LMFDB - Embedded newform 1849.4.a.i.1.21

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			1.21
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)

$f(q)$	$=$	$q-1.06456 q^{2} -7.81960 q^{3} -6.86672 q^{4} -6.14081 q^{5} +8.32441 q^{6} +5.24909 q^{7} +15.8265 q^{8} +34.1462 q^{9} +O(q^{10})$	\(q-1.06456 q^{2} -7.81960 q^{3} -6.86672 q^{4} -6.14081 q^{5} +8.32441 q^{6} +5.24909 q^{7} +15.8265 q^{8} +34.1462 q^{9} +6.53724 q^{10} -14.5177 q^{11} +53.6950 q^{12} -49.9353 q^{13} -5.58795 q^{14} +48.0187 q^{15} +38.0856 q^{16} +75.6572 q^{17} -36.3506 q^{18} -128.126 q^{19} +42.1672 q^{20} -41.0458 q^{21} +15.4549 q^{22} -131.825 q^{23} -123.757 q^{24} -87.2904 q^{25} +53.1589 q^{26} -55.8805 q^{27} -36.0440 q^{28} +36.6667 q^{29} -51.1187 q^{30} -251.659 q^{31} -167.156 q^{32} +113.523 q^{33} -80.5414 q^{34} -32.2337 q^{35} -234.472 q^{36} +264.673 q^{37} +136.397 q^{38} +390.474 q^{39} -97.1874 q^{40} -0.0646232 q^{41} +43.6956 q^{42} +99.6890 q^{44} -209.685 q^{45} +140.335 q^{46} +346.105 q^{47} -297.814 q^{48} -315.447 q^{49} +92.9256 q^{50} -591.610 q^{51} +342.892 q^{52} +468.928 q^{53} +59.4880 q^{54} +89.1505 q^{55} +83.0745 q^{56} +1001.89 q^{57} -39.0338 q^{58} +586.702 q^{59} -329.731 q^{60} +592.038 q^{61} +267.906 q^{62} +179.236 q^{63} -126.738 q^{64} +306.643 q^{65} -120.851 q^{66} -472.805 q^{67} -519.517 q^{68} +1030.82 q^{69} +34.3146 q^{70} +548.204 q^{71} +540.414 q^{72} +328.014 q^{73} -281.759 q^{74} +682.576 q^{75} +879.804 q^{76} -76.2047 q^{77} -415.682 q^{78} +801.655 q^{79} -233.876 q^{80} -484.984 q^{81} +0.0687950 q^{82} -1348.75 q^{83} +281.850 q^{84} -464.597 q^{85} -286.719 q^{87} -229.764 q^{88} +1491.49 q^{89} +223.222 q^{90} -262.115 q^{91} +905.205 q^{92} +1967.88 q^{93} -368.448 q^{94} +786.796 q^{95} +1307.09 q^{96} -281.945 q^{97} +335.811 q^{98} -495.724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.06456	−0.376378	−0.188189	−	0.982133i	$-0.560262\pi$
$2$	−1.06456	−0.376378	−0.188189	+	0.982133i	$0.560262\pi$
$3$	−7.81960	−1.50488	−0.752442	−	0.658659i	$-0.771124\pi$
$3$	−7.81960	−1.50488	−0.752442	+	0.658659i	$0.771124\pi$
$4$	−6.86672	−0.858340
$5$	−6.14081	−0.549251	−0.274626	−	0.961551i	$-0.588554\pi$
$5$	−6.14081	−0.549251	−0.274626	+	0.961551i	$0.588554\pi$
$6$	8.32441	0.566404
$7$	5.24909	0.283424	0.141712	−	0.989908i	$-0.454739\pi$
$7$	5.24909	0.283424	0.141712	+	0.989908i	$0.454739\pi$
$8$	15.8265	0.699438
$9$	34.1462	1.26467
$10$	6.53724	0.206726
$11$	−14.5177	−0.397932	−0.198966	−	0.980006i	$-0.563758\pi$
$11$	−14.5177	−0.397932	−0.198966	+	0.980006i	$0.563758\pi$
$12$	53.6950	1.29170
$13$	−49.9353	−1.06535	−0.532675	−	0.846320i	$-0.678813\pi$
$13$	−49.9353	−1.06535	−0.532675	+	0.846320i	$0.678813\pi$
$14$	−5.58795	−0.106675
$15$	48.0187	0.826559
$16$	38.0856	0.595087
$17$	75.6572	1.07939	0.539693	−	0.841862i	$-0.318540\pi$
$17$	75.6572	1.07939	0.539693	+	0.841862i	$0.318540\pi$
$18$	−36.3506	−0.475995
$19$	−128.126	−1.54706	−0.773528	−	0.633762i	$-0.781510\pi$
$19$	−128.126	−1.54706	−0.773528	+	0.633762i	$0.781510\pi$
$20$	42.1672	0.471444
$21$	−41.0458	−0.426520
$22$	15.4549	0.149773
$23$	−131.825	−1.19510	−0.597552	−	0.801830i	$-0.703860\pi$
$23$	−131.825	−1.19510	−0.597552	+	0.801830i	$0.703860\pi$
$24$	−123.757	−1.05257
$25$	−87.2904	−0.698323
$26$	53.1589	0.400974
$27$	−55.8805	−0.398304
$28$	−36.0440	−0.243274
$29$	36.6667	0.234788	0.117394	−	0.993085i	$-0.462546\pi$
$29$	36.6667	0.234788	0.117394	+	0.993085i	$0.462546\pi$
$30$	−51.1187	−0.311098
$31$	−251.659	−1.45804	−0.729022	−	0.684491i	$-0.760025\pi$
$31$	−251.659	−1.45804	−0.729022	+	0.684491i	$0.760025\pi$
$32$	−167.156	−0.923415
$33$	113.523	0.598841
$34$	−80.5414	−0.406257
$35$	−32.2337	−0.155671
$36$	−234.472	−1.08552
$37$	264.673	1.17600	0.588000	−	0.808861i	$-0.299916\pi$
$37$	264.673	1.17600	0.588000	+	0.808861i	$0.299916\pi$
$38$	136.397	0.582277
$39$	390.474	1.60323
$40$	−97.1874	−0.384167
$41$	−0.0646232	−0.000246157 0	−0.000123079	−	1.00000i	$-0.500039\pi$
$41$	−0.0646232	−0.000246157 0	−0.000123079		1.00000i	$0.500039\pi$
$42$	43.6956	0.160533
$43$	0	0
$43$	0	0
$44$	99.6890	0.341561
$45$	−209.685	−0.694624
$46$	140.335	0.449810
$47$	346.105	1.07414	0.537070	−	0.843538i	$-0.319531\pi$
$47$	346.105	1.07414	0.537070	+	0.843538i	$0.319531\pi$
$48$	−297.814	−0.895537
$49$	−315.447	−0.919671
$50$	92.9256	0.262833
$51$	−591.610	−1.62435
$52$	342.892	0.914433
$53$	468.928	1.21532	0.607662	−	0.794196i	$-0.292107\pi$
$53$	468.928	1.21532	0.607662	+	0.794196i	$0.292107\pi$
$54$	59.4880	0.149913
$55$	89.1505	0.218565
$56$	83.0745	0.198237
$57$	1001.89	2.32814
$58$	−39.0338	−0.0883688
$59$	586.702	1.29461	0.647306	−	0.762230i	$-0.275895\pi$
$59$	586.702	1.29461	0.647306	+	0.762230i	$0.275895\pi$
$60$	−329.731	−0.709468
$61$	592.038	1.24267	0.621333	−	0.783546i	$-0.286591\pi$
$61$	592.038	1.24267	0.621333	+	0.783546i	$0.286591\pi$
$62$	267.906	0.548775
$63$	179.236	0.358439
$64$	−126.738	−0.247534
$65$	306.643	0.585145
$66$	−120.851	−0.225390
$67$	−472.805	−0.862125	−0.431062	−	0.902322i	$-0.641861\pi$
$67$	−472.805	−0.862125	−0.431062	+	0.902322i	$0.641861\pi$
$68$	−519.517	−0.926481
$69$	1030.82	1.79849
$70$	34.3146	0.0585911
$71$	548.204	0.916336	0.458168	−	0.888866i	$-0.348506\pi$
$71$	548.204	0.916336	0.458168	+	0.888866i	$0.348506\pi$
$72$	540.414	0.884561
$73$	328.014	0.525905	0.262953	−	0.964809i	$-0.415304\pi$
$73$	328.014	0.525905	0.262953	+	0.964809i	$0.415304\pi$
$74$	−281.759	−0.442620
