LMFDB - Embedded newform 2013.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.53773$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53773 q^{2} -1.00000 q^{3} +4.44007 q^{4} +0.994065 q^{5} -2.53773 q^{6} +4.88646 q^{7} +6.19224 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.53773 q^{2} -1.00000 q^{3} +4.44007 q^{4} +0.994065 q^{5} -2.53773 q^{6} +4.88646 q^{7} +6.19224 q^{8} +1.00000 q^{9} +2.52267 q^{10} +1.00000 q^{11} -4.44007 q^{12} +4.29008 q^{13} +12.4005 q^{14} -0.994065 q^{15} +6.83409 q^{16} -3.82389 q^{17} +2.53773 q^{18} -2.93110 q^{19} +4.41372 q^{20} -4.88646 q^{21} +2.53773 q^{22} -5.41371 q^{23} -6.19224 q^{24} -4.01184 q^{25} +10.8871 q^{26} -1.00000 q^{27} +21.6962 q^{28} -2.31016 q^{29} -2.52267 q^{30} -6.92787 q^{31} +4.95859 q^{32} -1.00000 q^{33} -9.70401 q^{34} +4.85746 q^{35} +4.44007 q^{36} +0.949760 q^{37} -7.43834 q^{38} -4.29008 q^{39} +6.15549 q^{40} -4.66091 q^{41} -12.4005 q^{42} +4.23337 q^{43} +4.44007 q^{44} +0.994065 q^{45} -13.7385 q^{46} +8.27575 q^{47} -6.83409 q^{48} +16.8775 q^{49} -10.1810 q^{50} +3.82389 q^{51} +19.0483 q^{52} -11.5324 q^{53} -2.53773 q^{54} +0.994065 q^{55} +30.2582 q^{56} +2.93110 q^{57} -5.86257 q^{58} +5.12033 q^{59} -4.41372 q^{60} -1.00000 q^{61} -17.5811 q^{62} +4.88646 q^{63} -1.08461 q^{64} +4.26462 q^{65} -2.53773 q^{66} -6.83412 q^{67} -16.9784 q^{68} +5.41371 q^{69} +12.3269 q^{70} +4.72943 q^{71} +6.19224 q^{72} +15.9491 q^{73} +2.41023 q^{74} +4.01184 q^{75} -13.0143 q^{76} +4.88646 q^{77} -10.8871 q^{78} -6.64878 q^{79} +6.79353 q^{80} +1.00000 q^{81} -11.8281 q^{82} -8.78161 q^{83} -21.6962 q^{84} -3.80120 q^{85} +10.7431 q^{86} +2.31016 q^{87} +6.19224 q^{88} +0.0660596 q^{89} +2.52267 q^{90} +20.9633 q^{91} -24.0372 q^{92} +6.92787 q^{93} +21.0016 q^{94} -2.91370 q^{95} -4.95859 q^{96} +11.3016 q^{97} +42.8306 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.53773	1.79445	0.897223	−	0.441578i	$-0.145581\pi$
$2$	2.53773	1.79445	0.897223	+	0.441578i	$0.145581\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.44007	2.22004
$5$	0.994065	0.444559	0.222280	−	0.974983i	$-0.428650\pi$
$5$	0.994065	0.444559	0.222280	+	0.974983i	$0.428650\pi$
$6$	−2.53773	−1.03602
$7$	4.88646	1.84691	0.923455	−	0.383707i	$-0.125353\pi$
$7$	4.88646	1.84691	0.923455	+	0.383707i	$0.125353\pi$
$8$	6.19224	2.18929
$9$	1.00000	0.333333
$10$	2.52267	0.797737
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.44007	−1.28174
$13$	4.29008	1.18985	0.594927	−	0.803779i	$-0.297181\pi$
$13$	4.29008	1.18985	0.594927	+	0.803779i	$0.297181\pi$
$14$	12.4005	3.31418
$15$	−0.994065	−0.256666
$16$	6.83409	1.70852
$17$	−3.82389	−0.927431	−0.463715	−	0.885984i	$-0.653484\pi$
$17$	−3.82389	−0.927431	−0.463715	+	0.885984i	$0.653484\pi$
$18$	2.53773	0.598149
$19$	−2.93110	−0.672441	−0.336220	−	0.941783i	$-0.609149\pi$
$19$	−2.93110	−0.672441	−0.336220	+	0.941783i	$0.609149\pi$
$20$	4.41372	0.986937
$21$	−4.88646	−1.06631
$22$	2.53773	0.541046
$23$	−5.41371	−1.12884	−0.564418	−	0.825489i	$-0.690899\pi$
$23$	−5.41371	−1.12884	−0.564418	+	0.825489i	$0.690899\pi$
$24$	−6.19224	−1.26399
$25$	−4.01184	−0.802367
$26$	10.8871	2.13513
$27$	−1.00000	−0.192450
$28$	21.6962	4.10021
$29$	−2.31016	−0.428986	−0.214493	−	0.976725i	$-0.568810\pi$
$29$	−2.31016	−0.428986	−0.214493	+	0.976725i	$0.568810\pi$
$30$	−2.52267	−0.460574
$31$	−6.92787	−1.24428	−0.622141	−	0.782905i	$-0.713737\pi$
$31$	−6.92787	−1.24428	−0.622141	+	0.782905i	$0.713737\pi$
$32$	4.95859	0.876564
$33$	−1.00000	−0.174078
$34$	−9.70401	−1.66422
$35$	4.85746	0.821061
$36$	4.44007	0.740012
$37$	0.949760	0.156140	0.0780698	−	0.996948i	$-0.475124\pi$
$37$	0.949760	0.156140	0.0780698	+	0.996948i	$0.475124\pi$
$38$	−7.43834	−1.20666
$39$	−4.29008	−0.686963
$40$	6.15549	0.973268
$41$	−4.66091	−0.727912	−0.363956	−	0.931416i	$-0.618574\pi$
$41$	−4.66091	−0.727912	−0.363956	+	0.931416i	$0.618574\pi$
$42$	−12.4005	−1.91344
$43$	4.23337	0.645583	0.322791	−	0.946470i	$-0.395379\pi$
$43$	4.23337	0.645583	0.322791	+	0.946470i	$0.395379\pi$
$44$	4.44007	0.669366
$45$	0.994065	0.148186
$46$	−13.7385	−2.02563
$47$	8.27575	1.20714	0.603571	−	0.797309i	$-0.293744\pi$
$47$	8.27575	1.20714	0.603571	+	0.797309i	$0.293744\pi$
$48$	−6.83409	−0.986416
$49$	16.8775	2.41108
$50$	−10.1810	−1.43980
$51$	3.82389	0.535452
$52$	19.0483	2.64152
$53$	−11.5324	−1.58410	−0.792051	−	0.610455i	$-0.790987\pi$
$53$	−11.5324	−1.58410	−0.792051	+	0.610455i	$0.790987\pi$
$54$	−2.53773	−0.345341
$55$	0.994065	0.134040
$56$	30.2582	4.04342
$57$	2.93110	0.388234
$58$	−5.86257	−0.769793
$59$	5.12033	0.666610	0.333305	−	0.942819i	$-0.391836\pi$
$59$	5.12033	0.666610	0.333305	+	0.942819i	$0.391836\pi$
$60$	−4.41372	−0.569809
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−17.5811	−2.23280
$63$	4.88646	0.615637
$64$	−1.08461	−0.135577
$65$	4.26462	0.528961
$66$	−2.53773	−0.312373
$67$	−6.83412	−0.834920	−0.417460	−	0.908695i	$-0.637080\pi$
$67$	−6.83412	−0.834920	−0.417460	+	0.908695i	$0.637080\pi$
$68$	−16.9784	−2.05893
$69$	5.41371	0.651734
$70$	12.3269	1.47335
$71$	4.72943	0.561280	0.280640	−	0.959813i	$-0.409453\pi$
$71$	4.72943	0.561280	0.280640	+	0.959813i	$0.409453\pi$
$72$	6.19224	0.729763
$73$	15.9491	1.86670	0.933348	−	0.358972i	$-0.116873\pi$
$73$	15.9491	1.86670	0.933348	+	0.358972i	$0.116873\pi$
$74$	2.41023	0.280184
$75$	4.01184	0.463247
$76$	−13.0143	−1.49284
$77$	4.88646	0.556864
$78$	−10.8871	−1.23272
$79$	−6.64878	−0.748046	−0.374023	−	0.927419i	$-0.622022\pi$
