LMFDB - Embedded newform 5290.2.a.bk.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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.10043$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.10043 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.10043 q^{6} -4.03086 q^{7} +1.00000 q^{8} -1.78906 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.10043 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.10043 q^{6} -4.03086 q^{7} +1.00000 q^{8} -1.78906 q^{9} -1.00000 q^{10} +0.737876 q^{11} -1.10043 q^{12} -5.77330 q^{13} -4.03086 q^{14} +1.10043 q^{15} +1.00000 q^{16} -2.90932 q^{17} -1.78906 q^{18} -7.37166 q^{19} -1.00000 q^{20} +4.43567 q^{21} +0.737876 q^{22} -1.10043 q^{24} +1.00000 q^{25} -5.77330 q^{26} +5.27001 q^{27} -4.03086 q^{28} -5.57201 q^{29} +1.10043 q^{30} +1.13423 q^{31} +1.00000 q^{32} -0.811979 q^{33} -2.90932 q^{34} +4.03086 q^{35} -1.78906 q^{36} +6.51538 q^{37} -7.37166 q^{38} +6.35310 q^{39} -1.00000 q^{40} -2.10226 q^{41} +4.43567 q^{42} -5.93446 q^{43} +0.737876 q^{44} +1.78906 q^{45} +10.3100 q^{47} -1.10043 q^{48} +9.24780 q^{49} +1.00000 q^{50} +3.20149 q^{51} -5.77330 q^{52} +2.64344 q^{53} +5.27001 q^{54} -0.737876 q^{55} -4.03086 q^{56} +8.11198 q^{57} -5.57201 q^{58} +12.9481 q^{59} +1.10043 q^{60} -10.3037 q^{61} +1.13423 q^{62} +7.21144 q^{63} +1.00000 q^{64} +5.77330 q^{65} -0.811979 q^{66} +7.21540 q^{67} -2.90932 q^{68} +4.03086 q^{70} -1.82541 q^{71} -1.78906 q^{72} +14.3165 q^{73} +6.51538 q^{74} -1.10043 q^{75} -7.37166 q^{76} -2.97427 q^{77} +6.35310 q^{78} -5.44210 q^{79} -1.00000 q^{80} -0.432092 q^{81} -2.10226 q^{82} -16.4300 q^{83} +4.43567 q^{84} +2.90932 q^{85} -5.93446 q^{86} +6.13160 q^{87} +0.737876 q^{88} -7.74561 q^{89} +1.78906 q^{90} +23.2713 q^{91} -1.24814 q^{93} +10.3100 q^{94} +7.37166 q^{95} -1.10043 q^{96} +9.28624 q^{97} +9.24780 q^{98} -1.32010 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * 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
$3$	−1.10043	−0.635332	−0.317666	−	0.948203i	$-0.602899\pi$
$3$	−1.10043	−0.635332	−0.317666	+	0.948203i	$0.602899\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.10043	−0.449248
$7$	−4.03086	−1.52352	−0.761760	−	0.647859i	$-0.775665\pi$
$7$	−4.03086	−1.52352	−0.761760	+	0.647859i	$0.775665\pi$
$8$	1.00000	0.353553
$9$	−1.78906	−0.596353
$10$	−1.00000	−0.316228
$11$	0.737876	0.222478	0.111239	−	0.993794i	$-0.464518\pi$
$11$	0.737876	0.222478	0.111239	+	0.993794i	$0.464518\pi$
$12$	−1.10043	−0.317666
$13$	−5.77330	−1.60122	−0.800612	−	0.599183i	$-0.795492\pi$
$13$	−5.77330	−1.60122	−0.800612	+	0.599183i	$0.795492\pi$
$14$	−4.03086	−1.07729
$15$	1.10043	0.284129
$16$	1.00000	0.250000
$17$	−2.90932	−0.705613	−0.352807	−	0.935696i	$-0.614773\pi$
$17$	−2.90932	−0.705613	−0.352807	+	0.935696i	$0.614773\pi$
$18$	−1.78906	−0.421685
$19$	−7.37166	−1.69118	−0.845588	−	0.533836i	$-0.820750\pi$
$19$	−7.37166	−1.69118	−0.845588	+	0.533836i	$0.820750\pi$
$20$	−1.00000	−0.223607
$21$	4.43567	0.967941
$22$	0.737876	0.157316
$23$	0	0
$23$	0	0
$24$	−1.10043	−0.224624
$25$	1.00000	0.200000
$26$	−5.77330	−1.13224
$27$	5.27001	1.01421
$28$	−4.03086	−0.761760
$29$	−5.57201	−1.03470	−0.517348	−	0.855775i	$-0.673081\pi$
$29$	−5.57201	−1.03470	−0.517348	+	0.855775i	$0.673081\pi$
$30$	1.10043	0.200910
$31$	1.13423	0.203714	0.101857	−	0.994799i	$-0.467522\pi$
$31$	1.13423	0.203714	0.101857	+	0.994799i	$0.467522\pi$
$32$	1.00000	0.176777
$33$	−0.811979	−0.141347
$34$	−2.90932	−0.498944
$35$	4.03086	0.681339
$36$	−1.78906	−0.298176
$37$	6.51538	1.07112	0.535561	−	0.844496i	$-0.320100\pi$
$37$	6.51538	1.07112	0.535561	+	0.844496i	$0.320100\pi$
$38$	−7.37166	−1.19584
$39$	6.35310	1.01731
$40$	−1.00000	−0.158114
$41$	−2.10226	−0.328319	−0.164159	−	0.986434i	$-0.552491\pi$
$41$	−2.10226	−0.328319	−0.164159	+	0.986434i	$0.552491\pi$
$42$	4.43567	0.684438
$43$	−5.93446	−0.904997	−0.452498	−	0.891765i	$-0.649467\pi$
$43$	−5.93446	−0.904997	−0.452498	+	0.891765i	$0.649467\pi$
$44$	0.737876	0.111239
$45$	1.78906	0.266697
$46$	0	0
$47$	10.3100	1.50386	0.751931	−	0.659242i	$-0.229123\pi$
$47$	10.3100	1.50386	0.751931	+	0.659242i	$0.229123\pi$
$48$	−1.10043	−0.158833
$49$	9.24780	1.32111
$50$	1.00000	0.141421
$51$	3.20149	0.448299
$52$	−5.77330	−0.800612
$53$	2.64344	0.363104	0.181552	−	0.983381i	$-0.441888\pi$
$53$	2.64344	0.363104	0.181552	+	0.983381i	$0.441888\pi$
$54$	5.27001	0.717158
$55$	−0.737876	−0.0994952
$56$	−4.03086	−0.538646
$57$	8.11198	1.07446
$58$	−5.57201	−0.731641
$59$	12.9481	1.68570	0.842851	−	0.538146i	$-0.180875\pi$
$59$	12.9481	1.68570	0.842851	+	0.538146i	$0.180875\pi$
$60$	1.10043	0.142065
$61$	−10.3037	−1.31926	−0.659630	−	0.751591i	$-0.729287\pi$
$61$	−10.3037	−1.31926	−0.659630	+	0.751591i	$0.729287\pi$
$62$	1.13423	0.144047
$63$	7.21144	0.908556
$64$	1.00000	0.125000
$65$	5.77330	0.716089
$66$	−0.811979	−0.0999477
$67$	7.21540	0.881502	0.440751	−	0.897629i	$-0.354712\pi$
$67$	7.21540	0.881502	0.440751	+	0.897629i	$0.354712\pi$
$68$	−2.90932	−0.352807
$69$	0	0
$70$	4.03086	0.481779
$71$	−1.82541	−0.216636	−0.108318	−	0.994116i	$-0.534546\pi$
$71$	−1.82541	−0.216636	−0.108318	+	0.994116i	$0.534546\pi$
$72$	−1.78906	−0.210843
$73$	14.3165	1.67562	0.837810	−	0.545963i	$-0.183836\pi$
$73$	14.3165	1.67562	0.837810	+	0.545963i	$0.183836\pi$
$74$	6.51538	0.757398
$75$	−1.10043	−0.127066
$76$	−7.37166	−0.845588
$77$	−2.97427	−0.338950
$78$	6.35310	0.719346
