LMFDB - Embedded newform 1849.4.a.i.1.15

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			1.15
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)

$f(q)$	$=$	$q-3.06679 q^{2} -2.01332 q^{3} +1.40518 q^{4} -11.9365 q^{5} +6.17442 q^{6} -10.6583 q^{7} +20.2249 q^{8} -22.9465 q^{9} +O(q^{10})$	\(q-3.06679 q^{2} -2.01332 q^{3} +1.40518 q^{4} -11.9365 q^{5} +6.17442 q^{6} -10.6583 q^{7} +20.2249 q^{8} -22.9465 q^{9} +36.6067 q^{10} +65.4818 q^{11} -2.82908 q^{12} -61.8987 q^{13} +32.6868 q^{14} +24.0320 q^{15} -73.2669 q^{16} -22.8412 q^{17} +70.3722 q^{18} +36.6127 q^{19} -16.7730 q^{20} +21.4586 q^{21} -200.819 q^{22} -143.179 q^{23} -40.7192 q^{24} +17.4799 q^{25} +189.830 q^{26} +100.558 q^{27} -14.9769 q^{28} +213.016 q^{29} -73.7010 q^{30} -307.040 q^{31} +62.8949 q^{32} -131.836 q^{33} +70.0492 q^{34} +127.223 q^{35} -32.2441 q^{36} -83.7905 q^{37} -112.284 q^{38} +124.622 q^{39} -241.414 q^{40} +59.1767 q^{41} -65.8090 q^{42} +92.0140 q^{44} +273.901 q^{45} +439.100 q^{46} +201.957 q^{47} +147.510 q^{48} -229.400 q^{49} -53.6072 q^{50} +45.9867 q^{51} -86.9790 q^{52} +406.354 q^{53} -308.391 q^{54} -781.624 q^{55} -215.563 q^{56} -73.7131 q^{57} -653.274 q^{58} +164.777 q^{59} +33.7694 q^{60} -150.450 q^{61} +941.626 q^{62} +244.572 q^{63} +393.250 q^{64} +738.853 q^{65} +404.312 q^{66} +169.033 q^{67} -32.0962 q^{68} +288.265 q^{69} -390.166 q^{70} +1039.96 q^{71} -464.092 q^{72} +374.665 q^{73} +256.968 q^{74} -35.1926 q^{75} +51.4477 q^{76} -697.926 q^{77} -382.188 q^{78} +465.164 q^{79} +874.550 q^{80} +417.101 q^{81} -181.482 q^{82} +1307.62 q^{83} +30.1533 q^{84} +272.644 q^{85} -428.869 q^{87} +1324.36 q^{88} -66.7489 q^{89} -839.997 q^{90} +659.736 q^{91} -201.193 q^{92} +618.169 q^{93} -619.359 q^{94} -437.028 q^{95} -126.628 q^{96} -953.889 q^{97} +703.522 q^{98} -1502.58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.06679	−1.08427	−0.542137	−	0.840290i	$-0.682384\pi$
$2$	−3.06679	−1.08427	−0.542137	+	0.840290i	$0.682384\pi$
$3$	−2.01332	−0.387463	−0.193732	−	0.981055i	$-0.562059\pi$
$3$	−2.01332	−0.387463	−0.193732	+	0.981055i	$0.562059\pi$
$4$	1.40518	0.175648
$5$	−11.9365	−1.06763	−0.533816	−	0.845600i	$-0.679243\pi$
$5$	−11.9365	−1.06763	−0.533816	+	0.845600i	$0.679243\pi$
$6$	6.17442	0.420116
$7$	−10.6583	−0.575495	−0.287748	−	0.957706i	$-0.592906\pi$
$7$	−10.6583	−0.575495	−0.287748	+	0.957706i	$0.592906\pi$
$8$	20.2249	0.893823
$9$	−22.9465	−0.849872
$10$	36.6067	1.15761
$11$	65.4818	1.79487	0.897433	−	0.441152i	$-0.145430\pi$
$11$	65.4818	1.79487	0.897433	+	0.441152i	$0.145430\pi$
$12$	−2.82908	−0.0680572
$13$	−61.8987	−1.32058	−0.660292	−	0.751009i	$-0.729568\pi$
$13$	−61.8987	−1.32058	−0.660292	+	0.751009i	$0.729568\pi$
$14$	32.6868	0.623994
$15$	24.0320	0.413669
$16$	−73.2669	−1.14480
$17$	−22.8412	−0.325871	−0.162936	−	0.986637i	$-0.552096\pi$
$17$	−22.8412	−0.325871	−0.162936	+	0.986637i	$0.552096\pi$
$18$	70.3722	0.921493
$19$	36.6127	0.442081	0.221041	−	0.975265i	$-0.429055\pi$
$19$	36.6127	0.442081	0.221041	+	0.975265i	$0.429055\pi$
$20$	−16.7730	−0.187528
$21$	21.4586	0.222983
$22$	−200.819	−1.94612
$23$	−143.179	−1.29804	−0.649020	−	0.760772i	$-0.724821\pi$
$23$	−143.179	−1.29804	−0.649020	+	0.760772i	$0.724821\pi$
$24$	−40.7192	−0.346324
$25$	17.4799	0.139839
$26$	189.830	1.43187
$27$	100.558	0.716758
$28$	−14.9769	−0.101085
$29$	213.016	1.36400	0.682001	−	0.731351i	$-0.261110\pi$
$29$	213.016	1.36400	0.682001	+	0.731351i	$0.261110\pi$
$30$	−73.7010	−0.448530
$31$	−307.040	−1.77890	−0.889452	−	0.457029i	$-0.848913\pi$
$31$	−307.040	−1.77890	−0.889452	+	0.457029i	$0.848913\pi$
$32$	62.8949	0.347449
$33$	−131.836	−0.695445
$34$	70.0492	0.353334
$35$	127.223	0.614417
$36$	−32.2441	−0.149278
$37$	−83.7905	−0.372299	−0.186150	−	0.982521i	$-0.559601\pi$
$37$	−83.7905	−0.372299	−0.186150	+	0.982521i	$0.559601\pi$
$38$	−112.284	−0.479337
$39$	124.622	0.511678
$40$	−241.414	−0.954274
$41$	59.1767	0.225411	0.112705	−	0.993628i	$-0.464048\pi$
$41$	59.1767	0.225411	0.112705	+	0.993628i	$0.464048\pi$
$42$	−65.8090	−0.241775
$43$	0	0
$43$	0	0
$44$	92.0140	0.315265
$45$	273.901	0.907351
$46$	439.100	1.40743
$47$	201.957	0.626775	0.313388	−	0.949625i	$-0.398536\pi$
$47$	201.957	0.626775	0.313388	+	0.949625i	$0.398536\pi$
$48$	147.510	0.443567
$49$	−229.400	−0.668805
$50$	−53.6072	−0.151624
$51$	45.9867	0.126263
$52$	−86.9790	−0.231958
$53$	406.354	1.05315	0.526576	−	0.850128i	$-0.323476\pi$
$53$	406.354	1.05315	0.526576	+	0.850128i	$0.323476\pi$
$54$	−308.391	−0.777161
$55$	−781.624	−1.91626
$56$	−215.563	−0.514391
$57$	−73.7131	−0.171290
$58$	−653.274	−1.47895
$59$	164.777	0.363595	0.181798	−	0.983336i	$-0.441808\pi$
$59$	164.777	0.363595	0.181798	+	0.983336i	$0.441808\pi$
$60$	33.7694	0.0726601
$61$	−150.450	−0.315790	−0.157895	−	0.987456i	$-0.550471\pi$
$61$	−150.450	−0.315790	−0.157895	+	0.987456i	$0.550471\pi$
$62$	941.626	1.92882
$63$	244.572	0.489097
$64$	393.250	0.768067
$65$	738.853	1.40990
$66$	404.312	0.754052
$67$	169.033	0.308220	0.154110	−	0.988054i	$-0.450749\pi$
$67$	169.033	0.308220	0.154110	+	0.988054i	$0.450749\pi$
$68$	−32.0962	−0.0572387
$69$	288.265	0.502943
$70$	−390.166	−0.666196
$71$	1039.96	1.73832	0.869162	−	0.494528i	$-0.164659\pi$
$71$	1039.96	1.73832	0.869162	+	0.494528i	$0.164659\pi$
$72$	−464.092	−0.759635
$73$	374.665	0.600701	0.300351	−	0.953829i	$-0.402896\pi$
$73$	374.665	0.600701	0.300351	+	0.953829i	$0.402896\pi$
