LMFDB - Embedded newform 507.4.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.6
Root			$2.05129$ 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)

$f(q)$	$=$	$q+1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} -17.8886 q^{5} -3.15386 q^{6} +30.1975 q^{7} -15.6587 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} -17.8886 q^{5} -3.15386 q^{6} +30.1975 q^{7} -15.6587 q^{8} +9.00000 q^{9} -18.8061 q^{10} +50.8457 q^{11} +20.6844 q^{12} +31.7462 q^{14} +53.6659 q^{15} +38.6966 q^{16} -2.99137 q^{17} +9.46157 q^{18} -72.7016 q^{19} +123.339 q^{20} -90.5926 q^{21} +53.4533 q^{22} -41.9071 q^{23} +46.9761 q^{24} +195.003 q^{25} -27.0000 q^{27} -208.206 q^{28} -135.233 q^{29} +56.4182 q^{30} +316.820 q^{31} +165.951 q^{32} -152.537 q^{33} -3.14479 q^{34} -540.192 q^{35} -62.0532 q^{36} -261.777 q^{37} -76.4301 q^{38} +280.113 q^{40} -198.911 q^{41} -95.2386 q^{42} -201.351 q^{43} -350.571 q^{44} -160.998 q^{45} -44.0563 q^{46} -97.3687 q^{47} -116.090 q^{48} +568.890 q^{49} +205.004 q^{50} +8.97412 q^{51} -150.458 q^{53} -28.3847 q^{54} -909.560 q^{55} -472.853 q^{56} +218.105 q^{57} -142.168 q^{58} -497.812 q^{59} -370.016 q^{60} +525.066 q^{61} +333.068 q^{62} +271.778 q^{63} -135.112 q^{64} -160.360 q^{66} -777.584 q^{67} +20.6249 q^{68} +125.721 q^{69} -567.896 q^{70} -1012.16 q^{71} -140.928 q^{72} -612.910 q^{73} -275.202 q^{74} -585.010 q^{75} +501.263 q^{76} +1535.41 q^{77} +718.804 q^{79} -692.230 q^{80} +81.0000 q^{81} -209.112 q^{82} -397.730 q^{83} +624.617 q^{84} +53.5116 q^{85} -211.677 q^{86} +405.699 q^{87} -796.176 q^{88} +648.413 q^{89} -169.255 q^{90} +288.941 q^{92} -950.460 q^{93} -102.362 q^{94} +1300.53 q^{95} -497.852 q^{96} -272.412 q^{97} +598.066 q^{98} +457.611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.05129	0.371686	0.185843	−	0.982579i	$-0.440498\pi$
$2$	1.05129	0.371686	0.185843	+	0.982579i	$0.440498\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.89480	−0.861850
$5$	−17.8886	−1.60001	−0.800004	−	0.599994i	$-0.795169\pi$
$5$	−17.8886	−1.60001	−0.800004	+	0.599994i	$0.795169\pi$
$6$	−3.15386	−0.214593
$7$	30.1975	1.63051	0.815256	−	0.579100i	$-0.196596\pi$
$7$	30.1975	1.63051	0.815256	+	0.579100i	$0.196596\pi$
$8$	−15.6587	−0.692023
$9$	9.00000	0.333333
$10$	−18.8061	−0.594700
$11$	50.8457	1.39369	0.696843	−	0.717224i	$-0.254587\pi$
$11$	50.8457	1.39369	0.696843	+	0.717224i	$0.254587\pi$
$12$	20.6844	0.497589
$13$	0	0
$13$	0	0
$14$	31.7462	0.606038
$15$	53.6659	0.923765
$16$	38.6966	0.604635
$17$	−2.99137	−0.0426773	−0.0213387	−	0.999772i	$-0.506793\pi$
$17$	−2.99137	−0.0426773	−0.0213387	+	0.999772i	$0.506793\pi$
$18$	9.46157	0.123895
$19$	−72.7016	−0.877836	−0.438918	−	0.898527i	$-0.644638\pi$
$19$	−72.7016	−0.877836	−0.438918	+	0.898527i	$0.644638\pi$
$20$	123.339	1.37897
$21$	−90.5926	−0.941377
$22$	53.4533	0.518013
$23$	−41.9071	−0.379923	−0.189961	−	0.981792i	$-0.560836\pi$
$23$	−41.9071	−0.379923	−0.189961	+	0.981792i	$0.560836\pi$
$24$	46.9761	0.399539
$25$	195.003	1.56003
$26$	0	0
$27$	−27.0000	−0.192450
$28$	−208.206	−1.40526
$29$	−135.233	−0.865935	−0.432967	−	0.901410i	$-0.642534\pi$
$29$	−135.233	−0.865935	−0.432967	+	0.901410i	$0.642534\pi$
$30$	56.4182	0.343350
$31$	316.820	1.83557	0.917783	−	0.397082i	$-0.129977\pi$
$31$	316.820	1.83557	0.917783	+	0.397082i	$0.129977\pi$
$32$	165.951	0.916757
$33$	−152.537	−0.804645
$34$	−3.14479	−0.0158625
$35$	−540.192	−2.60883
$36$	−62.0532	−0.287283
$37$	−261.777	−1.16313	−0.581565	−	0.813500i	$-0.697559\pi$
$37$	−261.777	−1.16313	−0.581565	+	0.813500i	$0.697559\pi$
$38$	−76.4301	−0.326279
$39$	0	0
$40$	280.113	1.10724
$41$	−198.911	−0.757674	−0.378837	−	0.925463i	$-0.623676\pi$
$41$	−198.911	−0.757674	−0.378837	+	0.925463i	$0.623676\pi$
$42$	−95.2386	−0.349896
$43$	−201.351	−0.714085	−0.357043	−	0.934088i	$-0.616215\pi$
$43$	−201.351	−0.714085	−0.357043	+	0.934088i	$0.616215\pi$
$44$	−350.571	−1.20115
$45$	−160.998	−0.533336
$46$	−44.0563	−0.141212
$47$	−97.3687	−0.302185	−0.151092	−	0.988520i	$-0.548279\pi$
$47$	−97.3687	−0.302185	−0.151092	+	0.988520i	$0.548279\pi$
$48$	−116.090	−0.349086
$49$	568.890	1.65857
$50$	205.004	0.579839
$51$	8.97412	0.0246398
$52$	0	0
$53$	−150.458	−0.389943	−0.194972	−	0.980809i	$-0.562461\pi$
$53$	−150.458	−0.389943	−0.194972	+	0.980809i	$0.562461\pi$
$54$	−28.3847	−0.0715309
$55$	−909.560	−2.22991
$56$	−472.853	−1.12835
$57$	218.105	0.506819
$58$	−142.168	−0.321855
$59$	−497.812	−1.09847	−0.549234	−	0.835668i	$-0.685081\pi$
$59$	−497.812	−1.09847	−0.549234	+	0.835668i	$0.685081\pi$
$60$	−370.016	−0.796147
$61$	525.066	1.10209	0.551047	−	0.834474i	$-0.314228\pi$
$61$	525.066	1.10209	0.551047	+	0.834474i	$0.314228\pi$
$62$	333.068	0.682253
$63$	271.778	0.543504
$64$	−135.112	−0.263890
$65$	0	0
$66$	−160.360	−0.299075
$67$	−777.584	−1.41787	−0.708933	−	0.705276i	$-0.750823\pi$
$67$	−777.584	−1.41787	−0.708933	+	0.705276i	$0.750823\pi$
$68$	20.6249	0.0367814
$69$	125.721	0.219349
$70$	−567.896	−0.969666
$71$	−1012.16	−1.69185	−0.845924	−	0.533303i	$-0.820951\pi$
$71$	−1012.16	−1.69185	−0.845924	+	0.533303i	$0.820951\pi$
$72$	−140.928	−0.230674
$73$	−612.910	−0.982680	−0.491340	−	0.870968i	$-0.663493\pi$
$73$	−612.910	−0.982680	−0.491340	+	0.870968i	$0.663493\pi$
$74$	−275.202	−0.432318
$75$	−585.010	−0.900682
$76$	501.263	0.756563
$77$	1535.41	2.27242
$78$	0	0
$79$	718.804	1.02369	0.511846	−	0.859077i	$-0.328962\pi$
$79$	718.804	1.02369	0.511846	+	0.859077i	$0.328962\pi$
$80$	−692.230	−0.967421
$81$	81.0000	0.111111
$82$	−209.112	−0.281616
$83$	−397.730	−0.525982	−0.262991	−	0.964798i	$-0.584709\pi$
$83$	−397.730	−0.525982	−0.262991	+	0.964798i	$0.584709\pi$
