LMFDB - Embedded newform 1849.4.a.i.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} +O(q^{10})$	\(q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} -1.87262 q^{10} +36.0498 q^{11} +12.2514 q^{12} +72.5269 q^{13} -1.14503 q^{14} -2.97924 q^{15} -20.3395 q^{16} -42.3970 q^{17} +33.4516 q^{18} -54.5057 q^{19} -3.37245 q^{20} -1.82168 q^{21} -74.5453 q^{22} -113.780 q^{23} -79.7566 q^{24} -124.180 q^{25} -149.974 q^{26} +142.045 q^{27} -2.06211 q^{28} -18.9616 q^{29} +6.16060 q^{30} +45.5688 q^{31} -151.889 q^{32} -118.597 q^{33} +87.6703 q^{34} +0.501455 q^{35} +60.2437 q^{36} +56.1166 q^{37} +112.709 q^{38} -238.601 q^{39} +21.9547 q^{40} -51.8970 q^{41} +3.76695 q^{42} -134.250 q^{44} -14.6498 q^{45} +235.280 q^{46} +133.140 q^{47} +66.9133 q^{48} -342.693 q^{49} +256.785 q^{50} +139.479 q^{51} -270.092 q^{52} -368.545 q^{53} -293.727 q^{54} +32.6464 q^{55} +13.4244 q^{56} +179.314 q^{57} +39.2097 q^{58} +489.535 q^{59} +11.0947 q^{60} +592.623 q^{61} -94.2291 q^{62} -8.95775 q^{63} +476.798 q^{64} +65.6798 q^{65} +245.241 q^{66} +1060.37 q^{67} +157.887 q^{68} +374.318 q^{69} -1.03693 q^{70} -489.493 q^{71} -392.188 q^{72} +511.754 q^{73} -116.040 q^{74} +408.530 q^{75} +202.980 q^{76} +19.9619 q^{77} +493.389 q^{78} +197.197 q^{79} -18.4193 q^{80} -30.5219 q^{81} +107.315 q^{82} +391.934 q^{83} +6.78397 q^{84} -38.3944 q^{85} +62.3804 q^{87} +873.971 q^{88} +836.377 q^{89} +30.2935 q^{90} +40.1604 q^{91} +423.721 q^{92} -149.913 q^{93} -275.313 q^{94} -49.3599 q^{95} +499.687 q^{96} -1193.25 q^{97} +708.636 q^{98} -583.179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.06784	−0.731093	−0.365547	−	0.930793i	$-0.619118\pi$
$2$	−2.06784	−0.731093	−0.365547	+	0.930793i	$0.619118\pi$
$3$	−3.28982	−0.633127	−0.316563	−	0.948571i	$-0.602529\pi$
$3$	−3.28982	−0.633127	−0.316563	+	0.948571i	$0.602529\pi$
$4$	−3.72402	−0.465503
$5$	0.905592	0.0809986	0.0404993	−	0.999180i	$-0.487105\pi$
$5$	0.905592	0.0809986	0.0404993	+	0.999180i	$0.487105\pi$
$6$	6.80284	0.462875
$7$	0.553732	0.0298987	0.0149493	−	0.999888i	$-0.495241\pi$
$7$	0.553732	0.0298987	0.0149493	+	0.999888i	$0.495241\pi$
$8$	24.2434	1.07142
$9$	−16.1771	−0.599151
$10$	−1.87262	−0.0592175
$11$	36.0498	0.988128	0.494064	−	0.869425i	$-0.335511\pi$
$11$	36.0498	0.988128	0.494064	+	0.869425i	$0.335511\pi$
$12$	12.2514	0.294722
$13$	72.5269	1.54733	0.773667	−	0.633593i	$-0.218420\pi$
$13$	72.5269	1.54733	0.773667	+	0.633593i	$0.218420\pi$
$14$	−1.14503	−0.0218587
$15$	−2.97924	−0.0512824
$16$	−20.3395	−0.317804
$17$	−42.3970	−0.604869	−0.302435	−	0.953170i	$-0.597799\pi$
$17$	−42.3970	−0.604869	−0.302435	+	0.953170i	$0.597799\pi$
$18$	33.4516	0.438035
$19$	−54.5057	−0.658130	−0.329065	−	0.944307i	$-0.606733\pi$
$19$	−54.5057	−0.658130	−0.329065	+	0.944307i	$0.606733\pi$
$20$	−3.37245	−0.0377051
$21$	−1.82168	−0.0189297
$22$	−74.5453	−0.722414
$23$	−113.780	−1.03152	−0.515758	−	0.856734i	$-0.672490\pi$
$23$	−113.780	−1.03152	−0.515758	+	0.856734i	$0.672490\pi$
$24$	−79.7566	−0.678344
$25$	−124.180	−0.993439
$26$	−149.974	−1.13125
$27$	142.045	1.01246
$28$	−2.06211	−0.0139179
$29$	−18.9616	−0.121417	−0.0607084	−	0.998156i	$-0.519336\pi$
$29$	−18.9616	−0.121417	−0.0607084	+	0.998156i	$0.519336\pi$
$30$	6.16060	0.0374922
$31$	45.5688	0.264013	0.132006	−	0.991249i	$-0.457858\pi$
$31$	45.5688	0.264013	0.132006	+	0.991249i	$0.457858\pi$
$32$	−151.889	−0.839074
$33$	−118.597	−0.625611
$34$	87.6703	0.442216
$35$	0.501455	0.00242175
$36$	60.2437	0.278906
$37$	56.1166	0.249338	0.124669	−	0.992198i	$-0.460213\pi$
$37$	56.1166	0.249338	0.124669	+	0.992198i	$0.460213\pi$
$38$	112.709	0.481154
$39$	−238.601	−0.979658
$40$	21.9547	0.0867835
$41$	−51.8970	−0.197682	−0.0988409	−	0.995103i	$-0.531513\pi$
$41$	−51.8970	−0.197682	−0.0988409	+	0.995103i	$0.531513\pi$
$42$	3.76695	0.0138393
$43$	0	0
$43$	0	0
$44$	−134.250	−0.459977
$45$	−14.6498	−0.0485304
$46$	235.280	0.754134
$47$	133.140	0.413202	0.206601	−	0.978425i	$-0.433760\pi$
$47$	133.140	0.413202	0.206601	+	0.978425i	$0.433760\pi$
$48$	66.9133	0.201210
$49$	−342.693	−0.999106
$50$	256.785	0.726297
$51$	139.479	0.382959
$52$	−270.092	−0.720288
$53$	−368.545	−0.955162	−0.477581	−	0.878588i	$-0.658486\pi$
$53$	−368.545	−0.955162	−0.477581	+	0.878588i	$0.658486\pi$
$54$	−293.727	−0.740206
$55$	32.6464	0.0800371
$56$	13.4244	0.0320340
$57$	179.314	0.416679
$58$	39.2097	0.0887670
$59$	489.535	1.08020	0.540102	−	0.841599i	$-0.318386\pi$
$59$	489.535	1.08020	0.540102	+	0.841599i	$0.318386\pi$
$60$	11.0947	0.0238721
$61$	592.623	1.24389	0.621947	−	0.783059i	$-0.286342\pi$
$61$	592.623	1.24389	0.621947	+	0.783059i	$0.286342\pi$
$62$	−94.2291	−0.193018
$63$	−8.95775	−0.0179138
$64$	476.798	0.931246
$65$	65.6798	0.125332
$66$	245.241	0.457380
$67$	1060.37	1.93350	0.966751	−	0.255719i	$-0.0823121\pi$
$67$	1060.37	1.93350	0.966751	+	0.255719i	$0.0823121\pi$
$68$	157.887	0.281568
$69$	374.318	0.653080
$70$	−1.03693	−0.00177053
$71$	−489.493	−0.818199	−0.409099	−	0.912490i	$-0.634157\pi$
$71$	−489.493	−0.818199	−0.409099	+	0.912490i	$0.634157\pi$
$72$	−392.188	−0.641941
$73$	511.754	0.820497	0.410248	−	0.911974i	$-0.365442\pi$
$73$	511.754	0.820497	0.410248	+	0.911974i	$0.365442\pi$
$74$	−116.040	−0.182289
$75$	408.530	0.628973
$76$	202.980	0.306361
$77$	19.9619	0.0295438
$78$	493.389	0.716222
$79$	197.197	0.280840	0.140420	−	0.990092i	$-0.455155\pi$
$79$	197.197	0.280840	0.140420	+	0.990092i	$0.455155\pi$
$80$	−18.4193	−0.0257417
