LMFDB - Embedded newform 2013.2.a.h.1.14

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.57087$ 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)

$f(q)$	$=$	$q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +10.3020 q^{10} -1.00000 q^{11} -4.60938 q^{12} -4.75237 q^{13} +5.25159 q^{14} -4.00721 q^{15} +8.02760 q^{16} -0.339679 q^{17} +2.57087 q^{18} +4.54116 q^{19} +18.4707 q^{20} -2.04273 q^{21} -2.57087 q^{22} -4.75749 q^{23} -6.70837 q^{24} +11.0577 q^{25} -12.2177 q^{26} -1.00000 q^{27} +9.41571 q^{28} -4.28494 q^{29} -10.3020 q^{30} +1.81765 q^{31} +7.22118 q^{32} +1.00000 q^{33} -0.873272 q^{34} +8.18565 q^{35} +4.60938 q^{36} -2.11204 q^{37} +11.6747 q^{38} +4.75237 q^{39} +26.8819 q^{40} -10.2585 q^{41} -5.25159 q^{42} -9.89546 q^{43} -4.60938 q^{44} +4.00721 q^{45} -12.2309 q^{46} -5.22451 q^{47} -8.02760 q^{48} -2.82726 q^{49} +28.4280 q^{50} +0.339679 q^{51} -21.9055 q^{52} +9.68455 q^{53} -2.57087 q^{54} -4.00721 q^{55} +13.7034 q^{56} -4.54116 q^{57} -11.0160 q^{58} -2.04679 q^{59} -18.4707 q^{60} +1.00000 q^{61} +4.67295 q^{62} +2.04273 q^{63} +2.50953 q^{64} -19.0437 q^{65} +2.57087 q^{66} +5.30981 q^{67} -1.56571 q^{68} +4.75749 q^{69} +21.0442 q^{70} +11.4906 q^{71} +6.70837 q^{72} -4.51365 q^{73} -5.42978 q^{74} -11.0577 q^{75} +20.9319 q^{76} -2.04273 q^{77} +12.2177 q^{78} +5.49270 q^{79} +32.1683 q^{80} +1.00000 q^{81} -26.3733 q^{82} +14.2207 q^{83} -9.41571 q^{84} -1.36117 q^{85} -25.4399 q^{86} +4.28494 q^{87} -6.70837 q^{88} -6.05470 q^{89} +10.3020 q^{90} -9.70780 q^{91} -21.9291 q^{92} -1.81765 q^{93} -13.4315 q^{94} +18.1974 q^{95} -7.22118 q^{96} +13.6004 q^{97} -7.26851 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * 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 $

$2$	2.57087	1.81788	0.908940	−	0.416927i	$-0.136893\pi$
$2$	2.57087	1.81788	0.908940	+	0.416927i	$0.136893\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.60938	2.30469
$5$	4.00721	1.79208	0.896040	−	0.443974i	$-0.146432\pi$
$5$	4.00721	1.79208	0.896040	+	0.443974i	$0.146432\pi$
$6$	−2.57087	−1.04955
$7$	2.04273	0.772079	0.386040	−	0.922482i	$-0.373843\pi$
$7$	2.04273	0.772079	0.386040	+	0.922482i	$0.373843\pi$
$8$	6.70837	2.37177
$9$	1.00000	0.333333
$10$	10.3020	3.25779
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.60938	−1.33061
$13$	−4.75237	−1.31807	−0.659035	−	0.752112i	$-0.729035\pi$
$13$	−4.75237	−1.31807	−0.659035	+	0.752112i	$0.729035\pi$
$14$	5.25159	1.40355
$15$	−4.00721	−1.03466
$16$	8.02760	2.00690
$17$	−0.339679	−0.0823844	−0.0411922	−	0.999151i	$-0.513116\pi$
$17$	−0.339679	−0.0823844	−0.0411922	+	0.999151i	$0.513116\pi$
$18$	2.57087	0.605960
$19$	4.54116	1.04181	0.520907	−	0.853613i	$-0.325594\pi$
$19$	4.54116	1.04181	0.520907	+	0.853613i	$0.325594\pi$
$20$	18.4707	4.13018
$21$	−2.04273	−0.445760
$22$	−2.57087	−0.548112
$23$	−4.75749	−0.992006	−0.496003	−	0.868321i	$-0.665200\pi$
$23$	−4.75749	−0.992006	−0.496003	+	0.868321i	$0.665200\pi$
$24$	−6.70837	−1.36934
$25$	11.0577	2.21155
$26$	−12.2177	−2.39609
$27$	−1.00000	−0.192450
$28$	9.41571	1.77940
$29$	−4.28494	−0.795693	−0.397846	−	0.917452i	$-0.630242\pi$
$29$	−4.28494	−0.795693	−0.397846	+	0.917452i	$0.630242\pi$
$30$	−10.3020	−1.88088
$31$	1.81765	0.326460	0.163230	−	0.986588i	$-0.447809\pi$
$31$	1.81765	0.326460	0.163230	+	0.986588i	$0.447809\pi$
$32$	7.22118	1.27654
$33$	1.00000	0.174078
$34$	−0.873272	−0.149765
$35$	8.18565	1.38363
$36$	4.60938	0.768229
$37$	−2.11204	−0.347217	−0.173609	−	0.984815i	$-0.555543\pi$
$37$	−2.11204	−0.347217	−0.173609	+	0.984815i	$0.555543\pi$
$38$	11.6747	1.89389
$39$	4.75237	0.760988
$40$	26.8819	4.25039
$41$	−10.2585	−1.60211	−0.801056	−	0.598589i	$-0.795728\pi$
$41$	−10.2585	−1.60211	−0.801056	+	0.598589i	$0.795728\pi$
$42$	−5.25159	−0.810338
$43$	−9.89546	−1.50904	−0.754522	−	0.656275i	$-0.772131\pi$
$43$	−9.89546	−1.50904	−0.754522	+	0.656275i	$0.772131\pi$
$44$	−4.60938	−0.694890
$45$	4.00721	0.597360
$46$	−12.2309	−1.80335
$47$	−5.22451	−0.762074	−0.381037	−	0.924560i	$-0.624433\pi$
$47$	−5.22451	−0.762074	−0.381037	+	0.924560i	$0.624433\pi$
$48$	−8.02760	−1.15868
$49$	−2.82726	−0.403894
$50$	28.4280	4.02033
$51$	0.339679	0.0475646
$52$	−21.9055	−3.03774
$53$	9.68455	1.33028	0.665138	−	0.746721i	$-0.268373\pi$
$53$	9.68455	1.33028	0.665138	+	0.746721i	$0.268373\pi$
$54$	−2.57087	−0.349851
$55$	−4.00721	−0.540332
$56$	13.7034	1.83119
$57$	−4.54116	−0.601492
$58$	−11.0160	−1.44647
$59$	−2.04679	−0.266469	−0.133235	−	0.991085i	$-0.542536\pi$
$59$	−2.04679	−0.266469	−0.133235	+	0.991085i	$0.542536\pi$
$60$	−18.4707	−2.38456
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	4.67295	0.593465
$63$	2.04273	0.257360
$64$	2.50953	0.313691
$65$	−19.0437	−2.36209
$66$	2.57087	0.316452
$67$	5.30981	0.648697	0.324348	−	0.945938i	$-0.394855\pi$
$67$	5.30981	0.648697	0.324348	+	0.945938i	$0.394855\pi$
$68$	−1.56571	−0.189870
$69$	4.75749	0.572735
$70$	21.0442	2.51527
$71$	11.4906	1.36368	0.681841	−	0.731500i	$-0.261180\pi$
$71$	11.4906	1.36368	0.681841	+	0.731500i	$0.261180\pi$
$72$	6.70837	0.790589
$73$	−4.51365	−0.528283	−0.264142	−	0.964484i	$-0.585089\pi$
$73$	−4.51365	−0.528283	−0.264142	+	0.964484i	$0.585089\pi$
$74$	−5.42978	−0.631199
$75$	−11.0577	−1.27684
$76$	20.9319	2.40106
$77$	−2.04273	−0.232791
$78$	12.2177	1.38339
$79$	5.49270	0.617977	0.308989	−	0.951066i	$-0.400009\pi$
$79$	5.49270	0.617977	0.308989	+	0.951066i	$0.400009\pi$