$84$	624.617	0.811326
$85$	53.5116	0.0682841
$86$	−211.677	−0.265415
$87$	405.699	0.499948
$88$	−796.176	−0.964462
$89$	648.413	0.772265	0.386133	−	0.922443i	$-0.373811\pi$
$89$	648.413	0.772265	0.386133	+	0.922443i	$0.373811\pi$
$90$	−169.255	−0.198233
$91$	0	0
$92$	288.941	0.327436
$93$	−950.460	−1.05976
$94$	−102.362	−0.112318
$95$	1300.53	1.40454
$96$	−497.852	−0.529290
$97$	−272.412	−0.285147	−0.142574	−	0.989784i	$-0.545538\pi$
$97$	−272.412	−0.285147	−0.142574	+	0.989784i	$0.545538\pi$
$98$	598.066	0.616467
$99$	457.611	0.464562
$100$	−1344.51	−1.34451
$101$	416.057	0.409893	0.204947	−	0.978773i	$-0.434298\pi$
$101$	416.057	0.409893	0.204947	+	0.978773i	$0.434298\pi$
$102$	9.43436	0.00915824
$103$	261.509	0.250168	0.125084	−	0.992146i	$-0.460080\pi$
$103$	261.509	0.250168	0.125084	+	0.992146i	$0.460080\pi$
$104$	0	0
$105$	1620.58	1.50621
$106$	−158.174	−0.144936
$107$	1041.57	0.941052	0.470526	−	0.882386i	$-0.344064\pi$
$107$	1041.57	0.941052	0.470526	+	0.882386i	$0.344064\pi$
$108$	186.160	0.165863
$109$	609.644	0.535718	0.267859	−	0.963458i	$-0.413684\pi$
$109$	609.644	0.535718	0.267859	+	0.963458i	$0.413684\pi$
$110$	−956.207	−0.828825
$111$	785.330	0.671533
$112$	1168.54	0.985865
$113$	−333.997	−0.278051	−0.139025	−	0.990289i	$-0.544397\pi$
$113$	−333.997	−0.278051	−0.139025	+	0.990289i	$0.544397\pi$
$114$	229.290	0.188377
$115$	749.660	0.607880
$116$	932.403	0.746306
$117$	0	0
$118$	−523.343	−0.408285
$119$	−90.3320	−0.0695859
$120$	−840.338	−0.639266
$121$	1254.28	0.942361
$122$	551.994	0.409633
$123$	596.732	0.437443
$124$	−2184.41	−1.58198
$125$	−1252.26	−0.896048
$126$	285.716	0.202013
$127$	−1110.44	−0.775872	−0.387936	−	0.921686i	$-0.626812\pi$
$127$	−1110.44	−0.775872	−0.387936	+	0.921686i	$0.626812\pi$
$128$	−1469.65	−1.01484
$129$	604.052	0.412277
$130$	0	0
$131$	−557.489	−0.371817	−0.185909	−	0.982567i	$-0.559523\pi$
$131$	−557.489	−0.371817	−0.185909	+	0.982567i	$0.559523\pi$
$132$	1051.71	0.693483
$133$	−2195.41	−1.43132
$134$	−817.463	−0.527000
$135$	482.993	0.307922
$136$	46.8410	0.0295337
$137$	1364.89	0.851170	0.425585	−	0.904918i	$-0.360068\pi$
$137$	1364.89	0.851170	0.425585	+	0.904918i	$0.360068\pi$
$138$	132.169	0.0815287
$139$	−1936.99	−1.18197	−0.590985	−	0.806683i	$-0.701261\pi$
$139$	−1936.99	−1.18197	−0.590985	+	0.806683i	$0.701261\pi$
$140$	3724.52	2.24842
$141$	292.106	0.174467
$142$	−1064.07	−0.628836
$143$	0	0
$144$	348.270	0.201545
$145$	2419.13	1.38550
$146$	−644.343	−0.365248
$147$	−1706.67	−0.957577
$148$	1804.90	1.00244
$149$	−3499.94	−1.92434	−0.962169	−	0.272452i	$-0.912165\pi$
$149$	−3499.94	−1.92434	−0.962169	+	0.272452i	$0.912165\pi$
$150$	−615.013	−0.334770
$151$	−672.434	−0.362397	−0.181198	−	0.983447i	$-0.557998\pi$
$151$	−672.434	−0.362397	−0.181198	+	0.983447i	$0.557998\pi$
$152$	1138.41	0.607482
$153$	−26.9224	−0.0142258
$154$	1614.16	0.844627
$155$	−5667.48	−2.93692
$156$	0	0
$157$	1272.02	0.646612	0.323306	−	0.946295i	$-0.395206\pi$
$157$	1272.02	0.646612	0.323306	+	0.946295i	$0.395206\pi$
$158$	755.668	0.380492
$159$	451.374	0.225134
$160$	−2968.63	−1.46682
$161$	−1265.49	−0.619469
$162$	85.1541	0.0412984
$163$	−1476.22	−0.709366	−0.354683	−	0.934987i	$-0.615411\pi$
$163$	−1476.22	−0.709366	−0.354683	+	0.934987i	$0.615411\pi$
$164$	1371.45	0.653001
$165$	2728.68	1.28744
$166$	−418.127	−0.195500
$167$	−3234.78	−1.49889	−0.749446	−	0.662066i	$-0.769680\pi$
$167$	−3234.78	−1.49889	−0.749446	+	0.662066i	$0.769680\pi$
$168$	1418.56	0.651454
$169$	0	0
$170$	56.2559	0.0253802
$171$	−654.314	−0.292612
$172$	1388.27	0.615434
$173$	424.597	0.186598	0.0932991	−	0.995638i	$-0.470259\pi$
$173$	424.597	0.186598	0.0932991	+	0.995638i	$0.470259\pi$
$174$	426.505	0.185823
$175$	5888.62	2.54364
$176$	1967.56	0.842671
$177$	1493.44	0.634201
$178$	681.667	0.287040
$179$	−4400.04	−1.83729	−0.918644	−	0.395086i	$-0.870715\pi$
$179$	−4400.04	−1.83729	−0.918644	+	0.395086i	$0.870715\pi$
$180$	1110.05	0.459656
$181$	−345.151	−0.141740	−0.0708698	−	0.997486i	$-0.522577\pi$
$181$	−345.151	−0.141740	−0.0708698	+	0.997486i	$0.522577\pi$
$182$	0	0
$183$	−1575.20	−0.636295
$184$	656.209	0.262915
$185$	4682.83	1.86102
$186$	−999.205	−0.393899
$187$	−152.098	−0.0594788
$188$	671.338	0.260438
$189$	−815.333	−0.313792
$190$	1367.23	0.522049
$191$	−4076.61	−1.54436	−0.772181	−	0.635402i	$-0.780834\pi$
$191$	−4076.61	−1.54436	−0.772181	+	0.635402i	$0.780834\pi$
$192$	405.335	0.152357
$193$	−3221.08	−1.20134	−0.600670	−	0.799497i	$-0.705099\pi$
$193$	−3221.08	−1.20134	−0.600670	+	0.799497i	$0.705099\pi$
$194$	−286.383	−0.105985
$195$	0	0
$196$	−3922.38	−1.42944
$197$	−3068.80	−1.10986	−0.554931	−	0.831897i	$-0.687255\pi$
$197$	−3068.80	−1.10986	−0.554931	+	0.831897i	$0.687255\pi$
$198$	481.080	0.172671
$199$	3992.05	1.42206	0.711028	−	0.703164i	$-0.248230\pi$
$199$	3992.05	1.42206	0.711028	+	0.703164i	$0.248230\pi$
$200$	−3053.50	−1.07957
$201$	2332.75	0.818605
$202$	437.395	0.152351
$203$	−4083.70	−1.41192
$204$	−61.8747	−0.0212358
$205$	3558.24	1.21228
$206$	274.921	0.0929838
$207$	−377.163	−0.126641
$208$	0	0
$209$	−3696.56	−1.22343
$210$	1703.69	0.559837
$211$	2868.29	0.935837	0.467918	−	0.883772i	$-0.345004\pi$
$211$	2868.29	0.935837	0.467918	+	0.883772i	$0.345004\pi$
$212$	1037.38	0.336072
$213$	3036.48	0.976789
$214$	1094.99	0.349775
$215$	3601.89	1.14254
$216$	422.784	0.133180
$217$	9567.18	2.99291
$218$	640.909	0.199119
$219$	1838.73	0.567351
$220$	6271.23	1.92185
$221$	0	0
$222$	825.606	0.249599
$223$	3099.47	0.930745	0.465372	−	0.885115i	$-0.345920\pi$
$223$	3099.47	0.930745	0.465372	+	0.885115i	$0.345920\pi$
$224$	5011.30	1.49478
$225$	1755.03	0.520009
$226$	−351.126	−0.103347
