LMFDB - Embedded newform 490.4.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{177}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 44 $ x^2 - x - 44
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.15207$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -4.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} +8.30413 q^{6} -8.00000 q^{8} -9.76034 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -4.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} +8.30413 q^{6} -8.00000 q^{8} -9.76034 q^{9} -10.0000 q^{10} +30.7603 q^{11} -16.6083 q^{12} +27.5438 q^{13} -20.7603 q^{15} +16.0000 q^{16} -5.84793 q^{17} +19.5207 q^{18} -33.3917 q^{19} +20.0000 q^{20} -61.5207 q^{22} -71.0413 q^{23} +33.2165 q^{24} +25.0000 q^{25} -55.0876 q^{26} +152.631 q^{27} -59.8017 q^{29} +41.5207 q^{30} +48.3041 q^{31} -32.0000 q^{32} -127.719 q^{33} +11.6959 q^{34} -39.0413 q^{36} -266.562 q^{37} +66.7835 q^{38} -114.364 q^{39} -40.0000 q^{40} +437.779 q^{41} +25.5207 q^{43} +123.041 q^{44} -48.8017 q^{45} +142.083 q^{46} -494.622 q^{47} -66.4331 q^{48} -50.0000 q^{50} +24.2810 q^{51} +110.175 q^{52} -378.959 q^{53} -305.263 q^{54} +153.802 q^{55} +138.645 q^{57} +119.603 q^{58} +619.474 q^{59} -83.0413 q^{60} +44.0364 q^{61} -96.6083 q^{62} +64.0000 q^{64} +137.719 q^{65} +255.438 q^{66} +358.479 q^{67} -23.3917 q^{68} +294.968 q^{69} +851.207 q^{71} +78.0827 q^{72} +800.119 q^{73} +533.124 q^{74} -103.802 q^{75} -133.567 q^{76} +228.727 q^{78} +578.364 q^{79} +80.0000 q^{80} -370.207 q^{81} -875.557 q^{82} +1094.91 q^{83} -29.2397 q^{85} -51.0413 q^{86} +248.301 q^{87} -246.083 q^{88} +1344.33 q^{89} +97.6034 q^{90} -284.165 q^{92} -200.562 q^{93} +989.243 q^{94} -166.959 q^{95} +132.866 q^{96} +902.926 q^{97} -300.231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9} - 20 q^{10} - 5 q^{11} + 20 q^{12} + 95 q^{13} + 25 q^{15} + 32 q^{16} - 25 q^{17} - 94 q^{18} - 120 q^{19} + 40 q^{20} + 10 q^{22} + 124 q^{23} - 40 q^{24} + 50 q^{25} - 190 q^{26} + 425 q^{27} + 213 q^{29} - 50 q^{30} + 70 q^{31} - 64 q^{32} - 455 q^{33} + 50 q^{34} + 188 q^{36} - 134 q^{37} + 240 q^{38} + 503 q^{39} - 80 q^{40} + 370 q^{41} - 82 q^{43} - 20 q^{44} + 235 q^{45} - 248 q^{46} + 115 q^{47} + 80 q^{48} - 100 q^{50} - 151 q^{51} + 380 q^{52} - 1024 q^{53} - 850 q^{54} - 25 q^{55} - 654 q^{57} - 426 q^{58} + 760 q^{59} + 100 q^{60} - 790 q^{61} - 140 q^{62} + 128 q^{64} + 475 q^{65} + 910 q^{66} + 850 q^{67} - 100 q^{68} + 2080 q^{69} + 372 q^{71} - 376 q^{72} + 190 q^{73} + 268 q^{74} + 125 q^{75} - 480 q^{76} - 1006 q^{78} + 425 q^{79} + 160 q^{80} + 590 q^{81} - 740 q^{82} + 2110 q^{83} - 125 q^{85} + 164 q^{86} + 2745 q^{87} + 40 q^{88} + 560 q^{89} - 470 q^{90} + 496 q^{92} - 2 q^{93} - 230 q^{94} - 600 q^{95} - 160 q^{96} + 675 q^{97} - 2330 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9 - 20 * q^10 - 5 * q^11 + 20 * q^12 + 95 * q^13 + 25 * q^15 + 32 * q^16 - 25 * q^17 - 94 * q^18 - 120 * q^19 + 40 * q^20 + 10 * q^22 + 124 * q^23 - 40 * q^24 + 50 * q^25 - 190 * q^26 + 425 * q^27 + 213 * q^29 - 50 * q^30 + 70 * q^31 - 64 * q^32 - 455 * q^33 + 50 * q^34 + 188 * q^36 - 134 * q^37 + 240 * q^38 + 503 * q^39 - 80 * q^40 + 370 * q^41 - 82 * q^43 - 20 * q^44 + 235 * q^45 - 248 * q^46 + 115 * q^47 + 80 * q^48 - 100 * q^50 - 151 * q^51 + 380 * q^52 - 1024 * q^53 - 850 * q^54 - 25 * q^55 - 654 * q^57 - 426 * q^58 + 760 * q^59 + 100 * q^60 - 790 * q^61 - 140 * q^62 + 128 * q^64 + 475 * q^65 + 910 * q^66 + 850 * q^67 - 100 * q^68 + 2080 * q^69 + 372 * q^71 - 376 * q^72 + 190 * q^73 + 268 * q^74 + 125 * q^75 - 480 * q^76 - 1006 * q^78 + 425 * q^79 + 160 * q^80 + 590 * q^81 - 740 * q^82 + 2110 * q^83 - 125 * q^85 + 164 * q^86 + 2745 * q^87 + 40 * q^88 + 560 * q^89 - 470 * q^90 + 496 * q^92 - 2 * q^93 - 230 * q^94 - 600 * q^95 - 160 * q^96 + 675 * q^97 - 2330 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−4.15207	−0.799066	−0.399533	−	0.916719i	$-0.630828\pi$
$3$	−4.15207	−0.799066	−0.399533	+	0.916719i	$0.630828\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	8.30413	0.565025
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	−9.76034	−0.361494
$10$	−10.0000	−0.316228
$11$	30.7603	0.843145	0.421572	−	0.906795i	$-0.361478\pi$
$11$	30.7603	0.843145	0.421572	+	0.906795i	$0.361478\pi$
$12$	−16.6083	−0.399533
$13$	27.5438	0.587637	0.293818	−	0.955861i	$-0.405074\pi$
$13$	27.5438	0.587637	0.293818	+	0.955861i	$0.405074\pi$
$14$	0	0
$15$	−20.7603	−0.357353
$16$	16.0000	0.250000
$17$	−5.84793	−0.0834313	−0.0417156	−	0.999130i	$-0.513282\pi$
$17$	−5.84793	−0.0834313	−0.0417156	+	0.999130i	$0.513282\pi$
$18$	19.5207	0.255615
$19$	−33.3917	−0.403189	−0.201594	−	0.979469i	$-0.564612\pi$
$19$	−33.3917	−0.403189	−0.201594	+	0.979469i	$0.564612\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−61.5207	−0.596193
$23$	−71.0413	−0.644050	−0.322025	−	0.946731i	$-0.604363\pi$
$23$	−71.0413	−0.644050	−0.322025	+	0.946731i	$0.604363\pi$
$24$	33.2165	0.282512
$25$	25.0000	0.200000
$26$	−55.0876	−0.415522
$27$	152.631	1.08792
$28$	0	0
$29$	−59.8017	−0.382927	−0.191464	−	0.981500i	$-0.561323\pi$
$29$	−59.8017	−0.382927	−0.191464	+	0.981500i	$0.561323\pi$
$30$	41.5207	0.252687
$31$	48.3041	0.279861	0.139930	−	0.990161i	$-0.455312\pi$
$31$	48.3041	0.279861	0.139930	+	0.990161i	$0.455312\pi$
$32$	−32.0000	−0.176777
$33$	−127.719	−0.673728
$34$	11.6959	0.0589948
$35$	0	0
$36$	−39.0413	−0.180747
$37$	−266.562	−1.18439	−0.592196	−	0.805794i	$-0.701739\pi$
$37$	−266.562	−1.18439	−0.592196	+	0.805794i	$0.701739\pi$
$38$	66.7835	0.285098
$39$	−114.364	−0.469560
$40$	−40.0000	−0.158114
$41$	437.779	1.66755	0.833775	−	0.552105i	$-0.186175\pi$
$41$	437.779	1.66755	0.833775	+	0.552105i	$0.186175\pi$
$42$	0	0
$43$	25.5207	0.0905085	0.0452543	−	0.998976i	$-0.485590\pi$
