LMFDB - Embedded newform 1849.4.a.i.1.36

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			1.36
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)

$f(q)$	$=$	$q+2.34509 q^{2} -2.42890 q^{3} -2.50055 q^{4} +18.7081 q^{5} -5.69599 q^{6} +0.512587 q^{7} -24.6247 q^{8} -21.1004 q^{9} +O(q^{10})$	\(q+2.34509 q^{2} -2.42890 q^{3} -2.50055 q^{4} +18.7081 q^{5} -5.69599 q^{6} +0.512587 q^{7} -24.6247 q^{8} -21.1004 q^{9} +43.8722 q^{10} +5.04244 q^{11} +6.07358 q^{12} -48.6308 q^{13} +1.20206 q^{14} -45.4401 q^{15} -37.7429 q^{16} -6.35958 q^{17} -49.4825 q^{18} +123.762 q^{19} -46.7805 q^{20} -1.24502 q^{21} +11.8250 q^{22} +141.010 q^{23} +59.8111 q^{24} +224.993 q^{25} -114.044 q^{26} +116.831 q^{27} -1.28175 q^{28} -206.672 q^{29} -106.561 q^{30} +164.801 q^{31} +108.487 q^{32} -12.2476 q^{33} -14.9138 q^{34} +9.58954 q^{35} +52.7627 q^{36} -365.186 q^{37} +290.233 q^{38} +118.119 q^{39} -460.682 q^{40} -175.812 q^{41} -2.91969 q^{42} -12.6089 q^{44} -394.749 q^{45} +330.680 q^{46} +219.602 q^{47} +91.6737 q^{48} -342.737 q^{49} +527.630 q^{50} +15.4468 q^{51} +121.604 q^{52} +34.4084 q^{53} +273.980 q^{54} +94.3346 q^{55} -12.6223 q^{56} -300.605 q^{57} -484.665 q^{58} -771.285 q^{59} +113.625 q^{60} -432.289 q^{61} +386.473 q^{62} -10.8158 q^{63} +556.356 q^{64} -909.791 q^{65} -28.7217 q^{66} -644.829 q^{67} +15.9024 q^{68} -342.498 q^{69} +22.4883 q^{70} -919.149 q^{71} +519.593 q^{72} +98.7029 q^{73} -856.394 q^{74} -546.486 q^{75} -309.472 q^{76} +2.58469 q^{77} +277.001 q^{78} +411.930 q^{79} -706.098 q^{80} +285.940 q^{81} -412.295 q^{82} +271.229 q^{83} +3.11324 q^{84} -118.976 q^{85} +501.986 q^{87} -124.169 q^{88} +115.517 q^{89} -925.723 q^{90} -24.9276 q^{91} -352.601 q^{92} -400.285 q^{93} +514.986 q^{94} +2315.35 q^{95} -263.505 q^{96} +623.381 q^{97} -803.750 q^{98} -106.398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.34509	0.829115	0.414557	−	0.910023i	$-0.363936\pi$
$2$	2.34509	0.829115	0.414557	+	0.910023i	$0.363936\pi$
$3$	−2.42890	−0.467442	−0.233721	−	0.972304i	$-0.575090\pi$
$3$	−2.42890	−0.467442	−0.233721	+	0.972304i	$0.575090\pi$
$4$	−2.50055	−0.312569
$5$	18.7081	1.67330	0.836652	−	0.547735i	$-0.184510\pi$
$5$	18.7081	1.67330	0.836652	+	0.547735i	$0.184510\pi$
$6$	−5.69599	−0.387563
$7$	0.512587	0.0276771	0.0138386	−	0.999904i	$-0.495595\pi$
$7$	0.512587	0.0276771	0.0138386	+	0.999904i	$0.495595\pi$
$8$	−24.6247	−1.08827
$9$	−21.1004	−0.781498
$10$	43.8722	1.38736
$11$	5.04244	0.138214	0.0691070	−	0.997609i	$-0.477985\pi$
$11$	5.04244	0.138214	0.0691070	+	0.997609i	$0.477985\pi$
$12$	6.07358	0.146108
$13$	−48.6308	−1.03752	−0.518760	−	0.854920i	$-0.673606\pi$
$13$	−48.6308	−1.03752	−0.518760	+	0.854920i	$0.673606\pi$
$14$	1.20206	0.0229475
$15$	−45.4401	−0.782173
$16$	−37.7429	−0.589732
$17$	−6.35958	−0.0907308	−0.0453654	−	0.998970i	$-0.514445\pi$
$17$	−6.35958	−0.0907308	−0.0453654	+	0.998970i	$0.514445\pi$
$18$	−49.4825	−0.647951
$19$	123.762	1.49436	0.747182	−	0.664620i	$-0.231406\pi$
$19$	123.762	1.49436	0.747182	+	0.664620i	$0.231406\pi$
$20$	−46.7805	−0.523022
$21$	−1.24502	−0.0129375
$22$	11.8250	0.114595
$23$	141.010	1.27837	0.639185	−	0.769053i	$-0.279272\pi$
$23$	141.010	1.27837	0.639185	+	0.769053i	$0.279272\pi$
$24$	59.8111	0.508703
$25$	224.993	1.79995
$26$	−114.044	−0.860224
$27$	116.831	0.832747
$28$	−1.28175	−0.00865100
$29$	−206.672	−1.32338	−0.661690	−	0.749777i	$-0.730161\pi$
$29$	−206.672	−1.32338	−0.661690	+	0.749777i	$0.730161\pi$
$30$	−106.561	−0.648511
$31$	164.801	0.954809	0.477405	−	0.878684i	$-0.341578\pi$
$31$	164.801	0.954809	0.477405	+	0.878684i	$0.341578\pi$
$32$	108.487	0.599314
$33$	−12.2476	−0.0646071
$34$	−14.9138	−0.0752263
$35$	9.58954	0.0463122
$36$	52.7627	0.244272
$37$	−365.186	−1.62260	−0.811300	−	0.584630i	$-0.801240\pi$
$37$	−365.186	−1.62260	−0.811300	+	0.584630i	$0.801240\pi$
$38$	290.233	1.23900
$39$	118.119	0.484981
$40$	−460.682	−1.82101
$41$	−175.812	−0.669689	−0.334844	−	0.942273i	$-0.608684\pi$
$41$	−175.812	−0.669689	−0.334844	+	0.942273i	$0.608684\pi$
$42$	−2.91969	−0.0107266
$43$	0	0
$43$	0	0
$44$	−12.6089	−0.0432013
$45$	−394.749	−1.30768
$46$	330.680	1.05992
$47$	219.602	0.681537	0.340768	−	0.940147i	$-0.389313\pi$
$47$	219.602	0.681537	0.340768	+	0.940147i	$0.389313\pi$
$48$	91.6737	0.275666
$49$	−342.737	−0.999234
$50$	527.630	1.49236
$51$	15.4468	0.0424114
$52$	121.604	0.324296
$53$	34.4084	0.0891765	0.0445883	−	0.999005i	$-0.485802\pi$
$53$	34.4084	0.0891765	0.0445883	+	0.999005i	$0.485802\pi$
$54$	273.980	0.690443
$55$	94.3346	0.231274
$56$	−12.6223	−0.0301202
$57$	−300.605	−0.698529
$58$	−484.665	−1.09723
$59$	−771.285	−1.70191	−0.850956	−	0.525238i	$-0.823976\pi$
$59$	−771.285	−1.70191	−0.850956	+	0.525238i	$0.823976\pi$
$60$	113.625	0.244483
$61$	−432.289	−0.907360	−0.453680	−	0.891165i	$-0.649889\pi$
$61$	−432.289	−0.907360	−0.453680	+	0.891165i	$0.649889\pi$
$62$	386.473	0.791647
$63$	−10.8158	−0.0216296
$64$	556.356	1.08663
$65$	−909.791	−1.73609
$66$	−28.7217	−0.0535667
$67$	−644.829	−1.17580	−0.587899	−	0.808935i	$-0.700045\pi$
$67$	−644.829	−1.17580	−0.587899	+	0.808935i	$0.700045\pi$
$68$	15.9024	0.0283596
$69$	−342.498	−0.597564
$70$	22.4883	0.0383982
$71$	−919.149	−1.53638	−0.768190	−	0.640222i	$-0.778842\pi$
$71$	−919.149	−1.53638	−0.768190	+	0.640222i	$0.778842\pi$
$72$	519.593	0.850481
$73$	98.7029	0.158251	0.0791253	−	0.996865i	$-0.474787\pi$
$73$	98.7029	0.158251	0.0791253	+	0.996865i	$0.474787\pi$
$74$	−856.394	−1.34532