$227$	258.860	0.0756879	0.0378440	−	0.999284i	$-0.487951\pi$
$227$	258.860	0.0756879	0.0378440	+	0.999284i	$0.487951\pi$
$228$	−1503.79	−0.436802
$229$	804.986	0.232292	0.116146	−	0.993232i	$-0.462946\pi$
$229$	804.986	0.232292	0.116146	+	0.993232i	$0.462946\pi$
$230$	788.107	0.225940
$231$	−4606.24	−1.31198
$232$	2117.57	0.599247
$233$	−1717.65	−0.482947	−0.241474	−	0.970407i	$-0.577631\pi$
$233$	−1717.65	−0.482947	−0.241474	+	0.970407i	$0.577631\pi$
$234$	0	0
$235$	1741.79	0.483498
$236$	3432.32	0.946715
$237$	−2156.41	−0.591029
$238$	−94.9647	−0.0258641
$239$	−2355.26	−0.637445	−0.318722	−	0.947848i	$-0.603254\pi$
$239$	−2355.26	−0.637445	−0.318722	+	0.947848i	$0.603254\pi$
$240$	2076.69	0.558541
$241$	2170.07	0.580027	0.290014	−	0.957023i	$-0.406340\pi$
$241$	2170.07	0.580027	0.290014	+	0.957023i	$0.406340\pi$
$242$	1318.61	0.350262
$243$	−243.000	−0.0641500
$244$	−3620.22	−0.949840
$245$	−10176.7	−2.65373
$246$	627.335	0.162591
$247$	0	0
$248$	−4960.98	−1.27025
$249$	1193.19	0.303676
$250$	−1316.49	−0.333048
$251$	2860.82	0.719416	0.359708	−	0.933065i	$-0.382876\pi$
$251$	2860.82	0.719416	0.359708	+	0.933065i	$0.382876\pi$
$252$	−1873.85	−0.468419
$253$	−2130.79	−0.529493
$254$	−1167.39	−0.288381
$255$	−160.535	−0.0394238
$256$	−464.125	−0.113312
$257$	2276.69	0.552593	0.276296	−	0.961073i	$-0.410893\pi$
$257$	2276.69	0.552593	0.276296	+	0.961073i	$0.410893\pi$
$258$	635.031	0.153238
$259$	−7905.00	−1.89650
$260$	0	0
$261$	−1217.10	−0.288645
$262$	−586.080	−0.138199
$263$	−3933.20	−0.922172	−0.461086	−	0.887355i	$-0.652540\pi$
$263$	−3933.20	−0.922172	−0.461086	+	0.887355i	$0.652540\pi$
$264$	2388.53	0.556833
$265$	2691.49	0.623912
$266$	−2308.00	−0.532002
$267$	−1945.24	−0.445868
$268$	5361.29	1.22199
$269$	−1622.92	−0.367848	−0.183924	−	0.982940i	$-0.558880\pi$
$269$	−1622.92	−0.367848	−0.183924	+	0.982940i	$0.558880\pi$
$270$	507.764	0.114450
$271$	−1554.77	−0.348508	−0.174254	−	0.984701i	$-0.555751\pi$
$271$	−1554.77	−0.348508	−0.174254	+	0.984701i	$0.555751\pi$
$272$	−115.756	−0.0258042
$273$	0	0
$274$	1434.89	0.316368
$275$	9915.08	2.17419
$276$	−866.822	−0.189046
$277$	−8258.33	−1.79132	−0.895658	−	0.444743i	$-0.853295\pi$
$277$	−8258.33	−1.79132	−0.895658	+	0.444743i	$0.853295\pi$
$278$	−2036.33	−0.439321
$279$	2851.38	0.611855
$280$	8458.70	1.80537
$281$	5023.16	1.06639	0.533197	−	0.845991i	$-0.320991\pi$
$281$	5023.16	1.06639	0.533197	+	0.845991i	$0.320991\pi$
$282$	307.087	0.0648467
$283$	−4804.71	−1.00922	−0.504612	−	0.863346i	$-0.668364\pi$
$283$	−4804.71	−1.00922	−0.504612	+	0.863346i	$0.668364\pi$
$284$	6978.64	1.45812
$285$	−3901.60	−0.810914
$286$	0	0
$287$	−6006.61	−1.23540
$288$	1493.56	0.305586
$289$	−4904.05	−0.998179
$290$	2543.20	0.514971
$291$	817.237	0.164630
$292$	4225.89	0.846923
$293$	−2496.53	−0.497778	−0.248889	−	0.968532i	$-0.580065\pi$
$293$	−2496.53	−0.497778	−0.248889	+	0.968532i	$0.580065\pi$
$294$	−1794.20	−0.355917
$295$	8905.18	1.75756
$296$	4099.08	0.804912
$297$	−1372.83	−0.268215
$298$	−3679.44	−0.715249
$299$	0	0
$300$	4033.53	0.776253
$301$	−6080.29	−1.16433
$302$	−706.920	−0.134698
$303$	−1248.17	−0.236652
$304$	−2813.31	−0.530770
$305$	−9392.71	−1.76336
$306$	−28.3031	−0.00528751
$307$	1914.68	0.355950	0.177975	−	0.984035i	$-0.443045\pi$
$307$	1914.68	0.355950	0.177975	+	0.984035i	$0.443045\pi$
$308$	−10586.4	−1.95849
$309$	−784.528	−0.144434
$310$	−5958.14	−1.09161
$311$	3171.99	0.578350	0.289175	−	0.957276i	$-0.406619\pi$
$311$	3171.99	0.578350	0.289175	+	0.957276i	$0.406619\pi$
$312$	0	0
$313$	1240.50	0.224017	0.112009	−	0.993707i	$-0.464272\pi$
$313$	1240.50	0.224017	0.112009	+	0.993707i	$0.464272\pi$
$314$	1337.25	0.240336
$315$	−4861.73	−0.869611
$316$	−4956.01	−0.882270
$317$	9521.41	1.68699	0.843495	−	0.537137i	$-0.180494\pi$
$317$	9521.41	1.68699	0.843495	+	0.537137i	$0.180494\pi$
$318$	474.523	0.0836790
$319$	−6876.01	−1.20684
$320$	2416.96	0.422226
$321$	−3124.72	−0.543317
$322$	−1330.39	−0.230248
$323$	217.477	0.0374637
$324$	−558.479	−0.0957611
$325$	0	0
$326$	−1551.93	−0.263661
$327$	−1828.93	−0.309297
$328$	3114.68	0.524327
$329$	−2940.29	−0.492716
$330$	2868.62	0.478522
$331$	−1997.12	−0.331637	−0.165818	−	0.986156i	$-0.553027\pi$
$331$	−1997.12	−0.331637	−0.165818	+	0.986156i	$0.553027\pi$
$332$	2742.27	0.453317
$333$	−2355.99	−0.387710
$334$	−3400.68	−0.557116
$335$	13909.9	2.26860
$336$	−3505.63	−0.569190
$337$	5200.25	0.840581	0.420290	−	0.907390i	$-0.361928\pi$
$337$	5200.25	0.840581	0.420290	+	0.907390i	$0.361928\pi$
$338$	0	0
$339$	1001.99	0.160533
$340$	−368.952	−0.0588506
$341$	16108.9	2.55820
$342$	−687.871	−0.108760
$343$	6821.32	1.07381
$344$	3152.88	0.494163
$345$	−2248.98	−0.350960
$346$	446.372	0.0693558
$347$	4622.17	0.715075	0.357538	−	0.933899i	$-0.383616\pi$
$347$	4622.17	0.715075	0.357538	+	0.933899i	$0.383616\pi$
$348$	−2797.21	−0.430880
$349$	9870.06	1.51385	0.756923	−	0.653504i	$-0.226702\pi$
$349$	9870.06	1.51385	0.756923	+	0.653504i	$0.226702\pi$
$350$	6190.62	0.945436
$351$	0	0
$352$	8437.87	1.27767
$353$	−8962.46	−1.35134	−0.675671	−	0.737203i	$-0.736146\pi$
$353$	−8962.46	−1.35134	−0.675671	+	0.737203i	$0.736146\pi$
$354$	1570.03	0.235723
$355$	18106.2	2.70697
$356$	−4470.68	−0.665577
$357$	270.996	0.0401754
$358$	−4625.70	−0.682893
$359$	−9174.16	−1.34873	−0.674365	−	0.738399i	$-0.735582\pi$
$359$	−9174.16	−1.34873	−0.674365	+	0.738399i	$0.735582\pi$
$360$	2521.01	0.369081
$361$	−1573.48	−0.229404
$362$	−362.852	−0.0526826
$363$	−3762.85	−0.544072
$364$	0	0
$365$	10964.1	1.57230
$366$	−1655.98	−0.236502
$367$	10360.7	1.47364	0.736818	−	0.676092i	$-0.236328\pi$
$367$	10360.7	1.47364	0.736818	+	0.676092i	$0.236328\pi$
