LMFDB - Embedded newform 387.8.a.b.1.9

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			1.9
Root			$13.1261$ 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)

$f(q)$	$=$	$q+15.1261 q^{2} +100.799 q^{4} -12.0619 q^{5} -1248.65 q^{7} -411.441 q^{8} +O(q^{10})$	\(q+15.1261 q^{2} +100.799 q^{4} -12.0619 q^{5} -1248.65 q^{7} -411.441 q^{8} -182.450 q^{10} +2043.21 q^{11} +9460.36 q^{13} -18887.2 q^{14} -19125.8 q^{16} +19027.5 q^{17} -28326.9 q^{19} -1215.83 q^{20} +30905.9 q^{22} -2087.68 q^{23} -77979.5 q^{25} +143098. q^{26} -125863. q^{28} +111967. q^{29} +7978.79 q^{31} -236635. q^{32} +287812. q^{34} +15061.1 q^{35} -185038. q^{37} -428475. q^{38} +4962.76 q^{40} +421826. q^{41} +79507.0 q^{43} +205954. q^{44} -31578.5 q^{46} -197368. q^{47} +735581. q^{49} -1.17953e6 q^{50} +953597. q^{52} +2.01317e6 q^{53} -24645.0 q^{55} +513745. q^{56} +1.69363e6 q^{58} +856041. q^{59} +2.61554e6 q^{61} +120688. q^{62} -1.13126e6 q^{64} -114110. q^{65} +2.93249e6 q^{67} +1.91796e6 q^{68} +227816. q^{70} +3.20003e6 q^{71} +4.19984e6 q^{73} -2.79891e6 q^{74} -2.85533e6 q^{76} -2.55125e6 q^{77} +7.83389e6 q^{79} +230694. q^{80} +6.38059e6 q^{82} -5.57533e6 q^{83} -229508. q^{85} +1.20263e6 q^{86} -840660. q^{88} +889160. q^{89} -1.18127e7 q^{91} -210437. q^{92} -2.98542e6 q^{94} +341676. q^{95} +1.05709e7 q^{97} +1.11265e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	15.1261	1.33697	0.668486	−	0.743725i	$-0.266943\pi$
$2$	15.1261	1.33697	0.668486	+	0.743725i	$0.266943\pi$
$3$	0	0
$3$	0	0
$4$	100.799	0.787495
$5$	−12.0619	−0.0431540	−0.0215770	−	0.999767i	$-0.506869\pi$
$5$	−12.0619	−0.0431540	−0.0215770	+	0.999767i	$0.506869\pi$
$6$	0	0
$7$	−1248.65	−1.37593	−0.687966	−	0.725743i	$-0.741496\pi$
$7$	−1248.65	−1.37593	−0.687966	+	0.725743i	$0.741496\pi$
$8$	−411.441	−0.284114
$9$	0	0
$10$	−182.450	−0.0576956
$11$	2043.21	0.462849	0.231424	−	0.972853i	$-0.425661\pi$
$11$	2043.21	0.462849	0.231424	+	0.972853i	$0.425661\pi$
$12$	0	0
$13$	9460.36	1.19428	0.597139	−	0.802137i	$-0.296304\pi$
$13$	9460.36	1.19428	0.597139	+	0.802137i	$0.296304\pi$
$14$	−18887.2	−1.83958
$15$	0	0
$16$	−19125.8	−1.16735
$17$	19027.5	0.939312	0.469656	−	0.882849i	$-0.344378\pi$
$17$	19027.5	0.939312	0.469656	+	0.882849i	$0.344378\pi$
$18$	0	0
$19$	−28326.9	−0.947460	−0.473730	−	0.880670i	$-0.657093\pi$
$19$	−28326.9	−0.947460	−0.473730	+	0.880670i	$0.657093\pi$
$20$	−1215.83	−0.0339835
$21$	0	0
$22$	30905.9	0.618816
$23$	−2087.68	−0.0357781	−0.0178890	−	0.999840i	$-0.505695\pi$
$23$	−2087.68	−0.0357781	−0.0178890	+	0.999840i	$0.505695\pi$
$24$	0	0
$25$	−77979.5	−0.998138
$26$	143098.	1.59672
$27$	0	0
$28$	−125863.	−1.08354
$29$	111967.	0.852508	0.426254	−	0.904603i	$-0.359833\pi$
$29$	111967.	0.852508	0.426254	+	0.904603i	$0.359833\pi$
$30$	0	0
$31$	7978.79	0.0481029	0.0240514	−	0.999711i	$-0.492343\pi$
$31$	7978.79	0.0481029	0.0240514	+	0.999711i	$0.492343\pi$
$32$	−236635.	−1.27660
$33$	0	0
$34$	287812.	1.25583
$35$	15061.1	0.0593769
$36$	0	0
$37$	−185038.	−0.600559	−0.300279	−	0.953851i	$-0.597080\pi$
$37$	−185038.	−0.600559	−0.300279	+	0.953851i	$0.597080\pi$
$38$	−428475.	−1.26673
$39$	0	0
$40$	4962.76	0.0122606
$41$	421826.	0.955851	0.477925	−	0.878400i	$-0.341389\pi$
$41$	421826.	0.955851	0.477925	+	0.878400i	$0.341389\pi$
$42$	0	0
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	205954.	0.364491
$45$	0	0
$46$	−31578.5	−0.0478343
$47$	−197368.	−0.277290	−0.138645	−	0.990342i	$-0.544275\pi$
$47$	−197368.	−0.277290	−0.138645	+	0.990342i	$0.544275\pi$
$48$	0	0
$49$	735581.	0.893191
$50$	−1.17953e6	−1.33448
$51$	0	0
$52$	953597.	0.940488
$53$	2.01317e6	1.85744	0.928722	−	0.370778i	$-0.120909\pi$
$53$	2.01317e6	1.85744	0.928722	+	0.370778i	$0.120909\pi$
$54$	0	0
$55$	−24645.0	−0.0199738
$56$	513745.	0.390921
$57$	0	0
$58$	1.69363e6	1.13978
$59$	856041.	0.542641	0.271321	−	0.962489i	$-0.412540\pi$
$59$	856041.	0.542641	0.271321	+	0.962489i	$0.412540\pi$
$60$	0	0
$61$	2.61554e6	1.47539	0.737695	−	0.675135i	$-0.235914\pi$
$61$	2.61554e6	1.47539	0.737695	+	0.675135i	$0.235914\pi$
$62$	120688.	0.0643122
$63$	0	0
$64$	−1.13126e6	−0.539427
$65$	−114110.	−0.0515379
$66$	0	0
$67$	2.93249e6	1.19117	0.595587	−	0.803291i	$-0.296920\pi$
$67$	2.93249e6	1.19117	0.595587	+	0.803291i	$0.296920\pi$
$68$	1.91796e6	0.739703
$69$	0	0
$70$	227816.	0.0793853
$71$	3.20003e6	1.06109	0.530543	−	0.847658i	$-0.321988\pi$
$71$	3.20003e6	1.06109	0.530543	+	0.847658i	$0.321988\pi$
$72$	0	0
$73$	4.19984e6	1.26358	0.631790	−	0.775140i	$-0.282321\pi$
$73$	4.19984e6	1.26358	0.631790	+	0.775140i	$0.282321\pi$
$74$	−2.79891e6	−0.802930
$75$	0	0
$76$	−2.85533e6	−0.746119
$77$	−2.55125e6	−0.636849
$78$	0	0
$79$	7.83389e6	1.78765	0.893825	−	0.448416i	$-0.148012\pi$
$79$	7.83389e6	1.78765	0.893825	+	0.448416i	$0.148012\pi$
$80$	230694.	0.0503756
$81$	0	0
$82$	6.38059e6	1.27795
$83$	−5.57533e6	−1.07028	−0.535140	−	0.844764i	$-0.679741\pi$
$83$	−5.57533e6	−1.07028	−0.535140	+	0.844764i	$0.679741\pi$
$84$	0	0
$85$	−229508.	−0.0405351
