LMFDB - Embedded newform 387.8.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,8,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("387.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	387.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:	$120.893004862$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 $ x^11 - 2x^10 - 977x^9 + 2592x^8 + 344686x^7 - 1160956x^6 - 53409536x^5 + 209758592x^4 + 3410917248x^3 - 14180732672x^2 - 60918607872x + 238240894976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.52766$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.52766 q^{2} -97.4450 q^{4} -304.619 q^{5} +1421.71 q^{7} -1246.18 q^{8} +O(q^{10})$	\(q+5.52766 q^{2} -97.4450 q^{4} -304.619 q^{5} +1421.71 q^{7} -1246.18 q^{8} -1683.83 q^{10} +7143.27 q^{11} -1897.38 q^{13} +7858.73 q^{14} +5584.49 q^{16} -1140.96 q^{17} -16176.5 q^{19} +29683.6 q^{20} +39485.6 q^{22} -91608.2 q^{23} +14667.6 q^{25} -10488.0 q^{26} -138539. q^{28} +229144. q^{29} -212418. q^{31} +190381. q^{32} -6306.85 q^{34} -433079. q^{35} -482724. q^{37} -89418.0 q^{38} +379611. q^{40} +384844. q^{41} +79507.0 q^{43} -696076. q^{44} -506379. q^{46} -380758. q^{47} +1.19772e6 q^{49} +81077.5 q^{50} +184890. q^{52} +361687. q^{53} -2.17598e6 q^{55} -1.77171e6 q^{56} +1.26663e6 q^{58} +1.95582e6 q^{59} -479312. q^{61} -1.17417e6 q^{62} +337544. q^{64} +577976. q^{65} -2.46363e6 q^{67} +111181. q^{68} -2.39392e6 q^{70} +1.56017e6 q^{71} +2.98243e6 q^{73} -2.66833e6 q^{74} +1.57632e6 q^{76} +1.01557e7 q^{77} +2.64376e6 q^{79} -1.70114e6 q^{80} +2.12728e6 q^{82} -5.54958e6 q^{83} +347559. q^{85} +439488. q^{86} -8.90183e6 q^{88} +9.15035e6 q^{89} -2.69752e6 q^{91} +8.92676e6 q^{92} -2.10470e6 q^{94} +4.92766e6 q^{95} +4.33147e6 q^{97} +6.62056e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) $ 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8} - 1333 q^{10} - 1333 q^{11} - 17967 q^{13} + 22352 q^{14} - 34406 q^{16} + 63095 q^{17} - 54524 q^{19} + 280995 q^{20} - 289358 q^{22} + 138139 q^{23} + 3455 q^{25} + 132946 q^{26} - 12704 q^{28} + 308658 q^{29} - 209523 q^{31} + 644934 q^{32} + 762435 q^{34} + 578892 q^{35} - 298472 q^{37} + 369707 q^{38} + 2633173 q^{40} + 1346735 q^{41} + 874577 q^{43} - 3134292 q^{44} + 3588111 q^{46} - 499284 q^{47} + 2544563 q^{49} - 3049745 q^{50} + 983088 q^{52} + 2210495 q^{53} - 1855072 q^{55} + 469976 q^{56} + 4397067 q^{58} + 5824216 q^{59} - 4453034 q^{61} - 1002789 q^{62} + 4757538 q^{64} + 2162872 q^{65} - 6859513 q^{67} + 9397005 q^{68} + 845078 q^{70} + 10726554 q^{71} - 4456898 q^{73} - 1046637 q^{74} + 5861267 q^{76} + 17019816 q^{77} - 15541320 q^{79} + 15680911 q^{80} + 20233655 q^{82} + 11146767 q^{83} - 12471976 q^{85} + 1908168 q^{86} - 24463544 q^{88} + 13531356 q^{89} - 19746448 q^{91} + 26023161 q^{92} + 20288857 q^{94} + 12291624 q^{95} - 10999901 q^{97} - 29909168 q^{98}+O(q^{100}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8 - 1333 * q^10 - 1333 * q^11 - 17967 * q^13 + 22352 * q^14 - 34406 * q^16 + 63095 * q^17 - 54524 * q^19 + 280995 * q^20 - 289358 * q^22 + 138139 * q^23 + 3455 * q^25 + 132946 * q^26 - 12704 * q^28 + 308658 * q^29 - 209523 * q^31 + 644934 * q^32 + 762435 * q^34 + 578892 * q^35 - 298472 * q^37 + 369707 * q^38 + 2633173 * q^40 + 1346735 * q^41 + 874577 * q^43 - 3134292 * q^44 + 3588111 * q^46 - 499284 * q^47 + 2544563 * q^49 - 3049745 * q^50 + 983088 * q^52 + 2210495 * q^53 - 1855072 * q^55 + 469976 * q^56 + 4397067 * q^58 + 5824216 * q^59 - 4453034 * q^61 - 1002789 * q^62 + 4757538 * q^64 + 2162872 * q^65 - 6859513 * q^67 + 9397005 * q^68 + 845078 * q^70 + 10726554 * q^71 - 4456898 * q^73 - 1046637 * q^74 + 5861267 * q^76 + 17019816 * q^77 - 15541320 * q^79 + 15680911 * q^80 + 20233655 * q^82 + 11146767 * q^83 - 12471976 * q^85 + 1908168 * q^86 - 24463544 * q^88 + 13531356 * q^89 - 19746448 * q^91 + 26023161 * q^92 + 20288857 * q^94 + 12291624 * q^95 - 10999901 * q^97 - 29909168 * q^98

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 $

$2$	5.52766	0.488581	0.244290	−	0.969702i	$-0.421445\pi$
$2$	5.52766	0.488581	0.244290	+	0.969702i	$0.421445\pi$
$3$	0	0
$3$	0	0
$4$	−97.4450	−0.761289
$5$	−304.619	−1.08984	−0.544919	−	0.838489i	$-0.683439\pi$
$5$	−304.619	−1.08984	−0.544919	+	0.838489i	$0.683439\pi$
$6$	0	0
$7$	1421.71	1.56663	0.783317	−	0.621622i	$-0.213526\pi$
$7$	1421.71	1.56663	0.783317	+	0.621622i	$0.213526\pi$
$8$	−1246.18	−0.860532
$9$	0	0
$10$	−1683.83	−0.532473
$11$	7143.27	1.61817	0.809083	−	0.587695i	$-0.199964\pi$
$11$	7143.27	1.61817	0.809083	+	0.587695i	$0.199964\pi$
$12$	0	0
$13$	−1897.38	−0.239525	−0.119763	−	0.992803i	$-0.538213\pi$
$13$	−1897.38	−0.239525	−0.119763	+	0.992803i	$0.538213\pi$
$14$	7858.73	0.765427
$15$	0	0
$16$	5584.49	0.340850
$17$	−1140.96	−0.0563249	−0.0281624	−	0.999603i	$-0.508966\pi$
$17$	−1140.96	−0.0563249	−0.0281624	+	0.999603i	$0.508966\pi$
$18$	0	0
$19$	−16176.5	−0.541061	−0.270531	−	0.962711i	$-0.587199\pi$
$19$	−16176.5	−0.541061	−0.270531	+	0.962711i	$0.587199\pi$
$20$	29683.6	0.829681
$21$	0	0
$22$	39485.6	0.790604
$23$	−91608.2	−1.56995	−0.784977	−	0.619525i	$-0.787325\pi$
$23$	−91608.2	−1.56995	−0.784977	+	0.619525i	$0.787325\pi$
$24$	0	0
$25$	14667.6	0.187745
$26$	−10488.0	−0.117027
$27$	0	0
$28$	−138539.	−1.19266
$29$	229144.	1.74468	0.872341	−	0.488898i	$-0.162601\pi$
$29$	229144.	1.74468	0.872341	+	0.488898i	$0.162601\pi$
$30$	0	0
$31$	−212418.	−1.28064	−0.640318	−	0.768110i	$-0.721197\pi$
$31$	−212418.	−1.28064	−0.640318	+	0.768110i	$0.721197\pi$
$32$	190381.	1.02706
$33$	0	0
$34$	−6306.85	−0.0275192
