LMFDB - Embedded newform 1849.4.a.l.1.6

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:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-4.53463 q^{2} +3.33693 q^{3} +12.5629 q^{4} -15.3423 q^{5} -15.1318 q^{6} -5.56073 q^{7} -20.6909 q^{8} -15.8649 q^{9} +O(q^{10})$	\(q-4.53463 q^{2} +3.33693 q^{3} +12.5629 q^{4} -15.3423 q^{5} -15.1318 q^{6} -5.56073 q^{7} -20.6909 q^{8} -15.8649 q^{9} +69.5716 q^{10} -47.0754 q^{11} +41.9214 q^{12} -26.7976 q^{13} +25.2159 q^{14} -51.1962 q^{15} -6.67737 q^{16} +108.036 q^{17} +71.9413 q^{18} +94.6225 q^{19} -192.743 q^{20} -18.5558 q^{21} +213.470 q^{22} -17.0909 q^{23} -69.0442 q^{24} +110.386 q^{25} +121.517 q^{26} -143.037 q^{27} -69.8587 q^{28} +48.5387 q^{29} +232.156 q^{30} -245.035 q^{31} +195.807 q^{32} -157.088 q^{33} -489.905 q^{34} +85.3144 q^{35} -199.308 q^{36} -100.513 q^{37} -429.078 q^{38} -89.4217 q^{39} +317.446 q^{40} -391.549 q^{41} +84.1436 q^{42} -591.402 q^{44} +243.404 q^{45} +77.5010 q^{46} -39.8096 q^{47} -22.2820 q^{48} -312.078 q^{49} -500.560 q^{50} +360.510 q^{51} -336.654 q^{52} +64.6359 q^{53} +648.621 q^{54} +722.246 q^{55} +115.056 q^{56} +315.749 q^{57} -220.105 q^{58} -794.094 q^{59} -643.171 q^{60} -825.534 q^{61} +1111.14 q^{62} +88.2203 q^{63} -834.491 q^{64} +411.136 q^{65} +712.334 q^{66} -709.119 q^{67} +1357.25 q^{68} -57.0313 q^{69} -386.869 q^{70} +42.6703 q^{71} +328.258 q^{72} -1054.35 q^{73} +455.790 q^{74} +368.351 q^{75} +1188.73 q^{76} +261.774 q^{77} +405.494 q^{78} -1023.82 q^{79} +102.446 q^{80} -48.9544 q^{81} +1775.53 q^{82} +264.392 q^{83} -233.114 q^{84} -1657.53 q^{85} +161.970 q^{87} +974.033 q^{88} -40.7355 q^{89} -1103.75 q^{90} +149.014 q^{91} -214.711 q^{92} -817.666 q^{93} +180.522 q^{94} -1451.73 q^{95} +653.394 q^{96} +1102.61 q^{97} +1415.16 q^{98} +746.846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * 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 $

$2$	−4.53463	−1.60323	−0.801617	−	0.597838i	$-0.796027\pi$
$2$	−4.53463	−1.60323	−0.801617	+	0.597838i	$0.796027\pi$
$3$	3.33693	0.642193	0.321097	−	0.947046i	$-0.395949\pi$
$3$	3.33693	0.642193	0.321097	+	0.947046i	$0.395949\pi$
$4$	12.5629	1.57036
$5$	−15.3423	−1.37226	−0.686129	−	0.727480i	$-0.740691\pi$
$5$	−15.3423	−1.37226	−0.686129	+	0.727480i	$0.740691\pi$
$6$	−15.1318	−1.02959
$7$	−5.56073	−0.300251	−0.150126	−	0.988667i	$-0.547968\pi$
$7$	−5.56073	−0.300251	−0.150126	+	0.988667i	$0.547968\pi$
$8$	−20.6909	−0.914417
$9$	−15.8649	−0.587588
$10$	69.5716	2.20005
$11$	−47.0754	−1.29034	−0.645172	−	0.764037i	$-0.723214\pi$
$11$	−47.0754	−1.29034	−0.645172	+	0.764037i	$0.723214\pi$
$12$	41.9214	1.00847
$13$	−26.7976	−0.571716	−0.285858	−	0.958272i	$-0.592279\pi$
$13$	−26.7976	−0.571716	−0.285858	+	0.958272i	$0.592279\pi$
$14$	25.2159	0.481373
$15$	−51.1962	−0.881254
$16$	−6.67737	−0.104334
$17$	108.036	1.54133	0.770666	−	0.637239i	$-0.219924\pi$
$17$	108.036	1.54133	0.770666	+	0.637239i	$0.219924\pi$
$18$	71.9413	0.942040
$19$	94.6225	1.14252	0.571260	−	0.820769i	$-0.306455\pi$
$19$	94.6225	1.14252	0.571260	+	0.820769i	$0.306455\pi$
$20$	−192.743	−2.15493
$21$	−18.5558	−0.192819
$22$	213.470	2.06872
$23$	−17.0909	−0.154944	−0.0774718	−	0.996995i	$-0.524685\pi$
$23$	−17.0909	−0.154944	−0.0774718	+	0.996995i	$0.524685\pi$
$24$	−69.0442	−0.587232
$25$	110.386	0.883089
$26$	121.517	0.916594
$27$	−143.037	−1.01954
$28$	−69.8587	−0.471502
$29$	48.5387	0.310807	0.155404	−	0.987851i	$-0.450332\pi$
$29$	48.5387	0.310807	0.155404	+	0.987851i	$0.450332\pi$
$30$	232.156	1.41286
$31$	−245.035	−1.41966	−0.709832	−	0.704371i	$-0.751229\pi$
$31$	−245.035	−1.41966	−0.709832	+	0.704371i	$0.751229\pi$
$32$	195.807	1.08169
$33$	−157.088	−0.828650
$34$	−489.905	−2.47112
$35$	85.3144	0.412022
$36$	−199.308	−0.922723
$37$	−100.513	−0.446602	−0.223301	−	0.974750i	$-0.571683\pi$
$37$	−100.513	−0.446602	−0.223301	+	0.974750i	$0.571683\pi$
$38$	−429.078	−1.83173
$39$	−89.4217	−0.367152
$40$	317.446	1.25482
$41$	−391.549	−1.49146	−0.745729	−	0.666250i	$-0.767898\pi$
$41$	−391.549	−1.49146	−0.745729	+	0.666250i	$0.767898\pi$
$42$	84.1436	0.309134
$43$	0	0
$43$	0	0
$44$	−591.402	−2.02630
$45$	243.404	0.806321
$46$	77.5010	0.248411
$47$	−39.8096	−0.123549	−0.0617747	−	0.998090i	$-0.519676\pi$
$47$	−39.8096	−0.123549	−0.0617747	+	0.998090i	$0.519676\pi$
$48$	−22.2820	−0.0670026
$49$	−312.078	−0.909849
$50$	−500.560	−1.41580
$51$	360.510	0.989834
$52$	−336.654	−0.897799
$53$	64.6359	0.167517	0.0837587	−	0.996486i	$-0.473308\pi$
$53$	64.6359	0.167517	0.0837587	+	0.996486i	$0.473308\pi$
$54$	648.621	1.63456
$55$	722.246	1.77068
$56$	115.056	0.274555
$57$	315.749	0.733719
$58$	−220.105	−0.498296
$59$	−794.094	−1.75224	−0.876121	−	0.482091i	$-0.839877\pi$
$59$	−794.094	−1.75224	−0.876121	+	0.482091i	$0.839877\pi$
$60$	−643.171	−1.38388
$61$	−825.534	−1.73277	−0.866384	−	0.499379i	$-0.833562\pi$
$61$	−825.534	−1.73277	−0.866384	+	0.499379i	$0.833562\pi$
$62$	1111.14	2.27605
$63$	88.2203	0.176424
$64$	−834.491	−1.62987
$65$	411.136	0.784541
$66$	712.334	1.32852
$67$	−709.119	−1.29303	−0.646513	−	0.762903i	$-0.723773\pi$
$67$	−709.119	−1.29303	−0.646513	+	0.762903i	$0.723773\pi$
$68$	1357.25	2.42044
$69$	−57.0313	−0.0995037
$70$	−386.869	−0.660567
$71$	42.6703	0.0713243	0.0356622	−	0.999364i	$-0.488646\pi$
$71$	42.6703	0.0713243	0.0356622	+	0.999364i	$0.488646\pi$
$72$	328.258	0.537300
$73$	−1054.35	−1.69045	−0.845223	−	0.534414i	$-0.820532\pi$
$73$	−1054.35	−1.69045	−0.845223	+	0.534414i	$0.820532\pi$
