LMFDB - Embedded newform 507.4.a.q.1.4

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			1.4
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	$-0.559502\pi$
$2$	−1.05129	−0.371686	−0.185843	+	0.982579i	$0.559502\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.89480	−0.861850
$5$	17.8886	1.60001	0.800004	−	0.599994i	$-0.204831\pi$
$5$	17.8886	1.60001	0.800004	+	0.599994i	$0.204831\pi$
$6$	3.15386	0.214593
$7$	−30.1975	−1.63051	−0.815256	−	0.579100i	$-0.803404\pi$
$7$	−30.1975	−1.63051	−0.815256	+	0.579100i	$0.803404\pi$
$8$	15.6587	0.692023
$9$	9.00000	0.333333
$10$	−18.8061	−0.594700
$11$	−50.8457	−1.39369	−0.696843	−	0.717224i	$-0.745413\pi$
$11$	−50.8457	−1.39369	−0.696843	+	0.717224i	$0.745413\pi$
$12$	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	$-0.355362\pi$
$19$	72.7016	0.877836	0.438918	+	0.898527i	$0.355362\pi$
$20$	−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	$-0.870023\pi$
$31$	−316.820	−1.83557	−0.917783	+	0.397082i	$0.870023\pi$
$32$	−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	$-0.302441\pi$
$37$	261.777	1.16313	0.581565	+	0.813500i	$0.302441\pi$
$38$	−76.4301	−0.326279
$39$	0	0
$40$	280.113	1.10724
$41$	198.911	0.757674	0.378837	−	0.925463i	$-0.376324\pi$
$41$	198.911	0.757674	0.378837	+	0.925463i	$0.376324\pi$
$42$	−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	$-0.451721\pi$
$47$	97.3687	0.302185	0.151092	+	0.988520i	$0.451721\pi$
$48$	−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	$-0.314919\pi$
$59$	497.812	1.09847	0.549234	+	0.835668i	$0.314919\pi$
$60$	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	$-0.249177\pi$
$67$	777.584	1.41787	0.708933	+	0.705276i	$0.249177\pi$
$68$	20.6249	0.0367814
$69$	125.721	0.219349
$70$	567.896	0.969666
$71$	1012.16	1.69185	0.845924	−	0.533303i	$-0.179049\pi$
$71$	1012.16	1.69185	0.845924	+	0.533303i	$0.179049\pi$
$72$	140.928	0.230674
$73$	612.910	0.982680	0.491340	−	0.870968i	$-0.336507\pi$
$73$	612.910	0.982680	0.491340	+	0.870968i	$0.336507\pi$
$74$	−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	$-0.415291\pi$
$83$	397.730	0.525982	0.262991	+	0.964798i	$0.415291\pi$
$84$	−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	$-0.626189\pi$
$89$	−648.413	−0.772265	−0.386133	+	0.922443i	$0.626189\pi$
$90$	−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	$-0.454462\pi$
$97$	272.412	0.285147	0.142574	+	0.989784i	$0.454462\pi$
$98$	−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	$-0.586316\pi$
$109$	−609.644	−0.535718	−0.267859	+	0.963458i	$0.586316\pi$
$110$	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	$-0.639932\pi$
$137$	−1364.89	−0.851170	−0.425585	+	0.904918i	$0.639932\pi$
$138$	−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	$-0.0878347\pi$
$149$	3499.94	1.92434	0.962169	+	0.272452i	$0.0878347\pi$
$150$	615.013	0.334770
$151$	672.434	0.362397	0.181198	−	0.983447i	$-0.442002\pi$
$151$	672.434	0.362397	0.181198	+	0.983447i	$0.442002\pi$
$152$	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	$-0.384589\pi$
$163$	1476.22	0.709366	0.354683	+	0.934987i	$0.384589\pi$
$164$	−1371.45	−0.653001
$165$	2728.68	1.28744
$166$	−418.127	−0.195500
$167$	3234.78	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$167$	3234.78	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$168$	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	$-0.294901\pi$
$193$	3221.08	1.20134	0.600670	+	0.799497i	$0.294901\pi$
$194$	−286.383	−0.105985
$195$	0	0
$196$	−3922.38	−1.42944
$197$	3068.80	1.10986	0.554931	−	0.831897i	$-0.312745\pi$
$197$	3068.80	1.10986	0.554931	+	0.831897i	$0.312745\pi$
$198$	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	$-0.654080\pi$
