LMFDB - Embedded newform 387.8.a.b.1.1

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			1.1
Root			$-19.3827$ 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)

$f(q)$	$=$	$q-17.3827 q^{2} +174.160 q^{4} +230.747 q^{5} -1110.68 q^{7} -802.384 q^{8} +O(q^{10})$	\(q-17.3827 q^{2} +174.160 q^{4} +230.747 q^{5} -1110.68 q^{7} -802.384 q^{8} -4011.02 q^{10} +607.968 q^{11} +13041.8 q^{13} +19306.6 q^{14} -8344.81 q^{16} +20609.8 q^{17} -24170.2 q^{19} +40186.9 q^{20} -10568.2 q^{22} -60316.5 q^{23} -24880.7 q^{25} -226703. q^{26} -193435. q^{28} +77712.2 q^{29} +34644.3 q^{31} +247761. q^{32} -358255. q^{34} -256286. q^{35} +489896. q^{37} +420144. q^{38} -185148. q^{40} +809882. q^{41} +79507.0 q^{43} +105884. q^{44} +1.04847e6 q^{46} -289158. q^{47} +410063. q^{49} +432494. q^{50} +2.27136e6 q^{52} -892274. q^{53} +140287. q^{55} +891191. q^{56} -1.35085e6 q^{58} +1.51749e6 q^{59} -160538. q^{61} -602213. q^{62} -3.23863e6 q^{64} +3.00937e6 q^{65} -2.42938e6 q^{67} +3.58940e6 q^{68} +4.45495e6 q^{70} -993231. q^{71} -2.67982e6 q^{73} -8.51574e6 q^{74} -4.20947e6 q^{76} -675257. q^{77} -4.46840e6 q^{79} -1.92554e6 q^{80} -1.40780e7 q^{82} +4.10044e6 q^{83} +4.75566e6 q^{85} -1.38205e6 q^{86} -487824. q^{88} +2.96316e6 q^{89} -1.44853e7 q^{91} -1.05047e7 q^{92} +5.02636e6 q^{94} -5.57721e6 q^{95} -9.83610e6 q^{97} -7.12801e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−17.3827	−1.53643	−0.768216	−	0.640191i	$-0.778855\pi$
$2$	−17.3827	−1.53643	−0.768216	+	0.640191i	$0.778855\pi$
$3$	0	0
$3$	0	0
$4$	174.160	1.36062
$5$	230.747	0.825547	0.412773	−	0.910834i	$-0.364560\pi$
$5$	230.747	0.825547	0.412773	+	0.910834i	$0.364560\pi$
$6$	0	0
$7$	−1110.68	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$7$	−1110.68	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$8$	−802.384	−0.554074
$9$	0	0
$10$	−4011.02	−1.26840
$11$	607.968	0.137723	0.0688615	−	0.997626i	$-0.478063\pi$
$11$	607.968	0.137723	0.0688615	+	0.997626i	$0.478063\pi$
$12$	0	0
$13$	13041.8	1.64640	0.823202	−	0.567748i	$-0.192185\pi$
$13$	13041.8	1.64640	0.823202	+	0.567748i	$0.192185\pi$
$14$	19306.6	1.88044
$15$	0	0
$16$	−8344.81	−0.509327
$17$	20609.8	1.01743	0.508713	−	0.860936i	$-0.330122\pi$
$17$	20609.8	1.01743	0.508713	+	0.860936i	$0.330122\pi$
$18$	0	0
$19$	−24170.2	−0.808430	−0.404215	−	0.914664i	$-0.632455\pi$
$19$	−24170.2	−0.808430	−0.404215	+	0.914664i	$0.632455\pi$
$20$	40186.9	1.12326
$21$	0	0
$22$	−10568.2	−0.211602
$23$	−60316.5	−1.03369	−0.516843	−	0.856080i	$-0.672893\pi$
$23$	−60316.5	−1.03369	−0.516843	+	0.856080i	$0.672893\pi$
$24$	0	0
$25$	−24880.7	−0.318472
$26$	−226703.	−2.52959
$27$	0	0
$28$	−193435.	−1.66526
$29$	77712.2	0.591693	0.295846	−	0.955236i	$-0.404398\pi$
$29$	77712.2	0.591693	0.295846	+	0.955236i	$0.404398\pi$
$30$	0	0
$31$	34644.3	0.208865	0.104433	−	0.994532i	$-0.466697\pi$
$31$	34644.3	0.208865	0.104433	+	0.994532i	$0.466697\pi$
$32$	247761.	1.33662
$33$	0	0
$34$	−358255.	−1.56320
$35$	−256286.	−1.01038
$36$	0	0
$37$	489896.	1.59000	0.795002	−	0.606607i	$-0.207470\pi$
$37$	489896.	1.59000	0.795002	+	0.606607i	$0.207470\pi$
$38$	420144.	1.24210
$39$	0	0
$40$	−185148.	−0.457414
$41$	809882.	1.83518	0.917589	−	0.397529i	$-0.130132\pi$
$41$	809882.	1.83518	0.917589	+	0.397529i	$0.130132\pi$
$42$	0	0
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	105884.	0.187389
$45$	0	0
$46$	1.04847e6	1.58819
$47$	−289158.	−0.406249	−0.203125	−	0.979153i	$-0.565110\pi$
$47$	−289158.	−0.406249	−0.203125	+	0.979153i	$0.565110\pi$
$48$	0	0
$49$	410063.	0.497925
$50$	432494.	0.489311
$51$	0	0
$52$	2.27136e6	2.24014
$53$	−892274.	−0.823252	−0.411626	−	0.911353i	$-0.635039\pi$
$53$	−892274.	−0.823252	−0.411626	+	0.911353i	$0.635039\pi$
$54$	0	0
$55$	140287.	0.113697
$56$	891191.	0.678129
$57$	0	0
$58$	−1.35085e6	−0.909096
$59$	1.51749e6	0.961930	0.480965	−	0.876740i	$-0.340286\pi$
$59$	1.51749e6	0.961930	0.480965	+	0.876740i	$0.340286\pi$
$60$	0	0
$61$	−160538.	−0.0905570	−0.0452785	−	0.998974i	$-0.514418\pi$
$61$	−160538.	−0.0905570	−0.0452785	+	0.998974i	$0.514418\pi$
$62$	−602213.	−0.320907
$63$	0	0
$64$	−3.23863e6	−1.54430
$65$	3.00937e6	1.35918
$66$	0	0
$67$	−2.42938e6	−0.986811	−0.493406	−	0.869799i	$-0.664248\pi$
$67$	−2.42938e6	−0.986811	−0.493406	+	0.869799i	$0.664248\pi$
$68$	3.58940e6	1.38433
$69$	0	0
$70$	4.45495e6	1.55239
$71$	−993231.	−0.329341	−0.164671	−	0.986349i	$-0.552656\pi$
$71$	−993231.	−0.329341	−0.164671	+	0.986349i	$0.552656\pi$
$72$	0	0
$73$	−2.67982e6	−0.806262	−0.403131	−	0.915142i	$-0.632078\pi$
$73$	−2.67982e6	−0.806262	−0.403131	+	0.915142i	$0.632078\pi$
$74$	−8.51574e6	−2.44293
$75$	0	0
$76$	−4.20947e6	−1.09997
$77$	−675257.	−0.168559
$78$	0	0
$79$	−4.46840e6	−1.01966	−0.509832	−	0.860274i	$-0.670292\pi$
$79$	−4.46840e6	−1.01966	−0.509832	+	0.860274i	$0.670292\pi$
$80$	−1.92554e6	−0.420473
$81$	0	0
$82$	−1.40780e7	−2.81963
$83$	4.10044e6	0.787150	0.393575	−	0.919292i	$-0.371238\pi$
$83$	4.10044e6	0.787150	0.393575	+	0.919292i	$0.371238\pi$
