LMFDB - Embedded newform 507.4.a.q.1.3

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} - 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			1.3
Root			$2.86460$ 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)

$f(q)$	$=$	$q-1.86460 q^{2} -3.00000 q^{3} -4.52327 q^{4} -2.36060 q^{5} +5.59380 q^{6} -4.86461 q^{7} +23.3509 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.86460 q^{2} -3.00000 q^{3} -4.52327 q^{4} -2.36060 q^{5} +5.59380 q^{6} -4.86461 q^{7} +23.3509 q^{8} +9.00000 q^{9} +4.40158 q^{10} -35.1633 q^{11} +13.5698 q^{12} +9.07054 q^{14} +7.08181 q^{15} -7.35391 q^{16} -33.1102 q^{17} -16.7814 q^{18} -104.145 q^{19} +10.6776 q^{20} +14.5938 q^{21} +65.5656 q^{22} -86.3184 q^{23} -70.0526 q^{24} -119.428 q^{25} -27.0000 q^{27} +22.0039 q^{28} -118.190 q^{29} -13.2047 q^{30} +262.589 q^{31} -173.095 q^{32} +105.490 q^{33} +61.7373 q^{34} +11.4834 q^{35} -40.7094 q^{36} -59.6265 q^{37} +194.189 q^{38} -55.1222 q^{40} -76.9932 q^{41} -27.2116 q^{42} -344.731 q^{43} +159.053 q^{44} -21.2454 q^{45} +160.949 q^{46} +415.931 q^{47} +22.0617 q^{48} -319.336 q^{49} +222.685 q^{50} +99.3307 q^{51} +141.710 q^{53} +50.3442 q^{54} +83.0067 q^{55} -113.593 q^{56} +312.436 q^{57} +220.376 q^{58} +598.746 q^{59} -32.0329 q^{60} +791.010 q^{61} -489.624 q^{62} -43.7814 q^{63} +381.584 q^{64} -196.697 q^{66} +22.1123 q^{67} +149.766 q^{68} +258.955 q^{69} -21.4120 q^{70} -599.641 q^{71} +210.158 q^{72} +776.246 q^{73} +111.180 q^{74} +358.283 q^{75} +471.076 q^{76} +171.056 q^{77} -1276.41 q^{79} +17.3597 q^{80} +81.0000 q^{81} +143.562 q^{82} +493.338 q^{83} -66.0117 q^{84} +78.1601 q^{85} +642.785 q^{86} +354.569 q^{87} -821.095 q^{88} +1251.31 q^{89} +39.6142 q^{90} +390.441 q^{92} -787.767 q^{93} -775.545 q^{94} +245.845 q^{95} +519.285 q^{96} -76.4923 q^{97} +595.433 q^{98} -316.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.86460	−0.659236	−0.329618	−	0.944114i	$-0.606920\pi$
$2$	−1.86460	−0.659236	−0.329618	+	0.944114i	$0.606920\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.52327	−0.565408
$5$	−2.36060	−0.211139	−0.105569	−	0.994412i	$-0.533667\pi$
$5$	−2.36060	−0.211139	−0.105569	+	0.994412i	$0.533667\pi$
$6$	5.59380	0.380610
$7$	−4.86461	−0.262664	−0.131332	−	0.991338i	$-0.541925\pi$
$7$	−4.86461	−0.262664	−0.131332	+	0.991338i	$0.541925\pi$
$8$	23.3509	1.03197
$9$	9.00000	0.333333
$10$	4.40158	0.139190
$11$	−35.1633	−0.963832	−0.481916	−	0.876218i	$-0.660059\pi$
$11$	−35.1633	−0.963832	−0.481916	+	0.876218i	$0.660059\pi$
$12$	13.5698	0.326439
$13$	0	0
$13$	0	0
$14$	9.07054	0.173157
$15$	7.08181	0.121901
$16$	−7.35391	−0.114905
$17$	−33.1102	−0.472377	−0.236189	−	0.971707i	$-0.575898\pi$
$17$	−33.1102	−0.472377	−0.236189	+	0.971707i	$0.575898\pi$
$18$	−16.7814	−0.219745
$19$	−104.145	−1.25750	−0.628751	−	0.777607i	$-0.716434\pi$
$19$	−104.145	−1.25750	−0.628751	+	0.777607i	$0.716434\pi$
$20$	10.6776	0.119380
$21$	14.5938	0.151649
$22$	65.5656	0.635392
$23$	−86.3184	−0.782549	−0.391275	−	0.920274i	$-0.627966\pi$
$23$	−86.3184	−0.782549	−0.391275	+	0.920274i	$0.627966\pi$
$24$	−70.0526	−0.595810
$25$	−119.428	−0.955420
$26$	0	0
$27$	−27.0000	−0.192450
$28$	22.0039	0.148512
$29$	−118.190	−0.756802	−0.378401	−	0.925642i	$-0.623526\pi$
$29$	−118.190	−0.756802	−0.378401	+	0.925642i	$0.623526\pi$
$30$	−13.2047	−0.0803615
$31$	262.589	1.52137	0.760684	−	0.649122i	$-0.224864\pi$
$31$	262.589	1.52137	0.760684	+	0.649122i	$0.224864\pi$
$32$	−173.095	−0.956224
$33$	105.490	0.556468
$34$	61.7373	0.311408
$35$	11.4834	0.0554586
$36$	−40.7094	−0.188469
$37$	−59.6265	−0.264933	−0.132467	−	0.991187i	$-0.542290\pi$
$37$	−59.6265	−0.264933	−0.132467	+	0.991187i	$0.542290\pi$
$38$	194.189	0.828990
$39$	0	0
$40$	−55.1222	−0.217890
$41$	−76.9932	−0.293276	−0.146638	−	0.989190i	$-0.546845\pi$
$41$	−76.9932	−0.293276	−0.146638	+	0.989190i	$0.546845\pi$
$42$	−27.2116	−0.0999725
$43$	−344.731	−1.22258	−0.611290	−	0.791406i	$-0.709349\pi$
$43$	−344.731	−1.22258	−0.611290	+	0.791406i	$0.709349\pi$
$44$	159.053	0.544959
$45$	−21.2454	−0.0703796
$46$	160.949	0.515884
$47$	415.931	1.29085	0.645423	−	0.763825i	$-0.276681\pi$
$47$	415.931	1.29085	0.645423	+	0.763825i	$0.276681\pi$
$48$	22.0617	0.0663404
$49$	−319.336	−0.931008
$50$	222.685	0.629847
$51$	99.3307	0.272727
$52$	0	0
$53$	141.710	0.367271	0.183636	−	0.982994i	$-0.441213\pi$
$53$	141.710	0.367271	0.183636	+	0.982994i	$0.441213\pi$
$54$	50.3442	0.126870
$55$	83.0067	0.203502
$56$	−113.593	−0.271062
$57$	312.436	0.726019
$58$	220.376	0.498911
$59$	598.746	1.32119	0.660594	−	0.750744i	$-0.270305\pi$
$59$	598.746	1.32119	0.660594	+	0.750744i	$0.270305\pi$
$60$	−32.0329	−0.0689239
$61$	791.010	1.66030	0.830151	−	0.557539i	$-0.188254\pi$
$61$	791.010	1.66030	0.830151	+	0.557539i	$0.188254\pi$
$62$	−489.624	−1.00294
$63$	−43.7814	−0.0875547
$64$	381.584	0.745281
$65$	0	0
$66$	−196.697	−0.366844
$67$	22.1123	0.0403201	0.0201601	−	0.999797i	$-0.493582\pi$
$67$	22.1123	0.0403201	0.0201601	+	0.999797i	$0.493582\pi$
$68$	149.766	0.267086
$69$	258.955	0.451805
$70$	−21.4120	−0.0365603
$71$	−599.641	−1.00231	−0.501157	−	0.865356i	$-0.667092\pi$
$71$	−599.641	−1.00231	−0.501157	+	0.865356i	$0.667092\pi$
$72$	210.158	0.343991
$73$	776.246	1.24456	0.622279	−	0.782795i	$-0.286207\pi$
$73$	776.246	1.24456	0.622279	+	0.782795i	$0.286207\pi$
$74$	111.180	0.174653
$75$	358.283	0.551612
$76$	471.076	0.711002
$77$	171.056	0.253164
$78$	0	0