$74$	256.968	0.403674
$75$	−35.1926	−0.0541826
$76$	51.4477	0.0776507
$77$	−697.926	−1.03294
$78$	−382.188	−0.554799
$79$	465.164	0.662468	0.331234	−	0.943549i	$-0.392535\pi$
$79$	465.164	0.662468	0.331234	+	0.943549i	$0.392535\pi$
$80$	874.550	1.22222
$81$	417.101	0.572155
$82$	−181.482	−0.244407
$83$	1307.62	1.72928	0.864641	−	0.502391i	$-0.167546\pi$
$83$	1307.62	1.72928	0.864641	+	0.502391i	$0.167546\pi$
$84$	30.1533	0.0391666
$85$	272.644	0.347911
$86$	0	0
$87$	−428.869	−0.528501
$88$	1324.36	1.60429
$89$	−66.7489	−0.0794986	−0.0397493	−	0.999210i	$-0.512656\pi$
$89$	−66.7489	−0.0794986	−0.0397493	+	0.999210i	$0.512656\pi$
$90$	−839.997	−0.983816
$91$	659.736	0.759990
$92$	−201.193	−0.227998
$93$	618.169	0.689260
$94$	−619.359	−0.679596
$95$	−437.028	−0.471980
$96$	−126.628	−0.134624
$97$	−953.889	−0.998482	−0.499241	−	0.866463i	$-0.666388\pi$
$97$	−953.889	−0.998482	−0.499241	+	0.866463i	$0.666388\pi$
$98$	703.522	0.725167
$99$	−1502.58	−1.52541
$100$	24.5625	0.0245625
$101$	−1507.22	−1.48489	−0.742446	−	0.669905i	$-0.766335\pi$
$101$	−1507.22	−1.48489	−0.742446	+	0.669905i	$0.766335\pi$
$102$	−141.031	−0.136904
$103$	1071.84	1.02536	0.512679	−	0.858581i	$-0.328653\pi$
$103$	1071.84	1.02536	0.512679	+	0.858581i	$0.328653\pi$
$104$	−1251.89	−1.18037
$105$	−256.141	−0.238064
$106$	−1246.20	−1.14190
$107$	924.397	0.835186	0.417593	−	0.908634i	$-0.362874\pi$
$107$	924.397	0.835186	0.417593	+	0.908634i	$0.362874\pi$
$108$	141.303	0.125897
$109$	−1584.45	−1.39232	−0.696161	−	0.717886i	$-0.745110\pi$
$109$	−1584.45	−1.39232	−0.696161	+	0.717886i	$0.745110\pi$
$110$	2397.07	2.07775
$111$	168.697	0.144252
$112$	780.902	0.658825
$113$	1539.52	1.28164	0.640822	−	0.767690i	$-0.278594\pi$
$113$	1539.52	1.28164	0.640822	+	0.767690i	$0.278594\pi$
$114$	226.063	0.185725
$115$	1709.06	1.38583
$116$	299.326	0.239584
$117$	1420.36	1.12233
$118$	−505.335	−0.394236
$119$	243.449	0.187537
$120$	486.044	0.369746
$121$	2956.87	2.22154
$122$	461.399	0.342403
$123$	−119.142	−0.0873385
$124$	−431.448	−0.312461
$125$	1283.41	0.918336
$126$	−750.049	−0.530315
$127$	−626.337	−0.437625	−0.218813	−	0.975767i	$-0.570218\pi$
$127$	−626.337	−0.437625	−0.218813	+	0.975767i	$0.570218\pi$
$128$	−1709.17	−1.18024
$129$	0	0
$130$	−2265.91	−1.52872
$131$	−1299.79	−0.866894	−0.433447	−	0.901179i	$-0.642703\pi$
$131$	−1299.79	−0.866894	−0.433447	+	0.901179i	$0.642703\pi$
$132$	−185.254	−0.122153
$133$	−390.230	−0.254416
$134$	−518.389	−0.334194
$135$	−1200.31	−0.765234
$136$	−461.962	−0.291271
$137$	1833.35	1.14331	0.571656	−	0.820493i	$-0.306301\pi$
$137$	1833.35	1.14331	0.571656	+	0.820493i	$0.306301\pi$
$138$	−884.048	−0.545327
$139$	354.867	0.216543	0.108271	−	0.994121i	$-0.465468\pi$
$139$	354.867	0.216543	0.108271	+	0.994121i	$0.465468\pi$
$140$	178.772	0.107921
$141$	−406.604	−0.242853
$142$	−3189.35	−1.88482
$143$	−4053.24	−2.37027
$144$	1681.22	0.972930
$145$	−2542.66	−1.45625
$146$	−1149.02	−0.651324
$147$	461.856	0.259138
$148$	−117.741	−0.0653937
$149$	−3282.46	−1.80476	−0.902382	−	0.430938i	$-0.858183\pi$
$149$	−3282.46	−1.80476	−0.902382	+	0.430938i	$0.858183\pi$
$150$	107.928	0.0587488
$151$	124.151	0.0669093	0.0334546	−	0.999440i	$-0.489349\pi$
$151$	124.151	0.0669093	0.0334546	+	0.999440i	$0.489349\pi$
$152$	740.489	0.395142
$153$	524.128	0.276949
$154$	2140.39	1.11999
$155$	3664.98	1.89921
$156$	175.117	0.0898753
$157$	1119.99	0.569332	0.284666	−	0.958627i	$-0.408117\pi$
$157$	1119.99	0.569332	0.284666	+	0.958627i	$0.408117\pi$
$158$	−1426.56	−0.718297
$159$	−818.121	−0.408058
$160$	−750.745	−0.370947
$161$	1526.05	0.747015
$162$	−1279.16	−0.620372
$163$	2820.81	1.35548	0.677739	−	0.735303i	$-0.262960\pi$
$163$	2820.81	1.35548	0.677739	+	0.735303i	$0.262960\pi$
$164$	83.1542	0.0395930
$165$	1573.66	0.742479
$166$	−4010.20	−1.87501
$167$	1945.07	0.901281	0.450640	−	0.892706i	$-0.351196\pi$
$167$	1945.07	0.901281	0.450640	+	0.892706i	$0.351196\pi$
$168$	433.998	0.199308
$169$	1634.44	0.743944
$170$	−836.142	−0.377231
$171$	−840.136	−0.375712
$172$	0	0
$173$	−1105.62	−0.485889	−0.242945	−	0.970040i	$-0.578113\pi$
$173$	−1105.62	−0.485889	−0.242945	+	0.970040i	$0.578113\pi$
$174$	1315.25	0.573039
$175$	−186.307	−0.0804769
$176$	−4797.65	−2.05475
$177$	−331.748	−0.140880
$178$	204.705	0.0861982
$179$	−1154.35	−0.482014	−0.241007	−	0.970523i	$-0.577478\pi$
$179$	−1154.35	−0.482014	−0.241007	+	0.970523i	$0.577478\pi$
$180$	384.882	0.159374
$181$	−3547.67	−1.45688	−0.728442	−	0.685108i	$-0.759755\pi$
$181$	−3547.67	−1.45688	−0.728442	+	0.685108i	$0.759755\pi$
$182$	−2023.27	−0.824037
$183$	302.905	0.122357
$184$	−2895.78	−1.16022
$185$	1000.17	0.397479
$186$	−1895.79	−0.747346
$187$	−1495.69	−0.584895
$188$	283.787	0.110092
$189$	−1071.78	−0.412491
$190$	1340.27	0.511755
$191$	2388.85	0.904979	0.452490	−	0.891770i	$-0.350536\pi$
$191$	2388.85	0.904979	0.452490	+	0.891770i	$0.350536\pi$
$192$	−791.738	−0.297598
$193$	775.397	0.289193	0.144597	−	0.989491i	$-0.453812\pi$
$193$	775.397	0.289193	0.144597	+	0.989491i	$0.453812\pi$
$194$	2925.37	1.08263
$195$	−1487.55	−0.546284
$196$	−322.350	−0.117474
$197$	3582.80	1.29576	0.647878	−	0.761744i	$-0.275657\pi$
$197$	3582.80	1.29576	0.647878	+	0.761744i	$0.275657\pi$
$198$	4608.10	1.65396
$199$	−3110.52	−1.10804	−0.554018	−	0.832505i	$-0.686906\pi$
$199$	−3110.52	−1.10804	−0.554018	+	0.832505i	$0.686906\pi$
$200$	353.529	0.124992
$201$	−340.318	−0.119424
$202$	4622.33	1.61003