$84$	0	0
$85$	4.75566e6	0.839932
$86$	−1.38205e6	−0.234304
$87$	0	0
$88$	−487824.	−0.0763087
$89$	2.96316e6	0.445543	0.222772	−	0.974871i	$-0.428490\pi$
$89$	2.96316e6	0.445543	0.222772	+	0.974871i	$0.428490\pi$
$90$	0	0
$91$	−1.44853e7	−2.01503
$92$	−1.05047e7	−1.40646
$93$	0	0
$94$	5.02636e6	0.624175
$95$	−5.57721e6	−0.667397
$96$	0	0
$97$	−9.83610e6	−1.09426	−0.547132	−	0.837046i	$-0.684280\pi$
$97$	−9.83610e6	−1.09426	−0.547132	+	0.837046i	$0.684280\pi$
$98$	−7.12801e6	−0.765028
$99$	0	0
$100$	−4.33321e6	−0.433321
$101$	1.11991e7	1.08158	0.540788	−	0.841159i	$-0.318126\pi$
$101$	1.11991e7	1.08158	0.540788	+	0.841159i	$0.318126\pi$
$102$	0	0
$103$	2.09902e6	0.189272	0.0946359	−	0.995512i	$-0.469831\pi$
$103$	2.09902e6	0.189272	0.0946359	+	0.995512i	$0.469831\pi$
$104$	−1.04646e7	−0.912229
$105$	0	0
$106$	1.55102e7	1.26487
$107$	−1.39300e7	−1.09928	−0.549639	−	0.835402i	$-0.685235\pi$
$107$	−1.39300e7	−1.09928	−0.549639	+	0.835402i	$0.685235\pi$
$108$	0	0
$109$	2.48819e7	1.84031	0.920154	−	0.391557i	$-0.128063\pi$
$109$	2.48819e7	1.84031	0.920154	+	0.391557i	$0.128063\pi$
$110$	−2.43857e6	−0.174687
$111$	0	0
$112$	9.26840e6	0.623364
$113$	1.72023e7	1.12153	0.560766	−	0.827974i	$-0.310507\pi$
$113$	1.72023e7	1.12153	0.560766	+	0.827974i	$0.310507\pi$
$114$	0	0
$115$	−1.39179e7	−0.853357
$116$	1.35343e7	0.805071
$117$	0	0
$118$	−2.63781e7	−1.47794
$119$	−2.28908e7	−1.24522
$120$	0	0
$121$	−1.91175e7	−0.981032
$122$	2.79058e6	0.139135
$123$	0	0
$124$	6.03365e6	0.284187
$125$	−2.37683e7	−1.08846
$126$	0	0
$127$	−3.68734e7	−1.59735	−0.798675	−	0.601763i	$-0.794465\pi$
$127$	−3.68734e7	−1.59735	−0.798675	+	0.601763i	$0.794465\pi$
$128$	2.45829e7	1.03609
$129$	0	0
$130$	−5.23110e7	−2.08829
$131$	−2.41863e7	−0.939981	−0.469991	−	0.882671i	$-0.655743\pi$
$131$	−2.41863e7	−0.939981	−0.469991	+	0.882671i	$0.655743\pi$
$132$	0	0
$133$	2.68453e7	0.989435
$134$	4.22293e7	1.51617
$135$	0	0
$136$	−1.65370e7	−0.563729
$137$	4.37084e6	0.145226	0.0726128	−	0.997360i	$-0.476866\pi$
$137$	4.37084e6	0.145226	0.0726128	+	0.997360i	$0.476866\pi$
$138$	0	0
$139$	2.60325e7	0.822174	0.411087	−	0.911596i	$-0.365149\pi$
$139$	2.60325e7	0.822174	0.411087	+	0.911596i	$0.365149\pi$
$140$	−4.46347e7	−1.37475
$141$	0	0
$142$	1.72651e7	0.506010
$143$	7.92901e6	0.226748
$144$	0	0
$145$	1.79319e7	0.488470
$146$	4.65827e7	1.23877
$147$	0	0
$148$	8.53202e7	2.16340
$149$	−2.65502e7	−0.657530	−0.328765	−	0.944412i	$-0.606632\pi$
$149$	−2.65502e7	−0.657530	−0.328765	+	0.944412i	$0.606632\pi$
$150$	0	0
$151$	5.28071e7	1.24817	0.624084	−	0.781357i	$-0.285472\pi$
$151$	5.28071e7	1.24817	0.624084	+	0.781357i	$0.285472\pi$
$152$	1.93938e7	0.447930
$153$	0	0
$154$	1.17378e7	0.258979
$155$	7.99408e6	0.172428
$156$	0	0
$157$	−6.72632e7	−1.38717	−0.693584	−	0.720376i	$-0.743969\pi$
$157$	−6.72632e7	−1.38717	−0.693584	+	0.720376i	$0.743969\pi$
$158$	7.76730e7	1.56664
$159$	0	0
$160$	5.71702e7	1.10344
$161$	6.69922e7	1.26513
$162$	0	0
$163$	5.59234e7	1.01143	0.505717	−	0.862700i	$-0.331228\pi$
$163$	5.59234e7	1.01143	0.505717	+	0.862700i	$0.331228\pi$
$164$	1.41049e8	2.49699
$165$	0	0
$166$	−7.12770e7	−1.20940
$167$	−1.13304e7	−0.188252	−0.0941258	−	0.995560i	$-0.530006\pi$
$167$	−1.13304e7	−0.188252	−0.0941258	+	0.995560i	$0.530006\pi$
$168$	0	0
$169$	1.07341e8	1.71065
$170$	−8.26664e7	−1.29050
$171$	0	0
$172$	1.38469e7	0.207493
$173$	3.43489e7	0.504373	0.252186	−	0.967679i	$-0.418850\pi$
$173$	3.43489e7	0.504373	0.252186	+	0.967679i	$0.418850\pi$
$174$	0	0
$175$	2.76344e7	0.389778
$176$	−5.07338e6	−0.0701460
$177$	0	0
$178$	−5.15078e7	−0.684547
$179$	−1.06394e8	−1.38654	−0.693268	−	0.720680i	$-0.743830\pi$
$179$	−1.06394e8	−1.38654	−0.693268	+	0.720680i	$0.743830\pi$
$180$	0	0
$181$	−1.03201e8	−1.29363	−0.646815	−	0.762647i	$-0.723899\pi$
$181$	−1.03201e8	−1.29363	−0.646815	+	0.762647i	$0.723899\pi$
$182$	2.51794e8	3.09596
$183$	0	0
$184$	4.83970e7	0.572739
$185$	1.13042e8	1.31262
$186$	0	0
$187$	1.25301e7	0.140123
$188$	−5.03597e7	−0.552752
$189$	0	0
$190$	9.69471e7	1.02541
$191$	−6.61411e7	−0.686839	−0.343419	−	0.939182i	$-0.611585\pi$
$191$	−6.61411e7	−0.686839	−0.343419	+	0.939182i	$0.611585\pi$
$192$	0	0
$193$	5.13623e7	0.514273	0.257136	−	0.966375i	$-0.417221\pi$
$193$	5.13623e7	0.514273	0.257136	+	0.966375i	$0.417221\pi$
$194$	1.70978e8	1.68126
$195$	0	0
$196$	7.14164e7	0.677488
$197$	9.19611e7	0.856983	0.428492	−	0.903546i	$-0.359045\pi$
$197$	9.19611e7	0.856983	0.428492	+	0.903546i	$0.359045\pi$
$198$	0	0
$199$	6.18358e7	0.556230	0.278115	−	0.960548i	$-0.410290\pi$
$199$	6.18358e7	0.556230	0.278115	+	0.960548i	$0.410290\pi$
$200$	1.99639e7	0.176457
$201$	0	0
$202$	−1.94670e8	−1.66177
$203$	−8.63132e7	−0.724171
$204$	0	0
$205$	1.86878e8	1.51503
$206$	−3.64867e7	−0.290803
$207$	0	0
$208$	−1.08832e8	−0.838558
$209$	−1.46947e7	−0.111339
$210$	0	0
$211$	1.45231e8	1.06431	0.532157	−	0.846646i	$-0.321382\pi$
$211$	1.45231e8	1.06431	0.532157	+	0.846646i	$0.321382\pi$
