LMFDB - Embedded newform 2013.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
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			1.7
Root			$0.171582$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.171582 q^{2} -1.00000 q^{3} -1.97056 q^{4} -0.133072 q^{5} -0.171582 q^{6} +0.615329 q^{7} -0.681275 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.171582 q^{2} -1.00000 q^{3} -1.97056 q^{4} -0.133072 q^{5} -0.171582 q^{6} +0.615329 q^{7} -0.681275 q^{8} +1.00000 q^{9} -0.0228327 q^{10} +1.00000 q^{11} +1.97056 q^{12} -4.70459 q^{13} +0.105579 q^{14} +0.133072 q^{15} +3.82423 q^{16} +2.34281 q^{17} +0.171582 q^{18} -7.85906 q^{19} +0.262226 q^{20} -0.615329 q^{21} +0.171582 q^{22} +1.86581 q^{23} +0.681275 q^{24} -4.98229 q^{25} -0.807221 q^{26} -1.00000 q^{27} -1.21254 q^{28} +4.53951 q^{29} +0.0228327 q^{30} +3.06900 q^{31} +2.01872 q^{32} -1.00000 q^{33} +0.401984 q^{34} -0.0818830 q^{35} -1.97056 q^{36} +9.24562 q^{37} -1.34847 q^{38} +4.70459 q^{39} +0.0906587 q^{40} +1.52969 q^{41} -0.105579 q^{42} +1.17504 q^{43} -1.97056 q^{44} -0.133072 q^{45} +0.320139 q^{46} -7.78342 q^{47} -3.82423 q^{48} -6.62137 q^{49} -0.854870 q^{50} -2.34281 q^{51} +9.27067 q^{52} -11.1113 q^{53} -0.171582 q^{54} -0.133072 q^{55} -0.419208 q^{56} +7.85906 q^{57} +0.778896 q^{58} +11.0751 q^{59} -0.262226 q^{60} -1.00000 q^{61} +0.526584 q^{62} +0.615329 q^{63} -7.30207 q^{64} +0.626049 q^{65} -0.171582 q^{66} +11.2239 q^{67} -4.61665 q^{68} -1.86581 q^{69} -0.0140496 q^{70} -6.59487 q^{71} -0.681275 q^{72} +4.36946 q^{73} +1.58638 q^{74} +4.98229 q^{75} +15.4867 q^{76} +0.615329 q^{77} +0.807221 q^{78} +11.7882 q^{79} -0.508897 q^{80} +1.00000 q^{81} +0.262467 q^{82} +10.8873 q^{83} +1.21254 q^{84} -0.311763 q^{85} +0.201616 q^{86} -4.53951 q^{87} -0.681275 q^{88} +15.1533 q^{89} -0.0228327 q^{90} -2.89487 q^{91} -3.67669 q^{92} -3.06900 q^{93} -1.33549 q^{94} +1.04582 q^{95} -2.01872 q^{96} +15.1739 q^{97} -1.13611 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.171582	0.121327	0.0606633	−	0.998158i	$-0.480678\pi$
$2$	0.171582	0.121327	0.0606633	+	0.998158i	$0.480678\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97056	−0.985280
$5$	−0.133072	−0.0595116	−0.0297558	−	0.999557i	$-0.509473\pi$
$5$	−0.133072	−0.0595116	−0.0297558	+	0.999557i	$0.509473\pi$
$6$	−0.171582	−0.0700479
$7$	0.615329	0.232572	0.116286	−	0.993216i	$-0.462901\pi$
$7$	0.615329	0.232572	0.116286	+	0.993216i	$0.462901\pi$
$8$	−0.681275	−0.240867
$9$	1.00000	0.333333
$10$	−0.0228327	−0.00722034
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.97056	0.568852
$13$	−4.70459	−1.30482	−0.652409	−	0.757867i	$-0.726241\pi$
$13$	−4.70459	−1.30482	−0.652409	+	0.757867i	$0.726241\pi$
$14$	0.105579	0.0282172
$15$	0.133072	0.0343590
$16$	3.82423	0.956056
$17$	2.34281	0.568215	0.284108	−	0.958792i	$-0.408303\pi$
$17$	2.34281	0.568215	0.284108	+	0.958792i	$0.408303\pi$
$18$	0.171582	0.0404422
$19$	−7.85906	−1.80299	−0.901496	−	0.432788i	$-0.857530\pi$
$19$	−7.85906	−1.80299	−0.901496	+	0.432788i	$0.857530\pi$
$20$	0.262226	0.0586356
$21$	−0.615329	−0.134276
$22$	0.171582	0.0365813
$23$	1.86581	0.389048	0.194524	−	0.980898i	$-0.437684\pi$
$23$	1.86581	0.389048	0.194524	+	0.980898i	$0.437684\pi$
$24$	0.681275	0.139065
$25$	−4.98229	−0.996458
$26$	−0.807221	−0.158309
$27$	−1.00000	−0.192450
$28$	−1.21254	−0.229149
$29$	4.53951	0.842965	0.421482	−	0.906837i	$-0.361510\pi$
$29$	4.53951	0.842965	0.421482	+	0.906837i	$0.361510\pi$
$30$	0.0228327	0.00416867
$31$	3.06900	0.551208	0.275604	−	0.961271i	$-0.411122\pi$
$31$	3.06900	0.551208	0.275604	+	0.961271i	$0.411122\pi$
$32$	2.01872	0.356862
$33$	−1.00000	−0.174078
$34$	0.401984	0.0689396
$35$	−0.0818830	−0.0138408
$36$	−1.97056	−0.328427
$37$	9.24562	1.51997	0.759986	−	0.649940i	$-0.225206\pi$
$37$	9.24562	1.51997	0.759986	+	0.649940i	$0.225206\pi$
$38$	−1.34847	−0.218751
$39$	4.70459	0.753337
$40$	0.0906587	0.0143344
$41$	1.52969	0.238897	0.119449	−	0.992840i	$-0.461887\pi$
$41$	1.52969	0.238897	0.119449	+	0.992840i	$0.461887\pi$
$42$	−0.105579	−0.0162912
$43$	1.17504	0.179193	0.0895963	−	0.995978i	$-0.471442\pi$
$43$	1.17504	0.179193	0.0895963	+	0.995978i	$0.471442\pi$
$44$	−1.97056	−0.297073
$45$	−0.133072	−0.0198372
$46$	0.320139	0.0472019
$47$	−7.78342	−1.13533	−0.567664	−	0.823260i	$-0.692153\pi$
$47$	−7.78342	−1.13533	−0.567664	+	0.823260i	$0.692153\pi$
$48$	−3.82423	−0.551979
$49$	−6.62137	−0.945910
$50$	−0.854870	−0.120897
$51$	−2.34281	−0.328059
$52$	9.27067	1.28561
$53$	−11.1113	−1.52626	−0.763130	−	0.646246i	$-0.776338\pi$
$53$	−11.1113	−1.52626	−0.763130	+	0.646246i	$0.776338\pi$
$54$	−0.171582	−0.0233493
$55$	−0.133072	−0.0179434
$56$	−0.419208	−0.0560191
$57$	7.85906	1.04096
$58$	0.778896	0.102274
$59$	11.0751	1.44185	0.720925	−	0.693013i	$-0.243717\pi$
$59$	11.0751	1.44185	0.720925	+	0.693013i	$0.243717\pi$
$60$	−0.262226	−0.0338533
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.526584	0.0668762
$63$	0.615329	0.0775242
$64$	−7.30207	−0.912759
$65$	0.626049	0.0776518
$66$	−0.171582	−0.0211202
$67$	11.2239	1.37121	0.685607	−	0.727972i	$-0.259537\pi$
$67$	11.2239	1.37121	0.685607	+	0.727972i	$0.259537\pi$
$68$	−4.61665	−0.559851
$69$	−1.86581	−0.224617
$70$	−0.0140496	−0.00167925
$71$	−6.59487	−0.782668	−0.391334	−	0.920249i	$-0.627986\pi$
$71$	−6.59487	−0.782668	−0.391334	+	0.920249i	$0.627986\pi$
$72$	−0.681275	−0.0802891
$73$	4.36946	0.511406	0.255703	−	0.966755i	$-0.417693\pi$
$73$	4.36946	0.511406	0.255703	+	0.966755i	$0.417693\pi$
$74$	1.58638	0.184413
$75$	4.98229	0.575306
$76$	15.4867	1.77645
$77$	0.615329	0.0701232
