LMFDB - Embedded newform 5290.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{24})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 1 $ x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.93185$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} -3.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} -3.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} -0.378937 q^{11} +2.41421 q^{12} -0.964724 q^{13} +3.18154 q^{14} -2.41421 q^{15} +1.00000 q^{16} -3.19980 q^{17} -2.82843 q^{18} +7.39595 q^{19} -1.00000 q^{20} -7.68092 q^{21} +0.378937 q^{22} -2.41421 q^{24} +1.00000 q^{25} +0.964724 q^{26} -0.414214 q^{27} -3.18154 q^{28} +0.545866 q^{29} +2.41421 q^{30} +10.1463 q^{31} -1.00000 q^{32} -0.914836 q^{33} +3.19980 q^{34} +3.18154 q^{35} +2.82843 q^{36} -4.82843 q^{37} -7.39595 q^{38} -2.32905 q^{39} +1.00000 q^{40} -6.26330 q^{41} +7.68092 q^{42} +4.21441 q^{43} -0.378937 q^{44} -2.82843 q^{45} +2.54587 q^{47} +2.41421 q^{48} +3.12220 q^{49} -1.00000 q^{50} -7.72500 q^{51} -0.964724 q^{52} -9.58114 q^{53} +0.414214 q^{54} +0.378937 q^{55} +3.18154 q^{56} +17.8554 q^{57} -0.545866 q^{58} +3.00000 q^{59} -2.41421 q^{60} -9.75663 q^{61} -10.1463 q^{62} -8.99876 q^{63} +1.00000 q^{64} +0.964724 q^{65} +0.914836 q^{66} -13.7143 q^{67} -3.19980 q^{68} -3.18154 q^{70} +11.2521 q^{71} -2.82843 q^{72} -6.78799 q^{73} +4.82843 q^{74} +2.41421 q^{75} +7.39595 q^{76} +1.20560 q^{77} +2.32905 q^{78} +16.6091 q^{79} -1.00000 q^{80} -9.48528 q^{81} +6.26330 q^{82} -13.9917 q^{83} -7.68092 q^{84} +3.19980 q^{85} -4.21441 q^{86} +1.31784 q^{87} +0.378937 q^{88} -17.7067 q^{89} +2.82843 q^{90} +3.06931 q^{91} +24.4952 q^{93} -2.54587 q^{94} -7.39595 q^{95} -2.41421 q^{96} -14.7712 q^{97} -3.12220 q^{98} -1.07180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} + 4 q^{28} - 12 q^{29} + 4 q^{30} + 28 q^{31} - 4 q^{32} - 16 q^{33} + 12 q^{34} - 4 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} + 4 q^{40} - 8 q^{41} - 4 q^{42} + 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} - 16 q^{51} - 8 q^{52} - 20 q^{53} - 4 q^{54} - 4 q^{56} + 12 q^{57} + 12 q^{58} + 12 q^{59} - 4 q^{60} - 28 q^{62} + 4 q^{64} + 8 q^{65} + 16 q^{66} - 12 q^{67} - 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} - 24 q^{77} + 16 q^{78} + 4 q^{79} - 4 q^{80} - 4 q^{81} + 8 q^{82} - 12 q^{83} + 4 q^{84} + 12 q^{85} - 12 q^{86} + 4 q^{87} - 40 q^{89} - 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} - 16 q^{97} - 12 q^{98} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 12 * q^17 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 + 4 * q^28 - 12 * q^29 + 4 * q^30 + 28 * q^31 - 4 * q^32 - 16 * q^33 + 12 * q^34 - 4 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 + 4 * q^40 - 8 * q^41 - 4 * q^42 + 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 - 16 * q^51 - 8 * q^52 - 20 * q^53 - 4 * q^54 - 4 * q^56 + 12 * q^57 + 12 * q^58 + 12 * q^59 - 4 * q^60 - 28 * q^62 + 4 * q^64 + 8 * q^65 + 16 * q^66 - 12 * q^67 - 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 - 24 * q^77 + 16 * q^78 + 4 * q^79 - 4 * q^80 - 4 * q^81 + 8 * q^82 - 12 * q^83 + 4 * q^84 + 12 * q^85 - 12 * q^86 + 4 * q^87 - 40 * q^89 - 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 - 16 * q^97 - 12 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.41421	1.39385	0.696923	−	0.717146i	$-0.254552\pi$
$3$	2.41421	1.39385	0.696923	+	0.717146i	$0.254552\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.41421	−0.985599
$7$	−3.18154	−1.20251	−0.601255	−	0.799057i	$-0.705332\pi$
$7$	−3.18154	−1.20251	−0.601255	+	0.799057i	$0.705332\pi$
$8$	−1.00000	−0.353553
$9$	2.82843	0.942809
$10$	1.00000	0.316228
$11$	−0.378937	−0.114254	−0.0571270	−	0.998367i	$-0.518194\pi$
$11$	−0.378937	−0.114254	−0.0571270	+	0.998367i	$0.518194\pi$
$12$	2.41421	0.696923
$13$	−0.964724	−0.267566	−0.133783	−	0.991011i	$-0.542713\pi$
$13$	−0.964724	−0.267566	−0.133783	+	0.991011i	$0.542713\pi$
$14$	3.18154	0.850302
$15$	−2.41421	−0.623347
$16$	1.00000	0.250000
$17$	−3.19980	−0.776066	−0.388033	−	0.921646i	$-0.626845\pi$
$17$	−3.19980	−0.776066	−0.388033	+	0.921646i	$0.626845\pi$
$18$	−2.82843	−0.666667
$19$	7.39595	1.69675	0.848374	−	0.529397i	$-0.177582\pi$
$19$	7.39595	1.69675	0.848374	+	0.529397i	$0.177582\pi$
$20$	−1.00000	−0.223607
$21$	−7.68092	−1.67611
$22$	0.378937	0.0807897
$23$	0	0
$23$	0	0
$24$	−2.41421	−0.492799
$25$	1.00000	0.200000
$26$	0.964724	0.189198
$27$	−0.414214	−0.0797154
$28$	−3.18154	−0.601255
$29$	0.545866	0.101365	0.0506824	−	0.998715i	$-0.483860\pi$
$29$	0.545866	0.101365	0.0506824	+	0.998715i	$0.483860\pi$
$30$	2.41421	0.440773
$31$	10.1463	1.82232	0.911161	−	0.412050i	$-0.135187\pi$
$31$	10.1463	1.82232	0.911161	+	0.412050i	$0.135187\pi$
$32$	−1.00000	−0.176777
$33$	−0.914836	−0.159252
$34$	3.19980	0.548761
$35$	3.18154	0.537779
$36$	2.82843	0.471405
$37$	−4.82843	−0.793789	−0.396894	−	0.917864i	$-0.629912\pi$
$37$	−4.82843	−0.793789	−0.396894	+	0.917864i	$0.629912\pi$
$38$	−7.39595	−1.19978
$39$	−2.32905	−0.372946
$40$	1.00000	0.158114
$41$	−6.26330	−0.978164	−0.489082	−	0.872238i	$-0.662668\pi$
$41$	−6.26330	−0.978164	−0.489082	+	0.872238i	$0.662668\pi$
$42$	7.68092	1.18519
$43$	4.21441	0.642692	0.321346	−	0.946962i	$-0.395865\pi$
$43$	4.21441	0.642692	0.321346	+	0.946962i	$0.395865\pi$
$44$	−0.378937	−0.0571270
$45$	−2.82843	−0.421637
$46$	0	0
$47$	2.54587	0.371353	0.185676	−	0.982611i	$-0.440552\pi$
$47$	2.54587	0.371353	0.185676	+	0.982611i	$0.440552\pi$
$48$	2.41421	0.348462
$49$	3.12220	0.446029
$50$	−1.00000	−0.141421
$51$	−7.72500	−1.08172
$52$	−0.964724	−0.133783
$53$	−9.58114	−1.31607	−0.658036	−	0.752987i	$-0.728612\pi$
$53$	−9.58114	−1.31607	−0.658036	+	0.752987i	$0.728612\pi$
$54$	0.414214	0.0563673
