LMFDB - Embedded newform 241.2.a.b.1.1

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:	$0$
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} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.59703$ 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)

$f(q)$	$=$	$q-2.59703 q^{2} -1.20534 q^{3} +4.74454 q^{4} +3.49051 q^{5} +3.13029 q^{6} -0.744578 q^{7} -7.12764 q^{8} -1.54716 q^{9} +O(q^{10})$	\(q-2.59703 q^{2} -1.20534 q^{3} +4.74454 q^{4} +3.49051 q^{5} +3.13029 q^{6} -0.744578 q^{7} -7.12764 q^{8} -1.54716 q^{9} -9.06493 q^{10} +6.28793 q^{11} -5.71878 q^{12} -4.06994 q^{13} +1.93369 q^{14} -4.20724 q^{15} +9.02158 q^{16} -1.60034 q^{17} +4.01801 q^{18} +2.14421 q^{19} +16.5608 q^{20} +0.897468 q^{21} -16.3299 q^{22} +9.25572 q^{23} +8.59122 q^{24} +7.18363 q^{25} +10.5697 q^{26} +5.48087 q^{27} -3.53268 q^{28} +3.13090 q^{29} +10.9263 q^{30} -3.15223 q^{31} -9.17399 q^{32} -7.57908 q^{33} +4.15612 q^{34} -2.59895 q^{35} -7.34056 q^{36} +4.19928 q^{37} -5.56857 q^{38} +4.90566 q^{39} -24.8791 q^{40} -4.52694 q^{41} -2.33075 q^{42} +6.99535 q^{43} +29.8333 q^{44} -5.40037 q^{45} -24.0373 q^{46} -4.82023 q^{47} -10.8741 q^{48} -6.44560 q^{49} -18.6561 q^{50} +1.92895 q^{51} -19.3100 q^{52} +3.71179 q^{53} -14.2339 q^{54} +21.9481 q^{55} +5.30708 q^{56} -2.58450 q^{57} -8.13103 q^{58} +3.34128 q^{59} -19.9614 q^{60} +10.8630 q^{61} +8.18643 q^{62} +1.15198 q^{63} +5.78192 q^{64} -14.2062 q^{65} +19.6831 q^{66} +5.80682 q^{67} -7.59287 q^{68} -11.1563 q^{69} +6.74955 q^{70} +15.7805 q^{71} +11.0276 q^{72} -1.64682 q^{73} -10.9056 q^{74} -8.65870 q^{75} +10.1733 q^{76} -4.68186 q^{77} -12.7401 q^{78} -11.4813 q^{79} +31.4899 q^{80} -1.96482 q^{81} +11.7566 q^{82} -4.74454 q^{83} +4.25807 q^{84} -5.58599 q^{85} -18.1671 q^{86} -3.77380 q^{87} -44.8181 q^{88} -7.95332 q^{89} +14.0249 q^{90} +3.03039 q^{91} +43.9141 q^{92} +3.79951 q^{93} +12.5182 q^{94} +7.48438 q^{95} +11.0578 q^{96} -5.49759 q^{97} +16.7394 q^{98} -9.72843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * 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 $

$2$	−2.59703	−1.83637	−0.918187	−	0.396147i	$-0.870347\pi$
$2$	−2.59703	−1.83637	−0.918187	+	0.396147i	$0.870347\pi$
$3$	−1.20534	−0.695902	−0.347951	−	0.937513i	$-0.613123\pi$
$3$	−1.20534	−0.695902	−0.347951	+	0.937513i	$0.613123\pi$
$4$	4.74454	2.37227
$5$	3.49051	1.56100	0.780501	−	0.625155i	$-0.214964\pi$
$5$	3.49051	1.56100	0.780501	+	0.625155i	$0.214964\pi$
$6$	3.13029	1.27794
$7$	−0.744578	−0.281424	−0.140712	−	0.990051i	$-0.544939\pi$
$7$	−0.744578	−0.281424	−0.140712	+	0.990051i	$0.544939\pi$
$8$	−7.12764	−2.52000
$9$	−1.54716	−0.515720
$10$	−9.06493	−2.86658
$11$	6.28793	1.89588	0.947941	−	0.318445i	$-0.103161\pi$
$11$	6.28793	1.89588	0.947941	+	0.318445i	$0.103161\pi$
$12$	−5.71878	−1.65087
$13$	−4.06994	−1.12880	−0.564399	−	0.825502i	$-0.690892\pi$
$13$	−4.06994	−1.12880	−0.564399	+	0.825502i	$0.690892\pi$
$14$	1.93369	0.516800
$15$	−4.20724	−1.08630
$16$	9.02158	2.25539
$17$	−1.60034	−0.388139	−0.194070	−	0.980988i	$-0.562169\pi$
$17$	−1.60034	−0.388139	−0.194070	+	0.980988i	$0.562169\pi$
$18$	4.01801	0.947055
$19$	2.14421	0.491916	0.245958	−	0.969280i	$-0.420897\pi$
$19$	2.14421	0.491916	0.245958	+	0.969280i	$0.420897\pi$
$20$	16.5608	3.70312
$21$	0.897468	0.195844
$22$	−16.3299	−3.48155
$23$	9.25572	1.92995	0.964975	−	0.262340i	$-0.0844943\pi$
$23$	9.25572	1.92995	0.964975	+	0.262340i	$0.0844943\pi$
$24$	8.59122	1.75367
$25$	7.18363	1.43673
$26$	10.5697	2.07290
$27$	5.48087	1.05479
$28$	−3.53268	−0.667614
$29$	3.13090	0.581394	0.290697	−	0.956815i	$-0.406113\pi$
$29$	3.13090	0.581394	0.290697	+	0.956815i	$0.406113\pi$
$30$	10.9263	1.99486
$31$	−3.15223	−0.566158	−0.283079	−	0.959097i	$-0.591356\pi$
$31$	−3.15223	−0.566158	−0.283079	+	0.959097i	$0.591356\pi$
$32$	−9.17399	−1.62175
$33$	−7.57908	−1.31935
$34$	4.15612	0.712769
$35$	−2.59895	−0.439303
$36$	−7.34056	−1.22343
$37$	4.19928	0.690358	0.345179	−	0.938537i	$-0.387818\pi$
$37$	4.19928	0.690358	0.345179	+	0.938537i	$0.387818\pi$
$38$	−5.56857	−0.903342
$39$	4.90566	0.785534
$40$	−24.8791	−3.93372
$41$	−4.52694	−0.706990	−0.353495	−	0.935436i	$-0.615007\pi$
$41$	−4.52694	−0.706990	−0.353495	+	0.935436i	$0.615007\pi$
$42$	−2.33075	−0.359642
$43$	6.99535	1.06678	0.533391	−	0.845869i	$-0.320918\pi$
$43$	6.99535	1.06678	0.533391	+	0.845869i	$0.320918\pi$
$44$	29.8333	4.49754
$45$	−5.40037	−0.805039
$46$	−24.0373	−3.54411
$47$	−4.82023	−0.703102	−0.351551	−	0.936169i	$-0.614346\pi$
$47$	−4.82023	−0.703102	−0.351551	+	0.936169i	$0.614346\pi$
$48$	−10.8741	−1.56953
$49$	−6.44560	−0.920800
$50$	−18.6561	−2.63837
$51$	1.92895	0.270107
$52$	−19.3100	−2.67782
$53$	3.71179	0.509853	0.254927	−	0.966960i	$-0.417949\pi$
$53$	3.71179	0.509853	0.254927	+	0.966960i	$0.417949\pi$
$54$	−14.2339	−1.93699
$55$	21.9481	2.95948
$56$	5.30708	0.709189
$57$	−2.58450	−0.342325
$58$	−8.13103	−1.06766
$59$	3.34128	0.434997	0.217499	−	0.976061i	$-0.430210\pi$
$59$	3.34128	0.434997	0.217499	+	0.976061i	$0.430210\pi$
$60$	−19.9614	−2.57701
$61$	10.8630	1.39087	0.695434	−	0.718590i	$-0.255212\pi$
$61$	10.8630	1.39087	0.695434	+	0.718590i	$0.255212\pi$
$62$	8.18643	1.03968
$63$	1.15198	0.145136
$64$	5.78192	0.722740
$65$	−14.2062	−1.76206
$66$	19.6831	2.42282
$67$	5.80682	0.709416	0.354708	−	0.934977i	$-0.384580\pi$
$67$	5.80682	0.709416	0.354708	+	0.934977i	$0.384580\pi$
$68$	−7.59287	−0.920771
$69$	−11.1563	−1.34306
$70$	6.74955	0.806725
$71$	15.7805	1.87281	0.936403	−	0.350927i	$-0.114134\pi$
