LMFDB - Embedded newform 5239.2.a.m.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 19 x^{15} + 90 x^{14} + 116 x^{13} - 776 x^{12} - 146 x^{11} + 3232 x^{10} + \cdots - 1 $ x^17 - 4x^16 - 19x^15 + 90x^14 + 116x^13 - 776x^12 - 146x^11 + 3232x^10 - 995x^9 - 6763x^8 + 3668x^7 + 6782x^6 - 4160x^5 - 2876x^4 + 1449x^3 + 392x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.182983$ of defining polynomial
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.182983 q^{2} -1.75533 q^{3} -1.96652 q^{4} -3.62872 q^{5} -0.321197 q^{6} -3.69449 q^{7} -0.725806 q^{8} +0.0811940 q^{9} +O(q^{10})$	\(q+0.182983 q^{2} -1.75533 q^{3} -1.96652 q^{4} -3.62872 q^{5} -0.321197 q^{6} -3.69449 q^{7} -0.725806 q^{8} +0.0811940 q^{9} -0.663994 q^{10} -6.06887 q^{11} +3.45189 q^{12} -0.676030 q^{14} +6.36961 q^{15} +3.80022 q^{16} -5.58543 q^{17} +0.0148572 q^{18} +0.655112 q^{19} +7.13593 q^{20} +6.48506 q^{21} -1.11050 q^{22} +3.67741 q^{23} +1.27403 q^{24} +8.16758 q^{25} +5.12348 q^{27} +7.26528 q^{28} +0.0957801 q^{29} +1.16553 q^{30} -1.00000 q^{31} +2.14699 q^{32} +10.6529 q^{33} -1.02204 q^{34} +13.4063 q^{35} -0.159669 q^{36} -5.04992 q^{37} +0.119875 q^{38} +2.63375 q^{40} -4.04773 q^{41} +1.18666 q^{42} +10.6868 q^{43} +11.9345 q^{44} -0.294630 q^{45} +0.672904 q^{46} -8.90265 q^{47} -6.67066 q^{48} +6.64925 q^{49} +1.49453 q^{50} +9.80430 q^{51} +1.86810 q^{53} +0.937510 q^{54} +22.0222 q^{55} +2.68148 q^{56} -1.14994 q^{57} +0.0175262 q^{58} -3.27713 q^{59} -12.5259 q^{60} -4.52127 q^{61} -0.182983 q^{62} -0.299970 q^{63} -7.20758 q^{64} +1.94930 q^{66} -1.84876 q^{67} +10.9839 q^{68} -6.45508 q^{69} +2.45312 q^{70} +10.5275 q^{71} -0.0589311 q^{72} +12.6192 q^{73} -0.924052 q^{74} -14.3368 q^{75} -1.28829 q^{76} +22.4214 q^{77} -16.9523 q^{79} -13.7899 q^{80} -9.23699 q^{81} -0.740668 q^{82} -12.3567 q^{83} -12.7530 q^{84} +20.2680 q^{85} +1.95550 q^{86} -0.168126 q^{87} +4.40482 q^{88} +3.79668 q^{89} -0.0539124 q^{90} -7.23169 q^{92} +1.75533 q^{93} -1.62904 q^{94} -2.37722 q^{95} -3.76868 q^{96} +10.1945 q^{97} +1.21670 q^{98} -0.492756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.182983	0.129389	0.0646944	−	0.997905i	$-0.479393\pi$
$2$	0.182983	0.129389	0.0646944	+	0.997905i	$0.479393\pi$
$3$	−1.75533	−1.01344	−0.506721	−	0.862110i	$-0.669143\pi$
$3$	−1.75533	−1.01344	−0.506721	+	0.862110i	$0.669143\pi$
$4$	−1.96652	−0.983259
$5$	−3.62872	−1.62281	−0.811406	−	0.584483i	$-0.801297\pi$
$5$	−3.62872	−1.62281	−0.811406	+	0.584483i	$0.801297\pi$
$6$	−0.321197	−0.131128
$7$	−3.69449	−1.39639	−0.698193	−	0.715910i	$-0.746012\pi$
$7$	−3.69449	−1.39639	−0.698193	+	0.715910i	$0.746012\pi$
$8$	−0.725806	−0.256611
$9$	0.0811940	0.0270647
$10$	−0.663994	−0.209973
$11$	−6.06887	−1.82983	−0.914917	−	0.403643i	$-0.867744\pi$
$11$	−6.06887	−1.82983	−0.914917	+	0.403643i	$0.867744\pi$
$12$	3.45189	0.996476
$13$	0	0
$13$	0	0
$14$	−0.676030	−0.180677
$15$	6.36961	1.64463
$16$	3.80022	0.950056
$17$	−5.58543	−1.35467	−0.677333	−	0.735676i	$-0.736865\pi$
$17$	−5.58543	−1.35467	−0.677333	+	0.735676i	$0.736865\pi$
$18$	0.0148572	0.00350186
$19$	0.655112	0.150293	0.0751465	−	0.997173i	$-0.476058\pi$
$19$	0.655112	0.150293	0.0751465	+	0.997173i	$0.476058\pi$
$20$	7.13593	1.59564
$21$	6.48506	1.41516
$22$	−1.11050	−0.236760
$23$	3.67741	0.766793	0.383396	−	0.923584i	$-0.374754\pi$
$23$	3.67741	0.766793	0.383396	+	0.923584i	$0.374754\pi$
$24$	1.27403	0.260061
$25$	8.16758	1.63352
$26$	0	0
$27$	5.12348	0.986014
$28$	7.26528	1.37301
$29$	0.0957801	0.0177859	0.00889296	−	0.999960i	$-0.497169\pi$
$29$	0.0957801	0.0177859	0.00889296	+	0.999960i	$0.497169\pi$
$30$	1.16553	0.212796
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.14699	0.379538
$33$	10.6529	1.85443
$34$	−1.02204	−0.175279
$35$	13.4063	2.26607
$36$	−0.159669	−0.0266116
$37$	−5.04992	−0.830202	−0.415101	−	0.909775i	$-0.636254\pi$
$37$	−5.04992	−0.830202	−0.415101	+	0.909775i	$0.636254\pi$
$38$	0.119875	0.0194462
$39$	0	0
$40$	2.63375	0.416432
$41$	−4.04773	−0.632150	−0.316075	−	0.948734i	$-0.602365\pi$
$41$	−4.04773	−0.632150	−0.316075	+	0.948734i	$0.602365\pi$
$42$	1.18666	0.183105
$43$	10.6868	1.62972	0.814860	−	0.579658i	$-0.196814\pi$
$43$	10.6868	1.62972	0.814860	+	0.579658i	$0.196814\pi$
$44$	11.9345	1.79920
$45$	−0.294630	−0.0439209
$46$	0.672904	0.0992143
$47$	−8.90265	−1.29859	−0.649293	−	0.760539i	$-0.724935\pi$
$47$	−8.90265	−1.29859	−0.649293	+	0.760539i	$0.724935\pi$
$48$	−6.67066	−0.962827
$49$	6.64925	0.949893
$50$	1.49453	0.211359
$51$	9.80430	1.37288
$52$	0	0
$53$	1.86810	0.256604	0.128302	−	0.991735i	$-0.459047\pi$
$53$	1.86810	0.256604	0.128302	+	0.991735i	$0.459047\pi$
$54$	0.937510	0.127579
$55$	22.0222	2.96947
$56$	2.68148	0.358328
$57$	−1.14994	−0.152313
$58$	0.0175262	0.00230130
$59$	−3.27713	−0.426646	−0.213323	−	0.976982i	$-0.568429\pi$
$59$	−3.27713	−0.426646	−0.213323	+	0.976982i	$0.568429\pi$
$60$	−12.5259	−1.61709
$61$	−4.52127	−0.578889	−0.289445	−	0.957195i	$-0.593471\pi$
$61$	−4.52127	−0.578889	−0.289445	+	0.957195i	$0.593471\pi$
$62$	−0.182983	−0.0232389
$63$	−0.299970	−0.0377927
$64$	−7.20758	−0.900948
$65$	0	0
$66$	1.94930	0.239942
$67$	−1.84876	−0.225862	−0.112931	−	0.993603i	$-0.536024\pi$
$67$	−1.84876	−0.225862	−0.112931	+	0.993603i	$0.536024\pi$
$68$	10.9839	1.33199
$69$	−6.45508	−0.777100
$70$	2.45312	0.293204
$71$	10.5275	1.24939	0.624693	−	0.780870i	$-0.285224\pi$
$71$	10.5275	1.24939	0.624693	+	0.780870i	$0.285224\pi$