$79$	−6.64878	−0.748046	−0.374023	+	0.927419i	$0.622022\pi$
$80$	6.79353	0.759540
$81$	1.00000	0.111111
$82$	−11.8281	−1.30620
$83$	−8.78161	−0.963906	−0.481953	−	0.876197i	$-0.660072\pi$
$83$	−8.78161	−0.963906	−0.481953	+	0.876197i	$0.660072\pi$
$84$	−21.6962	−2.36725
$85$	−3.80120	−0.412298
$86$	10.7431	1.15846
$87$	2.31016	0.247675
$88$	6.19224	0.660095
$89$	0.0660596	0.00700230	0.00350115	−	0.999994i	$-0.498886\pi$
$89$	0.0660596	0.00700230	0.00350115	+	0.999994i	$0.498886\pi$
$90$	2.52267	0.265912
$91$	20.9633	2.19755
$92$	−24.0372	−2.50606
$93$	6.92787	0.718387
$94$	21.0016	2.16615
$95$	−2.91370	−0.298940
$96$	−4.95859	−0.506084
$97$	11.3016	1.14751	0.573753	−	0.819028i	$-0.305487\pi$
$97$	11.3016	1.14751	0.573753	+	0.819028i	$0.305487\pi$
$98$	42.8306	4.32654
$99$	1.00000	0.100504
$100$	−17.8128	−1.78128
$101$	−6.79683	−0.676310	−0.338155	−	0.941091i	$-0.609803\pi$
$101$	−6.79683	−0.676310	−0.338155	+	0.941091i	$0.609803\pi$
$102$	9.70401	0.960840
$103$	12.1574	1.19790	0.598952	−	0.800785i	$-0.295584\pi$
$103$	12.1574	1.19790	0.598952	+	0.800785i	$0.295584\pi$
$104$	26.5652	2.60493
$105$	−4.85746	−0.474040
$106$	−29.2662	−2.84258
$107$	3.63314	0.351229	0.175614	−	0.984459i	$-0.443809\pi$
$107$	3.63314	0.351229	0.175614	+	0.984459i	$0.443809\pi$
$108$	−4.44007	−0.427246
$109$	4.81079	0.460790	0.230395	−	0.973097i	$-0.425998\pi$
$109$	4.81079	0.460790	0.230395	+	0.973097i	$0.425998\pi$
$110$	2.52267	0.240527
$111$	−0.949760	−0.0901472
$112$	33.3945	3.15549
$113$	−4.35919	−0.410078	−0.205039	−	0.978754i	$-0.565732\pi$
$113$	−4.35919	−0.410078	−0.205039	+	0.978754i	$0.565732\pi$
$114$	7.43834	0.696664
$115$	−5.38157	−0.501834
$116$	−10.2573	−0.952365
$117$	4.29008	0.396618
$118$	12.9940	1.19620
$119$	−18.6853	−1.71288
$120$	−6.15549	−0.561917
$121$	1.00000	0.0909091
$122$	−2.53773	−0.229755
$123$	4.66091	0.420260
$124$	−30.7602	−2.76235
$125$	−8.95835	−0.801259
$126$	12.4005	1.10473
$127$	−20.5780	−1.82600	−0.913001	−	0.407957i	$-0.866241\pi$
$127$	−20.5780	−1.82600	−0.913001	+	0.407957i	$0.866241\pi$
$128$	−12.6696	−1.11985
$129$	−4.23337	−0.372727
$130$	10.8225	0.949192
$131$	8.91370	0.778794	0.389397	−	0.921070i	$-0.372683\pi$
$131$	8.91370	0.778794	0.389397	+	0.921070i	$0.372683\pi$
$132$	−4.44007	−0.386459
$133$	−14.3227	−1.24194
$134$	−17.3431	−1.49822
$135$	−0.994065	−0.0855555
$136$	−23.6785	−2.03041
$137$	−11.8906	−1.01589	−0.507943	−	0.861391i	$-0.669594\pi$
$137$	−11.8906	−1.01589	−0.507943	+	0.861391i	$0.669594\pi$
$138$	13.7385	1.16950
$139$	3.99386	0.338755	0.169377	−	0.985551i	$-0.445824\pi$
$139$	3.99386	0.338755	0.169377	+	0.985551i	$0.445824\pi$
$140$	21.5675	1.82278
$141$	−8.27575	−0.696944
$142$	12.0020	1.00719
$143$	4.29008	0.358755
$144$	6.83409	0.569508
$145$	−2.29645	−0.190710
$146$	40.4744	3.34969
$147$	−16.8775	−1.39204
$148$	4.21700	0.346636
$149$	18.2887	1.49827	0.749134	−	0.662418i	$-0.230470\pi$
$149$	18.2887	1.49827	0.749134	+	0.662418i	$0.230470\pi$
$150$	10.1810	0.831271
$151$	11.2751	0.917554	0.458777	−	0.888551i	$-0.348288\pi$
$151$	11.2751	0.917554	0.458777	+	0.888551i	$0.348288\pi$
$152$	−18.1501	−1.47217
$153$	−3.82389	−0.309144
$154$	12.4005	0.999263
$155$	−6.88675	−0.553157
$156$	−19.0483	−1.52508
$157$	−16.6823	−1.33139	−0.665695	−	0.746224i	$-0.731865\pi$
$157$	−16.6823	−1.33139	−0.665695	+	0.746224i	$0.731865\pi$
$158$	−16.8728	−1.34233
$159$	11.5324	0.914582
$160$	4.92916	0.389685
$161$	−26.4539	−2.08486
$162$	2.53773	0.199383
$163$	10.4676	0.819882	0.409941	−	0.912112i	$-0.365549\pi$
$163$	10.4676	0.819882	0.409941	+	0.912112i	$0.365549\pi$
$164$	−20.6948	−1.61599
$165$	−0.994065	−0.0773878
$166$	−22.2853	−1.72968
$167$	−21.0144	−1.62614	−0.813070	−	0.582166i	$-0.802205\pi$
$167$	−21.0144	−1.62614	−0.813070	+	0.582166i	$0.802205\pi$
$168$	−30.2582	−2.33447
$169$	5.40481	0.415754
$170$	−9.64641	−0.739846
$171$	−2.93110	−0.224147
$172$	18.7965	1.43322
$173$	3.21998	0.244811	0.122405	−	0.992480i	$-0.460939\pi$
$173$	3.21998	0.244811	0.122405	+	0.992480i	$0.460939\pi$
$174$	5.86257	0.444440
$175$	−19.6037	−1.48190
$176$	6.83409	0.515139
$177$	−5.12033	−0.384867
$178$	0.167641	0.0125652
$179$	−7.27099	−0.543460	−0.271730	−	0.962374i	$-0.587596\pi$
$179$	−7.27099	−0.543460	−0.271730	+	0.962374i	$0.587596\pi$
$180$	4.41372	0.328979
$181$	13.4180	0.997355	0.498678	−	0.866788i	$-0.333819\pi$
$181$	13.4180	0.997355	0.498678	+	0.866788i	$0.333819\pi$
$182$	53.1993	3.94339
$183$	1.00000	0.0739221
$184$	−33.5230	−2.47135
$185$	0.944123	0.0694133
$186$	17.5811	1.28911
$187$	−3.82389	−0.279631
$188$	36.7449	2.67990
$189$	−4.88646	−0.355438
$190$	−7.39419	−0.536431
$191$	16.2153	1.17329	0.586647	−	0.809843i	$-0.300448\pi$
$191$	16.2153	1.17329	0.586647	+	0.809843i	$0.300448\pi$
$192$	1.08461	0.0782752
$193$	15.4786	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$193$	15.4786	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$194$	28.6805	2.05914
$195$	−4.26462	−0.305396
$196$	74.9374	5.35267
$197$	−17.7360	−1.26364	−0.631818	−	0.775117i	$-0.717691\pi$
$197$	−17.7360	−1.26364	−0.631818	+	0.775117i	$0.717691\pi$
$198$	2.53773	0.180349
$199$	−2.42918	−0.172200	−0.0861000	−	0.996286i	$-0.527440\pi$
$199$	−2.42918	−0.172200	−0.0861000	+	0.996286i	$0.527440\pi$
$200$	−24.8423	−1.75661
$201$	6.83412	0.482041
$202$	−17.2485	−1.21360
$203$	−11.2885	−0.792299
$204$	16.9784	1.18872
$205$	−4.63325	−0.323600
$206$	30.8522	2.14957
$207$	−5.41371	−0.376279
$208$	29.3188	2.03289
