LMFDB - Embedded newform 2013.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} + \cdots - 35 $ x^13 - 4x^12 - 11x^11 + 57x^10 + 28x^9 - 290x^8 + 51x^7 + 644x^6 - 259x^5 - 640x^4 + 274x^3 + 256x^2 - 74x - 35
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.312603$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.312603 q^{2} +1.00000 q^{3} -1.90228 q^{4} -0.566394 q^{5} -0.312603 q^{6} +3.64999 q^{7} +1.21987 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.312603 q^{2} +1.00000 q^{3} -1.90228 q^{4} -0.566394 q^{5} -0.312603 q^{6} +3.64999 q^{7} +1.21987 q^{8} +1.00000 q^{9} +0.177056 q^{10} +1.00000 q^{11} -1.90228 q^{12} -4.95192 q^{13} -1.14100 q^{14} -0.566394 q^{15} +3.42322 q^{16} +4.81571 q^{17} -0.312603 q^{18} +5.92245 q^{19} +1.07744 q^{20} +3.64999 q^{21} -0.312603 q^{22} -2.51849 q^{23} +1.21987 q^{24} -4.67920 q^{25} +1.54799 q^{26} +1.00000 q^{27} -6.94331 q^{28} -1.74831 q^{29} +0.177056 q^{30} -0.640532 q^{31} -3.50984 q^{32} +1.00000 q^{33} -1.50541 q^{34} -2.06733 q^{35} -1.90228 q^{36} +8.32847 q^{37} -1.85138 q^{38} -4.95192 q^{39} -0.690924 q^{40} +1.27159 q^{41} -1.14100 q^{42} -8.66727 q^{43} -1.90228 q^{44} -0.566394 q^{45} +0.787289 q^{46} +7.48555 q^{47} +3.42322 q^{48} +6.32245 q^{49} +1.46273 q^{50} +4.81571 q^{51} +9.41994 q^{52} +5.68854 q^{53} -0.312603 q^{54} -0.566394 q^{55} +4.45250 q^{56} +5.92245 q^{57} +0.546528 q^{58} +8.26974 q^{59} +1.07744 q^{60} +1.00000 q^{61} +0.200232 q^{62} +3.64999 q^{63} -5.74926 q^{64} +2.80474 q^{65} -0.312603 q^{66} +2.72272 q^{67} -9.16082 q^{68} -2.51849 q^{69} +0.646255 q^{70} -1.89197 q^{71} +1.21987 q^{72} -5.86057 q^{73} -2.60351 q^{74} -4.67920 q^{75} -11.2662 q^{76} +3.64999 q^{77} +1.54799 q^{78} +8.84072 q^{79} -1.93889 q^{80} +1.00000 q^{81} -0.397505 q^{82} +7.12240 q^{83} -6.94331 q^{84} -2.72759 q^{85} +2.70942 q^{86} -1.74831 q^{87} +1.21987 q^{88} -0.680778 q^{89} +0.177056 q^{90} -18.0745 q^{91} +4.79088 q^{92} -0.640532 q^{93} -2.34001 q^{94} -3.35444 q^{95} -3.50984 q^{96} +7.68043 q^{97} -1.97642 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * 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 $

$2$	−0.312603	−0.221044	−0.110522	−	0.993874i	$-0.535252\pi$
$2$	−0.312603	−0.221044	−0.110522	+	0.993874i	$0.535252\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90228	−0.951140
$5$	−0.566394	−0.253299	−0.126649	−	0.991948i	$-0.540422\pi$
$5$	−0.566394	−0.253299	−0.126649	+	0.991948i	$0.540422\pi$
$6$	−0.312603	−0.127620
$7$	3.64999	1.37957	0.689784	−	0.724015i	$-0.257706\pi$
$7$	3.64999	1.37957	0.689784	+	0.724015i	$0.257706\pi$
$8$	1.21987	0.431287
$9$	1.00000	0.333333
$10$	0.177056	0.0559902
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.90228	−0.549141
$13$	−4.95192	−1.37342	−0.686708	−	0.726933i	$-0.740945\pi$
$13$	−4.95192	−1.37342	−0.686708	+	0.726933i	$0.740945\pi$
$14$	−1.14100	−0.304945
$15$	−0.566394	−0.146242
$16$	3.42322	0.855806
$17$	4.81571	1.16798	0.583990	−	0.811761i	$-0.301491\pi$
$17$	4.81571	1.16798	0.583990	+	0.811761i	$0.301491\pi$
$18$	−0.312603	−0.0736813
$19$	5.92245	1.35870	0.679352	−	0.733813i	$-0.262261\pi$
$19$	5.92245	1.35870	0.679352	+	0.733813i	$0.262261\pi$
$20$	1.07744	0.240923
$21$	3.64999	0.796494
$22$	−0.312603	−0.0666472
$23$	−2.51849	−0.525142	−0.262571	−	0.964913i	$-0.584570\pi$
$23$	−2.51849	−0.525142	−0.262571	+	0.964913i	$0.584570\pi$
$24$	1.21987	0.249004
$25$	−4.67920	−0.935840
$26$	1.54799	0.303585
$27$	1.00000	0.192450
$28$	−6.94331	−1.31216
$29$	−1.74831	−0.324653	−0.162327	−	0.986737i	$-0.551900\pi$
$29$	−1.74831	−0.324653	−0.162327	+	0.986737i	$0.551900\pi$
$30$	0.177056	0.0323259
$31$	−0.640532	−0.115043	−0.0575215	−	0.998344i	$-0.518320\pi$
$31$	−0.640532	−0.115043	−0.0575215	+	0.998344i	$0.518320\pi$
$32$	−3.50984	−0.620458
$33$	1.00000	0.174078
$34$	−1.50541	−0.258175
$35$	−2.06733	−0.349443
$36$	−1.90228	−0.317047
$37$	8.32847	1.36919	0.684596	−	0.728923i	$-0.259979\pi$
$37$	8.32847	1.36919	0.684596	+	0.728923i	$0.259979\pi$
$38$	−1.85138	−0.300333
$39$	−4.95192	−0.792942
$40$	−0.690924	−0.109245
$41$	1.27159	0.198590	0.0992949	−	0.995058i	$-0.468341\pi$
$41$	1.27159	0.198590	0.0992949	+	0.995058i	$0.468341\pi$
$42$	−1.14100	−0.176060
$43$	−8.66727	−1.32175	−0.660873	−	0.750498i	$-0.729814\pi$
$43$	−8.66727	−1.32175	−0.660873	+	0.750498i	$0.729814\pi$
$44$	−1.90228	−0.286779
$45$	−0.566394	−0.0844330
$46$	0.787289	0.116079
$47$	7.48555	1.09188	0.545940	−	0.837825i	$-0.316173\pi$
$47$	7.48555	1.09188	0.545940	+	0.837825i	$0.316173\pi$
$48$	3.42322	0.494100
$49$	6.32245	0.903208
$50$	1.46273	0.206862
$51$	4.81571	0.674334
$52$	9.41994	1.30631
$53$	5.68854	0.781381	0.390690	−	0.920522i	$-0.372236\pi$
$53$	5.68854	0.781381	0.390690	+	0.920522i	$0.372236\pi$
$54$	−0.312603	−0.0425399
$55$	−0.566394	−0.0763725
$56$	4.45250	0.594990
$57$	5.92245	0.784448
$58$	0.546528	0.0717627
$59$	8.26974	1.07663	0.538315	−	0.842744i	$-0.319061\pi$
$59$	8.26974	1.07663	0.538315	+	0.842744i	$0.319061\pi$
$60$	1.07744	0.139097
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	0.200232	0.0254295
$63$	3.64999	0.459856
$64$	−5.74926	−0.718658
$65$	2.80474	0.347885
$66$	−0.312603	−0.0384788
$67$	2.72272	0.332633	0.166317	−	0.986072i	$-0.446813\pi$
$67$	2.72272	0.332633	0.166317	+	0.986072i	$0.446813\pi$
$68$	−9.16082	−1.11091
$69$	−2.51849	−0.303191
$70$	0.646255	0.0772422
$71$	−1.89197	−0.224536	−0.112268	−	0.993678i	$-0.535812\pi$
$71$	−1.89197	−0.224536	−0.112268	+	0.993678i	$0.535812\pi$
$72$	1.21987	0.143762
$73$	−5.86057	−0.685928	−0.342964	−	0.939349i	$-0.611431\pi$