$55$	0.378937	0.0510959
$56$	3.18154	0.425151
$57$	17.8554	2.36501
$58$	−0.545866	−0.0716757
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	−2.41421	−0.311674
$61$	−9.75663	−1.24921	−0.624604	−	0.780941i	$-0.714740\pi$
$61$	−9.75663	−1.24921	−0.624604	+	0.780941i	$0.714740\pi$
$62$	−10.1463	−1.28858
$63$	−8.99876	−1.13374
$64$	1.00000	0.125000
$65$	0.964724	0.119659
$66$	0.914836	0.112608
$67$	−13.7143	−1.67547	−0.837735	−	0.546078i	$-0.816120\pi$
$67$	−13.7143	−1.67547	−0.837735	+	0.546078i	$0.816120\pi$
$68$	−3.19980	−0.388033
$69$	0	0
$70$	−3.18154	−0.380267
$71$	11.2521	1.33538	0.667689	−	0.744440i	$-0.267284\pi$
$71$	11.2521	1.33538	0.667689	+	0.744440i	$0.267284\pi$
$72$	−2.82843	−0.333333
$73$	−6.78799	−0.794474	−0.397237	−	0.917716i	$-0.630031\pi$
$73$	−6.78799	−0.794474	−0.397237	+	0.917716i	$0.630031\pi$
$74$	4.82843	0.561293
$75$	2.41421	0.278769
$76$	7.39595	0.848374
$77$	1.20560	0.137391
$78$	2.32905	0.263713
$79$	16.6091	1.86867	0.934336	−	0.356393i	$-0.115994\pi$
$79$	16.6091	1.86867	0.934336	+	0.356393i	$0.115994\pi$
$80$	−1.00000	−0.111803
$81$	−9.48528	−1.05392
$82$	6.26330	0.691666
$83$	−13.9917	−1.53579	−0.767895	−	0.640576i	$-0.778696\pi$
$83$	−13.9917	−1.53579	−0.767895	+	0.640576i	$0.778696\pi$
$84$	−7.68092	−0.838057
$85$	3.19980	0.347067
$86$	−4.21441	−0.454452
$87$	1.31784	0.141287
$88$	0.378937	0.0403949
$89$	−17.7067	−1.87691	−0.938455	−	0.345400i	$-0.887743\pi$
$89$	−17.7067	−1.87691	−0.938455	+	0.345400i	$0.887743\pi$
$90$	2.82843	0.298142
$91$	3.06931	0.321751
$92$	0	0
$93$	24.4952	2.54004
$94$	−2.54587	−0.262586
$95$	−7.39595	−0.758809
$96$	−2.41421	−0.246400
$97$	−14.7712	−1.49979	−0.749896	−	0.661555i	$-0.769897\pi$
$97$	−14.7712	−1.49979	−0.749896	+	0.661555i	$0.769897\pi$
$98$	−3.12220	−0.315390
$99$	−1.07180	−0.107720
$100$	1.00000	0.100000
$101$	−9.36433	−0.931785	−0.465893	−	0.884841i	$-0.654267\pi$
$101$	−9.36433	−0.931785	−0.465893	+	0.884841i	$0.654267\pi$
$102$	7.72500	0.764889
$103$	−8.19756	−0.807730	−0.403865	−	0.914819i	$-0.632333\pi$
$103$	−8.19756	−0.807730	−0.403865	+	0.914819i	$0.632333\pi$
$104$	0.964724	0.0945990
$105$	7.68092	0.749581
$106$	9.58114	0.930603
$107$	5.07107	0.490239	0.245119	−	0.969493i	$-0.421173\pi$
$107$	5.07107	0.490239	0.245119	+	0.969493i	$0.421173\pi$
$108$	−0.414214	−0.0398577
$109$	2.90895	0.278627	0.139313	−	0.990248i	$-0.455510\pi$
$109$	2.90895	0.278627	0.139313	+	0.990248i	$0.455510\pi$
$110$	−0.378937	−0.0361303
$111$	−11.6569	−1.10642
$112$	−3.18154	−0.300627
$113$	−1.52228	−0.143204	−0.0716021	−	0.997433i	$-0.522811\pi$
$113$	−1.52228	−0.143204	−0.0716021	+	0.997433i	$0.522811\pi$
$114$	−17.8554	−1.67231
$115$	0	0
$116$	0.545866	0.0506824
$117$	−2.72865	−0.252264
$118$	−3.00000	−0.276172
$119$	10.1803	0.933226
$120$	2.41421	0.220387
$121$	−10.8564	−0.986946
$122$	9.75663	0.883324
$123$	−15.1210	−1.36341
$124$	10.1463	0.911161
$125$	−1.00000	−0.0894427
$126$	8.99876	0.801673
$127$	8.21682	0.729125	0.364562	−	0.931179i	$-0.381219\pi$
$127$	8.21682	0.729125	0.364562	+	0.931179i	$0.381219\pi$
$128$	−1.00000	−0.0883883
$129$	10.1745	0.895814
$130$	−0.964724	−0.0846119
$131$	−17.8776	−1.56197	−0.780986	−	0.624549i	$-0.785283\pi$
$131$	−17.8776	−1.56197	−0.780986	+	0.624549i	$0.785283\pi$
$132$	−0.914836	−0.0796262
$133$	−23.5305	−2.04036
$134$	13.7143	1.18474
$135$	0.414214	0.0356498
$136$	3.19980	0.274381
$137$	9.05621	0.773724	0.386862	−	0.922138i	$-0.373559\pi$
$137$	9.05621	0.773724	0.386862	+	0.922138i	$0.373559\pi$
$138$	0	0
$139$	17.4336	1.47870	0.739351	−	0.673320i	$-0.235133\pi$
$139$	17.4336	1.47870	0.739351	+	0.673320i	$0.235133\pi$
$140$	3.18154	0.268889
$141$	6.14626	0.517609
$142$	−11.2521	−0.944255
$143$	0.365570	0.0305705
$144$	2.82843	0.235702
$145$	−0.545866	−0.0453317
$146$	6.78799	0.561778
$147$	7.53766	0.621696
$148$	−4.82843	−0.396894
$149$	−9.93942	−0.814269	−0.407134	−	0.913368i	$-0.633472\pi$
$149$	−9.93942	−0.814269	−0.407134	+	0.913368i	$0.633472\pi$
$150$	−2.41421	−0.197120
$151$	9.39355	0.764436	0.382218	−	0.924072i	$-0.375160\pi$
$151$	9.39355	0.764436	0.382218	+	0.924072i	$0.375160\pi$
$152$	−7.39595	−0.599891
$153$	−9.05040	−0.731682
$154$	−1.20560	−0.0971504
$155$	−10.1463	−0.814968
$156$	−2.32905	−0.186473
$157$	−0.672195	−0.0536470	−0.0268235	−	0.999640i	$-0.508539\pi$
$157$	−0.672195	−0.0536470	−0.0268235	+	0.999640i	$0.508539\pi$
$158$	−16.6091	−1.32135
$159$	−23.1309	−1.83440
$160$	1.00000	0.0790569
$161$	0	0
$162$	9.48528	0.745234
$163$	−13.9202	−1.09031	−0.545156	−	0.838335i	$-0.683529\pi$
$163$	−13.9202	−1.09031	−0.545156	+	0.838335i	$0.683529\pi$
$164$	−6.26330	−0.489082
$165$	0.914836	0.0712199
$166$	13.9917	1.08597
$167$	21.9301	1.69700	0.848502	−	0.529192i	$-0.177505\pi$
$167$	21.9301	1.69700	0.848502	+	0.529192i	$0.177505\pi$
$168$	7.68092	0.592596
$169$	−12.0693	−0.928408
$170$	−3.19980	−0.245414
$171$	20.9189	1.59971
$172$	4.21441	0.321346
$173$	−2.50454	−0.190416	−0.0952082	−	0.995457i	$-0.530352\pi$
$173$	−2.50454	−0.190416	−0.0952082	+	0.995457i	$0.530352\pi$
$174$	−1.31784	−0.0999050
$175$	−3.18154	−0.240502
$176$	−0.378937	−0.0285635
$177$	7.24264	0.544390
$178$	17.7067	1.32718
$179$	−25.2360	−1.88623	−0.943114	−	0.332468i	$-0.892119\pi$
$179$	−25.2360	−1.88623	−0.943114	+	0.332468i	$0.892119\pi$
$180$	−2.82843	−0.210819
$181$	−6.67220	−0.495940	−0.247970	−	0.968768i	$-0.579764\pi$
$181$	−6.67220	−0.495940	−0.247970	+	0.968768i	$0.579764\pi$
$182$	−3.06931	−0.227512
$183$	−23.5546	−1.74121
$184$	0	0
$185$	4.82843	0.354993
$186$	−24.4952	−1.79608
$187$	1.21252	0.0886685
$188$	2.54587	0.185676
$189$	1.31784	0.0958586
$190$	7.39595	0.536559
$191$	−8.91624	−0.645157	−0.322578	−	0.946543i	$-0.604550\pi$
$191$	−8.91624	−0.645157	−0.322578	+	0.946543i	$0.604550\pi$