$79$	−5.44210	−0.612284	−0.306142	−	0.951986i	$-0.599038\pi$
$79$	−5.44210	−0.612284	−0.306142	+	0.951986i	$0.599038\pi$
$80$	−1.00000	−0.111803
$81$	−0.432092	−0.0480102
$82$	−2.10226	−0.232156
$83$	−16.4300	−1.80343	−0.901713	−	0.432335i	$-0.857690\pi$
$83$	−16.4300	−1.80343	−0.901713	+	0.432335i	$0.857690\pi$
$84$	4.43567	0.483971
$85$	2.90932	0.315560
$86$	−5.93446	−0.639929
$87$	6.13160	0.657376
$88$	0.737876	0.0786578
$89$	−7.74561	−0.821033	−0.410517	−	0.911853i	$-0.634652\pi$
$89$	−7.74561	−0.821033	−0.410517	+	0.911853i	$0.634652\pi$
$90$	1.78906	0.188583
$91$	23.2713	2.43950
$92$	0	0
$93$	−1.24814	−0.129426
$94$	10.3100	1.06339
$95$	7.37166	0.756317
$96$	−1.10043	−0.112312
$97$	9.28624	0.942875	0.471438	−	0.881899i	$-0.343735\pi$
$97$	9.28624	0.942875	0.471438	+	0.881899i	$0.343735\pi$
$98$	9.24780	0.934169
$99$	−1.32010	−0.132675
$100$	1.00000	0.100000
$101$	−14.9778	−1.49035	−0.745175	−	0.666869i	$-0.767634\pi$
$101$	−14.9778	−1.49035	−0.745175	+	0.666869i	$0.767634\pi$
$102$	3.20149	0.316995
$103$	1.94560	0.191706	0.0958529	−	0.995396i	$-0.469442\pi$
$103$	1.94560	0.191706	0.0958529	+	0.995396i	$0.469442\pi$
$104$	−5.77330	−0.566118
$105$	−4.43567	−0.432877
$106$	2.64344	0.256753
$107$	−8.43976	−0.815902	−0.407951	−	0.913004i	$-0.633757\pi$
$107$	−8.43976	−0.815902	−0.407951	+	0.913004i	$0.633757\pi$
$108$	5.27001	0.507107
$109$	7.06370	0.676580	0.338290	−	0.941042i	$-0.390152\pi$
$109$	7.06370	0.676580	0.338290	+	0.941042i	$0.390152\pi$
$110$	−0.737876	−0.0703537
$111$	−7.16971	−0.680519
$112$	−4.03086	−0.380880
$113$	−3.24150	−0.304935	−0.152467	−	0.988308i	$-0.548722\pi$
$113$	−3.24150	−0.304935	−0.152467	+	0.988308i	$0.548722\pi$
$114$	8.11198	0.759757
$115$	0	0
$116$	−5.57201	−0.517348
$117$	10.3288	0.954895
$118$	12.9481	1.19197
$119$	11.7270	1.07502
$120$	1.10043	0.100455
$121$	−10.4555	−0.950504
$122$	−10.3037	−0.932857
$123$	2.31339	0.208591
$124$	1.13423	0.101857
$125$	−1.00000	−0.0894427
$126$	7.21144	0.642446
$127$	1.22247	0.108477	0.0542385	−	0.998528i	$-0.482727\pi$
$127$	1.22247	0.108477	0.0542385	+	0.998528i	$0.482727\pi$
$128$	1.00000	0.0883883
$129$	6.53044	0.574973
$130$	5.77330	0.506352
$131$	−5.03867	−0.440231	−0.220116	−	0.975474i	$-0.570643\pi$
$131$	−5.03867	−0.440231	−0.220116	+	0.975474i	$0.570643\pi$
$132$	−0.811979	−0.0706737
$133$	29.7141	2.57654
$134$	7.21540	0.623316
$135$	−5.27001	−0.453571
$136$	−2.90932	−0.249472
$137$	5.29346	0.452251	0.226125	−	0.974098i	$-0.427394\pi$
$137$	5.29346	0.452251	0.226125	+	0.974098i	$0.427394\pi$
$138$	0	0
$139$	−7.03580	−0.596769	−0.298384	−	0.954446i	$-0.596448\pi$
$139$	−7.03580	−0.596769	−0.298384	+	0.954446i	$0.596448\pi$
$140$	4.03086	0.340669
$141$	−11.3454	−0.955452
$142$	−1.82541	−0.153185
$143$	−4.25998	−0.356237
$144$	−1.78906	−0.149088
$145$	5.57201	0.462731
$146$	14.3165	1.18484
$147$	−10.1765	−0.839346
$148$	6.51538	0.535561
$149$	3.27791	0.268537	0.134269	−	0.990945i	$-0.457132\pi$
$149$	3.27791	0.268537	0.134269	+	0.990945i	$0.457132\pi$
$150$	−1.10043	−0.0898495
$151$	10.7845	0.877633	0.438816	−	0.898577i	$-0.355398\pi$
$151$	10.7845	0.877633	0.438816	+	0.898577i	$0.355398\pi$
$152$	−7.37166	−0.597921
$153$	5.20494	0.420795
$154$	−2.97427	−0.239674
$155$	−1.13423	−0.0911035
$156$	6.35310	0.508655
$157$	23.7655	1.89669	0.948346	−	0.317238i	$-0.102755\pi$
$157$	23.7655	1.89669	0.948346	+	0.317238i	$0.102755\pi$
$158$	−5.44210	−0.432950
$159$	−2.90891	−0.230692
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−0.432092	−0.0339483
$163$	−20.9790	−1.64320	−0.821602	−	0.570061i	$-0.806920\pi$
$163$	−20.9790	−1.64320	−0.821602	+	0.570061i	$0.806920\pi$
$164$	−2.10226	−0.164159
$165$	0.811979	0.0632125
$166$	−16.4300	−1.27521
$167$	8.75366	0.677378	0.338689	−	0.940898i	$-0.390016\pi$
$167$	8.75366	0.677378	0.338689	+	0.940898i	$0.390016\pi$
$168$	4.43567	0.342219
$169$	20.3310	1.56392
$170$	2.90932	0.223135
$171$	13.1883	1.00854
$172$	−5.93446	−0.452498
$173$	9.31210	0.707986	0.353993	−	0.935248i	$-0.384824\pi$
$173$	9.31210	0.707986	0.353993	+	0.935248i	$0.384824\pi$
$174$	6.13160	0.464835
$175$	−4.03086	−0.304704
$176$	0.737876	0.0556195
$177$	−14.2485	−1.07098
$178$	−7.74561	−0.580558
$179$	9.60165	0.717661	0.358831	−	0.933403i	$-0.383176\pi$
$179$	9.60165	0.717661	0.358831	+	0.933403i	$0.383176\pi$
$180$	1.78906	0.133349
$181$	−7.43822	−0.552878	−0.276439	−	0.961031i	$-0.589154\pi$
$181$	−7.43822	−0.552878	−0.276439	+	0.961031i	$0.589154\pi$
$182$	23.2713	1.72499
$183$	11.3385	0.838168
$184$	0	0
$185$	−6.51538	−0.479020
$186$	−1.24814	−0.0915179
$187$	−2.14672	−0.156983
$188$	10.3100	0.751931
$189$	−21.2427	−1.54518
$190$	7.37166	0.534797
$191$	−14.7109	−1.06444	−0.532222	−	0.846605i	$-0.678643\pi$
$191$	−14.7109	−1.06444	−0.532222	+	0.846605i	$0.678643\pi$
$192$	−1.10043	−0.0794165
$193$	4.37071	0.314610	0.157305	−	0.987550i	$-0.449719\pi$
$193$	4.37071	0.314610	0.157305	+	0.987550i	$0.449719\pi$
$194$	9.28624	0.666714
$195$	−6.35310	−0.454955
$196$	9.24780	0.660557
$197$	11.4366	0.814824	0.407412	−	0.913244i	$-0.366431\pi$
$197$	11.4366	0.814824	0.407412	+	0.913244i	$0.366431\pi$
$198$	−1.32010	−0.0938157
$199$	−15.6770	−1.11131	−0.555656	−	0.831413i	$-0.687533\pi$
$199$	−15.6770	−1.11131	−0.555656	+	0.831413i	$0.687533\pi$
$200$	1.00000	0.0707107
$201$	−7.94003	−0.560047
$202$	−14.9778	−1.05384
$203$	22.4600	1.57638
$204$	3.20149	0.224149
$205$	2.10226	0.146829
$206$	1.94560	0.135557
$207$	0	0
$208$	−5.77330	−0.400306