$79$	−1276.41	−1.81781	−0.908904	−	0.417006i	$-0.863080\pi$
$79$	−1276.41	−1.81781	−0.908904	+	0.417006i	$0.863080\pi$
$80$	17.3597	0.0242609
$81$	81.0000	0.111111
$82$	143.562	0.193338
$83$	493.338	0.652420	0.326210	−	0.945297i	$-0.394228\pi$
$83$	493.338	0.652420	0.326210	+	0.945297i	$0.394228\pi$
$84$	−66.0117	−0.0857437
$85$	78.1601	0.0997371
$86$	642.785	0.805969
$87$	354.569	0.436940
$88$	−821.095	−0.994648
$89$	1251.31	1.49032	0.745161	−	0.666885i	$-0.232373\pi$
$89$	1251.31	1.49032	0.745161	+	0.666885i	$0.232373\pi$
$90$	39.6142	0.0463967
$91$	0	0
$92$	390.441	0.442460
$93$	−787.767	−0.878362
$94$	−775.545	−0.850972
$95$	245.845	0.265507
$96$	519.285	0.552076
$97$	−76.4923	−0.0800682	−0.0400341	−	0.999198i	$-0.512747\pi$
$97$	−76.4923	−0.0800682	−0.0400341	+	0.999198i	$0.512747\pi$
$98$	595.433	0.613753
$99$	−316.470	−0.321277
$100$	540.203	0.540203
$101$	1218.67	1.20062	0.600310	−	0.799768i	$-0.295044\pi$
$101$	1218.67	1.20062	0.600310	+	0.799768i	$0.295044\pi$
$102$	−185.212	−0.179791
$103$	−989.436	−0.946524	−0.473262	−	0.880922i	$-0.656924\pi$
$103$	−989.436	−0.946524	−0.473262	+	0.880922i	$0.656924\pi$
$104$	0	0
$105$	−34.4502	−0.0320190
$106$	−264.232	−0.242118
$107$	−1126.11	−1.01743	−0.508717	−	0.860934i	$-0.669880\pi$
$107$	−1126.11	−1.01743	−0.508717	+	0.860934i	$0.669880\pi$
$108$	122.128	0.108813
$109$	−44.7158	−0.0392935	−0.0196468	−	0.999807i	$-0.506254\pi$
$109$	−44.7158	−0.0392935	−0.0196468	+	0.999807i	$0.506254\pi$
$110$	−154.774	−0.134156
$111$	178.879	0.152959
$112$	35.7739	0.0301814
$113$	1570.11	1.30711	0.653554	−	0.756880i	$-0.273277\pi$
$113$	1570.11	1.30711	0.653554	+	0.756880i	$0.273277\pi$
$114$	−582.567	−0.478618
$115$	203.764	0.165226
$116$	534.603	0.427902
$117$	0	0
$118$	−1116.42	−0.870974
$119$	161.068	0.124076
$120$	165.367	0.125799
$121$	−94.5390	−0.0710285
$122$	−1474.92	−1.09453
$123$	230.980	0.169323
$124$	−1187.76	−0.860194
$125$	576.996	0.412865
$126$	81.6349	0.0577192
$127$	691.316	0.483027	0.241513	−	0.970397i	$-0.422356\pi$
$127$	691.316	0.483027	0.241513	+	0.970397i	$0.422356\pi$
$128$	673.258	0.464907
$129$	1034.19	0.705857
$130$	0	0
$131$	2768.65	1.84655	0.923274	−	0.384143i	$-0.125503\pi$
$131$	2768.65	1.84655	0.923274	+	0.384143i	$0.125503\pi$
$132$	−477.160	−0.314632
$133$	506.625	0.330301
$134$	−41.2306	−0.0265804
$135$	63.7363	0.0406337
$136$	−773.153	−0.487480
$137$	1345.44	0.839041	0.419520	−	0.907746i	$-0.362198\pi$
$137$	1345.44	0.839041	0.419520	+	0.907746i	$0.362198\pi$
$138$	−482.848	−0.297846
$139$	1859.48	1.13467	0.567334	−	0.823488i	$-0.307975\pi$
$139$	1859.48	1.13467	0.567334	+	0.823488i	$0.307975\pi$
$140$	−51.9425	−0.0313567
$141$	−1247.79	−0.745271
$142$	1118.09	0.660761
$143$	0	0
$144$	−66.1852	−0.0383016
$145$	278.999	0.159790
$146$	−1447.39	−0.820457
$147$	958.007	0.537518
$148$	269.706	0.149796
$149$	1425.71	0.783885	0.391942	−	0.919990i	$-0.371803\pi$
$149$	1425.71	0.783885	0.391942	+	0.919990i	$0.371803\pi$
$150$	−668.054	−0.363642
$151$	−1692.79	−0.912299	−0.456149	−	0.889903i	$-0.650772\pi$
$151$	−1692.79	−0.912299	−0.456149	+	0.889903i	$0.650772\pi$
$152$	−2431.88	−1.29771
$153$	−297.992	−0.157459
$154$	−318.951	−0.166895
$155$	−619.869	−0.321220
$156$	0	0
$157$	−527.380	−0.268086	−0.134043	−	0.990976i	$-0.542796\pi$
$157$	−527.380	−0.268086	−0.134043	+	0.990976i	$0.542796\pi$
$158$	2379.99	1.19836
$159$	−425.130	−0.212044
$160$	408.609	0.201896
$161$	419.905	0.205548
$162$	−151.033	−0.0732484
$163$	−2970.91	−1.42760	−0.713802	−	0.700348i	$-0.753028\pi$
$163$	−2970.91	−1.42760	−0.713802	+	0.700348i	$0.753028\pi$
$164$	348.261	0.165821
$165$	−249.020	−0.117492
$166$	−919.877	−0.430098
$167$	−406.803	−0.188499	−0.0942497	−	0.995549i	$-0.530045\pi$
$167$	−406.803	−0.188499	−0.0942497	+	0.995549i	$0.530045\pi$
$168$	340.778	0.156498
$169$	0	0
$170$	−145.737	−0.0657503
$171$	−937.307	−0.419167
$172$	1559.31	0.691257
$173$	−2892.70	−1.27126	−0.635629	−	0.771994i	$-0.719259\pi$
$173$	−2892.70	−1.27126	−0.635629	+	0.771994i	$0.719259\pi$
$174$	−661.129	−0.288046
$175$	580.968	0.250955
$176$	258.588	0.110749
$177$	−1796.24	−0.762788
$178$	−2333.19	−0.982473
$179$	3772.31	1.57517	0.787586	−	0.616204i	$-0.211330\pi$
$179$	3772.31	1.57517	0.787586	+	0.616204i	$0.211330\pi$
$180$	96.0988	0.0397932
$181$	−1673.88	−0.687395	−0.343698	−	0.939080i	$-0.611679\pi$
$181$	−1673.88	−0.687395	−0.343698	+	0.939080i	$0.611679\pi$
$182$	0	0
$183$	−2373.03	−0.958576
$184$	−2015.61	−0.807570
$185$	140.754	0.0559377
$186$	1468.87	0.579048
$187$	1164.27	0.455292
$188$	−1881.37	−0.729856
$189$	131.344	0.0505497
$190$	−458.403	−0.175032
$191$	−5024.84	−1.90359	−0.951793	−	0.306740i	$-0.900762\pi$
$191$	−5024.84	−1.90359	−0.951793	+	0.306740i	$0.900762\pi$
$192$	−1144.75	−0.430288
$193$	−2398.57	−0.894575	−0.447287	−	0.894390i	$-0.647610\pi$
$193$	−2398.57	−0.894575	−0.447287	+	0.894390i	$0.647610\pi$
$194$	142.628	0.0527838
$195$	0	0
$196$	1444.44	0.526400
$197$	4579.71	1.65630	0.828150	−	0.560507i	$-0.189394\pi$
$197$	4579.71	1.65630	0.828150	+	0.560507i	$0.189394\pi$
$198$	590.090	0.211797
$199$	177.539	0.0632431	0.0316215	−	0.999500i	$-0.489933\pi$
$199$	177.539	0.0632431	0.0316215	+	0.999500i	$0.489933\pi$
$200$	−2788.74	−0.985968
$201$	−66.3369	−0.0232788
$202$	−2272.34	−0.791491
$203$	574.946	0.198785
$204$	−449.299	−0.154202
$205$	181.750	0.0619220
$206$	1844.90	0.623983
$207$	−776.866	−0.260850
$208$	0	0
$209$	3662.09	1.21202
