LMFDB - Embedded newform 289.4.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2555057.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 21x^{2} - 4x + 36 $ x^4 - x^3 - 21x^2 - 4x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.58184$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58184 q^{2} +4.98387 q^{3} -5.49778 q^{4} +14.4471 q^{5} -7.88368 q^{6} -29.4104 q^{7} +21.3513 q^{8} -2.16104 q^{9} +O(q^{10})$	\(q-1.58184 q^{2} +4.98387 q^{3} -5.49778 q^{4} +14.4471 q^{5} -7.88368 q^{6} -29.4104 q^{7} +21.3513 q^{8} -2.16104 q^{9} -22.8530 q^{10} +13.5324 q^{11} -27.4002 q^{12} +45.7656 q^{13} +46.5225 q^{14} +72.0024 q^{15} +10.2079 q^{16} +3.41842 q^{18} +113.386 q^{19} -79.4269 q^{20} -146.578 q^{21} -21.4060 q^{22} +144.513 q^{23} +106.412 q^{24} +83.7182 q^{25} -72.3938 q^{26} -145.335 q^{27} +161.692 q^{28} -1.26688 q^{29} -113.896 q^{30} -30.0858 q^{31} -186.958 q^{32} +67.4435 q^{33} -424.894 q^{35} +11.8809 q^{36} +398.512 q^{37} -179.358 q^{38} +228.090 q^{39} +308.464 q^{40} +184.595 q^{41} +231.862 q^{42} +135.605 q^{43} -74.3979 q^{44} -31.2207 q^{45} -228.596 q^{46} +247.542 q^{47} +50.8748 q^{48} +521.971 q^{49} -132.429 q^{50} -251.609 q^{52} -635.182 q^{53} +229.896 q^{54} +195.503 q^{55} -627.951 q^{56} +565.100 q^{57} +2.00399 q^{58} +625.420 q^{59} -395.853 q^{60} -166.873 q^{61} +47.5909 q^{62} +63.5570 q^{63} +214.074 q^{64} +661.179 q^{65} -106.685 q^{66} +159.984 q^{67} +720.232 q^{69} +672.115 q^{70} +19.4559 q^{71} -46.1411 q^{72} +336.039 q^{73} -630.382 q^{74} +417.241 q^{75} -623.370 q^{76} -397.992 q^{77} -360.801 q^{78} +1072.15 q^{79} +147.474 q^{80} -665.982 q^{81} -291.999 q^{82} +47.1944 q^{83} +805.852 q^{84} -214.506 q^{86} -6.31394 q^{87} +288.934 q^{88} -626.312 q^{89} +49.3862 q^{90} -1345.98 q^{91} -794.499 q^{92} -149.944 q^{93} -391.572 q^{94} +1638.09 q^{95} -931.774 q^{96} +692.045 q^{97} -825.674 q^{98} -29.2439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9} - 7 q^{10} + 10 q^{11} - 29 q^{12} - 22 q^{13} + 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} + 330 q^{20} - 352 q^{21} - 79 q^{22} + 380 q^{23} + 159 q^{24} + 378 q^{25} - 448 q^{26} - 494 q^{27} + 608 q^{28} - 78 q^{29} + 313 q^{30} + 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} + 512 q^{37} - 524 q^{38} + 12 q^{39} + 1381 q^{40} + 840 q^{41} + 1455 q^{42} - 114 q^{43} - 1041 q^{44} + 648 q^{45} - 1051 q^{46} + 10 q^{47} + 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} + 581 q^{54} - 1316 q^{55} + 411 q^{56} + 358 q^{57} - 376 q^{58} + 996 q^{59} - 217 q^{60} + 448 q^{61} - 73 q^{62} + 766 q^{63} - 150 q^{64} - 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} + 1116 q^{71} - 39 q^{72} + 540 q^{73} + 1630 q^{74} + 1070 q^{75} - 873 q^{76} - 894 q^{77} - 1245 q^{78} + 940 q^{79} + 307 q^{80} + 1080 q^{81} - 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} - 2252 q^{88} + 784 q^{89} - 2069 q^{90} - 2858 q^{91} - 1566 q^{92} - 1550 q^{93} + 1119 q^{94} + 2494 q^{95} - 2643 q^{96} - 518 q^{97} - 1877 q^{98} - 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9 - 7 * q^10 + 10 * q^11 - 29 * q^12 - 22 * q^13 + 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 + 330 * q^20 - 352 * q^21 - 79 * q^22 + 380 * q^23 + 159 * q^24 + 378 * q^25 - 448 * q^26 - 494 * q^27 + 608 * q^28 - 78 * q^29 + 313 * q^30 + 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 + 512 * q^37 - 524 * q^38 + 12 * q^39 + 1381 * q^40 + 840 * q^41 + 1455 * q^42 - 114 * q^43 - 1041 * q^44 + 648 * q^45 - 1051 * q^46 + 10 * q^47 + 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 + 581 * q^54 - 1316 * q^55 + 411 * q^56 + 358 * q^57 - 376 * q^58 + 996 * q^59 - 217 * q^60 + 448 * q^61 - 73 * q^62 + 766 * q^63 - 150 * q^64 - 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 + 1116 * q^71 - 39 * q^72 + 540 * q^73 + 1630 * q^74 + 1070 * q^75 - 873 * q^76 - 894 * q^77 - 1245 * q^78 + 940 * q^79 + 307 * q^80 + 1080 * q^81 - 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 - 2252 * q^88 + 784 * q^89 - 2069 * q^90 - 2858 * q^91 - 1566 * q^92 - 1550 * q^93 + 1119 * q^94 + 2494 * q^95 - 2643 * q^96 - 518 * q^97 - 1877 * q^98 - 1406 * 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 $

$2$	−1.58184	−0.559265	−0.279632	−	0.960107i	$-0.590213\pi$
$2$	−1.58184	−0.559265	−0.279632	+	0.960107i	$0.590213\pi$
$3$	4.98387	0.959146	0.479573	−	0.877502i	$-0.340792\pi$
$3$	4.98387	0.959146	0.479573	+	0.877502i	$0.340792\pi$
$4$	−5.49778	−0.687223
$5$	14.4471	1.29219	0.646093	−	0.763259i	$-0.276402\pi$
$5$	14.4471	1.29219	0.646093	+	0.763259i	$0.276402\pi$
$6$	−7.88368	−0.536417
$7$	−29.4104	−1.58801	−0.794006	−	0.607910i	$-0.792008\pi$
$7$	−29.4104	−1.58801	−0.794006	+	0.607910i	$0.792008\pi$
$8$	21.3513	0.943604
$9$	−2.16104	−0.0800385
$10$	−22.8530	−0.722674
$11$	13.5324	0.370923	0.185462	−	0.982651i	$-0.440622\pi$
$11$	13.5324	0.370923	0.185462	+	0.982651i	$0.440622\pi$
$12$	−27.4002	−0.659147
$13$	45.7656	0.976391	0.488196	−	0.872734i	$-0.337655\pi$
$13$	45.7656	0.976391	0.488196	+	0.872734i	$0.337655\pi$
$14$	46.5225	0.888119
$15$	72.0024	1.23940
$16$	10.2079	0.159498
$17$	0	0
$17$	0	0
$18$	3.41842	0.0447627
$19$	113.386	1.36908	0.684539	−	0.728976i	$-0.260004\pi$
$19$	113.386	1.36908	0.684539	+	0.728976i	$0.260004\pi$
$20$	−79.4269	−0.888020
$21$	−146.578	−1.52314
$22$	−21.4060	−0.207444
$23$	144.513	1.31013	0.655065	−	0.755573i	$-0.272641\pi$
$23$	144.513	1.31013	0.655065	+	0.755573i	$0.272641\pi$
$24$	106.412	0.905055
$25$	83.7182	0.669745
$26$	−72.3938	−0.546061
$27$	−145.335	−1.03591
$28$	161.692	1.09132
$29$	−1.26688	−0.00811217	−0.00405608	−	0.999992i	$-0.501291\pi$
$29$	−1.26688	−0.00811217	−0.00405608	+	0.999992i	$0.501291\pi$
$30$	−113.896	−0.693150
$31$	−30.0858	−0.174309	−0.0871544	−	0.996195i	$-0.527777\pi$
$31$	−30.0858	−0.174309	−0.0871544	+	0.996195i	$0.527777\pi$
$32$	−186.958	−1.03281
$33$	67.4435	0.355770
$34$	0	0
$35$	−424.894	−2.05201
$36$	11.8809	0.0550043