$80$	32.1683	3.59652
$81$	1.00000	0.111111
$82$	−26.3733	−2.91245
$83$	14.2207	1.56092	0.780460	−	0.625206i	$-0.214985\pi$
$83$	14.2207	1.56092	0.780460	+	0.625206i	$0.214985\pi$
$84$	−9.41571	−1.02734
$85$	−1.36117	−0.147639
$86$	−25.4399	−2.74326
$87$	4.28494	0.459393
$88$	−6.70837	−0.715115
$89$	−6.05470	−0.641797	−0.320899	−	0.947114i	$-0.603985\pi$
$89$	−6.05470	−0.641797	−0.320899	+	0.947114i	$0.603985\pi$
$90$	10.3020	1.08593
$91$	−9.70780	−1.01765
$92$	−21.9291	−2.28626
$93$	−1.81765	−0.188482
$94$	−13.4315	−1.38536
$95$	18.1974	1.86701
$96$	−7.22118	−0.737009
$97$	13.6004	1.38092	0.690458	−	0.723373i	$-0.257409\pi$
$97$	13.6004	1.38092	0.690458	+	0.723373i	$0.257409\pi$
$98$	−7.26851	−0.734231
$99$	−1.00000	−0.100504
$100$	50.9693	5.09693
$101$	−10.2656	−1.02147	−0.510735	−	0.859738i	$-0.670627\pi$
$101$	−10.2656	−1.02147	−0.510735	+	0.859738i	$0.670627\pi$
$102$	0.873272	0.0864668
$103$	10.8307	1.06718	0.533590	−	0.845743i	$-0.320843\pi$
$103$	10.8307	1.06718	0.533590	+	0.845743i	$0.320843\pi$
$104$	−31.8807	−3.12616
$105$	−8.18565	−0.798837
$106$	24.8977	2.41828
$107$	−10.3745	−1.00294	−0.501471	−	0.865174i	$-0.667208\pi$
$107$	−10.3745	−1.00294	−0.501471	+	0.865174i	$0.667208\pi$
$108$	−4.60938	−0.443537
$109$	−15.9251	−1.52534	−0.762672	−	0.646786i	$-0.776113\pi$
$109$	−15.9251	−1.52534	−0.762672	+	0.646786i	$0.776113\pi$
$110$	−10.3020	−0.982259
$111$	2.11204	0.200466
$112$	16.3982	1.54949
$113$	4.50235	0.423546	0.211773	−	0.977319i	$-0.432076\pi$
$113$	4.50235	0.423546	0.211773	+	0.977319i	$0.432076\pi$
$114$	−11.6747	−1.09344
$115$	−19.0643	−1.77775
$116$	−19.7509	−1.83382
$117$	−4.75237	−0.439357
$118$	−5.26203	−0.484409
$119$	−0.693873	−0.0636072
$120$	−26.8819	−2.45397
$121$	1.00000	0.0909091
$122$	2.57087	0.232756
$123$	10.2585	0.924980
$124$	8.37824	0.752388
$125$	24.2746	2.17119
$126$	5.25159	0.467849
$127$	−12.2578	−1.08770	−0.543852	−	0.839181i	$-0.683035\pi$
$127$	−12.2578	−1.08770	−0.543852	+	0.839181i	$0.683035\pi$
$128$	−7.99069	−0.706284
$129$	9.89546	0.871246
$130$	−48.9590	−4.29399
$131$	14.1653	1.23763	0.618814	−	0.785538i	$-0.287614\pi$
$131$	14.1653	1.23763	0.618814	+	0.785538i	$0.287614\pi$
$132$	4.60938	0.401195
$133$	9.27637	0.804363
$134$	13.6508	1.17925
$135$	−4.00721	−0.344886
$136$	−2.27870	−0.195397
$137$	11.8311	1.01080	0.505401	−	0.862885i	$-0.331345\pi$
$137$	11.8311	1.01080	0.505401	+	0.862885i	$0.331345\pi$
$138$	12.2309	1.04116
$139$	21.4652	1.82066	0.910328	−	0.413887i	$-0.135829\pi$
$139$	21.4652	1.82066	0.910328	+	0.413887i	$0.135829\pi$
$140$	37.7307	3.18883
$141$	5.22451	0.439983
$142$	29.5408	2.47901
$143$	4.75237	0.397413
$144$	8.02760	0.668967
$145$	−17.1706	−1.42594
$146$	−11.6040	−0.960356
$147$	2.82726	0.233188
$148$	−9.73519	−0.800227
$149$	5.71869	0.468493	0.234247	−	0.972177i	$-0.424738\pi$
$149$	5.71869	0.468493	0.234247	+	0.972177i	$0.424738\pi$
$150$	−28.4280	−2.32114
$151$	4.53058	0.368694	0.184347	−	0.982861i	$-0.440983\pi$
$151$	4.53058	0.368694	0.184347	+	0.982861i	$0.440983\pi$
$152$	30.4638	2.47094
$153$	−0.339679	−0.0274615
$154$	−5.25159	−0.423185
$155$	7.28371	0.585042
$156$	21.9055	1.75384
$157$	−10.4733	−0.835859	−0.417930	−	0.908479i	$-0.637244\pi$
$157$	−10.4733	−0.835859	−0.417930	+	0.908479i	$0.637244\pi$
$158$	14.1210	1.12341
$159$	−9.68455	−0.768035
$160$	28.9368	2.28766
$161$	−9.71827	−0.765907
$162$	2.57087	0.201987
$163$	12.0156	0.941136	0.470568	−	0.882364i	$-0.344049\pi$
$163$	12.0156	0.941136	0.470568	+	0.882364i	$0.344049\pi$
$164$	−47.2854	−3.69237
$165$	4.00721	0.311961
$166$	36.5595	2.83756
$167$	7.72247	0.597582	0.298791	−	0.954318i	$-0.403417\pi$
$167$	7.72247	0.597582	0.298791	+	0.954318i	$0.403417\pi$
$168$	−13.7034	−1.05724
$169$	9.58501	0.737308
$170$	−3.49938	−0.268391
$171$	4.54116	0.347271
$172$	−45.6119	−3.47787
$173$	14.5915	1.10937	0.554684	−	0.832061i	$-0.312839\pi$
$173$	14.5915	1.10937	0.554684	+	0.832061i	$0.312839\pi$
$174$	11.0160	0.835122
$175$	22.5880	1.70749
$176$	−8.02760	−0.605103
$177$	2.04679	0.153846
$178$	−15.5659	−1.16671
$179$	−13.1655	−0.984037	−0.492019	−	0.870585i	$-0.663741\pi$
$179$	−13.1655	−0.984037	−0.492019	+	0.870585i	$0.663741\pi$
$180$	18.4707	1.37673
$181$	−7.26104	−0.539709	−0.269854	−	0.962901i	$-0.586976\pi$
$181$	−7.26104	−0.539709	−0.269854	+	0.962901i	$0.586976\pi$
$182$	−24.9575	−1.84997
$183$	−1.00000	−0.0739221
$184$	−31.9150	−2.35281
$185$	−8.46339	−0.622241
$186$	−4.67295	−0.342637
$187$	0.339679	0.0248398
$188$	−24.0818	−1.75634
$189$	−2.04273	−0.148587
$190$	46.7832	3.39401
$191$	3.04371	0.220235	0.110118	−	0.993919i	$-0.464877\pi$
$191$	3.04371	0.220235	0.110118	+	0.993919i	$0.464877\pi$
$192$	−2.50953	−0.181110
$193$	6.85641	0.493535	0.246768	−	0.969075i	$-0.420632\pi$
$193$	6.85641	0.493535	0.246768	+	0.969075i	$0.420632\pi$
$194$	34.9650	2.51034
$195$	19.0437	1.36375
$196$	−13.0319	−0.930850
$197$	−12.1375	−0.864763	−0.432381	−	0.901691i	$-0.642327\pi$
$197$	−12.1375	−0.864763	−0.432381	+	0.901691i	$0.642327\pi$
$198$	−2.57087	−0.182704
$199$	−13.8050	−0.978613	−0.489306	−	0.872112i	$-0.662750\pi$
$199$	−13.8050	−0.978613	−0.489306	+	0.872112i	$0.662750\pi$
$200$	74.1794	5.24528
$201$	−5.30981	−0.374525
$202$	−26.3916	−1.85691
$203$	−8.75297	−0.614338
$204$	1.56571	0.109622
$205$	−41.1081	−2.87111
$206$	27.8443	1.94001
$207$	−4.75749	−0.330669
$208$	−38.1501	−2.64523
$209$	−4.54116	−0.314119
$210$	−21.0442	−1.45219
