LMFDB - Embedded newform 2013.2.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-2.54331$ 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)

$f(q)$	$=$	$q+2.54331 q^{2} -1.00000 q^{3} +4.46845 q^{4} +0.329781 q^{5} -2.54331 q^{6} +0.595463 q^{7} +6.27804 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54331 q^{2} -1.00000 q^{3} +4.46845 q^{4} +0.329781 q^{5} -2.54331 q^{6} +0.595463 q^{7} +6.27804 q^{8} +1.00000 q^{9} +0.838736 q^{10} -1.00000 q^{11} -4.46845 q^{12} +0.0829823 q^{13} +1.51445 q^{14} -0.329781 q^{15} +7.03014 q^{16} +6.96049 q^{17} +2.54331 q^{18} +1.08146 q^{19} +1.47361 q^{20} -0.595463 q^{21} -2.54331 q^{22} +3.20203 q^{23} -6.27804 q^{24} -4.89124 q^{25} +0.211050 q^{26} -1.00000 q^{27} +2.66080 q^{28} +8.72957 q^{29} -0.838736 q^{30} -3.05943 q^{31} +5.32378 q^{32} +1.00000 q^{33} +17.7027 q^{34} +0.196372 q^{35} +4.46845 q^{36} -5.63463 q^{37} +2.75050 q^{38} -0.0829823 q^{39} +2.07038 q^{40} -0.0715670 q^{41} -1.51445 q^{42} +11.3684 q^{43} -4.46845 q^{44} +0.329781 q^{45} +8.14377 q^{46} +11.2549 q^{47} -7.03014 q^{48} -6.64542 q^{49} -12.4400 q^{50} -6.96049 q^{51} +0.370802 q^{52} -8.24041 q^{53} -2.54331 q^{54} -0.329781 q^{55} +3.73835 q^{56} -1.08146 q^{57} +22.2021 q^{58} -0.674261 q^{59} -1.47361 q^{60} +1.00000 q^{61} -7.78108 q^{62} +0.595463 q^{63} -0.520247 q^{64} +0.0273660 q^{65} +2.54331 q^{66} +0.140859 q^{67} +31.1026 q^{68} -3.20203 q^{69} +0.499437 q^{70} -12.8499 q^{71} +6.27804 q^{72} -1.10649 q^{73} -14.3306 q^{74} +4.89124 q^{75} +4.83247 q^{76} -0.595463 q^{77} -0.211050 q^{78} +14.9245 q^{79} +2.31841 q^{80} +1.00000 q^{81} -0.182017 q^{82} -1.08794 q^{83} -2.66080 q^{84} +2.29543 q^{85} +28.9134 q^{86} -8.72957 q^{87} -6.27804 q^{88} -1.53437 q^{89} +0.838736 q^{90} +0.0494129 q^{91} +14.3081 q^{92} +3.05943 q^{93} +28.6246 q^{94} +0.356646 q^{95} -5.32378 q^{96} -8.74805 q^{97} -16.9014 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.54331	1.79840	0.899198	−	0.437543i	$-0.144151\pi$
$2$	2.54331	1.79840	0.899198	+	0.437543i	$0.144151\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.46845	2.23422
$5$	0.329781	0.147482	0.0737412	−	0.997277i	$-0.476506\pi$
$5$	0.329781	0.147482	0.0737412	+	0.997277i	$0.476506\pi$
$6$	−2.54331	−1.03830
$7$	0.595463	0.225064	0.112532	−	0.993648i	$-0.464104\pi$
$7$	0.595463	0.225064	0.112532	+	0.993648i	$0.464104\pi$
$8$	6.27804	2.21962
$9$	1.00000	0.333333
$10$	0.838736	0.265232
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.46845	−1.28993
$13$	0.0829823	0.0230152	0.0115076	−	0.999934i	$-0.496337\pi$
$13$	0.0829823	0.0230152	0.0115076	+	0.999934i	$0.496337\pi$
$14$	1.51445	0.404754
$15$	−0.329781	−0.0851490
$16$	7.03014	1.75754
$17$	6.96049	1.68817	0.844083	−	0.536213i	$-0.180146\pi$
$17$	6.96049	1.68817	0.844083	+	0.536213i	$0.180146\pi$
$18$	2.54331	0.599465
$19$	1.08146	0.248105	0.124052	−	0.992276i	$-0.460411\pi$
$19$	1.08146	0.248105	0.124052	+	0.992276i	$0.460411\pi$
$20$	1.47361	0.329509
$21$	−0.595463	−0.129941
$22$	−2.54331	−0.542237
$23$	3.20203	0.667669	0.333835	−	0.942632i	$-0.391657\pi$
$23$	3.20203	0.667669	0.333835	+	0.942632i	$0.391657\pi$
$24$	−6.27804	−1.28150
$25$	−4.89124	−0.978249
$26$	0.211050	0.0413903
$27$	−1.00000	−0.192450
$28$	2.66080	0.502844
$29$	8.72957	1.62104	0.810521	−	0.585710i	$-0.199184\pi$
$29$	8.72957	1.62104	0.810521	+	0.585710i	$0.199184\pi$
$30$	−0.838736	−0.153132
$31$	−3.05943	−0.549489	−0.274745	−	0.961517i	$-0.588593\pi$
$31$	−3.05943	−0.549489	−0.274745	+	0.961517i	$0.588593\pi$
$32$	5.32378	0.941119
$33$	1.00000	0.174078
$34$	17.7027	3.03599
$35$	0.196372	0.0331930
$36$	4.46845	0.744742
$37$	−5.63463	−0.926328	−0.463164	−	0.886273i	$-0.653286\pi$
$37$	−5.63463	−0.926328	−0.463164	+	0.886273i	$0.653286\pi$
$38$	2.75050	0.446190
$39$	−0.0829823	−0.0132878
$40$	2.07038	0.327355
$41$	−0.0715670	−0.0111769	−0.00558844	−	0.999984i	$-0.501779\pi$
$41$	−0.0715670	−0.0111769	−0.00558844	+	0.999984i	$0.501779\pi$
$42$	−1.51445	−0.233685
$43$	11.3684	1.73366	0.866831	−	0.498603i	$-0.166153\pi$
$43$	11.3684	1.73366	0.866831	+	0.498603i	$0.166153\pi$
$44$	−4.46845	−0.673644
$45$	0.329781	0.0491608
$46$	8.14377	1.20073
$47$	11.2549	1.64169	0.820845	−	0.571151i	$-0.193503\pi$
$47$	11.2549	1.64169	0.820845	+	0.571151i	$0.193503\pi$
$48$	−7.03014	−1.01471
$49$	−6.64542	−0.949346
$50$	−12.4400	−1.75928
$51$	−6.96049	−0.974663
$52$	0.370802	0.0514210
$53$	−8.24041	−1.13191	−0.565954	−	0.824437i	$-0.691492\pi$
$53$	−8.24041	−1.13191	−0.565954	+	0.824437i	$0.691492\pi$
$54$	−2.54331	−0.346101
$55$	−0.329781	−0.0444676
$56$	3.73835	0.499557
$57$	−1.08146	−0.143243
$58$	22.2021	2.91527
$59$	−0.674261	−0.0877813	−0.0438907	−	0.999036i	$-0.513975\pi$
$59$	−0.674261	−0.0877813	−0.0438907	+	0.999036i	$0.513975\pi$
$60$	−1.47361	−0.190242
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−7.78108	−0.988199
$63$	0.595463	0.0750213
$64$	−0.520247	−0.0650309
$65$	0.0273660	0.00339433
$66$	2.54331	0.313060
$67$	0.140859	0.0172087	0.00860433	−	0.999963i	$-0.497261\pi$
$67$	0.140859	0.0172087	0.00860433	+	0.999963i	$0.497261\pi$
$68$	31.1026	3.77174
$69$	−3.20203	−0.385479
$70$	0.499437	0.0596941
$71$	−12.8499	−1.52500	−0.762500	−	0.646988i	$-0.776028\pi$
$71$	−12.8499	−1.52500	−0.762500	+	0.646988i	$0.776028\pi$
$72$	6.27804	0.739875
$73$	−1.10649	−0.129505	−0.0647527	−	0.997901i	$-0.520626\pi$
$73$	−1.10649	−0.129505	−0.0647527	+	0.997901i	$0.520626\pi$
$74$	−14.3306	−1.66590
$75$	4.89124	0.564792
$76$	4.83247	0.554322
$77$	−0.595463	−0.0678594
$78$	−0.211050	−0.0238967
