LMFDB - Embedded newform 5290.2.a.bk.1.14

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			1.14
Root			$3.15164$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.15164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.15164 q^{6} -0.586101 q^{7} +1.00000 q^{8} +6.93286 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.15164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.15164 q^{6} -0.586101 q^{7} +1.00000 q^{8} +6.93286 q^{9} -1.00000 q^{10} +1.70208 q^{11} +3.15164 q^{12} +6.24681 q^{13} -0.586101 q^{14} -3.15164 q^{15} +1.00000 q^{16} +2.23343 q^{17} +6.93286 q^{18} -1.53474 q^{19} -1.00000 q^{20} -1.84718 q^{21} +1.70208 q^{22} +3.15164 q^{24} +1.00000 q^{25} +6.24681 q^{26} +12.3950 q^{27} -0.586101 q^{28} -0.273904 q^{29} -3.15164 q^{30} -8.90264 q^{31} +1.00000 q^{32} +5.36436 q^{33} +2.23343 q^{34} +0.586101 q^{35} +6.93286 q^{36} -8.46576 q^{37} -1.53474 q^{38} +19.6877 q^{39} -1.00000 q^{40} -3.08937 q^{41} -1.84718 q^{42} +7.42460 q^{43} +1.70208 q^{44} -6.93286 q^{45} -5.72656 q^{47} +3.15164 q^{48} -6.65649 q^{49} +1.00000 q^{50} +7.03896 q^{51} +6.24681 q^{52} +10.2861 q^{53} +12.3950 q^{54} -1.70208 q^{55} -0.586101 q^{56} -4.83696 q^{57} -0.273904 q^{58} -6.50953 q^{59} -3.15164 q^{60} +11.7092 q^{61} -8.90264 q^{62} -4.06336 q^{63} +1.00000 q^{64} -6.24681 q^{65} +5.36436 q^{66} -13.1665 q^{67} +2.23343 q^{68} +0.586101 q^{70} +7.94527 q^{71} +6.93286 q^{72} +1.43479 q^{73} -8.46576 q^{74} +3.15164 q^{75} -1.53474 q^{76} -0.997594 q^{77} +19.6877 q^{78} +11.8322 q^{79} -1.00000 q^{80} +18.2660 q^{81} -3.08937 q^{82} +4.34511 q^{83} -1.84718 q^{84} -2.23343 q^{85} +7.42460 q^{86} -0.863248 q^{87} +1.70208 q^{88} -10.7471 q^{89} -6.93286 q^{90} -3.66127 q^{91} -28.0580 q^{93} -5.72656 q^{94} +1.53474 q^{95} +3.15164 q^{96} +3.88552 q^{97} -6.65649 q^{98} +11.8003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.15164	1.81960	0.909801	−	0.415044i	$-0.136234\pi$
$3$	3.15164	1.81960	0.909801	+	0.415044i	$0.136234\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.15164	1.28665
$7$	−0.586101	−0.221526	−0.110763	−	0.993847i	$-0.535329\pi$
$7$	−0.586101	−0.221526	−0.110763	+	0.993847i	$0.535329\pi$
$8$	1.00000	0.353553
$9$	6.93286	2.31095
$10$	−1.00000	−0.316228
$11$	1.70208	0.513198	0.256599	−	0.966518i	$-0.417398\pi$
$11$	1.70208	0.513198	0.256599	+	0.966518i	$0.417398\pi$
$12$	3.15164	0.909801
$13$	6.24681	1.73255	0.866277	−	0.499564i	$-0.166507\pi$
$13$	6.24681	1.73255	0.866277	+	0.499564i	$0.166507\pi$
$14$	−0.586101	−0.156642
$15$	−3.15164	−0.813751
$16$	1.00000	0.250000
$17$	2.23343	0.541685	0.270843	−	0.962624i	$-0.412698\pi$
$17$	2.23343	0.541685	0.270843	+	0.962624i	$0.412698\pi$
$18$	6.93286	1.63409
$19$	−1.53474	−0.352094	−0.176047	−	0.984382i	$-0.556331\pi$
$19$	−1.53474	−0.352094	−0.176047	+	0.984382i	$0.556331\pi$
$20$	−1.00000	−0.223607
$21$	−1.84718	−0.403088
$22$	1.70208	0.362885
$23$	0	0
$23$	0	0
$24$	3.15164	0.643327
$25$	1.00000	0.200000
$26$	6.24681	1.22510
$27$	12.3950	2.38541
$28$	−0.586101	−0.110763
$29$	−0.273904	−0.0508627	−0.0254313	−	0.999677i	$-0.508096\pi$
$29$	−0.273904	−0.0508627	−0.0254313	+	0.999677i	$0.508096\pi$
$30$	−3.15164	−0.575409
$31$	−8.90264	−1.59896	−0.799481	−	0.600691i	$-0.794892\pi$
$31$	−8.90264	−1.59896	−0.799481	+	0.600691i	$0.794892\pi$
$32$	1.00000	0.176777
$33$	5.36436	0.933815
$34$	2.23343	0.383029
$35$	0.586101	0.0990692
$36$	6.93286	1.15548
$37$	−8.46576	−1.39176	−0.695881	−	0.718157i	$-0.744986\pi$
$37$	−8.46576	−1.39176	−0.695881	+	0.718157i	$0.744986\pi$
$38$	−1.53474	−0.248968
$39$	19.6877	3.15256
$40$	−1.00000	−0.158114
$41$	−3.08937	−0.482478	−0.241239	−	0.970466i	$-0.577554\pi$
$41$	−3.08937	−0.482478	−0.241239	+	0.970466i	$0.577554\pi$
$42$	−1.84718	−0.285027
$43$	7.42460	1.13224	0.566120	−	0.824323i	$-0.308444\pi$
$43$	7.42460	1.13224	0.566120	+	0.824323i	$0.308444\pi$
$44$	1.70208	0.256599
$45$	−6.93286	−1.03349
$46$	0	0
$47$	−5.72656	−0.835304	−0.417652	−	0.908607i	$-0.637147\pi$
$47$	−5.72656	−0.835304	−0.417652	+	0.908607i	$0.637147\pi$
$48$	3.15164	0.454901
$49$	−6.65649	−0.950926
$50$	1.00000	0.141421
$51$	7.03896	0.985652
$52$	6.24681	0.866277
$53$	10.2861	1.41291	0.706455	−	0.707758i	$-0.250293\pi$
$53$	10.2861	1.41291	0.706455	+	0.707758i	$0.250293\pi$
$54$	12.3950	1.68674
$55$	−1.70208	−0.229509
$56$	−0.586101	−0.0783211
$57$	−4.83696	−0.640671
$58$	−0.273904	−0.0359654
$59$	−6.50953	−0.847469	−0.423734	−	0.905787i	$-0.639281\pi$
$59$	−6.50953	−0.847469	−0.423734	+	0.905787i	$0.639281\pi$
$60$	−3.15164	−0.406875
$61$	11.7092	1.49921	0.749606	−	0.661884i	$-0.230243\pi$
$61$	11.7092	1.49921	0.749606	+	0.661884i	$0.230243\pi$
$62$	−8.90264	−1.13064
$63$	−4.06336	−0.511935
$64$	1.00000	0.125000
$65$	−6.24681	−0.774822
$66$	5.36436	0.660307
$67$	−13.1665	−1.60854	−0.804271	−	0.594262i	$-0.797444\pi$
$67$	−13.1665	−1.60854	−0.804271	+	0.594262i	$0.797444\pi$
$68$	2.23343	0.270843
$69$	0	0
$70$	0.586101	0.0700525
$71$	7.94527	0.942930	0.471465	−	0.881885i	$-0.343725\pi$
$71$	7.94527	0.942930	0.471465	+	0.881885i	$0.343725\pi$
$72$	6.93286	0.817045
$73$	1.43479	0.167929	0.0839647	−	0.996469i	$-0.473242\pi$
$73$	1.43479	0.167929	0.0839647	+	0.996469i	$0.473242\pi$
$74$	−8.46576	−0.984125
$75$	3.15164	0.363920
$76$	−1.53474	−0.176047
$77$	−0.997594	−0.113686
$78$	19.6877	2.22920
$79$	11.8322	1.33123	0.665615	−	0.746295i	$-0.268169\pi$
$79$	11.8322	1.33123	0.665615	+	0.746295i	$0.268169\pi$