$203$	−2270.39	−0.784976
$204$	64.6198	0.0221779
$205$	−706.363	−0.240656
$206$	−3287.11	−1.11177
$207$	3285.46	1.10317
$208$	4535.13	1.51180
$209$	2397.47	0.793476
$210$	785.528	0.258127
$211$	1101.39	0.359350	0.179675	−	0.983726i	$-0.442495\pi$
$211$	1101.39	0.359350	0.179675	+	0.983726i	$0.442495\pi$
$212$	571.003	0.184984
$213$	−2093.78	−0.673537
$214$	−2834.93	−0.905569
$215$	0	0
$216$	2033.78	0.640654
$217$	3272.53	1.02375
$218$	4859.18	1.50966
$219$	−754.320	−0.232750
$220$	−1098.33	−0.336587
$221$	1413.84	0.430341
$222$	−517.358	−0.156409
$223$	2413.48	0.724748	0.362374	−	0.932033i	$-0.381966\pi$
$223$	2413.48	0.724748	0.362374	+	0.932033i	$0.381966\pi$
$224$	−670.354	−0.199955
$225$	−401.104	−0.118846
$226$	−4721.38	−1.38965
$227$	2233.25	0.652979	0.326489	−	0.945201i	$-0.394134\pi$
$227$	2233.25	0.652979	0.326489	+	0.945201i	$0.394134\pi$
$228$	−103.581	−0.0300868
$229$	−1359.76	−0.392381	−0.196190	−	0.980566i	$-0.562857\pi$
$229$	−1359.76	−0.392381	−0.196190	+	0.980566i	$0.562857\pi$
$230$	−5241.31	−1.50262
$231$	1405.15	0.400225
$232$	4308.22	1.21918
$233$	−6996.98	−1.96733	−0.983665	−	0.180012i	$-0.942386\pi$
$233$	−6996.98	−1.96733	−0.983665	+	0.180012i	$0.942386\pi$
$234$	−4355.94	−1.21691
$235$	−2410.66	−0.669166
$236$	231.542	0.0638648
$237$	−936.523	−0.256682
$238$	−746.607	−0.203342
$239$	4353.01	1.17813	0.589064	−	0.808086i	$-0.299496\pi$
$239$	4353.01	1.17813	0.589064	+	0.808086i	$0.299496\pi$
$240$	−1760.75	−0.473566
$241$	−3059.19	−0.817676	−0.408838	−	0.912607i	$-0.634066\pi$
$241$	−3059.19	−0.817676	−0.408838	+	0.912607i	$0.634066\pi$
$242$	−9068.09	−2.40876
$243$	−3554.83	−0.938447
$244$	−211.411	−0.0554679
$245$	2738.23	0.714038
$246$	365.382	0.0946988
$247$	−2266.28	−0.583805
$248$	−6209.85	−1.59002
$249$	−2632.66	−0.670033
$250$	−3935.95	−0.995727
$251$	6105.23	1.53529	0.767647	−	0.640873i	$-0.221427\pi$
$251$	6105.23	1.53529	0.767647	+	0.640873i	$0.221427\pi$
$252$	343.668	0.0859090
$253$	−9375.63	−2.32980
$254$	1920.84	0.474505
$255$	−548.920	−0.134803
$256$	2095.67	0.511639
$257$	1695.01	0.411409	0.205704	−	0.978614i	$-0.434051\pi$
$257$	1695.01	0.411409	0.205704	+	0.978614i	$0.434051\pi$
$258$	0	0
$259$	893.066	0.214257
$260$	1038.22	0.247646
$261$	−4887.98	−1.15923
$262$	3986.18	0.939950
$263$	1328.61	0.311505	0.155752	−	0.987796i	$-0.450220\pi$
$263$	1328.61	0.311505	0.155752	+	0.987796i	$0.450220\pi$
$264$	−2666.37	−0.621604
$265$	−4850.45	−1.12438
$266$	1196.75	0.275856
$267$	134.387	0.0308028
$268$	237.523	0.0541382
$269$	−4979.49	−1.12864	−0.564321	−	0.825555i	$-0.690862\pi$
$269$	−4979.49	−1.12864	−0.564321	+	0.825555i	$0.690862\pi$
$270$	3681.11	0.829723
$271$	−2747.64	−0.615894	−0.307947	−	0.951404i	$-0.599642\pi$
$271$	−2747.64	−0.615894	−0.307947	+	0.951404i	$0.599642\pi$
$272$	1673.51	0.373056
$273$	−1328.26	−0.294468
$274$	−5622.50	−1.23966
$275$	1144.62	0.250993
$276$	405.066	0.0883409
$277$	5590.40	1.21262	0.606308	−	0.795230i	$-0.292650\pi$
$277$	5590.40	1.21262	0.606308	+	0.795230i	$0.292650\pi$
$278$	−1088.30	−0.234792
$279$	7045.51	1.51184
$280$	2573.07	0.549180
$281$	3044.07	0.646243	0.323121	−	0.946358i	$-0.395268\pi$
$281$	3044.07	0.646243	0.323121	+	0.946358i	$0.395268\pi$
$282$	1246.97	0.263318
$283$	−3571.65	−0.750221	−0.375111	−	0.926980i	$-0.622395\pi$
$283$	−3571.65	−0.750221	−0.375111	+	0.926980i	$0.622395\pi$
$284$	1461.34	0.305333
$285$	879.877	0.182875
$286$	12430.4	2.57002
$287$	−630.724	−0.129723
$288$	−1443.22	−0.295287
$289$	−4391.28	−0.893808
$290$	7797.80	1.57898
$291$	1920.48	0.386875
$292$	526.473	0.105512
$293$	−3424.66	−0.682835	−0.341417	−	0.939912i	$-0.610907\pi$
$293$	−3424.66	−0.682835	−0.341417	+	0.939912i	$0.610907\pi$
$294$	−1416.41	−0.280976
$295$	−1966.86	−0.388186
$296$	−1694.65	−0.332770
$297$	6584.74	1.28648
$298$	10066.6	1.95686
$299$	8862.59	1.71417
$300$	−49.4522	−0.00951707
$301$	0	0
$302$	−380.746	−0.0725479
$303$	3034.52	0.575342
$304$	−2682.50	−0.506093
$305$	1795.85	0.337148
$306$	−1607.39	−0.300288
$307$	−1249.32	−0.232256	−0.116128	−	0.993234i	$-0.537048\pi$
$307$	−1249.32	−0.232256	−0.116128	+	0.993234i	$0.537048\pi$
$308$	−980.715	−0.181433
$309$	−2157.96	−0.397289
$310$	−11239.7	−2.05927
$311$	−2947.84	−0.537481	−0.268740	−	0.963213i	$-0.586607\pi$
$311$	−2947.84	−0.537481	−0.268740	+	0.963213i	$0.586607\pi$
$312$	2520.46	0.457350
$313$	8598.81	1.55282	0.776411	−	0.630226i	$-0.217038\pi$
$313$	8598.81	1.55282	0.776411	+	0.630226i	$0.217038\pi$
$314$	−3434.78	−0.617311
$315$	−2919.33	−0.522176
$316$	653.641	0.116361
$317$	−1852.66	−0.328252	−0.164126	−	0.986439i	$-0.552480\pi$
$317$	−1852.66	−0.328252	−0.164126	+	0.986439i	$0.552480\pi$
$318$	2509.00	0.442446
$319$	13948.7	2.44820
$320$	−4694.03	−0.820013
$321$	−1861.11	−0.323604
$322$	−4680.07	−0.809969
$323$	−836.281	−0.144062
$324$	586.103	0.100498
$325$	−1081.98	−0.184670
$326$	−8650.82	−1.46971
$327$	3190.01	0.539474
$328$	1196.84	0.201477
$329$	−2152.52	−0.360706
$330$	−4826.07	−0.805050
$331$	−316.494	−0.0525562	−0.0262781	−	0.999655i	$-0.508366\pi$
$331$	−316.494	−0.0525562	−0.0262781	+	0.999655i	$0.508366\pi$
$332$	1837.45	0.303745
$333$	1922.70	0.316407
$334$	−5965.11	−0.977234
$335$	−2017.67	−0.329065
$336$	−1572.21	−0.255270
$337$	−2975.67	−0.480994	−0.240497	−	0.970650i	$-0.577310\pi$
$337$	−2975.67	−0.480994	−0.240497	+	0.970650i	$0.577310\pi$
$338$	−5012.49	−0.806638
$339$	−3099.54	−0.496590
$340$	383.116	0.0611099
$341$	−20105.5	−3.19289