$81$	−30.5219	−0.0418681
$82$	107.315	0.144524
$83$	391.934	0.518318	0.259159	−	0.965835i	$-0.416555\pi$
$83$	391.934	0.518318	0.259159	+	0.965835i	$0.416555\pi$
$84$	6.78397	0.00881181
$85$	−38.3944	−0.0489936
$86$	0	0
$87$	62.3804	0.0768722
$88$	873.971	1.05870
$89$	836.377	0.996133	0.498066	−	0.867139i	$-0.334044\pi$
$89$	836.377	0.996133	0.498066	+	0.867139i	$0.334044\pi$
$90$	30.2935	0.0354802
$91$	40.1604	0.0462633
$92$	423.721	0.480174
$93$	−149.913	−0.167154
$94$	−275.313	−0.302089
$95$	−49.3599	−0.0533076
$96$	499.687	0.531240
$97$	−1193.25	−1.24903	−0.624514	−	0.781013i	$-0.714703\pi$
$97$	−1193.25	−1.24903	−0.624514	+	0.781013i	$0.714703\pi$
$98$	708.636	0.730440
$99$	−583.179	−0.592038
$100$	462.449	0.462449
$101$	−1774.91	−1.74862	−0.874309	−	0.485370i	$-0.838685\pi$
$101$	−1774.91	−1.74862	−0.874309	+	0.485370i	$0.838685\pi$
$102$	−288.420	−0.279979
$103$	−1820.25	−1.74131	−0.870655	−	0.491894i	$-0.836305\pi$
$103$	−1820.25	−1.74131	−0.870655	+	0.491894i	$0.836305\pi$
$104$	1758.30	1.65784
$105$	−1.64970	−0.00153328
$106$	762.094	0.698313
$107$	−656.760	−0.593378	−0.296689	−	0.954974i	$-0.595882\pi$
$107$	−656.760	−0.593378	−0.296689	+	0.954974i	$0.595882\pi$
$108$	−528.978	−0.471305
$109$	518.425	0.455560	0.227780	−	0.973713i	$-0.426853\pi$
$109$	518.425	0.455560	0.227780	+	0.973713i	$0.426853\pi$
$110$	−67.5076	−0.0585145
$111$	−184.614	−0.157863
$112$	−11.2626	−0.00950194
$113$	1702.26	1.41713	0.708564	−	0.705647i	$-0.249343\pi$
$113$	1702.26	1.41713	0.708564	+	0.705647i	$0.249343\pi$
$114$	−370.793	−0.304631
$115$	−103.039	−0.0835514
$116$	70.6136	0.0565199
$117$	−1173.27	−0.927086
$118$	−1012.28	−0.789730
$119$	−23.4765	−0.0180848
$120$	−72.2270	−0.0549449
$121$	−31.4145	−0.0236022
$122$	−1225.45	−0.909402
$123$	170.732	0.125158
$124$	−169.699	−0.122899
$125$	−225.655	−0.161466
$126$	18.5232	0.0130967
$127$	−1281.78	−0.895587	−0.447793	−	0.894137i	$-0.647790\pi$
$127$	−1281.78	−0.895587	−0.447793	+	0.894137i	$0.647790\pi$
$128$	229.166	0.158247
$129$	0	0
$130$	−135.816	−0.0916293
$131$	2387.94	1.59263	0.796316	−	0.604880i	$-0.206779\pi$
$131$	2387.94	1.59263	0.796316	+	0.604880i	$0.206779\pi$
$132$	441.659	0.291223
$133$	−30.1815	−0.0196772
$134$	−2192.68	−1.41357
$135$	128.635	0.0820083
$136$	−1027.85	−0.648069
$137$	3079.35	1.92034	0.960169	−	0.279418i	$-0.0901416\pi$
$137$	3079.35	1.92034	0.960169	+	0.279418i	$0.0901416\pi$
$138$	−774.030	−0.477463
$139$	−59.2952	−0.0361824	−0.0180912	−	0.999836i	$-0.505759\pi$
$139$	−59.2952	−0.0361824	−0.0180912	+	0.999836i	$0.505759\pi$
$140$	−1.86743	−0.00112733
$141$	−438.007	−0.261609
$142$	1012.19	0.598180
$143$	2614.58	1.52896
$144$	329.033	0.190413
$145$	−17.1715	−0.00983460
$146$	−1058.23	−0.599859
$147$	1127.40	0.632561
$148$	−208.979	−0.116068
$149$	−2972.79	−1.63450	−0.817251	−	0.576283i	$-0.804503\pi$
$149$	−2972.79	−1.63450	−0.817251	+	0.576283i	$0.804503\pi$
$150$	−844.776	−0.459838
$151$	181.367	0.0977443	0.0488722	−	0.998805i	$-0.484437\pi$
$151$	181.367	0.0977443	0.0488722	+	0.998805i	$0.484437\pi$
$152$	−1321.41	−0.705133
$153$	685.859	0.362408
$154$	−41.2781	−0.0215992
$155$	41.2667	0.0213847
$156$	888.554	0.456034
$157$	−1001.66	−0.509180	−0.254590	−	0.967049i	$-0.581940\pi$
$157$	−1001.66	−0.509180	−0.254590	+	0.967049i	$0.581940\pi$
$158$	−407.773	−0.205321
$159$	1212.45	0.604739
$160$	−137.549	−0.0679639
$161$	−63.0038	−0.0308410
$162$	63.1144	0.0306095
$163$	2683.64	1.28956	0.644781	−	0.764367i	$-0.276948\pi$
$163$	2683.64	1.28956	0.644781	+	0.764367i	$0.276948\pi$
$164$	193.266	0.0920214
$165$	−107.401	−0.0506736
$166$	−810.459	−0.378939
$167$	−1580.13	−0.732178	−0.366089	−	0.930580i	$-0.619304\pi$
$167$	−1580.13	−0.732178	−0.366089	+	0.930580i	$0.619304\pi$
$168$	−44.1638	−0.0202816
$169$	3063.15	1.39424
$170$	79.3936	0.0358189
$171$	881.742	0.394319
$172$	0	0
$173$	−1218.41	−0.535456	−0.267728	−	0.963495i	$-0.586273\pi$
$173$	−1218.41	−0.535456	−0.267728	+	0.963495i	$0.586273\pi$
$174$	−128.993	−0.0562008
$175$	−68.7623	−0.0297025
$176$	−733.234	−0.314032
$177$	−1610.48	−0.683906
$178$	−1729.50	−0.728266
$179$	3175.63	1.32602	0.663011	−	0.748610i	$-0.269278\pi$
$179$	3175.63	1.32602	0.663011	+	0.748610i	$0.269278\pi$
$180$	54.5563	0.0225910
$181$	−2654.51	−1.09010	−0.545050	−	0.838403i	$-0.683490\pi$
$181$	−2654.51	−1.09010	−0.545050	+	0.838403i	$0.683490\pi$
$182$	−83.0455	−0.0338228
$183$	−1949.62	−0.787543
$184$	−2758.43	−1.10519
$185$	50.8187	0.0201960
$186$	309.997	0.122205
$187$	−1528.40	−0.597689
$188$	−495.817	−0.192346
$189$	78.6547	0.0302714
$190$	102.069	0.0389728
$191$	757.828	0.287092	0.143546	−	0.989644i	$-0.454150\pi$
$191$	757.828	0.287092	0.143546	+	0.989644i	$0.454150\pi$
$192$	−1568.58	−0.589597
$193$	2143.88	0.799584	0.399792	−	0.916606i	$-0.369082\pi$
$193$	2143.88	0.799584	0.399792	+	0.916606i	$0.369082\pi$
$194$	2467.45	0.913156
$195$	−216.075	−0.0793510
$196$	1276.20	0.465087
$197$	−2151.99	−0.778289	−0.389144	−	0.921177i	$-0.627229\pi$
$197$	−2151.99	−0.778289	−0.389144	+	0.921177i	$0.627229\pi$
$198$	1205.92	0.432835
$199$	3651.57	1.30077	0.650384	−	0.759605i	$-0.274608\pi$
$199$	3651.57	1.30077	0.650384	+	0.759605i	$0.274608\pi$
$200$	−3010.55	−1.06439
$201$	−3488.43	−1.22415
$202$	3670.24	1.27840
$203$	−10.4997	−0.00363020
$204$	−519.421	−0.178268
$205$	−46.9975	−0.0160120
$206$	3764.00	1.27306
$207$	1840.63	0.618033
$208$	−1475.16	−0.491750
$209$	−1964.92	−0.650316
$210$	3.41132	0.00112097