$80$	−1.00000	−0.111803
$81$	18.2660	2.02955
$82$	−3.08937	−0.341163
$83$	4.34511	0.476938	0.238469	−	0.971150i	$-0.423354\pi$
$83$	4.34511	0.476938	0.238469	+	0.971150i	$0.423354\pi$
$84$	−1.84718	−0.201544
$85$	−2.23343	−0.242249
$86$	7.42460	0.800615
$87$	−0.863248	−0.0925499
$88$	1.70208	0.181443
$89$	−10.7471	−1.13919	−0.569594	−	0.821926i	$-0.692900\pi$
$89$	−10.7471	−1.13919	−0.569594	+	0.821926i	$0.692900\pi$
$90$	−6.93286	−0.730787
$91$	−3.66127	−0.383805
$92$	0	0
$93$	−28.0580	−2.90948
$94$	−5.72656	−0.590649
$95$	1.53474	0.157461
$96$	3.15164	0.321663
$97$	3.88552	0.394515	0.197258	−	0.980352i	$-0.436796\pi$
$97$	3.88552	0.394515	0.197258	+	0.980352i	$0.436796\pi$
$98$	−6.65649	−0.672407
$99$	11.8003	1.18598
$100$	1.00000	0.100000
$101$	17.2834	1.71976	0.859882	−	0.510493i	$-0.170537\pi$
$101$	17.2834	1.71976	0.859882	+	0.510493i	$0.170537\pi$
$102$	7.03896	0.696961
$103$	−1.54651	−0.152382	−0.0761910	−	0.997093i	$-0.524276\pi$
$103$	−1.54651	−0.152382	−0.0761910	+	0.997093i	$0.524276\pi$
$104$	6.24681	0.612550
$105$	1.84718	0.180267
$106$	10.2861	0.999078
$107$	−4.19431	−0.405479	−0.202740	−	0.979233i	$-0.564985\pi$
$107$	−4.19431	−0.405479	−0.202740	+	0.979233i	$0.564985\pi$
$108$	12.3950	1.19271
$109$	20.1253	1.92766	0.963829	−	0.266521i	$-0.0858742\pi$
$109$	20.1253	1.92766	0.963829	+	0.266521i	$0.0858742\pi$
$110$	−1.70208	−0.162287
$111$	−26.6811	−2.53245
$112$	−0.586101	−0.0553814
$113$	−20.1906	−1.89937	−0.949686	−	0.313203i	$-0.898598\pi$
$113$	−20.1906	−1.89937	−0.949686	+	0.313203i	$0.898598\pi$
$114$	−4.83696	−0.453023
$115$	0	0
$116$	−0.273904	−0.0254313
$117$	43.3083	4.00385
$118$	−6.50953	−0.599251
$119$	−1.30901	−0.119997
$120$	−3.15164	−0.287704
$121$	−8.10291	−0.736628
$122$	11.7092	1.06010
$123$	−9.73658	−0.877918
$124$	−8.90264	−0.799481
$125$	−1.00000	−0.0894427
$126$	−4.06336	−0.361993
$127$	3.09642	0.274763	0.137381	−	0.990518i	$-0.456131\pi$
$127$	3.09642	0.274763	0.137381	+	0.990518i	$0.456131\pi$
$128$	1.00000	0.0883883
$129$	23.3997	2.06023
$130$	−6.24681	−0.547882
$131$	−2.81139	−0.245632	−0.122816	−	0.992429i	$-0.539193\pi$
$131$	−2.81139	−0.245632	−0.122816	+	0.992429i	$0.539193\pi$
$132$	5.36436	0.466908
$133$	0.899515	0.0779979
$134$	−13.1665	−1.13741
$135$	−12.3950	−1.06679
$136$	2.23343	0.191515
$137$	−11.7641	−1.00508	−0.502539	−	0.864555i	$-0.667601\pi$
$137$	−11.7641	−1.00508	−0.502539	+	0.864555i	$0.667601\pi$
$138$	0	0
$139$	−16.1372	−1.36874	−0.684368	−	0.729137i	$-0.739922\pi$
$139$	−16.1372	−1.36874	−0.684368	+	0.729137i	$0.739922\pi$
$140$	0.586101	0.0495346
$141$	−18.0481	−1.51992
$142$	7.94527	0.666752
$143$	10.6326	0.889142
$144$	6.93286	0.577738
$145$	0.273904	0.0227465
$146$	1.43479	0.118744
$147$	−20.9789	−1.73031
$148$	−8.46576	−0.695881
$149$	−4.77884	−0.391498	−0.195749	−	0.980654i	$-0.562714\pi$
$149$	−4.77884	−0.391498	−0.195749	+	0.980654i	$0.562714\pi$
$150$	3.15164	0.257331
$151$	5.45532	0.443948	0.221974	−	0.975053i	$-0.428750\pi$
$151$	5.45532	0.443948	0.221974	+	0.975053i	$0.428750\pi$
$152$	−1.53474	−0.124484
$153$	15.4840	1.25181
$154$	−0.997594	−0.0803884
$155$	8.90264	0.715078
$156$	19.6877	1.57628
$157$	−5.44221	−0.434336	−0.217168	−	0.976134i	$-0.569682\pi$
$157$	−5.44221	−0.434336	−0.217168	+	0.976134i	$0.569682\pi$
$158$	11.8322	0.941322
$159$	32.4182	2.57093
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	18.2660	1.43511
$163$	−3.21035	−0.251454	−0.125727	−	0.992065i	$-0.540126\pi$
$163$	−3.21035	−0.251454	−0.125727	+	0.992065i	$0.540126\pi$
$164$	−3.08937	−0.241239
$165$	−5.36436	−0.417615
$166$	4.34511	0.337246
$167$	−8.55460	−0.661974	−0.330987	−	0.943635i	$-0.607382\pi$
$167$	−8.55460	−0.661974	−0.330987	+	0.943635i	$0.607382\pi$
$168$	−1.84718	−0.142513
$169$	26.0227	2.00174
$170$	−2.23343	−0.171296
$171$	−10.6402	−0.813673
$172$	7.42460	0.566120
$173$	16.0483	1.22013	0.610065	−	0.792351i	$-0.291143\pi$
$173$	16.0483	1.22013	0.610065	+	0.792351i	$0.291143\pi$
$174$	−0.863248	−0.0654426
$175$	−0.586101	−0.0443051
$176$	1.70208	0.128299
$177$	−20.5157	−1.54206
$178$	−10.7471	−0.805528
$179$	−0.883737	−0.0660536	−0.0330268	−	0.999454i	$-0.510515\pi$
$179$	−0.883737	−0.0660536	−0.0330268	+	0.999454i	$0.510515\pi$
$180$	−6.93286	−0.516745
$181$	5.84106	0.434162	0.217081	−	0.976154i	$-0.430346\pi$
$181$	5.84106	0.434162	0.217081	+	0.976154i	$0.430346\pi$
$182$	−3.66127	−0.271391
$183$	36.9033	2.72797
$184$	0	0
$185$	8.46576	0.622415
$186$	−28.0580	−2.05731
$187$	3.80148	0.277992
$188$	−5.72656	−0.417652
$189$	−7.26471	−0.528430
$190$	1.53474	0.111342
$191$	−13.0027	−0.940839	−0.470420	−	0.882443i	$-0.655897\pi$
$191$	−13.0027	−0.940839	−0.470420	+	0.882443i	$0.655897\pi$
$192$	3.15164	0.227450
$193$	−2.25851	−0.162571	−0.0812855	−	0.996691i	$-0.525903\pi$
$193$	−2.25851	−0.162571	−0.0812855	+	0.996691i	$0.525903\pi$
$194$	3.88552	0.278964
$195$	−19.6877	−1.40987
$196$	−6.65649	−0.475463
$197$	5.95055	0.423959	0.211980	−	0.977274i	$-0.432009\pi$
$197$	5.95055	0.423959	0.211980	+	0.977274i	$0.432009\pi$
$198$	11.8003	0.838611
$199$	−20.6146	−1.46133	−0.730664	−	0.682737i	$-0.760789\pi$
$199$	−20.6146	−1.46133	−0.730664	+	0.682737i	$0.760789\pi$
$200$	1.00000	0.0707107
$201$	−41.4961	−2.92691
$202$	17.2834	1.21606
$203$	0.160535	0.0112674
$204$	7.03896	0.492826
$205$	3.08937	0.215771
$206$	−1.54651	−0.107750
$207$	0	0
$208$	6.24681	0.433138
$209$	−2.61226	−0.180694
$210$	1.84718	0.127468