$209$	−5.43937	−0.376249
$210$	−4.43567	−0.306090
$211$	0.615129	0.0423472	0.0211736	−	0.999776i	$-0.493260\pi$
$211$	0.615129	0.0423472	0.0211736	+	0.999776i	$0.493260\pi$
$212$	2.64344	0.181552
$213$	2.00873	0.137636
$214$	−8.43976	−0.576930
$215$	5.93446	0.404727
$216$	5.27001	0.358579
$217$	−4.57191	−0.310362
$218$	7.06370	0.478414
$219$	−15.7543	−1.06457
$220$	−0.737876	−0.0497476
$221$	16.7964	1.12985
$222$	−7.16971	−0.481199
$223$	13.9032	0.931024	0.465512	−	0.885042i	$-0.345870\pi$
$223$	13.9032	0.931024	0.465512	+	0.885042i	$0.345870\pi$
$224$	−4.03086	−0.269323
$225$	−1.78906	−0.119271
$226$	−3.24150	−0.215621
$227$	−8.00035	−0.531002	−0.265501	−	0.964111i	$-0.585537\pi$
$227$	−8.00035	−0.531002	−0.265501	+	0.964111i	$0.585537\pi$
$228$	8.11198	0.537229
$229$	−16.7061	−1.10397	−0.551986	−	0.833853i	$-0.686130\pi$
$229$	−16.7061	−1.10397	−0.551986	+	0.833853i	$0.686130\pi$
$230$	0	0
$231$	3.27297	0.215346
$232$	−5.57201	−0.365821
$233$	6.28825	0.411957	0.205978	−	0.978557i	$-0.433962\pi$
$233$	6.28825	0.411957	0.205978	+	0.978557i	$0.433962\pi$
$234$	10.3288	0.675213
$235$	−10.3100	−0.672548
$236$	12.9481	0.842851
$237$	5.98863	0.389004
$238$	11.7270	0.760151
$239$	4.31982	0.279426	0.139713	−	0.990192i	$-0.455382\pi$
$239$	4.31982	0.279426	0.139713	+	0.990192i	$0.455382\pi$
$240$	1.10043	0.0710323
$241$	5.00515	0.322410	0.161205	−	0.986921i	$-0.448462\pi$
$241$	5.00515	0.322410	0.161205	+	0.986921i	$0.448462\pi$
$242$	−10.4555	−0.672108
$243$	−15.3346	−0.983712
$244$	−10.3037	−0.659630
$245$	−9.24780	−0.590820
$246$	2.31339	0.147496
$247$	42.5588	2.70795
$248$	1.13423	0.0720236
$249$	18.0800	1.14577
$250$	−1.00000	−0.0632456
$251$	−6.02318	−0.380180	−0.190090	−	0.981767i	$-0.560878\pi$
$251$	−6.02318	−0.380180	−0.190090	+	0.981767i	$0.560878\pi$
$252$	7.21144	0.454278
$253$	0	0
$254$	1.22247	0.0767048
$255$	−3.20149	−0.200485
$256$	1.00000	0.0625000
$257$	−23.0530	−1.43800	−0.719002	−	0.695008i	$-0.755401\pi$
$257$	−23.0530	−1.43800	−0.719002	+	0.695008i	$0.755401\pi$
$258$	6.53044	0.406568
$259$	−26.2626	−1.63188
$260$	5.77330	0.358045
$261$	9.96866	0.617045
$262$	−5.03867	−0.311290
$263$	1.14714	0.0707357	0.0353678	−	0.999374i	$-0.488740\pi$
$263$	1.14714	0.0707357	0.0353678	+	0.999374i	$0.488740\pi$
$264$	−0.811979	−0.0499739
$265$	−2.64344	−0.162385
$266$	29.7141	1.82189
$267$	8.52349	0.521629
$268$	7.21540	0.440751
$269$	−14.5898	−0.889553	−0.444777	−	0.895642i	$-0.646717\pi$
$269$	−14.5898	−0.889553	−0.444777	+	0.895642i	$0.646717\pi$
$270$	−5.27001	−0.320723
$271$	−9.19145	−0.558341	−0.279170	−	0.960242i	$-0.590059\pi$
$271$	−9.19145	−0.558341	−0.279170	+	0.960242i	$0.590059\pi$
$272$	−2.90932	−0.176403
$273$	−25.6084	−1.54989
$274$	5.29346	0.319789
$275$	0.737876	0.0444956
$276$	0	0
$277$	22.8877	1.37519	0.687596	−	0.726094i	$-0.258666\pi$
$277$	22.8877	1.37519	0.687596	+	0.726094i	$0.258666\pi$
$278$	−7.03580	−0.421979
$279$	−2.02920	−0.121485
$280$	4.03086	0.240890
$281$	22.4336	1.33828	0.669138	−	0.743138i	$-0.266663\pi$
$281$	22.4336	1.33828	0.669138	+	0.743138i	$0.266663\pi$
$282$	−11.3454	−0.675607
$283$	21.7271	1.29154	0.645772	−	0.763531i	$-0.276536\pi$
$283$	21.7271	1.29154	0.645772	+	0.763531i	$0.276536\pi$
$284$	−1.82541	−0.108318
$285$	−8.11198	−0.480512
$286$	−4.25998	−0.251898
$287$	8.47392	0.500200
$288$	−1.78906	−0.105421
$289$	−8.53587	−0.502110
$290$	5.57201	0.327200
$291$	−10.2188	−0.599039
$292$	14.3165	0.837810
$293$	−26.5654	−1.55197	−0.775985	−	0.630752i	$-0.782747\pi$
$293$	−26.5654	−1.55197	−0.775985	+	0.630752i	$0.782747\pi$
$294$	−10.1765	−0.593507
$295$	−12.9481	−0.753869
$296$	6.51538	0.378699
$297$	3.88862	0.225640
$298$	3.27791	0.189884
$299$	0	0
$300$	−1.10043	−0.0635332
$301$	23.9209	1.37878
$302$	10.7845	0.620580
$303$	16.4820	0.946867
$304$	−7.37166	−0.422794
$305$	10.3037	0.589991
$306$	5.20494	0.297547
$307$	15.3616	0.876734	0.438367	−	0.898796i	$-0.355557\pi$
$307$	15.3616	0.876734	0.438367	+	0.898796i	$0.355557\pi$
$308$	−2.97427	−0.169475
$309$	−2.14099	−0.121797
$310$	−1.13423	−0.0644199
$311$	4.16462	0.236154	0.118077	−	0.993004i	$-0.462327\pi$
$311$	4.16462	0.236154	0.118077	+	0.993004i	$0.462327\pi$
$312$	6.35310	0.359673
$313$	11.7221	0.662574	0.331287	−	0.943530i	$-0.392517\pi$
$313$	11.7221	0.662574	0.331287	+	0.943530i	$0.392517\pi$
$314$	23.7655	1.34116
$315$	−7.21144	−0.406318
$316$	−5.44210	−0.306142
$317$	33.4427	1.87833	0.939164	−	0.343468i	$-0.111602\pi$
$317$	33.4427	1.87833	0.939164	+	0.343468i	$0.111602\pi$
$318$	−2.90891	−0.163124
$319$	−4.11145	−0.230197
$320$	−1.00000	−0.0559017
$321$	9.28735	0.518369
$322$	0	0
$323$	21.4465	1.19332
$324$	−0.432092	−0.0240051
$325$	−5.77330	−0.320245
$326$	−20.9790	−1.16192
$327$	−7.77309	−0.429853
$328$	−2.10226	−0.116078
$329$	−41.5580	−2.29116
$330$	0.811979	0.0446980
$331$	−15.2387	−0.837592	−0.418796	−	0.908080i	$-0.637548\pi$
$331$	−15.2387	−0.837592	−0.418796	+	0.908080i	$0.637548\pi$
$332$	−16.4300	−0.901713
$333$	−11.6564	−0.638767
$334$	8.75366	0.478979
$335$	−7.21540	−0.394220
$336$	4.43567	0.241985
$337$	−9.19452	−0.500857	−0.250429	−	0.968135i	$-0.580572\pi$
$337$	−9.19452	−0.500857	−0.250429	+	0.968135i	$0.580572\pi$
$338$	20.3310	1.10586
$339$	3.56704	0.193735
$340$	2.90932	0.157780
$341$	0.836921	0.0453218
$342$	13.1883	0.713144
$343$	−9.06054	−0.489223
$344$	−5.93446	−0.319965
$345$	0	0
$346$	9.31210	0.500622
$347$	−28.3879	−1.52394	−0.761971	−	0.647611i	$-0.775768\pi$
