LMFDB - Embedded newform 5290.2.a.bf.1.5

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.252973568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 18x^{3} + 19x^{2} - 20x + 4 $ x^6 - 2x^5 - 11x^4 + 18x^3 + 19x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.34768$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.34768 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34768 q^{6} +0.277858 q^{7} -1.00000 q^{8} -1.18376 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.34768 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34768 q^{6} +0.277858 q^{7} -1.00000 q^{8} -1.18376 q^{9} -1.00000 q^{10} -4.27485 q^{11} +1.34768 q^{12} -6.06352 q^{13} -0.277858 q^{14} +1.34768 q^{15} +1.00000 q^{16} -3.97244 q^{17} +1.18376 q^{18} +7.73762 q^{19} +1.00000 q^{20} +0.374463 q^{21} +4.27485 q^{22} -1.34768 q^{24} +1.00000 q^{25} +6.06352 q^{26} -5.63837 q^{27} +0.277858 q^{28} +8.24729 q^{29} -1.34768 q^{30} +5.37900 q^{31} -1.00000 q^{32} -5.76112 q^{33} +3.97244 q^{34} +0.277858 q^{35} -1.18376 q^{36} -6.34138 q^{37} -7.73762 q^{38} -8.17168 q^{39} -1.00000 q^{40} +10.3809 q^{41} -0.374463 q^{42} +1.11536 q^{43} -4.27485 q^{44} -1.18376 q^{45} -1.35019 q^{47} +1.34768 q^{48} -6.92279 q^{49} -1.00000 q^{50} -5.35357 q^{51} -6.06352 q^{52} +9.08831 q^{53} +5.63837 q^{54} -4.27485 q^{55} -0.277858 q^{56} +10.4278 q^{57} -8.24729 q^{58} +6.30241 q^{59} +1.34768 q^{60} +5.68906 q^{61} -5.37900 q^{62} -0.328918 q^{63} +1.00000 q^{64} -6.06352 q^{65} +5.76112 q^{66} -2.89902 q^{67} -3.97244 q^{68} -0.277858 q^{70} -11.9336 q^{71} +1.18376 q^{72} -2.40378 q^{73} +6.34138 q^{74} +1.34768 q^{75} +7.73762 q^{76} -1.18780 q^{77} +8.17168 q^{78} +12.0048 q^{79} +1.00000 q^{80} -4.04742 q^{81} -10.3809 q^{82} +8.05143 q^{83} +0.374463 q^{84} -3.97244 q^{85} -1.11536 q^{86} +11.1147 q^{87} +4.27485 q^{88} +12.7108 q^{89} +1.18376 q^{90} -1.68480 q^{91} +7.24916 q^{93} +1.35019 q^{94} +7.73762 q^{95} -1.34768 q^{96} +18.5287 q^{97} +6.92279 q^{98} +5.06041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - 6 q^{10} + 10 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 6 q^{16} - 10 q^{17} - 8 q^{18} + 2 q^{19} + 6 q^{20} + 12 q^{21} - 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{30} - 2 q^{31} - 6 q^{32} - 22 q^{33} + 10 q^{34} + 2 q^{35} + 8 q^{36} - 4 q^{37} - 2 q^{38} + 24 q^{39} - 6 q^{40} + 6 q^{41} - 12 q^{42} + 12 q^{43} + 10 q^{44} + 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} + 34 q^{51} - 2 q^{52} + 36 q^{53} + 8 q^{54} + 10 q^{55} - 2 q^{56} + 32 q^{57} + 16 q^{59} - 2 q^{60} - 10 q^{61} + 2 q^{62} - 48 q^{63} + 6 q^{64} - 2 q^{65} + 22 q^{66} + 16 q^{67} - 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} + 4 q^{74} - 2 q^{75} + 2 q^{76} - 16 q^{77} - 24 q^{78} - 20 q^{79} + 6 q^{80} + 34 q^{81} - 6 q^{82} + 8 q^{83} + 12 q^{84} - 10 q^{85} - 12 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} + 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} + 2 q^{97} - 8 q^{98} + 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - 6 * q^10 + 10 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 6 * q^16 - 10 * q^17 - 8 * q^18 + 2 * q^19 + 6 * q^20 + 12 * q^21 - 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^30 - 2 * q^31 - 6 * q^32 - 22 * q^33 + 10 * q^34 + 2 * q^35 + 8 * q^36 - 4 * q^37 - 2 * q^38 + 24 * q^39 - 6 * q^40 + 6 * q^41 - 12 * q^42 + 12 * q^43 + 10 * q^44 + 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 + 34 * q^51 - 2 * q^52 + 36 * q^53 + 8 * q^54 + 10 * q^55 - 2 * q^56 + 32 * q^57 + 16 * q^59 - 2 * q^60 - 10 * q^61 + 2 * q^62 - 48 * q^63 + 6 * q^64 - 2 * q^65 + 22 * q^66 + 16 * q^67 - 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 + 4 * q^74 - 2 * q^75 + 2 * q^76 - 16 * q^77 - 24 * q^78 - 20 * q^79 + 6 * q^80 + 34 * q^81 - 6 * q^82 + 8 * q^83 + 12 * q^84 - 10 * q^85 - 12 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 + 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 + 2 * q^97 - 8 * q^98 + 50 * 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
$3$	1.34768	0.778082	0.389041	−	0.921220i	$-0.372806\pi$
$3$	1.34768	0.778082	0.389041	+	0.921220i	$0.372806\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.34768	−0.550187
$7$	0.277858	0.105021	0.0525103	−	0.998620i	$-0.483278\pi$
$7$	0.277858	0.105021	0.0525103	+	0.998620i	$0.483278\pi$
$8$	−1.00000	−0.353553
$9$	−1.18376	−0.394588
$10$	−1.00000	−0.316228
$11$	−4.27485	−1.28891	−0.644457	−	0.764640i	$-0.722917\pi$
$11$	−4.27485	−1.28891	−0.644457	+	0.764640i	$0.722917\pi$
$12$	1.34768	0.389041
$13$	−6.06352	−1.68172	−0.840859	−	0.541254i	$-0.817950\pi$
$13$	−6.06352	−1.68172	−0.840859	+	0.541254i	$0.817950\pi$
$14$	−0.277858	−0.0742607
$15$	1.34768	0.347969
$16$	1.00000	0.250000
$17$	−3.97244	−0.963458	−0.481729	−	0.876320i	$-0.659991\pi$
$17$	−3.97244	−0.963458	−0.481729	+	0.876320i	$0.659991\pi$
$18$	1.18376	0.279016
$19$	7.73762	1.77513	0.887566	−	0.460681i	$-0.152395\pi$
$19$	7.73762	1.77513	0.887566	+	0.460681i	$0.152395\pi$
$20$	1.00000	0.223607
$21$	0.374463	0.0817146
$22$	4.27485	0.911400
$23$	0	0
$23$	0	0
$24$	−1.34768	−0.275094
$25$	1.00000	0.200000
$26$	6.06352	1.18915
$27$	−5.63837	−1.08510
$28$	0.277858	0.0525103
$29$	8.24729	1.53148	0.765741	−	0.643149i	$-0.222372\pi$
$29$	8.24729	1.53148	0.765741	+	0.643149i	$0.222372\pi$
$30$	−1.34768	−0.246051
$31$	5.37900	0.966096	0.483048	−	0.875594i	$-0.339530\pi$
$31$	5.37900	0.966096	0.483048	+	0.875594i	$0.339530\pi$
$32$	−1.00000	−0.176777
$33$	−5.76112	−1.00288
$34$	3.97244	0.681268
$35$	0.277858	0.0469666
$36$	−1.18376	−0.197294
$37$	−6.34138	−1.04252	−0.521258	−	0.853399i	$-0.674537\pi$
$37$	−6.34138	−1.04252	−0.521258	+	0.853399i	$0.674537\pi$
$38$	−7.73762	−1.25521
$39$	−8.17168	−1.30852
$40$	−1.00000	−0.158114
$41$	10.3809	1.62122	0.810609	−	0.585587i	$-0.199136\pi$
$41$	10.3809	1.62122	0.810609	+	0.585587i	$0.199136\pi$
$42$	−0.374463	−0.0577810