$342$	2576.52	0.407375
$343$	6100.83	0.960389
$344$	0	0
$345$	−3440.88	−0.536958
$346$	3390.71	0.526837
$347$	−3588.41	−0.555147	−0.277573	−	0.960704i	$-0.589530\pi$
$347$	−3588.41	−0.555147	−0.277573	+	0.960704i	$0.589530\pi$
$348$	−602.640	−0.0928301
$349$	−10696.8	−1.64065	−0.820325	−	0.571898i	$-0.806207\pi$
$349$	−10696.8	−1.64065	−0.820325	+	0.571898i	$0.806207\pi$
$350$	571.362	0.0872589
$351$	−6224.43	−0.946539
$352$	4118.47	0.623623
$353$	−7340.86	−1.10684	−0.553420	−	0.832902i	$-0.686678\pi$
$353$	−7340.86	−1.10684	−0.553420	+	0.832902i	$0.686678\pi$
$354$	1017.40	0.152752
$355$	−12413.5	−1.85589
$356$	−93.7946	−0.0139638
$357$	−490.141	−0.0726639
$358$	3540.16	0.522635
$359$	8011.90	1.17786	0.588931	−	0.808184i	$-0.299549\pi$
$359$	8011.90	1.17786	0.588931	+	0.808184i	$0.299549\pi$
$360$	5539.63	0.811011
$361$	−5518.51	−0.804564
$362$	10879.9	1.57966
$363$	−5953.12	−0.860766
$364$	927.050	0.133491
$365$	−4472.18	−0.641328
$366$	−928.944	−0.132669
$367$	−8926.05	−1.26958	−0.634790	−	0.772685i	$-0.718913\pi$
$367$	−8926.05	−1.26958	−0.634790	+	0.772685i	$0.718913\pi$
$368$	10490.3	1.48599
$369$	−1357.90	−0.191570
$370$	−3067.29	−0.430976
$371$	−4331.05	−0.606084
$372$	868.642	0.121067
$373$	3809.92	0.528874	0.264437	−	0.964403i	$-0.414814\pi$
$373$	3809.92	0.528874	0.264437	+	0.964403i	$0.414814\pi$
$374$	4586.95	0.634186
$375$	−2583.92	−0.355821
$376$	4084.56	0.560226
$377$	−13185.4	−1.80128
$378$	3286.93	0.447253
$379$	2451.19	0.332214	0.166107	−	0.986108i	$-0.446880\pi$
$379$	2451.19	0.332214	0.166107	+	0.986108i	$0.446880\pi$
$380$	−614.105	−0.0829024
$381$	1261.02	0.169564
$382$	−7326.09	−0.981244
$383$	−3346.93	−0.446528	−0.223264	−	0.974758i	$-0.571671\pi$
$383$	−3346.93	−0.446528	−0.223264	+	0.974758i	$0.571671\pi$
$384$	3441.11	0.457301
$385$	8330.80	1.10280
$386$	−2377.98	−0.313564
$387$	0	0
$388$	−1340.39	−0.175381
$389$	−5274.35	−0.687455	−0.343727	−	0.939069i	$-0.611690\pi$
$389$	−5274.35	−0.687455	−0.343727	+	0.939069i	$0.611690\pi$
$390$	4561.99	0.592321
$391$	3270.39	0.422994
$392$	−4639.60	−0.597793
$393$	2616.89	0.335890
$394$	−10987.7	−1.40495
$395$	−5552.42	−0.707273
$396$	−2111.40	−0.267935
$397$	−9500.83	−1.20109	−0.600545	−	0.799591i	$-0.705050\pi$
$397$	−9500.83	−1.20109	−0.600545	+	0.799591i	$0.705050\pi$
$398$	9539.32	1.20141
$399$	785.658	0.0985767
$400$	−1280.70	−0.160087
$401$	−14475.4	−1.80266	−0.901330	−	0.433132i	$-0.857408\pi$
$401$	−14475.4	−1.80266	−0.901330	+	0.433132i	$0.857408\pi$
$402$	1043.68	0.129488
$403$	19005.4	2.34919
$404$	−2117.92	−0.260819
$405$	−4978.72	−0.610851
$406$	6962.81	0.851129
$407$	−5486.76	−0.668227
$408$	930.077	0.112857
$409$	−12284.3	−1.48513	−0.742567	−	0.669772i	$-0.766392\pi$
$409$	−12284.3	−1.48513	−0.742567	+	0.669772i	$0.766392\pi$
$410$	2166.26	0.260937
$411$	−3691.12	−0.442992
$412$	1506.14	0.180102
$413$	−1756.24	−0.209247
$414$	−10075.8	−1.19613
$415$	−15608.4	−1.84624
$416$	−3893.11	−0.458835
$417$	−714.462	−0.0839025
$418$	−7352.53	−0.860345
$419$	−2550.74	−0.297403	−0.148701	−	0.988882i	$-0.547509\pi$
$419$	−2550.74	−0.297403	−0.148701	+	0.988882i	$0.547509\pi$
$420$	−359.925	−0.0418155
$421$	4680.41	0.541827	0.270913	−	0.962604i	$-0.412674\pi$
$421$	4680.41	0.541827	0.270913	+	0.962604i	$0.412674\pi$
$422$	−3377.73	−0.389634
$423$	−4634.21	−0.532679
$424$	8218.47	0.941331
$425$	−399.263	−0.0455696
$426$	6421.18	0.730298
$427$	1603.55	0.181736
$428$	1298.95	0.146699
$429$	8160.46	0.918394
$430$	0	0
$431$	6700.14	0.748803	0.374402	−	0.927267i	$-0.377848\pi$
$431$	6700.14	0.748803	0.374402	+	0.927267i	$0.377848\pi$
$432$	−7367.60	−0.820541
$433$	11197.9	1.24281	0.621407	−	0.783488i	$-0.286562\pi$
$433$	11197.9	1.24281	0.621407	+	0.783488i	$0.286562\pi$
$434$	−10036.2	−1.11002
$435$	5119.19	0.564245
$436$	−2226.45	−0.244559
$437$	−5242.18	−0.573838
$438$	2313.34	0.252364
$439$	13944.1	1.51598	0.757992	−	0.652264i	$-0.226181\pi$
$439$	13944.1	1.51598	0.757992	+	0.652264i	$0.226181\pi$
$440$	−15808.3	−1.71279
$441$	5263.94	0.568399
$442$	−4335.95	−0.466607
$443$	2589.51	0.277723	0.138862	−	0.990312i	$-0.455656\pi$
$443$	2589.51	0.277723	0.138862	+	0.990312i	$0.455656\pi$
$444$	237.050	0.0253377
$445$	796.748	0.0848753
$446$	−7401.64	−0.785825
$447$	6608.64	0.699280
$448$	−4191.39	−0.442019
$449$	−13244.7	−1.39211	−0.696056	−	0.717987i	$-0.745064\pi$
$449$	−13244.7	−1.39211	−0.696056	+	0.717987i	$0.745064\pi$
$450$	1230.10	0.128861
$451$	3875.00	0.404582
$452$	2163.31	0.225118
$453$	−249.957	−0.0259249
$454$	−6848.91	−0.708007
$455$	−7874.93	−0.811390
$456$	−1490.84	−0.153103
$457$	−7940.24	−0.812754	−0.406377	−	0.913705i	$-0.633208\pi$
$457$	−7940.24	−0.812754	−0.406377	+	0.913705i	$0.633208\pi$
$458$	4170.08	0.425448
$459$	−2296.88	−0.233571
$460$	2401.54	0.243418
$461$	5251.72	0.530579	0.265290	−	0.964169i	$-0.414532\pi$
$461$	5251.72	0.530579	0.265290	+	0.964169i	$0.414532\pi$
$462$	−4309.29	−0.433953
$463$	−9045.26	−0.907924	−0.453962	−	0.891021i	$-0.649990\pi$
$463$	−9045.26	−0.907924	−0.453962	+	0.891021i	$0.649990\pi$
$464$	−15607.0	−1.56150
$465$	−7378.78	−0.735876
$466$	21458.3	2.13312
$467$	−11982.6	−1.18734	−0.593671	−	0.804708i	$-0.702322\pi$
$467$	−11982.6	−1.18734	−0.593671	+	0.804708i	$0.702322\pi$
$468$	1995.87	0.197135
$469$	−1801.61	−0.177379
$470$	7392.97	0.725558
$471$	−2254.90	−0.220595
$472$	3332.59	0.324989
$473$	0	0
$474$	2872.12	0.278314
$475$	639.988	0.0618203
$476$	342.091	0.0329406
