LMFDB - Embedded newform 1849.4.a.j.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.06679 q^{2} +2.01332 q^{3} +1.40518 q^{4} +11.9365 q^{5} +6.17442 q^{6} +10.6583 q^{7} -20.2249 q^{8} -22.9465 q^{9} +O(q^{10})$	\(q+3.06679 q^{2} +2.01332 q^{3} +1.40518 q^{4} +11.9365 q^{5} +6.17442 q^{6} +10.6583 q^{7} -20.2249 q^{8} -22.9465 q^{9} +36.6067 q^{10} +65.4818 q^{11} +2.82908 q^{12} -61.8987 q^{13} +32.6868 q^{14} +24.0320 q^{15} -73.2669 q^{16} -22.8412 q^{17} -70.3722 q^{18} -36.6127 q^{19} +16.7730 q^{20} +21.4586 q^{21} +200.819 q^{22} -143.179 q^{23} -40.7192 q^{24} +17.4799 q^{25} -189.830 q^{26} -100.558 q^{27} +14.9769 q^{28} -213.016 q^{29} +73.7010 q^{30} -307.040 q^{31} -62.8949 q^{32} +131.836 q^{33} -70.0492 q^{34} +127.223 q^{35} -32.2441 q^{36} +83.7905 q^{37} -112.284 q^{38} -124.622 q^{39} -241.414 q^{40} +59.1767 q^{41} +65.8090 q^{42} +92.0140 q^{44} -273.901 q^{45} -439.100 q^{46} +201.957 q^{47} -147.510 q^{48} -229.400 q^{49} +53.6072 q^{50} -45.9867 q^{51} -86.9790 q^{52} +406.354 q^{53} -308.391 q^{54} +781.624 q^{55} -215.563 q^{56} -73.7131 q^{57} -653.274 q^{58} +164.777 q^{59} +33.7694 q^{60} +150.450 q^{61} -941.626 q^{62} -244.572 q^{63} +393.250 q^{64} -738.853 q^{65} +404.312 q^{66} +169.033 q^{67} -32.0962 q^{68} -288.265 q^{69} +390.166 q^{70} -1039.96 q^{71} +464.092 q^{72} -374.665 q^{73} +256.968 q^{74} +35.1926 q^{75} -51.4477 q^{76} +697.926 q^{77} -382.188 q^{78} +465.164 q^{79} -874.550 q^{80} +417.101 q^{81} +181.482 q^{82} +1307.62 q^{83} +30.1533 q^{84} -272.644 q^{85} -428.869 q^{87} -1324.36 q^{88} +66.7489 q^{89} -839.997 q^{90} -659.736 q^{91} -201.193 q^{92} -618.169 q^{93} +619.359 q^{94} -437.028 q^{95} -126.628 q^{96} -953.889 q^{97} -703.522 q^{98} -1502.58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.317616\pi$
$2$	3.06679	1.08427	0.542137	+	0.840290i	$0.317616\pi$
$3$	2.01332	0.387463	0.193732	−	0.981055i	$-0.437941\pi$
$3$	2.01332	0.387463	0.193732	+	0.981055i	$0.437941\pi$
$4$	1.40518	0.175648
$5$	11.9365	1.06763	0.533816	−	0.845600i	$-0.320757\pi$
$5$	11.9365	1.06763	0.533816	+	0.845600i	$0.320757\pi$
$6$	6.17442	0.420116
$7$	10.6583	0.575495	0.287748	−	0.957706i	$-0.407094\pi$
$7$	10.6583	0.575495	0.287748	+	0.957706i	$0.407094\pi$
$8$	−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	$-0.570945\pi$
$19$	−36.6127	−0.442081	−0.221041	+	0.975265i	$0.570945\pi$
$20$	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	$-0.738890\pi$
$29$	−213.016	−1.36400	−0.682001	+	0.731351i	$0.738890\pi$
$30$	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	$-0.440399\pi$
$37$	83.7905	0.372299	0.186150	+	0.982521i	$0.440399\pi$
$38$	−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	$-0.449529\pi$
$61$	150.450	0.315790	0.157895	+	0.987456i	$0.449529\pi$
$62$	−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	$-0.835341\pi$
$71$	−1039.96	−1.73832	−0.869162	+	0.494528i	$0.835341\pi$
$72$	464.092	0.759635
$73$	−374.665	−0.600701	−0.300351	−	0.953829i	$-0.597104\pi$
$73$	−374.665	−0.600701	−0.300351	+	0.953829i	$0.597104\pi$
$74$	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	$-0.487344\pi$
$89$	66.7489	0.0794986	0.0397493	+	0.999210i	$0.487344\pi$
$90$	−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	$-0.721406\pi$
$113$	−1539.52	−1.28164	−0.640822	+	0.767690i	$0.721406\pi$
$114$	−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	$-0.357297\pi$
