LMFDB - Embedded newform 2013.2.a.h.1.11

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			1.11
Root			$-1.69494$ 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)

$f(q)$	$=$	$q+1.69494 q^{2} -1.00000 q^{3} +0.872835 q^{4} +1.13650 q^{5} -1.69494 q^{6} +4.14659 q^{7} -1.91048 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.69494 q^{2} -1.00000 q^{3} +0.872835 q^{4} +1.13650 q^{5} -1.69494 q^{6} +4.14659 q^{7} -1.91048 q^{8} +1.00000 q^{9} +1.92630 q^{10} -1.00000 q^{11} -0.872835 q^{12} +2.80864 q^{13} +7.02824 q^{14} -1.13650 q^{15} -4.98383 q^{16} -0.763911 q^{17} +1.69494 q^{18} +3.34950 q^{19} +0.991974 q^{20} -4.14659 q^{21} -1.69494 q^{22} +3.86313 q^{23} +1.91048 q^{24} -3.70838 q^{25} +4.76049 q^{26} -1.00000 q^{27} +3.61929 q^{28} +2.17513 q^{29} -1.92630 q^{30} +6.15568 q^{31} -4.62635 q^{32} +1.00000 q^{33} -1.29479 q^{34} +4.71258 q^{35} +0.872835 q^{36} +3.38312 q^{37} +5.67721 q^{38} -2.80864 q^{39} -2.17125 q^{40} +1.67214 q^{41} -7.02824 q^{42} +5.23257 q^{43} -0.872835 q^{44} +1.13650 q^{45} +6.54779 q^{46} -12.4466 q^{47} +4.98383 q^{48} +10.1942 q^{49} -6.28549 q^{50} +0.763911 q^{51} +2.45148 q^{52} +4.85562 q^{53} -1.69494 q^{54} -1.13650 q^{55} -7.92198 q^{56} -3.34950 q^{57} +3.68672 q^{58} -11.2371 q^{59} -0.991974 q^{60} +1.00000 q^{61} +10.4335 q^{62} +4.14659 q^{63} +2.12626 q^{64} +3.19201 q^{65} +1.69494 q^{66} +3.11299 q^{67} -0.666769 q^{68} -3.86313 q^{69} +7.98757 q^{70} -0.313422 q^{71} -1.91048 q^{72} +4.11415 q^{73} +5.73420 q^{74} +3.70838 q^{75} +2.92356 q^{76} -4.14659 q^{77} -4.76049 q^{78} +0.122521 q^{79} -5.66410 q^{80} +1.00000 q^{81} +2.83418 q^{82} -2.98302 q^{83} -3.61929 q^{84} -0.868182 q^{85} +8.86891 q^{86} -2.17513 q^{87} +1.91048 q^{88} +12.3890 q^{89} +1.92630 q^{90} +11.6463 q^{91} +3.37187 q^{92} -6.15568 q^{93} -21.0963 q^{94} +3.80669 q^{95} +4.62635 q^{96} +0.287224 q^{97} +17.2786 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.69494	1.19851	0.599253	−	0.800560i	$-0.295464\pi$
$2$	1.69494	1.19851	0.599253	+	0.800560i	$0.295464\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.872835	0.436418
$5$	1.13650	0.508256	0.254128	−	0.967171i	$-0.418211\pi$
$5$	1.13650	0.508256	0.254128	+	0.967171i	$0.418211\pi$
$6$	−1.69494	−0.691958
$7$	4.14659	1.56726	0.783632	−	0.621225i	$-0.213365\pi$
$7$	4.14659	1.56726	0.783632	+	0.621225i	$0.213365\pi$
$8$	−1.91048	−0.675457
$9$	1.00000	0.333333
$10$	1.92630	0.609149
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.872835	−0.251966
$13$	2.80864	0.778977	0.389488	−	0.921031i	$-0.372652\pi$
$13$	2.80864	0.778977	0.389488	+	0.921031i	$0.372652\pi$
$14$	7.02824	1.87838
$15$	−1.13650	−0.293442
$16$	−4.98383	−1.24596
$17$	−0.763911	−0.185276	−0.0926379	−	0.995700i	$-0.529530\pi$
$17$	−0.763911	−0.185276	−0.0926379	+	0.995700i	$0.529530\pi$
$18$	1.69494	0.399502
$19$	3.34950	0.768428	0.384214	−	0.923244i	$-0.374473\pi$
$19$	3.34950	0.768428	0.384214	+	0.923244i	$0.374473\pi$
$20$	0.991974	0.221812
$21$	−4.14659	−0.904860
$22$	−1.69494	−0.361363
$23$	3.86313	0.805518	0.402759	−	0.915306i	$-0.368051\pi$
$23$	3.86313	0.805518	0.402759	+	0.915306i	$0.368051\pi$
$24$	1.91048	0.389975
$25$	−3.70838	−0.741675
$26$	4.76049	0.933609
$27$	−1.00000	−0.192450
$28$	3.61929	0.683982
$29$	2.17513	0.403911	0.201955	−	0.979395i	$-0.435270\pi$
$29$	2.17513	0.403911	0.201955	+	0.979395i	$0.435270\pi$
$30$	−1.92630	−0.351692
$31$	6.15568	1.10559	0.552796	−	0.833317i	$-0.313561\pi$
$31$	6.15568	1.10559	0.552796	+	0.833317i	$0.313561\pi$
$32$	−4.62635	−0.817831
$33$	1.00000	0.174078
$34$	−1.29479	−0.222054
$35$	4.71258	0.796572
$36$	0.872835	0.145473
$37$	3.38312	0.556181	0.278091	−	0.960555i	$-0.410298\pi$
$37$	3.38312	0.556181	0.278091	+	0.960555i	$0.410298\pi$
$38$	5.67721	0.920965
$39$	−2.80864	−0.449743
$40$	−2.17125	−0.343305
$41$	1.67214	0.261144	0.130572	−	0.991439i	$-0.458319\pi$
$41$	1.67214	0.261144	0.130572	+	0.991439i	$0.458319\pi$
$42$	−7.02824	−1.08448
$43$	5.23257	0.797959	0.398980	−	0.916960i	$-0.369364\pi$
$43$	5.23257	0.797959	0.398980	+	0.916960i	$0.369364\pi$
$44$	−0.872835	−0.131585
$45$	1.13650	0.169419
$46$	6.54779	0.965419
$47$	−12.4466	−1.81553	−0.907764	−	0.419481i	$-0.862212\pi$
$47$	−12.4466	−1.81553	−0.907764	+	0.419481i	$0.862212\pi$
$48$	4.98383	0.719354
$49$	10.1942	1.45632
$50$	−6.28549	−0.888903
$51$	0.763911	0.106969
$52$	2.45148	0.339959
$53$	4.85562	0.666971	0.333485	−	0.942755i	$-0.391775\pi$
$53$	4.85562	0.666971	0.333485	+	0.942755i	$0.391775\pi$
$54$	−1.69494	−0.230653
$55$	−1.13650	−0.153245
$56$	−7.92198	−1.05862
$57$	−3.34950	−0.443652
$58$	3.68672	0.484090
$59$	−11.2371	−1.46295	−0.731473	−	0.681871i	$-0.761167\pi$
$59$	−11.2371	−1.46295	−0.731473	+	0.681871i	$0.761167\pi$
$60$	−0.991974	−0.128063
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	10.4335	1.32506
$63$	4.14659	0.522421
$64$	2.12626	0.265782
$65$	3.19201	0.395920
$66$	1.69494	0.208633
$67$	3.11299	0.380313	0.190156	−	0.981754i	$-0.439101\pi$
$67$	3.11299	0.380313	0.190156	+	0.981754i	$0.439101\pi$
$68$	−0.666769	−0.0808576
$69$	−3.86313	−0.465066
$70$	7.98757	0.954697
$71$	−0.313422	−0.0371964	−0.0185982	−	0.999827i	$-0.505920\pi$
$71$	−0.313422	−0.0371964	−0.0185982	+	0.999827i	$0.505920\pi$
$72$	−1.91048	−0.225152
$73$	4.11415	0.481525	0.240762	−	0.970584i	$-0.422603\pi$
$73$	4.11415	0.481525	0.240762	+	0.970584i	$0.422603\pi$
$74$	5.73420	0.666587
$75$	3.70838	0.428206
$76$	2.92356	0.335355
$77$	−4.14659	−0.472548
$78$	−4.76049	−0.539019
$79$	0.122521	0.0137846	0.00689232	−	0.999976i	$-0.497806\pi$
