LMFDB - Embedded newform 9251.2.a.t.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-2.48400$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48400 q^{2} +1.60954 q^{3} +4.17025 q^{4} -1.24863 q^{5} +3.99809 q^{6} -4.33788 q^{7} +5.39091 q^{8} -0.409386 q^{9} +O(q^{10})$	\(q+2.48400 q^{2} +1.60954 q^{3} +4.17025 q^{4} -1.24863 q^{5} +3.99809 q^{6} -4.33788 q^{7} +5.39091 q^{8} -0.409386 q^{9} -3.10161 q^{10} -1.00000 q^{11} +6.71218 q^{12} +3.41292 q^{13} -10.7753 q^{14} -2.00972 q^{15} +5.05050 q^{16} -3.22679 q^{17} -1.01691 q^{18} +7.88973 q^{19} -5.20712 q^{20} -6.98199 q^{21} -2.48400 q^{22} -5.25089 q^{23} +8.67687 q^{24} -3.44091 q^{25} +8.47770 q^{26} -5.48754 q^{27} -18.0901 q^{28} -4.99215 q^{30} -7.46621 q^{31} +1.76363 q^{32} -1.60954 q^{33} -8.01535 q^{34} +5.41643 q^{35} -1.70724 q^{36} +0.156756 q^{37} +19.5981 q^{38} +5.49323 q^{39} -6.73127 q^{40} +5.92116 q^{41} -17.3433 q^{42} -3.19801 q^{43} -4.17025 q^{44} +0.511173 q^{45} -13.0432 q^{46} -3.78287 q^{47} +8.12898 q^{48} +11.8172 q^{49} -8.54723 q^{50} -5.19364 q^{51} +14.2328 q^{52} -12.7243 q^{53} -13.6310 q^{54} +1.24863 q^{55} -23.3851 q^{56} +12.6988 q^{57} -4.93175 q^{59} -8.38106 q^{60} +10.8056 q^{61} -18.5461 q^{62} +1.77587 q^{63} -5.72015 q^{64} -4.26149 q^{65} -3.99809 q^{66} -4.44829 q^{67} -13.4565 q^{68} -8.45151 q^{69} +13.4544 q^{70} -6.95540 q^{71} -2.20696 q^{72} +3.38107 q^{73} +0.389381 q^{74} -5.53828 q^{75} +32.9022 q^{76} +4.33788 q^{77} +13.6452 q^{78} -11.8638 q^{79} -6.30623 q^{80} -7.60425 q^{81} +14.7082 q^{82} +10.8180 q^{83} -29.1167 q^{84} +4.02908 q^{85} -7.94384 q^{86} -5.39091 q^{88} -2.57416 q^{89} +1.26975 q^{90} -14.8049 q^{91} -21.8976 q^{92} -12.0172 q^{93} -9.39666 q^{94} -9.85139 q^{95} +2.83863 q^{96} -13.6920 q^{97} +29.3540 q^{98} +0.409386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * 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 $

$2$	2.48400	1.75645	0.878226	−	0.478245i	$-0.158727\pi$
$2$	2.48400	1.75645	0.878226	+	0.478245i	$0.158727\pi$
$3$	1.60954	0.929267	0.464634	−	0.885503i	$-0.346186\pi$
$3$	1.60954	0.929267	0.464634	+	0.885503i	$0.346186\pi$
$4$	4.17025	2.08513
$5$	−1.24863	−0.558406	−0.279203	−	0.960232i	$-0.590070\pi$
$5$	−1.24863	−0.558406	−0.279203	+	0.960232i	$0.590070\pi$
$6$	3.99809	1.63221
$7$	−4.33788	−1.63957	−0.819783	−	0.572674i	$-0.805906\pi$
$7$	−4.33788	−1.63957	−0.819783	+	0.572674i	$0.805906\pi$
$8$	5.39091	1.90597
$9$	−0.409386	−0.136462
$10$	−3.10161	−0.980814
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.71218	1.93764
$13$	3.41292	0.946575	0.473287	−	0.880908i	$-0.343067\pi$
$13$	3.41292	0.946575	0.473287	+	0.880908i	$0.343067\pi$
$14$	−10.7753	−2.87982
$15$	−2.00972	−0.518909
$16$	5.05050	1.26263
$17$	−3.22679	−0.782612	−0.391306	−	0.920261i	$-0.627977\pi$
$17$	−3.22679	−0.782612	−0.391306	+	0.920261i	$0.627977\pi$
$18$	−1.01691	−0.239689
$19$	7.88973	1.81003	0.905014	−	0.425381i	$-0.139860\pi$
$19$	7.88973	1.81003	0.905014	+	0.425381i	$0.139860\pi$
$20$	−5.20712	−1.16435
$21$	−6.98199	−1.52360
$22$	−2.48400	−0.529590
$23$	−5.25089	−1.09489	−0.547443	−	0.836843i	$-0.684399\pi$
$23$	−5.25089	−1.09489	−0.547443	+	0.836843i	$0.684399\pi$
$24$	8.67687	1.77116
$25$	−3.44091	−0.688183
$26$	8.47770	1.66261
$27$	−5.48754	−1.05608
$28$	−18.0901	−3.41870
$29$	0	0
$29$	0	0
$30$	−4.99215	−0.911438
$31$	−7.46621	−1.34097	−0.670486	−	0.741922i	$-0.733914\pi$
$31$	−7.46621	−1.34097	−0.670486	+	0.741922i	$0.733914\pi$
$32$	1.76363	0.311769
$33$	−1.60954	−0.280185
$34$	−8.01535	−1.37462
$35$	5.41643	0.915544
$36$	−1.70724	−0.284540
$37$	0.156756	0.0257705	0.0128852	−	0.999917i	$-0.495898\pi$
$37$	0.156756	0.0257705	0.0128852	+	0.999917i	$0.495898\pi$
$38$	19.5981	3.17923
$39$	5.49323	0.879621
$40$	−6.73127	−1.06431
$41$	5.92116	0.924731	0.462365	−	0.886690i	$-0.347001\pi$
$41$	5.92116	0.924731	0.462365	+	0.886690i	$0.347001\pi$
$42$	−17.3433	−2.67612
$43$	−3.19801	−0.487691	−0.243846	−	0.969814i	$-0.578409\pi$
$43$	−3.19801	−0.487691	−0.243846	+	0.969814i	$0.578409\pi$
$44$	−4.17025	−0.628689
$45$	0.511173	0.0762012
$46$	−13.0432	−1.92312
$47$	−3.78287	−0.551789	−0.275894	−	0.961188i	$-0.588974\pi$
$47$	−3.78287	−0.551789	−0.275894	+	0.961188i	$0.588974\pi$
$48$	8.12898	1.17332
$49$	11.8172	1.68818
$50$	−8.54723	−1.20876
$51$	−5.19364	−0.727256
$52$	14.2328	1.97373
$53$	−12.7243	−1.74782	−0.873909	−	0.486089i	$-0.838423\pi$
$53$	−12.7243	−1.74782	−0.873909	+	0.486089i	$0.838423\pi$
$54$	−13.6310	−1.85495
$55$	1.24863	0.168366
$56$	−23.3851	−3.12497
$57$	12.6988	1.68200
$58$	0	0
$59$	−4.93175	−0.642060	−0.321030	−	0.947069i	$-0.604029\pi$
$59$	−4.93175	−0.642060	−0.321030	+	0.947069i	$0.604029\pi$
$60$	−8.38106	−1.08199
$61$	10.8056	1.38351	0.691756	−	0.722132i	$-0.256838\pi$
$61$	10.8056	1.38351	0.691756	+	0.722132i	$0.256838\pi$
$62$	−18.5461	−2.35535
$63$	1.77587	0.223738
$64$	−5.72015	−0.715018
$65$	−4.26149	−0.528573
$66$	−3.99809	−0.492131
$67$	−4.44829	−0.543446	−0.271723	−	0.962376i	$-0.587593\pi$
$67$	−4.44829	−0.543446	−0.271723	+	0.962376i	$0.587593\pi$
$68$	−13.4565	−1.63184
$69$	−8.45151	−1.01744
$70$	13.4544	1.60811
$71$	−6.95540	−0.825454	−0.412727	−	0.910855i	$-0.635424\pi$
$71$	−6.95540	−0.825454	−0.412727	+	0.910855i	$0.635424\pi$
$72$	−2.20696	−0.260093
$73$	3.38107	0.395724	0.197862	−	0.980230i	$-0.436600\pi$
$73$	3.38107	0.395724	0.197862	+	0.980230i	$0.436600\pi$
$74$	0.389381	0.0452647
