LMFDB - Embedded newform 2013.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.12
Root			$2.30577$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30577 q^{2} +1.00000 q^{3} +3.31659 q^{4} -2.09861 q^{5} +2.30577 q^{6} +3.60849 q^{7} +3.03576 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.30577 q^{2} +1.00000 q^{3} +3.31659 q^{4} -2.09861 q^{5} +2.30577 q^{6} +3.60849 q^{7} +3.03576 q^{8} +1.00000 q^{9} -4.83892 q^{10} +1.00000 q^{11} +3.31659 q^{12} +2.44670 q^{13} +8.32036 q^{14} -2.09861 q^{15} +0.366596 q^{16} +3.44250 q^{17} +2.30577 q^{18} -3.95594 q^{19} -6.96024 q^{20} +3.60849 q^{21} +2.30577 q^{22} +0.849566 q^{23} +3.03576 q^{24} -0.595826 q^{25} +5.64153 q^{26} +1.00000 q^{27} +11.9679 q^{28} +6.57886 q^{29} -4.83892 q^{30} +3.69177 q^{31} -5.22624 q^{32} +1.00000 q^{33} +7.93762 q^{34} -7.57282 q^{35} +3.31659 q^{36} -7.31015 q^{37} -9.12149 q^{38} +2.44670 q^{39} -6.37089 q^{40} -1.36595 q^{41} +8.32036 q^{42} +1.86998 q^{43} +3.31659 q^{44} -2.09861 q^{45} +1.95891 q^{46} +1.31253 q^{47} +0.366596 q^{48} +6.02119 q^{49} -1.37384 q^{50} +3.44250 q^{51} +8.11469 q^{52} +3.81778 q^{53} +2.30577 q^{54} -2.09861 q^{55} +10.9545 q^{56} -3.95594 q^{57} +15.1694 q^{58} +9.31071 q^{59} -6.96024 q^{60} +1.00000 q^{61} +8.51239 q^{62} +3.60849 q^{63} -12.7837 q^{64} -5.13467 q^{65} +2.30577 q^{66} -6.57801 q^{67} +11.4174 q^{68} +0.849566 q^{69} -17.4612 q^{70} +1.57572 q^{71} +3.03576 q^{72} -10.7030 q^{73} -16.8556 q^{74} -0.595826 q^{75} -13.1202 q^{76} +3.60849 q^{77} +5.64153 q^{78} -10.4459 q^{79} -0.769343 q^{80} +1.00000 q^{81} -3.14957 q^{82} +7.24446 q^{83} +11.9679 q^{84} -7.22446 q^{85} +4.31176 q^{86} +6.57886 q^{87} +3.03576 q^{88} -7.28594 q^{89} -4.83892 q^{90} +8.82887 q^{91} +2.81766 q^{92} +3.69177 q^{93} +3.02640 q^{94} +8.30198 q^{95} -5.22624 q^{96} -9.05193 q^{97} +13.8835 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.30577	1.63043	0.815214	−	0.579160i	$-0.196619\pi$
$2$	2.30577	1.63043	0.815214	+	0.579160i	$0.196619\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.31659	1.65830
$5$	−2.09861	−0.938528	−0.469264	−	0.883058i	$-0.655481\pi$
$5$	−2.09861	−0.938528	−0.469264	+	0.883058i	$0.655481\pi$
$6$	2.30577	0.941328
$7$	3.60849	1.36388	0.681940	−	0.731408i	$-0.261136\pi$
$7$	3.60849	1.36388	0.681940	+	0.731408i	$0.261136\pi$
$8$	3.03576	1.07330
$9$	1.00000	0.333333
$10$	−4.83892	−1.53020
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.31659	0.957417
$13$	2.44670	0.678591	0.339296	−	0.940680i	$-0.389811\pi$
$13$	2.44670	0.678591	0.339296	+	0.940680i	$0.389811\pi$
$14$	8.32036	2.22371
$15$	−2.09861	−0.541859
$16$	0.366596	0.0916490
$17$	3.44250	0.834928	0.417464	−	0.908693i	$-0.362919\pi$
$17$	3.44250	0.834928	0.417464	+	0.908693i	$0.362919\pi$
$18$	2.30577	0.543476
$19$	−3.95594	−0.907554	−0.453777	−	0.891115i	$-0.649924\pi$
$19$	−3.95594	−0.907554	−0.453777	+	0.891115i	$0.649924\pi$
$20$	−6.96024	−1.55636
$21$	3.60849	0.787437
$22$	2.30577	0.491593
$23$	0.849566	0.177147	0.0885734	−	0.996070i	$-0.471769\pi$
$23$	0.849566	0.177147	0.0885734	+	0.996070i	$0.471769\pi$
$24$	3.03576	0.619672
$25$	−0.595826	−0.119165
$26$	5.64153	1.10639
$27$	1.00000	0.192450
$28$	11.9679	2.26172
$29$	6.57886	1.22166	0.610832	−	0.791760i	$-0.290835\pi$
$29$	6.57886	1.22166	0.610832	+	0.791760i	$0.290835\pi$
$30$	−4.83892	−0.883463
$31$	3.69177	0.663062	0.331531	−	0.943444i	$-0.392435\pi$
$31$	3.69177	0.663062	0.331531	+	0.943444i	$0.392435\pi$
$32$	−5.22624	−0.923877
$33$	1.00000	0.174078
$34$	7.93762	1.36129
$35$	−7.57282	−1.28004
$36$	3.31659	0.552765
$37$	−7.31015	−1.20178	−0.600891	−	0.799331i	$-0.705187\pi$
$37$	−7.31015	−1.20178	−0.600891	+	0.799331i	$0.705187\pi$
$38$	−9.12149	−1.47970
$39$	2.44670	0.391785
$40$	−6.37089	−1.00733
$41$	−1.36595	−0.213326	−0.106663	−	0.994295i	$-0.534017\pi$
$41$	−1.36595	−0.213326	−0.106663	+	0.994295i	$0.534017\pi$
$42$	8.32036	1.28386
$43$	1.86998	0.285170	0.142585	−	0.989783i	$-0.454459\pi$
$43$	1.86998	0.285170	0.142585	+	0.989783i	$0.454459\pi$
$44$	3.31659	0.499995
$45$	−2.09861	−0.312843
$46$	1.95891	0.288825
$47$	1.31253	0.191453	0.0957263	−	0.995408i	$-0.469483\pi$
$47$	1.31253	0.191453	0.0957263	+	0.995408i	$0.469483\pi$
$48$	0.366596	0.0529136
$49$	6.02119	0.860170
$50$	−1.37384	−0.194290
$51$	3.44250	0.482046
$52$	8.11469	1.12530
$53$	3.81778	0.524413	0.262206	−	0.965012i	$-0.415550\pi$
$53$	3.81778	0.524413	0.262206	+	0.965012i	$0.415550\pi$
$54$	2.30577	0.313776
$55$	−2.09861	−0.282977
$56$	10.9545	1.46386
$57$	−3.95594	−0.523977
$58$	15.1694	1.99183
$59$	9.31071	1.21215	0.606076	−	0.795407i	$-0.292743\pi$
$59$	9.31071	1.21215	0.606076	+	0.795407i	$0.292743\pi$
$60$	−6.96024	−0.898563
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	8.51239	1.08107
$63$	3.60849	0.454627
$64$	−12.7837	−1.59796
$65$	−5.13467	−0.636877
$66$	2.30577	0.283821
$67$	−6.57801	−0.803632	−0.401816	−	0.915721i	$-0.631621\pi$
$67$	−6.57801	−0.803632	−0.401816	+	0.915721i	$0.631621\pi$
$68$	11.4174	1.38456
$69$	0.849566	0.102276
$70$	−17.4612	−2.08701
$71$	1.57572	0.187004	0.0935020	−	0.995619i	$-0.470194\pi$
$71$	1.57572	0.187004	0.0935020	+	0.995619i	$0.470194\pi$
$72$	3.03576	0.357768
$73$	−10.7030	−1.25269	−0.626343	−	0.779548i	$-0.715449\pi$
$73$	−10.7030	−1.25269	−0.626343	+	0.779548i	$0.715449\pi$
$74$	−16.8556	−1.95942
$75$	−0.595826	−0.0688000
$76$	−13.1202	−1.50499
$77$	3.60849	0.411225
$78$	5.64153	0.638777
$79$	−10.4459	−1.17526	−0.587629	−	0.809130i	$-0.699939\pi$
