LMFDB - Embedded newform 289.4.a.i.1.12

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} + \cdots + 29352 $ x^12 - 72x^10 - 17x^9 + 1872x^8 + 627x^7 - 20922x^6 - 5163x^5 + 93255x^4 - 4607x^3 - 117822x^2 + 21960x + 29352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-4.44354$ 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)

$f(q)$	$=$	$q+4.44354 q^{2} +0.537336 q^{3} +11.7450 q^{4} +17.2592 q^{5} +2.38767 q^{6} -6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} +O(q^{10})$	\(q+4.44354 q^{2} +0.537336 q^{3} +11.7450 q^{4} +17.2592 q^{5} +2.38767 q^{6} -6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} +76.6918 q^{10} +55.3227 q^{11} +6.31102 q^{12} +58.6637 q^{13} -28.4725 q^{14} +9.27398 q^{15} -20.0149 q^{16} -118.692 q^{18} -91.1866 q^{19} +202.709 q^{20} -3.44305 q^{21} +245.829 q^{22} +120.879 q^{23} +8.94185 q^{24} +172.879 q^{25} +260.674 q^{26} -28.8610 q^{27} -75.2576 q^{28} -215.755 q^{29} +41.2093 q^{30} -17.5166 q^{31} -222.065 q^{32} +29.7269 q^{33} -110.590 q^{35} -313.724 q^{36} -8.40485 q^{37} -405.191 q^{38} +31.5221 q^{39} +287.211 q^{40} +99.9530 q^{41} -15.2993 q^{42} -81.5297 q^{43} +649.766 q^{44} -461.015 q^{45} +537.130 q^{46} +195.351 q^{47} -10.7547 q^{48} -301.942 q^{49} +768.195 q^{50} +689.006 q^{52} +260.322 q^{53} -128.245 q^{54} +954.825 q^{55} -106.630 q^{56} -48.9979 q^{57} -958.715 q^{58} -536.401 q^{59} +108.923 q^{60} -265.689 q^{61} -77.8357 q^{62} +171.156 q^{63} -826.636 q^{64} +1012.49 q^{65} +132.093 q^{66} +514.794 q^{67} +64.9526 q^{69} -491.412 q^{70} -704.023 q^{71} -444.504 q^{72} +184.948 q^{73} -37.3473 q^{74} +92.8943 q^{75} -1070.99 q^{76} -354.487 q^{77} +140.070 q^{78} -34.8358 q^{79} -345.440 q^{80} +705.696 q^{81} +444.145 q^{82} -647.682 q^{83} -40.4386 q^{84} -362.280 q^{86} -115.933 q^{87} +920.630 q^{88} -1060.24 q^{89} -2048.53 q^{90} -375.895 q^{91} +1419.72 q^{92} -9.41231 q^{93} +868.051 q^{94} -1573.81 q^{95} -119.324 q^{96} -256.409 q^{97} -1341.69 q^{98} -1477.74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q + 18 * q^3 + 48 * q^4 + 30 * q^5 - 9 * q^6 + 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9} + 60 q^{10} + 162 q^{11} + 216 q^{12} - 72 q^{13} + 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} + 129 q^{20} + 246 q^{21} + 456 q^{22} + 282 q^{23} + 72 q^{24} + 444 q^{25} + 528 q^{26} + 1092 q^{27} + 120 q^{28} + 648 q^{29} - 1890 q^{30} + 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} - 30 q^{37} - 60 q^{38} + 1758 q^{39} - 450 q^{40} + 318 q^{41} + 804 q^{42} + 486 q^{43} + 2448 q^{44} + 486 q^{45} + 1617 q^{46} - 888 q^{47} + 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} + 933 q^{54} + 972 q^{55} + 2661 q^{56} - 156 q^{57} + 201 q^{58} - 792 q^{59} + 1458 q^{60} + 1212 q^{61} + 2817 q^{62} + 2112 q^{63} - 1857 q^{64} + 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} + 2802 q^{71} + 1455 q^{72} + 726 q^{73} + 270 q^{74} - 264 q^{75} + 675 q^{76} - 1008 q^{77} - 3090 q^{78} - 444 q^{79} - 1143 q^{80} + 2520 q^{81} - 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} - 3750 q^{88} - 906 q^{89} - 7755 q^{90} + 2280 q^{91} + 87 q^{92} + 132 q^{93} + 735 q^{94} + 966 q^{95} - 5046 q^{96} - 3246 q^{97} + 1911 q^{98} - 282 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 + 48 * q^4 + 30 * q^5 - 9 * q^6 + 24 * q^7 - 51 * q^8 + 108 * q^9 + 60 * q^10 + 162 * q^11 + 216 * q^12 - 72 * q^13 + 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 + 129 * q^20 + 246 * q^21 + 456 * q^22 + 282 * q^23 + 72 * q^24 + 444 * q^25 + 528 * q^26 + 1092 * q^27 + 120 * q^28 + 648 * q^29 - 1890 * q^30 + 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 - 30 * q^37 - 60 * q^38 + 1758 * q^39 - 450 * q^40 + 318 * q^41 + 804 * q^42 + 486 * q^43 + 2448 * q^44 + 486 * q^45 + 1617 * q^46 - 888 * q^47 + 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 + 933 * q^54 + 972 * q^55 + 2661 * q^56 - 156 * q^57 + 201 * q^58 - 792 * q^59 + 1458 * q^60 + 1212 * q^61 + 2817 * q^62 + 2112 * q^63 - 1857 * q^64 + 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 + 2802 * q^71 + 1455 * q^72 + 726 * q^73 + 270 * q^74 - 264 * q^75 + 675 * q^76 - 1008 * q^77 - 3090 * q^78 - 444 * q^79 - 1143 * q^80 + 2520 * q^81 - 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 - 3750 * q^88 - 906 * q^89 - 7755 * q^90 + 2280 * q^91 + 87 * q^92 + 132 * q^93 + 735 * q^94 + 966 * q^95 - 5046 * q^96 - 3246 * q^97 + 1911 * q^98 - 282 * 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 $

$2$	4.44354	1.57103	0.785514	−	0.618844i	$-0.212399\pi$
$2$	4.44354	1.57103	0.785514	+	0.618844i	$0.212399\pi$
$3$	0.537336	0.103410	0.0517052	−	0.998662i	$-0.483534\pi$
$3$	0.537336	0.103410	0.0517052	+	0.998662i	$0.483534\pi$
$4$	11.7450	1.46813
$5$	17.2592	1.54371	0.771854	−	0.635800i	$-0.219330\pi$
$5$	17.2592	1.54371	0.771854	+	0.635800i	$0.219330\pi$
$6$	2.38767	0.162461
$7$	−6.40763	−0.345979	−0.172990	−	0.984924i	$-0.555343\pi$
$7$	−6.40763	−0.345979	−0.172990	+	0.984924i	$0.555343\pi$
$8$	16.6411	0.735439
$9$	−26.7113	−0.989306
$10$	76.6918	2.42521
$11$	55.3227	1.51640	0.758201	−	0.652020i	$-0.226078\pi$
$11$	55.3227	1.51640	0.758201	+	0.652020i	$0.226078\pi$
$12$	6.31102	0.151819
$13$	58.6637	1.25157	0.625784	−	0.779996i	$-0.284779\pi$
$13$	58.6637	1.25157	0.625784	+	0.779996i	$0.284779\pi$
$14$	−28.4725	−0.543543
$15$	9.27398	0.159635
$16$	−20.0149	−0.312732
$17$	0	0
$17$	0	0
$18$	−118.692	−1.55423
$19$	−91.1866	−1.10103	−0.550517	−	0.834824i	$-0.685569\pi$
$19$	−91.1866	−1.10103	−0.550517	+	0.834824i	$0.685569\pi$
$20$	202.709	2.26636
$21$	−3.44305	−0.0357779
$22$	245.829	2.38231
$23$	120.879	1.09587	0.547935	−	0.836521i	$-0.315414\pi$
$23$	120.879	1.09587	0.547935	+	0.836521i	$0.315414\pi$
$24$	8.94185	0.0760520
$25$	172.879	1.38303
$26$	260.674	1.96625
$27$	−28.8610	−0.205715
$28$	−75.2576	−0.507941
$29$	−215.755	−1.38154	−0.690771	−	0.723074i	$-0.742729\pi$
$29$	−215.755	−1.38154	−0.690771	+	0.723074i	$0.742729\pi$
$30$	41.2093	0.250792
$31$	−17.5166	−0.101486	−0.0507432	−	0.998712i	$-0.516159\pi$