$192$	2.41421	0.174231
$193$	−10.8571	−0.781514	−0.390757	−	0.920494i	$-0.627787\pi$
$193$	−10.8571	−0.781514	−0.390757	+	0.920494i	$0.627787\pi$
$194$	14.7712	1.06051
$195$	2.32905	0.166787
$196$	3.12220	0.223014
$197$	−17.5687	−1.25172	−0.625859	−	0.779937i	$-0.715251\pi$
$197$	−17.5687	−1.25172	−0.625859	+	0.779937i	$0.715251\pi$
$198$	1.07180	0.0761693
$199$	7.45997	0.528823	0.264412	−	0.964410i	$-0.414822\pi$
$199$	7.45997	0.528823	0.264412	+	0.964410i	$0.414822\pi$
$200$	−1.00000	−0.0707107
$201$	−33.1093	−2.33535
$202$	9.36433	0.658872
$203$	−1.73670	−0.121892
$204$	−7.72500	−0.540858
$205$	6.26330	0.437448
$206$	8.19756	0.571151
$207$	0	0
$208$	−0.964724	−0.0668916
$209$	−2.80260	−0.193860
$210$	−7.68092	−0.530034
$211$	−22.2820	−1.53396	−0.766978	−	0.641673i	$-0.778240\pi$
$211$	−22.2820	−1.53396	−0.766978	+	0.641673i	$0.778240\pi$
$212$	−9.58114	−0.658036
$213$	27.1650	1.86131
$214$	−5.07107	−0.346651
$215$	−4.21441	−0.287421
$216$	0.414214	0.0281837
$217$	−32.2808	−2.19136
$218$	−2.90895	−0.197019
$219$	−16.3877	−1.10738
$220$	0.378937	0.0255480
$221$	3.08692	0.207649
$222$	11.6569	0.782357
$223$	−12.2633	−0.821212	−0.410606	−	0.911813i	$-0.634683\pi$
$223$	−12.2633	−0.821212	−0.410606	+	0.911813i	$0.634683\pi$
$224$	3.18154	0.212576
$225$	2.82843	0.188562
$226$	1.52228	0.101261
$227$	−10.1920	−0.676466	−0.338233	−	0.941062i	$-0.609829\pi$
$227$	−10.1920	−0.676466	−0.338233	+	0.941062i	$0.609829\pi$
$228$	17.8554	1.18250
$229$	4.28256	0.283000	0.141500	−	0.989938i	$-0.454808\pi$
$229$	4.28256	0.283000	0.141500	+	0.989938i	$0.454808\pi$
$230$	0	0
$231$	2.91059	0.191503
$232$	−0.545866	−0.0358379
$233$	−2.86783	−0.187878	−0.0939390	−	0.995578i	$-0.529946\pi$
$233$	−2.86783	−0.187878	−0.0939390	+	0.995578i	$0.529946\pi$
$234$	2.72865	0.178377
$235$	−2.54587	−0.166074
$236$	3.00000	0.195283
$237$	40.0980	2.60464
$238$	−10.1803	−0.659891
$239$	−6.30463	−0.407813	−0.203906	−	0.978990i	$-0.565364\pi$
$239$	−6.30463	−0.407813	−0.203906	+	0.978990i	$0.565364\pi$
$240$	−2.41421	−0.155837
$241$	19.5887	1.26182	0.630910	−	0.775856i	$-0.282682\pi$
$241$	19.5887	1.26182	0.630910	+	0.775856i	$0.282682\pi$
$242$	10.8564	0.697876
$243$	−21.6569	−1.38929
$244$	−9.75663	−0.624604
$245$	−3.12220	−0.199470
$246$	15.1210	0.964077
$247$	−7.13505	−0.453993
$248$	−10.1463	−0.644288
$249$	−33.7790	−2.14066
$250$	1.00000	0.0632456
$251$	−14.4970	−0.915041	−0.457520	−	0.889199i	$-0.651262\pi$
$251$	−14.4970	−0.915041	−0.457520	+	0.889199i	$0.651262\pi$
$252$	−8.99876	−0.566868
$253$	0	0
$254$	−8.21682	−0.515569
$255$	7.72500	0.483758
$256$	1.00000	0.0625000
$257$	3.61501	0.225498	0.112749	−	0.993623i	$-0.464034\pi$
$257$	3.61501	0.225498	0.112749	+	0.993623i	$0.464034\pi$
$258$	−10.1745	−0.633436
$259$	15.3618	0.954538
$260$	0.964724	0.0598296
$261$	1.54394	0.0955676
$262$	17.8776	1.10448
$263$	3.72940	0.229965	0.114982	−	0.993368i	$-0.463319\pi$
$263$	3.72940	0.229965	0.114982	+	0.993368i	$0.463319\pi$
$264$	0.914836	0.0563042
$265$	9.58114	0.588565
$266$	23.5305	1.44275
$267$	−42.7479	−2.61613
$268$	−13.7143	−0.837735
$269$	27.8471	1.69787	0.848934	−	0.528498i	$-0.177245\pi$
$269$	27.8471	1.69787	0.848934	+	0.528498i	$0.177245\pi$
$270$	−0.414214	−0.0252082
$271$	1.11512	0.0677385	0.0338693	−	0.999426i	$-0.489217\pi$
$271$	1.11512	0.0677385	0.0338693	+	0.999426i	$0.489217\pi$
$272$	−3.19980	−0.194016
$273$	7.40996	0.448471
$274$	−9.05621	−0.547105
$275$	−0.378937	−0.0228508
$276$	0	0
$277$	−11.5033	−0.691166	−0.345583	−	0.938388i	$-0.612319\pi$
$277$	−11.5033	−0.691166	−0.345583	+	0.938388i	$0.612319\pi$
$278$	−17.4336	−1.04560
$279$	28.6980	1.71810
$280$	−3.18154	−0.190133
$281$	10.5534	0.629565	0.314782	−	0.949164i	$-0.398068\pi$
$281$	10.5534	0.629565	0.314782	+	0.949164i	$0.398068\pi$
$282$	−6.14626	−0.366005
$283$	14.0330	0.834177	0.417089	−	0.908866i	$-0.363050\pi$
$283$	14.0330	0.834177	0.417089	+	0.908866i	$0.363050\pi$
$284$	11.2521	0.667689
$285$	−17.8554	−1.05766
$286$	−0.365570	−0.0216166
$287$	19.9270	1.17625
$288$	−2.82843	−0.166667
$289$	−6.76127	−0.397722
$290$	0.545866	0.0320544
$291$	−35.6609	−2.09048
$292$	−6.78799	−0.397237
$293$	−0.849820	−0.0496470	−0.0248235	−	0.999692i	$-0.507902\pi$
$293$	−0.849820	−0.0496470	−0.0248235	+	0.999692i	$0.507902\pi$
$294$	−7.53766	−0.439605
$295$	−3.00000	−0.174667
$296$	4.82843	0.280647
$297$	0.156961	0.00910780
$298$	9.93942	0.575775
$299$	0	0
$300$	2.41421	0.139385
$301$	−13.4083	−0.772843
$302$	−9.39355	−0.540538
$303$	−22.6075	−1.29877
$304$	7.39595	0.424187
$305$	9.75663	0.558663
$306$	9.05040	0.517377
$307$	9.57650	0.546560	0.273280	−	0.961935i	$-0.411892\pi$
$307$	9.57650	0.546560	0.273280	+	0.961935i	$0.411892\pi$
$308$	1.20560	0.0686957
$309$	−19.7907	−1.12585
$310$	10.1463	0.576269
$311$	−15.0331	−0.852451	−0.426226	−	0.904617i	$-0.640157\pi$
$311$	−15.0331	−0.852451	−0.426226	+	0.904617i	$0.640157\pi$
$312$	2.32905	0.131856
$313$	24.0623	1.36008	0.680040	−	0.733175i	$-0.261963\pi$
$313$	24.0623	1.36008	0.680040	+	0.733175i	$0.261963\pi$
$314$	0.672195	0.0379342
$315$	8.99876	0.507022
$316$	16.6091	0.934336
$317$	−1.49546	−0.0839935	−0.0419968	−	0.999118i	$-0.513372\pi$
$317$	−1.49546	−0.0839935	−0.0419968	+	0.999118i	$0.513372\pi$
$318$	23.1309	1.29712
$319$	−0.206849	−0.0115813
$320$	−1.00000	−0.0559017
$321$	12.2426	0.683318
$322$	0	0
$323$	−23.6656	−1.31679
$324$	−9.48528	−0.526960
$325$	−0.964724	−0.0535132
$326$	13.9202	0.770966
$327$	7.02282	0.388363
$328$	6.26330	0.345833
$329$	−8.09978	−0.446555
$330$	−0.914836	−0.0503601
$331$	−28.8471	−1.58558	−0.792791	−	0.609494i	$-0.791373\pi$
$331$	−28.8471	−1.58558	−0.792791	+	0.609494i	$0.791373\pi$
$332$	−13.9917	−0.767895
$333$	−13.6569	−0.748391
$334$	−21.9301	−1.19996
$335$	13.7143	0.749293
$336$	−7.68092	−0.419028