$131$	1299.79	0.866894	0.433447	+	0.901179i	$0.357297\pi$
$132$	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	$-0.693699\pi$
$137$	−1833.35	−1.14331	−0.571656	+	0.820493i	$0.693699\pi$
$138$	−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	$-0.141817\pi$
$149$	3282.46	1.80476	0.902382	+	0.430938i	$0.141817\pi$
$150$	107.928	0.0587488
$151$	−124.151	−0.0669093	−0.0334546	−	0.999440i	$-0.510651\pi$
$151$	−124.151	−0.0669093	−0.0334546	+	0.999440i	$0.510651\pi$
$152$	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	$-0.591883\pi$
$157$	−1119.99	−0.569332	−0.284666	+	0.958627i	$0.591883\pi$
$158$	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	$-0.737040\pi$
$163$	−2820.81	−1.35548	−0.677739	+	0.735303i	$0.737040\pi$
$164$	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	$-0.422522\pi$
$179$	1154.35	0.482014	0.241007	+	0.970523i	$0.422522\pi$
$180$	−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	$-0.649464\pi$
$191$	−2388.85	−0.904979	−0.452490	+	0.891770i	$0.649464\pi$
$192$	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	$-0.313094\pi$
$199$	3110.52	1.10804	0.554018	+	0.832505i	$0.313094\pi$
$200$	−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	$-0.557505\pi$
$211$	−1101.39	−0.359350	−0.179675	+	0.983726i	$0.557505\pi$
$212$	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	$-0.618034\pi$
$223$	−2413.48	−0.724748	−0.362374	+	0.932033i	$0.618034\pi$
$224$	−670.354	−0.199955
$225$	−401.104	−0.118846
$226$	−4721.38	−1.38965
$227$	−2233.25	−0.652979	−0.326489	−	0.945201i	$-0.605866\pi$
$227$	−2233.25	−0.652979	−0.326489	+	0.945201i	$0.605866\pi$
$228$	−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	$-0.0576135\pi$
$233$	6996.98	1.96733	0.983665	+	0.180012i	$0.0576135\pi$
$234$	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	$-0.365934\pi$
$241$	3059.19	0.817676	0.408838	+	0.912607i	$0.365934\pi$
$242$	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	$-0.565949\pi$
$257$	−1695.01	−0.411409	−0.205704	+	0.978614i	$0.565949\pi$
$258$	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	$-0.549780\pi$
$263$	−1328.61	−0.311505	−0.155752	+	0.987796i	$0.549780\pi$
$264$	−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	$-0.707350\pi$
$277$	−5590.40	−1.21262	−0.606308	+	0.795230i	$0.707350\pi$
$278$	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	$-0.782962\pi$
$313$	−8598.81	−1.55282	−0.776411	+	0.630226i	$0.782962\pi$
$314$	−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	$-0.491634\pi$
$331$	316.494	0.0525562	0.0262781	+	0.999655i	$0.491634\pi$
$332$	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	$-0.410470\pi$
$347$	3588.41	0.555147	0.277573	+	0.960704i	$0.410470\pi$
$348$	−602.640	−0.0928301
$349$	10696.8	1.64065	0.820325	−	0.571898i	$-0.193793\pi$
$349$	10696.8	1.64065	0.820325	+	0.571898i	$0.193793\pi$
$350$	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	$-0.585186\pi$
$373$	−3809.92	−0.528874	−0.264437	+	0.964403i	$0.585186\pi$
$374$	−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	$-0.428329\pi$
$383$	3346.93	0.446528	0.223264	+	0.974758i	$0.428329\pi$
$384$	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	$-0.388310\pi$
$389$	5274.35	0.687455	0.343727	+	0.939069i	$0.388310\pi$
$390$	−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	$-0.233608\pi$
$409$	12284.3	1.48513	0.742567	+	0.669772i	$0.233608\pi$
