LMFDB - Embedded newform 2013.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.10
Root			$1.88022$ 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)

$f(q)$	$=$	$q+1.88022 q^{2} +1.00000 q^{3} +1.53524 q^{4} +1.27827 q^{5} +1.88022 q^{6} +0.0298223 q^{7} -0.873847 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.88022 q^{2} +1.00000 q^{3} +1.53524 q^{4} +1.27827 q^{5} +1.88022 q^{6} +0.0298223 q^{7} -0.873847 q^{8} +1.00000 q^{9} +2.40344 q^{10} -1.00000 q^{11} +1.53524 q^{12} +5.58822 q^{13} +0.0560727 q^{14} +1.27827 q^{15} -4.71351 q^{16} +1.33955 q^{17} +1.88022 q^{18} +6.70962 q^{19} +1.96246 q^{20} +0.0298223 q^{21} -1.88022 q^{22} +3.41259 q^{23} -0.873847 q^{24} -3.36602 q^{25} +10.5071 q^{26} +1.00000 q^{27} +0.0457846 q^{28} +1.60973 q^{29} +2.40344 q^{30} -6.25509 q^{31} -7.11477 q^{32} -1.00000 q^{33} +2.51865 q^{34} +0.0381211 q^{35} +1.53524 q^{36} +1.71832 q^{37} +12.6156 q^{38} +5.58822 q^{39} -1.11701 q^{40} +0.668829 q^{41} +0.0560727 q^{42} +2.57228 q^{43} -1.53524 q^{44} +1.27827 q^{45} +6.41643 q^{46} -0.587690 q^{47} -4.71351 q^{48} -6.99911 q^{49} -6.32887 q^{50} +1.33955 q^{51} +8.57927 q^{52} +7.62049 q^{53} +1.88022 q^{54} -1.27827 q^{55} -0.0260602 q^{56} +6.70962 q^{57} +3.02664 q^{58} +10.5438 q^{59} +1.96246 q^{60} -1.00000 q^{61} -11.7610 q^{62} +0.0298223 q^{63} -3.95034 q^{64} +7.14327 q^{65} -1.88022 q^{66} -8.58956 q^{67} +2.05653 q^{68} +3.41259 q^{69} +0.0716763 q^{70} +2.03577 q^{71} -0.873847 q^{72} -3.80905 q^{73} +3.23083 q^{74} -3.36602 q^{75} +10.3009 q^{76} -0.0298223 q^{77} +10.5071 q^{78} +7.69951 q^{79} -6.02516 q^{80} +1.00000 q^{81} +1.25755 q^{82} -0.742344 q^{83} +0.0457846 q^{84} +1.71231 q^{85} +4.83647 q^{86} +1.60973 q^{87} +0.873847 q^{88} -13.4255 q^{89} +2.40344 q^{90} +0.166654 q^{91} +5.23915 q^{92} -6.25509 q^{93} -1.10499 q^{94} +8.57673 q^{95} -7.11477 q^{96} +1.56491 q^{97} -13.1599 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.88022	1.32952	0.664760	−	0.747057i	$-0.268534\pi$
$2$	1.88022	1.32952	0.664760	+	0.747057i	$0.268534\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.53524	0.767622
$5$	1.27827	0.571661	0.285831	−	0.958280i	$-0.407731\pi$
$5$	1.27827	0.571661	0.285831	+	0.958280i	$0.407731\pi$
$6$	1.88022	0.767598
$7$	0.0298223	0.0112718	0.00563589	−	0.999984i	$-0.498206\pi$
$7$	0.0298223	0.0112718	0.00563589	+	0.999984i	$0.498206\pi$
$8$	−0.873847	−0.308951
$9$	1.00000	0.333333
$10$	2.40344	0.760035
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.53524	0.443187
$13$	5.58822	1.54989	0.774946	−	0.632027i	$-0.217777\pi$
$13$	5.58822	1.54989	0.774946	+	0.632027i	$0.217777\pi$
$14$	0.0560727	0.0149861
$15$	1.27827	0.330049
$16$	−4.71351	−1.17838
$17$	1.33955	0.324888	0.162444	−	0.986718i	$-0.448062\pi$
$17$	1.33955	0.324888	0.162444	+	0.986718i	$0.448062\pi$
$18$	1.88022	0.443173
$19$	6.70962	1.53929	0.769647	−	0.638470i	$-0.220432\pi$
$19$	6.70962	1.53929	0.769647	+	0.638470i	$0.220432\pi$
$20$	1.96246	0.438820
$21$	0.0298223	0.00650777
$22$	−1.88022	−0.400865
$23$	3.41259	0.711574	0.355787	−	0.934567i	$-0.384213\pi$
$23$	3.41259	0.711574	0.355787	+	0.934567i	$0.384213\pi$
$24$	−0.873847	−0.178373
$25$	−3.36602	−0.673203
$26$	10.5071	2.06061
$27$	1.00000	0.192450
$28$	0.0457846	0.00865247
$29$	1.60973	0.298918	0.149459	−	0.988768i	$-0.452247\pi$
$29$	1.60973	0.298918	0.149459	+	0.988768i	$0.452247\pi$
$30$	2.40344	0.438806
$31$	−6.25509	−1.12345	−0.561724	−	0.827325i	$-0.689862\pi$
$31$	−6.25509	−1.12345	−0.561724	+	0.827325i	$0.689862\pi$
$32$	−7.11477	−1.25773
$33$	−1.00000	−0.174078
$34$	2.51865	0.431944
$35$	0.0381211	0.00644365
$36$	1.53524	0.255874
$37$	1.71832	0.282490	0.141245	−	0.989975i	$-0.454889\pi$
$37$	1.71832	0.282490	0.141245	+	0.989975i	$0.454889\pi$
$38$	12.6156	2.04652
$39$	5.58822	0.894831
$40$	−1.11701	−0.176616
$41$	0.668829	0.104454	0.0522268	−	0.998635i	$-0.483368\pi$
$41$	0.668829	0.104454	0.0522268	+	0.998635i	$0.483368\pi$
$42$	0.0560727	0.00865221
$43$	2.57228	0.392270	0.196135	−	0.980577i	$-0.437161\pi$
$43$	2.57228	0.392270	0.196135	+	0.980577i	$0.437161\pi$
$44$	−1.53524	−0.231447
$45$	1.27827	0.190554
$46$	6.41643	0.946051
$47$	−0.587690	−0.0857233	−0.0428617	−	0.999081i	$-0.513647\pi$
$47$	−0.587690	−0.0857233	−0.0428617	+	0.999081i	$0.513647\pi$
$48$	−4.71351	−0.680337
$49$	−6.99911	−0.999873
$50$	−6.32887	−0.895037
$51$	1.33955	0.187574
$52$	8.57927	1.18973
$53$	7.62049	1.04675	0.523377	−	0.852101i	$-0.324672\pi$
$53$	7.62049	1.04675	0.523377	+	0.852101i	$0.324672\pi$
$54$	1.88022	0.255866
$55$	−1.27827	−0.172362
$56$	−0.0260602	−0.00348243
$57$	6.70962	0.888711
$58$	3.02664	0.397418
$59$	10.5438	1.37269	0.686345	−	0.727276i	$-0.259214\pi$
$59$	10.5438	1.37269	0.686345	+	0.727276i	$0.259214\pi$
$60$	1.96246	0.253353
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−11.7610	−1.49365
$63$	0.0298223	0.00375726
$64$	−3.95034	−0.493792
$65$	7.14327	0.886014
$66$	−1.88022	−0.231440
$67$	−8.58956	−1.04938	−0.524691	−	0.851293i	$-0.675819\pi$
$67$	−8.58956	−1.04938	−0.524691	+	0.851293i	$0.675819\pi$
$68$	2.05653	0.249391
$69$	3.41259	0.410827
$70$	0.0716763	0.00856695
$71$	2.03577	0.241601	0.120801	−	0.992677i	$-0.461454\pi$
$71$	2.03577	0.241601	0.120801	+	0.992677i	$0.461454\pi$
$72$	−0.873847	−0.102984
$73$	−3.80905	−0.445816	−0.222908	−	0.974840i	$-0.571555\pi$
$73$	−3.80905	−0.445816	−0.222908	+	0.974840i	$0.571555\pi$
$74$	3.23083	0.375576
$75$	−3.36602	−0.388674
$76$	10.3009	1.18159
$77$	−0.0298223	−0.00339857
$78$	10.5071	1.18970
$79$	7.69951	0.866262	0.433131	−	0.901331i	$-0.357409\pi$