$37$	398.512	1.77067	0.885337	−	0.464950i	$-0.153928\pi$
$37$	398.512	1.77067	0.885337	+	0.464950i	$0.153928\pi$
$38$	−179.358	−0.765677
$39$	228.090	0.936502
$40$	308.464	1.21931
$41$	184.595	0.703143	0.351571	−	0.936161i	$-0.385647\pi$
$41$	184.595	0.703143	0.351571	+	0.936161i	$0.385647\pi$
$42$	231.862	0.851836
$43$	135.605	0.480921	0.240460	−	0.970659i	$-0.422702\pi$
$43$	135.605	0.480921	0.240460	+	0.970659i	$0.422702\pi$
$44$	−74.3979	−0.254907
$45$	−31.2207	−0.103425
$46$	−228.596	−0.732709
$47$	247.542	0.768249	0.384124	−	0.923281i	$-0.374503\pi$
$47$	247.542	0.768249	0.384124	+	0.923281i	$0.374503\pi$
$48$	50.8748	0.152982
$49$	521.971	1.52178
$50$	−132.429	−0.374565
$51$	0	0
$52$	−251.609	−0.670998
$53$	−635.182	−1.64621	−0.823103	−	0.567892i	$-0.807759\pi$
$53$	−635.182	−1.64621	−0.823103	+	0.567892i	$0.807759\pi$
$54$	229.896	0.579351
$55$	195.503	0.479302
$56$	−627.951	−1.49845
$57$	565.100	1.31315
$58$	2.00399	0.00453685
$59$	625.420	1.38005	0.690023	−	0.723788i	$-0.257600\pi$
$59$	625.420	1.38005	0.690023	+	0.723788i	$0.257600\pi$
$60$	−395.853	−0.851741
$61$	−166.873	−0.350261	−0.175130	−	0.984545i	$-0.556035\pi$
$61$	−166.873	−0.350261	−0.175130	+	0.984545i	$0.556035\pi$
$62$	47.5909	0.0974847
$63$	63.5570	0.127102
$64$	214.074	0.418114
$65$	661.179	1.26168
$66$	−106.685	−0.198970
$67$	159.984	0.291719	0.145859	−	0.989305i	$-0.453405\pi$
$67$	159.984	0.291719	0.145859	+	0.989305i	$0.453405\pi$
$68$	0	0
$69$	720.232	1.25661
$70$	672.115	1.14762
$71$	19.4559	0.0325211	0.0162605	−	0.999868i	$-0.494824\pi$
$71$	19.4559	0.0325211	0.0162605	+	0.999868i	$0.494824\pi$
$72$	−46.1411	−0.0755247
$73$	336.039	0.538772	0.269386	−	0.963032i	$-0.413179\pi$
$73$	336.039	0.538772	0.269386	+	0.963032i	$0.413179\pi$
$74$	−630.382	−0.990276
$75$	417.241	0.642384
$76$	−623.370	−0.940862
$77$	−397.992	−0.589031
$78$	−360.801	−0.523753
$79$	1072.15	1.52691	0.763457	−	0.645859i	$-0.223500\pi$
$79$	1072.15	1.52691	0.763457	+	0.645859i	$0.223500\pi$
$80$	147.474	0.206101
$81$	−665.982	−0.913555
$82$	−291.999	−0.393243
$83$	47.1944	0.0624128	0.0312064	−	0.999513i	$-0.490065\pi$
$83$	47.1944	0.0624128	0.0312064	+	0.999513i	$0.490065\pi$
$84$	805.852	1.04673
$85$	0	0
$86$	−214.506	−0.268962
$87$	−6.31394	−0.00778075
$88$	288.934	0.350005
$89$	−626.312	−0.745944	−0.372972	−	0.927843i	$-0.621661\pi$
$89$	−626.312	−0.745944	−0.372972	+	0.927843i	$0.621661\pi$
$90$	49.3862	0.0578418
$91$	−1345.98	−1.55052
$92$	−794.499	−0.900351
$93$	−149.944	−0.167188
$94$	−391.572	−0.429655
$95$	1638.09	1.76910
$96$	−931.774	−0.990612
$97$	692.045	0.724398	0.362199	−	0.932101i	$-0.382026\pi$
$97$	692.045	0.724398	0.362199	+	0.932101i	$0.382026\pi$
$98$	−825.674	−0.851079
$99$	−29.2439	−0.0296882
$100$	−460.264	−0.460264
$101$	−551.668	−0.543496	−0.271748	−	0.962369i	$-0.587602\pi$
$101$	−551.668	−0.543496	−0.271748	+	0.962369i	$0.587602\pi$
$102$	0	0
$103$	−175.990	−0.168358	−0.0841789	−	0.996451i	$-0.526827\pi$
$103$	−175.990	−0.168358	−0.0841789	+	0.996451i	$0.526827\pi$
$104$	977.156	0.921327
$105$	−2117.62	−1.96817
$106$	1004.76	0.920665
$107$	148.521	0.134188	0.0670938	−	0.997747i	$-0.478627\pi$
$107$	148.521	0.134188	0.0670938	+	0.997747i	$0.478627\pi$
$108$	799.019	0.711904
$109$	−703.114	−0.617854	−0.308927	−	0.951086i	$-0.599970\pi$
$109$	−703.114	−0.617854	−0.308927	+	0.951086i	$0.599970\pi$
$110$	−309.254	−0.268057
$111$	1986.13	1.69834
$112$	−300.218	−0.253285
$113$	−1987.05	−1.65421	−0.827104	−	0.562048i	$-0.810014\pi$
$113$	−1987.05	−1.65421	−0.827104	+	0.562048i	$0.810014\pi$
$114$	−893.898	−0.734396
$115$	2087.79	1.69293
$116$	6.96500	0.00557487
$117$	−98.9012	−0.0781489
$118$	−989.314	−0.771811
$119$	0	0
$120$	1537.35	1.16950
$121$	−1147.88	−0.862416
$122$	263.966	0.195888
$123$	919.996	0.674417
$124$	165.405	0.119789
$125$	−596.402	−0.426750
$126$	−100.537	−0.0710837
$127$	−1561.88	−1.09130	−0.545649	−	0.838014i	$-0.683717\pi$
$127$	−1561.88	−1.09130	−0.545649	+	0.838014i	$0.683717\pi$
$128$	1157.03	0.798970
$129$	675.838	0.461273
$130$	−1045.88	−0.705613
$131$	1317.70	0.878839	0.439419	−	0.898282i	$-0.355184\pi$
$131$	1317.70	0.878839	0.439419	+	0.898282i	$0.355184\pi$
$132$	−370.790	−0.244493
$133$	−3334.72	−2.17411
$134$	−253.069	−0.163148
$135$	−2099.66	−1.33859
$136$	0	0
$137$	485.214	0.302588	0.151294	−	0.988489i	$-0.451656\pi$
$137$	485.214	0.302588	0.151294	+	0.988489i	$0.451656\pi$
$138$	−1139.29	−0.702775
$139$	−1016.66	−0.620376	−0.310188	−	0.950675i	$-0.600392\pi$
$139$	−1016.66	−0.620376	−0.310188	+	0.950675i	$0.600392\pi$
$140$	2335.98	1.41019
$141$	1233.72	0.736863
$142$	−30.7762	−0.0181879
$143$	619.316	0.362166
$144$	−22.0596	−0.0127660
$145$	−18.3026	−0.0104824
$146$	−531.559	−0.301316
$147$	2601.44	1.45961
$148$	−2190.93	−1.21685
$149$	−1322.91	−0.727364	−0.363682	−	0.931523i	$-0.618481\pi$
$149$	−1322.91	−0.727364	−0.363682	+	0.931523i	$0.618481\pi$
$150$	−660.008	−0.359263
$151$	−1467.32	−0.790785	−0.395392	−	0.918512i	$-0.629391\pi$
$151$	−1467.32	−0.790785	−0.395392	+	0.918512i	$0.629391\pi$
$152$	2420.94	1.29187
$153$	0	0
$154$	629.559	0.329424
$155$	−434.652	−0.225239
$156$	−1253.99	−0.643586
$157$	−3403.23	−1.72998	−0.864991	−	0.501788i	$-0.832676\pi$
$157$	−3403.23	−1.72998	−0.864991	+	0.501788i	$0.832676\pi$
$158$	−1695.97	−0.853949
$159$	−3165.66	−1.57895
$160$	−2701.00	−1.33458
$161$	−4250.17	−2.08050
$162$	1053.48	0.510919
$163$	−378.056	−0.181667	−0.0908333	−	0.995866i	$-0.528953\pi$
$163$	−378.056	−0.181667	−0.0908333	+	0.995866i	$0.528953\pi$
$164$	−1014.86	−0.483216
$165$	974.362	0.459721
$166$	−74.6540	−0.0349053
$167$	572.418	0.265240	0.132620	−	0.991167i	$-0.457661\pi$
$167$	572.418	0.265240	0.132620	+	0.991167i	$0.457661\pi$
$168$	−3129.63	−1.43724
$169$	−102.512	−0.0466601
$170$	0	0
$171$	−245.031	−0.109579
$172$	−745.528	−0.330500
$173$	3321.64	1.45977	0.729884	−	0.683571i	$-0.239574\pi$
$173$	3321.64	1.45977	0.729884	+	0.683571i	$0.239574\pi$
$174$	9.98764	0.00435150
$175$	−2462.18	−1.06356
$176$	138.137	0.0591616
