LMFDB - Embedded newform 507.4.a.p.1.7

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:	$0$
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} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 $ x^9 - 56x^7 - 27x^6 + 945x^5 + 763x^4 - 4139x^3 - 2478x^2 + 63*x + 27
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			1.7
Root			$-4.83218$ 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)

$f(q)$	$=$	$q+4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} +8.08864 q^{5} +12.0907 q^{6} +5.95078 q^{7} +0.978887 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} +8.08864 q^{5} +12.0907 q^{6} +5.95078 q^{7} +0.978887 q^{8} +9.00000 q^{9} +32.5992 q^{10} +17.2359 q^{11} +24.7287 q^{12} +23.9831 q^{14} +24.2659 q^{15} -61.9979 q^{16} +92.9299 q^{17} +36.2722 q^{18} +13.3832 q^{19} +66.6738 q^{20} +17.8523 q^{21} +69.4648 q^{22} +219.710 q^{23} +2.93666 q^{24} -59.5738 q^{25} +27.0000 q^{27} +49.0516 q^{28} -199.485 q^{29} +97.7977 q^{30} +307.777 q^{31} -257.698 q^{32} +51.7076 q^{33} +374.531 q^{34} +48.1337 q^{35} +74.1860 q^{36} -333.777 q^{37} +53.9376 q^{38} +7.91787 q^{40} -200.689 q^{41} +71.9493 q^{42} +116.806 q^{43} +142.073 q^{44} +72.7978 q^{45} +885.487 q^{46} +338.610 q^{47} -185.994 q^{48} -307.588 q^{49} -240.097 q^{50} +278.790 q^{51} -26.6215 q^{53} +108.817 q^{54} +139.415 q^{55} +5.82514 q^{56} +40.1496 q^{57} -803.976 q^{58} -280.058 q^{59} +200.021 q^{60} -207.084 q^{61} +1240.42 q^{62} +53.5570 q^{63} -542.603 q^{64} +208.394 q^{66} -285.981 q^{67} +766.011 q^{68} +659.131 q^{69} +193.991 q^{70} -317.673 q^{71} +8.80999 q^{72} -63.0668 q^{73} -1345.20 q^{74} -178.721 q^{75} +110.316 q^{76} +102.567 q^{77} -623.835 q^{79} -501.479 q^{80} +81.0000 q^{81} -808.824 q^{82} +659.874 q^{83} +147.155 q^{84} +751.677 q^{85} +470.755 q^{86} -598.456 q^{87} +16.8720 q^{88} +1273.19 q^{89} +293.393 q^{90} +1811.05 q^{92} +923.331 q^{93} +1364.68 q^{94} +108.252 q^{95} -773.094 q^{96} +603.746 q^{97} -1239.66 q^{98} +155.123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 6 q^{2} + 27 q^{3} + 44 q^{4} + 33 q^{5} + 18 q^{6} + 83 q^{7} + 87 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q + 6 * q^2 + 27 * q^3 + 44 * q^4 + 33 * q^5 + 18 * q^6 + 83 * q^7 + 87 * q^8 + 81 * q^9	\( 9 q + 6 q^{2} + 27 q^{3} + 44 q^{4} + 33 q^{5} + 18 q^{6} + 83 q^{7} + 87 q^{8} + 81 q^{9} - 54 q^{10} + 85 q^{11} + 132 q^{12} + 158 q^{14} + 99 q^{15} + 216 q^{16} + 178 q^{17} + 54 q^{18} + 352 q^{19} + 402 q^{20} + 249 q^{21} - 630 q^{22} + 150 q^{23} + 261 q^{24} - 20 q^{25} + 243 q^{27} + 940 q^{28} - 97 q^{29} - 162 q^{30} + 717 q^{31} + 707 q^{32} + 255 q^{33} + 632 q^{34} - 418 q^{35} + 396 q^{36} + 1108 q^{37} - 660 q^{38} - 1506 q^{40} + 334 q^{41} + 474 q^{42} + 242 q^{43} - 307 q^{44} + 297 q^{45} + 979 q^{46} - 184 q^{47} + 648 q^{48} - 38 q^{49} - 2031 q^{50} + 534 q^{51} - 151 q^{53} + 162 q^{54} + 2064 q^{55} + 2276 q^{56} + 1056 q^{57} + 1161 q^{58} + 537 q^{59} + 1206 q^{60} - 1340 q^{61} + 347 q^{62} + 747 q^{63} + 893 q^{64} - 1890 q^{66} + 2308 q^{67} + 2785 q^{68} + 450 q^{69} - 1420 q^{70} + 96 q^{71} + 783 q^{72} + 2505 q^{73} - 1191 q^{74} - 60 q^{75} + 2409 q^{76} - 2142 q^{77} - 1591 q^{79} - 2671 q^{80} + 729 q^{81} + 1517 q^{82} + 1539 q^{83} + 2820 q^{84} + 4296 q^{85} - 3763 q^{86} - 291 q^{87} - 3716 q^{88} - 592 q^{89} - 486 q^{90} + 515 q^{92} + 2151 q^{93} - 692 q^{94} + 4158 q^{95} + 2121 q^{96} + 1445 q^{97} + 1457 q^{98} + 765 q^{99}+O(q^{100}) \) 9 * q + 6 * q^2 + 27 * q^3 + 44 * q^4 + 33 * q^5 + 18 * q^6 + 83 * q^7 + 87 * q^8 + 81 * q^9 - 54 * q^10 + 85 * q^11 + 132 * q^12 + 158 * q^14 + 99 * q^15 + 216 * q^16 + 178 * q^17 + 54 * q^18 + 352 * q^19 + 402 * q^20 + 249 * q^21 - 630 * q^22 + 150 * q^23 + 261 * q^24 - 20 * q^25 + 243 * q^27 + 940 * q^28 - 97 * q^29 - 162 * q^30 + 717 * q^31 + 707 * q^32 + 255 * q^33 + 632 * q^34 - 418 * q^35 + 396 * q^36 + 1108 * q^37 - 660 * q^38 - 1506 * q^40 + 334 * q^41 + 474 * q^42 + 242 * q^43 - 307 * q^44 + 297 * q^45 + 979 * q^46 - 184 * q^47 + 648 * q^48 - 38 * q^49 - 2031 * q^50 + 534 * q^51 - 151 * q^53 + 162 * q^54 + 2064 * q^55 + 2276 * q^56 + 1056 * q^57 + 1161 * q^58 + 537 * q^59 + 1206 * q^60 - 1340 * q^61 + 347 * q^62 + 747 * q^63 + 893 * q^64 - 1890 * q^66 + 2308 * q^67 + 2785 * q^68 + 450 * q^69 - 1420 * q^70 + 96 * q^71 + 783 * q^72 + 2505 * q^73 - 1191 * q^74 - 60 * q^75 + 2409 * q^76 - 2142 * q^77 - 1591 * q^79 - 2671 * q^80 + 729 * q^81 + 1517 * q^82 + 1539 * q^83 + 2820 * q^84 + 4296 * q^85 - 3763 * q^86 - 291 * q^87 - 3716 * q^88 - 592 * q^89 - 486 * q^90 + 515 * q^92 + 2151 * q^93 - 692 * q^94 + 4158 * q^95 + 2121 * q^96 + 1445 * q^97 + 1457 * q^98 + 765 * 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 $

$2$	4.03025	1.42491	0.712454	−	0.701719i	$-0.247584\pi$
$2$	4.03025	1.42491	0.712454	+	0.701719i	$0.247584\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	8.24289	1.03036
$5$	8.08864	0.723470	0.361735	−	0.932281i	$-0.382184\pi$
$5$	8.08864	0.723470	0.361735	+	0.932281i	$0.382184\pi$
$6$	12.0907	0.822671
$7$	5.95078	0.321312	0.160656	−	0.987010i	$-0.448639\pi$
$7$	5.95078	0.321312	0.160656	+	0.987010i	$0.448639\pi$
$8$	0.978887	0.0432611
$9$	9.00000	0.333333
$10$	32.5992	1.03088
$11$	17.2359	0.472437	0.236219	−	0.971700i	$-0.424092\pi$
$11$	17.2359	0.472437	0.236219	+	0.971700i	$0.424092\pi$
$12$	24.7287	0.594879
$13$	0	0
$13$	0	0
$14$	23.9831	0.457840
$15$	24.2659	0.417696
$16$	−61.9979	−0.968718
$17$	92.9299	1.32581	0.662907	−	0.748702i	$-0.269323\pi$
$17$	92.9299	1.32581	0.662907	+	0.748702i	$0.269323\pi$
$18$	36.2722	0.474969
$19$	13.3832	0.161596	0.0807979	−	0.996731i	$-0.474253\pi$
$19$	13.3832	0.161596	0.0807979	+	0.996731i	$0.474253\pi$
$20$	66.6738	0.745435
$21$	17.8523	0.185510
$22$	69.4648	0.673179
$23$	219.710	1.99186	0.995930	−	0.0901293i	$-0.0287280\pi$
$23$	219.710	1.99186	0.995930	+	0.0901293i	$0.0287280\pi$
$24$	2.93666	0.0249768
$25$	−59.5738	−0.476591
$26$	0	0
$27$	27.0000	0.192450
$28$	49.0516	0.331067
$29$	−199.485	−1.27736	−0.638681	−	0.769471i	$-0.720520\pi$