$73$	−5.86057	−0.685928	−0.342964	+	0.939349i	$0.611431\pi$
$74$	−2.60351	−0.302652
$75$	−4.67920	−0.540307
$76$	−11.2662	−1.29232
$77$	3.64999	0.415955
$78$	1.54799	0.175275
$79$	8.84072	0.994659	0.497330	−	0.867562i	$-0.334314\pi$
$79$	8.84072	0.994659	0.497330	+	0.867562i	$0.334314\pi$
$80$	−1.93889	−0.216775
$81$	1.00000	0.111111
$82$	−0.397505	−0.0438970
$83$	7.12240	0.781785	0.390892	−	0.920436i	$-0.372166\pi$
$83$	7.12240	0.781785	0.390892	+	0.920436i	$0.372166\pi$
$84$	−6.94331	−0.757577
$85$	−2.72759	−0.295848
$86$	2.70942	0.292164
$87$	−1.74831	−0.187439
$88$	1.21987	0.130038
$89$	−0.680778	−0.0721623	−0.0360812	−	0.999349i	$-0.511487\pi$
$89$	−0.680778	−0.0721623	−0.0360812	+	0.999349i	$0.511487\pi$
$90$	0.177056	0.0186634
$91$	−18.0745	−1.89472
$92$	4.79088	0.499483
$93$	−0.640532	−0.0664201
$94$	−2.34001	−0.241353
$95$	−3.35444	−0.344158
$96$	−3.50984	−0.358222
$97$	7.68043	0.779830	0.389915	−	0.920851i	$-0.372504\pi$
$97$	7.68043	0.779830	0.389915	+	0.920851i	$0.372504\pi$
$98$	−1.97642	−0.199648
$99$	1.00000	0.100504
$100$	8.90114	0.890114
$101$	5.75759	0.572901	0.286451	−	0.958095i	$-0.407525\pi$
$101$	5.75759	0.572901	0.286451	+	0.958095i	$0.407525\pi$
$102$	−1.50541	−0.149057
$103$	0.367680	0.0362286	0.0181143	−	0.999836i	$-0.494234\pi$
$103$	0.367680	0.0362286	0.0181143	+	0.999836i	$0.494234\pi$
$104$	−6.04068	−0.592337
$105$	−2.06733	−0.201751
$106$	−1.77826	−0.172719
$107$	10.3242	0.998075	0.499038	−	0.866580i	$-0.333687\pi$
$107$	10.3242	0.998075	0.499038	+	0.866580i	$0.333687\pi$
$108$	−1.90228	−0.183047
$109$	5.75458	0.551188	0.275594	−	0.961274i	$-0.411125\pi$
$109$	5.75458	0.551188	0.275594	+	0.961274i	$0.411125\pi$
$110$	0.177056	0.0168817
$111$	8.32847	0.790503
$112$	12.4947	1.18064
$113$	3.31944	0.312266	0.156133	−	0.987736i	$-0.450097\pi$
$113$	3.31944	0.312266	0.156133	+	0.987736i	$0.450097\pi$
$114$	−1.85138	−0.173397
$115$	1.42646	0.133018
$116$	3.32578	0.308791
$117$	−4.95192	−0.457805
$118$	−2.58515	−0.237982
$119$	17.5773	1.61131
$120$	−0.690924	−0.0630724
$121$	1.00000	0.0909091
$122$	−0.312603	−0.0283018
$123$	1.27159	0.114656
$124$	1.21847	0.109422
$125$	5.48224	0.490346
$126$	−1.14100	−0.101648
$127$	−4.18381	−0.371253	−0.185626	−	0.982620i	$-0.559431\pi$
$127$	−4.18381	−0.371253	−0.185626	+	0.982620i	$0.559431\pi$
$128$	8.81692	0.779313
$129$	−8.66727	−0.763110
$130$	−0.876770	−0.0768978
$131$	−11.5884	−1.01249	−0.506244	−	0.862391i	$-0.668966\pi$
$131$	−11.5884	−1.01249	−0.506244	+	0.862391i	$0.668966\pi$
$132$	−1.90228	−0.165572
$133$	21.6169	1.87442
$134$	−0.851132	−0.0735266
$135$	−0.566394	−0.0487474
$136$	5.87451	0.503735
$137$	7.91940	0.676600	0.338300	−	0.941038i	$-0.390148\pi$
$137$	7.91940	0.676600	0.338300	+	0.941038i	$0.390148\pi$
$138$	0.787289	0.0670185
$139$	1.64236	0.139303	0.0696516	−	0.997571i	$-0.477811\pi$
$139$	1.64236	0.139303	0.0696516	+	0.997571i	$0.477811\pi$
$140$	3.93264	0.332369
$141$	7.48555	0.630397
$142$	0.591437	0.0496323
$143$	−4.95192	−0.414100
$144$	3.42322	0.285269
$145$	0.990233	0.0822344
$146$	1.83203	0.151620
$147$	6.32245	0.521467
$148$	−15.8431	−1.30229
$149$	11.3148	0.926944	0.463472	−	0.886112i	$-0.346604\pi$
$149$	11.3148	0.926944	0.463472	+	0.886112i	$0.346604\pi$
$150$	1.46273	0.119432
$151$	−7.66180	−0.623508	−0.311754	−	0.950163i	$-0.600917\pi$
$151$	−7.66180	−0.623508	−0.311754	+	0.950163i	$0.600917\pi$
$152$	7.22459	0.585992
$153$	4.81571	0.389327
$154$	−1.14100	−0.0919444
$155$	0.362793	0.0291402
$156$	9.41994	0.754199
$157$	8.82636	0.704420	0.352210	−	0.935921i	$-0.385430\pi$
$157$	8.82636	0.704420	0.352210	+	0.935921i	$0.385430\pi$
$158$	−2.76364	−0.219863
$159$	5.68854	0.451130
$160$	1.98795	0.157161
$161$	−9.19248	−0.724469
$162$	−0.312603	−0.0245604
$163$	−5.69791	−0.446295	−0.223147	−	0.974785i	$-0.571633\pi$
$163$	−5.69791	−0.446295	−0.223147	+	0.974785i	$0.571633\pi$
$164$	−2.41893	−0.188887
$165$	−0.566394	−0.0440937
$166$	−2.22648	−0.172809
$167$	−6.58782	−0.509781	−0.254891	−	0.966970i	$-0.582039\pi$
$167$	−6.58782	−0.509781	−0.254891	+	0.966970i	$0.582039\pi$
$168$	4.45250	0.343518
$169$	11.5215	0.886271
$170$	0.852652	0.0653954
$171$	5.92245	0.452901
$172$	16.4876	1.25716
$173$	17.4016	1.32302	0.661509	−	0.749937i	$-0.269916\pi$
$173$	17.4016	1.32302	0.661509	+	0.749937i	$0.269916\pi$
$174$	0.546528	0.0414322
$175$	−17.0790	−1.29105
$176$	3.42322	0.258035
$177$	8.26974	0.621592
$178$	0.212813	0.0159510
$179$	12.2137	0.912894	0.456447	−	0.889751i	$-0.349122\pi$
$179$	12.2137	0.912894	0.456447	+	0.889751i	$0.349122\pi$
$180$	1.07744	0.0803075
$181$	−5.01121	−0.372480	−0.186240	−	0.982504i	$-0.559630\pi$
$181$	−5.01121	−0.372480	−0.186240	+	0.982504i	$0.559630\pi$
$182$	5.65014	0.418816
$183$	1.00000	0.0739221
$184$	−3.07222	−0.226487
$185$	−4.71719	−0.346815
$186$	0.200232	0.0146818
$187$	4.81571	0.352159
$188$	−14.2396	−1.03853
$189$	3.64999	0.265498
$190$	1.04861	0.0760741
$191$	14.1607	1.02463	0.512316	−	0.858797i	$-0.328788\pi$
$191$	14.1607	1.02463	0.512316	+	0.858797i	$0.328788\pi$
$192$	−5.74926	−0.414917
$193$	24.7548	1.78189	0.890946	−	0.454110i	$-0.150043\pi$
$193$	24.7548	1.78189	0.890946	+	0.454110i	$0.150043\pi$
$194$	−2.40093	−0.172377
$195$	2.80474	0.200851
$196$	−12.0271	−0.859077
$197$	−8.63717	−0.615373	−0.307686	−	0.951488i	$-0.599555\pi$
$197$	−8.63717	−0.615373	−0.307686	+	0.951488i	$0.599555\pi$
$198$	−0.312603	−0.0222157
$199$	−14.9776	−1.06174	−0.530868	−	0.847455i	$-0.678134\pi$
$199$	−14.9776	−1.06174	−0.530868	+	0.847455i	$0.678134\pi$
$200$	−5.70799	−0.403616
$201$	2.72272	0.192046