$86$	1.20263e6	0.203886
$87$	0	0
$88$	−840660.	−0.131502
$89$	889160.	0.133695	0.0668474	−	0.997763i	$-0.478706\pi$
$89$	889160.	0.133695	0.0668474	+	0.997763i	$0.478706\pi$
$90$	0	0
$91$	−1.18127e7	−1.64325
$92$	−210437.	−0.0281750
$93$	0	0
$94$	−2.98542e6	−0.370730
$95$	341676.	0.0408866
$96$	0	0
$97$	1.05709e7	1.17601	0.588003	−	0.808859i	$-0.299914\pi$
$97$	1.05709e7	1.17601	0.588003	+	0.808859i	$0.299914\pi$
$98$	1.11265e7	1.19417
$99$	0	0
$100$	−7.86028e6	−0.786028
$101$	−613031.	−0.0592049	−0.0296024	−	0.999562i	$-0.509424\pi$
$101$	−613031.	−0.0592049	−0.0296024	+	0.999562i	$0.509424\pi$
$102$	0	0
$103$	−1.58867e7	−1.43253	−0.716265	−	0.697828i	$-0.754150\pi$
$103$	−1.58867e7	−1.43253	−0.716265	+	0.697828i	$0.754150\pi$
$104$	−3.89238e6	−0.339311
$105$	0	0
$106$	3.04515e7	2.48335
$107$	2.82221e6	0.222713	0.111357	−	0.993781i	$-0.464480\pi$
$107$	2.82221e6	0.222713	0.111357	+	0.993781i	$0.464480\pi$
$108$	0	0
$109$	−2.05758e6	−0.152183	−0.0760913	−	0.997101i	$-0.524244\pi$
$109$	−2.05758e6	−0.152183	−0.0760913	+	0.997101i	$0.524244\pi$
$110$	−372783.	−0.0267044
$111$	0	0
$112$	2.38814e7	1.60619
$113$	−1.63742e6	−0.106754	−0.0533770	−	0.998574i	$-0.516999\pi$
$113$	−1.63742e6	−0.106754	−0.0533770	+	0.998574i	$0.516999\pi$
$114$	0	0
$115$	25181.4	0.00154396
$116$	1.12862e7	0.671346
$117$	0	0
$118$	1.29486e7	0.725496
$119$	−2.37586e7	−1.29243
$120$	0	0
$121$	−1.53125e7	−0.785771
$122$	3.95629e7	1.97255
$123$	0	0
$124$	804256.	0.0378808
$125$	1.88292e6	0.0862276
$126$	0	0
$127$	6.60627e6	0.286183	0.143091	−	0.989709i	$-0.454296\pi$
$127$	6.60627e6	0.286183	0.143091	+	0.989709i	$0.454296\pi$
$128$	1.31777e7	0.555397
$129$	0	0
$130$	−1.72604e6	−0.0689047
$131$	5.79186e6	0.225096	0.112548	−	0.993646i	$-0.464099\pi$
$131$	5.79186e6	0.225096	0.112548	+	0.993646i	$0.464099\pi$
$132$	0	0
$133$	3.53703e7	1.30364
$134$	4.43572e7	1.59257
$135$	0	0
$136$	−7.82868e6	−0.266872
$137$	−2.00914e7	−0.667556	−0.333778	−	0.942652i	$-0.608324\pi$
$137$	−2.00914e7	−0.667556	−0.333778	+	0.942652i	$0.608324\pi$
$138$	0	0
$139$	2.57362e7	0.812817	0.406408	−	0.913692i	$-0.366781\pi$
$139$	2.57362e7	0.812817	0.406408	+	0.913692i	$0.366781\pi$
$140$	1.51815e6	0.0467590
$141$	0	0
$142$	4.84041e7	1.41864
$143$	1.93295e7	0.552770
$144$	0	0
$145$	−1.35054e6	−0.0367891
$146$	6.35272e7	1.68937
$147$	0	0
$148$	−1.86517e7	−0.472937
$149$	−2.86333e7	−0.709121	−0.354560	−	0.935033i	$-0.615369\pi$
$149$	−2.86333e7	−0.709121	−0.354560	+	0.935033i	$0.615369\pi$
$150$	0	0
$151$	−6.67796e7	−1.57843	−0.789213	−	0.614119i	$-0.789511\pi$
$151$	−6.67796e7	−1.57843	−0.789213	+	0.614119i	$0.789511\pi$
$152$	1.16548e7	0.269186
$153$	0	0
$154$	−3.85906e7	−0.851449
$155$	−96239.3	−0.00207583
$156$	0	0
$157$	−8.44900e7	−1.74243	−0.871217	−	0.490898i	$-0.836669\pi$
$157$	−8.44900e7	−1.74243	−0.871217	+	0.490898i	$0.836669\pi$
$158$	1.18496e8	2.39004
$159$	0	0
$160$	2.85426e6	0.0550902
$161$	2.60678e6	0.0492282
$162$	0	0
$163$	6.39006e7	1.15571	0.577854	−	0.816140i	$-0.303890\pi$
$163$	6.39006e7	1.15571	0.577854	+	0.816140i	$0.303890\pi$
$164$	4.25198e7	0.752727
$165$	0	0
$166$	−8.43330e7	−1.43093
$167$	1.62544e7	0.270061	0.135031	−	0.990841i	$-0.456887\pi$
$167$	1.62544e7	0.270061	0.135031	+	0.990841i	$0.456887\pi$
$168$	0	0
$169$	2.67498e7	0.426302
$170$	−3.47156e6	−0.0541942
$171$	0	0
$172$	8.01425e6	0.120092
$173$	1.19428e8	1.75366	0.876830	−	0.480801i	$-0.159654\pi$
$173$	1.19428e8	1.75366	0.876830	+	0.480801i	$0.159654\pi$
$174$	0	0
$175$	9.73690e7	1.37337
$176$	−3.90781e7	−0.540305
$177$	0	0
$178$	1.34495e7	0.178746
$179$	−6.67618e7	−0.870047	−0.435023	−	0.900419i	$-0.643260\pi$
$179$	−6.67618e7	−0.870047	−0.435023	+	0.900419i	$0.643260\pi$
$180$	0	0
$181$	1.24721e8	1.56339	0.781693	−	0.623664i	$-0.214357\pi$
$181$	1.24721e8	1.56339	0.781693	+	0.623664i	$0.214357\pi$
$182$	−1.78680e8	−2.19698
$183$	0	0
$184$	858957.	0.0101650
$185$	2.23191e6	0.0259165
$186$	0	0
$187$	3.88772e7	0.434759
$188$	−1.98946e7	−0.218365
$189$	0	0
$190$	5.16822e6	0.0546643
$191$	−7.43805e7	−0.772400	−0.386200	−	0.922415i	$-0.626213\pi$
$191$	−7.43805e7	−0.772400	−0.386200	+	0.922415i	$0.626213\pi$
$192$	0	0
$193$	9.08749e7	0.909900	0.454950	−	0.890517i	$-0.349657\pi$
$193$	9.08749e7	0.909900	0.454950	+	0.890517i	$0.349657\pi$
$194$	1.59896e8	1.57229
$195$	0	0
$196$	7.41460e7	0.703383
$197$	1.24750e8	1.16254	0.581270	−	0.813711i	$-0.302556\pi$
$197$	1.24750e8	1.16254	0.581270	+	0.813711i	$0.302556\pi$
$198$	0	0
$199$	−1.75151e8	−1.57553	−0.787767	−	0.615973i	$-0.788763\pi$
$199$	−1.75151e8	−1.57553	−0.787767	+	0.615973i	$0.788763\pi$
$200$	3.20839e7	0.283585
$201$	0	0
$202$	−9.27277e6	−0.0791553
$203$	−1.39808e8	−1.17299
$204$	0	0
$205$	−5.08803e6	−0.0412487
$206$	−2.40304e8	−1.91525
$207$	0	0
$208$	−1.80937e8	−1.39414
$209$	−5.78778e7	−0.438530
$210$	0	0
$211$	8.95521e7	0.656277	0.328138	−	0.944630i	$-0.393579\pi$
$211$	8.95521e7	0.656277	0.328138	+	0.944630i	$0.393579\pi$
$212$	2.02926e8	1.46273
$213$	0	0
$214$	4.26891e7	0.297761