$79$	0.122521	0.0137846	0.00689232	+	0.999976i	$0.497806\pi$
$80$	−5.66410	−0.633266
$81$	1.00000	0.111111
$82$	2.83418	0.312983
$83$	−2.98302	−0.327430	−0.163715	−	0.986508i	$-0.552348\pi$
$83$	−2.98302	−0.327430	−0.163715	+	0.986508i	$0.552348\pi$
$84$	−3.61929	−0.394897
$85$	−0.868182	−0.0941676
$86$	8.86891	0.956359
$87$	−2.17513	−0.233198
$88$	1.91048	0.203658
$89$	12.3890	1.31323	0.656617	−	0.754224i	$-0.271987\pi$
$89$	12.3890	1.31323	0.656617	+	0.754224i	$0.271987\pi$
$90$	1.92630	0.203050
$91$	11.6463	1.22086
$92$	3.37187	0.351542
$93$	−6.15568	−0.638314
$94$	−21.0963	−2.17592
$95$	3.80669	0.390558
$96$	4.62635	0.472175
$97$	0.287224	0.0291632	0.0145816	−	0.999894i	$-0.495358\pi$
$97$	0.287224	0.0291632	0.0145816	+	0.999894i	$0.495358\pi$
$98$	17.2786	1.74540
$99$	−1.00000	−0.100504
$100$	−3.23680	−0.323680
$101$	8.25985	0.821886	0.410943	−	0.911661i	$-0.365200\pi$
$101$	8.25985	0.821886	0.410943	+	0.911661i	$0.365200\pi$
$102$	1.29479	0.128203
$103$	11.1319	1.09686	0.548428	−	0.836198i	$-0.315226\pi$
$103$	11.1319	1.09686	0.548428	+	0.836198i	$0.315226\pi$
$104$	−5.36586	−0.526165
$105$	−4.71258	−0.459901
$106$	8.23000	0.799368
$107$	20.5662	1.98821	0.994104	−	0.108435i	$-0.0345838\pi$
$107$	20.5662	1.98821	0.994104	+	0.108435i	$0.0345838\pi$
$108$	−0.872835	−0.0839886
$109$	−2.42639	−0.232406	−0.116203	−	0.993225i	$-0.537072\pi$
$109$	−2.42639	−0.232406	−0.116203	+	0.993225i	$0.537072\pi$
$110$	−1.92630	−0.183665
$111$	−3.38312	−0.321111
$112$	−20.6659	−1.95274
$113$	−0.194417	−0.0182892	−0.00914462	−	0.999958i	$-0.502911\pi$
$113$	−0.194417	−0.0182892	−0.00914462	+	0.999958i	$0.502911\pi$
$114$	−5.67721	−0.531720
$115$	4.39043	0.409410
$116$	1.89853	0.176274
$117$	2.80864	0.259659
$118$	−19.0462	−1.75335
$119$	−3.16763	−0.290376
$120$	2.17125	0.198208
$121$	1.00000	0.0909091
$122$	1.69494	0.153453
$123$	−1.67214	−0.150771
$124$	5.37289	0.482500
$125$	−9.89704	−0.885218
$126$	7.02824	0.626125
$127$	−1.09170	−0.0968730	−0.0484365	−	0.998826i	$-0.515424\pi$
$127$	−1.09170	−0.0968730	−0.0484365	+	0.998826i	$0.515424\pi$
$128$	12.8566	1.13637
$129$	−5.23257	−0.460702
$130$	5.41028	0.474513
$131$	−8.56374	−0.748217	−0.374109	−	0.927385i	$-0.622051\pi$
$131$	−8.56374	−0.748217	−0.374109	+	0.927385i	$0.622051\pi$
$132$	0.872835	0.0759706
$133$	13.8890	1.20433
$134$	5.27635	0.455807
$135$	−1.13650	−0.0978140
$136$	1.45944	0.125146
$137$	−15.2173	−1.30010	−0.650049	−	0.759892i	$-0.725252\pi$
$137$	−15.2173	−1.30010	−0.650049	+	0.759892i	$0.725252\pi$
$138$	−6.54779	−0.557385
$139$	−7.34342	−0.622861	−0.311430	−	0.950269i	$-0.600808\pi$
$139$	−7.34342	−0.622861	−0.311430	+	0.950269i	$0.600808\pi$
$140$	4.11331	0.347638
$141$	12.4466	1.04820
$142$	−0.531233	−0.0445801
$143$	−2.80864	−0.234870
$144$	−4.98383	−0.415319
$145$	2.47202	0.205290
$146$	6.97325	0.577111
$147$	−10.1942	−0.840805
$148$	2.95291	0.242727
$149$	8.97409	0.735186	0.367593	−	0.929987i	$-0.380182\pi$
$149$	8.97409	0.735186	0.367593	+	0.929987i	$0.380182\pi$
$150$	6.28549	0.513208
$151$	5.70128	0.463963	0.231982	−	0.972720i	$-0.425479\pi$
$151$	5.70128	0.463963	0.231982	+	0.972720i	$0.425479\pi$
$152$	−6.39915	−0.519040
$153$	−0.763911	−0.0617586
$154$	−7.02824	−0.566352
$155$	6.99590	0.561924
$156$	−2.45148	−0.196276
$157$	−0.592821	−0.0473123	−0.0236561	−	0.999720i	$-0.507531\pi$
$157$	−0.592821	−0.0473123	−0.0236561	+	0.999720i	$0.507531\pi$
$158$	0.207665	0.0165210
$159$	−4.85562	−0.385076
$160$	−5.25783	−0.415668
$161$	16.0188	1.26246
$162$	1.69494	0.133167
$163$	−20.0035	−1.56680	−0.783398	−	0.621521i	$-0.786515\pi$
$163$	−20.0035	−1.56680	−0.783398	+	0.621521i	$0.786515\pi$
$164$	1.45950	0.113968
$165$	1.13650	0.0884761
$166$	−5.05606	−0.392426
$167$	1.97988	0.153208	0.0766038	−	0.997062i	$-0.475592\pi$
$167$	1.97988	0.153208	0.0766038	+	0.997062i	$0.475592\pi$
$168$	7.92198	0.611194
$169$	−5.11154	−0.393195
$170$	−1.47152	−0.112860
$171$	3.34950	0.256143
$172$	4.56717	0.348244
$173$	−5.75321	−0.437408	−0.218704	−	0.975791i	$-0.570183\pi$
$173$	−5.75321	−0.437408	−0.218704	+	0.975791i	$0.570183\pi$
$174$	−3.68672	−0.279489
$175$	−15.3771	−1.16240
$176$	4.98383	0.375670
$177$	11.2371	0.844632
$178$	20.9987	1.57392
$179$	−21.2013	−1.58466	−0.792329	−	0.610095i	$-0.791131\pi$
$179$	−21.2013	−1.58466	−0.792329	+	0.610095i	$0.791131\pi$
$180$	0.991974	0.0739374
$181$	−18.2793	−1.35869	−0.679345	−	0.733819i	$-0.737736\pi$
$181$	−18.2793	−1.35869	−0.679345	+	0.733819i	$0.737736\pi$
$182$	19.7398	1.46321
$183$	−1.00000	−0.0739221
$184$	−7.38044	−0.544093
$185$	3.84490	0.282683
$186$	−10.4335	−0.765023
$187$	0.763911	0.0558627
$188$	−10.8639	−0.792328
$189$	−4.14659	−0.301620
$190$	6.45213	0.468087
$191$	−6.81813	−0.493342	−0.246671	−	0.969099i	$-0.579337\pi$
$191$	−6.81813	−0.493342	−0.246671	+	0.969099i	$0.579337\pi$
$192$	−2.12626	−0.153449
$193$	−25.6061	−1.84317	−0.921583	−	0.388181i	$-0.873104\pi$
$193$	−25.6061	−1.84317	−0.921583	+	0.388181i	$0.873104\pi$
$194$	0.486828	0.0349522
$195$	−3.19201	−0.228585
$196$	8.89787	0.635562
$197$	−4.60372	−0.328002	−0.164001	−	0.986460i	$-0.552440\pi$
$197$	−4.60372	−0.328002	−0.164001	+	0.986460i	$0.552440\pi$
$198$	−1.69494	−0.120454
$199$	−10.2809	−0.728796	−0.364398	−	0.931243i	$-0.618725\pi$
$199$	−10.2809	−0.728796	−0.364398	+	0.931243i	$0.618725\pi$
$200$	7.08478	0.500970
$201$	−3.11299	−0.219574
$202$	14.0000	0.985035
$203$	9.01936	0.633035
$204$	0.666769	0.0466831
$205$	1.90038	0.132728
$206$	18.8679	1.31459
$207$	3.86313	0.268506
$208$	−13.9978	−0.970572
