LMFDB - Embedded newform 1183.2.a.q.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
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			1.11
Root			$-2.07140$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07140 q^{2} -3.01646 q^{3} +2.29068 q^{4} +2.69245 q^{5} -6.24828 q^{6} -1.00000 q^{7} +0.602118 q^{8} +6.09903 q^{9} +O(q^{10})$	\(q+2.07140 q^{2} -3.01646 q^{3} +2.29068 q^{4} +2.69245 q^{5} -6.24828 q^{6} -1.00000 q^{7} +0.602118 q^{8} +6.09903 q^{9} +5.57713 q^{10} -1.66028 q^{11} -6.90975 q^{12} -2.07140 q^{14} -8.12167 q^{15} -3.33414 q^{16} +6.90851 q^{17} +12.6335 q^{18} +7.92373 q^{19} +6.16755 q^{20} +3.01646 q^{21} -3.43909 q^{22} +1.95034 q^{23} -1.81626 q^{24} +2.24929 q^{25} -9.34811 q^{27} -2.29068 q^{28} -2.71657 q^{29} -16.8232 q^{30} +1.76567 q^{31} -8.11056 q^{32} +5.00816 q^{33} +14.3103 q^{34} -2.69245 q^{35} +13.9709 q^{36} +4.20030 q^{37} +16.4132 q^{38} +1.62117 q^{40} +7.08279 q^{41} +6.24828 q^{42} -3.56471 q^{43} -3.80317 q^{44} +16.4213 q^{45} +4.03993 q^{46} +1.53115 q^{47} +10.0573 q^{48} +1.00000 q^{49} +4.65917 q^{50} -20.8392 q^{51} +12.7174 q^{53} -19.3636 q^{54} -4.47022 q^{55} -0.602118 q^{56} -23.9016 q^{57} -5.62710 q^{58} -4.52186 q^{59} -18.6042 q^{60} +2.89049 q^{61} +3.65741 q^{62} -6.09903 q^{63} -10.1319 q^{64} +10.3739 q^{66} +1.27141 q^{67} +15.8252 q^{68} -5.88313 q^{69} -5.57713 q^{70} +2.93807 q^{71} +3.67234 q^{72} +14.6180 q^{73} +8.70049 q^{74} -6.78490 q^{75} +18.1507 q^{76} +1.66028 q^{77} +2.91352 q^{79} -8.97701 q^{80} +9.90109 q^{81} +14.6713 q^{82} +2.33012 q^{83} +6.90975 q^{84} +18.6008 q^{85} -7.38392 q^{86} +8.19444 q^{87} -0.999683 q^{88} -7.64714 q^{89} +34.0151 q^{90} +4.46761 q^{92} -5.32609 q^{93} +3.17163 q^{94} +21.3343 q^{95} +24.4652 q^{96} -12.9169 q^{97} +2.07140 q^{98} -10.1261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9} - 6 q^{10} - 12 q^{11} + 13 q^{12} + 3 q^{14} - 11 q^{15} + 13 q^{16} + 31 q^{17} + 29 q^{18} + 3 q^{19} + 18 q^{20} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 6 q^{24} + 32 q^{25} + 32 q^{27} - 15 q^{28} + 15 q^{29} - 10 q^{30} + 21 q^{31} + 3 q^{32} + 29 q^{33} - 3 q^{34} - 4 q^{35} + 49 q^{36} - 5 q^{37} + 45 q^{38} - 20 q^{40} + 16 q^{41} + 2 q^{42} - 22 q^{43} - 35 q^{44} - 5 q^{45} - 2 q^{46} + 4 q^{47} + 11 q^{48} + 12 q^{49} - 13 q^{50} + 18 q^{51} + 53 q^{53} + 5 q^{54} - 26 q^{55} + 12 q^{56} + 8 q^{57} - 32 q^{58} + 26 q^{59} - 38 q^{60} + 22 q^{61} + 19 q^{62} - 26 q^{63} + 2 q^{64} - 34 q^{66} - 12 q^{67} + 34 q^{68} + 3 q^{69} + 6 q^{70} - 21 q^{71} + 4 q^{72} + 15 q^{73} - 40 q^{74} + 15 q^{75} - 43 q^{76} + 12 q^{77} + 2 q^{79} - 13 q^{80} + 36 q^{81} - 32 q^{82} + 9 q^{83} - 13 q^{84} + 39 q^{85} - 44 q^{86} + 27 q^{87} - 48 q^{88} + 22 q^{89} - 26 q^{90} + 52 q^{92} + 53 q^{93} - 44 q^{94} + 29 q^{95} + 114 q^{96} - 9 q^{97} - 3 q^{98} - 37 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9 - 6 * q^10 - 12 * q^11 + 13 * q^12 + 3 * q^14 - 11 * q^15 + 13 * q^16 + 31 * q^17 + 29 * q^18 + 3 * q^19 + 18 * q^20 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 6 * q^24 + 32 * q^25 + 32 * q^27 - 15 * q^28 + 15 * q^29 - 10 * q^30 + 21 * q^31 + 3 * q^32 + 29 * q^33 - 3 * q^34 - 4 * q^35 + 49 * q^36 - 5 * q^37 + 45 * q^38 - 20 * q^40 + 16 * q^41 + 2 * q^42 - 22 * q^43 - 35 * q^44 - 5 * q^45 - 2 * q^46 + 4 * q^47 + 11 * q^48 + 12 * q^49 - 13 * q^50 + 18 * q^51 + 53 * q^53 + 5 * q^54 - 26 * q^55 + 12 * q^56 + 8 * q^57 - 32 * q^58 + 26 * q^59 - 38 * q^60 + 22 * q^61 + 19 * q^62 - 26 * q^63 + 2 * q^64 - 34 * q^66 - 12 * q^67 + 34 * q^68 + 3 * q^69 + 6 * q^70 - 21 * q^71 + 4 * q^72 + 15 * q^73 - 40 * q^74 + 15 * q^75 - 43 * q^76 + 12 * q^77 + 2 * q^79 - 13 * q^80 + 36 * q^81 - 32 * q^82 + 9 * q^83 - 13 * q^84 + 39 * q^85 - 44 * q^86 + 27 * q^87 - 48 * q^88 + 22 * q^89 - 26 * q^90 + 52 * q^92 + 53 * q^93 - 44 * q^94 + 29 * q^95 + 114 * q^96 - 9 * q^97 - 3 * q^98 - 37 * 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 $

$2$	2.07140	1.46470	0.732349	−	0.680929i	$-0.238424\pi$
$2$	2.07140	1.46470	0.732349	+	0.680929i	$0.238424\pi$
$3$	−3.01646	−1.74155	−0.870777	−	0.491678i	$-0.836384\pi$
$3$	−3.01646	−1.74155	−0.870777	+	0.491678i	$0.836384\pi$
$4$	2.29068	1.14534
$5$	2.69245	1.20410	0.602050	−	0.798458i	$-0.294351\pi$
$5$	2.69245	1.20410	0.602050	+	0.798458i	$0.294351\pi$
$6$	−6.24828	−2.55085
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.602118	0.212881
$9$	6.09903	2.03301
$10$	5.57713	1.76364
$11$	−1.66028	−0.500593	−0.250296	−	0.968169i	$-0.580528\pi$
$11$	−1.66028	−0.500593	−0.250296	+	0.968169i	$0.580528\pi$
$12$	−6.90975	−1.99467
$13$	0	0
$13$	0	0
$14$	−2.07140	−0.553604
$15$	−8.12167	−2.09701
$16$	−3.33414	−0.833535
$17$	6.90851	1.67556	0.837780	−	0.546008i	$-0.183853\pi$
$17$	6.90851	1.67556	0.837780	+	0.546008i	$0.183853\pi$
$18$	12.6335	2.97775
$19$	7.92373	1.81783	0.908914	−	0.416984i	$-0.136913\pi$
$19$	7.92373	1.81783	0.908914	+	0.416984i	$0.136913\pi$
$20$	6.16755	1.37911
$21$	3.01646	0.658246
$22$	−3.43909	−0.733217
$23$	1.95034	0.406674	0.203337	−	0.979109i	$-0.434821\pi$
$23$	1.95034	0.406674	0.203337	+	0.979109i	$0.434821\pi$
$24$	−1.81626	−0.370743
$25$	2.24929	0.449858
$26$	0	0
$27$	−9.34811	−1.79904
$28$	−2.29068	−0.432898
$29$	−2.71657	−0.504455	−0.252228	−	0.967668i	$-0.581163\pi$
$29$	−2.71657	−0.504455	−0.252228	+	0.967668i	$0.581163\pi$
$30$	−16.8232	−3.07148
$31$	1.76567	0.317124	0.158562	−	0.987349i	$-0.449314\pi$
$31$	1.76567	0.317124	0.158562	+	0.987349i	$0.449314\pi$
$32$	−8.11056	−1.43376
$33$	5.00816	0.871809
$34$	14.3103	2.45419
$35$	−2.69245	−0.455107
$36$	13.9709	2.32849
$37$	4.20030	0.690526	0.345263	−	0.938506i	$-0.387790\pi$
$37$	4.20030	0.690526	0.345263	+	0.938506i	$0.387790\pi$
$38$	16.4132	2.66257
$39$	0	0
$40$	1.62117	0.256330
$41$	7.08279	1.10615	0.553073	−	0.833133i	$-0.313455\pi$
$41$	7.08279	1.10615	0.553073	+	0.833133i	$0.313455\pi$