$79$	−10.4459	−1.17526	−0.587629	+	0.809130i	$0.699939\pi$
$80$	−0.769343	−0.0860151
$81$	1.00000	0.111111
$82$	−3.14957	−0.347812
$83$	7.24446	0.795183	0.397591	−	0.917563i	$-0.369846\pi$
$83$	7.24446	0.795183	0.397591	+	0.917563i	$0.369846\pi$
$84$	11.9679	1.30580
$85$	−7.22446	−0.783603
$86$	4.31176	0.464949
$87$	6.57886	0.705328
$88$	3.03576	0.323613
$89$	−7.28594	−0.772309	−0.386154	−	0.922434i	$-0.626197\pi$
$89$	−7.28594	−0.772309	−0.386154	+	0.922434i	$0.626197\pi$
$90$	−4.83892	−0.510067
$91$	8.82887	0.925517
$92$	2.81766	0.293762
$93$	3.69177	0.382819
$94$	3.02640	0.312150
$95$	8.30198	0.851765
$96$	−5.22624	−0.533400
$97$	−9.05193	−0.919085	−0.459542	−	0.888156i	$-0.651987\pi$
$97$	−9.05193	−0.919085	−0.459542	+	0.888156i	$0.651987\pi$
$98$	13.8835	1.40245
$99$	1.00000	0.100504
$100$	−1.97611	−0.197611
$101$	−13.1346	−1.30694	−0.653472	−	0.756951i	$-0.726688\pi$
$101$	−13.1346	−1.30694	−0.653472	+	0.756951i	$0.726688\pi$
$102$	7.93762	0.785941
$103$	−0.0774333	−0.00762973	−0.00381487	−	0.999993i	$-0.501214\pi$
$103$	−0.0774333	−0.00762973	−0.00381487	+	0.999993i	$0.501214\pi$
$104$	7.42758	0.728335
$105$	−7.57282	−0.739031
$106$	8.80294	0.855017
$107$	10.0443	0.971017	0.485509	−	0.874232i	$-0.338634\pi$
$107$	10.0443	0.971017	0.485509	+	0.874232i	$0.338634\pi$
$108$	3.31659	0.319139
$109$	−0.477338	−0.0457207	−0.0228603	−	0.999739i	$-0.507277\pi$
$109$	−0.477338	−0.0457207	−0.0228603	+	0.999739i	$0.507277\pi$
$110$	−4.83892	−0.461373
$111$	−7.31015	−0.693849
$112$	1.32286	0.124998
$113$	7.10555	0.668434	0.334217	−	0.942496i	$-0.391528\pi$
$113$	7.10555	0.668434	0.334217	+	0.942496i	$0.391528\pi$
$114$	−9.12149	−0.854306
$115$	−1.78291	−0.166257
$116$	21.8194	2.02588
$117$	2.44670	0.226197
$118$	21.4684	1.97633
$119$	12.4222	1.13874
$120$	−6.37089	−0.581580
$121$	1.00000	0.0909091
$122$	2.30577	0.208755
$123$	−1.36595	−0.123164
$124$	12.2441	1.09955
$125$	11.7435	1.05037
$126$	8.32036	0.741236
$127$	−9.72051	−0.862556	−0.431278	−	0.902219i	$-0.641937\pi$
$127$	−9.72051	−0.862556	−0.431278	+	0.902219i	$0.641937\pi$
$128$	−19.0239	−1.68149
$129$	1.86998	0.164643
$130$	−11.8394	−1.03838
$131$	−15.9897	−1.39703	−0.698515	−	0.715595i	$-0.746155\pi$
$131$	−15.9897	−1.39703	−0.698515	+	0.715595i	$0.746155\pi$
$132$	3.31659	0.288672
$133$	−14.2749	−1.23780
$134$	−15.1674	−1.31026
$135$	−2.09861	−0.180620
$136$	10.4506	0.896131
$137$	5.95848	0.509067	0.254534	−	0.967064i	$-0.418078\pi$
$137$	5.95848	0.509067	0.254534	+	0.967064i	$0.418078\pi$
$138$	1.95891	0.166753
$139$	−18.8845	−1.60176	−0.800882	−	0.598822i	$-0.795636\pi$
$139$	−18.8845	−1.60176	−0.800882	+	0.598822i	$0.795636\pi$
$140$	−25.1159	−2.12268
$141$	1.31253	0.110535
$142$	3.63326	0.304896
$143$	2.44670	0.204603
$144$	0.366596	0.0305497
$145$	−13.8065	−1.14657
$146$	−24.6786	−2.04241
$147$	6.02119	0.496619
$148$	−24.2448	−1.99291
$149$	−1.10720	−0.0907052	−0.0453526	−	0.998971i	$-0.514441\pi$
$149$	−1.10720	−0.0907052	−0.0453526	+	0.998971i	$0.514441\pi$
$150$	−1.37384	−0.112174
$151$	−3.65928	−0.297788	−0.148894	−	0.988853i	$-0.547571\pi$
$151$	−3.65928	−0.297788	−0.148894	+	0.988853i	$0.547571\pi$
$152$	−12.0093	−0.974081
$153$	3.44250	0.278309
$154$	8.32036	0.670474
$155$	−7.74760	−0.622302
$156$	8.11469	0.649695
$157$	16.3738	1.30677	0.653386	−	0.757025i	$-0.273348\pi$
$157$	16.3738	1.30677	0.653386	+	0.757025i	$0.273348\pi$
$158$	−24.0859	−1.91617
$159$	3.81778	0.302770
$160$	10.9678	0.867084
$161$	3.06565	0.241607
$162$	2.30577	0.181159
$163$	−22.6137	−1.77124	−0.885620	−	0.464411i	$-0.846266\pi$
$163$	−22.6137	−1.77124	−0.885620	+	0.464411i	$0.846266\pi$
$164$	−4.53030	−0.353757
$165$	−2.09861	−0.163377
$166$	16.7041	1.29649
$167$	6.60139	0.510831	0.255416	−	0.966831i	$-0.417788\pi$
$167$	6.60139	0.510831	0.255416	+	0.966831i	$0.417788\pi$
$168$	10.9545	0.845159
$169$	−7.01368	−0.539514
$170$	−16.6580	−1.27761
$171$	−3.95594	−0.302518
$172$	6.20197	0.472896
$173$	3.71475	0.282427	0.141213	−	0.989979i	$-0.454900\pi$
$173$	3.71475	0.282427	0.141213	+	0.989979i	$0.454900\pi$
$174$	15.1694	1.14999
$175$	−2.15003	−0.162527
$176$	0.366596	0.0276332
$177$	9.31071	0.699836
$178$	−16.7997	−1.25919
$179$	0.0221268	0.00165384	0.000826918	−	1.00000i	$-0.499737\pi$
$179$	0.0221268	0.00165384	0.000826918		1.00000i	$0.499737\pi$
$180$	−6.96024	−0.518786
$181$	2.65161	0.197093	0.0985463	−	0.995132i	$-0.468581\pi$
$181$	2.65161	0.197093	0.0985463	+	0.995132i	$0.468581\pi$
$182$	20.3574	1.50899
$183$	1.00000	0.0739221
$184$	2.57908	0.190132
$185$	15.3412	1.12791
$186$	8.51239	0.624159
$187$	3.44250	0.251740
$188$	4.35314	0.317485
$189$	3.60849	0.262479
$190$	19.1425	1.38874
$191$	−15.8081	−1.14383	−0.571916	−	0.820312i	$-0.693800\pi$
$191$	−15.8081	−1.14383	−0.571916	+	0.820312i	$0.693800\pi$
$192$	−12.7837	−0.922585
$193$	0.933750	0.0672128	0.0336064	−	0.999435i	$-0.489301\pi$
$193$	0.933750	0.0672128	0.0336064	+	0.999435i	$0.489301\pi$
$194$	−20.8717	−1.49850
$195$	−5.13467	−0.367701
$196$	19.9698	1.42642
$197$	−2.77360	−0.197611	−0.0988053	−	0.995107i	$-0.531502\pi$
$197$	−2.77360	−0.197611	−0.0988053	+	0.995107i	$0.531502\pi$
$198$	2.30577	0.163864
$199$	−25.9480	−1.83940	−0.919702	−	0.392618i	$-0.871569\pi$
$199$	−25.9480	−1.83940	−0.919702	+	0.392618i	$0.871569\pi$
$200$	−1.80879	−0.127900
$201$	−6.57801	−0.463977
$202$	−30.2855	−2.13088
$203$	23.7397	1.66620
$204$	11.4174	0.799375
$205$	2.86660	0.200212
$206$	−0.178544	−0.0124397
$207$	0.849566	0.0590489
$208$	0.896949	0.0621922
