LMFDB - Embedded newform 1183.2.a.q.1.2

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			1.2
Root			$2.47725$ 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)

$f(q)$	$=$	$q-2.47725 q^{2} +0.982981 q^{3} +4.13677 q^{4} -1.35413 q^{5} -2.43509 q^{6} -1.00000 q^{7} -5.29330 q^{8} -2.03375 q^{9} +O(q^{10})$	\(q-2.47725 q^{2} +0.982981 q^{3} +4.13677 q^{4} -1.35413 q^{5} -2.43509 q^{6} -1.00000 q^{7} -5.29330 q^{8} -2.03375 q^{9} +3.35452 q^{10} +3.34694 q^{11} +4.06636 q^{12} +2.47725 q^{14} -1.33108 q^{15} +4.83930 q^{16} +0.692094 q^{17} +5.03810 q^{18} -7.45343 q^{19} -5.60172 q^{20} -0.982981 q^{21} -8.29121 q^{22} +8.25231 q^{23} -5.20321 q^{24} -3.16633 q^{25} -4.94808 q^{27} -4.13677 q^{28} +1.07995 q^{29} +3.29742 q^{30} +11.0557 q^{31} -1.40155 q^{32} +3.28998 q^{33} -1.71449 q^{34} +1.35413 q^{35} -8.41314 q^{36} -5.43331 q^{37} +18.4640 q^{38} +7.16781 q^{40} +4.30075 q^{41} +2.43509 q^{42} +4.19825 q^{43} +13.8455 q^{44} +2.75396 q^{45} -20.4430 q^{46} +12.1411 q^{47} +4.75694 q^{48} +1.00000 q^{49} +7.84380 q^{50} +0.680315 q^{51} -4.51915 q^{53} +12.2576 q^{54} -4.53219 q^{55} +5.29330 q^{56} -7.32657 q^{57} -2.67530 q^{58} +1.38180 q^{59} -5.50638 q^{60} -6.49906 q^{61} -27.3877 q^{62} +2.03375 q^{63} -6.20662 q^{64} -8.15010 q^{66} +3.86290 q^{67} +2.86303 q^{68} +8.11186 q^{69} -3.35452 q^{70} -2.65952 q^{71} +10.7652 q^{72} +10.2115 q^{73} +13.4597 q^{74} -3.11245 q^{75} -30.8331 q^{76} -3.34694 q^{77} +1.27930 q^{79} -6.55304 q^{80} +1.23738 q^{81} -10.6540 q^{82} -9.49352 q^{83} -4.06636 q^{84} -0.937185 q^{85} -10.4001 q^{86} +1.06157 q^{87} -17.7164 q^{88} +8.29790 q^{89} -6.82224 q^{90} +34.1379 q^{92} +10.8675 q^{93} -30.0765 q^{94} +10.0929 q^{95} -1.37769 q^{96} +10.2683 q^{97} -2.47725 q^{98} -6.80684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47725	−1.75168	−0.875840	−	0.482602i	$-0.839692\pi$
$2$	−2.47725	−1.75168	−0.875840	+	0.482602i	$0.839692\pi$
$3$	0.982981	0.567524	0.283762	−	0.958895i	$-0.408417\pi$
$3$	0.982981	0.567524	0.283762	+	0.958895i	$0.408417\pi$
$4$	4.13677	2.06838
$5$	−1.35413	−0.605585	−0.302792	−	0.953057i	$-0.597919\pi$
$5$	−1.35413	−0.605585	−0.302792	+	0.953057i	$0.597919\pi$
$6$	−2.43509	−0.994121
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−5.29330	−1.87146
$9$	−2.03375	−0.677916
$10$	3.35452	1.06079
$11$	3.34694	1.00914	0.504570	−	0.863371i	$-0.331651\pi$
$11$	3.34694	1.00914	0.504570	+	0.863371i	$0.331651\pi$
$12$	4.06636	1.17386
$13$	0	0
$13$	0	0
$14$	2.47725	0.662073
$15$	−1.33108	−0.343684
$16$	4.83930	1.20982
$17$	0.692094	0.167858	0.0839288	−	0.996472i	$-0.473253\pi$
$17$	0.692094	0.167858	0.0839288	+	0.996472i	$0.473253\pi$
$18$	5.03810	1.18749
$19$	−7.45343	−1.70993	−0.854967	−	0.518683i	$-0.826422\pi$
$19$	−7.45343	−1.70993	−0.854967	+	0.518683i	$0.826422\pi$
$20$	−5.60172	−1.25258
$21$	−0.982981	−0.214504
$22$	−8.29121	−1.76769
$23$	8.25231	1.72073	0.860363	−	0.509682i	$-0.170237\pi$
$23$	8.25231	1.72073	0.860363	+	0.509682i	$0.170237\pi$
$24$	−5.20321	−1.06210
$25$	−3.16633	−0.633267
$26$	0	0
$27$	−4.94808	−0.952258
$28$	−4.13677	−0.781775
$29$	1.07995	0.200541	0.100271	−	0.994960i	$-0.468029\pi$
$29$	1.07995	0.200541	0.100271	+	0.994960i	$0.468029\pi$
$30$	3.29742	0.602025
$31$	11.0557	1.98566	0.992830	−	0.119537i	$-0.0381412\pi$
$31$	11.0557	1.98566	0.992830	+	0.119537i	$0.0381412\pi$
$32$	−1.40155	−0.247761
$33$	3.28998	0.572712
$34$	−1.71449	−0.294033
$35$	1.35413	0.228890
$36$	−8.41314	−1.40219
$37$	−5.43331	−0.893230	−0.446615	−	0.894726i	$-0.647371\pi$
$37$	−5.43331	−0.893230	−0.446615	+	0.894726i	$0.647371\pi$
$38$	18.4640	2.99526
$39$	0	0
$40$	7.16781	1.13333
$41$	4.30075	0.671665	0.335832	−	0.941922i	$-0.390982\pi$
$41$	4.30075	0.671665	0.335832	+	0.941922i	$0.390982\pi$
$42$	2.43509	0.375742
$43$	4.19825	0.640227	0.320114	−	0.947379i	$-0.396279\pi$
$43$	4.19825	0.640227	0.320114	+	0.947379i	$0.396279\pi$
$44$	13.8455	2.08729
$45$	2.75396	0.410536
$46$	−20.4430	−3.01416
$47$	12.1411	1.77096	0.885481	−	0.464676i	$-0.153829\pi$
$47$	12.1411	1.77096	0.885481	+	0.464676i	$0.153829\pi$
$48$	4.75694	0.686605
$49$	1.00000	0.142857
$50$	7.84380	1.10928
$51$	0.680315	0.0952632
$52$	0	0
$53$	−4.51915	−0.620753	−0.310377	−	0.950614i	$-0.600455\pi$
$53$	−4.51915	−0.620753	−0.310377	+	0.950614i	$0.600455\pi$
$54$	12.2576	1.66805
$55$	−4.53219	−0.611121
$56$	5.29330	0.707347
$57$	−7.32657	−0.970428
$58$	−2.67530	−0.351284
$59$	1.38180	0.179895	0.0899474	−	0.995947i	$-0.471330\pi$
$59$	1.38180	0.179895	0.0899474	+	0.995947i	$0.471330\pi$
$60$	−5.50638	−0.710870
$61$	−6.49906	−0.832120	−0.416060	−	0.909337i	$-0.636589\pi$
$61$	−6.49906	−0.832120	−0.416060	+	0.909337i	$0.636589\pi$
$62$	−27.3877	−3.47824
$63$	2.03375	0.256228
$64$	−6.20662	−0.775827
$65$	0	0
$66$	−8.15010	−1.00321
$67$	3.86290	0.471929	0.235964	−	0.971762i	$-0.424175\pi$
$67$	3.86290	0.471929	0.235964	+	0.971762i	$0.424175\pi$
$68$	2.86303	0.347194
$69$	8.11186	0.976553
$70$	−3.35452	−0.400941
$71$	−2.65952	−0.315627	−0.157813	−	0.987469i	$-0.550444\pi$
$71$	−2.65952	−0.315627	−0.157813	+	0.987469i	$0.550444\pi$
$72$	10.7652	1.26870
$73$	10.2115	1.19517	0.597585	−	0.801806i	$-0.296127\pi$
$73$	10.2115	1.19517	0.597585	+	0.801806i	$0.296127\pi$
$74$	13.4597	1.56465
$75$	−3.11245	−0.359394
$76$	−30.8331	−3.53680
$77$	−3.34694	−0.381419
$78$	0	0
$79$	1.27930	0.143932	0.0719662	−	0.997407i	$-0.477073\pi$