$79$	14.9245	1.67913	0.839567	−	0.543256i	$-0.182809\pi$
$79$	14.9245	1.67913	0.839567	+	0.543256i	$0.182809\pi$
$80$	2.31841	0.259206
$81$	1.00000	0.111111
$82$	−0.182017	−0.0201005
$83$	−1.08794	−0.119417	−0.0597087	−	0.998216i	$-0.519017\pi$
$83$	−1.08794	−0.119417	−0.0597087	+	0.998216i	$0.519017\pi$
$84$	−2.66080	−0.290317
$85$	2.29543	0.248975
$86$	28.9134	3.11781
$87$	−8.72957	−0.935909
$88$	−6.27804	−0.669242
$89$	−1.53437	−0.162642	−0.0813212	−	0.996688i	$-0.525914\pi$
$89$	−1.53437	−0.162642	−0.0813212	+	0.996688i	$0.525914\pi$
$90$	0.838736	0.0884106
$91$	0.0494129	0.00517988
$92$	14.3081	1.49172
$93$	3.05943	0.317248
$94$	28.6246	2.95241
$95$	0.356646	0.0365911
$96$	−5.32378	−0.543356
$97$	−8.74805	−0.888230	−0.444115	−	0.895970i	$-0.646482\pi$
$97$	−8.74805	−0.888230	−0.444115	+	0.895970i	$0.646482\pi$
$98$	−16.9014	−1.70730
$99$	−1.00000	−0.100504
$100$	−21.8563	−2.18563
$101$	9.88085	0.983181	0.491590	−	0.870827i	$-0.336416\pi$
$101$	9.88085	0.983181	0.491590	+	0.870827i	$0.336416\pi$
$102$	−17.7027	−1.75283
$103$	−7.23771	−0.713153	−0.356577	−	0.934266i	$-0.616056\pi$
$103$	−7.23771	−0.713153	−0.356577	+	0.934266i	$0.616056\pi$
$104$	0.520967	0.0510850
$105$	−0.196372	−0.0191640
$106$	−20.9580	−2.03562
$107$	−16.9166	−1.63539	−0.817695	−	0.575652i	$-0.804748\pi$
$107$	−16.9166	−1.63539	−0.817695	+	0.575652i	$0.804748\pi$
$108$	−4.46845	−0.429977
$109$	5.79446	0.555008	0.277504	−	0.960724i	$-0.410493\pi$
$109$	5.79446	0.555008	0.277504	+	0.960724i	$0.410493\pi$
$110$	−0.838736	−0.0799704
$111$	5.63463	0.534816
$112$	4.18619	0.395558
$113$	−12.3271	−1.15964	−0.579818	−	0.814746i	$-0.696876\pi$
$113$	−12.3271	−1.15964	−0.579818	+	0.814746i	$0.696876\pi$
$114$	−2.75050	−0.257608
$115$	1.05597	0.0984695
$116$	39.0077	3.62177
$117$	0.0829823	0.00767172
$118$	−1.71486	−0.157865
$119$	4.14471	0.379945
$120$	−2.07038	−0.188999
$121$	1.00000	0.0909091
$122$	2.54331	0.230261
$123$	0.0715670	0.00645298
$124$	−13.6709	−1.22768
$125$	−3.26194	−0.291757
$126$	1.51445	0.134918
$127$	−7.99339	−0.709299	−0.354649	−	0.934999i	$-0.615400\pi$
$127$	−7.99339	−0.709299	−0.354649	+	0.934999i	$0.615400\pi$
$128$	−11.9707	−1.05807
$129$	−11.3684	−1.00093
$130$	0.0696003	0.00610435
$131$	−15.8726	−1.38680	−0.693398	−	0.720555i	$-0.743887\pi$
$131$	−15.8726	−1.38680	−0.693398	+	0.720555i	$0.743887\pi$
$132$	4.46845	0.388929
$133$	0.643972	0.0558395
$134$	0.358249	0.0309480
$135$	−0.329781	−0.0283830
$136$	43.6982	3.74709
$137$	−16.9666	−1.44956	−0.724778	−	0.688983i	$-0.758058\pi$
$137$	−16.9666	−1.44956	−0.724778	+	0.688983i	$0.758058\pi$
$138$	−8.14377	−0.693243
$139$	15.7351	1.33463	0.667315	−	0.744775i	$-0.267443\pi$
$139$	15.7351	1.33463	0.667315	+	0.744775i	$0.267443\pi$
$140$	0.877480	0.0741606
$141$	−11.2549	−0.947830
$142$	−32.6813	−2.74255
$143$	−0.0829823	−0.00693933
$144$	7.03014	0.585845
$145$	2.87885	0.239075
$146$	−2.81416	−0.232902
$147$	6.64542	0.548105
$148$	−25.1781	−2.06963
$149$	−15.3791	−1.25990	−0.629950	−	0.776635i	$-0.716925\pi$
$149$	−15.3791	−1.25990	−0.629950	+	0.776635i	$0.716925\pi$
$150$	12.4400	1.01572
$151$	16.5708	1.34851	0.674257	−	0.738497i	$-0.264464\pi$
$151$	16.5708	1.34851	0.674257	+	0.738497i	$0.264464\pi$
$152$	6.78948	0.550699
$153$	6.96049	0.562722
$154$	−1.51445	−0.122038
$155$	−1.00894	−0.0810400
$156$	−0.370802	−0.0296879
$157$	−6.06333	−0.483907	−0.241953	−	0.970288i	$-0.577788\pi$
$157$	−6.06333	−0.483907	−0.241953	+	0.970288i	$0.577788\pi$
$158$	37.9576	3.01975
$159$	8.24041	0.653507
$160$	1.75568	0.138799
$161$	1.90669	0.150268
$162$	2.54331	0.199822
$163$	17.8621	1.39907	0.699535	−	0.714598i	$-0.253390\pi$
$163$	17.8621	1.39907	0.699535	+	0.714598i	$0.253390\pi$
$164$	−0.319793	−0.0249717
$165$	0.329781	0.0256734
$166$	−2.76698	−0.214759
$167$	21.2052	1.64091	0.820455	−	0.571711i	$-0.193720\pi$
$167$	21.2052	1.64091	0.820455	+	0.571711i	$0.193720\pi$
$168$	−3.73835	−0.288420
$169$	−12.9931	−0.999470
$170$	5.83801	0.447755
$171$	1.08146	0.0827016
$172$	50.7990	3.87339
$173$	2.96793	0.225647	0.112824	−	0.993615i	$-0.464010\pi$
$173$	2.96793	0.225647	0.112824	+	0.993615i	$0.464010\pi$
$174$	−22.2021	−1.68313
$175$	−2.91256	−0.220169
$176$	−7.03014	−0.529917
$177$	0.674261	0.0506806
$178$	−3.90237	−0.292495
$179$	1.16838	0.0873291	0.0436646	−	0.999046i	$-0.486097\pi$
$179$	1.16838	0.0873291	0.0436646	+	0.999046i	$0.486097\pi$
$180$	1.47361	0.109836
$181$	−11.0228	−0.819318	−0.409659	−	0.912239i	$-0.634352\pi$
$181$	−11.0228	−0.819318	−0.409659	+	0.912239i	$0.634352\pi$
$182$	0.125673	0.00931548
$183$	−1.00000	−0.0739221
$184$	20.1025	1.48197
$185$	−1.85819	−0.136617
$186$	7.78108	0.570537
$187$	−6.96049	−0.509001
$188$	50.2918	3.66790
$189$	−0.595463	−0.0433136
$190$	0.907063	0.0658052
$191$	−15.3640	−1.11170	−0.555849	−	0.831283i	$-0.687607\pi$
$191$	−15.3640	−1.11170	−0.555849	+	0.831283i	$0.687607\pi$
$192$	0.520247	0.0375456
$193$	−11.1185	−0.800324	−0.400162	−	0.916444i	$-0.631046\pi$
$193$	−11.1185	−0.800324	−0.400162	+	0.916444i	$0.631046\pi$
$194$	−22.2490	−1.59739
$195$	−0.0273660	−0.00195972
$196$	−29.6947	−2.12105
$197$	−17.7144	−1.26210	−0.631050	−	0.775742i	$-0.717376\pi$
$197$	−17.7144	−1.26210	−0.631050	+	0.775742i	$0.717376\pi$
$198$	−2.54331	−0.180746
$199$	24.5173	1.73798	0.868992	−	0.494826i	$-0.164768\pi$
$199$	24.5173	1.73798	0.868992	+	0.494826i	$0.164768\pi$
$200$	−30.7074	−2.17134
$201$	−0.140859	−0.00993542
$202$	25.1301	1.76815
$203$	5.19814	0.364838
$204$	−31.1026	−2.17762
$205$	−0.0236014	−0.00164839
$206$	−18.4078	−1.28253
$207$	3.20203	0.222556