$72$	−0.0589311	−0.00694510
$73$	12.6192	1.47696	0.738481	−	0.674274i	$-0.235543\pi$
$73$	12.6192	1.47696	0.738481	+	0.674274i	$0.235543\pi$
$74$	−0.924052	−0.107419
$75$	−14.3368	−1.65547
$76$	−1.28829	−0.147777
$77$	22.4214	2.55515
$78$	0	0
$79$	−16.9523	−1.90728	−0.953639	−	0.300952i	$-0.902696\pi$
$79$	−16.9523	−1.90728	−0.953639	+	0.300952i	$0.902696\pi$
$80$	−13.7899	−1.54176
$81$	−9.23699	−1.02633
$82$	−0.740668	−0.0817930
$83$	−12.3567	−1.35633	−0.678163	−	0.734911i	$-0.737224\pi$
$83$	−12.3567	−1.35633	−0.678163	+	0.734911i	$0.737224\pi$
$84$	−12.7530	−1.39146
$85$	20.2680	2.19837
$86$	1.95550	0.210867
$87$	−0.168126	−0.0180250
$88$	4.40482	0.469556
$89$	3.79668	0.402447	0.201223	−	0.979545i	$-0.435508\pi$
$89$	3.79668	0.402447	0.201223	+	0.979545i	$0.435508\pi$
$90$	−0.0539124	−0.00568286
$91$	0	0
$92$	−7.23169	−0.753955
$93$	1.75533	0.182020
$94$	−1.62904	−0.168022
$95$	−2.37722	−0.243897
$96$	−3.76868	−0.384640
$97$	10.1945	1.03509	0.517547	−	0.855655i	$-0.326845\pi$
$97$	10.1945	1.03509	0.517547	+	0.855655i	$0.326845\pi$
$98$	1.21670	0.122905
$99$	−0.492756	−0.0495239
$100$	−16.0617	−1.60617
$101$	2.88901	0.287468	0.143734	−	0.989616i	$-0.454089\pi$
$101$	2.88901	0.287468	0.143734	+	0.989616i	$0.454089\pi$
$102$	1.79402	0.177635
$103$	13.5970	1.33975	0.669875	−	0.742474i	$-0.266348\pi$
$103$	13.5970	1.33975	0.669875	+	0.742474i	$0.266348\pi$
$104$	0	0
$105$	−23.5324	−2.29653
$106$	0.341832	0.0332016
$107$	−12.1537	−1.17494	−0.587470	−	0.809246i	$-0.699876\pi$
$107$	−12.1537	−1.17494	−0.587470	+	0.809246i	$0.699876\pi$
$108$	−10.0754	−0.969506
$109$	−0.634560	−0.0607798	−0.0303899	−	0.999538i	$-0.509675\pi$
$109$	−0.634560	−0.0607798	−0.0303899	+	0.999538i	$0.509675\pi$
$110$	4.02970	0.384216
$111$	8.86430	0.841362
$112$	−14.0399	−1.32664
$113$	−16.2274	−1.52654	−0.763271	−	0.646079i	$-0.776408\pi$
$113$	−16.2274	−1.52654	−0.763271	+	0.646079i	$0.776408\pi$
$114$	−0.210420	−0.0197076
$115$	−13.3443	−1.24436
$116$	−0.188353	−0.0174882
$117$	0	0
$118$	−0.599660	−0.0552032
$119$	20.6353	1.89164
$120$	−4.62310	−0.422029
$121$	25.8312	2.34829
$122$	−0.827317	−0.0749018
$123$	7.10512	0.640647
$124$	1.96652	0.176598
$125$	−11.4943	−1.02808
$126$	−0.0548896	−0.00488995
$127$	−16.5399	−1.46768	−0.733838	−	0.679325i	$-0.762273\pi$
$127$	−16.5399	−1.46768	−0.733838	+	0.679325i	$0.762273\pi$
$128$	−5.61285	−0.496110
$129$	−18.7589	−1.65163
$130$	0	0
$131$	8.84045	0.772393	0.386197	−	0.922416i	$-0.373789\pi$
$131$	8.84045	0.772393	0.386197	+	0.922416i	$0.373789\pi$
$132$	−20.9491	−1.82338
$133$	−2.42030	−0.209867
$134$	−0.338292	−0.0292239
$135$	−18.5916	−1.60011
$136$	4.05394	0.347623
$137$	−11.9686	−1.02255	−0.511274	−	0.859418i	$-0.670826\pi$
$137$	−11.9686	−1.02255	−0.511274	+	0.859418i	$0.670826\pi$
$138$	−1.18117	−0.100548
$139$	10.8866	0.923385	0.461693	−	0.887040i	$-0.347242\pi$
$139$	10.8866	0.923385	0.461693	+	0.887040i	$0.347242\pi$
$140$	−26.3636	−2.22813
$141$	15.6271	1.31604
$142$	1.92636	0.161657
$143$	0	0
$144$	0.308556	0.0257130
$145$	−0.347559	−0.0288632
$146$	2.30910	0.191102
$147$	−11.6716	−0.962661
$148$	9.93076	0.816304
$149$	11.8566	0.971332	0.485666	−	0.874145i	$-0.338577\pi$
$149$	11.8566	0.971332	0.485666	+	0.874145i	$0.338577\pi$
$150$	−2.62340	−0.214200
$151$	7.01530	0.570897	0.285449	−	0.958394i	$-0.407857\pi$
$151$	7.01530	0.570897	0.285449	+	0.958394i	$0.407857\pi$
$152$	−0.475485	−0.0385669
$153$	−0.453504	−0.0366636
$154$	4.10274	0.330608
$155$	3.62872	0.291466
$156$	0	0
$157$	2.09749	0.167398	0.0836992	−	0.996491i	$-0.473327\pi$
$157$	2.09749	0.167398	0.0836992	+	0.996491i	$0.473327\pi$
$158$	−3.10198	−0.246780
$159$	−3.27915	−0.260053
$160$	−7.79082	−0.615918
$161$	−13.5861	−1.07074
$162$	−1.69021	−0.132796
$163$	−7.09025	−0.555351	−0.277676	−	0.960675i	$-0.589564\pi$
$163$	−7.09025	−0.555351	−0.277676	+	0.960675i	$0.589564\pi$
$164$	7.95994	0.621567
$165$	−38.6563	−3.00939
$166$	−2.26107	−0.175493
$167$	3.90278	0.302006	0.151003	−	0.988533i	$-0.451750\pi$
$167$	3.90278	0.302006	0.151003	+	0.988533i	$0.451750\pi$
$168$	−4.70690	−0.363145
$169$	0	0
$170$	3.70870	0.284444
$171$	0.0531912	0.00406763
$172$	−21.0157	−1.60244
$173$	−0.641945	−0.0488062	−0.0244031	−	0.999702i	$-0.507769\pi$
$173$	−0.641945	−0.0488062	−0.0244031	+	0.999702i	$0.507769\pi$
$174$	−0.0307642	−0.00233223
$175$	−30.1750	−2.28102
$176$	−23.0631	−1.73844
$177$	5.75246	0.432381
$178$	0.694728	0.0520721
$179$	−9.54860	−0.713696	−0.356848	−	0.934162i	$-0.616149\pi$
$179$	−9.54860	−0.713696	−0.356848	+	0.934162i	$0.616149\pi$
$180$	0.579395	0.0431856
$181$	12.1439	0.902651	0.451325	−	0.892359i	$-0.350951\pi$
$181$	12.1439	0.902651	0.451325	+	0.892359i	$0.350951\pi$
$182$	0	0
$183$	7.93634	0.586671
$184$	−2.66909	−0.196768
$185$	18.3247	1.34726
$186$	0.321197	0.0235513
$187$	33.8973	2.47881
$188$	17.5072	1.27685
$189$	−18.9286	−1.37686
$190$	−0.434991	−0.0315576
$191$	19.1875	1.38836	0.694179	−	0.719803i	$-0.255768\pi$
$191$	19.1875	1.38836	0.694179	+	0.719803i	$0.255768\pi$
$192$	12.6517	0.913059
$193$	−9.16619	−0.659797	−0.329899	−	0.944016i	$-0.607015\pi$
$193$	−9.16619	−0.659797	−0.329899	+	0.944016i	$0.607015\pi$
$194$	1.86542	0.133929
$195$	0	0
$196$	−13.0759	−0.933990
$197$	3.73178	0.265879	0.132939	−	0.991124i	$-0.457558\pi$
$197$	3.73178	0.265879	0.132939	+	0.991124i	$0.457558\pi$
$198$	−0.0901661	−0.00640783
$199$	−5.06193	−0.358831	−0.179415	−	0.983773i	$-0.557421\pi$