$79$	7.69951	0.866262	0.433131	+	0.901331i	$0.357409\pi$
$80$	−6.02516	−0.673633
$81$	1.00000	0.111111
$82$	1.25755	0.138873
$83$	−0.742344	−0.0814828	−0.0407414	−	0.999170i	$-0.512972\pi$
$83$	−0.742344	−0.0814828	−0.0407414	+	0.999170i	$0.512972\pi$
$84$	0.0457846	0.00499551
$85$	1.71231	0.185726
$86$	4.83647	0.521530
$87$	1.60973	0.172581
$88$	0.873847	0.0931524
$89$	−13.4255	−1.42310	−0.711552	−	0.702634i	$-0.752007\pi$
$89$	−13.4255	−1.42310	−0.711552	+	0.702634i	$0.752007\pi$
$90$	2.40344	0.253345
$91$	0.166654	0.0174701
$92$	5.23915	0.546219
$93$	−6.25509	−0.648623
$94$	−1.10499	−0.113971
$95$	8.57673	0.879954
$96$	−7.11477	−0.726148
$97$	1.56491	0.158893	0.0794464	−	0.996839i	$-0.474685\pi$
$97$	1.56491	0.158893	0.0794464	+	0.996839i	$0.474685\pi$
$98$	−13.1599	−1.32935
$99$	−1.00000	−0.100504
$100$	−5.16766	−0.516766
$101$	−13.7243	−1.36561	−0.682807	−	0.730598i	$-0.739241\pi$
$101$	−13.7243	−1.36561	−0.682807	+	0.730598i	$0.739241\pi$
$102$	2.51865	0.249383
$103$	−8.90102	−0.877043	−0.438522	−	0.898721i	$-0.644498\pi$
$103$	−8.90102	−0.877043	−0.438522	+	0.898721i	$0.644498\pi$
$104$	−4.88324	−0.478842
$105$	0.0381211	0.00372024
$106$	14.3282	1.39168
$107$	−8.38029	−0.810154	−0.405077	−	0.914283i	$-0.632755\pi$
$107$	−8.38029	−0.810154	−0.405077	+	0.914283i	$0.632755\pi$
$108$	1.53524	0.147729
$109$	−11.9870	−1.14814	−0.574072	−	0.818805i	$-0.694637\pi$
$109$	−11.9870	−1.14814	−0.574072	+	0.818805i	$0.694637\pi$
$110$	−2.40344	−0.229159
$111$	1.71832	0.163096
$112$	−0.140568	−0.0132824
$113$	1.22669	0.115398	0.0576988	−	0.998334i	$-0.481624\pi$
$113$	1.22669	0.115398	0.0576988	+	0.998334i	$0.481624\pi$
$114$	12.6156	1.18156
$115$	4.36222	0.406779
$116$	2.47132	0.229456
$117$	5.58822	0.516631
$118$	19.8248	1.82502
$119$	0.0399484	0.00366206
$120$	−1.11701	−0.101969
$121$	1.00000	0.0909091
$122$	−1.88022	−0.170228
$123$	0.668829	0.0603063
$124$	−9.60309	−0.862383
$125$	−10.6941	−0.956506
$126$	0.0560727	0.00499535
$127$	−6.73121	−0.597298	−0.298649	−	0.954363i	$-0.596536\pi$
$127$	−6.73121	−0.597298	−0.298649	+	0.954363i	$0.596536\pi$
$128$	6.80202	0.601220
$129$	2.57228	0.226477
$130$	13.4310	1.17797
$131$	−1.11554	−0.0974650	−0.0487325	−	0.998812i	$-0.515518\pi$
$131$	−1.11554	−0.0974650	−0.0487325	+	0.998812i	$0.515518\pi$
$132$	−1.53524	−0.133626
$133$	0.200097	0.0173506
$134$	−16.1503	−1.39517
$135$	1.27827	0.110016
$136$	−1.17056	−0.100374
$137$	4.67046	0.399025	0.199512	−	0.979895i	$-0.436064\pi$
$137$	4.67046	0.399025	0.199512	+	0.979895i	$0.436064\pi$
$138$	6.41643	0.546203
$139$	−3.77266	−0.319993	−0.159996	−	0.987118i	$-0.551148\pi$
$139$	−3.77266	−0.319993	−0.159996	+	0.987118i	$0.551148\pi$
$140$	0.0585252	0.00494628
$141$	−0.587690	−0.0494924
$142$	3.82770	0.321214
$143$	−5.58822	−0.467310
$144$	−4.71351	−0.392793
$145$	2.05767	0.170880
$146$	−7.16187	−0.592720
$147$	−6.99911	−0.577277
$148$	2.63804	0.216845
$149$	−7.87763	−0.645360	−0.322680	−	0.946508i	$-0.604584\pi$
$149$	−7.87763	−0.645360	−0.322680	+	0.946508i	$0.604584\pi$
$150$	−6.32887	−0.516750
$151$	18.2796	1.48757	0.743785	−	0.668419i	$-0.233029\pi$
$151$	18.2796	1.48757	0.743785	+	0.668419i	$0.233029\pi$
$152$	−5.86318	−0.475567
$153$	1.33955	0.108296
$154$	−0.0560727	−0.00451847
$155$	−7.99572	−0.642232
$156$	8.57927	0.686892
$157$	−21.7284	−1.73412	−0.867059	−	0.498206i	$-0.833992\pi$
$157$	−21.7284	−1.73412	−0.867059	+	0.498206i	$0.833992\pi$
$158$	14.4768	1.15171
$159$	7.62049	0.604344
$160$	−9.09462	−0.718993
$161$	0.101771	0.00802071
$162$	1.88022	0.147724
$163$	−10.1629	−0.796023	−0.398012	−	0.917380i	$-0.630300\pi$
$163$	−10.1629	−0.796023	−0.398012	+	0.917380i	$0.630300\pi$
$164$	1.02682	0.0801809
$165$	−1.27827	−0.0995135
$166$	−1.39577	−0.108333
$167$	−11.2296	−0.868970	−0.434485	−	0.900679i	$-0.643070\pi$
$167$	−11.2296	−0.868970	−0.434485	+	0.900679i	$0.643070\pi$
$168$	−0.0260602	−0.00201058
$169$	18.2282	1.40217
$170$	3.21952	0.246926
$171$	6.70962	0.513098
$172$	3.94908	0.301115
$173$	11.3300	0.861404	0.430702	−	0.902494i	$-0.358266\pi$
$173$	11.3300	0.861404	0.430702	+	0.902494i	$0.358266\pi$
$174$	3.02664	0.229449
$175$	−0.100383	−0.00758821
$176$	4.71351	0.355295
$177$	10.5438	0.792523
$178$	−25.2430	−1.89204
$179$	−9.37041	−0.700377	−0.350189	−	0.936679i	$-0.613883\pi$
$179$	−9.37041	−0.700377	−0.350189	+	0.936679i	$0.613883\pi$
$180$	1.96246	0.146273
$181$	−17.0680	−1.26865	−0.634327	−	0.773065i	$-0.718723\pi$
$181$	−17.0680	−1.26865	−0.634327	+	0.773065i	$0.718723\pi$
$182$	0.313346	0.0232268
$183$	−1.00000	−0.0739221
$184$	−2.98208	−0.219842
$185$	2.19648	0.161489
$186$	−11.7610	−0.862357
$187$	−1.33955	−0.0979573
$188$	−0.902247	−0.0658031
$189$	0.0298223	0.00216926
$190$	16.1262	1.16992
$191$	21.8340	1.57985	0.789927	−	0.613201i	$-0.210118\pi$
$191$	21.8340	1.57985	0.789927	+	0.613201i	$0.210118\pi$
$192$	−3.95034	−0.285091
$193$	10.7246	0.771975	0.385988	−	0.922504i	$-0.373861\pi$
$193$	10.7246	0.771975	0.385988	+	0.922504i	$0.373861\pi$
$194$	2.94239	0.211251
$195$	7.14327	0.511540
$196$	−10.7453	−0.767524
$197$	−14.5895	−1.03946	−0.519730	−	0.854331i	$-0.673967\pi$
$197$	−14.5895	−1.03946	−0.519730	+	0.854331i	$0.673967\pi$
$198$	−1.88022	−0.133622
$199$	19.4483	1.37865	0.689326	−	0.724451i	$-0.257907\pi$
$199$	19.4483	1.37865	0.689326	+	0.724451i	$0.257907\pi$
$200$	2.94138	0.207987
$201$	−8.58956	−0.605861
$202$	−25.8047	−1.81561
$203$	0.0480058	0.00336935
$204$	2.05653	0.143986
$205$	0.854947	0.0597121
$206$	−16.7359	−1.16605
$207$	3.41259	0.237191
$208$	−26.3401	−1.82636
