LMFDB - Embedded newform 9.24.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,24,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	9.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:	$30.1683633611$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{530401}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 132600 $ x^2 - x - 132600
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$364.643$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1563.86 q^{2} -5.94295e6 q^{4} -1.13630e8 q^{5} +7.85264e9 q^{7} +2.24125e10 q^{8} +O(q^{10})$	\(q-1563.86 q^{2} -5.94295e6 q^{4} -1.13630e8 q^{5} +7.85264e9 q^{7} +2.24125e10 q^{8} +1.77701e11 q^{10} -1.03137e12 q^{11} +8.08921e12 q^{13} -1.22804e13 q^{14} +1.48030e13 q^{16} +1.38649e14 q^{17} -1.41905e14 q^{19} +6.75297e14 q^{20} +1.61292e15 q^{22} -4.80770e15 q^{23} +9.90836e14 q^{25} -1.26504e16 q^{26} -4.66679e16 q^{28} +1.45614e16 q^{29} -8.10883e16 q^{31} -2.11160e17 q^{32} -2.16828e17 q^{34} -8.92295e17 q^{35} +1.19418e18 q^{37} +2.21919e17 q^{38} -2.54674e18 q^{40} -6.63767e18 q^{41} -1.06144e19 q^{43} +6.12940e18 q^{44} +7.51856e18 q^{46} -1.16951e19 q^{47} +3.42952e19 q^{49} -1.54953e18 q^{50} -4.80738e19 q^{52} +7.56809e19 q^{53} +1.17195e20 q^{55} +1.75998e20 q^{56} -2.27720e19 q^{58} +4.19627e19 q^{59} +7.45869e19 q^{61} +1.26811e20 q^{62} +2.06047e20 q^{64} -9.19177e20 q^{65} -1.29554e21 q^{67} -8.23985e20 q^{68} +1.39542e21 q^{70} +2.37787e21 q^{71} -3.03208e21 q^{73} -1.86752e21 q^{74} +8.43334e20 q^{76} -8.09899e21 q^{77} +3.75756e20 q^{79} -1.68207e21 q^{80} +1.03804e22 q^{82} +9.99994e21 q^{83} -1.57547e22 q^{85} +1.65994e22 q^{86} -2.31157e22 q^{88} +5.36043e21 q^{89} +6.35217e22 q^{91} +2.85719e22 q^{92} +1.82895e22 q^{94} +1.61246e22 q^{95} +1.11058e22 q^{97} -5.36328e22 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1242 q^{2} - 6458716 q^{4} + 46808820 q^{5} - 211963904 q^{7} - 2571869016 q^{8}+O(q^{10}) $ 2 * q + 1242 * q^2 - 6458716 * q^4 + 46808820 * q^5 - 211963904 * q^7 - 2571869016 * q^8	$ 2 q + 1242 q^{2} - 6458716 q^{4} + 46808820 q^{5} - 211963904 q^{7} - 2571869016 q^{8} + 627869790180 q^{10} - 1468972366488 q^{11} + 10491654264748 q^{13} - 34908555004416 q^{14} - 50973150676720 q^{16} + 210888011520828 q^{17} - 907382448537944 q^{19} + 592549041758760 q^{20} + 385075304370504 q^{22} - 10\!\cdots\!12 q^{23}+ \cdots + 52\!\cdots\!18 q^{98}+O(q^{100}) $ 2 * q + 1242 * q^2 - 6458716 * q^4 + 46808820 * q^5 - 211963904 * q^7 - 2571869016 * q^8 + 627869790180 * q^10 - 1468972366488 * q^11 + 10491654264748 * q^13 - 34908555004416 * q^14 - 50973150676720 * q^16 + 210888011520828 * q^17 - 907382448537944 * q^19 + 592549041758760 * q^20 + 385075304370504 * q^22 - 10116923323892112 * q^23 + 14810505797591150 * q^25 - 5909481699569604 * q^26 - 42508434042586112 * q^28 - 18478753545176892 * q^29 - 272793622592745488 * q^31 - 186134219136906336 * q^32 - 14135605903588212 * q^34 - 2186169652458823680 * q^35 - 478995036787364 * q^37 - 1925903087124629112 * q^38 - 6555203866715785200 * q^40 - 5555714961308771412 * q^41 - 1198322147609320040 * q^43 + 6355093136294718288 * q^44 - 7378368693556745808 * q^46 - 26308565672855777280 * q^47 + 71964232849356271890 * q^49 + 37226516336176411350 * q^50 - 49312907988586886888 * q^52 + 41127501899415224628 * q^53 + 46986672525187689360 * q^55 + 377486892221258373120 * q^56 - 115477922638933597836 * q^58 + 307537061909444286696 * q^59 + 594961179098503751020 * q^61 - 411087431199774869712 * q^62 + 828036632782207954496 * q^64 - 533732415162776445960 * q^65 - 1630225825126993264088 * q^67 - 861243436942941889224 * q^68 - 2235006928450834744320 * q^70 + 383942598581649272976 * q^71 - 2812202351440561692428 * q^73 - 5219558875357315020756 * q^74 + 1238138884710050927056 * q^76 - 4569917579124061519872 * q^77 + 21069388575313284880 * q^79 - 12235121810092022582880 * q^80 + 13416177399661303790652 * q^82 + 14817262080324402696024 * q^83 - 4164778183840982876520 * q^85 + 43019621516128896935352 * q^86 - 12182478384106427357664 * q^88 + 43449805260884456557164 * q^89 + 44146945026523904417792 * q^91 + 31310234209098260658144 * q^92 - 22713687421447503614976 * q^94 - 106687644602844474428400 * q^95 + 107136573045242168450692 * q^97 + 52061241480597067368618 * 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 $

$2$	−1563.86	−0.539949	−0.269974	−	0.962867i	$-0.587015\pi$
$2$	−1563.86	−0.539949	−0.269974	+	0.962867i	$0.587015\pi$
$3$	0	0
$3$	0	0
$4$	−5.94295e6	−0.708455
$5$	−1.13630e8	−1.04073	−0.520365	−	0.853944i	$-0.674204\pi$
$5$	−1.13630e8	−1.04073	−0.520365	+	0.853944i	$0.674204\pi$
$6$	0	0
$7$	7.85264e9	1.50103	0.750513	−	0.660856i	$-0.229807\pi$
$7$	7.85264e9	1.50103	0.750513	+	0.660856i	$0.229807\pi$
$8$	2.24125e10	0.922478
$9$	0	0
$10$	1.77701e11	0.561941
$11$	−1.03137e12	−1.08993	−0.544966	−	0.838458i	$-0.683457\pi$
$11$	−1.03137e12	−1.08993	−0.544966	+	0.838458i	$0.683457\pi$
$12$	0	0
$13$	8.08921e12	1.25187	0.625933	−	0.779877i	$-0.284718\pi$
$13$	8.08921e12	1.25187	0.625933	+	0.779877i	$0.284718\pi$
$14$	−1.22804e13	−0.810477
$15$	0	0
$16$	1.48030e13	0.210364
$17$	1.38649e14	0.981193	0.490597	−	0.871387i	$-0.336779\pi$
$17$	1.38649e14	0.981193	0.490597	+	0.871387i	$0.336779\pi$
$18$	0	0
$19$	−1.41905e14	−0.279467	−0.139734	−	0.990189i	$-0.544625\pi$
$19$	−1.41905e14	−0.279467	−0.139734	+	0.990189i	$0.544625\pi$
$20$	6.75297e14	0.737310
$21$	0	0
$22$	1.61292e15	0.588508
$23$	−4.80770e15	−1.05212	−0.526062	−	0.850446i	$-0.676332\pi$
$23$	−4.80770e15	−1.05212	−0.526062	+	0.850446i	$0.676332\pi$
$24$	0	0
$25$	9.90836e14	0.0831174
$26$	−1.26504e16	−0.675944
$27$	0	0
$28$	−4.66679e16	−1.06341
$29$	1.45614e16	0.221629	0.110814	−	0.993841i	$-0.464654\pi$
