LMFDB - Embedded newform 2013.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 55 x^{10} + 32 x^{9} - 266 x^{8} + 13 x^{7} + 534 x^{6} - 141 x^{5} + \cdots - 11 $ x^13 - 4x^12 - 11x^11 + 55x^10 + 32x^9 - 266x^8 + 13x^7 + 534x^6 - 141x^5 - 404x^4 + 98x^3 + 118x^2 - 16x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.534142$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.534142 q^{2} +1.00000 q^{3} -1.71469 q^{4} +3.62612 q^{5} -0.534142 q^{6} +4.31243 q^{7} +1.98417 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.534142 q^{2} +1.00000 q^{3} -1.71469 q^{4} +3.62612 q^{5} -0.534142 q^{6} +4.31243 q^{7} +1.98417 q^{8} +1.00000 q^{9} -1.93686 q^{10} -1.00000 q^{11} -1.71469 q^{12} -1.21915 q^{13} -2.30345 q^{14} +3.62612 q^{15} +2.36956 q^{16} +0.492960 q^{17} -0.534142 q^{18} +0.909227 q^{19} -6.21767 q^{20} +4.31243 q^{21} +0.534142 q^{22} +9.05847 q^{23} +1.98417 q^{24} +8.14872 q^{25} +0.651199 q^{26} +1.00000 q^{27} -7.39450 q^{28} -3.36455 q^{29} -1.93686 q^{30} -1.80170 q^{31} -5.23402 q^{32} -1.00000 q^{33} -0.263311 q^{34} +15.6374 q^{35} -1.71469 q^{36} -2.52082 q^{37} -0.485656 q^{38} -1.21915 q^{39} +7.19484 q^{40} -3.50527 q^{41} -2.30345 q^{42} +1.17586 q^{43} +1.71469 q^{44} +3.62612 q^{45} -4.83851 q^{46} -6.47062 q^{47} +2.36956 q^{48} +11.5971 q^{49} -4.35257 q^{50} +0.492960 q^{51} +2.09047 q^{52} +7.40180 q^{53} -0.534142 q^{54} -3.62612 q^{55} +8.55661 q^{56} +0.909227 q^{57} +1.79715 q^{58} -12.4433 q^{59} -6.21767 q^{60} -1.00000 q^{61} +0.962363 q^{62} +4.31243 q^{63} -1.94340 q^{64} -4.42078 q^{65} +0.534142 q^{66} -1.39825 q^{67} -0.845275 q^{68} +9.05847 q^{69} -8.35258 q^{70} -12.1125 q^{71} +1.98417 q^{72} -9.92547 q^{73} +1.34647 q^{74} +8.14872 q^{75} -1.55905 q^{76} -4.31243 q^{77} +0.651199 q^{78} +4.62242 q^{79} +8.59228 q^{80} +1.00000 q^{81} +1.87231 q^{82} -2.80042 q^{83} -7.39450 q^{84} +1.78753 q^{85} -0.628078 q^{86} -3.36455 q^{87} -1.98417 q^{88} +12.0828 q^{89} -1.93686 q^{90} -5.25750 q^{91} -15.5325 q^{92} -1.80170 q^{93} +3.45623 q^{94} +3.29696 q^{95} -5.23402 q^{96} +2.52978 q^{97} -6.19449 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.534142	−0.377695	−0.188848	−	0.982006i	$-0.560475\pi$
$2$	−0.534142	−0.377695	−0.188848	+	0.982006i	$0.560475\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.71469	−0.857346
$5$	3.62612	1.62165	0.810824	−	0.585290i	$-0.199019\pi$
$5$	3.62612	1.62165	0.810824	+	0.585290i	$0.199019\pi$
$6$	−0.534142	−0.218062
$7$	4.31243	1.62995	0.814973	−	0.579498i	$-0.196751\pi$
$7$	4.31243	1.62995	0.814973	+	0.579498i	$0.196751\pi$
$8$	1.98417	0.701511
$9$	1.00000	0.333333
$10$	−1.93686	−0.612489
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.71469	−0.494989
$13$	−1.21915	−0.338131	−0.169066	−	0.985605i	$-0.554075\pi$
$13$	−1.21915	−0.338131	−0.169066	+	0.985605i	$0.554075\pi$
$14$	−2.30345	−0.615623
$15$	3.62612	0.936259
$16$	2.36956	0.592389
$17$	0.492960	0.119560	0.0597802	−	0.998212i	$-0.480960\pi$
$17$	0.492960	0.119560	0.0597802	+	0.998212i	$0.480960\pi$
$18$	−0.534142	−0.125898
$19$	0.909227	0.208591	0.104296	−	0.994546i	$-0.466741\pi$
$19$	0.909227	0.208591	0.104296	+	0.994546i	$0.466741\pi$
$20$	−6.21767	−1.39031
$21$	4.31243	0.941050
$22$	0.534142	0.113879
$23$	9.05847	1.88882	0.944411	−	0.328768i	$-0.106633\pi$
$23$	9.05847	1.88882	0.944411	+	0.328768i	$0.106633\pi$
$24$	1.98417	0.405017
$25$	8.14872	1.62974
$26$	0.651199	0.127711
$27$	1.00000	0.192450
$28$	−7.39450	−1.39743
$29$	−3.36455	−0.624781	−0.312391	−	0.949954i	$-0.601130\pi$
$29$	−3.36455	−0.624781	−0.312391	+	0.949954i	$0.601130\pi$
$30$	−1.93686	−0.353621
$31$	−1.80170	−0.323595	−0.161797	−	0.986824i	$-0.551729\pi$
$31$	−1.80170	−0.323595	−0.161797	+	0.986824i	$0.551729\pi$
$32$	−5.23402	−0.925253
$33$	−1.00000	−0.174078
$34$	−0.263311	−0.0451574
$35$	15.6374	2.64320
$36$	−1.71469	−0.285782
$37$	−2.52082	−0.414420	−0.207210	−	0.978296i	$-0.566438\pi$
$37$	−2.52082	−0.414420	−0.207210	+	0.978296i	$0.566438\pi$
$38$	−0.485656	−0.0787839
$39$	−1.21915	−0.195220
$40$	7.19484	1.13760
$41$	−3.50527	−0.547432	−0.273716	−	0.961811i	$-0.588253\pi$
$41$	−3.50527	−0.547432	−0.273716	+	0.961811i	$0.588253\pi$
$42$	−2.30345	−0.355430
$43$	1.17586	0.179318	0.0896588	−	0.995973i	$-0.471422\pi$
$43$	1.17586	0.179318	0.0896588	+	0.995973i	$0.471422\pi$
$44$	1.71469	0.258500
$45$	3.62612	0.540549
$46$	−4.83851	−0.713399
$47$	−6.47062	−0.943837	−0.471919	−	0.881642i	$-0.656438\pi$
$47$	−6.47062	−0.943837	−0.471919	+	0.881642i	$0.656438\pi$
$48$	2.36956	0.342016
$49$	11.5971	1.65673
$50$	−4.35257	−0.615546
$51$	0.492960	0.0690283
$52$	2.09047	0.289896
$53$	7.40180	1.01672	0.508358	−	0.861146i	$-0.330253\pi$
$53$	7.40180	1.01672	0.508358	+	0.861146i	$0.330253\pi$
$54$	−0.534142	−0.0726875
$55$	−3.62612	−0.488945
$56$	8.55661	1.14343
$57$	0.909227	0.120430
$58$	1.79715	0.235977
$59$	−12.4433	−1.61997	−0.809987	−	0.586448i	$-0.800526\pi$
$59$	−12.4433	−1.61997	−0.809987	+	0.586448i	$0.800526\pi$
$60$	−6.21767	−0.802698
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.962363	0.122220
$63$	4.31243	0.543316
$64$	−1.94340	−0.242925
$65$	−4.42078	−0.548330
$66$	0.534142	0.0657483
$67$	−1.39825	−0.170824	−0.0854118	−	0.996346i	$-0.527221\pi$
$67$	−1.39825	−0.170824	−0.0854118	+	0.996346i	$0.527221\pi$
$68$	−0.845275	−0.102505
$69$	9.05847	1.09051
$70$	−8.35258	−0.998324
$71$	−12.1125	−1.43749	−0.718747	−	0.695272i	$-0.755284\pi$
$71$	−12.1125	−1.43749	−0.718747	+	0.695272i	$0.755284\pi$
$72$	1.98417	0.233837
$73$	−9.92547	−1.16169	−0.580844	−	0.814015i	$-0.697277\pi$