$211$	−5708.59	−1.86254	−0.931270	−	0.364331i	$-0.881298\pi$
$211$	−5708.59	−1.86254	−0.931270	+	0.364331i	$0.881298\pi$
$212$	1372.47	0.444631
$213$	1610.34	0.518024
$214$	1358.08	0.433814
$215$	0	0
$216$	3443.66	1.08477
$217$	25.2329	0.00789364
$218$	−1072.02	−0.333057
$219$	−1683.58	−0.519478
$220$	−121.576	−0.0372575
$221$	−3074.92	−0.935935
$222$	381.752	0.115412
$223$	−3393.14	−1.01893	−0.509465	−	0.860491i	$-0.670157\pi$
$223$	−3393.14	−1.01893	−0.509465	+	0.860491i	$0.670157\pi$
$224$	−84.1056	−0.0250872
$225$	2008.87	0.595220
$226$	−3520.01	−1.03605
$227$	−5880.28	−1.71933	−0.859664	−	0.510859i	$-0.829327\pi$
$227$	−5880.28	−1.71933	−0.859664	+	0.510859i	$0.829327\pi$
$228$	−667.769	−0.193965
$229$	3582.01	1.03365	0.516826	−	0.856091i	$-0.327114\pi$
$229$	3582.01	1.03365	0.516826	+	0.856091i	$0.327114\pi$
$230$	213.068	0.0610839
$231$	−65.6711	−0.0187049
$232$	−459.695	−0.130088
$233$	1730.14	0.486459	0.243230	−	0.969969i	$-0.421793\pi$
$233$	1730.14	0.486459	0.243230	+	0.969969i	$0.421793\pi$
$234$	2426.14	0.677786
$235$	120.571	0.0334688
$236$	−1823.04	−0.502838
$237$	−648.743	−0.177808
$238$	48.5458	0.0132217
$239$	−4199.88	−1.13668	−0.568342	−	0.822792i	$-0.692415\pi$
$239$	−4199.88	−1.13668	−0.568342	+	0.822792i	$0.692415\pi$
$240$	60.5962	0.0162978
$241$	6623.20	1.77028	0.885141	−	0.465322i	$-0.154062\pi$
$241$	6623.20	1.77028	0.885141	+	0.465322i	$0.154062\pi$
$242$	64.9602	0.0172554
$243$	−3734.80	−0.985957
$244$	−2206.94	−0.579036
$245$	−310.340	−0.0809262
$246$	−353.047	−0.0915019
$247$	−3953.13	−1.01835
$248$	1104.74	0.282868
$249$	−1289.39	−0.328161
$250$	466.620	0.118047
$251$	−2718.52	−0.683631	−0.341816	−	0.939767i	$-0.611042\pi$
$251$	−2718.52	−0.683631	−0.341816	+	0.939767i	$0.611042\pi$
$252$	33.3589	0.00833893
$253$	−4101.76	−1.01927
$254$	2650.52	0.654757
$255$	126.311	0.0310192
$256$	−4288.26	−1.04694
$257$	1570.63	0.381219	0.190609	−	0.981666i	$-0.438954\pi$
$257$	1570.63	0.381219	0.190609	+	0.981666i	$0.438954\pi$
$258$	0	0
$259$	31.0735	0.00745488
$260$	−244.593	−0.0583424
$261$	306.744	0.0727469
$262$	−4937.88	−1.16436
$263$	−5434.10	−1.27407	−0.637036	−	0.770834i	$-0.719840\pi$
$263$	−5434.10	−1.27407	−0.637036	+	0.770834i	$0.719840\pi$
$264$	−2875.21	−0.670291
$265$	−333.752	−0.0773668
$266$	62.4107	0.0143859
$267$	−2751.53	−0.630678
$268$	−3948.84	−0.900051
$269$	1749.35	0.396505	0.198252	−	0.980151i	$-0.436473\pi$
$269$	1749.35	0.396505	0.198252	+	0.980151i	$0.436473\pi$
$270$	−265.997	−0.0599557
$271$	4745.81	1.06379	0.531895	−	0.846810i	$-0.321480\pi$
$271$	4745.81	1.06379	0.531895	+	0.846810i	$0.321480\pi$
$272$	862.333	0.192230
$273$	−132.121	−0.0292905
$274$	−6367.61	−1.40395
$275$	−4476.66	−0.981646
$276$	−1393.97	−0.304011
$277$	−5996.54	−1.30071	−0.650356	−	0.759630i	$-0.725380\pi$
$277$	−5996.54	−1.30071	−0.650356	+	0.759630i	$0.725380\pi$
$278$	122.613	0.0264527
$279$	−737.169	−0.158183
$280$	12.1570	0.00259471
$281$	2534.71	0.538107	0.269054	−	0.963125i	$-0.413289\pi$
$281$	2534.71	0.538107	0.269054	+	0.963125i	$0.413289\pi$
$282$	905.731	0.191261
$283$	6608.32	1.38807	0.694035	−	0.719942i	$-0.255831\pi$
$283$	6608.32	1.38807	0.694035	+	0.719942i	$0.255831\pi$
$284$	1822.88	0.380874
$285$	162.385	0.0337505
$286$	−5406.54	−1.11782
$287$	−28.7370	−0.00591043
$288$	2457.11	0.502732
$289$	−3115.50	−0.634133
$290$	35.5080	0.00719001
$291$	3925.57	0.790794
$292$	−1905.78	−0.381943
$293$	6937.69	1.38329	0.691646	−	0.722237i	$-0.256886\pi$
$293$	6937.69	1.38329	0.691646	+	0.722237i	$0.256886\pi$
$294$	−2331.29	−0.462461
$295$	443.319	0.0874951
$296$	1360.46	0.267146
$297$	5120.69	1.00045
$298$	6147.27	1.19497
$299$	−8252.14	−1.59610
$300$	−1521.37	−0.292789
$301$	0	0
$302$	−375.038	−0.0714602
$303$	5839.15	1.10710
$304$	1108.62	0.209156
$305$	536.674	0.100754
$306$	−1418.25	−0.264954
$307$	−1685.77	−0.313394	−0.156697	−	0.987647i	$-0.550085\pi$
$307$	−1685.77	−0.313394	−0.156697	+	0.987647i	$0.550085\pi$
$308$	−74.3385	−0.0137527
$309$	5988.32	1.10247
$310$	−85.3332	−0.0156342
$311$	5016.27	0.914620	0.457310	−	0.889307i	$-0.348813\pi$
$311$	5016.27	0.914620	0.457310	+	0.889307i	$0.348813\pi$
$312$	−5784.50	−1.04962
$313$	−5995.54	−1.08271	−0.541354	−	0.840794i	$-0.682088\pi$
$313$	−5995.54	−1.08271	−0.541354	+	0.840794i	$0.682088\pi$
$314$	2071.28	0.372258
$315$	−8.11207	−0.00145099
$316$	−734.366	−0.130732
$317$	−7839.42	−1.38898	−0.694488	−	0.719504i	$-0.744369\pi$
$317$	−7839.42	−1.38898	−0.694488	+	0.719504i	$0.744369\pi$
$318$	−2507.16	−0.442120
$319$	−683.563	−0.119975
$320$	431.785	0.0754297
$321$	2160.62	0.375683
$322$	130.282	0.0225476
$323$	2310.88	0.398082
$324$	113.664	0.0194897
$325$	−9006.38	−1.53718
$326$	−5549.34	−0.942790
$327$	−1705.52	−0.288427
$328$	−1258.16	−0.211800
$329$	73.7239	0.0123542
$330$	222.088	0.0370471
$331$	−8960.38	−1.48794	−0.743968	−	0.668215i	$-0.767059\pi$
$331$	−8960.38	−1.48794	−0.743968	+	0.668215i	$0.767059\pi$
$332$	−1459.57	−0.241278
$333$	−907.801	−0.149391
$334$	3267.45	0.535291
$335$	960.262	0.156611
$336$	37.0520	0.00601593
$337$	−11341.3	−1.83324	−0.916618	−	0.399765i	$-0.869092\pi$
$337$	−11341.3	−1.83324	−0.916618	+	0.399765i	$0.869092\pi$
$338$	−6334.12	−1.01932
$339$	−5600.14	−0.897221
$340$	142.982	0.0228067
$341$	1642.74	0.260878
$342$	−1823.30	−0.288284
$343$	−379.690	−0.0597707
$344$	0	0
$345$	338.979	0.0528986
$346$	2519.48	0.391468
$347$	−4636.21	−0.717247	−0.358623	−	0.933482i	$-0.616754\pi$