$29$	1.45614e16	0.221629	0.110814	+	0.993841i	$0.464654\pi$
$30$	0	0
$31$	−8.10883e16	−0.573190	−0.286595	−	0.958052i	$-0.592523\pi$
$31$	−8.10883e16	−0.573190	−0.286595	+	0.958052i	$0.592523\pi$
$32$	−2.11160e17	−1.03606
$33$	0	0
$34$	−2.16828e17	−0.529794
$35$	−8.92295e17	−1.56216
$36$	0	0
$37$	1.19418e18	1.10344	0.551720	−	0.834029i	$-0.313972\pi$
$37$	1.19418e18	1.10344	0.551720	+	0.834029i	$0.313972\pi$
$38$	2.21919e17	0.150898
$39$	0	0
$40$	−2.54674e18	−0.960050
$41$	−6.63767e18	−1.88365	−0.941827	−	0.336098i	$-0.890893\pi$
$41$	−6.63767e18	−1.88365	−0.941827	+	0.336098i	$0.890893\pi$
$42$	0	0
$43$	−1.06144e19	−1.74184	−0.870920	−	0.491425i	$-0.836476\pi$
$43$	−1.06144e19	−1.74184	−0.870920	+	0.491425i	$0.836476\pi$
$44$	6.12940e18	0.772168
$45$	0	0
$46$	7.51856e18	0.568094
$47$	−1.16951e19	−0.690049	−0.345024	−	0.938594i	$-0.612129\pi$
$47$	−1.16951e19	−0.690049	−0.345024	+	0.938594i	$0.612129\pi$
$48$	0	0
$49$	3.42952e19	1.25308
$50$	−1.54953e18	−0.0448791
$51$	0	0
$52$	−4.80738e19	−0.886891
$53$	7.56809e19	1.12154	0.560769	−	0.827972i	$-0.310506\pi$
$53$	7.56809e19	1.12154	0.560769	+	0.827972i	$0.310506\pi$
$54$	0	0
$55$	1.17195e20	1.13432
$56$	1.75998e20	1.38466
$57$	0	0
$58$	−2.27720e19	−0.119668
$59$	4.19627e19	0.181161	0.0905806	−	0.995889i	$-0.471128\pi$
$59$	4.19627e19	0.181161	0.0905806	+	0.995889i	$0.471128\pi$
$60$	0	0
$61$	7.45869e19	0.219467	0.109734	−	0.993961i	$-0.465000\pi$
$61$	7.45869e19	0.219467	0.109734	+	0.993961i	$0.465000\pi$
$62$	1.26811e20	0.309493
$63$	0	0
$64$	2.06047e20	0.349058
$65$	−9.19177e20	−1.30285
$66$	0	0
$67$	−1.29554e21	−1.29595	−0.647976	−	0.761661i	$-0.724384\pi$
$67$	−1.29554e21	−1.29595	−0.647976	+	0.761661i	$0.724384\pi$
$68$	−8.23985e20	−0.695131
$69$	0	0
$70$	1.39542e21	0.843487
$71$	2.37787e21	1.22101	0.610503	−	0.792014i	$-0.290967\pi$
$71$	2.37787e21	1.22101	0.610503	+	0.792014i	$0.290967\pi$
$72$	0	0
$73$	−3.03208e21	−1.13117	−0.565585	−	0.824690i	$-0.691349\pi$
$73$	−3.03208e21	−1.13117	−0.565585	+	0.824690i	$0.691349\pi$
$74$	−1.86752e21	−0.595801
$75$	0	0
$76$	8.43334e20	0.197990
$77$	−8.09899e21	−1.63602
$78$	0	0
$79$	3.75756e20	0.0565190	0.0282595	−	0.999601i	$-0.491004\pi$
$79$	3.75756e20	0.0565190	0.0282595	+	0.999601i	$0.491004\pi$
$80$	−1.68207e21	−0.218932
$81$	0	0
$82$	1.03804e22	1.01708
$83$	9.99994e21	0.852314	0.426157	−	0.904649i	$-0.359867\pi$
$83$	9.99994e21	0.852314	0.426157	+	0.904649i	$0.359867\pi$
$84$	0	0
$85$	−1.57547e22	−1.02116
$86$	1.65994e22	0.940505
$87$	0	0
$88$	−2.31157e22	−1.00544
$89$	5.36043e21	0.204746	0.102373	−	0.994746i	$-0.467357\pi$
$89$	5.36043e21	0.204746	0.102373	+	0.994746i	$0.467357\pi$
$90$	0	0
$91$	6.35217e22	1.87908
$92$	2.85719e22	0.745383
$93$	0	0
$94$	1.82895e22	0.372591
$95$	1.61246e22	0.290850
$96$	0	0
$97$	1.11058e22	0.157643	0.0788214	−	0.996889i	$-0.474884\pi$
$97$	1.11058e22	0.157643	0.0788214	+	0.996889i	$0.474884\pi$
$98$	−5.36328e22	−0.676598
$99$	0	0
$100$	−5.88849e21	−0.0588849
$101$	−8.99589e22	−0.802321	−0.401160	−	0.916008i	$-0.631393\pi$
$101$	−8.99589e22	−0.802321	−0.401160	+	0.916008i	$0.631393\pi$
$102$	0	0
$103$	−8.83460e22	−0.628867	−0.314434	−	0.949279i	$-0.601815\pi$
$103$	−8.83460e22	−0.628867	−0.314434	+	0.949279i	$0.601815\pi$
$104$	1.81300e23	1.15482
$105$	0	0
$106$	−1.18354e23	−0.605573
$107$	−2.32082e23	−1.06593	−0.532963	−	0.846138i	$-0.678922\pi$
$107$	−2.32082e23	−1.06593	−0.532963	+	0.846138i	$0.678922\pi$
$108$	0	0
$109$	−2.76863e23	−1.02768	−0.513842	−	0.857885i	$-0.671778\pi$
$109$	−2.76863e23	−1.02768	−0.513842	+	0.857885i	$0.671778\pi$
$110$	−1.83276e23	−0.612477
$111$	0	0
$112$	1.16243e23	0.315762
$113$	−3.71795e23	−0.911803	−0.455901	−	0.890030i	$-0.650683\pi$
$113$	−3.71795e23	−0.911803	−0.455901	+	0.890030i	$0.650683\pi$
$114$	0	0
$115$	5.46299e23	1.09498
$116$	−8.65376e22	−0.157014
$117$	0	0
$118$	−6.56237e22	−0.0978178
$119$	1.08876e24	1.47280
$120$	0	0
$121$	1.68298e23	0.187952
$122$	−1.16643e23	−0.118501
$123$	0	0
$124$	4.81904e23	0.406080
$125$	1.24199e24	0.954227
$126$	0	0
$127$	−1.60553e24	−1.02772	−0.513861	−	0.857874i	$-0.671785\pi$
$127$	−1.60553e24	−1.02772	−0.513861	+	0.857874i	$0.671785\pi$
$128$	1.44911e24	0.847591
$129$	0	0
$130$	1.43746e24	0.703474
$131$	−2.07814e24	−0.931228	−0.465614	−	0.884988i	$-0.654166\pi$
$131$	−2.07814e24	−0.931228	−0.465614	+	0.884988i	$0.654166\pi$
$132$	0	0
$133$	−1.11433e24	−0.419487
$134$	2.02603e24	0.699748
$135$	0	0
$136$	3.10748e24	0.905130
$137$	−4.86669e24	−1.30301	−0.651504	−	0.758645i	$-0.725862\pi$
$137$	−4.86669e24	−1.30301	−0.651504	+	0.758645i	$0.725862\pi$
$138$	0	0
$139$	9.05962e23	0.205324	0.102662	−	0.994716i	$-0.467264\pi$
$139$	9.05962e23	0.205324	0.102662	+	0.994716i	$0.467264\pi$
$140$	5.30287e24	1.10672
$141$	0	0
$142$	−3.71866e24	−0.659281
$143$	−8.34299e24	−1.36445
$144$	0	0
$145$	−1.65461e24	−0.230655
$146$	4.74175e24	0.610774
$147$	0	0
$148$	−7.09694e24	−0.781738
$149$	−9.86509e24	−1.00568	−0.502839	−	0.864380i	$-0.667711\pi$
$149$	−9.86509e24	−1.00568	−0.502839	+	0.864380i	$0.667711\pi$
$150$	0	0
$151$	−4.82721e24	−0.422145	−0.211072	−	0.977470i	$-0.567696\pi$
$151$	−4.82721e24	−0.422145	−0.211072	+	0.977470i	$0.567696\pi$
$152$	−3.18045e24	−0.257802
$153$	0	0
$154$	1.26657e25	0.883365
$155$	9.21406e24	0.596536
$156$	0	0
$157$	1.87063e24	0.104506	0.0522529	−	0.998634i	$-0.483360\pi$
$157$	1.87063e24	0.104506	0.0522529	+	0.998634i	$0.483360\pi$
$158$	−5.87629e23	−0.0305174
$159$	0	0
$160$	2.39941e25	1.07826
$161$	−3.77531e25	−1.57927
$162$	0	0
$163$	−3.92032e25	−1.42286	−0.711432	−	0.702755i	$-0.751953\pi$
$163$	−3.92032e25	−1.42286	−0.711432	+	0.702755i	$0.751953\pi$
$164$	3.94473e25	1.33448
$165$	0	0