$211$	0.303311	0.0208808	0.0104404	−	0.999945i	$-0.496677\pi$
$211$	0.303311	0.0208808	0.0104404	+	0.999945i	$0.496677\pi$
$212$	10.2861	0.706455
$213$	25.0407	1.71576
$214$	−4.19431	−0.286717
$215$	−7.42460	−0.506353
$216$	12.3950	0.843371
$217$	5.21785	0.354211
$218$	20.1253	1.36306
$219$	4.52195	0.305565
$220$	−1.70208	−0.114754
$221$	13.9518	0.938499
$222$	−26.6811	−1.79072
$223$	−13.0872	−0.876381	−0.438190	−	0.898882i	$-0.644380\pi$
$223$	−13.0872	−0.876381	−0.438190	+	0.898882i	$0.644380\pi$
$224$	−0.586101	−0.0391605
$225$	6.93286	0.462191
$226$	−20.1906	−1.34306
$227$	−21.5293	−1.42895	−0.714475	−	0.699661i	$-0.753335\pi$
$227$	−21.5293	−1.42895	−0.714475	+	0.699661i	$0.753335\pi$
$228$	−4.83696	−0.320336
$229$	11.6468	0.769640	0.384820	−	0.922992i	$-0.374263\pi$
$229$	11.6468	0.769640	0.384820	+	0.922992i	$0.374263\pi$
$230$	0	0
$231$	−3.14406	−0.206864
$232$	−0.273904	−0.0179827
$233$	14.9008	0.976185	0.488092	−	0.872792i	$-0.337693\pi$
$233$	14.9008	0.976185	0.488092	+	0.872792i	$0.337693\pi$
$234$	43.3083	2.83115
$235$	5.72656	0.373559
$236$	−6.50953	−0.423734
$237$	37.2910	2.42231
$238$	−1.30901	−0.0848508
$239$	14.0873	0.911234	0.455617	−	0.890176i	$-0.349419\pi$
$239$	14.0873	0.911234	0.455617	+	0.890176i	$0.349419\pi$
$240$	−3.15164	−0.203438
$241$	0.805703	0.0518999	0.0259499	−	0.999663i	$-0.491739\pi$
$241$	0.805703	0.0518999	0.0259499	+	0.999663i	$0.491739\pi$
$242$	−8.10291	−0.520875
$243$	20.3829	1.30756
$244$	11.7092	0.749606
$245$	6.65649	0.425267
$246$	−9.73658	−0.620782
$247$	−9.58725	−0.610022
$248$	−8.90264	−0.565318
$249$	13.6942	0.867838
$250$	−1.00000	−0.0632456
$251$	18.1838	1.14775	0.573876	−	0.818942i	$-0.305439\pi$
$251$	18.1838	1.14775	0.573876	+	0.818942i	$0.305439\pi$
$252$	−4.06336	−0.255968
$253$	0	0
$254$	3.09642	0.194287
$255$	−7.03896	−0.440797
$256$	1.00000	0.0625000
$257$	−16.0600	−1.00180	−0.500898	−	0.865506i	$-0.666997\pi$
$257$	−16.0600	−1.00180	−0.500898	+	0.865506i	$0.666997\pi$
$258$	23.3997	1.45680
$259$	4.96180	0.308311
$260$	−6.24681	−0.387411
$261$	−1.89894	−0.117541
$262$	−2.81139	−0.173688
$263$	7.97560	0.491797	0.245898	−	0.969296i	$-0.420917\pi$
$263$	7.97560	0.491797	0.245898	+	0.969296i	$0.420917\pi$
$264$	5.36436	0.330154
$265$	−10.2861	−0.631872
$266$	0.899515	0.0551528
$267$	−33.8710	−2.07287
$268$	−13.1665	−0.804271
$269$	18.0501	1.10054	0.550268	−	0.834988i	$-0.314526\pi$
$269$	18.0501	1.10054	0.550268	+	0.834988i	$0.314526\pi$
$270$	−12.3950	−0.754334
$271$	−22.8448	−1.38772	−0.693861	−	0.720109i	$-0.744092\pi$
$271$	−22.8448	−1.38772	−0.693861	+	0.720109i	$0.744092\pi$
$272$	2.23343	0.135421
$273$	−11.5390	−0.698372
$274$	−11.7641	−0.710697
$275$	1.70208	0.102640
$276$	0	0
$277$	20.9373	1.25800	0.629000	−	0.777405i	$-0.283465\pi$
$277$	20.9373	1.25800	0.629000	+	0.777405i	$0.283465\pi$
$278$	−16.1372	−0.967842
$279$	−61.7208	−3.69513
$280$	0.586101	0.0350263
$281$	2.88646	0.172192	0.0860960	−	0.996287i	$-0.472561\pi$
$281$	2.88646	0.172192	0.0860960	+	0.996287i	$0.472561\pi$
$282$	−18.0481	−1.07475
$283$	−2.86080	−0.170057	−0.0850285	−	0.996379i	$-0.527098\pi$
$283$	−2.86080	−0.170057	−0.0850285	+	0.996379i	$0.527098\pi$
$284$	7.94527	0.471465
$285$	4.83696	0.286517
$286$	10.6326	0.628719
$287$	1.81068	0.106881
$288$	6.93286	0.408523
$289$	−12.0118	−0.706577
$290$	0.273904	0.0160842
$291$	12.2458	0.717861
$292$	1.43479	0.0839647
$293$	2.79775	0.163446	0.0817232	−	0.996655i	$-0.473958\pi$
$293$	2.79775	0.163446	0.0817232	+	0.996655i	$0.473958\pi$
$294$	−20.9789	−1.22351
$295$	6.50953	0.378999
$296$	−8.46576	−0.492062
$297$	21.0973	1.22419
$298$	−4.77884	−0.276831
$299$	0	0
$300$	3.15164	0.181960
$301$	−4.35157	−0.250820
$302$	5.45532	0.313918
$303$	54.4712	3.12929
$304$	−1.53474	−0.0880236
$305$	−11.7092	−0.670468
$306$	15.4840	0.885163
$307$	−28.5926	−1.63187	−0.815933	−	0.578147i	$-0.803776\pi$
$307$	−28.5926	−1.63187	−0.815933	+	0.578147i	$0.803776\pi$
$308$	−0.997594	−0.0568432
$309$	−4.87405	−0.277275
$310$	8.90264	0.505636
$311$	−17.2586	−0.978645	−0.489323	−	0.872103i	$-0.662756\pi$
$311$	−17.2586	−0.978645	−0.489323	+	0.872103i	$0.662756\pi$
$312$	19.6877	1.11460
$313$	30.4579	1.72158	0.860791	−	0.508959i	$-0.169970\pi$
$313$	30.4579	1.72158	0.860791	+	0.508959i	$0.169970\pi$
$314$	−5.44221	−0.307122
$315$	4.06336	0.228944
$316$	11.8322	0.665615
$317$	8.82463	0.495641	0.247820	−	0.968806i	$-0.420286\pi$
$317$	8.82463	0.495641	0.247820	+	0.968806i	$0.420286\pi$
$318$	32.4182	1.81792
$319$	−0.466207	−0.0261026
$320$	−1.00000	−0.0559017
$321$	−13.2190	−0.737811
$322$	0	0
$323$	−3.42774	−0.190724
$324$	18.2660	1.01478
$325$	6.24681	0.346511
$326$	−3.21035	−0.177805
$327$	63.4279	3.50757
$328$	−3.08937	−0.170582
$329$	3.35634	0.185041
$330$	−5.36436	−0.295298
$331$	5.93397	0.326160	0.163080	−	0.986613i	$-0.447857\pi$
$331$	5.93397	0.326160	0.163080	+	0.986613i	$0.447857\pi$
$332$	4.34511	0.238469
$333$	−58.6919	−3.21630
$334$	−8.55460	−0.468087
$335$	13.1665	0.719362
$336$	−1.84718	−0.100772
$337$	−25.8103	−1.40598	−0.702989	−	0.711201i	$-0.748151\pi$
$337$	−25.8103	−1.40598	−0.702989	+	0.711201i	$0.748151\pi$
$338$	26.0227	1.41545
$339$	−63.6336	−3.45610
$340$	−2.23343	−0.121125
$341$	−15.1530	−0.820583
$342$	−10.6402	−0.575354
$343$	8.00409	0.432180
$344$	7.42460	0.400307
$345$	0	0
$346$	16.0483	0.862762
$347$	27.4313	1.47259	0.736295	−	0.676660i	$-0.236573\pi$
$347$	27.4313	1.47259	0.736295	+	0.676660i	$0.236573\pi$
$348$	−0.863248	−0.0462749