$75$	−5.53828	−0.639506
$76$	32.9022	3.77414
$77$	4.33788	0.494348
$78$	13.6452	1.54501
$79$	−11.8638	−1.33478	−0.667390	−	0.744708i	$-0.732589\pi$
$79$	−11.8638	−1.33478	−0.667390	+	0.744708i	$0.732589\pi$
$80$	−6.30623	−0.705058
$81$	−7.60425	−0.844916
$82$	14.7082	1.62425
$83$	10.8180	1.18743	0.593713	−	0.804677i	$-0.297661\pi$
$83$	10.8180	1.18743	0.593713	+	0.804677i	$0.297661\pi$
$84$	−29.1167	−3.17689
$85$	4.02908	0.437015
$86$	−7.94384	−0.856607
$87$	0	0
$88$	−5.39091	−0.574673
$89$	−2.57416	−0.272860	−0.136430	−	0.990650i	$-0.543563\pi$
$89$	−2.57416	−0.272860	−0.136430	+	0.990650i	$0.543563\pi$
$90$	1.26975	0.133844
$91$	−14.8049	−1.55197
$92$	−21.8976	−2.28298
$93$	−12.0172	−1.24612
$94$	−9.39666	−0.969191
$95$	−9.85139	−1.01073
$96$	2.83863	0.289717
$97$	−13.6920	−1.39021	−0.695104	−	0.718909i	$-0.744642\pi$
$97$	−13.6920	−1.39021	−0.695104	+	0.718909i	$0.744642\pi$
$98$	29.3540	2.96520
$99$	0.409386	0.0411448
$100$	−14.3495	−1.43495
$101$	−15.2789	−1.52031	−0.760153	−	0.649744i	$-0.774876\pi$
$101$	−15.2789	−1.52031	−0.760153	+	0.649744i	$0.774876\pi$
$102$	−12.9010	−1.27739
$103$	17.3172	1.70632	0.853158	−	0.521652i	$-0.174684\pi$
$103$	17.3172	1.70632	0.853158	+	0.521652i	$0.174684\pi$
$104$	18.3988	1.80415
$105$	8.71795	0.850785
$106$	−31.6072	−3.06996
$107$	−4.57513	−0.442294	−0.221147	−	0.975240i	$-0.570980\pi$
$107$	−4.57513	−0.442294	−0.221147	+	0.975240i	$0.570980\pi$
$108$	−22.8844	−2.20205
$109$	−8.58602	−0.822391	−0.411196	−	0.911547i	$-0.634889\pi$
$109$	−8.58602	−0.822391	−0.411196	+	0.911547i	$0.634889\pi$
$110$	3.10161	0.295727
$111$	0.252304	0.0239477
$112$	−21.9085	−2.07016
$113$	4.50753	0.424033	0.212017	−	0.977266i	$-0.431997\pi$
$113$	4.50753	0.424033	0.212017	+	0.977266i	$0.431997\pi$
$114$	31.5439	2.95435
$115$	6.55644	0.611391
$116$	0	0
$117$	−1.39720	−0.129171
$118$	−12.2505	−1.12775
$119$	13.9974	1.28314
$120$	−10.8342	−0.989026
$121$	1.00000	0.0909091
$122$	26.8410	2.43007
$123$	9.53034	0.859322
$124$	−31.1360	−2.79610
$125$	10.5396	0.942691
$126$	4.41126	0.392986
$127$	7.87006	0.698355	0.349177	−	0.937057i	$-0.386461\pi$
$127$	7.87006	0.698355	0.349177	+	0.937057i	$0.386461\pi$
$128$	−17.7361	−1.56766
$129$	−5.14731	−0.453196
$130$	−10.5855	−0.928414
$131$	0.585436	0.0511498	0.0255749	−	0.999673i	$-0.491858\pi$
$131$	0.585436	0.0511498	0.0255749	+	0.999673i	$0.491858\pi$
$132$	−6.71218	−0.584220
$133$	−34.2247	−2.96766
$134$	−11.0496	−0.954537
$135$	6.85193	0.589720
$136$	−17.3953	−1.49164
$137$	13.0489	1.11484	0.557421	−	0.830230i	$-0.311791\pi$
$137$	13.0489	1.11484	0.557421	+	0.830230i	$0.311791\pi$
$138$	−20.9936	−1.78709
$139$	9.78669	0.830096	0.415048	−	0.909799i	$-0.363765\pi$
$139$	9.78669	0.830096	0.415048	+	0.909799i	$0.363765\pi$
$140$	22.5879	1.90902
$141$	−6.08868	−0.512759
$142$	−17.2772	−1.44987
$143$	−3.41292	−0.285403
$144$	−2.06760	−0.172300
$145$	0	0
$146$	8.39856	0.695070
$147$	19.0203	1.56877
$148$	0.653711	0.0537347
$149$	3.59653	0.294639	0.147319	−	0.989089i	$-0.452935\pi$
$149$	3.59653	0.294639	0.147319	+	0.989089i	$0.452935\pi$
$150$	−13.7571	−1.12326
$151$	−13.3410	−1.08567	−0.542837	−	0.839838i	$-0.682650\pi$
$151$	−13.3410	−1.08567	−0.542837	+	0.839838i	$0.682650\pi$
$152$	42.5328	3.44987
$153$	1.32100	0.106797
$154$	10.7753	0.868299
$155$	9.32257	0.748807
$156$	22.9082	1.83412
$157$	−15.2824	−1.21967	−0.609836	−	0.792528i	$-0.708765\pi$
$157$	−15.2824	−1.21967	−0.609836	+	0.792528i	$0.708765\pi$
$158$	−29.4696	−2.34448
$159$	−20.4803	−1.62419
$160$	−2.20213	−0.174094
$161$	22.7778	1.79514
$162$	−18.8889	−1.48406
$163$	−10.6468	−0.833923	−0.416961	−	0.908924i	$-0.636905\pi$
$163$	−10.6468	−0.833923	−0.416961	+	0.908924i	$0.636905\pi$
$164$	24.6928	1.92818
$165$	2.00972	0.156457
$166$	26.8718	2.08566
$167$	18.7552	1.45132	0.725661	−	0.688052i	$-0.241534\pi$
$167$	18.7552	1.45132	0.725661	+	0.688052i	$0.241534\pi$
$168$	−37.6393	−2.90393
$169$	−1.35195	−0.103996
$170$	10.0082	0.767597
$171$	−3.22994	−0.247000
$172$	−13.3365	−1.01690
$173$	−0.562371	−0.0427563	−0.0213782	−	0.999771i	$-0.506805\pi$
$173$	−0.562371	−0.0427563	−0.0213782	+	0.999771i	$0.506805\pi$
$174$	0	0
$175$	14.9263	1.12832
$176$	−5.05050	−0.380696
$177$	−7.93785	−0.596645
$178$	−6.39421	−0.479267
$179$	8.72682	0.652273	0.326137	−	0.945323i	$-0.394253\pi$
$179$	8.72682	0.652273	0.326137	+	0.945323i	$0.394253\pi$
$180$	2.13172	0.158889
$181$	−21.4433	−1.59387	−0.796934	−	0.604066i	$-0.793546\pi$
$181$	−21.4433	−1.59387	−0.796934	+	0.604066i	$0.793546\pi$
$182$	−36.7753	−2.72597
$183$	17.3920	1.28565
$184$	−28.3071	−2.08682
$185$	−0.195731	−0.0143904
$186$	−29.8506	−2.18875
$187$	3.22679	0.235966
$188$	−15.7755	−1.15055
$189$	23.8043	1.73151
$190$	−24.4708	−1.77530
$191$	−1.16055	−0.0839745	−0.0419872	−	0.999118i	$-0.513369\pi$
$191$	−1.16055	−0.0839745	−0.0419872	+	0.999118i	$0.513369\pi$
$192$	−9.20680	−0.664443
$193$	−3.20830	−0.230938	−0.115469	−	0.993311i	$-0.536837\pi$
$193$	−3.20830	−0.230938	−0.115469	+	0.993311i	$0.536837\pi$
$194$	−34.0108	−2.44183
$195$	−6.85904	−0.491186
$196$	49.2809	3.52006
$197$	15.8476	1.12909	0.564546	−	0.825402i	$-0.309051\pi$
$197$	15.8476	1.12909	0.564546	+	0.825402i	$0.309051\pi$
$198$	1.01691	0.0722690
$199$	8.30490	0.588719	0.294359	−	0.955695i	$-0.404894\pi$
$199$	8.30490	0.588719	0.294359	+	0.955695i	$0.404894\pi$
$200$	−18.5496	−1.31166
$201$	−7.15970	−0.505006
$202$	−37.9527	−2.67035