$166$	−1.56385e25	−0.460206
$167$	4.64021e25	1.27438	0.637188	−	0.770708i	$-0.280097\pi$
$167$	4.64021e25	1.27438	0.637188	+	0.770708i	$0.280097\pi$
$168$	0	0
$169$	2.36815e25	0.567168
$170$	2.46381e25	0.551372
$171$	0	0
$172$	6.30809e25	1.23402
$173$	4.74788e25	0.868900	0.434450	−	0.900696i	$-0.356943\pi$
$173$	4.74788e25	0.868900	0.434450	+	0.900696i	$0.356943\pi$
$174$	0	0
$175$	7.78068e24	0.124761
$176$	−1.52674e25	−0.229282
$177$	0	0
$178$	−8.38295e24	−0.110552
$179$	−5.97561e25	−0.738878	−0.369439	−	0.929255i	$-0.620450\pi$
$179$	−5.97561e25	−0.738878	−0.369439	+	0.929255i	$0.620450\pi$
$180$	0	0
$181$	3.92753e25	0.427381	0.213691	−	0.976901i	$-0.431452\pi$
$181$	3.92753e25	0.427381	0.213691	+	0.976901i	$0.431452\pi$
$182$	−9.93389e25	−1.01461
$183$	0	0
$184$	−1.07753e26	−0.970562
$185$	−1.35694e26	−1.14838
$186$	0	0
$187$	−1.42999e26	−1.06943
$188$	6.95036e25	0.488869
$189$	0	0
$190$	−2.52167e25	−0.157044
$191$	9.94591e25	0.583124	0.291562	−	0.956552i	$-0.405825\pi$
$191$	9.94591e25	0.583124	0.291562	+	0.956552i	$0.405825\pi$
$192$	0	0
$193$	2.11752e26	1.10133	0.550667	−	0.834725i	$-0.314373\pi$
$193$	2.11752e26	1.10133	0.550667	+	0.834725i	$0.314373\pi$
$194$	−1.73679e25	−0.0851190
$195$	0	0
$196$	−2.03815e26	−0.887750
$197$	−2.43182e26	−0.999009	−0.499505	−	0.866311i	$-0.666485\pi$
$197$	−2.43182e26	−0.999009	−0.499505	+	0.866311i	$0.666485\pi$
$198$	0	0
$199$	−2.49955e26	−0.914220	−0.457110	−	0.889410i	$-0.651115\pi$
$199$	−2.49955e26	−0.914220	−0.457110	+	0.889410i	$0.651115\pi$
$200$	2.22072e25	0.0766740
$201$	0	0
$202$	1.40683e26	0.433212
$203$	1.14345e26	0.332670
$204$	0	0
$205$	7.54238e26	1.96037
$206$	1.38161e26	0.339556
$207$	0	0
$208$	1.19745e26	0.263347
$209$	1.46357e26	0.304600
$210$	0	0
$211$	−2.68608e26	−0.501038	−0.250519	−	0.968112i	$-0.580601\pi$
$211$	−2.68608e26	−0.501038	−0.250519	+	0.968112i	$0.580601\pi$
$212$	−4.49768e26	−0.794560
$213$	0	0
$214$	3.62943e26	0.575546
$215$	1.20611e27	1.81278
$216$	0	0
$217$	−6.36757e26	−0.860373
$218$	4.32974e26	0.554897
$219$	0	0
$220$	−6.96483e26	−0.803618
$221$	1.12156e27	1.22832
$222$	0	0
$223$	4.28148e25	0.0422754	0.0211377	−	0.999777i	$-0.493271\pi$
$223$	4.28148e25	0.0422754	0.0211377	+	0.999777i	$0.493271\pi$
$224$	−1.65816e27	−1.55516
$225$	0	0
$226$	5.81434e26	0.492327
$227$	−1.04141e27	−0.838154	−0.419077	−	0.907951i	$-0.637646\pi$
$227$	−1.04141e27	−0.838154	−0.419077	+	0.907951i	$0.637646\pi$
$228$	0	0
$229$	3.17314e26	0.230877	0.115439	−	0.993315i	$-0.463173\pi$
$229$	3.17314e26	0.230877	0.115439	+	0.993315i	$0.463173\pi$
$230$	−8.54334e26	−0.591232
$231$	0	0
$232$	3.26358e26	0.204448
$233$	−1.07463e27	−0.640715	−0.320357	−	0.947297i	$-0.603803\pi$
$233$	−1.07463e27	−0.640715	−0.320357	+	0.947297i	$0.603803\pi$
$234$	0	0
$235$	1.32892e27	0.718154
$236$	−2.49382e26	−0.128345
$237$	0	0
$238$	−1.70267e27	−0.795235
$239$	2.91187e27	1.29598	0.647988	−	0.761651i	$-0.275611\pi$
$239$	2.91187e27	1.29598	0.647988	+	0.761651i	$0.275611\pi$
$240$	0	0
$241$	−1.77639e27	−0.718362	−0.359181	−	0.933268i	$-0.616944\pi$
$241$	−1.77639e27	−0.718362	−0.359181	+	0.933268i	$0.616944\pi$
$242$	−2.63194e26	−0.101484
$243$	0	0
$244$	−4.43266e26	−0.155483
$245$	−3.89696e27	−1.30411
$246$	0	0
$247$	−1.14790e27	−0.349855
$248$	−1.81739e27	−0.528756
$249$	0	0
$250$	−1.94229e27	−0.515234
$251$	4.39892e27	1.11455	0.557274	−	0.830329i	$-0.311847\pi$
$251$	4.39892e27	1.11455	0.557274	+	0.830329i	$0.311847\pi$
$252$	0	0
$253$	4.95853e27	1.14674
$254$	2.51082e27	0.554917
$255$	0	0
$256$	−3.99465e27	−0.806714
$257$	−3.06305e27	−0.591457	−0.295729	−	0.955272i	$-0.595562\pi$
$257$	−3.06305e27	−0.591457	−0.295729	+	0.955272i	$0.595562\pi$
$258$	0	0
$259$	9.37744e27	1.65629
$260$	5.46263e27	0.923013
$261$	0	0
$262$	3.24992e27	0.502815
$263$	−4.37920e27	−0.648491	−0.324246	−	0.945973i	$-0.605110\pi$
$263$	−4.37920e27	−0.648491	−0.324246	+	0.945973i	$0.605110\pi$
$264$	0	0
$265$	−8.59962e27	−1.16722
$266$	1.74265e27	0.226502
$267$	0	0
$268$	7.69930e27	0.918124
$269$	1.36648e28	1.56118	0.780588	−	0.625046i	$-0.214920\pi$
$269$	1.36648e28	1.56118	0.780588	+	0.625046i	$0.214920\pi$
$270$	0	0
$271$	−7.06980e27	−0.741755	−0.370878	−	0.928682i	$-0.620943\pi$
$271$	−7.06980e27	−0.741755	−0.370878	+	0.928682i	$0.620943\pi$
$272$	2.05243e27	0.206408
$273$	0	0
$274$	7.61081e27	0.703558
$275$	−1.02192e27	−0.0905923
$276$	0	0
$277$	1.02188e28	0.833460	0.416730	−	0.909030i	$-0.363176\pi$
$277$	1.02188e28	0.833460	0.416730	+	0.909030i	$0.363176\pi$
$278$	−1.41680e27	−0.110865
$279$	0	0
$280$	−1.99986e28	−1.44106
$281$	8.03841e26	0.0555965	0.0277983	−	0.999614i	$-0.491150\pi$
$281$	8.03841e26	0.0555965	0.0277983	+	0.999614i	$0.491150\pi$
$282$	0	0
$283$	−2.15414e28	−1.37318	−0.686592	−	0.727043i	$-0.740894\pi$
$283$	−2.15414e28	−1.37318	−0.686592	+	0.727043i	$0.740894\pi$
$284$	−1.41316e28	−0.865028
$285$	0	0
$286$	1.30473e28	0.736733
$287$	−5.21232e28	−2.82741
$288$	0	0
$289$	−7.43986e26	−0.0372597
$290$	2.58758e27	0.124542
$291$	0	0
$292$	1.80195e28	0.801383
$293$	2.33106e28	0.996725	0.498363	−	0.866969i	$-0.333935\pi$
$293$	2.33106e28	0.996725	0.498363	+	0.866969i	$0.333935\pi$
$294$	0	0
$295$	−4.76822e27	−0.188540
$296$	2.67645e28	1.01790
$297$	0	0
$298$	1.54276e28	0.543015
$299$	−3.88905e28	−1.31712
$300$	0	0
$301$	−8.33511e28	−2.61455
$302$	7.54907e27	0.227936
$303$	0	0
$304$	−2.10062e27	−0.0587898
$305$	−8.47531e27	−0.228406
$306$	0	0
$307$	6.97395e28	1.74336	0.871681	−	0.490074i	$-0.163030\pi$
$307$	6.97395e28	1.74336	0.871681	+	0.490074i	$0.163030\pi$
$308$	4.81319e28	1.15904
$309$	0	0
$310$	−1.44095e28	−0.322099
$311$	4.01460e28	0.864765	0.432382	−	0.901690i	$-0.357673\pi$
$311$	4.01460e28	0.864765	0.432382	+	0.901690i	$0.357673\pi$