$349$	3.55776	0.190442	0.0952212	−	0.995456i	$-0.469644\pi$
$349$	3.55776	0.190442	0.0952212	+	0.995456i	$0.469644\pi$
$350$	−0.586101	−0.0313284
$351$	77.4290	4.13286
$352$	1.70208	0.0907214
$353$	13.4092	0.713700	0.356850	−	0.934162i	$-0.383851\pi$
$353$	13.4092	0.713700	0.356850	+	0.934162i	$0.383851\pi$
$354$	−20.5157	−1.09040
$355$	−7.94527	−0.421691
$356$	−10.7471	−0.569594
$357$	−4.12555	−0.218347
$358$	−0.883737	−0.0467069
$359$	2.51760	0.132874	0.0664369	−	0.997791i	$-0.478837\pi$
$359$	2.51760	0.132874	0.0664369	+	0.997791i	$0.478837\pi$
$360$	−6.93286	−0.365394
$361$	−16.6446	−0.876030
$362$	5.84106	0.306999
$363$	−25.5375	−1.34037
$364$	−3.66127	−0.191902
$365$	−1.43479	−0.0751003
$366$	36.9033	1.92897
$367$	30.4898	1.59155	0.795777	−	0.605590i	$-0.207063\pi$
$367$	30.4898	1.59155	0.795777	+	0.605590i	$0.207063\pi$
$368$	0	0
$369$	−21.4181	−1.11498
$370$	8.46576	0.440114
$371$	−6.02872	−0.312995
$372$	−28.0580	−1.45474
$373$	−28.3933	−1.47015	−0.735074	−	0.677987i	$-0.762852\pi$
$373$	−28.3933	−1.47015	−0.735074	+	0.677987i	$0.762852\pi$
$374$	3.80148	0.196570
$375$	−3.15164	−0.162750
$376$	−5.72656	−0.295325
$377$	−1.71103	−0.0881223
$378$	−7.26471	−0.373656
$379$	18.5845	0.954623	0.477312	−	0.878734i	$-0.341611\pi$
$379$	18.5845	0.954623	0.477312	+	0.878734i	$0.341611\pi$
$380$	1.53474	0.0787307
$381$	9.75881	0.499959
$382$	−13.0027	−0.665274
$383$	−8.49534	−0.434092	−0.217046	−	0.976161i	$-0.569642\pi$
$383$	−8.49534	−0.434092	−0.217046	+	0.976161i	$0.569642\pi$
$384$	3.15164	0.160832
$385$	0.997594	0.0508421
$386$	−2.25851	−0.114955
$387$	51.4737	2.61655
$388$	3.88552	0.197258
$389$	−5.92367	−0.300342	−0.150171	−	0.988660i	$-0.547982\pi$
$389$	−5.92367	−0.300342	−0.150171	+	0.988660i	$0.547982\pi$
$390$	−19.6877	−0.996927
$391$	0	0
$392$	−6.65649	−0.336203
$393$	−8.86050	−0.446953
$394$	5.95055	0.299785
$395$	−11.8322	−0.595345
$396$	11.8003	0.592988
$397$	−11.3130	−0.567781	−0.283890	−	0.958857i	$-0.591625\pi$
$397$	−11.3130	−0.567781	−0.283890	+	0.958857i	$0.591625\pi$
$398$	−20.6146	−1.03332
$399$	2.83495	0.141925
$400$	1.00000	0.0500000
$401$	2.22352	0.111037	0.0555187	−	0.998458i	$-0.482319\pi$
$401$	2.22352	0.111037	0.0555187	+	0.998458i	$0.482319\pi$
$402$	−41.4961	−2.06964
$403$	−55.6131	−2.77029
$404$	17.2834	0.859882
$405$	−18.2660	−0.907643
$406$	0.160535	0.00796724
$407$	−14.4094	−0.714249
$408$	7.03896	0.348481
$409$	−17.6432	−0.872398	−0.436199	−	0.899850i	$-0.643676\pi$
$409$	−17.6432	−0.872398	−0.436199	+	0.899850i	$0.643676\pi$
$410$	3.08937	0.152573
$411$	−37.0763	−1.82884
$412$	−1.54651	−0.0761910
$413$	3.81524	0.187736
$414$	0	0
$415$	−4.34511	−0.213293
$416$	6.24681	0.306275
$417$	−50.8586	−2.49055
$418$	−2.61226	−0.127770
$419$	0.825594	0.0403329	0.0201664	−	0.999797i	$-0.493580\pi$
$419$	0.825594	0.0403329	0.0201664	+	0.999797i	$0.493580\pi$
$420$	1.84718	0.0901333
$421$	−18.0318	−0.878816	−0.439408	−	0.898288i	$-0.644812\pi$
$421$	−18.0318	−0.878816	−0.439408	+	0.898288i	$0.644812\pi$
$422$	0.303311	0.0147649
$423$	−39.7014	−1.93035
$424$	10.2861	0.499539
$425$	2.23343	0.108337
$426$	25.0407	1.21322
$427$	−6.86279	−0.332114
$428$	−4.19431	−0.202740
$429$	33.5102	1.61789
$430$	−7.42460	−0.358046
$431$	−6.40236	−0.308391	−0.154196	−	0.988040i	$-0.549279\pi$
$431$	−6.40236	−0.308391	−0.154196	+	0.988040i	$0.549279\pi$
$432$	12.3950	0.596353
$433$	−19.8963	−0.956154	−0.478077	−	0.878318i	$-0.658666\pi$
$433$	−19.8963	−0.956154	−0.478077	+	0.878318i	$0.658666\pi$
$434$	5.21785	0.250465
$435$	0.863248	0.0413896
$436$	20.1253	0.963829
$437$	0	0
$438$	4.52195	0.216067
$439$	−21.8528	−1.04298	−0.521489	−	0.853258i	$-0.674623\pi$
$439$	−21.8528	−1.04298	−0.521489	+	0.853258i	$0.674623\pi$
$440$	−1.70208	−0.0811437
$441$	−46.1485	−2.19755
$442$	13.9518	0.663619
$443$	8.85999	0.420951	0.210475	−	0.977599i	$-0.432499\pi$
$443$	8.85999	0.420951	0.210475	+	0.977599i	$0.432499\pi$
$444$	−26.6811	−1.26623
$445$	10.7471	0.509460
$446$	−13.0872	−0.619695
$447$	−15.0612	−0.712371
$448$	−0.586101	−0.0276907
$449$	−8.85606	−0.417943	−0.208972	−	0.977922i	$-0.567012\pi$
$449$	−8.85606	−0.417943	−0.208972	+	0.977922i	$0.567012\pi$
$450$	6.93286	0.326818
$451$	−5.25836	−0.247607
$452$	−20.1906	−0.949686
$453$	17.1932	0.807808
$454$	−21.5293	−1.01042
$455$	3.66127	0.171643
$456$	−4.83696	−0.226512
$457$	8.97376	0.419775	0.209887	−	0.977726i	$-0.432690\pi$
$457$	8.97376	0.419775	0.209887	+	0.977726i	$0.432690\pi$
$458$	11.6468	0.544218
$459$	27.6832	1.29214
$460$	0	0
$461$	−17.5927	−0.819374	−0.409687	−	0.912226i	$-0.634362\pi$
$461$	−17.5927	−0.819374	−0.409687	+	0.912226i	$0.634362\pi$
$462$	−3.14406	−0.146275
$463$	−33.6039	−1.56171	−0.780854	−	0.624714i	$-0.785216\pi$
$463$	−33.6039	−1.56171	−0.780854	+	0.624714i	$0.785216\pi$
$464$	−0.273904	−0.0127157
$465$	28.0580	1.30116
$466$	14.9008	0.690267
$467$	−4.05576	−0.187678	−0.0938390	−	0.995587i	$-0.529914\pi$
$467$	−4.05576	−0.187678	−0.0938390	+	0.995587i	$0.529914\pi$
$468$	43.3083	2.00193
$469$	7.71690	0.356333
$470$	5.72656	0.264146
$471$	−17.1519	−0.790318
$472$	−6.50953	−0.299625
$473$	12.6373	0.581063
$474$	37.2910	1.71283
$475$	−1.53474	−0.0704188
$476$	−1.30901	−0.0599986
$477$	71.3123	3.26517
$478$	14.0873	0.644340
$479$	0.0944147	0.00431392	0.00215696	−	0.999998i	$-0.499313\pi$
$479$	0.0944147	0.00431392	0.00215696	+	0.999998i	$0.499313\pi$
$480$	−3.15164	−0.143852
$481$	−52.8840	−2.41130
$482$	0.805703	0.0366988