$208$	0.583378	0.0404500
$209$	−1.08146	−0.0748064
$210$	−0.499437	−0.0344644
$211$	9.34349	0.643232	0.321616	−	0.946870i	$-0.395774\pi$
$211$	9.34349	0.643232	0.321616	+	0.946870i	$0.395774\pi$
$212$	−36.8219	−2.52894
$213$	12.8499	0.880459
$214$	−43.0243	−2.94108
$215$	3.74907	0.255685
$216$	−6.27804	−0.427167
$217$	−1.82178	−0.123670
$218$	14.7371	0.998124
$219$	1.10649	0.0747700
$220$	−1.47361	−0.0993507
$221$	0.577597	0.0388534
$222$	14.3306	0.961810
$223$	−23.8528	−1.59730	−0.798652	−	0.601793i	$-0.794453\pi$
$223$	−23.8528	−1.59730	−0.798652	+	0.601793i	$0.794453\pi$
$224$	3.17011	0.211812
$225$	−4.89124	−0.326083
$226$	−31.3517	−2.08548
$227$	4.98647	0.330964	0.165482	−	0.986213i	$-0.447082\pi$
$227$	4.98647	0.330964	0.165482	+	0.986213i	$0.447082\pi$
$228$	−4.83247	−0.320038
$229$	0.915859	0.0605217	0.0302608	−	0.999542i	$-0.490366\pi$
$229$	0.915859	0.0605217	0.0302608	+	0.999542i	$0.490366\pi$
$230$	2.68566	0.177087
$231$	0.595463	0.0391786
$232$	54.8046	3.59810
$233$	7.32305	0.479749	0.239875	−	0.970804i	$-0.422894\pi$
$233$	7.32305	0.479749	0.239875	+	0.970804i	$0.422894\pi$
$234$	0.211050	0.0137968
$235$	3.71164	0.242120
$236$	−3.01290	−0.196123
$237$	−14.9245	−0.969448
$238$	10.5413	0.683292
$239$	−24.5442	−1.58763	−0.793817	−	0.608157i	$-0.791909\pi$
$239$	−24.5442	−1.58763	−0.793817	+	0.608157i	$0.791909\pi$
$240$	−2.31841	−0.149652
$241$	18.3505	1.18206	0.591031	−	0.806649i	$-0.298721\pi$
$241$	18.3505	1.18206	0.591031	+	0.806649i	$0.298721\pi$
$242$	2.54331	0.163490
$243$	−1.00000	−0.0641500
$244$	4.46845	0.286063
$245$	−2.19153	−0.140012
$246$	0.182017	0.0116050
$247$	0.0897424	0.00571017
$248$	−19.2072	−1.21966
$249$	1.08794	0.0689456
$250$	−8.29614	−0.524694
$251$	2.34673	0.148125	0.0740623	−	0.997254i	$-0.476404\pi$
$251$	2.34673	0.148125	0.0740623	+	0.997254i	$0.476404\pi$
$252$	2.66080	0.167615
$253$	−3.20203	−0.201310
$254$	−20.3297	−1.27560
$255$	−2.29543	−0.143746
$256$	−29.4048	−1.83780
$257$	−2.07933	−0.129705	−0.0648527	−	0.997895i	$-0.520658\pi$
$257$	−2.07933	−0.129705	−0.0648527	+	0.997895i	$0.520658\pi$
$258$	−28.9134	−1.80007
$259$	−3.35522	−0.208483
$260$	0.122283	0.00758370
$261$	8.72957	0.540347
$262$	−40.3690	−2.49401
$263$	−24.1181	−1.48718	−0.743591	−	0.668634i	$-0.766879\pi$
$263$	−24.1181	−1.48718	−0.743591	+	0.668634i	$0.766879\pi$
$264$	6.27804	0.386387
$265$	−2.71753	−0.166936
$266$	1.63782	0.100421
$267$	1.53437	0.0939016
$268$	0.629421	0.0384480
$269$	−13.9942	−0.853243	−0.426622	−	0.904430i	$-0.640296\pi$
$269$	−13.9942	−0.853243	−0.426622	+	0.904430i	$0.640296\pi$
$270$	−0.838736	−0.0510439
$271$	−24.2791	−1.47485	−0.737426	−	0.675428i	$-0.763959\pi$
$271$	−24.2791	−1.47485	−0.737426	+	0.675428i	$0.763959\pi$
$272$	48.9332	2.96701
$273$	−0.0494129	−0.00299061
$274$	−43.1514	−2.60687
$275$	4.89124	0.294953
$276$	−14.3081	−0.861247
$277$	−16.3119	−0.980085	−0.490043	−	0.871699i	$-0.663019\pi$
$277$	−16.3119	−0.980085	−0.490043	+	0.871699i	$0.663019\pi$
$278$	40.0192	2.40019
$279$	−3.05943	−0.183163
$280$	1.23283	0.0736759
$281$	13.7085	0.817778	0.408889	−	0.912584i	$-0.365916\pi$
$281$	13.7085	0.817778	0.408889	+	0.912584i	$0.365916\pi$
$282$	−28.6246	−1.70457
$283$	31.0223	1.84409	0.922043	−	0.387087i	$-0.126519\pi$
$283$	31.0223	1.84409	0.922043	+	0.387087i	$0.126519\pi$
$284$	−57.4190	−3.40719
$285$	−0.356646	−0.0211259
$286$	−0.211050	−0.0124797
$287$	−0.0426155	−0.00251551
$288$	5.32378	0.313706
$289$	31.4484	1.84990
$290$	7.32181	0.429951
$291$	8.74805	0.512820
$292$	−4.94431	−0.289344
$293$	4.76769	0.278531	0.139266	−	0.990255i	$-0.455526\pi$
$293$	4.76769	0.278531	0.139266	+	0.990255i	$0.455526\pi$
$294$	16.9014	0.985710
$295$	−0.222358	−0.0129462
$296$	−35.3745	−2.05610
$297$	1.00000	0.0580259
$298$	−39.1138	−2.26580
$299$	0.265712	0.0153665
$300$	21.8563	1.26187
$301$	6.76945	0.390185
$302$	42.1448	2.42516
$303$	−9.88085	−0.567640
$304$	7.60284	0.436053
$305$	0.329781	0.0188832
$306$	17.7027	1.01200
$307$	−9.09194	−0.518905	−0.259452	−	0.965756i	$-0.583542\pi$
$307$	−9.09194	−0.518905	−0.259452	+	0.965756i	$0.583542\pi$
$308$	−2.66080	−0.151613
$309$	7.23771	0.411739
$310$	−2.56605	−0.145742
$311$	0.130155	0.00738041	0.00369020	−	0.999993i	$-0.498825\pi$
$311$	0.130155	0.00738041	0.00369020	+	0.999993i	$0.498825\pi$
$312$	−0.520967	−0.0294939
$313$	−18.8073	−1.06305	−0.531526	−	0.847042i	$-0.678381\pi$
$313$	−18.8073	−1.06305	−0.531526	+	0.847042i	$0.678381\pi$
$314$	−15.4210	−0.870255
$315$	0.196372	0.0110643
$316$	66.6892	3.75156
$317$	21.5314	1.20932	0.604661	−	0.796483i	$-0.293308\pi$
$317$	21.5314	1.20932	0.604661	+	0.796483i	$0.293308\pi$
$318$	20.9580	1.17526
$319$	−8.72957	−0.488762
$320$	−0.171568	−0.00959092
$321$	16.9166	0.944193
$322$	4.84931	0.270242
$323$	7.52751	0.418842
$324$	4.46845	0.248247
$325$	−0.405887	−0.0225146
$326$	45.4290	2.51608
$327$	−5.79446	−0.320434
$328$	−0.449301	−0.0248085
$329$	6.70186	0.369485
$330$	0.838736	0.0461709
$331$	−5.77423	−0.317380	−0.158690	−	0.987328i	$-0.550727\pi$
$331$	−5.77423	−0.317380	−0.158690	+	0.987328i	$0.550727\pi$
$332$	−4.86142	−0.266805
$333$	−5.63463	−0.308776
$334$	53.9316	2.95100
$335$	0.0464526	0.00253797
$336$	−4.18619	−0.228376
$337$	−16.2916	−0.887462	−0.443731	−	0.896160i	$-0.646345\pi$
$337$	−16.2916	−0.887462	−0.443731	+	0.896160i	$0.646345\pi$
$338$	−33.0456	−1.79744
$339$	12.3271	0.669517
$340$	10.2570	0.556266
$341$	3.05943	0.165677
$342$	2.75050	0.148730
$343$	−8.12535	−0.438728
$344$	71.3712	3.84808
$345$	−1.05597	−0.0568514
$346$	7.54837	0.405803