$79$	1.27930	0.143932	0.0719662	+	0.997407i	$0.477073\pi$
$80$	−6.55304	−0.732652
$81$	1.23738	0.137487
$82$	−10.6540	−1.17654
$83$	−9.49352	−1.04205	−0.521024	−	0.853542i	$-0.674450\pi$
$83$	−9.49352	−1.04205	−0.521024	+	0.853542i	$0.674450\pi$
$84$	−4.06636	−0.443676
$85$	−0.937185	−0.101652
$86$	−10.4001	−1.12147
$87$	1.06157	0.113812
$88$	−17.7164	−1.88857
$89$	8.29790	0.879576	0.439788	−	0.898102i	$-0.355054\pi$
$89$	8.29790	0.879576	0.439788	+	0.898102i	$0.355054\pi$
$90$	−6.82224	−0.719128
$91$	0	0
$92$	34.1379	3.55912
$93$	10.8675	1.12691
$94$	−30.0765	−3.10216
$95$	10.0929	1.03551
$96$	−1.37769	−0.140610
$97$	10.2683	1.04258	0.521292	−	0.853379i	$-0.325450\pi$
$97$	10.2683	1.04258	0.521292	+	0.853379i	$0.325450\pi$
$98$	−2.47725	−0.250240
$99$	−6.80684	−0.684113
$100$	−13.0984	−1.30984
$101$	13.0574	1.29926	0.649632	−	0.760249i	$-0.274923\pi$
$101$	13.0574	1.29926	0.649632	+	0.760249i	$0.274923\pi$
$102$	−1.68531	−0.166871
$103$	0.0458921	0.00452188	0.00226094	−	0.999997i	$-0.499280\pi$
$103$	0.0458921	0.00452188	0.00226094	+	0.999997i	$0.499280\pi$
$104$	0	0
$105$	1.33108	0.129900
$106$	11.1951	1.08736
$107$	5.71462	0.552453	0.276226	−	0.961093i	$-0.410916\pi$
$107$	5.71462	0.552453	0.276226	+	0.961093i	$0.410916\pi$
$108$	−20.4690	−1.96963
$109$	−12.6142	−1.20822	−0.604112	−	0.796899i	$-0.706472\pi$
$109$	−12.6142	−1.20822	−0.604112	+	0.796899i	$0.706472\pi$
$110$	11.2274	1.07049
$111$	−5.34084	−0.506930
$112$	−4.83930	−0.457271
$113$	11.4224	1.07453	0.537267	−	0.843412i	$-0.319457\pi$
$113$	11.4224	1.07453	0.537267	+	0.843412i	$0.319457\pi$
$114$	18.1498	1.69988
$115$	−11.1747	−1.04205
$116$	4.46749	0.414796
$117$	0	0
$118$	−3.42306	−0.315118
$119$	−0.692094	−0.0634442
$120$	7.04582	0.643193
$121$	0.202019	0.0183654
$122$	16.0998	1.45761
$123$	4.22756	0.381186
$124$	45.7348	4.10710
$125$	11.0583	0.989082
$126$	−5.03810	−0.448830
$127$	15.1460	1.34399	0.671995	−	0.740555i	$-0.265438\pi$
$127$	15.1460	1.34399	0.671995	+	0.740555i	$0.265438\pi$
$128$	18.1784	1.60676
$129$	4.12680	0.363344
$130$	0	0
$131$	15.4359	1.34864	0.674321	−	0.738438i	$-0.264436\pi$
$131$	15.4359	1.34864	0.674321	+	0.738438i	$0.264436\pi$
$132$	13.6099	1.18459
$133$	7.45343	0.646294
$134$	−9.56938	−0.826668
$135$	6.70034	0.576673
$136$	−3.66346	−0.314139
$137$	−1.45737	−0.124512	−0.0622558	−	0.998060i	$-0.519829\pi$
$137$	−1.45737	−0.124512	−0.0622558	+	0.998060i	$0.519829\pi$
$138$	−20.0951	−1.71061
$139$	1.84411	0.156415	0.0782076	−	0.996937i	$-0.475080\pi$
$139$	1.84411	0.156415	0.0782076	+	0.996937i	$0.475080\pi$
$140$	5.60172	0.473431
$141$	11.9345	1.00506
$142$	6.58829	0.552877
$143$	0	0
$144$	−9.84192	−0.820160
$145$	−1.46239	−0.121445
$146$	−25.2965	−2.09355
$147$	0.982981	0.0810749
$148$	−22.4763	−1.84754
$149$	−20.2755	−1.66104	−0.830518	−	0.556992i	$-0.811955\pi$
$149$	−20.2755	−1.66104	−0.830518	+	0.556992i	$0.811955\pi$
$150$	7.71030	0.629544
$151$	10.1798	0.828422	0.414211	−	0.910181i	$-0.364057\pi$
$151$	10.1798	0.828422	0.414211	+	0.910181i	$0.364057\pi$
$152$	39.4532	3.20008
$153$	−1.40755	−0.113793
$154$	8.29121	0.668125
$155$	−14.9708	−1.20249
$156$	0	0
$157$	11.0029	0.878127	0.439064	−	0.898456i	$-0.355310\pi$
$157$	11.0029	0.878127	0.439064	+	0.898456i	$0.355310\pi$
$158$	−3.16914	−0.252124
$159$	−4.44224	−0.352293
$160$	1.89787	0.150040
$161$	−8.25231	−0.650373
$162$	−3.06530	−0.240833
$163$	25.0175	1.95952	0.979762	−	0.200164i	$-0.0641476\pi$
$163$	25.0175	1.95952	0.979762	+	0.200164i	$0.0641476\pi$
$164$	17.7912	1.38926
$165$	−4.45506	−0.346826
$166$	23.5178	1.82534
$167$	8.22613	0.636557	0.318279	−	0.947997i	$-0.396895\pi$
$167$	8.22613	0.636557	0.318279	+	0.947997i	$0.396895\pi$
$168$	5.20321	0.401437
$169$	0	0
$170$	2.32164	0.178062
$171$	15.1584	1.15919
$172$	17.3672	1.32423
$173$	9.15205	0.695818	0.347909	−	0.937528i	$-0.386892\pi$
$173$	9.15205	0.695818	0.347909	+	0.937528i	$0.386892\pi$
$174$	−2.62977	−0.199362
$175$	3.16633	0.239352
$176$	16.1968	1.22088
$177$	1.35828	0.102095
$178$	−20.5560	−1.54074
$179$	−16.9164	−1.26439	−0.632196	−	0.774809i	$-0.717846\pi$
$179$	−16.9164	−1.26439	−0.632196	+	0.774809i	$0.717846\pi$
$180$	11.3925	0.849145
$181$	−3.26162	−0.242434	−0.121217	−	0.992626i	$-0.538680\pi$
$181$	−3.26162	−0.242434	−0.121217	+	0.992626i	$0.538680\pi$
$182$	0	0
$183$	−6.38845	−0.472248
$184$	−43.6820	−3.22028
$185$	7.35740	0.540927
$186$	−26.9216	−1.97399
$187$	2.31640	0.169392
$188$	50.2249	3.66303
$189$	4.94808	0.359920
$190$	−25.0026	−1.81388
$191$	1.18333	0.0856230	0.0428115	−	0.999083i	$-0.486369\pi$
$191$	1.18333	0.0856230	0.0428115	+	0.999083i	$0.486369\pi$
$192$	−6.10098	−0.440301
$193$	−4.53144	−0.326180	−0.163090	−	0.986611i	$-0.552146\pi$
$193$	−4.53144	−0.326180	−0.163090	+	0.986611i	$0.552146\pi$
$194$	−25.4370	−1.82627
$195$	0	0
$196$	4.13677	0.295483
$197$	−12.6500	−0.901278	−0.450639	−	0.892706i	$-0.648804\pi$
$197$	−12.6500	−0.901278	−0.450639	+	0.892706i	$0.648804\pi$
$198$	16.8622	1.19835
$199$	21.2820	1.50864	0.754320	−	0.656506i	$-0.227967\pi$
$199$	21.2820	1.50864	0.754320	+	0.656506i	$0.227967\pi$
$200$	16.7604	1.18514
$201$	3.79716	0.267831
$202$	−32.3465	−2.27590
$203$	−1.07995	−0.0757975
$204$	2.81430	0.197041
$205$	−5.82377	−0.406750
$206$	−0.113686	−0.00792089
$207$	−16.7831	−1.16651
$208$	0	0
$209$	−24.9462	−1.72556
$210$	−3.29742	−0.227544