$212$	−1.55398e8	−1.12014
$213$	0	0
$214$	2.42142e8	1.68897
$215$	1.83460e7	0.125895
$216$	0	0
$217$	−3.84787e7	−0.255630
$218$	−4.32515e8	−2.82751
$219$	0	0
$220$	2.44324e7	0.154699
$221$	2.68789e8	1.67509
$222$	0	0
$223$	1.18865e8	0.717775	0.358888	−	0.933381i	$-0.383156\pi$
$223$	1.18865e8	0.717775	0.358888	+	0.933381i	$0.383156\pi$
$224$	−2.75183e8	−1.63589
$225$	0	0
$226$	−2.99023e8	−1.72316
$227$	2.33026e8	1.32225	0.661125	−	0.750276i	$-0.270079\pi$
$227$	2.33026e8	1.32225	0.661125	+	0.750276i	$0.270079\pi$
$228$	0	0
$229$	2.52042e8	1.38691	0.693457	−	0.720498i	$-0.256087\pi$
$229$	2.52042e8	1.38691	0.693457	+	0.720498i	$0.256087\pi$
$230$	2.41931e8	1.31112
$231$	0	0
$232$	−6.23551e7	−0.327841
$233$	−1.61379e8	−0.835799	−0.417899	−	0.908493i	$-0.637234\pi$
$233$	−1.61379e8	−0.835799	−0.417899	+	0.908493i	$0.637234\pi$
$234$	0	0
$235$	−6.67224e7	−0.335378
$236$	2.64286e8	1.30882
$237$	0	0
$238$	3.97906e8	1.91320
$239$	3.28589e8	1.55690	0.778449	−	0.627707i	$-0.216007\pi$
$239$	3.28589e8	1.55690	0.778449	+	0.627707i	$0.216007\pi$
$240$	0	0
$241$	−5.95088e7	−0.273855	−0.136928	−	0.990581i	$-0.543723\pi$
$241$	−5.95088e7	−0.273855	−0.136928	+	0.990581i	$0.543723\pi$
$242$	3.32315e8	1.50729
$243$	0	0
$244$	−2.79592e7	−0.123214
$245$	9.46209e7	0.411060
$246$	0	0
$247$	−3.15223e8	−1.33100
$248$	−2.77981e7	−0.115727
$249$	0	0
$250$	4.13158e8	1.67235
$251$	1.34270e8	0.535944	0.267972	−	0.963427i	$-0.413646\pi$
$251$	1.34270e8	0.535944	0.267972	+	0.963427i	$0.413646\pi$
$252$	0	0
$253$	−3.66705e7	−0.142362
$254$	6.40960e8	2.45422
$255$	0	0
$256$	−1.27732e7	−0.0475837
$257$	2.54950e8	0.936892	0.468446	−	0.883492i	$-0.344814\pi$
$257$	2.54950e8	0.936892	0.468446	+	0.883492i	$0.344814\pi$
$258$	0	0
$259$	−5.44117e8	−1.94600
$260$	5.24111e8	1.84934
$261$	0	0
$262$	4.20424e8	1.44422
$263$	−1.82117e8	−0.617314	−0.308657	−	0.951173i	$-0.599879\pi$
$263$	−1.82117e8	−0.617314	−0.308657	+	0.951173i	$0.599879\pi$
$264$	0	0
$265$	−2.05890e8	−0.679633
$266$	−4.66645e8	−1.52020
$267$	0	0
$268$	−4.23101e8	−1.34268
$269$	4.86909e8	1.52516	0.762579	−	0.646895i	$-0.223933\pi$
$269$	4.86909e8	1.52516	0.762579	+	0.646895i	$0.223933\pi$
$270$	0	0
$271$	−5.57858e7	−0.170267	−0.0851336	−	0.996370i	$-0.527132\pi$
$271$	−5.57858e7	−0.170267	−0.0851336	+	0.996370i	$0.527132\pi$
$272$	−1.71985e8	−0.518202
$273$	0	0
$274$	−7.59772e7	−0.223129
$275$	−1.51266e7	−0.0438610
$276$	0	0
$277$	6.88409e8	1.94611	0.973055	−	0.230572i	$-0.0740596\pi$
$277$	6.88409e8	1.94611	0.973055	+	0.230572i	$0.0740596\pi$
$278$	−4.52516e8	−1.26322
$279$	0	0
$280$	2.05640e8	0.559828
$281$	−2.36816e8	−0.636707	−0.318353	−	0.947972i	$-0.603130\pi$
$281$	−2.36816e8	−0.636707	−0.318353	+	0.947972i	$0.603130\pi$
$282$	0	0
$283$	3.02454e8	0.793245	0.396623	−	0.917982i	$-0.370182\pi$
$283$	3.02454e8	0.793245	0.396623	+	0.917982i	$0.370182\pi$
$284$	−1.72981e8	−0.448109
$285$	0	0
$286$	−1.37828e8	−0.348383
$287$	−8.99518e8	−2.24607
$288$	0	0
$289$	1.44250e7	0.0351539
$290$	−3.11705e8	−0.750501
$291$	0	0
$292$	−4.66718e8	−1.09702
$293$	6.95562e8	1.61547	0.807735	−	0.589546i	$-0.200693\pi$
$293$	6.95562e8	1.61547	0.807735	+	0.589546i	$0.200693\pi$
$294$	0	0
$295$	3.50157e8	0.794118
$296$	−3.93085e8	−0.880979
$297$	0	0
$298$	4.61515e8	1.01025
$299$	−7.86637e8	−1.70187
$300$	0	0
$301$	−8.83067e7	−0.186643
$302$	−9.17932e8	−1.91773
$303$	0	0
$304$	2.01696e8	0.411755
$305$	−3.70436e7	−0.0747591
$306$	0	0
$307$	6.66587e8	1.31484	0.657420	−	0.753525i	$-0.271648\pi$
$307$	6.66587e8	1.31484	0.657420	+	0.753525i	$0.271648\pi$
$308$	−1.17603e8	−0.229345
$309$	0	0
$310$	−1.38959e8	−0.264924
$311$	8.68038e8	1.63635	0.818177	−	0.574967i	$-0.194985\pi$
$311$	8.68038e8	1.63635	0.818177	+	0.574967i	$0.194985\pi$
$312$	0	0
$313$	6.01957e8	1.10958	0.554792	−	0.831989i	$-0.312798\pi$
$313$	6.01957e8	1.10958	0.554792	+	0.831989i	$0.312798\pi$
$314$	1.16922e9	2.13129
$315$	0	0
$316$	−7.78215e8	−1.38738
$317$	8.81210e8	1.55372	0.776859	−	0.629675i	$-0.216812\pi$
$317$	8.81210e8	1.55372	0.776859	+	0.629675i	$0.216812\pi$
$318$	0	0
$319$	4.72466e7	0.0814897
$320$	−7.47305e8	−1.27489
$321$	0	0
$322$	−1.16451e9	−1.94378
$323$	−4.98143e8	−0.822517
$324$	0	0
$325$	−3.24489e8	−0.524334
$326$	−9.72103e8	−1.55400
$327$	0	0
$328$	−6.49837e8	−1.01682
$329$	3.21161e8	0.497208
$330$	0	0
$331$	−8.76684e8	−1.32876	−0.664378	−	0.747397i	$-0.731303\pi$
$331$	−8.76684e8	−1.32876	−0.664378	+	0.747397i	$0.731303\pi$
$332$	7.14133e8	1.07102
$333$	0	0
$334$	1.96954e8	0.289236
$335$	−5.60574e8	−0.814659
$336$	0	0
$337$	−3.84104e8	−0.546694	−0.273347	−	0.961916i	$-0.588131\pi$
$337$	−3.84104e8	−0.546694	−0.273347	+	0.961916i	$0.588131\pi$
$338$	−1.86587e9	−2.62829
$339$	0	0
$340$	8.28244e8	1.14283
$341$	2.10626e7	0.0287655
$342$	0	0
$343$	4.59244e8	0.614488
$344$	−6.37952e7	−0.0844954
$345$	0	0
$346$	−5.97078e8	−0.774934
$347$	9.79801e8	1.25888	0.629441	−	0.777049i	$-0.283284\pi$
$347$	9.79801e8	1.25888	0.629441	+	0.777049i	$0.283284\pi$
$348$	0	0
