LMFDB - Embedded newform 507.4.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,4,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.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:	$29.9139683729$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 48x^{7} + 29x^{6} + 772x^{5} - 150x^{4} - 4745x^{3} - 966x^{2} + 9428x + 5144 $ x^9 - x^8 - 48x^7 + 29x^6 + 772x^5 - 150x^4 - 4745x^3 - 966x^2 + 9428*x + 5144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 13^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.614643$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61464 q^{2} -3.00000 q^{3} -5.39293 q^{4} -1.20859 q^{5} +4.84393 q^{6} -28.2769 q^{7} +21.6248 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.61464 q^{2} -3.00000 q^{3} -5.39293 q^{4} -1.20859 q^{5} +4.84393 q^{6} -28.2769 q^{7} +21.6248 q^{8} +9.00000 q^{9} +1.95145 q^{10} +31.7768 q^{11} +16.1788 q^{12} +45.6572 q^{14} +3.62578 q^{15} +8.22709 q^{16} -16.0963 q^{17} -14.5318 q^{18} +58.5273 q^{19} +6.51785 q^{20} +84.8308 q^{21} -51.3081 q^{22} +152.860 q^{23} -64.8744 q^{24} -123.539 q^{25} -27.0000 q^{27} +152.496 q^{28} +265.310 q^{29} -5.85434 q^{30} +56.9241 q^{31} -186.282 q^{32} -95.3303 q^{33} +25.9899 q^{34} +34.1753 q^{35} -48.5363 q^{36} -444.864 q^{37} -94.5007 q^{38} -26.1356 q^{40} +189.276 q^{41} -136.972 q^{42} -132.752 q^{43} -171.370 q^{44} -10.8773 q^{45} -246.814 q^{46} -113.693 q^{47} -24.6813 q^{48} +456.586 q^{49} +199.472 q^{50} +48.2890 q^{51} +300.506 q^{53} +43.5954 q^{54} -38.4051 q^{55} -611.483 q^{56} -175.582 q^{57} -428.381 q^{58} -513.561 q^{59} -19.5536 q^{60} +619.902 q^{61} -91.9121 q^{62} -254.493 q^{63} +234.963 q^{64} +153.924 q^{66} -597.308 q^{67} +86.8064 q^{68} -458.580 q^{69} -55.1809 q^{70} -826.673 q^{71} +194.623 q^{72} +332.560 q^{73} +718.297 q^{74} +370.618 q^{75} -315.633 q^{76} -898.549 q^{77} +679.621 q^{79} -9.94319 q^{80} +81.0000 q^{81} -305.614 q^{82} -88.2682 q^{83} -457.487 q^{84} +19.4539 q^{85} +214.347 q^{86} -795.931 q^{87} +687.166 q^{88} -1484.39 q^{89} +17.5630 q^{90} -824.363 q^{92} -170.772 q^{93} +183.574 q^{94} -70.7356 q^{95} +558.847 q^{96} -154.995 q^{97} -737.223 q^{98} +285.991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9	\( 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9} + 198 q^{10} - 37 q^{11} - 96 q^{12} + 98 q^{14} + 123 q^{15} + 32 q^{16} - 134 q^{17} - 72 q^{18} + 72 q^{19} - 356 q^{20} + 3 q^{21} + 274 q^{22} + 226 q^{23} + 333 q^{24} + 612 q^{25} - 243 q^{27} - 132 q^{28} - 547 q^{29} - 594 q^{30} + 521 q^{31} - 721 q^{32} + 111 q^{33} + 100 q^{34} + 138 q^{35} + 288 q^{36} - 584 q^{37} - 416 q^{38} + 1342 q^{40} - 482 q^{41} - 294 q^{42} + 158 q^{43} - 1453 q^{44} - 369 q^{45} - 1537 q^{46} - 1500 q^{47} - 96 q^{48} + 642 q^{49} - 2777 q^{50} + 402 q^{51} + 1399 q^{53} + 216 q^{54} - 1408 q^{55} - 616 q^{56} - 216 q^{57} - 1455 q^{58} - 1541 q^{59} + 1068 q^{60} + 2092 q^{61} - 293 q^{62} - 9 q^{63} + 2481 q^{64} - 822 q^{66} - 252 q^{67} - 1579 q^{68} - 678 q^{69} - 2492 q^{70} - 2352 q^{71} - 999 q^{72} - 903 q^{73} + 1037 q^{74} - 1836 q^{75} + 485 q^{76} - 1686 q^{77} - 115 q^{79} - 5701 q^{80} + 729 q^{81} - 5147 q^{82} - 1207 q^{83} + 396 q^{84} - 4308 q^{85} - 5691 q^{86} + 1641 q^{87} - 484 q^{88} - 2336 q^{89} + 1782 q^{90} + 2087 q^{92} - 1563 q^{93} - 468 q^{94} - 222 q^{95} + 2163 q^{96} - 2155 q^{97} - 5593 q^{98} - 333 q^{99}+O(q^{100}) \) 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9 + 198 * q^10 - 37 * q^11 - 96 * q^12 + 98 * q^14 + 123 * q^15 + 32 * q^16 - 134 * q^17 - 72 * q^18 + 72 * q^19 - 356 * q^20 + 3 * q^21 + 274 * q^22 + 226 * q^23 + 333 * q^24 + 612 * q^25 - 243 * q^27 - 132 * q^28 - 547 * q^29 - 594 * q^30 + 521 * q^31 - 721 * q^32 + 111 * q^33 + 100 * q^34 + 138 * q^35 + 288 * q^36 - 584 * q^37 - 416 * q^38 + 1342 * q^40 - 482 * q^41 - 294 * q^42 + 158 * q^43 - 1453 * q^44 - 369 * q^45 - 1537 * q^46 - 1500 * q^47 - 96 * q^48 + 642 * q^49 - 2777 * q^50 + 402 * q^51 + 1399 * q^53 + 216 * q^54 - 1408 * q^55 - 616 * q^56 - 216 * q^57 - 1455 * q^58 - 1541 * q^59 + 1068 * q^60 + 2092 * q^61 - 293 * q^62 - 9 * q^63 + 2481 * q^64 - 822 * q^66 - 252 * q^67 - 1579 * q^68 - 678 * q^69 - 2492 * q^70 - 2352 * q^71 - 999 * q^72 - 903 * q^73 + 1037 * q^74 - 1836 * q^75 + 485 * q^76 - 1686 * q^77 - 115 * q^79 - 5701 * q^80 + 729 * q^81 - 5147 * q^82 - 1207 * q^83 + 396 * q^84 - 4308 * q^85 - 5691 * q^86 + 1641 * q^87 - 484 * q^88 - 2336 * q^89 + 1782 * q^90 + 2087 * q^92 - 1563 * q^93 - 468 * q^94 - 222 * q^95 + 2163 * q^96 - 2155 * q^97 - 5593 * q^98 - 333 * 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 $

$2$	−1.61464	−0.570863	−0.285431	−	0.958399i	$-0.592137\pi$
$2$	−1.61464	−0.570863	−0.285431	+	0.958399i	$0.592137\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.39293	−0.674116
$5$	−1.20859	−0.108100	−0.0540499	−	0.998538i	$-0.517213\pi$
$5$	−1.20859	−0.108100	−0.0540499	+	0.998538i	$0.517213\pi$
$6$	4.84393	0.329588
$7$	−28.2769	−1.52681	−0.763406	−	0.645919i	$-0.776474\pi$
$7$	−28.2769	−1.52681	−0.763406	+	0.645919i	$0.776474\pi$
$8$	21.6248	0.955690
$9$	9.00000	0.333333
$10$	1.95145	0.0617101
$11$	31.7768	0.871005	0.435502	−	0.900188i	$-0.356571\pi$
$11$	31.7768	0.871005	0.435502	+	0.900188i	$0.356571\pi$
$12$	16.1788	0.389201
$13$	0	0
$13$	0	0
$14$	45.6572	0.871600
$15$	3.62578	0.0624114
$16$	8.22709	0.128548
$17$	−16.0963	−0.229643	−0.114822	−	0.993386i	$-0.536630\pi$
$17$	−16.0963	−0.229643	−0.114822	+	0.993386i	$0.536630\pi$
$18$	−14.5318	−0.190288
$19$	58.5273	0.706688	0.353344	−	0.935493i	$-0.385044\pi$
$19$	58.5273	0.706688	0.353344	+	0.935493i	$0.385044\pi$
$20$	6.51785	0.0728718
$21$	84.8308	0.881505
$22$	−51.3081	−0.497224
$23$	152.860	1.38580	0.692902	−	0.721031i	$-0.256332\pi$
$23$	152.860	1.38580	0.692902	+	0.721031i	$0.256332\pi$
$24$	−64.8744	−0.551768
$25$	−123.539	−0.988314
$26$	0	0
$27$	−27.0000	−0.192450
$28$	152.496	1.02925
$29$	265.310	1.69886	0.849429	−	0.527703i	$-0.176947\pi$
$29$	265.310	1.69886	0.849429	+	0.527703i	$0.176947\pi$