$43$	1.11536	0.170090	0.0850452	−	0.996377i	$-0.472897\pi$
$43$	1.11536	0.170090	0.0850452	+	0.996377i	$0.472897\pi$
$44$	−4.27485	−0.644457
$45$	−1.18376	−0.176465
$46$	0	0
$47$	−1.35019	−0.196945	−0.0984726	−	0.995140i	$-0.531396\pi$
$47$	−1.35019	−0.196945	−0.0984726	+	0.995140i	$0.531396\pi$
$48$	1.34768	0.194521
$49$	−6.92279	−0.988971
$50$	−1.00000	−0.141421
$51$	−5.35357	−0.749650
$52$	−6.06352	−0.840859
$53$	9.08831	1.24838	0.624188	−	0.781275i	$-0.285430\pi$
$53$	9.08831	1.24838	0.624188	+	0.781275i	$0.285430\pi$
$54$	5.63837	0.767285
$55$	−4.27485	−0.576420
$56$	−0.277858	−0.0371304
$57$	10.4278	1.38120
$58$	−8.24729	−1.08292
$59$	6.30241	0.820503	0.410252	−	0.911972i	$-0.365441\pi$
$59$	6.30241	0.820503	0.410252	+	0.911972i	$0.365441\pi$
$60$	1.34768	0.173985
$61$	5.68906	0.728409	0.364205	−	0.931319i	$-0.381341\pi$
$61$	5.68906	0.728409	0.364205	+	0.931319i	$0.381341\pi$
$62$	−5.37900	−0.683133
$63$	−0.328918	−0.0414398
$64$	1.00000	0.125000
$65$	−6.06352	−0.752087
$66$	5.76112	0.709145
$67$	−2.89902	−0.354172	−0.177086	−	0.984195i	$-0.556667\pi$
$67$	−2.89902	−0.354172	−0.177086	+	0.984195i	$0.556667\pi$
$68$	−3.97244	−0.481729
$69$	0	0
$70$	−0.277858	−0.0332104
$71$	−11.9336	−1.41626	−0.708130	−	0.706082i	$-0.750461\pi$
$71$	−11.9336	−1.41626	−0.708130	+	0.706082i	$0.750461\pi$
$72$	1.18376	0.139508
$73$	−2.40378	−0.281341	−0.140671	−	0.990056i	$-0.544926\pi$
$73$	−2.40378	−0.281341	−0.140671	+	0.990056i	$0.544926\pi$
$74$	6.34138	0.737171
$75$	1.34768	0.155616
$76$	7.73762	0.887566
$77$	−1.18780	−0.135362
$78$	8.17168	0.925260
$79$	12.0048	1.35065	0.675323	−	0.737522i	$-0.264004\pi$
$79$	12.0048	1.35065	0.675323	+	0.737522i	$0.264004\pi$
$80$	1.00000	0.111803
$81$	−4.04742	−0.449713
$82$	−10.3809	−1.14637
$83$	8.05143	0.883759	0.441880	−	0.897074i	$-0.354312\pi$
$83$	8.05143	0.883759	0.441880	+	0.897074i	$0.354312\pi$
$84$	0.374463	0.0408573
$85$	−3.97244	−0.430872
$86$	−1.11536	−0.120272
$87$	11.1147	1.19162
$88$	4.27485	0.455700
$89$	12.7108	1.34735	0.673673	−	0.739030i	$-0.264716\pi$
$89$	12.7108	1.34735	0.673673	+	0.739030i	$0.264716\pi$
$90$	1.18376	0.124780
$91$	−1.68480	−0.176615
$92$	0	0
$93$	7.24916	0.751702
$94$	1.35019	0.139261
$95$	7.73762	0.793863
$96$	−1.34768	−0.137547
$97$	18.5287	1.88130	0.940652	−	0.339372i	$-0.110214\pi$
$97$	18.5287	1.88130	0.940652	+	0.339372i	$0.110214\pi$
$98$	6.92279	0.699308
$99$	5.06041	0.508590
$100$	1.00000	0.100000
$101$	13.1995	1.31340	0.656700	−	0.754152i	$-0.271952\pi$
$101$	13.1995	1.31340	0.656700	+	0.754152i	$0.271952\pi$
$102$	5.35357	0.530083
$103$	0.713182	0.0702719	0.0351360	−	0.999383i	$-0.488814\pi$
$103$	0.713182	0.0702719	0.0351360	+	0.999383i	$0.488814\pi$
$104$	6.06352	0.594577
$105$	0.374463	0.0365439
$106$	−9.08831	−0.882734
$107$	13.7586	1.33010	0.665048	−	0.746801i	$-0.268411\pi$
$107$	13.7586	1.33010	0.665048	+	0.746801i	$0.268411\pi$
$108$	−5.63837	−0.542552
$109$	−5.38076	−0.515383	−0.257692	−	0.966227i	$-0.582962\pi$
$109$	−5.38076	−0.515383	−0.257692	+	0.966227i	$0.582962\pi$
$110$	4.27485	0.407591
$111$	−8.54614	−0.811164
$112$	0.277858	0.0262551
$113$	−2.46857	−0.232223	−0.116112	−	0.993236i	$-0.537043\pi$
$113$	−2.46857	−0.232223	−0.116112	+	0.993236i	$0.537043\pi$
$114$	−10.4278	−0.976655
$115$	0	0
$116$	8.24729	0.765741
$117$	7.17778	0.663586
$118$	−6.30241	−0.580183
$119$	−1.10378	−0.101183
$120$	−1.34768	−0.123026
$121$	7.27431	0.661301
$122$	−5.68906	−0.515063
$123$	13.9901	1.26144
$124$	5.37900	0.483048
$125$	1.00000	0.0894427
$126$	0.328918	0.0293024
$127$	4.43850	0.393853	0.196926	−	0.980418i	$-0.436904\pi$
$127$	4.43850	0.393853	0.196926	+	0.980418i	$0.436904\pi$
$128$	−1.00000	−0.0883883
$129$	1.50314	0.132344
$130$	6.06352	0.531806
$131$	−14.2284	−1.24314	−0.621571	−	0.783357i	$-0.713505\pi$
$131$	−14.2284	−1.24314	−0.621571	+	0.783357i	$0.713505\pi$
$132$	−5.76112	−0.501441
$133$	2.14996	0.186425
$134$	2.89902	0.250437
$135$	−5.63837	−0.485273
$136$	3.97244	0.340634
$137$	13.5386	1.15668	0.578340	−	0.815796i	$-0.303701\pi$
$137$	13.5386	1.15668	0.578340	+	0.815796i	$0.303701\pi$
$138$	0	0
$139$	−6.03970	−0.512280	−0.256140	−	0.966640i	$-0.582451\pi$
$139$	−6.03970	−0.512280	−0.256140	+	0.966640i	$0.582451\pi$
$140$	0.277858	0.0234833
$141$	−1.81962	−0.153240
$142$	11.9336	1.00145
$143$	25.9206	2.16759
$144$	−1.18376	−0.0986469
$145$	8.24729	0.684900
$146$	2.40378	0.198938
$147$	−9.32970	−0.769501
$148$	−6.34138	−0.521258
$149$	8.15834	0.668357	0.334179	−	0.942510i	$-0.391541\pi$
$149$	8.15834	0.668357	0.334179	+	0.942510i	$0.391541\pi$
$150$	−1.34768	−0.110037
$151$	−5.59650	−0.455437	−0.227718	−	0.973727i	$-0.573127\pi$
$151$	−5.59650	−0.455437	−0.227718	+	0.973727i	$0.573127\pi$
$152$	−7.73762	−0.627604
$153$	4.70243	0.380169
$154$	1.18780	0.0957157
$155$	5.37900	0.432051
$156$	−8.17168	−0.654258
$157$	0.961498	0.0767359	0.0383679	−	0.999264i	$-0.487784\pi$
$157$	0.961498	0.0767359	0.0383679	+	0.999264i	$0.487784\pi$
$158$	−12.0048	−0.955051
$159$	12.2481	0.971339
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	4.04742	0.317995
$163$	−8.67987	−0.679860	−0.339930	−	0.940451i	$-0.610403\pi$
$163$	−8.67987	−0.679860	−0.339930	+	0.940451i	$0.610403\pi$
$164$	10.3809	0.810609
$165$	−5.76112	−0.448502
$166$	−8.05143	−0.624912
$167$	4.05637	0.313892	0.156946	−	0.987607i	$-0.449835\pi$
$167$	4.05637	0.313892	0.156946	+	0.987607i	$0.449835\pi$
$168$	−0.374463	−0.0288905
$169$	23.7663	1.82818
$170$	3.97244	0.304672
$171$	−9.15951	−0.700445
$172$	1.11536	0.0850452
$173$	13.0629	0.993155	0.496577	−	0.867993i	$-0.334590\pi$
$173$	13.0629	0.993155	0.496577	+	0.867993i	$0.334590\pi$
$174$	−11.1147	−0.842602
$175$	0.277858	0.0210041
$176$	−4.27485	−0.322229
$177$	8.49362	0.638419
$178$	−12.7108	−0.952717
$179$	3.78992	0.283272	0.141636	−	0.989919i	$-0.454764\pi$
$179$	3.78992	0.283272	0.141636	+	0.989919i	$0.454764\pi$
$180$	−1.18376	−0.0882325
$181$	7.20164	0.535293	0.267647	−	0.963517i	$-0.413754\pi$