$177$	3117.01	1.32367
$178$	990.726	0.417180
$179$	−2093.76	−0.874273	−0.437137	−	0.899395i	$-0.644007\pi$
$179$	−2093.76	−0.874273	−0.437137	+	0.899395i	$0.644007\pi$
$180$	171.645	0.0710758
$181$	−682.032	−0.280083	−0.140042	−	0.990146i	$-0.544724\pi$
$181$	−682.032	−0.280083	−0.140042	+	0.990146i	$0.544724\pi$
$182$	2129.13	0.867152
$183$	−831.673	−0.335951
$184$	3085.54	1.23624
$185$	5757.33	2.28804
$186$	237.187	0.0935021
$187$	0	0
$188$	−1360.93	−0.527958
$189$	4274.35	1.64504
$190$	−2591.20	−0.989398
$191$	1921.15	0.727799	0.363900	−	0.931438i	$-0.381445\pi$
$191$	1921.15	0.727799	0.363900	+	0.931438i	$0.381445\pi$
$192$	1066.92	0.401032
$193$	69.6893	0.0259914	0.0129957	−	0.999916i	$-0.495863\pi$
$193$	69.6893	0.0259914	0.0129957	+	0.999916i	$0.495863\pi$
$194$	−1094.70	−0.405130
$195$	3295.23	1.21014
$196$	−2869.68	−1.04580
$197$	3043.10	1.10057	0.550285	−	0.834977i	$-0.314519\pi$
$197$	3043.10	1.10057	0.550285	+	0.834977i	$0.314519\pi$
$198$	46.2592	0.0166035
$199$	1255.72	0.447315	0.223657	−	0.974668i	$-0.428200\pi$
$199$	1255.72	0.447315	0.223657	+	0.974668i	$0.428200\pi$
$200$	1787.49	0.631975
$201$	797.340	0.279801
$202$	872.651	0.303958
$203$	37.2593	0.0128822
$204$	0	0
$205$	2666.85	0.908591
$206$	278.389	0.0941566
$207$	−312.297	−0.104861
$208$	467.170	0.155733
$209$	1534.38	0.507823
$210$	3349.73	1.10073
$211$	1060.15	0.345894	0.172947	−	0.984931i	$-0.444671\pi$
$211$	1060.15	0.345894	0.172947	+	0.984931i	$0.444671\pi$
$212$	3492.09	1.13131
$213$	96.9658	0.0311924
$214$	−234.937	−0.0750464
$215$	1959.10	0.621439
$216$	−3103.09	−0.977494
$217$	884.835	0.276804
$218$	1112.21	0.345544
$219$	1674.77	0.516761
$220$	−1074.83	−0.329387
$221$	0	0
$222$	−3141.74	−0.949819
$223$	−1398.85	−0.420064	−0.210032	−	0.977695i	$-0.567357\pi$
$223$	−1398.85	−0.420064	−0.210032	+	0.977695i	$0.567357\pi$
$224$	5498.50	1.64011
$225$	−180.918	−0.0536054
$226$	3143.19	0.925141
$227$	2436.65	0.712451	0.356226	−	0.934400i	$-0.384063\pi$
$227$	2436.65	0.712451	0.356226	+	0.934400i	$0.384063\pi$
$228$	−3106.80	−0.902424
$229$	5027.28	1.45071	0.725354	−	0.688376i	$-0.241676\pi$
$229$	5027.28	1.45071	0.725354	+	0.688376i	$0.241676\pi$
$230$	−3302.54	−0.946797
$231$	−1983.54	−0.564967
$232$	−27.0495	−0.00765467
$233$	−891.120	−0.250555	−0.125277	−	0.992122i	$-0.539982\pi$
$233$	−891.120	−0.250555	−0.125277	+	0.992122i	$0.539982\pi$
$234$	156.446	0.0437059
$235$	3576.26	0.992721
$236$	−3438.42	−0.948399
$237$	5343.45	1.46453
$238$	0	0
$239$	−161.975	−0.0438382	−0.0219191	−	0.999760i	$-0.506978\pi$
$239$	−161.975	−0.0438382	−0.0219191	+	0.999760i	$0.506978\pi$
$240$	734.992	0.197681
$241$	3467.39	0.926782	0.463391	−	0.886154i	$-0.346633\pi$
$241$	3467.39	0.926782	0.463391	+	0.886154i	$0.346633\pi$
$242$	1815.75	0.482319
$243$	604.873	0.159682
$244$	917.432	0.240707
$245$	7540.96	1.96642
$246$	−1455.29	−0.377177
$247$	5189.17	1.33676
$248$	−642.372	−0.164478
$249$	235.211	0.0598630
$250$	943.412	0.238666
$251$	−4328.65	−1.08853	−0.544267	−	0.838912i	$-0.683192\pi$
$251$	−4328.65	−1.08853	−0.544267	+	0.838912i	$0.683192\pi$
$252$	−349.423	−0.0873474
$253$	1955.60	0.485958
$254$	2470.65	0.610324
$255$	0	0
$256$	−3542.83	−0.864950
$257$	−4567.47	−1.10860	−0.554301	−	0.832316i	$-0.687014\pi$
$257$	−4567.47	−1.10860	−0.554301	+	0.832316i	$0.687014\pi$
$258$	−1069.07	−0.257974
$259$	−11720.4	−2.81185
$260$	−3635.02	−0.867055
$261$	2.73777	0.000649285 0
$262$	−2084.39	−0.491504
$263$	4711.02	1.10454	0.552270	−	0.833665i	$-0.313762\pi$
$263$	4711.02	1.10454	0.552270	+	0.833665i	$0.313762\pi$
$264$	1440.01	0.335706
$265$	−9176.52	−2.12721
$266$	5274.99	1.21590
$267$	−3121.46	−0.715469
$268$	−879.558	−0.200476
$269$	−3659.09	−0.829362	−0.414681	−	0.909967i	$-0.636107\pi$
$269$	−3659.09	−0.829362	−0.414681	+	0.909967i	$0.636107\pi$
$270$	3321.33	0.748629
$271$	−7702.43	−1.72653	−0.863264	−	0.504753i	$-0.831584\pi$
$271$	−7702.43	−1.72653	−0.863264	+	0.504753i	$0.831584\pi$
$272$	0	0
$273$	−6708.21	−1.48718
$274$	−767.530	−0.169227
$275$	1132.90	0.248424
$276$	−3959.68	−0.863568
$277$	−3252.61	−0.705526	−0.352763	−	0.935713i	$-0.614758\pi$
$277$	−3252.61	−0.705526	−0.352763	+	0.935713i	$0.614758\pi$
$278$	1608.20	0.346954
$279$	65.0166	0.0139514
$280$	−9072.06	−1.93628
$281$	−6839.31	−1.45195	−0.725977	−	0.687719i	$-0.758612\pi$
$281$	−6839.31	−1.45195	−0.725977	+	0.687719i	$0.758612\pi$
$282$	−1951.54	−0.412101
$283$	3131.30	0.657726	0.328863	−	0.944378i	$-0.393335\pi$
$283$	3131.30	0.657726	0.328863	+	0.944378i	$0.393335\pi$
$284$	−106.965	−0.0223492
$285$	8164.05	1.69683
$286$	−979.659	−0.202547
$287$	−5429.00	−1.11660
$288$	404.023	0.0826642
$289$	0	0
$290$	28.9519	0.00586245
$291$	3449.06	0.694803
$292$	−1847.47	−0.370256
$293$	5396.03	1.07590	0.537951	−	0.842976i	$-0.319198\pi$
$293$	5396.03	1.07590	0.537951	+	0.842976i	$0.319198\pi$
$294$	−4115.05	−0.816309
$295$	9035.49	1.78328
$296$	8508.76	1.67082
$297$	−1966.72	−0.384245
$298$	2092.64	0.406789
$299$	6613.70	1.27920
$300$	−2293.90	−0.441461
$301$	−3988.20	−0.763708
$302$	2321.06	0.442258
$303$	−2749.44	−0.521292
$304$	1157.43	0.218365
$305$	−2410.83	−0.452602
$306$	0	0
$307$	2156.62	0.400927	0.200463	−	0.979701i	$-0.435755\pi$
$307$	2156.62	0.400927	0.200463	+	0.979701i	$0.435755\pi$
$308$	2188.07	0.404795
$309$	−877.113	−0.161480
$310$	687.550	0.125968
$311$	2729.42	0.497656	0.248828	−	0.968548i	$-0.419955\pi$
$311$	2729.42	0.497656	0.248828	+	0.968548i	$0.419955\pi$
$312$	4870.02	0.883687
$313$	−5014.77	−0.905595	−0.452798	−	0.891613i	$-0.649574\pi$
$313$	−5014.77	−0.905595	−0.452798	+	0.891613i	$0.649574\pi$
$314$	5383.36	0.967518
$315$	918.213	0.164240
$316$	−5894.44	−1.04933
$317$	−1164.53	−0.206329	−0.103165	−	0.994664i	$-0.532897\pi$
$317$	−1164.53	−0.206329	−0.103165	+	0.994664i	$0.532897\pi$
$318$	5007.57	0.883052
$319$	−17.1438	−0.00300899
$320$	3092.75	0.540281
$321$	740.210	0.128706
$322$	6723.09	1.16355
$323$	0	0
$324$	3661.42	0.627816
$325$	3831.41	0.653934
$326$	598.024	0.101600
