LMFDB - Embedded newform 507.4.a.r.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 $ x^10 - 70x^8 + 1645x^6 - 14700x^4 + 44100x^2 - 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.04224$ 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)

$f(q)$	$=$	$q-2.04224 q^{2} +3.00000 q^{3} -3.82924 q^{4} -12.0825 q^{5} -6.12673 q^{6} -29.7373 q^{7} +24.1582 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.04224 q^{2} +3.00000 q^{3} -3.82924 q^{4} -12.0825 q^{5} -6.12673 q^{6} -29.7373 q^{7} +24.1582 q^{8} +9.00000 q^{9} +24.6753 q^{10} -28.0636 q^{11} -11.4877 q^{12} +60.7308 q^{14} -36.2474 q^{15} -18.7029 q^{16} -50.6556 q^{17} -18.3802 q^{18} -105.148 q^{19} +46.2667 q^{20} -89.2119 q^{21} +57.3126 q^{22} -160.592 q^{23} +72.4746 q^{24} +20.9857 q^{25} +27.0000 q^{27} +113.871 q^{28} +140.105 q^{29} +74.0259 q^{30} -223.593 q^{31} -155.070 q^{32} -84.1907 q^{33} +103.451 q^{34} +359.300 q^{35} -34.4632 q^{36} +228.352 q^{37} +214.739 q^{38} -291.890 q^{40} +295.902 q^{41} +182.192 q^{42} +192.103 q^{43} +107.462 q^{44} -108.742 q^{45} +327.968 q^{46} -36.9300 q^{47} -56.1088 q^{48} +541.307 q^{49} -42.8579 q^{50} -151.967 q^{51} +149.102 q^{53} -55.1406 q^{54} +339.077 q^{55} -718.399 q^{56} -315.445 q^{57} -286.128 q^{58} -438.867 q^{59} +138.800 q^{60} +286.146 q^{61} +456.631 q^{62} -267.636 q^{63} +466.313 q^{64} +171.938 q^{66} +537.128 q^{67} +193.973 q^{68} -481.776 q^{69} -733.777 q^{70} -102.729 q^{71} +217.424 q^{72} +75.5209 q^{73} -466.350 q^{74} +62.9571 q^{75} +402.639 q^{76} +834.535 q^{77} +17.5526 q^{79} +225.977 q^{80} +81.0000 q^{81} -604.304 q^{82} -1463.08 q^{83} +341.614 q^{84} +612.044 q^{85} -392.322 q^{86} +420.315 q^{87} -677.965 q^{88} +334.905 q^{89} +222.078 q^{90} +614.946 q^{92} -670.779 q^{93} +75.4200 q^{94} +1270.45 q^{95} -465.209 q^{96} +748.756 q^{97} -1105.48 q^{98} -252.572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) $ 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9	$ 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9} + 80 q^{10} + 180 q^{12} - 60 q^{14} + 500 q^{16} + 210 q^{17} + 580 q^{22} - 120 q^{23} + 960 q^{25} + 270 q^{27} + 990 q^{29} + 240 q^{30} - 120 q^{35} + 540 q^{36} + 1380 q^{38} + 2000 q^{40} - 180 q^{42} - 740 q^{43} + 1500 q^{48} + 1550 q^{49} + 630 q^{51} + 330 q^{53} + 520 q^{55} - 5340 q^{56} + 2750 q^{61} - 1560 q^{62} + 3140 q^{64} + 1740 q^{66} + 1200 q^{68} - 360 q^{69} - 4380 q^{74} + 2880 q^{75} + 4320 q^{77} + 1100 q^{79} + 810 q^{81} - 4780 q^{82} + 2970 q^{87} + 6340 q^{88} + 720 q^{90} - 1740 q^{92} + 6460 q^{94} - 2760 q^{95}+O(q^{100}) $ 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9 + 80 * q^10 + 180 * q^12 - 60 * q^14 + 500 * q^16 + 210 * q^17 + 580 * q^22 - 120 * q^23 + 960 * q^25 + 270 * q^27 + 990 * q^29 + 240 * q^30 - 120 * q^35 + 540 * q^36 + 1380 * q^38 + 2000 * q^40 - 180 * q^42 - 740 * q^43 + 1500 * q^48 + 1550 * q^49 + 630 * q^51 + 330 * q^53 + 520 * q^55 - 5340 * q^56 + 2750 * q^61 - 1560 * q^62 + 3140 * q^64 + 1740 * q^66 + 1200 * q^68 - 360 * q^69 - 4380 * q^74 + 2880 * q^75 + 4320 * q^77 + 1100 * q^79 + 810 * q^81 - 4780 * q^82 + 2970 * q^87 + 6340 * q^88 + 720 * q^90 - 1740 * q^92 + 6460 * q^94 - 2760 * q^95

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 $

$2$	−2.04224	−0.722042	−0.361021	−	0.932558i	$-0.617572\pi$
$2$	−2.04224	−0.722042	−0.361021	+	0.932558i	$0.617572\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−3.82924	−0.478656
$5$	−12.0825	−1.08069	−0.540344	−	0.841444i	$-0.681706\pi$
$5$	−12.0825	−1.08069	−0.540344	+	0.841444i	$0.681706\pi$
$6$	−6.12673	−0.416871
$7$	−29.7373	−1.60566	−0.802832	−	0.596206i	$-0.796674\pi$
$7$	−29.7373	−1.60566	−0.802832	+	0.596206i	$0.796674\pi$
$8$	24.1582	1.06765
$9$	9.00000	0.333333
$10$	24.6753	0.780302
$11$	−28.0636	−0.769226	−0.384613	−	0.923078i	$-0.625665\pi$
$11$	−28.0636	−0.769226	−0.384613	+	0.923078i	$0.625665\pi$
$12$	−11.4877	−0.276352
$13$	0	0
$13$	0	0
$14$	60.7308	1.15936
$15$	−36.2474	−0.623935
$16$	−18.7029	−0.292233
$17$	−50.6556	−0.722693	−0.361347	−	0.932432i	$-0.617683\pi$
$17$	−50.6556	−0.722693	−0.361347	+	0.932432i	$0.617683\pi$
$18$	−18.3802	−0.240681
$19$	−105.148	−1.26962	−0.634808	−	0.772670i	$-0.718921\pi$
$19$	−105.148	−1.26962	−0.634808	+	0.772670i	$0.718921\pi$
$20$	46.2667	0.517277
$21$	−89.2119	−0.927030
$22$	57.3126	0.555413
$23$	−160.592	−1.45590	−0.727951	−	0.685629i	$-0.759527\pi$
$23$	−160.592	−1.45590	−0.727951	+	0.685629i	$0.759527\pi$
$24$	72.4746	0.616409
$25$	20.9857	0.167886
$26$	0	0
$27$	27.0000	0.192450
$28$	113.871	0.768560
$29$	140.105	0.897132	0.448566	−	0.893750i	$-0.351935\pi$
$29$	140.105	0.897132	0.448566	+	0.893750i	$0.351935\pi$
$30$	74.0259	0.450507
$31$	−223.593	−1.29544	−0.647718	−	0.761880i	$-0.724276\pi$
$31$	−223.593	−1.29544	−0.647718	+	0.761880i	$0.724276\pi$
$32$	−155.070	−0.856647
$33$	−84.1907	−0.444113
$34$	103.451	0.521815
$35$	359.300	1.73522
$36$	−34.4632	−0.159552
$37$	228.352	1.01462	0.507308	−	0.861765i	$-0.330641\pi$
$37$	228.352	1.01462	0.507308	+	0.861765i	$0.330641\pi$
$38$	214.739	0.916716
$39$	0	0
$40$	−291.890	−1.15380
$41$	295.902	1.12713	0.563563	−	0.826073i	$-0.309430\pi$
$41$	295.902	1.12713	0.563563	+	0.826073i	$0.309430\pi$
$42$	182.192	0.669354
$43$	192.103	0.681291	0.340645	−	0.940192i	$-0.389354\pi$
$43$	192.103	0.681291	0.340645	+	0.940192i	$0.389354\pi$
$44$	107.462	0.368194
$45$	−108.742	−0.360229
$46$	327.968	1.05122
$47$	−36.9300	−0.114613	−0.0573063	−	0.998357i	$-0.518251\pi$
$47$	−36.9300	−0.114613	−0.0573063	+	0.998357i	$0.518251\pi$
$48$	−56.1088	−0.168721
$49$	541.307	1.57815
$50$	−42.8579	−0.121220
$51$	−151.967	−0.417247
$52$	0	0
$53$	149.102	0.386429	0.193214	−	0.981157i	$-0.438109\pi$
$53$	149.102	0.386429	0.193214	+	0.981157i	$0.438109\pi$