$211$	6.82090	0.469570	0.234785	−	0.972047i	$-0.424561\pi$
$211$	6.82090	0.469570	0.234785	+	0.972047i	$0.424561\pi$
$212$	−18.6947	−1.28396
$213$	−2.61425	−0.179126
$214$	−14.1565	−0.967720
$215$	−5.68497	−0.387712
$216$	26.1917	1.78212
$217$	−11.0557	−0.750509
$218$	31.2486	2.11642
$219$	10.0377	0.678288
$220$	−18.7486	−1.26403
$221$	0	0
$222$	13.2306	0.887979
$223$	12.4587	0.834297	0.417148	−	0.908838i	$-0.363030\pi$
$223$	12.4587	0.834297	0.417148	+	0.908838i	$0.363030\pi$
$224$	1.40155	0.0936448
$225$	6.43953	0.429302
$226$	−28.2962	−1.88224
$227$	−7.81480	−0.518686	−0.259343	−	0.965785i	$-0.583506\pi$
$227$	−7.81480	−0.518686	−0.259343	+	0.965785i	$0.583506\pi$
$228$	−30.3083	−2.00722
$229$	−14.9634	−0.988806	−0.494403	−	0.869233i	$-0.664613\pi$
$229$	−14.9634	−0.988806	−0.494403	+	0.869233i	$0.664613\pi$
$230$	27.6825	1.82533
$231$	−3.28998	−0.216465
$232$	−5.71649	−0.375306
$233$	13.2274	0.866556	0.433278	−	0.901260i	$-0.357357\pi$
$233$	13.2274	0.866556	0.433278	+	0.901260i	$0.357357\pi$
$234$	0	0
$235$	−16.4406	−1.07247
$236$	5.71618	0.372091
$237$	1.25753	0.0816851
$238$	1.71449	0.111134
$239$	7.69420	0.497697	0.248848	−	0.968542i	$-0.419948\pi$
$239$	7.69420	0.497697	0.248848	+	0.968542i	$0.419948\pi$
$240$	−6.44151	−0.415798
$241$	−9.00075	−0.579789	−0.289895	−	0.957059i	$-0.593620\pi$
$241$	−9.00075	−0.579789	−0.289895	+	0.957059i	$0.593620\pi$
$242$	−0.500452	−0.0321703
$243$	16.0606	1.03029
$244$	−26.8851	−1.72114
$245$	−1.35413	−0.0865121
$246$	−10.4727	−0.667716
$247$	0	0
$248$	−58.5211	−3.71609
$249$	−9.33194	−0.591388
$250$	−27.3941	−1.73255
$251$	−3.21852	−0.203151	−0.101576	−	0.994828i	$-0.532388\pi$
$251$	−3.21852	−0.203151	−0.101576	+	0.994828i	$0.532388\pi$
$252$	8.41314	0.529978
$253$	27.6200	1.73645
$254$	−37.5204	−2.35424
$255$	−0.921235	−0.0576900
$256$	−32.6193	−2.03870
$257$	5.74593	0.358422	0.179211	−	0.983811i	$-0.442646\pi$
$257$	5.74593	0.358422	0.179211	+	0.983811i	$0.442646\pi$
$258$	−10.2231	−0.636463
$259$	5.43331	0.337609
$260$	0	0
$261$	−2.19634	−0.135950
$262$	−38.2386	−2.36239
$263$	−4.51679	−0.278517	−0.139259	−	0.990256i	$-0.544472\pi$
$263$	−4.51679	−0.278517	−0.139259	+	0.990256i	$0.544472\pi$
$264$	−17.4149	−1.07181
$265$	6.11952	0.375919
$266$	−18.4640	−1.13210
$267$	8.15668	0.499180
$268$	15.9799	0.976130
$269$	1.67968	0.102412	0.0512058	−	0.998688i	$-0.483694\pi$
$269$	1.67968	0.102412	0.0512058	+	0.998688i	$0.483694\pi$
$270$	−16.5984	−1.01015
$271$	−16.2674	−0.988174	−0.494087	−	0.869412i	$-0.664498\pi$
$271$	−16.2674	−0.988174	−0.494087	+	0.869412i	$0.664498\pi$
$272$	3.34925	0.203078
$273$	0	0
$274$	3.61027	0.218104
$275$	−10.5975	−0.639055
$276$	33.5569	2.01989
$277$	−6.96973	−0.418770	−0.209385	−	0.977833i	$-0.567146\pi$
$277$	−6.96973	−0.418770	−0.209385	+	0.977833i	$0.567146\pi$
$278$	−4.56831	−0.273989
$279$	−22.4845	−1.34611
$280$	−7.16781	−0.428359
$281$	15.7742	0.941012	0.470506	−	0.882397i	$-0.344071\pi$
$281$	15.7742	0.941012	0.470506	+	0.882397i	$0.344071\pi$
$282$	−29.5647	−1.76055
$283$	−27.5891	−1.64000	−0.820000	−	0.572363i	$-0.806027\pi$
$283$	−27.5891	−1.64000	−0.820000	+	0.572363i	$0.806027\pi$
$284$	−11.0018	−0.652837
$285$	9.92113	0.587677
$286$	0	0
$287$	−4.30075	−0.253865
$288$	2.85039	0.167961
$289$	−16.5210	−0.971824
$290$	3.62270	0.212732
$291$	10.0935	0.591691
$292$	42.2427	2.47207
$293$	−6.96652	−0.406989	−0.203494	−	0.979076i	$-0.565230\pi$
$293$	−6.96652	−0.406989	−0.203494	+	0.979076i	$0.565230\pi$
$294$	−2.43509	−0.142017
$295$	−1.87113	−0.108942
$296$	28.7601	1.67165
$297$	−16.5609	−0.960963
$298$	50.2275	2.90960
$299$	0	0
$300$	−12.8755	−0.743365
$301$	−4.19825	−0.241983
$302$	−25.2180	−1.45113
$303$	12.8352	0.737364
$304$	−36.0694	−2.06872
$305$	8.80057	0.503919
$306$	3.48684	0.199330
$307$	23.3723	1.33393	0.666965	−	0.745089i	$-0.267593\pi$
$307$	23.3723	1.33393	0.666965	+	0.745089i	$0.267593\pi$
$308$	−13.8455	−0.788921
$309$	0.0451111	0.00256628
$310$	37.0865	2.10637
$311$	0.213388	0.0121001	0.00605006	−	0.999982i	$-0.498074\pi$
$311$	0.213388	0.0121001	0.00605006	+	0.999982i	$0.498074\pi$
$312$	0	0
$313$	−13.2875	−0.751052	−0.375526	−	0.926812i	$-0.622538\pi$
$313$	−13.2875	−0.751052	−0.375526	+	0.926812i	$0.622538\pi$
$314$	−27.2569	−1.53820
$315$	−2.75396	−0.155168
$316$	5.29216	0.297707
$317$	−9.25588	−0.519862	−0.259931	−	0.965627i	$-0.583700\pi$
$317$	−9.25588	−0.519862	−0.259931	+	0.965627i	$0.583700\pi$
$318$	11.0045	0.617104
$319$	3.61452	0.202374
$320$	8.40456	0.469829
$321$	5.61736	0.313530
$322$	20.4430	1.13925
$323$	−5.15847	−0.287025
$324$	5.11876	0.284375
$325$	0	0
$326$	−61.9747	−3.43246
$327$	−12.3995	−0.685697
$328$	−22.7652	−1.25700
$329$	−12.1411	−0.669361
$330$	11.0363	0.607528
$331$	−14.1218	−0.776204	−0.388102	−	0.921617i	$-0.626869\pi$
$331$	−14.1218	−0.776204	−0.388102	+	0.921617i	$0.626869\pi$
$332$	−39.2725	−2.15536
$333$	11.0500	0.605535
$334$	−20.3782	−1.11504
$335$	−5.23087	−0.285793
$336$	−4.75694	−0.259512
$337$	27.8977	1.51968	0.759842	−	0.650108i	$-0.225276\pi$
$337$	27.8977	1.51968	0.759842	+	0.650108i	$0.225276\pi$
$338$	0	0
$339$	11.2280	0.609824
$340$	−3.87691	−0.210255
$341$	37.0027	2.00381
$342$	−37.5511	−2.03053
$343$	−1.00000	−0.0539949
$344$	−22.2226	−1.19816
$345$	−10.9845	−0.591386
$346$	−22.6719	−1.21885
$347$	0.430164	0.0230924	0.0115462	−	0.999933i	$-0.496325\pi$
$347$	0.430164	0.0230924	0.0115462	+	0.999933i	$0.496325\pi$