$327$	−3504.23	−0.592612
$328$	3941.34	0.663488
$329$	−7280.30	−1.21999
$330$	−1541.28	−0.257106
$331$	2144.03	0.356032	0.178016	−	0.984028i	$-0.443032\pi$
$331$	2144.03	0.356032	0.178016	+	0.984028i	$0.443032\pi$
$332$	−259.465	−0.0428915
$333$	−861.200	−0.141722
$334$	−905.474	−0.148339
$335$	2311.30	0.376955
$336$	−1496.25	−0.242937
$337$	−1955.09	−0.316025	−0.158012	−	0.987437i	$-0.550509\pi$
$337$	−1955.09	−0.316025	−0.158012	+	0.987437i	$0.550509\pi$
$338$	162.158	0.0260954
$339$	−9903.18	−1.58663
$340$	0	0
$341$	−407.132	−0.0646552
$342$	387.600	0.0612836
$343$	−5263.61	−0.828595
$344$	2895.35	0.453799
$345$	10405.3	1.62377
$346$	−5254.31	−0.816397
$347$	−10906.7	−1.68732	−0.843662	−	0.536875i	$-0.819605\pi$
$347$	−10906.7	−1.68732	−0.843662	+	0.536875i	$0.819605\pi$
$348$	34.7127	0.00534711
$349$	9245.27	1.41802	0.709009	−	0.705200i	$-0.249143\pi$
$349$	9245.27	1.41802	0.709009	+	0.705200i	$0.249143\pi$
$350$	3894.78	0.594814
$351$	−6651.33	−1.01146
$352$	−2529.98	−0.383092
$353$	−4026.13	−0.607051	−0.303526	−	0.952823i	$-0.598164\pi$
$353$	−4026.13	−0.607051	−0.303526	+	0.952823i	$0.598164\pi$
$354$	−4930.61	−0.740280
$355$	281.081	0.0420233
$356$	3443.33	0.512630
$357$	0	0
$358$	3311.99	0.488950
$359$	−10382.3	−1.52634	−0.763171	−	0.646197i	$-0.776359\pi$
$359$	−10382.3	−1.52634	−0.763171	+	0.646197i	$0.776359\pi$
$360$	−666.604	−0.0975919
$361$	5997.34	0.874375
$362$	1078.87	0.156641
$363$	−5720.86	−0.827183
$364$	7399.92	1.06555
$365$	4854.78	0.696194
$366$	1315.57	0.187886
$367$	12159.2	1.72945	0.864723	−	0.502249i	$-0.167494\pi$
$367$	12159.2	1.72945	0.864723	+	0.502249i	$0.167494\pi$
$368$	1475.17	0.208963
$369$	−398.916	−0.0562785
$370$	−9107.18	−1.27962
$371$	18680.9	2.61419
$372$	824.358	0.114895
$373$	11494.5	1.59561	0.797807	−	0.602913i	$-0.205993\pi$
$373$	11494.5	1.59561	0.797807	+	0.602913i	$0.205993\pi$
$374$	0	0
$375$	−2972.39	−0.409316
$376$	5285.35	0.724923
$377$	−57.9793	−0.00792065
$378$	−6761.34	−0.920016
$379$	−1085.96	−0.147182	−0.0735908	−	0.997289i	$-0.523446\pi$
$379$	−1085.96	−0.147182	−0.0735908	+	0.997289i	$0.523446\pi$
$380$	−9005.88	−1.21577
$381$	−7784.23	−1.04671
$382$	−3038.95	−0.407032
$383$	−8246.14	−1.10015	−0.550076	−	0.835115i	$-0.685401\pi$
$383$	−8246.14	−1.10015	−0.550076	+	0.835115i	$0.685401\pi$
$384$	5766.50	0.766329
$385$	−5749.82	−0.761138
$386$	−110.237	−0.0145361
$387$	−293.048	−0.0384922
$388$	−3804.72	−0.497823
$389$	−3801.18	−0.495443	−0.247722	−	0.968831i	$-0.579682\pi$
$389$	−3801.18	−0.495443	−0.247722	+	0.968831i	$0.579682\pi$
$390$	−5212.53	−0.676786
$391$	0	0
$392$	11144.8	1.43596
$393$	6567.24	0.842935
$394$	−4813.70	−0.615510
$395$	15489.4	1.97306
$396$	160.777	0.0204024
$397$	−8372.90	−1.05850	−0.529249	−	0.848466i	$-0.677526\pi$
$397$	−8372.90	−1.05850	−0.529249	+	0.848466i	$0.677526\pi$
$398$	−1986.35	−0.250167
$399$	−16619.8	−2.08529
$400$	854.586	0.106823
$401$	−2173.63	−0.270688	−0.135344	−	0.990799i	$-0.543214\pi$
$401$	−2173.63	−0.270688	−0.135344	+	0.990799i	$0.543214\pi$
$402$	−1261.26	−0.156483
$403$	−1376.89	−0.170194
$404$	3032.95	0.373503
$405$	−9621.49	−1.18048
$406$	−58.9382	−0.00720457
$407$	5392.80	0.656785
$408$	0	0
$409$	4538.13	0.548646	0.274323	−	0.961638i	$-0.411546\pi$
$409$	4538.13	0.548646	0.274323	+	0.961638i	$0.411546\pi$
$410$	−4218.54	−0.508143
$411$	2418.24	0.290227
$412$	967.557	0.115699
$413$	−18393.8	−2.19153
$414$	494.005	0.0586449
$415$	681.822	0.0806490
$416$	−8556.23	−1.00842
$417$	−5066.91	−0.595031
$418$	−2427.14	−0.284008
$419$	4239.67	0.494323	0.247161	−	0.968974i	$-0.420502\pi$
$419$	4239.67	0.494323	0.247161	+	0.968974i	$0.420502\pi$
$420$	11642.2	1.35257
$421$	14001.6	1.62090	0.810448	−	0.585811i	$-0.199224\pi$
$421$	14001.6	1.62090	0.810448	+	0.585811i	$0.199224\pi$
$422$	−1676.98	−0.193446
$423$	−534.948	−0.0614895
$424$	−13562.0	−1.55337
$425$	0	0
$426$	−153.384	−0.0174448
$427$	4907.80	0.556218
$428$	−816.537	−0.0922168
$429$	3086.59	0.347371
$430$	−3098.98	−0.347549
$431$	6401.94	0.715477	0.357738	−	0.933822i	$-0.383548\pi$
$431$	6401.94	0.715477	0.357738	+	0.933822i	$0.383548\pi$
$432$	−1483.56	−0.165227
$433$	13.2865	0.00147462	0.000737310	−	1.00000i	$-0.499765\pi$
$433$	13.2865	0.00147462	0.000737310		1.00000i	$0.499765\pi$
$434$	−1399.67	−0.154807
$435$	−91.2180	−0.0100542
$436$	3865.57	0.424603
$437$	16385.7	1.79367
$438$	−2649.22	−0.289006
$439$	−14294.8	−1.55410	−0.777052	−	0.629437i	$-0.783286\pi$
$439$	−14294.8	−1.55410	−0.777052	+	0.629437i	$0.783286\pi$
$440$	4174.25	0.452272
$441$	−1128.00	−0.121801
$442$	0	0
$443$	16530.3	1.77286	0.886430	−	0.462862i	$-0.153177\pi$
$443$	16530.3	1.77286	0.886430	+	0.462862i	$0.153177\pi$
$444$	−10919.3	−1.16713
$445$	−9048.39	−0.963898
$446$	2212.76	0.234927
$447$	−6593.22	−0.697648
$448$	−6296.01	−0.663970
$449$	16571.9	1.74182	0.870910	−	0.491443i	$-0.163530\pi$
$449$	16571.9	1.74182	0.870910	+	0.491443i	$0.163530\pi$
$450$	286.184	0.0299796
$451$	2498.00	0.260812
$452$	10924.4	1.13681
$453$	−7312.91	−0.758478
$454$	−3854.40	−0.398449
$455$	−19445.5	−2.00356
$456$	12065.6	1.23909
$457$	−14718.1	−1.50653	−0.753263	−	0.657719i	$-0.771521\pi$
$457$	−14718.1	−1.50653	−0.753263	+	0.657719i	$0.771521\pi$
$458$	−7952.35	−0.811329
$459$	0	0
$460$	−11478.2	−1.16342
$461$	−15330.5	−1.54884	−0.774419	−	0.632672i	$-0.781958\pi$
$461$	−15330.5	−1.54884	−0.774419	+	0.632672i	$0.781958\pi$
$462$	3137.64	0.315966
$463$	11158.0	1.11999	0.559993	−	0.828497i	$-0.310804\pi$
$463$	11158.0	1.11999	0.559993	+	0.828497i	$0.310804\pi$
$464$	−12.9321	−0.00129388
$465$	−2166.25	−0.216037
$466$	1409.61	0.140126
$467$	−14748.4	−1.46140	−0.730700	−	0.682699i	$-0.760806\pi$
$467$	−14748.4	−1.46140	−0.730700	+	0.682699i	$0.760806\pi$
$468$	543.737	0.0537057
$469$	−4705.19	−0.463253
$470$	−5657.07	−0.555194
$471$	−16961.2	−1.65931
$472$	13353.5	1.30222
$473$	1835.06	0.178385
$474$	−8452.48	−0.819062
$475$	9492.45	0.916934
$476$	0	0
$477$	1372.65	0.131760
$478$	256.219	0.0245171