$54$	−55.1406	−0.138957
$55$	339.077	0.831293
$56$	−718.399	−1.71429
$57$	−315.445	−0.733013
$58$	−286.128	−0.647767
$59$	−438.867	−0.968400	−0.484200	−	0.874957i	$-0.660889\pi$
$59$	−438.867	−0.968400	−0.484200	+	0.874957i	$0.660889\pi$
$60$	138.800	0.298650
$61$	286.146	0.600610	0.300305	−	0.953843i	$-0.402912\pi$
$61$	286.146	0.600610	0.300305	+	0.953843i	$0.402912\pi$
$62$	456.631	0.935358
$63$	−267.636	−0.535221
$64$	466.313	0.910768
$65$	0	0
$66$	171.938	0.320668
$67$	537.128	0.979412	0.489706	−	0.871888i	$-0.337104\pi$
$67$	537.128	0.979412	0.489706	+	0.871888i	$0.337104\pi$
$68$	193.973	0.345921
$69$	−481.776	−0.840566
$70$	−733.777	−1.25290
$71$	−102.729	−0.171713	−0.0858567	−	0.996307i	$-0.527363\pi$
$71$	−102.729	−0.171713	−0.0858567	+	0.996307i	$0.527363\pi$
$72$	217.424	0.355884
$73$	75.5209	0.121083	0.0605414	−	0.998166i	$-0.480717\pi$
$73$	75.5209	0.121083	0.0605414	+	0.998166i	$0.480717\pi$
$74$	−466.350	−0.732596
$75$	62.9571	0.0969288
$76$	402.639	0.607709
$77$	834.535	1.23512
$78$	0	0
$79$	17.5526	0.0249978	0.0124989	−	0.999922i	$-0.496021\pi$
$79$	17.5526	0.0249978	0.0124989	+	0.999922i	$0.496021\pi$
$80$	225.977	0.315813
$81$	81.0000	0.111111
$82$	−604.304	−0.813831
$83$	−1463.08	−1.93487	−0.967434	−	0.253122i	$-0.918543\pi$
$83$	−1463.08	−1.93487	−0.967434	+	0.253122i	$0.918543\pi$
$84$	341.614	0.443728
$85$	612.044	0.781005
$86$	−392.322	−0.491920
$87$	420.315	0.517960
$88$	−677.965	−0.821265
$89$	334.905	0.398875	0.199438	−	0.979911i	$-0.436089\pi$
$89$	334.905	0.398875	0.199438	+	0.979911i	$0.436089\pi$
$90$	222.078	0.260101
$91$	0	0
$92$	614.946	0.696876
$93$	−670.779	−0.747920
$94$	75.4200	0.0827551
$95$	1270.45	1.37206
$96$	−465.209	−0.494585
$97$	748.756	0.783760	0.391880	−	0.920016i	$-0.371825\pi$
$97$	748.756	0.783760	0.391880	+	0.920016i	$0.371825\pi$
$98$	−1105.48	−1.13949
$99$	−252.572	−0.256409
$100$	−80.3594	−0.0803594
$101$	−784.002	−0.772387	−0.386194	−	0.922418i	$-0.626210\pi$
$101$	−784.002	−0.772387	−0.386194	+	0.922418i	$0.626210\pi$
$102$	310.353	0.301270
$103$	396.040	0.378864	0.189432	−	0.981894i	$-0.439335\pi$
$103$	396.040	0.378864	0.189432	+	0.981894i	$0.439335\pi$
$104$	0	0
$105$	1077.90	1.00183
$106$	−304.502	−0.279018
$107$	−1436.59	−1.29795	−0.648974	−	0.760810i	$-0.724802\pi$
$107$	−1436.59	−1.29795	−0.648974	+	0.760810i	$0.724802\pi$
$108$	−103.390	−0.0921173
$109$	1977.92	1.73807	0.869037	−	0.494746i	$-0.164739\pi$
$109$	1977.92	1.73807	0.869037	+	0.494746i	$0.164739\pi$
$110$	−692.477	−0.600228
$111$	685.056	0.585789
$112$	556.175	0.469228
$113$	122.405	0.101902	0.0509509	−	0.998701i	$-0.483775\pi$
$113$	122.405	0.101902	0.0509509	+	0.998701i	$0.483775\pi$
$114$	644.216	0.529266
$115$	1940.35	1.57338
$116$	−536.496	−0.429417
$117$	0	0
$118$	896.273	0.699225
$119$	1506.36	1.16040
$120$	−875.671	−0.666145
$121$	−543.436	−0.408291
$122$	−584.379	−0.433665
$123$	887.706	0.650746
$124$	856.192	0.620067
$125$	1256.75	0.899256
$126$	546.577	0.386452
$127$	2309.61	1.61374	0.806868	−	0.590731i	$-0.201161\pi$
$127$	2309.61	1.61374	0.806868	+	0.590731i	$0.201161\pi$
$128$	288.232	0.199034
$129$	576.310	0.393343
$130$	0	0
$131$	−1444.26	−0.963250	−0.481625	−	0.876377i	$-0.659953\pi$
$131$	−1444.26	−0.963250	−0.481625	+	0.876377i	$0.659953\pi$
$132$	322.387	0.212577
$133$	3126.83	2.03858
$134$	−1096.94	−0.707176
$135$	−326.226	−0.207978
$136$	−1223.75	−0.771584
$137$	735.918	0.458932	0.229466	−	0.973317i	$-0.426302\pi$
$137$	735.918	0.458932	0.229466	+	0.973317i	$0.426302\pi$
$138$	983.904	0.606924
$139$	−1505.14	−0.918449	−0.459225	−	0.888320i	$-0.651873\pi$
$139$	−1505.14	−0.918449	−0.459225	+	0.888320i	$0.651873\pi$
$140$	−1375.85	−0.830573
$141$	−110.790	−0.0661716
$142$	209.797	0.123984
$143$	0	0
$144$	−168.326	−0.0974111
$145$	−1692.81	−0.969520
$146$	−154.232	−0.0874269
$147$	1623.92	0.911148
$148$	−874.415	−0.485652
$149$	−427.843	−0.235237	−0.117618	−	0.993059i	$-0.537526\pi$
$149$	−427.843	−0.235237	−0.117618	+	0.993059i	$0.537526\pi$
$150$	−128.574	−0.0699867
$151$	1601.83	0.863278	0.431639	−	0.902046i	$-0.357935\pi$
$151$	1601.83	0.863278	0.431639	+	0.902046i	$0.357935\pi$
$152$	−2540.20	−1.35551
$153$	−455.900	−0.240898
$154$	−1704.32	−0.891807
$155$	2701.55	1.39996
$156$	0	0
$157$	−730.346	−0.371261	−0.185631	−	0.982620i	$-0.559433\pi$
$157$	−730.346	−0.371261	−0.185631	+	0.982620i	$0.559433\pi$
$158$	−35.8467	−0.0180495
$159$	447.306	0.223105
$160$	1873.62	0.925767
$161$	4775.58	2.33769
$162$	−165.422	−0.0802269
$163$	−1898.36	−0.912215	−0.456107	−	0.889925i	$-0.650757\pi$
$163$	−1898.36	−0.912215	−0.456107	+	0.889925i	$0.650757\pi$
$164$	−1133.08	−0.539505
$165$	1017.23	0.479947
$166$	2987.97	1.39706
$167$	−1427.50	−0.661457	−0.330729	−	0.943726i	$-0.607294\pi$
$167$	−1427.50	−0.661457	−0.330729	+	0.943726i	$0.607294\pi$
$168$	−2155.20	−0.989745
$169$	0	0
$170$	−1249.94	−0.563919
$171$	−946.336	−0.423205
$172$	−735.611	−0.326104
$173$	−2044.40	−0.898454	−0.449227	−	0.893418i	$-0.648301\pi$
$173$	−2044.40	−0.898454	−0.449227	+	0.893418i	$0.648301\pi$
$174$	−858.385	−0.373988
$175$	−624.058	−0.269568
$176$	524.871	0.224793
$177$	−1316.60	−0.559106
$178$	−683.958	−0.288004
$179$	−3889.72	−1.62420	−0.812098	−	0.583521i	$-0.801675\pi$
$179$	−3889.72	−1.62420	−0.812098	+	0.583521i	$0.801675\pi$
$180$	416.400	0.172426
$181$	−2477.02	−1.01721	−0.508606	−	0.861000i	$-0.669839\pi$
$181$	−2477.02	−1.01721	−0.508606	+	0.861000i	$0.669839\pi$
$182$	0	0
$183$	858.437	0.346762
$184$	−3879.61	−1.55440
$185$	−2759.05	−1.09648
$186$	1369.89	0.540029
$187$	1421.58	0.555914
$188$	141.414	0.0548600
$189$	−802.907	−0.309010
$190$	−2594.57	−0.990683
$191$	2276.81	0.862535	0.431267	−	0.902224i	$-0.358067\pi$
$191$	2276.81	0.862535	0.431267	+	0.902224i	$0.358067\pi$
