LMFDB - Embedded newform 2013.2.a.c.1.1

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 $ x^12 - 5x^11 - 5x^10 + 48x^9 - 173x^7 + 29x^6 + 281x^5 - 41x^4 - 201x^3 + 8x^2 + 49x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73351$ 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)

$f(q)$	$=$	$q-2.73351 q^{2} +1.00000 q^{3} +5.47208 q^{4} -3.64694 q^{5} -2.73351 q^{6} -3.96128 q^{7} -9.49098 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73351 q^{2} +1.00000 q^{3} +5.47208 q^{4} -3.64694 q^{5} -2.73351 q^{6} -3.96128 q^{7} -9.49098 q^{8} +1.00000 q^{9} +9.96895 q^{10} +1.00000 q^{11} +5.47208 q^{12} +2.49181 q^{13} +10.8282 q^{14} -3.64694 q^{15} +14.9995 q^{16} -4.84898 q^{17} -2.73351 q^{18} -0.0465231 q^{19} -19.9564 q^{20} -3.96128 q^{21} -2.73351 q^{22} +7.87558 q^{23} -9.49098 q^{24} +8.30017 q^{25} -6.81139 q^{26} +1.00000 q^{27} -21.6765 q^{28} +4.43593 q^{29} +9.96895 q^{30} +10.7837 q^{31} -22.0194 q^{32} +1.00000 q^{33} +13.2547 q^{34} +14.4466 q^{35} +5.47208 q^{36} -5.41262 q^{37} +0.127171 q^{38} +2.49181 q^{39} +34.6130 q^{40} -1.28084 q^{41} +10.8282 q^{42} +6.56966 q^{43} +5.47208 q^{44} -3.64694 q^{45} -21.5280 q^{46} +0.000570449 q^{47} +14.9995 q^{48} +8.69175 q^{49} -22.6886 q^{50} -4.84898 q^{51} +13.6354 q^{52} -9.54719 q^{53} -2.73351 q^{54} -3.64694 q^{55} +37.5964 q^{56} -0.0465231 q^{57} -12.1257 q^{58} -7.63076 q^{59} -19.9564 q^{60} -1.00000 q^{61} -29.4773 q^{62} -3.96128 q^{63} +30.1913 q^{64} -9.08748 q^{65} -2.73351 q^{66} -8.92768 q^{67} -26.5340 q^{68} +7.87558 q^{69} -39.4898 q^{70} +10.4879 q^{71} -9.49098 q^{72} -13.5644 q^{73} +14.7955 q^{74} +8.30017 q^{75} -0.254578 q^{76} -3.96128 q^{77} -6.81139 q^{78} -8.55077 q^{79} -54.7024 q^{80} +1.00000 q^{81} +3.50118 q^{82} +3.71971 q^{83} -21.6765 q^{84} +17.6839 q^{85} -17.9582 q^{86} +4.43593 q^{87} -9.49098 q^{88} -13.8620 q^{89} +9.96895 q^{90} -9.87077 q^{91} +43.0958 q^{92} +10.7837 q^{93} -0.00155933 q^{94} +0.169667 q^{95} -22.0194 q^{96} -6.11297 q^{97} -23.7590 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * 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 $

$2$	−2.73351	−1.93288	−0.966442	−	0.256884i	$-0.917304\pi$
$2$	−2.73351	−1.93288	−0.966442	+	0.256884i	$0.917304\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.47208	2.73604
$5$	−3.64694	−1.63096	−0.815480	−	0.578785i	$-0.803527\pi$
$5$	−3.64694	−1.63096	−0.815480	+	0.578785i	$0.803527\pi$
$6$	−2.73351	−1.11595
$7$	−3.96128	−1.49722	−0.748612	−	0.663009i	$-0.769279\pi$
$7$	−3.96128	−1.49722	−0.748612	+	0.663009i	$0.769279\pi$
$8$	−9.49098	−3.35557
$9$	1.00000	0.333333
$10$	9.96895	3.15246
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.47208	1.57965
$13$	2.49181	0.691104	0.345552	−	0.938400i	$-0.387692\pi$
$13$	2.49181	0.691104	0.345552	+	0.938400i	$0.387692\pi$
$14$	10.8282	2.89396
$15$	−3.64694	−0.941636
$16$	14.9995	3.74988
$17$	−4.84898	−1.17605	−0.588026	−	0.808842i	$-0.700095\pi$
$17$	−4.84898	−1.17605	−0.588026	+	0.808842i	$0.700095\pi$
$18$	−2.73351	−0.644295
$19$	−0.0465231	−0.0106731	−0.00533656	−	0.999986i	$-0.501699\pi$
$19$	−0.0465231	−0.0106731	−0.00533656	+	0.999986i	$0.501699\pi$
$20$	−19.9564	−4.46238
$21$	−3.96128	−0.864423
$22$	−2.73351	−0.582787
$23$	7.87558	1.64217	0.821086	−	0.570804i	$-0.193369\pi$
$23$	7.87558	1.64217	0.821086	+	0.570804i	$0.193369\pi$
$24$	−9.49098	−1.93734
$25$	8.30017	1.66003
$26$	−6.81139	−1.33582
$27$	1.00000	0.192450
$28$	−21.6765	−4.09647
$29$	4.43593	0.823732	0.411866	−	0.911245i	$-0.364877\pi$
$29$	4.43593	0.823732	0.411866	+	0.911245i	$0.364877\pi$
$30$	9.96895	1.82007
$31$	10.7837	1.93680	0.968402	−	0.249394i	$-0.0802314\pi$
$31$	10.7837	1.93680	0.968402	+	0.249394i	$0.0802314\pi$
$32$	−22.0194	−3.89252
$33$	1.00000	0.174078
$34$	13.2547	2.27317
$35$	14.4466	2.44191
$36$	5.47208	0.912014
$37$	−5.41262	−0.889830	−0.444915	−	0.895573i	$-0.646766\pi$
$37$	−5.41262	−0.889830	−0.444915	+	0.895573i	$0.646766\pi$
$38$	0.127171	0.0206299
$39$	2.49181	0.399009
$40$	34.6130	5.47280
$41$	−1.28084	−0.200033	−0.100017	−	0.994986i	$-0.531890\pi$
$41$	−1.28084	−0.200033	−0.100017	+	0.994986i	$0.531890\pi$
$42$	10.8282	1.67083
$43$	6.56966	1.00186	0.500932	−	0.865487i	$-0.332991\pi$
$43$	6.56966	1.00186	0.500932	+	0.865487i	$0.332991\pi$
$44$	5.47208	0.824948
$45$	−3.64694	−0.543654
$46$	−21.5280	−3.17413
$47$	0.000570449 0	8.32086e−5 0	4.16043e−5	−	1.00000i	$-0.499987\pi$
$47$	0.000570449 0	8.32086e−5 0	4.16043e−5		1.00000i	$0.499987\pi$
$48$	14.9995	2.16500
$49$	8.69175	1.24168
$50$	−22.6886	−3.20865
$51$	−4.84898	−0.678993
$52$	13.6354	1.89089
$53$	−9.54719	−1.31141	−0.655704	−	0.755018i	$-0.727628\pi$
$53$	−9.54719	−1.31141	−0.655704	+	0.755018i	$0.727628\pi$
$54$	−2.73351	−0.371984
$55$	−3.64694	−0.491753
$56$	37.5964	5.02403
$57$	−0.0465231	−0.00616213
$58$	−12.1257	−1.59218
$59$	−7.63076	−0.993440	−0.496720	−	0.867911i	$-0.665462\pi$
$59$	−7.63076	−0.993440	−0.496720	+	0.867911i	$0.665462\pi$
$60$	−19.9564	−2.57635
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−29.4773	−3.74362
$63$	−3.96128	−0.499075
$64$	30.1913	3.77391
$65$	−9.08748	−1.12716
$66$	−2.73351	−0.336472
$67$	−8.92768	−1.09069	−0.545345	−	0.838212i	$-0.683601\pi$
$67$	−8.92768	−1.09069	−0.545345	+	0.838212i	$0.683601\pi$
$68$	−26.5340	−3.21772
$69$	7.87558	0.948109
$70$	−39.4898	−4.71994
$71$	10.4879	1.24469	0.622343	−	0.782745i	$-0.286181\pi$
$71$	10.4879	1.24469	0.622343	+	0.782745i	$0.286181\pi$
$72$	−9.49098	−1.11852
$73$	−13.5644	−1.58759	−0.793797	−	0.608183i	$-0.791899\pi$