$209$	−3.95594	−0.273638
$210$	−17.4612	−1.20494
$211$	15.7399	1.08358	0.541791	−	0.840513i	$-0.317746\pi$
$211$	15.7399	1.08358	0.541791	+	0.840513i	$0.317746\pi$
$212$	12.6620	0.869631
$213$	1.57572	0.107967
$214$	23.1598	1.58317
$215$	−3.92437	−0.267640
$216$	3.03576	0.206557
$217$	13.3217	0.904337
$218$	−1.10063	−0.0745443
$219$	−10.7030	−0.723239
$220$	−6.96024	−0.469259
$221$	8.42274	0.566575
$222$	−16.8556	−1.13127
$223$	9.57624	0.641272	0.320636	−	0.947202i	$-0.396103\pi$
$223$	9.57624	0.641272	0.320636	+	0.947202i	$0.396103\pi$
$224$	−18.8588	−1.26006
$225$	−0.595826	−0.0397217
$226$	16.3838	1.08983
$227$	−1.89689	−0.125901	−0.0629505	−	0.998017i	$-0.520051\pi$
$227$	−1.89689	−0.125901	−0.0629505	+	0.998017i	$0.520051\pi$
$228$	−13.1202	−0.868908
$229$	11.3024	0.746886	0.373443	−	0.927653i	$-0.378177\pi$
$229$	11.3024	0.746886	0.373443	+	0.927653i	$0.378177\pi$
$230$	−4.11098	−0.271070
$231$	3.60849	0.237421
$232$	19.9718	1.31122
$233$	−11.3109	−0.741004	−0.370502	−	0.928832i	$-0.620814\pi$
$233$	−11.3109	−0.741004	−0.370502	+	0.928832i	$0.620814\pi$
$234$	5.64153	0.368798
$235$	−2.75450	−0.179684
$236$	30.8798	2.01011
$237$	−10.4459	−0.678536
$238$	28.6428	1.85664
$239$	−22.3403	−1.44508	−0.722538	−	0.691331i	$-0.757025\pi$
$239$	−22.3403	−1.44508	−0.722538	+	0.691331i	$0.757025\pi$
$240$	−0.769343	−0.0496609
$241$	5.71726	0.368281	0.184141	−	0.982900i	$-0.441050\pi$
$241$	5.71726	0.368281	0.184141	+	0.982900i	$0.441050\pi$
$242$	2.30577	0.148221
$243$	1.00000	0.0641500
$244$	3.31659	0.212323
$245$	−12.6361	−0.807294
$246$	−3.14957	−0.200809
$247$	−9.67897	−0.615858
$248$	11.2073	0.711667
$249$	7.24446	0.459099
$250$	27.0778	1.71255
$251$	9.70844	0.612791	0.306396	−	0.951904i	$-0.400877\pi$
$251$	9.70844	0.612791	0.306396	+	0.951904i	$0.400877\pi$
$252$	11.9679	0.753906
$253$	0.849566	0.0534117
$254$	−22.4133	−1.40634
$255$	−7.22446	−0.452414
$256$	−18.2973	−1.14358
$257$	−10.8338	−0.675794	−0.337897	−	0.941183i	$-0.609716\pi$
$257$	−10.8338	−0.675794	−0.337897	+	0.941183i	$0.609716\pi$
$258$	4.31176	0.268438
$259$	−26.3786	−1.63909
$260$	−17.0296	−1.05613
$261$	6.57886	0.407221
$262$	−36.8687	−2.27776
$263$	−28.2215	−1.74021	−0.870107	−	0.492862i	$-0.835951\pi$
$263$	−28.2215	−1.74021	−0.870107	+	0.492862i	$0.835951\pi$
$264$	3.03576	0.186838
$265$	−8.01205	−0.492176
$266$	−32.9148	−2.01814
$267$	−7.28594	−0.445893
$268$	−21.8166	−1.33266
$269$	25.5430	1.55739	0.778693	−	0.627405i	$-0.215883\pi$
$269$	25.5430	1.55739	0.778693	+	0.627405i	$0.215883\pi$
$270$	−4.83892	−0.294488
$271$	12.0251	0.730475	0.365238	−	0.930914i	$-0.380988\pi$
$271$	12.0251	0.730475	0.365238	+	0.930914i	$0.380988\pi$
$272$	1.26201	0.0765203
$273$	8.82887	0.534348
$274$	13.7389	0.829997
$275$	−0.595826	−0.0359296
$276$	2.81766	0.169603
$277$	3.26431	0.196133	0.0980667	−	0.995180i	$-0.468734\pi$
$277$	3.26431	0.196133	0.0980667	+	0.995180i	$0.468734\pi$
$278$	−43.5434	−2.61156
$279$	3.69177	0.221021
$280$	−22.9893	−1.37387
$281$	5.40234	0.322277	0.161138	−	0.986932i	$-0.448483\pi$
$281$	5.40234	0.322277	0.161138	+	0.986932i	$0.448483\pi$
$282$	3.02640	0.180220
$283$	16.7426	0.995244	0.497622	−	0.867394i	$-0.334207\pi$
$283$	16.7426	0.995244	0.497622	+	0.867394i	$0.334207\pi$
$284$	5.22603	0.310108
$285$	8.30198	0.491767
$286$	5.64153	0.333590
$287$	−4.92902	−0.290951
$288$	−5.22624	−0.307959
$289$	−5.14922	−0.302895
$290$	−31.8346	−1.86939
$291$	−9.05193	−0.530634
$292$	−35.4973	−2.07732
$293$	−12.2361	−0.714841	−0.357421	−	0.933943i	$-0.616344\pi$
$293$	−12.2361	−0.714841	−0.357421	+	0.933943i	$0.616344\pi$
$294$	13.8835	0.809702
$295$	−19.5396	−1.13764
$296$	−22.1919	−1.28988
$297$	1.00000	0.0580259
$298$	−2.55295	−0.147888
$299$	2.07863	0.120210
$300$	−1.97611	−0.114091
$301$	6.74781	0.388938
$302$	−8.43747	−0.485522
$303$	−13.1346	−0.754564
$304$	−1.45023	−0.0831764
$305$	−2.09861	−0.120166
$306$	7.93762	0.453763
$307$	19.9409	1.13809	0.569045	−	0.822306i	$-0.307313\pi$
$307$	19.9409	1.13809	0.569045	+	0.822306i	$0.307313\pi$
$308$	11.9679	0.681933
$309$	−0.0774333	−0.00440503
$310$	−17.8642	−1.01462
$311$	26.8239	1.52104	0.760521	−	0.649314i	$-0.224944\pi$
$311$	26.8239	1.52104	0.760521	+	0.649314i	$0.224944\pi$
$312$	7.42758	0.420504
$313$	−14.8393	−0.838768	−0.419384	−	0.907809i	$-0.637754\pi$
$313$	−14.8393	−0.838768	−0.419384	+	0.907809i	$0.637754\pi$
$314$	37.7543	2.13060
$315$	−7.57282	−0.426680
$316$	−34.6449	−1.94893
$317$	−29.2085	−1.64051	−0.820257	−	0.571996i	$-0.806169\pi$
$317$	−29.2085	−1.64051	−0.820257	+	0.571996i	$0.806169\pi$
$318$	8.80294	0.493644
$319$	6.57886	0.368345
$320$	26.8281	1.49973
$321$	10.0443	0.560617
$322$	7.06869	0.393923
$323$	−13.6183	−0.757742
$324$	3.31659	0.184255
$325$	−1.45780	−0.0808644
$326$	−52.1420	−2.88788
$327$	−0.477338	−0.0263968
$328$	−4.14670	−0.228963
$329$	4.73626	0.261119
$330$	−4.83892	−0.266374
$331$	11.9108	0.654674	0.327337	−	0.944908i	$-0.393849\pi$
$331$	11.9108	0.654674	0.327337	+	0.944908i	$0.393849\pi$
$332$	24.0269	1.31865
$333$	−7.31015	−0.400594
$334$	15.2213	0.832873
$335$	13.8047	0.754231
$336$	1.32286	0.0721678
$337$	13.2602	0.722331	0.361165	−	0.932502i	$-0.382379\pi$
$337$	13.2602	0.722331	0.361165	+	0.932502i	$0.382379\pi$
$338$	−16.1720	−0.879639
$339$	7.10555	0.385920
$340$	−23.9606	−1.29945
$341$	3.69177	0.199921
$342$	−9.12149	−0.493234
$343$	−3.53203	−0.190711
$344$	5.67682	0.306074
$345$	−1.78291	−0.0959886
$346$	8.56536	0.460477
$347$	−16.6739	−0.895104	−0.447552	−	0.894258i	$-0.647704\pi$
