LMFDB - Embedded newform 1849.4.a.j.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.84969 q^{2} +3.08645 q^{3} -4.57866 q^{4} +18.1899 q^{5} -5.70896 q^{6} -24.2083 q^{7} +23.2666 q^{8} -17.4738 q^{9} +O(q^{10})$	\(q-1.84969 q^{2} +3.08645 q^{3} -4.57866 q^{4} +18.1899 q^{5} -5.70896 q^{6} -24.2083 q^{7} +23.2666 q^{8} -17.4738 q^{9} -33.6456 q^{10} +49.5002 q^{11} -14.1318 q^{12} -23.1645 q^{13} +44.7778 q^{14} +56.1421 q^{15} -6.40651 q^{16} -2.27673 q^{17} +32.3211 q^{18} +103.752 q^{19} -83.2854 q^{20} -74.7178 q^{21} -91.5597 q^{22} -159.479 q^{23} +71.8111 q^{24} +205.872 q^{25} +42.8469 q^{26} -137.266 q^{27} +110.842 q^{28} -309.695 q^{29} -103.845 q^{30} +93.3796 q^{31} -174.283 q^{32} +152.780 q^{33} +4.21124 q^{34} -440.347 q^{35} +80.0068 q^{36} -1.12136 q^{37} -191.909 q^{38} -71.4959 q^{39} +423.216 q^{40} +386.766 q^{41} +138.204 q^{42} -226.645 q^{44} -317.847 q^{45} +294.985 q^{46} +214.825 q^{47} -19.7734 q^{48} +243.043 q^{49} -380.798 q^{50} -7.02702 q^{51} +106.062 q^{52} -96.4065 q^{53} +253.899 q^{54} +900.402 q^{55} -563.245 q^{56} +320.226 q^{57} +572.838 q^{58} -135.840 q^{59} -257.056 q^{60} -374.631 q^{61} -172.723 q^{62} +423.012 q^{63} +373.620 q^{64} -421.359 q^{65} -282.594 q^{66} +266.093 q^{67} +10.4244 q^{68} -492.223 q^{69} +814.503 q^{70} +438.610 q^{71} -406.556 q^{72} -809.464 q^{73} +2.07417 q^{74} +635.413 q^{75} -475.047 q^{76} -1198.32 q^{77} +132.245 q^{78} -1055.64 q^{79} -116.534 q^{80} +48.1284 q^{81} -715.396 q^{82} -429.900 q^{83} +342.108 q^{84} -41.4135 q^{85} -955.857 q^{87} +1151.70 q^{88} -136.454 q^{89} +587.917 q^{90} +560.773 q^{91} +730.200 q^{92} +288.211 q^{93} -397.358 q^{94} +1887.24 q^{95} -537.914 q^{96} +25.6218 q^{97} -449.553 q^{98} -864.958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.84969	−0.653962	−0.326981	−	0.945031i	$-0.606031\pi$
$2$	−1.84969	−0.653962	−0.326981	+	0.945031i	$0.606031\pi$
$3$	3.08645	0.593987	0.296994	−	0.954879i	$-0.404016\pi$
$3$	3.08645	0.593987	0.296994	+	0.954879i	$0.404016\pi$
$4$	−4.57866	−0.572333
$5$	18.1899	1.62695	0.813476	−	0.581598i	$-0.197572\pi$
$5$	18.1899	1.62695	0.813476	+	0.581598i	$0.197572\pi$
$6$	−5.70896	−0.388445
$7$	−24.2083	−1.30713	−0.653563	−	0.756872i	$-0.726727\pi$
$7$	−24.2083	−1.30713	−0.653563	+	0.756872i	$0.726727\pi$
$8$	23.2666	1.02825
$9$	−17.4738	−0.647179
$10$	−33.6456	−1.06397
$11$	49.5002	1.35681	0.678403	−	0.734690i	$-0.262673\pi$
$11$	49.5002	1.35681	0.678403	+	0.734690i	$0.262673\pi$
$12$	−14.1318	−0.339959
$13$	−23.1645	−0.494205	−0.247102	−	0.968989i	$-0.579478\pi$
$13$	−23.1645	−0.494205	−0.247102	+	0.968989i	$0.579478\pi$
$14$	44.7778	0.854812
$15$	56.1421	0.966389
$16$	−6.40651	−0.100102
$17$	−2.27673	−0.0324817	−0.0162409	−	0.999868i	$-0.505170\pi$
$17$	−2.27673	−0.0324817	−0.0162409	+	0.999868i	$0.505170\pi$
$18$	32.3211	0.423231
$19$	103.752	1.25276	0.626379	−	0.779519i	$-0.284536\pi$
$19$	103.752	1.25276	0.626379	+	0.779519i	$0.284536\pi$
$20$	−83.2854	−0.931159
$21$	−74.7178	−0.776417
$22$	−91.5597	−0.887300
$23$	−159.479	−1.44581	−0.722905	−	0.690948i	$-0.757193\pi$
$23$	−159.479	−1.44581	−0.722905	+	0.690948i	$0.757193\pi$
$24$	71.8111	0.610766
$25$	205.872	1.64697
$26$	42.8469	0.323191
$27$	−137.266	−0.978404
$28$	110.842	0.748112
$29$	−309.695	−1.98306	−0.991532	−	0.129863i	$-0.958546\pi$
$29$	−309.695	−1.98306	−0.991532	+	0.129863i	$0.958546\pi$
$30$	−103.845	−0.631982
$31$	93.3796	0.541015	0.270508	−	0.962718i	$-0.412809\pi$
$31$	93.3796	0.541015	0.270508	+	0.962718i	$0.412809\pi$
$32$	−174.283	−0.962784
$33$	152.780	0.805925
$34$	4.21124	0.0212418
$35$	−440.347	−2.12663
$36$	80.0068	0.370402
$37$	−1.12136	−0.00498247	−0.00249123	−	0.999997i	$-0.500793\pi$
$37$	−1.12136	−0.00498247	−0.00249123	+	0.999997i	$0.500793\pi$
$38$	−191.909	−0.819257
$39$	−71.4959	−0.293551
$40$	423.216	1.67291
$41$	386.766	1.47324	0.736619	−	0.676308i	$-0.236421\pi$
$41$	386.766	1.47324	0.736619	+	0.676308i	$0.236421\pi$
$42$	138.204	0.507747
$43$	0	0
$43$	0	0
$44$	−226.645	−0.776545
$45$	−317.847	−1.05293
$46$	294.985	0.945505
$47$	214.825	0.666710	0.333355	−	0.942801i	$-0.391819\pi$
$47$	214.825	0.666710	0.333355	+	0.942801i	$0.391819\pi$
$48$	−19.7734	−0.0594592
$49$	243.043	0.708581
$50$	−380.798	−1.07706
$51$	−7.02702	−0.0192937
$52$	106.062	0.282850
$53$	−96.4065	−0.249858	−0.124929	−	0.992166i	$-0.539870\pi$
$53$	−96.4065	−0.249858	−0.124929	+	0.992166i	$0.539870\pi$
$54$	253.899	0.639839
$55$	900.402	2.20746
$56$	−563.245	−1.34405
$57$	320.226	0.744122
$58$	572.838	1.29685
$59$	−135.840	−0.299744	−0.149872	−	0.988705i	$-0.547886\pi$
$59$	−135.840	−0.299744	−0.149872	+	0.988705i	$0.547886\pi$
$60$	−257.056	−0.553097
$61$	−374.631	−0.786337	−0.393169	−	0.919466i	$-0.628621\pi$
$61$	−374.631	−0.786337	−0.393169	+	0.919466i	$0.628621\pi$
$62$	−172.723	−0.353804
$63$	423.012	0.845945
$64$	373.620	0.729726
$65$	−421.359	−0.804048
$66$	−282.594	−0.527045
$67$	266.093	0.485200	0.242600	−	0.970126i	$-0.422000\pi$
$67$	266.093	0.485200	0.242600	+	0.970126i	$0.422000\pi$
$68$	10.4244	0.0185904
$69$	−492.223	−0.858792
$70$	814.503	1.39074
$71$	438.610	0.733147	0.366574	−	0.930389i	$-0.380531\pi$
$71$	438.610	0.733147	0.366574	+	0.930389i	$0.380531\pi$
$72$	−406.556	−0.665460
$73$	−809.464	−1.29782	−0.648908	−	0.760867i	$-0.724774\pi$
$73$	−809.464	−1.29782	−0.648908	+	0.760867i	$0.724774\pi$
$74$	2.07417	0.00325835
$75$	635.413	0.978282
$76$	−475.047	−0.716995
$77$	−1198.32	−1.77352