$73$	−13.5644	−1.58759	−0.793797	+	0.608183i	$0.791899\pi$
$74$	14.7955	1.71994
$75$	8.30017	0.958421
$76$	−0.254578	−0.0292021
$77$	−3.96128	−0.451430
$78$	−6.81139	−0.771238
$79$	−8.55077	−0.962036	−0.481018	−	0.876711i	$-0.659733\pi$
$79$	−8.55077	−0.962036	−0.481018	+	0.876711i	$0.659733\pi$
$80$	−54.7024	−6.11591
$81$	1.00000	0.111111
$82$	3.50118	0.386641
$83$	3.71971	0.408291	0.204146	−	0.978941i	$-0.434558\pi$
$83$	3.71971	0.408291	0.204146	+	0.978941i	$0.434558\pi$
$84$	−21.6765	−2.36510
$85$	17.6839	1.91809
$86$	−17.9582	−1.93649
$87$	4.43593	0.475582
$88$	−9.49098	−1.01174
$89$	−13.8620	−1.46937	−0.734684	−	0.678409i	$-0.762670\pi$
$89$	−13.8620	−1.46937	−0.734684	+	0.678409i	$0.762670\pi$
$90$	9.96895	1.05082
$91$	−9.87077	−1.03474
$92$	43.0958	4.49305
$93$	10.7837	1.11821
$94$	−0.00155933	−0.000160833 0
$95$	0.169667	0.0174074
$96$	−22.0194	−2.24735
$97$	−6.11297	−0.620678	−0.310339	−	0.950626i	$-0.600443\pi$
$97$	−6.11297	−0.620678	−0.310339	+	0.950626i	$0.600443\pi$
$98$	−23.7590	−2.40002
$99$	1.00000	0.100504
$100$	45.4192	4.54192
$101$	−15.6307	−1.55531	−0.777655	−	0.628691i	$-0.783591\pi$
$101$	−15.6307	−1.55531	−0.777655	+	0.628691i	$0.783591\pi$
$102$	13.2547	1.31242
$103$	−9.08974	−0.895639	−0.447819	−	0.894124i	$-0.647799\pi$
$103$	−9.08974	−0.895639	−0.447819	+	0.894124i	$0.647799\pi$
$104$	−23.6497	−2.31905
$105$	14.4466	1.40984
$106$	26.0973	2.53480
$107$	12.4016	1.19891	0.599453	−	0.800410i	$-0.295385\pi$
$107$	12.4016	1.19891	0.599453	+	0.800410i	$0.295385\pi$
$108$	5.47208	0.526551
$109$	6.19519	0.593392	0.296696	−	0.954972i	$-0.404115\pi$
$109$	6.19519	0.593392	0.296696	+	0.954972i	$0.404115\pi$
$110$	9.96895	0.950502
$111$	−5.41262	−0.513743
$112$	−59.4173	−5.61441
$113$	11.2098	1.05453	0.527263	−	0.849702i	$-0.323218\pi$
$113$	11.2098	1.05453	0.527263	+	0.849702i	$0.323218\pi$
$114$	0.127171	0.0119107
$115$	−28.7218	−2.67832
$116$	24.2738	2.25376
$117$	2.49181	0.230368
$118$	20.8588	1.92020
$119$	19.2082	1.76081
$120$	34.6130	3.15972
$121$	1.00000	0.0909091
$122$	2.73351	0.247480
$123$	−1.28084	−0.115489
$124$	59.0091	5.29918
$125$	−12.0355	−1.07649
$126$	10.8282	0.964653
$127$	1.57944	0.140153	0.0700763	−	0.997542i	$-0.477676\pi$
$127$	1.57944	0.140153	0.0700763	+	0.997542i	$0.477676\pi$
$128$	−38.4893	−3.40201
$129$	6.56966	0.578426
$130$	24.8407	2.17868
$131$	−11.9942	−1.04794	−0.523970	−	0.851736i	$-0.675550\pi$
$131$	−11.9942	−1.04794	−0.523970	+	0.851736i	$0.675550\pi$
$132$	5.47208	0.476284
$133$	0.184291	0.0159800
$134$	24.4039	2.10818
$135$	−3.64694	−0.313879
$136$	46.0216	3.94632
$137$	9.02980	0.771468	0.385734	−	0.922610i	$-0.373948\pi$
$137$	9.02980	0.771468	0.385734	+	0.922610i	$0.373948\pi$
$138$	−21.5280	−1.83258
$139$	−7.43255	−0.630421	−0.315210	−	0.949022i	$-0.602075\pi$
$139$	−7.43255	−0.630421	−0.315210	+	0.949022i	$0.602075\pi$
$140$	79.0527	6.68118
$141$	0.000570449 0	4.80405e−5 0
$142$	−28.6688	−2.40583
$143$	2.49181	0.208376
$144$	14.9995	1.24996
$145$	−16.1776	−1.34347
$146$	37.0784	3.06863
$147$	8.69175	0.716884
$148$	−29.6183	−2.43461
$149$	−9.09929	−0.745443	−0.372722	−	0.927943i	$-0.621575\pi$
$149$	−9.09929	−0.745443	−0.372722	+	0.927943i	$0.621575\pi$
$150$	−22.6886	−1.85252
$151$	10.5174	0.855891	0.427946	−	0.903804i	$-0.359237\pi$
$151$	10.5174	0.855891	0.427946	+	0.903804i	$0.359237\pi$
$152$	0.441549	0.0358144
$153$	−4.84898	−0.392017
$154$	10.8282	0.872562
$155$	−39.3274	−3.15885
$156$	13.6354	1.09171
$157$	−19.3242	−1.54224	−0.771118	−	0.636692i	$-0.780302\pi$
$157$	−19.3242	−1.54224	−0.771118	+	0.636692i	$0.780302\pi$
$158$	23.3736	1.85951
$159$	−9.54719	−0.757141
$160$	80.3035	6.34855
$161$	−31.1974	−2.45870
$162$	−2.73351	−0.214765
$163$	2.98353	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$163$	2.98353	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$164$	−7.00885	−0.547299
$165$	−3.64694	−0.283914
$166$	−10.1679	−0.789180
$167$	−6.61012	−0.511507	−0.255753	−	0.966742i	$-0.582323\pi$
$167$	−6.61012	−0.511507	−0.255753	+	0.966742i	$0.582323\pi$
$168$	37.5964	2.90063
$169$	−6.79088	−0.522375
$170$	−48.3393	−3.70745
$171$	−0.0465231	−0.00355771
$172$	35.9497	2.74114
$173$	7.02661	0.534223	0.267111	−	0.963666i	$-0.413931\pi$
$173$	7.02661	0.534223	0.267111	+	0.963666i	$0.413931\pi$
$174$	−12.1257	−0.919244
$175$	−32.8793	−2.48544
$176$	14.9995	1.13063
$177$	−7.63076	−0.573563
$178$	37.8919	2.84012
$179$	22.3293	1.66897	0.834486	−	0.551029i	$-0.185765\pi$
$179$	22.3293	1.66897	0.834486	+	0.551029i	$0.185765\pi$
$180$	−19.9564	−1.48746
$181$	15.6618	1.16413	0.582067	−	0.813141i	$-0.302244\pi$
$181$	15.6618	1.16413	0.582067	+	0.813141i	$0.302244\pi$
$182$	26.9818	2.00003
$183$	−1.00000	−0.0739221
$184$	−74.7470	−5.51042
$185$	19.7395	1.45128
$186$	−29.4773	−2.16138
$187$	−4.84898	−0.354593
$188$	0.00312155	0.000227662 0
$189$	−3.96128	−0.288141
$190$	−0.463786	−0.0336466
$191$	−21.8177	−1.57868	−0.789338	−	0.613959i	$-0.789576\pi$
$191$	−21.8177	−1.57868	−0.789338	+	0.613959i	$0.789576\pi$
$192$	30.1913	2.17887
$193$	0.455455	0.0327843	0.0163922	−	0.999866i	$-0.494782\pi$
$193$	0.455455	0.0327843	0.0163922	+	0.999866i	$0.494782\pi$
$194$	16.7099	1.19970
$195$	−9.08748	−0.650768
$196$	47.5620	3.39728
$197$	23.1632	1.65031	0.825155	−	0.564906i	$-0.191088\pi$
$197$	23.1632	1.65031	0.825155	+	0.564906i	$0.191088\pi$
$198$	−2.73351	−0.194262
$199$	4.75326	0.336949	0.168475	−	0.985706i	$-0.446116\pi$
$199$	4.75326	0.336949	0.168475	+	0.985706i	$0.446116\pi$
$200$	−78.7767	−5.57035
$201$	−8.92768	−0.629710