$209$	−2.93110	−0.202748
$210$	−12.3269	−0.850638
$211$	−23.4818	−1.61655	−0.808276	−	0.588804i	$-0.799599\pi$
$211$	−23.4818	−1.61655	−0.808276	+	0.588804i	$0.799599\pi$
$212$	−51.2048	−3.51676
$213$	−4.72943	−0.324055
$214$	9.21992	0.630261
$215$	4.20824	0.287000
$216$	−6.19224	−0.421329
$217$	−33.8528	−2.29808
$218$	12.2085	0.826863
$219$	−15.9491	−1.07774
$220$	4.41372	0.297573
$221$	−16.4048	−1.10351
$222$	−2.41023	−0.161764
$223$	19.8001	1.32591	0.662957	−	0.748657i	$-0.269301\pi$
$223$	19.8001	1.32591	0.662957	+	0.748657i	$0.269301\pi$
$224$	24.2300	1.61893
$225$	−4.01184	−0.267456
$226$	−11.0624	−0.735862
$227$	22.2706	1.47815	0.739077	−	0.673621i	$-0.235262\pi$
$227$	22.2706	1.47815	0.739077	+	0.673621i	$0.235262\pi$
$228$	13.0143	0.861893
$229$	4.54201	0.300144	0.150072	−	0.988675i	$-0.452049\pi$
$229$	4.54201	0.300144	0.150072	+	0.988675i	$0.452049\pi$
$230$	−13.6570	−0.900515
$231$	−4.88646	−0.321506
$232$	−14.3051	−0.939175
$233$	−9.10518	−0.596500	−0.298250	−	0.954488i	$-0.596403\pi$
$233$	−9.10518	−0.596500	−0.298250	+	0.954488i	$0.596403\pi$
$234$	10.8871	0.711710
$235$	8.22663	0.536646
$236$	22.7346	1.47990
$237$	6.64878	0.431885
$238$	−47.4183	−3.07367
$239$	−7.66236	−0.495637	−0.247818	−	0.968807i	$-0.579714\pi$
$239$	−7.66236	−0.495637	−0.247818	+	0.968807i	$0.579714\pi$
$240$	−6.79353	−0.438520
$241$	−3.33162	−0.214608	−0.107304	−	0.994226i	$-0.534222\pi$
$241$	−3.33162	−0.214608	−0.107304	+	0.994226i	$0.534222\pi$
$242$	2.53773	0.163131
$243$	−1.00000	−0.0641500
$244$	−4.44007	−0.284246
$245$	16.7774	1.07187
$246$	11.8281	0.754134
$247$	−12.5747	−0.800107
$248$	−42.8991	−2.72409
$249$	8.78161	0.556512
$250$	−22.7339	−1.43782
$251$	29.0747	1.83518	0.917589	−	0.397529i	$-0.130132\pi$
$251$	29.0747	1.83518	0.917589	+	0.397529i	$0.130132\pi$
$252$	21.6962	1.36674
$253$	−5.41371	−0.340357
$254$	−52.2214	−3.27666
$255$	3.80120	0.238040
$256$	−29.9829	−1.87393
$257$	−20.2898	−1.26564	−0.632822	−	0.774297i	$-0.718104\pi$
$257$	−20.2898	−1.26564	−0.632822	+	0.774297i	$0.718104\pi$
$258$	−10.7431	−0.668839
$259$	4.64097	0.288376
$260$	18.9352	1.17431
$261$	−2.31016	−0.142995
$262$	22.6206	1.39750
$263$	32.3400	1.99417	0.997085	−	0.0762942i	$-0.0243088\pi$
$263$	32.3400	1.99417	0.997085	+	0.0762942i	$0.0243088\pi$
$264$	−6.19224	−0.381106
$265$	−11.4640	−0.704227
$266$	−36.3472	−2.22859
$267$	−0.0660596	−0.00404278
$268$	−30.3440	−1.85355
$269$	17.3768	1.05948	0.529742	−	0.848159i	$-0.322289\pi$
$269$	17.3768	1.05948	0.529742	+	0.848159i	$0.322289\pi$
$270$	−2.52267	−0.153525
$271$	−11.5350	−0.700701	−0.350350	−	0.936619i	$-0.613937\pi$
$271$	−11.5350	−0.700701	−0.350350	+	0.936619i	$0.613937\pi$
$272$	−26.1328	−1.58454
$273$	−20.9633	−1.26876
$274$	−30.1752	−1.82295
$275$	−4.01184	−0.241923
$276$	24.0372	1.44687
$277$	−11.7386	−0.705307	−0.352653	−	0.935754i	$-0.614721\pi$
$277$	−11.7386	−0.705307	−0.352653	+	0.935754i	$0.614721\pi$
$278$	10.1353	0.607877
$279$	−6.92787	−0.414761
$280$	30.0786	1.79754
$281$	7.78483	0.464404	0.232202	−	0.972668i	$-0.425407\pi$
$281$	7.78483	0.464404	0.232202	+	0.972668i	$0.425407\pi$
$282$	−21.0016	−1.25063
$283$	−24.6554	−1.46561	−0.732806	−	0.680438i	$-0.761790\pi$
$283$	−24.6554	−1.46561	−0.732806	+	0.680438i	$0.761790\pi$
$284$	20.9990	1.24606
$285$	2.91370	0.172593
$286$	10.8871	0.643766
$287$	−22.7754	−1.34439
$288$	4.95859	0.292188
$289$	−2.37783	−0.139873
$290$	−5.82777	−0.342219
$291$	−11.3016	−0.662513
$292$	70.8150	4.14413
$293$	−13.4592	−0.786297	−0.393149	−	0.919475i	$-0.628614\pi$
$293$	−13.4592	−0.786297	−0.393149	+	0.919475i	$0.628614\pi$
$294$	−42.8306	−2.49793
$295$	5.08994	0.296348
$296$	5.88114	0.341835
$297$	−1.00000	−0.0580259
$298$	46.4118	2.68856
$299$	−23.2252	−1.34315
$300$	17.8128	1.02842
$301$	20.6862	1.19233
$302$	28.6131	1.64650
$303$	6.79683	0.390467
$304$	−20.0314	−1.14888
$305$	−0.994065	−0.0569200
$306$	−9.70401	−0.554741
$307$	15.7969	0.901579	0.450789	−	0.892630i	$-0.351143\pi$
$307$	15.7969	0.901579	0.450789	+	0.892630i	$0.351143\pi$
$308$	21.6962	1.23626
$309$	−12.1574	−0.691610
$310$	−17.4767	−0.992611
$311$	20.8528	1.18246	0.591228	−	0.806504i	$-0.298643\pi$
$311$	20.8528	1.18246	0.591228	+	0.806504i	$0.298643\pi$
$312$	−26.5652	−1.50396
$313$	7.74049	0.437518	0.218759	−	0.975779i	$-0.429799\pi$
$313$	7.74049	0.437518	0.218759	+	0.975779i	$0.429799\pi$
$314$	−42.3351	−2.38911
$315$	4.85746	0.273687
$316$	−29.5211	−1.66069
$317$	3.37084	0.189325	0.0946627	−	0.995509i	$-0.469823\pi$
$317$	3.37084	0.189325	0.0946627	+	0.995509i	$0.469823\pi$
$318$	29.2662	1.64117
$319$	−2.31016	−0.129344
$320$	−1.07818	−0.0602719
$321$	−3.63314	−0.202782
$322$	−67.1328	−3.74116
$323$	11.2082	0.623642
$324$	4.44007	0.246671
$325$	−17.2111	−0.954700
$326$	26.5638	1.47123
$327$	−4.81079	−0.266037
$328$	−28.8615	−1.59361
$329$	40.4391	2.22948
$330$	−2.52267	−0.138868
$331$	11.3276	0.622622	0.311311	−	0.950308i	$-0.399232\pi$
$331$	11.3276	0.622622	0.311311	+	0.950308i	$0.399232\pi$
$332$	−38.9910	−2.13991
$333$	0.949760	0.0520465
$334$	−53.3288	−2.91802
$335$	−6.79355	−0.371172
$336$	−33.3945	−1.82182
$337$	27.5129	1.49872	0.749362	−	0.662161i	$-0.230360\pi$
$337$	27.5129	1.49872	0.749362	+	0.662161i	$0.230360\pi$
$338$	13.7159	0.746049
$339$	4.35919	0.236758
$340$	−16.8776	−0.915316
$341$	−6.92787	−0.375165
$342$	−7.43834	−0.402219
$343$	48.2662	2.60613
$344$	26.2140	1.41337
$345$	5.38157	0.289734
$346$	8.17145	0.439300
$347$	−7.46395	−0.400686	−0.200343	−	0.979726i	$-0.564206\pi$