$192$	1398.94	0.525832
$193$	−3922.42	−1.46291	−0.731456	−	0.681888i	$-0.761159\pi$
$193$	−3922.42	−1.46291	−0.731456	+	0.681888i	$0.761159\pi$
$194$	−1529.14	−0.565907
$195$	0	0
$196$	−2072.80	−0.755392
$197$	5063.23	1.83117	0.915584	−	0.402128i	$-0.131729\pi$
$197$	5063.23	1.83117	0.915584	+	0.402128i	$0.131729\pi$
$198$	515.814	0.185138
$199$	3270.06	1.16487	0.582433	−	0.812879i	$-0.302101\pi$
$199$	3270.06	1.16487	0.582433	+	0.812879i	$0.302101\pi$
$200$	506.977	0.179243
$201$	1611.38	0.565464
$202$	1601.12	0.557696
$203$	−4166.34	−1.44049
$204$	581.918	0.199718
$205$	−3575.22	−1.21807
$206$	−808.810	−0.273555
$207$	−1445.33	−0.485301
$208$	0	0
$209$	2950.84	0.976622
$210$	−2201.33	−0.723363
$211$	−2812.18	−0.917527	−0.458764	−	0.888558i	$-0.651708\pi$
$211$	−2812.18	−0.917527	−0.458764	+	0.888558i	$0.651708\pi$
$212$	−570.948	−0.184966
$213$	−308.186	−0.0991388
$214$	2933.87	0.937173
$215$	−2321.08	−0.736262
$216$	652.271	0.205470
$217$	6649.05	2.08003
$218$	−4039.39	−1.25496
$219$	226.563	0.0699072
$220$	−1298.41	−0.397903
$221$	0	0
$222$	−1399.05	−0.422964
$223$	917.736	0.275588	0.137794	−	0.990461i	$-0.455999\pi$
$223$	917.736	0.275588	0.137794	+	0.990461i	$0.455999\pi$
$224$	4611.35	1.37549
$225$	188.871	0.0559619
$226$	−249.981	−0.0735774
$227$	1336.39	0.390746	0.195373	−	0.980729i	$-0.437408\pi$
$227$	1336.39	0.390746	0.195373	+	0.980729i	$0.437408\pi$
$228$	1207.92	0.350861
$229$	−164.820	−0.0475617	−0.0237808	−	0.999717i	$-0.507570\pi$
$229$	−164.820	−0.0475617	−0.0237808	+	0.999717i	$0.507570\pi$
$230$	−3962.66	−1.13604
$231$	2503.60	0.713096
$232$	3384.68	0.957824
$233$	−4243.42	−1.19312	−0.596558	−	0.802570i	$-0.703465\pi$
$233$	−4243.42	−1.19312	−0.596558	+	0.802570i	$0.703465\pi$
$234$	0	0
$235$	446.205	0.123860
$236$	1680.53	0.463530
$237$	52.6579	0.0144325
$238$	−3076.35	−0.837859
$239$	2491.07	0.674200	0.337100	−	0.941469i	$-0.390554\pi$
$239$	2491.07	0.674200	0.337100	+	0.941469i	$0.390554\pi$
$240$	677.932	0.182335
$241$	−2917.40	−0.779776	−0.389888	−	0.920862i	$-0.627486\pi$
$241$	−2917.40	−0.779776	−0.389888	+	0.920862i	$0.627486\pi$
$242$	1109.83	0.294803
$243$	243.000	0.0641500
$244$	−1095.72	−0.287485
$245$	−6540.32	−1.70549
$246$	−1812.91	−0.469866
$247$	0	0
$248$	−5401.60	−1.38307
$249$	−4389.25	−1.11710
$250$	−2566.58	−0.649300
$251$	−1313.88	−0.330403	−0.165202	−	0.986260i	$-0.552827\pi$
$251$	−1313.88	−0.330403	−0.165202	+	0.986260i	$0.552827\pi$
$252$	1024.84	0.256187
$253$	4506.79	1.11992
$254$	−4716.78	−1.16519
$255$	1836.13	0.450914
$256$	−4319.15	−1.05448
$257$	−987.582	−0.239703	−0.119851	−	0.992792i	$-0.538242\pi$
$257$	−987.582	−0.239703	−0.119851	+	0.992792i	$0.538242\pi$
$258$	−1176.97	−0.284010
$259$	−6790.57	−1.62913
$260$	0	0
$261$	1260.94	0.299044
$262$	2949.53	0.695507
$263$	−6986.45	−1.63803	−0.819017	−	0.573769i	$-0.805481\pi$
$263$	−6986.45	−1.63803	−0.819017	+	0.573769i	$0.805481\pi$
$264$	−2033.90	−0.474158
$265$	−1801.52	−0.417609
$266$	−6385.74	−1.47194
$267$	1004.72	0.230291
$268$	−2056.79	−0.468801
$269$	−5904.34	−1.33827	−0.669134	−	0.743142i	$-0.733335\pi$
$269$	−5904.34	−1.33827	−0.669134	+	0.743142i	$0.733335\pi$
$270$	666.233	0.150169
$271$	2131.54	0.477793	0.238897	−	0.971045i	$-0.423214\pi$
$271$	2131.54	0.477793	0.238897	+	0.971045i	$0.423214\pi$
$272$	947.408	0.211195
$273$	0	0
$274$	−1502.92	−0.331368
$275$	−588.934	−0.129142
$276$	1844.84	0.402342
$277$	4032.41	0.874673	0.437336	−	0.899298i	$-0.355922\pi$
$277$	4032.41	0.874673	0.437336	+	0.899298i	$0.355922\pi$
$278$	3073.86	0.663159
$279$	−2012.34	−0.431812
$280$	8680.03	1.85261
$281$	2298.29	0.487916	0.243958	−	0.969786i	$-0.421554\pi$
$281$	2298.29	0.487916	0.243958	+	0.969786i	$0.421554\pi$
$282$	226.260	0.0477787
$283$	6656.80	1.39825	0.699127	−	0.714998i	$-0.253572\pi$
$283$	6656.80	1.39825	0.699127	+	0.714998i	$0.253572\pi$
$284$	393.373	0.0821916
$285$	3811.35	0.792158
$286$	0	0
$287$	−8799.33	−1.80978
$288$	−1395.63	−0.285549
$289$	−2347.01	−0.477715
$290$	3457.13	0.700034
$291$	2246.27	0.452504
$292$	−289.188	−0.0579570
$293$	−7466.99	−1.48883	−0.744413	−	0.667719i	$-0.767271\pi$
$293$	−7466.99	−1.48883	−0.744413	+	0.667719i	$0.767271\pi$
$294$	−3316.44	−0.657887
$295$	5302.59	1.04654
$296$	5516.57	1.08326
$297$	−757.717	−0.148038
$298$	873.759	0.169851
$299$	0	0
$300$	−241.078	−0.0463955
$301$	−5712.64	−1.09392
$302$	−3271.32	−0.623323
$303$	−2352.01	−0.445938
$304$	1966.58	0.371024
$305$	−3457.34	−0.649071
$306$	931.059	0.173938
$307$	3965.99	0.737299	0.368650	−	0.929568i	$-0.379820\pi$
$307$	3965.99	0.737299	0.368650	+	0.929568i	$0.379820\pi$
$308$	−3195.64	−0.591196
$309$	1188.12	0.218737
$310$	−5517.23	−1.01083
$311$	7372.29	1.34419	0.672097	−	0.740463i	$-0.265394\pi$
$311$	7372.29	1.34419	0.672097	+	0.740463i	$0.265394\pi$
$312$	0	0
$313$	8249.55	1.48975	0.744875	−	0.667204i	$-0.232509\pi$
$313$	8249.55	1.48975	0.744875	+	0.667204i	$0.232509\pi$
$314$	1491.54	0.268066
$315$	3233.70	0.578407
$316$	−67.2133	−0.0119653
$317$	5575.26	0.987817	0.493909	−	0.869514i	$-0.335568\pi$
$317$	5575.26	0.987817	0.493909	+	0.869514i	$0.335568\pi$
$318$	−913.507	−0.161091
$319$	−3931.85	−0.690098
$320$	−5634.21	−0.984256
$321$	−4309.77	−0.749371
$322$	−9752.88	−1.68791
$323$	5326.35	0.917543
$324$	−310.169	−0.0531840
$325$	0	0
$326$	3876.91	0.658657
$327$	5933.75	1.00348
$328$	7148.46	1.20338
$329$	1098.20	0.184029
$330$	−2077.43	−0.346542
$331$	4157.36	0.690361	0.345180	−	0.938536i	$-0.387818\pi$
$331$	4157.36	0.690361	0.345180	+	0.938536i	$0.387818\pi$
$332$	5602.50	0.926136
$333$	2055.17	0.338206
$334$	2915.30	0.477600
$335$	−6489.82	−1.05844
$336$	1668.52	0.270909
$337$	3225.18	0.521326	0.260663	−	0.965430i	$-0.416059\pi$
$337$	3225.18	0.521326	0.260663	+	0.965430i	$0.416059\pi$