$29$	−199.485	−1.27736	−0.638681	+	0.769471i	$0.720520\pi$
$30$	97.7977	0.595178
$31$	307.777	1.78317	0.891586	−	0.452851i	$-0.149593\pi$
$31$	307.777	1.78317	0.891586	+	0.452851i	$0.149593\pi$
$32$	−257.698	−1.42359
$33$	51.7076	0.272762
$34$	374.531	1.88916
$35$	48.1337	0.232460
$36$	74.1860	0.343454
$37$	−333.777	−1.48304	−0.741521	−	0.670930i	$-0.765895\pi$
$37$	−333.777	−1.48304	−0.741521	+	0.670930i	$0.765895\pi$
$38$	53.9376	0.230259
$39$	0	0
$40$	7.91787	0.0312981
$41$	−200.689	−0.764446	−0.382223	−	0.924070i	$-0.624841\pi$
$41$	−200.689	−0.764446	−0.382223	+	0.924070i	$0.624841\pi$
$42$	71.9493	0.264334
$43$	116.806	0.414248	0.207124	−	0.978315i	$-0.433590\pi$
$43$	116.806	0.414248	0.207124	+	0.978315i	$0.433590\pi$
$44$	142.073	0.486781
$45$	72.7978	0.241157
$46$	885.487	2.83822
$47$	338.610	1.05088	0.525440	−	0.850831i	$-0.323901\pi$
$47$	338.610	1.05088	0.525440	+	0.850831i	$0.323901\pi$
$48$	−185.994	−0.559289
$49$	−307.588	−0.896759
$50$	−240.097	−0.679097
$51$	278.790	0.765459
$52$	0	0
$53$	−26.6215	−0.0689951	−0.0344975	−	0.999405i	$-0.510983\pi$
$53$	−26.6215	−0.0689951	−0.0344975	+	0.999405i	$0.510983\pi$
$54$	108.817	0.274224
$55$	139.415	0.341794
$56$	5.82514	0.0139003
$57$	40.1496	0.0932973
$58$	−803.976	−1.82012
$59$	−280.058	−0.617973	−0.308987	−	0.951066i	$-0.599990\pi$
$59$	−280.058	−0.617973	−0.308987	+	0.951066i	$0.599990\pi$
$60$	200.021	0.430377
$61$	−207.084	−0.434663	−0.217332	−	0.976098i	$-0.569735\pi$
$61$	−207.084	−0.434663	−0.217332	+	0.976098i	$0.569735\pi$
$62$	1240.42	2.54086
$63$	53.5570	0.107104
$64$	−542.603	−1.05977
$65$	0	0
$66$	208.394	0.388660
$67$	−285.981	−0.521465	−0.260732	−	0.965411i	$-0.583964\pi$
$67$	−285.981	−0.521465	−0.260732	+	0.965411i	$0.583964\pi$
$68$	766.011	1.36607
$69$	659.131	1.15000
$70$	193.991	0.331233
$71$	−317.673	−0.530998	−0.265499	−	0.964111i	$-0.585537\pi$
$71$	−317.673	−0.530998	−0.265499	+	0.964111i	$0.585537\pi$
$72$	8.80999	0.0144204
$73$	−63.0668	−0.101115	−0.0505576	−	0.998721i	$-0.516100\pi$
$73$	−63.0668	−0.101115	−0.0505576	+	0.998721i	$0.516100\pi$
$74$	−1345.20	−2.11320
$75$	−178.721	−0.275160
$76$	110.316	0.166502
$77$	102.567	0.151800
$78$	0	0
$79$	−623.835	−0.888443	−0.444221	−	0.895917i	$-0.646520\pi$
$79$	−623.835	−0.888443	−0.444221	+	0.895917i	$0.646520\pi$
$80$	−501.479	−0.700838
$81$	81.0000	0.111111
$82$	−808.824	−1.08926
$83$	659.874	0.872658	0.436329	−	0.899787i	$-0.356278\pi$
$83$	659.874	0.872658	0.436329	+	0.899787i	$0.356278\pi$
$84$	147.155	0.191142
$85$	751.677	0.959186
$86$	470.755	0.590265
$87$	−598.456	−0.737486
$88$	16.8720	0.0204382
$89$	1273.19	1.51638	0.758191	−	0.652032i	$-0.226083\pi$
$89$	1273.19	1.51638	0.758191	+	0.652032i	$0.226083\pi$
$90$	293.393	0.343626
$91$	0	0
$92$	1811.05	2.05233
$93$	923.331	1.02952
$94$	1364.68	1.49741
$95$	108.252	0.116910
$96$	−773.094	−0.821912
$97$	603.746	0.631970	0.315985	−	0.948764i	$-0.397665\pi$
$97$	603.746	0.631970	0.315985	+	0.948764i	$0.397665\pi$
$98$	−1239.66	−1.27780
$99$	155.123	0.157479
$100$	−491.060	−0.491060
$101$	−740.588	−0.729616	−0.364808	−	0.931083i	$-0.618865\pi$
$101$	−740.588	−0.729616	−0.364808	+	0.931083i	$0.618865\pi$
$102$	1123.59	1.09071
$103$	−1888.57	−1.80666	−0.903332	−	0.428942i	$-0.858887\pi$
$103$	−1888.57	−1.80666	−0.903332	+	0.428942i	$0.858887\pi$
$104$	0	0
$105$	144.401	0.134211
$106$	−107.291	−0.0983116
$107$	−919.463	−0.830728	−0.415364	−	0.909655i	$-0.636346\pi$
$107$	−919.463	−0.830728	−0.415364	+	0.909655i	$0.636346\pi$
$108$	222.558	0.198293
$109$	1570.40	1.37998	0.689988	−	0.723821i	$-0.257616\pi$
$109$	1570.40	1.37998	0.689988	+	0.723821i	$0.257616\pi$
$110$	561.876	0.487025
$111$	−1001.33	−0.856234
$112$	−368.936	−0.311260
$113$	−1324.66	−1.10277	−0.551386	−	0.834250i	$-0.685901\pi$
$113$	−1324.66	−1.10277	−0.551386	+	0.834250i	$0.685901\pi$
$114$	161.813	0.132940
$115$	1777.16	1.44105
$116$	−1644.34	−1.31614
$117$	0	0
$118$	−1128.70	−0.880555
$119$	553.006	0.426000
$120$	23.7536	0.0180700
$121$	−1033.92	−0.776803
$122$	−834.601	−0.619354
$123$	−602.066	−0.441353
$124$	2536.97	1.83731
$125$	−1492.95	−1.06827
$126$	215.848	0.152613
$127$	−2350.39	−1.64223	−0.821115	−	0.570763i	$-0.806648\pi$
$127$	−2350.39	−1.64223	−0.821115	+	0.570763i	$0.806648\pi$
$128$	−125.240	−0.0864824
$129$	350.417	0.239166
$130$	0	0
$131$	2308.69	1.53978	0.769890	−	0.638177i	$-0.220311\pi$
$131$	2308.69	1.53978	0.769890	+	0.638177i	$0.220311\pi$
$132$	426.220	0.281043
$133$	79.6405	0.0519226
$134$	−1152.57	−0.743039
$135$	218.393	0.139232
$136$	90.9680	0.0573562
$137$	−374.912	−0.233802	−0.116901	−	0.993144i	$-0.537296\pi$
$137$	−374.912	−0.233802	−0.116901	+	0.993144i	$0.537296\pi$
$138$	2656.46	1.63864
$139$	487.711	0.297605	0.148802	−	0.988867i	$-0.452458\pi$
$139$	487.711	0.297605	0.148802	+	0.988867i	$0.452458\pi$
$140$	396.761	0.239517
$141$	1015.83	0.606726
$142$	−1280.30	−0.756623
$143$	0	0
$144$	−557.981	−0.322906
$145$	−1613.57	−0.924134
$146$	−254.175	−0.144080
$147$	−922.765	−0.517744
$148$	−2751.28	−1.52807
$149$	1055.91	0.580558	0.290279	−	0.956942i	$-0.406252\pi$
$149$	1055.91	0.580558	0.290279	+	0.956942i	$0.406252\pi$
$150$	−720.292	−0.392077
$151$	−888.560	−0.478874	−0.239437	−	0.970912i	$-0.576963\pi$
$151$	−888.560	−0.478874	−0.239437	+	0.970912i	$0.576963\pi$
$152$	13.1007	0.00699081
$153$	836.369	0.441938
$154$	413.370	0.216301
$155$	2489.50	1.29007
$156$	0	0
$157$	−3648.56	−1.85469	−0.927346	−	0.374206i	$-0.877915\pi$
$157$	−3648.56	−1.85469	−0.927346	+	0.374206i	$0.877915\pi$
$158$	−2514.21	−1.26595
$159$	−79.8644	−0.0398343
$160$	−2084.43	−1.02993
$161$	1307.45	0.640008
$162$	326.450	0.158323
$163$	1386.49	0.666249	0.333125	−	0.942883i	$-0.391897\pi$
$163$	1386.49	0.666249	0.333125	+	0.942883i	$0.391897\pi$
$164$	−1654.25	−0.787655
$165$	418.244	0.197335
$166$	2659.46	1.24346
$167$	−3376.19	−1.56442	−0.782209	−	0.623017i	$-0.785907\pi$
$167$	−3376.19	−1.56442	−0.782209	+	0.623017i	$0.785907\pi$
$168$	17.4754	0.00802535
$169$	0	0
$170$	3029.44	1.36675
$171$	120.449	0.0538652
$172$	962.815	0.426825
$173$	341.817	0.150219	0.0751095	−	0.997175i	$-0.476069\pi$