$30$	−5.85434	−0.0356284
$31$	56.9241	0.329802	0.164901	−	0.986310i	$-0.447269\pi$
$31$	56.9241	0.329802	0.164901	+	0.986310i	$0.447269\pi$
$32$	−186.282	−1.02907
$33$	−95.3303	−0.502875
$34$	25.9899	0.131095
$35$	34.1753	0.165048
$36$	−48.5363	−0.224705
$37$	−444.864	−1.97663	−0.988314	−	0.152434i	$-0.951289\pi$
$37$	−444.864	−1.97663	−0.988314	+	0.152434i	$0.951289\pi$
$38$	−94.5007	−0.403422
$39$	0	0
$40$	−26.1356	−0.103310
$41$	189.276	0.720976	0.360488	−	0.932764i	$-0.382610\pi$
$41$	189.276	0.720976	0.360488	+	0.932764i	$0.382610\pi$
$42$	−136.972	−0.503218
$43$	−132.752	−0.470802	−0.235401	−	0.971898i	$-0.575640\pi$
$43$	−132.752	−0.470802	−0.235401	+	0.971898i	$0.575640\pi$
$44$	−171.370	−0.587158
$45$	−10.8773	−0.0360333
$46$	−246.814	−0.791104
$47$	−113.693	−0.352847	−0.176424	−	0.984314i	$-0.556453\pi$
$47$	−113.693	−0.352847	−0.176424	+	0.984314i	$0.556453\pi$
$48$	−24.6813	−0.0742173
$49$	456.586	1.33115
$50$	199.472	0.564192
$51$	48.2890	0.132585
$52$	0	0
$53$	300.506	0.778824	0.389412	−	0.921064i	$-0.372678\pi$
$53$	300.506	0.778824	0.389412	+	0.921064i	$0.372678\pi$
$54$	43.5954	0.109863
$55$	−38.4051	−0.0941554
$56$	−611.483	−1.45916
$57$	−175.582	−0.408007
$58$	−428.381	−0.969814
$59$	−513.561	−1.13322	−0.566610	−	0.823986i	$-0.691745\pi$
$59$	−513.561	−1.13322	−0.566610	+	0.823986i	$0.691745\pi$
$60$	−19.5536	−0.0420725
$61$	619.902	1.30115	0.650577	−	0.759441i	$-0.274527\pi$
$61$	619.902	1.30115	0.650577	+	0.759441i	$0.274527\pi$
$62$	−91.9121	−0.188272
$63$	−254.493	−0.508937
$64$	234.963	0.458911
$65$	0	0
$66$	153.924	0.287072
$67$	−597.308	−1.08915	−0.544573	−	0.838713i	$-0.683308\pi$
$67$	−597.308	−1.08915	−0.544573	+	0.838713i	$0.683308\pi$
$68$	86.8064	0.154806
$69$	−458.580	−0.800095
$70$	−55.1809	−0.0942197
$71$	−826.673	−1.38180	−0.690902	−	0.722949i	$-0.742786\pi$
$71$	−826.673	−1.38180	−0.690902	+	0.722949i	$0.742786\pi$
$72$	194.623	0.318563
$73$	332.560	0.533194	0.266597	−	0.963808i	$-0.414101\pi$
$73$	332.560	0.533194	0.266597	+	0.963808i	$0.414101\pi$
$74$	718.297	1.12838
$75$	370.618	0.570604
$76$	−315.633	−0.476390
$77$	−898.549	−1.32986
$78$	0	0
$79$	679.621	0.967891	0.483945	−	0.875098i	$-0.339203\pi$
$79$	679.621	0.967891	0.483945	+	0.875098i	$0.339203\pi$
$80$	−9.94319	−0.0138960
$81$	81.0000	0.111111
$82$	−305.614	−0.411578
$83$	−88.2682	−0.116731	−0.0583656	−	0.998295i	$-0.518589\pi$
$83$	−88.2682	−0.116731	−0.0583656	+	0.998295i	$0.518589\pi$
$84$	−457.487	−0.594237
$85$	19.4539	0.0248244
$86$	214.347	0.268763
$87$	−795.931	−0.980836
$88$	687.166	0.832411
$89$	−1484.39	−1.76792	−0.883959	−	0.467564i	$-0.845132\pi$
$89$	−1484.39	−1.76792	−0.883959	+	0.467564i	$0.845132\pi$
$90$	17.5630	0.0205700
$91$	0	0
$92$	−824.363	−0.934193
$93$	−170.772	−0.190411
$94$	183.574	0.201427
$95$	−70.7356	−0.0763929
$96$	558.847	0.594136
$97$	−154.995	−0.162241	−0.0811206	−	0.996704i	$-0.525850\pi$
$97$	−154.995	−0.162241	−0.0811206	+	0.996704i	$0.525850\pi$
$98$	−737.223	−0.759906
$99$	285.991	0.290335
$100$	666.238	0.666238
$101$	−1963.48	−1.93440	−0.967198	−	0.254025i	$-0.918246\pi$
$101$	−1963.48	−1.93440	−0.967198	+	0.254025i	$0.918246\pi$
$102$	−77.9696	−0.0756876
$103$	−1620.75	−1.55046	−0.775228	−	0.631682i	$-0.782365\pi$
$103$	−1620.75	−1.55046	−0.775228	+	0.631682i	$0.782365\pi$
$104$	0	0
$105$	−102.526	−0.0952905
$106$	−485.210	−0.444601
$107$	321.126	0.290135	0.145068	−	0.989422i	$-0.453660\pi$
$107$	321.126	0.290135	0.145068	+	0.989422i	$0.453660\pi$
$108$	145.609	0.129734
$109$	1305.27	1.14699	0.573495	−	0.819209i	$-0.305587\pi$
$109$	1305.27	1.14699	0.573495	+	0.819209i	$0.305587\pi$
$110$	62.0106	0.0537498
$111$	1334.59	1.14121
$112$	−232.637	−0.196269
$113$	−1086.88	−0.904820	−0.452410	−	0.891810i	$-0.649436\pi$
$113$	−1086.88	−0.904820	−0.452410	+	0.891810i	$0.649436\pi$
$114$	283.502	0.232916
$115$	−184.745	−0.149805
$116$	−1430.80	−1.14523
$117$	0	0
$118$	829.217	0.646912
$119$	455.155	0.350622
$120$	78.4067	0.0596460
$121$	−321.238	−0.241351
$122$	−1000.92	−0.742780
$123$	−567.829	−0.416256
$124$	−306.988	−0.222325
$125$	300.383	0.214936
$126$	410.915	0.290533
$127$	1326.41	0.926774	0.463387	−	0.886156i	$-0.346634\pi$
$127$	1326.41	0.926774	0.463387	+	0.886156i	$0.346634\pi$
$128$	1110.88	0.767098
$129$	398.256	0.271817
$130$	0	0
$131$	2379.32	1.58689	0.793443	−	0.608644i	$-0.208286\pi$
$131$	2379.32	1.58689	0.793443	+	0.608644i	$0.208286\pi$
$132$	514.109	0.338996
$133$	−1654.97	−1.07898
$134$	964.440	0.621753
$135$	32.6320	0.0208038
$136$	−348.080	−0.219468
$137$	−1633.55	−1.01871	−0.509355	−	0.860556i	$-0.670116\pi$
$137$	−1633.55	−1.01871	−0.509355	+	0.860556i	$0.670116\pi$
$138$	740.443	0.456744
$139$	−1254.97	−0.765791	−0.382895	−	0.923792i	$-0.625073\pi$
$139$	−1254.97	−0.765791	−0.382895	+	0.923792i	$0.625073\pi$
$140$	−184.305	−0.111261
$141$	341.079	0.203716
$142$	1334.78	0.788820
$143$	0	0
$144$	74.0438	0.0428494
$145$	−320.652	−0.183646
$146$	−536.965	−0.304380
$147$	−1369.76	−0.768542
$148$	2399.12	1.33248
$149$	−461.974	−0.254002	−0.127001	−	0.991903i	$-0.540535\pi$
$149$	−461.974	−0.254002	−0.127001	+	0.991903i	$0.540535\pi$
$150$	−598.416	−0.325736
$151$	766.065	0.412857	0.206429	−	0.978462i	$-0.433816\pi$
$151$	766.065	0.412857	0.206429	+	0.978462i	$0.433816\pi$
$152$	1265.64	0.675375
$153$	−144.867	−0.0765478
$154$	1450.84	0.759167
$155$	−68.7980	−0.0356516
$156$	0	0
$157$	−3424.00	−1.74054	−0.870270	−	0.492576i	$-0.836055\pi$
$157$	−3424.00	−1.74054	−0.870270	+	0.492576i	$0.836055\pi$
$158$	−1097.35	−0.552533
$159$	−901.517	−0.449654
$160$	225.139	0.111243
$161$	−4322.41	−2.11586
$162$	−130.786	−0.0634292
$163$	1722.36	0.827640	0.413820	−	0.910359i	$-0.364194\pi$
$163$	1722.36	0.827640	0.413820	+	0.910359i	$0.364194\pi$
$164$	−1020.75	−0.486021
$165$	115.215	0.0543607
$166$	142.522	0.0666375
$167$	2360.22	1.09365	0.546824	−	0.837247i	$-0.315837\pi$
$167$	2360.22	1.09365	0.546824	+	0.837247i	$0.315837\pi$
$168$	1834.45	0.842446
$169$	0	0
$170$	−31.4111	−0.0141713
$171$	526.746	0.235563
$172$	715.921	0.317375