$348$	4.39146	0.235407
$349$	−27.0848	−1.44982	−0.724909	−	0.688844i	$-0.758118\pi$
$349$	−27.0848	−1.44982	−0.724909	+	0.688844i	$0.758118\pi$
$350$	−7.84380	−0.419269
$351$	0	0
$352$	−4.69089	−0.250025
$353$	27.1110	1.44297	0.721485	−	0.692430i	$-0.243460\pi$
$353$	27.1110	1.44297	0.721485	+	0.692430i	$0.243460\pi$
$354$	−3.36480	−0.178837
$355$	3.60133	0.191139
$356$	34.3265	1.81930
$357$	−0.680315	−0.0360061
$358$	41.9062	2.21481
$359$	−22.9394	−1.21070	−0.605348	−	0.795961i	$-0.706966\pi$
$359$	−22.9394	−1.21070	−0.605348	+	0.795961i	$0.706966\pi$
$360$	−14.5775	−0.768304
$361$	36.5536	1.92387
$362$	8.07984	0.424667
$363$	0.198581	0.0104228
$364$	0	0
$365$	−13.8277	−0.723777
$366$	15.8258	0.827227
$367$	−0.540610	−0.0282196	−0.0141098	−	0.999900i	$-0.504491\pi$
$367$	−0.540610	−0.0282196	−0.0141098	+	0.999900i	$0.504491\pi$
$368$	39.9354	2.08178
$369$	−8.74665	−0.455332
$370$	−18.2261	−0.947530
$371$	4.51915	0.234623
$372$	44.9564	2.33088
$373$	4.04819	0.209607	0.104804	−	0.994493i	$-0.466579\pi$
$373$	4.04819	0.209607	0.104804	+	0.994493i	$0.466579\pi$
$374$	−5.73830	−0.296720
$375$	10.8701	0.561328
$376$	−64.2665	−3.31429
$377$	0	0
$378$	−12.2576	−0.630464
$379$	−25.5845	−1.31419	−0.657093	−	0.753810i	$-0.728214\pi$
$379$	−25.5845	−1.31419	−0.657093	+	0.753810i	$0.728214\pi$
$380$	41.7520	2.14183
$381$	14.8882	0.762747
$382$	−2.93141	−0.149984
$383$	−10.3550	−0.529115	−0.264558	−	0.964370i	$-0.585226\pi$
$383$	−10.3550	−0.529115	−0.264558	+	0.964370i	$0.585226\pi$
$384$	17.8690	0.911876
$385$	4.53219	0.230982
$386$	11.2255	0.571363
$387$	−8.53819	−0.434020
$388$	42.4774	2.15646
$389$	−15.6867	−0.795348	−0.397674	−	0.917527i	$-0.630183\pi$
$389$	−15.6867	−0.795348	−0.397674	+	0.917527i	$0.630183\pi$
$390$	0	0
$391$	5.71138	0.288837
$392$	−5.29330	−0.267352
$393$	15.1732	0.765387
$394$	31.3373	1.57875
$395$	−1.73234	−0.0871633
$396$	−28.1583	−1.41501
$397$	17.2121	0.863850	0.431925	−	0.901909i	$-0.357834\pi$
$397$	17.2121	0.863850	0.431925	+	0.901909i	$0.357834\pi$
$398$	−52.7208	−2.64266
$399$	7.32657	0.366787
$400$	−15.3228	−0.766142
$401$	−28.6309	−1.42976	−0.714881	−	0.699247i	$-0.753519\pi$
$401$	−28.6309	−1.42976	−0.714881	+	0.699247i	$0.753519\pi$
$402$	−9.40651	−0.469154
$403$	0	0
$404$	54.0156	2.68738
$405$	−1.67557	−0.0832599
$406$	2.67530	0.132773
$407$	−18.1850	−0.901395
$408$	−3.60111	−0.178282
$409$	−21.7941	−1.07765	−0.538826	−	0.842417i	$-0.681132\pi$
$409$	−21.7941	−1.07765	−0.538826	+	0.842417i	$0.681132\pi$
$410$	14.4269	0.712496
$411$	−1.43257	−0.0706633
$412$	0.189845	0.00935299
$413$	−1.38180	−0.0679939
$414$	41.5760	2.04335
$415$	12.8554	0.631049
$416$	0	0
$417$	1.81272	0.0887694
$418$	61.7979	3.02264
$419$	−6.96938	−0.340477	−0.170238	−	0.985403i	$-0.554454\pi$
$419$	−6.96938	−0.340477	−0.170238	+	0.985403i	$0.554454\pi$
$420$	5.50638	0.268684
$421$	−8.00034	−0.389913	−0.194956	−	0.980812i	$-0.562457\pi$
$421$	−8.00034	−0.389913	−0.194956	+	0.980812i	$0.562457\pi$
$422$	−16.8971	−0.822536
$423$	−24.6920	−1.20056
$424$	23.9212	1.16172
$425$	−2.19140	−0.106299
$426$	6.47616	0.313771
$427$	6.49906	0.314512
$428$	23.6400	1.14268
$429$	0	0
$430$	14.0831	0.679147
$431$	−26.7240	−1.28725	−0.643624	−	0.765342i	$-0.722570\pi$
$431$	−26.7240	−1.28725	−0.643624	+	0.765342i	$0.722570\pi$
$432$	−23.9452	−1.15207
$433$	−25.6499	−1.23266	−0.616329	−	0.787489i	$-0.711381\pi$
$433$	−25.6499	−1.23266	−0.616329	+	0.787489i	$0.711381\pi$
$434$	27.3877	1.31465
$435$	−1.43750	−0.0689228
$436$	−52.1821	−2.49907
$437$	−61.5080	−2.94233
$438$	−24.8660	−1.18814
$439$	−29.7851	−1.42156	−0.710782	−	0.703413i	$-0.751659\pi$
$439$	−29.7851	−1.42156	−0.710782	+	0.703413i	$0.751659\pi$
$440$	23.9903	1.14369
$441$	−2.03375	−0.0968452
$442$	0	0
$443$	31.7157	1.50686	0.753429	−	0.657530i	$-0.228399\pi$
$443$	31.7157	1.50686	0.753429	+	0.657530i	$0.228399\pi$
$444$	−22.0938	−1.04852
$445$	−11.2364	−0.532658
$446$	−30.8633	−1.46142
$447$	−19.9304	−0.942678
$448$	6.20662	0.293235
$449$	25.0667	1.18297	0.591485	−	0.806316i	$-0.298542\pi$
$449$	25.0667	1.18297	0.591485	+	0.806316i	$0.298542\pi$
$450$	−15.9523	−0.752000
$451$	14.3944	0.677804
$452$	47.2520	2.22255
$453$	10.0066	0.470150
$454$	19.3592	0.908573
$455$	0	0
$456$	38.7818	1.81612
$457$	−20.3303	−0.951011	−0.475505	−	0.879713i	$-0.657735\pi$
$457$	−20.3303	−0.951011	−0.475505	+	0.879713i	$0.657735\pi$
$458$	37.0680	1.73207
$459$	−3.42454	−0.159844
$460$	−46.2271	−2.15535
$461$	30.1317	1.40337	0.701687	−	0.712486i	$-0.252431\pi$
$461$	30.1317	1.40337	0.701687	+	0.712486i	$0.252431\pi$
$462$	8.15010	0.379177
$463$	−10.7592	−0.500023	−0.250011	−	0.968243i	$-0.580434\pi$
$463$	−10.7592	−0.500023	−0.250011	+	0.968243i	$0.580434\pi$
$464$	5.22619	0.242620
$465$	−14.7160	−0.682440
$466$	−32.7676	−1.51793
$467$	−7.00596	−0.324197	−0.162099	−	0.986775i	$-0.551826\pi$
$467$	−7.00596	−0.324197	−0.162099	+	0.986775i	$0.551826\pi$
$468$	0	0
$469$	−3.86290	−0.178372
$470$	40.7275	1.87862
$471$	10.8156	0.498358
$472$	−7.31428	−0.336667
$473$	14.0513	0.646079
$474$	−3.11521	−0.143086
$475$	23.6000	1.08284
$476$	−2.86303	−0.131227
$477$	9.19082	0.420819
$478$	−19.0605	−0.871805
$479$	12.4047	0.566787	0.283394	−	0.959004i	$-0.408540\pi$
$479$	12.4047	0.566787	0.283394	+	0.959004i	$0.408540\pi$
$480$	1.86557	0.0851514
$481$	0	0
$482$	22.2971	1.01561
$483$	−8.11186	−0.369102
$484$	0.835706	0.0379866