$349$	−1.02828e9	−1.29485	−0.647427	−	0.762128i	$-0.724155\pi$
$349$	−1.02828e9	−1.29485	−0.647427	+	0.762128i	$0.724155\pi$
$350$	−4.80362e8	−0.598867
$351$	0	0
$352$	1.50631e8	0.184083
$353$	1.21223e9	1.46680	0.733402	−	0.679795i	$-0.237931\pi$
$353$	1.21223e9	1.46680	0.733402	+	0.679795i	$0.237931\pi$
$354$	0	0
$355$	−2.29185e8	−0.271887
$356$	5.16063e8	0.606217
$357$	0	0
$358$	1.84942e9	2.13032
$359$	−1.13679e9	−1.29673	−0.648365	−	0.761330i	$-0.724547\pi$
$359$	−1.13679e9	−1.29673	−0.648365	+	0.761330i	$0.724547\pi$
$360$	0	0
$361$	−3.09674e8	−0.346441
$362$	1.79392e9	1.98757
$363$	0	0
$364$	−2.52275e9	−2.74170
$365$	−6.18362e8	−0.665607
$366$	0	0
$367$	1.53409e9	1.62002	0.810009	−	0.586418i	$-0.199462\pi$
$367$	1.53409e9	1.62002	0.810009	+	0.586418i	$0.199462\pi$
$368$	5.03330e8	0.526484
$369$	0	0
$370$	−1.96498e9	−2.01676
$371$	9.91029e8	1.00758
$372$	0	0
$373$	−8.11683e8	−0.809852	−0.404926	−	0.914350i	$-0.632703\pi$
$373$	−8.11683e8	−0.809852	−0.404926	+	0.914350i	$0.632703\pi$
$374$	−2.17808e8	−0.215289
$375$	0	0
$376$	2.32016e8	0.225092
$377$	1.01351e9	0.974166
$378$	0	0
$379$	2.21198e8	0.208710	0.104355	−	0.994540i	$-0.466722\pi$
$379$	2.21198e8	0.208710	0.104355	+	0.994540i	$0.466722\pi$
$380$	−9.71325e8	−0.908076
$381$	0	0
$382$	1.14971e9	1.05528
$383$	−1.31039e9	−1.19180	−0.595901	−	0.803058i	$-0.703205\pi$
$383$	−1.31039e9	−1.19180	−0.595901	+	0.803058i	$0.703205\pi$
$384$	0	0
$385$	−1.55814e8	−0.139153
$386$	−8.92817e8	−0.790145
$387$	0	0
$388$	−1.71305e9	−1.48888
$389$	−2.22960e8	−0.192045	−0.0960226	−	0.995379i	$-0.530612\pi$
$389$	−2.22960e8	−0.192045	−0.0960226	+	0.995379i	$0.530612\pi$
$390$	0	0
$391$	−1.24311e9	−1.05170
$392$	−3.29028e8	−0.275887
$393$	0	0
$394$	−1.59854e9	−1.31670
$395$	−1.03107e9	−0.841780
$396$	0	0
$397$	−6.55657e8	−0.525909	−0.262954	−	0.964808i	$-0.584697\pi$
$397$	−6.55657e8	−0.525909	−0.262954	+	0.964808i	$0.584697\pi$
$398$	−1.07488e9	−0.854610
$399$	0	0
$400$	2.07624e8	0.162207
$401$	7.45083e8	0.577031	0.288516	−	0.957475i	$-0.406838\pi$
$401$	7.45083e8	0.577031	0.288516	+	0.957475i	$0.406838\pi$
$402$	0	0
$403$	4.51825e8	0.343877
$404$	1.95043e9	1.47162
$405$	0	0
$406$	1.50036e9	1.11264
$407$	2.97841e8	0.218980
$408$	0	0
$409$	−4.87681e8	−0.352456	−0.176228	−	0.984349i	$-0.556390\pi$
$409$	−4.87681e8	−0.352456	−0.176228	+	0.984349i	$0.556390\pi$
$410$	−3.24846e9	−2.32773
$411$	0	0
$412$	3.65565e8	0.257528
$413$	−1.68544e9	−1.17730
$414$	0	0
$415$	9.46167e8	0.649829
$416$	3.23125e9	2.20062
$417$	0	0
$418$	2.55434e8	0.171065
$419$	−1.39810e9	−0.928518	−0.464259	−	0.885700i	$-0.653679\pi$
$419$	−1.39810e9	−0.928518	−0.464259	+	0.885700i	$0.653679\pi$
$420$	0	0
$421$	−2.54250e9	−1.66063	−0.830316	−	0.557293i	$-0.811840\pi$
$421$	−2.54250e9	−1.66063	−0.830316	+	0.557293i	$0.811840\pi$
$422$	−2.52451e9	−1.63525
$423$	0	0
$424$	7.15947e8	0.456142
$425$	−5.12785e8	−0.324022
$426$	0	0
$427$	1.78306e8	0.110833
$428$	−2.42605e9	−1.49570
$429$	0	0
$430$	−3.18904e8	−0.193429
$431$	−6.45199e8	−0.388171	−0.194086	−	0.980985i	$-0.562174\pi$
$431$	−6.45199e8	−0.388171	−0.194086	+	0.980985i	$0.562174\pi$
$432$	0	0
$433$	−1.41525e9	−0.837770	−0.418885	−	0.908039i	$-0.637579\pi$
$433$	−1.41525e9	−0.837770	−0.418885	+	0.908039i	$0.637579\pi$
$434$	6.68865e8	0.392757
$435$	0	0
$436$	4.33342e9	2.50397
$437$	1.45786e9	0.835663
$438$	0	0
$439$	3.20780e9	1.80959	0.904797	−	0.425844i	$-0.140023\pi$
$439$	3.20780e9	1.80959	0.904797	+	0.425844i	$0.140023\pi$
$440$	−1.12564e8	−0.0629964
$441$	0	0
$442$	−4.67230e9	−2.57367
$443$	3.24734e9	1.77466	0.887328	−	0.461138i	$-0.152559\pi$
$443$	3.24734e9	1.77466	0.887328	+	0.461138i	$0.152559\pi$
$444$	0	0
$445$	6.83741e8	0.367817
$446$	−2.06621e9	−1.10281
$447$	0	0
$448$	3.59707e9	1.89006
$449$	9.00041e8	0.469246	0.234623	−	0.972086i	$-0.424615\pi$
$449$	9.00041e8	0.469246	0.234623	+	0.972086i	$0.424615\pi$
$450$	0	0
$451$	4.92383e8	0.252746
$452$	2.99595e9	1.52598
$453$	0	0
$454$	−4.05063e9	−2.03155
$455$	−3.34244e9	−1.66350
$456$	0	0
$457$	3.56466e9	1.74708	0.873538	−	0.486756i	$-0.161820\pi$
$457$	3.56466e9	1.74708	0.873538	+	0.486756i	$0.161820\pi$
$458$	−4.38119e9	−2.13090
$459$	0	0
$460$	−2.42394e9	−1.16110
$461$	−2.12032e9	−1.00797	−0.503986	−	0.863712i	$-0.668134\pi$
$461$	−2.12032e9	−1.00797	−0.503986	+	0.863712i	$0.668134\pi$
$462$	0	0
$463$	−1.32103e9	−0.618555	−0.309278	−	0.950972i	$-0.600087\pi$
$463$	−1.32103e9	−0.618555	−0.309278	+	0.950972i	$0.600087\pi$
$464$	−6.48494e8	−0.301365
$465$	0	0
$466$	2.80521e9	1.28415
$467$	−2.75292e7	−0.0125079	−0.00625395	−	0.999980i	$-0.501991\pi$
$467$	−2.75292e7	−0.0125079	−0.00625395	+	0.999980i	$0.501991\pi$
$468$	0	0
$469$	2.69826e9	1.20776
$470$	1.15982e9	0.515285
$471$	0	0
$472$	−1.21761e9	−0.532980
$473$	4.83377e7	0.0210026
$474$	0	0
$475$	6.01370e8	0.257463
$476$	−3.98667e9	−1.69428
$477$	0	0
$478$	−5.71178e9	−2.39207
$479$	−3.09426e9	−1.28642	−0.643209	−	0.765691i	$-0.722397\pi$
$479$	−3.09426e9	−1.28642	−0.643209	+	0.765691i	$0.722397\pi$