$483$	0	0
$484$	−8.10291	−0.368314
$485$	−3.88552	−0.176433
$486$	20.3829	0.924586
$487$	−16.1849	−0.733409	−0.366705	−	0.930337i	$-0.619514\pi$
$487$	−16.1849	−0.733409	−0.366705	+	0.930337i	$0.619514\pi$
$488$	11.7092	0.530051
$489$	−10.1179	−0.457546
$490$	6.65649	0.300709
$491$	8.73443	0.394179	0.197090	−	0.980385i	$-0.436851\pi$
$491$	8.73443	0.394179	0.197090	+	0.980385i	$0.436851\pi$
$492$	−9.73658	−0.438959
$493$	−0.611744	−0.0275516
$494$	−9.58725	−0.431351
$495$	−11.8003	−0.530384
$496$	−8.90264	−0.399740
$497$	−4.65673	−0.208883
$498$	13.6942	0.613654
$499$	−11.0247	−0.493534	−0.246767	−	0.969075i	$-0.579368\pi$
$499$	−11.0247	−0.493534	−0.246767	+	0.969075i	$0.579368\pi$
$500$	−1.00000	−0.0447214
$501$	−26.9610	−1.20453
$502$	18.1838	0.811584
$503$	−26.0574	−1.16184	−0.580920	−	0.813960i	$-0.697307\pi$
$503$	−26.0574	−1.16184	−0.580920	+	0.813960i	$0.697307\pi$
$504$	−4.06336	−0.180996
$505$	−17.2834	−0.769102
$506$	0	0
$507$	82.0141	3.64238
$508$	3.09642	0.137381
$509$	−13.2217	−0.586040	−0.293020	−	0.956106i	$-0.594660\pi$
$509$	−13.2217	−0.586040	−0.293020	+	0.956106i	$0.594660\pi$
$510$	−7.03896	−0.311691
$511$	−0.840933	−0.0372007
$512$	1.00000	0.0441942
$513$	−19.0231	−0.839890
$514$	−16.0600	−0.708377
$515$	1.54651	0.0681473
$516$	23.3997	1.03011
$517$	−9.74708	−0.428676
$518$	4.96180	0.218009
$519$	50.5786	2.22015
$520$	−6.24681	−0.273941
$521$	−14.6199	−0.640509	−0.320255	−	0.947331i	$-0.603768\pi$
$521$	−14.6199	−0.640509	−0.320255	+	0.947331i	$0.603768\pi$
$522$	−1.89894	−0.0831142
$523$	2.31930	0.101416	0.0507079	−	0.998714i	$-0.483852\pi$
$523$	2.31930	0.101416	0.0507079	+	0.998714i	$0.483852\pi$
$524$	−2.81139	−0.122816
$525$	−1.84718	−0.0806177
$526$	7.97560	0.347753
$527$	−19.8834	−0.866134
$528$	5.36436	0.233454
$529$	0	0
$530$	−10.2861	−0.446801
$531$	−45.1297	−1.95846
$532$	0.899515	0.0389989
$533$	−19.2987	−0.835919
$534$	−33.8710	−1.46574
$535$	4.19431	0.181336
$536$	−13.1665	−0.568706
$537$	−2.78522	−0.120191
$538$	18.0501	0.778196
$539$	−11.3299	−0.488013
$540$	−12.3950	−0.533395
$541$	10.9391	0.470308	0.235154	−	0.971958i	$-0.424441\pi$
$541$	10.9391	0.470308	0.235154	+	0.971958i	$0.424441\pi$
$542$	−22.8448	−0.981268
$543$	18.4089	0.790003
$544$	2.23343	0.0957573
$545$	−20.1253	−0.862075
$546$	−11.5390	−0.493824
$547$	−28.7469	−1.22913	−0.614564	−	0.788867i	$-0.710668\pi$
$547$	−28.7469	−1.22913	−0.614564	+	0.788867i	$0.710668\pi$
$548$	−11.7641	−0.502539
$549$	81.1784	3.46461
$550$	1.70208	0.0725771
$551$	0.420372	0.0179085
$552$	0	0
$553$	−6.93489	−0.294902
$554$	20.9373	0.889540
$555$	26.6811	1.13255
$556$	−16.1372	−0.684368
$557$	−6.79417	−0.287878	−0.143939	−	0.989587i	$-0.545977\pi$
$557$	−6.79417	−0.287878	−0.143939	+	0.989587i	$0.545977\pi$
$558$	−61.7208	−2.61285
$559$	46.3801	1.96167
$560$	0.586101	0.0247673
$561$	11.9809	0.505834
$562$	2.88646	0.121758
$563$	39.0015	1.64372	0.821858	−	0.569693i	$-0.192938\pi$
$563$	39.0015	1.64372	0.821858	+	0.569693i	$0.192938\pi$
$564$	−18.0481	−0.759961
$565$	20.1906	0.849425
$566$	−2.86080	−0.120248
$567$	−10.7057	−0.449597
$568$	7.94527	0.333376
$569$	44.4696	1.86426	0.932131	−	0.362121i	$-0.117947\pi$
$569$	44.4696	1.86426	0.932131	+	0.362121i	$0.117947\pi$
$570$	4.83696	0.202598
$571$	0.240915	0.0100820	0.00504100	−	0.999987i	$-0.498395\pi$
$571$	0.240915	0.0100820	0.00504100	+	0.999987i	$0.498395\pi$
$572$	10.6326	0.444571
$573$	−40.9797	−1.71195
$574$	1.81068	0.0755764
$575$	0	0
$576$	6.93286	0.288869
$577$	−7.07715	−0.294626	−0.147313	−	0.989090i	$-0.547062\pi$
$577$	−7.07715	−0.294626	−0.147313	+	0.989090i	$0.547062\pi$
$578$	−12.0118	−0.499625
$579$	−7.11801	−0.295814
$580$	0.273904	0.0113732
$581$	−2.54668	−0.105654
$582$	12.2458	0.507604
$583$	17.5079	0.725101
$584$	1.43479	0.0593720
$585$	−43.3083	−1.79058
$586$	2.79775	0.115574
$587$	26.5919	1.09756	0.548782	−	0.835966i	$-0.315092\pi$
$587$	26.5919	1.09756	0.548782	+	0.835966i	$0.315092\pi$
$588$	−20.9789	−0.865154
$589$	13.6633	0.562985
$590$	6.50953	0.267993
$591$	18.7540	0.771438
$592$	−8.46576	−0.347941
$593$	−36.5178	−1.49961	−0.749804	−	0.661660i	$-0.769852\pi$
$593$	−36.5178	−1.49961	−0.749804	+	0.661660i	$0.769852\pi$
$594$	21.0973	0.865632
$595$	1.30901	0.0536643
$596$	−4.77884	−0.195749
$597$	−64.9698	−2.65904
$598$	0	0
$599$	−21.6301	−0.883783	−0.441892	−	0.897068i	$-0.645692\pi$
$599$	−21.6301	−0.883783	−0.441892	+	0.897068i	$0.645692\pi$
$600$	3.15164	0.128665
$601$	−15.3369	−0.625604	−0.312802	−	0.949818i	$-0.601268\pi$
$601$	−15.3369	−0.625604	−0.312802	+	0.949818i	$0.601268\pi$
$602$	−4.35157	−0.177357
$603$	−91.2814	−3.71727
$604$	5.45532	0.221974
$605$	8.10291	0.329430
$606$	54.4712	2.21274
$607$	24.2992	0.986273	0.493136	−	0.869952i	$-0.335850\pi$
$607$	24.2992	0.986273	0.493136	+	0.869952i	$0.335850\pi$
$608$	−1.53474	−0.0622421
$609$	0.505951	0.0205022
$610$	−11.7092	−0.474092
$611$	−35.7727	−1.44721
$612$	15.4840	0.625905
$613$	−33.5137	−1.35361	−0.676804	−	0.736164i	$-0.736635\pi$
$613$	−33.5137	−1.35361	−0.676804	+	0.736164i	$0.736635\pi$
$614$	−28.5926	−1.15390
$615$	9.73658	0.392617
$616$	−0.997594	−0.0401942
$617$	−26.9418	−1.08464	−0.542319	−	0.840173i	$-0.682454\pi$
$617$	−26.9418	−1.08464	−0.542319	+	0.840173i	$0.682454\pi$
$618$	−4.87405	−0.196063
$619$	−7.71942	−0.310270	−0.155135	−	0.987893i	$-0.549581\pi$
$619$	−7.71942	−0.310270	−0.155135	+	0.987893i	$0.549581\pi$
$620$	8.90264	0.357539
$621$	0	0
$622$	−17.2586	−0.692007
