2.59049
$791$	−4203.97	−0.188971
$792$	−26510.5	−1.18940
$793$	−33635.9	−1.50623
$794$	24444.3	1.09257
$795$	−816.979	−0.0364469
$796$	12305.5	0.547934
$797$	23799.0	1.05772	0.528860	−	0.848709i	$-0.322620\pi$
$797$	23799.0	1.05772	0.528860	+	0.848709i	$0.322620\pi$
$798$	1360.80	0.0603658
$799$	9636.57	0.426680
$800$	9063.93	0.400573
$801$	26000.4	1.14691
$802$	52873.4	2.32796
$803$	3896.49	0.171238
$804$	21736.1	0.953451
$805$	144.041	0.00630657
$806$	44910.2	1.96265
$807$	−757.348	−0.0330358
$808$	−28828.4	−1.25517
$809$	2665.36	0.115833	0.0579166	−	0.998321i	$-0.481554\pi$
$809$	2665.36	0.115833	0.0579166	+	0.998321i	$0.481554\pi$
$810$	28899.0	1.25359
$811$	36736.8	1.59063	0.795317	−	0.606194i	$-0.207305\pi$
$811$	36736.8	1.59063	0.795317	+	0.606194i	$0.207305\pi$
$812$	−12812.1	−0.553715
$813$	−1508.16	−0.0650597
$814$	88273.9	3.80098
$815$	−5314.16	−0.228401
$816$	−386.140	−0.0165657
$817$	0	0
$818$	20927.2	0.894504
$819$	3911.46	0.166883
$820$	−41239.8	−1.75629
$821$	−13460.1	−0.572180	−0.286090	−	0.958203i	$-0.592356\pi$
$821$	−13460.1	−0.572180	−0.286090	+	0.958203i	$0.592356\pi$
$822$	1090.88	0.0462880
$823$	−25589.3	−1.08382	−0.541912	−	0.840435i	$-0.682300\pi$
$823$	−25589.3	−1.08382	−0.541912	+	0.840435i	$0.682300\pi$
$824$	−35355.5	−1.49474
$825$	4376.43	0.184688
$826$	1710.08	0.0720355
$827$	24201.4	1.01761	0.508807	−	0.860881i	$-0.330087\pi$
$827$	24201.4	1.01761	0.508807	+	0.860881i	$0.330087\pi$
$828$	759.222	0.0318657
$829$	15933.9	0.667560	0.333780	−	0.942651i	$-0.391676\pi$
$829$	15933.9	0.667560	0.333780	+	0.942651i	$0.391676\pi$
$830$	49349.2	2.06378
$831$	3902.95	0.162926
$832$	31538.0	1.31416
$833$	8077.41	0.335973
$834$	8046.38	0.334081
$835$	−22751.6	−0.942935
$836$	−27289.7	−1.12899
$837$	23464.7	0.969006
$838$	−14953.2	−0.616406
$839$	23536.8	0.968512	0.484256	−	0.874926i	$-0.339090\pi$
$839$	23536.8	0.968512	0.484256	+	0.874926i	$0.339090\pi$
$840$	−1982.40	−0.0814275
$841$	32296.1	1.32421
$842$	1094.33	0.0447898
$843$	10493.1	0.428709
$844$	−11728.3	−0.478323
$845$	10056.0	0.409394
$846$	−41854.7	−1.70094
$847$	7450.91	0.302263
$848$	316.493	0.0128165
$849$	−1971.27	−0.0796864
$850$	5092.94	0.205513
$851$	−901.629	−0.0363190
$852$	−9668.90	−0.388792
$853$	14346.0	0.575845	0.287923	−	0.957654i	$-0.407035\pi$
$853$	14346.0	0.575845	0.287923	+	0.957654i	$0.407035\pi$
$854$	−17423.4	−0.698145
$855$	12402.9	0.496107
$856$	−3330.07	−0.132967
$857$	−25049.7	−0.998462	−0.499231	−	0.866469i	$-0.666384\pi$
$857$	−25049.7	−0.998462	−0.499231	+	0.866469i	$0.666384\pi$
$858$	16519.1	0.657288
$859$	26179.1	1.03983	0.519917	−	0.854217i	$-0.325963\pi$
$859$	26179.1	1.03983	0.519917	+	0.854217i	$0.325963\pi$
$860$	0	0
$861$	−1926.43	−0.0762516
$862$	74181.7	2.93113
$863$	−10987.8	−0.433404	−0.216702	−	0.976238i	$-0.569530\pi$
$863$	−10987.8	−0.433404	−0.216702	+	0.976238i	$0.569530\pi$
$864$	17875.3	0.703852
$865$	−15425.6	−0.606342
$866$	−28163.0	−1.10510
$867$	7517.42	0.294469
$868$	14156.2	0.553561
$869$	−53884.4	−2.10346
$870$	24592.0	0.958331
$871$	37694.8	1.46641
$872$	8857.20	0.343971
$873$	27104.1	1.05078
$874$	458.062	0.0177279
$875$	4504.05	0.174017
$876$	1535.78	0.0592341
$877$	43452.2	1.67306	0.836531	−	0.547919i	$-0.184580\pi$