$202$	−1.79984	−0.126636
$203$	−6.38133	−0.447882
$204$	−9.16082	−0.641386
$205$	−0.720223	−0.0503026
$206$	−0.114938	−0.00800812
$207$	−2.51849	−0.175047
$208$	−16.9515	−1.17538
$209$	5.92245	0.409665
$210$	0.646255	0.0445958
$211$	−8.99241	−0.619063	−0.309532	−	0.950889i	$-0.600172\pi$
$211$	−8.99241	−0.619063	−0.309532	+	0.950889i	$0.600172\pi$
$212$	−10.8212	−0.743202
$213$	−1.89197	−0.129636
$214$	−3.22737	−0.220618
$215$	4.90908	0.334797
$216$	1.21987	0.0830013
$217$	−2.33794	−0.158710
$218$	−1.79890	−0.121837
$219$	−5.86057	−0.396021
$220$	1.07744	0.0726409
$221$	−23.8470	−1.60412
$222$	−2.60351	−0.174736
$223$	−28.6287	−1.91712	−0.958561	−	0.284888i	$-0.908043\pi$
$223$	−28.6287	−1.91712	−0.958561	+	0.284888i	$0.908043\pi$
$224$	−12.8109	−0.855964
$225$	−4.67920	−0.311947
$226$	−1.03767	−0.0690245
$227$	−25.8521	−1.71586	−0.857932	−	0.513763i	$-0.828251\pi$
$227$	−25.8521	−1.71586	−0.857932	+	0.513763i	$0.828251\pi$
$228$	−11.2662	−0.746120
$229$	−22.3266	−1.47538	−0.737691	−	0.675139i	$-0.764084\pi$
$229$	−22.3266	−1.47538	−0.737691	+	0.675139i	$0.764084\pi$
$230$	−0.445915	−0.0294028
$231$	3.64999	0.240152
$232$	−2.13271	−0.140019
$233$	29.6483	1.94232	0.971161	−	0.238424i	$-0.0766309\pi$
$233$	29.6483	1.94232	0.971161	+	0.238424i	$0.0766309\pi$
$234$	1.54799	0.101195
$235$	−4.23977	−0.276572
$236$	−15.7314	−1.02402
$237$	8.84072	0.574267
$238$	−5.49472	−0.356170
$239$	−20.1797	−1.30531	−0.652657	−	0.757653i	$-0.726346\pi$
$239$	−20.1797	−1.30531	−0.652657	+	0.757653i	$0.726346\pi$
$240$	−1.93889	−0.125155
$241$	−9.92548	−0.639356	−0.319678	−	0.947526i	$-0.603575\pi$
$241$	−9.92548	−0.639356	−0.319678	+	0.947526i	$0.603575\pi$
$242$	−0.312603	−0.0200949
$243$	1.00000	0.0641500
$244$	−1.90228	−0.121781
$245$	−3.58100	−0.228781
$246$	−0.397505	−0.0253440
$247$	−29.3275	−1.86607
$248$	−0.781363	−0.0496166
$249$	7.12240	0.451364
$250$	−1.71376	−0.108388
$251$	30.4348	1.92103	0.960513	−	0.278237i	$-0.0897499\pi$
$251$	30.4348	1.92103	0.960513	+	0.278237i	$0.0897499\pi$
$252$	−6.94331	−0.437387
$253$	−2.51849	−0.158336
$254$	1.30787	0.0820632
$255$	−2.72759	−0.170808
$256$	8.74233	0.546395
$257$	−21.9651	−1.37015	−0.685074	−	0.728474i	$-0.740230\pi$
$257$	−21.9651	−1.37015	−0.685074	+	0.728474i	$0.740230\pi$
$258$	2.70942	0.168681
$259$	30.3989	1.88889
$260$	−5.33539	−0.330887
$261$	−1.74831	−0.108218
$262$	3.62259	0.223804
$263$	10.7441	0.662509	0.331254	−	0.943541i	$-0.392528\pi$
$263$	10.7441	0.662509	0.331254	+	0.943541i	$0.392528\pi$
$264$	1.21987	0.0750775
$265$	−3.22195	−0.197923
$266$	−6.75752	−0.414330
$267$	−0.680778	−0.0416629
$268$	−5.17938	−0.316381
$269$	−1.67222	−0.101957	−0.0509784	−	0.998700i	$-0.516234\pi$
$269$	−1.67222	−0.101957	−0.0509784	+	0.998700i	$0.516234\pi$
$270$	0.177056	0.0107753
$271$	−19.2595	−1.16993	−0.584965	−	0.811058i	$-0.698892\pi$
$271$	−19.2595	−1.16993	−0.584965	+	0.811058i	$0.698892\pi$
$272$	16.4852	0.999565
$273$	−18.0745	−1.09392
$274$	−2.47563	−0.149558
$275$	−4.67920	−0.282166
$276$	4.79088	0.288377
$277$	−9.37301	−0.563169	−0.281585	−	0.959536i	$-0.590860\pi$
$277$	−9.37301	−0.563169	−0.281585	+	0.959536i	$0.590860\pi$
$278$	−0.513407	−0.0307921
$279$	−0.640532	−0.0383476
$280$	−2.52187	−0.150710
$281$	23.2121	1.38472	0.692360	−	0.721552i	$-0.256571\pi$
$281$	23.2121	1.38472	0.692360	+	0.721552i	$0.256571\pi$
$282$	−2.34001	−0.139345
$283$	13.6668	0.812406	0.406203	−	0.913783i	$-0.366853\pi$
$283$	13.6668	0.812406	0.406203	+	0.913783i	$0.366853\pi$
$284$	3.59906	0.213565
$285$	−3.35444	−0.198700
$286$	1.54799	0.0915344
$287$	4.64131	0.273968
$288$	−3.50984	−0.206819
$289$	6.19103	0.364178
$290$	−0.309550	−0.0181774
$291$	7.68043	0.450235
$292$	11.1484	0.652413
$293$	−29.1764	−1.70450	−0.852252	−	0.523132i	$-0.824764\pi$
$293$	−29.1764	−1.70450	−0.852252	+	0.523132i	$0.824764\pi$
$294$	−1.97642	−0.115267
$295$	−4.68393	−0.272709
$296$	10.1596	0.590515
$297$	1.00000	0.0580259
$298$	−3.53704	−0.204895
$299$	12.4714	0.721238
$300$	8.90114	0.513908
$301$	−31.6355	−1.82344
$302$	2.39510	0.137823
$303$	5.75759	0.330765
$304$	20.2739	1.16279
$305$	−0.566394	−0.0324316
$306$	−1.50541	−0.0860583
$307$	5.90000	0.336731	0.168365	−	0.985725i	$-0.446151\pi$
$307$	5.90000	0.336731	0.168365	+	0.985725i	$0.446151\pi$
$308$	−6.94331	−0.395632
$309$	0.367680	0.0209166
$310$	−0.113410	−0.00644127
$311$	−11.7271	−0.664983	−0.332492	−	0.943106i	$-0.607889\pi$
$311$	−11.7271	−0.664983	−0.332492	+	0.943106i	$0.607889\pi$
$312$	−6.04068	−0.341986
$313$	26.0462	1.47222	0.736109	−	0.676864i	$-0.236661\pi$
$313$	26.0462	1.47222	0.736109	+	0.676864i	$0.236661\pi$
$314$	−2.75915	−0.155708
$315$	−2.06733	−0.116481
$316$	−16.8175	−0.946060
$317$	9.64392	0.541656	0.270828	−	0.962628i	$-0.412702\pi$
$317$	9.64392	0.541656	0.270828	+	0.962628i	$0.412702\pi$
$318$	−1.77826	−0.0997196
$319$	−1.74831	−0.0978867
$320$	3.25634	0.182035
$321$	10.3242	0.576239
$322$	2.87360	0.160139
$323$	28.5208	1.58694
$324$	−1.90228	−0.105682
$325$	23.1710	1.28530
$326$	1.78118	0.0986507
$327$	5.75458	0.318229
$328$	1.55117	0.0856493
$329$	27.3222	1.50632
$330$	0.177056	0.00974664
$331$	−10.7136	−0.588875	−0.294437	−	0.955671i	$-0.595132\pi$
$331$	−10.7136	−0.588875	−0.294437	+	0.955671i	$0.595132\pi$
$332$	−13.5488	−0.743586
$333$	8.32847	0.456397
$334$	2.05937	0.112684
$335$	−1.54213	−0.0842557
$336$	12.4947	0.681644
$337$	−10.9557	−0.596795	−0.298398	−	0.954442i	$-0.596452\pi$
$337$	−10.9557	−0.596795	−0.298398	+	0.954442i	$0.596452\pi$
$338$	−3.60167	−0.195905
$339$	3.31944	0.180287
$340$	5.18863	0.281393