$31$	−17.5166	−0.101486	−0.0507432	+	0.998712i	$0.516159\pi$
$32$	−222.065	−1.22675
$33$	29.7269	0.156812
$34$	0	0
$35$	−110.590	−0.534091
$36$	−313.724	−1.45243
$37$	−8.40485	−0.0373446	−0.0186723	−	0.999826i	$-0.505944\pi$
$37$	−8.40485	−0.0373446	−0.0186723	+	0.999826i	$0.505944\pi$
$38$	−405.191	−1.72975
$39$	31.5221	0.129425
$40$	287.211	1.13530
$41$	99.9530	0.380733	0.190366	−	0.981713i	$-0.439032\pi$
$41$	99.9530	0.380733	0.190366	+	0.981713i	$0.439032\pi$
$42$	−15.2993	−0.0562080
$43$	−81.5297	−0.289143	−0.144572	−	0.989494i	$-0.546180\pi$
$43$	−81.5297	−0.289143	−0.144572	+	0.989494i	$0.546180\pi$
$44$	649.766	2.22627
$45$	−461.015	−1.52720
$46$	537.130	1.72164
$47$	195.351	0.606275	0.303137	−	0.952947i	$-0.401966\pi$
$47$	195.351	0.606275	0.303137	+	0.952947i	$0.401966\pi$
$48$	−10.7547	−0.0323398
$49$	−301.942	−0.880298
$50$	768.195	2.17278
$51$	0	0
$52$	689.006	1.83746
$53$	260.322	0.674678	0.337339	−	0.941383i	$-0.390473\pi$
$53$	260.322	0.674678	0.337339	+	0.941383i	$0.390473\pi$
$54$	−128.245	−0.323184
$55$	954.825	2.34088
$56$	−106.630	−0.254447
$57$	−48.9979	−0.113858
$58$	−958.715	−2.17044
$59$	−536.401	−1.18362	−0.591809	−	0.806078i	$-0.701586\pi$
$59$	−536.401	−1.18362	−0.591809	+	0.806078i	$0.701586\pi$
$60$	108.923	0.234365
$61$	−265.689	−0.557671	−0.278836	−	0.960339i	$-0.589948\pi$
$61$	−265.689	−0.557671	−0.278836	+	0.960339i	$0.589948\pi$
$62$	−77.8357	−0.159438
$63$	171.156	0.342280
$64$	−826.636	−1.61452
$65$	1012.49	1.93206
$66$	132.093	0.246356
$67$	514.794	0.938687	0.469344	−	0.883016i	$-0.344491\pi$
$67$	514.794	0.938687	0.469344	+	0.883016i	$0.344491\pi$
$68$	0	0
$69$	64.9526	0.113324
$70$	−491.412	−0.839071
$71$	−704.023	−1.17679	−0.588396	−	0.808573i	$-0.700240\pi$
$71$	−704.023	−1.17679	−0.588396	+	0.808573i	$0.700240\pi$
$72$	−444.504	−0.727574
$73$	184.948	0.296528	0.148264	−	0.988948i	$-0.452632\pi$
$73$	184.948	0.296528	0.148264	+	0.988948i	$0.452632\pi$
$74$	−37.3473	−0.0586693
$75$	92.8943	0.143020
$76$	−1070.99	−1.61646
$77$	−354.487	−0.524644
$78$	140.070	0.203330
$79$	−34.8358	−0.0496118	−0.0248059	−	0.999692i	$-0.507897\pi$
$79$	−34.8358	−0.0496118	−0.0248059	+	0.999692i	$0.507897\pi$
$80$	−345.440	−0.482767
$81$	705.696	0.968033
$82$	444.145	0.598141
$83$	−647.682	−0.856534	−0.428267	−	0.903652i	$-0.640876\pi$
$83$	−647.682	−0.856534	−0.428267	+	0.903652i	$0.640876\pi$
$84$	−40.4386	−0.0525264
$85$	0	0
$86$	−362.280	−0.454252
$87$	−115.933	−0.142866
$88$	920.630	1.11522
$89$	−1060.24	−1.26275	−0.631377	−	0.775476i	$-0.717510\pi$
$89$	−1060.24	−1.26275	−0.631377	+	0.775476i	$0.717510\pi$
$90$	−2048.53	−2.39927
$91$	−375.895	−0.433017
$92$	1419.72	1.60887
$93$	−9.41231	−0.0104947
$94$	868.051	0.952474
$95$	−1573.81	−1.69967
$96$	−119.324	−0.126859
$97$	−256.409	−0.268395	−0.134198	−	0.990955i	$-0.542846\pi$
$97$	−256.409	−0.268395	−0.134198	+	0.990955i	$0.542846\pi$
$98$	−1341.69	−1.38297
$99$	−1477.74	−1.50019
$100$	2030.47	2.03047
$101$	−1465.07	−1.44337	−0.721685	−	0.692222i	$-0.756632\pi$
$101$	−1465.07	−1.44337	−0.721685	+	0.692222i	$0.756632\pi$
$102$	0	0
$103$	−25.6805	−0.0245668	−0.0122834	−	0.999925i	$-0.503910\pi$
$103$	−25.6805	−0.0245668	−0.0122834	+	0.999925i	$0.503910\pi$
$104$	976.227	0.920452
$105$	−59.4242	−0.0552306
$106$	1156.75	1.05994
$107$	2030.70	1.83472	0.917359	−	0.398060i	$-0.130317\pi$
$107$	2030.70	1.83472	0.917359	+	0.398060i	$0.130317\pi$
$108$	−338.973	−0.302015
$109$	−716.479	−0.629598	−0.314799	−	0.949158i	$-0.601937\pi$
$109$	−716.479	−0.629598	−0.314799	+	0.949158i	$0.601937\pi$
$110$	4242.80	3.67759
$111$	−4.51623	−0.00386182
$112$	128.248	0.108199
$113$	16.9632	0.0141218	0.00706090	−	0.999975i	$-0.497752\pi$
$113$	16.9632	0.0141218	0.00706090	+	0.999975i	$0.497752\pi$
$114$	−217.724	−0.178875
$115$	2086.27	1.69170
$116$	−2534.05	−2.02828
$117$	−1566.98	−1.23818
$118$	−2383.52	−1.85950
$119$	0	0
$120$	154.329	0.117402
$121$	1729.60	1.29948
$122$	−1180.60	−0.876117
$123$	53.7084	0.0393717
$124$	−205.733	−0.148995
$125$	826.356	0.591292
$126$	760.537	0.537730
$127$	−1138.85	−0.795724	−0.397862	−	0.917445i	$-0.630248\pi$
$127$	−1138.85	−0.795724	−0.397862	+	0.917445i	$0.630248\pi$
$128$	−1896.67	−1.30971
$129$	−43.8089	−0.0299004
$130$	4499.02	3.03531
$131$	−618.036	−0.412199	−0.206100	−	0.978531i	$-0.566077\pi$
$131$	−618.036	−0.412199	−0.206100	+	0.978531i	$0.566077\pi$
$132$	349.143	0.230219
$133$	584.290	0.380935
$134$	2287.50	1.47470
$135$	−498.117	−0.317564
$136$	0	0
$137$	−2255.17	−1.40637	−0.703183	−	0.711009i	$-0.748238\pi$
$137$	−2255.17	−1.40637	−0.703183	+	0.711009i	$0.748238\pi$
$138$	288.619	0.178036
$139$	1014.29	0.618930	0.309465	−	0.950911i	$-0.399850\pi$
$139$	1014.29	0.618930	0.309465	+	0.950911i	$0.399850\pi$
$140$	−1298.88	−0.784113
$141$	104.969	0.0626951
$142$	−3128.35	−1.84877
$143$	3245.44	1.89788
$144$	534.622	0.309388
$145$	−3723.76	−2.13270
$146$	821.822	0.465853
$147$	−162.245	−0.0910320
$148$	−98.7150	−0.0548265
$149$	−345.080	−0.189732	−0.0948661	−	0.995490i	$-0.530242\pi$
$149$	−345.080	−0.189732	−0.0948661	+	0.995490i	$0.530242\pi$
$150$	412.779	0.224688
$151$	2555.94	1.37748	0.688741	−	0.725007i	$-0.258164\pi$
$151$	2555.94	1.37748	0.688741	+	0.725007i	$0.258164\pi$
$152$	−1517.44	−0.809743
$153$	0	0
$154$	−1575.18	−0.824230
$155$	−302.322	−0.156665
$156$	370.228	0.190012
$157$	3651.08	1.85598	0.927988	−	0.372610i	$-0.121537\pi$
$157$	3651.08	1.85598	0.927988	+	0.372610i	$0.121537\pi$
$158$	−154.794	−0.0779415
$159$	139.880	0.0697688
$160$	−3832.66	−1.89374
$161$	−774.547	−0.379148
$162$	3135.79	1.52081
$163$	211.756	0.101755	0.0508773	−	0.998705i	$-0.483798\pi$
$163$	211.756	0.101755	0.0508773	+	0.998705i	$0.483798\pi$
$164$	1173.95	0.558963
$165$	513.062	0.242072
$166$	−2878.00	−1.34564
$167$	977.319	0.452858	0.226429	−	0.974028i	$-0.427295\pi$
$167$	977.319	0.452858	0.226429	+	0.974028i	$0.427295\pi$
$168$	−57.2960	−0.0263124
$169$	1244.43	0.566424
$170$	0	0
$171$	2435.71	1.08926
$172$	−957.567	−0.424499
$173$	3607.58	1.58543	0.792714	−	0.609594i	$-0.208667\pi$