$347$	−16.6739	−0.895104	−0.447552	+	0.894258i	$0.647704\pi$
$348$	21.8194	1.16964
$349$	−0.284417	−0.0152245	−0.00761224	−	0.999971i	$-0.502423\pi$
$349$	−0.284417	−0.0152245	−0.00761224	+	0.999971i	$0.502423\pi$
$350$	−4.95748	−0.264989
$351$	2.44670	0.130595
$352$	−5.22624	−0.278559
$353$	7.72741	0.411289	0.205644	−	0.978627i	$-0.434071\pi$
$353$	7.72741	0.411289	0.205644	+	0.978627i	$0.434071\pi$
$354$	21.4684	1.14103
$355$	−3.30683	−0.175508
$356$	−24.1645	−1.28072
$357$	12.4222	0.657453
$358$	0.0510194	0.00269646
$359$	−10.6405	−0.561584	−0.280792	−	0.959769i	$-0.590597\pi$
$359$	−10.6405	−0.561584	−0.280792	+	0.959769i	$0.590597\pi$
$360$	−6.37089	−0.335775
$361$	−3.35057	−0.176346
$362$	6.11401	0.321345
$363$	1.00000	0.0524864
$364$	29.2818	1.53478
$365$	22.4614	1.17568
$366$	2.30577	0.120525
$367$	−21.2539	−1.10944	−0.554722	−	0.832036i	$-0.687175\pi$
$367$	−21.2539	−1.10944	−0.554722	+	0.832036i	$0.687175\pi$
$368$	0.311447	0.0162353
$369$	−1.36595	−0.0711085
$370$	35.3733	1.83897
$371$	13.7764	0.715236
$372$	12.2441	0.634827
$373$	−5.68945	−0.294588	−0.147294	−	0.989093i	$-0.547056\pi$
$373$	−5.68945	−0.294588	−0.147294	+	0.989093i	$0.547056\pi$
$374$	7.93762	0.410444
$375$	11.7435	0.606430
$376$	3.98454	0.205487
$377$	16.0965	0.829010
$378$	8.32036	0.427953
$379$	16.8224	0.864109	0.432054	−	0.901848i	$-0.357789\pi$
$379$	16.8224	0.864109	0.432054	+	0.901848i	$0.357789\pi$
$380$	27.5343	1.41248
$381$	−9.72051	−0.497997
$382$	−36.4498	−1.86493
$383$	31.0487	1.58651	0.793256	−	0.608888i	$-0.208384\pi$
$383$	31.0487	1.58651	0.793256	+	0.608888i	$0.208384\pi$
$384$	−19.0239	−0.970808
$385$	−7.57282	−0.385947
$386$	2.15302	0.109586
$387$	1.86998	0.0950566
$388$	−30.0216	−1.52411
$389$	14.5335	0.736880	0.368440	−	0.929652i	$-0.379892\pi$
$389$	14.5335	0.736880	0.368440	+	0.929652i	$0.379892\pi$
$390$	−11.8394	−0.599510
$391$	2.92463	0.147905
$392$	18.2789	0.923224
$393$	−15.9897	−0.806576
$394$	−6.39528	−0.322190
$395$	21.9220	1.10301
$396$	3.31659	0.166665
$397$	29.9888	1.50510	0.752548	−	0.658537i	$-0.228824\pi$
$397$	29.9888	1.50510	0.752548	+	0.658537i	$0.228824\pi$
$398$	−59.8302	−2.99901
$399$	−14.2749	−0.714641
$400$	−0.218427	−0.0109214
$401$	12.7323	0.635819	0.317910	−	0.948121i	$-0.397019\pi$
$401$	12.7323	0.635819	0.317910	+	0.948121i	$0.397019\pi$
$402$	−15.1674	−0.756481
$403$	9.03264	0.449948
$404$	−43.5622	−2.16730
$405$	−2.09861	−0.104281
$406$	54.7385	2.71662
$407$	−7.31015	−0.362351
$408$	10.4506	0.517382
$409$	5.25522	0.259854	0.129927	−	0.991524i	$-0.458526\pi$
$409$	5.25522	0.259854	0.129927	+	0.991524i	$0.458526\pi$
$410$	6.60973	0.326431
$411$	5.95848	0.293910
$412$	−0.256815	−0.0126524
$413$	33.5976	1.65323
$414$	1.95891	0.0962750
$415$	−15.2033	−0.746301
$416$	−12.7870	−0.626935
$417$	−18.8845	−0.924779
$418$	−9.12149	−0.446147
$419$	−8.30152	−0.405556	−0.202778	−	0.979225i	$-0.564997\pi$
$419$	−8.30152	−0.405556	−0.202778	+	0.979225i	$0.564997\pi$
$420$	−25.1159	−1.22553
$421$	26.9565	1.31378	0.656888	−	0.753988i	$-0.271872\pi$
$421$	26.9565	1.31378	0.656888	+	0.753988i	$0.271872\pi$
$422$	36.2927	1.76670
$423$	1.31253	0.0638175
$424$	11.5899	0.562854
$425$	−2.05113	−0.0994943
$426$	3.63326	0.176032
$427$	3.60849	0.174627
$428$	33.3128	1.61023
$429$	2.44670	0.118128
$430$	−9.04871	−0.436368
$431$	2.04059	0.0982916	0.0491458	−	0.998792i	$-0.484350\pi$
$431$	2.04059	0.0982916	0.0491458	+	0.998792i	$0.484350\pi$
$432$	0.366596	0.0176379
$433$	39.8409	1.91463	0.957315	−	0.289046i	$-0.0933379\pi$
$433$	39.8409	1.91463	0.957315	+	0.289046i	$0.0933379\pi$
$434$	30.7169	1.47446
$435$	−13.8065	−0.661970
$436$	−1.58313	−0.0758184
$437$	−3.36083	−0.160770
$438$	−24.6786	−1.17919
$439$	29.4294	1.40459	0.702295	−	0.711886i	$-0.252159\pi$
$439$	29.4294	1.40459	0.702295	+	0.711886i	$0.252159\pi$
$440$	−6.37089	−0.303720
$441$	6.02119	0.286723
$442$	19.4209	0.923759
$443$	−12.7009	−0.603440	−0.301720	−	0.953397i	$-0.597561\pi$
$443$	−12.7009	−0.603440	−0.301720	+	0.953397i	$0.597561\pi$
$444$	−24.2448	−1.15061
$445$	15.2904	0.724833
$446$	22.0806	1.04555
$447$	−1.10720	−0.0523687
$448$	−46.1299	−2.17943
$449$	2.91417	0.137528	0.0687642	−	0.997633i	$-0.478094\pi$
$449$	2.91417	0.137528	0.0687642	+	0.997633i	$0.478094\pi$
$450$	−1.37384	−0.0647634
$451$	−1.36595	−0.0643201
$452$	23.5662	1.10846
$453$	−3.65928	−0.171928
$454$	−4.37380	−0.205272
$455$	−18.5284	−0.868624
$456$	−12.0093	−0.562386
$457$	7.73512	0.361834	0.180917	−	0.983498i	$-0.442093\pi$
$457$	7.73512	0.361834	0.180917	+	0.983498i	$0.442093\pi$
$458$	26.0608	1.21774
$459$	3.44250	0.160682
$460$	−5.91318	−0.275704
$461$	10.8482	0.505253	0.252626	−	0.967564i	$-0.418706\pi$
$461$	10.8482	0.505253	0.252626	+	0.967564i	$0.418706\pi$
$462$	8.32036	0.387098
$463$	−4.66601	−0.216848	−0.108424	−	0.994105i	$-0.534580\pi$
$463$	−4.66601	−0.216848	−0.108424	+	0.994105i	$0.534580\pi$
$464$	2.41178	0.111964
$465$	−7.74760	−0.359286
$466$	−26.0805	−1.20815
$467$	−24.7863	−1.14697	−0.573486	−	0.819215i	$-0.694409\pi$
$467$	−24.7863	−1.14697	−0.573486	+	0.819215i	$0.694409\pi$
$468$	8.11469	0.375102
$469$	−23.7367	−1.09606
$470$	−6.35125	−0.292961
$471$	16.3738	0.754465
$472$	28.2651	1.30101
$473$	1.86998	0.0859819
$474$	−24.0859	−1.10630
$475$	2.35705	0.108149
$476$	41.1994	1.88837
$477$	3.81778	0.174804
$478$	−51.5118	−2.35609
$479$	1.13037	0.0516481	0.0258240	−	0.999667i	$-0.491779\pi$
$479$	1.13037	0.0516481	0.0258240	+	0.999667i	$0.491779\pi$