$75$	−546.486	−0.841371
$76$	−309.472	−0.467091
$77$	2.58469	0.00382536
$78$	277.001	0.402105
$79$	411.930	0.586655	0.293327	−	0.956012i	$-0.405237\pi$
$79$	411.930	0.586655	0.293327	+	0.956012i	$0.405237\pi$
$80$	−706.098	−0.986802
$81$	285.940	0.392237
$82$	−412.295	−0.555249
$83$	271.229	0.358689	0.179345	−	0.983786i	$-0.442602\pi$
$83$	271.229	0.358689	0.179345	+	0.983786i	$0.442602\pi$
$84$	3.11324	0.00404384
$85$	−118.976	−0.151820
$86$	0	0
$87$	501.986	0.618604
$88$	−124.169	−0.150414
$89$	115.517	0.137582	0.0687908	−	0.997631i	$-0.478086\pi$
$89$	115.517	0.137582	0.0687908	+	0.997631i	$0.478086\pi$
$90$	−925.723	−1.08422
$91$	−24.9276	−0.0287156
$92$	−352.601	−0.399578
$93$	−400.285	−0.446318
$94$	514.986	0.565072
$95$	2315.35	2.50053
$96$	−263.505	−0.280145
$97$	623.381	0.652523	0.326261	−	0.945280i	$-0.394211\pi$
$97$	623.381	0.652523	0.326261	+	0.945280i	$0.394211\pi$
$98$	−803.750	−0.828480
$99$	−106.398	−0.108014
$100$	−562.606	−0.562606
$101$	134.852	0.132854	0.0664270	−	0.997791i	$-0.478840\pi$
$101$	134.852	0.132854	0.0664270	+	0.997791i	$0.478840\pi$
$102$	36.2241	0.0351639
$103$	−246.042	−0.235371	−0.117686	−	0.993051i	$-0.537547\pi$
$103$	−246.042	−0.235371	−0.117686	+	0.993051i	$0.537547\pi$
$104$	1197.52	1.12910
$105$	−23.2920	−0.0216483
$106$	80.6908	0.0739376
$107$	−615.063	−0.555704	−0.277852	−	0.960624i	$-0.589623\pi$
$107$	−615.063	−0.555704	−0.277852	+	0.960624i	$0.589623\pi$
$108$	−292.142	−0.260291
$109$	1860.95	1.63529	0.817646	−	0.575721i	$-0.195279\pi$
$109$	1860.95	1.63529	0.817646	+	0.575721i	$0.195279\pi$
$110$	221.223	0.191753
$111$	887.001	0.758472
$112$	−19.3465	−0.0163221
$113$	−2228.96	−1.85560	−0.927802	−	0.373072i	$-0.878304\pi$
$113$	−2228.96	−1.85560	−0.927802	+	0.373072i	$0.878304\pi$
$114$	−704.947	−0.579161
$115$	2638.02	2.13910
$116$	516.793	0.413647
$117$	1026.13	0.810820
$118$	−1808.73	−1.41108
$119$	−3.25984	−0.00251117
$120$	1118.95	0.851215
$121$	−1305.57	−0.980897
$122$	−1013.76	−0.752306
$123$	427.030	0.313041
$124$	−412.092	−0.298443
$125$	1870.68	1.33855
$126$	−25.3641	−0.0179334
$127$	453.295	0.316720	0.158360	−	0.987381i	$-0.449379\pi$
$127$	453.295	0.316720	0.158360	+	0.987381i	$0.449379\pi$
$128$	436.806	0.301629
$129$	0	0
$130$	−2133.54	−1.43942
$131$	−995.763	−0.664124	−0.332062	−	0.943258i	$-0.607744\pi$
$131$	−995.763	−0.664124	−0.332062	+	0.943258i	$0.607744\pi$
$132$	30.6257	0.0201941
$133$	63.4388	0.0413597
$134$	−1512.18	−0.974871
$135$	2185.69	1.39344
$136$	156.603	0.0987397
$137$	−2491.26	−1.55359	−0.776797	−	0.629751i	$-0.783157\pi$
$137$	−2491.26	−1.55359	−0.776797	+	0.629751i	$0.783157\pi$
$138$	−803.189	−0.495449
$139$	−1951.81	−1.19101	−0.595506	−	0.803351i	$-0.703048\pi$
$139$	−1951.81	−1.19101	−0.595506	+	0.803351i	$0.703048\pi$
$140$	−23.9791	−0.0144757
$141$	−533.391	−0.318579
$142$	−2155.49	−1.27384
$143$	−245.218	−0.143400
$144$	796.391	0.460875
$145$	−3866.44	−2.21442
$146$	231.467	0.131208
$147$	832.475	0.467084
$148$	913.165	0.507174
$149$	−2006.42	−1.10317	−0.551585	−	0.834119i	$-0.685977\pi$
$149$	−2006.42	−1.10317	−0.551585	+	0.834119i	$0.685977\pi$
$150$	−1281.56	−0.697593
$151$	3455.23	1.86213	0.931067	−	0.364847i	$-0.118879\pi$
$151$	3455.23	1.86213	0.931067	+	0.364847i	$0.118879\pi$
$152$	−3047.60	−1.62627
$153$	134.190	0.0709059
$154$	6.06134	0.00317167
$155$	3083.11	1.59769
$156$	−295.363	−0.151590
$157$	−380.367	−0.193354	−0.0966771	−	0.995316i	$-0.530821\pi$
$157$	−380.367	−0.193354	−0.0966771	+	0.995316i	$0.530821\pi$
$158$	966.013	0.486404
$159$	−83.5746	−0.0416849
$160$	2029.59	1.00283
$161$	72.2797	0.0353816
$162$	670.556	0.325209
$163$	−1067.78	−0.513096	−0.256548	−	0.966532i	$-0.582585\pi$
$163$	−1067.78	−0.513096	−0.256548	+	0.966532i	$0.582585\pi$
$164$	439.627	0.209324
$165$	−229.129	−0.108107
$166$	636.056	0.297395
$167$	−4232.47	−1.96119	−0.980593	−	0.196055i	$-0.937187\pi$
$167$	−4232.47	−1.96119	−0.980593	+	0.196055i	$0.937187\pi$
$168$	30.6584	0.0140794
$169$	167.959	0.0764490
$170$	−279.009	−0.125876
$171$	−2611.43	−1.16784
$172$	0	0
$173$	−3617.39	−1.58974	−0.794869	−	0.606781i	$-0.792461\pi$
$173$	−3617.39	−1.58974	−0.794869	+	0.606781i	$0.792461\pi$
$174$	1177.20	0.512894
$175$	115.329	0.0498173
$176$	−190.316	−0.0815093
$177$	1873.37	0.795545
$178$	270.897	0.114071
$179$	643.127	0.268545	0.134272	−	0.990944i	$-0.457130\pi$
$179$	643.127	0.268545	0.134272	+	0.990944i	$0.457130\pi$
$180$	987.090	0.408741
$181$	3174.93	1.30382	0.651909	−	0.758297i	$-0.273968\pi$
$181$	3174.93	1.30382	0.651909	+	0.758297i	$0.273968\pi$
$182$	−58.4574	−0.0238085
$183$	1049.99	0.424138
$184$	−3472.32	−1.39121
$185$	−6831.94	−2.71510
$186$	−938.704	−0.370049
$187$	−32.0678	−0.0125403
$188$	−549.125	−0.213027
$189$	59.8862	0.0230480
$190$	5429.71	2.07322
$191$	−464.296	−0.175892	−0.0879458	−	0.996125i	$-0.528030\pi$
$191$	−464.296	−0.175892	−0.0879458	+	0.996125i	$0.528030\pi$
$192$	−1351.33	−0.507938
$193$	−3898.46	−1.45397	−0.726987	−	0.686651i	$-0.759080\pi$
$193$	−3898.46	−1.45397	−0.726987	+	0.686651i	$0.759080\pi$
$194$	1461.88	0.541017
$195$	2209.79	0.811521
$196$	857.031	0.312329
$197$	2153.97	0.779005	0.389503	−	0.921025i	$-0.372647\pi$
$197$	2153.97	0.779005	0.389503	+	0.921025i	$0.372647\pi$
$198$	−249.512	−0.0895560
$199$	3038.98	1.08255	0.541275	−	0.840845i	$-0.317942\pi$
$199$	3038.98	1.08255	0.541275	+	0.840845i	$0.317942\pi$
$200$	−5540.40	−1.95883
$201$	1566.23	0.549617
$202$	316.240	0.110151
$203$	−105.937	−0.0366274