$43$	25.5207	0.0905085	0.0452543	+	0.998976i	$0.485590\pi$
$44$	123.041	0.421572
$45$	−48.8017	−0.161665
$46$	142.083	0.455412
$47$	−494.622	−1.53506	−0.767532	−	0.641011i	$-0.778515\pi$
$47$	−494.622	−1.53506	−0.767532	+	0.641011i	$0.778515\pi$
$48$	−66.4331	−0.199766
$49$	0	0
$50$	−50.0000	−0.141421
$51$	24.2810	0.0666671
$52$	110.175	0.293818
$53$	−378.959	−0.982150	−0.491075	−	0.871117i	$-0.663396\pi$
$53$	−378.959	−0.982150	−0.491075	+	0.871117i	$0.663396\pi$
$54$	−305.263	−0.769278
$55$	153.802	0.377066
$56$	0	0
$57$	138.645	0.322174
$58$	119.603	0.270771
$59$	619.474	1.36693	0.683464	−	0.729985i	$-0.260473\pi$
$59$	619.474	1.36693	0.683464	+	0.729985i	$0.260473\pi$
$60$	−83.0413	−0.178677
$61$	44.0364	0.0924310	0.0462155	−	0.998931i	$-0.485284\pi$
$61$	44.0364	0.0924310	0.0462155	+	0.998931i	$0.485284\pi$
$62$	−96.6083	−0.197891
$63$	0	0
$64$	64.0000	0.125000
$65$	137.719	0.262799
$66$	255.438	0.476398
$67$	358.479	0.653660	0.326830	−	0.945083i	$-0.394020\pi$
$67$	358.479	0.653660	0.326830	+	0.945083i	$0.394020\pi$
$68$	−23.3917	−0.0417156
$69$	294.968	0.514638
$70$	0	0
$71$	851.207	1.42281	0.711406	−	0.702781i	$-0.248059\pi$
$71$	851.207	1.42281	0.711406	+	0.702781i	$0.248059\pi$
$72$	78.0827	0.127807
$73$	800.119	1.28283	0.641417	−	0.767193i	$-0.278347\pi$
$73$	800.119	1.28283	0.641417	+	0.767193i	$0.278347\pi$
$74$	533.124	0.837492
$75$	−103.802	−0.159813
$76$	−133.567	−0.201594
$77$	0	0
$78$	228.727	0.332029
$79$	578.364	0.823684	0.411842	−	0.911255i	$-0.364886\pi$
$79$	578.364	0.823684	0.411842	+	0.911255i	$0.364886\pi$
$80$	80.0000	0.111803
$81$	−370.207	−0.507828
$82$	−875.557	−1.17914
$83$	1094.91	1.44798	0.723989	−	0.689811i	$-0.242306\pi$
$83$	1094.91	1.44798	0.723989	+	0.689811i	$0.242306\pi$
$84$	0	0
$85$	−29.2397	−0.0373116
$86$	−51.0413	−0.0639992
$87$	248.301	0.305984
$88$	−246.083	−0.298097
$89$	1344.33	1.60111	0.800555	−	0.599259i	$-0.204538\pi$
$89$	1344.33	1.60111	0.800555	+	0.599259i	$0.204538\pi$
$90$	97.6034	0.114314
$91$	0	0
$92$	−284.165	−0.322025
$93$	−200.562	−0.223627
$94$	989.243	1.08545
$95$	−166.959	−0.180312
$96$	132.866	0.141256
$97$	902.926	0.945136	0.472568	−	0.881294i	$-0.343327\pi$
$97$	902.926	0.945136	0.472568	+	0.881294i	$0.343327\pi$
$98$	0	0
$99$	−300.231	−0.304792
$100$	100.000	0.100000
$101$	596.783	0.587942	0.293971	−	0.955814i	$-0.405023\pi$
$101$	596.783	0.587942	0.293971	+	0.955814i	$0.405023\pi$
$102$	−48.5620	−0.0471408
$103$	850.410	0.813528	0.406764	−	0.913533i	$-0.366657\pi$
$103$	850.410	0.813528	0.406764	+	0.913533i	$0.366657\pi$
$104$	−220.350	−0.207761
$105$	0	0
$106$	757.917	0.694485
$107$	305.851	0.276334	0.138167	−	0.990409i	$-0.455879\pi$
$107$	305.851	0.276334	0.138167	+	0.990409i	$0.455879\pi$
$108$	610.526	0.543962
$109$	951.008	0.835689	0.417844	−	0.908519i	$-0.362786\pi$
$109$	951.008	0.835689	0.417844	+	0.908519i	$0.362786\pi$
$110$	−307.603	−0.266626
$111$	1106.78	0.946408
$112$	0	0
$113$	−1821.14	−1.51609	−0.758047	−	0.652200i	$-0.773846\pi$
$113$	−1821.14	−1.51609	−0.758047	+	0.652200i	$0.773846\pi$
$114$	−277.289	−0.227812
$115$	−355.207	−0.288028
$116$	−239.207	−0.191464
$117$	−268.837	−0.212427
$118$	−1238.95	−0.966563
$119$	0	0
$120$	166.083	0.126343
$121$	−384.802	−0.289107
$122$	−88.0729	−0.0653586
$123$	−1817.69	−1.33248
$124$	193.217	0.139930
$125$	125.000	0.0894427
$126$	0	0
$127$	−934.810	−0.653157	−0.326579	−	0.945170i	$-0.605896\pi$
$127$	−934.810	−0.653157	−0.326579	+	0.945170i	$0.605896\pi$
$128$	−128.000	−0.0883883
$129$	−105.964	−0.0723223
$130$	−275.438	−0.185827
$131$	1249.18	0.833140	0.416570	−	0.909104i	$-0.363232\pi$
$131$	1249.18	0.833140	0.416570	+	0.909104i	$0.363232\pi$
$132$	−510.876	−0.336864
$133$	0	0
$134$	−716.959	−0.462207
$135$	763.157	0.486534
$136$	46.7835	0.0294974
$137$	1745.93	1.08880	0.544399	−	0.838827i	$-0.316758\pi$
$137$	1745.93	1.08880	0.544399	+	0.838827i	$0.316758\pi$
$138$	−589.937	−0.363904
$139$	−765.676	−0.467222	−0.233611	−	0.972330i	$-0.575054\pi$
$139$	−765.676	−0.467222	−0.233611	+	0.972330i	$0.575054\pi$
$140$	0	0
$141$	2053.70	1.22662
$142$	−1702.41	−1.00608
$143$	847.257	0.495463
$144$	−156.165	−0.0903735
$145$	−299.008	−0.171250
$146$	−1600.24	−0.907100
$147$	0	0
$148$	−1066.25	−0.592196
$149$	−1727.29	−0.949698	−0.474849	−	0.880067i	$-0.657497\pi$
$149$	−1727.29	−0.949698	−0.474849	+	0.880067i	$0.657497\pi$
$150$	207.603	0.113005
$151$	1811.65	0.976359	0.488180	−	0.872743i	$-0.337661\pi$
$151$	1811.65	0.976359	0.488180	+	0.872743i	$0.337661\pi$
$152$	267.134	0.142549
$153$	57.0778	0.0301599
$154$	0	0
$155$	241.521	0.125157
$156$	−457.455	−0.234780
$157$	−3370.59	−1.71339	−0.856695	−	0.515823i	$-0.827486\pi$
$157$	−3370.59	−1.71339	−0.856695	+	0.515823i	$0.827486\pi$
$158$	−1156.73	−0.582432
$159$	1573.46	0.784803
$160$	−160.000	−0.0790569
$161$	0	0
$162$	740.413	0.359089
$163$	499.207	0.239883	0.119941	−	0.992781i	$-0.461729\pi$
$163$	499.207	0.239883	0.119941	+	0.992781i	$0.461729\pi$
$164$	1751.11	0.833775
$165$	−638.595	−0.301300
$166$	−2189.82	−1.02388
$167$	2568.55	1.19018	0.595090	−	0.803659i	$-0.297116\pi$
$167$	2568.55	1.19018	0.595090	+	0.803659i	$0.297116\pi$
$168$	0	0
$169$	−1438.34	−0.654683
$170$	58.4793	0.0263833
$171$	325.915	0.145750
$172$	102.083	0.0452543
$173$	1754.80	0.771183	0.385592	−	0.922670i	$-0.373997\pi$
$173$	1754.80	0.771183	0.385592	+	0.922670i	$0.373997\pi$
$174$	−496.601	−0.216363
$175$	0	0
$176$	492.165	0.210786
$177$	−2572.10	−1.09226
$178$	−2688.66	−1.13216
$179$	1374.58	0.573971	0.286986	−	0.957935i	$-0.407347\pi$
$179$	1374.58	0.573971	0.286986	+	0.957935i	$0.407347\pi$
$180$	−195.207	−0.0808325
$181$	−2412.69	−0.990795	−0.495398	−	0.868666i	$-0.664978\pi$
$181$	−2412.69	−0.990795	−0.495398	+	0.868666i	$0.664978\pi$
$182$	0	0
$183$	−182.842	−0.0738584
