LMFDB - Embedded newform 507.4.a.r.1.9

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			1.9
Root			$5.04537$ 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)

$f(q)$	$=$	$q+5.04537 q^{2} +3.00000 q^{3} +17.4557 q^{4} +20.1174 q^{5} +15.1361 q^{6} -15.4279 q^{7} +47.7076 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.04537 q^{2} +3.00000 q^{3} +17.4557 q^{4} +20.1174 q^{5} +15.1361 q^{6} -15.4279 q^{7} +47.7076 q^{8} +9.00000 q^{9} +101.500 q^{10} -26.9372 q^{11} +52.3672 q^{12} -77.8394 q^{14} +60.3522 q^{15} +101.057 q^{16} +23.2334 q^{17} +45.4083 q^{18} +45.0794 q^{19} +351.164 q^{20} -46.2837 q^{21} -135.908 q^{22} -142.010 q^{23} +143.123 q^{24} +279.710 q^{25} +27.0000 q^{27} -269.305 q^{28} +2.29068 q^{29} +304.499 q^{30} +37.7740 q^{31} +128.207 q^{32} -80.8116 q^{33} +117.221 q^{34} -310.369 q^{35} +157.102 q^{36} -313.840 q^{37} +227.442 q^{38} +959.753 q^{40} +5.86820 q^{41} -233.518 q^{42} -360.898 q^{43} -470.209 q^{44} +181.057 q^{45} -716.493 q^{46} +209.748 q^{47} +303.170 q^{48} -104.980 q^{49} +1411.24 q^{50} +69.7003 q^{51} +276.886 q^{53} +136.225 q^{54} -541.906 q^{55} -736.028 q^{56} +135.238 q^{57} +11.5573 q^{58} +543.189 q^{59} +1053.49 q^{60} +205.788 q^{61} +190.583 q^{62} -138.851 q^{63} -161.602 q^{64} -407.724 q^{66} -492.578 q^{67} +405.557 q^{68} -426.030 q^{69} -1565.93 q^{70} -826.859 q^{71} +429.369 q^{72} -66.1205 q^{73} -1583.44 q^{74} +839.129 q^{75} +786.894 q^{76} +415.584 q^{77} +317.642 q^{79} +2033.00 q^{80} +81.0000 q^{81} +29.6072 q^{82} -141.450 q^{83} -807.915 q^{84} +467.396 q^{85} -1820.86 q^{86} +6.87204 q^{87} -1285.11 q^{88} -641.320 q^{89} +913.497 q^{90} -2478.89 q^{92} +113.322 q^{93} +1058.26 q^{94} +906.880 q^{95} +384.621 q^{96} +1114.92 q^{97} -529.663 q^{98} -242.435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.04537	1.78381	0.891903	−	0.452226i	$-0.149370\pi$
$2$	5.04537	1.78381	0.891903	+	0.452226i	$0.149370\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.4557	2.18197
$5$	20.1174	1.79935	0.899677	−	0.436556i	$-0.143802\pi$
$5$	20.1174	1.79935	0.899677	+	0.436556i	$0.143802\pi$
$6$	15.1361	1.02988
$7$	−15.4279	−0.833028	−0.416514	−	0.909129i	$-0.636748\pi$
$7$	−15.4279	−0.833028	−0.416514	+	0.909129i	$0.636748\pi$
$8$	47.7076	2.10840
$9$	9.00000	0.333333
$10$	101.500	3.20970
$11$	−26.9372	−0.738352	−0.369176	−	0.929359i	$-0.620360\pi$
$11$	−26.9372	−0.738352	−0.369176	+	0.929359i	$0.620360\pi$
$12$	52.3672	1.25976
$13$	0	0
$13$	0	0
$14$	−77.8394	−1.48596
$15$	60.3522	1.03886
$16$	101.057	1.57901
$17$	23.2334	0.331467	0.165733	−	0.986171i	$-0.447001\pi$
$17$	23.2334	0.331467	0.165733	+	0.986171i	$0.447001\pi$
$18$	45.4083	0.594602
$19$	45.0794	0.544312	0.272156	−	0.962253i	$-0.412263\pi$
$19$	45.0794	0.544312	0.272156	+	0.962253i	$0.412263\pi$
$20$	351.164	3.92613
$21$	−46.2837	−0.480949
$22$	−135.908	−1.31708
$23$	−142.010	−1.28744	−0.643720	−	0.765261i	$-0.722610\pi$
$23$	−142.010	−1.28744	−0.643720	+	0.765261i	$0.722610\pi$
$24$	143.123	1.21729
$25$	279.710	2.23768
$26$	0	0
$27$	27.0000	0.192450
$28$	−269.305	−1.81764
$29$	2.29068	0.0146679	0.00733394	−	0.999973i	$-0.497666\pi$
$29$	2.29068	0.0146679	0.00733394	+	0.999973i	$0.497666\pi$
$30$	304.499	1.85312
$31$	37.7740	0.218852	0.109426	−	0.993995i	$-0.465099\pi$
$31$	37.7740	0.218852	0.109426	+	0.993995i	$0.465099\pi$
$32$	128.207	0.708251
$33$	−80.8116	−0.426288
$34$	117.221	0.591273
$35$	−310.369	−1.49891
$36$	157.102	0.727322
$37$	−313.840	−1.39446	−0.697228	−	0.716849i	$-0.745584\pi$
$37$	−313.840	−1.39446	−0.697228	+	0.716849i	$0.745584\pi$
$38$	227.442	0.970947
$39$	0	0
$40$	959.753	3.79376
$41$	5.86820	0.0223527	0.0111763	−	0.999938i	$-0.496442\pi$
$41$	5.86820	0.0223527	0.0111763	+	0.999938i	$0.496442\pi$
$42$	−233.518	−0.857920
$43$	−360.898	−1.27992	−0.639958	−	0.768410i	$-0.721048\pi$
$43$	−360.898	−1.27992	−0.639958	+	0.768410i	$0.721048\pi$
$44$	−470.209	−1.61106
$45$	181.057	0.599785
$46$	−716.493	−2.29655
$47$	209.748	0.650956	0.325478	−	0.945550i	$-0.394475\pi$
$47$	209.748	0.650956	0.325478	+	0.945550i	$0.394475\pi$
$48$	303.170	0.911642
$49$	−104.980	−0.306064
$50$	1411.24	3.99158
$51$	69.7003	0.191372
$52$	0	0
$53$	276.886	0.717609	0.358804	−	0.933413i	$-0.383185\pi$
$53$	276.886	0.717609	0.358804	+	0.933413i	$0.383185\pi$
$54$	136.225	0.343294
$55$	−541.906	−1.32856
$56$	−736.028	−1.75636
$57$	135.238	0.314259
$58$	11.5573	0.0261647
$59$	543.189	1.19860	0.599298	−	0.800526i	$-0.295447\pi$
$59$	543.189	1.19860	0.599298	+	0.800526i	$0.295447\pi$
$60$	1053.49	2.26675
$61$	205.788	0.431942	0.215971	−	0.976400i	$-0.430708\pi$
$61$	205.788	0.431942	0.215971	+	0.976400i	$0.430708\pi$
$62$	190.583	0.390389
$63$	−138.851	−0.277676
$64$	−161.602	−0.315629
$65$	0	0
$66$	−407.724	−0.760415
$67$	−492.578	−0.898179	−0.449090	−	0.893487i	$-0.648252\pi$
$67$	−492.578	−0.898179	−0.449090	+	0.893487i	$0.648252\pi$
$68$	405.557	0.723249
$69$	−426.030	−0.743304
$70$	−1565.93	−2.67377
$71$	−826.859	−1.38211	−0.691057	−	0.722800i	$-0.742855\pi$
$71$	−826.859	−1.38211	−0.691057	+	0.722800i	$0.742855\pi$
$72$	429.369	0.702800
$73$	−66.1205	−0.106011	−0.0530056	−	0.998594i	$-0.516880\pi$
$73$	−66.1205	−0.106011	−0.0530056	+	0.998594i	$0.516880\pi$
$74$	−1583.44	−2.48744
$75$	839.129	1.29192
$76$	786.894	1.18767
$77$	415.584	0.615068
$78$	0	0
$79$	317.642	0.452374	0.226187	−	0.974084i	$-0.427374\pi$