$210$	64.2359	0.0211081
$211$	4363.80	1.42378	0.711888	−	0.702293i	$-0.247841\pi$
$211$	4363.80	1.42378	0.711888	+	0.702293i	$0.247841\pi$
$212$	−640.992	−0.207658
$213$	1798.92	0.578687
$214$	2099.75	0.670729
$215$	813.773	0.258134
$216$	−630.474	−0.198603
$217$	−1277.39	−0.399609
$218$	83.3770	0.0259037
$219$	−2328.74	−0.718546
$220$	−375.462	−0.115062
$221$	0	0
$222$	−333.539	−0.100836
$223$	1691.78	0.508026	0.254013	−	0.967201i	$-0.418249\pi$
$223$	1691.78	0.508026	0.254013	+	0.967201i	$0.418249\pi$
$224$	842.039	0.251166
$225$	−1074.85	−0.318473
$226$	−2927.62	−0.861692
$227$	3553.37	1.03897	0.519484	−	0.854480i	$-0.326124\pi$
$227$	3553.37	1.03897	0.519484	+	0.854480i	$0.326124\pi$
$228$	−1413.23	−0.410497
$229$	−3780.28	−1.09086	−0.545432	−	0.838155i	$-0.683635\pi$
$229$	−3780.28	−1.09086	−0.545432	+	0.838155i	$0.683635\pi$
$230$	−379.937	−0.108923
$231$	−513.167	−0.146164
$232$	−2759.83	−0.780999
$233$	−6588.54	−1.85249	−0.926243	−	0.376926i	$-0.876981\pi$
$233$	−6588.54	−1.85249	−0.926243	+	0.376926i	$0.876981\pi$
$234$	0	0
$235$	−981.849	−0.272548
$236$	−2708.29	−0.747010
$237$	3829.22	1.04951
$238$	−300.328	−0.0817956
$239$	−3252.33	−0.880233	−0.440117	−	0.897941i	$-0.645063\pi$
$239$	−3252.33	−0.880233	−0.440117	+	0.897941i	$0.645063\pi$
$240$	−52.0790	−0.0140070
$241$	3173.99	0.848360	0.424180	−	0.905578i	$-0.360562\pi$
$241$	3173.99	0.848360	0.424180	+	0.905578i	$0.360562\pi$
$242$	176.277	0.0468245
$243$	−243.000	−0.0641500
$244$	−3577.95	−0.938749
$245$	753.825	0.196572
$246$	−430.685	−0.111624
$247$	0	0
$248$	6131.69	1.57001
$249$	−1480.01	−0.376675
$250$	−1075.87	−0.272175
$251$	−1493.79	−0.375647	−0.187823	−	0.982203i	$-0.560143\pi$
$251$	−1493.79	−0.375647	−0.187823	+	0.982203i	$0.560143\pi$
$252$	198.035	0.0495041
$253$	3035.24	0.754246
$254$	−1289.03	−0.318428
$255$	−234.480	−0.0575833
$256$	−4308.03	−1.05177
$257$	2979.55	0.723188	0.361594	−	0.932336i	$-0.382233\pi$
$257$	2979.55	0.723188	0.361594	+	0.932336i	$0.382233\pi$
$258$	−1928.36	−0.465326
$259$	290.059	0.0695884
$260$	0	0
$261$	−1063.71	−0.252267
$262$	−5162.42	−1.21731
$263$	1090.01	0.255562	0.127781	−	0.991802i	$-0.459214\pi$
$263$	1090.01	0.255562	0.127781	+	0.991802i	$0.459214\pi$
$264$	2463.29	0.574260
$265$	−334.521	−0.0775451
$266$	−944.653	−0.217746
$267$	−3753.93	−0.860438
$268$	−100.020	−0.0227973
$269$	−4586.58	−1.03959	−0.519793	−	0.854292i	$-0.673991\pi$
$269$	−4586.58	−1.03959	−0.519793	+	0.854292i	$0.673991\pi$
$270$	−118.843	−0.0267872
$271$	−5480.65	−1.22851	−0.614254	−	0.789108i	$-0.710543\pi$
$271$	−5480.65	−1.22851	−0.614254	+	0.789108i	$0.710543\pi$
$272$	243.490	0.0542784
$273$	0	0
$274$	−2508.71	−0.553126
$275$	4199.47	0.920864
$276$	−1171.32	−0.255454
$277$	3856.51	0.836518	0.418259	−	0.908328i	$-0.362640\pi$
$277$	3856.51	0.836518	0.418259	+	0.908328i	$0.362640\pi$
$278$	−3467.18	−0.748013
$279$	2363.30	0.507123
$280$	268.148	0.0572317
$281$	5331.62	1.13188	0.565939	−	0.824447i	$-0.308514\pi$
$281$	5331.62	1.13188	0.565939	+	0.824447i	$0.308514\pi$
$282$	2326.64	0.491309
$283$	5430.68	1.14071	0.570354	−	0.821399i	$-0.306806\pi$
$283$	5430.68	1.14071	0.570354	+	0.821399i	$0.306806\pi$
$284$	2712.34	0.566717
$285$	−737.536	−0.153291
$286$	0	0
$287$	374.542	0.0770331
$288$	−1557.85	−0.318741
$289$	−3816.71	−0.776860
$290$	−520.221	−0.105339
$291$	229.477	0.0462274
$292$	−3511.17	−0.703684
$293$	−950.151	−0.189449	−0.0947243	−	0.995504i	$-0.530197\pi$
$293$	−950.151	−0.189449	−0.0947243	+	0.995504i	$0.530197\pi$
$294$	−1786.30	−0.354351
$295$	−1413.40	−0.278954
$296$	−1392.33	−0.273404
$297$	949.410	0.185489
$298$	−2658.38	−0.516765
$299$	0	0
$300$	−1620.61	−0.311886
$301$	1676.98	0.321128
$302$	3156.37	0.601420
$303$	−3656.02	−0.693178
$304$	765.874	0.144493
$305$	−1867.26	−0.350554
$306$	555.636	0.103803
$307$	−9212.70	−1.71269	−0.856346	−	0.516403i	$-0.827271\pi$
$307$	−9212.70	−1.71269	−0.856346	+	0.516403i	$0.827271\pi$
$308$	−773.731	−0.143141
$309$	2968.31	0.546476
$310$	1155.81	0.211759
$311$	2395.47	0.436767	0.218383	−	0.975863i	$-0.429922\pi$
$311$	2395.47	0.436767	0.218383	+	0.975863i	$0.429922\pi$
$312$	0	0
$313$	−3760.86	−0.679157	−0.339578	−	0.940578i	$-0.610284\pi$
$313$	−3760.86	−0.679157	−0.339578	+	0.940578i	$0.610284\pi$
$314$	983.353	0.176732
$315$	103.351	0.0184862
$316$	5773.52	1.02780
$317$	1509.19	0.267396	0.133698	−	0.991022i	$-0.457315\pi$
$317$	1509.19	0.267396	0.133698	+	0.991022i	$0.457315\pi$
$318$	792.697	0.139787
$319$	4155.94	0.729430
$320$	−900.769	−0.157358
$321$	3378.34	0.587416
$322$	−782.955	−0.135504
$323$	3448.27	0.594015
$324$	−366.385	−0.0628232
$325$	0	0
$326$	5539.55	0.941127
$327$	134.147	0.0226861
$328$	−1797.86	−0.302653
$329$	−2023.34	−0.339059
$330$	464.323	0.0774550
$331$	1508.07	0.250426	0.125213	−	0.992130i	$-0.460039\pi$
$331$	1508.07	0.250426	0.125213	+	0.992130i	$0.460039\pi$
$332$	−2231.50	−0.368884
$333$	−536.638	−0.0883111
$334$	758.525	0.124265
$335$	−52.1984	−0.00851314
$336$	−107.322	−0.0174252
$337$	8030.49	1.29807	0.649033	−	0.760760i	$-0.275173\pi$
$337$	8030.49	1.29807	0.649033	+	0.760760i	$0.275173\pi$
$338$	0	0
$339$	−4710.32	−0.754659
$340$	−353.539	−0.0563922
$341$	−9233.51	−1.46634
$342$	1747.70	0.276330
$343$	3222.00	0.507206
$344$	−8049.77	−1.26167
$345$	−611.291	−0.0953936
$346$	5393.72	0.838059
$347$	6414.73	0.992394	0.496197	−	0.868210i	$-0.334729\pi$
$347$	6414.73	0.992394	0.496197	+	0.868210i	$0.334729\pi$
