LMFDB - Embedded newform 241.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.73684$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73684 q^{2} -2.37146 q^{3} +1.01662 q^{4} -2.63180 q^{5} -4.11885 q^{6} -2.01025 q^{7} -1.70797 q^{8} +2.62382 q^{9} +O(q^{10})$	\(q+1.73684 q^{2} -2.37146 q^{3} +1.01662 q^{4} -2.63180 q^{5} -4.11885 q^{6} -2.01025 q^{7} -1.70797 q^{8} +2.62382 q^{9} -4.57103 q^{10} -3.39618 q^{11} -2.41088 q^{12} +5.63669 q^{13} -3.49150 q^{14} +6.24122 q^{15} -4.99972 q^{16} +0.866432 q^{17} +4.55716 q^{18} +2.46437 q^{19} -2.67556 q^{20} +4.76723 q^{21} -5.89863 q^{22} -6.37847 q^{23} +4.05038 q^{24} +1.92640 q^{25} +9.79005 q^{26} +0.892104 q^{27} -2.04367 q^{28} -4.52212 q^{29} +10.8400 q^{30} -3.51511 q^{31} -5.26780 q^{32} +8.05390 q^{33} +1.50486 q^{34} +5.29060 q^{35} +2.66743 q^{36} -5.19315 q^{37} +4.28022 q^{38} -13.3672 q^{39} +4.49504 q^{40} +1.35422 q^{41} +8.27994 q^{42} +8.49015 q^{43} -3.45264 q^{44} -6.90537 q^{45} -11.0784 q^{46} -9.44537 q^{47} +11.8566 q^{48} -2.95888 q^{49} +3.34585 q^{50} -2.05471 q^{51} +5.73040 q^{52} +9.71877 q^{53} +1.54945 q^{54} +8.93808 q^{55} +3.43345 q^{56} -5.84415 q^{57} -7.85421 q^{58} +6.03110 q^{59} +6.34497 q^{60} +4.45402 q^{61} -6.10520 q^{62} -5.27454 q^{63} +0.850111 q^{64} -14.8347 q^{65} +13.9884 q^{66} -10.9216 q^{67} +0.880836 q^{68} +15.1263 q^{69} +9.18894 q^{70} -3.01063 q^{71} -4.48140 q^{72} -0.255916 q^{73} -9.01969 q^{74} -4.56837 q^{75} +2.50534 q^{76} +6.82718 q^{77} -23.2167 q^{78} -10.3262 q^{79} +13.1583 q^{80} -9.98704 q^{81} +2.35207 q^{82} -16.8148 q^{83} +4.84649 q^{84} -2.28028 q^{85} +14.7461 q^{86} +10.7240 q^{87} +5.80057 q^{88} -17.4574 q^{89} -11.9935 q^{90} -11.3312 q^{91} -6.48451 q^{92} +8.33594 q^{93} -16.4051 q^{94} -6.48574 q^{95} +12.4924 q^{96} +0.273223 q^{97} -5.13911 q^{98} -8.91095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * q^98 - 20 * 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 $

$2$	1.73684	1.22813	0.614067	−	0.789254i	$-0.289533\pi$
$2$	1.73684	1.22813	0.614067	+	0.789254i	$0.289533\pi$
$3$	−2.37146	−1.36916	−0.684581	−	0.728937i	$-0.740015\pi$
$3$	−2.37146	−1.36916	−0.684581	+	0.728937i	$0.740015\pi$
$4$	1.01662	0.508312
$5$	−2.63180	−1.17698	−0.588489	−	0.808505i	$-0.700277\pi$
$5$	−2.63180	−1.17698	−0.588489	+	0.808505i	$0.700277\pi$
$6$	−4.11885	−1.68151
$7$	−2.01025	−0.759805	−0.379902	−	0.925027i	$-0.624042\pi$
$7$	−2.01025	−0.759805	−0.379902	+	0.925027i	$0.624042\pi$
$8$	−1.70797	−0.603858
$9$	2.62382	0.874605
$10$	−4.57103	−1.44549
$11$	−3.39618	−1.02399	−0.511993	−	0.858989i	$-0.671093\pi$
$11$	−3.39618	−1.02399	−0.511993	+	0.858989i	$0.671093\pi$
$12$	−2.41088	−0.695962
$13$	5.63669	1.56334	0.781669	−	0.623694i	$-0.214369\pi$
$13$	5.63669	1.56334	0.781669	+	0.623694i	$0.214369\pi$
$14$	−3.49150	−0.933141
$15$	6.24122	1.61148
$16$	−4.99972	−1.24993
$17$	0.866432	0.210141	0.105070	−	0.994465i	$-0.466493\pi$
$17$	0.866432	0.210141	0.105070	+	0.994465i	$0.466493\pi$
$18$	4.55716	1.07413
$19$	2.46437	0.565365	0.282682	−	0.959214i	$-0.408776\pi$
$19$	2.46437	0.565365	0.282682	+	0.959214i	$0.408776\pi$
$20$	−2.67556	−0.598273
$21$	4.76723	1.04030
$22$	−5.89863	−1.25759
$23$	−6.37847	−1.33000	−0.665001	−	0.746842i	$-0.731569\pi$
$23$	−6.37847	−1.33000	−0.665001	+	0.746842i	$0.731569\pi$
$24$	4.05038	0.826780
$25$	1.92640	0.385279
$26$	9.79005	1.91999
$27$	0.892104	0.171686
$28$	−2.04367	−0.386218
$29$	−4.52212	−0.839737	−0.419868	−	0.907585i	$-0.637924\pi$
$29$	−4.52212	−0.839737	−0.419868	+	0.907585i	$0.637924\pi$
$30$	10.8400	1.97911
$31$	−3.51511	−0.631332	−0.315666	−	0.948870i	$-0.602228\pi$
$31$	−3.51511	−0.631332	−0.315666	+	0.948870i	$0.602228\pi$
$32$	−5.26780	−0.931224
$33$	8.05390	1.40200
$34$	1.50486	0.258081
$35$	5.29060	0.894274
$36$	2.66743	0.444572
$37$	−5.19315	−0.853748	−0.426874	−	0.904311i	$-0.640385\pi$
$37$	−5.19315	−0.853748	−0.426874	+	0.904311i	$0.640385\pi$
$38$	4.28022	0.694344
$39$	−13.3672	−2.14046
$40$	4.49504	0.710729
$41$	1.35422	0.211494	0.105747	−	0.994393i	$-0.466277\pi$
$41$	1.35422	0.211494	0.105747	+	0.994393i	$0.466277\pi$
$42$	8.27994	1.27762
$43$	8.49015	1.29474	0.647368	−	0.762178i	$-0.275870\pi$
$43$	8.49015	1.29474	0.647368	+	0.762178i	$0.275870\pi$
$44$	−3.45264	−0.520505
$45$	−6.90537	−1.02939
$46$	−11.0784	−1.63342
$47$	−9.44537	−1.37775	−0.688875	−	0.724880i	$-0.741895\pi$
$47$	−9.44537	−1.37775	−0.688875	+	0.724880i	$0.741895\pi$
$48$	11.8566	1.71136
$49$	−2.95888	−0.422697
$50$	3.34585	0.473174
$51$	−2.05471	−0.287717
$52$	5.73040	0.794663
$53$	9.71877	1.33498	0.667488	−	0.744620i	$-0.267369\pi$
$53$	9.71877	1.33498	0.667488	+	0.744620i	$0.267369\pi$
$54$	1.54945	0.210853
$55$	8.93808	1.20521
$56$	3.43345	0.458814
$57$	−5.84415	−0.774076
$58$	−7.85421	−1.03131
$59$	6.03110	0.785182	0.392591	−	0.919713i	$-0.371579\pi$
$59$	6.03110	0.785182	0.392591	+	0.919713i	$0.371579\pi$
$60$	6.34497	0.819132
$61$	4.45402	0.570279	0.285140	−	0.958486i	$-0.407960\pi$
$61$	4.45402	0.570279	0.285140	+	0.958486i	$0.407960\pi$
$62$	−6.10520	−0.775361
$63$	−5.27454	−0.664529
$64$	0.850111	0.106264
$65$	−14.8347	−1.84002
$66$	13.9884	1.72185
$67$	−10.9216	−1.33428	−0.667141	−	0.744932i	$-0.732482\pi$
$67$	−10.9216	−1.33428	−0.667141	+	0.744932i	$0.732482\pi$
$68$	0.880836	0.106817
$69$	15.1263	1.82099
$70$	9.18894	1.09829
$71$	−3.01063	−0.357296	−0.178648	−	0.983913i	$-0.557172\pi$
$71$	−3.01063	−0.357296	−0.178648	+	0.983913i	$0.557172\pi$
$72$	−4.48140	−0.528138
$73$	−0.255916	−0.0299527	−0.0149764	−	0.999888i	$-0.504767\pi$