$71$	15.7805	1.87281	0.936403	+	0.350927i	$0.114134\pi$
$72$	11.0276	1.29961
$73$	−1.64682	−0.192745	−0.0963727	−	0.995345i	$-0.530724\pi$
$73$	−1.64682	−0.192745	−0.0963727	+	0.995345i	$0.530724\pi$
$74$	−10.9056	−1.26775
$75$	−8.65870	−0.999821
$76$	10.1733	1.16696
$77$	−4.68186	−0.533547
$78$	−12.7401	−1.44253
$79$	−11.4813	−1.29174	−0.645872	−	0.763446i	$-0.723506\pi$
$79$	−11.4813	−1.29174	−0.645872	+	0.763446i	$0.723506\pi$
$80$	31.4899	3.52067
$81$	−1.96482	−0.218313
$82$	11.7566	1.29830
$83$	−4.74454	−0.520781	−0.260390	−	0.965503i	$-0.583851\pi$
$83$	−4.74454	−0.520781	−0.260390	+	0.965503i	$0.583851\pi$
$84$	4.25807	0.464594
$85$	−5.58599	−0.605886
$86$	−18.1671	−1.95901
$87$	−3.77380	−0.404594
$88$	−44.8181	−4.77762
$89$	−7.95332	−0.843050	−0.421525	−	0.906817i	$-0.638505\pi$
$89$	−7.95332	−0.843050	−0.421525	+	0.906817i	$0.638505\pi$
$90$	14.0249	1.47835
$91$	3.03039	0.317671
$92$	43.9141	4.57836
$93$	3.79951	0.393991
$94$	12.5182	1.29116
$95$	7.48438	0.767882
$96$	11.0578	1.12858
$97$	−5.49759	−0.558195	−0.279098	−	0.960263i	$-0.590035\pi$
$97$	−5.49759	−0.558195	−0.279098	+	0.960263i	$0.590035\pi$
$98$	16.7394	1.69093
$99$	−9.72843	−0.977744
$100$	34.0830	3.40830
$101$	−10.4008	−1.03492	−0.517459	−	0.855708i	$-0.673122\pi$
$101$	−10.4008	−1.03492	−0.517459	+	0.855708i	$0.673122\pi$
$102$	−5.00953	−0.496018
$103$	−16.9464	−1.66978	−0.834888	−	0.550420i	$-0.814468\pi$
$103$	−16.9464	−1.66978	−0.834888	+	0.550420i	$0.814468\pi$
$104$	29.0091	2.84457
$105$	3.13262	0.305712
$106$	−9.63961	−0.936281
$107$	−0.873633	−0.0844573	−0.0422287	−	0.999108i	$-0.513446\pi$
$107$	−0.873633	−0.0844573	−0.0422287	+	0.999108i	$0.513446\pi$
$108$	26.0042	2.50225
$109$	−9.90349	−0.948582	−0.474291	−	0.880368i	$-0.657296\pi$
$109$	−9.90349	−0.948582	−0.474291	+	0.880368i	$0.657296\pi$
$110$	−56.9996	−5.43470
$111$	−5.06155	−0.480421
$112$	−6.71727	−0.634722
$113$	5.23192	0.492177	0.246089	−	0.969247i	$-0.420855\pi$
$113$	5.23192	0.492177	0.246089	+	0.969247i	$0.420855\pi$
$114$	6.71201	0.628638
$115$	32.3071	3.01266
$116$	14.8547	1.37922
$117$	6.29685	0.582144
$118$	−8.67738	−0.798818
$119$	1.19158	0.109232
$120$	29.9877	2.73749
$121$	28.5381	2.59437
$122$	−28.2115	−2.55415
$123$	5.45650	0.491996
$124$	−14.9559	−1.34308
$125$	7.62196	0.681729
$126$	−2.99172	−0.266524
$127$	−3.50226	−0.310775	−0.155388	−	0.987854i	$-0.549663\pi$
$127$	−3.50226	−0.310775	−0.155388	+	0.987854i	$0.549663\pi$
$128$	3.33219	0.294527
$129$	−8.43177	−0.742376
$130$	36.8937	3.23579
$131$	−13.2883	−1.16100	−0.580500	−	0.814260i	$-0.697143\pi$
$131$	−13.2883	−1.16100	−0.580500	+	0.814260i	$0.697143\pi$
$132$	−35.9593	−3.12985
$133$	−1.59653	−0.138437
$134$	−15.0805	−1.30275
$135$	19.1310	1.64653
$136$	11.4066	0.978111
$137$	−9.37803	−0.801219	−0.400610	−	0.916249i	$-0.631202\pi$
$137$	−9.37803	−0.801219	−0.400610	+	0.916249i	$0.631202\pi$
$138$	28.9731	2.46636
$139$	3.48685	0.295751	0.147875	−	0.989006i	$-0.452757\pi$
$139$	3.48685	0.295751	0.147875	+	0.989006i	$0.452757\pi$
$140$	−12.3308	−1.04215
$141$	5.81000	0.489291
$142$	−40.9825	−3.43917
$143$	−25.5915	−2.14007
$144$	−13.9578	−1.16315
$145$	10.9284	0.907557
$146$	4.27683	0.353953
$147$	7.76913	0.640787
$148$	19.9237	1.63771
$149$	−8.39873	−0.688051	−0.344025	−	0.938960i	$-0.611791\pi$
$149$	−8.39873	−0.688051	−0.344025	+	0.938960i	$0.611791\pi$
$150$	22.4869	1.83604
$151$	−6.68837	−0.544292	−0.272146	−	0.962256i	$-0.587733\pi$
$151$	−6.68837	−0.544292	−0.272146	+	0.962256i	$0.587733\pi$
$152$	−15.2832	−1.23963
$153$	2.47598	0.200171
$154$	12.1589	0.979792
$155$	−11.0029	−0.883773
$156$	23.2751	1.86350
$157$	−11.9755	−0.955752	−0.477876	−	0.878427i	$-0.658593\pi$
$157$	−11.9755	−0.955752	−0.477876	+	0.878427i	$0.658593\pi$
$158$	29.8171	2.37213
$159$	−4.47396	−0.354808
$160$	−32.0218	−2.53155
$161$	−6.89161	−0.543135
$162$	5.10268	0.400905
$163$	−13.7742	−1.07888	−0.539438	−	0.842025i	$-0.681363\pi$
$163$	−13.7742	−1.07888	−0.539438	+	0.842025i	$0.681363\pi$
$164$	−21.4783	−1.67717
$165$	−26.4548	−2.05951
$166$	12.3217	0.956348
$167$	7.34847	0.568642	0.284321	−	0.958729i	$-0.408232\pi$
$167$	7.34847	0.568642	0.284321	+	0.958729i	$0.408232\pi$
$168$	−6.39683	−0.493526
$169$	3.56442	0.274187
$170$	14.5070	1.11263
$171$	−3.31744	−0.253691
$172$	33.1897	2.53069
$173$	14.4542	1.09893	0.549467	−	0.835515i	$-0.314831\pi$
$173$	14.4542	1.09893	0.549467	+	0.835515i	$0.314831\pi$
$174$	9.80065	0.742985
$175$	−5.34877	−0.404329
$176$	56.7270	4.27596
$177$	−4.02737	−0.302716
$178$	20.6550	1.54816
$179$	10.4351	0.779953	0.389976	−	0.920825i	$-0.372483\pi$
$179$	10.4351	0.779953	0.389976	+	0.920825i	$0.372483\pi$
$180$	−25.6223	−1.90977
$181$	25.3704	1.88577	0.942883	−	0.333125i	$-0.108103\pi$
$181$	25.3704	1.88577	0.942883	+	0.333125i	$0.108103\pi$
$182$	−7.87000	−0.583363
$183$	−13.0936	−0.967908
$184$	−65.9714	−4.86348
$185$	14.6576	1.07765
$186$	−9.86741	−0.723514
$187$	−10.0628	−0.735867
$188$	−22.8698	−1.66795
$189$	−4.08093	−0.296844
$190$	−19.4371	−1.41012
$191$	−16.4111	−1.18747	−0.593733	−	0.804662i	$-0.702346\pi$
$191$	−16.4111	−1.18747	−0.593733	+	0.804662i	$0.702346\pi$
$192$	−6.96916	−0.502956
$193$	−8.05553	−0.579850	−0.289925	−	0.957049i	$-0.593630\pi$
$193$	−8.05553	−0.579850	−0.289925	+	0.957049i	$0.593630\pi$
$194$	14.2774	1.02506
$195$	17.1232	1.22622
$196$	−30.5814	−2.18439
$197$	1.16210	0.0827963	0.0413981	−	0.999143i	$-0.486819\pi$
$197$	1.16210	0.0827963	0.0413981	+	0.999143i	$0.486819\pi$
$198$	25.2650	1.79550