$173$	4240.41	1.86354	0.931769	−	0.363052i	$-0.118265\pi$
$173$	4240.41	1.86354	0.931769	+	0.363052i	$0.118265\pi$
$174$	1285.14	0.559923
$175$	3493.31	1.50897
$176$	261.430	0.111966
$177$	1540.68	0.654264
$178$	2396.76	1.00924
$179$	−145.366	−0.0606991	−0.0303496	−	0.999539i	$-0.509662\pi$
$179$	−145.366	−0.0606991	−0.0303496	+	0.999539i	$0.509662\pi$
$180$	58.6607	0.0242906
$181$	1447.40	0.594388	0.297194	−	0.954817i	$-0.403949\pi$
$181$	1447.40	0.594388	0.297194	+	0.954817i	$0.403949\pi$
$182$	0	0
$183$	−1859.71	−0.751221
$184$	3305.57	1.32440
$185$	537.659	0.213673
$186$	275.736	0.108699
$187$	−511.490	−0.200020
$188$	613.138	0.237860
$189$	763.478	0.293835
$190$	114.213	0.0436098
$191$	−3772.56	−1.42918	−0.714589	−	0.699544i	$-0.753386\pi$
$191$	−3772.56	−1.42918	−0.714589	+	0.699544i	$0.753386\pi$
$192$	−704.888	−0.264953
$193$	−4396.27	−1.63964	−0.819819	−	0.572622i	$-0.805926\pi$
$193$	−4396.27	−1.63964	−0.819819	+	0.572622i	$0.805926\pi$
$194$	250.262	0.0926175
$195$	0	0
$196$	−2462.33	−0.897352
$197$	−1220.50	−0.441405	−0.220703	−	0.975341i	$-0.570835\pi$
$197$	−1220.50	−0.441405	−0.220703	+	0.975341i	$0.570835\pi$
$198$	−461.773	−0.165741
$199$	1851.42	0.659516	0.329758	−	0.944066i	$-0.393033\pi$
$199$	1851.42	0.659516	0.329758	+	0.944066i	$0.393033\pi$
$200$	−2671.51	−0.944522
$201$	1791.93	0.628819
$202$	3170.33	1.10427
$203$	−7502.16	−2.59384
$204$	−260.419	−0.0893774
$205$	−228.758	−0.0779373
$206$	2616.93	0.885097
$207$	1375.74	0.461935
$208$	0	0
$209$	1859.81	0.615529
$210$	165.543	0.0543978
$211$	565.901	0.184636	0.0923180	−	0.995730i	$-0.470572\pi$
$211$	565.901	0.184636	0.0923180	+	0.995730i	$0.470572\pi$
$212$	−1620.61	−0.525017
$213$	2480.02	0.797785
$214$	−518.505	−0.165627
$215$	160.443	0.0508936
$216$	−583.870	−0.183923
$217$	−1609.64	−0.503546
$218$	−2107.54	−0.654774
$219$	−997.679	−0.307840
$220$	207.116	0.0634717
$221$	0	0
$222$	−2154.89	−0.651472
$223$	−1073.79	−0.322448	−0.161224	−	0.986918i	$-0.551544\pi$
$223$	−1073.79	−0.322448	−0.161224	+	0.986918i	$0.551544\pi$
$224$	5267.49	1.57120
$225$	−1111.85	−0.329438
$226$	1754.92	0.516528
$227$	5756.24	1.68306	0.841531	−	0.540208i	$-0.181655\pi$
$227$	5756.24	1.68306	0.841531	+	0.540208i	$0.181655\pi$
$228$	946.900	0.275044
$229$	−2577.30	−0.743725	−0.371862	−	0.928288i	$-0.621281\pi$
$229$	−2577.30	−0.743725	−0.371862	+	0.928288i	$0.621281\pi$
$230$	298.298	0.0855182
$231$	2695.65	0.767795
$232$	5737.28	1.62358
$233$	−347.566	−0.0977246	−0.0488623	−	0.998806i	$-0.515560\pi$
$233$	−347.566	−0.0977246	−0.0488623	+	0.998806i	$0.515560\pi$
$234$	0	0
$235$	137.408	0.0381427
$236$	2769.60	0.763921
$237$	−2038.86	−0.558812
$238$	−734.914	−0.200157
$239$	−2201.35	−0.595788	−0.297894	−	0.954599i	$-0.596284\pi$
$239$	−2201.35	−0.595788	−0.297894	+	0.954599i	$0.596284\pi$
$240$	29.8296	0.00802288
$241$	−699.561	−0.186982	−0.0934910	−	0.995620i	$-0.529803\pi$
$241$	−699.561	−0.186982	−0.0934910	+	0.995620i	$0.529803\pi$
$242$	518.685	0.137778
$243$	−243.000	−0.0641500
$244$	−3343.09	−0.877128
$245$	−551.826	−0.143897
$246$	916.842	0.237625
$247$	0	0
$248$	1230.97	0.315189
$249$	264.804	0.0673948
$250$	−485.011	−0.122699
$251$	6033.42	1.51724	0.758618	−	0.651536i	$-0.225875\pi$
$251$	6033.42	1.51724	0.758618	+	0.651536i	$0.225875\pi$
$252$	1372.46	0.343083
$253$	4857.39	1.20704
$254$	−2141.69	−0.529061
$255$	−58.3618	−0.0143324
$256$	−3673.37	−0.896819
$257$	−3501.49	−0.849872	−0.424936	−	0.905223i	$-0.639703\pi$
$257$	−3501.49	−0.849872	−0.424936	+	0.905223i	$0.639703\pi$
$258$	−643.041	−0.155170
$259$	12579.4	3.01794
$260$	0	0
$261$	2387.79	0.566286
$262$	−3841.75	−0.905894
$263$	−66.3098	−0.0155469	−0.00777346	−	0.999970i	$-0.502474\pi$
$263$	−66.3098	−0.0155469	−0.00777346	+	0.999970i	$0.502474\pi$
$264$	−2061.50	−0.480592
$265$	−363.189	−0.0841907
$266$	2672.19	0.615949
$267$	4453.16	1.02071
$268$	3221.24	0.734211
$269$	3128.48	0.709096	0.354548	−	0.935038i	$-0.384635\pi$
$269$	3128.48	0.709096	0.354548	+	0.935038i	$0.384635\pi$
$270$	−52.6890	−0.0118761
$271$	1260.57	0.282561	0.141280	−	0.989970i	$-0.454878\pi$
$271$	1260.57	0.282561	0.141280	+	0.989970i	$0.454878\pi$
$272$	−132.426	−0.0295202
$273$	0	0
$274$	2637.60	0.581544
$275$	−3925.68	−0.860826
$276$	2473.09	0.539357
$277$	−1534.66	−0.332884	−0.166442	−	0.986051i	$-0.553228\pi$
$277$	−1534.66	−0.332884	−0.166442	+	0.986051i	$0.553228\pi$
$278$	2026.32	0.437161
$279$	512.317	0.109934
$280$	739.034	0.157735
$281$	−652.474	−0.138517	−0.0692586	−	0.997599i	$-0.522063\pi$
$281$	−652.474	−0.138517	−0.0692586	+	0.997599i	$0.522063\pi$
$282$	−550.721	−0.116294
$283$	922.235	0.193714	0.0968572	−	0.995298i	$-0.469121\pi$
$283$	922.235	0.193714	0.0968572	+	0.995298i	$0.469121\pi$
$284$	4458.19	0.931496
$285$	212.207	0.0441054
$286$	0	0
$287$	−5352.16	−1.10079
$288$	−1676.54	−0.343024
$289$	−4653.91	−0.947264
$290$	517.739	0.104837
$291$	464.986	0.0936700
$292$	−1793.47	−0.359434
$293$	−5570.98	−1.11078	−0.555392	−	0.831588i	$-0.687432\pi$
$293$	−5570.98	−1.11078	−0.555392	+	0.831588i	$0.687432\pi$
$294$	2211.67	0.438732
$295$	620.686	0.122501
$296$	−9620.10	−1.88904
$297$	−857.972	−0.167625
$298$	745.923	0.145000
$299$	0	0
$300$	−1998.72	−0.384653
$301$	3753.82	0.718825
$302$	−1236.92	−0.235685
$303$	5890.45	1.11682
$304$	481.509	0.0908435
$305$	−749.209	−0.140654
$306$	233.909	0.0436983
$307$	7069.91	1.31434	0.657168	−	0.753744i	$-0.271754\pi$
$307$	7069.91	1.31434	0.657168	+	0.753744i	$0.271754\pi$
$308$	4845.81	0.896480
$309$	4862.24	0.895156
$310$	111.084	0.0203521
$311$	−6857.82	−1.25039	−0.625195	−	0.780468i	$-0.714981\pi$
$311$	−6857.82	−1.25039	−0.625195	+	0.780468i	$0.714981\pi$
$312$	0	0
$313$	3820.23	0.689879	0.344940	−	0.938625i	$-0.387899\pi$
$313$	3820.23	0.689879	0.344940	+	0.938625i	$0.387899\pi$
$314$	5528.53	0.993609
$315$	307.578	0.0550160
$316$	−3665.15	−0.652471
$317$	−6324.21	−1.12051	−0.560257	−	0.828319i	$-0.689298\pi$
$317$	−6324.21	−1.12051	−0.560257	+	0.828319i	$0.689298\pi$
$318$	1455.63	0.256691
$319$	8430.70	1.47971
$320$	−283.974	−0.0496082