$480$	10.9678	0.500611
$481$	−17.8857	−0.815518
$482$	13.1827	0.600456
$483$	3.06565	0.139492
$484$	3.31659	0.150754
$485$	18.9965	0.862587
$486$	2.30577	0.104592
$487$	25.9042	1.17383	0.586916	−	0.809647i	$-0.300342\pi$
$487$	25.9042	1.17383	0.586916	+	0.809647i	$0.300342\pi$
$488$	3.03576	0.137422
$489$	−22.6137	−1.02263
$490$	−29.1361	−1.31623
$491$	34.4568	1.55502	0.777508	−	0.628873i	$-0.216484\pi$
$491$	34.4568	1.55502	0.777508	+	0.628873i	$0.216484\pi$
$492$	−4.53030	−0.204242
$493$	22.6477	1.02000
$494$	−22.3175	−1.00411
$495$	−2.09861	−0.0943256
$496$	1.35339	0.0607689
$497$	5.68598	0.255051
$498$	16.7041	0.748528
$499$	−22.1313	−0.990735	−0.495368	−	0.868683i	$-0.664967\pi$
$499$	−22.1313	−0.990735	−0.495368	+	0.868683i	$0.664967\pi$
$500$	38.9483	1.74182
$501$	6.60139	0.294929
$502$	22.3855	0.999112
$503$	−24.1431	−1.07649	−0.538244	−	0.842789i	$-0.680912\pi$
$503$	−24.1431	−1.07649	−0.538244	+	0.842789i	$0.680912\pi$
$504$	10.9545	0.487953
$505$	27.5645	1.22660
$506$	1.95891	0.0870840
$507$	−7.01368	−0.311489
$508$	−32.2390	−1.43037
$509$	27.8837	1.23592	0.617961	−	0.786209i	$-0.287959\pi$
$509$	27.8837	1.23592	0.617961	+	0.786209i	$0.287959\pi$
$510$	−16.6580	−0.737628
$511$	−38.6215	−1.70851
$512$	−4.14171	−0.183040
$513$	−3.95594	−0.174659
$514$	−24.9803	−1.10183
$515$	0.162503	0.00716072
$516$	6.20197	0.273027
$517$	1.31253	0.0577251
$518$	−60.8231	−2.67241
$519$	3.71475	0.163059
$520$	−15.5876	−0.683562
$521$	43.5182	1.90657	0.953283	−	0.302078i	$-0.0976804\pi$
$521$	43.5182	1.90657	0.953283	+	0.302078i	$0.0976804\pi$
$522$	15.1694	0.663945
$523$	25.2483	1.10403	0.552016	−	0.833833i	$-0.313859\pi$
$523$	25.2483	1.10403	0.552016	+	0.833833i	$0.313859\pi$
$524$	−53.0314	−2.31669
$525$	−2.15003	−0.0938350
$526$	−65.0725	−2.83730
$527$	12.7089	0.553609
$528$	0.366596	0.0159540
$529$	−22.2782	−0.968619
$530$	−18.4740	−0.802458
$531$	9.31071	0.404050
$532$	−47.3442	−2.05263
$533$	−3.34206	−0.144761
$534$	−16.7997	−0.726996
$535$	−21.0791	−0.911327
$536$	−19.9693	−0.862541
$537$	0.0221268	0.000954842 0
$538$	58.8964	2.53921
$539$	6.02119	0.259351
$540$	−6.96024	−0.299521
$541$	28.8646	1.24098	0.620492	−	0.784213i	$-0.286933\pi$
$541$	28.8646	1.24098	0.620492	+	0.784213i	$0.286933\pi$
$542$	27.7272	1.19099
$543$	2.65161	0.113791
$544$	−17.9913	−0.771370
$545$	1.00175	0.0429101
$546$	20.3574	0.871215
$547$	13.7523	0.588006	0.294003	−	0.955805i	$-0.405012\pi$
$547$	13.7523	0.588006	0.294003	+	0.955805i	$0.405012\pi$
$548$	19.7618	0.844184
$549$	1.00000	0.0426790
$550$	−1.37384	−0.0585807
$551$	−26.0255	−1.10873
$552$	2.57908	0.109773
$553$	−37.6940	−1.60291
$554$	7.52676	0.319782
$555$	15.3412	0.651197
$556$	−62.6323	−2.65620
$557$	9.73016	0.412280	0.206140	−	0.978523i	$-0.433910\pi$
$557$	9.73016	0.412280	0.206140	+	0.978523i	$0.433910\pi$
$558$	8.51239	0.360358
$559$	4.57528	0.193514
$560$	−2.77617	−0.117314
$561$	3.44250	0.145342
$562$	12.4566	0.525449
$563$	18.6299	0.785157	0.392578	−	0.919719i	$-0.371583\pi$
$563$	18.6299	0.785157	0.392578	+	0.919719i	$0.371583\pi$
$564$	4.35314	0.183300
$565$	−14.9118	−0.627344
$566$	38.6046	1.62267
$567$	3.60849	0.151542
$568$	4.78352	0.200712
$569$	7.57312	0.317482	0.158741	−	0.987320i	$-0.449257\pi$
$569$	7.57312	0.317482	0.158741	+	0.987320i	$0.449257\pi$
$570$	19.1425	0.801790
$571$	−19.6633	−0.822883	−0.411442	−	0.911436i	$-0.634975\pi$
$571$	−19.6633	−0.822883	−0.411442	+	0.911436i	$0.634975\pi$
$572$	8.11469	0.339292
$573$	−15.8081	−0.660391
$574$	−11.3652	−0.474374
$575$	−0.506193	−0.0211097
$576$	−12.7837	−0.532655
$577$	−15.6768	−0.652633	−0.326317	−	0.945261i	$-0.605808\pi$
$577$	−15.6768	−0.652633	−0.326317	+	0.945261i	$0.605808\pi$
$578$	−11.8729	−0.493849
$579$	0.933750	0.0388053
$580$	−45.7904	−1.90134
$581$	26.1415	1.08453
$582$	−20.8717	−0.865160
$583$	3.81778	0.158116
$584$	−32.4916	−1.34451
$585$	−5.13467	−0.212292
$586$	−28.2137	−1.16550
$587$	12.6646	0.522722	0.261361	−	0.965241i	$-0.415829\pi$
$587$	12.6646	0.522722	0.261361	+	0.965241i	$0.415829\pi$
$588$	19.9698	0.823542
$589$	−14.6044	−0.601764
$590$	−45.0538	−1.85484
$591$	−2.77360	−0.114090
$592$	−2.67987	−0.110142
$593$	−26.1463	−1.07370	−0.536850	−	0.843678i	$-0.680386\pi$
$593$	−26.1463	−1.07370	−0.536850	+	0.843678i	$0.680386\pi$
$594$	2.30577	0.0946070
$595$	−26.0694	−1.06874
$596$	−3.67212	−0.150416
$597$	−25.9480	−1.06198
$598$	4.79285	0.195994
$599$	−8.73226	−0.356791	−0.178395	−	0.983959i	$-0.557091\pi$
$599$	−8.73226	−0.356791	−0.178395	+	0.983959i	$0.557091\pi$
$600$	−1.80879	−0.0738433
$601$	−37.8295	−1.54310	−0.771550	−	0.636169i	$-0.780518\pi$
$601$	−37.8295	−1.54310	−0.771550	+	0.636169i	$0.780518\pi$
$602$	15.5589	0.634135
$603$	−6.57801	−0.267877
$604$	−12.1363	−0.493821
$605$	−2.09861	−0.0853207
$606$	−30.2855	−1.23026
$607$	−6.10934	−0.247970	−0.123985	−	0.992284i	$-0.539568\pi$
$607$	−6.10934	−0.247970	−0.123985	+	0.992284i	$0.539568\pi$
$608$	20.6747	0.838468
$609$	23.7397	0.961983
$610$	−4.83892	−0.195922
$611$	3.21137	0.129918
$612$	11.4174	0.461519
$613$	−17.5729	−0.709761	−0.354881	−	0.934912i	$-0.615478\pi$
$613$	−17.5729	−0.709761	−0.354881	+	0.934912i	$0.615478\pi$
$614$	45.9793	1.85557
$615$	2.86660	0.115592
$616$	10.9545	0.441370
$617$	−12.4187	−0.499956	−0.249978	−	0.968251i	$-0.580423\pi$
$617$	−12.4187	−0.499956	−0.249978	+	0.968251i	$0.580423\pi$
$618$	−0.178544	−0.00718208
$619$	43.2786	1.73951	0.869756	−	0.493481i	$-0.164276\pi$
$619$	43.2786	1.73951	0.869756	+	0.493481i	$0.164276\pi$
