LMFDB - Embedded newform 289.4.a.h.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:	$1$
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} - 4607 x^{3} - 117822 x^{2} + 21960 x + 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	$-0.516466\pi$
$3$	−0.537336	−0.103410	−0.0517052	+	0.998662i	$0.516466\pi$
$4$	11.7450	1.46813
$5$	−17.2592	−1.54371	−0.771854	−	0.635800i	$-0.780670\pi$
$5$	−17.2592	−1.54371	−0.771854	+	0.635800i	$0.780670\pi$
$6$	−2.38767	−0.162461
$7$	6.40763	0.345979	0.172990	−	0.984924i	$-0.444657\pi$
$7$	6.40763	0.345979	0.172990	+	0.984924i	$0.444657\pi$
$8$	16.6411	0.735439
$9$	−26.7113	−0.989306
$10$	−76.6918	−2.42521
$11$	−55.3227	−1.51640	−0.758201	−	0.652020i	$-0.773922\pi$
$11$	−55.3227	−1.51640	−0.758201	+	0.652020i	$0.773922\pi$
$12$	−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	$-0.684586\pi$
$23$	−120.879	−1.09587	−0.547935	+	0.836521i	$0.684586\pi$
$24$	−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	$-0.257271\pi$
$29$	215.755	1.38154	0.690771	+	0.723074i	$0.257271\pi$
$30$	41.2093	0.250792
$31$	17.5166	0.101486	0.0507432	−	0.998712i	$-0.483841\pi$
$31$	17.5166	0.101486	0.0507432	+	0.998712i	$0.483841\pi$
$32$	−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	$-0.494056\pi$
$37$	8.40485	0.0373446	0.0186723	+	0.999826i	$0.494056\pi$
$38$	−405.191	−1.72975
$39$	−31.5221	−0.129425
$40$	−287.211	−1.13530
$41$	−99.9530	−0.380733	−0.190366	−	0.981713i	$-0.560968\pi$
$41$	−99.9530	−0.380733	−0.190366	+	0.981713i	$0.560968\pi$
$42$	−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	$-0.410052\pi$
$61$	265.689	0.557671	0.278836	+	0.960339i	$0.410052\pi$
$62$	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	$-0.299760\pi$
$71$	704.023	1.17679	0.588396	+	0.808573i	$0.299760\pi$
$72$	−444.504	−0.727574
$73$	−184.948	−0.296528	−0.148264	−	0.988948i	$-0.547368\pi$
$73$	−184.948	−0.296528	−0.148264	+	0.988948i	$0.547368\pi$
$74$	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	$-0.492103\pi$
$79$	34.8358	0.0496118	0.0248059	+	0.999692i	$0.492103\pi$
$80$	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	$-0.457154\pi$
$97$	256.409	0.268395	0.134198	+	0.990955i	$0.457154\pi$
$98$	−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	$-0.869683\pi$
$107$	−2030.70	−1.83472	−0.917359	+	0.398060i	$0.869683\pi$
$108$	338.973	0.302015
$109$	716.479	0.629598	0.314799	−	0.949158i	$-0.398063\pi$
$109$	716.479	0.629598	0.314799	+	0.949158i	$0.398063\pi$
$110$	4242.80	3.67759
$111$	−4.51623	−0.00386182
$112$	−128.248	−0.108199
$113$	−16.9632	−0.0141218	−0.00706090	−	0.999975i	$-0.502248\pi$
$113$	−16.9632	−0.0141218	−0.00706090	+	0.999975i	$0.502248\pi$
$114$	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	$-0.433923\pi$
$131$	618.036	0.412199	0.206100	+	0.978531i	$0.433923\pi$
$132$	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	$-0.600150\pi$
$139$	−1014.29	−0.618930	−0.309465	+	0.950911i	$0.600150\pi$
$140$	−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	$-0.516202\pi$
$163$	−211.756	−0.101755	−0.0508773	+	0.998705i	$0.516202\pi$
$164$	−1173.95	−0.558963
$165$	−513.062	−0.242072
$166$	−2878.00	−1.34564
$167$	−977.319	−0.452858	−0.226429	−	0.974028i	$-0.572705\pi$
$167$	−977.319	−0.452858	−0.226429	+	0.974028i	$0.572705\pi$
$168$	−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	$-0.791333\pi$