$78$	0.807221	0.0913998
$79$	11.7882	1.32628	0.663141	−	0.748495i	$-0.269223\pi$
$79$	11.7882	1.32628	0.663141	+	0.748495i	$0.269223\pi$
$80$	−0.508897	−0.0568964
$81$	1.00000	0.111111
$82$	0.262467	0.0289846
$83$	10.8873	1.19503	0.597517	−	0.801856i	$-0.296154\pi$
$83$	10.8873	1.19503	0.597517	+	0.801856i	$0.296154\pi$
$84$	1.21254	0.132299
$85$	−0.311763	−0.0338154
$86$	0.201616	0.0217408
$87$	−4.53951	−0.486686
$88$	−0.681275	−0.0726242
$89$	15.1533	1.60625	0.803123	−	0.595813i	$-0.203170\pi$
$89$	15.1533	1.60625	0.803123	+	0.595813i	$0.203170\pi$
$90$	−0.0228327	−0.00240678
$91$	−2.89487	−0.303465
$92$	−3.67669	−0.383321
$93$	−3.06900	−0.318240
$94$	−1.33549	−0.137745
$95$	1.04582	0.107299
$96$	−2.01872	−0.206035
$97$	15.1739	1.54068	0.770340	−	0.637633i	$-0.220086\pi$
$97$	15.1739	1.54068	0.770340	+	0.637633i	$0.220086\pi$
$98$	−1.13611	−0.114764
$99$	1.00000	0.100504
$100$	9.81790	0.981790
$101$	14.9729	1.48986	0.744931	−	0.667141i	$-0.232482\pi$
$101$	14.9729	1.48986	0.744931	+	0.667141i	$0.232482\pi$
$102$	−0.401984	−0.0398023
$103$	2.65906	0.262005	0.131003	−	0.991382i	$-0.458180\pi$
$103$	2.65906	0.262005	0.131003	+	0.991382i	$0.458180\pi$
$104$	3.20512	0.314288
$105$	0.0818830	0.00799097
$106$	−1.90650	−0.185176
$107$	9.97635	0.964450	0.482225	−	0.876047i	$-0.339829\pi$
$107$	9.97635	0.964450	0.482225	+	0.876047i	$0.339829\pi$
$108$	1.97056	0.189617
$109$	−8.83359	−0.846104	−0.423052	−	0.906105i	$-0.639041\pi$
$109$	−8.83359	−0.846104	−0.423052	+	0.906105i	$0.639041\pi$
$110$	−0.0228327	−0.00217701
$111$	−9.24562	−0.877556
$112$	2.35316	0.222352
$113$	−4.24584	−0.399415	−0.199707	−	0.979856i	$-0.563999\pi$
$113$	−4.24584	−0.399415	−0.199707	+	0.979856i	$0.563999\pi$
$114$	1.34847	0.126296
$115$	−0.248287	−0.0231529
$116$	−8.94537	−0.830556
$117$	−4.70459	−0.434939
$118$	1.90028	0.174935
$119$	1.44160	0.132151
$120$	−0.0906587	−0.00827597
$121$	1.00000	0.0909091
$122$	−0.171582	−0.0155343
$123$	−1.52969	−0.137927
$124$	−6.04764	−0.543094
$125$	1.32836	0.118812
$126$	0.105579	0.00940574
$127$	19.3085	1.71335	0.856675	−	0.515856i	$-0.172526\pi$
$127$	19.3085	1.71335	0.856675	+	0.515856i	$0.172526\pi$
$128$	−5.29034	−0.467604
$129$	−1.17504	−0.103457
$130$	0.107419	0.00942123
$131$	16.1882	1.41437	0.707187	−	0.707027i	$-0.249964\pi$
$131$	16.1882	1.41437	0.707187	+	0.707027i	$0.249964\pi$
$132$	1.97056	0.171515
$133$	−4.83590	−0.419326
$134$	1.92581	0.166365
$135$	0.133072	0.0114530
$136$	−1.59610	−0.136864
$137$	−16.9876	−1.45135	−0.725674	−	0.688038i	$-0.758472\pi$
$137$	−16.9876	−1.45135	−0.725674	+	0.688038i	$0.758472\pi$
$138$	−0.320139	−0.0272520
$139$	0.981625	0.0832604	0.0416302	−	0.999133i	$-0.486745\pi$
$139$	0.981625	0.0832604	0.0416302	+	0.999133i	$0.486745\pi$
$140$	0.161355	0.0136370
$141$	7.78342	0.655482
$142$	−1.13156	−0.0949584
$143$	−4.70459	−0.393417
$144$	3.82423	0.318685
$145$	−0.604081	−0.0501662
$146$	0.749719	0.0620472
$147$	6.62137	0.546121
$148$	−18.2191	−1.49760
$149$	19.9181	1.63175	0.815876	−	0.578227i	$-0.196255\pi$
$149$	19.9181	1.63175	0.815876	+	0.578227i	$0.196255\pi$
$150$	0.854870	0.0697999
$151$	−9.27179	−0.754528	−0.377264	−	0.926106i	$-0.623135\pi$
$151$	−9.27179	−0.754528	−0.377264	+	0.926106i	$0.623135\pi$
$152$	5.35418	0.434282
$153$	2.34281	0.189405
$154$	0.105579	0.00850781
$155$	−0.408397	−0.0328033
$156$	−9.27067	−0.742248
$157$	9.62702	0.768320	0.384160	−	0.923267i	$-0.374491\pi$
$157$	9.62702	0.768320	0.384160	+	0.923267i	$0.374491\pi$
$158$	2.02265	0.160913
$159$	11.1113	0.881186
$160$	−0.268635	−0.0212374
$161$	1.14809	0.0904818
$162$	0.171582	0.0134807
$163$	17.0593	1.33619	0.668093	−	0.744077i	$-0.267111\pi$
$163$	17.0593	1.33619	0.668093	+	0.744077i	$0.267111\pi$
$164$	−3.01434	−0.235381
$165$	0.133072	0.0103596
$166$	1.86806	0.144989
$167$	8.92176	0.690387	0.345193	−	0.938532i	$-0.387813\pi$
$167$	8.92176	0.690387	0.345193	+	0.938532i	$0.387813\pi$
$168$	0.419208	0.0323426
$169$	9.13314	0.702549
$170$	−0.0534928	−0.00410271
$171$	−7.85906	−0.600997
$172$	−2.31549	−0.176555
$173$	3.85738	0.293271	0.146636	−	0.989191i	$-0.453156\pi$
$173$	3.85738	0.293271	0.146636	+	0.989191i	$0.453156\pi$
$174$	−0.778896	−0.0590480
$175$	−3.06575	−0.231749
$176$	3.82423	0.288262
$177$	−11.0751	−0.832453
$178$	2.60003	0.194880
$179$	−10.4383	−0.780194	−0.390097	−	0.920774i	$-0.627558\pi$
$179$	−10.4383	−0.780194	−0.390097	+	0.920774i	$0.627558\pi$
$180$	0.262226	0.0195452
$181$	13.9705	1.03842	0.519208	−	0.854648i	$-0.326227\pi$
$181$	13.9705	1.03842	0.519208	+	0.854648i	$0.326227\pi$
$182$	−0.496706	−0.0368183
$183$	1.00000	0.0739221
$184$	−1.27113	−0.0937089
$185$	−1.23033	−0.0904559
$186$	−0.526584	−0.0386110
$187$	2.34281	0.171323
$188$	15.3377	1.11862
$189$	−0.615329	−0.0447586
$190$	0.179444	0.0130182
$191$	−24.4448	−1.76876	−0.884382	−	0.466763i	$-0.845420\pi$
$191$	−24.4448	−1.76876	−0.884382	+	0.466763i	$0.845420\pi$
$192$	7.30207	0.526982
$193$	−6.16239	−0.443578	−0.221789	−	0.975095i	$-0.571190\pi$
$193$	−6.16239	−0.443578	−0.221789	+	0.975095i	$0.571190\pi$
$194$	2.60357	0.186926
$195$	−0.626049	−0.0448323
$196$	13.0478	0.931986
$197$	−16.1438	−1.15020	−0.575100	−	0.818083i	$-0.695037\pi$
$197$	−16.1438	−1.15020	−0.575100	+	0.818083i	$0.695037\pi$
$198$	0.171582	0.0121938
$199$	−11.7030	−0.829600	−0.414800	−	0.909913i	$-0.636149\pi$
$199$	−11.7030	−0.829600	−0.414800	+	0.909913i	$0.636149\pi$
$200$	3.39431	0.240014
$201$	−11.2239	−0.791670
$202$	2.56908	0.180760
$203$	2.79329	0.196050
$204$	4.61665	0.323230
$205$	−0.203559	−0.0142172
$206$	0.456247	0.0317882
$207$	1.86581	0.129683