$35$	−433079.	−1.70738
$36$	0	0
$37$	−482724.	−1.56672	−0.783362	−	0.621566i	$-0.786497\pi$
$37$	−482724.	−1.56672	−0.783362	+	0.621566i	$0.786497\pi$
$38$	−89418.0	−0.264352
$39$	0	0
$40$	379611.	0.937839
$41$	384844.	0.872049	0.436025	−	0.899935i	$-0.356386\pi$
$41$	384844.	0.872049	0.436025	+	0.899935i	$0.356386\pi$
$42$	0	0
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	−696076.	−1.23189
$45$	0	0
$46$	−506379.	−0.767049
$47$	−380758.	−0.534941	−0.267471	−	0.963566i	$-0.586188\pi$
$47$	−380758.	−0.534941	−0.267471	+	0.963566i	$0.586188\pi$
$48$	0	0
$49$	1.19772e6	1.45435
$50$	81077.5	0.0917287
$51$	0	0
$52$	184890.	0.182348
$53$	361687.	0.333709	0.166854	−	0.985982i	$-0.446639\pi$
$53$	361687.	0.333709	0.166854	+	0.985982i	$0.446639\pi$
$54$	0	0
$55$	−2.17598e6	−1.76354
$56$	−1.77171e6	−1.34814
$57$	0	0
$58$	1.26663e6	0.852418
$59$	1.95582e6	1.23979	0.619894	−	0.784685i	$-0.287176\pi$
$59$	1.95582e6	1.23979	0.619894	+	0.784685i	$0.287176\pi$
$60$	0	0
$61$	−479312.	−0.270374	−0.135187	−	0.990820i	$-0.543163\pi$
$61$	−479312.	−0.270374	−0.135187	+	0.990820i	$0.543163\pi$
$62$	−1.17417e6	−0.625694
$63$	0	0
$64$	337544.	0.160954
$65$	577976.	0.261044
$66$	0	0
$67$	−2.46363e6	−1.00072	−0.500362	−	0.865816i	$-0.666800\pi$
$67$	−2.46363e6	−1.00072	−0.500362	+	0.865816i	$0.666800\pi$
$68$	111181.	0.0428795
$69$	0	0
$70$	−2.39392e6	−0.834191
$71$	1.56017e6	0.517332	0.258666	−	0.965967i	$-0.416717\pi$
$71$	1.56017e6	0.517332	0.258666	+	0.965967i	$0.416717\pi$
$72$	0	0
$73$	2.98243e6	0.897305	0.448652	−	0.893706i	$-0.351904\pi$
$73$	2.98243e6	0.897305	0.448652	+	0.893706i	$0.351904\pi$
$74$	−2.66833e6	−0.765471
$75$	0	0
$76$	1.57632e6	0.411904
$77$	1.01557e7	2.53507
$78$	0	0
$79$	2.64376e6	0.603292	0.301646	−	0.953420i	$-0.402464\pi$
$79$	2.64376e6	0.603292	0.301646	+	0.953420i	$0.402464\pi$
$80$	−1.70114e6	−0.371471
$81$	0	0
$82$	2.12728e6	0.426066
$83$	−5.54958e6	−1.06534	−0.532668	−	0.846324i	$-0.678810\pi$
$83$	−5.54958e6	−1.06534	−0.532668	+	0.846324i	$0.678810\pi$
$84$	0	0
$85$	347559.	0.0613850
$86$	439488.	0.0745078
$87$	0	0
$88$	−8.90183e6	−1.39248
$89$	9.15035e6	1.37585	0.687927	−	0.725779i	$-0.258521\pi$
$89$	9.15035e6	1.37585	0.687927	+	0.725779i	$0.258521\pi$
$90$	0	0
$91$	−2.69752e6	−0.375249
$92$	8.92676e6	1.19519
$93$	0	0
$94$	−2.10470e6	−0.261362
$95$	4.92766e6	0.589669
$96$	0	0
$97$	4.33147e6	0.481875	0.240937	−	0.970541i	$-0.422545\pi$
$97$	4.33147e6	0.481875	0.240937	+	0.970541i	$0.422545\pi$
$98$	6.62056e6	0.710565
$99$	0	0
$100$	−1.42928e6	−0.142928
$101$	5.03114e6	0.485894	0.242947	−	0.970040i	$-0.421886\pi$
$101$	5.03114e6	0.485894	0.242947	+	0.970040i	$0.421886\pi$
$102$	0	0
$103$	1.58973e7	1.43348	0.716741	−	0.697339i	$-0.245633\pi$
$103$	1.58973e7	1.43348	0.716741	+	0.697339i	$0.245633\pi$
$104$	2.36448e6	0.206119
$105$	0	0
$106$	1.99928e6	0.163044
$107$	1.56322e7	1.23361	0.616805	−	0.787116i	$-0.288427\pi$
$107$	1.56322e7	1.23361	0.616805	+	0.787116i	$0.288427\pi$
$108$	0	0
$109$	1.27583e7	0.943624	0.471812	−	0.881699i	$-0.343600\pi$
$109$	1.27583e7	0.943624	0.471812	+	0.881699i	$0.343600\pi$
$110$	−1.20280e7	−0.861630
$111$	0	0
$112$	7.93952e6	0.533987
$113$	1.58622e7	1.03416	0.517081	−	0.855937i	$-0.327019\pi$
$113$	1.58622e7	1.03416	0.517081	+	0.855937i	$0.327019\pi$
$114$	0	0
$115$	2.79056e7	1.71099
$116$	−2.23290e7	−1.32821
$117$	0	0
$118$	1.08111e7	0.605737
$119$	−1.62212e6	−0.0882405
$120$	0	0
$121$	3.15392e7	1.61846
$122$	−2.64948e6	−0.132099
$123$	0	0
$124$	2.06991e7	0.974934
$125$	1.93303e7	0.885225
$126$	0	0
$127$	−2.44940e7	−1.06108	−0.530539	−	0.847660i	$-0.678011\pi$
$127$	−2.44940e7	−1.06108	−0.530539	+	0.847660i	$0.678011\pi$
$128$	−2.25029e7	−0.948425
$129$	0	0
$130$	3.19486e6	0.127541
$131$	−3.59703e7	−1.39796	−0.698979	−	0.715142i	$-0.746362\pi$
$131$	−3.59703e7	−1.39796	−0.698979	+	0.715142i	$0.746362\pi$
$132$	0	0
$133$	−2.29983e7	−0.847645
$134$	−1.36181e7	−0.488934
$135$	0	0
$136$	1.42185e6	0.0484693
$137$	1.88193e7	0.625289	0.312644	−	0.949870i	$-0.398785\pi$
$137$	1.88193e7	0.625289	0.312644	+	0.949870i	$0.398785\pi$
$138$	0	0
$139$	−3.72014e7	−1.17492	−0.587459	−	0.809254i	$-0.699872\pi$
$139$	−3.72014e7	−1.17492	−0.587459	+	0.809254i	$0.699872\pi$
$140$	4.22014e7	1.29981
$141$	0	0
$142$	8.62411e6	0.252758
$143$	−1.35535e7	−0.387592
$144$	0	0
$145$	−6.98017e7	−1.90142
$146$	1.64858e7	0.438406
$147$	0	0
$148$	4.70390e7	1.19273
$149$	4.39692e7	1.08892	0.544461	−	0.838786i	$-0.316734\pi$
$149$	4.39692e7	1.08892	0.544461	+	0.838786i	$0.316734\pi$
$150$	0	0
$151$	−3.09651e7	−0.731902	−0.365951	−	0.930634i	$-0.619256\pi$
$151$	−3.09651e7	−0.731902	−0.365951	+	0.930634i	$0.619256\pi$
$152$	2.01588e7	0.465600
$153$	0	0
$154$	5.61370e7	1.23859
$155$	6.47065e7	1.39568
$156$	0	0
$157$	−1.67885e6	−0.0346228	−0.0173114	−	0.999850i	$-0.505511\pi$
$157$	−1.67885e6	−0.0346228	−0.0173114	+	0.999850i	$0.505511\pi$
$158$	1.46138e7	0.294757
$159$	0	0
$160$	−5.79935e7	−1.11933
$161$	−1.30240e8	−2.45954
$162$	0	0
$163$	8.30485e6	0.150202	0.0751009	−	0.997176i	$-0.476072\pi$
$163$	8.30485e6	0.150202	0.0751009	+	0.997176i	$0.476072\pi$
$164$	−3.75011e7	−0.663881
$165$	0	0
$166$	−3.06762e7	−0.520502
$167$	−4.62254e7	−0.768021	−0.384010	−	0.923329i	$-0.625457\pi$
$167$	−4.62254e7	−0.768021	−0.384010	+	0.923329i	$0.625457\pi$
$168$	0	0
$169$	−5.91485e7	−0.942628
$170$	1.92119e6	0.0299915
$171$	0	0
$172$	−7.74756e6	−0.116095
$173$	4.56672e7	0.670568	0.335284	−	0.942117i	$-0.391168\pi$
$173$	4.56672e7	0.670568	0.335284	+	0.942117i	$0.391168\pi$
$174$	0	0
$175$	2.08531e7	0.294128
$176$	3.98915e7	0.551552