$337$	4.91991	0.268005	0.134002	−	0.990981i	$-0.457217\pi$
$337$	4.91991	0.268005	0.134002	+	0.990981i	$0.457217\pi$
$338$	12.0693	0.656484
$339$	−3.67511	−0.199605
$340$	3.19980	0.173534
$341$	−3.84480	−0.208208
$342$	−20.9189	−1.13117
$343$	12.3374	0.666156
$344$	−4.21441	−0.227226
$345$	0	0
$346$	2.50454	0.134645
$347$	16.4979	0.885654	0.442827	−	0.896607i	$-0.353976\pi$
$347$	16.4979	0.885654	0.442827	+	0.896607i	$0.353976\pi$
$348$	1.31784	0.0706435
$349$	26.2900	1.40727	0.703637	−	0.710560i	$-0.251558\pi$
$349$	26.2900	1.40727	0.703637	+	0.710560i	$0.251558\pi$
$350$	3.18154	0.170060
$351$	0.399602	0.0213292
$352$	0.378937	0.0201974
$353$	15.8466	0.843430	0.421715	−	0.906729i	$-0.361428\pi$
$353$	15.8466	0.843430	0.421715	+	0.906729i	$0.361428\pi$
$354$	−7.24264	−0.384942
$355$	−11.2521	−0.597199
$356$	−17.7067	−0.938455
$357$	24.5774	1.30077
$358$	25.2360	1.33377
$359$	25.5719	1.34963	0.674815	−	0.737987i	$-0.264223\pi$
$359$	25.5719	1.34963	0.674815	+	0.737987i	$0.264223\pi$
$360$	2.82843	0.149071
$361$	35.7001	1.87895
$362$	6.67220	0.350683
$363$	−26.2097	−1.37565
$364$	3.06931	0.160875
$365$	6.78799	0.355300
$366$	23.5546	1.23122
$367$	24.8808	1.29876	0.649382	−	0.760462i	$-0.275027\pi$
$367$	24.8808	1.29876	0.649382	+	0.760462i	$0.275027\pi$
$368$	0	0
$369$	−17.7153	−0.922222
$370$	−4.82843	−0.251018
$371$	30.4828	1.58259
$372$	24.4952	1.27002
$373$	20.1463	1.04313	0.521567	−	0.853210i	$-0.325348\pi$
$373$	20.1463	1.04313	0.521567	+	0.853210i	$0.325348\pi$
$374$	−1.21252	−0.0626981
$375$	−2.41421	−0.124669
$376$	−2.54587	−0.131293
$377$	−0.526610	−0.0271218
$378$	−1.31784	−0.0677822
$379$	−5.96661	−0.306484	−0.153242	−	0.988189i	$-0.548971\pi$
$379$	−5.96661	−0.306484	−0.153242	+	0.988189i	$0.548971\pi$
$380$	−7.39595	−0.379404
$381$	19.8372	1.01629
$382$	8.91624	0.456195
$383$	24.7685	1.26561	0.632806	−	0.774310i	$-0.281903\pi$
$383$	24.7685	1.26561	0.632806	+	0.774310i	$0.281903\pi$
$384$	−2.41421	−0.123200
$385$	−1.20560	−0.0614433
$386$	10.8571	0.552614
$387$	11.9202	0.605936
$388$	−14.7712	−0.749896
$389$	−24.4901	−1.24170	−0.620848	−	0.783931i	$-0.713212\pi$
$389$	−24.4901	−1.24170	−0.620848	+	0.783931i	$0.713212\pi$
$390$	−2.32905	−0.117936
$391$	0	0
$392$	−3.12220	−0.157695
$393$	−43.1603	−2.17715
$394$	17.5687	0.885098
$395$	−16.6091	−0.835696
$396$	−1.07180	−0.0538598
$397$	12.7142	0.638108	0.319054	−	0.947737i	$-0.396635\pi$
$397$	12.7142	0.638108	0.319054	+	0.947737i	$0.396635\pi$
$398$	−7.45997	−0.373935
$399$	−56.8077	−2.84394
$400$	1.00000	0.0500000
$401$	17.3020	0.864021	0.432011	−	0.901868i	$-0.357804\pi$
$401$	17.3020	0.864021	0.432011	+	0.901868i	$0.357804\pi$
$402$	33.1093	1.65134
$403$	−9.78834	−0.487592
$404$	−9.36433	−0.465893
$405$	9.48528	0.471327
$406$	1.73670	0.0861907
$407$	1.82967	0.0906935
$408$	7.72500	0.382445
$409$	−27.7228	−1.37080	−0.685401	−	0.728166i	$-0.740373\pi$
$409$	−27.7228	−1.37080	−0.685401	+	0.728166i	$0.740373\pi$
$410$	−6.26330	−0.309323
$411$	21.8636	1.07845
$412$	−8.19756	−0.403865
$413$	−9.54462	−0.469660
$414$	0	0
$415$	13.9917	0.686826
$416$	0.964724	0.0472995
$417$	42.0885	2.06108
$418$	2.80260	0.137080
$419$	2.39521	0.117013	0.0585067	−	0.998287i	$-0.481366\pi$
$419$	2.39521	0.117013	0.0585067	+	0.998287i	$0.481366\pi$
$420$	7.68092	0.374790
$421$	−0.479091	−0.0233495	−0.0116747	−	0.999932i	$-0.503716\pi$
$421$	−0.479091	−0.0233495	−0.0116747	+	0.999932i	$0.503716\pi$
$422$	22.2820	1.08467
$423$	7.20080	0.350115
$424$	9.58114	0.465301
$425$	−3.19980	−0.155213
$426$	−27.1650	−1.31615
$427$	31.0411	1.50218
$428$	5.07107	0.245119
$429$	0.882564	0.0426106
$430$	4.21441	0.203237
$431$	32.2843	1.55508	0.777539	−	0.628834i	$-0.216468\pi$
$431$	32.2843	1.55508	0.777539	+	0.628834i	$0.216468\pi$
$432$	−0.414214	−0.0199289
$433$	−5.89366	−0.283231	−0.141616	−	0.989922i	$-0.545230\pi$
$433$	−5.89366	−0.283231	−0.141616	+	0.989922i	$0.545230\pi$
$434$	32.2808	1.54953
$435$	−1.31784	−0.0631855
$436$	2.90895	0.139313
$437$	0	0
$438$	16.3877	0.783033
$439$	−26.5784	−1.26852	−0.634260	−	0.773120i	$-0.718695\pi$
$439$	−26.5784	−1.26852	−0.634260	+	0.773120i	$0.718695\pi$
$440$	−0.378937	−0.0180651
$441$	8.83092	0.420520
$442$	−3.08692	−0.146830
$443$	7.27186	0.345497	0.172748	−	0.984966i	$-0.444735\pi$
$443$	7.27186	0.345497	0.172748	+	0.984966i	$0.444735\pi$
$444$	−11.6569	−0.553210
$445$	17.7067	0.839380
$446$	12.2633	0.580684
$447$	−23.9959	−1.13497
$448$	−3.18154	−0.150314
$449$	−5.53250	−0.261095	−0.130547	−	0.991442i	$-0.541673\pi$
$449$	−5.53250	−0.261095	−0.130547	+	0.991442i	$0.541673\pi$
$450$	−2.82843	−0.133333
$451$	2.37340	0.111759
$452$	−1.52228	−0.0716021
$453$	22.6780	1.06551
$454$	10.1920	0.478334
$455$	−3.06931	−0.143891
$456$	−17.8554	−0.836156
$457$	16.0942	0.752857	0.376428	−	0.926446i	$-0.377152\pi$
$457$	16.0942	0.752857	0.376428	+	0.926446i	$0.377152\pi$
$458$	−4.28256	−0.200111
$459$	1.32540	0.0618644
$460$	0	0
$461$	−10.2540	−0.477577	−0.238789	−	0.971072i	$-0.576750\pi$
$461$	−10.2540	−0.477577	−0.238789	+	0.971072i	$0.576750\pi$
$462$	−2.91059	−0.135413
$463$	−2.87175	−0.133461	−0.0667307	−	0.997771i	$-0.521257\pi$
$463$	−2.87175	−0.133461	−0.0667307	+	0.997771i	$0.521257\pi$
$464$	0.545866	0.0253412
$465$	−24.4952	−1.13594
$466$	2.86783	0.132850
$467$	22.4450	1.03863	0.519316	−	0.854583i	$-0.326187\pi$
$467$	22.4450	1.03863	0.519316	+	0.854583i	$0.326187\pi$
$468$	−2.72865	−0.126132
$469$	43.6326	2.01477
$470$	2.54587	0.117432
$471$	−1.62282	−0.0747757
$472$	−3.00000	−0.138086
$473$	−1.59700	−0.0734301
$474$	−40.0980	−1.84176
$475$	7.39595	0.339350
$476$	10.1803	0.466613
$477$	−27.0996	−1.24080
$478$	6.30463	0.288367
$479$	−13.3226	−0.608727	−0.304364	−	0.952556i	$-0.598444\pi$
$479$	−13.3226	−0.608727	−0.304364	+	0.952556i	$0.598444\pi$