$199$	−5.06193	−0.358831	−0.179415	+	0.983773i	$0.557421\pi$
$200$	−5.92808	−0.419179
$201$	3.24518	0.228898
$202$	0.528641	0.0371951
$203$	−0.353859	−0.0248360
$204$	−19.2803	−1.34989
$205$	14.6881	1.02586
$206$	2.48802	0.173349
$207$	0.298584	0.0207530
$208$	0	0
$209$	−3.97579	−0.275011
$210$	−4.30604	−0.297145
$211$	12.9580	0.892066	0.446033	−	0.895016i	$-0.352836\pi$
$211$	12.9580	0.892066	0.446033	+	0.895016i	$0.352836\pi$
$212$	−3.67366	−0.252308
$213$	−18.4793	−1.26618
$214$	−2.22392	−0.152024
$215$	−38.7793	−2.64473
$216$	−3.71865	−0.253022
$217$	3.69449	0.250798
$218$	−0.116114	−0.00786422
$219$	−22.1509	−1.49682
$220$	−43.3071	−2.91976
$221$	0	0
$222$	1.62202	0.108863
$223$	3.49445	0.234006	0.117003	−	0.993132i	$-0.462671\pi$
$223$	3.49445	0.234006	0.117003	+	0.993132i	$0.462671\pi$
$224$	−7.93203	−0.529981
$225$	0.663159	0.0442106
$226$	−2.96933	−0.197517
$227$	13.6598	0.906632	0.453316	−	0.891350i	$-0.350241\pi$
$227$	13.6598	0.906632	0.453316	+	0.891350i	$0.350241\pi$
$228$	2.26138	0.149763
$229$	−2.79089	−0.184427	−0.0922135	−	0.995739i	$-0.529394\pi$
$229$	−2.79089	−0.184427	−0.0922135	+	0.995739i	$0.529394\pi$
$230$	−2.44178	−0.161006
$231$	−39.3570	−2.58950
$232$	−0.0695178	−0.00456407
$233$	8.36588	0.548067	0.274033	−	0.961720i	$-0.411642\pi$
$233$	8.36588	0.548067	0.274033	+	0.961720i	$0.411642\pi$
$234$	0	0
$235$	32.3052	2.10736
$236$	6.44453	0.419503
$237$	29.7569	1.93292
$238$	3.77592	0.244756
$239$	13.8007	0.892695	0.446348	−	0.894860i	$-0.352725\pi$
$239$	13.8007	0.892695	0.446348	+	0.894860i	$0.352725\pi$
$240$	24.2059	1.56249
$241$	−0.530190	−0.0341525	−0.0170763	−	0.999854i	$-0.505436\pi$
$241$	−0.530190	−0.0341525	−0.0170763	+	0.999854i	$0.505436\pi$
$242$	4.72667	0.303842
$243$	0.843563	0.0541146
$244$	8.89116	0.569198
$245$	−24.1282	−1.54150
$246$	1.30012	0.0828925
$247$	0	0
$248$	0.725806	0.0460887
$249$	21.6902	1.37456
$250$	−2.10326	−0.133022
$251$	9.36623	0.591191	0.295596	−	0.955313i	$-0.404482\pi$
$251$	9.36623	0.591191	0.295596	+	0.955313i	$0.404482\pi$
$252$	0.589897	0.0371600
$253$	−22.3177	−1.40310
$254$	−3.02652	−0.189901
$255$	−35.5770	−2.22792
$256$	13.3881	0.836757
$257$	0.239217	0.0149219	0.00746097	−	0.999972i	$-0.497625\pi$
$257$	0.239217	0.0149219	0.00746097	+	0.999972i	$0.497625\pi$
$258$	−3.43256	−0.213702
$259$	18.6569	1.15928
$260$	0	0
$261$	0.00777677	0.000481370 0
$262$	1.61765	0.0999390
$263$	−20.9621	−1.29258	−0.646291	−	0.763091i	$-0.723681\pi$
$263$	−20.9621	−1.29258	−0.646291	+	0.763091i	$0.723681\pi$
$264$	−7.73193	−0.475868
$265$	−6.77882	−0.416420
$266$	−0.442875	−0.0271544
$267$	−6.66443	−0.407857
$268$	3.63561	0.222080
$269$	−14.0249	−0.855114	−0.427557	−	0.903988i	$-0.640626\pi$
$269$	−14.0249	−0.855114	−0.427557	+	0.903988i	$0.640626\pi$
$270$	−3.40196	−0.207037
$271$	16.6138	1.00922	0.504609	−	0.863348i	$-0.331637\pi$
$271$	16.6138	1.00922	0.504609	+	0.863348i	$0.331637\pi$
$272$	−21.2259	−1.28701
$273$	0	0
$274$	−2.19006	−0.132306
$275$	−49.5680	−2.98906
$276$	12.6940	0.764090
$277$	15.6722	0.941654	0.470827	−	0.882226i	$-0.343956\pi$
$277$	15.6722	0.941654	0.470827	+	0.882226i	$0.343956\pi$
$278$	1.99206	0.119476
$279$	−0.0811940	−0.00486096
$280$	−9.73034	−0.581499
$281$	−16.6078	−0.990739	−0.495370	−	0.868682i	$-0.664967\pi$
$281$	−16.6078	−0.990739	−0.495370	+	0.868682i	$0.664967\pi$
$282$	2.85950	0.170281
$283$	4.44925	0.264480	0.132240	−	0.991218i	$-0.457783\pi$
$283$	4.44925	0.264480	0.132240	+	0.991218i	$0.457783\pi$
$284$	−20.7025	−1.22847
$285$	4.17281	0.247176
$286$	0	0
$287$	14.9543	0.882725
$288$	0.174323	0.0102721
$289$	14.1971	0.835122
$290$	−0.0635975	−0.00373457
$291$	−17.8947	−1.04901
$292$	−24.8158	−1.45224
$293$	−5.12140	−0.299195	−0.149598	−	0.988747i	$-0.547798\pi$
$293$	−5.12140	−0.299195	−0.149598	+	0.988747i	$0.547798\pi$
$294$	−2.13572	−0.124557
$295$	11.8918	0.692366
$296$	3.66527	0.213039
$297$	−31.0937	−1.80424
$298$	2.16956	0.125679
$299$	0	0
$300$	28.1936	1.62776
$301$	−39.4822	−2.27572
$302$	1.28368	0.0738676
$303$	−5.07118	−0.291332
$304$	2.48957	0.142787
$305$	16.4064	0.939428
$306$	−0.0829836	−0.00474386
$307$	−9.50377	−0.542409	−0.271204	−	0.962522i	$-0.587422\pi$
$307$	−9.50377	−0.542409	−0.271204	+	0.962522i	$0.587422\pi$
$308$	−44.0920	−2.51238
$309$	−23.8672	−1.35776
$310$	0.663994	0.0377123
$311$	−23.0295	−1.30589	−0.652943	−	0.757407i	$-0.726466\pi$
$311$	−23.0295	−1.30589	−0.652943	+	0.757407i	$0.726466\pi$
$312$	0	0
$313$	5.15180	0.291197	0.145599	−	0.989344i	$-0.453489\pi$
$313$	5.15180	0.291197	0.145599	+	0.989344i	$0.453489\pi$
$314$	0.383806	0.0216594
$315$	1.08851	0.0613305
$316$	33.3369	1.87535
$317$	5.49179	0.308450	0.154225	−	0.988036i	$-0.450712\pi$
$317$	5.49179	0.308450	0.154225	+	0.988036i	$0.450712\pi$
$318$	−0.600029	−0.0336479
$319$	−0.581277	−0.0325453
$320$	26.1543	1.46207
$321$	21.3338	1.19073
$322$	−2.48604	−0.138541
$323$	−3.65909	−0.203597
$324$	18.1647	1.00915
$325$	0	0
$326$	−1.29740	−0.0718562
$327$	1.11386	0.0615968
$328$	2.93787	0.162217
$329$	32.8908	1.81333
$330$	−7.07346	−0.389381
$331$	−15.8721	−0.872412	−0.436206	−	0.899847i	$-0.643678\pi$
$331$	−15.8721	−0.872412	−0.436206	+	0.899847i	$0.643678\pi$
$332$	24.2997	1.33362
$333$	−0.410024	−0.0224692
$334$	0.714143	0.0390762
$335$	6.70862	0.366531
$336$	24.6447	1.34448
$337$	−0.555177	−0.0302424	−0.0151212	−	0.999886i	$-0.504813\pi$
$337$	−0.555177	−0.0302424	−0.0151212	+	0.999886i	$0.504813\pi$
$338$	0	0
$339$	28.4844	1.54706