$209$	−3.34950	−0.231690
$210$	−7.98757	−0.551194
$211$	19.2901	1.32798	0.663991	−	0.747740i	$-0.268861\pi$
$211$	19.2901	1.32798	0.663991	+	0.747740i	$0.268861\pi$
$212$	4.23816	0.291078
$213$	0.313422	0.0214753
$214$	34.8585	2.38288
$215$	5.94680	0.405568
$216$	1.91048	0.129992
$217$	25.5251	1.73275
$218$	−4.11259	−0.278540
$219$	−4.11415	−0.278009
$220$	−0.991974	−0.0668789
$221$	−2.14555	−0.144325
$222$	−5.73420	−0.384854
$223$	21.7966	1.45961	0.729803	−	0.683657i	$-0.239612\pi$
$223$	21.7966	1.45961	0.729803	+	0.683657i	$0.239612\pi$
$224$	−19.1836	−1.28176
$225$	−3.70838	−0.247225
$226$	−0.329526	−0.0219198
$227$	−19.0029	−1.26127	−0.630633	−	0.776081i	$-0.717205\pi$
$227$	−19.0029	−1.26127	−0.630633	+	0.776081i	$0.717205\pi$
$228$	−2.92356	−0.193617
$229$	−28.4656	−1.88106	−0.940529	−	0.339713i	$-0.889670\pi$
$229$	−28.4656	−1.88106	−0.940529	+	0.339713i	$0.889670\pi$
$230$	7.44153	0.490680
$231$	4.14659	0.272826
$232$	−4.15554	−0.272824
$233$	−7.38981	−0.484123	−0.242061	−	0.970261i	$-0.577824\pi$
$233$	−7.38981	−0.484123	−0.242061	+	0.970261i	$0.577824\pi$
$234$	4.76049	0.311203
$235$	−14.1456	−0.922754
$236$	−9.80813	−0.638455
$237$	−0.122521	−0.00795856
$238$	−5.36895	−0.348017
$239$	10.8094	0.699205	0.349602	−	0.936898i	$-0.386317\pi$
$239$	10.8094	0.699205	0.349602	+	0.936898i	$0.386317\pi$
$240$	5.66410	0.365616
$241$	−26.6577	−1.71718	−0.858588	−	0.512666i	$-0.828658\pi$
$241$	−26.6577	−1.71718	−0.858588	+	0.512666i	$0.828658\pi$
$242$	1.69494	0.108955
$243$	−1.00000	−0.0641500
$244$	0.872835	0.0558775
$245$	11.5857	0.740182
$246$	−2.83418	−0.180701
$247$	9.40754	0.598587
$248$	−11.7603	−0.746780
$249$	2.98302	0.189042
$250$	−16.7749	−1.06094
$251$	12.8841	0.813236	0.406618	−	0.913598i	$-0.366708\pi$
$251$	12.8841	0.813236	0.406618	+	0.913598i	$0.366708\pi$
$252$	3.61929	0.227994
$253$	−3.86313	−0.242873
$254$	−1.85038	−0.116103
$255$	0.868182	0.0543677
$256$	17.5387	1.09617
$257$	−26.0777	−1.62668	−0.813341	−	0.581788i	$-0.802353\pi$
$257$	−26.0777	−1.62668	−0.813341	+	0.581788i	$0.802353\pi$
$258$	−8.86891	−0.552154
$259$	14.0284	0.871683
$260$	2.78610	0.172786
$261$	2.17513	0.134637
$262$	−14.5151	−0.896743
$263$	−21.6443	−1.33464	−0.667322	−	0.744769i	$-0.732559\pi$
$263$	−21.6443	−1.33464	−0.667322	+	0.744769i	$0.732559\pi$
$264$	−1.91048	−0.117582
$265$	5.51839	0.338992
$266$	23.5411	1.44340
$267$	−12.3890	−0.758196
$268$	2.71713	0.165975
$269$	−1.70348	−0.103863	−0.0519315	−	0.998651i	$-0.516538\pi$
$269$	−1.70348	−0.103863	−0.0519315	+	0.998651i	$0.516538\pi$
$270$	−1.92630	−0.117231
$271$	21.2091	1.28836	0.644180	−	0.764874i	$-0.277199\pi$
$271$	21.2091	1.28836	0.644180	+	0.764874i	$0.277199\pi$
$272$	3.80720	0.230846
$273$	−11.6463	−0.704865
$274$	−25.7924	−1.55818
$275$	3.70838	0.223624
$276$	−3.37187	−0.202963
$277$	−4.64693	−0.279207	−0.139603	−	0.990207i	$-0.544583\pi$
$277$	−4.64693	−0.279207	−0.139603	+	0.990207i	$0.544583\pi$
$278$	−12.4467	−0.746503
$279$	6.15568	0.368531
$280$	−9.00330	−0.538050
$281$	−3.70914	−0.221269	−0.110634	−	0.993861i	$-0.535288\pi$
$281$	−3.70914	−0.221269	−0.110634	+	0.993861i	$0.535288\pi$
$282$	21.0963	1.25627
$283$	1.52229	0.0904910	0.0452455	−	0.998976i	$-0.485593\pi$
$283$	1.52229	0.0904910	0.0452455	+	0.998976i	$0.485593\pi$
$284$	−0.273566	−0.0162331
$285$	−3.80669	−0.225489
$286$	−4.76049	−0.281494
$287$	6.93367	0.409281
$288$	−4.62635	−0.272610
$289$	−16.4164	−0.965673
$290$	4.18994	0.246042
$291$	−0.287224	−0.0168374
$292$	3.59098	0.210146
$293$	−25.9504	−1.51604	−0.758018	−	0.652234i	$-0.773832\pi$
$293$	−25.9504	−1.51604	−0.758018	+	0.652234i	$0.773832\pi$
$294$	−17.2786	−1.00771
$295$	−12.7709	−0.743551
$296$	−6.46339	−0.375677
$297$	1.00000	0.0580259
$298$	15.2106	0.881125
$299$	10.8501	0.627480
$300$	3.23680	0.186877
$301$	21.6973	1.25061
$302$	9.66335	0.556063
$303$	−8.25985	−0.474516
$304$	−16.6933	−0.957428
$305$	1.13650	0.0650756
$306$	−1.29479	−0.0740180
$307$	12.7503	0.727700	0.363850	−	0.931458i	$-0.381462\pi$
$307$	12.7503	0.727700	0.363850	+	0.931458i	$0.381462\pi$
$308$	−3.61929	−0.206228
$309$	−11.1319	−0.633271
$310$	11.8577	0.673470
$311$	2.42241	0.137362	0.0686812	−	0.997639i	$-0.478121\pi$
$311$	2.42241	0.137362	0.0686812	+	0.997639i	$0.478121\pi$
$312$	5.36586	0.303782
$313$	1.39019	0.0785779	0.0392890	−	0.999228i	$-0.487491\pi$
$313$	1.39019	0.0785779	0.0392890	+	0.999228i	$0.487491\pi$
$314$	−1.00480	−0.0567040
$315$	4.71258	0.265524
$316$	0.106940	0.00601586
$317$	4.56623	0.256465	0.128233	−	0.991744i	$-0.459070\pi$
$317$	4.56623	0.256465	0.128233	+	0.991744i	$0.459070\pi$
$318$	−8.23000	−0.461516
$319$	−2.17513	−0.121784
$320$	2.41648	0.135085
$321$	−20.5662	−1.14789
$322$	27.1510	1.51307
$323$	−2.55872	−0.142371
$324$	0.872835	0.0484908
$325$	−10.4155	−0.577748
$326$	−33.9048	−1.87781
$327$	2.42639	0.134180
$328$	−3.19459	−0.176391
$329$	−51.6111	−2.84541
$330$	1.92630	0.106039
$331$	8.68359	0.477293	0.238647	−	0.971106i	$-0.423296\pi$
$331$	8.68359	0.477293	0.238647	+	0.971106i	$0.423296\pi$
$332$	−2.60369	−0.142896
$333$	3.38312	0.185394
$334$	3.35579	0.183620
$335$	3.53790	0.193296
$336$	20.6659	1.12742
$337$	−19.3769	−1.05553	−0.527764	−	0.849391i	$-0.676969\pi$
$337$	−19.3769	−1.05553	−0.527764	+	0.849391i	$0.676969\pi$
$338$	−8.66377	−0.471247
$339$	0.194417	0.0105593
$340$	−0.757780	−0.0410964
$341$	−6.15568	−0.333349
$342$	5.67721	0.306988
$343$	13.2451	0.715168
$344$	−9.99673	−0.538987
$345$	−4.39043	−0.236373
$346$	−9.75137	−0.524237
$347$	12.5548	0.673978	0.336989	−	0.941509i	$-0.390591\pi$