$368$	−1621.66	−0.229715
$369$	−1790.20	−0.252558
$370$	4922.99	0.691713
$371$	−4543.46	−0.635807
$372$	6553.23	0.913358
$373$	−5480.60	−0.760790	−0.380395	−	0.924824i	$-0.624212\pi$
$373$	−5480.60	−0.760790	−0.380395	+	0.924824i	$0.624212\pi$
$374$	−159.899	−0.0221074
$375$	3756.79	0.517333
$376$	1524.67	0.209119
$377$	0	0
$378$	−857.148	−0.116632
$379$	4262.83	0.577748	0.288874	−	0.957367i	$-0.406719\pi$
$379$	4262.83	0.577748	0.288874	+	0.957367i	$0.406719\pi$
$380$	−8966.91	−1.21051
$381$	3331.33	0.447950
$382$	−4285.68	−0.574017
$383$	−901.981	−0.120337	−0.0601685	−	0.998188i	$-0.519164\pi$
$383$	−901.981	−0.120337	−0.0601685	+	0.998188i	$0.519164\pi$
$384$	4408.94	0.585919
$385$	−27466.4	−3.63590
$386$	−3386.28	−0.446520
$387$	−1812.15	−0.238028
$388$	1878.23	0.245754
$389$	−1093.46	−0.142521	−0.0712606	−	0.997458i	$-0.522702\pi$
$389$	−1093.46	−0.142521	−0.0712606	+	0.997458i	$0.522702\pi$
$390$	0	0
$391$	125.360	0.0162141
$392$	−8908.07	−1.14777
$393$	1672.47	0.214669
$394$	−3226.18	−0.412519
$395$	−12858.4	−1.63792
$396$	−3155.14	−0.400383
$397$	2587.62	0.327126	0.163563	−	0.986533i	$-0.447701\pi$
$397$	2587.62	0.327126	0.163563	+	0.986533i	$0.447701\pi$
$398$	4196.79	0.528558
$399$	6586.22	0.826374
$400$	7545.98	0.943247
$401$	422.775	0.0526494	0.0263247	−	0.999653i	$-0.491620\pi$
$401$	422.775	0.0526494	0.0263247	+	0.999653i	$0.491620\pi$
$402$	2452.39	0.304264
$403$	0	0
$404$	−2868.63	−0.353267
$405$	−1448.98	−0.177779
$406$	−4293.13	−0.524789
$407$	−13310.2	−1.62104
$408$	−140.523	−0.0170513
$409$	−3028.09	−0.366087	−0.183044	−	0.983105i	$-0.558595\pi$
$409$	−3028.09	−0.366087	−0.183044	+	0.983105i	$0.558595\pi$
$410$	3740.73	0.450588
$411$	−4094.66	−0.491423
$412$	−1803.05	−0.215607
$413$	−15032.7	−1.79107
$414$	−396.506	−0.0470706
$415$	7114.84	0.841576
$416$	0	0
$417$	5810.98	0.682410
$418$	−3886.14	−0.454730
$419$	−9629.51	−1.12275	−0.561375	−	0.827562i	$-0.689727\pi$
$419$	−9629.51	−1.12275	−0.561375	+	0.827562i	$0.689727\pi$
$420$	−11173.6	−1.29813
$421$	−8288.54	−0.959521	−0.479761	−	0.877399i	$-0.659277\pi$
$421$	−8288.54	−0.959521	−0.479761	+	0.877399i	$0.659277\pi$
$422$	3015.40	0.347837
$423$	−876.319	−0.100728
$424$	2355.97	0.269850
$425$	−583.328	−0.0665778
$426$	3192.21	0.363058
$427$	15855.7	1.79698
$428$	−7181.43	−0.811046
$429$	0	0
$430$	3786.61	0.424667
$431$	−3873.84	−0.432938	−0.216469	−	0.976289i	$-0.569454\pi$
$431$	−3873.84	−0.432938	−0.216469	+	0.976289i	$0.569454\pi$
$432$	−1044.81	−0.116362
$433$	3016.87	0.334830	0.167415	−	0.985886i	$-0.446458\pi$
$433$	3016.87	0.334830	0.167415	+	0.985886i	$0.446458\pi$
$434$	10057.8	1.11242
$435$	−7257.40	−0.799921
$436$	−4203.37	−0.461709
$437$	3046.71	0.333510
$438$	1933.03	0.210876
$439$	−2862.77	−0.311235	−0.155618	−	0.987817i	$-0.549737\pi$
$439$	−2862.77	−0.311235	−0.155618	+	0.987817i	$0.549737\pi$
$440$	14242.5	1.54315
$441$	5120.01	0.552857
$442$	0	0
$443$	13067.0	1.40143	0.700713	−	0.713443i	$-0.252865\pi$
$443$	13067.0	1.40143	0.700713	+	0.713443i	$0.252865\pi$
$444$	−5414.69	−0.578761
$445$	−11599.2	−1.23563
$446$	3258.43	0.345944
$447$	10499.8	1.11102
$448$	−4080.04	−0.430276
$449$	9527.11	1.00136	0.500682	−	0.865631i	$-0.333083\pi$
$449$	9527.11	1.00136	0.500682	+	0.865631i	$0.333083\pi$
$450$	1845.04	0.193280
$451$	−10113.7	−1.05596
$452$	2302.84	0.239638
$453$	2017.30	0.209230
$454$	272.136	0.0281321
$455$	0	0
$456$	−3415.23	−0.350730
$457$	−6223.04	−0.636983	−0.318492	−	0.947926i	$-0.603176\pi$
$457$	−6223.04	−0.636983	−0.318492	+	0.947926i	$0.603176\pi$
$458$	846.270	0.0863397
$459$	80.7671	0.00821325
$460$	−5168.76	−0.523901
$461$	−17482.6	−1.76626	−0.883128	−	0.469132i	$-0.844567\pi$
$461$	−17482.6	−1.76626	−0.883128	+	0.469132i	$0.844567\pi$
$462$	−4842.47	−0.487645
$463$	3280.46	0.329278	0.164639	−	0.986354i	$-0.447354\pi$
$463$	3280.46	0.329278	0.164639	+	0.986354i	$0.447354\pi$
$464$	−5233.06	−0.523575
$465$	17002.4	1.69563
$466$	−1805.74	−0.179504
$467$	8459.42	0.838234	0.419117	−	0.907932i	$-0.362340\pi$
$467$	8459.42	0.838234	0.419117	+	0.907932i	$0.362340\pi$
$468$	0	0
$469$	−23481.1	−2.31185
$470$	1831.12	0.179709
$471$	−3816.05	−0.373321
$472$	7795.09	0.760165
$473$	−10237.8	−0.995211
$474$	−2267.00	−0.219677
$475$	−14177.0	−1.36945
$476$	622.821	0.0599726
$477$	−1354.12	−0.129981
$478$	−2476.05	−0.236929
$479$	−17593.9	−1.67826	−0.839129	−	0.543933i	$-0.816935\pi$
$479$	−17593.9	−1.67826	−0.839129	+	0.543933i	$0.816935\pi$
$480$	8905.90	0.846868
$481$	0	0
$482$	2281.36	0.215588
$483$	3796.47	0.357651
$484$	−8648.02	−0.812174
$485$	4873.08	0.456238
$486$	−255.462	−0.0238436
$487$	−12736.9	−1.18515	−0.592573	−	0.805517i	$-0.701888\pi$
$487$	−12736.9	−1.18515	−0.592573	+	0.805517i	$0.701888\pi$
$488$	−8221.84	−0.762675
$489$	4428.67	0.409553
$490$	−10698.6	−0.986352
$491$	−5458.09	−0.501671	−0.250835	−	0.968030i	$-0.580705\pi$
$491$	−5458.09	−0.501671	−0.250835	+	0.968030i	$0.580705\pi$
$492$	−4114.35	−0.377010
$493$	404.532	0.0369558
$494$	0	0
$495$	−8186.04	−0.743303
$496$	12259.9	1.10985
$497$	−30564.7	−2.75858
$498$	1254.38	0.112872
$499$	18109.7	1.62466	0.812328	−	0.583201i	$-0.198200\pi$
$499$	18109.7	1.62466	0.812328	+	0.583201i	$0.198200\pi$
$500$	8634.12	0.772259
$501$	9704.35	0.865386
$502$	3007.54	0.267396
$503$	19414.1	1.72094	0.860469	−	0.509503i	$-0.170171\pi$
$503$	19414.1	1.72094	0.860469	+	0.509503i	$0.170171\pi$
$504$	−4255.68	−0.376117
$505$	−7442.70	−0.655833
$506$	−2240.07	−0.196805
$507$	0	0
$508$	7656.27	0.668686
$509$	−16124.1	−1.40410	−0.702051	−	0.712126i	$-0.747732\pi$
$509$	−16124.1	−1.40410	−0.702051	+	0.712126i	$0.747732\pi$
$510$	−168.768	−0.0146533
$511$	−18508.3	−1.60227