$73$	−9.92547	−1.16169	−0.580844	+	0.814015i	$0.697277\pi$
$74$	1.34647	0.156524
$75$	8.14872	0.940933
$76$	−1.55905	−0.178835
$77$	−4.31243	−0.491447
$78$	0.651199	0.0737338
$79$	4.62242	0.520063	0.260031	−	0.965600i	$-0.416267\pi$
$79$	4.62242	0.520063	0.260031	+	0.965600i	$0.416267\pi$
$80$	8.59228	0.960647
$81$	1.00000	0.111111
$82$	1.87231	0.206762
$83$	−2.80042	−0.307386	−0.153693	−	0.988119i	$-0.549117\pi$
$83$	−2.80042	−0.307386	−0.153693	+	0.988119i	$0.549117\pi$
$84$	−7.39450	−0.806806
$85$	1.78753	0.193885
$86$	−0.628078	−0.0677274
$87$	−3.36455	−0.360718
$88$	−1.98417	−0.211513
$89$	12.0828	1.28077	0.640387	−	0.768053i	$-0.278774\pi$
$89$	12.0828	1.28077	0.640387	+	0.768053i	$0.278774\pi$
$90$	−1.93686	−0.204163
$91$	−5.25750	−0.551136
$92$	−15.5325	−1.61937
$93$	−1.80170	−0.186828
$94$	3.45623	0.356483
$95$	3.29696	0.338261
$96$	−5.23402	−0.534195
$97$	2.52978	0.256861	0.128430	−	0.991719i	$-0.459006\pi$
$97$	2.52978	0.256861	0.128430	+	0.991719i	$0.459006\pi$
$98$	−6.19449	−0.625738
$99$	−1.00000	−0.100504
$100$	−13.9725	−1.39725
$101$	−3.20857	−0.319264	−0.159632	−	0.987177i	$-0.551031\pi$
$101$	−3.20857	−0.319264	−0.159632	+	0.987177i	$0.551031\pi$
$102$	−0.263311	−0.0260716
$103$	−11.5401	−1.13708	−0.568542	−	0.822654i	$-0.692492\pi$
$103$	−11.5401	−1.13708	−0.568542	+	0.822654i	$0.692492\pi$
$104$	−2.41900	−0.237203
$105$	15.6374	1.52605
$106$	−3.95361	−0.384009
$107$	−10.8292	−1.04690	−0.523450	−	0.852056i	$-0.675355\pi$
$107$	−10.8292	−1.04690	−0.523450	+	0.852056i	$0.675355\pi$
$108$	−1.71469	−0.164996
$109$	6.23060	0.596783	0.298391	−	0.954444i	$-0.403550\pi$
$109$	6.23060	0.596783	0.298391	+	0.954444i	$0.403550\pi$
$110$	1.93686	0.184672
$111$	−2.52082	−0.239265
$112$	10.2186	0.965562
$113$	2.26940	0.213487	0.106744	−	0.994287i	$-0.465958\pi$
$113$	2.26940	0.213487	0.106744	+	0.994287i	$0.465958\pi$
$114$	−0.485656	−0.0454859
$115$	32.8471	3.06300
$116$	5.76917	0.535654
$117$	−1.21915	−0.112710
$118$	6.64646	0.611856
$119$	2.12586	0.194877
$120$	7.19484	0.656796
$121$	1.00000	0.0909091
$122$	0.534142	0.0483589
$123$	−3.50527	−0.316060
$124$	3.08936	0.277433
$125$	11.4176	1.02122
$126$	−2.30345	−0.205208
$127$	3.48898	0.309597	0.154798	−	0.987946i	$-0.450527\pi$
$127$	3.48898	0.309597	0.154798	+	0.987946i	$0.450527\pi$
$128$	11.5061	1.01701
$129$	1.17586	0.103529
$130$	2.36132	0.207102
$131$	21.6610	1.89253	0.946266	−	0.323390i	$-0.104823\pi$
$131$	21.6610	1.89253	0.946266	+	0.323390i	$0.104823\pi$
$132$	1.71469	0.149245
$133$	3.92098	0.339992
$134$	0.746864	0.0645192
$135$	3.62612	0.312086
$136$	0.978118	0.0838730
$137$	21.3976	1.82812	0.914062	−	0.405575i	$-0.132929\pi$
$137$	21.3976	1.82812	0.914062	+	0.405575i	$0.132929\pi$
$138$	−4.83851	−0.411881
$139$	−6.56067	−0.556469	−0.278235	−	0.960513i	$-0.589749\pi$
$139$	−6.56067	−0.556469	−0.278235	+	0.960513i	$0.589749\pi$
$140$	−26.8133	−2.26614
$141$	−6.47062	−0.544925
$142$	6.46981	0.542934
$143$	1.21915	0.101950
$144$	2.36956	0.197463
$145$	−12.2003	−1.01318
$146$	5.30161	0.438764
$147$	11.5971	0.956512
$148$	4.32243	0.355301
$149$	15.9721	1.30849	0.654244	−	0.756283i	$-0.272987\pi$
$149$	15.9721	1.30849	0.654244	+	0.756283i	$0.272987\pi$
$150$	−4.35257	−0.355386
$151$	−17.1351	−1.39444	−0.697218	−	0.716860i	$-0.745579\pi$
$151$	−17.1351	−1.39444	−0.697218	+	0.716860i	$0.745579\pi$
$152$	1.80406	0.146329
$153$	0.492960	0.0398535
$154$	2.30345	0.185617
$155$	−6.53317	−0.524757
$156$	2.09047	0.167371
$157$	1.67936	0.134027	0.0670137	−	0.997752i	$-0.478653\pi$
$157$	1.67936	0.134027	0.0670137	+	0.997752i	$0.478653\pi$
$158$	−2.46903	−0.196425
$159$	7.40180	0.587001
$160$	−18.9792	−1.50044
$161$	39.0640	3.07868
$162$	−0.534142	−0.0419661
$163$	5.03166	0.394110	0.197055	−	0.980392i	$-0.436862\pi$
$163$	5.03166	0.394110	0.197055	+	0.980392i	$0.436862\pi$
$164$	6.01047	0.469339
$165$	−3.62612	−0.282293
$166$	1.49582	0.116098
$167$	16.5787	1.28290	0.641450	−	0.767165i	$-0.278333\pi$
$167$	16.5787	1.28290	0.641450	+	0.767165i	$0.278333\pi$
$168$	8.55661	0.660157
$169$	−11.5137	−0.885667
$170$	−0.954795	−0.0732294
$171$	0.909227	0.0695304
$172$	−2.01625	−0.153737
$173$	−10.7498	−0.817289	−0.408644	−	0.912694i	$-0.633998\pi$
$173$	−10.7498	−0.817289	−0.408644	+	0.912694i	$0.633998\pi$
$174$	1.79715	0.136241
$175$	35.1408	2.65640
$176$	−2.36956	−0.178612
$177$	−12.4433	−0.935292
$178$	−6.45392	−0.483742
$179$	15.8180	1.18229	0.591145	−	0.806565i	$-0.298676\pi$
$179$	15.8180	1.18229	0.591145	+	0.806565i	$0.298676\pi$
$180$	−6.21767	−0.463438
$181$	−15.4710	−1.14995	−0.574975	−	0.818171i	$-0.694988\pi$
$181$	−15.4710	−1.14995	−0.574975	+	0.818171i	$0.694988\pi$
$182$	2.80825	0.208162
$183$	−1.00000	−0.0739221
$184$	17.9736	1.32503
$185$	−9.14078	−0.672043
$186$	0.962363	0.0705639
$187$	−0.492960	−0.0360488
$188$	11.0951	0.809195
$189$	4.31243	0.313683
$190$	−1.76105	−0.127760
$191$	18.2591	1.32119	0.660593	−	0.750745i	$-0.270305\pi$
$191$	18.2591	1.32119	0.660593	+	0.750745i	$0.270305\pi$
$192$	−1.94340	−0.140253
$193$	−14.9462	−1.07585	−0.537926	−	0.842992i	$-0.680792\pi$
$193$	−14.9462	−1.07585	−0.537926	+	0.842992i	$0.680792\pi$
$194$	−1.35126	−0.0970150
$195$	−4.42078	−0.316579
$196$	−19.8854	−1.42039
$197$	−5.53663	−0.394469	−0.197234	−	0.980356i	$-0.563196\pi$
$197$	−5.53663	−0.394469	−0.197234	+	0.980356i	$0.563196\pi$
$198$	0.534142	0.0379598
$199$	1.42160	0.100774	0.0503872	−	0.998730i	$-0.483954\pi$
$199$	1.42160	0.100774	0.0503872	+	0.998730i	$0.483954\pi$
$200$	16.1685	1.14328
$201$	−1.39825	−0.0986250