$181$	7.20164	0.535293	0.267647	+	0.963517i	$0.413754\pi$
$182$	1.68480	0.124886
$183$	7.66702	0.566763
$184$	0	0
$185$	−6.34138	−0.466228
$186$	−7.24916	−0.531534
$187$	16.9816	1.24182
$188$	−1.35019	−0.0984726
$189$	−1.56667	−0.113958
$190$	−7.73762	−0.561346
$191$	13.7381	0.994055	0.497028	−	0.867735i	$-0.334425\pi$
$191$	13.7381	0.994055	0.497028	+	0.867735i	$0.334425\pi$
$192$	1.34768	0.0972603
$193$	−4.59398	−0.330682	−0.165341	−	0.986236i	$-0.552872\pi$
$193$	−4.59398	−0.330682	−0.165341	+	0.986236i	$0.552872\pi$
$194$	−18.5287	−1.33028
$195$	−8.17168	−0.585186
$196$	−6.92279	−0.494485
$197$	−14.8453	−1.05769	−0.528843	−	0.848720i	$-0.677374\pi$
$197$	−14.8453	−1.05769	−0.528843	+	0.848720i	$0.677374\pi$
$198$	−5.06041	−0.359627
$199$	−20.3774	−1.44451	−0.722256	−	0.691626i	$-0.756895\pi$
$199$	−20.3774	−1.44451	−0.722256	+	0.691626i	$0.756895\pi$
$200$	−1.00000	−0.0707107
$201$	−3.90695	−0.275575
$202$	−13.1995	−0.928714
$203$	2.29158	0.160837
$204$	−5.35357	−0.374825
$205$	10.3809	0.725031
$206$	−0.713182	−0.0496898
$207$	0	0
$208$	−6.06352	−0.420430
$209$	−33.0771	−2.28799
$210$	−0.374463	−0.0258404
$211$	−22.4403	−1.54485	−0.772426	−	0.635104i	$-0.780957\pi$
$211$	−22.4403	−1.54485	−0.772426	+	0.635104i	$0.780957\pi$
$212$	9.08831	0.624188
$213$	−16.0827	−1.10197
$214$	−13.7586	−0.940520
$215$	1.11536	0.0760668
$216$	5.63837	0.383642
$217$	1.49460	0.101460
$218$	5.38076	0.364431
$219$	−3.23952	−0.218907
$220$	−4.27485	−0.288210
$221$	24.0870	1.62027
$222$	8.54614	0.573579
$223$	−18.3132	−1.22634	−0.613172	−	0.789949i	$-0.710107\pi$
$223$	−18.3132	−1.22634	−0.613172	+	0.789949i	$0.710107\pi$
$224$	−0.277858	−0.0185652
$225$	−1.18376	−0.0789175
$226$	2.46857	0.164207
$227$	−3.91481	−0.259835	−0.129918	−	0.991525i	$-0.541471\pi$
$227$	−3.91481	−0.259835	−0.129918	+	0.991525i	$0.541471\pi$
$228$	10.4278	0.690599
$229$	6.38567	0.421977	0.210989	−	0.977489i	$-0.432332\pi$
$229$	6.38567	0.421977	0.210989	+	0.977489i	$0.432332\pi$
$230$	0	0
$231$	−1.60077	−0.105323
$232$	−8.24729	−0.541461
$233$	−23.2287	−1.52176	−0.760880	−	0.648892i	$-0.775233\pi$
$233$	−23.2287	−1.52176	−0.760880	+	0.648892i	$0.775233\pi$
$234$	−7.17778	−0.469226
$235$	−1.35019	−0.0880766
$236$	6.30241	0.410252
$237$	16.1786	1.05091
$238$	1.10378	0.0715471
$239$	19.7495	1.27749	0.638744	−	0.769419i	$-0.279454\pi$
$239$	19.7495	1.27749	0.638744	+	0.769419i	$0.279454\pi$
$240$	1.34768	0.0869923
$241$	9.97224	0.642368	0.321184	−	0.947017i	$-0.395919\pi$
$241$	9.97224	0.642368	0.321184	+	0.947017i	$0.395919\pi$
$242$	−7.27431	−0.467610
$243$	11.4605	0.735191
$244$	5.68906	0.364205
$245$	−6.92279	−0.442281
$246$	−13.9901	−0.891974
$247$	−46.9172	−2.98527
$248$	−5.37900	−0.341567
$249$	10.8507	0.687638
$250$	−1.00000	−0.0632456
$251$	−11.9987	−0.757354	−0.378677	−	0.925529i	$-0.623621\pi$
$251$	−11.9987	−0.757354	−0.378677	+	0.925529i	$0.623621\pi$
$252$	−0.328918	−0.0207199
$253$	0	0
$254$	−4.43850	−0.278496
$255$	−5.35357	−0.335254
$256$	1.00000	0.0625000
$257$	16.6156	1.03646	0.518228	−	0.855243i	$-0.326592\pi$
$257$	16.6156	1.03646	0.518228	+	0.855243i	$0.326592\pi$
$258$	−1.50314	−0.0935816
$259$	−1.76200	−0.109486
$260$	−6.06352	−0.376044
$261$	−9.76283	−0.604304
$262$	14.2284	0.879035
$263$	6.52125	0.402118	0.201059	−	0.979579i	$-0.435562\pi$
$263$	6.52125	0.402118	0.201059	+	0.979579i	$0.435562\pi$
$264$	5.76112	0.354572
$265$	9.08831	0.558290
$266$	−2.14996	−0.131823
$267$	17.1301	1.04835
$268$	−2.89902	−0.177086
$269$	−3.20535	−0.195434	−0.0977169	−	0.995214i	$-0.531154\pi$
$269$	−3.20535	−0.195434	−0.0977169	+	0.995214i	$0.531154\pi$
$270$	5.63837	0.343140
$271$	15.4955	0.941283	0.470641	−	0.882325i	$-0.344023\pi$
$271$	15.4955	0.941283	0.470641	+	0.882325i	$0.344023\pi$
$272$	−3.97244	−0.240865
$273$	−2.27057	−0.137421
$274$	−13.5386	−0.817897
$275$	−4.27485	−0.257783
$276$	0	0
$277$	−14.7617	−0.886947	−0.443473	−	0.896288i	$-0.646254\pi$
$277$	−14.7617	−0.886947	−0.443473	+	0.896288i	$0.646254\pi$
$278$	6.03970	0.362237
$279$	−6.36746	−0.381210
$280$	−0.277858	−0.0166052
$281$	−10.1441	−0.605144	−0.302572	−	0.953127i	$-0.597845\pi$
$281$	−10.1441	−0.605144	−0.302572	+	0.953127i	$0.597845\pi$
$282$	1.81962	0.108357
$283$	4.15812	0.247175	0.123587	−	0.992334i	$-0.460560\pi$
$283$	4.15812	0.247175	0.123587	+	0.992334i	$0.460560\pi$
$284$	−11.9336	−0.708130
$285$	10.4278	0.617691
$286$	−25.9206	−1.53272
$287$	2.88441	0.170261
$288$	1.18376	0.0697539
$289$	−1.21972	−0.0717482
$290$	−8.24729	−0.484297
$291$	24.9707	1.46381
$292$	−2.40378	−0.140671
$293$	7.33132	0.428300	0.214150	−	0.976801i	$-0.431302\pi$
$293$	7.33132	0.428300	0.214150	+	0.976801i	$0.431302\pi$
$294$	9.32970	0.544119
$295$	6.30241	0.366940
$296$	6.34138	0.368585
$297$	24.1032	1.39861
$298$	−8.15834	−0.472600
$299$	0	0
$300$	1.34768	0.0778082
$301$	0.309911	0.0178630
$302$	5.59650	0.322043
$303$	17.7887	1.02193
$304$	7.73762	0.443783
$305$	5.68906	0.325755
$306$	−4.70243	−0.268820
$307$	20.7155	1.18230	0.591148	−	0.806563i	$-0.298675\pi$
$307$	20.7155	1.18230	0.591148	+	0.806563i	$0.298675\pi$
$308$	−1.18780	−0.0676812
$309$	0.961140	0.0546774
$310$	−5.37900	−0.305506
$311$	35.0989	1.99027	0.995137	−	0.0985036i	$-0.0314056\pi$
$311$	35.0989	1.99027	0.995137	+	0.0985036i	$0.0314056\pi$
$312$	8.17168	0.462630
$313$	23.1708	1.30969	0.654847	−	0.755762i	$-0.272733\pi$
$313$	23.1708	1.30969	0.654847	+	0.755762i	$0.272733\pi$
$314$	−0.961498	−0.0542604
$315$	−0.328918	−0.0185324
$316$	12.0048	0.675323
$317$	−18.4670	−1.03721	−0.518606	−	0.855014i	$-0.673549\pi$
$317$	−18.4670	−1.03721	−0.518606	+	0.855014i	$0.673549\pi$
$318$	−12.2481	−0.686840
$319$	−35.2559	−1.97395
$320$	1.00000	0.0559017
$321$	18.5422	1.03492
$322$	0	0
$323$	−30.7372	−1.71026
$324$	−4.04742	−0.224856
$325$	−6.06352	−0.336344
$326$	8.67987	0.480734
$327$	−7.25153	−0.401011
$328$	−10.3809	−0.573187
$329$	−0.375161	−0.0206833