$321$	−963.379	−0.167510
$322$	6979.16	1.20787
$323$	−942.075	−0.162286
$324$	−436.827	−0.0749018
$325$	0	0
$326$	−2780.99	−0.472469
$327$	−3915.80	−0.662215
$328$	4093.06	0.689030
$329$	3214.89	0.538731
$330$	−186.032	−0.0310325
$331$	−7928.22	−1.31654	−0.658269	−	0.752783i	$-0.728711\pi$
$331$	−7928.22	−1.31654	−0.658269	+	0.752783i	$0.728711\pi$
$332$	476.024	0.0786904
$333$	−4003.78	−0.658876
$334$	−3810.91	−0.624323
$335$	721.902	0.117737
$336$	697.911	0.113316
$337$	−9305.11	−1.50410	−0.752050	−	0.659106i	$-0.770935\pi$
$337$	−9305.11	−1.50410	−0.752050	+	0.659106i	$0.770935\pi$
$338$	0	0
$339$	3260.63	0.522398
$340$	−104.914	−0.0167345
$341$	1808.86	0.287259
$342$	−850.506	−0.134474
$343$	−3211.86	−0.505609
$344$	−2870.73	−0.449940
$345$	554.236	0.0864901
$346$	−6846.74	−1.06382
$347$	−2063.17	−0.319184	−0.159592	−	0.987183i	$-0.551018\pi$
$347$	−2063.17	−0.319184	−0.159592	+	0.987183i	$0.551018\pi$
$348$	4292.40	0.661197
$349$	−3148.44	−0.482900	−0.241450	−	0.970413i	$-0.577623\pi$
$349$	−3148.44	−0.482900	−0.241450	+	0.970413i	$0.577623\pi$
$350$	−5640.46	−0.861414
$351$	0	0
$352$	−5919.44	−0.896328
$353$	−4543.87	−0.685116	−0.342558	−	0.939497i	$-0.611293\pi$
$353$	−4543.87	−0.685116	−0.342558	+	0.939497i	$0.611293\pi$
$354$	−2487.65	−0.373495
$355$	999.111	0.149373
$356$	8005.19	1.19178
$357$	−1365.47	−0.202432
$358$	234.714	0.0346509
$359$	−21.5084	−0.00316204	−0.00158102	−	0.999999i	$-0.500503\pi$
$359$	−21.5084	−0.00316204	−0.00158102	+	0.999999i	$0.500503\pi$
$360$	−235.220	−0.0344366
$361$	−3433.56	−0.500591
$362$	−2337.03	−0.339314
$363$	963.714	0.139344
$364$	0	0
$365$	−401.929	−0.0576381
$366$	3002.76	0.428844
$367$	−13050.8	−1.85626	−0.928129	−	0.372258i	$-0.878584\pi$
$367$	−13050.8	−1.85626	−0.928129	+	0.372258i	$0.878584\pi$
$368$	1257.59	0.178143
$369$	1703.49	0.240325
$370$	−868.128	−0.121978
$371$	−8497.39	−1.18912
$372$	920.963	0.128359
$373$	−10150.6	−1.40905	−0.704527	−	0.709677i	$-0.748841\pi$
$373$	−10150.6	−1.40905	−0.704527	+	0.709677i	$0.748841\pi$
$374$	825.873	0.114184
$375$	−901.148	−0.124094
$376$	−2458.59	−0.337213
$377$	0	0
$378$	−1232.74	−0.167739
$379$	3443.65	0.466724	0.233362	−	0.972390i	$-0.425027\pi$
$379$	3443.65	0.466724	0.233362	+	0.972390i	$0.425027\pi$
$380$	381.472	0.0514977
$381$	−3979.24	−0.535073
$382$	6091.34	0.815865
$383$	−5784.45	−0.771728	−0.385864	−	0.922556i	$-0.626097\pi$
$383$	−5784.45	−0.771728	−0.385864	+	0.922556i	$0.626097\pi$
$384$	−3332.63	−0.442884
$385$	1085.98	0.143758
$386$	7098.40	0.936008
$387$	−1194.77	−0.156934
$388$	835.879	0.109369
$389$	−2235.07	−0.291318	−0.145659	−	0.989335i	$-0.546530\pi$
$389$	−2235.07	−0.291318	−0.145659	+	0.989335i	$0.546530\pi$
$390$	0	0
$391$	−2460.49	−0.318241
$392$	9873.57	1.27217
$393$	−7137.96	−0.916189
$394$	1970.67	0.251982
$395$	−821.385	−0.104629
$396$	−1542.33	−0.195719
$397$	−3585.93	−0.453332	−0.226666	−	0.973973i	$-0.572783\pi$
$397$	−3585.93	−0.453332	−0.226666	+	0.973973i	$0.572783\pi$
$398$	−2989.38	−0.376493
$399$	4964.92	0.622949
$400$	−1016.37	−0.127046
$401$	4130.00	0.514321	0.257160	−	0.966369i	$-0.417213\pi$
$401$	4130.00	0.514321	0.257160	+	0.966369i	$0.417213\pi$
$402$	−2893.32	−0.358969
$403$	0	0
$404$	10588.9	1.30401
$405$	−97.8960	−0.0120111
$406$	12113.3	1.48072
$407$	−14136.3	−1.72165
$408$	1044.24	0.126710
$409$	−10133.6	−1.22512	−0.612558	−	0.790425i	$-0.709860\pi$
$409$	−10133.6	−1.22512	−0.612558	+	0.790425i	$0.709860\pi$
$410$	369.363	0.0444915
$411$	4900.64	0.588153
$412$	8740.57	1.04519
$413$	14521.9	1.73021
$414$	−2221.33	−0.263701
$415$	106.680	0.0126186
$416$	0	0
$417$	3764.90	0.442129
$418$	−3002.92	−0.351382
$419$	−7801.05	−0.909561	−0.454781	−	0.890604i	$-0.650282\pi$
$419$	−7801.05	−0.909561	−0.454781	+	0.890604i	$0.650282\pi$
$420$	552.915	0.0642369
$421$	−12154.2	−1.40704	−0.703518	−	0.710678i	$-0.748388\pi$
$421$	−12154.2	−1.40704	−0.703518	+	0.710678i	$0.748388\pi$
$422$	−913.728	−0.105402
$423$	−1023.24	−0.117616
$424$	6498.38	0.744314
$425$	1988.53	0.226960
$426$	−4004.35	−0.455425
$427$	−17528.9	−1.98662
$428$	−1731.81	−0.195585
$429$	0	0
$430$	−259.058	−0.0290532
$431$	−13124.4	−1.46678	−0.733390	−	0.679808i	$-0.762063\pi$
$431$	−13124.4	−1.46678	−0.733390	+	0.679808i	$0.762063\pi$
$432$	−222.131	−0.0247391
$433$	−4457.79	−0.494752	−0.247376	−	0.968920i	$-0.579568\pi$
$433$	−4457.79	−0.494752	−0.247376	+	0.968920i	$0.579568\pi$
$434$	2598.99	0.287456
$435$	961.956	0.106028
$436$	−7039.21	−0.773204
$437$	8946.48	0.979332
$438$	1610.89	0.175734
$439$	−4830.11	−0.525122	−0.262561	−	0.964915i	$-0.584567\pi$
$439$	−4830.11	−0.525122	−0.262561	+	0.964915i	$0.584567\pi$
$440$	−830.503	−0.0899834
$441$	4109.27	0.443718
$442$	0	0
$443$	9154.26	0.981788	0.490894	−	0.871219i	$-0.336670\pi$
$443$	9154.26	0.981788	0.490894	+	0.871219i	$0.336670\pi$
$444$	−7197.36	−0.769305
$445$	1794.02	0.191112
$446$	1733.78	0.184074
$447$	1385.92	0.146648
$448$	−6644.02	−0.700671
$449$	2576.20	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$449$	2576.20	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$450$	1795.25	0.188064
$451$	6014.59	0.627973
$452$	5861.44	0.609954
$453$	−2298.19	−0.238363
$454$	−9294.28	−0.960797
$455$	0	0
$456$	−3796.92	−0.389928
$457$	1489.35	0.152448	0.0762240	−	0.997091i	$-0.475714\pi$
$457$	1489.35	0.152448	0.0762240	+	0.997091i	$0.475714\pi$
$458$	4161.42	0.424565
$459$	434.601	0.0441949
$460$	996.319	0.100986
$461$	−13869.1	−1.40118	−0.700592	−	0.713562i	$-0.747081\pi$
$461$	−13869.1	−1.40118	−0.700592	+	0.713562i	$0.747081\pi$
$462$	−4352.51	−0.438305
$463$	10538.6	1.05782	0.528908	−	0.848679i	$-0.322602\pi$
$463$	10538.6	1.05782	0.528908	+	0.848679i	$0.322602\pi$
$464$	2182.73	0.218385
$465$	206.394	0.0205834
$466$	561.196	0.0557873
$467$	12356.9	1.22443	0.612214	−	0.790692i	$-0.290279\pi$
$467$	12356.9	1.22443	0.612214	+	0.790692i	$0.290279\pi$
$468$	0	0
$469$	16890.1	1.66292
$470$	−221.866	−0.0217742
$471$	10272.0	1.00490
$472$	−11105.6	−1.08301
$473$	−4218.42	−0.410070
$474$	3292.04	0.319005
$475$	−7230.42	−0.698430