$341$	−0.640532	−0.0346868
$342$	−1.85138	−0.100111
$343$	−2.47304	−0.133532
$344$	−10.5729	−0.570052
$345$	1.42646	0.0767979
$346$	−5.43979	−0.292445
$347$	−26.6990	−1.43328	−0.716638	−	0.697445i	$-0.754320\pi$
$347$	−26.6990	−1.43328	−0.716638	+	0.697445i	$0.754320\pi$
$348$	3.32578	0.178280
$349$	−14.7551	−0.789821	−0.394911	−	0.918719i	$-0.629224\pi$
$349$	−14.7551	−0.789821	−0.394911	+	0.918719i	$0.629224\pi$
$350$	5.33896	0.285380
$351$	−4.95192	−0.264314
$352$	−3.50984	−0.187075
$353$	−32.6873	−1.73977	−0.869885	−	0.493254i	$-0.835807\pi$
$353$	−32.6873	−1.73977	−0.869885	+	0.493254i	$0.835807\pi$
$354$	−2.58515	−0.137399
$355$	1.07160	0.0568747
$356$	1.29503	0.0686364
$357$	17.5773	0.930289
$358$	−3.81804	−0.201790
$359$	27.4476	1.44863	0.724316	−	0.689469i	$-0.242156\pi$
$359$	27.4476	1.44863	0.724316	+	0.689469i	$0.242156\pi$
$360$	−0.690924	−0.0364149
$361$	16.0755	0.846077
$362$	1.56652	0.0823345
$363$	1.00000	0.0524864
$364$	34.3827	1.80214
$365$	3.31939	0.173745
$366$	−0.312603	−0.0163400
$367$	−8.92108	−0.465676	−0.232838	−	0.972515i	$-0.574801\pi$
$367$	−8.92108	−0.465676	−0.232838	+	0.972515i	$0.574801\pi$
$368$	−8.62137	−0.449420
$369$	1.27159	0.0661966
$370$	1.47461	0.0766613
$371$	20.7631	1.07797
$372$	1.21847	0.0631748
$373$	−1.36928	−0.0708985	−0.0354492	−	0.999371i	$-0.511286\pi$
$373$	−1.36928	−0.0708985	−0.0354492	+	0.999371i	$0.511286\pi$
$374$	−1.50541	−0.0778427
$375$	5.48224	0.283101
$376$	9.13136	0.470914
$377$	8.65751	0.445884
$378$	−1.14100	−0.0586867
$379$	−27.3808	−1.40646	−0.703228	−	0.710965i	$-0.748258\pi$
$379$	−27.3808	−1.40646	−0.703228	+	0.710965i	$0.748258\pi$
$380$	6.38108	0.327343
$381$	−4.18381	−0.214343
$382$	−4.42668	−0.226489
$383$	4.54888	0.232437	0.116218	−	0.993224i	$-0.462923\pi$
$383$	4.54888	0.232437	0.116218	+	0.993224i	$0.462923\pi$
$384$	8.81692	0.449937
$385$	−2.06733	−0.105361
$386$	−7.73844	−0.393876
$387$	−8.66727	−0.440582
$388$	−14.6103	−0.741727
$389$	−11.1014	−0.562863	−0.281432	−	0.959581i	$-0.590809\pi$
$389$	−11.1014	−0.562863	−0.281432	+	0.959581i	$0.590809\pi$
$390$	−0.876770	−0.0443970
$391$	−12.1283	−0.613356
$392$	7.71254	0.389542
$393$	−11.5884	−0.584560
$394$	2.70001	0.136024
$395$	−5.00733	−0.251946
$396$	−1.90228	−0.0955931
$397$	−14.6290	−0.734208	−0.367104	−	0.930180i	$-0.619651\pi$
$397$	−14.6290	−0.734208	−0.367104	+	0.930180i	$0.619651\pi$
$398$	4.68205	0.234690
$399$	21.6169	1.08220
$400$	−16.0179	−0.800897
$401$	−15.2401	−0.761054	−0.380527	−	0.924770i	$-0.624257\pi$
$401$	−15.2401	−0.761054	−0.380527	+	0.924770i	$0.624257\pi$
$402$	−0.851132	−0.0424506
$403$	3.17186	0.158002
$404$	−10.9525	−0.544909
$405$	−0.566394	−0.0281443
$406$	1.99482	0.0990015
$407$	8.32847	0.412827
$408$	5.87451	0.290832
$409$	15.5725	0.770011	0.385005	−	0.922914i	$-0.374200\pi$
$409$	15.5725	0.770011	0.385005	+	0.922914i	$0.374200\pi$
$410$	0.225144	0.0111191
$411$	7.91940	0.390635
$412$	−0.699431	−0.0344585
$413$	30.1845	1.48528
$414$	0.787289	0.0386931
$415$	−4.03408	−0.198025
$416$	17.3805	0.852147
$417$	1.64236	0.0804267
$418$	−1.85138	−0.0905539
$419$	15.5105	0.757738	0.378869	−	0.925450i	$-0.376313\pi$
$419$	15.5105	0.757738	0.378869	+	0.925450i	$0.376313\pi$
$420$	3.93264	0.191893
$421$	−13.5039	−0.658140	−0.329070	−	0.944306i	$-0.606735\pi$
$421$	−13.5039	−0.658140	−0.329070	+	0.944306i	$0.606735\pi$
$422$	2.81106	0.136840
$423$	7.48555	0.363960
$424$	6.93925	0.337000
$425$	−22.5336	−1.09304
$426$	0.591437	0.0286552
$427$	3.64999	0.176636
$428$	−19.6395	−0.949309
$429$	−4.95192	−0.239081
$430$	−1.53460	−0.0740048
$431$	30.3369	1.46128	0.730639	−	0.682764i	$-0.239222\pi$
$431$	30.3369	1.46128	0.730639	+	0.682764i	$0.239222\pi$
$432$	3.42322	0.164700
$433$	−28.9624	−1.39184	−0.695921	−	0.718118i	$-0.745004\pi$
$433$	−28.9624	−1.39184	−0.695921	+	0.718118i	$0.745004\pi$
$434$	0.730847	0.0350818
$435$	0.990233	0.0474780
$436$	−10.9468	−0.524257
$437$	−14.9157	−0.713513
$438$	1.83203	0.0875380
$439$	−22.2488	−1.06188	−0.530938	−	0.847411i	$-0.678160\pi$
$439$	−22.2488	−1.06188	−0.530938	+	0.847411i	$0.678160\pi$
$440$	−0.690924	−0.0329385
$441$	6.32245	0.301069
$442$	7.45465	0.354582
$443$	−9.53995	−0.453257	−0.226628	−	0.973981i	$-0.572770\pi$
$443$	−9.53995	−0.453257	−0.226628	+	0.973981i	$0.572770\pi$
$444$	−15.8431	−0.751879
$445$	0.385588	0.0182786
$446$	8.94943	0.423768
$447$	11.3148	0.535171
$448$	−20.9848	−0.991437
$449$	5.84158	0.275681	0.137841	−	0.990454i	$-0.455984\pi$
$449$	5.84158	0.275681	0.137841	+	0.990454i	$0.455984\pi$
$450$	1.46273	0.0689539
$451$	1.27159	0.0598771
$452$	−6.31449	−0.297009
$453$	−7.66180	−0.359983
$454$	8.08145	0.379281
$455$	10.2373	0.479931
$456$	7.22459	0.338323
$457$	−39.0411	−1.82626	−0.913132	−	0.407664i	$-0.866343\pi$
$457$	−39.0411	−1.82626	−0.913132	+	0.407664i	$0.866343\pi$
$458$	6.97936	0.326124
$459$	4.81571	0.224778
$460$	−2.71352	−0.126519
$461$	35.5532	1.65588	0.827939	−	0.560818i	$-0.189513\pi$
$461$	35.5532	1.65588	0.827939	+	0.560818i	$0.189513\pi$
$462$	−1.14100	−0.0530841
$463$	−2.38286	−0.110741	−0.0553704	−	0.998466i	$-0.517634\pi$
$463$	−2.38286	−0.110741	−0.0553704	+	0.998466i	$0.517634\pi$
$464$	−5.98487	−0.277840
$465$	0.362793	0.0168241
$466$	−9.26814	−0.429338
$467$	3.86895	0.179034	0.0895168	−	0.995985i	$-0.471468\pi$
$467$	3.86895	0.179034	0.0895168	+	0.995985i	$0.471468\pi$
$468$	9.41994	0.435437
$469$	9.93792	0.458890
$470$	1.32536	0.0611345
$471$	8.82636	0.406697
$472$	10.0880	0.464337
$473$	−8.66727	−0.398521
$474$	−2.76364	−0.126938
$475$	−27.7123	−1.27153
$476$	−33.4369	−1.53258
$477$	5.68854	0.260460