$177$	0	0
$178$	5.05800e7	0.672216
$179$	−7.68660e7	−1.00173	−0.500863	−	0.865527i	$-0.666984\pi$
$179$	−7.68660e7	−1.00173	−0.500863	+	0.865527i	$0.666984\pi$
$180$	0	0
$181$	7.38362e7	0.925538	0.462769	−	0.886479i	$-0.346856\pi$
$181$	7.38362e7	0.925538	0.462769	+	0.886479i	$0.346856\pi$
$182$	−1.49110e7	−0.183339
$183$	0	0
$184$	1.14161e8	1.35100
$185$	1.47047e8	1.70747
$186$	0	0
$187$	−8.15021e6	−0.0911430
$188$	3.71029e7	0.407245
$189$	0	0
$190$	2.72384e7	0.288101
$191$	4.61537e7	0.479280	0.239640	−	0.970862i	$-0.422971\pi$
$191$	4.61537e7	0.479280	0.239640	+	0.970862i	$0.422971\pi$
$192$	0	0
$193$	1.04470e8	1.04603	0.523013	−	0.852325i	$-0.324808\pi$
$193$	1.04470e8	1.04603	0.523013	+	0.852325i	$0.324808\pi$
$194$	2.39429e7	0.235435
$195$	0	0
$196$	−1.16711e8	−1.10718
$197$	−3.24556e7	−0.302453	−0.151226	−	0.988499i	$-0.548322\pi$
$197$	−3.24556e7	−0.302453	−0.151226	+	0.988499i	$0.548322\pi$
$198$	0	0
$199$	1.90706e8	1.71545	0.857725	−	0.514109i	$-0.171877\pi$
$199$	1.90706e8	1.71545	0.857725	+	0.514109i	$0.171877\pi$
$200$	−1.82785e7	−0.161561
$201$	0	0
$202$	2.78104e7	0.237398
$203$	3.25777e8	2.73328
$204$	0	0
$205$	−1.17231e8	−0.950392
$206$	8.78747e7	0.700372
$207$	0	0
$208$	−1.05959e7	−0.0816422
$209$	−1.15553e8	−0.875526
$210$	0	0
$211$	−4.93604e6	−0.0361735	−0.0180867	−	0.999836i	$-0.505758\pi$
$211$	−4.93604e6	−0.0361735	−0.0180867	+	0.999836i	$0.505758\pi$
$212$	−3.52446e7	−0.254049
$213$	0	0
$214$	8.64097e7	0.602718
$215$	−2.42193e7	−0.166199
$216$	0	0
$217$	−3.01997e8	−2.00629
$218$	7.05233e7	0.461036
$219$	0	0
$220$	2.12038e8	1.34256
$221$	2.16484e6	0.0134912
$222$	0	0
$223$	2.77562e8	1.67608	0.838038	−	0.545612i	$-0.183703\pi$
$223$	2.77562e8	1.67608	0.838038	+	0.545612i	$0.183703\pi$
$224$	2.70666e8	1.60903
$225$	0	0
$226$	8.76807e7	0.505271
$227$	1.27335e8	0.722535	0.361267	−	0.932462i	$-0.382344\pi$
$227$	1.27335e8	0.722535	0.361267	+	0.932462i	$0.382344\pi$
$228$	0	0
$229$	1.66075e8	0.913861	0.456931	−	0.889502i	$-0.348949\pi$
$229$	1.66075e8	0.913861	0.456931	+	0.889502i	$0.348949\pi$
$230$	1.54252e8	0.835959
$231$	0	0
$232$	−2.85556e8	−1.50135
$233$	1.97183e8	1.02123	0.510616	−	0.859809i	$-0.329417\pi$
$233$	1.97183e8	1.02123	0.510616	+	0.859809i	$0.329417\pi$
$234$	0	0
$235$	1.15986e8	0.582999
$236$	−1.90585e8	−0.943837
$237$	0	0
$238$	−8.96652e6	−0.0431126
$239$	−7.22966e7	−0.342551	−0.171275	−	0.985223i	$-0.554789\pi$
$239$	−7.22966e7	−0.342551	−0.171275	+	0.985223i	$0.554789\pi$
$240$	0	0
$241$	−3.09906e8	−1.42617	−0.713084	−	0.701079i	$-0.752702\pi$
$241$	−3.09906e8	−1.42617	−0.713084	+	0.701079i	$0.752702\pi$
$242$	1.74338e8	0.790748
$243$	0	0
$244$	4.67066e7	0.205832
$245$	−3.64847e8	−1.58500
$246$	0	0
$247$	3.06929e7	0.129598
$248$	2.64712e8	1.10203
$249$	0	0
$250$	1.06851e8	0.432504
$251$	−1.11482e8	−0.444988	−0.222494	−	0.974934i	$-0.571420\pi$
$251$	−1.11482e8	−0.444988	−0.222494	+	0.974934i	$0.571420\pi$
$252$	0	0
$253$	−6.54383e8	−2.54045
$254$	−1.35395e8	−0.518422
$255$	0	0
$256$	−1.67594e8	−0.624336
$257$	−8.26622e7	−0.303767	−0.151884	−	0.988398i	$-0.548534\pi$
$257$	−8.26622e7	−0.303767	−0.151884	+	0.988398i	$0.548534\pi$
$258$	0	0
$259$	−6.86293e8	−2.45448
$260$	−5.63209e7	−0.198730
$261$	0	0
$262$	−1.98831e8	−0.683015
$263$	2.74508e8	0.930486	0.465243	−	0.885183i	$-0.345967\pi$
$263$	2.74508e8	0.930486	0.465243	+	0.885183i	$0.345967\pi$
$264$	0	0
$265$	−1.10177e8	−0.363688
$266$	−1.27126e8	−0.414143
$267$	0	0
$268$	2.40069e8	0.761840
$269$	9.06481e7	0.283940	0.141970	−	0.989871i	$-0.454656\pi$
$269$	9.06481e7	0.283940	0.141970	+	0.989871i	$0.454656\pi$
$270$	0	0
$271$	2.46059e8	0.751011	0.375505	−	0.926820i	$-0.377469\pi$
$271$	2.46059e8	0.751011	0.375505	+	0.926820i	$0.377469\pi$
$272$	−6.37169e6	−0.0191983
$273$	0	0
$274$	1.04026e8	0.305504
$275$	1.04775e8	0.303803
$276$	0	0
$277$	6.60621e8	1.86755	0.933777	−	0.357857i	$-0.116492\pi$
$277$	6.60621e8	1.86755	0.933777	+	0.357857i	$0.116492\pi$
$278$	−2.05637e8	−0.574042
$279$	0	0
$280$	5.39696e8	1.46925
$281$	−2.01108e7	−0.0540700	−0.0270350	−	0.999634i	$-0.508607\pi$
$281$	−2.01108e7	−0.0540700	−0.0270350	+	0.999634i	$0.508607\pi$
$282$	0	0
$283$	2.51117e8	0.658602	0.329301	−	0.944225i	$-0.393187\pi$
$283$	2.51117e8	0.658602	0.329301	+	0.944225i	$0.393187\pi$
$284$	−1.52031e8	−0.393839
$285$	0	0
$286$	−7.49190e7	−0.189370
$287$	5.47136e8	1.36618
$288$	0	0
$289$	−4.09037e8	−0.996828
$290$	−3.85840e8	−0.928997
$291$	0	0
$292$	−2.90623e8	−0.683108
$293$	3.74733e8	0.870333	0.435166	−	0.900350i	$-0.356690\pi$
$293$	3.74733e8	0.870333	0.435166	+	0.900350i	$0.356690\pi$
$294$	0	0
$295$	−5.95780e8	−1.35117
$296$	6.01562e8	1.34822
$297$	0	0
$298$	2.43047e8	0.532027
$299$	1.73815e8	0.376044
$300$	0	0
$301$	1.13036e8	0.238910
$302$	−1.71164e8	−0.357593
$303$	0	0
$304$	−9.03373e7	−0.184421
$305$	1.46008e8	0.294663
$306$	0	0
$307$	3.69155e8	0.728156	0.364078	−	0.931369i	$-0.381384\pi$
$307$	3.69155e8	0.728156	0.364078	+	0.931369i	$0.381384\pi$
$308$	−9.89619e8	−1.92992
$309$	0	0
$310$	3.57676e8	0.681904
$311$	7.67471e8	1.44677	0.723387	−	0.690443i	$-0.242584\pi$
$311$	7.67471e8	1.44677	0.723387	+	0.690443i	$0.242584\pi$
$312$	0	0
$313$	3.94815e8	0.727761	0.363881	−	0.931446i	$-0.381452\pi$
$313$	3.94815e8	0.727761	0.363881	+	0.931446i	$0.381452\pi$
$314$	−9.28008e6	−0.0169160
$315$	0	0
$316$	−2.57621e8	−0.459279
$317$	−5.25976e8	−0.927381	−0.463691	−	0.885997i	$-0.653475\pi$
$317$	−5.25976e8	−0.927381	−0.463691	+	0.885997i	$0.653475\pi$
$318$	0	0
$319$	1.63684e9	2.82318
$320$	−1.02822e8	−0.175413
$321$	0	0
$322$	−7.19924e8	−1.20169