$173$	341.817	0.150219	0.0751095	+	0.997175i	$0.476069\pi$
$174$	−2411.93	−1.05085
$175$	−354.511	−0.153134
$176$	−1068.59	−0.457658
$177$	−840.174	−0.356787
$178$	5131.28	2.16070
$179$	−2885.55	−1.20489	−0.602446	−	0.798159i	$-0.705807\pi$
$179$	−2885.55	−1.20489	−0.602446	+	0.798159i	$0.705807\pi$
$180$	600.064	0.248478
$181$	3795.62	1.55871	0.779354	−	0.626584i	$-0.215547\pi$
$181$	3795.62	1.55871	0.779354	+	0.626584i	$0.215547\pi$
$182$	0	0
$183$	−621.253	−0.250953
$184$	215.072	0.0861701
$185$	−2699.80	−1.07294
$186$	3721.25	1.46696
$187$	1601.73	0.626363
$188$	2791.12	1.08278
$189$	160.671	0.0618365
$190$	436.282	0.166586
$191$	−2805.90	−1.06297	−0.531486	−	0.847067i	$-0.678366\pi$
$191$	−2805.90	−1.06297	−0.531486	+	0.847067i	$0.678366\pi$
$192$	−1627.81	−0.611859
$193$	−2485.64	−0.927048	−0.463524	−	0.886084i	$-0.653415\pi$
$193$	−2485.64	−0.927048	−0.463524	+	0.886084i	$0.653415\pi$
$194$	2433.24	0.900499
$195$	0	0
$196$	−2535.41	−0.923985
$197$	2750.70	0.994818	0.497409	−	0.867516i	$-0.334285\pi$
$197$	2750.70	0.994818	0.497409	+	0.867516i	$0.334285\pi$
$198$	625.183	0.224393
$199$	3998.53	1.42436	0.712182	−	0.701994i	$-0.247707\pi$
$199$	3998.53	1.42436	0.712182	+	0.701994i	$0.247707\pi$
$200$	−58.3161	−0.0206178
$201$	−857.943	−0.301068
$202$	−2984.75	−1.03964
$203$	−1187.09	−0.410432
$204$	2298.03	0.788698
$205$	−1623.30	−0.553054
$206$	−7611.41	−2.57433
$207$	1977.39	0.663953
$208$	0	0
$209$	230.671	0.0763438
$210$	581.973	0.191238
$211$	−1375.80	−0.448882	−0.224441	−	0.974488i	$-0.572056\pi$
$211$	−1375.80	−0.448882	−0.224441	+	0.974488i	$0.572056\pi$
$212$	−219.438	−0.0710898
$213$	−953.020	−0.306572
$214$	−3705.66	−1.18371
$215$	944.799	0.299696
$216$	26.4300	0.00832561
$217$	1831.51	0.572955
$218$	6329.12	1.96634
$219$	−189.200	−0.0583789
$220$	1149.18	0.352171
$221$	0	0
$222$	−4035.61	−1.22005
$223$	1694.37	0.508805	0.254403	−	0.967098i	$-0.418121\pi$
$223$	1694.37	0.508805	0.254403	+	0.967098i	$0.418121\pi$
$224$	−1533.50	−0.457418
$225$	−536.164	−0.158864
$226$	−5338.70	−1.57135
$227$	−405.400	−0.118534	−0.0592672	−	0.998242i	$-0.518876\pi$
$227$	−405.400	−0.118534	−0.0592672	+	0.998242i	$0.518876\pi$
$228$	330.949	0.0961299
$229$	2359.54	0.680884	0.340442	−	0.940265i	$-0.389423\pi$
$229$	2359.54	0.680884	0.340442	+	0.940265i	$0.389423\pi$
$230$	7162.39	2.05337
$231$	307.701	0.0876416
$232$	−195.274	−0.0552601
$233$	938.507	0.263878	0.131939	−	0.991258i	$-0.457880\pi$
$233$	938.507	0.263878	0.131939	+	0.991258i	$0.457880\pi$
$234$	0	0
$235$	2738.90	0.760280
$236$	−2308.49	−0.636736
$237$	−1871.51	−0.512943
$238$	2228.75	0.607010
$239$	4664.25	1.26237	0.631183	−	0.775634i	$-0.282570\pi$
$239$	4664.25	1.26237	0.631183	+	0.775634i	$0.282570\pi$
$240$	−1504.44	−0.404629
$241$	−3774.94	−1.00898	−0.504492	−	0.863416i	$-0.668320\pi$
$241$	−3774.94	−1.00898	−0.504492	+	0.863416i	$0.668320\pi$
$242$	−4166.97	−1.10687
$243$	243.000	0.0641500
$244$	−1706.97	−0.447860
$245$	−2487.97	−0.648778
$246$	−2426.47	−0.628887
$247$	0	0
$248$	301.279	0.0771421
$249$	1979.62	0.503829
$250$	−6016.96	−1.52219
$251$	−960.695	−0.241588	−0.120794	−	0.992678i	$-0.538544\pi$
$251$	−960.695	−0.241588	−0.120794	+	0.992678i	$0.538544\pi$
$252$	441.464	0.110356
$253$	3786.90	0.941029
$254$	−9472.64	−2.34003
$255$	2255.03	0.553787
$256$	3836.08	0.936542
$257$	−16.7302	−0.00406070	−0.00203035	−	0.999998i	$-0.500646\pi$
$257$	−16.7302	−0.00406070	−0.00203035	+	0.999998i	$0.500646\pi$
$258$	1412.27	0.340790
$259$	−1986.23	−0.476519
$260$	0	0
$261$	−1795.37	−0.425788
$262$	9304.58	2.19404
$263$	−400.736	−0.0939560	−0.0469780	−	0.998896i	$-0.514959\pi$
$263$	−400.736	−0.0939560	−0.0469780	+	0.998896i	$0.514959\pi$
$264$	50.6159	0.0118000
$265$	−215.332	−0.0499159
$266$	320.971	0.0739849
$267$	3819.57	0.875484
$268$	−2357.31	−0.537297
$269$	2236.97	0.507027	0.253514	−	0.967332i	$-0.418414\pi$
$269$	2236.97	0.507027	0.253514	+	0.967332i	$0.418414\pi$
$270$	880.179	0.198393
$271$	−4018.89	−0.900850	−0.450425	−	0.892814i	$-0.648727\pi$
$271$	−4018.89	−0.900850	−0.450425	+	0.892814i	$0.648727\pi$
$272$	−5761.46	−1.28434
$273$	0	0
$274$	−1510.99	−0.333147
$275$	−1026.81	−0.225159
$276$	5433.14	1.18492
$277$	6792.95	1.47346	0.736731	−	0.676186i	$-0.236368\pi$
$277$	6792.95	1.47346	0.736731	+	0.676186i	$0.236368\pi$
$278$	1965.59	0.424059
$279$	2769.99	0.594391
$280$	47.1175	0.0100565
$281$	−7286.80	−1.54695	−0.773477	−	0.633824i	$-0.781484\pi$
$281$	−7286.80	−1.54695	−0.773477	+	0.633824i	$0.781484\pi$
$282$	4094.04	0.864528
$283$	−2429.77	−0.510369	−0.255185	−	0.966892i	$-0.582136\pi$
$283$	−2429.77	−0.510369	−0.255185	+	0.966892i	$0.582136\pi$
$284$	−2618.54	−0.547120
$285$	324.756	0.0674979
$286$	0	0
$287$	−1194.25	−0.245626
$288$	−2319.28	−0.474531
$289$	3722.97	0.757780
$290$	−6503.07	−1.31681
$291$	1811.24	0.364868
$292$	−519.853	−0.104185
$293$	4211.25	0.839672	0.419836	−	0.907600i	$-0.362088\pi$
$293$	4211.25	0.839672	0.419836	+	0.907600i	$0.362088\pi$
$294$	−3718.97	−0.737737
$295$	−2265.29	−0.447085
$296$	−326.730	−0.0641580
$297$	465.368	0.0909206
$298$	4255.56	0.827242
$299$	0	0
$300$	−1473.18	−0.283514
$301$	695.084	0.133103
$302$	−3581.12	−0.682351
$303$	−2221.76	−0.421244
$304$	−829.731	−0.156541
$305$	−1675.03	−0.314466
$306$	3370.78	0.629720
$307$	8212.27	1.52671	0.763353	−	0.645982i	$-0.223552\pi$
$307$	8212.27	1.52671	0.763353	+	0.645982i	$0.223552\pi$
$308$	845.447	0.156408
$309$	−5665.71	−1.04308
$310$	10033.3	1.83823
$311$	−4238.55	−0.772818	−0.386409	−	0.922328i	$-0.626285\pi$
$311$	−4238.55	−0.772818	−0.386409	+	0.922328i	$0.626285\pi$
$312$	0	0
$313$	3807.82	0.687638	0.343819	−	0.939036i	$-0.388279\pi$
$313$	3807.82	0.687638	0.343819	+	0.939036i	$0.388279\pi$
$314$	−14704.6	−2.64276
$315$	433.204	0.0774865
$316$	−5142.20	−0.915416
$317$	−10497.7	−1.85996	−0.929981	−	0.367608i	$-0.880177\pi$
$317$	−10497.7	−1.85996	−0.929981	+	0.367608i	$0.880177\pi$
$318$	−321.873	−0.0567602
$319$	−3438.31	−0.603474
$320$	−4388.92	−0.766713
$321$	−2758.39	−0.479621
$322$	5269.34	0.911953
$323$	1243.70	0.214246