$199$	−15.8123	−1.12090	−0.560451	−	0.828188i	$-0.689372\pi$
$199$	−15.8123	−1.12090	−0.560451	+	0.828188i	$0.689372\pi$
$200$	−51.2023	−3.62055
$201$	−6.99918	−0.493684
$202$	27.0112	1.90050
$203$	−2.33120	−0.163618
$204$	9.15198	0.640767
$205$	−15.8013	−1.10361
$206$	44.0102	3.06633
$207$	−14.3201	−0.995314
$208$	−36.7173	−2.54589
$209$	13.4827	0.932615
$210$	−8.13549	−0.561402
$211$	−6.41779	−0.441819	−0.220910	−	0.975294i	$-0.570903\pi$
$211$	−6.41779	−0.441819	−0.220910	+	0.975294i	$0.570903\pi$
$212$	17.6107	1.20951
$213$	−19.0209	−1.30329
$214$	2.26885	0.155095
$215$	24.4173	1.66525
$216$	−39.0656	−2.65808
$217$	2.34708	0.159330
$218$	25.7196	1.74195
$219$	1.98497	0.134132
$220$	104.133	7.02067
$221$	6.51329	0.438131
$222$	13.1450	0.882234
$223$	15.6352	1.04701	0.523506	−	0.852022i	$-0.324624\pi$
$223$	15.6352	1.04701	0.523506	+	0.852022i	$0.324624\pi$
$224$	6.83075	0.456399
$225$	−11.1142	−0.740948
$226$	−13.5874	−0.903821
$227$	−6.01020	−0.398911	−0.199456	−	0.979907i	$-0.563917\pi$
$227$	−6.01020	−0.398911	−0.199456	+	0.979907i	$0.563917\pi$
$228$	−12.2623	−0.812088
$229$	−10.7079	−0.707595	−0.353798	−	0.935322i	$-0.615110\pi$
$229$	−10.7079	−0.707595	−0.353798	+	0.935322i	$0.615110\pi$
$230$	−83.9024	−5.53236
$231$	5.64322	0.371297
$232$	−22.3159	−1.46511
$233$	2.77571	0.181843	0.0909214	−	0.995858i	$-0.471019\pi$
$233$	2.77571	0.181843	0.0909214	+	0.995858i	$0.471019\pi$
$234$	−16.3531	−1.06903
$235$	−16.8250	−1.09754
$236$	15.8528	1.03193
$237$	13.8388	0.898928
$238$	−3.09456	−0.200590
$239$	9.74488	0.630344	0.315172	−	0.949035i	$-0.397938\pi$
$239$	9.74488	0.630344	0.315172	+	0.949035i	$0.397938\pi$
$240$	−37.9559	−2.45005
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−74.1141	−4.76423
$243$	−14.0743	−0.902868
$244$	51.5400	3.29951
$245$	−22.4984	−1.43737
$246$	−14.1707	−0.903489
$247$	−8.72682	−0.555274
$248$	22.4680	1.42672
$249$	5.71877	0.362413
$250$	−19.7944	−1.25191
$251$	1.47018	0.0927970	0.0463985	−	0.998923i	$-0.485226\pi$
$251$	1.47018	0.0927970	0.0463985	+	0.998923i	$0.485226\pi$
$252$	5.46562	0.344302
$253$	58.1993	3.65896
$254$	9.09545	0.570699
$255$	6.73301	0.421638
$256$	−20.2176	−1.26360
$257$	19.0717	1.18966	0.594829	−	0.803852i	$-0.297220\pi$
$257$	19.0717	1.18966	0.594829	+	0.803852i	$0.297220\pi$
$258$	21.8975	1.36328
$259$	−3.12669	−0.194283
$260$	−67.4017	−4.18007
$261$	−4.84401	−0.299836
$262$	34.5099	2.13203
$263$	−11.0150	−0.679217	−0.339608	−	0.940567i	$-0.610295\pi$
$263$	−11.0150	−0.679217	−0.339608	+	0.940567i	$0.610295\pi$
$264$	54.0210	3.32476
$265$	12.9560	0.795882
$266$	4.14624	0.254222
$267$	9.58644	0.586681
$268$	27.5507	1.68293
$269$	−9.48636	−0.578393	−0.289197	−	0.957270i	$-0.593388\pi$
$269$	−9.48636	−0.578393	−0.289197	+	0.957270i	$0.593388\pi$
$270$	−49.6837	−3.02365
$271$	21.3477	1.29678	0.648390	−	0.761308i	$-0.275443\pi$
$271$	21.3477	1.29678	0.648390	+	0.761308i	$0.275443\pi$
$272$	−14.4376	−0.875407
$273$	−3.65264	−0.221068
$274$	24.3550	1.47134
$275$	45.1701	2.72386
$276$	−52.9314	−3.18609
$277$	−18.2788	−1.09827	−0.549135	−	0.835734i	$-0.685043\pi$
$277$	−18.2788	−1.09827	−0.549135	+	0.835734i	$0.685043\pi$
$278$	−9.05544	−0.543109
$279$	4.87701	0.291979
$280$	18.5244	1.10704
$281$	11.5147	0.686909	0.343454	−	0.939169i	$-0.388403\pi$
$281$	11.5147	0.686909	0.343454	+	0.939169i	$0.388403\pi$
$282$	−15.0887	−0.898521
$283$	25.1735	1.49641	0.748205	−	0.663468i	$-0.230916\pi$
$283$	25.1735	1.49641	0.748205	+	0.663468i	$0.230916\pi$
$284$	74.8714	4.44280
$285$	−9.02121	−0.534371
$286$	66.4618	3.92997
$287$	3.37066	0.198964
$288$	14.1936	0.836367
$289$	−14.4389	−0.849348
$290$	−28.3814	−1.66661
$291$	6.62645	0.388449
$292$	−7.81339	−0.457244
$293$	−0.319785	−0.0186820	−0.00934102	−	0.999956i	$-0.502973\pi$
$293$	−0.319785	−0.0186820	−0.00934102	+	0.999956i	$0.502973\pi$
$294$	−20.1766	−1.17673
$295$	11.6627	0.679031
$296$	−29.9310	−1.73970
$297$	34.4633	1.99976
$298$	21.8117	1.26352
$299$	−37.6702	−2.17853
$300$	−41.0815	−2.37184
$301$	−5.20859	−0.300218
$302$	17.3699	0.999523
$303$	12.5365	0.720202
$304$	19.3442	1.10946
$305$	37.9174	2.17115
$306$	−6.43018	−0.367589
$307$	−8.24844	−0.470763	−0.235382	−	0.971903i	$-0.575634\pi$
$307$	−8.24844	−0.470763	−0.235382	+	0.971903i	$0.575634\pi$
$308$	−22.2132	−1.26572
$309$	20.4261	1.16200
$310$	28.5748	1.62294
$311$	−11.0098	−0.624306	−0.312153	−	0.950032i	$-0.601050\pi$
$311$	−11.0098	−0.624306	−0.312153	+	0.950032i	$0.601050\pi$
$312$	−34.9657	−1.97955
$313$	−10.3244	−0.583570	−0.291785	−	0.956484i	$-0.594249\pi$
$313$	−10.3244	−0.583570	−0.291785	+	0.956484i	$0.594249\pi$
$314$	31.1008	1.75512
$315$	4.02100	0.226557
$316$	−54.4733	−3.06437
$317$	−29.1691	−1.63830	−0.819149	−	0.573581i	$-0.805554\pi$
$317$	−29.1691	−1.63830	−0.819149	+	0.573581i	$0.805554\pi$
$318$	11.6190	0.651560
$319$	19.6869	1.10225
$320$	20.1818	1.12820
$321$	1.05302	0.0587740
$322$	17.8977	0.997398
$323$	−3.43147	−0.190932
$324$	−9.32216	−0.517898
$325$	−29.2369	−1.62177
$326$	35.7719	1.98122
$327$	11.9371	0.660121
$328$	32.2664	1.78162
$329$	3.58903	0.197870
$330$	68.7039	3.78202
$331$	14.3362	0.787988	0.393994	−	0.919113i	$-0.371093\pi$
$331$	14.3362	0.787988	0.393994	+	0.919113i	$0.371093\pi$
$332$	−22.5107	−1.23543
$333$	−6.49696	−0.356031
$334$	−19.0842	−1.04424
$335$	20.2687	1.10740
$336$	8.09658	0.441705
$337$	5.47393	0.298184	0.149092	−	0.988823i	$-0.452365\pi$
$337$	5.47393	0.298184	0.149092	+	0.988823i	$0.452365\pi$
$338$	−9.25690	−0.503509
$339$	−6.30623	−0.342507