$512$	11269.2	0.972724
$513$	1962.94	0.168940
$514$	2393.46	0.205391
$515$	−4678.05	−0.400271
$516$	−4164.81	−0.355321
$517$	−4950.78	−0.421151
$518$	−8310.41	−0.704901
$519$	−1273.79	−0.107733
$520$	0	0
$521$	18662.7	1.56934	0.784672	−	0.619911i	$-0.212831\pi$
$521$	18662.7	1.56934	0.784672	+	0.619911i	$0.212831\pi$
$522$	−1279.51	−0.107285
$523$	−2290.01	−0.191463	−0.0957314	−	0.995407i	$-0.530519\pi$
$523$	−2290.01	−0.191463	−0.0957314	+	0.995407i	$0.530519\pi$
$524$	3843.77	0.320450
$525$	−17665.9	−1.46857
$526$	−4134.91	−0.342758
$527$	−947.727	−0.0783370
$528$	−5902.67	−0.486517
$529$	−10410.8	−0.855659
$530$	2829.52	0.231899
$531$	−4480.31	−0.366156
$532$	15136.9	1.23359
$533$	0	0
$534$	−2045.00	−0.165723
$535$	−18632.3	−1.50569
$536$	12175.9	0.981195
$537$	13200.1	1.06076
$538$	−1706.15	−0.136724
$539$	28925.6	2.31153
$540$	−3330.14	−0.265382
$541$	11740.6	0.933029	0.466514	−	0.884514i	$-0.345510\pi$
$541$	11740.6	0.933029	0.466514	+	0.884514i	$0.345510\pi$
$542$	−1634.51	−0.129535
$543$	1035.45	0.0818334
$544$	−496.420	−0.0391247
$545$	−10905.7	−0.857153
$546$	0	0
$547$	312.599	0.0244347	0.0122174	−	0.999925i	$-0.496111\pi$
$547$	312.599	0.0244347	0.0122174	+	0.999925i	$0.496111\pi$
$548$	−9410.63	−0.733581
$549$	4725.59	0.367365
$550$	10423.6	0.808114
$551$	9831.64	0.760149
$552$	−1968.63	−0.151794
$553$	21706.1	1.66914
$554$	−8681.86	−0.665806
$555$	−14048.5	−1.07446
$556$	13355.2	1.01868
$557$	7567.62	0.575674	0.287837	−	0.957679i	$-0.407064\pi$
$557$	7567.62	0.575674	0.287837	+	0.957679i	$0.407064\pi$
$558$	2997.61	0.227418
$559$	0	0
$560$	−20903.6	−1.57739
$561$	456.295	0.0343401
$562$	5280.78	0.396363
$563$	13068.3	0.978261	0.489131	−	0.872211i	$-0.337314\pi$
$563$	13068.3	0.978261	0.489131	+	0.872211i	$0.337314\pi$
$564$	−2014.01	−0.150364
$565$	5974.74	0.444884
$566$	−5051.12	−0.375114
$567$	2446.00	0.181168
$568$	15849.1	1.17080
$569$	−5959.19	−0.439055	−0.219528	−	0.975606i	$-0.570452\pi$
$569$	−5959.19	−0.439055	−0.219528	+	0.975606i	$0.570452\pi$
$570$	−4101.69	−0.301405
$571$	−5460.53	−0.400203	−0.200102	−	0.979775i	$-0.564127\pi$
$571$	−5460.53	−0.400203	−0.200102	+	0.979775i	$0.564127\pi$
$572$	0	0
$573$	12229.8	0.891638
$574$	−6314.66	−0.459179
$575$	−8172.02	−0.592690
$576$	−1216.00	−0.0879633
$577$	−8560.26	−0.617623	−0.308811	−	0.951123i	$-0.599931\pi$
$577$	−8560.26	−0.617623	−0.308811	+	0.951123i	$0.599931\pi$
$578$	−5155.56	−0.371009
$579$	9663.24	0.693594
$580$	−16679.4	−1.19410
$581$	−12010.4	−0.857620
$582$	859.149	0.0611905
$583$	−7650.14	−0.543458
$584$	9597.36	0.680037
$585$	0	0
$586$	−2624.57	−0.185017
$587$	25603.9	1.80032	0.900158	−	0.435564i	$-0.143451\pi$
$587$	25603.9	1.80032	0.900158	+	0.435564i	$0.143451\pi$
$588$	11767.1	0.825287
$589$	−23033.3	−1.61133
$590$	9361.89	0.653259
$591$	9206.39	0.640779
$592$	−10129.9	−0.703269
$593$	−16311.5	−1.12956	−0.564782	−	0.825240i	$-0.691040\pi$
$593$	−16311.5	−1.12956	−0.564782	+	0.825240i	$0.691040\pi$
$594$	−1443.24	−0.0996916
$595$	1615.92	0.111338
$596$	24131.4	1.65849
$597$	−11976.2	−0.821024
$598$	0	0
$599$	6549.91	0.446782	0.223391	−	0.974729i	$-0.428287\pi$
$599$	6549.91	0.446782	0.223391	+	0.974729i	$0.428287\pi$
$600$	9160.49	0.623292
$601$	11467.3	0.778306	0.389153	−	0.921173i	$-0.372768\pi$
$601$	11467.3	0.778306	0.389153	+	0.921173i	$0.372768\pi$
$602$	−6392.12	−0.432763
$603$	−6998.26	−0.472622
$604$	4636.30	0.312332
$605$	−22437.4	−1.50779
$606$	−1312.18	−0.0879601
$607$	17594.3	1.17649	0.588245	−	0.808682i	$-0.299819\pi$
$607$	17594.3	1.17649	0.588245	+	0.808682i	$0.299819\pi$
$608$	−12064.9	−0.804762
$609$	12251.1	0.815171
$610$	−9874.42	−0.655416
$611$	0	0
$612$	185.624	0.0122605
$613$	12783.2	0.842265	0.421132	−	0.906999i	$-0.361633\pi$
$613$	12783.2	0.842265	0.421132	+	0.906999i	$0.361633\pi$
$614$	2012.87	0.132301
$615$	−10674.7	−0.699913
$616$	−24042.5	−1.57257
$617$	9767.34	0.637307	0.318653	−	0.947871i	$-0.396769\pi$
$617$	9767.34	0.637307	0.318653	+	0.947871i	$0.396769\pi$
$618$	−824.763	−0.0536842
$619$	24677.0	1.60235	0.801173	−	0.598433i	$-0.204210\pi$
$619$	24677.0	1.60235	0.801173	+	0.598433i	$0.204210\pi$
$620$	39076.1	2.53119
$621$	1131.49	0.0731162
$622$	3334.66	0.214964
$623$	19580.5	1.25919
$624$	0	0
$625$	−1974.11	−0.126343
$626$	1304.12	0.0832639
$627$	11089.7	0.706346
$628$	−8770.30	−0.557282
$629$	783.071	0.0496393
$630$	−5111.07	−0.323222
$631$	22666.9	1.43004	0.715021	−	0.699103i	$-0.246417\pi$
$631$	22666.9	1.43004	0.715021	+	0.699103i	$0.246417\pi$
$632$	−11255.5	−0.708419
$633$	−8604.88	−0.540306
$634$	10009.7	0.627030
$635$	19864.3	1.24140
$636$	−3112.13	−0.194032
$637$	0	0
$638$	−7228.64	−0.448565
$639$	−9109.44	−0.563950
$640$	26290.0	1.62375
$641$	−10770.3	−0.663653	−0.331826	−	0.943341i	$-0.607665\pi$
$641$	−10770.3	−0.663653	−0.331826	+	0.943341i	$0.607665\pi$
$642$	−3284.97	−0.201943
$643$	−21220.8	−1.30151	−0.650753	−	0.759289i	$-0.725547\pi$
$643$	−21220.8	−1.30151	−0.650753	+	0.759289i	$0.725547\pi$
$644$	8725.29	0.533889
$645$	−10805.7	−0.659647
$646$	228.631	0.0139247
$647$	−19430.5	−1.18067	−0.590334	−	0.807159i	$-0.701004\pi$
$647$	−19430.5	−1.18067	−0.590334	+	0.807159i	$0.701004\pi$
$648$	−1268.35	−0.0768914
$649$	−25311.6	−1.53092
$650$	0	0
$651$	−28701.5	−1.72796
$652$	10178.3	0.611367
$653$	28307.3	1.69640	0.848201	−	0.529674i	$-0.177686\pi$
$653$	28307.3	1.69640	0.848201	+	0.529674i	$0.177686\pi$
$654$	−1922.73	−0.114961
$655$	9972.72	0.594910
$656$	−7697.17	−0.458116
$657$	−5516.19	−0.327560
$658$	−3091.09	−0.183136
$659$	25525.5	1.50885	0.754425	−	0.656387i	$-0.227916\pi$
$659$	25525.5	1.50885	0.754425	+	0.656387i	$0.227916\pi$
$660$	−18813.7	−1.10958