$215$	−959005.	−0.00658092
$216$	0	0
$217$	−9.96271e6	−0.0661863
$218$	−3.11233e7	−0.203464
$219$	0	0
$220$	−2.48420e6	−0.0157292
$221$	1.80007e8	1.12180
$222$	0	0
$223$	−1.68028e8	−1.01464	−0.507322	−	0.861757i	$-0.669364\pi$
$223$	−1.68028e8	−1.01464	−0.507322	+	0.861757i	$0.669364\pi$
$224$	2.95474e8	1.75651
$225$	0	0
$226$	−2.47677e7	−0.142727
$227$	−1.05659e8	−0.599538	−0.299769	−	0.954012i	$-0.596910\pi$
$227$	−1.05659e8	−0.599538	−0.299769	+	0.954012i	$0.596910\pi$
$228$	0	0
$229$	−2.91314e8	−1.60301	−0.801506	−	0.597987i	$-0.795967\pi$
$229$	−2.91314e8	−1.60301	−0.801506	+	0.597987i	$0.795967\pi$
$230$	380897.	0.00206424
$231$	0	0
$232$	−4.60680e7	−0.242209
$233$	2.72762e8	1.41266	0.706332	−	0.707881i	$-0.250349\pi$
$233$	2.72762e8	1.41266	0.706332	+	0.707881i	$0.250349\pi$
$234$	0	0
$235$	2.38064e6	0.0119662
$236$	8.62884e7	0.427327
$237$	0	0
$238$	−3.59376e8	−1.72794
$239$	−2.25857e8	−1.07014	−0.535069	−	0.844808i	$-0.679715\pi$
$239$	−2.25857e8	−1.07014	−0.535069	+	0.844808i	$0.679715\pi$
$240$	0	0
$241$	2.02550e8	0.932122	0.466061	−	0.884753i	$-0.345673\pi$
$241$	2.02550e8	0.932122	0.466061	+	0.884753i	$0.345673\pi$
$242$	−2.31618e8	−1.05055
$243$	0	0
$244$	2.63644e8	1.16186
$245$	−8.87250e6	−0.0385447
$246$	0	0
$247$	−2.67982e8	−1.13153
$248$	−3.28280e6	−0.0136667
$249$	0	0
$250$	2.84812e7	0.115284
$251$	−4.56654e8	−1.82276	−0.911379	−	0.411567i	$-0.864981\pi$
$251$	−4.56654e8	−1.82276	−0.911379	+	0.411567i	$0.864981\pi$
$252$	0	0
$253$	−4.26557e6	−0.0165598
$254$	9.99272e7	0.382618
$255$	0	0
$256$	3.44128e8	1.28198
$257$	−6.13602e7	−0.225487	−0.112743	−	0.993624i	$-0.535964\pi$
$257$	−6.13602e7	−0.225487	−0.112743	+	0.993624i	$0.535964\pi$
$258$	0	0
$259$	2.31048e8	0.826328
$260$	−1.15022e7	−0.0405858
$261$	0	0
$262$	8.76083e7	0.300947
$263$	5.34920e8	1.81319	0.906596	−	0.422000i	$-0.138672\pi$
$263$	5.34920e8	1.81319	0.906596	+	0.422000i	$0.138672\pi$
$264$	0	0
$265$	−2.42827e7	−0.0801560
$266$	5.35015e8	1.74293
$267$	0	0
$268$	2.95593e8	0.938043
$269$	1.68231e8	0.526956	0.263478	−	0.964665i	$-0.415130\pi$
$269$	1.68231e8	0.526956	0.263478	+	0.964665i	$0.415130\pi$
$270$	0	0
$271$	3.63723e8	1.11014	0.555071	−	0.831803i	$-0.312691\pi$
$271$	3.63723e8	1.11014	0.555071	+	0.831803i	$0.312691\pi$
$272$	−3.63916e8	−1.09650
$273$	0	0
$274$	−3.03904e8	−0.892504
$275$	−1.59329e8	−0.461987
$276$	0	0
$277$	−2.54748e8	−0.720165	−0.360083	−	0.932920i	$-0.617252\pi$
$277$	−2.54748e8	−0.720165	−0.360083	+	0.932920i	$0.617252\pi$
$278$	3.89289e8	1.08671
$279$	0	0
$280$	−6.19674e6	−0.0168698
$281$	5.70700e8	1.53439	0.767195	−	0.641414i	$-0.221652\pi$
$281$	5.70700e8	1.53439	0.767195	+	0.641414i	$0.221652\pi$
$282$	0	0
$283$	−2.06689e8	−0.542083	−0.271041	−	0.962568i	$-0.587368\pi$
$283$	−2.06689e8	−0.542083	−0.271041	+	0.962568i	$0.587368\pi$
$284$	3.22561e8	0.835599
$285$	0	0
$286$	2.92380e8	0.739039
$287$	−5.26713e8	−1.31519
$288$	0	0
$289$	−4.82937e7	−0.117692
$290$	−2.04284e7	−0.0491860
$291$	0	0
$292$	4.23341e8	0.995062
$293$	−8.14731e8	−1.89225	−0.946123	−	0.323808i	$-0.895037\pi$
$293$	−8.14731e8	−1.89225	−0.946123	+	0.323808i	$0.895037\pi$
$294$	0	0
$295$	−1.03255e7	−0.0234171
$296$	7.61323e7	0.170627
$297$	0	0
$298$	−4.33111e8	−0.948075
$299$	−1.97502e7	−0.0427290
$300$	0	0
$301$	−9.92763e7	−0.209828
$302$	−1.01012e9	−2.11031
$303$	0	0
$304$	5.41774e8	1.10601
$305$	−3.15484e7	−0.0636689
$306$	0	0
$307$	−1.50628e8	−0.297112	−0.148556	−	0.988904i	$-0.547463\pi$
$307$	−1.50628e8	−0.297112	−0.148556	+	0.988904i	$0.547463\pi$
$308$	−2.57165e8	−0.501515
$309$	0	0
$310$	−1.45573e6	−0.00277533
$311$	6.59750e8	1.24371	0.621853	−	0.783134i	$-0.286380\pi$
$311$	6.59750e8	1.24371	0.621853	+	0.783134i	$0.286380\pi$
$312$	0	0
$313$	−3.46916e8	−0.639469	−0.319735	−	0.947507i	$-0.603594\pi$
$313$	−3.46916e8	−0.639469	−0.319735	+	0.947507i	$0.603594\pi$
$314$	−1.27801e9	−2.32959
$315$	0	0
$316$	7.89650e8	1.40776
$317$	9.98461e8	1.76045	0.880225	−	0.474557i	$-0.157392\pi$
$317$	9.98461e8	1.76045	0.880225	+	0.474557i	$0.157392\pi$
$318$	0	0
$319$	2.28773e8	0.394582
$320$	1.36452e7	0.0232784
$321$	0	0
$322$	3.94305e7	0.0658167
$323$	−5.38989e8	−0.889961
$324$	0	0
$325$	−7.37714e8	−1.19205
$326$	9.66567e8	1.54515
$327$	0	0
$328$	−1.73556e8	−0.271570
$329$	2.46444e8	0.381533
$330$	0	0
$331$	7.96597e8	1.20737	0.603686	−	0.797222i	$-0.293698\pi$
$331$	7.96597e8	1.20737	0.603686	+	0.797222i	$0.293698\pi$
$332$	−5.61989e8	−0.842839
$333$	0	0
$334$	2.45865e8	0.361065
$335$	−3.53714e7	−0.0514039
$336$	0	0
$337$	−1.10141e9	−1.56764	−0.783818	−	0.620991i	$-0.786730\pi$
$337$	−1.10141e9	−1.56764	−0.783818	+	0.620991i	$0.786730\pi$
$338$	4.04621e8	0.569954
$339$	0	0
$340$	−2.31342e7	−0.0319211
$341$	1.63024e7	0.0222643
$342$	0	0
$343$	1.09834e8	0.146963
$344$	−3.27124e7	−0.0433269
$345$	0	0
$346$	1.80648e9	2.34459
$347$	5.91060e8	0.759414	0.379707	−	0.925107i	$-0.376025\pi$
$347$	5.91060e8	0.759414	0.379707	+	0.925107i	$0.376025\pi$
$348$	0	0
$349$	1.16064e9	1.46153	0.730764	−	0.682631i	$-0.239164\pi$