$211$	13.4936	0.928938	0.464469	−	0.885589i	$-0.346245\pi$
$211$	13.4936	0.928938	0.464469	+	0.885589i	$0.346245\pi$
$212$	44.6398	3.06587
$213$	−11.4906	−0.787322
$214$	−26.6715	−1.82323
$215$	−39.6532	−2.70432
$216$	−6.70837	−0.456447
$217$	3.71297	0.252053
$218$	−40.9413	−2.77289
$219$	4.51365	0.305004
$220$	−18.4707	−1.24530
$221$	1.61428	0.108588
$222$	5.42978	0.364423
$223$	−3.65818	−0.244970	−0.122485	−	0.992470i	$-0.539086\pi$
$223$	−3.65818	−0.244970	−0.122485	+	0.992470i	$0.539086\pi$
$224$	14.7509	0.985588
$225$	11.0577	0.737183
$226$	11.5750	0.769956
$227$	−6.72165	−0.446131	−0.223066	−	0.974803i	$-0.571606\pi$
$227$	−6.72165	−0.446131	−0.223066	+	0.974803i	$0.571606\pi$
$228$	−20.9319	−1.38625
$229$	−1.23766	−0.0817871	−0.0408935	−	0.999164i	$-0.513020\pi$
$229$	−1.23766	−0.0817871	−0.0408935	+	0.999164i	$0.513020\pi$
$230$	−49.0118	−3.23174
$231$	2.04273	0.134402
$232$	−28.7449	−1.88720
$233$	12.9299	0.847065	0.423532	−	0.905881i	$-0.360790\pi$
$233$	12.9299	0.847065	0.423532	+	0.905881i	$0.360790\pi$
$234$	−12.2177	−0.798698
$235$	−20.9357	−1.36570
$236$	−9.43442	−0.614128
$237$	−5.49270	−0.356789
$238$	−1.78386	−0.115630
$239$	−18.5458	−1.19963	−0.599814	−	0.800140i	$-0.704759\pi$
$239$	−18.5458	−1.19963	−0.599814	+	0.800140i	$0.704759\pi$
$240$	−32.1683	−2.07645
$241$	−27.7936	−1.79034	−0.895171	−	0.445723i	$-0.852947\pi$
$241$	−27.7936	−1.79034	−0.895171	+	0.445723i	$0.852947\pi$
$242$	2.57087	0.165262
$243$	−1.00000	−0.0641500
$244$	4.60938	0.295085
$245$	−11.3294	−0.723810
$246$	26.3733	1.68150
$247$	−21.5813	−1.37318
$248$	12.1935	0.774287
$249$	−14.2207	−0.901197
$250$	62.4070	3.94696
$251$	−4.56250	−0.287982	−0.143991	−	0.989579i	$-0.545994\pi$
$251$	−4.56250	−0.287982	−0.143991	+	0.989579i	$0.545994\pi$
$252$	9.41571	0.593134
$253$	4.75749	0.299101
$254$	−31.5132	−1.97732
$255$	1.36117	0.0852396
$256$	−25.5621	−1.59763
$257$	−16.8127	−1.04874	−0.524372	−	0.851489i	$-0.675700\pi$
$257$	−16.8127	−1.04874	−0.524372	+	0.851489i	$0.675700\pi$
$258$	25.4399	1.58382
$259$	−4.31433	−0.268079
$260$	−87.7798	−5.44387
$261$	−4.28494	−0.265231
$262$	36.4171	2.24986
$263$	−8.19724	−0.505463	−0.252732	−	0.967536i	$-0.581329\pi$
$263$	−8.19724	−0.505463	−0.252732	+	0.967536i	$0.581329\pi$
$264$	6.70837	0.412872
$265$	38.8081	2.38396
$266$	23.8483	1.46224
$267$	6.05470	0.370542
$268$	24.4749	1.49504
$269$	12.7223	0.775690	0.387845	−	0.921725i	$-0.373220\pi$
$269$	12.7223	0.775690	0.387845	+	0.921725i	$0.373220\pi$
$270$	−10.3020	−0.626961
$271$	28.9215	1.75686	0.878428	−	0.477875i	$-0.158593\pi$
$271$	28.9215	1.75686	0.878428	+	0.477875i	$0.158593\pi$
$272$	−2.72681	−0.165337
$273$	9.70780	0.587543
$274$	30.4163	1.83752
$275$	−11.0577	−0.666807
$276$	21.9291	1.31998
$277$	9.01259	0.541514	0.270757	−	0.962648i	$-0.412726\pi$
$277$	9.01259	0.541514	0.270757	+	0.962648i	$0.412726\pi$
$278$	55.1843	3.30974
$279$	1.81765	0.108820
$280$	54.9124	3.28164
$281$	−20.0391	−1.19543	−0.597715	−	0.801708i	$-0.703925\pi$
$281$	−20.0391	−1.19543	−0.597715	+	0.801708i	$0.703925\pi$
$282$	13.4315	0.799837
$283$	29.2872	1.74094	0.870471	−	0.492221i	$-0.163815\pi$
$283$	29.2872	1.74094	0.870471	+	0.492221i	$0.163815\pi$
$284$	52.9645	3.14286
$285$	−18.1974	−1.07792
$286$	12.2177	0.722449
$287$	−20.9554	−1.23696
$288$	7.22118	0.425512
$289$	−16.8846	−0.993213
$290$	−44.1435	−2.59220
$291$	−13.6004	−0.797272
$292$	−20.8051	−1.21753
$293$	31.2913	1.82806	0.914029	−	0.405649i	$-0.132954\pi$
$293$	31.2913	1.82806	0.914029	+	0.405649i	$0.132954\pi$
$294$	7.26851	0.423908
$295$	−8.20191	−0.477534
$296$	−14.1683	−0.823518
$297$	1.00000	0.0580259
$298$	14.7020	0.851665
$299$	22.6094	1.30753
$300$	−50.9693	−2.94271
$301$	−20.2137	−1.16510
$302$	11.6475	0.670241
$303$	10.2656	0.589746
$304$	36.4547	2.09082
$305$	4.00721	0.229452
$306$	−0.873272	−0.0499216
$307$	0.203717	0.0116268	0.00581338	−	0.999983i	$-0.498150\pi$
$307$	0.203717	0.0116268	0.00581338	+	0.999983i	$0.498150\pi$
$308$	−9.41571	−0.536510
$309$	−10.8307	−0.616137
$310$	18.7255	1.06354
$311$	−15.4938	−0.878573	−0.439287	−	0.898347i	$-0.644769\pi$
$311$	−15.4938	−0.878573	−0.439287	+	0.898347i	$0.644769\pi$
$312$	31.8807	1.80489
$313$	−27.2007	−1.53747	−0.768737	−	0.639565i	$-0.779114\pi$
$313$	−27.2007	−1.53747	−0.768737	+	0.639565i	$0.779114\pi$
$314$	−26.9255	−1.51949
$315$	8.18565	0.461209
$316$	25.3179	1.42425
$317$	−11.9050	−0.668653	−0.334327	−	0.942457i	$-0.608509\pi$
$317$	−11.9050	−0.668653	−0.334327	+	0.942457i	$0.608509\pi$
$318$	−24.8977	−1.39620
$319$	4.28494	0.239910
$320$	10.0562	0.562159
$321$	10.3745	0.579049
$322$	−24.9844	−1.39233
$323$	−1.54254	−0.0858292
$324$	4.60938	0.256076
$325$	−52.5505	−2.91497
$326$	30.8906	1.71087
$327$	15.9251	0.880657
$328$	−68.8180	−3.79984
$329$	−10.6723	−0.588381
$330$	10.3020	0.567108
$331$	−5.44265	−0.299155	−0.149577	−	0.988750i	$-0.547791\pi$
$331$	−5.44265	−0.299155	−0.149577	+	0.988750i	$0.547791\pi$
$332$	65.5483	3.59743
$333$	−2.11204	−0.115739
$334$	19.8535	1.08633
$335$	21.2775	1.16252
$336$	−16.3982	−0.894596
$337$	11.5595	0.629687	0.314843	−	0.949144i	$-0.398048\pi$
$337$	11.5595	0.629687	0.314843	+	0.949144i	$0.398048\pi$
$338$	24.6418	1.34034
$339$	−4.50235	−0.244534
$340$	−6.27413	−0.340263
$341$	−1.81765	−0.0984314
$342$	11.6747	0.631298
$343$	−20.0744	−1.08392
$344$	−66.3824	−3.57910
$345$	19.0643	1.02639
$346$	37.5128	2.01670
$347$	−34.9338	−1.87535	−0.937673	−	0.347519i	$-0.887024\pi$