$324$	667.674	0.114485
$325$	0	0
$326$	5587.91	0.949343
$327$	4711.21	0.796730
$328$	−196.452	−0.0330708
$329$	2014.99	0.337660
$330$	1685.63	0.281184
$331$	11905.2	1.97695	0.988474	−	0.151389i	$-0.0483746\pi$
$331$	11905.2	1.97695	0.988474	+	0.151389i	$0.0483746\pi$
$332$	5439.27	0.899152
$333$	−3003.99	−0.494347
$334$	−13606.9	−2.22915
$335$	−2313.20	−0.377264
$336$	−1106.81	−0.179706
$337$	8981.18	1.45174	0.725869	−	0.687833i	$-0.241438\pi$
$337$	8981.18	1.45174	0.725869	+	0.687833i	$0.241438\pi$
$338$	0	0
$339$	−3973.97	−0.636686
$340$	6195.99	0.988308
$341$	5304.80	0.842437
$342$	485.439	0.0767530
$343$	−3871.51	−0.609451
$344$	114.339	0.0179208
$345$	5331.48	0.831992
$346$	1377.61	0.214048
$347$	−5712.87	−0.883813	−0.441906	−	0.897061i	$-0.645698\pi$
$347$	−5712.87	−0.883813	−0.441906	+	0.897061i	$0.645698\pi$
$348$	−4933.01	−0.759876
$349$	9507.28	1.45820	0.729102	−	0.684406i	$-0.239938\pi$
$349$	9507.28	1.45820	0.729102	+	0.684406i	$0.239938\pi$
$350$	−1428.77	−0.218202
$351$	0	0
$352$	−4441.65	−0.672559
$353$	−3972.96	−0.599035	−0.299518	−	0.954091i	$-0.596826\pi$
$353$	−3972.96	−0.599035	−0.299518	+	0.954091i	$0.596826\pi$
$354$	−3386.11	−0.508389
$355$	−2569.55	−0.384162
$356$	10494.8	1.56242
$357$	1659.02	0.245951
$358$	−11629.5	−1.71686
$359$	−109.866	−0.0161519	−0.00807594	−	0.999967i	$-0.502571\pi$
$359$	−109.866	−0.0161519	−0.00807594	+	0.999967i	$0.502571\pi$
$360$	71.2609	0.0104327
$361$	−6679.89	−0.973887
$362$	15297.3	2.22101
$363$	−3101.77	−0.448487
$364$	0	0
$365$	−510.125	−0.0731539
$366$	−2503.80	−0.357584
$367$	7020.02	0.998480	0.499240	−	0.866464i	$-0.333613\pi$
$367$	7020.02	0.998480	0.499240	+	0.866464i	$0.333613\pi$
$368$	−13621.6	−1.92955
$369$	−1806.20	−0.254815
$370$	−10880.9	−1.52884
$371$	−158.418	−0.0221689
$372$	7610.91	1.06077
$373$	2227.18	0.309166	0.154583	−	0.987980i	$-0.450597\pi$
$373$	2227.18	0.309166	0.154583	+	0.987980i	$0.450597\pi$
$374$	6455.36	0.892510
$375$	−4478.86	−0.616766
$376$	331.461	0.0454622
$377$	0	0
$378$	647.544	0.0881113
$379$	−11004.6	−1.49147	−0.745734	−	0.666244i	$-0.767901\pi$
$379$	−11004.6	−1.49147	−0.745734	+	0.666244i	$0.767901\pi$
$380$	892.309	0.120459
$381$	−7051.16	−0.948142
$382$	−11308.5	−1.51464
$383$	−4436.85	−0.591938	−0.295969	−	0.955198i	$-0.595643\pi$
$383$	−4436.85	−0.591938	−0.295969	+	0.955198i	$0.595643\pi$
$384$	−375.720	−0.0499306
$385$	829.627	0.109823
$386$	−10017.7	−1.32096
$387$	1051.25	0.138083
$388$	4976.61	0.651157
$389$	−2561.58	−0.333874	−0.166937	−	0.985968i	$-0.553388\pi$
$389$	−2561.58	−0.333874	−0.166937	+	0.985968i	$0.553388\pi$
$390$	0	0
$391$	20417.7	2.64083
$392$	−301.094	−0.0387948
$393$	6926.07	0.888992
$394$	11086.0	1.41752
$395$	−5045.98	−0.642762
$396$	1278.66	0.162260
$397$	2206.90	0.278996	0.139498	−	0.990222i	$-0.455451\pi$
$397$	2206.90	0.278996	0.139498	+	0.990222i	$0.455451\pi$
$398$	16115.1	2.02959
$399$	238.922	0.0299775
$400$	3693.45	0.461682
$401$	−8071.02	−1.00511	−0.502553	−	0.864546i	$-0.667606\pi$
$401$	−8071.02	−1.00511	−0.502553	+	0.864546i	$0.667606\pi$
$402$	−3457.72	−0.428994
$403$	0	0
$404$	−6104.58	−0.751768
$405$	655.180	0.0803856
$406$	−4784.28	−0.584827
$407$	−5752.93	−0.700644
$408$	272.904	0.0331146
$409$	6298.36	0.761452	0.380726	−	0.924688i	$-0.375674\pi$
$409$	6298.36	0.761452	0.380726	+	0.924688i	$0.375674\pi$
$410$	−6542.29	−0.788051
$411$	−1124.74	−0.134986
$412$	−15567.3	−1.86152
$413$	−1666.56	−0.198562
$414$	7969.38	0.946072
$415$	5337.49	0.631342
$416$	0	0
$417$	1463.13	0.171822
$418$	929.662	0.108783
$419$	−1432.01	−0.166965	−0.0834824	−	0.996509i	$-0.526604\pi$
$419$	−1432.01	−0.166965	−0.0834824	+	0.996509i	$0.526604\pi$
$420$	1190.28	0.138285
$421$	9641.43	1.11614	0.558069	−	0.829794i	$-0.311542\pi$
$421$	9641.43	1.11614	0.558069	+	0.829794i	$0.311542\pi$
$422$	−5544.82	−0.639615
$423$	3047.49	0.350293
$424$	−26.0594	−0.00298480
$425$	−5536.19	−0.631870
$426$	−3840.90	−0.436837
$427$	−1232.31	−0.139662
$428$	−7579.03	−0.855949
$429$	0	0
$430$	3807.77	0.427040
$431$	3370.61	0.376698	0.188349	−	0.982102i	$-0.439686\pi$
$431$	3370.61	0.376698	0.188349	+	0.982102i	$0.439686\pi$
$432$	−1673.94	−0.186430
$433$	6248.91	0.693541	0.346770	−	0.937950i	$-0.387278\pi$
$433$	6248.91	0.693541	0.346770	+	0.937950i	$0.387278\pi$
$434$	7381.45	0.816407
$435$	−4840.70	−0.533549
$436$	12944.7	1.42187
$437$	2940.43	0.321876
$438$	−762.524	−0.0831845
$439$	2866.16	0.311604	0.155802	−	0.987788i	$-0.450204\pi$
$439$	2866.16	0.311604	0.155802	+	0.987788i	$0.450204\pi$
$440$	136.471	0.0147864
$441$	−2768.29	−0.298920
$442$	0	0
$443$	10776.3	1.15575	0.577877	−	0.816124i	$-0.303881\pi$
$443$	10776.3	1.15575	0.577877	+	0.816124i	$0.303881\pi$
$444$	−8253.85	−0.882230
$445$	10298.4	1.09706
$446$	6828.74	0.725000
$447$	3167.72	0.335185
$448$	−3228.91	−0.340517
$449$	13834.9	1.45414	0.727069	−	0.686564i	$-0.240882\pi$
$449$	13834.9	1.45414	0.727069	+	0.686564i	$0.240882\pi$
$450$	−2160.87	−0.226366
$451$	−3459.04	−0.361153
$452$	−10919.0	−1.13625
$453$	−2665.68	−0.276478
$454$	−1633.86	−0.168901
$455$	0	0
$456$	39.3020	0.00403615
$457$	17233.0	1.76395	0.881976	−	0.471295i	$-0.156213\pi$
$457$	17233.0	1.76395	0.881976	+	0.471295i	$0.156213\pi$
$458$	9509.51	0.970197
$459$	2509.11	0.255153
$460$	14648.9	1.48480
$461$	11485.0	1.16033	0.580164	−	0.814500i	$-0.302988\pi$
$461$	11485.0	1.16033	0.580164	+	0.814500i	$0.302988\pi$
$462$	1240.11	0.124881
$463$	1613.61	0.161967	0.0809837	−	0.996715i	$-0.474194\pi$
$463$	1613.61	0.161967	0.0809837	+	0.996715i	$0.474194\pi$
$464$	12367.7	1.23740
$465$	7468.49	0.744824
$466$	3782.41	0.376002
$467$	−8149.20	−0.807495	−0.403747	−	0.914871i	$-0.632293\pi$
$467$	−8149.20	−0.807495	−0.403747	+	0.914871i	$0.632293\pi$
$468$	0	0
$469$	−1701.81	−0.167553
$470$	11038.4	1.08333
$471$	−10945.7	−1.07081
$472$	−274.145	−0.0267342
$473$	2013.24	0.195706
$474$	−7542.63	−0.730896
$475$	−797.289	−0.0770150
$476$	4558.36	0.438933
$477$	−239.593	−0.0229984
$478$	18798.1	1.79875
$479$	1827.62	0.174334	0.0871670	−	0.996194i	$-0.472219\pi$
$479$	1827.62	0.174334	0.0871670	+	0.996194i	$0.472219\pi$