$75$	682.576	1.05090
$76$	879.804	1.32790
$77$	−76.2047	−0.112784
$78$	−415.682	−0.603419
$79$	801.655	1.14169	0.570843	−	0.821059i	$-0.306616\pi$
$79$	801.655	1.14169	0.570843	+	0.821059i	$0.306616\pi$
$80$	−233.876	−0.326852
$81$	−484.984	−0.665273
$82$	0.0687950	9.26480e−5 0
$83$	−1348.75	−1.78368	−0.891838	−	0.452356i	$-0.850584\pi$
$83$	−1348.75	−1.78368	−0.891838	+	0.452356i	$0.850584\pi$
$84$	281.850	0.366099
$85$	−464.597	−0.592854
$86$	0	0
$87$	−286.719	−0.353328
$88$	−229.764	−0.278329
$89$	1491.49	1.77638	0.888189	−	0.459478i	$-0.151964\pi$
$89$	1491.49	1.77638	0.888189	+	0.459478i	$0.151964\pi$
$90$	223.222	0.261441
$91$	−262.115	−0.301946
$92$	905.205	1.02581
$93$	1967.88	2.19419
$94$	−368.448	−0.404282
$95$	786.796	0.849722
$96$	1307.09	1.38963
$97$	−281.945	−0.295125	−0.147563	−	0.989053i	$-0.547143\pi$
$97$	−281.945	−0.295125	−0.147563	+	0.989053i	$0.547143\pi$
$98$	335.811	0.346143
$99$	−495.724	−0.503254
$100$	599.399	0.599399
$101$	1102.45	1.08612	0.543060	−	0.839694i	$-0.317266\pi$
$101$	1102.45	1.08612	0.543060	+	0.839694i	$0.317266\pi$
$102$	629.802	0.611370
$103$	−1857.59	−1.77703	−0.888514	−	0.458849i	$-0.848262\pi$
$103$	−1857.59	−1.77703	−0.888514	+	0.458849i	$0.848262\pi$
$104$	−790.299	−0.745146
$105$	252.055	0.234267
$106$	−499.200	−0.457421
$107$	187.602	0.169497	0.0847487	−	0.996402i	$-0.472991\pi$
$107$	187.602	0.169497	0.0847487	+	0.996402i	$0.472991\pi$
$108$	383.716	0.341880
$109$	116.470	0.102347	0.0511733	−	0.998690i	$-0.483704\pi$
$109$	116.470	0.102347	0.0511733	+	0.998690i	$0.483704\pi$
$110$	−94.9058	−0.0822628
$111$	−2069.64	−1.76974
$112$	199.915	0.168662
$113$	−1240.45	−1.03267	−0.516334	−	0.856387i	$-0.672704\pi$
$113$	−1240.45	−1.03267	−0.516334	+	0.856387i	$0.672704\pi$
$114$	−1066.57	−0.876260
$115$	809.512	0.656412
$116$	−251.780	−0.201528
$117$	−1705.10	−1.34732
$118$	−624.578	−0.487263
$119$	397.132	0.305924
$120$	759.967	0.578126
$121$	−1120.24	−0.841650
$122$	−630.258	−0.467712
$123$	0.505328	0.000370438 0
$124$	1728.07	1.25150
$125$	1303.64	0.932806
$126$	−190.807	−0.134909
$127$	92.3145	0.0645007	0.0322503	−	0.999480i	$-0.489733\pi$
$127$	92.3145	0.0645007	0.0322503	+	0.999480i	$0.489733\pi$
$128$	1472.17	1.01658
$129$	0	0
$130$	−326.439	−0.220235
$131$	1721.43	1.14811	0.574055	−	0.818817i	$-0.305370\pi$
$131$	1721.43	1.14811	0.574055	+	0.818817i	$0.305370\pi$
$132$	−779.528	−0.514009
$133$	−672.544	−0.438473
$134$	503.328	0.324485
$135$	343.152	0.218769
$136$	1197.39	0.754964
$137$	1677.68	1.04624	0.523118	−	0.852261i	$-0.324769\pi$
$137$	1677.68	1.04624	0.523118	+	0.852261i	$0.324769\pi$
$138$	−1097.36	−0.676912
$139$	2819.71	1.72061	0.860306	−	0.509778i	$-0.170272\pi$
$139$	2819.71	1.72061	0.860306	+	0.509778i	$0.170272\pi$
$140$	221.340	0.133619
$141$	−2706.40	−1.61646
$142$	−583.594	−0.344888
$143$	724.946	0.423937
$144$	1300.48	0.752592
$145$	−225.163	−0.128957
$146$	−349.189	−0.197939
$147$	2466.67	1.38400
$148$	−1817.43	−1.00941
$149$	971.666	0.534241	0.267121	−	0.963663i	$-0.413928\pi$
$149$	971.666	0.534241	0.267121	+	0.963663i	$0.413928\pi$
$150$	−726.641	−0.395533
$151$	−876.678	−0.472470	−0.236235	−	0.971696i	$-0.575914\pi$
$151$	−876.678	−0.472470	−0.236235	+	0.971696i	$0.575914\pi$
$152$	−2027.78	−1.08207
$153$	2583.41	1.36507
$154$	81.1242	0.0424492
$155$	1545.39	0.800832
$156$	−2681.28	−1.37611
$157$	2191.29	1.11391	0.556955	−	0.830543i	$-0.311970\pi$
$157$	2191.29	1.11391	0.556955	+	0.830543i	$0.311970\pi$
$158$	−853.407	−0.429705
$159$	−3666.83	−1.82892
$160$	1026.47	0.507187
$161$	−691.961	−0.338721
$162$	516.293	0.250394
$163$	212.798	0.102255	0.0511276	−	0.998692i	$-0.483718\pi$
$163$	212.798	0.102255	0.0511276	+	0.998692i	$0.483718\pi$
$164$	0.443749	0.000211287 0
$165$	−697.122	−0.328914
$166$	1435.83	0.671335
$167$	268.336	0.124338	0.0621691	−	0.998066i	$-0.480198\pi$
$167$	268.336	0.124338	0.0621691	+	0.998066i	$0.480198\pi$
$168$	−649.610	−0.298324
$169$	296.533	0.134972
$170$	494.590	0.223137
$171$	−4375.01	−1.95652
$172$	0	0
$173$	−310.456	−0.136437	−0.0682183	−	0.997670i	$-0.521731\pi$
$173$	−310.456	−0.136437	−0.0682183	+	0.997670i	$0.521731\pi$
$174$	305.229	0.132985
$175$	−458.195	−0.197922
$176$	−552.915	−0.236804
$177$	−4587.78	−1.94824
$178$	−1587.78	−0.668589
$179$	−3308.82	−1.38163	−0.690817	−	0.723030i	$-0.742749\pi$
$179$	−3308.82	−1.38163	−0.690817	+	0.723030i	$0.742749\pi$
$180$	1439.85	0.596223
$181$	1215.01	0.498957	0.249479	−	0.968380i	$-0.419741\pi$
$181$	1215.01	0.498957	0.249479	+	0.968380i	$0.419741\pi$
$182$	279.036	0.113646
$183$	−4629.50	−1.87007
$184$	−2086.32	−0.835901
$185$	−1625.31	−0.645919
$186$	−2094.92	−0.825842
$187$	−1098.37	−0.429523
$188$	−2376.61	−0.921977
$189$	−293.322	−0.112889
$190$	−837.589	−0.319816
$191$	3262.00	1.23576	0.617880	−	0.786273i	$-0.287992\pi$
$191$	3262.00	1.23576	0.617880	+	0.786273i	$0.287992\pi$
$192$	991.038	0.372511
$193$	−596.437	−0.222448	−0.111224	−	0.993795i	$-0.535477\pi$
$193$	−596.437	−0.222448	−0.111224	+	0.993795i	$0.535477\pi$
$194$	300.146	0.111079
$195$	−2397.83	−0.880575
$196$	2166.09	0.789390
$197$	3156.54	1.14160	0.570798	−	0.821091i	$-0.306634\pi$
$197$	3156.54	1.14160	0.570798	+	0.821091i	$0.306634\pi$
$198$	527.727	0.189414
$199$	1617.31	0.576120	0.288060	−	0.957612i	$-0.406990\pi$
$199$	1617.31	0.576120	0.288060	+	0.957612i	$0.406990\pi$
$200$	−1381.50	−0.488434
$201$	3697.15	1.29740
$202$	−1173.62	−0.408791
$203$	192.467	0.0665445
$204$	4062.42	1.39425
$205$	0.396839	0.000135202 0