$338$	0	0
$339$	367.215	0.0588330
$340$	−2343.67	−0.373833
$341$	6274.82	0.996483
$342$	1932.65	0.305572
$343$	−5897.11	−0.928321
$344$	4640.87	0.727381
$345$	5821.04	0.908389
$346$	4175.15	0.648721
$347$	3290.49	0.509057	0.254529	−	0.967065i	$-0.418080\pi$
$347$	3290.49	0.509057	0.254529	+	0.967065i	$0.418080\pi$
$348$	−1609.49	−0.247924
$349$	4491.52	0.688899	0.344449	−	0.938805i	$-0.388066\pi$
$349$	4491.52	0.688899	0.344449	+	0.938805i	$0.388066\pi$
$350$	1274.48	0.194639
$351$	0	0
$352$	4351.81	0.658955
$353$	−5897.88	−0.889270	−0.444635	−	0.895712i	$-0.646667\pi$
$353$	−5897.88	−0.889270	−0.444635	+	0.895712i	$0.646667\pi$
$354$	2688.82	0.403698
$355$	1241.21	0.185569
$356$	−1282.43	−0.190924
$357$	4519.08	0.669958
$358$	7943.75	1.17274
$359$	9277.20	1.36388	0.681938	−	0.731410i	$-0.261137\pi$
$359$	9277.20	1.36388	0.681938	+	0.731410i	$0.261137\pi$
$360$	−2627.01	−0.384599
$361$	4197.19	0.611924
$362$	5058.67	0.734469
$363$	−1630.31	−0.235727
$364$	0	0
$365$	−912.477	−0.130853
$366$	−1753.14	−0.250377
$367$	−6574.36	−0.935092	−0.467546	−	0.883969i	$-0.654862\pi$
$367$	−6574.36	−0.935092	−0.467546	+	0.883969i	$0.654862\pi$
$368$	3003.54	0.425463
$369$	2663.12	0.375708
$370$	5634.65	0.791707
$371$	−4433.89	−0.620474
$372$	2568.58	0.357996
$373$	−5345.55	−0.742043	−0.371021	−	0.928624i	$-0.620992\pi$
$373$	−5345.55	−0.742043	−0.371021	+	0.928624i	$0.620992\pi$
$374$	−2903.20	−0.401393
$375$	3770.24	0.519186
$376$	−892.162	−0.122366
$377$	0	0
$378$	1639.73	0.223118
$379$	1038.51	0.140751	0.0703757	−	0.997521i	$-0.477580\pi$
$379$	1038.51	0.140751	0.0703757	+	0.997521i	$0.477580\pi$
$380$	−4864.87	−0.656743
$381$	6928.82	0.931691
$382$	−4649.80	−0.622786
$383$	−6749.19	−0.900437	−0.450219	−	0.892918i	$-0.648654\pi$
$383$	−6749.19	−0.900437	−0.450219	+	0.892918i	$0.648654\pi$
$384$	864.696	0.114912
$385$	−10083.2	−1.33478
$386$	8010.54	1.05628
$387$	1728.93	0.227097
$388$	−2867.17	−0.375151
$389$	−1246.11	−0.162417	−0.0812083	−	0.996697i	$-0.525878\pi$
$389$	−1246.11	−0.162417	−0.0812083	+	0.996697i	$0.525878\pi$
$390$	0	0
$391$	8134.89	1.05217
$392$	13077.0	1.68492
$393$	−4332.78	−0.556133
$394$	−10340.3	−1.32218
$395$	−212.079	−0.0270148
$396$	967.161	0.122731
$397$	−8355.69	−1.05632	−0.528161	−	0.849144i	$-0.677118\pi$
$397$	−8355.69	−1.05632	−0.528161	+	0.849144i	$0.677118\pi$
$398$	−6678.25	−0.841082
$399$	9380.49	1.17697
$400$	−392.494	−0.0490618
$401$	−3283.66	−0.408923	−0.204461	−	0.978875i	$-0.565544\pi$
$401$	−3283.66	−0.408923	−0.204461	+	0.978875i	$0.565544\pi$
$402$	−3290.83	−0.408288
$403$	0	0
$404$	3002.14	0.369708
$405$	−978.679	−0.120076
$406$	8508.68	1.04010
$407$	−6408.37	−0.780470
$408$	−3671.24	−0.445474
$409$	−10928.9	−1.32127	−0.660636	−	0.750706i	$-0.729713\pi$
$409$	−10928.9	−1.32127	−0.660636	+	0.750706i	$0.729713\pi$
$410$	7301.47	0.879497
$411$	2207.75	0.264965
$412$	−1516.53	−0.181345
$413$	13050.7	1.55492
$414$	2951.71	0.350408
$415$	17677.6	2.09099
$416$	0	0
$417$	−4515.43	−0.530267
$418$	−6026.33	−0.705162
$419$	7302.94	0.851485	0.425742	−	0.904844i	$-0.360013\pi$
$419$	7302.94	0.851485	0.425742	+	0.904844i	$0.360013\pi$
$420$	−4127.54	−0.479531
$421$	−7580.99	−0.877612	−0.438806	−	0.898582i	$-0.644599\pi$
$421$	−7580.99	−0.877612	−0.438806	+	0.898582i	$0.644599\pi$
$422$	5743.15	0.662493
$423$	−332.370	−0.0382042
$424$	3602.03	0.412571
$425$	−1063.04	−0.121330
$426$	629.391	0.0715823
$427$	−8509.19	−0.964377
$428$	5501.06	0.621270
$429$	0	0
$430$	4740.21	0.531612
$431$	10056.7	1.12394	0.561968	−	0.827159i	$-0.310044\pi$
$431$	10056.7	1.12394	0.561968	+	0.827159i	$0.310044\pi$
$432$	−504.979	−0.0562403
$433$	2733.38	0.303367	0.151683	−	0.988429i	$-0.451531\pi$
$433$	2733.38	0.303367	0.151683	+	0.988429i	$0.451531\pi$
$434$	−13579.0	−1.50187
$435$	−5078.44	−0.559752
$436$	−7573.93	−0.831939
$437$	16886.0	1.84844
$438$	−462.696	−0.0504759
$439$	6744.23	0.733223	0.366611	−	0.930374i	$-0.380518\pi$
$439$	6744.23	0.733223	0.366611	+	0.930374i	$0.380518\pi$
$440$	8191.48	0.887531
$441$	4871.76	0.526051
$442$	0	0
$443$	8655.69	0.928317	0.464158	−	0.885752i	$-0.346357\pi$
$443$	8655.69	0.928317	0.464158	+	0.885752i	$0.346357\pi$
$444$	−2623.25	−0.280391
$445$	−4046.48	−0.431059
$446$	−1874.24	−0.198986
$447$	−1283.53	−0.135814
$448$	−13866.9	−1.46239
$449$	6522.46	0.685555	0.342777	−	0.939417i	$-0.388632\pi$
$449$	6522.46	0.685555	0.342777	+	0.939417i	$0.388632\pi$
$450$	−385.721	−0.0404068
$451$	−8304.07	−0.867014
$452$	−468.719	−0.0487759
$453$	4805.49	0.498414
$454$	−2729.23	−0.282135
$455$	0	0
$456$	−7620.59	−0.782602
$457$	−1551.23	−0.158782	−0.0793909	−	0.996844i	$-0.525298\pi$
$457$	−1551.23	−0.158782	−0.0793909	+	0.996844i	$0.525298\pi$
$458$	336.603	0.0343415
$459$	−1367.70	−0.139082
$460$	−7430.06	−0.753105
$461$	7766.25	0.784621	0.392310	−	0.919833i	$-0.371676\pi$
$461$	7766.25	0.784621	0.392310	+	0.919833i	$0.371676\pi$
$462$	−5112.97	−0.514885
$463$	−2004.52	−0.201205	−0.100603	−	0.994927i	$-0.532077\pi$
$463$	−2004.52	−0.201205	−0.100603	+	0.994927i	$0.532077\pi$
$464$	−2620.37	−0.262172
$465$	8104.66	0.808268
$466$	8666.10	0.861479
$467$	18674.3	1.85042	0.925209	−	0.379458i	$-0.123889\pi$
$467$	18674.3	1.85042	0.925209	+	0.379458i	$0.123889\pi$
$468$	0	0
$469$	−15972.7	−1.57261
$470$	−911.259	−0.0894324
$471$	−2191.04	−0.214348
$472$	−10602.2	−1.03391
$473$	−5391.11	−0.524067
$474$	−107.540	−0.0104209
$475$	−2206.61	−0.213150
$476$	−5768.22	−0.555433
$477$	1341.92	0.128810
$478$	−5087.36	−0.486800
$479$	−9313.02	−0.888357	−0.444178	−	0.895938i	$-0.646504\pi$
$479$	−9313.02	−0.888357	−0.444178	+	0.895938i	$0.646504\pi$
$480$	5620.86	0.534492
$481$	0	0
$482$	5958.03	0.563031
$483$	14326.7	1.34967
$484$	2080.95	0.195431
$485$	−9046.81	−0.846999
$486$	−496.265	−0.0463190