$480$	−6253.28	−0.594629
$481$	0	0
$482$	−15213.9	−1.43771
$483$	3922.34	0.369509
$484$	−8522.52	−0.800387
$485$	4883.49	0.457212
$486$	979.350	0.0914078
$487$	−7838.95	−0.729398	−0.364699	−	0.931125i	$-0.618828\pi$
$487$	−7838.95	−0.729398	−0.364699	+	0.931125i	$0.618828\pi$
$488$	−202.712	−0.0188040
$489$	4159.48	0.384659
$490$	−10027.1	−0.924449
$491$	17196.1	1.58055	0.790273	−	0.612755i	$-0.209939\pi$
$491$	17196.1	1.58055	0.790273	+	0.612755i	$0.209939\pi$
$492$	−4962.76	−0.454753
$493$	−18538.2	−1.69354
$494$	0	0
$495$	1254.73	0.113931
$496$	−19081.5	−1.72739
$497$	−1890.40	−0.170616
$498$	7978.37	0.717910
$499$	5355.28	0.480431	0.240216	−	0.970720i	$-0.422782\pi$
$499$	5355.28	0.480431	0.240216	+	0.970720i	$0.422782\pi$
$500$	−12306.2	−1.10070
$501$	−10128.6	−0.903217
$502$	−3871.84	−0.344240
$503$	2979.80	0.264141	0.132071	−	0.991240i	$-0.457837\pi$
$503$	2979.80	0.264141	0.132071	+	0.991240i	$0.457837\pi$
$504$	52.4263	0.00463344
$505$	−5990.35	−0.527856
$506$	15262.1	1.34088
$507$	0	0
$508$	−19374.0	−1.69209
$509$	15353.7	1.33701	0.668507	−	0.743706i	$-0.266934\pi$
$509$	15353.7	1.33701	0.668507	+	0.743706i	$0.266934\pi$
$510$	9088.33	0.789094
$511$	−375.297	−0.0324895
$512$	16462.3	1.42097
$513$	361.347	0.0310991
$514$	−67.4267	−0.00578611
$515$	−15276.0	−1.30707
$516$	2888.44	0.246428
$517$	5836.24	0.496475
$518$	−8005.00	−0.678995
$519$	1025.45	0.0867289
$520$	0	0
$521$	433.801	0.0364783	0.0182391	−	0.999834i	$-0.494194\pi$
$521$	433.801	0.0364783	0.0182391	+	0.999834i	$0.494194\pi$
$522$	−7235.78	−0.606708
$523$	18900.3	1.58021	0.790106	−	0.612970i	$-0.210026\pi$
$523$	18900.3	1.58021	0.790106	+	0.612970i	$0.210026\pi$
$524$	19030.3	1.58653
$525$	−1063.53	−0.0884121
$526$	−1615.06	−0.133879
$527$	28601.7	2.36415
$528$	−3205.76	−0.264229
$529$	36105.7	2.96751
$530$	−867.839	−0.0711255
$531$	−2520.52	−0.205991
$532$	656.468	0.0534990
$533$	0	0
$534$	15393.8	1.24748
$535$	−7437.21	−0.601007
$536$	−279.943	−0.0225592
$537$	−8656.64	−0.695645
$538$	9015.53	0.722467
$539$	−5301.55	−0.423662
$540$	1800.19	0.143459
$541$	13247.5	1.05278	0.526391	−	0.850243i	$-0.323545\pi$
$541$	13247.5	1.05278	0.526391	+	0.850243i	$0.323545\pi$
$542$	−16197.1	−1.28363
$543$	11386.9	0.899920
$544$	−23947.9	−1.88742
$545$	12702.4	0.998372
$546$	0	0
$547$	−5543.52	−0.433316	−0.216658	−	0.976248i	$-0.569516\pi$
$547$	−5543.52	−0.433316	−0.216658	+	0.976248i	$0.569516\pi$
$548$	−3090.36	−0.240901
$549$	−1863.76	−0.144888
$550$	−4138.28	−0.320831
$551$	−2669.76	−0.206416
$552$	645.215	0.0497503
$553$	−3712.31	−0.285467
$554$	27377.3	2.09955
$555$	−8099.40	−0.619460
$556$	4020.14	0.306640
$557$	6733.19	0.512198	0.256099	−	0.966651i	$-0.417563\pi$
$557$	6733.19	0.512198	0.256099	+	0.966651i	$0.417563\pi$
$558$	11163.7	0.846952
$559$	0	0
$560$	−2984.19	−0.225188
$561$	4805.18	0.361631
$562$	−29367.6	−2.20427
$563$	24282.4	1.81773	0.908863	−	0.417096i	$-0.136952\pi$
$563$	24282.4	1.81773	0.908863	+	0.417096i	$0.136952\pi$
$564$	8373.37	0.625146
$565$	−10714.7	−0.797823
$566$	−9792.55	−0.727229
$567$	482.013	0.0357013
$568$	−310.966	−0.0229716
$569$	−19876.2	−1.46441	−0.732207	−	0.681082i	$-0.761510\pi$
$569$	−19876.2	−1.46441	−0.732207	+	0.681082i	$0.761510\pi$
$570$	1308.85	0.0961782
$571$	225.014	0.0164913	0.00824567	−	0.999966i	$-0.497375\pi$
$571$	225.014	0.0164913	0.00824567	+	0.999966i	$0.497375\pi$
$572$	0	0
$573$	−8417.70	−0.613707
$574$	−4813.14	−0.349994
$575$	−13089.0	−0.949302
$576$	−4883.43	−0.353257
$577$	−12258.1	−0.884424	−0.442212	−	0.896910i	$-0.645806\pi$
$577$	−12258.1	−0.884424	−0.442212	+	0.896910i	$0.645806\pi$
$578$	15004.5	1.07977
$579$	−7456.92	−0.535231
$580$	−13300.4	−0.952191
$581$	3926.77	0.280395
$582$	7299.73	0.519903
$583$	−458.844	−0.0325958
$584$	−61.7353	−0.00437436
$585$	0	0
$586$	16972.4	1.19645
$587$	10282.3	0.722992	0.361496	−	0.932374i	$-0.382266\pi$
$587$	10282.3	0.722992	0.361496	+	0.932374i	$0.382266\pi$
$588$	−7606.24	−0.533463
$589$	4119.04	0.288153
$590$	−9129.67	−0.637055
$591$	8252.10	0.574359
$592$	20693.5	1.43665
$593$	12355.1	0.855586	0.427793	−	0.903877i	$-0.359291\pi$
$593$	12355.1	0.855586	0.427793	+	0.903877i	$0.359291\pi$
$594$	1875.55	0.129553
$595$	4473.07	0.308198
$596$	8703.71	0.598184
$597$	11995.6	0.822357
$598$	0	0
$599$	13035.2	0.889157	0.444578	−	0.895740i	$-0.353354\pi$
$599$	13035.2	0.889157	0.444578	+	0.895740i	$0.353354\pi$
$600$	−174.948	−0.0119037
$601$	−5153.36	−0.349767	−0.174884	−	0.984589i	$-0.555955\pi$
$601$	−5153.36	−0.349767	−0.174884	+	0.984589i	$0.555955\pi$
$602$	2801.36	0.189659
$603$	−2573.83	−0.173822
$604$	−7324.30	−0.493413
$605$	−8363.05	−0.561994
$606$	−8954.25	−0.600234
$607$	−1406.55	−0.0940530	−0.0470265	−	0.998894i	$-0.514975\pi$
$607$	−1406.55	−0.0940530	−0.0470265	+	0.998894i	$0.514975\pi$
$608$	−3448.83	−0.230047
$609$	−3561.28	−0.236963
$610$	−6750.79	−0.448085
$611$	0	0
$612$	6894.10	0.455355
$613$	−15984.3	−1.05318	−0.526590	−	0.850120i	$-0.676530\pi$
$613$	−15984.3	−1.05318	−0.526590	+	0.850120i	$0.676530\pi$
$614$	33097.5	2.17541
$615$	−4869.90	−0.319306
$616$	100.401	0.00656703
$617$	−10324.4	−0.673652	−0.336826	−	0.941567i	$-0.609353\pi$
$617$	−10324.4	−0.673652	−0.336826	+	0.941567i	$0.609353\pi$
$618$	−22834.2	−1.48629
$619$	−7423.00	−0.481996	−0.240998	−	0.970526i	$-0.577475\pi$
$619$	−7423.00	−0.481996	−0.240998	+	0.970526i	$0.577475\pi$
$620$	20520.6	1.32924
$621$	5932.18	0.383334
$622$	−17082.4	−1.10119
$623$	7576.48	0.487232
$624$	0	0
$625$	−4629.23	−0.296271
$626$	15346.4	0.979820
$627$	692.014	0.0440771
$628$	−30074.6	−1.91100
$629$	−31017.8	−1.96624
$630$	1745.92	0.110411
$631$	1190.30	0.0750954	0.0375477	−	0.999295i	$-0.488045\pi$
$631$	1190.30	0.0750954	0.0375477	+	0.999295i	$0.488045\pi$
$632$	−610.665	−0.0384350
$633$	−4127.41	−0.259162
$634$	−42308.2	−2.65027
$635$	−19011.5	−1.18810
$636$	−658.313	−0.0410437
$637$	0	0
$638$	−13857.2	−0.859894
$639$	−2859.06	−0.176999
$640$	−1013.02	−0.0625674
$641$	705.064	0.0434451	0.0217226	−	0.999764i	$-0.493085\pi$
$641$	705.064	0.0434451	0.0217226	+	0.999764i	$0.493085\pi$