$206$	1977.51	0.668834
$207$	−4501.32	−1.51142
$208$	−1901.81	−0.633977
$209$	1860.09	0.615623
$210$	−268.326	−0.0881728
$211$	−3160.29	−1.03110	−0.515552	−	0.856858i	$-0.672413\pi$
$211$	−3160.29	−1.03110	−0.515552	+	0.856858i	$0.672413\pi$
$212$	−3220.00	−1.04316
$213$	−4286.74	−1.37898
$214$	−199.713	−0.0637950
$215$	0	0
$216$	−884.391	−0.278589
$217$	−1320.98	−0.413245
$218$	−123.989	−0.0385209
$219$	−2564.94	−0.791426
$220$	−612.171	−0.187603
$221$	−3777.97	−1.14993
$222$	2203.25	0.666091
$223$	3030.41	0.910006	0.455003	−	0.890490i	$-0.349638\pi$
$223$	3030.41	0.910006	0.455003	+	0.890490i	$0.349638\pi$
$224$	−877.417	−0.261718
$225$	−2980.64	−0.883152
$226$	1320.53	0.388673
$227$	−4911.55	−1.43608	−0.718041	−	0.696000i	$-0.754961\pi$
$227$	−4911.55	−1.43608	−0.718041	+	0.696000i	$0.754961\pi$
$228$	−6879.72	−1.99833
$229$	−5122.08	−1.47806	−0.739031	−	0.673671i	$-0.764716\pi$
$229$	−5122.08	−1.47806	−0.739031	+	0.673671i	$0.764716\pi$
$230$	−861.771	−0.247059
$231$	595.891	0.169726
$232$	580.305	0.164219
$233$	−1455.82	−0.409332	−0.204666	−	0.978832i	$-0.565611\pi$
$233$	−1455.82	−0.409332	−0.204666	+	0.978832i	$0.565611\pi$
$234$	1815.18	0.507102
$235$	−2125.37	−0.589973
$236$	−4028.72	−1.11122
$237$	−6268.62	−1.71810
$238$	−422.769	−0.115143
$239$	5646.52	1.52821	0.764107	−	0.645089i	$-0.223180\pi$
$239$	5646.52	1.52821	0.764107	+	0.645089i	$0.223180\pi$
$240$	1828.82	0.491875
$241$	−2920.77	−0.780677	−0.390339	−	0.920671i	$-0.627642\pi$
$241$	−2920.77	−0.780677	−0.390339	+	0.920671i	$0.627642\pi$
$242$	1192.56	0.316778
$243$	5301.16	1.39946
$244$	−4065.36	−1.06663
$245$	1937.10	0.505130
$246$	−0.537950	−0.000139425 0
$247$	6398.00	1.64816
$248$	−3982.88	−1.01981
$249$	10546.7	2.68422
$250$	−1387.79	−0.351087
$251$	−2486.12	−0.625189	−0.312594	−	0.949887i	$-0.601198\pi$
$251$	−2486.12	−0.625189	−0.312594	+	0.949887i	$0.601198\pi$
$252$	−1230.77	−0.307663
$253$	1913.79	0.475570
$254$	−98.2740	−0.0242766
$255$	3632.96	0.892177
$256$	−553.304	−0.135084
$257$	−7326.49	−1.77826	−0.889132	−	0.457650i	$-0.848691\pi$
$257$	−7326.49	−1.77826	−0.889132	+	0.457650i	$0.848691\pi$
$258$	0	0
$259$	1389.29	0.333307
$260$	−2105.63	−0.502253
$261$	1252.03	0.296930
$262$	−1832.56	−0.432123
$263$	−251.220	−0.0589008	−0.0294504	−	0.999566i	$-0.509376\pi$
$263$	−251.220	−0.0589008	−0.0294504	+	0.999566i	$0.509376\pi$
$264$	1796.66	0.418852
$265$	−2879.60	−0.667518
$266$	715.961	0.165031
$267$	−11662.9	−2.67324
$268$	3246.62	0.739996
$269$	−4741.17	−1.07463	−0.537313	−	0.843383i	$-0.680560\pi$
$269$	−4741.17	−1.07463	−0.537313	+	0.843383i	$0.680560\pi$
$270$	−365.304	−0.0823397
$271$	3799.34	0.851637	0.425819	−	0.904809i	$-0.359986\pi$
$271$	3799.34	0.851637	0.425819	+	0.904809i	$0.359986\pi$
$272$	2881.45	0.642329
$273$	2049.63	0.454394
$274$	−1785.99	−0.393779
$275$	1267.26	0.277885
$276$	−7078.34	−1.54372
$277$	4768.63	1.03437	0.517183	−	0.855875i	$-0.326981\pi$
$277$	4768.63	1.03437	0.517183	+	0.855875i	$0.326981\pi$
$278$	−3001.75	−0.647600
$279$	−8593.21	−1.84395
$280$	−510.145	−0.108882
$281$	2410.33	0.511703	0.255851	−	0.966716i	$-0.417644\pi$
$281$	2410.33	0.511703	0.255851	+	0.966716i	$0.417644\pi$
$282$	2881.12	0.608398
$283$	−8196.95	−1.72176	−0.860880	−	0.508808i	$-0.830086\pi$
$283$	−8196.95	−1.72176	−0.860880	+	0.508808i	$0.830086\pi$
$284$	−3764.36	−0.786528
$285$	−6152.44	−1.27873
$286$	−771.746	−0.159560
$287$	−0.339213	−6.97669e−5 0
$288$	−5707.74	−1.16782
$289$	811.018	0.165076
$290$	239.699	0.0485366
$291$	2204.70	0.444129
$292$	−2252.38	−0.451405
$293$	4556.22	0.908455	0.454227	−	0.890886i	$-0.349915\pi$
$293$	4556.22	0.908455	0.454227	+	0.890886i	$0.349915\pi$
$294$	−2625.91	−0.520906
$295$	−3602.83	−0.711067
$296$	4188.84	0.822538
$297$	811.257	0.158498
$298$	−1034.39	−0.201076
$299$	6582.71	1.27320
$300$	−4687.06	−0.902025
$301$	0	0
$302$	933.273	0.177827
$303$	−8620.74	−1.63448
$304$	−4879.74	−0.920633
$305$	−3635.59	−0.682536
$306$	−2750.18	−0.513783
$307$	592.948	0.110232	0.0551162	−	0.998480i	$-0.482447\pi$
$307$	592.948	0.110232	0.0551162	+	0.998480i	$0.482447\pi$
$308$	523.276	0.0968066
$309$	14525.6	2.67422
$310$	−1645.16	−0.301415
$311$	462.957	0.0844113	0.0422056	−	0.999109i	$-0.486562\pi$
$311$	462.957	0.0844113	0.0422056	+	0.999109i	$0.486562\pi$
$312$	6179.83	1.12136
$313$	−2003.19	−0.361748	−0.180874	−	0.983506i	$-0.557893\pi$
$313$	−2003.19	−0.361748	−0.180874	+	0.983506i	$0.557893\pi$
$314$	−2332.75	−0.419251
$315$	−1100.66	−0.196873
$316$	−5504.74	−0.979955
$317$	7514.15	1.33135	0.665673	−	0.746244i	$-0.268145\pi$
$317$	7514.15	1.33135	0.665673	+	0.746244i	$0.268145\pi$
$318$	3903.55	0.688365
$319$	−532.317	−0.0934295
$320$	778.272	0.135959
$321$	−1466.98	−0.255074
$322$	736.631	0.127487
$323$	−9693.64	−1.66987
$324$	3330.25	0.571031
$325$	4358.87	0.743959
$326$	−226.535	−0.0384866
$327$	−910.747	−0.154020
$328$	−1.02276	−0.000172172 0
$329$	1816.74	0.304437
$330$	742.125	0.123796
$331$	45.1750	0.00750164	0.00375082	−	0.999993i	$-0.498806\pi$
$331$	45.1750	0.00750164	0.00375082	+	0.999993i	$0.498806\pi$
$332$	9261.52	1.53100
$333$	9037.58	1.48726
$334$	−285.659	−0.0467981
$335$	2903.41	0.473523
$336$	−1563.25	−0.253817
$337$	−3243.02	−0.524209	−0.262105	−	0.965039i	$-0.584417\pi$
$337$	−3243.02	−0.524209	−0.262105	+	0.965039i	$0.584417\pi$
$338$	−315.676	−0.0508003
$339$	9699.82	1.55405
$340$	3190.26	0.508870
$341$	3653.51	0.580202
$342$	4657.45	0.736391
$343$	−3456.25	−0.544081
$344$	0	0
