LMFDB - Embedded newform 2013.2.a.g.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} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} + \cdots - 35 $ x^13 - 4x^12 - 11x^11 + 57x^10 + 28x^9 - 290x^8 + 51x^7 + 644x^6 - 259x^5 - 640x^4 + 274x^3 + 256x^2 - 74x - 35
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.88247$ 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)

$f(q)$	$=$	$q+1.88247 q^{2} +1.00000 q^{3} +1.54370 q^{4} +3.12160 q^{5} +1.88247 q^{6} +2.89419 q^{7} -0.858967 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.88247 q^{2} +1.00000 q^{3} +1.54370 q^{4} +3.12160 q^{5} +1.88247 q^{6} +2.89419 q^{7} -0.858967 q^{8} +1.00000 q^{9} +5.87632 q^{10} +1.00000 q^{11} +1.54370 q^{12} +0.612006 q^{13} +5.44823 q^{14} +3.12160 q^{15} -4.70439 q^{16} -5.09716 q^{17} +1.88247 q^{18} +2.06821 q^{19} +4.81882 q^{20} +2.89419 q^{21} +1.88247 q^{22} +0.735761 q^{23} -0.858967 q^{24} +4.74437 q^{25} +1.15208 q^{26} +1.00000 q^{27} +4.46777 q^{28} +0.761613 q^{29} +5.87632 q^{30} -4.32662 q^{31} -7.13795 q^{32} +1.00000 q^{33} -9.59527 q^{34} +9.03450 q^{35} +1.54370 q^{36} -1.64079 q^{37} +3.89335 q^{38} +0.612006 q^{39} -2.68135 q^{40} +6.49247 q^{41} +5.44823 q^{42} -9.20961 q^{43} +1.54370 q^{44} +3.12160 q^{45} +1.38505 q^{46} +3.57602 q^{47} -4.70439 q^{48} +1.37634 q^{49} +8.93115 q^{50} -5.09716 q^{51} +0.944756 q^{52} -3.52427 q^{53} +1.88247 q^{54} +3.12160 q^{55} -2.48601 q^{56} +2.06821 q^{57} +1.43371 q^{58} -12.3226 q^{59} +4.81882 q^{60} +1.00000 q^{61} -8.14475 q^{62} +2.89419 q^{63} -4.02821 q^{64} +1.91044 q^{65} +1.88247 q^{66} +3.24324 q^{67} -7.86851 q^{68} +0.735761 q^{69} +17.0072 q^{70} +2.36763 q^{71} -0.858967 q^{72} -7.36624 q^{73} -3.08874 q^{74} +4.74437 q^{75} +3.19270 q^{76} +2.89419 q^{77} +1.15208 q^{78} -1.49514 q^{79} -14.6852 q^{80} +1.00000 q^{81} +12.2219 q^{82} +7.31386 q^{83} +4.46777 q^{84} -15.9113 q^{85} -17.3368 q^{86} +0.761613 q^{87} -0.858967 q^{88} -9.67208 q^{89} +5.87632 q^{90} +1.77126 q^{91} +1.13580 q^{92} -4.32662 q^{93} +6.73175 q^{94} +6.45612 q^{95} -7.13795 q^{96} -5.41968 q^{97} +2.59092 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.88247	1.33111	0.665555	−	0.746349i	$-0.268195\pi$
$2$	1.88247	1.33111	0.665555	+	0.746349i	$0.268195\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.54370	0.771851
$5$	3.12160	1.39602	0.698010	−	0.716088i	$-0.254069\pi$
$5$	3.12160	1.39602	0.698010	+	0.716088i	$0.254069\pi$
$6$	1.88247	0.768516
$7$	2.89419	1.09390	0.546951	−	0.837165i	$-0.315789\pi$
$7$	2.89419	1.09390	0.546951	+	0.837165i	$0.315789\pi$
$8$	−0.858967	−0.303691
$9$	1.00000	0.333333
$10$	5.87632	1.85826
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.54370	0.445629
$13$	0.612006	0.169740	0.0848700	−	0.996392i	$-0.472953\pi$
$13$	0.612006	0.169740	0.0848700	+	0.996392i	$0.472953\pi$
$14$	5.44823	1.45610
$15$	3.12160	0.805993
$16$	−4.70439	−1.17610
$17$	−5.09716	−1.23624	−0.618122	−	0.786082i	$-0.712106\pi$
$17$	−5.09716	−1.23624	−0.618122	+	0.786082i	$0.712106\pi$
$18$	1.88247	0.443703
$19$	2.06821	0.474480	0.237240	−	0.971451i	$-0.423757\pi$
$19$	2.06821	0.474480	0.237240	+	0.971451i	$0.423757\pi$
$20$	4.81882	1.07752
$21$	2.89419	0.631564
$22$	1.88247	0.401344
$23$	0.735761	0.153417	0.0767084	−	0.997054i	$-0.475559\pi$
$23$	0.735761	0.153417	0.0767084	+	0.997054i	$0.475559\pi$
$24$	−0.858967	−0.175336
$25$	4.74437	0.948874
$26$	1.15208	0.225942
$27$	1.00000	0.192450
$28$	4.46777	0.844329
$29$	0.761613	0.141428	0.0707140	−	0.997497i	$-0.477472\pi$
$29$	0.761613	0.141428	0.0707140	+	0.997497i	$0.477472\pi$
$30$	5.87632	1.07286
$31$	−4.32662	−0.777085	−0.388542	−	0.921431i	$-0.627021\pi$
$31$	−4.32662	−0.777085	−0.388542	+	0.921431i	$0.627021\pi$
$32$	−7.13795	−1.26182
$33$	1.00000	0.174078
$34$	−9.59527	−1.64558
$35$	9.03450	1.52711
$36$	1.54370	0.257284
$37$	−1.64079	−0.269744	−0.134872	−	0.990863i	$-0.543062\pi$
$37$	−1.64079	−0.269744	−0.134872	+	0.990863i	$0.543062\pi$
$38$	3.89335	0.631585
$39$	0.612006	0.0979994
$40$	−2.68135	−0.423959
$41$	6.49247	1.01395	0.506977	−	0.861960i	$-0.330763\pi$
$41$	6.49247	1.01395	0.506977	+	0.861960i	$0.330763\pi$
$42$	5.44823	0.840681
$43$	−9.20961	−1.40445	−0.702226	−	0.711954i	$-0.747811\pi$
$43$	−9.20961	−1.40445	−0.702226	+	0.711954i	$0.747811\pi$
$44$	1.54370	0.232722
$45$	3.12160	0.465340
$46$	1.38505	0.204215
$47$	3.57602	0.521616	0.260808	−	0.965391i	$-0.416011\pi$
$47$	3.57602	0.521616	0.260808	+	0.965391i	$0.416011\pi$
$48$	−4.70439	−0.679020
$49$	1.37634	0.196620
$50$	8.93115	1.26306
$51$	−5.09716	−0.713746
$52$	0.944756	0.131014
$53$	−3.52427	−0.484095	−0.242048	−	0.970264i	$-0.577819\pi$
$53$	−3.52427	−0.484095	−0.242048	+	0.970264i	$0.577819\pi$
$54$	1.88247	0.256172
$55$	3.12160	0.420916
$56$	−2.48601	−0.332208
$57$	2.06821	0.273941
$58$	1.43371	0.188256
$59$	−12.3226	−1.60427	−0.802133	−	0.597145i	$-0.796302\pi$
$59$	−12.3226	−1.60427	−0.802133	+	0.597145i	$0.796302\pi$
$60$	4.81882	0.622107
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−8.14475	−1.03438
$63$	2.89419	0.364634
$64$	−4.02821	−0.503526
$65$	1.91044	0.236961
$66$	1.88247	0.231716
$67$	3.24324	0.396225	0.198112	−	0.980179i	$-0.436519\pi$
$67$	3.24324	0.396225	0.198112	+	0.980179i	$0.436519\pi$
$68$	−7.86851	−0.954196
$69$	0.735761	0.0885752
$70$	17.0072	2.03275
$71$	2.36763	0.280986	0.140493	−	0.990082i	$-0.455131\pi$
$71$	2.36763	0.280986	0.140493	+	0.990082i	$0.455131\pi$
$72$	−0.858967	−0.101230
$73$	−7.36624	−0.862153	−0.431077	−	0.902315i	$-0.641866\pi$