$480$	2.41421	0.110193
$481$	4.65810	0.212391
$482$	−19.5887	−0.892241
$483$	0	0
$484$	−10.8564	−0.493473
$485$	14.7712	0.670728
$486$	21.6569	0.982375
$487$	−40.4151	−1.83138	−0.915691	−	0.401884i	$-0.868355\pi$
$487$	−40.4151	−1.83138	−0.915691	+	0.401884i	$0.868355\pi$
$488$	9.75663	0.441662
$489$	−33.6062	−1.51973
$490$	3.12220	0.141047
$491$	33.7274	1.52210	0.761048	−	0.648695i	$-0.224685\pi$
$491$	33.7274	1.52210	0.761048	+	0.648695i	$0.224685\pi$
$492$	−15.1210	−0.681705
$493$	−1.74666	−0.0786657
$494$	7.13505	0.321021
$495$	1.07180	0.0481737
$496$	10.1463	0.455581
$497$	−35.7990	−1.60580
$498$	33.7790	1.51367
$499$	−30.9211	−1.38422	−0.692109	−	0.721793i	$-0.743318\pi$
$499$	−30.9211	−1.38422	−0.692109	+	0.721793i	$0.743318\pi$
$500$	−1.00000	−0.0447214
$501$	52.9440	2.36536
$502$	14.4970	0.647032
$503$	−24.1751	−1.07792	−0.538958	−	0.842333i	$-0.681182\pi$
$503$	−24.1751	−1.07792	−0.538958	+	0.842333i	$0.681182\pi$
$504$	8.99876	0.400836
$505$	9.36433	0.416707
$506$	0	0
$507$	−29.1379	−1.29406
$508$	8.21682	0.364562
$509$	1.69302	0.0750419	0.0375210	−	0.999296i	$-0.488054\pi$
$509$	1.69302	0.0750419	0.0375210	+	0.999296i	$0.488054\pi$
$510$	−7.72500	−0.342069
$511$	21.5963	0.955363
$512$	−1.00000	−0.0441942
$513$	−3.06350	−0.135257
$514$	−3.61501	−0.159451
$515$	8.19756	0.361228
$516$	10.1745	0.447907
$517$	−0.964724	−0.0424285
$518$	−15.3618	−0.674960
$519$	−6.04649	−0.265411
$520$	−0.964724	−0.0423059
$521$	−21.9822	−0.963056	−0.481528	−	0.876431i	$-0.659918\pi$
$521$	−21.9822	−0.963056	−0.481528	+	0.876431i	$0.659918\pi$
$522$	−1.54394	−0.0675765
$523$	−4.91003	−0.214701	−0.107350	−	0.994221i	$-0.534237\pi$
$523$	−4.91003	−0.214701	−0.107350	+	0.994221i	$0.534237\pi$
$524$	−17.8776	−0.780986
$525$	−7.68092	−0.335223
$526$	−3.72940	−0.162609
$527$	−32.4660	−1.41424
$528$	−0.914836	−0.0398131
$529$	0	0
$530$	−9.58114	−0.416178
$531$	8.48528	0.368230
$532$	−23.5305	−1.02018
$533$	6.04236	0.261724
$534$	42.7479	1.84988
$535$	−5.07107	−0.219241
$536$	13.7143	0.592368
$537$	−60.9251	−2.62911
$538$	−27.8471	−1.20057
$539$	−1.18312	−0.0509605
$540$	0.414214	0.0178249
$541$	31.1498	1.33924	0.669618	−	0.742706i	$-0.266458\pi$
$541$	31.1498	1.33924	0.669618	+	0.742706i	$0.266458\pi$
$542$	−1.11512	−0.0478984
$543$	−16.1081	−0.691265
$544$	3.19980	0.137190
$545$	−2.90895	−0.124606
$546$	−7.40996	−0.317117
$547$	19.1127	0.817200	0.408600	−	0.912714i	$-0.366017\pi$
$547$	19.1127	0.817200	0.408600	+	0.912714i	$0.366017\pi$
$548$	9.05621	0.386862
$549$	−27.5959	−1.17777
$550$	0.378937	0.0161579
$551$	4.03720	0.171990
$552$	0	0
$553$	−52.8426	−2.24710
$554$	11.5033	0.488728
$555$	11.6569	0.494806
$556$	17.4336	0.739351
$557$	6.38138	0.270388	0.135194	−	0.990819i	$-0.456834\pi$
$557$	6.38138	0.270388	0.135194	+	0.990819i	$0.456834\pi$
$558$	−28.6980	−1.21488
$559$	−4.06574	−0.171963
$560$	3.18154	0.134445
$561$	2.92729	0.123590
$562$	−10.5534	−0.445170
$563$	−14.4336	−0.608304	−0.304152	−	0.952624i	$-0.598373\pi$
$563$	−14.4336	−0.608304	−0.304152	+	0.952624i	$0.598373\pi$
$564$	6.14626	0.258804
$565$	1.52228	0.0640429
$566$	−14.0330	−0.589852
$567$	30.1778	1.26735
$568$	−11.2521	−0.472127
$569$	1.15404	0.0483799	0.0241900	−	0.999707i	$-0.492299\pi$
$569$	1.15404	0.0483799	0.0241900	+	0.999707i	$0.492299\pi$
$570$	17.8554	0.747881
$571$	−35.6984	−1.49393	−0.746966	−	0.664862i	$-0.768490\pi$
$571$	−35.6984	−1.49393	−0.746966	+	0.664862i	$0.768490\pi$
$572$	0.365570	0.0152852
$573$	−21.5257	−0.899250
$574$	−19.9270	−0.831735
$575$	0	0
$576$	2.82843	0.117851
$577$	−35.2426	−1.46717	−0.733584	−	0.679599i	$-0.762154\pi$
$577$	−35.2426	−1.46717	−0.733584	+	0.679599i	$0.762154\pi$
$578$	6.76127	0.281232
$579$	−26.2114	−1.08931
$580$	−0.545866	−0.0226659
$581$	44.5152	1.84680
$582$	35.6609	1.47819
$583$	3.63065	0.150366
$584$	6.78799	0.280889
$585$	2.72865	0.112816
$586$	0.849820	0.0351058
$587$	47.9659	1.97977	0.989883	−	0.141886i	$-0.0453166\pi$
$587$	47.9659	1.97977	0.989883	+	0.141886i	$0.0453166\pi$
$588$	7.53766	0.310848
$589$	75.0413	3.09202
$590$	3.00000	0.123508
$591$	−42.4146	−1.74470
$592$	−4.82843	−0.198447
$593$	2.31195	0.0949404	0.0474702	−	0.998873i	$-0.484884\pi$
$593$	2.31195	0.0949404	0.0474702	+	0.998873i	$0.484884\pi$
$594$	−0.156961	−0.00644019
$595$	−10.1803	−0.417351
$596$	−9.93942	−0.407134
$597$	18.0100	0.737099
$598$	0	0
$599$	9.03795	0.369281	0.184640	−	0.982806i	$-0.440888\pi$
$599$	9.03795	0.369281	0.184640	+	0.982806i	$0.440888\pi$
$600$	−2.41421	−0.0985599
$601$	3.20610	0.130780	0.0653898	−	0.997860i	$-0.479171\pi$
$601$	3.20610	0.130780	0.0653898	+	0.997860i	$0.479171\pi$
$602$	13.4083	0.546483
$603$	−38.7899	−1.57965
$604$	9.39355	0.382218
$605$	10.8564	0.441376
$606$	22.6075	0.918366
$607$	42.9168	1.74194	0.870969	−	0.491338i	$-0.163492\pi$
$607$	42.9168	1.74194	0.870969	+	0.491338i	$0.163492\pi$
$608$	−7.39595	−0.299946
$609$	−4.19275	−0.169899
$610$	−9.75663	−0.395034
$611$	−2.45606	−0.0993615
$612$	−9.05040	−0.365841
$613$	29.8420	1.20531	0.602653	−	0.798004i	$-0.294110\pi$
$613$	29.8420	1.20531	0.602653	+	0.798004i	$0.294110\pi$
$614$	−9.57650	−0.386476
$615$	15.1210	0.609736
$616$	−1.20560	−0.0485752
$617$	10.0888	0.406158	0.203079	−	0.979162i	$-0.434905\pi$
$617$	10.0888	0.406158	0.203079	+	0.979162i	$0.434905\pi$
$618$	19.7907	0.796097
$619$	18.9416	0.761326	0.380663	−	0.924714i	$-0.375696\pi$
$619$	18.9416	0.761326	0.380663	+	0.924714i	$0.375696\pi$
$620$	−10.1463	−0.407484
$621$	0	0
$622$	15.0331	0.602774
$623$	56.3347	2.25700
$624$	−2.32905	−0.0932366
$625$	1.00000	0.0400000
$626$	−24.0623	−0.961721
$627$	−6.76608	−0.270211
$628$	−0.672195	−0.0268235
$629$	15.4500	0.616032
$630$	−8.99876	−0.358519
$631$	20.2665	0.806796	0.403398	−	0.915025i	$-0.367829\pi$