$347$	−18.5188	−0.994143	−0.497072	−	0.867710i	$-0.665591\pi$
$347$	−18.5188	−0.994143	−0.497072	+	0.867710i	$0.665591\pi$
$348$	−39.0077	−2.09103
$349$	9.92712	0.531387	0.265693	−	0.964058i	$-0.414399\pi$
$349$	9.92712	0.531387	0.265693	+	0.964058i	$0.414399\pi$
$350$	−7.40755	−0.395950
$351$	−0.0829823	−0.00442927
$352$	−5.32378	−0.283758
$353$	14.8318	0.789415	0.394707	−	0.918807i	$-0.370846\pi$
$353$	14.8318	0.789415	0.394707	+	0.918807i	$0.370846\pi$
$354$	1.71486	0.0911437
$355$	−4.23764	−0.224911
$356$	−6.85623	−0.363380
$357$	−4.14471	−0.219362
$358$	2.97157	0.157052
$359$	27.5857	1.45592	0.727959	−	0.685621i	$-0.240469\pi$
$359$	27.5857	1.45592	0.727959	+	0.685621i	$0.240469\pi$
$360$	2.07038	0.109118
$361$	−17.8304	−0.938444
$362$	−28.0344	−1.47346
$363$	−1.00000	−0.0524864
$364$	0.220799	0.0115730
$365$	−0.364900	−0.0190998
$366$	−2.54331	−0.132941
$367$	−25.3367	−1.32256	−0.661281	−	0.750138i	$-0.729987\pi$
$367$	−25.3367	−1.32256	−0.661281	+	0.750138i	$0.729987\pi$
$368$	22.5107	1.17345
$369$	−0.0715670	−0.00372563
$370$	−4.72597	−0.245692
$371$	−4.90686	−0.254752
$372$	13.6709	0.708803
$373$	22.9549	1.18856	0.594281	−	0.804258i	$-0.297437\pi$
$373$	22.9549	1.18856	0.594281	+	0.804258i	$0.297437\pi$
$374$	−17.7027	−0.915385
$375$	3.26194	0.168446
$376$	70.6585	3.64393
$377$	0.724400	0.0373085
$378$	−1.51445	−0.0778949
$379$	−2.82059	−0.144884	−0.0724420	−	0.997373i	$-0.523079\pi$
$379$	−2.82059	−0.144884	−0.0724420	+	0.997373i	$0.523079\pi$
$380$	1.59365	0.0817527
$381$	7.99339	0.409514
$382$	−39.0754	−1.99927
$383$	25.6130	1.30876	0.654382	−	0.756164i	$-0.272929\pi$
$383$	25.6130	1.30876	0.654382	+	0.756164i	$0.272929\pi$
$384$	11.9707	0.610877
$385$	−0.196372	−0.0100081
$386$	−28.2777	−1.43930
$387$	11.3684	0.577887
$388$	−39.0902	−1.98450
$389$	−2.02580	−0.102712	−0.0513562	−	0.998680i	$-0.516354\pi$
$389$	−2.02580	−0.102712	−0.0513562	+	0.998680i	$0.516354\pi$
$390$	−0.0696003	−0.00352435
$391$	22.2877	1.12714
$392$	−41.7203	−2.10719
$393$	15.8726	0.800667
$394$	−45.0533	−2.26975
$395$	4.92180	0.247643
$396$	−4.46845	−0.224548
$397$	1.07995	0.0542011	0.0271006	−	0.999633i	$-0.491373\pi$
$397$	1.07995	0.0542011	0.0271006	+	0.999633i	$0.491373\pi$
$398$	62.3552	3.12558
$399$	−0.643972	−0.0322389
$400$	−34.3861	−1.71931
$401$	3.50052	0.174807	0.0874037	−	0.996173i	$-0.472143\pi$
$401$	3.50052	0.174807	0.0874037	+	0.996173i	$0.472143\pi$
$402$	−0.358249	−0.0178678
$403$	−0.253878	−0.0126466
$404$	44.1521	2.19665
$405$	0.329781	0.0163869
$406$	13.2205	0.656123
$407$	5.63463	0.279298
$408$	−43.6982	−2.16339
$409$	−27.1693	−1.34344	−0.671719	−	0.740806i	$-0.734444\pi$
$409$	−27.1693	−1.34344	−0.671719	+	0.740806i	$0.734444\pi$
$410$	−0.0600258	−0.00296446
$411$	16.9666	0.836901
$412$	−32.3414	−1.59334
$413$	−0.401498	−0.0197564
$414$	8.14377	0.400244
$415$	−0.358783	−0.0176120
$416$	0.441779	0.0216600
$417$	−15.7351	−0.770549
$418$	−2.75050	−0.134531
$419$	−15.6757	−0.765810	−0.382905	−	0.923788i	$-0.625076\pi$
$419$	−15.6757	−0.765810	−0.382905	+	0.923788i	$0.625076\pi$
$420$	−0.877480	−0.0428166
$421$	−1.40707	−0.0685762	−0.0342881	−	0.999412i	$-0.510916\pi$
$421$	−1.40707	−0.0685762	−0.0342881	+	0.999412i	$0.510916\pi$
$422$	23.7634	1.15679
$423$	11.2549	0.547230
$424$	−51.7337	−2.51241
$425$	−34.0454	−1.65145
$426$	32.6813	1.58341
$427$	0.595463	0.0288165
$428$	−75.5910	−3.65383
$429$	0.0829823	0.00400642
$430$	9.53507	0.459822
$431$	−23.5382	−1.13379	−0.566897	−	0.823789i	$-0.691856\pi$
$431$	−23.5382	−1.13379	−0.566897	+	0.823789i	$0.691856\pi$
$432$	−7.03014	−0.338238
$433$	29.2710	1.40668	0.703338	−	0.710856i	$-0.251692\pi$
$433$	29.2710	1.40668	0.703338	+	0.710856i	$0.251692\pi$
$434$	−4.63335	−0.222408
$435$	−2.87885	−0.138030
$436$	25.8922	1.24001
$437$	3.46288	0.165652
$438$	2.81416	0.134466
$439$	−17.0691	−0.814664	−0.407332	−	0.913280i	$-0.633541\pi$
$439$	−17.0691	−0.814664	−0.407332	+	0.913280i	$0.633541\pi$
$440$	−2.07038	−0.0987014
$441$	−6.64542	−0.316449
$442$	1.46901	0.0698738
$443$	−32.9257	−1.56435	−0.782173	−	0.623061i	$-0.785889\pi$
$443$	−32.9257	−1.56435	−0.782173	+	0.623061i	$0.785889\pi$
$444$	25.1781	1.19490
$445$	−0.506004	−0.0239869
$446$	−60.6653	−2.87258
$447$	15.3791	0.727404
$448$	−0.309788	−0.0146361
$449$	−30.7700	−1.45213	−0.726064	−	0.687627i	$-0.758652\pi$
$449$	−30.7700	−1.45213	−0.726064	+	0.687627i	$0.758652\pi$
$450$	−12.4400	−0.586426
$451$	0.0715670	0.00336996
$452$	−55.0831	−2.59089
$453$	−16.5708	−0.778565
$454$	12.6822	0.595204
$455$	0.0162954	0.000763942 0
$456$	−6.78948	−0.317946
$457$	−11.8994	−0.556632	−0.278316	−	0.960490i	$-0.589776\pi$
$457$	−11.8994	−0.556632	−0.278316	+	0.960490i	$0.589776\pi$
$458$	2.32932	0.108842
$459$	−6.96049	−0.324888
$460$	4.71854	0.220003
$461$	9.53778	0.444218	0.222109	−	0.975022i	$-0.428706\pi$
$461$	9.53778	0.444218	0.222109	+	0.975022i	$0.428706\pi$
$462$	1.51445	0.0704586
$463$	22.8038	1.05978	0.529890	−	0.848066i	$-0.322233\pi$
$463$	22.8038	1.05978	0.529890	+	0.848066i	$0.322233\pi$
$464$	61.3701	2.84904
$465$	1.00894	0.0467885
$466$	18.6248	0.862778
$467$	41.0776	1.90084	0.950422	−	0.310962i	$-0.100651\pi$
$467$	41.0776	1.90084	0.950422	+	0.310962i	$0.100651\pi$
$468$	0.370802	0.0171403
$469$	0.0838763	0.00387305
$470$	9.43986	0.435428
$471$	6.06333	0.279384
$472$	−4.23304	−0.194842
$473$	−11.3684	−0.522719
$474$	−37.9576	−1.74345
$475$	−5.28970	−0.242708
$476$	18.5204	0.848883
$477$	−8.24041	−0.377303
$478$	−62.4237	−2.85519
$479$	−11.8369	−0.540841	−0.270421	−	0.962742i	$-0.587163\pi$