$202$	42.7266	3.00624
$203$	−17.5720	−1.23331
$204$	−26.5340	−1.85775
$205$	4.67113	0.326246
$206$	24.8469	1.73117
$207$	7.87558	0.547391
$208$	37.3760	2.59156
$209$	−0.0465231	−0.00321807
$210$	−39.4898	−2.72506
$211$	−25.2215	−1.73632	−0.868162	−	0.496282i	$-0.834698\pi$
$211$	−25.2215	−1.73632	−0.868162	+	0.496282i	$0.834698\pi$
$212$	−52.2430	−3.58806
$213$	10.4879	0.718620
$214$	−33.8999	−2.31735
$215$	−23.9592	−1.63400
$216$	−9.49098	−0.645779
$217$	−42.7172	−2.89983
$218$	−16.9346	−1.14696
$219$	−13.5644	−0.916597
$220$	−19.9564	−1.34546
$221$	−12.0827	−0.812774
$222$	14.7955	0.993007
$223$	−6.05952	−0.405776	−0.202888	−	0.979202i	$-0.565033\pi$
$223$	−6.05952	−0.405776	−0.202888	+	0.979202i	$0.565033\pi$
$224$	87.2251	5.82797
$225$	8.30017	0.553344
$226$	−30.6420	−2.03828
$227$	−11.2156	−0.744402	−0.372201	−	0.928152i	$-0.621397\pi$
$227$	−11.2156	−0.744402	−0.372201	+	0.928152i	$0.621397\pi$
$228$	−0.254578	−0.0168598
$229$	22.6663	1.49783	0.748916	−	0.662665i	$-0.230575\pi$
$229$	22.6663	1.49783	0.748916	+	0.662665i	$0.230575\pi$
$230$	78.5113	5.17688
$231$	−3.96128	−0.260633
$232$	−42.1013	−2.76409
$233$	−7.95089	−0.520880	−0.260440	−	0.965490i	$-0.583868\pi$
$233$	−7.95089	−0.520880	−0.260440	+	0.965490i	$0.583868\pi$
$234$	−6.81139	−0.445275
$235$	−0.00208039	−0.000135710 0
$236$	−41.7561	−2.71809
$237$	−8.55077	−0.555432
$238$	−52.5058	−3.40345
$239$	21.7846	1.40913	0.704563	−	0.709642i	$-0.251143\pi$
$239$	21.7846	1.40913	0.704563	+	0.709642i	$0.251143\pi$
$240$	−54.7024	−3.53102
$241$	−4.08238	−0.262970	−0.131485	−	0.991318i	$-0.541974\pi$
$241$	−4.08238	−0.262970	−0.131485	+	0.991318i	$0.541974\pi$
$242$	−2.73351	−0.175717
$243$	1.00000	0.0641500
$244$	−5.47208	−0.350314
$245$	−31.6983	−2.02513
$246$	3.50118	0.223227
$247$	−0.115927	−0.00737624
$248$	−102.348	−6.49908
$249$	3.71971	0.235727
$250$	32.8992	2.08073
$251$	−17.4417	−1.10091	−0.550454	−	0.834865i	$-0.685546\pi$
$251$	−17.4417	−1.10091	−0.550454	+	0.834865i	$0.685546\pi$
$252$	−21.6765	−1.36549
$253$	7.87558	0.495134
$254$	−4.31742	−0.270899
$255$	17.6839	1.10741
$256$	44.8285	2.80178
$257$	−5.20391	−0.324611	−0.162306	−	0.986741i	$-0.551893\pi$
$257$	−5.20391	−0.324611	−0.162306	+	0.986741i	$0.551893\pi$
$258$	−17.9582	−1.11803
$259$	21.4409	1.33227
$260$	−49.7275	−3.08397
$261$	4.43593	0.274577
$262$	32.7864	2.02555
$263$	8.82731	0.544315	0.272158	−	0.962253i	$-0.412263\pi$
$263$	8.82731	0.544315	0.272158	+	0.962253i	$0.412263\pi$
$264$	−9.49098	−0.584129
$265$	34.8180	2.13885
$266$	−0.503761	−0.0308876
$267$	−13.8620	−0.848341
$268$	−48.8530	−2.98417
$269$	21.3260	1.30027	0.650135	−	0.759819i	$-0.274712\pi$
$269$	21.3260	1.30027	0.650135	+	0.759819i	$0.274712\pi$
$270$	9.96895	0.606691
$271$	−17.7756	−1.07979	−0.539895	−	0.841732i	$-0.681536\pi$
$271$	−17.7756	−1.07979	−0.539895	+	0.841732i	$0.681536\pi$
$272$	−72.7325	−4.41005
$273$	−9.87077	−0.597406
$274$	−24.6831	−1.49116
$275$	8.30017	0.500519
$276$	43.0958	2.59406
$277$	−22.8321	−1.37185	−0.685924	−	0.727673i	$-0.740602\pi$
$277$	−22.8321	−1.37185	−0.685924	+	0.727673i	$0.740602\pi$
$278$	20.3170	1.21853
$279$	10.7837	0.645601
$280$	−137.112	−8.19400
$281$	4.80146	0.286431	0.143215	−	0.989692i	$-0.454256\pi$
$281$	4.80146	0.286431	0.143215	+	0.989692i	$0.454256\pi$
$282$	−0.00155933	−9.28567e−5 0
$283$	−21.8710	−1.30009	−0.650047	−	0.759894i	$-0.725251\pi$
$283$	−21.8710	−1.30009	−0.650047	+	0.759894i	$0.725251\pi$
$284$	57.3907	3.40551
$285$	0.169667	0.0100502
$286$	−6.81139	−0.402766
$287$	5.07376	0.299494
$288$	−22.0194	−1.29751
$289$	6.51264	0.383096
$290$	44.2216	2.59678
$291$	−6.11297	−0.358349
$292$	−74.2255	−4.34372
$293$	4.29126	0.250698	0.125349	−	0.992113i	$-0.459995\pi$
$293$	4.29126	0.250698	0.125349	+	0.992113i	$0.459995\pi$
$294$	−23.7590	−1.38565
$295$	27.8289	1.62026
$296$	51.3711	2.98588
$297$	1.00000	0.0580259
$298$	24.8730	1.44086
$299$	19.6245	1.13491
$300$	45.4192	2.62228
$301$	−26.0243	−1.50001
$302$	−28.7493	−1.65434
$303$	−15.6307	−0.897959
$304$	−0.697824	−0.0400229
$305$	3.64694	0.208823
$306$	13.2547	0.757724
$307$	−16.6202	−0.948566	−0.474283	−	0.880373i	$-0.657293\pi$
$307$	−16.6202	−0.948566	−0.474283	+	0.880373i	$0.657293\pi$
$308$	−21.6765	−1.23513
$309$	−9.08974	−0.517097
$310$	107.502	6.10569
$311$	−1.40402	−0.0796148	−0.0398074	−	0.999207i	$-0.512674\pi$
$311$	−1.40402	−0.0796148	−0.0398074	+	0.999207i	$0.512674\pi$
$312$	−23.6497	−1.33890
$313$	7.92475	0.447933	0.223967	−	0.974597i	$-0.428099\pi$
$313$	7.92475	0.447933	0.223967	+	0.974597i	$0.428099\pi$
$314$	52.8228	2.98096
$315$	14.4466	0.813971
$316$	−46.7905	−2.63217
$317$	0.811864	0.0455988	0.0227994	−	0.999740i	$-0.492742\pi$
$317$	0.811864	0.0455988	0.0227994	+	0.999740i	$0.492742\pi$
$318$	26.0973	1.46347
$319$	4.43593	0.248364
$320$	−110.106	−6.15510
$321$	12.4016	0.692189
$322$	85.2784	4.75238
$323$	0.225590	0.0125521
$324$	5.47208	0.304005
$325$	20.6824	1.14726
$326$	−8.15551	−0.451692
$327$	6.19519	0.342595
$328$	12.1564	0.671225
$329$	−0.00225971	−0.000124582 0
$330$	9.96895	0.548773
$331$	−0.889505	−0.0488916	−0.0244458	−	0.999701i	$-0.507782\pi$
$331$	−0.889505	−0.0488916	−0.0244458	+	0.999701i	$0.507782\pi$
$332$	20.3546	1.11710
$333$	−5.41262	−0.296610
$334$	18.0688	0.988683
$335$	32.5587	1.77887
$336$	−59.4173	−3.24148
$337$	1.39890	0.0762027	0.0381013	−	0.999274i	$-0.487869\pi$
$337$	1.39890	0.0762027	0.0381013	+	0.999274i	$0.487869\pi$
$338$	18.5629	1.00969
$339$	11.2098	0.608831
$340$	96.7680	5.24798
$341$	10.7837	0.583968