$312$	0	0
$313$	7.08075e28	1.41683	0.708417	−	0.705794i	$-0.249409\pi$
$313$	7.08075e28	1.41683	0.708417	+	0.705794i	$0.249409\pi$
$314$	−2.92539e27	−0.0564278
$315$	0	0
$316$	−2.23310e27	−0.0400412
$317$	3.21150e28	0.555298	0.277649	−	0.960683i	$-0.410445\pi$
$317$	3.21150e28	0.555298	0.277649	+	0.960683i	$0.410445\pi$
$318$	0	0
$319$	−1.50182e28	−0.241560
$320$	−2.34132e28	−0.363275
$321$	0	0
$322$	5.90406e28	0.852723
$323$	−1.96750e28	−0.274211
$324$	0	0
$325$	8.01509e27	0.104052
$326$	6.13082e28	0.768274
$327$	0	0
$328$	−1.48767e29	−1.73763
$329$	−9.18377e28	−1.03578
$330$	0	0
$331$	8.40986e28	0.884640	0.442320	−	0.896857i	$-0.354155\pi$
$331$	8.40986e28	0.884640	0.442320	+	0.896857i	$0.354155\pi$
$332$	−5.94292e28	−0.603826
$333$	0	0
$334$	−7.25663e28	−0.688098
$335$	1.47212e29	1.34874
$336$	0	0
$337$	−1.63996e29	−1.40311	−0.701553	−	0.712618i	$-0.747510\pi$
$337$	−1.63996e29	−1.40311	−0.701553	+	0.712618i	$0.747510\pi$
$338$	−3.70345e28	−0.306242
$339$	0	0
$340$	9.36294e28	0.723444
$341$	8.36322e28	0.624738
$342$	0	0
$343$	5.43907e28	0.379877
$344$	−2.37896e29	−1.60681
$345$	0	0
$346$	−7.42502e28	−0.469162
$347$	−6.78465e28	−0.414704	−0.207352	−	0.978266i	$-0.566485\pi$
$347$	−6.78465e28	−0.414704	−0.207352	+	0.978266i	$0.566485\pi$
$348$	0	0
$349$	1.82821e29	1.04601	0.523003	−	0.852331i	$-0.324812\pi$
$349$	1.82821e29	1.04601	0.523003	+	0.852331i	$0.324812\pi$
$350$	−1.21679e28	−0.0673647
$351$	0	0
$352$	2.17784e29	1.12924
$353$	−1.44105e29	−0.723218	−0.361609	−	0.932330i	$-0.617772\pi$
$353$	−1.44105e29	−0.723218	−0.361609	+	0.932330i	$0.617772\pi$
$354$	0	0
$355$	−2.70198e29	−1.27074
$356$	−3.18568e28	−0.145053
$357$	0	0
$358$	9.34501e28	0.398956
$359$	3.54388e28	0.146519	0.0732593	−	0.997313i	$-0.476660\pi$
$359$	3.54388e28	0.146519	0.0732593	+	0.997313i	$0.476660\pi$
$360$	0	0
$361$	−2.37693e29	−0.921898
$362$	−6.14210e28	−0.230764
$363$	0	0
$364$	−3.77506e29	−1.33125
$365$	3.44535e29	1.17724
$366$	0	0
$367$	1.57063e29	0.503981	0.251990	−	0.967730i	$-0.418915\pi$
$367$	1.57063e29	0.503981	0.251990	+	0.967730i	$0.418915\pi$
$368$	−7.11686e28	−0.221329
$369$	0	0
$370$	2.12207e29	0.620068
$371$	5.94295e29	1.68346
$372$	0	0
$373$	4.68656e29	1.24796	0.623982	−	0.781438i	$-0.285514\pi$
$373$	4.68656e29	1.24796	0.623982	+	0.781438i	$0.285514\pi$
$374$	2.23630e29	0.577440
$375$	0	0
$376$	−2.62118e29	−0.636555
$377$	1.17790e29	0.277449
$378$	0	0
$379$	4.57537e28	0.101409	0.0507044	−	0.998714i	$-0.483853\pi$
$379$	4.57537e28	0.101409	0.0507044	+	0.998714i	$0.483853\pi$
$380$	−9.58280e28	−0.206054
$381$	0	0
$382$	−1.55540e29	−0.314857
$383$	−4.53749e29	−0.891312	−0.445656	−	0.895204i	$-0.647030\pi$
$383$	−4.53749e29	−0.891312	−0.445656	+	0.895204i	$0.647030\pi$
$384$	0	0
$385$	9.20288e29	1.70265
$386$	−3.31151e29	−0.594664
$387$	0	0
$388$	−6.60011e28	−0.111683
$389$	−3.59874e29	−0.591195	−0.295597	−	0.955313i	$-0.595519\pi$
$389$	−3.59874e29	−0.591195	−0.295597	+	0.955313i	$0.595519\pi$
$390$	0	0
$391$	−6.66583e29	−1.03234
$392$	7.68642e29	1.15594
$393$	0	0
$394$	3.80302e29	0.539414
$395$	−4.26971e28	−0.0588210
$396$	0	0
$397$	−9.62669e28	−0.125137	−0.0625686	−	0.998041i	$-0.519929\pi$
$397$	−9.62669e28	−0.125137	−0.0625686	+	0.998041i	$0.519929\pi$
$398$	3.90894e29	0.493632
$399$	0	0
$400$	1.46674e28	0.0174849
$401$	−4.97920e29	−0.576766	−0.288383	−	0.957515i	$-0.593118\pi$
$401$	−4.97920e29	−0.576766	−0.288383	+	0.957515i	$0.593118\pi$
$402$	0	0
$403$	−6.55941e29	−0.717557
$404$	5.34621e29	0.568408
$405$	0	0
$406$	−1.78820e29	−0.179625
$407$	−1.23164e30	−1.20267
$408$	0	0
$409$	−1.48649e30	−1.37197	−0.685985	−	0.727616i	$-0.740628\pi$
$409$	−1.48649e30	−1.37197	−0.685985	+	0.727616i	$0.740628\pi$
$410$	−1.17952e30	−1.05850
$411$	0	0
$412$	5.25036e29	0.445524
$413$	3.29518e29	0.271928
$414$	0	0
$415$	−1.13629e30	−0.887028
$416$	−1.70812e30	−1.29701
$417$	0	0
$418$	−2.28881e29	−0.164469
$419$	5.07194e29	0.354579	0.177289	−	0.984159i	$-0.443267\pi$
$419$	5.07194e29	0.354579	0.177289	+	0.984159i	$0.443267\pi$
$420$	0	0
$421$	2.56153e30	1.69533	0.847666	−	0.530531i	$-0.178007\pi$
$421$	2.56153e30	1.69533	0.847666	+	0.530531i	$0.178007\pi$
$422$	4.20065e29	0.270535
$423$	0	0
$424$	1.69620e30	1.03459
$425$	1.37379e29	0.0815542
$426$	0	0
$427$	5.85704e29	0.329426
$428$	1.37925e30	0.755161
$429$	0	0
$430$	−1.88619e30	−0.978811
$431$	1.21646e30	0.614625	0.307312	−	0.951609i	$-0.400570\pi$
$431$	1.21646e30	0.614625	0.307312	+	0.951609i	$0.400570\pi$
$432$	0	0
$433$	1.79430e30	0.859577	0.429789	−	0.902930i	$-0.358588\pi$
$433$	1.79430e30	0.859577	0.429789	+	0.902930i	$0.358588\pi$
$434$	9.95798e29	0.464558
$435$	0	0
$436$	1.64538e30	0.728068
$437$	6.82236e29	0.294034
$438$	0	0
$439$	−3.97063e30	−1.62374	−0.811871	−	0.583837i	$-0.801551\pi$
$439$	−3.97063e30	−1.62374	−0.811871	+	0.583837i	$0.801551\pi$
$440$	2.62663e30	1.04639
$441$	0	0
$442$	−1.75397e30	−0.663231
$443$	1.28735e30	0.474301	0.237151	−	0.971473i	$-0.423787\pi$
$443$	1.28735e30	0.474301	0.237151	+	0.971473i	$0.423787\pi$
$444$	0	0
$445$	−6.09105e29	−0.213085
$446$	−6.69562e28	−0.0228265
$447$	0	0
$448$	1.61802e30	0.523945
$449$	−3.17012e30	−1.00056	−0.500279	−	0.865864i	$-0.666769\pi$
$449$	−3.17012e30	−1.00056	−0.500279	+	0.865864i	$0.666769\pi$
$450$	0	0
$451$	6.84590e30	2.05305
$452$	2.20956e30	0.645971
$453$	0	0
$454$	1.62862e30	0.452560
$455$	−7.21796e30	−1.95562
$456$	0	0
$457$	−6.89795e30	−1.77699	−0.888493	−	0.458891i	$-0.848247\pi$
$457$	−6.89795e30	−1.77699	−0.888493	+	0.458891i	$0.848247\pi$
$458$	−4.96234e29	−0.124662
$459$	0	0
$460$	−3.24663e30	−0.775742
$461$	1.25314e30	0.292038	0.146019	−	0.989282i	$-0.453354\pi$
$461$	1.25314e30	0.292038	0.146019	+	0.989282i	$0.453354\pi$
$462$	0	0