$347$	12.5548	0.673978	0.336989	+	0.941509i	$0.390591\pi$
$348$	−1.89853	−0.101772
$349$	23.5352	1.25981	0.629907	−	0.776671i	$-0.283093\pi$
$349$	23.5352	1.25981	0.629907	+	0.776671i	$0.283093\pi$
$350$	−26.0634	−1.39315
$351$	−2.80864	−0.149914
$352$	4.62635	0.246585
$353$	−29.5091	−1.57061	−0.785306	−	0.619108i	$-0.787494\pi$
$353$	−29.5091	−1.57061	−0.785306	+	0.619108i	$0.787494\pi$
$354$	19.0462	1.01230
$355$	−0.356203	−0.0189053
$356$	10.8136	0.573118
$357$	3.16763	0.167649
$358$	−35.9350	−1.89922
$359$	−5.82428	−0.307394	−0.153697	−	0.988118i	$-0.549118\pi$
$359$	−5.82428	−0.307394	−0.153697	+	0.988118i	$0.549118\pi$
$360$	−2.17125	−0.114435
$361$	−7.78086	−0.409519
$362$	−30.9824	−1.62840
$363$	−1.00000	−0.0524864
$364$	10.1653	0.532806
$365$	4.67572	0.244738
$366$	−1.69494	−0.0885961
$367$	32.4023	1.69139	0.845693	−	0.533670i	$-0.179188\pi$
$367$	32.4023	1.69139	0.845693	+	0.533670i	$0.179188\pi$
$368$	−19.2532	−1.00364
$369$	1.67214	0.0870479
$370$	6.51689	0.338797
$371$	20.1343	1.04532
$372$	−5.37289	−0.278571
$373$	4.55651	0.235927	0.117964	−	0.993018i	$-0.462363\pi$
$373$	4.55651	0.235927	0.117964	+	0.993018i	$0.462363\pi$
$374$	1.29479	0.0669518
$375$	9.89704	0.511081
$376$	23.7791	1.22631
$377$	6.10915	0.314637
$378$	−7.02824	−0.361494
$379$	−26.0481	−1.33800	−0.669001	−	0.743262i	$-0.733278\pi$
$379$	−26.0481	−1.33800	−0.669001	+	0.743262i	$0.733278\pi$
$380$	3.32261	0.170447
$381$	1.09170	0.0559297
$382$	−11.5563	−0.591274
$383$	9.19798	0.469995	0.234997	−	0.971996i	$-0.424492\pi$
$383$	9.19798	0.469995	0.234997	+	0.971996i	$0.424492\pi$
$384$	−12.8566	−0.656085
$385$	−4.71258	−0.240176
$386$	−43.4009	−2.20905
$387$	5.23257	0.265986
$388$	0.250699	0.0127273
$389$	4.77997	0.242354	0.121177	−	0.992631i	$-0.461333\pi$
$389$	4.77997	0.242354	0.121177	+	0.992631i	$0.461333\pi$
$390$	−5.41028	−0.273960
$391$	−2.95109	−0.149243
$392$	−19.4759	−0.983679
$393$	8.56374	0.431984
$394$	−7.80306	−0.393112
$395$	0.139244	0.00700613
$396$	−0.872835	−0.0438616
$397$	−0.984062	−0.0493886	−0.0246943	−	0.999695i	$-0.507861\pi$
$397$	−0.984062	−0.0493886	−0.0246943	+	0.999695i	$0.507861\pi$
$398$	−17.4256	−0.873466
$399$	−13.8890	−0.695320
$400$	18.4819	0.924096
$401$	18.2690	0.912312	0.456156	−	0.889900i	$-0.349226\pi$
$401$	18.2690	0.912312	0.456156	+	0.889900i	$0.349226\pi$
$402$	−5.27635	−0.263160
$403$	17.2891	0.861231
$404$	7.20949	0.358685
$405$	1.13650	0.0564729
$406$	15.2873	0.758696
$407$	−3.38312	−0.167695
$408$	−1.45944	−0.0722530
$409$	29.2832	1.44796	0.723981	−	0.689820i	$-0.242310\pi$
$409$	29.2832	1.44796	0.723981	+	0.689820i	$0.242310\pi$
$410$	3.22103	0.159075
$411$	15.2173	0.750612
$412$	9.71630	0.478688
$413$	−46.5956	−2.29282
$414$	6.54779	0.321806
$415$	−3.39020	−0.166418
$416$	−12.9938	−0.637071
$417$	7.34342	0.359609
$418$	−5.67721	−0.277681
$419$	−30.2004	−1.47539	−0.737694	−	0.675135i	$-0.764085\pi$
$419$	−30.2004	−1.47539	−0.737694	+	0.675135i	$0.764085\pi$
$420$	−4.11331	−0.200709
$421$	26.3462	1.28404	0.642018	−	0.766689i	$-0.278097\pi$
$421$	26.3462	1.28404	0.642018	+	0.766689i	$0.278097\pi$
$422$	32.6956	1.59160
$423$	−12.4466	−0.605176
$424$	−9.27657	−0.450510
$425$	2.83287	0.137414
$426$	0.531233	0.0257383
$427$	4.14659	0.200668
$428$	17.9509	0.867689
$429$	2.80864	0.135602
$430$	10.0795	0.486076
$431$	27.7478	1.33656	0.668282	−	0.743908i	$-0.267030\pi$
$431$	27.7478	1.33656	0.668282	+	0.743908i	$0.267030\pi$
$432$	4.98383	0.239785
$433$	−7.30026	−0.350828	−0.175414	−	0.984495i	$-0.556126\pi$
$433$	−7.30026	−0.350828	−0.175414	+	0.984495i	$0.556126\pi$
$434$	43.2636	2.07672
$435$	−2.47202	−0.118524
$436$	−2.11784	−0.101426
$437$	12.9395	0.618982
$438$	−6.97325	−0.333195
$439$	1.66481	0.0794573	0.0397286	−	0.999211i	$-0.487351\pi$
$439$	1.66481	0.0794573	0.0397286	+	0.999211i	$0.487351\pi$
$440$	2.17125	0.103510
$441$	10.1942	0.485439
$442$	−3.63659	−0.172975
$443$	−2.28757	−0.108686	−0.0543428	−	0.998522i	$-0.517306\pi$
$443$	−2.28757	−0.108686	−0.0543428	+	0.998522i	$0.517306\pi$
$444$	−2.95291	−0.140139
$445$	14.0801	0.667460
$446$	36.9440	1.74935
$447$	−8.97409	−0.424460
$448$	8.81671	0.416551
$449$	−10.2005	−0.481390	−0.240695	−	0.970601i	$-0.577375\pi$
$449$	−10.2005	−0.481390	−0.240695	+	0.970601i	$0.577375\pi$
$450$	−6.28549	−0.296301
$451$	−1.67214	−0.0787378
$452$	−0.169694	−0.00798174
$453$	−5.70128	−0.267869
$454$	−32.2088	−1.51163
$455$	13.2360	0.620511
$456$	6.39915	0.299668
$457$	−32.8187	−1.53520	−0.767598	−	0.640932i	$-0.778548\pi$
$457$	−32.8187	−1.53520	−0.767598	+	0.640932i	$0.778548\pi$
$458$	−48.2476	−2.25446
$459$	0.763911	0.0356563
$460$	3.83212	0.178674
$461$	17.3153	0.806455	0.403228	−	0.915100i	$-0.367888\pi$
$461$	17.3153	0.806455	0.403228	+	0.915100i	$0.367888\pi$
$462$	7.02824	0.326983
$463$	−28.6210	−1.33013	−0.665066	−	0.746785i	$-0.731597\pi$
$463$	−28.6210	−1.33013	−0.665066	+	0.746785i	$0.731597\pi$
$464$	−10.8405	−0.503256
$465$	−6.99590	−0.324427
$466$	−12.5253	−0.580224
$467$	−16.1513	−0.747393	−0.373696	−	0.927551i	$-0.621910\pi$
$467$	−16.1513	−0.747393	−0.373696	+	0.927551i	$0.621910\pi$
$468$	2.45148	0.113320
$469$	12.9083	0.596050
$470$	−23.9759	−1.10593
$471$	0.592821	0.0273157
$472$	21.4683	0.988157
$473$	−5.23257	−0.240594
$474$	−0.207665	−0.00953839
$475$	−12.4212	−0.569924
$476$	−2.76482	−0.126725
$477$	4.85562	0.222324
$478$	18.3214	0.838001
$479$	15.7906	0.721493	0.360747	−	0.932664i	$-0.382522\pi$
$479$	15.7906	0.721493	0.360747	+	0.932664i	$0.382522\pi$
$480$	5.25783	0.239986