$347$	−28.3879	−1.52394	−0.761971	+	0.647611i	$0.775768\pi$
$348$	6.13160	0.328688
$349$	2.68077	0.143498	0.0717491	−	0.997423i	$-0.477142\pi$
$349$	2.68077	0.143498	0.0717491	+	0.997423i	$0.477142\pi$
$350$	−4.03086	−0.215458
$351$	−30.4253	−1.62398
$352$	0.737876	0.0393289
$353$	−14.4593	−0.769594	−0.384797	−	0.923001i	$-0.625728\pi$
$353$	−14.4593	−0.769594	−0.384797	+	0.923001i	$0.625728\pi$
$354$	−14.2485	−0.757298
$355$	1.82541	0.0968826
$356$	−7.74561	−0.410517
$357$	−12.9048	−0.682992
$358$	9.60165	0.507463
$359$	15.7837	0.833034	0.416517	−	0.909128i	$-0.363251\pi$
$359$	15.7837	0.833034	0.416517	+	0.909128i	$0.363251\pi$
$360$	1.78906	0.0942917
$361$	35.3414	1.86008
$362$	−7.43822	−0.390944
$363$	11.5056	0.603886
$364$	23.2713	1.21975
$365$	−14.3165	−0.749360
$366$	11.3385	0.592674
$367$	−18.1412	−0.946963	−0.473482	−	0.880804i	$-0.657003\pi$
$367$	−18.1412	−0.946963	−0.473482	+	0.880804i	$0.657003\pi$
$368$	0	0
$369$	3.76107	0.195794
$370$	−6.51538	−0.338719
$371$	−10.6553	−0.553197
$372$	−1.24814	−0.0647129
$373$	27.3094	1.41403	0.707014	−	0.707199i	$-0.250042\pi$
$373$	27.3094	1.41403	0.707014	+	0.707199i	$0.250042\pi$
$374$	−2.14672	−0.111004
$375$	1.10043	0.0568258
$376$	10.3100	0.531696
$377$	32.1689	1.65678
$378$	−21.2427	−1.09260
$379$	−1.95905	−0.100630	−0.0503149	−	0.998733i	$-0.516023\pi$
$379$	−1.95905	−0.100630	−0.0503149	+	0.998733i	$0.516023\pi$
$380$	7.37166	0.378158
$381$	−1.34524	−0.0689190
$382$	−14.7109	−0.752675
$383$	−0.187725	−0.00959232	−0.00479616	−	0.999988i	$-0.501527\pi$
$383$	−0.187725	−0.00959232	−0.00479616	+	0.999988i	$0.501527\pi$
$384$	−1.10043	−0.0561560
$385$	2.97427	0.151583
$386$	4.37071	0.222463
$387$	10.6171	0.539697
$388$	9.28624	0.471438
$389$	−0.461916	−0.0234201	−0.0117100	−	0.999931i	$-0.503728\pi$
$389$	−0.461916	−0.0234201	−0.0117100	+	0.999931i	$0.503728\pi$
$390$	−6.35310	−0.321701
$391$	0	0
$392$	9.24780	0.467084
$393$	5.54470	0.279693
$394$	11.4366	0.576168
$395$	5.44210	0.273822
$396$	−1.32010	−0.0663377
$397$	−9.14855	−0.459153	−0.229576	−	0.973291i	$-0.573734\pi$
$397$	−9.14855	−0.459153	−0.229576	+	0.973291i	$0.573734\pi$
$398$	−15.6770	−0.785816
$399$	−32.6982	−1.63696
$400$	1.00000	0.0500000
$401$	25.3201	1.26443	0.632214	−	0.774794i	$-0.282146\pi$
$401$	25.3201	1.26443	0.632214	+	0.774794i	$0.282146\pi$
$402$	−7.94003	−0.396013
$403$	−6.54824	−0.326191
$404$	−14.9778	−0.745175
$405$	0.432092	0.0214708
$406$	22.4600	1.11467
$407$	4.80754	0.238301
$408$	3.20149	0.158498
$409$	36.9772	1.82840	0.914202	−	0.405260i	$-0.132819\pi$
$409$	36.9772	1.82840	0.914202	+	0.405260i	$0.132819\pi$
$410$	2.10226	0.103823
$411$	−5.82507	−0.287329
$412$	1.94560	0.0958529
$413$	−52.1920	−2.56820
$414$	0	0
$415$	16.4300	0.806517
$416$	−5.77330	−0.283059
$417$	7.74239	0.379146
$418$	−5.43937	−0.266048
$419$	13.3635	0.652851	0.326425	−	0.945223i	$-0.394156\pi$
$419$	13.3635	0.652851	0.326425	+	0.945223i	$0.394156\pi$
$420$	−4.43567	−0.216438
$421$	9.23034	0.449859	0.224930	−	0.974375i	$-0.427785\pi$
$421$	9.23034	0.449859	0.224930	+	0.974375i	$0.427785\pi$
$422$	0.615129	0.0299440
$423$	−18.4451	−0.896833
$424$	2.64344	0.128377
$425$	−2.90932	−0.141123
$426$	2.00873	0.0973232
$427$	41.5329	2.00992
$428$	−8.43976	−0.407951
$429$	4.68780	0.226329
$430$	5.93446	0.286185
$431$	−23.1846	−1.11676	−0.558380	−	0.829585i	$-0.688577\pi$
$431$	−23.1846	−1.11676	−0.558380	+	0.829585i	$0.688577\pi$
$432$	5.27001	0.253554
$433$	−12.9492	−0.622299	−0.311150	−	0.950361i	$-0.600714\pi$
$433$	−12.9492	−0.622299	−0.311150	+	0.950361i	$0.600714\pi$
$434$	−4.57191	−0.219459
$435$	−6.13160	−0.293988
$436$	7.06370	0.338290
$437$	0	0
$438$	−15.7543	−0.752768
$439$	3.04386	0.145276	0.0726379	−	0.997358i	$-0.476858\pi$
$439$	3.04386	0.145276	0.0726379	+	0.997358i	$0.476858\pi$
$440$	−0.737876	−0.0351769
$441$	−16.5449	−0.787850
$442$	16.7964	0.798921
$443$	−7.27680	−0.345731	−0.172866	−	0.984945i	$-0.555303\pi$
$443$	−7.27680	−0.345731	−0.172866	+	0.984945i	$0.555303\pi$
$444$	−7.16971	−0.340259
$445$	7.74561	0.367177
$446$	13.9032	0.658333
$447$	−3.60711	−0.170610
$448$	−4.03086	−0.190440
$449$	24.9498	1.17745	0.588727	−	0.808332i	$-0.299629\pi$
$449$	24.9498	1.17745	0.588727	+	0.808332i	$0.299629\pi$
$450$	−1.78906	−0.0843370
$451$	−1.55121	−0.0730436
$452$	−3.24150	−0.152467
$453$	−11.8676	−0.557588
$454$	−8.00035	−0.375475
$455$	−23.2713	−1.09098
$456$	8.11198	0.379878
$457$	14.0095	0.655335	0.327667	−	0.944793i	$-0.393738\pi$
$457$	14.0095	0.655335	0.327667	+	0.944793i	$0.393738\pi$
$458$	−16.7061	−0.780626
$459$	−15.3321	−0.715643
$460$	0	0
$461$	4.80312	0.223704	0.111852	−	0.993725i	$-0.464322\pi$
$461$	4.80312	0.223704	0.111852	+	0.993725i	$0.464322\pi$
$462$	3.27297	0.152272
$463$	−7.62109	−0.354182	−0.177091	−	0.984194i	$-0.556669\pi$
$463$	−7.62109	−0.354182	−0.177091	+	0.984194i	$0.556669\pi$
$464$	−5.57201	−0.258674
$465$	1.24814	0.0578810
$466$	6.28825	0.291297
$467$	9.82287	0.454548	0.227274	−	0.973831i	$-0.427019\pi$
$467$	9.82287	0.454548	0.227274	+	0.973831i	$0.427019\pi$
$468$	10.3288	0.477447
$469$	−29.0843	−1.34299
$470$	−10.3100	−0.475563
$471$	−26.1522	−1.20503
$472$	12.9481	0.595986
$473$	−4.37889	−0.201342
$474$	5.98863	0.275067
$475$	−7.37166	−0.338235
$476$	11.7270	0.537508
$477$	−4.72927	−0.216538
$478$	4.31982	0.197584
$479$	−35.5465	−1.62416	−0.812082	−	0.583544i	$-0.801666\pi$
$479$	−35.5465	−1.62416	−0.812082	+	0.583544i	$0.801666\pi$