$480$	0	0
$481$	6.38914e9	2.61779
$482$	1.03443e9	0.420760
$483$	0	0
$484$	−3.32951e9	−1.33482
$485$	−2.26965e9	−0.903366
$486$	0	0
$487$	2.45364e9	0.962629	0.481315	−	0.876548i	$-0.340159\pi$
$487$	2.45364e9	0.962629	0.481315	+	0.876548i	$0.340159\pi$
$488$	1.28813e8	0.0501753
$489$	0	0
$490$	−1.64477e9	−0.631566
$491$	3.55312e9	1.35464	0.677321	−	0.735688i	$-0.263141\pi$
$491$	3.55312e9	1.35464	0.677321	+	0.735688i	$0.263141\pi$
$492$	0	0
$493$	1.60163e9	0.602003
$494$	5.47945e9	2.04500
$495$	0	0
$496$	−2.89100e8	−0.106381
$497$	1.10316e9	0.403080
$498$	0	0
$499$	1.61280e9	0.581069	0.290534	−	0.956865i	$-0.406167\pi$
$499$	1.61280e9	0.581069	0.290534	+	0.956865i	$0.406167\pi$
$500$	−4.13948e9	−1.48099
$501$	0	0
$502$	−2.33397e9	−0.823442
$503$	3.82508e9	1.34015	0.670074	−	0.742294i	$-0.266262\pi$
$503$	3.82508e9	1.34015	0.670074	+	0.742294i	$0.266262\pi$
$504$	0	0
$505$	2.58415e9	0.892891
$506$	6.37435e8	0.218730
$507$	0	0
$508$	−6.42186e9	−2.17339
$509$	−9.34320e8	−0.314039	−0.157019	−	0.987596i	$-0.550189\pi$
$509$	−9.34320e8	−0.314039	−0.157019	+	0.987596i	$0.550189\pi$
$510$	0	0
$511$	2.97642e9	0.986782
$512$	−2.92457e9	−0.962981
$513$	0	0
$514$	−4.43174e9	−1.43947
$515$	4.84343e8	0.156253
$516$	0	0
$517$	−1.75799e8	−0.0559499
$518$	9.45825e9	2.98990
$519$	0	0
$520$	−2.41467e9	−0.753088
$521$	−1.99243e9	−0.617237	−0.308619	−	0.951186i	$-0.599867\pi$
$521$	−1.99243e9	−0.617237	−0.308619	+	0.951186i	$0.599867\pi$
$522$	0	0
$523$	−2.41120e9	−0.737017	−0.368509	−	0.929624i	$-0.620132\pi$
$523$	−2.41120e9	−0.737017	−0.368509	+	0.929624i	$0.620132\pi$
$524$	−4.21228e9	−1.27896
$525$	0	0
$526$	3.16570e9	0.948460
$527$	7.14012e8	0.212505
$528$	0	0
$529$	2.33258e8	0.0685081
$530$	3.57893e9	1.04421
$531$	0	0
$532$	4.67537e9	1.34625
$533$	1.05623e10	3.02145
$534$	0	0
$535$	−3.21431e9	−0.907506
$536$	1.94930e9	0.546766
$537$	0	0
$538$	−8.46382e9	−2.34330
$539$	2.49305e8	0.0685757
$540$	0	0
$541$	4.57719e9	1.24282	0.621410	−	0.783486i	$-0.286560\pi$
$541$	4.57719e9	1.24282	0.621410	+	0.783486i	$0.286560\pi$
$542$	9.69710e8	0.261604
$543$	0	0
$544$	5.10630e9	1.35991
$545$	5.74143e9	1.51926
$546$	0	0
$547$	1.95785e9	0.511475	0.255737	−	0.966746i	$-0.417682\pi$
$547$	1.95785e9	0.511475	0.255737	+	0.966746i	$0.417682\pi$
$548$	7.61225e8	0.197597
$549$	0	0
$550$	2.62943e8	0.0673894
$551$	−1.87832e9	−0.478342
$552$	0	0
$553$	4.96295e9	1.24796
$554$	−1.19664e10	−2.99007
$555$	0	0
$556$	4.53381e9	1.11867
$557$	5.46100e9	1.33899	0.669497	−	0.742814i	$-0.266510\pi$
$557$	5.46100e9	1.33899	0.669497	+	0.742814i	$0.266510\pi$
$558$	0	0
$559$	1.03692e9	0.251074
$560$	2.13866e9	0.514616
$561$	0	0
$562$	4.11652e9	0.978256
$563$	−1.67608e9	−0.395836	−0.197918	−	0.980219i	$-0.563418\pi$
$563$	−1.67608e9	−0.395836	−0.197918	+	0.980219i	$0.563418\pi$
$564$	0	0
$565$	3.96938e9	0.925877
$566$	−5.25749e9	−1.21877
$567$	0	0
$568$	7.96953e8	0.182479
$569$	6.70164e8	0.152506	0.0762532	−	0.997088i	$-0.475704\pi$
$569$	6.70164e8	0.152506	0.0762532	+	0.997088i	$0.475704\pi$
$570$	0	0
$571$	−4.11196e9	−0.924320	−0.462160	−	0.886797i	$-0.652925\pi$
$571$	−4.11196e9	−0.924320	−0.462160	+	0.886797i	$0.652925\pi$
$572$	1.38092e9	0.308518
$573$	0	0
$574$	1.56361e10	3.45094
$575$	1.50071e9	0.329201
$576$	0	0
$577$	3.72343e9	0.806915	0.403458	−	0.914998i	$-0.367808\pi$
$577$	3.72343e9	0.806915	0.403458	+	0.914998i	$0.367808\pi$
$578$	−2.50746e8	−0.0540116
$579$	0	0
$580$	3.12301e9	0.664624
$581$	−4.55427e9	−0.963391
$582$	0	0
$583$	−5.42474e8	−0.113381
$584$	2.15025e9	0.446729
$585$	0	0
$586$	−1.20908e10	−2.48206
$587$	5.57358e9	1.13737	0.568684	−	0.822556i	$-0.307453\pi$
$587$	5.57358e9	1.13737	0.568684	+	0.822556i	$0.307453\pi$
$588$	0	0
$589$	−8.37359e8	−0.168853
$590$	−6.08668e9	−1.22011
$591$	0	0
$592$	−4.08809e9	−0.809832
$593$	7.08618e9	1.39547	0.697735	−	0.716356i	$-0.254191\pi$
$593$	7.08618e9	1.39547	0.697735	+	0.716356i	$0.254191\pi$
$594$	0	0
$595$	−5.28200e9	−1.02799
$596$	−4.62397e9	−0.894650
$597$	0	0
$598$	1.36739e10	2.61480
$599$	9.43000e9	1.79274	0.896371	−	0.443304i	$-0.146194\pi$
$599$	9.43000e9	1.79274	0.896371	+	0.443304i	$0.146194\pi$
$600$	0	0
$601$	−8.09030e9	−1.52021	−0.760106	−	0.649799i	$-0.774853\pi$
$601$	−8.09030e9	−1.52021	−0.760106	+	0.649799i	$0.774853\pi$
$602$	1.53501e9	0.286764
$603$	0	0
$604$	9.19688e9	1.69829
$605$	−4.41132e9	−0.809888
$606$	0	0
$607$	−5.71746e9	−1.03763	−0.518815	−	0.854886i	$-0.673627\pi$
$607$	−5.71746e9	−1.03763	−0.518815	+	0.854886i	$0.673627\pi$
$608$	−5.98843e9	−1.08056
$609$	0	0
$610$	6.43920e8	0.114862
$611$	−3.77115e9	−0.668851
$612$	0	0
$613$	−2.69282e9	−0.472166	−0.236083	−	0.971733i	$-0.575864\pi$
$613$	−2.69282e9	−0.472166	−0.236083	+	0.971733i	$0.575864\pi$
$614$	−1.15871e10	−2.02016
$615$	0	0
$616$	5.41816e8	0.0933940
$617$	−3.24038e9	−0.555390	−0.277695	−	0.960669i	$-0.589571\pi$
$617$	−3.24038e9	−0.555390	−0.277695	+	0.960669i	$0.589571\pi$
$618$	0	0
$619$	−2.96275e9	−0.502086	−0.251043	−	0.967976i	$-0.580773\pi$