$73$	−7.36624	−0.862153	−0.431077	+	0.902315i	$0.641866\pi$
$74$	−3.08874	−0.359059
$75$	4.74437	0.547833
$76$	3.19270	0.366228
$77$	2.89419	0.329824
$78$	1.15208	0.130448
$79$	−1.49514	−0.168216	−0.0841080	−	0.996457i	$-0.526804\pi$
$79$	−1.49514	−0.168216	−0.0841080	+	0.996457i	$0.526804\pi$
$80$	−14.6852	−1.64186
$81$	1.00000	0.111111
$82$	12.2219	1.34968
$83$	7.31386	0.802801	0.401400	−	0.915903i	$-0.368524\pi$
$83$	7.31386	0.802801	0.401400	+	0.915903i	$0.368524\pi$
$84$	4.46777	0.487474
$85$	−15.9113	−1.72582
$86$	−17.3368	−1.86948
$87$	0.761613	0.0816535
$88$	−0.858967	−0.0915662
$89$	−9.67208	−1.02524	−0.512619	−	0.858616i	$-0.671325\pi$
$89$	−9.67208	−1.02524	−0.512619	+	0.858616i	$0.671325\pi$
$90$	5.87632	0.619419
$91$	1.77126	0.185679
$92$	1.13580	0.118415
$93$	−4.32662	−0.448650
$94$	6.73175	0.694327
$95$	6.45612	0.662384
$96$	−7.13795	−0.728514
$97$	−5.41968	−0.550285	−0.275143	−	0.961403i	$-0.588725\pi$
$97$	−5.41968	−0.550285	−0.275143	+	0.961403i	$0.588725\pi$
$98$	2.59092	0.261723
$99$	1.00000	0.100504
$100$	7.32390	0.732390
$101$	12.3803	1.23188	0.615942	−	0.787791i	$-0.288776\pi$
$101$	12.3803	1.23188	0.615942	+	0.787791i	$0.288776\pi$
$102$	−9.59527	−0.950073
$103$	9.12585	0.899197	0.449598	−	0.893231i	$-0.351567\pi$
$103$	9.12585	0.899197	0.449598	+	0.893231i	$0.351567\pi$
$104$	−0.525693	−0.0515485
$105$	9.03450	0.881677
$106$	−6.63434	−0.644384
$107$	−6.74514	−0.652077	−0.326039	−	0.945356i	$-0.605714\pi$
$107$	−6.74514	−0.652077	−0.326039	+	0.945356i	$0.605714\pi$
$108$	1.54370	0.148543
$109$	19.9344	1.90937	0.954686	−	0.297614i	$-0.0961908\pi$
$109$	19.9344	1.90937	0.954686	+	0.297614i	$0.0961908\pi$
$110$	5.87632	0.560285
$111$	−1.64079	−0.155737
$112$	−13.6154	−1.28653
$113$	7.56976	0.712103	0.356052	−	0.934466i	$-0.384123\pi$
$113$	7.56976	0.712103	0.356052	+	0.934466i	$0.384123\pi$
$114$	3.89335	0.364646
$115$	2.29675	0.214173
$116$	1.17570	0.109161
$117$	0.612006	0.0565800
$118$	−23.1970	−2.13545
$119$	−14.7522	−1.35233
$120$	−2.68135	−0.244773
$121$	1.00000	0.0909091
$122$	1.88247	0.170431
$123$	6.49247	0.585406
$124$	−6.67902	−0.599794
$125$	−0.797969	−0.0713725
$126$	5.44823	0.485367
$127$	−4.37829	−0.388511	−0.194255	−	0.980951i	$-0.562229\pi$
$127$	−4.37829	−0.388511	−0.194255	+	0.980951i	$0.562229\pi$
$128$	6.69289	0.591574
$129$	−9.20961	−0.810861
$130$	3.59635	0.315420
$131$	4.67606	0.408549	0.204275	−	0.978914i	$-0.434516\pi$
$131$	4.67606	0.408549	0.204275	+	0.978914i	$0.434516\pi$
$132$	1.54370	0.134362
$133$	5.98580	0.519034
$134$	6.10531	0.527419
$135$	3.12160	0.268664
$136$	4.37830	0.375436
$137$	11.2825	0.963926	0.481963	−	0.876192i	$-0.339924\pi$
$137$	11.2825	0.963926	0.481963	+	0.876192i	$0.339924\pi$
$138$	1.38505	0.117903
$139$	7.24871	0.614828	0.307414	−	0.951576i	$-0.400536\pi$
$139$	7.24871	0.614828	0.307414	+	0.951576i	$0.400536\pi$
$140$	13.9466	1.17870
$141$	3.57602	0.301155
$142$	4.45700	0.374023
$143$	0.612006	0.0511785
$144$	−4.70439	−0.392032
$145$	2.37745	0.197436
$146$	−13.8667	−1.14762
$147$	1.37634	0.113519
$148$	−2.53289	−0.208202
$149$	4.14184	0.339313	0.169656	−	0.985503i	$-0.445734\pi$
$149$	4.14184	0.339313	0.169656	+	0.985503i	$0.445734\pi$
$150$	8.93115	0.729225
$151$	−13.8303	−1.12550	−0.562748	−	0.826629i	$-0.690256\pi$
$151$	−13.8303	−1.12550	−0.562748	+	0.826629i	$0.690256\pi$
$152$	−1.77653	−0.144095
$153$	−5.09716	−0.412081
$154$	5.44823	0.439031
$155$	−13.5060	−1.08483
$156$	0.944756	0.0756410
$157$	−4.73773	−0.378112	−0.189056	−	0.981966i	$-0.560543\pi$
$157$	−4.73773	−0.378112	−0.189056	+	0.981966i	$0.560543\pi$
$158$	−2.81455	−0.223914
$159$	−3.52427	−0.279493
$160$	−22.2818	−1.76153
$161$	2.12943	0.167823
$162$	1.88247	0.147901
$163$	4.98268	0.390274	0.195137	−	0.980776i	$-0.437485\pi$
$163$	4.98268	0.390274	0.195137	+	0.980776i	$0.437485\pi$
$164$	10.0224	0.782621
$165$	3.12160	0.243016
$166$	13.7681	1.06862
$167$	4.39380	0.340002	0.170001	−	0.985444i	$-0.445623\pi$
$167$	4.39380	0.340002	0.170001	+	0.985444i	$0.445623\pi$
$168$	−2.48601	−0.191800
$169$	−12.6254	−0.971188
$170$	−29.9526	−2.29726
$171$	2.06821	0.158160
$172$	−14.2169	−1.08403
$173$	−7.03421	−0.534801	−0.267401	−	0.963585i	$-0.586165\pi$
$173$	−7.03421	−0.534801	−0.267401	+	0.963585i	$0.586165\pi$
$174$	1.43371	0.108690
$175$	13.7311	1.03797
$176$	−4.70439	−0.354607
$177$	−12.3226	−0.926224
$178$	−18.2074	−1.36470
$179$	−15.8954	−1.18808	−0.594040	−	0.804435i	$-0.702468\pi$
$179$	−15.8954	−1.18808	−0.594040	+	0.804435i	$0.702468\pi$
$180$	4.81882	0.359174
$181$	−5.01234	−0.372564	−0.186282	−	0.982496i	$-0.559644\pi$
$181$	−5.01234	−0.372564	−0.186282	+	0.982496i	$0.559644\pi$
$182$	3.33435	0.247159
$183$	1.00000	0.0739221
$184$	−0.631995	−0.0465913
$185$	−5.12189	−0.376569
$186$	−8.14475	−0.597202
$187$	−5.09716	−0.372742
$188$	5.52031	0.402610
$189$	2.89419	0.210521
$190$	12.1535	0.881705
$191$	−15.4877	−1.12065	−0.560325	−	0.828273i	$-0.689324\pi$
$191$	−15.4877	−1.12065	−0.560325	+	0.828273i	$0.689324\pi$
$192$	−4.02821	−0.290711
$193$	13.4034	0.964797	0.482399	−	0.875952i	$-0.339766\pi$
$193$	13.4034	0.964797	0.482399	+	0.875952i	$0.339766\pi$
$194$	−10.2024	−0.732490
$195$	1.91044	0.136809
$196$	2.12466	0.151761
$197$	4.47438	0.318786	0.159393	−	0.987215i	$-0.449046\pi$
$197$	4.47438	0.318786	0.159393	+	0.987215i	$0.449046\pi$
$198$	1.88247	0.133781
$199$	−4.95661	−0.351365	−0.175683	−	0.984447i	$-0.556213\pi$
$199$	−4.95661	−0.351365	−0.175683	+	0.984447i	$0.556213\pi$