$42$	6.24828	0.964131
$43$	−3.56471	−0.543613	−0.271806	−	0.962352i	$-0.587621\pi$
$43$	−3.56471	−0.543613	−0.271806	+	0.962352i	$0.587621\pi$
$44$	−3.80317	−0.573350
$45$	16.4213	2.44795
$46$	4.03993	0.595655
$47$	1.53115	0.223342	0.111671	−	0.993745i	$-0.464380\pi$
$47$	1.53115	0.223342	0.111671	+	0.993745i	$0.464380\pi$
$48$	10.0573	1.45165
$49$	1.00000	0.142857
$50$	4.65917	0.658907
$51$	−20.8392	−2.91808
$52$	0	0
$53$	12.7174	1.74687	0.873437	−	0.486938i	$-0.161886\pi$
$53$	12.7174	1.74687	0.873437	+	0.486938i	$0.161886\pi$
$54$	−19.3636	−2.63506
$55$	−4.47022	−0.602764
$56$	−0.602118	−0.0804614
$57$	−23.9016	−3.16585
$58$	−5.62710	−0.738875
$59$	−4.52186	−0.588697	−0.294348	−	0.955698i	$-0.595103\pi$
$59$	−4.52186	−0.588697	−0.294348	+	0.955698i	$0.595103\pi$
$60$	−18.6042	−2.40179
$61$	2.89049	0.370089	0.185045	−	0.982730i	$-0.440757\pi$
$61$	2.89049	0.370089	0.185045	+	0.982730i	$0.440757\pi$
$62$	3.65741	0.464492
$63$	−6.09903	−0.768406
$64$	−10.1319	−1.26649
$65$	0	0
$66$	10.3739	1.27694
$67$	1.27141	0.155328	0.0776639	−	0.996980i	$-0.475254\pi$
$67$	1.27141	0.155328	0.0776639	+	0.996980i	$0.475254\pi$
$68$	15.8252	1.91909
$69$	−5.88313	−0.708245
$70$	−5.57713	−0.666595
$71$	2.93807	0.348685	0.174342	−	0.984685i	$-0.444220\pi$
$71$	2.93807	0.348685	0.174342	+	0.984685i	$0.444220\pi$
$72$	3.67234	0.432789
$73$	14.6180	1.71091	0.855456	−	0.517876i	$-0.173277\pi$
$73$	14.6180	1.71091	0.855456	+	0.517876i	$0.173277\pi$
$74$	8.70049	1.01141
$75$	−6.78490	−0.783453
$76$	18.1507	2.08203
$77$	1.66028	0.189206
$78$	0	0
$79$	2.91352	0.327797	0.163898	−	0.986477i	$-0.447593\pi$
$79$	2.91352	0.327797	0.163898	+	0.986477i	$0.447593\pi$
$80$	−8.97701	−1.00366
$81$	9.90109	1.10012
$82$	14.6713	1.62017
$83$	2.33012	0.255764	0.127882	−	0.991789i	$-0.459182\pi$
$83$	2.33012	0.255764	0.127882	+	0.991789i	$0.459182\pi$
$84$	6.90975	0.753916
$85$	18.6008	2.01754
$86$	−7.38392	−0.796229
$87$	8.19444	0.878536
$88$	−0.999683	−0.106567
$89$	−7.64714	−0.810595	−0.405298	−	0.914185i	$-0.632832\pi$
$89$	−7.64714	−0.810595	−0.405298	+	0.914185i	$0.632832\pi$
$90$	34.0151	3.58551
$91$	0	0
$92$	4.46761	0.465781
$93$	−5.32609	−0.552289
$94$	3.17163	0.327128
$95$	21.3343	2.18885
$96$	24.4652	2.49697
$97$	−12.9169	−1.31151	−0.655755	−	0.754974i	$-0.727649\pi$
$97$	−12.9169	−1.31151	−0.655755	+	0.754974i	$0.727649\pi$
$98$	2.07140	0.209243
$99$	−10.1261	−1.01771
$100$	5.15241	0.515241
$101$	−18.0307	−1.79412	−0.897061	−	0.441908i	$-0.854302\pi$
$101$	−18.0307	−1.79412	−0.897061	+	0.441908i	$0.854302\pi$
$102$	−43.1663	−4.27410
$103$	0.209846	0.0206767	0.0103384	−	0.999947i	$-0.496709\pi$
$103$	0.209846	0.0206767	0.0103384	+	0.999947i	$0.496709\pi$
$104$	0	0
$105$	8.12167	0.792594
$106$	26.3428	2.55864
$107$	−4.45174	−0.430365	−0.215183	−	0.976574i	$-0.569035\pi$
$107$	−4.45174	−0.430365	−0.215183	+	0.976574i	$0.569035\pi$
$108$	−21.4135	−2.06052
$109$	−13.3139	−1.27524	−0.637619	−	0.770352i	$-0.720080\pi$
$109$	−13.3139	−1.27524	−0.637619	+	0.770352i	$0.720080\pi$
$110$	−9.25959	−0.882868
$111$	−12.6701	−1.20259
$112$	3.33414	0.315047
$113$	9.85466	0.927049	0.463524	−	0.886084i	$-0.346585\pi$
$113$	9.85466	0.927049	0.463524	+	0.886084i	$0.346585\pi$
$114$	−49.5097	−4.63701
$115$	5.25120	0.489677
$116$	−6.22281	−0.577773
$117$	0	0
$118$	−9.36657	−0.862263
$119$	−6.90851	−0.633302
$120$	−4.89020	−0.446412
$121$	−8.24348	−0.749407
$122$	5.98735	0.542069
$123$	−21.3649	−1.92641
$124$	4.04460	0.363216
$125$	−7.40615	−0.662426
$126$	−12.6335	−1.12548
$127$	8.17792	0.725673	0.362836	−	0.931853i	$-0.381808\pi$
$127$	8.17792	0.725673	0.362836	+	0.931853i	$0.381808\pi$
$128$	−4.76607	−0.421265
$129$	10.7528	0.946731
$130$	0	0
$131$	−2.36055	−0.206242	−0.103121	−	0.994669i	$-0.532883\pi$
$131$	−2.36055	−0.206242	−0.103121	+	0.994669i	$0.532883\pi$
$132$	11.4721	0.998519
$133$	−7.92373	−0.687074
$134$	2.63360	0.227508
$135$	−25.1693	−2.16623
$136$	4.15974	0.356695
$137$	−11.6888	−0.998638	−0.499319	−	0.866418i	$-0.666416\pi$
$137$	−11.6888	−0.998638	−0.499319	+	0.866418i	$0.666416\pi$
$138$	−12.1863	−1.03737
$139$	−17.0059	−1.44242	−0.721211	−	0.692715i	$-0.756414\pi$
$139$	−17.0059	−1.44242	−0.721211	+	0.692715i	$0.756414\pi$
$140$	−6.16755	−0.521253
$141$	−4.61866	−0.388962
$142$	6.08591	0.510718
$143$	0	0
$144$	−20.3350	−1.69459
$145$	−7.31424	−0.607415
$146$	30.2797	2.50597
$147$	−3.01646	−0.248793
$148$	9.62156	0.790888
$149$	−0.211752	−0.0173474	−0.00867372	−	0.999962i	$-0.502761\pi$
$149$	−0.211752	−0.0173474	−0.00867372	+	0.999962i	$0.502761\pi$
$150$	−14.0542	−1.14752
$151$	−13.7721	−1.12076	−0.560380	−	0.828236i	$-0.689345\pi$
$151$	−13.7721	−1.12076	−0.560380	+	0.828236i	$0.689345\pi$
$152$	4.77102	0.386981
$153$	42.1352	3.40643
$154$	3.43909	0.277130
$155$	4.75399	0.381850
$156$	0	0
$157$	0.811199	0.0647407	0.0323704	−	0.999476i	$-0.489694\pi$
$157$	0.811199	0.0647407	0.0323704	+	0.999476i	$0.489694\pi$
$158$	6.03506	0.480123
$159$	−38.3616	−3.04227
$160$	−21.8373	−1.72639
$161$	−1.95034	−0.153708
$162$	20.5091	1.61135
$163$	−5.11460	−0.400606	−0.200303	−	0.979734i	$-0.564193\pi$
$163$	−5.11460	−0.400606	−0.200303	+	0.979734i	$0.564193\pi$
$164$	16.2244	1.26691
$165$	13.4842	1.04975
$166$	4.82660	0.374617
$167$	−5.06523	−0.391959	−0.195980	−	0.980608i	$-0.562789\pi$
$167$	−5.06523	−0.391959	−0.195980	+	0.980608i	$0.562789\pi$
$168$	1.81626	0.140128
$169$	0	0
$170$	38.5297	2.95509
$171$	48.3271	3.69566
$172$	−8.16561	−0.622622
$173$	10.8223	0.822806	0.411403	−	0.911454i	$-0.365039\pi$
$173$	10.8223	0.822806	0.411403	+	0.911454i	$0.365039\pi$
$174$	16.9739	1.28679
$175$	−2.24929	−0.170030
$176$	5.53560	0.417262
$177$	13.6400	1.02525
$178$	−15.8403	−1.18728
$179$	−7.55404	−0.564616	−0.282308	−	0.959324i	$-0.591100\pi$
$179$	−7.55404	−0.564616	−0.282308	+	0.959324i	$0.591100\pi$
$180$	37.6161	2.80374