$184$	568.331	0.227706
$185$	−1332.81	−0.529676
$186$	401.124	0.158128
$187$	−179.884	−0.0703446
$188$	−1978.49	−0.767532
$189$	0	0
$190$	333.917	0.127500
$191$	4838.63	1.83304	0.916521	−	0.399987i	$-0.130986\pi$
$191$	4838.63	1.83304	0.916521	+	0.399987i	$0.130986\pi$
$192$	−265.732	−0.0998832
$193$	−156.942	−0.0585333	−0.0292666	−	0.999572i	$-0.509317\pi$
$193$	−156.942	−0.0585333	−0.0292666	+	0.999572i	$0.509317\pi$
$194$	−1805.85	−0.668312
$195$	−571.819	−0.209994
$196$	0	0
$197$	−2862.00	−1.03507	−0.517536	−	0.855662i	$-0.673151\pi$
$197$	−2862.00	−1.03507	−0.517536	+	0.855662i	$0.673151\pi$
$198$	600.462	0.215520
$199$	−4423.75	−1.57584	−0.787918	−	0.615781i	$-0.788841\pi$
$199$	−4423.75	−1.57584	−0.787918	+	0.615781i	$0.788841\pi$
$200$	−200.000	−0.0707107
$201$	−1488.43	−0.522317
$202$	−1193.57	−0.415738
$203$	0	0
$204$	97.1240	0.0333335
$205$	2188.89	0.745751
$206$	−1700.82	−0.575251
$207$	693.387	0.232820
$208$	440.701	0.146909
$209$	−1027.14	−0.339947
$210$	0	0
$211$	6021.74	1.96471	0.982354	−	0.187031i	$-0.0598865\pi$
$211$	6021.74	1.96471	0.982354	+	0.187031i	$0.0598865\pi$
$212$	−1515.83	−0.491075
$213$	−3534.27	−1.13692
$214$	−611.703	−0.195398
$215$	127.603	0.0404766
$216$	−1221.05	−0.384639
$217$	0	0
$218$	−1902.02	−0.590921
$219$	−3322.15	−1.02507
$220$	615.207	0.188533
$221$	−161.074	−0.0490273
$222$	−2213.57	−0.669211
$223$	−221.279	−0.0664481	−0.0332241	−	0.999448i	$-0.510577\pi$
$223$	−221.279	−0.0664481	−0.0332241	+	0.999448i	$0.510577\pi$
$224$	0	0
$225$	−244.008	−0.0722988
$226$	3642.28	1.07204
$227$	−1879.36	−0.549504	−0.274752	−	0.961515i	$-0.588596\pi$
$227$	−1879.36	−0.549504	−0.274752	+	0.961515i	$0.588596\pi$
$228$	554.579	0.161087
$229$	1936.08	0.558690	0.279345	−	0.960191i	$-0.409883\pi$
$229$	1936.08	0.558690	0.279345	+	0.960191i	$0.409883\pi$
$230$	710.413	0.203666
$231$	0	0
$232$	478.413	0.135385
$233$	2331.06	0.655419	0.327710	−	0.944778i	$-0.393723\pi$
$233$	2331.06	0.655419	0.327710	+	0.944778i	$0.393723\pi$
$234$	537.673	0.150209
$235$	−2473.11	−0.686501
$236$	2477.90	0.683464
$237$	−2401.41	−0.658177
$238$	0	0
$239$	3040.15	0.822807	0.411404	−	0.911453i	$-0.365039\pi$
$239$	3040.15	0.822807	0.411404	+	0.911453i	$0.365039\pi$
$240$	−332.165	−0.0893383
$241$	−5386.78	−1.43981	−0.719903	−	0.694075i	$-0.755814\pi$
$241$	−5386.78	−1.43981	−0.719903	+	0.694075i	$0.755814\pi$
$242$	769.603	0.204430
$243$	−2583.92	−0.682135
$244$	176.146	0.0462155
$245$	0	0
$246$	3635.37	0.942207
$247$	−919.735	−0.236929
$248$	−386.433	−0.0989457
$249$	−4546.15	−1.15703
$250$	−250.000	−0.0632456
$251$	2751.98	0.692046	0.346023	−	0.938226i	$-0.387532\pi$
$251$	2751.98	0.692046	0.346023	+	0.938226i	$0.387532\pi$
$252$	0	0
$253$	−2185.26	−0.543027
$254$	1869.62	0.461852
$255$	121.405	0.0298144
$256$	256.000	0.0625000
$257$	5135.80	1.24655	0.623273	−	0.782004i	$-0.285802\pi$
$257$	5135.80	1.24655	0.623273	+	0.782004i	$0.285802\pi$
$258$	211.927	0.0511396
$259$	0	0
$260$	550.876	0.131400
$261$	583.685	0.138426
$262$	−2498.36	−0.589119
$263$	−3811.93	−0.893741	−0.446871	−	0.894599i	$-0.647462\pi$
$263$	−3811.93	−0.893741	−0.446871	+	0.894599i	$0.647462\pi$
$264$	1021.75	0.238199
$265$	−1894.79	−0.439231
$266$	0	0
$267$	−5581.75	−1.27939
$268$	1433.92	0.326830
$269$	−6682.65	−1.51468	−0.757339	−	0.653022i	$-0.773501\pi$
$269$	−6682.65	−1.51468	−0.757339	+	0.653022i	$0.773501\pi$
$270$	−1526.31	−0.344032
$271$	1151.35	0.258080	0.129040	−	0.991639i	$-0.458810\pi$
$271$	1151.35	0.258080	0.129040	+	0.991639i	$0.458810\pi$
$272$	−93.5669	−0.0208578
$273$	0	0
$274$	−3491.87	−0.769896
$275$	769.008	0.168629
$276$	1179.87	0.257319
$277$	5916.22	1.28329	0.641644	−	0.767002i	$-0.278253\pi$
$277$	5916.22	1.28329	0.641644	+	0.767002i	$0.278253\pi$
$278$	1531.35	0.330376
$279$	−471.465	−0.101168
$280$	0	0
$281$	7433.32	1.57806	0.789030	−	0.614355i	$-0.210584\pi$
$281$	7433.32	1.57806	0.789030	+	0.614355i	$0.210584\pi$
$282$	−4107.40	−0.867349
$283$	3643.23	0.765256	0.382628	−	0.923903i	$-0.375019\pi$
$283$	3643.23	0.765256	0.382628	+	0.923903i	$0.375019\pi$
$284$	3404.83	0.711406
$285$	693.224	0.144081
$286$	−1694.51	−0.350345
$287$	0	0
$288$	312.331	0.0639037
$289$	−4878.80	−0.993039
$290$	598.017	0.121092
$291$	−3749.01	−0.755226
$292$	3200.48	0.641417
$293$	2863.46	0.570939	0.285469	−	0.958388i	$-0.407851\pi$
$293$	2863.46	0.570939	0.285469	+	0.958388i	$0.407851\pi$
$294$	0	0
$295$	3097.37	0.611308
$296$	2132.50	0.418746
$297$	4694.99	0.917277
$298$	3454.58	0.671538
$299$	−1956.75	−0.378467
$300$	−415.207	−0.0799066
$301$	0	0
$302$	−3623.31	−0.690390
$303$	−2477.89	−0.469805
$304$	−534.268	−0.100797
$305$	220.182	0.0413364
$306$	−114.156	−0.0213263
$307$	−5534.57	−1.02891	−0.514454	−	0.857518i	$-0.672005\pi$
$307$	−5534.57	−1.02891	−0.514454	+	0.857518i	$0.672005\pi$
$308$	0	0
$309$	−3530.96	−0.650062
$310$	−483.041	−0.0884997
$311$	4416.84	0.805325	0.402662	−	0.915349i	$-0.368085\pi$
$311$	4416.84	0.805325	0.402662	+	0.915349i	$0.368085\pi$
$312$	914.910	0.166015
$313$	−538.259	−0.0972018	−0.0486009	−	0.998818i	$-0.515476\pi$
$313$	−538.259	−0.0972018	−0.0486009	+	0.998818i	$0.515476\pi$
$314$	6741.18	1.21155
$315$	0	0
$316$	2313.45	0.411842
$317$	−4113.57	−0.728837	−0.364418	−	0.931235i	$-0.618732\pi$
$317$	−4113.57	−0.728837	−0.364418	+	0.931235i	$0.618732\pi$
$318$	−3146.92	−0.554939
$319$	−1839.52	−0.322863
$320$	320.000	0.0559017
$321$	−1269.92	−0.220809
$322$	0	0
$323$	195.273	0.0336386
$324$	−1480.83	−0.253914
$325$	688.595	0.117527
$326$	−998.413	−0.169623
$327$	−3948.65	−0.667770
$328$	−3502.23	−0.589568
$329$	0	0
$330$	1277.19	0.213051
$331$	2729.42	0.453240	0.226620	−	0.973983i	$-0.427232\pi$
$331$	2729.42	0.453240	0.226620	+	0.973983i	$0.427232\pi$
$332$	4379.65	0.723989
$333$	2601.74	0.428151