$74$	455.790	0.716007
$75$	368.351	0.567114
$76$	1188.73	1.79417
$77$	261.774	0.387427
$78$	405.494	0.588631
$79$	−1023.82	−1.45808	−0.729041	−	0.684470i	$-0.760034\pi$
$79$	−1023.82	−1.45808	−0.729041	+	0.684470i	$0.760034\pi$
$80$	102.446	0.143173
$81$	−48.9544	−0.0671529
$82$	1775.53	2.39115
$83$	264.392	0.349648	0.174824	−	0.984600i	$-0.444064\pi$
$83$	264.392	0.349648	0.174824	+	0.984600i	$0.444064\pi$
$84$	−233.114	−0.302795
$85$	−1657.53	−2.11510
$86$	0	0
$87$	161.970	0.199598
$88$	974.033	1.17991
$89$	−40.7355	−0.0485163	−0.0242582	−	0.999706i	$-0.507722\pi$
$89$	−40.7355	−0.0485163	−0.0242582	+	0.999706i	$0.507722\pi$
$90$	−1103.75	−1.29272
$91$	149.014	0.171658
$92$	−214.711	−0.243317
$93$	−817.666	−0.911699
$94$	180.522	0.198079
$95$	−1451.73	−1.56783
$96$	653.394	0.694653
$97$	1102.61	1.15415	0.577076	−	0.816691i	$-0.304194\pi$
$97$	1102.61	1.15415	0.577076	+	0.816691i	$0.304194\pi$
$98$	1415.16	1.45870
$99$	746.846	0.758190
$100$	1386.77	1.38677
$101$	1484.66	1.46267	0.731333	−	0.682021i	$-0.238899\pi$
$101$	1484.66	1.46267	0.731333	+	0.682021i	$0.238899\pi$
$102$	−1634.78	−1.58693
$103$	−382.419	−0.365834	−0.182917	−	0.983128i	$-0.558554\pi$
$103$	−382.419	−0.365834	−0.182917	+	0.983128i	$0.558554\pi$
$104$	554.466	0.522787
$105$	284.689	0.264598
$106$	−293.100	−0.268570
$107$	−723.378	−0.653566	−0.326783	−	0.945099i	$-0.605965\pi$
$107$	−723.378	−0.653566	−0.326783	+	0.945099i	$0.605965\pi$
$108$	−1796.96	−1.60104
$109$	−706.345	−0.620693	−0.310347	−	0.950623i	$-0.600445\pi$
$109$	−706.345	−0.620693	−0.310347	+	0.950623i	$0.600445\pi$
$110$	−3275.12	−2.83882
$111$	−335.406	−0.286805
$112$	37.1311	0.0313264
$113$	393.099	0.327254	0.163627	−	0.986522i	$-0.447681\pi$
$113$	393.099	0.327254	0.163627	+	0.986522i	$0.447681\pi$
$114$	−1431.81	−1.17632
$115$	262.214	0.212622
$116$	609.785	0.488078
$117$	425.140	0.335933
$118$	3600.92	2.80925
$119$	−600.761	−0.462787
$120$	1059.30	0.805834
$121$	885.098	0.664987
$122$	3743.49	2.77803
$123$	−1306.57	−0.957804
$124$	−3078.34	−2.22938
$125$	224.210	0.160431
$126$	−400.046	−0.282849
$127$	1426.09	0.996416	0.498208	−	0.867058i	$-0.333992\pi$
$127$	1426.09	0.996416	0.498208	+	0.867058i	$0.333992\pi$
$128$	2217.66	1.53137
$129$	0	0
$130$	−1864.35	−1.25780
$131$	−1069.95	−0.713602	−0.356801	−	0.934180i	$-0.616133\pi$
$131$	−1069.95	−0.713602	−0.356801	+	0.934180i	$0.616133\pi$
$132$	−1973.47	−1.30128
$133$	−526.170	−0.343043
$134$	3215.59	2.07302
$135$	2194.52	1.39907
$136$	−2235.37	−1.40942
$137$	2303.23	1.43634	0.718168	−	0.695870i	$-0.244981\pi$
$137$	2303.23	1.43634	0.718168	+	0.695870i	$0.244981\pi$
$138$	258.616	0.159528
$139$	842.729	0.514240	0.257120	−	0.966379i	$-0.417226\pi$
$139$	842.729	0.514240	0.257120	+	0.966379i	$0.417226\pi$
$140$	1071.79	0.647022
$141$	−132.842	−0.0793426
$142$	−193.494	−0.114350
$143$	1261.51	0.737710
$144$	105.936	0.0613053
$145$	−744.695	−0.426507
$146$	4781.09	2.71018
$147$	−1041.38	−0.584299
$148$	−1262.73	−0.701325
$149$	−2013.58	−1.10711	−0.553553	−	0.832814i	$-0.686728\pi$
$149$	−2013.58	−1.10711	−0.553553	+	0.832814i	$0.686728\pi$
$150$	−1670.34	−0.909216
$151$	−263.419	−0.141965	−0.0709825	−	0.997478i	$-0.522613\pi$
$151$	−263.419	−0.141965	−0.0709825	+	0.997478i	$0.522613\pi$
$152$	−1957.82	−1.04474
$153$	−1713.98	−0.905668
$154$	−1187.05	−0.621136
$155$	3759.40	1.94814
$156$	−1123.39	−0.576560
$157$	1965.01	0.998884	0.499442	−	0.866347i	$-0.333538\pi$
$157$	1965.01	0.998884	0.499442	+	0.866347i	$0.333538\pi$
$158$	4642.63	2.33765
$159$	215.686	0.107579
$160$	−3004.12	−1.48435
$161$	95.0380	0.0465220
$162$	221.990	0.107662
$163$	1319.80	0.634200	0.317100	−	0.948392i	$-0.397291\pi$
$163$	1319.80	0.634200	0.317100	+	0.948392i	$0.397291\pi$
$164$	−4918.98	−2.34212
$165$	2410.09	1.13712
$166$	−1198.92	−0.560568
$167$	2680.31	1.24197	0.620984	−	0.783823i	$-0.286733\pi$
$167$	2680.31	1.24197	0.620984	+	0.783823i	$0.286733\pi$
$168$	383.936	0.176317
$169$	−1478.89	−0.673141
$170$	7516.26	3.39101
$171$	−1501.17	−0.671331
$172$	0	0
$173$	−1312.55	−0.576828	−0.288414	−	0.957506i	$-0.593128\pi$
$173$	−1312.55	−0.576828	−0.288414	+	0.957506i	$0.593128\pi$
$174$	−734.476	−0.320003
$175$	−613.828	−0.265149
$176$	314.340	0.134627
$177$	−2649.84	−1.12528
$178$	184.720	0.0777830
$179$	−2101.08	−0.877328	−0.438664	−	0.898651i	$-0.644548\pi$
$179$	−2101.08	−0.877328	−0.438664	+	0.898651i	$0.644548\pi$
$180$	3057.85	1.26621
$181$	−1789.20	−0.734753	−0.367377	−	0.930072i	$-0.619744\pi$
$181$	−1789.20	−0.734753	−0.367377	+	0.930072i	$0.619744\pi$
$182$	−675.723	−0.275209
$183$	−2754.75	−1.11277
$184$	353.626	0.141683
$185$	1542.10	0.612853
$186$	3707.81	1.46167
$187$	−5085.86	−1.98885
$188$	−500.122	−0.194017
$189$	795.392	0.306118
$190$	6583.04	2.51360
$191$	6.00110	0.00227342	0.00113671	−	0.999999i	$-0.499638\pi$
$191$	6.00110	0.00227342	0.00113671	+	0.999999i	$0.499638\pi$
$192$	−2784.64	−1.04669
$193$	−3101.58	−1.15677	−0.578385	−	0.815764i	$-0.696317\pi$
$193$	−3101.58	−1.15677	−0.578385	+	0.815764i	$0.696317\pi$
$194$	−4999.91	−1.85037
$195$	1371.93	0.503827
$196$	−3920.60	−1.42879
$197$	−3754.54	−1.35787	−0.678934	−	0.734199i	$-0.737558\pi$
$197$	−3754.54	−1.35787	−0.678934	+	0.734199i	$0.737558\pi$
$198$	−3386.67	−1.21556
$199$	2365.23	0.842547	0.421274	−	0.906934i	$-0.361583\pi$
$199$	2365.23	0.842547	0.421274	+	0.906934i	$0.361583\pi$
$200$	−2283.99	−0.807512
$201$	−2366.28	−0.830372
$202$	−6732.39	−2.34500