$345$	−6330.06	−0.987824
$346$	330.498	0.0513517
$347$	3928.20	0.607715	0.303857	−	0.952718i	$-0.401725\pi$
$347$	3928.20	0.607715	0.303857	+	0.952718i	$0.401725\pi$
$348$	1968.82	0.303275
$349$	9860.04	1.51231	0.756154	−	0.654393i	$-0.227076\pi$
$349$	9860.04	1.51231	0.756154	+	0.654393i	$0.227076\pi$
$350$	487.775	0.0744933
$351$	2790.41	0.424333
$352$	2426.72	0.367456
$353$	3705.00	0.558633	0.279316	−	0.960199i	$-0.409892\pi$
$353$	3705.00	0.558633	0.279316	+	0.960199i	$0.409892\pi$
$354$	4883.95	0.733274
$355$	−3366.42	−0.503299
$356$	−10241.6	−1.52474
$357$	−3105.41	−0.460380
$358$	3522.42	0.520016
$359$	3869.65	0.568892	0.284446	−	0.958692i	$-0.408190\pi$
$359$	3869.65	0.568892	0.284446	+	0.958692i	$0.408190\pi$
$360$	−3318.58	−0.485846
$361$	9557.21	1.39338
$362$	−1293.45	−0.187796
$363$	8759.80	1.26659
$364$	1799.87	0.259172
$365$	−2014.27	−0.288854
$366$	4928.36	0.703852
$367$	−10876.6	−1.54702	−0.773508	−	0.633786i	$-0.781500\pi$
$367$	−10876.6	−1.54702	−0.773508	+	0.633786i	$0.781500\pi$
$368$	−5020.63	−0.711191
$369$	−2.20664	−0.000311309 0
$370$	1730.23	0.243109
$371$	2461.44	0.344452
$372$	−13512.9	−1.88336
$373$	10131.1	1.40634	0.703172	−	0.711020i	$-0.251766\pi$
$373$	10131.1	1.40634	0.703172	+	0.711020i	$0.251766\pi$
$374$	1169.28	0.161663
$375$	−10193.9	−1.40376
$376$	5477.62	0.751294
$377$	−1830.96	−0.250131
$378$	312.258	0.0424889
$379$	−8606.22	−1.16642	−0.583208	−	0.812323i	$-0.698203\pi$
$379$	−8606.22	−1.16642	−0.583208	+	0.812323i	$0.698203\pi$
$380$	−5402.71	−0.729350
$381$	−721.862	−0.0970660
$382$	−3472.58	−0.465112
$383$	−3345.75	−0.446370	−0.223185	−	0.974776i	$-0.571645\pi$
$383$	−3345.75	−0.446370	−0.223185	+	0.974776i	$0.571645\pi$
$384$	−11511.8	−1.52984
$385$	467.959	0.0619465
$386$	634.941	0.0837245
$387$	0	0
$388$	1936.03	0.253318
$389$	−3603.72	−0.469706	−0.234853	−	0.972031i	$-0.575461\pi$
$389$	−3603.72	−0.469706	−0.234853	+	0.972031i	$0.575461\pi$
$390$	2552.62	0.331429
$391$	−9973.51	−1.28998
$392$	−4992.41	−0.643252
$393$	−13460.9	−1.72777
$394$	−3360.32	−0.429671
$395$	−4922.81	−0.627072
$396$	3404.00	0.431963
$397$	4178.70	0.528270	0.264135	−	0.964486i	$-0.414914\pi$
$397$	4178.70	0.528270	0.264135	+	0.964486i	$0.414914\pi$
$398$	−1721.71	−0.216839
$399$	5259.02	0.659851
$400$	−3324.51	−0.415563
$401$	−6248.54	−0.778147	−0.389074	−	0.921207i	$-0.627205\pi$
$401$	−6248.54	−0.778147	−0.389074	+	0.921207i	$0.627205\pi$
$402$	−3935.83	−0.488311
$403$	12566.7	1.55333
$404$	−7570.23	−0.932260
$405$	2978.20	0.365402
$406$	−204.892	−0.0250458
$407$	−3842.44	−0.467968
$408$	−9363.09	−1.13613
$409$	−2173.77	−0.262802	−0.131401	−	0.991329i	$-0.541948\pi$
$409$	−2173.77	−0.262802	−0.131401	+	0.991329i	$0.541948\pi$
$410$	−0.422457	−5.08870e−5 0
$411$	−13118.8	−1.57446
$412$	12755.6	1.52529
$413$	3079.65	0.366925
$414$	4791.91	0.568864
$415$	8282.45	0.979685
$416$	8346.98	0.983761
$417$	−22049.1	−2.58932
$418$	−1980.17	−0.231707
$419$	−9987.39	−1.16448	−0.582238	−	0.813018i	$-0.697823\pi$
$419$	−9987.39	−1.16448	−0.582238	+	0.813018i	$0.697823\pi$
$420$	−1730.79	−0.201080
$421$	−6981.99	−0.808269	−0.404134	−	0.914700i	$-0.632427\pi$
$421$	−6981.99	−0.808269	−0.404134	+	0.914700i	$0.632427\pi$
$422$	3364.30	0.388085
$423$	11818.2	1.35844
$424$	7421.47	0.850043
$425$	−6604.15	−0.753761
$426$	4563.48	0.519017
$427$	3107.66	0.352202
$428$	−1288.21	−0.145486
$429$	−5668.79	−0.637976
$430$	0	0
$431$	222.271	0.0248408	0.0124204	−	0.999923i	$-0.496046\pi$
$431$	222.271	0.0248408	0.0124204	+	0.999923i	$0.496046\pi$
$432$	−2128.24	−0.237026
$433$	5956.90	0.661132	0.330566	−	0.943783i	$-0.392760\pi$
$433$	5956.90	0.661132	0.330566	+	0.943783i	$0.392760\pi$
$434$	1406.26	0.155536
$435$	1760.69	0.194066
$436$	−799.765	−0.0878481
$437$	16890.2	1.84889
$438$	2730.52	0.297875
$439$	6259.09	0.680478	0.340239	−	0.940339i	$-0.389492\pi$
$439$	6259.09	0.680478	0.340239	+	0.940339i	$0.389492\pi$
$440$	1410.94	0.152872
$441$	−10771.3	−1.16308
$442$	4021.86	0.432806
$443$	10832.7	1.16180	0.580902	−	0.813974i	$-0.302700\pi$
$443$	10832.7	1.16180	0.580902	+	0.813974i	$0.302700\pi$
$444$	14211.6	1.51904
$445$	−9158.96	−0.975677
$446$	−3226.04	−0.342506
$447$	−7598.04	−0.803971
$448$	−665.257	−0.0701573
$449$	−10794.8	−1.13461	−0.567305	−	0.823508i	$-0.692014\pi$
$449$	−10794.8	−1.13461	−0.567305	+	0.823508i	$0.692014\pi$
$450$	3173.06	0.332398
$451$	0.938180	9.79538e−5 0
$452$	8517.81	0.886381
$453$	6855.27	0.711013
$454$	5228.62	0.540509
$455$	1609.60	0.165844
$456$	15856.4	1.62839
$457$	−12577.4	−1.28741	−0.643706	−	0.765273i	$-0.722604\pi$
$457$	−12577.4	−1.28741	−0.643706	+	0.765273i	$0.722604\pi$
$458$	5452.74	0.556310
$459$	−4227.76	−0.429924
$460$	−5558.69	−0.563425
$461$	−14738.5	−1.48902	−0.744510	−	0.667611i	$-0.767317\pi$
$461$	−14738.5	−1.48902	−0.744510	+	0.667611i	$0.767317\pi$
$462$	−634.359	−0.0638811
$463$	−877.733	−0.0881030	−0.0440515	−	0.999029i	$-0.514027\pi$
$463$	−877.733	−0.0881030	−0.0440515	+	0.999029i	$0.514027\pi$
$464$	1396.47	0.139719
$465$	−12084.4	−1.20516
$466$	1549.81	0.154063
$467$	−3211.66	−0.318239	−0.159120	−	0.987259i	$-0.550866\pi$
$467$	−3211.66	−0.318239	−0.159120	+	0.987259i	$0.550866\pi$
$468$	11708.4	1.15646
$469$	−2481.80	−0.244347
$470$	2262.57	0.222052
$471$	−17135.0	−1.67630
$472$	9285.43	0.905501
$473$	0	0
$474$	6673.30	0.646656
$475$	11184.2	1.08035
$476$	−2726.99	−0.262587
$477$	16012.1	1.53699
$478$	−6011.04	−0.575186
$479$	−6177.44	−0.589258	−0.294629	−	0.955612i	$-0.595196\pi$