$208$	−17.9914	−1.24748
$209$	−7.85906	−0.543622
$210$	0.0140496	0.000969517 0
$211$	−13.0881	−0.901019	−0.450509	−	0.892772i	$-0.648758\pi$
$211$	−13.0881	−0.901019	−0.450509	+	0.892772i	$0.648758\pi$
$212$	21.8955	1.50379
$213$	6.59487	0.451873
$214$	1.71176	0.117013
$215$	−0.156365	−0.0106640
$216$	0.681275	0.0463549
$217$	1.88844	0.128196
$218$	−1.51568	−0.102655
$219$	−4.36946	−0.295261
$220$	0.262226	0.0176793
$221$	−11.0220	−0.741417
$222$	−1.58638	−0.106471
$223$	2.06775	0.138467	0.0692334	−	0.997600i	$-0.477945\pi$
$223$	2.06775	0.138467	0.0692334	+	0.997600i	$0.477945\pi$
$224$	1.24218	0.0829963
$225$	−4.98229	−0.332153
$226$	−0.728508	−0.0484596
$227$	−6.15200	−0.408322	−0.204161	−	0.978937i	$-0.565447\pi$
$227$	−6.15200	−0.408322	−0.204161	+	0.978937i	$0.565447\pi$
$228$	−15.4867	−1.02563
$229$	19.5963	1.29496	0.647479	−	0.762083i	$-0.275823\pi$
$229$	19.5963	1.29496	0.647479	+	0.762083i	$0.275823\pi$
$230$	−0.0426015	−0.00280906
$231$	−0.615329	−0.0404857
$232$	−3.09265	−0.203043
$233$	−20.5752	−1.34792	−0.673962	−	0.738766i	$-0.735409\pi$
$233$	−20.5752	−1.34792	−0.673962	+	0.738766i	$0.735409\pi$
$234$	−0.807221	−0.0527697
$235$	1.03575	0.0675652
$236$	−21.8241	−1.42063
$237$	−11.7882	−0.765729
$238$	0.247352	0.0160335
$239$	−23.1378	−1.49666	−0.748330	−	0.663327i	$-0.769144\pi$
$239$	−23.1378	−1.49666	−0.748330	+	0.663327i	$0.769144\pi$
$240$	0.508897	0.0328492
$241$	0.0983366	0.00633442	0.00316721	−	0.999995i	$-0.498992\pi$
$241$	0.0983366	0.00633442	0.00316721	+	0.999995i	$0.498992\pi$
$242$	0.171582	0.0110297
$243$	−1.00000	−0.0641500
$244$	1.97056	0.126152
$245$	0.881119	0.0562926
$246$	−0.262467	−0.0167343
$247$	36.9736	2.35257
$248$	−2.09083	−0.132768
$249$	−10.8873	−0.689953
$250$	0.227923	0.0144151
$251$	−3.43655	−0.216913	−0.108457	−	0.994101i	$-0.534591\pi$
$251$	−3.43655	−0.216913	−0.108457	+	0.994101i	$0.534591\pi$
$252$	−1.21254	−0.0763830
$253$	1.86581	0.117302
$254$	3.31298	0.207875
$255$	0.311763	0.0195233
$256$	13.6964	0.856027
$257$	−12.4152	−0.774439	−0.387220	−	0.921988i	$-0.626564\pi$
$257$	−12.4152	−0.774439	−0.387220	+	0.921988i	$0.626564\pi$
$258$	−0.201616	−0.0125521
$259$	5.68910	0.353503
$260$	−1.23367	−0.0765087
$261$	4.53951	0.280988
$262$	2.77761	0.171601
$263$	4.10959	0.253408	0.126704	−	0.991941i	$-0.459560\pi$
$263$	4.10959	0.253408	0.126704	+	0.991941i	$0.459560\pi$
$264$	0.681275	0.0419296
$265$	1.47861	0.0908301
$266$	−0.829753	−0.0508754
$267$	−15.1533	−0.927367
$268$	−22.1173	−1.35103
$269$	17.7222	1.08054	0.540270	−	0.841492i	$-0.318322\pi$
$269$	17.7222	1.08054	0.540270	+	0.841492i	$0.318322\pi$
$270$	0.0228327	0.00138956
$271$	6.97502	0.423702	0.211851	−	0.977302i	$-0.432051\pi$
$271$	6.97502	0.423702	0.211851	+	0.977302i	$0.432051\pi$
$272$	8.95944	0.543246
$273$	2.89487	0.175205
$274$	−2.91476	−0.176087
$275$	−4.98229	−0.300444
$276$	3.67669	0.221311
$277$	−2.67748	−0.160874	−0.0804371	−	0.996760i	$-0.525632\pi$
$277$	−2.67748	−0.160874	−0.0804371	+	0.996760i	$0.525632\pi$
$278$	0.168429	0.0101017
$279$	3.06900	0.183736
$280$	0.0557849	0.00333379
$281$	−16.1747	−0.964905	−0.482452	−	0.875922i	$-0.660254\pi$
$281$	−16.1747	−0.964905	−0.482452	+	0.875922i	$0.660254\pi$
$282$	1.33549	0.0795274
$283$	14.1430	0.840715	0.420357	−	0.907359i	$-0.361905\pi$
$283$	14.1430	0.840715	0.420357	+	0.907359i	$0.361905\pi$
$284$	12.9956	0.771147
$285$	−1.04582	−0.0619490
$286$	−0.807221	−0.0477320
$287$	0.941262	0.0555609
$288$	2.01872	0.118954
$289$	−11.5112	−0.677131
$290$	−0.103649	−0.00608649
$291$	−15.1739	−0.889512
$292$	−8.61028	−0.503878
$293$	−8.25000	−0.481970	−0.240985	−	0.970529i	$-0.577471\pi$
$293$	−8.25000	−0.481970	−0.240985	+	0.970529i	$0.577471\pi$
$294$	1.13611	0.0662591
$295$	−1.47378	−0.0858068
$296$	−6.29882	−0.366111
$297$	−1.00000	−0.0580259
$298$	3.41758	0.197975
$299$	−8.77786	−0.507637
$300$	−9.81790	−0.566837
$301$	0.723038	0.0416752
$302$	−1.59087	−0.0915443
$303$	−14.9729	−0.860173
$304$	−30.0548	−1.72376
$305$	0.133072	0.00761968
$306$	0.401984	0.0229799
$307$	−5.17139	−0.295147	−0.147573	−	0.989051i	$-0.547146\pi$
$307$	−5.17139	−0.295147	−0.147573	+	0.989051i	$0.547146\pi$
$308$	−1.21254	−0.0690910
$309$	−2.65906	−0.151269
$310$	−0.0700735	−0.00397991
$311$	5.56505	0.315565	0.157783	−	0.987474i	$-0.449565\pi$
$311$	5.56505	0.315565	0.157783	+	0.987474i	$0.449565\pi$
$312$	−3.20512	−0.181454
$313$	−26.1339	−1.47718	−0.738589	−	0.674156i	$-0.764507\pi$
$313$	−26.1339	−1.47718	−0.738589	+	0.674156i	$0.764507\pi$
$314$	1.65182	0.0932176
$315$	−0.0818830	−0.00461359
$316$	−23.2294	−1.30676
$317$	−9.26111	−0.520156	−0.260078	−	0.965588i	$-0.583748\pi$
$317$	−9.26111	−0.520156	−0.260078	+	0.965588i	$0.583748\pi$
$318$	1.90650	0.106911
$319$	4.53951	0.254163
$320$	0.971702	0.0543198
$321$	−9.97635	−0.556825
$322$	0.196991	0.0109779
$323$	−18.4123	−1.02449
$324$	−1.97056	−0.109476
$325$	23.4396	1.30020
$326$	2.92706	0.162115
$327$	8.83359	0.488499
$328$	−1.04214	−0.0575425
$329$	−4.78936	−0.264046
$330$	0.0228327	0.00125690
$331$	−2.06884	−0.113714	−0.0568569	−	0.998382i	$-0.518108\pi$
$331$	−2.06884	−0.113714	−0.0568569	+	0.998382i	$0.518108\pi$
$332$	−21.4540	−1.17744
$333$	9.24562	0.506657
$334$	1.53081	0.0837622
$335$	−1.49358	−0.0816031
$336$	−2.35316	−0.128375
$337$	−0.238290	−0.0129805	−0.00649024	−	0.999979i	$-0.502066\pi$
$337$	−0.238290	−0.0129805	−0.00649024	+	0.999979i	$0.502066\pi$
$338$	1.56708	0.0852379
$339$	4.24584	0.230602
$340$	0.614347	0.0333176
$341$	3.06900	0.166195
$342$	−1.34847	−0.0729169
$343$	−8.38162	−0.452565
$344$	−0.800529	−0.0431616
$345$	0.248287	0.0133673