$349$	1.16064e9	1.46153	0.730764	+	0.682631i	$0.239164\pi$
$350$	1.47281e9	1.83616
$351$	0	0
$352$	−4.83495e8	−0.590871
$353$	2.28005e8	0.275888	0.137944	−	0.990440i	$-0.455951\pi$
$353$	2.28005e8	0.275888	0.137944	+	0.990440i	$0.455951\pi$
$354$	0	0
$355$	−3.85985e7	−0.0457900
$356$	8.96267e7	0.105284
$357$	0	0
$358$	−1.00985e9	−1.16323
$359$	1.34720e9	1.53674	0.768371	−	0.640005i	$-0.221068\pi$
$359$	1.34720e9	1.53674	0.768371	+	0.640005i	$0.221068\pi$
$360$	0	0
$361$	−9.14611e7	−0.102320
$362$	1.88655e9	2.09020
$363$	0	0
$364$	−1.19071e9	−1.29405
$365$	−5.06580e7	−0.0545285
$366$	0	0
$367$	−9.77318e8	−1.03206	−0.516030	−	0.856571i	$-0.672591\pi$
$367$	−9.77318e8	−1.03206	−0.516030	+	0.856571i	$0.672591\pi$
$368$	3.99286e7	0.0417654
$369$	0	0
$370$	3.37602e7	0.0346496
$371$	−2.51375e9	−2.55572
$372$	0	0
$373$	6.10073e8	0.608696	0.304348	−	0.952561i	$-0.401561\pi$
$373$	6.10073e8	0.608696	0.304348	+	0.952561i	$0.401561\pi$
$374$	5.88060e8	0.581261
$375$	0	0
$376$	8.12054e7	0.0787820
$377$	1.05925e9	1.01813
$378$	0	0
$379$	3.49421e8	0.329695	0.164847	−	0.986319i	$-0.447287\pi$
$379$	3.49421e8	0.329695	0.164847	+	0.986319i	$0.447287\pi$
$380$	3.44407e7	0.0321980
$381$	0	0
$382$	−1.12509e9	−1.03268
$383$	−6.97644e8	−0.634509	−0.317255	−	0.948340i	$-0.602761\pi$
$383$	−6.97644e8	−0.634509	−0.317255	+	0.948340i	$0.602761\pi$
$384$	0	0
$385$	3.07730e7	0.0274825
$386$	1.37458e9	1.21651
$387$	0	0
$388$	1.06554e9	0.926098
$389$	−1.70449e9	−1.46815	−0.734077	−	0.679067i	$-0.762385\pi$
$389$	−1.70449e9	−1.46815	−0.734077	+	0.679067i	$0.762385\pi$
$390$	0	0
$391$	−3.97233e7	−0.0336068
$392$	−3.02648e8	−0.253768
$393$	0	0
$394$	1.88698e9	1.55428
$395$	−9.44915e7	−0.0771442
$396$	0	0
$397$	−1.51386e7	−0.0121428	−0.00607138	−	0.999982i	$-0.501933\pi$
$397$	−1.51386e7	−0.0121428	−0.00607138	+	0.999982i	$0.501933\pi$
$398$	−2.64936e9	−2.10645
$399$	0	0
$400$	1.49142e9	1.16517
$401$	1.18655e9	0.918928	0.459464	−	0.888196i	$-0.348042\pi$
$401$	1.18655e9	0.918928	0.459464	+	0.888196i	$0.348042\pi$
$402$	0	0
$403$	7.54822e7	0.0574482
$404$	−6.17931e7	−0.0466235
$405$	0	0
$406$	−2.11475e9	−1.56826
$407$	−3.78072e8	−0.277968
$408$	0	0
$409$	1.78027e9	1.28663	0.643315	−	0.765602i	$-0.277559\pi$
$409$	1.78027e9	1.28663	0.643315	+	0.765602i	$0.277559\pi$
$410$	−7.69620e7	−0.0551484
$411$	0	0
$412$	−1.60137e9	−1.12811
$413$	−1.06890e9	−0.746638
$414$	0	0
$415$	6.72490e7	0.0461868
$416$	−2.23865e9	−1.52461
$417$	0	0
$418$	−8.75466e8	−0.586303
$419$	−1.26485e9	−0.840023	−0.420012	−	0.907519i	$-0.637974\pi$
$419$	−1.26485e9	−0.840023	−0.420012	+	0.907519i	$0.637974\pi$
$420$	0	0
$421$	2.11626e8	0.138224	0.0691118	−	0.997609i	$-0.477983\pi$
$421$	2.11626e8	0.138224	0.0691118	+	0.997609i	$0.477983\pi$
$422$	1.35457e9	0.877424
$423$	0	0
$424$	−8.28301e8	−0.527725
$425$	−1.48375e9	−0.937563
$426$	0	0
$427$	−3.26589e9	−2.03004
$428$	2.84477e8	0.175385
$429$	0	0
$430$	−1.45060e7	−0.00879850
$431$	−3.00302e8	−0.180671	−0.0903353	−	0.995911i	$-0.528794\pi$
$431$	−3.00302e8	−0.180671	−0.0903353	+	0.995911i	$0.528794\pi$
$432$	0	0
$433$	−1.41630e9	−0.838392	−0.419196	−	0.907896i	$-0.637688\pi$
$433$	−1.41630e9	−0.838392	−0.419196	+	0.907896i	$0.637688\pi$
$434$	−1.50697e8	−0.0884893
$435$	0	0
$436$	−2.07403e8	−0.119843
$437$	5.91374e7	0.0338983
$438$	0	0
$439$	1.52173e9	0.858445	0.429223	−	0.903199i	$-0.358788\pi$
$439$	1.52173e9	0.858445	0.429223	+	0.903199i	$0.358788\pi$
$440$	1.01400e7	0.00567482
$441$	0	0
$442$	2.72280e9	1.49982
$443$	−2.81273e8	−0.153715	−0.0768574	−	0.997042i	$-0.524489\pi$
$443$	−2.81273e8	−0.153715	−0.0768574	+	0.997042i	$0.524489\pi$
$444$	0	0
$445$	−1.07250e7	−0.00576946
$446$	−2.54160e9	−1.35655
$447$	0	0
$448$	1.41255e9	0.742215
$449$	−2.07207e9	−1.08029	−0.540146	−	0.841571i	$-0.681631\pi$
$449$	−2.07207e9	−1.08029	−0.540146	+	0.841571i	$0.681631\pi$
$450$	0	0
$451$	8.61880e8	0.442414
$452$	−1.65050e8	−0.0840682
$453$	0	0
$454$	−1.59821e9	−0.801566
$455$	1.42483e8	0.0709126
$456$	0	0
$457$	6.18336e8	0.303053	0.151526	−	0.988453i	$-0.451581\pi$
$457$	6.18336e8	0.303053	0.151526	+	0.988453i	$0.451581\pi$
$458$	−4.40644e9	−2.14318
$459$	0	0
$460$	2.53827e6	0.00121586
$461$	−1.04519e9	−0.496867	−0.248433	−	0.968649i	$-0.579916\pi$
$461$	−1.04519e9	−0.496867	−0.248433	+	0.968649i	$0.579916\pi$
$462$	0	0
$463$	−6.19870e8	−0.290246	−0.145123	−	0.989414i	$-0.546358\pi$
$463$	−6.19870e8	−0.290246	−0.145123	+	0.989414i	$0.546358\pi$
$464$	−2.14147e9	−0.995173
$465$	0	0
$466$	4.12584e9	1.88869
$467$	4.18640e9	1.90209	0.951047	−	0.309047i	$-0.100010\pi$
$467$	4.18640e9	1.90209	0.951047	+	0.309047i	$0.100010\pi$
$468$	0	0
$469$	−3.66165e9	−1.63897
$470$	3.60098e7	0.0159985
$471$	0	0
$472$	−3.52210e8	−0.154172
$473$	1.62450e8	0.0705838
$474$	0	0
$475$	2.20891e9	0.945695
$476$	−2.39485e9	−1.01778
$477$	0	0
$478$	−3.41633e9	−1.43075
$479$	−2.16526e9	−0.900193	−0.450097	−	0.892980i	$-0.648610\pi$
$479$	−2.16526e9	−0.900193	−0.450097	+	0.892980i	$0.648610\pi$
$480$	0	0