$485$	−13.9045	−0.631373
$486$	−39.7860	−1.80473
$487$	−4.21898	−0.191180	−0.0955900	−	0.995421i	$-0.530474\pi$
$487$	−4.21898	−0.191180	−0.0955900	+	0.995421i	$0.530474\pi$
$488$	34.4015	1.55728
$489$	24.5918	1.11208
$490$	3.35452	0.151542
$491$	8.08942	0.365070	0.182535	−	0.983199i	$-0.441570\pi$
$491$	8.08942	0.365070	0.182535	+	0.983199i	$0.441570\pi$
$492$	17.4884	0.788438
$493$	0.747425	0.0336624
$494$	0	0
$495$	9.21734	0.414289
$496$	53.5018	2.40230
$497$	2.65952	0.119296
$498$	23.1176	1.03592
$499$	35.5855	1.59302	0.796512	−	0.604623i	$-0.206676\pi$
$499$	35.5855	1.59302	0.796512	+	0.604623i	$0.206676\pi$
$500$	45.7455	2.04580
$501$	8.08613	0.361262
$502$	7.97307	0.355856
$503$	−37.2077	−1.65901	−0.829505	−	0.558500i	$-0.811377\pi$
$503$	−37.2077	−1.65901	−0.829505	+	0.558500i	$0.811377\pi$
$504$	−10.7652	−0.479522
$505$	−17.6815	−0.786815
$506$	−68.4216	−3.04171
$507$	0	0
$508$	62.6555	2.77989
$509$	29.2315	1.29566	0.647832	−	0.761783i	$-0.275676\pi$
$509$	29.2315	1.29566	0.647832	+	0.761783i	$0.275676\pi$
$510$	2.28213	0.101054
$511$	−10.2115	−0.451732
$512$	44.4492	1.96440
$513$	36.8801	1.62830
$514$	−14.2341	−0.627840
$515$	−0.0621438	−0.00273839
$516$	17.0716	0.751535
$517$	40.6356	1.78715
$518$	−13.4597	−0.591383
$519$	8.99629	0.394893
$520$	0	0
$521$	34.1215	1.49489	0.747444	−	0.664324i	$-0.231281\pi$
$521$	34.1215	1.49489	0.747444	+	0.664324i	$0.231281\pi$
$522$	5.44089	0.238141
$523$	−13.6495	−0.596850	−0.298425	−	0.954433i	$-0.596461\pi$
$523$	−13.6495	−0.596850	−0.298425	+	0.954433i	$0.596461\pi$
$524$	63.8548	2.78951
$525$	3.11245	0.135838
$526$	11.1892	0.487873
$527$	7.65157	0.333308
$528$	15.9212	0.692881
$529$	45.1006	1.96090
$530$	−15.1596	−0.658490
$531$	−2.81023	−0.121954
$532$	30.8331	1.33678
$533$	0	0
$534$	−20.2061	−0.874404
$535$	−7.73833	−0.334557
$536$	−20.4475	−0.883198
$537$	−16.6285	−0.717573
$538$	−4.16098	−0.179392
$539$	3.34694	0.144163
$540$	27.7177	1.19278
$541$	9.86414	0.424092	0.212046	−	0.977260i	$-0.431987\pi$
$541$	9.86414	0.424092	0.212046	+	0.977260i	$0.431987\pi$
$542$	40.2984	1.73096
$543$	−3.20611	−0.137587
$544$	−0.970002	−0.0415885
$545$	17.0813	0.731683
$546$	0	0
$547$	−27.8424	−1.19046	−0.595228	−	0.803557i	$-0.702938\pi$
$547$	−27.8424	−1.19046	−0.595228	+	0.803557i	$0.702938\pi$
$548$	−6.02880	−0.257538
$549$	13.2175	0.564107
$550$	26.2527	1.11942
$551$	−8.04931	−0.342912
$552$	−42.9385	−1.82758
$553$	−1.27930	−0.0544013
$554$	17.2658	0.733552
$555$	7.23218	0.306989
$556$	7.62864	0.323526
$557$	−2.24905	−0.0952954	−0.0476477	−	0.998864i	$-0.515172\pi$
$557$	−2.24905	−0.0952954	−0.0476477	+	0.998864i	$0.515172\pi$
$558$	55.6997	2.35796
$559$	0	0
$560$	6.55304	0.276916
$561$	2.27698	0.0961340
$562$	−39.0767	−1.64835
$563$	30.8047	1.29826	0.649131	−	0.760676i	$-0.275133\pi$
$563$	30.8047	1.29826	0.649131	+	0.760676i	$0.275133\pi$
$564$	49.3701	2.07886
$565$	−15.4675	−0.650721
$566$	68.3450	2.87276
$567$	−1.23738	−0.0519651
$568$	14.0776	0.590684
$569$	−16.0245	−0.671783	−0.335891	−	0.941901i	$-0.609038\pi$
$569$	−16.0245	−0.671783	−0.335891	+	0.941901i	$0.609038\pi$
$570$	−24.5771	−1.02942
$571$	8.25263	0.345362	0.172681	−	0.984978i	$-0.444757\pi$
$571$	8.25263	0.345362	0.172681	+	0.984978i	$0.444757\pi$
$572$	0	0
$573$	1.16319	0.0485931
$574$	10.6540	0.444691
$575$	−26.1296	−1.08968
$576$	12.6227	0.525946
$577$	11.8605	0.493760	0.246880	−	0.969046i	$-0.420595\pi$
$577$	11.8605	0.493760	0.246880	+	0.969046i	$0.420595\pi$
$578$	40.9267	1.70232
$579$	−4.45432	−0.185115
$580$	−6.04956	−0.251194
$581$	9.49352	0.393857
$582$	−25.0041	−1.03645
$583$	−15.1253	−0.626428
$584$	−54.0527	−2.23672
$585$	0	0
$586$	17.2578	0.712914
$587$	8.16634	0.337061	0.168531	−	0.985696i	$-0.446098\pi$
$587$	8.16634	0.337061	0.168531	+	0.985696i	$0.446098\pi$
$588$	4.06636	0.167694
$589$	−82.4027	−3.39535
$590$	4.63527	0.190831
$591$	−12.4347	−0.511497
$592$	−26.2934	−1.08065
$593$	−21.7045	−0.891296	−0.445648	−	0.895208i	$-0.647027\pi$
$593$	−21.7045	−0.891296	−0.445648	+	0.895208i	$0.647027\pi$
$594$	41.0256	1.68330
$595$	0.937185	0.0384208
$596$	−83.8751	−3.43566
$597$	20.9198	0.856190
$598$	0	0
$599$	−12.5895	−0.514392	−0.257196	−	0.966359i	$-0.582799\pi$
$599$	−12.5895	−0.514392	−0.257196	+	0.966359i	$0.582799\pi$
$600$	16.4751	0.672594
$601$	9.71667	0.396351	0.198176	−	0.980167i	$-0.436498\pi$
$601$	9.71667	0.396351	0.198176	+	0.980167i	$0.436498\pi$
$602$	10.4001	0.423877
$603$	−7.85618	−0.319928
$604$	42.1116	1.71349
$605$	−0.273560	−0.0111218
$606$	−31.7960	−1.29163
$607$	−19.5676	−0.794223	−0.397111	−	0.917770i	$-0.629987\pi$
$607$	−19.5676	−0.794223	−0.397111	+	0.917770i	$0.629987\pi$
$608$	10.4463	0.423654
$609$	−1.06157	−0.0430169
$610$	−21.8012	−0.882705
$611$	0	0
$612$	−5.82269	−0.235368
$613$	−1.16145	−0.0469105	−0.0234552	−	0.999725i	$-0.507467\pi$
$613$	−1.16145	−0.0469105	−0.0234552	+	0.999725i	$0.507467\pi$
$614$	−57.8991	−2.33662
$615$	−5.72466	−0.230841
$616$	17.7164	0.713813
$617$	−5.76897	−0.232250	−0.116125	−	0.993235i	$-0.537047\pi$
$617$	−5.76897	−0.232250	−0.116125	+	0.993235i	$0.537047\pi$
$618$	−0.111751	−0.00449530
$619$	22.1428	0.889995	0.444997	−	0.895532i	$-0.353205\pi$
$619$	22.1428	0.889995	0.444997	+	0.895532i	$0.353205\pi$
$620$	−61.9308	−2.48720
$621$	−40.8331	−1.63857
$622$	−0.528615	−0.0211955
$623$	−8.29790	−0.332448
$624$	0	0
$625$	0.857342	0.0342937