$323$	1.84568e7	0.0304752
$324$	0	0
$325$	−2.78299e7	−0.0449698
$326$	4.59064e7	0.0733857
$327$	0	0
$328$	−4.79586e8	−0.750426
$329$	−5.41327e8	−0.838058
$330$	0	0
$331$	1.17755e9	1.78477	0.892386	−	0.451273i	$-0.149030\pi$
$331$	1.17755e9	1.78477	0.892386	+	0.451273i	$0.149030\pi$
$332$	5.40778e8	0.811028
$333$	0	0
$334$	−2.55518e8	−0.375240
$335$	7.50469e8	1.09063
$336$	0	0
$337$	−4.76656e8	−0.678423	−0.339212	−	0.940710i	$-0.610160\pi$
$337$	−4.76656e8	−0.678423	−0.339212	+	0.940710i	$0.610160\pi$
$338$	−3.26953e8	−0.460550
$339$	0	0
$340$	−3.38679e7	−0.0467317
$341$	−1.51736e9	−2.07228
$342$	0	0
$343$	5.31965e8	0.711793
$344$	−9.90803e7	−0.131230
$345$	0	0
$346$	2.52433e8	0.327626
$347$	−1.08505e8	−0.139411	−0.0697057	−	0.997568i	$-0.522206\pi$
$347$	−1.08505e8	−0.139411	−0.0697057	+	0.997568i	$0.522206\pi$
$348$	0	0
$349$	−7.46559e8	−0.940102	−0.470051	−	0.882639i	$-0.655765\pi$
$349$	−7.46559e8	−0.940102	−0.470051	+	0.882639i	$0.655765\pi$
$350$	1.15269e8	0.143705
$351$	0	0
$352$	1.35994e9	1.66196
$353$	4.13749e8	0.500640	0.250320	−	0.968163i	$-0.419464\pi$
$353$	4.13749e8	0.500640	0.250320	+	0.968163i	$0.419464\pi$
$354$	0	0
$355$	−4.75259e8	−0.563807
$356$	−8.91656e8	−1.04742
$357$	0	0
$358$	−4.24889e8	−0.489424
$359$	1.58431e8	0.180721	0.0903607	−	0.995909i	$-0.471198\pi$
$359$	1.58431e8	0.180721	0.0903607	+	0.995909i	$0.471198\pi$
$360$	0	0
$361$	−6.32193e8	−0.707253
$362$	4.08141e8	0.452200
$363$	0	0
$364$	2.62860e8	0.285673
$365$	−9.08504e8	−0.977916
$366$	0	0
$367$	5.61609e7	0.0593065	0.0296533	−	0.999560i	$-0.490560\pi$
$367$	5.61609e7	0.0593065	0.0296533	+	0.999560i	$0.490560\pi$
$368$	−5.11585e8	−0.535119
$369$	0	0
$370$	8.12824e8	0.834239
$371$	5.14214e8	0.522800
$372$	0	0
$373$	1.21691e9	1.21416	0.607080	−	0.794641i	$-0.292341\pi$
$373$	1.21691e9	1.21416	0.607080	+	0.794641i	$0.292341\pi$
$374$	−4.50516e7	−0.0445307
$375$	0	0
$376$	4.74494e8	0.460334
$377$	−4.34773e8	−0.417896
$378$	0	0
$379$	−1.99936e9	−1.88649	−0.943245	−	0.332098i	$-0.892244\pi$
$379$	−1.99936e9	−1.88649	−0.943245	+	0.332098i	$0.892244\pi$
$380$	−4.80176e8	−0.448908
$381$	0	0
$382$	2.55122e8	0.234167
$383$	7.65586e8	0.696303	0.348151	−	0.937438i	$-0.386809\pi$
$383$	7.65586e8	0.696303	0.348151	+	0.937438i	$0.386809\pi$
$384$	0	0
$385$	−3.09361e9	−2.76282
$386$	5.77476e8	0.511068
$387$	0	0
$388$	−4.22080e8	−0.366846
$389$	6.56361e8	0.565352	0.282676	−	0.959215i	$-0.408778\pi$
$389$	6.56361e8	0.565352	0.282676	+	0.959215i	$0.408778\pi$
$390$	0	0
$391$	1.04522e8	0.0884275
$392$	−1.49257e9	−1.25151
$393$	0	0
$394$	−1.79403e8	−0.147773
$395$	−8.05339e8	−0.657490
$396$	0	0
$397$	9.12150e8	0.731644	0.365822	−	0.930685i	$-0.380788\pi$
$397$	9.12150e8	0.731644	0.365822	+	0.930685i	$0.380788\pi$
$398$	1.05416e9	0.838136
$399$	0	0
$400$	8.19110e7	0.0639930
$401$	1.15178e8	0.0891997	0.0445999	−	0.999005i	$-0.485799\pi$
$401$	1.15178e8	0.0891997	0.0445999	+	0.999005i	$0.485799\pi$
$402$	0	0
$403$	4.03037e8	0.306745
$404$	−4.90259e8	−0.369906
$405$	0	0
$406$	1.80078e9	1.33543
$407$	−3.44823e9	−2.53522
$408$	0	0
$409$	−8.39721e8	−0.606881	−0.303440	−	0.952850i	$-0.598135\pi$
$409$	−8.39721e8	−0.606881	−0.303440	+	0.952850i	$0.598135\pi$
$410$	−6.48011e8	−0.464343
$411$	0	0
$412$	−1.54911e9	−1.09129
$413$	2.78061e9	1.94230
$414$	0	0
$415$	1.69051e9	1.16104
$416$	−3.61223e8	−0.246008
$417$	0	0
$418$	−6.38738e8	−0.427765
$419$	−9.18009e8	−0.609674	−0.304837	−	0.952404i	$-0.598602\pi$
$419$	−9.18009e8	−0.609674	−0.304837	+	0.952404i	$0.598602\pi$
$420$	0	0
$421$	9.86735e7	0.0644486	0.0322243	−	0.999481i	$-0.489741\pi$
$421$	9.86735e7	0.0644486	0.0322243	+	0.999481i	$0.489741\pi$
$422$	−2.72847e7	−0.0176737
$423$	0	0
$424$	−4.50728e8	−0.287167
$425$	−1.67352e7	−0.0105747
$426$	0	0
$427$	−6.81443e8	−0.423577
$428$	−1.52328e9	−0.939134
$429$	0	0
$430$	−1.33876e8	−0.0812014
$431$	−2.42488e9	−1.45888	−0.729440	−	0.684045i	$-0.760219\pi$
$431$	−2.42488e9	−1.45888	−0.729440	+	0.684045i	$0.760219\pi$
$432$	0	0
$433$	1.63675e9	0.968888	0.484444	−	0.874822i	$-0.339022\pi$
$433$	1.63675e9	0.968888	0.484444	+	0.874822i	$0.339022\pi$
$434$	−1.66934e9	−0.980233
$435$	0	0
$436$	−1.24323e9	−0.718370
$437$	1.48190e9	0.849441
$438$	0	0
$439$	−1.40300e9	−0.791465	−0.395733	−	0.918366i	$-0.629509\pi$
$439$	−1.40300e9	−0.791465	−0.395733	+	0.918366i	$0.629509\pi$
$440$	2.71166e9	1.51758
$441$	0	0
$442$	1.19665e7	0.00659156
$443$	−4.39909e8	−0.240409	−0.120204	−	0.992749i	$-0.538355\pi$
$443$	−4.39909e8	−0.240409	−0.120204	+	0.992749i	$0.538355\pi$
$444$	0	0
$445$	−2.78737e9	−1.49946
$446$	1.53427e9	0.818898
$447$	0	0
$448$	4.79890e8	0.252156
$449$	−2.11015e9	−1.10015	−0.550073	−	0.835116i	$-0.685400\pi$
$449$	−2.11015e9	−1.10015	−0.550073	+	0.835116i	$0.685400\pi$
$450$	0	0
$451$	2.74904e9	1.41112
$452$	−1.54569e9	−0.787295
$453$	0	0
$454$	7.03866e8	0.353016
$455$	8.21715e8	0.408960
$456$	0	0
$457$	−2.13547e9	−1.04661	−0.523307	−	0.852144i	$-0.675302\pi$
$457$	−2.13547e9	−1.04661	−0.523307	+	0.852144i	$0.675302\pi$
$458$	9.18006e8	0.446495
$459$	0	0
$460$	−2.71926e9	−1.30256
$461$	−7.44367e8	−0.353862	−0.176931	−	0.984223i	$-0.556617\pi$
$461$	−7.44367e8	−0.353862	−0.176931	+	0.984223i	$0.556617\pi$
$462$	0	0
$463$	1.70021e9	0.796105	0.398052	−	0.917363i	$-0.369686\pi$
$463$	1.70021e9	0.796105	0.398052	+	0.917363i	$0.369686\pi$
$464$	1.27965e9	0.594675
$465$	0	0
$466$	1.08996e9	0.498954
$467$	3.93170e9	1.78637	0.893185	−	0.449689i	$-0.148465\pi$
$467$	3.93170e9	1.78637	0.893185	+	0.449689i	$0.148465\pi$
$468$	0	0
$469$	−3.50257e9	−1.56777
$470$	6.41131e8	0.284842
$471$	0	0