$330$	5.76112	0.317139
$331$	7.92476	0.435584	0.217792	−	0.975995i	$-0.430115\pi$
$331$	7.92476	0.435584	0.217792	+	0.975995i	$0.430115\pi$
$332$	8.05143	0.441880
$333$	7.50669	0.411364
$334$	−4.05637	−0.221955
$335$	−2.89902	−0.158390
$336$	0.374463	0.0204287
$337$	−11.2629	−0.613531	−0.306766	−	0.951785i	$-0.599247\pi$
$337$	−11.2629	−0.613531	−0.306766	+	0.951785i	$0.599247\pi$
$338$	−23.7663	−1.29272
$339$	−3.32683	−0.180689
$340$	−3.97244	−0.215436
$341$	−22.9944	−1.24522
$342$	9.15951	0.495289
$343$	−3.86856	−0.208883
$344$	−1.11536	−0.0601361
$345$	0	0
$346$	−13.0629	−0.702266
$347$	−1.56472	−0.0839988	−0.0419994	−	0.999118i	$-0.513373\pi$
$347$	−1.56472	−0.0839988	−0.0419994	+	0.999118i	$0.513373\pi$
$348$	11.1147	0.595810
$349$	−19.4881	−1.04317	−0.521586	−	0.853199i	$-0.674659\pi$
$349$	−19.4881	−1.04317	−0.521586	+	0.853199i	$0.674659\pi$
$350$	−0.277858	−0.0148521
$351$	34.1884	1.82484
$352$	4.27485	0.227850
$353$	9.29507	0.494727	0.247363	−	0.968923i	$-0.420436\pi$
$353$	9.29507	0.494727	0.247363	+	0.968923i	$0.420436\pi$
$354$	−8.49362	−0.451431
$355$	−11.9336	−0.633371
$356$	12.7108	0.673673
$357$	−1.48753	−0.0787286
$358$	−3.78992	−0.200304
$359$	−9.59454	−0.506380	−0.253190	−	0.967417i	$-0.581480\pi$
$359$	−9.59454	−0.506380	−0.253190	+	0.967417i	$0.581480\pi$
$360$	1.18376	0.0623898
$361$	40.8707	2.15109
$362$	−7.20164	−0.378510
$363$	9.80343	0.514546
$364$	−1.68480	−0.0883075
$365$	−2.40378	−0.125820
$366$	−7.66702	−0.400762
$367$	−31.4194	−1.64008	−0.820040	−	0.572306i	$-0.806049\pi$
$367$	−31.4194	−1.64008	−0.820040	+	0.572306i	$0.806049\pi$
$368$	0	0
$369$	−12.2885	−0.639713
$370$	6.34138	0.329673
$371$	2.52526	0.131105
$372$	7.24916	0.375851
$373$	−4.71067	−0.243909	−0.121955	−	0.992536i	$-0.538916\pi$
$373$	−4.71067	−0.243909	−0.121955	+	0.992536i	$0.538916\pi$
$374$	−16.9816	−0.878096
$375$	1.34768	0.0695938
$376$	1.35019	0.0696307
$377$	−50.0076	−2.57552
$378$	1.56667	0.0805806
$379$	17.0505	0.875823	0.437911	−	0.899018i	$-0.355718\pi$
$379$	17.0505	0.875823	0.437911	+	0.899018i	$0.355718\pi$
$380$	7.73762	0.396931
$381$	5.98166	0.306450
$382$	−13.7381	−0.702903
$383$	31.1949	1.59399	0.796994	−	0.603988i	$-0.206422\pi$
$383$	31.1949	1.59399	0.796994	+	0.603988i	$0.206422\pi$
$384$	−1.34768	−0.0687734
$385$	−1.18780	−0.0605359
$386$	4.59398	0.233828
$387$	−1.32032	−0.0671156
$388$	18.5287	0.940652
$389$	−15.1218	−0.766704	−0.383352	−	0.923602i	$-0.625230\pi$
$389$	−15.1218	−0.766704	−0.383352	+	0.923602i	$0.625230\pi$
$390$	8.17168	0.413789
$391$	0	0
$392$	6.92279	0.349654
$393$	−19.1753	−0.967268
$394$	14.8453	0.747896
$395$	12.0048	0.604027
$396$	5.06041	0.254295
$397$	30.8304	1.54734	0.773668	−	0.633592i	$-0.218420\pi$
$397$	30.8304	1.54734	0.773668	+	0.633592i	$0.218420\pi$
$398$	20.3774	1.02142
$399$	2.89745	0.145054
$400$	1.00000	0.0500000
$401$	−13.8814	−0.693202	−0.346601	−	0.938013i	$-0.612664\pi$
$401$	−13.8814	−0.693202	−0.346601	+	0.938013i	$0.612664\pi$
$402$	3.90695	0.194861
$403$	−32.6157	−1.62470
$404$	13.1995	0.656700
$405$	−4.04742	−0.201118
$406$	−2.29158	−0.113729
$407$	27.1084	1.34371
$408$	5.35357	0.265041
$409$	−15.0967	−0.746484	−0.373242	−	0.927734i	$-0.621754\pi$
$409$	−15.0967	−0.746484	−0.373242	+	0.927734i	$0.621754\pi$
$410$	−10.3809	−0.512674
$411$	18.2457	0.899993
$412$	0.713182	0.0351360
$413$	1.75118	0.0861697
$414$	0	0
$415$	8.05143	0.395229
$416$	6.06352	0.297289
$417$	−8.13957	−0.398596
$418$	33.0771	1.61785
$419$	12.4593	0.608675	0.304338	−	0.952564i	$-0.401565\pi$
$419$	12.4593	0.608675	0.304338	+	0.952564i	$0.401565\pi$
$420$	0.374463	0.0182719
$421$	16.4512	0.801780	0.400890	−	0.916126i	$-0.368701\pi$
$421$	16.4512	0.801780	0.400890	+	0.916126i	$0.368701\pi$
$422$	22.4403	1.09238
$423$	1.59830	0.0777122
$424$	−9.08831	−0.441367
$425$	−3.97244	−0.192692
$426$	16.0827	0.779209
$427$	1.58075	0.0764979
$428$	13.7586	0.665048
$429$	34.9327	1.68657
$430$	−1.11536	−0.0537873
$431$	15.4875	0.746008	0.373004	−	0.927830i	$-0.378328\pi$
$431$	15.4875	0.746008	0.373004	+	0.927830i	$0.378328\pi$
$432$	−5.63837	−0.271276
$433$	−27.3666	−1.31515	−0.657577	−	0.753388i	$-0.728418\pi$
$433$	−27.3666	−1.31515	−0.657577	+	0.753388i	$0.728418\pi$
$434$	−1.49460	−0.0717430
$435$	11.1147	0.532909
$436$	−5.38076	−0.257692
$437$	0	0
$438$	3.23952	0.154790
$439$	−7.07033	−0.337448	−0.168724	−	0.985663i	$-0.553965\pi$
$439$	−7.07033	−0.337448	−0.168724	+	0.985663i	$0.553965\pi$
$440$	4.27485	0.203795
$441$	8.19495	0.390236
$442$	−24.0870	−1.14570
$443$	−28.3768	−1.34822	−0.674110	−	0.738631i	$-0.735473\pi$
$443$	−28.3768	−1.34822	−0.674110	+	0.738631i	$0.735473\pi$
$444$	−8.54614	−0.405582
$445$	12.7108	0.602551
$446$	18.3132	0.867157
$447$	10.9948	0.520037
$448$	0.277858	0.0131276
$449$	−25.0706	−1.18315	−0.591577	−	0.806249i	$-0.701494\pi$
$449$	−25.0706	−1.18315	−0.591577	+	0.806249i	$0.701494\pi$
$450$	1.18376	0.0558031
$451$	−44.3766	−2.08961
$452$	−2.46857	−0.116112
$453$	−7.54229	−0.354368
$454$	3.91481	0.183731
$455$	−1.68480	−0.0789846
$456$	−10.4278	−0.488327
$457$	−30.4575	−1.42474	−0.712371	−	0.701803i	$-0.752379\pi$
$457$	−30.4575	−1.42474	−0.712371	+	0.701803i	$0.752379\pi$
$458$	−6.38567	−0.298383
$459$	22.3981	1.04545
$460$	0	0
$461$	−12.2536	−0.570705	−0.285353	−	0.958423i	$-0.592111\pi$
$461$	−12.2536	−0.570705	−0.285353	+	0.958423i	$0.592111\pi$
$462$	1.60077	0.0744747
$463$	−32.8134	−1.52497	−0.762483	−	0.647008i	$-0.776020\pi$
$463$	−32.8134	−1.52497	−0.762483	+	0.647008i	$0.776020\pi$
$464$	8.24729	0.382871
$465$	7.24916	0.336172
$466$	23.2287	1.07605
$467$	31.2283	1.44507	0.722537	−	0.691332i	$-0.242976\pi$
$467$	31.2283	1.44507	0.722537	+	0.691332i	$0.242976\pi$
$468$	7.17778	0.331793
$469$	−0.805517	−0.0371953
$470$	1.35019	0.0622796
$471$	1.29579	0.0597068
$472$	−6.30241	−0.290092
$473$	−4.76798	−0.219232
$474$	−16.1786	−0.743108
$475$	7.73762	0.355026
$476$	−1.10378	−0.0505914
$477$	−10.7584	−0.492593