$479$	−6177.44	−0.589258	−0.294629	+	0.955612i	$0.595196\pi$
$480$	−8026.62	−0.763257
$481$	−13216.5	−1.25285
$482$	3109.32	0.293829
$483$	5410.86	0.509736
$484$	7692.35	0.722422
$485$	1731.37	0.162098
$486$	−5643.38	−0.526726
$487$	15600.7	1.45161	0.725807	−	0.687899i	$-0.241467\pi$
$487$	15600.7	1.45161	0.725807	+	0.687899i	$0.241467\pi$
$488$	9369.86	0.869168
$489$	−1663.99	−0.153882
$490$	−2062.15	−0.190120
$491$	−108.625	−0.00998406	−0.00499203	−	0.999988i	$-0.501589\pi$
$491$	−108.625	−0.00998406	−0.00499203	+	0.999988i	$0.501589\pi$
$492$	−3.46994	−0.000317962 0
$493$	2774.10	0.253427
$494$	−6811.03	−0.620329
$495$	3044.15	0.276413
$496$	−9584.59	−0.867663
$497$	2877.57	0.259712
$498$	−11227.6	−1.01028
$499$	1133.22	0.101663	0.0508317	−	0.998707i	$-0.483813\pi$
$499$	1133.22	0.101663	0.0508317	+	0.998707i	$0.483813\pi$
$500$	−8951.70	−0.800664
$501$	−2098.28	−0.187115
$502$	2646.61	0.235307
$503$	12385.7	1.09791	0.548956	−	0.835852i	$-0.315026\pi$
$503$	12385.7	1.09791	0.548956	+	0.835852i	$0.315026\pi$
$504$	2836.68	0.250706
$505$	−6769.95	−0.596552
$506$	−2037.34	−0.178994
$507$	−2318.77	−0.203117
$508$	−633.897	−0.0553635
$509$	−5798.36	−0.504927	−0.252464	−	0.967606i	$-0.581241\pi$
$509$	−5798.36	−0.504927	−0.252464	+	0.967606i	$0.581241\pi$
$510$	−3867.50	−0.335795
$511$	1721.77	0.149054
$512$	−11188.3	−0.965739
$513$	7159.73	0.616199
$514$	7799.46	0.669299
$515$	11407.1	0.976035
$516$	0	0
$517$	−5024.65	−0.427435
$518$	−1478.98	−0.125449
$519$	2427.64	0.205321
$520$	4853.08	0.409272
$521$	−1523.74	−0.128131	−0.0640653	−	0.997946i	$-0.520407\pi$
$521$	−1523.74	−0.128131	−0.0640653	+	0.997946i	$0.520407\pi$
$522$	−1332.86	−0.111758
$523$	7712.81	0.644852	0.322426	−	0.946595i	$-0.395502\pi$
$523$	7712.81	0.644852	0.322426	+	0.946595i	$0.395502\pi$
$524$	−11820.6	−0.985468
$525$	3582.90	0.297849
$526$	267.438	0.0221690
$527$	−19039.8	−1.57379
$528$	4323.58	0.356363
$529$	5210.81	0.428274
$530$	3065.50	0.251239
$531$	20033.7	1.63726
$532$	4618.17	0.376359
$533$	3.22698	0.000262244 0
$534$	12415.8	1.00615
$535$	−1152.03	−0.0930966
$536$	−7482.84	−0.603003
$537$	25873.6	2.07920
$538$	5047.24	0.404465
$539$	4579.57	0.365966
$540$	−2356.33	−0.187778
$541$	−17909.6	−1.42328	−0.711640	−	0.702544i	$-0.752047\pi$
$541$	−17909.6	−1.42328	−0.711640	+	0.702544i	$0.752047\pi$
$542$	−4044.62	−0.320537
$543$	−9500.92	−0.750872
$544$	−12646.6	−0.996722
$545$	−715.219	−0.0562139
$546$	−2181.95	−0.171024
$547$	6691.92	0.523082	0.261541	−	0.965192i	$-0.415769\pi$
$547$	6691.92	0.523082	0.261541	+	0.965192i	$0.415769\pi$
$548$	−11520.2	−0.898025
$549$	20215.8	1.57157
$550$	−1349.07	−0.104590
$551$	−4697.95	−0.363230
$552$	16314.2	1.25793
$553$	4207.96	0.323581
$554$	−5076.48	−0.389312
$555$	12709.3	0.972032
$556$	−19362.2	−1.47687
$557$	9117.59	0.693581	0.346790	−	0.937943i	$-0.387271\pi$
$557$	9117.59	0.693581	0.346790	+	0.937943i	$0.387271\pi$
$558$	9147.96	0.694021
$559$	0	0
$560$	−1227.64	−0.0926378
$561$	8588.81	0.646381
$562$	−2565.94	−0.192593
$563$	16518.8	1.23656	0.618282	−	0.785956i	$-0.287829\pi$
$563$	16518.8	1.23656	0.618282	+	0.785956i	$0.287829\pi$
$564$	18584.1	1.38747
$565$	7617.36	0.567194
$566$	8726.12	0.648032
$567$	−2545.72	−0.188554
$568$	8676.13	0.640920
$569$	25394.8	1.87101	0.935505	−	0.353313i	$-0.114945\pi$
$569$	25394.8	1.87101	0.935505	+	0.353313i	$0.114945\pi$
$570$	6549.62	0.481286
$571$	13697.9	1.00392	0.501960	−	0.864891i	$-0.332613\pi$
$571$	13697.9	1.00392	0.501960	+	0.864891i	$0.332613\pi$
$572$	−4978.00	−0.363882
$573$	−25507.6	−1.85967
$574$	0.361111	2.62587e−5 0
$575$	11507.1	0.834569
$576$	−4327.61	−0.313051
$577$	−763.733	−0.0551033	−0.0275517	−	0.999620i	$-0.508771\pi$
$577$	−763.733	−0.0551033	−0.0275517	+	0.999620i	$0.508771\pi$
$578$	−863.375	−0.0621309
$579$	4663.90	0.334759
$580$	1546.13	0.110689
$581$	−7079.73	−0.505537
$582$	−2347.02	−0.167160
$583$	−6807.75	−0.483616
$584$	5191.29	0.367838
$585$	10470.7	0.740018
$586$	−4850.36	−0.341922
$587$	−7553.03	−0.531085	−0.265543	−	0.964099i	$-0.585551\pi$
$587$	−7553.03	−0.531085	−0.265543	+	0.964099i	$0.585551\pi$
$588$	−16937.9	−1.18794
$589$	32244.0	2.25567
$590$	3835.42	0.267630
$591$	−24682.9	−1.71797
$592$	10080.2	0.699822
$593$	−23780.6	−1.64680	−0.823401	−	0.567460i	$-0.807926\pi$
$593$	−23780.6	−1.64680	−0.823401	+	0.567460i	$0.807926\pi$
$594$	−863.629	−0.0596551
$595$	−2438.71	−0.168029
$596$	−6672.16	−0.458561
$597$	−12646.7	−0.866993
$598$	−7007.67	−0.479206
$599$	−5509.20	−0.375792	−0.187896	−	0.982189i	$-0.560167\pi$
$599$	−5509.20	−0.375792	−0.187896	+	0.982189i	$0.560167\pi$
$600$	10802.8	0.735036
$601$	−19229.4	−1.30513	−0.652565	−	0.757733i	$-0.726307\pi$
$601$	−19229.4	−1.30513	−0.652565	+	0.757733i	$0.726307\pi$
$602$	0	0
$603$	−16144.5	−1.09031
$604$	6019.90	0.405540
$605$	6879.16	0.462277
$606$	9177.26	0.615183
$607$	−16273.8	−1.08820	−0.544098	−	0.839022i	$-0.683128\pi$
$607$	−16273.8	−1.08820	−0.544098	+	0.839022i	$0.683128\pi$
$608$	21417.0	1.42858
$609$	−1505.01	−0.100142
$610$	3870.29	0.256891
$611$	−17282.8	−1.14434
$612$	−17739.5	−1.17170
$613$	22778.0	1.50081	0.750404	−	0.660979i	$-0.229859\pi$
$613$	22778.0	1.50081	0.750404	+	0.660979i	$0.229859\pi$
$614$	−631.227	−0.0414890
$615$	−3.10312	−0.000203463 0
$616$	−1206.05	−0.0788850
$617$	−2928.42	−0.191076	−0.0955379	−	0.995426i	$-0.530457\pi$
$617$	−2928.42	−0.191076	−0.0955379	+	0.995426i	$0.530457\pi$
$618$	−15463.4	−1.00652