$623$	6.29888	0.252359
$624$	19.6877	0.788140
$625$	1.00000	0.0400000
$626$	30.4579	1.21734
$627$	−8.23292	−0.328791
$628$	−5.44221	−0.217168
$629$	−18.9077	−0.753898
$630$	4.06336	0.161888
$631$	3.78473	0.150668	0.0753338	−	0.997158i	$-0.475998\pi$
$631$	3.78473	0.150668	0.0753338	+	0.997158i	$0.475998\pi$
$632$	11.8322	0.470661
$633$	0.955927	0.0379947
$634$	8.82463	0.350471
$635$	−3.09642	−0.122878
$636$	32.4182	1.28547
$637$	−41.5818	−1.64753
$638$	−0.466207	−0.0184573
$639$	55.0834	2.17907
$640$	−1.00000	−0.0395285
$641$	−7.16289	−0.282917	−0.141459	−	0.989944i	$-0.545179\pi$
$641$	−7.16289	−0.282917	−0.141459	+	0.989944i	$0.545179\pi$
$642$	−13.2190	−0.521711
$643$	−42.6671	−1.68263	−0.841313	−	0.540548i	$-0.818217\pi$
$643$	−42.6671	−1.68263	−0.841313	+	0.540548i	$0.818217\pi$
$644$	0	0
$645$	−23.3997	−0.921362
$646$	−3.42774	−0.134862
$647$	21.5811	0.848440	0.424220	−	0.905559i	$-0.360548\pi$
$647$	21.5811	0.848440	0.424220	+	0.905559i	$0.360548\pi$
$648$	18.2660	0.717555
$649$	−11.0798	−0.434919
$650$	6.24681	0.245020
$651$	16.4448	0.644523
$652$	−3.21035	−0.125727
$653$	−18.1083	−0.708634	−0.354317	−	0.935125i	$-0.615287\pi$
$653$	−18.1083	−0.708634	−0.354317	+	0.935125i	$0.615287\pi$
$654$	63.4279	2.48023
$655$	2.81139	0.109850
$656$	−3.08937	−0.120620
$657$	9.94720	0.388077
$658$	3.35634	0.130844
$659$	8.14959	0.317463	0.158731	−	0.987322i	$-0.449260\pi$
$659$	8.14959	0.317463	0.158731	+	0.987322i	$0.449260\pi$
$660$	−5.36436	−0.208807
$661$	17.8455	0.694110	0.347055	−	0.937845i	$-0.387182\pi$
$661$	17.8455	0.694110	0.347055	+	0.937845i	$0.387182\pi$
$662$	5.93397	0.230630
$663$	43.9711	1.70770
$664$	4.34511	0.168623
$665$	−0.899515	−0.0348817
$666$	−58.6919	−2.27427
$667$	0	0
$668$	−8.55460	−0.330987
$669$	−41.2461	−1.59466
$670$	13.1665	0.508666
$671$	19.9301	0.769392
$672$	−1.84718	−0.0712566
$673$	9.58138	0.369335	0.184668	−	0.982801i	$-0.440879\pi$
$673$	9.58138	0.369335	0.184668	+	0.982801i	$0.440879\pi$
$674$	−25.8103	−0.994176
$675$	12.3950	0.477083
$676$	26.0227	1.00087
$677$	−25.3498	−0.974272	−0.487136	−	0.873326i	$-0.661958\pi$
$677$	−25.3498	−0.974272	−0.487136	+	0.873326i	$0.661958\pi$
$678$	−63.6336	−2.44383
$679$	−2.27731	−0.0873952
$680$	−2.23343	−0.0856480
$681$	−67.8527	−2.60012
$682$	−15.1530	−0.580240
$683$	18.7764	0.718457	0.359229	−	0.933250i	$-0.383040\pi$
$683$	18.7764	0.718457	0.359229	+	0.933250i	$0.383040\pi$
$684$	−10.6402	−0.406837
$685$	11.7641	0.449484
$686$	8.00409	0.305597
$687$	36.7065	1.40044
$688$	7.42460	0.283060
$689$	64.2555	2.44794
$690$	0	0
$691$	46.2070	1.75780	0.878898	−	0.477010i	$-0.158280\pi$
$691$	46.2070	1.75780	0.878898	+	0.477010i	$0.158280\pi$
$692$	16.0483	0.610065
$693$	−6.91618	−0.262724
$694$	27.4313	1.04128
$695$	16.1372	0.612117
$696$	−0.863248	−0.0327213
$697$	−6.89987	−0.261351
$698$	3.55776	0.134663
$699$	46.9620	1.77627
$700$	−0.586101	−0.0221526
$701$	49.6988	1.87710	0.938549	−	0.345145i	$-0.112170\pi$
$701$	49.6988	1.87710	0.938549	+	0.345145i	$0.112170\pi$
$702$	77.4290	2.92237
$703$	12.9928	0.490032
$704$	1.70208	0.0641497
$705$	18.0481	0.679730
$706$	13.4092	0.504662
$707$	−10.1298	−0.380972
$708$	−20.5157	−0.771028
$709$	−5.59825	−0.210247	−0.105123	−	0.994459i	$-0.533524\pi$
$709$	−5.59825	−0.210247	−0.105123	+	0.994459i	$0.533524\pi$
$710$	−7.94527	−0.298181
$711$	82.0312	3.07641
$712$	−10.7471	−0.402764
$713$	0	0
$714$	−4.12555	−0.154395
$715$	−10.6326	−0.397637
$716$	−0.883737	−0.0330268
$717$	44.3983	1.65808
$718$	2.51760	0.0939559
$719$	−32.5301	−1.21317	−0.606583	−	0.795020i	$-0.707460\pi$
$719$	−32.5301	−1.21317	−0.606583	+	0.795020i	$0.707460\pi$
$720$	−6.93286	−0.258372
$721$	0.906411	0.0337565
$722$	−16.6446	−0.619447
$723$	2.53929	0.0944372
$724$	5.84106	0.217081
$725$	−0.273904	−0.0101725
$726$	−25.5375	−0.947785
$727$	5.01312	0.185926	0.0929631	−	0.995670i	$-0.470366\pi$
$727$	5.01312	0.185926	0.0929631	+	0.995670i	$0.470366\pi$
$728$	−3.66127	−0.135696
$729$	9.44170	0.349693
$730$	−1.43479	−0.0531040
$731$	16.5823	0.613318
$732$	36.9033	1.36398
$733$	−19.9073	−0.735294	−0.367647	−	0.929965i	$-0.619837\pi$
$733$	−19.9073	−0.735294	−0.367647	+	0.929965i	$0.619837\pi$
$734$	30.4898	1.12540
$735$	20.9789	0.773817
$736$	0	0
$737$	−22.4105	−0.825500
$738$	−21.4181	−0.788413
$739$	20.1621	0.741676	0.370838	−	0.928698i	$-0.379071\pi$
$739$	20.1621	0.741676	0.370838	+	0.928698i	$0.379071\pi$
$740$	8.46576	0.311208
$741$	−30.2156	−1.11000
$742$	−6.02872	−0.221321
$743$	−37.1533	−1.36302	−0.681510	−	0.731808i	$-0.738677\pi$
$743$	−37.1533	−1.36302	−0.681510	+	0.731808i	$0.738677\pi$
$744$	−28.0580	−1.02865
$745$	4.77884	0.175083
$746$	−28.3933	−1.03955
$747$	30.1240	1.10218
$748$	3.80148	0.138996
$749$	2.45829	0.0898240
$750$	−3.15164	−0.115082
$751$	6.40163	0.233599	0.116799	−	0.993156i	$-0.462737\pi$
$751$	6.40163	0.233599	0.116799	+	0.993156i	$0.462737\pi$
$752$	−5.72656	−0.208826
$753$	57.3089	2.08845
$754$	−1.71103	−0.0623119
$755$	−5.45532	−0.198539
$756$	−7.26471	−0.264215
$757$	−3.60100	−0.130881	−0.0654403	−	0.997856i	$-0.520845\pi$
$757$	−3.60100	−0.130881	−0.0654403	+	0.997856i	$0.520845\pi$
$758$	18.5845	0.675021
$759$	0	0
$760$	1.53474	0.0556710
$761$	22.1708	0.803692	0.401846	−	0.915707i	$-0.368369\pi$
$761$	22.1708	0.803692	0.401846	+	0.915707i	$0.368369\pi$
$762$	9.75881	0.353524
$763$	−11.7955	−0.427025
$764$	−13.0027	−0.470420
$765$	−15.4840	−0.559826
$766$	−8.49534	−0.306949
$767$	−40.6638	−1.46828