$203$	0	0
$204$	−21.6588	−1.51642
$205$	−7.39337	−0.516375
$206$	43.0160	2.99706
$207$	2.14964	0.149410
$208$	17.2370	1.19517
$209$	−7.88973	−0.545744
$210$	21.6554	1.49436
$211$	1.95912	0.134871	0.0674357	−	0.997724i	$-0.478518\pi$
$211$	1.95912	0.134871	0.0674357	+	0.997724i	$0.478518\pi$
$212$	−53.0636	−3.64442
$213$	−11.1950	−0.767068
$214$	−11.3646	−0.776869
$215$	3.99314	0.272330
$216$	−29.5828	−2.01285
$217$	32.3876	2.19861
$218$	−21.3277	−1.44449
$219$	5.44196	0.367733
$220$	5.20712	0.351064
$221$	−11.0128	−0.740801
$222$	0.626724	0.0420630
$223$	−3.34094	−0.223726	−0.111863	−	0.993724i	$-0.535682\pi$
$223$	−3.34094	−0.223726	−0.111863	+	0.993724i	$0.535682\pi$
$224$	−7.65042	−0.511165
$225$	1.40866	0.0939108
$226$	11.1967	0.744794
$227$	24.6860	1.63847	0.819234	−	0.573459i	$-0.194399\pi$
$227$	24.6860	1.63847	0.819234	+	0.573459i	$0.194399\pi$
$228$	52.9573	3.50718
$229$	27.8093	1.83769	0.918844	−	0.394620i	$-0.129124\pi$
$229$	27.8093	1.83769	0.918844	+	0.394620i	$0.129124\pi$
$230$	16.2862	1.07388
$231$	6.98199	0.459381
$232$	0	0
$233$	−6.55755	−0.429600	−0.214800	−	0.976658i	$-0.568910\pi$
$233$	−6.55755	−0.429600	−0.214800	+	0.976658i	$0.568910\pi$
$234$	−3.47065	−0.226884
$235$	4.72342	0.308122
$236$	−20.5667	−1.33878
$237$	−19.0952	−1.24037
$238$	34.7696	2.25378
$239$	25.4157	1.64401	0.822003	−	0.569483i	$-0.192857\pi$
$239$	25.4157	1.64401	0.822003	+	0.569483i	$0.192857\pi$
$240$	−10.1501	−0.655187
$241$	−3.09174	−0.199156	−0.0995781	−	0.995030i	$-0.531749\pi$
$241$	−3.09174	−0.199156	−0.0995781	+	0.995030i	$0.531749\pi$
$242$	2.48400	0.159678
$243$	4.22329	0.270924
$244$	45.0619	2.88480
$245$	−14.7554	−0.942688
$246$	23.6734	1.50936
$247$	26.9270	1.71333
$248$	−40.2497	−2.55586
$249$	17.4119	1.10344
$250$	26.1804	1.65579
$251$	9.93897	0.627342	0.313671	−	0.949532i	$-0.398441\pi$
$251$	9.93897	0.627342	0.313671	+	0.949532i	$0.398441\pi$
$252$	7.40582	0.466523
$253$	5.25089	0.330121
$254$	19.5492	1.22663
$255$	6.48496	0.406104
$256$	−32.6162	−2.03851
$257$	25.8038	1.60960	0.804798	−	0.593549i	$-0.202274\pi$
$257$	25.8038	1.60960	0.804798	+	0.593549i	$0.202274\pi$
$258$	−12.7859	−0.796017
$259$	−0.679988	−0.0422524
$260$	−17.7715	−1.10214
$261$	0	0
$262$	1.45422	0.0898422
$263$	−26.7419	−1.64898	−0.824488	−	0.565880i	$-0.808537\pi$
$263$	−26.7419	−1.64898	−0.824488	+	0.565880i	$0.808537\pi$
$264$	−8.67687	−0.534024
$265$	15.8880	0.975993
$266$	−85.0142	−5.21256
$267$	−4.14321	−0.253560
$268$	−18.5505	−1.13315
$269$	−20.1985	−1.23152	−0.615762	−	0.787932i	$-0.711152\pi$
$269$	−20.1985	−1.23152	−0.615762	+	0.787932i	$0.711152\pi$
$270$	17.0202	1.03582
$271$	1.03904	0.0631173	0.0315586	−	0.999502i	$-0.489953\pi$
$271$	1.03904	0.0631173	0.0315586	+	0.999502i	$0.489953\pi$
$272$	−16.2969	−0.988146
$273$	−23.8290	−1.44220
$274$	32.4134	1.95817
$275$	3.44091	0.207495
$276$	−35.2449	−2.12150
$277$	−19.3845	−1.16470	−0.582351	−	0.812937i	$-0.697867\pi$
$277$	−19.3845	−1.16470	−0.582351	+	0.812937i	$0.697867\pi$
$278$	24.3101	1.45803
$279$	3.05656	0.182992
$280$	29.1995	1.74500
$281$	21.2565	1.26806	0.634028	−	0.773310i	$-0.281400\pi$
$281$	21.2565	1.26806	0.634028	+	0.773310i	$0.281400\pi$
$282$	−15.1243	−0.900638
$283$	13.5808	0.807293	0.403646	−	0.914915i	$-0.367743\pi$
$283$	13.5808	0.807293	0.403646	+	0.914915i	$0.367743\pi$
$284$	−29.0058	−1.72118
$285$	−15.8562	−0.939239
$286$	−8.47770	−0.501297
$287$	−25.6853	−1.51616
$288$	−0.722006	−0.0425446
$289$	−6.58782	−0.387519
$290$	0	0
$291$	−22.0377	−1.29187
$292$	14.0999	0.825134
$293$	3.61548	0.211219	0.105609	−	0.994408i	$-0.466321\pi$
$293$	3.61548	0.211219	0.105609	+	0.994408i	$0.466321\pi$
$294$	47.2464	2.75547
$295$	6.15795	0.358530
$296$	0.845056	0.0491179
$297$	5.48754	0.318419
$298$	8.93377	0.517519
$299$	−17.9209	−1.03639
$300$	−23.0960	−1.33345
$301$	13.8726	0.799602
$302$	−33.1390	−1.90693
$303$	−24.5920	−1.41277
$304$	39.8471	2.28539
$305$	−13.4922	−0.772561
$306$	3.28137	0.187583
$307$	11.3363	0.646998	0.323499	−	0.946228i	$-0.395141\pi$
$307$	11.3363	0.646998	0.323499	+	0.946228i	$0.395141\pi$
$308$	18.0901	1.03078
$309$	27.8727	1.58562
$310$	23.1573	1.31524
$311$	−6.55098	−0.371472	−0.185736	−	0.982600i	$-0.559467\pi$
$311$	−6.55098	−0.371472	−0.185736	+	0.982600i	$0.559467\pi$
$312$	29.6135	1.67653
$313$	−26.1586	−1.47857	−0.739284	−	0.673393i	$-0.764836\pi$
$313$	−26.1586	−1.47857	−0.739284	+	0.673393i	$0.764836\pi$
$314$	−37.9616	−2.14230
$315$	−2.21741	−0.124937
$316$	−49.4750	−2.78319
$317$	−24.5458	−1.37863	−0.689315	−	0.724461i	$-0.742089\pi$
$317$	−24.5458	−1.37863	−0.689315	+	0.724461i	$0.742089\pi$
$318$	−50.8730	−2.85282
$319$	0	0
$320$	7.14237	0.399271
$321$	−7.36384	−0.411010
$322$	56.5800	3.15308
$323$	−25.4585	−1.41655
$324$	−31.7116	−1.76176
$325$	−11.7436	−0.651416
$326$	−26.4467	−1.46475
$327$	−13.8195	−0.764222
$328$	31.9204	1.76251
$329$	16.4097	0.904694
$330$	4.99215	0.274809
$331$	9.23848	0.507793	0.253896	−	0.967231i	$-0.418288\pi$
$331$	9.23848	0.507793	0.253896	+	0.967231i	$0.418288\pi$
$332$	45.1136	2.47593
$333$	−0.0641736	−0.00351669
$334$	46.5880	2.54918
$335$	5.55429	0.303463
$336$	−35.2626	−1.92373
$337$	7.74981	0.422159	0.211080	−	0.977469i	$-0.432302\pi$
$337$	7.74981	0.422159	0.211080	+	0.977469i	$0.432302\pi$
$338$	−3.35824	−0.182664
$339$	7.25505	0.394040
$340$	16.8023	0.911232
$341$	7.46621	0.404318
$342$	−8.02318	−0.433844
$343$	−20.8966	−1.12831