$481$	−1.75053e9	−0.717235
$482$	3.06380e9	1.24622
$483$	0	0
$484$	−1.54349e9	−0.618791
$485$	−1.27505e8	−0.0507493
$486$	0	0
$487$	−4.04525e9	−1.58706	−0.793531	−	0.608530i	$-0.791760\pi$
$487$	−4.04525e9	−1.58706	−0.793531	+	0.608530i	$0.791760\pi$
$488$	−1.07614e9	−0.419178
$489$	0	0
$490$	−1.34206e8	−0.0515332
$491$	−2.63031e9	−1.00282	−0.501408	−	0.865211i	$-0.667184\pi$
$491$	−2.63031e9	−1.00282	−0.501408	+	0.865211i	$0.667184\pi$
$492$	0	0
$493$	2.13046e9	0.800772
$494$	−4.05353e9	−1.51283
$495$	0	0
$496$	−1.52601e8	−0.0561527
$497$	−3.99572e9	−1.45998
$498$	0	0
$499$	3.10184e8	0.111755	0.0558775	−	0.998438i	$-0.482204\pi$
$499$	3.10184e8	0.111755	0.0558775	+	0.998438i	$0.482204\pi$
$500$	1.89797e8	0.0679037
$501$	0	0
$502$	−6.90740e9	−2.43698
$503$	−4.58242e9	−1.60549	−0.802743	−	0.596325i	$-0.796627\pi$
$503$	−4.58242e9	−1.60549	−0.802743	+	0.596325i	$0.796627\pi$
$504$	0	0
$505$	7.39432e6	0.00255493
$506$	−6.45216e7	−0.0221400
$507$	0	0
$508$	6.65908e8	0.225367
$509$	5.65113e8	0.189943	0.0949714	−	0.995480i	$-0.469724\pi$
$509$	5.65113e8	0.189943	0.0949714	+	0.995480i	$0.469724\pi$
$510$	0	0
$511$	−5.24412e9	−1.73860
$512$	3.51858e9	1.15857
$513$	0	0
$514$	−9.28141e8	−0.301469
$515$	1.91624e8	0.0618194
$516$	0	0
$517$	−4.03265e8	−0.128344
$518$	3.49486e9	1.10478
$519$	0	0
$520$	4.69494e7	0.0146426
$521$	5.02091e9	1.55543	0.777714	−	0.628618i	$-0.216379\pi$
$521$	5.02091e9	1.55543	0.777714	+	0.628618i	$0.216379\pi$
$522$	0	0
$523$	4.46410e9	1.36452	0.682258	−	0.731112i	$-0.260998\pi$
$523$	4.46410e9	1.36452	0.682258	+	0.731112i	$0.260998\pi$
$524$	5.83815e8	0.177262
$525$	0	0
$526$	8.09126e9	2.42419
$527$	1.51816e8	0.0451836
$528$	0	0
$529$	−3.40047e9	−0.998720
$530$	−3.67303e8	−0.107166
$531$	0	0
$532$	3.56530e9	1.02661
$533$	3.99063e9	1.14155
$534$	0	0
$535$	−3.40412e7	−0.00961096
$536$	−1.20655e9	−0.338429
$537$	0	0
$538$	2.54469e9	0.704525
$539$	1.50295e9	0.413412
$540$	0	0
$541$	−4.10317e9	−1.11411	−0.557056	−	0.830475i	$-0.688069\pi$
$541$	−4.10317e9	−1.11411	−0.557056	+	0.830475i	$0.688069\pi$
$542$	5.50172e9	1.48423
$543$	0	0
$544$	−4.50256e9	−1.19912
$545$	2.48184e7	0.00656728
$546$	0	0
$547$	−1.85474e9	−0.484539	−0.242269	−	0.970209i	$-0.577892\pi$
$547$	−1.85474e9	−0.484539	−0.242269	+	0.970209i	$0.577892\pi$
$548$	−2.02520e9	−0.525697
$549$	0	0
$550$	−2.41002e9	−0.617663
$551$	−3.17168e9	−0.807717
$552$	0	0
$553$	−9.78177e9	−2.45969
$554$	−3.85335e9	−0.962841
$555$	0	0
$556$	2.59419e9	0.640089
$557$	5.61884e9	1.37770	0.688848	−	0.724906i	$-0.258117\pi$
$557$	5.61884e9	1.37770	0.688848	+	0.724906i	$0.258117\pi$
$558$	0	0
$559$	7.52165e8	0.182126
$560$	−2.88055e8	−0.0693135
$561$	0	0
$562$	8.63247e9	2.05144
$563$	4.77175e9	1.12693	0.563467	−	0.826139i	$-0.309467\pi$
$563$	4.77175e9	1.12693	0.563467	+	0.826139i	$0.309467\pi$
$564$	0	0
$565$	1.97503e7	0.00460686
$566$	−3.12641e9	−0.724749
$567$	0	0
$568$	−1.31662e9	−0.301469
$569$	3.47483e9	0.790753	0.395377	−	0.918519i	$-0.370614\pi$
$569$	3.47483e9	0.790753	0.395377	+	0.918519i	$0.370614\pi$
$570$	0	0
$571$	3.59894e9	0.809000	0.404500	−	0.914538i	$-0.367446\pi$
$571$	3.59894e9	0.809000	0.404500	+	0.914538i	$0.367446\pi$
$572$	1.94840e9	0.435304
$573$	0	0
$574$	−7.96712e9	−1.75837
$575$	1.62796e8	0.0357114
$576$	0	0
$577$	4.67766e9	1.01371	0.506855	−	0.862032i	$-0.330808\pi$
$577$	4.67766e9	1.01371	0.506855	+	0.862032i	$0.330808\pi$
$578$	−7.30496e8	−0.157351
$579$	0	0
$580$	−1.36133e8	−0.0289712
$581$	6.96163e9	1.47263
$582$	0	0
$583$	4.11334e9	0.859715
$584$	−1.72798e9	−0.359000
$585$	0	0
$586$	−1.23237e10	−2.52988
$587$	−5.27917e9	−1.07729	−0.538644	−	0.842533i	$-0.681063\pi$
$587$	−5.27917e9	−1.07729	−0.538644	+	0.842533i	$0.681063\pi$
$588$	0	0
$589$	−2.26014e8	−0.0455755
$590$	−1.56184e8	−0.0313080
$591$	0	0
$592$	3.53901e9	0.701060
$593$	4.65728e9	0.917151	0.458575	−	0.888655i	$-0.348360\pi$
$593$	4.65728e9	0.917151	0.458575	+	0.888655i	$0.348360\pi$
$594$	0	0
$595$	2.86574e8	0.0557735
$596$	−2.88622e9	−0.558429
$597$	0	0
$598$	−2.98744e8	−0.0571274
$599$	8.21418e9	1.56160	0.780801	−	0.624780i	$-0.214811\pi$
$599$	8.21418e9	1.56160	0.780801	+	0.624780i	$0.214811\pi$
$600$	0	0
$601$	4.53542e9	0.852229	0.426115	−	0.904669i	$-0.359882\pi$
$601$	4.53542e9	0.852229	0.426115	+	0.904669i	$0.359882\pi$
$602$	−1.50166e9	−0.280534
$603$	0	0
$604$	−6.73134e9	−1.24300
$605$	1.84697e8	0.0339091
$606$	0	0
$607$	2.58768e9	0.469625	0.234812	−	0.972041i	$-0.424552\pi$
$607$	2.58768e9	0.469625	0.234812	+	0.972041i	$0.424552\pi$
$608$	6.70312e9	1.20952
$609$	0	0
$610$	−4.77204e8	−0.0851235
$611$	−1.86717e9	−0.331162
$612$	0	0
$613$	4.69723e9	0.823626	0.411813	−	0.911268i	$-0.364896\pi$
$613$	4.69723e9	0.823626	0.411813	+	0.911268i	$0.364896\pi$
$614$	−2.27841e9	−0.397231
$615$	0	0
$616$	1.04969e9	0.180937
$617$	6.31709e9	1.08273	0.541363	−	0.840789i	$-0.317908\pi$
$617$	6.31709e9	1.08273	0.541363	+	0.840789i	$0.317908\pi$
$618$	0	0
$619$	1.92907e9	0.326912	0.163456	−	0.986551i	$-0.447736\pi$