$203$	−269.911	−0.0933202
$204$	4529.04	1.55439
$205$	6007.27	2.04666
$206$	1734.13	0.586517
$207$	271.145	0.0910430
$208$	178.937	0.0596494
$209$	−4454.40	−1.47424
$210$	−1290.96	−0.424212
$211$	3728.35	1.21645	0.608223	−	0.793766i	$-0.291883\pi$
$211$	3728.35	1.21645	0.608223	+	0.793766i	$0.291883\pi$
$212$	812.012	0.263062
$213$	142.388	0.0458040
$214$	3280.25	1.04782
$215$	0	0
$216$	2959.57	0.932283
$217$	1362.57	0.426256
$218$	3203.01	0.995116
$219$	−3518.30	−1.08559
$220$	9073.47	2.78061
$221$	−2895.11	−0.881204
$222$	1520.94	0.459815
$223$	−2959.21	−0.888624	−0.444312	−	0.895872i	$-0.646552\pi$
$223$	−2959.21	−0.888624	−0.444312	+	0.895872i	$0.646552\pi$
$224$	−1088.83	−0.324778
$225$	−1751.26	−0.518892
$226$	−1782.56	−0.524664
$227$	2242.02	0.655541	0.327771	−	0.944757i	$-0.393703\pi$
$227$	2242.02	0.655541	0.327771	+	0.944757i	$0.393703\pi$
$228$	3966.71	1.15220
$229$	−2286.84	−0.659907	−0.329953	−	0.943997i	$-0.607033\pi$
$229$	−2286.84	−0.659907	−0.329953	+	0.943997i	$0.607033\pi$
$230$	−1189.04	−0.340883
$231$	873.522	0.248803
$232$	−1004.31	−0.284207
$233$	−1578.46	−0.443813	−0.221906	−	0.975068i	$-0.571228\pi$
$233$	−1578.46	−0.443813	−0.221906	+	0.975068i	$0.571228\pi$
$234$	−1927.85	−0.538579
$235$	610.771	0.169542
$236$	−9976.10	−2.75165
$237$	−3416.41	−0.936371
$238$	2724.23	0.741956
$239$	4323.15	1.17005	0.585024	−	0.811016i	$-0.301085\pi$
$239$	4323.15	1.17005	0.585024	+	0.811016i	$0.301085\pi$
$240$	341.856	0.0919447
$241$	−4289.68	−1.14657	−0.573284	−	0.819357i	$-0.694331\pi$
$241$	−4289.68	−1.14657	−0.573284	+	0.819357i	$0.694331\pi$
$242$	−4013.59	−1.06613
$243$	3698.65	0.976413
$244$	−10371.1	−2.72107
$245$	4788.00	1.24855
$246$	5924.83	1.53558
$247$	−2535.65	−0.653197
$248$	5069.99	1.29817
$249$	882.259	0.224542
$250$	−1016.71	−0.257209
$251$	1692.79	0.425690	0.212845	−	0.977086i	$-0.431727\pi$
$251$	1692.79	0.425690	0.212845	+	0.977086i	$0.431727\pi$
$252$	1108.30	0.277049
$253$	804.563	0.199930
$254$	−6466.78	−1.59749
$255$	−5531.05	−1.35831
$256$	−3380.32	−0.825273
$257$	−1880.62	−0.456458	−0.228229	−	0.973607i	$-0.573294\pi$
$257$	−1880.62	−0.456458	−0.228229	+	0.973607i	$0.573294\pi$
$258$	0	0
$259$	558.927	0.134093
$260$	5165.05	1.23201
$261$	−770.060	−0.182626
$262$	4851.82	1.14407
$263$	4168.52	0.977346	0.488673	−	0.872467i	$-0.337481\pi$
$263$	4168.52	0.977346	0.488673	+	0.872467i	$0.337481\pi$
$264$	3250.28	0.757732
$265$	−991.663	−0.229877
$266$	2385.99	0.549978
$267$	−135.932	−0.0311569
$268$	−8908.57	−2.03051
$269$	4437.76	1.00586	0.502928	−	0.864328i	$-0.332256\pi$
$269$	4437.76	1.00586	0.502928	+	0.864328i	$0.332256\pi$
$270$	−9951.34	−2.24303
$271$	4849.83	1.08711	0.543554	−	0.839374i	$-0.317078\pi$
$271$	4849.83	1.08711	0.543554	+	0.839374i	$0.317078\pi$
$272$	−721.399	−0.160813
$273$	497.250	0.110238
$274$	−10444.3	−2.30278
$275$	−5196.48	−1.13949
$276$	−716.476	−0.156256
$277$	489.600	0.106199	0.0530996	−	0.998589i	$-0.483090\pi$
$277$	489.600	0.106199	0.0530996	+	0.998589i	$0.483090\pi$
$278$	−3821.46	−0.824447
$279$	3887.45	0.834177
$280$	−1765.23	−0.376760
$281$	−312.504	−0.0663432	−0.0331716	−	0.999450i	$-0.510561\pi$
$281$	−312.504	−0.0663432	−0.0331716	+	0.999450i	$0.510561\pi$
$282$	602.389	0.127205
$283$	1547.45	0.325040	0.162520	−	0.986705i	$-0.448038\pi$
$283$	1547.45	0.325040	0.162520	+	0.986705i	$0.448038\pi$
$284$	536.061	0.112005
$285$	−4844.32	−1.00685
$286$	−5720.47	−1.18272
$287$	2177.30	0.447812
$288$	−3106.45	−0.635587
$289$	6758.85	1.37571
$290$	3376.92	0.683791
$291$	3679.32	0.741188
$292$	−13245.7	−2.65460
$293$	−5190.12	−1.03485	−0.517424	−	0.855729i	$-0.673109\pi$
$293$	−5190.12	−1.03485	−0.517424	+	0.855729i	$0.673109\pi$
$294$	4722.29	0.936768
$295$	12183.2	2.40453
$296$	2079.71	0.408380
$297$	6733.54	1.31555
$298$	9130.83	1.77495
$299$	457.995	0.0885837
$300$	4627.55	0.890572
$301$	0	0
$302$	1194.51	0.227603
$303$	4954.22	0.939314
$304$	−631.830	−0.119204
$305$	12665.6	2.37780
$306$	7772.27	1.45200
$307$	−3979.88	−0.739882	−0.369941	−	0.929055i	$-0.620622\pi$
$307$	−3979.88	−0.739882	−0.369941	+	0.929055i	$0.620622\pi$
$308$	3288.63	0.608400
$309$	−1276.11	−0.234936
$310$	−17047.5	−3.12333
$311$	−1170.33	−0.213387	−0.106694	−	0.994292i	$-0.534026\pi$
$311$	−1170.33	−0.213387	−0.106694	+	0.994292i	$0.534026\pi$
$312$	1850.21	0.335730
$313$	−639.068	−0.115407	−0.0577033	−	0.998334i	$-0.518378\pi$
$313$	−639.068	−0.115407	−0.0577033	+	0.998334i	$0.518378\pi$
$314$	−8910.59	−1.60144
$315$	−1353.50	−0.242099
$316$	−12862.1	−2.28971
$317$	8151.43	1.44426	0.722129	−	0.691758i	$-0.243164\pi$
$317$	8151.43	1.44426	0.722129	+	0.691758i	$0.243164\pi$
$318$	−978.055	−0.172474
$319$	−2284.98	−0.401048
$320$	12803.0	2.23659
$321$	−2413.86	−0.419716
$322$	−430.962	−0.0745856
$323$	10222.7	1.76100
$324$	−615.008	−0.105454
$325$	−2958.08	−0.504876
$326$	−5984.80	−1.01677
$327$	−2357.03	−0.398605
$328$	8101.51	1.36381
$329$	221.370	0.0370959
$330$	−10928.8	−1.82307
$331$	−6295.50	−1.04541	−0.522707	−	0.852513i	$-0.675078\pi$
$331$	−6295.50	−1.04541	−0.522707	+	0.852513i	$0.675078\pi$
$332$	3321.52	0.549073
$333$	1594.63	0.262418
$334$	−12154.2	−1.99117
$335$	10879.5	1.77436
$336$	123.904	0.0201176
$337$	−8697.19	−1.40583	−0.702917	−	0.711271i	$-0.748120\pi$
$337$	−8697.19	−1.40583	−0.702917	+	0.711271i	$0.748120\pi$
$338$	6706.22	1.07920
$339$	1311.75	0.210160
$340$	−20823.3	−3.32147
$341$	11535.1	1.83186
$342$	6807.27	1.07630
$343$	3642.71	0.573435
$344$	0	0
$345$	874.991	0.136545