$204$	−38.6254	−0.0132565
$205$	−3289.11	−1.12059
$206$	−576.990	−0.195150
$207$	−2975.36	−0.999043
$208$	1835.47	0.611860
$209$	624.062	0.206542
$210$	−54.6220	−0.0179489
$211$	−969.498	−0.316318	−0.158159	−	0.987414i	$-0.550556\pi$
$211$	−969.498	−0.316318	−0.158159	+	0.987414i	$0.550556\pi$
$212$	−86.0398	−0.0278738
$213$	2232.52	0.718169
$214$	−1442.38	−0.460743
$215$	0	0
$216$	−2876.94	−0.906254
$217$	84.4748	0.0264264
$218$	4364.10	1.35584
$219$	−239.740	−0.0739730
$220$	−235.888	−0.0722890
$221$	309.272	0.0941351
$222$	2080.10	0.628860
$223$	−446.780	−0.134164	−0.0670821	−	0.997747i	$-0.521369\pi$
$223$	−446.780	−0.134164	−0.0670821	+	0.997747i	$0.521369\pi$
$224$	55.6093	0.0165873
$225$	−4747.46	−1.40665
$226$	−5227.13	−1.53851
$227$	552.010	0.161402	0.0807009	−	0.996738i	$-0.474284\pi$
$227$	552.010	0.161402	0.0807009	+	0.996738i	$0.474284\pi$
$228$	751.678	0.218338
$229$	−393.795	−0.113636	−0.0568181	−	0.998385i	$-0.518096\pi$
$229$	−393.795	−0.113636	−0.0568181	+	0.998385i	$0.518096\pi$
$230$	6186.40	1.77356
$231$	−6.27796	−0.00178814
$232$	5089.25	1.44020
$233$	−335.082	−0.0942143	−0.0471071	−	0.998890i	$-0.515000\pi$
$233$	−335.082	−0.0942143	−0.0471071	+	0.998890i	$0.515000\pi$
$234$	2406.37	0.672263
$235$	4108.34	1.14042
$236$	1928.64	0.531964
$237$	−1000.54	−0.274227
$238$	−7.64462	−0.00208205
$239$	−5612.62	−1.51904	−0.759520	−	0.650485i	$-0.774566\pi$
$239$	−5612.62	−1.51904	−0.759520	+	0.650485i	$0.774566\pi$
$240$	1715.04	0.461273
$241$	−2947.42	−0.787800	−0.393900	−	0.919153i	$-0.628874\pi$
$241$	−2947.42	−0.787800	−0.393900	+	0.919153i	$0.628874\pi$
$242$	−3061.69	−0.813276
$243$	−3848.96	−1.01610
$244$	1080.96	0.283612
$245$	−6411.97	−1.67202
$246$	1001.42	0.259547
$247$	−6018.64	−1.55043
$248$	−4058.18	−1.03909
$249$	−658.788	−0.167667
$250$	4386.93	1.10981
$251$	1443.00	0.362874	0.181437	−	0.983403i	$-0.441925\pi$
$251$	1443.00	0.362874	0.181437	+	0.983403i	$0.441925\pi$
$252$	27.0455	0.00676073
$253$	711.032	0.176689
$254$	1063.02	0.262597
$255$	288.980	0.0709672
$256$	−3426.50	−0.836547
$257$	7394.73	1.79483	0.897414	−	0.441189i	$-0.145443\pi$
$257$	7394.73	1.79483	0.897414	+	0.441189i	$0.145443\pi$
$258$	0	0
$259$	−187.190	−0.0449089
$260$	2274.98	0.542646
$261$	4360.87	1.03422
$262$	−2335.16	−0.550635
$263$	7763.59	1.82024	0.910121	−	0.414343i	$-0.135988\pi$
$263$	7763.59	1.82024	0.910121	+	0.414343i	$0.135988\pi$
$264$	301.594	0.0703099
$265$	643.716	0.149219
$266$	148.770	0.0342919
$267$	−280.579	−0.0643114
$268$	1612.43	0.367517
$269$	6410.90	1.45308	0.726541	−	0.687123i	$-0.241127\pi$
$269$	6410.90	1.45308	0.726541	+	0.687123i	$0.241127\pi$
$270$	5125.64	1.15532
$271$	1239.58	0.277857	0.138929	−	0.990302i	$-0.455634\pi$
$271$	1239.58	0.277857	0.138929	+	0.990302i	$0.455634\pi$
$272$	240.029	0.0535069
$273$	60.5466	0.0134229
$274$	−5842.22	−1.28811
$275$	1134.52	0.248778
$276$	856.433	0.186780
$277$	−1265.98	−0.274605	−0.137302	−	0.990529i	$-0.543843\pi$
$277$	−1265.98	−0.274605	−0.137302	+	0.990529i	$0.543843\pi$
$278$	−4577.18	−0.987485
$279$	−3477.37	−0.746181
$280$	−236.140	−0.0504002
$281$	−2547.49	−0.540821	−0.270410	−	0.962745i	$-0.587159\pi$
$281$	−2547.49	−0.540821	−0.270410	+	0.962745i	$0.587159\pi$
$282$	−1250.85	−0.264139
$283$	−2198.22	−0.461733	−0.230866	−	0.972985i	$-0.574156\pi$
$283$	−2198.22	−0.461733	−0.230866	+	0.972985i	$0.574156\pi$
$284$	2298.38	0.480224
$285$	−5623.76	−1.16885
$286$	−575.059	−0.118895
$287$	−90.1191	−0.0185351
$288$	−2289.13	−0.468363
$289$	−4872.56	−0.991768
$290$	−9067.16	−1.83601
$291$	−1514.13	−0.305017
$292$	−246.811	−0.0494642
$293$	3476.05	0.693082	0.346541	−	0.938035i	$-0.387356\pi$
$293$	3476.05	0.693082	0.346541	+	0.938035i	$0.387356\pi$
$294$	1952.23	0.387266
$295$	−14429.3	−2.84781
$296$	8992.61	1.76583
$297$	589.115	0.115097
$298$	−4705.24	−0.914655
$299$	−6857.41	−1.32634
$300$	1366.52	0.262986
$301$	0	0
$302$	8102.82	1.54392
$303$	−327.542	−0.0621015
$304$	−4671.13	−0.881275
$305$	−8087.31	−1.51829
$306$	314.688	0.0587892
$307$	1861.37	0.346039	0.173019	−	0.984918i	$-0.444648\pi$
$307$	1861.37	0.346039	0.173019	+	0.984918i	$0.444648\pi$
$308$	−6.46315	−0.00119569
$309$	597.611	0.110022
$310$	7230.17	1.32467
$311$	−7750.28	−1.41311	−0.706556	−	0.707657i	$-0.749752\pi$
$311$	−7750.28	−1.41311	−0.706556	+	0.707657i	$0.749752\pi$
$312$	−2908.66	−0.527790
$313$	1674.83	0.302451	0.151225	−	0.988499i	$-0.451678\pi$
$313$	1674.83	0.302451	0.151225	+	0.988499i	$0.451678\pi$
$314$	−891.996	−0.160313
$315$	−202.344	−0.0361929
$316$	−1030.05	−0.183370
$317$	−4814.34	−0.852998	−0.426499	−	0.904488i	$-0.640253\pi$
$317$	−4814.34	−0.852998	−0.426499	+	0.904488i	$0.640253\pi$
$318$	−195.990	−0.0345616
$319$	−1042.13	−0.182910
$320$	10408.4	1.81827
$321$	1493.93	0.259760
$322$	169.502	0.0293354
$323$	−787.073	−0.135585
$324$	−715.008	−0.122601
$325$	−10941.6	−1.86748
$326$	−2504.03	−0.425415
$327$	−4520.07	−0.764404
$328$	4329.33	0.728802
$329$	112.565	0.0188630
$330$	−537.329	−0.0896333
$331$	−10848.9	−1.80154	−0.900768	−	0.434301i	$-0.856995\pi$
$331$	−10848.9	−1.80154	−0.900768	+	0.434301i	$0.856995\pi$
$332$	−678.220	−0.112115
$333$	7705.58	1.26806
$334$	−9925.52	−1.62605
$335$	−12063.5	−1.96747
$336$	46.9908	0.00762964
$337$	−8725.22	−1.41037	−0.705183	−	0.709026i	$-0.749135\pi$
$337$	−8725.22	−1.41037	−0.705183	+	0.709026i	$0.749135\pi$
$338$	393.878	0.0633850
$339$	5413.93	0.867388
$340$	297.504	0.0474542
$341$	830.999	0.131968
$342$	−6124.04	−0.968275