$223$	−3099.47	−0.930745	−0.465372	+	0.885115i	$0.654080\pi$
$224$	5011.30	1.49478
$225$	1755.03	0.520009
$226$	351.126	0.103347
$227$	−258.860	−0.0756879	−0.0378440	−	0.999284i	$-0.512049\pi$
$227$	−258.860	−0.0756879	−0.0378440	+	0.999284i	$0.512049\pi$
$228$	1503.79	0.436802
$229$	−804.986	−0.232292	−0.116146	−	0.993232i	$-0.537054\pi$
$229$	−804.986	−0.232292	−0.116146	+	0.993232i	$0.537054\pi$
$230$	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	$-0.396746\pi$
$239$	2355.26	0.637445	0.318722	+	0.947848i	$0.396746\pi$
$240$	−2076.69	−0.558541
$241$	−2170.07	−0.580027	−0.290014	−	0.957023i	$-0.593660\pi$
$241$	−2170.07	−0.580027	−0.290014	+	0.957023i	$0.593660\pi$
$242$	−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	$-0.444249\pi$
$271$	1554.77	0.348508	0.174254	+	0.984701i	$0.444249\pi$
$272$	−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	$-0.679009\pi$
$281$	−5023.16	−1.06639	−0.533197	+	0.845991i	$0.679009\pi$
$282$	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	$-0.419935\pi$
$293$	2496.53	0.497778	0.248889	+	0.968532i	$0.419935\pi$
$294$	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	$-0.556955\pi$
$307$	−1914.68	−0.355950	−0.177975	+	0.984035i	$0.556955\pi$
$308$	−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	$-0.819506\pi$
$317$	−9521.41	−1.68699	−0.843495	+	0.537137i	$0.819506\pi$
$318$	−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	$-0.446973\pi$
$331$	1997.12	0.331637	0.165818	+	0.986156i	$0.446973\pi$
$332$	−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	$-0.773298\pi$
$349$	−9870.06	−1.51385	−0.756923	+	0.653504i	$0.773298\pi$
$350$	6190.62	0.945436
$351$	0	0
$352$	8437.87	1.27767
$353$	8962.46	1.35134	0.675671	−	0.737203i	$-0.263854\pi$
$353$	8962.46	1.35134	0.675671	+	0.737203i	$0.263854\pi$
$354$	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	$-0.264418\pi$
$359$	9174.16	1.34873	0.674365	+	0.738399i	$0.264418\pi$
$360$	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	$-0.593281\pi$
$379$	−4262.83	−0.577748	−0.288874	+	0.957367i	$0.593281\pi$
$380$	−8966.91	−1.21051
$381$	3331.33	0.447950
$382$	4285.68	0.574017
$383$	901.981	0.120337	0.0601685	−	0.998188i	$-0.480836\pi$
$383$	901.981	0.120337	0.0601685	+	0.998188i	$0.480836\pi$
$384$	−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	$-0.552299\pi$
$397$	−2587.62	−0.327126	−0.163563	+	0.986533i	$0.552299\pi$
$398$	−4196.79	−0.528558
$399$	6586.22	0.826374
$400$	7545.98	0.943247
$401$	−422.775	−0.0526494	−0.0263247	−	0.999653i	$-0.508380\pi$
$401$	−422.775	−0.0526494	−0.0263247	+	0.999653i	$0.508380\pi$
$402$	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	$-0.441405\pi$
$409$	3028.09	0.366087	0.183044	+	0.983105i	$0.441405\pi$
$410$	−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	$-0.340723\pi$
$421$	8288.54	0.959521	0.479761	+	0.877399i	$0.340723\pi$
$422$	−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	$-0.430546\pi$
$431$	3873.84	0.432938	0.216469	+	0.976289i	$0.430546\pi$
$432$	−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	$-0.666917\pi$
$449$	−9527.11	−1.00136	−0.500682	+	0.865631i	$0.666917\pi$
$450$	−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	$-0.396824\pi$
$457$	6223.04	0.636983	0.318492	+	0.947926i	$0.396824\pi$
$458$	846.270	0.0863397
$459$	80.7671	0.00821325
$460$	5168.76	0.523901
$461$	17482.6	1.76626	0.883128	−	0.469132i	$-0.155433\pi$
$461$	17482.6	1.76626	0.883128	+	0.469132i	$0.155433\pi$
$462$	4842.47	0.487645
$463$	−3280.46	−0.329278	−0.164639	−	0.986354i	$-0.552646\pi$
$463$	−3280.46	−0.329278	−0.164639	+	0.986354i	$0.552646\pi$
$464$	−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	$-0.183065\pi$