$209$	−6.70962	−0.464114
$210$	0.0716763	0.00494613
$211$	−21.2613	−1.46369	−0.731843	−	0.681473i	$-0.761340\pi$
$211$	−21.2613	−1.46369	−0.731843	+	0.681473i	$0.761340\pi$
$212$	11.6993	0.803511
$213$	2.03577	0.139489
$214$	−15.7568	−1.07711
$215$	3.28808	0.224245
$216$	−0.873847	−0.0594577
$217$	−0.186542	−0.0126633
$218$	−22.5382	−1.52648
$219$	−3.80905	−0.257392
$220$	−1.96246	−0.132309
$221$	7.48568	0.503541
$222$	3.23083	0.216839
$223$	−9.20342	−0.616306	−0.308153	−	0.951337i	$-0.599711\pi$
$223$	−9.20342	−0.616306	−0.308153	+	0.951337i	$0.599711\pi$
$224$	−0.212179	−0.0141768
$225$	−3.36602	−0.224401
$226$	2.30646	0.153423
$227$	9.75094	0.647193	0.323596	−	0.946195i	$-0.395108\pi$
$227$	9.75094	0.647193	0.323596	+	0.946195i	$0.395108\pi$
$228$	10.3009	0.682194
$229$	8.00584	0.529041	0.264521	−	0.964380i	$-0.414786\pi$
$229$	8.00584	0.529041	0.264521	+	0.964380i	$0.414786\pi$
$230$	8.20195	0.540821
$231$	−0.0298223	−0.00196217
$232$	−1.40665	−0.0923513
$233$	6.15569	0.403273	0.201636	−	0.979460i	$-0.435374\pi$
$233$	6.15569	0.403273	0.201636	+	0.979460i	$0.435374\pi$
$234$	10.5071	0.686871
$235$	−0.751228	−0.0490047
$236$	16.1873	1.05371
$237$	7.69951	0.500137
$238$	0.0751120	0.00486879
$239$	23.9973	1.55225	0.776127	−	0.630576i	$-0.217181\pi$
$239$	23.9973	1.55225	0.776127	+	0.630576i	$0.217181\pi$
$240$	−6.02516	−0.388922
$241$	−17.6264	−1.13542	−0.567708	−	0.823230i	$-0.692170\pi$
$241$	−17.6264	−1.13542	−0.567708	+	0.823230i	$0.692170\pi$
$242$	1.88022	0.120865
$243$	1.00000	0.0641500
$244$	−1.53524	−0.0982839
$245$	−8.94678	−0.571589
$246$	1.25755	0.0801784
$247$	37.4948	2.38574
$248$	5.46599	0.347091
$249$	−0.742344	−0.0470441
$250$	−20.1072	−1.27169
$251$	7.69236	0.485538	0.242769	−	0.970084i	$-0.421944\pi$
$251$	7.69236	0.485538	0.242769	+	0.970084i	$0.421944\pi$
$252$	0.0457846	0.00288416
$253$	−3.41259	−0.214548
$254$	−12.6562	−0.794120
$255$	1.71231	0.107229
$256$	20.6900	1.29313
$257$	−4.61272	−0.287734	−0.143867	−	0.989597i	$-0.545954\pi$
$257$	−4.61272	−0.287734	−0.143867	+	0.989597i	$0.545954\pi$
$258$	4.83647	0.301106
$259$	0.0512443	0.00318417
$260$	10.9667	0.680123
$261$	1.60973	0.0996395
$262$	−2.09746	−0.129582
$263$	−9.97272	−0.614944	−0.307472	−	0.951557i	$-0.599483\pi$
$263$	−9.97272	−0.614944	−0.307472	+	0.951557i	$0.599483\pi$
$264$	0.873847	0.0537815
$265$	9.74107	0.598389
$266$	0.376227	0.0230679
$267$	−13.4255	−0.821629
$268$	−13.1871	−0.805528
$269$	21.8938	1.33489	0.667444	−	0.744660i	$-0.267388\pi$
$269$	21.8938	1.33489	0.667444	+	0.744660i	$0.267388\pi$
$270$	2.40344	0.146269
$271$	18.1929	1.10514	0.552571	−	0.833466i	$-0.313647\pi$
$271$	18.1929	1.10514	0.552571	+	0.833466i	$0.313647\pi$
$272$	−6.31397	−0.382841
$273$	0.166654	0.0100863
$274$	8.78152	0.530511
$275$	3.36602	0.202978
$276$	5.23915	0.315360
$277$	24.8770	1.49471	0.747357	−	0.664423i	$-0.231323\pi$
$277$	24.8770	1.49471	0.747357	+	0.664423i	$0.231323\pi$
$278$	−7.09344	−0.425436
$279$	−6.25509	−0.374483
$280$	−0.0333120	−0.00199077
$281$	−16.7545	−0.999487	−0.499744	−	0.866173i	$-0.666572\pi$
$281$	−16.7545	−0.999487	−0.499744	+	0.866173i	$0.666572\pi$
$282$	−1.10499	−0.0658011
$283$	−10.4893	−0.623527	−0.311763	−	0.950160i	$-0.600920\pi$
$283$	−10.4893	−0.623527	−0.311763	+	0.950160i	$0.600920\pi$
$284$	3.12540	0.185458
$285$	8.57673	0.508042
$286$	−10.5071	−0.621298
$287$	0.0199461	0.00117738
$288$	−7.11477	−0.419242
$289$	−15.2056	−0.894448
$290$	3.86888	0.227188
$291$	1.56491	0.0917368
$292$	−5.84782	−0.342218
$293$	−23.2899	−1.36061	−0.680305	−	0.732930i	$-0.738152\pi$
$293$	−23.2899	−1.36061	−0.680305	+	0.732930i	$0.738152\pi$
$294$	−13.1599	−0.767501
$295$	13.4779	0.784714
$296$	−1.50155	−0.0872757
$297$	−1.00000	−0.0580259
$298$	−14.8117	−0.858019
$299$	19.0703	1.10286
$300$	−5.16766	−0.298355
$301$	0.0767116	0.00442158
$302$	34.3697	1.97775
$303$	−13.7243	−0.788438
$304$	−31.6259	−1.81387
$305$	−1.27827	−0.0731937
$306$	2.51865	0.143981
$307$	−5.37282	−0.306643	−0.153321	−	0.988176i	$-0.548997\pi$
$307$	−5.37282	−0.306643	−0.153321	+	0.988176i	$0.548997\pi$
$308$	−0.0457846	−0.00260882
$309$	−8.90102	−0.506361
$310$	−15.0337	−0.853859
$311$	0.901161	0.0511001	0.0255501	−	0.999674i	$-0.491866\pi$
$311$	0.901161	0.0511001	0.0255501	+	0.999674i	$0.491866\pi$
$312$	−4.88324	−0.276459
$313$	4.66099	0.263455	0.131727	−	0.991286i	$-0.457948\pi$
$313$	4.66099	0.263455	0.131727	+	0.991286i	$0.457948\pi$
$314$	−40.8543	−2.30554
$315$	0.0381211	0.00214788
$316$	11.8206	0.664962
$317$	−7.15317	−0.401762	−0.200881	−	0.979616i	$-0.564380\pi$
$317$	−7.15317	−0.401762	−0.200881	+	0.979616i	$0.564380\pi$
$318$	14.3282	0.803487
$319$	−1.60973	−0.0901273
$320$	−5.04961	−0.282282
$321$	−8.38029	−0.467742
$322$	0.191353	0.0106637
$323$	8.98785	0.500097
$324$	1.53524	0.0852913
$325$	−18.8100	−1.04339
$326$	−19.1086	−1.05833
$327$	−11.9870	−0.662881
$328$	−0.584454	−0.0322711
$329$	−0.0175263	−0.000966255 0
$330$	−2.40344	−0.132305
$331$	3.97759	0.218628	0.109314	−	0.994007i	$-0.465135\pi$
$331$	3.97759	0.218628	0.109314	+	0.994007i	$0.465135\pi$
$332$	−1.13968	−0.0625480
$333$	1.71832	0.0941633
$334$	−21.1141	−1.15531
$335$	−10.9798	−0.599891
$336$	−0.140568	−0.00766862
$337$	−19.6675	−1.07135	−0.535677	−	0.844423i	$-0.679944\pi$
$337$	−19.6675	−1.07135	−0.535677	+	0.844423i	$0.679944\pi$
$338$	34.2731	1.86421
$339$	1.22669	0.0666248
$340$	2.62881	0.142567
$341$	6.25509	0.338732
$342$	12.6156	0.682173
$343$	−0.417486	−0.0225421
$344$	−2.24778	−0.121192
$345$	4.36222	0.234854
$346$	21.3029	1.14525
$347$	14.8057	0.794812	0.397406	−	0.917643i	$-0.369910\pi$