$343$	−351.500	−0.0553330
$344$	0	0
$345$	−6407.49	−0.999907
$346$	−8483.10	−1.31808
$347$	5950.59	0.920589	0.460295	−	0.887766i	$-0.347744\pi$
$347$	5950.59	0.920589	0.460295	+	0.887766i	$0.347744\pi$
$348$	−1255.24	−0.193356
$349$	5162.99	0.791887	0.395944	−	0.918275i	$-0.370418\pi$
$349$	5162.99	0.791887	0.395944	+	0.918275i	$0.370418\pi$
$350$	270.456	0.0413043
$351$	−5681.60	−0.863992
$352$	547.042	0.0828336
$353$	−6312.98	−0.951859	−0.475929	−	0.879484i	$-0.657888\pi$
$353$	−6312.98	−0.951859	−0.475929	+	0.879484i	$0.657888\pi$
$354$	4393.23	0.659598
$355$	−17195.5	−2.57083
$356$	−288.855	−0.0430037
$357$	7.91783	0.00117383
$358$	1508.19	0.222655
$359$	−2094.51	−0.307921	−0.153961	−	0.988077i	$-0.549203\pi$
$359$	−2094.51	−0.307921	−0.153961	+	0.988077i	$0.549203\pi$
$360$	9720.60	1.42311
$361$	8457.99	1.23312
$362$	7445.51	1.08101
$363$	3171.11	0.458513
$364$	62.3325	0.00897559
$365$	1846.54	0.264801
$366$	2462.32	0.351659
$367$	11071.4	1.57473	0.787363	−	0.616489i	$-0.211446\pi$
$367$	11071.4	1.57473	0.787363	+	0.616489i	$0.211446\pi$
$368$	−5322.10	−0.753896
$369$	3709.71	0.523360
$370$	−16021.5	−2.25113
$371$	17.6373	0.00246815
$372$	1000.93	0.139505
$373$	−1517.88	−0.210705	−0.105353	−	0.994435i	$-0.533597\pi$
$373$	−1517.88	−0.210705	−0.105353	+	0.994435i	$0.533597\pi$
$374$	−75.2019	−0.0103973
$375$	−4543.71	−0.625696
$376$	−5407.64	−0.741696
$377$	10050.6	1.37303
$378$	140.439	0.0191095
$379$	13541.0	1.83524	0.917618	−	0.397463i	$-0.130109\pi$
$379$	13541.0	1.83524	0.917618	+	0.397463i	$0.130109\pi$
$380$	−5789.64	−0.781585
$381$	−1101.01	−0.148048
$382$	−1088.82	−0.145834
$383$	−1160.65	−0.154847	−0.0774235	−	0.996998i	$-0.524669\pi$
$383$	−1160.65	−0.154847	−0.0774235	+	0.996998i	$0.524669\pi$
$384$	−1060.96	−0.140994
$385$	48.3547	0.00640100
$386$	−9142.24	−1.20551
$387$	0	0
$388$	−1558.79	−0.203958
$389$	2125.41	0.277024	0.138512	−	0.990361i	$-0.455768\pi$
$389$	2125.41	0.277024	0.138512	+	0.990361i	$0.455768\pi$
$390$	5182.16	0.672844
$391$	−896.761	−0.115988
$392$	8439.82	1.08744
$393$	2418.61	0.310440
$394$	5051.26	0.645885
$395$	7706.43	0.981652
$396$	266.053	0.0337618
$397$	1017.45	0.128626	0.0643128	−	0.997930i	$-0.479514\pi$
$397$	1017.45	0.128626	0.0643128	+	0.997930i	$0.479514\pi$
$398$	7126.69	0.897559
$399$	−154.086	−0.0193333
$400$	−8491.89	−1.06149
$401$	4536.33	0.564922	0.282461	−	0.959279i	$-0.408849\pi$
$401$	4536.33	0.564922	0.282461	+	0.959279i	$0.408849\pi$
$402$	3672.94	0.455696
$403$	−8014.40	−0.990634
$404$	−337.203	−0.0415260
$405$	5349.40	0.656331
$406$	−248.433	−0.0303683
$407$	−1841.43	−0.224266
$408$	−380.373	−0.0461551
$409$	12621.0	1.52584	0.762918	−	0.646495i	$-0.223766\pi$
$409$	12621.0	1.52584	0.762918	+	0.646495i	$0.223766\pi$
$410$	−7713.27	−0.929100
$411$	6051.01	0.726215
$412$	615.239	0.0735696
$413$	−395.351	−0.0471040
$414$	−6977.50	−0.828322
$415$	5074.18	0.600196
$416$	−5275.84	−0.621801
$417$	4740.76	0.556729
$418$	1463.48	0.171247
$419$	7940.92	0.925869	0.462934	−	0.886392i	$-0.346797\pi$
$419$	7940.92	0.925869	0.462934	+	0.886392i	$0.346797\pi$
$420$	58.2429	0.00676657
$421$	−3246.56	−0.375838	−0.187919	−	0.982185i	$-0.560174\pi$
$421$	−3246.56	−0.375838	−0.187919	+	0.982185i	$0.560174\pi$
$422$	−2273.56	−0.262264
$423$	−4633.70	−0.532619
$424$	−847.298	−0.0970482
$425$	−1430.86	−0.163311
$426$	5235.47	0.595444
$427$	−221.586	−0.0251131
$428$	1537.99	0.173696
$429$	595.611	0.0670312
$430$	0	0
$431$	−10024.0	−1.12028	−0.560141	−	0.828398i	$-0.689253\pi$
$431$	−10024.0	−1.12028	−0.560141	+	0.828398i	$0.689253\pi$
$432$	−4409.55	−0.491098
$433$	−9624.64	−1.06820	−0.534100	−	0.845421i	$-0.679349\pi$
$433$	−9624.64	−1.06820	−0.534100	+	0.845421i	$0.679349\pi$
$434$	198.101	0.0219105
$435$	9391.21	1.03511
$436$	−4653.40	−0.511141
$437$	17451.6	1.91035
$438$	−562.211	−0.0613321
$439$	−7330.44	−0.796954	−0.398477	−	0.917178i	$-0.630461\pi$
$439$	−7330.44	−0.796954	−0.398477	+	0.917178i	$0.630461\pi$
$440$	−2322.96	−0.251689
$441$	7231.91	0.780899
$442$	725.270	0.0780488
$443$	−1082.51	−0.116098	−0.0580492	−	0.998314i	$-0.518488\pi$
$443$	−1082.51	−0.116098	−0.0580492	+	0.998314i	$0.518488\pi$
$444$	−2217.99	−0.237074
$445$	2161.10	0.230216
$446$	−1047.74	−0.111238
$447$	4873.39	0.515668
$448$	285.181	0.0300749
$449$	−5924.49	−0.622703	−0.311352	−	0.950295i	$-0.600782\pi$
$449$	−5924.49	−0.622703	−0.311352	+	0.950295i	$0.600782\pi$
$450$	−11133.2	−1.16628
$451$	−886.523	−0.0925604
$452$	5573.63	0.580004
$453$	−8392.40	−0.870440
$454$	1294.51	0.133821
$455$	−466.347	−0.0480499
$456$	7402.33	0.760188
$457$	9192.85	0.940970	0.470485	−	0.882408i	$-0.344079\pi$
$457$	9192.85	0.940970	0.470485	+	0.882408i	$0.344079\pi$
$458$	−923.485	−0.0942175
$459$	−742.997	−0.0755559
$460$	−6596.50	−0.668616
$461$	−1014.04	−0.102448	−0.0512242	−	0.998687i	$-0.516312\pi$
$461$	−1014.04	−0.102448	−0.0512242	+	0.998687i	$0.516312\pi$
$462$	−14.7224	−0.00148257
$463$	−11579.2	−1.16227	−0.581134	−	0.813808i	$-0.697391\pi$
$463$	−11579.2	−1.16227	−0.581134	+	0.813808i	$0.697391\pi$
$464$	7800.40	0.780441
$465$	−7488.57	−0.746826
$466$	−785.797	−0.0781145
$467$	11479.0	1.13744	0.568721	−	0.822530i	$-0.307438\pi$
$467$	11479.0	1.13744	0.568721	+	0.822530i	$0.307438\pi$
$468$	−2565.89	−0.253437
$469$	−330.531	−0.0325427
$470$	9634.42	0.945538
$471$	923.875	0.0903820
$472$	18992.7	1.85214
$473$	0	0
$474$	−2346.35	−0.227366
$475$	27845.6	2.68977
$476$	8.15139	0.000784912 0
$477$	−726.032	−0.0696913
$478$	−13162.1	−1.25946