$340$	−26.5030	−1.43733
$341$	−19.8210	−1.07337
$342$	8.61547	0.465871
$343$	10.0113	0.540559
$344$	−49.8604	−2.68829
$345$	−38.9410	−2.09651
$346$	−37.5380	−2.01805
$347$	−24.3460	−1.30696	−0.653480	−	0.756944i	$-0.726691\pi$
$347$	−24.3460	−1.30696	−0.653480	+	0.756944i	$0.726691\pi$
$348$	−17.9049	−0.959805
$349$	−32.0868	−1.71757	−0.858783	−	0.512339i	$-0.828779\pi$
$349$	−32.0868	−1.71757	−0.858783	+	0.512339i	$0.828779\pi$
$350$	13.8909	0.742499
$351$	−22.3068	−1.19065
$352$	−57.6854	−3.07464
$353$	13.4079	0.713631	0.356816	−	0.934175i	$-0.383862\pi$
$353$	13.4079	0.713631	0.356816	+	0.934175i	$0.383862\pi$
$354$	10.4592	0.555899
$355$	55.0821	2.92345
$356$	−37.7348	−1.99994
$357$	−1.43625	−0.0760146
$358$	−27.1001	−1.43228
$359$	26.1416	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$359$	26.1416	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$360$	38.4919	2.02870
$361$	−14.4024	−0.758019
$362$	−65.8875	−3.46297
$363$	−34.3980	−1.80543
$364$	14.3778	0.753602
$365$	−5.74822	−0.300876
$366$	34.0044	1.77744
$367$	4.22872	0.220737	0.110369	−	0.993891i	$-0.464797\pi$
$367$	4.22872	0.220737	0.110369	+	0.993891i	$0.464797\pi$
$368$	83.5012	4.35280
$369$	7.00391	0.364609
$370$	−38.0662	−1.97897
$371$	−2.76372	−0.143485
$372$	18.0269	0.934652
$373$	−35.5776	−1.84214	−0.921070	−	0.389398i	$-0.872683\pi$
$373$	−35.5776	−1.84214	−0.921070	+	0.389398i	$0.872683\pi$
$374$	26.1334	1.35133
$375$	−9.18704	−0.474417
$376$	34.3568	1.77182
$377$	−12.7426	−0.656277
$378$	10.5983	0.545117
$379$	−10.5187	−0.540310	−0.270155	−	0.962817i	$-0.587075\pi$
$379$	−10.5187	−0.540310	−0.270155	+	0.962817i	$0.587075\pi$
$380$	35.5100	1.82162
$381$	4.22140	0.216269
$382$	42.6201	2.18063
$383$	14.8054	0.756519	0.378260	−	0.925700i	$-0.376523\pi$
$383$	14.8054	0.756519	0.378260	+	0.925700i	$0.376523\pi$
$384$	−4.01641	−0.204962
$385$	−16.3420	−0.832867
$386$	20.9204	1.06482
$387$	−10.8229	−0.550160
$388$	−26.0835	−1.32419
$389$	−8.90749	−0.451628	−0.225814	−	0.974170i	$-0.572504\pi$
$389$	−8.90749	−0.451628	−0.225814	+	0.974170i	$0.572504\pi$
$390$	−44.4694	−2.25180
$391$	−14.8123	−0.749090
$392$	45.9419	2.32042
$393$	16.0168	0.807943
$394$	−3.01801	−0.152045
$395$	−40.0754	−2.01641
$396$	−46.1569	−2.31947
$397$	32.7082	1.64158	0.820789	−	0.571232i	$-0.193534\pi$
$397$	32.7082	1.64158	0.820789	+	0.571232i	$0.193534\pi$
$398$	41.0648	2.05839
$399$	1.92436	0.0963386
$400$	64.8076	3.24038
$401$	−16.3591	−0.816933	−0.408467	−	0.912773i	$-0.633936\pi$
$401$	−16.3591	−0.816933	−0.408467	+	0.912773i	$0.633936\pi$
$402$	18.1771	0.906589
$403$	12.8294	0.639078
$404$	−49.3470	−2.45511
$405$	−6.85821	−0.340787
$406$	6.05419	0.300464
$407$	26.4048	1.30884
$408$	−13.7489	−0.680670
$409$	−27.1198	−1.34099	−0.670494	−	0.741915i	$-0.733918\pi$
$409$	−27.1198	−1.34099	−0.670494	+	0.741915i	$0.733918\pi$
$410$	41.0364	2.02664
$411$	11.3037	0.557570
$412$	−80.4028	−3.96116
$413$	−2.48784	−0.122419
$414$	37.1896	1.82777
$415$	−16.5608	−0.812939
$416$	37.3376	1.83063
$417$	−4.20284	−0.205814
$418$	−35.0148	−1.71263
$419$	−1.69471	−0.0827921	−0.0413960	−	0.999143i	$-0.513181\pi$
$419$	−1.69471	−0.0827921	−0.0413960	+	0.999143i	$0.513181\pi$
$420$	14.8628	0.725232
$421$	6.27194	0.305676	0.152838	−	0.988251i	$-0.451159\pi$
$421$	6.27194	0.305676	0.152838	+	0.988251i	$0.451159\pi$
$422$	16.6672	0.811345
$423$	7.45766	0.362604
$424$	−26.4563	−1.28483
$425$	−11.4962	−0.557650
$426$	49.3977	2.39333
$427$	−8.08837	−0.391424
$428$	−4.14499	−0.200356
$429$	30.8464	1.48928
$430$	−63.4124	−3.05802
$431$	26.2043	1.26222	0.631108	−	0.775695i	$-0.282600\pi$
$431$	26.2043	1.26222	0.631108	+	0.775695i	$0.282600\pi$
$432$	49.4460	2.37897
$433$	−1.61920	−0.0778136	−0.0389068	−	0.999243i	$-0.512388\pi$
$433$	−1.61920	−0.0778136	−0.0389068	+	0.999243i	$0.512388\pi$
$434$	−6.09543	−0.292590
$435$	−13.1725	−0.631571
$436$	−46.9875	−2.25029
$437$	19.8462	0.949374
$438$	−5.15502	−0.246316
$439$	−35.8451	−1.71080	−0.855398	−	0.517972i	$-0.826687\pi$
$439$	−35.8451	−1.71080	−0.855398	+	0.517972i	$0.826687\pi$
$440$	−156.438	−7.45788
$441$	9.97238	0.474875
$442$	−16.9152	−0.804573
$443$	19.6847	0.935250	0.467625	−	0.883927i	$-0.345110\pi$
$443$	19.6847	0.935250	0.467625	+	0.883927i	$0.345110\pi$
$444$	−24.0147	−1.13969
$445$	−27.7611	−1.31600
$446$	−40.6051	−1.92271
$447$	10.1233	0.478816
$448$	−4.30509	−0.203396
$449$	23.0445	1.08754	0.543769	−	0.839235i	$-0.316997\pi$
$449$	23.0445	1.08754	0.543769	+	0.839235i	$0.316997\pi$
$450$	28.8639	1.36066
$451$	−28.4651	−1.34037
$452$	24.8230	1.16758
$453$	8.06175	0.378774
$454$	15.6086	0.732550
$455$	10.5776	0.495885
$456$	18.4214	0.862660
$457$	9.75545	0.456341	0.228170	−	0.973621i	$-0.426726\pi$
$457$	9.75545	0.456341	0.228170	+	0.973621i	$0.426726\pi$
$458$	27.8086	1.29941
$459$	−8.77125	−0.409407
$460$	153.282	7.14683
$461$	29.0597	1.35345	0.676724	−	0.736237i	$-0.263399\pi$
$461$	29.0597	1.35345	0.676724	+	0.736237i	$0.263399\pi$
$462$	−14.6556	−0.681839
$463$	34.1246	1.58591	0.792953	−	0.609282i	$-0.208542\pi$
$463$	34.1246	1.58591	0.792953	+	0.609282i	$0.208542\pi$
$464$	28.2457	1.31127
$465$	13.2622	0.615020
$466$	−7.20859	−0.333931
$467$	−12.0061	−0.555577	−0.277789	−	0.960642i	$-0.589601\pi$
$467$	−12.0061	−0.555577	−0.277789	+	0.960642i	$0.589601\pi$
$468$	29.8757	1.38100
$469$	−4.32363	−0.199647
$470$	43.6950	2.01550
$471$	14.4346	0.665110
$472$	−23.8154	−1.09619
$473$	43.9863	2.02249
$474$	−35.9398	−1.65077
$475$	15.4032	0.706748
$476$	5.65349	0.259127
$477$	−5.74273	−0.262941