$348$	−1603.81	−0.247050
$349$	3381.63	0.518667	0.259333	−	0.965788i	$-0.416497\pi$
$349$	3381.63	0.518667	0.259333	+	0.965788i	$0.416497\pi$
$350$	−1083.27	−0.165438
$351$	0	0
$352$	6086.60	0.921639
$353$	6521.67	0.983325	0.491662	−	0.870786i	$-0.336389\pi$
$353$	6521.67	0.983325	0.491662	+	0.870786i	$0.336389\pi$
$354$	3349.26	0.502857
$355$	1415.52	0.211627
$356$	−5660.01	−0.842640
$357$	−483.205	−0.0716356
$358$	−7033.85	−1.03841
$359$	2259.11	0.332121	0.166060	−	0.986116i	$-0.446895\pi$
$359$	2259.11	0.332121	0.166060	+	0.986116i	$0.446895\pi$
$360$	−496.100	−0.0726298
$361$	3987.22	0.581312
$362$	3121.12	0.453155
$363$	283.617	0.0410083
$364$	0	0
$365$	−1832.41	−0.262775
$366$	4424.75	0.631927
$367$	3404.86	0.484284	0.242142	−	0.970241i	$-0.422150\pi$
$367$	3404.86	0.484284	0.242142	+	0.970241i	$0.422150\pi$
$368$	634.778	0.0899187
$369$	−692.939	−0.0977587
$370$	−262.451	−0.0368761
$371$	−689.363	−0.0964689
$372$	3563.28	0.496633
$373$	11445.0	1.58874	0.794372	−	0.607431i	$-0.207800\pi$
$373$	11445.0	1.58874	0.794372	+	0.607431i	$0.207800\pi$
$374$	−2170.89	−0.300145
$375$	−1730.99	−0.238368
$376$	9712.36	1.33212
$377$	0	0
$378$	−244.905	−0.0333242
$379$	−3587.91	−0.486276	−0.243138	−	0.969992i	$-0.578177\pi$
$379$	−3587.91	−0.486276	−0.243138	+	0.969992i	$0.578177\pi$
$380$	−1112.02	−0.150120
$381$	−2073.95	−0.278876
$382$	9369.32	1.25491
$383$	11338.6	1.51273	0.756367	−	0.654148i	$-0.226972\pi$
$383$	11338.6	1.51273	0.756367	+	0.654148i	$0.226972\pi$
$384$	−2019.77	−0.268414
$385$	−403.795	−0.0534527
$386$	4472.37	0.589735
$387$	−3102.58	−0.407527
$388$	345.995	0.0452713
$389$	4424.87	0.576735	0.288367	−	0.957520i	$-0.406888\pi$
$389$	4424.87	0.576735	0.288367	+	0.957520i	$0.406888\pi$
$390$	0	0
$391$	2858.02	0.369658
$392$	−7456.77	−0.960775
$393$	−8305.94	−1.06610
$394$	−8539.33	−1.09189
$395$	3013.09	0.383810
$396$	1431.48	0.181653
$397$	11640.3	1.47156	0.735780	−	0.677221i	$-0.236816\pi$
$397$	11640.3	1.47156	0.735780	+	0.677221i	$0.236816\pi$
$398$	−331.038	−0.0416921
$399$	−1519.88	−0.190699
$400$	878.260	0.109782
$401$	10195.9	1.26972	0.634861	−	0.772626i	$-0.281057\pi$
$401$	10195.9	1.26972	0.634861	+	0.772626i	$0.281057\pi$
$402$	123.692	0.0153462
$403$	0	0
$404$	−5512.39	−0.678840
$405$	−191.209	−0.0234599
$406$	−1072.04	−0.131046
$407$	2096.67	0.255351
$408$	2319.46	0.281447
$409$	−2195.22	−0.265395	−0.132697	−	0.991157i	$-0.542364\pi$
$409$	−2195.22	−0.265395	−0.132697	+	0.991157i	$0.542364\pi$
$410$	−338.892	−0.0408212
$411$	−4036.32	−0.484420
$412$	4475.48	0.535173
$413$	−2912.66	−0.347028
$414$	1448.54	0.171961
$415$	−1164.57	−0.137751
$416$	0	0
$417$	−5578.43	−0.655100
$418$	−6828.34	−0.799007
$419$	−7413.03	−0.864320	−0.432160	−	0.901797i	$-0.642248\pi$
$419$	−7413.03	−0.864320	−0.432160	+	0.901797i	$0.642248\pi$
$420$	155.828	0.0181038
$421$	2671.47	0.309263	0.154631	−	0.987972i	$-0.450581\pi$
$421$	2671.47	0.309263	0.154631	+	0.987972i	$0.450581\pi$
$422$	−8136.75	−0.938603
$423$	3743.38	0.430282
$424$	3309.05	0.379014
$425$	3954.27	0.451319
$426$	−3354.27	−0.381491
$427$	−3847.95	−0.436101
$428$	5093.71	0.575266
$429$	0	0
$430$	−1517.36	−0.170171
$431$	−1243.06	−0.138924	−0.0694619	−	0.997585i	$-0.522128\pi$
$431$	−1243.06	−0.138924	−0.0694619	+	0.997585i	$0.522128\pi$
$432$	198.556	0.0221135
$433$	−965.341	−0.107139	−0.0535697	−	0.998564i	$-0.517060\pi$
$433$	−965.341	−0.107139	−0.0535697	+	0.998564i	$0.517060\pi$
$434$	2381.83	0.263436
$435$	−836.997	−0.0922550
$436$	202.261	0.0222169
$437$	8989.65	0.984057
$438$	4342.17	0.473691
$439$	−5443.94	−0.591857	−0.295928	−	0.955210i	$-0.595629\pi$
$439$	−5443.94	−0.591857	−0.295928	+	0.955210i	$0.595629\pi$
$440$	1938.28	0.210009
$441$	−2874.02	−0.310336
$442$	0	0
$443$	−9917.30	−1.06362	−0.531812	−	0.846862i	$-0.678489\pi$
$443$	−9917.30	−1.06362	−0.531812	+	0.846862i	$0.678489\pi$
$444$	−809.119	−0.0864845
$445$	−2953.85	−0.314665
$446$	−3154.49	−0.334909
$447$	−4277.13	−0.452576
$448$	−1856.26	−0.195759
$449$	6519.89	0.685284	0.342642	−	0.939466i	$-0.388678\pi$
$449$	6519.89	0.685284	0.342642	+	0.939466i	$0.388678\pi$
$450$	2004.16	0.209949
$451$	2707.34	0.282669
$452$	−7102.01	−0.739050
$453$	5078.36	0.526716
$454$	−6625.62	−0.684924
$455$	0	0
$456$	7295.64	0.749232
$457$	8414.81	0.861331	0.430665	−	0.902512i	$-0.358279\pi$
$457$	8414.81	0.861331	0.430665	+	0.902512i	$0.358279\pi$
$458$	7048.71	0.719137
$459$	893.976	0.0909090
$460$	−921.677	−0.0934204
$461$	−3286.81	−0.332065	−0.166033	−	0.986120i	$-0.553096\pi$
$461$	−3286.81	−0.332065	−0.166033	+	0.986120i	$0.553096\pi$
$462$	956.852	0.0963567
$463$	10342.8	1.03817	0.519085	−	0.854723i	$-0.326273\pi$
$463$	10342.8	1.03817	0.519085	+	0.854723i	$0.326273\pi$
$464$	869.156	0.0869603
$465$	1859.61	0.185456
$466$	12285.0	1.22122
$467$	−6152.69	−0.609662	−0.304831	−	0.952406i	$-0.598600\pi$
$467$	−6152.69	−0.609662	−0.304831	+	0.952406i	$0.598600\pi$
$468$	0	0
$469$	−107.568	−0.0105906
$470$	1830.75	0.179673
$471$	1582.14	0.154780
$472$	13981.2	1.36343
$473$	12121.9	1.17836
$474$	−7139.96	−0.691876
$475$	12437.8	1.20144
$476$	−728.555	−0.0701539
$477$	1275.39	0.122424
$478$	6064.30	0.580281
$479$	−18873.6	−1.80032	−0.900161	−	0.435557i	$-0.856552\pi$
$479$	−18873.6	−1.80032	−0.900161	+	0.435557i	$0.856552\pi$
$480$	−1225.83	−0.116565
$481$	0	0
$482$	−5918.22	−0.559269
$483$	−1259.71	−0.118673
$484$	427.625	0.0401601
$485$	180.568	0.0169055