$202$	1.71383	0.120585
$203$	−14.5094	−1.01836
$204$	−0.845275	−0.0591811
$205$	−12.7105	−0.887742
$206$	6.16407	0.429471
$207$	9.05847	0.629607
$208$	−2.88884	−0.200305
$209$	−0.909227	−0.0628926
$210$	−8.35258	−0.576383
$211$	−18.4855	−1.27259	−0.636296	−	0.771445i	$-0.719534\pi$
$211$	−18.4855	−1.27259	−0.636296	+	0.771445i	$0.719534\pi$
$212$	−12.6918	−0.871677
$213$	−12.1125	−0.829937
$214$	5.78434	0.395409
$215$	4.26382	0.290790
$216$	1.98417	0.135006
$217$	−7.76971	−0.527442
$218$	−3.32802	−0.225402
$219$	−9.92547	−0.670701
$220$	6.21767	0.419196
$221$	−0.600993	−0.0404271
$222$	1.34647	0.0903694
$223$	11.2160	0.751077	0.375538	−	0.926807i	$-0.377458\pi$
$223$	11.2160	0.751077	0.375538	+	0.926807i	$0.377458\pi$
$224$	−22.5714	−1.50811
$225$	8.14872	0.543248
$226$	−1.21218	−0.0806331
$227$	22.4464	1.48982	0.744911	−	0.667163i	$-0.232492\pi$
$227$	22.4464	1.48982	0.744911	+	0.667163i	$0.232492\pi$
$228$	−1.55905	−0.103250
$229$	21.4818	1.41955	0.709777	−	0.704426i	$-0.248795\pi$
$229$	21.4818	1.41955	0.709777	+	0.704426i	$0.248795\pi$
$230$	−17.5450	−1.15688
$231$	−4.31243	−0.283737
$232$	−6.67585	−0.438291
$233$	−4.14079	−0.271272	−0.135636	−	0.990759i	$-0.543308\pi$
$233$	−4.14079	−0.271272	−0.135636	+	0.990759i	$0.543308\pi$
$234$	0.651199	0.0425702
$235$	−23.4632	−1.53057
$236$	21.3363	1.38888
$237$	4.62242	0.300258
$238$	−1.13551	−0.0736042
$239$	−10.5358	−0.681507	−0.340753	−	0.940153i	$-0.610682\pi$
$239$	−10.5358	−0.681507	−0.340753	+	0.940153i	$0.610682\pi$
$240$	8.59228	0.554630
$241$	−11.8063	−0.760513	−0.380257	−	0.924881i	$-0.624164\pi$
$241$	−11.8063	−0.760513	−0.380257	+	0.924881i	$0.624164\pi$
$242$	−0.534142	−0.0343359
$243$	1.00000	0.0641500
$244$	1.71469	0.109772
$245$	42.0524	2.68663
$246$	1.87231	0.119374
$247$	−1.10848	−0.0705312
$248$	−3.57488	−0.227005
$249$	−2.80042	−0.177469
$250$	−6.09862	−0.385711
$251$	13.7725	0.869314	0.434657	−	0.900596i	$-0.356870\pi$
$251$	13.7725	0.869314	0.434657	+	0.900596i	$0.356870\pi$
$252$	−7.39450	−0.465810
$253$	−9.05847	−0.569501
$254$	−1.86361	−0.116933
$255$	1.78753	0.111940
$256$	−2.25909	−0.141193
$257$	−29.9006	−1.86515	−0.932574	−	0.360980i	$-0.882442\pi$
$257$	−29.9006	−1.86515	−0.932574	+	0.360980i	$0.882442\pi$
$258$	−0.628078	−0.0391024
$259$	−10.8709	−0.675482
$260$	7.58028	0.470109
$261$	−3.36455	−0.208260
$262$	−11.5701	−0.714800
$263$	−6.38562	−0.393754	−0.196877	−	0.980428i	$-0.563080\pi$
$263$	−6.38562	−0.393754	−0.196877	+	0.980428i	$0.563080\pi$
$264$	−1.98417	−0.122117
$265$	26.8398	1.64875
$266$	−2.09436	−0.128413
$267$	12.0828	0.739455
$268$	2.39757	0.146455
$269$	26.0111	1.58592	0.792962	−	0.609272i	$-0.208538\pi$
$269$	26.0111	1.58592	0.792962	+	0.609272i	$0.208538\pi$
$270$	−1.93686	−0.117874
$271$	−0.817061	−0.0496329	−0.0248165	−	0.999692i	$-0.507900\pi$
$271$	−0.817061	−0.0496329	−0.0248165	+	0.999692i	$0.507900\pi$
$272$	1.16810	0.0708263
$273$	−5.25750	−0.318199
$274$	−11.4294	−0.690474
$275$	−8.14872	−0.491386
$276$	−15.5325	−0.934946
$277$	4.93273	0.296379	0.148190	−	0.988959i	$-0.452655\pi$
$277$	4.93273	0.296379	0.148190	+	0.988959i	$0.452655\pi$
$278$	3.50433	0.210176
$279$	−1.80170	−0.107865
$280$	31.0273	1.85423
$281$	−21.8269	−1.30209	−0.651043	−	0.759041i	$-0.725668\pi$
$281$	−21.8269	−1.30209	−0.651043	+	0.759041i	$0.725668\pi$
$282$	3.45623	0.205815
$283$	−5.17215	−0.307452	−0.153726	−	0.988113i	$-0.549127\pi$
$283$	−5.17215	−0.307452	−0.153726	+	0.988113i	$0.549127\pi$
$284$	20.7693	1.23243
$285$	3.29696	0.195295
$286$	−0.651199	−0.0385062
$287$	−15.1163	−0.892285
$288$	−5.23402	−0.308418
$289$	−16.7570	−0.985705
$290$	6.51666	0.382672
$291$	2.52978	0.148299
$292$	17.0191	0.995969
$293$	−9.66881	−0.564858	−0.282429	−	0.959288i	$-0.591140\pi$
$293$	−9.66881	−0.564858	−0.282429	+	0.959288i	$0.591140\pi$
$294$	−6.19449	−0.361270
$295$	−45.1207	−2.62703
$296$	−5.00174	−0.290720
$297$	−1.00000	−0.0580259
$298$	−8.53138	−0.494210
$299$	−11.0436	−0.638670
$300$	−13.9725	−0.806705
$301$	5.07084	0.292278
$302$	9.15258	0.526672
$303$	−3.20857	−0.184327
$304$	2.15447	0.123567
$305$	−3.62612	−0.207631
$306$	−0.263311	−0.0150525
$307$	19.6167	1.11958	0.559791	−	0.828634i	$-0.310881\pi$
$307$	19.6167	1.11958	0.559791	+	0.828634i	$0.310881\pi$
$308$	7.39450	0.421341
$309$	−11.5401	−0.656496
$310$	3.48964	0.198198
$311$	14.3311	0.812641	0.406321	−	0.913731i	$-0.366812\pi$
$311$	14.3311	0.812641	0.406321	+	0.913731i	$0.366812\pi$
$312$	−2.41900	−0.136949
$313$	−32.1674	−1.81821	−0.909103	−	0.416570i	$-0.863232\pi$
$313$	−32.1674	−1.81821	−0.909103	+	0.416570i	$0.863232\pi$
$314$	−0.897016	−0.0506215
$315$	15.6374	0.881067
$316$	−7.92603	−0.445874
$317$	−25.8443	−1.45156	−0.725781	−	0.687926i	$-0.758521\pi$
$317$	−25.8443	−1.45156	−0.725781	+	0.687926i	$0.758521\pi$
$318$	−3.95361	−0.221707
$319$	3.36455	0.188379
$320$	−7.04700	−0.393939
$321$	−10.8292	−0.604428
$322$	−20.8657	−1.16280
$323$	0.448213	0.0249392
$324$	−1.71469	−0.0952607
$325$	−9.93451	−0.551067
$326$	−2.68762	−0.148854
$327$	6.23060	0.344553
$328$	−6.95507	−0.384029
$329$	−27.9041	−1.53840
$330$	1.93686	0.106621
$331$	6.95974	0.382542	0.191271	−	0.981537i	$-0.438739\pi$
$331$	6.95974	0.382542	0.191271	+	0.981537i	$0.438739\pi$
$332$	4.80186	0.263536
$333$	−2.52082	−0.138140
$334$	−8.85538	−0.484545
$335$	−5.07022	−0.277016
$336$	10.2186	0.557468
$337$	−27.1628	−1.47965	−0.739825	−	0.672799i	$-0.765092\pi$
$337$	−27.1628	−1.47965	−0.739825	+	0.672799i	$0.765092\pi$
$338$	6.14993	0.334512
$339$	2.26940	0.123257
$340$	−3.06507	−0.166227
$341$	1.80170	0.0975675