$78$	132.245	0.191972
$79$	−1055.64	−1.50341	−0.751704	−	0.659501i	$-0.770768\pi$
$79$	−1055.64	−1.50341	−0.751704	+	0.659501i	$0.770768\pi$
$80$	−116.534	−0.162861
$81$	48.1284	0.0660197
$82$	−715.396	−0.963443
$83$	−429.900	−0.568526	−0.284263	−	0.958746i	$-0.591749\pi$
$83$	−429.900	−0.568526	−0.284263	+	0.958746i	$0.591749\pi$
$84$	342.108	0.444369
$85$	−41.4135	−0.0528462
$86$	0	0
$87$	−955.857	−1.17791
$88$	1151.70	1.39513
$89$	−136.454	−0.162517	−0.0812587	−	0.996693i	$-0.525894\pi$
$89$	−136.454	−0.162517	−0.0812587	+	0.996693i	$0.525894\pi$
$90$	587.917	0.688576
$91$	560.773	0.645988
$92$	730.200	0.827485
$93$	288.211	0.321356
$94$	−397.358	−0.436003
$95$	1887.24	2.03818
$96$	−537.914	−0.571882
$97$	25.6218	0.0268196	0.0134098	−	0.999910i	$-0.495731\pi$
$97$	25.6218	0.0268196	0.0134098	+	0.999910i	$0.495731\pi$
$98$	−449.553	−0.463385
$99$	−864.958	−0.878096
$100$	−942.618	−0.942618
$101$	−1661.81	−1.63719	−0.818593	−	0.574373i	$-0.805246\pi$
$101$	−1661.81	−1.63719	−0.818593	+	0.574373i	$0.805246\pi$
$102$	12.9978	0.0126174
$103$	22.0462	0.0210901	0.0105450	−	0.999944i	$-0.496643\pi$
$103$	22.0462	0.0210901	0.0105450	+	0.999944i	$0.496643\pi$
$104$	−538.957	−0.508165
$105$	−1359.11	−1.26319
$106$	178.322	0.163397
$107$	−891.422	−0.805392	−0.402696	−	0.915334i	$-0.631927\pi$
$107$	−891.422	−0.805392	−0.402696	+	0.915334i	$0.631927\pi$
$108$	628.496	0.559973
$109$	1372.93	1.20644	0.603222	−	0.797573i	$-0.293883\pi$
$109$	1372.93	1.20644	0.603222	+	0.797573i	$0.293883\pi$
$110$	−1665.46	−1.44359
$111$	−3.46104	−0.00295952
$112$	155.091	0.130846
$113$	938.442	0.781249	0.390625	−	0.920550i	$-0.372259\pi$
$113$	938.442	0.781249	0.390625	+	0.920550i	$0.372259\pi$
$114$	−592.317	−0.486628
$115$	−2900.90	−2.35226
$116$	1417.99	1.13497
$117$	404.772	0.319839
$118$	251.262	0.196021
$119$	55.1159	0.0424577
$120$	1306.24	0.993687
$121$	1119.27	0.840921
$122$	692.949	0.514235
$123$	1193.73	0.875085
$124$	−427.554	−0.309641
$125$	1471.05	1.05260
$126$	−782.440	−0.553216
$127$	−2503.68	−1.74934	−0.874669	−	0.484721i	$-0.838921\pi$
$127$	−2503.68	−1.74934	−0.874669	+	0.484721i	$0.838921\pi$
$128$	703.181	0.485570
$129$	0	0
$130$	779.381	0.525817
$131$	168.167	0.112159	0.0560794	−	0.998426i	$-0.482140\pi$
$131$	168.167	0.112159	0.0560794	+	0.998426i	$0.482140\pi$
$132$	−699.527	−0.461258
$133$	−2511.67	−1.63751
$134$	−492.188	−0.317303
$135$	−2496.86	−1.59182
$136$	−52.9718	−0.0333992
$137$	−357.390	−0.222875	−0.111438	−	0.993771i	$-0.535546\pi$
$137$	−357.390	−0.222875	−0.111438	+	0.993771i	$0.535546\pi$
$138$	910.457	0.561618
$139$	493.366	0.301056	0.150528	−	0.988606i	$-0.451903\pi$
$139$	493.366	0.301056	0.150528	+	0.988606i	$0.451903\pi$
$140$	2016.20	1.21714
$141$	663.045	0.396017
$142$	−811.291	−0.479451
$143$	−1146.64	−0.670540
$144$	111.946	0.0647837
$145$	−5633.31	−3.22635
$146$	1497.25	0.848723
$147$	750.140	0.420888
$148$	5.13435	0.00285163
$149$	−187.920	−0.103322	−0.0516610	−	0.998665i	$-0.516452\pi$
$149$	−187.920	−0.103322	−0.0516610	+	0.998665i	$0.516452\pi$
$150$	−1175.31	−0.639760
$151$	1664.02	0.896794	0.448397	−	0.893834i	$-0.351995\pi$
$151$	1664.02	0.896794	0.448397	+	0.893834i	$0.351995\pi$
$152$	2413.96	1.28814
$153$	39.7833	0.0210215
$154$	2216.51	1.15981
$155$	1698.56	0.880206
$156$	327.356	0.168009
$157$	3303.37	1.67922	0.839611	−	0.543188i	$-0.182783\pi$
$157$	3303.37	1.67922	0.839611	+	0.543188i	$0.182783\pi$
$158$	1952.61	0.983172
$159$	−297.554	−0.148412
$160$	−3170.18	−1.56640
$161$	3860.71	1.88986
$162$	−89.0223	−0.0431744
$163$	1552.90	0.746212	0.373106	−	0.927789i	$-0.378293\pi$
$163$	1552.90	0.746212	0.373106	+	0.927789i	$0.378293\pi$
$164$	−1770.87	−0.843183
$165$	2779.04	1.31120
$166$	795.180	0.371795
$167$	2180.15	1.01021	0.505105	−	0.863058i	$-0.331454\pi$
$167$	2180.15	1.01021	0.505105	+	0.863058i	$0.331454\pi$
$168$	−1738.43	−0.798348
$169$	−1660.41	−0.755762
$170$	76.6020	0.0345594
$171$	−1812.95	−0.810759
$172$	0	0
$173$	−1547.13	−0.679918	−0.339959	−	0.940440i	$-0.610413\pi$
$173$	−1547.13	−0.679918	−0.339959	+	0.940440i	$0.610413\pi$
$174$	1768.03	0.770312
$175$	−4983.81	−2.15280
$176$	−317.123	−0.135819
$177$	−419.264	−0.178044
$178$	252.396	0.106280
$179$	−2721.23	−1.13628	−0.568140	−	0.822932i	$-0.692337\pi$
$179$	−2721.23	−1.13628	−0.568140	+	0.822932i	$0.692337\pi$
$180$	1455.31	0.602626
$181$	−973.771	−0.399889	−0.199944	−	0.979807i	$-0.564076\pi$
$181$	−973.771	−0.399889	−0.199944	+	0.979807i	$0.564076\pi$
$182$	−1037.25	−0.422452
$183$	−1156.28	−0.467074
$184$	−3710.52	−1.48665
$185$	−20.3975	−0.00810624
$186$	−533.100	−0.210155
$187$	−112.699	−0.0440713
$188$	−983.610	−0.381580
$189$	3322.99	1.27890
$190$	−3490.80	−1.33289
$191$	−741.917	−0.281064	−0.140532	−	0.990076i	$-0.544881\pi$
$191$	−741.917	−0.281064	−0.140532	+	0.990076i	$0.544881\pi$
$192$	1153.16	0.433448
$193$	437.336	0.163109	0.0815547	−	0.996669i	$-0.474011\pi$
$193$	437.336	0.163109	0.0815547	+	0.996669i	$0.474011\pi$
$194$	−47.3923	−0.0175390
$195$	−1300.50	−0.477594
$196$	−1112.81	−0.405544
$197$	1769.20	0.639848	0.319924	−	0.947443i	$-0.396343\pi$
$197$	1769.20	0.639848	0.319924	+	0.947443i	$0.396343\pi$
$198$	1599.90	0.574242
$199$	−2442.81	−0.870181	−0.435091	−	0.900387i	$-0.643284\pi$
$199$	−2442.81	−0.870181	−0.435091	+	0.900387i	$0.643284\pi$
$200$	4789.93	1.69350
$201$	821.282	0.288203
$202$	3073.82	1.07066
$203$	7497.19	2.59212
$204$	32.1744	0.0110424
$205$	7035.24	2.39689
$206$	−40.7785	−0.0137921