$877$	43452.2	1.67306	0.836531	+	0.547919i	$0.184580\pi$
$878$	20054.9	0.770865
$879$	−11308.1	−0.433917
$880$	−6381.00	−0.244436
$881$	−10548.4	−0.403389	−0.201694	−	0.979449i	$-0.564645\pi$
$881$	−10548.4	−0.403389	−0.201694	+	0.979449i	$0.564645\pi$
$882$	−35082.8	−1.33934
$883$	−12217.7	−0.465637	−0.232818	−	0.972520i	$-0.574795\pi$
$883$	−12217.7	−0.465637	−0.232818	+	0.972520i	$0.574795\pi$
$884$	11697.8	0.445068
$885$	−1997.38	−0.0758658
$886$	61513.5	2.33249
$887$	39821.5	1.50741	0.753706	−	0.657212i	$-0.228264\pi$
$887$	39821.5	1.50741	0.753706	+	0.657212i	$0.228264\pi$
$888$	12408.9	0.468934
$889$	−6905.80	−0.260532
$890$	−64074.6	−2.41324
$891$	−27072.2	−1.01790
$892$	54362.4	2.04057
$893$	−15366.4	−0.575829
$894$	−21580.1	−0.807322
$895$	−58780.3	−2.19532
$896$	9398.77	0.350436
$897$	−168.726	−0.00628049
$898$	16622.6	0.617710
$899$	−62631.6	−2.32356
$900$	−13460.5	−0.498537
$901$	890.635	0.0329316
$902$	63487.4	2.34357
$903$	0	0
$904$	19475.6	0.716538
$905$	34063.4	1.25117
$906$	10691.4	0.392049
$907$	−32895.0	−1.20426	−0.602128	−	0.798399i	$-0.705680\pi$
$907$	−32895.0	−1.20426	−0.602128	+	0.798399i	$0.705680\pi$
$908$	−16086.5	−0.587938
$909$	−34414.6	−1.25573
$910$	−9639.29	−0.351142
$911$	14491.2	0.527019	0.263509	−	0.964657i	$-0.415120\pi$
$911$	14491.2	0.527019	0.263509	+	0.964657i	$0.415120\pi$
$912$	615.734	0.0223563
$913$	−46229.7	−1.67577
$914$	−43645.2	−1.57949
$915$	20350.6	0.735267
$916$	33833.3	1.22040
$917$	241.496	0.00869675
$918$	10043.9	0.361110
$919$	3819.84	0.137111	0.0685554	−	0.997647i	$-0.478161\pi$
$919$	3819.84	0.137111	0.0685554	+	0.997647i	$0.478161\pi$
$920$	−667.298	−0.0239132
$921$	−13835.5	−0.495000
$922$	−28873.9	−1.03136
$923$	−16767.8	−0.597962
$924$	5206.99	0.185387
$925$	15985.3	0.568208
$926$	−37832.8	−1.34262
$927$	−42206.5	−1.49541
$928$	−47712.4	−1.68775
$929$	−6597.01	−0.232983	−0.116491	−	0.993192i	$-0.537165\pi$
$929$	−6597.01	−0.232983	−0.116491	+	0.993192i	$0.537165\pi$
$930$	−27171.8	−0.958064
$931$	−12880.1	−0.453415
$932$	−22692.7	−0.797559
$933$	−6871.16	−0.241106
$934$	53784.6	1.88425
$935$	−17956.6	−0.628068
$936$	−18120.5	−0.632787
$937$	22841.5	0.796370	0.398185	−	0.917305i	$-0.369640\pi$
$937$	22841.5	0.796370	0.398185	+	0.917305i	$0.369640\pi$
$938$	19525.9	0.679685
$939$	12714.1	0.441862
$940$	62765.6	2.17786
$941$	36677.3	1.27061	0.635306	−	0.772261i	$-0.280874\pi$
$941$	36677.3	1.27061	0.635306	+	0.772261i	$0.280874\pi$
$942$	20769.7	0.718378
$943$	−648.460	−0.0223932
$944$	773.775	0.0266782
$945$	−5036.34	−0.173367
$946$	0	0
$947$	−19733.4	−0.677138	−0.338569	−	0.940942i	$-0.609943\pi$
$947$	−19733.4	−0.677138	−0.338569	+	0.940942i	$0.609943\pi$
$948$	−21238.2	−0.727622
$949$	2663.34	0.0911020
$950$	−8121.13	−0.277352
$951$	10450.4	0.356338
$952$	2161.12	0.0735739
$953$	12496.6	0.424768	0.212384	−	0.977186i	$-0.431877\pi$
$953$	12496.6	0.424768	0.212384	+	0.977186i	$0.431877\pi$
$954$	−3868.32	−0.131280
$955$	−39050.0	−1.32317
$956$	31309.9	1.05924
$957$	−23037.5	−0.778157
$958$	24021.1	0.810111
$959$	596.315	0.0200793
$960$	−19081.3	−0.641507
$961$	39411.0	1.32291
$962$	60337.4	2.02220
$963$	−3975.35	−0.133026
$964$	−25159.6	−0.840597
$965$	10986.4	0.366491
$966$	−87.4002	−0.00291103