$486$	453.098	0.0422900
$487$	−8546.70	−0.795252	−0.397626	−	0.917548i	$-0.630166\pi$
$487$	−8546.70	−0.795252	−0.397626	+	0.917548i	$0.630166\pi$
$488$	18470.8	1.71339
$489$	8912.72	0.824227
$490$	−1405.58	−0.129587
$491$	861.293	0.0791642	0.0395821	−	0.999216i	$-0.487397\pi$
$491$	861.293	0.0791642	0.0395821	+	0.999216i	$0.487397\pi$
$492$	−1044.78	−0.0957367
$493$	3913.29	0.357496
$494$	0	0
$495$	747.060	0.0678341
$496$	−1931.06	−0.174813
$497$	2917.02	0.263272
$498$	2759.63	0.248317
$499$	−3549.02	−0.318389	−0.159194	−	0.987247i	$-0.550890\pi$
$499$	−3549.02	−0.318389	−0.159194	+	0.987247i	$0.550890\pi$
$500$	−2609.91	−0.233437
$501$	1220.41	0.108830
$502$	2785.33	0.247640
$503$	4578.66	0.405870	0.202935	−	0.979192i	$-0.434952\pi$
$503$	4578.66	0.405870	0.202935	+	0.979192i	$0.434952\pi$
$504$	−1022.34	−0.0903540
$505$	−2876.81	−0.253497
$506$	−5659.52	−0.497226
$507$	0	0
$508$	−3127.01	−0.273107
$509$	−11402.5	−0.992945	−0.496473	−	0.868052i	$-0.665372\pi$
$509$	−11402.5	−0.992945	−0.496473	+	0.868052i	$0.665372\pi$
$510$	437.212	0.0379609
$511$	−3776.13	−0.326901
$512$	2646.69	0.228453
$513$	2811.92	0.242006
$514$	−5555.67	−0.476751
$515$	2335.67	0.199848
$516$	−4677.93	−0.399098
$517$	−14625.5	−1.24416
$518$	−540.844	−0.0458752
$519$	8678.09	0.733961
$520$	0	0
$521$	4027.26	0.338651	0.169326	−	0.985560i	$-0.445841\pi$
$521$	4027.26	0.338651	0.169326	+	0.985560i	$0.445841\pi$
$522$	1983.39	0.166304
$523$	2560.78	0.214102	0.107051	−	0.994254i	$-0.465859\pi$
$523$	2560.78	0.214102	0.107051	+	0.994254i	$0.465859\pi$
$524$	−12523.3	−1.04405
$525$	−1742.90	−0.144889
$526$	−2032.43	−0.168476
$527$	−8694.39	−0.718660
$528$	−775.764	−0.0639409
$529$	−4716.13	−0.387617
$530$	623.748	0.0511205
$531$	5388.71	0.440396
$532$	−2291.60	−0.186755
$533$	0	0
$534$	6999.58	0.567231
$535$	2658.31	0.214820
$536$	516.342	0.0416093
$537$	−11316.9	−0.909426
$538$	8552.13	0.685332
$539$	11228.9	0.897335
$540$	−288.296	−0.0229746
$541$	15461.8	1.22875	0.614376	−	0.789013i	$-0.289408\pi$
$541$	15461.8	1.22875	0.614376	+	0.789013i	$0.289408\pi$
$542$	10219.2	0.809876
$543$	5021.64	0.396868
$544$	5731.22	0.451698
$545$	105.556	0.00829639
$546$	0	0
$547$	−5589.73	−0.436928	−0.218464	−	0.975845i	$-0.570105\pi$
$547$	−5589.73	−0.436928	−0.218464	+	0.975845i	$0.570105\pi$
$548$	−6085.78	−0.474401
$549$	7119.09	0.553434
$550$	−7830.34	−0.607067
$551$	12308.9	0.951680
$552$	6046.83	0.466251
$553$	6209.21	0.477473
$554$	−7190.85	−0.551462
$555$	−422.263	−0.0322956
$556$	−8410.91	−0.641550
$557$	−15283.9	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$557$	−15283.9	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$558$	−4406.61	−0.334313
$559$	0	0
$560$	−84.4479	−0.00637246
$561$	−3492.80	−0.262863
$562$	−9941.34	−0.746175
$563$	20834.6	1.55964	0.779818	−	0.626007i	$-0.215312\pi$
$563$	20834.6	1.55964	0.779818	+	0.626007i	$0.215312\pi$
$564$	5644.10	0.421382
$565$	−3706.40	−0.275981
$566$	−10126.0	−0.751995
$567$	−394.033	−0.0291849
$568$	−14002.2	−1.03436
$569$	−2621.05	−0.193111	−0.0965556	−	0.995328i	$-0.530783\pi$
$569$	−2621.05	−0.193111	−0.0965556	+	0.995328i	$0.530783\pi$
$570$	1375.21	0.101055
$571$	−5483.96	−0.401921	−0.200960	−	0.979599i	$-0.564406\pi$
$571$	−5483.96	−0.401921	−0.200960	+	0.979599i	$0.564406\pi$
$572$	0	0
$573$	15074.5	1.09904
$574$	−698.370	−0.0507830
$575$	10308.8	0.747664
$576$	3434.26	0.248427
$577$	−26965.7	−1.94558	−0.972789	−	0.231692i	$-0.925574\pi$
$577$	−26965.7	−1.94558	−0.972789	+	0.231692i	$0.925574\pi$
$578$	7116.64	0.512134
$579$	7195.71	0.516483
$580$	−1261.99	−0.0903468
$581$	−2399.89	−0.171367
$582$	−427.883	−0.0304748
$583$	−4983.00	−0.353987
$584$	18126.0	1.28435
$585$	0	0
$586$	1771.65	0.124891
$587$	−521.211	−0.0366485	−0.0183243	−	0.999832i	$-0.505833\pi$
$587$	−521.211	−0.0366485	−0.0183243	+	0.999832i	$0.505833\pi$
$588$	−4333.32	−0.303917
$589$	−27347.4	−1.91312
$590$	2635.43	0.183896
$591$	−13739.1	−0.956265
$592$	438.488	0.0304421
$593$	−4324.86	−0.299496	−0.149748	−	0.988724i	$-0.547846\pi$
$593$	−4324.86	−0.299496	−0.149748	+	0.988724i	$0.547846\pi$
$594$	−1770.27	−0.122281
$595$	−380.218	−0.0261974
$596$	−6448.87	−0.443215
$597$	−532.616	−0.0365134
$598$	0	0
$599$	−22325.2	−1.52284	−0.761422	−	0.648257i	$-0.775498\pi$
$599$	−22325.2	−1.52284	−0.761422	+	0.648257i	$0.775498\pi$
$600$	8366.22	0.569249
$601$	1909.74	0.129617	0.0648086	−	0.997898i	$-0.479356\pi$
$601$	1909.74	0.129617	0.0648086	+	0.997898i	$0.479356\pi$
$602$	−3126.90	−0.211699
$603$	199.011	0.0134400
$604$	7656.93	0.515821
$605$	223.169	0.0149969
$606$	6817.02	0.456968
$607$	6709.42	0.448644	0.224322	−	0.974515i	$-0.427983\pi$
$607$	6709.42	0.448644	0.224322	+	0.974515i	$0.427983\pi$
$608$	18027.0	1.20245
$609$	−1724.84	−0.114768
$610$	3481.69	0.231098
$611$	0	0
$612$	1347.90	0.0890287
$613$	18099.7	1.19256	0.596281	−	0.802776i	$-0.296644\pi$
$613$	18099.7	1.19256	0.596281	+	0.802776i	$0.296644\pi$
$614$	17178.0	1.12907
$615$	−545.251	−0.0357507
$616$	3994.30	0.261258
$617$	−1455.96	−0.0949994	−0.0474997	−	0.998871i	$-0.515125\pi$
$617$	−1455.96	−0.0949994	−0.0474997	+	0.998871i	$0.515125\pi$
$618$	−5534.71	−0.360256
$619$	−19567.5	−1.27057	−0.635287	−	0.772276i	$-0.719118\pi$
$619$	−19567.5	−1.27057	−0.635287	+	0.772276i	$0.719118\pi$
$620$	2803.83	0.181620
$621$	2330.60	0.150602
$622$	−4466.59	−0.287932
$623$	−6087.13	−0.391454
$624$	0	0
$625$	13566.4	0.868249
$626$	7012.49	0.447724