$173$	3607.58	1.58543	0.792714	+	0.609594i	$0.208667\pi$
$174$	−515.152	−0.224446
$175$	−1107.75	−0.478501
$176$	−1107.28	−0.474228
$177$	−288.228	−0.122398
$178$	−4711.21	−1.98382
$179$	3180.10	1.32789	0.663943	−	0.747783i	$-0.268882\pi$
$179$	3180.10	1.32789	0.663943	+	0.747783i	$0.268882\pi$
$180$	−5414.62	−2.24212
$181$	−1094.34	−0.449401	−0.224701	−	0.974428i	$-0.572140\pi$
$181$	−1094.34	−0.449401	−0.224701	+	0.974428i	$0.572140\pi$
$182$	−1670.30	−0.680281
$183$	−142.764	−0.0576690
$184$	2011.56	0.805945
$185$	−145.061	−0.0576491
$186$	−41.8239	−0.0164875
$187$	0	0
$188$	2294.40	0.890088
$189$	184.931	0.0711731
$190$	−6993.26	−2.67023
$191$	−2323.98	−0.880406	−0.440203	−	0.897898i	$-0.645094\pi$
$191$	−2323.98	−0.880406	−0.440203	+	0.897898i	$0.645094\pi$
$192$	−444.182	−0.166959
$193$	2521.70	0.940498	0.470249	−	0.882534i	$-0.344164\pi$
$193$	2521.70	0.940498	0.470249	+	0.882534i	$0.344164\pi$
$194$	−1139.36	−0.421656
$195$	544.046	0.199795
$196$	−3546.31	−1.29239
$197$	−2196.87	−0.794521	−0.397260	−	0.917706i	$-0.630039\pi$
$197$	−2196.87	−0.794521	−0.397260	+	0.917706i	$0.630039\pi$
$198$	−6566.39	−2.35683
$199$	3596.88	1.28129	0.640643	−	0.767839i	$-0.278668\pi$
$199$	3596.88	1.28129	0.640643	+	0.767839i	$0.278668\pi$
$200$	2876.90	1.01714
$201$	276.617	0.0970700
$202$	−6510.11	−2.26757
$203$	1382.48	0.477985
$204$	0	0
$205$	1725.11	0.587740
$206$	−114.112	−0.0385951
$207$	−3228.83	−1.08415
$208$	−1174.15	−0.391406
$209$	−5044.69	−1.66961
$210$	−264.054	−0.0867687
$211$	3677.29	1.19979	0.599893	−	0.800080i	$-0.295210\pi$
$211$	3677.29	1.19979	0.599893	+	0.800080i	$0.295210\pi$
$212$	3057.48	0.990513
$213$	−378.297	−0.121692
$214$	9023.47	2.88239
$215$	−1407.14	−0.446353
$216$	−480.278	−0.151291
$217$	112.240	0.0351122
$218$	−3183.70	−0.989116
$219$	99.3792	0.0306640
$220$	11214.4	3.43671
$221$	0	0
$222$	−20.0680	−0.00606702
$223$	972.699	0.292093	0.146047	−	0.989278i	$-0.453345\pi$
$223$	972.699	0.292093	0.146047	+	0.989278i	$0.453345\pi$
$224$	1422.91	0.424430
$225$	−4617.82	−1.36824
$226$	75.3766	0.0221857
$227$	4696.68	1.37326	0.686629	−	0.727008i	$-0.259090\pi$
$227$	4696.68	1.37326	0.686629	+	0.727008i	$0.259090\pi$
$228$	−575.480	−0.167158
$229$	−2105.80	−0.607664	−0.303832	−	0.952726i	$-0.598266\pi$
$229$	−2105.80	−0.607664	−0.303832	+	0.952726i	$0.598266\pi$
$230$	9270.42	2.65771
$231$	−190.479	−0.0542537
$232$	−3590.40	−1.01604
$233$	641.400	0.180341	0.0901706	−	0.995926i	$-0.471259\pi$
$233$	641.400	0.180341	0.0901706	+	0.995926i	$0.471259\pi$
$234$	−6962.94	−1.94522
$235$	3371.60	0.935911
$236$	−6300.03	−1.73770
$237$	−18.7185	−0.00513038
$238$	0	0
$239$	4322.85	1.16997	0.584984	−	0.811045i	$-0.301101\pi$
$239$	4322.85	1.16997	0.584984	+	0.811045i	$0.301101\pi$
$240$	−185.617	−0.0499231
$241$	2462.38	0.658156	0.329078	−	0.944303i	$-0.393262\pi$
$241$	2462.38	0.658156	0.329078	+	0.944303i	$0.393262\pi$
$242$	7685.56	2.04151
$243$	1158.44	0.305820
$244$	−3120.52	−0.818732
$245$	−5211.28	−1.35892
$246$	238.655	0.0618540
$247$	−5349.35	−1.37802
$248$	−291.495	−0.0746370
$249$	−348.023	−0.0885746
$250$	3671.94	0.928936
$251$	2631.96	0.661865	0.330932	−	0.943654i	$-0.392637\pi$
$251$	2631.96	0.661865	0.330932	+	0.943654i	$0.392637\pi$
$252$	2010.23	0.502509
$253$	6687.35	1.66178
$254$	−5060.54	−1.25010
$255$	0	0
$256$	−1814.81	−0.443068
$257$	−3375.79	−0.819361	−0.409680	−	0.912229i	$-0.634360\pi$
$257$	−3375.79	−0.819361	−0.409680	+	0.912229i	$0.634360\pi$
$258$	−194.666	−0.0469744
$259$	53.8552	0.0129204
$260$	11891.7	2.83650
$261$	5763.09	1.36677
$262$	−2746.27	−0.647576
$263$	−1603.60	−0.375977	−0.187989	−	0.982171i	$-0.560197\pi$
$263$	−1603.60	−0.375977	−0.187989	+	0.982171i	$0.560197\pi$
$264$	494.688	0.115325
$265$	4492.94	1.04151
$266$	2596.31	0.598459
$267$	−569.705	−0.130582
$268$	6046.26	1.37811
$269$	−6543.59	−1.48316	−0.741580	−	0.670864i	$-0.765923\pi$
$269$	−6543.59	−1.48316	−0.741580	+	0.670864i	$0.765923\pi$
$270$	−2213.40	−0.498901
$271$	−356.005	−0.0797998	−0.0398999	−	0.999204i	$-0.512704\pi$
$271$	−356.005	−0.0797998	−0.0398999	+	0.999204i	$0.512704\pi$
$272$	0	0
$273$	−201.982	−0.0447784
$274$	−10020.9	−2.20944
$275$	9564.15	2.09724
$276$	762.869	0.166374
$277$	3175.91	0.688887	0.344444	−	0.938807i	$-0.388068\pi$
$277$	3175.91	0.688887	0.344444	+	0.938807i	$0.388068\pi$
$278$	4507.05	0.972356
$279$	467.891	0.100401
$280$	−1840.34	−0.392791
$281$	1667.30	0.353960	0.176980	−	0.984214i	$-0.443367\pi$
$281$	1667.30	0.353960	0.176980	+	0.984214i	$0.443367\pi$
$282$	466.435	0.0984957
$283$	7800.28	1.63844	0.819220	−	0.573479i	$-0.194407\pi$
$283$	7800.28	1.63844	0.819220	+	0.573479i	$0.194407\pi$
$284$	−8268.76	−1.72768
$285$	−845.663	−0.175764
$286$	14421.2	2.98162
$287$	−640.461	−0.131726
$288$	5931.65	1.21363
$289$	0	0
$290$	−16546.6	−3.35052
$291$	−137.778	−0.0277549
$292$	2172.21	0.435340
$293$	−2403.16	−0.479161	−0.239580	−	0.970877i	$-0.577010\pi$
$293$	−2403.16	−0.479161	−0.239580	+	0.970877i	$0.577010\pi$
$294$	−720.939	−0.143014
$295$	−9257.84	−1.82716
$296$	−139.866	−0.0274646
$297$	−1596.67	−0.311947
$298$	−1533.38	−0.298074
$299$	7091.21	1.37156
$300$	1091.04	0.209971
$301$	522.412	0.100038
$302$	11357.4	2.16406
$303$	−787.238	−0.149259
$304$	1825.09	0.344329
$305$	−4585.57	−0.860881
$306$	0	0
$307$	−4027.80	−0.748791	−0.374395	−	0.927269i	$-0.622150\pi$
$307$	−4027.80	−0.748791	−0.374395	+	0.927269i	$0.622150\pi$
$308$	−4163.46	−0.770244
$309$	−13.7991	−0.00254046
$310$	−1343.38	−0.246125
$311$	3944.44	0.719192	0.359596	−	0.933108i	$-0.382915\pi$
$311$	3944.44	0.719192	0.359596	+	0.933108i	$0.382915\pi$
$312$	524.562	0.0951843
$313$	6540.41	1.18111	0.590553	−	0.806999i	$-0.298910\pi$
$313$	6540.41	1.18111	0.590553	+	0.806999i	$0.298910\pi$
$314$	16223.7	2.91579
$315$	2954.01	0.528380
$316$	−409.147	−0.0728364
$317$	−3711.41	−0.657582	−0.328791	−	0.944403i	$-0.606641\pi$
$317$	−3711.41	−0.657582	−0.328791	+	0.944403i	$0.606641\pi$
$318$	621.563	0.109609
$319$	−11936.2	−2.09497
$320$	−14267.1	−2.49235