$478$	−19.7495	−0.903321
$479$	22.4845	1.02734	0.513670	−	0.857988i	$-0.328285\pi$
$479$	22.4845	1.02734	0.513670	+	0.857988i	$0.328285\pi$
$480$	−1.34768	−0.0615128
$481$	38.4511	1.75322
$482$	−9.97224	−0.454223
$483$	0	0
$484$	7.27431	0.330650
$485$	18.5287	0.841345
$486$	−11.4605	−0.519858
$487$	33.7784	1.53064	0.765322	−	0.643648i	$-0.222580\pi$
$487$	33.7784	1.53064	0.765322	+	0.643648i	$0.222580\pi$
$488$	−5.68906	−0.257532
$489$	−11.6977	−0.528987
$490$	6.92279	0.312740
$491$	−20.1215	−0.908070	−0.454035	−	0.890984i	$-0.650016\pi$
$491$	−20.1215	−0.908070	−0.454035	+	0.890984i	$0.650016\pi$
$492$	13.9901	0.630721
$493$	−32.7619	−1.47552
$494$	46.9172	2.11091
$495$	5.06041	0.227448
$496$	5.37900	0.241524
$497$	−3.31586	−0.148736
$498$	−10.8507	−0.486233
$499$	28.4999	1.27583	0.637914	−	0.770107i	$-0.279797\pi$
$499$	28.4999	1.27583	0.637914	+	0.770107i	$0.279797\pi$
$500$	1.00000	0.0447214
$501$	5.46669	0.244234
$502$	11.9987	0.535530
$503$	−28.6550	−1.27766	−0.638832	−	0.769347i	$-0.720582\pi$
$503$	−28.6550	−1.27766	−0.638832	+	0.769347i	$0.720582\pi$
$504$	0.328918	0.0146512
$505$	13.1995	0.587370
$506$	0	0
$507$	32.0293	1.42247
$508$	4.43850	0.196926
$509$	7.91020	0.350614	0.175307	−	0.984514i	$-0.443908\pi$
$509$	7.91020	0.350614	0.175307	+	0.984514i	$0.443908\pi$
$510$	5.35357	0.237060
$511$	−0.667910	−0.0295466
$512$	−1.00000	−0.0441942
$513$	−43.6275	−1.92620
$514$	−16.6156	−0.732885
$515$	0.713182	0.0314266
$516$	1.50314	0.0661722
$517$	5.77185	0.253846
$518$	1.76200	0.0774180
$519$	17.6046	0.772756
$520$	6.06352	0.265903
$521$	−5.28345	−0.231472	−0.115736	−	0.993280i	$-0.536923\pi$
$521$	−5.28345	−0.231472	−0.115736	+	0.993280i	$0.536923\pi$
$522$	9.76283	0.427308
$523$	5.47277	0.239308	0.119654	−	0.992816i	$-0.461822\pi$
$523$	5.47277	0.239308	0.119654	+	0.992816i	$0.461822\pi$
$524$	−14.2284	−0.621571
$525$	0.374463	0.0163429
$526$	−6.52125	−0.284340
$527$	−21.3677	−0.930793
$528$	−5.76112	−0.250720
$529$	0	0
$530$	−9.08831	−0.394771
$531$	−7.46056	−0.323761
$532$	2.14996	0.0932126
$533$	−62.9446	−2.72643
$534$	−17.1301	−0.741292
$535$	13.7586	0.594837
$536$	2.89902	0.125219
$537$	5.10760	0.220409
$538$	3.20535	0.138193
$539$	29.5939	1.27470
$540$	−5.63837	−0.242637
$541$	18.1605	0.780781	0.390391	−	0.920649i	$-0.372340\pi$
$541$	18.1605	0.780781	0.390391	+	0.920649i	$0.372340\pi$
$542$	−15.4955	−0.665587
$543$	9.70549	0.416502
$544$	3.97244	0.170317
$545$	−5.38076	−0.230486
$546$	2.27057	0.0971713
$547$	21.5357	0.920802	0.460401	−	0.887711i	$-0.347706\pi$
$547$	21.5357	0.920802	0.460401	+	0.887711i	$0.347706\pi$
$548$	13.5386	0.578340
$549$	−6.73450	−0.287421
$550$	4.27485	0.182280
$551$	63.8143	2.71858
$552$	0	0
$553$	3.33563	0.141846
$554$	14.7617	0.627166
$555$	−8.54614	−0.362764
$556$	−6.03970	−0.256140
$557$	−2.51720	−0.106657	−0.0533287	−	0.998577i	$-0.516983\pi$
$557$	−2.51720	−0.106657	−0.0533287	+	0.998577i	$0.516983\pi$
$558$	6.36746	0.269556
$559$	−6.76300	−0.286044
$560$	0.277858	0.0117417
$561$	22.8857	0.966235
$562$	10.1441	0.427901
$563$	−10.3194	−0.434912	−0.217456	−	0.976070i	$-0.569776\pi$
$563$	−10.3194	−0.434912	−0.217456	+	0.976070i	$0.569776\pi$
$564$	−1.81962	−0.0766198
$565$	−2.46857	−0.103853
$566$	−4.15812	−0.174779
$567$	−1.12461	−0.0472291
$568$	11.9336	0.500724
$569$	−0.168656	−0.00707041	−0.00353521	−	0.999994i	$-0.501125\pi$
$569$	−0.168656	−0.00707041	−0.00353521	+	0.999994i	$0.501125\pi$
$570$	−10.4278	−0.436773
$571$	44.4122	1.85859	0.929296	−	0.369335i	$-0.120414\pi$
$571$	44.4122	1.85859	0.929296	+	0.369335i	$0.120414\pi$
$572$	25.9206	1.08380
$573$	18.5146	0.773457
$574$	−2.88441	−0.120393
$575$	0	0
$576$	−1.18376	−0.0493235
$577$	−44.5205	−1.85341	−0.926707	−	0.375784i	$-0.877373\pi$
$577$	−44.5205	−1.85341	−0.926707	+	0.375784i	$0.877373\pi$
$578$	1.21972	0.0507336
$579$	−6.19121	−0.257298
$580$	8.24729	0.342450
$581$	2.23716	0.0928129
$582$	−24.9707	−1.03507
$583$	−38.8511	−1.60905
$584$	2.40378	0.0994691
$585$	7.17778	0.296764
$586$	−7.33132	−0.302854
$587$	−27.3786	−1.13004	−0.565018	−	0.825078i	$-0.691131\pi$
$587$	−27.3786	−1.13004	−0.565018	+	0.825078i	$0.691131\pi$
$588$	−9.32970	−0.384750
$589$	41.6206	1.71495
$590$	−6.30241	−0.259466
$591$	−20.0067	−0.822966
$592$	−6.34138	−0.260629
$593$	−15.6138	−0.641183	−0.320591	−	0.947218i	$-0.603882\pi$
$593$	−15.6138	−0.641183	−0.320591	+	0.947218i	$0.603882\pi$
$594$	−24.1032	−0.988964
$595$	−1.10378	−0.0452504
$596$	8.15834	0.334179
$597$	−27.4621	−1.12395
$598$	0	0
$599$	−8.10235	−0.331053	−0.165526	−	0.986205i	$-0.552932\pi$
$599$	−8.10235	−0.331053	−0.165526	+	0.986205i	$0.552932\pi$
$600$	−1.34768	−0.0550187
$601$	45.3241	1.84881	0.924405	−	0.381413i	$-0.124562\pi$
$601$	45.3241	1.84881	0.924405	+	0.381413i	$0.124562\pi$
$602$	−0.309911	−0.0126310
$603$	3.43176	0.139752
$604$	−5.59650	−0.227718
$605$	7.27431	0.295743
$606$	−17.7887	−0.722616
$607$	16.3012	0.661644	0.330822	−	0.943693i	$-0.392674\pi$
$607$	16.3012	0.661644	0.330822	+	0.943693i	$0.392674\pi$
$608$	−7.73762	−0.313802
$609$	3.08831	0.125145
$610$	−5.68906	−0.230343
$611$	8.18690	0.331206
$612$	4.70243	0.190084
$613$	−27.4162	−1.10733	−0.553664	−	0.832740i	$-0.686771\pi$
$613$	−27.4162	−1.10733	−0.553664	+	0.832740i	$0.686771\pi$
$614$	−20.7155	−0.836010
$615$	13.9901	0.564134
$616$	1.18780	0.0478579
$617$	36.8679	1.48425	0.742123	−	0.670264i	$-0.233819\pi$
$617$	36.8679	1.48425	0.742123	+	0.670264i	$0.233819\pi$
$618$	−0.961140	−0.0386627
$619$	−42.6906	−1.71588	−0.857940	−	0.513750i	$-0.828256\pi$
$619$	−42.6906	−1.71588	−0.857940	+	0.513750i	$0.828256\pi$
$620$	5.37900	0.216026
$621$	0	0
$622$	−35.0989	−1.40734
$623$	3.53181	0.141499
$624$	−8.17168	−0.327129
$625$	1.00000	0.0400000
$626$	−23.1708	−0.926093
$627$	−44.5773	−1.78025
$628$	0.961498	0.0383679
$629$	25.1908	1.00442
$630$	0.328918	0.0131044
$631$	−26.5097	−1.05533	−0.527667	−	0.849451i	$-0.676933\pi$