$73$	−0.255916	−0.0299527	−0.0149764	+	0.999888i	$0.504767\pi$
$74$	−9.01969	−1.04852
$75$	−4.56837	−0.527510
$76$	2.50534	0.287382
$77$	6.82718	0.778030
$78$	−23.2167	−2.62877
$79$	−10.3262	−1.16179	−0.580893	−	0.813980i	$-0.697297\pi$
$79$	−10.3262	−1.16179	−0.580893	+	0.813980i	$0.697297\pi$
$80$	13.1583	1.47114
$81$	−9.98704	−1.10967
$82$	2.35207	0.259743
$83$	−16.8148	−1.84567	−0.922833	−	0.385201i	$-0.874132\pi$
$83$	−16.8148	−1.84567	−0.922833	+	0.385201i	$0.874132\pi$
$84$	4.84649	0.528795
$85$	−2.28028	−0.247331
$86$	14.7461	1.59011
$87$	10.7240	1.14974
$88$	5.80057	0.618343
$89$	−17.4574	−1.85048	−0.925241	−	0.379380i	$-0.876137\pi$
$89$	−17.4574	−1.85048	−0.925241	+	0.379380i	$0.876137\pi$
$90$	−11.9935	−1.26423
$91$	−11.3312	−1.18783
$92$	−6.48451	−0.676056
$93$	8.33594	0.864397
$94$	−16.4051	−1.69206
$95$	−6.48574	−0.665423
$96$	12.4924	1.27500
$97$	0.273223	0.0277416	0.0138708	−	0.999904i	$-0.495585\pi$
$97$	0.273223	0.0277416	0.0138708	+	0.999904i	$0.495585\pi$
$98$	−5.13911	−0.519128
$99$	−8.91095	−0.895584
$100$	1.95842	0.195842
$101$	7.47149	0.743441	0.371721	−	0.928345i	$-0.378768\pi$
$101$	7.47149	0.743441	0.371721	+	0.928345i	$0.378768\pi$
$102$	−3.56870	−0.353354
$103$	14.5145	1.43015	0.715077	−	0.699046i	$-0.246392\pi$
$103$	14.5145	1.43015	0.715077	+	0.699046i	$0.246392\pi$
$104$	−9.62730	−0.944035
$105$	−12.5464	−1.22441
$106$	16.8800	1.63953
$107$	16.7492	1.61921	0.809605	−	0.586976i	$-0.199682\pi$
$107$	16.7492	1.61921	0.809605	+	0.586976i	$0.199682\pi$
$108$	0.906935	0.0872698
$109$	−6.01965	−0.576578	−0.288289	−	0.957543i	$-0.593086\pi$
$109$	−6.01965	−0.576578	−0.288289	+	0.957543i	$0.593086\pi$
$110$	15.5240	1.48016
$111$	12.3153	1.16892
$112$	10.0507	0.949703
$113$	18.9246	1.78028	0.890139	−	0.455689i	$-0.150607\pi$
$113$	18.9246	1.78028	0.890139	+	0.455689i	$0.150607\pi$
$114$	−10.1504	−0.950669
$115$	16.7869	1.56539
$116$	−4.59730	−0.426848
$117$	14.7896	1.36730
$118$	10.4751	0.964308
$119$	−1.74175	−0.159666
$120$	−10.6598	−0.973103
$121$	0.534035	0.0485487
$122$	7.73594	0.700379
$123$	−3.21149	−0.289570
$124$	−3.57355	−0.320914
$125$	8.08912	0.723513
$126$	−9.16104	−0.816131
$127$	−13.7300	−1.21834	−0.609172	−	0.793038i	$-0.708498\pi$
$127$	−13.7300	−1.21834	−0.609172	+	0.793038i	$0.708498\pi$
$128$	12.0121	1.06173
$129$	−20.1340	−1.77270
$130$	−25.7655	−2.25978
$131$	−14.3193	−1.25108	−0.625542	−	0.780190i	$-0.715122\pi$
$131$	−14.3193	−1.25108	−0.625542	+	0.780190i	$0.715122\pi$
$132$	8.18779	0.712656
$133$	−4.95401	−0.429567
$134$	−18.9690	−1.63868
$135$	−2.34784	−0.202070
$136$	−1.47984	−0.126895
$137$	10.1743	0.869252	0.434626	−	0.900611i	$-0.356881\pi$
$137$	10.1743	0.869252	0.434626	+	0.900611i	$0.356881\pi$
$138$	26.2720	2.23642
$139$	8.00345	0.678844	0.339422	−	0.940634i	$-0.389769\pi$
$139$	8.00345	0.678844	0.339422	+	0.940634i	$0.389769\pi$
$140$	5.37855	0.454570
$141$	22.3993	1.88636
$142$	−5.22899	−0.438807
$143$	−19.1432	−1.60084
$144$	−13.1184	−1.09320
$145$	11.9013	0.988352
$146$	−0.444486	−0.0367860
$147$	7.01686	0.578741
$148$	−5.27948	−0.433971
$149$	−15.5640	−1.27505	−0.637527	−	0.770428i	$-0.720042\pi$
$149$	−15.5640	−1.27505	−0.637527	+	0.770428i	$0.720042\pi$
$150$	−7.93454	−0.647853
$151$	−2.43764	−0.198372	−0.0991862	−	0.995069i	$-0.531624\pi$
$151$	−2.43764	−0.198372	−0.0991862	+	0.995069i	$0.531624\pi$
$152$	−4.20907	−0.341400
$153$	2.27336	0.183790
$154$	11.8577	0.955524
$155$	9.25108	0.743065
$156$	−13.5894	−1.08802
$157$	12.1633	0.970735	0.485367	−	0.874310i	$-0.338686\pi$
$157$	12.1633	0.970735	0.485367	+	0.874310i	$0.338686\pi$
$158$	−17.9350	−1.42683
$159$	−23.0477	−1.82780
$160$	13.8638	1.09603
$161$	12.8223	1.01054
$162$	−17.3459	−1.36282
$163$	4.23026	0.331340	0.165670	−	0.986181i	$-0.447021\pi$
$163$	4.23026	0.331340	0.165670	+	0.986181i	$0.447021\pi$
$164$	1.37674	0.107505
$165$	−21.1963	−1.65013
$166$	−29.2047	−2.26672
$167$	14.3677	1.11181	0.555903	−	0.831247i	$-0.312372\pi$
$167$	14.3677	1.11181	0.555903	+	0.831247i	$0.312372\pi$
$168$	−8.14229	−0.628191
$169$	18.7723	1.44402
$170$	−3.96049	−0.303756
$171$	6.46605	0.494471
$172$	8.63129	0.658130
$173$	1.08253	0.0823030	0.0411515	−	0.999153i	$-0.486897\pi$
$173$	1.08253	0.0823030	0.0411515	+	0.999153i	$0.486897\pi$
$174$	18.6259	1.41203
$175$	−3.87255	−0.292737
$176$	16.9800	1.27991
$177$	−14.3025	−1.07504
$178$	−30.3208	−2.27264
$179$	−24.0238	−1.79562	−0.897810	−	0.440382i	$-0.854843\pi$
$179$	−24.0238	−1.79562	−0.897810	+	0.440382i	$0.854843\pi$
$180$	−7.02017	−0.523252
$181$	−4.72624	−0.351298	−0.175649	−	0.984453i	$-0.556202\pi$
$181$	−4.72624	−0.351298	−0.175649	+	0.984453i	$0.556202\pi$
$182$	−19.6805	−1.45882
$183$	−10.5625	−0.780805
$184$	10.8942	0.803133
$185$	13.6674	1.00484
$186$	14.4782	1.06159
$187$	−2.94256	−0.215181
$188$	−9.60239	−0.700327
$189$	−1.79336	−0.130447
$190$	−11.2647	−0.817228
$191$	−24.3499	−1.76190	−0.880948	−	0.473213i	$-0.843094\pi$
$191$	−24.3499	−1.76190	−0.880948	+	0.473213i	$0.843094\pi$
$192$	−2.01600	−0.145492
$193$	3.22480	0.232126	0.116063	−	0.993242i	$-0.462973\pi$
$193$	3.22480	0.232126	0.116063	+	0.993242i	$0.462973\pi$
$194$	0.474545	0.0340704
$195$	35.1798	2.51928
$196$	−3.00807	−0.214862
$197$	−3.60952	−0.257167	−0.128584	−	0.991699i	$-0.541043\pi$
$197$	−3.60952	−0.257167	−0.128584	+	0.991699i	$0.541043\pi$
$198$	−15.4769	−1.09990
$199$	11.6028	0.822499	0.411249	−	0.911523i	$-0.365093\pi$
$199$	11.6028	0.822499	0.411249	+	0.911523i	$0.365093\pi$
$200$	−3.29023	−0.232654
