LMFDB - Embedded newform 1849.4.a.j.1.43

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			1.43
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	$-0.205299\pi$
$2$	4.52050	1.59824	0.799120	+	0.601172i	$0.205299\pi$
$3$	1.75128	0.337034	0.168517	−	0.985699i	$-0.446102\pi$
$3$	1.75128	0.337034	0.168517	+	0.985699i	$0.446102\pi$
$4$	12.4349	1.55437
$5$	13.0472	1.16698	0.583488	−	0.812122i	$-0.301687\pi$
$5$	13.0472	1.16698	0.583488	+	0.812122i	$0.301687\pi$
$6$	7.91667	0.538661
$7$	−4.32755	−0.233666	−0.116833	−	0.993152i	$-0.537274\pi$
$7$	−4.32755	−0.233666	−0.116833	+	0.993152i	$0.537274\pi$
$8$	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	$-0.577082\pi$
$19$	−39.7201	−0.479601	−0.239800	+	0.970822i	$0.577082\pi$
$20$	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	$-0.224086\pi$
$29$	238.086	1.52454	0.762268	+	0.647262i	$0.224086\pi$
$30$	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	$-0.787429\pi$
$37$	−353.428	−1.57036	−0.785178	+	0.619270i	$0.787429\pi$
$38$	−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	$-0.884345\pi$
$61$	−890.643	−1.86943	−0.934714	+	0.355400i	$0.884345\pi$
$62$	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	$-0.621010\pi$
$71$	−443.994	−0.742146	−0.371073	+	0.928604i	$0.621010\pi$
$72$	−479.813	−0.785369
$73$	70.5226	0.113069	0.0565346	−	0.998401i	$-0.481995\pi$
$73$	70.5226	0.113069	0.0565346	+	0.998401i	$0.481995\pi$
$74$	−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	$-0.276047\pi$
$89$	1086.38	1.29389	0.646944	+	0.762537i	$0.276047\pi$
$90$	−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	$-0.367494\pi$
$113$	971.442	0.808722	0.404361	+	0.914599i	$0.367494\pi$
$114$	−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	$-0.505924\pi$
$131$	−55.8044	−0.0372187	−0.0186094	+	0.999827i	$0.505924\pi$
$132$	−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	$-0.513681\pi$
$137$	−137.795	−0.0859316	−0.0429658	+	0.999077i	$0.513681\pi$
$138$	−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	$-0.230352\pi$
$149$	2725.90	1.49876	0.749378	+	0.662142i	$0.230352\pi$
$150$	358.065	0.194906
$151$	−1350.49	−0.727822	−0.363911	−	0.931434i	$-0.618559\pi$
$151$	−1350.49	−0.727822	−0.363911	+	0.931434i	$0.618559\pi$
$152$	−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	$-0.732344\pi$
$157$	−2623.54	−1.33364	−0.666818	+	0.745220i	$0.732344\pi$
$158$	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	$-0.531200\pi$
$163$	−407.303	−0.195721	−0.0978603	+	0.995200i	$0.531200\pi$
$164$	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	$-0.889737\pi$
$179$	−4505.20	−1.88120	−0.940600	+	0.339517i	$0.889737\pi$
$180$	−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	$-0.691866\pi$
$191$	−2992.98	−1.13384	−0.566922	+	0.823771i	$0.691866\pi$
$192$	−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	$-0.556399\pi$
$199$	−989.587	−0.352512	−0.176256	+	0.984344i	$0.556399\pi$
$200$	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	$-0.450828\pi$
$211$	943.172	0.307728	0.153864	+	0.988092i	$0.450828\pi$
$212$	−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	$-0.727921\pi$
$223$	−4371.74	−1.31280	−0.656398	+	0.754415i	$0.727921\pi$
$224$	867.240	0.258682
$225$	−1082.47	−0.320733
$226$	4391.41	1.29253
$227$	1293.65	0.378249	0.189124	−	0.981953i	$-0.439435\pi$
$227$	1293.65	0.378249	0.189124	+	0.981953i	$0.439435\pi$
$228$	−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	$-0.417413\pi$
$233$	1824.91	0.513108	0.256554	+	0.966530i	$0.417413\pi$
$234$	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	$-0.412845\pi$
$241$	2023.30	0.540797	0.270398	+	0.962749i	$0.412845\pi$
$242$	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	$-0.533661\pi$
$257$	−869.760	−0.211106	−0.105553	+	0.994414i	$0.533661\pi$
$258$	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	$-0.307522\pi$
$263$	4849.52	1.13701	0.568506	+	0.822679i	$0.307522\pi$
$264$	−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	$-0.422293\pi$