$476$	−2454.62	−0.236360
$477$	2704.55	0.259608
$478$	3554.39	0.340113
$479$	−4204.24	−0.401037	−0.200518	−	0.979690i	$-0.564263\pi$
$479$	−4204.24	−0.401037	−0.200518	+	0.979690i	$0.564263\pi$
$480$	−675.418	−0.0642260
$481$	0	0
$482$	1129.54	0.106741
$483$	12967.2	1.22159
$484$	1732.41	0.162699
$485$	187.326	0.0175382
$486$	392.358	0.0366209
$487$	12581.8	1.17071	0.585355	−	0.810777i	$-0.300955\pi$
$487$	12581.8	1.17071	0.585355	+	0.810777i	$0.300955\pi$
$488$	13405.3	1.24350
$489$	−5167.07	−0.477838
$490$	891.002	0.0821457
$491$	3085.05	0.283557	0.141778	−	0.989898i	$-0.454718\pi$
$491$	3085.05	0.283557	0.141778	+	0.989898i	$0.454718\pi$
$492$	3062.26	0.280605
$493$	−4270.53	−0.390131
$494$	0	0
$495$	−345.646	−0.0313851
$496$	468.319	0.0423955
$497$	23375.8	2.10975
$498$	−427.565	−0.0384732
$499$	6275.13	0.562953	0.281477	−	0.959568i	$-0.409176\pi$
$499$	6275.13	0.562953	0.281477	+	0.959568i	$0.409176\pi$
$500$	−1619.94	−0.144892
$501$	−7080.66	−0.631418
$502$	−9741.83	−0.866133
$503$	−17843.6	−1.58173	−0.790863	−	0.611994i	$-0.790368\pi$
$503$	−17843.6	−1.58173	−0.790863	+	0.611994i	$0.790368\pi$
$504$	−5503.35	−0.486386
$505$	2373.05	0.209108
$506$	−7842.96	−0.689055
$507$	0	0
$508$	−7153.26	−0.624753
$509$	−10033.0	−0.873684	−0.436842	−	0.899538i	$-0.643903\pi$
$509$	−10033.0	−0.873684	−0.436842	+	0.899538i	$0.643903\pi$
$510$	94.2334	0.00818182
$511$	−9403.77	−0.814086
$512$	−2955.83	−0.255138
$513$	−1580.24	−0.136002
$514$	5653.66	0.485160
$515$	1958.82	0.167604
$516$	−2147.76	−0.183236
$517$	−3612.79	−0.307332
$518$	−20311.2	−1.72283
$519$	−12721.2	−1.07591
$520$	0	0
$521$	−2406.44	−0.202357	−0.101179	−	0.994868i	$-0.532261\pi$
$521$	−2406.44	−0.202357	−0.101179	+	0.994868i	$0.532261\pi$
$522$	−3855.43	−0.323271
$523$	1987.60	0.166179	0.0830895	−	0.996542i	$-0.473521\pi$
$523$	1987.60	0.166179	0.0830895	+	0.996542i	$0.473521\pi$
$524$	−12831.5	−1.06975
$525$	−10479.9	−0.871204
$526$	107.067	0.00887515
$527$	−916.270	−0.0757369
$528$	−784.290	−0.0646436
$529$	11199.2	0.920455
$530$	586.421	0.0480613
$531$	−4622.05	−0.377740
$532$	8925.15	0.727358
$533$	0	0
$534$	−7190.27	−0.582684
$535$	−388.111	−0.0313635
$536$	−12916.7	−1.04089
$537$	436.097	0.0350447
$538$	−5051.38	−0.404797
$539$	14508.8	1.15944
$540$	−175.982	−0.0140242
$541$	−9255.22	−0.735514	−0.367757	−	0.929922i	$-0.619874\pi$
$541$	−9255.22	−0.735514	−0.367757	+	0.929922i	$0.619874\pi$
$542$	−2035.37	−0.161303
$543$	−4342.19	−0.343170
$544$	2998.46	0.236320
$545$	−1577.54	−0.123989
$546$	0	0
$547$	−7539.31	−0.589319	−0.294660	−	0.955602i	$-0.595206\pi$
$547$	−7539.31	−0.589319	−0.294660	+	0.955602i	$0.595206\pi$
$548$	8809.60	0.686729
$549$	5579.12	0.433718
$550$	6338.57	0.491414
$551$	15527.9	1.20056
$552$	−9916.70	−0.764643
$553$	−19217.6	−1.47779
$554$	2477.93	0.190031
$555$	−1612.98	−0.123364
$556$	6767.94	0.516232
$557$	−13615.2	−1.03572	−0.517860	−	0.855465i	$-0.673271\pi$
$557$	−13615.2	−1.03572	−0.517860	+	0.855465i	$0.673271\pi$
$558$	−827.209	−0.0627573
$559$	0	0
$560$	281.163	0.0212166
$561$	1534.47	0.115482
$562$	1053.51	0.0790743
$563$	−4751.68	−0.355700	−0.177850	−	0.984058i	$-0.556914\pi$
$563$	−4751.68	−0.355700	−0.177850	+	0.984058i	$0.556914\pi$
$564$	−1839.41	−0.137329
$565$	1313.59	0.0978109
$566$	−1489.08	−0.110584
$567$	−2290.43	−0.169646
$568$	−17876.6	−1.32058
$569$	17296.9	1.27438	0.637191	−	0.770706i	$-0.280096\pi$
$569$	17296.9	1.27438	0.637191	+	0.770706i	$0.280096\pi$
$570$	−342.638	−0.0251782
$571$	3685.46	0.270108	0.135054	−	0.990838i	$-0.456879\pi$
$571$	3685.46	0.270108	0.135054	+	0.990838i	$0.456879\pi$
$572$	0	0
$573$	11317.7	0.825137
$574$	8641.83	0.628402
$575$	−18884.2	−1.36961
$576$	2114.66	0.152970
$577$	10066.3	0.726287	0.363143	−	0.931733i	$-0.381704\pi$
$577$	10066.3	0.726287	0.363143	+	0.931733i	$0.381704\pi$
$578$	7514.40	0.540758
$579$	13188.8	0.946646
$580$	1729.25	0.123799
$581$	2495.95	0.178227
$582$	−750.787	−0.0534727
$583$	9549.10	0.678359
$584$	7191.53	0.509568
$585$	0	0
$586$	8995.14	0.634106
$587$	19809.2	1.39286	0.696432	−	0.717622i	$-0.254770\pi$
$587$	19809.2	1.39286	0.696432	+	0.717622i	$0.254770\pi$
$588$	7387.00	0.518086
$589$	3331.61	0.233067
$590$	−1002.19	−0.0699311
$591$	3661.49	0.254845
$592$	−3659.94	−0.254092
$593$	5085.44	0.352165	0.176082	−	0.984375i	$-0.443657\pi$
$593$	5085.44	0.352165	0.176082	+	0.984375i	$0.443657\pi$
$594$	1385.32	0.0956908
$595$	−550.097	−0.0379022
$596$	2491.39	0.171227
$597$	−5554.26	−0.380772
$598$	0	0
$599$	−20473.7	−1.39655	−0.698273	−	0.715832i	$-0.746048\pi$
$599$	−20473.7	−1.39655	−0.698273	+	0.715832i	$0.746048\pi$
$600$	8014.54	0.545320
$601$	6131.90	0.416182	0.208091	−	0.978109i	$-0.433275\pi$
$601$	6131.90	0.416182	0.208091	+	0.978109i	$0.433275\pi$
$602$	−6061.07	−0.410350
$603$	−5375.78	−0.363049
$604$	−4131.33	−0.278314
$605$	388.246	0.0260900
$606$	−9510.98	−0.637553
$607$	27464.1	1.83647	0.918233	−	0.396041i	$-0.129616\pi$
$607$	27464.1	1.83647	0.918233	+	0.396041i	$0.129616\pi$
$608$	−10902.6	−0.727234
$609$	22506.5	1.49755
$610$	1209.71	0.0802943
$611$	0	0
$612$	781.258	0.0516021
$613$	−13563.4	−0.893669	−0.446835	−	0.894617i	$-0.647449\pi$
$613$	−13563.4	−0.893669	−0.446835	+	0.894617i	$0.647449\pi$
$614$	−11415.4	−0.750305
$615$	686.274	0.0449971
$616$	−19431.0	−1.27093
$617$	−4983.73	−0.325182	−0.162591	−	0.986694i	$-0.551985\pi$
$617$	−4983.73	−0.325182	−0.162591	+	0.986694i	$0.551985\pi$
$618$	−7850.78	−0.511011
$619$	−10088.7	−0.655085	−0.327543	−	0.944836i	$-0.606221\pi$
$619$	−10088.7	−0.655085	−0.327543	+	0.944836i	$0.606221\pi$
$620$	371.023	0.0240333
$621$	−4127.22	−0.266698
$622$	11072.9	0.713801
$623$	41973.9	2.69928
$624$	0	0
$625$	15079.4	0.965080
$626$	−6168.31	−0.393826
$627$	−5579.42	−0.355376
$628$	18465.4	1.17333
$629$	7160.69	0.453919
$630$	−496.628	−0.0314066
$631$	6909.71	0.435929	0.217964	−	0.975957i	$-0.430058\pi$
$631$	6909.71	0.435929	0.217964	+	0.975957i	$0.430058\pi$
$632$	14696.7	0.925004
$633$	−1697.70	−0.106600
$634$	10211.3	0.639660
$635$	−1603.10	−0.100184
$636$	4861.82	0.303119