$201$	25.9000	1.82685
$202$	12.9768	0.913045
$203$	9.09061	0.638036
$204$	−2.08887	−0.146250
$205$	−3.56405	−0.248924
$206$	25.2094	1.75642
$207$	−16.7359	−1.16323
$208$	−28.1819	−1.95406
$209$	−8.36944	−0.578926
$210$	−21.7912	−1.50373
$211$	25.9439	1.78605	0.893025	−	0.450007i	$-0.148579\pi$
$211$	25.9439	1.78605	0.893025	+	0.450007i	$0.148579\pi$
$212$	9.88034	0.678585
$213$	7.13958	0.489196
$214$	29.0908	1.98861
$215$	−22.3444	−1.52388
$216$	−1.52369	−0.103674
$217$	7.06626	0.479689
$218$	−10.4552	−0.708115
$219$	0.606895	0.0410102
$220$	9.08667	0.612623
$221$	4.88381	0.328521
$222$	21.3898	1.43559
$223$	−4.40090	−0.294706	−0.147353	−	0.989084i	$-0.547075\pi$
$223$	−4.40090	−0.294706	−0.147353	+	0.989084i	$0.547075\pi$
$224$	10.5896	0.707548
$225$	5.05451	0.336967
$226$	32.8691	2.18642
$227$	−23.0781	−1.53175	−0.765873	−	0.642991i	$-0.777693\pi$
$227$	−23.0781	−1.53175	−0.765873	+	0.642991i	$0.777693\pi$
$228$	−5.94130	−0.393472
$229$	3.21172	0.212236	0.106118	−	0.994354i	$-0.466158\pi$
$229$	3.21172	0.212236	0.106118	+	0.994354i	$0.466158\pi$
$230$	29.1562	1.92250
$231$	−16.1904	−1.06525
$232$	7.72364	0.507082
$233$	7.13210	0.467239	0.233620	−	0.972328i	$-0.424943\pi$
$233$	7.13210	0.467239	0.233620	+	0.972328i	$0.424943\pi$
$234$	25.6873	1.67923
$235$	24.8584	1.62158
$236$	6.13136	0.399117
$237$	24.4881	1.59067
$238$	−3.02514	−0.196091
$239$	3.66241	0.236902	0.118451	−	0.992960i	$-0.462207\pi$
$239$	3.66241	0.236902	0.118451	+	0.992960i	$0.462207\pi$
$240$	−31.2044	−2.01423
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	0.927536	0.0596243
$243$	21.0075	1.34763
$244$	4.52807	0.289880
$245$	7.78719	0.497506
$246$	−5.57785	−0.355630
$247$	13.8909	0.883856
$248$	6.00370	0.381235
$249$	39.8756	2.52702
$250$	14.0495	0.888571
$251$	1.41613	0.0893854	0.0446927	−	0.999001i	$-0.485769\pi$
$251$	1.41613	0.0893854	0.0446927	+	0.999001i	$0.485769\pi$
$252$	−5.36222	−0.337788
$253$	21.6624	1.36190
$254$	−23.8469	−1.49629
$255$	5.40759	0.338636
$256$	19.1629	1.19768
$257$	−11.0690	−0.690466	−0.345233	−	0.938517i	$-0.612200\pi$
$257$	−11.0690	−0.690466	−0.345233	+	0.938517i	$0.612200\pi$
$258$	−34.9697	−2.17712
$259$	10.4395	0.648682
$260$	−15.0813	−0.935302
$261$	−11.8652	−0.734438
$262$	−24.8704	−1.53650
$263$	−3.31569	−0.204454	−0.102227	−	0.994761i	$-0.532597\pi$
$263$	−3.31569	−0.204454	−0.102227	+	0.994761i	$0.532597\pi$
$264$	−13.7558	−0.846612
$265$	−25.5779	−1.57124
$266$	−8.60433	−0.527565
$267$	41.3995	2.53361
$268$	−11.1031	−0.678231
$269$	−14.3455	−0.874663	−0.437332	−	0.899300i	$-0.644076\pi$
$269$	−14.3455	−0.874663	−0.437332	+	0.899300i	$0.644076\pi$
$270$	−4.07784	−0.248169
$271$	−1.55240	−0.0943014	−0.0471507	−	0.998888i	$-0.515014\pi$
$271$	−1.55240	−0.0943014	−0.0471507	+	0.998888i	$0.515014\pi$
$272$	−4.33192	−0.262661
$273$	26.8714	1.62633
$274$	17.6712	1.06756
$275$	−6.54239	−0.394521
$276$	15.3777	0.925631
$277$	18.0089	1.08205	0.541024	−	0.841007i	$-0.318037\pi$
$277$	18.0089	1.08205	0.541024	+	0.841007i	$0.318037\pi$
$278$	13.9007	0.833711
$279$	−9.22300	−0.552167
$280$	−9.03618	−0.540015
$281$	−11.5476	−0.688873	−0.344436	−	0.938810i	$-0.611930\pi$
$281$	−11.5476	−0.688873	−0.344436	+	0.938810i	$0.611930\pi$
$282$	38.9041	2.31671
$283$	−1.84755	−0.109825	−0.0549126	−	0.998491i	$-0.517488\pi$
$283$	−1.84755	−0.109825	−0.0549126	+	0.998491i	$0.517488\pi$
$284$	−3.06068	−0.181618
$285$	15.3807	0.911071
$286$	−33.2488	−1.96604
$287$	−2.72233	−0.160694
$288$	−13.8217	−0.814453
$289$	−16.2493	−0.955841
$290$	20.6708	1.21383
$291$	−0.647937	−0.0379827
$292$	−0.260171	−0.0152253
$293$	−3.03213	−0.177139	−0.0885694	−	0.996070i	$-0.528229\pi$
$293$	−3.03213	−0.177139	−0.0885694	+	0.996070i	$0.528229\pi$
$294$	12.1872	0.710771
$295$	−15.8727	−0.924143
$296$	8.86974	0.515543
$297$	−3.02975	−0.175804
$298$	−27.0322	−1.56594
$299$	−35.9535	−2.07924
$300$	−4.64431	−0.268140
$301$	−17.0674	−0.983746
$302$	−4.23380	−0.243628
$303$	−17.7183	−1.01789
$304$	−12.3212	−0.706667
$305$	−11.7221	−0.671207
$306$	3.94847	0.225719
$307$	8.40693	0.479809	0.239905	−	0.970796i	$-0.422884\pi$
$307$	8.40693	0.479809	0.239905	+	0.970796i	$0.422884\pi$
$308$	6.94068	0.395482
$309$	−34.4205	−1.95811
$310$	16.0677	0.912583
$311$	2.94070	0.166752	0.0833759	−	0.996518i	$-0.473430\pi$
$311$	2.94070	0.166752	0.0833759	+	0.996518i	$0.473430\pi$
$312$	22.8307	1.29254
$313$	16.5110	0.933258	0.466629	−	0.884453i	$-0.345468\pi$
$313$	16.5110	0.933258	0.466629	+	0.884453i	$0.345468\pi$
$314$	21.1257	1.19219
$315$	13.8816	0.782137
$316$	−10.4978	−0.590550
$317$	−20.3799	−1.14465	−0.572325	−	0.820027i	$-0.693959\pi$
$317$	−20.3799	−1.14465	−0.572325	+	0.820027i	$0.693959\pi$
$318$	−40.0302	−2.24478
$319$	15.3579	0.859879
$320$	−2.23733	−0.125070
$321$	−39.7201	−2.21696
$322$	22.2704	1.24108
$323$	2.13521	0.118806
$324$	−10.1531	−0.564059
$325$	10.8585	0.602322
$326$	7.34731	0.406930
$327$	14.2754	0.789429
$328$	−2.31297	−0.127713
$329$	18.9876	1.04682
$330$	−36.8146	−2.02658
$331$	9.08522	0.499369	0.249684	−	0.968327i	$-0.419673\pi$
$331$	9.08522	0.499369	0.249684	+	0.968327i	$0.419673\pi$
$332$	−17.0943	−0.938174
$333$	−13.6259	−0.746693
$334$	24.9545	1.36545
$335$	28.7434	1.57042
$336$	−23.8349	−1.30030
$337$	−34.1864	−1.86225	−0.931125	−	0.364700i	$-0.881171\pi$
$337$	−34.1864	−1.86225	−0.931125	+	0.364700i	$0.881171\pi$
$338$	32.6046	1.77345
$339$	−44.8789	−2.43749
$340$	−2.31819	−0.125721
$341$	11.9379	0.646476
$342$	11.2305	0.607277
$343$	20.0199	1.08097
$344$	−14.5009	−0.781837