$334$	−5137.09	−0.841584
$335$	1792.40	0.292326
$336$	0	0
$337$	−10463.2	−1.69130	−0.845650	−	0.533738i	$-0.820787\pi$
$337$	−10463.2	−1.69130	−0.845650	+	0.533738i	$0.820787\pi$
$338$	2876.68	0.462931
$339$	7561.50	1.21146
$340$	−116.959	−0.0186558
$341$	1485.85	0.235963
$342$	−651.829	−0.103061
$343$	0	0
$344$	−204.165	−0.0319996
$345$	1474.84	0.230153
$346$	−3509.59	−0.545309
$347$	9776.50	1.51248	0.756239	−	0.654296i	$-0.227035\pi$
$347$	9776.50	1.51248	0.756239	+	0.654296i	$0.227035\pi$
$348$	993.202	0.152992
$349$	−9228.60	−1.41546	−0.707730	−	0.706483i	$-0.750281\pi$
$349$	−9228.60	−1.41546	−0.707730	+	0.706483i	$0.750281\pi$
$350$	0	0
$351$	4204.05	0.639303
$352$	−984.331	−0.149048
$353$	1749.13	0.263731	0.131865	−	0.991268i	$-0.457903\pi$
$353$	1749.13	0.263731	0.131865	+	0.991268i	$0.457903\pi$
$354$	5144.20	0.772348
$355$	4256.03	0.636301
$356$	5377.32	0.800555
$357$	0	0
$358$	−2749.16	−0.405859
$359$	−7715.57	−1.13430	−0.567148	−	0.823616i	$-0.691953\pi$
$359$	−7715.57	−1.13430	−0.567148	+	0.823616i	$0.691953\pi$
$360$	390.413	0.0571572
$361$	−5743.99	−0.837439
$362$	4825.38	0.700598
$363$	1597.72	0.231016
$364$	0	0
$365$	4000.60	0.573701
$366$	365.685	0.0522258
$367$	12115.1	1.72317	0.861585	−	0.507613i	$-0.169472\pi$
$367$	12115.1	1.72317	0.861585	+	0.507613i	$0.169472\pi$
$368$	−1136.66	−0.161012
$369$	−4272.87	−0.602809
$370$	2665.62	0.374538
$371$	0	0
$372$	−802.248	−0.111814
$373$	−1859.65	−0.258148	−0.129074	−	0.991635i	$-0.541200\pi$
$373$	−1859.65	−0.258148	−0.129074	+	0.991635i	$0.541200\pi$
$374$	359.769	0.0497412
$375$	−519.008	−0.0714706
$376$	3956.97	0.542727
$377$	−1647.17	−0.225022
$378$	0	0
$379$	−5734.05	−0.777146	−0.388573	−	0.921418i	$-0.627032\pi$
$379$	−5734.05	−0.777146	−0.388573	+	0.921418i	$0.627032\pi$
$380$	−667.835	−0.0901558
$381$	3881.39	0.521916
$382$	−9677.26	−1.29616
$383$	−6511.70	−0.868753	−0.434377	−	0.900731i	$-0.643031\pi$
$383$	−6511.70	−0.868753	−0.434377	+	0.900731i	$0.643031\pi$
$384$	531.465	0.0706281
$385$	0	0
$386$	313.884	0.0413893
$387$	−249.090	−0.0327183
$388$	3611.70	0.472568
$389$	2341.29	0.305162	0.152581	−	0.988291i	$-0.451241\pi$
$389$	2341.29	0.305162	0.152581	+	0.988291i	$0.451241\pi$
$390$	1143.64	0.148488
$391$	415.445	0.0537339
$392$	0	0
$393$	−5186.68	−0.665734
$394$	5724.00	0.731906
$395$	2891.82	0.368362
$396$	−1200.92	−0.152396
$397$	5258.22	0.664741	0.332371	−	0.943149i	$-0.392151\pi$
$397$	5258.22	0.664741	0.332371	+	0.943149i	$0.392151\pi$
$398$	8847.50	1.11428
$399$	0	0
$400$	400.000	0.0500000
$401$	15091.6	1.87939	0.939697	−	0.342008i	$-0.111107\pi$
$401$	15091.6	1.87939	0.939697	+	0.342008i	$0.111107\pi$
$402$	2976.86	0.369334
$403$	1330.48	0.164456
$404$	2387.13	0.293971
$405$	−1851.03	−0.227108
$406$	0	0
$407$	−8199.54	−0.998614
$408$	−194.248	−0.0235704
$409$	−129.019	−0.0155980	−0.00779899	−	0.999970i	$-0.502483\pi$
$409$	−129.019	−0.0155980	−0.00779899	+	0.999970i	$0.502483\pi$
$410$	−4377.79	−0.527325
$411$	−7249.24	−0.870021
$412$	3401.64	0.406764
$413$	0	0
$414$	−1386.77	−0.164629
$415$	5474.56	0.647556
$416$	−881.402	−0.103880
$417$	3179.14	0.373341
$418$	2054.28	0.240378
$419$	13177.3	1.53640	0.768200	−	0.640210i	$-0.221153\pi$
$419$	13177.3	1.53640	0.768200	+	0.640210i	$0.221153\pi$
$420$	0	0
$421$	12260.2	1.41930	0.709650	−	0.704554i	$-0.248853\pi$
$421$	12260.2	1.41930	0.709650	+	0.704554i	$0.248853\pi$
$422$	−12043.5	−1.38926
$423$	4827.67	0.554916
$424$	3031.67	0.347243
$425$	−146.198	−0.0166863
$426$	7068.54	0.803924
$427$	0	0
$428$	1223.41	0.138167
$429$	−3517.87	−0.395907
$430$	−255.207	−0.0286213
$431$	−7530.20	−0.841571	−0.420785	−	0.907160i	$-0.638245\pi$
$431$	−7530.20	−0.841571	−0.420785	+	0.907160i	$0.638245\pi$
$432$	2442.10	0.271981
$433$	−8716.73	−0.967435	−0.483717	−	0.875224i	$-0.660714\pi$
$433$	−8716.73	−0.967435	−0.483717	+	0.875224i	$0.660714\pi$
$434$	0	0
$435$	1241.50	0.136840
$436$	3804.03	0.417844
$437$	2372.19	0.259674
$438$	6644.30	0.724833
$439$	−15682.4	−1.70496	−0.852481	−	0.522758i	$-0.824903\pi$
$439$	−15682.4	−1.70496	−0.852481	+	0.522758i	$0.824903\pi$
$440$	−1230.41	−0.133313
$441$	0	0
$442$	322.149	0.0346675
$443$	−8720.40	−0.935256	−0.467628	−	0.883925i	$-0.654891\pi$
$443$	−8720.40	−0.935256	−0.467628	+	0.883925i	$0.654891\pi$
$444$	4427.13	0.473204
$445$	6721.65	0.716038
$446$	442.558	0.0469859
$447$	7171.82	0.758871
$448$	0	0
$449$	2140.07	0.224935	0.112468	−	0.993655i	$-0.464125\pi$
$449$	2140.07	0.224935	0.112468	+	0.993655i	$0.464125\pi$
$450$	488.017	0.0511230
$451$	13466.2	1.40599
$452$	−7284.56	−0.758047
$453$	−7522.11	−0.780175
$454$	3758.72	0.388558
$455$	0	0
$456$	−1109.16	−0.113906
$457$	5191.79	0.531426	0.265713	−	0.964052i	$-0.414393\pi$
$457$	5191.79	0.531426	0.265713	+	0.964052i	$0.414393\pi$
$458$	−3872.17	−0.395053
$459$	−892.578	−0.0907668
$460$	−1420.83	−0.144014
$461$	8683.45	0.877285	0.438643	−	0.898662i	$-0.355459\pi$
$461$	8683.45	0.877285	0.438643	+	0.898662i	$0.355459\pi$
$462$	0	0
$463$	11705.0	1.17490	0.587448	−	0.809262i	$-0.300133\pi$
$463$	11705.0	1.17490	0.587448	+	0.809262i	$0.300133\pi$
$464$	−956.827	−0.0957318
$465$	−1002.81	−0.100009
$466$	−4662.12	−0.463451
$467$	−3787.90	−0.375339	−0.187669	−	0.982232i	$-0.560093\pi$
$467$	−3787.90	−0.375339	−0.187669	+	0.982232i	$0.560093\pi$
$468$	−1075.35	−0.106214
$469$	0	0
$470$	4946.22	0.485430
$471$	13994.9	1.36911
$472$	−4955.80	−0.483282
$473$	785.025	0.0763118
$474$	4802.81	0.465402
$475$	−834.793	−0.0806378
$476$	0	0
$477$	3698.76	0.355041
$478$	−6080.30	−0.581813
$479$	−114.043	−0.0108785	−0.00543923	−	0.999985i	$-0.501731\pi$
$479$	−114.043	−0.0108785	−0.00543923	+	0.999985i	$0.501731\pi$
$480$	664.331	0.0631717
$481$	−7342.13	−0.695992
$482$	10773.6	1.01810
$483$	0	0
$484$	−1539.21	−0.144554
$485$	4514.63	0.422678