$619$	1.92907e9	0.326912	0.163456	+	0.986551i	$0.447736\pi$
$620$	−9.70086e6	−0.00163470
$621$	0	0
$622$	9.97945e9	1.66280
$623$	−1.11025e9	−0.183955
$624$	0	0
$625$	6.06944e9	0.994417
$626$	−5.24750e9	−0.854953
$627$	0	0
$628$	−8.51653e9	−1.37216
$629$	−3.52081e9	−0.564112
$630$	0	0
$631$	−5.13248e9	−0.813251	−0.406626	−	0.913595i	$-0.633295\pi$
$631$	−5.13248e9	−0.813251	−0.406626	+	0.913595i	$0.633295\pi$
$632$	−3.22318e9	−0.507896
$633$	0	0
$634$	1.51028e10	2.35367
$635$	−7.96842e7	−0.0123499
$636$	0	0
$637$	6.95886e9	1.06672
$638$	3.46045e9	0.527546
$639$	0	0
$640$	−1.58948e8	−0.0239676
$641$	1.08820e10	1.63195	0.815976	−	0.578086i	$-0.196200\pi$
$641$	1.08820e10	1.63195	0.815976	+	0.578086i	$0.196200\pi$
$642$	0	0
$643$	5.44950e9	0.808385	0.404192	−	0.914674i	$-0.367553\pi$
$643$	5.44950e9	0.808385	0.404192	+	0.914674i	$0.367553\pi$
$644$	2.62762e8	0.0387669
$645$	0	0
$646$	−8.15280e9	−1.18985
$647$	−2.41640e9	−0.350754	−0.175377	−	0.984501i	$-0.556114\pi$
$647$	−2.41640e9	−0.350754	−0.175377	+	0.984501i	$0.556114\pi$
$648$	0	0
$649$	1.74907e9	0.251161
$650$	−1.11587e10	−1.59374
$651$	0	0
$652$	6.44113e9	0.910114
$653$	−7.41937e9	−1.04273	−0.521363	−	0.853335i	$-0.674576\pi$
$653$	−7.41937e9	−1.04273	−0.521363	+	0.853335i	$0.674576\pi$
$654$	0	0
$655$	−6.98608e7	−0.00971380
$656$	−8.06777e9	−1.11581
$657$	0	0
$658$	3.72774e9	0.510099
$659$	4.19463e9	0.570945	0.285473	−	0.958387i	$-0.407849\pi$
$659$	4.19463e9	0.570945	0.285473	+	0.958387i	$0.407849\pi$
$660$	0	0
$661$	−5.21211e9	−0.701954	−0.350977	−	0.936384i	$-0.614151\pi$
$661$	−5.21211e9	−0.701954	−0.350977	+	0.936384i	$0.614151\pi$
$662$	1.20494e10	1.61422
$663$	0	0
$664$	2.29392e9	0.304081
$665$	−4.26633e8	−0.0562573
$666$	0	0
$667$	−2.33752e8	−0.0305011
$668$	1.63843e9	0.212672
$669$	0	0
$670$	−5.35032e8	−0.0687255
$671$	5.34410e9	0.682882
$672$	0	0
$673$	−1.45876e10	−1.84473	−0.922363	−	0.386325i	$-0.873744\pi$
$673$	−1.45876e10	−1.84473	−0.922363	+	0.386325i	$0.873744\pi$
$674$	−1.66601e10	−2.09589
$675$	0	0
$676$	2.69636e9	0.335711
$677$	5.06173e9	0.626958	0.313479	−	0.949595i	$-0.398505\pi$
$677$	5.06173e9	0.626958	0.313479	+	0.949595i	$0.398505\pi$
$678$	0	0
$679$	−1.31993e10	−1.61810
$680$	9.44287e7	0.0115166
$681$	0	0
$682$	2.46591e8	0.0297668
$683$	−3.88726e9	−0.466844	−0.233422	−	0.972376i	$-0.574992\pi$
$683$	−3.88726e9	−0.466844	−0.233422	+	0.972376i	$0.574992\pi$
$684$	0	0
$685$	2.42340e8	0.0288077
$686$	1.66136e9	0.196485
$687$	0	0
$688$	−1.52064e9	−0.178019
$689$	1.90453e10	2.21831
$690$	0	0
$691$	−6.93681e9	−0.799810	−0.399905	−	0.916557i	$-0.630957\pi$
$691$	−6.93681e9	−0.799810	−0.399905	+	0.916557i	$0.630957\pi$
$692$	1.20383e10	1.38100
$693$	0	0
$694$	8.94045e9	1.01532
$695$	−3.10428e8	−0.0350763
$696$	0	0
$697$	8.02629e9	0.897842
$698$	1.75559e10	1.95402
$699$	0	0
$700$	9.81473e9	1.08152
$701$	−3.87694e9	−0.425085	−0.212543	−	0.977152i	$-0.568174\pi$
$701$	−3.87694e9	−0.425085	−0.212543	+	0.977152i	$0.568174\pi$
$702$	0	0
$703$	5.24155e9	0.569005
$704$	−2.31141e9	−0.249673
$705$	0	0
$706$	3.44883e9	0.368855
$707$	7.65460e8	0.0814619
$708$	0	0
$709$	−1.10614e10	−1.16559	−0.582797	−	0.812618i	$-0.698042\pi$
$709$	−1.10614e10	−1.16559	−0.582797	+	0.812618i	$0.698042\pi$
$710$	−5.83845e8	−0.0612200
$711$	0	0
$712$	−3.65836e8	−0.0379846
$713$	−1.66572e7	−0.00172103
$714$	0	0
$715$	−2.33151e8	−0.0238542
$716$	−6.72955e9	−0.685157
$717$	0	0
$718$	2.03779e10	2.05458
$719$	1.72872e10	1.73450	0.867249	−	0.497875i	$-0.165886\pi$
$719$	1.72872e10	1.73450	0.867249	+	0.497875i	$0.165886\pi$
$720$	0	0
$721$	1.98369e10	1.97107
$722$	−1.38345e9	−0.136799
$723$	0	0
$724$	1.25718e10	1.23116
$725$	−8.73116e9	−0.850921
$726$	0	0
$727$	5.92252e9	0.571658	0.285829	−	0.958281i	$-0.407731\pi$
$727$	5.92252e9	0.571658	0.285829	+	0.958281i	$0.407731\pi$
$728$	4.86021e9	0.466869
$729$	0	0
$730$	−7.66259e8	−0.0729030
$731$	1.51282e9	0.143244
$732$	0	0
$733$	1.69133e10	1.58623	0.793114	−	0.609074i	$-0.208459\pi$
$733$	1.69133e10	1.58623	0.793114	+	0.609074i	$0.208459\pi$
$734$	−1.47830e10	−1.37983
$735$	0	0
$736$	4.94018e8	0.0456741
$737$	5.99170e9	0.551333
$738$	0	0
$739$	−2.73492e9	−0.249281	−0.124640	−	0.992202i	$-0.539778\pi$
$739$	−2.73492e9	−0.249281	−0.124640	+	0.992202i	$0.539778\pi$
$740$	2.24975e8	0.0204091
$741$	0	0
$742$	−3.80232e10	−3.41692
$743$	9.30626e9	0.832366	0.416183	−	0.909281i	$-0.363368\pi$
$743$	9.30626e9	0.832366	0.416183	+	0.909281i	$0.363368\pi$
$744$	0	0
$745$	3.45373e8	0.0306014
$746$	9.22803e9	0.813810
$747$	0	0
$748$	3.91879e9	0.342371
$749$	−3.52395e9	−0.306438
$750$	0	0
$751$	2.13212e9	0.183684	0.0918421	−	0.995774i	$-0.470725\pi$
$751$	2.13212e9	0.183684	0.0918421	+	0.995774i	$0.470725\pi$
$752$	3.77483e9	0.323694
$753$	0	0
$754$	1.60224e10	1.36122
$755$	8.05489e8	0.0681154
$756$	0	0
$757$	1.54717e10	1.29630	0.648148	−	0.761515i	$-0.275544\pi$
$757$	1.54717e10	1.29630	0.648148	+	0.761515i	$0.275544\pi$
$758$	5.28539e9	0.440793
$759$	0	0
$760$	−1.40579e8	−0.0116165
$761$	1.05745e8	0.00869787	0.00434894	−	0.999991i	$-0.498616\pi$