$181$	14.0359	1.04328	0.521641	−	0.853165i	$-0.325320\pi$
$181$	14.0359	1.04328	0.521641	+	0.853165i	$0.325320\pi$
$182$	0	0
$183$	−8.71905	−0.644530
$184$	1.17434	0.0865732
$185$	11.3091	0.831463
$186$	−11.0324	−0.808937
$187$	−11.4701	−0.838773
$188$	3.50739	0.255802
$189$	9.34811	0.679975
$190$	44.1917	3.20600
$191$	−27.1486	−1.96440	−0.982202	−	0.187825i	$-0.939856\pi$
$191$	−27.1486	−1.96440	−0.982202	+	0.187825i	$0.939856\pi$
$192$	30.5625	2.20566
$193$	8.95507	0.644600	0.322300	−	0.946638i	$-0.395544\pi$
$193$	8.95507	0.644600	0.322300	+	0.946638i	$0.395544\pi$
$194$	−26.7560	−1.92097
$195$	0	0
$196$	2.29068	0.163620
$197$	−15.9211	−1.13433	−0.567164	−	0.823605i	$-0.691959\pi$
$197$	−15.9211	−1.13433	−0.567164	+	0.823605i	$0.691959\pi$
$198$	−20.9751	−1.49064
$199$	4.27396	0.302973	0.151486	−	0.988459i	$-0.451594\pi$
$199$	4.27396	0.302973	0.151486	+	0.988459i	$0.451594\pi$
$200$	1.35434	0.0957662
$201$	−3.83516	−0.270512
$202$	−37.3487	−2.62785
$203$	2.71657	0.190666
$204$	−47.7361	−3.34219
$205$	19.0701	1.33191
$206$	0.434673	0.0302851
$207$	11.8952	0.826773
$208$	0	0
$209$	−13.1556	−0.909992
$210$	16.8232	1.16091
$211$	21.2984	1.46624	0.733122	−	0.680097i	$-0.238062\pi$
$211$	21.2984	1.46624	0.733122	+	0.680097i	$0.238062\pi$
$212$	29.1316	2.00077
$213$	−8.86257	−0.607253
$214$	−9.22131	−0.630356
$215$	−9.59780	−0.654564
$216$	−5.62866	−0.382982
$217$	−1.76567	−0.119862
$218$	−27.5783	−1.86784
$219$	−44.0947	−2.97965
$220$	−10.2398	−0.690371
$221$	0	0
$222$	−26.2447	−1.76143
$223$	−9.63999	−0.645541	−0.322771	−	0.946477i	$-0.604614\pi$
$223$	−9.63999	−0.645541	−0.322771	+	0.946477i	$0.604614\pi$
$224$	8.11056	0.541910
$225$	13.7185	0.914567
$226$	20.4129	1.35785
$227$	13.1175	0.870636	0.435318	−	0.900277i	$-0.356636\pi$
$227$	13.1175	0.870636	0.435318	+	0.900277i	$0.356636\pi$
$228$	−54.7510	−3.62597
$229$	14.5532	0.961704	0.480852	−	0.876802i	$-0.340327\pi$
$229$	14.5532	0.961704	0.480852	+	0.876802i	$0.340327\pi$
$230$	10.8773	0.717229
$231$	−5.00816	−0.329513
$232$	−1.63570	−0.107389
$233$	2.85570	0.187083	0.0935417	−	0.995615i	$-0.470181\pi$
$233$	2.85570	0.187083	0.0935417	+	0.995615i	$0.470181\pi$
$234$	0	0
$235$	4.12256	0.268926
$236$	−10.3582	−0.674258
$237$	−8.78852	−0.570876
$238$	−14.3103	−0.927596
$239$	4.12813	0.267026	0.133513	−	0.991047i	$-0.457374\pi$
$239$	4.12813	0.267026	0.133513	+	0.991047i	$0.457374\pi$
$240$	27.0788	1.74793
$241$	−6.07256	−0.391168	−0.195584	−	0.980687i	$-0.562660\pi$
$241$	−6.07256	−0.391168	−0.195584	+	0.980687i	$0.562660\pi$
$242$	−17.0755	−1.09765
$243$	−1.82194	−0.116877
$244$	6.62119	0.423878
$245$	2.69245	0.172014
$246$	−44.2553	−2.82161
$247$	0	0
$248$	1.06314	0.0675097
$249$	−7.02872	−0.445427
$250$	−15.3411	−0.970254
$251$	−3.59902	−0.227168	−0.113584	−	0.993528i	$-0.536233\pi$
$251$	−3.59902	−0.227168	−0.113584	+	0.993528i	$0.536233\pi$
$252$	−13.9709	−0.880087
$253$	−3.23811	−0.203578
$254$	16.9397	1.06289
$255$	−56.1086	−3.51366
$256$	10.3914	0.649462
$257$	7.71112	0.481006	0.240503	−	0.970648i	$-0.422688\pi$
$257$	7.71112	0.481006	0.240503	+	0.970648i	$0.422688\pi$
$258$	22.2733	1.38668
$259$	−4.20030	−0.260994
$260$	0	0
$261$	−16.5685	−1.02556
$262$	−4.88964	−0.302083
$263$	−9.29078	−0.572894	−0.286447	−	0.958096i	$-0.592474\pi$
$263$	−9.29078	−0.572894	−0.286447	+	0.958096i	$0.592474\pi$
$264$	3.01550	0.185592
$265$	34.2411	2.10341
$266$	−16.4132	−1.00636
$267$	23.0673	1.41170
$268$	2.91240	0.177903
$269$	1.41823	0.0864708	0.0432354	−	0.999065i	$-0.486233\pi$
$269$	1.41823	0.0864708	0.0432354	+	0.999065i	$0.486233\pi$
$270$	−52.1356	−3.17287
$271$	13.4966	0.819863	0.409931	−	0.912116i	$-0.365553\pi$
$271$	13.4966	0.819863	0.409931	+	0.912116i	$0.365553\pi$
$272$	−23.0339	−1.39664
$273$	0	0
$274$	−24.2121	−1.46270
$275$	−3.73445	−0.225196
$276$	−13.4764	−0.811183
$277$	−15.0626	−0.905022	−0.452511	−	0.891759i	$-0.649472\pi$
$277$	−15.0626	−0.905022	−0.452511	+	0.891759i	$0.649472\pi$
$278$	−35.2260	−2.11271
$279$	10.7689	0.644717
$280$	−1.62117	−0.0968836
$281$	−11.7731	−0.702323	−0.351162	−	0.936315i	$-0.614213\pi$
$281$	−11.7731	−0.702323	−0.351162	+	0.936315i	$0.614213\pi$
$282$	−9.56708	−0.569711
$283$	−10.9857	−0.653031	−0.326516	−	0.945192i	$-0.605875\pi$
$283$	−10.9857	−0.653031	−0.326516	+	0.945192i	$0.605875\pi$
$284$	6.73018	0.399363
$285$	−64.3539	−3.81200
$286$	0	0
$287$	−7.08279	−0.418084
$288$	−49.4666	−2.91485
$289$	30.7275	1.80750
$290$	−15.1507	−0.889680
$291$	38.9632	2.28406
$292$	33.4853	1.95958
$293$	8.32168	0.486157	0.243079	−	0.970007i	$-0.421843\pi$
$293$	8.32168	0.486157	0.243079	+	0.970007i	$0.421843\pi$
$294$	−6.24828	−0.364407
$295$	−12.1749	−0.708850
$296$	2.52908	0.147000
$297$	15.5205	0.900588
$298$	−0.438623	−0.0254088
$299$	0	0
$300$	−15.5420	−0.897321
$301$	3.56471	0.205466
$302$	−28.5275	−1.64158
$303$	54.3889	3.12456
$304$	−26.4188	−1.51522
$305$	7.78250	0.445625
$306$	87.2787	4.98939
$307$	−13.8619	−0.791138	−0.395569	−	0.918436i	$-0.629453\pi$
$307$	−13.8619	−0.791138	−0.395569	+	0.918436i	$0.629453\pi$
$308$	3.80317	0.216706
$309$	−0.632991	−0.0360096
$310$	9.84740	0.559295
$311$	12.8881	0.730820	0.365410	−	0.930847i	$-0.380929\pi$
$311$	12.8881	0.730820	0.365410	+	0.930847i	$0.380929\pi$
$312$	0	0
$313$	20.5315	1.16051	0.580256	−	0.814434i	$-0.302953\pi$
$313$	20.5315	1.16051	0.580256	+	0.814434i	$0.302953\pi$
$314$	1.68031	0.0948256
$315$	−16.4213	−0.925238
$316$	6.67395	0.375439
$317$	−10.5405	−0.592014	−0.296007	−	0.955186i	$-0.595655\pi$
$317$	−10.5405	−0.592014	−0.296007	+	0.955186i	$0.595655\pi$
$318$	−79.4621	−4.45601
$319$	4.51027	0.252527
$320$	−27.2797	−1.52498
$321$	13.4285	0.749505
$322$	−4.03993	−0.225137
$323$	54.7412	3.04588
$324$	22.6803	1.26001
$325$	0	0
$326$	−10.5944	−0.586767
$327$	40.1608	2.22090
$328$	4.26467	0.235477
$329$	−1.53115	−0.0844152
$330$	27.9312	1.53756
$331$	12.6309	0.694256	0.347128	−	0.937818i	$-0.387157\pi$