$200$	−4.07526	−0.288164
$201$	3.24324	0.228761
$202$	23.3055	1.63977
$203$	2.20425	0.154708
$204$	−7.86851	−0.550906
$205$	20.2669	1.41550
$206$	17.1792	1.19693
$207$	0.735761	0.0511389
$208$	−2.87911	−0.199631
$209$	2.06821	0.143061
$210$	17.0072	1.17361
$211$	3.19557	0.219992	0.109996	−	0.993932i	$-0.464916\pi$
$211$	3.19557	0.219992	0.109996	+	0.993932i	$0.464916\pi$
$212$	−5.44042	−0.373650
$213$	2.36763	0.162227
$214$	−12.6975	−0.867986
$215$	−28.7487	−1.96065
$216$	−0.858967	−0.0584453
$217$	−12.5221	−0.850054
$218$	37.5260	2.54158
$219$	−7.36624	−0.497764
$220$	4.81882	0.324885
$221$	−3.11950	−0.209840
$222$	−3.08874	−0.207303
$223$	12.6949	0.850112	0.425056	−	0.905167i	$-0.360254\pi$
$223$	12.6949	0.850112	0.425056	+	0.905167i	$0.360254\pi$
$224$	−20.6586	−1.38031
$225$	4.74437	0.316291
$226$	14.2499	0.947887
$227$	−1.98758	−0.131920	−0.0659601	−	0.997822i	$-0.521011\pi$
$227$	−1.98758	−0.131920	−0.0659601	+	0.997822i	$0.521011\pi$
$228$	3.19270	0.211442
$229$	0.684015	0.0452010	0.0226005	−	0.999745i	$-0.492805\pi$
$229$	0.684015	0.0452010	0.0226005	+	0.999745i	$0.492805\pi$
$230$	4.32357	0.285088
$231$	2.89419	0.190424
$232$	−0.654200	−0.0429504
$233$	−2.69089	−0.176286	−0.0881431	−	0.996108i	$-0.528093\pi$
$233$	−2.69089	−0.176286	−0.0881431	+	0.996108i	$0.528093\pi$
$234$	1.15208	0.0753141
$235$	11.1629	0.728186
$236$	−19.0224	−1.23825
$237$	−1.49514	−0.0971195
$238$	−27.7705	−1.80010
$239$	−7.37296	−0.476917	−0.238458	−	0.971153i	$-0.576642\pi$
$239$	−7.37296	−0.476917	−0.238458	+	0.971153i	$0.576642\pi$
$240$	−14.6852	−0.947926
$241$	1.15121	0.0741559	0.0370780	−	0.999312i	$-0.488195\pi$
$241$	1.15121	0.0741559	0.0370780	+	0.999312i	$0.488195\pi$
$242$	1.88247	0.121010
$243$	1.00000	0.0641500
$244$	1.54370	0.0988254
$245$	4.29638	0.274486
$246$	12.2219	0.779240
$247$	1.26576	0.0805382
$248$	3.71643	0.235993
$249$	7.31386	0.463497
$250$	−1.50215	−0.0950046
$251$	20.0298	1.26427	0.632136	−	0.774858i	$-0.282178\pi$
$251$	20.0298	1.26427	0.632136	+	0.774858i	$0.282178\pi$
$252$	4.46777	0.281443
$253$	0.735761	0.0462569
$254$	−8.24201	−0.517150
$255$	−15.9113	−0.996404
$256$	20.6556	1.29098
$257$	−3.44723	−0.215032	−0.107516	−	0.994203i	$-0.534290\pi$
$257$	−3.44723	−0.215032	−0.107516	+	0.994203i	$0.534290\pi$
$258$	−17.3368	−1.07934
$259$	−4.74876	−0.295073
$260$	2.94915	0.182898
$261$	0.761613	0.0471426
$262$	8.80255	0.543824
$263$	23.1517	1.42759	0.713797	−	0.700353i	$-0.246974\pi$
$263$	23.1517	1.42759	0.713797	+	0.700353i	$0.246974\pi$
$264$	−0.858967	−0.0528658
$265$	−11.0013	−0.675807
$266$	11.2681	0.690891
$267$	−9.67208	−0.591922
$268$	5.00660	0.305827
$269$	−13.9885	−0.852896	−0.426448	−	0.904512i	$-0.640235\pi$
$269$	−13.9885	−0.852896	−0.426448	+	0.904512i	$0.640235\pi$
$270$	5.87632	0.357622
$271$	15.0767	0.915847	0.457924	−	0.888992i	$-0.348593\pi$
$271$	15.0767	0.915847	0.457924	+	0.888992i	$0.348593\pi$
$272$	23.9790	1.45394
$273$	1.77126	0.107202
$274$	21.2389	1.28309
$275$	4.74437	0.286096
$276$	1.13580	0.0683669
$277$	−17.8552	−1.07282	−0.536408	−	0.843959i	$-0.680219\pi$
$277$	−17.8552	−1.07282	−0.536408	+	0.843959i	$0.680219\pi$
$278$	13.6455	0.818403
$279$	−4.32662	−0.259028
$280$	−7.76034	−0.463769
$281$	−10.5356	−0.628500	−0.314250	−	0.949340i	$-0.601753\pi$
$281$	−10.5356	−0.628500	−0.314250	+	0.949340i	$0.601753\pi$
$282$	6.73175	0.400870
$283$	−23.4431	−1.39355	−0.696774	−	0.717291i	$-0.745382\pi$
$283$	−23.4431	−1.39355	−0.696774	+	0.717291i	$0.745382\pi$
$284$	3.65491	0.216879
$285$	6.45612	0.382428
$286$	1.15208	0.0681242
$287$	18.7904	1.10917
$288$	−7.13795	−0.420607
$289$	8.98108	0.528299
$290$	4.47548	0.262809
$291$	−5.41968	−0.317707
$292$	−11.3713	−0.665454
$293$	−16.5925	−0.969345	−0.484673	−	0.874696i	$-0.661061\pi$
$293$	−16.5925	−0.969345	−0.484673	+	0.874696i	$0.661061\pi$
$294$	2.59092	0.151106
$295$	−38.4662	−2.23959
$296$	1.40938	0.0819188
$297$	1.00000	0.0580259
$298$	7.79690	0.451662
$299$	0.450290	0.0260410
$300$	7.32390	0.422846
$301$	−26.6544	−1.53633
$302$	−26.0352	−1.49816
$303$	12.3803	0.711229
$304$	−9.72966	−0.558035
$305$	3.12160	0.178742
$306$	−9.59527	−0.548525
$307$	−2.89781	−0.165387	−0.0826933	−	0.996575i	$-0.526352\pi$
$307$	−2.89781	−0.165387	−0.0826933	+	0.996575i	$0.526352\pi$
$308$	4.46777	0.254575
$309$	9.12585	0.519152
$310$	−25.4246	−1.44402
$311$	10.4745	0.593956	0.296978	−	0.954884i	$-0.404021\pi$
$311$	10.4745	0.593956	0.296978	+	0.954884i	$0.404021\pi$
$312$	−0.525693	−0.0297615
$313$	−31.7744	−1.79599	−0.897997	−	0.440002i	$-0.854978\pi$
$313$	−31.7744	−1.79599	−0.897997	+	0.440002i	$0.854978\pi$
$314$	−8.91866	−0.503309
$315$	9.03450	0.509036
$316$	−2.30805	−0.129838
$317$	16.7759	0.942228	0.471114	−	0.882072i	$-0.343852\pi$
$317$	16.7759	0.942228	0.471114	+	0.882072i	$0.343852\pi$
$318$	−6.63434	−0.372035
$319$	0.761613	0.0426421
$320$	−12.5745	−0.702933
$321$	−6.74514	−0.376477
$322$	4.00860	0.223391
$323$	−10.5420	−0.586573
$324$	1.54370	0.0857613
$325$	2.90359	0.161062
$326$	9.37976	0.519497
$327$	19.9344	1.10238
$328$	−5.57682	−0.307928
$329$	10.3497	0.570596
$330$	5.87632	0.323481
$331$	−20.7792	−1.14213	−0.571065	−	0.820905i	$-0.693470\pi$
$331$	−20.7792	−1.14213	−0.571065	+	0.820905i	$0.693470\pi$
$332$	11.2904	0.619643
$333$	−1.64079	−0.0899147
$334$	8.27121	0.452580
$335$	10.1241	0.553138
$336$	−13.6154	−0.742781
$337$	1.27358	0.0693766	0.0346883	−	0.999398i	$-0.488956\pi$
$337$	1.27358	0.0693766	0.0346883	+	0.999398i	$0.488956\pi$
$338$	−23.7671	−1.29276