$478$	−25.3077	−1.15755
$479$	7.47517	0.341549	0.170775	−	0.985310i	$-0.445373\pi$
$479$	7.47517	0.341549	0.170775	+	0.985310i	$0.445373\pi$
$480$	38.5972	1.76171
$481$	−17.0908	−0.779275
$482$	−2.59703	−0.118291
$483$	8.30672	0.377969
$484$	135.400	6.15455
$485$	−19.1894	−0.871344
$486$	36.5514	1.65800
$487$	21.7985	0.987783	0.493891	−	0.869524i	$-0.335574\pi$
$487$	21.7985	0.987783	0.493891	+	0.869524i	$0.335574\pi$
$488$	−77.4277	−3.50499
$489$	16.6025	0.750793
$490$	58.4289	2.63955
$491$	−12.8909	−0.581758	−0.290879	−	0.956760i	$-0.593948\pi$
$491$	−12.8909	−0.581758	−0.290879	+	0.956760i	$0.593948\pi$
$492$	25.8886	1.16715
$493$	−5.01051	−0.225662
$494$	22.6638	1.01969
$495$	−33.9571	−1.52626
$496$	−28.4381	−1.27691
$497$	−11.7498	−0.527053
$498$	−14.8518	−0.665525
$499$	−24.9744	−1.11801	−0.559004	−	0.829165i	$-0.688816\pi$
$499$	−24.9744	−1.11801	−0.559004	+	0.829165i	$0.688816\pi$
$500$	36.1627	1.61725
$501$	−8.85740	−0.395719
$502$	−3.81810	−0.170410
$503$	11.1640	0.497779	0.248890	−	0.968532i	$-0.419934\pi$
$503$	11.1640	0.497779	0.248890	+	0.968532i	$0.419934\pi$
$504$	−8.21090	−0.365743
$505$	−36.3041	−1.61551
$506$	−151.145	−6.71922
$507$	−4.29634	−0.190807
$508$	−16.6166	−0.737242
$509$	18.6656	0.827337	0.413668	−	0.910428i	$-0.364247\pi$
$509$	18.6656	0.827337	0.413668	+	0.910428i	$0.364247\pi$
$510$	−17.4858	−0.774284
$511$	1.22618	0.0542432
$512$	45.8413	2.02592
$513$	11.7521	0.518870
$514$	−49.5296	−2.18466
$515$	−59.1514	−2.60652
$516$	−40.0049	−1.76112
$517$	−30.3092	−1.33300
$518$	8.12010	0.356777
$519$	−17.4222	−0.764751
$520$	101.256	4.44038
$521$	−37.9249	−1.66152	−0.830760	−	0.556631i	$-0.812094\pi$
$521$	−37.9249	−1.66152	−0.830760	+	0.556631i	$0.812094\pi$
$522$	12.5800	0.550612
$523$	23.8400	1.04245	0.521225	−	0.853419i	$-0.325475\pi$
$523$	23.8400	1.04245	0.521225	+	0.853419i	$0.325475\pi$
$524$	−63.0467	−2.75421
$525$	6.44708	0.281374
$526$	28.6063	1.24730
$527$	5.04464	0.219748
$528$	−68.3753	−2.97565
$529$	62.6683	2.72471
$530$	−33.6471	−1.46154
$531$	−5.16949	−0.224337
$532$	−7.57482	−0.328410
$533$	18.4244	0.798049
$534$	−24.8962	−1.07737
$535$	−3.04942	−0.131838
$536$	−41.3889	−1.78773
$537$	−12.5778	−0.542771
$538$	24.6363	1.06215
$539$	−40.5295	−1.74573
$540$	90.7677	3.90602
$541$	37.7424	1.62267	0.811337	−	0.584579i	$-0.198740\pi$
$541$	37.7424	1.62267	0.811337	+	0.584579i	$0.198740\pi$
$542$	−55.4405	−2.38137
$543$	−30.5799	−1.31231
$544$	14.6815	0.629464
$545$	−34.5682	−1.48074
$546$	9.48601	0.405964
$547$	−22.1817	−0.948423	−0.474211	−	0.880411i	$-0.657267\pi$
$547$	−22.1817	−0.948423	−0.474211	+	0.880411i	$0.657267\pi$
$548$	−44.4944	−1.90071
$549$	−16.8068	−0.717298
$550$	−117.308	−5.00203
$551$	6.71332	0.285997
$552$	79.5179	3.38451
$553$	8.54870	0.363528
$554$	47.4706	2.01683
$555$	−17.6674	−0.749939
$556$	16.5435	0.701601
$557$	4.36041	0.184757	0.0923783	−	0.995724i	$-0.470553\pi$
$557$	4.36041	0.184757	0.0923783	+	0.995724i	$0.470553\pi$
$558$	−12.6657	−0.536182
$559$	−28.4707	−1.20418
$560$	−23.4467	−0.990802
$561$	12.1291	0.512091
$562$	−29.9039	−1.26142
$563$	5.45151	0.229754	0.114877	−	0.993380i	$-0.463353\pi$
$563$	5.45151	0.229754	0.114877	+	0.993380i	$0.463353\pi$
$564$	27.5658	1.16073
$565$	18.2620	0.768289
$566$	−65.3762	−2.74797
$567$	1.46296	0.0614386
$568$	−112.478	−4.71947
$569$	−17.0647	−0.715388	−0.357694	−	0.933839i	$-0.616437\pi$
$569$	−17.0647	−0.715388	−0.357694	+	0.933839i	$0.616437\pi$
$570$	23.4283	0.981304
$571$	−12.7567	−0.533853	−0.266926	−	0.963717i	$-0.586008\pi$
$571$	−12.7567	−0.533853	−0.266926	+	0.963717i	$0.586008\pi$
$572$	−121.420	−5.07682
$573$	19.7809	0.826360
$574$	−8.75370	−0.365372
$575$	66.4896	2.77281
$576$	−8.94555	−0.372731
$577$	−28.2866	−1.17759	−0.588794	−	0.808283i	$-0.700397\pi$
$577$	−28.2866	−1.17759	−0.588794	+	0.808283i	$0.700397\pi$
$578$	37.4982	1.55972
$579$	9.70964	0.403519
$580$	51.8504	2.15297
$581$	3.53268	0.146560
$582$	−17.2091	−0.713339
$583$	23.3395	0.966622
$584$	11.7379	0.485718
$585$	21.9792	0.908728
$586$	0.830490	0.0343072
$587$	15.2711	0.630308	0.315154	−	0.949041i	$-0.397944\pi$
$587$	15.2711	0.630308	0.315154	+	0.949041i	$0.397944\pi$
$588$	36.8610	1.52012
$589$	−6.75906	−0.278502
$590$	−30.2884	−1.24696
$591$	−1.40072	−0.0576181
$592$	37.8841	1.55703
$593$	14.5819	0.598808	0.299404	−	0.954126i	$-0.403212\pi$
$593$	14.5819	0.598808	0.299404	+	0.954126i	$0.403212\pi$
$594$	−89.5021	−3.67231
$595$	4.15921	0.170511
$596$	−39.8481	−1.63224
$597$	19.0591	0.780038
$598$	97.8305	4.00059
$599$	24.4860	1.00047	0.500235	−	0.865890i	$-0.333247\pi$
$599$	24.4860	1.00047	0.500235	+	0.865890i	$0.333247\pi$
$600$	61.7161	2.51955
$601$	10.0479	0.409863	0.204931	−	0.978776i	$-0.434303\pi$
$601$	10.0479	0.409863	0.204931	+	0.978776i	$0.434303\pi$
$602$	13.5268	0.551312
$603$	−8.98408	−0.365860
$604$	−31.7332	−1.29121
$605$	99.6123	4.04982
$606$	−32.5576	−1.32256
$607$	−5.94024	−0.241107	−0.120553	−	0.992707i	$-0.538467\pi$
$607$	−5.94024	−0.241107	−0.120553	+	0.992707i	$0.538467\pi$
$608$	−19.6710	−0.797763
$609$	2.80989	0.113862
$610$	−98.4725	−3.98704
$611$	19.6180	0.793661
$612$	11.7474	0.474860
$613$	15.6857	0.633539	0.316769	−	0.948503i	$-0.397402\pi$
$613$	15.6857	0.633539	0.316769	+	0.948503i	$0.397402\pi$
$614$	21.4214	0.864497
$615$	19.0459	0.768006
$616$	33.3706	1.34454
$617$	−6.45067	−0.259694	−0.129847	−	0.991534i	$-0.541449\pi$
$617$	−6.45067	−0.259694	−0.129847	+	0.991534i	$0.541449\pi$
$618$	−53.0471	−2.13387
$619$	−3.10687	−0.124876	−0.0624379	−	0.998049i	$-0.519888\pi$