$79$	317.642	0.452374	0.226187	+	0.974084i	$0.427374\pi$
$80$	2033.00	2.84120
$81$	81.0000	0.111111
$82$	29.6072	0.0398728
$83$	−141.450	−0.187063	−0.0935313	−	0.995616i	$-0.529816\pi$
$83$	−141.450	−0.187063	−0.0935313	+	0.995616i	$0.529816\pi$
$84$	−807.915	−1.04941
$85$	467.396	0.596426
$86$	−1820.86	−2.28312
$87$	6.87204	0.00846851
$88$	−1285.11	−1.55674
$89$	−641.320	−0.763818	−0.381909	−	0.924200i	$-0.624733\pi$
$89$	−641.320	−0.763818	−0.381909	+	0.924200i	$0.624733\pi$
$90$	913.497	1.06990
$91$	0	0
$92$	−2478.89	−2.80915
$93$	113.322	0.126354
$94$	1058.26	1.16118
$95$	906.880	0.979410
$96$	384.621	0.408909
$97$	1114.92	1.16704	0.583522	−	0.812097i	$-0.301674\pi$
$97$	1114.92	1.16704	0.583522	+	0.812097i	$0.301674\pi$
$98$	−529.663	−0.545960
$99$	−242.435	−0.246117
$100$	4882.53	4.88253
$101$	1589.91	1.56635	0.783177	−	0.621799i	$-0.213598\pi$
$101$	1589.91	1.56635	0.783177	+	0.621799i	$0.213598\pi$
$102$	351.664	0.341371
$103$	527.502	0.504625	0.252312	−	0.967646i	$-0.418809\pi$
$103$	527.502	0.504625	0.252312	+	0.967646i	$0.418809\pi$
$104$	0	0
$105$	−931.107	−0.865398
$106$	1396.99	1.28008
$107$	1751.96	1.58289	0.791443	−	0.611243i	$-0.209330\pi$
$107$	1751.96	1.58289	0.791443	+	0.611243i	$0.209330\pi$
$108$	471.305	0.419920
$109$	−967.122	−0.849848	−0.424924	−	0.905229i	$-0.639699\pi$
$109$	−967.122	−0.849848	−0.424924	+	0.905229i	$0.639699\pi$
$110$	−2734.12	−2.36989
$111$	−941.519	−0.805090
$112$	−1559.09	−1.31536
$113$	1910.97	1.59088	0.795439	−	0.606033i	$-0.207240\pi$
$113$	1910.97	1.59088	0.795439	+	0.606033i	$0.207240\pi$
$114$	682.326	0.560577
$115$	−2856.87	−2.31656
$116$	39.9855	0.0320048
$117$	0	0
$118$	2740.59	2.13806
$119$	−358.443	−0.276121
$120$	2879.26	2.19033
$121$	−605.387	−0.454836
$122$	1038.28	0.770501
$123$	17.6046	0.0129053
$124$	659.372	0.477527
$125$	3112.35	2.22702
$126$	−700.555	−0.495320
$127$	1233.11	0.861584	0.430792	−	0.902451i	$-0.358234\pi$
$127$	1233.11	0.861584	0.430792	+	0.902451i	$0.358234\pi$
$128$	−1841.00	−1.27127
$129$	−1082.69	−0.738960
$130$	0	0
$131$	−1274.90	−0.850292	−0.425146	−	0.905125i	$-0.639777\pi$
$131$	−1274.90	−0.850292	−0.425146	+	0.905125i	$0.639777\pi$
$132$	−1410.63	−0.930145
$133$	−695.480	−0.453427
$134$	−2485.24	−1.60218
$135$	543.170	0.346286
$136$	1108.41	0.698864
$137$	−2031.32	−1.26677	−0.633385	−	0.773837i	$-0.718335\pi$
$137$	−2031.32	−1.26677	−0.633385	+	0.773837i	$0.718335\pi$
$138$	−2149.48	−1.32591
$139$	−1445.66	−0.882156	−0.441078	−	0.897469i	$-0.645404\pi$
$139$	−1445.66	−0.882156	−0.441078	+	0.897469i	$0.645404\pi$
$140$	−5417.72	−3.27058
$141$	629.245	0.375830
$142$	−4171.81	−2.46542
$143$	0	0
$144$	909.510	0.526337
$145$	46.0825	0.0263927
$146$	−333.602	−0.189103
$147$	−314.940	−0.176706
$148$	−5478.30	−3.04266
$149$	−966.318	−0.531301	−0.265650	−	0.964069i	$-0.585587\pi$
$149$	−966.318	−0.531301	−0.265650	+	0.964069i	$0.585587\pi$
$150$	4233.71	2.30454
$151$	−1463.09	−0.788505	−0.394252	−	0.919002i	$-0.628996\pi$
$151$	−1463.09	−0.788505	−0.394252	+	0.919002i	$0.628996\pi$
$152$	2150.63	1.14763
$153$	209.101	0.110489
$154$	2096.78	1.09716
$155$	759.914	0.393792
$156$	0	0
$157$	−66.0424	−0.0335717	−0.0167859	−	0.999859i	$-0.505343\pi$
$157$	−66.0424	−0.0335717	−0.0167859	+	0.999859i	$0.505343\pi$
$158$	1602.62	0.806948
$159$	830.659	0.414312
$160$	2579.19	1.27439
$161$	2190.92	1.07247
$162$	408.675	0.198201
$163$	−3525.24	−1.69398	−0.846988	−	0.531612i	$-0.821587\pi$
$163$	−3525.24	−1.69398	−0.846988	+	0.531612i	$0.821587\pi$
$164$	102.434	0.0487728
$165$	−1625.72	−0.767043
$166$	−713.669	−0.333683
$167$	−260.652	−0.120777	−0.0603887	−	0.998175i	$-0.519234\pi$
$167$	−260.652	−0.120777	−0.0603887	+	0.998175i	$0.519234\pi$
$168$	−2208.08	−1.01403
$169$	0	0
$170$	2358.19	1.06391
$171$	405.715	0.181437
$172$	−6299.74	−2.79273
$173$	911.753	0.400689	0.200345	−	0.979725i	$-0.435794\pi$
$173$	911.753	0.400689	0.200345	+	0.979725i	$0.435794\pi$
$174$	34.6720	0.0151062
$175$	−4315.33	−1.86405
$176$	−2722.18	−1.16587
$177$	1629.57	0.692009
$178$	−3235.70	−1.36250
$179$	2690.48	1.12344	0.561721	−	0.827327i	$-0.310139\pi$
$179$	2690.48	1.12344	0.561721	+	0.827327i	$0.310139\pi$
$180$	3160.47	1.30871
$181$	4773.85	1.96043	0.980213	−	0.197944i	$-0.0634265\pi$
$181$	4773.85	1.96043	0.980213	+	0.197944i	$0.0634265\pi$
$182$	0	0
$183$	617.364	0.249382
$184$	−6774.96	−2.71444
$185$	−6313.63	−2.50912
$186$	571.750	0.225391
$187$	−625.844	−0.244739
$188$	3661.31	1.42036
$189$	−416.553	−0.160316
$190$	4575.54	1.74708
$191$	−2057.47	−0.779443	−0.389721	−	0.920933i	$-0.627429\pi$
$191$	−2057.47	−0.779443	−0.389721	+	0.920933i	$0.627429\pi$
$192$	−484.806	−0.182228
$193$	−729.873	−0.272215	−0.136107	−	0.990694i	$-0.543459\pi$
$193$	−729.873	−0.272215	−0.136107	+	0.990694i	$0.543459\pi$
$194$	5625.20	2.08178
$195$	0	0
$196$	−1832.50	−0.667822
$197$	1701.11	0.615225	0.307613	−	0.951512i	$-0.400470\pi$
$197$	1701.11	0.615225	0.307613	+	0.951512i	$0.400470\pi$
$198$	−1223.17	−0.439026
$199$	−1840.88	−0.655761	−0.327881	−	0.944719i	$-0.606334\pi$
$199$	−1840.88	−0.655761	−0.327881	+	0.944719i	$0.606334\pi$
$200$	13344.3	4.71792
$201$	−1477.73	−0.518564
$202$	8021.66	2.79407
$203$	−35.3404	−0.0122188
$204$	1216.67	0.417568
$205$	118.053	0.0402204
$206$	2661.44	0.900153
$207$	−1278.09	−0.429147
$208$	0	0
$209$	−1214.31	−0.401894
$210$	−4697.78	−1.54370
$211$	142.970	0.0466467	0.0233234	−	0.999728i	$-0.492575\pi$