$478$	6.30823	0.288532
$479$	8.53831	0.390125	0.195063	−	0.980791i	$-0.437509\pi$
$479$	8.53831	0.390125	0.195063	+	0.980791i	$0.437509\pi$
$480$	1.98795	0.0907372
$481$	−41.2419	−1.88047
$482$	3.10274	0.141326
$483$	−9.19248	−0.418272
$484$	−1.90228	−0.0864672
$485$	−4.35015	−0.197530
$486$	−0.312603	−0.0141800
$487$	−28.6951	−1.30030	−0.650150	−	0.759805i	$-0.725294\pi$
$487$	−28.6951	−1.30030	−0.650150	+	0.759805i	$0.725294\pi$
$488$	1.21987	0.0552207
$489$	−5.69791	−0.257668
$490$	1.11943	0.0505707
$491$	−16.4259	−0.741291	−0.370645	−	0.928774i	$-0.620863\pi$
$491$	−16.4259	−0.741291	−0.370645	+	0.928774i	$0.620863\pi$
$492$	−2.41893	−0.109054
$493$	−8.41936	−0.379189
$494$	9.16788	0.412482
$495$	−0.566394	−0.0254575
$496$	−2.19268	−0.0984545
$497$	−6.90569	−0.309763
$498$	−2.22648	−0.0997711
$499$	10.8763	0.486888	0.243444	−	0.969915i	$-0.421723\pi$
$499$	10.8763	0.486888	0.243444	+	0.969915i	$0.421723\pi$
$500$	−10.4287	−0.466388
$501$	−6.58782	−0.294322
$502$	−9.51400	−0.424631
$503$	−3.47751	−0.155055	−0.0775273	−	0.996990i	$-0.524702\pi$
$503$	−3.47751	−0.155055	−0.0775273	+	0.996990i	$0.524702\pi$
$504$	4.45250	0.198330
$505$	−3.26106	−0.145115
$506$	0.787289	0.0349993
$507$	11.5215	0.511689
$508$	7.95877	0.353113
$509$	−29.0169	−1.28615	−0.643077	−	0.765802i	$-0.722342\pi$
$509$	−29.0169	−1.28615	−0.643077	+	0.765802i	$0.722342\pi$
$510$	0.852652	0.0377561
$511$	−21.3910	−0.946284
$512$	−20.3667	−0.900090
$513$	5.92245	0.261483
$514$	6.86637	0.302863
$515$	−0.208252	−0.00917667
$516$	16.4876	0.725824
$517$	7.48555	0.329214
$518$	−9.50278	−0.417528
$519$	17.4016	0.763845
$520$	3.42140	0.150038
$521$	28.6613	1.25567	0.627837	−	0.778345i	$-0.283941\pi$
$521$	28.6613	1.25567	0.627837	+	0.778345i	$0.283941\pi$
$522$	0.546528	0.0239209
$523$	−2.18310	−0.0954601	−0.0477301	−	0.998860i	$-0.515199\pi$
$523$	−2.18310	−0.0954601	−0.0477301	+	0.998860i	$0.515199\pi$
$524$	22.0445	0.963017
$525$	−17.0790	−0.745391
$526$	−3.35864	−0.146444
$527$	−3.08461	−0.134368
$528$	3.42322	0.148977
$529$	−16.6572	−0.724226
$530$	1.00719	0.0437496
$531$	8.26974	0.358876
$532$	−41.1214	−1.78284
$533$	−6.29684	−0.272746
$534$	0.212813	0.00920933
$535$	−5.84754	−0.252811
$536$	3.32135	0.143461
$537$	12.2137	0.527060
$538$	0.522740	0.0225369
$539$	6.32245	0.272327
$540$	1.07744	0.0463656
$541$	20.7325	0.891359	0.445680	−	0.895193i	$-0.352962\pi$
$541$	20.7325	0.891359	0.445680	+	0.895193i	$0.352962\pi$
$542$	6.02058	0.258606
$543$	−5.01121	−0.215052
$544$	−16.9024	−0.724683
$545$	−3.25935	−0.139615
$546$	5.65014	0.241804
$547$	21.8138	0.932692	0.466346	−	0.884602i	$-0.345570\pi$
$547$	21.8138	0.932692	0.466346	+	0.884602i	$0.345570\pi$
$548$	−15.0649	−0.643541
$549$	1.00000	0.0426790
$550$	1.46273	0.0623711
$551$	−10.3543	−0.441108
$552$	−3.07222	−0.130762
$553$	32.2686	1.37220
$554$	2.93003	0.124485
$555$	−4.71719	−0.200234
$556$	−3.12423	−0.132497
$557$	−10.7557	−0.455735	−0.227867	−	0.973692i	$-0.573175\pi$
$557$	−10.7557	−0.455735	−0.227867	+	0.973692i	$0.573175\pi$
$558$	0.200232	0.00847651
$559$	42.9196	1.81531
$560$	−7.07694	−0.299055
$561$	4.81571	0.203319
$562$	−7.25619	−0.306084
$563$	27.3894	1.15433	0.577163	−	0.816629i	$-0.304160\pi$
$563$	27.3894	1.15433	0.577163	+	0.816629i	$0.304160\pi$
$564$	−14.2396	−0.599595
$565$	−1.88011	−0.0790967
$566$	−4.27228	−0.179577
$567$	3.64999	0.153285
$568$	−2.30795	−0.0968396
$569$	1.23800	0.0518996	0.0259498	−	0.999663i	$-0.491739\pi$
$569$	1.23800	0.0518996	0.0259498	+	0.999663i	$0.491739\pi$
$570$	1.04861	0.0439214
$571$	−46.1278	−1.93039	−0.965194	−	0.261535i	$-0.915771\pi$
$571$	−46.1278	−1.93039	−0.965194	+	0.261535i	$0.915771\pi$
$572$	9.41994	0.393867
$573$	14.1607	0.591572
$574$	−1.45089	−0.0605589
$575$	11.7845	0.491449
$576$	−5.74926	−0.239553
$577$	11.2998	0.470417	0.235209	−	0.971945i	$-0.424423\pi$
$577$	11.2998	0.470417	0.235209	+	0.971945i	$0.424423\pi$
$578$	−1.93534	−0.0804994
$579$	24.7548	1.02878
$580$	−1.88370	−0.0782164
$581$	25.9967	1.07852
$582$	−2.40093	−0.0995217
$583$	5.68854	0.235595
$584$	−7.14911	−0.295832
$585$	2.80474	0.115962
$586$	9.12064	0.376770
$587$	31.2722	1.29074	0.645372	−	0.763869i	$-0.276703\pi$
$587$	31.2722	1.29074	0.645372	+	0.763869i	$0.276703\pi$
$588$	−12.0271	−0.495988
$589$	−3.79352	−0.156309
$590$	1.46421	0.0602806
$591$	−8.63717	−0.355286
$592$	28.5102	1.17176
$593$	−37.1701	−1.52639	−0.763197	−	0.646166i	$-0.776371\pi$
$593$	−37.1701	−1.52639	−0.763197	+	0.646166i	$0.776371\pi$
$594$	−0.312603	−0.0128263
$595$	−9.95567	−0.408143
$596$	−21.5239	−0.881653
$597$	−14.9776	−0.612994
$598$	−3.89859	−0.159425
$599$	−6.09028	−0.248842	−0.124421	−	0.992230i	$-0.539707\pi$
$599$	−6.09028	−0.248842	−0.124421	+	0.992230i	$0.539707\pi$
$600$	−5.70799	−0.233028
$601$	14.5166	0.592145	0.296073	−	0.955165i	$-0.404323\pi$
$601$	14.5166	0.592145	0.296073	+	0.955165i	$0.404323\pi$
$602$	9.88935	0.403060
$603$	2.72272	0.110878
$604$	14.5749	0.593044
$605$	−0.566394	−0.0230272
$606$	−1.79984	−0.0731135
$607$	−21.7734	−0.883755	−0.441878	−	0.897075i	$-0.645687\pi$
$607$	−21.7734	−0.883755	−0.441878	+	0.897075i	$0.645687\pi$
$608$	−20.7869	−0.843019
$609$	−6.38133	−0.258585
$610$	0.177056	0.00716881
$611$	−37.0678	−1.49960
$612$	−9.16082	−0.370304
$613$	−8.54328	−0.345060	−0.172530	−	0.985004i	$-0.555194\pi$
$613$	−8.54328	−0.345060	−0.172530	+	0.985004i	$0.555194\pi$
$614$	−1.84436	−0.0744323
$615$	−0.720223	−0.0290422
$616$	4.45250	0.179396
$617$	−8.41289	−0.338690	−0.169345	−	0.985557i	$-0.554165\pi$
$617$	−8.41289	−0.338690	−0.169345	+	0.985557i	$0.554165\pi$