$347$	−4636.21	−0.717247	−0.358623	+	0.933482i	$0.616754\pi$
$348$	−232.306	−0.0357842
$349$	−5902.79	−0.905355	−0.452678	−	0.891674i	$-0.649531\pi$
$349$	−5902.79	−0.905355	−0.452678	+	0.891674i	$0.649531\pi$
$350$	142.190	0.0217153
$351$	10302.1	1.56662
$352$	−5475.55	−0.829113
$353$	9876.87	1.48921	0.744607	−	0.667503i	$-0.232637\pi$
$353$	9876.87	1.48921	0.744607	+	0.667503i	$0.232637\pi$
$354$	3330.23	0.499999
$355$	−443.281	−0.0662730
$356$	−3114.69	−0.463702
$357$	77.2337	0.0114500
$358$	−6566.71	−0.969445
$359$	−7475.25	−1.09897	−0.549483	−	0.835505i	$-0.685175\pi$
$359$	−7475.25	−1.09897	−0.549483	+	0.835505i	$0.685175\pi$
$360$	−355.162	−0.0519964
$361$	−3888.13	−0.566866
$362$	5489.11	0.796965
$363$	103.348	0.0149432
$364$	−149.558	−0.0215357
$365$	463.440	0.0664591
$366$	4031.52	0.575767
$367$	4041.24	0.574799	0.287400	−	0.957811i	$-0.407209\pi$
$367$	4041.24	0.574799	0.287400	+	0.957811i	$0.407209\pi$
$368$	2314.24	0.327820
$369$	839.541	0.118441
$370$	−105.085	−0.0147652
$371$	−204.075	−0.0285581
$372$	558.280	0.0778104
$373$	−5634.47	−0.782149	−0.391075	−	0.920359i	$-0.627897\pi$
$373$	−5634.47	−0.782149	−0.391075	+	0.920359i	$0.627897\pi$
$374$	3160.50	0.436966
$375$	742.366	0.102228
$376$	3227.77	0.442712
$377$	−1375.23	−0.187872
$378$	−162.646	−0.0221312
$379$	2008.13	0.272165	0.136082	−	0.990698i	$-0.456549\pi$
$379$	2008.13	0.272165	0.136082	+	0.990698i	$0.456549\pi$
$380$	183.817	0.0248148
$381$	4216.83	0.567020
$382$	−1567.07	−0.209891
$383$	−205.436	−0.0274080	−0.0137040	−	0.999906i	$-0.504362\pi$
$383$	−205.436	−0.0274080	−0.0137040	+	0.999906i	$0.504362\pi$
$384$	−753.915	−0.100190
$385$	18.0773	0.00239300
$386$	−4433.20	−0.584570
$387$	0	0
$388$	4443.68	0.581426
$389$	−3601.09	−0.469363	−0.234682	−	0.972072i	$-0.575405\pi$
$389$	−3601.09	−0.469363	−0.234682	+	0.972072i	$0.575405\pi$
$390$	446.809	0.0580130
$391$	4823.95	0.623932
$392$	−8308.07	−1.07046
$393$	−7855.89	−1.00834
$394$	4449.98	0.569002
$395$	178.580	0.0227477
$396$	2171.77	0.275595
$397$	−12924.6	−1.63392	−0.816962	−	0.576691i	$-0.804344\pi$
$397$	−12924.6	−1.63392	−0.816962	+	0.576691i	$0.804344\pi$
$398$	−7550.87	−0.950983
$399$	99.2918	0.0124582
$400$	2525.75	0.315719
$401$	4108.28	0.511615	0.255807	−	0.966728i	$-0.417659\pi$
$401$	4108.28	0.511615	0.255807	+	0.966728i	$0.417659\pi$
$402$	7213.52	0.894969
$403$	3304.96	0.408516
$404$	6609.81	0.813986
$405$	−27.6404	−0.00339126
$406$	21.7116	0.00265402
$407$	2022.99	0.246378
$408$	3381.44	0.410310
$409$	3060.09	0.369956	0.184978	−	0.982743i	$-0.440779\pi$
$409$	3060.09	0.369956	0.184978	+	0.982743i	$0.440779\pi$
$410$	97.1836	0.0117062
$411$	−10130.5	−1.21582
$412$	6778.67	0.810585
$413$	271.071	0.0322967
$414$	−3806.14	−0.451840
$415$	354.933	0.0419830
$416$	−11016.0	−1.29833
$417$	195.071	0.0229081
$418$	4063.14	0.475442
$419$	−4245.76	−0.495033	−0.247516	−	0.968884i	$-0.579614\pi$
$419$	−4245.76	−0.495033	−0.247516	+	0.968884i	$0.579614\pi$
$420$	6.14351	0.000713745 0
$421$	15790.0	1.82792	0.913962	−	0.405800i	$-0.133007\pi$
$421$	15790.0	1.82792	0.913962	+	0.405800i	$0.133007\pi$
$422$	11804.5	1.36169
$423$	−2153.82	−0.247570
$424$	−8934.81	−1.02338
$425$	5264.85	0.600901
$426$	−3329.94	−0.378723
$427$	328.154	0.0371908
$428$	2445.79	0.276219
$429$	−8601.50	−0.968028
$430$	0	0
$431$	9935.16	1.11035	0.555174	−	0.831734i	$-0.312652\pi$
$431$	9935.16	1.11035	0.555174	+	0.831734i	$0.312652\pi$
$432$	−2889.12	−0.321766
$433$	−5897.25	−0.654512	−0.327256	−	0.944936i	$-0.606124\pi$
$433$	−5897.25	−0.654512	−0.327256	+	0.944936i	$0.606124\pi$
$434$	−52.1776	−0.00577098
$435$	56.4912	0.00622655
$436$	−1930.62	−0.212065
$437$	6201.68	0.678871
$438$	3481.38	0.379787
$439$	5213.48	0.566801	0.283401	−	0.959002i	$-0.408537\pi$
$439$	5213.48	0.566801	0.283401	+	0.959002i	$0.408537\pi$
$440$	791.461	0.0857532
$441$	5543.77	0.598615
$442$	6358.46	0.684256
$443$	−86.4536	−0.00927208	−0.00463604	−	0.999989i	$-0.501476\pi$
$443$	−86.4536	−0.00927208	−0.00463604	+	0.999989i	$0.501476\pi$
$444$	687.505	0.0734855
$445$	757.417	0.0806854
$446$	7016.49	0.744933
$447$	9779.96	1.03485
$448$	264.018	0.0278430
$449$	−4606.22	−0.484145	−0.242072	−	0.970258i	$-0.577827\pi$
$449$	−4606.22	−0.484145	−0.242072	+	0.970258i	$0.577827\pi$
$450$	−4154.02	−0.435161
$451$	−1870.88	−0.195335
$452$	−6339.26	−0.659677
$453$	−596.664	−0.0618846
$454$	12159.5	1.25699
$455$	36.3690	0.00374726
$456$	4347.19	0.446438
$457$	1481.01	0.151595	0.0757973	−	0.997123i	$-0.475850\pi$
$457$	1481.01	0.151595	0.0757973	+	0.997123i	$0.475850\pi$
$458$	−7407.05	−0.755695
$459$	−6022.28	−0.612409
$460$	383.718	0.0388934
$461$	−10609.9	−1.07192	−0.535958	−	0.844244i	$-0.680050\pi$
$461$	−10609.9	−1.07192	−0.535958	+	0.844244i	$0.680050\pi$
$462$	135.798	0.0136751
$463$	−9170.50	−0.920495	−0.460247	−	0.887791i	$-0.652239\pi$
$463$	−9170.50	−0.920495	−0.460247	+	0.887791i	$0.652239\pi$
$464$	385.670	0.0385868
$465$	−135.760	−0.0135392
$466$	−3577.65	−0.355647
$467$	−3075.80	−0.304777	−0.152389	−	0.988321i	$-0.548697\pi$
$467$	−3075.80	−0.304777	−0.152389	+	0.988321i	$0.548697\pi$
$468$	4369.29	0.431561
$469$	587.160	0.0578092
$470$	−249.321	−0.0244688
$471$	3295.29	0.322375
$472$	11868.0	1.15735
$473$	0	0
$474$	1341.50	0.129994
$475$	6768.51	0.653812
$476$	87.4272	0.00841853
$477$	5961.98	0.572286
$478$	8684.69	0.831022
$479$	−8567.68	−0.817259	−0.408630	−	0.912700i	$-0.633993\pi$
$479$	−8567.68	−0.817259	−0.408630	+	0.912700i	$0.633993\pi$