$207$	2786.70	0.935697
$208$	148.403	0.0494708
$209$	5135.75	1.69975
$210$	2513.92	0.826081
$211$	−2447.16	−0.798433	−0.399217	−	0.916857i	$-0.630718\pi$
$211$	−2447.16	−0.798433	−0.399217	+	0.916857i	$0.630718\pi$
$212$	441.413	0.143002
$213$	1353.75	0.435480
$214$	1648.85	0.526696
$215$	0	0
$216$	−3193.71	−1.00604
$217$	−2260.56	−0.707175
$218$	−2539.48	−0.788970
$219$	−2498.37	−0.770886
$220$	−4122.64	−1.26340
$221$	52.7393	0.0160526
$222$	6.40183	0.00193542
$223$	1162.40	0.349059	0.174529	−	0.984652i	$-0.444160\pi$
$223$	1162.40	0.349059	0.174529	+	0.984652i	$0.444160\pi$
$224$	4219.09	1.25848
$225$	−3597.37	−1.06589
$226$	−1735.82	−0.510908
$227$	3586.53	1.04866	0.524332	−	0.851514i	$-0.324315\pi$
$227$	3586.53	1.04866	0.524332	+	0.851514i	$0.324315\pi$
$228$	−1466.21	−0.425886
$229$	−3162.75	−0.912666	−0.456333	−	0.889809i	$-0.650837\pi$
$229$	−3162.75	−0.912666	−0.456333	+	0.889809i	$0.650837\pi$
$230$	5365.75	1.53829
$231$	−3698.54	−1.05345
$232$	−7205.53	−2.03908
$233$	−3331.29	−0.936652	−0.468326	−	0.883556i	$-0.655143\pi$
$233$	−3331.29	−0.936652	−0.468326	+	0.883556i	$0.655143\pi$
$234$	−748.700	−0.209163
$235$	3907.63	1.08471
$236$	621.967	0.171553
$237$	−3258.19	−0.893005
$238$	−101.947	−0.0277657
$239$	−3470.98	−0.939410	−0.469705	−	0.882823i	$-0.655640\pi$
$239$	−3470.98	−0.939410	−0.469705	+	0.882823i	$0.655640\pi$
$240$	−359.675	−0.0967372
$241$	−3904.03	−1.04349	−0.521744	−	0.853102i	$-0.674718\pi$
$241$	−3904.03	−1.04349	−0.521744	+	0.853102i	$0.674718\pi$
$242$	−2070.29	−0.549931
$243$	3854.73	1.01762
$244$	1715.31	0.450047
$245$	4420.93	1.15283
$246$	−2208.03	−0.572273
$247$	−2403.36	−0.619119
$248$	2172.62	0.556297
$249$	−1326.86	−0.337697
$250$	−2720.98	−0.688359
$251$	−5320.94	−1.33807	−0.669034	−	0.743232i	$-0.733292\pi$
$251$	−5320.94	−1.33807	−0.669034	+	0.743232i	$0.733292\pi$
$252$	−1936.83	−0.484162
$253$	−7894.22	−1.96168
$254$	4631.03	1.14400
$255$	−127.821	−0.0313900
$256$	−4289.62	−1.04727
$257$	21.4980	0.00521793	0.00260896	−	0.999997i	$-0.499170\pi$
$257$	21.4980	0.00521793	0.00260896	+	0.999997i	$0.499170\pi$
$258$	0	0
$259$	27.1464	0.00651272
$260$	1929.26	0.460183
$261$	5411.55	1.28340
$262$	−311.056	−0.0733477
$263$	−2887.95	−0.677105	−0.338553	−	0.940947i	$-0.609937\pi$
$263$	−2887.95	−0.677105	−0.338553	+	0.940947i	$0.609937\pi$
$264$	3554.66	0.828690
$265$	−1753.62	−0.406506
$266$	4645.80	1.07087
$267$	−421.157	−0.0965333
$268$	−1218.35	−0.277696
$269$	−6873.83	−1.55801	−0.779005	−	0.627018i	$-0.784275\pi$
$269$	−6873.83	−1.55801	−0.779005	+	0.627018i	$0.784275\pi$
$270$	4618.40	1.04099
$271$	−6722.51	−1.50688	−0.753438	−	0.657518i	$-0.771606\pi$
$271$	−6722.51	−1.50688	−0.753438	+	0.657518i	$0.771606\pi$
$272$	14.5859	0.00325147
$273$	1730.80	0.383709
$274$	661.060	0.145752
$275$	10190.7	2.23462
$276$	2253.72	0.491515
$277$	−7511.83	−1.62939	−0.814697	−	0.579887i	$-0.803097\pi$
$277$	−7511.83	−1.62939	−0.814697	+	0.579887i	$0.803097\pi$
$278$	−912.571	−0.196879
$279$	−1631.70	−0.350134
$280$	−10245.4	−2.18670
$281$	−6564.63	−1.39364	−0.696820	−	0.717246i	$-0.745403\pi$
$281$	−6564.63	−1.39364	−0.696820	+	0.717246i	$0.745403\pi$
$282$	−1226.42	−0.258981
$283$	982.494	0.206372	0.103186	−	0.994662i	$-0.467096\pi$
$283$	982.494	0.206372	0.103186	+	0.994662i	$0.467096\pi$
$284$	−2008.25	−0.419605
$285$	5824.87	1.21065
$286$	2120.93	0.438508
$287$	−9362.97	−1.92571
$288$	3045.38	0.623094
$289$	−4907.82	−0.998945
$290$	10419.8	2.10991
$291$	79.0805	0.0159305
$292$	3706.26	0.742783
$293$	4099.32	0.817354	0.408677	−	0.912679i	$-0.365990\pi$
$293$	4099.32	0.817354	0.408677	+	0.912679i	$0.365990\pi$
$294$	−1387.52	−0.275245
$295$	−2470.92	−0.487669
$296$	−26.0903	−0.00512321
$297$	−6794.70	−1.32750
$298$	347.592	0.0675687
$299$	3694.24	0.714526
$300$	−2909.34	−0.559903
$301$	0	0
$302$	−3077.91	−0.586470
$303$	−5129.08	−0.972468
$304$	−664.690	−0.125403
$305$	−6814.49	−1.27933
$306$	−73.5865	−0.0137473
$307$	6286.95	1.16878	0.584390	−	0.811473i	$-0.301334\pi$
$307$	6286.95	1.16878	0.584390	+	0.811473i	$0.301334\pi$
$308$	5486.69	1.01504
$309$	68.0445	0.0125272
$310$	−3141.81	−0.575622
$311$	−9190.56	−1.67572	−0.837860	−	0.545885i	$-0.816193\pi$
$311$	−9190.56	−1.67572	−0.837860	+	0.545885i	$0.816193\pi$
$312$	−1663.46	−0.301843
$313$	−2173.57	−0.392516	−0.196258	−	0.980552i	$-0.562879\pi$
$313$	−2173.57	−0.392516	−0.196258	+	0.980552i	$0.562879\pi$
$314$	−6110.20	−1.09815
$315$	7694.54	1.37631
$316$	4833.44	0.860450
$317$	8485.50	1.50345	0.751724	−	0.659478i	$-0.229223\pi$
$317$	8485.50	1.50345	0.751724	+	0.659478i	$0.229223\pi$
$318$	550.381	0.0970560
$319$	−15329.9	−2.69063
$320$	6796.10	1.18723
$321$	−2751.33	−0.478393
$322$	−7141.10	−1.23589
$323$	−236.216	−0.0406917
$324$	−220.364	−0.0377853
$325$	−4768.91	−0.813943
$326$	−2872.38	−0.487995
$327$	4237.47	0.716613
$328$	8998.73	1.51485
$329$	−5200.54	−0.871475
$330$	−5140.36	−0.857477
$331$	−3108.26	−0.516149	−0.258075	−	0.966125i	$-0.583088\pi$
$331$	−3108.26	−0.516149	−0.258075	+	0.966125i	$0.583088\pi$
$332$	1968.37	0.325386
$333$	19.5945	0.00322455
$334$	−4032.59	−0.660640
$335$	4840.20	0.789398
$336$	478.680	0.0777207
$337$	6066.72	0.980639	0.490319	−	0.871543i	$-0.336880\pi$
$337$	6066.72	0.980639	0.490319	+	0.871543i	$0.336880\pi$
$338$	3071.23	0.494240
$339$	2896.45	0.464052
$340$	189.619	0.0302456
$341$	4622.30	0.734052
$342$	3353.39	0.530206
$343$	2419.79	0.380922
$344$	0	0
$345$	−8953.48	−1.39721
$346$	2861.70	0.444641