$342$	−0.485656	−0.0262613
$343$	19.8246	1.07043
$344$	2.33312	0.125793
$345$	32.8471	1.76843
$346$	5.74189	0.308686
$347$	−24.5634	−1.31863	−0.659315	−	0.751867i	$-0.729154\pi$
$347$	−24.5634	−1.31863	−0.659315	+	0.751867i	$0.729154\pi$
$348$	5.76917	0.309260
$349$	19.9223	1.06642	0.533209	−	0.845984i	$-0.320986\pi$
$349$	19.9223	1.06642	0.533209	+	0.845984i	$0.320986\pi$
$350$	−18.7702	−1.00331
$351$	−1.21915	−0.0650734
$352$	5.23402	0.278974
$353$	1.49470	0.0795546	0.0397773	−	0.999209i	$-0.487335\pi$
$353$	1.49470	0.0795546	0.0397773	+	0.999209i	$0.487335\pi$
$354$	6.64646	0.353255
$355$	−43.9215	−2.33111
$356$	−20.7183	−1.09807
$357$	2.12586	0.112512
$358$	−8.44903	−0.446545
$359$	13.4291	0.708762	0.354381	−	0.935101i	$-0.384692\pi$
$359$	13.4291	0.708762	0.354381	+	0.935101i	$0.384692\pi$
$360$	7.19484	0.379201
$361$	−18.1733	−0.956490
$362$	8.26371	0.434331
$363$	1.00000	0.0524864
$364$	9.01500	0.472515
$365$	−35.9909	−1.88385
$366$	0.534142	0.0279200
$367$	−17.3863	−0.907557	−0.453778	−	0.891115i	$-0.649924\pi$
$367$	−17.3863	−0.907557	−0.453778	+	0.891115i	$0.649924\pi$
$368$	21.4645	1.11892
$369$	−3.50527	−0.182477
$370$	4.88247	0.253828
$371$	31.9198	1.65719
$372$	3.08936	0.160176
$373$	−10.2747	−0.532002	−0.266001	−	0.963973i	$-0.585702\pi$
$373$	−10.2747	−0.532002	−0.266001	+	0.963973i	$0.585702\pi$
$374$	0.263311	0.0136155
$375$	11.4176	0.589603
$376$	−12.8388	−0.662112
$377$	4.10189	0.211258
$378$	−2.30345	−0.118477
$379$	−14.6983	−0.755003	−0.377501	−	0.926009i	$-0.623217\pi$
$379$	−14.6983	−0.755003	−0.377501	+	0.926009i	$0.623217\pi$
$380$	−5.65328	−0.290007
$381$	3.48898	0.178746
$382$	−9.75297	−0.499005
$383$	28.1057	1.43613	0.718067	−	0.695973i	$-0.245027\pi$
$383$	28.1057	1.43613	0.718067	+	0.695973i	$0.245027\pi$
$384$	11.5061	0.587168
$385$	−15.6374	−0.796955
$386$	7.98340	0.406344
$387$	1.17586	0.0597726
$388$	−4.33780	−0.220218
$389$	26.0871	1.32267	0.661334	−	0.750091i	$-0.269991\pi$
$389$	26.0871	1.32267	0.661334	+	0.750091i	$0.269991\pi$
$390$	2.36132	0.119570
$391$	4.46547	0.225828
$392$	23.0106	1.16221
$393$	21.6610	1.09265
$394$	2.95735	0.148989
$395$	16.7614	0.843359
$396$	1.71469	0.0861665
$397$	28.9690	1.45391	0.726957	−	0.686683i	$-0.240934\pi$
$397$	28.9690	1.45391	0.726957	+	0.686683i	$0.240934\pi$
$398$	−0.759335	−0.0380620
$399$	3.92098	0.196295
$400$	19.3088	0.965442
$401$	15.6855	0.783297	0.391648	−	0.920115i	$-0.371905\pi$
$401$	15.6855	0.783297	0.391648	+	0.920115i	$0.371905\pi$
$402$	0.746864	0.0372502
$403$	2.19654	0.109418
$404$	5.50171	0.273720
$405$	3.62612	0.180183
$406$	7.75008	0.384630
$407$	2.52082	0.124952
$408$	0.978118	0.0484241
$409$	−27.7465	−1.37197	−0.685987	−	0.727614i	$-0.740629\pi$
$409$	−27.7465	−1.37197	−0.685987	+	0.727614i	$0.740629\pi$
$410$	6.78922	0.335296
$411$	21.3976	1.05547
$412$	19.7878	0.974875
$413$	−53.6607	−2.64047
$414$	−4.83851	−0.237800
$415$	−10.1546	−0.498472
$416$	6.38106	0.312857
$417$	−6.56067	−0.321278
$418$	0.485656	0.0237542
$419$	29.3305	1.43289	0.716445	−	0.697643i	$-0.245768\pi$
$419$	29.3305	1.43289	0.716445	+	0.697643i	$0.245768\pi$
$420$	−26.8133	−1.30836
$421$	20.6444	1.00615	0.503073	−	0.864244i	$-0.332203\pi$
$421$	20.6444	1.00615	0.503073	+	0.864244i	$0.332203\pi$
$422$	9.87387	0.480652
$423$	−6.47062	−0.314612
$424$	14.6864	0.713237
$425$	4.01699	0.194853
$426$	6.46981	0.313463
$427$	−4.31243	−0.208693
$428$	18.5688	0.897556
$429$	1.21915	0.0588611
$430$	−2.27748	−0.109830
$431$	−29.1418	−1.40371	−0.701857	−	0.712318i	$-0.747645\pi$
$431$	−29.1418	−1.40371	−0.701857	+	0.712318i	$0.747645\pi$
$432$	2.36956	0.114005
$433$	18.2972	0.879307	0.439654	−	0.898167i	$-0.355101\pi$
$433$	18.2972	0.879307	0.439654	+	0.898167i	$0.355101\pi$
$434$	4.15013	0.199213
$435$	−12.2003	−0.584957
$436$	−10.6836	−0.511650
$437$	8.23621	0.393991
$438$	5.30161	0.253321
$439$	21.3407	1.01854	0.509268	−	0.860608i	$-0.329916\pi$
$439$	21.3407	1.01854	0.509268	+	0.860608i	$0.329916\pi$
$440$	−7.19484	−0.343001
$441$	11.5971	0.552242
$442$	0.321015	0.0152691
$443$	20.8404	0.990159	0.495080	−	0.868848i	$-0.335139\pi$
$443$	20.8404	0.990159	0.495080	+	0.868848i	$0.335139\pi$
$444$	4.32243	0.205133
$445$	43.8136	2.07696
$446$	−5.99092	−0.283678
$447$	15.9721	0.755456
$448$	−8.38079	−0.395955
$449$	−13.0657	−0.616607	−0.308304	−	0.951288i	$-0.599761\pi$
$449$	−13.0657	−0.616607	−0.308304	+	0.951288i	$0.599761\pi$
$450$	−4.35257	−0.205182
$451$	3.50527	0.165057
$452$	−3.89132	−0.183032
$453$	−17.1351	−0.805078
$454$	−11.9896	−0.562699
$455$	−19.0643	−0.893749
$456$	1.80406	0.0844830
$457$	−31.7457	−1.48500	−0.742500	−	0.669846i	$-0.766360\pi$
$457$	−31.7457	−1.48500	−0.742500	+	0.669846i	$0.766360\pi$
$458$	−11.4743	−0.536159
$459$	0.492960	0.0230094
$460$	−56.3226	−2.62606
$461$	−21.5585	−1.00408	−0.502041	−	0.864844i	$-0.667417\pi$
$461$	−21.5585	−1.00408	−0.502041	+	0.864844i	$0.667417\pi$
$462$	2.30345	0.107166
$463$	−20.3433	−0.945434	−0.472717	−	0.881214i	$-0.656727\pi$
$463$	−20.3433	−0.945434	−0.472717	+	0.881214i	$0.656727\pi$
$464$	−7.97249	−0.370114
$465$	−6.53317	−0.302969
$466$	2.21177	0.102458
$467$	−1.24480	−0.0576027	−0.0288013	−	0.999585i	$-0.509169\pi$
$467$	−1.24480	−0.0576027	−0.0288013	+	0.999585i	$0.509169\pi$
$468$	2.09047	0.0966319
$469$	−6.02986	−0.278433
$470$	12.5327	0.578090
$471$	1.67936	0.0773808
$472$	−24.6896	−1.13643
$473$	−1.17586	−0.0540663
$474$	−2.46903	−0.113406
$475$	7.40904	0.339950
$476$	−3.64519	−0.167077
$477$	7.40180	0.338905
$478$	5.62763	0.257402
$479$	14.9723	0.684102	0.342051	−	0.939681i	$-0.388878\pi$