$347$	−34.9338	−1.87535	−0.937673	+	0.347519i	$0.887024\pi$
$348$	19.7509	1.05876
$349$	−16.4637	−0.881281	−0.440641	−	0.897684i	$-0.645249\pi$
$349$	−16.4637	−0.881281	−0.440641	+	0.897684i	$0.645249\pi$
$350$	58.0708	3.10401
$351$	4.75237	0.253663
$352$	−7.22118	−0.384890
$353$	36.1064	1.92175	0.960876	−	0.276980i	$-0.0893335\pi$
$353$	36.1064	1.92175	0.960876	+	0.276980i	$0.0893335\pi$
$354$	5.26203	0.279674
$355$	46.0452	2.44383
$356$	−27.9084	−1.47914
$357$	0.693873	0.0367237
$358$	−33.8469	−1.78886
$359$	−16.1146	−0.850498	−0.425249	−	0.905076i	$-0.639813\pi$
$359$	−16.1146	−0.850498	−0.425249	+	0.905076i	$0.639813\pi$
$360$	26.8819	1.41680
$361$	1.62217	0.0853773
$362$	−18.6672	−0.981126
$363$	−1.00000	−0.0524864
$364$	−44.7469	−2.34538
$365$	−18.0872	−0.946725
$366$	−2.57087	−0.134382
$367$	35.8180	1.86969	0.934843	−	0.355061i	$-0.115540\pi$
$367$	35.8180	1.86969	0.934843	+	0.355061i	$0.115540\pi$
$368$	−38.1913	−1.99086
$369$	−10.2585	−0.534038
$370$	−21.7583	−1.13116
$371$	19.7829	1.02708
$372$	−8.37824	−0.434392
$373$	−18.3914	−0.952273	−0.476137	−	0.879371i	$-0.657963\pi$
$373$	−18.3914	−0.952273	−0.476137	+	0.879371i	$0.657963\pi$
$374$	0.873272	0.0451558
$375$	−24.2746	−1.25354
$376$	−35.0480	−1.80746
$377$	20.3636	1.04878
$378$	−5.25159	−0.270113
$379$	−5.27053	−0.270729	−0.135364	−	0.990796i	$-0.543221\pi$
$379$	−5.27053	−0.270729	−0.135364	+	0.990796i	$0.543221\pi$
$380$	83.8787	4.30289
$381$	12.2578	0.627986
$382$	7.82499	0.400361
$383$	32.5167	1.66153	0.830763	−	0.556626i	$-0.187904\pi$
$383$	32.5167	1.66153	0.830763	+	0.556626i	$0.187904\pi$
$384$	7.99069	0.407773
$385$	−8.18565	−0.417179
$386$	17.6269	0.897188
$387$	−9.89546	−0.503014
$388$	62.6895	3.18258
$389$	−24.3758	−1.23590	−0.617950	−	0.786217i	$-0.712037\pi$
$389$	−24.3758	−1.23590	−0.617950	+	0.786217i	$0.712037\pi$
$390$	48.9590	2.47914
$391$	1.61602	0.0817258
$392$	−18.9663	−0.957942
$393$	−14.1653	−0.714544
$394$	−31.2040	−1.57203
$395$	22.0104	1.10746
$396$	−4.60938	−0.231630
$397$	−18.0276	−0.904779	−0.452390	−	0.891820i	$-0.649428\pi$
$397$	−18.0276	−0.904779	−0.452390	+	0.891820i	$0.649428\pi$
$398$	−35.4909	−1.77900
$399$	−9.27637	−0.464399
$400$	88.7671	4.43836
$401$	−29.1981	−1.45808	−0.729042	−	0.684469i	$-0.760034\pi$
$401$	−29.1981	−1.45808	−0.729042	+	0.684469i	$0.760034\pi$
$402$	−13.6508	−0.680842
$403$	−8.63815	−0.430297
$404$	−47.3182	−2.35417
$405$	4.00721	0.199120
$406$	−22.5027	−1.11679
$407$	2.11204	0.104690
$408$	2.27870	0.112812
$409$	2.63476	0.130280	0.0651401	−	0.997876i	$-0.479251\pi$
$409$	2.63476	0.130280	0.0651401	+	0.997876i	$0.479251\pi$
$410$	−105.684	−5.21934
$411$	−11.8311	−0.583587
$412$	49.9227	2.45952
$413$	−4.18103	−0.205735
$414$	−12.2309	−0.601116
$415$	56.9852	2.79729
$416$	−34.3177	−1.68257
$417$	−21.4652	−1.05116
$418$	−11.6747	−0.571030
$419$	32.0724	1.56684	0.783420	−	0.621492i	$-0.213473\pi$
$419$	32.0724	1.56684	0.783420	+	0.621492i	$0.213473\pi$
$420$	−37.7307	−1.84107
$421$	6.02368	0.293576	0.146788	−	0.989168i	$-0.453106\pi$
$421$	6.02368	0.293576	0.146788	+	0.989168i	$0.453106\pi$
$422$	34.6903	1.68870
$423$	−5.22451	−0.254025
$424$	64.9676	3.15510
$425$	−3.75609	−0.182197
$426$	−29.5408	−1.43126
$427$	2.04273	0.0988546
$428$	−47.8200	−2.31147
$429$	−4.75237	−0.229447
$430$	−101.943	−4.91614
$431$	−19.6288	−0.945487	−0.472744	−	0.881200i	$-0.656736\pi$
$431$	−19.6288	−0.945487	−0.472744	+	0.881200i	$0.656736\pi$
$432$	−8.02760	−0.386228
$433$	27.8579	1.33876	0.669382	−	0.742919i	$-0.266559\pi$
$433$	27.8579	1.33876	0.669382	+	0.742919i	$0.266559\pi$
$434$	9.54557	0.458202
$435$	17.1706	0.823269
$436$	−73.4046	−3.51544
$437$	−21.6046	−1.03349
$438$	11.6040	0.554462
$439$	−25.4823	−1.21620	−0.608102	−	0.793859i	$-0.708069\pi$
$439$	−25.4823	−1.21620	−0.608102	+	0.793859i	$0.708069\pi$
$440$	−26.8819	−1.28154
$441$	−2.82726	−0.134631
$442$	4.15011	0.197401
$443$	29.0256	1.37905	0.689524	−	0.724263i	$-0.257820\pi$
$443$	29.0256	1.37905	0.689524	+	0.724263i	$0.257820\pi$
$444$	9.73519	0.462012
$445$	−24.2625	−1.15015
$446$	−9.40471	−0.445326
$447$	−5.71869	−0.270485
$448$	5.12629	0.242194
$449$	23.3018	1.09968	0.549840	−	0.835270i	$-0.314689\pi$
$449$	23.3018	1.09968	0.549840	+	0.835270i	$0.314689\pi$
$450$	28.4280	1.34011
$451$	10.2585	0.483055
$452$	20.7530	0.976141
$453$	−4.53058	−0.212865
$454$	−17.2805	−0.811013
$455$	−38.9012	−1.82372
$456$	−30.4638	−1.42660
$457$	38.8508	1.81737	0.908683	−	0.417487i	$-0.137089\pi$
$457$	38.8508	1.81737	0.908683	+	0.417487i	$0.137089\pi$
$458$	−3.18187	−0.148679
$459$	0.339679	0.0158549
$460$	−87.8745	−4.09717
$461$	2.42547	0.112965	0.0564827	−	0.998404i	$-0.482011\pi$
$461$	2.42547	0.112965	0.0564827	+	0.998404i	$0.482011\pi$
$462$	5.25159	0.244326
$463$	37.3362	1.73516	0.867581	−	0.497295i	$-0.165673\pi$
$463$	37.3362	1.73516	0.867581	+	0.497295i	$0.165673\pi$
$464$	−34.3978	−1.59688
$465$	−7.28371	−0.337774
$466$	33.2411	1.53986
$467$	−7.55898	−0.349788	−0.174894	−	0.984587i	$-0.555958\pi$
$467$	−7.55898	−0.349788	−0.174894	+	0.984587i	$0.555958\pi$
$468$	−21.9055	−1.01258
$469$	10.8465	0.500845
$470$	−53.8231	−2.48267
$471$	10.4733	0.482583
$472$	−13.7306	−0.632003
$473$	9.89546	0.454994
$474$	−14.1210	−0.648600
$475$	50.2150	2.30402
$476$	−3.19832	−0.146595
$477$	9.68455	0.443425
$478$	−47.6788	−2.18078
$479$	−35.7614	−1.63398	−0.816990	−	0.576651i	$-0.804359\pi$