$479$	11310.1	1.07886	0.539429	−	0.842031i	$-0.318640\pi$
$479$	11310.1	1.07886	0.539429	+	0.842031i	$0.318640\pi$
$480$	−4929.68	−0.468767
$481$	17759.3	1.68348
$482$	−6911.96	−0.653177
$483$	−175.560	−0.0165389
$484$	3264.65	0.306597
$485$	11662.3	1.09187
$486$	−9026.17	−0.842460
$487$	13942.4	1.29731	0.648657	−	0.761081i	$-0.275331\pi$
$487$	13942.4	1.29731	0.648657	+	0.761081i	$0.275331\pi$
$488$	10645.0	0.987453
$489$	2593.52	0.239843
$490$	−15036.6	−1.38630
$491$	6614.78	0.607986	0.303993	−	0.952674i	$-0.401680\pi$
$491$	6614.78	0.607986	0.303993	+	0.952674i	$0.401680\pi$
$492$	−1067.81	−0.0978467
$493$	1314.35	0.120071
$494$	−14114.3	−1.28549
$495$	−1990.50	−0.180740
$496$	−6220.06	−0.563082
$497$	−471.144	−0.0425226
$498$	−1544.92	−0.139015
$499$	1025.76	0.0920229	0.0460114	−	0.998941i	$-0.485349\pi$
$499$	1025.76	0.0920229	0.0460114	+	0.998941i	$0.485349\pi$
$500$	−4677.74	−0.418389
$501$	10280.2	0.916741
$502$	3383.96	0.300864
$503$	3411.78	0.302433	0.151217	−	0.988501i	$-0.451681\pi$
$503$	3411.78	0.302433	0.151217	+	0.988501i	$0.451681\pi$
$504$	266.337	0.0235389
$505$	2522.82	0.222305
$506$	1667.44	0.146495
$507$	−407.955	−0.0357355
$508$	−1133.49	−0.0989967
$509$	−334.899	−0.0291634	−0.0145817	−	0.999894i	$-0.504642\pi$
$509$	−334.899	−0.0291634	−0.0145817	+	0.999894i	$0.504642\pi$
$510$	677.685	0.0588400
$511$	50.5938	0.00437992
$512$	−11529.9	−0.995223
$513$	14459.2	1.24443
$514$	17341.3	1.48812
$515$	−4602.98	−0.393847
$516$	0	0
$517$	1107.33	0.0941979
$518$	−438.977	−0.0372346
$519$	8786.27	0.743111
$520$	22403.4	1.88933
$521$	−15973.0	−1.34317	−0.671585	−	0.740928i	$-0.734386\pi$
$521$	−15973.0	−1.34317	−0.671585	+	0.740928i	$0.734386\pi$
$522$	10226.6	0.857486
$523$	−4623.45	−0.386557	−0.193279	−	0.981144i	$-0.561912\pi$
$523$	−4623.45	−0.386557	−0.193279	+	0.981144i	$0.561912\pi$
$524$	2489.95	0.207584
$525$	−280.122	−0.0232867
$526$	18206.3	1.50919
$527$	−1048.06	−0.0866307
$528$	462.260	0.0381009
$529$	7716.68	0.634230
$530$	1509.57	0.123720
$531$	16274.5	1.33004
$532$	−158.632	−0.0129277
$533$	8549.89	0.694816
$534$	−657.983	−0.0533216
$535$	−11506.7	−0.929862
$536$	15878.8	1.27959
$537$	−1562.09	−0.125529
$538$	15034.1	1.20477
$539$	−1728.23	−0.138108
$540$	−5465.42	−0.435545
$541$	5776.76	0.459080	0.229540	−	0.973299i	$-0.426278\pi$
$541$	5776.76	0.459080	0.229540	+	0.973299i	$0.426278\pi$
$542$	2906.93	0.230376
$543$	−7711.60	−0.609459
$544$	−689.934	−0.0543763
$545$	34814.9	2.73634
$546$	141.987	0.0111291
$547$	20861.6	1.63067	0.815334	−	0.578990i	$-0.196553\pi$
$547$	20861.6	1.63067	0.815334	+	0.578990i	$0.196553\pi$
$548$	6229.51	0.485605
$549$	9121.49	0.709100
$550$	2660.54	0.206265
$551$	−25578.1	−1.97761
$552$	8433.93	0.650311
$553$	211.150	0.0162369
$554$	−2968.85	−0.227679
$555$	16594.1	1.26915
$556$	4880.60	0.372273
$557$	−4932.51	−0.375219	−0.187610	−	0.982244i	$-0.560074\pi$
$557$	−4932.51	−0.375219	−0.187610	+	0.982244i	$0.560074\pi$
$558$	−8154.75	−0.618670
$559$	0	0
$560$	−361.937	−0.0273118
$561$	77.8895	0.00586185
$562$	−5974.10	−0.448403
$563$	−14078.4	−1.05388	−0.526939	−	0.849903i	$-0.676660\pi$
$563$	−14078.4	−1.05388	−0.526939	+	0.849903i	$0.676660\pi$
$564$	1333.77	0.0995778
$565$	−41699.7	−3.10499
$566$	−5155.02	−0.382830
$567$	146.569	0.0108560
$568$	22633.8	1.67200
$569$	−7165.14	−0.527905	−0.263953	−	0.964536i	$-0.585026\pi$
$569$	−7165.14	−0.527905	−0.263953	+	0.964536i	$0.585026\pi$
$570$	−13188.2	−0.969112
$571$	−15291.1	−1.12069	−0.560344	−	0.828260i	$-0.689331\pi$
$571$	−15291.1	−1.12069	−0.560344	+	0.828260i	$0.689331\pi$
$572$	613.180	0.0448223
$573$	1127.73	0.0822192
$574$	−211.337	−0.0153677
$575$	31726.2	2.30100
$576$	−11739.4	−0.849201
$577$	−10271.5	−0.741089	−0.370545	−	0.928815i	$-0.620829\pi$
$577$	−10271.5	−0.741089	−0.370545	+	0.928815i	$0.620829\pi$
$578$	−11426.6	−0.822290
$579$	9468.97	0.679649
$580$	9668.23	0.692157
$581$	139.028	0.00992749
$582$	−3550.77	−0.252894
$583$	173.502	0.0123254
$584$	−2430.53	−0.172219
$585$	19197.0	1.35675
$586$	8151.66	0.574645
$587$	−5869.33	−0.412697	−0.206349	−	0.978479i	$-0.566158\pi$
$587$	−5869.33	−0.412697	−0.206349	+	0.978479i	$0.566158\pi$
$588$	−2081.64	−0.145996
$589$	20396.0	1.42683
$590$	−33838.0	−2.36117
$591$	−5231.78	−0.364140
$592$	13783.2	0.956900
$593$	13637.1	0.944367	0.472184	−	0.881500i	$-0.343466\pi$
$593$	13637.1	0.944367	0.472184	+	0.881500i	$0.343466\pi$
$594$	1381.53	0.0954289
$595$	−60.9854	−0.00420195
$596$	5017.15	0.344816
$597$	−7381.38	−0.506030
$598$	−16081.3	−1.09968
$599$	2989.04	0.203888	0.101944	−	0.994790i	$-0.467494\pi$
$599$	2989.04	0.203888	0.101944	+	0.994790i	$0.467494\pi$
$600$	13457.1	0.915639
$601$	−3752.57	−0.254693	−0.127347	−	0.991858i	$-0.540646\pi$
$601$	−3752.57	−0.254693	−0.127347	+	0.991858i	$0.540646\pi$
$602$	0	0
$603$	13606.2	0.918883
$604$	−8639.96	−0.582045
$605$	−24424.8	−1.64134
$606$	−768.115	−0.0514893
$607$	9165.95	0.612906	0.306453	−	0.951886i	$-0.400858\pi$
$607$	9165.95	0.612906	0.306453	+	0.951886i	$0.400858\pi$
$608$	13426.6	0.895593
$609$	257.312	0.0171212
$610$	−18965.5	−1.25884
$611$	−10679.4	−0.707108
$612$	−335.548	−0.0221630
$613$	8403.46	0.553691	0.276846	−	0.960914i	$-0.410711\pi$
$613$	8403.46	0.553691	0.276846	+	0.960914i	$0.410711\pi$
$614$	4365.08	0.286906
$615$	7988.93	0.523812
$616$	−63.6474	−0.00416303
$617$	−14381.6	−0.938380	−0.469190	−	0.883097i	$-0.655454\pi$
$617$	−14381.6	−0.938380	−0.469190	+	0.883097i	$0.655454\pi$
$618$	1401.45	0.0912212