$642$	−11117.0	−0.683415
$643$	14641.4	0.897976	0.448988	−	0.893538i	$-0.351785\pi$
$643$	14641.4	0.897976	0.448988	+	0.893538i	$0.351785\pi$
$644$	10777.1	0.659439
$645$	2834.40	0.173030
$646$	5012.42	0.305280
$647$	1520.83	0.0924111	0.0462056	−	0.998932i	$-0.485287\pi$
$647$	1520.83	0.0924111	0.0462056	+	0.998932i	$0.485287\pi$
$648$	79.2899	0.00480679
$649$	−4827.04	−0.291954
$650$	0	0
$651$	5494.54	0.330796
$652$	11428.7	0.686477
$653$	−22054.4	−1.32168	−0.660838	−	0.750529i	$-0.729799\pi$
$653$	−22054.4	−1.32168	−0.660838	+	0.750529i	$0.729799\pi$
$654$	18987.3	1.13527
$655$	18674.2	1.11398
$656$	12442.3	0.740532
$657$	−567.601	−0.0337051
$658$	8120.92	0.481134
$659$	−12652.3	−0.747895	−0.373947	−	0.927450i	$-0.621996\pi$
$659$	−12652.3	−0.747895	−0.373947	+	0.927450i	$0.621996\pi$
$660$	3447.54	0.203326
$661$	−10893.2	−0.640994	−0.320497	−	0.947250i	$-0.603850\pi$
$661$	−10893.2	−0.640994	−0.320497	+	0.947250i	$0.603850\pi$
$662$	47981.0	2.81697
$663$	0	0
$664$	645.942	0.0377522
$665$	644.184	0.0375645
$666$	−12106.8	−0.704399
$667$	−43829.0	−2.54433
$668$	−27829.6	−1.61191
$669$	5083.12	0.293759
$670$	−9322.76	−0.537567
$671$	−3569.28	−0.205351
$672$	−4600.51	−0.264090
$673$	−9019.75	−0.516621	−0.258310	−	0.966062i	$-0.583166\pi$
$673$	−9019.75	−0.516621	−0.258310	+	0.966062i	$0.583166\pi$
$674$	36196.4	2.06859
$675$	−1608.49	−0.0917199
$676$	0	0
$677$	−24923.6	−1.41491	−0.707454	−	0.706760i	$-0.750156\pi$
$677$	−24923.6	−1.41491	−0.707454	+	0.706760i	$0.750156\pi$
$678$	−16016.1	−0.907218
$679$	3592.76	0.203060
$680$	735.807	0.0414955
$681$	−1216.20	−0.0684359
$682$	21379.7	1.20039
$683$	−24634.2	−1.38009	−0.690044	−	0.723767i	$-0.742409\pi$
$683$	−24634.2	−1.38009	−0.690044	+	0.723767i	$0.742409\pi$
$684$	992.846	0.0555006
$685$	−3032.53	−0.169149
$686$	−15603.1	−0.868411
$687$	7078.61	0.393109
$688$	−7241.70	−0.401290
$689$	0	0
$690$	21487.2	1.18551
$691$	−10340.2	−0.569264	−0.284632	−	0.958637i	$-0.591871\pi$
$691$	−10340.2	−0.569264	−0.284632	+	0.958637i	$0.591871\pi$
$692$	2817.56	0.154780
$693$	923.102	0.0505999
$694$	−23024.3	−1.25935
$695$	3944.92	0.215308
$696$	−585.821	−0.0319045
$697$	−18650.0	−1.01351
$698$	38316.7	2.07780
$699$	2815.52	0.152350
$700$	−2922.19	−0.157784
$701$	−20833.9	−1.12252	−0.561258	−	0.827641i	$-0.689683\pi$
$701$	−20833.9	−1.12252	−0.561258	+	0.827641i	$0.689683\pi$
$702$	0	0
$703$	−4467.00	−0.239653
$704$	−9352.23	−0.500676
$705$	8216.69	0.438948
$706$	−16012.0	−0.853569
$707$	−4407.07	−0.234434
$708$	−6925.46	−0.367619
$709$	9189.56	0.486772	0.243386	−	0.969930i	$-0.421742\pi$
$709$	9189.56	0.486772	0.243386	+	0.969930i	$0.421742\pi$
$710$	−10355.9	−0.547395
$711$	−5614.52	−0.296148
$712$	1246.31	0.0656004
$713$	67621.8	3.55183
$714$	6686.25	0.350457
$715$	0	0
$716$	−23785.2	−1.24147
$717$	13992.8	0.728827
$718$	−442.788	−0.0230149
$719$	7503.22	0.389183	0.194592	−	0.980884i	$-0.437662\pi$
$719$	7503.22	0.389183	0.194592	+	0.980884i	$0.437662\pi$
$720$	−4513.31	−0.233613
$721$	−11238.5	−0.580503
$722$	−26921.6	−1.38770
$723$	−11324.8	−0.582537
$724$	31286.8	1.60603
$725$	11884.1	0.608779
$726$	−12500.9	−0.639053
$727$	−20727.2	−1.05740	−0.528700	−	0.848809i	$-0.677320\pi$
$727$	−20727.2	−1.05740	−0.528700	+	0.848809i	$0.677320\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−2055.93	−0.104237
$731$	10854.7	0.549216
$732$	−5120.92	−0.258572
$733$	17361.3	0.874836	0.437418	−	0.899258i	$-0.355893\pi$
$733$	17361.3	0.874836	0.437418	+	0.899258i	$0.355893\pi$
$734$	28292.4	1.42274
$735$	−7463.92	−0.374572
$736$	−56618.9	−2.83560
$737$	−4929.13	−0.246359
$738$	−7279.42	−0.363088
$739$	18093.8	0.900663	0.450331	−	0.892861i	$-0.351306\pi$
$739$	18093.8	0.900663	0.450331	+	0.892861i	$0.351306\pi$
$740$	−22254.1	−1.10551
$741$	0	0
$742$	−638.466	−0.0315887
$743$	−14875.3	−0.734482	−0.367241	−	0.930126i	$-0.619698\pi$
$743$	−14875.3	−0.734482	−0.367241	+	0.930126i	$0.619698\pi$
$744$	903.837	0.0445380
$745$	8540.85	0.420017
$746$	8976.07	0.440533
$747$	5938.87	0.290886
$748$	13202.9	0.645380
$749$	−5471.52	−0.266923
$750$	−18050.9	−0.878834
$751$	−17750.9	−0.862502	−0.431251	−	0.902232i	$-0.641928\pi$
$751$	−17750.9	−0.862502	−0.431251	+	0.902232i	$0.641928\pi$
$752$	−20993.1	−1.01801
$753$	−2882.09	−0.139481
$754$	0	0
$755$	−7187.25	−0.346451
$756$	1324.39	0.0637139
$757$	−10220.3	−0.490702	−0.245351	−	0.969434i	$-0.578903\pi$
$757$	−10220.3	−0.490702	−0.245351	+	0.969434i	$0.578903\pi$
$758$	−44351.1	−2.12520
$759$	11360.7	0.543303
$760$	105.967	0.00505765
$761$	−14112.0	−0.672221	−0.336110	−	0.941823i	$-0.609112\pi$
$761$	−14112.0	−0.672221	−0.336110	+	0.941823i	$0.609112\pi$
$762$	−28417.9	−1.35101
$763$	9345.13	0.443403
$764$	−23128.7	−1.09525
$765$	6765.10	0.319729
$766$	−17881.6	−0.843457
$767$	0	0
$768$	11508.2	0.540713
$769$	−22736.7	−1.06620	−0.533100	−	0.846052i	$-0.678973\pi$
$769$	−22736.7	−1.06620	−0.533100	+	0.846052i	$0.678973\pi$
$770$	3343.60	0.156487
$771$	−50.1905	−0.00234444
$772$	−20488.8	−0.955194
$773$	−343.173	−0.0159678	−0.00798388	−	0.999968i	$-0.502541\pi$
$773$	−343.173	−0.0159678	−0.00798388	+	0.999968i	$0.502541\pi$
$774$	4236.80	0.196755
$775$	−18335.4	−0.849844
$776$	590.999	0.0273397
$777$	−5958.69	−0.275118
$778$	−10323.8	−0.475740
$779$	−2685.86	−0.123531
$780$	0	0
$781$	−5475.37	−0.250863
$782$	82288.3	3.76294
$783$	−5386.11	−0.245829
$784$	19069.8	0.868706
$785$	−29511.9	−1.34181
$786$	27913.8	1.26673
$787$	−19086.4	−0.864496	−0.432248	−	0.901755i	$-0.642279\pi$
$787$	−19086.4	−0.864496	−0.432248	+	0.901755i	$0.642279\pi$
$788$	22673.7	1.02502
$789$	−1202.21	−0.0542455
$790$	−20336.6	−0.915876
$791$	−7882.74	−0.354334
$792$	151.848	0.00681272
$793$	0	0
$794$	8894.36	0.397543
$795$	−645.995	−0.0288190
$796$	32959.5	1.46761
$797$	12031.1	0.534709	0.267354	−	0.963598i	$-0.413851\pi$
$797$	12031.1	0.534709	0.267354	+	0.963598i	$0.413851\pi$
$798$	962.913	0.0427152
$799$	31467.0	1.39327
$800$	15352.1	0.678471
$801$	11458.7	0.505461
$802$	−32528.2	−1.43218
$803$	−1087.01	−0.0477706
$804$	−7071.93	−0.310208
$805$	10575.5	0.463027
$806$	0	0