$345$	−39.8094	−2.14327
$346$	1.88018	0.101079
$347$	−9.13414	−0.490346	−0.245173	−	0.969479i	$-0.578845\pi$
$347$	−9.13414	−0.490346	−0.245173	+	0.969479i	$0.578845\pi$
$348$	10.9023	0.584425
$349$	−20.3980	−1.09188	−0.545940	−	0.837824i	$-0.683827\pi$
$349$	−20.3980	−1.09188	−0.545940	+	0.837824i	$0.683827\pi$
$350$	−6.72601	−0.359520
$351$	5.02852	0.268402
$352$	17.8904	0.953561
$353$	13.2353	0.704444	0.352222	−	0.935916i	$-0.385426\pi$
$353$	13.2353	0.704444	0.352222	+	0.935916i	$0.385426\pi$
$354$	−24.8412	−1.32029
$355$	7.92339	0.420530
$356$	−17.7476	−0.940622
$357$	4.13048	0.218608
$358$	−41.7255	−2.20526
$359$	35.7474	1.88668	0.943339	−	0.331831i	$-0.107666\pi$
$359$	35.7474	1.88668	0.943339	+	0.331831i	$0.107666\pi$
$360$	11.7942	0.621607
$361$	−12.9269	−0.680363
$362$	−8.20873	−0.431441
$363$	−1.26644	−0.0664710
$364$	−11.5196	−0.603789
$365$	0.673522	0.0352537
$366$	−18.3455	−0.958933
$367$	−34.7219	−1.81247	−0.906234	−	0.422777i	$-0.861055\pi$
$367$	−34.7219	−1.81247	−0.906234	+	0.422777i	$0.861055\pi$
$368$	31.8906	1.66241
$369$	3.55323	0.184974
$370$	23.7381	1.23408
$371$	−19.5372	−1.01432
$372$	8.47452	0.439383
$373$	−34.9987	−1.81217	−0.906083	−	0.423100i	$-0.860942\pi$
$373$	−34.9987	−1.81217	−0.906083	+	0.423100i	$0.860942\pi$
$374$	−5.11076	−0.264271
$375$	−19.1830	−0.990607
$376$	16.1324	0.831966
$377$	−25.4898	−1.31279
$378$	−3.11478	−0.160207
$379$	17.4032	0.893943	0.446972	−	0.894548i	$-0.352502\pi$
$379$	17.4032	0.893943	0.446972	+	0.894548i	$0.352502\pi$
$380$	−6.59356	−0.338242
$381$	32.5602	1.66811
$382$	−42.2919	−2.16384
$383$	7.58514	0.387582	0.193791	−	0.981043i	$-0.437922\pi$
$383$	7.58514	0.387582	0.193791	+	0.981043i	$0.437922\pi$
$384$	−28.4862	−1.45368
$385$	−17.9678	−0.915725
$386$	5.60097	0.285082
$387$	22.2766	1.13238
$388$	0.277765	0.0141014
$389$	−9.68216	−0.490905	−0.245452	−	0.969409i	$-0.578937\pi$
$389$	−9.68216	−0.490905	−0.245452	+	0.969409i	$0.578937\pi$
$390$	61.1018	3.09401
$391$	−5.52651	−0.279488
$392$	5.05368	0.255249
$393$	33.9577	1.71294
$394$	−6.26917	−0.315836
$395$	27.1765	1.36740
$396$	−9.05909	−0.455236
$397$	−8.54563	−0.428893	−0.214446	−	0.976736i	$-0.568795\pi$
$397$	−8.54563	−0.428893	−0.214446	+	0.976736i	$0.568795\pi$
$398$	20.1522	1.01014
$399$	11.7482	0.588147
$400$	−9.63145	−0.481573
$401$	23.0124	1.14918	0.574592	−	0.818440i	$-0.305161\pi$
$401$	23.0124	1.14918	0.574592	+	0.818440i	$0.305161\pi$
$402$	44.9843	2.24361
$403$	−19.8136	−0.986986
$404$	7.59570	0.377900
$405$	26.2839	1.30606
$406$	15.7890	0.783593
$407$	17.6369	0.874227
$408$	3.50938	0.173740
$409$	−24.2236	−1.19778	−0.598891	−	0.800831i	$-0.704392\pi$
$409$	−24.2236	−1.19778	−0.598891	+	0.800831i	$0.704392\pi$
$410$	−6.19020	−0.305712
$411$	−24.1280	−1.19015
$412$	14.7558	0.726965
$413$	−12.1240	−0.596585
$414$	−29.0677	−1.42860
$415$	44.2533	2.17231
$416$	−29.6930	−1.45582
$417$	−18.9799	−0.929448
$418$	−14.5364	−0.710999
$419$	27.7565	1.35600	0.677998	−	0.735064i	$-0.262848\pi$
$419$	27.7565	1.35600	0.677998	+	0.735064i	$0.262848\pi$
$420$	−12.7550	−0.622380
$421$	−33.1205	−1.61420	−0.807098	−	0.590418i	$-0.798963\pi$
$421$	−33.1205	−1.61420	−0.807098	+	0.590418i	$0.798963\pi$
$422$	45.0604	2.19351
$423$	−24.7829	−1.20499
$424$	−16.5994	−0.806137
$425$	1.66909	0.0809628
$426$	12.4003	0.600798
$427$	−8.95372	−0.433301
$428$	17.0277	0.823064
$429$	45.3974	2.19181
$430$	−38.8087	−1.87152
$431$	−5.07371	−0.244392	−0.122196	−	0.992506i	$-0.538994\pi$
$431$	−5.07371	−0.244392	−0.122196	+	0.992506i	$0.538994\pi$
$432$	−4.46027	−0.214595
$433$	11.6416	0.559457	0.279729	−	0.960079i	$-0.409755\pi$
$433$	11.6416	0.559457	0.279729	+	0.960079i	$0.409755\pi$
$434$	12.2730	0.589122
$435$	−28.2235	−1.35321
$436$	−6.11973	−0.293082
$437$	−15.7189	−0.751937
$438$	1.05408	0.0503660
$439$	−14.7945	−0.706105	−0.353052	−	0.935604i	$-0.614856\pi$
$439$	−14.7945	−0.706105	−0.353052	+	0.935604i	$0.614856\pi$
$440$	−15.2660	−0.727777
$441$	−7.76356	−0.369693
$442$	8.48241	0.403467
$443$	−2.54544	−0.120937	−0.0604687	−	0.998170i	$-0.519260\pi$
$443$	−2.54544	−0.120937	−0.0604687	+	0.998170i	$0.519260\pi$
$444$	12.5201	0.594176
$445$	45.9445	2.17798
$446$	−7.64367	−0.361938
$447$	36.9094	1.74575
$448$	−1.70894	−0.0807398
$449$	−13.1558	−0.620860	−0.310430	−	0.950596i	$-0.600473\pi$
$449$	−13.1558	−0.620860	−0.310430	+	0.950596i	$0.600473\pi$
$450$	8.77889	0.413841
$451$	−4.59919	−0.216567
$452$	19.2392	0.904937
$453$	5.78077	0.271604
$454$	−40.0830	−1.88119
$455$	29.8215	1.39805
$456$	9.98163	0.467432
$457$	5.54809	0.259528	0.129764	−	0.991545i	$-0.458578\pi$
$457$	5.54809	0.259528	0.129764	+	0.991545i	$0.458578\pi$
$458$	5.57825	0.260655
$459$	0.772948	0.0360781
$460$	17.0660	0.795704
$461$	−32.2282	−1.50102	−0.750508	−	0.660861i	$-0.770191\pi$
$461$	−32.2282	−1.50102	−0.750508	+	0.660861i	$0.770191\pi$
$462$	−28.1202	−1.30827
$463$	−18.5042	−0.859965	−0.429983	−	0.902837i	$-0.641480\pi$
$463$	−18.5042	−0.859965	−0.429983	+	0.902837i	$0.641480\pi$
$464$	22.6094	1.04961
$465$	−21.9386	−1.01738
$466$	12.3873	0.573832
$467$	20.9192	0.968026	0.484013	−	0.875061i	$-0.339179\pi$
$467$	20.9192	0.968026	0.484013	+	0.875061i	$0.339179\pi$
$468$	15.0355	0.695017
$469$	21.9551	1.01379
$470$	43.1751	1.99152
$471$	−28.8447	−1.32909
$472$	−10.3009	−0.474139
$473$	−28.8341	−1.32579
$474$	42.5320	1.95356
$475$	4.74735	0.217823
$476$	−1.77070	−0.0811600
$477$	25.5003	1.16758
$478$	6.36103	0.290947
$479$	−9.86001	−0.450515	−0.225258	−	0.974299i	$-0.572322\pi$
$479$	−9.86001	−0.450515	−0.225258	+	0.974299i	$0.572322\pi$