$347$	14.8057	0.794812	0.397406	+	0.917643i	$0.369910\pi$
$348$	2.47132	0.132477
$349$	−32.1526	−1.72109	−0.860546	−	0.509373i	$-0.829877\pi$
$349$	−32.1526	−1.72109	−0.860546	+	0.509373i	$0.829877\pi$
$350$	−0.188742	−0.0100887
$351$	5.58822	0.298277
$352$	7.11477	0.379219
$353$	−2.07749	−0.110574	−0.0552868	−	0.998471i	$-0.517607\pi$
$353$	−2.07749	−0.110574	−0.0552868	+	0.998471i	$0.517607\pi$
$354$	19.8248	1.05367
$355$	2.60227	0.138114
$356$	−20.6115	−1.09241
$357$	0.0399484	0.00211429
$358$	−17.6185	−0.931165
$359$	−8.95752	−0.472760	−0.236380	−	0.971661i	$-0.575961\pi$
$359$	−8.95752	−0.472760	−0.236380	+	0.971661i	$0.575961\pi$
$360$	−1.11701	−0.0588719
$361$	26.0190	1.36942
$362$	−32.0917	−1.68670
$363$	1.00000	0.0524864
$364$	0.255854	0.0134104
$365$	−4.86901	−0.254856
$366$	−1.88022	−0.0982809
$367$	6.69870	0.349669	0.174835	−	0.984598i	$-0.444061\pi$
$367$	6.69870	0.349669	0.174835	+	0.984598i	$0.444061\pi$
$368$	−16.0853	−0.838503
$369$	0.668829	0.0348179
$370$	4.12988	0.214702
$371$	0.227261	0.0117988
$372$	−9.60309	−0.497897
$373$	−34.7971	−1.80172	−0.900862	−	0.434107i	$-0.857064\pi$
$373$	−34.7971	−1.80172	−0.900862	+	0.434107i	$0.857064\pi$
$374$	−2.51865	−0.130236
$375$	−10.6941	−0.552239
$376$	0.513550	0.0264843
$377$	8.99550	0.463292
$378$	0.0560727	0.00288407
$379$	7.77701	0.399478	0.199739	−	0.979849i	$-0.435991\pi$
$379$	7.77701	0.399478	0.199739	+	0.979849i	$0.435991\pi$
$380$	13.1674	0.675472
$381$	−6.73121	−0.344850
$382$	41.0528	2.10045
$383$	24.8333	1.26892	0.634462	−	0.772954i	$-0.281222\pi$
$383$	24.8333	1.26892	0.634462	+	0.772954i	$0.281222\pi$
$384$	6.80202	0.347114
$385$	−0.0381211	−0.00194283
$386$	20.1647	1.02636
$387$	2.57228	0.130757
$388$	2.40252	0.121970
$389$	26.7412	1.35583	0.677916	−	0.735140i	$-0.262883\pi$
$389$	26.7412	1.35583	0.677916	+	0.735140i	$0.262883\pi$
$390$	13.4310	0.680103
$391$	4.57132	0.231181
$392$	6.11615	0.308912
$393$	−1.11554	−0.0562715
$394$	−27.4316	−1.38198
$395$	9.84208	0.495209
$396$	−1.53524	−0.0771489
$397$	16.7943	0.842880	0.421440	−	0.906856i	$-0.361525\pi$
$397$	16.7943	0.842880	0.421440	+	0.906856i	$0.361525\pi$
$398$	36.5672	1.83295
$399$	0.200097	0.0100174
$400$	15.8658	0.793288
$401$	−14.3276	−0.715486	−0.357743	−	0.933820i	$-0.616454\pi$
$401$	−14.3276	−0.715486	−0.357743	+	0.933820i	$0.616454\pi$
$402$	−16.1503	−0.805504
$403$	−34.9548	−1.74122
$404$	−21.0701	−1.04828
$405$	1.27827	0.0635179
$406$	0.0902617	0.00447961
$407$	−1.71832	−0.0851740
$408$	−1.17056	−0.0579512
$409$	4.28656	0.211957	0.105978	−	0.994368i	$-0.466203\pi$
$409$	4.28656	0.211957	0.105978	+	0.994368i	$0.466203\pi$
$410$	1.60749	0.0793884
$411$	4.67046	0.230377
$412$	−13.6652	−0.673238
$413$	0.314442	0.0154727
$414$	6.41643	0.315350
$415$	−0.948919	−0.0465806
$416$	−39.7589	−1.94934
$417$	−3.77266	−0.184748
$418$	−12.6156	−0.617049
$419$	10.7345	0.524414	0.262207	−	0.965012i	$-0.415550\pi$
$419$	10.7345	0.524414	0.262207	+	0.965012i	$0.415550\pi$
$420$	0.0585252	0.00285574
$421$	−7.07807	−0.344964	−0.172482	−	0.985013i	$-0.555179\pi$
$421$	−7.07807	−0.344964	−0.172482	+	0.985013i	$0.555179\pi$
$422$	−39.9760	−1.94600
$423$	−0.587690	−0.0285744
$424$	−6.65913	−0.323396
$425$	−4.50893	−0.218715
$426$	3.82770	0.185453
$427$	−0.0298223	−0.00144320
$428$	−12.8658	−0.621891
$429$	−5.58822	−0.269802
$430$	6.18233	0.298139
$431$	−18.2462	−0.878890	−0.439445	−	0.898269i	$-0.644825\pi$
$431$	−18.2462	−0.878890	−0.439445	+	0.898269i	$0.644825\pi$
$432$	−4.71351	−0.226779
$433$	−5.19879	−0.249838	−0.124919	−	0.992167i	$-0.539867\pi$
$433$	−5.19879	−0.249838	−0.124919	+	0.992167i	$0.539867\pi$
$434$	−0.350740	−0.0168361
$435$	2.05767	0.0986577
$436$	−18.4029	−0.881340
$437$	22.8972	1.09532
$438$	−7.16187	−0.342207
$439$	−35.1802	−1.67906	−0.839529	−	0.543315i	$-0.817169\pi$
$439$	−35.1802	−1.67906	−0.839529	+	0.543315i	$0.817169\pi$
$440$	1.11701	0.0532516
$441$	−6.99911	−0.333291
$442$	14.0747	0.669468
$443$	−13.3949	−0.636409	−0.318204	−	0.948022i	$-0.603080\pi$
$443$	−13.3949	−0.636409	−0.318204	+	0.948022i	$0.603080\pi$
$444$	2.63804	0.125196
$445$	−17.1615	−0.813533
$446$	−17.3045	−0.819391
$447$	−7.87763	−0.372599
$448$	−0.117808	−0.00556592
$449$	17.7582	0.838061	0.419030	−	0.907972i	$-0.362370\pi$
$449$	17.7582	0.838061	0.419030	+	0.907972i	$0.362370\pi$
$450$	−6.32887	−0.298346
$451$	−0.668829	−0.0314939
$452$	1.88327	0.0885817
$453$	18.2796	0.858849
$454$	18.3340	0.860455
$455$	0.213029	0.00998696
$456$	−5.86318	−0.274569
$457$	21.6364	1.01211	0.506054	−	0.862502i	$-0.331104\pi$
$457$	21.6364	1.01211	0.506054	+	0.862502i	$0.331104\pi$
$458$	15.0528	0.703370
$459$	1.33955	0.0625247
$460$	6.69707	0.312252
$461$	9.15352	0.426322	0.213161	−	0.977017i	$-0.431624\pi$
$461$	9.15352	0.426322	0.213161	+	0.977017i	$0.431624\pi$
$462$	−0.0560727	−0.00260874
$463$	−7.70387	−0.358029	−0.179015	−	0.983846i	$-0.557291\pi$
$463$	−7.70387	−0.358029	−0.179015	+	0.983846i	$0.557291\pi$
$464$	−7.58746	−0.352239
$465$	−7.99572	−0.370793
$466$	11.5741	0.536159
$467$	−10.5122	−0.486448	−0.243224	−	0.969970i	$-0.578205\pi$
$467$	−10.5122	−0.486448	−0.243224	+	0.969970i	$0.578205\pi$
$468$	8.57927	0.396577
$469$	−0.256161	−0.0118284
$470$	−1.41248	−0.0651527
$471$	−21.7284	−1.00119
$472$	−9.21369	−0.424094
$473$	−2.57228	−0.118274
$474$	14.4768	0.664941
$475$	−22.5847	−1.03626
$476$	0.0613305	0.00281108
$477$	7.62049	0.348918
$478$	45.1203	2.06375
$479$	22.2273	1.01559	0.507795	−	0.861478i	$-0.330461\pi$
$479$	22.2273	1.01559	0.507795	+	0.861478i	$0.330461\pi$