$807$	6710.91	0.292732
$808$	−724.952	−0.0315640
$809$	10175.4	0.442210	0.221105	−	0.975250i	$-0.429034\pi$
$809$	10175.4	0.442210	0.221105	+	0.975250i	$0.429034\pi$
$810$	2640.54	0.114542
$811$	26754.1	1.15840	0.579201	−	0.815185i	$-0.303365\pi$
$811$	26754.1	1.15840	0.579201	+	0.815185i	$0.303365\pi$
$812$	−9785.08	−0.422893
$813$	−12056.7	−0.520106
$814$	−23185.7	−0.998353
$815$	11214.9	0.482011
$816$	−17284.4	−0.741513
$817$	1563.23	0.0669408
$818$	25383.9	1.08500
$819$	0	0
$820$	−13380.7	−0.569845
$821$	−15777.5	−0.670693	−0.335347	−	0.942095i	$-0.608853\pi$
$821$	−15777.5	−0.670693	−0.335347	+	0.942095i	$0.608853\pi$
$822$	−4532.97	−0.192342
$823$	−13863.9	−0.587197	−0.293599	−	0.955929i	$-0.594853\pi$
$823$	−13863.9	−0.587197	−0.293599	+	0.955929i	$0.594853\pi$
$824$	−1848.70	−0.0781583
$825$	−3080.42	−0.129996
$826$	−6716.66	−0.282933
$827$	−26835.0	−1.12835	−0.564175	−	0.825655i	$-0.690806\pi$
$827$	−26835.0	−1.12835	−0.564175	+	0.825655i	$0.690806\pi$
$828$	16299.4	0.684111
$829$	625.251	0.0261953	0.0130976	−	0.999914i	$-0.495831\pi$
$829$	625.251	0.0261953	0.0130976	+	0.999914i	$0.495831\pi$
$830$	21511.4	0.899604
$831$	20378.9	0.850704
$832$	0	0
$833$	−28584.2	−1.18893
$834$	5896.78	0.244831
$835$	−27308.8	−1.13181
$836$	1901.40	0.0786617
$837$	8309.98	0.343172
$838$	−5771.35	−0.237909
$839$	−27307.4	−1.12367	−0.561833	−	0.827251i	$-0.689904\pi$
$839$	−27307.4	−1.12367	−0.561833	+	0.827251i	$0.689904\pi$
$840$	141.353	0.00580610
$841$	15405.4	0.631656
$842$	38857.3	1.59039
$843$	−21860.4	−0.893135
$844$	−11340.6	−0.462510
$845$	0	0
$846$	12282.1	0.499135
$847$	−6152.66	−0.249596
$848$	1650.48	0.0668368
$849$	−7289.30	−0.294662
$850$	−22312.2	−0.900356
$851$	−73334.2	−2.95401
$852$	−7855.63	−0.315880
$853$	44801.9	1.79834	0.899172	−	0.437595i	$-0.144170\pi$
$853$	44801.9	1.79834	0.899172	+	0.437595i	$0.144170\pi$
$854$	−4966.53	−0.199006
$855$	974.268	0.0389699
$856$	−900.051	−0.0359382
$857$	−25167.1	−1.00314	−0.501571	−	0.865116i	$-0.667244\pi$
$857$	−25167.1	−1.00314	−0.501571	+	0.865116i	$0.667244\pi$
$858$	0	0
$859$	4059.10	0.161228	0.0806138	−	0.996745i	$-0.474312\pi$
$859$	4059.10	0.161228	0.0806138	+	0.996745i	$0.474312\pi$
$860$	7787.87	0.308795
$861$	−3582.76	−0.141812
$862$	13584.4	0.536759
$863$	818.924	0.0323019	0.0161509	−	0.999870i	$-0.494859\pi$
$863$	818.924	0.0323019	0.0161509	+	0.999870i	$0.494859\pi$
$864$	−6957.85	−0.273971
$865$	2764.84	0.108679
$866$	25184.6	0.988231
$867$	11168.9	0.437505
$868$	15096.9	0.590350
$869$	−10752.3	−0.419733
$870$	−19509.2	−0.760258
$871$	0	0
$872$	1537.25	0.0596993
$873$	5433.71	0.210657
$874$	11850.7	0.458644
$875$	−8884.23	−0.343248
$876$	−1559.56	−0.0601513
$877$	190.251	0.00732533	0.00366267	−	0.999993i	$-0.498834\pi$
$877$	190.251	0.00732533	0.00366267	+	0.999993i	$0.498834\pi$
$878$	11551.3	0.444007
$879$	12633.8	0.484785
$880$	−8643.43	−0.331102
$881$	−19803.4	−0.757315	−0.378657	−	0.925537i	$-0.623614\pi$
$881$	−19803.4	−0.757315	−0.378657	+	0.925537i	$0.623614\pi$
$882$	−11156.9	−0.425933
$883$	19652.1	0.748974	0.374487	−	0.927232i	$-0.377819\pi$
$883$	19652.1	0.748974	0.374487	+	0.927232i	$0.377819\pi$
$884$	0	0
$885$	−6795.87	−0.258125
$886$	43431.2	1.64684
$887$	−26295.0	−0.995379	−0.497689	−	0.867355i	$-0.665818\pi$
$887$	−26295.0	−0.995379	−0.497689	+	0.867355i	$0.665818\pi$
$888$	−980.189	−0.0370417
$889$	−13986.6	−0.527668
$890$	41505.1	1.56321
$891$	1396.11	0.0524930
$892$	13966.5	0.524253
$893$	4531.69	0.169818
$894$	12766.7	0.477608
$895$	−23340.2	−0.871704
$896$	−745.275	−0.0277878
$897$	0	0
$898$	55758.0	2.07201
$899$	−61397.0	−2.27776
$900$	−4419.54	−0.163687
$901$	−2473.93	−0.0914746
$902$	−13940.8	−0.514609
$903$	2085.25	0.0768470
$904$	−1296.69	−0.0477072
$905$	30701.4	1.12768
$906$	−10743.3	−0.393956
$907$	42417.3	1.55286	0.776429	−	0.630204i	$-0.217029\pi$
$907$	42417.3	1.55286	0.776429	+	0.630204i	$0.217029\pi$
$908$	−3341.66	−0.122133
$909$	−6665.29	−0.243205
$910$	0	0
$911$	−872.245	−0.0317220	−0.0158610	−	0.999874i	$-0.505049\pi$
$911$	−872.245	−0.0317220	−0.0158610	+	0.999874i	$0.505049\pi$
$912$	−2489.19	−0.0903788
$913$	11373.5	0.412276
$914$	69453.2	2.51347
$915$	−5025.10	−0.181557
$916$	19449.4	0.701557
$917$	13738.5	0.494749
$918$	10112.3	0.363569
$919$	−17181.4	−0.616716	−0.308358	−	0.951270i	$-0.599779\pi$
$919$	−17181.4	−0.616716	−0.308358	+	0.951270i	$0.599779\pi$
$920$	1739.64	0.0623415
$921$	24636.8	0.881444
$922$	46287.5	1.65336
$923$	0	0
$924$	2536.34	0.0903025
$925$	19884.4	0.706804
$926$	6503.25	0.230788
$927$	−16997.1	−0.602221
$928$	51407.0	1.81845
$929$	−56042.9	−1.97923	−0.989617	−	0.143728i	$-0.954091\pi$
$929$	−56042.9	−1.97923	−0.989617	+	0.143728i	$0.954091\pi$
$930$	30099.9	1.06130
$931$	−4116.52	−0.144912
$932$	7736.00	0.271890
$933$	−12715.7	−0.446187
$934$	−32843.3	−1.15060
$935$	12955.8	0.453155
$936$	0	0
$937$	−36672.5	−1.27859	−0.639295	−	0.768961i	$-0.720774\pi$
$937$	−36672.5	−1.27859	−0.639295	+	0.768961i	$0.720774\pi$
$938$	−6858.71	−0.238747
$939$	11423.5	0.397008
$940$	22576.4	0.783363
$941$	21069.0	0.729895	0.364947	−	0.931028i	$-0.381087\pi$
$941$	21069.0	0.729895	0.364947	+	0.931028i	$0.381087\pi$
$942$	−44113.7	−1.52580
$943$	−44093.4	−1.52267
$944$	17363.0	0.598642
$945$	1299.61	0.0447369
$946$	8113.87	0.278863
$947$	1838.70	0.0630938	0.0315469	−	0.999502i	$-0.489957\pi$
$947$	1838.70	0.0630938	0.0315469	+	0.999502i	$0.489957\pi$
$948$	−15426.6	−0.528516
$949$	0	0
$950$	−3213.27	−0.109739
$951$	−31493.0	−1.07385
$952$	541.330	0.0184292
$953$	13599.8	0.462266	0.231133	−	0.972922i	$-0.425757\pi$
$953$	13599.8	0.462266	0.231133	+	0.972922i	$0.425757\pi$
$954$	−965.620	−0.0327705
$955$	−22695.9	−0.769029
$956$	38446.9	1.30069
$957$	−10314.9	−0.348416
$958$	7365.75	0.248410
$959$	−2231.02	−0.0751235
$960$	−13166.8	−0.442662
$961$	64935.6	2.17971
$962$	0	0
$963$	−8275.17	−0.276909
$964$	−31116.4	−1.03962
$965$	−20105.5	−0.670692
$966$	15808.0	0.526516
$967$	−2081.30	−0.0692141	−0.0346070	−	0.999401i	$-0.511018\pi$
$967$	−2081.30	−0.0692141	−0.0346070	+	0.999401i	$0.511018\pi$