$477$	−9324.43	−0.895044
$478$	−13349.8	−1.27741
$479$	5589.14	0.533140	0.266570	−	0.963816i	$-0.414110\pi$
$479$	5589.14	0.533140	0.266570	+	0.963816i	$0.414110\pi$
$480$	1511.49	0.143729
$481$	5186.52	0.491653
$482$	9381.89	0.886584
$483$	−3072.42	−0.289441
$484$	4154.95	0.390209
$485$	11386.1	1.06601
$486$	10901.9	1.01753
$487$	9311.43	0.866409	0.433205	−	0.901296i	$-0.357383\pi$
$487$	9311.43	0.866409	0.433205	+	0.901296i	$0.357383\pi$
$488$	−3042.84	−0.282260
$489$	−5679.19	−0.525198
$490$	−8397.58	−0.774212
$491$	12911.8	1.18677	0.593383	−	0.804920i	$-0.297792\pi$
$491$	12911.8	1.18677	0.593383	+	0.804920i	$0.297792\pi$
$492$	−167.416	−0.0153408
$493$	−4865.55	−0.444489
$494$	6950.20	0.633005
$495$	17935.6	1.62857
$496$	22495.9	2.03648
$497$	−11084.3	−1.00040
$498$	8073.82	0.726499
$499$	−6845.56	−0.614127	−0.307064	−	0.951689i	$-0.599346\pi$
$499$	−6845.56	−0.614127	−0.307064	+	0.951689i	$0.599346\pi$
$500$	1803.43	0.161304
$501$	−3916.04	−0.349213
$502$	−18723.4	−1.66468
$503$	5914.10	0.524248	0.262124	−	0.965034i	$-0.415577\pi$
$503$	5914.10	0.524248	0.262124	+	0.965034i	$0.415577\pi$
$504$	4946.44	0.437166
$505$	17990.9	1.58532
$506$	28753.1	2.52614
$507$	−3290.66	−0.288251
$508$	−880.118	−0.0768680
$509$	−5224.84	−0.454984	−0.227492	−	0.973780i	$-0.573053\pi$
$509$	−5224.84	−0.454984	−0.227492	+	0.973780i	$0.573053\pi$
$510$	1683.42	0.146163
$511$	−3993.30	−0.345701
$512$	7246.41	0.625487
$513$	3681.72	0.316865
$514$	−5198.25	−0.446079
$515$	−12794.0	−1.09471
$516$	0	0
$517$	13224.5	1.12498
$518$	−2738.84	−0.232313
$519$	2225.97	0.188264
$520$	14943.2	1.26020
$521$	1983.41	0.166785	0.0833923	−	0.996517i	$-0.473425\pi$
$521$	1983.41	0.166785	0.0833923	+	0.996517i	$0.473425\pi$
$522$	14990.4	1.25692
$523$	−588.084	−0.0491685	−0.0245843	−	0.999698i	$-0.507826\pi$
$523$	−588.084	−0.0491685	−0.0245843	+	0.999698i	$0.507826\pi$
$524$	−1826.44	−0.152268
$525$	375.095	0.0311818
$526$	−4074.57	−0.337756
$527$	7013.17	0.579694
$528$	9659.21	0.796142
$529$	8333.24	0.684905
$530$	14875.3	1.21913
$531$	−3781.06	−0.309009
$532$	−548.346	−0.0446876
$533$	−3662.96	−0.297674
$534$	−412.136	−0.0333986
$535$	−11034.1	−0.891671
$536$	3418.68	0.275494
$537$	2324.08	0.186763
$538$	15271.0	1.22376
$539$	−15021.5	−1.20042
$540$	−1686.66	−0.134412
$541$	−14115.0	−1.12173	−0.560863	−	0.827909i	$-0.689530\pi$
$541$	−14115.0	−1.12173	−0.560863	+	0.827909i	$0.689530\pi$
$542$	8426.42	0.667797
$543$	7142.58	0.564489
$544$	−1436.60	−0.113224
$545$	18912.8	1.48649
$546$	4073.49	0.319284
$547$	9946.81	0.777504	0.388752	−	0.921342i	$-0.372906\pi$
$547$	9946.81	0.777504	0.388752	+	0.921342i	$0.372906\pi$
$548$	2576.20	0.200820
$549$	3452.32	0.268381
$550$	−3510.30	−0.272145
$551$	7799.09	0.602999
$552$	5830.13	0.449542
$553$	−4957.86	−0.381247
$554$	−17144.6	−1.31481
$555$	−2013.65	−0.154009
$556$	498.654	0.0380353
$557$	−12763.4	−0.970918	−0.485459	−	0.874259i	$-0.661347\pi$
$557$	−12763.4	−0.970918	−0.485459	+	0.874259i	$0.661347\pi$
$558$	−21607.1	−1.63925
$559$	0	0
$560$	−9321.24	−0.703383
$561$	3011.29	0.226626
$562$	−9335.53	−0.700704
$563$	2108.25	0.157819	0.0789096	−	0.996882i	$-0.474856\pi$
$563$	2108.25	0.157819	0.0789096	+	0.996882i	$0.474856\pi$
$564$	−571.353	−0.0426566
$565$	−18376.5	−1.36832
$566$	10953.5	0.813445
$567$	−4445.59	−0.329272
$568$	21033.2	1.55375
$569$	6912.66	0.509304	0.254652	−	0.967033i	$-0.418039\pi$
$569$	6912.66	0.509304	0.254652	+	0.967033i	$0.418039\pi$
$570$	−2698.39	−0.198287
$571$	−24459.8	−1.79266	−0.896330	−	0.443387i	$-0.853777\pi$
$571$	−24459.8	−1.79266	−0.896330	+	0.443387i	$0.853777\pi$
$572$	−5695.55	−0.416334
$573$	−4809.51	−0.350646
$574$	1934.30	0.140655
$575$	−2502.76	−0.181517
$576$	−9023.73	−0.652758
$577$	−22269.4	−1.60674	−0.803370	−	0.595480i	$-0.796962\pi$
$577$	−22269.4	−1.60674	−0.803370	+	0.595480i	$0.796962\pi$
$578$	13467.1	0.969132
$579$	−1561.12	−0.112052
$580$	−3572.91	−0.255788
$581$	−13937.1	−0.995193
$582$	−5889.71	−0.419478
$583$	26608.8	1.89027
$584$	7577.55	0.536920
$585$	−16954.1	−1.19823
$586$	10502.7	0.740379
$587$	−23935.8	−1.68303	−0.841514	−	0.540235i	$-0.818336\pi$
$587$	−23935.8	−1.68303	−0.841514	+	0.540235i	$0.818336\pi$
$588$	648.993	0.0455170
$589$	−11241.6	−0.786419
$590$	6031.93	0.420900
$591$	−7213.32	−0.502058
$592$	6139.07	0.426207
$593$	25229.9	1.74717	0.873583	−	0.486675i	$-0.161791\pi$
$593$	25229.9	1.74717	0.873583	+	0.486675i	$0.161791\pi$
$594$	−20194.0	−1.39490
$595$	−2905.93	−0.200221
$596$	−4612.46	−0.317003
$597$	6262.48	0.429324
$598$	−27179.7	−1.85863
$599$	−11758.7	−0.802086	−0.401043	−	0.916059i	$-0.631352\pi$
$599$	−11758.7	−0.802086	−0.401043	+	0.916059i	$0.631352\pi$
$600$	−711.768	−0.0484297
$601$	18453.3	1.25246	0.626228	−	0.779640i	$-0.284598\pi$
$601$	18453.3	1.25246	0.626228	+	0.779640i	$0.284598\pi$
$602$	0	0
$603$	−3878.73	−0.261947
$604$	174.456	0.0117525
$605$	−35294.7	−2.37179
$606$	−9306.22	−0.623828
$607$	26742.0	1.78818	0.894088	−	0.447892i	$-0.147825\pi$
$607$	26742.0	1.78818	0.894088	+	0.447892i	$0.147825\pi$
$608$	2302.76	0.153600
$609$	4571.02	0.304150
$610$	−5507.49	−0.365560
$611$	−12500.9	−0.827710
$612$	736.496	0.0486456
$613$	−2389.43	−0.157436	−0.0787179	−	0.996897i	$-0.525083\pi$
$613$	−2389.43	−0.157436	−0.0787179	+	0.996897i	$0.525083\pi$
$614$	3831.40	0.251829
$615$	1422.13	0.0932454
$616$	−14115.5	−0.923262
$617$	16915.3	1.10371	0.551853	−	0.833942i	$-0.313921\pi$