$480$	452.513	0.0430298
$481$	4069.96	0.385809
$482$	−13695.8	−1.29424
$483$	207.271	0.0195263
$484$	116.988	0.0109869
$485$	−1080.59	−0.101170
$486$	7722.98	0.720827
$487$	−7868.75	−0.732171	−0.366085	−	0.930581i	$-0.619302\pi$
$487$	−7868.75	−0.732171	−0.366085	+	0.930581i	$0.619302\pi$
$488$	14367.2	1.33273
$489$	−8828.69	−0.816457
$490$	641.736	0.0591646
$491$	−16285.2	−1.49683	−0.748414	−	0.663232i	$-0.769184\pi$
$491$	−16285.2	−1.49683	−0.748414	+	0.663232i	$0.769184\pi$
$492$	−635.810	−0.0582612
$493$	803.916	0.0734413
$494$	8174.45	0.744506
$495$	−528.123	−0.0479542
$496$	−926.845	−0.0839044
$497$	−271.048	−0.0244631
$498$	2666.27	0.239916
$499$	−16520.2	−1.48206	−0.741030	−	0.671472i	$-0.765662\pi$
$499$	−16520.2	−1.48206	−0.741030	+	0.671472i	$0.765662\pi$
$500$	840.346	0.0751628
$501$	5198.33	0.463562
$502$	5621.47	0.499798
$503$	−1294.17	−0.114720	−0.0573600	−	0.998354i	$-0.518268\pi$
$503$	−1294.17	−0.114720	−0.0573600	+	0.998354i	$0.518268\pi$
$504$	−217.167	−0.0191932
$505$	−1607.35	−0.141636
$506$	8481.80	0.745182
$507$	−10077.2	−0.882732
$508$	4773.37	0.416898
$509$	−5448.73	−0.474480	−0.237240	−	0.971451i	$-0.576243\pi$
$509$	−5448.73	−0.474480	−0.237240	+	0.971451i	$0.576243\pi$
$510$	−261.191	−0.0226779
$511$	283.374	0.0245318
$512$	7034.13	0.607163
$513$	−7742.25	−0.666333
$514$	−3247.82	−0.278706
$515$	−1648.41	−0.141044
$516$	0	0
$517$	4799.67	0.408296
$518$	−64.2552	−0.00545021
$519$	4008.35	0.339012
$520$	1592.30	0.134283
$521$	16148.0	1.35788	0.678942	−	0.734192i	$-0.262439\pi$
$521$	16148.0	1.35788	0.678942	+	0.734192i	$0.262439\pi$
$522$	−634.298	−0.0531848
$523$	−4443.77	−0.371534	−0.185767	−	0.982594i	$-0.559477\pi$
$523$	−4443.77	−0.371534	−0.185767	+	0.982594i	$0.559477\pi$
$524$	−8892.72	−0.741375
$525$	226.216	0.0188055
$526$	11236.9	0.931465
$527$	−1931.98	−0.159693
$528$	2412.21	0.198822
$529$	778.997	0.0640254
$530$	690.147	0.0565624
$531$	−7919.24	−0.647205
$532$	112.397	0.00915980
$533$	−3763.93	−0.305880
$534$	5689.74	0.461085
$535$	−594.757	−0.0480628
$536$	25707.0	2.07159
$537$	−10447.3	−0.839540
$538$	−3617.38	−0.289882
$539$	−12354.0	−0.987245
$540$	−479.039	−0.0381751
$541$	−12789.1	−1.01635	−0.508176	−	0.861253i	$-0.669680\pi$
$541$	−12789.1	−1.01635	−0.508176	+	0.861253i	$0.669680\pi$
$542$	−9813.59	−0.777730
$543$	8732.87	0.690172
$544$	6439.62	0.507530
$545$	469.481	0.0368998
$546$	273.205	0.0214141
$547$	−6699.60	−0.523682	−0.261841	−	0.965111i	$-0.584330\pi$
$547$	−6699.60	−0.523682	−0.261841	+	0.965111i	$0.584330\pi$
$548$	−11467.6	−0.893923
$549$	−9586.89	−0.745280
$550$	9257.03	0.717674
$551$	1033.52	0.0799080
$552$	9074.75	0.699723
$553$	109.194	0.00839676
$554$	12399.9	0.950942
$555$	−167.185	−0.0127867
$556$	220.817	0.0168430
$557$	−1895.56	−0.144197	−0.0720983	−	0.997398i	$-0.522970\pi$
$557$	−1895.56	−0.144197	−0.0720983	+	0.997398i	$0.522970\pi$
$558$	1524.35	0.115647
$559$	0	0
$560$	−10.1993	−0.000769644 0
$561$	5028.17	0.378413
$562$	−5241.38	−0.393406
$563$	−3891.98	−0.291345	−0.145673	−	0.989333i	$-0.546535\pi$
$563$	−3891.98	−0.291345	−0.145673	+	0.989333i	$0.546535\pi$
$564$	1631.15	0.121780
$565$	1541.56	0.114785
$566$	−13665.0	−1.01481
$567$	−16.9009	−0.00125180
$568$	−11867.0	−0.876634
$569$	−15271.0	−1.12512	−0.562559	−	0.826757i	$-0.690183\pi$
$569$	−15271.0	−1.12512	−0.562559	+	0.826757i	$0.690183\pi$
$570$	−335.788	−0.0246747
$571$	14055.6	1.03014	0.515070	−	0.857148i	$-0.327766\pi$
$571$	14055.6	1.03014	0.515070	+	0.857148i	$0.327766\pi$
$572$	−9736.74	−0.711737
$573$	−2493.12	−0.181765
$574$	59.4237	0.00432107
$575$	14129.2	1.02475
$576$	−7713.19	−0.557957
$577$	7860.86	0.567161	0.283581	−	0.958948i	$-0.408478\pi$
$577$	7860.86	0.567161	0.283581	+	0.958948i	$0.408478\pi$
$578$	6442.36	0.463610
$579$	−7052.98	−0.506238
$580$	63.9471	0.00457803
$581$	217.026	0.0154970
$582$	−8117.46	−0.578144
$583$	−13286.0	−0.943823
$584$	12406.7	0.879096
$585$	−1062.51	−0.0750927
$586$	−14346.1	−1.01131
$587$	10247.7	0.720562	0.360281	−	0.932844i	$-0.382681\pi$
$587$	10247.7	0.720562	0.360281	+	0.932844i	$0.382681\pi$
$588$	−4198.46	−0.294459
$589$	−2483.76	−0.173755
$590$	−916.715	−0.0639671
$591$	7079.66	0.492755
$592$	−1141.38	−0.0792407
$593$	−16157.0	−1.11887	−0.559435	−	0.828874i	$-0.688982\pi$
$593$	−16157.0	−1.11887	−0.559435	+	0.828874i	$0.688982\pi$
$594$	−10588.8	−0.731419
$595$	−21.2602	−0.00146484
$596$	11070.7	0.760865
$597$	−12013.0	−0.823551
$598$	17064.1	1.16690
$599$	−14102.1	−0.961933	−0.480967	−	0.876739i	$-0.659714\pi$
$599$	−14102.1	−0.961933	−0.480967	+	0.876739i	$0.659714\pi$
$600$	9904.17	0.673894
$601$	−12470.6	−0.846397	−0.423198	−	0.906037i	$-0.639093\pi$
$601$	−12470.6	−0.846397	−0.423198	+	0.906037i	$0.639093\pi$
$602$	0	0
$603$	−17153.7	−1.15846
$604$	−675.413	−0.0455003
$605$	−28.4487	−0.00191174
$606$	−12074.4	−0.809391
$607$	−18569.3	−1.24169	−0.620844	−	0.783934i	$-0.713210\pi$
$607$	−18569.3	−1.24169	−0.620844	+	0.783934i	$0.713210\pi$
$608$	8278.80	0.552220
$609$	34.5420	0.00229838
$610$	−1109.76	−0.0736604
$611$	9656.24	0.639361
$612$	−2554.15	−0.168702
$613$	25890.1	1.70586	0.852928	−	0.522028i	$-0.174824\pi$
$613$	25890.1	1.70586	0.852928	+	0.522028i	$0.174824\pi$
$614$	3485.91	0.229120
$615$	154.614	0.0101376
$616$	483.945	0.0316537
$617$	−24758.2	−1.61544	−0.807720	−	0.589566i	$-0.799299\pi$
$617$	−24758.2	−1.61544	−0.807720	+	0.589566i	$0.799299\pi$
$618$	−12382.9	−0.806009
$619$	−5979.48	−0.388264	−0.194132	−	0.980975i	$-0.562189\pi$