$211$	142.970	0.0466467	0.0233234	+	0.999728i	$0.492575\pi$
$212$	4833.25	1.56580
$213$	−2480.58	−0.797964
$214$	8839.31	2.82356
$215$	−7260.32	−2.30302
$216$	1288.11	0.405762
$217$	−582.773	−0.182310
$218$	−4879.48	−1.51597
$219$	−198.361	−0.0612056
$220$	−9459.37	−2.89887
$221$	0	0
$222$	−4750.31	−1.43613
$223$	−2338.71	−0.702295	−0.351148	−	0.936320i	$-0.614208\pi$
$223$	−2338.71	−0.702295	−0.351148	+	0.936320i	$0.614208\pi$
$224$	−1977.96	−0.589993
$225$	2517.39	0.745892
$226$	9641.57	2.83782
$227$	3279.36	0.958850	0.479425	−	0.877583i	$-0.340845\pi$
$227$	3279.36	0.958850	0.479425	+	0.877583i	$0.340845\pi$
$228$	2360.68	0.685702
$229$	1143.72	0.330041	0.165021	−	0.986290i	$-0.447231\pi$
$229$	1143.72	0.330041	0.165021	+	0.986290i	$0.447231\pi$
$230$	−14414.0	−4.13230
$231$	1246.75	0.355110
$232$	109.283	0.0309258
$233$	−4238.17	−1.19164	−0.595819	−	0.803118i	$-0.703173\pi$
$233$	−4238.17	−1.19164	−0.595819	+	0.803118i	$0.703173\pi$
$234$	0	0
$235$	4219.59	1.17130
$236$	9481.75	2.61529
$237$	952.927	0.261178
$238$	−1808.48	−0.492547
$239$	−3310.03	−0.895849	−0.447924	−	0.894072i	$-0.647837\pi$
$239$	−3310.03	−0.895849	−0.447924	+	0.894072i	$0.647837\pi$
$240$	6098.99	1.64037
$241$	5702.86	1.52429	0.762145	−	0.647407i	$-0.224146\pi$
$241$	5702.86	1.52429	0.762145	+	0.647407i	$0.224146\pi$
$242$	−3054.40	−0.811340
$243$	243.000	0.0641500
$244$	3592.18	0.942483
$245$	−2111.93	−0.550718
$246$	88.8217	0.0230206
$247$	0	0
$248$	1802.11	0.461427
$249$	−424.351	−0.108001
$250$	15703.0	3.97257
$251$	−3910.23	−0.983313	−0.491657	−	0.870789i	$-0.663608\pi$
$251$	−3910.23	−0.983313	−0.491657	+	0.870789i	$0.663608\pi$
$252$	−2423.75	−0.605880
$253$	3825.35	0.950585
$254$	6221.51	1.53690
$255$	1402.19	0.344347
$256$	−7995.69	−1.95207
$257$	6972.80	1.69242	0.846209	−	0.532851i	$-0.178879\pi$
$257$	6972.80	1.69242	0.846209	+	0.532851i	$0.178879\pi$
$258$	−5462.59	−1.31816
$259$	4841.88	1.16162
$260$	0	0
$261$	20.6161	0.00488930
$262$	−6432.32	−1.51676
$263$	281.691	0.0660449	0.0330224	−	0.999455i	$-0.489487\pi$
$263$	281.691	0.0660449	0.0330224	+	0.999455i	$0.489487\pi$
$264$	−3855.33	−0.898785
$265$	5570.23	1.29123
$266$	−3508.95	−0.808826
$267$	−1923.96	−0.440990
$268$	−8598.31	−1.95980
$269$	4333.13	0.982139	0.491070	−	0.871120i	$-0.336606\pi$
$269$	4333.13	0.982139	0.491070	+	0.871120i	$0.336606\pi$
$270$	2740.49	0.617707
$271$	−428.596	−0.0960715	−0.0480357	−	0.998846i	$-0.515296\pi$
$271$	−428.596	−0.0960715	−0.0480357	+	0.998846i	$0.515296\pi$
$272$	2347.89	0.523390
$273$	0	0
$274$	−10248.8	−2.25967
$275$	−7534.59	−1.65219
$276$	−7436.67	−1.62187
$277$	8938.75	1.93891	0.969454	−	0.245274i	$-0.0788779\pi$
$277$	8938.75	1.93891	0.969454	+	0.245274i	$0.0788779\pi$
$278$	−7293.91	−1.57360
$279$	339.966	0.0729506
$280$	−14807.0	−3.16031
$281$	−775.819	−0.164703	−0.0823514	−	0.996603i	$-0.526243\pi$
$281$	−775.819	−0.164703	−0.0823514	+	0.996603i	$0.526243\pi$
$282$	3174.77	0.670408
$283$	−4014.53	−0.843248	−0.421624	−	0.906771i	$-0.638540\pi$
$283$	−4014.53	−0.843248	−0.421624	+	0.906771i	$0.638540\pi$
$284$	−14433.4	−3.01573
$285$	2720.64	0.565463
$286$	0	0
$287$	−90.5340	−0.0186204
$288$	1153.86	0.236084
$289$	−4373.21	−0.890130
$290$	232.503	0.0470795
$291$	3344.77	0.673793
$292$	−1154.18	−0.231313
$293$	4956.21	0.988208	0.494104	−	0.869403i	$-0.335496\pi$
$293$	4956.21	0.988208	0.494104	+	0.869403i	$0.335496\pi$
$294$	−1588.99	−0.315210
$295$	10927.5	2.15670
$296$	−14972.5	−2.94007
$297$	−727.304	−0.142096
$298$	−4875.43	−0.947738
$299$	0	0
$300$	14647.6	2.81893
$301$	5567.89	1.06621
$302$	−7381.80	−1.40654
$303$	4769.72	0.904334
$304$	4555.58	0.859474
$305$	4139.92	0.777217
$306$	1054.99	0.197091
$307$	3894.90	0.724084	0.362042	−	0.932162i	$-0.382080\pi$
$307$	3894.90	0.724084	0.362042	+	0.932162i	$0.382080\pi$
$308$	7254.33	1.34206
$309$	1582.51	0.291345
$310$	3834.04	0.702448
$311$	3097.44	0.564758	0.282379	−	0.959303i	$-0.408876\pi$
$311$	3097.44	0.564758	0.282379	+	0.959303i	$0.408876\pi$
$312$	0	0
$313$	4487.36	0.810353	0.405177	−	0.914238i	$-0.367210\pi$
$313$	4487.36	0.810353	0.405177	+	0.914238i	$0.367210\pi$
$314$	−333.208	−0.0598854
$315$	−2793.32	−0.499638
$316$	5544.68	0.987065
$317$	−6820.62	−1.20847	−0.604233	−	0.796807i	$-0.706521\pi$
$317$	−6820.62	−1.20847	−0.604233	+	0.796807i	$0.706521\pi$
$318$	4190.98	0.739052
$319$	−61.7045	−0.0108301
$320$	−3251.01	−0.567928
$321$	5255.89	0.913880
$322$	11054.0	1.91309
$323$	1047.35	0.180421
$324$	1413.91	0.242441
$325$	0	0
$326$	−17786.1	−3.02173
$327$	−2901.37	−0.490660
$328$	279.958	0.0471283
$329$	−3235.98	−0.542265
$330$	−8202.35	−1.36826
$331$	−5012.96	−0.832438	−0.416219	−	0.909264i	$-0.636645\pi$
$331$	−5012.96	−0.832438	−0.416219	+	0.909264i	$0.636645\pi$
$332$	−2469.12	−0.408164
$333$	−2824.56	−0.464819
$334$	−1315.08	−0.215444
$335$	−9909.39	−1.61614
$336$	−4677.28	−0.759424
$337$	3220.79	0.520616	0.260308	−	0.965526i	$-0.416176\pi$
$337$	3220.79	0.520616	0.260308	+	0.965526i	$0.416176\pi$
$338$	0	0
$339$	5732.92	0.918494
$340$	8158.74	1.30138
$341$	−1017.52	−0.161590
$342$	2046.98	0.323649
$343$	6911.39	1.08799
$344$	−17217.6	−2.69858
$345$	−8570.62	−1.33747
$346$	4600.13	0.714753
$347$	−3360.71	−0.519921	−0.259960	−	0.965619i	$-0.583710\pi$
$347$	−3360.71	−0.519921	−0.259960	+	0.965619i	$0.583710\pi$
$348$	119.957	0.0184780
$349$	−4591.32	−0.704205	−0.352102	−	0.935961i	$-0.614533\pi$
$349$	−4591.32	−0.704205	−0.352102	+	0.935961i	$0.614533\pi$