$340$	−39.8573	−2.16156
$341$	6.06887	0.328648
$342$	0.00973310	0.000526306 0
$343$	1.29584	0.0699690
$344$	−7.75654	−0.418204
$345$	23.4236	1.26109
$346$	−0.117465	−0.00631497
$347$	−0.223016	−0.0119721	−0.00598606	−	0.999982i	$-0.501905\pi$
$347$	−0.223016	−0.0119721	−0.00598606	+	0.999982i	$0.501905\pi$
$348$	0.330623	0.0177232
$349$	15.4324	0.826075	0.413037	−	0.910714i	$-0.364468\pi$
$349$	15.4324	0.826075	0.413037	+	0.910714i	$0.364468\pi$
$350$	−5.52153	−0.295138
$351$	0	0
$352$	−13.0298	−0.694491
$353$	24.6102	1.30987	0.654935	−	0.755685i	$-0.272696\pi$
$353$	24.6102	1.30987	0.654935	+	0.755685i	$0.272696\pi$
$354$	1.05260	0.0559452
$355$	−38.2014	−2.02752
$356$	−7.46623	−0.395709
$357$	−36.2219	−1.91706
$358$	−1.74723	−0.0923442
$359$	−17.8709	−0.943191	−0.471595	−	0.881815i	$-0.656322\pi$
$359$	−17.8709	−0.943191	−0.471595	+	0.881815i	$0.656322\pi$
$360$	0.213844	0.0112706
$361$	−18.5708	−0.977412
$362$	2.22214	0.116793
$363$	−45.3423	−2.37986
$364$	0	0
$365$	−45.7914	−2.39683
$366$	1.45222	0.0759086
$367$	−9.80199	−0.511660	−0.255830	−	0.966722i	$-0.582349\pi$
$367$	−9.80199	−0.511660	−0.255830	+	0.966722i	$0.582349\pi$
$368$	13.9750	0.728496
$369$	−0.328652	−0.0171089
$370$	3.35312	0.174320
$371$	−6.90169	−0.358318
$372$	−3.45189	−0.178972
$373$	23.1345	1.19786	0.598928	−	0.800803i	$-0.295593\pi$
$373$	23.1345	1.19786	0.598928	+	0.800803i	$0.295593\pi$
$374$	6.20263	0.320731
$375$	20.1763	1.04190
$376$	6.46160	0.333232
$377$	0	0
$378$	−3.46362	−0.178149
$379$	16.2603	0.835236	0.417618	−	0.908623i	$-0.362865\pi$
$379$	16.2603	0.835236	0.417618	+	0.908623i	$0.362865\pi$
$380$	4.67484	0.239814
$381$	29.0330	1.48740
$382$	3.51099	0.179638
$383$	33.9676	1.73567	0.867833	−	0.496856i	$-0.165512\pi$
$383$	33.9676	1.73567	0.867833	+	0.496856i	$0.165512\pi$
$384$	9.85242	0.502779
$385$	−81.3608	−4.14653
$386$	−1.67726	−0.0853703
$387$	0.867703	0.0441078
$388$	−20.0476	−1.01776
$389$	−14.2901	−0.724536	−0.362268	−	0.932074i	$-0.617997\pi$
$389$	−14.2901	−0.724536	−0.362268	+	0.932074i	$0.617997\pi$
$390$	0	0
$391$	−20.5399	−1.03875
$392$	−4.82607	−0.243753
$393$	−15.5179	−0.782776
$394$	0.682854	0.0344017
$395$	61.5150	3.09515
$396$	0.969013	0.0486948
$397$	−17.8971	−0.898232	−0.449116	−	0.893473i	$-0.648261\pi$
$397$	−17.8971	−0.898232	−0.449116	+	0.893473i	$0.648261\pi$
$398$	−0.926249	−0.0464287
$399$	4.24844	0.212688
$400$	31.0386	1.55193
$401$	−22.1692	−1.10708	−0.553539	−	0.832823i	$-0.686723\pi$
$401$	−22.1692	−1.10708	−0.553539	+	0.832823i	$0.686723\pi$
$402$	0.593815	0.0296168
$403$	0	0
$404$	−5.68129	−0.282655
$405$	33.5184	1.66554
$406$	−0.0647502	−0.00321350
$407$	30.6473	1.51913
$408$	−7.11602	−0.352295
$409$	−24.9061	−1.23153	−0.615764	−	0.787931i	$-0.711152\pi$
$409$	−24.9061	−1.23153	−0.615764	+	0.787931i	$0.711152\pi$
$410$	2.68767	0.132735
$411$	21.0089	1.03629
$412$	−26.7387	−1.31732
$413$	12.1073	0.595762
$414$	0.0546358	0.00268520
$415$	44.8391	2.20106
$416$	0	0
$417$	−19.1095	−0.935798
$418$	−0.727503	−0.0355833
$419$	14.6498	0.715688	0.357844	−	0.933781i	$-0.383512\pi$
$419$	14.6498	0.715688	0.357844	+	0.933781i	$0.383512\pi$
$420$	46.2769	2.25808
$421$	−1.42223	−0.0693153	−0.0346576	−	0.999399i	$-0.511034\pi$
$421$	−1.42223	−0.0693153	−0.0346576	+	0.999399i	$0.511034\pi$
$422$	2.37110	0.115423
$423$	−0.722842	−0.0351458
$424$	−1.35588	−0.0658474
$425$	−45.6195	−2.21287
$426$	−3.38140	−0.163830
$427$	16.7038	0.808353
$428$	23.9004	1.15527
$429$	0	0
$430$	−7.09597	−0.342198
$431$	9.77669	0.470927	0.235463	−	0.971883i	$-0.424339\pi$
$431$	9.77669	0.470927	0.235463	+	0.971883i	$0.424339\pi$
$432$	19.4704	0.936768
$433$	9.83002	0.472401	0.236200	−	0.971704i	$-0.424098\pi$
$433$	9.83002	0.472401	0.236200	+	0.971704i	$0.424098\pi$
$434$	0.676030	0.0324505
$435$	0.610082	0.0292512
$436$	1.24787	0.0597623
$437$	2.40912	0.115244
$438$	−4.05324	−0.193671
$439$	−4.03805	−0.192725	−0.0963627	−	0.995346i	$-0.530721\pi$
$439$	−4.03805	−0.192725	−0.0963627	+	0.995346i	$0.530721\pi$
$440$	−15.9839	−0.762001
$441$	0.539879	0.0257085
$442$	0	0
$443$	3.22763	0.153349	0.0766746	−	0.997056i	$-0.475570\pi$
$443$	3.22763	0.153349	0.0766746	+	0.997056i	$0.475570\pi$
$444$	−17.4318	−0.827276
$445$	−13.7771	−0.653096
$446$	0.639426	0.0302777
$447$	−20.8123	−0.984388
$448$	26.6283	1.25807
$449$	−7.19988	−0.339783	−0.169892	−	0.985463i	$-0.554342\pi$
$449$	−7.19988	−0.339783	−0.169892	+	0.985463i	$0.554342\pi$
$450$	0.121347	0.00572035
$451$	24.5652	1.15673
$452$	31.9114	1.50098
$453$	−12.3142	−0.578571
$454$	2.49951	0.117308
$455$	0	0
$456$	0.834634	0.0390853
$457$	25.7767	1.20578	0.602892	−	0.797823i	$-0.294015\pi$
$457$	25.7767	1.20578	0.602892	+	0.797823i	$0.294015\pi$
$458$	−0.510685	−0.0238628
$459$	−28.6168	−1.33572
$460$	26.2417	1.22353
$461$	−6.81554	−0.317431	−0.158716	−	0.987324i	$-0.550735\pi$
$461$	−6.81554	−0.317431	−0.158716	+	0.987324i	$0.550735\pi$
$462$	−7.20167	−0.335052
$463$	32.9799	1.53271	0.766353	−	0.642419i	$-0.222069\pi$
$463$	32.9799	1.53271	0.766353	+	0.642419i	$0.222069\pi$
$464$	0.363986	0.0168976
$465$	−6.36961	−0.295383
$466$	1.53082	0.0709136
$467$	11.0482	0.511252	0.255626	−	0.966776i	$-0.417718\pi$
$467$	11.0482	0.511252	0.255626	+	0.966776i	$0.417718\pi$
$468$	0	0
$469$	6.83021	0.315390
$470$	5.91131	0.272669
$471$	−3.68180	−0.169648
$472$	2.37856	0.109482
$473$	−64.8567	−2.98211
$474$	5.44501	0.250098
$475$	5.35068	0.245506
$476$	−40.5797	−1.85997