$480$	−9.09462	−0.415111
$481$	9.60235	0.437829
$482$	−33.1416	−1.50956
$483$	0.101771	0.00463076
$484$	1.53524	0.0697838
$485$	2.00039	0.0908328
$486$	1.88022	0.0852887
$487$	6.57806	0.298081	0.149040	−	0.988831i	$-0.452382\pi$
$487$	6.57806	0.298081	0.149040	+	0.988831i	$0.452382\pi$
$488$	0.873847	0.0395572
$489$	−10.1629	−0.459584
$490$	−16.8219	−0.759938
$491$	12.9133	0.582769	0.291384	−	0.956606i	$-0.405884\pi$
$491$	12.9133	0.582769	0.291384	+	0.956606i	$0.405884\pi$
$492$	1.02682	0.0462924
$493$	2.15630	0.0971149
$494$	70.4987	3.17189
$495$	−1.27827	−0.0574541
$496$	29.4835	1.32385
$497$	0.0607114	0.00272328
$498$	−1.39577	−0.0625461
$499$	34.3660	1.53843	0.769217	−	0.638988i	$-0.220647\pi$
$499$	34.3660	1.53843	0.769217	+	0.638988i	$0.220647\pi$
$500$	−16.4180	−0.734235
$501$	−11.2296	−0.501700
$502$	14.4634	0.645532
$503$	−21.4268	−0.955373	−0.477687	−	0.878530i	$-0.658525\pi$
$503$	−21.4268	−0.955373	−0.477687	+	0.878530i	$0.658525\pi$
$504$	−0.0260602	−0.00116081
$505$	−17.5434	−0.780669
$506$	−6.41643	−0.285245
$507$	18.2282	0.809542
$508$	−10.3340	−0.458499
$509$	−11.0074	−0.487896	−0.243948	−	0.969788i	$-0.578443\pi$
$509$	−11.0074	−0.487896	−0.243948	+	0.969788i	$0.578443\pi$
$510$	3.21952	0.142563
$511$	−0.113595	−0.00502514
$512$	25.2978	1.11802
$513$	6.70962	0.296237
$514$	−8.67295	−0.382547
$515$	−11.3779	−0.501372
$516$	3.94908	0.173849
$517$	0.587690	0.0258466
$518$	0.0963508	0.00423341
$519$	11.3300	0.497332
$520$	−6.24212	−0.273735
$521$	42.8741	1.87835	0.939175	−	0.343440i	$-0.111592\pi$
$521$	42.8741	1.87835	0.939175	+	0.343440i	$0.111592\pi$
$522$	3.02664	0.132473
$523$	−15.8294	−0.692172	−0.346086	−	0.938203i	$-0.612489\pi$
$523$	−15.8294	−0.692172	−0.346086	+	0.938203i	$0.612489\pi$
$524$	−1.71262	−0.0748163
$525$	−0.100383	−0.00438105
$526$	−18.7510	−0.817581
$527$	−8.37899	−0.364994
$528$	4.71351	0.205129
$529$	−11.3542	−0.493663
$530$	18.3154	0.795570
$531$	10.5438	0.457563
$532$	0.307197	0.0133187
$533$	3.73756	0.161892
$534$	−25.2430	−1.09237
$535$	−10.7123	−0.463133
$536$	7.50596	0.324208
$537$	−9.37041	−0.404363
$538$	41.1653	1.77476
$539$	6.99911	0.301473
$540$	1.96246	0.0844509
$541$	12.6615	0.544360	0.272180	−	0.962246i	$-0.412255\pi$
$541$	12.6615	0.544360	0.272180	+	0.962246i	$0.412255\pi$
$542$	34.2068	1.46931
$543$	−17.0680	−0.732458
$544$	−9.53056	−0.408620
$545$	−15.3226	−0.656349
$546$	0.313346	0.0134100
$547$	38.1275	1.63021	0.815106	−	0.579312i	$-0.196679\pi$
$547$	38.1275	1.63021	0.815106	+	0.579312i	$0.196679\pi$
$548$	7.17030	0.306300
$549$	−1.00000	−0.0426790
$550$	6.32887	0.269864
$551$	10.8007	0.460123
$552$	−2.98208	−0.126926
$553$	0.229617	0.00976432
$554$	46.7743	1.98725
$555$	2.19648	0.0932355
$556$	−5.79195	−0.245633
$557$	14.8321	0.628455	0.314228	−	0.949348i	$-0.398254\pi$
$557$	14.8321	0.628455	0.314228	+	0.949348i	$0.398254\pi$
$558$	−11.7610	−0.497882
$559$	14.3745	0.607976
$560$	−0.179684	−0.00759305
$561$	−1.33955	−0.0565557
$562$	−31.5021	−1.32884
$563$	−2.52615	−0.106464	−0.0532322	−	0.998582i	$-0.516952\pi$
$563$	−2.52615	−0.106464	−0.0532322	+	0.998582i	$0.516952\pi$
$564$	−0.902247	−0.0379914
$565$	1.56805	0.0659683
$566$	−19.7223	−0.828991
$567$	0.0298223	0.00125242
$568$	−1.77895	−0.0746431
$569$	10.0494	0.421291	0.210645	−	0.977563i	$-0.432443\pi$
$569$	10.0494	0.421291	0.210645	+	0.977563i	$0.432443\pi$
$570$	16.1262	0.675452
$571$	−19.7352	−0.825891	−0.412946	−	0.910756i	$-0.635500\pi$
$571$	−19.7352	−0.825891	−0.412946	+	0.910756i	$0.635500\pi$
$572$	−8.57927	−0.358717
$573$	21.8340	0.912129
$574$	0.0375031	0.00156535
$575$	−11.4868	−0.479034
$576$	−3.95034	−0.164597
$577$	−1.47224	−0.0612900	−0.0306450	−	0.999530i	$-0.509756\pi$
$577$	−1.47224	−0.0612900	−0.0306450	+	0.999530i	$0.509756\pi$
$578$	−28.5900	−1.18919
$579$	10.7246	0.445700
$580$	3.15902	0.131171
$581$	−0.0221384	−0.000918457 0
$582$	2.94239	0.121966
$583$	−7.62049	−0.315608
$584$	3.32852	0.137735
$585$	7.14327	0.295338
$586$	−43.7902	−1.80896
$587$	37.3090	1.53991	0.769953	−	0.638101i	$-0.220280\pi$
$587$	37.3090	1.53991	0.769953	+	0.638101i	$0.220280\pi$
$588$	−10.7453	−0.443130
$589$	−41.9693	−1.72932
$590$	25.3415	1.04329
$591$	−14.5895	−0.600132
$592$	−8.09933	−0.332880
$593$	23.1904	0.952314	0.476157	−	0.879360i	$-0.342029\pi$
$593$	23.1904	0.952314	0.476157	+	0.879360i	$0.342029\pi$
$594$	−1.88022	−0.0771465
$595$	0.0510650	0.00209346
$596$	−12.0941	−0.495393
$597$	19.4483	0.795966
$598$	35.8564	1.46628
$599$	10.9690	0.448183	0.224091	−	0.974568i	$-0.428059\pi$
$599$	10.9690	0.448183	0.224091	+	0.974568i	$0.428059\pi$
$600$	2.94138	0.120081
$601$	8.97680	0.366171	0.183086	−	0.983097i	$-0.441391\pi$
$601$	8.97680	0.366171	0.183086	+	0.983097i	$0.441391\pi$
$602$	0.144235	0.00587858
$603$	−8.58956	−0.349794
$604$	28.0636	1.14189
$605$	1.27827	0.0519692
$606$	−25.8047	−1.04824
$607$	21.8511	0.886907	0.443453	−	0.896297i	$-0.353753\pi$
$607$	21.8511	0.886907	0.443453	+	0.896297i	$0.353753\pi$
$608$	−47.7374	−1.93601
$609$	0.0480058	0.00194529
$610$	−2.40344	−0.0973125
$611$	−3.28414	−0.132862
$612$	2.05653	0.0831303
$613$	6.69910	0.270574	0.135287	−	0.990806i	$-0.456804\pi$
$613$	6.69910	0.270574	0.135287	+	0.990806i	$0.456804\pi$
$614$	−10.1021	−0.407688
$615$	0.854947	0.0344748
$616$	0.0260602	0.00104999
$617$	14.6447	0.589572	0.294786	−	0.955563i	$-0.404752\pi$
$617$	14.6447	0.589572	0.294786	+	0.955563i	$0.404752\pi$
$618$	−16.7359	−0.673217
$619$	4.61819	0.185621	0.0928103	−	0.995684i	$-0.470415\pi$
$619$	4.61819	0.185621	0.0928103	+	0.995684i	$0.470415\pi$