$627$	−10986.3	−0.699760
$628$	2385.48	0.151578
$629$	1974.25	0.125148
$630$	−192.708	−0.0121868
$631$	−31211.1	−1.96909	−0.984544	−	0.175136i	$-0.943963\pi$
$631$	−31211.1	−1.96909	−0.984544	+	0.175136i	$0.943963\pi$
$632$	−29805.2	−1.87593
$633$	−13091.4	−0.822017
$634$	−2814.03	−0.176277
$635$	−1631.92	−0.101986
$636$	1922.98	0.119891
$637$	0	0
$638$	−7749.17	−0.480866
$639$	−5396.77	−0.334105
$640$	−1589.29	−0.0981600
$641$	19040.1	1.17323	0.586614	−	0.809866i	$-0.300460\pi$
$641$	19040.1	1.17323	0.586614	+	0.809866i	$0.300460\pi$
$642$	−6299.25	−0.387246
$643$	2224.04	0.136404	0.0682020	−	0.997672i	$-0.478274\pi$
$643$	2224.04	0.136404	0.0682020	+	0.997672i	$0.478274\pi$
$644$	−1899.34	−0.116218
$645$	−2441.32	−0.149034
$646$	−6429.65	−0.391596
$647$	−22766.2	−1.38335	−0.691677	−	0.722207i	$-0.743128\pi$
$647$	−22766.2	−1.38335	−0.691677	+	0.722207i	$0.743128\pi$
$648$	1891.42	0.114664
$649$	−21053.9	−1.27340
$650$	0	0
$651$	3832.18	0.230714
$652$	13438.2	0.807179
$653$	−26796.6	−1.60587	−0.802935	−	0.596066i	$-0.796730\pi$
$653$	−26796.6	−1.60587	−0.802935	+	0.596066i	$0.796730\pi$
$654$	−250.131	−0.0149555
$655$	−6535.67	−0.389878
$656$	566.201	0.0336989
$657$	6986.22	0.414853
$658$	3772.72	0.223520
$659$	−17395.3	−1.02826	−0.514132	−	0.857711i	$-0.671886\pi$
$659$	−17395.3	−1.02826	−0.514132	+	0.857711i	$0.671886\pi$
$660$	1126.38	0.0664310
$661$	28033.4	1.64958	0.824790	−	0.565439i	$-0.191293\pi$
$661$	28033.4	1.64958	0.824790	+	0.565439i	$0.191293\pi$
$662$	−2811.94	−0.165089
$663$	0	0
$664$	11519.9	0.673280
$665$	−1195.94	−0.0697392
$666$	1000.62	0.0582178
$667$	10201.9	0.592235
$668$	1840.08	0.106579
$669$	−5075.33	−0.293309
$670$	97.3291	0.00561216
$671$	−27814.5	−1.60025
$672$	−2526.12	−0.145010
$673$	20885.3	1.19624	0.598120	−	0.801407i	$-0.295915\pi$
$673$	20885.3	1.19624	0.598120	+	0.801407i	$0.295915\pi$
$674$	−14973.6	−0.855732
$675$	3224.54	0.183871
$676$	0	0
$677$	8938.84	0.507456	0.253728	−	0.967276i	$-0.418343\pi$
$677$	8938.84	0.507456	0.253728	+	0.967276i	$0.418343\pi$
$678$	8782.86	0.497498
$679$	372.105	0.0210310
$680$	1825.11	0.102926
$681$	−10660.1	−0.599848
$682$	17216.8	0.966665
$683$	−18061.8	−1.01188	−0.505940	−	0.862569i	$-0.668854\pi$
$683$	−18061.8	−1.01188	−0.505940	+	0.862569i	$0.668854\pi$
$684$	4239.69	0.237001
$685$	−3176.05	−0.177154
$686$	−6007.74	−0.334368
$687$	11340.8	0.629811
$688$	2535.12	0.140480
$689$	0	0
$690$	1139.81	0.0628868
$691$	−1933.75	−0.106459	−0.0532295	−	0.998582i	$-0.516951\pi$
$691$	−1933.75	−0.106459	−0.0532295	+	0.998582i	$0.516951\pi$
$692$	13084.4	0.718780
$693$	1539.50	0.0843880
$694$	−11960.9	−0.654222
$695$	−4389.49	−0.239572
$696$	8279.50	0.450910
$697$	2549.26	0.138537
$698$	−6305.39	−0.341923
$699$	19765.6	1.06953
$700$	−2627.87	−0.141892
$701$	8894.15	0.479212	0.239606	−	0.970870i	$-0.422982\pi$
$701$	8894.15	0.479212	0.239606	+	0.970870i	$0.422982\pi$
$702$	0	0
$703$	6209.81	0.333154
$704$	−13417.8	−0.718326
$705$	2945.55	0.157356
$706$	−12160.3	−0.648243
$707$	−5928.37	−0.315360
$708$	8124.86	0.431287
$709$	−20617.1	−1.09209	−0.546044	−	0.837757i	$-0.683867\pi$
$709$	−20617.1	−1.09209	−0.546044	+	0.837757i	$0.683867\pi$
$710$	−2639.37	−0.139512
$711$	−11487.6	−0.605936
$712$	29219.2	1.53797
$713$	−22666.3	−1.19055
$714$	900.983	0.0472247
$715$	0	0
$716$	−17063.2	−0.890616
$717$	9756.99	0.508203
$718$	−4212.34	−0.218946
$719$	12900.0	0.669107	0.334553	−	0.942377i	$-0.391415\pi$
$719$	12900.0	0.669107	0.334553	+	0.942377i	$0.391415\pi$
$720$	156.237	0.00808696
$721$	4813.21	0.248618
$722$	−7434.56	−0.383221
$723$	−9521.97	−0.489801
$724$	7571.41	0.388659
$725$	14115.1	0.723064
$726$	−528.832	−0.0270342
$727$	−3681.32	−0.187803	−0.0939013	−	0.995582i	$-0.529934\pi$
$727$	−3681.32	−0.187803	−0.0939013	+	0.995582i	$0.529934\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	3416.71	0.173230
$731$	11414.1	0.577519
$732$	10733.8	0.541987
$733$	−14330.0	−0.722088	−0.361044	−	0.932549i	$-0.617580\pi$
$733$	−14330.0	−0.722088	−0.361044	+	0.932549i	$0.617580\pi$
$734$	−6348.70	−0.319257
$735$	−2261.47	−0.113491
$736$	14941.3	0.748292
$737$	−777.542	−0.0388618
$738$	1292.05	0.0644460
$739$	3980.74	0.198151	0.0990757	−	0.995080i	$-0.468411\pi$
$739$	3980.74	0.198151	0.0990757	+	0.995080i	$0.468411\pi$
$740$	−636.670	−0.0316276
$741$	0	0
$742$	1285.39	0.0635957
$743$	−34167.8	−1.68707	−0.843536	−	0.537073i	$-0.819530\pi$
$743$	−34167.8	−1.68707	−0.843536	+	0.537073i	$0.819530\pi$
$744$	−18395.1	−0.906446
$745$	−3365.54	−0.165508
$746$	−21340.4	−1.04736
$747$	4440.04	0.217473
$748$	−5266.29	−0.257426
$749$	5478.10	0.267243
$750$	3227.60	0.157141
$751$	−1667.87	−0.0810407	−0.0405204	−	0.999179i	$-0.512902\pi$
$751$	−1667.87	−0.0810407	−0.0405204	+	0.999179i	$0.512902\pi$
$752$	−3058.72	−0.148325
$753$	4481.38	0.216880
$754$	0	0
$755$	3996.00	0.192622
$756$	−594.106	−0.0285812
$757$	26775.5	1.28556	0.642782	−	0.766049i	$-0.277780\pi$
$757$	26775.5	1.28556	0.642782	+	0.766049i	$0.277780\pi$
$758$	6690.02	0.320571
$759$	−9105.73	−0.435464
$760$	5740.71	0.273997
$761$	−25360.3	−1.20803	−0.604014	−	0.796974i	$-0.706433\pi$
$761$	−25360.3	−1.20803	−0.604014	+	0.796974i	$0.706433\pi$
$762$	3867.09	0.183845
$763$	217.525	0.0103210
$764$	22728.7	1.07630
$765$	703.441	0.0332457
$766$	−21142.0	−0.997248
$767$	0	0
$768$	12924.1	0.607237
$769$	−21088.5	−0.988906	−0.494453	−	0.869204i	$-0.664632\pi$
$769$	−21088.5	−0.988906	−0.494453	+	0.869204i	$0.664632\pi$