$761$	1.05745e8	0.00869787	0.00434894	+	0.999991i	$0.498616\pi$
$762$	0	0
$763$	2.56920e9	0.209393
$764$	−7.49750e9	−0.608261
$765$	0	0
$766$	−1.05526e10	−0.848321
$767$	8.09846e9	0.648065
$768$	0	0
$769$	1.45940e10	1.15726	0.578632	−	0.815589i	$-0.303587\pi$
$769$	1.45940e10	1.15726	0.578632	+	0.815589i	$0.303587\pi$
$770$	4.65475e8	0.0367434
$771$	0	0
$772$	9.16013e9	0.716541
$773$	−7.67773e9	−0.597867	−0.298934	−	0.954274i	$-0.596631\pi$
$773$	−7.67773e9	−0.597867	−0.298934	+	0.954274i	$0.596631\pi$
$774$	0	0
$775$	−6.22182e8	−0.0480133
$776$	−4.34928e9	−0.334119
$777$	0	0
$778$	−2.57823e10	−1.96288
$779$	−1.19490e10	−0.905630
$780$	0	0
$781$	6.53835e9	0.491122
$782$	−6.00859e8	−0.0449313
$783$	0	0
$784$	−1.40686e10	−1.04266
$785$	1.01911e9	0.0751930
$786$	0	0
$787$	−9.73198e9	−0.711688	−0.355844	−	0.934545i	$-0.615807\pi$
$787$	−9.73198e9	−0.711688	−0.355844	+	0.934545i	$0.615807\pi$
$788$	1.25747e10	0.915494
$789$	0	0
$790$	−1.42929e9	−0.103140
$791$	2.04456e9	0.146886
$792$	0	0
$793$	2.47439e10	1.76203
$794$	−2.28988e8	−0.0162345
$795$	0	0
$796$	−1.76551e10	−1.24073
$797$	4.83086e9	0.338003	0.169001	−	0.985616i	$-0.445946\pi$
$797$	4.83086e9	0.338003	0.169001	+	0.985616i	$0.445946\pi$
$798$	0	0
$799$	−3.75542e9	−0.260462
$800$	1.84527e10	1.27422
$801$	0	0
$802$	1.79479e10	1.22858
$803$	8.58116e9	0.584846
$804$	0	0
$805$	−3.14427e7	−0.00212439
$806$	1.14175e9	0.0768067
$807$	0	0
$808$	2.52226e8	0.0168209
$809$	−1.46263e10	−0.971216	−0.485608	−	0.874177i	$-0.661402\pi$
$809$	−1.46263e10	−0.971216	−0.485608	+	0.874177i	$0.661402\pi$
$810$	0	0
$811$	2.93692e9	0.193339	0.0966694	−	0.995317i	$-0.469181\pi$
$811$	2.93692e9	0.193339	0.0966694	+	0.995317i	$0.469181\pi$
$812$	−1.40925e10	−0.923727
$813$	0	0
$814$	−5.71876e9	−0.371635
$815$	−7.70762e8	−0.0498734
$816$	0	0
$817$	−2.25218e9	−0.144486
$818$	2.69285e10	1.72019
$819$	0	0
$820$	−5.12869e8	−0.0324832
$821$	−1.70106e10	−1.07280	−0.536401	−	0.843964i	$-0.680216\pi$
$821$	−1.70106e10	−1.07280	−0.536401	+	0.843964i	$0.680216\pi$
$822$	0	0
$823$	7.47291e9	0.467294	0.233647	−	0.972321i	$-0.424934\pi$
$823$	7.47291e9	0.467294	0.233647	+	0.972321i	$0.424934\pi$
$824$	6.53644e9	0.407002
$825$	0	0
$826$	−1.61682e10	−0.998234
$827$	2.00025e10	1.22975	0.614873	−	0.788626i	$-0.289207\pi$
$827$	2.00025e10	1.22975	0.614873	+	0.788626i	$0.289207\pi$
$828$	0	0
$829$	−8.27952e9	−0.504736	−0.252368	−	0.967631i	$-0.581209\pi$
$829$	−8.27952e9	−0.504736	−0.252368	+	0.967631i	$0.581209\pi$
$830$	1.01722e9	0.0617504
$831$	0	0
$832$	−1.07021e10	−0.644226
$833$	1.39963e10	0.838985
$834$	0	0
$835$	−1.96059e8	−0.0116542
$836$	−5.83404e9	−0.345340
$837$	0	0
$838$	−1.91323e10	−1.12309
$839$	−1.26666e10	−0.740443	−0.370222	−	0.928943i	$-0.620718\pi$
$839$	−1.26666e10	−0.740443	−0.370222	+	0.928943i	$0.620718\pi$
$840$	0	0
$841$	−4.71317e9	−0.273229
$842$	3.20108e9	0.184801
$843$	0	0
$844$	9.02679e9	0.516814
$845$	−3.22654e8	−0.0183966
$846$	0	0
$847$	1.91199e10	1.08117
$848$	−3.85036e10	−2.16828
$849$	0	0
$850$	−2.24434e10	−1.25350
$851$	3.86301e8	0.0214868
$852$	0	0
$853$	−3.00382e10	−1.65711	−0.828556	−	0.559906i	$-0.810837\pi$
$853$	−3.00382e10	−1.65711	−0.828556	+	0.559906i	$0.810837\pi$
$854$	−4.94002e10	−2.71410
$855$	0	0
$856$	−1.16117e9	−0.0632759
$857$	−1.76722e10	−0.959088	−0.479544	−	0.877518i	$-0.659198\pi$
$857$	−1.76722e10	−0.959088	−0.479544	+	0.877518i	$0.659198\pi$
$858$	0	0
$859$	1.84797e9	0.0994763	0.0497382	−	0.998762i	$-0.484161\pi$
$859$	1.84797e9	0.0994763	0.0497382	+	0.998762i	$0.484161\pi$
$860$	−9.66671e7	−0.00518244
$861$	0	0
$862$	−4.54240e9	−0.241551
$863$	5.58485e9	0.295784	0.147892	−	0.989004i	$-0.452751\pi$
$863$	5.58485e9	0.295784	0.147892	+	0.989004i	$0.452751\pi$
$864$	0	0
$865$	−1.44053e9	−0.0756774
$866$	−2.14231e10	−1.12091
$867$	0	0
$868$	−1.00423e9	−0.0521214
$869$	1.60063e10	0.827411
$870$	0	0
$871$	2.77424e10	1.42259
$872$	8.46574e8	0.0432372
$873$	0	0
$874$	8.94519e8	0.0453210
$875$	−2.35110e9	−0.118643
$876$	0	0
$877$	−2.49280e10	−1.24793	−0.623963	−	0.781454i	$-0.714478\pi$
$877$	−2.49280e10	−1.24793	−0.623963	+	0.781454i	$0.714478\pi$
$878$	2.30179e10	1.14772
$879$	0	0
$880$	4.71356e8	0.0233163
$881$	7.08433e9	0.349047	0.174523	−	0.984653i	$-0.444162\pi$
$881$	7.08433e9	0.349047	0.174523	+	0.984653i	$0.444162\pi$
$882$	0	0
$883$	−1.79072e9	−0.0875316	−0.0437658	−	0.999042i	$-0.513936\pi$
$883$	−1.79072e9	−0.0875316	−0.0437658	+	0.999042i	$0.513936\pi$
$884$	1.81446e10	0.883412
$885$	0	0
$886$	−4.25457e9	−0.205512
$887$	−6.97503e9	−0.335593	−0.167797	−	0.985822i	$-0.553665\pi$
$887$	−6.97503e9	−0.335593	−0.167797	+	0.985822i	$0.553665\pi$
$888$	0	0
$889$	−8.24891e9	−0.393768
$890$	−1.62227e8	−0.00771361
$891$	0	0
$892$	−1.69371e10	−0.799026
$893$	5.59082e9	0.262722
$894$	0	0
$895$	8.05275e8	0.0375460
$896$	−1.64543e10	−0.764189
$897$	0	0
$898$	−3.13423e10	−1.44432
$899$	8.93364e8	0.0410081
$900$	0	0
$901$	3.83056e10	1.74472
$902$	1.30369e10	0.591495
$903$	0	0
$904$	6.73699e8	0.0303303