$410$	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	$-0.452491\pi$
$419$	2550.74	0.297403	0.148701	+	0.988882i	$0.452491\pi$
$420$	359.925	0.0418155
$421$	−4680.41	−0.541827	−0.270913	−	0.962604i	$-0.587326\pi$
$421$	−4680.41	−0.541827	−0.270913	+	0.962604i	$0.587326\pi$
$422$	−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	$-0.713438\pi$
$433$	−11197.9	−1.24281	−0.621407	+	0.783488i	$0.713438\pi$
$434$	−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	$-0.254936\pi$
$449$	13244.7	1.39211	0.696056	+	0.717987i	$0.254936\pi$
$450$	−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	$-0.366792\pi$
$457$	7940.24	0.812754	0.406377	+	0.913705i	$0.366792\pi$
$458$	−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	$-0.350010\pi$
$463$	9045.26	0.907924	0.453962	+	0.891021i	$0.350010\pi$
$464$	15607.0	1.56150
$465$	−7378.78	−0.735876
$466$	21458.3	2.13312
$467$	11982.6	1.18734	0.593671	−	0.804708i	$-0.297678\pi$
$467$	11982.6	1.18734	0.593671	+	0.804708i	$0.297678\pi$
$468$	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	$-0.702208\pi$
$491$	−12911.8	−1.18677	−0.593383	+	0.804920i	$0.702208\pi$
$492$	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	$-0.400654\pi$
$499$	6845.56	0.614127	0.307064	+	0.951689i	$0.400654\pi$
$500$	−1803.43	−0.161304
$501$	3916.04	0.349213
$502$	18723.4	1.66468
$503$	−5914.10	−0.524248	−0.262124	−	0.965034i	$-0.584423\pi$
$503$	−5914.10	−0.524248	−0.262124	+	0.965034i	$0.584423\pi$
$504$	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	$-0.526575\pi$
$521$	−1983.41	−0.166785	−0.0833923	+	0.996517i	$0.526575\pi$
$522$	14990.4	1.25692
$523$	588.084	0.0491685	0.0245843	−	0.999698i	$-0.492174\pi$
$523$	588.084	0.0491685	0.0245843	+	0.999698i	$0.492174\pi$
$524$	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	$-0.146223\pi$
$571$	24459.8	1.79266	0.896330	+	0.443387i	$0.146223\pi$
$572$	−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	$-0.203038\pi$
$577$	22269.4	1.60674	0.803370	+	0.595480i	$0.203038\pi$
$578$	−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	$-0.181664\pi$
$587$	23935.8	1.68303	0.841514	+	0.540235i	$0.181664\pi$
$588$	−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	$-0.838209\pi$
$593$	−25229.9	−1.74717	−0.873583	+	0.486675i	$0.838209\pi$
$594$	−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	$-0.715402\pi$
$601$	−18453.3	−1.25246	−0.626228	+	0.779640i	$0.715402\pi$
$602$	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	$-0.852175\pi$
$607$	−26742.0	−1.78818	−0.894088	+	0.447892i	$0.852175\pi$
$608$	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	$-0.600312\pi$
$631$	−9825.75	−0.619900	−0.309950	+	0.950753i	$0.600312\pi$
$632$	−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	$-0.553247\pi$
$641$	−5404.26	−0.333004	−0.166502	+	0.986041i	$0.553247\pi$
$642$	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	$-0.410380\pi$
$647$	9145.13	0.555691	0.277846	+	0.960626i	$0.410380\pi$
$648$	−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	$-0.498462\pi$
$653$	161.209	0.00966091	0.00483046	+	0.999988i	$0.498462\pi$
$654$	−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	$-0.603959\pi$
$673$	−11202.5	−0.641642	−0.320821	+	0.947140i	$0.603959\pi$
$674$	−9125.74	−0.521529
$675$	−1757.75	−0.100231
$676$	2296.70	0.130672
$677$	29615.8	1.68128	0.840640	−	0.541594i	$-0.182179\pi$