$477$	0.151679	0.00694490
$478$	2.52530	0.115505
$479$	3.10615	0.141924	0.0709618	−	0.997479i	$-0.477393\pi$
$479$	3.10615	0.141924	0.0709618	+	0.997479i	$0.477393\pi$
$480$	13.6755	0.624197
$481$	0	0
$482$	−0.0970159	−0.00441895
$483$	23.8482	1.08513
$484$	−50.7975	−2.30898
$485$	−36.9929	−1.67976
$486$	0.154358	0.00700182
$487$	−17.0632	−0.773206	−0.386603	−	0.922246i	$-0.626352\pi$
$487$	−17.0632	−0.773206	−0.386603	+	0.922246i	$0.626352\pi$
$488$	3.28157	0.148550
$489$	12.4458	0.562816
$490$	−4.41506	−0.199452
$491$	20.1958	0.911422	0.455711	−	0.890128i	$-0.349385\pi$
$491$	20.1958	0.911422	0.455711	+	0.890128i	$0.349385\pi$
$492$	−13.9723	−0.629922
$493$	−0.534974	−0.0240940
$494$	0	0
$495$	1.78807	0.0803679
$496$	−3.80022	−0.170635
$497$	−38.8938	−1.74463
$498$	3.96894	0.177852
$499$	−14.7606	−0.660775	−0.330388	−	0.943845i	$-0.607180\pi$
$499$	−14.7606	−0.660775	−0.330388	+	0.943845i	$0.607180\pi$
$500$	22.6037	1.01087
$501$	−6.85068	−0.306066
$502$	1.71386	0.0764935
$503$	−26.9128	−1.19998	−0.599991	−	0.800007i	$-0.704829\pi$
$503$	−26.9128	−1.19998	−0.599991	+	0.800007i	$0.704829\pi$
$504$	0.217720	0.00969804
$505$	−10.4834	−0.466506
$506$	−4.08377	−0.181546
$507$	0	0
$508$	32.5259	1.44310
$509$	−25.9581	−1.15057	−0.575286	−	0.817952i	$-0.695109\pi$
$509$	−25.9581	−1.15057	−0.575286	+	0.817952i	$0.695109\pi$
$510$	−6.51000	−0.288268
$511$	−46.6214	−2.06241
$512$	13.6755	0.604377
$513$	3.35645	0.148191
$514$	0.0437727	0.00193073
$515$	−49.3396	−2.17416
$516$	36.8896	1.62398
$517$	54.0291	2.37620
$518$	3.41390	0.149998
$519$	1.12683	0.0494622
$520$	0	0
$521$	−20.9303	−0.916973	−0.458486	−	0.888701i	$-0.651608\pi$
$521$	−20.9303	−0.916973	−0.458486	+	0.888701i	$0.651608\pi$
$522$	0.00142302	6.22839e−5 0
$523$	37.9535	1.65959	0.829796	−	0.558067i	$-0.188457\pi$
$523$	37.9535	1.65959	0.829796	+	0.558067i	$0.188457\pi$
$524$	−17.3849	−0.759462
$525$	52.9673	2.31168
$526$	−3.83572	−0.167245
$527$	5.58543	0.243305
$528$	40.4834	1.76181
$529$	−9.47667	−0.412029
$530$	−1.24041	−0.0538800
$531$	−0.266083	−0.0115470
$532$	4.75957	0.206354
$533$	0	0
$534$	−1.21948	−0.0527720
$535$	44.1023	1.90671
$536$	1.34184	0.0579586
$537$	16.7610	0.723290
$538$	−2.56632	−0.110642
$539$	−40.3534	−1.73815
$540$	36.5608	1.57333
$541$	−27.9959	−1.20364	−0.601818	−	0.798633i	$-0.705557\pi$
$541$	−27.9959	−1.20364	−0.601818	+	0.798633i	$0.705557\pi$
$542$	3.04005	0.130581
$543$	−21.3166	−0.914784
$544$	−11.9919	−0.514147
$545$	2.30264	0.0986342
$546$	0	0
$547$	26.1073	1.11627	0.558133	−	0.829751i	$-0.311518\pi$
$547$	26.1073	1.11627	0.558133	+	0.829751i	$0.311518\pi$
$548$	23.5365	1.00543
$549$	−0.367100	−0.0156675
$550$	−9.07012	−0.386751
$551$	0.0627467	0.00267310
$552$	4.68513	0.199413
$553$	62.6300	2.66330
$554$	2.86776	0.121839
$555$	−32.1660	−1.36537
$556$	−21.4086	−0.907927
$557$	8.71912	0.369441	0.184721	−	0.982791i	$-0.440862\pi$
$557$	8.71912	0.369441	0.184721	+	0.982791i	$0.440862\pi$
$558$	−0.0148572	−0.000628953 0
$559$	0	0
$560$	50.9468	2.15289
$561$	−59.5010	−2.51213
$562$	−3.03895	−0.128191
$563$	33.3778	1.40671	0.703354	−	0.710840i	$-0.251685\pi$
$563$	33.3778	1.40671	0.703354	+	0.710840i	$0.251685\pi$
$564$	−30.7310	−1.29401
$565$	58.8845	2.47729
$566$	0.814138	0.0342208
$567$	34.1260	1.43316
$568$	−7.64094	−0.320607
$569$	4.82522	0.202284	0.101142	−	0.994872i	$-0.467750\pi$
$569$	4.82522	0.202284	0.101142	+	0.994872i	$0.467750\pi$
$570$	0.763554	0.0319817
$571$	−4.77441	−0.199803	−0.0999013	−	0.994997i	$-0.531853\pi$
$571$	−4.77441	−0.199803	−0.0999013	+	0.994997i	$0.531853\pi$
$572$	0	0
$573$	−33.6804	−1.40702
$574$	2.73639	0.114215
$575$	30.0355	1.25257
$576$	−0.585213	−0.0243839
$577$	−29.8805	−1.24394	−0.621970	−	0.783041i	$-0.713667\pi$
$577$	−29.8805	−1.24394	−0.621970	+	0.783041i	$0.713667\pi$
$578$	2.59783	0.108055
$579$	16.0897	0.668666
$580$	0.683481	0.0283800
$581$	45.6518	1.89396
$582$	−3.27444	−0.135730
$583$	−11.3373	−0.469542
$584$	−9.15908	−0.379005
$585$	0	0
$586$	−0.937130	−0.0387125
$587$	42.2540	1.74401	0.872005	−	0.489498i	$-0.162820\pi$
$587$	42.2540	1.74401	0.872005	+	0.489498i	$0.162820\pi$
$588$	22.9525	0.946545
$589$	−0.655112	−0.0269934
$590$	2.17600	0.0895843
$591$	−6.55052	−0.269452
$592$	−19.1908	−0.788739
$593$	−19.6901	−0.808574	−0.404287	−	0.914632i	$-0.632480\pi$
$593$	−19.6901	−0.808574	−0.404287	+	0.914632i	$0.632480\pi$
$594$	−5.68963	−0.233448
$595$	−74.8797	−3.06977
$596$	−23.3162	−0.955070
$597$	8.88538	0.363654
$598$	0	0
$599$	19.0162	0.776979	0.388490	−	0.921453i	$-0.372997\pi$
$599$	19.0162	0.776979	0.388490	+	0.921453i	$0.372997\pi$
$600$	10.4058	0.424813
$601$	−10.8422	−0.442263	−0.221131	−	0.975244i	$-0.570975\pi$
$601$	−10.8422	−0.442263	−0.221131	+	0.975244i	$0.570975\pi$
$602$	−7.22458	−0.294452
$603$	−0.150108	−0.00611287
$604$	−13.7957	−0.561340
$605$	−93.7341	−3.81083
$606$	−0.927941	−0.0376950
$607$	−10.8186	−0.439112	−0.219556	−	0.975600i	$-0.570461\pi$
$607$	−10.8186	−0.439112	−0.219556	+	0.975600i	$0.570461\pi$
$608$	1.40652	0.0570419
$609$	0.621140	0.0251699
$610$	3.00210	0.121551
$611$	0	0
$612$	0.891823	0.0360498
$613$	−45.3425	−1.83137	−0.915683	−	0.401901i	$-0.868350\pi$
$613$	−45.3425	−1.83137	−0.915683	+	0.401901i	$0.868350\pi$
$614$	−1.73903	−0.0701816
$615$	−25.7825	−1.03965
$616$	−16.2736	−0.655681
$617$	−38.9534	−1.56820	−0.784102	−	0.620632i	$-0.786876\pi$
$617$	−38.9534	−1.56820	−0.784102	+	0.620632i	$0.786876\pi$
$618$	−4.36730	−0.175679