$346$	0.661856	0.0355816
$347$	27.9023	1.49787	0.748937	−	0.662641i	$-0.230564\pi$
$347$	27.9023	1.49787	0.748937	+	0.662641i	$0.230564\pi$
$348$	8.94537	0.479522
$349$	30.6969	1.64317	0.821585	−	0.570086i	$-0.193090\pi$
$349$	30.6969	1.64317	0.821585	+	0.570086i	$0.193090\pi$
$350$	−0.526026	−0.0281173
$351$	4.70459	0.251112
$352$	2.01872	0.107598
$353$	32.2120	1.71447	0.857236	−	0.514924i	$-0.172180\pi$
$353$	32.2120	1.71447	0.857236	+	0.514924i	$0.172180\pi$
$354$	−1.90028	−0.100999
$355$	0.877593	0.0465778
$356$	−29.8605	−1.58260
$357$	−1.44160	−0.0762976
$358$	−1.79102	−0.0946582
$359$	−25.4721	−1.34437	−0.672184	−	0.740384i	$-0.734644\pi$
$359$	−25.4721	−1.34437	−0.672184	+	0.740384i	$0.734644\pi$
$360$	0.0906587	0.00477813
$361$	42.7648	2.25078
$362$	2.39708	0.125987
$363$	−1.00000	−0.0524864
$364$	5.70451	0.298998
$365$	−0.581452	−0.0304346
$366$	0.171582	0.00896872
$367$	35.8891	1.87340	0.936698	−	0.350138i	$-0.113865\pi$
$367$	35.8891	1.87340	0.936698	+	0.350138i	$0.113865\pi$
$368$	7.13527	0.371952
$369$	1.52969	0.0796324
$370$	−0.211103	−0.0109747
$371$	−6.83713	−0.354966
$372$	6.04764	0.313556
$373$	26.2640	1.35990	0.679950	−	0.733259i	$-0.262002\pi$
$373$	26.2640	1.35990	0.679950	+	0.733259i	$0.262002\pi$
$374$	0.401984	0.0207861
$375$	−1.32836	−0.0685964
$376$	5.30265	0.273463
$377$	−21.3565	−1.09992
$378$	−0.105579	−0.00543041
$379$	−22.5811	−1.15991	−0.579957	−	0.814647i	$-0.696931\pi$
$379$	−22.5811	−1.15991	−0.579957	+	0.814647i	$0.696931\pi$
$380$	−2.06085	−0.105719
$381$	−19.3085	−0.989203
$382$	−4.19428	−0.214598
$383$	1.52359	0.0778520	0.0389260	−	0.999242i	$-0.487606\pi$
$383$	1.52359	0.0778520	0.0389260	+	0.999242i	$0.487606\pi$
$384$	5.29034	0.269971
$385$	−0.0818830	−0.00417315
$386$	−1.05735	−0.0538179
$387$	1.17504	0.0597308
$388$	−29.9012	−1.51800
$389$	−21.4415	−1.08713	−0.543563	−	0.839369i	$-0.682925\pi$
$389$	−21.4415	−1.08713	−0.543563	+	0.839369i	$0.682925\pi$
$390$	−0.107419	−0.00543935
$391$	4.37124	0.221063
$392$	4.51098	0.227839
$393$	−16.1882	−0.816589
$394$	−2.76999	−0.139550
$395$	−1.56869	−0.0789291
$396$	−1.97056	−0.0990244
$397$	−7.89768	−0.396373	−0.198187	−	0.980164i	$-0.563505\pi$
$397$	−7.89768	−0.396373	−0.198187	+	0.980164i	$0.563505\pi$
$398$	−2.00801	−0.100653
$399$	4.83590	0.242098
$400$	−19.0534	−0.952670
$401$	11.0900	0.553807	0.276903	−	0.960898i	$-0.410692\pi$
$401$	11.0900	0.553807	0.276903	+	0.960898i	$0.410692\pi$
$402$	−1.92581	−0.0960507
$403$	−14.4384	−0.719226
$404$	−29.5051	−1.46793
$405$	−0.133072	−0.00661240
$406$	0.479277	0.0237861
$407$	9.24562	0.458289
$408$	1.59610	0.0790187
$409$	1.82984	0.0904797	0.0452399	−	0.998976i	$-0.485595\pi$
$409$	1.82984	0.0904797	0.0452399	+	0.998976i	$0.485595\pi$
$410$	−0.0349270	−0.00172492
$411$	16.9876	0.837937
$412$	−5.23985	−0.258149
$413$	6.81481	0.335335
$414$	0.320139	0.0157340
$415$	−1.44879	−0.0711183
$416$	−9.49723	−0.465640
$417$	−0.981625	−0.0480704
$418$	−1.34847	−0.0659558
$419$	29.0901	1.42115	0.710573	−	0.703623i	$-0.248436\pi$
$419$	29.0901	1.42115	0.710573	+	0.703623i	$0.248436\pi$
$420$	−0.161355	−0.00787334
$421$	−0.0560143	−0.00272997	−0.00136499	−	0.999999i	$-0.500434\pi$
$421$	−0.0560143	−0.00272997	−0.00136499	+	0.999999i	$0.500434\pi$
$422$	−2.24567	−0.109318
$423$	−7.78342	−0.378443
$424$	7.56988	0.367626
$425$	−11.6726	−0.566203
$426$	1.13156	0.0548243
$427$	−0.615329	−0.0297779
$428$	−19.6590	−0.950253
$429$	4.70459	0.227140
$430$	−0.0268294	−0.00129383
$431$	−2.07838	−0.100112	−0.0500561	−	0.998746i	$-0.515940\pi$
$431$	−2.07838	−0.100112	−0.0500561	+	0.998746i	$0.515940\pi$
$432$	−3.82423	−0.183993
$433$	−5.73899	−0.275798	−0.137899	−	0.990446i	$-0.544035\pi$
$433$	−5.73899	−0.275798	−0.137899	+	0.990446i	$0.544035\pi$
$434$	0.324022	0.0155536
$435$	0.604081	0.0289635
$436$	17.4071	0.833650
$437$	−14.6635	−0.701450
$438$	−0.749719	−0.0358230
$439$	32.6721	1.55935	0.779677	−	0.626182i	$-0.215383\pi$
$439$	32.6721	1.55935	0.779677	+	0.626182i	$0.215383\pi$
$440$	0.0906587	0.00432198
$441$	−6.62137	−0.315303
$442$	−1.89117	−0.0899537
$443$	−25.8218	−1.22683	−0.613415	−	0.789761i	$-0.710205\pi$
$443$	−25.8218	−1.22683	−0.613415	+	0.789761i	$0.710205\pi$
$444$	18.2191	0.864638
$445$	−2.01648	−0.0955903
$446$	0.354788	0.0167997
$447$	−19.9181	−0.942093
$448$	−4.49318	−0.212283
$449$	−18.6591	−0.880579	−0.440290	−	0.897856i	$-0.645124\pi$
$449$	−18.6591	−0.880579	−0.440290	+	0.897856i	$0.645124\pi$
$450$	−0.854870	−0.0402990
$451$	1.52969	0.0720303
$452$	8.36667	0.393535
$453$	9.27179	0.435627
$454$	−1.05557	−0.0495404
$455$	0.385226	0.0180597
$456$	−5.35418	−0.250733
$457$	−4.37660	−0.204729	−0.102364	−	0.994747i	$-0.532641\pi$
$457$	−4.37660	−0.204729	−0.102364	+	0.994747i	$0.532641\pi$
$458$	3.36236	0.157113
$459$	−2.34281	−0.109353
$460$	0.489264	0.0228120
$461$	−36.4443	−1.69738	−0.848689	−	0.528891i	$-0.822608\pi$
$461$	−36.4443	−1.69738	−0.848689	+	0.528891i	$0.822608\pi$
$462$	−0.105579	−0.00491199
$463$	14.5793	0.677557	0.338779	−	0.940866i	$-0.389986\pi$
$463$	14.5793	0.677557	0.338779	+	0.940866i	$0.389986\pi$
$464$	17.3601	0.805922
$465$	0.408397	0.0189390
$466$	−3.53032	−0.163539
$467$	26.5701	1.22952	0.614760	−	0.788714i	$-0.289253\pi$
$467$	26.5701	1.22952	0.614760	+	0.788714i	$0.289253\pi$
$468$	9.27067	0.428537
$469$	6.90637	0.318906
$470$	0.177717	0.00819745
$471$	−9.62702	−0.443590
$472$	−7.54517	−0.347295
$473$	1.17504	0.0540286
$474$	−2.02265	−0.0929033
$475$	39.1561	1.79661
$476$	−2.84076	−0.130206
$477$	−11.1113	−0.508753
$478$	−3.97002	−0.181585
$479$	4.66442	0.213123	0.106561	−	0.994306i	$-0.466016\pi$