$350$	−21772.4	−3.32510
$351$	0	0
$352$	−3453.54	−0.522938
$353$	1740.09	0.262367	0.131183	−	0.991358i	$-0.458122\pi$
$353$	1740.09	0.262367	0.131183	+	0.991358i	$0.458122\pi$
$354$	8221.76	1.23441
$355$	−16634.2	−2.48691
$356$	−11194.7	−1.66662
$357$	−1075.33	−0.159419
$358$	13574.5	2.00400
$359$	1425.49	0.209567	0.104784	−	0.994495i	$-0.466585\pi$
$359$	1425.49	0.209567	0.104784	+	0.994495i	$0.466585\pi$
$360$	8637.78	1.26459
$361$	−4826.85	−0.703725
$362$	24085.8	3.49702
$363$	−1816.16	−0.262600
$364$	0	0
$365$	−1330.17	−0.190752
$366$	3114.83	0.444849
$367$	10849.2	1.54312	0.771559	−	0.636158i	$-0.219477\pi$
$367$	10849.2	1.54312	0.771559	+	0.636158i	$0.219477\pi$
$368$	−14351.1	−2.03288
$369$	52.8138	0.00745089
$370$	−31854.6	−4.47579
$371$	−4271.77	−0.597788
$372$	1978.12	0.275700
$373$	−494.749	−0.0686786	−0.0343393	−	0.999410i	$-0.510933\pi$
$373$	−494.749	−0.0686786	−0.0343393	+	0.999410i	$0.510933\pi$
$374$	−3157.61	−0.436567
$375$	9337.06	1.28577
$376$	10006.6	1.37248
$377$	0	0
$378$	−2101.66	−0.285973
$379$	12643.3	1.71357	0.856786	−	0.515671i	$-0.172457\pi$
$379$	12643.3	1.71357	0.856786	+	0.515671i	$0.172457\pi$
$380$	15830.3	2.13704
$381$	3699.34	0.497436
$382$	−10380.7	−1.39037
$383$	−2321.51	−0.309722	−0.154861	−	0.987936i	$-0.549493\pi$
$383$	−2321.51	−0.309722	−0.154861	+	0.987936i	$0.549493\pi$
$384$	−5522.99	−0.733969
$385$	8360.47	1.10673
$386$	−3682.48	−0.485578
$387$	−3248.08	−0.426639
$388$	19461.8	2.54645
$389$	−10477.6	−1.36564	−0.682821	−	0.730586i	$-0.739247\pi$
$389$	−10477.6	−1.36564	−0.682821	+	0.730586i	$0.739247\pi$
$390$	0	0
$391$	−3299.38	−0.426744
$392$	−5008.35	−0.645306
$393$	−3824.69	−0.490916
$394$	8582.75	1.09744
$395$	6390.14	0.813982
$396$	−4231.88	−0.537020
$397$	1766.85	0.223364	0.111682	−	0.993744i	$-0.464376\pi$
$397$	1766.85	0.223364	0.111682	+	0.993744i	$0.464376\pi$
$398$	−9287.91	−1.16975
$399$	−2086.44	−0.261786
$400$	28266.5	3.53332
$401$	5001.65	0.622869	0.311434	−	0.950268i	$-0.399191\pi$
$401$	5001.65	0.622869	0.311434	+	0.950268i	$0.399191\pi$
$402$	−7455.71	−0.925018
$403$	0	0
$404$	27753.0	3.41773
$405$	1629.51	0.199928
$406$	−178.305	−0.0217959
$407$	8453.96	1.02960
$408$	3325.24	0.403490
$409$	11208.6	1.35508	0.677541	−	0.735485i	$-0.263046\pi$
$409$	11208.6	1.35508	0.677541	+	0.735485i	$0.263046\pi$
$410$	595.620	0.0717453
$411$	−6093.96	−0.731370
$412$	9207.94	1.10107
$413$	−8380.26	−0.998464
$414$	−6448.44	−0.765515
$415$	−2845.61	−0.336592
$416$	0	0
$417$	−4336.99	−0.509313
$418$	−6126.66	−0.716901
$419$	3285.19	0.383036	0.191518	−	0.981489i	$-0.438659\pi$
$419$	3285.19	0.383036	0.191518	+	0.981489i	$0.438659\pi$
$420$	−16253.2	−1.88827
$421$	13289.9	1.53850	0.769250	−	0.638948i	$-0.220630\pi$
$421$	13289.9	1.53850	0.769250	+	0.638948i	$0.220630\pi$
$422$	721.336	0.0832087
$423$	1887.74	0.216985
$424$	13209.6	1.51301
$425$	6498.61	0.741715
$426$	−12515.4	−1.42341
$427$	−3174.88	−0.359820
$428$	30581.8	3.45380
$429$	0	0
$430$	−36631.0	−4.10815
$431$	13692.3	1.53024	0.765119	−	0.643889i	$-0.222680\pi$
$431$	13692.3	1.53024	0.765119	+	0.643889i	$0.222680\pi$
$432$	2728.53	0.303881
$433$	−10002.5	−1.11014	−0.555070	−	0.831804i	$-0.687308\pi$
$433$	−10002.5	−1.11014	−0.555070	+	0.831804i	$0.687308\pi$
$434$	−2940.30	−0.325205
$435$	138.248	0.0152378
$436$	−16881.8	−1.85434
$437$	−6401.73	−0.700769
$438$	−1000.81	−0.109179
$439$	4487.21	0.487842	0.243921	−	0.969795i	$-0.421566\pi$
$439$	4487.21	0.487842	0.243921	+	0.969795i	$0.421566\pi$
$440$	−25853.1	−2.80113
$441$	−944.821	−0.102021
$442$	0	0
$443$	2035.35	0.218290	0.109145	−	0.994026i	$-0.465189\pi$
$443$	2035.35	0.218290	0.109145	+	0.994026i	$0.465189\pi$
$444$	−16434.9	−1.75668
$445$	−12901.7	−1.37438
$446$	−11799.7	−1.25276
$447$	−2898.95	−0.306747
$448$	2493.18	0.262928
$449$	−3575.58	−0.375818	−0.187909	−	0.982186i	$-0.560171\pi$
$449$	−3575.58	−0.375818	−0.187909	+	0.982186i	$0.560171\pi$
$450$	12701.1	1.33053
$451$	−158.073	−0.0165041
$452$	33357.4	3.47124
$453$	−4389.26	−0.455243
$454$	16545.6	1.71040
$455$	0	0
$456$	6451.90	0.662583
$457$	−8058.60	−0.824869	−0.412435	−	0.910987i	$-0.635321\pi$
$457$	−8058.60	−0.824869	−0.412435	+	0.910987i	$0.635321\pi$
$458$	5770.51	0.588730
$459$	627.303	0.0637908
$460$	−49868.8	−5.05466
$461$	−11692.1	−1.18125	−0.590626	−	0.806945i	$-0.701119\pi$
$461$	−11692.1	−1.18125	−0.590626	+	0.806945i	$0.701119\pi$
$462$	6290.33	0.633447
$463$	−1732.40	−0.173891	−0.0869455	−	0.996213i	$-0.527711\pi$
$463$	−1732.40	−0.173891	−0.0869455	+	0.996213i	$0.527711\pi$
$464$	231.489	0.0231607
$465$	2279.74	0.227356
$466$	−21383.1	−2.12565
$467$	10769.9	1.06718	0.533588	−	0.845745i	$-0.320843\pi$
$467$	10769.9	1.06718	0.533588	+	0.845745i	$0.320843\pi$
$468$	0	0
$469$	7599.44	0.748208
$470$	21289.4	2.08937
$471$	−198.127	−0.0193826
$472$	25914.2	2.52712
$473$	9721.58	0.945029
$474$	4807.87	0.465892
$475$	12609.1	1.21799
$476$	−6256.88	−0.602487
$477$	2491.98	0.239203
$478$	−16700.3	−1.59802
$479$	−7911.64	−0.754680	−0.377340	−	0.926075i	$-0.623161\pi$
$479$	−7911.64	−0.754680	−0.377340	+	0.926075i	$0.623161\pi$
$480$	7737.57	0.735772
$481$	0	0
$482$	28773.0	2.71904
$483$	6572.75	0.619193
$484$	−10567.5	−0.992438
$485$	22429.3	2.09993
$486$	1226.02	0.114431
$487$	10964.8	1.02025	0.510125	−	0.860100i	$-0.329599\pi$
$487$	10964.8	1.02025	0.510125	+	0.860100i	$0.329599\pi$
$488$	9817.66	0.910707
$489$	−10575.7	−0.978018