$487$	−3536.80	−0.329092	−0.164546	−	0.986369i	$-0.552616\pi$
$487$	−3536.80	−0.329092	−0.164546	+	0.986369i	$0.552616\pi$
$488$	6912.76	0.641241
$489$	−5695.08	−0.526667
$490$	13356.9	1.23144
$491$	−3361.78	−0.308992	−0.154496	−	0.987993i	$-0.549375\pi$
$491$	−3361.78	−0.308992	−0.154496	+	0.987993i	$0.549375\pi$
$492$	−3399.24	−0.311483
$493$	−7097.10	−0.648351
$494$	0	0
$495$	3051.69	0.277098
$496$	4181.84	0.378569
$497$	3054.87	0.275714
$498$	8963.91	0.806591
$499$	4027.43	0.361308	0.180654	−	0.983547i	$-0.442179\pi$
$499$	4027.43	0.361308	0.180654	+	0.983547i	$0.442179\pi$
$500$	−4812.40	−0.430434
$501$	−4282.50	−0.381892
$502$	2683.26	0.238565
$503$	1766.67	0.156604	0.0783022	−	0.996930i	$-0.475050\pi$
$503$	1766.67	0.156604	0.0783022	+	0.996930i	$0.475050\pi$
$504$	−6465.59	−0.571429
$505$	9472.67	0.834709
$506$	−9203.96	−0.808628
$507$	0	0
$508$	−8844.05	−0.772424
$509$	−6816.27	−0.593567	−0.296784	−	0.954945i	$-0.595914\pi$
$509$	−6816.27	−0.593567	−0.296784	+	0.954945i	$0.595914\pi$
$510$	−3749.83	−0.325579
$511$	−2245.79	−0.194418
$512$	6514.89	0.562344
$513$	−2839.01	−0.244338
$514$	2016.88	0.173076
$515$	−4785.13	−0.409433
$516$	−2206.83	−0.188276
$517$	1036.39	0.0881630
$518$	13868.0	1.17630
$519$	−6133.19	−0.518723
$520$	0	0
$521$	−5442.27	−0.457640	−0.228820	−	0.973469i	$-0.573487\pi$
$521$	−5442.27	−0.457640	−0.228820	+	0.973469i	$0.573487\pi$
$522$	−2575.15	−0.215922
$523$	20728.5	1.73307	0.866535	−	0.499117i	$-0.166342\pi$
$523$	20728.5	1.73307	0.866535	+	0.499117i	$0.166342\pi$
$524$	5530.43	0.461065
$525$	−1872.17	−0.155635
$526$	14268.0	1.18273
$527$	11326.2	0.936202
$528$	1574.61	0.129785
$529$	13622.8	1.11965
$530$	3679.13	0.301531
$531$	−3949.80	−0.322800
$532$	−11973.4	−0.975775
$533$	0	0
$534$	−2051.87	−0.166279
$535$	17357.5	1.40268
$536$	12976.0	1.04567
$537$	−11669.2	−0.937730
$538$	12058.1	0.966285
$539$	−15191.0	−1.21396
$540$	1249.20	0.0995500
$541$	−8577.44	−0.681651	−0.340825	−	0.940127i	$-0.610706\pi$
$541$	−8577.44	−0.681651	−0.340825	+	0.940127i	$0.610706\pi$
$542$	−4353.13	−0.344987
$543$	−7431.05	−0.587287
$544$	7855.14	0.619093
$545$	−23898.1	−1.87832
$546$	0	0
$547$	8723.99	0.681921	0.340961	−	0.940078i	$-0.389248\pi$
$547$	8723.99	0.681921	0.340961	+	0.940078i	$0.389248\pi$
$548$	−2818.01	−0.219671
$549$	2575.31	0.200203
$550$	1202.75	0.0932459
$551$	−14731.8	−1.13901
$552$	−11638.8	−0.897431
$553$	−521.968	−0.0401380
$554$	−8235.17	−0.631550
$555$	−8277.15	−0.633055
$556$	5763.56	0.439621
$557$	965.006	0.0734087	0.0367043	−	0.999326i	$-0.488314\pi$
$557$	965.006	0.0734087	0.0367043	+	0.999326i	$0.488314\pi$
$558$	4109.68	0.311786
$559$	0	0
$560$	−6719.95	−0.507089
$561$	4264.73	0.320957
$562$	−4693.66	−0.352296
$563$	−14605.2	−1.09331	−0.546657	−	0.837357i	$-0.684100\pi$
$563$	−14605.2	−1.09331	−0.546657	+	0.837357i	$0.684100\pi$
$564$	424.242	0.0316734
$565$	−1478.95	−0.110124
$566$	−13594.8	−1.00960
$567$	−2408.72	−0.178407
$568$	−2481.74	−0.183330
$569$	7802.48	0.574863	0.287432	−	0.957801i	$-0.407199\pi$
$569$	7802.48	0.574863	0.287432	+	0.957801i	$0.407199\pi$
$570$	−7783.71	−0.571971
$571$	11988.2	0.878618	0.439309	−	0.898336i	$-0.355223\pi$
$571$	11988.2	0.878618	0.439309	+	0.898336i	$0.355223\pi$
$572$	0	0
$573$	6830.43	0.497985
$574$	17970.4	1.30674
$575$	−3370.14	−0.244425
$576$	4196.82	0.303589
$577$	−5576.90	−0.402374	−0.201187	−	0.979553i	$-0.564480\pi$
$577$	−5576.90	−0.402374	−0.201187	+	0.979553i	$0.564480\pi$
$578$	4793.17	0.344930
$579$	−11767.3	−0.844613
$580$	6482.19	0.464066
$581$	43508.1	3.10675
$582$	−4587.43	−0.326727
$583$	−4184.33	−0.297251
$584$	1824.45	0.129274
$585$	0	0
$586$	15249.4	1.07499
$587$	−26754.0	−1.88119	−0.940593	−	0.339535i	$-0.889730\pi$
$587$	−26754.0	−1.88119	−0.940593	+	0.339535i	$0.889730\pi$
$588$	−6218.39	−0.436126
$589$	23510.5	1.64471
$590$	−10829.2	−0.755644
$591$	15189.7	1.05722
$592$	−4270.85	−0.296505
$593$	3589.40	0.248565	0.124283	−	0.992247i	$-0.460337\pi$
$593$	3589.40	0.248565	0.124283	+	0.992247i	$0.460337\pi$
$594$	1547.44	0.106889
$595$	−18200.5	−1.25403
$596$	1638.32	0.112597
$597$	9810.18	0.672536
$598$	0	0
$599$	−7462.78	−0.509050	−0.254525	−	0.967066i	$-0.581919\pi$
$599$	−7462.78	−0.509050	−0.254525	+	0.967066i	$0.581919\pi$
$600$	1520.93	0.103486
$601$	−16511.0	−1.12063	−0.560316	−	0.828279i	$-0.689320\pi$
$601$	−16511.0	−1.12063	−0.560316	+	0.828279i	$0.689320\pi$
$602$	11666.6	0.789858
$603$	4834.15	0.326471
$604$	−6133.80	−0.413213
$605$	6566.04	0.441235
$606$	4803.37	0.321986
$607$	−11953.6	−0.799309	−0.399654	−	0.916666i	$-0.630870\pi$
$607$	−11953.6	−0.799309	−0.399654	+	0.916666i	$0.630870\pi$
$608$	16305.3	1.08761
$609$	−12499.0	−0.831669
$610$	7060.73	0.468657
$611$	0	0
$612$	1745.75	0.115307
$613$	4575.65	0.301482	0.150741	−	0.988573i	$-0.451834\pi$
$613$	4575.65	0.301482	0.150741	+	0.988573i	$0.451834\pi$
$614$	−8099.51	−0.532361
$615$	−10725.7	−0.703253
$616$	20160.9	1.31868
$617$	19231.0	1.25480	0.627400	−	0.778697i	$-0.284119\pi$
$617$	19231.0	1.25480	0.627400	+	0.778697i	$0.284119\pi$
$618$	−2426.43	−0.157937
$619$	11715.6	0.760727	0.380363	−	0.924837i	$-0.375799\pi$
$619$	11715.6	0.760727	0.380363	+	0.924837i	$0.375799\pi$
$620$	−10344.9	−0.670099
$621$	−4335.99	−0.280189
$622$	−15056.0	−0.970564
$623$	−9959.17	−0.640459
$624$	0	0
$625$	−17807.8	−1.13970
$626$	−16847.6	−1.07566
$627$	8852.52	0.563853
$628$	2796.68	0.177706
$629$	−11567.3	−0.733256
$630$	−6603.99	−0.417634
$631$	8780.09	0.553930	0.276965	−	0.960880i	$-0.410671\pi$
$631$	8780.09	0.553930	0.276965	+	0.960880i	$0.410671\pi$
$632$	424.040	0.0266889
$633$	−8436.53	−0.529735
$634$	−11386.0	−0.713245
$635$	−27905.7	−1.74395
$636$	−1712.84	−0.106790
$637$	0	0
$638$	8029.78	0.498279
$639$	−924.558	−0.0572378
$640$	−3482.55	−0.215094