$617$	16915.3	1.10371	0.551853	+	0.833942i	$0.313921\pi$
$618$	6618.01	0.430769
$619$	18741.2	1.21692	0.608460	−	0.793584i	$-0.291787\pi$
$619$	18741.2	1.21692	0.608460	+	0.793584i	$0.291787\pi$
$620$	5149.97	0.333593
$621$	−14397.8	−0.930380
$622$	9040.39	0.582776
$623$	711.432	0.0457511
$624$	−9130.65	−0.585767
$625$	−17504.4	−1.12028
$626$	−26370.7	−1.68368
$627$	−4826.87	−0.307443
$628$	1573.79	0.100002
$629$	1913.88	0.121322
$630$	8952.96	0.566182
$631$	9825.75	0.619900	0.309950	−	0.950753i	$-0.399688\pi$
$631$	9825.75	0.619900	0.309950	+	0.950753i	$0.399688\pi$
$632$	9407.89	0.592129
$633$	−2217.45	−0.139235
$634$	5681.73	0.355915
$635$	7476.26	0.467223
$636$	−1149.61	−0.0716746
$637$	14199.6	0.883214
$638$	−42777.6	−2.65452
$639$	−23863.6	−1.47735
$640$	20401.5	1.26007
$641$	5404.26	0.333004	0.166502	−	0.986041i	$-0.446753\pi$
$641$	5404.26	0.333004	0.166502	+	0.986041i	$0.446753\pi$
$642$	5707.62	0.350875
$643$	24177.5	1.48284	0.741422	−	0.671039i	$-0.234152\pi$
$643$	24177.5	1.48284	0.741422	+	0.671039i	$0.234152\pi$
$644$	2144.38	0.131212
$645$	0	0
$646$	2564.70	0.156202
$647$	−9145.13	−0.555691	−0.277846	−	0.960626i	$-0.589620\pi$
$647$	−9145.13	−0.555691	−0.277846	+	0.960626i	$0.589620\pi$
$648$	8435.82	0.511405
$649$	10789.9	0.652604
$650$	3318.21	0.200232
$651$	−6588.65	−0.396666
$652$	3963.76	0.238087
$653$	−161.209	−0.00966091	−0.00483046	−	0.999988i	$-0.501538\pi$
$653$	−161.209	−0.00966091	−0.00483046	+	0.999988i	$0.501538\pi$
$654$	−9783.08	−0.584937
$655$	15514.9	0.925524
$656$	−4335.70	−0.258050
$657$	−8597.26	−0.510519
$658$	6601.33	0.391104
$659$	−8406.91	−0.496945	−0.248472	−	0.968639i	$-0.579929\pi$
$659$	−8406.91	−0.496945	−0.248472	+	0.968639i	$0.579929\pi$
$660$	2211.28	0.130415
$661$	−17911.7	−1.05399	−0.526994	−	0.849869i	$-0.676681\pi$
$661$	−17911.7	−1.05399	−0.526994	+	0.849869i	$0.676681\pi$
$662$	970.621	0.0569853
$663$	−2846.52	−0.166741
$664$	26446.6	1.54567
$665$	4657.98	0.271622
$666$	−5896.52	−0.343071
$667$	−30499.4	−1.77053
$668$	2733.18	0.158308
$669$	−4859.11	−0.280813
$670$	6187.75	0.356797
$671$	−9851.77	−0.566801
$672$	1349.64	0.0774753
$673$	11202.5	0.641642	0.320821	−	0.947140i	$-0.396041\pi$
$673$	11202.5	0.641642	0.320821	+	0.947140i	$0.396041\pi$
$674$	9125.74	0.521529
$675$	1757.75	0.100231
$676$	2296.70	0.130672
$677$	−29615.8	−1.68128	−0.840640	−	0.541594i	$-0.817821\pi$
$677$	−29615.8	−1.68128	−0.840640	+	0.541594i	$0.817821\pi$
$678$	9505.64	0.538439
$679$	10166.9	0.574622
$680$	5514.20	0.310971
$681$	−4496.25	−0.253005
$682$	61659.4	3.46197
$683$	24045.9	1.34713	0.673566	−	0.739127i	$-0.264762\pi$
$683$	24045.9	1.34713	0.673566	+	0.739127i	$0.264762\pi$
$684$	−1180.55	−0.0659931
$685$	−21883.8	−1.22064
$686$	−18709.9	−1.04132
$687$	2737.62	0.152033
$688$	0	0
$689$	−25152.8	−1.39078
$690$	10552.4	0.582209
$691$	21794.1	1.19983	0.599917	−	0.800062i	$-0.295200\pi$
$691$	21794.1	1.19983	0.599917	+	0.800062i	$0.295200\pi$
$692$	−1553.60	−0.0853455
$693$	16015.0	0.877864
$694$	11004.9	0.601931
$695$	−4235.87	−0.231188
$696$	−8673.83	−0.472386
$697$	−1351.67	−0.0734550
$698$	32804.8	1.77891
$699$	14087.2	0.762268
$700$	−261.795	−0.0141356
$701$	−25915.8	−1.39633	−0.698164	−	0.715937i	$-0.746000\pi$
$701$	−25915.8	−1.39633	−0.698164	+	0.715937i	$0.746000\pi$
$702$	19089.0	1.02631
$703$	−3067.80	−0.164587
$704$	25750.7	1.37858
$705$	4853.42	0.259277
$706$	22512.9	1.20012
$707$	16064.5	0.854549
$708$	−466.167	−0.0247453
$709$	−26358.5	−1.39621	−0.698106	−	0.715995i	$-0.745973\pi$
$709$	−26358.5	−1.39621	−0.698106	+	0.715995i	$0.745973\pi$
$710$	38069.6	2.01229
$711$	−10673.9	−0.563013
$712$	−1349.99	−0.0710576
$713$	43961.7	2.30909
$714$	1503.16	0.0787875
$715$	48381.5	2.53058
$716$	−1622.08	−0.0846648
$717$	−8764.00	−0.456482
$718$	−24570.8	−1.27712
$719$	522.060	0.0270787	0.0135393	−	0.999908i	$-0.495690\pi$
$719$	522.060	0.0270787	0.0135393	+	0.999908i	$0.495690\pi$
$720$	−20067.9	−1.03873
$721$	−11424.0	−0.590088
$722$	16924.1	0.872367
$723$	6159.13	0.316819
$724$	−4985.12	−0.255899
$725$	3723.50	0.190741
$726$	18257.0	0.933305
$727$	8443.21	0.430731	0.215366	−	0.976534i	$-0.430906\pi$
$727$	8443.21	0.430731	0.215366	+	0.976534i	$0.430906\pi$
$728$	13343.1	0.679296
$729$	−4104.71	−0.208541
$730$	13715.2	0.695375
$731$	0	0
$732$	425.637	0.0214918
$733$	9103.47	0.458723	0.229362	−	0.973341i	$-0.426336\pi$
$733$	9103.47	0.458723	0.229362	+	0.973341i	$0.426336\pi$
$734$	27374.3	1.37657
$735$	−5512.94	−0.276664
$736$	−9005.24	−0.451002
$737$	11068.6	0.553212
$738$	4164.39	0.207715
$739$	1195.87	0.0595275	0.0297638	−	0.999557i	$-0.490524\pi$
$739$	1195.87	0.0595275	0.0297638	+	0.999557i	$0.490524\pi$
$740$	1405.42	0.0698164
$741$	4562.75	0.226203
$742$	13282.4	0.657160
$743$	−18356.6	−0.906379	−0.453189	−	0.891414i	$-0.649714\pi$
$743$	−18356.6	−0.906379	−0.453189	+	0.891414i	$0.649714\pi$
$744$	12502.4	0.616076
$745$	39181.1	1.92682
$746$	−11684.2	−0.573444
$747$	−30005.4	−1.46967
$748$	−2101.72	−0.102736
$749$	−9852.52	−0.480645
$750$	7924.33	0.385808
$751$	37294.3	1.81210	0.906052	−	0.423167i	$-0.139082\pi$
$751$	37294.3	1.81210	0.906052	+	0.423167i	$0.139082\pi$
$752$	−14796.8	−0.717530
$753$	−12291.8	−0.594870
$754$	40436.8	1.95308
$755$	−1481.93	−0.0714345
$756$	−1506.05	−0.0724532
$757$	14854.1	0.713187	0.356593	−	0.934260i	$-0.383938\pi$
$757$	14854.1	0.713187	0.356593	+	0.934260i	$0.383938\pi$
$758$	−7517.27	−0.360211
$759$	18876.1	0.902714
$760$	−8838.84	−0.421867