$342$	0.127171	0.00687664
$343$	−6.70150	−0.361847
$344$	−62.3525	−3.36182
$345$	−28.7218	−1.54633
$346$	−19.2073	−1.03259
$347$	−25.4056	−1.36384	−0.681922	−	0.731425i	$-0.738855\pi$
$347$	−25.4056	−1.36384	−0.681922	+	0.731425i	$0.738855\pi$
$348$	24.2738	1.30121
$349$	−11.0467	−0.591315	−0.295658	−	0.955294i	$-0.595539\pi$
$349$	−11.0467	−0.591315	−0.295658	+	0.955294i	$0.595539\pi$
$350$	89.8759	4.80407
$351$	2.49181	0.133003
$352$	−22.0194	−1.17364
$353$	−0.252241	−0.0134254	−0.00671272	−	0.999977i	$-0.502137\pi$
$353$	−0.252241	−0.0134254	−0.00671272	+	0.999977i	$0.502137\pi$
$354$	20.8588	1.10863
$355$	−38.2488	−2.03003
$356$	−75.8540	−4.02025
$357$	19.2082	1.01661
$358$	−61.0374	−3.22593
$359$	32.5118	1.71591	0.857953	−	0.513728i	$-0.171736\pi$
$359$	32.5118	1.71591	0.857953	+	0.513728i	$0.171736\pi$
$360$	34.6130	1.82427
$361$	−18.9978	−0.999886
$362$	−42.8118	−2.25014
$363$	1.00000	0.0524864
$364$	−54.0136	−2.83108
$365$	49.4685	2.58930
$366$	2.73351	0.142883
$367$	20.9788	1.09509	0.547543	−	0.836778i	$-0.315563\pi$
$367$	20.9788	1.09509	0.547543	+	0.836778i	$0.315563\pi$
$368$	118.130	6.15795
$369$	−1.28084	−0.0666777
$370$	−53.9582	−2.80515
$371$	37.8191	1.96347
$372$	59.0091	3.05948
$373$	−26.5886	−1.37671	−0.688353	−	0.725375i	$-0.741666\pi$
$373$	−26.5886	−1.37671	−0.688353	+	0.725375i	$0.741666\pi$
$374$	13.2547	0.685387
$375$	−12.0355	−0.621511
$376$	−0.00541412	−0.000279212 0
$377$	11.0535	0.569284
$378$	10.8282	0.556943
$379$	−12.8737	−0.661276	−0.330638	−	0.943758i	$-0.607264\pi$
$379$	−12.8737	−0.661276	−0.330638	+	0.943758i	$0.607264\pi$
$380$	0.928431	0.0476275
$381$	1.57944	0.0809172
$382$	59.6390	3.05140
$383$	−19.8514	−1.01436	−0.507179	−	0.861841i	$-0.669312\pi$
$383$	−19.8514	−1.01436	−0.507179	+	0.861841i	$0.669312\pi$
$384$	−38.4893	−1.96415
$385$	14.4466	0.736265
$386$	−1.24499	−0.0633683
$387$	6.56966	0.333955
$388$	−33.4507	−1.69820
$389$	−35.7712	−1.81367	−0.906836	−	0.421484i	$-0.861510\pi$
$389$	−35.7712	−1.81367	−0.906836	+	0.421484i	$0.861510\pi$
$390$	24.8407	1.25786
$391$	−38.1886	−1.93128
$392$	−82.4932	−4.16654
$393$	−11.9942	−0.605029
$394$	−63.3169	−3.18986
$395$	31.1841	1.56904
$396$	5.47208	0.274983
$397$	−10.7271	−0.538375	−0.269188	−	0.963088i	$-0.586755\pi$
$397$	−10.7271	−0.538375	−0.269188	+	0.963088i	$0.586755\pi$
$398$	−12.9931	−0.651284
$399$	0.184291	0.00922609
$400$	124.499	6.22493
$401$	−35.1051	−1.75306	−0.876532	−	0.481343i	$-0.840149\pi$
$401$	−35.1051	−1.75306	−0.876532	+	0.481343i	$0.840149\pi$
$402$	24.4039	1.21716
$403$	26.8709	1.33853
$404$	−85.5324	−4.25539
$405$	−3.64694	−0.181218
$406$	48.0332	2.38385
$407$	−5.41262	−0.268294
$408$	46.0216	2.27841
$409$	−13.4048	−0.662824	−0.331412	−	0.943486i	$-0.607525\pi$
$409$	−13.4048	−0.662824	−0.331412	+	0.943486i	$0.607525\pi$
$410$	−12.7686	−0.630596
$411$	9.02980	0.445407
$412$	−49.7398	−2.45051
$413$	30.2276	1.48740
$414$	−21.5280	−1.05804
$415$	−13.5656	−0.665907
$416$	−54.8682	−2.69014
$417$	−7.43255	−0.363974
$418$	0.127171	0.00622015
$419$	20.8940	1.02074	0.510369	−	0.859956i	$-0.329509\pi$
$419$	20.8940	1.02074	0.510369	+	0.859956i	$0.329509\pi$
$420$	79.0527	3.85738
$421$	17.4927	0.852541	0.426270	−	0.904596i	$-0.359827\pi$
$421$	17.4927	0.852541	0.426270	+	0.904596i	$0.359827\pi$
$422$	68.9434	3.35611
$423$	0.000570449 0	2.77362e−5 0
$424$	90.6121	4.40051
$425$	−40.2474	−1.95228
$426$	−28.6688	−1.38901
$427$	3.96128	0.191700
$428$	67.8625	3.28026
$429$	2.49181	0.120306
$430$	65.4926	3.15833
$431$	2.88306	0.138872	0.0694361	−	0.997586i	$-0.477880\pi$
$431$	2.88306	0.138872	0.0694361	+	0.997586i	$0.477880\pi$
$432$	14.9995	0.721665
$433$	3.43061	0.164865	0.0824323	−	0.996597i	$-0.473731\pi$
$433$	3.43061	0.164865	0.0824323	+	0.996597i	$0.473731\pi$
$434$	116.768	5.60503
$435$	−16.1776	−0.775655
$436$	33.9006	1.62354
$437$	−0.366396	−0.0175271
$438$	37.0784	1.77168
$439$	16.7134	0.797687	0.398843	−	0.917019i	$-0.369412\pi$
$439$	16.7134	0.797687	0.398843	+	0.917019i	$0.369412\pi$
$440$	34.6130	1.65011
$441$	8.69175	0.413893
$442$	33.0283	1.57100
$443$	−23.9890	−1.13975	−0.569875	−	0.821731i	$-0.693009\pi$
$443$	−23.9890	−1.13975	−0.569875	+	0.821731i	$0.693009\pi$
$444$	−29.6183	−1.40562
$445$	50.5539	2.39648
$446$	16.5638	0.784317
$447$	−9.09929	−0.430382
$448$	−119.596	−5.65039
$449$	−33.8675	−1.59831	−0.799154	−	0.601127i	$-0.794719\pi$
$449$	−33.8675	−1.59831	−0.799154	+	0.601127i	$0.794719\pi$
$450$	−22.6886	−1.06955
$451$	−1.28084	−0.0603123
$452$	61.3408	2.88523
$453$	10.5174	0.494149
$454$	30.6578	1.43884
$455$	35.9981	1.68762
$456$	0.441549	0.0206774
$457$	35.1111	1.64243	0.821215	−	0.570619i	$-0.193297\pi$
$457$	35.1111	1.64243	0.821215	+	0.570619i	$0.193297\pi$
$458$	−61.9586	−2.89513
$459$	−4.84898	−0.226331
$460$	−157.168	−7.32799
$461$	−18.4997	−0.861619	−0.430809	−	0.902443i	$-0.641772\pi$
$461$	−18.4997	−0.861619	−0.430809	+	0.902443i	$0.641772\pi$
$462$	10.8282	0.503774
$463$	6.23727	0.289871	0.144935	−	0.989441i	$-0.453703\pi$
$463$	6.23727	0.289871	0.144935	+	0.989441i	$0.453703\pi$
$464$	66.5368	3.08890
$465$	−39.3274	−1.82376
$466$	21.7338	1.00680
$467$	−33.7421	−1.56140	−0.780700	−	0.624906i	$-0.785137\pi$
$467$	−33.7421	−1.56140	−0.780700	+	0.624906i	$0.785137\pi$
$468$	13.6354	0.630296
$469$	35.3651	1.63301
$470$	0.00568678	0.000262312 0
$471$	−19.3242	−0.890410
$472$	72.4233	3.33355
$473$	6.56966	0.302073
$474$	23.3736	1.07359
$475$	−0.386149	−0.0177177
$476$	105.109	4.81765
$477$	−9.54719	−0.437136
$478$	−59.5483	−2.72368