$619$	20695.9	1.34384	0.671921	−	0.740623i	$-0.265470\pi$
$619$	20695.9	1.34384	0.671921	+	0.740623i	$0.265470\pi$
$620$	−7709.47	−0.499386
$621$	16474.3	1.06456
$622$	−18175.1	−1.17163
$623$	59.2125	0.00380786
$624$	−4458.17	−0.286009
$625$	6872.81	0.439860
$626$	3927.64	0.250767
$627$	−1515.79	−0.0965465
$628$	951.127	0.0604365
$629$	2322.43	0.147220
$630$	−474.514	−0.0300081
$631$	−18686.0	−1.17889	−0.589444	−	0.807809i	$-0.700653\pi$
$631$	−18686.0	−1.17889	−0.589444	+	0.807809i	$0.700653\pi$
$632$	−10143.7	−0.638439
$633$	2354.81	0.147860
$634$	−11290.1	−0.707233
$635$	8480.29	0.529969
$636$	208.982	0.0130294
$637$	16667.6	1.03673
$638$	−2443.89	−0.151653
$639$	19394.5	1.20068
$640$	8171.81	0.504717
$641$	−2741.94	−0.168955	−0.0844774	−	0.996425i	$-0.526922\pi$
$641$	−2741.94	−0.168955	−0.0844774	+	0.996425i	$0.526922\pi$
$642$	3503.39	0.215371
$643$	−9202.37	−0.564395	−0.282198	−	0.959356i	$-0.591063\pi$
$643$	−9202.37	−0.564395	−0.282198	+	0.959356i	$0.591063\pi$
$644$	−180.739	−0.0110592
$645$	0	0
$646$	−1845.76	−0.112415
$647$	8101.38	0.492269	0.246135	−	0.969236i	$-0.420839\pi$
$647$	8101.38	0.492269	0.246135	+	0.969236i	$0.420839\pi$
$648$	−7041.21	−0.426859
$649$	−3889.16	−0.235228
$650$	−25659.1	−1.54836
$651$	−205.181	−0.0123528
$652$	2670.02	0.160378
$653$	2590.36	0.155235	0.0776175	−	0.996983i	$-0.475269\pi$
$653$	2590.36	0.155235	0.0776175	+	0.996983i	$0.475269\pi$
$654$	−10600.0	−0.633779
$655$	−18628.8	−1.11128
$656$	6635.66	0.394937
$657$	−2082.67	−0.123673
$658$	263.976	0.0156396
$659$	−5952.63	−0.351869	−0.175934	−	0.984402i	$-0.556295\pi$
$659$	−5952.63	−0.351869	−0.175934	+	0.984402i	$0.556295\pi$
$660$	572.949	0.0337909
$661$	−23326.7	−1.37262	−0.686311	−	0.727309i	$-0.740771\pi$
$661$	−23326.7	−1.37262	−0.686311	+	0.727309i	$0.740771\pi$
$662$	−25441.6	−1.49368
$663$	−751.190	−0.0440027
$664$	−6678.94	−0.390351
$665$	1186.82	0.0692073
$666$	18070.3	1.05137
$667$	−29142.7	−1.69177
$668$	10583.5	0.613005
$669$	1085.19	0.0627140
$670$	−28290.1	−1.63126
$671$	−2179.79	−0.125410
$672$	−135.069	−0.00775360
$673$	20507.9	1.17462	0.587311	−	0.809362i	$-0.300187\pi$
$673$	20507.9	1.17462	0.587311	+	0.809362i	$0.300187\pi$
$674$	−20461.4	−1.16935
$675$	26286.2	1.49890
$676$	−419.988	−0.0238956
$677$	29831.9	1.69355	0.846774	−	0.531953i	$-0.178542\pi$
$677$	29831.9	1.69355	0.846774	+	0.531953i	$0.178542\pi$
$678$	12696.2	0.719164
$679$	319.537	0.0180600
$680$	2929.74	0.165221
$681$	−1340.78	−0.0754460
$682$	1948.77	0.109417
$683$	−6248.79	−0.350078	−0.175039	−	0.984562i	$-0.556005\pi$
$683$	−6248.79	−0.350078	−0.175039	+	0.984562i	$0.556005\pi$
$684$	6530.00	0.365031
$685$	−46606.7	−2.59964
$686$	−824.300	−0.0458774
$687$	956.489	0.0531184
$688$	0	0
$689$	−1673.31	−0.0925225
$690$	−15026.2	−0.829037
$691$	−17494.1	−0.963107	−0.481554	−	0.876417i	$-0.659927\pi$
$691$	−17494.1	−0.963107	−0.481554	+	0.876417i	$0.659927\pi$
$692$	9045.45	0.496902
$693$	−54.5382	−0.00298951
$694$	13954.7	0.763274
$695$	−36514.7	−1.99292
$696$	−12361.3	−0.673208
$697$	1118.09	0.0607614
$698$	12107.7	0.656566
$699$	813.880	0.0440397
$700$	−288.385	−0.0155713
$701$	25115.2	1.35319	0.676596	−	0.736354i	$-0.263454\pi$
$701$	25115.2	1.35319	0.676596	+	0.736354i	$0.263454\pi$
$702$	−13323.9	−0.716349
$703$	−45196.1	−2.42476
$704$	2805.39	0.150188
$705$	−9978.74	−0.533080
$706$	−14804.5	−0.789200
$707$	69.1233	0.00367701
$708$	−4684.46	−0.248662
$709$	18394.0	0.974331	0.487165	−	0.873310i	$-0.338031\pi$
$709$	18394.0	0.974331	0.487165	+	0.873310i	$0.338031\pi$
$710$	−40325.1	−2.13151
$711$	−8691.90	−0.458469
$712$	−2844.57	−0.149726
$713$	23238.5	1.22060
$714$	18.5680	0.000973237 0
$715$	−4587.57	−0.239952
$716$	−1608.17	−0.0839387
$717$	13632.5	0.710063
$718$	−4911.81	−0.255302
$719$	30052.0	1.55876	0.779382	−	0.626549i	$-0.215533\pi$
$719$	30052.0	1.55876	0.779382	+	0.626549i	$0.215533\pi$
$720$	14899.0	0.771183
$721$	−126.118	−0.00651439
$722$	19834.8	1.02240
$723$	7158.99	0.368251
$724$	−7939.07	−0.407532
$725$	−46499.8	−2.38201
$726$	7436.54	0.380160
$727$	−4166.51	−0.212555	−0.106277	−	0.994337i	$-0.533893\pi$
$727$	−4166.51	−0.212555	−0.106277	+	0.994337i	$0.533893\pi$
$728$	613.835	0.0312503
$729$	1628.36	0.0827293
$730$	4330.31	0.219551
$731$	0	0
$732$	−2625.54	−0.132572
$733$	−23201.4	−1.16912	−0.584559	−	0.811351i	$-0.698733\pi$
$733$	−23201.4	−1.16912	−0.584559	+	0.811351i	$0.698733\pi$
$734$	25963.5	1.30563
$735$	15574.0	0.781574
$736$	15297.8	0.766145
$737$	−3251.51	−0.162512
$738$	8699.62	0.433926
$739$	−27055.3	−1.34675	−0.673373	−	0.739303i	$-0.735155\pi$
$739$	−27055.3	−1.34675	−0.673373	+	0.739303i	$0.735155\pi$
$740$	17083.6	0.848656
$741$	14618.7	0.724738
$742$	41.3611	0.00204638
$743$	−16610.7	−0.820172	−0.410086	−	0.912047i	$-0.634501\pi$
$743$	−16610.7	−0.820172	−0.410086	+	0.912047i	$0.634501\pi$
$744$	9856.91	0.485715
$745$	−37536.3	−1.84594
$746$	−3559.58	−0.174699
$747$	−5723.05	−0.280315
$748$	80.1871	0.00391969
$749$	−315.273	−0.0153803
$750$	−10655.4	−0.518774
$751$	5199.15	0.252623	0.126311	−	0.991991i	$-0.459686\pi$
$751$	5199.15	0.252623	0.126311	+	0.991991i	$0.459686\pi$
$752$	−8288.41	−0.401924
$753$	−3504.90	−0.169622
$754$	23569.7	1.13840
$755$	64640.7	3.11592
$756$	−149.748	−0.00720409
$757$	−30028.9	−1.44177	−0.720884	−	0.693056i	$-0.756264\pi$
$757$	−30028.9	−1.44177	−0.720884	+	0.693056i	$0.756264\pi$
$758$	31754.9	1.52162
$759$	−1727.03	−0.0825917
$760$	−57014.9	−2.72125
$761$	13045.8	0.621433	0.310716	−	0.950503i	$-0.399431\pi$