$479$	17593.9	1.67826	0.839129	+	0.543933i	$0.183065\pi$
$480$	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	$-0.298112\pi$
$487$	12736.9	1.18515	0.592573	+	0.805517i	$0.298112\pi$
$488$	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	$-0.801800\pi$
$499$	−18109.7	−1.62466	−0.812328	+	0.583201i	$0.801800\pi$
$500$	−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	$-0.252268\pi$
$509$	16124.1	1.40410	0.702051	+	0.712126i	$0.252268\pi$
$510$	−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	$-0.654490\pi$
$541$	−11740.6	−0.933029	−0.466514	+	0.884514i	$0.654490\pi$
$542$	−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	$-0.592936\pi$
$557$	−7567.62	−0.575674	−0.287837	+	0.957679i	$0.592936\pi$
$558$	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	$-0.400069\pi$
$577$	8560.26	0.617623	0.308811	+	0.951123i	$0.400069\pi$
$578$	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	$-0.856549\pi$
$587$	−25603.9	−1.80032	−0.900158	+	0.435564i	$0.856549\pi$
$588$	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	$-0.308960\pi$
$593$	16311.5	1.12956	0.564782	+	0.825240i	$0.308960\pi$
$594$	−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	$-0.638367\pi$
$613$	−12783.2	−0.842265	−0.421132	+	0.906999i	$0.638367\pi$
$614$	2012.87	0.132301
$615$	−10674.7	−0.699913
$616$	24042.5	1.57257
$617$	−9767.34	−0.637307	−0.318653	−	0.947871i	$-0.603231\pi$
$617$	−9767.34	−0.637307	−0.318653	+	0.947871i	$0.603231\pi$
$618$	824.763	0.0536842
$619$	−24677.0	−1.60235	−0.801173	−	0.598433i	$-0.795790\pi$
$619$	−24677.0	−1.60235	−0.801173	+	0.598433i	$0.795790\pi$
$620$	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	$-0.753583\pi$
$631$	−22666.9	−1.43004	−0.715021	+	0.699103i	$0.753583\pi$
$632$	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	$-0.274453\pi$
$643$	21220.8	1.30151	0.650753	+	0.759289i	$0.274453\pi$
$644$	−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	$-0.221798\pi$
$661$	26065.8	1.53380	0.766901	+	0.641765i	$0.221798\pi$
$662$	−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	$-0.297299\pi$
$683$	21227.9	1.18926	0.594629	+	0.804000i	$0.297299\pi$
$684$	−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	$-0.398662\pi$
$691$	11371.3	0.626025	0.313012	+	0.949749i	$0.398662\pi$
$692$	−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	$-0.580339\pi$
$709$	−9428.79	−0.499444	−0.249722	+	0.968318i	$0.580339\pi$
$710$	−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	$-0.521632\pi$
$733$	−2695.20	−0.135811	−0.0679056	+	0.997692i	$0.521632\pi$
$734$	−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	$-0.515686\pi$
$739$	−1979.17	−0.0985181	−0.0492590	+	0.998786i	$0.515686\pi$
$740$	−32287.1	−1.60392
$741$	0	0
$742$	−4776.47	−0.236320
$743$	−19324.2	−0.954156	−0.477078	−	0.878861i	$-0.658304\pi$
$743$	−19324.2	−0.954156	−0.477078	+	0.878861i	$0.658304\pi$
$744$	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	$-0.316262\pi$
$761$	22912.0	1.09141	0.545704	+	0.837978i	$0.316262\pi$
$762$	−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	$-0.632244\pi$
$769$	−17213.9	−0.807215	−0.403607	+	0.914932i	$0.632244\pi$
$770$	−28875.1	−1.35141
$771$	−6830.08	−0.319039
$772$	−22208.7	−1.03537
$773$	−19732.2	−0.918136	−0.459068	−	0.888401i	$-0.651817\pi$
$773$	−19732.2	−0.918136	−0.459068	+	0.888401i	$0.651817\pi$
$774$	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	$-0.211389\pi$
$787$	34771.8	1.57494	0.787472	+	0.616350i	$0.211389\pi$
$788$	−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	$-0.560725\pi$
$811$	−8758.70	−0.379235	−0.189618	+	0.981858i	$0.560725\pi$
$812$	−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	$-0.571506\pi$