$479$	3.25254	0.148612	0.0743062	−	0.997235i	$-0.476326\pi$
$479$	3.25254	0.148612	0.0743062	+	0.997235i	$0.476326\pi$
$480$	80.3035	3.66534
$481$	−13.4872	−0.614965
$482$	11.1592	0.508290
$483$	−31.1974	−1.41953
$484$	5.47208	0.248731
$485$	22.2936	1.01230
$486$	−2.73351	−0.123995
$487$	−29.2275	−1.32442	−0.662211	−	0.749317i	$-0.730382\pi$
$487$	−29.2275	−1.32442	−0.662211	+	0.749317i	$0.730382\pi$
$488$	9.49098	0.429636
$489$	2.98353	0.134920
$490$	86.6476	3.91434
$491$	8.51904	0.384459	0.192229	−	0.981350i	$-0.438428\pi$
$491$	8.51904	0.384459	0.192229	+	0.981350i	$0.438428\pi$
$492$	−7.00885	−0.315983
$493$	−21.5097	−0.968750
$494$	0.316887	0.0142574
$495$	−3.64694	−0.163918
$496$	161.750	7.26279
$497$	−41.5456	−1.86357
$498$	−10.1679	−0.455633
$499$	−11.6950	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$499$	−11.6950	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$500$	−65.8593	−2.94532
$501$	−6.61012	−0.295318
$502$	47.6770	2.12793
$503$	15.7000	0.700029	0.350014	−	0.936744i	$-0.386177\pi$
$503$	15.7000	0.700029	0.350014	+	0.936744i	$0.386177\pi$
$504$	37.5964	1.67468
$505$	57.0041	2.53665
$506$	−21.5280	−0.957036
$507$	−6.79088	−0.301593
$508$	8.64283	0.383464
$509$	−4.33869	−0.192309	−0.0961545	−	0.995366i	$-0.530654\pi$
$509$	−4.33869	−0.192309	−0.0961545	+	0.995366i	$0.530654\pi$
$510$	−48.3393	−2.14050
$511$	53.7324	2.37698
$512$	−45.5605	−2.01351
$513$	−0.0465231	−0.00205404
$514$	14.2250	0.627436
$515$	33.1497	1.46075
$516$	35.9497	1.58260
$517$	0.000570449 0	2.50883e−5 0
$518$	−58.6090	−2.57513
$519$	7.02661	0.308434
$520$	86.2491	3.78227
$521$	−24.1662	−1.05874	−0.529370	−	0.848391i	$-0.677572\pi$
$521$	−24.1662	−1.05874	−0.529370	+	0.848391i	$0.677572\pi$
$522$	−12.1257	−0.530726
$523$	−1.28085	−0.0560078	−0.0280039	−	0.999608i	$-0.508915\pi$
$523$	−1.28085	−0.0560078	−0.0280039	+	0.999608i	$0.508915\pi$
$524$	−65.6334	−2.86721
$525$	−32.8793	−1.43497
$526$	−24.1296	−1.05210
$527$	−52.2898	−2.27778
$528$	14.9995	0.652771
$529$	39.0248	1.69673
$530$	−95.1754	−4.13416
$531$	−7.63076	−0.331147
$532$	1.00846	0.0437221
$533$	−3.19160	−0.138244
$534$	37.8919	1.63974
$535$	−45.2278	−1.95537
$536$	84.7324	3.65988
$537$	22.3293	0.963581
$538$	−58.2949	−2.51327
$539$	8.69175	0.374380
$540$	−19.9564	−0.858785
$541$	−28.2362	−1.21397	−0.606986	−	0.794713i	$-0.707621\pi$
$541$	−28.2362	−1.21397	−0.606986	+	0.794713i	$0.707621\pi$
$542$	48.5898	2.08711
$543$	15.6618	0.672113
$544$	106.772	4.57780
$545$	−22.5935	−0.967799
$546$	26.9818	1.15472
$547$	18.7087	0.799925	0.399963	−	0.916531i	$-0.369023\pi$
$547$	18.7087	0.799925	0.399963	+	0.916531i	$0.369023\pi$
$548$	49.4118	2.11077
$549$	−1.00000	−0.0426790
$550$	−22.6886	−0.967445
$551$	−0.206373	−0.00879179
$552$	−74.7470	−3.18144
$553$	33.8720	1.44038
$554$	62.4118	2.65162
$555$	19.7395	0.837895
$556$	−40.6715	−1.72486
$557$	−24.7519	−1.04877	−0.524386	−	0.851480i	$-0.675705\pi$
$557$	−24.7519	−1.04877	−0.524386	+	0.851480i	$0.675705\pi$
$558$	−29.4773	−1.24787
$559$	16.3704	0.692392
$560$	216.691	9.15689
$561$	−4.84898	−0.204724
$562$	−13.1248	−0.553638
$563$	−5.89926	−0.248624	−0.124312	−	0.992243i	$-0.539672\pi$
$563$	−5.89926	−0.248624	−0.124312	+	0.992243i	$0.539672\pi$
$564$	0.00312155	0.000131441 0
$565$	−40.8813	−1.71989
$566$	59.7845	2.51293
$567$	−3.96128	−0.166358
$568$	−99.5406	−4.17663
$569$	−21.8777	−0.917161	−0.458581	−	0.888653i	$-0.651642\pi$
$569$	−21.8777	−0.917161	−0.458581	+	0.888653i	$0.651642\pi$
$570$	−0.463786	−0.0194259
$571$	0.305750	0.0127953	0.00639763	−	0.999980i	$-0.497964\pi$
$571$	0.305750	0.0127953	0.00639763	+	0.999980i	$0.497964\pi$
$572$	13.6354	0.570125
$573$	−21.8177	−0.911449
$574$	−13.8692	−0.578888
$575$	65.3686	2.72606
$576$	30.1913	1.25797
$577$	−3.24969	−0.135286	−0.0676432	−	0.997710i	$-0.521548\pi$
$577$	−3.24969	−0.135286	−0.0676432	+	0.997710i	$0.521548\pi$
$578$	−17.8024	−0.740481
$579$	0.455455	0.0189280
$580$	−88.5250	−3.67580
$581$	−14.7348	−0.611304
$582$	16.7099	0.692647
$583$	−9.54719	−0.395404
$584$	128.739	5.32728
$585$	−9.08748	−0.375721
$586$	−11.7302	−0.484571
$587$	43.1427	1.78069	0.890345	−	0.455286i	$-0.150463\pi$
$587$	43.1427	1.78069	0.890345	+	0.455286i	$0.150463\pi$
$588$	47.5620	1.96142
$589$	−0.501689	−0.0206717
$590$	−76.0706	−3.13178
$591$	23.1632	0.952807
$592$	−81.1868	−3.33676
$593$	5.14139	0.211132	0.105566	−	0.994412i	$-0.466335\pi$
$593$	5.14139	0.211132	0.105566	+	0.994412i	$0.466335\pi$
$594$	−2.73351	−0.112157
$595$	−70.0511	−2.87181
$596$	−49.7921	−2.03956
$597$	4.75326	0.194538
$598$	−53.6437	−2.19365
$599$	2.04207	0.0834367	0.0417183	−	0.999129i	$-0.486717\pi$
$599$	2.04207	0.0834367	0.0417183	+	0.999129i	$0.486717\pi$
$600$	−78.7767	−3.21604
$601$	7.94702	0.324166	0.162083	−	0.986777i	$-0.448179\pi$
$601$	7.94702	0.324166	0.162083	+	0.986777i	$0.448179\pi$
$602$	71.1376	2.89935
$603$	−8.92768	−0.363563
$604$	57.5519	2.34175
$605$	−3.64694	−0.148269
$606$	42.7266	1.73565
$607$	−18.0641	−0.733198	−0.366599	−	0.930379i	$-0.619478\pi$
$607$	−18.0641	−0.733198	−0.366599	+	0.930379i	$0.619478\pi$
$608$	1.02441	0.0415453
$609$	−17.5720	−0.712052
$610$	−9.96895	−0.403631
$611$	0.00142145	5.75058e−5 0
$612$	−26.5340	−1.07257
$613$	0.125725	0.00507800	0.00253900	−	0.999997i	$-0.499192\pi$
$613$	0.125725	0.00507800	0.00253900	+	0.999997i	$0.499192\pi$
$614$	45.4315	1.83347
$615$	4.67113	0.188358
$616$	37.5964	1.51480
$617$	5.30198	0.213450	0.106725	−	0.994289i	$-0.465964\pi$
$617$	5.30198	0.213450	0.106725	+	0.994289i	$0.465964\pi$
$618$	24.8469	0.999489