$321$	1091.17	0.189729
$322$	−3441.73	−0.595652
$323$	0	0
$324$	8288.41	1.42119
$325$	10141.7	1.73096
$326$	940.945	0.159859
$327$	−384.990	−0.0651070
$328$	1663.33	0.280005
$329$	−1251.74	−0.209759
$330$	2279.81	0.380301
$331$	3510.10	0.582877	0.291439	−	0.956590i	$-0.405866\pi$
$331$	3510.10	0.582877	0.291439	+	0.956590i	$0.405866\pi$
$332$	−7607.03	−1.25750
$333$	224.504	0.0369452
$334$	4342.75	0.711451
$335$	8884.92	1.44906
$336$	68.9121	0.0111889
$337$	−5718.46	−0.924346	−0.462173	−	0.886790i	$-0.652930\pi$
$337$	−5718.46	−0.924346	−0.462173	+	0.886790i	$0.652930\pi$
$338$	5529.68	0.889867
$339$	9.11494	0.00146034
$340$	0	0
$341$	−969.067	−0.153894
$342$	10823.2	1.71126
$343$	4132.55	0.650544
$344$	−1356.74	−0.212647
$345$	1121.03	0.174940
$346$	16030.4	2.49075
$347$	677.787	0.104857	0.0524287	−	0.998625i	$-0.483304\pi$
$347$	677.787	0.104857	0.0524287	+	0.998625i	$0.483304\pi$
$348$	−1361.63	−0.209745
$349$	12161.8	1.86534	0.932670	−	0.360731i	$-0.117473\pi$
$349$	12161.8	1.86534	0.932670	+	0.360731i	$0.117473\pi$
$350$	−4922.31	−0.751738
$351$	−1693.09	−0.257466
$352$	−12285.3	−1.86025
$353$	5681.58	0.856657	0.428328	−	0.903623i	$-0.359103\pi$
$353$	5681.58	0.856657	0.428328	+	0.903623i	$0.359103\pi$
$354$	−1280.75	−0.192291
$355$	−12150.9	−1.81662
$356$	−12452.5	−1.85388
$357$	0	0
$358$	14130.9	2.08614
$359$	−5883.91	−0.865017	−0.432508	−	0.901630i	$-0.642371\pi$
$359$	−5883.91	−0.865017	−0.432508	+	0.901630i	$0.642371\pi$
$360$	−7671.78	−1.12316
$361$	1456.00	0.212276
$362$	−4862.74	−0.706022
$363$	929.379	0.134380
$364$	−4414.89	−0.635723
$365$	3192.05	0.457752
$366$	−634.377	−0.0905996
$367$	−11526.1	−1.63939	−0.819695	−	0.572801i	$-0.805857\pi$
$367$	−11526.1	−1.63939	−0.819695	+	0.572801i	$0.805857\pi$
$368$	−2419.37	−0.342714
$369$	−2669.87	−0.376661
$370$	−644.583	−0.0905683
$371$	−1668.05	−0.233425
$372$	−110.548	−0.0154076
$373$	3533.27	0.490471	0.245236	−	0.969464i	$-0.421135\pi$
$373$	3533.27	0.490471	0.245236	+	0.969464i	$0.421135\pi$
$374$	0	0
$375$	444.031	0.0611458
$376$	3250.86	0.445878
$377$	−12657.0	−1.72909
$378$	821.746	0.111815
$379$	−13568.8	−1.83901	−0.919503	−	0.393082i	$-0.871409\pi$
$379$	−13568.8	−1.83901	−0.919503	+	0.393082i	$0.871409\pi$
$380$	−18484.4	−2.49534
$381$	−611.947	−0.0822861
$382$	−10326.7	−1.38314
$383$	−12948.4	−1.72750	−0.863748	−	0.503923i	$-0.831889\pi$
$383$	−12948.4	−1.72750	−0.863748	+	0.503923i	$0.831889\pi$
$384$	−1019.15	−0.135438
$385$	−6118.16	−0.809897
$386$	11205.3	1.47755
$387$	2177.76	0.286051
$388$	−3011.52	−0.394038
$389$	8901.44	1.16021	0.580104	−	0.814542i	$-0.303012\pi$
$389$	8901.44	1.16021	0.580104	+	0.814542i	$0.303012\pi$
$390$	2417.49	0.313883
$391$	0	0
$392$	−5024.64	−0.647405
$393$	−332.093	−0.0426257
$394$	−9761.88	−1.24821
$395$	−601.237	−0.0765862
$396$	−17356.1	−2.20246
$397$	−7180.09	−0.907703	−0.453852	−	0.891077i	$-0.649950\pi$
$397$	−7180.09	−0.907703	−0.453852	+	0.891077i	$0.649950\pi$
$398$	15982.9	2.01293
$399$	313.960	0.0393926
$400$	−3460.15	−0.432519
$401$	5087.50	0.633560	0.316780	−	0.948499i	$-0.397398\pi$
$401$	5087.50	0.633560	0.316780	+	0.948499i	$0.397398\pi$
$402$	1229.16	0.152500
$403$	−1027.59	−0.127017
$404$	−17207.3	−2.11905
$405$	12179.7	1.49436
$406$	6143.09	0.750927
$407$	−464.979	−0.0566294
$408$	0	0
$409$	−5287.62	−0.639256	−0.319628	−	0.947543i	$-0.603558\pi$
$409$	−5287.62	−0.639256	−0.319628	+	0.947543i	$0.603558\pi$
$410$	7665.57	0.923355
$411$	−1211.78	−0.145433
$412$	−301.618	−0.0360671
$413$	3437.06	0.409507
$414$	−14347.4	−1.70323
$415$	−11178.5	−1.32224
$416$	−13027.2	−1.53536
$417$	545.017	0.0640038
$418$	−22416.3	−2.62300
$419$	15292.9	1.78307	0.891533	−	0.452956i	$-0.149630\pi$
$419$	15292.9	1.78307	0.891533	+	0.452956i	$0.149630\pi$
$420$	−697.938	−0.0810854
$421$	−1484.20	−0.171818	−0.0859089	−	0.996303i	$-0.527379\pi$
$421$	−1484.20	−0.171818	−0.0859089	+	0.996303i	$0.527379\pi$
$422$	16340.2	1.88490
$423$	−5218.08	−0.599792
$424$	4332.04	0.496185
$425$	0	0
$426$	−1680.98	−0.191182
$427$	1702.43	0.192943
$428$	23850.6	2.69360
$429$	1743.89	0.196261
$430$	−6252.66	−0.701232
$431$	2361.94	0.263969	0.131984	−	0.991252i	$-0.457865\pi$
$431$	2361.94	0.263969	0.131984	+	0.991252i	$0.457865\pi$
$432$	577.649	0.0643337
$433$	−12384.3	−1.37449	−0.687244	−	0.726426i	$-0.741180\pi$
$433$	−12384.3	−1.37449	−0.687244	+	0.726426i	$0.741180\pi$
$434$	498.742	0.0551622
$435$	−2000.91	−0.220543
$436$	−8415.05	−0.924330
$437$	−11022.5	−1.20659
$438$	441.595	0.0481740
$439$	7612.65	0.827636	0.413818	−	0.910360i	$-0.364195\pi$
$439$	7612.65	0.827636	0.413818	+	0.910360i	$0.364195\pi$
$440$	15889.3	1.72158
$441$	8065.26	0.870885
$442$	0	0
$443$	11492.3	1.23254	0.616272	−	0.787533i	$-0.288642\pi$
$443$	11492.3	1.23254	0.616272	+	0.787533i	$0.288642\pi$
$444$	−53.0432	−0.00566963
$445$	−18298.9	−1.94932
$446$	4322.22	0.458886
$447$	−185.424	−0.0196203
$448$	5296.78	0.558592
$449$	−13654.4	−1.43517	−0.717584	−	0.696472i	$-0.754752\pi$
$449$	−13654.4	−1.43517	−0.717584	+	0.696472i	$0.754752\pi$
$450$	−20519.5	−2.14955
$451$	5529.67	0.577344
$452$	199.233	0.0207326
$453$	1373.40	0.142446
$454$	20869.9	2.15743
$455$	−6487.64	−0.668451
$456$	−815.377	−0.0837358
$457$	12274.9	1.25645	0.628223	−	0.778034i	$-0.283783\pi$
$457$	12274.9	1.25645	0.628223	+	0.778034i	$0.283783\pi$
$458$	−9357.20	−0.954657
$459$	0	0
$460$	24503.3	2.48363
$461$	−932.142	−0.0941739	−0.0470869	−	0.998891i	$-0.514994\pi$
$461$	−932.142	−0.0941739	−0.0470869	+	0.998891i	$0.514994\pi$
$462$	−846.400	−0.0852340
$463$	5569.01	0.558993	0.279496	−	0.960147i	$-0.409832\pi$
$463$	5569.01	0.558993	0.279496	+	0.960147i	$0.409832\pi$
$464$	4318.31	0.432053
$465$	−162.449	−0.0162008
$466$	2850.08	0.283321
$467$	14662.2	1.45286	0.726428	−	0.687243i	$-0.241179\pi$
$467$	14662.2	1.45286	0.726428	+	0.687243i	$0.241179\pi$
$468$	−18404.2	−1.81781
$469$	−3298.61	−0.324766
$470$	14981.8	1.47034
$471$	1961.86	0.191927
$472$	−8926.29	−0.870478
$473$	−4510.45	−0.438458
$474$	−83.1765	−0.00805996
$475$	−15764.3	−1.52277
$476$	0	0