$479$	−11.8369	−0.540841	−0.270421	+	0.962742i	$0.587163\pi$
$480$	−1.75568	−0.0801354
$481$	−0.467575	−0.0213196
$482$	46.6712	2.12581
$483$	−1.90669	−0.0867574
$484$	4.46845	0.203111
$485$	−2.88494	−0.130998
$486$	−2.54331	−0.115367
$487$	23.2203	1.05221	0.526105	−	0.850420i	$-0.323652\pi$
$487$	23.2203	1.05221	0.526105	+	0.850420i	$0.323652\pi$
$488$	6.27804	0.284194
$489$	−17.8621	−0.807754
$490$	−5.57376	−0.251797
$491$	−10.6561	−0.480901	−0.240451	−	0.970661i	$-0.577295\pi$
$491$	−10.6561	−0.480901	−0.240451	+	0.970661i	$0.577295\pi$
$492$	0.319793	0.0144174
$493$	60.7621	2.73659
$494$	0.228243	0.0102691
$495$	−0.329781	−0.0148225
$496$	−21.5082	−0.965747
$497$	−7.65163	−0.343223
$498$	2.76698	0.123991
$499$	41.6152	1.86295	0.931475	−	0.363804i	$-0.118522\pi$
$499$	41.6152	1.86295	0.931475	+	0.363804i	$0.118522\pi$
$500$	−14.5758	−0.651851
$501$	−21.2052	−0.947380
$502$	5.96848	0.266386
$503$	31.7709	1.41660	0.708298	−	0.705914i	$-0.249463\pi$
$503$	31.7709	1.41660	0.708298	+	0.705914i	$0.249463\pi$
$504$	3.73835	0.166519
$505$	3.25851	0.145002
$506$	−8.14377	−0.362035
$507$	12.9931	0.577044
$508$	−35.7181	−1.58473
$509$	29.3708	1.30184	0.650920	−	0.759147i	$-0.274383\pi$
$509$	29.3708	1.30184	0.650920	+	0.759147i	$0.274383\pi$
$510$	−5.83801	−0.258511
$511$	−0.658877	−0.0291470
$512$	−50.8442	−2.24702
$513$	−1.08146	−0.0477478
$514$	−5.28840	−0.233261
$515$	−2.38686	−0.105178
$516$	−50.7990	−2.23630
$517$	−11.2549	−0.494988
$518$	−8.53338	−0.374935
$519$	−2.96793	−0.130278
$520$	0.171805	0.00753414
$521$	−3.61714	−0.158470	−0.0792350	−	0.996856i	$-0.525248\pi$
$521$	−3.61714	−0.158470	−0.0792350	+	0.996856i	$0.525248\pi$
$522$	22.2021	0.971757
$523$	−21.7716	−0.952004	−0.476002	−	0.879444i	$-0.657914\pi$
$523$	−21.7716	−0.952004	−0.476002	+	0.879444i	$0.657914\pi$
$524$	−70.9259	−3.09841
$525$	2.91256	0.127114
$526$	−61.3398	−2.67454
$527$	−21.2951	−0.927629
$528$	7.03014	0.305948
$529$	−12.7470	−0.554218
$530$	−6.91153	−0.300218
$531$	−0.674261	−0.0292604
$532$	2.87756	0.124758
$533$	−0.00593879	−0.000257238 0
$534$	3.90237	0.168872
$535$	−5.57877	−0.241191
$536$	0.884319	0.0381967
$537$	−1.16838	−0.0504195
$538$	−35.5917	−1.53447
$539$	6.64542	0.286239
$540$	−1.47361	−0.0634140
$541$	39.5580	1.70073	0.850366	−	0.526191i	$-0.176380\pi$
$541$	39.5580	1.70073	0.850366	+	0.526191i	$0.176380\pi$
$542$	−61.7494	−2.65236
$543$	11.0228	0.473034
$544$	37.0561	1.58877
$545$	1.91090	0.0818540
$546$	−0.125673	−0.00537829
$547$	22.9213	0.980046	0.490023	−	0.871710i	$-0.336988\pi$
$547$	22.9213	0.980046	0.490023	+	0.871710i	$0.336988\pi$
$548$	−75.8144	−3.23863
$549$	1.00000	0.0426790
$550$	12.4400	0.530442
$551$	9.44072	0.402188
$552$	−20.1025	−0.855618
$553$	8.88697	0.377913
$554$	−41.4862	−1.76258
$555$	1.85819	0.0788759
$556$	70.3113	2.98186
$557$	4.36360	0.184892	0.0924458	−	0.995718i	$-0.470532\pi$
$557$	4.36360	0.184892	0.0924458	+	0.995718i	$0.470532\pi$
$558$	−7.78108	−0.329400
$559$	0.943374	0.0399005
$560$	1.38053	0.0583378
$561$	6.96049	0.293872
$562$	34.8649	1.47069
$563$	7.88133	0.332158	0.166079	−	0.986112i	$-0.446889\pi$
$563$	7.88133	0.332158	0.166079	+	0.986112i	$0.446889\pi$
$564$	−50.2918	−2.11767
$565$	−4.06524	−0.171026
$566$	78.8995	3.31640
$567$	0.595463	0.0250071
$568$	−80.6721	−3.38493
$569$	19.5591	0.819961	0.409980	−	0.912094i	$-0.365536\pi$
$569$	19.5591	0.819961	0.409980	+	0.912094i	$0.365536\pi$
$570$	−0.907063	−0.0379927
$571$	37.0732	1.55147	0.775733	−	0.631061i	$-0.217380\pi$
$571$	37.0732	1.55147	0.775733	+	0.631061i	$0.217380\pi$
$572$	−0.370802	−0.0155040
$573$	15.3640	0.641840
$574$	−0.108385	−0.00452389
$575$	−15.6619	−0.653147
$576$	−0.520247	−0.0216770
$577$	20.2481	0.842941	0.421471	−	0.906842i	$-0.361514\pi$
$577$	20.2481	0.842941	0.421471	+	0.906842i	$0.361514\pi$
$578$	79.9831	3.32686
$579$	11.1185	0.462067
$580$	12.8640	0.534147
$581$	−0.647830	−0.0268765
$582$	22.2490	0.922252
$583$	8.24041	0.341283
$584$	−6.94662	−0.287453
$585$	0.0273660	0.00113144
$586$	12.1257	0.500910
$587$	−14.4483	−0.596343	−0.298172	−	0.954512i	$-0.596377\pi$
$587$	−14.4483	−0.596343	−0.298172	+	0.954512i	$0.596377\pi$
$588$	29.6947	1.22459
$589$	−3.30866	−0.136331
$590$	−0.565527	−0.0232824
$591$	17.7144	0.728674
$592$	−39.6123	−1.62805
$593$	−14.6070	−0.599839	−0.299920	−	0.953964i	$-0.596960\pi$
$593$	−14.6070	−0.599839	−0.299920	+	0.953964i	$0.596960\pi$
$594$	2.54331	0.104353
$595$	1.36685	0.0560353
$596$	−68.7205	−2.81490
$597$	−24.5173	−1.00343
$598$	0.675789	0.0276351
$599$	3.38693	0.138386	0.0691932	−	0.997603i	$-0.477958\pi$
$599$	3.38693	0.138386	0.0691932	+	0.997603i	$0.477958\pi$
$600$	30.7074	1.25363
$601$	25.0307	1.02102	0.510512	−	0.859871i	$-0.329456\pi$
$601$	25.0307	1.02102	0.510512	+	0.859871i	$0.329456\pi$
$602$	17.2168	0.701706
$603$	0.140859	0.00573622
$604$	74.0459	3.01288
$605$	0.329781	0.0134075
$606$	−25.1301	−1.02084
$607$	41.4522	1.68249	0.841246	−	0.540652i	$-0.181822\pi$
$607$	41.4522	1.68249	0.841246	+	0.540652i	$0.181822\pi$
$608$	5.75747	0.233496
$609$	−5.19814	−0.210639
$610$	0.838736	0.0339594
$611$	0.933954	0.0377837
$612$	31.1026	1.25725
$613$	−22.4905	−0.908383	−0.454191	−	0.890904i	$-0.650072\pi$
$613$	−22.4905	−0.908383	−0.454191	+	0.890904i	$0.650072\pi$
$614$	−23.1237	−0.933195
$615$	0.0236014	0.000951701 0
$616$	−3.73835	−0.150622
$617$	19.0197	0.765703	0.382851	−	0.923810i	$-0.374942\pi$
$617$	19.0197	0.765703	0.382851	+	0.923810i	$0.374942\pi$
$618$	18.4078	0.740470
$619$	−19.8223	−0.796727	−0.398364	−	0.917228i	$-0.630422\pi$
$619$	−19.8223	−0.796727	−0.398364	+	0.917228i	$0.630422\pi$