$619$	−3.10687	−0.124876	−0.0624379	+	0.998049i	$0.519888\pi$
$620$	−52.2036	−2.09655
$621$	50.7294	2.03570
$622$	28.5926	1.14646
$623$	5.92187	0.237255
$624$	44.2568	1.77169
$625$	−9.31364	−0.372545
$626$	26.8127	1.07165
$627$	−16.2512	−0.649009
$628$	−56.8184	−2.26730
$629$	−6.72028	−0.267955
$630$	−10.4426	−0.416044
$631$	−29.4635	−1.17292	−0.586462	−	0.809976i	$-0.699480\pi$
$631$	−29.4635	−1.17292	−0.586462	+	0.809976i	$0.699480\pi$
$632$	81.8343	3.25520
$633$	7.73561	0.307463
$634$	75.7528	3.00853
$635$	−12.2246	−0.485120
$636$	−21.2269	−0.841700
$637$	26.2332	1.03940
$638$	−51.1274	−2.02415
$639$	−24.4150	−0.965843
$640$	11.6310	0.459756
$641$	−48.1471	−1.90169	−0.950847	−	0.309660i	$-0.899785\pi$
$641$	−48.1471	−1.90169	−0.950847	+	0.309660i	$0.899785\pi$
$642$	−2.73473	−0.107931
$643$	−44.2183	−1.74380	−0.871899	−	0.489686i	$-0.837112\pi$
$643$	−44.2183	−1.74380	−0.871899	+	0.489686i	$0.837112\pi$
$644$	−32.6975	−1.28846
$645$	−29.4311	−1.15885
$646$	8.91161	0.350622
$647$	45.0000	1.76913	0.884566	−	0.466415i	$-0.154454\pi$
$647$	45.0000	1.76913	0.884566	+	0.466415i	$0.154454\pi$
$648$	14.0045	0.550149
$649$	21.0097	0.824704
$650$	75.9291	2.97818
$651$	−2.82903	−0.110878
$652$	−65.3521	−2.55939
$653$	−32.3117	−1.26445	−0.632227	−	0.774784i	$-0.717859\pi$
$653$	−32.3117	−1.26445	−0.632227	+	0.774784i	$0.717859\pi$
$654$	−31.0008	−1.21223
$655$	−46.3827	−1.81232
$656$	−40.8402	−1.59454
$657$	2.54789	0.0994026
$658$	−9.32081	−0.363363
$659$	38.4217	1.49670	0.748349	−	0.663305i	$-0.230847\pi$
$659$	38.4217	1.49670	0.748349	+	0.663305i	$0.230847\pi$
$660$	−125.516	−4.88570
$661$	18.8765	0.734210	0.367105	−	0.930179i	$-0.380349\pi$
$661$	18.8765	0.734210	0.367105	+	0.930179i	$0.380349\pi$
$662$	−37.2315	−1.44704
$663$	−7.85072	−0.304897
$664$	33.8174	1.31237
$665$	−5.57271	−0.216100
$666$	16.8728	0.653806
$667$	28.9788	1.12206
$668$	34.8651	1.34897
$669$	−18.8457	−0.728618
$670$	−52.6384	−2.03360
$671$	68.3059	2.63692
$672$	−8.23336	−0.317609
$673$	−4.88197	−0.188186	−0.0940931	−	0.995563i	$-0.529995\pi$
$673$	−4.88197	−0.188186	−0.0940931	+	0.995563i	$0.529995\pi$
$674$	−14.2159	−0.547577
$675$	39.3725	1.51545
$676$	16.9116	0.650444
$677$	−14.1390	−0.543405	−0.271703	−	0.962381i	$-0.587587\pi$
$677$	−14.1390	−0.543405	−0.271703	+	0.962381i	$0.587587\pi$
$678$	16.3774	0.628972
$679$	4.09338	0.157090
$680$	39.8149	1.52683
$681$	7.24433	0.277603
$682$	51.4757	1.97111
$683$	−18.3055	−0.700440	−0.350220	−	0.936668i	$-0.613893\pi$
$683$	−18.3055	−0.700440	−0.350220	+	0.936668i	$0.613893\pi$
$684$	−15.7397	−0.601823
$685$	−32.7341	−1.25070
$686$	−25.9996	−0.992669
$687$	12.9066	0.492417
$688$	63.1091	2.40601
$689$	−15.1068	−0.575522
$690$	101.131	3.84998
$691$	12.6938	0.482895	0.241448	−	0.970414i	$-0.422378\pi$
$691$	12.6938	0.482895	0.241448	+	0.970414i	$0.422378\pi$
$692$	68.5786	2.60697
$693$	7.24358	0.275161
$694$	63.2271	2.40007
$695$	12.1709	0.461668
$696$	26.8983	1.01958
$697$	7.24465	0.274411
$698$	83.3302	3.15409
$699$	−3.34567	−0.126545
$700$	−25.3775	−0.959178
$701$	13.7325	0.518670	0.259335	−	0.965787i	$-0.416497\pi$
$701$	13.7325	0.518670	0.259335	+	0.965787i	$0.416497\pi$
$702$	57.9313	2.18648
$703$	9.00415	0.339598
$704$	36.3563	1.37023
$705$	20.2798	0.763783
$706$	−34.8207	−1.31049
$707$	7.74421	0.291251
$708$	−19.1080	−0.718123
$709$	37.0563	1.39168	0.695840	−	0.718197i	$-0.255032\pi$
$709$	37.0563	1.39168	0.695840	+	0.718197i	$0.255032\pi$
$710$	−143.049	−5.36855
$711$	17.7634	0.666178
$712$	56.6884	2.12449
$713$	−29.1762	−1.09266
$714$	3.72999	0.139591
$715$	−89.3273	−3.34065
$716$	49.5095	1.85026
$717$	−11.7459	−0.438658
$718$	−67.8905	−2.53365
$719$	−21.7402	−0.810771	−0.405386	−	0.914146i	$-0.632863\pi$
$719$	−21.7402	−0.810771	−0.405386	+	0.914146i	$0.632863\pi$
$720$	−48.7198	−1.81568
$721$	12.6179	0.469915
$722$	37.4033	1.39201
$723$	−1.20534	−0.0448270
$724$	120.371	4.47354
$725$	22.4912	0.835304
$726$	89.3325	3.31544
$727$	22.3166	0.827679	0.413839	−	0.910350i	$-0.364188\pi$
$727$	22.3166	0.827679	0.413839	+	0.910350i	$0.364188\pi$
$728$	−21.5995	−0.800531
$729$	22.8588	0.846621
$730$	14.9283	0.552520
$731$	−11.1949	−0.414060
$732$	−62.1232	−2.29614
$733$	−45.3568	−1.67529	−0.837645	−	0.546215i	$-0.816068\pi$
$733$	−45.3568	−1.67529	−0.837645	+	0.546215i	$0.816068\pi$
$734$	−10.9821	−0.405356
$735$	27.1182	1.00027
$736$	−84.9118	−3.12989
$737$	36.5129	1.34497
$738$	−18.1893	−0.669558
$739$	−12.2783	−0.451663	−0.225831	−	0.974166i	$-0.572510\pi$
$739$	−12.2783	−0.451663	−0.225831	+	0.974166i	$0.572510\pi$
$740$	69.5436	2.55647
$741$	10.5188	0.386417
$742$	7.17744	0.263492
$743$	23.7224	0.870291	0.435146	−	0.900360i	$-0.356697\pi$
$743$	23.7224	0.870291	0.435146	+	0.900360i	$0.356697\pi$
$744$	−27.0815	−0.992856
$745$	−29.3158	−1.07405
$746$	92.3960	3.38286
$747$	7.34056	0.268577
$748$	−47.7435	−1.74567
$749$	0.650488	0.0237683
$750$	23.8590	0.871207
$751$	18.8204	0.686765	0.343383	−	0.939196i	$-0.388427\pi$
$751$	18.8204	0.686765	0.343383	+	0.939196i	$0.388427\pi$
$752$	−43.4860	−1.58577
$753$	−1.77207	−0.0645777
$754$	33.0928	1.20517
$755$	−23.3458	−0.849640
$756$	−19.3621	−0.704194
$757$	20.4755	0.744195	0.372098	−	0.928194i	$-0.378639\pi$
$757$	20.4755	0.744195	0.372098	+	0.928194i	$0.378639\pi$
$758$	27.3173	0.992210
$759$	−70.1499	−2.54628
$760$	−53.3460	−1.93506
$761$	6.54100	0.237111	0.118555	−	0.992947i	$-0.462174\pi$
$761$	6.54100	0.237111	0.118555	+	0.992947i	$0.462174\pi$
$762$	−10.9631	−0.397151