$463$	4.87399e30	1.08070	0.540348	−	0.841442i	$-0.318293\pi$
$463$	4.87399e30	1.08070	0.540348	+	0.841442i	$0.318293\pi$
$464$	2.15553e29	0.0466227
$465$	0	0
$466$	1.68057e30	0.345953
$467$	−4.35835e30	−0.875343	−0.437671	−	0.899135i	$-0.644197\pi$
$467$	−4.35835e30	−0.875343	−0.437671	+	0.899135i	$0.644197\pi$
$468$	0	0
$469$	−1.01734e31	−1.94526
$470$	−2.07824e30	−0.387766
$471$	0	0
$472$	9.40490e29	0.167117
$473$	1.09474e31	1.89849
$474$	0	0
$475$	−1.40604e29	−0.0232286
$476$	−6.47046e30	−1.04341
$477$	0	0
$478$	−4.55376e30	−0.699760
$479$	−4.80333e30	−0.720582	−0.360291	−	0.932840i	$-0.617323\pi$
$479$	−4.80333e30	−0.720582	−0.360291	+	0.932840i	$0.617323\pi$
$480$	0	0
$481$	9.65995e30	1.38136
$482$	2.77803e30	0.387879
$483$	0	0
$484$	−1.00019e30	−0.133156
$485$	−1.26195e30	−0.164063
$486$	0	0
$487$	−3.71714e30	−0.460920	−0.230460	−	0.973082i	$-0.574023\pi$
$487$	−3.71714e30	−0.460920	−0.230460	+	0.973082i	$0.574023\pi$
$488$	1.67168e30	0.202454
$489$	0	0
$490$	6.09429e30	0.704155
$491$	−7.53933e30	−0.850933	−0.425466	−	0.904974i	$-0.639890\pi$
$491$	−7.53933e30	−0.850933	−0.425466	+	0.904974i	$0.639890\pi$
$492$	0	0
$493$	2.01892e30	0.217460
$494$	1.79515e30	0.188904
$495$	0	0
$496$	−1.20035e30	−0.120579
$497$	1.86726e31	1.83276
$498$	0	0
$499$	3.09263e30	0.289849	0.144925	−	0.989443i	$-0.453706\pi$
$499$	3.09263e30	0.289849	0.144925	+	0.989443i	$0.453706\pi$
$500$	−7.38106e30	−0.676027
$501$	0	0
$502$	−6.87930e30	−0.601799
$503$	4.43628e30	0.379304	0.189652	−	0.981851i	$-0.439264\pi$
$503$	4.43628e30	0.379304	0.189652	+	0.981851i	$0.439264\pi$
$504$	0	0
$505$	1.02220e31	0.834999
$506$	−7.75444e30	−0.619183
$507$	0	0
$508$	9.54158e30	0.728094
$509$	2.05052e31	1.52971	0.764855	−	0.644203i	$-0.222811\pi$
$509$	2.05052e31	1.52971	0.764855	+	0.644203i	$0.222811\pi$
$510$	0	0
$511$	−2.38098e31	−1.69791
$512$	−5.90893e30	−0.412007
$513$	0	0
$514$	4.79018e30	0.319357
$515$	1.00388e31	0.654481
$516$	0	0
$517$	1.20620e31	0.752106
$518$	−1.46650e31	−0.894313
$519$	0	0
$520$	−2.06011e31	−1.20185
$521$	2.13126e31	1.21620	0.608098	−	0.793862i	$-0.291933\pi$
$521$	2.13126e31	1.21620	0.608098	+	0.793862i	$0.291933\pi$
$522$	0	0
$523$	5.37551e30	0.293528	0.146764	−	0.989172i	$-0.453114\pi$
$523$	5.37551e30	0.293528	0.146764	+	0.989172i	$0.453114\pi$
$524$	1.23503e31	0.659733
$525$	0	0
$526$	6.84846e30	0.350152
$527$	−1.12428e31	−0.562410
$528$	0	0
$529$	2.23351e30	0.106966
$530$	1.34486e31	0.630238
$531$	0	0
$532$	6.62240e30	0.297188
$533$	−5.36935e31	−2.35808
$534$	0	0
$535$	2.63714e31	1.10934
$536$	−2.90362e31	−1.19549
$537$	0	0
$538$	−2.13698e31	−0.842955
$539$	−3.53711e31	−1.36577
$540$	0	0
$541$	−3.74692e30	−0.138646	−0.0693228	−	0.997594i	$-0.522084\pi$
$541$	−3.74692e30	−0.138646	−0.0693228	+	0.997594i	$0.522084\pi$
$542$	1.10562e31	0.400510
$543$	0	0
$544$	−2.92771e31	−1.01658
$545$	3.14599e31	1.06954
$546$	0	0
$547$	−3.43148e30	−0.111848	−0.0559239	−	0.998435i	$-0.517810\pi$
$547$	−3.43148e30	−0.111848	−0.0559239	+	0.998435i	$0.517810\pi$
$548$	2.89225e31	0.923123
$549$	0	0
$550$	1.59814e30	0.0489152
$551$	−2.06633e30	−0.0619379
$552$	0	0
$553$	2.95068e30	0.0848364
$554$	−1.59808e31	−0.450026
$555$	0	0
$556$	−5.38409e30	−0.145463
$557$	−3.40780e31	−0.901860	−0.450930	−	0.892559i	$-0.648908\pi$
$557$	−3.40780e31	−0.901860	−0.450930	+	0.892559i	$0.648908\pi$
$558$	0	0
$559$	−8.58622e31	−2.18055
$560$	−1.32087e31	−0.328622
$561$	0	0
$562$	−1.25709e30	−0.0300193
$563$	2.39242e31	0.559747	0.279873	−	0.960037i	$-0.409708\pi$
$563$	2.39242e31	0.559747	0.279873	+	0.960037i	$0.409708\pi$
$564$	0	0
$565$	4.22470e31	0.948940
$566$	3.36876e31	0.741450
$567$	0	0
$568$	5.32942e31	1.12635
$569$	1.92696e31	0.399101	0.199550	−	0.979888i	$-0.436052\pi$
$569$	1.92696e31	0.399101	0.199550	+	0.979888i	$0.436052\pi$
$570$	0	0
$571$	1.76715e31	0.351526	0.175763	−	0.984433i	$-0.443761\pi$
$571$	1.76715e31	0.351526	0.175763	+	0.984433i	$0.443761\pi$
$572$	4.95820e31	0.966651
$573$	0	0
$574$	8.15133e31	1.52666
$575$	−4.76364e30	−0.0874498
$576$	0	0
$577$	5.86874e31	1.03520	0.517599	−	0.855624i	$-0.326826\pi$
$577$	5.86874e31	1.03520	0.517599	+	0.855624i	$0.326826\pi$
$578$	1.16349e30	0.0201183
$579$	0	0
$580$	9.83327e30	0.163409
$581$	7.85259e31	1.27934
$582$	0	0
$583$	−7.80552e31	−1.22240
$584$	−6.79566e31	−1.04348
$585$	0	0
$586$	−3.64545e31	−0.538181
$587$	−6.89187e31	−0.997697	−0.498849	−	0.866689i	$-0.666244\pi$
$587$	−6.89187e31	−0.997697	−0.498849	+	0.866689i	$0.666244\pi$
$588$	0	0
$589$	1.15068e31	0.160188
$590$	7.45682e30	0.101802
$591$	0	0
$592$	1.76775e31	0.232124
$593$	7.35782e31	0.947589	0.473795	−	0.880635i	$-0.342884\pi$
$593$	7.35782e31	0.947589	0.473795	+	0.880635i	$0.342884\pi$
$594$	0	0
$595$	−1.23716e32	−1.53278
$596$	5.86278e31	0.712478
$597$	0	0
$598$	6.08193e31	0.711177
$599$	−1.35998e32	−1.56000	−0.779999	−	0.625780i	$-0.784781\pi$
$599$	−1.35998e32	−1.56000	−0.779999	+	0.625780i	$0.784781\pi$
$600$	0	0
$601$	−7.89659e31	−0.871732	−0.435866	−	0.900011i	$-0.643558\pi$
$601$	−7.89659e31	−0.871732	−0.435866	+	0.900011i	$0.643558\pi$
$602$	1.30349e32	1.41172
$603$	0	0
$604$	2.86879e31	0.299070
$605$	−1.91237e31	−0.195607
$606$	0	0
$607$	−4.65196e31	−0.458106	−0.229053	−	0.973414i	$-0.573563\pi$
$607$	−4.65196e31	−0.458106	−0.229053	+	0.973414i	$0.573563\pi$
$608$	2.99646e31	0.289546
$609$	0	0
$610$	1.32542e31	0.123327
$611$	−9.46044e31	−0.863849
$612$	0	0
$613$	1.41819e32	1.24721	0.623606	−	0.781739i	$-0.285667\pi$
$613$	1.41819e32	1.24721	0.623606	+	0.781739i	$0.285667\pi$
$614$	−1.09063e32	−0.941326
$615$	0	0
$616$	−1.81519e32	−1.50919
$617$	−2.38519e32	−1.94645	−0.973227	−	0.229848i	$-0.926177\pi$
$617$	−2.38519e32	−1.94645	−0.973227	+	0.229848i	$0.926177\pi$