$618$	−0.114938	−0.00462349
$619$	−2.02990	−0.0815887	−0.0407944	−	0.999168i	$-0.512989\pi$
$619$	−2.02990	−0.0815887	−0.0407944	+	0.999168i	$0.512989\pi$
$620$	−0.690134	−0.0277164
$621$	−2.51849	−0.101064
$622$	3.66593	0.146990
$623$	−2.48483	−0.0995528
$624$	−16.9515	−0.678605
$625$	20.2909	0.811636
$626$	−8.14212	−0.325425
$627$	5.92245	0.236520
$628$	−16.7902	−0.670002
$629$	40.1075	1.59919
$630$	0.646255	0.0257474
$631$	−22.5257	−0.896734	−0.448367	−	0.893850i	$-0.647994\pi$
$631$	−22.5257	−0.896734	−0.448367	+	0.893850i	$0.647994\pi$
$632$	10.7845	0.428984
$633$	−8.99241	−0.357416
$634$	−3.01472	−0.119730
$635$	2.36968	0.0940379
$636$	−10.8212	−0.429088
$637$	−31.3083	−1.24048
$638$	0.546528	0.0216373
$639$	−1.89197	−0.0748454
$640$	−4.99385	−0.197399
$641$	−43.0281	−1.69951	−0.849753	−	0.527181i	$-0.823249\pi$
$641$	−43.0281	−1.69951	−0.849753	+	0.527181i	$0.823249\pi$
$642$	−3.22737	−0.127374
$643$	10.5165	0.414729	0.207365	−	0.978264i	$-0.433511\pi$
$643$	10.5165	0.414729	0.207365	+	0.978264i	$0.433511\pi$
$644$	17.4867	0.689071
$645$	4.90908	0.193295
$646$	−8.91569	−0.350783
$647$	−39.4255	−1.54998	−0.774988	−	0.631976i	$-0.782244\pi$
$647$	−39.4255	−1.54998	−0.774988	+	0.631976i	$0.782244\pi$
$648$	1.21987	0.0479208
$649$	8.26974	0.324616
$650$	−7.24334	−0.284107
$651$	−2.33794	−0.0916310
$652$	10.8390	0.424488
$653$	−15.3931	−0.602378	−0.301189	−	0.953564i	$-0.597384\pi$
$653$	−15.3931	−0.602378	−0.301189	+	0.953564i	$0.597384\pi$
$654$	−1.79890	−0.0703425
$655$	6.56362	0.256462
$656$	4.35295	0.169954
$657$	−5.86057	−0.228643
$658$	−8.54101	−0.332963
$659$	43.9614	1.71249	0.856246	−	0.516568i	$-0.172791\pi$
$659$	43.9614	1.71249	0.856246	+	0.516568i	$0.172791\pi$
$660$	1.07744	0.0419392
$661$	47.0556	1.83025	0.915126	−	0.403168i	$-0.132091\pi$
$661$	47.0556	1.83025	0.915126	+	0.403168i	$0.132091\pi$
$662$	3.34912	0.130167
$663$	−23.8470	−0.926141
$664$	8.68836	0.337174
$665$	−12.2437	−0.474790
$666$	−2.60351	−0.100884
$667$	4.40311	0.170489
$668$	12.5319	0.484873
$669$	−28.6287	−1.10685
$670$	0.482075	0.0186242
$671$	1.00000	0.0386046
$672$	−12.8109	−0.494191
$673$	31.6606	1.22043	0.610213	−	0.792238i	$-0.291084\pi$
$673$	31.6606	1.22043	0.610213	+	0.792238i	$0.291084\pi$
$674$	3.42479	0.131918
$675$	−4.67920	−0.180102
$676$	−21.9172	−0.842968
$677$	−22.9417	−0.881723	−0.440861	−	0.897575i	$-0.645327\pi$
$677$	−22.9417	−0.881723	−0.440861	+	0.897575i	$0.645327\pi$
$678$	−1.03767	−0.0398513
$679$	28.0335	1.07583
$680$	−3.32729	−0.127596
$681$	−25.8521	−0.990655
$682$	0.200232	0.00766729
$683$	−8.30501	−0.317782	−0.158891	−	0.987296i	$-0.550792\pi$
$683$	−8.30501	−0.317782	−0.158891	+	0.987296i	$0.550792\pi$
$684$	−11.2662	−0.430772
$685$	−4.48550	−0.171382
$686$	0.773081	0.0295164
$687$	−22.3266	−0.851812
$688$	−29.6700	−1.13116
$689$	−28.1692	−1.07316
$690$	−0.445915	−0.0169757
$691$	46.0852	1.75316	0.876581	−	0.481254i	$-0.159819\pi$
$691$	46.0852	1.75316	0.876581	+	0.481254i	$0.159819\pi$
$692$	−33.1027	−1.25837
$693$	3.64999	0.138652
$694$	8.34619	0.316817
$695$	−0.930222	−0.0352853
$696$	−2.13271	−0.0808400
$697$	6.12363	0.231949
$698$	4.61249	0.174585
$699$	29.6483	1.12140
$700$	32.4891	1.22797
$701$	−13.9928	−0.528499	−0.264250	−	0.964454i	$-0.585124\pi$
$701$	−13.9928	−0.528499	−0.264250	+	0.964454i	$0.585124\pi$
$702$	1.54799	0.0584250
$703$	49.3250	1.86033
$704$	−5.74926	−0.216683
$705$	−4.23977	−0.159679
$706$	10.2182	0.384566
$707$	21.0152	0.790356
$708$	−15.7314	−0.591221
$709$	−5.40084	−0.202833	−0.101416	−	0.994844i	$-0.532337\pi$
$709$	−5.40084	−0.202833	−0.101416	+	0.994844i	$0.532337\pi$
$710$	−0.334986	−0.0125718
$711$	8.84072	0.331553
$712$	−0.830457	−0.0311227
$713$	1.61318	0.0604139
$714$	−5.49472	−0.205635
$715$	2.80474	0.104891
$716$	−23.2339	−0.868290
$717$	−20.1797	−0.753623
$718$	−8.58022	−0.320211
$719$	−36.5679	−1.36375	−0.681876	−	0.731468i	$-0.738836\pi$
$719$	−36.5679	−1.36375	−0.681876	+	0.731468i	$0.738836\pi$
$720$	−1.93889	−0.0722582
$721$	1.34203	0.0499799
$722$	−5.02524	−0.187020
$723$	−9.92548	−0.369133
$724$	9.53272	0.354281
$725$	8.18070	0.303824
$726$	−0.312603	−0.0116018
$727$	31.6255	1.17293	0.586463	−	0.809976i	$-0.300520\pi$
$727$	31.6255	1.17293	0.586463	+	0.809976i	$0.300520\pi$
$728$	−22.0484	−0.817169
$729$	1.00000	0.0370370
$730$	−1.03765	−0.0384052
$731$	−41.7390	−1.54377
$732$	−1.90228	−0.0703103
$733$	28.8516	1.06566	0.532829	−	0.846223i	$-0.321129\pi$
$733$	28.8516	1.06566	0.532829	+	0.846223i	$0.321129\pi$
$734$	2.78876	0.102935
$735$	−3.58100	−0.132087
$736$	8.83951	0.325829
$737$	2.72272	0.100293
$738$	−0.397505	−0.0146323
$739$	20.9977	0.772414	0.386207	−	0.922412i	$-0.373785\pi$
$739$	20.9977	0.772414	0.386207	+	0.922412i	$0.373785\pi$
$740$	8.97342	0.329869
$741$	−29.3275	−1.07737
$742$	−6.49062	−0.238278
$743$	−32.6365	−1.19732	−0.598659	−	0.801004i	$-0.704299\pi$
$743$	−32.6365	−1.19732	−0.598659	+	0.801004i	$0.704299\pi$
$744$	−0.781363	−0.0286461
$745$	−6.40862	−0.234794
$746$	0.428041	0.0156717
$747$	7.12240	0.260595
$748$	−9.16082	−0.334953
$749$	37.6832	1.37691
$750$	−1.71376	−0.0625778
$751$	4.22071	0.154016	0.0770079	−	0.997030i	$-0.475463\pi$
$751$	4.22071	0.154016	0.0770079	+	0.997030i	$0.475463\pi$
$752$	25.6247	0.934437
$753$	30.4348	1.10910
$754$	−2.70636	−0.0985600
$755$	4.33959	0.157934
$756$	−6.94331	−0.252526
$757$	−10.8908	−0.395832	−0.197916	−	0.980219i	$-0.563417\pi$
$757$	−10.8908	−0.395832	−0.197916	+	0.980219i	$0.563417\pi$
$758$	8.55931	0.310888
$759$	−2.51849	−0.0914155
$760$	−4.09196	−0.148431