$768$	3.15164	0.113725
$769$	−1.42436	−0.0513637	−0.0256819	−	0.999670i	$-0.508176\pi$
$769$	−1.42436	−0.0513637	−0.0256819	+	0.999670i	$0.508176\pi$
$770$	0.997594	0.0359508
$771$	−50.6154	−1.82287
$772$	−2.25851	−0.0812855
$773$	6.33786	0.227957	0.113978	−	0.993483i	$-0.463641\pi$
$773$	6.33786	0.227957	0.113978	+	0.993483i	$0.463641\pi$
$774$	51.4737	1.85018
$775$	−8.90264	−0.319792
$776$	3.88552	0.139482
$777$	15.6378	0.561003
$778$	−5.92367	−0.212374
$779$	4.74138	0.169878
$780$	−19.6877	−0.704934
$781$	13.5235	0.483909
$782$	0	0
$783$	−3.39503	−0.121329
$784$	−6.65649	−0.237732
$785$	5.44221	0.194241
$786$	−8.86050	−0.316043
$787$	−14.4402	−0.514739	−0.257369	−	0.966313i	$-0.582856\pi$
$787$	−14.4402	−0.514739	−0.257369	+	0.966313i	$0.582856\pi$
$788$	5.95055	0.211980
$789$	25.1363	0.894874
$790$	−11.8322	−0.420972
$791$	11.8337	0.420759
$792$	11.8003	0.419306
$793$	73.1453	2.59747
$794$	−11.3130	−0.401482
$795$	−32.4182	−1.14976
$796$	−20.6146	−0.730664
$797$	−29.9672	−1.06149	−0.530746	−	0.847531i	$-0.678088\pi$
$797$	−29.9672	−1.06149	−0.530746	+	0.847531i	$0.678088\pi$
$798$	2.83495	0.100356
$799$	−12.7898	−0.452472
$800$	1.00000	0.0353553
$801$	−74.5080	−2.63261
$802$	2.22352	0.0785153
$803$	2.44213	0.0861810
$804$	−41.4961	−1.46345
$805$	0	0
$806$	−55.6131	−1.95889
$807$	56.8876	2.00254
$808$	17.2834	0.608028
$809$	−32.2589	−1.13416	−0.567081	−	0.823662i	$-0.691927\pi$
$809$	−32.2589	−1.13416	−0.567081	+	0.823662i	$0.691927\pi$
$810$	−18.2660	−0.641800
$811$	−0.208582	−0.00732432	−0.00366216	−	0.999993i	$-0.501166\pi$
$811$	−0.208582	−0.00732432	−0.00366216	+	0.999993i	$0.501166\pi$
$812$	0.160535	0.00563369
$813$	−71.9987	−2.52510
$814$	−14.4094	−0.505050
$815$	3.21035	0.112454
$816$	7.03896	0.246413
$817$	−11.3948	−0.398655
$818$	−17.6432	−0.616879
$819$	−25.3830	−0.886955
$820$	3.08937	0.107885
$821$	24.5453	0.856635	0.428318	−	0.903628i	$-0.359106\pi$
$821$	24.5453	0.856635	0.428318	+	0.903628i	$0.359106\pi$
$822$	−37.0763	−1.29319
$823$	−13.5685	−0.472966	−0.236483	−	0.971636i	$-0.575995\pi$
$823$	−13.5685	−0.472966	−0.236483	+	0.971636i	$0.575995\pi$
$824$	−1.54651	−0.0538752
$825$	5.36436	0.186763
$826$	3.81524	0.132749
$827$	36.3082	1.26256	0.631280	−	0.775555i	$-0.282530\pi$
$827$	36.3082	1.26256	0.631280	+	0.775555i	$0.282530\pi$
$828$	0	0
$829$	23.1362	0.803555	0.401777	−	0.915737i	$-0.368393\pi$
$829$	23.1362	0.803555	0.401777	+	0.915737i	$0.368393\pi$
$830$	−4.34511	−0.150821
$831$	65.9869	2.28906
$832$	6.24681	0.216569
$833$	−14.8668	−0.515103
$834$	−50.8586	−1.76109
$835$	8.55460	0.296044
$836$	−2.61226	−0.0903469
$837$	−110.348	−3.81418
$838$	0.825594	0.0285197
$839$	17.4952	0.604000	0.302000	−	0.953308i	$-0.402346\pi$
$839$	17.4952	0.604000	0.302000	+	0.953308i	$0.402346\pi$
$840$	1.84718	0.0637339
$841$	−28.9250	−0.997413
$842$	−18.0318	−0.621417
$843$	9.09711	0.313321
$844$	0.303311	0.0104404
$845$	−26.0227	−0.895206
$846$	−39.7014	−1.36496
$847$	4.74913	0.163182
$848$	10.2861	0.353227
$849$	−9.01623	−0.309436
$850$	2.23343	0.0766059
$851$	0	0
$852$	25.0407	0.857879
$853$	0.0547774	0.00187554	0.000937771	−	1.00000i	$-0.499701\pi$
$853$	0.0547774	0.00187554	0.000937771		1.00000i	$0.499701\pi$
$854$	−6.86279	−0.234840
$855$	10.6402	0.363886
$856$	−4.19431	−0.143359
$857$	−31.3584	−1.07118	−0.535592	−	0.844477i	$-0.679911\pi$
$857$	−31.3584	−1.07118	−0.535592	+	0.844477i	$0.679911\pi$
$858$	33.5102	1.14402
$859$	5.98249	0.204120	0.102060	−	0.994778i	$-0.467457\pi$
$859$	5.98249	0.204120	0.102060	+	0.994778i	$0.467457\pi$
$860$	−7.42460	−0.253177
$861$	5.70663	0.194481
$862$	−6.40236	−0.218065
$863$	54.3457	1.84995	0.924975	−	0.380027i	$-0.124085\pi$
$863$	54.3457	1.84995	0.924975	+	0.380027i	$0.124085\pi$
$864$	12.3950	0.421685
$865$	−16.0483	−0.545659
$866$	−19.8963	−0.676103
$867$	−37.8569	−1.28569
$868$	5.21785	0.177105
$869$	20.1395	0.683184
$870$	0.863248	0.0292668
$871$	−82.2486	−2.78689
$872$	20.1253	0.681530
$873$	26.9378	0.911706
$874$	0	0
$875$	0.586101	0.0198138
$876$	4.52195	0.152782
$877$	26.6957	0.901449	0.450725	−	0.892663i	$-0.351166\pi$
$877$	26.6957	0.901449	0.450725	+	0.892663i	$0.351166\pi$
$878$	−21.8528	−0.737497
$879$	8.81751	0.297407
$880$	−1.70208	−0.0573772
$881$	19.5812	0.659709	0.329855	−	0.944032i	$-0.393000\pi$
$881$	19.5812	0.659709	0.329855	+	0.944032i	$0.393000\pi$
$882$	−46.1485	−1.55390
$883$	41.3492	1.39151	0.695755	−	0.718279i	$-0.255070\pi$
$883$	41.3492	1.39151	0.695755	+	0.718279i	$0.255070\pi$
$884$	13.9518	0.469250
$885$	20.5157	0.689628
$886$	8.85999	0.297657
$887$	33.4241	1.12227	0.561135	−	0.827724i	$-0.310365\pi$
$887$	33.4241	1.12227	0.561135	+	0.827724i	$0.310365\pi$
$888$	−26.6811	−0.895358
$889$	−1.81482	−0.0608670
$890$	10.7471	0.360243
$891$	31.0902	1.04156
$892$	−13.0872	−0.438190
$893$	8.78880	0.294106
$894$	−15.0612	−0.503722
$895$	0.883737	0.0295401
$896$	−0.586101	−0.0195803
$897$	0	0
$898$	−8.85606	−0.295530
$899$	2.43847	0.0813275
$900$	6.93286	0.231095
$901$	22.9733	0.765352
$902$	−5.25836	−0.175084
$903$	−13.7146	−0.456393
$904$	−20.1906	−0.671530
$905$	−5.84106	−0.194163
$906$	17.1932	0.571207
$907$	−7.14117	−0.237119	−0.118559	−	0.992947i	$-0.537828\pi$
$907$	−7.14117	−0.237119	−0.118559	+	0.992947i	$0.537828\pi$
$908$	−21.5293	−0.714475
$909$	119.823	3.97429
$910$	3.66127	0.121370
$911$	−41.0838	−1.36117	−0.680583	−	0.732671i	$-0.738273\pi$
$911$	−41.0838	−1.36117	−0.680583	+	0.732671i	$0.738273\pi$