$618$	0	0
$619$	1.46333e32	1.15054	0.575268	−	0.817965i	$-0.304898\pi$
$619$	1.46333e32	1.15054	0.575268	+	0.817965i	$0.304898\pi$
$620$	−5.47587e31	−0.422619
$621$	0	0
$622$	−6.27827e31	−0.466929
$623$	4.20935e31	0.307328
$624$	0	0
$625$	−1.52938e32	−1.07621
$626$	−1.10733e32	−0.765018
$627$	0	0
$628$	−1.11170e31	−0.0740377
$629$	1.65572e32	1.08269
$630$	0	0
$631$	2.57610e32	1.62414	0.812072	−	0.583557i	$-0.198339\pi$
$631$	2.57610e32	1.62414	0.812072	+	0.583557i	$0.198339\pi$
$632$	8.42164e30	0.0521375
$633$	0	0
$634$	−5.02233e31	−0.299833
$635$	1.82436e32	1.06958
$636$	0	0
$637$	2.77421e32	1.56869
$638$	2.34864e31	0.130430
$639$	0	0
$640$	−1.64662e32	−0.882113
$641$	2.91189e32	1.53217	0.766086	−	0.642739i	$-0.222202\pi$
$641$	2.91189e32	1.53217	0.766086	+	0.642739i	$0.222202\pi$
$642$	0	0
$643$	−3.58958e32	−1.82229	−0.911144	−	0.412088i	$-0.864800\pi$
$643$	−3.58958e32	−1.82229	−0.911144	+	0.412088i	$0.864800\pi$
$644$	2.24365e32	1.11884
$645$	0	0
$646$	3.07689e31	0.148060
$647$	−3.52744e32	−1.66748	−0.833740	−	0.552157i	$-0.813805\pi$
$647$	−3.52744e32	−1.66748	−0.833740	+	0.552157i	$0.813805\pi$
$648$	0	0
$649$	−4.32791e31	−0.197453
$650$	−1.25345e31	−0.0561827
$651$	0	0
$652$	2.32983e32	1.00804
$653$	2.22542e32	0.946041	0.473021	−	0.881051i	$-0.343164\pi$
$653$	2.22542e32	0.946041	0.473021	+	0.881051i	$0.343164\pi$
$654$	0	0
$655$	2.36139e32	0.969156
$656$	−9.82577e31	−0.396253
$657$	0	0
$658$	1.43621e32	0.559269
$659$	−1.21818e31	−0.0466152	−0.0233076	−	0.999728i	$-0.507420\pi$
$659$	−1.21818e31	−0.0466152	−0.0233076	+	0.999728i	$0.507420\pi$
$660$	0	0
$661$	−3.10145e32	−1.14617	−0.573084	−	0.819496i	$-0.694253\pi$
$661$	−3.10145e32	−1.14617	−0.573084	+	0.819496i	$0.694253\pi$
$662$	−1.31518e32	−0.477661
$663$	0	0
$664$	2.24124e32	0.786241
$665$	1.26621e32	0.436573
$666$	0	0
$667$	−7.00068e31	−0.233181
$668$	−2.75765e32	−0.902839
$669$	0	0
$670$	−2.30218e32	−0.728248
$671$	−7.69268e31	−0.239204
$672$	0	0
$673$	1.82996e32	0.549880	0.274940	−	0.961461i	$-0.411342\pi$
$673$	1.82996e32	0.549880	0.274940	+	0.961461i	$0.411342\pi$
$674$	2.56467e32	0.757605
$675$	0	0
$676$	−1.40738e32	−0.401813
$677$	5.90638e32	1.65788	0.828938	−	0.559341i	$-0.188946\pi$
$677$	5.90638e32	1.65788	0.828938	+	0.559341i	$0.188946\pi$
$678$	0	0
$679$	8.72096e31	0.236626
$680$	−3.53103e32	−0.941995
$681$	0	0
$682$	−1.30789e32	−0.337327
$683$	−3.47709e32	−0.881815	−0.440907	−	0.897553i	$-0.645343\pi$
$683$	−3.47709e32	−0.881815	−0.440907	+	0.897553i	$0.645343\pi$
$684$	0	0
$685$	5.53001e32	1.35608
$686$	−8.50594e31	−0.205114
$687$	0	0
$688$	−1.57125e32	−0.366420
$689$	6.12199e32	1.40402
$690$	0	0
$691$	−4.28793e32	−0.951151	−0.475576	−	0.879675i	$-0.657760\pi$
$691$	−4.28793e32	−0.951151	−0.475576	+	0.879675i	$0.657760\pi$
$692$	−2.82164e32	−0.615577
$693$	0	0
$694$	1.06102e32	0.223919
$695$	−1.02944e32	−0.213687
$696$	0	0
$697$	−9.20307e32	−1.84823
$698$	−2.85907e32	−0.564790
$699$	0	0
$700$	−4.62402e31	−0.0883878
$701$	−8.63465e32	−1.62363	−0.811816	−	0.583913i	$-0.801521\pi$
$701$	−8.63465e32	−1.62363	−0.811816	+	0.583913i	$0.801521\pi$
$702$	0	0
$703$	−1.69459e32	−0.308375
$704$	−2.12511e32	−0.380449
$705$	0	0
$706$	2.25359e32	0.390501
$707$	−7.06414e32	−1.20430
$708$	0	0
$709$	7.56772e32	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$709$	7.56772e32	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$710$	4.22551e32	0.686133
$711$	0	0
$712$	1.20141e32	0.188873
$713$	3.89848e32	0.603068
$714$	0	0
$715$	9.48013e32	1.42002
$716$	3.55128e32	0.523462
$717$	0	0
$718$	−5.54213e31	−0.0791126
$719$	3.98801e32	0.560240	0.280120	−	0.959965i	$-0.409626\pi$
$719$	3.98801e32	0.560240	0.280120	+	0.959965i	$0.409626\pi$
$720$	0	0
$721$	−6.93749e32	−0.943946
$722$	3.71718e32	0.497778
$723$	0	0
$724$	−2.33411e32	−0.302781
$725$	1.44279e31	0.0184212
$726$	0	0
$727$	−7.76270e32	−0.960211	−0.480106	−	0.877211i	$-0.659402\pi$
$727$	−7.76270e32	−0.960211	−0.480106	+	0.877211i	$0.659402\pi$
$728$	1.42368e33	1.73341
$729$	0	0
$730$	−5.38804e32	−0.635650
$731$	−1.47168e33	−1.70908
$732$	0	0
$733$	8.56762e32	0.964195	0.482097	−	0.876118i	$-0.339875\pi$
$733$	8.56762e32	0.964195	0.482097	+	0.876118i	$0.339875\pi$
$734$	−2.45624e32	−0.272124
$735$	0	0
$736$	1.01519e33	1.09007
$737$	1.33618e33	1.41250
$738$	0	0
$739$	−5.55833e32	−0.569552	−0.284776	−	0.958594i	$-0.591919\pi$
$739$	−5.55833e32	−0.569552	−0.284776	+	0.958594i	$0.591919\pi$
$740$	8.06424e32	0.813577
$741$	0	0
$742$	−9.29394e32	−0.908981
$743$	1.55682e33	1.49923	0.749613	−	0.661876i	$-0.230240\pi$
$743$	1.55682e33	1.49923	0.749613	+	0.661876i	$0.230240\pi$
$744$	0	0
$745$	1.12097e33	1.04664
$746$	−7.32911e32	−0.673837
$747$	0	0
$748$	8.49835e32	0.757646
$749$	−1.82245e33	−1.59998
$750$	0	0
$751$	1.66899e33	1.42100	0.710501	−	0.703696i	$-0.248468\pi$
$751$	1.66899e33	1.42100	0.710501	+	0.703696i	$0.248468\pi$
$752$	−1.73124e32	−0.145161
$753$	0	0
$754$	−1.84207e32	−0.149808
$755$	5.48515e32	0.439338
$756$	0	0
$757$	−7.88666e31	−0.0612760	−0.0306380	−	0.999531i	$-0.509754\pi$
$757$	−7.88666e31	−0.0612760	−0.0306380	+	0.999531i	$0.509754\pi$
$758$	−7.15524e31	−0.0547556
$759$	0	0
$760$	3.61394e32	0.268303
$761$	−7.62229e32	−0.557394	−0.278697	−	0.960379i	$-0.589902\pi$
$761$	−7.62229e32	−0.557394	−0.278697	+	0.960379i	$0.589902\pi$
$762$	0	0
$763$	−2.17410e33	−1.54258
$764$	−5.91081e32	−0.413117
$765$	0	0
$766$	7.09600e32	0.481263
$767$	3.39445e32	0.226789
$768$	0	0
$769$	−2.24557e33	−1.45604	−0.728020	−	0.685556i	$-0.759559\pi$
$769$	−2.24557e33	−1.45604	−0.728020	+	0.685556i	$0.759559\pi$
$770$	−1.43920e33	−0.919344
$771$	0	0
$772$	−1.25843e33	−0.780246
$773$	−1.77063e33	−1.08159	−0.540795	−	0.841154i	$-0.681877\pi$