$173$	−3607.58	−1.58543	−0.792714	+	0.609594i	$0.791333\pi$
$174$	−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	$-0.427860\pi$
$181$	1094.34	0.449401	0.224701	+	0.974428i	$0.427860\pi$
$182$	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	$-0.655836\pi$
$193$	−2521.70	−0.940498	−0.470249	+	0.882534i	$0.655836\pi$
$194$	1139.36	0.421656
$195$	544.046	0.199795
$196$	−3546.31	−1.29239
$197$	2196.87	0.794521	0.397260	−	0.917706i	$-0.369961\pi$
$197$	2196.87	0.794521	0.397260	+	0.917706i	$0.369961\pi$
$198$	6566.39	2.35683
$199$	−3596.88	−1.28129	−0.640643	−	0.767839i	$-0.721332\pi$
$199$	−3596.88	−1.28129	−0.640643	+	0.767839i	$0.721332\pi$
$200$	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	$-0.704790\pi$
$211$	−3677.29	−1.19979	−0.599893	+	0.800080i	$0.704790\pi$
$212$	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	$-0.740910\pi$
$227$	−4696.68	−1.37326	−0.686629	+	0.727008i	$0.740910\pi$
$228$	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	$-0.528741\pi$
$233$	−641.400	−0.180341	−0.0901706	+	0.995926i	$0.528741\pi$
$234$	−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	$-0.606738\pi$
$241$	−2462.38	−0.658156	−0.329078	+	0.944303i	$0.606738\pi$
$242$	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	$-0.234077\pi$
$269$	6543.59	1.48316	0.741580	+	0.670864i	$0.234077\pi$
$270$	−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	$-0.611932\pi$
$277$	−3175.91	−0.688887	−0.344444	+	0.938807i	$0.611932\pi$
$278$	−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	$-0.805593\pi$
$283$	−7800.28	−1.63844	−0.819220	+	0.573479i	$0.805593\pi$
$284$	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	$-0.617085\pi$
$311$	−3944.44	−0.719192	−0.359596	+	0.933108i	$0.617085\pi$
$312$	−524.562	−0.0951843
$313$	−6540.41	−1.18111	−0.590553	−	0.806999i	$-0.701090\pi$
$313$	−6540.41	−1.18111	−0.590553	+	0.806999i	$0.701090\pi$
$314$	16223.7	2.91579
$315$	2954.01	0.528380
$316$	409.147	0.0728364
$317$	3711.41	0.657582	0.328791	−	0.944403i	$-0.393359\pi$
$317$	3711.41	0.657582	0.328791	+	0.944403i	$0.393359\pi$
$318$	−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	$-0.347070\pi$
$337$	5718.46	0.924346	0.462173	+	0.886790i	$0.347070\pi$
$338$	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	$-0.516696\pi$
$347$	−677.787	−0.104857	−0.0524287	+	0.998625i	$0.516696\pi$
$348$	−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	$-0.194143\pi$
$367$	11526.1	1.63939	0.819695	+	0.572801i	$0.194143\pi$
$368$	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	$-0.128591\pi$
$379$	13568.8	1.83901	0.919503	+	0.393082i	$0.128591\pi$
$380$	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	$-0.350050\pi$
$397$	7180.09	0.907703	0.453852	+	0.891077i	$0.350050\pi$
$398$	−15982.9	−2.01293
$399$	313.960	0.0393926
$400$	−3460.15	−0.432519
$401$	−5087.50	−0.633560	−0.316780	−	0.948499i	$-0.602602\pi$
$401$	−5087.50	−0.633560	−0.316780	+	0.948499i	$0.602602\pi$
$402$	−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	$-0.850370\pi$
$419$	−15292.9	−1.78307	−0.891533	+	0.452956i	$0.850370\pi$
$420$	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	$-0.542135\pi$
$431$	−2361.94	−0.263969	−0.131984	+	0.991252i	$0.542135\pi$
$432$	−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	$-0.635805\pi$