$480$	1.10043	0.0502274
$481$	−37.6152	−1.71511
$482$	5.00515	0.227978
$483$	0	0
$484$	−10.4555	−0.475252
$485$	−9.28624	−0.421667
$486$	−15.3346	−0.695589
$487$	10.0536	0.455574	0.227787	−	0.973711i	$-0.426851\pi$
$487$	10.0536	0.455574	0.227787	+	0.973711i	$0.426851\pi$
$488$	−10.3037	−0.466429
$489$	23.0859	1.04398
$490$	−9.24780	−0.417773
$491$	27.7805	1.25372	0.626858	−	0.779133i	$-0.284340\pi$
$491$	27.7805	1.25372	0.626858	+	0.779133i	$0.284340\pi$
$492$	2.31339	0.104296
$493$	16.2108	0.730096
$494$	42.5588	1.91481
$495$	1.32010	0.0593342
$496$	1.13423	0.0509284
$497$	7.35795	0.330049
$498$	18.0800	0.810185
$499$	4.98775	0.223282	0.111641	−	0.993749i	$-0.464389\pi$
$499$	4.98775	0.223282	0.111641	+	0.993749i	$0.464389\pi$
$500$	−1.00000	−0.0447214
$501$	−9.63277	−0.430360
$502$	−6.02318	−0.268828
$503$	−11.1101	−0.495373	−0.247687	−	0.968840i	$-0.579670\pi$
$503$	−11.1101	−0.495373	−0.247687	+	0.968840i	$0.579670\pi$
$504$	7.21144	0.321223
$505$	14.9778	0.666504
$506$	0	0
$507$	−22.3727	−0.993608
$508$	1.22247	0.0542385
$509$	−21.5120	−0.953504	−0.476752	−	0.879038i	$-0.658186\pi$
$509$	−21.5120	−0.953504	−0.476752	+	0.879038i	$0.658186\pi$
$510$	−3.20149	−0.141765
$511$	−57.7077	−2.55284
$512$	1.00000	0.0441942
$513$	−38.8488	−1.71522
$514$	−23.0530	−1.01682
$515$	−1.94560	−0.0857335
$516$	6.53044	0.287487
$517$	7.60747	0.334576
$518$	−26.2626	−1.15391
$519$	−10.2473	−0.449806
$520$	5.77330	0.253176
$521$	−28.6408	−1.25478	−0.627389	−	0.778706i	$-0.715876\pi$
$521$	−28.6408	−1.25478	−0.627389	+	0.778706i	$0.715876\pi$
$522$	9.96866	0.436316
$523$	−25.3228	−1.10729	−0.553644	−	0.832753i	$-0.686763\pi$
$523$	−25.3228	−1.10729	−0.553644	+	0.832753i	$0.686763\pi$
$524$	−5.03867	−0.220116
$525$	4.43567	0.193588
$526$	1.14714	0.0500177
$527$	−3.29983	−0.143743
$528$	−0.811979	−0.0353369
$529$	0	0
$530$	−2.64344	−0.114824
$531$	−23.1650	−1.00527
$532$	29.7141	1.28827
$533$	12.1370	0.525712
$534$	8.52349	0.368847
$535$	8.43976	0.364883
$536$	7.21540	0.311658
$537$	−10.5659	−0.455953
$538$	−14.5898	−0.629009
$539$	6.82373	0.293919
$540$	−5.27001	−0.226785
$541$	19.3521	0.832011	0.416006	−	0.909362i	$-0.363430\pi$
$541$	19.3521	0.832011	0.416006	+	0.909362i	$0.363430\pi$
$542$	−9.19145	−0.394807
$543$	8.18522	0.351262
$544$	−2.90932	−0.124736
$545$	−7.06370	−0.302576
$546$	−25.6084	−1.09594
$547$	−24.1160	−1.03112	−0.515562	−	0.856852i	$-0.672417\pi$
$547$	−24.1160	−1.03112	−0.515562	+	0.856852i	$0.672417\pi$
$548$	5.29346	0.226125
$549$	18.4340	0.786744
$550$	0.737876	0.0314631
$551$	41.0750	1.74985
$552$	0	0
$553$	21.9363	0.932827
$554$	22.8877	0.972407
$555$	7.16971	0.304337
$556$	−7.03580	−0.298384
$557$	−24.4293	−1.03510	−0.517550	−	0.855653i	$-0.673156\pi$
$557$	−24.4293	−1.03510	−0.517550	+	0.855653i	$0.673156\pi$
$558$	−2.02920	−0.0859030
$559$	34.2614	1.44910
$560$	4.03086	0.170335
$561$	2.36231	0.0997366
$562$	22.4336	0.946305
$563$	41.6973	1.75733	0.878666	−	0.477438i	$-0.158434\pi$
$563$	41.6973	1.75733	0.878666	+	0.477438i	$0.158434\pi$
$564$	−11.3454	−0.477726
$565$	3.24150	0.136371
$566$	21.7271	0.913259
$567$	1.74170	0.0731445
$568$	−1.82541	−0.0765924
$569$	28.3866	1.19003	0.595014	−	0.803715i	$-0.297146\pi$
$569$	28.3866	1.19003	0.595014	+	0.803715i	$0.297146\pi$
$570$	−8.11198	−0.339774
$571$	8.38158	0.350758	0.175379	−	0.984501i	$-0.443885\pi$
$571$	8.38158	0.350758	0.175379	+	0.984501i	$0.443885\pi$
$572$	−4.25998	−0.178119
$573$	16.1883	0.676275
$574$	8.47392	0.353695
$575$	0	0
$576$	−1.78906	−0.0745441
$577$	−43.0208	−1.79098	−0.895490	−	0.445081i	$-0.853175\pi$
$577$	−43.0208	−1.79098	−0.895490	+	0.445081i	$0.853175\pi$
$578$	−8.53587	−0.355045
$579$	−4.80965	−0.199882
$580$	5.57201	0.231365
$581$	66.2269	2.74756
$582$	−10.2188	−0.423585
$583$	1.95053	0.0807827
$584$	14.3165	0.592421
$585$	−10.3288	−0.427042
$586$	−26.5654	−1.09741
$587$	−34.4985	−1.42390	−0.711952	−	0.702228i	$-0.752189\pi$
$587$	−34.4985	−1.42390	−0.711952	+	0.702228i	$0.752189\pi$
$588$	−10.1765	−0.419673
$589$	−8.36116	−0.344516
$590$	−12.9481	−0.533066
$591$	−12.5852	−0.517684
$592$	6.51538	0.267781
$593$	−28.8940	−1.18653	−0.593267	−	0.805006i	$-0.702162\pi$
$593$	−28.8940	−1.18653	−0.593267	+	0.805006i	$0.702162\pi$
$594$	3.88862	0.159552
$595$	−11.7270	−0.480762
$596$	3.27791	0.134269
$597$	17.2514	0.706052
$598$	0	0
$599$	18.2589	0.746038	0.373019	−	0.927824i	$-0.378323\pi$
$599$	18.2589	0.746038	0.373019	+	0.927824i	$0.378323\pi$
$600$	−1.10043	−0.0449248
$601$	−45.9045	−1.87248	−0.936242	−	0.351355i	$-0.885721\pi$
$601$	−45.9045	−1.87248	−0.936242	+	0.351355i	$0.885721\pi$
$602$	23.9209	0.974945
$603$	−12.9088	−0.525686
$604$	10.7845	0.438816
$605$	10.4555	0.425078
$606$	16.4820	0.669536
$607$	−17.7887	−0.722021	−0.361010	−	0.932562i	$-0.617568\pi$
$607$	−17.7887	−0.722021	−0.361010	+	0.932562i	$0.617568\pi$
$608$	−7.37166	−0.298960
$609$	−24.7156	−1.00153
$610$	10.3037	0.417187
$611$	−59.5225	−2.40802
$612$	5.20494	0.210397
$613$	10.0320	0.405190	0.202595	−	0.979263i	$-0.435062\pi$
$613$	10.0320	0.405190	0.202595	+	0.979263i	$0.435062\pi$
$614$	15.3616	0.619944
$615$	−2.31339	−0.0932849
$616$	−2.97427	−0.119837
$617$	13.4029	0.539581	0.269791	−	0.962919i	$-0.413046\pi$
$617$	13.4029	0.539581	0.269791	+	0.962919i	$0.413046\pi$
$618$	−2.14099	−0.0861234
$619$	−16.5462	−0.665049	−0.332525	−	0.943095i	$-0.607900\pi$
$619$	−16.5462	−0.665049	−0.332525	+	0.943095i	$0.607900\pi$