$331$	12.6309	0.694256	0.347128	+	0.937818i	$0.387157\pi$
$332$	5.33756	0.292937
$333$	25.6178	1.40385
$334$	−10.4921	−0.574102
$335$	3.42321	0.187030
$336$	−10.0573	−0.548671
$337$	28.9414	1.57654	0.788271	−	0.615329i	$-0.210977\pi$
$337$	28.9414	1.57654	0.788271	+	0.615329i	$0.210977\pi$
$338$	0	0
$339$	−29.7262	−1.61451
$340$	42.6086	2.31077
$341$	−2.93151	−0.158750
$342$	100.105	5.41303
$343$	−1.00000	−0.0539949
$344$	−2.14637	−0.115725
$345$	−15.8400	−0.852799
$346$	22.4173	1.20516
$347$	27.5087	1.47674	0.738371	−	0.674394i	$-0.235595\pi$
$347$	27.5087	1.47674	0.738371	+	0.674394i	$0.235595\pi$
$348$	18.7709	1.00622
$349$	−12.8635	−0.688566	−0.344283	−	0.938866i	$-0.611878\pi$
$349$	−12.8635	−0.688566	−0.344283	+	0.938866i	$0.611878\pi$
$350$	−4.65917	−0.249043
$351$	0	0
$352$	13.4658	0.717729
$353$	−9.21469	−0.490449	−0.245224	−	0.969466i	$-0.578862\pi$
$353$	−9.21469	−0.490449	−0.245224	+	0.969466i	$0.578862\pi$
$354$	28.2539	1.50168
$355$	7.91061	0.419851
$356$	−17.5172	−0.928408
$357$	20.8392	1.10293
$358$	−15.6474	−0.826992
$359$	−34.1609	−1.80295	−0.901473	−	0.432836i	$-0.857513\pi$
$359$	−34.1609	−1.80295	−0.901473	+	0.432836i	$0.857513\pi$
$360$	9.88758	0.521121
$361$	43.7855	2.30450
$362$	29.0740	1.52809
$363$	24.8661	1.30513
$364$	0	0
$365$	39.3583	2.06011
$366$	−18.0606	−0.944043
$367$	−12.2691	−0.640442	−0.320221	−	0.947343i	$-0.603757\pi$
$367$	−12.2691	−0.640442	−0.320221	+	0.947343i	$0.603757\pi$
$368$	−6.50271	−0.338977
$369$	43.1982	2.24881
$370$	23.4257	1.21784
$371$	−12.7174	−0.660256
$372$	−12.2004	−0.632560
$373$	−30.9879	−1.60450	−0.802248	−	0.596991i	$-0.796363\pi$
$373$	−30.9879	−1.60450	−0.802248	+	0.596991i	$0.796363\pi$
$374$	−23.7590	−1.22855
$375$	22.3403	1.15365
$376$	0.921935	0.0475452
$377$	0	0
$378$	19.3636	0.995958
$379$	−25.7797	−1.32421	−0.662107	−	0.749409i	$-0.730338\pi$
$379$	−25.7797	−1.32421	−0.662107	+	0.749409i	$0.730338\pi$
$380$	48.8700	2.50698
$381$	−24.6684	−1.26380
$382$	−56.2355	−2.87726
$383$	0.831967	0.0425115	0.0212558	−	0.999774i	$-0.493234\pi$
$383$	0.831967	0.0425115	0.0212558	+	0.999774i	$0.493234\pi$
$384$	14.3766	0.733655
$385$	4.47022	0.227823
$386$	18.5495	0.944144
$387$	−21.7413	−1.10517
$388$	−29.5884	−1.50213
$389$	21.1540	1.07255	0.536275	−	0.844043i	$-0.319831\pi$
$389$	21.1540	1.07255	0.536275	+	0.844043i	$0.319831\pi$
$390$	0	0
$391$	13.4740	0.681407
$392$	0.602118	0.0304115
$393$	7.12051	0.359182
$394$	−32.9788	−1.66145
$395$	7.84452	0.394700
$396$	−23.1957	−1.16563
$397$	−26.2413	−1.31701	−0.658507	−	0.752575i	$-0.728812\pi$
$397$	−26.2413	−1.31701	−0.658507	+	0.752575i	$0.728812\pi$
$398$	8.85306	0.443764
$399$	23.9016	1.19658
$400$	−7.49945	−0.374973
$401$	−13.0900	−0.653681	−0.326841	−	0.945079i	$-0.605984\pi$
$401$	−13.0900	−0.653681	−0.326841	+	0.945079i	$0.605984\pi$
$402$	−7.94414	−0.396218
$403$	0	0
$404$	−41.3026	−2.05488
$405$	26.6582	1.32466
$406$	5.62710	0.279268
$407$	−6.97368	−0.345672
$408$	−12.5477	−0.621203
$409$	−23.1164	−1.14303	−0.571516	−	0.820591i	$-0.693645\pi$
$409$	−23.1164	−1.14303	−0.571516	+	0.820591i	$0.693645\pi$
$410$	39.5017	1.95085
$411$	35.2587	1.73918
$412$	0.480690	0.0236819
$413$	4.52186	0.222506
$414$	24.6397	1.21097
$415$	6.27373	0.307966
$416$	0	0
$417$	51.2976	2.51206
$418$	−27.2505	−1.33286
$419$	26.8569	1.31205	0.656023	−	0.754741i	$-0.272237\pi$
$419$	26.8569	1.31205	0.656023	+	0.754741i	$0.272237\pi$
$420$	18.6042	0.907790
$421$	−18.5815	−0.905606	−0.452803	−	0.891611i	$-0.649576\pi$
$421$	−18.5815	−0.905606	−0.452803	+	0.891611i	$0.649576\pi$
$422$	44.1175	2.14761
$423$	9.33855	0.454056
$424$	7.65739	0.371876
$425$	15.5393	0.753765
$426$	−18.3579	−0.889443
$427$	−2.89049	−0.139881
$428$	−10.1975	−0.492915
$429$	0	0
$430$	−19.8808	−0.958739
$431$	30.3452	1.46168	0.730839	−	0.682550i	$-0.239129\pi$
$431$	30.3452	1.46168	0.730839	+	0.682550i	$0.239129\pi$
$432$	31.1679	1.49957
$433$	7.20269	0.346139	0.173070	−	0.984910i	$-0.444631\pi$
$433$	7.20269	0.346139	0.173070	+	0.984910i	$0.444631\pi$
$434$	−3.65741	−0.175561
$435$	22.0631	1.05785
$436$	−30.4978	−1.46058
$437$	15.4540	0.739264
$438$	−91.3377	−4.36428
$439$	37.1668	1.77387	0.886937	−	0.461889i	$-0.152828\pi$
$439$	37.1668	1.77387	0.886937	+	0.461889i	$0.152828\pi$
$440$	−2.69160	−0.128317
$441$	6.09903	0.290430
$442$	0	0
$443$	−16.2860	−0.773769	−0.386884	−	0.922128i	$-0.626449\pi$
$443$	−16.2860	−0.773769	−0.386884	+	0.922128i	$0.626449\pi$
$444$	−29.0231	−1.37737
$445$	−20.5896	−0.976039
$446$	−19.9682	−0.945523
$447$	0.638743	0.0302115
$448$	10.1319	0.478687
$449$	−24.4510	−1.15392	−0.576958	−	0.816774i	$-0.695760\pi$
$449$	−24.4510	−1.15392	−0.576958	+	0.816774i	$0.695760\pi$
$450$	28.4165	1.33956
$451$	−11.7594	−0.553729
$452$	22.5739	1.06179
$453$	41.5431	1.95186
$454$	27.1715	1.27522
$455$	0	0
$456$	−14.3916	−0.673948
$457$	38.0768	1.78116	0.890578	−	0.454831i	$-0.150300\pi$
$457$	38.0768	1.78116	0.890578	+	0.454831i	$0.150300\pi$
$458$	30.1455	1.40861
$459$	−64.5815	−3.01441
$460$	12.0288	0.560847
$461$	−23.8562	−1.11109	−0.555547	−	0.831485i	$-0.687491\pi$
$461$	−23.8562	−1.11109	−0.555547	+	0.831485i	$0.687491\pi$
$462$	−10.3739	−0.482637
$463$	3.70780	0.172316	0.0861581	−	0.996281i	$-0.472541\pi$
$463$	3.70780	0.172316	0.0861581	+	0.996281i	$0.472541\pi$
$464$	9.05744	0.420481
$465$	−14.3402	−0.665012
$466$	5.91529	0.274021
$467$	38.4670	1.78004	0.890020	−	0.455922i	$-0.150690\pi$
$467$	38.4670	1.78004	0.890020	+	0.455922i	$0.150690\pi$
$468$	0	0
$469$	−1.27141	−0.0587084
$470$	8.53944	0.393895
$471$	−2.44695	−0.112749
$472$	−2.72270	−0.125322
$473$	5.91841	0.272129
$474$	−18.2045	−0.836161
$475$	17.8228	0.817765
$476$	−15.8252	−0.725347
$477$	77.5640	3.55141
$478$	8.55098	0.391113
$479$	27.3349	1.24896	0.624482	−	0.781039i	$-0.285310\pi$
$479$	27.3349	1.24896	0.624482	+	0.781039i	$0.285310\pi$
$480$	65.8713	3.00660
$481$	0	0