$479$	14914.1	1.42264	0.711320	−	0.702868i	$-0.248098\pi$
$479$	14914.1	1.42264	0.711320	+	0.702868i	$0.248098\pi$
$480$	−13461.4	−1.28006
$481$	18238.1	1.72887
$482$	−5484.86	−0.518317
$483$	−21182.3	−1.99550
$484$	6310.77	0.592672
$485$	9998.04	0.936057
$486$	−956.813	−0.0893043
$487$	3034.34	0.282339	0.141169	−	0.989985i	$-0.454914\pi$
$487$	3034.34	0.282339	0.141169	+	0.989985i	$0.454914\pi$
$488$	−3562.96	−0.330507
$489$	−1884.18	−0.174245
$490$	−11928.6	−1.09975
$491$	10032.0	0.922073	0.461036	−	0.887381i	$-0.347478\pi$
$491$	10032.0	0.922073	0.461036	+	0.887381i	$0.347478\pi$
$492$	−5057.94	−0.463475
$493$	0	0
$494$	−8208.43	−0.747601
$495$	−422.490	−0.0383626
$496$	−307.112	−0.0278019
$497$	−572.207	−0.0516438
$498$	−372.066	−0.0334793
$499$	13921.2	1.24890	0.624449	−	0.781066i	$-0.285324\pi$
$499$	13921.2	1.24890	0.624449	+	0.781066i	$0.285324\pi$
$500$	3278.89	0.293273
$501$	2852.86	0.254404
$502$	6847.23	0.608779
$503$	−10270.2	−0.910387	−0.455194	−	0.890392i	$-0.650430\pi$
$503$	−10270.2	−0.910387	−0.455194	+	0.890392i	$0.650430\pi$
$504$	1357.03	0.119934
$505$	−7970.00	−0.702298
$506$	−3093.44	−0.271779
$507$	−510.908	−0.0447539
$508$	8586.90	0.749965
$509$	18020.5	1.56924	0.784621	−	0.619975i	$-0.212857\pi$
$509$	18020.5	1.56924	0.784621	+	0.619975i	$0.212857\pi$
$510$	0	0
$511$	−9883.03	−0.855576
$512$	−3652.06	−0.315234
$513$	−16478.9	−1.41825
$514$	7225.00	0.620002
$515$	−2542.55	−0.217550
$516$	−3715.61	−0.316998
$517$	3349.82	0.284962
$518$	18539.8	1.57257
$519$	16554.6	1.40013
$520$	14117.1	1.19053
$521$	−18326.3	−1.54106	−0.770529	−	0.637405i	$-0.780008\pi$
$521$	−18326.3	−1.54106	−0.770529	+	0.637405i	$0.780008\pi$
$522$	−4.33071	−0.000363122 0
$523$	−15369.6	−1.28502	−0.642512	−	0.766276i	$-0.722108\pi$
$523$	−15369.6	−1.28502	−0.642512	+	0.766276i	$0.722108\pi$
$524$	−7244.42	−0.603958
$525$	−12271.2	−1.02011
$526$	−7452.09	−0.617731
$527$	0	0
$528$	688.455	0.0567447
$529$	8716.90	0.716438
$530$	14515.8	1.18967
$531$	−1351.56	−0.110457
$532$	18333.6	1.49410
$533$	8448.08	0.686542
$534$	4937.65	0.400137
$535$	2145.70	0.173395
$536$	3415.87	0.275267
$537$	−10435.0	−0.838556
$538$	5788.09	0.463833
$539$	7063.50	0.564464
$540$	11543.5	0.919913
$541$	18606.9	1.47870	0.739348	−	0.673323i	$-0.235134\pi$
$541$	18606.9	1.47870	0.739348	+	0.673323i	$0.235134\pi$
$542$	12184.0	0.965586
$543$	−3399.16	−0.268641
$544$	0	0
$545$	−10157.9	−0.798382
$546$	10611.3	0.831725
$547$	−3946.20	−0.308459	−0.154230	−	0.988035i	$-0.549290\pi$
$547$	−3946.20	−0.308459	−0.154230	+	0.988035i	$0.549290\pi$
$548$	−2667.60	−0.207946
$549$	360.619	0.0280343
$550$	−1792.07	−0.138935
$551$	−143.646	−0.0111062
$552$	15377.9	1.18574
$553$	−31532.3	−2.42476
$554$	5145.11	0.394576
$555$	28693.8	2.19457
$556$	5589.39	0.426336
$557$	14883.1	1.13217	0.566084	−	0.824347i	$-0.308458\pi$
$557$	14883.1	1.13217	0.566084	+	0.824347i	$0.308458\pi$
$558$	−102.846	−0.00780253
$559$	6206.05	0.469567
$560$	−4337.27	−0.327291
$561$	0	0
$562$	10818.7	0.812027
$563$	25751.7	1.92771	0.963857	−	0.266420i	$-0.0858408\pi$
$563$	25751.7	1.92771	0.963857	+	0.266420i	$0.0858408\pi$
$564$	−6782.71	−0.506389
$565$	−28707.0	−2.13755
$566$	−4953.22	−0.367843
$567$	19586.8	1.45074
$568$	415.410	0.0306870
$569$	−2194.88	−0.161712	−0.0808561	−	0.996726i	$-0.525765\pi$
$569$	−2194.88	−0.161712	−0.0808561	+	0.996726i	$0.525765\pi$
$570$	−12914.2	−0.948977
$571$	−5227.87	−0.383151	−0.191576	−	0.981478i	$-0.561360\pi$
$571$	−5227.87	−0.383151	−0.191576	+	0.981478i	$0.561360\pi$
$572$	−3404.86	−0.248889
$573$	9574.77	0.698066
$574$	8587.81	0.624474
$575$	12098.3	0.877453
$576$	−462.623	−0.0334652
$577$	−6527.86	−0.470985	−0.235492	−	0.971876i	$-0.575670\pi$
$577$	−6527.86	−0.470985	−0.235492	+	0.971876i	$0.575670\pi$
$578$	0	0
$579$	347.323	0.0249296
$580$	100.624	0.00720376
$581$	−1388.01	−0.0991122
$582$	−5455.87	−0.388579
$583$	−8595.50	−0.610617
$584$	7174.87	0.508387
$585$	−1428.83	−0.100983
$586$	−8535.65	−0.601714
$587$	−6648.24	−0.467465	−0.233733	−	0.972301i	$-0.575094\pi$
$587$	−6648.24	−0.467465	−0.233733	+	0.972301i	$0.575094\pi$
$588$	−14302.1	−1.00308
$589$	−3411.30	−0.238642
$590$	−14292.7	−0.997324
$591$	15166.4	1.05561
$592$	4067.96	0.282419
$593$	−1450.60	−0.100453	−0.0502267	−	0.998738i	$-0.515994\pi$
$593$	−1450.60	−0.100453	−0.0502267	+	0.998738i	$0.515994\pi$
$594$	3111.04	0.214895
$595$	0	0
$596$	7273.09	0.499861
$597$	6258.35	0.429040
$598$	−10461.8	−0.715411
$599$	−10070.9	−0.686957	−0.343479	−	0.939161i	$-0.611605\pi$
$599$	−10070.9	−0.686957	−0.343479	+	0.939161i	$0.611605\pi$
$600$	8908.64	0.606156
$601$	9209.45	0.625060	0.312530	−	0.949908i	$-0.398823\pi$
$601$	9209.45	0.625060	0.312530	+	0.949908i	$0.398823\pi$
$602$	6308.69	0.427115
$603$	−345.732	−0.0233487
$604$	8066.99	0.543445
$605$	−16583.5	−1.11440
$606$	4349.18	0.291540
$607$	−5813.89	−0.388762	−0.194381	−	0.980926i	$-0.562270\pi$
$607$	−5813.89	−0.388762	−0.194381	+	0.980926i	$0.562270\pi$
$608$	−21198.4	−1.41399
$609$	185.695	0.0123559
$610$	3813.54	0.253124
$611$	11328.9	0.750111
$612$	0	0
$613$	−23778.5	−1.56673	−0.783365	−	0.621562i	$-0.786498\pi$
$613$	−23778.5	−1.56673	−0.783365	+	0.621562i	$0.786498\pi$
$614$	−3411.42	−0.224224
$615$	13291.3	0.871472
$616$	−8497.65	−0.555812
$617$	−19716.9	−1.28650	−0.643251	−	0.765655i	$-0.722415\pi$
$617$	−19716.9	−1.28650	−0.643251	+	0.765655i	$0.722415\pi$
$618$	1387.45	0.0903099
$619$	−6184.28	−0.401562	−0.200781	−	0.979636i	$-0.564348\pi$
$619$	−6184.28	−0.401562	−0.200781	+	0.979636i	$0.564348\pi$
$620$	2389.62	0.154790
$621$	−21002.7	−1.35718
$622$	−4317.50	−0.278322
$623$	18420.1	1.18457
$624$	2328.31	0.149370
$625$	−19081.0	−1.22119
$626$	7932.56	0.506468
$627$	7647.13	0.487077
$628$	18710.2	1.18888
$629$	0	0
$630$	−1452.47	−0.0918534
$631$	14216.8	0.896926	0.448463	−	0.893801i	$-0.351972\pi$
$631$	14216.8	0.896926	0.448463	+	0.893801i	$0.351972\pi$
$632$	22891.8	1.44080
$633$	5283.64	0.331763
$634$	1842.09	0.115393
$635$	−22564.7	−1.41016
$636$	17404.1	1.08509