$339$	7.56976	0.411133
$340$	−24.5623	−1.33208
$341$	−4.32662	−0.234300
$342$	3.89335	0.210528
$343$	−16.2759	−0.878818
$344$	7.91076	0.426519
$345$	2.29675	0.123653
$346$	−13.2417	−0.711879
$347$	28.1641	1.51193	0.755963	−	0.654615i	$-0.227169\pi$
$347$	28.1641	1.51193	0.755963	+	0.654615i	$0.227169\pi$
$348$	1.17570	0.0630243
$349$	−21.6485	−1.15882	−0.579409	−	0.815037i	$-0.696717\pi$
$349$	−21.6485	−1.15882	−0.579409	+	0.815037i	$0.696717\pi$
$350$	25.8484	1.38166
$351$	0.612006	0.0326665
$352$	−7.13795	−0.380454
$353$	1.15454	0.0614500	0.0307250	−	0.999528i	$-0.490218\pi$
$353$	1.15454	0.0614500	0.0307250	+	0.999528i	$0.490218\pi$
$354$	−23.1970	−1.23290
$355$	7.39078	0.392262
$356$	−14.9308	−0.791332
$357$	−14.7522	−0.780767
$358$	−29.9227	−1.58146
$359$	11.6273	0.613667	0.306834	−	0.951763i	$-0.400730\pi$
$359$	11.6273	0.613667	0.306834	+	0.951763i	$0.400730\pi$
$360$	−2.68135	−0.141320
$361$	−14.7225	−0.774869
$362$	−9.43559	−0.495924
$363$	1.00000	0.0524864
$364$	2.73430	0.143316
$365$	−22.9944	−1.20358
$366$	1.88247	0.0983984
$367$	19.3017	1.00754	0.503770	−	0.863838i	$-0.331946\pi$
$367$	19.3017	1.00754	0.503770	+	0.863838i	$0.331946\pi$
$368$	−3.46131	−0.180433
$369$	6.49247	0.337985
$370$	−9.64181	−0.501254
$371$	−10.1999	−0.529553
$372$	−6.67902	−0.346291
$373$	31.6290	1.63769	0.818843	−	0.574018i	$-0.194616\pi$
$373$	31.6290	1.63769	0.818843	+	0.574018i	$0.194616\pi$
$374$	−9.59527	−0.496160
$375$	−0.797969	−0.0412069
$376$	−3.07168	−0.158410
$377$	0.466112	0.0240060
$378$	5.44823	0.280227
$379$	3.94697	0.202742	0.101371	−	0.994849i	$-0.467677\pi$
$379$	3.94697	0.202742	0.101371	+	0.994849i	$0.467677\pi$
$380$	9.96633	0.511262
$381$	−4.37829	−0.224307
$382$	−29.1551	−1.49171
$383$	8.76935	0.448093	0.224046	−	0.974578i	$-0.428073\pi$
$383$	8.76935	0.448093	0.224046	+	0.974578i	$0.428073\pi$
$384$	6.69289	0.341545
$385$	9.03450	0.460441
$386$	25.2315	1.28425
$387$	−9.20961	−0.468151
$388$	−8.36638	−0.424738
$389$	−26.6960	−1.35354	−0.676770	−	0.736195i	$-0.736621\pi$
$389$	−26.6960	−1.35354	−0.676770	+	0.736195i	$0.736621\pi$
$390$	3.59635	0.182108
$391$	−3.75030	−0.189661
$392$	−1.18223	−0.0597116
$393$	4.67606	0.235876
$394$	8.42289	0.424339
$395$	−4.66721	−0.234833
$396$	1.54370	0.0775740
$397$	−14.7330	−0.739427	−0.369714	−	0.929146i	$-0.620544\pi$
$397$	−14.7330	−0.739427	−0.369714	+	0.929146i	$0.620544\pi$
$398$	−9.33069	−0.467705
$399$	5.98580	0.299665
$400$	−22.3194	−1.11597
$401$	18.2938	0.913548	0.456774	−	0.889583i	$-0.349005\pi$
$401$	18.2938	0.913548	0.456774	+	0.889583i	$0.349005\pi$
$402$	6.10531	0.304505
$403$	−2.64792	−0.131902
$404$	19.1115	0.950831
$405$	3.12160	0.155113
$406$	4.14944	0.205933
$407$	−1.64079	−0.0813309
$408$	4.37830	0.216758
$409$	−26.8010	−1.32522	−0.662611	−	0.748964i	$-0.730552\pi$
$409$	−26.8010	−1.32522	−0.662611	+	0.748964i	$0.730552\pi$
$410$	38.1518	1.88419
$411$	11.2825	0.556523
$412$	14.0876	0.694046
$413$	−35.6640	−1.75491
$414$	1.38505	0.0680715
$415$	22.8309	1.12073
$416$	−4.36847	−0.214182
$417$	7.24871	0.354971
$418$	3.89335	0.190430
$419$	−9.36955	−0.457732	−0.228866	−	0.973458i	$-0.573502\pi$
$419$	−9.36955	−0.457732	−0.228866	+	0.973458i	$0.573502\pi$
$420$	13.9466	0.680523
$421$	6.67779	0.325456	0.162728	−	0.986671i	$-0.447971\pi$
$421$	6.67779	0.325456	0.162728	+	0.986671i	$0.447971\pi$
$422$	6.01557	0.292833
$423$	3.57602	0.173872
$424$	3.02723	0.147015
$425$	−24.1828	−1.17304
$426$	4.45700	0.215942
$427$	2.89419	0.140060
$428$	−10.4125	−0.503307
$429$	0.612006	0.0295479
$430$	−54.1187	−2.60983
$431$	25.4516	1.22596	0.612979	−	0.790099i	$-0.289971\pi$
$431$	25.4516	1.22596	0.612979	+	0.790099i	$0.289971\pi$
$432$	−4.70439	−0.226340
$433$	−19.6754	−0.945540	−0.472770	−	0.881186i	$-0.656746\pi$
$433$	−19.6754	−0.945540	−0.472770	+	0.881186i	$0.656746\pi$
$434$	−23.5725	−1.13151
$435$	2.37745	0.113990
$436$	30.7728	1.47375
$437$	1.52171	0.0727932
$438$	−13.8667	−0.662579
$439$	−2.68583	−0.128188	−0.0640938	−	0.997944i	$-0.520416\pi$
$439$	−2.68583	−0.128188	−0.0640938	+	0.997944i	$0.520416\pi$
$440$	−2.68135	−0.127828
$441$	1.37634	0.0655400
$442$	−5.87237	−0.279320
$443$	−33.3146	−1.58282	−0.791412	−	0.611283i	$-0.790654\pi$
$443$	−33.3146	−1.58282	−0.791412	+	0.611283i	$0.790654\pi$
$444$	−2.53289	−0.120206
$445$	−30.1924	−1.43125
$446$	23.8978	1.13159
$447$	4.14184	0.195902
$448$	−11.6584	−0.550808
$449$	3.56896	0.168430	0.0842149	−	0.996448i	$-0.473162\pi$
$449$	3.56896	0.168430	0.0842149	+	0.996448i	$0.473162\pi$
$450$	8.93115	0.421018
$451$	6.49247	0.305719
$452$	11.6855	0.549638
$453$	−13.8303	−0.649805
$454$	−3.74156	−0.175600
$455$	5.52917	0.259211
$456$	−1.77653	−0.0831934
$457$	19.1421	0.895428	0.447714	−	0.894177i	$-0.352238\pi$
$457$	19.1421	0.895428	0.447714	+	0.894177i	$0.352238\pi$
$458$	1.28764	0.0601675
$459$	−5.09716	−0.237915
$460$	3.54550	0.165310
$461$	7.73587	0.360296	0.180148	−	0.983640i	$-0.442342\pi$
$461$	7.73587	0.360296	0.180148	+	0.983640i	$0.442342\pi$
$462$	5.44823	0.253475
$463$	25.3911	1.18002	0.590012	−	0.807395i	$-0.299123\pi$
$463$	25.3911	1.18002	0.590012	+	0.807395i	$0.299123\pi$
$464$	−3.58292	−0.166333
$465$	−13.5060	−0.626325
$466$	−5.06553	−0.234656
$467$	39.5896	1.83199	0.915993	−	0.401194i	$-0.131405\pi$
$467$	39.5896	1.83199	0.915993	+	0.401194i	$0.131405\pi$
$468$	0.944756	0.0436713
$469$	9.38656	0.433431
$470$	21.0138	0.969295
$471$	−4.73773	−0.218303
$472$	10.5847	0.487201
$473$	−9.20961	−0.423458
$474$	−2.81455	−0.129277
$475$	9.81236	0.450222