$347$	−7.46395	−0.400686	−0.200343	+	0.979726i	$0.564206\pi$
$348$	10.2573	0.549848
$349$	−8.64667	−0.462845	−0.231423	−	0.972853i	$-0.574338\pi$
$349$	−8.64667	−0.462845	−0.231423	+	0.972853i	$0.574338\pi$
$350$	−49.7489	−2.65919
$351$	−4.29008	−0.228988
$352$	4.95859	0.264294
$353$	33.8131	1.79969	0.899845	−	0.436210i	$-0.143680\pi$
$353$	33.8131	1.79969	0.899845	+	0.436210i	$0.143680\pi$
$354$	−12.9940	−0.690624
$355$	4.70136	0.249522
$356$	0.293309	0.0155454
$357$	18.6853	0.988932
$358$	−18.4518	−0.975209
$359$	4.96562	0.262076	0.131038	−	0.991377i	$-0.458169\pi$
$359$	4.96562	0.262076	0.131038	+	0.991377i	$0.458169\pi$
$360$	6.15549	0.324423
$361$	−10.4087	−0.547824
$362$	34.0514	1.78970
$363$	−1.00000	−0.0524864
$364$	93.0787	4.87865
$365$	15.8544	0.829857
$366$	2.53773	0.132649
$367$	28.2934	1.47690	0.738451	−	0.674307i	$-0.235558\pi$
$367$	28.2934	1.47690	0.738451	+	0.674307i	$0.235558\pi$
$368$	−36.9978	−1.92864
$369$	−4.66091	−0.242637
$370$	2.39593	0.124558
$371$	−56.3528	−2.92569
$372$	30.7602	1.59484
$373$	−18.5022	−0.958007	−0.479003	−	0.877813i	$-0.659002\pi$
$373$	−18.5022	−0.958007	−0.479003	+	0.877813i	$0.659002\pi$
$374$	−9.70401	−0.501782
$375$	8.95835	0.462607
$376$	51.2454	2.64278
$377$	−9.91079	−0.510432
$378$	−12.4005	−0.637814
$379$	10.1763	0.522721	0.261361	−	0.965241i	$-0.415829\pi$
$379$	10.1763	0.522721	0.261361	+	0.965241i	$0.415829\pi$
$380$	−12.9371	−0.663657
$381$	20.5780	1.05424
$382$	41.1499	2.10541
$383$	−18.0563	−0.922634	−0.461317	−	0.887235i	$-0.652623\pi$
$383$	−18.0563	−0.922634	−0.461317	+	0.887235i	$0.652623\pi$
$384$	12.6696	0.646545
$385$	4.85746	0.247559
$386$	39.2804	1.99932
$387$	4.23337	0.215194
$388$	50.1801	2.54751
$389$	12.9240	0.655271	0.327636	−	0.944804i	$-0.393748\pi$
$389$	12.9240	0.655271	0.327636	+	0.944804i	$0.393748\pi$
$390$	−10.8225	−0.548016
$391$	20.7014	1.04692
$392$	104.510	5.27854
$393$	−8.91370	−0.449637
$394$	−45.0091	−2.26753
$395$	−6.60932	−0.332551
$396$	4.44007	0.223122
$397$	25.2642	1.26798	0.633988	−	0.773343i	$-0.281417\pi$
$397$	25.2642	1.26798	0.633988	+	0.773343i	$0.281417\pi$
$398$	−6.16460	−0.309004
$399$	14.3227	0.717033
$400$	−27.4173	−1.37086
$401$	−33.4265	−1.66924	−0.834620	−	0.550826i	$-0.814313\pi$
$401$	−33.4265	−1.66924	−0.834620	+	0.550826i	$0.814313\pi$
$402$	17.3431	0.864997
$403$	−29.7211	−1.48052
$404$	−30.1784	−1.50143
$405$	0.994065	0.0493955
$406$	−28.6472	−1.42174
$407$	0.949760	0.0470779
$408$	23.6785	1.17226
$409$	−3.25363	−0.160882	−0.0804408	−	0.996759i	$-0.525633\pi$
$409$	−3.25363	−0.160882	−0.0804408	+	0.996759i	$0.525633\pi$
$410$	−11.7579	−0.580683
$411$	11.8906	0.586522
$412$	53.9797	2.65939
$413$	25.0203	1.23117
$414$	−13.7385	−0.675212
$415$	−8.72948	−0.428513
$416$	21.2728	1.04298
$417$	−3.99386	−0.195580
$418$	−7.43834	−0.363821
$419$	−35.2785	−1.72347	−0.861735	−	0.507359i	$-0.830622\pi$
$419$	−35.2785	−1.72347	−0.861735	+	0.507359i	$0.830622\pi$
$420$	−21.5675	−1.05239
$421$	7.26689	0.354167	0.177083	−	0.984196i	$-0.443334\pi$
$421$	7.26689	0.354167	0.177083	+	0.984196i	$0.443334\pi$
$422$	−59.5904	−2.90081
$423$	8.27575	0.402381
$424$	−71.4116	−3.46806
$425$	15.3408	0.744140
$426$	−12.0020	−0.581500
$427$	−4.88646	−0.236473
$428$	16.1314	0.779740
$429$	−4.29008	−0.207127
$430$	10.6794	0.515005
$431$	−7.77524	−0.374520	−0.187260	−	0.982310i	$-0.559961\pi$
$431$	−7.77524	−0.374520	−0.187260	+	0.982310i	$0.559961\pi$
$432$	−6.83409	−0.328805
$433$	−35.7180	−1.71650	−0.858250	−	0.513232i	$-0.828448\pi$
$433$	−35.7180	−1.71650	−0.858250	+	0.513232i	$0.828448\pi$
$434$	−85.9092	−4.12378
$435$	2.29645	0.110106
$436$	21.3603	1.02297
$437$	15.8681	0.759075
$438$	−40.4744	−1.93394
$439$	15.8024	0.754205	0.377103	−	0.926172i	$-0.376920\pi$
$439$	15.8024	0.754205	0.377103	+	0.926172i	$0.376920\pi$
$440$	6.15549	0.293451
$441$	16.8775	0.803692
$442$	−41.6310	−1.98018
$443$	−2.20489	−0.104757	−0.0523787	−	0.998627i	$-0.516680\pi$
$443$	−2.20489	−0.104757	−0.0523787	+	0.998627i	$0.516680\pi$
$444$	−4.21700	−0.200130
$445$	0.0656675	0.00311294
$446$	50.2473	2.37928
$447$	−18.2887	−0.865026
$448$	−5.29993	−0.250398
$449$	−11.0478	−0.521379	−0.260690	−	0.965423i	$-0.583950\pi$
$449$	−11.0478	−0.521379	−0.260690	+	0.965423i	$0.583950\pi$
$450$	−10.1810	−0.479935
$451$	−4.66091	−0.219474
$452$	−19.3551	−0.910387
$453$	−11.2751	−0.529750
$454$	56.5169	2.65247
$455$	20.8389	0.976943
$456$	18.1501	0.849955
$457$	−32.3367	−1.51265	−0.756324	−	0.654197i	$-0.773007\pi$
$457$	−32.3367	−1.51265	−0.756324	+	0.654197i	$0.773007\pi$
$458$	11.5264	0.538593
$459$	3.82389	0.178484
$460$	−23.8946	−1.11409
$461$	−15.6990	−0.731175	−0.365587	−	0.930777i	$-0.619132\pi$
$461$	−15.6990	−0.731175	−0.365587	+	0.930777i	$0.619132\pi$
$462$	−12.4005	−0.576925
$463$	−5.21953	−0.242572	−0.121286	−	0.992618i	$-0.538702\pi$
$463$	−5.21953	−0.242572	−0.121286	+	0.992618i	$0.538702\pi$
$464$	−15.7879	−0.732933
$465$	6.88675	0.319366
$466$	−23.1065	−1.07039
$467$	38.1044	1.76326	0.881630	−	0.471941i	$-0.156446\pi$
$467$	38.1044	1.76326	0.881630	+	0.471941i	$0.156446\pi$
$468$	19.0483	0.880507
$469$	−33.3947	−1.54202
$470$	20.8770	0.962982
$471$	16.6823	0.768679
$472$	31.7063	1.45940
$473$	4.23337	0.194650
$474$	16.8728	0.774994
$475$	11.7591	0.539544
$476$	−82.9642	−3.80266
$477$	−11.5324	−0.528034
$478$	−19.4450	−0.889393
$479$	−13.9545	−0.637597	−0.318799	−	0.947822i	$-0.603279\pi$
$479$	−13.9545	−0.637597	−0.318799	+	0.947822i	$0.603279\pi$
$480$	−4.92916	−0.224984