$620$	−12.2754	−0.492991
$621$	3.41259	0.136942
$622$	1.69438	0.0679386
$623$	−0.400381	−0.0160409
$624$	−26.3401	−1.05445
$625$	3.16015	0.126406
$626$	8.76370	0.350268
$627$	−6.70962	−0.267957
$628$	−33.3584	−1.33115
$629$	2.30177	0.0917775
$630$	0.0716763	0.00285565
$631$	−7.21368	−0.287172	−0.143586	−	0.989638i	$-0.545863\pi$
$631$	−7.21368	−0.287172	−0.143586	+	0.989638i	$0.545863\pi$
$632$	−6.72819	−0.267633
$633$	−21.2613	−0.845060
$634$	−13.4496	−0.534151
$635$	−8.60433	−0.341452
$636$	11.6993	0.463907
$637$	−39.1126	−1.54970
$638$	−3.02664	−0.119826
$639$	2.03577	0.0805338
$640$	8.69485	0.343694
$641$	42.0066	1.65916	0.829580	−	0.558387i	$-0.188580\pi$
$641$	42.0066	1.65916	0.829580	+	0.558387i	$0.188580\pi$
$642$	−15.7568	−0.621873
$643$	3.82823	0.150971	0.0754853	−	0.997147i	$-0.475949\pi$
$643$	3.82823	0.150971	0.0754853	+	0.997147i	$0.475949\pi$
$644$	0.156244	0.00615687
$645$	3.28808	0.129468
$646$	16.8992	0.664889
$647$	−26.9638	−1.06006	−0.530028	−	0.847980i	$-0.677819\pi$
$647$	−26.9638	−1.06006	−0.530028	+	0.847980i	$0.677819\pi$
$648$	−0.873847	−0.0343279
$649$	−10.5438	−0.413882
$650$	−35.3671	−1.38721
$651$	−0.186542	−0.00731114
$652$	−15.6026	−0.611045
$653$	3.40054	0.133073	0.0665366	−	0.997784i	$-0.478805\pi$
$653$	3.40054	0.133073	0.0665366	+	0.997784i	$0.478805\pi$
$654$	−22.5382	−0.881313
$655$	−1.42596	−0.0557170
$656$	−3.15254	−0.123086
$657$	−3.80905	−0.148605
$658$	−0.0329533	−0.00128466
$659$	32.0857	1.24988	0.624941	−	0.780672i	$-0.285123\pi$
$659$	32.0857	1.24988	0.624941	+	0.780672i	$0.285123\pi$
$660$	−1.96246	−0.0763887
$661$	1.07251	0.0417157	0.0208578	−	0.999782i	$-0.493360\pi$
$661$	1.07251	0.0417157	0.0208578	+	0.999782i	$0.493360\pi$
$662$	7.47876	0.290670
$663$	7.48568	0.290720
$664$	0.648695	0.0251742
$665$	0.255778	0.00991866
$666$	3.23083	0.125192
$667$	5.49333	0.212703
$668$	−17.2401	−0.667040
$669$	−9.20342	−0.355825
$670$	−20.6445	−0.797567
$671$	1.00000	0.0386046
$672$	−0.212179	−0.00818499
$673$	10.2363	0.394578	0.197289	−	0.980345i	$-0.436786\pi$
$673$	10.2363	0.394578	0.197289	+	0.980345i	$0.436786\pi$
$674$	−36.9792	−1.42439
$675$	−3.36602	−0.129558
$676$	27.9847	1.07633
$677$	−35.6445	−1.36993	−0.684965	−	0.728576i	$-0.740182\pi$
$677$	−35.6445	−1.36993	−0.684965	+	0.728576i	$0.740182\pi$
$678$	2.30646	0.0885790
$679$	0.0466694	0.00179101
$680$	−1.49629	−0.0573802
$681$	9.75094	0.373657
$682$	11.7610	0.450351
$683$	−26.9142	−1.02984	−0.514921	−	0.857238i	$-0.672179\pi$
$683$	−26.9142	−1.02984	−0.514921	+	0.857238i	$0.672179\pi$
$684$	10.3009	0.393865
$685$	5.97013	0.228107
$686$	−0.784968	−0.0299702
$687$	8.00584	0.305442
$688$	−12.1245	−0.462242
$689$	42.5849	1.62236
$690$	8.20195	0.312243
$691$	−2.50922	−0.0954551	−0.0477276	−	0.998860i	$-0.515198\pi$
$691$	−2.50922	−0.0954551	−0.0477276	+	0.998860i	$0.515198\pi$
$692$	17.3943	0.661233
$693$	−0.0298223	−0.00113286
$694$	27.8380	1.05672
$695$	−4.82249	−0.182927
$696$	−1.40665	−0.0533190
$697$	0.895928	0.0339357
$698$	−60.4542	−2.28822
$699$	6.15569	0.232830
$700$	−0.154112	−0.00582487
$701$	−1.91591	−0.0723628	−0.0361814	−	0.999345i	$-0.511519\pi$
$701$	−1.91591	−0.0723628	−0.0361814	+	0.999345i	$0.511519\pi$
$702$	10.5071	0.396565
$703$	11.5293	0.434835
$704$	3.95034	0.148884
$705$	−0.751228	−0.0282929
$706$	−3.90615	−0.147010
$707$	−0.409290	−0.0153929
$708$	16.1873	0.608358
$709$	−2.61979	−0.0983884	−0.0491942	−	0.998789i	$-0.515665\pi$
$709$	−2.61979	−0.0983884	−0.0491942	+	0.998789i	$0.515665\pi$
$710$	4.89285	0.183625
$711$	7.69951	0.288754
$712$	11.7319	0.439670
$713$	−21.3460	−0.799416
$714$	0.0751120	0.00281100
$715$	−7.14327	−0.267143
$716$	−14.3859	−0.537625
$717$	23.9973	0.896195
$718$	−16.8422	−0.628544
$719$	36.1632	1.34866	0.674331	−	0.738429i	$-0.264432\pi$
$719$	36.1632	1.34866	0.674331	+	0.738429i	$0.264432\pi$
$720$	−6.02516	−0.224544
$721$	−0.265449	−0.00988585
$722$	48.9216	1.82067
$723$	−17.6264	−0.655533
$724$	−26.2035	−0.973847
$725$	−5.41836	−0.201233
$726$	1.88022	0.0697817
$727$	36.6906	1.36078	0.680389	−	0.732851i	$-0.261811\pi$
$727$	36.6906	1.36078	0.680389	+	0.732851i	$0.261811\pi$
$728$	−0.145630	−0.00539740
$729$	1.00000	0.0370370
$730$	−9.15483	−0.338835
$731$	3.44569	0.127444
$732$	−1.53524	−0.0567442
$733$	30.2021	1.11554	0.557770	−	0.829996i	$-0.311657\pi$
$733$	30.2021	1.11554	0.557770	+	0.829996i	$0.311657\pi$
$734$	12.5951	0.464892
$735$	−8.94678	−0.330007
$736$	−24.2798	−0.894964
$737$	8.58956	0.316401
$738$	1.25755	0.0462910
$739$	−46.7194	−1.71860	−0.859301	−	0.511471i	$-0.829101\pi$
$739$	−46.7194	−1.71860	−0.859301	+	0.511471i	$0.829101\pi$
$740$	3.37214	0.123962
$741$	37.4948	1.37741
$742$	0.427301	0.0156867
$743$	12.0904	0.443554	0.221777	−	0.975097i	$-0.428814\pi$
$743$	12.0904	0.443554	0.221777	+	0.975097i	$0.428814\pi$
$744$	5.46599	0.200393
$745$	−10.0698	−0.368928
$746$	−65.4263	−2.39543
$747$	−0.742344	−0.0271609
$748$	−2.05653	−0.0751942
$749$	−0.249920	−0.00913188
$750$	−20.1072	−0.734212
$751$	−27.1495	−0.990701	−0.495350	−	0.868693i	$-0.664960\pi$
$751$	−27.1495	−0.990701	−0.495350	+	0.868693i	$0.664960\pi$
$752$	2.77008	0.101015
$753$	7.69236	0.280325
$754$	16.9135	0.615955
$755$	23.3663	0.850386
$756$	0.0457846	0.00166517
$757$	−30.1523	−1.09590	−0.547952	−	0.836510i	$-0.684592\pi$
$757$	−30.1523	−1.09590	−0.547952	+	0.836510i	$0.684592\pi$
$758$	14.6225	0.531114
$759$	−3.41259	−0.123869
$760$	−7.49475	−0.271863
$761$	−22.1105	−0.801504	−0.400752	−	0.916186i	$-0.631251\pi$
$761$	−22.1105	−0.801504	−0.400752	+	0.916186i	$0.631251\pi$
$762$	−12.6562	−0.458485