$661$	−26065.8	−1.53380	−0.766901	−	0.641765i	$-0.778202\pi$
$661$	−26065.8	−1.53380	−0.766901	+	0.641765i	$0.778202\pi$
$662$	−2099.55	−0.123265
$663$	0	0
$664$	6227.92	0.363991
$665$	39272.8	2.29013
$666$	−2476.82	−0.144106
$667$	5667.21	0.328988
$668$	22303.2	1.29182
$669$	−9298.42	−0.537366
$670$	14623.3	0.843205
$671$	26697.3	1.53597
$672$	−15033.9	−0.863014
$673$	27351.3	1.56659	0.783295	−	0.621650i	$-0.213537\pi$
$673$	27351.3	1.56659	0.783295	+	0.621650i	$0.213537\pi$
$674$	5466.95	0.312432
$675$	−5265.09	−0.300227
$676$	0	0
$677$	−20998.8	−1.19209	−0.596047	−	0.802949i	$-0.703263\pi$
$677$	−20998.8	−1.19209	−0.596047	+	0.802949i	$0.703263\pi$
$678$	1053.38	0.0596677
$679$	−8226.17	−0.464936
$680$	−837.921	−0.0472541
$681$	−776.581	−0.0436985
$682$	16935.1	0.950847
$683$	−21227.9	−1.18926	−0.594629	−	0.804000i	$-0.702701\pi$
$683$	−21227.9	−1.18926	−0.594629	+	0.804000i	$0.702701\pi$
$684$	4511.36	0.252188
$685$	−24416.0	−1.36188
$686$	7171.15	0.399119
$687$	−2414.96	−0.134114
$688$	−7791.59	−0.431761
$689$	0	0
$690$	−2364.32	−0.130447
$691$	−11371.3	−0.626025	−0.313012	−	0.949749i	$-0.601338\pi$
$691$	−11371.3	−0.626025	−0.313012	+	0.949749i	$0.601338\pi$
$692$	−2927.51	−0.160820
$693$	13818.7	0.757474
$694$	4859.22	0.265783
$695$	34650.2	1.89116
$696$	−6352.71	−0.345975
$697$	595.016	0.0323355
$698$	10376.3	0.562675
$699$	5152.94	0.278830
$700$	−40600.8	−2.19224
$701$	−8695.98	−0.468534	−0.234267	−	0.972172i	$-0.575269\pi$
$701$	−8695.98	−0.468534	−0.234267	+	0.972172i	$0.575269\pi$
$702$	0	0
$703$	19031.6	1.02104
$704$	−6869.84	−0.367780
$705$	−5225.38	−0.279148
$706$	−9422.11	−0.502274
$707$	12563.9	0.668336
$708$	−10296.9	−0.546586
$709$	9428.79	0.499444	0.249722	−	0.968318i	$-0.419661\pi$
$709$	9428.79	0.499444	0.249722	+	0.968318i	$0.419661\pi$
$710$	19034.7	1.00614
$711$	6469.23	0.341231
$712$	−10153.3	−0.534425
$713$	−13277.0	−0.697374
$714$	284.894	0.0149326
$715$	0	0
$716$	30337.4	1.58347
$717$	7065.79	0.368029
$718$	−9644.66	−0.501303
$719$	790.174	0.0409854	0.0204927	−	0.999790i	$-0.493477\pi$
$719$	790.174	0.0409854	0.0204927	+	0.999790i	$0.493477\pi$
$720$	−6230.07	−0.322474
$721$	7896.93	0.407902
$722$	−1654.18	−0.0852663
$723$	−6510.21	−0.334879
$724$	2379.75	0.122158
$725$	−26370.9	−1.35088
$726$	−3955.83	−0.202224
$727$	−1591.88	−0.0812101	−0.0406050	−	0.999175i	$-0.512929\pi$
$727$	−1591.88	−0.0812101	−0.0406050	+	0.999175i	$0.512929\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	11526.4	0.584400
$731$	602.314	0.0304752
$732$	10860.7	0.548391
$733$	2695.20	0.135811	0.0679056	−	0.997692i	$-0.478368\pi$
$733$	2695.20	0.135811	0.0679056	+	0.997692i	$0.478368\pi$
$734$	10892.1	0.547729
$735$	30530.0	1.53213
$736$	−6954.50	−0.348297
$737$	−39536.8	−1.97606
$738$	−1882.01	−0.0938721
$739$	1979.17	0.0985181	0.0492590	−	0.998786i	$-0.484314\pi$
$739$	1979.17	0.0985181	0.0492590	+	0.998786i	$0.484314\pi$
$740$	−32287.1	−1.60392
$741$	0	0
$742$	−4776.47	−0.236320
$743$	19324.2	0.954156	0.477078	−	0.878861i	$-0.341696\pi$
$743$	19324.2	0.954156	0.477078	+	0.878861i	$0.341696\pi$
$744$	14883.0	0.733381
$745$	62609.2	3.07896
$746$	−5761.67	−0.282775
$747$	−3579.57	−0.175327
$748$	1048.69	0.0512618
$749$	31452.9	1.53440
$750$	3949.46	0.192285
$751$	13898.2	0.675303	0.337652	−	0.941271i	$-0.390367\pi$
$751$	13898.2	0.675303	0.337652	+	0.941271i	$0.390367\pi$
$752$	−3767.84	−0.182712
$753$	−8582.46	−0.415355
$754$	0	0
$755$	12028.9	0.579838
$756$	5621.56	0.270442
$757$	16195.7	0.777601	0.388800	−	0.921322i	$-0.372890\pi$
$757$	16195.7	0.777601	0.388800	+	0.921322i	$0.372890\pi$
$758$	4481.45	0.214741
$759$	6392.38	0.305703
$760$	−20364.6	−0.971977
$761$	−22912.0	−1.09141	−0.545704	−	0.837978i	$-0.683738\pi$
$761$	−22912.0	−1.09141	−0.545704	+	0.837978i	$0.683738\pi$
$762$	3502.17	0.166497
$763$	18409.7	0.873495
$764$	28107.4	1.33101
$765$	481.604	0.0227614
$766$	−948.240	−0.0447275
$767$	0	0
$768$	1392.37	0.0654205
$769$	17213.9	0.807215	0.403607	−	0.914932i	$-0.367756\pi$
$769$	17213.9	0.807215	0.403607	+	0.914932i	$0.367756\pi$
$770$	−28875.1	−1.35141
$771$	−6830.08	−0.319039
$772$	22208.7	1.03537
$773$	19732.2	0.918136	0.459068	−	0.888401i	$-0.348183\pi$
$773$	19732.2	0.918136	0.459068	+	0.888401i	$0.348183\pi$
$774$	−1905.09	−0.0884717
$775$	61781.0	2.86353
$776$	4265.62	0.197328
$777$	23715.0	1.09494
$778$	−1149.54	−0.0529731
$779$	14461.1	0.665113
$780$	0	0
$781$	−51463.9	−2.35791
$782$	131.789	0.00602654
$783$	3651.29	0.166649
$784$	22014.1	1.00283
$785$	−22754.7	−1.03458
$786$	1758.24	0.0797892
$787$	−34771.8	−1.57494	−0.787472	−	0.616350i	$-0.788611\pi$
$787$	−34771.8	−1.57494	−0.787472	+	0.616350i	$0.788611\pi$
$788$	21158.7	0.956534
$789$	11799.6	0.532416
$790$	−13517.9	−0.608790
$791$	−10085.9	−0.453365
$792$	−7165.59	−0.321487
$793$	0	0
$794$	2720.33	0.121588
$795$	−8074.46	−0.360216
$796$	−27524.4	−1.22560
$797$	−16429.2	−0.730178	−0.365089	−	0.930973i	$-0.618961\pi$
$797$	−16429.2	−0.730178	−0.365089	+	0.930973i	$0.618961\pi$
$798$	6924.00	0.307151
$799$	291.266	0.0128964
$800$	32360.9	1.43017
$801$	5835.71	0.257422
$802$	444.458	0.0195690
$803$	−31163.8	−1.36955
$804$	−16083.9	−0.705515
$805$	22637.9	0.991156
$806$	0	0
$807$	4868.76	0.212377
$808$	−6514.91	−0.283656
$809$	−1805.75	−0.0784755	−0.0392378	−	0.999230i	$-0.512493\pi$
$809$	−1805.75	−0.0784755	−0.0392378	+	0.999230i	$0.512493\pi$
$810$	−1523.29	−0.0660778
$811$	8758.70	0.379235	0.189618	−	0.981858i	$-0.439275\pi$
$811$	8758.70	0.379235	0.189618	+	0.981858i	$0.439275\pi$
$812$	28156.3	1.21686
$813$	4664.31	0.201211
$814$	−13992.8	−0.602516
$815$	26407.6	1.13499
$816$	347.268	0.0148981
$817$	14638.5	0.626850
$818$	−3183.39	−0.136069
$819$	0	0