$481$	4.07455	0.185783
$482$	−8.45475	−0.385103
$483$	26.4539	1.20369
$484$	4.44007	0.201821
$485$	11.2346	0.510135
$486$	−2.53773	−0.115114
$487$	−28.5606	−1.29421	−0.647103	−	0.762403i	$-0.724020\pi$
$487$	−28.5606	−1.29421	−0.647103	+	0.762403i	$0.724020\pi$
$488$	−6.19224	−0.280310
$489$	−10.4676	−0.473359
$490$	42.5764	1.92341
$491$	3.97165	0.179238	0.0896189	−	0.995976i	$-0.471435\pi$
$491$	3.97165	0.179238	0.0896189	+	0.995976i	$0.471435\pi$
$492$	20.6948	0.932992
$493$	8.83382	0.397855
$494$	−31.9111	−1.43575
$495$	0.994065	0.0446799
$496$	−47.3457	−2.12589
$497$	23.1102	1.03663
$498$	22.2853	0.998630
$499$	−24.1339	−1.08038	−0.540192	−	0.841542i	$-0.681648\pi$
$499$	−24.1339	−1.08038	−0.540192	+	0.841542i	$0.681648\pi$
$500$	−39.7757	−1.77882
$501$	21.0144	0.938852
$502$	73.7837	3.29313
$503$	−13.5112	−0.602433	−0.301217	−	0.953556i	$-0.597393\pi$
$503$	−13.5112	−0.602433	−0.301217	+	0.953556i	$0.597393\pi$
$504$	30.2582	1.34781
$505$	−6.75649	−0.300660
$506$	−13.7385	−0.610752
$507$	−5.40481	−0.240036
$508$	−91.3678	−4.05379
$509$	−25.6211	−1.13563	−0.567817	−	0.823155i	$-0.692212\pi$
$509$	−25.6211	−1.13563	−0.567817	+	0.823155i	$0.692212\pi$
$510$	9.64641	0.427150
$511$	77.9345	3.44762
$512$	−50.7492	−2.24282
$513$	2.93110	0.129411
$514$	−51.4901	−2.27113
$515$	12.0852	0.532539
$516$	−18.7965	−0.827468
$517$	8.27575	0.363967
$518$	11.7775	0.517475
$519$	−3.21998	−0.141342
$520$	26.4076	1.15805
$521$	1.69899	0.0744343	0.0372172	−	0.999307i	$-0.488151\pi$
$521$	1.69899	0.0744343	0.0372172	+	0.999307i	$0.488151\pi$
$522$	−5.86257	−0.256598
$523$	−6.21946	−0.271958	−0.135979	−	0.990712i	$-0.543418\pi$
$523$	−6.21946	−0.271958	−0.135979	+	0.990712i	$0.543418\pi$
$524$	39.5775	1.72895
$525$	19.6037	0.855575
$526$	82.0702	3.57843
$527$	26.4914	1.15399
$528$	−6.83409	−0.297416
$529$	6.30822	0.274271
$530$	−29.0925	−1.26370
$531$	5.12033	0.222203
$532$	−63.5939	−2.75714
$533$	−19.9957	−0.866109
$534$	−0.167641	−0.00725455
$535$	3.61157	0.156142
$536$	−42.3185	−1.82788
$537$	7.27099	0.313767
$538$	44.0977	1.90119
$539$	16.8775	0.726967
$540$	−4.41372	−0.189936
$541$	29.7950	1.28099	0.640493	−	0.767964i	$-0.278730\pi$
$541$	29.7950	1.28099	0.640493	+	0.767964i	$0.278730\pi$
$542$	−29.2727	−1.25737
$543$	−13.4180	−0.575823
$544$	−18.9611	−0.812952
$545$	4.78224	0.204849
$546$	−53.1993	−2.27672
$547$	−7.33226	−0.313505	−0.156752	−	0.987638i	$-0.550102\pi$
$547$	−7.33226	−0.313505	−0.156752	+	0.987638i	$0.550102\pi$
$548$	−52.7953	−2.25530
$549$	−1.00000	−0.0426790
$550$	−10.1810	−0.434117
$551$	6.77132	0.288468
$552$	33.5230	1.42683
$553$	−32.4890	−1.38157
$554$	−29.7895	−1.26563
$555$	−0.944123	−0.0400758
$556$	17.7330	0.752048
$557$	28.4514	1.20552	0.602762	−	0.797921i	$-0.294067\pi$
$557$	28.4514	1.20552	0.602762	+	0.797921i	$0.294067\pi$
$558$	−17.5811	−0.744266
$559$	18.1615	0.768149
$560$	33.1963	1.40280
$561$	3.82389	0.161445
$562$	19.7558	0.833348
$563$	−13.4623	−0.567369	−0.283684	−	0.958918i	$-0.591557\pi$
$563$	−13.4623	−0.567369	−0.283684	+	0.958918i	$0.591557\pi$
$564$	−36.7449	−1.54724
$565$	−4.33331	−0.182304
$566$	−62.5687	−2.62996
$567$	4.88646	0.205212
$568$	29.2858	1.22880
$569$	−9.09616	−0.381331	−0.190666	−	0.981655i	$-0.561065\pi$
$569$	−9.09616	−0.381331	−0.190666	+	0.981655i	$0.561065\pi$
$570$	7.39419	0.309709
$571$	46.0280	1.92621	0.963107	−	0.269120i	$-0.0867329\pi$
$571$	46.0280	1.92621	0.963107	+	0.269120i	$0.0867329\pi$
$572$	19.0483	0.796448
$573$	−16.2153	−0.677402
$574$	−57.7977	−2.41243
$575$	21.7189	0.905741
$576$	−1.08461	−0.0451922
$577$	−7.77431	−0.323649	−0.161824	−	0.986820i	$-0.551738\pi$
$577$	−7.77431	−0.323649	−0.161824	+	0.986820i	$0.551738\pi$
$578$	−6.03430	−0.250994
$579$	−15.4786	−0.643267
$580$	−10.1964	−0.423383
$581$	−42.9110	−1.78025
$582$	−28.6805	−1.18884
$583$	−11.5324	−0.477625
$584$	98.7605	4.08674
$585$	4.26462	0.176320
$586$	−34.1559	−1.41097
$587$	37.6111	1.55238	0.776188	−	0.630501i	$-0.217151\pi$
$587$	37.6111	1.55238	0.776188	+	0.630501i	$0.217151\pi$
$588$	−74.9374	−3.09037
$589$	20.3063	0.836706
$590$	12.9169	0.531780
$591$	17.7360	0.729560
$592$	6.49075	0.266768
$593$	24.6250	1.01123	0.505614	−	0.862760i	$-0.331266\pi$
$593$	24.6250	1.01123	0.505614	+	0.862760i	$0.331266\pi$
$594$	−2.53773	−0.104124
$595$	−18.5744	−0.761477
$596$	81.2031	3.32621
$597$	2.42918	0.0994198
$598$	−58.9394	−2.41021
$599$	−22.6718	−0.926343	−0.463171	−	0.886269i	$-0.653289\pi$
$599$	−22.6718	−0.926343	−0.463171	+	0.886269i	$0.653289\pi$
$600$	24.8423	1.01418
$601$	−29.1465	−1.18891	−0.594455	−	0.804129i	$-0.702632\pi$
$601$	−29.1465	−1.18891	−0.594455	+	0.804129i	$0.702632\pi$
$602$	52.4960	2.13958
$603$	−6.83412	−0.278307
$604$	50.0622	2.03700
$605$	0.994065	0.0404145
$606$	17.2485	0.700673
$607$	8.63031	0.350293	0.175147	−	0.984542i	$-0.443960\pi$
$607$	8.63031	0.350293	0.175147	+	0.984542i	$0.443960\pi$
$608$	−14.5341	−0.589437
$609$	11.2885	0.457434
$610$	−2.52267	−0.102140
$611$	35.5036	1.43632
$612$	−16.9784	−0.686310
$613$	−17.1543	−0.692854	−0.346427	−	0.938077i	$-0.612605\pi$
$613$	−17.1543	−0.692854	−0.346427	+	0.938077i	$0.612605\pi$
$614$	40.0884	1.61783
$615$	4.63325	0.186831
$616$	30.2582	1.21914
$617$	−43.1267	−1.73622	−0.868108	−	0.496376i	$-0.834664\pi$
$617$	−43.1267	−1.73622	−0.868108	+	0.496376i	$0.834664\pi$
$618$	−30.8522	−1.24106
$619$	−16.8162	−0.675902	−0.337951	−	0.941164i	$-0.609734\pi$
$619$	−16.8162	−0.675902	−0.337951	+	0.941164i	$0.609734\pi$