$619$	−21693.7	−1.40863	−0.704316	−	0.709886i	$-0.748746\pi$
$619$	−21693.7	−1.40863	−0.704316	+	0.709886i	$0.748746\pi$
$620$	−10611.8	−0.687386
$621$	7366.44	0.476015
$622$	−492.844	−0.0317705
$623$	7828.96	0.503468
$624$	14871.4	0.954061
$625$	2905.92	0.185979
$626$	2132.51	0.136154
$627$	−14545.2	−0.926441
$628$	−15047.0	−0.956113
$629$	20024.4	1.26936
$630$	1171.71	0.0740986
$631$	6428.64	0.405579	0.202789	−	0.979222i	$-0.434999\pi$
$631$	6428.64	0.405579	0.202789	+	0.979222i	$0.434999\pi$
$632$	12687.4	0.798538
$633$	24712.2	1.55169
$634$	−7999.23	−0.501089
$635$	−566.886	−0.0354271
$636$	25179.1	1.56984
$637$	15751.9	0.979772
$638$	566.681	0.0351648
$639$	18719.1	1.15887
$640$	−9040.30	−0.558358
$641$	−16640.2	−1.02535	−0.512675	−	0.858583i	$-0.671345\pi$
$641$	−16640.2	−1.02535	−0.512675	+	0.858583i	$0.671345\pi$
$642$	1561.68	0.0960041
$643$	−22067.1	−1.35341	−0.676705	−	0.736254i	$-0.736593\pi$
$643$	−22067.1	−1.35341	−0.676705	+	0.736254i	$0.736593\pi$
$644$	4751.50	0.290738
$645$	0	0
$646$	10319.4	0.628502
$647$	21490.3	1.30583	0.652914	−	0.757432i	$-0.273546\pi$
$647$	21490.3	1.30583	0.652914	+	0.757432i	$0.273546\pi$
$648$	−7675.58	−0.465317
$649$	−8517.57	−0.515168
$650$	−4640.27	−0.280010
$651$	10329.6	0.621885
$652$	−1461.22	−0.0877698
$653$	−6820.47	−0.408738	−0.204369	−	0.978894i	$-0.565514\pi$
$653$	−6820.47	−0.408738	−0.204369	+	0.978894i	$0.565514\pi$
$654$	969.542	0.0579695
$655$	−10571.0	−0.630600
$656$	−2.46121	−0.000146485 0
$657$	11200.4	0.665099
$658$	−1934.02	−0.114583
$659$	22489.9	1.32941	0.664705	−	0.747106i	$-0.268557\pi$
$659$	22489.9	1.32941	0.664705	+	0.747106i	$0.268557\pi$
$660$	4786.94	0.282320
$661$	4415.60	0.259829	0.129915	−	0.991525i	$-0.458530\pi$
$661$	4415.60	0.259829	0.129915	+	0.991525i	$0.458530\pi$
$662$	−48.0913	−0.00282345
$663$	29542.2	1.73050
$664$	−21346.0	−1.24757
$665$	4129.96	0.240832
$666$	−9621.01	−0.559770
$667$	−4833.59	−0.280596
$668$	−1842.59	−0.106724
$669$	−23696.6	−1.36945
$670$	−3090.84	−0.178223
$671$	−8595.03	−0.494497
$672$	6861.05	0.393855
$673$	12380.3	0.709099	0.354550	−	0.935037i	$-0.384634\pi$
$673$	12380.3	0.709099	0.354550	+	0.935037i	$0.384634\pi$
$674$	3452.38	0.197301
$675$	4877.83	0.278145
$676$	−2036.21	−0.115852
$677$	13581.0	0.770988	0.385494	−	0.922710i	$-0.374031\pi$
$677$	13581.0	0.770988	0.385494	+	0.922710i	$0.374031\pi$
$678$	−10326.0	−0.584908
$679$	−1479.95	−0.0836456
$680$	−7352.93	−0.414665
$681$	38406.4	2.16114
$682$	−3889.37	−0.218375
$683$	−11883.8	−0.665772	−0.332886	−	0.942967i	$-0.608022\pi$
$683$	−11883.8	−0.665772	−0.332886	+	0.942967i	$0.608022\pi$
$684$	30042.0	1.67936
$685$	−10302.3	−0.574646
$686$	3679.37	0.204780
$687$	40052.6	2.22431
$688$	0	0
$689$	−23416.0	−1.29475
$690$	6738.71	0.371795
$691$	−29404.3	−1.61880	−0.809401	−	0.587256i	$-0.800208\pi$
$691$	−29404.3	−1.61880	−0.809401	+	0.587256i	$0.800208\pi$
$692$	2131.81	0.117109
$693$	−2602.10	−0.142634
$694$	−4181.80	−0.228730
$695$	−17315.3	−0.945048
$696$	−4537.75	−0.247131
$697$	−4.88921	−0.000265699 0
$698$	−10496.6	−0.569199
$699$	11384.0	0.615996
$700$	3146.30	0.169884
$701$	−3434.39	−0.185043	−0.0925214	−	0.995711i	$-0.529493\pi$
$701$	−3434.39	−0.185043	−0.0925214	+	0.995711i	$0.529493\pi$
$702$	−2970.55	−0.159710
$703$	−33911.4	−1.81934
$704$	1839.94	0.0985019
$705$	16619.5	0.887840
$706$	−3944.18	−0.210257
$707$	5786.87	0.307832
$708$	31503.0	1.67225
$709$	9505.59	0.503512	0.251756	−	0.967791i	$-0.418992\pi$
$709$	9505.59	0.503512	0.251756	+	0.967791i	$0.418992\pi$
$710$	3583.74	0.189430
$711$	27373.5	1.44386
$712$	23605.0	1.24247
$713$	33175.0	1.74251
$714$	3305.89	0.173277
$715$	−4451.76	−0.232848
$716$	22720.7	1.18591
$717$	−44153.6	−2.29978
$718$	−4119.46	−0.214118
$719$	−30161.2	−1.56443	−0.782214	−	0.623010i	$-0.785909\pi$
$719$	−30161.2	−1.56443	−0.782214	+	0.623010i	$0.785909\pi$
$720$	−7985.99	−0.413362
$721$	−9750.66	−0.503653
$722$	−10174.2	−0.524438
$723$	22839.3	1.17483
$724$	−8343.16	−0.428275
$725$	−3200.65	−0.163958
$726$	−9325.31	−0.476714
$727$	13578.6	0.692713	0.346356	−	0.938103i	$-0.387419\pi$
$727$	13578.6	0.692713	0.346356	+	0.938103i	$0.387419\pi$
$728$	−4148.35	−0.211192
$729$	−28358.4	−1.44076
$730$	2144.30	0.108718
$731$	0	0
$732$	31789.5	1.60515
$733$	−30598.7	−1.54187	−0.770934	−	0.636915i	$-0.780210\pi$
$733$	−30598.7	−1.54187	−0.770934	+	0.636915i	$0.780210\pi$
$734$	11578.8	0.582263
$735$	−15147.4	−0.760162
$736$	22035.3	1.10358
$737$	6864.05	0.343067
$738$	2.34909	0.000117170 0
$739$	−6419.22	−0.319533	−0.159766	−	0.987155i	$-0.551074\pi$
$739$	−6419.22	−0.319533	−0.159766	+	0.987155i	$0.551074\pi$
$740$	11160.5	0.554418
$741$	−50029.8	−2.48028
$742$	−2620.35	−0.129644
$743$	−30806.9	−1.52113	−0.760563	−	0.649264i	$-0.775077\pi$
$743$	−30806.9	−1.52113	−0.760563	+	0.649264i	$0.775077\pi$
$744$	31144.5	1.53470
$745$	−5966.82	−0.293433
$746$	−10785.1	−0.529317
$747$	−46054.8	−2.25577
$748$	7542.19	0.368676
$749$	984.742	0.0480396
$750$	10852.0	0.528345
$751$	−19700.5	−0.957233	−0.478616	−	0.878024i	$-0.658862\pi$
$751$	−19700.5	−0.957233	−0.478616	+	0.878024i	$0.658862\pi$
$752$	13181.6	0.639207
$753$	19440.5	0.940836
$754$	1949.16	0.0941437
$755$	5383.51	0.259505
$756$	2014.16	0.0968971
$757$	−11597.2	−0.556813	−0.278406	−	0.960463i	$-0.589806\pi$
$757$	−11597.2	−0.556813	−0.278406	+	0.960463i	$0.589806\pi$
$758$	9161.81	0.439013
$759$	−14965.1	−0.715678
$760$	12452.2	0.594328
$761$	35405.7	1.68654	0.843269	−	0.537492i	$-0.180628\pi$