$637$	0	0
$638$	−13612.6	−0.844713
$639$	−7440.06	−0.460601
$640$	−1342.60	−0.0829232
$641$	24827.6	1.52984	0.764922	−	0.644123i	$-0.222778\pi$
$641$	24827.6	1.52984	0.764922	+	0.644123i	$0.222778\pi$
$642$	1555.51	0.0956250
$643$	9712.36	0.595674	0.297837	−	0.954617i	$-0.403735\pi$
$643$	9712.36	0.595674	0.297837	+	0.954617i	$0.403735\pi$
$644$	23310.5	1.42634
$645$	−481.329	−0.0293834
$646$	1521.12	0.0926432
$647$	422.401	0.0256666	0.0128333	−	0.999918i	$-0.495915\pi$
$647$	422.401	0.0256666	0.0128333	+	0.999918i	$0.495915\pi$
$648$	1751.61	0.106188
$649$	−16319.3	−0.987039
$650$	0	0
$651$	4828.92	0.290722
$652$	−9288.54	−0.557925
$653$	−5691.05	−0.341053	−0.170527	−	0.985353i	$-0.554547\pi$
$653$	−5691.05	−0.341053	−0.170527	+	0.985353i	$0.554547\pi$
$654$	6322.62	0.378034
$655$	−2875.63	−0.171542
$656$	1557.19	0.0926802
$657$	2993.04	0.177731
$658$	−5190.90	−0.307542
$659$	−11497.8	−0.679655	−0.339827	−	0.940488i	$-0.610369\pi$
$659$	−11497.8	−0.679655	−0.339827	+	0.940488i	$0.610369\pi$
$660$	−621.348	−0.0366454
$661$	22058.8	1.29802	0.649008	−	0.760781i	$-0.275184\pi$
$661$	22058.8	1.29802	0.649008	+	0.760781i	$0.275184\pi$
$662$	12801.2	0.751562
$663$	0	0
$664$	−1908.78	−0.111559
$665$	2000.19	0.116638
$666$	6464.67	0.376128
$667$	40555.3	2.35429
$668$	−12728.5	−0.737246
$669$	3221.36	0.186166
$670$	−1165.61	−0.0672114
$671$	19698.5	1.13331
$672$	−15802.5	−0.907133
$673$	−4767.64	−0.273074	−0.136537	−	0.990635i	$-0.543597\pi$
$673$	−4767.64	−0.273074	−0.136537	+	0.990635i	$0.543597\pi$
$674$	15024.4	0.858634
$675$	3335.56	0.190201
$676$	0	0
$677$	−14024.5	−0.796165	−0.398082	−	0.917350i	$-0.630324\pi$
$677$	−14024.5	−0.796165	−0.398082	+	0.917350i	$0.630324\pi$
$678$	−5264.75	−0.298218
$679$	4382.80	0.247712
$680$	420.687	0.0237244
$681$	−17268.7	−0.971717
$682$	−2920.67	−0.163986
$683$	4652.81	0.260666	0.130333	−	0.991470i	$-0.458395\pi$
$683$	4652.81	0.260666	0.130333	+	0.991470i	$0.458395\pi$
$684$	−2840.70	−0.158797
$685$	1974.29	0.110122
$686$	5186.00	0.288633
$687$	7731.91	0.429390
$688$	−1092.16	−0.0605207
$689$	0	0
$690$	−894.894	−0.0493740
$691$	10978.9	0.604426	0.302213	−	0.953240i	$-0.402275\pi$
$691$	10978.9	0.604426	0.302213	+	0.953240i	$0.402275\pi$
$692$	−22868.2	−1.25624
$693$	−8086.95	−0.443287
$694$	3331.28	0.182210
$695$	1516.74	0.0827818
$696$	−17211.8	−0.937375
$697$	−3046.66	−0.165567
$698$	5083.60	0.275669
$699$	1042.70	0.0564213
$700$	−18839.2	−1.01722
$701$	−4451.47	−0.239843	−0.119921	−	0.992783i	$-0.538264\pi$
$701$	−4451.47	−0.239843	−0.119921	+	0.992783i	$0.538264\pi$
$702$	0	0
$703$	−26036.7	−1.39686
$704$	7466.35	0.399714
$705$	−412.225	−0.0220217
$706$	7336.74	0.391107
$707$	55521.3	2.95346
$708$	−8308.79	−0.441050
$709$	18370.9	0.973107	0.486554	−	0.873651i	$-0.338254\pi$
$709$	18370.9	0.973107	0.486554	+	0.873651i	$0.338254\pi$
$710$	−1613.21	−0.0852713
$711$	6116.59	0.322630
$712$	−32099.6	−1.68958
$713$	8701.42	0.457042
$714$	2204.74	0.115561
$715$	0	0
$716$	783.947	0.0409183
$717$	6604.04	0.343978
$718$	34.7284	0.00180509
$719$	−31594.0	−1.63874	−0.819372	−	0.573263i	$-0.805677\pi$
$719$	−31594.0	−1.63874	−0.819372	+	0.573263i	$0.805677\pi$
$720$	−89.4887	−0.00463201
$721$	45829.8	2.36725
$722$	5543.97	0.285769
$723$	2098.68	0.107954
$724$	−7805.71	−0.400687
$725$	−32776.2	−1.67901
$726$	−1556.05	−0.0795463
$727$	−21370.5	−1.09022	−0.545109	−	0.838365i	$-0.683512\pi$
$727$	−21370.5	−1.09022	−0.545109	+	0.838365i	$0.683512\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	648.972	0.0329035
$731$	2136.82	0.108116
$732$	10029.3	0.506410
$733$	−13371.4	−0.673785	−0.336893	−	0.941543i	$-0.609376\pi$
$733$	−13371.4	−0.673785	−0.336893	+	0.941543i	$0.609376\pi$
$734$	21072.4	1.05967
$735$	1655.48	0.0830792
$736$	−28475.1	−1.42610
$737$	−18980.5	−0.948652
$738$	−2750.53	−0.137193
$739$	6426.29	0.319885	0.159942	−	0.987126i	$-0.448869\pi$
$739$	6426.29	0.319885	0.159942	+	0.987126i	$0.448869\pi$
$740$	−2899.56	−0.144040
$741$	0	0
$742$	13720.2	0.678822
$743$	−25071.8	−1.23795	−0.618975	−	0.785411i	$-0.712452\pi$
$743$	−25071.8	−1.23795	−0.618975	+	0.785411i	$0.712452\pi$
$744$	−3692.92	−0.181974
$745$	558.338	0.0274576
$746$	16389.6	0.804376
$747$	−794.413	−0.0389104
$748$	2758.43	0.134837
$749$	−9080.47	−0.442982
$750$	1455.03	0.0708404
$751$	5426.94	0.263691	0.131846	−	0.991270i	$-0.457910\pi$
$751$	5426.94	0.263691	0.131846	+	0.991270i	$0.457910\pi$
$752$	−935.362	−0.0453579
$753$	−18100.3	−0.875977
$754$	0	0
$755$	−925.860	−0.0446298
$756$	−4117.38	−0.198079
$757$	−2227.69	−0.106957	−0.0534786	−	0.998569i	$-0.517031\pi$
$757$	−2227.69	−0.106957	−0.0534786	+	0.998569i	$0.517031\pi$
$758$	−5560.26	−0.266435
$759$	−14572.2	−0.696886
$760$	−1529.64	−0.0730079
$761$	30769.6	1.46570	0.732851	−	0.680390i	$-0.238189\pi$
$761$	30769.6	1.46570	0.732851	+	0.680390i	$0.238189\pi$
$762$	6425.06	0.305453
$763$	−36909.0	−1.75124
$764$	20345.2	0.963432
$765$	175.085	0.00827480
$766$	9339.83	0.440551
$767$	0	0
$768$	11020.1	0.517779
$769$	1346.49	0.0631415	0.0315707	−	0.999502i	$-0.489949\pi$
$769$	1346.49	0.0631415	0.0315707	+	0.999502i	$0.489949\pi$
$770$	−1753.47	−0.0820658
$771$	10504.5	0.490674
$772$	23708.8	1.10531
$773$	−18487.6	−0.860226	−0.430113	−	0.902775i	$-0.641526\pi$
$773$	−18487.6	−0.860226	−0.430113	+	0.902775i	$0.641526\pi$
$774$	1929.12	0.0895877
$775$	−7032.36	−0.325948
$776$	−3351.75	−0.155052
$777$	−37738.2	−1.74241
$778$	3608.84	0.166302
$779$	11077.8	0.509505
$780$	0	0
$781$	−26269.0	−1.20356
$782$	3972.81	0.181672
$783$	−7163.38	−0.326945
$784$	3756.37	0.171117
$785$	4138.22	0.188152
$786$	11525.3	0.523018
$787$	−1388.74	−0.0629010	−0.0314505	−	0.999505i	$-0.510013\pi$
$787$	−1388.74	−0.0629010	−0.0314505	+	0.999505i	$0.510013\pi$
$788$	6582.05	0.297558
$789$	198.929	0.00897601
$790$	1326.24	0.0597287
$791$	30733.5	1.38149
$792$	6184.49	0.277470
$793$	0	0
$794$	5790.00	0.258790
$795$	1089.57	0.0486075
$796$	−9984.57	−0.444590
$797$	27516.6	1.22295	0.611473	−	0.791265i	$-0.290577\pi$
$797$	27516.6	1.22295	0.611473	+	0.791265i	$0.290577\pi$