$477$	−6953.53	−0.667464
$478$	19208.8	1.83805
$479$	−12651.6	−1.20682	−0.603409	−	0.797432i	$-0.706191\pi$
$479$	−12651.6	−1.20682	−0.603409	+	0.797432i	$0.706191\pi$
$480$	−2059.43	−0.195833
$481$	−493.060	−0.0467393
$482$	10941.7	1.03398
$483$	−416.192	−0.0392079
$484$	20314.2	1.90780
$485$	−4425.40	−0.414324
$486$	5147.58	0.480451
$487$	−13319.7	−1.23937	−0.619683	−	0.784852i	$-0.712739\pi$
$487$	−13319.7	−1.23937	−0.619683	+	0.784852i	$0.712739\pi$
$488$	−4421.34	−0.410133
$489$	113.784	0.0105225
$490$	−23156.5	−2.13491
$491$	−19380.9	−1.78136	−0.890679	−	0.454633i	$-0.849771\pi$
$491$	−19380.9	−1.78136	−0.890679	+	0.454633i	$0.849771\pi$
$492$	630.805	0.0578026
$493$	0	0
$494$	−23770.0	−2.16491
$495$	−25504.6	−2.31585
$496$	350.593	0.0317381
$497$	4511.12	0.407146
$498$	−1546.45	−0.139153
$499$	−20101.1	−1.80330	−0.901650	−	0.432466i	$-0.857644\pi$
$499$	−20101.1	−1.80330	−0.901650	+	0.432466i	$0.857644\pi$
$500$	9705.56	0.868091
$501$	525.149	0.0468302
$502$	11695.2	1.03981
$503$	6166.84	0.546652	0.273326	−	0.961921i	$-0.411876\pi$
$503$	6166.84	0.546652	0.273326	+	0.961921i	$0.411876\pi$
$504$	2848.22	0.251726
$505$	−25286.0	−2.22814
$506$	29715.5	2.61070
$507$	668.679	0.0585741
$508$	−13375.8	−1.16822
$509$	14496.0	1.26233	0.631165	−	0.775649i	$-0.282577\pi$
$509$	14496.0	1.26233	0.631165	+	0.775649i	$0.282577\pi$
$510$	0	0
$511$	−1185.08	−0.102592
$512$	7109.16	0.613639
$513$	2631.74	0.226499
$514$	−15000.4	−1.28724
$515$	−443.225	−0.0379239
$516$	−514.535	−0.0438976
$517$	10807.4	0.919357
$518$	239.307	0.0202984
$519$	1938.48	0.163950
$520$	16848.9	1.42091
$521$	2642.20	0.222182	0.111091	−	0.993810i	$-0.464565\pi$
$521$	2642.20	0.222182	0.111091	+	0.993810i	$0.464565\pi$
$522$	25608.5	2.14723
$523$	12574.5	1.05133	0.525665	−	0.850692i	$-0.323817\pi$
$523$	12574.5	1.05133	0.525665	+	0.850692i	$0.323817\pi$
$524$	−7258.84	−0.605160
$525$	−595.232	−0.0494820
$526$	−7125.63	−0.590670
$527$	0	0
$528$	−594.980	−0.0490401
$529$	2444.72	0.200930
$530$	19964.5	1.63623
$531$	14328.0	1.17096
$532$	6862.49	0.559261
$533$	5863.61	0.476513
$534$	−2531.50	−0.205148
$535$	35048.2	2.83227
$536$	8566.72	0.690347
$537$	1708.78	0.137317
$538$	−29076.7	−2.33008
$539$	−16704.3	−1.33489
$540$	−5850.39	−0.466224
$541$	−18289.3	−1.45345	−0.726726	−	0.686927i	$-0.758959\pi$
$541$	−18289.3	−1.45345	−0.726726	+	0.686927i	$0.758959\pi$
$542$	−1581.92	−0.125368
$543$	−588.028	−0.0464728
$544$	0	0
$545$	−12365.8	−0.971916
$546$	−897.515	−0.0703481
$547$	9989.86	0.780869	0.390435	−	0.920631i	$-0.372325\pi$
$547$	9989.86	0.780869	0.390435	+	0.920631i	$0.372325\pi$
$548$	−26487.0	−2.06472
$549$	7096.88	0.551708
$550$	42498.6	3.29482
$551$	19674.0	1.52112
$552$	1080.88	0.0833431
$553$	223.215	0.0171647
$554$	14112.3	1.08226
$555$	−77.9464	−0.00596152
$556$	11912.9	0.908668
$557$	−4181.95	−0.318124	−0.159062	−	0.987269i	$-0.550847\pi$
$557$	−4181.95	−0.318124	−0.159062	+	0.987269i	$0.550847\pi$
$558$	2079.09	0.157733
$559$	−4782.84	−0.361883
$560$	2213.45	0.167027
$561$	0	0
$562$	7408.70	0.556080
$563$	10429.1	0.780697	0.390348	−	0.920667i	$-0.372355\pi$
$563$	10429.1	0.780697	0.390348	+	0.920667i	$0.372355\pi$
$564$	1232.87	0.0920443
$565$	292.771	0.0217999
$566$	34660.8	2.57403
$567$	−4521.84	−0.334920
$568$	−11715.7	−0.865458
$569$	8440.98	0.621906	0.310953	−	0.950425i	$-0.399352\pi$
$569$	8440.98	0.621906	0.310953	+	0.950425i	$0.399352\pi$
$570$	−3757.73	−0.276130
$571$	−27092.6	−1.98562	−0.992811	−	0.119694i	$-0.961809\pi$
$571$	−27092.6	−1.98562	−0.992811	+	0.119694i	$0.961809\pi$
$572$	38117.7	2.78633
$573$	−1248.76	−0.0910431
$574$	−2845.91	−0.206944
$575$	20897.5	1.51562
$576$	22080.5	1.59726
$577$	−10864.3	−0.783857	−0.391929	−	0.919996i	$-0.628192\pi$
$577$	−10864.3	−0.783857	−0.391929	+	0.919996i	$0.628192\pi$
$578$	0	0
$579$	1355.00	0.0972572
$580$	−43735.5	−3.13107
$581$	4150.11	0.296343
$582$	−612.220	−0.0436037
$583$	14401.7	1.02308
$584$	3077.73	0.218078
$585$	−27044.8	−1.91140
$586$	−10678.5	−0.752774
$587$	25173.8	1.77008	0.885038	−	0.465518i	$-0.154132\pi$
$587$	25173.8	1.77008	0.885038	+	0.465518i	$0.154132\pi$
$588$	−1905.56	−0.133646
$589$	1597.28	0.111740
$590$	−41137.5	−2.87052
$591$	−1180.46	−0.0821617
$592$	168.222	0.0116788
$593$	777.712	0.0538563	0.0269282	−	0.999637i	$-0.491427\pi$
$593$	777.712	0.0538563	0.0269282	+	0.999637i	$0.491427\pi$
$594$	−7094.86	−0.490077
$595$	0	0
$596$	−4052.97	−0.278551
$597$	1932.73	0.132498
$598$	31510.0	2.15475
$599$	6690.40	0.456365	0.228182	−	0.973618i	$-0.426722\pi$
$599$	6690.40	0.456365	0.228182	+	0.973618i	$0.426722\pi$
$600$	1545.86	0.105182
$601$	1574.80	0.106884	0.0534421	−	0.998571i	$-0.482981\pi$
$601$	1574.80	0.106884	0.0534421	+	0.998571i	$0.482981\pi$
$602$	2321.36	0.157162
$603$	−13750.8	−0.928649
$604$	30019.6	2.02232
$605$	29851.6	2.00601
$606$	−3498.12	−0.234491
$607$	24567.4	1.64276	0.821382	−	0.570378i	$-0.193203\pi$
$607$	24567.4	1.64276	0.821382	+	0.570378i	$0.193203\pi$
$608$	20249.4	1.35069
$609$	742.856	0.0494286
$610$	−20376.1	−1.35247
$611$	11460.0	0.758795
$612$	0	0
$613$	−27992.8	−1.84440	−0.922201	−	0.386710i	$-0.873611\pi$
$613$	−27992.8	−1.84440	−0.922201	+	0.386710i	$0.873611\pi$
$614$	−17897.7	−1.17637
$615$	926.962	0.0607784
$616$	−5899.05	−0.385843
$617$	3787.41	0.247124	0.123562	−	0.992337i	$-0.460568\pi$
$617$	3787.41	0.247124	0.123562	+	0.992337i	$0.460568\pi$
$618$	−61.3167	−0.00399113
$619$	−4066.72	−0.264063	−0.132032	−	0.991246i	$-0.542150\pi$
$619$	−4066.72	−0.264063	−0.132032	+	0.991246i	$0.542150\pi$
$620$	−3550.78	−0.230004
$621$	−3488.69	−0.225437
$622$	17527.3	1.12987
$623$	6793.62	0.436887
$624$	−630.911	−0.0404754
$625$	−7347.68	−0.470251
$626$	29062.6	1.85555
$627$	−2710.70	−0.172655
$628$	42882.0	2.72481
$629$	0	0
$630$	13126.2	0.830099
$631$	−11686.8	−0.737309	−0.368655	−	0.929566i	$-0.620182\pi$
$631$	−11686.8	−0.737309	−0.368655	+	0.929566i	$0.620182\pi$
$632$	−579.705	−0.0364864
$633$	1975.94	0.124070
$634$	−16491.8	−1.03308
$635$	−19655.7	−1.22836
$636$	1642.90	0.102429
$637$	−17713.1	−1.10175