$479$	14.9723	0.684102	0.342051	+	0.939681i	$0.388878\pi$
$480$	−18.9792	−0.866277
$481$	3.07326	0.140128
$482$	6.30626	0.287242
$483$	39.0640	1.77748
$484$	−1.71469	−0.0779406
$485$	9.17329	0.416538
$486$	−0.534142	−0.0242292
$487$	−19.3857	−0.878450	−0.439225	−	0.898377i	$-0.644747\pi$
$487$	−19.3857	−0.878450	−0.439225	+	0.898377i	$0.644747\pi$
$488$	−1.98417	−0.0898193
$489$	5.03166	0.227540
$490$	−22.4619	−1.01473
$491$	−12.6872	−0.572565	−0.286282	−	0.958145i	$-0.592420\pi$
$491$	−12.6872	−0.572565	−0.286282	+	0.958145i	$0.592420\pi$
$492$	6.01047	0.270973
$493$	−1.65859	−0.0746991
$494$	0.592088	0.0266393
$495$	−3.62612	−0.162982
$496$	−4.26923	−0.191694
$497$	−52.2345	−2.34304
$498$	1.49582	0.0670293
$499$	4.49897	0.201402	0.100701	−	0.994917i	$-0.467892\pi$
$499$	4.49897	0.201402	0.100701	+	0.994917i	$0.467892\pi$
$500$	−19.5777	−0.875541
$501$	16.5787	0.740682
$502$	−7.35648	−0.328336
$503$	−35.1228	−1.56605	−0.783024	−	0.621991i	$-0.786324\pi$
$503$	−35.1228	−1.56605	−0.783024	+	0.621991i	$0.786324\pi$
$504$	8.55661	0.381142
$505$	−11.6346	−0.517734
$506$	4.83851	0.215098
$507$	−11.5137	−0.511340
$508$	−5.98253	−0.265432
$509$	−0.331366	−0.0146875	−0.00734377	−	0.999973i	$-0.502338\pi$
$509$	−0.331366	−0.0146875	−0.00734377	+	0.999973i	$0.502338\pi$
$510$	−0.954795	−0.0422790
$511$	−42.8029	−1.89349
$512$	−21.8055	−0.963677
$513$	0.909227	0.0401434
$514$	15.9712	0.704457
$515$	−41.8459	−1.84395
$516$	−2.01625	−0.0887603
$517$	6.47062	0.284578
$518$	5.80658	0.255127
$519$	−10.7498	−0.471862
$520$	−8.77159	−0.384660
$521$	11.5442	0.505762	0.252881	−	0.967497i	$-0.418622\pi$
$521$	11.5442	0.505762	0.252881	+	0.967497i	$0.418622\pi$
$522$	1.79715	0.0786590
$523$	−16.4599	−0.719741	−0.359871	−	0.933002i	$-0.617179\pi$
$523$	−16.4599	−0.719741	−0.359871	+	0.933002i	$0.617179\pi$
$524$	−37.1420	−1.62255
$525$	35.1408	1.53367
$526$	3.41083	0.148719
$527$	−0.888167	−0.0386892
$528$	−2.36956	−0.103122
$529$	59.0559	2.56765
$530$	−14.3362	−0.622727
$531$	−12.4433	−0.539991
$532$	−6.72328	−0.291491
$533$	4.27345	0.185104
$534$	−6.45392	−0.279289
$535$	−39.2680	−1.69770
$536$	−2.77437	−0.119835
$537$	15.8180	0.682595
$538$	−13.8936	−0.598996
$539$	−11.5971	−0.499522
$540$	−6.21767	−0.267566
$541$	−19.3268	−0.830924	−0.415462	−	0.909611i	$-0.636380\pi$
$541$	−19.3268	−0.830924	−0.415462	+	0.909611i	$0.636380\pi$
$542$	0.436426	0.0187461
$543$	−15.4710	−0.663925
$544$	−2.58017	−0.110624
$545$	22.5929	0.967772
$546$	2.80825	0.120182
$547$	9.18213	0.392599	0.196300	−	0.980544i	$-0.437107\pi$
$547$	9.18213	0.392599	0.196300	+	0.980544i	$0.437107\pi$
$548$	−36.6904	−1.56734
$549$	−1.00000	−0.0426790
$550$	4.35257	0.185594
$551$	−3.05914	−0.130324
$552$	17.9736	0.765006
$553$	19.9339	0.847675
$554$	−2.63478	−0.111941
$555$	−9.14078	−0.388004
$556$	11.2495	0.477087
$557$	−27.0866	−1.14770	−0.573848	−	0.818962i	$-0.694550\pi$
$557$	−27.0866	−1.14770	−0.573848	+	0.818962i	$0.694550\pi$
$558$	0.962363	0.0407401
$559$	−1.43356	−0.0606329
$560$	37.0537	1.56580
$561$	−0.492960	−0.0208128
$562$	11.6587	0.491792
$563$	−15.3958	−0.648854	−0.324427	−	0.945911i	$-0.605171\pi$
$563$	−15.3958	−0.648854	−0.324427	+	0.945911i	$0.605171\pi$
$564$	11.0951	0.467189
$565$	8.22910	0.346201
$566$	2.76266	0.116123
$567$	4.31243	0.181105
$568$	−24.0334	−1.00842
$569$	8.58984	0.360105	0.180052	−	0.983657i	$-0.442373\pi$
$569$	8.58984	0.360105	0.180052	+	0.983657i	$0.442373\pi$
$570$	−1.76105	−0.0737621
$571$	30.5350	1.27785	0.638924	−	0.769270i	$-0.279380\pi$
$571$	30.5350	1.27785	0.638924	+	0.769270i	$0.279380\pi$
$572$	−2.09047	−0.0874068
$573$	18.2591	0.762787
$574$	8.07423	0.337012
$575$	73.8149	3.07829
$576$	−1.94340	−0.0809750
$577$	−30.0446	−1.25077	−0.625387	−	0.780315i	$-0.715059\pi$
$577$	−30.0446	−1.25077	−0.625387	+	0.780315i	$0.715059\pi$
$578$	8.95061	0.372296
$579$	−14.9462	−0.621144
$580$	20.9197	0.868642
$581$	−12.0766	−0.501023
$582$	−1.35126	−0.0560116
$583$	−7.40180	−0.306551
$584$	−19.6938	−0.814937
$585$	−4.42078	−0.182777
$586$	5.16452	0.213344
$587$	29.0280	1.19811	0.599057	−	0.800706i	$-0.295542\pi$
$587$	29.0280	1.19811	0.599057	+	0.800706i	$0.295542\pi$
$588$	−19.8854	−0.820062
$589$	−1.63816	−0.0674990
$590$	24.1008	0.992216
$591$	−5.53663	−0.227747
$592$	−5.97322	−0.245498
$593$	−40.3838	−1.65836	−0.829182	−	0.558979i	$-0.811193\pi$
$593$	−40.3838	−1.65836	−0.829182	+	0.558979i	$0.811193\pi$
$594$	0.534142	0.0219161
$595$	7.70861	0.316022
$596$	−27.3873	−1.12183
$597$	1.42160	0.0581821
$598$	5.89887	0.241223
$599$	34.3217	1.40235	0.701173	−	0.712992i	$-0.252660\pi$
$599$	34.3217	1.40235	0.701173	+	0.712992i	$0.252660\pi$
$600$	16.1685	0.660075
$601$	−27.5446	−1.12357	−0.561785	−	0.827284i	$-0.689885\pi$
$601$	−27.5446	−1.12357	−0.561785	+	0.827284i	$0.689885\pi$
$602$	−2.70855	−0.110392
$603$	−1.39825	−0.0569412
$604$	29.3814	1.19551
$605$	3.62612	0.147423
$606$	1.71383	0.0696196
$607$	−7.48437	−0.303781	−0.151891	−	0.988397i	$-0.548536\pi$
$607$	−7.48437	−0.303781	−0.151891	+	0.988397i	$0.548536\pi$
$608$	−4.75892	−0.193000
$609$	−14.5094	−0.587951
$610$	1.93686	0.0784212
$611$	7.88866	0.319141
$612$	−0.845275	−0.0341682
$613$	42.2994	1.70846	0.854229	−	0.519897i	$-0.174030\pi$
$613$	42.2994	1.70846	0.854229	+	0.519897i	$0.174030\pi$
$614$	−10.4781	−0.422861
$615$	−12.7105	−0.512538
$616$	−8.55661	−0.344756
$617$	−8.67487	−0.349237	−0.174619	−	0.984636i	$-0.555869\pi$
$617$	−8.67487	−0.349237	−0.174619	+	0.984636i	$0.555869\pi$
$618$	6.16407	0.247955