$346$	5951.93	0.924791
$347$	−668.082	−0.103356	−0.0516780	−	0.998664i	$-0.516457\pi$
$347$	−668.082	−0.103356	−0.0516780	+	0.998664i	$0.516457\pi$
$348$	2034.81	0.313441
$349$	−11598.1	−1.77889	−0.889444	−	0.457044i	$-0.848908\pi$
$349$	−11598.1	−1.77889	−0.889444	+	0.457044i	$0.848908\pi$
$350$	2783.48	0.425095
$351$	3833.05	0.582886
$352$	−9217.68	−1.39575
$353$	7934.08	1.19628	0.598142	−	0.801390i	$-0.295906\pi$
$353$	7934.08	1.19628	0.598142	+	0.801390i	$0.295906\pi$
$354$	12016.0	1.80408
$355$	−654.660	−0.0978753
$356$	−511.755	−0.0761880
$357$	−2004.70	−0.297199
$358$	9527.60	1.40656
$359$	−11897.8	−1.74914	−0.874570	−	0.484899i	$-0.838856\pi$
$359$	−11897.8	−1.74914	−0.874570	+	0.484899i	$0.838856\pi$
$360$	−5036.24	−0.737314
$361$	2094.42	0.305354
$362$	8113.37	1.17798
$363$	2953.51	0.427050
$364$	1872.04	0.269565
$365$	16176.2	2.31973
$366$	12491.8	1.78403
$367$	9301.79	1.32302	0.661512	−	0.749935i	$-0.269915\pi$
$367$	9301.79	1.32302	0.661512	+	0.749935i	$0.269915\pi$
$368$	114.122	0.0161659
$369$	6211.88	0.876362
$370$	−6992.87	−0.982546
$371$	−359.423	−0.0502973
$372$	−10272.2	−1.43169
$373$	11919.0	1.65453	0.827265	−	0.561811i	$-0.189895\pi$
$373$	11919.0	1.65453	0.827265	+	0.561811i	$0.189895\pi$
$374$	23062.5	3.18859
$375$	748.173	0.103028
$376$	823.696	0.112976
$377$	−1300.72	−0.177693
$378$	−3606.81	−0.490778
$379$	−2056.42	−0.278710	−0.139355	−	0.990242i	$-0.544503\pi$
$379$	−2056.42	−0.278710	−0.139355	+	0.990242i	$0.544503\pi$
$380$	−18237.8	−2.46206
$381$	4758.76	0.639892
$382$	−27.2127	−0.00364483
$383$	1903.72	0.253983	0.126992	−	0.991904i	$-0.459468\pi$
$383$	1903.72	0.253983	0.126992	+	0.991904i	$0.459468\pi$
$384$	7400.17	0.983433
$385$	−4016.21	−0.531650
$386$	14064.5	1.85457
$387$	0	0
$388$	13851.9	1.81243
$389$	6277.83	0.818248	0.409124	−	0.912479i	$-0.365834\pi$
$389$	6277.83	0.818248	0.409124	+	0.912479i	$0.365834\pi$
$390$	−6221.21	−0.807752
$391$	−1846.44	−0.238820
$392$	6457.18	0.831982
$393$	−3570.35	−0.458271
$394$	17025.5	2.17698
$395$	15707.7	2.00086
$396$	9382.52	1.19063
$397$	4659.76	0.589085	0.294543	−	0.955638i	$-0.404833\pi$
$397$	4659.76	0.589085	0.294543	+	0.955638i	$0.404833\pi$
$398$	−10725.5	−1.35080
$399$	−1755.80	−0.220300
$400$	−737.089	−0.0921362
$401$	5853.34	0.728933	0.364466	−	0.931217i	$-0.381251\pi$
$401$	5853.34	0.728933	0.364466	+	0.931217i	$0.381251\pi$
$402$	10730.2	1.33128
$403$	6566.34	0.811645
$404$	18651.6	2.29691
$405$	751.074	0.0921510
$406$	1223.94	0.149614
$407$	4731.71	0.576270
$408$	−7459.28	−0.905121
$409$	2287.05	0.276497	0.138249	−	0.990398i	$-0.455853\pi$
$409$	2287.05	0.276497	0.138249	+	0.990398i	$0.455853\pi$
$410$	−27240.7	−3.28128
$411$	7685.72	0.922405
$412$	−4804.28	−0.574490
$413$	4415.75	0.526113
$414$	−1229.54	−0.145963
$415$	−4056.38	−0.479807
$416$	−5247.14	−0.618419
$417$	2812.13	0.330241
$418$	20199.0	2.36356
$419$	5013.93	0.584597	0.292299	−	0.956327i	$-0.405580\pi$
$419$	5013.93	0.584597	0.292299	+	0.956327i	$0.405580\pi$
$420$	3576.50	0.415513
$421$	−4203.07	−0.486568	−0.243284	−	0.969955i	$-0.578225\pi$
$421$	−4203.07	−0.486568	−0.243284	+	0.969955i	$0.578225\pi$
$422$	−16906.7	−1.95025
$423$	631.574	0.0725962
$424$	−1337.37	−0.153181
$425$	11925.7	1.36113
$426$	−645.676	−0.0734345
$427$	4590.57	0.520266
$428$	−9087.70	−1.02633
$429$	4209.57	0.473752
$430$	0	0
$431$	2466.18	0.275619	0.137809	−	0.990459i	$-0.455994\pi$
$431$	2466.18	0.275619	0.137809	+	0.990459i	$0.455994\pi$
$432$	955.113	0.106372
$433$	9329.00	1.03539	0.517694	−	0.855566i	$-0.326791\pi$
$433$	9329.00	1.03539	0.517694	+	0.855566i	$0.326791\pi$
$434$	−6178.77	−0.683388
$435$	−2485.00	−0.273900
$436$	−8873.71	−0.974710
$437$	−1617.19	−0.177026
$438$	15954.2	1.74046
$439$	−4218.24	−0.458600	−0.229300	−	0.973356i	$-0.573644\pi$
$439$	−4218.24	−0.458600	−0.229300	+	0.973356i	$0.573644\pi$
$440$	−14943.9	−1.61914
$441$	4951.08	0.534616
$442$	13128.3	1.41278
$443$	−6631.94	−0.711271	−0.355635	−	0.934625i	$-0.615735\pi$
$443$	−6631.94	−0.711271	−0.355635	+	0.934625i	$0.615735\pi$
$444$	−4213.66	−0.450386
$445$	624.976	0.0665769
$446$	13418.9	1.42467
$447$	−6719.18	−0.710976
$448$	4640.38	0.489369
$449$	16157.3	1.69824	0.849120	−	0.528200i	$-0.177133\pi$
$449$	16157.3	1.69824	0.849120	+	0.528200i	$0.177133\pi$
$450$	7941.32	0.831906
$451$	18432.4	1.92449
$452$	4938.45	0.513906
$453$	−879.011	−0.0911690
$454$	−10166.7	−1.05099
$455$	−2286.22	−0.235559
$456$	−6533.13	−0.670925
$457$	−1401.42	−0.143448	−0.0717241	−	0.997425i	$-0.522850\pi$
$457$	−1401.42	−0.143448	−0.0717241	+	0.997425i	$0.522850\pi$
$458$	10370.0	1.05799
$459$	−15453.2	−1.57145
$460$	3294.16	0.333893
$461$	1225.40	0.123802	0.0619009	−	0.998082i	$-0.480284\pi$
$461$	1225.40	0.123802	0.0619009	+	0.998082i	$0.480284\pi$
$462$	−3961.10	−0.398890
$463$	3958.51	0.397338	0.198669	−	0.980067i	$-0.436338\pi$
$463$	3958.51	0.397338	0.198669	+	0.980067i	$0.436338\pi$
$464$	−324.111	−0.0324277
$465$	12544.9	1.25109
$466$	7157.73	0.711536
$467$	−1913.41	−0.189598	−0.0947990	−	0.995496i	$-0.530221\pi$
$467$	−1913.41	−0.189598	−0.0947990	+	0.995496i	$0.530221\pi$
$468$	5340.97	0.527535
$469$	3943.22	0.388233
$470$	−2769.62	−0.271815
$471$	6557.11	0.641477
$472$	16430.5	1.60228
$473$	0	0
$474$	15492.2	1.50122
$475$	10445.0	1.00895
$476$	−7547.28	−0.726741
$477$	−1025.44	−0.0984312
$478$	−19603.9	−1.87586
$479$	−1527.15	−0.145673	−0.0728365	−	0.997344i	$-0.523205\pi$
$479$	−1527.15	−0.145673	−0.0728365	+	0.997344i	$0.523205\pi$