$821$	−10480.4	−0.445518	−0.222759	+	0.974874i	$0.571506\pi$
$822$	−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	$-0.428950\pi$
$827$	10529.0	0.442720	0.221360	+	0.975192i	$0.428950\pi$
$828$	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	$-0.814993\pi$
$839$	−40623.1	−1.67159	−0.835796	+	0.549041i	$0.814993\pi$
$840$	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	$-0.195676\pi$
$853$	40704.0	1.63385	0.816927	+	0.576742i	$0.195676\pi$
$854$	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	$-0.258545\pi$
$863$	34878.2	1.37575	0.687873	+	0.725831i	$0.258545\pi$
$864$	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	$-0.259432\pi$
$877$	35625.1	1.37169	0.685846	+	0.727747i	$0.259432\pi$
$878$	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	$-0.557267\pi$
$929$	−10133.6	−0.357881	−0.178940	+	0.983860i	$0.557267\pi$
$930$	−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	$-0.654903\pi$
$941$	−26998.8	−0.935321	−0.467660	+	0.883908i	$0.654903\pi$
$942$	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	$-0.409531\pi$
$947$	16343.4	0.560812	0.280406	+	0.959882i	$0.409531\pi$
$948$	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	$-0.252543\pi$
$967$	42185.0	1.40287	0.701436	+	0.712732i	$0.252543\pi$
$968$	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	$-0.664450\pi$
$977$	−30169.0	−0.987915	−0.493957	+	0.869486i	$0.664450\pi$
$978$	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	$-0.375859\pi$
$983$	23434.7	0.760378	0.380189	+	0.924909i	$0.375859\pi$
$984$	−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.q.1.4	yes	9
3.2	odd	2		1521.4.a.be.1.6		9
13.5	odd	4		507.4.b.j.337.10		18
13.8	odd	4		507.4.b.j.337.9		18
13.12	even	2		507.4.a.n.1.6	✓	9
39.38	odd	2		1521.4.a.bj.1.4		9

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

\(f(q)\)	\(=\)	\(q-1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} +17.8886 q^{5} +3.15386 q^{6} -30.1975 q^{7} +15.6587 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.05129 q^{2} -3.00000 q^{3} -6.89480 q^{4} +17.8886 q^{5} +3.15386 q^{6} -30.1975 q^{7} +15.6587 q^{8} +9.00000 q^{9} -18.8061 q^{10} -50.8457 q^{11} +20.6844 q^{12} +31.7462 q^{14} -53.6659 q^{15} +38.6966 q^{16} -2.99137 q^{17} -9.46157 q^{18} +72.7016 q^{19} -123.339 q^{20} +90.5926 q^{21} +53.4533 q^{22} -41.9071 q^{23} -46.9761 q^{24} +195.003 q^{25} -27.0000 q^{27} +208.206 q^{28} -135.233 q^{29} +56.4182 q^{30} -316.820 q^{31} -165.951 q^{32} +152.537 q^{33} +3.14479 q^{34} -540.192 q^{35} -62.0532 q^{36} +261.777 q^{37} -76.4301 q^{38} +280.113 q^{40} +198.911 q^{41} -95.2386 q^{42} -201.351 q^{43} +350.571 q^{44} +160.998 q^{45} +44.0563 q^{46} +97.3687 q^{47} -116.090 q^{48} +568.890 q^{49} -205.004 q^{50} +8.97412 q^{51} -150.458 q^{53} +28.3847 q^{54} -909.560 q^{55} -472.853 q^{56} -218.105 q^{57} +142.168 q^{58} +497.812 q^{59} +370.016 q^{60} +525.066 q^{61} +333.068 q^{62} -271.778 q^{63} -135.112 q^{64} -160.360 q^{66} +777.584 q^{67} +20.6249 q^{68} +125.721 q^{69} +567.896 q^{70} +1012.16 q^{71} +140.928 q^{72} +612.910 q^{73} -275.202 q^{74} -585.010 q^{75} -501.263 q^{76} +1535.41 q^{77} +718.804 q^{79} +692.230 q^{80} +81.0000 q^{81} -209.112 q^{82} +397.730 q^{83} -624.617 q^{84} -53.5116 q^{85} +211.677 q^{86} +405.699 q^{87} -796.176 q^{88} -648.413 q^{89} -169.255 q^{90} +288.941 q^{92} +950.460 q^{93} -102.362 q^{94} +1300.53 q^{95} +497.852 q^{96} +272.412 q^{97} -598.066 q^{98} -457.611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{2} - 27 q^{3} + 32 q^{4} + 41 q^{5} - 24 q^{6} + q^{7} + 111 q^{8} + 81 q^{9}+O(q^{10}) \) 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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