$480$	−32.8775	−1.50064
$481$	−29.2722	−1.33470
$482$	−1.73684	−0.0791110
$483$	−30.4077	−1.38360
$484$	0.542913	0.0246779
$485$	−0.719069	−0.0326512
$486$	36.4868	1.65507
$487$	−25.9290	−1.17496	−0.587478	−	0.809240i	$-0.699879\pi$
$487$	−25.9290	−1.17496	−0.587478	+	0.809240i	$0.699879\pi$
$488$	−7.60734	−0.344368
$489$	−10.0319	−0.453658
$490$	13.5251	0.611003
$491$	−22.5594	−1.01809	−0.509046	−	0.860739i	$-0.670002\pi$
$491$	−22.5594	−1.01809	−0.509046	+	0.860739i	$0.670002\pi$
$492$	−3.26487	−0.147192
$493$	−3.91811	−0.176463
$494$	24.1263	1.08549
$495$	23.4519	1.05408
$496$	17.5746	0.789122
$497$	6.05213	0.271475
$498$	69.2577	3.10351
$499$	39.8682	1.78475	0.892373	−	0.451298i	$-0.149039\pi$
$499$	39.8682	1.78475	0.892373	+	0.451298i	$0.149039\pi$
$500$	8.22360	0.367771
$501$	−34.0724	−1.52224
$502$	2.45960	0.109777
$503$	−19.7008	−0.878416	−0.439208	−	0.898386i	$-0.644741\pi$
$503$	−19.7008	−0.878416	−0.439208	+	0.898386i	$0.644741\pi$
$504$	9.00875	0.401282
$505$	−19.6635	−0.875015
$506$	37.6242	1.67260
$507$	−44.5178	−1.97710
$508$	−13.9583	−0.619298
$509$	−23.4312	−1.03857	−0.519284	−	0.854602i	$-0.673801\pi$
$509$	−23.4312	−1.03857	−0.519284	+	0.854602i	$0.673801\pi$
$510$	9.39213	0.415891
$511$	0.514457	0.0227582
$512$	9.25877	0.409184
$513$	2.19847	0.0970650
$514$	−19.2251	−0.847985
$515$	−38.1993	−1.68326
$516$	−20.4687	−0.901086
$517$	32.0782	1.41080
$518$	18.1319	0.796668
$519$	−2.56717	−0.112686
$520$	25.3372	1.11111
$521$	−5.76181	−0.252430	−0.126215	−	0.992003i	$-0.540283\pi$
$521$	−5.76181	−0.252430	−0.126215	+	0.992003i	$0.540283\pi$
$522$	−20.6080	−0.901988
$523$	42.0766	1.83988	0.919942	−	0.392056i	$-0.128236\pi$
$523$	42.0766	1.83988	0.919942	+	0.392056i	$0.128236\pi$
$524$	−14.5574	−0.635941
$525$	9.18358	0.400804
$526$	−5.75883	−0.251097
$527$	−3.04560	−0.132669
$528$	−40.2673	−1.75241
$529$	17.6849	0.768907
$530$	−44.4248	−1.92969
$531$	15.8245	0.686724
$532$	−5.03636	−0.218354
$533$	7.63334	0.330637
$534$	71.9045	3.11161
$535$	−44.0807	−1.90578
$536$	18.6537	0.805717
$537$	56.9714	2.45850
$538$	−24.9160	−1.07420
$539$	10.0489	0.432836
$540$	−2.38688	−0.102715
$541$	7.25557	0.311941	0.155971	−	0.987762i	$-0.450149\pi$
$541$	7.25557	0.311941	0.155971	+	0.987762i	$0.450149\pi$
$542$	−2.69627	−0.115815
$543$	11.2081	0.480984
$544$	−4.56419	−0.195688
$545$	15.8426	0.678620
$546$	46.6715	1.99735
$547$	−27.6574	−1.18254	−0.591272	−	0.806472i	$-0.701374\pi$
$547$	−27.6574	−1.18254	−0.591272	+	0.806472i	$0.701374\pi$
$548$	10.3435	0.441851
$549$	11.6865	0.498769
$550$	−11.3631	−0.484524
$551$	−11.1442	−0.474758
$552$	−25.8352	−1.09962
$553$	20.7582	0.882730
$554$	31.2786	1.32890
$555$	−32.4116	−1.37579
$556$	8.13650	0.345065
$557$	26.7523	1.13353	0.566766	−	0.823878i	$-0.308194\pi$
$557$	26.7523	1.13353	0.566766	+	0.823878i	$0.308194\pi$
$558$	−16.0189	−0.678135
$559$	47.8564	2.02411
$560$	−26.4515	−1.11778
$561$	6.97816	0.294618
$562$	−20.0564	−0.846028
$563$	20.2482	0.853362	0.426681	−	0.904402i	$-0.359683\pi$
$563$	20.2482	0.853362	0.426681	+	0.904402i	$0.359683\pi$
$564$	22.7717	0.958861
$565$	−49.8059	−2.09535
$566$	−3.20890	−0.134880
$567$	20.0765	0.843133
$568$	5.14206	0.215756
$569$	41.1274	1.72415	0.862076	−	0.506779i	$-0.169164\pi$
$569$	41.1274	1.72415	0.862076	+	0.506779i	$0.169164\pi$
$570$	26.7138	1.11892
$571$	25.2419	1.05634	0.528170	−	0.849139i	$-0.322878\pi$
$571$	25.2419	1.05634	0.528170	+	0.849139i	$0.322878\pi$
$572$	−19.4615	−0.813725
$573$	57.7448	2.41232
$574$	−4.72827	−0.197354
$575$	−12.2875	−0.512423
$576$	2.23054	0.0929390
$577$	4.90936	0.204379	0.102190	−	0.994765i	$-0.467415\pi$
$577$	4.90936	0.204379	0.102190	+	0.994765i	$0.467415\pi$
$578$	−28.2225	−1.17390
$579$	−7.64748	−0.317818
$580$	12.0992	0.502391
$581$	33.8020	1.40234
$582$	−1.12536	−0.0466479
$583$	−33.0067	−1.36700
$584$	0.437097	0.0180872
$585$	−38.9235	−1.60929
$586$	−5.26633	−0.217550
$587$	0.733495	0.0302746	0.0151373	−	0.999885i	$-0.495181\pi$
$587$	0.733495	0.0302746	0.0151373	+	0.999885i	$0.495181\pi$
$588$	7.13351	0.294181
$589$	−8.66253	−0.356933
$590$	−27.5683	−1.13497
$591$	8.55982	0.352104
$592$	25.9643	1.06713
$593$	43.2540	1.77623	0.888115	−	0.459621i	$-0.152015\pi$
$593$	43.2540	1.77623	0.888115	+	0.459621i	$0.152015\pi$
$594$	−5.26219	−0.215910
$595$	4.58394	0.187923
$596$	−15.8227	−0.648125
$597$	−27.5155	−1.12613
$598$	−62.4455	−2.55359
$599$	−21.1031	−0.862251	−0.431126	−	0.902292i	$-0.641883\pi$
$599$	−21.1031	−0.862251	−0.431126	+	0.902292i	$0.641883\pi$
$600$	7.80264	0.318541
$601$	−16.1436	−0.658512	−0.329256	−	0.944241i	$-0.606798\pi$
$601$	−16.1436	−0.658512	−0.329256	+	0.944241i	$0.606798\pi$
$602$	−29.6433	−1.20817
$603$	−28.6562	−1.16697
$604$	−2.47816	−0.100835
$605$	−1.40548	−0.0571408
$606$	−30.7740	−1.25011
$607$	−32.2628	−1.30951	−0.654753	−	0.755843i	$-0.727227\pi$
$607$	−32.2628	−1.30951	−0.654753	+	0.755843i	$0.727227\pi$
$608$	−12.9818	−0.526481
$609$	−21.5580	−0.873574
$610$	−20.3595	−0.824331
$611$	−53.2407	−2.15389
$612$	2.31115	0.0934227
$613$	−44.6321	−1.80267	−0.901337	−	0.433119i	$-0.857413\pi$
$613$	−44.6321	−1.80267	−0.901337	+	0.433119i	$0.857413\pi$
$614$	14.6015	0.589270
$615$	8.45200	0.340818
$616$	−11.6606	−0.469820
$617$	20.2532	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$617$	20.2532	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$618$	−59.7830	−2.40482
$619$	23.9533	0.962766	0.481383	−	0.876510i	$-0.340135\pi$
$619$	23.9533	0.962766	0.481383	+	0.876510i	$0.340135\pi$