$481$	9.50197	0.433252
$482$	−45.1834	−2.05805
$483$	−16.0188	−0.728881
$484$	0.872835	0.0396743
$485$	0.326429	0.0148224
$486$	−1.69494	−0.0768842
$487$	−7.39301	−0.335009	−0.167505	−	0.985871i	$-0.553571\pi$
$487$	−7.39301	−0.335009	−0.167505	+	0.985871i	$0.553571\pi$
$488$	−1.91048	−0.0864834
$489$	20.0035	0.904590
$490$	19.6371	0.887113
$491$	−23.8693	−1.07721	−0.538604	−	0.842559i	$-0.681048\pi$
$491$	−23.8693	−1.07721	−0.538604	+	0.842559i	$0.681048\pi$
$492$	−1.45950	−0.0657993
$493$	−1.66160	−0.0748349
$494$	15.9452	0.717411
$495$	−1.13650	−0.0510817
$496$	−30.6788	−1.37752
$497$	−1.29963	−0.0582965
$498$	5.05606	0.226567
$499$	25.5180	1.14234	0.571172	−	0.820830i	$-0.306489\pi$
$499$	25.5180	1.14234	0.571172	+	0.820830i	$0.306489\pi$
$500$	−8.63848	−0.386325
$501$	−1.97988	−0.0884545
$502$	21.8378	0.974669
$503$	−0.804971	−0.0358919	−0.0179459	−	0.999839i	$-0.505713\pi$
$503$	−0.804971	−0.0358919	−0.0179459	+	0.999839i	$0.505713\pi$
$504$	−7.92198	−0.352873
$505$	9.38729	0.417729
$506$	−6.54779	−0.291085
$507$	5.11154	0.227011
$508$	−0.952877	−0.0422771
$509$	33.1176	1.46791	0.733955	−	0.679198i	$-0.237672\pi$
$509$	33.1176	1.46791	0.733955	+	0.679198i	$0.237672\pi$
$510$	1.47152	0.0651600
$511$	17.0597	0.754677
$512$	4.01391	0.177391
$513$	−3.34950	−0.147884
$514$	−44.2002	−1.94959
$515$	12.6513	0.557485
$516$	−4.56717	−0.201058
$517$	12.4466	0.547402
$518$	23.7774	1.04472
$519$	5.75321	0.252538
$520$	−6.09827	−0.267427
$521$	9.15916	0.401270	0.200635	−	0.979666i	$-0.435699\pi$
$521$	9.15916	0.401270	0.200635	+	0.979666i	$0.435699\pi$
$522$	3.68672	0.161363
$523$	21.3574	0.933893	0.466947	−	0.884285i	$-0.345354\pi$
$523$	21.3574	0.933893	0.466947	+	0.884285i	$0.345354\pi$
$524$	−7.47473	−0.326535
$525$	15.3771	0.671113
$526$	−36.6858	−1.59958
$527$	−4.70239	−0.204839
$528$	−4.98383	−0.216893
$529$	−8.07623	−0.351141
$530$	9.35337	0.406284
$531$	−11.2371	−0.487648
$532$	12.1228	0.525590
$533$	4.69643	0.203425
$534$	−20.9987	−0.908703
$535$	23.3734	1.01052
$536$	−5.94732	−0.256885
$537$	21.2013	0.914902
$538$	−2.88731	−0.124481
$539$	−10.1942	−0.439096
$540$	−0.991974	−0.0426878
$541$	−24.7604	−1.06453	−0.532266	−	0.846577i	$-0.678659\pi$
$541$	−24.7604	−1.06453	−0.532266	+	0.846577i	$0.678659\pi$
$542$	35.9482	1.54411
$543$	18.2793	0.784440
$544$	3.53412	0.151524
$545$	−2.75758	−0.118122
$546$	−19.7398	−0.844785
$547$	2.04043	0.0872427	0.0436213	−	0.999048i	$-0.486110\pi$
$547$	2.04043	0.0872427	0.0436213	+	0.999048i	$0.486110\pi$
$548$	−13.2822	−0.567386
$549$	1.00000	0.0426790
$550$	6.28549	0.268014
$551$	7.28558	0.310376
$552$	7.38044	0.314132
$553$	0.508042	0.0216042
$554$	−7.87628	−0.334631
$555$	−3.84490	−0.163207
$556$	−6.40960	−0.271827
$557$	−6.92621	−0.293473	−0.146737	−	0.989176i	$-0.546877\pi$
$557$	−6.92621	−0.293473	−0.146737	+	0.989176i	$0.546877\pi$
$558$	10.4335	0.441686
$559$	14.6964	0.621592
$560$	−23.4867	−0.992495
$561$	−0.763911	−0.0322524
$562$	−6.28679	−0.265192
$563$	24.0659	1.01426	0.507128	−	0.861871i	$-0.330707\pi$
$563$	24.0659	1.01426	0.507128	+	0.861871i	$0.330707\pi$
$564$	10.8639	0.457451
$565$	−0.220954	−0.00929562
$566$	2.58020	0.108454
$567$	4.14659	0.174140
$568$	0.598787	0.0251245
$569$	−10.8199	−0.453594	−0.226797	−	0.973942i	$-0.572825\pi$
$569$	−10.8199	−0.453594	−0.226797	+	0.973942i	$0.572825\pi$
$570$	−6.45213	−0.270250
$571$	23.3189	0.975867	0.487933	−	0.872881i	$-0.337751\pi$
$571$	23.3189	0.975867	0.487933	+	0.872881i	$0.337751\pi$
$572$	−2.45148	−0.102502
$573$	6.81813	0.284831
$574$	11.7522	0.490526
$575$	−14.3259	−0.597433
$576$	2.12626	0.0885940
$577$	19.0741	0.794066	0.397033	−	0.917804i	$-0.370040\pi$
$577$	19.0741	0.794066	0.397033	+	0.917804i	$0.370040\pi$
$578$	−27.8249	−1.15737
$579$	25.6061	1.06415
$580$	2.15767	0.0895923
$581$	−12.3694	−0.513168
$582$	−0.486828	−0.0201797
$583$	−4.85562	−0.201099
$584$	−7.86001	−0.325249
$585$	3.19201	0.131973
$586$	−43.9844	−1.81698
$587$	−19.9932	−0.825206	−0.412603	−	0.910911i	$-0.635380\pi$
$587$	−19.9932	−0.825206	−0.412603	+	0.910911i	$0.635380\pi$
$588$	−8.89787	−0.366942
$589$	20.6184	0.849568
$590$	−21.6460	−0.891151
$591$	4.60372	0.189372
$592$	−16.8609	−0.692978
$593$	20.8462	0.856052	0.428026	−	0.903766i	$-0.359209\pi$
$593$	20.8462	0.856052	0.428026	+	0.903766i	$0.359209\pi$
$594$	1.69494	0.0695444
$595$	−3.60000	−0.147585
$596$	7.83290	0.320848
$597$	10.2809	0.420770
$598$	18.3904	0.752039
$599$	−35.7082	−1.45900	−0.729498	−	0.683983i	$-0.760246\pi$
$599$	−35.7082	−1.45900	−0.729498	+	0.683983i	$0.760246\pi$
$600$	−7.08478	−0.289235
$601$	−25.3646	−1.03464	−0.517322	−	0.855791i	$-0.673071\pi$
$601$	−25.3646	−1.03464	−0.517322	+	0.855791i	$0.673071\pi$
$602$	36.7758	1.49887
$603$	3.11299	0.126771
$604$	4.97628	0.202482
$605$	1.13650	0.0462051
$606$	−14.0000	−0.568710
$607$	31.9208	1.29562	0.647812	−	0.761800i	$-0.275684\pi$
$607$	31.9208	1.29562	0.647812	+	0.761800i	$0.275684\pi$
$608$	−15.4959	−0.628444
$609$	−9.01936	−0.365483
$610$	1.92630	0.0779935
$611$	−34.9581	−1.41425
$612$	−0.666769	−0.0269525
$613$	12.6456	0.510751	0.255376	−	0.966842i	$-0.417801\pi$
$613$	12.6456	0.510751	0.255376	+	0.966842i	$0.417801\pi$
$614$	21.6111	0.872153
$615$	−1.90038	−0.0766306
$616$	7.92198	0.319186
$617$	−11.8467	−0.476930	−0.238465	−	0.971151i	$-0.576644\pi$
$617$	−11.8467	−0.476930	−0.238465	+	0.971151i	$0.576644\pi$
$618$	−18.8679	−0.758979
$619$	5.81776	0.233835	0.116918	−	0.993142i	$-0.462699\pi$
$619$	5.81776	0.233835	0.116918	+	0.993142i	$0.462699\pi$
$620$	6.10627	0.245234