$479$	−35.7614	−1.63398	−0.816990	+	0.576651i	$0.804359\pi$
$480$	−28.9368	−1.32078
$481$	10.0372	0.457657
$482$	−71.4537	−3.25463
$483$	9.71827	0.442197
$484$	4.60938	0.209517
$485$	54.4998	2.47471
$486$	−2.57087	−0.116617
$487$	−6.39232	−0.289664	−0.144832	−	0.989456i	$-0.546264\pi$
$487$	−6.39232	−0.289664	−0.144832	+	0.989456i	$0.546264\pi$
$488$	6.70837	0.303674
$489$	−12.0156	−0.543365
$490$	−29.1265	−1.31580
$491$	16.7893	0.757691	0.378846	−	0.925460i	$-0.376321\pi$
$491$	16.7893	0.757691	0.378846	+	0.925460i	$0.376321\pi$
$492$	47.2854	2.13179
$493$	1.45550	0.0655526
$494$	−55.4827	−2.49628
$495$	−4.00721	−0.180111
$496$	14.5914	0.655172
$497$	23.4722	1.05287
$498$	−36.5595	−1.63827
$499$	2.39493	0.107212	0.0536060	−	0.998562i	$-0.482929\pi$
$499$	2.39493	0.107212	0.0536060	+	0.998562i	$0.482929\pi$
$500$	111.891	5.00392
$501$	−7.72247	−0.345014
$502$	−11.7296	−0.523517
$503$	2.97796	0.132781	0.0663903	−	0.997794i	$-0.478852\pi$
$503$	2.97796	0.132781	0.0663903	+	0.997794i	$0.478852\pi$
$504$	13.7034	0.610397
$505$	−41.1366	−1.83055
$506$	12.2309	0.543730
$507$	−9.58501	−0.425685
$508$	−56.5008	−2.50682
$509$	−13.6035	−0.602964	−0.301482	−	0.953472i	$-0.597481\pi$
$509$	−13.6035	−0.602964	−0.301482	+	0.953472i	$0.597481\pi$
$510$	3.49938	0.154955
$511$	−9.22017	−0.407876
$512$	−49.7355	−2.19802
$513$	−4.54116	−0.200497
$514$	−43.2232	−1.90649
$515$	43.4009	1.91247
$516$	45.6119	2.00795
$517$	5.22451	0.229774
$518$	−11.0916	−0.487336
$519$	−14.5915	−0.640494
$520$	−127.752	−5.60232
$521$	4.86305	0.213054	0.106527	−	0.994310i	$-0.466027\pi$
$521$	4.86305	0.213054	0.106527	+	0.994310i	$0.466027\pi$
$522$	−11.0160	−0.482158
$523$	4.06198	0.177618	0.0888091	−	0.996049i	$-0.471694\pi$
$523$	4.06198	0.177618	0.0888091	+	0.996049i	$0.471694\pi$
$524$	65.2932	2.85234
$525$	−22.5880	−0.985820
$526$	−21.0740	−0.918872
$527$	−0.617419	−0.0268952
$528$	8.02760	0.349357
$529$	−0.366250	−0.0159239
$530$	99.7705	4.33375
$531$	−2.04679	−0.0888230
$532$	42.7583	1.85381
$533$	48.7523	2.11170
$534$	15.5659	0.673601
$535$	−41.5729	−1.79735
$536$	35.6202	1.53856
$537$	13.1655	0.568134
$538$	32.7073	1.41011
$539$	2.82726	0.121779
$540$	−18.4707	−0.794854
$541$	43.0563	1.85113	0.925566	−	0.378585i	$-0.123589\pi$
$541$	43.0563	1.85113	0.925566	+	0.378585i	$0.123589\pi$
$542$	74.3534	3.19375
$543$	7.26104	0.311601
$544$	−2.45289	−0.105167
$545$	−63.8150	−2.73354
$546$	24.9575	1.06808
$547$	8.25809	0.353090	0.176545	−	0.984293i	$-0.443508\pi$
$547$	8.25809	0.353090	0.176545	+	0.984293i	$0.443508\pi$
$548$	54.5341	2.32958
$549$	1.00000	0.0426790
$550$	−28.4280	−1.21217
$551$	−19.4586	−0.828964
$552$	31.9150	1.35839
$553$	11.2201	0.477127
$554$	23.1702	0.984408
$555$	8.46339	0.359251
$556$	98.9413	4.19605
$557$	−12.2925	−0.520852	−0.260426	−	0.965494i	$-0.583863\pi$
$557$	−12.2925	−0.520852	−0.260426	+	0.965494i	$0.583863\pi$
$558$	4.67295	0.197822
$559$	47.0269	1.98902
$560$	65.7111	2.77680
$561$	−0.339679	−0.0143413
$562$	−51.5179	−2.17315
$563$	−20.3279	−0.856719	−0.428359	−	0.903609i	$-0.640908\pi$
$563$	−20.3279	−0.856719	−0.428359	+	0.903609i	$0.640908\pi$
$564$	24.0818	1.01402
$565$	18.0419	0.759028
$566$	75.2935	3.16482
$567$	2.04273	0.0857866
$568$	77.0831	3.23434
$569$	−6.99933	−0.293427	−0.146714	−	0.989179i	$-0.546870\pi$
$569$	−6.99933	−0.293427	−0.146714	+	0.989179i	$0.546870\pi$
$570$	−46.7832	−1.95953
$571$	−28.0828	−1.17523	−0.587615	−	0.809141i	$-0.699933\pi$
$571$	−28.0828	−1.17523	−0.587615	+	0.809141i	$0.699933\pi$
$572$	21.9055	0.915913
$573$	−3.04371	−0.127153
$574$	−53.8736	−2.24864
$575$	−52.6071	−2.19387
$576$	2.50953	0.104564
$577$	−20.0459	−0.834523	−0.417262	−	0.908786i	$-0.637010\pi$
$577$	−20.0459	−0.834523	−0.417262	+	0.908786i	$0.637010\pi$
$578$	−43.4082	−1.80554
$579$	−6.85641	−0.284943
$580$	−79.1460	−3.28636
$581$	29.0489	1.20515
$582$	−34.9650	−1.44934
$583$	−9.68455	−0.401093
$584$	−30.2793	−1.25296
$585$	−19.0437	−0.787362
$586$	80.4459	3.32319
$587$	−16.2870	−0.672235	−0.336118	−	0.941820i	$-0.609114\pi$
$587$	−16.2870	−0.672235	−0.336118	+	0.941820i	$0.609114\pi$
$588$	13.0319	0.537426
$589$	8.25425	0.340111
$590$	−21.0861	−0.868099
$591$	12.1375	0.499271
$592$	−16.9546	−0.696830
$593$	−36.0721	−1.48130	−0.740652	−	0.671889i	$-0.765483\pi$
$593$	−36.0721	−1.48130	−0.740652	+	0.671889i	$0.765483\pi$
$594$	2.57087	0.105484
$595$	−2.78050	−0.113989
$596$	26.3596	1.07973
$597$	13.8050	0.565002
$598$	58.1258	2.37694
$599$	−12.5585	−0.513125	−0.256563	−	0.966528i	$-0.582590\pi$
$599$	−12.5585	−0.513125	−0.256563	+	0.966528i	$0.582590\pi$
$600$	−74.1794	−3.02836
$601$	35.2090	1.43621	0.718103	−	0.695936i	$-0.245010\pi$
$601$	35.2090	1.43621	0.718103	+	0.695936i	$0.245010\pi$
$602$	−51.9669	−2.11801
$603$	5.30981	0.216232
$604$	20.8832	0.849724
$605$	4.00721	0.162916
$606$	26.3916	1.07209
$607$	1.60580	0.0651773	0.0325886	−	0.999469i	$-0.489625\pi$
$607$	1.60580	0.0651773	0.0325886	+	0.999469i	$0.489625\pi$
$608$	32.7926	1.32991
$609$	8.75297	0.354688
$610$	10.3020	0.417117
$611$	24.8288	1.00447
$612$	−1.56571	−0.0632901
$613$	−2.16291	−0.0873591	−0.0436796	−	0.999046i	$-0.513908\pi$
$613$	−2.16291	−0.0873591	−0.0436796	+	0.999046i	$0.513908\pi$
$614$	0.523731	0.0211361
$615$	41.1081	1.65764
$616$	−13.7034	−0.552125
$617$	−14.6864	−0.591253	−0.295627	−	0.955304i	$-0.595528\pi$
$617$	−14.6864	−0.591253	−0.295627	+	0.955304i	$0.595528\pi$
$618$	−27.8443	−1.12006