$626$	32.9164	1.31560
$627$	−24.5216	−0.979299
$628$	45.5164	1.81630
$629$	−3.76036	−0.149935
$630$	6.82224	0.271805
$631$	−1.53311	−0.0610321	−0.0305160	−	0.999534i	$-0.509715\pi$
$631$	−1.53311	−0.0610321	−0.0305160	+	0.999534i	$0.509715\pi$
$632$	−6.77172	−0.269364
$633$	6.70481	0.266492
$634$	22.9291	0.910632
$635$	−20.5096	−0.813900
$636$	−18.3765	−0.728676
$637$	0	0
$638$	−8.95407	−0.354495
$639$	5.40879	0.213968
$640$	−24.6159	−0.973031
$641$	6.98425	0.275861	0.137931	−	0.990442i	$-0.455955\pi$
$641$	6.98425	0.275861	0.137931	+	0.990442i	$0.455955\pi$
$642$	−13.9156	−0.549205
$643$	−2.00673	−0.0791376	−0.0395688	−	0.999217i	$-0.512598\pi$
$643$	−2.00673	−0.0791376	−0.0395688	+	0.999217i	$0.512598\pi$
$644$	−34.1379	−1.34522
$645$	−5.58822	−0.220036
$646$	12.7788	0.502776
$647$	−31.7091	−1.24661	−0.623306	−	0.781978i	$-0.714211\pi$
$647$	−31.7091	−1.24661	−0.623306	+	0.781978i	$0.714211\pi$
$648$	−6.54983	−0.257302
$649$	4.62480	0.181539
$650$	0	0
$651$	−10.8675	−0.425932
$652$	103.492	4.05305
$653$	32.9719	1.29029	0.645144	−	0.764061i	$-0.276797\pi$
$653$	32.9719	1.29029	0.645144	+	0.764061i	$0.276797\pi$
$654$	30.7168	1.20112
$655$	−20.9022	−0.816717
$656$	20.8126	0.812596
$657$	−20.7677	−0.810225
$658$	30.0765	1.17251
$659$	4.53941	0.176830	0.0884151	−	0.996084i	$-0.471820\pi$
$659$	4.53941	0.176830	0.0884151	+	0.996084i	$0.471820\pi$
$660$	−18.4295	−0.717368
$661$	−3.74518	−0.145671	−0.0728354	−	0.997344i	$-0.523205\pi$
$661$	−3.74518	−0.145671	−0.0728354	+	0.997344i	$0.523205\pi$
$662$	34.9832	1.35966
$663$	0	0
$664$	50.2520	1.95016
$665$	−10.0929	−0.391386
$666$	−27.3736	−1.06070
$667$	8.91206	0.345076
$668$	34.0296	1.31664
$669$	12.2467	0.473484
$670$	12.9582	0.500618
$671$	−21.7520	−0.839726
$672$	1.37769	0.0531457
$673$	−12.6511	−0.487665	−0.243833	−	0.969817i	$-0.578405\pi$
$673$	−12.6511	−0.487665	−0.243833	+	0.969817i	$0.578405\pi$
$674$	−69.1095	−2.66200
$675$	15.6673	0.603033
$676$	0	0
$677$	9.61317	0.369464	0.184732	−	0.982789i	$-0.440858\pi$
$677$	9.61317	0.369464	0.184732	+	0.982789i	$0.440858\pi$
$678$	−27.8147	−1.06822
$679$	−10.2683	−0.394059
$680$	4.96080	0.190238
$681$	−7.68180	−0.294367
$682$	−91.6650	−3.51003
$683$	2.24054	0.0857320	0.0428660	−	0.999081i	$-0.486351\pi$
$683$	2.24054	0.0857320	0.0428660	+	0.999081i	$0.486351\pi$
$684$	62.7067	2.39765
$685$	1.97347	0.0754023
$686$	2.47725	0.0945818
$687$	−14.7087	−0.561171
$688$	20.3166	0.774563
$689$	0	0
$690$	27.2114	1.03592
$691$	−16.7892	−0.638693	−0.319346	−	0.947638i	$-0.603463\pi$
$691$	−16.7892	−0.638693	−0.319346	+	0.947638i	$0.603463\pi$
$692$	37.8599	1.43922
$693$	6.80684	0.258570
$694$	−1.06562	−0.0404505
$695$	−2.49716	−0.0947227
$696$	−5.61920	−0.212995
$697$	2.97653	0.112744
$698$	67.0959	2.53962
$699$	13.0023	0.491791
$700$	13.0984	0.495072
$701$	−50.3596	−1.90206	−0.951028	−	0.309106i	$-0.899970\pi$
$701$	−50.3596	−1.90206	−0.951028	+	0.309106i	$0.899970\pi$
$702$	0	0
$703$	40.4967	1.52736
$704$	−20.7732	−0.782919
$705$	−16.1608	−0.608651
$706$	−67.1606	−2.52762
$707$	−13.0574	−0.491076
$708$	5.61889	0.211171
$709$	−10.1451	−0.381006	−0.190503	−	0.981687i	$-0.561012\pi$
$709$	−10.1451	−0.381006	−0.190503	+	0.981687i	$0.561012\pi$
$710$	−8.92140	−0.334814
$711$	−2.60177	−0.0975741
$712$	−43.9233	−1.64609
$713$	91.2349	3.41677
$714$	1.68531	0.0630712
$715$	0	0
$716$	−69.9792	−2.61525
$717$	7.56325	0.282455
$718$	56.8266	2.12075
$719$	5.86968	0.218902	0.109451	−	0.993992i	$-0.465091\pi$
$719$	5.86968	0.218902	0.109451	+	0.993992i	$0.465091\pi$
$720$	13.3272	0.496676
$721$	−0.0458921	−0.00170911
$722$	−90.5523	−3.37001
$723$	−8.84757	−0.329045
$724$	−13.4926	−0.501447
$725$	−3.41947	−0.126996
$726$	−0.491935	−0.0182574
$727$	−41.0582	−1.52276	−0.761382	−	0.648304i	$-0.775479\pi$
$727$	−41.0582	−1.52276	−0.761382	+	0.648304i	$0.775479\pi$
$728$	0	0
$729$	12.0751	0.447225
$730$	34.2547	1.26783
$731$	2.90558	0.107467
$732$	−26.4275	−0.976790
$733$	19.8655	0.733748	0.366874	−	0.930271i	$-0.380428\pi$
$733$	19.8655	0.733748	0.366874	+	0.930271i	$0.380428\pi$
$734$	1.33923	0.0494317
$735$	−1.33108	−0.0490977
$736$	−11.5660	−0.426328
$737$	12.9289	0.476243
$738$	21.6676	0.797597
$739$	32.3664	1.19062	0.595309	−	0.803497i	$-0.297030\pi$
$739$	32.3664	1.19062	0.595309	+	0.803497i	$0.297030\pi$
$740$	30.4358	1.11884
$741$	0	0
$742$	−11.1951	−0.410984
$743$	−46.4032	−1.70237	−0.851185	−	0.524866i	$-0.824115\pi$
$743$	−46.4032	−1.70237	−0.851185	+	0.524866i	$0.824115\pi$
$744$	−57.5251	−2.10897
$745$	27.4557	1.00590
$746$	−10.0284	−0.367165
$747$	19.3074	0.706422
$748$	9.58240	0.350367
$749$	−5.71462	−0.208808
$750$	−26.9279	−0.983267
$751$	−33.2309	−1.21261	−0.606306	−	0.795232i	$-0.707349\pi$
$751$	−33.2309	−1.21261	−0.606306	+	0.795232i	$0.707349\pi$
$752$	58.7544	2.14255
$753$	−3.16374	−0.115293
$754$	0	0
$755$	−13.7848	−0.501680
$756$	20.4690	0.744452
$757$	22.3961	0.814001	0.407001	−	0.913428i	$-0.366575\pi$
$757$	22.3961	0.814001	0.407001	+	0.913428i	$0.366575\pi$
$758$	63.3791	2.30203
$759$	27.1499	0.985480
$760$	−53.4248	−1.93792
$761$	−37.9167	−1.37448	−0.687240	−	0.726430i	$-0.741178\pi$
$761$	−37.9167	−1.37448	−0.687240	+	0.726430i	$0.741178\pi$
$762$	−36.8819	−1.33609
$763$	12.6142	0.456666
$764$	4.89518	0.177101
$765$	1.90600	0.0689115
$766$	25.6519	0.926841
$767$	0	0
$768$	−32.0641	−1.15701
$769$	5.88438	0.212196	0.106098	−	0.994356i	$-0.466164\pi$