$620$	−25.6956	−1.03196
$621$	0.849566	0.0340919
$622$	61.8497	2.47995
$623$	−26.2912	−1.05334
$624$	0.896949	0.0359067
$625$	−21.6659	−0.866635
$626$	−34.2161	−1.36755
$627$	−3.95594	−0.157985
$628$	54.3052	2.16702
$629$	−25.1652	−1.00340
$630$	−17.4612	−0.695671
$631$	18.2006	0.724553	0.362276	−	0.932071i	$-0.382000\pi$
$631$	18.2006	0.724553	0.362276	+	0.932071i	$0.382000\pi$
$632$	−31.7113	−1.26141
$633$	15.7399	0.625606
$634$	−67.3482	−2.67474
$635$	20.3996	0.809533
$636$	12.6620	0.502082
$637$	14.7320	0.583704
$638$	15.1694	0.600561
$639$	1.57572	0.0623346
$640$	39.9237	1.57812
$641$	43.7711	1.72886	0.864428	−	0.502756i	$-0.167681\pi$
$641$	43.7711	1.72886	0.864428	+	0.502756i	$0.167681\pi$
$642$	23.1598	0.914046
$643$	−7.68280	−0.302980	−0.151490	−	0.988459i	$-0.548407\pi$
$643$	−7.68280	−0.302980	−0.151490	+	0.988459i	$0.548407\pi$
$644$	10.1675	0.400656
$645$	−3.92437	−0.154522
$646$	−31.4007	−1.23544
$647$	19.6661	0.773154	0.386577	−	0.922257i	$-0.373657\pi$
$647$	19.6661	0.773154	0.386577	+	0.922257i	$0.373657\pi$
$648$	3.03576	0.119256
$649$	9.31071	0.365477
$650$	−3.36137	−0.131844
$651$	13.3217	0.522119
$652$	−75.0003	−2.93724
$653$	−44.2287	−1.73080	−0.865401	−	0.501079i	$-0.832936\pi$
$653$	−44.2287	−1.73080	−0.865401	+	0.501079i	$0.832936\pi$
$654$	−1.10063	−0.0430382
$655$	33.5563	1.31115
$656$	−0.500752	−0.0195511
$657$	−10.7030	−0.417562
$658$	10.9207	0.425735
$659$	14.1182	0.549969	0.274984	−	0.961449i	$-0.411327\pi$
$659$	14.1182	0.549969	0.274984	+	0.961449i	$0.411327\pi$
$660$	−6.96024	−0.270927
$661$	−7.40942	−0.288193	−0.144097	−	0.989564i	$-0.546028\pi$
$661$	−7.40942	−0.288193	−0.144097	+	0.989564i	$0.546028\pi$
$662$	27.4635	1.06740
$663$	8.42274	0.327112
$664$	21.9925	0.853473
$665$	29.9576	1.16171
$666$	−16.8556	−0.653139
$667$	5.58917	0.216414
$668$	21.8941	0.847109
$669$	9.57624	0.370239
$670$	31.8305	1.22972
$671$	1.00000	0.0386046
$672$	−18.8588	−0.727495
$673$	−22.9392	−0.884242	−0.442121	−	0.896956i	$-0.645774\pi$
$673$	−22.9392	−0.884242	−0.442121	+	0.896956i	$0.645774\pi$
$674$	30.5751	1.17771
$675$	−0.595826	−0.0229333
$676$	−23.2615	−0.894674
$677$	11.1592	0.428882	0.214441	−	0.976737i	$-0.431207\pi$
$677$	11.1592	0.428882	0.214441	+	0.976737i	$0.431207\pi$
$678$	16.3838	0.629215
$679$	−32.6638	−1.25352
$680$	−21.9318	−0.841044
$681$	−1.89689	−0.0726889
$682$	8.51239	0.325956
$683$	−25.6000	−0.979558	−0.489779	−	0.871847i	$-0.662923\pi$
$683$	−25.6000	−0.979558	−0.489779	+	0.871847i	$0.662923\pi$
$684$	−13.1202	−0.501664
$685$	−12.5045	−0.477774
$686$	−8.14405	−0.310941
$687$	11.3024	0.431215
$688$	0.685528	0.0261355
$689$	9.34095	0.355862
$690$	−4.11098	−0.156503
$691$	35.4260	1.34767	0.673834	−	0.738883i	$-0.264646\pi$
$691$	35.4260	1.34767	0.673834	+	0.738883i	$0.264646\pi$
$692$	12.3203	0.468347
$693$	3.60849	0.137075
$694$	−38.4463	−1.45940
$695$	39.6313	1.50330
$696$	19.9718	0.757031
$697$	−4.70228	−0.178111
$698$	−0.655801	−0.0248224
$699$	−11.3109	−0.427819
$700$	−7.13077	−0.269518
$701$	−30.1134	−1.13737	−0.568684	−	0.822556i	$-0.692547\pi$
$701$	−30.1134	−1.13737	−0.568684	+	0.822556i	$0.692547\pi$
$702$	5.64153	0.212926
$703$	28.9185	1.09068
$704$	−12.7837	−0.481804
$705$	−2.75450	−0.103740
$706$	17.8177	0.670576
$707$	−47.3961	−1.78252
$708$	30.8798	1.16053
$709$	−20.6377	−0.775067	−0.387533	−	0.921856i	$-0.626673\pi$
$709$	−20.6377	−0.775067	−0.387533	+	0.921856i	$0.626673\pi$
$710$	−7.62481	−0.286154
$711$	−10.4459	−0.391753
$712$	−22.1184	−0.828922
$713$	3.13640	0.117459
$714$	28.6428	1.07193
$715$	−5.13467	−0.192026
$716$	0.0733856	0.00274255
$717$	−22.3403	−0.834315
$718$	−24.5346	−0.915622
$719$	−10.6305	−0.396452	−0.198226	−	0.980156i	$-0.563518\pi$
$719$	−10.6305	−0.396452	−0.198226	+	0.980156i	$0.563518\pi$
$720$	−0.769343	−0.0286717
$721$	−0.279417	−0.0104060
$722$	−7.72566	−0.287519
$723$	5.71726	0.212627
$724$	8.79430	0.326838
$725$	−3.91985	−0.145580
$726$	2.30577	0.0855753
$727$	−26.9274	−0.998682	−0.499341	−	0.866406i	$-0.666424\pi$
$727$	−26.9274	−0.998682	−0.499341	+	0.866406i	$0.666424\pi$
$728$	26.8024	0.993361
$729$	1.00000	0.0370370
$730$	51.7908	1.91686
$731$	6.43741	0.238096
$732$	3.31659	0.122585
$733$	−33.7895	−1.24804	−0.624022	−	0.781406i	$-0.714503\pi$
$733$	−33.7895	−1.24804	−0.624022	+	0.781406i	$0.714503\pi$
$734$	−49.0066	−1.80887
$735$	−12.6361	−0.466091
$736$	−4.44003	−0.163662
$737$	−6.57801	−0.242304
$738$	−3.14957	−0.115937
$739$	44.5870	1.64016	0.820080	−	0.572249i	$-0.193929\pi$
$739$	44.5870	1.64016	0.820080	+	0.572249i	$0.193929\pi$
$740$	50.8804	1.87040
$741$	−9.67897	−0.355566
$742$	31.7653	1.16614
$743$	38.2112	1.40183	0.700917	−	0.713243i	$-0.252774\pi$
$743$	38.2112	1.40183	0.700917	+	0.713243i	$0.252774\pi$
$744$	11.2073	0.410881
$745$	2.32358	0.0851293
$746$	−13.1186	−0.480305
$747$	7.24446	0.265061
$748$	11.4174	0.417460
$749$	36.2447	1.32435
$750$	27.0778	0.988741
$751$	−34.7514	−1.26810	−0.634048	−	0.773294i	$-0.718608\pi$
$751$	−34.7514	−1.26810	−0.634048	+	0.773294i	$0.718608\pi$
$752$	0.481169	0.0175464
$753$	9.70844	0.353795
$754$	37.1148	1.35164
$755$	7.67941	0.279482
$756$	11.9679	0.435268
$757$	−14.4650	−0.525740	−0.262870	−	0.964831i	$-0.584669\pi$
$757$	−14.4650	−0.525740	−0.262870	+	0.964831i	$0.584669\pi$
$758$	38.7887	1.40887
$759$	0.849566	0.0308373
$760$	25.2028	0.914202
$761$	47.7651	1.73148	0.865742	−	0.500490i	$-0.166847\pi$
$761$	47.7651	1.73148	0.865742	+	0.500490i	$0.166847\pi$
$762$	−22.4133	−0.811948