$619$	47.1847	1.89651	0.948257	−	0.317505i	$-0.102845\pi$
$619$	47.1847	1.89651	0.948257	+	0.317505i	$0.102845\pi$
$620$	33.5734	1.34834
$621$	4.75749	0.190912
$622$	−39.8326	−1.59714
$623$	−12.3681	−0.495518
$624$	38.1501	1.52723
$625$	41.9849	1.67940
$626$	−69.9294	−2.79494
$627$	4.54116	0.181357
$628$	−48.2753	−1.92639
$629$	0.717416	0.0286053
$630$	21.0442	0.838423
$631$	44.0652	1.75421	0.877104	−	0.480300i	$-0.159472\pi$
$631$	44.0652	1.75421	0.877104	+	0.480300i	$0.159472\pi$
$632$	36.8471	1.46570
$633$	−13.4936	−0.536323
$634$	−30.6063	−1.21553
$635$	−49.1196	−1.94925
$636$	−44.6398	−1.77008
$637$	13.4362	0.532360
$638$	11.0160	0.436128
$639$	11.4906	0.454561
$640$	−32.0204	−1.26572
$641$	−32.9295	−1.30064	−0.650319	−	0.759661i	$-0.725365\pi$
$641$	−32.9295	−1.30064	−0.650319	+	0.759661i	$0.725365\pi$
$642$	26.6715	1.05264
$643$	34.3960	1.35645	0.678223	−	0.734856i	$-0.262750\pi$
$643$	34.3960	1.35645	0.678223	+	0.734856i	$0.262750\pi$
$644$	−44.7952	−1.76518
$645$	39.6532	1.56134
$646$	−3.96567	−0.156027
$647$	40.6293	1.59730	0.798652	−	0.601793i	$-0.205547\pi$
$647$	40.6293	1.59730	0.798652	+	0.601793i	$0.205547\pi$
$648$	6.70837	0.263530
$649$	2.04679	0.0803435
$650$	−135.100	−5.29908
$651$	−3.71297	−0.145523
$652$	55.3845	2.16903
$653$	−0.882411	−0.0345314	−0.0172657	−	0.999851i	$-0.505496\pi$
$653$	−0.882411	−0.0345314	−0.0172657	+	0.999851i	$0.505496\pi$
$654$	40.9413	1.60093
$655$	56.7633	2.21793
$656$	−82.3514	−3.21528
$657$	−4.51365	−0.176094
$658$	−27.4370	−1.06961
$659$	24.8985	0.969906	0.484953	−	0.874540i	$-0.338837\pi$
$659$	24.8985	0.969906	0.484953	+	0.874540i	$0.338837\pi$
$660$	18.4707	0.718973
$661$	40.3972	1.57127	0.785635	−	0.618690i	$-0.212336\pi$
$661$	40.3972	1.57127	0.785635	+	0.618690i	$0.212336\pi$
$662$	−13.9923	−0.543828
$663$	−1.61428	−0.0626935
$664$	95.3974	3.70214
$665$	37.1724	1.44148
$666$	−5.42978	−0.210400
$667$	20.3856	0.789332
$668$	35.5958	1.37724
$669$	3.65818	0.141433
$670$	54.7018	2.11331
$671$	−1.00000	−0.0386046
$672$	−14.7509	−0.569029
$673$	−4.08661	−0.157527	−0.0787636	−	0.996893i	$-0.525097\pi$
$673$	−4.08661	−0.157527	−0.0787636	+	0.996893i	$0.525097\pi$
$674$	29.7180	1.14469
$675$	−11.0577	−0.425613
$676$	44.1809	1.69927
$677$	−3.16188	−0.121521	−0.0607604	−	0.998152i	$-0.519353\pi$
$677$	−3.16188	−0.121521	−0.0607604	+	0.998152i	$0.519353\pi$
$678$	−11.5750	−0.444534
$679$	27.7820	1.06618
$680$	−9.13121	−0.350166
$681$	6.72165	0.257574
$682$	−4.67295	−0.178936
$683$	−2.84581	−0.108892	−0.0544459	−	0.998517i	$-0.517339\pi$
$683$	−2.84581	−0.108892	−0.0544459	+	0.998517i	$0.517339\pi$
$684$	20.9319	0.800353
$685$	47.4098	1.81144
$686$	−51.6088	−1.97043
$687$	1.23766	0.0472198
$688$	−79.4368	−3.02850
$689$	−46.0246	−1.75340
$690$	49.0118	1.86585
$691$	24.9625	0.949620	0.474810	−	0.880088i	$-0.342517\pi$
$691$	24.9625	0.949620	0.474810	+	0.880088i	$0.342517\pi$
$692$	67.2576	2.55675
$693$	−2.04273	−0.0775969
$694$	−89.8104	−3.40915
$695$	86.0157	3.26276
$696$	28.7449	1.08957
$697$	3.48461	0.131989
$698$	−42.3260	−1.60206
$699$	−12.9299	−0.489053
$700$	104.116	3.93523
$701$	3.42189	0.129243	0.0646216	−	0.997910i	$-0.479416\pi$
$701$	3.42189	0.129243	0.0646216	+	0.997910i	$0.479416\pi$
$702$	12.2177	0.461128
$703$	−9.59112	−0.361736
$704$	−2.50953	−0.0945815
$705$	20.9357	0.788485
$706$	92.8250	3.49351
$707$	−20.9699	−0.788655
$708$	9.43442	0.354567
$709$	−52.0319	−1.95410	−0.977050	−	0.213008i	$-0.931674\pi$
$709$	−52.0319	−1.95410	−0.977050	+	0.213008i	$0.931674\pi$
$710$	118.376	4.44258
$711$	5.49270	0.205992
$712$	−40.6172	−1.52219
$713$	−8.64747	−0.323850
$714$	1.78386	0.0667592
$715$	19.0437	0.712196
$716$	−60.6849	−2.26790
$717$	18.5458	0.692605
$718$	−41.4287	−1.54610
$719$	−10.9759	−0.409332	−0.204666	−	0.978832i	$-0.565611\pi$
$719$	−10.9759	−0.409332	−0.204666	+	0.978832i	$0.565611\pi$
$720$	32.1683	1.19884
$721$	22.1242	0.823947
$722$	4.17038	0.155206
$723$	27.7936	1.03365
$724$	−33.4689	−1.24386
$725$	−47.3817	−1.75971
$726$	−2.57087	−0.0954140
$727$	32.1350	1.19182	0.595911	−	0.803051i	$-0.296791\pi$
$727$	32.1350	1.19182	0.595911	+	0.803051i	$0.296791\pi$
$728$	−65.1235	−2.41364
$729$	1.00000	0.0370370
$730$	−46.4998	−1.72103
$731$	3.36128	0.124322
$732$	−4.60938	−0.170367
$733$	17.1024	0.631693	0.315846	−	0.948810i	$-0.397712\pi$
$733$	17.1024	0.631693	0.315846	+	0.948810i	$0.397712\pi$
$734$	92.0835	3.39887
$735$	11.3294	0.417892
$736$	−34.3547	−1.26633
$737$	−5.30981	−0.195589
$738$	−26.3733	−0.970816
$739$	43.8812	1.61420	0.807098	−	0.590417i	$-0.201037\pi$
$739$	43.8812	1.61420	0.807098	+	0.590417i	$0.201037\pi$
$740$	−39.0109	−1.43407
$741$	21.5813	0.792808
$742$	50.8593	1.86711
$743$	−34.0979	−1.25093	−0.625465	−	0.780252i	$-0.715091\pi$
$743$	−34.0979	−1.25093	−0.625465	+	0.780252i	$0.715091\pi$
$744$	−12.1935	−0.447035
$745$	22.9160	0.839577
$746$	−47.2820	−1.73112
$747$	14.2207	0.520306
$748$	1.56571	0.0572480
$749$	−21.1923	−0.774351
$750$	−62.4070	−2.27878
$751$	−0.462726	−0.0168851	−0.00844255	−	0.999964i	$-0.502687\pi$
$751$	−0.462726	−0.0168851	−0.00844255	+	0.999964i	$0.502687\pi$
$752$	−41.9403	−1.52941
$753$	4.56250	0.166267
$754$	52.3522	1.90655
$755$	18.1550	0.660728
$756$	−9.41571	−0.342446
$757$	−15.0488	−0.546957	−0.273479	−	0.961878i	$-0.588174\pi$
$757$	−15.0488	−0.546957	−0.273479	+	0.961878i	$0.588174\pi$
$758$	−13.5498	−0.492153
$759$	−4.75749	−0.172686
$760$	122.075	4.42812