$344$	−17.2401	−0.929527
$345$	10.5528	0.568146
$346$	−1.39693	−0.0750994
$347$	−15.5385	−0.834151	−0.417076	−	0.908872i	$-0.636945\pi$
$347$	−15.5385	−0.834151	−0.417076	+	0.908872i	$0.636945\pi$
$348$	0	0
$349$	−28.8052	−1.54191	−0.770954	−	0.636890i	$-0.780220\pi$
$349$	−28.8052	−1.54191	−0.770954	+	0.636890i	$0.780220\pi$
$350$	37.0769	1.98184
$351$	−18.7285	−0.999656
$352$	−1.76363	−0.0940018
$353$	4.64212	0.247075	0.123537	−	0.992340i	$-0.460576\pi$
$353$	4.64212	0.247075	0.123537	+	0.992340i	$0.460576\pi$
$354$	−19.7176	−1.04798
$355$	8.68475	0.460939
$356$	−10.7349	−0.568949
$357$	22.5294	1.19238
$358$	21.6774	1.14569
$359$	−9.64431	−0.509007	−0.254504	−	0.967072i	$-0.581912\pi$
$359$	−9.64431	−0.509007	−0.254504	+	0.967072i	$0.581912\pi$
$360$	2.75569	0.145237
$361$	43.2478	2.27620
$362$	−53.2652	−2.79955
$363$	1.60954	0.0844789
$364$	−61.7400	−3.23606
$365$	−4.22171	−0.220975
$366$	43.2017	2.25819
$367$	−20.7081	−1.08095	−0.540477	−	0.841359i	$-0.681756\pi$
$367$	−20.7081	−1.08095	−0.540477	+	0.841359i	$0.681756\pi$
$368$	−26.5196	−1.38243
$369$	−2.42404	−0.126191
$370$	−0.486195	−0.0252761
$371$	55.1966	2.86566
$372$	−50.1146	−2.59832
$373$	9.52134	0.492996	0.246498	−	0.969143i	$-0.420720\pi$
$373$	9.52134	0.492996	0.246498	+	0.969143i	$0.420720\pi$
$374$	8.01535	0.414464
$375$	16.9639	0.876012
$376$	−20.3931	−1.05169
$377$	0	0
$378$	59.1299	3.04131
$379$	−0.203466	−0.0104513	−0.00522566	−	0.999986i	$-0.501663\pi$
$379$	−0.203466	−0.0104513	−0.00522566	+	0.999986i	$0.501663\pi$
$380$	−41.0828	−2.10750
$381$	12.6672	0.648958
$382$	−2.88281	−0.147497
$383$	33.2197	1.69745	0.848723	−	0.528838i	$-0.177372\pi$
$383$	33.2197	1.69745	0.848723	+	0.528838i	$0.177372\pi$
$384$	−28.5469	−1.45678
$385$	−5.41643	−0.276047
$386$	−7.96941	−0.405632
$387$	1.30922	0.0665513
$388$	−57.0989	−2.89876
$389$	5.39070	0.273319	0.136660	−	0.990618i	$-0.456363\pi$
$389$	5.39070	0.273319	0.136660	+	0.990618i	$0.456363\pi$
$390$	−17.0378	−0.862745
$391$	16.9435	0.856871
$392$	63.7056	3.21762
$393$	0.942282	0.0475318
$394$	39.3653	1.98320
$395$	14.8135	0.745349
$396$	1.70724	0.0857922
$397$	2.58905	0.129941	0.0649703	−	0.997887i	$-0.479305\pi$
$397$	2.58905	0.129941	0.0649703	+	0.997887i	$0.479305\pi$
$398$	20.6294	1.03406
$399$	−55.0860	−2.75775
$400$	−17.3783	−0.868917
$401$	−30.9159	−1.54387	−0.771933	−	0.635704i	$-0.780710\pi$
$401$	−30.9159	−1.54387	−0.771933	+	0.635704i	$0.780710\pi$
$402$	−17.7847	−0.887020
$403$	−25.4816	−1.26933
$404$	−63.7168	−3.17003
$405$	9.49492	0.471806
$406$	0	0
$407$	−0.156756	−0.00777010
$408$	−27.9985	−1.38613
$409$	−27.3291	−1.35134	−0.675668	−	0.737206i	$-0.736145\pi$
$409$	−27.3291	−1.35134	−0.675668	+	0.737206i	$0.736145\pi$
$410$	−18.3651	−0.906989
$411$	21.0027	1.03599
$412$	72.2172	3.55789
$413$	21.3934	1.05270
$414$	5.33971	0.262432
$415$	−13.5077	−0.663066
$416$	6.01914	0.295112
$417$	15.7521	0.771382
$418$	−19.5981	−0.958574
$419$	32.0078	1.56368	0.781842	−	0.623477i	$-0.214280\pi$
$419$	32.0078	1.56368	0.781842	+	0.623477i	$0.214280\pi$
$420$	36.3561	1.77399
$421$	−16.6276	−0.810378	−0.405189	−	0.914233i	$-0.632794\pi$
$421$	−16.6276	−0.810378	−0.405189	+	0.914233i	$0.632794\pi$
$422$	4.86645	0.236895
$423$	1.54866	0.0752982
$424$	−68.5956	−3.33130
$425$	11.1031	0.538580
$426$	−27.8083	−1.34732
$427$	−46.8733	−2.26836
$428$	−19.0794	−0.922239
$429$	−5.49323	−0.265216
$430$	9.91895	0.478334
$431$	14.2553	0.686652	0.343326	−	0.939216i	$-0.388446\pi$
$431$	14.2553	0.686652	0.343326	+	0.939216i	$0.388446\pi$
$432$	−27.7148	−1.33343
$433$	4.19527	0.201612	0.100806	−	0.994906i	$-0.467858\pi$
$433$	4.19527	0.201612	0.100806	+	0.994906i	$0.467858\pi$
$434$	80.4507	3.86176
$435$	0	0
$436$	−35.8059	−1.71479
$437$	−41.4281	−1.98178
$438$	13.5178	0.645906
$439$	15.8189	0.754993	0.377497	−	0.926011i	$-0.376785\pi$
$439$	15.8189	0.754993	0.377497	+	0.926011i	$0.376785\pi$
$440$	6.73127	0.320901
$441$	−4.83781	−0.230372
$442$	−27.3558	−1.30118
$443$	−26.3718	−1.25296	−0.626480	−	0.779437i	$-0.715505\pi$
$443$	−26.3718	−1.25296	−0.626480	+	0.779437i	$0.715505\pi$
$444$	1.05217	0.0499339
$445$	3.21418	0.152367
$446$	−8.29888	−0.392964
$447$	5.78875	0.273798
$448$	24.8133	1.17232
$449$	10.0615	0.474832	0.237416	−	0.971408i	$-0.423699\pi$
$449$	10.0615	0.474832	0.237416	+	0.971408i	$0.423699\pi$
$450$	3.49911	0.164950
$451$	−5.92116	−0.278817
$452$	18.7976	0.884163
$453$	−21.4728	−1.00888
$454$	61.3200	2.87789
$455$	18.4859	0.866631
$456$	68.4582	3.20585
$457$	−19.0783	−0.892447	−0.446223	−	0.894922i	$-0.647231\pi$
$457$	−19.0783	−0.892447	−0.446223	+	0.894922i	$0.647231\pi$
$458$	69.0782	3.22781
$459$	17.7071	0.826498
$460$	27.3420	1.27483
$461$	31.3326	1.45930	0.729652	−	0.683819i	$-0.239682\pi$
$461$	31.3326	1.45930	0.729652	+	0.683819i	$0.239682\pi$
$462$	17.3433	0.806882
$463$	−39.7402	−1.84688	−0.923442	−	0.383738i	$-0.874637\pi$
$463$	−39.7402	−1.84688	−0.923442	+	0.383738i	$0.874637\pi$
$464$	0	0
$465$	15.0050	0.695842
$466$	−16.2890	−0.754571
$467$	−9.22574	−0.426917	−0.213458	−	0.976952i	$-0.568473\pi$
$467$	−9.22574	−0.426917	−0.213458	+	0.976952i	$0.568473\pi$
$468$	−5.82669	−0.269339
$469$	19.2962	0.891015
$470$	11.7330	0.541202
$471$	−24.5977	−1.13340
$472$	−26.5866	−1.22375
$473$	3.19801	0.147044
$474$	−47.4325	−2.17865
$475$	−27.1479	−1.24563
$476$	58.3729	2.67552
$477$	5.20916	0.238511
$478$	63.1326	2.88762