$637$	23888.3	1.48585
$638$	27.1187	0.00168282
$639$	−42.0450	−0.00260294
$640$	16715.7	1.03242
$641$	−14249.8	−0.878058	−0.439029	−	0.898473i	$-0.644677\pi$
$641$	−14249.8	−0.878058	−0.439029	+	0.898473i	$0.644677\pi$
$642$	−1170.89	−0.0719805
$643$	−1767.83	−0.108424	−0.0542118	−	0.998529i	$-0.517265\pi$
$643$	−1767.83	−0.108424	−0.0542118	+	0.998529i	$0.517265\pi$
$644$	23366.5	1.42977
$645$	9763.89	0.596051
$646$	0	0
$647$	−14274.5	−0.867369	−0.433685	−	0.901065i	$-0.642787\pi$
$647$	−14274.5	−0.867369	−0.433685	+	0.901065i	$0.642787\pi$
$648$	−14219.6	−0.862035
$649$	8463.40	0.511891
$650$	−6060.68	−0.365722
$651$	4409.90	0.265496
$652$	2078.47	0.124845
$653$	−14516.1	−0.869924	−0.434962	−	0.900449i	$-0.643238\pi$
$653$	−14516.1	−0.869924	−0.434962	+	0.900449i	$0.643238\pi$
$654$	5543.13	0.331427
$655$	19036.9	1.13562
$656$	1884.32	0.112150
$657$	−726.193	−0.0431225
$658$	11516.3	0.682296
$659$	23248.8	1.37427	0.687135	−	0.726530i	$-0.258868\pi$
$659$	23248.8	1.37427	0.687135	+	0.726530i	$0.258868\pi$
$660$	−5356.83	−0.315931
$661$	−28695.7	−1.68855	−0.844277	−	0.535907i	$-0.819970\pi$
$661$	−28695.7	−1.68855	−0.844277	+	0.535907i	$0.819970\pi$
$662$	−3391.51	−0.199116
$663$	0	0
$664$	1007.66	0.0588930
$665$	−48177.0	−2.80936
$666$	1362.28	0.0792602
$667$	−183.079	−0.0106280
$668$	−3147.03	−0.182279
$669$	−6971.71	−0.402903
$670$	−3656.11	−0.210818
$671$	−2258.18	−0.129920
$672$	27403.8	1.57310
$673$	6852.55	0.392491	0.196246	−	0.980555i	$-0.437125\pi$
$673$	6852.55	0.392491	0.196246	+	0.980555i	$0.437125\pi$
$674$	3092.63	0.176742
$675$	−12167.2	−0.693799
$676$	563.590	0.0320659
$677$	2123.19	0.120533	0.0602665	−	0.998182i	$-0.480805\pi$
$677$	2123.19	0.120533	0.0602665	+	0.998182i	$0.480805\pi$
$678$	15665.2	0.887345
$679$	−20353.3	−1.15035
$680$	0	0
$681$	12144.0	0.683345
$682$	644.017	0.0361594
$683$	4035.12	0.226061	0.113030	−	0.993592i	$-0.463944\pi$
$683$	4035.12	0.226061	0.113030	+	0.993592i	$0.463944\pi$
$684$	1347.13	0.0753052
$685$	7009.92	0.391001
$686$	8326.18	0.463404
$687$	25055.3	1.39144
$688$	1384.24	0.0767060
$689$	−29069.5	−1.60734
$690$	−16459.4	−0.908116
$691$	−20015.0	−1.10189	−0.550947	−	0.834540i	$-0.685733\pi$
$691$	−20015.0	−1.10189	−0.550947	+	0.834540i	$0.685733\pi$
$692$	−18261.7	−1.00319
$693$	860.076	0.0471451
$694$	17252.6	0.943661
$695$	−14687.8	−0.801641
$696$	−134.811	−0.00734195
$697$	0	0
$698$	−14624.5	−0.793047
$699$	−4441.23	−0.240319
$700$	13536.6	0.730905
$701$	19025.4	1.02508	0.512539	−	0.858664i	$-0.328705\pi$
$701$	19025.4	1.02508	0.512539	+	0.858664i	$0.328705\pi$
$702$	10521.3	0.565673
$703$	45185.6	2.42419
$704$	2896.93	0.155088
$705$	17823.6	0.952164
$706$	6368.69	0.339502
$707$	16224.8	0.863077
$708$	−17136.6	−0.909653
$709$	11992.4	0.635237	0.317619	−	0.948219i	$-0.397117\pi$
$709$	11992.4	0.635237	0.317619	+	0.948219i	$0.397117\pi$
$710$	−444.626	−0.0235021
$711$	−2316.96	−0.122212
$712$	−13372.6	−0.703876
$713$	−4347.78	−0.228367
$714$	0	0
$715$	8947.31	0.467987
$716$	11511.0	0.600821
$717$	−807.265	−0.0420472
$718$	16423.1	0.853629
$719$	12005.7	0.622721	0.311361	−	0.950292i	$-0.399215\pi$
$719$	12005.7	0.622721	0.311361	+	0.950292i	$0.399215\pi$
$720$	−318.697	−0.0164960
$721$	5175.95	0.267354
$722$	−9486.83	−0.489007
$723$	17281.0	0.888919
$724$	3749.66	0.192479
$725$	−106.060	−0.00543309
$726$	9049.49	0.462614
$727$	−22403.9	−1.14294	−0.571468	−	0.820624i	$-0.693626\pi$
$727$	−22403.9	−1.14294	−0.571468	+	0.820624i	$0.693626\pi$
$728$	−28738.5	−1.46308
$729$	20996.1	1.06671
$730$	−7679.48	−0.389357
$731$	0	0
$732$	4572.36	0.230873
$733$	−17400.5	−0.876810	−0.438405	−	0.898777i	$-0.644457\pi$
$733$	−17400.5	−0.876810	−0.438405	+	0.898777i	$0.644457\pi$
$734$	−19233.9	−0.967218
$735$	37583.2	1.88609
$736$	−27017.8	−1.35311
$737$	2164.96	0.108205
$738$	631.022	0.0314746
$739$	−7691.26	−0.382852	−0.191426	−	0.981507i	$-0.561311\pi$
$739$	−7691.26	−0.382852	−0.191426	+	0.981507i	$0.561311\pi$
$740$	−31652.6	−1.57239
$741$	25862.1	1.28214
$742$	−29550.3	−1.46203
$743$	33377.5	1.64805	0.824027	−	0.566551i	$-0.191723\pi$
$743$	33377.5	1.64805	0.824027	+	0.566551i	$0.191723\pi$
$744$	−3201.50	−0.157759
$745$	−19112.2	−0.939890
$746$	−18182.5	−0.892371
$747$	−101.989	−0.00499543
$748$	0	0
$749$	−4368.06	−0.213092
$750$	4701.84	0.228916
$751$	30285.6	1.47155	0.735777	−	0.677224i	$-0.236817\pi$
$751$	30285.6	1.47155	0.735777	+	0.677224i	$0.236817\pi$
$752$	2526.88	0.122534
$753$	−21573.4	−1.04406
$754$	91.7139	0.00442974
$755$	−21198.4	−1.02184
$756$	−23499.5	−1.13051
$757$	−13809.3	−0.663023	−0.331511	−	0.943451i	$-0.607559\pi$
$757$	−13809.3	−0.663023	−0.331511	+	0.943451i	$0.607559\pi$
$758$	1717.81	0.0823135
$759$	9746.44	0.466104
$760$	34975.5	1.66933
$761$	33269.2	1.58477	0.792383	−	0.610023i	$-0.208840\pi$
$761$	33269.2	1.58477	0.792383	+	0.610023i	$0.208840\pi$
$762$	12313.4	0.585390
$763$	20678.8	0.981159
$764$	−10562.1	−0.500160
$765$	0	0
$766$	13044.1	0.615276
$767$	28622.7	1.34746
$768$	−17657.0	−0.829613
$769$	−22932.1	−1.07536	−0.537681	−	0.843148i	$-0.680700\pi$
$769$	−22932.1	−1.07536	−0.537681	+	0.843148i	$0.680700\pi$
$770$	9095.29	0.425677
$771$	−22763.7	−1.06331
$772$	−383.137	−0.0178619
$773$	3142.46	0.146218	0.0731090	−	0.997324i	$-0.476708\pi$
$773$	3142.46	0.146218	0.0731090	+	0.997324i	$0.476708\pi$
$774$	463.555	0.0215273
$775$	−2518.73	−0.116742
$776$	14776.1	0.683545
$777$	−58412.9	−2.69698
$778$	6012.85	0.277084
$779$	20930.4	0.962657
$780$	−18116.5	−0.831633
$781$	263.285	0.0120628
$782$	0	0
$783$	184.121	0.00840351
$784$	5328.22	0.242721
$785$	−49166.7	−2.23546
$786$	−10388.3	−0.471424
$787$	−11712.3	−0.530492	−0.265246	−	0.964181i	$-0.585453\pi$
$787$	−11712.3	−0.530492	−0.265246	+	0.964181i	$0.585453\pi$
$788$	−16730.3	−0.756337
$789$	23479.1	1.05942
$790$	−24501.8	−1.10346
$791$	58439.8	2.62690
$792$	−624.397	−0.0280139
$793$	−7637.04	−0.341991
$794$	13244.6	0.591981
$795$	−45734.6	−2.04030
$796$	−6903.68	−0.307405