$641$	24991.7	1.53996	0.769980	−	0.638068i	$-0.220266\pi$
$641$	24991.7	1.53996	0.769980	+	0.638068i	$0.220266\pi$
$642$	8801.60	0.541077
$643$	2353.86	0.144365	0.0721827	−	0.997391i	$-0.477004\pi$
$643$	2353.86	0.144365	0.0721827	+	0.997391i	$0.477004\pi$
$644$	−18286.8	−1.11895
$645$	−6963.24	−0.425081
$646$	−10877.7	−0.662504
$647$	−5910.80	−0.359162	−0.179581	−	0.983743i	$-0.557474\pi$
$647$	−5910.80	−0.359162	−0.179581	+	0.983743i	$0.557474\pi$
$648$	1956.81	0.118628
$649$	12316.2	0.744918
$650$	0	0
$651$	19947.2	1.20091
$652$	7269.28	0.436637
$653$	5924.34	0.355034	0.177517	−	0.984118i	$-0.443194\pi$
$653$	5924.34	0.355034	0.177517	+	0.984118i	$0.443194\pi$
$654$	−12118.2	−0.724553
$655$	17450.2	1.04097
$656$	−5534.23	−0.329383
$657$	679.688	0.0403610
$658$	−2242.79	−0.132877
$659$	−12839.5	−0.758964	−0.379482	−	0.925199i	$-0.623898\pi$
$659$	−12839.5	−0.758964	−0.379482	+	0.925199i	$0.623898\pi$
$660$	−3895.22	−0.229729
$661$	−10265.5	−0.604057	−0.302028	−	0.953299i	$-0.597664\pi$
$661$	−10265.5	−0.604057	−0.302028	+	0.953299i	$0.597664\pi$
$662$	−8490.35	−0.498469
$663$	0	0
$664$	−35345.4	−2.06577
$665$	−37779.8	−2.20306
$666$	−4197.15	−0.244199
$667$	−22499.7	−1.30614
$668$	5466.25	0.316610
$669$	2753.21	0.159111
$670$	13253.8	0.764236
$671$	−8030.27	−0.462004
$672$	13834.1	0.794137
$673$	9862.82	0.564909	0.282454	−	0.959281i	$-0.408851\pi$
$673$	9862.82	0.564909	0.282454	+	0.959281i	$0.408851\pi$
$674$	−6586.61	−0.376419
$675$	566.614	0.0323096
$676$	0	0
$677$	32615.5	1.85158	0.925788	−	0.378043i	$-0.123403\pi$
$677$	32615.5	1.85158	0.925788	+	0.378043i	$0.123403\pi$
$678$	−749.943	−0.0424799
$679$	−22266.0	−1.25845
$680$	14785.9	0.833841
$681$	4009.17	0.225597
$682$	−12814.7	−0.719502
$683$	21627.4	1.21164	0.605820	−	0.795602i	$-0.292845\pi$
$683$	21627.4	1.21164	0.605820	+	0.795602i	$0.292845\pi$
$684$	3623.75	0.202570
$685$	−8891.70	−0.495962
$686$	12043.3	0.670286
$687$	−494.461	−0.0274598
$688$	−3592.90	−0.199096
$689$	0	0
$690$	−11888.0	−0.655895
$691$	−14233.1	−0.783580	−0.391790	−	0.920055i	$-0.628144\pi$
$691$	−14233.1	−0.783580	−0.391790	+	0.920055i	$0.628144\pi$
$692$	7828.49	0.430050
$693$	7510.81	0.411706
$694$	−6719.98	−0.367561
$695$	18185.8	0.992557
$696$	10154.0	0.553000
$697$	−14989.1	−0.814566
$698$	−9172.78	−0.497414
$699$	−12730.3	−0.688845
$700$	2389.67	0.129030
$701$	−28747.0	−1.54887	−0.774437	−	0.632651i	$-0.781967\pi$
$701$	−28747.0	−1.54887	−0.774437	+	0.632651i	$0.781967\pi$
$702$	0	0
$703$	−24010.8	−1.28817
$704$	−13086.4	−0.700586
$705$	1338.61	0.0715109
$706$	12044.9	0.642090
$707$	23314.1	1.24019
$708$	5041.59	0.267619
$709$	1818.65	0.0963339	0.0481670	−	0.998839i	$-0.484662\pi$
$709$	1818.65	0.0963339	0.0481670	+	0.998839i	$0.484662\pi$
$710$	−2534.86	−0.133988
$711$	157.974	0.00833260
$712$	8090.70	0.425859
$713$	35907.3	1.88603
$714$	−9229.06	−0.483738
$715$	0	0
$716$	14894.7	0.777431
$717$	7473.20	0.389249
$718$	−18946.3	−0.984776
$719$	26141.8	1.35595	0.677973	−	0.735087i	$-0.262859\pi$
$719$	26141.8	1.35595	0.677973	+	0.735087i	$0.262859\pi$
$720$	2033.80	0.105271
$721$	−11777.2	−0.608328
$722$	−8571.68	−0.441835
$723$	−8752.19	−0.450204
$724$	9485.10	0.486894
$725$	2940.20	0.150616
$726$	3329.48	0.170205
$727$	−1340.10	−0.0683652	−0.0341826	−	0.999416i	$-0.510883\pi$
$727$	−1340.10	−0.0683652	−0.0341826	+	0.999416i	$0.510883\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	1863.50	0.0944811
$731$	−9731.11	−0.492364
$732$	−3287.16	−0.165980
$733$	32517.1	1.63854	0.819269	−	0.573409i	$-0.194380\pi$
$733$	32517.1	1.63854	0.819269	+	0.573409i	$0.194380\pi$
$734$	13426.4	0.675176
$735$	−19620.9	−0.984666
$736$	24903.0	1.24719
$737$	−15073.7	−0.753389
$738$	−5438.73	−0.271277
$739$	22170.5	1.10359	0.551797	−	0.833978i	$-0.313942\pi$
$739$	22170.5	1.10359	0.551797	+	0.833978i	$0.313942\pi$
$740$	10565.1	0.524838
$741$	0	0
$742$	9055.07	0.448008
$743$	30387.8	1.50043	0.750216	−	0.661193i	$-0.229949\pi$
$743$	30387.8	1.50043	0.750216	+	0.661193i	$0.229949\pi$
$744$	−16204.8	−0.798518
$745$	5169.39	0.254217
$746$	10916.9	0.535786
$747$	−13167.7	−0.644956
$748$	−5443.57	−0.266092
$749$	42720.3	2.08407
$750$	−7699.75	−0.374874
$751$	−16898.3	−0.821077	−0.410539	−	0.911843i	$-0.634659\pi$
$751$	−16898.3	−0.821077	−0.410539	+	0.911843i	$0.634659\pi$
$752$	690.699	0.0334936
$753$	−3941.63	−0.190758
$754$	0	0
$755$	−19354.0	−0.932934
$756$	3074.53	0.147909
$757$	32925.8	1.58086	0.790428	−	0.612555i	$-0.209858\pi$
$757$	32925.8	1.58086	0.790428	+	0.612555i	$0.209858\pi$
$758$	−2120.89	−0.101628
$759$	13520.4	0.646585
$760$	30691.8	1.46488
$761$	16792.0	0.799882	0.399941	−	0.916541i	$-0.369031\pi$
$761$	16792.0	0.799882	0.399941	+	0.916541i	$0.369031\pi$
$762$	−14150.3	−0.672720
$763$	−58817.9	−2.79076
$764$	−8718.46	−0.412857
$765$	5508.39	0.260335
$766$	13783.5	0.650153
$767$	0	0
$768$	−12957.4	−0.608804
$769$	1541.57	0.0722891	0.0361445	−	0.999347i	$-0.488492\pi$
$769$	1541.57	0.0722891	0.0361445	+	0.999347i	$0.488492\pi$
$770$	20592.4	0.963765
$771$	−2962.75	−0.138393
$772$	15019.9	0.700231
$773$	38071.2	1.77144	0.885721	−	0.464218i	$-0.153665\pi$
$773$	38071.2	1.77144	0.885721	+	0.464218i	$0.153665\pi$
$774$	−3530.90	−0.163973
$775$	−4692.26	−0.217485
$776$	18088.6	0.836782
$777$	−20371.7	−0.940580
$778$	2544.85	0.117272
$779$	−31113.6	−1.43102
$780$	0	0
$781$	2882.93	0.132086
$782$	−16613.4	−0.759712
$783$	3782.83	0.172653
$784$	−10124.0	−0.461189
$785$	8824.38	0.401217
$786$	8848.60	0.401551
$787$	−20049.8	−0.908129	−0.454065	−	0.890969i	$-0.650027\pi$
$787$	−20049.8	−0.908129	−0.454065	+	0.890969i	$0.650027\pi$
$788$	−19388.3	−0.876498
$789$	−20959.4	−0.945720
$790$	433.117	0.0195058
$791$	−3640.00	−0.163620
$792$	−6101.69	−0.273755
$793$	0	0
$794$	17064.4	0.762709