$479$	−6.28701	−0.287261	−0.143630	−	0.989631i	$-0.545878\pi$
$479$	−6.28701	−0.287261	−0.143630	+	0.989631i	$0.545878\pi$
$480$	−3.54441	−0.161779
$481$	0.534996	0.0243937
$482$	−7.67987	−0.349808
$483$	36.6617	1.66816
$484$	4.17025	0.189557
$485$	17.0962	0.776300
$486$	10.4906	0.475865
$487$	21.1188	0.956985	0.478492	−	0.878092i	$-0.341183\pi$
$487$	21.1188	0.956985	0.478492	+	0.878092i	$0.341183\pi$
$488$	58.2518	2.63694
$489$	−17.1365	−0.774937
$490$	−36.6524	−1.65579
$491$	36.3430	1.64014	0.820069	−	0.572265i	$-0.193935\pi$
$491$	36.3430	1.64014	0.820069	+	0.572265i	$0.193935\pi$
$492$	39.7439	1.79179
$493$	0	0
$494$	66.8868	3.00938
$495$	−0.511173	−0.0229755
$496$	−37.7081	−1.69314
$497$	30.1717	1.35339
$498$	43.2512	1.93813
$499$	−42.3905	−1.89766	−0.948830	−	0.315788i	$-0.897731\pi$
$499$	−42.3905	−1.89766	−0.948830	+	0.315788i	$0.897731\pi$
$500$	43.9528	1.96563
$501$	30.1872	1.34867
$502$	24.6884	1.10190
$503$	−14.9151	−0.665033	−0.332516	−	0.943097i	$-0.607898\pi$
$503$	−14.9151	−0.665033	−0.332516	+	0.943097i	$0.607898\pi$
$504$	9.57354	0.426439
$505$	19.0777	0.848948
$506$	13.0432	0.579842
$507$	−2.17602	−0.0966403
$508$	32.8201	1.45616
$509$	23.7542	1.05289	0.526443	−	0.850210i	$-0.323525\pi$
$509$	23.7542	1.05289	0.526443	+	0.850210i	$0.323525\pi$
$510$	16.1086	0.713303
$511$	−14.6667	−0.648815
$512$	−45.5463	−2.01288
$513$	−43.2952	−1.91153
$514$	64.0966	2.82718
$515$	−21.6229	−0.952818
$516$	−21.4656	−0.944970
$517$	3.78287	0.166371
$518$	−1.68909	−0.0742144
$519$	−0.905158	−0.0397320
$520$	−22.9733	−1.00745
$521$	−7.05079	−0.308901	−0.154450	−	0.988001i	$-0.549361\pi$
$521$	−7.05079	−0.308901	−0.154450	+	0.988001i	$0.549361\pi$
$522$	0	0
$523$	11.8210	0.516896	0.258448	−	0.966025i	$-0.416789\pi$
$523$	11.8210	0.516896	0.258448	+	0.966025i	$0.416789\pi$
$524$	2.44142	0.106654
$525$	24.0244	1.04851
$526$	−66.4268	−2.89635
$527$	24.0919	1.04946
$528$	−8.12898	−0.353768
$529$	4.57188	0.198777
$530$	39.4658	1.71429
$531$	2.01899	0.0876167
$532$	−142.726	−6.18795
$533$	20.2085	0.875327
$534$	−10.2917	−0.445367
$535$	5.71266	0.246980
$536$	−23.9803	−1.03579
$537$	14.0462	0.606136
$538$	−50.1731	−2.16312
$539$	−11.8172	−0.509005
$540$	28.5743	1.22964
$541$	10.4848	0.450777	0.225388	−	0.974269i	$-0.427635\pi$
$541$	10.4848	0.450777	0.225388	+	0.974269i	$0.427635\pi$
$542$	2.58098	0.110863
$543$	−34.5138	−1.48113
$544$	−5.69087	−0.243994
$545$	10.7208	0.459228
$546$	−59.1912	−2.53315
$547$	27.2345	1.16446	0.582231	−	0.813024i	$-0.302180\pi$
$547$	27.2345	1.16446	0.582231	+	0.813024i	$0.302180\pi$
$548$	54.4171	2.32459
$549$	−4.42365	−0.188797
$550$	8.54723	0.364455
$551$	0	0
$552$	−45.5613	−1.93922
$553$	51.4637	2.18846
$554$	−48.1511	−2.04575
$555$	−0.315036	−0.0133725
$556$	40.8130	1.73086
$557$	22.2134	0.941214	0.470607	−	0.882343i	$-0.344035\pi$
$557$	22.2134	0.941214	0.470607	+	0.882343i	$0.344035\pi$
$558$	7.59250	0.321416
$559$	−10.9146	−0.461636
$560$	27.3557	1.15599
$561$	5.19364	0.219276
$562$	52.8011	2.22728
$563$	−40.8563	−1.72189	−0.860944	−	0.508699i	$-0.830126\pi$
$563$	−40.8563	−1.72189	−0.860944	+	0.508699i	$0.830126\pi$
$564$	−25.3913	−1.06917
$565$	−5.62826	−0.236783
$566$	33.7346	1.41797
$567$	32.9863	1.38530
$568$	−37.4959	−1.57329
$569$	−8.88645	−0.372540	−0.186270	−	0.982499i	$-0.559640\pi$
$569$	−8.88645	−0.372540	−0.186270	+	0.982499i	$0.559640\pi$
$570$	−39.3867	−1.64973
$571$	29.0605	1.21615	0.608073	−	0.793881i	$-0.291943\pi$
$571$	29.0605	1.21615	0.608073	+	0.793881i	$0.291943\pi$
$572$	−14.2328	−0.595101
$573$	−1.86795	−0.0780348
$574$	−63.8023	−2.66306
$575$	18.0679	0.753482
$576$	2.34175	0.0975728
$577$	22.5698	0.939595	0.469798	−	0.882774i	$-0.344327\pi$
$577$	22.5698	0.939595	0.469798	+	0.882774i	$0.344327\pi$
$578$	−16.3641	−0.680658
$579$	−5.16388	−0.214604
$580$	0	0
$581$	−46.9271	−1.94686
$582$	−54.7417	−2.26912
$583$	12.7243	0.526987
$584$	18.2270	0.754239
$585$	1.74460	0.0721301
$586$	8.98085	0.370995
$587$	19.8969	0.821234	0.410617	−	0.911808i	$-0.365313\pi$
$587$	19.8969	0.821234	0.410617	+	0.911808i	$0.365313\pi$
$588$	79.3195	3.27108
$589$	−58.9064	−2.42720
$590$	15.2964	0.629741
$591$	25.5073	1.04923
$592$	0.791695	0.0325385
$593$	−10.0453	−0.412512	−0.206256	−	0.978498i	$-0.566128\pi$
$593$	−10.0453	−0.412512	−0.206256	+	0.978498i	$0.566128\pi$
$594$	13.6310	0.559288
$595$	−17.4777	−0.716515
$596$	14.9984	0.614359
$597$	13.3671	0.547077
$598$	−44.5155	−1.82037
$599$	23.3547	0.954246	0.477123	−	0.878836i	$-0.341680\pi$
$599$	23.3547	0.954246	0.477123	+	0.878836i	$0.341680\pi$
$600$	−29.8564	−1.21888
$601$	−43.1901	−1.76176	−0.880881	−	0.473339i	$-0.843049\pi$
$601$	−43.1901	−1.76176	−0.880881	+	0.473339i	$0.843049\pi$
$602$	34.4595	1.40446
$603$	1.82107	0.0741597
$604$	−55.6352	−2.26377
$605$	−1.24863	−0.0507642
$606$	−61.0864	−2.48147
$607$	32.3539	1.31320	0.656602	−	0.754237i	$-0.271993\pi$
$607$	32.3539	1.31320	0.656602	+	0.754237i	$0.271993\pi$
$608$	13.9146	0.564310
$609$	0	0
$610$	−33.5146	−1.35697
$611$	−12.9107	−0.522309
$612$	5.50892	0.222685
$613$	41.6093	1.68059	0.840293	−	0.542133i	$-0.182383\pi$
$613$	41.6093	1.68059	0.840293	+	0.542133i	$0.182383\pi$
$614$	28.1594	1.13642
$615$	−11.8999	−0.479851
$616$	23.3851	0.942214
$617$	17.9049	0.720823	0.360412	−	0.932793i	$-0.382636\pi$
$617$	17.9049	0.720823	0.360412	+	0.932793i	$0.382636\pi$
$618$	69.2359	2.78507
$619$	−15.8354	−0.636477	−0.318239	−	0.948011i	$-0.603091\pi$