$476$	−22.7730	−1.04380
$477$	−3.52427	−0.161365
$478$	−13.8794	−0.634828
$479$	7.82772	0.357658	0.178829	−	0.983880i	$-0.442769\pi$
$479$	7.82772	0.357658	0.178829	+	0.983880i	$0.442769\pi$
$480$	−22.2818	−1.01702
$481$	−1.00417	−0.0457864
$482$	2.16712	0.0987096
$483$	2.12943	0.0968926
$484$	1.54370	0.0701683
$485$	−16.9181	−0.768210
$486$	1.88247	0.0853907
$487$	−1.81531	−0.0822596	−0.0411298	−	0.999154i	$-0.513096\pi$
$487$	−1.81531	−0.0822596	−0.0411298	+	0.999154i	$0.513096\pi$
$488$	−0.858967	−0.0388836
$489$	4.98268	0.225325
$490$	8.08781	0.365370
$491$	−11.0929	−0.500615	−0.250307	−	0.968166i	$-0.580532\pi$
$491$	−11.0929	−0.500615	−0.250307	+	0.968166i	$0.580532\pi$
$492$	10.0224	0.451847
$493$	−3.88206	−0.174839
$494$	2.38275	0.107205
$495$	3.12160	0.140305
$496$	20.3541	0.913927
$497$	6.85237	0.307371
$498$	13.7681	0.616965
$499$	7.50790	0.336100	0.168050	−	0.985778i	$-0.446253\pi$
$499$	7.50790	0.336100	0.168050	+	0.985778i	$0.446253\pi$
$500$	−1.23183	−0.0550890
$501$	4.39380	0.196300
$502$	37.7056	1.68288
$503$	−0.897861	−0.0400336	−0.0200168	−	0.999800i	$-0.506372\pi$
$503$	−0.897861	−0.0400336	−0.0200168	+	0.999800i	$0.506372\pi$
$504$	−2.48601	−0.110736
$505$	38.6463	1.71974
$506$	1.38505	0.0615730
$507$	−12.6254	−0.560716
$508$	−6.75878	−0.299872
$509$	27.5580	1.22149	0.610744	−	0.791828i	$-0.290871\pi$
$509$	27.5580	1.22149	0.610744	+	0.791828i	$0.290871\pi$
$510$	−29.9526	−1.32632
$511$	−21.3193	−0.943111
$512$	25.4978	1.12686
$513$	2.06821	0.0913137
$514$	−6.48932	−0.286232
$515$	28.4872	1.25530
$516$	−14.2169	−0.625864
$517$	3.57602	0.157273
$518$	−8.93941	−0.392775
$519$	−7.03421	−0.308768
$520$	−1.64100	−0.0719627
$521$	−36.2046	−1.58615	−0.793076	−	0.609122i	$-0.791522\pi$
$521$	−36.2046	−1.58615	−0.793076	+	0.609122i	$0.791522\pi$
$522$	1.43371	0.0627520
$523$	−6.50599	−0.284487	−0.142244	−	0.989832i	$-0.545432\pi$
$523$	−6.50599	−0.284487	−0.142244	+	0.989832i	$0.545432\pi$
$524$	7.21845	0.315339
$525$	13.7311	0.599275
$526$	43.5824	1.90028
$527$	22.0535	0.960666
$528$	−4.70439	−0.204732
$529$	−22.4587	−0.976463
$530$	−20.7097	−0.899573
$531$	−12.3226	−0.534755
$532$	9.24029	0.400617
$533$	3.97343	0.172108
$534$	−18.2074	−0.787913
$535$	−21.0556	−0.910314
$536$	−2.78584	−0.120330
$537$	−15.8954	−0.685939
$538$	−26.3330	−1.13530
$539$	1.37634	0.0592831
$540$	4.81882	0.207369
$541$	34.8334	1.49761	0.748803	−	0.662793i	$-0.230629\pi$
$541$	34.8334	1.49761	0.748803	+	0.662793i	$0.230629\pi$
$542$	28.3816	1.21909
$543$	−5.01234	−0.215100
$544$	36.3833	1.55992
$545$	62.2273	2.66552
$546$	3.33435	0.142697
$547$	14.8639	0.635537	0.317768	−	0.948168i	$-0.397067\pi$
$547$	14.8639	0.635537	0.317768	+	0.948168i	$0.397067\pi$
$548$	17.4168	0.744007
$549$	1.00000	0.0426790
$550$	8.93115	0.380825
$551$	1.57518	0.0671047
$552$	−0.631995	−0.0268995
$553$	−4.32721	−0.184012
$554$	−33.6120	−1.42804
$555$	−5.12189	−0.217412
$556$	11.1899	0.474556
$557$	22.9924	0.974219	0.487109	−	0.873341i	$-0.338051\pi$
$557$	22.9924	0.974219	0.487109	+	0.873341i	$0.338051\pi$
$558$	−8.14475	−0.344795
$559$	−5.63634	−0.238392
$560$	−42.5018	−1.79603
$561$	−5.09716	−0.215202
$562$	−19.8329	−0.836602
$563$	36.3407	1.53158	0.765789	−	0.643091i	$-0.222348\pi$
$563$	36.3407	1.53158	0.765789	+	0.643091i	$0.222348\pi$
$564$	5.52031	0.232447
$565$	23.6297	0.994111
$566$	−44.1310	−1.85496
$567$	2.89419	0.121545
$568$	−2.03372	−0.0853328
$569$	−8.88595	−0.372518	−0.186259	−	0.982501i	$-0.559636\pi$
$569$	−8.88595	−0.372518	−0.186259	+	0.982501i	$0.559636\pi$
$570$	12.1535	0.509053
$571$	−16.8135	−0.703624	−0.351812	−	0.936071i	$-0.614434\pi$
$571$	−16.8135	−0.703624	−0.351812	+	0.936071i	$0.614434\pi$
$572$	0.944756	0.0395022
$573$	−15.4877	−0.647007
$574$	35.3725	1.47642
$575$	3.49072	0.145573
$576$	−4.02821	−0.167842
$577$	−4.40239	−0.183274	−0.0916370	−	0.995792i	$-0.529210\pi$
$577$	−4.40239	−0.183274	−0.0916370	+	0.995792i	$0.529210\pi$
$578$	16.9066	0.703223
$579$	13.4034	0.557026
$580$	3.67007	0.152392
$581$	21.1677	0.878184
$582$	−10.2024	−0.422903
$583$	−3.52427	−0.145960
$584$	6.32736	0.261828
$585$	1.91044	0.0789869
$586$	−31.2350	−1.29030
$587$	−2.69850	−0.111379	−0.0556894	−	0.998448i	$-0.517736\pi$
$587$	−2.69850	−0.111379	−0.0556894	+	0.998448i	$0.517736\pi$
$588$	2.12466	0.0876195
$589$	−8.94837	−0.368711
$590$	−72.4116	−2.98114
$591$	4.47438	0.184051
$592$	7.71891	0.317245
$593$	20.9299	0.859487	0.429743	−	0.902951i	$-0.358604\pi$
$593$	20.9299	0.859487	0.429743	+	0.902951i	$0.358604\pi$
$594$	1.88247	0.0772388
$595$	−46.0503	−1.88788
$596$	6.39377	0.261899
$597$	−4.95661	−0.202861
$598$	0.847659	0.0346634
$599$	34.2115	1.39784	0.698922	−	0.715198i	$-0.253663\pi$
$599$	34.2115	1.39784	0.698922	+	0.715198i	$0.253663\pi$
$600$	−4.07526	−0.166372
$601$	41.0075	1.67273	0.836365	−	0.548174i	$-0.184677\pi$
$601$	41.0075	1.67273	0.836365	+	0.548174i	$0.184677\pi$
$602$	−50.1761	−2.04503
$603$	3.24324	0.132075
$604$	−21.3499	−0.868715
$605$	3.12160	0.126911
$606$	23.3055	0.946723
$607$	37.3275	1.51507	0.757537	−	0.652792i	$-0.226402\pi$
$607$	37.3275	1.51507	0.757537	+	0.652792i	$0.226402\pi$
$608$	−14.7628	−0.598710
$609$	2.20425	0.0893208
$610$	5.87632	0.237925
$611$	2.18854	0.0885390
$612$	−7.86851	−0.318065
$613$	−26.6605	−1.07681	−0.538404	−	0.842687i	$-0.680972\pi$
$613$	−26.6605	−1.07681	−0.538404	+	0.842687i	$0.680972\pi$
$614$	−5.45504	−0.220148
$615$	20.2669	0.817240
$616$	−2.48601	−0.100164
$617$	36.4605	1.46784	0.733922	−	0.679234i	$-0.237688\pi$