$482$	−12.5787	−0.572943
$483$	5.88313	0.267692
$484$	−18.8832	−0.858326
$485$	−34.7780	−1.57919
$486$	−3.77395	−0.171190
$487$	26.4037	1.19646	0.598232	−	0.801323i	$-0.295870\pi$
$487$	26.4037	1.19646	0.598232	+	0.801323i	$0.295870\pi$
$488$	1.74042	0.0787849
$489$	15.4280	0.697678
$490$	5.57713	0.251949
$491$	−26.1680	−1.18095	−0.590473	−	0.807058i	$-0.701059\pi$
$491$	−26.1680	−1.18095	−0.590473	+	0.807058i	$0.701059\pi$
$492$	−48.9403	−2.20640
$493$	−18.7675	−0.845245
$494$	0	0
$495$	−27.2640	−1.22543
$496$	−5.88700	−0.264334
$497$	−2.93807	−0.131790
$498$	−14.5593	−0.652416
$499$	−0.380977	−0.0170549	−0.00852743	−	0.999964i	$-0.502714\pi$
$499$	−0.380977	−0.0170549	−0.00852743	+	0.999964i	$0.502714\pi$
$500$	−16.9651	−0.758704
$501$	15.2791	0.682618
$502$	−7.45500	−0.332733
$503$	28.9398	1.29036	0.645181	−	0.764030i	$-0.276782\pi$
$503$	28.9398	1.29036	0.645181	+	0.764030i	$0.276782\pi$
$504$	−3.67234	−0.163579
$505$	−48.5468	−2.16030
$506$	−6.70741	−0.298181
$507$	0	0
$508$	18.7330	0.831143
$509$	−14.3808	−0.637420	−0.318710	−	0.947852i	$-0.603250\pi$
$509$	−14.3808	−0.637420	−0.318710	+	0.947852i	$0.603250\pi$
$510$	−116.223	−5.14645
$511$	−14.6180	−0.646664
$512$	31.0568	1.37253
$513$	−74.0719	−3.27035
$514$	15.9728	0.704529
$515$	0.564999	0.0248968
$516$	24.6312	1.08433
$517$	−2.54214	−0.111803
$518$	−8.70049	−0.382278
$519$	−32.6451	−1.43296
$520$	0	0
$521$	−9.56341	−0.418981	−0.209490	−	0.977811i	$-0.567180\pi$
$521$	−9.56341	−0.418981	−0.209490	+	0.977811i	$0.567180\pi$
$522$	−34.3199	−1.50214
$523$	31.6128	1.38233	0.691167	−	0.722695i	$-0.257097\pi$
$523$	31.6128	1.38233	0.691167	+	0.722695i	$0.257097\pi$
$524$	−5.40727	−0.236218
$525$	6.78490	0.296117
$526$	−19.2449	−0.839117
$527$	12.1982	0.531361
$528$	−16.6979	−0.726684
$529$	−19.1962	−0.834616
$530$	70.9268	3.08086
$531$	−27.5790	−1.19683
$532$	−18.1507	−0.786935
$533$	0	0
$534$	47.7815	2.06771
$535$	−11.9861	−0.518203
$536$	0.765540	0.0330663
$537$	22.7865	0.983309
$538$	2.93771	0.126654
$539$	−1.66028	−0.0715133
$540$	−57.6549	−2.48107
$541$	−8.73575	−0.375579	−0.187790	−	0.982209i	$-0.560132\pi$
$541$	−8.73575	−0.375579	−0.187790	+	0.982209i	$0.560132\pi$
$542$	27.9569	1.20085
$543$	−42.3388	−1.81693
$544$	−56.0319	−2.40235
$545$	−35.8469	−1.53551
$546$	0	0
$547$	−30.0145	−1.28333	−0.641664	−	0.766986i	$-0.721755\pi$
$547$	−30.0145	−1.28333	−0.641664	+	0.766986i	$0.721755\pi$
$548$	−26.7752	−1.14378
$549$	17.6292	0.752395
$550$	−7.73553	−0.329844
$551$	−21.5254	−0.917013
$552$	−3.54234	−0.150772
$553$	−2.91352	−0.123896
$554$	−31.2005	−1.32558
$555$	−34.1135	−1.44804
$556$	−38.9551	−1.65207
$557$	−46.6749	−1.97768	−0.988840	−	0.148978i	$-0.952402\pi$
$557$	−46.6749	−1.97768	−0.988840	+	0.148978i	$0.952402\pi$
$558$	22.3067	0.944316
$559$	0	0
$560$	8.97701	0.379348
$561$	34.5990	1.46077
$562$	−24.3867	−1.02869
$563$	37.2742	1.57092	0.785459	−	0.618913i	$-0.212427\pi$
$563$	37.2742	1.57092	0.785459	+	0.618913i	$0.212427\pi$
$564$	−10.5799	−0.445494
$565$	26.5332	1.11626
$566$	−22.7557	−0.956494
$567$	−9.90109	−0.415807
$568$	1.76906	0.0742283
$569$	29.1429	1.22173	0.610866	−	0.791734i	$-0.290821\pi$
$569$	29.1429	1.22173	0.610866	+	0.791734i	$0.290821\pi$
$570$	−133.302	−5.58343
$571$	−36.4299	−1.52454	−0.762271	−	0.647257i	$-0.775916\pi$
$571$	−36.4299	−1.52454	−0.762271	+	0.647257i	$0.775916\pi$
$572$	0	0
$573$	81.8927	3.42112
$574$	−14.6713	−0.612367
$575$	4.38689	0.182946
$576$	−61.7948	−2.57478
$577$	8.28861	0.345059	0.172530	−	0.985004i	$-0.444806\pi$
$577$	8.28861	0.345059	0.172530	+	0.985004i	$0.444806\pi$
$578$	63.6488	2.64744
$579$	−27.0126	−1.12261
$580$	−16.7546	−0.695697
$581$	−2.33012	−0.0966697
$582$	80.7083	3.34547
$583$	−21.1145	−0.874472
$584$	8.80178	0.364220
$585$	0	0
$586$	17.2375	0.712074
$587$	−4.32673	−0.178583	−0.0892916	−	0.996006i	$-0.528460\pi$
$587$	−4.32673	−0.178583	−0.0892916	+	0.996006i	$0.528460\pi$
$588$	−6.90975	−0.284953
$589$	13.9907	0.576478
$590$	−25.2190	−1.03825
$591$	48.0252	1.97549
$592$	−14.0044	−0.575577
$593$	−46.9105	−1.92638	−0.963192	−	0.268813i	$-0.913369\pi$
$593$	−46.9105	−1.92638	−0.963192	+	0.268813i	$0.913369\pi$
$594$	32.1490	1.31909
$595$	−18.6008	−0.762559
$596$	−0.485057	−0.0198687
$597$	−12.8922	−0.527644
$598$	0	0
$599$	11.2181	0.458359	0.229179	−	0.973384i	$-0.426396\pi$
$599$	11.2181	0.458359	0.229179	+	0.973384i	$0.426396\pi$
$600$	−4.08531	−0.166782
$601$	−2.04589	−0.0834535	−0.0417267	−	0.999129i	$-0.513286\pi$
$601$	−2.04589	−0.0834535	−0.0417267	+	0.999129i	$0.513286\pi$
$602$	7.38392	0.300946
$603$	7.75438	0.315783
$604$	−31.5476	−1.28365
$605$	−22.1952	−0.902361
$606$	112.661	4.57654
$607$	−47.0883	−1.91125	−0.955627	−	0.294581i	$-0.904820\pi$
$607$	−47.0883	−1.91125	−0.955627	+	0.294581i	$0.904820\pi$
$608$	−64.2659	−2.60633
$609$	−8.19444	−0.332055
$610$	16.1206	0.652706
$611$	0	0
$612$	96.5184	3.90153
$613$	19.4975	0.787495	0.393748	−	0.919219i	$-0.371178\pi$
$613$	19.4975	0.787495	0.393748	+	0.919219i	$0.371178\pi$
$614$	−28.7134	−1.15878
$615$	−57.5241	−2.31959
$616$	0.999683	0.0402784
$617$	−30.0788	−1.21093	−0.605464	−	0.795873i	$-0.707012\pi$
$617$	−30.0788	−1.21093	−0.605464	+	0.795873i	$0.707012\pi$
$618$	−1.31118	−0.0527432
$619$	−30.4696	−1.22468	−0.612339	−	0.790595i	$-0.709771\pi$
$619$	−30.4696	−1.22468	−0.612339	+	0.790595i	$0.709771\pi$
$620$	10.8899	0.437348
$621$	−18.2320	−0.731625
$622$	26.6965	1.07043
$623$	7.64714	0.306376
$624$	0	0
$625$	−31.1871	−1.24749
$626$	42.5290	1.69980
$627$	39.6833	1.58480
$628$	1.85820	0.0741502
$629$	29.0178	1.15702
$630$	−34.0151	−1.35519
$631$	41.3087	1.64447	0.822236	−	0.569146i	$-0.192726\pi$
$631$	41.3087	1.64447	0.822236	+	0.569146i	$0.192726\pi$
$632$	1.75428	0.0697817
$633$	−64.2459	−2.55354
$634$	−21.8336	−0.867123
$635$	22.0186	0.873783
$636$	−87.8743	−3.48444
$637$	0	0
$638$	9.34256	0.369875
$639$	17.9194	0.708880