$620$	−30.5777	−1.22803
$621$	5.41371	0.217245
$622$	52.9189	2.12185
$623$	0.322798	0.0129326
$624$	−29.3188	−1.17369
$625$	11.1540	0.446160
$626$	19.6433	0.785103
$627$	2.93110	0.117057
$628$	−74.0705	−2.95574
$629$	−3.63178	−0.144809
$630$	12.3269	0.491116
$631$	37.2478	1.48281	0.741406	−	0.671057i	$-0.234160\pi$
$631$	37.2478	1.48281	0.741406	+	0.671057i	$0.234160\pi$
$632$	−41.1709	−1.63769
$633$	23.4818	0.933317
$634$	8.55429	0.339734
$635$	−20.4559	−0.811766
$636$	51.2048	2.03040
$637$	72.4060	2.86883
$638$	−5.86257	−0.232101
$639$	4.72943	0.187093
$640$	−12.5944	−0.497839
$641$	−15.9557	−0.630213	−0.315107	−	0.949056i	$-0.602040\pi$
$641$	−15.9557	−0.630213	−0.315107	+	0.949056i	$0.602040\pi$
$642$	−9.21992	−0.363881
$643$	35.2795	1.39129	0.695644	−	0.718387i	$-0.255119\pi$
$643$	35.2795	1.39129	0.695644	+	0.718387i	$0.255119\pi$
$644$	−117.457	−4.62846
$645$	−4.20824	−0.165699
$646$	28.4434	1.11909
$647$	−25.5200	−1.00329	−0.501647	−	0.865072i	$-0.667273\pi$
$647$	−25.5200	−1.00329	−0.501647	+	0.865072i	$0.667273\pi$
$648$	6.19224	0.243254
$649$	5.12033	0.200990
$650$	−43.6771	−1.71316
$651$	33.8528	1.32680
$652$	46.4767	1.82017
$653$	−3.73660	−0.146225	−0.0731123	−	0.997324i	$-0.523293\pi$
$653$	−3.73660	−0.146225	−0.0731123	+	0.997324i	$0.523293\pi$
$654$	−12.2085	−0.477390
$655$	8.86080	0.346220
$656$	−31.8531	−1.24365
$657$	15.9491	0.622232
$658$	102.624	4.00069
$659$	−13.9968	−0.545237	−0.272618	−	0.962122i	$-0.587890\pi$
$659$	−13.9968	−0.545237	−0.272618	+	0.962122i	$0.587890\pi$
$660$	−4.41372	−0.171804
$661$	16.3657	0.636551	0.318275	−	0.947998i	$-0.396896\pi$
$661$	16.3657	0.636551	0.318275	+	0.947998i	$0.396896\pi$
$662$	28.7464	1.11726
$663$	16.4048	0.637110
$664$	−54.3778	−2.11027
$665$	−14.2377	−0.552115
$666$	2.41023	0.0933947
$667$	12.5065	0.484255
$668$	−93.3053	−3.61009
$669$	−19.8001	−0.765517
$670$	−17.2402	−0.666047
$671$	−1.00000	−0.0386046
$672$	−24.2300	−0.934692
$673$	27.6477	1.06574	0.532871	−	0.846196i	$-0.321113\pi$
$673$	27.6477	1.06574	0.532871	+	0.846196i	$0.321113\pi$
$674$	69.8203	2.68938
$675$	4.01184	0.154416
$676$	23.9977	0.922989
$677$	29.5915	1.13729	0.568647	−	0.822581i	$-0.307467\pi$
$677$	29.5915	1.13729	0.568647	+	0.822581i	$0.307467\pi$
$678$	11.0624	0.424850
$679$	55.2250	2.11934
$680$	−23.5379	−0.902639
$681$	−22.2706	−0.853413
$682$	−17.5811	−0.673214
$683$	−4.11331	−0.157391	−0.0786957	−	0.996899i	$-0.525076\pi$
$683$	−4.11331	−0.157391	−0.0786957	+	0.996899i	$0.525076\pi$
$684$	−13.0143	−0.497614
$685$	−11.8201	−0.451622
$686$	122.487	4.67656
$687$	−4.54201	−0.173288
$688$	28.9312	1.10299
$689$	−49.4751	−1.88485
$690$	13.6570	0.519912
$691$	34.3281	1.30590	0.652951	−	0.757400i	$-0.273531\pi$
$691$	34.3281	1.30590	0.652951	+	0.757400i	$0.273531\pi$
$692$	14.2970	0.543489
$693$	4.88646	0.185621
$694$	−18.9415	−0.719009
$695$	3.97016	0.150597
$696$	14.3051	0.542233
$697$	17.8228	0.675088
$698$	−21.9429	−0.830551
$699$	9.10518	0.344389
$700$	−87.0418	−3.28987
$701$	−3.38074	−0.127689	−0.0638443	−	0.997960i	$-0.520336\pi$
$701$	−3.38074	−0.127689	−0.0638443	+	0.997960i	$0.520336\pi$
$702$	−10.8871	−0.410906
$703$	−2.78384	−0.104995
$704$	−1.08461	−0.0408779
$705$	−8.22663	−0.309833
$706$	85.8085	3.22945
$707$	−33.2124	−1.24908
$708$	−22.7346	−0.854419
$709$	28.0573	1.05371	0.526856	−	0.849954i	$-0.323371\pi$
$709$	28.0573	1.05371	0.526856	+	0.849954i	$0.323371\pi$
$710$	11.9308	0.447754
$711$	−6.64878	−0.249349
$712$	0.409057	0.0153301
$713$	37.5055	1.40459
$714$	47.4183	1.77458
$715$	4.26462	0.159488
$716$	−32.2837	−1.20650
$717$	7.66236	0.286156
$718$	12.6014	0.470280
$719$	0.0861753	0.00321380	0.00160690	−	0.999999i	$-0.499489\pi$
$719$	0.0861753	0.00321380	0.00160690	+	0.999999i	$0.499489\pi$
$720$	6.79353	0.253180
$721$	59.4067	2.21242
$722$	−26.4143	−0.983040
$723$	3.33162	0.123904
$724$	59.5771	2.21416
$725$	9.26799	0.344205
$726$	−2.53773	−0.0941840
$727$	−12.6578	−0.469453	−0.234727	−	0.972061i	$-0.575419\pi$
$727$	−12.6578	−0.469453	−0.234727	+	0.972061i	$0.575419\pi$
$728$	129.810	4.81108
$729$	1.00000	0.0370370
$730$	40.2342	1.48913
$731$	−16.1880	−0.598733
$732$	4.44007	0.164110
$733$	25.0980	0.927016	0.463508	−	0.886093i	$-0.346591\pi$
$733$	25.0980	0.927016	0.463508	+	0.886093i	$0.346591\pi$
$734$	71.8009	2.65022
$735$	−16.7774	−0.618842
$736$	−26.8444	−0.989497
$737$	−6.83412	−0.251738
$738$	−11.8281	−0.435399
$739$	31.4481	1.15684	0.578419	−	0.815740i	$-0.303670\pi$
$739$	31.4481	1.15684	0.578419	+	0.815740i	$0.303670\pi$
$740$	4.19197	0.154100
$741$	12.5747	0.461942
$742$	−143.008	−5.25000
$743$	2.21453	0.0812431	0.0406215	−	0.999175i	$-0.487066\pi$
$743$	2.21453	0.0812431	0.0406215	+	0.999175i	$0.487066\pi$
$744$	42.8991	1.57276
$745$	18.1802	0.666069
$746$	−46.9535	−1.71909
$747$	−8.78161	−0.321302
$748$	−16.9784	−0.620790
$749$	17.7532	0.648688
$750$	22.7339	0.830123
$751$	34.7061	1.26644	0.633222	−	0.773970i	$-0.281732\pi$
$751$	34.7061	1.26644	0.633222	+	0.773970i	$0.281732\pi$
$752$	56.5572	2.06243
$753$	−29.0747	−1.05954
$754$	−25.1509	−0.915942
$755$	11.2082	0.407907
$756$	−21.6962	−0.789085
$757$	−23.4680	−0.852960	−0.426480	−	0.904497i	$-0.640247\pi$
$757$	−23.4680	−0.852960	−0.426480	+	0.904497i	$0.640247\pi$
$758$	25.8247	0.937995
$759$	5.41371	0.196505
$760$	−18.0424	−0.654465
$761$	−5.93914	−0.215294	−0.107647	−	0.994189i	$-0.534332\pi$
$761$	−5.93914	−0.215294	−0.107647	+	0.994189i	$0.534332\pi$
$762$	52.2214	1.89178
$763$	23.5078	0.851038
$764$	71.9969	2.60476