$638$	−53038.8	−3.29126
$639$	18805.4	1.16421
$640$	−32734.9	−2.02181
$641$	23652.6	1.45744	0.728721	−	0.684810i	$-0.240115\pi$
$641$	23652.6	1.45744	0.728721	+	0.684810i	$0.240115\pi$
$642$	4848.64	0.298069
$643$	−2712.61	−0.166368	−0.0831841	−	0.996534i	$-0.526509\pi$
$643$	−2712.61	−0.166368	−0.0831841	+	0.996534i	$0.526509\pi$
$644$	−9097.06	−0.556637
$645$	−756.105	−0.0461575
$646$	0	0
$647$	3672.97	0.223183	0.111592	−	0.993754i	$-0.464405\pi$
$647$	3672.97	0.223183	0.111592	+	0.993754i	$0.464405\pi$
$648$	11743.5	0.711929
$649$	−29675.2	−1.79484
$650$	45065.2	2.71939
$651$	60.3106	0.00363097
$652$	2487.08	0.149389
$653$	−26090.8	−1.56357	−0.781785	−	0.623548i	$-0.785691\pi$
$653$	−26090.8	−1.56357	−0.781785	+	0.623548i	$0.785691\pi$
$654$	−1710.72	−0.102285
$655$	−10666.8	−0.636315
$656$	−2000.54	−0.119067
$657$	−4940.19	−0.293357
$658$	−5562.14	−0.329536
$659$	−14303.7	−0.845515	−0.422758	−	0.906243i	$-0.638938\pi$
$659$	−14303.7	−0.845515	−0.422758	+	0.906243i	$0.638938\pi$
$660$	6025.92	0.355392
$661$	−9780.49	−0.575517	−0.287759	−	0.957703i	$-0.592910\pi$
$661$	−9780.49	−0.575517	−0.287759	+	0.957703i	$0.592910\pi$
$662$	15597.2	0.915716
$663$	0	0
$664$	−10778.1	−0.629928
$665$	10084.4	0.588052
$666$	997.593	0.0580419
$667$	−26080.2	−1.51399
$668$	11478.6	0.664852
$669$	522.667	0.0302055
$670$	39480.4	2.27651
$671$	−14698.6	−0.845654
$672$	764.582	0.0438905
$673$	−21380.1	−1.22458	−0.612289	−	0.790634i	$-0.709751\pi$
$673$	−21380.1	−1.22458	−0.612289	+	0.790634i	$0.709751\pi$
$674$	−25410.2	−1.45217
$675$	−4989.47	−0.284511
$676$	14615.9	0.831581
$677$	−7244.51	−0.411269	−0.205635	−	0.978629i	$-0.565926\pi$
$677$	−7244.51	−0.411269	−0.205635	+	0.978629i	$0.565926\pi$
$678$	40.5026	0.00229424
$679$	1642.97	0.0928593
$680$	0	0
$681$	2523.70	0.142009
$682$	−4306.08	−0.241772
$683$	−4140.24	−0.231950	−0.115975	−	0.993252i	$-0.536999\pi$
$683$	−4140.24	−0.231950	−0.115975	+	0.993252i	$0.536999\pi$
$684$	28607.4	1.59917
$685$	−38922.4	−2.17102
$686$	18363.1	1.02202
$687$	−1131.52	−0.0628388
$688$	1631.81	0.0904244
$689$	15271.4	0.844406
$690$	4981.33	0.274835
$691$	30750.3	1.69290	0.846451	−	0.532466i	$-0.178735\pi$
$691$	30750.3	1.69290	0.846451	+	0.532466i	$0.178735\pi$
$692$	42371.0	2.32761
$693$	9468.81	0.519034
$694$	3011.77	0.164734
$695$	17505.9	0.955448
$696$	−1929.25	−0.105069
$697$	0	0
$698$	54041.2	2.93050
$699$	344.647	0.0186492
$700$	−13010.5	−0.702500
$701$	−20466.3	−1.10271	−0.551356	−	0.834270i	$-0.685890\pi$
$701$	−20466.3	−1.10271	−0.551356	+	0.834270i	$0.685890\pi$
$702$	−7523.32	−0.404487
$703$	766.410	0.0411176
$704$	−45731.8	−2.44827
$705$	1811.68	0.0967830
$706$	25246.3	1.34583
$707$	9387.65	0.499376
$708$	−3385.24	−0.179696
$709$	−24814.8	−1.31444	−0.657222	−	0.753697i	$-0.728269\pi$
$709$	−24814.8	−1.31444	−0.657222	+	0.753697i	$0.728269\pi$
$710$	−53992.8	−2.85396
$711$	930.509	0.0490813
$712$	−17643.5	−0.928678
$713$	−2117.39	−0.111216
$714$	0	0
$715$	56013.6	2.92978
$716$	37350.3	1.94950
$717$	2322.83	0.120987
$718$	−26145.4	−1.35897
$719$	24507.8	1.27119	0.635597	−	0.772021i	$-0.280754\pi$
$719$	24507.8	1.27119	0.635597	+	0.772021i	$0.280754\pi$
$720$	9227.14	0.477604
$721$	164.551	0.00849960
$722$	6469.79	0.333491
$723$	1323.12	0.0680601
$724$	−12853.0	−0.659778
$725$	−37299.6	−1.91072
$726$	4129.73	0.211114
$727$	−7468.67	−0.381015	−0.190507	−	0.981686i	$-0.561013\pi$
$727$	−7468.67	−0.381015	−0.190507	+	0.981686i	$0.561013\pi$
$728$	−6255.30	−0.318457
$729$	−18431.3	−0.936408
$730$	14184.0	0.719140
$731$	0	0
$732$	−1676.77	−0.0846654
$733$	2801.95	0.141190	0.0705952	−	0.997505i	$-0.477510\pi$
$733$	2801.95	0.141190	0.0705952	+	0.997505i	$0.477510\pi$
$734$	−51216.5	−2.57552
$735$	−2800.21	−0.140527
$736$	−26843.0	−1.34436
$737$	28479.8	1.42343
$738$	−11863.7	−0.591745
$739$	5867.20	0.292055	0.146027	−	0.989281i	$-0.453351\pi$
$739$	5867.20	0.292055	0.146027	+	0.989281i	$0.453351\pi$
$740$	−1703.74	−0.0846361
$741$	−2874.40	−0.142502
$742$	−7412.02	−0.366717
$743$	23585.7	1.16457	0.582286	−	0.812984i	$-0.302159\pi$
$743$	23585.7	1.16457	0.582286	+	0.812984i	$0.302159\pi$
$744$	−156.631	−0.00771824
$745$	−5955.80	−0.292891
$746$	15700.2	0.770543
$747$	17300.4	0.847375
$748$	0	0
$749$	−13011.9	−0.634775
$750$	1973.07	0.0960616
$751$	−15142.8	−0.735775	−0.367887	−	0.929870i	$-0.619919\pi$
$751$	−15142.8	−0.735775	−0.367887	+	0.929870i	$0.619919\pi$
$752$	−3909.93	−0.189602
$753$	1414.25	0.0684437
$754$	−56241.8	−2.71645
$755$	44113.5	2.12643
$756$	2172.01	0.104491
$757$	−13149.7	−0.631353	−0.315676	−	0.948867i	$-0.602231\pi$
$757$	−13149.7	−0.631353	−0.315676	+	0.948867i	$0.602231\pi$
$758$	−60293.5	−2.88913
$759$	3593.36	0.171845
$760$	−26189.8	−1.25001
$761$	−12831.3	−0.611213	−0.305607	−	0.952158i	$-0.598859\pi$
$761$	−12831.3	−0.611213	−0.305607	+	0.952158i	$0.598859\pi$
$762$	−2719.21	−0.129274
$763$	4590.93	0.217828
$764$	−27295.2	−1.29255
$765$	0	0
$766$	−57536.6	−2.71394
$767$	−31467.3	−1.48138
$768$	−975.162	−0.0458179
$769$	−11365.1	−0.532949	−0.266474	−	0.963842i	$-0.585859\pi$
$769$	−11365.1	−0.532949	−0.266474	+	0.963842i	$0.585859\pi$
$770$	−27186.3	−1.27237
$771$	−1813.93	−0.0847304
$772$	29617.4	1.38077
$773$	−16551.8	−0.770150	−0.385075	−	0.922885i	$-0.625824\pi$
$773$	−16551.8	−0.770150	−0.385075	+	0.922885i	$0.625824\pi$
$774$	9676.96	0.449394
$775$	−3028.26	−0.140359
$776$	−4266.91	−0.197388
$777$	28.9383	0.00133611
$778$	39553.9	1.82272
$779$	−9114.37	−0.419199
$780$	6389.83	0.293324
$781$	−38948.5	−1.78449
$782$	0	0
$783$	6226.91	0.284204
$784$	6043.33	0.275298
$785$	63014.7	2.86509
$786$	−1475.67	−0.0669661
$787$	−32051.7	−1.45174	−0.725870	−	0.687832i	$-0.758562\pi$
$787$	−32051.7	−1.45174	−0.725870	+	0.687832i	$0.758562\pi$
$788$	−25802.3	−1.16646
$789$	−861.670	−0.0388799
$790$	−2671.62	−0.120319
$791$	−108.694	−0.00488585
$792$	−24591.2	−1.10330
$793$	−15586.3	−0.697964
$794$	−31905.0	−1.42603
$795$	2414.22	0.107703
$796$	42245.4	1.88109
$797$	27679.0	1.23016	0.615082	−	0.788463i	$-0.289123\pi$