$640$	−12.8324	−0.507245
$641$	23.9080	0.944308	0.472154	−	0.881516i	$-0.343477\pi$
$641$	23.9080	0.944308	0.472154	+	0.881516i	$0.343477\pi$
$642$	27.8157	1.09780
$643$	−20.3926	−0.804204	−0.402102	−	0.915595i	$-0.631720\pi$
$643$	−20.3926	−0.804204	−0.402102	+	0.915595i	$0.631720\pi$
$644$	−4.46761	−0.176049
$645$	28.9514	1.13996
$646$	113.391	4.46129
$647$	29.1050	1.14424	0.572118	−	0.820171i	$-0.306122\pi$
$647$	29.1050	1.14424	0.572118	+	0.820171i	$0.306122\pi$
$648$	5.96163	0.234195
$649$	7.50755	0.294697
$650$	0	0
$651$	5.32609	0.208746
$652$	−11.7159	−0.458831
$653$	−41.8362	−1.63718	−0.818588	−	0.574382i	$-0.805243\pi$
$653$	−41.8362	−1.63718	−0.818588	+	0.574382i	$0.805243\pi$
$654$	83.1889	3.25294
$655$	−6.35567	−0.248337
$656$	−23.6150	−0.922011
$657$	89.1559	3.47830
$658$	−3.17163	−0.123643
$659$	−8.39738	−0.327116	−0.163558	−	0.986534i	$-0.552297\pi$
$659$	−8.39738	−0.327116	−0.163558	+	0.986534i	$0.552297\pi$
$660$	30.8881	1.20232
$661$	−17.4149	−0.677362	−0.338681	−	0.940901i	$-0.609981\pi$
$661$	−17.4149	−0.677362	−0.338681	+	0.940901i	$0.609981\pi$
$662$	26.1636	1.01688
$663$	0	0
$664$	1.40301	0.0544472
$665$	−21.3343	−0.827307
$666$	53.0646	2.05621
$667$	−5.29825	−0.205149
$668$	−11.6028	−0.448927
$669$	29.0786	1.12424
$670$	7.09083	0.273943
$671$	−4.79902	−0.185264
$672$	−24.4652	−0.943765
$673$	−26.0000	−1.00223	−0.501114	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501114	+	0.865382i	$0.667076\pi$
$674$	59.9492	2.30916
$675$	−21.0266	−0.809315
$676$	0	0
$677$	27.2989	1.04918	0.524592	−	0.851354i	$-0.324218\pi$
$677$	27.2989	1.04918	0.524592	+	0.851354i	$0.324218\pi$
$678$	−61.5747	−2.36476
$679$	12.9169	0.495704
$680$	11.1999	0.429496
$681$	−39.5683	−1.51626
$682$	−6.07232	−0.232521
$683$	−6.81285	−0.260686	−0.130343	−	0.991469i	$-0.541608\pi$
$683$	−6.81285	−0.260686	−0.130343	+	0.991469i	$0.541608\pi$
$684$	110.702	4.23280
$685$	−31.4714	−1.20246
$686$	−2.07140	−0.0790863
$687$	−43.8992	−1.67486
$688$	11.8852	0.453120
$689$	0	0
$690$	−32.8110	−1.24909
$691$	−29.5695	−1.12488	−0.562438	−	0.826840i	$-0.690136\pi$
$691$	−29.5695	−1.12488	−0.562438	+	0.826840i	$0.690136\pi$
$692$	24.7905	0.942393
$693$	10.1261	0.384658
$694$	56.9813	2.16298
$695$	−45.7876	−1.73682
$696$	4.93402	0.187023
$697$	48.9315	1.85341
$698$	−26.6454	−1.00854
$699$	−8.61412	−0.325816
$700$	−5.15241	−0.194743
$701$	5.36856	0.202768	0.101384	−	0.994847i	$-0.467673\pi$
$701$	5.36856	0.202768	0.101384	+	0.994847i	$0.467673\pi$
$702$	0	0
$703$	33.2821	1.25526
$704$	16.8218	0.633995
$705$	−12.4355	−0.468349
$706$	−19.0873	−0.718359
$707$	18.0307	0.678114
$708$	31.2450	1.17426
$709$	24.2656	0.911313	0.455657	−	0.890156i	$-0.349405\pi$
$709$	24.2656	0.911313	0.455657	+	0.890156i	$0.349405\pi$
$710$	16.3860	0.614956
$711$	17.7697	0.666414
$712$	−4.60448	−0.172560
$713$	3.44367	0.128966
$714$	43.1663	1.61546
$715$	0	0
$716$	−17.3039	−0.646678
$717$	−12.4523	−0.465041
$718$	−70.7608	−2.64077
$719$	−42.1440	−1.57170	−0.785852	−	0.618414i	$-0.787775\pi$
$719$	−42.1440	−1.57170	−0.785852	+	0.618414i	$0.787775\pi$
$720$	−54.7511	−2.04045
$721$	−0.209846	−0.00781506
$722$	90.6971	3.37540
$723$	18.3176	0.681241
$724$	32.1518	1.19491
$725$	−6.11037	−0.226933
$726$	51.5076	1.91163
$727$	−20.2269	−0.750174	−0.375087	−	0.926990i	$-0.622387\pi$
$727$	−20.2269	−0.750174	−0.375087	+	0.926990i	$0.622387\pi$
$728$	0	0
$729$	−24.2075	−0.896573
$730$	81.5267	3.01744
$731$	−24.6268	−0.910856
$732$	−19.9726	−0.738207
$733$	18.1077	0.668821	0.334411	−	0.942427i	$-0.391463\pi$
$733$	18.1077	0.668821	0.334411	+	0.942427i	$0.391463\pi$
$734$	−25.4142	−0.938054
$735$	−8.12167	−0.299572
$736$	−15.8184	−0.583073
$737$	−2.11090	−0.0777559
$738$	89.4805	3.29382
$739$	−13.7353	−0.505263	−0.252631	−	0.967563i	$-0.581296\pi$
$739$	−13.7353	−0.505263	−0.252631	+	0.967563i	$0.581296\pi$
$740$	25.9056	0.952308
$741$	0	0
$742$	−26.3428	−0.967076
$743$	−3.37426	−0.123790	−0.0618949	−	0.998083i	$-0.519714\pi$
$743$	−3.37426	−0.123790	−0.0618949	+	0.998083i	$0.519714\pi$
$744$	−3.20693	−0.117572
$745$	−0.570133	−0.0208881
$746$	−64.1883	−2.35010
$747$	14.2115	0.519971
$748$	−26.2742	−0.960681
$749$	4.45174	0.162663
$750$	46.2757	1.68975
$751$	−4.27988	−0.156175	−0.0780875	−	0.996947i	$-0.524881\pi$
$751$	−4.27988	−0.156175	−0.0780875	+	0.996947i	$0.524881\pi$
$752$	−5.10508	−0.186163
$753$	10.8563	0.395626
$754$	0	0
$755$	−37.0808	−1.34951
$756$	21.4135	0.778803
$757$	−2.70914	−0.0984655	−0.0492328	−	0.998787i	$-0.515678\pi$
$757$	−2.70914	−0.0984655	−0.0492328	+	0.998787i	$0.515678\pi$
$758$	−53.4000	−1.93957
$759$	9.76763	0.354543
$760$	12.8457	0.465964
$761$	27.7059	1.00434	0.502169	−	0.864770i	$-0.332536\pi$
$761$	27.7059	1.00434	0.502169	+	0.864770i	$0.332536\pi$
$762$	−51.0979	−1.85108
$763$	13.3139	0.481995
$764$	−62.1888	−2.24991
$765$	113.447	4.10169
$766$	1.72333	0.0622666
$767$	0	0
$768$	−31.3452	−1.13107
$769$	−41.4393	−1.49434	−0.747169	−	0.664634i	$-0.768588\pi$
$769$	−41.4393	−1.49434	−0.747169	+	0.664634i	$0.768588\pi$
$770$	9.25959	0.333693
$771$	−23.2603	−0.837699
$772$	20.5132	0.738287
$773$	19.4987	0.701319	0.350660	−	0.936503i	$-0.385957\pi$
$773$	19.4987	0.701319	0.350660	+	0.936503i	$0.385957\pi$
$774$	−45.0348	−1.61874
$775$	3.97152	0.142661
$776$	−7.77748	−0.279195
$777$	12.6701	0.454536
$778$	43.8183	1.57096
$779$	56.1221	2.01078
$780$	0	0
$781$	−4.87801	−0.174549
$782$	27.9099	0.998056
$783$	25.3948	0.907537
$784$	−3.33414	−0.119076
$785$	2.18411	0.0779543
$786$	14.7494	0.526093
$787$	8.20762	0.292570	0.146285	−	0.989242i	$-0.453268\pi$
$787$	8.20762	0.292570	0.146285	+	0.989242i	$0.453268\pi$
$788$	−36.4701	−1.29919
$789$	28.0253	0.997726
$790$	16.2491	0.578117
$791$	−9.85466	−0.350391
$792$	−6.09710	−0.216651
$793$	0	0
$794$	−54.3562	−1.92903
$795$	−103.287	−3.66320
$796$	9.79028	0.347007
$797$	−19.0306	−0.674098	−0.337049	−	0.941487i	$-0.609429\pi$