$619$	18.7219	0.752496	0.376248	−	0.926519i	$-0.377214\pi$
$619$	18.7219	0.752496	0.376248	+	0.926519i	$0.377214\pi$
$620$	11.2024	0.449899
$621$	9.05847	0.363504
$622$	−7.65483	−0.306931
$623$	52.1063	2.08759
$624$	−2.88884	−0.115646
$625$	0.658006	0.0263202
$626$	17.1819	0.686728
$627$	−0.909227	−0.0363110
$628$	−2.87958	−0.114908
$629$	−1.24266	−0.0495482
$630$	−8.35258	−0.332775
$631$	−2.06390	−0.0821626	−0.0410813	−	0.999156i	$-0.513080\pi$
$631$	−2.06390	−0.0821626	−0.0410813	+	0.999156i	$0.513080\pi$
$632$	9.17168	0.364830
$633$	−18.4855	−0.734732
$634$	13.8045	0.548248
$635$	12.6514	0.502057
$636$	−12.6918	−0.503263
$637$	−14.1386	−0.560191
$638$	−1.79715	−0.0711497
$639$	−12.1125	−0.479165
$640$	41.7224	1.64922
$641$	1.83897	0.0726350	0.0363175	−	0.999340i	$-0.488437\pi$
$641$	1.83897	0.0726350	0.0363175	+	0.999340i	$0.488437\pi$
$642$	5.78434	0.228290
$643$	−20.5058	−0.808670	−0.404335	−	0.914611i	$-0.632497\pi$
$643$	−20.5058	−0.808670	−0.404335	+	0.914611i	$0.632497\pi$
$644$	−66.9828	−2.63949
$645$	4.26382	0.167888
$646$	−0.239409	−0.00941943
$647$	−5.70352	−0.224228	−0.112114	−	0.993695i	$-0.535762\pi$
$647$	−5.70352	−0.224228	−0.112114	+	0.993695i	$0.535762\pi$
$648$	1.98417	0.0779457
$649$	12.4433	0.488440
$650$	5.30644	0.208136
$651$	−7.76971	−0.304519
$652$	−8.62775	−0.337889
$653$	−45.7322	−1.78964	−0.894819	−	0.446429i	$-0.852696\pi$
$653$	−45.7322	−1.78964	−0.894819	+	0.446429i	$0.852696\pi$
$654$	−3.32802	−0.130136
$655$	78.5453	3.06902
$656$	−8.30594	−0.324293
$657$	−9.92547	−0.387230
$658$	14.9048	0.581048
$659$	−2.76046	−0.107532	−0.0537661	−	0.998554i	$-0.517123\pi$
$659$	−2.76046	−0.107532	−0.0537661	+	0.998554i	$0.517123\pi$
$660$	6.21767	0.242023
$661$	−39.3593	−1.53090	−0.765449	−	0.643497i	$-0.777483\pi$
$661$	−39.3593	−1.53090	−0.765449	+	0.643497i	$0.777483\pi$
$662$	−3.71749	−0.144484
$663$	−0.600993	−0.0233406
$664$	−5.55651	−0.215635
$665$	14.2179	0.551348
$666$	1.34647	0.0521748
$667$	−30.4777	−1.18010
$668$	−28.4274	−1.09989
$669$	11.2160	0.433634
$670$	2.70822	0.104628
$671$	1.00000	0.0386046
$672$	−22.5714	−0.870710
$673$	37.2480	1.43580	0.717902	−	0.696144i	$-0.245103\pi$
$673$	37.2480	1.43580	0.717902	+	0.696144i	$0.245103\pi$
$674$	14.5088	0.558857
$675$	8.14872	0.313644
$676$	19.7424	0.759323
$677$	−2.89189	−0.111144	−0.0555721	−	0.998455i	$-0.517698\pi$
$677$	−2.89189	−0.111144	−0.0555721	+	0.998455i	$0.517698\pi$
$678$	−1.21218	−0.0465535
$679$	10.9095	0.418669
$680$	3.54677	0.136012
$681$	22.4464	0.860150
$682$	−0.962363	−0.0368508
$683$	51.1425	1.95691	0.978457	−	0.206449i	$-0.0661906\pi$
$683$	51.1425	1.95691	0.978457	+	0.206449i	$0.0661906\pi$
$684$	−1.55905	−0.0596116
$685$	77.5903	2.96457
$686$	−10.5892	−0.404296
$687$	21.4818	0.819580
$688$	2.78628	0.106226
$689$	−9.02390	−0.343783
$690$	−17.5450	−0.667926
$691$	−5.49790	−0.209150	−0.104575	−	0.994517i	$-0.533348\pi$
$691$	−5.49790	−0.209150	−0.104575	+	0.994517i	$0.533348\pi$
$692$	18.4325	0.700699
$693$	−4.31243	−0.163816
$694$	13.1203	0.498041
$695$	−23.7898	−0.902397
$696$	−6.67585	−0.253047
$697$	−1.72796	−0.0654512
$698$	−10.6413	−0.402781
$699$	−4.14079	−0.156619
$700$	−60.2557	−2.27745
$701$	2.46512	0.0931063	0.0465531	−	0.998916i	$-0.485176\pi$
$701$	2.46512	0.0931063	0.0465531	+	0.998916i	$0.485176\pi$
$702$	0.651199	0.0245779
$703$	−2.29200	−0.0864443
$704$	1.94340	0.0732447
$705$	−23.4632	−0.883676
$706$	−0.798379	−0.0300474
$707$	−13.8367	−0.520384
$708$	21.3363	0.801869
$709$	−9.77187	−0.366990	−0.183495	−	0.983021i	$-0.558741\pi$
$709$	−9.77187	−0.366990	−0.183495	+	0.983021i	$0.558741\pi$
$710$	23.4603	0.880449
$711$	4.62242	0.173354
$712$	23.9743	0.898477
$713$	−16.3206	−0.611213
$714$	−1.13551	−0.0424954
$715$	4.42078	0.165328
$716$	−27.1229	−1.01363
$717$	−10.5358	−0.393468
$718$	−7.17305	−0.267696
$719$	−5.87214	−0.218994	−0.109497	−	0.993987i	$-0.534924\pi$
$719$	−5.87214	−0.218994	−0.109497	+	0.993987i	$0.534924\pi$
$720$	8.59228	0.320216
$721$	−49.7661	−1.85339
$722$	9.70712	0.361262
$723$	−11.8063	−0.439082
$724$	26.5280	0.985906
$725$	−27.4168	−1.01823
$726$	−0.534142	−0.0198239
$727$	−24.9562	−0.925576	−0.462788	−	0.886469i	$-0.653151\pi$
$727$	−24.9562	−0.925576	−0.462788	+	0.886469i	$0.653151\pi$
$728$	−10.4318	−0.386628
$729$	1.00000	0.0370370
$730$	19.2242	0.711521
$731$	0.579655	0.0214393
$732$	1.71469	0.0633769
$733$	−3.63477	−0.134253	−0.0671266	−	0.997744i	$-0.521383\pi$
$733$	−3.63477	−0.134253	−0.0671266	+	0.997744i	$0.521383\pi$
$734$	9.28674	0.342780
$735$	42.0524	1.55113
$736$	−47.4122	−1.74764
$737$	1.39825	0.0515052
$738$	1.87231	0.0689208
$739$	−54.0129	−1.98690	−0.993448	−	0.114282i	$-0.963543\pi$
$739$	−54.0129	−1.98690	−0.993448	+	0.114282i	$0.963543\pi$
$740$	15.6736	0.576174
$741$	−1.10848	−0.0407212
$742$	−17.0497	−0.625913
$743$	−20.2219	−0.741870	−0.370935	−	0.928659i	$-0.620963\pi$
$743$	−20.2219	−0.741870	−0.370935	+	0.928659i	$0.620963\pi$
$744$	−3.57488	−0.131062
$745$	57.9168	2.12191
$746$	5.48813	0.200935
$747$	−2.80042	−0.102462
$748$	0.845275	0.0309063
$749$	−46.7003	−1.70639
$750$	−6.09862	−0.222690
$751$	−6.50255	−0.237281	−0.118641	−	0.992937i	$-0.537854\pi$
$751$	−6.50255	−0.237281	−0.118641	+	0.992937i	$0.537854\pi$
$752$	−15.3325	−0.559119
$753$	13.7725	0.501898
$754$	−2.19099	−0.0797912
$755$	−62.1339	−2.26128
$756$	−7.39450	−0.268935
$757$	−25.3404	−0.921013	−0.460507	−	0.887656i	$-0.652332\pi$
$757$	−25.3404	−0.921013	−0.460507	+	0.887656i	$0.652332\pi$
$758$	7.85100	0.285161
$759$	−9.05847	−0.328802
$760$	6.54174	0.237294
$761$	38.1316	1.38227	0.691135	−	0.722725i	$-0.257111\pi$