$619$	19.0810	0.766931	0.383465	−	0.923555i	$-0.374731\pi$
$619$	19.0810	0.766931	0.383465	+	0.923555i	$0.374731\pi$
$620$	−215.203	−8.64275
$621$	7.87558	0.316036
$622$	3.83791	0.153886
$623$	54.9113	2.19997
$624$	37.3760	1.49624
$625$	2.39192	0.0956769
$626$	−21.6624	−0.865803
$627$	−0.0465231	−0.00185795
$628$	−105.743	−4.21962
$629$	26.2457	1.04649
$630$	−39.4898	−1.57331
$631$	−28.8352	−1.14791	−0.573955	−	0.818887i	$-0.694592\pi$
$631$	−28.8352	−1.14791	−0.573955	+	0.818887i	$0.694592\pi$
$632$	81.1551	3.22818
$633$	−25.2215	−1.00247
$634$	−2.21924	−0.0881373
$635$	−5.76012	−0.228584
$636$	−52.2430	−2.07157
$637$	21.6582	0.858129
$638$	−12.1257	−0.480060
$639$	10.4879	0.414895
$640$	140.368	5.54854
$641$	−36.6121	−1.44609	−0.723045	−	0.690801i	$-0.757258\pi$
$641$	−36.6121	−1.44609	−0.723045	+	0.690801i	$0.757258\pi$
$642$	−33.8999	−1.33792
$643$	10.2211	0.403081	0.201540	−	0.979480i	$-0.435405\pi$
$643$	10.2211	0.403081	0.201540	+	0.979480i	$0.435405\pi$
$644$	−170.715	−6.72710
$645$	−23.9592	−0.943391
$646$	−0.616651	−0.0242618
$647$	14.8266	0.582895	0.291448	−	0.956587i	$-0.405863\pi$
$647$	14.8266	0.582895	0.291448	+	0.956587i	$0.405863\pi$
$648$	−9.49098	−0.372841
$649$	−7.63076	−0.299533
$650$	−56.5357	−2.21751
$651$	−42.7172	−1.67422
$652$	16.3261	0.639380
$653$	32.8234	1.28448	0.642240	−	0.766503i	$-0.278005\pi$
$653$	32.8234	1.28448	0.642240	+	0.766503i	$0.278005\pi$
$654$	−16.9346	−0.662196
$655$	43.7422	1.70915
$656$	−19.2119	−0.750100
$657$	−13.5644	−0.529198
$658$	0.00617694	0.000240802 0
$659$	27.2740	1.06245	0.531223	−	0.847232i	$-0.321733\pi$
$659$	27.2740	1.06245	0.531223	+	0.847232i	$0.321733\pi$
$660$	−19.9564	−0.776800
$661$	37.8805	1.47338	0.736690	−	0.676230i	$-0.236388\pi$
$661$	37.8805	1.47338	0.736690	+	0.676230i	$0.236388\pi$
$662$	2.43147	0.0945019
$663$	−12.0827	−0.469255
$664$	−35.3037	−1.37005
$665$	−0.672098	−0.0260628
$666$	14.7955	0.573313
$667$	34.9355	1.35271
$668$	−36.1711	−1.39950
$669$	−6.05952	−0.234275
$670$	−88.9996	−3.43835
$671$	−1.00000	−0.0386046
$672$	87.2251	3.36478
$673$	−15.5129	−0.597980	−0.298990	−	0.954256i	$-0.596650\pi$
$673$	−15.5129	−0.597980	−0.298990	+	0.954256i	$0.596650\pi$
$674$	−3.82390	−0.147291
$675$	8.30017	0.319474
$676$	−37.1602	−1.42924
$677$	18.4113	0.707603	0.353802	−	0.935320i	$-0.384889\pi$
$677$	18.4113	0.707603	0.353802	+	0.935320i	$0.384889\pi$
$678$	−30.6420	−1.17680
$679$	24.2152	0.929294
$680$	−167.838	−6.43629
$681$	−11.2156	−0.429781
$682$	−29.4773	−1.12874
$683$	−17.0633	−0.652907	−0.326454	−	0.945213i	$-0.605854\pi$
$683$	−17.0633	−0.652907	−0.326454	+	0.945213i	$0.605854\pi$
$684$	−0.254578	−0.00973403
$685$	−32.9311	−1.25823
$686$	18.3186	0.699409
$687$	22.6663	0.864773
$688$	98.5418	3.75687
$689$	−23.7898	−0.906319
$690$	78.5113	2.98887
$691$	−5.56534	−0.211715	−0.105858	−	0.994381i	$-0.533759\pi$
$691$	−5.56534	−0.211715	−0.105858	+	0.994381i	$0.533759\pi$
$692$	38.4502	1.46166
$693$	−3.96128	−0.150477
$694$	69.4464	2.63615
$695$	27.1061	1.02819
$696$	−42.1013	−1.59585
$697$	6.21076	0.235249
$698$	30.1962	1.14294
$699$	−7.95089	−0.300730
$700$	−179.918	−6.80027
$701$	20.5225	0.775123	0.387562	−	0.921844i	$-0.373317\pi$
$701$	20.5225	0.775123	0.387562	+	0.921844i	$0.373317\pi$
$702$	−6.81139	−0.257079
$703$	0.251812	0.00949726
$704$	30.1913	1.13788
$705$	−0.00208039	−7.83521e−5 0
$706$	0.689504	0.0259498
$707$	61.9175	2.32865
$708$	−41.7561	−1.56929
$709$	10.8572	0.407751	0.203875	−	0.978997i	$-0.434646\pi$
$709$	10.8572	0.407751	0.203875	+	0.978997i	$0.434646\pi$
$710$	104.553	3.92382
$711$	−8.55077	−0.320679
$712$	131.564	4.93057
$713$	84.9277	3.18057
$714$	−52.5058	−1.96498
$715$	−9.08748	−0.339853
$716$	122.188	4.56638
$717$	21.7846	0.813559
$718$	−88.8713	−3.31665
$719$	−4.63514	−0.172861	−0.0864307	−	0.996258i	$-0.527546\pi$
$719$	−4.63514	−0.172861	−0.0864307	+	0.996258i	$0.527546\pi$
$720$	−54.7024	−2.03864
$721$	36.0070	1.34097
$722$	51.9308	1.93266
$723$	−4.08238	−0.151826
$724$	85.7028	3.18512
$725$	36.8190	1.36742
$726$	−2.73351	−0.101450
$727$	11.4366	0.424160	0.212080	−	0.977252i	$-0.431976\pi$
$727$	11.4366	0.424160	0.212080	+	0.977252i	$0.431976\pi$
$728$	93.6832	3.47213
$729$	1.00000	0.0370370
$730$	−135.223	−5.00482
$731$	−31.8562	−1.17824
$732$	−5.47208	−0.202254
$733$	7.97524	0.294572	0.147286	−	0.989094i	$-0.452946\pi$
$733$	7.97524	0.294572	0.147286	+	0.989094i	$0.452946\pi$
$734$	−57.3458	−2.11667
$735$	−31.6983	−1.16921
$736$	−173.416	−6.39219
$737$	−8.92768	−0.328855
$738$	3.50118	0.128880
$739$	5.04646	0.185637	0.0928186	−	0.995683i	$-0.470412\pi$
$739$	5.04646	0.185637	0.0928186	+	0.995683i	$0.470412\pi$
$740$	108.016	3.97076
$741$	−0.115927	−0.00425867
$742$	−103.379	−3.79516
$743$	−7.43485	−0.272758	−0.136379	−	0.990657i	$-0.543547\pi$
$743$	−7.43485	−0.272758	−0.136379	+	0.990657i	$0.543547\pi$
$744$	−102.348	−3.75224
$745$	33.1846	1.21579
$746$	72.6803	2.66101
$747$	3.71971	0.136097
$748$	−26.5340	−0.970181
$749$	−49.1262	−1.79503
$750$	32.8992	1.20131
$751$	−33.0659	−1.20659	−0.603296	−	0.797518i	$-0.706146\pi$
$751$	−33.0659	−1.20659	−0.603296	+	0.797518i	$0.706146\pi$
$752$	0.00855647	0.000312022 0
$753$	−17.4417	−0.635610
$754$	−30.2149	−1.10036
$755$	−38.3562	−1.39593
$756$	−21.6765	−0.788365
$757$	29.1687	1.06015	0.530077	−	0.847949i	$-0.322163\pi$
$757$	29.1687	1.06015	0.530077	+	0.847949i	$0.322163\pi$
$758$	35.1903	1.27817
$759$	7.87558	0.285865
$760$	−1.61030	−0.0584118
$761$	27.4535	0.995190	0.497595	−	0.867410i	$-0.334217\pi$
$761$	27.4535	0.995190	0.497595	+	0.867410i	$0.334217\pi$