$620$	−4.50840	−0.181062
$621$	−3.20203	−0.128493
$622$	0.331025	0.0132729
$623$	−0.913658	−0.0366050
$624$	−0.583378	−0.0233538
$625$	23.3805	0.935220
$626$	−47.8329	−1.91179
$627$	1.08146	0.0431895
$628$	−27.0937	−1.08116
$629$	−39.2198	−1.56380
$630$	0.499437	0.0198980
$631$	−8.96489	−0.356886	−0.178443	−	0.983950i	$-0.557106\pi$
$631$	−8.96489	−0.356886	−0.178443	+	0.983950i	$0.557106\pi$
$632$	93.6965	3.72704
$633$	−9.34349	−0.371370
$634$	54.7611	2.17484
$635$	−2.63607	−0.104609
$636$	36.8219	1.46008
$637$	−0.551453	−0.0218494
$638$	−22.2021	−0.878988
$639$	−12.8499	−0.508333
$640$	−3.94771	−0.156047
$641$	−2.96210	−0.116996	−0.0584980	−	0.998288i	$-0.518631\pi$
$641$	−2.96210	−0.116996	−0.0584980	+	0.998288i	$0.518631\pi$
$642$	43.0243	1.69803
$643$	30.3611	1.19733	0.598663	−	0.801001i	$-0.295699\pi$
$643$	30.3611	1.19733	0.598663	+	0.801001i	$0.295699\pi$
$644$	8.51995	0.335733
$645$	−3.74907	−0.147620
$646$	19.1448	0.753243
$647$	44.6983	1.75727	0.878636	−	0.477491i	$-0.158454\pi$
$647$	44.6983	1.75727	0.878636	+	0.477491i	$0.158454\pi$
$648$	6.27804	0.246625
$649$	0.674261	0.0264671
$650$	−1.03230	−0.0404901
$651$	1.82178	0.0714011
$652$	79.8161	3.12584
$653$	−21.4840	−0.840733	−0.420366	−	0.907355i	$-0.638098\pi$
$653$	−21.4840	−0.840733	−0.420366	+	0.907355i	$0.638098\pi$
$654$	−14.7371	−0.576267
$655$	−5.23448	−0.204528
$656$	−0.503126	−0.0196438
$657$	−1.10649	−0.0431685
$658$	17.0449	0.664481
$659$	−26.1584	−1.01899	−0.509493	−	0.860475i	$-0.670167\pi$
$659$	−26.1584	−1.01899	−0.509493	+	0.860475i	$0.670167\pi$
$660$	1.47361	0.0573601
$661$	49.2767	1.91664	0.958320	−	0.285697i	$-0.0922249\pi$
$661$	49.2767	1.91664	0.958320	+	0.285697i	$0.0922249\pi$
$662$	−14.6857	−0.570775
$663$	−0.577597	−0.0224320
$664$	−6.83016	−0.265061
$665$	0.212370	0.00823534
$666$	−14.3306	−0.555301
$667$	27.9523	1.08232
$668$	94.7545	3.66616
$669$	23.8528	0.922204
$670$	0.118143	0.00456428
$671$	−1.00000	−0.0386046
$672$	−3.17011	−0.122290
$673$	−7.96941	−0.307198	−0.153599	−	0.988133i	$-0.549086\pi$
$673$	−7.96941	−0.307198	−0.153599	+	0.988133i	$0.549086\pi$
$674$	−41.4348	−1.59601
$675$	4.89124	0.188264
$676$	−58.0591	−2.23304
$677$	13.0772	0.502596	0.251298	−	0.967910i	$-0.419143\pi$
$677$	13.0772	0.502596	0.251298	+	0.967910i	$0.419143\pi$
$678$	31.3517	1.20406
$679$	−5.20914	−0.199909
$680$	14.4108	0.552630
$681$	−4.98647	−0.191082
$682$	7.78108	0.297953
$683$	29.5060	1.12902	0.564508	−	0.825427i	$-0.309066\pi$
$683$	29.5060	1.12902	0.564508	+	0.825427i	$0.309066\pi$
$684$	4.83247	0.184774
$685$	−5.59526	−0.213784
$686$	−20.6653	−0.789006
$687$	−0.915859	−0.0349422
$688$	79.9213	3.04697
$689$	−0.683809	−0.0260510
$690$	−2.68566	−0.102241
$691$	1.06947	0.0406846	0.0203423	−	0.999793i	$-0.493524\pi$
$691$	1.06947	0.0406846	0.0203423	+	0.999793i	$0.493524\pi$
$692$	13.2620	0.504147
$693$	−0.595463	−0.0226198
$694$	−47.0992	−1.78786
$695$	5.18912	0.196835
$696$	−54.8046	−2.07736
$697$	−0.498141	−0.0188684
$698$	25.2478	0.955643
$699$	−7.32305	−0.276983
$700$	−13.0146	−0.491906
$701$	−2.52697	−0.0954424	−0.0477212	−	0.998861i	$-0.515196\pi$
$701$	−2.52697	−0.0954424	−0.0477212	+	0.998861i	$0.515196\pi$
$702$	−0.211050	−0.00796558
$703$	−6.09365	−0.229826
$704$	0.520247	0.0196076
$705$	−3.71164	−0.139788
$706$	37.7218	1.41968
$707$	5.88368	0.221279
$708$	3.01290	0.113232
$709$	−8.02051	−0.301217	−0.150608	−	0.988594i	$-0.548123\pi$
$709$	−8.02051	−0.301217	−0.150608	+	0.988594i	$0.548123\pi$
$710$	−10.7777	−0.404478
$711$	14.9245	0.559711
$712$	−9.63281	−0.361005
$713$	−9.79637	−0.366877
$714$	−10.5413	−0.394499
$715$	−0.0273660	−0.00102343
$716$	5.22087	0.195113
$717$	24.5442	0.916621
$718$	70.1591	2.61831
$719$	−17.4383	−0.650339	−0.325170	−	0.945656i	$-0.605421\pi$
$719$	−17.4383	−0.650339	−0.325170	+	0.945656i	$0.605421\pi$
$720$	2.31841	0.0864019
$721$	−4.30979	−0.160505
$722$	−45.3484	−1.68769
$723$	−18.3505	−0.682463
$724$	−49.2548	−1.83054
$725$	−42.6985	−1.58578
$726$	−2.54331	−0.0943913
$727$	−21.4232	−0.794541	−0.397271	−	0.917701i	$-0.630043\pi$
$727$	−21.4232	−0.794541	−0.397271	+	0.917701i	$0.630043\pi$
$728$	0.310217	0.0114974
$729$	1.00000	0.0370370
$730$	−0.928057	−0.0343489
$731$	79.1294	2.92671
$732$	−4.46845	−0.165159
$733$	24.8791	0.918929	0.459464	−	0.888196i	$-0.348041\pi$
$733$	24.8791	0.918929	0.459464	+	0.888196i	$0.348041\pi$
$734$	−64.4391	−2.37849
$735$	2.19153	0.0808359
$736$	17.0469	0.628356
$737$	−0.140859	−0.00518861
$738$	−0.182017	−0.00670015
$739$	−3.44825	−0.126846	−0.0634230	−	0.997987i	$-0.520202\pi$
$739$	−3.44825	−0.126846	−0.0634230	+	0.997987i	$0.520202\pi$
$740$	−8.30325	−0.305233
$741$	−0.0897424	−0.00329677
$742$	−12.4797	−0.458144
$743$	−18.1232	−0.664874	−0.332437	−	0.943125i	$-0.607871\pi$
$743$	−18.1232	−0.664874	−0.332437	+	0.943125i	$0.607871\pi$
$744$	19.2072	0.704171
$745$	−5.07171	−0.185813
$746$	58.3816	2.13750
$747$	−1.08794	−0.0398058
$748$	−31.1026	−1.13722
$749$	−10.0732	−0.368067
$750$	8.29614	0.302932
$751$	12.9982	0.474310	0.237155	−	0.971472i	$-0.423785\pi$
$751$	12.9982	0.474310	0.237155	+	0.971472i	$0.423785\pi$
$752$	79.1233	2.88533
$753$	−2.34673	−0.0855197
$754$	1.84238	0.0670954
$755$	5.46474	0.198882
$756$	−2.66080	−0.0967723
$757$	−16.0448	−0.583158	−0.291579	−	0.956547i	$-0.594181\pi$
$757$	−16.0448	−0.583158	−0.291579	+	0.956547i	$0.594181\pi$
$758$	−7.17365	−0.260559
$759$	3.20203	0.116226
$760$	2.23904	0.0812185
$761$	40.4165	1.46510	0.732549	−	0.680714i	$-0.238330\pi$
$761$	40.4165	1.46510	0.732549	+	0.680714i	$0.238330\pi$