$765$	−3.80120	−0.137433
$766$	−45.8220	−1.65562
$767$	21.9666	0.793169
$768$	29.9829	1.08191
$769$	−4.29907	−0.155028	−0.0775142	−	0.996991i	$-0.524698\pi$
$769$	−4.29907	−0.155028	−0.0775142	+	0.996991i	$0.524698\pi$
$770$	12.3269	0.444231
$771$	20.2898	0.730720
$772$	68.7260	2.47350
$773$	−19.6190	−0.705646	−0.352823	−	0.935690i	$-0.614778\pi$
$773$	−19.6190	−0.705646	−0.352823	+	0.935690i	$0.614778\pi$
$774$	10.7431	0.386154
$775$	27.7935	0.998371
$776$	69.9824	2.51222
$777$	−4.64097	−0.166494
$778$	32.7975	1.17585
$779$	13.6616	0.489477
$780$	−18.9352	−0.677989
$781$	4.72943	0.169232
$782$	52.5347	1.87864
$783$	2.31016	0.0825585
$784$	115.343	4.11938
$785$	−16.5833	−0.591882
$786$	−22.6206	−0.806849
$787$	−19.9085	−0.709662	−0.354831	−	0.934931i	$-0.615462\pi$
$787$	−19.9085	−0.709662	−0.354831	+	0.934931i	$0.615462\pi$
$788$	−78.7490	−2.80532
$789$	−32.3400	−1.15133
$790$	−16.7727	−0.596744
$791$	−21.3010	−0.757376
$792$	6.19224	0.220032
$793$	−4.29008	−0.152345
$794$	64.1138	2.27531
$795$	11.4640	0.406586
$796$	−10.7857	−0.382290
$797$	−31.1383	−1.10298	−0.551488	−	0.834183i	$-0.685940\pi$
$797$	−31.1383	−1.10298	−0.551488	+	0.834183i	$0.685940\pi$
$798$	36.3472	1.28668
$799$	−31.6456	−1.11954
$800$	−19.8931	−0.703326
$801$	0.0660596	0.00233410
$802$	−84.8274	−2.99536
$803$	15.9491	0.562830
$804$	30.3440	1.07015
$805$	−26.2969	−0.926843
$806$	−75.4242	−2.65670
$807$	−17.3768	−0.611694
$808$	−42.0876	−1.48064
$809$	28.9916	1.01929	0.509645	−	0.860385i	$-0.329777\pi$
$809$	28.9916	1.01929	0.509645	+	0.860385i	$0.329777\pi$
$810$	2.52267	0.0886375
$811$	52.5821	1.84641	0.923204	−	0.384309i	$-0.125560\pi$
$811$	52.5821	1.84641	0.923204	+	0.384309i	$0.125560\pi$
$812$	−50.1219	−1.75893
$813$	11.5350	0.404550
$814$	2.41023	0.0844787
$815$	10.4054	0.364486
$816$	26.1328	0.914832
$817$	−12.4084	−0.434116
$818$	−8.25684	−0.288693
$819$	20.9633	0.732518
$820$	−20.5719	−0.718403
$821$	−3.62268	−0.126432	−0.0632162	−	0.998000i	$-0.520136\pi$
$821$	−3.62268	−0.126432	−0.0632162	+	0.998000i	$0.520136\pi$
$822$	30.1752	1.05248
$823$	52.2870	1.82261	0.911306	−	0.411730i	$-0.135075\pi$
$823$	52.2870	1.82261	0.911306	+	0.411730i	$0.135075\pi$
$824$	75.2815	2.62256
$825$	4.01184	0.139674
$826$	63.4947	2.20926
$827$	−21.6441	−0.752637	−0.376319	−	0.926490i	$-0.622810\pi$
$827$	−21.6441	−0.752637	−0.376319	+	0.926490i	$0.622810\pi$
$828$	−24.0372	−0.835352
$829$	23.1504	0.804048	0.402024	−	0.915629i	$-0.368307\pi$
$829$	23.1504	0.804048	0.402024	+	0.915629i	$0.368307\pi$
$830$	−22.1531	−0.768944
$831$	11.7386	0.407209
$832$	−4.65308	−0.161317
$833$	−64.5379	−2.23611
$834$	−10.1353	−0.350958
$835$	−20.8896	−0.722916
$836$	−13.0143	−0.450109
$837$	6.92787	0.239462
$838$	−89.5274	−3.09267
$839$	45.0573	1.55555	0.777776	−	0.628541i	$-0.216348\pi$
$839$	45.0573	1.55555	0.777776	+	0.628541i	$0.216348\pi$
$840$	−30.0786	−1.03781
$841$	−23.6631	−0.815971
$842$	18.4414	0.635533
$843$	−7.78483	−0.268124
$844$	−104.261	−3.58880
$845$	5.37273	0.184827
$846$	21.0016	0.722050
$847$	4.88646	0.167901
$848$	−78.8137	−2.70647
$849$	24.6554	0.846171
$850$	38.9309	1.33532
$851$	−5.14172	−0.176256
$852$	−20.9990	−0.719414
$853$	−25.4763	−0.872291	−0.436146	−	0.899876i	$-0.643657\pi$
$853$	−25.4763	−0.872291	−0.436146	+	0.899876i	$0.643657\pi$
$854$	−12.4005	−0.424337
$855$	−2.91370	−0.0996466
$856$	22.4973	0.768941
$857$	−19.0519	−0.650802	−0.325401	−	0.945576i	$-0.605499\pi$
$857$	−19.0519	−0.650802	−0.325401	+	0.945576i	$0.605499\pi$
$858$	−10.8871	−0.371678
$859$	−0.566950	−0.0193441	−0.00967204	−	0.999953i	$-0.503079\pi$
$859$	−0.566950	−0.0193441	−0.00967204	+	0.999953i	$0.503079\pi$
$860$	18.6849	0.637150
$861$	22.7754	0.776183
$862$	−19.7315	−0.672056
$863$	5.04043	0.171578	0.0857891	−	0.996313i	$-0.472659\pi$
$863$	5.04043	0.171578	0.0857891	+	0.996313i	$0.472659\pi$
$864$	−4.95859	−0.168695
$865$	3.20087	0.108833
$866$	−90.6427	−3.08017
$867$	2.37783	0.0807555
$868$	−150.309	−5.10181
$869$	−6.64878	−0.225544
$870$	5.82777	0.197580
$871$	−29.3189	−0.993434
$872$	29.7896	1.00880
$873$	11.3016	0.382502
$874$	40.2690	1.36212
$875$	−43.7746	−1.47985
$876$	−70.8150	−2.39262
$877$	21.1269	0.713406	0.356703	−	0.934218i	$-0.383901\pi$
$877$	21.1269	0.713406	0.356703	+	0.934218i	$0.383901\pi$
$878$	40.1021	1.35338
$879$	13.4592	0.453969
$880$	6.79353	0.229010
$881$	−43.4917	−1.46527	−0.732635	−	0.680621i	$-0.761710\pi$
$881$	−43.4917	−1.46527	−0.732635	+	0.680621i	$0.761710\pi$
$882$	42.8306	1.44218
$883$	−11.2005	−0.376925	−0.188463	−	0.982080i	$-0.560350\pi$
$883$	−11.2005	−0.376925	−0.188463	+	0.982080i	$0.560350\pi$
$884$	−72.8386	−2.44983
$885$	−5.08994	−0.171096
$886$	−5.59541	−0.187981
$887$	−36.9615	−1.24105	−0.620523	−	0.784188i	$-0.713080\pi$
$887$	−36.9615	−1.24105	−0.620523	+	0.784188i	$0.713080\pi$
$888$	−5.88114	−0.197358
$889$	−100.554	−3.37246
$890$	0.166646	0.00558600
$891$	1.00000	0.0335013
$892$	87.9139	2.94358
$893$	−24.2571	−0.811731
$894$	−46.4118	−1.55224
$895$	−7.22784	−0.241600
$896$	−61.9098	−2.06826
$897$	23.2252	0.775468
$898$	−28.0364	−0.935587
$899$	16.0045	0.533780
$900$	−17.8128	−0.593761
$901$	44.0988	1.46914
$902$	−11.8281	−0.393834
$903$	−20.6862	−0.688394
$904$	−26.9931	−0.897778
$905$	13.3384	0.443384
$906$	−28.6131	−0.950608
$907$	52.8559	1.75505	0.877526	−	0.479529i	$-0.159193\pi$
$907$	52.8559	1.75505	0.877526	+	0.479529i	$0.159193\pi$
$908$	98.8832	3.28155
$909$	−6.79683	−0.225437
$910$	52.8835	1.75307