$439$	−7612.65	−0.827636	−0.413818	+	0.910360i	$0.635805\pi$
$440$	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	$-0.245248\pi$
$449$	13654.4	1.43517	0.717584	+	0.696472i	$0.245248\pi$
$450$	−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	$-0.293809\pi$
$479$	12651.6	1.20682	0.603409	+	0.797432i	$0.293809\pi$
$480$	−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	$-0.287261\pi$
$487$	13319.7	1.23937	0.619683	+	0.784852i	$0.287261\pi$
$488$	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	$-0.142356\pi$
$499$	20101.1	1.80330	0.901650	+	0.432466i	$0.142356\pi$
$500$	−9705.56	−0.868091
$501$	525.149	0.0468302
$502$	11695.2	1.03981
$503$	−6166.84	−0.546652	−0.273326	−	0.961921i	$-0.588124\pi$
$503$	−6166.84	−0.546652	−0.273326	+	0.961921i	$0.588124\pi$
$504$	−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	$-0.535435\pi$
$521$	−2642.20	−0.222182	−0.111091	+	0.993810i	$0.535435\pi$
$522$	−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	$-0.241041\pi$
$541$	18289.3	1.45345	0.726726	+	0.686927i	$0.241041\pi$
$542$	−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	$-0.627675\pi$
$547$	−9989.86	−0.780869	−0.390435	+	0.920631i	$0.627675\pi$
$548$	−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	$-0.0381913\pi$
$571$	27092.6	1.98562	0.992811	+	0.119694i	$0.0381913\pi$
$572$	−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	$-0.517019\pi$
$601$	−1574.80	−0.106884	−0.0534421	+	0.998571i	$0.517019\pi$
$602$	−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	$-0.806797\pi$
$607$	−24567.4	−1.64276	−0.821382	+	0.570378i	$0.806797\pi$
$608$	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	$-0.539432\pi$
$617$	−3787.41	−0.247124	−0.123562	+	0.992337i	$0.539432\pi$
$618$	61.3167	0.00399113
$619$	4066.72	0.264063	0.132032	−	0.991246i	$-0.457850\pi$
$619$	4066.72	0.264063	0.132032	+	0.991246i	$0.457850\pi$
$620$	−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	$-0.759885\pi$
$641$	−23652.6	−1.45744	−0.728721	+	0.684810i	$0.759885\pi$
$642$	4848.64	0.298069
$643$	2712.61	0.166368	0.0831841	−	0.996534i	$-0.473491\pi$
$643$	2712.61	0.166368	0.0831841	+	0.996534i	$0.473491\pi$
$644$	−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	$-0.214309\pi$
$653$	26090.8	1.56357	0.781785	+	0.623548i	$0.214309\pi$
$654$	−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	$-0.290249\pi$
$673$	21380.1	1.22458	0.612289	+	0.790634i	$0.290249\pi$
$674$	25410.2	1.45217
$675$	4989.47	0.284511
$676$	14615.9	0.831581
$677$	7244.51	0.411269	0.205635	−	0.978629i	$-0.434074\pi$
$677$	7244.51	0.411269	0.205635	+	0.978629i	$0.434074\pi$
$678$	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	$-0.463001\pi$
$683$	4140.24	0.231950	0.115975	+	0.993252i	$0.463001\pi$
$684$	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	$-0.821265\pi$
$691$	−30750.3	−1.69290	−0.846451	+	0.532466i	$0.821265\pi$
$692$	−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	$-0.271731\pi$
$709$	24814.8	1.31444	0.657222	+	0.753697i	$0.271731\pi$
$710$	−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	$-0.719246\pi$
$719$	−24507.8	−1.27119	−0.635597	+	0.772021i	$0.719246\pi$
$720$	−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	$-0.697841\pi$
$743$	−23585.7	−1.16457	−0.582286	+	0.812984i	$0.697841\pi$