$820$	−24533.4	−1.04481
$821$	10480.4	0.445518	0.222759	−	0.974874i	$-0.428494\pi$
$821$	10480.4	0.445518	0.222759	+	0.974874i	$0.428494\pi$
$822$	−4304.66	−0.182655
$823$	−38187.3	−1.61741	−0.808703	−	0.588217i	$-0.799830\pi$
$823$	−38187.3	−1.61741	−0.808703	+	0.588217i	$0.799830\pi$
$824$	−4094.89	−0.173122
$825$	−29745.2	−1.25527
$826$	−15803.7	−0.665714
$827$	−10529.0	−0.442720	−0.221360	−	0.975192i	$-0.571050\pi$
$827$	−10529.0	−0.442720	−0.221360	+	0.975192i	$0.571050\pi$
$828$	2600.47	0.109145
$829$	9131.19	0.382557	0.191278	−	0.981536i	$-0.438737\pi$
$829$	9131.19	0.382557	0.191278	+	0.981536i	$0.438737\pi$
$830$	7479.73	0.312801
$831$	24775.0	1.03422
$832$	0	0
$833$	−1701.76	−0.0707834
$834$	6109.00	0.253642
$835$	57865.8	2.39824
$836$	25487.0	1.05441
$837$	−8554.14	−0.353255
$838$	−10123.4	−0.417310
$839$	40623.1	1.67159	0.835796	−	0.549041i	$-0.185007\pi$
$839$	40623.1	1.67159	0.835796	+	0.549041i	$0.185007\pi$
$840$	−25376.1	−1.04233
$841$	−6101.07	−0.250157
$842$	−8713.62	−0.356640
$843$	−15069.5	−0.615683
$844$	−19776.3	−0.806551
$845$	0	0
$846$	−921.261	−0.0374393
$847$	37876.2	1.53653
$848$	−5822.22	−0.235773
$849$	14414.1	0.582675
$850$	−613.244	−0.0247460
$851$	10970.3	0.441900
$852$	−20935.9	−0.841846
$853$	−40704.0	−1.63385	−0.816927	−	0.576742i	$-0.804324\pi$
$853$	−40704.0	−1.63385	−0.816927	+	0.576742i	$0.804324\pi$
$854$	16668.8	0.667911
$855$	11704.8	0.468182
$856$	−16309.7	−0.651229
$857$	45984.1	1.83289	0.916445	−	0.400160i	$-0.131045\pi$
$857$	45984.1	1.83289	0.916445	+	0.400160i	$0.131045\pi$
$858$	0	0
$859$	7787.52	0.309321	0.154660	−	0.987968i	$-0.450572\pi$
$859$	7787.52	0.309321	0.154660	+	0.987968i	$0.450572\pi$
$860$	−24834.3	−0.984700
$861$	18019.8	0.713257
$862$	−4072.51	−0.160917
$863$	−34878.2	−1.37575	−0.687873	−	0.725831i	$-0.741455\pi$
$863$	−34878.2	−1.37575	−0.687873	+	0.725831i	$0.741455\pi$
$864$	−4480.67	−0.176430
$865$	−7595.46	−0.298559
$866$	3171.59	0.124452
$867$	14712.2	0.576299
$868$	−65963.8	−2.57944
$869$	36548.1	1.42671
$870$	−7629.59	−0.297319
$871$	0	0
$872$	−9546.22	−0.370729
$873$	−2451.71	−0.0950491
$874$	3202.96	0.123961
$875$	−37815.3	−1.46102
$876$	−12677.7	−0.488971
$877$	−35625.1	−1.37169	−0.685846	−	0.727747i	$-0.740568\pi$
$877$	−35625.1	−1.37169	−0.685846	+	0.727747i	$0.740568\pi$
$878$	−3009.58	−0.115682
$879$	7489.59	0.287392
$880$	−35196.9	−1.34828
$881$	15602.6	0.596669	0.298335	−	0.954461i	$-0.403569\pi$
$881$	15602.6	0.596669	0.298335	+	0.954461i	$0.403569\pi$
$882$	5382.59	0.205489
$883$	−25341.6	−0.965812	−0.482906	−	0.875672i	$-0.660419\pi$
$883$	−25341.6	−0.965812	−0.482906	+	0.875672i	$0.660419\pi$
$884$	0	0
$885$	−26715.6	−1.01473
$886$	13737.1	0.520890
$887$	−5091.34	−0.192729	−0.0963644	−	0.995346i	$-0.530721\pi$
$887$	−5091.34	−0.192729	−0.0963644	+	0.995346i	$0.530721\pi$
$888$	−12297.2	−0.464716
$889$	−33532.6	−1.26507
$890$	−12194.1	−0.459266
$891$	4118.50	0.154854
$892$	−21370.2	−0.802162
$893$	7078.86	0.265269
$894$	11038.3	0.412949
$895$	78710.8	2.93968
$896$	−44379.7	−1.65471
$897$	0	0
$898$	10015.7	0.372192
$899$	−42844.5	−1.58948
$900$	−12100.6	−0.448170
$901$	450.076	0.0166417
$902$	−10632.4	−0.392485
$903$	18240.9	0.672223
$904$	5229.95	0.192418
$905$	6174.28	0.226785
$906$	2120.76	0.0777677
$907$	−551.828	−0.0202019	−0.0101010	−	0.999949i	$-0.503215\pi$
$907$	−551.828	−0.0202019	−0.0101010	+	0.999949i	$0.503215\pi$
$908$	−1784.79	−0.0652316
$909$	3744.51	0.136631
$910$	0	0
$911$	37661.8	1.36969	0.684847	−	0.728687i	$-0.259869\pi$
$911$	37661.8	1.36969	0.684847	+	0.728687i	$0.259869\pi$
$912$	8439.92	0.306440
$913$	−20222.8	−0.733054
$914$	−6542.19	−0.236757
$915$	28178.1	1.01808
$916$	−5550.22	−0.200201
$917$	−16834.8	−0.606252
$918$	84.9092	0.00305275
$919$	16265.4	0.583836	0.291918	−	0.956443i	$-0.405707\pi$
$919$	16265.4	0.583836	0.291918	+	0.956443i	$0.405707\pi$
$920$	−11738.7	−0.420667
$921$	−5744.04	−0.205508
$922$	−18379.2	−0.656492
$923$	0	0
$924$	31759.1	1.13073
$925$	−51047.3	−1.81451
$926$	3448.70	0.122388
$927$	2353.58	0.0833893
$928$	−22442.0	−0.793852
$929$	10133.6	0.357881	0.178940	−	0.983860i	$-0.442733\pi$
$929$	10133.6	0.357881	0.178940	+	0.983860i	$0.442733\pi$
$930$	17874.4	0.630242
$931$	−41359.2	−1.45595
$932$	11842.8	0.416228
$933$	−9515.96	−0.333911
$934$	8893.26	0.311559
$935$	2720.83	0.0951666
$936$	0	0
$937$	−45619.6	−1.59053	−0.795265	−	0.606261i	$-0.792669\pi$
$937$	−45619.6	−1.59053	−0.795265	+	0.606261i	$0.792669\pi$
$938$	−24685.3	−0.859280
$939$	−3721.51	−0.129336
$940$	−12009.3	−0.416703
$941$	26998.8	0.935321	0.467660	−	0.883908i	$-0.345097\pi$
$941$	26998.8	0.935321	0.467660	+	0.883908i	$0.345097\pi$
$942$	−4011.76	−0.138758
$943$	8335.76	0.287858
$944$	−19263.7	−0.664173
$945$	14585.2	0.502070
$946$	−10762.9	−0.369905
$947$	−16343.4	−0.560812	−0.280406	−	0.959882i	$-0.590469\pi$
$947$	−16343.4	−0.560812	−0.280406	+	0.959882i	$0.590469\pi$
$948$	14868.0	0.509379
$949$	0	0
$950$	−14904.1	−0.509004
$951$	−28564.2	−0.973984
$952$	1414.48	0.0481550
$953$	−19617.5	−0.666812	−0.333406	−	0.942783i	$-0.608198\pi$
$953$	−19617.5	−0.666812	−0.333406	+	0.942783i	$0.608198\pi$
$954$	−1423.57	−0.0483121
$955$	72925.0	2.47099
$956$	16239.1	0.549382
$957$	20628.0	0.696770
$958$	−18496.2	−0.623784
$959$	41216.2	1.38784
$960$	−7250.89	−0.243772
$961$	70583.9	2.36930
$962$	0	0
$963$	9374.15	0.313684
$964$	−14962.2	−0.499896
$965$	57620.8	1.92215
$966$	3991.17	0.132934
$967$	−42185.0	−1.40287	−0.701436	−	0.712732i	$-0.747457\pi$
$967$	−42185.0	−1.40287	−0.701436	+	0.712732i	$0.747457\pi$
$968$	−19640.4	−0.652135
$969$	−652.432	−0.0216297
$970$	5123.00	0.169577
$971$	−42711.7	−1.41162	−0.705811	−	0.708400i	$-0.749417\pi$