$762$	20.3297	0.736468
$763$	3.45039	0.124912
$764$	−68.6532	−2.48379
$765$	2.29543	0.0829916
$766$	65.1419	2.35367
$767$	−0.0559518	−0.00202030
$768$	29.4048	1.06105
$769$	25.1456	0.906774	0.453387	−	0.891314i	$-0.350216\pi$
$769$	25.1456	0.906774	0.453387	+	0.891314i	$0.350216\pi$
$770$	−0.499437	−0.0179984
$771$	2.07933	0.0748854
$772$	−49.6822	−1.78810
$773$	−16.3560	−0.588284	−0.294142	−	0.955762i	$-0.595034\pi$
$773$	−16.3560	−0.588284	−0.294142	+	0.955762i	$0.595034\pi$
$774$	28.9134	1.03927
$775$	14.9644	0.537537
$776$	−54.9206	−1.97154
$777$	3.35522	0.120368
$778$	−5.15226	−0.184717
$779$	−0.0773971	−0.00277304
$780$	−0.122283	−0.00437845
$781$	12.8499	0.459805
$782$	56.6846	2.02704
$783$	−8.72957	−0.311970
$784$	−46.7183	−1.66851
$785$	−1.99957	−0.0713677
$786$	40.3690	1.43992
$787$	28.0304	0.999175	0.499588	−	0.866263i	$-0.333485\pi$
$787$	28.0304	0.999175	0.499588	+	0.866263i	$0.333485\pi$
$788$	−79.1560	−2.81981
$789$	24.1181	0.858625
$790$	12.5177	0.445359
$791$	−7.34034	−0.260992
$792$	−6.27804	−0.223081
$793$	0.0829823	0.00294679
$794$	2.74665	0.0974751
$795$	2.71753	0.0963808
$796$	109.554	3.88305
$797$	−35.6574	−1.26305	−0.631525	−	0.775356i	$-0.717571\pi$
$797$	−35.6574	−1.26305	−0.631525	+	0.775356i	$0.717571\pi$
$798$	−1.63782	−0.0579783
$799$	78.3393	2.77144
$800$	−26.0399	−0.920649
$801$	−1.53437	−0.0542141
$802$	8.90292	0.314373
$803$	1.10649	0.0390473
$804$	−0.629421	−0.0221980
$805$	0.628790	0.0221619
$806$	−0.645692	−0.0227435
$807$	13.9942	0.492620
$808$	62.0324	2.18229
$809$	13.6655	0.480452	0.240226	−	0.970717i	$-0.422778\pi$
$809$	13.6655	0.480452	0.240226	+	0.970717i	$0.422778\pi$
$810$	0.838736	0.0294702
$811$	47.8791	1.68126	0.840631	−	0.541608i	$-0.182184\pi$
$811$	47.8791	1.68126	0.840631	+	0.541608i	$0.182184\pi$
$812$	23.2276	0.815130
$813$	24.2791	0.851506
$814$	14.3306	0.502289
$815$	5.89059	0.206338
$816$	−48.9332	−1.71300
$817$	12.2945	0.430130
$818$	−69.1002	−2.41603
$819$	0.0494129	0.00172663
$820$	−0.105462	−0.00368288
$821$	8.04263	0.280690	0.140345	−	0.990103i	$-0.455179\pi$
$821$	8.04263	0.280690	0.140345	+	0.990103i	$0.455179\pi$
$822$	43.1514	1.50508
$823$	12.4433	0.433745	0.216872	−	0.976200i	$-0.430414\pi$
$823$	12.4433	0.433745	0.216872	+	0.976200i	$0.430414\pi$
$824$	−45.4387	−1.58293
$825$	−4.89124	−0.170291
$826$	−1.02114	−0.0355298
$827$	12.2012	0.424278	0.212139	−	0.977240i	$-0.431957\pi$
$827$	12.2012	0.424278	0.212139	+	0.977240i	$0.431957\pi$
$828$	14.3081	0.497241
$829$	−21.1707	−0.735288	−0.367644	−	0.929967i	$-0.619835\pi$
$829$	−21.1707	−0.735288	−0.367644	+	0.929967i	$0.619835\pi$
$830$	−0.912497	−0.0316732
$831$	16.3119	0.565852
$832$	−0.0431713	−0.00149670
$833$	−46.2554	−1.60265
$834$	−40.0192	−1.38575
$835$	6.99307	0.242005
$836$	−4.83247	−0.167134
$837$	3.05943	0.105749
$838$	−39.8683	−1.37723
$839$	−39.8488	−1.37573	−0.687867	−	0.725837i	$-0.741453\pi$
$839$	−39.8488	−1.37573	−0.687867	+	0.725837i	$0.741453\pi$
$840$	−1.23283	−0.0425368
$841$	47.2055	1.62777
$842$	−3.57861	−0.123327
$843$	−13.7085	−0.472144
$844$	41.7509	1.43713
$845$	−4.28488	−0.147404
$846$	28.6246	0.984136
$847$	0.595463	0.0204604
$848$	−57.9313	−1.98937
$849$	−31.0223	−1.06468
$850$	−86.5883	−2.96995
$851$	−18.0423	−0.618481
$852$	57.4190	1.96714
$853$	47.3637	1.62170	0.810851	−	0.585252i	$-0.199005\pi$
$853$	47.3637	1.62170	0.810851	+	0.585252i	$0.199005\pi$
$854$	1.51445	0.0518234
$855$	0.356646	0.0121970
$856$	−106.203	−3.62995
$857$	0.0360945	0.00123297	0.000616483	−	1.00000i	$-0.499804\pi$
$857$	0.0360945	0.00123297	0.000616483		1.00000i	$0.499804\pi$
$858$	0.211050	0.00720513
$859$	−6.64544	−0.226740	−0.113370	−	0.993553i	$-0.536164\pi$
$859$	−6.64544	−0.226740	−0.113370	+	0.993553i	$0.536164\pi$
$860$	16.7525	0.571257
$861$	0.0426155	0.00145233
$862$	−59.8650	−2.03901
$863$	29.7608	1.01307	0.506535	−	0.862219i	$-0.330926\pi$
$863$	29.7608	1.01307	0.506535	+	0.862219i	$0.330926\pi$
$864$	−5.32378	−0.181119
$865$	0.978765	0.0332790
$866$	74.4454	2.52976
$867$	−31.4484	−1.06804
$868$	−8.14052	−0.276307
$869$	−14.9245	−0.506278
$870$	−7.32181	−0.248233
$871$	0.0116888	0.000396060 0
$872$	36.3779	1.23191
$873$	−8.74805	−0.296077
$874$	8.80719	0.297908
$875$	−1.94237	−0.0656640
$876$	4.94431	0.167053
$877$	−16.7597	−0.565934	−0.282967	−	0.959130i	$-0.591319\pi$
$877$	−16.7597	−0.565934	−0.282967	+	0.959130i	$0.591319\pi$
$878$	−43.4121	−1.46509
$879$	−4.76769	−0.160810
$880$	−2.31841	−0.0781534
$881$	24.3345	0.819851	0.409925	−	0.912119i	$-0.365555\pi$
$881$	24.3345	0.819851	0.409925	+	0.912119i	$0.365555\pi$
$882$	−16.9014	−0.569100
$883$	26.7278	0.899461	0.449731	−	0.893164i	$-0.351520\pi$
$883$	26.7278	0.899461	0.449731	+	0.893164i	$0.351520\pi$
$884$	2.58096	0.0868072
$885$	0.222358	0.00747449
$886$	−83.7404	−2.81331
$887$	42.4352	1.42484	0.712418	−	0.701756i	$-0.247600\pi$
$887$	42.4352	1.42484	0.712418	+	0.701756i	$0.247600\pi$
$888$	35.3745	1.18709
$889$	−4.75977	−0.159638
$890$	−1.28693	−0.0431379
$891$	−1.00000	−0.0335013
$892$	−106.585	−3.56874
$893$	12.1717	0.407311
$894$	39.1138	1.30816
$895$	0.385311	0.0128795
$896$	−7.12812	−0.238134
$897$	−0.265712	−0.00887186
$898$	−78.2579	−2.61150
$899$	−26.7075	−0.890745
$900$	−21.8563	−0.728543
$901$	−57.3573	−1.91085
$902$	0.182017	0.00606052
$903$	−6.76945	−0.225273
$904$	−77.3901	−2.57396
$905$	−3.63511	−0.120835
$906$	−42.1448	−1.40017
$907$	−7.59234	−0.252100	−0.126050	−	0.992024i	$-0.540230\pi$
$907$	−7.59234	−0.252100	−0.126050	+	0.992024i	$0.540230\pi$
$908$	22.2818	0.739448