$277$	2228.63	0.483412	0.241706	+	0.970350i	$0.422293\pi$
$278$	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	$-0.272452\pi$
$313$	7259.87	1.31103	0.655515	+	0.755182i	$0.272452\pi$
$314$	−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	$-0.711034\pi$
$331$	−7412.74	−1.23094	−0.615470	+	0.788161i	$0.711034\pi$
$332$	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	$-0.441141\pi$
$347$	2376.88	0.367716	0.183858	+	0.982953i	$0.441141\pi$
$348$	5184.83	0.798666
$349$	2443.29	0.374747	0.187373	−	0.982289i	$-0.440003\pi$
$349$	2443.29	0.374747	0.187373	+	0.982289i	$0.440003\pi$
$350$	−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	$-0.546333\pi$
$373$	−2089.79	−0.290095	−0.145047	+	0.989425i	$0.546333\pi$
$374$	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	$-0.438219\pi$
$383$	2891.35	0.385747	0.192874	+	0.981224i	$0.438219\pi$
$384$	−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	$-0.325243\pi$
$389$	8007.52	1.04370	0.521848	+	0.853039i	$0.325243\pi$
$390$	−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	$-0.409718\pi$
$409$	4629.41	0.559681	0.279840	+	0.960047i	$0.409718\pi$
$410$	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	$-0.561770\pi$
$419$	−3307.85	−0.385678	−0.192839	+	0.981230i	$0.561770\pi$
$420$	−1229.59	−0.142852
$421$	242.081	0.0280245	0.0140122	−	0.999902i	$-0.495540\pi$
$421$	242.081	0.0280245	0.0140122	+	0.999902i	$0.495540\pi$
$422$	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	$-0.612367\pi$
$433$	−6230.06	−0.691450	−0.345725	+	0.938336i	$0.612367\pi$
$434$	−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	$-0.438098\pi$
$449$	3677.16	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$450$	−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	$-0.664515\pi$
$457$	−9654.94	−0.988270	−0.494135	+	0.869385i	$0.664515\pi$
$458$	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	$-0.637981\pi$
$463$	−8369.16	−0.840060	−0.420030	+	0.907510i	$0.637981\pi$
$464$	−2107.47	−0.210855
$465$	6010.80	0.599450
$466$	8249.53	0.820069
$467$	11897.9	1.17895	0.589475	−	0.807786i	$-0.299334\pi$
$467$	11897.9	1.17895	0.589475	+	0.807786i	$0.299334\pi$
$468$	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	$-0.463952\pi$
$491$	2458.96	0.226011	0.113006	+	0.993594i	$0.463952\pi$
$492$	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	$-0.371695\pi$
$499$	8744.82	0.784513	0.392256	+	0.919856i	$0.371695\pi$
$500$	−12942.1	−1.15758
$501$	3053.87	0.272329
$502$	−9947.20	−0.884393
$503$	−12931.7	−1.14631	−0.573157	−	0.819446i	$-0.694281\pi$
$503$	−12931.7	−1.14631	−0.573157	+	0.819446i	$0.694281\pi$
$504$	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	$-0.472787\pi$
$521$	2030.86	0.170775	0.0853875	+	0.996348i	$0.472787\pi$
$522$	−25758.4	−2.15980
$523$	−13361.0	−1.11708	−0.558542	−	0.829477i	$-0.688639\pi$
$523$	−13361.0	−1.11708	−0.558542	+	0.829477i	$0.688639\pi$
$524$	−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	$-0.665449\pi$
$571$	−13553.9	−0.993365	−0.496682	+	0.867932i	$0.665449\pi$
$572$	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	$-0.573266\pi$
$577$	−6324.19	−0.456290	−0.228145	+	0.973627i	$0.573266\pi$
$578$	−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	$-0.770999\pi$
$587$	−21394.9	−1.50437	−0.752183	+	0.658954i	$0.770999\pi$
$588$	−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	$-0.296342\pi$
$593$	17243.2	1.19409	0.597043	+	0.802209i	$0.296342\pi$
$594$	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	$-0.464807\pi$
$601$	3251.39	0.220677	0.110338	+	0.993894i	$0.464807\pi$
$602$	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	$-0.345600\pi$
$607$	13945.8	0.932526	0.466263	+	0.884646i	$0.345600\pi$
$608$	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	$-0.598288\pi$
$631$	−9633.83	−0.607792	−0.303896	+	0.952705i	$0.598288\pi$
$632$	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	$-0.608042\pi$