$971$	−42711.7	−1.41162	−0.705811	+	0.708400i	$0.749417\pi$
$972$	1675.44	0.0552877
$973$	−58492.4	−1.92722
$974$	−13390.2	−0.440502
$975$	0	0
$976$	20318.3	0.666365
$977$	30169.0	0.987915	0.493957	−	0.869486i	$-0.335550\pi$
$977$	30169.0	0.987915	0.493957	+	0.869486i	$0.335550\pi$
$978$	4655.79	0.152225
$979$	32969.0	1.07630
$980$	70166.1	2.28712
$981$	5486.79	0.178573
$982$	−5738.01	−0.186464
$983$	−23434.7	−0.760378	−0.380189	−	0.924909i	$-0.624141\pi$
$983$	−23434.7	−0.760378	−0.380189	+	0.924909i	$0.624141\pi$
$984$	−9344.04	−0.302721
$985$	54896.6	1.77579
$986$	425.278	0.0137359
$987$	8820.88	0.284470
$988$	0	0
$989$	8438.01	0.271297
$990$	−8605.86	−0.276275
$991$	−41688.8	−1.33632	−0.668158	−	0.744019i	$-0.732917\pi$
$991$	−41688.8	−1.33632	−0.668158	+	0.744019i	$0.732917\pi$
$992$	52576.5	1.68277
$993$	5991.37	0.191471
$994$	−32132.2	−1.02532
$995$	−71412.4	−2.27530
$996$	−8226.80	−0.261723
$997$	−46249.7	−1.46915	−0.734574	−	0.678528i	$-0.762618\pi$
$997$	−46249.7	−1.46915	−0.734574	+	0.678528i	$0.762618\pi$
$998$	19038.5	0.603861
$999$	7067.97	0.223844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.n.1.6	✓	9
3.2	odd	2		1521.4.a.bj.1.4		9
13.5	odd	4		507.4.b.j.337.9		18
13.8	odd	4		507.4.b.j.337.10		18
13.12	even	2		507.4.a.q.1.4	yes	9
39.38	odd	2		1521.4.a.be.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.4.a.n.1.6	✓	9	1.1	even	1	trivial
507.4.a.q.1.4	yes	9	13.12	even	2
507.4.b.j.337.9		18	13.5	odd	4
507.4.b.j.337.10		18	13.8	odd	4
1521.4.a.be.1.6		9	39.38	odd	2
1521.4.a.bj.1.4		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} -17.8886 q^{5} -3.15386 q^{6} +30.1975 q^{7} -15.6587 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} -17.8886 q^{5} -3.15386 q^{6} +30.1975 q^{7} -15.6587 q^{8} +9.00000 q^{9} -18.8061 q^{10} +50.8457 q^{11} +20.6844 q^{12} +31.7462 q^{14} +53.6659 q^{15} +38.6966 q^{16} -2.99137 q^{17} +9.46157 q^{18} -72.7016 q^{19} +123.339 q^{20} -90.5926 q^{21} +53.4533 q^{22} -41.9071 q^{23} +46.9761 q^{24} +195.003 q^{25} -27.0000 q^{27} -208.206 q^{28} -135.233 q^{29} +56.4182 q^{30} +316.820 q^{31} +165.951 q^{32} -152.537 q^{33} -3.14479 q^{34} -540.192 q^{35} -62.0532 q^{36} -261.777 q^{37} -76.4301 q^{38} +280.113 q^{40} -198.911 q^{41} -95.2386 q^{42} -201.351 q^{43} -350.571 q^{44} -160.998 q^{45} -44.0563 q^{46} -97.3687 q^{47} -116.090 q^{48} +568.890 q^{49} +205.004 q^{50} +8.97412 q^{51} -150.458 q^{53} -28.3847 q^{54} -909.560 q^{55} -472.853 q^{56} +218.105 q^{57} -142.168 q^{58} -497.812 q^{59} -370.016 q^{60} +525.066 q^{61} +333.068 q^{62} +271.778 q^{63} -135.112 q^{64} -160.360 q^{66} -777.584 q^{67} +20.6249 q^{68} +125.721 q^{69} -567.896 q^{70} -1012.16 q^{71} -140.928 q^{72} -612.910 q^{73} -275.202 q^{74} -585.010 q^{75} +501.263 q^{76} +1535.41 q^{77} +718.804 q^{79} -692.230 q^{80} +81.0000 q^{81} -209.112 q^{82} -397.730 q^{83} +624.617 q^{84} +53.5116 q^{85} -211.677 q^{86} +405.699 q^{87} -796.176 q^{88} +648.413 q^{89} -169.255 q^{90} +288.941 q^{92} -950.460 q^{93} -102.362 q^{94} +1300.53 q^{95} -497.852 q^{96} -272.412 q^{97} +598.066 q^{98} +457.611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9	\( 9 q - 8 q^{2} - 27 q^{3} + 32 q^{4} - 41 q^{5} + 24 q^{6} - q^{7} - 111 q^{8} + 81 q^{9} + 198 q^{10} - 37 q^{11} - 96 q^{12} + 98 q^{14} + 123 q^{15} + 32 q^{16} - 134 q^{17} - 72 q^{18} + 72 q^{19} - 356 q^{20} + 3 q^{21} + 274 q^{22} + 226 q^{23} + 333 q^{24} + 612 q^{25} - 243 q^{27} - 132 q^{28} - 547 q^{29} - 594 q^{30} + 521 q^{31} - 721 q^{32} + 111 q^{33} + 100 q^{34} + 138 q^{35} + 288 q^{36} - 584 q^{37} - 416 q^{38} + 1342 q^{40} - 482 q^{41} - 294 q^{42} + 158 q^{43} - 1453 q^{44} - 369 q^{45} - 1537 q^{46} - 1500 q^{47} - 96 q^{48} + 642 q^{49} - 2777 q^{50} + 402 q^{51} + 1399 q^{53} + 216 q^{54} - 1408 q^{55} - 616 q^{56} - 216 q^{57} - 1455 q^{58} - 1541 q^{59} + 1068 q^{60} + 2092 q^{61} - 293 q^{62} - 9 q^{63} + 2481 q^{64} - 822 q^{66} - 252 q^{67} - 1579 q^{68} - 678 q^{69} - 2492 q^{70} - 2352 q^{71} - 999 q^{72} - 903 q^{73} + 1037 q^{74} - 1836 q^{75} + 485 q^{76} - 1686 q^{77} - 115 q^{79} - 5701 q^{80} + 729 q^{81} - 5147 q^{82} - 1207 q^{83} + 396 q^{84} - 4308 q^{85} - 5691 q^{86} + 1641 q^{87} - 484 q^{88} - 2336 q^{89} + 1782 q^{90} + 2087 q^{92} - 1563 q^{93} - 468 q^{94} - 222 q^{95} + 2163 q^{96} - 2155 q^{97} - 5593 q^{98} - 333 q^{99}+O(q^{100}) \) 9 * q - 8 * q^2 - 27 * q^3 + 32 * q^4 - 41 * q^5 + 24 * q^6 - q^7 - 111 * q^8 + 81 * q^9 + 198 * q^10 - 37 * q^11 - 96 * q^12 + 98 * q^14 + 123 * q^15 + 32 * q^16 - 134 * q^17 - 72 * q^18 + 72 * q^19 - 356 * q^20 + 3 * q^21 + 274 * q^22 + 226 * q^23 + 333 * q^24 + 612 * q^25 - 243 * q^27 - 132 * q^28 - 547 * q^29 - 594 * q^30 + 521 * q^31 - 721 * q^32 + 111 * q^33 + 100 * q^34 + 138 * q^35 + 288 * q^36 - 584 * q^37 - 416 * q^38 + 1342 * q^40 - 482 * q^41 - 294 * q^42 + 158 * q^43 - 1453 * q^44 - 369 * q^45 - 1537 * q^46 - 1500 * q^47 - 96 * q^48 + 642 * q^49 - 2777 * q^50 + 402 * q^51 + 1399 * q^53 + 216 * q^54 - 1408 * q^55 - 616 * q^56 - 216 * q^57 - 1455 * q^58 - 1541 * q^59 + 1068 * q^60 + 2092 * q^61 - 293 * q^62 - 9 * q^63 + 2481 * q^64 - 822 * q^66 - 252 * q^67 - 1579 * q^68 - 678 * q^69 - 2492 * q^70 - 2352 * q^71 - 999 * q^72 - 903 * q^73 + 1037 * q^74 - 1836 * q^75 + 485 * q^76 - 1686 * q^77 - 115 * q^79 - 5701 * q^80 + 729 * q^81 - 5147 * q^82 - 1207 * q^83 + 396 * q^84 - 4308 * q^85 - 5691 * q^86 + 1641 * q^87 - 484 * q^88 - 2336 * q^89 + 1782 * q^90 + 2087 * q^92 - 1563 * q^93 - 468 * q^94 - 222 * q^95 + 2163 * q^96 - 2155 * q^97 - 5593 * q^98 - 333 * q^99

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