$797$	−19.0306	−0.674098	−0.337049	+	0.941487i	$0.609429\pi$
$798$	49.5097	1.75262
$799$	10.5780	0.374222
$800$	−18.2430	−0.644988
$801$	−46.6402	−1.64795
$802$	−27.1145	−0.957446
$803$	−24.2700	−0.856470
$804$	−8.78514	−0.309828
$805$	−5.25120	−0.185080
$806$	0	0
$807$	−4.27802	−0.150594
$808$	−10.8566	−0.381934
$809$	54.1432	1.90357	0.951786	−	0.306763i	$-0.0992458\pi$
$809$	54.1432	1.90357	0.951786	+	0.306763i	$0.0992458\pi$
$810$	55.2197	1.94022
$811$	−14.6232	−0.513490	−0.256745	−	0.966479i	$-0.582650\pi$
$811$	−14.6232	−0.513490	−0.256745	+	0.966479i	$0.582650\pi$
$812$	6.22281	0.218378
$813$	−40.7121	−1.42784
$814$	−14.4452	−0.506306
$815$	−13.7708	−0.482370
$816$	69.4810	2.43232
$817$	−28.2458	−0.988195
$818$	−47.8832	−1.67420
$819$	0	0
$820$	43.6834	1.52549
$821$	−23.4777	−0.819377	−0.409688	−	0.912226i	$-0.634363\pi$
$821$	−23.4777	−0.819377	−0.409688	+	0.912226i	$0.634363\pi$
$822$	73.0347	2.54738
$823$	−8.76789	−0.305629	−0.152815	−	0.988255i	$-0.548834\pi$
$823$	−8.76789	−0.305629	−0.152815	+	0.988255i	$0.548834\pi$
$824$	0.126352	0.00440167
$825$	11.2648	0.392191
$826$	9.36657	0.325905
$827$	43.3077	1.50596	0.752978	−	0.658046i	$-0.228617\pi$
$827$	43.3077	1.50596	0.752978	+	0.658046i	$0.228617\pi$
$828$	27.2481	0.946937
$829$	−42.6665	−1.48187	−0.740935	−	0.671577i	$-0.765617\pi$
$829$	−42.6665	−1.48187	−0.740935	+	0.671577i	$0.765617\pi$
$830$	12.9954	0.451077
$831$	45.4356	1.57614
$832$	0	0
$833$	6.90851	0.239366
$834$	106.258	3.67940
$835$	−13.6379	−0.471959
$836$	−30.1353	−1.04225
$837$	−16.5057	−0.570521
$838$	55.6313	1.92175
$839$	50.3058	1.73675	0.868374	−	0.495910i	$-0.165165\pi$
$839$	50.3058	1.73675	0.868374	+	0.495910i	$0.165165\pi$
$840$	4.89020	0.168728
$841$	−21.6202	−0.745525
$842$	−38.4896	−1.32644
$843$	35.5130	1.22313
$844$	48.7879	1.67935
$845$	0	0
$846$	19.3438	0.665055
$847$	8.24348	0.283249
$848$	−42.4017	−1.45608
$849$	33.1379	1.13729
$850$	32.1880	1.10404
$851$	8.19203	0.280819
$852$	−20.3013	−0.695512
$853$	−26.3263	−0.901395	−0.450697	−	0.892677i	$-0.648825\pi$
$853$	−26.3263	−0.901395	−0.450697	+	0.892677i	$0.648825\pi$
$854$	−5.98735	−0.204883
$855$	130.118	4.44995
$856$	−2.68047	−0.0916166
$857$	15.9118	0.543537	0.271768	−	0.962363i	$-0.412392\pi$
$857$	15.9118	0.543537	0.271768	+	0.962363i	$0.412392\pi$
$858$	0	0
$859$	−18.7577	−0.640004	−0.320002	−	0.947417i	$-0.603684\pi$
$859$	−18.7577	−0.640004	−0.320002	+	0.947417i	$0.603684\pi$
$860$	−21.9855	−0.749700
$861$	21.3649	0.728116
$862$	62.8569	2.14092
$863$	−6.96807	−0.237196	−0.118598	−	0.992942i	$-0.537840\pi$
$863$	−6.96807	−0.237196	−0.118598	+	0.992942i	$0.537840\pi$
$864$	75.8184	2.57939
$865$	29.1386	0.990741
$866$	14.9196	0.506990
$867$	−92.6883	−3.14786
$868$	−4.04460	−0.137283
$869$	−4.83726	−0.164093
$870$	45.7015	1.54943
$871$	0	0
$872$	−8.01652	−0.271474
$873$	−78.7804	−2.66631
$874$	32.0113	1.08280
$875$	7.40615	0.250373
$876$	−101.007	−3.41271
$877$	−44.0601	−1.48780	−0.743902	−	0.668289i	$-0.767027\pi$
$877$	−44.0601	−1.48780	−0.743902	+	0.668289i	$0.767027\pi$
$878$	76.9872	2.59819
$879$	−25.1020	−0.846670
$880$	14.9043	0.502425
$881$	−20.2850	−0.683418	−0.341709	−	0.939806i	$-0.611006\pi$
$881$	−20.2850	−0.683418	−0.341709	+	0.939806i	$0.611006\pi$
$882$	12.6335	0.425392
$883$	21.6871	0.729829	0.364915	−	0.931041i	$-0.381098\pi$
$883$	21.6871	0.729829	0.364915	+	0.931041i	$0.381098\pi$
$884$	0	0
$885$	36.7251	1.23450
$886$	−33.7347	−1.13334
$887$	−5.15797	−0.173188	−0.0865939	−	0.996244i	$-0.527598\pi$
$887$	−5.15797	−0.173188	−0.0865939	+	0.996244i	$0.527598\pi$
$888$	−7.62886	−0.256008
$889$	−8.17792	−0.274278
$890$	−42.6491	−1.42960
$891$	−16.4386	−0.550713
$892$	−22.0821	−0.739365
$893$	12.1324	0.405997
$894$	1.32309	0.0442507
$895$	−20.3389	−0.679854
$896$	4.76607	0.159223
$897$	0	0
$898$	−50.6478	−1.69014
$899$	−4.79659	−0.159975
$900$	31.4247	1.04749
$901$	87.8585	2.92699
$902$	−24.3584	−0.811045
$903$	−10.7528	−0.357831
$904$	5.93367	0.197351
$905$	37.7910	1.25622
$906$	86.0522	2.85889
$907$	45.3868	1.50704	0.753521	−	0.657423i	$-0.228354\pi$
$907$	45.3868	1.50704	0.753521	+	0.657423i	$0.228354\pi$
$908$	30.0479	0.997175
$909$	−109.970	−3.64747
$910$	0	0
$911$	−46.2828	−1.53342	−0.766708	−	0.641996i	$-0.778107\pi$
$911$	−46.2828	−1.53342	−0.766708	+	0.641996i	$0.778107\pi$
$912$	79.6913	2.63884
$913$	−3.86865	−0.128034
$914$	78.8720	2.60886
$915$	−23.4756	−0.776080
$916$	33.3368	1.10148
$917$	2.36055	0.0779523
$918$	−133.774	−4.41519
$919$	31.6537	1.04416	0.522079	−	0.852897i	$-0.325157\pi$
$919$	31.6537	1.04416	0.522079	+	0.852897i	$0.325157\pi$
$920$	3.16184	0.104243
$921$	41.8137	1.37781
$922$	−49.4157	−1.62742
$923$	0	0
$924$	−11.4721	−0.377405
$925$	9.44771	0.310639
$926$	7.68033	0.252391
$927$	1.27986	0.0420360
$928$	22.0329	0.723267
$929$	12.4113	0.407202	0.203601	−	0.979054i	$-0.434735\pi$
$929$	12.4113	0.407202	0.203601	+	0.979054i	$0.434735\pi$
$930$	−29.7043	−0.974042
$931$	7.92373	0.259690
$932$	6.54151	0.214274
$933$	−38.8766	−1.27276
$934$	79.6804	2.60722
$935$	−30.8825	−1.00997
$936$	0	0
$937$	−30.9889	−1.01236	−0.506182	−	0.862427i	$-0.668943\pi$
$937$	−30.9889	−1.01236	−0.506182	+	0.862427i	$0.668943\pi$
$938$	−2.63360	−0.0859900
$939$	−61.9326	−2.02109
$940$	9.44346	0.308012
$941$	25.8705	0.843353	0.421677	−	0.906746i	$-0.361442\pi$
$941$	25.8705	0.843353	0.421677	+	0.906746i	$0.361442\pi$
$942$	−5.06860	−0.165144
$943$	13.8139	0.449841
$944$	15.0765	0.490699
$945$	25.1693	0.818758
$946$	12.2594	0.398586
$947$	−6.91522	−0.224714	−0.112357	−	0.993668i	$-0.535840\pi$
$947$	−6.91522	−0.224714	−0.112357	+	0.993668i	$0.535840\pi$
$948$	−20.1317	−0.653848
$949$	0	0
$950$	36.9180	1.19778
$951$	31.7951	1.03103
$952$	−4.15974	−0.134818
$953$	13.3445	0.432271	0.216136	−	0.976363i	$-0.430655\pi$
$953$	13.3445	0.432271	0.216136	+	0.976363i	$0.430655\pi$
$954$	160.666	5.20175