$769$	5.88438	0.212196	0.106098	+	0.994356i	$0.466164\pi$
$770$	−11.2274	−0.404606
$771$	5.64814	0.203413
$772$	−18.7455	−0.674665
$773$	18.1883	0.654188	0.327094	−	0.944992i	$-0.393931\pi$
$773$	18.1883	0.654188	0.327094	+	0.944992i	$0.393931\pi$
$774$	21.1512	0.760265
$775$	−35.0060	−1.25745
$776$	−54.3530	−1.95116
$777$	5.34084	0.191601
$778$	38.8599	1.39320
$779$	−32.0553	−1.14850
$780$	0	0
$781$	−8.90125	−0.318512
$782$	−14.1485	−0.505949
$783$	−5.34367	−0.190967
$784$	4.83930	0.172832
$785$	−14.8994	−0.531781
$786$	−37.5878	−1.34071
$787$	8.90957	0.317592	0.158796	−	0.987311i	$-0.449239\pi$
$787$	8.90957	0.317592	0.158796	+	0.987311i	$0.449239\pi$
$788$	−52.3302	−1.86419
$789$	−4.43992	−0.158065
$790$	4.29143	0.152682
$791$	−11.4224	−0.406135
$792$	36.0307	1.28029
$793$	0	0
$794$	−42.6387	−1.51319
$795$	6.01537	0.213343
$796$	88.0386	3.12045
$797$	47.3677	1.67785	0.838925	−	0.544248i	$-0.183185\pi$
$797$	47.3677	1.67785	0.838925	+	0.544248i	$0.183185\pi$
$798$	−18.1498	−0.642494
$799$	8.40279	0.297269
$800$	4.43776	0.156899
$801$	−16.8758	−0.596279
$802$	70.9260	2.50448
$803$	34.1774	1.20609
$804$	15.7080	0.553977
$805$	11.1747	0.393856
$806$	0	0
$807$	1.65109	0.0581211
$808$	−69.1170	−2.43153
$809$	49.5112	1.74072	0.870361	−	0.492414i	$-0.163885\pi$
$809$	49.5112	1.74072	0.870361	+	0.492414i	$0.163885\pi$
$810$	4.15081	0.145845
$811$	41.3191	1.45091	0.725456	−	0.688269i	$-0.241629\pi$
$811$	41.3191	1.45091	0.725456	+	0.688269i	$0.241629\pi$
$812$	−4.46749	−0.156778
$813$	−15.9905	−0.560813
$814$	45.0487	1.57896
$815$	−33.8770	−1.18666
$816$	3.29225	0.115252
$817$	−31.2914	−1.09475
$818$	53.9895	1.88770
$819$	0	0
$820$	−24.0916	−0.841315
$821$	18.1127	0.632137	0.316068	−	0.948736i	$-0.397637\pi$
$821$	18.1127	0.632137	0.316068	+	0.948736i	$0.397637\pi$
$822$	3.54883	0.123780
$823$	−50.6779	−1.76652	−0.883261	−	0.468882i	$-0.844657\pi$
$823$	−50.6779	−1.76652	−0.883261	+	0.468882i	$0.844657\pi$
$824$	−0.242921	−0.00846255
$825$	−10.4172	−0.362679
$826$	3.42306	0.119103
$827$	−4.24466	−0.147601	−0.0738007	−	0.997273i	$-0.523513\pi$
$827$	−4.24466	−0.147601	−0.0738007	+	0.997273i	$0.523513\pi$
$828$	−69.4278	−2.41278
$829$	31.8934	1.10770	0.553852	−	0.832615i	$-0.313158\pi$
$829$	31.8934	1.10770	0.553852	+	0.832615i	$0.313158\pi$
$830$	−31.8462	−1.10540
$831$	−6.85111	−0.237662
$832$	0	0
$833$	0.692094	0.0239796
$834$	−4.49056	−0.155496
$835$	−11.1392	−0.385490
$836$	−103.197	−3.56913
$837$	−54.7044	−1.89086
$838$	17.2649	0.596406
$839$	43.0363	1.48578	0.742889	−	0.669414i	$-0.233455\pi$
$839$	43.0363	1.48578	0.742889	+	0.669414i	$0.233455\pi$
$840$	−7.04582	−0.243104
$841$	−27.8337	−0.959783
$842$	19.8188	0.683002
$843$	15.5058	0.534047
$844$	28.2165	0.971250
$845$	0	0
$846$	61.1681	2.10300
$847$	−0.202019	−0.00694146
$848$	−21.8695	−0.751003
$849$	−27.1195	−0.930740
$850$	5.42865	0.186201
$851$	−44.8373	−1.53700
$852$	−10.8146	−0.370501
$853$	−19.3374	−0.662101	−0.331050	−	0.943613i	$-0.607403\pi$
$853$	−19.3374	−0.662101	−0.331050	+	0.943613i	$0.607403\pi$
$854$	−16.0998	−0.550924
$855$	−20.5264	−0.701989
$856$	−30.2492	−1.03390
$857$	46.1320	1.57584	0.787920	−	0.615778i	$-0.211158\pi$
$857$	46.1320	1.57584	0.787920	+	0.615778i	$0.211158\pi$
$858$	0	0
$859$	0.0356597	0.00121669	0.000608347	−	1.00000i	$-0.499806\pi$
$859$	0.0356597	0.00121669	0.000608347		1.00000i	$0.499806\pi$
$860$	−23.5174	−0.801937
$861$	−4.22756	−0.144075
$862$	66.2019	2.25485
$863$	53.6734	1.82707	0.913533	−	0.406765i	$-0.133343\pi$
$863$	53.6734	1.82707	0.913533	+	0.406765i	$0.133343\pi$
$864$	6.93496	0.235932
$865$	−12.3931	−0.421377
$866$	63.5413	2.15922
$867$	−16.2398	−0.551534
$868$	−45.7348	−1.55234
$869$	4.28174	0.145248
$870$	3.56105	0.120731
$871$	0	0
$872$	66.7709	2.26115
$873$	−20.8830	−0.706784
$874$	152.371	5.15401
$875$	−11.0583	−0.373838
$876$	41.5238	1.40296
$877$	−31.8812	−1.07655	−0.538275	−	0.842769i	$-0.680924\pi$
$877$	−31.8812	−1.07655	−0.538275	+	0.842769i	$0.680924\pi$
$878$	73.7850	2.49012
$879$	−6.84796	−0.230976
$880$	−21.9326	−0.739349
$881$	40.5926	1.36760	0.683799	−	0.729670i	$-0.260326\pi$
$881$	40.5926	1.36760	0.683799	+	0.729670i	$0.260326\pi$
$882$	5.03810	0.169642
$883$	−7.42994	−0.250037	−0.125019	−	0.992154i	$-0.539899\pi$
$883$	−7.42994	−0.250037	−0.125019	+	0.992154i	$0.539899\pi$
$884$	0	0
$885$	−1.83929	−0.0618270
$886$	−78.5676	−2.63953
$887$	−31.6297	−1.06202	−0.531010	−	0.847365i	$-0.678187\pi$
$887$	−31.6297	−1.06202	−0.531010	+	0.847365i	$0.678187\pi$
$888$	28.2707	0.948701
$889$	−15.1460	−0.507981
$890$	27.8354	0.933046
$891$	4.14144	0.138744
$892$	51.5388	1.72565
$893$	−90.4928	−3.02823
$894$	49.3727	1.65127
$895$	22.9070	0.765697
$896$	−18.1784	−0.607299
$897$	0	0
$898$	−62.0964	−2.07218
$899$	11.9396	0.398207
$900$	26.6388	0.887961
$901$	−3.12768	−0.104198
$902$	−35.6584	−1.18730
$903$	−4.12680	−0.137331
$904$	−60.4625	−2.01095
$905$	4.41665	0.146815
$906$	−24.7888	−0.823552
$907$	30.4198	1.01007	0.505037	−	0.863098i	$-0.331479\pi$
$907$	30.4198	1.01007	0.505037	+	0.863098i	$0.331479\pi$
$908$	−32.3280	−1.07284
$909$	−26.5556	−0.880792
$910$	0	0
$911$	−3.61427	−0.119746	−0.0598731	−	0.998206i	$-0.519070\pi$
$911$	−3.61427	−0.119746	−0.0598731	+	0.998206i	$0.519070\pi$
$912$	−35.4555	−1.17405
$913$	−31.7742	−1.05157
$914$	50.3632	1.66587
$915$	8.65079	0.285986
$916$	−61.8999	−2.04523
$917$	−15.4359	−0.509739