$797$	−12691.2	−0.564045	−0.282022	−	0.959408i	$-0.591005\pi$
$797$	−12691.2	−0.564045	−0.282022	+	0.959408i	$0.591005\pi$
$798$	26289.9	1.16623
$799$	0	0
$800$	−15651.8	−0.691717
$801$	1353.49	0.0597042
$802$	3438.33	0.151386
$803$	4547.39	0.199843
$804$	−4383.60	−0.192286
$805$	−61402.6	−2.68839
$806$	2178.03	0.0951832
$807$	−18236.4	−0.795480
$808$	−11778.9	−0.512845
$809$	22034.9	0.957610	0.478805	−	0.877921i	$-0.341070\pi$
$809$	22034.9	0.957610	0.478805	+	0.877921i	$0.341070\pi$
$810$	15219.7	0.660203
$811$	2987.60	0.129357	0.0646787	−	0.997906i	$-0.479398\pi$
$811$	2987.60	0.129357	0.0646787	+	0.997906i	$0.479398\pi$
$812$	−204.843	−0.00885295
$813$	−38387.9	−1.65599
$814$	−8530.55	−0.367316
$815$	−5461.81	−0.234747
$816$	0	0
$817$	15375.7	0.658418
$818$	−7178.59	−0.306838
$819$	2908.72	0.124101
$820$	−14661.8	−0.624405
$821$	39918.9	1.69693	0.848465	−	0.529251i	$-0.177527\pi$
$821$	39918.9	1.69693	0.848465	+	0.529251i	$0.177527\pi$
$822$	−3825.27	−0.162313
$823$	−15017.3	−0.636050	−0.318025	−	0.948082i	$-0.603020\pi$
$823$	−15017.3	−0.636050	−0.318025	+	0.948082i	$0.603020\pi$
$824$	−3757.63	−0.158863
$825$	5646.25	0.238275
$826$	29096.1	1.22564
$827$	−3898.57	−0.163926	−0.0819628	−	0.996635i	$-0.526119\pi$
$827$	−3898.57	−0.163926	−0.0819628	+	0.996635i	$0.526119\pi$
$828$	1716.94	0.0720627
$829$	−4410.66	−0.184787	−0.0923937	−	0.995723i	$-0.529452\pi$
$829$	−4410.66	−0.184787	−0.0923937	+	0.995723i	$0.529452\pi$
$830$	−1078.53	−0.0451041
$831$	−16210.6	−0.676702
$832$	9797.23	0.408243
$833$	0	0
$834$	8015.05	0.332780
$835$	8269.77	0.342739
$836$	−8435.67	−0.348988
$837$	4372.52	0.180569
$838$	−6706.47	−0.276457
$839$	−29154.8	−1.19969	−0.599843	−	0.800118i	$-0.704770\pi$
$839$	−29154.8	−1.19969	−0.599843	+	0.800118i	$0.704770\pi$
$840$	−45214.0	−1.85718
$841$	−24387.4	−0.999934
$842$	−22148.3	−0.906510
$843$	−34086.2	−1.39264
$844$	−5828.46	−0.237706
$845$	−1481.00	−0.0602936
$846$	846.202	0.0343889
$847$	33759.5	1.36953
$848$	−6483.86	−0.262567
$849$	15606.0	0.630856
$850$	0	0
$851$	57590.0	2.31981
$852$	−533.097	−0.0214362
$853$	−24310.2	−0.975808	−0.487904	−	0.872897i	$-0.662238\pi$
$853$	−24310.2	−0.975808	−0.487904	+	0.872897i	$0.662238\pi$
$854$	−7763.35	−0.311073
$855$	−3539.99	−0.141596
$856$	3171.12	0.126620
$857$	−13081.1	−0.521403	−0.260701	−	0.965419i	$-0.583954\pi$
$857$	−13081.1	−0.521403	−0.260701	+	0.965419i	$0.583954\pi$
$858$	−4882.49	−0.194272
$859$	1740.97	0.0691514	0.0345757	−	0.999402i	$-0.488992\pi$
$859$	1740.97	0.0691514	0.0345757	+	0.999402i	$0.488992\pi$
$860$	−10770.7	−0.427067
$861$	−27057.4	−1.07098
$862$	−10126.8	−0.400141
$863$	−15561.9	−0.613826	−0.306913	−	0.951738i	$-0.599296\pi$
$863$	−15561.9	−0.613826	−0.306913	+	0.951738i	$0.599296\pi$
$864$	27171.5	1.06990
$865$	47988.0	1.88629
$866$	−21.0172	−0.000824703 0
$867$	0	0
$868$	−4864.63	−0.190226
$869$	14508.7	0.566368
$870$	144.292	0.00562295
$871$	7321.76	0.284832
$872$	−15012.4	−0.583010
$873$	−1495.54	−0.0579797
$874$	−25919.5	−1.00314
$875$	17540.4	0.677685
$876$	−9207.54	−0.355130
$877$	−32043.6	−1.23379	−0.616895	−	0.787045i	$-0.711610\pi$
$877$	−32043.6	−1.23379	−0.616895	+	0.787045i	$0.711610\pi$
$878$	22612.0	0.869156
$879$	26893.1	1.03195
$880$	1995.67	0.0764478
$881$	−38673.0	−1.47892	−0.739458	−	0.673202i	$-0.764918\pi$
$881$	−38673.0	−1.47892	−0.739458	+	0.673202i	$0.764918\pi$
$882$	1784.31	0.0681191
$883$	−45977.4	−1.75228	−0.876140	−	0.482056i	$-0.839890\pi$
$883$	−45977.4	−1.75228	−0.876140	+	0.482056i	$0.839890\pi$
$884$	0	0
$885$	45031.7	1.71042
$886$	−26148.3	−0.991499
$887$	−5325.60	−0.201596	−0.100798	−	0.994907i	$-0.532140\pi$
$887$	−5325.60	−0.201596	−0.100798	+	0.994907i	$0.532140\pi$
$888$	42406.5	1.60256
$889$	45935.6	1.73299
$890$	14313.1	0.539074
$891$	−9012.30	−0.338859
$892$	7690.60	0.288677
$893$	28067.7	1.05179
$894$	10429.4	0.390170
$895$	−30248.7	−1.12972
$896$	−34028.8	−1.26877
$897$	32961.8	1.22694
$898$	−26214.1	−0.974139
$899$	38.1150	0.00141402
$900$	994.649	0.0368389
$901$	0	0
$902$	−3951.44	−0.145863
$903$	−19876.7	−0.732507
$904$	−42426.1	−1.56092
$905$	−9853.37	−0.361919
$906$	11567.9	0.424190
$907$	−12188.4	−0.446207	−0.223104	−	0.974795i	$-0.571619\pi$
$907$	−12188.4	−0.446207	−0.223104	+	0.974795i	$0.571619\pi$
$908$	−13396.2	−0.489613
$909$	1192.18	0.0435006
$910$	30759.7	1.12052
$911$	24738.8	0.899707	0.449854	−	0.893102i	$-0.351476\pi$
$911$	24738.8	0.899707	0.449854	+	0.893102i	$0.351476\pi$
$912$	5768.48	0.209444
$913$	638.652	0.0231504
$914$	23281.6	0.842547
$915$	−12015.3	−0.434111
$916$	−27638.9	−0.996959
$917$	−38754.0	−1.39561
$918$	0	0
$919$	1584.70	0.0568820	0.0284410	−	0.999595i	$-0.490946\pi$
$919$	1584.70	0.0568820	0.0284410	+	0.999595i	$0.490946\pi$
$920$	44577.0	1.59746
$921$	10748.3	0.384548
$922$	24250.5	0.866211
$923$	890.412	0.0317533
$924$	10905.1	0.388258
$925$	33362.7	1.18590
$926$	−17650.1	−0.626369
$927$	380.322	0.0134751
$928$	236.852	0.00837829
$929$	−7266.92	−0.256642	−0.128321	−	0.991733i	$-0.540959\pi$
$929$	−7266.92	−0.256642	−0.128321	+	0.991733i	$0.540959\pi$
$930$	3426.66	0.120822
$931$	59184.1	2.08344
$932$	4899.19	0.172187
$933$	13603.1	0.477325
$934$	23329.6	0.817310
$935$	0	0
$936$	−2111.67	−0.0737416
$937$	−3617.62	−0.126129	−0.0630643	−	0.998009i	$-0.520087\pi$
$937$	−3617.62	−0.126129	−0.0630643	+	0.998009i	$0.520087\pi$
$938$	7442.86	0.259081
$939$	−24992.9	−0.868598
$940$	−19661.5	−0.682220
$941$	35841.7	1.24166	0.620832	−	0.783944i	$-0.286795\pi$
$941$	35841.7	1.24166	0.620832	+	0.783944i	$0.286795\pi$
$942$	26830.0	0.927991
$943$	26676.3	0.921208
$944$	6384.21	0.220115
$945$	61751.9	2.12570
$946$	−2902.77	−0.0997643
$947$	33544.8	1.15107	0.575534	−	0.817778i	$-0.304794\pi$
$947$	33544.8	1.15107	0.575534	+	0.817778i	$0.304794\pi$
$948$	−29377.1	−1.00646
$949$	15379.0	0.526052
$950$	−15015.5	−0.512809
$951$	−5803.85	−0.197900
$952$	0	0
$953$	−51190.9	−1.74002	−0.870008	−	0.493038i	$-0.835886\pi$
$953$	−51190.9	−1.74002	−0.870008	+	0.493038i	$0.835886\pi$