$479$	4.66442	0.213123	0.106561	+	0.994306i	$0.466016\pi$
$480$	0.268635	0.0122614
$481$	−43.4968	−1.98329
$482$	0.0168728	0.000768533 0
$483$	−1.14809	−0.0522397
$484$	−1.97056	−0.0895709
$485$	−2.01923	−0.0916884
$486$	−0.171582	−0.00778310
$487$	16.2253	0.735240	0.367620	−	0.929976i	$-0.380173\pi$
$487$	16.2253	0.735240	0.367620	+	0.929976i	$0.380173\pi$
$488$	0.681275	0.0308399
$489$	−17.0593	−0.771448
$490$	0.151184	0.00682979
$491$	37.8484	1.70808	0.854038	−	0.520210i	$-0.174146\pi$
$491$	37.8484	1.70808	0.854038	+	0.520210i	$0.174146\pi$
$492$	3.01434	0.135897
$493$	10.6352	0.478986
$494$	6.34400	0.285430
$495$	−0.133072	−0.00598114
$496$	11.7365	0.526986
$497$	−4.05802	−0.182027
$498$	−1.86806	−0.0837096
$499$	−12.9470	−0.579586	−0.289793	−	0.957089i	$-0.593587\pi$
$499$	−12.9470	−0.579586	−0.289793	+	0.957089i	$0.593587\pi$
$500$	−2.61762	−0.117063
$501$	−8.92176	−0.398595
$502$	−0.589650	−0.0263174
$503$	−22.8525	−1.01894	−0.509471	−	0.860488i	$-0.670159\pi$
$503$	−22.8525	−1.01894	−0.509471	+	0.860488i	$0.670159\pi$
$504$	−0.419208	−0.0186730
$505$	−1.99248	−0.0886641
$506$	0.320139	0.0142319
$507$	−9.13314	−0.405617
$508$	−38.0485	−1.68813
$509$	1.26053	0.0558720	0.0279360	−	0.999610i	$-0.491107\pi$
$509$	1.26053	0.0558720	0.0279360	+	0.999610i	$0.491107\pi$
$510$	0.0534928	0.00236870
$511$	2.68865	0.118939
$512$	12.9307	0.571463
$513$	7.85906	0.346986
$514$	−2.13022	−0.0939601
$515$	−0.353847	−0.0155924
$516$	2.31549	0.101934
$517$	−7.78342	−0.342314
$518$	0.976146	0.0428894
$519$	−3.85738	−0.169320
$520$	−0.426512	−0.0187038
$521$	33.2078	1.45486	0.727430	−	0.686182i	$-0.240715\pi$
$521$	33.2078	1.45486	0.727430	+	0.686182i	$0.240715\pi$
$522$	0.778896	0.0340914
$523$	22.8888	1.00086	0.500428	−	0.865778i	$-0.333176\pi$
$523$	22.8888	1.00086	0.500428	+	0.865778i	$0.333176\pi$
$524$	−31.8999	−1.39355
$525$	3.06575	0.133800
$526$	0.705131	0.0307452
$527$	7.19008	0.313205
$528$	−3.82423	−0.166428
$529$	−19.5188	−0.848642
$530$	0.253702	0.0110201
$531$	11.0751	0.480617
$532$	9.52944	0.413154
$533$	−7.19656	−0.311717
$534$	−2.60003	−0.112514
$535$	−1.32757	−0.0573959
$536$	−7.64654	−0.330280
$537$	10.4383	0.450445
$538$	3.04080	0.131098
$539$	−6.62137	−0.285203
$540$	−0.262226	−0.0112844
$541$	−7.47250	−0.321268	−0.160634	−	0.987014i	$-0.551354\pi$
$541$	−7.47250	−0.321268	−0.160634	+	0.987014i	$0.551354\pi$
$542$	1.19679	0.0514064
$543$	−13.9705	−0.599530
$544$	4.72948	0.202775
$545$	1.17550	0.0503530
$546$	0.496706	0.0212571
$547$	42.4596	1.81544	0.907721	−	0.419574i	$-0.137820\pi$
$547$	42.4596	1.81544	0.907721	+	0.419574i	$0.137820\pi$
$548$	33.4751	1.42998
$549$	−1.00000	−0.0426790
$550$	−0.854870	−0.0364518
$551$	−35.6762	−1.51986
$552$	1.27113	0.0541029
$553$	7.25365	0.308457
$554$	−0.459407	−0.0195183
$555$	1.23033	0.0522247
$556$	−1.93435	−0.0820348
$557$	33.5690	1.42236	0.711182	−	0.703008i	$-0.248160\pi$
$557$	33.5690	1.42236	0.711182	+	0.703008i	$0.248160\pi$
$558$	0.526584	0.0222921
$559$	−5.52810	−0.233814
$560$	−0.313139	−0.0132325
$561$	−2.34281	−0.0989136
$562$	−2.77529	−0.117069
$563$	−6.90978	−0.291212	−0.145606	−	0.989343i	$-0.546513\pi$
$563$	−6.90978	−0.291212	−0.145606	+	0.989343i	$0.546513\pi$
$564$	−15.3377	−0.645833
$565$	0.565002	0.0237698
$566$	2.42668	0.102001
$567$	0.615329	0.0258414
$568$	4.49293	0.188519
$569$	−43.2342	−1.81247	−0.906236	−	0.422772i	$-0.861057\pi$
$569$	−43.2342	−1.81247	−0.906236	+	0.422772i	$0.861057\pi$
$570$	−0.179444	−0.00751607
$571$	36.9917	1.54805	0.774027	−	0.633153i	$-0.218240\pi$
$571$	36.9917	1.54805	0.774027	+	0.633153i	$0.218240\pi$
$572$	9.27067	0.387626
$573$	24.4448	1.02120
$574$	0.161503	0.00674102
$575$	−9.29600	−0.387670
$576$	−7.30207	−0.304253
$577$	−43.0272	−1.79125	−0.895623	−	0.444815i	$-0.853270\pi$
$577$	−43.0272	−1.79125	−0.895623	+	0.444815i	$0.853270\pi$
$578$	−1.97512	−0.0821540
$579$	6.16239	0.256100
$580$	1.19038	0.0494277
$581$	6.69925	0.277932
$582$	−2.60357	−0.107922
$583$	−11.1113	−0.460184
$584$	−2.97680	−0.123181
$585$	0.626049	0.0258839
$586$	−1.41555	−0.0584758
$587$	2.31390	0.0955048	0.0477524	−	0.998859i	$-0.484794\pi$
$587$	2.31390	0.0955048	0.0477524	+	0.998859i	$0.484794\pi$
$588$	−13.0478	−0.538082
$589$	−24.1194	−0.993823
$590$	−0.252874	−0.0104107
$591$	16.1438	0.664069
$592$	35.3573	1.45318
$593$	10.2698	0.421731	0.210865	−	0.977515i	$-0.432372\pi$
$593$	10.2698	0.421731	0.210865	+	0.977515i	$0.432372\pi$
$594$	−0.171582	−0.00704008
$595$	−0.191837	−0.00786453
$596$	−39.2498	−1.60773
$597$	11.7030	0.478970
$598$	−1.50612	−0.0615898
$599$	21.7905	0.890335	0.445167	−	0.895447i	$-0.353144\pi$
$599$	21.7905	0.890335	0.445167	+	0.895447i	$0.353144\pi$
$600$	−3.39431	−0.138572
$601$	−20.7713	−0.847279	−0.423640	−	0.905831i	$-0.639248\pi$
$601$	−20.7713	−0.847279	−0.423640	+	0.905831i	$0.639248\pi$
$602$	0.124060	0.00505632
$603$	11.2239	0.457071
$604$	18.2706	0.743421
$605$	−0.133072	−0.00541015
$606$	−2.56908	−0.104362
$607$	1.14578	0.0465057	0.0232528	−	0.999730i	$-0.492598\pi$
$607$	1.14578	0.0465057	0.0232528	+	0.999730i	$0.492598\pi$
$608$	−15.8652	−0.643420
$609$	−2.79329	−0.113190
$610$	0.0228327	0.000924470 0
$611$	36.6178	1.48140
$612$	−4.61665	−0.186617
$613$	13.2402	0.534766	0.267383	−	0.963590i	$-0.413841\pi$
$613$	13.2402	0.534766	0.267383	+	0.963590i	$0.413841\pi$
$614$	−0.887316	−0.0358092
$615$	0.203559	0.00820828
$616$	−0.419208	−0.0168904
$617$	−19.1708	−0.771787	−0.385894	−	0.922543i	$-0.626107\pi$
$617$	−19.1708	−0.771787	−0.385894	+	0.922543i	$0.626107\pi$
$618$	−0.456247	−0.0183529
$619$	3.63574	0.146133	0.0730663	−	0.997327i	$-0.476722\pi$