$773$	−1.77063e33	−1.08159	−0.540795	+	0.841154i	$0.681877\pi$
$774$	0	0
$775$	−8.03452e31	−0.0476421
$776$	2.48909e32	0.145422
$777$	0	0
$778$	5.62793e32	0.319215
$779$	9.41917e32	0.526419
$780$	0	0
$781$	−2.45247e33	−1.33081
$782$	1.04244e33	0.557410
$783$	0	0
$784$	5.07673e32	0.263602
$785$	−2.12559e32	−0.108762
$786$	0	0
$787$	1.41877e33	0.705024	0.352512	−	0.935807i	$-0.385328\pi$
$787$	1.41877e33	0.705024	0.352512	+	0.935807i	$0.385328\pi$
$788$	1.44522e33	0.707753
$789$	0	0
$790$	6.67723e31	0.0317603
$791$	−2.91957e33	−1.36864
$792$	0	0
$793$	6.03349e32	0.274743
$794$	1.50548e32	0.0675676
$795$	0	0
$796$	1.48547e33	0.647684
$797$	−2.58083e33	−1.10915	−0.554573	−	0.832135i	$-0.687118\pi$
$797$	−2.58083e33	−1.10915	−0.554573	+	0.832135i	$0.687118\pi$
$798$	0	0
$799$	−1.62152e33	−0.677071
$800$	−2.09225e32	−0.0861149
$801$	0	0
$802$	7.78677e32	0.311424
$803$	3.12720e33	1.23290
$804$	0	0
$805$	4.28989e33	1.64359
$806$	1.02580e33	0.387444
$807$	0	0
$808$	−2.01621e33	−0.740124
$809$	1.24432e33	0.450323	0.225161	−	0.974321i	$-0.427709\pi$
$809$	1.24432e33	0.450323	0.225161	+	0.974321i	$0.427709\pi$
$810$	0	0
$811$	1.55059e32	0.0545453	0.0272727	−	0.999628i	$-0.491318\pi$
$811$	1.55059e32	0.0545453	0.0272727	+	0.999628i	$0.491318\pi$
$812$	−6.79549e32	−0.235682
$813$	0	0
$814$	1.92611e33	0.649383
$815$	4.45465e33	1.48082
$816$	0	0
$817$	1.50624e33	0.486787
$818$	2.32466e33	0.740793
$819$	0	0
$820$	−4.48240e33	−1.38884
$821$	−5.00186e33	−1.52822	−0.764108	−	0.645088i	$-0.776821\pi$
$821$	−5.00186e33	−1.52822	−0.764108	+	0.645088i	$0.776821\pi$
$822$	0	0
$823$	2.77022e33	0.823030	0.411515	−	0.911403i	$-0.365000\pi$
$823$	2.77022e33	0.823030	0.411515	+	0.911403i	$0.365000\pi$
$824$	−1.98006e33	−0.580116
$825$	0	0
$826$	−5.15319e32	−0.146827
$827$	2.81604e33	0.791270	0.395635	−	0.918408i	$-0.370525\pi$
$827$	2.81604e33	0.791270	0.395635	+	0.918408i	$0.370525\pi$
$828$	0	0
$829$	−6.05152e32	−0.165382	−0.0826908	−	0.996575i	$-0.526351\pi$
$829$	−6.05152e32	−0.165382	−0.0826908	+	0.996575i	$0.526351\pi$
$830$	1.77700e33	0.478950
$831$	0	0
$832$	1.66676e33	0.436974
$833$	4.75500e33	1.22951
$834$	0	0
$835$	−5.27266e33	−1.32628
$836$	−8.69791e32	−0.215796
$837$	0	0
$838$	−7.93180e32	−0.191454
$839$	2.21831e33	0.528152	0.264076	−	0.964502i	$-0.414933\pi$
$839$	2.21831e33	0.528152	0.264076	+	0.964502i	$0.414933\pi$
$840$	0	0
$841$	−4.10469e33	−0.950881
$842$	−4.00587e33	−0.915392
$843$	0	0
$844$	1.59632e33	0.354963
$845$	−2.69093e33	−0.590268
$846$	0	0
$847$	1.32158e33	0.282121
$848$	1.12031e33	0.235931
$849$	0	0
$850$	−2.14841e32	−0.0440351
$851$	−5.74124e33	−1.16096
$852$	0	0
$853$	9.69232e33	1.90772	0.953858	−	0.300257i	$-0.0970723\pi$
$853$	9.69232e33	1.90772	0.953858	+	0.300257i	$0.0970723\pi$
$854$	−9.15958e32	−0.177873
$855$	0	0
$856$	−5.20154e33	−0.983295
$857$	3.54610e33	0.661411	0.330705	−	0.943734i	$-0.392713\pi$
$857$	3.54610e33	0.661411	0.330705	+	0.943734i	$0.392713\pi$
$858$	0	0
$859$	9.58348e33	1.74021	0.870105	−	0.492866i	$-0.164051\pi$
$859$	9.58348e33	1.74021	0.870105	+	0.492866i	$0.164051\pi$
$860$	−7.16788e33	−1.28428
$861$	0	0
$862$	−1.90238e33	−0.331866
$863$	−3.43280e33	−0.590915	−0.295457	−	0.955356i	$-0.595472\pi$
$863$	−3.43280e33	−0.590915	−0.295457	+	0.955356i	$0.595472\pi$
$864$	0	0
$865$	−5.39502e33	−0.904290
$866$	−2.80604e33	−0.464128
$867$	0	0
$868$	3.78422e33	0.609536
$869$	−3.87544e32	−0.0616018
$870$	0	0
$871$	−1.04799e34	−1.62236
$872$	−6.20519e33	−0.948016
$873$	0	0
$874$	−1.06692e33	−0.158764
$875$	9.75287e33	1.43232
$876$	0	0
$877$	−8.57680e33	−1.22696	−0.613480	−	0.789711i	$-0.710231\pi$
$877$	−8.57680e33	−1.22696	−0.613480	+	0.789711i	$0.710231\pi$
$878$	6.20950e33	0.876738
$879$	0	0
$880$	1.73484e33	0.238621
$881$	8.23643e33	1.11819	0.559096	−	0.829103i	$-0.311148\pi$
$881$	8.23643e33	1.11819	0.559096	+	0.829103i	$0.311148\pi$
$882$	0	0
$883$	1.05626e34	1.39709	0.698545	−	0.715566i	$-0.253831\pi$
$883$	1.05626e34	1.39709	0.698545	+	0.715566i	$0.253831\pi$
$884$	−6.66539e33	−0.870211
$885$	0	0
$886$	−2.01324e33	−0.256098
$887$	−6.30164e33	−0.791283	−0.395642	−	0.918405i	$-0.629478\pi$
$887$	−6.30164e33	−0.791283	−0.395642	+	0.918405i	$0.629478\pi$
$888$	0	0
$889$	−1.26076e34	−1.54264
$890$	9.52555e32	0.115055
$891$	0	0
$892$	−2.54446e32	−0.0299502
$893$	1.65960e33	0.192846
$894$	0	0
$895$	6.79008e33	0.768972
$896$	1.13793e34	1.27226
$897$	0	0
$898$	4.95762e33	0.540250
$899$	−1.18076e33	−0.127035
$900$	0	0
$901$	1.04931e34	1.10045
$902$	−1.07060e34	−1.10854
$903$	0	0
$904$	−8.33286e33	−0.841118
$905$	−4.46285e33	−0.444788
$906$	0	0
$907$	1.10592e34	1.07458	0.537292	−	0.843396i	$-0.319447\pi$
$907$	1.10592e34	1.07458	0.537292	+	0.843396i	$0.319447\pi$
$908$	6.18904e33	0.593795
$909$	0	0
$910$	1.12879e34	1.05593
$911$	8.48544e33	0.783814	0.391907	−	0.920005i	$-0.371815\pi$
$911$	8.48544e33	0.783814	0.391907	+	0.920005i	$0.371815\pi$
$912$	0	0
$913$	−1.03137e34	−0.928964
$914$	1.07874e34	0.959481
$915$	0	0
$916$	−1.88578e33	−0.163566
$917$	−1.63189e34	−1.39780
$918$	0	0
$919$	2.82637e33	0.236102	0.118051	−	0.993008i	$-0.462335\pi$
$919$	2.82637e33	0.236102	0.118051	+	0.993008i	$0.462335\pi$
$920$	1.22439e34	1.01009
$921$	0	0
$922$	−1.95973e33	−0.157685
$923$	1.92351e34	1.52853
$924$	0	0
$925$	1.18323e33	0.0917150
$926$	−7.62223e33	−0.583520
$927$	0	0
$928$	−3.07478e33	−0.229621
$929$	−2.09040e34	−1.54187	−0.770936	−	0.636913i	$-0.780211\pi$
$929$	−2.09040e34	−1.54187	−0.770936	+	0.636913i	$0.780211\pi$
$930$	0	0
$931$	−4.86665e33	−0.350194
$932$	6.38646e33	0.453918
$933$	0	0
$934$	6.81585e33	0.472640
$935$	1.62489e34	1.11299
$936$	0	0
$937$	−9.77881e33	−0.653553	−0.326776	−	0.945102i	$-0.605962\pi$