$968$	−1012.10	−0.0336054
$969$	3731.10	0.123695
$970$	19681.6	0.651484
$971$	1636.62	0.0540904	0.0270452	−	0.999634i	$-0.491390\pi$
$971$	1636.62	0.0540904	0.0270452	+	0.999634i	$0.491390\pi$
$972$	2003.02	0.0660977
$973$	2902.26	0.0956240
$974$	−31592.9	−1.03932
$975$	0	0
$976$	12838.8	0.421066
$977$	29387.1	0.962311	0.481156	−	0.876635i	$-0.340217\pi$
$977$	29387.1	0.962311	0.481156	+	0.876635i	$0.340217\pi$
$978$	16763.7	0.548104
$979$	21944.6	0.716396
$980$	−20508.1	−0.668476
$981$	14133.6	0.459992
$982$	69304.4	2.25213
$983$	−24084.4	−0.781457	−0.390728	−	0.920506i	$-0.627777\pi$
$983$	−24084.4	−0.781457	−0.390728	+	0.920506i	$0.627777\pi$
$984$	−589.355	−0.0190934
$985$	22249.4	0.719722
$986$	−74713.4	−2.41314
$987$	6044.98	0.194948
$988$	0	0
$989$	25663.4	0.825125
$990$	5056.88	0.162342
$991$	1413.43	0.0453068	0.0226534	−	0.999743i	$-0.492789\pi$
$991$	1413.43	0.0453068	0.0226534	+	0.999743i	$0.492789\pi$
$992$	−79313.5	−2.53851
$993$	35715.7	1.14139
$994$	−7618.79	−0.243112
$995$	32342.7	1.03049
$996$	16317.8	0.519126
$997$	−33357.4	−1.05962	−0.529809	−	0.848117i	$-0.677737\pi$
$997$	−33357.4	−1.05962	−0.529809	+	0.848117i	$0.677737\pi$
$998$	21583.1	0.684570
$999$	−9011.97	−0.285411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.p.1.7	yes	9
3.2	odd	2		1521.4.a.bf.1.3		9
13.5	odd	4		507.4.b.k.337.4		18
13.8	odd	4		507.4.b.k.337.15		18
13.12	even	2		507.4.a.o.1.3	✓	9
39.38	odd	2		1521.4.a.bi.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.4.a.o.1.3	✓	9	13.12	even	2
507.4.a.p.1.7	yes	9	1.1	even	1	trivial
507.4.b.k.337.4		18	13.5	odd	4
507.4.b.k.337.15		18	13.8	odd	4
1521.4.a.bf.1.3		9	3.2	odd	2
1521.4.a.bi.1.7		9	39.38	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)

\(f(q)\)	\(=\)	\(q+4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} +8.08864 q^{5} +12.0907 q^{6} +5.95078 q^{7} +0.978887 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} +8.08864 q^{5} +12.0907 q^{6} +5.95078 q^{7} +0.978887 q^{8} +9.00000 q^{9} +32.5992 q^{10} +17.2359 q^{11} +24.7287 q^{12} +23.9831 q^{14} +24.2659 q^{15} -61.9979 q^{16} +92.9299 q^{17} +36.2722 q^{18} +13.3832 q^{19} +66.6738 q^{20} +17.8523 q^{21} +69.4648 q^{22} +219.710 q^{23} +2.93666 q^{24} -59.5738 q^{25} +27.0000 q^{27} +49.0516 q^{28} -199.485 q^{29} +97.7977 q^{30} +307.777 q^{31} -257.698 q^{32} +51.7076 q^{33} +374.531 q^{34} +48.1337 q^{35} +74.1860 q^{36} -333.777 q^{37} +53.9376 q^{38} +7.91787 q^{40} -200.689 q^{41} +71.9493 q^{42} +116.806 q^{43} +142.073 q^{44} +72.7978 q^{45} +885.487 q^{46} +338.610 q^{47} -185.994 q^{48} -307.588 q^{49} -240.097 q^{50} +278.790 q^{51} -26.6215 q^{53} +108.817 q^{54} +139.415 q^{55} +5.82514 q^{56} +40.1496 q^{57} -803.976 q^{58} -280.058 q^{59} +200.021 q^{60} -207.084 q^{61} +1240.42 q^{62} +53.5570 q^{63} -542.603 q^{64} +208.394 q^{66} -285.981 q^{67} +766.011 q^{68} +659.131 q^{69} +193.991 q^{70} -317.673 q^{71} +8.80999 q^{72} -63.0668 q^{73} -1345.20 q^{74} -178.721 q^{75} +110.316 q^{76} +102.567 q^{77} -623.835 q^{79} -501.479 q^{80} +81.0000 q^{81} -808.824 q^{82} +659.874 q^{83} +147.155 q^{84} +751.677 q^{85} +470.755 q^{86} -598.456 q^{87} +16.8720 q^{88} +1273.19 q^{89} +293.393 q^{90} +1811.05 q^{92} +923.331 q^{93} +1364.68 q^{94} +108.252 q^{95} -773.094 q^{96} +603.746 q^{97} -1239.66 q^{98} +155.123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 6 q^{2} + 27 q^{3} + 44 q^{4} + 33 q^{5} + 18 q^{6} + 83 q^{7} + 87 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q + 6 * q^2 + 27 * q^3 + 44 * q^4 + 33 * q^5 + 18 * q^6 + 83 * q^7 + 87 * q^8 + 81 * q^9	\( 9 q + 6 q^{2} + 27 q^{3} + 44 q^{4} + 33 q^{5} + 18 q^{6} + 83 q^{7} + 87 q^{8} + 81 q^{9} - 54 q^{10} + 85 q^{11} + 132 q^{12} + 158 q^{14} + 99 q^{15} + 216 q^{16} + 178 q^{17} + 54 q^{18} + 352 q^{19} + 402 q^{20} + 249 q^{21} - 630 q^{22} + 150 q^{23} + 261 q^{24} - 20 q^{25} + 243 q^{27} + 940 q^{28} - 97 q^{29} - 162 q^{30} + 717 q^{31} + 707 q^{32} + 255 q^{33} + 632 q^{34} - 418 q^{35} + 396 q^{36} + 1108 q^{37} - 660 q^{38} - 1506 q^{40} + 334 q^{41} + 474 q^{42} + 242 q^{43} - 307 q^{44} + 297 q^{45} + 979 q^{46} - 184 q^{47} + 648 q^{48} - 38 q^{49} - 2031 q^{50} + 534 q^{51} - 151 q^{53} + 162 q^{54} + 2064 q^{55} + 2276 q^{56} + 1056 q^{57} + 1161 q^{58} + 537 q^{59} + 1206 q^{60} - 1340 q^{61} + 347 q^{62} + 747 q^{63} + 893 q^{64} - 1890 q^{66} + 2308 q^{67} + 2785 q^{68} + 450 q^{69} - 1420 q^{70} + 96 q^{71} + 783 q^{72} + 2505 q^{73} - 1191 q^{74} - 60 q^{75} + 2409 q^{76} - 2142 q^{77} - 1591 q^{79} - 2671 q^{80} + 729 q^{81} + 1517 q^{82} + 1539 q^{83} + 2820 q^{84} + 4296 q^{85} - 3763 q^{86} - 291 q^{87} - 3716 q^{88} - 592 q^{89} - 486 q^{90} + 515 q^{92} + 2151 q^{93} - 692 q^{94} + 4158 q^{95} + 2121 q^{96} + 1445 q^{97} + 1457 q^{98} + 765 q^{99}+O(q^{100}) \) 9 * q + 6 * q^2 + 27 * q^3 + 44 * q^4 + 33 * q^5 + 18 * q^6 + 83 * q^7 + 87 * q^8 + 81 * q^9 - 54 * q^10 + 85 * q^11 + 132 * q^12 + 158 * q^14 + 99 * q^15 + 216 * q^16 + 178 * q^17 + 54 * q^18 + 352 * q^19 + 402 * q^20 + 249 * q^21 - 630 * q^22 + 150 * q^23 + 261 * q^24 - 20 * q^25 + 243 * q^27 + 940 * q^28 - 97 * q^29 - 162 * q^30 + 717 * q^31 + 707 * q^32 + 255 * q^33 + 632 * q^34 - 418 * q^35 + 396 * q^36 + 1108 * q^37 - 660 * q^38 - 1506 * q^40 + 334 * q^41 + 474 * q^42 + 242 * q^43 - 307 * q^44 + 297 * q^45 + 979 * q^46 - 184 * q^47 + 648 * q^48 - 38 * q^49 - 2031 * q^50 + 534 * q^51 - 151 * q^53 + 162 * q^54 + 2064 * q^55 + 2276 * q^56 + 1056 * q^57 + 1161 * q^58 + 537 * q^59 + 1206 * q^60 - 1340 * q^61 + 347 * q^62 + 747 * q^63 + 893 * q^64 - 1890 * q^66 + 2308 * q^67 + 2785 * q^68 + 450 * q^69 - 1420 * q^70 + 96 * q^71 + 783 * q^72 + 2505 * q^73 - 1191 * q^74 - 60 * q^75 + 2409 * q^76 - 2142 * q^77 - 1591 * q^79 - 2671 * q^80 + 729 * q^81 + 1517 * q^82 + 1539 * q^83 + 2820 * q^84 + 4296 * q^85 - 3763 * q^86 - 291 * q^87 - 3716 * q^88 - 592 * q^89 - 486 * q^90 + 515 * q^92 + 2151 * q^93 - 692 * q^94 + 4158 * q^95 + 2121 * q^96 + 1445 * q^97 + 1457 * q^98 + 765 * q^99

Introduction

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