$641$	−10806.5	−0.665885	−0.332943	+	0.942947i	$0.608042\pi$
$642$	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	$-0.367842\pi$
$647$	13276.4	0.806722	0.403361	+	0.915041i	$0.367842\pi$
$648$	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	$-0.427257\pi$
$653$	7560.53	0.453088	0.226544	+	0.974001i	$0.427257\pi$
$654$	−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	$-0.776819\pi$
$673$	−26681.2	−1.52821	−0.764105	+	0.645091i	$0.776819\pi$
$674$	54295.2	3.10293
$675$	−4034.36	−0.230048
$676$	−9584.15	−0.545297
$677$	−24196.9	−1.37365	−0.686826	−	0.726821i	$-0.740997\pi$
$677$	−24196.9	−1.37365	−0.686826	+	0.726821i	$0.740997\pi$
$678$	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	$-0.333523\pi$
$691$	18145.5	0.998970	0.499485	+	0.866322i	$0.333523\pi$
$692$	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	$-0.578424\pi$
$727$	−9561.59	−0.487785	−0.243892	+	0.969802i	$0.578424\pi$
$728$	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	$-0.391158\pi$
$733$	13308.7	0.670623	0.335312	+	0.942107i	$0.391158\pi$
$734$	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	$-0.631818\pi$
$739$	−16167.3	−0.804768	−0.402384	+	0.915471i	$0.631818\pi$
$740$	−57340.5	−2.84849
$741$	2627.03	0.130238
$742$	699.466	0.0346068
$743$	−25680.2	−1.26799	−0.633994	−	0.773338i	$-0.718585\pi$
$743$	−25680.2	−1.26799	−0.633994	+	0.773338i	$0.718585\pi$
$744$	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	$-0.599753\pi$
$751$	−12689.2	−0.616559	−0.308279	+	0.951296i	$0.599753\pi$
$752$	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	$-0.362569\pi$
$757$	17431.3	0.836926	0.418463	+	0.908234i	$0.362569\pi$
$758$	−58576.5	−2.80685
$759$	246.847	0.0118050
$760$	−10389.7	−0.495886
$761$	16997.5	0.809670	0.404835	−	0.914390i	$-0.367329\pi$
$761$	16997.5	0.809670	0.404835	+	0.914390i	$0.367329\pi$
$762$	−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	$-0.358665\pi$
$773$	18464.3	0.859138	0.429569	+	0.903034i	$0.358665\pi$
$774$	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	$-0.792695\pi$
$811$	−36736.8	−1.59063	−0.795317	+	0.606194i	$0.792695\pi$
$812$	−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	$-0.608324\pi$
$829$	−15933.9	−0.667560	−0.333780	+	0.942651i	$0.608324\pi$
$830$	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	$-0.660910\pi$
$839$	−23536.8	−0.968512	−0.484256	+	0.874926i	$0.660910\pi$
$840$	−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	$-0.674037\pi$
$859$	−26179.1	−1.03983	−0.519917	+	0.854217i	$0.674037\pi$
$860$	0	0
$861$	−1926.43	−0.0762516
$862$	−74181.7	−2.93113
$863$	10987.8	0.433404	0.216702	−	0.976238i	$-0.430470\pi$
$863$	10987.8	0.433404	0.216702	+	0.976238i	$0.430470\pi$
$864$	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	$-0.771736\pi$
$887$	−39821.5	−1.50741	−0.753706	+	0.657212i	$0.771736\pi$
$888$	−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	$-0.584880\pi$
$911$	−14491.2	−0.527019	−0.263509	+	0.964657i	$0.584880\pi$
$912$	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	$-0.462835\pi$
$929$	6597.01	0.232983	0.116491	+	0.993192i	$0.462835\pi$
$930$	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	$-0.630360\pi$
$937$	−22841.5	−0.796370	−0.398185	+	0.917305i	$0.630360\pi$
$938$	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	$-0.568123\pi$
$953$	−12496.6	−0.424768	−0.212384	+	0.977186i	$0.568123\pi$
$954$	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	$-0.444742\pi$
$983$	10646.8	0.345453	0.172727	+	0.984970i	$0.444742\pi$
$984$	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	$-0.499649\pi$
$991$	68.7730	0.00220449	0.00110224	+	0.999999i	$0.499649\pi$
$992$	−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	$-0.148821\pi$
$997$	56204.3	1.78536	0.892682	+	0.450686i	$0.148821\pi$
$998$	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.j.1.43	yes	50
43.42	odd	2		1849.4.a.i.1.8	✓	50

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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