$761$	−35725.3	−1.70176	−0.850881	−	0.525358i	$-0.823931\pi$
$761$	−35725.3	−1.70176	−0.850881	+	0.525358i	$0.823931\pi$
$762$	−3867.27	−0.183853
$763$	16887.6	0.801275
$764$	3356.77	0.158958
$765$	−6256.25	−0.295680
$766$	10264.3	0.484158
$767$	−10199.5	−0.480158
$768$	−4219.26	−0.198241
$769$	6836.30	0.320576	0.160288	−	0.987070i	$-0.448758\pi$
$769$	6836.30	0.320576	0.160288	+	0.987070i	$0.448758\pi$
$770$	−25548.8	−1.19573
$771$	−3412.60	−0.159406
$772$	1089.58	0.0507962
$773$	−16076.5	−0.748034	−0.374017	−	0.927422i	$-0.622020\pi$
$773$	−16076.5	−0.748034	−0.374017	+	0.927422i	$0.622020\pi$
$774$	0	0
$775$	−5367.03	−0.248761
$776$	−19292.3	−0.892466
$777$	−1798.03	−0.0830166
$778$	16175.3	0.745389
$779$	2166.62	0.0996499
$780$	−2090.28	−0.0959538
$781$	68098.7	3.12006
$782$	−10029.6	−0.458641
$783$	21420.5	0.977659
$784$	16807.4	0.765645
$785$	−13368.8	−0.607837
$786$	−8025.45	−0.364196
$787$	−23639.9	−1.07074	−0.535370	−	0.844618i	$-0.679828\pi$
$787$	−23639.9	−1.07074	−0.535370	+	0.844618i	$0.679828\pi$
$788$	5034.49	0.227597
$789$	−2674.92	−0.120697
$790$	17028.1	0.766877
$791$	−16408.7	−0.737580
$792$	−30389.6	−1.36344
$793$	9312.68	0.417028
$794$	29137.0	1.30231
$795$	9765.49	0.435656
$796$	−4370.86	−0.194624
$797$	25100.7	1.11557	0.557786	−	0.829985i	$-0.311651\pi$
$797$	25100.7	1.11557	0.557786	+	0.829985i	$0.311651\pi$
$798$	−2409.45	−0.106884
$799$	−4612.95	−0.204248
$800$	1099.40	0.0485870
$801$	1531.66	0.0675636
$802$	44393.0	1.95458
$803$	24533.7	1.07818
$804$	−478.210	−0.0209766
$805$	−18215.7	−0.797538
$806$	−58285.4	−2.54717
$807$	10025.3	0.437308
$808$	−30483.4	−1.32723
$809$	13162.4	0.572021	0.286011	−	0.958226i	$-0.407671\pi$
$809$	13162.4	0.572021	0.286011	+	0.958226i	$0.407671\pi$
$810$	15268.7	0.662329
$811$	25843.3	1.11897	0.559484	−	0.828841i	$-0.311000\pi$
$811$	25843.3	1.11897	0.559484	+	0.828841i	$0.311000\pi$
$812$	−3190.32	−0.137880
$813$	5531.87	0.238636
$814$	16826.7	0.724541
$815$	−33670.6	−1.44715
$816$	−3369.31	−0.144546
$817$	0	0
$818$	37673.4	1.61029
$819$	−15138.7	−0.645894
$820$	−992.570	−0.0422708
$821$	20649.7	0.877805	0.438903	−	0.898535i	$-0.355367\pi$
$821$	20649.7	0.877805	0.438903	+	0.898535i	$0.355367\pi$
$822$	11319.9	0.480324
$823$	−33853.1	−1.43384	−0.716918	−	0.697158i	$-0.754448\pi$
$823$	−33853.1	−1.43384	−0.716918	+	0.697158i	$0.754448\pi$
$824$	21677.9	0.916488
$825$	−2304.48	−0.0972505
$826$	5386.03	0.226881
$827$	12153.3	0.511019	0.255509	−	0.966807i	$-0.417757\pi$
$827$	12153.3	0.511019	0.255509	+	0.966807i	$0.417757\pi$
$828$	4616.68	0.193769
$829$	4628.02	0.193894	0.0969468	−	0.995290i	$-0.469092\pi$
$829$	4628.02	0.193894	0.0969468	+	0.995290i	$0.469092\pi$
$830$	47867.8	2.00182
$831$	−11255.3	−0.469844
$832$	−24341.7	−1.01430
$833$	5239.79	0.217945
$834$	2191.10	0.0909732
$835$	−23217.3	−0.962236
$836$	3368.89	0.139372
$837$	−30875.4	−1.27504
$838$	7822.57	0.322466
$839$	−29113.1	−1.19797	−0.598984	−	0.800761i	$-0.704429\pi$
$839$	−29113.1	−1.19797	−0.598984	+	0.800761i	$0.704429\pi$
$840$	−5180.42	−0.212787
$841$	20986.7	0.860500
$842$	−14353.8	−0.587488
$843$	−6128.69	−0.250395
$844$	1547.66	0.0631192
$845$	−19509.5	−0.794259
$846$	14212.1	0.577569
$847$	−31515.3	−1.27849
$848$	−29772.3	−1.20564
$849$	7190.87	0.290683
$850$	1224.45	0.0494099
$851$	11997.0	0.483259
$852$	−2942.15	−0.118305
$853$	−2836.73	−0.113866	−0.0569331	−	0.998378i	$-0.518132\pi$
$853$	−2836.73	−0.113866	−0.0569331	+	0.998378i	$0.518132\pi$
$854$	−4917.74	−0.197051
$855$	10028.3	0.401123
$856$	18695.8	0.746508
$857$	−2323.85	−0.0926269	−0.0463134	−	0.998927i	$-0.514747\pi$
$857$	−2323.85	−0.0926269	−0.0463134	+	0.998927i	$0.514747\pi$
$858$	−25026.4	−0.995789
$859$	20417.4	0.810981	0.405490	−	0.914099i	$-0.367101\pi$
$859$	20417.4	0.810981	0.405490	+	0.914099i	$0.367101\pi$
$860$	0	0
$861$	1269.85	0.0502629
$862$	−20547.9	−0.811907
$863$	−11193.8	−0.441532	−0.220766	−	0.975327i	$-0.570856\pi$
$863$	−11193.8	−0.441532	−0.220766	+	0.975327i	$0.570856\pi$
$864$	6324.61	0.249037
$865$	13197.2	0.518751
$866$	−34341.7	−1.34755
$867$	8841.04	0.346318
$868$	4598.51	0.179820
$869$	30459.8	1.18904
$870$	−15699.5	−0.611795
$871$	−10462.9	−0.407030
$872$	−32045.4	−1.24449
$873$	21888.5	0.848582
$874$	16076.6	0.622198
$875$	−13679.0	−0.528498
$876$	−1059.96	−0.0408820
$877$	−14906.8	−0.573966	−0.286983	−	0.957936i	$-0.592652\pi$
$877$	−14906.8	−0.573966	−0.286983	+	0.957936i	$0.592652\pi$
$878$	−42763.7	−1.64374
$879$	6894.93	0.264574
$880$	57267.2	2.19372
$881$	32192.4	1.23109	0.615544	−	0.788102i	$-0.288936\pi$
$881$	32192.4	1.23109	0.615544	+	0.788102i	$0.288936\pi$
$882$	−16143.4	−0.616300
$883$	−15047.5	−0.573486	−0.286743	−	0.958008i	$-0.592573\pi$
$883$	−15047.5	−0.573486	−0.286743	+	0.958008i	$0.592573\pi$
$884$	1986.71	0.0755885
$885$	3959.91	0.150408
$886$	−7941.48	−0.301128
$887$	45336.4	1.71618	0.858088	−	0.513502i	$-0.171652\pi$
$887$	45336.4	1.71618	0.858088	+	0.513502i	$0.171652\pi$
$888$	3411.88	0.128936
$889$	6675.70	0.251851
$890$	−2443.46	−0.0920280
$891$	27312.5	1.02694
$892$	3391.39	0.127301
$893$	7394.20	0.277086
$894$	−20267.3	−0.758210
$895$	13778.9	0.514614
$896$	18216.9	0.679224
$897$	−17843.2	−0.664178
$898$	40618.8	1.50943
$899$	−65404.4	−2.42643
$900$	−563.624	−0.0208750
$901$	−9281.64	−0.343192
$902$	−11883.8	−0.438678
$903$	0	0
$904$	31136.6	1.14556
$905$	42346.7	1.55542
$906$	766.564	0.0281097
$907$	1995.61	0.0730573	0.0365287	−	0.999333i	$-0.488370\pi$