$472$	−2.43731e9	−1.06688
$473$	5.67940e8	0.246768
$474$	0	0
$475$	−2.37270e8	−0.101582
$476$	1.58067e8	0.0671766
$477$	0	0
$478$	−3.99631e8	−0.167364
$479$	1.45058e9	0.603071	0.301536	−	0.953455i	$-0.402501\pi$
$479$	1.45058e9	0.603071	0.301536	+	0.953455i	$0.402501\pi$
$480$	0	0
$481$	9.15908e8	0.375270
$482$	−1.71305e9	−0.696798
$483$	0	0
$484$	−3.07334e9	−1.23212
$485$	−1.31945e9	−0.525165
$486$	0	0
$487$	4.29131e9	1.68360	0.841800	−	0.539790i	$-0.181496\pi$
$487$	4.29131e9	1.68360	0.841800	+	0.539790i	$0.181496\pi$
$488$	5.97311e8	0.232665
$489$	0	0
$490$	−2.01675e9	−0.774400
$491$	3.50889e8	0.133778	0.0668889	−	0.997760i	$-0.478693\pi$
$491$	3.50889e8	0.133778	0.0668889	+	0.997760i	$0.478693\pi$
$492$	0	0
$493$	−2.61445e8	−0.0982690
$494$	1.69660e8	0.0633190
$495$	0	0
$496$	−1.18625e9	−0.436505
$497$	2.21812e9	0.810470
$498$	0	0
$499$	−3.72276e9	−1.34126	−0.670630	−	0.741792i	$-0.733976\pi$
$499$	−3.72276e9	−1.34126	−0.670630	+	0.741792i	$0.733976\pi$
$500$	−1.88364e9	−0.673912
$501$	0	0
$502$	−6.16236e8	−0.217412
$503$	−5.48803e9	−1.92277	−0.961387	−	0.275199i	$-0.911256\pi$
$503$	−5.48803e9	−1.92277	−0.961387	+	0.275199i	$0.911256\pi$
$504$	0	0
$505$	−1.53258e9	−0.529545
$506$	−3.61720e9	−1.24121
$507$	0	0
$508$	2.38682e9	0.807788
$509$	−3.85451e8	−0.129556	−0.0647778	−	0.997900i	$-0.520634\pi$
$509$	−3.85451e8	−0.129556	−0.0647778	+	0.997900i	$0.520634\pi$
$510$	0	0
$511$	4.24015e9	1.40575
$512$	1.95397e9	0.643387
$513$	0	0
$514$	−4.56928e8	−0.148415
$515$	−4.84261e9	−1.56226
$516$	0	0
$517$	−2.71986e9	−0.865623
$518$	−3.79359e9	−1.19921
$519$	0	0
$520$	−7.20264e8	−0.224636
$521$	3.74846e9	1.16124	0.580618	−	0.814176i	$-0.302811\pi$
$521$	3.74846e9	1.16124	0.580618	+	0.814176i	$0.302811\pi$
$522$	0	0
$523$	2.64980e9	0.809949	0.404974	−	0.914328i	$-0.367280\pi$
$523$	2.64980e9	0.809949	0.404974	+	0.914328i	$0.367280\pi$
$524$	3.50512e9	1.06425
$525$	0	0
$526$	1.51739e9	0.454617
$527$	2.42361e8	0.0721316
$528$	0	0
$529$	4.98724e9	1.46476
$530$	−6.09019e8	−0.177691
$531$	0	0
$532$	2.24106e9	0.645303
$533$	−7.30193e8	−0.208878
$534$	0	0
$535$	−4.76187e9	−1.34443
$536$	3.07014e9	0.861155
$537$	0	0
$538$	5.01072e8	0.138727
$539$	8.55561e9	2.35337
$540$	0	0
$541$	−5.07052e9	−1.37677	−0.688386	−	0.725344i	$-0.741681\pi$
$541$	−5.07052e9	−1.37677	−0.688386	+	0.725344i	$0.741681\pi$
$542$	1.36013e9	0.366929
$543$	0	0
$544$	−2.17217e8	−0.0578493
$545$	−3.88641e9	−1.02840
$546$	0	0
$547$	3.00582e9	0.785249	0.392624	−	0.919699i	$-0.371567\pi$
$547$	3.00582e9	0.785249	0.392624	+	0.919699i	$0.371567\pi$
$548$	−1.83384e9	−0.476026
$549$	0	0
$550$	5.79159e8	0.148432
$551$	−3.70675e9	−0.943980
$552$	0	0
$553$	3.75866e9	0.945138
$554$	3.65169e9	0.912450
$555$	0	0
$556$	3.62509e9	0.894452
$557$	−5.43732e9	−1.33319	−0.666594	−	0.745421i	$-0.732249\pi$
$557$	−5.43732e9	−1.33319	−0.666594	+	0.745421i	$0.732249\pi$
$558$	0	0
$559$	−1.50855e8	−0.0365273
$560$	−2.41853e9	−0.581959
$561$	0	0
$562$	−1.11166e8	−0.0264176
$563$	4.80656e9	1.13516	0.567578	−	0.823320i	$-0.307881\pi$
$563$	4.80656e9	1.13516	0.567578	+	0.823320i	$0.307881\pi$
$564$	0	0
$565$	−4.83192e9	−1.12707
$566$	1.38809e9	0.321780
$567$	0	0
$568$	−1.94426e9	−0.445180
$569$	−7.07656e9	−1.61038	−0.805191	−	0.593015i	$-0.797937\pi$
$569$	−7.07656e9	−1.61038	−0.805191	+	0.593015i	$0.797937\pi$
$570$	0	0
$571$	−3.80378e9	−0.855045	−0.427523	−	0.904005i	$-0.640614\pi$
$571$	−3.80378e9	−0.855045	−0.427523	+	0.904005i	$0.640614\pi$
$572$	1.32072e9	0.295069
$573$	0	0
$574$	3.02438e9	0.667490
$575$	−1.34367e9	−0.294751
$576$	0	0
$577$	−2.81170e8	−0.0609332	−0.0304666	−	0.999536i	$-0.509699\pi$
$577$	−2.81170e8	−0.0609332	−0.0304666	+	0.999536i	$0.509699\pi$
$578$	−2.26102e9	−0.487031
$579$	0	0
$580$	6.80182e9	1.44753
$581$	−7.88989e9	−1.66899
$582$	0	0
$583$	2.58363e9	0.539996
$584$	−3.71665e9	−0.772159
$585$	0	0
$586$	2.07140e9	0.425228
$587$	−8.79495e8	−0.179473	−0.0897367	−	0.995966i	$-0.528603\pi$
$587$	−8.79495e8	−0.179473	−0.0897367	+	0.995966i	$0.528603\pi$
$588$	0	0
$589$	3.43618e9	0.692902
$590$	−3.29327e9	−0.660154
$591$	0	0
$592$	−2.69576e9	−0.534018
$593$	6.78081e8	0.133534	0.0667668	−	0.997769i	$-0.478732\pi$
$593$	6.78081e8	0.133534	0.0667668	+	0.997769i	$0.478732\pi$
$594$	0	0
$595$	4.94128e8	0.0961678
$596$	−4.28458e9	−0.828985
$597$	0	0
$598$	9.60791e8	0.183728
$599$	6.13578e9	1.16648	0.583238	−	0.812301i	$-0.301785\pi$
$599$	6.13578e9	1.16648	0.583238	+	0.812301i	$0.301785\pi$
$600$	0	0
$601$	−4.78315e8	−0.0898780	−0.0449390	−	0.998990i	$-0.514309\pi$
$601$	−4.78315e8	−0.0898780	−0.0449390	+	0.998990i	$0.514309\pi$
$602$	6.24824e8	0.116727
$603$	0	0
$604$	3.01739e9	0.557189
$605$	−9.60743e9	−1.76386
$606$	0	0
$607$	−8.97283e9	−1.62843	−0.814215	−	0.580563i	$-0.802832\pi$
$607$	−8.97283e9	−1.62843	−0.814215	+	0.580563i	$0.802832\pi$
$608$	−3.07969e9	−0.555705
$609$	0	0
$610$	8.07080e8	0.143967
$611$	7.22440e8	0.128132
$612$	0	0
$613$	7.77928e9	1.36404	0.682021	−	0.731333i	$-0.261101\pi$
$613$	7.77928e9	1.36404	0.682021	+	0.731333i	$0.261101\pi$
$614$	2.04056e9	0.355763
$615$	0	0
$616$	−1.26558e10	−2.18151
$617$	8.81774e9	1.51133	0.755665	−	0.654958i	$-0.227314\pi$
$617$	8.81774e9	1.51133	0.755665	+	0.654958i	$0.227314\pi$
$618$	0	0
$619$	−4.50857e9	−0.764050	−0.382025	−	0.924152i	$-0.624773\pi$
$619$	−4.50857e9	−0.764050	−0.382025	+	0.924152i	$0.624773\pi$
$620$	−6.30533e9	−1.06252
$621$	0	0
$622$	4.24232e9	0.706865
$623$	1.30091e10	2.15546
$624$	0	0
$625$	−7.03428e9	−1.15250
$626$	2.18240e9	0.355570
$627$	0	0
$628$	1.63595e8	0.0263579
$629$	5.50770e8	0.0882456
$630$	0	0