$954$	−2171.32	−0.0736886
$955$	27755.0	0.940452
$956$	890.506	0.0301266
$957$	−85.4425	−0.00288606
$958$	−23591.8	−0.795633
$959$	−14270.3	−0.480514
$960$	15413.9	0.518209
$961$	−28885.8	−0.969616
$962$	−28849.8	−0.966896
$963$	−320.960	−0.0107402
$964$	−19063.0	−0.636906
$965$	1006.81	0.0335858
$966$	33507.0	1.11602
$967$	11754.1	0.390885	0.195442	−	0.980715i	$-0.437386\pi$
$967$	11754.1	0.390885	0.195442	+	0.980715i	$0.437386\pi$
$968$	−24508.7	−0.813779
$969$	0	0
$970$	−15815.3	−0.523503
$971$	−16608.7	−0.548919	−0.274459	−	0.961599i	$-0.588499\pi$
$971$	−16608.7	−0.548919	−0.274459	+	0.961599i	$0.588499\pi$
$972$	−3325.46	−0.109737
$973$	29900.4	0.985164
$974$	−4799.84	−0.157902
$975$	19095.3	0.627218
$976$	−1703.42	−0.0558659
$977$	−47963.6	−1.57062	−0.785308	−	0.619105i	$-0.787496\pi$
$977$	−47963.6	−1.57062	−0.785308	+	0.619105i	$0.787496\pi$
$978$	2980.48	0.0974490
$979$	−8475.48	−0.276688
$980$	−41458.5	−1.35137
$981$	1519.46	0.0494521
$982$	−15869.0	−0.515683
$983$	−49858.2	−1.61773	−0.808866	−	0.587993i	$-0.799918\pi$
$983$	−49858.2	−1.61773	−0.808866	+	0.587993i	$0.799918\pi$
$984$	19643.1	0.636382
$985$	43964.0	1.42214
$986$	0	0
$987$	−36284.1	−1.17015
$988$	−28528.9	−0.918649
$989$	19596.7	0.630068
$990$	668.311	0.0214549
$991$	−50467.6	−1.61772	−0.808858	−	0.588005i	$-0.799914\pi$
$991$	−50467.6	−1.61772	−0.808858	+	0.588005i	$0.799914\pi$
$992$	5624.78	0.180027
$993$	10685.6	0.341487
$994$	905.139	0.0288826
$995$	18141.5	0.578014
$996$	−1293.14	−0.0411392
$997$	40927.6	1.30009	0.650046	−	0.759895i	$-0.274750\pi$
$997$	40927.6	1.30009	0.650046	+	0.759895i	$0.274750\pi$
$998$	−22021.2	−0.698465
$999$	−57917.6	−1.83427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.c.1.2	✓	4
17.4	even	4		289.4.b.d.288.5		8
17.13	even	4		289.4.b.d.288.6		8
17.16	even	2		289.4.a.d.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.c.1.2	✓	4	1.1	even	1	trivial
289.4.a.d.1.2	yes	4	17.16	even	2
289.4.b.d.288.5		8	17.4	even	4
289.4.b.d.288.6		8	17.13	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-1.58184 q^{2} +4.98387 q^{3} -5.49778 q^{4} +14.4471 q^{5} -7.88368 q^{6} -29.4104 q^{7} +21.3513 q^{8} -2.16104 q^{9} +O(q^{10})\)	\(q-1.58184 q^{2} +4.98387 q^{3} -5.49778 q^{4} +14.4471 q^{5} -7.88368 q^{6} -29.4104 q^{7} +21.3513 q^{8} -2.16104 q^{9} -22.8530 q^{10} +13.5324 q^{11} -27.4002 q^{12} +45.7656 q^{13} +46.5225 q^{14} +72.0024 q^{15} +10.2079 q^{16} +3.41842 q^{18} +113.386 q^{19} -79.4269 q^{20} -146.578 q^{21} -21.4060 q^{22} +144.513 q^{23} +106.412 q^{24} +83.7182 q^{25} -72.3938 q^{26} -145.335 q^{27} +161.692 q^{28} -1.26688 q^{29} -113.896 q^{30} -30.0858 q^{31} -186.958 q^{32} +67.4435 q^{33} -424.894 q^{35} +11.8809 q^{36} +398.512 q^{37} -179.358 q^{38} +228.090 q^{39} +308.464 q^{40} +184.595 q^{41} +231.862 q^{42} +135.605 q^{43} -74.3979 q^{44} -31.2207 q^{45} -228.596 q^{46} +247.542 q^{47} +50.8748 q^{48} +521.971 q^{49} -132.429 q^{50} -251.609 q^{52} -635.182 q^{53} +229.896 q^{54} +195.503 q^{55} -627.951 q^{56} +565.100 q^{57} +2.00399 q^{58} +625.420 q^{59} -395.853 q^{60} -166.873 q^{61} +47.5909 q^{62} +63.5570 q^{63} +214.074 q^{64} +661.179 q^{65} -106.685 q^{66} +159.984 q^{67} +720.232 q^{69} +672.115 q^{70} +19.4559 q^{71} -46.1411 q^{72} +336.039 q^{73} -630.382 q^{74} +417.241 q^{75} -623.370 q^{76} -397.992 q^{77} -360.801 q^{78} +1072.15 q^{79} +147.474 q^{80} -665.982 q^{81} -291.999 q^{82} +47.1944 q^{83} +805.852 q^{84} -214.506 q^{86} -6.31394 q^{87} +288.934 q^{88} -626.312 q^{89} +49.3862 q^{90} -1345.98 q^{91} -794.499 q^{92} -149.944 q^{93} -391.572 q^{94} +1638.09 q^{95} -931.774 q^{96} +692.045 q^{97} -825.674 q^{98} -29.2439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9} - 7 q^{10} + 10 q^{11} - 29 q^{12} - 22 q^{13} + 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} + 330 q^{20} - 352 q^{21} - 79 q^{22} + 380 q^{23} + 159 q^{24} + 378 q^{25} - 448 q^{26} - 494 q^{27} + 608 q^{28} - 78 q^{29} + 313 q^{30} + 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} + 512 q^{37} - 524 q^{38} + 12 q^{39} + 1381 q^{40} + 840 q^{41} + 1455 q^{42} - 114 q^{43} - 1041 q^{44} + 648 q^{45} - 1051 q^{46} + 10 q^{47} + 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} + 581 q^{54} - 1316 q^{55} + 411 q^{56} + 358 q^{57} - 376 q^{58} + 996 q^{59} - 217 q^{60} + 448 q^{61} - 73 q^{62} + 766 q^{63} - 150 q^{64} - 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} + 1116 q^{71} - 39 q^{72} + 540 q^{73} + 1630 q^{74} + 1070 q^{75} - 873 q^{76} - 894 q^{77} - 1245 q^{78} + 940 q^{79} + 307 q^{80} + 1080 q^{81} - 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} - 2252 q^{88} + 784 q^{89} - 2069 q^{90} - 2858 q^{91} - 1566 q^{92} - 1550 q^{93} + 1119 q^{94} + 2494 q^{95} - 2643 q^{96} - 518 q^{97} - 1877 q^{98} - 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9 - 7 * q^10 + 10 * q^11 - 29 * q^12 - 22 * q^13 + 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 + 330 * q^20 - 352 * q^21 - 79 * q^22 + 380 * q^23 + 159 * q^24 + 378 * q^25 - 448 * q^26 - 494 * q^27 + 608 * q^28 - 78 * q^29 + 313 * q^30 + 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 + 512 * q^37 - 524 * q^38 + 12 * q^39 + 1381 * q^40 + 840 * q^41 + 1455 * q^42 - 114 * q^43 - 1041 * q^44 + 648 * q^45 - 1051 * q^46 + 10 * q^47 + 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 + 581 * q^54 - 1316 * q^55 + 411 * q^56 + 358 * q^57 - 376 * q^58 + 996 * q^59 - 217 * q^60 + 448 * q^61 - 73 * q^62 + 766 * q^63 - 150 * q^64 - 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 + 1116 * q^71 - 39 * q^72 + 540 * q^73 + 1630 * q^74 + 1070 * q^75 - 873 * q^76 - 894 * q^77 - 1245 * q^78 + 940 * q^79 + 307 * q^80 + 1080 * q^81 - 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 - 2252 * q^88 + 784 * q^89 - 2069 * q^90 - 2858 * q^91 - 1566 * q^92 - 1550 * q^93 + 1119 * q^94 + 2494 * q^95 - 2643 * q^96 - 518 * q^97 - 1877 * q^98 - 1406 * q^99

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