$620$	9.40488	0.377709
$621$	−5.69026	−0.228342
$622$	5.10754	0.204794
$623$	35.0938	1.40600
$624$	66.8322	2.67543
$625$	−30.9210	−1.23684
$626$	28.6770	1.14617
$627$	19.8478	0.792644
$628$	12.3655	0.493436
$629$	−4.49951	−0.179407
$630$	24.1101	0.960568
$631$	−3.46481	−0.137932	−0.0689659	−	0.997619i	$-0.521970\pi$
$631$	−3.46481	−0.137932	−0.0689659	+	0.997619i	$0.521970\pi$
$632$	17.6368	0.701554
$633$	−61.5248	−2.44539
$634$	−35.3967	−1.40578
$635$	36.1348	1.43396
$636$	−23.4308	−0.929092
$637$	−16.6783	−0.660818
$638$	26.6743	1.05605
$639$	−7.89934	−0.312493
$640$	−31.6135	−1.24963
$641$	−28.9401	−1.14307	−0.571533	−	0.820579i	$-0.693651\pi$
$641$	−28.9401	−1.14307	−0.571533	+	0.820579i	$0.693651\pi$
$642$	−68.9876	−2.72272
$643$	18.6657	0.736103	0.368052	−	0.929805i	$-0.380025\pi$
$643$	18.6657	0.736103	0.368052	+	0.929805i	$0.380025\pi$
$644$	13.0355	0.513671
$645$	52.9888	2.08643
$646$	3.70852	0.145910
$647$	24.6633	0.969615	0.484808	−	0.874621i	$-0.338890\pi$
$647$	24.6633	0.969615	0.484808	+	0.874621i	$0.338890\pi$
$648$	17.0576	0.670084
$649$	−20.4827	−0.804016
$650$	18.8595	0.739731
$651$	−16.7574	−0.656772
$652$	4.30059	0.168424
$653$	12.4942	0.488937	0.244469	−	0.969657i	$-0.421386\pi$
$653$	12.4942	0.488937	0.244469	+	0.969657i	$0.421386\pi$
$654$	24.7941	0.969525
$655$	37.6856	1.47250
$656$	−6.77074	−0.264353
$657$	−0.671477	−0.0261968
$658$	32.9785	1.28564
$659$	34.3869	1.33952	0.669762	−	0.742576i	$-0.266396\pi$
$659$	34.3869	1.33952	0.669762	+	0.742576i	$0.266396\pi$
$660$	−21.5487	−0.838781
$661$	19.4957	0.758295	0.379147	−	0.925336i	$-0.376217\pi$
$661$	19.4957	0.758295	0.379147	+	0.925336i	$0.376217\pi$
$662$	15.7796	0.613292
$663$	−11.5818	−0.449798
$664$	28.7192	1.11452
$665$	13.0380	0.505591
$666$	−23.6660	−0.917039
$667$	28.8442	1.11685
$668$	14.6066	0.565145
$669$	10.4365	0.403500
$670$	49.9228	1.92869
$671$	−15.1267	−0.583958
$672$	−25.1128	−0.968748
$673$	−26.1090	−1.00643	−0.503215	−	0.864161i	$-0.667850\pi$
$673$	−26.1090	−1.00643	−0.503215	+	0.864161i	$0.667850\pi$
$674$	−59.3764	−2.28709
$675$	1.71855	0.0661469
$676$	19.0844	0.734015
$677$	−20.5707	−0.790597	−0.395298	−	0.918553i	$-0.629359\pi$
$677$	−20.5707	−0.790597	−0.395298	+	0.918553i	$0.629359\pi$
$678$	−77.9477	−2.99356
$679$	−0.549247	−0.0210782
$680$	3.89465	0.149353
$681$	54.7287	2.09721
$682$	20.7343	0.793959
$683$	23.7002	0.906864	0.453432	−	0.891291i	$-0.350199\pi$
$683$	23.7002	0.906864	0.453432	+	0.891291i	$0.350199\pi$
$684$	6.57354	0.251346
$685$	−26.7768	−1.02309
$686$	34.7714	1.32758
$687$	−7.61646	−0.290586
$688$	−42.4484	−1.61833
$689$	54.7818	2.08702
$690$	−69.1427	−2.63222
$691$	−7.36209	−0.280067	−0.140034	−	0.990147i	$-0.544721\pi$
$691$	−7.36209	−0.280067	−0.140034	+	0.990147i	$0.544721\pi$
$692$	1.10052	0.0418356
$693$	17.9133	0.680469
$694$	−15.8646	−0.602211
$695$	−21.0635	−0.798985
$696$	−18.3163	−0.694278
$697$	1.17334	0.0444435
$698$	−35.4282	−1.34098
$699$	−16.9135	−0.639727
$700$	−3.93692	−0.148802
$701$	−28.4805	−1.07569	−0.537846	−	0.843043i	$-0.680762\pi$
$701$	−28.4805	−1.07569	−0.537846	+	0.843043i	$0.680762\pi$
$702$	8.73375	0.329634
$703$	−12.7978	−0.482679
$704$	−2.88713	−0.108813
$705$	−58.9506	−2.22021
$706$	22.9876	0.865151
$707$	−15.0196	−0.564870
$708$	−14.5403	−0.546457
$709$	32.8736	1.23459	0.617297	−	0.786730i	$-0.288228\pi$
$709$	32.8736	1.23459	0.617297	+	0.786730i	$0.288228\pi$
$710$	13.7617	0.516467
$711$	−27.0940	−1.01610
$712$	29.8167	1.11743
$713$	22.4210	0.839674
$714$	7.17400	0.268480
$715$	50.3812	1.88415
$716$	−24.4231	−0.912736
$717$	−8.68526	−0.324357
$718$	62.0877	2.31709
$719$	−13.3988	−0.499690	−0.249845	−	0.968286i	$-0.580380\pi$
$719$	−13.3988	−0.499690	−0.249845	+	0.968286i	$0.580380\pi$
$720$	34.5250	1.28667
$721$	−29.1778	−1.08664
$722$	−22.4520	−0.835576
$723$	2.37146	0.0881955
$724$	−4.80481	−0.178569
$725$	−8.71140	−0.323533
$726$	−2.19961	−0.0816353
$727$	24.5791	0.911587	0.455793	−	0.890086i	$-0.349356\pi$
$727$	24.5791	0.911587	0.455793	+	0.890086i	$0.349356\pi$
$728$	19.3533	0.717282
$729$	−19.8574	−0.735459
$730$	1.16980	0.0432963
$731$	7.35613	0.272076
$732$	−10.7381	−0.396893
$733$	2.08207	0.0769029	0.0384515	−	0.999260i	$-0.487758\pi$
$733$	2.08207	0.0769029	0.0384515	+	0.999260i	$0.487758\pi$
$734$	−60.3065	−2.22595
$735$	−18.4670	−0.681166
$736$	33.6005	1.23853
$737$	37.0916	1.36629
$738$	6.17141	0.227173
$739$	−46.1104	−1.69620	−0.848099	−	0.529838i	$-0.822253\pi$
$739$	−46.1104	−1.69620	−0.848099	+	0.529838i	$0.822253\pi$
$740$	13.8946	0.510774
$741$	−32.9417	−1.21014
$742$	−33.9331	−1.24572
$743$	16.5456	0.606998	0.303499	−	0.952832i	$-0.401845\pi$
$743$	16.5456	0.606998	0.303499	+	0.952832i	$0.401845\pi$
$744$	−14.2375	−0.521973
$745$	40.9614	1.50071
$746$	−60.7873	−2.22558
$747$	−44.1190	−1.61423
$748$	−2.99148	−0.109379
$749$	−33.6702	−1.23028
$750$	−33.3179	−1.21660
$751$	36.4121	1.32870	0.664349	−	0.747423i	$-0.268709\pi$
$751$	36.4121	1.32870	0.664349	+	0.747423i	$0.268709\pi$
$752$	47.2243	1.72209
$753$	−3.35830	−0.122383
$754$	−44.2718	−1.61228
$755$	6.41540	0.233480
$756$	−1.82317	−0.0663080
$757$	16.3953	0.595898	0.297949	−	0.954582i	$-0.403697\pi$
$757$	16.3953	0.595898	0.297949	+	0.954582i	$0.403697\pi$
$758$	30.2267	1.09788
$759$	−51.3715	−1.86467
$760$	11.0774	0.401821
$761$	44.2450	1.60388	0.801940	−	0.597404i	$-0.203801\pi$
$761$	44.2450	1.60388	0.801940	+	0.597404i	$0.203801\pi$
$762$	56.5520	2.04866
$763$	12.1010	0.438087
$764$	−24.7547	−0.895593
$765$	−5.98303	−0.216317