$619$	−23.9690	−0.963394	−0.481697	−	0.876338i	$-0.659979\pi$
$619$	−23.9690	−0.963394	−0.481697	+	0.876338i	$0.659979\pi$
$620$	−7.13593	−0.286586
$621$	18.8411	0.756068
$622$	−4.21402	−0.168967
$623$	−14.0268	−0.561971
$624$	0	0
$625$	0.871501	0.0348601
$626$	0.942694	0.0376776
$627$	6.97884	0.278708
$628$	−4.12476	−0.164596
$629$	28.2060	1.12465
$630$	0.199179	0.00793547
$631$	25.8377	1.02858	0.514291	−	0.857616i	$-0.328055\pi$
$631$	25.8377	1.02858	0.514291	+	0.857616i	$0.328055\pi$
$632$	12.3041	0.489429
$633$	−22.7456	−0.904058
$634$	1.00491	0.0399099
$635$	60.0185	2.38176
$636$	6.44850	0.255699
$637$	0	0
$638$	−0.106364	−0.00421099
$639$	0.854772	0.0338143
$640$	20.3674	0.805093
$641$	5.13945	0.202996	0.101498	−	0.994836i	$-0.467636\pi$
$641$	5.13945	0.202996	0.101498	+	0.994836i	$0.467636\pi$
$642$	3.90372	0.154068
$643$	37.7706	1.48953	0.744764	−	0.667328i	$-0.232562\pi$
$643$	37.7706	1.48953	0.744764	+	0.667328i	$0.232562\pi$
$644$	26.7174	1.05281
$645$	68.0706	2.68028
$646$	−0.669551	−0.0263432
$647$	23.2264	0.913126	0.456563	−	0.889691i	$-0.349080\pi$
$647$	23.2264	0.913126	0.456563	+	0.889691i	$0.349080\pi$
$648$	6.70426	0.263368
$649$	19.8885	0.780691
$650$	0	0
$651$	−6.48506	−0.254169
$652$	13.9431	0.546054
$653$	28.7681	1.12578	0.562892	−	0.826530i	$-0.309689\pi$
$653$	28.7681	1.12578	0.562892	+	0.826530i	$0.309689\pi$
$654$	0.203819	0.00796993
$655$	−32.0795	−1.25345
$656$	−15.3823	−0.600578
$657$	1.02460	0.0399735
$658$	6.01846	0.234624
$659$	49.8266	1.94097	0.970485	−	0.241161i	$-0.0775282\pi$
$659$	49.8266	1.94097	0.970485	+	0.241161i	$0.0775282\pi$
$660$	76.0183	2.95901
$661$	0.921328	0.0358355	0.0179178	−	0.999839i	$-0.494296\pi$
$661$	0.921328	0.0358355	0.0179178	+	0.999839i	$0.494296\pi$
$662$	−2.90434	−0.112880
$663$	0	0
$664$	8.96859	0.348049
$665$	8.78260	0.340575
$666$	−0.0750275	−0.00290726
$667$	0.352223	0.0136381
$668$	−7.67488	−0.296950
$669$	−6.13392	−0.237151
$670$	1.22756	0.0474250
$671$	27.4390	1.05927
$672$	13.9234	0.537105
$673$	23.7932	0.917160	0.458580	−	0.888653i	$-0.348358\pi$
$673$	23.7932	0.917160	0.458580	+	0.888653i	$0.348358\pi$
$674$	−0.101588	−0.00391303
$675$	41.8464	1.61067
$676$	0	0
$677$	−7.86948	−0.302449	−0.151224	−	0.988499i	$-0.548322\pi$
$677$	−7.86948	−0.302449	−0.151224	+	0.988499i	$0.548322\pi$
$678$	5.21217	0.200172
$679$	−37.6634	−1.44539
$680$	−14.7106	−0.564126
$681$	−23.9775	−0.918819
$682$	1.11050	0.0425233
$683$	−6.18989	−0.236849	−0.118425	−	0.992963i	$-0.537784\pi$
$683$	−6.18989	−0.236849	−0.118425	+	0.992963i	$0.537784\pi$
$684$	−0.104601	−0.00399954
$685$	43.4307	1.65940
$686$	0.237118	0.00905320
$687$	4.89893	0.186906
$688$	40.6122	1.54832
$689$	0	0
$690$	4.28613	0.163170
$691$	−21.2108	−0.806896	−0.403448	−	0.915003i	$-0.632188\pi$
$691$	−21.2108	−0.806896	−0.403448	+	0.915003i	$0.632188\pi$
$692$	1.26240	0.0479891
$693$	1.82048	0.0691544
$694$	−0.0408082	−0.00154906
$695$	−39.5042	−1.49848
$696$	0.122027	0.00462542
$697$	22.6083	0.856352
$698$	2.82386	0.106885
$699$	−14.6849	−0.555434
$700$	59.3397	2.24283
$701$	27.0442	1.02144	0.510722	−	0.859746i	$-0.329378\pi$
$701$	27.0442	1.02144	0.510722	+	0.859746i	$0.329378\pi$
$702$	0	0
$703$	−3.30827	−0.124774
$704$	43.7419	1.64858
$705$	−56.7064	−2.13569
$706$	4.50326	0.169482
$707$	−10.6734	−0.401416
$708$	−11.3123	−0.425142
$709$	22.8348	0.857580	0.428790	−	0.903404i	$-0.358940\pi$
$709$	22.8348	0.857580	0.428790	+	0.903404i	$0.358940\pi$
$710$	−6.99021	−0.262338
$711$	−1.37642	−0.0516199
$712$	−2.75565	−0.103272
$713$	−3.67741	−0.137720
$714$	−6.62800	−0.248046
$715$	0	0
$716$	18.7775	0.701748
$717$	−24.2249	−0.904695
$718$	−3.27008	−0.122038
$719$	7.01652	0.261672	0.130836	−	0.991404i	$-0.458234\pi$
$719$	7.01652	0.261672	0.130836	+	0.991404i	$0.458234\pi$
$720$	−1.11966	−0.0417273
$721$	−50.2339	−1.87081
$722$	−3.39815	−0.126466
$723$	0.930660	0.0346116
$724$	−23.8812	−0.887539
$725$	0.782292	0.0290536
$726$	−8.29689	−0.307926
$727$	26.0514	0.966193	0.483097	−	0.875567i	$-0.339512\pi$
$727$	26.0514	0.966193	0.483097	+	0.875567i	$0.339512\pi$
$728$	0	0
$729$	26.2302	0.971490
$730$	−8.37906	−0.310123
$731$	−59.6903	−2.20773
$732$	−15.6069	−0.576849
$733$	1.78078	0.0657747	0.0328873	−	0.999459i	$-0.489530\pi$
$733$	1.78078	0.0657747	0.0328873	+	0.999459i	$0.489530\pi$
$734$	−1.79360	−0.0662030
$735$	42.3531	1.56222
$736$	7.89536	0.291027
$737$	11.2199	0.413289
$738$	−0.0601378	−0.00221370
$739$	7.92219	0.291422	0.145711	−	0.989327i	$-0.453453\pi$
$739$	7.92219	0.291422	0.145711	+	0.989327i	$0.453453\pi$
$740$	−36.0359	−1.32471
$741$	0	0
$742$	−1.26289	−0.0463623
$743$	19.5615	0.717641	0.358821	−	0.933407i	$-0.383179\pi$
$743$	19.5615	0.717641	0.358821	+	0.933407i	$0.383179\pi$
$744$	−1.27403	−0.0467083
$745$	−43.0243	−1.57629
$746$	4.23322	0.154989
$747$	−1.00329	−0.0367086
$748$	−66.6596	−2.43732
$749$	44.9017	1.64067
$750$	3.69192	0.134810
$751$	−13.7133	−0.500406	−0.250203	−	0.968193i	$-0.580497\pi$
$751$	−13.7133	−0.500406	−0.250203	+	0.968193i	$0.580497\pi$
$752$	−33.8321	−1.23373
$753$	−16.4409	−0.599138
$754$	0	0
$755$	−25.4565	−0.926458
$756$	37.2235	1.35380
$757$	−51.4909	−1.87147	−0.935735	−	0.352703i	$-0.885262\pi$
$757$	−51.4909	−1.87147	−0.935735	+	0.352703i	$0.885262\pi$
$758$	2.97536	0.108070
$759$	39.1750	1.42196
$760$	1.72540	0.0625868
$761$	5.14548	0.186523	0.0932617	−	0.995642i	$-0.470271\pi$
$761$	5.14548	0.186523	0.0932617	+	0.995642i	$0.470271\pi$