$619$	−5979.48	−0.388264	−0.194132	+	0.980975i	$0.562189\pi$
$620$	−153.678	−0.00995462
$621$	−16161.9	−1.04437
$622$	−10372.9	−0.668672
$623$	463.128	0.0297831
$624$	4853.01	0.311340
$625$	15318.1	0.980361
$626$	12397.8	0.791561
$627$	6464.23	0.411733
$628$	3730.21	0.237025
$629$	−2379.17	−0.150817
$630$	16.7745	0.00106081
$631$	20733.7	1.30808	0.654038	−	0.756462i	$-0.273074\pi$
$631$	20733.7	1.30808	0.654038	+	0.756462i	$0.273074\pi$
$632$	4780.74	0.300898
$633$	18780.3	1.17922
$634$	16210.7	1.01547
$635$	−1160.77	−0.0725413
$636$	−4515.19	−0.281508
$637$	−24854.5	−1.54595
$638$	1413.50	0.0877132
$639$	7918.56	0.490224
$640$	207.531	0.0128178
$641$	−8796.35	−0.542020	−0.271010	−	0.962577i	$-0.587358\pi$
$641$	−8796.35	−0.542020	−0.271010	+	0.962577i	$0.587358\pi$
$642$	−4467.83	−0.274659
$643$	12217.2	0.749299	0.374650	−	0.927166i	$-0.377763\pi$
$643$	12217.2	0.749299	0.374650	+	0.927166i	$0.377763\pi$
$644$	234.628	0.0143566
$645$	0	0
$646$	−4778.53	−0.291035
$647$	−11313.8	−0.687469	−0.343734	−	0.939067i	$-0.611692\pi$
$647$	−11313.8	−0.687469	−0.343734	+	0.939067i	$0.611692\pi$
$648$	−739.955	−0.0448583
$649$	17647.6	1.06738
$650$	18623.8	1.12382
$651$	−83.0117	−0.00499767
$652$	−9993.92	−0.600295
$653$	−6663.14	−0.399309	−0.199655	−	0.979866i	$-0.563982\pi$
$653$	−6663.14	−0.399309	−0.199655	+	0.979866i	$0.563982\pi$
$654$	3526.76	0.210867
$655$	2162.50	0.129001
$656$	1055.56	0.0628241
$657$	−8278.67	−0.491601
$658$	−152.449	−0.00903206
$659$	8919.91	0.527269	0.263634	−	0.964623i	$-0.415079\pi$
$659$	8919.91	0.527269	0.263634	+	0.964623i	$0.415079\pi$
$660$	399.963	0.0235887
$661$	20327.5	1.19614	0.598070	−	0.801444i	$-0.295934\pi$
$661$	20327.5	1.19614	0.598070	+	0.801444i	$0.295934\pi$
$662$	18528.7	1.08782
$663$	10115.9	0.592565
$664$	9501.84	0.555336
$665$	−27.3321	−0.00159383
$666$	1877.19	0.109219
$667$	2157.46	0.125243
$668$	5884.42	0.340831
$669$	11162.8	0.645112
$670$	−1985.67	−0.114497
$671$	21363.9	1.22913
$672$	276.692	0.0158834
$673$	28022.2	1.60502	0.802509	−	0.596640i	$-0.203498\pi$
$673$	28022.2	1.60502	0.802509	+	0.596640i	$0.203498\pi$
$674$	23452.1	1.34027
$675$	−17639.1	−1.00582
$676$	−11407.2	−0.649024
$677$	17930.8	1.01793	0.508963	−	0.860788i	$-0.330029\pi$
$677$	17930.8	1.01793	0.508963	+	0.860788i	$0.330029\pi$
$678$	11580.2	0.655952
$679$	−660.738	−0.0373443
$680$	−930.812	−0.0524927
$681$	19345.1	1.08855
$682$	−3396.94	−0.190726
$683$	18761.7	1.05110	0.525548	−	0.850764i	$-0.323860\pi$
$683$	18761.7	1.05110	0.525548	+	0.850764i	$0.323860\pi$
$684$	−3283.63	−0.183556
$685$	2788.63	0.155545
$686$	785.140	0.0436979
$687$	−11784.2	−0.654432
$688$	0	0
$689$	−26729.5	−1.47796
$690$	−700.956	−0.0386738
$691$	28630.0	1.57617	0.788087	−	0.615564i	$-0.211072\pi$
$691$	28630.0	1.57617	0.788087	+	0.615564i	$0.211072\pi$
$692$	4537.38	0.249256
$693$	−322.925	−0.0177012
$694$	9586.95	0.524374
$695$	−53.6973	−0.00293073
$696$	1512.32	0.0823624
$697$	2200.28	0.119572
$698$	12206.0	0.661899
$699$	−5691.84	−0.307990
$700$	256.072	0.0138266
$701$	−15943.9	−0.859046	−0.429523	−	0.903056i	$-0.641318\pi$
$701$	−15943.9	−0.859046	−0.429523	+	0.903056i	$0.641318\pi$
$702$	−21303.1	−1.14535
$703$	−3058.67	−0.164097
$704$	17188.5	0.920191
$705$	−396.656	−0.0211900
$706$	−20423.8	−1.08875
$707$	−982.825	−0.0522814
$708$	5997.48	0.318360
$709$	−1364.07	−0.0722552	−0.0361276	−	0.999347i	$-0.511502\pi$
$709$	−1364.07	−0.0722552	−0.0361276	+	0.999347i	$0.511502\pi$
$710$	916.636	0.0484517
$711$	−3190.07	−0.168266
$712$	20276.7	1.06728
$713$	−5184.84	−0.272333
$714$	−159.707	−0.00837100
$715$	2367.74	0.123844
$716$	−11826.1	−0.617267
$717$	13816.9	0.719665
$718$	15457.6	0.803446
$719$	36789.0	1.90820	0.954101	−	0.299484i	$-0.0968145\pi$
$719$	36789.0	1.90820	0.954101	+	0.299484i	$0.0968145\pi$
$720$	297.970	0.0154232
$721$	−1007.93	−0.0520629
$722$	8040.05	0.414432
$723$	−21789.2	−1.12081
$724$	9885.46	0.507445
$725$	2354.65	0.120620
$726$	−213.708	−0.0109248
$727$	−6053.05	−0.308797	−0.154398	−	0.988009i	$-0.549344\pi$
$727$	−6053.05	−0.308797	−0.154398	+	0.988009i	$0.549344\pi$
$728$	973.627	0.0495673
$729$	13110.9	0.666104
$730$	−958.322	−0.0485878
$731$	0	0
$732$	7260.44	0.366603
$733$	−970.290	−0.0488929	−0.0244464	−	0.999701i	$-0.507782\pi$
$733$	−970.290	−0.0488929	−0.0244464	+	0.999701i	$0.507782\pi$
$734$	−8356.66	−0.420232
$735$	1020.97	0.0512366
$736$	17282.0	0.865519
$737$	38226.0	1.91055
$738$	−1736.04	−0.0865915
$739$	1221.27	0.0607920	0.0303960	−	0.999538i	$-0.490323\pi$
$739$	1221.27	0.0607920	0.0303960	+	0.999538i	$0.490323\pi$
$740$	−189.250	−0.00940131
$741$	13005.1	0.644742
$742$	421.996	0.0208786
$743$	366.531	0.0180979	0.00904893	−	0.999959i	$-0.497120\pi$
$743$	366.531	0.0180979	0.00904893	+	0.999959i	$0.497120\pi$
$744$	−3634.41	−0.179091
$745$	−2692.14	−0.132392
$746$	11651.2	0.571824
$747$	−6340.35	−0.310550
$748$	5691.80	0.278226
$749$	−363.669	−0.0177412
$750$	−1535.10	−0.0747385
$751$	−37377.3	−1.81613	−0.908067	−	0.418825i	$-0.862442\pi$
$751$	−37377.3	−1.81613	−0.908067	+	0.418825i	$0.862442\pi$
$752$	−2708.00	−0.131317
$753$	8943.45	0.432825
$754$	2843.76	0.137352
$755$	164.244	0.00791716
$756$	−292.912	−0.0140914
$757$	−21396.5	−1.02730	−0.513651	−	0.857999i	$-0.671707\pi$
$757$	−21396.5	−1.02730	−0.513651	+	0.857999i	$0.671707\pi$
$758$	−4152.49	−0.198978
$759$	13494.1	0.645327
$760$	−1196.65	−0.0571148
$761$	−4078.78	−0.194291	−0.0971456	−	0.995270i	$-0.530971\pi$