$347$	−1685.20	−0.260710	−0.130355	−	0.991467i	$-0.541612\pi$
$347$	−1685.20	−0.260710	−0.130355	+	0.991467i	$0.541612\pi$
$348$	4376.55	0.674160
$349$	−6257.79	−0.959805	−0.479902	−	0.877322i	$-0.659328\pi$
$349$	−6257.79	−0.959805	−0.479902	+	0.877322i	$0.659328\pi$
$350$	9218.49	1.40785
$351$	3179.70	0.483532
$352$	−8627.01	−1.30631
$353$	5204.31	0.784695	0.392347	−	0.919817i	$-0.371663\pi$
$353$	5204.31	0.784695	0.392347	+	0.919817i	$0.371663\pi$
$354$	775.506	0.116434
$355$	7978.27	1.19280
$356$	624.775	0.0930141
$357$	170.112	0.0252193
$358$	5033.41	0.743084
$359$	6365.10	0.935758	0.467879	−	0.883793i	$-0.345018\pi$
$359$	6365.10	0.935758	0.467879	+	0.883793i	$0.345018\pi$
$360$	−7395.21	−1.08267
$361$	3905.53	0.569403
$362$	1801.17	0.261512
$363$	3454.56	0.499496
$364$	−2567.59	−0.369721
$365$	−14724.0	−2.11148
$366$	2138.75	0.305449
$367$	6551.85	0.931891	0.465945	−	0.884813i	$-0.345714\pi$
$367$	6551.85	0.931891	0.465945	+	0.884813i	$0.345714\pi$
$368$	1021.70	0.144728
$369$	−6758.29	−0.953449
$370$	37.7289	0.00530117
$371$	2333.84	0.326595
$372$	−1319.62	−0.183923
$373$	−5826.94	−0.808868	−0.404434	−	0.914567i	$-0.632531\pi$
$373$	−5826.94	−0.808868	−0.404434	+	0.914567i	$0.632531\pi$
$374$	208.457	0.0288210
$375$	4540.32	0.625230
$376$	4998.23	0.685543
$377$	7173.91	0.980040
$378$	−6146.48	−0.836351
$379$	−1125.98	−0.152607	−0.0763033	−	0.997085i	$-0.524312\pi$
$379$	−1125.98	−0.152607	−0.0763033	+	0.997085i	$0.524312\pi$
$380$	−8641.05	−1.16652
$381$	−7727.49	−1.03908
$382$	1372.31	0.183805
$383$	8568.62	1.14318	0.571588	−	0.820541i	$-0.306328\pi$
$383$	8568.62	1.14318	0.571588	+	0.820541i	$0.306328\pi$
$384$	2170.33	0.288423
$385$	−21797.2	−2.88543
$386$	−808.933	−0.106667
$387$	0	0
$388$	−117.314	−0.0153498
$389$	−14675.3	−1.91277	−0.956383	−	0.292117i	$-0.905640\pi$
$389$	−14675.3	−1.91277	−0.956383	+	0.292117i	$0.905640\pi$
$390$	2405.52	0.312329
$391$	363.091	0.0469623
$392$	5654.78	0.728596
$393$	519.039	0.0666210
$394$	−3272.46	−0.418437
$395$	−19202.0	−2.44597
$396$	3960.35	0.502563
$397$	−10358.3	−1.30950	−0.654748	−	0.755848i	$-0.727225\pi$
$397$	−10358.3	−1.30950	−0.654748	+	0.755848i	$0.727225\pi$
$398$	4518.43	0.569066
$399$	−7752.14	−0.972662
$400$	−1318.92	−0.164865
$401$	2134.79	0.265851	0.132926	−	0.991126i	$-0.457563\pi$
$401$	2134.79	0.265851	0.132926	+	0.991126i	$0.457563\pi$
$402$	−1519.11	−0.188474
$403$	−2163.09	−0.267372
$404$	7608.85	0.937016
$405$	875.449	0.107411
$406$	−13867.4	−1.69515
$407$	−55.5077	−0.00676024
$408$	−163.495	−0.0198387
$409$	−2284.74	−0.276218	−0.138109	−	0.990417i	$-0.544102\pi$
$409$	−2284.74	−0.276218	−0.138109	+	0.990417i	$0.544102\pi$
$410$	−13013.0	−1.56748
$411$	−1103.07	−0.132385
$412$	−100.942	−0.0120705
$413$	3288.46	0.391803
$414$	−5154.53	−0.611911
$415$	−7819.83	−0.924965
$416$	4037.16	0.475813
$417$	1522.75	0.178823
$418$	−9499.53	−1.11157
$419$	−2378.66	−0.277340	−0.138670	−	0.990339i	$-0.544283\pi$
$419$	−2378.66	−0.277340	−0.138670	+	0.990339i	$0.544283\pi$
$420$	6222.90	0.722967
$421$	14655.8	1.69663	0.848313	−	0.529496i	$-0.177619\pi$
$421$	14655.8	1.69663	0.848313	+	0.529496i	$0.177619\pi$
$422$	4526.48	0.522145
$423$	−3753.81	−0.431481
$424$	−2243.05	−0.256915
$425$	−468.715	−0.0534965
$426$	−2504.01	−0.284788
$427$	9069.19	1.02784
$428$	4081.52	0.460953
$429$	−3539.06	−0.398292
$430$	0	0
$431$	−2467.24	−0.275738	−0.137869	−	0.990450i	$-0.544025\pi$
$431$	−2467.24	−0.275738	−0.137869	+	0.990450i	$0.544025\pi$
$432$	879.397	0.0979399
$433$	−14202.3	−1.57626	−0.788128	−	0.615512i	$-0.788949\pi$
$433$	−14202.3	−1.57626	−0.788128	+	0.615512i	$0.788949\pi$
$434$	4181.33	0.462466
$435$	−17386.9	−1.91641
$436$	−6286.17	−0.690488
$437$	−16546.3	−1.81125
$438$	4621.19	0.504131
$439$	−11109.1	−1.20776	−0.603881	−	0.797075i	$-0.706380\pi$
$439$	−11109.1	−1.20776	−0.603881	+	0.797075i	$0.706380\pi$
$440$	20949.3	2.26981
$441$	−4246.90	−0.458578
$442$	−97.5511	−0.0104978
$443$	−3377.46	−0.362230	−0.181115	−	0.983462i	$-0.557971\pi$
$443$	−3377.46	−0.362230	−0.181115	+	0.983462i	$0.557971\pi$
$444$	15.8469	0.00169383
$445$	−2482.07	−0.264408
$446$	−2150.07	−0.228271
$447$	−580.004	−0.0613719
$448$	−9044.71	−0.953845
$449$	8468.28	0.890073	0.445036	−	0.895512i	$-0.353191\pi$
$449$	8468.28	0.890073	0.445036	+	0.895512i	$0.353191\pi$
$450$	6654.00	0.697050
$451$	19145.0	1.99890
$452$	−4296.81	−0.447135
$453$	5135.91	0.532684
$454$	−6633.96	−0.685787
$455$	10200.4	1.05099
$456$	7450.56	0.765142
$457$	1014.40	0.103833	0.0519163	−	0.998651i	$-0.483467\pi$
$457$	1014.40	0.103833	0.0519163	+	0.998651i	$0.483467\pi$
$458$	5850.10	0.596850
$459$	312.519	0.0317802
$460$	13282.2	1.34628
$461$	−7226.46	−0.730086	−0.365043	−	0.930991i	$-0.618946\pi$
$461$	−7226.46	−0.730086	−0.365043	+	0.930991i	$0.618946\pi$
$462$	6841.14	0.688914
$463$	−15866.5	−1.59261	−0.796304	−	0.604897i	$-0.793214\pi$
$463$	−15866.5	−1.59261	−0.796304	+	0.604897i	$0.793214\pi$
$464$	1984.06	0.198508
$465$	5242.53	0.522831
$466$	6161.84	0.612535
$467$	15440.6	1.52999	0.764996	−	0.644035i	$-0.222741\pi$
$467$	15440.6	1.52999	0.764996	+	0.644035i	$0.222741\pi$
$468$	−1853.31	−0.183054
$469$	−6441.66	−0.634218
$470$	−7227.89	−0.709357
$471$	10195.7	0.997437
$472$	−3160.53	−0.308211
$473$	0	0
$474$	6026.63	0.583992
$475$	21359.7	2.06326
$476$	−252.357	−0.0243000
$477$	1684.59	0.161703
$478$	6420.22	0.614339
$479$	−15315.4	−1.46092	−0.730460	−	0.682956i	$-0.760694\pi$