$631$	−1.47926e9	−0.234391	−0.117195	−	0.993109i	$-0.537390\pi$
$631$	−1.47926e9	−0.234391	−0.117195	+	0.993109i	$0.537390\pi$
$632$	−3.29461e9	−0.519152
$633$	0	0
$634$	−2.90741e9	−0.453101
$635$	7.46135e9	1.15640
$636$	0	0
$637$	−2.27252e9	−0.348353
$638$	9.04790e9	1.37935
$639$	0	0
$640$	6.85480e9	1.03363
$641$	−6.56349e9	−0.984309	−0.492155	−	0.870508i	$-0.663791\pi$
$641$	−6.56349e9	−0.984309	−0.492155	+	0.870508i	$0.663791\pi$
$642$	0	0
$643$	6.43261e9	0.954221	0.477110	−	0.878843i	$-0.341684\pi$
$643$	6.43261e9	0.954221	0.477110	+	0.878843i	$0.341684\pi$
$644$	1.26913e10	1.87242
$645$	0	0
$646$	1.02023e8	0.0148896
$647$	−1.74903e8	−0.0253882	−0.0126941	−	0.999919i	$-0.504041\pi$
$647$	−1.74903e8	−0.0253882	−0.0126941	+	0.999919i	$0.504041\pi$
$648$	0	0
$649$	1.39710e10	2.00618
$650$	−1.53834e8	−0.0219714
$651$	0	0
$652$	−8.09266e8	−0.114347
$653$	1.10036e10	1.54646	0.773230	−	0.634126i	$-0.218640\pi$
$653$	1.10036e10	1.54646	0.773230	+	0.634126i	$0.218640\pi$
$654$	0	0
$655$	1.09572e10	1.52355
$656$	2.14915e9	0.297238
$657$	0	0
$658$	−2.99227e9	−0.409459
$659$	1.09969e10	1.49683	0.748416	−	0.663230i	$-0.230815\pi$
$659$	1.09969e10	1.49683	0.748416	+	0.663230i	$0.230815\pi$
$660$	0	0
$661$	1.20713e10	1.62574	0.812869	−	0.582447i	$-0.197905\pi$
$661$	1.20713e10	1.62574	0.812869	+	0.582447i	$0.197905\pi$
$662$	6.50911e9	0.872005
$663$	0	0
$664$	6.91579e9	0.916755
$665$	7.00570e9	0.923795
$666$	0	0
$667$	−2.09915e10	−2.73907
$668$	4.50443e9	0.584686
$669$	0	0
$670$	4.14834e9	0.532859
$671$	−3.42386e9	−0.437509
$672$	0	0
$673$	4.08129e9	0.516113	0.258057	−	0.966130i	$-0.416918\pi$
$673$	4.08129e9	0.516113	0.258057	+	0.966130i	$0.416918\pi$
$674$	−2.63479e9	−0.331464
$675$	0	0
$676$	5.76372e9	0.717612
$677$	7.05725e9	0.874128	0.437064	−	0.899430i	$-0.356018\pi$
$677$	7.05725e9	0.874128	0.437064	+	0.899430i	$0.356018\pi$
$678$	0	0
$679$	6.15809e9	0.754922
$680$	−4.33122e8	−0.0528237
$681$	0	0
$682$	−8.38745e9	−1.01248
$683$	−7.13819e9	−0.857266	−0.428633	−	0.903479i	$-0.641005\pi$
$683$	−7.13819e9	−0.857266	−0.428633	+	0.903479i	$0.641005\pi$
$684$	0	0
$685$	−5.73270e9	−0.681463
$686$	2.94052e9	0.347768
$687$	0	0
$688$	4.44006e8	0.0519791
$689$	−6.86257e8	−0.0799317
$690$	0	0
$691$	−1.09452e10	−1.26197	−0.630987	−	0.775793i	$-0.717350\pi$
$691$	−1.09452e10	−1.26197	−0.630987	+	0.775793i	$0.717350\pi$
$692$	−4.45004e9	−0.510496
$693$	0	0
$694$	−5.99781e8	−0.0681137
$695$	1.13322e10	1.28047
$696$	0	0
$697$	−4.39093e8	−0.0491181
$698$	−4.12672e9	−0.459316
$699$	0	0
$700$	−2.03203e9	−0.223917
$701$	−1.00558e10	−1.10256	−0.551282	−	0.834319i	$-0.685861\pi$
$701$	−1.00558e10	−1.10256	−0.551282	+	0.834319i	$0.685861\pi$
$702$	0	0
$703$	7.80877e9	0.847694
$704$	2.41117e9	0.260450
$705$	0	0
$706$	2.28706e9	0.244603
$707$	7.15282e9	0.761218
$708$	0	0
$709$	1.17573e10	1.23892	0.619462	−	0.785027i	$-0.287351\pi$
$709$	1.17573e10	1.23892	0.619462	+	0.785027i	$0.287351\pi$
$710$	−2.62707e9	−0.275465
$711$	0	0
$712$	−1.14030e10	−1.18397
$713$	1.94592e10	2.01054
$714$	0	0
$715$	4.12864e9	0.422412
$716$	7.49021e9	0.762603
$717$	0	0
$718$	8.75753e8	0.0882970
$719$	1.29980e9	0.130414	0.0652072	−	0.997872i	$-0.479229\pi$
$719$	1.29980e9	0.130414	0.0652072	+	0.997872i	$0.479229\pi$
$720$	0	0
$721$	2.26013e10	2.24574
$722$	−3.49455e9	−0.345550
$723$	0	0
$724$	−7.19497e9	−0.704602
$725$	3.36100e9	0.327556
$726$	0	0
$727$	1.55479e10	1.50073	0.750363	−	0.661026i	$-0.229879\pi$
$727$	1.55479e10	1.50073	0.750363	+	0.661026i	$0.229879\pi$
$728$	3.36160e9	0.322914
$729$	0	0
$730$	−5.02190e9	−0.477791
$731$	−9.07145e7	−0.00858946
$732$	0	0
$733$	2.52604e9	0.236906	0.118453	−	0.992960i	$-0.462206\pi$
$733$	2.52604e9	0.236906	0.118453	+	0.992960i	$0.462206\pi$
$734$	3.10438e8	0.0289760
$735$	0	0
$736$	−1.74404e10	−1.61244
$737$	−1.75984e10	−1.61934
$738$	0	0
$739$	−8.96231e9	−0.816892	−0.408446	−	0.912783i	$-0.633929\pi$
$739$	−8.96231e9	−0.816892	−0.408446	+	0.912783i	$0.633929\pi$
$740$	−1.43290e10	−1.29988
$741$	0	0
$742$	2.84240e9	0.255430
$743$	−9.22267e9	−0.824890	−0.412445	−	0.910983i	$-0.635325\pi$
$743$	−9.22267e9	−0.824890	−0.412445	+	0.910983i	$0.635325\pi$
$744$	0	0
$745$	−1.33939e10	−1.18675
$746$	6.72664e9	0.593215
$747$	0	0
$748$	7.94197e8	0.0693862
$749$	2.22245e10	1.93262
$750$	0	0
$751$	1.49684e10	1.28954	0.644770	−	0.764377i	$-0.276953\pi$
$751$	1.49684e10	1.28954	0.644770	+	0.764377i	$0.276953\pi$
$752$	−2.12634e9	−0.182335
$753$	0	0
$754$	−2.40328e9	−0.204176
$755$	9.43255e9	0.797654
$756$	0	0
$757$	−1.31799e10	−1.10427	−0.552136	−	0.833754i	$-0.686187\pi$
$757$	−1.31799e10	−1.10427	−0.552136	+	0.833754i	$0.686187\pi$
$758$	−1.10518e10	−0.921702
$759$	0	0
$760$	−6.14076e9	−0.507428
$761$	5.65319e9	0.464994	0.232497	−	0.972597i	$-0.425310\pi$
$761$	5.65319e9	0.464994	0.232497	+	0.972597i	$0.425310\pi$
$762$	0	0
$763$	1.81385e10	1.47831
$764$	−4.49745e9	−0.364871
$765$	0	0
$766$	4.23190e9	0.340200
$767$	−3.71093e9	−0.296961
$768$	0	0
$769$	2.55751e9	0.202803	0.101402	−	0.994846i	$-0.467667\pi$
$769$	2.55751e9	0.202803	0.101402	+	0.994846i	$0.467667\pi$
$770$	−1.71004e10	−1.34986
$771$	0	0
$772$	−1.01801e10	−0.796328
$773$	−6.24612e9	−0.486387	−0.243194	−	0.969978i	$-0.578195\pi$
$773$	−6.24612e9	−0.486387	−0.243194	+	0.969978i	$0.578195\pi$
$774$	0	0
$775$	−3.11566e9	−0.240433
$776$	−5.39780e9	−0.414668
$777$	0	0
$778$	3.62814e9	0.276220
$779$	−6.22542e9	−0.471832
$780$	0	0
$781$	1.11448e10	0.837128
$782$	5.77760e8	0.0432040
$783$	0	0
$784$	6.68863e9	0.495713
$785$	5.11408e8	0.0377332
$786$	0	0
$787$	−2.24074e10	−1.63863	−0.819314	−	0.573345i	$-0.805646\pi$