$619$	−2.96275e9	−0.502086	−0.251043	+	0.967976i	$0.580773\pi$
$620$	1.39225e9	0.234610
$621$	0	0
$622$	−1.50889e10	−2.51415
$623$	−3.29112e9	−0.545299
$624$	0	0
$625$	−3.54067e9	−0.580103
$626$	−1.04637e10	−1.70480
$627$	0	0
$628$	−1.17146e10	−1.88741
$629$	1.00967e10	1.61771
$630$	0	0
$631$	−2.21319e9	−0.350685	−0.175342	−	0.984508i	$-0.556103\pi$
$631$	−2.21319e9	−0.350685	−0.175342	+	0.984508i	$0.556103\pi$
$632$	3.58537e9	0.564969
$633$	0	0
$634$	−1.53179e10	−2.38718
$635$	−8.50843e9	−1.31869
$636$	0	0
$637$	5.34796e9	0.819786
$638$	−8.21275e8	−0.125203
$639$	0	0
$640$	5.67243e9	0.855341
$641$	3.46476e9	0.519600	0.259800	−	0.965662i	$-0.416343\pi$
$641$	3.46476e9	0.519600	0.259800	+	0.965662i	$0.416343\pi$
$642$	0	0
$643$	6.65219e9	0.986794	0.493397	−	0.869804i	$-0.335755\pi$
$643$	6.65219e9	0.986794	0.493397	+	0.869804i	$0.335755\pi$
$644$	1.16674e10	1.72136
$645$	0	0
$646$	8.65908e9	1.26374
$647$	5.79744e9	0.841533	0.420766	−	0.907169i	$-0.361761\pi$
$647$	5.79744e9	0.841533	0.420766	+	0.907169i	$0.361761\pi$
$648$	0	0
$649$	9.22585e8	0.132480
$650$	5.64051e9	0.805604
$651$	0	0
$652$	9.73962e9	1.37618
$653$	−5.81937e9	−0.817861	−0.408931	−	0.912566i	$-0.634098\pi$
$653$	−5.81937e9	−0.817861	−0.408931	+	0.912566i	$0.634098\pi$
$654$	0	0
$655$	−5.58092e9	−0.775999
$656$	−6.75832e9	−0.934706
$657$	0	0
$658$	−5.58267e9	−0.763926
$659$	6.30400e9	0.858059	0.429029	−	0.903290i	$-0.358856\pi$
$659$	6.30400e9	0.858059	0.429029	+	0.903290i	$0.358856\pi$
$660$	0	0
$661$	−5.51668e9	−0.742973	−0.371486	−	0.928438i	$-0.621152\pi$
$661$	−5.51668e9	−0.742973	−0.371486	+	0.928438i	$0.621152\pi$
$662$	1.52392e10	2.04154
$663$	0	0
$664$	−3.29013e9	−0.436139
$665$	6.19448e9	0.816825
$666$	0	0
$667$	−4.68733e9	−0.611625
$668$	−1.97331e9	−0.256140
$669$	0	0
$670$	9.74431e9	1.25167
$671$	−9.76017e7	−0.0124718
$672$	0	0
$673$	5.21617e9	0.659628	0.329814	−	0.944046i	$-0.393014\pi$
$673$	5.21617e9	0.659628	0.329814	+	0.944046i	$0.393014\pi$
$674$	6.67678e9	0.839958
$675$	0	0
$676$	1.86944e10	2.32755
$677$	−3.56727e9	−0.441851	−0.220925	−	0.975291i	$-0.570908\pi$
$677$	−3.56727e9	−0.441851	−0.220925	+	0.975291i	$0.570908\pi$
$678$	0	0
$679$	1.09247e10	1.33927
$680$	−3.81586e9	−0.465384
$681$	0	0
$682$	−3.66127e8	−0.0441963
$683$	6.40635e9	0.769375	0.384688	−	0.923047i	$-0.374309\pi$
$683$	6.40635e9	0.769375	0.384688	+	0.923047i	$0.374309\pi$
$684$	0	0
$685$	1.00856e9	0.119890
$686$	−7.98291e9	−0.944120
$687$	0	0
$688$	−6.63471e8	−0.0776716
$689$	−1.16369e10	−1.35541
$690$	0	0
$691$	−1.21339e10	−1.39903	−0.699513	−	0.714620i	$-0.746600\pi$
$691$	−1.21339e10	−1.39903	−0.699513	+	0.714620i	$0.746600\pi$
$692$	5.98220e9	0.686261
$693$	0	0
$694$	−1.70316e10	−1.93419
$695$	6.00693e9	0.678744
$696$	0	0
$697$	1.66915e10	1.86716
$698$	1.78743e10	1.98946
$699$	0	0
$700$	4.81280e9	0.530341
$701$	−1.62846e10	−1.78552	−0.892759	−	0.450535i	$-0.851233\pi$
$701$	−1.62846e10	−1.78552	−0.892759	+	0.450535i	$0.851233\pi$
$702$	0	0
$703$	−1.18409e10	−1.28541
$704$	−1.96898e9	−0.212686
$705$	0	0
$706$	−2.10718e10	−2.25364
$707$	−1.24386e10	−1.32374
$708$	0	0
$709$	−3.23891e9	−0.341301	−0.170650	−	0.985332i	$-0.554587\pi$
$709$	−3.23891e9	−0.341301	−0.170650	+	0.985332i	$0.554587\pi$
$710$	3.98387e9	0.417735
$711$	0	0
$712$	−2.37759e9	−0.246864
$713$	−2.08962e9	−0.215901
$714$	0	0
$715$	1.82960e9	0.187191
$716$	−1.85295e10	−1.88655
$717$	0	0
$718$	1.97605e10	1.99234
$719$	−8.54046e9	−0.856900	−0.428450	−	0.903565i	$-0.640940\pi$
$719$	−8.54046e9	−0.856900	−0.428450	+	0.903565i	$0.640940\pi$
$720$	0	0
$721$	−2.33133e9	−0.231649
$722$	5.38298e9	0.532283
$723$	0	0
$724$	−1.79735e10	−1.76014
$725$	−1.93353e9	−0.188438
$726$	0	0
$727$	−9.39101e9	−0.906445	−0.453223	−	0.891397i	$-0.649726\pi$
$727$	−9.39101e9	−0.906445	−0.453223	+	0.891397i	$0.649726\pi$
$728$	1.16228e10	1.11648
$729$	0	0
$730$	1.07488e10	1.02266
$731$	1.63862e9	0.155156
$732$	0	0
$733$	6.63206e9	0.621991	0.310996	−	0.950411i	$-0.399338\pi$
$733$	6.63206e9	0.621991	0.310996	+	0.950411i	$0.399338\pi$
$734$	−2.66667e10	−2.48905
$735$	0	0
$736$	−1.49441e10	−1.38165
$737$	−1.47699e9	−0.135907
$738$	0	0
$739$	9.73593e9	0.887405	0.443703	−	0.896174i	$-0.353665\pi$
$739$	9.73593e9	0.887405	0.443703	+	0.896174i	$0.353665\pi$
$740$	1.96874e10	1.78598
$741$	0	0
$742$	−1.72268e10	−1.54807
$743$	1.04679e9	0.0936265	0.0468132	−	0.998904i	$-0.485093\pi$
$743$	1.04679e9	0.0936265	0.0468132	+	0.998904i	$0.485093\pi$
$744$	0	0
$745$	−6.12638e9	−0.542822
$746$	1.41093e10	1.24428
$747$	0	0
$748$	2.18224e9	0.190654
$749$	1.54717e10	1.34540
$750$	0	0
$751$	1.53753e10	1.32460	0.662300	−	0.749239i	$-0.269580\pi$
$751$	1.53753e10	1.32460	0.662300	+	0.749239i	$0.269580\pi$
$752$	2.41297e9	0.206914
$753$	0	0
$754$	−1.76176e10	−1.49674
$755$	1.21851e10	1.03042
$756$	0	0
$757$	−1.40954e9	−0.118098	−0.0590489	−	0.998255i	$-0.518807\pi$
$757$	−1.40954e9	−0.118098	−0.0590489	+	0.998255i	$0.518807\pi$
$758$	−3.84502e9	−0.320669
$759$	0	0