$761$	35405.7	1.68654	0.843269	+	0.537492i	$0.180628\pi$
$762$	768.464	0.0365335
$763$	611.360	0.0290075
$764$	−22399.2	−1.06070
$765$	−15864.2	−0.749768
$766$	3561.74	0.168004
$767$	−29297.2	−1.37922
$768$	4326.62	0.203286
$769$	−22021.1	−1.03264	−0.516321	−	0.856395i	$-0.672699\pi$
$769$	−22021.1	−1.03264	−0.516321	+	0.856395i	$0.672699\pi$
$770$	−498.169	−0.0233153
$771$	57290.3	2.67608
$772$	4095.57	0.190936
$773$	4710.78	0.219191	0.109596	−	0.993976i	$-0.465044\pi$
$773$	4710.78	0.219191	0.109596	+	0.993976i	$0.465044\pi$
$774$	0	0
$775$	21967.4	1.01819
$776$	−4462.19	−0.206422
$777$	−10863.7	−0.501588
$778$	3836.36	0.176787
$779$	8.27989	0.000380819 0
$780$	16465.2	0.755832
$781$	−7958.67	−0.364639
$782$	10617.4	0.485519
$783$	−2048.95	−0.0935168
$784$	−12014.0	−0.547284
$785$	−13456.3	−0.611816
$786$	14329.9	0.650294
$787$	23336.9	1.05701	0.528506	−	0.848929i	$-0.322752\pi$
$787$	23336.9	1.05701	0.528506	+	0.848929i	$0.322752\pi$
$788$	−21675.1	−0.979877
$789$	1964.44	0.0886389
$790$	5240.61	0.236016
$791$	−6511.23	−0.292683
$792$	−7845.57	−0.351995
$793$	−29563.6	−1.32388
$794$	−4448.47	−0.198829
$795$	22517.3	1.00454
$796$	−11105.6	−0.494506
$797$	−35188.8	−1.56393	−0.781964	−	0.623324i	$-0.785782\pi$
$797$	−35188.8	−1.56393	−0.781964	+	0.623324i	$0.785782\pi$
$798$	−5598.53	−0.248353
$799$	26185.3	1.15941
$800$	14591.1	0.644842
$801$	50928.7	2.24654
$802$	6651.92	0.292877
$803$	−4762.00	−0.209275
$804$	−25387.3	−1.11361
$805$	4249.20	0.186043
$806$	−13377.9	−0.584638
$807$	37074.1	1.61719
$808$	17447.9	0.759673
$809$	34912.8	1.51727	0.758634	−	0.651517i	$-0.225867\pi$
$809$	34912.8	1.51727	0.758634	+	0.651517i	$0.225867\pi$
$810$	−3170.46	−0.137529
$811$	12039.2	0.521274	0.260637	−	0.965437i	$-0.416067\pi$
$811$	12039.2	0.521274	0.260637	+	0.965437i	$0.416067\pi$
$812$	−1321.62	−0.0571178
$813$	−29709.4	−1.28161
$814$	4090.50	0.176133
$815$	−1306.75	−0.0561638
$816$	−22531.8	−0.966631
$817$	0	0
$818$	2314.10	0.0989128
$819$	−8950.22	−0.381863
$820$	−2.72498	−0.000116049 0
$821$	−15367.9	−0.653282	−0.326641	−	0.945148i	$-0.605917\pi$
$821$	−15367.9	−0.653282	−0.326641	+	0.945148i	$0.605917\pi$
$822$	13965.7	0.592592
$823$	−13492.2	−0.571458	−0.285729	−	0.958311i	$-0.592236\pi$
$823$	−13492.2	−0.571458	−0.285729	+	0.958311i	$0.592236\pi$
$824$	−29399.1	−1.24292
$825$	−9909.44	−0.418185
$826$	−3278.47	−0.138102
$827$	−20247.3	−0.851351	−0.425675	−	0.904876i	$-0.639963\pi$
$827$	−20247.3	−0.851351	−0.425675	+	0.904876i	$0.639963\pi$
$828$	30909.3	1.29731
$829$	19359.2	0.811063	0.405531	−	0.914081i	$-0.367086\pi$
$829$	19359.2	0.811063	0.405531	+	0.914081i	$0.367086\pi$
$830$	−8817.14	−0.368732
$831$	−37288.8	−1.55660
$832$	6328.68	0.263711
$833$	−23865.9	−0.992680
$834$	23472.5	0.974562
$835$	−1647.80	−0.0682929
$836$	−12772.7	−0.528414
$837$	14062.8	0.580744
$838$	10632.1	0.438283
$839$	−8186.73	−0.336874	−0.168437	−	0.985712i	$-0.553872\pi$
$839$	−8186.73	−0.336874	−0.168437	+	0.985712i	$0.553872\pi$
$840$	3989.13	0.163855
$841$	−23044.6	−0.944875
$842$	7432.72	0.304214
$843$	−18847.9	−0.770053
$844$	21700.8	0.885038
$845$	−1820.95	−0.0741334
$846$	−12581.1	−0.511286
$847$	−5880.22	−0.238544
$848$	17859.4	0.723224
$849$	64096.9	2.59105
$850$	7030.49	0.283699
$851$	−34890.5	−1.40544
$852$	29435.8	1.18363
$853$	−35270.2	−1.41574	−0.707871	−	0.706342i	$-0.750344\pi$
$853$	−35270.2	−1.41574	−0.707871	+	0.706342i	$0.750344\pi$
$854$	−3308.28	−0.132561
$855$	26866.1	1.07462
$856$	2969.08	0.118553
$857$	24977.7	0.995593	0.497797	−	0.867294i	$-0.334143\pi$
$857$	24977.7	0.995593	0.497797	+	0.867294i	$0.334143\pi$
$858$	6034.75	0.240120
$859$	31619.8	1.25594	0.627972	−	0.778236i	$-0.283885\pi$
$859$	31619.8	1.25594	0.627972	+	0.778236i	$0.283885\pi$
$860$	0	0
$861$	2.65251	0.000104991 0
$862$	−236.620	−0.00934953
$863$	18436.6	0.727220	0.363610	−	0.931551i	$-0.381544\pi$
$863$	18436.6	0.727220	0.363610	+	0.931551i	$0.381544\pi$
$864$	9340.76	0.367800
$865$	1906.45	0.0749379
$866$	−6341.46	−0.248835
$867$	−6341.84	−0.248420
$868$	9070.81	0.354704
$869$	−11638.2	−0.454313
$870$	−1874.35	−0.0730420
$871$	23609.7	0.918465
$872$	1843.30	0.0715850
$873$	−9627.34	−0.373237
$874$	−17980.5	−0.695882
$875$	6842.90	0.264380
$876$	17612.7	0.679313
$877$	48236.4	1.85727	0.928635	−	0.370994i	$-0.120983\pi$
$877$	48236.4	1.85727	0.928635	+	0.370994i	$0.120983\pi$
$878$	−6663.15	−0.256117
$879$	−35627.8	−1.36712
$880$	3395.35	0.130065
$881$	33308.7	1.27378	0.636888	−	0.770956i	$-0.280221\pi$
$881$	33308.7	1.27378	0.636888	+	0.770956i	$0.280221\pi$
$882$	11466.7	0.437759
$883$	31091.7	1.18496	0.592479	−	0.805586i	$-0.298149\pi$
$883$	31091.7	1.18496	0.592479	+	0.805586i	$0.298149\pi$
$884$	25942.2	0.987027
$885$	28172.7	1.07007
$886$	−11532.1	−0.437277
$887$	6550.91	0.247980	0.123990	−	0.992283i	$-0.460431\pi$
$887$	6550.91	0.247980	0.123990	+	0.992283i	$0.460431\pi$
$888$	−32755.0	−1.23782
$889$	484.567	0.0182810
$890$	9750.23	0.367223
$891$	7040.86	0.264734
$892$	−20809.0	−0.781094
$893$	−44345.0	−1.66176
$894$	8088.55	0.302597
$895$	20318.8	0.758864
$896$	7727.54	0.288124
$897$	−51474.2	−1.91602
$898$	11491.7	0.427042
$899$	−9227.52	−0.342330
$900$	20467.2	0.758044
$901$	35477.8	1.31181
$902$	−0.998746	−3.68676e−5 0
$903$	0	0
$904$	−19631.9	−0.722287
$905$	−7461.17	−0.274053
$906$	−7297.83	−0.267609
$907$	−46718.5	−1.71032	−0.855160	−	0.518364i	$-0.826541\pi$
$907$	−46718.5	−1.71032	−0.855160	+	0.518364i	$0.826541\pi$
$908$	33726.2	1.23265
$909$	37644.5	1.37359