$480$	−10024.6	−0.953243
$481$	2693.51	0.255329
$482$	19452.1	1.83822
$483$	317.136	0.0298761
$484$	11119.4	1.04427
$485$	−16916.5	−1.58379
$486$	−16772.0	−1.56542
$487$	−1636.23	−0.152248	−0.0761240	−	0.997098i	$-0.524254\pi$
$487$	−1636.23	−0.152248	−0.0761240	+	0.997098i	$0.524254\pi$
$488$	17081.0	1.58447
$489$	4404.08	0.407279
$490$	−21711.8	−2.00171
$491$	−15362.3	−1.41200	−0.705998	−	0.708214i	$-0.749501\pi$
$491$	−15362.3	−1.41200	−0.705998	+	0.708214i	$0.749501\pi$
$492$	−16414.3	−1.50409
$493$	5243.94	0.479057
$494$	11498.2	1.04723
$495$	−11458.3	−1.04043
$496$	1636.19	0.148119
$497$	−237.278	−0.0214152
$498$	−4000.72	−0.359993
$499$	−3149.23	−0.282523	−0.141262	−	0.989972i	$-0.545116\pi$
$499$	−3149.23	−0.282523	−0.141262	+	0.989972i	$0.545116\pi$
$500$	2816.72	0.251935
$501$	8944.03	0.797584
$502$	−7676.19	−0.682480
$503$	−15088.1	−1.33746	−0.668731	−	0.743505i	$-0.733162\pi$
$503$	−15088.1	−1.33746	−0.668731	+	0.743505i	$0.733162\pi$
$504$	−1825.36	−0.161325
$505$	−22778.1	−2.00715
$506$	−3648.39	−0.320535
$507$	−4934.96	−0.432287
$508$	17915.7	1.56473
$509$	−4490.78	−0.391061	−0.195531	−	0.980698i	$-0.562643\pi$
$509$	−4490.78	−0.391061	−0.195531	+	0.980698i	$0.562643\pi$
$510$	25081.3	2.17768
$511$	5862.97	0.507558
$512$	−2412.76	−0.208262
$513$	−13534.5	−1.16484
$514$	8527.91	0.731809
$515$	5867.19	0.502018
$516$	0	0
$517$	1874.05	0.159421
$518$	−2534.53	−0.214982
$519$	−4379.89	−0.370435
$520$	−8506.78	−0.717398
$521$	−8322.56	−0.699842	−0.349921	−	0.936779i	$-0.613792\pi$
$521$	−8322.56	−0.699842	−0.349921	+	0.936779i	$0.613792\pi$
$522$	3491.94	0.292793
$523$	−607.497	−0.0507916	−0.0253958	−	0.999677i	$-0.508085\pi$
$523$	−607.497	−0.0507916	−0.0253958	+	0.999677i	$0.508085\pi$
$524$	−13441.6	−1.12061
$525$	−2048.30	−0.170277
$526$	−18902.7	−1.56691
$527$	−26472.7	−2.18818
$528$	1048.93	0.0864563
$529$	−11874.9	−0.975992
$530$	4496.83	0.368546
$531$	12598.2	1.02960
$532$	−6610.21	−0.538701
$533$	10492.6	0.852690
$534$	616.400	0.0499517
$535$	11098.3	0.896861
$536$	14672.3	1.18236
$537$	−7011.15	−0.563414
$538$	−20123.6	−1.61262
$539$	14691.2	1.17402
$540$	27569.5	2.19704
$541$	24878.3	1.97708	0.988542	−	0.150949i	$-0.0482330\pi$
$541$	24878.3	1.97708	0.988542	+	0.150949i	$0.0482330\pi$
$542$	−21992.2	−1.74289
$543$	−5970.45	−0.471854
$544$	21154.2	1.66724
$545$	10837.0	0.851750
$546$	−2254.84	−0.176737
$547$	11419.9	0.892653	0.446327	−	0.894870i	$-0.352732\pi$
$547$	11419.9	0.892653	0.446327	+	0.894870i	$0.352732\pi$
$548$	28935.1	2.25556
$549$	13097.0	1.01815
$550$	23564.1	1.82687
$551$	4592.85	0.355104
$552$	1180.03	0.0909879
$553$	5693.18	0.437791
$554$	−2220.15	−0.170262
$555$	5145.90	0.393570
$556$	10587.1	0.807541
$557$	22723.6	1.72860	0.864300	−	0.502977i	$-0.167762\pi$
$557$	22723.6	1.72860	0.864300	+	0.502977i	$0.167762\pi$
$558$	−17628.1	−1.33738
$559$	0	0
$560$	−569.676	−0.0429879
$561$	−16971.2	−1.27723
$562$	1417.09	0.106364
$563$	19118.0	1.43113	0.715566	−	0.698545i	$-0.246169\pi$
$563$	19118.0	1.43113	0.715566	+	0.698545i	$0.246169\pi$
$564$	−1668.88	−0.124596
$565$	−6031.05	−0.449076
$566$	−7017.10	−0.521114
$567$	272.222	0.0201627
$568$	−882.886	−0.0652202
$569$	10290.8	0.758198	0.379099	−	0.925356i	$-0.376234\pi$
$569$	10290.8	0.758198	0.379099	+	0.925356i	$0.376234\pi$
$570$	21967.2	1.61422
$571$	−19387.7	−1.42093	−0.710465	−	0.703732i	$-0.751516\pi$
$571$	−19387.7	−1.42093	−0.710465	+	0.703732i	$0.751516\pi$
$572$	15848.1	1.15847
$573$	20.0253	0.00145998
$574$	−9873.25	−0.717947
$575$	−1886.60	−0.136829
$576$	13239.1	0.957689
$577$	−2596.32	−0.187324	−0.0936621	−	0.995604i	$-0.529857\pi$
$577$	−2596.32	−0.187324	−0.0936621	+	0.995604i	$0.529857\pi$
$578$	−30648.9	−2.20558
$579$	−10349.8	−0.742870
$580$	−9355.50	−0.669769
$581$	−1470.21	−0.104982
$582$	−16684.4	−1.18830
$583$	−3042.76	−0.216155
$584$	21815.5	1.54577
$585$	−6522.62	−0.460987
$586$	23535.3	1.65910
$587$	−15835.5	−1.11346	−0.556730	−	0.830694i	$-0.687944\pi$
$587$	−15835.5	−1.11346	−0.556730	+	0.830694i	$0.687944\pi$
$588$	−13082.8	−0.917559
$589$	−23185.8	−1.62200
$590$	−55246.5	−3.85502
$591$	−12528.7	−0.872014
$592$	671.164	0.0465957
$593$	−12647.9	−0.875863	−0.437932	−	0.899008i	$-0.644289\pi$
$593$	−12647.9	−0.875863	−0.437932	+	0.899008i	$0.644289\pi$
$594$	−30534.1	−2.10914
$595$	9217.05	0.635063
$596$	−25296.3	−1.73855
$597$	7892.63	0.541078
$598$	−2076.84	−0.142020
$599$	−19556.1	−1.33396	−0.666978	−	0.745078i	$-0.732412\pi$
$599$	−19556.1	−1.33396	−0.666978	+	0.745078i	$0.732412\pi$
$600$	−7621.52	−0.518579
$601$	−12683.1	−0.860822	−0.430411	−	0.902633i	$-0.641631\pi$
$601$	−12683.1	−0.860822	−0.430411	+	0.902633i	$0.641631\pi$
$602$	0	0
$603$	11250.1	0.759766
$604$	−3309.29	−0.222936
$605$	−13579.4	−0.912533
$606$	−22465.5	−1.50594
$607$	19151.8	1.28064	0.640321	−	0.768108i	$-0.278802\pi$
$607$	19151.8	1.28064	0.640321	+	0.768108i	$0.278802\pi$
$608$	18527.7	1.23585
$609$	−900.674	−0.0599296
$610$	−57433.8	−3.81217
$611$	1066.80	0.0706352
$612$	−21532.5	−1.42222
$613$	2222.58	0.146442	0.0732212	−	0.997316i	$-0.476672\pi$
$613$	2222.58	0.146442	0.0732212	+	0.997316i	$0.476672\pi$
$614$	18047.3	1.18620
$615$	20045.9	1.31435
$616$	−5416.34	−0.354270
$617$	−2823.15	−0.184207	−0.0921036	−	0.995749i	$-0.529359\pi$
$617$	−2823.15	−0.184207	−0.0921036	+	0.995749i	$0.529359\pi$
$618$	5786.68	0.376658
$619$	−473.132	−0.0307218	−0.0153609	−	0.999882i	$-0.504890\pi$
$619$	−473.132	−0.0307218	−0.0153609	+	0.999882i	$0.504890\pi$