$761$	−4078.78	−0.194291	−0.0971456	+	0.995270i	$0.530971\pi$
$762$	−8719.74	−0.414544
$763$	287.068	0.0136207
$764$	−2822.17	−0.133642
$765$	621.108	0.0293545
$766$	424.809	0.0200378
$767$	35504.5	1.67144
$768$	14107.6	0.662845
$769$	−6968.46	−0.326774	−0.163387	−	0.986562i	$-0.552242\pi$
$769$	−6968.46	−0.326774	−0.163387	+	0.986562i	$0.552242\pi$
$770$	−37.3811	−0.00174951
$771$	−5167.10	−0.241360
$772$	−7983.85	−0.372208
$773$	25350.9	1.17957	0.589785	−	0.807561i	$-0.299213\pi$
$773$	25350.9	1.17957	0.589785	+	0.807561i	$0.299213\pi$
$774$	0	0
$775$	−5658.73	−0.262281
$776$	−28928.4	−1.33823
$777$	−102.226	−0.00471989
$778$	7446.48	0.343148
$779$	2828.68	0.130100
$780$	804.668	0.0369381
$781$	−17646.1	−0.808485
$782$	−9975.17	−0.456153
$783$	−2693.40	−0.122930
$784$	6970.21	0.317520
$785$	−907.096	−0.0412429
$786$	16244.7	0.737189
$787$	−28392.5	−1.28600	−0.643000	−	0.765866i	$-0.722311\pi$
$787$	−28392.5	−1.28600	−0.643000	+	0.765866i	$0.722311\pi$
$788$	8014.06	0.362296
$789$	17877.2	0.806649
$790$	−369.276	−0.0166307
$791$	942.597	0.0423703
$792$	−14138.3	−0.634320
$793$	42981.1	1.92472
$794$	26726.1	1.19455
$795$	1097.98	0.0489830
$796$	−13598.5	−0.605511
$797$	−29905.5	−1.32912	−0.664559	−	0.747236i	$-0.731381\pi$
$797$	−29905.5	−1.32912	−0.664559	+	0.747236i	$0.731381\pi$
$798$	−205.320	−0.00910808
$799$	−5644.74	−0.249933
$800$	18861.5	0.833569
$801$	−13530.1	−0.596833
$802$	−8495.28	−0.374038
$803$	18448.6	0.810756
$804$	12991.0	0.569846
$805$	−57.0558	−0.00249808
$806$	−6834.14	−0.298663
$807$	−5755.05	−0.251038
$808$	−43030.0	−1.87350
$809$	−28881.4	−1.25515	−0.627575	−	0.778556i	$-0.715952\pi$
$809$	−28881.4	−1.25515	−0.627575	+	0.778556i	$0.715952\pi$
$810$	57.1559	0.00247933
$811$	18301.8	0.792431	0.396216	−	0.918157i	$-0.370323\pi$
$811$	18301.8	0.792431	0.396216	+	0.918157i	$0.370323\pi$
$812$	39.1010	0.00168987
$813$	−15612.9	−0.673514
$814$	−4183.23	−0.180125
$815$	2430.28	0.104453
$816$	−2836.92	−0.121706
$817$	0	0
$818$	−6327.80	−0.270472
$819$	−649.678	−0.0277187
$820$	175.020	0.00745361
$821$	−12725.8	−0.540966	−0.270483	−	0.962725i	$-0.587183\pi$
$821$	−12725.8	−0.540966	−0.270483	+	0.962725i	$0.587183\pi$
$822$	20948.3	0.888876
$823$	33139.0	1.40359	0.701795	−	0.712379i	$-0.252382\pi$
$823$	33139.0	1.40359	0.701795	+	0.712379i	$0.252382\pi$
$824$	−44129.2	−1.86567
$825$	14727.4	0.621506
$826$	−560.533	−0.0236119
$827$	−25709.7	−1.08103	−0.540516	−	0.841334i	$-0.681771\pi$
$827$	−25709.7	−1.08103	−0.540516	+	0.841334i	$0.681771\pi$
$828$	−6854.56	−0.287696
$829$	19624.3	0.822173	0.411086	−	0.911596i	$-0.365149\pi$
$829$	19624.3	0.822173	0.411086	+	0.911596i	$0.365149\pi$
$830$	−733.945	−0.0306935
$831$	19727.6	0.823516
$832$	34580.7	1.44095
$833$	14529.2	0.604329
$834$	−403.376	−0.0167479
$835$	−1430.95	−0.0593055
$836$	7317.39	0.302724
$837$	6472.81	0.267304
$838$	8779.56	0.361915
$839$	−42930.4	−1.76653	−0.883266	−	0.468872i	$-0.844661\pi$
$839$	−42930.4	−1.76653	−0.883266	+	0.468872i	$0.844661\pi$
$840$	−39.9944	−0.00164278
$841$	−24029.5	−0.985258
$842$	−32651.2	−1.33638
$843$	−8338.74	−0.340690
$844$	21258.9	0.867017
$845$	2773.96	0.112932
$846$	4453.75	0.180997
$847$	−17.3952	−0.000705674 0
$848$	7496.02	0.303555
$849$	−21740.2	−0.878824
$850$	−10886.9	−0.439315
$851$	−6384.97	−0.257196
$852$	−5996.96	−0.241141
$853$	29843.9	1.19793	0.598965	−	0.800775i	$-0.295579\pi$
$853$	29843.9	1.19793	0.598965	+	0.800775i	$0.295579\pi$
$854$	−678.571	−0.0271899
$855$	798.499	0.0319393
$856$	−15922.1	−0.635756
$857$	−1444.80	−0.0575887	−0.0287943	−	0.999585i	$-0.509167\pi$
$857$	−1444.80	−0.0575887	−0.0287943	+	0.999585i	$0.509167\pi$
$858$	17786.6	0.707719
$859$	43783.6	1.73909	0.869545	−	0.493854i	$-0.164412\pi$
$859$	43783.6	1.73909	0.869545	+	0.493854i	$0.164412\pi$
$860$	0	0
$861$	94.5397	0.00374205
$862$	−20544.4	−0.811767
$863$	−16285.3	−0.642362	−0.321181	−	0.947018i	$-0.604080\pi$
$863$	−16285.3	−0.642362	−0.321181	+	0.947018i	$0.604080\pi$
$864$	−21575.0	−0.849533
$865$	−1103.38	−0.0433712
$866$	12194.6	0.478510
$867$	10249.4	0.401487
$868$	−93.9678	−0.00367451
$869$	7108.91	0.277506
$870$	−116.815	−0.00455219
$871$	76905.3	2.99177
$872$	12568.4	0.488096
$873$	19303.2	0.748356
$874$	−12824.1	−0.496318
$875$	−124.953	−0.00482762
$876$	6269.69	0.241819
$877$	22308.4	0.858951	0.429476	−	0.903078i	$-0.358698\pi$
$877$	22308.4	0.858951	0.429476	+	0.903078i	$0.358698\pi$
$878$	−10780.7	−0.414385
$879$	−22823.8	−0.875799
$880$	−664.011	−0.0254361
$881$	−2607.01	−0.0996962	−0.0498481	−	0.998757i	$-0.515874\pi$
$881$	−2607.01	−0.0996962	−0.0498481	+	0.998757i	$0.515874\pi$
$882$	−11463.7	−0.437643
$883$	15569.0	0.593363	0.296682	−	0.954976i	$-0.404120\pi$
$883$	15569.0	0.593363	0.296682	+	0.954976i	$0.404120\pi$
$884$	11451.1	0.435680
$885$	−1458.44	−0.0553955
$886$	178.772	0.00677876
$887$	−10165.1	−0.384793	−0.192396	−	0.981317i	$-0.561626\pi$
$887$	−10165.1	−0.384793	−0.192396	+	0.981317i	$0.561626\pi$
$888$	−4475.67	−0.169137
$889$	−709.762	−0.0267769
$890$	−1566.22	−0.0589885
$891$	−1100.31	−0.0413711
$892$	12636.1	0.474315
$893$	−7256.89	−0.271940
$894$	−20223.4	−0.756569
$895$	2875.83	0.107406
$896$	126.896	0.00473137
$897$	27148.1	1.01053
$898$	9524.94	0.353955
$899$	−864.059	−0.0320556
$900$	−7481.06	−0.277076
$901$	15625.2	0.577748
$902$	3868.68	0.142808
$903$	0	0
$904$	41268.7	1.51834
$905$	−2403.90	−0.0882967
$906$	1233.81	0.0452434
$907$	2372.67	0.0868613	0.0434307	−	0.999056i	$-0.486171\pi$