$762$	−4.31742	−0.156404
$763$	−24.5409	−0.888440
$764$	−119.388	−4.31932
$765$	17.6839	0.639364
$766$	54.2640	1.96064
$767$	−19.0144	−0.686570
$768$	44.8285	1.61761
$769$	2.71137	0.0977746	0.0488873	−	0.998804i	$-0.484432\pi$
$769$	2.71137	0.0977746	0.0488873	+	0.998804i	$0.484432\pi$
$770$	−39.4898	−1.42311
$771$	−5.20391	−0.187414
$772$	2.49228	0.0896993
$773$	−31.1512	−1.12043	−0.560215	−	0.828347i	$-0.689281\pi$
$773$	−31.1512	−1.12043	−0.560215	+	0.828347i	$0.689281\pi$
$774$	−17.9582	−0.645496
$775$	89.5062	3.21516
$776$	58.0181	2.08273
$777$	21.4409	0.769189
$778$	97.7810	3.50562
$779$	0.0595884	0.00213498
$780$	−49.7275	−1.78053
$781$	10.4879	0.375287
$782$	104.389	3.73294
$783$	4.43593	0.158527
$784$	130.372	4.65615
$785$	70.4740	2.51533
$786$	32.7864	1.16945
$787$	7.90376	0.281739	0.140869	−	0.990028i	$-0.455010\pi$
$787$	7.90376	0.281739	0.140869	+	0.990028i	$0.455010\pi$
$788$	126.751	4.51532
$789$	8.82731	0.314261
$790$	−85.2422	−3.03278
$791$	−44.4050	−1.57886
$792$	−9.49098	−0.337247
$793$	−2.49181	−0.0884868
$794$	29.3225	1.04062
$795$	34.8180	1.23487
$796$	26.0102	0.921908
$797$	−52.9448	−1.87540	−0.937701	−	0.347444i	$-0.887050\pi$
$797$	−52.9448	−1.87540	−0.937701	+	0.347444i	$0.887050\pi$
$798$	−0.503761	−0.0178330
$799$	−0.00276610	−9.78575e−5 0
$800$	−182.765	−6.46171
$801$	−13.8620	−0.489790
$802$	95.9601	3.38847
$803$	−13.5644	−0.478677
$804$	−48.8530	−1.72291
$805$	113.775	4.01004
$806$	−73.4518	−2.58723
$807$	21.3260	0.750711
$808$	148.350	5.21895
$809$	−33.9262	−1.19278	−0.596391	−	0.802694i	$-0.703399\pi$
$809$	−33.9262	−1.19278	−0.596391	+	0.802694i	$0.703399\pi$
$810$	9.96895	0.350273
$811$	0.744633	0.0261476	0.0130738	−	0.999915i	$-0.495838\pi$
$811$	0.744633	0.0261476	0.0130738	+	0.999915i	$0.495838\pi$
$812$	−96.1553	−3.37439
$813$	−17.7756	−0.623418
$814$	14.7955	0.518581
$815$	−10.8807	−0.381136
$816$	−72.7325	−2.54615
$817$	−0.305641	−0.0106930
$818$	36.6421	1.28116
$819$	−9.87077	−0.344912
$820$	25.5608	0.892623
$821$	31.7241	1.10718	0.553590	−	0.832790i	$-0.313258\pi$
$821$	31.7241	1.10718	0.553590	+	0.832790i	$0.313258\pi$
$822$	−24.6831	−0.860921
$823$	11.6796	0.407124	0.203562	−	0.979062i	$-0.434748\pi$
$823$	11.6796	0.407124	0.203562	+	0.979062i	$0.434748\pi$
$824$	86.2705	3.00538
$825$	8.30017	0.288975
$826$	−82.6274	−2.87497
$827$	−20.3695	−0.708318	−0.354159	−	0.935185i	$-0.615233\pi$
$827$	−20.3695	−0.708318	−0.354159	+	0.935185i	$0.615233\pi$
$828$	43.0958	1.49768
$829$	−20.8722	−0.724922	−0.362461	−	0.931999i	$-0.618063\pi$
$829$	−20.8722	−0.724922	−0.362461	+	0.931999i	$0.618063\pi$
$830$	37.0816	1.28712
$831$	−22.8321	−0.792037
$832$	75.2309	2.60816
$833$	−42.1462	−1.46028
$834$	20.3170	0.703519
$835$	24.1067	0.834247
$836$	−0.254578	−0.00880477
$837$	10.7837	0.372738
$838$	−57.1139	−1.97297
$839$	−20.4940	−0.707530	−0.353765	−	0.935334i	$-0.615099\pi$
$839$	−20.4940	−0.707530	−0.353765	+	0.935334i	$0.615099\pi$
$840$	−137.112	−4.73081
$841$	−9.32253	−0.321466
$842$	−47.8164	−1.64786
$843$	4.80146	0.165371
$844$	−138.014	−4.75065
$845$	24.7659	0.851973
$846$	−0.00155933	−5.36108e−5 0
$847$	−3.96128	−0.136111
$848$	−143.203	−4.91762
$849$	−21.8710	−0.750609
$850$	110.017	3.77354
$851$	−42.6275	−1.46125
$852$	57.3907	1.96617
$853$	20.7580	0.710739	0.355370	−	0.934726i	$-0.384355\pi$
$853$	20.7580	0.710739	0.355370	+	0.934726i	$0.384355\pi$
$854$	−10.8282	−0.370534
$855$	0.169667	0.00580248
$856$	−117.703	−4.02301
$857$	34.8179	1.18936	0.594679	−	0.803963i	$-0.297279\pi$
$857$	34.8179	1.18936	0.594679	+	0.803963i	$0.297279\pi$
$858$	−6.81139	−0.232537
$859$	−24.7818	−0.845544	−0.422772	−	0.906236i	$-0.638943\pi$
$859$	−24.7818	−0.845544	−0.422772	+	0.906236i	$0.638943\pi$
$860$	−131.106	−4.47069
$861$	5.07376	0.172913
$862$	−7.88088	−0.268424
$863$	−24.0402	−0.818337	−0.409168	−	0.912459i	$-0.634181\pi$
$863$	−24.0402	−0.818337	−0.409168	+	0.912459i	$0.634181\pi$
$864$	−22.0194	−0.749116
$865$	−25.6256	−0.871297
$866$	−9.37761	−0.318664
$867$	6.51264	0.221181
$868$	−233.752	−7.93405
$869$	−8.55077	−0.290065
$870$	44.2216	1.49925
$871$	−22.2461	−0.753780
$872$	−58.7984	−1.99117
$873$	−6.11297	−0.206893
$874$	1.00155	0.0338779
$875$	47.6760	1.61174
$876$	−74.2255	−2.50785
$877$	4.16282	0.140568	0.0702842	−	0.997527i	$-0.477609\pi$
$877$	4.16282	0.140568	0.0702842	+	0.997527i	$0.477609\pi$
$878$	−45.6862	−1.54184
$879$	4.29126	0.144741
$880$	−54.7024	−1.84402
$881$	26.8981	0.906221	0.453110	−	0.891454i	$-0.350314\pi$
$881$	26.8981	0.906221	0.453110	+	0.891454i	$0.350314\pi$
$882$	−23.7590	−0.800007
$883$	13.4617	0.453023	0.226512	−	0.974008i	$-0.427268\pi$
$883$	13.4617	0.453023	0.226512	+	0.974008i	$0.427268\pi$
$884$	−66.1178	−2.22378
$885$	27.8289	0.935458
$886$	65.5741	2.20301
$887$	−6.91141	−0.232063	−0.116031	−	0.993246i	$-0.537017\pi$
$887$	−6.91141	−0.232063	−0.116031	+	0.993246i	$0.537017\pi$
$888$	51.3711	1.72390
$889$	−6.25661	−0.209840
$890$	−138.190	−4.63212
$891$	1.00000	0.0335013
$892$	−33.1582	−1.11022
$893$	−2.65390e−5 0	−8.88095e−7 0
$894$	24.8730	0.831878
$895$	−81.4337	−2.72203
$896$	152.467	5.09357
$897$	19.6245	0.655242
$898$	92.5772	3.08934
$899$	47.8356	1.59541
$900$	45.4192	1.51397
$901$	46.2942	1.54228
$902$	3.50118	0.116577
$903$	−26.0243	−0.866034
$904$	−106.392	−3.53853
$905$	−57.1177	−1.89866
$906$	−28.7493	−0.955133
$907$	37.3712	1.24089	0.620444	−	0.784250i	$-0.286952\pi$
$907$	37.3712	1.24089	0.620444	+	0.784250i	$0.286952\pi$
$908$	−61.3724	−2.03672
$909$	−15.6307	−0.518437