$763$	−0.357480	−0.0129416
$764$	33.5205	1.21273
$765$	1.71231	0.0619086
$766$	46.6922	1.68706
$767$	58.9212	2.12752
$768$	20.6900	0.746586
$769$	−23.3843	−0.843259	−0.421630	−	0.906768i	$-0.638542\pi$
$769$	−23.3843	−0.843259	−0.421630	+	0.906768i	$0.638542\pi$
$770$	−0.0716763	−0.00258303
$771$	−4.61272	−0.166123
$772$	16.4649	0.592585
$773$	49.4566	1.77883	0.889415	−	0.457100i	$-0.151112\pi$
$773$	49.4566	1.77883	0.889415	+	0.457100i	$0.151112\pi$
$774$	4.83647	0.173843
$775$	21.0547	0.756309
$776$	−1.36749	−0.0490901
$777$	0.0512443	0.00183838
$778$	50.2794	1.80260
$779$	4.48759	0.160785
$780$	10.9667	0.392669
$781$	−2.03577	−0.0728455
$782$	8.59510	0.307360
$783$	1.60973	0.0575269
$784$	32.9904	1.17823
$785$	−27.7749	−0.991328
$786$	−2.09746	−0.0748140
$787$	−14.0106	−0.499425	−0.249713	−	0.968320i	$-0.580336\pi$
$787$	−14.0106	−0.499425	−0.249713	+	0.968320i	$0.580336\pi$
$788$	−22.3985	−0.797912
$789$	−9.97272	−0.355038
$790$	18.5053	0.658389
$791$	0.0365829	0.00130074
$792$	0.873847	0.0310508
$793$	−5.58822	−0.198443
$794$	31.5770	1.12063
$795$	9.74107	0.345480
$796$	29.8579	1.05828
$797$	29.6569	1.05050	0.525252	−	0.850947i	$-0.323971\pi$
$797$	29.6569	1.05050	0.525252	+	0.850947i	$0.323971\pi$
$798$	0.376227	0.0133183
$799$	−0.787237	−0.0278505
$800$	23.9484	0.846705
$801$	−13.4255	−0.474368
$802$	−26.9391	−0.951253
$803$	3.80905	0.134418
$804$	−13.1871	−0.465072
$805$	0.130092	0.00458513
$806$	−65.7229	−2.31499
$807$	21.8938	0.770698
$808$	11.9929	0.421909
$809$	−28.7985	−1.01250	−0.506250	−	0.862387i	$-0.668969\pi$
$809$	−28.7985	−1.01250	−0.506250	+	0.862387i	$0.668969\pi$
$810$	2.40344	0.0844483
$811$	34.4307	1.20902	0.604512	−	0.796596i	$-0.293368\pi$
$811$	34.4307	1.20902	0.604512	+	0.796596i	$0.293368\pi$
$812$	0.0737006	0.00258638
$813$	18.1929	0.638054
$814$	−3.23083	−0.113240
$815$	−12.9910	−0.455056
$816$	−6.31397	−0.221033
$817$	17.2591	0.603818
$818$	8.05970	0.281801
$819$	0.166654	0.00582335
$820$	1.31255	0.0458363
$821$	39.8355	1.39027	0.695134	−	0.718880i	$-0.255345\pi$
$821$	39.8355	1.39027	0.695134	+	0.718880i	$0.255345\pi$
$822$	8.78152	0.306291
$823$	−37.9114	−1.32151	−0.660754	−	0.750602i	$-0.729763\pi$
$823$	−37.9114	−1.32151	−0.660754	+	0.750602i	$0.729763\pi$
$824$	7.77812	0.270964
$825$	3.36602	0.117190
$826$	0.591221	0.0205712
$827$	−10.8584	−0.377584	−0.188792	−	0.982017i	$-0.560457\pi$
$827$	−10.8584	−0.377584	−0.188792	+	0.982017i	$0.560457\pi$
$828$	5.23915	0.182073
$829$	−36.4132	−1.26468	−0.632342	−	0.774690i	$-0.717906\pi$
$829$	−36.4132	−1.26468	−0.632342	+	0.774690i	$0.717906\pi$
$830$	−1.78418	−0.0619298
$831$	24.8770	0.862973
$832$	−22.0753	−0.765325
$833$	−9.37563	−0.324846
$834$	−7.09344	−0.245626
$835$	−14.3545	−0.496757
$836$	−10.3009	−0.356264
$837$	−6.25509	−0.216208
$838$	20.1832	0.697218
$839$	28.0543	0.968542	0.484271	−	0.874918i	$-0.339085\pi$
$839$	28.0543	0.968542	0.484271	+	0.874918i	$0.339085\pi$
$840$	−0.0333120	−0.00114937
$841$	−26.4088	−0.910648
$842$	−13.3084	−0.458636
$843$	−16.7545	−0.577054
$844$	−32.6412	−1.12356
$845$	23.3006	0.801565
$846$	−1.10499	−0.0379903
$847$	0.0298223	0.00102471
$848$	−35.9193	−1.23347
$849$	−10.4893	−0.359993
$850$	−8.47781	−0.290786
$851$	5.86392	0.201012
$852$	3.12540	0.107074
$853$	−47.5752	−1.62894	−0.814471	−	0.580204i	$-0.802973\pi$
$853$	−47.5752	−1.62894	−0.814471	+	0.580204i	$0.802973\pi$
$854$	−0.0560727	−0.00191877
$855$	8.57673	0.293318
$856$	7.32309	0.250298
$857$	40.4027	1.38013	0.690065	−	0.723748i	$-0.257582\pi$
$857$	40.4027	1.38013	0.690065	+	0.723748i	$0.257582\pi$
$858$	−10.5071	−0.358707
$859$	−35.8636	−1.22365	−0.611825	−	0.790993i	$-0.709564\pi$
$859$	−35.8636	−1.22365	−0.611825	+	0.790993i	$0.709564\pi$
$860$	5.04801	0.172136
$861$	0.0199461	0.000679760 0
$862$	−34.3070	−1.16850
$863$	35.3569	1.20356	0.601782	−	0.798661i	$-0.294458\pi$
$863$	35.3569	1.20356	0.601782	+	0.798661i	$0.294458\pi$
$864$	−7.11477	−0.242049
$865$	14.4828	0.492431
$866$	−9.77488	−0.332164
$867$	−15.2056	−0.516410
$868$	−0.286387	−0.00972060
$869$	−7.69951	−0.261188
$870$	3.86888	0.131167
$871$	−48.0003	−1.62643
$872$	10.4748	0.354721
$873$	1.56491	0.0529643
$874$	43.0518	1.45625
$875$	−0.318922	−0.0107815
$876$	−5.84782	−0.197579
$877$	27.6647	0.934170	0.467085	−	0.884212i	$-0.345304\pi$
$877$	27.6647	0.934170	0.467085	+	0.884212i	$0.345304\pi$
$878$	−66.1466	−2.23234
$879$	−23.2899	−0.785548
$880$	6.02516	0.203108
$881$	−6.81227	−0.229511	−0.114756	−	0.993394i	$-0.536608\pi$
$881$	−6.81227	−0.229511	−0.114756	+	0.993394i	$0.536608\pi$
$882$	−13.1599	−0.443117
$883$	−16.0376	−0.539707	−0.269853	−	0.962901i	$-0.586975\pi$
$883$	−16.0376	−0.539707	−0.269853	+	0.962901i	$0.586975\pi$
$884$	11.4923	0.386529
$885$	13.4779	0.453055
$886$	−25.1853	−0.846118
$887$	43.1339	1.44829	0.724147	−	0.689646i	$-0.242234\pi$
$887$	43.1339	1.44829	0.724147	+	0.689646i	$0.242234\pi$
$888$	−1.50155	−0.0503886
$889$	−0.200741	−0.00673262
$890$	−32.2675	−1.08161
$891$	−1.00000	−0.0335013
$892$	−14.1295	−0.473090
$893$	−3.94318	−0.131953
$894$	−14.8117	−0.495378
$895$	−11.9779	−0.400379
$896$	0.202852	0.00677682
$897$	19.0703	0.636738
$898$	33.3894	1.11422
$899$	−10.0690	−0.335819
$900$	−5.16766	−0.172255
$901$	10.2080	0.340078
$902$	−1.25755	−0.0418718
$903$	0.0767116	0.00255280
$904$	−1.07194	−0.0356522
$905$	−21.8176	−0.725241
$906$	34.3697	1.14186
$907$	4.97879	0.165318	0.0826590	−	0.996578i	$-0.473659\pi$
$907$	4.97879	0.165318	0.0826590	+	0.996578i	$0.473659\pi$
$908$	14.9701	0.496799
$909$	−13.7243	−0.455205
$910$	0.400543	0.0132779