$795$	−5404.55	−0.241106
$796$	−12521.9	−0.557570
$797$	−22401.9	−0.995627	−0.497813	−	0.867284i	$-0.665864\pi$
$797$	−22401.9	−0.995627	−0.497813	+	0.867284i	$0.665864\pi$
$798$	−19157.2	−0.849823
$799$	1870.71	0.0828298
$800$	−3254.24	−0.143819
$801$	3014.15	0.132958
$802$	6706.02	0.295259
$803$	−2119.39	−0.0931401
$804$	−6170.38	−0.270662
$805$	−57700.7	−2.52631
$806$	0	0
$807$	−17713.0	−0.772649
$808$	−18940.1	−0.824640
$809$	−41966.4	−1.82381	−0.911903	−	0.410406i	$-0.865387\pi$
$809$	−41966.4	−1.82381	−0.911903	+	0.410406i	$0.865387\pi$
$810$	1998.70	0.0867002
$811$	13029.1	0.564133	0.282067	−	0.959395i	$-0.408980\pi$
$811$	13029.1	0.564133	0.282067	+	0.959395i	$0.408980\pi$
$812$	15953.9	0.689500
$813$	6394.63	0.275854
$814$	13087.4	0.563532
$815$	22936.8	0.985819
$816$	2842.22	0.121933
$817$	−20199.4	−0.864977
$818$	22319.5	0.954014
$819$	0	0
$820$	13690.4	0.583036
$821$	−8898.14	−0.378255	−0.189127	−	0.981953i	$-0.560566\pi$
$821$	−8898.14	−0.378255	−0.189127	+	0.981953i	$0.560566\pi$
$822$	−4508.77	−0.191316
$823$	22723.6	0.962448	0.481224	−	0.876598i	$-0.340192\pi$
$823$	22723.6	0.962448	0.481224	+	0.876598i	$0.340192\pi$
$824$	9567.61	0.404494
$825$	−1766.80	−0.0745602
$826$	−26652.7	−1.12272
$827$	−19073.3	−0.801989	−0.400994	−	0.916081i	$-0.631335\pi$
$827$	−19073.3	−0.801989	−0.400994	+	0.916081i	$0.631335\pi$
$828$	5534.52	0.232292
$829$	42503.8	1.78072	0.890361	−	0.455255i	$-0.150452\pi$
$829$	42503.8	1.78072	0.890361	+	0.455255i	$0.150452\pi$
$830$	−36102.0	−1.50978
$831$	12097.2	0.504992
$832$	0	0
$833$	−27420.2	−1.14052
$834$	9221.59	0.382875
$835$	17247.7	0.714829
$836$	−11299.5	−0.467465
$837$	−6037.01	−0.249307
$838$	−14914.4	−0.614808
$839$	19427.2	0.799408	0.399704	−	0.916644i	$-0.369113\pi$
$839$	19427.2	0.799408	0.399704	+	0.916644i	$0.369113\pi$
$840$	26040.1	1.06960
$841$	−4759.60	−0.195154
$842$	15482.2	0.633673
$843$	6894.86	0.281698
$844$	10768.5	0.439180
$845$	0	0
$846$	678.780	0.0275850
$847$	16160.3	0.655578
$848$	−2788.64	−0.112927
$849$	19970.4	0.807282
$850$	2170.99	0.0876052
$851$	−36671.5	−1.47718
$852$	1180.12	0.0474533
$853$	−26851.8	−1.07783	−0.538914	−	0.842361i	$-0.681165\pi$
$853$	−26851.8	−1.07783	−0.538914	+	0.842361i	$0.681165\pi$
$854$	17377.8	0.696320
$855$	11434.1	0.457353
$856$	−34705.4	−1.38576
$857$	41539.4	1.65573	0.827864	−	0.560929i	$-0.189556\pi$
$857$	41539.4	1.65573	0.827864	+	0.560929i	$0.189556\pi$
$858$	0	0
$859$	−11936.2	−0.474107	−0.237054	−	0.971497i	$-0.576182\pi$
$859$	−11936.2	−0.474107	−0.237054	+	0.971497i	$0.576182\pi$
$860$	8887.99	0.352416
$861$	−26398.0	−1.04488
$862$	−20538.3	−0.811529
$863$	−41128.6	−1.62229	−0.811143	−	0.584848i	$-0.801154\pi$
$863$	−41128.6	−1.62229	−0.811143	+	0.584848i	$0.801154\pi$
$864$	−4186.88	−0.164862
$865$	24701.3	0.970948
$866$	−5582.22	−0.219043
$867$	−7041.04	−0.275809
$868$	−25460.8	−0.995619
$869$	−492.590	−0.0192290
$870$	10371.4	0.404165
$871$	0	0
$872$	47782.9	1.85566
$873$	6738.81	0.261253
$874$	−34485.3	−1.33465
$875$	−37372.3	−1.44390
$876$	−867.564	−0.0334615
$877$	6406.86	0.246687	0.123343	−	0.992364i	$-0.460638\pi$
$877$	6406.86	0.246687	0.123343	+	0.992364i	$0.460638\pi$
$878$	−13773.4	−0.529417
$879$	−22401.0	−0.859574
$880$	−6341.73	−0.242931
$881$	−2938.07	−0.112357	−0.0561783	−	0.998421i	$-0.517892\pi$
$881$	−2938.07	−0.112357	−0.0561783	+	0.998421i	$0.517892\pi$
$882$	−9949.32	−0.379831
$883$	3022.06	0.115176	0.0575881	−	0.998340i	$-0.481659\pi$
$883$	3022.06	0.115176	0.0575881	+	0.998340i	$0.481659\pi$
$884$	0	0
$885$	15907.8	0.604219
$886$	−17677.0	−0.670284
$887$	−10060.4	−0.380830	−0.190415	−	0.981704i	$-0.560983\pi$
$887$	−10060.4	−0.380830	−0.190415	+	0.981704i	$0.560983\pi$
$888$	16549.7	0.625419
$889$	−68681.5	−2.59112
$890$	8263.89	0.311243
$891$	−2273.15	−0.0854696
$892$	−3514.24	−0.131912
$893$	3883.13	0.145514
$894$	2621.28	0.0980634
$895$	46997.3	1.75525
$896$	−8571.24	−0.319582
$897$	0	0
$898$	−13320.5	−0.494999
$899$	−31326.5	−1.16218
$900$	−723.234	−0.0267865
$901$	−7552.84	−0.279269
$902$	16958.9	0.626020
$903$	−17137.9	−0.631577
$904$	2957.09	0.108796
$905$	29928.4	1.09929
$906$	−9813.97	−0.359876
$907$	−43158.6	−1.58000	−0.789999	−	0.613108i	$-0.789919\pi$
$907$	−43158.6	−1.58000	−0.789999	+	0.613108i	$0.789919\pi$
$908$	−5117.36	−0.187033
$909$	−7056.02	−0.257462
$910$	0	0
$911$	−32665.9	−1.18800	−0.594001	−	0.804464i	$-0.702453\pi$
$911$	−32665.9	−1.18800	−0.594001	+	0.804464i	$0.702453\pi$
$912$	5899.75	0.214211
$913$	41059.3	1.48835
$914$	3167.98	0.114647
$915$	−10372.0	−0.374741
$916$	631.137	0.0227657
$917$	42948.4	1.54665
$918$	2793.18	0.100423
$919$	18989.9	0.681633	0.340816	−	0.940130i	$-0.389297\pi$
$919$	18989.9	0.681633	0.340816	+	0.940130i	$0.389297\pi$
$920$	46875.3	1.67982
$921$	11898.0	0.425680
$922$	−15860.6	−0.566529
$923$	0	0
$924$	−9586.91	−0.341327
$925$	4792.12	0.170340
$926$	4093.72	0.145279
$927$	3564.36	0.126288
$928$	−21726.0	−0.768525
$929$	5596.81	0.197659	0.0988295	−	0.995104i	$-0.468490\pi$
$929$	5596.81	0.197659	0.0988295	+	0.995104i	$0.468490\pi$
$930$	−16551.7	−0.583603
$931$	−56917.6	−2.00365
$932$	16249.1	0.571091
$933$	22116.9	0.776070
$934$	−38137.5	−1.33608
$935$	−17176.1	−0.600770
$936$	0	0
$937$	40294.4	1.40487	0.702433	−	0.711750i	$-0.252097\pi$
$937$	40294.4	1.40487	0.702433	+	0.711750i	$0.252097\pi$
$938$	32620.2	1.13549
$939$	24748.6	0.860108
$940$	−1708.63	−0.0592865
$941$	−43648.8	−1.51213	−0.756063	−	0.654499i	$-0.772880\pi$
$941$	−43648.8	−1.51213	−0.756063	+	0.654499i	$0.772880\pi$
$942$	4474.63	0.154768
$943$	−47519.5	−1.64098
$944$	8208.10	0.282999
$945$	9701.09	0.333943
$946$	11010.0	0.378398
$947$	10486.6	0.359839	0.179919	−	0.983681i	$-0.442416\pi$
$947$	10486.6	0.359839	0.179919	+	0.983681i	$0.442416\pi$