$617$	36.4605	1.46784	0.733922	+	0.679234i	$0.237688\pi$
$618$	17.1792	0.691047
$619$	−25.6753	−1.03198	−0.515989	−	0.856595i	$-0.672576\pi$
$619$	−25.6753	−1.03198	−0.515989	+	0.856595i	$0.672576\pi$
$620$	−20.8492	−0.837325
$621$	0.735761	0.0295251
$622$	19.7180	0.790620
$623$	−27.9929	−1.12151
$624$	−2.87911	−0.115257
$625$	−26.2128	−1.04851
$626$	−59.8144	−2.39066
$627$	2.06821	0.0825964
$628$	−7.31365	−0.291847
$629$	8.36337	0.333470
$630$	17.0072	0.677583
$631$	−48.5748	−1.93373	−0.966866	−	0.255283i	$-0.917831\pi$
$631$	−48.5748	−1.93373	−0.966866	+	0.255283i	$0.917831\pi$
$632$	1.28427	0.0510856
$633$	3.19557	0.127012
$634$	31.5802	1.25421
$635$	−13.6673	−0.542369
$636$	−5.44042	−0.215727
$637$	0.842328	0.0333743
$638$	1.43371	0.0567613
$639$	2.36763	0.0936619
$640$	20.8925	0.825849
$641$	0.709297	0.0280156	0.0140078	−	0.999902i	$-0.495541\pi$
$641$	0.709297	0.0280156	0.0140078	+	0.999902i	$0.495541\pi$
$642$	−12.6975	−0.501132
$643$	−13.1202	−0.517409	−0.258704	−	0.965957i	$-0.583296\pi$
$643$	−13.1202	−0.517409	−0.258704	+	0.965957i	$0.583296\pi$
$644$	3.28721	0.129534
$645$	−28.7487	−1.13198
$646$	−19.8450	−0.780793
$647$	38.0246	1.49490	0.747451	−	0.664317i	$-0.231278\pi$
$647$	38.0246	1.49490	0.747451	+	0.664317i	$0.231278\pi$
$648$	−0.858967	−0.0337434
$649$	−12.3226	−0.483704
$650$	5.46592	0.214391
$651$	−12.5221	−0.490779
$652$	7.69178	0.301233
$653$	−17.3803	−0.680143	−0.340071	−	0.940400i	$-0.610451\pi$
$653$	−17.3803	−0.680143	−0.340071	+	0.940400i	$0.610451\pi$
$654$	37.5260	1.46738
$655$	14.5968	0.570343
$656$	−30.5431	−1.19251
$657$	−7.36624	−0.287384
$658$	19.4830	0.759525
$659$	43.3771	1.68973	0.844866	−	0.534977i	$-0.179680\pi$
$659$	43.3771	1.68973	0.844866	+	0.534977i	$0.179680\pi$
$660$	4.81882	0.187572
$661$	22.6577	0.881283	0.440642	−	0.897683i	$-0.354751\pi$
$661$	22.6577	0.881283	0.440642	+	0.897683i	$0.354751\pi$
$662$	−39.1164	−1.52030
$663$	−3.11950	−0.121151
$664$	−6.28237	−0.243803
$665$	18.6852	0.724583
$666$	−3.08874	−0.119686
$667$	0.560365	0.0216974
$668$	6.78272	0.262431
$669$	12.6949	0.490812
$670$	19.0583	0.736287
$671$	1.00000	0.0386046
$672$	−20.6586	−0.796922
$673$	−11.6680	−0.449769	−0.224885	−	0.974385i	$-0.572201\pi$
$673$	−11.6680	−0.449769	−0.224885	+	0.974385i	$0.572201\pi$
$674$	2.39749	0.0923478
$675$	4.74437	0.182611
$676$	−19.4899	−0.749613
$677$	−12.7856	−0.491390	−0.245695	−	0.969347i	$-0.579016\pi$
$677$	−12.7856	−0.491390	−0.245695	+	0.969347i	$0.579016\pi$
$678$	14.2499	0.547263
$679$	−15.6856	−0.601958
$680$	13.6673	0.524116
$681$	−1.98758	−0.0761642
$682$	−8.14475	−0.311879
$683$	−3.82853	−0.146495	−0.0732474	−	0.997314i	$-0.523336\pi$
$683$	−3.82853	−0.146495	−0.0732474	+	0.997314i	$0.523336\pi$
$684$	3.19270	0.122076
$685$	35.2193	1.34566
$686$	−30.6390	−1.16980
$687$	0.684015	0.0260968
$688$	43.3256	1.65177
$689$	−2.15687	−0.0821703
$690$	4.32357	0.164595
$691$	−37.1229	−1.41222	−0.706111	−	0.708101i	$-0.749552\pi$
$691$	−37.1229	−1.41222	−0.706111	+	0.708101i	$0.749552\pi$
$692$	−10.8587	−0.412787
$693$	2.89419	0.109941
$694$	53.0181	2.01254
$695$	22.6276	0.858313
$696$	−0.654200	−0.0247974
$697$	−33.0932	−1.25349
$698$	−40.7527	−1.54251
$699$	−2.69089	−0.101779
$700$	21.1968	0.801162
$701$	25.9726	0.980971	0.490485	−	0.871449i	$-0.336819\pi$
$701$	25.9726	0.980971	0.490485	+	0.871449i	$0.336819\pi$
$702$	1.15208	0.0434826
$703$	−3.39350	−0.127988
$704$	−4.02821	−0.151819
$705$	11.1629	0.420418
$706$	2.17339	0.0817967
$707$	35.8309	1.34756
$708$	−19.0224	−0.714907
$709$	25.3724	0.952881	0.476441	−	0.879207i	$-0.341927\pi$
$709$	25.3724	0.952881	0.476441	+	0.879207i	$0.341927\pi$
$710$	13.9129	0.522144
$711$	−1.49514	−0.0560720
$712$	8.30800	0.311356
$713$	−3.18336	−0.119218
$714$	−27.7705	−1.03929
$715$	1.91044	0.0714463
$716$	−24.5378	−0.917022
$717$	−7.37296	−0.275348
$718$	21.8881	0.816858
$719$	46.9467	1.75082	0.875409	−	0.483384i	$-0.160592\pi$
$719$	46.9467	1.75082	0.875409	+	0.483384i	$0.160592\pi$
$720$	−14.6852	−0.547285
$721$	26.4120	0.983633
$722$	−27.7147	−1.03143
$723$	1.15121	0.0428140
$724$	−7.73756	−0.287564
$725$	3.61337	0.134197
$726$	1.88247	0.0698651
$727$	−5.13672	−0.190510	−0.0952551	−	0.995453i	$-0.530367\pi$
$727$	−5.13672	−0.190510	−0.0952551	+	0.995453i	$0.530367\pi$
$728$	−1.52146	−0.0563889
$729$	1.00000	0.0370370
$730$	−43.2864	−1.60210
$731$	46.9429	1.73625
$732$	1.54370	0.0570569
$733$	−51.6818	−1.90891	−0.954456	−	0.298352i	$-0.903563\pi$
$733$	−51.6818	−1.90891	−0.954456	+	0.298352i	$0.903563\pi$
$734$	36.3349	1.34114
$735$	4.29638	0.158474
$736$	−5.25182	−0.193585
$737$	3.24324	0.119466
$738$	12.2219	0.449894
$739$	−28.3068	−1.04128	−0.520642	−	0.853775i	$-0.674307\pi$
$739$	−28.3068	−1.04128	−0.520642	+	0.853775i	$0.674307\pi$
$740$	−7.90667	−0.290655
$741$	1.26576	0.0464988
$742$	−19.2010	−0.704892
$743$	50.3055	1.84553	0.922765	−	0.385362i	$-0.125923\pi$
$743$	50.3055	1.84553	0.922765	+	0.385362i	$0.125923\pi$
$744$	3.71643	0.136251
$745$	12.9292	0.473688
$746$	59.5406	2.17994
$747$	7.31386	0.267600
$748$	−7.86851	−0.287701
$749$	−19.5217	−0.713308
$750$	−1.50215	−0.0548509
$751$	46.7001	1.70411	0.852055	−	0.523452i	$-0.175356\pi$
$751$	46.7001	1.70411	0.852055	+	0.523452i	$0.175356\pi$
$752$	−16.8230	−0.613470
$753$	20.0298	0.729928
$754$	0.877443	0.0319546
$755$	−43.1727	−1.57121
$756$	4.46777	0.162491
$757$	21.8545	0.794314	0.397157	−	0.917751i	$-0.369997\pi$
$757$	21.8545	0.794314	0.397157	+	0.917751i	$0.369997\pi$
$758$	7.43006	0.269872