$490$	−10655.4	−0.982375
$491$	−9139.37	−0.840029	−0.420014	−	0.907518i	$-0.637975\pi$
$491$	−9139.37	−0.840029	−0.420014	+	0.907518i	$0.637975\pi$
$492$	307.301	0.0281590
$493$	53.2204	0.00486192
$494$	0	0
$495$	−4877.16	−0.442852
$496$	3817.31	0.345569
$497$	12756.7	1.15134
$498$	−2141.01	−0.192652
$499$	12577.5	1.12835	0.564175	−	0.825655i	$-0.309194\pi$
$499$	12577.5	1.12835	0.564175	+	0.825655i	$0.309194\pi$
$500$	54328.4	4.85928
$501$	−781.955	−0.0697309
$502$	−19728.6	−1.75404
$503$	13214.6	1.17139	0.585696	−	0.810531i	$-0.300821\pi$
$503$	13214.6	1.17139	0.585696	+	0.810531i	$0.300821\pi$
$504$	−6624.25	−0.585452
$505$	31984.8	2.81842
$506$	19300.3	1.69566
$507$	0	0
$508$	21524.9	1.87995
$509$	−21719.8	−1.89138	−0.945689	−	0.325073i	$-0.894611\pi$
$509$	−21719.8	−1.89138	−0.945689	+	0.325073i	$0.894611\pi$
$510$	7074.56	0.614248
$511$	1020.10	0.0883103
$512$	−25613.2	−2.21085
$513$	1217.14	0.104753
$514$	35180.4	3.01895
$515$	10612.0	0.907999
$516$	−18899.2	−1.61239
$517$	−5650.03	−0.480635
$518$	24429.1	2.07211
$519$	2735.26	0.231338
$520$	0	0
$521$	−4627.05	−0.389088	−0.194544	−	0.980894i	$-0.562323\pi$
$521$	−4627.05	−0.389088	−0.194544	+	0.980894i	$0.562323\pi$
$522$	104.016	0.00872156
$523$	13784.0	1.15245	0.576224	−	0.817292i	$-0.304526\pi$
$523$	13784.0	1.15245	0.576224	+	0.817292i	$0.304526\pi$
$524$	−22254.3	−1.85531
$525$	−12946.0	−1.07621
$526$	1421.23	0.117811
$527$	877.619	0.0725421
$528$	−8166.55	−0.673113
$529$	7999.85	0.657504
$530$	28103.9	2.30331
$531$	4888.70	0.399532
$532$	−12140.1	−0.989362
$533$	0	0
$534$	−9707.09	−0.786642
$535$	35245.0	2.84817
$536$	−23499.7	−1.89372
$537$	8071.45	0.648620
$538$	21862.2	1.75195
$539$	2827.87	0.225983
$540$	9481.42	0.755584
$541$	−454.638	−0.0361302	−0.0180651	−	0.999837i	$-0.505751\pi$
$541$	−454.638	−0.0361302	−0.0180651	+	0.999837i	$0.505751\pi$
$542$	−2162.43	−0.171373
$543$	14321.5	1.13185
$544$	2978.69	0.234762
$545$	−19456.0	−1.52918
$546$	0	0
$547$	11611.4	0.907621	0.453810	−	0.891098i	$-0.350064\pi$
$547$	11611.4	0.907621	0.453810	+	0.891098i	$0.350064\pi$
$548$	−35458.2	−2.76405
$549$	1852.09	0.143981
$550$	−38014.8	−2.94719
$551$	103.263	0.00798390
$552$	−20324.9	−1.56718
$553$	−4900.55	−0.376840
$554$	45099.3	3.45864
$555$	−18940.9	−1.44864
$556$	−25235.1	−1.92483
$557$	−4883.93	−0.371524	−0.185762	−	0.982595i	$-0.559475\pi$
$557$	−4883.93	−0.371524	−0.185762	+	0.982595i	$0.559475\pi$
$558$	1715.25	0.130130
$559$	0	0
$560$	−31364.9	−2.36680
$561$	−1877.53	−0.141300
$562$	−3914.29	−0.293798
$563$	19617.3	1.46851	0.734256	−	0.678873i	$-0.237531\pi$
$563$	19617.3	1.46851	0.734256	+	0.678873i	$0.237531\pi$
$564$	10983.9	0.820048
$565$	38443.8	2.86256
$566$	−20254.8	−1.50419
$567$	−1249.66	−0.0925587
$568$	−39447.5	−2.91405
$569$	7475.19	0.550749	0.275374	−	0.961337i	$-0.411198\pi$
$569$	7475.19	0.550749	0.275374	+	0.961337i	$0.411198\pi$
$570$	13726.6	1.00868
$571$	−7799.56	−0.571631	−0.285816	−	0.958285i	$-0.592265\pi$
$571$	−7799.56	−0.571631	−0.285816	+	0.958285i	$0.592265\pi$
$572$	0	0
$573$	−6172.42	−0.450011
$574$	−456.777	−0.0332152
$575$	−39721.6	−2.88088
$576$	−1454.42	−0.105210
$577$	−13136.1	−0.947771	−0.473885	−	0.880587i	$-0.657149\pi$
$577$	−13136.1	−0.947771	−0.473885	+	0.880587i	$0.657149\pi$
$578$	−22064.4	−1.58782
$579$	−2189.62	−0.157163
$580$	804.404	0.0575880
$581$	2182.28	0.155828
$582$	16875.6	1.20192
$583$	−7458.54	−0.529848
$584$	−3154.45	−0.223514
$585$	0	0
$586$	25005.9	1.76277
$587$	−22150.7	−1.55751	−0.778754	−	0.627330i	$-0.784148\pi$
$587$	−22150.7	−1.55751	−0.778754	+	0.627330i	$0.784148\pi$
$588$	−5497.51	−0.385567
$589$	1702.83	0.119124
$590$	55133.4	3.84713
$591$	5103.34	0.355201
$592$	−31715.6	−2.20186
$593$	22770.3	1.57684	0.788419	−	0.615138i	$-0.210900\pi$
$593$	22770.3	1.57684	0.788419	+	0.615138i	$0.210900\pi$
$594$	−3669.52	−0.253472
$595$	−7210.94	−0.496840
$596$	−16867.8	−1.15928
$597$	−5522.64	−0.378604
$598$	0	0
$599$	−7214.11	−0.492088	−0.246044	−	0.969259i	$-0.579131\pi$
$599$	−7214.11	−0.492088	−0.246044	+	0.969259i	$0.579131\pi$
$600$	40032.8	2.72389
$601$	27276.7	1.85132	0.925658	−	0.378360i	$-0.123512\pi$
$601$	27276.7	1.85132	0.925658	+	0.378360i	$0.123512\pi$
$602$	28092.1	1.90191
$603$	−4433.20	−0.299393
$604$	−25539.2	−1.72049
$605$	−12178.8	−0.818412
$606$	24065.0	1.61316
$607$	11566.2	0.773403	0.386701	−	0.922205i	$-0.373614\pi$
$607$	11566.2	0.773403	0.386701	+	0.922205i	$0.373614\pi$
$608$	5779.50	0.385509
$609$	−106.021	−0.00705450
$610$	20887.4	1.38640
$611$	0	0
$612$	3650.01	0.241083
$613$	−24476.6	−1.61272	−0.806362	−	0.591422i	$-0.798567\pi$
$613$	−24476.6	−1.61272	−0.806362	+	0.591422i	$0.798567\pi$
$614$	19651.2	1.29163
$615$	354.159	0.0232212
$616$	19826.5	1.29681
$617$	−2423.28	−0.158116	−0.0790581	−	0.996870i	$-0.525191\pi$
$617$	−2423.28	−0.158116	−0.0790581	+	0.996870i	$0.525191\pi$
$618$	7984.33	0.519704
$619$	−17223.4	−1.11836	−0.559182	−	0.829045i	$-0.688885\pi$
$619$	−17223.4	−1.11836	−0.559182	+	0.829045i	$0.688885\pi$
$620$	13264.8	0.859240
$621$	−3834.27	−0.247768
$622$	15627.7	1.00742
$623$	9894.22	0.636282
$624$	0	0
$625$	27648.7	1.76952
$626$	22640.4	1.44551
$627$	−3642.94	−0.232033
$628$	−1152.82	−0.0732523
$629$	−7291.57	−0.462216
$630$	−14093.3	−0.891257
$631$	−9242.58	−0.583108	−0.291554	−	0.956554i	$-0.594172\pi$
$631$	−9242.58	−0.583108	−0.291554	+	0.956554i	$0.594172\pi$
$632$	15154.0	0.953786