$619$	3.63574	0.146133	0.0730663	+	0.997327i	$0.476722\pi$
$620$	0.804771	0.0323204
$621$	−1.86581	−0.0748723
$622$	0.954861	0.0382864
$623$	9.32426	0.373569
$624$	17.9914	0.720232
$625$	24.7347	0.989388
$626$	−4.48411	−0.179221
$627$	7.85906	0.313860
$628$	−18.9706	−0.757010
$629$	21.6608	0.863671
$630$	−0.0140496	−0.000559751 0
$631$	34.0488	1.35546	0.677732	−	0.735309i	$-0.262963\pi$
$631$	34.0488	1.35546	0.677732	+	0.735309i	$0.262963\pi$
$632$	−8.03105	−0.319458
$633$	13.0881	0.520203
$634$	−1.58904	−0.0631087
$635$	−2.56942	−0.101964
$636$	−21.8955	−0.868215
$637$	31.1508	1.23424
$638$	0.778896	0.0308368
$639$	−6.59487	−0.260889
$640$	0.703996	0.0278279
$641$	1.72492	0.0681302	0.0340651	−	0.999420i	$-0.489155\pi$
$641$	1.72492	0.0681302	0.0340651	+	0.999420i	$0.489155\pi$
$642$	−1.71176	−0.0675577
$643$	−37.6517	−1.48484	−0.742420	−	0.669935i	$-0.766322\pi$
$643$	−37.6517	−1.48484	−0.742420	+	0.669935i	$0.766322\pi$
$644$	−2.26237	−0.0891499
$645$	0.156365	0.00615688
$646$	−3.15921	−0.124298
$647$	46.6191	1.83279	0.916393	−	0.400279i	$-0.131087\pi$
$647$	46.6191	1.83279	0.916393	+	0.400279i	$0.131087\pi$
$648$	−0.681275	−0.0267630
$649$	11.0751	0.434734
$650$	4.02181	0.157748
$651$	−1.88844	−0.0740139
$652$	−33.6164	−1.31652
$653$	−32.6575	−1.27799	−0.638993	−	0.769212i	$-0.720649\pi$
$653$	−32.6575	−1.27799	−0.638993	+	0.769212i	$0.720649\pi$
$654$	1.51568	0.0592679
$655$	−2.15420	−0.0841716
$656$	5.84988	0.228399
$657$	4.36946	0.170469
$658$	−0.821767	−0.0320358
$659$	36.3322	1.41530	0.707651	−	0.706562i	$-0.249755\pi$
$659$	36.3322	1.41530	0.707651	+	0.706562i	$0.249755\pi$
$660$	−0.262226	−0.0102071
$661$	20.6126	0.801736	0.400868	−	0.916136i	$-0.368709\pi$
$661$	20.6126	0.801736	0.400868	+	0.916136i	$0.368709\pi$
$662$	−0.354975	−0.0137965
$663$	11.0220	0.428058
$664$	−7.41723	−0.287844
$665$	0.643523	0.0249548
$666$	1.58638	0.0614710
$667$	8.46985	0.327954
$668$	−17.5809	−0.680224
$669$	−2.06775	−0.0799438
$670$	−0.256271	−0.00990063
$671$	−1.00000	−0.0386046
$672$	−1.24218	−0.0479180
$673$	−5.41924	−0.208896	−0.104448	−	0.994530i	$-0.533308\pi$
$673$	−5.41924	−0.208896	−0.104448	+	0.994530i	$0.533308\pi$
$674$	−0.0408862	−0.00157488
$675$	4.98229	0.191769
$676$	−17.9974	−0.692208
$677$	−15.1357	−0.581713	−0.290857	−	0.956767i	$-0.593940\pi$
$677$	−15.1357	−0.581713	−0.290857	+	0.956767i	$0.593940\pi$
$678$	0.728508	0.0279782
$679$	9.33697	0.358320
$680$	0.212396	0.00814502
$681$	6.15200	0.235745
$682$	0.526584	0.0201639
$683$	5.25700	0.201154	0.100577	−	0.994929i	$-0.467931\pi$
$683$	5.25700	0.201154	0.100577	+	0.994929i	$0.467931\pi$
$684$	15.4867	0.592150
$685$	2.26057	0.0863721
$686$	−1.43813	−0.0549082
$687$	−19.5963	−0.747644
$688$	4.49363	0.171318
$689$	52.2742	1.99149
$690$	0.0426015	0.00162181
$691$	−37.8441	−1.43966	−0.719828	−	0.694152i	$-0.755780\pi$
$691$	−37.8441	−1.43966	−0.719828	+	0.694152i	$0.755780\pi$
$692$	−7.60120	−0.288954
$693$	0.615329	0.0233744
$694$	4.78753	0.181732
$695$	−0.130627	−0.00495496
$696$	3.09265	0.117227
$697$	3.58377	0.135745
$698$	5.26703	0.199360
$699$	20.5752	0.778224
$700$	6.04124	0.228337
$701$	−26.2157	−0.990154	−0.495077	−	0.868849i	$-0.664860\pi$
$701$	−26.2157	−0.990154	−0.495077	+	0.868849i	$0.664860\pi$
$702$	0.807221	0.0304666
$703$	−72.6619	−2.74049
$704$	−7.30207	−0.275207
$705$	−1.03575	−0.0390088
$706$	5.52699	0.208011
$707$	9.21328	0.346501
$708$	21.8241	0.820199
$709$	−22.3870	−0.840762	−0.420381	−	0.907348i	$-0.638104\pi$
$709$	−22.3870	−0.840762	−0.420381	+	0.907348i	$0.638104\pi$
$710$	0.150579	0.00565113
$711$	11.7882	0.442094
$712$	−10.3236	−0.386892
$713$	5.72616	0.214446
$714$	−0.247352	−0.00925692
$715$	0.626049	0.0234129
$716$	20.5693	0.768709
$717$	23.1378	0.864097
$718$	−4.37055	−0.163108
$719$	−21.7396	−0.810751	−0.405376	−	0.914150i	$-0.632859\pi$
$719$	−21.7396	−0.810751	−0.405376	+	0.914150i	$0.632859\pi$
$720$	−0.508897	−0.0189655
$721$	1.63620	0.0609352
$722$	7.33765	0.273079
$723$	−0.0983366	−0.00365718
$724$	−27.5296	−1.02313
$725$	−22.6171	−0.839979
$726$	−0.171582	−0.00636799
$727$	−24.4460	−0.906653	−0.453327	−	0.891344i	$-0.649763\pi$
$727$	−24.4460	−0.906653	−0.453327	+	0.891344i	$0.649763\pi$
$728$	1.97220	0.0730947
$729$	1.00000	0.0370370
$730$	−0.0997666	−0.00369253
$731$	2.75291	0.101820
$732$	−1.97056	−0.0728340
$733$	13.6034	0.502452	0.251226	−	0.967928i	$-0.419166\pi$
$733$	13.6034	0.502452	0.251226	+	0.967928i	$0.419166\pi$
$734$	6.15792	0.227293
$735$	−0.881119	−0.0325006
$736$	3.76654	0.138837
$737$	11.2239	0.413436
$738$	0.262467	0.00966153
$739$	1.68561	0.0620061	0.0310031	−	0.999519i	$-0.490130\pi$
$739$	1.68561	0.0620061	0.0310031	+	0.999519i	$0.490130\pi$
$740$	2.42445	0.0891244
$741$	−36.9736	−1.35826
$742$	−1.17313	−0.0430668
$743$	45.8835	1.68330	0.841652	−	0.540020i	$-0.181583\pi$
$743$	45.8835	1.68330	0.841652	+	0.540020i	$0.181583\pi$
$744$	2.09083	0.0766536
$745$	−2.65054	−0.0971082
$746$	4.50643	0.164992
$747$	10.8873	0.398344
$748$	−4.61665	−0.168801
$749$	6.13873	0.224304
$750$	−0.227923	−0.00832257
$751$	−47.2695	−1.72489	−0.862445	−	0.506151i	$-0.831068\pi$
$751$	−47.2695	−1.72489	−0.862445	+	0.506151i	$0.831068\pi$
$752$	−29.7655	−1.08544
$753$	3.43655	0.125235
$754$	−3.66438	−0.133449
$755$	1.23382	0.0449032
$756$	1.21254	0.0440997
$757$	−33.4045	−1.21411	−0.607054	−	0.794661i	$-0.707649\pi$
$757$	−33.4045	−1.21411	−0.607054	+	0.794661i	$0.707649\pi$
$758$	−3.87451	−0.140728
$759$	−1.86581	−0.0677245
$760$	−0.712492	−0.0258448
$761$	19.2821	0.698974	0.349487	−	0.936941i	$-0.386356\pi$
$761$	19.2821	0.698974	0.349487	+	0.936941i	$0.386356\pi$