$621$	−3.86313	−0.155022
$622$	4.10585	0.164630
$623$	51.3722	2.05818
$624$	13.9978	0.560360
$625$	7.29394	0.291758
$626$	2.35629	0.0941762
$627$	3.34950	0.133766
$628$	−0.517435	−0.0206479
$629$	−2.58440	−0.103047
$630$	7.98757	0.318232
$631$	28.1087	1.11899	0.559495	−	0.828834i	$-0.310995\pi$
$631$	28.1087	1.11899	0.559495	+	0.828834i	$0.310995\pi$
$632$	−0.234073	−0.00931093
$633$	−19.2901	−0.766711
$634$	7.73951	0.307375
$635$	−1.24072	−0.0492363
$636$	−4.23816	−0.168054
$637$	28.6319	1.13444
$638$	−3.68672	−0.145959
$639$	−0.313422	−0.0123988
$640$	14.6115	0.577568
$641$	−17.8256	−0.704069	−0.352034	−	0.935987i	$-0.614510\pi$
$641$	−17.8256	−0.704069	−0.352034	+	0.935987i	$0.614510\pi$
$642$	−34.8585	−1.37576
$643$	−21.3216	−0.840842	−0.420421	−	0.907329i	$-0.638118\pi$
$643$	−21.3216	−0.840842	−0.420421	+	0.907329i	$0.638118\pi$
$644$	13.9818	0.550960
$645$	−5.94680	−0.234155
$646$	−4.33689	−0.170633
$647$	−37.4930	−1.47400	−0.737000	−	0.675893i	$-0.763758\pi$
$647$	−37.4930	−1.47400	−0.737000	+	0.675893i	$0.763758\pi$
$648$	−1.91048	−0.0750508
$649$	11.2371	0.441095
$650$	−17.6537	−0.692435
$651$	−25.5251	−1.00041
$652$	−17.4598	−0.683777
$653$	26.0148	1.01804	0.509018	−	0.860756i	$-0.330009\pi$
$653$	26.0148	1.01804	0.509018	+	0.860756i	$0.330009\pi$
$654$	4.11259	0.160815
$655$	−9.73266	−0.380286
$656$	−8.33364	−0.325374
$657$	4.11415	0.160508
$658$	−87.4779	−3.41024
$659$	−1.69718	−0.0661127	−0.0330564	−	0.999453i	$-0.510524\pi$
$659$	−1.69718	−0.0661127	−0.0330564	+	0.999453i	$0.510524\pi$
$660$	0.991974	0.0386125
$661$	28.7729	1.11914	0.559569	−	0.828784i	$-0.310967\pi$
$661$	28.7729	1.11914	0.559569	+	0.828784i	$0.310967\pi$
$662$	14.7182	0.572039
$663$	2.14555	0.0833264
$664$	5.69901	0.221165
$665$	15.7848	0.612108
$666$	5.73420	0.222196
$667$	8.40280	0.325358
$668$	1.72811	0.0668625
$669$	−21.7966	−0.842704
$670$	5.99655	0.231667
$671$	−1.00000	−0.0386046
$672$	19.1836	0.740022
$673$	−31.1045	−1.19899	−0.599496	−	0.800378i	$-0.704632\pi$
$673$	−31.1045	−1.19899	−0.599496	+	0.800378i	$0.704632\pi$
$674$	−32.8428	−1.26506
$675$	3.70838	0.142735
$676$	−4.46153	−0.171597
$677$	24.6673	0.948043	0.474021	−	0.880513i	$-0.342802\pi$
$677$	24.6673	0.948043	0.474021	+	0.880513i	$0.342802\pi$
$678$	0.329526	0.0126554
$679$	1.19100	0.0457064
$680$	1.65865	0.0636062
$681$	19.0029	0.728192
$682$	−10.4335	−0.399520
$683$	42.6506	1.63198	0.815990	−	0.578066i	$-0.196193\pi$
$683$	42.6506	1.63198	0.815990	+	0.578066i	$0.196193\pi$
$684$	2.92356	0.111785
$685$	−17.2944	−0.660783
$686$	22.4497	0.857133
$687$	28.4656	1.08603
$688$	−26.0782	−0.994223
$689$	13.6377	0.519555
$690$	−7.44153	−0.283294
$691$	−13.0177	−0.495218	−0.247609	−	0.968860i	$-0.579645\pi$
$691$	−13.0177	−0.495218	−0.247609	+	0.968860i	$0.579645\pi$
$692$	−5.02160	−0.190893
$693$	−4.14659	−0.157516
$694$	21.2797	0.807767
$695$	−8.34577	−0.316573
$696$	4.15554	0.157515
$697$	−1.27736	−0.0483836
$698$	39.8909	1.50989
$699$	7.38981	0.279508
$700$	−13.4217	−0.507292
$701$	28.0409	1.05909	0.529545	−	0.848282i	$-0.322362\pi$
$701$	28.0409	1.05909	0.529545	+	0.848282i	$0.322362\pi$
$702$	−4.76049	−0.179673
$703$	11.3318	0.427385
$704$	−2.12626	−0.0801363
$705$	14.1456	0.532752
$706$	−50.0163	−1.88239
$707$	34.2502	1.28811
$708$	9.80813	0.368612
$709$	−25.5510	−0.959587	−0.479794	−	0.877381i	$-0.659288\pi$
$709$	−25.5510	−0.959587	−0.479794	+	0.877381i	$0.659288\pi$
$710$	−0.603744	−0.0226581
$711$	0.122521	0.00459488
$712$	−23.6690	−0.887033
$713$	23.7802	0.890575
$714$	5.36895	0.200928
$715$	−3.19201	−0.119374
$716$	−18.5052	−0.691572
$717$	−10.8094	−0.403686
$718$	−9.87182	−0.368413
$719$	29.5599	1.10240	0.551200	−	0.834373i	$-0.314170\pi$
$719$	29.5599	1.10240	0.551200	+	0.834373i	$0.314170\pi$
$720$	−5.66410	−0.211089
$721$	46.1594	1.71906
$722$	−13.1881	−0.490811
$723$	26.6577	0.991412
$724$	−15.9548	−0.592956
$725$	−8.06619	−0.299571
$726$	−1.69494	−0.0629053
$727$	46.5039	1.72473	0.862367	−	0.506285i	$-0.168981\pi$
$727$	46.5039	1.72473	0.862367	+	0.506285i	$0.168981\pi$
$728$	−22.2500	−0.824640
$729$	1.00000	0.0370370
$730$	7.92508	0.293320
$731$	−3.99722	−0.147843
$732$	−0.872835	−0.0322609
$733$	30.3793	1.12209	0.561043	−	0.827787i	$-0.310400\pi$
$733$	30.3793	1.12209	0.561043	+	0.827787i	$0.310400\pi$
$734$	54.9201	2.02714
$735$	−11.5857	−0.427344
$736$	−17.8722	−0.658777
$737$	−3.11299	−0.114669
$738$	2.83418	0.104328
$739$	24.5413	0.902765	0.451382	−	0.892331i	$-0.350931\pi$
$739$	24.5413	0.902765	0.451382	+	0.892331i	$0.350931\pi$
$740$	3.35597	0.123368
$741$	−9.40754	−0.345595
$742$	34.1264	1.25282
$743$	−24.7861	−0.909313	−0.454657	−	0.890667i	$-0.650238\pi$
$743$	−24.7861	−0.909313	−0.454657	+	0.890667i	$0.650238\pi$
$744$	11.7603	0.431154
$745$	10.1990	0.373663
$746$	7.72304	0.282760
$747$	−2.98302	−0.109143
$748$	0.666769	0.0243795
$749$	85.2795	3.11605
$750$	16.7749	0.612534
$751$	23.7265	0.865793	0.432897	−	0.901444i	$-0.357491\pi$
$751$	23.7265	0.865793	0.432897	+	0.901444i	$0.357491\pi$
$752$	62.0319	2.26207
$753$	−12.8841	−0.469522
$754$	10.3547	0.377095
$755$	6.47948	0.235812
$756$	−3.61929	−0.131632
$757$	−12.6491	−0.459739	−0.229869	−	0.973222i	$-0.573830\pi$
$757$	−12.6491	−0.459739	−0.229869	+	0.973222i	$0.573830\pi$
$758$	−44.1501	−1.60360
$759$	3.86313	0.140223
$760$	−7.27261	−0.263805
$761$	−14.7959	−0.536352	−0.268176	−	0.963370i	$-0.586421\pi$
$761$	−14.7959	−0.536352	−0.268176	+	0.963370i	$0.586421\pi$
$762$	1.85038	0.0670320
$763$	−10.0612	−0.364241
$764$	−5.95110	−0.215303
$765$	−0.868182	−0.0313892