$633$	428.910	0.0269315
$634$	−34412.5	−2.15567
$635$	24807.0	1.55029
$636$	14499.8	0.904014
$637$	0	0
$638$	−311.322	−0.0193187
$639$	−7441.73	−0.460705
$640$	−37036.1	−2.28747
$641$	−11598.8	−0.714706	−0.357353	−	0.933969i	$-0.616321\pi$
$641$	−11598.8	−0.714706	−0.357353	+	0.933969i	$0.616321\pi$
$642$	26517.9	1.63018
$643$	−25363.9	−1.55561	−0.777804	−	0.628507i	$-0.783666\pi$
$643$	−25363.9	−1.55561	−0.777804	+	0.628507i	$0.783666\pi$
$644$	38244.0	2.34010
$645$	−21781.0	−1.32965
$646$	5284.26	0.321837
$647$	−6590.09	−0.400438	−0.200219	−	0.979751i	$-0.564165\pi$
$647$	−6590.09	−0.400438	−0.200219	+	0.979751i	$0.564165\pi$
$648$	3864.32	0.234267
$649$	−14632.0	−0.884985
$650$	0	0
$651$	−1748.32	−0.105257
$652$	−61535.6	−3.69620
$653$	15698.2	0.940765	0.470382	−	0.882463i	$-0.344116\pi$
$653$	15698.2	0.940765	0.470382	+	0.882463i	$0.344116\pi$
$654$	−14638.5	−0.875243
$655$	−25647.6	−1.52998
$656$	593.021	0.0352951
$657$	−595.084	−0.0353371
$658$	−16326.7	−0.967295
$659$	2840.81	0.167925	0.0839624	−	0.996469i	$-0.473242\pi$
$659$	2840.81	0.167925	0.0839624	+	0.996469i	$0.473242\pi$
$660$	−28378.1	−1.67366
$661$	−20819.1	−1.22507	−0.612533	−	0.790445i	$-0.709849\pi$
$661$	−20819.1	−1.22507	−0.612533	+	0.790445i	$0.709849\pi$
$662$	−25292.2	−1.48491
$663$	0	0
$664$	−6748.26	−0.394403
$665$	−13991.3	−0.815876
$666$	−14250.9	−0.829147
$667$	−325.300	−0.0188840
$668$	−4549.87	−0.263532
$669$	−7016.14	−0.405470
$670$	−49996.5	−2.88289
$671$	−5543.36	−0.318925
$672$	−5933.89	−0.340632
$673$	31264.5	1.79073	0.895364	−	0.445335i	$-0.146916\pi$
$673$	31264.5	1.79073	0.895364	+	0.445335i	$0.146916\pi$
$674$	16250.1	0.928679
$675$	7552.16	0.430641
$676$	0	0
$677$	−27953.2	−1.58689	−0.793447	−	0.608639i	$-0.791716\pi$
$677$	−27953.2	−1.58689	−0.793447	+	0.608639i	$0.791716\pi$
$678$	28924.7	1.63842
$679$	−17200.9	−0.972180
$680$	22298.4	1.25750
$681$	9838.09	0.553592
$682$	−5133.79	−0.288245
$683$	34709.9	1.94456	0.972282	−	0.233811i	$-0.0751196\pi$
$683$	34709.9	1.94456	0.972282	+	0.233811i	$0.0751196\pi$
$684$	7082.05	0.395890
$685$	−40864.9	−2.27937
$686$	34870.5	1.94076
$687$	3431.17	0.190549
$688$	−36471.1	−2.02100
$689$	0	0
$690$	−43241.9	−2.38578
$691$	11860.8	0.652974	0.326487	−	0.945202i	$-0.394135\pi$
$691$	11860.8	0.652974	0.326487	+	0.945202i	$0.394135\pi$
$692$	15915.3	0.874291
$693$	3740.26	0.205023
$694$	−16956.0	−0.927438
$695$	−29083.0	−1.58731
$696$	327.849	0.0178550
$697$	136.338	0.00740916
$698$	−23164.9	−1.25617
$699$	−12714.5	−0.687993
$700$	−75327.2	−4.06729
$701$	16100.5	0.867486	0.433743	−	0.901037i	$-0.357193\pi$
$701$	16100.5	0.867486	0.433743	+	0.901037i	$0.357193\pi$
$702$	0	0
$703$	−14147.7	−0.759019
$704$	4353.10	0.233045
$705$	12658.8	0.676251
$706$	8779.38	0.468012
$707$	−24528.9	−1.30482
$708$	28445.3	1.50994
$709$	28465.5	1.50782	0.753910	−	0.656978i	$-0.228166\pi$
$709$	28465.5	1.50782	0.753910	+	0.656978i	$0.228166\pi$
$710$	−83925.9	−4.43617
$711$	2858.78	0.150791
$712$	−30595.9	−1.61043
$713$	−5364.28	−0.281759
$714$	−5425.43	−0.284372
$715$	0	0
$716$	46964.4	2.45131
$717$	−9930.08	−0.517218
$718$	7192.14	0.373828
$719$	−27822.1	−1.44310	−0.721550	−	0.692362i	$-0.756570\pi$
$719$	−27822.1	−1.44310	−0.721550	+	0.692362i	$0.756570\pi$
$720$	18297.0	0.947067
$721$	−8138.25	−0.420367
$722$	−24353.2	−1.25531
$723$	17108.6	0.880049
$724$	83331.0	4.27758
$725$	640.725	0.0328220
$726$	−9163.20	−0.468427
$727$	866.153	0.0441869	0.0220934	−	0.999756i	$-0.492967\pi$
$727$	866.153	0.0441869	0.0220934	+	0.999756i	$0.492967\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−6711.20	−0.340264
$731$	−8384.90	−0.424250
$732$	10776.5	0.544143
$733$	23120.1	1.16502	0.582511	−	0.812823i	$-0.302070\pi$
$733$	23120.1	1.16502	0.582511	+	0.812823i	$0.302070\pi$
$734$	54738.3	2.75262
$735$	−6335.78	−0.317957
$736$	−18206.7	−0.911831
$737$	13268.7	0.663172
$738$	266.465	0.0132909
$739$	−20765.1	−1.03364	−0.516819	−	0.856095i	$-0.672884\pi$
$739$	−20765.1	−1.03364	−0.516819	+	0.856095i	$0.672884\pi$
$740$	−110209.	−5.47482
$741$	0	0
$742$	−21552.7	−1.06634
$743$	36995.8	1.82671	0.913354	−	0.407166i	$-0.133483\pi$
$743$	36995.8	1.82671	0.913354	+	0.407166i	$0.133483\pi$
$744$	5406.32	0.266405
$745$	−19439.8	−0.955999
$746$	−2496.19	−0.122509
$747$	−1273.05	−0.0623542
$748$	−10924.6	−0.534013
$749$	−27029.1	−1.31859
$750$	47108.9	2.29356
$751$	−34429.1	−1.67289	−0.836443	−	0.548055i	$-0.815369\pi$
$751$	−34429.1	−1.67289	−0.836443	+	0.548055i	$0.815369\pi$
$752$	21196.5	1.02787
$753$	−11730.7	−0.567716
$754$	0	0
$755$	−29433.5	−1.41880
$756$	−7271.24	−0.349805
$757$	4268.88	0.204960	0.102480	−	0.994735i	$-0.467322\pi$
$757$	4268.88	0.204960	0.102480	+	0.994735i	$0.467322\pi$
$758$	63790.2	3.05668
$759$	11476.1	0.548820
$760$	43265.1	2.06499
$761$	7342.11	0.349739	0.174869	−	0.984592i	$-0.444050\pi$
$761$	7342.11	0.349739	0.174869	+	0.984592i	$0.444050\pi$
$762$	18664.5	0.887329
$763$	14920.7	0.707947
$764$	−35914.7	−1.70072
$765$	4206.57	0.198809
$766$	−11712.9	−0.552484
$767$	0	0
$768$	−23987.1	−1.12703
$769$	14728.5	0.690666	0.345333	−	0.938480i	$-0.387766\pi$
$769$	14728.5	0.690666	0.345333	+	0.938480i	$0.387766\pi$
$770$	42181.7	1.97418
$771$	20918.4	0.977118
$772$	−12740.5	−0.593963
$773$	−9937.41	−0.462385	−0.231193	−	0.972908i	$-0.574263\pi$
$773$	−9937.41	−0.462385	−0.231193	+	0.972908i	$0.574263\pi$
$774$	−16387.8	−0.761041
$775$	10565.7	0.489719