$620$	−1.13423	−0.0455517
$621$	0	0
$622$	4.16462	0.166986
$623$	31.2214	1.25086
$624$	6.35310	0.254327
$625$	1.00000	0.0400000
$626$	11.7221	0.468511
$627$	5.98564	0.239043
$628$	23.7655	0.948346
$629$	−18.9553	−0.755798
$630$	−7.21144	−0.287311
$631$	16.1021	0.641013	0.320506	−	0.947246i	$-0.396147\pi$
$631$	16.1021	0.641013	0.320506	+	0.947246i	$0.396147\pi$
$632$	−5.44210	−0.216475
$633$	−0.676905	−0.0269046
$634$	33.4427	1.32818
$635$	−1.22247	−0.0485124
$636$	−2.90891	−0.115346
$637$	−53.3903	−2.11540
$638$	−4.11145	−0.162774
$639$	3.26576	0.129192
$640$	−1.00000	−0.0395285
$641$	17.0583	0.673762	0.336881	−	0.941547i	$-0.390628\pi$
$641$	17.0583	0.673762	0.336881	+	0.941547i	$0.390628\pi$
$642$	9.28735	0.366542
$643$	2.27337	0.0896531	0.0448266	−	0.998995i	$-0.485726\pi$
$643$	2.27337	0.0896531	0.0448266	+	0.998995i	$0.485726\pi$
$644$	0	0
$645$	−6.53044	−0.257136
$646$	21.4465	0.843802
$647$	29.3272	1.15297	0.576485	−	0.817107i	$-0.304424\pi$
$647$	29.3272	1.15297	0.576485	+	0.817107i	$0.304424\pi$
$648$	−0.432092	−0.0169742
$649$	9.55411	0.375032
$650$	−5.77330	−0.226447
$651$	5.03106	0.197183
$652$	−20.9790	−0.821602
$653$	−21.7848	−0.852506	−0.426253	−	0.904604i	$-0.640167\pi$
$653$	−21.7848	−0.852506	−0.426253	+	0.904604i	$0.640167\pi$
$654$	−7.77309	−0.303952
$655$	5.03867	0.196877
$656$	−2.10226	−0.0820796
$657$	−25.6131	−0.999260
$658$	−41.5580	−1.62010
$659$	8.99728	0.350484	0.175242	−	0.984525i	$-0.443929\pi$
$659$	8.99728	0.350484	0.175242	+	0.984525i	$0.443929\pi$
$660$	0.811979	0.0316062
$661$	45.3027	1.76207	0.881036	−	0.473050i	$-0.156847\pi$
$661$	45.3027	1.76207	0.881036	+	0.473050i	$0.156847\pi$
$662$	−15.2387	−0.592267
$663$	−18.4832	−0.717827
$664$	−16.4300	−0.637607
$665$	−29.7141	−1.15226
$666$	−11.6564	−0.451676
$667$	0	0
$668$	8.75366	0.338689
$669$	−15.2994	−0.591509
$670$	−7.21540	−0.278755
$671$	−7.60289	−0.293506
$672$	4.43567	0.171109
$673$	25.4992	0.982921	0.491460	−	0.870900i	$-0.336463\pi$
$673$	25.4992	0.982921	0.491460	+	0.870900i	$0.336463\pi$
$674$	−9.19452	−0.354160
$675$	5.27001	0.202843
$676$	20.3310	0.781960
$677$	35.6556	1.37035	0.685177	−	0.728376i	$-0.259725\pi$
$677$	35.6556	1.37035	0.685177	+	0.728376i	$0.259725\pi$
$678$	3.56704	0.136991
$679$	−37.4315	−1.43649
$680$	2.90932	0.111567
$681$	8.80381	0.337363
$682$	0.836921	0.0320473
$683$	−10.9725	−0.419852	−0.209926	−	0.977717i	$-0.567322\pi$
$683$	−10.9725	−0.419852	−0.209926	+	0.977717i	$0.567322\pi$
$684$	13.1883	0.504269
$685$	−5.29346	−0.202253
$686$	−9.06054	−0.345933
$687$	18.3839	0.701389
$688$	−5.93446	−0.226249
$689$	−15.2614	−0.581411
$690$	0	0
$691$	−43.7845	−1.66564	−0.832821	−	0.553542i	$-0.813276\pi$
$691$	−43.7845	−1.66564	−0.832821	+	0.553542i	$0.813276\pi$
$692$	9.31210	0.353993
$693$	5.32115	0.202134
$694$	−28.3879	−1.07759
$695$	7.03580	0.266883
$696$	6.13160	0.232418
$697$	6.11616	0.231666
$698$	2.68077	0.101468
$699$	−6.91976	−0.261729
$700$	−4.03086	−0.152352
$701$	−43.6102	−1.64714	−0.823568	−	0.567218i	$-0.808020\pi$
$701$	−43.6102	−1.64714	−0.823568	+	0.567218i	$0.808020\pi$
$702$	−30.4253	−1.14833
$703$	−48.0292	−1.81146
$704$	0.737876	0.0278097
$705$	11.3454	0.427291
$706$	−14.4593	−0.544185
$707$	60.3734	2.27058
$708$	−14.2485	−0.535491
$709$	10.8351	0.406922	0.203461	−	0.979083i	$-0.434781\pi$
$709$	10.8351	0.406922	0.203461	+	0.979083i	$0.434781\pi$
$710$	1.82541	0.0685063
$711$	9.73623	0.365137
$712$	−7.74561	−0.290279
$713$	0	0
$714$	−12.9048	−0.482949
$715$	4.25998	0.159314
$716$	9.60165	0.358831
$717$	−4.75365	−0.177528
$718$	15.7837	0.589044
$719$	5.12796	0.191241	0.0956203	−	0.995418i	$-0.469517\pi$
$719$	5.12796	0.191241	0.0956203	+	0.995418i	$0.469517\pi$
$720$	1.78906	0.0666743
$721$	−7.84244	−0.292068
$722$	35.3414	1.31527
$723$	−5.50781	−0.204838
$724$	−7.43822	−0.276439
$725$	−5.57201	−0.206939
$726$	11.5056	0.427012
$727$	−8.05373	−0.298696	−0.149348	−	0.988785i	$-0.547717\pi$
$727$	−8.05373	−0.298696	−0.149348	+	0.988785i	$0.547717\pi$
$728$	23.2713	0.862493
$729$	18.1708	0.672994
$730$	−14.3165	−0.529877
$731$	17.2652	0.638578
$732$	11.3385	0.419084
$733$	30.3020	1.11923	0.559614	−	0.828753i	$-0.310949\pi$
$733$	30.3020	1.11923	0.559614	+	0.828753i	$0.310949\pi$
$734$	−18.1412	−0.669604
$735$	10.1765	0.375367
$736$	0	0
$737$	5.32407	0.196115
$738$	3.76107	0.138447
$739$	45.9349	1.68974	0.844871	−	0.534970i	$-0.179677\pi$
$739$	45.9349	1.68974	0.844871	+	0.534970i	$0.179677\pi$
$740$	−6.51538	−0.239510
$741$	−46.8329	−1.72045
$742$	−10.6553	−0.391169
$743$	−20.7623	−0.761695	−0.380848	−	0.924638i	$-0.624368\pi$
$743$	−20.7623	−0.761695	−0.380848	+	0.924638i	$0.624368\pi$
$744$	−1.24814	−0.0457589
$745$	−3.27791	−0.120093
$746$	27.3094	0.999869
$747$	29.3942	1.07548
$748$	−2.14672	−0.0784917
$749$	34.0195	1.24304
$750$	1.10043	0.0401819
$751$	26.0653	0.951137	0.475568	−	0.879679i	$-0.342242\pi$
$751$	26.0653	0.951137	0.475568	+	0.879679i	$0.342242\pi$
$752$	10.3100	0.375966
$753$	6.62808	0.241541
$754$	32.1689	1.17152
$755$	−10.7845	−0.392489
$756$	−21.2427	−0.772588
$757$	18.3885	0.668340	0.334170	−	0.942513i	$-0.391544\pi$
$757$	18.3885	0.668340	0.334170	+	0.942513i	$0.391544\pi$
$758$	−1.95905	−0.0711560
$759$	0	0
$760$	7.37166	0.267398
$761$	6.45686	0.234061	0.117031	−	0.993128i	$-0.462662\pi$
$761$	6.45686	0.234061	0.117031	+	0.993128i	$0.462662\pi$
$762$	−1.34524	−0.0487331
$763$	−28.4728	−1.03078
$764$	−14.7109	−0.532222
$765$	−5.20494	−0.188185