$905$	−1.50438e9	−0.0674663
$906$	0	0
$907$	−6.43630e9	−0.286425	−0.143213	−	0.989692i	$-0.545743\pi$
$907$	−6.43630e9	−0.286425	−0.143213	+	0.989692i	$0.545743\pi$
$908$	−1.06504e10	−0.472133
$909$	0	0
$910$	2.15522e9	0.0948082
$911$	−1.55350e10	−0.680766	−0.340383	−	0.940287i	$-0.610557\pi$
$911$	−1.55350e10	−0.680766	−0.340383	+	0.940287i	$0.610557\pi$
$912$	0	0
$913$	−1.13916e10	−0.495377
$914$	9.35302e9	0.405173
$915$	0	0
$916$	−2.93642e10	−1.26236
$917$	−7.23199e9	−0.309717
$918$	0	0
$919$	3.73555e10	1.58763	0.793816	−	0.608158i	$-0.208091\pi$
$919$	3.73555e10	1.58763	0.793816	+	0.608158i	$0.208091\pi$
$920$	−1.03607e7	−0.000438662 0
$921$	0	0
$922$	−1.58096e10	−0.664297
$923$	3.02735e10	1.26723
$924$	0	0
$925$	1.44292e10	0.599440
$926$	−9.37622e9	−0.388051
$927$	0	0
$928$	−2.64954e10	−1.08831
$929$	−2.51045e10	−1.02730	−0.513649	−	0.858001i	$-0.671706\pi$
$929$	−2.51045e10	−1.02730	−0.513649	+	0.858001i	$0.671706\pi$
$930$	0	0
$931$	−2.08367e10	−0.846262
$932$	2.74943e10	1.11247
$933$	0	0
$934$	6.33240e10	2.54305
$935$	−4.68933e8	−0.0187616
$936$	0	0
$937$	−3.29027e10	−1.30660	−0.653300	−	0.757099i	$-0.726616\pi$
$937$	−3.29027e10	−1.30660	−0.653300	+	0.757099i	$0.726616\pi$
$938$	−5.53866e10	−2.19126
$939$	0	0
$940$	2.39967e8	0.00942330
$941$	−1.27046e10	−0.497048	−0.248524	−	0.968626i	$-0.579946\pi$
$941$	−1.27046e10	−0.497048	−0.248524	+	0.968626i	$0.579946\pi$
$942$	0	0
$943$	−8.80638e8	−0.0341985
$944$	−1.63725e10	−0.633450
$945$	0	0
$946$	2.45723e9	0.0943685
$947$	2.04335e9	0.0781840	0.0390920	−	0.999236i	$-0.487553\pi$
$947$	2.04335e9	0.0781840	0.0390920	+	0.999236i	$0.487553\pi$
$948$	0	0
$949$	3.97320e10	1.50907
$950$	3.34123e10	1.26437
$951$	0	0
$952$	9.77527e9	0.367197
$953$	1.23244e10	0.461253	0.230626	−	0.973042i	$-0.425922\pi$
$953$	1.23244e10	0.461253	0.230626	+	0.973042i	$0.425922\pi$
$954$	0	0
$955$	8.97170e8	0.0333321
$956$	−2.27662e10	−0.842729
$957$	0	0
$958$	−3.27520e10	−1.20353
$959$	2.50871e10	0.918512
$960$	0	0
$961$	−2.74490e10	−0.997686
$962$	−2.64787e10	−0.958923
$963$	0	0
$964$	2.04169e10	0.734041
$965$	−1.09612e9	−0.0392658
$966$	0	0
$967$	1.28161e10	0.455788	0.227894	−	0.973686i	$-0.426816\pi$
$967$	1.28161e10	0.455788	0.227894	+	0.973686i	$0.426816\pi$
$968$	6.30017e9	0.223248
$969$	0	0
$970$	−1.92865e9	−0.0678504
$971$	−2.66467e10	−0.934063	−0.467032	−	0.884241i	$-0.654677\pi$
$971$	−2.66467e10	−0.934063	−0.467032	+	0.884241i	$0.654677\pi$
$972$	0	0
$973$	−3.21355e10	−1.11838
$974$	−6.11889e10	−2.12186
$975$	0	0
$976$	−5.00243e10	−1.72229
$977$	−8.47518e9	−0.290749	−0.145374	−	0.989377i	$-0.546439\pi$
$977$	−8.47518e9	−0.290749	−0.145374	+	0.989377i	$0.546439\pi$
$978$	0	0
$979$	1.81674e9	0.0618805
$980$	−8.94342e8	−0.0303538
$981$	0	0
$982$	−3.97863e10	−1.34074
$983$	2.76800e9	0.0929455	0.0464727	−	0.998920i	$-0.485202\pi$
$983$	2.76800e9	0.0929455	0.0464727	+	0.998920i	$0.485202\pi$
$984$	0	0
$985$	−1.50472e9	−0.0501682
$986$	3.22255e10	1.07061
$987$	0	0
$988$	−2.70124e10	−0.891075
$989$	−1.65985e8	−0.00545610
$990$	0	0
$991$	2.88798e10	0.942621	0.471310	−	0.881967i	$-0.343781\pi$
$991$	2.88798e10	0.942621	0.471310	+	0.881967i	$0.343781\pi$
$992$	−1.88806e9	−0.0614080
$993$	0	0
$994$	−6.04397e10	−1.95196
$995$	2.11266e9	0.0679906
$996$	0	0
$997$	4.99664e9	0.159678	0.0798390	−	0.996808i	$-0.474559\pi$
$997$	4.99664e9	0.159678	0.0798390	+	0.996808i	$0.474559\pi$
$998$	4.69187e9	0.149413
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.b.1.9		11
3.2	odd	2		43.8.a.a.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.3	✓	11	3.2	odd	2
387.8.a.b.1.9		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)

\(f(q)\)	\(=\)	\(q+15.1261 q^{2} +100.799 q^{4} -12.0619 q^{5} -1248.65 q^{7} -411.441 q^{8} +O(q^{10})\)	\(q+15.1261 q^{2} +100.799 q^{4} -12.0619 q^{5} -1248.65 q^{7} -411.441 q^{8} -182.450 q^{10} +2043.21 q^{11} +9460.36 q^{13} -18887.2 q^{14} -19125.8 q^{16} +19027.5 q^{17} -28326.9 q^{19} -1215.83 q^{20} +30905.9 q^{22} -2087.68 q^{23} -77979.5 q^{25} +143098. q^{26} -125863. q^{28} +111967. q^{29} +7978.79 q^{31} -236635. q^{32} +287812. q^{34} +15061.1 q^{35} -185038. q^{37} -428475. q^{38} +4962.76 q^{40} +421826. q^{41} +79507.0 q^{43} +205954. q^{44} -31578.5 q^{46} -197368. q^{47} +735581. q^{49} -1.17953e6 q^{50} +953597. q^{52} +2.01317e6 q^{53} -24645.0 q^{55} +513745. q^{56} +1.69363e6 q^{58} +856041. q^{59} +2.61554e6 q^{61} +120688. q^{62} -1.13126e6 q^{64} -114110. q^{65} +2.93249e6 q^{67} +1.91796e6 q^{68} +227816. q^{70} +3.20003e6 q^{71} +4.19984e6 q^{73} -2.79891e6 q^{74} -2.85533e6 q^{76} -2.55125e6 q^{77} +7.83389e6 q^{79} +230694. q^{80} +6.38059e6 q^{82} -5.57533e6 q^{83} -229508. q^{85} +1.20263e6 q^{86} -840660. q^{88} +889160. q^{89} -1.18127e7 q^{91} -210437. q^{92} -2.98542e6 q^{94} +341676. q^{95} +1.05709e7 q^{97} +1.11265e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) \) 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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