$619$	−15.8354	−0.636477	−0.318239	+	0.948011i	$0.603091\pi$
$620$	38.8775	1.56136
$621$	28.8145	1.15629
$622$	−16.2726	−0.652473
$623$	11.1664	0.447373
$624$	27.7436	1.11063
$625$	4.04445	0.161778
$626$	−64.9778	−2.59704
$627$	−12.6988	−0.507142
$628$	−63.7317	−2.54317
$629$	−0.505818	−0.0201683
$630$	−5.50805	−0.219446
$631$	−40.1785	−1.59948	−0.799740	−	0.600346i	$-0.795030\pi$
$631$	−40.1785	−1.59948	−0.799740	+	0.600346i	$0.795030\pi$
$632$	−63.9565	−2.54405
$633$	3.15328	0.125332
$634$	−60.9718	−2.42150
$635$	−9.82682	−0.389965
$636$	−85.4079	−3.38664
$637$	40.3313	1.59799
$638$	0	0
$639$	2.84744	0.112643
$640$	22.1459	0.875393
$641$	−14.6768	−0.579701	−0.289850	−	0.957072i	$-0.593606\pi$
$641$	−14.6768	−0.579701	−0.289850	+	0.957072i	$0.593606\pi$
$642$	−18.2918	−0.721919
$643$	−23.6287	−0.931827	−0.465913	−	0.884830i	$-0.654274\pi$
$643$	−23.6287	−0.931827	−0.465913	+	0.884830i	$0.654274\pi$
$644$	94.9890	3.74309
$645$	6.42711	0.253067
$646$	−63.2389	−2.48810
$647$	−15.7214	−0.618073	−0.309037	−	0.951050i	$-0.600007\pi$
$647$	−15.7214	−0.618073	−0.309037	+	0.951050i	$0.600007\pi$
$648$	−40.9938	−1.61039
$649$	4.93175	0.193588
$650$	−29.1710	−1.14418
$651$	52.1290	2.04310
$652$	−44.3999	−1.73883
$653$	40.7072	1.59300	0.796498	−	0.604641i	$-0.206683\pi$
$653$	40.7072	1.59300	0.796498	+	0.604641i	$0.206683\pi$
$654$	−34.3277	−1.34232
$655$	−0.730995	−0.0285623
$656$	29.9049	1.16759
$657$	−1.38416	−0.0540013
$658$	40.7616	1.58905
$659$	−0.583461	−0.0227284	−0.0113642	−	0.999935i	$-0.503617\pi$
$659$	−0.583461	−0.0227284	−0.0113642	+	0.999935i	$0.503617\pi$
$660$	8.38106	0.326232
$661$	6.57327	0.255671	0.127835	−	0.991795i	$-0.459197\pi$
$661$	6.57327	0.255671	0.127835	+	0.991795i	$0.459197\pi$
$662$	22.9484	0.891914
$663$	−17.7255	−0.688402
$664$	58.3186	2.26320
$665$	42.7342	1.65716
$666$	−0.159407	−0.00617690
$667$	0	0
$668$	78.2140	3.02619
$669$	−5.37737	−0.207901
$670$	13.7969	0.533019
$671$	−10.8056	−0.417144
$672$	−12.3137	−0.475009
$673$	−8.76740	−0.337958	−0.168979	−	0.985620i	$-0.554047\pi$
$673$	−8.76740	−0.337958	−0.168979	+	0.985620i	$0.554047\pi$
$674$	19.2505	0.741502
$675$	18.8821	0.726774
$676$	−5.63797	−0.216845
$677$	3.06135	0.117657	0.0588286	−	0.998268i	$-0.481263\pi$
$677$	3.06135	0.117657	0.0588286	+	0.998268i	$0.481263\pi$
$678$	18.0215	0.692113
$679$	59.3941	2.27934
$680$	21.7204	0.832939
$681$	39.7331	1.52257
$682$	18.5461	0.710166
$683$	−13.0361	−0.498812	−0.249406	−	0.968399i	$-0.580235\pi$
$683$	−13.0361	−0.498812	−0.249406	+	0.968399i	$0.580235\pi$
$684$	−13.4697	−0.515026
$685$	−16.2933	−0.622534
$686$	−51.9072	−1.98183
$687$	44.7601	1.70770
$688$	−16.1515	−0.615771
$689$	−43.4271	−1.65444
$690$	26.2133	0.997922
$691$	−5.54561	−0.210965	−0.105483	−	0.994421i	$-0.533639\pi$
$691$	−5.54561	−0.210965	−0.105483	+	0.994421i	$0.533639\pi$
$692$	−2.34523	−0.0891523
$693$	−1.77587	−0.0674597
$694$	−38.5977	−1.46515
$695$	−12.2200	−0.463531
$696$	0	0
$697$	−19.1064	−0.723705
$698$	−71.5522	−2.70829
$699$	−10.5546	−0.399213
$700$	62.2464	2.35269
$701$	−10.6100	−0.400734	−0.200367	−	0.979721i	$-0.564213\pi$
$701$	−10.6100	−0.400734	−0.200367	+	0.979721i	$0.564213\pi$
$702$	−46.5217	−1.75585
$703$	1.23676	0.0466453
$704$	5.72015	0.215586
$705$	7.60253	0.286328
$706$	11.5310	0.433975
$707$	66.2780	2.49264
$708$	−33.1028	−1.24408
$709$	−37.6366	−1.41347	−0.706735	−	0.707478i	$-0.749833\pi$
$709$	−37.6366	−1.41347	−0.706735	+	0.707478i	$0.749833\pi$
$710$	21.5729	0.809617
$711$	4.85687	0.182147
$712$	−13.8771	−0.520065
$713$	39.2043	1.46821
$714$	55.9631	2.09437
$715$	4.26149	0.159371
$716$	36.3930	1.36007
$717$	40.9076	1.52772
$718$	−23.9565	−0.894047
$719$	−43.8029	−1.63357	−0.816786	−	0.576941i	$-0.804246\pi$
$719$	−43.8029	−1.63357	−0.816786	+	0.576941i	$0.804246\pi$
$720$	2.58168	0.0962136
$721$	−75.1201	−2.79762
$722$	107.428	3.99804
$723$	−4.97627	−0.185069
$724$	−89.4240	−3.32342
$725$	0	0
$726$	3.99809	0.148383
$727$	−2.87556	−0.106649	−0.0533243	−	0.998577i	$-0.516982\pi$
$727$	−2.87556	−0.106649	−0.0533243	+	0.998577i	$0.516982\pi$
$728$	−79.8117	−2.95802
$729$	29.6103	1.09668
$730$	−10.4867	−0.388131
$731$	10.3193	0.381673
$732$	72.5289	2.68075
$733$	20.9951	0.775473	0.387737	−	0.921770i	$-0.373257\pi$
$733$	20.9951	0.775473	0.387737	+	0.921770i	$0.373257\pi$
$734$	−51.4389	−1.89864
$735$	−23.7494	−0.876010
$736$	−9.26064	−0.341352
$737$	4.44829	0.163855
$738$	−6.02132	−0.221648
$739$	−37.5062	−1.37969	−0.689844	−	0.723958i	$-0.742321\pi$
$739$	−37.5062	−1.37969	−0.689844	+	0.723958i	$0.742321\pi$
$740$	−0.816246	−0.0300058
$741$	43.3401	1.59214
$742$	137.108	5.03340
$743$	14.9862	0.549789	0.274894	−	0.961474i	$-0.411357\pi$
$743$	14.9862	0.549789	0.274894	+	0.961474i	$0.411357\pi$
$744$	−64.7834	−2.37507
$745$	−4.49074	−0.164528
$746$	23.6510	0.865925
$747$	−4.42872	−0.162038
$748$	13.4565	0.492020
$749$	19.8464	0.725171
$750$	42.1383	1.53867
$751$	−30.2396	−1.10346	−0.551728	−	0.834024i	$-0.686032\pi$
$751$	−30.2396	−1.10346	−0.551728	+	0.834024i	$0.686032\pi$
$752$	−19.1054	−0.696703
$753$	15.9972	0.582969
$754$	0	0
$755$	16.6580	0.606247
$756$	99.2700	3.61041
$757$	−11.9060	−0.432730	−0.216365	−	0.976313i	$-0.569420\pi$
$757$	−11.9060	−0.432730	−0.216365	+	0.976313i	$0.569420\pi$
$758$	−0.505408	−0.0183573
$759$	8.45151	0.306771
$760$	−53.1079	−1.92643
$761$	2.34210	0.0849009	0.0424505	−	0.999099i	$-0.486484\pi$