$762$	−3.31298	−0.120017
$763$	−5.43556	−0.196781
$764$	48.1700	1.74273
$765$	−0.311763	−0.0112718
$766$	0.261421	0.00944551
$767$	−52.1036	−1.88135
$768$	−13.6964	−0.494227
$769$	−27.7997	−1.00248	−0.501242	−	0.865307i	$-0.667123\pi$
$769$	−27.7997	−1.00248	−0.501242	+	0.865307i	$0.667123\pi$
$770$	−0.0140496	−0.000506314 0
$771$	12.4152	0.447123
$772$	12.1434	0.437049
$773$	15.4428	0.555438	0.277719	−	0.960662i	$-0.410422\pi$
$773$	15.4428	0.555438	0.277719	+	0.960662i	$0.410422\pi$
$774$	0.201616	0.00724694
$775$	−15.2906	−0.549256
$776$	−10.3376	−0.371100
$777$	−5.68910	−0.204095
$778$	−3.67896	−0.131897
$779$	−12.0219	−0.430730
$780$	1.23367	0.0441723
$781$	−6.59487	−0.235983
$782$	0.750024	0.0268208
$783$	−4.53951	−0.162229
$784$	−25.3216	−0.904343
$785$	−1.28109	−0.0457239
$786$	−2.77761	−0.0990740
$787$	−39.8594	−1.42083	−0.710417	−	0.703781i	$-0.751494\pi$
$787$	−39.8594	−1.42083	−0.710417	+	0.703781i	$0.751494\pi$
$788$	31.8124	1.13327
$789$	−4.10959	−0.146305
$790$	−0.269158	−0.00957620
$791$	−2.61259	−0.0928929
$792$	−0.681275	−0.0242081
$793$	4.70459	0.167065
$794$	−1.35510	−0.0480906
$795$	−1.47861	−0.0524408
$796$	23.0614	0.817388
$797$	−17.9931	−0.637348	−0.318674	−	0.947864i	$-0.603238\pi$
$797$	−17.9931	−0.637348	−0.318674	+	0.947864i	$0.603238\pi$
$798$	0.829753	0.0293729
$799$	−18.2351	−0.645111
$800$	−10.0578	−0.355598
$801$	15.1533	0.535415
$802$	1.90284	0.0671915
$803$	4.36946	0.154195
$804$	22.1173	0.780017
$805$	−0.152778	−0.00538472
$806$	−2.47736	−0.0872612
$807$	−17.7222	−0.623850
$808$	−10.2007	−0.358859
$809$	−36.0517	−1.26751	−0.633755	−	0.773534i	$-0.718487\pi$
$809$	−36.0517	−1.26751	−0.633755	+	0.773534i	$0.718487\pi$
$810$	−0.0228327	−0.000802260 0
$811$	17.6858	0.621032	0.310516	−	0.950568i	$-0.399498\pi$
$811$	17.6858	0.621032	0.310516	+	0.950568i	$0.399498\pi$
$812$	−5.50434	−0.193165
$813$	−6.97502	−0.244625
$814$	1.58638	0.0556026
$815$	−2.27011	−0.0795186
$816$	−8.95944	−0.313643
$817$	−9.23474	−0.323082
$818$	0.313967	0.0109776
$819$	−2.89487	−0.101155
$820$	0.401125	0.0140079
$821$	−14.5517	−0.507858	−0.253929	−	0.967223i	$-0.581723\pi$
$821$	−14.5517	−0.507858	−0.253929	+	0.967223i	$0.581723\pi$
$822$	2.91476	0.101664
$823$	48.1384	1.67800	0.838999	−	0.544133i	$-0.183141\pi$
$823$	48.1384	1.67800	0.838999	+	0.544133i	$0.183141\pi$
$824$	−1.81156	−0.0631085
$825$	4.98229	0.173461
$826$	1.16930	0.0406850
$827$	27.5769	0.958943	0.479472	−	0.877557i	$-0.340828\pi$
$827$	27.5769	0.958943	0.479472	+	0.877557i	$0.340828\pi$
$828$	−3.67669	−0.127774
$829$	−10.6222	−0.368926	−0.184463	−	0.982839i	$-0.559055\pi$
$829$	−10.6222	−0.368926	−0.184463	+	0.982839i	$0.559055\pi$
$830$	−0.248586	−0.00862855
$831$	2.67748	0.0928808
$832$	34.3532	1.19098
$833$	−15.5126	−0.537481
$834$	−0.168429	−0.00583222
$835$	−1.18724	−0.0410860
$836$	15.4867	0.535620
$837$	−3.06900	−0.106080
$838$	4.99134	0.172423
$839$	−48.1933	−1.66382	−0.831909	−	0.554912i	$-0.812752\pi$
$839$	−48.1933	−1.66382	−0.831909	+	0.554912i	$0.812752\pi$
$840$	−0.0557849	−0.00192476
$841$	−8.39289	−0.289410
$842$	−0.00961104	−0.000331218 0
$843$	16.1747	0.557088
$844$	25.7908	0.887756
$845$	−1.21536	−0.0418098
$846$	−1.33549	−0.0459152
$847$	0.615329	0.0211430
$848$	−42.4922	−1.45919
$849$	−14.1430	−0.485387
$850$	−2.00280	−0.0686955
$851$	17.2506	0.591342
$852$	−12.9956	−0.445222
$853$	46.5258	1.59301	0.796507	−	0.604629i	$-0.206679\pi$
$853$	46.5258	1.59301	0.796507	+	0.604629i	$0.206679\pi$
$854$	−0.105579	−0.00361285
$855$	1.04582	0.0357663
$856$	−6.79664	−0.232304
$857$	−10.3918	−0.354979	−0.177489	−	0.984123i	$-0.556798\pi$
$857$	−10.3918	−0.354979	−0.177489	+	0.984123i	$0.556798\pi$
$858$	0.807221	0.0275581
$859$	57.1315	1.94930	0.974651	−	0.223732i	$-0.0718241\pi$
$859$	57.1315	1.94930	0.974651	+	0.223732i	$0.0718241\pi$
$860$	0.308127	0.0105071
$861$	−0.941262	−0.0320781
$862$	−0.356613	−0.0121463
$863$	21.5752	0.734429	0.367214	−	0.930136i	$-0.380312\pi$
$863$	21.5752	0.734429	0.367214	+	0.930136i	$0.380312\pi$
$864$	−2.01872	−0.0686782
$865$	−0.513309	−0.0174530
$866$	−0.984706	−0.0334617
$867$	11.5112	0.390942
$868$	−3.72129	−0.126309
$869$	11.7882	0.399889
$870$	0.103649	0.00351404
$871$	−52.8036	−1.78918
$872$	6.01811	0.203799
$873$	15.1739	0.513560
$874$	−2.51599	−0.0851045
$875$	0.817380	0.0276325
$876$	8.61028	0.290914
$877$	−19.6961	−0.665092	−0.332546	−	0.943087i	$-0.607908\pi$
$877$	−19.6961	−0.665092	−0.332546	+	0.943087i	$0.607908\pi$
$878$	5.60594	0.189191
$879$	8.25000	0.278266
$880$	−0.508897	−0.0171549
$881$	−13.2882	−0.447691	−0.223845	−	0.974625i	$-0.571861\pi$
$881$	−13.2882	−0.447691	−0.223845	+	0.974625i	$0.571861\pi$
$882$	−1.13611	−0.0382547
$883$	12.8872	0.433688	0.216844	−	0.976206i	$-0.430424\pi$
$883$	12.8872	0.433688	0.216844	+	0.976206i	$0.430424\pi$
$884$	21.7194	0.730504
$885$	1.47378	0.0495406
$886$	−4.43055	−0.148847
$887$	1.36425	0.0458071	0.0229036	−	0.999738i	$-0.492709\pi$
$887$	1.36425	0.0458071	0.0229036	+	0.999738i	$0.492709\pi$
$888$	6.29882	0.211374
$889$	11.8811	0.398478
$890$	−0.345991	−0.0115976
$891$	1.00000	0.0335013
$892$	−4.07463	−0.136429
$893$	61.1703	2.04699
$894$	−3.41758	−0.114301
$895$	1.38904	0.0464306
$896$	−3.25530	−0.108752
$897$	8.77786	0.293084
$898$	−3.20157	−0.106838
$899$	13.9317	0.464649
$900$	9.81790	0.327263
$901$	−26.0318	−0.867244
$902$	0.262467	0.00873919
$903$	−0.723038	−0.0240612
$904$	2.89258	0.0962059
$905$	−1.85908	−0.0617978
$906$	1.59087	0.0528531
$907$	52.3304	1.73760	0.868802	−	0.495160i	$-0.164890\pi$
$907$	52.3304	1.73760	0.868802	+	0.495160i	$0.164890\pi$