$762$	5.31255	0.192453
$763$	2.34438	0.0848721
$764$	−37.7325	−1.36511
$765$	1.64564	0.0594981
$766$	6.21551	0.224576
$767$	0	0
$768$	−23.5006	−0.848005
$769$	0.171319	0.00617794	0.00308897	−	0.999995i	$-0.499017\pi$
$769$	0.171319	0.00617794	0.00308897	+	0.999995i	$0.499017\pi$
$770$	−14.8877	−0.536514
$771$	−0.419905	−0.0151225
$772$	18.0255	0.648751
$773$	27.9300	1.00457	0.502285	−	0.864702i	$-0.332493\pi$
$773$	27.9300	1.00457	0.502285	+	0.864702i	$0.332493\pi$
$774$	0.158775	0.00570706
$775$	−8.16758	−0.293388
$776$	−7.39922	−0.265617
$777$	−32.7491	−1.17487
$778$	−2.61485	−0.0937467
$779$	−2.65172	−0.0950077
$780$	0	0
$781$	−63.8902	−2.28617
$782$	−3.75846	−0.134402
$783$	0.490727	0.0175372
$784$	25.2686	0.902451
$785$	−7.61121	−0.271656
$786$	−2.83952	−0.101282
$787$	−33.7150	−1.20181	−0.600905	−	0.799321i	$-0.705193\pi$
$787$	−33.7150	−1.20181	−0.600905	+	0.799321i	$0.705193\pi$
$788$	−7.33862	−0.261427
$789$	36.7955	1.30996
$790$	11.2562	0.400478
$791$	59.9518	2.13164
$792$	0.357645	0.0127084
$793$	0	0
$794$	−3.27488	−0.116221
$795$	11.8991	0.422017
$796$	9.95438	0.352824
$797$	−39.5708	−1.40167	−0.700835	−	0.713323i	$-0.747189\pi$
$797$	−39.5708	−1.40167	−0.700835	+	0.713323i	$0.747189\pi$
$798$	0.777394	0.0275194
$799$	49.7252	1.75915
$800$	17.5357	0.619981
$801$	0.308268	0.0108921
$802$	−4.05659	−0.143243
$803$	−76.5841	−2.70260
$804$	−6.38171	−0.225066
$805$	49.3003	1.73761
$806$	0	0
$807$	24.6184	0.866608
$808$	−2.09686	−0.0737674
$809$	46.4315	1.63245	0.816223	−	0.577737i	$-0.196064\pi$
$809$	46.4315	1.63245	0.816223	+	0.577737i	$0.196064\pi$
$810$	6.13331	0.215503
$811$	−28.5286	−1.00178	−0.500888	−	0.865512i	$-0.666993\pi$
$811$	−28.5286	−1.00178	−0.500888	+	0.865512i	$0.666993\pi$
$812$	0.695869	0.0244202
$813$	−29.1628	−1.02278
$814$	5.60795	0.196559
$815$	25.7285	0.901231
$816$	37.2585	1.30431
$817$	7.00104	0.244935
$818$	−4.55740	−0.159346
$819$	0	0
$820$	−28.8844	−1.00869
$821$	4.14769	0.144755	0.0723776	−	0.997377i	$-0.476941\pi$
$821$	4.14769	0.144755	0.0723776	+	0.997377i	$0.476941\pi$
$822$	3.84428	0.134085
$823$	32.5020	1.13295	0.566474	−	0.824080i	$-0.308307\pi$
$823$	32.5020	1.13295	0.566474	+	0.824080i	$0.308307\pi$
$824$	−9.86877	−0.343795
$825$	87.0084	3.02924
$826$	2.21544	0.0770849
$827$	22.4355	0.780160	0.390080	−	0.920781i	$-0.372447\pi$
$827$	22.4355	0.780160	0.390080	+	0.920781i	$0.372447\pi$
$828$	−0.587170	−0.0204056
$829$	−3.46797	−0.120448	−0.0602238	−	0.998185i	$-0.519181\pi$
$829$	−3.46797	−0.120448	−0.0602238	+	0.998185i	$0.519181\pi$
$830$	8.20480	0.284793
$831$	−27.5100	−0.954311
$832$	0	0
$833$	−37.1389	−1.28679
$834$	−3.49672	−0.121082
$835$	−14.1621	−0.490099
$836$	7.81846	0.270407
$837$	−5.12348	−0.177093
$838$	2.68066	0.0926020
$839$	31.1379	1.07500	0.537499	−	0.843264i	$-0.319369\pi$
$839$	31.1379	1.07500	0.537499	+	0.843264i	$0.319369\pi$
$840$	17.0800	0.589316
$841$	−28.9908	−0.999684
$842$	−0.260244	−0.00896862
$843$	29.1523	1.00406
$844$	−25.4822	−0.877132
$845$	0	0
$846$	−0.132268	−0.00454747
$847$	−95.4330	−3.27912
$848$	7.09921	0.243788
$849$	−7.80992	−0.268036
$850$	−8.34760	−0.286320
$851$	−18.5706	−0.636593
$852$	36.3399	1.24498
$853$	29.4896	1.00970	0.504852	−	0.863206i	$-0.331547\pi$
$853$	29.4896	1.00970	0.504852	+	0.863206i	$0.331547\pi$
$854$	3.05651	0.104592
$855$	−0.193016	−0.00660100
$856$	8.82122	0.301503
$857$	8.01476	0.273779	0.136889	−	0.990586i	$-0.456289\pi$
$857$	8.01476	0.273779	0.136889	+	0.990586i	$0.456289\pi$
$858$	0	0
$859$	−2.43673	−0.0831401	−0.0415700	−	0.999136i	$-0.513236\pi$
$859$	−2.43673	−0.0831401	−0.0415700	+	0.999136i	$0.513236\pi$
$860$	76.2602	2.60045
$861$	−26.2498	−0.894590
$862$	1.78897	0.0609326
$863$	22.1106	0.752655	0.376327	−	0.926487i	$-0.377187\pi$
$863$	22.1106	0.752655	0.376327	+	0.926487i	$0.377187\pi$
$864$	11.0001	0.374229
$865$	2.32944	0.0792032
$866$	1.79873	0.0611233
$867$	−24.9206	−0.846348
$868$	−7.26528	−0.246600
$869$	102.881	3.49000
$870$	0.111635	0.00378477
$871$	0	0
$872$	0.460568	0.0155968
$873$	0.827732	0.0280145
$874$	0.440828	0.0149112
$875$	42.4654	1.43559
$876$	43.5600	1.47176
$877$	50.1668	1.69401	0.847007	−	0.531582i	$-0.178402\pi$
$877$	50.1668	1.69401	0.847007	+	0.531582i	$0.178402\pi$
$878$	−0.738895	−0.0249365
$879$	8.98976	0.303217
$880$	83.6893	2.82117
$881$	−44.5341	−1.50039	−0.750196	−	0.661216i	$-0.770041\pi$
$881$	−44.5341	−1.50039	−0.750196	+	0.661216i	$0.770041\pi$
$882$	0.0987889	0.00332640
$883$	−29.1534	−0.981090	−0.490545	−	0.871416i	$-0.663202\pi$
$883$	−29.1534	−0.981090	−0.490545	+	0.871416i	$0.663202\pi$
$884$	0	0
$885$	−20.8740	−0.701673
$886$	0.590602	0.0198417
$887$	43.8419	1.47207	0.736034	−	0.676945i	$-0.236697\pi$
$887$	43.8419	1.47207	0.736034	+	0.676945i	$0.236697\pi$
$888$	−6.43376	−0.215903
$889$	61.1063	2.04944
$890$	−2.52097	−0.0845032
$891$	56.0581	1.87802
$892$	−6.87189	−0.230088
$893$	−5.83224	−0.195168
$894$	−3.80830	−0.127369
$895$	34.6492	1.15819
$896$	20.7366	0.692761
$897$	0	0
$898$	−1.31746	−0.0439641
$899$	−0.0957801	−0.00319445
$900$	−1.30411	−0.0434705
$901$	−10.4342	−0.347613
$902$	4.49502	0.149668
$903$	69.3044	2.30631
$904$	11.7779	0.391728
$905$	−44.0669	−1.46483
$906$	−2.25329	−0.0748606
$907$	25.4318	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$907$	25.4318	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$908$	−26.8622	−0.891453
$909$	0.234571	0.00778022
$910$	0	0
$911$	−23.9869	−0.794721	−0.397360	−	0.917663i	$-0.630074\pi$