$486$	5167.85	0.482342
$487$	2891.74	0.269070	0.134535	−	0.990909i	$-0.457046\pi$
$487$	2891.74	0.269070	0.134535	+	0.990909i	$0.457046\pi$
$488$	−352.292	−0.0326793
$489$	−2072.74	−0.191682
$490$	0	0
$491$	−226.858	−0.0208513	−0.0104256	−	0.999946i	$-0.503319\pi$
$491$	−226.858	−0.0208513	−0.0104256	+	0.999946i	$0.503319\pi$
$492$	−7270.74	−0.666241
$493$	349.716	0.0319481
$494$	1839.47	0.167534
$495$	−1501.16	−0.136307
$496$	772.866	0.0699652
$497$	0	0
$498$	9092.30	0.818144
$499$	−4995.69	−0.448172	−0.224086	−	0.974569i	$-0.571940\pi$
$499$	−4995.69	−0.448172	−0.224086	+	0.974569i	$0.571940\pi$
$500$	500.000	0.0447214
$501$	−10664.8	−0.951032
$502$	−5503.97	−0.489351
$503$	16990.9	1.50613	0.753067	−	0.657943i	$-0.228573\pi$
$503$	16990.9	1.50613	0.753067	+	0.657943i	$0.228573\pi$
$504$	0	0
$505$	2983.92	0.262936
$506$	4370.51	0.383978
$507$	5972.08	0.523135
$508$	−3739.24	−0.326579
$509$	1834.32	0.159735	0.0798674	−	0.996806i	$-0.474550\pi$
$509$	1834.32	0.159735	0.0798674	+	0.996806i	$0.474550\pi$
$510$	−242.810	−0.0210820
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−5096.63	−0.438639
$514$	−10271.6	−0.881442
$515$	4252.05	0.363821
$516$	−423.854	−0.0361611
$517$	−15214.7	−1.29428
$518$	0	0
$519$	−7286.03	−0.616226
$520$	−1101.75	−0.0929135
$521$	−18825.9	−1.58306	−0.791532	−	0.611127i	$-0.790716\pi$
$521$	−18825.9	−1.58306	−0.791532	+	0.611127i	$0.790716\pi$
$522$	−1167.37	−0.0978819
$523$	−2418.07	−0.202169	−0.101085	−	0.994878i	$-0.532231\pi$
$523$	−2418.07	−0.202169	−0.101085	+	0.994878i	$0.532231\pi$
$524$	4996.72	0.416570
$525$	0	0
$526$	7623.87	0.631970
$527$	−282.479	−0.0233491
$528$	−2043.50	−0.168432
$529$	−7120.13	−0.585200
$530$	3789.59	0.310583
$531$	−6046.28	−0.494136
$532$	0	0
$533$	12058.1	0.979913
$534$	11163.5	0.904667
$535$	1529.26	0.123580
$536$	−2867.83	−0.231104
$537$	−5707.34	−0.458641
$538$	13365.3	1.07104
$539$	0	0
$540$	3052.63	0.243267
$541$	1150.28	0.0914130	0.0457065	−	0.998955i	$-0.485446\pi$
$541$	1150.28	0.0914130	0.0457065	+	0.998955i	$0.485446\pi$
$542$	−2302.71	−0.182490
$543$	10017.7	0.791710
$544$	187.134	0.0147487
$545$	4755.04	0.373731
$546$	0	0
$547$	−22420.1	−1.75250	−0.876248	−	0.481860i	$-0.839961\pi$
$547$	−22420.1	−1.75250	−0.876248	+	0.481860i	$0.839961\pi$
$548$	6983.74	0.544399
$549$	−429.811	−0.0334132
$550$	−1538.02	−0.119239
$551$	1996.88	0.154392
$552$	−2359.75	−0.181952
$553$	0	0
$554$	−11832.4	−0.907422
$555$	5533.92	0.423246
$556$	−3062.71	−0.233611
$557$	7265.31	0.552677	0.276338	−	0.961060i	$-0.410879\pi$
$557$	7265.31	0.552677	0.276338	+	0.961060i	$0.410879\pi$
$558$	942.929	0.0715365
$559$	702.936	0.0531861
$560$	0	0
$561$	746.892	0.0562100
$562$	−14866.6	−1.11586
$563$	4126.64	0.308912	0.154456	−	0.988000i	$-0.450638\pi$
$563$	4126.64	0.308912	0.154456	+	0.988000i	$0.450638\pi$
$564$	8214.81	0.613308
$565$	−9105.70	−0.678017
$566$	−7286.45	−0.541118
$567$	0	0
$568$	−6809.65	−0.503040
$569$	1840.74	0.135620	0.0678102	−	0.997698i	$-0.478399\pi$
$569$	1840.74	0.135620	0.0678102	+	0.997698i	$0.478399\pi$
$570$	−1386.45	−0.101880
$571$	−2985.42	−0.218802	−0.109401	−	0.993998i	$-0.534893\pi$
$571$	−2985.42	−0.218802	−0.109401	+	0.993998i	$0.534893\pi$
$572$	3389.03	0.247731
$573$	−20090.3	−1.46472
$574$	0	0
$575$	−1776.03	−0.128810
$576$	−624.662	−0.0451867
$577$	−8718.99	−0.629075	−0.314537	−	0.949245i	$-0.601849\pi$
$577$	−8718.99	−0.629075	−0.314537	+	0.949245i	$0.601849\pi$
$578$	9757.60	0.702185
$579$	651.633	0.0467719
$580$	−1196.03	−0.0856252
$581$	0	0
$582$	7498.02	0.534025
$583$	−11656.9	−0.828095
$584$	−6400.95	−0.453550
$585$	−1344.18	−0.0950003
$586$	−5726.92	−0.403715
$587$	18460.2	1.29801	0.649007	−	0.760782i	$-0.275185\pi$
$587$	18460.2	1.29801	0.649007	+	0.760782i	$0.275185\pi$
$588$	0	0
$589$	−1612.96	−0.112837
$590$	−6194.74	−0.432260
$591$	11883.2	0.827090
$592$	−4264.99	−0.296098
$593$	18071.2	1.25143	0.625714	−	0.780052i	$-0.284808\pi$
$593$	18071.2	1.25143	0.625714	+	0.780052i	$0.284808\pi$
$594$	−9389.99	−0.648612
$595$	0	0
$596$	−6909.16	−0.474849
$597$	18367.7	1.25920
$598$	3913.50	0.267617
$599$	−4497.11	−0.306756	−0.153378	−	0.988168i	$-0.549015\pi$
$599$	−4497.11	−0.306756	−0.153378	+	0.988168i	$0.549015\pi$
$600$	830.413	0.0565025
$601$	−27009.9	−1.83320	−0.916602	−	0.399801i	$-0.869079\pi$
$601$	−27009.9	−1.83320	−0.916602	+	0.399801i	$0.869079\pi$
$602$	0	0
$603$	−3498.88	−0.236294
$604$	7246.61	0.488180
$605$	−1924.01	−0.129293
$606$	4955.77	0.332202
$607$	−9392.57	−0.628060	−0.314030	−	0.949413i	$-0.601679\pi$
$607$	−9392.57	−0.628060	−0.314030	+	0.949413i	$0.601679\pi$
$608$	1068.54	0.0712744
$609$	0	0
$610$	−440.364	−0.0292292
$611$	−13623.8	−0.902059
$612$	228.311	0.0150800
$613$	−238.429	−0.0157097	−0.00785485	−	0.999969i	$-0.502500\pi$
$613$	−238.429	−0.0157097	−0.00785485	+	0.999969i	$0.502500\pi$
$614$	11069.1	0.727548
$615$	−9088.43	−0.595904
$616$	0	0
$617$	−24963.3	−1.62883	−0.814413	−	0.580286i	$-0.802941\pi$
$617$	−24963.3	−1.62883	−0.814413	+	0.580286i	$0.802941\pi$
$618$	7061.92	0.459663
$619$	17460.9	1.13378	0.566892	−	0.823792i	$-0.308146\pi$
$619$	17460.9	1.13378	0.566892	+	0.823792i	$0.308146\pi$
$620$	966.083	0.0625787
$621$	−10843.1	−0.700677
$622$	−8833.68	−0.569451
$623$	0	0
$624$	−1829.82	−0.117390
$625$	625.000	0.0400000
$626$	1076.52	0.0687321
$627$	4264.76	0.271640
$628$	−13482.4	−0.856695
$629$	1558.84	0.0988154
$630$	0	0
$631$	−1439.72	−0.0908310	−0.0454155	−	0.998968i	$-0.514461\pi$
$631$	−1439.72	−0.0908310	−0.0454155	+	0.998968i	$0.514461\pi$
$632$	−4626.91	−0.291216
$633$	−25002.7	−1.56993
$634$	8227.14	0.515365
$635$	−4674.05	−0.292101
$636$	6293.85	0.392401
$637$	0	0
$638$	3679.04	0.228299
$639$	−8308.06	−0.514338
$640$	−640.000	−0.0395285
$641$	−19940.7	−1.22872	−0.614360	−	0.789026i	$-0.710586\pi$