$760$	4.47506e9	0.369787
$761$	1.37074e10	1.12748	0.563740	−	0.825952i	$-0.309362\pi$
$761$	1.37074e10	1.12748	0.563740	+	0.825952i	$0.309362\pi$
$762$	0	0
$763$	−2.76358e10	−2.25235
$764$	−1.15191e10	−0.934529
$765$	0	0
$766$	2.27781e10	1.83112
$767$	1.97908e10	1.58373
$768$	0	0
$769$	−3.22094e9	−0.255412	−0.127706	−	0.991812i	$-0.540761\pi$
$769$	−3.22094e9	−0.255412	−0.127706	+	0.991812i	$0.540761\pi$
$770$	2.70847e9	0.213799
$771$	0	0
$772$	8.94524e9	0.699732
$773$	−1.47558e10	−1.14904	−0.574518	−	0.818492i	$-0.694810\pi$
$773$	−1.47558e10	−1.14904	−0.574518	+	0.818492i	$0.694810\pi$
$774$	0	0
$775$	−8.61973e8	−0.0665178
$776$	7.89234e9	0.606303
$777$	0	0
$778$	3.87566e9	0.295064
$779$	−1.95750e10	−1.48361
$780$	0	0
$781$	−6.03853e8	−0.0453579
$782$	2.16087e10	1.61586
$783$	0	0
$784$	−3.42190e9	−0.253607
$785$	−1.55208e10	−1.14517
$786$	0	0
$787$	−5.55719e9	−0.406390	−0.203195	−	0.979138i	$-0.565133\pi$
$787$	−5.55719e9	−0.406390	−0.203195	+	0.979138i	$0.565133\pi$
$788$	1.60159e10	1.16603
$789$	0	0
$790$	1.79228e10	1.29334
$791$	−1.91062e10	−1.37264
$792$	0	0
$793$	−2.09370e9	−0.149094
$794$	1.13971e10	0.808023
$795$	0	0
$796$	1.07693e10	0.756820
$797$	1.17611e10	0.822891	0.411446	−	0.911434i	$-0.365024\pi$
$797$	1.17611e10	0.822891	0.411446	+	0.911434i	$0.365024\pi$
$798$	0	0
$799$	−5.95949e9	−0.413328
$800$	−6.16446e9	−0.425677
$801$	0	0
$802$	−1.29516e10	−0.886569
$803$	−1.62925e9	−0.111041
$804$	0	0
$805$	1.54583e10	1.04442
$806$	−7.85396e9	−0.528343
$807$	0	0
$808$	−8.98595e9	−0.599273
$809$	−1.25815e10	−0.835433	−0.417717	−	0.908577i	$-0.637170\pi$
$809$	−1.25815e10	−0.835433	−0.417717	+	0.908577i	$0.637170\pi$
$810$	0	0
$811$	2.43090e10	1.60027	0.800136	−	0.599818i	$-0.204760\pi$
$811$	2.43090e10	1.60027	0.800136	+	0.599818i	$0.204760\pi$
$812$	−1.50323e10	−0.985325
$813$	0	0
$814$	−5.17730e9	−0.336448
$815$	1.29042e10	0.834986
$816$	0	0
$817$	−1.92170e9	−0.123284
$818$	8.47724e9	0.541524
$819$	0	0
$820$	3.25467e10	2.06138
$821$	9.75294e9	0.615084	0.307542	−	0.951534i	$-0.400494\pi$
$821$	9.75294e9	0.615084	0.307542	+	0.951534i	$0.400494\pi$
$822$	0	0
$823$	−1.00621e10	−0.629202	−0.314601	−	0.949224i	$-0.601871\pi$
$823$	−1.00621e10	−0.629202	−0.314601	+	0.949224i	$0.601871\pi$
$824$	−1.68422e9	−0.104871
$825$	0	0
$826$	2.92976e10	1.80885
$827$	1.80699e10	1.11093	0.555464	−	0.831541i	$-0.312541\pi$
$827$	1.80699e10	1.11093	0.555464	+	0.831541i	$0.312541\pi$
$828$	0	0
$829$	−5.71510e9	−0.348404	−0.174202	−	0.984710i	$-0.555735\pi$
$829$	−5.71510e9	−0.348404	−0.174202	+	0.984710i	$0.555735\pi$
$830$	−1.64470e10	−0.998419
$831$	0	0
$832$	−4.22376e10	−2.54254
$833$	8.45131e9	0.506601
$834$	0	0
$835$	−2.61447e9	−0.155410
$836$	−2.55923e9	−0.151491
$837$	0	0
$838$	2.43029e10	1.42660
$839$	1.09882e10	0.642332	0.321166	−	0.947023i	$-0.395925\pi$
$839$	1.09882e10	0.642332	0.321166	+	0.947023i	$0.395925\pi$
$840$	0	0
$841$	−1.12107e10	−0.649900
$842$	4.41956e10	2.55145
$843$	0	0
$844$	2.52933e10	1.44813
$845$	2.47686e10	1.41222
$846$	0	0
$847$	2.12334e10	1.20068
$848$	7.44586e9	0.419305
$849$	0	0
$850$	8.91362e9	0.497838
$851$	−2.95488e10	−1.64357
$852$	0	0
$853$	2.69850e10	1.48868	0.744338	−	0.667803i	$-0.232765\pi$
$853$	2.69850e10	1.48868	0.744338	+	0.667803i	$0.232765\pi$
$854$	−3.09944e9	−0.170287
$855$	0	0
$856$	1.11772e10	0.609082
$857$	−4.73891e9	−0.257185	−0.128593	−	0.991698i	$-0.541046\pi$
$857$	−4.73891e9	−0.257185	−0.128593	+	0.991698i	$0.541046\pi$
$858$	0	0
$859$	−1.73970e10	−0.936479	−0.468239	−	0.883602i	$-0.655111\pi$
$859$	−1.73970e10	−0.936479	−0.468239	+	0.883602i	$0.655111\pi$
$860$	3.19514e9	0.171295
$861$	0	0
$862$	1.12153e10	0.596399
$863$	−9.17138e9	−0.485732	−0.242866	−	0.970060i	$-0.578088\pi$
$863$	−9.17138e9	−0.485732	−0.242866	+	0.970060i	$0.578088\pi$
$864$	0	0
$865$	7.92592e9	0.416383
$866$	2.46009e10	1.28718
$867$	0	0
$868$	−6.70144e9	−0.347816
$869$	−2.71664e9	−0.140431
$870$	0	0
$871$	−3.16836e10	−1.62469
$872$	−1.99648e10	−1.01967
$873$	0	0
$874$	−2.53416e10	−1.28394
$875$	2.63989e10	1.33216
$876$	0	0
$877$	−4.84972e9	−0.242783	−0.121392	−	0.992605i	$-0.538736\pi$
$877$	−4.84972e9	−0.242783	−0.121392	+	0.992605i	$0.538736\pi$
$878$	−5.57603e10	−2.78032
$879$	0	0
$880$	−1.17067e9	−0.0579088
$881$	5.10633e9	0.251590	0.125795	−	0.992056i	$-0.459852\pi$
$881$	5.10633e9	0.251590	0.125795	+	0.992056i	$0.459852\pi$
$882$	0	0
$883$	2.88460e10	1.41001	0.705006	−	0.709201i	$-0.250944\pi$
$883$	2.88460e10	1.41001	0.705006	+	0.709201i	$0.250944\pi$
$884$	4.68123e10	2.27917
$885$	0	0
$886$	−5.64476e10	−2.72664
$887$	7.47479e9	0.359638	0.179819	−	0.983700i	$-0.442449\pi$
$887$	7.47479e9	0.359638	0.179819	+	0.983700i	$0.442449\pi$
$888$	0	0
$889$	4.09544e10	1.95499
$890$	−1.18853e10	−0.565126
$891$	0	0
$892$	2.07016e10	0.976622
$893$	6.98900e9	0.328424
$894$	0	0
$895$	−2.45501e10	−1.14465
$896$	−2.73037e10	−1.26807
$897$	0	0
$898$	−1.56452e10	−0.720964
$899$	2.69229e9	0.123584
$900$	0	0
$901$	−1.83896e10	−0.837597
$902$	−8.55896e9	−0.388328