$766$	13.1742	0.476003
$767$	33.9954	1.22750
$768$	−45.4441	−1.63982
$769$	−21.3439	−0.769680	−0.384840	−	0.922983i	$-0.625743\pi$
$769$	−21.3439	−0.769680	−0.384840	+	0.922983i	$0.625743\pi$
$770$	−31.2073	−1.12463
$771$	26.2497	0.945360
$772$	3.27841	0.117993
$773$	20.7861	0.747623	0.373812	−	0.927505i	$-0.378051\pi$
$773$	20.7861	0.747623	0.373812	+	0.927505i	$0.378051\pi$
$774$	38.6909	1.39072
$775$	−6.77150	−0.243239
$776$	−0.466656	−0.0167520
$777$	−24.7570	−0.888151
$778$	−16.8164	−0.602897
$779$	3.33731	0.119571
$780$	35.7647	1.28058
$781$	10.2246	0.365866
$782$	−9.59868	−0.343248
$783$	−4.03420	−0.144171
$784$	14.7936	0.528342
$785$	−32.0114	−1.14253
$786$	58.9791	2.10372
$787$	−28.9072	−1.03043	−0.515215	−	0.857061i	$-0.672288\pi$
$787$	−28.9072	−1.03043	−0.515215	+	0.857061i	$0.672288\pi$
$788$	−3.66952	−0.130721
$789$	7.86302	0.279931
$790$	47.2013	1.67935
$791$	−38.0433	−1.35266
$792$	15.2196	0.540806
$793$	25.1060	0.891539
$794$	−14.8424	−0.526738
$795$	60.6570	2.15128
$796$	11.7957	0.418086
$797$	21.6563	0.767106	0.383553	−	0.923519i	$-0.374700\pi$
$797$	21.6563	0.767106	0.383553	+	0.923519i	$0.374700\pi$
$798$	20.4048	0.722323
$799$	−8.18377	−0.289521
$800$	−10.1479	−0.358781
$801$	−45.8050	−1.61844
$802$	39.9689	1.41135
$803$	0.869138	0.0306712
$804$	26.3306	0.928609
$805$	−33.7459	−1.18939
$806$	−34.4131	−1.21215
$807$	34.0199	1.19756
$808$	−12.7611	−0.448933
$809$	4.12546	0.145043	0.0725217	−	0.997367i	$-0.476895\pi$
$809$	4.12546	0.145043	0.0725217	+	0.997367i	$0.476895\pi$
$810$	45.6511	1.60402
$811$	−27.4598	−0.964243	−0.482121	−	0.876104i	$-0.660134\pi$
$811$	−27.4598	−0.964243	−0.482121	+	0.876104i	$0.660134\pi$
$812$	9.24173	0.324321
$813$	3.68145	0.129114
$814$	30.6325	1.07367
$815$	−11.1332	−0.389980
$816$	10.2730	0.359626
$817$	20.9228	0.731998
$818$	−42.0726	−1.47104
$819$	−29.7309	−1.03888
$820$	−3.62330	−0.126531
$821$	26.7943	0.935127	0.467564	−	0.883959i	$-0.345132\pi$
$821$	26.7943	0.935127	0.467564	+	0.883959i	$0.345132\pi$
$822$	−41.9066	−1.46166
$823$	29.5890	1.03141	0.515704	−	0.856767i	$-0.327531\pi$
$823$	29.5890	1.03141	0.515704	+	0.856767i	$0.327531\pi$
$824$	−24.7903	−0.863611
$825$	15.5150	0.540163
$826$	−21.0575	−0.732686
$827$	−41.2969	−1.43603	−0.718017	−	0.696025i	$-0.754950\pi$
$827$	−41.2969	−1.43603	−0.718017	+	0.696025i	$0.754950\pi$
$828$	−17.0142	−0.591283
$829$	−3.90138	−0.135501	−0.0677503	−	0.997702i	$-0.521582\pi$
$829$	−3.90138	−0.135501	−0.0677503	+	0.997702i	$0.521582\pi$
$830$	76.8610	2.66789
$831$	−42.7073	−1.48150
$832$	4.79182	0.166126
$833$	−2.56367	−0.0888258
$834$	−32.9650	−1.14149
$835$	−37.8130	−1.30857
$836$	−8.50857	−0.294275
$837$	−3.13584	−0.108391
$838$	48.2088	1.66534
$839$	18.4300	0.636274	0.318137	−	0.948045i	$-0.396943\pi$
$839$	18.4300	0.636274	0.318137	+	0.948045i	$0.396943\pi$
$840$	21.4289	0.739368
$841$	−8.55043	−0.294842
$842$	−57.5252	−1.98245
$843$	27.3847	0.943179
$844$	26.3752	0.907871
$845$	−49.4051	−1.69959
$846$	−43.0441	−1.47989
$847$	−1.07355	−0.0368875
$848$	−48.5912	−1.66863
$849$	4.38138	0.150368
$850$	2.89895	0.0994332
$851$	33.1243	1.13549
$852$	7.25827	0.248664
$853$	37.7897	1.29389	0.646947	−	0.762535i	$-0.276046\pi$
$853$	37.7897	1.29389	0.646947	+	0.762535i	$0.276046\pi$
$854$	−15.5512	−0.532151
$855$	−17.0174	−0.581982
$856$	−28.6072	−0.977773
$857$	−58.1926	−1.98782	−0.993910	−	0.110194i	$-0.964853\pi$
$857$	−58.1926	−1.98782	−0.993910	+	0.110194i	$0.964853\pi$
$858$	78.8481	2.69183
$859$	35.3869	1.20738	0.603692	−	0.797218i	$-0.293696\pi$
$859$	35.3869	1.20738	0.603692	+	0.797218i	$0.293696\pi$
$860$	−22.7159	−0.774605
$861$	6.45590	0.220016
$862$	−8.81224	−0.300146
$863$	27.4547	0.934568	0.467284	−	0.884107i	$-0.345233\pi$
$863$	27.4547	0.934568	0.467284	+	0.884107i	$0.345233\pi$
$864$	−4.69942	−0.159878
$865$	−2.84900	−0.0968689
$866$	20.2196	0.687088
$867$	38.5345	1.30870
$868$	7.18373	0.243832
$869$	35.0696	1.18965
$870$	−49.0198	−1.66193
$871$	−61.5615	−2.08593
$872$	10.2814	0.348172
$873$	0.716886	0.0242629
$874$	−27.3013	−0.923479
$875$	−16.2612	−0.549729
$876$	0.616984	0.0208460
$877$	−14.8517	−0.501505	−0.250752	−	0.968051i	$-0.580678\pi$
$877$	−14.8517	−0.501505	−0.250752	+	0.968051i	$0.580678\pi$
$878$	−25.6958	−0.867191
$879$	7.19056	0.242532
$880$	−44.6879	−1.50643
$881$	37.8714	1.27592	0.637960	−	0.770070i	$-0.279779\pi$
$881$	37.8714	1.27592	0.637960	+	0.770070i	$0.279779\pi$
$882$	−13.4841	−0.454033
$883$	−15.3679	−0.517171	−0.258586	−	0.965988i	$-0.583256\pi$
$883$	−15.3679	−0.517171	−0.258586	+	0.965988i	$0.583256\pi$
$884$	4.96500	0.166991
$885$	37.6414	1.26530
$886$	−4.42102	−0.148527
$887$	2.72841	0.0916111	0.0458056	−	0.998950i	$-0.485415\pi$
$887$	2.72841	0.0916111	0.0458056	+	0.998950i	$0.485415\pi$
$888$	−21.0342	−0.705862
$889$	27.6008	0.925703
$890$	79.7984	2.67485
$891$	33.9178	1.13629
$892$	−4.47406	−0.149803
$893$	−23.2769	−0.778931
$894$	64.1058	2.14402
$895$	63.2259	2.11341
$896$	−24.1474	−0.806707
$897$	85.2622	2.84682
$898$	−22.8495	−0.762499
$899$	15.8958	0.530153
$900$	5.13854	0.171285
$901$	8.42066	0.280533
$902$	−7.98807	−0.265973
$903$	40.4745	1.34691
$904$	−32.3227	−1.07504
$905$	12.4385	0.413471
$906$	10.0403	0.333566
$907$	−6.49334	−0.215608	−0.107804	−	0.994172i	$-0.534382\pi$
$907$	−6.49334	−0.215608	−0.107804	+	0.994172i	$0.534382\pi$
$908$	−23.4617	−0.778605
$909$	19.6038	0.650218
$910$	51.7952	1.71699
$911$	−32.2049	−1.06699	−0.533497	−	0.845802i	$-0.679123\pi$
$911$	−32.2049	−1.06699	−0.533497	+	0.845802i	$0.679123\pi$