$761$	13045.8	0.621433	0.310716	+	0.950503i	$0.399431\pi$
$762$	−2581.97	−0.122749
$763$	953.900	0.0452602
$764$	1161.00	0.0549782
$765$	2510.44	0.118647
$766$	−2721.83	−0.128386
$767$	37508.2	1.76577
$768$	8322.63	0.391038
$769$	18935.3	0.887938	0.443969	−	0.896042i	$-0.353570\pi$
$769$	18935.3	0.887938	0.443969	+	0.896042i	$0.353570\pi$
$770$	113.396	0.00530716
$771$	−17961.1	−0.838978
$772$	9748.28	0.454467
$773$	−7052.59	−0.328155	−0.164078	−	0.986447i	$-0.552465\pi$
$773$	−7052.59	−0.328155	−0.164078	+	0.986447i	$0.552465\pi$
$774$	0	0
$775$	37079.1	1.71861
$776$	−15350.6	−0.710121
$777$	454.665	0.0209923
$778$	4984.28	0.229685
$779$	−21758.8	−1.00076
$780$	−5525.69	−0.253656
$781$	−4634.76	−0.212349
$782$	−2102.99	−0.0961670
$783$	−24145.7	−1.10204
$784$	12935.9	0.589281
$785$	−7115.95	−0.323540
$786$	5671.86	0.257390
$787$	31343.9	1.41968	0.709841	−	0.704362i	$-0.248767\pi$
$787$	31343.9	1.41968	0.709841	+	0.704362i	$0.248767\pi$
$788$	−5386.11	−0.243492
$789$	−18857.0	−0.850858
$790$	18072.3	0.813902
$791$	−1142.54	−0.0513578
$792$	2620.02	0.117548
$793$	21022.6	0.941405
$794$	2386.01	0.106645
$795$	−1563.52	−0.0697515
$796$	−7599.12	−0.338371
$797$	35516.9	1.57851	0.789255	−	0.614066i	$-0.210467\pi$
$797$	35516.9	1.57851	0.789255	+	0.614066i	$0.210467\pi$
$798$	−361.347	−0.0160295
$799$	−1396.58	−0.0618364
$800$	24408.9	1.07873
$801$	−2437.46	−0.107520
$802$	10638.1	0.468385
$803$	497.704	0.0218725
$804$	−3916.42	−0.171793
$805$	1352.22	0.0592042
$806$	−18794.5	−0.821350
$807$	−15571.4	−0.679232
$808$	−3320.69	−0.144581
$809$	−18244.6	−0.792886	−0.396443	−	0.918059i	$-0.629756\pi$
$809$	−18244.6	−0.792886	−0.396443	+	0.918059i	$0.629756\pi$
$810$	12544.8	0.544174
$811$	26372.1	1.14186	0.570930	−	0.820999i	$-0.306583\pi$
$811$	26372.1	1.14186	0.570930	+	0.820999i	$0.306583\pi$
$812$	264.902	0.0114486
$813$	−3010.82	−0.129882
$814$	−4318.32	−0.185942
$815$	−19976.1	−0.858565
$816$	−583.006	−0.0250114
$817$	0	0
$818$	29597.3	1.26509
$819$	525.982	0.0224412
$820$	8224.58	0.350262
$821$	−3948.12	−0.167832	−0.0839162	−	0.996473i	$-0.526743\pi$
$821$	−3948.12	−0.167832	−0.0839162	+	0.996473i	$0.526743\pi$
$822$	14190.2	0.602116
$823$	−36600.5	−1.55020	−0.775100	−	0.631839i	$-0.782301\pi$
$823$	−36600.5	−1.55020	−0.775100	+	0.631839i	$0.782301\pi$
$824$	6058.71	0.256147
$825$	−2755.63	−0.116289
$826$	−927.134	−0.0390546
$827$	8511.44	0.357886	0.178943	−	0.983859i	$-0.442732\pi$
$827$	8511.44	0.357886	0.178943	+	0.983859i	$0.442732\pi$
$828$	7440.04	0.312270
$829$	20202.2	0.846382	0.423191	−	0.906041i	$-0.360910\pi$
$829$	20202.2	0.846382	0.423191	+	0.906041i	$0.360910\pi$
$830$	11899.4	0.497632
$831$	3074.95	0.128362
$832$	−27056.1	−1.12740
$833$	2179.66	0.0906613
$834$	11117.5	0.461592
$835$	−79181.4	−3.28166
$836$	−1560.50	−0.0645585
$837$	19253.9	0.795115
$838$	18622.2	0.767652
$839$	−5893.79	−0.242522	−0.121261	−	0.992621i	$-0.538694\pi$
$839$	−5893.79	−0.242522	−0.121261	+	0.992621i	$0.538694\pi$
$840$	573.561	0.0235592
$841$	18324.3	0.751336
$842$	−7613.48	−0.311613
$843$	6187.61	0.252803
$844$	2424.28	0.0988709
$845$	3142.19	0.127922
$846$	−10866.4	−0.441603
$847$	−669.221	−0.0271484
$848$	−1298.67	−0.0525903
$849$	5339.25	0.215833
$850$	−3355.50	−0.135403
$851$	−51494.7	−2.07428
$852$	−5582.53	−0.224477
$853$	29634.1	1.18951	0.594756	−	0.803906i	$-0.297249\pi$
$853$	29634.1	1.18951	0.594756	+	0.803906i	$0.297249\pi$
$854$	−519.639	−0.0208217
$855$	−48854.9	−1.95415
$856$	15145.8	0.604756
$857$	18851.6	0.751411	0.375705	−	0.926739i	$-0.377401\pi$
$857$	18851.6	0.751411	0.375705	+	0.926739i	$0.377401\pi$
$858$	1396.76	0.0555765
$859$	−8874.89	−0.352511	−0.176256	−	0.984344i	$-0.556399\pi$
$859$	−8874.89	−0.352511	−0.176256	+	0.984344i	$0.556399\pi$
$860$	0	0
$861$	218.890	0.00866407
$862$	−23507.3	−0.928842
$863$	34956.5	1.37883	0.689417	−	0.724365i	$-0.257867\pi$
$863$	34956.5	1.37883	0.689417	+	0.724365i	$0.257867\pi$
$864$	12674.7	0.499077
$865$	−67674.5	−2.66012
$866$	−22570.7	−0.885660
$867$	11835.0	0.463594
$868$	−211.233	−0.00826005
$869$	2077.13	0.0810839
$870$	22023.2	0.858227
$871$	31358.6	1.21991
$872$	−45825.4	−1.77964
$873$	−13153.6	−0.509945
$874$	40925.6	1.58390
$875$	958.889	0.0370473
$876$	599.480	0.0231216
$877$	−21331.6	−0.821341	−0.410670	−	0.911784i	$-0.634705\pi$
$877$	−21331.6	−0.821341	−0.410670	+	0.911784i	$0.634705\pi$
$878$	−17190.6	−0.660767
$879$	−8442.98	−0.323976
$880$	−3560.46	−0.136390
$881$	28864.1	1.10381	0.551905	−	0.833907i	$-0.313901\pi$
$881$	28864.1	1.10381	0.551905	+	0.833907i	$0.313901\pi$
$882$	16959.5	0.647455
$883$	−14623.5	−0.557327	−0.278663	−	0.960389i	$-0.589891\pi$
$883$	−14623.5	−0.557327	−0.278663	+	0.960389i	$0.589891\pi$
$884$	−773.349	−0.0294237
$885$	35047.3	1.33119
$886$	−2538.58	−0.0962589
$887$	31615.5	1.19678	0.598390	−	0.801205i	$-0.295807\pi$
$887$	31615.5	1.19678	0.598390	+	0.801205i	$0.295807\pi$
$888$	−21842.2	−0.825422
$889$	232.353	0.00876589
$890$	5067.98	0.190875
$891$	1441.84	0.0542126
$892$	1117.20	0.0419355
$893$	27178.3	1.01846
$894$	11428.6	0.427548
$895$	12031.7	0.449357
$896$	223.901	0.00834823
$897$	16656.0	0.619985
$898$	−13893.5	−0.516293
$899$	−34059.7	−1.26358
$900$	11871.2	0.439676
$901$	−218.823	−0.00809106
$902$	−2078.98	−0.0767432
$903$	0	0
$904$	54887.7	2.01940
$905$	59397.0	2.18168
$906$	−19681.0	−0.721695
$907$	−32362.1	−1.18475	−0.592373	−	0.805664i	$-0.701809\pi$
$907$	−32362.1	−1.18475	−0.592373	+	0.805664i	$0.701809\pi$