$763$	−1.72247	−0.0623575
$764$	−52.4289	−1.89681
$765$	−7.22446	−0.261201
$766$	71.5912	2.58669
$767$	22.7805	0.822555
$768$	−18.2973	−0.660247
$769$	11.9740	0.431792	0.215896	−	0.976416i	$-0.430733\pi$
$769$	11.9740	0.431792	0.215896	+	0.976416i	$0.430733\pi$
$770$	−17.4612	−0.629258
$771$	−10.8338	−0.390170
$772$	3.09687	0.111459
$773$	35.9717	1.29381	0.646906	−	0.762570i	$-0.276063\pi$
$773$	35.9717	1.29381	0.646906	+	0.762570i	$0.276063\pi$
$774$	4.31176	0.154983
$775$	−2.19965	−0.0790138
$776$	−27.4795	−0.986457
$777$	−26.3786	−0.946327
$778$	33.5111	1.20143
$779$	5.40361	0.193604
$780$	−17.0296	−0.609757
$781$	1.57572	0.0563838
$782$	6.74353	0.241148
$783$	6.57886	0.235109
$784$	2.20734	0.0788337
$785$	−34.3623	−1.22644
$786$	−36.8687	−1.31506
$787$	30.2154	1.07706	0.538532	−	0.842605i	$-0.318979\pi$
$787$	30.2154	1.07706	0.538532	+	0.842605i	$0.318979\pi$
$788$	−9.19888	−0.327697
$789$	−28.2215	−1.00471
$790$	50.5471	1.79838
$791$	25.6403	0.911663
$792$	3.03576	0.107871
$793$	2.44670	0.0868847
$794$	69.1475	2.45395
$795$	−8.01205	−0.284158
$796$	−86.0588	−3.05027
$797$	15.2674	0.540799	0.270400	−	0.962748i	$-0.412844\pi$
$797$	15.2674	0.540799	0.270400	+	0.962748i	$0.412844\pi$
$798$	−32.9148	−1.16517
$799$	4.51839	0.159849
$800$	3.11393	0.110094
$801$	−7.28594	−0.257436
$802$	29.3577	1.03666
$803$	−10.7030	−0.377699
$804$	−21.8166	−0.769411
$805$	−6.43361	−0.226755
$806$	20.8272	0.733608
$807$	25.5430	0.899157
$808$	−39.8736	−1.40275
$809$	6.43517	0.226249	0.113124	−	0.993581i	$-0.463914\pi$
$809$	6.43517	0.226249	0.113124	+	0.993581i	$0.463914\pi$
$810$	−4.83892	−0.170022
$811$	43.3815	1.52333	0.761666	−	0.647970i	$-0.224382\pi$
$811$	43.3815	1.52333	0.761666	+	0.647970i	$0.224382\pi$
$812$	78.7350	2.76306
$813$	12.0251	0.421740
$814$	−16.8556	−0.590787
$815$	47.4573	1.66236
$816$	1.26201	0.0441790
$817$	−7.39753	−0.258807
$818$	12.1174	0.423673
$819$	8.82887	0.308506
$820$	9.50734	0.332011
$821$	−5.47573	−0.191104	−0.0955521	−	0.995424i	$-0.530462\pi$
$821$	−5.47573	−0.191104	−0.0955521	+	0.995424i	$0.530462\pi$
$822$	13.7389	0.479199
$823$	25.1073	0.875187	0.437593	−	0.899173i	$-0.355831\pi$
$823$	25.1073	0.875187	0.437593	+	0.899173i	$0.355831\pi$
$824$	−0.235069	−0.00818902
$825$	−0.595826	−0.0207440
$826$	77.4684	2.69547
$827$	13.3525	0.464312	0.232156	−	0.972679i	$-0.425422\pi$
$827$	13.3525	0.464312	0.232156	+	0.972679i	$0.425422\pi$
$828$	2.81766	0.0979205
$829$	−40.1501	−1.39447	−0.697235	−	0.716843i	$-0.745586\pi$
$829$	−40.1501	−1.39447	−0.697235	+	0.716843i	$0.745586\pi$
$830$	−35.0554	−1.21679
$831$	3.26431	0.113238
$832$	−31.2778	−1.08436
$833$	20.7279	0.718180
$834$	−43.5434	−1.50779
$835$	−13.8538	−0.479429
$836$	−13.1202	−0.453772
$837$	3.69177	0.127606
$838$	−19.1414	−0.661230
$839$	−14.9067	−0.514636	−0.257318	−	0.966327i	$-0.582839\pi$
$839$	−14.9067	−0.514636	−0.257318	+	0.966327i	$0.582839\pi$
$840$	−22.9893	−0.793205
$841$	14.2814	0.492461
$842$	62.1555	2.14202
$843$	5.40234	0.186067
$844$	52.2029	1.79690
$845$	14.7190	0.506349
$846$	3.02640	0.104050
$847$	3.60849	0.123989
$848$	1.39958	0.0480619
$849$	16.7426	0.574604
$850$	−4.72944	−0.162218
$851$	−6.21045	−0.212892
$852$	5.22603	0.179041
$853$	−48.0187	−1.64413	−0.822065	−	0.569394i	$-0.807178\pi$
$853$	−48.0187	−1.64413	−0.822065	+	0.569394i	$0.807178\pi$
$854$	8.32036	0.284717
$855$	8.30198	0.283922
$856$	30.4920	1.04220
$857$	−20.1607	−0.688677	−0.344339	−	0.938846i	$-0.611897\pi$
$857$	−20.1607	−0.688677	−0.344339	+	0.938846i	$0.611897\pi$
$858$	5.64153	0.192599
$859$	−17.8960	−0.610603	−0.305301	−	0.952256i	$-0.598757\pi$
$859$	−17.8960	−0.610603	−0.305301	+	0.952256i	$0.598757\pi$
$860$	−13.0155	−0.443826
$861$	−4.92902	−0.167980
$862$	4.70513	0.160257
$863$	−55.4665	−1.88810	−0.944051	−	0.329799i	$-0.893019\pi$
$863$	−55.4665	−1.88810	−0.944051	+	0.329799i	$0.893019\pi$
$864$	−5.22624	−0.177800
$865$	−7.79581	−0.265066
$866$	91.8641	3.12167
$867$	−5.14922	−0.174877
$868$	44.1827	1.49966
$869$	−10.4459	−0.354354
$870$	−31.8346	−1.07929
$871$	−16.0944	−0.545337
$872$	−1.44908	−0.0490722
$873$	−9.05193	−0.306362
$874$	−7.74931	−0.262124
$875$	42.3762	1.43258
$876$	−35.4973	−1.19934
$877$	−16.2524	−0.548805	−0.274402	−	0.961615i	$-0.588480\pi$
$877$	−16.2524	−0.548805	−0.274402	+	0.961615i	$0.588480\pi$
$878$	67.8576	2.29008
$879$	−12.2361	−0.412714
$880$	−0.769343	−0.0259345
$881$	−18.5210	−0.623990	−0.311995	−	0.950084i	$-0.600997\pi$
$881$	−18.5210	−0.623990	−0.311995	+	0.950084i	$0.600997\pi$
$882$	13.8835	0.467482
$883$	31.7350	1.06797	0.533983	−	0.845495i	$-0.320695\pi$
$883$	31.7350	1.06797	0.533983	+	0.845495i	$0.320695\pi$
$884$	27.9348	0.939548
$885$	−19.5396	−0.656815
$886$	−29.2855	−0.983866
$887$	−33.6355	−1.12937	−0.564685	−	0.825307i	$-0.691002\pi$
$887$	−33.6355	−1.12937	−0.564685	+	0.825307i	$0.691002\pi$
$888$	−22.1919	−0.744711
$889$	−35.0764	−1.17642
$890$	35.2561	1.18179
$891$	1.00000	0.0335013
$892$	31.7605	1.06342
$893$	−5.19230	−0.173754
$894$	−2.55295	−0.0853833
$895$	−0.0464356	−0.00155217
$896$	−68.6474	−2.29335
$897$	2.07863	0.0694034
$898$	6.71943	0.224230
$899$	24.2876	0.810038
$900$	−1.97611	−0.0658704
$901$	13.1427	0.437847
$902$	−3.14957	−0.104869
$903$	6.74781	0.224553
$904$	21.5707	0.717432
$905$	−5.56470	−0.184977
$906$	−8.43747	−0.280316
$907$	−45.7768	−1.51999	−0.759996	−	0.649927i	$-0.774799\pi$
$907$	−45.7768	−1.51999	−0.759996	+	0.649927i	$0.774799\pi$
$908$	−6.29121	−0.208781
$909$	−13.1346	−0.435648
$910$	−42.7223	−1.41623