$763$	7.37392	0.266954
$764$	−77.8632	−2.81699
$765$	8.64242	0.312467
$766$	−38.4499	−1.38925
$767$	−13.5988	−0.491024
$768$	24.3691	0.879343
$769$	−10.7564	−0.387885	−0.193942	−	0.981013i	$-0.562127\pi$
$769$	−10.7564	−0.387885	−0.193942	+	0.981013i	$0.562127\pi$
$770$	42.4407	1.52946
$771$	−22.9878	−0.827886
$772$	−38.2198	−1.37556
$773$	−24.6229	−0.885624	−0.442812	−	0.896614i	$-0.646019\pi$
$773$	−24.6229	−0.885624	−0.442812	+	0.896614i	$0.646019\pi$
$774$	28.1074	1.01030
$775$	−22.6445	−0.813413
$776$	39.1848	1.40665
$777$	3.76872	0.135202
$778$	23.1330	0.829357
$779$	−9.70673	−0.347780
$780$	81.2418	2.90892
$781$	99.2269	3.55062
$782$	38.4679	1.37561
$783$	17.1601	0.613250
$784$	−58.1495	−2.07677
$785$	−41.8007	−1.49193
$786$	−41.5961	−1.48369
$787$	−10.1240	−0.360883	−0.180441	−	0.983586i	$-0.557753\pi$
$787$	−10.1240	−0.360883	−0.180441	+	0.983586i	$0.557753\pi$
$788$	5.51363	0.196415
$789$	13.2769	0.472669
$790$	104.077	3.70289
$791$	−3.89557	−0.138511
$792$	69.3407	2.46392
$793$	−44.2119	−1.57001
$794$	−84.9440	−3.01455
$795$	−15.6164	−0.553856
$796$	−75.0219	−2.65908
$797$	−8.60700	−0.304876	−0.152438	−	0.988313i	$-0.548712\pi$
$797$	−8.60700	−0.304876	−0.152438	+	0.988313i	$0.548712\pi$
$798$	−4.99762	−0.176914
$799$	7.71400	0.272902
$800$	−65.9025	−2.33000
$801$	12.3051	0.434778
$802$	42.4849	1.50020
$803$	−10.3551	−0.365423
$804$	−33.2079	−1.17115
$805$	−24.0552	−0.847834
$806$	−33.3183	−1.17359
$807$	11.4343	0.402505
$808$	74.1332	2.60800
$809$	23.7331	0.834411	0.417205	−	0.908812i	$-0.363010\pi$
$809$	23.7331	0.834411	0.417205	+	0.908812i	$0.363010\pi$
$810$	17.8109	0.625813
$811$	35.1374	1.23384	0.616920	−	0.787026i	$-0.288380\pi$
$811$	35.1374	1.23384	0.616920	+	0.787026i	$0.288380\pi$
$812$	−11.0605	−0.388147
$813$	−25.7312	−0.902432
$814$	−68.5739	−2.40351
$815$	−48.0788	−1.68413
$816$	17.4022	0.609198
$817$	14.9995	0.524767
$818$	70.4308	2.46256
$819$	−4.68850	−0.163829
$820$	−74.9700	−2.61807
$821$	18.3525	0.640508	0.320254	−	0.947332i	$-0.396232\pi$
$821$	18.3525	0.640508	0.320254	+	0.947332i	$0.396232\pi$
$822$	−29.3560	−1.02391
$823$	−0.411745	−0.0143525	−0.00717626	−	0.999974i	$-0.502284\pi$
$823$	−0.411745	−0.0143525	−0.00717626	+	0.999974i	$0.502284\pi$
$824$	120.788	4.20784
$825$	−54.4453	−1.89554
$826$	6.46099	0.224807
$827$	−10.9496	−0.380756	−0.190378	−	0.981711i	$-0.560971\pi$
$827$	−10.9496	−0.380756	−0.190378	+	0.981711i	$0.560971\pi$
$828$	−67.9422	−2.36115
$829$	6.76398	0.234923	0.117461	−	0.993077i	$-0.462524\pi$
$829$	6.76398	0.234923	0.117461	+	0.993077i	$0.462524\pi$
$830$	43.0089	1.49286
$831$	22.0322	0.764288
$832$	−23.5321	−0.815827
$833$	10.3152	0.357399
$834$	10.9149	0.377951
$835$	25.6499	0.887651
$836$	63.9690	2.21241
$837$	−17.2770	−0.597179
$838$	4.40121	0.152037
$839$	3.28222	0.113315	0.0566574	−	0.998394i	$-0.481956\pi$
$839$	3.28222	0.113315	0.0566574	+	0.998394i	$0.481956\pi$
$840$	−22.3282	−0.770395
$841$	−19.1974	−0.661981
$842$	−16.2884	−0.561335
$843$	−13.8791	−0.478021
$844$	−30.4495	−1.04811
$845$	12.4416	0.428006
$846$	−19.3677	−0.665876
$847$	−21.2488	−0.730118
$848$	33.4862	1.14992
$849$	−30.3426	−1.04136
$850$	29.8560	1.02405
$851$	38.8674	1.33236
$852$	−90.2454	−3.09175
$853$	−36.1823	−1.23886	−0.619429	−	0.785053i	$-0.712636\pi$
$853$	−36.1823	−1.23886	−0.619429	+	0.785053i	$0.712636\pi$
$854$	21.0057	0.718800
$855$	−11.5795	−0.396012
$856$	6.22694	0.212832
$857$	−25.4700	−0.870037	−0.435019	−	0.900421i	$-0.643258\pi$
$857$	−25.4700	−0.870037	−0.435019	+	0.900421i	$0.643258\pi$
$858$	−80.1089	−2.73487
$859$	3.88904	0.132692	0.0663461	−	0.997797i	$-0.478866\pi$
$859$	3.88904	0.132692	0.0663461	+	0.997797i	$0.478866\pi$
$860$	115.849	3.95042
$861$	−4.06279	−0.138459
$862$	−68.0532	−2.31790
$863$	−4.43810	−0.151075	−0.0755373	−	0.997143i	$-0.524067\pi$
$863$	−4.43810	−0.151075	−0.0755373	+	0.997143i	$0.524067\pi$
$864$	−50.2814	−1.71061
$865$	50.4526	1.71544
$866$	4.20509	0.142895
$867$	17.4038	0.591063
$868$	11.1358	0.377975
$869$	−72.1934	−2.44899
$870$	34.2092	1.15980
$871$	−23.6334	−0.800788
$872$	70.5885	2.39043
$873$	8.50564	0.287872
$874$	−51.5411	−1.74341
$875$	−5.67515	−0.191855
$876$	9.41778	0.318197
$877$	29.5579	0.998101	0.499050	−	0.866573i	$-0.333682\pi$
$877$	29.5579	0.998101	0.499050	+	0.866573i	$0.333682\pi$
$878$	93.0907	3.14166
$879$	0.385449	0.0130009
$880$	198.006	6.67478
$881$	−48.9852	−1.65035	−0.825177	−	0.564874i	$-0.808925\pi$
$881$	−48.9852	−1.65035	−0.825177	+	0.564874i	$0.808925\pi$
$882$	−25.8985	−0.872048
$883$	10.8101	0.363790	0.181895	−	0.983318i	$-0.441777\pi$
$883$	10.8101	0.363790	0.181895	+	0.983318i	$0.441777\pi$
$884$	30.9026	1.03937
$885$	−14.0576	−0.472540
$886$	−51.1218	−1.71747
$887$	−13.9186	−0.467340	−0.233670	−	0.972316i	$-0.575074\pi$
$887$	−13.9186	−0.467340	−0.233670	+	0.972316i	$0.575074\pi$
$888$	36.0769	1.21066
$889$	2.60770	0.0874596
$890$	72.0963	2.41667
$891$	−12.3546	−0.413896
$892$	74.1819	2.48379
$893$	−10.3356	−0.345867
$894$	−26.2905	−0.879286
$895$	36.4236	1.21751
$896$	−2.48107	−0.0828869
$897$	45.4054	1.51604
$898$	−59.8472	−1.99713
$899$	−9.86933	−0.329161
$900$	−52.7318	−1.75773
$901$	−5.94012	−0.197894
$902$	73.9246	2.46142
$903$	6.27811	0.208922
$904$	−37.2912	−1.24029
$905$	88.5554	2.94368
$906$	−20.9366	−0.695571
$907$	−45.3560	−1.50602	−0.753011	−	0.658008i	$-0.771399\pi$
$907$	−45.3560	−1.50602	−0.753011	+	0.658008i	$0.771399\pi$
$908$	−28.5156	−0.946325
$909$	16.0917	0.533728
$910$	−27.4703	−0.910630
$911$	3.51366	0.116413	0.0582064	−	0.998305i	$-0.481462\pi$