$912$	−4.83696	−0.160168
$913$	7.39574	0.244763
$914$	8.97376	0.296825
$915$	−36.9033	−1.21999
$916$	11.6468	0.384820
$917$	1.64776	0.0544138
$918$	27.6832	0.913683
$919$	1.24485	0.0410639	0.0205319	−	0.999789i	$-0.493464\pi$
$919$	1.24485	0.0410639	0.0205319	+	0.999789i	$0.493464\pi$
$920$	0	0
$921$	−90.1137	−2.96935
$922$	−17.5927	−0.579385
$923$	49.6326	1.63368
$924$	−3.14406	−0.103432
$925$	−8.46576	−0.278353
$926$	−33.6039	−1.10429
$927$	−10.7217	−0.352148
$928$	−0.273904	−0.00899134
$929$	38.1174	1.25059	0.625295	−	0.780388i	$-0.284979\pi$
$929$	38.1174	1.25059	0.625295	+	0.780388i	$0.284979\pi$
$930$	28.0580	0.920057
$931$	10.2160	0.334816
$932$	14.9008	0.488092
$933$	−54.3929	−1.78075
$934$	−4.05576	−0.132708
$935$	−3.80148	−0.124322
$936$	43.3083	1.41557
$937$	40.5884	1.32597	0.662983	−	0.748634i	$-0.269290\pi$
$937$	40.5884	1.32597	0.662983	+	0.748634i	$0.269290\pi$
$938$	7.71690	0.251966
$939$	95.9924	3.13259
$940$	5.72656	0.186780
$941$	46.8604	1.52761	0.763803	−	0.645450i	$-0.223330\pi$
$941$	46.8604	1.52761	0.763803	+	0.645450i	$0.223330\pi$
$942$	−17.1519	−0.558840
$943$	0	0
$944$	−6.50953	−0.211867
$945$	7.26471	0.236321
$946$	12.6373	0.410874
$947$	21.1898	0.688576	0.344288	−	0.938864i	$-0.388120\pi$
$947$	21.1898	0.688576	0.344288	+	0.938864i	$0.388120\pi$
$948$	37.2910	1.21116
$949$	8.96286	0.290947
$950$	−1.53474	−0.0497936
$951$	27.8121	0.901869
$952$	−1.30901	−0.0424254
$953$	18.0045	0.583221	0.291611	−	0.956537i	$-0.405809\pi$
$953$	18.0045	0.583221	0.291611	+	0.956537i	$0.405809\pi$
$954$	71.3123	2.30882
$955$	13.0027	0.420756
$956$	14.0873	0.455617
$957$	−1.46932	−0.0474964
$958$	0.0944147	0.00305040
$959$	6.89497	0.222650
$960$	−3.15164	−0.101719
$961$	48.2571	1.55668
$962$	−52.8840	−1.70505
$963$	−29.0786	−0.937044
$964$	0.805703	0.0259499
$965$	2.25851	0.0727039
$966$	0	0
$967$	44.5708	1.43330	0.716650	−	0.697433i	$-0.245674\pi$
$967$	44.5708	1.43330	0.716650	+	0.697433i	$0.245674\pi$
$968$	−8.10291	−0.260437
$969$	−10.8030	−0.347042
$970$	−3.88552	−0.124757
$971$	−60.3006	−1.93514	−0.967569	−	0.252608i	$-0.918712\pi$
$971$	−60.3006	−1.93514	−0.967569	+	0.252608i	$0.918712\pi$
$972$	20.3829	0.653781
$973$	9.45801	0.303210
$974$	−16.1849	−0.518599
$975$	19.6877	0.630512
$976$	11.7092	0.374803
$977$	1.13366	0.0362690	0.0181345	−	0.999836i	$-0.494227\pi$
$977$	1.13366	0.0362690	0.0181345	+	0.999836i	$0.494227\pi$
$978$	−10.1179	−0.323534
$979$	−18.2924	−0.584628
$980$	6.65649	0.212634
$981$	139.526	4.45473
$982$	8.73443	0.278727
$983$	−35.4229	−1.12982	−0.564908	−	0.825154i	$-0.691088\pi$
$983$	−35.4229	−1.12982	−0.564908	+	0.825154i	$0.691088\pi$
$984$	−9.73658	−0.310391
$985$	−5.95055	−0.189600
$986$	−0.611744	−0.0194819
$987$	10.5780	0.336701
$988$	−9.58725	−0.305011
$989$	0	0
$990$	−11.8003	−0.375038
$991$	−26.0397	−0.827178	−0.413589	−	0.910464i	$-0.635725\pi$
$991$	−26.0397	−0.827178	−0.413589	+	0.910464i	$0.635725\pi$
$992$	−8.90264	−0.282659
$993$	18.7018	0.593482
$994$	−4.65673	−0.147703
$995$	20.6146	0.653526
$996$	13.6942	0.433919
$997$	39.8804	1.26303	0.631513	−	0.775365i	$-0.282434\pi$
$997$	39.8804	1.26303	0.631513	+	0.775365i	$0.282434\pi$
$998$	−11.0247	−0.348981
$999$	−104.933	−3.31993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.14		15
23.13	even	11		230.2.g.d.31.3	✓	30
23.16	even	11		230.2.g.d.141.3	yes	30
23.22	odd	2		5290.2.a.bl.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.31.3	✓	30	23.13	even	11
230.2.g.d.141.3	yes	30	23.16	even	11
5290.2.a.bk.1.14		15	1.1	even	1	trivial
5290.2.a.bl.1.14		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.15164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.15164 q^{6} -0.586101 q^{7} +1.00000 q^{8} +6.93286 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.15164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.15164 q^{6} -0.586101 q^{7} +1.00000 q^{8} +6.93286 q^{9} -1.00000 q^{10} +1.70208 q^{11} +3.15164 q^{12} +6.24681 q^{13} -0.586101 q^{14} -3.15164 q^{15} +1.00000 q^{16} +2.23343 q^{17} +6.93286 q^{18} -1.53474 q^{19} -1.00000 q^{20} -1.84718 q^{21} +1.70208 q^{22} +3.15164 q^{24} +1.00000 q^{25} +6.24681 q^{26} +12.3950 q^{27} -0.586101 q^{28} -0.273904 q^{29} -3.15164 q^{30} -8.90264 q^{31} +1.00000 q^{32} +5.36436 q^{33} +2.23343 q^{34} +0.586101 q^{35} +6.93286 q^{36} -8.46576 q^{37} -1.53474 q^{38} +19.6877 q^{39} -1.00000 q^{40} -3.08937 q^{41} -1.84718 q^{42} +7.42460 q^{43} +1.70208 q^{44} -6.93286 q^{45} -5.72656 q^{47} +3.15164 q^{48} -6.65649 q^{49} +1.00000 q^{50} +7.03896 q^{51} +6.24681 q^{52} +10.2861 q^{53} +12.3950 q^{54} -1.70208 q^{55} -0.586101 q^{56} -4.83696 q^{57} -0.273904 q^{58} -6.50953 q^{59} -3.15164 q^{60} +11.7092 q^{61} -8.90264 q^{62} -4.06336 q^{63} +1.00000 q^{64} -6.24681 q^{65} +5.36436 q^{66} -13.1665 q^{67} +2.23343 q^{68} +0.586101 q^{70} +7.94527 q^{71} +6.93286 q^{72} +1.43479 q^{73} -8.46576 q^{74} +3.15164 q^{75} -1.53474 q^{76} -0.997594 q^{77} +19.6877 q^{78} +11.8322 q^{79} -1.00000 q^{80} +18.2660 q^{81} -3.08937 q^{82} +4.34511 q^{83} -1.84718 q^{84} -2.23343 q^{85} +7.42460 q^{86} -0.863248 q^{87} +1.70208 q^{88} -10.7471 q^{89} -6.93286 q^{90} -3.66127 q^{91} -28.0580 q^{93} -5.72656 q^{94} +1.53474 q^{95} +3.15164 q^{96} +3.88552 q^{97} -6.65649 q^{98} +11.8003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 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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