$620$	47228.8	3.05928
$621$	2444.64	0.157971
$622$	5307.03	0.342110
$623$	226.519	0.0145671
$624$	597.102	0.0383064
$625$	−17238.2	−1.10324
$626$	2897.94	0.185024
$627$	−14864.0	−0.946750
$628$	24686.1	1.56861
$629$	−10859.1	−0.688362
$630$	6137.63	0.388141
$631$	−5193.02	−0.327624	−0.163812	−	0.986492i	$-0.552379\pi$
$631$	−5193.02	−0.327624	−0.163812	+	0.986492i	$0.552379\pi$
$632$	21183.7	1.33330
$633$	12441.3	0.781194
$634$	−36963.7	−2.31548
$635$	−21879.5	−1.36734
$636$	2709.63	0.168937
$637$	8362.94	0.520175
$638$	10361.5	0.642974
$639$	−676.958	−0.0419093
$640$	−34023.9	−2.10143
$641$	10049.5	0.619240	0.309620	−	0.950860i	$-0.399798\pi$
$641$	10049.5	0.619240	0.309620	+	0.950860i	$0.399798\pi$
$642$	10946.0	0.672903
$643$	−18093.4	−1.10969	−0.554847	−	0.831952i	$-0.687223\pi$
$643$	−18093.4	−1.10969	−0.554847	+	0.831952i	$0.687223\pi$
$644$	1193.95	0.0730562
$645$	0	0
$646$	−46356.0	−2.82330
$647$	−27692.1	−1.68267	−0.841336	−	0.540512i	$-0.818231\pi$
$647$	−27692.1	−1.68267	−0.841336	+	0.540512i	$0.818231\pi$
$648$	1012.91	0.0614057
$649$	37382.4	2.26099
$650$	13413.8	0.809434
$651$	4546.82	0.273739
$652$	16580.5	0.995922
$653$	−5851.06	−0.350643	−0.175321	−	0.984511i	$-0.556096\pi$
$653$	−5851.06	−0.350643	−0.175321	+	0.984511i	$0.556096\pi$
$654$	10688.2	0.639057
$655$	16415.5	0.979246
$656$	2614.52	0.155610
$657$	16727.2	0.993285
$658$	−1003.83	−0.0594734
$659$	−21457.2	−1.26837	−0.634184	−	0.773182i	$-0.718664\pi$
$659$	−21457.2	−1.26837	−0.634184	+	0.773182i	$0.718664\pi$
$660$	30277.6	1.78569
$661$	20593.3	1.21178	0.605890	−	0.795548i	$-0.292817\pi$
$661$	20593.3	1.21178	0.605890	+	0.795548i	$0.292817\pi$
$662$	28547.7	1.67604
$663$	−9660.79	−0.565904
$664$	−5470.51	−0.319724
$665$	8072.66	0.470744
$666$	−7231.05	−0.420717
$667$	−829.571	−0.0481576
$668$	33672.4	1.95034
$669$	−9874.68	−0.570668
$670$	−49334.6	−2.84472
$671$	38862.4	2.23587
$672$	−3633.35	−0.208570
$673$	19282.2	1.10442	0.552210	−	0.833705i	$-0.313785\pi$
$673$	19282.2	1.10442	0.552210	+	0.833705i	$0.313785\pi$
$674$	39438.6	2.25388
$675$	−15789.3	−0.900343
$676$	−18579.1	−1.05707
$677$	15121.1	0.858423	0.429211	−	0.903204i	$-0.358792\pi$
$677$	15121.1	0.858423	0.429211	+	0.903204i	$0.358792\pi$
$678$	−5948.29	−0.336936
$679$	−6131.29	−0.346535
$680$	34295.7	1.93409
$681$	7481.46	0.420984
$682$	−52307.6	−2.93689
$683$	4213.32	0.236044	0.118022	−	0.993011i	$-0.462345\pi$
$683$	4213.32	0.236044	0.118022	+	0.993011i	$0.462345\pi$
$684$	−18859.0	−1.05423
$685$	−35336.8	−1.97102
$686$	−16518.4	−0.919350
$687$	−7631.04	−0.423788
$688$	0	0
$689$	−1732.08	−0.0957724
$690$	−3967.76	−0.218913
$691$	34542.1	1.90165	0.950826	−	0.309725i	$-0.100237\pi$
$691$	34542.1	1.90165	0.950826	+	0.309725i	$0.100237\pi$
$692$	−16489.4	−0.905827
$693$	−4153.01	−0.227648
$694$	3029.51	0.165704
$695$	−12929.4	−0.705669
$696$	−3351.31	−0.182516
$697$	−42301.6	−2.29883
$698$	52593.1	2.85197
$699$	−5267.22	−0.285014
$700$	−7711.43	−0.416378
$701$	32460.7	1.74896	0.874482	−	0.485058i	$-0.161201\pi$
$701$	32460.7	1.74896	0.874482	+	0.485058i	$0.161201\pi$
$702$	−17381.5	−0.934503
$703$	−9510.82	−0.510252
$704$	39284.0	2.10309
$705$	2038.10	0.108878
$706$	−35978.1	−1.91792
$707$	−8255.80	−0.439167
$708$	−33289.6	−1.76709
$709$	−31304.1	−1.65818	−0.829091	−	0.559113i	$-0.811142\pi$
$709$	−31304.1	−1.65818	−0.829091	+	0.559113i	$0.811142\pi$
$710$	2968.64	0.156917
$711$	16242.7	0.856751
$712$	842.854	0.0443642
$713$	4187.87	0.219968
$714$	9090.57	0.476479
$715$	−19354.4	−1.01233
$716$	−26395.5	−1.37772
$717$	14426.1	0.751397
$718$	53952.1	2.80428
$719$	−11067.7	−0.574071	−0.287035	−	0.957920i	$-0.592670\pi$
$719$	−11067.7	−0.574071	−0.287035	+	0.957920i	$0.592670\pi$
$720$	−1625.30	−0.0841267
$721$	2126.53	0.109842
$722$	−9497.42	−0.489553
$723$	−14314.4	−0.736318
$724$	−22477.5	−1.15383
$725$	5358.00	0.274470
$726$	−13393.1	−0.684661
$727$	21160.6	1.07951	0.539754	−	0.841823i	$-0.318517\pi$
$727$	21160.6	1.07951	0.539754	+	0.841823i	$0.318517\pi$
$728$	−3083.23	−0.156967
$729$	13663.9	0.694199
$730$	−73353.0	−3.71906
$731$	0	0
$732$	−34607.6	−1.74745
$733$	−10312.5	−0.519647	−0.259824	−	0.965656i	$-0.583664\pi$
$733$	−10312.5	−0.519647	−0.259824	+	0.965656i	$0.583664\pi$
$734$	−42180.2	−2.12112
$735$	15977.2	0.801808
$736$	−3346.51	−0.167601
$737$	33382.1	1.66845
$738$	−28168.6	−1.40501
$739$	23357.4	1.16267	0.581337	−	0.813663i	$-0.302530\pi$
$739$	23357.4	1.16267	0.581337	+	0.813663i	$0.302530\pi$
$740$	19373.2	0.962398
$741$	−8461.31	−0.419479
$742$	1629.85	0.0806383
$743$	−19675.6	−0.971504	−0.485752	−	0.874097i	$-0.661454\pi$
$743$	−19675.6	−0.971504	−0.485752	+	0.874097i	$0.661454\pi$
$744$	16918.2	0.833673
$745$	30892.9	1.51923
$746$	−54048.0	−2.65260
$747$	−4194.55	−0.205449
$748$	−63892.9	−3.12320
$749$	4022.51	0.196234
$750$	−3392.69	−0.165178
$751$	−17954.3	−0.872385	−0.436192	−	0.899853i	$-0.643673\pi$
$751$	−17954.3	−0.872385	−0.436192	+	0.899853i	$0.643673\pi$
$752$	265.823	0.0128904
$753$	5648.74	0.273375
$754$	5898.28	0.284884
$755$	4041.45	0.194813
$756$	9992.40	0.480714
$757$	−17228.1	−0.827168	−0.413584	−	0.910466i	$-0.635723\pi$
$757$	−17228.1	−0.827168	−0.413584	+	0.910466i	$0.635723\pi$
$758$	9325.10	0.446837
$759$	2684.77	0.128394
$760$	30037.5	1.43365
$761$	−12816.7	−0.610519	−0.305260	−	0.952269i	$-0.598743\pi$
$761$	−12816.7	−0.610519	−0.305260	+	0.952269i	$0.598743\pi$
$762$	−21579.2	−1.02590
$763$	3927.79	0.186364
$764$	75.3910	0.00357009