$766$	−0.187725	−0.00678279
$767$	−74.7534	−2.69919
$768$	−1.10043	−0.0397083
$769$	−48.6466	−1.75424	−0.877120	−	0.480271i	$-0.840538\pi$
$769$	−48.6466	−1.75424	−0.877120	+	0.480271i	$0.840538\pi$
$770$	2.97427	0.107185
$771$	25.3681	0.913611
$772$	4.37071	0.157305
$773$	37.4647	1.34751	0.673756	−	0.738954i	$-0.264680\pi$
$773$	37.4647	1.34751	0.673756	+	0.738954i	$0.264680\pi$
$774$	10.6171	0.381624
$775$	1.13423	0.0407427
$776$	9.28624	0.333357
$777$	28.9001	1.03678
$778$	−0.461916	−0.0165605
$779$	15.4972	0.555244
$780$	−6.35310	−0.227477
$781$	−1.34692	−0.0481967
$782$	0	0
$783$	−29.3646	−1.04940
$784$	9.24780	0.330278
$785$	−23.7655	−0.848226
$786$	5.54470	0.197773
$787$	42.3454	1.50945	0.754725	−	0.656042i	$-0.227770\pi$
$787$	42.3454	1.50945	0.754725	+	0.656042i	$0.227770\pi$
$788$	11.4366	0.407412
$789$	−1.26234	−0.0449407
$790$	5.44210	0.193621
$791$	13.0660	0.464574
$792$	−1.32010	−0.0469078
$793$	59.4866	2.11243
$794$	−9.14855	−0.324670
$795$	2.90891	0.103169
$796$	−15.6770	−0.555656
$797$	43.9677	1.55742	0.778708	−	0.627387i	$-0.215875\pi$
$797$	43.9677	1.55742	0.778708	+	0.627387i	$0.215875\pi$
$798$	−32.6982	−1.15751
$799$	−29.9950	−1.06115
$800$	1.00000	0.0353553
$801$	13.8574	0.489626
$802$	25.3201	0.894085
$803$	10.5638	0.372788
$804$	−7.94003	−0.280023
$805$	0	0
$806$	−6.54824	−0.230652
$807$	16.0550	0.565162
$808$	−14.9778	−0.526918
$809$	26.9085	0.946053	0.473027	−	0.881048i	$-0.343161\pi$
$809$	26.9085	0.946053	0.473027	+	0.881048i	$0.343161\pi$
$810$	0.432092	0.0151822
$811$	−48.2761	−1.69520	−0.847602	−	0.530633i	$-0.821954\pi$
$811$	−48.2761	−1.69520	−0.847602	+	0.530633i	$0.821954\pi$
$812$	22.4600	0.788191
$813$	10.1145	0.354732
$814$	4.80754	0.168504
$815$	20.9790	0.734864
$816$	3.20149	0.112075
$817$	43.7468	1.53051
$818$	36.9772	1.29288
$819$	−41.6338	−1.45480
$820$	2.10226	0.0734143
$821$	15.8510	0.553204	0.276602	−	0.960985i	$-0.410792\pi$
$821$	15.8510	0.553204	0.276602	+	0.960985i	$0.410792\pi$
$822$	−5.82507	−0.203173
$823$	−29.7919	−1.03848	−0.519241	−	0.854628i	$-0.673785\pi$
$823$	−29.7919	−1.03848	−0.519241	+	0.854628i	$0.673785\pi$
$824$	1.94560	0.0677783
$825$	−0.811979	−0.0282695
$826$	−52.1920	−1.81599
$827$	10.4602	0.363736	0.181868	−	0.983323i	$-0.441786\pi$
$827$	10.4602	0.363736	0.181868	+	0.983323i	$0.441786\pi$
$828$	0	0
$829$	−21.1020	−0.732902	−0.366451	−	0.930437i	$-0.619427\pi$
$829$	−21.1020	−0.732902	−0.366451	+	0.930437i	$0.619427\pi$
$830$	16.4300	0.570293
$831$	−25.1863	−0.873703
$832$	−5.77330	−0.200153
$833$	−26.9048	−0.932196
$834$	7.74239	0.268097
$835$	−8.75366	−0.302933
$836$	−5.43937	−0.188125
$837$	5.97740	0.206609
$838$	13.3635	0.461635
$839$	2.16678	0.0748055	0.0374027	−	0.999300i	$-0.488092\pi$
$839$	2.16678	0.0748055	0.0374027	+	0.999300i	$0.488092\pi$
$840$	−4.43567	−0.153045
$841$	2.04734	0.0705978
$842$	9.23034	0.318098
$843$	−24.6866	−0.850250
$844$	0.615129	0.0211736
$845$	−20.3310	−0.699406
$846$	−18.4451	−0.634156
$847$	42.1448	1.44811
$848$	2.64344	0.0907761
$849$	−23.9091	−0.820559
$850$	−2.90932	−0.0997888
$851$	0	0
$852$	2.00873	0.0688179
$853$	−23.0006	−0.787526	−0.393763	−	0.919212i	$-0.628827\pi$
$853$	−23.0006	−0.787526	−0.393763	+	0.919212i	$0.628827\pi$
$854$	41.5329	1.42123
$855$	−13.1883	−0.451032
$856$	−8.43976	−0.288465
$857$	18.4299	0.629554	0.314777	−	0.949166i	$-0.398070\pi$
$857$	18.4299	0.629554	0.314777	+	0.949166i	$0.398070\pi$
$858$	4.68780	0.160039
$859$	−37.8972	−1.29303	−0.646517	−	0.762899i	$-0.723775\pi$
$859$	−37.8972	−1.29303	−0.646517	+	0.762899i	$0.723775\pi$
$860$	5.93446	0.202363
$861$	−9.32494	−0.317793
$862$	−23.1846	−0.789669
$863$	−8.78358	−0.298996	−0.149498	−	0.988762i	$-0.547766\pi$
$863$	−8.78358	−0.298996	−0.149498	+	0.988762i	$0.547766\pi$
$864$	5.27001	0.179289
$865$	−9.31210	−0.316621
$866$	−12.9492	−0.440032
$867$	9.39310	0.319007
$868$	−4.57191	−0.155181
$869$	−4.01559	−0.136220
$870$	−6.13160	−0.207881
$871$	−41.6567	−1.41148
$872$	7.06370	0.239207
$873$	−16.6136	−0.562286
$874$	0	0
$875$	4.03086	0.136268
$876$	−15.7543	−0.532287
$877$	38.8448	1.31170	0.655848	−	0.754893i	$-0.272311\pi$
$877$	38.8448	1.31170	0.655848	+	0.754893i	$0.272311\pi$
$878$	3.04386	0.102725
$879$	29.2333	0.986016
$880$	−0.737876	−0.0248738
$881$	38.6626	1.30258	0.651288	−	0.758831i	$-0.274229\pi$
$881$	38.6626	1.30258	0.651288	+	0.758831i	$0.274229\pi$
$882$	−16.5449	−0.557094
$883$	−53.6177	−1.80438	−0.902190	−	0.431340i	$-0.858041\pi$
$883$	−53.6177	−1.80438	−0.902190	+	0.431340i	$0.858041\pi$
$884$	16.7964	0.564923
$885$	14.2485	0.478957
$886$	−7.27680	−0.244469
$887$	−7.28504	−0.244608	−0.122304	−	0.992493i	$-0.539028\pi$
$887$	−7.28504	−0.244608	−0.122304	+	0.992493i	$0.539028\pi$
$888$	−7.16971	−0.240600
$889$	−4.92762	−0.165267
$890$	7.74561	0.259634
$891$	−0.318830	−0.0106812
$892$	13.9032	0.465512
$893$	−76.0016	−2.54330
$894$	−3.60711	−0.120640
$895$	−9.60165	−0.320948
$896$	−4.03086	−0.134661
$897$	0	0
$898$	24.9498	0.832586
$899$	−6.31994	−0.210782
$900$	−1.78906	−0.0596353
$901$	−7.69061	−0.256211
$902$	−1.55121	−0.0516496
$903$	−26.3233	−0.875984
$904$	−3.24150	−0.107811
$905$	7.43822	0.247255
$906$	−11.8676	−0.394275
$907$	−33.3962	−1.10890	−0.554452	−	0.832216i	$-0.687072\pi$
$907$	−33.3962	−1.10890	−0.554452	+	0.832216i	$0.687072\pi$
$908$	−8.00035	−0.265501
$909$	26.7962	0.888774
$910$	−23.2713	−0.771437
$911$	−9.17625	−0.304023	−0.152011	−	0.988379i	$-0.548575\pi$