$744$	−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	$-0.380081\pi$
$751$	15142.8	0.735775	0.367887	+	0.929870i	$0.380081\pi$
$752$	−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	$-0.241438\pi$
$787$	32051.7	1.45174	0.725870	+	0.687832i	$0.241438\pi$
$788$	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	$-0.551677\pi$
$809$	−7438.60	−0.323272	−0.161636	+	0.986850i	$0.551677\pi$
$810$	−54121.1	−2.34768
$811$	−10261.1	−0.444288	−0.222144	−	0.975014i	$-0.571306\pi$
$811$	−10261.1	−0.444288	−0.222144	+	0.975014i	$0.571306\pi$
$812$	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	$-0.347108\pi$
$821$	21739.5	0.924134	0.462067	+	0.886845i	$0.347108\pi$
$822$	5384.60	0.228479
$823$	−23728.9	−1.00503	−0.502514	−	0.864569i	$-0.667592\pi$
$823$	−23728.9	−1.00503	−0.502514	+	0.864569i	$0.667592\pi$
$824$	−427.352	−0.0180674
$825$	5139.16	0.216876
$826$	−15272.7	−0.643347
$827$	−21101.5	−0.887270	−0.443635	−	0.896207i	$-0.646311\pi$
$827$	−21101.5	−0.887270	−0.443635	+	0.896207i	$0.646311\pi$
$828$	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	$-0.491570\pi$
$839$	1287.05	0.0529607	0.0264803	+	0.999649i	$0.491570\pi$
$840$	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	$-0.618842\pi$
$853$	−18173.4	−0.729479	−0.364740	+	0.931110i	$0.618842\pi$
$854$	7564.83	0.303118
$855$	−42038.4	−1.68150
$856$	−33793.0	−1.34932
$857$	39590.2	1.57803	0.789017	−	0.614371i	$-0.210590\pi$
$857$	39590.2	1.57803	0.789017	+	0.614371i	$0.210590\pi$
$858$	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	$-0.761023\pi$
$877$	−37979.1	−1.46233	−0.731164	+	0.682202i	$0.761023\pi$
$878$	−33827.1	−1.30024
$879$	1291.30	0.0495502
$880$	−19110.7	−0.732069
$881$	−18289.7	−0.699427	−0.349714	−	0.936857i	$-0.613721\pi$
$881$	−18289.7	−0.699427	−0.349714	+	0.936857i	$0.613721\pi$
$882$	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	$-0.908993\pi$
$887$	−50689.5	−1.91881	−0.959406	+	0.282028i	$0.908993\pi$
$888$	−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	$-0.803702\pi$
$907$	−44568.0	−1.63160	−0.815798	+	0.578338i	$0.803702\pi$
$908$	−55162.5	−2.01612
$909$	39134.0	1.42794
$910$	−28828.1	−1.05016
$911$	7809.03	0.284001	0.142000	−	0.989867i	$-0.454647\pi$
$911$	7809.03	0.284001	0.142000	+	0.989867i	$0.454647\pi$
$912$	−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	$-0.414268\pi$
$929$	15068.9	0.532180	0.266090	+	0.963948i	$0.414268\pi$
$930$	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	$-0.704714\pi$
$941$	−34621.7	−1.19940	−0.599701	+	0.800224i	$0.704714\pi$
$942$	−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	$-0.613422\pi$
$947$	−20331.6	−0.697665	−0.348832	+	0.937185i	$0.613422\pi$
$948$	−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	$-0.394309\pi$
$983$	20092.8	0.651944	0.325972	+	0.945379i	$0.394309\pi$
$984$	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	$-0.545638\pi$
$991$	−8915.20	−0.285773	−0.142886	+	0.989739i	$0.545638\pi$
$992$	−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	$-0.564068\pi$
$997$	−12587.1	−0.399837	−0.199919	+	0.979812i	$0.564068\pi$
$998$	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.h.1.12	✓	12
17.4	even	4		289.4.b.f.288.2		24
17.13	even	4		289.4.b.f.288.1		24
17.16	even	2		289.4.a.i.1.12	yes	12

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