$479$	−15315.4	−1.46092	−0.730460	+	0.682956i	$0.760694\pi$
$480$	−9784.59	−0.930424
$481$	25.9758	0.00246236
$482$	7221.23	0.682402
$483$	11915.9	1.12255
$484$	−5124.74	−0.481287
$485$	466.058	0.0436343
$486$	−7130.04	−0.665484
$487$	−4260.84	−0.396462	−0.198231	−	0.980155i	$-0.563520\pi$
$487$	−4260.84	−0.396462	−0.198231	+	0.980155i	$0.563520\pi$
$488$	−8716.38	−0.808549
$489$	4792.95	0.443240
$490$	−8177.32	−0.753906
$491$	8952.64	0.822865	0.411433	−	0.911440i	$-0.365029\pi$
$491$	8952.64	0.822865	0.411433	+	0.911440i	$0.365029\pi$
$492$	−5465.71	−0.500840
$493$	705.092	0.0644133
$494$	4445.47	0.404881
$495$	−15733.5	−1.42862
$496$	−598.237	−0.0541565
$497$	−10618.0	−0.958317
$498$	2454.28	0.220841
$499$	736.403	0.0660640	0.0330320	−	0.999454i	$-0.489484\pi$
$499$	736.403	0.0660640	0.0330320	+	0.999454i	$0.489484\pi$
$500$	−6735.44	−0.602436
$501$	6728.93	0.600052
$502$	9842.07	0.875046
$503$	995.504	0.0882451	0.0441226	−	0.999026i	$-0.485951\pi$
$503$	995.504	0.0882451	0.0441226	+	0.999026i	$0.485951\pi$
$504$	9842.04	0.869840
$505$	−30228.1	−2.66363
$506$	14601.8	1.28287
$507$	−5124.76	−0.448913
$508$	11463.5	1.00120
$509$	−12419.0	−1.08146	−0.540731	−	0.841195i	$-0.681852\pi$
$509$	−12419.0	−1.08146	−0.540731	+	0.841195i	$0.681852\pi$
$510$	236.428	0.0205279
$511$	19595.8	1.69641
$512$	2309.00	0.199306
$513$	−14241.7	−1.22570
$514$	−39.7645	−0.00341233
$515$	401.018	0.0343125
$516$	0	0
$517$	10633.8	0.904596
$518$	−50.2122	−0.00425907
$519$	−4775.13	−0.403863
$520$	−9803.57	−0.826760
$521$	10956.4	0.921325	0.460662	−	0.887575i	$-0.347612\pi$
$521$	10956.4	0.921325	0.460662	+	0.887575i	$0.347612\pi$
$522$	−10009.7	−0.839294
$523$	7978.77	0.667088	0.333544	−	0.942734i	$-0.391755\pi$
$523$	7978.77	0.667088	0.333544	+	0.942734i	$0.391755\pi$
$524$	−769.980	−0.0641922
$525$	−15382.3	−1.27874
$526$	5341.80	0.442801
$527$	−212.600	−0.0175731
$528$	−978.785	−0.0806745
$529$	13266.5	1.09036
$530$	3243.65	0.265840
$531$	2373.65	0.193988
$532$	11500.1	0.937203
$533$	−8959.23	−0.728082
$534$	779.008	0.0631291
$535$	−16214.9	−1.31034
$536$	6191.07	0.498906
$537$	−8398.93	−0.674936
$538$	12714.4	1.01888
$539$	12030.7	0.961406
$540$	11432.3	0.911049
$541$	15193.0	1.20739	0.603697	−	0.797214i	$-0.293694\pi$
$541$	15193.0	1.20739	0.603697	+	0.797214i	$0.293694\pi$
$542$	12434.5	0.985441
$543$	−3005.49	−0.237529
$544$	396.795	0.0312729
$545$	24973.4	1.96283
$546$	−3201.43	−0.250931
$547$	−5211.42	−0.407357	−0.203678	−	0.979038i	$-0.565290\pi$
$547$	−5211.42	−0.407357	−0.203678	+	0.979038i	$0.565290\pi$
$548$	1636.37	0.127559
$549$	6546.24	0.508901
$550$	−18849.6	−1.46136
$551$	−32131.5	−2.48430
$552$	−11452.3	−0.883051
$553$	25555.4	1.96515
$554$	13894.5	1.06556
$555$	−62.9558	−0.00481500
$556$	−2258.96	−0.172304
$557$	−5979.23	−0.454844	−0.227422	−	0.973796i	$-0.573030\pi$
$557$	−5979.23	−0.454844	−0.227422	+	0.973796i	$0.573030\pi$
$558$	3018.13	0.228974
$559$	0	0
$560$	2821.09	0.212880
$561$	−347.839	−0.0261778
$562$	12142.5	0.911389
$563$	−12821.9	−0.959819	−0.479910	−	0.877318i	$-0.659331\pi$
$563$	−12821.9	−0.959819	−0.479910	+	0.877318i	$0.659331\pi$
$564$	−3035.86	−0.226654
$565$	17070.1	1.27106
$566$	−1817.30	−0.134959
$567$	−1165.11	−0.0862961
$568$	10205.0	0.753857
$569$	−17386.3	−1.28097	−0.640486	−	0.767970i	$-0.721267\pi$
$569$	−17386.3	−1.28097	−0.640486	+	0.767970i	$0.721267\pi$
$570$	−10774.2	−0.791721
$571$	−17303.9	−1.26821	−0.634105	−	0.773247i	$-0.718631\pi$
$571$	−17303.9	−1.26821	−0.634105	+	0.773247i	$0.718631\pi$
$572$	5250.10	0.383772
$573$	−2289.89	−0.166949
$574$	17318.5	1.25934
$575$	−32832.2	−2.38121
$576$	−6528.57	−0.472264
$577$	26932.4	1.94317	0.971587	−	0.236683i	$-0.0760604\pi$
$577$	26932.4	1.94317	0.971587	+	0.236683i	$0.0760604\pi$
$578$	9077.92	0.653272
$579$	1349.81	0.0968849
$580$	25793.0	1.84655
$581$	10407.2	0.743135
$582$	−146.274	−0.0104180
$583$	−4772.14	−0.339008
$584$	−18833.4	−1.33447
$585$	7362.75	0.520363
$586$	−7582.45	−0.534519
$587$	−11169.9	−0.785406	−0.392703	−	0.919665i	$-0.628460\pi$
$587$	−11169.9	−0.785406	−0.392703	+	0.919665i	$0.628460\pi$
$588$	−3434.64	−0.240888
$589$	9688.34	0.677761
$590$	4570.42	0.318917
$591$	5460.54	0.380062
$592$	7.18404	0.000498753 0
$593$	1545.81	0.107047	0.0535234	−	0.998567i	$-0.482955\pi$
$593$	1545.81	0.107047	0.0535234	+	0.998567i	$0.482955\pi$
$594$	12568.1	0.868137
$595$	1002.55	0.0690767
$596$	860.421	0.0591346
$597$	−7539.60	−0.516877
$598$	−6833.18	−0.467273
$599$	7624.14	0.520057	0.260028	−	0.965601i	$-0.416268\pi$
$599$	7624.14	0.520057	0.260028	+	0.965601i	$0.416268\pi$
$600$	14783.9	1.00592
$601$	13723.7	0.931448	0.465724	−	0.884930i	$-0.345794\pi$
$601$	13723.7	0.931448	0.465724	+	0.884930i	$0.345794\pi$
$602$	0	0
$603$	−4649.66	−0.314011
$604$	−7618.98	−0.513265
$605$	20359.3	1.36814
$606$	9487.18	0.635958
$607$	−15914.5	−1.06417	−0.532083	−	0.846692i	$-0.678591\pi$
$607$	−15914.5	−1.06417	−0.532083	+	0.846692i	$0.678591\pi$
$608$	−18082.2	−1.20614
$609$	23139.7	1.53968
$610$	12604.7	0.836636
$611$	−4976.29	−0.329491
$612$	−182.154	−0.0120313
$613$	19139.8	1.26109	0.630546	−	0.776152i	$-0.282831\pi$
$613$	19139.8	1.26109	0.630546	+	0.776152i	$0.282831\pi$
$614$	−11628.9	−0.764338
$615$	21713.9	1.42372
$616$	−27880.7	−1.82361
$617$	−20419.1	−1.33232	−0.666160	−	0.745809i	$-0.732063\pi$
$617$	−20419.1	−1.33232	−0.666160	+	0.745809i	$0.732063\pi$
$618$	−125.861	−0.00819234
$619$	−741.929	−0.0481755	−0.0240878	−	0.999710i	$-0.507668\pi$