$911$	−9.17625	−0.304023	−0.152011	+	0.988379i	$0.548575\pi$
$912$	8.11198	0.268615
$913$	−12.1233	−0.401222
$914$	14.0095	0.463391
$915$	−11.3385	−0.374840
$916$	−16.7061	−0.551986
$917$	20.3102	0.670701
$918$	−15.3321	−0.506036
$919$	24.5778	0.810746	0.405373	−	0.914151i	$-0.367142\pi$
$919$	24.5778	0.810746	0.405373	+	0.914151i	$0.367142\pi$
$920$	0	0
$921$	−16.9043	−0.557017
$922$	4.80312	0.158182
$923$	10.5386	0.346883
$924$	3.27297	0.107673
$925$	6.51538	0.214224
$926$	−7.62109	−0.250445
$927$	−3.48080	−0.114324
$928$	−5.57201	−0.182910
$929$	38.4578	1.26176	0.630880	−	0.775880i	$-0.282694\pi$
$929$	38.4578	1.26176	0.630880	+	0.775880i	$0.282694\pi$
$930$	1.24814	0.0409280
$931$	−68.1717	−2.23424
$932$	6.28825	0.205978
$933$	−4.58287	−0.150036
$934$	9.82287	0.321414
$935$	2.14672	0.0702051
$936$	10.3288	0.337606
$937$	53.0345	1.73256	0.866282	−	0.499556i	$-0.166504\pi$
$937$	53.0345	1.73256	0.866282	+	0.499556i	$0.166504\pi$
$938$	−29.0843	−0.949634
$939$	−12.8994	−0.420955
$940$	−10.3100	−0.336274
$941$	−1.49214	−0.0486425	−0.0243213	−	0.999704i	$-0.507742\pi$
$941$	−1.49214	−0.0486425	−0.0243213	+	0.999704i	$0.507742\pi$
$942$	−26.1522	−0.852084
$943$	0	0
$944$	12.9481	0.421426
$945$	21.2427	0.691024
$946$	−4.37889	−0.142370
$947$	−13.8806	−0.451060	−0.225530	−	0.974236i	$-0.572411\pi$
$947$	−13.8806	−0.451060	−0.225530	+	0.974236i	$0.572411\pi$
$948$	5.98863	0.194502
$949$	−82.6534	−2.68304
$950$	−7.37166	−0.239168
$951$	−36.8013	−1.19336
$952$	11.7270	0.380076
$953$	−8.24634	−0.267125	−0.133563	−	0.991040i	$-0.542642\pi$
$953$	−8.24634	−0.267125	−0.133563	+	0.991040i	$0.542642\pi$
$954$	−4.72927	−0.153116
$955$	14.7109	0.476034
$956$	4.31982	0.139713
$957$	4.52436	0.146252
$958$	−35.5465	−1.14846
$959$	−21.3372	−0.689013
$960$	1.10043	0.0355162
$961$	−29.7135	−0.958501
$962$	−37.6152	−1.21276
$963$	15.0992	0.486566
$964$	5.00515	0.161205
$965$	−4.37071	−0.140698
$966$	0	0
$967$	−12.0301	−0.386862	−0.193431	−	0.981114i	$-0.561962\pi$
$967$	−12.0301	−0.386862	−0.193431	+	0.981114i	$0.561962\pi$
$968$	−10.4555	−0.336054
$969$	−23.6003	−0.758152
$970$	−9.28624	−0.298163
$971$	−16.0727	−0.515797	−0.257898	−	0.966172i	$-0.583030\pi$
$971$	−16.0727	−0.515797	−0.257898	+	0.966172i	$0.583030\pi$
$972$	−15.3346	−0.491856
$973$	28.3603	0.909189
$974$	10.0536	0.322139
$975$	6.35310	0.203462
$976$	−10.3037	−0.329815
$977$	33.0252	1.05657	0.528285	−	0.849067i	$-0.322835\pi$
$977$	33.0252	1.05657	0.528285	+	0.849067i	$0.322835\pi$
$978$	23.0859	0.738206
$979$	−5.71530	−0.182662
$980$	−9.24780	−0.295410
$981$	−12.6374	−0.403480
$982$	27.7805	0.886512
$983$	32.3802	1.03277	0.516384	−	0.856357i	$-0.327278\pi$
$983$	32.3802	1.03277	0.516384	+	0.856357i	$0.327278\pi$
$984$	2.31339	0.0737482
$985$	−11.4366	−0.364400
$986$	16.2108	0.516256
$987$	45.7315	1.45565
$988$	42.5588	1.35398
$989$	0	0
$990$	1.32010	0.0419556
$991$	47.7157	1.51574	0.757869	−	0.652407i	$-0.226241\pi$
$991$	47.7157	1.51574	0.757869	+	0.652407i	$0.226241\pi$
$992$	1.13423	0.0360118
$993$	16.7690	0.532149
$994$	7.35795	0.233380
$995$	15.6770	0.496994
$996$	18.0800	0.572887
$997$	−18.3474	−0.581069	−0.290534	−	0.956865i	$-0.593833\pi$
$997$	−18.3474	−0.581069	−0.290534	+	0.956865i	$0.593833\pi$
$998$	4.98775	0.157884
$999$	34.3362	1.08635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.5		15
23.4	even	11		230.2.g.d.131.1	✓	30
23.6	even	11		230.2.g.d.151.1	yes	30
23.22	odd	2		5290.2.a.bl.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.131.1	✓	30	23.4	even	11
230.2.g.d.151.1	yes	30	23.6	even	11
5290.2.a.bk.1.5		15	1.1	even	1	trivial
5290.2.a.bl.1.5		15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.10043 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.10043 q^{6} -4.03086 q^{7} +1.00000 q^{8} -1.78906 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.10043 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.10043 q^{6} -4.03086 q^{7} +1.00000 q^{8} -1.78906 q^{9} -1.00000 q^{10} +0.737876 q^{11} -1.10043 q^{12} -5.77330 q^{13} -4.03086 q^{14} +1.10043 q^{15} +1.00000 q^{16} -2.90932 q^{17} -1.78906 q^{18} -7.37166 q^{19} -1.00000 q^{20} +4.43567 q^{21} +0.737876 q^{22} -1.10043 q^{24} +1.00000 q^{25} -5.77330 q^{26} +5.27001 q^{27} -4.03086 q^{28} -5.57201 q^{29} +1.10043 q^{30} +1.13423 q^{31} +1.00000 q^{32} -0.811979 q^{33} -2.90932 q^{34} +4.03086 q^{35} -1.78906 q^{36} +6.51538 q^{37} -7.37166 q^{38} +6.35310 q^{39} -1.00000 q^{40} -2.10226 q^{41} +4.43567 q^{42} -5.93446 q^{43} +0.737876 q^{44} +1.78906 q^{45} +10.3100 q^{47} -1.10043 q^{48} +9.24780 q^{49} +1.00000 q^{50} +3.20149 q^{51} -5.77330 q^{52} +2.64344 q^{53} +5.27001 q^{54} -0.737876 q^{55} -4.03086 q^{56} +8.11198 q^{57} -5.57201 q^{58} +12.9481 q^{59} +1.10043 q^{60} -10.3037 q^{61} +1.13423 q^{62} +7.21144 q^{63} +1.00000 q^{64} +5.77330 q^{65} -0.811979 q^{66} +7.21540 q^{67} -2.90932 q^{68} +4.03086 q^{70} -1.82541 q^{71} -1.78906 q^{72} +14.3165 q^{73} +6.51538 q^{74} -1.10043 q^{75} -7.37166 q^{76} -2.97427 q^{77} +6.35310 q^{78} -5.44210 q^{79} -1.00000 q^{80} -0.432092 q^{81} -2.10226 q^{82} -16.4300 q^{83} +4.43567 q^{84} +2.90932 q^{85} -5.93446 q^{86} +6.13160 q^{87} +0.737876 q^{88} -7.74561 q^{89} +1.78906 q^{90} +23.2713 q^{91} -1.24814 q^{93} +10.3100 q^{94} +7.37166 q^{95} -1.10043 q^{96} +9.28624 q^{97} +9.24780 q^{98} -1.32010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * q^99

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