$787$	−2.24074e10	−1.63863	−0.819314	+	0.573345i	$0.805646\pi$
$788$	3.16263e9	0.230254
$789$	0	0
$790$	−4.45164e9	−0.321237
$791$	2.25514e10	1.62015
$792$	0	0
$793$	9.09436e8	0.0647613
$794$	5.04206e9	0.357467
$795$	0	0
$796$	−1.85833e10	−1.30595
$797$	−7.81380e9	−0.546712	−0.273356	−	0.961913i	$-0.588134\pi$
$797$	−7.81380e9	−0.546712	−0.273356	+	0.961913i	$0.588134\pi$
$798$	0	0
$799$	4.34430e8	0.0301305
$800$	2.79243e9	0.192826
$801$	0	0
$802$	6.36664e8	0.0435813
$803$	2.13043e10	1.45199
$804$	0	0
$805$	3.96736e10	2.68050
$806$	2.22785e9	0.149870
$807$	0	0
$808$	−6.26972e9	−0.418127
$809$	−1.22193e9	−0.0811386	−0.0405693	−	0.999177i	$-0.512917\pi$
$809$	−1.22193e9	−0.0811386	−0.0405693	+	0.999177i	$0.512917\pi$
$810$	0	0
$811$	−1.05088e10	−0.691797	−0.345898	−	0.938272i	$-0.612426\pi$
$811$	−1.05088e10	−0.691797	−0.345898	+	0.938272i	$0.612426\pi$
$812$	−3.17453e10	−2.08082
$813$	0	0
$814$	−1.90606e10	−1.23866
$815$	−2.52981e9	−0.163695
$816$	0	0
$817$	−1.28614e9	−0.0825111
$818$	−4.64169e9	−0.296510
$819$	0	0
$820$	1.14235e10	0.723523
$821$	1.87258e10	1.18097	0.590486	−	0.807048i	$-0.298936\pi$
$821$	1.87258e10	1.18097	0.590486	+	0.807048i	$0.298936\pi$
$822$	0	0
$823$	−3.81070e9	−0.238290	−0.119145	−	0.992877i	$-0.538015\pi$
$823$	−3.81070e9	−0.238290	−0.119145	+	0.992877i	$0.538015\pi$
$824$	−1.98109e10	−1.23356
$825$	0	0
$826$	1.53703e10	0.948968
$827$	−1.63714e10	−1.00651	−0.503254	−	0.864139i	$-0.667864\pi$
$827$	−1.63714e10	−1.00651	−0.503254	+	0.864139i	$0.667864\pi$
$828$	0	0
$829$	−6.71162e9	−0.409153	−0.204577	−	0.978851i	$-0.565582\pi$
$829$	−6.71162e9	−0.409153	−0.204577	+	0.978851i	$0.565582\pi$
$830$	9.34453e9	0.567263
$831$	0	0
$832$	−6.40448e8	−0.0385525
$833$	−1.36655e9	−0.0819158
$834$	0	0
$835$	1.40811e10	0.837018
$836$	1.12601e10	0.666529
$837$	0	0
$838$	−5.07444e9	−0.297875
$839$	1.35926e10	0.794577	0.397289	−	0.917694i	$-0.369951\pi$
$839$	1.35926e10	0.794577	0.397289	+	0.917694i	$0.369951\pi$
$840$	0	0
$841$	3.52573e10	2.04391
$842$	5.45434e8	0.0314883
$843$	0	0
$844$	4.80993e8	0.0275385
$845$	1.80177e10	1.02731
$846$	0	0
$847$	4.48396e10	2.53554
$848$	2.01984e9	0.113745
$849$	0	0
$850$	−9.25064e7	−0.00516661
$851$	4.42214e10	2.45968
$852$	0	0
$853$	−8.31755e9	−0.458853	−0.229427	−	0.973326i	$-0.573685\pi$
$853$	−8.31755e9	−0.458853	−0.229427	+	0.973326i	$0.573685\pi$
$854$	−3.76679e9	−0.206951
$855$	0	0
$856$	−1.94806e10	−1.06156
$857$	5.32901e8	0.0289210	0.0144605	−	0.999895i	$-0.495397\pi$
$857$	5.32901e8	0.0289210	0.0144605	+	0.999895i	$0.495397\pi$
$858$	0	0
$859$	−3.23176e10	−1.73965	−0.869827	−	0.493357i	$-0.835770\pi$
$859$	−3.23176e10	−1.73965	−0.869827	+	0.493357i	$0.835770\pi$
$860$	2.36005e9	0.126525
$861$	0	0
$862$	−1.34039e10	−0.712780
$863$	−5.97266e9	−0.316323	−0.158161	−	0.987413i	$-0.550557\pi$
$863$	−5.97266e9	−0.316323	−0.158161	+	0.987413i	$0.550557\pi$
$864$	0	0
$865$	−1.39111e10	−0.730810
$866$	9.04737e9	0.473380
$867$	0	0
$868$	2.94281e10	1.52737
$869$	1.88851e10	0.976226
$870$	0	0
$871$	4.67444e9	0.239699
$872$	−1.58991e10	−0.812018
$873$	0	0
$874$	8.19143e9	0.415020
$875$	2.74821e10	1.38683
$876$	0	0
$877$	−7.05767e9	−0.353315	−0.176658	−	0.984272i	$-0.556529\pi$
$877$	−7.05767e9	−0.353315	−0.176658	+	0.984272i	$0.556529\pi$
$878$	−7.75530e9	−0.386695
$879$	0	0
$880$	−1.21517e10	−0.601102
$881$	−2.62054e10	−1.29114	−0.645572	−	0.763700i	$-0.723381\pi$
$881$	−2.62054e10	−1.29114	−0.645572	+	0.763700i	$0.723381\pi$
$882$	0	0
$883$	−5.36619e8	−0.0262303	−0.0131152	−	0.999914i	$-0.504175\pi$
$883$	−5.36619e8	−0.0262303	−0.0131152	+	0.999914i	$0.504175\pi$
$884$	−2.10952e8	−0.0102707
$885$	0	0
$886$	−2.43167e9	−0.117459
$887$	2.81727e10	1.35549	0.677744	−	0.735298i	$-0.262958\pi$
$887$	2.81727e10	1.35549	0.677744	+	0.735298i	$0.262958\pi$
$888$	0	0
$889$	−3.48234e10	−1.66232
$890$	−1.54076e10	−0.732606
$891$	0	0
$892$	−2.70471e10	−1.27598
$893$	6.15932e9	0.289436
$894$	0	0
$895$	2.34148e10	1.09172
$896$	−3.19926e10	−1.48584
$897$	0	0
$898$	−1.16642e10	−0.537510
$899$	−4.86744e10	−2.23430
$900$	0	0
$901$	−4.12672e8	−0.0187961
$902$	1.51958e10	0.689446
$903$	0	0
$904$	−1.97672e10	−0.889928
$905$	−2.24919e10	−1.00869
$906$	0	0
$907$	3.54442e9	0.157732	0.0788659	−	0.996885i	$-0.474870\pi$
$907$	3.54442e9	0.157732	0.0788659	+	0.996885i	$0.474870\pi$
$908$	−1.24082e10	−0.550058
$909$	0	0
$910$	4.54216e9	0.199810
$911$	−9.71330e9	−0.425650	−0.212825	−	0.977090i	$-0.568266\pi$
$911$	−9.71330e9	−0.425650	−0.212825	+	0.977090i	$0.568266\pi$
$912$	0	0
$913$	−3.96421e10	−1.72389
$914$	−1.18041e10	−0.511355
$915$	0	0
$916$	−1.61832e10	−0.695713
$917$	−5.11393e10	−2.19009
$918$	0	0
$919$	1.30593e10	0.555029	0.277515	−	0.960721i	$-0.410489\pi$
$919$	1.30593e10	0.555029	0.277515	+	0.960721i	$0.410489\pi$
$920$	−3.47755e10	−1.47236
$921$	0	0
$922$	−4.11461e9	−0.172890
$923$	−2.96024e9	−0.123914
$924$	0	0
$925$	−7.08040e9	−0.294145
$926$	9.39820e9	0.388961
$927$	0	0
$928$	4.36246e10	1.79190
$929$	1.76183e10	0.720955	0.360478	−	0.932768i	$-0.382614\pi$
$929$	1.76183e10	0.720955	0.360478	+	0.932768i	$0.382614\pi$
$930$	0	0
$931$	−1.93748e10	−0.786890
$932$	−1.92145e10	−0.777452
$933$	0	0
$934$	2.17331e10	0.872786
$935$	2.48271e9	0.0993310
$936$	0	0
$937$	2.93955e10	1.16733	0.583664	−	0.811996i	$-0.301619\pi$
$937$	2.93955e10	1.16733	0.583664	+	0.811996i	$0.301619\pi$
$938$	−1.93610e10	−0.765982
$939$	0	0
$940$	−1.13022e10	−0.443831
$941$	−5.66655e9	−0.221694	−0.110847	−	0.993837i	$-0.535356\pi$
$941$	−5.66655e9	−0.221694	−0.110847	+	0.993837i	$0.535356\pi$
$942$	0	0
$943$	−3.52548e10	−1.36908