$641$	−19940.7	−1.22872	−0.614360	+	0.789026i	$0.710586\pi$
$642$	2539.83	0.156136
$643$	−11612.1	−0.712188	−0.356094	−	0.934450i	$-0.615892\pi$
$643$	−11612.1	−0.712188	−0.356094	+	0.934450i	$0.615892\pi$
$644$	0	0
$645$	−529.818	−0.0323435
$646$	−390.545	−0.0237861
$647$	−32202.8	−1.95676	−0.978378	−	0.206825i	$-0.933687\pi$
$647$	−32202.8	−1.95676	−0.978378	+	0.206825i	$0.933687\pi$
$648$	2961.65	0.179544
$649$	19055.2	1.15252
$650$	−1377.19	−0.0831044
$651$	0	0
$652$	1996.83	0.119941
$653$	−29927.9	−1.79352	−0.896760	−	0.442517i	$-0.854086\pi$
$653$	−29927.9	−1.79352	−0.896760	+	0.442517i	$0.854086\pi$
$654$	7897.30	0.472185
$655$	6245.90	0.372592
$656$	7004.46	0.416887
$657$	−7809.43	−0.463737
$658$	0	0
$659$	12500.6	0.738932	0.369466	−	0.929244i	$-0.379541\pi$
$659$	12500.6	0.738932	0.369466	+	0.929244i	$0.379541\pi$
$660$	−2554.38	−0.150650
$661$	−18712.3	−1.10110	−0.550548	−	0.834804i	$-0.685581\pi$
$661$	−18712.3	−1.10110	−0.550548	+	0.834804i	$0.685581\pi$
$662$	−5458.84	−0.320489
$663$	668.791	0.0391760
$664$	−8759.30	−0.511938
$665$	0	0
$666$	−5203.47	−0.302748
$667$	4248.39	0.246624
$668$	10274.2	0.595090
$669$	918.765	0.0530964
$670$	−3584.79	−0.206705
$671$	1354.58	0.0779327
$672$	0	0
$673$	14934.4	0.855394	0.427697	−	0.903922i	$-0.359325\pi$
$673$	14934.4	0.855394	0.427697	+	0.903922i	$0.359325\pi$
$674$	20926.4	1.19593
$675$	3815.78	0.217585
$676$	−5753.36	−0.327342
$677$	19564.4	1.11066	0.555332	−	0.831628i	$-0.312591\pi$
$677$	19564.4	1.11066	0.555332	+	0.831628i	$0.312591\pi$
$678$	−15123.0	−0.856630
$679$	0	0
$680$	233.917	0.0131916
$681$	7803.22	0.439090
$682$	−2971.70	−0.166851
$683$	7644.99	0.428298	0.214149	−	0.976801i	$-0.431302\pi$
$683$	7644.99	0.428298	0.214149	+	0.976801i	$0.431302\pi$
$684$	1303.66	0.0728752
$685$	8729.67	0.486925
$686$	0	0
$687$	−8038.75	−0.446430
$688$	408.331	0.0226271
$689$	−10438.0	−0.577148
$690$	−2949.68	−0.162743
$691$	35496.8	1.95421	0.977106	−	0.212753i	$-0.0682430\pi$
$691$	35496.8	1.95421	0.977106	+	0.212753i	$0.0682430\pi$
$692$	7019.19	0.385592
$693$	0	0
$694$	−19553.0	−1.06948
$695$	−3828.38	−0.208948
$696$	−1986.40	−0.108182
$697$	−2560.10	−0.139126
$698$	18457.2	1.00088
$699$	−9678.71	−0.523723
$700$	0	0
$701$	2739.01	0.147576	0.0737881	−	0.997274i	$-0.476491\pi$
$701$	2739.01	0.147576	0.0737881	+	0.997274i	$0.476491\pi$
$702$	−8408.10	−0.452056
$703$	8900.97	0.477534
$704$	1968.66	0.105393
$705$	10268.5	0.548560
$706$	−3498.27	−0.186486
$707$	0	0
$708$	−10288.4	−0.546132
$709$	−16989.9	−0.899958	−0.449979	−	0.893039i	$-0.648568\pi$
$709$	−16989.9	−0.899958	−0.449979	+	0.893039i	$0.648568\pi$
$710$	−8512.07	−0.449933
$711$	−5645.02	−0.297757
$712$	−10754.6	−0.566078
$713$	−3431.59	−0.180244
$714$	0	0
$715$	4236.28	0.221578
$716$	5498.32	0.286986
$717$	−12622.9	−0.657477
$718$	15431.1	0.802068
$719$	11354.5	0.588944	0.294472	−	0.955660i	$-0.404856\pi$
$719$	11354.5	0.588944	0.294472	+	0.955660i	$0.404856\pi$
$720$	−780.827	−0.0404163
$721$	0	0
$722$	11488.0	0.592159
$723$	22366.3	1.15050
$724$	−9650.76	−0.495398
$725$	−1495.04	−0.0765855
$726$	−3195.45	−0.163353
$727$	4622.31	0.235808	0.117904	−	0.993025i	$-0.462383\pi$
$727$	4622.31	0.235808	0.117904	+	0.993025i	$0.462383\pi$
$728$	0	0
$729$	20724.2	1.05290
$730$	−8001.19	−0.405668
$731$	−149.243	−0.00755124
$732$	−731.369	−0.0369292
$733$	19453.2	0.980248	0.490124	−	0.871653i	$-0.336952\pi$
$733$	19453.2	0.980248	0.490124	+	0.871653i	$0.336952\pi$
$734$	−24230.2	−1.21847
$735$	0	0
$736$	2273.32	0.113853
$737$	11026.9	0.551130
$738$	8545.73	0.426250
$739$	−2942.53	−0.146472	−0.0732359	−	0.997315i	$-0.523333\pi$
$739$	−2942.53	−0.146472	−0.0732359	+	0.997315i	$0.523333\pi$
$740$	−5331.24	−0.264838
$741$	3818.80	0.189321
$742$	0	0
$743$	10024.1	0.494949	0.247475	−	0.968894i	$-0.420399\pi$
$743$	10024.1	0.494949	0.247475	+	0.968894i	$0.420399\pi$
$744$	1604.50	0.0790641
$745$	−8636.45	−0.424718
$746$	3719.30	0.182538
$747$	−10686.7	−0.523436
$748$	−719.538	−0.0351723
$749$	0	0
$750$	1038.02	0.0505374
$751$	−29173.4	−1.41751	−0.708757	−	0.705453i	$-0.750744\pi$
$751$	−29173.4	−1.41751	−0.708757	+	0.705453i	$0.750744\pi$
$752$	−7913.95	−0.383766
$753$	−11426.4	−0.552991
$754$	3294.33	0.159115
$755$	9058.27	0.436641
$756$	0	0
$757$	32859.3	1.57766	0.788831	−	0.614610i	$-0.210687\pi$
$757$	32859.3	1.57766	0.788831	+	0.614610i	$0.210687\pi$
$758$	11468.1	0.549525
$759$	9073.33	0.433914
$760$	1335.67	0.0637498
$761$	20356.9	0.969692	0.484846	−	0.874600i	$-0.338876\pi$
$761$	20356.9	0.969692	0.484846	+	0.874600i	$0.338876\pi$
$762$	−7762.79	−0.369050
$763$	0	0
$764$	19354.5	0.916521
$765$	285.389	0.0134879
$766$	13023.4	0.614301
$767$	17062.7	0.803256
$768$	−1062.93	−0.0499416
$769$	−9679.87	−0.453921	−0.226960	−	0.973904i	$-0.572879\pi$
$769$	−9679.87	−0.453921	−0.226960	+	0.973904i	$0.572879\pi$
$770$	0	0
$771$	−21324.2	−0.996073
$772$	−627.767	−0.0292666
$773$	−18548.7	−0.863066	−0.431533	−	0.902097i	$-0.642027\pi$
$773$	−18548.7	−0.863066	−0.431533	+	0.902097i	$0.642027\pi$
$774$	498.181	0.0231353
$775$	1207.60	0.0559721
$776$	−7223.41	−0.334156
$777$	0	0
$778$	−4682.58	−0.215782
$779$	−14618.2	−0.672337
$780$	−2287.27	−0.104997
$781$	26183.4	1.19964
$782$	−830.890	−0.0379956
$783$	−9127.61	−0.416596
$784$	0	0
$785$	−16852.9	−0.766251
$786$	10373.4	0.470745
$787$	6816.97	0.308766	0.154383	−	0.988011i	$-0.450661\pi$
$787$	6816.97	0.308766	0.154383	+	0.988011i	$0.450661\pi$
$788$	−11448.0	−0.517536
$789$	15827.4	0.714158
$790$	−5783.64	−0.260472
$791$	0	0
$792$	2401.85	0.107760
$793$	1212.93	0.0543158
$794$	−10516.4	−0.470043
$795$	7867.31	0.350974
$796$	−17695.0	−0.787918
$797$	−6021.63	−0.267625	−0.133812	−	0.991007i	$-0.542722\pi$
$797$	−6021.63	−0.267625	−0.133812	+	0.991007i	$0.542722\pi$