$967$	−1702.88	−0.0566297	−0.0283149	−	0.999599i	$-0.509014\pi$
$967$	−1702.88	−0.0566297	−0.0283149	+	0.999599i	$0.509014\pi$
$968$	−34517.7	−1.14612
$969$	1732.72	0.0574437
$970$	−66794.6	−2.21097
$971$	−3923.91	−0.129685	−0.0648426	−	0.997896i	$-0.520655\pi$
$971$	−3923.91	−0.129685	−0.0648426	+	0.997896i	$0.520655\pi$
$972$	−40618.0	−1.34035
$973$	4398.45	0.144921
$974$	−48787.5	−1.60498
$975$	2991.40	0.0982579
$976$	−7883.71	−0.258557
$977$	−24540.8	−0.803614	−0.401807	−	0.915724i	$-0.631618\pi$
$977$	−24540.8	−0.803614	−0.401807	+	0.915724i	$0.631618\pi$
$978$	3224.49	0.105427
$979$	60024.2	1.95953
$980$	52610.3	1.71487
$981$	10573.5	0.344124
$982$	11115.8	0.361220
$983$	−10646.8	−0.345453	−0.172727	−	0.984970i	$-0.555258\pi$
$983$	−10646.8	−0.345453	−0.172727	+	0.984970i	$0.555258\pi$
$984$	8924.56	0.289131
$985$	−18149.1	−0.587085
$986$	−26809.2	−0.865900
$987$	2931.96	0.0945547
$988$	−18653.2	−0.600645
$989$	0	0
$990$	77991.3	2.50376
$991$	−68.7730	−0.00220449	−0.00110224	−	0.999999i	$-0.500351\pi$
$991$	−68.7730	−0.00220449	−0.00110224	+	0.999999i	$0.500351\pi$
$992$	52717.6	1.68729
$993$	−12981.8	−0.414869
$994$	−8685.72	−0.277157
$995$	−12911.3	−0.411373
$996$	−18221.2	−0.579678
$997$	−56204.3	−1.78536	−0.892682	−	0.450686i	$-0.851179\pi$
$997$	−56204.3	−1.78536	−0.892682	+	0.450686i	$0.851179\pi$
$998$	39531.0	1.25384
$999$	31525.1	0.998407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.8	✓	50
43.42	odd	2		1849.4.a.j.1.43	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.8	✓	50	1.1	even	1	trivial
1849.4.a.j.1.43	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)

\(f(q)\)	\(=\)	\(q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +O(q^{10})\)	\(q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +58.9799 q^{10} -55.2516 q^{11} -21.7771 q^{12} -37.7658 q^{13} -19.5627 q^{14} +22.8493 q^{15} -8.85170 q^{16} -24.9093 q^{17} +108.189 q^{18} +39.7201 q^{19} -162.241 q^{20} -7.57876 q^{21} +249.765 q^{22} -2.55110 q^{23} +35.1100 q^{24} +45.2293 q^{25} +170.720 q^{26} +89.1980 q^{27} +53.8129 q^{28} -238.086 q^{29} -103.290 q^{30} +263.063 q^{31} +200.400 q^{32} +96.7611 q^{33} +112.603 q^{34} -56.4624 q^{35} -297.606 q^{36} +353.428 q^{37} -179.555 q^{38} +66.1386 q^{39} +261.573 q^{40} +254.188 q^{41} +34.2598 q^{42} -687.051 q^{44} +312.259 q^{45} +11.5323 q^{46} -386.866 q^{47} +15.5018 q^{48} -324.272 q^{49} -204.459 q^{50} +43.6232 q^{51} -469.616 q^{52} -35.7551 q^{53} -403.220 q^{54} +720.878 q^{55} -86.7595 q^{56} -69.5611 q^{57} +1076.27 q^{58} -87.4154 q^{59} +284.130 q^{60} +890.643 q^{61} -1189.18 q^{62} -103.571 q^{63} -835.093 q^{64} +492.738 q^{65} -437.409 q^{66} -998.120 q^{67} -309.746 q^{68} +4.46769 q^{69} +255.238 q^{70} +443.994 q^{71} +479.813 q^{72} -70.5226 q^{73} -1597.67 q^{74} -79.2092 q^{75} +493.917 q^{76} -239.104 q^{77} -298.980 q^{78} +975.256 q^{79} +115.490 q^{80} +489.980 q^{81} -1149.06 q^{82} +836.712 q^{83} -94.2415 q^{84} +324.997 q^{85} +416.956 q^{87} +1107.69 q^{88} -1086.38 q^{89} -1411.57 q^{90} -163.434 q^{91} -31.7228 q^{92} -460.697 q^{93} +1748.83 q^{94} -518.236 q^{95} -350.956 q^{96} -1132.50 q^{97} +1465.87 q^{98} +1322.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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