$911$	50.4914	1.67285	0.836427	−	0.548078i	$-0.184640\pi$
$911$	50.4914	1.67285	0.836427	+	0.548078i	$0.184640\pi$
$912$	−1.45023	−0.0480219
$913$	7.24446	0.239757
$914$	17.8354	0.589944
$915$	−2.09861	−0.0693780
$916$	37.4856	1.23856
$917$	−57.6988	−1.90538
$918$	7.93762	0.261980
$919$	30.8985	1.01925	0.509624	−	0.860397i	$-0.329784\pi$
$919$	30.8985	1.01925	0.509624	+	0.860397i	$0.329784\pi$
$920$	−5.41249	−0.178444
$921$	19.9409	0.657076
$922$	25.0136	0.823778
$923$	3.85531	0.126899
$924$	11.9679	0.393714
$925$	4.35558	0.143210
$926$	−10.7588	−0.353555
$927$	−0.0774333	−0.00254324
$928$	−34.3827	−1.12867
$929$	2.08208	0.0683108	0.0341554	−	0.999417i	$-0.489126\pi$
$929$	2.08208	0.0683108	0.0341554	+	0.999417i	$0.489126\pi$
$930$	−17.8642	−0.585790
$931$	−23.8194	−0.780651
$932$	−37.5138	−1.22880
$933$	26.8239	0.878174
$934$	−57.1515	−1.87006
$935$	−7.22446	−0.236265
$936$	7.42758	0.242778
$937$	41.4039	1.35261	0.676304	−	0.736623i	$-0.263581\pi$
$937$	41.4039	1.35261	0.676304	+	0.736623i	$0.263581\pi$
$938$	−54.7314	−1.78704
$939$	−14.8393	−0.484263
$940$	−9.13555	−0.297969
$941$	−14.4000	−0.469428	−0.234714	−	0.972064i	$-0.575415\pi$
$941$	−14.4000	−0.469428	−0.234714	+	0.972064i	$0.575415\pi$
$942$	37.7543	1.23010
$943$	−1.16046	−0.0377899
$944$	3.41327	0.111092
$945$	−7.57282	−0.246344
$946$	4.31176	0.140187
$947$	−4.30437	−0.139873	−0.0699366	−	0.997551i	$-0.522280\pi$
$947$	−4.30437	−0.139873	−0.0699366	+	0.997551i	$0.522280\pi$
$948$	−34.6449	−1.12521
$949$	−26.1869	−0.850062
$950$	5.43482	0.176329
$951$	−29.2085	−0.947151
$952$	37.7109	1.22222
$953$	9.62424	0.311760	0.155880	−	0.987776i	$-0.450179\pi$
$953$	9.62424	0.311760	0.155880	+	0.987776i	$0.450179\pi$
$954$	8.80294	0.285006
$955$	33.1750	1.07352
$956$	−74.0938	−2.39636
$957$	6.57886	0.212664
$958$	2.60638	0.0842085
$959$	21.5011	0.694307
$960$	26.8281	0.865872
$961$	−17.3708	−0.560349
$962$	−41.2404	−1.32964
$963$	10.0443	0.323672
$964$	18.9618	0.610719
$965$	−1.95958	−0.0630811
$966$	7.06869	0.227431
$967$	−3.58949	−0.115430	−0.0577151	−	0.998333i	$-0.518382\pi$
$967$	−3.58949	−0.115430	−0.0577151	+	0.998333i	$0.518382\pi$
$968$	3.03576	0.0975731
$969$	−13.6183	−0.437483
$970$	43.8016	1.40639
$971$	−43.1986	−1.38631	−0.693154	−	0.720789i	$-0.743780\pi$
$971$	−43.1986	−1.38631	−0.693154	+	0.720789i	$0.743780\pi$
$972$	3.31659	0.106380
$973$	−68.1446	−2.18462
$974$	59.7293	1.91385
$975$	−1.45780	−0.0466871
$976$	0.366596	0.0117345
$977$	−32.4986	−1.03972	−0.519862	−	0.854251i	$-0.674016\pi$
$977$	−32.4986	−1.03972	−0.519862	+	0.854251i	$0.674016\pi$
$978$	−52.1420	−1.66732
$979$	−7.28594	−0.232860
$980$	−41.9089	−1.33873
$981$	−0.477338	−0.0152402
$982$	79.4497	2.53534
$983$	38.6133	1.23157	0.615786	−	0.787913i	$-0.288838\pi$
$983$	38.6133	1.23157	0.615786	+	0.787913i	$0.288838\pi$
$984$	−4.14670	−0.132192
$985$	5.82070	0.185463
$986$	52.2204	1.66304
$987$	4.73626	0.150757
$988$	−32.1012	−1.02127
$989$	1.58867	0.0505169
$990$	−4.83892	−0.153791
$991$	−31.4660	−0.999550	−0.499775	−	0.866155i	$-0.666584\pi$
$991$	−31.4660	−0.999550	−0.499775	+	0.866155i	$0.666584\pi$
$992$	−19.2941	−0.612587
$993$	11.9108	0.377976
$994$	13.1106	0.415842
$995$	54.4547	1.72633
$996$	24.0269	0.761322
$997$	4.94619	0.156647	0.0783237	−	0.996928i	$-0.475043\pi$
$997$	4.94619	0.156647	0.0783237	+	0.996928i	$0.475043\pi$
$998$	−51.0299	−1.61532
$999$	−7.31015	−0.231283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.g.1.12	✓	13
3.2	odd	2		6039.2.a.h.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.g.1.12	✓	13	1.1	even	1	trivial
6039.2.a.h.1.2		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)

\(f(q)\)	\(=\)	\(q+2.30577 q^{2} +1.00000 q^{3} +3.31659 q^{4} -2.09861 q^{5} +2.30577 q^{6} +3.60849 q^{7} +3.03576 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.30577 q^{2} +1.00000 q^{3} +3.31659 q^{4} -2.09861 q^{5} +2.30577 q^{6} +3.60849 q^{7} +3.03576 q^{8} +1.00000 q^{9} -4.83892 q^{10} +1.00000 q^{11} +3.31659 q^{12} +2.44670 q^{13} +8.32036 q^{14} -2.09861 q^{15} +0.366596 q^{16} +3.44250 q^{17} +2.30577 q^{18} -3.95594 q^{19} -6.96024 q^{20} +3.60849 q^{21} +2.30577 q^{22} +0.849566 q^{23} +3.03576 q^{24} -0.595826 q^{25} +5.64153 q^{26} +1.00000 q^{27} +11.9679 q^{28} +6.57886 q^{29} -4.83892 q^{30} +3.69177 q^{31} -5.22624 q^{32} +1.00000 q^{33} +7.93762 q^{34} -7.57282 q^{35} +3.31659 q^{36} -7.31015 q^{37} -9.12149 q^{38} +2.44670 q^{39} -6.37089 q^{40} -1.36595 q^{41} +8.32036 q^{42} +1.86998 q^{43} +3.31659 q^{44} -2.09861 q^{45} +1.95891 q^{46} +1.31253 q^{47} +0.366596 q^{48} +6.02119 q^{49} -1.37384 q^{50} +3.44250 q^{51} +8.11469 q^{52} +3.81778 q^{53} +2.30577 q^{54} -2.09861 q^{55} +10.9545 q^{56} -3.95594 q^{57} +15.1694 q^{58} +9.31071 q^{59} -6.96024 q^{60} +1.00000 q^{61} +8.51239 q^{62} +3.60849 q^{63} -12.7837 q^{64} -5.13467 q^{65} +2.30577 q^{66} -6.57801 q^{67} +11.4174 q^{68} +0.849566 q^{69} -17.4612 q^{70} +1.57572 q^{71} +3.03576 q^{72} -10.7030 q^{73} -16.8556 q^{74} -0.595826 q^{75} -13.1202 q^{76} +3.60849 q^{77} +5.64153 q^{78} -10.4459 q^{79} -0.769343 q^{80} +1.00000 q^{81} -3.14957 q^{82} +7.24446 q^{83} +11.9679 q^{84} -7.22446 q^{85} +4.31176 q^{86} +6.57886 q^{87} +3.03576 q^{88} -7.28594 q^{89} -4.83892 q^{90} +8.82887 q^{91} +2.81766 q^{92} +3.69177 q^{93} +3.02640 q^{94} +8.30198 q^{95} -5.22624 q^{96} -9.05193 q^{97} +13.8835 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

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