$770$	752.916	0.0352379
$771$	−8938.65	−0.417533
$772$	10849.4	0.505800
$773$	36492.1	1.69797	0.848985	−	0.528416i	$-0.177214\pi$
$773$	36492.1	1.69797	0.848985	+	0.528416i	$0.177214\pi$
$774$	5785.07	0.268656
$775$	−31360.4	−1.45355
$776$	−1786.16	−0.0826283
$777$	−870.178	−0.0401769
$778$	−8250.61	−0.380204
$779$	8018.47	0.368795
$780$	0	0
$781$	21085.4	0.966063
$782$	−5329.07	−0.243692
$783$	3191.12	0.145647
$784$	2348.37	0.106977
$785$	1244.94	0.0566034
$786$	15487.3	0.702814
$787$	886.171	0.0401380	0.0200690	−	0.999799i	$-0.493611\pi$
$787$	886.171	0.0401380	0.0200690	+	0.999799i	$0.493611\pi$
$788$	−20715.3	−0.936485
$789$	−3270.03	−0.147549
$790$	−5618.20	−0.253021
$791$	−7637.95	−0.343330
$792$	−7389.86	−0.331549
$793$	0	0
$794$	−21704.5	−0.970105
$795$	1003.56	0.0447707
$796$	−803.054	−0.0357582
$797$	40373.6	1.79436	0.897181	−	0.441664i	$-0.145612\pi$
$797$	40373.6	1.79436	0.897181	+	0.441664i	$0.145612\pi$
$798$	2833.96	0.125716
$799$	−13771.6	−0.609767
$800$	20672.3	0.913596
$801$	11261.8	0.496774
$802$	−19011.3	−0.837046
$803$	−27295.4	−1.19954
$804$	300.060	0.0131620
$805$	−991.229	−0.0433990
$806$	0	0
$807$	13759.7	0.600205
$808$	28457.1	1.23901
$809$	12136.2	0.527425	0.263712	−	0.964601i	$-0.415053\pi$
$809$	12136.2	0.527425	0.263712	+	0.964601i	$0.415053\pi$
$810$	356.528	0.0154656
$811$	−17625.8	−0.763163	−0.381582	−	0.924335i	$-0.624620\pi$
$811$	−17625.8	−0.763163	−0.381582	+	0.924335i	$0.624620\pi$
$812$	−2600.63	−0.112395
$813$	16442.0	0.709280
$814$	−3909.44	−0.168337
$815$	7013.13	0.301423
$816$	−730.469	−0.0313377
$817$	35902.1	1.53740
$818$	4093.20	0.174958
$819$	0	0
$820$	−822.106	−0.0350112
$821$	4685.38	0.199173	0.0995865	−	0.995029i	$-0.468248\pi$
$821$	4685.38	0.199173	0.0995865	+	0.995029i	$0.468248\pi$
$822$	7526.12	0.319347
$823$	13493.1	0.571493	0.285747	−	0.958305i	$-0.407758\pi$
$823$	13493.1	0.571493	0.285747	+	0.958305i	$0.407758\pi$
$824$	−23104.2	−0.976788
$825$	−12598.4	−0.531661
$826$	5430.95	0.228773
$827$	−9203.58	−0.386989	−0.193494	−	0.981101i	$-0.561982\pi$
$827$	−9203.58	−0.386989	−0.193494	+	0.981101i	$0.561982\pi$
$828$	3513.97	0.147487
$829$	20033.6	0.839320	0.419660	−	0.907681i	$-0.362149\pi$
$829$	20033.6	0.839320	0.419660	+	0.907681i	$0.362149\pi$
$830$	2171.47	0.0908105
$831$	−11569.5	−0.482964
$832$	0	0
$833$	10573.3	0.439787
$834$	10401.5	0.431866
$835$	960.301	0.0397995
$836$	−16564.6	−0.685287
$837$	−7089.91	−0.292787
$838$	13822.3	0.569791
$839$	−22834.8	−0.939625	−0.469813	−	0.882766i	$-0.655679\pi$
$839$	−22834.8	−0.939625	−0.469813	+	0.882766i	$0.655679\pi$
$840$	−804.443	−0.0330428
$841$	−10420.2	−0.427250
$842$	−4981.22	−0.203877
$843$	−15994.9	−0.653490
$844$	−19738.6	−0.805014
$845$	0	0
$846$	−6979.91	−0.283657
$847$	459.895	0.0186566
$848$	−1042.12	−0.0422012
$849$	−16292.0	−0.658588
$850$	−7373.14	−0.297525
$851$	5146.86	0.207323
$852$	−8137.01	−0.327194
$853$	23922.2	0.960233	0.480117	−	0.877205i	$-0.340594\pi$
$853$	23922.2	0.960233	0.480117	+	0.877205i	$0.340594\pi$
$854$	7174.89	0.287494
$855$	2212.61	0.0885025
$856$	−26295.7	−1.04996
$857$	−13915.6	−0.554665	−0.277332	−	0.960774i	$-0.589450\pi$
$857$	−13915.6	−0.554665	−0.277332	+	0.960774i	$0.589450\pi$
$858$	0	0
$859$	−41260.9	−1.63889	−0.819443	−	0.573161i	$-0.805717\pi$
$859$	−41260.9	−1.63889	−0.819443	+	0.573161i	$0.805717\pi$
$860$	−3680.91	−0.145951
$861$	−1123.63	−0.0444751
$862$	2317.81	0.0915835
$863$	47277.7	1.86483	0.932417	−	0.361384i	$-0.117696\pi$
$863$	47277.7	1.86483	0.932417	+	0.361384i	$0.117696\pi$
$864$	4673.56	0.184025
$865$	6828.51	0.268412
$866$	1799.97	0.0706300
$867$	11450.1	0.448520
$868$	5777.99	0.225942
$869$	44882.7	1.75206
$870$	1560.66	0.0608178
$871$	0	0
$872$	−1044.15	−0.0405499
$873$	−688.431	−0.0266894
$874$	−16762.1	−0.648726
$875$	−2806.86	−0.108445
$876$	10533.5	0.406272
$877$	−31051.0	−1.19558	−0.597788	−	0.801655i	$-0.703953\pi$
$877$	−31051.0	−1.19558	−0.597788	+	0.801655i	$0.703953\pi$
$878$	10150.8	0.390173
$879$	2850.45	0.109378
$880$	−610.424	−0.0233834
$881$	−24283.5	−0.928638	−0.464319	−	0.885668i	$-0.653701\pi$
$881$	−24283.5	−0.928638	−0.464319	+	0.885668i	$0.653701\pi$
$882$	5358.90	0.204584
$883$	15754.0	0.600412	0.300206	−	0.953874i	$-0.402945\pi$
$883$	15754.0	0.600412	0.300206	+	0.953874i	$0.402945\pi$
$884$	0	0
$885$	4240.20	0.161054
$886$	18491.8	0.701179
$887$	16246.0	0.614982	0.307491	−	0.951551i	$-0.400511\pi$
$887$	16246.0	0.614982	0.307491	+	0.951551i	$0.400511\pi$
$888$	4176.99	0.157850
$889$	−3362.98	−0.126874
$890$	5507.74	0.207438
$891$	−2848.23	−0.107092
$892$	−7652.36	−0.287242
$893$	−43317.2	−1.62324
$894$	7975.14	0.298354
$895$	−8904.93	−0.332580
$896$	−3275.13	−0.122114
$897$	0	0
$898$	−12157.0	−0.451764
$899$	−31035.3	−1.15137
$900$	4861.82	0.180068
$901$	−4692.05	−0.173490
$902$	−5048.11	−0.186345
$903$	−5030.94	−0.185403
$904$	36663.4	1.34890
$905$	3951.37	0.145136
$906$	−9469.12	−0.347230
$907$	−29623.9	−1.08451	−0.542253	−	0.840216i	$-0.682428\pi$
$907$	−29623.9	−1.08451	−0.542253	+	0.840216i	$0.682428\pi$
$908$	−16072.9	−0.587441
$909$	10968.1	0.400207
$910$	0	0
$911$	−1244.48	−0.0452594	−0.0226297	−	0.999744i	$-0.507204\pi$
$911$	−1244.48	−0.0452594	−0.0226297	+	0.999744i	$0.507204\pi$
$912$	−2297.62	−0.0834231
$913$	−17347.4	−0.628823
$914$	−15690.3	−0.567820
$915$	5601.78	0.202392
$916$	17099.2	0.616784
$917$	−13468.4	−0.485022
$918$	−1666.91	−0.0599305