$910$	−98.4012	−3.26197
$911$	−54.0645	−1.79124	−0.895618	−	0.444824i	$-0.853266\pi$
$911$	−54.0645	−1.79124	−0.895618	+	0.444824i	$0.853266\pi$
$912$	−0.697824	−0.0231073
$913$	3.71971	0.123105
$914$	−95.9767	−3.17463
$915$	3.64694	0.120564
$916$	124.032	4.09813
$917$	47.5125	1.56900
$918$	13.2547	0.437472
$919$	−19.5847	−0.646041	−0.323021	−	0.946392i	$-0.604698\pi$
$919$	−19.5847	−0.646041	−0.323021	+	0.946392i	$0.604698\pi$
$920$	272.598	8.98728
$921$	−16.6202	−0.547655
$922$	50.5692	1.66541
$923$	26.1339	0.860208
$924$	−21.6765	−0.713103
$925$	−44.9257	−1.47715
$926$	−17.0497	−0.560287
$927$	−9.08974	−0.298546
$928$	−97.6766	−3.20639
$929$	−0.822167	−0.0269744	−0.0134872	−	0.999909i	$-0.504293\pi$
$929$	−0.822167	−0.0269744	−0.0134872	+	0.999909i	$0.504293\pi$
$930$	107.502	3.52512
$931$	−0.404367	−0.0132526
$932$	−43.5079	−1.42515
$933$	−1.40402	−0.0459656
$934$	92.2345	3.01801
$935$	17.6839	0.578327
$936$	−23.6497	−0.773015
$937$	12.5109	0.408714	0.204357	−	0.978896i	$-0.434490\pi$
$937$	12.5109	0.408714	0.204357	+	0.978896i	$0.434490\pi$
$938$	−96.6708	−3.15641
$939$	7.92475	0.258614
$940$	−0.0113841	−0.000371308 0
$941$	31.3431	1.02176	0.510878	−	0.859653i	$-0.329320\pi$
$941$	31.3431	1.02176	0.510878	+	0.859653i	$0.329320\pi$
$942$	52.8228	1.72106
$943$	−10.0873	−0.328489
$944$	−114.458	−3.72528
$945$	14.4466	0.469946
$946$	−17.9582	−0.583873
$947$	−41.9864	−1.36438	−0.682188	−	0.731177i	$-0.738971\pi$
$947$	−41.9864	−1.36438	−0.682188	+	0.731177i	$0.738971\pi$
$948$	−46.7905	−1.51968
$949$	−33.7999	−1.09719
$950$	1.05554	0.0342463
$951$	0.811864	0.0263265
$952$	−182.304	−5.90852
$953$	28.8688	0.935152	0.467576	−	0.883953i	$-0.345127\pi$
$953$	28.8688	0.935152	0.467576	+	0.883953i	$0.345127\pi$
$954$	26.0973	0.844933
$955$	79.5679	2.57476
$956$	119.207	3.85543
$957$	4.43593	0.143393
$958$	−8.89085	−0.287250
$959$	−35.7696	−1.15506
$960$	−110.106	−3.55365
$961$	85.2875	2.75121
$962$	36.8675	1.18866
$963$	12.4016	0.399635
$964$	−22.3391	−0.719495
$965$	−1.66101	−0.0534700
$966$	85.2784	2.74379
$967$	−4.71947	−0.151768	−0.0758839	−	0.997117i	$-0.524178\pi$
$967$	−4.71947	−0.151768	−0.0758839	+	0.997117i	$0.524178\pi$
$968$	−9.49098	−0.305052
$969$	0.225590	0.00724698
$970$	−60.9399	−1.95666
$971$	−17.6533	−0.566522	−0.283261	−	0.959043i	$-0.591416\pi$
$971$	−17.6533	−0.566522	−0.283261	+	0.959043i	$0.591416\pi$
$972$	5.47208	0.175517
$973$	29.4424	0.943881
$974$	79.8936	2.55996
$975$	20.6824	0.662368
$976$	−14.9995	−0.480123
$977$	−35.4007	−1.13257	−0.566285	−	0.824210i	$-0.691620\pi$
$977$	−35.4007	−1.13257	−0.566285	+	0.824210i	$0.691620\pi$
$978$	−8.15551	−0.260784
$979$	−13.8620	−0.443031
$980$	−173.456	−5.54084
$981$	6.19519	0.197797
$982$	−23.2869	−0.743115
$983$	−53.5369	−1.70756	−0.853781	−	0.520633i	$-0.825696\pi$
$983$	−53.5369	−1.70756	−0.853781	+	0.520633i	$0.825696\pi$
$984$	12.1564	0.387532
$985$	−84.4748	−2.69159
$986$	58.7971	1.87248
$987$	−0.00225971	−7.19274e−5 0
$988$	−0.634360	−0.0201817
$989$	51.7399	1.64523
$990$	9.96895	0.316834
$991$	−53.7939	−1.70882	−0.854410	−	0.519600i	$-0.826081\pi$
$991$	−53.7939	−1.70882	−0.854410	+	0.519600i	$0.826081\pi$
$992$	−237.450	−7.53905
$993$	−0.889505	−0.0282276
$994$	113.565	3.60207
$995$	−17.3348	−0.549551
$996$	20.3546	0.644959
$997$	14.8273	0.469585	0.234792	−	0.972046i	$-0.424559\pi$
$997$	14.8273	0.469585	0.234792	+	0.972046i	$0.424559\pi$
$998$	31.9684	1.01194
$999$	−5.41262	−0.171248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.1	✓	12
3.2	odd	2		6039.2.a.f.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.1	✓	12	1.1	even	1	trivial
6039.2.a.f.1.12		12	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)

\(f(q)\)	\(=\)	\(q-2.73351 q^{2} +1.00000 q^{3} +5.47208 q^{4} -3.64694 q^{5} -2.73351 q^{6} -3.96128 q^{7} -9.49098 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73351 q^{2} +1.00000 q^{3} +5.47208 q^{4} -3.64694 q^{5} -2.73351 q^{6} -3.96128 q^{7} -9.49098 q^{8} +1.00000 q^{9} +9.96895 q^{10} +1.00000 q^{11} +5.47208 q^{12} +2.49181 q^{13} +10.8282 q^{14} -3.64694 q^{15} +14.9995 q^{16} -4.84898 q^{17} -2.73351 q^{18} -0.0465231 q^{19} -19.9564 q^{20} -3.96128 q^{21} -2.73351 q^{22} +7.87558 q^{23} -9.49098 q^{24} +8.30017 q^{25} -6.81139 q^{26} +1.00000 q^{27} -21.6765 q^{28} +4.43593 q^{29} +9.96895 q^{30} +10.7837 q^{31} -22.0194 q^{32} +1.00000 q^{33} +13.2547 q^{34} +14.4466 q^{35} +5.47208 q^{36} -5.41262 q^{37} +0.127171 q^{38} +2.49181 q^{39} +34.6130 q^{40} -1.28084 q^{41} +10.8282 q^{42} +6.56966 q^{43} +5.47208 q^{44} -3.64694 q^{45} -21.5280 q^{46} +0.000570449 q^{47} +14.9995 q^{48} +8.69175 q^{49} -22.6886 q^{50} -4.84898 q^{51} +13.6354 q^{52} -9.54719 q^{53} -2.73351 q^{54} -3.64694 q^{55} +37.5964 q^{56} -0.0465231 q^{57} -12.1257 q^{58} -7.63076 q^{59} -19.9564 q^{60} -1.00000 q^{61} -29.4773 q^{62} -3.96128 q^{63} +30.1913 q^{64} -9.08748 q^{65} -2.73351 q^{66} -8.92768 q^{67} -26.5340 q^{68} +7.87558 q^{69} -39.4898 q^{70} +10.4879 q^{71} -9.49098 q^{72} -13.5644 q^{73} +14.7955 q^{74} +8.30017 q^{75} -0.254578 q^{76} -3.96128 q^{77} -6.81139 q^{78} -8.55077 q^{79} -54.7024 q^{80} +1.00000 q^{81} +3.50118 q^{82} +3.71971 q^{83} -21.6765 q^{84} +17.6839 q^{85} -17.9582 q^{86} +4.43593 q^{87} -9.49098 q^{88} -13.8620 q^{89} +9.96895 q^{90} -9.87077 q^{91} +43.0958 q^{92} +10.7837 q^{93} -0.00155933 q^{94} +0.169667 q^{95} -22.0194 q^{96} -6.11297 q^{97} -23.7590 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

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