$912$	29.2191	0.967542
$913$	57.1061	1.88994
$914$	9.63615	0.318736
$915$	27.7985	0.918991
$916$	3.26511	0.107882
$917$	28.7855	0.950580
$918$	1.34249	0.0443087
$919$	−25.5609	−0.843177	−0.421588	−	0.906787i	$-0.638527\pi$
$919$	−25.5609	−0.843177	−0.421588	+	0.906787i	$0.638527\pi$
$920$	−28.6715	−0.945271
$921$	−19.9367	−0.656936
$922$	−55.9753	−1.84345
$923$	−16.9700	−0.558574
$924$	−16.4595	−0.541479
$925$	−10.0041	−0.328932
$926$	−32.1390	−1.05615
$927$	38.0833	1.25082
$928$	23.8216	0.781983
$929$	−43.9109	−1.44067	−0.720336	−	0.693626i	$-0.756012\pi$
$929$	−43.9109	−1.44067	−0.720336	+	0.693626i	$0.756012\pi$
$930$	−38.1038	−1.24947
$931$	−7.29177	−0.238978
$932$	7.25067	0.237503
$933$	−6.97375	−0.228310
$934$	36.3334	1.18886
$935$	7.74424	0.253264
$936$	−25.2603	−0.825658
$937$	37.5543	1.22684	0.613422	−	0.789755i	$-0.289792\pi$
$937$	37.5543	1.22684	0.613422	+	0.789755i	$0.289792\pi$
$938$	38.1326	1.24507
$939$	−39.1552	−1.27778
$940$	25.2716	0.824270
$941$	−20.6958	−0.674663	−0.337332	−	0.941386i	$-0.609524\pi$
$941$	−20.6958	−0.674663	−0.337332	+	0.941386i	$0.609524\pi$
$942$	−50.0987	−1.63230
$943$	−8.63787	−0.281288
$944$	−30.1538	−0.981423
$945$	4.71976	0.153534
$946$	−50.0802	−1.62825
$947$	−14.0412	−0.456276	−0.228138	−	0.973629i	$-0.573264\pi$
$947$	−14.0412	−0.456276	−0.228138	+	0.973629i	$0.573264\pi$
$948$	24.8952	0.808559
$949$	−1.44252	−0.0468262
$950$	8.24540	0.267516
$951$	48.3302	1.56721
$952$	2.97485	0.0964155
$953$	−32.4866	−1.05235	−0.526173	−	0.850378i	$-0.676373\pi$
$953$	−32.4866	−1.05235	−0.526173	+	0.850378i	$0.676373\pi$
$954$	44.2900	1.43394
$955$	64.0842	2.07371
$956$	3.72330	0.120420
$957$	−36.4207	−1.17731
$958$	−17.1253	−0.553293
$959$	−20.4530	−0.660461
$960$	5.30573	0.171242
$961$	−18.6440	−0.601419
$962$	−50.8412	−1.63919
$963$	43.9469	1.41617
$964$	−1.01662	−0.0327433
$965$	−8.48704	−0.273208
$966$	−52.8133	−1.69924
$967$	−53.7501	−1.72849	−0.864244	−	0.503073i	$-0.832203\pi$
$967$	−53.7501	−1.72849	−0.864244	+	0.503073i	$0.832203\pi$
$968$	−0.912116	−0.0293165
$969$	−5.06356	−0.162665
$970$	−1.24891	−0.0401001
$971$	34.1747	1.09672	0.548359	−	0.836243i	$-0.315253\pi$
$971$	34.1747	1.09672	0.548359	+	0.836243i	$0.315253\pi$
$972$	21.3568	0.685019
$973$	−16.0890	−0.515789
$974$	−45.0346	−1.44300
$975$	−25.7505	−0.824676
$976$	−22.2689	−0.712810
$977$	−8.90298	−0.284832	−0.142416	−	0.989807i	$-0.545487\pi$
$977$	−8.90298	−0.284832	−0.142416	+	0.989807i	$0.545487\pi$
$978$	−17.4238	−0.557153
$979$	59.2885	1.89487
$980$	7.91665	0.252888
$981$	−15.7945	−0.504278
$982$	−39.1822	−1.25035
$983$	22.5713	0.719912	0.359956	−	0.932969i	$-0.382792\pi$
$983$	22.5713	0.719912	0.359956	+	0.932969i	$0.382792\pi$
$984$	5.48512	0.174859
$985$	9.49955	0.302681
$986$	−6.80514	−0.216720
$987$	−45.0283	−1.43327
$988$	14.1218	0.449275
$989$	−54.1541	−1.72200
$990$	40.7322	1.29456
$991$	46.7740	1.48583	0.742913	−	0.669388i	$-0.233444\pi$
$991$	46.7740	1.48583	0.742913	+	0.669388i	$0.233444\pi$
$992$	18.5169	0.587912
$993$	−21.5452	−0.683717
$994$	10.5116	0.333408
$995$	−30.5362	−0.968063
$996$	40.5385	1.28451
$997$	−20.7833	−0.658214	−0.329107	−	0.944293i	$-0.606748\pi$
$997$	−20.7833	−0.658214	−0.329107	+	0.944293i	$0.606748\pi$
$998$	69.2448	2.19191
$999$	−4.63283	−0.146576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.a.1.7	✓	7
3.2	odd	2		2169.2.a.e.1.1		7
4.3	odd	2		3856.2.a.j.1.6		7
5.4	even	2		6025.2.a.f.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.7	✓	7	1.1	even	1	trivial
2169.2.a.e.1.1		7	3.2	odd	2
3856.2.a.j.1.6		7	4.3	odd	2
6025.2.a.f.1.1		7	5.4	even	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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73684 q^{2} -2.37146 q^{3} +1.01662 q^{4} -2.63180 q^{5} -4.11885 q^{6} -2.01025 q^{7} -1.70797 q^{8} +2.62382 q^{9} +O(q^{10})\)	\(q+1.73684 q^{2} -2.37146 q^{3} +1.01662 q^{4} -2.63180 q^{5} -4.11885 q^{6} -2.01025 q^{7} -1.70797 q^{8} +2.62382 q^{9} -4.57103 q^{10} -3.39618 q^{11} -2.41088 q^{12} +5.63669 q^{13} -3.49150 q^{14} +6.24122 q^{15} -4.99972 q^{16} +0.866432 q^{17} +4.55716 q^{18} +2.46437 q^{19} -2.67556 q^{20} +4.76723 q^{21} -5.89863 q^{22} -6.37847 q^{23} +4.05038 q^{24} +1.92640 q^{25} +9.79005 q^{26} +0.892104 q^{27} -2.04367 q^{28} -4.52212 q^{29} +10.8400 q^{30} -3.51511 q^{31} -5.26780 q^{32} +8.05390 q^{33} +1.50486 q^{34} +5.29060 q^{35} +2.66743 q^{36} -5.19315 q^{37} +4.28022 q^{38} -13.3672 q^{39} +4.49504 q^{40} +1.35422 q^{41} +8.27994 q^{42} +8.49015 q^{43} -3.45264 q^{44} -6.90537 q^{45} -11.0784 q^{46} -9.44537 q^{47} +11.8566 q^{48} -2.95888 q^{49} +3.34585 q^{50} -2.05471 q^{51} +5.73040 q^{52} +9.71877 q^{53} +1.54945 q^{54} +8.93808 q^{55} +3.43345 q^{56} -5.84415 q^{57} -7.85421 q^{58} +6.03110 q^{59} +6.34497 q^{60} +4.45402 q^{61} -6.10520 q^{62} -5.27454 q^{63} +0.850111 q^{64} -14.8347 q^{65} +13.9884 q^{66} -10.9216 q^{67} +0.880836 q^{68} +15.1263 q^{69} +9.18894 q^{70} -3.01063 q^{71} -4.48140 q^{72} -0.255916 q^{73} -9.01969 q^{74} -4.56837 q^{75} +2.50534 q^{76} +6.82718 q^{77} -23.2167 q^{78} -10.3262 q^{79} +13.1583 q^{80} -9.98704 q^{81} +2.35207 q^{82} -16.8148 q^{83} +4.84649 q^{84} -2.28028 q^{85} +14.7461 q^{86} +10.7240 q^{87} +5.80057 q^{88} -17.4574 q^{89} -11.9935 q^{90} -11.3312 q^{91} -6.48451 q^{92} +8.33594 q^{93} -16.4051 q^{94} -6.48574 q^{95} +12.4924 q^{96} +0.273223 q^{97} -5.13911 q^{98} -8.91095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * q^98 - 20 * q^99

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