$631$	−26.5097	−1.05533	−0.527667	+	0.849451i	$0.676933\pi$
$632$	−12.0048	−0.477526
$633$	−30.2423	−1.20202
$634$	18.4670	0.733419
$635$	4.43850	0.176136
$636$	12.2481	0.485669
$637$	41.9765	1.66317
$638$	35.2559	1.39579
$639$	14.1266	0.558839
$640$	−1.00000	−0.0395285
$641$	11.7209	0.462946	0.231473	−	0.972841i	$-0.425645\pi$
$641$	11.7209	0.462946	0.231473	+	0.972841i	$0.425645\pi$
$642$	−18.5422	−0.731802
$643$	40.8877	1.61245	0.806226	−	0.591607i	$-0.201506\pi$
$643$	40.8877	1.61245	0.806226	+	0.591607i	$0.201506\pi$
$644$	0	0
$645$	1.50314	0.0591862
$646$	30.7372	1.20934
$647$	42.3049	1.66318	0.831589	−	0.555392i	$-0.187432\pi$
$647$	42.3049	1.66318	0.831589	+	0.555392i	$0.187432\pi$
$648$	4.04742	0.158997
$649$	−26.9418	−1.05756
$650$	6.06352	0.237831
$651$	2.01424	0.0789442
$652$	−8.67987	−0.339930
$653$	−25.9966	−1.01733	−0.508663	−	0.860966i	$-0.669860\pi$
$653$	−25.9966	−1.01733	−0.508663	+	0.860966i	$0.669860\pi$
$654$	7.25153	0.283557
$655$	−14.2284	−0.555950
$656$	10.3809	0.405305
$657$	2.84551	0.111014
$658$	0.375161	0.0146253
$659$	−21.8135	−0.849731	−0.424866	−	0.905256i	$-0.639679\pi$
$659$	−21.8135	−0.849731	−0.424866	+	0.905256i	$0.639679\pi$
$660$	−5.76112	−0.224251
$661$	29.8428	1.16075	0.580375	−	0.814349i	$-0.302906\pi$
$661$	29.8428	1.16075	0.580375	+	0.814349i	$0.302906\pi$
$662$	−7.92476	−0.308005
$663$	32.4615	1.26070
$664$	−8.05143	−0.312456
$665$	2.14996	0.0833719
$666$	−7.50669	−0.290878
$667$	0	0
$668$	4.05637	0.156946
$669$	−24.6804	−0.954197
$670$	2.89902	0.111999
$671$	−24.3199	−0.938858
$672$	−0.374463	−0.0144452
$673$	0.408801	0.0157581	0.00787906	−	0.999969i	$-0.497492\pi$
$673$	0.408801	0.0157581	0.00787906	+	0.999969i	$0.497492\pi$
$674$	11.2629	0.433832
$675$	−5.63837	−0.217021
$676$	23.7663	0.914089
$677$	11.1643	0.429077	0.214539	−	0.976716i	$-0.431175\pi$
$677$	11.1643	0.429077	0.214539	+	0.976716i	$0.431175\pi$
$678$	3.32683	0.127766
$679$	5.14835	0.197576
$680$	3.97244	0.152336
$681$	−5.27591	−0.202173
$682$	22.9944	0.880500
$683$	22.9464	0.878018	0.439009	−	0.898483i	$-0.355330\pi$
$683$	22.9464	0.878018	0.439009	+	0.898483i	$0.355330\pi$
$684$	−9.15951	−0.350222
$685$	13.5386	0.517283
$686$	3.86856	0.147702
$687$	8.60583	0.328333
$688$	1.11536	0.0425226
$689$	−55.1072	−2.09942
$690$	0	0
$691$	28.9346	1.10072	0.550362	−	0.834926i	$-0.314490\pi$
$691$	28.9346	1.10072	0.550362	+	0.834926i	$0.314490\pi$
$692$	13.0629	0.496577
$693$	1.40608	0.0534124
$694$	1.56472	0.0593961
$695$	−6.03970	−0.229099
$696$	−11.1147	−0.421301
$697$	−41.2374	−1.56198
$698$	19.4881	0.737634
$699$	−31.3048	−1.18406
$700$	0.277858	0.0105021
$701$	−11.2336	−0.424287	−0.212143	−	0.977239i	$-0.568044\pi$
$701$	−11.2336	−0.424287	−0.212143	+	0.977239i	$0.568044\pi$
$702$	−34.1884	−1.29036
$703$	−49.0672	−1.85060
$704$	−4.27485	−0.161114
$705$	−1.81962	−0.0685308
$706$	−9.29507	−0.349825
$707$	3.66759	0.137934
$708$	8.49362	0.319210
$709$	−8.95220	−0.336207	−0.168103	−	0.985769i	$-0.553764\pi$
$709$	−8.95220	−0.336207	−0.168103	+	0.985769i	$0.553764\pi$
$710$	11.9336	0.447861
$711$	−14.2108	−0.532948
$712$	−12.7108	−0.476359
$713$	0	0
$714$	1.48753	0.0556696
$715$	25.9206	0.969376
$716$	3.78992	0.141636
$717$	26.6160	0.993991
$718$	9.59454	0.358065
$719$	−6.68364	−0.249258	−0.124629	−	0.992203i	$-0.539774\pi$
$719$	−6.68364	−0.249258	−0.124629	+	0.992203i	$0.539774\pi$
$720$	−1.18376	−0.0441162
$721$	0.198164	0.00738000
$722$	−40.8707	−1.52105
$723$	13.4394	0.499816
$724$	7.20164	0.267647
$725$	8.24729	0.306297
$726$	−9.80343	−0.363839
$727$	28.6131	1.06120	0.530601	−	0.847622i	$-0.321966\pi$
$727$	28.6131	1.06120	0.530601	+	0.847622i	$0.321966\pi$
$728$	1.68480	0.0624428
$729$	27.5873	1.02175
$730$	2.40378	0.0889679
$731$	−4.43069	−0.163875
$732$	7.66702	0.283381
$733$	−41.1371	−1.51943	−0.759716	−	0.650255i	$-0.774662\pi$
$733$	−41.1371	−1.51943	−0.759716	+	0.650255i	$0.774662\pi$
$734$	31.4194	1.15971
$735$	−9.32970	−0.344131
$736$	0	0
$737$	12.3929	0.456497
$738$	12.2885	0.452345
$739$	−37.6406	−1.38463	−0.692316	−	0.721594i	$-0.743410\pi$
$739$	−37.6406	−1.38463	−0.692316	+	0.721594i	$0.743410\pi$
$740$	−6.34138	−0.233114
$741$	−63.2293	−2.32279
$742$	−2.52526	−0.0927052
$743$	36.6092	1.34306	0.671530	−	0.740978i	$-0.265638\pi$
$743$	36.6092	1.34306	0.671530	+	0.740978i	$0.265638\pi$
$744$	−7.24916	−0.265767
$745$	8.15834	0.298898
$746$	4.71067	0.172470
$747$	−9.53099	−0.348721
$748$	16.9816	0.620908
$749$	3.82294	0.139687
$750$	−1.34768	−0.0492103
$751$	−5.42898	−0.198106	−0.0990531	−	0.995082i	$-0.531581\pi$
$751$	−5.42898	−0.198106	−0.0990531	+	0.995082i	$0.531581\pi$
$752$	−1.35019	−0.0492363
$753$	−16.1704	−0.589284
$754$	50.0076	1.82117
$755$	−5.59650	−0.203678
$756$	−1.56667	−0.0569791
$757$	45.4138	1.65059	0.825296	−	0.564700i	$-0.191008\pi$
$757$	45.4138	1.65059	0.825296	+	0.564700i	$0.191008\pi$
$758$	−17.0505	−0.619300
$759$	0	0
$760$	−7.73762	−0.280673
$761$	41.5516	1.50624	0.753122	−	0.657881i	$-0.228547\pi$
$761$	41.5516	1.50624	0.753122	+	0.657881i	$0.228547\pi$
$762$	−5.98166	−0.216693
$763$	−1.49509	−0.0541258
$764$	13.7381	0.497028
$765$	4.70243	0.170017
$766$	−31.1949	−1.12712
$767$	−38.2148	−1.37986
$768$	1.34768	0.0486302
$769$	3.94806	0.142371	0.0711853	−	0.997463i	$-0.477322\pi$
$769$	3.94806	0.142371	0.0711853	+	0.997463i	$0.477322\pi$
$770$	1.18780	0.0428054
$771$	22.3925	0.806448
$772$	−4.59398	−0.165341
$773$	−0.312432	−0.0112374	−0.00561869	−	0.999984i	$-0.501788\pi$
$773$	−0.312432	−0.0112374	−0.00561869	+	0.999984i	$0.501788\pi$
$774$	1.32032	0.0474579
$775$	5.37900	0.193219
$776$	−18.5287	−0.665142
$777$	−2.37462	−0.0851889
$778$	15.1218	0.542142
$779$	80.3232	2.87788
$780$	−8.17168	−0.292593
$781$	51.0144	1.82544
$782$	0	0
$783$	−46.5012	−1.66182
$784$	−6.92279	−0.247243
$785$	0.961498	0.0343173
$786$	19.1753	0.683962
$787$	28.7156	1.02360	0.511800	−	0.859104i	$-0.328979\pi$
$787$	28.7156	1.02360	0.511800	+	0.859104i	$0.328979\pi$