$631$	20.2665	0.806796	0.403398	+	0.915025i	$0.367829\pi$
$632$	−16.6091	−0.660675
$633$	−53.7935	−2.13810
$634$	1.49546	0.0593924
$635$	−8.21682	−0.326074
$636$	−23.1309	−0.917201
$637$	−3.01206	−0.119342
$638$	0.206849	0.00818923
$639$	31.8257	1.25901
$640$	1.00000	0.0395285
$641$	−18.2110	−0.719292	−0.359646	−	0.933089i	$-0.617103\pi$
$641$	−18.2110	−0.719292	−0.359646	+	0.933089i	$0.617103\pi$
$642$	−12.2426	−0.483178
$643$	−16.1507	−0.636921	−0.318461	−	0.947936i	$-0.603166\pi$
$643$	−16.1507	−0.636921	−0.318461	+	0.947936i	$0.603166\pi$
$644$	0	0
$645$	−10.1745	−0.400620
$646$	23.6656	0.931110
$647$	−25.5186	−1.00324	−0.501619	−	0.865089i	$-0.667262\pi$
$647$	−25.5186	−1.00324	−0.501619	+	0.865089i	$0.667262\pi$
$648$	9.48528	0.372617
$649$	−1.13681	−0.0446238
$650$	0.964724	0.0378396
$651$	−77.9326	−3.05442
$652$	−13.9202	−0.545156
$653$	−39.1723	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$653$	−39.1723	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$654$	−7.02282	−0.274614
$655$	17.8776	0.698535
$656$	−6.26330	−0.244541
$657$	−19.1993	−0.749038
$658$	8.09978	0.315762
$659$	1.10750	0.0431422	0.0215711	−	0.999767i	$-0.493133\pi$
$659$	1.10750	0.0431422	0.0215711	+	0.999767i	$0.493133\pi$
$660$	0.914836	0.0356099
$661$	−7.25939	−0.282358	−0.141179	−	0.989984i	$-0.545089\pi$
$661$	−7.25939	−0.282358	−0.141179	+	0.989984i	$0.545089\pi$
$662$	28.8471	1.12118
$663$	7.45249	0.289431
$664$	13.9917	0.542984
$665$	23.5305	0.912475
$666$	13.6569	0.529192
$667$	0	0
$668$	21.9301	0.848502
$669$	−29.6062	−1.14464
$670$	−13.7143	−0.529830
$671$	3.69715	0.142727
$672$	7.68092	0.296298
$673$	4.16156	0.160416	0.0802081	−	0.996778i	$-0.474442\pi$
$673$	4.16156	0.160416	0.0802081	+	0.996778i	$0.474442\pi$
$674$	−4.91991	−0.189508
$675$	−0.414214	−0.0159431
$676$	−12.0693	−0.464204
$677$	−45.6775	−1.75553	−0.877764	−	0.479094i	$-0.840965\pi$
$677$	−45.6775	−1.75553	−0.877764	+	0.479094i	$0.840965\pi$
$678$	3.67511	0.141142
$679$	46.9953	1.80351
$680$	−3.19980	−0.122707
$681$	−24.6056	−0.942890
$682$	3.84480	0.147225
$683$	−30.2920	−1.15909	−0.579545	−	0.814940i	$-0.696770\pi$
$683$	−30.2920	−1.15909	−0.579545	+	0.814940i	$0.696770\pi$
$684$	20.9189	0.799855
$685$	−9.05621	−0.346020
$686$	−12.3374	−0.471043
$687$	10.3390	0.394458
$688$	4.21441	0.160673
$689$	9.24316	0.352136
$690$	0	0
$691$	32.5637	1.23878	0.619390	−	0.785083i	$-0.287380\pi$
$691$	32.5637	1.23878	0.619390	+	0.785083i	$0.287380\pi$
$692$	−2.50454	−0.0952082
$693$	3.40996	0.129534
$694$	−16.4979	−0.626252
$695$	−17.4336	−0.661295
$696$	−1.31784	−0.0499525
$697$	20.0413	0.759119
$698$	−26.2900	−0.995093
$699$	−6.92356	−0.261873
$700$	−3.18154	−0.120251
$701$	−42.3103	−1.59804	−0.799019	−	0.601305i	$-0.794648\pi$
$701$	−42.3103	−1.59804	−0.799019	+	0.601305i	$0.794648\pi$
$702$	−0.399602	−0.0150820
$703$	−35.7108	−1.34686
$704$	−0.378937	−0.0142817
$705$	−6.14626	−0.231482
$706$	−15.8466	−0.596395
$707$	29.7930	1.12048
$708$	7.24264	0.272195
$709$	7.78119	0.292229	0.146114	−	0.989268i	$-0.453323\pi$
$709$	7.78119	0.292229	0.146114	+	0.989268i	$0.453323\pi$
$710$	11.2521	0.422284
$711$	46.9777	1.76180
$712$	17.7067	0.663588
$713$	0	0
$714$	−24.5774	−0.919786
$715$	−0.365570	−0.0136715
$716$	−25.2360	−0.943114
$717$	−15.2207	−0.568429
$718$	−25.5719	−0.954333
$719$	−45.8254	−1.70900	−0.854499	−	0.519453i	$-0.826136\pi$
$719$	−45.8254	−1.70900	−0.854499	+	0.519453i	$0.826136\pi$
$720$	−2.82843	−0.105409
$721$	26.0809	0.971302
$722$	−35.7001	−1.32862
$723$	47.2913	1.75878
$724$	−6.67220	−0.247970
$725$	0.545866	0.0202730
$726$	26.2097	0.972733
$727$	39.6130	1.46917	0.734583	−	0.678519i	$-0.237378\pi$
$727$	39.6130	1.46917	0.734583	+	0.678519i	$0.237378\pi$
$728$	−3.06931	−0.113756
$729$	−23.8284	−0.882534
$730$	−6.78799	−0.251235
$731$	−13.4853	−0.498771
$732$	−23.5546	−0.870603
$733$	−1.64689	−0.0608291	−0.0304146	−	0.999537i	$-0.509683\pi$
$733$	−1.64689	−0.0608291	−0.0304146	+	0.999537i	$0.509683\pi$
$734$	−24.8808	−0.918365
$735$	−7.53766	−0.278031
$736$	0	0
$737$	5.19686	0.191429
$738$	17.7153	0.652109
$739$	19.2913	0.709641	0.354821	−	0.934934i	$-0.384542\pi$
$739$	19.2913	0.709641	0.354821	+	0.934934i	$0.384542\pi$
$740$	4.82843	0.177497
$741$	−17.2255	−0.632796
$742$	−30.4828	−1.11906
$743$	−17.7321	−0.650527	−0.325263	−	0.945624i	$-0.605453\pi$
$743$	−17.7321	−0.650527	−0.325263	+	0.945624i	$0.605453\pi$
$744$	−24.4952	−0.898039
$745$	9.93942	0.364152
$746$	−20.1463	−0.737607
$747$	−39.5745	−1.44796
$748$	1.21252	0.0443343
$749$	−16.1338	−0.589517
$750$	2.41421	0.0881546
$751$	−14.7544	−0.538397	−0.269198	−	0.963085i	$-0.586759\pi$
$751$	−14.7544	−0.538397	−0.269198	+	0.963085i	$0.586759\pi$
$752$	2.54587	0.0928382
$753$	−34.9988	−1.27543
$754$	0.526610	0.0191780
$755$	−9.39355	−0.341866
$756$	1.31784	0.0479293
$757$	−22.9712	−0.834904	−0.417452	−	0.908699i	$-0.637077\pi$
$757$	−22.9712	−0.834904	−0.417452	+	0.908699i	$0.637077\pi$
$758$	5.96661	0.216717
$759$	0	0
$760$	7.39595	0.268279
$761$	1.11631	0.0404663	0.0202331	−	0.999795i	$-0.493559\pi$
$761$	1.11631	0.0404663	0.0202331	+	0.999795i	$0.493559\pi$
$762$	−19.8372	−0.718624
$763$	−9.25493	−0.335051
$764$	−8.91624	−0.322578
$765$	9.05040	0.327218
$766$	−24.7685	−0.894923
$767$	−2.89417	−0.104502
$768$	2.41421	0.0871154
$769$	−32.7065	−1.17943	−0.589714	−	0.807612i	$-0.700759\pi$
$769$	−32.7065	−1.17943	−0.589714	+	0.807612i	$0.700759\pi$
$770$	1.20560	0.0434470
$771$	8.72741	0.314310
$772$	−10.8571	−0.390757
$773$	32.1528	1.15646	0.578228	−	0.815876i	$-0.303745\pi$
$773$	32.1528	1.15646	0.578228	+	0.815876i	$0.303745\pi$
$774$	−11.9202	−0.428461
$775$	10.1463	0.364465
$776$	14.7712	0.530257
$777$	37.0868	1.33048
$778$	24.4901	0.878012
$779$	−46.3231	−1.65970