$797$	27679.0	1.23016	0.615082	+	0.788463i	$0.289123\pi$
$798$	1395.09	0.0618869
$799$	0	0
$800$	−38390.5	−1.69664
$801$	28320.3	1.24925
$802$	22606.5	0.995340
$803$	10231.8	0.449655
$804$	3248.87	0.142511
$805$	−13368.0	−0.585294
$806$	−4566.13	−0.199547
$807$	−3516.11	−0.153374
$808$	−24380.4	−1.06151
$809$	7438.60	0.323272	0.161636	−	0.986850i	$-0.448323\pi$
$809$	7438.60	0.323272	0.161636	+	0.986850i	$0.448323\pi$
$810$	54121.1	2.34768
$811$	10261.1	0.444288	0.222144	−	0.975014i	$-0.428694\pi$
$811$	10261.1	0.444288	0.222144	+	0.975014i	$0.428694\pi$
$812$	16237.2	0.701742
$813$	−191.294	−0.00825213
$814$	−2066.15	−0.0889663
$815$	3654.73	0.157079
$816$	0	0
$817$	7434.42	0.318357
$818$	−23495.7	−1.00429
$819$	10040.6	0.428386
$820$	20261.4	0.862876
$821$	−21739.5	−0.924134	−0.462067	−	0.886845i	$-0.652892\pi$
$821$	−21739.5	−0.924134	−0.462067	+	0.886845i	$0.652892\pi$
$822$	−5384.60	−0.228479
$823$	23728.9	1.00503	0.502514	−	0.864569i	$-0.332408\pi$
$823$	23728.9	1.00503	0.502514	+	0.864569i	$0.332408\pi$
$824$	−427.352	−0.0180674
$825$	5139.16	0.216876
$826$	15272.7	0.643347
$827$	21101.5	0.887270	0.443635	−	0.896207i	$-0.353689\pi$
$827$	21101.5	0.887270	0.443635	+	0.896207i	$0.353689\pi$
$828$	−37922.6	−1.59167
$829$	−1621.77	−0.0679448	−0.0339724	−	0.999423i	$-0.510816\pi$
$829$	−1621.77	−0.0679448	−0.0339724	+	0.999423i	$0.510816\pi$
$830$	−49671.9	−2.07727
$831$	1706.53	0.0712381
$832$	−48493.6	−2.02069
$833$	0	0
$834$	2421.80	0.100552
$835$	16867.7	0.699080
$836$	−59250.0	−2.45120
$837$	505.547	0.0208773
$838$	67954.3	2.80124
$839$	−1287.05	−0.0529607	−0.0264803	−	0.999649i	$-0.508430\pi$
$839$	−1287.05	−0.0529607	−0.0264803	+	0.999649i	$0.508430\pi$
$840$	−988.883	−0.0406187
$841$	22161.3	0.908658
$842$	−6595.08	−0.269930
$843$	895.900	0.0366031
$844$	43189.8	1.76144
$845$	21477.9	0.874392
$846$	−23186.7	−0.942289
$847$	−11082.7	−0.449592
$848$	−5210.30	−0.210994
$849$	4191.37	0.169432
$850$	0	0
$851$	−1015.97	−0.0409248
$852$	−4443.10	−0.178660
$853$	18173.4	0.729479	0.364740	−	0.931110i	$-0.381158\pi$
$853$	18173.4	0.729479	0.364740	+	0.931110i	$0.381158\pi$
$854$	7564.83	0.303118
$855$	42038.4	1.68150
$856$	33793.0	1.34932
$857$	−39590.2	−1.57803	−0.789017	−	0.614371i	$-0.789410\pi$
$857$	−39590.2	−1.57803	−0.789017	+	0.614371i	$0.789410\pi$
$858$	7749.04	0.308331
$859$	−17747.9	−0.704948	−0.352474	−	0.935822i	$-0.614659\pi$
$859$	−17747.9	−0.704948	−0.352474	+	0.935822i	$0.614659\pi$
$860$	−16526.8	−0.655302
$861$	−344.143	−0.0136218
$862$	10495.3	0.414702
$863$	−8155.37	−0.321683	−0.160841	−	0.986980i	$-0.551421\pi$
$863$	−8155.37	−0.321683	−0.160841	+	0.986980i	$0.551421\pi$
$864$	6409.03	0.252361
$865$	62263.8	2.44744
$866$	−55030.3	−2.15936
$867$	0	0
$868$	1318.26	0.0515491
$869$	−1927.21	−0.0752315
$870$	−8891.11	−0.346479
$871$	30199.7	1.17483
$872$	−11923.0	−0.463031
$873$	6849.00	0.265525
$874$	−48979.1	−1.89559
$875$	−5294.98	−0.204575
$876$	1167.21	0.0450187
$877$	37979.1	1.46233	0.731164	−	0.682202i	$-0.238977\pi$
$877$	37979.1	1.46233	0.731164	+	0.682202i	$0.238977\pi$
$878$	33827.1	1.30024
$879$	−1291.30	−0.0495502
$880$	−19110.7	−0.732069
$881$	18289.7	0.699427	0.349714	−	0.936857i	$-0.386279\pi$
$881$	18289.7	0.699427	0.349714	+	0.936857i	$0.386279\pi$
$882$	35838.3	1.36818
$883$	18414.9	0.701825	0.350912	−	0.936408i	$-0.385871\pi$
$883$	18414.9	0.701825	0.350912	+	0.936408i	$0.385871\pi$
$884$	0	0
$885$	−4974.57	−0.188947
$886$	51066.6	1.93636
$887$	50689.5	1.91881	0.959406	−	0.282028i	$-0.0910070\pi$
$887$	50689.5	1.91881	0.959406	+	0.282028i	$0.0910070\pi$
$888$	−75.1549	−0.00284013
$889$	7297.35	0.275304
$890$	−81311.6	−3.06244
$891$	39041.0	1.46793
$892$	11424.4	0.428830
$893$	−17813.4	−0.667529
$894$	−823.939	−0.0308240
$895$	54885.8	2.04987
$896$	12153.1	0.453133
$897$	3810.36	0.141833
$898$	−60673.8	−2.25469
$899$	3779.30	0.140208
$900$	−54236.4	−2.00875
$901$	0	0
$902$	24571.3	0.907023
$903$	280.711	0.0103449
$904$	282.286	0.0103857
$905$	−18887.4	−0.693744
$906$	6102.76	0.223786
$907$	44568.0	1.63160	0.815798	−	0.578338i	$-0.196298\pi$
$907$	44568.0	1.63160	0.815798	+	0.578338i	$0.196298\pi$
$908$	55162.5	2.01612
$909$	39134.0	1.42794
$910$	−28828.1	−1.05016
$911$	−7809.03	−0.284001	−0.142000	−	0.989867i	$-0.545353\pi$
$911$	−7809.03	−0.284001	−0.142000	+	0.989867i	$0.545353\pi$
$912$	980.685	0.0356072
$913$	−35831.5	−1.29885
$914$	54543.9	1.97391
$915$	−2463.99	−0.0890241
$916$	−24732.6	−0.892128
$917$	3960.15	0.142612
$918$	0	0
$919$	−36710.8	−1.31771	−0.658856	−	0.752269i	$-0.728959\pi$
$919$	−36710.8	−1.31771	−0.658856	+	0.752269i	$0.728959\pi$
$920$	34717.8	1.24414
$921$	−2164.28	−0.0774328
$922$	−4142.00	−0.147950
$923$	−41300.6	−1.47284
$924$	−2237.18	−0.0796512
$925$	−1453.02	−0.0516488
$926$	24746.1	0.878193
$927$	685.960	0.0243041
$928$	47911.7	1.69481
$929$	−15068.9	−0.532180	−0.266090	−	0.963948i	$-0.585732\pi$
$929$	−15068.9	−0.532180	−0.266090	+	0.963948i	$0.585732\pi$
$930$	−721.847	−0.0254519
$931$	27533.1	0.969238
$932$	7533.25	0.264764
$933$	2119.49	0.0743719
$934$	65151.8	2.28248
$935$	0	0
$936$	−26076.3	−0.910609
$937$	38416.7	1.33940	0.669700	−	0.742632i	$-0.266423\pi$
$937$	38416.7	1.33940	0.669700	+	0.742632i	$0.266423\pi$
$938$	−14657.5	−0.510217
$939$	3514.40	0.122139
$940$	39599.5	1.37404
$941$	34621.7	1.19940	0.599701	−	0.800224i	$-0.295286\pi$
$941$	34621.7	1.19940	0.599701	+	0.800224i	$0.295286\pi$
$942$	8717.59	0.301523
$943$	12082.2	0.417233
$944$	10736.0	0.370155
$945$	3191.75	0.109871
$946$	−20042.3	−0.688829
$947$	20331.6	0.697665	0.348832	−	0.937185i	$-0.386578\pi$
$947$	20331.6	0.697665	0.348832	+	0.937185i	$0.386578\pi$
$948$	−219.849	−0.00753204
$949$	10849.7	0.371124
$950$	−70049.1	−2.39231
$951$	−1994.28	−0.0680009
$952$	0	0
$953$	17934.5	0.609607	0.304803	−	0.952415i	$-0.401409\pi$
$953$	17934.5	0.609607	0.304803	+	0.952415i	$0.401409\pi$
$954$	−30898.2	−1.04860
$955$	−40110.0	−1.35909
$956$	50771.9	1.71766
$957$	−6413.73	−0.216642
$958$	−56217.8	−1.89594
$959$	14450.3	0.486573
$960$	−7666.21	−0.257735