$765$	26296.4	1.24281
$766$	−8632.67	−0.407195
$767$	21279.8	1.00178
$768$	−11279.9	−0.529985
$769$	−16838.5	−0.789614	−0.394807	−	0.918764i	$-0.629189\pi$
$769$	−16838.5	−0.789614	−0.394807	+	0.918764i	$0.629189\pi$
$770$	18212.0	0.852359
$771$	−6275.50	−0.293134
$772$	−38964.7	−1.81654
$773$	11690.7	0.543965	0.271983	−	0.962302i	$-0.412321\pi$
$773$	11690.7	0.543965	0.271983	+	0.962302i	$0.412321\pi$
$774$	0	0
$775$	−27048.5	−1.25369
$776$	−22813.9	−1.05538
$777$	1865.10	0.0861135
$778$	−28467.6	−1.31184
$779$	−37049.4	−1.70402
$780$	17235.4	0.791189
$781$	−2008.72	−0.0920329
$782$	8372.92	0.382884
$783$	−6942.84	−0.316880
$784$	2083.86	0.0949281
$785$	−30147.8	−1.37073
$786$	16190.2	0.734715
$787$	−20937.2	−0.948325	−0.474163	−	0.880437i	$-0.657249\pi$
$787$	−20937.2	−0.948325	−0.474163	+	0.880437i	$0.657249\pi$
$788$	−47167.8	−2.13234
$789$	13910.1	0.627645
$790$	−71228.7	−3.20785
$791$	−2185.92	−0.0982584
$792$	−15452.9	−0.693302
$793$	22122.3	0.990651
$794$	−21130.3	−0.944441
$795$	−3309.12	−0.147625
$796$	29714.1	1.32310
$797$	2263.84	0.100614	0.0503070	−	0.998734i	$-0.483980\pi$
$797$	2263.84	0.100614	0.0503070	+	0.998734i	$0.483980\pi$
$798$	7961.88	0.353192
$799$	−4300.88	−0.190431
$800$	21614.3	0.955228
$801$	646.263	0.0285076
$802$	−26542.7	−1.16865
$803$	49634.1	2.18126
$804$	−29727.3	−1.30398
$805$	−1458.10	−0.0638401
$806$	−29775.9	−1.30126
$807$	14808.5	0.645954
$808$	−30719.0	−1.33749
$809$	41722.8	1.81322	0.906611	−	0.421967i	$-0.138660\pi$
$809$	41722.8	1.81322	0.906611	+	0.421967i	$0.138660\pi$
$810$	−3405.84	−0.147740
$811$	−27390.6	−1.18596	−0.592980	−	0.805217i	$-0.702049\pi$
$811$	−27390.6	−1.18596	−0.592980	+	0.805217i	$0.702049\pi$
$812$	−3390.85	−0.146546
$813$	16183.6	0.698133
$814$	−21456.5	−0.923896
$815$	−20248.8	−0.870286
$816$	−2407.26	−0.103273
$817$	0	0
$818$	−10370.9	−0.443290
$819$	−2364.09	−0.100864
$820$	75468.5	3.21399
$821$	−29675.9	−1.26150	−0.630752	−	0.775984i	$-0.717254\pi$
$821$	−29675.9	−1.26150	−0.630752	+	0.775984i	$0.717254\pi$
$822$	−34851.9	−1.47883
$823$	−25520.1	−1.08089	−0.540445	−	0.841379i	$-0.681744\pi$
$823$	−25520.1	−1.08089	−0.540445	+	0.841379i	$0.681744\pi$
$824$	7912.60	0.334525
$825$	−17340.3	−0.731772
$826$	−20023.8	−0.843482
$827$	−8495.30	−0.357208	−0.178604	−	0.983921i	$-0.557158\pi$
$827$	−8495.30	−0.357208	−0.178604	+	0.983921i	$0.557158\pi$
$828$	3406.36	0.142970
$829$	20856.6	0.873800	0.436900	−	0.899510i	$-0.356076\pi$
$829$	20856.6	0.873800	0.436900	+	0.899510i	$0.356076\pi$
$830$	18394.2	0.769243
$831$	1633.76	0.0682005
$832$	22362.3	0.931820
$833$	−33715.8	−1.40238
$834$	−12752.0	−0.529454
$835$	−41122.2	−1.70430
$836$	−55960.0	−2.31509
$837$	35049.1	1.44740
$838$	−22736.3	−0.937246
$839$	3901.70	0.160550	0.0802752	−	0.996773i	$-0.474420\pi$
$839$	3901.70	0.160550	0.0802752	+	0.996773i	$0.474420\pi$
$840$	−5890.46	−0.241953
$841$	−22033.0	−0.903399
$842$	19059.4	0.780083
$843$	−1042.81	−0.0426052
$844$	46838.8	1.91026
$845$	22689.6	0.923722
$846$	−2863.95	−0.116389
$847$	−4921.79	−0.199663
$848$	−431.598	−0.0174777
$849$	5163.73	0.208738
$850$	−54078.7	−2.18222
$851$	1717.86	0.0691981
$852$	1788.80	0.0719287
$853$	−1841.86	−0.0739323	−0.0369662	−	0.999317i	$-0.511769\pi$
$853$	−1841.86	−0.0739323	−0.0369662	+	0.999317i	$0.511769\pi$
$854$	−20816.6	−0.834107
$855$	23031.5	0.921239
$856$	14967.3	0.597632
$857$	20314.0	0.809699	0.404849	−	0.914383i	$-0.367324\pi$
$857$	20314.0	0.809699	0.404849	+	0.914383i	$0.367324\pi$
$858$	−19088.8	−0.759536
$859$	9668.78	0.384045	0.192022	−	0.981391i	$-0.438495\pi$
$859$	9668.78	0.384045	0.192022	+	0.981391i	$0.438495\pi$
$860$	0	0
$861$	7265.51	0.287582
$862$	−11183.2	−0.441881
$863$	22251.2	0.877680	0.438840	−	0.898565i	$-0.355389\pi$
$863$	22251.2	0.877680	0.438840	+	0.898565i	$0.355389\pi$
$864$	−28007.6	−1.10282
$865$	20137.5	0.791557
$866$	−42303.6	−1.65997
$867$	22553.8	0.883469
$868$	17117.8	0.669374
$869$	48196.7	1.88143
$870$	11268.5	0.439126
$871$	19002.7	0.739243
$872$	14614.9	0.567572
$873$	−17492.7	−0.678165
$874$	7333.34	0.283814
$875$	−1246.77	−0.0481697
$876$	−44200.0	−1.70477
$877$	−42819.7	−1.64871	−0.824354	−	0.566074i	$-0.808462\pi$
$877$	−42819.7	−1.64871	−0.824354	+	0.566074i	$0.808462\pi$
$878$	19128.1	0.735243
$879$	−17319.1	−0.664572
$880$	−4822.70	−0.184742
$881$	26341.7	1.00735	0.503674	−	0.863894i	$-0.331981\pi$
$881$	26341.7	1.00735	0.503674	+	0.863894i	$0.331981\pi$
$882$	−22451.3	−0.857115
$883$	38448.2	1.46533	0.732664	−	0.680590i	$-0.238277\pi$
$883$	38448.2	1.46533	0.732664	+	0.680590i	$0.238277\pi$
$884$	−36370.9	−1.38381
$885$	40654.7	1.54417
$886$	30073.4	1.14033
$887$	5960.97	0.225648	0.112824	−	0.993615i	$-0.464010\pi$
$887$	5960.97	0.225648	0.112824	+	0.993615i	$0.464010\pi$
$888$	6939.85	0.262259
$889$	−7930.09	−0.299175
$890$	−2834.04	−0.106738
$891$	2304.55	0.0866503
$892$	−37176.1	−1.39546
$893$	−3766.88	−0.141158
$894$	30469.0	1.13986
$895$	32235.3	1.20392
$896$	−12331.8	−0.459795
$897$	1528.30	0.0568879
$898$	−73267.4	−2.72268
$899$	−11893.7	−0.441242
$900$	−22000.9	−0.814847
$901$	6983.02	0.258200
$902$	−83583.9	−3.08541
$903$	0	0
$904$	−8133.58	−0.299246
$905$	27450.5	1.00827
$906$	3985.99	0.146165
$907$	11008.3	0.403004	0.201502	−	0.979488i	$-0.435418\pi$
$907$	11008.3	0.403004	0.201502	+	0.979488i	$0.435418\pi$
$908$	28166.2	1.02943
$909$	−23553.9	−0.859445
$910$	10367.2	0.377657
$911$	46454.7	1.68947	0.844737	−	0.535181i	$-0.179757\pi$