$948$	−201.640	−0.00690819
$949$	0	0
$950$	4506.44	0.153903
$951$	16725.8	0.570317
$952$	36390.9	1.23890
$953$	33058.8	1.12369	0.561846	−	0.827242i	$-0.310091\pi$
$953$	33058.8	1.12369	0.561846	+	0.827242i	$0.310091\pi$
$954$	−2740.52	−0.0930059
$955$	−27509.5	−0.932131
$956$	−9538.90	−0.322709
$957$	−11795.5	−0.398428
$958$	19019.5	0.641431
$959$	−21884.2	−0.736891
$960$	−16902.6	−0.568260
$961$	20202.8	0.678152
$962$	0	0
$963$	−12929.3	−0.432650
$964$	11171.4	0.373244
$965$	47392.5	1.58095
$966$	−29258.7	−0.974515
$967$	53634.9	1.78364	0.891821	−	0.452389i	$-0.149428\pi$
$967$	53634.9	1.78364	0.891821	+	0.452389i	$0.149428\pi$
$968$	−13128.4	−0.435913
$969$	15979.1	0.529743
$970$	18475.8	0.611569
$971$	−4086.80	−0.135069	−0.0675344	−	0.997717i	$-0.521513\pi$
$971$	−4086.80	−0.135069	−0.0675344	+	0.997717i	$0.521513\pi$
$972$	−930.506	−0.0307058
$973$	44758.8	1.47472
$974$	7223.00	0.237618
$975$	0	0
$976$	−5351.76	−0.175518
$977$	−14381.0	−0.470919	−0.235459	−	0.971884i	$-0.575659\pi$
$977$	−14381.0	−0.470919	−0.235459	+	0.971884i	$0.575659\pi$
$978$	11630.7	0.380276
$979$	−9398.64	−0.306825
$980$	25044.5	0.816343
$981$	17801.3	0.579358
$982$	6865.57	0.223105
$983$	12916.5	0.419099	0.209549	−	0.977798i	$-0.432800\pi$
$983$	12916.5	0.419099	0.209549	+	0.977798i	$0.432800\pi$
$984$	21445.4	0.694770
$985$	−61176.2	−1.97892
$986$	14494.0	0.468137
$987$	3294.59	0.106249
$988$	0	0
$989$	−30850.3	−0.991893
$990$	−6232.30	−0.200076
$991$	−5838.98	−0.187166	−0.0935829	−	0.995611i	$-0.529832\pi$
$991$	−5838.98	−0.187166	−0.0935829	+	0.995611i	$0.529832\pi$
$992$	34672.5	1.10973
$993$	12472.1	0.398580
$994$	−6238.79	−0.199077
$995$	−39510.3	−1.25886
$996$	16807.5	0.534705
$997$	44290.1	1.40690	0.703452	−	0.710743i	$-0.251641\pi$
$997$	44290.1	1.40690	0.703452	+	0.710743i	$0.251641\pi$
$998$	−8224.99	−0.260879
$999$	6165.50	0.195263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.r.1.4		10
3.2	odd	2		1521.4.a.bk.1.7		10
13.2	odd	12		39.4.j.c.4.2	✓	10
13.5	odd	4		507.4.b.i.337.7		10
13.7	odd	12		39.4.j.c.10.2	yes	10
13.8	odd	4		507.4.b.i.337.4		10
13.12	even	2	inner	507.4.a.r.1.7		10
39.2	even	12		117.4.q.e.82.4		10
39.20	even	12		117.4.q.e.10.4		10
39.38	odd	2		1521.4.a.bk.1.4		10
52.7	even	12		624.4.bv.h.49.2		10
52.15	even	12		624.4.bv.h.433.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.2	✓	10	13.2	odd	12
39.4.j.c.10.2	yes	10	13.7	odd	12
117.4.q.e.10.4		10	39.20	even	12
117.4.q.e.82.4		10	39.2	even	12
507.4.a.r.1.4		10	1.1	even	1	trivial
507.4.a.r.1.7		10	13.12	even	2	inner
507.4.b.i.337.4		10	13.8	odd	4
507.4.b.i.337.7		10	13.5	odd	4
624.4.bv.h.49.2		10	52.7	even	12
624.4.bv.h.433.4		10	52.15	even	12
1521.4.a.bk.1.4		10	39.38	odd	2
1521.4.a.bk.1.7		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.04224 q^{2} +3.00000 q^{3} -3.82924 q^{4} -12.0825 q^{5} -6.12673 q^{6} -29.7373 q^{7} +24.1582 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.04224 q^{2} +3.00000 q^{3} -3.82924 q^{4} -12.0825 q^{5} -6.12673 q^{6} -29.7373 q^{7} +24.1582 q^{8} +9.00000 q^{9} +24.6753 q^{10} -28.0636 q^{11} -11.4877 q^{12} +60.7308 q^{14} -36.2474 q^{15} -18.7029 q^{16} -50.6556 q^{17} -18.3802 q^{18} -105.148 q^{19} +46.2667 q^{20} -89.2119 q^{21} +57.3126 q^{22} -160.592 q^{23} +72.4746 q^{24} +20.9857 q^{25} +27.0000 q^{27} +113.871 q^{28} +140.105 q^{29} +74.0259 q^{30} -223.593 q^{31} -155.070 q^{32} -84.1907 q^{33} +103.451 q^{34} +359.300 q^{35} -34.4632 q^{36} +228.352 q^{37} +214.739 q^{38} -291.890 q^{40} +295.902 q^{41} +182.192 q^{42} +192.103 q^{43} +107.462 q^{44} -108.742 q^{45} +327.968 q^{46} -36.9300 q^{47} -56.1088 q^{48} +541.307 q^{49} -42.8579 q^{50} -151.967 q^{51} +149.102 q^{53} -55.1406 q^{54} +339.077 q^{55} -718.399 q^{56} -315.445 q^{57} -286.128 q^{58} -438.867 q^{59} +138.800 q^{60} +286.146 q^{61} +456.631 q^{62} -267.636 q^{63} +466.313 q^{64} +171.938 q^{66} +537.128 q^{67} +193.973 q^{68} -481.776 q^{69} -733.777 q^{70} -102.729 q^{71} +217.424 q^{72} +75.5209 q^{73} -466.350 q^{74} +62.9571 q^{75} +402.639 q^{76} +834.535 q^{77} +17.5526 q^{79} +225.977 q^{80} +81.0000 q^{81} -604.304 q^{82} -1463.08 q^{83} +341.614 q^{84} +612.044 q^{85} -392.322 q^{86} +420.315 q^{87} -677.965 q^{88} +334.905 q^{89} +222.078 q^{90} +614.946 q^{92} -670.779 q^{93} +75.4200 q^{94} +1270.45 q^{95} -465.209 q^{96} +748.756 q^{97} -1105.48 q^{98} -252.572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) \) 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9	\( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9} + 80 q^{10} + 180 q^{12} - 60 q^{14} + 500 q^{16} + 210 q^{17} + 580 q^{22} - 120 q^{23} + 960 q^{25} + 270 q^{27} + 990 q^{29} + 240 q^{30} - 120 q^{35} + 540 q^{36} + 1380 q^{38} + 2000 q^{40} - 180 q^{42} - 740 q^{43} + 1500 q^{48} + 1550 q^{49} + 630 q^{51} + 330 q^{53} + 520 q^{55} - 5340 q^{56} + 2750 q^{61} - 1560 q^{62} + 3140 q^{64} + 1740 q^{66} + 1200 q^{68} - 360 q^{69} - 4380 q^{74} + 2880 q^{75} + 4320 q^{77} + 1100 q^{79} + 810 q^{81} - 4780 q^{82} + 2970 q^{87} + 6340 q^{88} + 720 q^{90} - 1740 q^{92} + 6460 q^{94} - 2760 q^{95}+O(q^{100}) \) 10 * q + 30 * q^3 + 60 * q^4 + 90 * q^9 + 80 * q^10 + 180 * q^12 - 60 * q^14 + 500 * q^16 + 210 * q^17 + 580 * q^22 - 120 * q^23 + 960 * q^25 + 270 * q^27 + 990 * q^29 + 240 * q^30 - 120 * q^35 + 540 * q^36 + 1380 * q^38 + 2000 * q^40 - 180 * q^42 - 740 * q^43 + 1500 * q^48 + 1550 * q^49 + 630 * q^51 + 330 * q^53 + 520 * q^55 - 5340 * q^56 + 2750 * q^61 - 1560 * q^62 + 3140 * q^64 + 1740 * q^66 + 1200 * q^68 - 360 * q^69 - 4380 * q^74 + 2880 * q^75 + 4320 * q^77 + 1100 * q^79 + 810 * q^81 - 4780 * q^82 + 2970 * q^87 + 6340 * q^88 + 720 * q^90 - 1740 * q^92 + 6460 * q^94 - 2760 * q^95

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