$961$	−29484.2	−0.989701
$962$	−2190.93	−0.0734287
$963$	−54242.5	−1.81510
$964$	28920.6	0.966256
$965$	43522.5	1.45185
$966$	−1849.37	−0.0615966
$967$	8758.07	0.291252	0.145626	−	0.989340i	$-0.453480\pi$
$967$	8758.07	0.291252	0.145626	+	0.989340i	$0.453480\pi$
$968$	28782.5	0.955686
$969$	0	0
$970$	−19664.4	−0.650914
$971$	−52844.2	−1.74650	−0.873250	−	0.487273i	$-0.837992\pi$
$971$	−52844.2	−1.74650	−0.873250	+	0.487273i	$0.837992\pi$
$972$	13605.9	0.448982
$973$	−6499.22	−0.214137
$974$	−59186.4	−1.94708
$975$	5449.52	0.178999
$976$	5317.72	0.174402
$977$	−45377.7	−1.48594	−0.742970	−	0.669325i	$-0.766583\pi$
$977$	−45377.7	−1.48594	−0.742970	+	0.669325i	$0.766583\pi$
$978$	505.604	0.0165311
$979$	−58655.3	−1.91484
$980$	−61206.5	−1.99507
$981$	19138.1	0.622866
$982$	−86119.6	−2.79856
$983$	−20092.8	−0.651944	−0.325972	−	0.945379i	$-0.605691\pi$
$983$	−20092.8	−0.651944	−0.325972	+	0.945379i	$0.605691\pi$
$984$	893.765	0.0289555
$985$	−37916.2	−1.22651
$986$	0	0
$987$	−672.604	−0.0216912
$988$	−62828.1	−2.02311
$989$	−9855.23	−0.316863
$990$	−113331.	−3.63826
$991$	8915.20	0.285773	0.142886	−	0.989739i	$-0.454362\pi$
$991$	8915.20	0.285773	0.142886	+	0.989739i	$0.454362\pi$
$992$	3889.83	0.124498
$993$	1886.10	0.0602756
$994$	20045.3	0.639637
$995$	62079.1	1.97793
$996$	−4087.53	−0.130039
$997$	12587.1	0.399837	0.199919	−	0.979812i	$-0.435932\pi$
$997$	12587.1	0.399837	0.199919	+	0.979812i	$0.435932\pi$
$998$	−89319.8	−2.83303
$999$	242.572	0.00768234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.i.1.12	yes	12
17.4	even	4		289.4.b.f.288.1		24
17.13	even	4		289.4.b.f.288.2		24
17.16	even	2		289.4.a.h.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.12	✓	12	17.16	even	2
289.4.a.i.1.12	yes	12	1.1	even	1	trivial
289.4.b.f.288.1		24	17.4	even	4
289.4.b.f.288.2		24	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)

\(f(q)\)	\(=\)	\(q+4.44354 q^{2} +0.537336 q^{3} +11.7450 q^{4} +17.2592 q^{5} +2.38767 q^{6} -6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} +O(q^{10})\)	\(q+4.44354 q^{2} +0.537336 q^{3} +11.7450 q^{4} +17.2592 q^{5} +2.38767 q^{6} -6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} +76.6918 q^{10} +55.3227 q^{11} +6.31102 q^{12} +58.6637 q^{13} -28.4725 q^{14} +9.27398 q^{15} -20.0149 q^{16} -118.692 q^{18} -91.1866 q^{19} +202.709 q^{20} -3.44305 q^{21} +245.829 q^{22} +120.879 q^{23} +8.94185 q^{24} +172.879 q^{25} +260.674 q^{26} -28.8610 q^{27} -75.2576 q^{28} -215.755 q^{29} +41.2093 q^{30} -17.5166 q^{31} -222.065 q^{32} +29.7269 q^{33} -110.590 q^{35} -313.724 q^{36} -8.40485 q^{37} -405.191 q^{38} +31.5221 q^{39} +287.211 q^{40} +99.9530 q^{41} -15.2993 q^{42} -81.5297 q^{43} +649.766 q^{44} -461.015 q^{45} +537.130 q^{46} +195.351 q^{47} -10.7547 q^{48} -301.942 q^{49} +768.195 q^{50} +689.006 q^{52} +260.322 q^{53} -128.245 q^{54} +954.825 q^{55} -106.630 q^{56} -48.9979 q^{57} -958.715 q^{58} -536.401 q^{59} +108.923 q^{60} -265.689 q^{61} -77.8357 q^{62} +171.156 q^{63} -826.636 q^{64} +1012.49 q^{65} +132.093 q^{66} +514.794 q^{67} +64.9526 q^{69} -491.412 q^{70} -704.023 q^{71} -444.504 q^{72} +184.948 q^{73} -37.3473 q^{74} +92.8943 q^{75} -1070.99 q^{76} -354.487 q^{77} +140.070 q^{78} -34.8358 q^{79} -345.440 q^{80} +705.696 q^{81} +444.145 q^{82} -647.682 q^{83} -40.4386 q^{84} -362.280 q^{86} -115.933 q^{87} +920.630 q^{88} -1060.24 q^{89} -2048.53 q^{90} -375.895 q^{91} +1419.72 q^{92} -9.41231 q^{93} +868.051 q^{94} -1573.81 q^{95} -119.324 q^{96} -256.409 q^{97} -1341.69 q^{98} -1477.74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q + 18 * q^3 + 48 * q^4 + 30 * q^5 - 9 * q^6 + 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9} + 60 q^{10} + 162 q^{11} + 216 q^{12} - 72 q^{13} + 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} + 129 q^{20} + 246 q^{21} + 456 q^{22} + 282 q^{23} + 72 q^{24} + 444 q^{25} + 528 q^{26} + 1092 q^{27} + 120 q^{28} + 648 q^{29} - 1890 q^{30} + 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} - 30 q^{37} - 60 q^{38} + 1758 q^{39} - 450 q^{40} + 318 q^{41} + 804 q^{42} + 486 q^{43} + 2448 q^{44} + 486 q^{45} + 1617 q^{46} - 888 q^{47} + 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} + 933 q^{54} + 972 q^{55} + 2661 q^{56} - 156 q^{57} + 201 q^{58} - 792 q^{59} + 1458 q^{60} + 1212 q^{61} + 2817 q^{62} + 2112 q^{63} - 1857 q^{64} + 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} + 2802 q^{71} + 1455 q^{72} + 726 q^{73} + 270 q^{74} - 264 q^{75} + 675 q^{76} - 1008 q^{77} - 3090 q^{78} - 444 q^{79} - 1143 q^{80} + 2520 q^{81} - 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} - 3750 q^{88} - 906 q^{89} - 7755 q^{90} + 2280 q^{91} + 87 q^{92} + 132 q^{93} + 735 q^{94} + 966 q^{95} - 5046 q^{96} - 3246 q^{97} + 1911 q^{98} - 282 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 + 48 * q^4 + 30 * q^5 - 9 * q^6 + 24 * q^7 - 51 * q^8 + 108 * q^9 + 60 * q^10 + 162 * q^11 + 216 * q^12 - 72 * q^13 + 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 + 129 * q^20 + 246 * q^21 + 456 * q^22 + 282 * q^23 + 72 * q^24 + 444 * q^25 + 528 * q^26 + 1092 * q^27 + 120 * q^28 + 648 * q^29 - 1890 * q^30 + 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 - 30 * q^37 - 60 * q^38 + 1758 * q^39 - 450 * q^40 + 318 * q^41 + 804 * q^42 + 486 * q^43 + 2448 * q^44 + 486 * q^45 + 1617 * q^46 - 888 * q^47 + 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 + 933 * q^54 + 972 * q^55 + 2661 * q^56 - 156 * q^57 + 201 * q^58 - 792 * q^59 + 1458 * q^60 + 1212 * q^61 + 2817 * q^62 + 2112 * q^63 - 1857 * q^64 + 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 + 2802 * q^71 + 1455 * q^72 + 726 * q^73 + 270 * q^74 - 264 * q^75 + 675 * q^76 - 1008 * q^77 - 3090 * q^78 - 444 * q^79 - 1143 * q^80 + 2520 * q^81 - 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 - 3750 * q^88 - 906 * q^89 - 7755 * q^90 + 2280 * q^91 + 87 * q^92 + 132 * q^93 + 735 * q^94 + 966 * q^95 - 5046 * q^96 - 3246 * q^97 + 1911 * q^98 - 282 * q^99

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