$911$	−23.9869	−0.794721	−0.397360	+	0.917663i	$0.630074\pi$
$912$	−4.37003	−0.144706
$913$	74.9914	2.48185
$914$	4.71671	0.156015
$915$	−28.7987	−0.952056
$916$	5.48833	0.181339
$917$	−32.6609	−1.07856
$918$	−5.23640	−0.172827
$919$	14.0002	0.461823	0.230911	−	0.972975i	$-0.425829\pi$
$919$	14.0002	0.461823	0.230911	+	0.972975i	$0.425829\pi$
$920$	9.68536	0.319317
$921$	16.6823	0.549700
$922$	−1.24713	−0.0410720
$923$	0	0
$924$	77.3962	2.54615
$925$	−41.2457	−1.35615
$926$	6.03477	0.198315
$927$	1.10399	0.0362599
$928$	0.205639	0.00675043
$929$	−10.5381	−0.345743	−0.172872	−	0.984944i	$-0.555305\pi$
$929$	−10.5381	−0.345743	−0.172872	+	0.984944i	$0.555305\pi$
$930$	−1.16553	−0.0382193
$931$	4.35600	0.142762
$932$	−16.4516	−0.538891
$933$	40.4245	1.32344
$934$	2.02164	0.0661502
$935$	−123.004	−4.02265
$936$	0	0
$937$	−4.24062	−0.138535	−0.0692675	−	0.997598i	$-0.522066\pi$
$937$	−4.24062	−0.138535	−0.0692675	+	0.997598i	$0.522066\pi$
$938$	1.24981	0.0408079
$939$	−9.04313	−0.295111
$940$	−63.5287	−2.07208
$941$	47.8587	1.56015	0.780074	−	0.625687i	$-0.215181\pi$
$941$	47.8587	1.56015	0.780074	+	0.625687i	$0.215181\pi$
$942$	−0.673708	−0.0219506
$943$	−14.8852	−0.484728
$944$	−12.4538	−0.405338
$945$	68.6866	2.23438
$946$	−11.8677	−0.385852
$947$	−44.1444	−1.43450	−0.717250	−	0.696816i	$-0.754600\pi$
$947$	−44.1444	−1.43450	−0.717250	+	0.696816i	$0.754600\pi$
$948$	−58.5174	−1.90056
$949$	0	0
$950$	0.979086	0.0317657
$951$	−9.63993	−0.312596
$952$	−14.9772	−0.485415
$953$	−27.4227	−0.888307	−0.444154	−	0.895951i	$-0.646496\pi$
$953$	−27.4227	−0.888307	−0.444154	+	0.895951i	$0.646496\pi$
$954$	0.0277547	0.000898592 0
$955$	−69.6259	−2.25304
$956$	−27.1394	−0.877750
$957$	1.02033	0.0329827
$958$	0.568373	0.0183633
$959$	44.2179	1.42787
$960$	−45.9095	−1.48172
$961$	1.00000	0.0322581
$962$	0	0
$963$	−0.986807	−0.0317994
$964$	1.04263	0.0335808
$965$	33.2615	1.07073
$966$	4.36382	0.140404
$967$	−0.954737	−0.0307023	−0.0153511	−	0.999882i	$-0.504887\pi$
$967$	−0.954737	−0.0307023	−0.0153511	+	0.999882i	$0.504887\pi$
$968$	−18.7484	−0.602598
$969$	6.42291	0.206334
$970$	−6.76908	−0.217342
$971$	−50.3590	−1.61610	−0.808048	−	0.589117i	$-0.799476\pi$
$971$	−50.3590	−1.61610	−0.808048	+	0.589117i	$0.799476\pi$
$972$	−1.65888	−0.0532087
$973$	−40.2203	−1.28940
$974$	−3.12227	−0.100044
$975$	0	0
$976$	−17.1818	−0.549977
$977$	−9.17280	−0.293464	−0.146732	−	0.989176i	$-0.546875\pi$
$977$	−9.17280	−0.293464	−0.146732	+	0.989176i	$0.546875\pi$
$978$	2.27736	0.0728221
$979$	−23.0415	−0.736411
$980$	47.4486	1.51569
$981$	−0.0515225	−0.00164499
$982$	3.69549	0.117928
$983$	15.2671	0.486946	0.243473	−	0.969908i	$-0.421713\pi$
$983$	15.2671	0.486946	0.243473	+	0.969908i	$0.421713\pi$
$984$	−5.15694	−0.164397
$985$	−13.5416	−0.431471
$986$	−0.0978912	−0.00311749
$987$	−57.7342	−1.83770
$988$	0	0
$989$	39.2997	1.24966
$990$	0.327187	0.0103987
$991$	15.6399	0.496817	0.248409	−	0.968655i	$-0.420092\pi$
$991$	15.6399	0.496817	0.248409	+	0.968655i	$0.420092\pi$
$992$	−2.14699	−0.0681670
$993$	27.8609	0.884139
$994$	−7.11692	−0.225735
$995$	18.3683	0.582315
$996$	−42.6541	−1.35155
$997$	14.7744	0.467911	0.233955	−	0.972247i	$-0.424833\pi$
$997$	14.7744	0.467911	0.233955	+	0.972247i	$0.424833\pi$
$998$	−2.70094	−0.0854969
$999$	−25.8732	−0.818591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.m.1.11		17
13.3	even	3		403.2.f.b.373.7	yes	34
13.9	even	3		403.2.f.b.94.7	✓	34
13.12	even	2		5239.2.a.n.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.7	✓	34	13.9	even	3
403.2.f.b.373.7	yes	34	13.3	even	3
5239.2.a.m.1.11		17	1.1	even	1	trivial
5239.2.a.n.1.7		17	13.12	even	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+0.182983 q^{2} -1.75533 q^{3} -1.96652 q^{4} -3.62872 q^{5} -0.321197 q^{6} -3.69449 q^{7} -0.725806 q^{8} +0.0811940 q^{9} +O(q^{10})\)	\(q+0.182983 q^{2} -1.75533 q^{3} -1.96652 q^{4} -3.62872 q^{5} -0.321197 q^{6} -3.69449 q^{7} -0.725806 q^{8} +0.0811940 q^{9} -0.663994 q^{10} -6.06887 q^{11} +3.45189 q^{12} -0.676030 q^{14} +6.36961 q^{15} +3.80022 q^{16} -5.58543 q^{17} +0.0148572 q^{18} +0.655112 q^{19} +7.13593 q^{20} +6.48506 q^{21} -1.11050 q^{22} +3.67741 q^{23} +1.27403 q^{24} +8.16758 q^{25} +5.12348 q^{27} +7.26528 q^{28} +0.0957801 q^{29} +1.16553 q^{30} -1.00000 q^{31} +2.14699 q^{32} +10.6529 q^{33} -1.02204 q^{34} +13.4063 q^{35} -0.159669 q^{36} -5.04992 q^{37} +0.119875 q^{38} +2.63375 q^{40} -4.04773 q^{41} +1.18666 q^{42} +10.6868 q^{43} +11.9345 q^{44} -0.294630 q^{45} +0.672904 q^{46} -8.90265 q^{47} -6.67066 q^{48} +6.64925 q^{49} +1.49453 q^{50} +9.80430 q^{51} +1.86810 q^{53} +0.937510 q^{54} +22.0222 q^{55} +2.68148 q^{56} -1.14994 q^{57} +0.0175262 q^{58} -3.27713 q^{59} -12.5259 q^{60} -4.52127 q^{61} -0.182983 q^{62} -0.299970 q^{63} -7.20758 q^{64} +1.94930 q^{66} -1.84876 q^{67} +10.9839 q^{68} -6.45508 q^{69} +2.45312 q^{70} +10.5275 q^{71} -0.0589311 q^{72} +12.6192 q^{73} -0.924052 q^{74} -14.3368 q^{75} -1.28829 q^{76} +22.4214 q^{77} -16.9523 q^{79} -13.7899 q^{80} -9.23699 q^{81} -0.740668 q^{82} -12.3567 q^{83} -12.7530 q^{84} +20.2680 q^{85} +1.95550 q^{86} -0.168126 q^{87} +4.40482 q^{88} +3.79668 q^{89} -0.0539124 q^{90} -7.23169 q^{92} +1.75533 q^{93} -1.62904 q^{94} -2.37722 q^{95} -3.76868 q^{96} +10.1945 q^{97} +1.21670 q^{98} -0.492756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

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