$911$	−6.97550	−0.231109	−0.115554	−	0.993301i	$-0.536864\pi$
$911$	−6.97550	−0.231109	−0.115554	+	0.993301i	$0.536864\pi$
$912$	20.0314	0.663306
$913$	−8.78161	−0.290629
$914$	−82.0619	−2.71437
$915$	0.994065	0.0328628
$916$	20.1668	0.666331
$917$	43.5565	1.43836
$918$	9.70401	0.320280
$919$	−33.6287	−1.10931	−0.554655	−	0.832081i	$-0.687150\pi$
$919$	−33.6287	−1.10931	−0.554655	+	0.832081i	$0.687150\pi$
$920$	−33.3240	−1.09866
$921$	−15.7969	−0.520527
$922$	−39.8398	−1.31205
$923$	20.2897	0.667842
$924$	−21.6962	−0.713754
$925$	−3.81028	−0.125281
$926$	−13.2458	−0.435282
$927$	12.1574	0.399301
$928$	−11.4552	−0.376034
$929$	−6.54384	−0.214696	−0.107348	−	0.994221i	$-0.534236\pi$
$929$	−6.54384	−0.214696	−0.107348	+	0.994221i	$0.534236\pi$
$930$	17.4767	0.573084
$931$	−49.4697	−1.62131
$932$	−40.4276	−1.32425
$933$	−20.8528	−0.682691
$934$	96.6986	3.16408
$935$	−3.80120	−0.124312
$936$	26.5652	0.868312
$937$	−35.2517	−1.15162	−0.575811	−	0.817583i	$-0.695314\pi$
$937$	−35.2517	−1.15162	−0.575811	+	0.817583i	$0.695314\pi$
$938$	−84.7466	−2.76708
$939$	−7.74049	−0.252601
$940$	36.5268	1.19137
$941$	2.92372	0.0953107	0.0476553	−	0.998864i	$-0.484825\pi$
$941$	2.92372	0.0953107	0.0476553	+	0.998864i	$0.484825\pi$
$942$	42.3351	1.37935
$943$	25.2328	0.821693
$944$	34.9928	1.13892
$945$	−4.85746	−0.158013
$946$	10.7431	0.349290
$947$	−23.8069	−0.773621	−0.386811	−	0.922159i	$-0.626423\pi$
$947$	−23.8069	−0.773621	−0.386811	+	0.922159i	$0.626423\pi$
$948$	29.5211	0.958799
$949$	68.4228	2.22110
$950$	29.8414	0.968183
$951$	−3.37084	−0.109307
$952$	−115.704	−3.74999
$953$	−43.2272	−1.40027	−0.700133	−	0.714012i	$-0.746876\pi$
$953$	−43.2272	−1.40027	−0.700133	+	0.714012i	$0.746876\pi$
$954$	−29.2662	−0.947528
$955$	16.1190	0.521599
$956$	−34.0214	−1.10033
$957$	2.31016	0.0746769
$958$	−35.4127	−1.14413
$959$	−58.1032	−1.87625
$960$	1.07818	0.0347980
$961$	16.9954	0.548239
$962$	10.3401	0.333378
$963$	3.63314	0.117076
$964$	−14.7926	−0.476438
$965$	15.3867	0.495315
$966$	67.1328	2.15996
$967$	−4.95474	−0.159334	−0.0796669	−	0.996822i	$-0.525386\pi$
$967$	−4.95474	−0.159334	−0.0796669	+	0.996822i	$0.525386\pi$
$968$	6.19224	0.199026
$969$	−11.2082	−0.360060
$970$	28.5103	0.915409
$971$	59.7469	1.91737	0.958685	−	0.284471i	$-0.0918181\pi$
$971$	59.7469	1.91737	0.958685	+	0.284471i	$0.0918181\pi$
$972$	−4.44007	−0.142415
$973$	19.5159	0.625650
$974$	−72.4791	−2.32238
$975$	17.2111	0.551196
$976$	−6.83409	−0.218754
$977$	−34.4068	−1.10077	−0.550386	−	0.834911i	$-0.685519\pi$
$977$	−34.4068	−1.10077	−0.550386	+	0.834911i	$0.685519\pi$
$978$	−26.5638	−0.849417
$979$	0.0660596	0.00211127
$980$	74.4927	2.37958
$981$	4.81079	0.153597
$982$	10.0790	0.321633
$983$	−25.9260	−0.826912	−0.413456	−	0.910524i	$-0.635679\pi$
$983$	−25.9260	−0.826912	−0.413456	+	0.910524i	$0.635679\pi$
$984$	28.8615	0.920070
$985$	−17.6307	−0.561761
$986$	22.4178	0.713929
$987$	−40.4391	−1.28719
$988$	−55.8324	−1.77627
$989$	−22.9182	−0.728757
$990$	2.52267	0.0801756
$991$	−43.2573	−1.37411	−0.687057	−	0.726604i	$-0.741098\pi$
$991$	−43.2573	−1.37411	−0.687057	+	0.726604i	$0.741098\pi$
$992$	−34.3525	−1.09069
$993$	−11.3276	−0.359471
$994$	58.6474	1.86018
$995$	−2.41476	−0.0765531
$996$	38.9910	1.23548
$997$	4.53605	0.143658	0.0718291	−	0.997417i	$-0.477116\pi$
$997$	4.53605	0.143658	0.0718291	+	0.997417i	$0.477116\pi$
$998$	−61.2454	−1.93869
$999$	−0.949760	−0.0300491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.12	✓	13
3.2	odd	2		6039.2.a.i.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.12	✓	13	1.1	even	1	trivial
6039.2.a.i.1.2		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)

\(f(q)\)	\(=\)	\(q+2.53773 q^{2} -1.00000 q^{3} +4.44007 q^{4} +0.994065 q^{5} -2.53773 q^{6} +4.88646 q^{7} +6.19224 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.53773 q^{2} -1.00000 q^{3} +4.44007 q^{4} +0.994065 q^{5} -2.53773 q^{6} +4.88646 q^{7} +6.19224 q^{8} +1.00000 q^{9} +2.52267 q^{10} +1.00000 q^{11} -4.44007 q^{12} +4.29008 q^{13} +12.4005 q^{14} -0.994065 q^{15} +6.83409 q^{16} -3.82389 q^{17} +2.53773 q^{18} -2.93110 q^{19} +4.41372 q^{20} -4.88646 q^{21} +2.53773 q^{22} -5.41371 q^{23} -6.19224 q^{24} -4.01184 q^{25} +10.8871 q^{26} -1.00000 q^{27} +21.6962 q^{28} -2.31016 q^{29} -2.52267 q^{30} -6.92787 q^{31} +4.95859 q^{32} -1.00000 q^{33} -9.70401 q^{34} +4.85746 q^{35} +4.44007 q^{36} +0.949760 q^{37} -7.43834 q^{38} -4.29008 q^{39} +6.15549 q^{40} -4.66091 q^{41} -12.4005 q^{42} +4.23337 q^{43} +4.44007 q^{44} +0.994065 q^{45} -13.7385 q^{46} +8.27575 q^{47} -6.83409 q^{48} +16.8775 q^{49} -10.1810 q^{50} +3.82389 q^{51} +19.0483 q^{52} -11.5324 q^{53} -2.53773 q^{54} +0.994065 q^{55} +30.2582 q^{56} +2.93110 q^{57} -5.86257 q^{58} +5.12033 q^{59} -4.41372 q^{60} -1.00000 q^{61} -17.5811 q^{62} +4.88646 q^{63} -1.08461 q^{64} +4.26462 q^{65} -2.53773 q^{66} -6.83412 q^{67} -16.9784 q^{68} +5.41371 q^{69} +12.3269 q^{70} +4.72943 q^{71} +6.19224 q^{72} +15.9491 q^{73} +2.41023 q^{74} +4.01184 q^{75} -13.0143 q^{76} +4.88646 q^{77} -10.8871 q^{78} -6.64878 q^{79} +6.79353 q^{80} +1.00000 q^{81} -11.8281 q^{82} -8.78161 q^{83} -21.6962 q^{84} -3.80120 q^{85} +10.7431 q^{86} +2.31016 q^{87} +6.19224 q^{88} +0.0660596 q^{89} +2.52267 q^{90} +20.9633 q^{91} -24.0372 q^{92} +6.92787 q^{93} +21.0016 q^{94} -2.91370 q^{95} -4.95859 q^{96} +11.3016 q^{97} +42.8306 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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