$798$	−8016.57	−0.355619
$799$	1830.04	0.0810290
$800$	23013.2	1.01705
$801$	−13359.5	−0.589306
$802$	−6668.48	−0.293606
$803$	10567.7	0.464414
$804$	−9663.72	−0.423897
$805$	5224.04	0.228724
$806$	0	0
$807$	−9385.45	−0.409397
$808$	−42459.9	−1.84868
$809$	31550.8	1.37116	0.685580	−	0.727998i	$-0.259549\pi$
$809$	31550.8	1.37116	0.685580	+	0.727998i	$0.259549\pi$
$810$	158.067	0.00685668
$811$	16536.1	0.715980	0.357990	−	0.933725i	$-0.383462\pi$
$811$	16536.1	0.715980	0.357990	+	0.933725i	$0.383462\pi$
$812$	40458.6	1.74855
$813$	−3781.70	−0.163137
$814$	22825.1	0.982826
$815$	−2081.63	−0.0894677
$816$	397.278	0.0170435
$817$	−7769.61	−0.332710
$818$	16362.1	0.699373
$819$	0	0
$820$	1233.68	0.0525388
$821$	3643.64	0.154889	0.0774445	−	0.996997i	$-0.475324\pi$
$821$	3643.64	0.154889	0.0774445	+	0.996997i	$0.475324\pi$
$822$	−7912.79	−0.335755
$823$	−26439.9	−1.11985	−0.559925	−	0.828543i	$-0.689170\pi$
$823$	−26439.9	−1.11985	−0.559925	+	0.828543i	$0.689170\pi$
$824$	−35048.3	−1.48175
$825$	11777.0	0.496998
$826$	−23447.7	−0.987713
$827$	−13793.7	−0.579995	−0.289997	−	0.957027i	$-0.593654\pi$
$827$	−13793.7	−0.579995	−0.289997	+	0.957027i	$0.593654\pi$
$828$	−7419.27	−0.311398
$829$	−34019.6	−1.42527	−0.712636	−	0.701534i	$-0.752499\pi$
$829$	−34019.6	−1.42527	−0.712636	+	0.701534i	$0.752499\pi$
$830$	−172.251	−0.00720350
$831$	4603.98	0.192190
$832$	0	0
$833$	−7349.36	−0.305691
$834$	−6078.97	−0.252395
$835$	−2852.54	−0.118223
$836$	−10029.8	−0.414938
$837$	−1536.95	−0.0634705
$838$	12595.9	0.519234
$839$	26565.2	1.09312	0.546562	−	0.837418i	$-0.315936\pi$
$839$	26565.2	1.09312	0.546562	+	0.837418i	$0.315936\pi$
$840$	−2217.10	−0.0910682
$841$	46000.5	1.88612
$842$	19624.8	0.803224
$843$	1957.42	0.0799729
$844$	−3051.86	−0.124466
$845$	0	0
$846$	1652.16	0.0671424
$847$	9083.63	0.368497
$848$	2472.29	0.100116
$849$	−2766.70	−0.111841
$850$	−3210.77	−0.129563
$851$	−68001.9	−2.73922
$852$	−13374.6	−0.537799
$853$	−15220.2	−0.610939	−0.305470	−	0.952202i	$-0.598813\pi$
$853$	−15220.2	−0.610939	−0.305470	+	0.952202i	$0.598813\pi$
$854$	28303.0	1.13408
$855$	−636.621	−0.0254643
$856$	6944.29	0.277279
$857$	39559.1	1.57680	0.788398	−	0.615165i	$-0.210911\pi$
$857$	39559.1	1.57680	0.788398	+	0.615165i	$0.210911\pi$
$858$	0	0
$859$	41510.0	1.64878	0.824390	−	0.566022i	$-0.191518\pi$
$859$	41510.0	1.64878	0.824390	+	0.566022i	$0.191518\pi$
$860$	−865.257	−0.0343082
$861$	16056.5	0.635544
$862$	21191.3	0.837330
$863$	34778.6	1.37182	0.685908	−	0.727688i	$-0.259405\pi$
$863$	34778.6	1.37182	0.685908	+	0.727688i	$0.259405\pi$
$864$	5029.62	0.198045
$865$	−5124.92	−0.201448
$866$	7197.74	0.282435
$867$	13961.7	0.546903
$868$	8680.67	0.339448
$869$	21596.2	0.843037
$870$	−1553.22	−0.0605275
$871$	0	0
$872$	28226.1	1.09617
$873$	−1394.96	−0.0540804
$874$	−14445.4	−0.559064
$875$	−8493.91	−0.328167
$876$	5380.41	0.207520
$877$	−28204.1	−1.08596	−0.542979	−	0.839746i	$-0.682704\pi$
$877$	−28204.1	−1.08596	−0.542979	+	0.839746i	$0.682704\pi$
$878$	7798.90	0.299772
$879$	16712.9	0.641312
$880$	−315.962	−0.0121035
$881$	−1006.27	−0.0384813	−0.0192406	−	0.999815i	$-0.506125\pi$
$881$	−1006.27	−0.0384813	−0.0192406	+	0.999815i	$0.506125\pi$
$882$	−6635.01	−0.253302
$883$	20823.5	0.793620	0.396810	−	0.917901i	$-0.370117\pi$
$883$	20823.5	0.793620	0.396810	+	0.917901i	$0.370117\pi$
$884$	0	0
$885$	−1862.06	−0.0707258
$886$	−14780.9	−0.560466
$887$	17301.0	0.654917	0.327458	−	0.944866i	$-0.393808\pi$
$887$	17301.0	0.654917	0.327458	+	0.944866i	$0.393808\pi$
$888$	28860.3	1.09064
$889$	−37507.0	−1.41501
$890$	−2896.70	−0.109098
$891$	2573.92	0.0967783
$892$	5790.85	0.217368
$893$	−6654.14	−0.249353
$894$	−2237.77	−0.0837161
$895$	175.688	0.00656156
$896$	−31412.2	−1.17121
$897$	0	0
$898$	−4159.64	−0.154576
$899$	15102.6	0.560287
$900$	5996.15	0.222079
$901$	−4837.04	−0.178852
$902$	−9711.42	−0.358486
$903$	−11261.5	−0.415014
$904$	−23503.5	−0.864728
$905$	−1749.31	−0.0642532
$906$	3710.76	0.136073
$907$	1878.58	0.0687732	0.0343866	−	0.999409i	$-0.489052\pi$
$907$	1878.58	0.0687732	0.0343866	+	0.999409i	$0.489052\pi$
$908$	−31043.0	−1.13458
$909$	−17671.4	−0.644799
$910$	0	0
$911$	−29940.8	−1.08890	−0.544448	−	0.838795i	$-0.683261\pi$
$911$	−29940.8	−1.08890	−0.544448	+	0.838795i	$0.683261\pi$
$912$	−1444.53	−0.0524485
$913$	−2804.88	−0.101673
$914$	−2404.77	−0.0870269
$915$	2247.63	0.0812069
$916$	13899.2	0.501357
$917$	−67279.9	−2.42288
$918$	−701.726	−0.0252292
$919$	10648.8	0.382233	0.191116	−	0.981567i	$-0.438789\pi$
$919$	10648.8	0.382233	0.191116	+	0.981567i	$0.438789\pi$
$920$	−3995.08	−0.143167
$921$	−21209.7	−0.758832
$922$	22393.6	0.799884
$923$	0	0
$924$	−14537.4	−0.517583
$925$	54958.2	1.95353
$926$	−17016.0	−0.603867
$927$	−14586.7	−0.516818
$928$	−49422.6	−1.74825
$929$	22670.9	0.800654	0.400327	−	0.916372i	$-0.368897\pi$
$929$	22670.9	0.800654	0.400327	+	0.916372i	$0.368897\pi$
$930$	−333.253	−0.0117503
$931$	26722.7	0.940711
$932$	1874.40	0.0658777
$933$	20573.5	0.721913
$934$	−19952.0	−0.698980
$935$	618.182	0.0216222
$936$	0	0
$937$	−18160.3	−0.633161	−0.316580	−	0.948566i	$-0.602535\pi$
$937$	−18160.3	−0.633161	−0.316580	+	0.948566i	$0.602535\pi$
$938$	−27271.4	−0.949300
$939$	−11460.7	−0.398302
$940$	−741.034	−0.0257126
$941$	17564.9	0.608503	0.304251	−	0.952592i	$-0.401594\pi$
$941$	17564.9	0.608503	0.304251	+	0.952592i	$0.401594\pi$
$942$	−16585.6	−0.573660
$943$	28932.8	0.999132
$944$	−4225.11	−0.145673
$945$	−922.733	−0.0317635
$946$	6811.25	0.234094
$947$	−40490.9	−1.38942	−0.694708	−	0.719292i	$-0.744467\pi$
$947$	−40490.9	−1.38942	−0.694708	+	0.719292i	$0.744467\pi$
$948$	10995.4	0.376704
$949$	0	0
$950$	11674.5	0.398708
$951$	18972.6	0.646930
$952$	9842.65	0.335086
$953$	−11971.4	−0.406917	−0.203458	−	0.979084i	$-0.565218\pi$
$953$	−11971.4	−0.406917	−0.203458	+	0.979084i	$0.565218\pi$
$954$	−4366.89	−0.148200
$955$	4559.49	0.154494
$956$	11871.7	0.401630
$957$	−25292.1	−0.854313
$958$	6788.35	0.228937
$959$	46191.7	1.55538
$960$	851.922	0.0286413
$961$	−26550.6	−0.891230