$903$	0	0
$904$	−1.38029e10	−0.621412
$905$	−2.38134e10	−1.06795
$906$	0	0
$907$	3.37329e9	0.150116	0.0750581	−	0.997179i	$-0.476086\pi$
$907$	3.37329e9	0.150116	0.0750581	+	0.997179i	$0.476086\pi$
$908$	4.05837e10	1.79908
$909$	0	0
$910$	5.81007e10	2.55586
$911$	1.87342e10	0.820958	0.410479	−	0.911870i	$-0.365362\pi$
$911$	1.87342e10	0.820958	0.410479	+	0.911870i	$0.365362\pi$
$912$	0	0
$913$	2.49294e9	0.108409
$914$	−6.19636e10	−2.68426
$915$	0	0
$916$	4.38956e10	1.88707
$917$	2.68632e10	1.15044
$918$	0	0
$919$	2.69873e10	1.14698	0.573489	−	0.819214i	$-0.305590\pi$
$919$	2.69873e10	1.14698	0.573489	+	0.819214i	$0.305590\pi$
$920$	1.11675e10	0.472823
$921$	0	0
$922$	3.68570e10	1.54868
$923$	−1.29535e10	−0.542229
$924$	0	0
$925$	−1.21889e10	−0.506372
$926$	2.29631e10	0.950368
$927$	0	0
$928$	1.92541e10	0.790868
$929$	−1.85412e10	−0.758721	−0.379360	−	0.925249i	$-0.623856\pi$
$929$	−1.85412e10	−0.758721	−0.379360	+	0.925249i	$0.623856\pi$
$930$	0	0
$931$	−9.91129e9	−0.402537
$932$	−2.81058e10	−1.13721
$933$	0	0
$934$	4.78533e8	0.0192176
$935$	2.89129e9	0.115678
$936$	0	0
$937$	4.42644e10	1.75779	0.878893	−	0.477020i	$-0.158283\pi$
$937$	4.42644e10	1.75779	0.878893	+	0.477020i	$0.158283\pi$
$938$	−4.69032e10	−1.85563
$939$	0	0
$940$	−1.16204e10	−0.456323
$941$	−3.74450e10	−1.46498	−0.732488	−	0.680780i	$-0.761641\pi$
$941$	−3.74450e10	−1.46498	−0.732488	+	0.680780i	$0.761641\pi$
$942$	0	0
$943$	−4.88493e10	−1.89700
$944$	−1.26632e10	−0.489937
$945$	0	0
$946$	−8.40242e8	−0.0322690
$947$	3.20475e10	1.22622	0.613111	−	0.789996i	$-0.289918\pi$
$947$	3.20475e10	1.22622	0.613111	+	0.789996i	$0.289918\pi$
$948$	0	0
$949$	−3.49498e10	−1.32743
$950$	−1.04535e10	−0.395574
$951$	0	0
$952$	1.83673e10	0.689946
$953$	−3.72778e10	−1.39517	−0.697583	−	0.716504i	$-0.745741\pi$
$953$	−3.72778e10	−1.39517	−0.697583	+	0.716504i	$0.745741\pi$
$954$	0	0
$955$	−1.52619e10	−0.567018
$956$	5.72270e10	2.11835
$957$	0	0
$958$	5.37867e10	1.97649
$959$	−4.85460e9	−0.177741
$960$	0	0
$961$	−2.63124e10	−0.956375
$962$	−1.11061e11	−4.02205
$963$	0	0
$964$	−1.03640e10	−0.372614
$965$	1.18517e10	0.424556
$966$	0	0
$967$	9.26852e8	0.0329623	0.0164812	−	0.999864i	$-0.494754\pi$
$967$	9.26852e8	0.0329623	0.0164812	+	0.999864i	$0.494754\pi$
$968$	1.53396e10	0.543564
$969$	0	0
$970$	3.94528e10	1.38796
$971$	1.22212e10	0.428398	0.214199	−	0.976790i	$-0.431286\pi$
$971$	1.22212e10	0.428398	0.214199	+	0.976790i	$0.431286\pi$
$972$	0	0
$973$	−2.89137e10	−1.00626
$974$	−4.26510e10	−1.47901
$975$	0	0
$976$	1.33966e9	0.0461231
$977$	1.62117e10	0.556157	0.278078	−	0.960558i	$-0.410303\pi$
$977$	1.62117e10	0.556157	0.278078	+	0.960558i	$0.410303\pi$
$978$	0	0
$979$	1.80151e9	0.0613616
$980$	1.64792e10	0.559298
$981$	0	0
$982$	−6.17630e10	−2.08132
$983$	7.23772e9	0.243033	0.121516	−	0.992589i	$-0.461224\pi$
$983$	7.23772e9	0.243033	0.121516	+	0.992589i	$0.461224\pi$
$984$	0	0
$985$	2.12198e10	0.707480
$986$	−2.78408e10	−0.924937
$987$	0	0
$988$	−5.48992e10	−1.81099
$989$	−4.79559e9	−0.157636
$990$	0	0
$991$	4.83836e10	1.57921	0.789606	−	0.613614i	$-0.210285\pi$
$991$	4.83836e10	1.57921	0.789606	+	0.613614i	$0.210285\pi$
$992$	8.58351e9	0.279173
$993$	0	0
$994$	−1.91759e10	−0.619305
$995$	1.42685e10	0.459194
$996$	0	0
$997$	−4.51500e10	−1.44286	−0.721431	−	0.692486i	$-0.756515\pi$
$997$	−4.51500e10	−1.44286	−0.721431	+	0.692486i	$0.756515\pi$
$998$	−2.80348e10	−0.892772
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.b.1.1		11
3.2	odd	2		43.8.a.a.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.11	✓	11	3.2	odd	2
387.8.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q-17.3827 q^{2} +174.160 q^{4} +230.747 q^{5} -1110.68 q^{7} -802.384 q^{8} +O(q^{10})\)	\(q-17.3827 q^{2} +174.160 q^{4} +230.747 q^{5} -1110.68 q^{7} -802.384 q^{8} -4011.02 q^{10} +607.968 q^{11} +13041.8 q^{13} +19306.6 q^{14} -8344.81 q^{16} +20609.8 q^{17} -24170.2 q^{19} +40186.9 q^{20} -10568.2 q^{22} -60316.5 q^{23} -24880.7 q^{25} -226703. q^{26} -193435. q^{28} +77712.2 q^{29} +34644.3 q^{31} +247761. q^{32} -358255. q^{34} -256286. q^{35} +489896. q^{37} +420144. q^{38} -185148. q^{40} +809882. q^{41} +79507.0 q^{43} +105884. q^{44} +1.04847e6 q^{46} -289158. q^{47} +410063. q^{49} +432494. q^{50} +2.27136e6 q^{52} -892274. q^{53} +140287. q^{55} +891191. q^{56} -1.35085e6 q^{58} +1.51749e6 q^{59} -160538. q^{61} -602213. q^{62} -3.23863e6 q^{64} +3.00937e6 q^{65} -2.42938e6 q^{67} +3.58940e6 q^{68} +4.45495e6 q^{70} -993231. q^{71} -2.67982e6 q^{73} -8.51574e6 q^{74} -4.20947e6 q^{76} -675257. q^{77} -4.46840e6 q^{79} -1.92554e6 q^{80} -1.40780e7 q^{82} +4.10044e6 q^{83} +4.75566e6 q^{85} -1.38205e6 q^{86} -487824. q^{88} +2.96316e6 q^{89} -1.44853e7 q^{91} -1.05047e7 q^{92} +5.02636e6 q^{94} -5.57721e6 q^{95} -9.83610e6 q^{97} -7.12801e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) \) 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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