$759$	0.735761	0.0267064
$760$	−5.54560	−0.201160
$761$	7.32772	0.265630	0.132815	−	0.991141i	$-0.457598\pi$
$761$	7.32772	0.265630	0.132815	+	0.991141i	$0.457598\pi$
$762$	−8.24201	−0.298577
$763$	57.6941	2.08867
$764$	−23.9084	−0.864975
$765$	−15.9113	−0.575274
$766$	16.5081	0.596460
$767$	−7.54151	−0.272308
$768$	20.6556	0.745345
$769$	−16.2012	−0.584230	−0.292115	−	0.956383i	$-0.594359\pi$
$769$	−16.2012	−0.584230	−0.292115	+	0.956383i	$0.594359\pi$
$770$	17.0072	0.612897
$771$	−3.44723	−0.124149
$772$	20.6908	0.744680
$773$	−54.9571	−1.97667	−0.988335	−	0.152294i	$-0.951334\pi$
$773$	−54.9571	−1.97667	−0.988335	+	0.152294i	$0.951334\pi$
$774$	−17.3368	−0.623160
$775$	−20.5271	−0.737356
$776$	4.65533	0.167117
$777$	−4.74876	−0.170361
$778$	−50.2544	−1.80171
$779$	13.4278	0.481101
$780$	2.94915	0.105596
$781$	2.36763	0.0847204
$782$	−7.05983	−0.252459
$783$	0.761613	0.0272178
$784$	−6.47483	−0.231244
$785$	−14.7893	−0.527853
$786$	8.80255	0.313977
$787$	20.7743	0.740525	0.370262	−	0.928927i	$-0.379268\pi$
$787$	20.7743	0.740525	0.370262	+	0.928927i	$0.379268\pi$
$788$	6.90711	0.246056
$789$	23.1517	0.824222
$790$	−8.78590	−0.312588
$791$	21.9083	0.778971
$792$	−0.858967	−0.0305221
$793$	0.612006	0.0217330
$794$	−27.7344	−0.984258
$795$	−11.0013	−0.390177
$796$	−7.65154	−0.271202
$797$	−23.3002	−0.825337	−0.412669	−	0.910881i	$-0.635403\pi$
$797$	−23.3002	−0.825337	−0.412669	+	0.910881i	$0.635403\pi$
$798$	11.2681	0.398886
$799$	−18.2275	−0.644844
$800$	−33.8651	−1.19731
$801$	−9.67208	−0.341746
$802$	34.4375	1.21603
$803$	−7.36624	−0.259949
$804$	5.00660	0.176569
$805$	6.64723	0.234284
$806$	−4.98464	−0.175576
$807$	−13.9885	−0.492420
$808$	−10.6343	−0.374112
$809$	12.6940	0.446296	0.223148	−	0.974785i	$-0.428367\pi$
$809$	12.6940	0.446296	0.223148	+	0.974785i	$0.428367\pi$
$810$	5.87632	0.206473
$811$	−0.417495	−0.0146602	−0.00733012	−	0.999973i	$-0.502333\pi$
$811$	−0.417495	−0.0146602	−0.00733012	+	0.999973i	$0.502333\pi$
$812$	3.40271	0.119412
$813$	15.0767	0.528765
$814$	−3.08874	−0.108260
$815$	15.5539	0.544830
$816$	23.9790	0.839434
$817$	−19.0474	−0.666385
$818$	−50.4521	−1.76401
$819$	1.77126	0.0618929
$820$	31.2860	1.09256
$821$	42.2687	1.47519	0.737594	−	0.675244i	$-0.235962\pi$
$821$	42.2687	1.47519	0.737594	+	0.675244i	$0.235962\pi$
$822$	21.2389	0.740793
$823$	−18.1385	−0.632270	−0.316135	−	0.948714i	$-0.602385\pi$
$823$	−18.1385	−0.632270	−0.316135	+	0.948714i	$0.602385\pi$
$824$	−7.83881	−0.273078
$825$	4.74437	0.165178
$826$	−67.1364	−2.33597
$827$	−22.9612	−0.798440	−0.399220	−	0.916855i	$-0.630719\pi$
$827$	−22.9612	−0.798440	−0.399220	+	0.916855i	$0.630719\pi$
$828$	1.13580	0.0394717
$829$	−16.3338	−0.567296	−0.283648	−	0.958929i	$-0.591545\pi$
$829$	−16.3338	−0.567296	−0.283648	+	0.958929i	$0.591545\pi$
$830$	42.9786	1.49181
$831$	−17.8552	−0.619391
$832$	−2.46529	−0.0854686
$833$	−7.01543	−0.243070
$834$	13.6455	0.472505
$835$	13.7157	0.474650
$836$	3.19270	0.110422
$837$	−4.32662	−0.149550
$838$	−17.6379	−0.609292
$839$	36.1415	1.24774	0.623872	−	0.781527i	$-0.285559\pi$
$839$	36.1415	1.24774	0.623872	+	0.781527i	$0.285559\pi$
$840$	−7.76034	−0.267757
$841$	−28.4199	−0.979998
$842$	12.5708	0.433217
$843$	−10.5356	−0.362865
$844$	4.93301	0.169801
$845$	−39.4116	−1.35580
$846$	6.73175	0.231442
$847$	2.89419	0.0994456
$848$	16.5795	0.569343
$849$	−23.4431	−0.804565
$850$	−45.5235	−1.56144
$851$	−1.20723	−0.0413833
$852$	3.65491	0.125215
$853$	28.6938	0.982456	0.491228	−	0.871031i	$-0.336548\pi$
$853$	28.6938	0.982456	0.491228	+	0.871031i	$0.336548\pi$
$854$	5.44823	0.186435
$855$	6.45612	0.220795
$856$	5.79385	0.198030
$857$	−20.6888	−0.706716	−0.353358	−	0.935488i	$-0.614960\pi$
$857$	−20.6888	−0.706716	−0.353358	+	0.935488i	$0.614960\pi$
$858$	1.15208	0.0393315
$859$	13.5802	0.463352	0.231676	−	0.972793i	$-0.425579\pi$
$859$	13.5802	0.463352	0.231676	+	0.972793i	$0.425579\pi$
$860$	−44.3795	−1.51333
$861$	18.7904	0.640377
$862$	47.9119	1.63188
$863$	27.8111	0.946702	0.473351	−	0.880874i	$-0.343044\pi$
$863$	27.8111	0.946702	0.473351	+	0.880874i	$0.343044\pi$
$864$	−7.13795	−0.242838
$865$	−21.9580	−0.746594
$866$	−37.0384	−1.25862
$867$	8.98108	0.305013
$868$	−19.3304	−0.656115
$869$	−1.49514	−0.0507190
$870$	4.47548	0.151733
$871$	1.98488	0.0672552
$872$	−17.1230	−0.579859
$873$	−5.41968	−0.183428
$874$	2.86458	0.0968957
$875$	−2.30947	−0.0780745
$876$	−11.3713	−0.384200
$877$	−50.7213	−1.71274	−0.856368	−	0.516367i	$-0.827284\pi$
$877$	−50.7213	−1.71274	−0.856368	+	0.516367i	$0.827284\pi$
$878$	−5.05600	−0.170632
$879$	−16.5925	−0.559652
$880$	−14.6852	−0.495038
$881$	−43.2148	−1.45594	−0.727971	−	0.685608i	$-0.759537\pi$
$881$	−43.2148	−1.45594	−0.727971	+	0.685608i	$0.759537\pi$
$882$	2.59092	0.0872409
$883$	6.52452	0.219568	0.109784	−	0.993955i	$-0.464984\pi$
$883$	6.52452	0.219568	0.109784	+	0.993955i	$0.464984\pi$
$884$	−4.81557	−0.161965
$885$	−38.4662	−1.29303
$886$	−62.7138	−2.10691
$887$	5.49555	0.184523	0.0922613	−	0.995735i	$-0.470590\pi$
$887$	5.49555	0.184523	0.0922613	+	0.995735i	$0.470590\pi$
$888$	1.40938	0.0472958
$889$	−12.6716	−0.424992
$890$	−56.8363	−1.90516
$891$	1.00000	0.0335013
$892$	19.5971	0.656160
$893$	7.39595	0.247496
$894$	7.79690	0.260767
$895$	−49.6192	−1.65859
$896$	19.3705	0.647123
$897$	0.450290	0.0150348
$898$	6.71848	0.224198
$899$	−3.29521	−0.109901
$900$	7.32390	0.244130
$901$	17.9638	0.598460
$902$	12.2219	0.406945
$903$	−26.6544	−0.887002
$904$	−6.50218	−0.216259
$905$	−15.6465	−0.520107