$911$	−46.5597	−1.54259	−0.771296	−	0.636476i	$-0.780391\pi$
$911$	−46.5597	−1.54259	−0.771296	+	0.636476i	$0.780391\pi$
$912$	−31.6259	−1.04724
$913$	0.742344	0.0245680
$914$	40.6812	1.34562
$915$	−1.27827	−0.0422584
$916$	12.2909	0.406103
$917$	−0.0332680	−0.00109861
$918$	2.51865	0.0831277
$919$	−2.86125	−0.0943839	−0.0471920	−	0.998886i	$-0.515027\pi$
$919$	−2.86125	−0.0943839	−0.0471920	+	0.998886i	$0.515027\pi$
$920$	−3.81191	−0.125675
$921$	−5.37282	−0.177040
$922$	17.2107	0.566803
$923$	11.3763	0.374456
$924$	−0.0457846	−0.00150620
$925$	−5.78389	−0.190173
$926$	−14.4850	−0.476007
$927$	−8.90102	−0.292348
$928$	−11.4528	−0.375957
$929$	−12.6025	−0.413476	−0.206738	−	0.978396i	$-0.566285\pi$
$929$	−12.6025	−0.413476	−0.206738	+	0.978396i	$0.566285\pi$
$930$	−15.0337	−0.492976
$931$	−46.9614	−1.53910
$932$	9.45048	0.309561
$933$	0.901161	0.0295027
$934$	−19.7654	−0.646742
$935$	−1.71231	−0.0559984
$936$	−4.88324	−0.159614
$937$	−13.0474	−0.426240	−0.213120	−	0.977026i	$-0.568363\pi$
$937$	−13.0474	−0.426240	−0.213120	+	0.977026i	$0.568363\pi$
$938$	−0.481640	−0.0157261
$939$	4.66099	0.152106
$940$	−1.15332	−0.0376171
$941$	3.70818	0.120883	0.0604416	−	0.998172i	$-0.480749\pi$
$941$	3.70818	0.120883	0.0604416	+	0.998172i	$0.480749\pi$
$942$	−40.8543	−1.33111
$943$	2.28244	0.0743264
$944$	−49.6985	−1.61755
$945$	0.0381211	0.00124008
$946$	−4.83647	−0.157247
$947$	47.5677	1.54574	0.772871	−	0.634564i	$-0.218820\pi$
$947$	47.5677	1.54574	0.772871	+	0.634564i	$0.218820\pi$
$948$	11.8206	0.383916
$949$	−21.2858	−0.690966
$950$	−42.4643	−1.37772
$951$	−7.15317	−0.231957
$952$	−0.0349088	−0.00113140
$953$	−7.37757	−0.238983	−0.119491	−	0.992835i	$-0.538126\pi$
$953$	−7.37757	−0.238983	−0.119491	+	0.992835i	$0.538126\pi$
$954$	14.3282	0.463893
$955$	27.9098	0.903141
$956$	36.8417	1.19154
$957$	−1.60973	−0.0520350
$958$	41.7922	1.35025
$959$	0.139284	0.00449772
$960$	−5.04961	−0.162976
$961$	8.12618	0.262135
$962$	18.0546	0.582102
$963$	−8.38029	−0.270051
$964$	−27.0608	−0.871570
$965$	13.7090	0.441308
$966$	0.191353	0.00615668
$967$	−36.9737	−1.18899	−0.594497	−	0.804098i	$-0.702649\pi$
$967$	−36.9737	−1.18899	−0.594497	+	0.804098i	$0.702649\pi$
$968$	−0.873847	−0.0280865
$969$	8.98785	0.288731
$970$	3.76117	0.120764
$971$	40.9475	1.31407	0.657034	−	0.753861i	$-0.271811\pi$
$971$	40.9475	1.31407	0.657034	+	0.753861i	$0.271811\pi$
$972$	1.53524	0.0492430
$973$	−0.112510	−0.00360689
$974$	12.3682	0.396304
$975$	−18.8100	−0.602403
$976$	4.71351	0.150876
$977$	2.35066	0.0752044	0.0376022	−	0.999293i	$-0.488028\pi$
$977$	2.35066	0.0752044	0.0376022	+	0.999293i	$0.488028\pi$
$978$	−19.1086	−0.611026
$979$	13.4255	0.429082
$980$	−13.7355	−0.438764
$981$	−11.9870	−0.382714
$982$	24.2799	0.774802
$983$	−42.1964	−1.34586	−0.672928	−	0.739708i	$-0.734964\pi$
$983$	−42.1964	−1.34586	−0.672928	+	0.739708i	$0.734964\pi$
$984$	−0.584454	−0.0186317
$985$	−18.6494	−0.594219
$986$	4.05433	0.129116
$987$	−0.0175263	−0.000557868 0
$988$	57.5637	1.83135
$989$	8.77814	0.279129
$990$	−2.40344	−0.0763864
$991$	31.5627	1.00262	0.501312	−	0.865267i	$-0.332851\pi$
$991$	31.5627	1.00262	0.501312	+	0.865267i	$0.332851\pi$
$992$	44.5036	1.41299
$993$	3.97759	0.126225
$994$	0.114151	0.00362065
$995$	24.8602	0.788123
$996$	−1.13968	−0.0361121
$997$	23.6223	0.748126	0.374063	−	0.927403i	$-0.377964\pi$
$997$	23.6223	0.748126	0.374063	+	0.927403i	$0.377964\pi$
$998$	64.6158	2.04538
$999$	1.71832	0.0543652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.10	✓	13
3.2	odd	2		6039.2.a.g.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.10	✓	13	1.1	even	1	trivial
6039.2.a.g.1.4		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)

\(f(q)\)	\(=\)	\(q+1.88022 q^{2} +1.00000 q^{3} +1.53524 q^{4} +1.27827 q^{5} +1.88022 q^{6} +0.0298223 q^{7} -0.873847 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.88022 q^{2} +1.00000 q^{3} +1.53524 q^{4} +1.27827 q^{5} +1.88022 q^{6} +0.0298223 q^{7} -0.873847 q^{8} +1.00000 q^{9} +2.40344 q^{10} -1.00000 q^{11} +1.53524 q^{12} +5.58822 q^{13} +0.0560727 q^{14} +1.27827 q^{15} -4.71351 q^{16} +1.33955 q^{17} +1.88022 q^{18} +6.70962 q^{19} +1.96246 q^{20} +0.0298223 q^{21} -1.88022 q^{22} +3.41259 q^{23} -0.873847 q^{24} -3.36602 q^{25} +10.5071 q^{26} +1.00000 q^{27} +0.0457846 q^{28} +1.60973 q^{29} +2.40344 q^{30} -6.25509 q^{31} -7.11477 q^{32} -1.00000 q^{33} +2.51865 q^{34} +0.0381211 q^{35} +1.53524 q^{36} +1.71832 q^{37} +12.6156 q^{38} +5.58822 q^{39} -1.11701 q^{40} +0.668829 q^{41} +0.0560727 q^{42} +2.57228 q^{43} -1.53524 q^{44} +1.27827 q^{45} +6.41643 q^{46} -0.587690 q^{47} -4.71351 q^{48} -6.99911 q^{49} -6.32887 q^{50} +1.33955 q^{51} +8.57927 q^{52} +7.62049 q^{53} +1.88022 q^{54} -1.27827 q^{55} -0.0260602 q^{56} +6.70962 q^{57} +3.02664 q^{58} +10.5438 q^{59} +1.96246 q^{60} -1.00000 q^{61} -11.7610 q^{62} +0.0298223 q^{63} -3.95034 q^{64} +7.14327 q^{65} -1.88022 q^{66} -8.58956 q^{67} +2.05653 q^{68} +3.41259 q^{69} +0.0716763 q^{70} +2.03577 q^{71} -0.873847 q^{72} -3.80905 q^{73} +3.23083 q^{74} -3.36602 q^{75} +10.3009 q^{76} -0.0298223 q^{77} +10.5071 q^{78} +7.69951 q^{79} -6.02516 q^{80} +1.00000 q^{81} +1.25755 q^{82} -0.742344 q^{83} +0.0457846 q^{84} +1.71231 q^{85} +4.83647 q^{86} +1.60973 q^{87} +0.873847 q^{88} -13.4255 q^{89} +2.40344 q^{90} +0.166654 q^{91} +5.23915 q^{92} -6.25509 q^{93} -1.10499 q^{94} +8.57673 q^{95} -7.11477 q^{96} +1.56491 q^{97} -13.1599 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

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