$761$	2.34210	0.0849009	0.0424505	+	0.999099i	$0.486484\pi$
$762$	31.4652	1.13986
$763$	37.2452	1.34836
$764$	−4.83979	−0.175097
$765$	−1.64945	−0.0596360
$766$	82.5176	2.98148
$767$	−16.8317	−0.607757
$768$	−52.4970	−1.89432
$769$	10.0078	0.360890	0.180445	−	0.983585i	$-0.442246\pi$
$769$	10.0078	0.360890	0.180445	+	0.983585i	$0.442246\pi$
$770$	−13.4544	−0.484863
$771$	41.5322	1.49574
$772$	−13.3794	−0.481536
$773$	8.26441	0.297250	0.148625	−	0.988894i	$-0.452515\pi$
$773$	8.26441	0.297250	0.148625	+	0.988894i	$0.452515\pi$
$774$	3.25210	0.116894
$775$	25.6906	0.922833
$776$	−73.8120	−2.64970
$777$	−1.09447	−0.0392638
$778$	13.3905	0.480072
$779$	46.7164	1.67379
$780$	−28.6039	−1.02418
$781$	6.95540	0.248884
$782$	42.0877	1.50505
$783$	0	0
$784$	59.6830	2.13154
$785$	19.0822	0.681072
$786$	2.34063	0.0834874
$787$	32.1568	1.14626	0.573132	−	0.819463i	$-0.305728\pi$
$787$	32.1568	1.14626	0.573132	+	0.819463i	$0.305728\pi$
$788$	66.0883	2.35430
$789$	−43.0421	−1.53234
$790$	36.7968	1.30917
$791$	−19.5532	−0.695230
$792$	2.20696	0.0784209
$793$	36.8786	1.30960
$794$	6.43120	0.228235
$795$	25.5724	0.906958
$796$	34.6335	1.22755
$797$	21.1780	0.750164	0.375082	−	0.926992i	$-0.377614\pi$
$797$	21.1780	0.750164	0.375082	+	0.926992i	$0.377614\pi$
$798$	−136.834	−4.84386
$799$	12.2065	0.431837
$800$	−6.06850	−0.214554
$801$	1.05383	0.0372351
$802$	−76.7951	−2.71173
$803$	−3.38107	−0.119315
$804$	−29.8578	−1.05300
$805$	−28.4411	−1.00242
$806$	−63.2963	−2.22952
$807$	−32.5103	−1.14442
$808$	−82.3671	−2.89766
$809$	−30.4346	−1.07002	−0.535011	−	0.844845i	$-0.679693\pi$
$809$	−30.4346	−1.07002	−0.535011	+	0.844845i	$0.679693\pi$
$810$	23.5854	0.828705
$811$	−25.3347	−0.889623	−0.444811	−	0.895624i	$-0.646729\pi$
$811$	−25.3347	−0.889623	−0.444811	+	0.895624i	$0.646729\pi$
$812$	0	0
$813$	1.67238	0.0586528
$814$	−0.389381	−0.0136478
$815$	13.2940	0.465667
$816$	−26.2305	−0.918252
$817$	−25.2314	−0.882735
$818$	−67.8854	−2.37356
$819$	6.06091	0.211785
$820$	−30.8322	−1.07671
$821$	11.5343	0.402548	0.201274	−	0.979535i	$-0.435492\pi$
$821$	11.5343	0.402548	0.201274	+	0.979535i	$0.435492\pi$
$822$	52.1706	1.81966
$823$	−52.1878	−1.81915	−0.909577	−	0.415536i	$-0.863594\pi$
$823$	−52.1878	−1.81915	−0.909577	+	0.415536i	$0.863594\pi$
$824$	93.3555	3.25219
$825$	5.53828	0.192818
$826$	53.1411	1.84902
$827$	45.2613	1.57389	0.786945	−	0.617023i	$-0.211662\pi$
$827$	45.2613	1.57389	0.786945	+	0.617023i	$0.211662\pi$
$828$	8.96455	0.311540
$829$	−7.36913	−0.255940	−0.127970	−	0.991778i	$-0.540846\pi$
$829$	−7.36913	−0.255940	−0.127970	+	0.991778i	$0.540846\pi$
$830$	−33.5531	−1.16464
$831$	−31.2001	−1.08232
$832$	−19.5224	−0.676818
$833$	−38.1318	−1.32119
$834$	39.1281	1.35490
$835$	−23.4184	−0.810427
$836$	−32.9022	−1.13795
$837$	40.9711	1.41617
$838$	79.5074	2.74654
$839$	23.7615	0.820338	0.410169	−	0.912010i	$-0.365470\pi$
$839$	23.7615	0.820338	0.410169	+	0.912010i	$0.365470\pi$
$840$	46.9977	1.62157
$841$	0	0
$842$	−41.3029	−1.42339
$843$	34.2131	1.17836
$844$	8.17002	0.281224
$845$	1.68809	0.0580721
$846$	3.84686	0.132258
$847$	−4.33788	−0.149051
$848$	−64.2642	−2.20684
$849$	21.8588	0.750191
$850$	27.5801	0.945990
$851$	−0.823108	−0.0282158
$852$	−46.6859	−1.59943
$853$	−10.1896	−0.348884	−0.174442	−	0.984667i	$-0.555812\pi$
$853$	−10.1896	−0.348884	−0.174442	+	0.984667i	$0.555812\pi$
$854$	−116.433	−3.98426
$855$	4.03302	0.137926
$856$	−24.6641	−0.843001
$857$	32.5344	1.11135	0.555676	−	0.831399i	$-0.312459\pi$
$857$	32.5344	1.11135	0.555676	+	0.831399i	$0.312459\pi$
$858$	−13.6452	−0.465839
$859$	−38.1391	−1.30129	−0.650644	−	0.759383i	$-0.725501\pi$
$859$	−38.1391	−1.30129	−0.650644	+	0.759383i	$0.725501\pi$
$860$	16.6524	0.567842
$861$	−41.3415	−1.40892
$862$	35.4101	1.20607
$863$	8.23738	0.280404	0.140202	−	0.990123i	$-0.455225\pi$
$863$	8.23738	0.280404	0.140202	+	0.990123i	$0.455225\pi$
$864$	−9.67799	−0.329252
$865$	0.702196	0.0238754
$866$	10.4211	0.354122
$867$	−10.6033	−0.360109
$868$	135.064	4.58438
$869$	11.8638	0.402451
$870$	0	0
$871$	−15.1817	−0.514412
$872$	−46.2864	−1.56746
$873$	5.60529	0.189710
$874$	−102.907	−3.48090
$875$	−45.7196	−1.54560
$876$	22.6943	0.766770
$877$	−50.9996	−1.72213	−0.861067	−	0.508491i	$-0.830203\pi$
$877$	−50.9996	−1.72213	−0.861067	+	0.508491i	$0.830203\pi$
$878$	39.2940	1.32611
$879$	5.81925	0.196279
$880$	6.30623	0.212583
$881$	−0.875343	−0.0294911	−0.0147455	−	0.999891i	$-0.504694\pi$
$881$	−0.875343	−0.0294911	−0.0147455	+	0.999891i	$0.504694\pi$
$882$	−12.0171	−0.404638
$883$	−1.89418	−0.0637442	−0.0318721	−	0.999492i	$-0.510147\pi$
$883$	−1.89418	−0.0637442	−0.0318721	+	0.999492i	$0.510147\pi$
$884$	−45.9261	−1.54466
$885$	9.91147	0.333170
$886$	−65.5074	−2.20077
$887$	−46.7093	−1.56835	−0.784173	−	0.620543i	$-0.786912\pi$
$887$	−46.7093	−1.56835	−0.784173	+	0.620543i	$0.786912\pi$
$888$	1.36015	0.0456436
$889$	−34.1394	−1.14500
$890$	7.98403	0.267625
$891$	7.60425	0.254752
$892$	−13.9325	−0.466496
$893$	−29.8459	−0.998754
$894$	14.3792	0.480914
$895$	−10.8966	−0.364233
$896$	76.9371	2.57029
$897$	−28.8444	−0.963086
$898$	24.9928	0.834021
$899$	0	0
$900$	5.87447	0.195816
$901$	41.0587	1.36786
$902$	−14.7082	−0.489728
$903$	22.3285	0.743044
$904$	24.2997	0.808196
$905$	26.7748	0.890026
$906$	−53.3385	−1.77205
$907$	55.4693	1.84183	0.920913	−	0.389768i	$-0.127445\pi$
$907$	55.4693	1.84183	0.920913	+	0.389768i	$0.127445\pi$
$908$	102.947	3.41641