$911$	46454.7	1.68947	0.844737	+	0.535181i	$0.179757\pi$
$912$	−2108.37	−0.0765518
$913$	−12446.4	−0.451166
$914$	6354.93	0.229981
$915$	42264.3	1.52701
$916$	−28729.3	−1.03629
$917$	5949.70	0.214260
$918$	70074.6	2.51940
$919$	−20767.9	−0.745452	−0.372726	−	0.927941i	$-0.621577\pi$
$919$	−20767.9	−0.745452	−0.372726	+	0.927941i	$0.621577\pi$
$920$	−5425.44	−0.194426
$921$	−13280.6	−0.475147
$922$	−5556.74	−0.198483
$923$	−1143.46	−0.0407773
$924$	10973.9	0.390710
$925$	−11095.3	−0.394389
$926$	−17950.4	−0.637026
$927$	6067.03	0.214960
$928$	9504.19	0.336197
$929$	−16007.8	−0.565339	−0.282669	−	0.959217i	$-0.591220\pi$
$929$	−16007.8	−0.565339	−0.282669	+	0.959217i	$0.591220\pi$
$930$	−56886.4	−2.00578
$931$	−29529.6	−1.03952
$932$	−19830.0	−0.696945
$933$	−3905.32	−0.137036
$934$	8676.62	0.303970
$935$	78028.8	2.72921
$936$	−8796.52	−0.307183
$937$	−47353.3	−1.65098	−0.825488	−	0.564419i	$-0.809100\pi$
$937$	−47353.3	−1.65098	−0.825488	+	0.564419i	$0.809100\pi$
$938$	−17881.0	−0.622427
$939$	−2132.53	−0.0741134
$940$	7673.03	0.266241
$941$	953.004	0.0330149	0.0165075	−	0.999864i	$-0.494745\pi$
$941$	953.004	0.0330149	0.0165075	+	0.999864i	$0.494745\pi$
$942$	−29734.1	−1.02844
$943$	6691.94	0.231092
$944$	5302.46	0.182818
$945$	−12203.1	−0.420072
$946$	0	0
$947$	−49178.4	−1.68752	−0.843761	−	0.536719i	$-0.819663\pi$
$947$	−49178.4	−1.68752	−0.843761	+	0.536719i	$0.819663\pi$
$948$	−42919.9	−1.47044
$949$	28254.1	0.966455
$950$	−47364.3	−1.61758
$951$	27200.8	0.927493
$952$	12430.3	0.423180
$953$	−28559.9	−0.970772	−0.485386	−	0.874300i	$-0.661321\pi$
$953$	−28559.9	−0.970772	−0.485386	+	0.874300i	$0.661321\pi$
$954$	4649.99	0.157808
$955$	−92.0706	−0.00311972
$956$	54311.1	1.83739
$957$	−7624.83	−0.257550
$958$	6925.07	0.233548
$959$	−12807.6	−0.431261
$960$	42722.8	1.43633
$961$	30251.2	1.01545
$962$	−12214.1	−0.409353
$963$	11476.3	0.384028
$964$	−53890.7	−1.80052
$965$	47585.4	1.58739
$966$	−1438.09	−0.0478984
$967$	42440.5	1.41137	0.705685	−	0.708526i	$-0.250640\pi$
$967$	42440.5	1.41137	0.705685	+	0.708526i	$0.250640\pi$
$968$	−18313.5	−0.608075
$969$	34112.4	1.13091
$970$	76710.1	2.53919
$971$	−16692.9	−0.551699	−0.275849	−	0.961201i	$-0.588959\pi$
$971$	−16692.9	−0.551699	−0.275849	+	0.961201i	$0.588959\pi$
$972$	46465.6	1.53332
$973$	−4686.19	−0.154401
$974$	7419.71	0.244089
$975$	−9870.92	−0.324228
$976$	5512.40	0.180786
$977$	−29557.2	−0.967879	−0.483940	−	0.875101i	$-0.660795\pi$
$977$	−29557.2	−0.967879	−0.483940	+	0.875101i	$0.660795\pi$
$978$	−19970.9	−0.652964
$979$	1917.64	0.0626028
$980$	60151.0	1.96067
$981$	11206.1	0.364712
$982$	69662.3	2.26376
$983$	19927.3	0.646574	0.323287	−	0.946301i	$-0.395212\pi$
$983$	19927.3	0.646574	0.323287	+	0.946301i	$0.395212\pi$
$984$	27034.2	0.875832
$985$	57603.3	1.86334
$986$	−23779.3	−0.768041
$987$	738.698	0.0238227
$988$	−31855.1	−1.02575
$989$	0	0
$990$	51959.3	1.66806
$991$	39265.8	1.25865	0.629323	−	0.777144i	$-0.283332\pi$
$991$	39265.8	1.25865	0.629323	+	0.777144i	$0.283332\pi$
$992$	−47979.5	−1.53563
$993$	−21007.7	−0.671357
$994$	1075.97	0.0343336
$995$	−36288.1	−1.15619
$996$	11083.7	0.352611
$997$	20423.8	0.648775	0.324388	−	0.945924i	$-0.394842\pi$
$997$	20423.8	0.648775	0.324388	+	0.945924i	$0.394842\pi$
$998$	14280.6	0.452950
$999$	14377.1	0.455328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.l.1.6		60
43.25	even	21		43.4.g.a.23.1	yes	120
43.31	even	21		43.4.g.a.15.1	✓	120
43.42	odd	2		1849.4.a.k.1.55		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.15.1	✓	120	43.31	even	21
43.4.g.a.23.1	yes	120	43.25	even	21
1849.4.a.k.1.55		60	43.42	odd	2
1849.4.a.l.1.6		60	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)

\(f(q)\)	\(=\)	\(q-4.53463 q^{2} +3.33693 q^{3} +12.5629 q^{4} -15.3423 q^{5} -15.1318 q^{6} -5.56073 q^{7} -20.6909 q^{8} -15.8649 q^{9} +O(q^{10})\)	\(q-4.53463 q^{2} +3.33693 q^{3} +12.5629 q^{4} -15.3423 q^{5} -15.1318 q^{6} -5.56073 q^{7} -20.6909 q^{8} -15.8649 q^{9} +69.5716 q^{10} -47.0754 q^{11} +41.9214 q^{12} -26.7976 q^{13} +25.2159 q^{14} -51.1962 q^{15} -6.67737 q^{16} +108.036 q^{17} +71.9413 q^{18} +94.6225 q^{19} -192.743 q^{20} -18.5558 q^{21} +213.470 q^{22} -17.0909 q^{23} -69.0442 q^{24} +110.386 q^{25} +121.517 q^{26} -143.037 q^{27} -69.8587 q^{28} +48.5387 q^{29} +232.156 q^{30} -245.035 q^{31} +195.807 q^{32} -157.088 q^{33} -489.905 q^{34} +85.3144 q^{35} -199.308 q^{36} -100.513 q^{37} -429.078 q^{38} -89.4217 q^{39} +317.446 q^{40} -391.549 q^{41} +84.1436 q^{42} -591.402 q^{44} +243.404 q^{45} +77.5010 q^{46} -39.8096 q^{47} -22.2820 q^{48} -312.078 q^{49} -500.560 q^{50} +360.510 q^{51} -336.654 q^{52} +64.6359 q^{53} +648.621 q^{54} +722.246 q^{55} +115.056 q^{56} +315.749 q^{57} -220.105 q^{58} -794.094 q^{59} -643.171 q^{60} -825.534 q^{61} +1111.14 q^{62} +88.2203 q^{63} -834.491 q^{64} +411.136 q^{65} +712.334 q^{66} -709.119 q^{67} +1357.25 q^{68} -57.0313 q^{69} -386.869 q^{70} +42.6703 q^{71} +328.258 q^{72} -1054.35 q^{73} +455.790 q^{74} +368.351 q^{75} +1188.73 q^{76} +261.774 q^{77} +405.494 q^{78} -1023.82 q^{79} +102.446 q^{80} -48.9544 q^{81} +1775.53 q^{82} +264.392 q^{83} -233.114 q^{84} -1657.53 q^{85} +161.970 q^{87} +974.033 q^{88} -40.7355 q^{89} -1103.75 q^{90} +149.014 q^{91} -214.711 q^{92} -817.666 q^{93} +180.522 q^{94} -1451.73 q^{95} +653.394 q^{96} +1102.61 q^{97} +1415.16 q^{98} +746.846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * q^99

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