$761$	−3.40565	−0.123455	−0.0617274	−	0.998093i	$-0.519661\pi$
$761$	−3.40565	−0.123455	−0.0617274	+	0.998093i	$0.519661\pi$
$762$	31.5132	1.14160
$763$	−32.5306	−1.17769
$764$	14.0296	0.507574
$765$	−1.36117	−0.0492131
$766$	83.5963	3.02046
$767$	9.72709	0.351225
$768$	25.5621	0.922393
$769$	16.3158	0.588363	0.294182	−	0.955750i	$-0.404953\pi$
$769$	16.3158	0.588363	0.294182	+	0.955750i	$0.404953\pi$
$770$	−21.0442	−0.758382
$771$	16.8127	0.605493
$772$	31.6038	1.13744
$773$	33.0741	1.18959	0.594797	−	0.803876i	$-0.297232\pi$
$773$	33.0741	1.18959	0.594797	+	0.803876i	$0.297232\pi$
$774$	−25.4399	−0.914420
$775$	20.0991	0.721982
$776$	91.2368	3.27521
$777$	4.31433	0.154776
$778$	−62.6669	−2.24672
$779$	−46.5857	−1.66910
$780$	87.7798	3.14302
$781$	−11.4906	−0.411166
$782$	4.15459	0.148568
$783$	4.28494	0.153131
$784$	−22.6961	−0.810575
$785$	−41.9687	−1.49793
$786$	−36.4171	−1.29896
$787$	13.5591	0.483328	0.241664	−	0.970360i	$-0.422307\pi$
$787$	13.5591	0.483328	0.241664	+	0.970360i	$0.422307\pi$
$788$	−55.9464	−1.99301
$789$	8.19724	0.291829
$790$	56.5860	2.01324
$791$	9.19709	0.327011
$792$	−6.70837	−0.238372
$793$	−4.75237	−0.168762
$794$	−46.3466	−1.64478
$795$	−38.8081	−1.37638
$796$	−63.6326	−2.25540
$797$	18.0188	0.638257	0.319129	−	0.947711i	$-0.396610\pi$
$797$	18.0188	0.638257	0.319129	+	0.947711i	$0.396610\pi$
$798$	−23.8483	−0.844222
$799$	1.77466	0.0627829
$800$	79.8500	2.82312
$801$	−6.05470	−0.213932
$802$	−75.0646	−2.65062
$803$	4.51365	0.159283
$804$	−24.4749	−0.863164
$805$	−38.9432	−1.37257
$806$	−22.2076	−0.782228
$807$	−12.7223	−0.447845
$808$	−68.8657	−2.42269
$809$	11.1179	0.390883	0.195441	−	0.980715i	$-0.437386\pi$
$809$	11.1179	0.390883	0.195441	+	0.980715i	$0.437386\pi$
$810$	10.3020	0.361976
$811$	9.75699	0.342614	0.171307	−	0.985218i	$-0.445201\pi$
$811$	9.75699	0.342614	0.171307	+	0.985218i	$0.445201\pi$
$812$	−40.3457	−1.41586
$813$	−28.9215	−1.01432
$814$	5.42978	0.190314
$815$	48.1491	1.68659
$816$	2.72681	0.0954575
$817$	−44.9369	−1.57214
$818$	6.77362	0.236834
$819$	−9.70780	−0.339218
$820$	−189.483	−6.61702
$821$	17.6656	0.616535	0.308268	−	0.951300i	$-0.400251\pi$
$821$	17.6656	0.616535	0.308268	+	0.951300i	$0.400251\pi$
$822$	−30.4163	−1.06089
$823$	45.2415	1.57702	0.788510	−	0.615022i	$-0.210853\pi$
$823$	45.2415	1.57702	0.788510	+	0.615022i	$0.210853\pi$
$824$	72.6563	2.53110
$825$	11.0577	0.384981
$826$	−10.7489	−0.374002
$827$	−26.0944	−0.907392	−0.453696	−	0.891157i	$-0.649895\pi$
$827$	−26.0944	−0.907392	−0.453696	+	0.891157i	$0.649895\pi$
$828$	−21.9291	−0.762088
$829$	−36.7769	−1.27732	−0.638658	−	0.769491i	$-0.720510\pi$
$829$	−36.7769	−1.27732	−0.638658	+	0.769491i	$0.720510\pi$
$830$	146.501	5.08514
$831$	−9.01259	−0.312643
$832$	−11.9262	−0.413467
$833$	0.960361	0.0332745
$834$	−55.1843	−1.91088
$835$	30.9456	1.07092
$836$	−20.9319	−0.723946
$837$	−1.81765	−0.0628272
$838$	82.4541	2.84833
$839$	−5.35112	−0.184741	−0.0923706	−	0.995725i	$-0.529444\pi$
$839$	−5.35112	−0.184741	−0.0923706	+	0.995725i	$0.529444\pi$
$840$	−54.9124	−1.89466
$841$	−10.6393	−0.366873
$842$	15.4861	0.533686
$843$	20.0391	0.690182
$844$	62.1971	2.14091
$845$	38.4092	1.32131
$846$	−13.4315	−0.461786
$847$	2.04273	0.0701890
$848$	77.7437	2.66973
$849$	−29.2872	−1.00513
$850$	−9.65641	−0.331212
$851$	10.0480	0.344442
$852$	−52.9645	−1.81453
$853$	44.6105	1.52744	0.763718	−	0.645550i	$-0.223372\pi$
$853$	44.6105	1.52744	0.763718	+	0.645550i	$0.223372\pi$
$854$	5.25159	0.179706
$855$	18.1974	0.622338
$856$	−69.5961	−2.37875
$857$	−7.03968	−0.240471	−0.120235	−	0.992745i	$-0.538365\pi$
$857$	−7.03968	−0.240471	−0.120235	+	0.992745i	$0.538365\pi$
$858$	−12.2177	−0.417106
$859$	55.9231	1.90807	0.954036	−	0.299693i	$-0.0968841\pi$
$859$	55.9231	1.90807	0.954036	+	0.299693i	$0.0968841\pi$
$860$	−182.776	−6.23263
$861$	20.9554	0.714158
$862$	−50.4632	−1.71878
$863$	−47.1465	−1.60489	−0.802443	−	0.596729i	$-0.796467\pi$
$863$	−47.1465	−1.60489	−0.802443	+	0.596729i	$0.796467\pi$
$864$	−7.22118	−0.245670
$865$	58.4711	1.98808
$866$	71.6190	2.43371
$867$	16.8846	0.573432
$868$	17.1145	0.580903
$869$	−5.49270	−0.186327
$870$	44.1435	1.49661
$871$	−25.2342	−0.855028
$872$	−106.831	−3.61776
$873$	13.6004	0.460305
$874$	−55.5425	−1.87875
$875$	49.5865	1.67633
$876$	20.8051	0.702940
$877$	−15.8127	−0.533957	−0.266979	−	0.963702i	$-0.586025\pi$
$877$	−15.8127	−0.533957	−0.266979	+	0.963702i	$0.586025\pi$
$878$	−65.5117	−2.21091
$879$	−31.2913	−1.05543
$880$	−32.1683	−1.08439
$881$	13.2185	0.445343	0.222672	−	0.974894i	$-0.428522\pi$
$881$	13.2185	0.445343	0.222672	+	0.974894i	$0.428522\pi$
$882$	−7.26851	−0.244744
$883$	−31.4226	−1.05746	−0.528728	−	0.848791i	$-0.677331\pi$
$883$	−31.4226	−1.05746	−0.528728	+	0.848791i	$0.677331\pi$
$884$	7.44083	0.250262
$885$	8.20191	0.275704
$886$	74.6211	2.50694
$887$	−26.4566	−0.888326	−0.444163	−	0.895946i	$-0.646499\pi$
$887$	−26.4566	−0.888326	−0.444163	+	0.895946i	$0.646499\pi$
$888$	14.1683	0.475459
$889$	−25.0394	−0.839793
$890$	−62.3757	−2.09084
$891$	−1.00000	−0.0335013
$892$	−16.8619	−0.564579
$893$	−23.7254	−0.793939
$894$	−14.7020	−0.491709
$895$	−52.7570	−1.76347
$896$	−16.3228	−0.545307
$897$	−22.6094	−0.754905
$898$	59.9059	1.99909
$899$	−7.78852	−0.259762
$900$	50.9693	1.69898
$901$	−3.28964	−0.109594
$902$	26.3733	0.878136
$903$	20.2137	0.672671
$904$	30.2035	1.00455
$905$	−29.0965	−0.967201
$906$	−11.6475	−0.386964