$908$	−1380.33	−0.0504491
$909$	−2845.43	−0.103825
$910$	−1093.63	−0.0398389
$911$	−35154.1	−1.27849	−0.639247	−	0.769002i	$-0.720754\pi$
$911$	−35154.1	−1.27849	−0.639247	+	0.769002i	$0.720754\pi$
$912$	11345.7	0.411945
$913$	1367.66	0.0495759
$914$	21558.1	0.780172
$915$	19643.3	0.709712
$916$	984.703	0.0355191
$917$	−510.416	−0.0183810
$918$	−1742.40	−0.0626445
$919$	−7359.98	−0.264182	−0.132091	−	0.991238i	$-0.542169\pi$
$919$	−7359.98	−0.264182	−0.132091	+	0.991238i	$0.542169\pi$
$920$	−64960.6	−2.32792
$921$	−4521.08	−0.161753
$922$	−2378.02	−0.0849415
$923$	44699.0	1.59403
$924$	15.6983	0.000558915 0
$925$	−82164.4	−2.92059
$926$	−27154.2	−0.963654
$927$	5191.59	0.183942
$928$	−22421.3	−0.793121
$929$	26410.1	0.932708	0.466354	−	0.884598i	$-0.345567\pi$
$929$	26410.1	0.932708	0.466354	+	0.884598i	$0.345567\pi$
$930$	−17561.4	−0.619205
$931$	−42417.8	−1.49322
$932$	837.888	0.0294484
$933$	18824.7	0.660548
$934$	26919.3	0.943070
$935$	−599.928	−0.0209837
$936$	−25268.2	−0.882391
$937$	26123.6	0.910800	0.455400	−	0.890287i	$-0.349496\pi$
$937$	26123.6	0.910800	0.455400	+	0.890287i	$0.349496\pi$
$938$	−775.126	−0.0269816
$939$	−4068.00	−0.141378
$940$	−10273.1	−0.356459
$941$	6602.83	0.228742	0.114371	−	0.993438i	$-0.463515\pi$
$941$	6602.83	0.228742	0.114371	+	0.993438i	$0.463515\pi$
$942$	2166.57	0.0749370
$943$	−24791.2	−0.856110
$944$	29110.5	1.00367
$945$	1120.36	0.0385664
$946$	0	0
$947$	−9913.13	−0.340162	−0.170081	−	0.985430i	$-0.554403\pi$
$947$	−9913.13	−0.340162	−0.170081	+	0.985430i	$0.554403\pi$
$948$	2501.89	0.0857148
$949$	−4800.00	−0.164188
$950$	65300.4	2.23013
$951$	11693.6	0.398727
$952$	80.2727	0.00273283
$953$	−12334.8	−0.419268	−0.209634	−	0.977780i	$-0.567227\pi$
$953$	−12334.8	−0.419268	−0.209634	+	0.977780i	$0.567227\pi$
$954$	−1702.61	−0.0577821
$955$	−8686.10	−0.294320
$956$	14034.6	0.474804
$957$	2531.24	0.0854997
$958$	26523.3	0.894497
$959$	−1276.99	−0.0429990
$960$	−25280.9	−0.849935
$961$	−2631.71	−0.0883389
$962$	41647.2	1.39580
$963$	12978.1	0.434282
$964$	7370.16	0.246242
$965$	−72932.7	−2.43294
$966$	−411.705	−0.0137126
$967$	−43542.0	−1.44800	−0.724000	−	0.689800i	$-0.757699\pi$
$967$	−43542.0	−1.44800	−0.724000	+	0.689800i	$0.757699\pi$
$968$	32149.4	1.06748
$969$	1911.72	0.0633781
$970$	27349.1	0.905285
$971$	−47860.8	−1.58180	−0.790900	−	0.611946i	$-0.790387\pi$
$971$	−47860.8	−1.58180	−0.790900	+	0.611946i	$0.790387\pi$
$972$	9624.52	0.317599
$973$	−1000.47	−0.0329638
$974$	32696.3	1.07562
$975$	26576.1	0.872940
$976$	16315.8	0.535100
$977$	2411.64	0.0789716	0.0394858	−	0.999220i	$-0.487428\pi$
$977$	2411.64	0.0789716	0.0394858	+	0.999220i	$0.487428\pi$
$978$	6082.04	0.198857
$979$	582.487	0.0190157
$980$	16033.4	0.522621
$981$	−39266.9	−1.27798
$982$	15512.3	0.504090
$983$	15548.6	0.504500	0.252250	−	0.967662i	$-0.418829\pi$
$983$	15548.6	0.504500	0.252250	+	0.967662i	$0.418829\pi$
$984$	−10515.5	−0.340673
$985$	40296.7	1.30351
$986$	3082.26	0.0995530
$987$	−273.410	−0.00881735
$988$	15049.9	0.484617
$989$	0	0
$990$	−4667.91	−0.149854
$991$	679.692	0.0217872	0.0108936	−	0.999941i	$-0.496532\pi$
$991$	679.692	0.0217872	0.0108936	+	0.999941i	$0.496532\pi$
$992$	17878.8	0.572231
$993$	26350.8	0.842114
$994$	−1104.88	−0.0352561
$995$	56853.6	1.81144
$996$	1647.33	0.0524073
$997$	42549.5	1.35161	0.675806	−	0.737080i	$-0.263796\pi$
$997$	42549.5	1.35161	0.675806	+	0.737080i	$0.263796\pi$
$998$	2405.51	0.0762976
$999$	−42665.1	−1.35122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.36	✓	50
43.42	odd	2		1849.4.a.j.1.15	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.36	✓	50	1.1	even	1	trivial
1849.4.a.j.1.15	yes	50	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.34509 q^{2} -2.42890 q^{3} -2.50055 q^{4} +18.7081 q^{5} -5.69599 q^{6} +0.512587 q^{7} -24.6247 q^{8} -21.1004 q^{9} +O(q^{10})\)	\(q+2.34509 q^{2} -2.42890 q^{3} -2.50055 q^{4} +18.7081 q^{5} -5.69599 q^{6} +0.512587 q^{7} -24.6247 q^{8} -21.1004 q^{9} +43.8722 q^{10} +5.04244 q^{11} +6.07358 q^{12} -48.6308 q^{13} +1.20206 q^{14} -45.4401 q^{15} -37.7429 q^{16} -6.35958 q^{17} -49.4825 q^{18} +123.762 q^{19} -46.7805 q^{20} -1.24502 q^{21} +11.8250 q^{22} +141.010 q^{23} +59.8111 q^{24} +224.993 q^{25} -114.044 q^{26} +116.831 q^{27} -1.28175 q^{28} -206.672 q^{29} -106.561 q^{30} +164.801 q^{31} +108.487 q^{32} -12.2476 q^{33} -14.9138 q^{34} +9.58954 q^{35} +52.7627 q^{36} -365.186 q^{37} +290.233 q^{38} +118.119 q^{39} -460.682 q^{40} -175.812 q^{41} -2.91969 q^{42} -12.6089 q^{44} -394.749 q^{45} +330.680 q^{46} +219.602 q^{47} +91.6737 q^{48} -342.737 q^{49} +527.630 q^{50} +15.4468 q^{51} +121.604 q^{52} +34.4084 q^{53} +273.980 q^{54} +94.3346 q^{55} -12.6223 q^{56} -300.605 q^{57} -484.665 q^{58} -771.285 q^{59} +113.625 q^{60} -432.289 q^{61} +386.473 q^{62} -10.8158 q^{63} +556.356 q^{64} -909.791 q^{65} -28.7217 q^{66} -644.829 q^{67} +15.9024 q^{68} -342.498 q^{69} +22.4883 q^{70} -919.149 q^{71} +519.593 q^{72} +98.7029 q^{73} -856.394 q^{74} -546.486 q^{75} -309.472 q^{76} +2.58469 q^{77} +277.001 q^{78} +411.930 q^{79} -706.098 q^{80} +285.940 q^{81} -412.295 q^{82} +271.229 q^{83} +3.11324 q^{84} -118.976 q^{85} +501.986 q^{87} -124.169 q^{88} +115.517 q^{89} -925.723 q^{90} -24.9276 q^{91} -352.601 q^{92} -400.285 q^{93} +514.986 q^{94} +2315.35 q^{95} -263.505 q^{96} +623.381 q^{97} -803.750 q^{98} -106.398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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