$955$	−73.0963	−2.36534
$956$	9.45622	0.305836
$957$	−13.6051	−0.439789
$958$	56.6215	1.82936
$959$	11.6888	0.377450
$960$	82.2880	2.65583
$961$	−27.8824	−0.899432
$962$	0	0
$963$	−27.1513	−0.874938
$964$	−13.9103	−0.448021
$965$	24.1111	0.776163
$966$	12.1863	0.392087
$967$	51.2060	1.64667	0.823337	−	0.567553i	$-0.192110\pi$
$967$	51.2060	1.64667	0.823337	+	0.567553i	$0.192110\pi$
$968$	−4.96354	−0.159534
$969$	−165.125	−5.30456
$970$	−72.0391	−2.31304
$971$	32.2622	1.03534	0.517671	−	0.855580i	$-0.326799\pi$
$971$	32.2622	1.03534	0.517671	+	0.855580i	$0.326799\pi$
$972$	−4.17348	−0.133864
$973$	17.0059	0.545184
$974$	54.6924	1.75246
$975$	0	0
$976$	−9.63730	−0.308482
$977$	38.6920	1.23787	0.618933	−	0.785444i	$-0.287565\pi$
$977$	38.6920	1.23787	0.618933	+	0.785444i	$0.287565\pi$
$978$	31.9575	1.02189
$979$	12.6964	0.405778
$980$	6.16755	0.197015
$981$	−81.2017	−2.59257
$982$	−54.2043	−1.72973
$983$	38.0339	1.21309	0.606547	−	0.795048i	$-0.292554\pi$
$983$	38.0339	1.21309	0.606547	+	0.795048i	$0.292554\pi$
$984$	−12.8642	−0.410096
$985$	−42.8667	−1.36585
$986$	−38.8749	−1.23803
$987$	4.61866	0.147014
$988$	0	0
$989$	−6.95240	−0.221073
$990$	−56.4746	−1.79488
$991$	−21.6138	−0.686585	−0.343293	−	0.939228i	$-0.611542\pi$
$991$	−21.6138	−0.686585	−0.343293	+	0.939228i	$0.611542\pi$
$992$	−14.3206	−0.454680
$993$	−38.1005	−1.20908
$994$	−6.08591	−0.193033
$995$	11.5074	0.364810
$996$	−16.1006	−0.510166
$997$	−15.2409	−0.482686	−0.241343	−	0.970440i	$-0.577588\pi$
$997$	−15.2409	−0.482686	−0.241343	+	0.970440i	$0.577588\pi$
$998$	−0.789153	−0.0249802
$999$	−39.2649	−1.24229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.q.1.11	✓	12
7.6	odd	2		8281.2.a.cn.1.11		12
13.5	odd	4		1183.2.c.j.337.5		24
13.8	odd	4		1183.2.c.j.337.20		24
13.12	even	2		1183.2.a.r.1.2	yes	12
91.90	odd	2		8281.2.a.cq.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.11	✓	12	1.1	even	1	trivial
1183.2.a.r.1.2	yes	12	13.12	even	2
1183.2.c.j.337.5		24	13.5	odd	4
1183.2.c.j.337.20		24	13.8	odd	4
8281.2.a.cn.1.11		12	7.6	odd	2
8281.2.a.cq.1.2		12	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07140 q^{2} -3.01646 q^{3} +2.29068 q^{4} +2.69245 q^{5} -6.24828 q^{6} -1.00000 q^{7} +0.602118 q^{8} +6.09903 q^{9} +O(q^{10})\)	\(q+2.07140 q^{2} -3.01646 q^{3} +2.29068 q^{4} +2.69245 q^{5} -6.24828 q^{6} -1.00000 q^{7} +0.602118 q^{8} +6.09903 q^{9} +5.57713 q^{10} -1.66028 q^{11} -6.90975 q^{12} -2.07140 q^{14} -8.12167 q^{15} -3.33414 q^{16} +6.90851 q^{17} +12.6335 q^{18} +7.92373 q^{19} +6.16755 q^{20} +3.01646 q^{21} -3.43909 q^{22} +1.95034 q^{23} -1.81626 q^{24} +2.24929 q^{25} -9.34811 q^{27} -2.29068 q^{28} -2.71657 q^{29} -16.8232 q^{30} +1.76567 q^{31} -8.11056 q^{32} +5.00816 q^{33} +14.3103 q^{34} -2.69245 q^{35} +13.9709 q^{36} +4.20030 q^{37} +16.4132 q^{38} +1.62117 q^{40} +7.08279 q^{41} +6.24828 q^{42} -3.56471 q^{43} -3.80317 q^{44} +16.4213 q^{45} +4.03993 q^{46} +1.53115 q^{47} +10.0573 q^{48} +1.00000 q^{49} +4.65917 q^{50} -20.8392 q^{51} +12.7174 q^{53} -19.3636 q^{54} -4.47022 q^{55} -0.602118 q^{56} -23.9016 q^{57} -5.62710 q^{58} -4.52186 q^{59} -18.6042 q^{60} +2.89049 q^{61} +3.65741 q^{62} -6.09903 q^{63} -10.1319 q^{64} +10.3739 q^{66} +1.27141 q^{67} +15.8252 q^{68} -5.88313 q^{69} -5.57713 q^{70} +2.93807 q^{71} +3.67234 q^{72} +14.6180 q^{73} +8.70049 q^{74} -6.78490 q^{75} +18.1507 q^{76} +1.66028 q^{77} +2.91352 q^{79} -8.97701 q^{80} +9.90109 q^{81} +14.6713 q^{82} +2.33012 q^{83} +6.90975 q^{84} +18.6008 q^{85} -7.38392 q^{86} +8.19444 q^{87} -0.999683 q^{88} -7.64714 q^{89} +34.0151 q^{90} +4.46761 q^{92} -5.32609 q^{93} +3.17163 q^{94} +21.3343 q^{95} +24.4652 q^{96} -12.9169 q^{97} +2.07140 q^{98} -10.1261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9} - 6 q^{10} - 12 q^{11} + 13 q^{12} + 3 q^{14} - 11 q^{15} + 13 q^{16} + 31 q^{17} + 29 q^{18} + 3 q^{19} + 18 q^{20} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 6 q^{24} + 32 q^{25} + 32 q^{27} - 15 q^{28} + 15 q^{29} - 10 q^{30} + 21 q^{31} + 3 q^{32} + 29 q^{33} - 3 q^{34} - 4 q^{35} + 49 q^{36} - 5 q^{37} + 45 q^{38} - 20 q^{40} + 16 q^{41} + 2 q^{42} - 22 q^{43} - 35 q^{44} - 5 q^{45} - 2 q^{46} + 4 q^{47} + 11 q^{48} + 12 q^{49} - 13 q^{50} + 18 q^{51} + 53 q^{53} + 5 q^{54} - 26 q^{55} + 12 q^{56} + 8 q^{57} - 32 q^{58} + 26 q^{59} - 38 q^{60} + 22 q^{61} + 19 q^{62} - 26 q^{63} + 2 q^{64} - 34 q^{66} - 12 q^{67} + 34 q^{68} + 3 q^{69} + 6 q^{70} - 21 q^{71} + 4 q^{72} + 15 q^{73} - 40 q^{74} + 15 q^{75} - 43 q^{76} + 12 q^{77} + 2 q^{79} - 13 q^{80} + 36 q^{81} - 32 q^{82} + 9 q^{83} - 13 q^{84} + 39 q^{85} - 44 q^{86} + 27 q^{87} - 48 q^{88} + 22 q^{89} - 26 q^{90} + 52 q^{92} + 53 q^{93} - 44 q^{94} + 29 q^{95} + 114 q^{96} - 9 q^{97} - 3 q^{98} - 37 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9 - 6 * q^10 - 12 * q^11 + 13 * q^12 + 3 * q^14 - 11 * q^15 + 13 * q^16 + 31 * q^17 + 29 * q^18 + 3 * q^19 + 18 * q^20 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 6 * q^24 + 32 * q^25 + 32 * q^27 - 15 * q^28 + 15 * q^29 - 10 * q^30 + 21 * q^31 + 3 * q^32 + 29 * q^33 - 3 * q^34 - 4 * q^35 + 49 * q^36 - 5 * q^37 + 45 * q^38 - 20 * q^40 + 16 * q^41 + 2 * q^42 - 22 * q^43 - 35 * q^44 - 5 * q^45 - 2 * q^46 + 4 * q^47 + 11 * q^48 + 12 * q^49 - 13 * q^50 + 18 * q^51 + 53 * q^53 + 5 * q^54 - 26 * q^55 + 12 * q^56 + 8 * q^57 - 32 * q^58 + 26 * q^59 - 38 * q^60 + 22 * q^61 + 19 * q^62 - 26 * q^63 + 2 * q^64 - 34 * q^66 - 12 * q^67 + 34 * q^68 + 3 * q^69 + 6 * q^70 - 21 * q^71 + 4 * q^72 + 15 * q^73 - 40 * q^74 + 15 * q^75 - 43 * q^76 + 12 * q^77 + 2 * q^79 - 13 * q^80 + 36 * q^81 - 32 * q^82 + 9 * q^83 - 13 * q^84 + 39 * q^85 - 44 * q^86 + 27 * q^87 - 48 * q^88 + 22 * q^89 - 26 * q^90 + 52 * q^92 + 53 * q^93 - 44 * q^94 + 29 * q^95 + 114 * q^96 - 9 * q^97 - 3 * q^98 - 37 * q^99

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