$909$	6.25496	0.207464
$910$	45.9189	1.52220
$911$	51.6651	1.71174	0.855871	−	0.517189i	$-0.173022\pi$
$911$	51.6651	1.71174	0.855871	+	0.517189i	$0.173022\pi$
$912$	64.1354	2.12374
$913$	−10.8180	−0.358022
$914$	−47.3906	−1.56754
$915$	−21.7162	−0.717916
$916$	115.972	3.83181
$917$	−2.53955	−0.0838634
$918$	43.9845	1.45171
$919$	−19.2269	−0.634237	−0.317119	−	0.948386i	$-0.602715\pi$
$919$	−19.2269	−0.634237	−0.317119	+	0.948386i	$0.602715\pi$
$920$	35.3452	1.16530
$921$	18.2462	0.601234
$922$	77.8301	2.56320
$923$	−23.7383	−0.781354
$924$	29.1167	0.957868
$925$	−0.539383	−0.0177348
$926$	−98.7147	−3.24396
$927$	−7.08943	−0.232847
$928$	0	0
$929$	−47.9439	−1.57299	−0.786494	−	0.617598i	$-0.788106\pi$
$929$	−47.9439	−1.57299	−0.786494	+	0.617598i	$0.788106\pi$
$930$	37.2725	1.22221
$931$	93.2348	3.05565
$932$	−27.3467	−0.895769
$933$	−10.5440	−0.345197
$934$	−22.9167	−0.749859
$935$	−4.02908	−0.131765
$936$	−7.53219	−0.246197
$937$	−8.76405	−0.286309	−0.143154	−	0.989700i	$-0.545725\pi$
$937$	−8.76405	−0.286309	−0.143154	+	0.989700i	$0.545725\pi$
$938$	47.9317	1.56503
$939$	−42.1032	−1.37399
$940$	19.6979	0.642474
$941$	−13.4937	−0.439883	−0.219941	−	0.975513i	$-0.570587\pi$
$941$	−13.4937	−0.439883	−0.219941	+	0.975513i	$0.570587\pi$
$942$	−61.1006	−1.99077
$943$	−31.0914	−1.01248
$944$	−24.9078	−0.810681
$945$	−29.7229	−0.966885
$946$	7.94384	0.258277
$947$	53.9459	1.75300	0.876502	−	0.481397i	$-0.159871\pi$
$947$	53.9459	1.75300	0.876502	+	0.481397i	$0.159871\pi$
$948$	−79.6319	−2.58632
$949$	11.5393	0.374582
$950$	−67.4353	−2.18789
$951$	−39.5075	−1.28112
$952$	75.4589	2.44564
$953$	0.580291	0.0187975	0.00939874	−	0.999956i	$-0.497008\pi$
$953$	0.580291	0.0187975	0.00939874	+	0.999956i	$0.497008\pi$
$954$	12.9395	0.418933
$955$	1.44910	0.0468919
$956$	105.990	3.42796
$957$	0	0
$958$	−15.6169	−0.504560
$959$	−56.6046	−1.82786
$960$	11.4959	0.371029
$961$	24.7443	0.798205
$962$	1.32893	0.0428464
$963$	1.87299	0.0603564
$964$	−12.8933	−0.415266
$965$	4.00599	0.128957
$966$	91.0676	2.93005
$967$	30.7659	0.989363	0.494682	−	0.869074i	$-0.335285\pi$
$967$	30.7659	0.989363	0.494682	+	0.869074i	$0.335285\pi$
$968$	5.39091	0.173270
$969$	−40.9765	−1.31635
$970$	42.4670	1.36353
$971$	−7.74336	−0.248496	−0.124248	−	0.992251i	$-0.539652\pi$
$971$	−7.74336	−0.248496	−0.124248	+	0.992251i	$0.539652\pi$
$972$	17.6122	0.564911
$973$	−42.4535	−1.36100
$974$	52.4591	1.68090
$975$	−18.9017	−0.605340
$976$	54.5735	1.74686
$977$	−31.9055	−1.02075	−0.510373	−	0.859953i	$-0.670493\pi$
$977$	−31.9055	−1.02075	−0.510373	+	0.859953i	$0.670493\pi$
$978$	−42.5669	−1.36114
$979$	2.57416	0.0822705
$980$	−61.5338	−1.96562
$981$	3.51500	0.112225
$982$	90.2760	2.88082
$983$	34.6333	1.10463	0.552316	−	0.833635i	$-0.313744\pi$
$983$	34.6333	1.10463	0.552316	+	0.833635i	$0.313744\pi$
$984$	51.3772	1.63784
$985$	−19.7878	−0.630492
$986$	0	0
$987$	26.4120	0.840703
$988$	112.293	3.57250
$989$	16.7924	0.533967
$990$	−1.26975	−0.0403554
$991$	−26.8122	−0.851717	−0.425859	−	0.904790i	$-0.640028\pi$
$991$	−26.8122	−0.851717	−0.425859	+	0.904790i	$0.640028\pi$
$992$	−13.1676	−0.418073
$993$	14.8697	0.471875
$994$	74.9465	2.37716
$995$	−10.3698	−0.328744
$996$	72.6121	2.30080
$997$	16.2461	0.514519	0.257259	−	0.966342i	$-0.417180\pi$
$997$	16.2461	0.514519	0.257259	+	0.966342i	$0.417180\pi$
$998$	−105.298	−3.33315
$999$	−0.860203	−0.0272156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.17	yes	18
29.28	even	2		9251.2.a.s.1.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.2	✓	18	29.28	even	2
9251.2.a.t.1.17	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+2.48400 q^{2} +1.60954 q^{3} +4.17025 q^{4} -1.24863 q^{5} +3.99809 q^{6} -4.33788 q^{7} +5.39091 q^{8} -0.409386 q^{9} +O(q^{10})\)	\(q+2.48400 q^{2} +1.60954 q^{3} +4.17025 q^{4} -1.24863 q^{5} +3.99809 q^{6} -4.33788 q^{7} +5.39091 q^{8} -0.409386 q^{9} -3.10161 q^{10} -1.00000 q^{11} +6.71218 q^{12} +3.41292 q^{13} -10.7753 q^{14} -2.00972 q^{15} +5.05050 q^{16} -3.22679 q^{17} -1.01691 q^{18} +7.88973 q^{19} -5.20712 q^{20} -6.98199 q^{21} -2.48400 q^{22} -5.25089 q^{23} +8.67687 q^{24} -3.44091 q^{25} +8.47770 q^{26} -5.48754 q^{27} -18.0901 q^{28} -4.99215 q^{30} -7.46621 q^{31} +1.76363 q^{32} -1.60954 q^{33} -8.01535 q^{34} +5.41643 q^{35} -1.70724 q^{36} +0.156756 q^{37} +19.5981 q^{38} +5.49323 q^{39} -6.73127 q^{40} +5.92116 q^{41} -17.3433 q^{42} -3.19801 q^{43} -4.17025 q^{44} +0.511173 q^{45} -13.0432 q^{46} -3.78287 q^{47} +8.12898 q^{48} +11.8172 q^{49} -8.54723 q^{50} -5.19364 q^{51} +14.2328 q^{52} -12.7243 q^{53} -13.6310 q^{54} +1.24863 q^{55} -23.3851 q^{56} +12.6988 q^{57} -4.93175 q^{59} -8.38106 q^{60} +10.8056 q^{61} -18.5461 q^{62} +1.77587 q^{63} -5.72015 q^{64} -4.26149 q^{65} -3.99809 q^{66} -4.44829 q^{67} -13.4565 q^{68} -8.45151 q^{69} +13.4544 q^{70} -6.95540 q^{71} -2.20696 q^{72} +3.38107 q^{73} +0.389381 q^{74} -5.53828 q^{75} +32.9022 q^{76} +4.33788 q^{77} +13.6452 q^{78} -11.8638 q^{79} -6.30623 q^{80} -7.60425 q^{81} +14.7082 q^{82} +10.8180 q^{83} -29.1167 q^{84} +4.02908 q^{85} -7.94384 q^{86} -5.39091 q^{88} -2.57416 q^{89} +1.26975 q^{90} -14.8049 q^{91} -21.8976 q^{92} -12.0172 q^{93} -9.39666 q^{94} -9.85139 q^{95} +2.83863 q^{96} -13.6920 q^{97} +29.3540 q^{98} +0.409386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

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