$909$	9.88085	0.327727
$910$	0.0414444	0.00137387
$911$	−30.6962	−1.01701	−0.508505	−	0.861059i	$-0.669802\pi$
$911$	−30.6962	−1.01701	−0.508505	+	0.861059i	$0.669802\pi$
$912$	−7.60284	−0.251755
$913$	1.08794	0.0360057
$914$	−30.2640	−1.00104
$915$	−0.329781	−0.0109022
$916$	4.09247	0.135219
$917$	−9.45155	−0.312118
$918$	−17.7027	−0.584276
$919$	−47.5570	−1.56876	−0.784380	−	0.620281i	$-0.787019\pi$
$919$	−47.5570	−1.56876	−0.784380	+	0.620281i	$0.787019\pi$
$920$	6.62941	0.218565
$921$	9.09194	0.299590
$922$	24.2576	0.798880
$923$	−1.06631	−0.0350981
$924$	2.66080	0.0875338
$925$	27.5604	0.906180
$926$	57.9972	1.90590
$927$	−7.23771	−0.237718
$928$	46.4743	1.52559
$929$	−24.6228	−0.807847	−0.403923	−	0.914793i	$-0.632354\pi$
$929$	−24.6228	−0.807847	−0.403923	+	0.914793i	$0.632354\pi$
$930$	2.56605	0.0841442
$931$	−7.18678	−0.235537
$932$	32.7227	1.07187
$933$	−0.130155	−0.00426108
$934$	104.473	3.41847
$935$	−2.29543	−0.0750687
$936$	0.520967	0.0170283
$937$	13.4835	0.440487	0.220244	−	0.975445i	$-0.429315\pi$
$937$	13.4835	0.440487	0.220244	+	0.975445i	$0.429315\pi$
$938$	0.213324	0.00696527
$939$	18.8073	0.613753
$940$	16.5853	0.540951
$941$	−51.2951	−1.67217	−0.836086	−	0.548598i	$-0.815162\pi$
$941$	−51.2951	−1.67217	−0.836086	+	0.548598i	$0.815162\pi$
$942$	15.4210	0.502442
$943$	−0.229160	−0.00746246
$944$	−4.74015	−0.154279
$945$	−0.196372	−0.00638799
$946$	−28.9134	−0.940054
$947$	36.6121	1.18973	0.594867	−	0.803824i	$-0.297205\pi$
$947$	36.6121	1.18973	0.594867	+	0.803824i	$0.297205\pi$
$948$	−66.6892	−2.16597
$949$	−0.0918195	−0.00298059
$950$	−13.4534	−0.436485
$951$	−21.5314	−0.698203
$952$	26.0207	0.843336
$953$	−34.3089	−1.11137	−0.555687	−	0.831392i	$-0.687545\pi$
$953$	−34.3089	−1.11137	−0.555687	+	0.831392i	$0.687545\pi$
$954$	−20.9580	−0.678539
$955$	−5.06675	−0.163956
$956$	−109.675	−3.54713
$957$	8.72957	0.282187
$958$	−30.1049	−0.972646
$959$	−10.1030	−0.326243
$960$	0.171568	0.00553732
$961$	−21.6399	−0.698062
$962$	−1.18919	−0.0383410
$963$	−16.9166	−0.545130
$964$	81.9984	2.64099
$965$	−3.66665	−0.118034
$966$	−4.84931	−0.156024
$967$	35.6507	1.14645	0.573225	−	0.819398i	$-0.305692\pi$
$967$	35.6507	1.14645	0.573225	+	0.819398i	$0.305692\pi$
$968$	6.27804	0.201784
$969$	−7.52751	−0.241819
$970$	−7.33730	−0.235587
$971$	2.45087	0.0786520	0.0393260	−	0.999226i	$-0.487479\pi$
$971$	2.45087	0.0786520	0.0393260	+	0.999226i	$0.487479\pi$
$972$	−4.46845	−0.143326
$973$	9.36965	0.300377
$974$	59.0564	1.89229
$975$	0.405887	0.0129988
$976$	7.03014	0.225029
$977$	−36.7003	−1.17415	−0.587073	−	0.809534i	$-0.699720\pi$
$977$	−36.7003	−1.17415	−0.587073	+	0.809534i	$0.699720\pi$
$978$	−45.4290	−1.45266
$979$	1.53437	0.0490385
$980$	−9.79275	−0.312818
$981$	5.79446	0.185003
$982$	−27.1017	−0.864851
$983$	−34.5193	−1.10099	−0.550497	−	0.834837i	$-0.685562\pi$
$983$	−34.5193	−1.10099	−0.550497	+	0.834837i	$0.685562\pi$
$984$	0.449301	0.0143232
$985$	−5.84187	−0.186138
$986$	154.537	4.92146
$987$	−6.70186	−0.213322
$988$	0.401009	0.0127578
$989$	36.4019	1.15751
$990$	−0.838736	−0.0266568
$991$	−36.6557	−1.16441	−0.582204	−	0.813043i	$-0.697809\pi$
$991$	−36.6557	−1.16441	−0.582204	+	0.813043i	$0.697809\pi$
$992$	−16.2877	−0.517135
$993$	5.77423	0.183240
$994$	−19.4605	−0.617250
$995$	8.08533	0.256322
$996$	4.86142	0.154040
$997$	17.8981	0.566840	0.283420	−	0.958996i	$-0.408531\pi$
$997$	17.8981	0.566840	0.283420	+	0.958996i	$0.408531\pi$
$998$	105.840	3.35032
$999$	5.63463	0.178272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.13	✓	14
3.2	odd	2		6039.2.a.j.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.13	✓	14	1.1	even	1	trivial
6039.2.a.j.1.2		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.54331 q^{2} -1.00000 q^{3} +4.46845 q^{4} +0.329781 q^{5} -2.54331 q^{6} +0.595463 q^{7} +6.27804 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54331 q^{2} -1.00000 q^{3} +4.46845 q^{4} +0.329781 q^{5} -2.54331 q^{6} +0.595463 q^{7} +6.27804 q^{8} +1.00000 q^{9} +0.838736 q^{10} -1.00000 q^{11} -4.46845 q^{12} +0.0829823 q^{13} +1.51445 q^{14} -0.329781 q^{15} +7.03014 q^{16} +6.96049 q^{17} +2.54331 q^{18} +1.08146 q^{19} +1.47361 q^{20} -0.595463 q^{21} -2.54331 q^{22} +3.20203 q^{23} -6.27804 q^{24} -4.89124 q^{25} +0.211050 q^{26} -1.00000 q^{27} +2.66080 q^{28} +8.72957 q^{29} -0.838736 q^{30} -3.05943 q^{31} +5.32378 q^{32} +1.00000 q^{33} +17.7027 q^{34} +0.196372 q^{35} +4.46845 q^{36} -5.63463 q^{37} +2.75050 q^{38} -0.0829823 q^{39} +2.07038 q^{40} -0.0715670 q^{41} -1.51445 q^{42} +11.3684 q^{43} -4.46845 q^{44} +0.329781 q^{45} +8.14377 q^{46} +11.2549 q^{47} -7.03014 q^{48} -6.64542 q^{49} -12.4400 q^{50} -6.96049 q^{51} +0.370802 q^{52} -8.24041 q^{53} -2.54331 q^{54} -0.329781 q^{55} +3.73835 q^{56} -1.08146 q^{57} +22.2021 q^{58} -0.674261 q^{59} -1.47361 q^{60} +1.00000 q^{61} -7.78108 q^{62} +0.595463 q^{63} -0.520247 q^{64} +0.0273660 q^{65} +2.54331 q^{66} +0.140859 q^{67} +31.1026 q^{68} -3.20203 q^{69} +0.499437 q^{70} -12.8499 q^{71} +6.27804 q^{72} -1.10649 q^{73} -14.3306 q^{74} +4.89124 q^{75} +4.83247 q^{76} -0.595463 q^{77} -0.211050 q^{78} +14.9245 q^{79} +2.31841 q^{80} +1.00000 q^{81} -0.182017 q^{82} -1.08794 q^{83} -2.66080 q^{84} +2.29543 q^{85} +28.9134 q^{86} -8.72957 q^{87} -6.27804 q^{88} -1.53437 q^{89} +0.838736 q^{90} +0.0494129 q^{91} +14.3081 q^{92} +3.05943 q^{93} +28.6246 q^{94} +0.356646 q^{95} -5.32378 q^{96} -8.74805 q^{97} -16.9014 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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