$761$	42.4300	1.53809	0.769044	−	0.639196i	$-0.220733\pi$
$761$	42.4300	1.53809	0.769044	+	0.639196i	$0.220733\pi$
$762$	1.30787	0.0473792
$763$	21.0042	0.760402
$764$	−26.9376	−0.974568
$765$	−2.72759	−0.0986161
$766$	−1.42199	−0.0513787
$767$	−40.9511	−1.47866
$768$	8.74233	0.315461
$769$	9.63948	0.347609	0.173804	−	0.984780i	$-0.444394\pi$
$769$	9.63948	0.347609	0.173804	+	0.984780i	$0.444394\pi$
$770$	0.646255	0.0232894
$771$	−21.9651	−0.791055
$772$	−47.0906	−1.69483
$773$	−33.6347	−1.20976	−0.604878	−	0.796318i	$-0.706778\pi$
$773$	−33.6347	−1.20976	−0.604878	+	0.796318i	$0.706778\pi$
$774$	2.70942	0.0973879
$775$	2.99718	0.107662
$776$	9.36909	0.336331
$777$	30.3989	1.09055
$778$	3.47033	0.124418
$779$	7.53096	0.269825
$780$	−5.33539	−0.191038
$781$	−1.89197	−0.0677002
$782$	3.79135	0.135579
$783$	−1.74831	−0.0624796
$784$	21.6432	0.772971
$785$	−4.99919	−0.178429
$786$	3.62259	0.129213
$787$	23.3713	0.833096	0.416548	−	0.909114i	$-0.363240\pi$
$787$	23.3713	0.833096	0.416548	+	0.909114i	$0.363240\pi$
$788$	16.4303	0.585305
$789$	10.7441	0.382500
$790$	1.56531	0.0556911
$791$	12.1159	0.430792
$792$	1.21987	0.0433460
$793$	−4.95192	−0.175848
$794$	4.57307	0.162292
$795$	−3.22195	−0.114271
$796$	28.4916	1.00986
$797$	3.91048	0.138516	0.0692582	−	0.997599i	$-0.477937\pi$
$797$	3.91048	0.138516	0.0692582	+	0.997599i	$0.477937\pi$
$798$	−6.75752	−0.239214
$799$	36.0482	1.27529
$800$	16.4232	0.580649
$801$	−0.680778	−0.0240541
$802$	4.76410	0.168226
$803$	−5.86057	−0.206815
$804$	−5.17938	−0.182663
$805$	5.20656	0.183507
$806$	−0.991535	−0.0349253
$807$	−1.67222	−0.0588648
$808$	7.02348	0.247085
$809$	13.4616	0.473286	0.236643	−	0.971597i	$-0.423953\pi$
$809$	13.4616	0.473286	0.236643	+	0.971597i	$0.423953\pi$
$810$	0.177056	0.00622113
$811$	11.3472	0.398455	0.199227	−	0.979953i	$-0.436157\pi$
$811$	11.3472	0.398455	0.199227	+	0.979953i	$0.436157\pi$
$812$	12.1391	0.425998
$813$	−19.2595	−0.675460
$814$	−2.60351	−0.0912529
$815$	3.22726	0.113046
$816$	16.4852	0.577099
$817$	−51.3315	−1.79586
$818$	−4.86802	−0.170206
$819$	−18.0745	−0.631573
$820$	1.37007	0.0478448
$821$	45.7887	1.59804	0.799019	−	0.601306i	$-0.205353\pi$
$821$	45.7887	1.59804	0.799019	+	0.601306i	$0.205353\pi$
$822$	−2.47563	−0.0863475
$823$	−55.5408	−1.93603	−0.968016	−	0.250889i	$-0.919277\pi$
$823$	−55.5408	−1.93603	−0.968016	+	0.250889i	$0.919277\pi$
$824$	0.448521	0.0156250
$825$	−4.67920	−0.162909
$826$	−9.43578	−0.328313
$827$	6.93826	0.241267	0.120633	−	0.992697i	$-0.461507\pi$
$827$	6.93826	0.241267	0.120633	+	0.992697i	$0.461507\pi$
$828$	4.79088	0.166494
$829$	−4.43162	−0.153917	−0.0769583	−	0.997034i	$-0.524521\pi$
$829$	−4.43162	−0.153917	−0.0769583	+	0.997034i	$0.524521\pi$
$830$	1.26107	0.0437722
$831$	−9.37301	−0.325146
$832$	28.4699	0.987016
$833$	30.4471	1.05493
$834$	−0.513407	−0.0177778
$835$	3.73130	0.129127
$836$	−11.2662	−0.389648
$837$	−0.640532	−0.0221400
$838$	−4.84863	−0.167493
$839$	−29.8533	−1.03065	−0.515324	−	0.856995i	$-0.672329\pi$
$839$	−29.8533	−1.03065	−0.515324	+	0.856995i	$0.672329\pi$
$840$	−2.52187	−0.0870127
$841$	−25.9434	−0.894600
$842$	4.22136	0.145478
$843$	23.2121	0.799468
$844$	17.1061	0.588815
$845$	−6.52572	−0.224492
$846$	−2.34001	−0.0804511
$847$	3.64999	0.125415
$848$	19.4731	0.668710
$849$	13.6668	0.469043
$850$	7.04409	0.241610
$851$	−20.9752	−0.719020
$852$	3.59906	0.123302
$853$	26.3547	0.902369	0.451184	−	0.892431i	$-0.351002\pi$
$853$	26.3547	0.902369	0.451184	+	0.892431i	$0.351002\pi$
$854$	−1.14100	−0.0390442
$855$	−3.35444	−0.114719
$856$	12.5941	0.430457
$857$	−31.8262	−1.08716	−0.543582	−	0.839356i	$-0.682932\pi$
$857$	−31.8262	−1.08716	−0.543582	+	0.839356i	$0.682932\pi$
$858$	1.54799	0.0528474
$859$	−11.8487	−0.404273	−0.202136	−	0.979357i	$-0.564788\pi$
$859$	−11.8487	−0.404273	−0.202136	+	0.979357i	$0.564788\pi$
$860$	−9.33845	−0.318438
$861$	4.64131	0.158176
$862$	−9.48342	−0.323006
$863$	−32.7734	−1.11562	−0.557810	−	0.829969i	$-0.688358\pi$
$863$	−32.7734	−1.11562	−0.557810	+	0.829969i	$0.688358\pi$
$864$	−3.50984	−0.119407
$865$	−9.85614	−0.335119
$866$	9.05373	0.307658
$867$	6.19103	0.210258
$868$	4.44741	0.150955
$869$	8.84072	0.299901
$870$	−0.309550	−0.0104947
$871$	−13.4827	−0.456844
$872$	7.01981	0.237721
$873$	7.68043	0.259943
$874$	4.66268	0.157718
$875$	20.0101	0.676466
$876$	11.1484	0.376671
$877$	24.9285	0.841776	0.420888	−	0.907113i	$-0.361718\pi$
$877$	24.9285	0.841776	0.420888	+	0.907113i	$0.361718\pi$
$878$	6.95504	0.234721
$879$	−29.1764	−0.984096
$880$	−1.93889	−0.0653600
$881$	−11.6811	−0.393547	−0.196773	−	0.980449i	$-0.563046\pi$
$881$	−11.6811	−0.393547	−0.196773	+	0.980449i	$0.563046\pi$
$882$	−1.97642	−0.0665495
$883$	0.105485	0.00354987	0.00177493	−	0.999998i	$-0.499435\pi$
$883$	0.105485	0.00354987	0.00177493	+	0.999998i	$0.499435\pi$
$884$	45.3637	1.52574
$885$	−4.68393	−0.157449
$886$	2.98222	0.100190
$887$	40.8981	1.37322	0.686612	−	0.727024i	$-0.259097\pi$
$887$	40.8981	1.37322	0.686612	+	0.727024i	$0.259097\pi$
$888$	10.1596	0.340934
$889$	−15.2709	−0.512168
$890$	−0.120536	−0.00404038
$891$	1.00000	0.0335013
$892$	54.4598	1.82345
$893$	44.3328	1.48354
$894$	−3.53704	−0.118296
$895$	−6.91776	−0.231235
$896$	32.1817	1.07512
$897$	12.4714	0.416407
$898$	−1.82610	−0.0609377
$899$	1.11985	0.0373491
$900$	8.90114	0.296705
$901$	27.3943	0.912637
$902$	−0.397505	−0.0132355
$903$	−31.6355	−1.05276
$904$	4.04926	0.134676
$905$	2.83832	0.0943489
$906$	2.39510	0.0795720
$907$	50.7488	1.68509	0.842543	−	0.538630i	$-0.181058\pi$
$907$	50.7488	1.68509	0.842543	+	0.538630i	$0.181058\pi$