$619$	−741.929	−0.0481755	−0.0240878	+	0.999710i	$0.507668\pi$
$620$	−7777.15	−0.503771
$621$	21891.0	1.41458
$622$	16999.6	1.09586
$623$	3303.31	0.212431
$624$	458.039	0.0293850
$625$	1024.24	0.0655512
$626$	4020.42	0.256691
$627$	15851.2	1.00963
$628$	−15125.0	−0.961074
$629$	2.55305	0.000161839 0
$630$	−14232.5	−0.900057
$631$	−14781.2	−0.932533	−0.466266	−	0.884644i	$-0.654401\pi$
$631$	−14781.2	−0.932533	−0.466266	+	0.884644i	$0.654401\pi$
$632$	−24561.2	−1.54587
$633$	−7553.03	−0.474259
$634$	−15695.5	−0.983199
$635$	−45541.7	−2.84609
$636$	1362.40	0.0849412
$637$	−5629.96	−0.350184
$638$	28355.6	1.75957
$639$	−7664.20	−0.474478
$640$	12790.8	0.790000
$641$	−3976.97	−0.245056	−0.122528	−	0.992465i	$-0.539100\pi$
$641$	−3976.97	−0.245056	−0.122528	+	0.992465i	$0.539100\pi$
$642$	5089.09	0.312851
$643$	−2640.34	−0.161936	−0.0809679	−	0.996717i	$-0.525801\pi$
$643$	−2640.34	−0.161936	−0.0809679	+	0.996717i	$0.525801\pi$
$644$	−17676.9	−1.08163
$645$	0	0
$646$	436.926	0.0266109
$647$	−11975.9	−0.727697	−0.363848	−	0.931458i	$-0.618537\pi$
$647$	−11975.9	−0.727697	−0.363848	+	0.931458i	$0.618537\pi$
$648$	1119.78	0.0678845
$649$	−6724.11	−0.406694
$650$	8820.98	0.532288
$651$	−6977.11	−0.420053
$652$	−7110.21	−0.427082
$653$	27053.1	1.62124	0.810619	−	0.585574i	$-0.199131\pi$
$653$	27053.1	1.62124	0.810619	+	0.585574i	$0.199131\pi$
$654$	−7837.98	−0.468638
$655$	3058.94	0.182477
$656$	−2477.82	−0.147474
$657$	14144.4	0.839919
$658$	9619.37	0.569912
$659$	27557.4	1.62896	0.814478	−	0.580194i	$-0.197023\pi$
$659$	27557.4	1.62896	0.814478	+	0.580194i	$0.197023\pi$
$660$	−12724.3	−0.750444
$661$	17087.7	1.00550	0.502751	−	0.864432i	$-0.332321\pi$
$661$	17087.7	1.00550	0.502751	+	0.864432i	$0.332321\pi$
$662$	5749.30	0.337542
$663$	162.777	0.00953505
$664$	−10002.3	−0.584585
$665$	−45687.0	−2.66416
$666$	−36.2437	−0.00210873
$667$	49389.7	2.86713
$668$	−9982.18	−0.578177
$669$	3587.69	0.207336
$670$	−8952.84	−0.516237
$671$	−18544.3	−1.06691
$672$	13022.0	0.747522
$673$	7916.77	0.453446	0.226723	−	0.973959i	$-0.427199\pi$
$673$	7916.77	0.453446	0.226723	+	0.973959i	$0.427199\pi$
$674$	−11221.5	−0.641301
$675$	−28259.2	−1.61141
$676$	7602.45	0.432547
$677$	19951.0	1.13262	0.566308	−	0.824194i	$-0.308371\pi$
$677$	19951.0	1.13262	0.566308	+	0.824194i	$0.308371\pi$
$678$	−5357.53	−0.303473
$679$	−620.262	−0.0350566
$680$	−963.550	−0.0543389
$681$	11069.7	0.622893
$682$	−8549.81	−0.480043
$683$	−28013.0	−1.56938	−0.784692	−	0.619886i	$-0.787179\pi$
$683$	−28013.0	−1.56938	−0.784692	+	0.619886i	$0.787179\pi$
$684$	8300.89	0.464024
$685$	−6500.89	−0.362608
$686$	−4475.85	−0.249109
$687$	−9761.68	−0.542112
$688$	0	0
$689$	2233.20	0.123481
$690$	16561.1	0.913726
$691$	21559.9	1.18694	0.593471	−	0.804855i	$-0.297757\pi$
$691$	21559.9	1.18694	0.593471	+	0.804855i	$0.297757\pi$
$692$	7083.77	0.389140
$693$	20939.2	1.14778
$694$	3117.10	0.170495
$695$	8974.26	0.489803
$696$	−22239.5	−1.21119
$697$	−880.564	−0.0478533
$698$	11574.9	0.627676
$699$	−10281.9	−0.556360
$700$	22819.2	1.23212
$701$	4705.35	0.253522	0.126761	−	0.991933i	$-0.459542\pi$
$701$	4705.35	0.253522	0.126761	+	0.991933i	$0.459542\pi$
$702$	−5881.44	−0.316212
$703$	−116.344	−0.00624183
$704$	18494.2	0.990097
$705$	12060.7	0.644302
$706$	−9626.33	−0.513161
$707$	40229.5	2.14001
$708$	1919.67	0.101900
$709$	−25069.4	−1.32793	−0.663963	−	0.747765i	$-0.731127\pi$
$709$	−25069.4	−1.32793	−0.663963	+	0.747765i	$0.731127\pi$
$710$	−14757.3	−0.780044
$711$	18446.1	0.972974
$712$	−3174.81	−0.167108
$713$	−14892.1	−0.782205
$714$	−314.654	−0.0164925
$715$	−20857.3	−1.09094
$716$	12459.6	0.650330
$717$	−10713.0	−0.557998
$718$	−11773.4	−0.611950
$719$	−31411.2	−1.62926	−0.814631	−	0.579979i	$-0.803061\pi$
$719$	−31411.2	−1.62926	−0.814631	+	0.579979i	$0.803061\pi$
$720$	2036.29	0.105400
$721$	−533.702	−0.0275674
$722$	−7224.01	−0.372368
$723$	−12049.6	−0.619819
$724$	4458.57	0.228869
$725$	−63757.4	−3.26606
$726$	−6389.84	−0.326652
$727$	21425.3	1.09301	0.546506	−	0.837455i	$-0.315958\pi$
$727$	21425.3	1.09301	0.546506	+	0.837455i	$0.315958\pi$
$728$	13047.3	0.664236
$729$	10598.0	0.538433
$730$	27234.9	1.38083
$731$	0	0
$732$	5294.21	0.267322
$733$	3241.88	0.163358	0.0816791	−	0.996659i	$-0.473972\pi$
$733$	3241.88	0.163358	0.0816791	+	0.996659i	$0.473972\pi$
$734$	−12118.9	−0.609422
$735$	13645.0	0.684765
$736$	27794.4	1.39200
$737$	13171.6	0.658322
$738$	12500.7	0.623520
$739$	352.220	0.0175326	0.00876632	−	0.999962i	$-0.497210\pi$
$739$	352.220	0.0175326	0.00876632	+	0.999962i	$0.497210\pi$
$740$	93.3933	0.00463947
$741$	−7417.86	−0.367749
$742$	−4316.87	−0.213581
$743$	23682.7	1.16936	0.584679	−	0.811265i	$-0.301221\pi$
$743$	23682.7	1.16936	0.584679	+	0.811265i	$0.301221\pi$
$744$	6705.69	0.330433
$745$	−3418.23	−0.168100
$746$	10778.0	0.528969
$747$	7512.00	0.367938
$748$	516.009	0.0252235
$749$	21579.8	1.05275
$750$	−8398.16	−0.408877
$751$	−3352.04	−0.162873	−0.0814364	−	0.996679i	$-0.525951\pi$
$751$	−3352.04	−0.162873	−0.0814364	+	0.996679i	$0.525951\pi$
$752$	−1376.28	−0.0667388
$753$	−16422.8	−0.794795
$754$	−13269.5	−0.640909
$755$	30268.3	1.45904
$756$	−15214.8	−0.731955
$757$	−20731.0	−0.995352	−0.497676	−	0.867363i	$-0.665813\pi$
$757$	−20731.0	−0.995352	−0.497676	+	0.867363i	$0.665813\pi$
$758$	2082.72	0.0997990
$759$	−24365.1	−1.16521
$760$	43909.6	2.09575
$761$	15049.1	0.716860	0.358430	−	0.933557i	$-0.383312\pi$
$761$	15049.1	0.716860	0.358430	+	0.933557i	$0.383312\pi$