$911$	3.51366	0.116413	0.0582064	+	0.998305i	$0.481462\pi$
$912$	−23.3163	−0.772079
$913$	−29.8333	−0.987339
$914$	−25.3352	−0.838013
$915$	−45.7033	−1.51091
$916$	−50.8039	−1.67861
$917$	9.89414	0.326733
$918$	22.7791	0.751824
$919$	22.3344	0.736743	0.368372	−	0.929679i	$-0.379915\pi$
$919$	22.3344	0.736743	0.368372	+	0.929679i	$0.379915\pi$
$920$	−230.274	−7.59190
$921$	9.94216	0.327605
$922$	−75.4689	−2.48544
$923$	−64.2259	−2.11402
$924$	26.7745	0.880816
$925$	30.1661	0.991854
$926$	−88.6226	−2.91232
$927$	26.2187	0.861137
$928$	−28.7229	−0.942874
$929$	18.1496	0.595470	0.297735	−	0.954648i	$-0.403769\pi$
$929$	18.1496	0.595470	0.297735	+	0.954648i	$0.403769\pi$
$930$	−34.4423	−1.12941
$931$	−13.8207	−0.452956
$932$	13.1695	0.431380
$933$	13.2705	0.434456
$934$	31.1802	1.02025
$935$	−35.1243	−1.14869
$936$	−44.8817	−1.46700
$937$	50.6507	1.65469	0.827343	−	0.561696i	$-0.189851\pi$
$937$	50.6507	1.65469	0.827343	+	0.561696i	$0.189851\pi$
$938$	11.2286	0.366626
$939$	12.4444	0.406107
$940$	−79.8270	−2.60367
$941$	44.9519	1.46539	0.732695	−	0.680558i	$-0.238262\pi$
$941$	44.9519	1.46539	0.732695	+	0.680558i	$0.238262\pi$
$942$	−37.4869	−1.22139
$943$	−41.9001	−1.36446
$944$	30.1436	0.981090
$945$	−14.2445	−0.463374
$946$	−114.234	−3.71405
$947$	18.5204	0.601832	0.300916	−	0.953651i	$-0.402708\pi$
$947$	18.5204	0.601832	0.300916	+	0.953651i	$0.402708\pi$
$948$	65.6588	2.13250
$949$	6.70245	0.217571
$950$	−40.0025	−1.29785
$951$	35.1586	1.14010
$952$	−8.49313	−0.275264
$953$	4.77064	0.154536	0.0772681	−	0.997010i	$-0.475380\pi$
$953$	4.77064	0.154536	0.0772681	+	0.997010i	$0.475380\pi$
$954$	14.9140	0.482859
$955$	−57.2831	−1.85364
$956$	46.2350	1.49535
$957$	−23.7294	−0.767062
$958$	−19.4132	−0.627212
$959$	6.98268	0.225482
$960$	−24.3259	−0.785115
$961$	−21.0634	−0.679465
$962$	44.3853	1.43104
$963$	1.35165	0.0435563
$964$	4.74454	0.152811
$965$	−28.1179	−0.905147
$966$	−21.5727	−0.694092
$967$	−42.9853	−1.38231	−0.691157	−	0.722705i	$-0.742898\pi$
$967$	−42.9853	−1.38231	−0.691157	+	0.722705i	$0.742898\pi$
$968$	−203.409	−6.53781
$969$	4.13608	0.132870
$970$	49.8352	1.60011
$971$	38.4332	1.23338	0.616690	−	0.787206i	$-0.288473\pi$
$971$	38.4332	1.23338	0.616690	+	0.787206i	$0.288473\pi$
$972$	−66.7762	−2.14185
$973$	−2.59623	−0.0832314
$974$	−56.6112	−1.81394
$975$	35.2404	1.12860
$976$	98.0016	3.13695
$977$	11.7197	0.374948	0.187474	−	0.982270i	$-0.439970\pi$
$977$	11.7197	0.374948	0.187474	+	0.982270i	$0.439970\pi$
$978$	−43.1172	−1.37874
$979$	−50.0099	−1.59832
$980$	−106.745	−3.40983
$981$	15.3223	0.489203
$982$	33.4780	1.06832
$983$	−24.4745	−0.780615	−0.390307	−	0.920685i	$-0.627631\pi$
$983$	−24.4745	−0.780615	−0.390307	+	0.920685i	$0.627631\pi$
$984$	−38.8920	−1.23983
$985$	4.05632	0.129245
$986$	13.0124	0.414400
$987$	−4.32600	−0.137698
$988$	−41.4047	−1.31726
$989$	64.7470	2.05884
$990$	88.1876	2.80278
$991$	22.7385	0.722313	0.361156	−	0.932505i	$-0.382382\pi$
$991$	22.7385	0.722313	0.361156	+	0.932505i	$0.382382\pi$
$992$	28.9185	0.918164
$993$	−17.2800	−0.548363
$994$	30.5146	0.967866
$995$	−55.1928	−1.74973
$996$	27.1329	0.859740
$997$	51.7206	1.63801	0.819005	−	0.573787i	$-0.194526\pi$
$997$	51.7206	1.63801	0.819005	+	0.573787i	$0.194526\pi$
$998$	64.8592	2.05308
$999$	23.0157	0.728184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.1	✓	12
3.2	odd	2		2169.2.a.h.1.12		12
4.3	odd	2		3856.2.a.n.1.9		12
5.4	even	2		6025.2.a.h.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.1	✓	12	1.1	even	1	trivial
2169.2.a.h.1.12		12	3.2	odd	2
3856.2.a.n.1.9		12	4.3	odd	2
6025.2.a.h.1.12		12	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)

\(f(q)\)	\(=\)	\(q-2.59703 q^{2} -1.20534 q^{3} +4.74454 q^{4} +3.49051 q^{5} +3.13029 q^{6} -0.744578 q^{7} -7.12764 q^{8} -1.54716 q^{9} +O(q^{10})\)	\(q-2.59703 q^{2} -1.20534 q^{3} +4.74454 q^{4} +3.49051 q^{5} +3.13029 q^{6} -0.744578 q^{7} -7.12764 q^{8} -1.54716 q^{9} -9.06493 q^{10} +6.28793 q^{11} -5.71878 q^{12} -4.06994 q^{13} +1.93369 q^{14} -4.20724 q^{15} +9.02158 q^{16} -1.60034 q^{17} +4.01801 q^{18} +2.14421 q^{19} +16.5608 q^{20} +0.897468 q^{21} -16.3299 q^{22} +9.25572 q^{23} +8.59122 q^{24} +7.18363 q^{25} +10.5697 q^{26} +5.48087 q^{27} -3.53268 q^{28} +3.13090 q^{29} +10.9263 q^{30} -3.15223 q^{31} -9.17399 q^{32} -7.57908 q^{33} +4.15612 q^{34} -2.59895 q^{35} -7.34056 q^{36} +4.19928 q^{37} -5.56857 q^{38} +4.90566 q^{39} -24.8791 q^{40} -4.52694 q^{41} -2.33075 q^{42} +6.99535 q^{43} +29.8333 q^{44} -5.40037 q^{45} -24.0373 q^{46} -4.82023 q^{47} -10.8741 q^{48} -6.44560 q^{49} -18.6561 q^{50} +1.92895 q^{51} -19.3100 q^{52} +3.71179 q^{53} -14.2339 q^{54} +21.9481 q^{55} +5.30708 q^{56} -2.58450 q^{57} -8.13103 q^{58} +3.34128 q^{59} -19.9614 q^{60} +10.8630 q^{61} +8.18643 q^{62} +1.15198 q^{63} +5.78192 q^{64} -14.2062 q^{65} +19.6831 q^{66} +5.80682 q^{67} -7.59287 q^{68} -11.1563 q^{69} +6.74955 q^{70} +15.7805 q^{71} +11.0276 q^{72} -1.64682 q^{73} -10.9056 q^{74} -8.65870 q^{75} +10.1733 q^{76} -4.68186 q^{77} -12.7401 q^{78} -11.4813 q^{79} +31.4899 q^{80} -1.96482 q^{81} +11.7566 q^{82} -4.74454 q^{83} +4.25807 q^{84} -5.58599 q^{85} -18.1671 q^{86} -3.77380 q^{87} -44.8181 q^{88} -7.95332 q^{89} +14.0249 q^{90} +3.03039 q^{91} +43.9141 q^{92} +3.79951 q^{93} +12.5182 q^{94} +7.48438 q^{95} +11.0578 q^{96} -5.49759 q^{97} +16.7394 q^{98} -9.72843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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