$776$	53190.3	2.46059
$777$	14525.7	0.670663
$778$	−52863.3	−2.43604
$779$	264.535	0.0121668
$780$	0	0
$781$	22273.3	1.02049
$782$	−16646.6	−0.761229
$783$	61.8484	0.00282284
$784$	−10608.9	−0.483279
$785$	−1328.60	−0.0604074
$786$	−19297.0	−0.875700
$787$	−36305.0	−1.64439	−0.822194	−	0.569207i	$-0.807250\pi$
$787$	−36305.0	−1.64439	−0.822194	+	0.569207i	$0.807250\pi$
$788$	29694.2	1.34240
$789$	845.072	0.0381310
$790$	32240.6	1.45199
$791$	−29482.3	−1.32525
$792$	−11566.0	−0.518914
$793$	0	0
$794$	8914.40	0.398439
$795$	16710.7	0.745493
$796$	−32133.9	−1.43085
$797$	−9150.73	−0.406694	−0.203347	−	0.979107i	$-0.565182\pi$
$797$	−9150.73	−0.406694	−0.203347	+	0.979107i	$0.565182\pi$
$798$	−10526.9	−0.466976
$799$	4873.17	0.215770
$800$	35860.7	1.58484
$801$	−5771.88	−0.254606
$802$	25235.1	1.11108
$803$	1781.10	0.0782736
$804$	−25794.9	−1.13149
$805$	44075.5	1.92976
$806$	0	0
$807$	12999.4	0.567038
$808$	75850.7	3.30250
$809$	30349.9	1.31897	0.659484	−	0.751719i	$-0.270775\pi$
$809$	30349.9	1.31897	0.659484	+	0.751719i	$0.270775\pi$
$810$	8221.47	0.356633
$811$	4238.72	0.183529	0.0917643	−	0.995781i	$-0.470749\pi$
$811$	4238.72	0.183529	0.0917643	+	0.995781i	$0.470749\pi$
$812$	−616.892	−0.0266609
$813$	−1285.79	−0.0554669
$814$	42653.3	1.83661
$815$	−70918.6	−3.04806
$816$	7043.68	0.302179
$817$	−16269.1	−0.696674
$818$	56551.4	2.41721
$819$	0	0
$820$	2060.70	0.0877595
$821$	−5934.48	−0.252271	−0.126136	−	0.992013i	$-0.540257\pi$
$821$	−5934.48	−0.252271	−0.126136	+	0.992013i	$0.540257\pi$
$822$	−30746.3	−1.30462
$823$	−22459.6	−0.951265	−0.475633	−	0.879644i	$-0.657781\pi$
$823$	−22459.6	−0.951265	−0.475633	+	0.879644i	$0.657781\pi$
$824$	25165.9	1.06395
$825$	−22603.8	−0.953894
$826$	−42281.5	−1.78107
$827$	−20138.4	−0.846772	−0.423386	−	0.905949i	$-0.639159\pi$
$827$	−20138.4	−0.846772	−0.423386	+	0.905949i	$0.639159\pi$
$828$	−22310.0	−0.936384
$829$	5845.70	0.244909	0.122455	−	0.992474i	$-0.460923\pi$
$829$	5845.70	0.244909	0.122455	+	0.992474i	$0.460923\pi$
$830$	−14357.2	−0.600415
$831$	26816.2	1.11943
$832$	0	0
$833$	−2439.05	−0.101450
$834$	−21881.7	−0.908516
$835$	−5243.63	−0.217322
$836$	−21196.7	−0.876919
$837$	1019.90	0.0421180
$838$	16575.0	0.683261
$839$	27779.9	1.14311	0.571554	−	0.820564i	$-0.306341\pi$
$839$	27779.9	1.14311	0.571554	+	0.820564i	$0.306341\pi$
$840$	−44420.9	−1.82460
$841$	−24383.8	−0.999785
$842$	67052.3	2.74439
$843$	−2327.46	−0.0950911
$844$	2495.65	0.101782
$845$	0	0
$846$	9524.32	0.387060
$847$	9339.85	0.378891
$848$	27981.2	1.13311
$849$	−12043.6	−0.486849
$850$	32787.9	1.32308
$851$	44568.4	1.79528
$852$	−43300.3	−1.74113
$853$	−16480.5	−0.661526	−0.330763	−	0.943714i	$-0.607306\pi$
$853$	−16480.5	−0.661526	−0.330763	+	0.943714i	$0.607306\pi$
$854$	−16018.4	−0.641849
$855$	8161.92	0.326470
$856$	83582.1	3.33736
$857$	−45445.2	−1.81141	−0.905704	−	0.423910i	$-0.860657\pi$
$857$	−45445.2	−1.81141	−0.905704	+	0.423910i	$0.860657\pi$
$858$	0	0
$859$	−28243.1	−1.12182	−0.560909	−	0.827877i	$-0.689548\pi$
$859$	−28243.1	−1.12182	−0.560909	+	0.827877i	$0.689548\pi$
$860$	−126734.	−5.02512
$861$	−271.602	−0.0107505
$862$	69082.5	2.72965
$863$	328.319	0.0129503	0.00647514	−	0.999979i	$-0.497939\pi$
$863$	328.319	0.0129503	0.00647514	+	0.999979i	$0.497939\pi$
$864$	3461.59	0.136303
$865$	18342.1	0.720982
$866$	−50466.4	−1.98027
$867$	−13119.6	−0.513917
$868$	−10172.7	−0.397793
$869$	−8556.40	−0.334011
$870$	697.510	0.0271814
$871$	0	0
$872$	−46139.1	−1.79182
$873$	10034.3	0.389015
$874$	−32299.1	−1.25004
$875$	−48017.0	−1.85517
$876$	−3462.54	−0.133549
$877$	−42480.0	−1.63563	−0.817815	−	0.575482i	$-0.804815\pi$
$877$	−42480.0	−1.63563	−0.817815	+	0.575482i	$0.804815\pi$
$878$	22639.6	0.870216
$879$	14868.6	0.570542
$880$	−54763.3	−2.09781
$881$	−5220.95	−0.199657	−0.0998287	−	0.995005i	$-0.531829\pi$
$881$	−5220.95	−0.199657	−0.0998287	+	0.995005i	$0.531829\pi$
$882$	−4766.97	−0.181987
$883$	11790.3	0.449349	0.224674	−	0.974434i	$-0.427868\pi$
$883$	11790.3	0.449349	0.224674	+	0.974434i	$0.427868\pi$
$884$	0	0
$885$	32782.6	1.24517
$886$	10269.1	0.389387
$887$	−49352.3	−1.86819	−0.934097	−	0.357019i	$-0.883793\pi$
$887$	−49352.3	−1.86819	−0.934097	+	0.357019i	$0.883793\pi$
$888$	−44917.6	−1.69745
$889$	−19024.4	−0.717724
$890$	−65093.8	−2.45163
$891$	−2181.91	−0.0820391
$892$	−40823.9	−1.53238
$893$	9455.33	0.354323
$894$	−14626.3	−0.547177
$895$	54125.5	2.02147
$896$	28402.7	1.05900
$897$	0	0
$898$	−18040.1	−0.670386
$899$	86.5281	0.00321009
$900$	43942.8	1.62751
$901$	6433.02	0.237863
$902$	−797.536	−0.0294402
$903$	16703.7	0.615574
$904$	91168.1	3.35421
$905$	96037.3	3.52750
$906$	−22145.4	−0.812066
$907$	6088.94	0.222910	0.111455	−	0.993769i	$-0.464449\pi$
$907$	6088.94	0.222910	0.111455	+	0.993769i	$0.464449\pi$
$908$	57243.7	2.09218
$909$	14309.2	0.522118
$910$	0	0
$911$	−30301.7	−1.10202	−0.551010	−	0.834499i	$-0.685757\pi$
$911$	−30301.7	−1.10202	−0.551010	+	0.834499i	$0.685757\pi$
$912$	13666.7	0.496218
$913$	3810.28	0.138118
$914$	−40658.6	−1.47141
$915$	12419.8	0.448726
$916$	19964.5	0.720139
$917$	19669.0	0.708317
$918$	3164.97	0.113790
$919$	34695.8	1.24538	0.622692	−	0.782467i	$-0.286039\pi$
$919$	34695.8	1.24538	0.622692	+	0.782467i	$0.286039\pi$
$920$	−136295.	−4.88424
$921$	11684.7	0.418050
$922$	−58991.2	−2.10713
$923$	0	0
$924$	21763.0	0.774837
$925$	−87783.9	−3.12034
$926$	−8740.61	−0.310188
$927$	4747.52	0.168208