$798$	0	0
$799$	2892.51	0.128072
$800$	−800.000	−0.0353553
$801$	−13121.1	−0.578792
$802$	−30183.1	−1.32893
$803$	24611.9	1.08161
$804$	−5953.72	−0.261159
$805$	0	0
$806$	−2660.96	−0.116288
$807$	27746.8	1.21033
$808$	−4774.27	−0.207869
$809$	−43546.7	−1.89249	−0.946244	−	0.323455i	$-0.895156\pi$
$809$	−43546.7	−1.89249	−0.946244	+	0.323455i	$0.895156\pi$
$810$	3702.07	0.160589
$811$	−1152.67	−0.0499084	−0.0249542	−	0.999689i	$-0.507944\pi$
$811$	−1152.67	−0.0499084	−0.0249542	+	0.999689i	$0.507944\pi$
$812$	0	0
$813$	−4780.49	−0.206223
$814$	16399.1	0.706127
$815$	2496.03	0.107279
$816$	388.496	0.0166668
$817$	−852.179	−0.0364920
$818$	258.038	0.0110294
$819$	0	0
$820$	8755.57	0.372875
$821$	11693.9	0.497099	0.248550	−	0.968619i	$-0.420046\pi$
$821$	11693.9	0.497099	0.248550	+	0.968619i	$0.420046\pi$
$822$	14498.5	0.615197
$823$	−31687.2	−1.34210	−0.671048	−	0.741414i	$-0.734156\pi$
$823$	−31687.2	−1.34210	−0.671048	+	0.741414i	$0.734156\pi$
$824$	−6803.28	−0.287626
$825$	−3192.97	−0.134746
$826$	0	0
$827$	15163.8	0.637602	0.318801	−	0.947822i	$-0.396720\pi$
$827$	15163.8	0.637602	0.318801	+	0.947822i	$0.396720\pi$
$828$	2773.55	0.116410
$829$	26856.9	1.12519	0.562593	−	0.826734i	$-0.309804\pi$
$829$	26856.9	1.12519	0.562593	+	0.826734i	$0.309804\pi$
$830$	−10949.1	−0.457891
$831$	−24564.5	−1.02543
$832$	1762.80	0.0734546
$833$	0	0
$834$	−6358.28	−0.263992
$835$	12842.7	0.532265
$836$	−4108.56	−0.169973
$837$	7372.73	0.304467
$838$	−26354.5	−1.08640
$839$	30204.8	1.24289	0.621446	−	0.783457i	$-0.286545\pi$
$839$	30204.8	1.24289	0.621446	+	0.783457i	$0.286545\pi$
$840$	0	0
$841$	−20812.8	−0.853367
$842$	−24520.4	−1.00360
$843$	−30863.7	−1.26097
$844$	24086.9	0.982354
$845$	−7191.70	−0.292783
$846$	−9655.35	−0.392385
$847$	0	0
$848$	−6063.34	−0.245538
$849$	−15126.9	−0.611490
$850$	292.397	0.0117990
$851$	18936.9	0.762808
$852$	−14137.1	−0.568460
$853$	14609.8	0.586435	0.293218	−	0.956046i	$-0.405274\pi$
$853$	14609.8	0.586435	0.293218	+	0.956046i	$0.405274\pi$
$854$	0	0
$855$	1629.57	0.0651815
$856$	−2446.81	−0.0976989
$857$	−9402.54	−0.374778	−0.187389	−	0.982286i	$-0.560002\pi$
$857$	−9402.54	−0.374778	−0.187389	+	0.982286i	$0.560002\pi$
$858$	7035.73	0.279949
$859$	−2224.92	−0.0883740	−0.0441870	−	0.999023i	$-0.514070\pi$
$859$	−2224.92	−0.0883740	−0.0441870	+	0.999023i	$0.514070\pi$
$860$	510.413	0.0202383
$861$	0	0
$862$	15060.4	0.595080
$863$	35688.5	1.40771	0.703853	−	0.710345i	$-0.251461\pi$
$863$	35688.5	1.40771	0.703853	+	0.710345i	$0.251461\pi$
$864$	−4884.20	−0.192319
$865$	8773.98	0.344884
$866$	17433.5	0.684080
$867$	20257.1	0.793504
$868$	0	0
$869$	17790.7	0.694484
$870$	−2483.01	−0.0967607
$871$	9873.88	0.384115
$872$	−7608.07	−0.295461
$873$	−8812.86	−0.341661
$874$	−4744.39	−0.183617
$875$	0	0
$876$	−13288.6	−0.512534
$877$	38959.0	1.50006	0.750029	−	0.661404i	$-0.230039\pi$
$877$	38959.0	1.50006	0.750029	+	0.661404i	$0.230039\pi$
$878$	31364.7	1.20559
$879$	−11889.3	−0.456218
$880$	2460.83	0.0942664
$881$	40111.1	1.53391	0.766957	−	0.641699i	$-0.221770\pi$
$881$	40111.1	1.53391	0.766957	+	0.641699i	$0.221770\pi$
$882$	0	0
$883$	−4293.98	−0.163651	−0.0818256	−	0.996647i	$-0.526075\pi$
$883$	−4293.98	−0.163651	−0.0818256	+	0.996647i	$0.526075\pi$
$884$	−644.297	−0.0245136
$885$	−12860.5	−0.488476
$886$	17440.8	0.661326
$887$	−26652.1	−1.00890	−0.504448	−	0.863442i	$-0.668304\pi$
$887$	−26652.1	−1.00890	−0.504448	+	0.863442i	$0.668304\pi$
$888$	−8854.27	−0.334606
$889$	0	0
$890$	−13443.3	−0.506315
$891$	−11387.7	−0.428173
$892$	−885.116	−0.0332241
$893$	16516.3	0.618920
$894$	−14343.6	−0.536603
$895$	6872.89	0.256688
$896$	0	0
$897$	8124.55	0.302420
$898$	−4280.13	−0.159053
$899$	−2888.67	−0.107166
$900$	−976.034	−0.0361494
$901$	2216.12	0.0819421
$902$	−26932.4	−0.994182
$903$	0	0
$904$	14569.1	0.536020
$905$	−12063.5	−0.443097
$906$	15044.2	0.551667
$907$	−16281.1	−0.596036	−0.298018	−	0.954560i	$-0.596326\pi$
$907$	−16281.1	−0.596036	−0.298018	+	0.954560i	$0.596326\pi$
$908$	−7517.44	−0.274752
$909$	−5824.81	−0.212538
$910$	0	0
$911$	−24281.9	−0.883091	−0.441545	−	0.897239i	$-0.645570\pi$
$911$	−24281.9	−0.883091	−0.441545	+	0.897239i	$0.645570\pi$
$912$	2218.32	0.0805436
$913$	33679.9	1.22086
$914$	−10383.6	−0.375775
$915$	−914.211	−0.0330305
$916$	7744.33	0.279345
$917$	0	0
$918$	1785.16	0.0641818
$919$	1504.18	0.0539917	0.0269959	−	0.999636i	$-0.491406\pi$
$919$	1504.18	0.0539917	0.0269959	+	0.999636i	$0.491406\pi$
$920$	2841.65	0.101833
$921$	22979.9	0.822165
$922$	−17366.9	−0.620334
$923$	23445.5	0.836096
$924$	0	0
$925$	−6664.05	−0.236879
$926$	−23410.0	−0.830777
$927$	−8300.29	−0.294085
$928$	1913.65	0.0676926
$929$	904.268	0.0319355	0.0159677	−	0.999873i	$-0.494917\pi$
$929$	904.268	0.0319355	0.0159677	+	0.999873i	$0.494917\pi$
$930$	2005.62	0.0707171
$931$	0	0
$932$	9324.23	0.327710
$933$	−18339.0	−0.643507
$934$	7575.80	0.265405
$935$	−899.422	−0.0314591
$936$	2150.69	0.0751043
$937$	−10330.7	−0.360182	−0.180091	−	0.983650i	$-0.557639\pi$
$937$	−10330.7	−0.360182	−0.180091	+	0.983650i	$0.557639\pi$
$938$	0	0
$939$	2234.89	0.0776707
$940$	−9892.43	−0.343251
$941$	−47994.9	−1.66269	−0.831344	−	0.555758i	$-0.812428\pi$
$941$	−47994.9	−1.66269	−0.831344	+	0.555758i	$0.812428\pi$
$942$	−27989.8	−0.968108
$943$	−31100.4	−1.07398
$944$	9911.59	0.341732
$945$	0	0
$946$	−1570.05	−0.0539606
$947$	8535.87	0.292902	0.146451	−	0.989218i	$-0.453215\pi$
$947$	8535.87	0.292902	0.146451	+	0.989218i	$0.453215\pi$
$948$	−9605.62	−0.329089
$949$	22038.3	0.753840
$950$	1669.59	0.0570195
$951$	17079.8	0.582388
$952$	0	0
$953$	−34893.0	−1.18604	−0.593020	−	0.805188i	$-0.702064\pi$
$953$	−34893.0	−1.18604	−0.593020	+	0.805188i	$0.702064\pi$
$954$	−7397.53	−0.251052
$955$	24193.1	0.819761
$956$	12160.6	0.411404