$908$	12.1229	0.402312
$909$	14.9729	0.496621
$910$	0.0660977	0.00219112
$911$	4.50180	0.149151	0.0745756	−	0.997215i	$-0.476240\pi$
$911$	4.50180	0.149151	0.0745756	+	0.997215i	$0.476240\pi$
$912$	30.0548	0.995214
$913$	10.8873	0.360316
$914$	−0.750944	−0.0248390
$915$	−0.133072	−0.00439922
$916$	−38.6156	−1.27590
$917$	9.96110	0.328944
$918$	−0.401984	−0.0132674
$919$	25.3477	0.836143	0.418072	−	0.908414i	$-0.362706\pi$
$919$	25.3477	0.836143	0.418072	+	0.908414i	$0.362706\pi$
$920$	0.169152	0.00557677
$921$	5.17139	0.170403
$922$	−6.25317	−0.205937
$923$	31.0262	1.02124
$924$	1.21254	0.0398897
$925$	−46.0644	−1.51459
$926$	2.50154	0.0822057
$927$	2.65906	0.0873351
$928$	9.16398	0.300822
$929$	20.9203	0.686372	0.343186	−	0.939267i	$-0.388494\pi$
$929$	20.9203	0.686372	0.343186	+	0.939267i	$0.388494\pi$
$930$	0.0700735	0.00229780
$931$	52.0377	1.70547
$932$	40.5446	1.32808
$933$	−5.56505	−0.182192
$934$	4.55895	0.149173
$935$	−0.311763	−0.0101957
$936$	3.20512	0.104763
$937$	33.7225	1.10167	0.550833	−	0.834615i	$-0.314310\pi$
$937$	33.7225	1.10167	0.550833	+	0.834615i	$0.314310\pi$
$938$	1.18501	0.0386918
$939$	26.1339	0.852849
$940$	−2.04102	−0.0665706
$941$	−45.8406	−1.49436	−0.747180	−	0.664621i	$-0.768593\pi$
$941$	−45.8406	−1.49436	−0.747180	+	0.664621i	$0.768593\pi$
$942$	−1.65182	−0.0538192
$943$	2.85411	0.0929425
$944$	42.3535	1.37849
$945$	0.0818830	0.00266366
$946$	0.201616	0.00655510
$947$	−31.2864	−1.01667	−0.508336	−	0.861159i	$-0.669739\pi$
$947$	−31.2864	−1.01667	−0.508336	+	0.861159i	$0.669739\pi$
$948$	23.2294	0.754457
$949$	−20.5565	−0.667292
$950$	6.71847	0.217976
$951$	9.26111	0.300312
$952$	−0.982127	−0.0318309
$953$	58.6406	1.89955	0.949777	−	0.312926i	$-0.101309\pi$
$953$	58.6406	1.89955	0.949777	+	0.312926i	$0.101309\pi$
$954$	−1.90650	−0.0617253
$955$	3.25292	0.105262
$956$	45.5944	1.47463
$957$	−4.53951	−0.146741
$958$	0.800329	0.0258574
$959$	−10.4530	−0.337544
$960$	−0.971702	−0.0313615
$961$	−21.5813	−0.696170
$962$	−7.46326	−0.240625
$963$	9.97635	0.321483
$964$	−0.193778	−0.00624117
$965$	0.820041	0.0263981
$966$	−0.196991	−0.00633807
$967$	−35.3660	−1.13729	−0.568647	−	0.822582i	$-0.692533\pi$
$967$	−35.3660	−1.13729	−0.568647	+	0.822582i	$0.692533\pi$
$968$	−0.681275	−0.0218970
$969$	18.4123	0.591488
$970$	−0.346462	−0.0111242
$971$	21.4189	0.687366	0.343683	−	0.939086i	$-0.388325\pi$
$971$	21.4189	0.687366	0.343683	+	0.939086i	$0.388325\pi$
$972$	1.97056	0.0632057
$973$	0.604022	0.0193641
$974$	2.78397	0.0892042
$975$	−23.4396	−0.750669
$976$	−3.82423	−0.122410
$977$	−50.4860	−1.61519	−0.807595	−	0.589737i	$-0.799231\pi$
$977$	−50.4860	−1.61519	−0.807595	+	0.589737i	$0.799231\pi$
$978$	−2.92706	−0.0935971
$979$	15.1533	0.484301
$980$	−1.73630	−0.0554640
$981$	−8.83359	−0.282035
$982$	6.49410	0.207235
$983$	−4.20465	−0.134107	−0.0670537	−	0.997749i	$-0.521360\pi$
$983$	−4.20465	−0.134107	−0.0670537	+	0.997749i	$0.521360\pi$
$984$	1.04214	0.0332222
$985$	2.14829	0.0684503
$986$	1.82481	0.0581137
$987$	4.78936	0.152447
$988$	−72.8587	−2.31794
$989$	2.19241	0.0697145
$990$	−0.0228327	−0.000725671 0
$991$	14.4063	0.457631	0.228816	−	0.973470i	$-0.426515\pi$
$991$	14.4063	0.457631	0.228816	+	0.973470i	$0.426515\pi$
$992$	6.19544	0.196705
$993$	2.06884	0.0656527
$994$	−0.696282	−0.0220847
$995$	1.55734	0.0493708
$996$	21.4540	0.679797
$997$	25.4235	0.805169	0.402585	−	0.915383i	$-0.368112\pi$
$997$	25.4235	0.805169	0.402585	+	0.915383i	$0.368112\pi$
$998$	−2.22147	−0.0703193
$999$	−9.24562	−0.292519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.7	✓	13
3.2	odd	2		6039.2.a.i.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.7	✓	13	1.1	even	1	trivial
6039.2.a.i.1.7		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.171582 q^{2} -1.00000 q^{3} -1.97056 q^{4} -0.133072 q^{5} -0.171582 q^{6} +0.615329 q^{7} -0.681275 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.171582 q^{2} -1.00000 q^{3} -1.97056 q^{4} -0.133072 q^{5} -0.171582 q^{6} +0.615329 q^{7} -0.681275 q^{8} +1.00000 q^{9} -0.0228327 q^{10} +1.00000 q^{11} +1.97056 q^{12} -4.70459 q^{13} +0.105579 q^{14} +0.133072 q^{15} +3.82423 q^{16} +2.34281 q^{17} +0.171582 q^{18} -7.85906 q^{19} +0.262226 q^{20} -0.615329 q^{21} +0.171582 q^{22} +1.86581 q^{23} +0.681275 q^{24} -4.98229 q^{25} -0.807221 q^{26} -1.00000 q^{27} -1.21254 q^{28} +4.53951 q^{29} +0.0228327 q^{30} +3.06900 q^{31} +2.01872 q^{32} -1.00000 q^{33} +0.401984 q^{34} -0.0818830 q^{35} -1.97056 q^{36} +9.24562 q^{37} -1.34847 q^{38} +4.70459 q^{39} +0.0906587 q^{40} +1.52969 q^{41} -0.105579 q^{42} +1.17504 q^{43} -1.97056 q^{44} -0.133072 q^{45} +0.320139 q^{46} -7.78342 q^{47} -3.82423 q^{48} -6.62137 q^{49} -0.854870 q^{50} -2.34281 q^{51} +9.27067 q^{52} -11.1113 q^{53} -0.171582 q^{54} -0.133072 q^{55} -0.419208 q^{56} +7.85906 q^{57} +0.778896 q^{58} +11.0751 q^{59} -0.262226 q^{60} -1.00000 q^{61} +0.526584 q^{62} +0.615329 q^{63} -7.30207 q^{64} +0.626049 q^{65} -0.171582 q^{66} +11.2239 q^{67} -4.61665 q^{68} -1.86581 q^{69} -0.0140496 q^{70} -6.59487 q^{71} -0.681275 q^{72} +4.36946 q^{73} +1.58638 q^{74} +4.98229 q^{75} +15.4867 q^{76} +0.615329 q^{77} +0.807221 q^{78} +11.7882 q^{79} -0.508897 q^{80} +1.00000 q^{81} +0.262467 q^{82} +10.8873 q^{83} +1.21254 q^{84} -0.311763 q^{85} +0.201616 q^{86} -4.53951 q^{87} -0.681275 q^{88} +15.1533 q^{89} -0.0228327 q^{90} -2.89487 q^{91} -3.67669 q^{92} -3.06900 q^{93} -1.33549 q^{94} +1.04582 q^{95} -2.01872 q^{96} +15.1739 q^{97} -1.13611 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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