$908$	49.1779	1.63203
$909$	5.75759	0.190967
$910$	−3.20020	−0.106086
$911$	−10.3513	−0.342954	−0.171477	−	0.985188i	$-0.554854\pi$
$911$	−10.3513	−0.342954	−0.171477	+	0.985188i	$0.554854\pi$
$912$	20.2739	0.671336
$913$	7.12240	0.235717
$914$	12.2044	0.403684
$915$	−0.566394	−0.0187244
$916$	42.4714	1.40329
$917$	−42.2978	−1.39679
$918$	−1.50541	−0.0496858
$919$	13.4653	0.444178	0.222089	−	0.975026i	$-0.428712\pi$
$919$	13.4653	0.444178	0.222089	+	0.975026i	$0.428712\pi$
$920$	1.74009	0.0573689
$921$	5.90000	0.194412
$922$	−11.1141	−0.366022
$923$	9.36891	0.308381
$924$	−6.94331	−0.228418
$925$	−38.9706	−1.28134
$926$	0.744889	0.0244786
$927$	0.367680	0.0120762
$928$	6.13630	0.201434
$929$	−53.3111	−1.74908	−0.874541	−	0.484952i	$-0.838837\pi$
$929$	−53.3111	−1.74908	−0.874541	+	0.484952i	$0.838837\pi$
$930$	−0.113410	−0.00371887
$931$	37.4444	1.22719
$932$	−56.3993	−1.84742
$933$	−11.7271	−0.383928
$934$	−1.20945	−0.0395743
$935$	−2.72759	−0.0892016
$936$	−6.04068	−0.197446
$937$	13.0959	0.427825	0.213913	−	0.976853i	$-0.431379\pi$
$937$	13.0959	0.427825	0.213913	+	0.976853i	$0.431379\pi$
$938$	−3.10662	−0.101435
$939$	26.0462	0.849985
$940$	8.06522	0.263058
$941$	−24.2906	−0.791850	−0.395925	−	0.918283i	$-0.629576\pi$
$941$	−24.2906	−0.791850	−0.395925	+	0.918283i	$0.629576\pi$
$942$	−2.75915	−0.0898979
$943$	−3.20250	−0.104288
$944$	28.3092	0.921386
$945$	−2.06733	−0.0672503
$946$	2.70942	0.0880907
$947$	13.2672	0.431126	0.215563	−	0.976490i	$-0.430841\pi$
$947$	13.2672	0.431126	0.215563	+	0.976490i	$0.430841\pi$
$948$	−16.8175	−0.546208
$949$	29.0211	0.942064
$950$	8.66297	0.281064
$951$	9.64392	0.312725
$952$	21.4419	0.694937
$953$	−2.00746	−0.0650281	−0.0325141	−	0.999471i	$-0.510351\pi$
$953$	−2.00746	−0.0650281	−0.0325141	+	0.999471i	$0.510351\pi$
$954$	−1.77826	−0.0575731
$955$	−8.02053	−0.259538
$956$	38.3874	1.24154
$957$	−1.74831	−0.0565149
$958$	−2.66910	−0.0862348
$959$	28.9058	0.933416
$960$	3.25634	0.105098
$961$	−30.5897	−0.986765
$962$	12.8924	0.415666
$963$	10.3242	0.332692
$964$	18.8810	0.608117
$965$	−14.0210	−0.451351
$966$	2.87360	0.0924566
$967$	16.8882	0.543089	0.271544	−	0.962426i	$-0.412466\pi$
$967$	16.8882	0.543089	0.271544	+	0.962426i	$0.412466\pi$
$968$	1.21987	0.0392079
$969$	28.5208	0.916220
$970$	1.35987	0.0436628
$971$	−32.5186	−1.04357	−0.521785	−	0.853077i	$-0.674734\pi$
$971$	−32.5186	−1.04357	−0.521785	+	0.853077i	$0.674734\pi$
$972$	−1.90228	−0.0610156
$973$	5.99460	0.192178
$974$	8.97019	0.287424
$975$	23.1710	0.742067
$976$	3.42322	0.109575
$977$	−4.98527	−0.159493	−0.0797464	−	0.996815i	$-0.525411\pi$
$977$	−4.98527	−0.159493	−0.0797464	+	0.996815i	$0.525411\pi$
$978$	1.78118	0.0569560
$979$	−0.680778	−0.0217578
$980$	6.81206	0.217603
$981$	5.75458	0.183729
$982$	5.13479	0.163858
$983$	33.5077	1.06873	0.534365	−	0.845254i	$-0.320551\pi$
$983$	33.5077	1.06873	0.534365	+	0.845254i	$0.320551\pi$
$984$	1.55117	0.0494496
$985$	4.89204	0.155873
$986$	2.63192	0.0838174
$987$	27.3222	0.869675
$988$	55.7891	1.77489
$989$	21.8284	0.694104
$990$	0.177056	0.00562722
$991$	9.41107	0.298953	0.149476	−	0.988765i	$-0.452241\pi$
$991$	9.41107	0.298953	0.149476	+	0.988765i	$0.452241\pi$
$992$	2.24817	0.0713793
$993$	−10.7136	−0.339987
$994$	2.15874	0.0684712
$995$	8.48323	0.268937
$996$	−13.5488	−0.429310
$997$	−12.4384	−0.393928	−0.196964	−	0.980411i	$-0.563108\pi$
$997$	−12.4384	−0.393928	−0.196964	+	0.980411i	$0.563108\pi$
$998$	−3.39995	−0.107624
$999$	8.32847	0.263501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.g.1.6	✓	13
3.2	odd	2		6039.2.a.h.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.g.1.6	✓	13	1.1	even	1	trivial
6039.2.a.h.1.8		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.312603 q^{2} +1.00000 q^{3} -1.90228 q^{4} -0.566394 q^{5} -0.312603 q^{6} +3.64999 q^{7} +1.21987 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.312603 q^{2} +1.00000 q^{3} -1.90228 q^{4} -0.566394 q^{5} -0.312603 q^{6} +3.64999 q^{7} +1.21987 q^{8} +1.00000 q^{9} +0.177056 q^{10} +1.00000 q^{11} -1.90228 q^{12} -4.95192 q^{13} -1.14100 q^{14} -0.566394 q^{15} +3.42322 q^{16} +4.81571 q^{17} -0.312603 q^{18} +5.92245 q^{19} +1.07744 q^{20} +3.64999 q^{21} -0.312603 q^{22} -2.51849 q^{23} +1.21987 q^{24} -4.67920 q^{25} +1.54799 q^{26} +1.00000 q^{27} -6.94331 q^{28} -1.74831 q^{29} +0.177056 q^{30} -0.640532 q^{31} -3.50984 q^{32} +1.00000 q^{33} -1.50541 q^{34} -2.06733 q^{35} -1.90228 q^{36} +8.32847 q^{37} -1.85138 q^{38} -4.95192 q^{39} -0.690924 q^{40} +1.27159 q^{41} -1.14100 q^{42} -8.66727 q^{43} -1.90228 q^{44} -0.566394 q^{45} +0.787289 q^{46} +7.48555 q^{47} +3.42322 q^{48} +6.32245 q^{49} +1.46273 q^{50} +4.81571 q^{51} +9.41994 q^{52} +5.68854 q^{53} -0.312603 q^{54} -0.566394 q^{55} +4.45250 q^{56} +5.92245 q^{57} +0.546528 q^{58} +8.26974 q^{59} +1.07744 q^{60} +1.00000 q^{61} +0.200232 q^{62} +3.64999 q^{63} -5.74926 q^{64} +2.80474 q^{65} -0.312603 q^{66} +2.72272 q^{67} -9.16082 q^{68} -2.51849 q^{69} +0.646255 q^{70} -1.89197 q^{71} +1.21987 q^{72} -5.86057 q^{73} -2.60351 q^{74} -4.67920 q^{75} -11.2662 q^{76} +3.64999 q^{77} +1.54799 q^{78} +8.84072 q^{79} -1.93889 q^{80} +1.00000 q^{81} -0.397505 q^{82} +7.12240 q^{83} -6.94331 q^{84} -2.72759 q^{85} +2.70942 q^{86} -1.74831 q^{87} +1.21987 q^{88} -0.680778 q^{89} +0.177056 q^{90} -18.0745 q^{91} +4.79088 q^{92} -0.640532 q^{93} -2.34001 q^{94} -3.35444 q^{95} -3.50984 q^{96} +7.68043 q^{97} -1.97642 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

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