$780$	2.32905	0.0833933
$781$	−4.26384	−0.152572
$782$	0	0
$783$	−0.226105	−0.00808034
$784$	3.12220	0.111507
$785$	0.672195	0.0239917
$786$	43.1603	1.53948
$787$	43.3113	1.54388	0.771940	−	0.635696i	$-0.219287\pi$
$787$	43.3113	1.54388	0.771940	+	0.635696i	$0.219287\pi$
$788$	−17.5687	−0.625859
$789$	9.00356	0.320535
$790$	16.6091	0.590926
$791$	4.84320	0.172204
$792$	1.07180	0.0380846
$793$	9.41245	0.334246
$794$	−12.7142	−0.451210
$795$	23.1309	0.820369
$796$	7.45997	0.264412
$797$	−53.7188	−1.90282	−0.951409	−	0.307931i	$-0.900363\pi$
$797$	−53.7188	−1.90282	−0.951409	+	0.307931i	$0.900363\pi$
$798$	56.8077	2.01097
$799$	−8.14626	−0.288194
$800$	−1.00000	−0.0353553
$801$	−50.0822	−1.76957
$802$	−17.3020	−0.610955
$803$	2.57222	0.0907718
$804$	−33.1093	−1.16767
$805$	0	0
$806$	9.78834	0.344780
$807$	67.2289	2.36657
$808$	9.36433	0.329436
$809$	3.88347	0.136536	0.0682679	−	0.997667i	$-0.478253\pi$
$809$	3.88347	0.136536	0.0682679	+	0.997667i	$0.478253\pi$
$810$	−9.48528	−0.333279
$811$	26.3686	0.925928	0.462964	−	0.886377i	$-0.346786\pi$
$811$	26.3686	0.925928	0.462964	+	0.886377i	$0.346786\pi$
$812$	−1.73670	−0.0609460
$813$	2.69213	0.0944171
$814$	−1.82967	−0.0641300
$815$	13.9202	0.487602
$816$	−7.72500	−0.270429
$817$	31.1696	1.09049
$818$	27.7228	0.969304
$819$	8.68131	0.303350
$820$	6.26330	0.218724
$821$	−19.2724	−0.672611	−0.336305	−	0.941753i	$-0.609177\pi$
$821$	−19.2724	−0.672611	−0.336305	+	0.941753i	$0.609177\pi$
$822$	−21.8636	−0.762581
$823$	23.0456	0.803318	0.401659	−	0.915789i	$-0.368434\pi$
$823$	23.0456	0.803318	0.401659	+	0.915789i	$0.368434\pi$
$824$	8.19756	0.285576
$825$	−0.914836	−0.0318505
$826$	9.54462	0.332100
$827$	−46.3594	−1.61207	−0.806037	−	0.591866i	$-0.798392\pi$
$827$	−46.3594	−1.61207	−0.806037	+	0.591866i	$0.798392\pi$
$828$	0	0
$829$	12.9939	0.451298	0.225649	−	0.974209i	$-0.427550\pi$
$829$	12.9939	0.451298	0.225649	+	0.974209i	$0.427550\pi$
$830$	−13.9917	−0.485659
$831$	−27.7714	−0.963379
$832$	−0.964724	−0.0334458
$833$	−9.99042	−0.346148
$834$	−42.0885	−1.45741
$835$	−21.9301	−0.758923
$836$	−2.80260	−0.0969301
$837$	−4.20272	−0.145267
$838$	−2.39521	−0.0827410
$839$	−34.1981	−1.18065	−0.590325	−	0.807166i	$-0.701000\pi$
$839$	−34.1981	−1.18065	−0.590325	+	0.807166i	$0.701000\pi$
$840$	−7.68092	−0.265017
$841$	−28.7020	−0.989725
$842$	0.479091	0.0165106
$843$	25.4782	0.877517
$844$	−22.2820	−0.766978
$845$	12.0693	0.415197
$846$	−7.20080	−0.247568
$847$	34.5401	1.18681
$848$	−9.58114	−0.329018
$849$	33.8787	1.16272
$850$	3.19980	0.109752
$851$	0	0
$852$	27.1650	0.930656
$853$	−23.9952	−0.821580	−0.410790	−	0.911730i	$-0.634747\pi$
$853$	−23.9952	−0.821580	−0.410790	+	0.911730i	$0.634747\pi$
$854$	−31.0411	−1.06221
$855$	−20.9189	−0.715412
$856$	−5.07107	−0.173326
$857$	−22.3839	−0.764620	−0.382310	−	0.924034i	$-0.624871\pi$
$857$	−22.3839	−0.764620	−0.382310	+	0.924034i	$0.624871\pi$
$858$	−0.882564	−0.0301302
$859$	2.36876	0.0808209	0.0404105	−	0.999183i	$-0.487133\pi$
$859$	2.36876	0.0808209	0.0404105	+	0.999183i	$0.487133\pi$
$860$	−4.21441	−0.143710
$861$	48.1079	1.63951
$862$	−32.2843	−1.09961
$863$	20.9558	0.713343	0.356672	−	0.934230i	$-0.383911\pi$
$863$	20.9558	0.713343	0.356672	+	0.934230i	$0.383911\pi$
$864$	0.414214	0.0140918
$865$	2.50454	0.0851568
$866$	5.89366	0.200275
$867$	−16.3232	−0.554364
$868$	−32.2808	−1.09568
$869$	−6.29382	−0.213503
$870$	1.31784	0.0446789
$871$	13.2305	0.448299
$872$	−2.90895	−0.0985094
$873$	−41.7794	−1.41402
$874$	0	0
$875$	3.18154	0.107556
$876$	−16.3877	−0.553688
$877$	−27.6307	−0.933021	−0.466510	−	0.884516i	$-0.654489\pi$
$877$	−27.6307	−0.933021	−0.466510	+	0.884516i	$0.654489\pi$
$878$	26.5784	0.896979
$879$	−2.05165	−0.0692004
$880$	0.378937	0.0127740
$881$	−42.2216	−1.42248	−0.711241	−	0.702949i	$-0.751866\pi$
$881$	−42.2216	−1.42248	−0.711241	+	0.702949i	$0.751866\pi$
$882$	−8.83092	−0.297352
$883$	−1.70658	−0.0574309	−0.0287155	−	0.999588i	$-0.509142\pi$
$883$	−1.70658	−0.0574309	−0.0287155	+	0.999588i	$0.509142\pi$
$884$	3.08692	0.103824
$885$	−7.24264	−0.243459
$886$	−7.27186	−0.244303
$887$	−42.2373	−1.41819	−0.709095	−	0.705113i	$-0.750896\pi$
$887$	−42.2373	−1.41819	−0.709095	+	0.705113i	$0.750896\pi$
$888$	11.6569	0.391178
$889$	−26.1421	−0.876779
$890$	−17.7067	−0.593531
$891$	3.59433	0.120415
$892$	−12.2633	−0.410606
$893$	18.8291	0.630092
$894$	23.9959	0.802542
$895$	25.2360	0.843547
$896$	3.18154	0.106288
$897$	0	0
$898$	5.53250	0.184622
$899$	5.53850	0.184719
$900$	2.82843	0.0942809
$901$	30.6577	1.02136
$902$	−2.37340	−0.0790256
$903$	−32.3706	−1.07722
$904$	1.52228	0.0506304
$905$	6.67220	0.221791
$906$	−22.6780	−0.753427
$907$	5.67924	0.188576	0.0942881	−	0.995545i	$-0.469943\pi$
$907$	5.67924	0.188576	0.0942881	+	0.995545i	$0.469943\pi$
$908$	−10.1920	−0.338233
$909$	−26.4863	−0.878496
$910$	3.06931	0.101747
$911$	−9.92162	−0.328718	−0.164359	−	0.986401i	$-0.552556\pi$
$911$	−9.92162	−0.328718	−0.164359	+	0.986401i	$0.552556\pi$
$912$	17.8554	0.591252
$913$	5.30198	0.175470
$914$	−16.0942	−0.532350
$915$	23.5546	0.778691
$916$	4.28256	0.141500
$917$	56.8783	1.87829
$918$	−1.32540	−0.0437447
$919$	−11.9150	−0.393040	−0.196520	−	0.980500i	$-0.562964\pi$
$919$	−11.9150	−0.393040	−0.196520	+	0.980500i	$0.562964\pi$
$920$	0	0
$921$	23.1197	0.761820
$922$	10.2540	0.337698
$923$	−10.8552	−0.357302
$924$	2.91059	0.0957513
$925$	−4.82843	−0.158758
$926$	2.87175	0.0943715
$927$	−23.1862	−0.761535
$928$	−0.545866	−0.0179189
$929$	24.8088	0.813951	0.406975	−	0.913439i	$-0.366583\pi$
$929$	24.8088	0.813951	0.406975	+	0.913439i	$0.366583\pi$
$930$	24.4952	0.803231
$931$	23.0916	0.756798
$932$	−2.86783	−0.0939390
$933$	−36.2932	−1.18819
$934$	−22.4450	−0.734423
$935$	−1.21252	−0.0396538
$936$	2.72865	0.0891887