$910$	−1713.51	−0.0624200
$911$	−18054.8	−0.656620	−0.328310	−	0.944570i	$-0.606479\pi$
$911$	−18054.8	−0.656620	−0.328310	+	0.944570i	$0.606479\pi$
$912$	38157.7	1.38545
$913$	19580.8	0.709781
$914$	13389.4	0.484553
$915$	28428.9	1.02714
$916$	35171.9	1.26868
$917$	9035.96	0.325402
$918$	4500.70	0.161814
$919$	−42321.3	−1.51910	−0.759548	−	0.650451i	$-0.774580\pi$
$919$	−42321.3	−1.51910	−0.759548	+	0.650451i	$0.774580\pi$
$920$	12811.7	0.459119
$921$	−4636.62	−0.165887
$922$	15689.9	0.560434
$923$	−27374.7	−0.976219
$924$	−4091.81	−0.145683
$925$	−23103.4	−0.821228
$926$	934.396	0.0331600
$927$	−63429.7	−2.24736
$928$	−6129.06	−0.216806
$929$	−32859.5	−1.16048	−0.580240	−	0.814446i	$-0.697041\pi$
$929$	−32859.5	−1.16048	−0.580240	+	0.814446i	$0.697041\pi$
$930$	12864.5	0.453595
$931$	40416.9	1.42278
$932$	9996.74	0.351346
$933$	−3620.14	−0.127029
$934$	3418.99	0.119778
$935$	6744.88	0.235916
$936$	−26985.7	−0.942367
$937$	−14.5879	−0.000508608 0	−0.000254304	−	1.00000i	$-0.500081\pi$
$937$	−14.5879	−0.000508608 0	−0.000254304		1.00000i	$0.500081\pi$
$938$	2642.01	0.0919668
$939$	15664.2	0.544389
$940$	14594.3	0.506397
$941$	9884.04	0.342413	0.171206	−	0.985235i	$-0.445233\pi$
$941$	9884.04	0.342413	0.171206	+	0.985235i	$0.445233\pi$
$942$	18241.2	0.630924
$943$	8.51894	0.000294183 0
$944$	22344.9	0.770408
$945$	1801.23	0.0620044
$946$	0	0
$947$	43165.9	1.48121	0.740603	−	0.671943i	$-0.234540\pi$
$947$	43165.9	1.48121	0.740603	+	0.671943i	$0.234540\pi$
$948$	43044.9	1.47472
$949$	−16379.4	−0.560273
$950$	−11906.2	−0.406618
$951$	−58757.6	−2.00352
$952$	6285.19	0.213975
$953$	−11414.8	−0.387998	−0.193999	−	0.981002i	$-0.562146\pi$
$953$	−11414.8	−0.387998	−0.193999	+	0.981002i	$0.562146\pi$
$954$	−17045.8	−0.578488
$955$	−20031.3	−0.678742
$956$	−38773.1	−1.31173
$957$	4162.50	0.140600
$958$	6576.23	0.221783
$959$	8806.31	0.296528
$960$	−6085.78	−0.204602
$961$	33541.4	1.12589
$962$	14069.7	0.471545
$963$	6405.91	0.214359
$964$	20056.1	0.670086
$965$	3662.61	0.122180
$966$	−5760.17	−0.191853
$967$	−21094.6	−0.701508	−0.350754	−	0.936468i	$-0.614075\pi$
$967$	−21094.6	−0.701508	−0.350754	+	0.936468i	$0.614075\pi$
$968$	−17729.4	−0.588682
$969$	75800.4	2.51296
$970$	−1843.14	−0.0610100
$971$	−17622.1	−0.582409	−0.291205	−	0.956661i	$-0.594056\pi$
$971$	−17622.1	−0.582409	−0.291205	+	0.956661i	$0.594056\pi$
$972$	−36401.6	−1.20121
$973$	14800.9	0.487663
$974$	−16607.8	−0.546355
$975$	−34084.7	−1.11957
$976$	22548.1	0.739495
$977$	29292.7	0.959218	0.479609	−	0.877482i	$-0.340778\pi$
$977$	29292.7	0.959218	0.479609	+	0.877482i	$0.340778\pi$
$978$	1771.42	0.0579178
$979$	−21653.0	−0.706878
$980$	−13301.5	−0.433573
$981$	3977.00	0.129435
$982$	115.637	0.00375778
$983$	−36585.0	−1.18706	−0.593531	−	0.804811i	$-0.702266\pi$
$983$	−36585.0	−1.18706	−0.593531	+	0.804811i	$0.702266\pi$
$984$	7.99755	0.000259098 0
$985$	−19383.7	−0.627023
$986$	−2953.19	−0.0953841
$987$	−14206.2	−0.458143
$988$	−43933.2	−1.41468
$989$	0	0
$990$	−3240.67	−0.104036
$991$	8841.74	0.283418	0.141709	−	0.989908i	$-0.454740\pi$
$991$	8841.74	0.283418	0.141709	+	0.989908i	$0.454740\pi$
$992$	42066.4	1.34638
$993$	−353.251	−0.0112891
$994$	−3063.34	−0.0977497
$995$	−9931.58	−0.316434
$996$	−72421.4	−2.30398
$997$	6013.86	0.191034	0.0955169	−	0.995428i	$-0.469550\pi$
$997$	6013.86	0.191034	0.0955169	+	0.995428i	$0.469550\pi$
$998$	−1206.38	−0.0382638
$999$	−14790.1	−0.468405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.21	✓	50
43.42	odd	2		1849.4.a.j.1.30	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.21	✓	50	1.1	even	1	trivial
1849.4.a.j.1.30	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)

\(f(q)\)	\(=\)	\(q-1.06456 q^{2} -7.81960 q^{3} -6.86672 q^{4} -6.14081 q^{5} +8.32441 q^{6} +5.24909 q^{7} +15.8265 q^{8} +34.1462 q^{9} +O(q^{10})\)	\(q-1.06456 q^{2} -7.81960 q^{3} -6.86672 q^{4} -6.14081 q^{5} +8.32441 q^{6} +5.24909 q^{7} +15.8265 q^{8} +34.1462 q^{9} +6.53724 q^{10} -14.5177 q^{11} +53.6950 q^{12} -49.9353 q^{13} -5.58795 q^{14} +48.0187 q^{15} +38.0856 q^{16} +75.6572 q^{17} -36.3506 q^{18} -128.126 q^{19} +42.1672 q^{20} -41.0458 q^{21} +15.4549 q^{22} -131.825 q^{23} -123.757 q^{24} -87.2904 q^{25} +53.1589 q^{26} -55.8805 q^{27} -36.0440 q^{28} +36.6667 q^{29} -51.1187 q^{30} -251.659 q^{31} -167.156 q^{32} +113.523 q^{33} -80.5414 q^{34} -32.2337 q^{35} -234.472 q^{36} +264.673 q^{37} +136.397 q^{38} +390.474 q^{39} -97.1874 q^{40} -0.0646232 q^{41} +43.6956 q^{42} +99.6890 q^{44} -209.685 q^{45} +140.335 q^{46} +346.105 q^{47} -297.814 q^{48} -315.447 q^{49} +92.9256 q^{50} -591.610 q^{51} +342.892 q^{52} +468.928 q^{53} +59.4880 q^{54} +89.1505 q^{55} +83.0745 q^{56} +1001.89 q^{57} -39.0338 q^{58} +586.702 q^{59} -329.731 q^{60} +592.038 q^{61} +267.906 q^{62} +179.236 q^{63} -126.738 q^{64} +306.643 q^{65} -120.851 q^{66} -472.805 q^{67} -519.517 q^{68} +1030.82 q^{69} +34.3146 q^{70} +548.204 q^{71} +540.414 q^{72} +328.014 q^{73} -281.759 q^{74} +682.576 q^{75} +879.804 q^{76} -76.2047 q^{77} -415.682 q^{78} +801.655 q^{79} -233.876 q^{80} -484.984 q^{81} +0.0687950 q^{82} -1348.75 q^{83} +281.850 q^{84} -464.597 q^{85} -286.719 q^{87} -229.764 q^{88} +1491.49 q^{89} +223.222 q^{90} -262.115 q^{91} +905.205 q^{92} +1967.88 q^{93} -368.448 q^{94} +786.796 q^{95} +1307.09 q^{96} -281.945 q^{97} +335.811 q^{98} -495.724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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