$957$	7637.81	0.257989
$958$	228.087	0.00769223
$959$	0	0
$960$	−1328.66	−0.0446691
$961$	−27457.7	−0.921678
$962$	14684.3	0.492141
$963$	−2985.21	−0.0998932
$964$	−21547.1	−0.719903
$965$	−784.709	−0.0261769
$966$	0	0
$967$	26199.3	0.871266	0.435633	−	0.900124i	$-0.356525\pi$
$967$	26199.3	0.871266	0.435633	+	0.900124i	$0.356525\pi$
$968$	3078.41	0.102215
$969$	−810.785	−0.0268794
$970$	−9029.26	−0.298878
$971$	27146.3	0.897186	0.448593	−	0.893736i	$-0.351925\pi$
$971$	27146.3	0.897186	0.448593	+	0.893736i	$0.351925\pi$
$972$	−10335.7	−0.341068
$973$	0	0
$974$	−5783.47	−0.190261
$975$	−2859.09	−0.0939120
$976$	704.583	0.0231077
$977$	27693.7	0.906857	0.453428	−	0.891293i	$-0.350201\pi$
$977$	27693.7	0.906857	0.453428	+	0.891293i	$0.350201\pi$
$978$	4145.48	0.135540
$979$	41352.1	1.34997
$980$	0	0
$981$	−9282.16	−0.302096
$982$	453.717	0.0147441
$983$	2569.25	0.0833636	0.0416818	−	0.999131i	$-0.486728\pi$
$983$	2569.25	0.0833636	0.0416818	+	0.999131i	$0.486728\pi$
$984$	14541.5	0.471103
$985$	−14310.0	−0.462898
$986$	−699.432	−0.0225907
$987$	0	0
$988$	−3678.94	−0.118464
$989$	−1813.02	−0.0582920
$990$	3002.31	0.0963836
$991$	32881.3	1.05399	0.526997	−	0.849867i	$-0.323318\pi$
$991$	32881.3	1.05399	0.526997	+	0.849867i	$0.323318\pi$
$992$	−1545.73	−0.0494728
$993$	−11332.7	−0.362169
$994$	0	0
$995$	−22118.7	−0.704735
$996$	−18184.6	−0.578515
$997$	43063.3	1.36793	0.683966	−	0.729514i	$-0.260254\pi$
$997$	43063.3	1.36793	0.683966	+	0.729514i	$0.260254\pi$
$998$	9991.37	0.316905
$999$	−40685.7	−1.28853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.u.1.1	yes	2
5.4	even	2		2450.4.a.bt.1.2		2
7.2	even	3		490.4.e.t.361.2		4
7.3	odd	6		490.4.e.x.471.1		4
7.4	even	3		490.4.e.t.471.2		4
7.5	odd	6		490.4.e.x.361.1		4
7.6	odd	2		490.4.a.p.1.2	✓	2
35.34	odd	2		2450.4.a.ca.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.p.1.2	✓	2	7.6	odd	2
490.4.a.u.1.1	yes	2	1.1	even	1	trivial
490.4.e.t.361.2		4	7.2	even	3
490.4.e.t.471.2		4	7.4	even	3
490.4.e.x.361.1		4	7.5	odd	6
490.4.e.x.471.1		4	7.3	odd	6
2450.4.a.bt.1.2		2	5.4	even	2
2450.4.a.ca.1.1		2	35.34	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -4.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} +8.30413 q^{6} -8.00000 q^{8} -9.76034 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -4.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} +8.30413 q^{6} -8.00000 q^{8} -9.76034 q^{9} -10.0000 q^{10} +30.7603 q^{11} -16.6083 q^{12} +27.5438 q^{13} -20.7603 q^{15} +16.0000 q^{16} -5.84793 q^{17} +19.5207 q^{18} -33.3917 q^{19} +20.0000 q^{20} -61.5207 q^{22} -71.0413 q^{23} +33.2165 q^{24} +25.0000 q^{25} -55.0876 q^{26} +152.631 q^{27} -59.8017 q^{29} +41.5207 q^{30} +48.3041 q^{31} -32.0000 q^{32} -127.719 q^{33} +11.6959 q^{34} -39.0413 q^{36} -266.562 q^{37} +66.7835 q^{38} -114.364 q^{39} -40.0000 q^{40} +437.779 q^{41} +25.5207 q^{43} +123.041 q^{44} -48.8017 q^{45} +142.083 q^{46} -494.622 q^{47} -66.4331 q^{48} -50.0000 q^{50} +24.2810 q^{51} +110.175 q^{52} -378.959 q^{53} -305.263 q^{54} +153.802 q^{55} +138.645 q^{57} +119.603 q^{58} +619.474 q^{59} -83.0413 q^{60} +44.0364 q^{61} -96.6083 q^{62} +64.0000 q^{64} +137.719 q^{65} +255.438 q^{66} +358.479 q^{67} -23.3917 q^{68} +294.968 q^{69} +851.207 q^{71} +78.0827 q^{72} +800.119 q^{73} +533.124 q^{74} -103.802 q^{75} -133.567 q^{76} +228.727 q^{78} +578.364 q^{79} +80.0000 q^{80} -370.207 q^{81} -875.557 q^{82} +1094.91 q^{83} -29.2397 q^{85} -51.0413 q^{86} +248.301 q^{87} -246.083 q^{88} +1344.33 q^{89} +97.6034 q^{90} -284.165 q^{92} -200.562 q^{93} +989.243 q^{94} -166.959 q^{95} +132.866 q^{96} +902.926 q^{97} -300.231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9} - 20 q^{10} - 5 q^{11} + 20 q^{12} + 95 q^{13} + 25 q^{15} + 32 q^{16} - 25 q^{17} - 94 q^{18} - 120 q^{19} + 40 q^{20} + 10 q^{22} + 124 q^{23} - 40 q^{24} + 50 q^{25} - 190 q^{26} + 425 q^{27} + 213 q^{29} - 50 q^{30} + 70 q^{31} - 64 q^{32} - 455 q^{33} + 50 q^{34} + 188 q^{36} - 134 q^{37} + 240 q^{38} + 503 q^{39} - 80 q^{40} + 370 q^{41} - 82 q^{43} - 20 q^{44} + 235 q^{45} - 248 q^{46} + 115 q^{47} + 80 q^{48} - 100 q^{50} - 151 q^{51} + 380 q^{52} - 1024 q^{53} - 850 q^{54} - 25 q^{55} - 654 q^{57} - 426 q^{58} + 760 q^{59} + 100 q^{60} - 790 q^{61} - 140 q^{62} + 128 q^{64} + 475 q^{65} + 910 q^{66} + 850 q^{67} - 100 q^{68} + 2080 q^{69} + 372 q^{71} - 376 q^{72} + 190 q^{73} + 268 q^{74} + 125 q^{75} - 480 q^{76} - 1006 q^{78} + 425 q^{79} + 160 q^{80} + 590 q^{81} - 740 q^{82} + 2110 q^{83} - 125 q^{85} + 164 q^{86} + 2745 q^{87} + 40 q^{88} + 560 q^{89} - 470 q^{90} + 496 q^{92} - 2 q^{93} - 230 q^{94} - 600 q^{95} - 160 q^{96} + 675 q^{97} - 2330 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9 - 20 * q^10 - 5 * q^11 + 20 * q^12 + 95 * q^13 + 25 * q^15 + 32 * q^16 - 25 * q^17 - 94 * q^18 - 120 * q^19 + 40 * q^20 + 10 * q^22 + 124 * q^23 - 40 * q^24 + 50 * q^25 - 190 * q^26 + 425 * q^27 + 213 * q^29 - 50 * q^30 + 70 * q^31 - 64 * q^32 - 455 * q^33 + 50 * q^34 + 188 * q^36 - 134 * q^37 + 240 * q^38 + 503 * q^39 - 80 * q^40 + 370 * q^41 - 82 * q^43 - 20 * q^44 + 235 * q^45 - 248 * q^46 + 115 * q^47 + 80 * q^48 - 100 * q^50 - 151 * q^51 + 380 * q^52 - 1024 * q^53 - 850 * q^54 - 25 * q^55 - 654 * q^57 - 426 * q^58 + 760 * q^59 + 100 * q^60 - 790 * q^61 - 140 * q^62 + 128 * q^64 + 475 * q^65 + 910 * q^66 + 850 * q^67 - 100 * q^68 + 2080 * q^69 + 372 * q^71 - 376 * q^72 + 190 * q^73 + 268 * q^74 + 125 * q^75 - 480 * q^76 - 1006 * q^78 + 425 * q^79 + 160 * q^80 + 590 * q^81 - 740 * q^82 + 2110 * q^83 - 125 * q^85 + 164 * q^86 + 2745 * q^87 + 40 * q^88 + 560 * q^89 - 470 * q^90 + 496 * q^92 - 2 * q^93 - 230 * q^94 - 600 * q^95 - 160 * q^96 + 675 * q^97 - 2330 * q^99

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