$766$	15.5901	0.563292
$767$	−31.5610	−1.13960
$768$	−17.5387	−0.632872
$769$	25.1700	0.907652	0.453826	−	0.891090i	$-0.350059\pi$
$769$	25.1700	0.907652	0.453826	+	0.891090i	$0.350059\pi$
$770$	−7.98757	−0.287852
$771$	26.0777	0.939165
$772$	−22.3499	−0.804390
$773$	−23.2571	−0.836500	−0.418250	−	0.908332i	$-0.637356\pi$
$773$	−23.2571	−0.836500	−0.418250	+	0.908332i	$0.637356\pi$
$774$	8.86891	0.318786
$775$	−22.8276	−0.819991
$776$	−0.548736	−0.0196985
$777$	−14.0284	−0.503266
$778$	8.10178	0.290463
$779$	5.60082	0.200670
$780$	−2.78610	−0.0997583
$781$	0.313422	0.0112151
$782$	−5.00193	−0.178869
$783$	−2.17513	−0.0777327
$784$	−50.8062	−1.81451
$785$	−0.673739	−0.0240468
$786$	14.5151	0.517735
$787$	34.9096	1.24439	0.622196	−	0.782862i	$-0.286241\pi$
$787$	34.9096	1.24439	0.622196	+	0.782862i	$0.286241\pi$
$788$	−4.01829	−0.143146
$789$	21.6443	0.770557
$790$	0.236011	0.00839689
$791$	−0.806168	−0.0286641
$792$	1.91048	0.0678860
$793$	2.80864	0.0997378
$794$	−1.66793	−0.0591926
$795$	−5.51839	−0.195717
$796$	−8.97355	−0.318059
$797$	24.0098	0.850472	0.425236	−	0.905082i	$-0.360191\pi$
$797$	24.0098	0.850472	0.425236	+	0.905082i	$0.360191\pi$
$798$	−23.5411	−0.833345
$799$	9.50812	0.336373
$800$	17.1562	0.606565
$801$	12.3890	0.437745
$802$	30.9650	1.09341
$803$	−4.11415	−0.145185
$804$	−2.71713	−0.0958258
$805$	18.2053	0.641653
$806$	29.3040	1.03219
$807$	1.70348	0.0599654
$808$	−15.7803	−0.555149
$809$	−50.4476	−1.77364	−0.886822	−	0.462112i	$-0.847092\pi$
$809$	−50.4476	−1.77364	−0.886822	+	0.462112i	$0.847092\pi$
$810$	1.92630	0.0676832
$811$	−31.5727	−1.10867	−0.554334	−	0.832295i	$-0.687027\pi$
$811$	−31.5727	−1.10867	−0.554334	+	0.832295i	$0.687027\pi$
$812$	7.87241	0.276268
$813$	−21.2091	−0.743835
$814$	−5.73420	−0.200984
$815$	−22.7339	−0.796334
$816$	−3.80720	−0.133279
$817$	17.5265	0.613174
$818$	49.6334	1.73539
$819$	11.6463	0.406954
$820$	1.65872	0.0579249
$821$	5.36610	0.187278	0.0936390	−	0.995606i	$-0.470150\pi$
$821$	5.36610	0.187278	0.0936390	+	0.995606i	$0.470150\pi$
$822$	25.7924	0.899613
$823$	−34.2346	−1.19334	−0.596671	−	0.802486i	$-0.703510\pi$
$823$	−34.2346	−1.19334	−0.596671	+	0.802486i	$0.703510\pi$
$824$	−21.2672	−0.740880
$825$	−3.70838	−0.129109
$826$	−78.9770	−2.74796
$827$	27.0655	0.941159	0.470579	−	0.882358i	$-0.344045\pi$
$827$	27.0655	0.941159	0.470579	+	0.882358i	$0.344045\pi$
$828$	3.37187	0.117181
$829$	−8.45949	−0.293810	−0.146905	−	0.989151i	$-0.546931\pi$
$829$	−8.45949	−0.293810	−0.146905	+	0.989151i	$0.546931\pi$
$830$	−5.74619	−0.199453
$831$	4.64693	0.161200
$832$	5.97189	0.207038
$833$	−7.78748	−0.269820
$834$	12.4467	0.430993
$835$	2.25013	0.0778688
$836$	−2.92356	−0.101113
$837$	−6.15568	−0.212771
$838$	−51.1881	−1.76826
$839$	−41.7580	−1.44165	−0.720824	−	0.693119i	$-0.756236\pi$
$839$	−41.7580	−1.44165	−0.720824	+	0.693119i	$0.756236\pi$
$840$	9.00330	0.310643
$841$	−24.2688	−0.836856
$842$	44.6554	1.53893
$843$	3.70914	0.127750
$844$	16.8370	0.579555
$845$	−5.80924	−0.199844
$846$	−21.0963	−0.725307
$847$	4.14659	0.142479
$848$	−24.1996	−0.831017
$849$	−1.52229	−0.0522450
$850$	4.80156	0.164692
$851$	13.0694	0.448014
$852$	0.273566	0.00937221
$853$	6.48751	0.222128	0.111064	−	0.993813i	$-0.464574\pi$
$853$	6.48751	0.222128	0.111064	+	0.993813i	$0.464574\pi$
$854$	7.02824	0.240501
$855$	3.80669	0.130186
$856$	−39.2913	−1.34295
$857$	−53.2173	−1.81787	−0.908933	−	0.416941i	$-0.863102\pi$
$857$	−53.2173	−1.81787	−0.908933	+	0.416941i	$0.863102\pi$
$858$	4.76049	0.162520
$859$	54.5457	1.86107	0.930537	−	0.366198i	$-0.119341\pi$
$859$	54.5457	1.86107	0.930537	+	0.366198i	$0.119341\pi$
$860$	5.19057	0.176997
$861$	−6.93367	−0.236299
$862$	47.0310	1.60188
$863$	9.97813	0.339660	0.169830	−	0.985473i	$-0.445678\pi$
$863$	9.97813	0.339660	0.169830	+	0.985473i	$0.445678\pi$
$864$	4.62635	0.157392
$865$	−6.53850	−0.222316
$866$	−12.3735	−0.420469
$867$	16.4164	0.557532
$868$	22.2792	0.756205
$869$	−0.122521	−0.00415622
$870$	−4.18994	−0.142052
$871$	8.74328	0.296255
$872$	4.63557	0.156980
$873$	0.287224	0.00972105
$874$	21.9318	0.741854
$875$	−41.0390	−1.38737
$876$	−3.59098	−0.121328
$877$	18.1582	0.613159	0.306580	−	0.951845i	$-0.400815\pi$
$877$	18.1582	0.613159	0.306580	+	0.951845i	$0.400815\pi$
$878$	2.82177	0.0952300
$879$	25.9504	0.875284
$880$	5.66410	0.190937
$881$	−26.6452	−0.897700	−0.448850	−	0.893607i	$-0.648166\pi$
$881$	−26.6452	−0.897700	−0.448850	+	0.893607i	$0.648166\pi$
$882$	17.2786	0.581801
$883$	−10.9254	−0.367668	−0.183834	−	0.982957i	$-0.558851\pi$
$883$	−10.9254	−0.367668	−0.183834	+	0.982957i	$0.558851\pi$
$884$	−1.87271	−0.0629862
$885$	12.7709	0.429290
$886$	−3.87730	−0.130260
$887$	−34.3580	−1.15363	−0.576814	−	0.816875i	$-0.695704\pi$
$887$	−34.3580	−1.15363	−0.576814	+	0.816875i	$0.695704\pi$
$888$	6.46339	0.216897
$889$	−4.52685	−0.151826
$890$	23.8649	0.799955
$891$	−1.00000	−0.0335013
$892$	19.0248	0.636998
$893$	−41.6900	−1.39510
$894$	−15.2106	−0.508718
$895$	−24.0952	−0.805412
$896$	53.3110	1.78099
$897$	−10.8501	−0.362276
$898$	−17.2892	−0.576949
$899$	13.3894	0.446561
$900$	−3.23680	−0.107893
$901$	−3.70926	−0.123573
$902$	−2.83418	−0.0943678
$903$	−21.6973	−0.722042
$904$	0.371430	0.0123536
$905$	−20.7743	−0.690563
$906$	−9.66335	−0.321043
$907$	−0.294342	−0.00977345	−0.00488673	−	0.999988i	$-0.501555\pi$
$907$	−0.294342	−0.00977345	−0.00488673	+	0.999988i	$0.501555\pi$
$908$	−16.5864	−0.550438
$909$	8.25985	0.273962
$910$	22.4342	0.743687
$911$	−5.06741	−0.167891	−0.0839454	−	0.996470i	$-0.526752\pi$