$762$	14293.4	0.679522
$763$	−33236.2	−1.57698
$764$	3396.99	0.160862
$765$	723.653	0.0342009
$766$	−15849.3	−0.747594
$767$	3146.66	0.148135
$768$	−13239.7	−0.622066
$769$	−7250.41	−0.339995	−0.169998	−	0.985444i	$-0.554376\pi$
$769$	−7250.41	−0.339995	−0.169998	+	0.985444i	$0.554376\pi$
$770$	40318.0	1.88696
$771$	66.3524	0.00309938
$772$	−2002.41	−0.0933529
$773$	2947.00	0.137123	0.0685615	−	0.997647i	$-0.478159\pi$
$773$	2947.00	0.137123	0.0685615	+	0.997647i	$0.478159\pi$
$774$	0	0
$775$	19224.2	0.891038
$776$	596.132	0.0275772
$777$	83.7859	0.00386847
$778$	27144.6	1.25088
$779$	40127.9	1.84561
$780$	5954.56	0.273343
$781$	21711.3	0.994738
$782$	−671.603	−0.0307116
$783$	42510.6	1.94024
$784$	−1557.06	−0.0709301
$785$	60088.0	2.73201
$786$	−960.058	−0.0435676
$787$	−27036.2	−1.22457	−0.612285	−	0.790637i	$-0.709749\pi$
$787$	−27036.2	−1.22457	−0.612285	+	0.790637i	$0.709749\pi$
$788$	−8100.56	−0.366206
$789$	−8913.51	−0.402192
$790$	35517.7	1.59958
$791$	−22718.1	−1.02119
$792$	−20124.6	−0.902899
$793$	8678.12	0.388612
$794$	19159.6	0.856361
$795$	−5412.47	−0.241460
$796$	11184.8	0.498034
$797$	33.4802	0.00148799	0.000743997	−	1.00000i	$-0.499763\pi$
$797$	33.4802	0.00148799	0.000743997		1.00000i	$0.499763\pi$
$798$	14339.0	0.636085
$799$	−489.098	−0.0216559
$800$	−35879.9	−1.58568
$801$	2384.37	0.105178
$802$	−3948.69	−0.173857
$803$	−40068.6	−1.76088
$804$	−3760.38	−0.164948
$805$	70225.9	3.07471
$806$	4001.03	0.174851
$807$	−21215.7	−0.925438
$808$	−38664.5	−1.68343
$809$	42225.4	1.83506	0.917531	−	0.397665i	$-0.130179\pi$
$809$	42225.4	1.83506	0.917531	+	0.397665i	$0.130179\pi$
$810$	−1619.31	−0.0702427
$811$	−5553.35	−0.240449	−0.120225	−	0.992747i	$-0.538361\pi$
$811$	−5553.35	−0.240449	−0.120225	+	0.992747i	$0.538361\pi$
$812$	−34327.1	−1.48355
$813$	−20748.7	−0.895066
$814$	102.672	0.00442094
$815$	28247.1	1.21405
$816$	45.0187	0.00193133
$817$	0	0
$818$	4226.04	0.180636
$819$	−9798.85	−0.418070
$820$	−32212.0	−1.37182
$821$	23869.5	1.01468	0.507338	−	0.861747i	$-0.330629\pi$
$821$	23869.5	1.01468	0.507338	+	0.861747i	$0.330629\pi$
$822$	2040.33	0.0865749
$823$	−26707.2	−1.13117	−0.565587	−	0.824689i	$-0.691350\pi$
$823$	−26707.2	−1.13117	−0.565587	+	0.824689i	$0.691350\pi$
$824$	512.940	0.0216858
$825$	31453.0	1.32734
$826$	−6082.62	−0.256225
$827$	14209.8	0.597489	0.298744	−	0.954333i	$-0.403432\pi$
$827$	14209.8	0.597489	0.298744	+	0.954333i	$0.403432\pi$
$828$	−12759.4	−0.535531
$829$	−26345.6	−1.10376	−0.551882	−	0.833922i	$-0.686090\pi$
$829$	−26345.6	−1.10376	−0.551882	+	0.833922i	$0.686090\pi$
$830$	14464.2	0.604892
$831$	−23184.9	−0.967839
$832$	−8654.70	−0.360634
$833$	−553.344	−0.0230159
$834$	−2816.60	−0.116944
$835$	39656.7	1.64356
$836$	−23514.9	−0.972823
$837$	−12817.9	−0.529331
$838$	4399.78	0.181370
$839$	−6078.93	−0.250141	−0.125070	−	0.992148i	$-0.539916\pi$
$839$	−6078.93	−0.250141	−0.125070	+	0.992148i	$0.539916\pi$
$840$	−31621.8	−1.29887
$841$	71521.8	2.93254
$842$	−27108.6	−1.10953
$843$	−20261.4	−0.827805
$844$	11204.7	0.456970
$845$	−30202.6	−1.22959
$846$	6943.36	0.282172
$847$	−27095.5	−1.09919
$848$	617.629	0.0250112
$849$	3032.42	0.122582
$850$	866.976	0.0349847
$851$	178.834	0.00720370
$852$	−6198.36	−0.249240
$853$	28429.0	1.14114	0.570569	−	0.821249i	$-0.306723\pi$
$853$	28429.0	1.14114	0.570569	+	0.821249i	$0.306723\pi$
$854$	−16775.1	−0.672170
$855$	−32977.3	−1.31907
$856$	−20740.3	−0.828142
$857$	−3079.93	−0.122764	−0.0613818	−	0.998114i	$-0.519551\pi$
$857$	−3079.93	−0.122764	−0.0613818	+	0.998114i	$0.519551\pi$
$858$	6546.14	0.260468
$859$	−14493.8	−0.575696	−0.287848	−	0.957676i	$-0.592940\pi$
$859$	−14493.8	−0.575696	−0.287848	+	0.957676i	$0.592940\pi$
$860$	0	0
$861$	−28898.3	−1.14385
$862$	4563.62	0.180322
$863$	32404.8	1.27818	0.639092	−	0.769130i	$-0.279310\pi$
$863$	32404.8	1.27818	0.639092	+	0.769130i	$0.279310\pi$
$864$	23923.1	0.941991
$865$	−28142.0	−1.10619
$866$	26269.8	1.03081
$867$	−15147.7	−0.593361
$868$	10350.4	0.404740
$869$	−52254.6	−2.03983
$870$	32160.3	1.25326
$871$	−6163.90	−0.239788
$872$	31943.3	1.24052
$873$	−447.712	−0.0173571
$874$	30605.4	1.18449
$875$	−35611.6	−1.37588
$876$	11439.2	0.441204
$877$	−19866.3	−0.764923	−0.382461	−	0.923971i	$-0.624924\pi$
$877$	−19866.3	−0.764923	−0.382461	+	0.923971i	$0.624924\pi$
$878$	20548.3	0.789831
$879$	12652.3	0.485498
$880$	−5768.43	−0.220970
$881$	14081.8	0.538512	0.269256	−	0.963069i	$-0.413222\pi$
$881$	14081.8	0.538512	0.269256	+	0.963069i	$0.413222\pi$
$882$	7855.42	0.299893
$883$	24474.0	0.932748	0.466374	−	0.884588i	$-0.345560\pi$
$883$	24474.0	0.932748	0.466374	+	0.884588i	$0.345560\pi$
$884$	−241.476	−0.00918744
$885$	−7626.36	−0.289669
$886$	6247.24	0.236885
$887$	−1361.28	−0.0515301	−0.0257651	−	0.999668i	$-0.508202\pi$
$887$	−1361.28	−0.0515301	−0.0257651	+	0.999668i	$0.508202\pi$
$888$	−80.5264	−0.00304312
$889$	60610.0	2.28661
$890$	4591.06	0.172913
$891$	2382.36	0.0895759
$892$	−5322.24	−0.199778
$893$	22288.5	0.835227
$894$	1072.83	0.0401349
$895$	−49498.8	−1.84867
$896$	−17022.8	−0.634702
$897$	11402.1	0.424419
$898$	−15663.6	−0.582074
$899$	−28919.2	−1.07287
$900$	16471.2	0.610043
$901$	219.492	0.00811580
$902$	−35412.2	−1.30720
$903$	0	0
$904$	21834.3	0.803317
$905$	−17712.8	−0.650600
$906$	−9499.81	−0.348356
$907$	10369.2	0.379609	0.189804	−	0.981822i	$-0.439215\pi$
$907$	10369.2	0.379609	0.189804	+	0.981822i	$0.439215\pi$
$908$	−16421.5	−0.600185
$909$	29038.1	1.05955