$919$	−27386.4	−0.983020	−0.491510	−	0.870872i	$-0.663555\pi$
$919$	−27386.4	−0.983020	−0.491510	+	0.870872i	$0.663555\pi$
$920$	4758.06	0.170509
$921$	27638.1	0.988823
$922$	6128.58	0.218909
$923$	0	0
$924$	2321.19	0.0826425
$925$	7121.04	0.253123
$926$	−19285.3	−0.684399
$927$	−8904.92	−0.315508
$928$	20458.0	0.723672
$929$	−40144.3	−1.41775	−0.708876	−	0.705333i	$-0.750797\pi$
$929$	−40144.3	−1.41775	−0.708876	+	0.705333i	$0.750797\pi$
$930$	−3467.42	−0.122259
$931$	33257.3	1.17074
$932$	29801.7	1.04741
$933$	−7186.40	−0.252167
$934$	11472.3	0.401911
$935$	−2748.37	−0.0961298
$936$	0	0
$937$	38928.8	1.35725	0.678627	−	0.734483i	$-0.262575\pi$
$937$	38928.8	1.35725	0.678627	+	0.734483i	$0.262575\pi$
$938$	200.571	0.00698173
$939$	11282.6	0.392111
$940$	4441.16	0.154101
$941$	20870.7	0.723025	0.361513	−	0.932367i	$-0.382260\pi$
$941$	20870.7	0.723025	0.361513	+	0.932367i	$0.382260\pi$
$942$	−2950.06	−0.102036
$943$	6645.93	0.229503
$944$	−4403.12	−0.151811
$945$	−310.052	−0.0106730
$946$	−22602.5	−0.776818
$947$	−35530.9	−1.21922	−0.609609	−	0.792702i	$-0.708673\pi$
$947$	−35530.9	−1.21922	−0.609609	+	0.792702i	$0.708673\pi$
$948$	−17320.6	−0.593403
$949$	0	0
$950$	−23191.5	−0.792034
$951$	−4527.57	−0.154381
$952$	3761.09	0.128044
$953$	−24920.3	−0.847060	−0.423530	−	0.905882i	$-0.639209\pi$
$953$	−24920.3	−0.847060	−0.423530	+	0.905882i	$0.639209\pi$
$954$	−2378.09	−0.0807060
$955$	11861.7	0.401921
$956$	14711.2	0.497691
$957$	−12467.8	−0.421137
$958$	35191.6	1.18684
$959$	−6545.03	−0.220386
$960$	2702.31	0.0908506
$961$	39162.1	1.31456
$962$	0	0
$963$	−10135.0	−0.339145
$964$	−14356.8	−0.479670
$965$	5662.07	0.188879
$966$	2348.86	0.0782334
$967$	34035.7	1.13187	0.565934	−	0.824451i	$-0.308516\pi$
$967$	34035.7	1.13187	0.565934	+	0.824451i	$0.308516\pi$
$968$	−2207.57	−0.0732995
$969$	−10344.8	−0.342955
$970$	−336.687	−0.0111447
$971$	27039.2	0.893646	0.446823	−	0.894622i	$-0.352555\pi$
$971$	27039.2	0.893646	0.446823	+	0.894622i	$0.352555\pi$
$972$	1099.15	0.0362710
$973$	−9045.62	−0.298036
$974$	15936.2	0.524259
$975$	0	0
$976$	−5817.02	−0.190777
$977$	57783.1	1.89216	0.946082	−	0.323926i	$-0.105003\pi$
$977$	57783.1	1.89216	0.946082	+	0.323926i	$0.105003\pi$
$978$	−16618.7	−0.543360
$979$	−44000.3	−1.43642
$980$	−3409.75	−0.111143
$981$	−402.442	−0.0130978
$982$	−1605.97	−0.0521879
$983$	52953.3	1.71816	0.859078	−	0.511845i	$-0.171038\pi$
$983$	52953.3	1.71816	0.859078	+	0.511845i	$0.171038\pi$
$984$	5393.58	0.174737
$985$	−10810.9	−0.349709
$986$	−7296.71	−0.235674
$987$	6070.02	0.195756
$988$	0	0
$989$	29756.6	0.956730
$990$	−1392.97	−0.0447186
$991$	9632.95	0.308780	0.154390	−	0.988010i	$-0.450659\pi$
$991$	9632.95	0.308780	0.154390	+	0.988010i	$0.450659\pi$
$992$	−45452.9	−1.45477
$993$	−4524.20	−0.144583
$994$	−5439.07	−0.173558
$995$	−419.098	−0.0133531
$996$	6694.50	0.212975
$997$	11816.6	0.375362	0.187681	−	0.982230i	$-0.439903\pi$
$997$	11816.6	0.375362	0.187681	+	0.982230i	$0.439903\pi$
$998$	6617.50	0.209893
$999$	1609.91	0.0509864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.q.1.3	yes	9
3.2	odd	2		1521.4.a.be.1.7		9
13.5	odd	4		507.4.b.j.337.12		18
13.8	odd	4		507.4.b.j.337.7		18
13.12	even	2		507.4.a.n.1.7	✓	9
39.38	odd	2		1521.4.a.bj.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.4.a.n.1.7	✓	9	13.12	even	2
507.4.a.q.1.3	yes	9	1.1	even	1	trivial
507.4.b.j.337.7		18	13.8	odd	4
507.4.b.j.337.12		18	13.5	odd	4
1521.4.a.be.1.7		9	3.2	odd	2
1521.4.a.bj.1.3		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)

\(f(q)\)	\(=\)	\(q-1.86460 q^{2} -3.00000 q^{3} -4.52327 q^{4} -2.36060 q^{5} +5.59380 q^{6} -4.86461 q^{7} +23.3509 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.86460 q^{2} -3.00000 q^{3} -4.52327 q^{4} -2.36060 q^{5} +5.59380 q^{6} -4.86461 q^{7} +23.3509 q^{8} +9.00000 q^{9} +4.40158 q^{10} -35.1633 q^{11} +13.5698 q^{12} +9.07054 q^{14} +7.08181 q^{15} -7.35391 q^{16} -33.1102 q^{17} -16.7814 q^{18} -104.145 q^{19} +10.6776 q^{20} +14.5938 q^{21} +65.5656 q^{22} -86.3184 q^{23} -70.0526 q^{24} -119.428 q^{25} -27.0000 q^{27} +22.0039 q^{28} -118.190 q^{29} -13.2047 q^{30} +262.589 q^{31} -173.095 q^{32} +105.490 q^{33} +61.7373 q^{34} +11.4834 q^{35} -40.7094 q^{36} -59.6265 q^{37} +194.189 q^{38} -55.1222 q^{40} -76.9932 q^{41} -27.2116 q^{42} -344.731 q^{43} +159.053 q^{44} -21.2454 q^{45} +160.949 q^{46} +415.931 q^{47} +22.0617 q^{48} -319.336 q^{49} +222.685 q^{50} +99.3307 q^{51} +141.710 q^{53} +50.3442 q^{54} +83.0067 q^{55} -113.593 q^{56} +312.436 q^{57} +220.376 q^{58} +598.746 q^{59} -32.0329 q^{60} +791.010 q^{61} -489.624 q^{62} -43.7814 q^{63} +381.584 q^{64} -196.697 q^{66} +22.1123 q^{67} +149.766 q^{68} +258.955 q^{69} -21.4120 q^{70} -599.641 q^{71} +210.158 q^{72} +776.246 q^{73} +111.180 q^{74} +358.283 q^{75} +471.076 q^{76} +171.056 q^{77} -1276.41 q^{79} +17.3597 q^{80} +81.0000 q^{81} +143.562 q^{82} +493.338 q^{83} -66.0117 q^{84} +78.1601 q^{85} +642.785 q^{86} +354.569 q^{87} -821.095 q^{88} +1251.31 q^{89} +39.6142 q^{90} +390.441 q^{92} -787.767 q^{93} -775.545 q^{94} +245.845 q^{95} +519.285 q^{96} -76.4923 q^{97} +595.433 q^{98} -316.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{2} - 27 q^{3} + 32 q^{4} + 41 q^{5} - 24 q^{6} + q^{7} + 111 q^{8} + 81 q^{9}+O(q^{10}) \) 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

Introduction

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