$937$	32.9338	1.07590	0.537950	−	0.842977i	$-0.319199\pi$
$937$	32.9338	1.07590	0.537950	+	0.842977i	$0.319199\pi$
$938$	−43.6326	−1.42466
$939$	58.0914	1.89574
$940$	−2.54587	−0.0830370
$941$	23.3320	0.760602	0.380301	−	0.924863i	$-0.375820\pi$
$941$	23.3320	0.760602	0.380301	+	0.924863i	$0.375820\pi$
$942$	1.62282	0.0528744
$943$	0	0
$944$	3.00000	0.0976417
$945$	−1.31784	−0.0428692
$946$	1.59700	0.0519229
$947$	42.6736	1.38670	0.693352	−	0.720599i	$-0.256133\pi$
$947$	42.6736	1.38670	0.693352	+	0.720599i	$0.256133\pi$
$948$	40.0980	1.30232
$949$	6.54854	0.212575
$950$	−7.39595	−0.239956
$951$	−3.61037	−0.117074
$952$	−10.1803	−0.329945
$953$	−33.2127	−1.07587	−0.537933	−	0.842988i	$-0.680794\pi$
$953$	−33.2127	−1.07587	−0.537933	+	0.842988i	$0.680794\pi$
$954$	27.0996	0.877381
$955$	8.91624	0.288523
$956$	−6.30463	−0.203906
$957$	−0.499378	−0.0161426
$958$	13.3226	0.430435
$959$	−28.8127	−0.930410
$960$	−2.41421	−0.0779184
$961$	71.9467	2.32086
$962$	−4.65810	−0.150183
$963$	14.3431	0.462201
$964$	19.5887	0.630910
$965$	10.8571	0.349504
$966$	0	0
$967$	−16.7178	−0.537609	−0.268805	−	0.963195i	$-0.586629\pi$
$967$	−16.7178	−0.537609	−0.268805	+	0.963195i	$0.586629\pi$
$968$	10.8564	0.348938
$969$	−57.1338	−1.83540
$970$	−14.7712	−0.474276
$971$	−26.1581	−0.839455	−0.419727	−	0.907650i	$-0.637874\pi$
$971$	−26.1581	−0.839455	−0.419727	+	0.907650i	$0.637874\pi$
$972$	−21.6569	−0.694644
$973$	−55.4658	−1.77815
$974$	40.4151	1.29498
$975$	−2.32905	−0.0745893
$976$	−9.75663	−0.312302
$977$	35.1898	1.12582	0.562911	−	0.826518i	$-0.309681\pi$
$977$	35.1898	1.12582	0.562911	+	0.826518i	$0.309681\pi$
$978$	33.6062	1.07461
$979$	6.70975	0.214444
$980$	−3.12220	−0.0997350
$981$	8.22775	0.262692
$982$	−33.7274	−1.07628
$983$	14.5238	0.463237	0.231619	−	0.972807i	$-0.425598\pi$
$983$	14.5238	0.463237	0.231619	+	0.972807i	$0.425598\pi$
$984$	15.1210	0.482038
$985$	17.5687	0.559785
$986$	1.74666	0.0556251
$987$	−19.5546	−0.622429
$988$	−7.13505	−0.226996
$989$	0	0
$990$	−1.07180	−0.0340639
$991$	−21.5531	−0.684658	−0.342329	−	0.939580i	$-0.611216\pi$
$991$	−21.5531	−0.684658	−0.342329	+	0.939580i	$0.611216\pi$
$992$	−10.1463	−0.322144
$993$	−69.6431	−2.21006
$994$	35.7990	1.13548
$995$	−7.45997	−0.236497
$996$	−33.7790	−1.07033
$997$	23.0318	0.729425	0.364713	−	0.931120i	$-0.381167\pi$
$997$	23.0318	0.729425	0.364713	+	0.931120i	$0.381167\pi$
$998$	30.9211	0.978789
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.u.1.3	✓	4
23.22	odd	2		5290.2.a.v.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.u.1.3	✓	4	1.1	even	1	trivial
5290.2.a.v.1.4	yes	4	23.22	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} -3.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} -3.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} -0.378937 q^{11} +2.41421 q^{12} -0.964724 q^{13} +3.18154 q^{14} -2.41421 q^{15} +1.00000 q^{16} -3.19980 q^{17} -2.82843 q^{18} +7.39595 q^{19} -1.00000 q^{20} -7.68092 q^{21} +0.378937 q^{22} -2.41421 q^{24} +1.00000 q^{25} +0.964724 q^{26} -0.414214 q^{27} -3.18154 q^{28} +0.545866 q^{29} +2.41421 q^{30} +10.1463 q^{31} -1.00000 q^{32} -0.914836 q^{33} +3.19980 q^{34} +3.18154 q^{35} +2.82843 q^{36} -4.82843 q^{37} -7.39595 q^{38} -2.32905 q^{39} +1.00000 q^{40} -6.26330 q^{41} +7.68092 q^{42} +4.21441 q^{43} -0.378937 q^{44} -2.82843 q^{45} +2.54587 q^{47} +2.41421 q^{48} +3.12220 q^{49} -1.00000 q^{50} -7.72500 q^{51} -0.964724 q^{52} -9.58114 q^{53} +0.414214 q^{54} +0.378937 q^{55} +3.18154 q^{56} +17.8554 q^{57} -0.545866 q^{58} +3.00000 q^{59} -2.41421 q^{60} -9.75663 q^{61} -10.1463 q^{62} -8.99876 q^{63} +1.00000 q^{64} +0.964724 q^{65} +0.914836 q^{66} -13.7143 q^{67} -3.19980 q^{68} -3.18154 q^{70} +11.2521 q^{71} -2.82843 q^{72} -6.78799 q^{73} +4.82843 q^{74} +2.41421 q^{75} +7.39595 q^{76} +1.20560 q^{77} +2.32905 q^{78} +16.6091 q^{79} -1.00000 q^{80} -9.48528 q^{81} +6.26330 q^{82} -13.9917 q^{83} -7.68092 q^{84} +3.19980 q^{85} -4.21441 q^{86} +1.31784 q^{87} +0.378937 q^{88} -17.7067 q^{89} +2.82843 q^{90} +3.06931 q^{91} +24.4952 q^{93} -2.54587 q^{94} -7.39595 q^{95} -2.41421 q^{96} -14.7712 q^{97} -3.12220 q^{98} -1.07180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} + 4 q^{28} - 12 q^{29} + 4 q^{30} + 28 q^{31} - 4 q^{32} - 16 q^{33} + 12 q^{34} - 4 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} + 4 q^{40} - 8 q^{41} - 4 q^{42} + 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} - 16 q^{51} - 8 q^{52} - 20 q^{53} - 4 q^{54} - 4 q^{56} + 12 q^{57} + 12 q^{58} + 12 q^{59} - 4 q^{60} - 28 q^{62} + 4 q^{64} + 8 q^{65} + 16 q^{66} - 12 q^{67} - 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} - 24 q^{77} + 16 q^{78} + 4 q^{79} - 4 q^{80} - 4 q^{81} + 8 q^{82} - 12 q^{83} + 4 q^{84} + 12 q^{85} - 12 q^{86} + 4 q^{87} - 40 q^{89} - 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} - 16 q^{97} - 12 q^{98} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 12 * q^17 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 + 4 * q^28 - 12 * q^29 + 4 * q^30 + 28 * q^31 - 4 * q^32 - 16 * q^33 + 12 * q^34 - 4 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 + 4 * q^40 - 8 * q^41 - 4 * q^42 + 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 - 16 * q^51 - 8 * q^52 - 20 * q^53 - 4 * q^54 - 4 * q^56 + 12 * q^57 + 12 * q^58 + 12 * q^59 - 4 * q^60 - 28 * q^62 + 4 * q^64 + 8 * q^65 + 16 * q^66 - 12 * q^67 - 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 - 24 * q^77 + 16 * q^78 + 4 * q^79 - 4 * q^80 - 4 * q^81 + 8 * q^82 - 12 * q^83 + 4 * q^84 + 12 * q^85 - 12 * q^86 + 4 * q^87 - 40 * q^89 - 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 - 16 * q^97 - 12 * q^98 - 32 * q^99

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