$911$	−5.06741	−0.167891	−0.0839454	+	0.996470i	$0.526752\pi$
$912$	16.6933	0.552771
$913$	2.98302	0.0987237
$914$	−55.6259	−1.83994
$915$	−1.13650	−0.0375714
$916$	−24.8458	−0.820927
$917$	−35.5103	−1.17265
$918$	1.29479	0.0427343
$919$	−1.35956	−0.0448476	−0.0224238	−	0.999749i	$-0.507138\pi$
$919$	−1.35956	−0.0448476	−0.0224238	+	0.999749i	$0.507138\pi$
$920$	−8.38784	−0.276539
$921$	−12.7503	−0.420138
$922$	29.3485	0.966542
$923$	−0.880290	−0.0289751
$924$	3.61929	0.119066
$925$	−12.5459	−0.412506
$926$	−48.5110	−1.59417
$927$	11.1319	0.365619
$928$	−10.0629	−0.330331
$929$	28.0140	0.919111	0.459555	−	0.888149i	$-0.348009\pi$
$929$	28.0140	0.919111	0.459555	+	0.888149i	$0.348009\pi$
$930$	−11.8577	−0.388828
$931$	34.1455	1.11907
$932$	−6.45009	−0.211280
$933$	−2.42241	−0.0793062
$934$	−27.3755	−0.895755
$935$	0.868182	0.0283926
$936$	−5.36586	−0.175388
$937$	−30.1476	−0.984879	−0.492439	−	0.870347i	$-0.663895\pi$
$937$	−30.1476	−0.984879	−0.492439	+	0.870347i	$0.663895\pi$
$938$	21.8789	0.714370
$939$	−1.39019	−0.0453670
$940$	−12.3467	−0.402706
$941$	−38.8303	−1.26583	−0.632916	−	0.774221i	$-0.718142\pi$
$941$	−38.8303	−1.26583	−0.632916	+	0.774221i	$0.718142\pi$
$942$	1.00480	0.0327381
$943$	6.45968	0.210356
$944$	56.0038	1.82277
$945$	−4.71258	−0.153300
$946$	−8.86891	−0.288353
$947$	8.12694	0.264090	0.132045	−	0.991244i	$-0.457846\pi$
$947$	8.12694	0.264090	0.132045	+	0.991244i	$0.457846\pi$
$948$	−0.106940	−0.00347326
$949$	11.5552	0.375097
$950$	−21.0532	−0.683057
$951$	−4.56623	−0.148070
$952$	6.05169	0.196136
$953$	−15.8810	−0.514436	−0.257218	−	0.966353i	$-0.582806\pi$
$953$	−15.8810	−0.514436	−0.257218	+	0.966353i	$0.582806\pi$
$954$	8.23000	0.266456
$955$	−7.74877	−0.250744
$956$	9.43486	0.305145
$957$	2.17513	0.0703119
$958$	26.7643	0.864714
$959$	−63.0997	−2.03760
$960$	−2.41648	−0.0779916
$961$	6.89236	0.222334
$962$	16.1053	0.519256
$963$	20.5662	0.662736
$964$	−23.2678	−0.749406
$965$	−29.1012	−0.936801
$966$	−27.1510	−0.873569
$967$	−12.2586	−0.394209	−0.197104	−	0.980383i	$-0.563154\pi$
$967$	−12.2586	−0.394209	−0.197104	+	0.980383i	$0.563154\pi$
$968$	−1.91048	−0.0614052
$969$	2.55872	0.0821979
$970$	0.553278	0.0177647
$971$	−31.0824	−0.997482	−0.498741	−	0.866751i	$-0.666204\pi$
$971$	−31.0824	−0.997482	−0.498741	+	0.866751i	$0.666204\pi$
$972$	−0.872835	−0.0279962
$973$	−30.4502	−0.976187
$974$	−12.5307	−0.401511
$975$	10.4155	0.333563
$976$	−4.98383	−0.159528
$977$	−33.1624	−1.06096	−0.530480	−	0.847697i	$-0.677988\pi$
$977$	−33.1624	−1.06096	−0.530480	+	0.847697i	$0.677988\pi$
$978$	33.9048	1.08416
$979$	−12.3890	−0.395955
$980$	10.1124	0.323029
$981$	−2.42639	−0.0774686
$982$	−40.4572	−1.29104
$983$	−15.8218	−0.504638	−0.252319	−	0.967644i	$-0.581193\pi$
$983$	−15.8218	−0.504638	−0.252319	+	0.967644i	$0.581193\pi$
$984$	3.19459	0.101840
$985$	−5.23212	−0.166709
$986$	−2.81633	−0.0896901
$987$	51.6111	1.64280
$988$	8.21123	0.261234
$989$	20.2141	0.642771
$990$	−1.92630	−0.0612217
$991$	−0.275528	−0.00875245	−0.00437623	−	0.999990i	$-0.501393\pi$
$991$	−0.275528	−0.00875245	−0.00437623	+	0.999990i	$0.501393\pi$
$992$	−28.4783	−0.904187
$993$	−8.68359	−0.275565
$994$	−2.20281	−0.0698687
$995$	−11.6842	−0.370415
$996$	2.60369	0.0825010
$997$	45.5754	1.44339	0.721694	−	0.692212i	$-0.243364\pi$
$997$	45.5754	1.44339	0.721694	+	0.692212i	$0.243364\pi$
$998$	43.2516	1.36911
$999$	−3.38312	−0.107037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.11	✓	14
3.2	odd	2		6039.2.a.j.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.11	✓	14	1.1	even	1	trivial
6039.2.a.j.1.4		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)

\(f(q)\)	\(=\)	\(q+1.69494 q^{2} -1.00000 q^{3} +0.872835 q^{4} +1.13650 q^{5} -1.69494 q^{6} +4.14659 q^{7} -1.91048 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.69494 q^{2} -1.00000 q^{3} +0.872835 q^{4} +1.13650 q^{5} -1.69494 q^{6} +4.14659 q^{7} -1.91048 q^{8} +1.00000 q^{9} +1.92630 q^{10} -1.00000 q^{11} -0.872835 q^{12} +2.80864 q^{13} +7.02824 q^{14} -1.13650 q^{15} -4.98383 q^{16} -0.763911 q^{17} +1.69494 q^{18} +3.34950 q^{19} +0.991974 q^{20} -4.14659 q^{21} -1.69494 q^{22} +3.86313 q^{23} +1.91048 q^{24} -3.70838 q^{25} +4.76049 q^{26} -1.00000 q^{27} +3.61929 q^{28} +2.17513 q^{29} -1.92630 q^{30} +6.15568 q^{31} -4.62635 q^{32} +1.00000 q^{33} -1.29479 q^{34} +4.71258 q^{35} +0.872835 q^{36} +3.38312 q^{37} +5.67721 q^{38} -2.80864 q^{39} -2.17125 q^{40} +1.67214 q^{41} -7.02824 q^{42} +5.23257 q^{43} -0.872835 q^{44} +1.13650 q^{45} +6.54779 q^{46} -12.4466 q^{47} +4.98383 q^{48} +10.1942 q^{49} -6.28549 q^{50} +0.763911 q^{51} +2.45148 q^{52} +4.85562 q^{53} -1.69494 q^{54} -1.13650 q^{55} -7.92198 q^{56} -3.34950 q^{57} +3.68672 q^{58} -11.2371 q^{59} -0.991974 q^{60} +1.00000 q^{61} +10.4335 q^{62} +4.14659 q^{63} +2.12626 q^{64} +3.19201 q^{65} +1.69494 q^{66} +3.11299 q^{67} -0.666769 q^{68} -3.86313 q^{69} +7.98757 q^{70} -0.313422 q^{71} -1.91048 q^{72} +4.11415 q^{73} +5.73420 q^{74} +3.70838 q^{75} +2.92356 q^{76} -4.14659 q^{77} -4.76049 q^{78} +0.122521 q^{79} -5.66410 q^{80} +1.00000 q^{81} +2.83418 q^{82} -2.98302 q^{83} -3.61929 q^{84} -0.868182 q^{85} +8.86891 q^{86} -2.17513 q^{87} +1.91048 q^{88} +12.3890 q^{89} +1.92630 q^{90} +11.6463 q^{91} +3.37187 q^{92} -6.15568 q^{93} -21.0963 q^{94} +3.80669 q^{95} +4.62635 q^{96} +0.287224 q^{97} +17.2786 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 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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