$907$	−34.1071	−1.13251	−0.566254	−	0.824231i	$-0.691608\pi$
$907$	−34.1071	−1.13251	−0.566254	+	0.824231i	$0.691608\pi$
$908$	−30.9826	−1.02819
$909$	−10.2656	−0.340490
$910$	−100.010	−3.31530
$911$	9.45811	0.313361	0.156681	−	0.987649i	$-0.449921\pi$
$911$	9.45811	0.313361	0.156681	+	0.987649i	$0.449921\pi$
$912$	−36.4547	−1.20713
$913$	−14.2207	−0.470635
$914$	99.8805	3.30375
$915$	−4.00721	−0.132474
$916$	−5.70485	−0.188494
$917$	28.9359	0.955546
$918$	0.873272	0.0288223
$919$	21.9708	0.724750	0.362375	−	0.932032i	$-0.381966\pi$
$919$	21.9708	0.724750	0.362375	+	0.932032i	$0.381966\pi$
$920$	−127.890	−4.21642
$921$	−0.203717	−0.00671272
$922$	6.23557	0.205357
$923$	−54.6075	−1.79743
$924$	9.41571	0.309754
$925$	−23.3544	−0.767887
$926$	95.9867	3.15432
$927$	10.8307	0.355727
$928$	−30.9423	−1.01573
$929$	−0.381863	−0.0125285	−0.00626425	−	0.999980i	$-0.501994\pi$
$929$	−0.381863	−0.0125285	−0.00626425	+	0.999980i	$0.501994\pi$
$930$	−18.7255	−0.614033
$931$	−12.8390	−0.420782
$932$	59.5987	1.95222
$933$	15.4938	0.507245
$934$	−19.4332	−0.635873
$935$	1.36117	0.0445149
$936$	−31.8807	−1.04205
$937$	−45.5441	−1.48786	−0.743931	−	0.668256i	$-0.767041\pi$
$937$	−45.5441	−1.48786	−0.743931	+	0.668256i	$0.767041\pi$
$938$	27.8850	0.910477
$939$	27.2007	0.887661
$940$	−96.5007	−3.14750
$941$	−24.7833	−0.807911	−0.403956	−	0.914779i	$-0.632365\pi$
$941$	−24.7833	−0.807911	−0.403956	+	0.914779i	$0.632365\pi$
$942$	26.9255	0.877279
$943$	48.8049	1.58931
$944$	−16.4308	−0.534777
$945$	−8.18565	−0.266279
$946$	25.4399	0.827124
$947$	3.66692	0.119159	0.0595794	−	0.998224i	$-0.481024\pi$
$947$	3.66692	0.119159	0.0595794	+	0.998224i	$0.481024\pi$
$948$	−25.3179	−0.822288
$949$	21.4505	0.696314
$950$	129.096	4.18844
$951$	11.9050	0.386047
$952$	−4.65476	−0.150862
$953$	−55.9404	−1.81209	−0.906044	−	0.423184i	$-0.860912\pi$
$953$	−55.9404	−1.81209	−0.906044	+	0.423184i	$0.860912\pi$
$954$	24.8977	0.806094
$955$	12.1968	0.394679
$956$	−85.4845	−2.76477
$957$	−4.28494	−0.138512
$958$	−91.9380	−2.97038
$959$	24.1678	0.780419
$960$	−10.0562	−0.324563
$961$	−27.6961	−0.893424
$962$	25.8043	0.831965
$963$	−10.3745	−0.334314
$964$	−128.111	−4.12618
$965$	27.4751	0.884454
$966$	24.9844	0.803861
$967$	40.3407	1.29727	0.648634	−	0.761100i	$-0.275341\pi$
$967$	40.3407	1.29727	0.648634	+	0.761100i	$0.275341\pi$
$968$	6.70837	0.215615
$969$	1.54254	0.0495535
$970$	140.112	4.49873
$971$	23.6883	0.760193	0.380096	−	0.924947i	$-0.375891\pi$
$971$	23.6883	0.760193	0.380096	+	0.924947i	$0.375891\pi$
$972$	−4.60938	−0.147846
$973$	43.8476	1.40569
$974$	−16.4338	−0.526574
$975$	52.5505	1.68296
$976$	8.02760	0.256957
$977$	10.2404	0.327620	0.163810	−	0.986492i	$-0.447622\pi$
$977$	10.2404	0.327620	0.163810	+	0.986492i	$0.447622\pi$
$978$	−30.8906	−0.987773
$979$	6.05470	0.193509
$980$	−52.2215	−1.66816
$981$	−15.9251	−0.508448
$982$	43.1632	1.37739
$983$	−26.3822	−0.841461	−0.420730	−	0.907186i	$-0.638226\pi$
$983$	−26.3822	−0.841461	−0.420730	+	0.907186i	$0.638226\pi$
$984$	68.8180	2.19384
$985$	−48.6376	−1.54972
$986$	3.74191	0.119167
$987$	10.6723	0.339702
$988$	−99.4763	−3.16476
$989$	47.0776	1.49698
$990$	−10.3020	−0.327420
$991$	35.8606	1.13915	0.569575	−	0.821939i	$-0.307108\pi$
$991$	35.8606	1.13915	0.569575	+	0.821939i	$0.307108\pi$
$992$	13.1256	0.416738
$993$	5.44265	0.172717
$994$	60.3439	1.91399
$995$	−55.3197	−1.75375
$996$	−65.5483	−2.07698
$997$	7.80670	0.247241	0.123620	−	0.992330i	$-0.460550\pi$
$997$	7.80670	0.247241	0.123620	+	0.992330i	$0.460550\pi$
$998$	6.15707	0.194899
$999$	2.11204	0.0668220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.14	✓	14
3.2	odd	2		6039.2.a.j.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.14	✓	14	1.1	even	1	trivial
6039.2.a.j.1.1		14	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)

\(f(q)\)	\(=\)	\(q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +10.3020 q^{10} -1.00000 q^{11} -4.60938 q^{12} -4.75237 q^{13} +5.25159 q^{14} -4.00721 q^{15} +8.02760 q^{16} -0.339679 q^{17} +2.57087 q^{18} +4.54116 q^{19} +18.4707 q^{20} -2.04273 q^{21} -2.57087 q^{22} -4.75749 q^{23} -6.70837 q^{24} +11.0577 q^{25} -12.2177 q^{26} -1.00000 q^{27} +9.41571 q^{28} -4.28494 q^{29} -10.3020 q^{30} +1.81765 q^{31} +7.22118 q^{32} +1.00000 q^{33} -0.873272 q^{34} +8.18565 q^{35} +4.60938 q^{36} -2.11204 q^{37} +11.6747 q^{38} +4.75237 q^{39} +26.8819 q^{40} -10.2585 q^{41} -5.25159 q^{42} -9.89546 q^{43} -4.60938 q^{44} +4.00721 q^{45} -12.2309 q^{46} -5.22451 q^{47} -8.02760 q^{48} -2.82726 q^{49} +28.4280 q^{50} +0.339679 q^{51} -21.9055 q^{52} +9.68455 q^{53} -2.57087 q^{54} -4.00721 q^{55} +13.7034 q^{56} -4.54116 q^{57} -11.0160 q^{58} -2.04679 q^{59} -18.4707 q^{60} +1.00000 q^{61} +4.67295 q^{62} +2.04273 q^{63} +2.50953 q^{64} -19.0437 q^{65} +2.57087 q^{66} +5.30981 q^{67} -1.56571 q^{68} +4.75749 q^{69} +21.0442 q^{70} +11.4906 q^{71} +6.70837 q^{72} -4.51365 q^{73} -5.42978 q^{74} -11.0577 q^{75} +20.9319 q^{76} -2.04273 q^{77} +12.2177 q^{78} +5.49270 q^{79} +32.1683 q^{80} +1.00000 q^{81} -26.3733 q^{82} +14.2207 q^{83} -9.41571 q^{84} -1.36117 q^{85} -25.4399 q^{86} +4.28494 q^{87} -6.70837 q^{88} -6.05470 q^{89} +10.3020 q^{90} -9.70780 q^{91} -21.9291 q^{92} -1.81765 q^{93} -13.4315 q^{94} +18.1974 q^{95} -7.22118 q^{96} +13.6004 q^{97} -7.26851 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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