$761$	38.1316	1.38227	0.691135	+	0.722725i	$0.257111\pi$
$762$	−1.86361	−0.0675114
$763$	26.8690	0.972724
$764$	−31.3088	−1.13271
$765$	1.78753	0.0646283
$766$	−15.0124	−0.542421
$767$	15.1702	0.547764
$768$	−2.25909	−0.0815177
$769$	−25.0980	−0.905058	−0.452529	−	0.891750i	$-0.649478\pi$
$769$	−25.0980	−0.905058	−0.452529	+	0.891750i	$0.649478\pi$
$770$	8.35258	0.301006
$771$	−29.9006	−1.07684
$772$	25.6282	0.922378
$773$	14.8328	0.533500	0.266750	−	0.963766i	$-0.414050\pi$
$773$	14.8328	0.533500	0.266750	+	0.963766i	$0.414050\pi$
$774$	−0.628078	−0.0225758
$775$	−14.6815	−0.527377
$776$	5.01953	0.180190
$777$	−10.8709	−0.389990
$778$	−13.9342	−0.499566
$779$	−3.18709	−0.114189
$780$	7.58028	0.271418
$781$	12.1125	0.433421
$782$	−2.38519	−0.0852943
$783$	−3.36455	−0.120239
$784$	27.4799	0.981427
$785$	6.08955	0.217345
$786$	−11.5701	−0.412690
$787$	20.9211	0.745758	0.372879	−	0.927880i	$-0.378371\pi$
$787$	20.9211	0.745758	0.372879	+	0.927880i	$0.378371\pi$
$788$	9.49363	0.338196
$789$	−6.38562	−0.227334
$790$	−8.95298	−0.318533
$791$	9.78663	0.347973
$792$	−1.98417	−0.0705045
$793$	1.21915	0.0432933
$794$	−15.4736	−0.549137
$795$	26.8398	0.951909
$796$	−2.43760	−0.0863986
$797$	−50.6551	−1.79430	−0.897148	−	0.441730i	$-0.854365\pi$
$797$	−50.6551	−1.79430	−0.897148	+	0.441730i	$0.854365\pi$
$798$	−2.09436	−0.0741396
$799$	−3.18976	−0.112846
$800$	−42.6506	−1.50793
$801$	12.0828	0.426925
$802$	−8.37828	−0.295847
$803$	9.92547	0.350262
$804$	2.39757	0.0845558
$805$	141.651	4.99253
$806$	−1.17327	−0.0413265
$807$	26.0111	0.915633
$808$	−6.36635	−0.223967
$809$	−17.7140	−0.622792	−0.311396	−	0.950280i	$-0.600797\pi$
$809$	−17.7140	−0.622792	−0.311396	+	0.950280i	$0.600797\pi$
$810$	−1.93686	−0.0680543
$811$	28.1935	0.990009	0.495004	−	0.868890i	$-0.335166\pi$
$811$	28.1935	0.990009	0.495004	+	0.868890i	$0.335166\pi$
$812$	24.8792	0.873087
$813$	−0.817061	−0.0286556
$814$	−1.34647	−0.0471939
$815$	18.2454	0.639108
$816$	1.16810	0.0408916
$817$	1.06913	0.0374041
$818$	14.8205	0.518188
$819$	−5.25750	−0.183712
$820$	21.7946	0.761102
$821$	−43.3355	−1.51242	−0.756210	−	0.654329i	$-0.772951\pi$
$821$	−43.3355	−1.51242	−0.756210	+	0.654329i	$0.772951\pi$
$822$	−11.4294	−0.398645
$823$	39.0773	1.36215	0.681075	−	0.732214i	$-0.261513\pi$
$823$	39.0773	1.36215	0.681075	+	0.732214i	$0.261513\pi$
$824$	−22.8976	−0.797677
$825$	−8.14872	−0.283702
$826$	28.6624	0.997293
$827$	2.15211	0.0748363	0.0374181	−	0.999300i	$-0.488087\pi$
$827$	2.15211	0.0748363	0.0374181	+	0.999300i	$0.488087\pi$
$828$	−15.5325	−0.539791
$829$	33.0029	1.14624	0.573119	−	0.819472i	$-0.305733\pi$
$829$	33.0029	1.14624	0.573119	+	0.819472i	$0.305733\pi$
$830$	5.42402	0.188270
$831$	4.93273	0.171115
$832$	2.36930	0.0821406
$833$	5.71690	0.198079
$834$	3.50433	0.121345
$835$	60.1163	2.08041
$836$	1.55905	0.0539207
$837$	−1.80170	−0.0622759
$838$	−15.6667	−0.541196
$839$	17.0342	0.588086	0.294043	−	0.955792i	$-0.404999\pi$
$839$	17.0342	0.588086	0.294043	+	0.955792i	$0.404999\pi$
$840$	31.0273	1.07054
$841$	−17.6798	−0.609648
$842$	−11.0270	−0.380016
$843$	−21.8269	−0.751760
$844$	31.6969	1.09105
$845$	−41.7499	−1.43624
$846$	3.45623	0.118828
$847$	4.31243	0.148177
$848$	17.5390	0.602291
$849$	−5.17215	−0.177508
$850$	−2.14564	−0.0735950
$851$	−22.8348	−0.782765
$852$	20.7693	0.711544
$853$	46.1109	1.57881	0.789404	−	0.613873i	$-0.210390\pi$
$853$	46.1109	1.57881	0.789404	+	0.613873i	$0.210390\pi$
$854$	2.30345	0.0788225
$855$	3.29696	0.112754
$856$	−21.4870	−0.734412
$857$	−19.3678	−0.661591	−0.330796	−	0.943702i	$-0.607317\pi$
$857$	−19.3678	−0.661591	−0.330796	+	0.943702i	$0.607317\pi$
$858$	−0.651199	−0.0222316
$859$	26.8064	0.914622	0.457311	−	0.889307i	$-0.348813\pi$
$859$	26.8064	0.914622	0.457311	+	0.889307i	$0.348813\pi$
$860$	−7.31114	−0.249308
$861$	−15.1163	−0.515161
$862$	15.5659	0.530176
$863$	19.7597	0.672627	0.336313	−	0.941750i	$-0.390820\pi$
$863$	19.7597	0.672627	0.336313	+	0.941750i	$0.390820\pi$
$864$	−5.23402	−0.178065
$865$	−38.9799	−1.32535
$866$	−9.77330	−0.332110
$867$	−16.7570	−0.569097
$868$	13.3227	0.452201
$869$	−4.62242	−0.156805
$870$	6.51666	0.220936
$871$	1.70468	0.0577608
$872$	12.3626	0.418650
$873$	2.52978	0.0856202
$874$	−4.39930	−0.148809
$875$	49.2377	1.66454
$876$	17.0191	0.575023
$877$	55.2507	1.86568	0.932842	−	0.360285i	$-0.117321\pi$
$877$	55.2507	1.86568	0.932842	+	0.360285i	$0.117321\pi$
$878$	−11.3990	−0.384696
$879$	−9.66881	−0.326121
$880$	−8.59228	−0.289646
$881$	−7.93825	−0.267446	−0.133723	−	0.991019i	$-0.542693\pi$
$881$	−7.93825	−0.267446	−0.133723	+	0.991019i	$0.542693\pi$
$882$	−6.19449	−0.208579
$883$	−28.2610	−0.951058	−0.475529	−	0.879700i	$-0.657743\pi$
$883$	−28.2610	−0.951058	−0.475529	+	0.879700i	$0.657743\pi$
$884$	1.03052	0.0346601
$885$	−45.1207	−1.51671
$886$	−11.1318	−0.373979
$887$	42.0820	1.41297	0.706487	−	0.707726i	$-0.250279\pi$
$887$	42.0820	1.41297	0.706487	+	0.707726i	$0.250279\pi$
$888$	−5.00174	−0.167847
$889$	15.0460	0.504626
$890$	−23.4027	−0.784460
$891$	−1.00000	−0.0335013
$892$	−19.2319	−0.643933
$893$	−5.88327	−0.196876
$894$	−8.53138	−0.285332
$895$	57.3578	1.91726
$896$	49.6193	1.65766
$897$	−11.0436	−0.368736
$898$	6.97892	0.232890
$899$	6.06191	0.202176
$900$	−13.9725	−0.465751
$901$	3.64879	0.121559
$902$	−1.87231	−0.0623412
$903$	5.07084	0.168747
$904$	4.50288	0.149764
$905$	−56.0997	−1.86482
$906$	9.15258	0.304074
$907$	−21.4152	−0.711079	−0.355540	−	0.934661i	$-0.615703\pi$
$907$	−21.4152	−0.711079	−0.355540	+	0.934661i	$0.615703\pi$