$962$	0	0
$963$	2890.14	0.0967117
$964$	3772.68	0.126048
$965$	5313.30	0.177245
$966$	−20937.5	−0.697362
$967$	341.617	0.0113605	0.00568027	−	0.999984i	$-0.498192\pi$
$967$	341.617	0.0113605	0.00568027	+	0.999984i	$0.498192\pi$
$968$	−6946.71	−0.230657
$969$	2826.23	0.0936960
$970$	−302.465	−0.0100119
$971$	−2743.85	−0.0906843	−0.0453422	−	0.998972i	$-0.514438\pi$
$971$	−2743.85	−0.0906843	−0.0453422	+	0.998972i	$0.514438\pi$
$972$	1310.48	0.0432446
$973$	35486.6	1.16922
$974$	−20315.1	−0.668314
$975$	0	0
$976$	5099.99	0.167261
$977$	19743.5	0.646520	0.323260	−	0.946310i	$-0.395221\pi$
$977$	19743.5	0.646520	0.323260	+	0.946310i	$0.395221\pi$
$978$	8342.97	0.272780
$979$	−47169.0	−1.53986
$980$	2975.96	0.0970035
$981$	11747.4	0.382330
$982$	−4981.26	−0.161872
$983$	−17848.8	−0.579135	−0.289567	−	0.957158i	$-0.593511\pi$
$983$	−17848.8	−0.579135	−0.289567	+	0.957158i	$0.593511\pi$
$984$	−12279.2	−0.397811
$985$	1475.08	0.0477158
$986$	6895.37	0.222711
$987$	−9644.67	−0.311037
$988$	0	0
$989$	−20292.4	−0.652439
$990$	558.095	0.0179166
$991$	38391.0	1.23061	0.615303	−	0.788291i	$-0.289034\pi$
$991$	38391.0	1.23061	0.615303	+	0.788291i	$0.289034\pi$
$992$	−10603.9	−0.339391
$993$	23784.6	0.760104
$994$	−37743.6	−1.20438
$995$	−2237.61	−0.0712935
$996$	−1428.07	−0.0454319
$997$	−7060.87	−0.224293	−0.112146	−	0.993692i	$-0.535773\pi$
$997$	−7060.87	−0.224293	−0.112146	+	0.993692i	$0.535773\pi$
$998$	−10132.1	−0.321369
$999$	12011.3	0.380402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.n.1.5	✓	9
3.2	odd	2		1521.4.a.bj.1.5		9
13.5	odd	4		507.4.b.j.337.11		18
13.8	odd	4		507.4.b.j.337.8		18
13.12	even	2		507.4.a.q.1.5	yes	9
39.38	odd	2		1521.4.a.be.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.4.a.n.1.5	✓	9	1.1	even	1	trivial
507.4.a.q.1.5	yes	9	13.12	even	2
507.4.b.j.337.8		18	13.8	odd	4
507.4.b.j.337.11		18	13.5	odd	4
1521.4.a.be.1.5		9	39.38	odd	2
1521.4.a.bj.1.5		9	3.2	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61464 q^{2} -3.00000 q^{3} -5.39293 q^{4} -1.20859 q^{5} +4.84393 q^{6} -28.2769 q^{7} +21.6248 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.61464 q^{2} -3.00000 q^{3} -5.39293 q^{4} -1.20859 q^{5} +4.84393 q^{6} -28.2769 q^{7} +21.6248 q^{8} +9.00000 q^{9} +1.95145 q^{10} +31.7768 q^{11} +16.1788 q^{12} +45.6572 q^{14} +3.62578 q^{15} +8.22709 q^{16} -16.0963 q^{17} -14.5318 q^{18} +58.5273 q^{19} +6.51785 q^{20} +84.8308 q^{21} -51.3081 q^{22} +152.860 q^{23} -64.8744 q^{24} -123.539 q^{25} -27.0000 q^{27} +152.496 q^{28} +265.310 q^{29} -5.85434 q^{30} +56.9241 q^{31} -186.282 q^{32} -95.3303 q^{33} +25.9899 q^{34} +34.1753 q^{35} -48.5363 q^{36} -444.864 q^{37} -94.5007 q^{38} -26.1356 q^{40} +189.276 q^{41} -136.972 q^{42} -132.752 q^{43} -171.370 q^{44} -10.8773 q^{45} -246.814 q^{46} -113.693 q^{47} -24.6813 q^{48} +456.586 q^{49} +199.472 q^{50} +48.2890 q^{51} +300.506 q^{53} +43.5954 q^{54} -38.4051 q^{55} -611.483 q^{56} -175.582 q^{57} -428.381 q^{58} -513.561 q^{59} -19.5536 q^{60} +619.902 q^{61} -91.9121 q^{62} -254.493 q^{63} +234.963 q^{64} +153.924 q^{66} -597.308 q^{67} +86.8064 q^{68} -458.580 q^{69} -55.1809 q^{70} -826.673 q^{71} +194.623 q^{72} +332.560 q^{73} +718.297 q^{74} +370.618 q^{75} -315.633 q^{76} -898.549 q^{77} +679.621 q^{79} -9.94319 q^{80} +81.0000 q^{81} -305.614 q^{82} -88.2682 q^{83} -457.487 q^{84} +19.4539 q^{85} +214.347 q^{86} -795.931 q^{87} +687.166 q^{88} -1484.39 q^{89} +17.5630 q^{90} -824.363 q^{92} -170.772 q^{93} +183.574 q^{94} -70.7356 q^{95} +558.847 q^{96} -154.995 q^{97} -737.223 q^{98} +285.991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9	\( 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9} + 198 q^{10} - 37 q^{11} - 96 q^{12} + 98 q^{14} + 123 q^{15} + 32 q^{16} - 134 q^{17} - 72 q^{18} + 72 q^{19} - 356 q^{20} + 3 q^{21} + 274 q^{22} + 226 q^{23} + 333 q^{24} + 612 q^{25} - 243 q^{27} - 132 q^{28} - 547 q^{29} - 594 q^{30} + 521 q^{31} - 721 q^{32} + 111 q^{33} + 100 q^{34} + 138 q^{35} + 288 q^{36} - 584 q^{37} - 416 q^{38} + 1342 q^{40} - 482 q^{41} - 294 q^{42} + 158 q^{43} - 1453 q^{44} - 369 q^{45} - 1537 q^{46} - 1500 q^{47} - 96 q^{48} + 642 q^{49} - 2777 q^{50} + 402 q^{51} + 1399 q^{53} + 216 q^{54} - 1408 q^{55} - 616 q^{56} - 216 q^{57} - 1455 q^{58} - 1541 q^{59} + 1068 q^{60} + 2092 q^{61} - 293 q^{62} - 9 q^{63} + 2481 q^{64} - 822 q^{66} - 252 q^{67} - 1579 q^{68} - 678 q^{69} - 2492 q^{70} - 2352 q^{71} - 999 q^{72} - 903 q^{73} + 1037 q^{74} - 1836 q^{75} + 485 q^{76} - 1686 q^{77} - 115 q^{79} - 5701 q^{80} + 729 q^{81} - 5147 q^{82} - 1207 q^{83} + 396 q^{84} - 4308 q^{85} - 5691 q^{86} + 1641 q^{87} - 484 q^{88} - 2336 q^{89} + 1782 q^{90} + 2087 q^{92} - 1563 q^{93} - 468 q^{94} - 222 q^{95} + 2163 q^{96} - 2155 q^{97} - 5593 q^{98} - 333 q^{99}+O(q^{100}) \) 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9 + 198 * q^10 - 37 * q^11 - 96 * q^12 + 98 * q^14 + 123 * q^15 + 32 * q^16 - 134 * q^17 - 72 * q^18 + 72 * q^19 - 356 * q^20 + 3 * q^21 + 274 * q^22 + 226 * q^23 + 333 * q^24 + 612 * q^25 - 243 * q^27 - 132 * q^28 - 547 * q^29 - 594 * q^30 + 521 * q^31 - 721 * q^32 + 111 * q^33 + 100 * q^34 + 138 * q^35 + 288 * q^36 - 584 * q^37 - 416 * q^38 + 1342 * q^40 - 482 * q^41 - 294 * q^42 + 158 * q^43 - 1453 * q^44 - 369 * q^45 - 1537 * q^46 - 1500 * q^47 - 96 * q^48 + 642 * q^49 - 2777 * q^50 + 402 * q^51 + 1399 * q^53 + 216 * q^54 - 1408 * q^55 - 616 * q^56 - 216 * q^57 - 1455 * q^58 - 1541 * q^59 + 1068 * q^60 + 2092 * q^61 - 293 * q^62 - 9 * q^63 + 2481 * q^64 - 822 * q^66 - 252 * q^67 - 1579 * q^68 - 678 * q^69 - 2492 * q^70 - 2352 * q^71 - 999 * q^72 - 903 * q^73 + 1037 * q^74 - 1836 * q^75 + 485 * q^76 - 1686 * q^77 - 115 * q^79 - 5701 * q^80 + 729 * q^81 - 5147 * q^82 - 1207 * q^83 + 396 * q^84 - 4308 * q^85 - 5691 * q^86 + 1641 * q^87 - 484 * q^88 - 2336 * q^89 + 1782 * q^90 + 2087 * q^92 - 1563 * q^93 - 468 * q^94 - 222 * q^95 + 2163 * q^96 - 2155 * q^97 - 5593 * q^98 - 333 * q^99

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