$910$	−18867.5	−0.687310
$911$	6938.26	0.252333	0.126166	−	0.992009i	$-0.459733\pi$
$911$	6938.26	0.252333	0.126166	+	0.992009i	$0.459733\pi$
$912$	−2051.53	−0.0744879
$913$	−21280.1	−0.771379
$914$	−1876.31	−0.0679026
$915$	−21032.6	−0.759908
$916$	14481.2	0.522349
$917$	−4071.04	−0.146606
$918$	−578.061	−0.0207831
$919$	−5381.77	−0.193175	−0.0965876	−	0.995324i	$-0.530793\pi$
$919$	−5381.77	−0.193175	−0.0965876	+	0.995324i	$0.530793\pi$
$920$	−67494.0	−2.41871
$921$	19404.4	0.694240
$922$	13366.7	0.477449
$923$	−10160.2	−0.362325
$924$	16934.4	0.602922
$925$	−230.857	−0.00820600
$926$	29348.0	1.04151
$927$	−385.232	−0.0136490
$928$	53974.4	1.90926
$929$	11294.7	0.398888	0.199444	−	0.979909i	$-0.436086\pi$
$929$	11294.7	0.398888	0.199444	+	0.979909i	$0.436086\pi$
$930$	−9697.03	−0.341912
$931$	25216.3	0.887680
$932$	15252.9	0.536077
$933$	−28366.2	−0.995356
$934$	−28560.3	−1.00056
$935$	−2049.98	−0.0717020
$936$	9417.65	0.328873
$937$	46811.1	1.63207	0.816037	−	0.578000i	$-0.196167\pi$
$937$	46811.1	1.63207	0.816037	+	0.578000i	$0.196167\pi$
$938$	11915.1	0.414755
$939$	−6708.61	−0.233149
$940$	−17891.7	−0.620813
$941$	416.802	0.0144393	0.00721963	−	0.999974i	$-0.497702\pi$
$941$	416.802	0.0144393	0.00721963	+	0.999974i	$0.497702\pi$
$942$	−18858.8	−0.652286
$943$	−61681.0	−2.13002
$944$	870.261	0.0300049
$945$	60444.7	2.08071
$946$	0	0
$947$	25431.0	0.872648	0.436324	−	0.899790i	$-0.356280\pi$
$947$	25431.0	0.872648	0.436324	+	0.899790i	$0.356280\pi$
$948$	14918.2	0.511097
$949$	18750.8	0.641387
$950$	−39508.7	−1.34930
$951$	26190.1	0.893029
$952$	1282.36	0.0436570
$953$	23225.7	0.789460	0.394730	−	0.918797i	$-0.370838\pi$
$953$	23225.7	0.789460	0.394730	+	0.918797i	$0.370838\pi$
$954$	−3115.96	−0.105747
$955$	−13495.4	−0.457278
$956$	15892.5	0.537656
$957$	−47315.1	−1.59820
$958$	28328.8	0.955387
$959$	8651.83	0.291326
$960$	20975.8	0.705200
$961$	−21071.3	−0.707303
$962$	−48.0471	−0.00161029
$963$	15576.6	0.521233
$964$	17875.2	0.597223
$965$	7955.09	0.265371
$966$	−22040.7	−0.734106
$967$	7103.25	0.236220	0.118110	−	0.993000i	$-0.462316\pi$
$967$	7103.25	0.236220	0.118110	+	0.993000i	$0.462316\pi$
$968$	26041.5	0.864674
$969$	−729.069	−0.0241704
$970$	−862.061	−0.0285352
$971$	−279.508	−0.00923774	−0.00461887	−	0.999989i	$-0.501470\pi$
$971$	−279.508	−0.00923774	−0.00461887	+	0.999989i	$0.501470\pi$
$972$	−17649.5	−0.582417
$973$	−11943.6	−0.393518
$974$	7881.20	0.259271
$975$	−14719.0	−0.483472
$976$	2400.08	0.0787137
$977$	2433.91	0.0797007	0.0398504	−	0.999206i	$-0.487312\pi$
$977$	2433.91	0.0797007	0.0398504	+	0.999206i	$0.487312\pi$
$978$	−8865.44	−0.289863
$979$	−6754.47	−0.220504
$980$	−20241.9	−0.659801
$981$	−23990.3	−0.780786
$982$	−16559.6	−0.538123
$983$	52451.6	1.70188	0.850940	−	0.525264i	$-0.176033\pi$
$983$	52451.6	1.70188	0.850940	+	0.525264i	$0.176033\pi$
$984$	27774.1	0.899803
$985$	32181.5	1.04100
$986$	−1304.20	−0.0421239
$987$	−16051.2	−0.517645
$988$	11004.2	0.354342
$989$	0	0
$990$	29102.0	0.934264
$991$	−6191.90	−0.198478	−0.0992392	−	0.995064i	$-0.531641\pi$
$991$	−6191.90	−0.198478	−0.0992392	+	0.995064i	$0.531641\pi$
$992$	−16274.4	−0.520881
$993$	−9593.48	−0.306586
$994$	19640.0	0.626703
$995$	−44434.4	−1.41574
$996$	6075.27	0.193275
$997$	−6156.43	−0.195563	−0.0977814	−	0.995208i	$-0.531175\pi$
$997$	−6156.43	−0.195563	−0.0977814	+	0.995208i	$0.531175\pi$
$998$	−1362.11	−0.0432033
$999$	153.926	0.00487486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.18	yes	50
43.42	odd	2		1849.4.a.i.1.33	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.33	✓	50	43.42	odd	2
1849.4.a.j.1.18	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)

\(f(q)\)	\(=\)	\(q-1.84969 q^{2} +3.08645 q^{3} -4.57866 q^{4} +18.1899 q^{5} -5.70896 q^{6} -24.2083 q^{7} +23.2666 q^{8} -17.4738 q^{9} +O(q^{10})\)	\(q-1.84969 q^{2} +3.08645 q^{3} -4.57866 q^{4} +18.1899 q^{5} -5.70896 q^{6} -24.2083 q^{7} +23.2666 q^{8} -17.4738 q^{9} -33.6456 q^{10} +49.5002 q^{11} -14.1318 q^{12} -23.1645 q^{13} +44.7778 q^{14} +56.1421 q^{15} -6.40651 q^{16} -2.27673 q^{17} +32.3211 q^{18} +103.752 q^{19} -83.2854 q^{20} -74.7178 q^{21} -91.5597 q^{22} -159.479 q^{23} +71.8111 q^{24} +205.872 q^{25} +42.8469 q^{26} -137.266 q^{27} +110.842 q^{28} -309.695 q^{29} -103.845 q^{30} +93.3796 q^{31} -174.283 q^{32} +152.780 q^{33} +4.21124 q^{34} -440.347 q^{35} +80.0068 q^{36} -1.12136 q^{37} -191.909 q^{38} -71.4959 q^{39} +423.216 q^{40} +386.766 q^{41} +138.204 q^{42} -226.645 q^{44} -317.847 q^{45} +294.985 q^{46} +214.825 q^{47} -19.7734 q^{48} +243.043 q^{49} -380.798 q^{50} -7.02702 q^{51} +106.062 q^{52} -96.4065 q^{53} +253.899 q^{54} +900.402 q^{55} -563.245 q^{56} +320.226 q^{57} +572.838 q^{58} -135.840 q^{59} -257.056 q^{60} -374.631 q^{61} -172.723 q^{62} +423.012 q^{63} +373.620 q^{64} -421.359 q^{65} -282.594 q^{66} +266.093 q^{67} +10.4244 q^{68} -492.223 q^{69} +814.503 q^{70} +438.610 q^{71} -406.556 q^{72} -809.464 q^{73} +2.07417 q^{74} +635.413 q^{75} -475.047 q^{76} -1198.32 q^{77} +132.245 q^{78} -1055.64 q^{79} -116.534 q^{80} +48.1284 q^{81} -715.396 q^{82} -429.900 q^{83} +342.108 q^{84} -41.4135 q^{85} -955.857 q^{87} +1151.70 q^{88} -136.454 q^{89} +587.917 q^{90} +560.773 q^{91} +730.200 q^{92} +288.211 q^{93} -397.358 q^{94} +1887.24 q^{95} -537.914 q^{96} +25.6218 q^{97} -449.553 q^{98} -864.958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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