$908$	−38.4887	−1.27729
$909$	−3.20857	−0.106421
$910$	10.1830	0.337565
$911$	6.72715	0.222880	0.111440	−	0.993771i	$-0.464454\pi$
$911$	6.72715	0.222880	0.111440	+	0.993771i	$0.464454\pi$
$912$	2.15447	0.0713415
$913$	2.80042	0.0926803
$914$	16.9567	0.560878
$915$	−3.62612	−0.119876
$916$	−36.8346	−1.21705
$917$	93.4117	3.08473
$918$	−0.263311	−0.00869055
$919$	−44.7382	−1.47578	−0.737888	−	0.674923i	$-0.764177\pi$
$919$	−44.7382	−1.47578	−0.737888	+	0.674923i	$0.764177\pi$
$920$	65.1742	2.14873
$921$	19.6167	0.646391
$922$	11.5153	0.379237
$923$	14.7670	0.486062
$924$	7.39450	0.243261
$925$	−20.5414	−0.675398
$926$	10.8662	0.357086
$927$	−11.5401	−0.379028
$928$	17.6101	0.578081
$929$	−38.6489	−1.26803	−0.634014	−	0.773322i	$-0.718594\pi$
$929$	−38.6489	−1.26803	−0.634014	+	0.773322i	$0.718594\pi$
$930$	3.48964	0.114430
$931$	10.5444	0.345578
$932$	7.10018	0.232574
$933$	14.3311	0.469179
$934$	0.664902	0.0217563
$935$	−1.78753	−0.0584585
$936$	−2.41900	−0.0790676
$937$	−39.2625	−1.28265	−0.641325	−	0.767269i	$-0.721615\pi$
$937$	−39.2625	−1.28265	−0.641325	+	0.767269i	$0.721615\pi$
$938$	3.22080	0.105163
$939$	−32.1674	−1.04974
$940$	40.2322	1.31223
$941$	19.1212	0.623332	0.311666	−	0.950192i	$-0.399113\pi$
$941$	19.1212	0.623332	0.311666	+	0.950192i	$0.399113\pi$
$942$	−0.897016	−0.0292264
$943$	−31.7524	−1.03400
$944$	−29.4850	−0.959654
$945$	15.6374	0.508684
$946$	0.628078	0.0204206
$947$	19.6358	0.638078	0.319039	−	0.947742i	$-0.396640\pi$
$947$	19.6358	0.638078	0.319039	+	0.947742i	$0.396640\pi$
$948$	−7.92603	−0.257425
$949$	12.1006	0.392803
$950$	−3.95748	−0.128397
$951$	−25.8443	−0.838059
$952$	4.21807	0.136708
$953$	−25.5350	−0.827160	−0.413580	−	0.910468i	$-0.635722\pi$
$953$	−25.5350	−0.827160	−0.413580	+	0.910468i	$0.635722\pi$
$954$	−3.95361	−0.128003
$955$	66.2098	2.14250
$956$	18.0657	0.584287
$957$	3.36455	0.108760
$958$	−7.99733	−0.258382
$959$	92.2759	2.97974
$960$	−7.04700	−0.227441
$961$	−27.7539	−0.895286
$962$	−1.64155	−0.0529258
$963$	−10.8292	−0.348967
$964$	20.2442	0.652023
$965$	−54.1967	−1.74465
$966$	−20.8657	−0.671344
$967$	55.0924	1.77165	0.885826	−	0.464018i	$-0.153593\pi$
$967$	55.0924	1.77165	0.885826	+	0.464018i	$0.153593\pi$
$968$	1.98417	0.0637737
$969$	0.448213	0.0143987
$970$	−4.89984	−0.157324
$971$	−7.43173	−0.238496	−0.119248	−	0.992865i	$-0.538048\pi$
$971$	−7.43173	−0.238496	−0.119248	+	0.992865i	$0.538048\pi$
$972$	−1.71469	−0.0549988
$973$	−28.2925	−0.907015
$974$	10.3547	0.331786
$975$	−9.93451	−0.318159
$976$	−2.36956	−0.0758476
$977$	22.8141	0.729889	0.364945	−	0.931029i	$-0.381088\pi$
$977$	22.8141	0.729889	0.364945	+	0.931029i	$0.381088\pi$
$978$	−2.68762	−0.0859406
$979$	−12.0828	−0.386168
$980$	−72.1069	−2.30337
$981$	6.23060	0.198928
$982$	6.77676	0.216255
$983$	28.4396	0.907081	0.453541	−	0.891236i	$-0.350161\pi$
$983$	28.4396	0.907081	0.453541	+	0.891236i	$0.350161\pi$
$984$	−6.95507	−0.221719
$985$	−20.0765	−0.639690
$986$	0.885922	0.0282135
$987$	−27.9041	−0.888198
$988$	1.90071	0.0604697
$989$	10.6515	0.338699
$990$	1.93686	0.0615575
$991$	−48.9700	−1.55558	−0.777791	−	0.628523i	$-0.783660\pi$
$991$	−48.9700	−1.55558	−0.777791	+	0.628523i	$0.783660\pi$
$992$	9.43014	0.299407
$993$	6.95974	0.220861
$994$	27.9006	0.884954
$995$	5.15488	0.163421
$996$	4.80186	0.152153
$997$	10.7047	0.339022	0.169511	−	0.985528i	$-0.445781\pi$
$997$	10.7047	0.339022	0.169511	+	0.985528i	$0.445781\pi$
$998$	−2.40309	−0.0760684
$999$	−2.52082	−0.0797552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.5	✓	13
3.2	odd	2		6039.2.a.g.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.5	✓	13	1.1	even	1	trivial
6039.2.a.g.1.9		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.534142 q^{2} +1.00000 q^{3} -1.71469 q^{4} +3.62612 q^{5} -0.534142 q^{6} +4.31243 q^{7} +1.98417 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.534142 q^{2} +1.00000 q^{3} -1.71469 q^{4} +3.62612 q^{5} -0.534142 q^{6} +4.31243 q^{7} +1.98417 q^{8} +1.00000 q^{9} -1.93686 q^{10} -1.00000 q^{11} -1.71469 q^{12} -1.21915 q^{13} -2.30345 q^{14} +3.62612 q^{15} +2.36956 q^{16} +0.492960 q^{17} -0.534142 q^{18} +0.909227 q^{19} -6.21767 q^{20} +4.31243 q^{21} +0.534142 q^{22} +9.05847 q^{23} +1.98417 q^{24} +8.14872 q^{25} +0.651199 q^{26} +1.00000 q^{27} -7.39450 q^{28} -3.36455 q^{29} -1.93686 q^{30} -1.80170 q^{31} -5.23402 q^{32} -1.00000 q^{33} -0.263311 q^{34} +15.6374 q^{35} -1.71469 q^{36} -2.52082 q^{37} -0.485656 q^{38} -1.21915 q^{39} +7.19484 q^{40} -3.50527 q^{41} -2.30345 q^{42} +1.17586 q^{43} +1.71469 q^{44} +3.62612 q^{45} -4.83851 q^{46} -6.47062 q^{47} +2.36956 q^{48} +11.5971 q^{49} -4.35257 q^{50} +0.492960 q^{51} +2.09047 q^{52} +7.40180 q^{53} -0.534142 q^{54} -3.62612 q^{55} +8.55661 q^{56} +0.909227 q^{57} +1.79715 q^{58} -12.4433 q^{59} -6.21767 q^{60} -1.00000 q^{61} +0.962363 q^{62} +4.31243 q^{63} -1.94340 q^{64} -4.42078 q^{65} +0.534142 q^{66} -1.39825 q^{67} -0.845275 q^{68} +9.05847 q^{69} -8.35258 q^{70} -12.1125 q^{71} +1.98417 q^{72} -9.92547 q^{73} +1.34647 q^{74} +8.14872 q^{75} -1.55905 q^{76} -4.31243 q^{77} +0.651199 q^{78} +4.62242 q^{79} +8.59228 q^{80} +1.00000 q^{81} +1.87231 q^{82} -2.80042 q^{83} -7.39450 q^{84} +1.78753 q^{85} -0.628078 q^{86} -3.36455 q^{87} -1.98417 q^{88} +12.0828 q^{89} -1.93686 q^{90} -5.25750 q^{91} -15.5325 q^{92} -1.80170 q^{93} +3.45623 q^{94} +3.29696 q^{95} -5.23402 q^{96} +2.52978 q^{97} -6.19449 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

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