$907$	2372.67	0.0868613	0.0434307	+	0.999056i	$0.486171\pi$
$908$	21898.3	0.800352
$909$	28712.9	1.04768
$910$	−75.2054	−0.00273960
$911$	37280.3	1.35582	0.677909	−	0.735146i	$-0.262886\pi$
$911$	37280.3	1.35582	0.677909	+	0.735146i	$0.262886\pi$
$912$	−3647.15	−0.132423
$913$	14129.1	0.512165
$914$	−3062.50	−0.110830
$915$	−1765.56	−0.0637899
$916$	−13339.5	−0.481168
$917$	1322.28	0.0476176
$918$	12453.1	0.447728
$919$	−23845.4	−0.855915	−0.427957	−	0.903799i	$-0.640767\pi$
$919$	−23845.4	−0.855915	−0.427957	+	0.903799i	$0.640767\pi$
$920$	−2498.01	−0.0895186
$921$	5545.88	0.198418
$922$	21939.7	0.783671
$923$	−35501.4	−1.26603
$924$	244.561	0.00870720
$925$	−6968.55	−0.247702
$926$	18963.2	0.672967
$927$	29446.4	1.04331
$928$	2880.06	0.101878
$929$	−51353.9	−1.81364	−0.906818	−	0.421523i	$-0.861496\pi$
$929$	−51353.9	−1.81364	−0.906818	+	0.421523i	$0.861496\pi$
$930$	280.731	0.00989842
$931$	18678.7	0.657541
$932$	−6443.06	−0.226448
$933$	−16502.6	−0.579070
$934$	6360.27	0.222821
$935$	−1384.11	−0.0484120
$936$	−28444.2	−0.993298
$937$	3092.80	0.107831	0.0539154	−	0.998546i	$-0.482830\pi$
$937$	3092.80	0.107831	0.0539154	+	0.998546i	$0.482830\pi$
$938$	−1214.15	−0.0422639
$939$	19724.3	0.685492
$940$	−449.008	−0.0155798
$941$	−37935.7	−1.31421	−0.657103	−	0.753801i	$-0.728218\pi$
$941$	−37935.7	−1.31421	−0.657103	+	0.753801i	$0.728218\pi$
$942$	−6814.14	−0.235686
$943$	5904.87	0.203912
$944$	−9956.90	−0.343294
$945$	71.2291	0.00245194
$946$	0	0
$947$	−54489.0	−1.86975	−0.934876	−	0.354974i	$-0.884490\pi$
$947$	−54489.0	−1.86975	−0.934876	+	0.354974i	$0.884490\pi$
$948$	2415.93	0.0827699
$949$	37115.9	1.26958
$950$	−13996.2	−0.477997
$951$	25790.3	0.879398
$952$	−569.152	−0.0193764
$953$	9955.68	0.338401	0.169200	−	0.985582i	$-0.445881\pi$
$953$	9955.68	0.338401	0.169200	+	0.985582i	$0.445881\pi$
$954$	−12328.4	−0.418394
$955$	686.283	0.0232540
$956$	15640.4	0.529130
$957$	2248.80	0.0759596
$958$	17716.6	0.597493
$959$	1705.13	0.0574156
$960$	−1420.49	−0.0477565
$961$	−27714.5	−0.930297
$962$	−8416.04	−0.282063
$963$	10624.5	0.355523
$964$	−24665.0	−0.824071
$965$	1941.48	0.0647652
$966$	−428.605	−0.0142755
$967$	−33247.1	−1.10564	−0.552820	−	0.833301i	$-0.686448\pi$
$967$	−33247.1	−1.10564	−0.552820	+	0.833301i	$0.686448\pi$
$968$	−761.595	−0.0252878
$969$	−7602.37	−0.252037
$970$	2234.50	0.0739644
$971$	−41308.7	−1.36525	−0.682626	−	0.730768i	$-0.739162\pi$
$971$	−41308.7	−1.36525	−0.682626	+	0.730768i	$0.739162\pi$
$972$	13908.5	0.458966
$973$	−32.8336	−0.00108181
$974$	16271.3	0.535285
$975$	29629.4	0.973231
$976$	−12053.6	−0.395315
$977$	45094.5	1.47666	0.738332	−	0.674437i	$-0.235614\pi$
$977$	45094.5	1.47666	0.738332	+	0.674437i	$0.235614\pi$
$978$	18256.4	0.596906
$979$	30151.2	0.984307
$980$	1155.71	0.0376714
$981$	−8386.59	−0.272949
$982$	33675.3	1.09432
$983$	−50236.2	−1.62999	−0.814997	−	0.579465i	$-0.803262\pi$
$983$	−50236.2	−1.62999	−0.814997	+	0.579465i	$0.803262\pi$
$984$	4139.13	0.134096
$985$	−1948.82	−0.0630403
$986$	−1662.37	−0.0536924
$987$	−242.538	−0.00782177
$988$	14721.5	0.474043
$989$	0	0
$990$	1092.08	0.0350590
$991$	−27459.8	−0.880210	−0.440105	−	0.897946i	$-0.645059\pi$
$991$	−27459.8	−0.880210	−0.440105	+	0.897946i	$0.645059\pi$
$992$	−6921.38	−0.221526
$993$	29478.1	0.942052
$994$	560.484	0.0178848
$995$	3306.83	0.105360
$996$	4801.73	0.152760
$997$	−47249.9	−1.50092	−0.750461	−	0.660915i	$-0.770168\pi$
$997$	−47249.9	−1.50092	−0.750461	+	0.660915i	$0.770168\pi$
$998$	34161.3	1.08352
$999$	7971.07	0.252446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.19	✓	50
43.42	odd	2		1849.4.a.j.1.32	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.19	✓	50	1.1	even	1	trivial
1849.4.a.j.1.32	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)

\(f(q)\)	\(=\)	\(q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} +O(q^{10})\)	\(q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} -1.87262 q^{10} +36.0498 q^{11} +12.2514 q^{12} +72.5269 q^{13} -1.14503 q^{14} -2.97924 q^{15} -20.3395 q^{16} -42.3970 q^{17} +33.4516 q^{18} -54.5057 q^{19} -3.37245 q^{20} -1.82168 q^{21} -74.5453 q^{22} -113.780 q^{23} -79.7566 q^{24} -124.180 q^{25} -149.974 q^{26} +142.045 q^{27} -2.06211 q^{28} -18.9616 q^{29} +6.16060 q^{30} +45.5688 q^{31} -151.889 q^{32} -118.597 q^{33} +87.6703 q^{34} +0.501455 q^{35} +60.2437 q^{36} +56.1166 q^{37} +112.709 q^{38} -238.601 q^{39} +21.9547 q^{40} -51.8970 q^{41} +3.76695 q^{42} -134.250 q^{44} -14.6498 q^{45} +235.280 q^{46} +133.140 q^{47} +66.9133 q^{48} -342.693 q^{49} +256.785 q^{50} +139.479 q^{51} -270.092 q^{52} -368.545 q^{53} -293.727 q^{54} +32.6464 q^{55} +13.4244 q^{56} +179.314 q^{57} +39.2097 q^{58} +489.535 q^{59} +11.0947 q^{60} +592.623 q^{61} -94.2291 q^{62} -8.95775 q^{63} +476.798 q^{64} +65.6798 q^{65} +245.241 q^{66} +1060.37 q^{67} +157.887 q^{68} +374.318 q^{69} -1.03693 q^{70} -489.493 q^{71} -392.188 q^{72} +511.754 q^{73} -116.040 q^{74} +408.530 q^{75} +202.980 q^{76} +19.9619 q^{77} +493.389 q^{78} +197.197 q^{79} -18.4193 q^{80} -30.5219 q^{81} +107.315 q^{82} +391.934 q^{83} +6.78397 q^{84} -38.3944 q^{85} +62.3804 q^{87} +873.971 q^{88} +836.377 q^{89} +30.2935 q^{90} +40.1604 q^{91} +423.721 q^{92} -149.913 q^{93} -275.313 q^{94} -49.3599 q^{95} +499.687 q^{96} -1193.25 q^{97} +708.636 q^{98} -583.179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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