$907$	1995.61	0.0730573	0.0365287	+	0.999333i	$0.488370\pi$
$908$	3138.13	0.114694
$909$	34585.5	1.26197
$910$	24150.7	0.879769
$911$	−14639.1	−0.532398	−0.266199	−	0.963918i	$-0.585768\pi$
$911$	−14639.1	−0.532398	−0.266199	+	0.963918i	$0.585768\pi$
$912$	5400.74	0.196092
$913$	85625.6	3.10383
$914$	24351.0	0.881248
$915$	−3615.62	−0.130632
$916$	−1910.71	−0.0689209
$917$	13853.6	0.498893
$918$	7044.04	0.253255
$919$	−3884.35	−0.139427	−0.0697133	−	0.997567i	$-0.522208\pi$
$919$	−3884.35	−0.139427	−0.0697133	+	0.997567i	$0.522208\pi$
$920$	34565.5	1.23869
$921$	2515.28	0.0899906
$922$	−16105.9	−0.575293
$923$	−64372.4	−2.29560
$924$	1974.49	0.0702988
$925$	−1464.65	−0.0520621
$926$	27739.9	0.984437
$927$	−24595.1	−0.871423
$928$	13397.6	0.473920
$929$	11634.6	0.410892	0.205446	−	0.978668i	$-0.434135\pi$
$929$	11634.6	0.410892	0.205446	+	0.978668i	$0.434135\pi$
$930$	22629.1	0.797891
$931$	−8398.97	−0.295666
$932$	−9832.05	−0.345557
$933$	5934.94	0.208254
$934$	36748.1	1.28740
$935$	17853.3	0.624453
$936$	28726.6	1.00316
$937$	−16593.3	−0.578527	−0.289263	−	0.957250i	$-0.593410\pi$
$937$	−16593.3	−0.578527	−0.289263	+	0.957250i	$0.593410\pi$
$938$	5525.16	0.192327
$939$	−17312.2	−0.601662
$940$	−3387.42	−0.117538
$941$	20113.2	0.696780	0.348390	−	0.937350i	$-0.386728\pi$
$941$	20113.2	0.696780	0.348390	+	0.937350i	$0.386728\pi$
$942$	6915.30	0.239185
$943$	−8472.87	−0.292592
$944$	−12072.7	−0.416242
$945$	12793.3	0.440389
$946$	0	0
$947$	−2781.93	−0.0954600	−0.0477300	−	0.998860i	$-0.515199\pi$
$947$	−2781.93	−0.0954600	−0.0477300	+	0.998860i	$0.515199\pi$
$948$	−1315.99	−0.0450857
$949$	−23191.2	−0.793277
$950$	−1962.71	−0.0670301
$951$	3730.01	0.127186
$952$	4923.74	0.167625
$953$	5315.57	0.180680	0.0903400	−	0.995911i	$-0.471205\pi$
$953$	5315.57	0.180680	0.0903400	+	0.995911i	$0.471205\pi$
$954$	28596.0	0.970472
$955$	−28514.5	−0.966185
$956$	6116.78	0.206936
$957$	−28083.1	−0.948588
$958$	−17140.7	−0.578070
$959$	−19540.4	−0.657971
$960$	9450.58	0.317725
$961$	64482.5	2.16450
$962$	−15906.0	−0.533086
$963$	−21211.7	−0.709801
$964$	−4298.73	−0.143623
$965$	−9255.52	−0.308752
$966$	9422.47	0.313833
$967$	−28577.3	−0.950344	−0.475172	−	0.879893i	$-0.657614\pi$
$967$	−28577.3	−0.950344	−0.475172	+	0.879893i	$0.657614\pi$
$968$	59802.4	1.98566
$969$	1683.70	0.0558186
$970$	−34918.7	−1.15585
$971$	28460.3	0.940612	0.470306	−	0.882503i	$-0.344144\pi$
$971$	28460.3	0.940612	0.470306	+	0.882503i	$0.344144\pi$
$972$	−4995.19	−0.164836
$973$	−3782.29	−0.124619
$974$	−28556.2	−0.939424
$975$	2178.38	0.0715527
$976$	11023.0	0.361515
$977$	1661.03	0.0543919	0.0271960	−	0.999630i	$-0.491342\pi$
$977$	1661.03	0.0543919	0.0271960	+	0.999630i	$0.491342\pi$
$978$	17416.9	0.569458
$979$	−4370.84	−0.142689
$980$	3847.72	0.125419
$981$	36357.7	1.18330
$982$	−39597.8	−1.28678
$983$	24756.7	0.803271	0.401636	−	0.915800i	$-0.368442\pi$
$983$	24756.7	0.803271	0.401636	+	0.915800i	$0.368442\pi$
$984$	−2409.63	−0.0780651
$985$	−42766.1	−1.38339
$986$	14921.6	0.481948
$987$	4333.71	0.139760
$988$	−3184.54	−0.102544
$989$	0	0
$990$	−55004.6	−1.76582
$991$	20329.5	0.651654	0.325827	−	0.945429i	$-0.394357\pi$
$991$	20329.5	0.651654	0.325827	+	0.945429i	$0.394357\pi$
$992$	−19311.3	−0.618077
$993$	637.204	0.0203636
$994$	33993.1	1.08470
$995$	37128.8	1.18298
$996$	−3699.38	−0.117690
$997$	51774.9	1.64466	0.822330	−	0.569011i	$-0.192674\pi$
$997$	51774.9	1.64466	0.822330	+	0.569011i	$0.192674\pi$
$998$	20993.9	0.665882
$999$	−8425.84	−0.266848

Twists

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

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

\(f(q)\)	\(=\)	\(q-3.06679 q^{2} -2.01332 q^{3} +1.40518 q^{4} -11.9365 q^{5} +6.17442 q^{6} -10.6583 q^{7} +20.2249 q^{8} -22.9465 q^{9} +O(q^{10})\)	\(q-3.06679 q^{2} -2.01332 q^{3} +1.40518 q^{4} -11.9365 q^{5} +6.17442 q^{6} -10.6583 q^{7} +20.2249 q^{8} -22.9465 q^{9} +36.6067 q^{10} +65.4818 q^{11} -2.82908 q^{12} -61.8987 q^{13} +32.6868 q^{14} +24.0320 q^{15} -73.2669 q^{16} -22.8412 q^{17} +70.3722 q^{18} +36.6127 q^{19} -16.7730 q^{20} +21.4586 q^{21} -200.819 q^{22} -143.179 q^{23} -40.7192 q^{24} +17.4799 q^{25} +189.830 q^{26} +100.558 q^{27} -14.9769 q^{28} +213.016 q^{29} -73.7010 q^{30} -307.040 q^{31} +62.8949 q^{32} -131.836 q^{33} +70.0492 q^{34} +127.223 q^{35} -32.2441 q^{36} -83.7905 q^{37} -112.284 q^{38} +124.622 q^{39} -241.414 q^{40} +59.1767 q^{41} -65.8090 q^{42} +92.0140 q^{44} +273.901 q^{45} +439.100 q^{46} +201.957 q^{47} +147.510 q^{48} -229.400 q^{49} -53.6072 q^{50} +45.9867 q^{51} -86.9790 q^{52} +406.354 q^{53} -308.391 q^{54} -781.624 q^{55} -215.563 q^{56} -73.7131 q^{57} -653.274 q^{58} +164.777 q^{59} +33.7694 q^{60} -150.450 q^{61} +941.626 q^{62} +244.572 q^{63} +393.250 q^{64} +738.853 q^{65} +404.312 q^{66} +169.033 q^{67} -32.0962 q^{68} +288.265 q^{69} -390.166 q^{70} +1039.96 q^{71} -464.092 q^{72} +374.665 q^{73} +256.968 q^{74} -35.1926 q^{75} +51.4477 q^{76} -697.926 q^{77} -382.188 q^{78} +465.164 q^{79} +874.550 q^{80} +417.101 q^{81} -181.482 q^{82} +1307.62 q^{83} +30.1533 q^{84} +272.644 q^{85} -428.869 q^{87} +1324.36 q^{88} -66.7489 q^{89} -839.997 q^{90} +659.736 q^{91} -201.193 q^{92} +618.169 q^{93} -619.359 q^{94} -437.028 q^{95} -126.628 q^{96} -953.889 q^{97} +703.522 q^{98} -1502.58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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