$788$	−14.8453	−0.528843
$789$	8.78855	0.312881
$790$	−12.0048	−0.427112
$791$	−0.685911	−0.0243882
$792$	−5.06041	−0.179814
$793$	−34.4957	−1.22498
$794$	−30.8304	−1.09413
$795$	12.2481	0.434396
$796$	−20.3774	−0.722256
$797$	13.4229	0.475465	0.237733	−	0.971331i	$-0.423596\pi$
$797$	13.4229	0.475465	0.237733	+	0.971331i	$0.423596\pi$
$798$	−2.89745	−0.102569
$799$	5.36354	0.189749
$800$	−1.00000	−0.0353553
$801$	−15.0466	−0.531646
$802$	13.8814	0.490168
$803$	10.2758	0.362625
$804$	−3.90695	−0.137787
$805$	0	0
$806$	32.6157	1.14884
$807$	−4.31978	−0.152064
$808$	−13.1995	−0.464357
$809$	20.5625	0.722939	0.361470	−	0.932384i	$-0.382275\pi$
$809$	20.5625	0.722939	0.361470	+	0.932384i	$0.382275\pi$
$810$	4.04742	0.142212
$811$	13.7871	0.484132	0.242066	−	0.970260i	$-0.422175\pi$
$811$	13.7871	0.484132	0.242066	+	0.970260i	$0.422175\pi$
$812$	2.29158	0.0804186
$813$	20.8829	0.732396
$814$	−27.1084	−0.950150
$815$	−8.67987	−0.304043
$816$	−5.35357	−0.187412
$817$	8.63021	0.301933
$818$	15.0967	0.527844
$819$	1.99440	0.0696901
$820$	10.3809	0.362516
$821$	−2.15092	−0.0750675	−0.0375338	−	0.999295i	$-0.511950\pi$
$821$	−2.15092	−0.0750675	−0.0375338	+	0.999295i	$0.511950\pi$
$822$	−18.2457	−0.636391
$823$	−25.6114	−0.892756	−0.446378	−	0.894845i	$-0.647286\pi$
$823$	−25.6114	−0.892756	−0.446378	+	0.894845i	$0.647286\pi$
$824$	−0.713182	−0.0248449
$825$	−5.76112	−0.200576
$826$	−1.75118	−0.0609312
$827$	22.6563	0.787836	0.393918	−	0.919146i	$-0.371119\pi$
$827$	22.6563	0.787836	0.393918	+	0.919146i	$0.371119\pi$
$828$	0	0
$829$	−1.71605	−0.0596008	−0.0298004	−	0.999556i	$-0.509487\pi$
$829$	−1.71605	−0.0596008	−0.0298004	+	0.999556i	$0.509487\pi$
$830$	−8.05143	−0.279469
$831$	−19.8941	−0.690118
$832$	−6.06352	−0.210215
$833$	27.5004	0.952832
$834$	8.13957	0.281850
$835$	4.05637	0.140377
$836$	−33.0771	−1.14400
$837$	−30.3288	−1.04832
$838$	−12.4593	−0.430399
$839$	−47.1414	−1.62750	−0.813750	−	0.581215i	$-0.802578\pi$
$839$	−47.1414	−1.62750	−0.813750	+	0.581215i	$0.802578\pi$
$840$	−0.374463	−0.0129202
$841$	39.0177	1.34544
$842$	−16.4512	−0.566944
$843$	−13.6709	−0.470852
$844$	−22.4403	−0.772426
$845$	23.7663	0.817586
$846$	−1.59830	−0.0549508
$847$	2.02123	0.0694502
$848$	9.08831	0.312094
$849$	5.60381	0.192322
$850$	3.97244	0.136254
$851$	0	0
$852$	−16.0827	−0.550984
$853$	39.4368	1.35029	0.675146	−	0.737684i	$-0.264081\pi$
$853$	39.4368	1.35029	0.675146	+	0.737684i	$0.264081\pi$
$854$	−1.58075	−0.0540922
$855$	−9.15951	−0.313248
$856$	−13.7586	−0.470260
$857$	−28.4657	−0.972370	−0.486185	−	0.873856i	$-0.661612\pi$
$857$	−28.4657	−0.972370	−0.486185	+	0.873856i	$0.661612\pi$
$858$	−34.9327	−1.19258
$859$	−31.7924	−1.08474	−0.542372	−	0.840138i	$-0.682474\pi$
$859$	−31.7924	−1.08474	−0.542372	+	0.840138i	$0.682474\pi$
$860$	1.11536	0.0380334
$861$	3.88726	0.132477
$862$	−15.4875	−0.527507
$863$	8.40378	0.286068	0.143034	−	0.989718i	$-0.454314\pi$
$863$	8.40378	0.286068	0.143034	+	0.989718i	$0.454314\pi$
$864$	5.63837	0.191821
$865$	13.0629	0.444152
$866$	27.3666	0.929954
$867$	−1.64379	−0.0558260
$868$	1.49460	0.0507300
$869$	−51.3187	−1.74087
$870$	−11.1147	−0.376823
$871$	17.5783	0.595617
$872$	5.38076	0.182216
$873$	−21.9336	−0.742340
$874$	0	0
$875$	0.277858	0.00939332
$876$	−3.23952	−0.109453
$877$	9.42234	0.318170	0.159085	−	0.987265i	$-0.449146\pi$
$877$	9.42234	0.318170	0.159085	+	0.987265i	$0.449146\pi$
$878$	7.07033	0.238612
$879$	9.88027	0.333253
$880$	−4.27485	−0.144105
$881$	20.1685	0.679493	0.339747	−	0.940517i	$-0.389659\pi$
$881$	20.1685	0.679493	0.339747	+	0.940517i	$0.389659\pi$
$882$	−8.19495	−0.275938
$883$	7.82701	0.263400	0.131700	−	0.991290i	$-0.457956\pi$
$883$	7.82701	0.263400	0.131700	+	0.991290i	$0.457956\pi$
$884$	24.0870	0.810133
$885$	8.49362	0.285510
$886$	28.3768	0.953336
$887$	9.43323	0.316737	0.158368	−	0.987380i	$-0.449377\pi$
$887$	9.43323	0.316737	0.158368	+	0.987380i	$0.449377\pi$
$888$	8.54614	0.286790
$889$	1.23327	0.0413626
$890$	−12.7108	−0.426068
$891$	17.3021	0.579641
$892$	−18.3132	−0.613172
$893$	−10.4472	−0.349604
$894$	−10.9948	−0.367722
$895$	3.78992	0.126683
$896$	−0.277858	−0.00928259
$897$	0	0
$898$	25.0706	0.836616
$899$	44.3621	1.47956
$900$	−1.18376	−0.0394588
$901$	−36.1028	−1.20276
$902$	44.3766	1.47758
$903$	0.417661	0.0138989
$904$	2.46857	0.0821033
$905$	7.20164	0.239390
$906$	7.54229	0.250576
$907$	51.8009	1.72002	0.860010	−	0.510278i	$-0.170457\pi$
$907$	51.8009	1.72002	0.860010	+	0.510278i	$0.170457\pi$
$908$	−3.91481	−0.129918
$909$	−15.6251	−0.518251
$910$	1.68480	0.0558506
$911$	40.3464	1.33674	0.668368	−	0.743830i	$-0.266993\pi$
$911$	40.3464	1.33674	0.668368	+	0.743830i	$0.266993\pi$
$912$	10.4278	0.345300
$913$	−34.4186	−1.13909
$914$	30.4575	1.00745
$915$	7.66702	0.253464
$916$	6.38567	0.210989
$917$	−3.95348	−0.130556
$918$	−22.3981	−0.739247
$919$	−45.7173	−1.50807	−0.754037	−	0.656832i	$-0.771896\pi$
$919$	−45.7173	−1.50807	−0.754037	+	0.656832i	$0.771896\pi$
$920$	0	0
$921$	27.9178	0.919924
$922$	12.2536	0.403550
$923$	72.3598	2.38175
$924$	−1.60077	−0.0526616
$925$	−6.34138	−0.208503
$926$	32.8134	1.07831
$927$	−0.844239	−0.0277284
$928$	−8.24729	−0.270730
$929$	12.2348	0.401411	0.200705	−	0.979652i	$-0.435677\pi$
$929$	12.2348	0.401411	0.200705	+	0.979652i	$0.435677\pi$
$930$	−7.24916	−0.237709
$931$	−53.5659	−1.75555
$932$	−23.2287	−0.760880
$933$	47.3020	1.54860
$934$	−31.2283	−1.02182
$935$	16.9816	0.555357
$936$	−7.17778	−0.234613
$937$	2.49312	0.0814468	0.0407234	−	0.999170i	$-0.487034\pi$
$937$	2.49312	0.0814468	0.0407234	+	0.999170i	$0.487034\pi$
$938$	0.805517	0.0263011
$939$	31.2268	1.01905
$940$	−1.35019	−0.0440383
$941$	−55.3082	−1.80300	−0.901498	−	0.432783i	$-0.857532\pi$
$941$	−55.3082	−1.80300	−0.901498	+	0.432783i	$0.857532\pi$
$942$	−1.29579	−0.0422191
$943$	0	0
$944$	6.30241	0.205126
$945$	−1.56667	−0.0509637
$946$	4.76798	0.155020
$947$	16.2348	0.527561	0.263780	−	0.964583i	$-0.415031\pi$