$918$	8.48343	0.279995
$919$	−23.5740	−0.777635	−0.388817	−	0.921315i	$-0.627116\pi$
$919$	−23.5740	−0.777635	−0.388817	+	0.921315i	$0.627116\pi$
$920$	59.1510	1.95015
$921$	22.9746	0.757037
$922$	−74.6437	−2.45826
$923$	0	0
$924$	−13.6099	−0.447732
$925$	17.2037	0.565653
$926$	26.6532	0.875880
$927$	−0.0933330	−0.00306546
$928$	−1.51360	−0.0496862
$929$	−12.9440	−0.424678	−0.212339	−	0.977196i	$-0.568108\pi$
$929$	−12.9440	−0.424678	−0.212339	+	0.977196i	$0.568108\pi$
$930$	36.4553	1.19542
$931$	−7.45343	−0.244276
$932$	54.7187	1.79237
$933$	0.209756	0.00686711
$934$	17.3555	0.567890
$935$	−3.13670	−0.102581
$936$	0	0
$937$	3.98151	0.130070	0.0650352	−	0.997883i	$-0.479284\pi$
$937$	3.98151	0.130070	0.0650352	+	0.997883i	$0.479284\pi$
$938$	9.56938	0.312451
$939$	−13.0613	−0.426240
$940$	−68.0110	−2.21827
$941$	8.25663	0.269158	0.134579	−	0.990903i	$-0.457032\pi$
$941$	8.25663	0.269158	0.134579	+	0.990903i	$0.457032\pi$
$942$	−26.7930	−0.872965
$943$	35.4911	1.15575
$944$	6.68694	0.217641
$945$	−6.70034	−0.217962
$946$	−34.8086	−1.13172
$947$	−25.6597	−0.833828	−0.416914	−	0.908946i	$-0.636888\pi$
$947$	−25.6597	−0.833828	−0.416914	+	0.908946i	$0.636888\pi$
$948$	5.20209	0.168956
$949$	0	0
$950$	−58.4632	−1.89680
$951$	−9.09835	−0.295034
$952$	3.66346	0.118734
$953$	5.32962	0.172643	0.0863217	−	0.996267i	$-0.472489\pi$
$953$	5.32962	0.172643	0.0863217	+	0.996267i	$0.472489\pi$
$954$	−22.7680	−0.737140
$955$	−1.60239	−0.0518520
$956$	31.8291	1.02943
$957$	3.55301	0.114852
$958$	−30.7297	−0.992830
$959$	1.45737	0.0470609
$960$	8.26152	0.266639
$961$	91.2281	2.94284
$962$	0	0
$963$	−11.6221	−0.374517
$964$	−37.2340	−1.19923
$965$	6.13615	0.197530
$966$	20.0951	0.646549
$967$	−2.30160	−0.0740145	−0.0370073	−	0.999315i	$-0.511782\pi$
$967$	−2.30160	−0.0740145	−0.0370073	+	0.999315i	$0.511782\pi$
$968$	−1.06935	−0.0343702
$969$	−5.07068	−0.162894
$970$	34.4450	1.10596
$971$	28.9098	0.927760	0.463880	−	0.885898i	$-0.346457\pi$
$971$	28.9098	0.927760	0.463880	+	0.885898i	$0.346457\pi$
$972$	66.4388	2.13102
$973$	−1.84411	−0.0591194
$974$	10.4515	0.334886
$975$	0	0
$976$	−31.4509	−1.00672
$977$	13.9475	0.446221	0.223111	−	0.974793i	$-0.428379\pi$
$977$	13.9475	0.446221	0.223111	+	0.974793i	$0.428379\pi$
$978$	−60.9199	−1.94800
$979$	27.7726	0.887616
$980$	−5.60172	−0.178940
$981$	25.6542	0.819075
$982$	−20.0395	−0.639487
$983$	21.0575	0.671630	0.335815	−	0.941928i	$-0.390988\pi$
$983$	21.0575	0.671630	0.335815	+	0.941928i	$0.390988\pi$
$984$	−22.3777	−0.713376
$985$	17.1298	0.545800
$986$	−1.85156	−0.0589657
$987$	−11.9345	−0.379878
$988$	0	0
$989$	34.6453	1.10166
$990$	−22.8337	−0.725701
$991$	−29.0676	−0.923364	−0.461682	−	0.887046i	$-0.652754\pi$
$991$	−29.0676	−0.923364	−0.461682	+	0.887046i	$0.652754\pi$
$992$	−15.4951	−0.491968
$993$	−13.8814	−0.440514
$994$	−6.58829	−0.208968
$995$	−28.8186	−0.913610
$996$	−38.6041	−1.22322
$997$	−17.2046	−0.544875	−0.272437	−	0.962174i	$-0.587830\pi$
$997$	−17.2046	−0.544875	−0.272437	+	0.962174i	$0.587830\pi$
$998$	−88.1541	−2.79047
$999$	26.8844	0.850586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.q.1.2	✓	12
7.6	odd	2		8281.2.a.cn.1.2		12
13.5	odd	4		1183.2.c.j.337.22		24
13.8	odd	4		1183.2.c.j.337.3		24
13.12	even	2		1183.2.a.r.1.11	yes	12
91.90	odd	2		8281.2.a.cq.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.2	✓	12	1.1	even	1	trivial
1183.2.a.r.1.11	yes	12	13.12	even	2
1183.2.c.j.337.3		24	13.8	odd	4
1183.2.c.j.337.22		24	13.5	odd	4
8281.2.a.cn.1.2		12	7.6	odd	2
8281.2.a.cq.1.11		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)

\(f(q)\)	\(=\)	\(q-2.47725 q^{2} +0.982981 q^{3} +4.13677 q^{4} -1.35413 q^{5} -2.43509 q^{6} -1.00000 q^{7} -5.29330 q^{8} -2.03375 q^{9} +O(q^{10})\)	\(q-2.47725 q^{2} +0.982981 q^{3} +4.13677 q^{4} -1.35413 q^{5} -2.43509 q^{6} -1.00000 q^{7} -5.29330 q^{8} -2.03375 q^{9} +3.35452 q^{10} +3.34694 q^{11} +4.06636 q^{12} +2.47725 q^{14} -1.33108 q^{15} +4.83930 q^{16} +0.692094 q^{17} +5.03810 q^{18} -7.45343 q^{19} -5.60172 q^{20} -0.982981 q^{21} -8.29121 q^{22} +8.25231 q^{23} -5.20321 q^{24} -3.16633 q^{25} -4.94808 q^{27} -4.13677 q^{28} +1.07995 q^{29} +3.29742 q^{30} +11.0557 q^{31} -1.40155 q^{32} +3.28998 q^{33} -1.71449 q^{34} +1.35413 q^{35} -8.41314 q^{36} -5.43331 q^{37} +18.4640 q^{38} +7.16781 q^{40} +4.30075 q^{41} +2.43509 q^{42} +4.19825 q^{43} +13.8455 q^{44} +2.75396 q^{45} -20.4430 q^{46} +12.1411 q^{47} +4.75694 q^{48} +1.00000 q^{49} +7.84380 q^{50} +0.680315 q^{51} -4.51915 q^{53} +12.2576 q^{54} -4.53219 q^{55} +5.29330 q^{56} -7.32657 q^{57} -2.67530 q^{58} +1.38180 q^{59} -5.50638 q^{60} -6.49906 q^{61} -27.3877 q^{62} +2.03375 q^{63} -6.20662 q^{64} -8.15010 q^{66} +3.86290 q^{67} +2.86303 q^{68} +8.11186 q^{69} -3.35452 q^{70} -2.65952 q^{71} +10.7652 q^{72} +10.2115 q^{73} +13.4597 q^{74} -3.11245 q^{75} -30.8331 q^{76} -3.34694 q^{77} +1.27930 q^{79} -6.55304 q^{80} +1.23738 q^{81} -10.6540 q^{82} -9.49352 q^{83} -4.06636 q^{84} -0.937185 q^{85} -10.4001 q^{86} +1.06157 q^{87} -17.7164 q^{88} +8.29790 q^{89} -6.82224 q^{90} +34.1379 q^{92} +10.8675 q^{93} -30.0765 q^{94} +10.0929 q^{95} -1.37769 q^{96} +10.2683 q^{97} -2.47725 q^{98} -6.80684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9}+O(q^{10}) \) 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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