$906$	−26.0352	−0.864961
$907$	5.03434	0.167162	0.0835812	−	0.996501i	$-0.473364\pi$
$907$	5.03434	0.167162	0.0835812	+	0.996501i	$0.473364\pi$
$908$	−3.06823	−0.101823
$909$	12.3803	0.410628
$910$	10.4085	0.345039
$911$	−28.6591	−0.949518	−0.474759	−	0.880116i	$-0.657465\pi$
$911$	−28.6591	−0.949518	−0.474759	+	0.880116i	$0.657465\pi$
$912$	−9.72966	−0.322181
$913$	7.31386	0.242053
$914$	36.0344	1.19191
$915$	3.12160	0.103197
$916$	1.05592	0.0348885
$917$	13.5334	0.446913
$918$	−9.59527	−0.316691
$919$	45.7713	1.50986	0.754928	−	0.655808i	$-0.227672\pi$
$919$	45.7713	1.50986	0.754928	+	0.655808i	$0.227672\pi$
$920$	−1.97283	−0.0650424
$921$	−2.89781	−0.0954860
$922$	14.5626	0.479593
$923$	1.44900	0.0476945
$924$	4.46777	0.146979
$925$	−7.78452	−0.255953
$926$	47.7980	1.57074
$927$	9.12585	0.299732
$928$	−5.43635	−0.178457
$929$	30.9109	1.01415	0.507077	−	0.861901i	$-0.330726\pi$
$929$	30.9109	1.01415	0.507077	+	0.861901i	$0.330726\pi$
$930$	−25.4246	−0.833707
$931$	2.84656	0.0932922
$932$	−4.15394	−0.136067
$933$	10.4745	0.342921
$934$	74.5262	2.43857
$935$	−15.9113	−0.520355
$936$	−0.525693	−0.0171828
$937$	46.3042	1.51269	0.756346	−	0.654172i	$-0.226983\pi$
$937$	46.3042	1.51269	0.756346	+	0.654172i	$0.226983\pi$
$938$	17.6699	0.576944
$939$	−31.7744	−1.03692
$940$	17.2322	0.562051
$941$	4.10685	0.133879	0.0669397	−	0.997757i	$-0.478676\pi$
$941$	4.10685	0.133879	0.0669397	+	0.997757i	$0.478676\pi$
$942$	−8.91866	−0.290586
$943$	4.77691	0.155558
$944$	57.9703	1.88677
$945$	9.03450	0.293892
$946$	−17.3368	−0.563669
$947$	−20.6827	−0.672097	−0.336049	−	0.941845i	$-0.609091\pi$
$947$	−20.6827	−0.672097	−0.336049	+	0.941845i	$0.609091\pi$
$948$	−2.30805	−0.0749618
$949$	−4.50819	−0.146342
$950$	18.4715	0.599295
$951$	16.7759	0.543996
$952$	12.6716	0.410690
$953$	−15.2308	−0.493374	−0.246687	−	0.969095i	$-0.579342\pi$
$953$	−15.2308	−0.493374	−0.246687	+	0.969095i	$0.579342\pi$
$954$	−6.63434	−0.214795
$955$	−48.3463	−1.56445
$956$	−11.3817	−0.368109
$957$	0.761613	0.0246194
$958$	14.7355	0.476081
$959$	32.6536	1.05444
$960$	−12.5745	−0.405839
$961$	−12.2803	−0.396140
$962$	−1.89033	−0.0609467
$963$	−6.74514	−0.217359
$964$	1.77713	0.0572374
$965$	41.8400	1.34688
$966$	4.00860	0.128975
$967$	−15.8808	−0.510692	−0.255346	−	0.966850i	$-0.582189\pi$
$967$	−15.8808	−0.510692	−0.255346	+	0.966850i	$0.582189\pi$
$968$	−0.858967	−0.0276082
$969$	−10.5420	−0.338658
$970$	−31.8478	−1.02257
$971$	49.4951	1.58837	0.794187	−	0.607674i	$-0.207897\pi$
$971$	49.4951	1.58837	0.794187	+	0.607674i	$0.207897\pi$
$972$	1.54370	0.0495143
$973$	20.9792	0.672561
$974$	−3.41727	−0.109497
$975$	2.90359	0.0929891
$976$	−4.70439	−0.150584
$977$	31.6358	1.01212	0.506059	−	0.862499i	$-0.331102\pi$
$977$	31.6358	1.01212	0.506059	+	0.862499i	$0.331102\pi$
$978$	9.37976	0.299932
$979$	−9.67208	−0.309121
$980$	6.63233	0.211862
$981$	19.9344	0.636458
$982$	−20.8820	−0.666373
$983$	−9.43029	−0.300780	−0.150390	−	0.988627i	$-0.548053\pi$
$983$	−9.43029	−0.300780	−0.150390	+	0.988627i	$0.548053\pi$
$984$	−5.57682	−0.177782
$985$	13.9672	0.445032
$986$	−7.30788	−0.232730
$987$	10.3497	0.329434
$988$	1.95395	0.0621636
$989$	−6.77608	−0.215467
$990$	5.87632	0.186762
$991$	−22.5480	−0.716259	−0.358130	−	0.933672i	$-0.616585\pi$
$991$	−22.5480	−0.716259	−0.358130	+	0.933672i	$0.616585\pi$
$992$	30.8832	0.980543
$993$	−20.7792	−0.659409
$994$	12.8994	0.409144
$995$	−15.4726	−0.490513
$996$	11.2904	0.357751
$997$	19.8731	0.629388	0.314694	−	0.949193i	$-0.398098\pi$
$997$	19.8731	0.629388	0.314694	+	0.949193i	$0.398098\pi$
$998$	14.1334	0.447386
$999$	−1.64079	−0.0519123

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.88247 q^{2} +1.00000 q^{3} +1.54370 q^{4} +3.12160 q^{5} +1.88247 q^{6} +2.89419 q^{7} -0.858967 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.88247 q^{2} +1.00000 q^{3} +1.54370 q^{4} +3.12160 q^{5} +1.88247 q^{6} +2.89419 q^{7} -0.858967 q^{8} +1.00000 q^{9} +5.87632 q^{10} +1.00000 q^{11} +1.54370 q^{12} +0.612006 q^{13} +5.44823 q^{14} +3.12160 q^{15} -4.70439 q^{16} -5.09716 q^{17} +1.88247 q^{18} +2.06821 q^{19} +4.81882 q^{20} +2.89419 q^{21} +1.88247 q^{22} +0.735761 q^{23} -0.858967 q^{24} +4.74437 q^{25} +1.15208 q^{26} +1.00000 q^{27} +4.46777 q^{28} +0.761613 q^{29} +5.87632 q^{30} -4.32662 q^{31} -7.13795 q^{32} +1.00000 q^{33} -9.59527 q^{34} +9.03450 q^{35} +1.54370 q^{36} -1.64079 q^{37} +3.89335 q^{38} +0.612006 q^{39} -2.68135 q^{40} +6.49247 q^{41} +5.44823 q^{42} -9.20961 q^{43} +1.54370 q^{44} +3.12160 q^{45} +1.38505 q^{46} +3.57602 q^{47} -4.70439 q^{48} +1.37634 q^{49} +8.93115 q^{50} -5.09716 q^{51} +0.944756 q^{52} -3.52427 q^{53} +1.88247 q^{54} +3.12160 q^{55} -2.48601 q^{56} +2.06821 q^{57} +1.43371 q^{58} -12.3226 q^{59} +4.81882 q^{60} +1.00000 q^{61} -8.14475 q^{62} +2.89419 q^{63} -4.02821 q^{64} +1.91044 q^{65} +1.88247 q^{66} +3.24324 q^{67} -7.86851 q^{68} +0.735761 q^{69} +17.0072 q^{70} +2.36763 q^{71} -0.858967 q^{72} -7.36624 q^{73} -3.08874 q^{74} +4.74437 q^{75} +3.19270 q^{76} +2.89419 q^{77} +1.15208 q^{78} -1.49514 q^{79} -14.6852 q^{80} +1.00000 q^{81} +12.2219 q^{82} +7.31386 q^{83} +4.46777 q^{84} -15.9113 q^{85} -17.3368 q^{86} +0.761613 q^{87} -0.858967 q^{88} -9.67208 q^{89} +5.87632 q^{90} +1.77126 q^{91} +1.13580 q^{92} -4.32662 q^{93} +6.73175 q^{94} +6.45612 q^{95} -7.13795 q^{96} -5.41968 q^{97} +2.59092 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

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