$928$	293.681	0.0103885
$929$	16990.8	0.600054	0.300027	−	0.953931i	$-0.403004\pi$
$929$	16990.8	0.600054	0.300027	+	0.953931i	$0.403004\pi$
$930$	11502.1	0.405559
$931$	−4732.44	−0.166594
$932$	−73980.4	−2.60012
$933$	9292.32	0.326063
$934$	54338.0	1.90363
$935$	−12590.3	−0.440372
$936$	0	0
$937$	9307.86	0.324519	0.162260	−	0.986748i	$-0.448122\pi$
$937$	9307.86	0.324519	0.162260	+	0.986748i	$0.448122\pi$
$938$	38342.0	1.33466
$939$	13462.1	0.467858
$940$	73656.0	2.55574
$941$	−52285.3	−1.81132	−0.905659	−	0.424006i	$-0.860623\pi$
$941$	−52285.3	−1.81132	−0.905659	+	0.424006i	$0.860623\pi$
$942$	−999.624	−0.0345749
$943$	−833.344	−0.0287777
$944$	54892.8	1.89260
$945$	−8379.96	−0.288466
$946$	49048.9	1.68575
$947$	−12348.5	−0.423731	−0.211865	−	0.977299i	$-0.567954\pi$
$947$	−12348.5	−0.423731	−0.211865	+	0.977299i	$0.567954\pi$
$948$	16634.0	0.569882
$949$	0	0
$950$	63617.7	2.17267
$951$	−20461.8	−0.697709
$952$	−17100.5	−0.582174
$953$	−25631.0	−0.871218	−0.435609	−	0.900136i	$-0.643467\pi$
$953$	−25631.0	−0.871218	−0.435609	+	0.900136i	$0.643467\pi$
$954$	12572.9	0.426692
$955$	−41391.0	−1.40249
$956$	−57778.9	−1.95471
$957$	−185.114	−0.00625274
$958$	−39917.1	−1.34620
$959$	31339.0	1.05525
$960$	−9753.03	−0.327893
$961$	−28364.1	−0.952104
$962$	0	0
$963$	15767.7	0.527629
$964$	99547.7	3.32595
$965$	−14683.1	−0.489811
$966$	33161.9	1.10452
$967$	11185.6	0.371981	0.185991	−	0.982552i	$-0.440451\pi$
$967$	11185.6	0.371981	0.185991	+	0.982552i	$0.440451\pi$
$968$	−28881.6	−0.958977
$969$	3142.05	0.104166
$970$	113164.	3.74586
$971$	−23541.3	−0.778039	−0.389019	−	0.921230i	$-0.627186\pi$
$971$	−23541.3	−0.778039	−0.389019	+	0.921230i	$0.627186\pi$
$972$	4241.74	0.139973
$973$	22303.6	0.734860
$974$	55321.3	1.81993
$975$	0	0
$976$	20796.3	0.682041
$977$	−24198.8	−0.792415	−0.396207	−	0.918161i	$-0.629674\pi$
$977$	−24198.8	−0.792415	−0.396207	+	0.918161i	$0.629674\pi$
$978$	−53358.4	−1.74459
$979$	17275.4	0.563966
$980$	−36865.2	−1.20165
$981$	−8704.10	−0.283283
$982$	−46111.5	−1.49845
$983$	33757.4	1.09532	0.547658	−	0.836702i	$-0.315520\pi$
$983$	33757.4	1.09532	0.547658	+	0.836702i	$0.315520\pi$
$984$	839.874	0.0272096
$985$	34222.0	1.10701
$986$	268.516	0.00867272
$987$	−9707.93	−0.313077
$988$	0	0
$989$	51251.1	1.64782
$990$	−24607.0	−0.789963
$991$	25298.5	0.810933	0.405466	−	0.914110i	$-0.367109\pi$
$991$	25298.5	0.810933	0.405466	+	0.914110i	$0.367109\pi$
$992$	4842.89	0.155002
$993$	−15038.9	−0.480608
$994$	64362.2	2.05377
$995$	−37033.7	−1.17995
$996$	−7407.36	−0.235654
$997$	−28766.1	−0.913773	−0.456886	−	0.889525i	$-0.651035\pi$
$997$	−28766.1	−0.913773	−0.456886	+	0.889525i	$0.651035\pi$
$998$	63458.2	2.01276
$999$	−8473.67	−0.268363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.r.1.9		10
3.2	odd	2		1521.4.a.bk.1.2		10
13.2	odd	12		39.4.j.c.4.5	✓	10
13.5	odd	4		507.4.b.i.337.2		10
13.7	odd	12		39.4.j.c.10.5	yes	10
13.8	odd	4		507.4.b.i.337.9		10
13.12	even	2	inner	507.4.a.r.1.2		10
39.2	even	12		117.4.q.e.82.1		10
39.20	even	12		117.4.q.e.10.1		10
39.38	odd	2		1521.4.a.bk.1.9		10
52.7	even	12		624.4.bv.h.49.5		10
52.15	even	12		624.4.bv.h.433.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.5	✓	10	13.2	odd	12
39.4.j.c.10.5	yes	10	13.7	odd	12
117.4.q.e.10.1		10	39.20	even	12
117.4.q.e.82.1		10	39.2	even	12
507.4.a.r.1.2		10	13.12	even	2	inner
507.4.a.r.1.9		10	1.1	even	1	trivial
507.4.b.i.337.2		10	13.5	odd	4
507.4.b.i.337.9		10	13.8	odd	4
624.4.bv.h.49.5		10	52.7	even	12
624.4.bv.h.433.1		10	52.15	even	12
1521.4.a.bk.1.2		10	3.2	odd	2
1521.4.a.bk.1.9		10	39.38	odd	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+5.04537 q^{2} +3.00000 q^{3} +17.4557 q^{4} +20.1174 q^{5} +15.1361 q^{6} -15.4279 q^{7} +47.7076 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.04537 q^{2} +3.00000 q^{3} +17.4557 q^{4} +20.1174 q^{5} +15.1361 q^{6} -15.4279 q^{7} +47.7076 q^{8} +9.00000 q^{9} +101.500 q^{10} -26.9372 q^{11} +52.3672 q^{12} -77.8394 q^{14} +60.3522 q^{15} +101.057 q^{16} +23.2334 q^{17} +45.4083 q^{18} +45.0794 q^{19} +351.164 q^{20} -46.2837 q^{21} -135.908 q^{22} -142.010 q^{23} +143.123 q^{24} +279.710 q^{25} +27.0000 q^{27} -269.305 q^{28} +2.29068 q^{29} +304.499 q^{30} +37.7740 q^{31} +128.207 q^{32} -80.8116 q^{33} +117.221 q^{34} -310.369 q^{35} +157.102 q^{36} -313.840 q^{37} +227.442 q^{38} +959.753 q^{40} +5.86820 q^{41} -233.518 q^{42} -360.898 q^{43} -470.209 q^{44} +181.057 q^{45} -716.493 q^{46} +209.748 q^{47} +303.170 q^{48} -104.980 q^{49} +1411.24 q^{50} +69.7003 q^{51} +276.886 q^{53} +136.225 q^{54} -541.906 q^{55} -736.028 q^{56} +135.238 q^{57} +11.5573 q^{58} +543.189 q^{59} +1053.49 q^{60} +205.788 q^{61} +190.583 q^{62} -138.851 q^{63} -161.602 q^{64} -407.724 q^{66} -492.578 q^{67} +405.557 q^{68} -426.030 q^{69} -1565.93 q^{70} -826.859 q^{71} +429.369 q^{72} -66.1205 q^{73} -1583.44 q^{74} +839.129 q^{75} +786.894 q^{76} +415.584 q^{77} +317.642 q^{79} +2033.00 q^{80} +81.0000 q^{81} +29.6072 q^{82} -141.450 q^{83} -807.915 q^{84} +467.396 q^{85} -1820.86 q^{86} +6.87204 q^{87} -1285.11 q^{88} -641.320 q^{89} +913.497 q^{90} -2478.89 q^{92} +113.322 q^{93} +1058.26 q^{94} +906.880 q^{95} +384.621 q^{96} +1114.92 q^{97} -529.663 q^{98} -242.435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) \) 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

Introduction

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