$677$	29615.8	1.68128	0.840640	+	0.541594i	$0.182179\pi$
$678$	−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	$-0.704800\pi$
$691$	−21794.1	−1.19983	−0.599917	+	0.800062i	$0.704800\pi$
$692$	−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	$-0.569094\pi$
$727$	−8443.21	−0.430731	−0.215366	+	0.976534i	$0.569094\pi$
$728$	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	$-0.573664\pi$
$733$	−9103.47	−0.458723	−0.229362	+	0.973341i	$0.573664\pi$
$734$	−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	$-0.509476\pi$
$739$	−1195.87	−0.0595275	−0.0297638	+	0.999557i	$0.509476\pi$
$740$	1405.42	0.0698164
$741$	4562.75	0.226203
$742$	13282.4	0.657160
$743$	18356.6	0.906379	0.453189	−	0.891414i	$-0.350286\pi$
$743$	18356.6	0.906379	0.453189	+	0.891414i	$0.350286\pi$
$744$	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	$-0.860918\pi$
$751$	−37294.3	−1.81210	−0.906052	+	0.423167i	$0.860918\pi$
$752$	−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	$-0.616062\pi$
$757$	−14854.1	−0.713187	−0.356593	+	0.934260i	$0.616062\pi$
$758$	7517.27	0.360211
$759$	−18876.1	−0.902714
$760$	8838.84	0.421867
$761$	35725.3	1.70176	0.850881	−	0.525358i	$-0.176069\pi$
$761$	35725.3	1.70176	0.850881	+	0.525358i	$0.176069\pi$
$762$	−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	$-0.377980\pi$
$773$	16076.5	0.748034	0.374017	+	0.927422i	$0.377980\pi$
$774$	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	$-0.689000\pi$
$811$	−25843.3	−1.11897	−0.559484	+	0.828841i	$0.689000\pi$
$812$	−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	$-0.530908\pi$
$829$	−4628.02	−0.193894	−0.0969468	+	0.995290i	$0.530908\pi$
$830$	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	$-0.295571\pi$
$839$	29113.1	1.19797	0.598984	+	0.800761i	$0.295571\pi$
$840$	−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	$-0.632899\pi$
$859$	−20417.4	−0.810981	−0.405490	+	0.914099i	$0.632899\pi$
$860$	0	0
$861$	1269.85	0.0502629
$862$	20547.9	0.811907
$863$	11193.8	0.441532	0.220766	−	0.975327i	$-0.429144\pi$
$863$	11193.8	0.441532	0.220766	+	0.975327i	$0.429144\pi$
$864$	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	$-0.828348\pi$
$887$	−45336.4	−1.71618	−0.858088	+	0.513502i	$0.828348\pi$
$888$	−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	$-0.414232\pi$
$911$	14639.1	0.532398	0.266199	+	0.963918i	$0.414232\pi$
$912$	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	$-0.565865\pi$
$929$	−11634.6	−0.410892	−0.205446	+	0.978668i	$0.565865\pi$
$930$	−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	$-0.406590\pi$
$937$	16593.3	0.578527	0.289263	+	0.957250i	$0.406590\pi$
$938$	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	$-0.528795\pi$
$953$	−5315.57	−0.180680	−0.0903400	+	0.995911i	$0.528795\pi$
$954$	−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	$-0.631558\pi$
$983$	−24756.7	−0.803271	−0.401636	+	0.915800i	$0.631558\pi$
$984$	−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	$-0.605643\pi$
$991$	−20329.5	−0.651654	−0.325827	+	0.945429i	$0.605643\pi$
$992$	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	$-0.807326\pi$
$997$	−51774.9	−1.64466	−0.822330	+	0.569011i	$0.807326\pi$
$998$	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.j.1.36	yes	50
43.42	odd	2		1849.4.a.i.1.15	✓	50

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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