$944$	1.09223e10	0.422582
$945$	0	0
$946$	3.13938e9	0.120566
$947$	−2.82326e10	−1.08025	−0.540126	−	0.841584i	$-0.681624\pi$
$947$	−2.82326e10	−1.08025	−0.540126	+	0.841584i	$0.681624\pi$
$948$	0	0
$949$	−5.65879e9	−0.214927
$950$	−1.31155e9	−0.0496308
$951$	0	0
$952$	2.02146e9	0.0759338
$953$	2.48053e10	0.928366	0.464183	−	0.885739i	$-0.346348\pi$
$953$	2.48053e10	0.928366	0.464183	+	0.885739i	$0.346348\pi$
$954$	0	0
$955$	−1.40593e10	−0.522338
$956$	7.04494e9	0.260780
$957$	0	0
$958$	8.01833e9	0.294649
$959$	2.67555e10	0.979599
$960$	0	0
$961$	1.76088e10	0.640027
$962$	5.06283e9	0.183350
$963$	0	0
$964$	3.01988e10	1.08573
$965$	−3.18236e10	−1.14000
$966$	0	0
$967$	−3.08573e10	−1.09740	−0.548700	−	0.836019i	$-0.684877\pi$
$967$	−3.08573e10	−1.09740	−0.548700	+	0.836019i	$0.684877\pi$
$968$	−3.93036e10	−1.39274
$969$	0	0
$970$	−7.29345e9	−0.256585
$971$	3.26691e9	0.114517	0.0572585	−	0.998359i	$-0.481764\pi$
$971$	3.26691e9	0.114517	0.0572585	+	0.998359i	$0.481764\pi$
$972$	0	0
$973$	−5.28896e10	−1.84067
$974$	2.37209e10	0.822574
$975$	0	0
$976$	−2.67671e9	−0.0921568
$977$	−1.92954e10	−0.661948	−0.330974	−	0.943640i	$-0.607377\pi$
$977$	−1.92954e10	−0.661948	−0.330974	+	0.943640i	$0.607377\pi$
$978$	0	0
$979$	6.53635e10	2.22636
$980$	3.55525e10	1.20664
$981$	0	0
$982$	1.93959e9	0.0653612
$983$	−4.50199e10	−1.51170	−0.755852	−	0.654742i	$-0.772777\pi$
$983$	−4.50199e10	−1.51170	−0.755852	+	0.654742i	$0.772777\pi$
$984$	0	0
$985$	9.88658e9	0.329624
$986$	−1.44518e9	−0.0480123
$987$	0	0
$988$	−2.99087e9	−0.0986615
$989$	−7.28349e9	−0.239416
$990$	0	0
$991$	−4.47544e10	−1.46076	−0.730379	−	0.683042i	$-0.760657\pi$
$991$	−4.47544e10	−1.46076	−0.730379	+	0.683042i	$0.760657\pi$
$992$	−4.04403e10	−1.31529
$993$	0	0
$994$	1.22610e10	0.395980
$995$	−5.80926e10	−1.86956
$996$	0	0
$997$	4.11948e10	1.31647	0.658233	−	0.752815i	$-0.271304\pi$
$997$	4.11948e10	1.31647	0.658233	+	0.752815i	$0.271304\pi$
$998$	−2.05781e10	−0.655314
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.b.1.6		11
3.2	odd	2		43.8.a.a.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.6	✓	11	3.2	odd	2
387.8.a.b.1.6		11	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q+5.52766 q^{2} -97.4450 q^{4} -304.619 q^{5} +1421.71 q^{7} -1246.18 q^{8} +O(q^{10})\)	\(q+5.52766 q^{2} -97.4450 q^{4} -304.619 q^{5} +1421.71 q^{7} -1246.18 q^{8} -1683.83 q^{10} +7143.27 q^{11} -1897.38 q^{13} +7858.73 q^{14} +5584.49 q^{16} -1140.96 q^{17} -16176.5 q^{19} +29683.6 q^{20} +39485.6 q^{22} -91608.2 q^{23} +14667.6 q^{25} -10488.0 q^{26} -138539. q^{28} +229144. q^{29} -212418. q^{31} +190381. q^{32} -6306.85 q^{34} -433079. q^{35} -482724. q^{37} -89418.0 q^{38} +379611. q^{40} +384844. q^{41} +79507.0 q^{43} -696076. q^{44} -506379. q^{46} -380758. q^{47} +1.19772e6 q^{49} +81077.5 q^{50} +184890. q^{52} +361687. q^{53} -2.17598e6 q^{55} -1.77171e6 q^{56} +1.26663e6 q^{58} +1.95582e6 q^{59} -479312. q^{61} -1.17417e6 q^{62} +337544. q^{64} +577976. q^{65} -2.46363e6 q^{67} +111181. q^{68} -2.39392e6 q^{70} +1.56017e6 q^{71} +2.98243e6 q^{73} -2.66833e6 q^{74} +1.57632e6 q^{76} +1.01557e7 q^{77} +2.64376e6 q^{79} -1.70114e6 q^{80} +2.12728e6 q^{82} -5.54958e6 q^{83} +347559. q^{85} +439488. q^{86} -8.90183e6 q^{88} +9.15035e6 q^{89} -2.69752e6 q^{91} +8.92676e6 q^{92} -2.10470e6 q^{94} +4.92766e6 q^{95} +4.33147e6 q^{97} +6.62056e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8} - 1333 q^{10} - 1333 q^{11} - 17967 q^{13} + 22352 q^{14} - 34406 q^{16} + 63095 q^{17} - 54524 q^{19} + 280995 q^{20} - 289358 q^{22} + 138139 q^{23} + 3455 q^{25} + 132946 q^{26} - 12704 q^{28} + 308658 q^{29} - 209523 q^{31} + 644934 q^{32} + 762435 q^{34} + 578892 q^{35} - 298472 q^{37} + 369707 q^{38} + 2633173 q^{40} + 1346735 q^{41} + 874577 q^{43} - 3134292 q^{44} + 3588111 q^{46} - 499284 q^{47} + 2544563 q^{49} - 3049745 q^{50} + 983088 q^{52} + 2210495 q^{53} - 1855072 q^{55} + 469976 q^{56} + 4397067 q^{58} + 5824216 q^{59} - 4453034 q^{61} - 1002789 q^{62} + 4757538 q^{64} + 2162872 q^{65} - 6859513 q^{67} + 9397005 q^{68} + 845078 q^{70} + 10726554 q^{71} - 4456898 q^{73} - 1046637 q^{74} + 5861267 q^{76} + 17019816 q^{77} - 15541320 q^{79} + 15680911 q^{80} + 20233655 q^{82} + 11146767 q^{83} - 12471976 q^{85} + 1908168 q^{86} - 24463544 q^{88} + 13531356 q^{89} - 19746448 q^{91} + 26023161 q^{92} + 20288857 q^{94} + 12291624 q^{95} - 10999901 q^{97} - 29909168 q^{98}+O(q^{100}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8 - 1333 * q^10 - 1333 * q^11 - 17967 * q^13 + 22352 * q^14 - 34406 * q^16 + 63095 * q^17 - 54524 * q^19 + 280995 * q^20 - 289358 * q^22 + 138139 * q^23 + 3455 * q^25 + 132946 * q^26 - 12704 * q^28 + 308658 * q^29 - 209523 * q^31 + 644934 * q^32 + 762435 * q^34 + 578892 * q^35 - 298472 * q^37 + 369707 * q^38 + 2633173 * q^40 + 1346735 * q^41 + 874577 * q^43 - 3134292 * q^44 + 3588111 * q^46 - 499284 * q^47 + 2544563 * q^49 - 3049745 * q^50 + 983088 * q^52 + 2210495 * q^53 - 1855072 * q^55 + 469976 * q^56 + 4397067 * q^58 + 5824216 * q^59 - 4453034 * q^61 - 1002789 * q^62 + 4757538 * q^64 + 2162872 * q^65 - 6859513 * q^67 + 9397005 * q^68 + 845078 * q^70 + 10726554 * q^71 - 4456898 * q^73 - 1046637 * q^74 + 5861267 * q^76 + 17019816 * q^77 - 15541320 * q^79 + 15680911 * q^80 + 20233655 * q^82 + 11146767 * q^83 - 12471976 * q^85 + 1908168 * q^86 - 24463544 * q^88 + 13531356 * q^89 - 19746448 * q^91 + 26023161 * q^92 + 20288857 * q^94 + 12291624 * q^95 - 10999901 * q^97 - 29909168 * q^98

Introduction

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