$947$	16.2348	0.527561	0.263780	+	0.964583i	$0.415031\pi$
$948$	16.1786	0.525457
$949$	14.5754	0.473137
$950$	−7.73762	−0.251041
$951$	−24.8876	−0.807036
$952$	1.10378	0.0357736
$953$	54.4450	1.76365	0.881824	−	0.471579i	$-0.156316\pi$
$953$	54.4450	1.76365	0.881824	+	0.471579i	$0.156316\pi$
$954$	10.7584	0.348316
$955$	13.7381	0.444555
$956$	19.7495	0.638744
$957$	−47.5136	−1.53590
$958$	−22.4845	−0.726440
$959$	3.76181	0.121475
$960$	1.34768	0.0434961
$961$	−2.06640	−0.0666581
$962$	−38.4511	−1.23971
$963$	−16.2869	−0.524839
$964$	9.97224	0.321184
$965$	−4.59398	−0.147886
$966$	0	0
$967$	24.9401	0.802020	0.401010	−	0.916074i	$-0.368659\pi$
$967$	24.9401	0.802020	0.401010	+	0.916074i	$0.368659\pi$
$968$	−7.27431	−0.233805
$969$	−41.4239	−1.33073
$970$	−18.5287	−0.594921
$971$	21.6631	0.695201	0.347600	−	0.937643i	$-0.386997\pi$
$971$	21.6631	0.695201	0.347600	+	0.937643i	$0.386997\pi$
$972$	11.4605	0.367595
$973$	−1.67818	−0.0538000
$974$	−33.7784	−1.08233
$975$	−8.17168	−0.261703
$976$	5.68906	0.182102
$977$	58.8859	1.88393	0.941963	−	0.335717i	$-0.108978\pi$
$977$	58.8859	1.88393	0.941963	+	0.335717i	$0.108978\pi$
$978$	11.6977	0.374051
$979$	−54.3368	−1.73661
$980$	−6.92279	−0.221141
$981$	6.36955	0.203364
$982$	20.1215	0.642103
$983$	12.2151	0.389600	0.194800	−	0.980843i	$-0.437594\pi$
$983$	12.2151	0.389600	0.194800	+	0.980843i	$0.437594\pi$
$984$	−13.9901	−0.445987
$985$	−14.8453	−0.473011
$986$	32.7619	1.04335
$987$	−0.505596	−0.0160933
$988$	−46.9172	−1.49264
$989$	0	0
$990$	−5.06041	−0.160830
$991$	11.2996	0.358944	0.179472	−	0.983763i	$-0.442561\pi$
$991$	11.2996	0.358944	0.179472	+	0.983763i	$0.442561\pi$
$992$	−5.37900	−0.170783
$993$	10.6800	0.338920
$994$	3.31586	0.105173
$995$	−20.3774	−0.646005
$996$	10.8507	0.343819
$997$	−55.4199	−1.75517	−0.877583	−	0.479425i	$-0.840845\pi$
$997$	−55.4199	−1.75517	−0.877583	+	0.479425i	$0.840845\pi$
$998$	−28.4999	−0.902147
$999$	35.7550	1.13124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bf.1.5	yes	6
23.22	odd	2		5290.2.a.be.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.be.1.5	✓	6	23.22	odd	2
5290.2.a.bf.1.5	yes	6	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.34768 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34768 q^{6} +0.277858 q^{7} -1.00000 q^{8} -1.18376 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.34768 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34768 q^{6} +0.277858 q^{7} -1.00000 q^{8} -1.18376 q^{9} -1.00000 q^{10} -4.27485 q^{11} +1.34768 q^{12} -6.06352 q^{13} -0.277858 q^{14} +1.34768 q^{15} +1.00000 q^{16} -3.97244 q^{17} +1.18376 q^{18} +7.73762 q^{19} +1.00000 q^{20} +0.374463 q^{21} +4.27485 q^{22} -1.34768 q^{24} +1.00000 q^{25} +6.06352 q^{26} -5.63837 q^{27} +0.277858 q^{28} +8.24729 q^{29} -1.34768 q^{30} +5.37900 q^{31} -1.00000 q^{32} -5.76112 q^{33} +3.97244 q^{34} +0.277858 q^{35} -1.18376 q^{36} -6.34138 q^{37} -7.73762 q^{38} -8.17168 q^{39} -1.00000 q^{40} +10.3809 q^{41} -0.374463 q^{42} +1.11536 q^{43} -4.27485 q^{44} -1.18376 q^{45} -1.35019 q^{47} +1.34768 q^{48} -6.92279 q^{49} -1.00000 q^{50} -5.35357 q^{51} -6.06352 q^{52} +9.08831 q^{53} +5.63837 q^{54} -4.27485 q^{55} -0.277858 q^{56} +10.4278 q^{57} -8.24729 q^{58} +6.30241 q^{59} +1.34768 q^{60} +5.68906 q^{61} -5.37900 q^{62} -0.328918 q^{63} +1.00000 q^{64} -6.06352 q^{65} +5.76112 q^{66} -2.89902 q^{67} -3.97244 q^{68} -0.277858 q^{70} -11.9336 q^{71} +1.18376 q^{72} -2.40378 q^{73} +6.34138 q^{74} +1.34768 q^{75} +7.73762 q^{76} -1.18780 q^{77} +8.17168 q^{78} +12.0048 q^{79} +1.00000 q^{80} -4.04742 q^{81} -10.3809 q^{82} +8.05143 q^{83} +0.374463 q^{84} -3.97244 q^{85} -1.11536 q^{86} +11.1147 q^{87} +4.27485 q^{88} +12.7108 q^{89} +1.18376 q^{90} -1.68480 q^{91} +7.24916 q^{93} +1.35019 q^{94} +7.73762 q^{95} -1.34768 q^{96} +18.5287 q^{97} +6.92279 q^{98} +5.06041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - 6 q^{10} + 10 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 6 q^{16} - 10 q^{17} - 8 q^{18} + 2 q^{19} + 6 q^{20} + 12 q^{21} - 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{30} - 2 q^{31} - 6 q^{32} - 22 q^{33} + 10 q^{34} + 2 q^{35} + 8 q^{36} - 4 q^{37} - 2 q^{38} + 24 q^{39} - 6 q^{40} + 6 q^{41} - 12 q^{42} + 12 q^{43} + 10 q^{44} + 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} + 34 q^{51} - 2 q^{52} + 36 q^{53} + 8 q^{54} + 10 q^{55} - 2 q^{56} + 32 q^{57} + 16 q^{59} - 2 q^{60} - 10 q^{61} + 2 q^{62} - 48 q^{63} + 6 q^{64} - 2 q^{65} + 22 q^{66} + 16 q^{67} - 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} + 4 q^{74} - 2 q^{75} + 2 q^{76} - 16 q^{77} - 24 q^{78} - 20 q^{79} + 6 q^{80} + 34 q^{81} - 6 q^{82} + 8 q^{83} + 12 q^{84} - 10 q^{85} - 12 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} + 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} + 2 q^{97} - 8 q^{98} + 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - 6 * q^10 + 10 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 6 * q^16 - 10 * q^17 - 8 * q^18 + 2 * q^19 + 6 * q^20 + 12 * q^21 - 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^30 - 2 * q^31 - 6 * q^32 - 22 * q^33 + 10 * q^34 + 2 * q^35 + 8 * q^36 - 4 * q^37 - 2 * q^38 + 24 * q^39 - 6 * q^40 + 6 * q^41 - 12 * q^42 + 12 * q^43 + 10 * q^44 + 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 + 34 * q^51 - 2 * q^52 + 36 * q^53 + 8 * q^54 + 10 * q^55 - 2 * q^56 + 32 * q^57 + 16 * q^59 - 2 * q^60 - 10 * q^61 + 2 * q^62 - 48 * q^63 + 6 * q^64 - 2 * q^65 + 22 * q^66 + 16 * q^67 - 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 + 4 * q^74 - 2 * q^75 + 2 * q^76 - 16 * q^77 - 24 * q^78 - 20 * q^79 + 6 * q^80 + 34 * q^81 - 6 * q^82 + 8 * q^83 + 12 * q^84 - 10 * q^85 - 12 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 + 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 + 2 * q^97 - 8 * q^98 + 50 * q^99

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