$937$	−9.77881e33	−0.653553	−0.326776	+	0.945102i	$0.605962\pi$
$938$	1.59097e34	1.05034
$939$	0	0
$940$	−7.89769e33	−0.508780
$941$	−2.28884e34	−1.45658	−0.728290	−	0.685270i	$-0.759684\pi$
$941$	−2.28884e34	−1.45658	−0.728290	+	0.685270i	$0.759684\pi$
$942$	0	0
$943$	3.19119e34	1.98184
$944$	6.21175e32	0.0381098
$945$	0	0
$946$	−1.71202e34	−1.02509
$947$	−1.58194e34	−0.935763	−0.467882	−	0.883791i	$-0.654983\pi$
$947$	−1.58194e34	−0.935763	−0.467882	+	0.883791i	$0.654983\pi$
$948$	0	0
$949$	−2.45271e34	−1.41607
$950$	2.19886e32	0.0125422
$951$	0	0
$952$	2.44019e34	1.35862
$953$	1.70079e34	0.935582	0.467791	−	0.883839i	$-0.345050\pi$
$953$	1.70079e34	0.935582	0.467791	+	0.883839i	$0.345050\pi$
$954$	0	0
$955$	−1.13015e34	−0.606874
$956$	−1.73051e34	−0.918140
$957$	0	0
$958$	7.51172e33	0.389078
$959$	−3.82163e34	−1.95585
$960$	0	0
$961$	−1.34380e34	−0.671453
$962$	−1.51068e34	−0.745863
$963$	0	0
$964$	1.05570e34	0.508927
$965$	−2.40614e34	−1.14619
$966$	0	0
$967$	−3.44351e34	−1.60176	−0.800880	−	0.598825i	$-0.795634\pi$
$967$	−3.44351e34	−1.60176	−0.800880	+	0.598825i	$0.795634\pi$
$968$	3.77198e33	0.173382
$969$	0	0
$970$	1.97351e33	0.0885859
$971$	−1.73462e33	−0.0769456	−0.0384728	−	0.999260i	$-0.512249\pi$
$971$	−1.73462e33	−0.0769456	−0.0384728	+	0.999260i	$0.512249\pi$
$972$	0	0
$973$	7.11419e33	0.308197
$974$	5.81308e33	0.248873
$975$	0	0
$976$	1.10411e33	0.0461680
$977$	−1.44173e33	−0.0595794	−0.0297897	−	0.999556i	$-0.509484\pi$
$977$	−1.44173e33	−0.0595794	−0.0297897	+	0.999556i	$0.509484\pi$
$978$	0	0
$979$	−5.52859e33	−0.223159
$980$	2.31594e34	0.923907
$981$	0	0
$982$	1.17904e34	0.459460
$983$	4.62857e34	1.78271	0.891357	−	0.453303i	$-0.149754\pi$
$983$	4.62857e34	1.78271	0.891357	+	0.453303i	$0.149754\pi$
$984$	0	0
$985$	2.76327e34	1.03970
$986$	−3.15731e33	−0.117418
$987$	0	0
$988$	6.82191e33	0.247857
$989$	5.10309e34	1.83263
$990$	0	0
$991$	−1.68657e34	−0.591776	−0.295888	−	0.955223i	$-0.595615\pi$
$991$	−1.68657e34	−0.591776	−0.295888	+	0.955223i	$0.595615\pi$
$992$	1.71226e34	0.593862
$993$	0	0
$994$	−2.92013e34	−0.989597
$995$	2.84023e34	0.951455
$996$	0	0
$997$	2.01747e34	0.660410	0.330205	−	0.943909i	$-0.392882\pi$
$997$	2.01747e34	0.660410	0.330205	+	0.943909i	$0.392882\pi$
$998$	−4.83644e33	−0.156504
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.24.a.c.1.1		2
3.2	odd	2		3.24.a.b.1.2	✓	2
12.11	even	2		48.24.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.24.a.b.1.2	✓	2	3.2	odd	2
9.24.a.c.1.1		2	1.1	even	1	trivial
48.24.a.g.1.2		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-1563.86 q^{2} -5.94295e6 q^{4} -1.13630e8 q^{5} +7.85264e9 q^{7} +2.24125e10 q^{8} +O(q^{10})\)	\(q-1563.86 q^{2} -5.94295e6 q^{4} -1.13630e8 q^{5} +7.85264e9 q^{7} +2.24125e10 q^{8} +1.77701e11 q^{10} -1.03137e12 q^{11} +8.08921e12 q^{13} -1.22804e13 q^{14} +1.48030e13 q^{16} +1.38649e14 q^{17} -1.41905e14 q^{19} +6.75297e14 q^{20} +1.61292e15 q^{22} -4.80770e15 q^{23} +9.90836e14 q^{25} -1.26504e16 q^{26} -4.66679e16 q^{28} +1.45614e16 q^{29} -8.10883e16 q^{31} -2.11160e17 q^{32} -2.16828e17 q^{34} -8.92295e17 q^{35} +1.19418e18 q^{37} +2.21919e17 q^{38} -2.54674e18 q^{40} -6.63767e18 q^{41} -1.06144e19 q^{43} +6.12940e18 q^{44} +7.51856e18 q^{46} -1.16951e19 q^{47} +3.42952e19 q^{49} -1.54953e18 q^{50} -4.80738e19 q^{52} +7.56809e19 q^{53} +1.17195e20 q^{55} +1.75998e20 q^{56} -2.27720e19 q^{58} +4.19627e19 q^{59} +7.45869e19 q^{61} +1.26811e20 q^{62} +2.06047e20 q^{64} -9.19177e20 q^{65} -1.29554e21 q^{67} -8.23985e20 q^{68} +1.39542e21 q^{70} +2.37787e21 q^{71} -3.03208e21 q^{73} -1.86752e21 q^{74} +8.43334e20 q^{76} -8.09899e21 q^{77} +3.75756e20 q^{79} -1.68207e21 q^{80} +1.03804e22 q^{82} +9.99994e21 q^{83} -1.57547e22 q^{85} +1.65994e22 q^{86} -2.31157e22 q^{88} +5.36043e21 q^{89} +6.35217e22 q^{91} +2.85719e22 q^{92} +1.82895e22 q^{94} +1.61246e22 q^{95} +1.11058e22 q^{97} -5.36328e22 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1242 q^{2} - 6458716 q^{4} + 46808820 q^{5} - 211963904 q^{7} - 2571869016 q^{8}+O(q^{10}) \) 2 * q + 1242 * q^2 - 6458716 * q^4 + 46808820 * q^5 - 211963904 * q^7 - 2571869016 * q^8	\( 2 q + 1242 q^{2} - 6458716 q^{4} + 46808820 q^{5} - 211963904 q^{7} - 2571869016 q^{8} + 627869790180 q^{10} - 1468972366488 q^{11} + 10491654264748 q^{13} - 34908555004416 q^{14} - 50973150676720 q^{16} + 210888011520828 q^{17} - 907382448537944 q^{19} + 592549041758760 q^{20} + 385075304370504 q^{22} - 10\!\cdots\!12 q^{23}+ \cdots + 52\!\cdots\!18 q^{98}+O(q^{100}) \) 2 * q + 1242 * q^2 - 6458716 * q^4 + 46808820 * q^5 - 211963904 * q^7 - 2571869016 * q^8 + 627869790180 * q^10 - 1468972366488 * q^11 + 10491654264748 * q^13 - 34908555004416 * q^14 - 50973150676720 * q^16 + 210888011520828 * q^17 - 907382448537944 * q^19 + 592549041758760 * q^20 + 385075304370504 * q^22 - 10116923323892112 * q^23 + 14810505797591150 * q^25 - 5909481699569604 * q^26 - 42508434042586112 * q^28 - 18478753545176892 * q^29 - 272793622592745488 * q^31 - 186134219136906336 * q^32 - 14135605903588212 * q^34 - 2186169652458823680 * q^35 - 478995036787364 * q^37 - 1925903087124629112 * q^38 - 6555203866715785200 * q^40 - 5555714961308771412 * q^41 - 1198322147609320040 * q^43 + 6355093136294718288 * q^44 - 7378368693556745808 * q^46 - 26308565672855777280 * q^47 + 71964232849356271890 * q^49 + 37226516336176411350 * q^50 - 49312907988586886888 * q^52 + 41127501899415224628 * q^53 + 46986672525187689360 * q^55 + 377486892221258373120 * q^56 - 115477922638933597836 * q^58 + 307537061909444286696 * q^59 + 594961179098503751020 * q^61 - 411087431199774869712 * q^62 + 828036632782207954496 * q^64 - 533732415162776445960 * q^65 - 1630225825126993264088 * q^67 - 861243436942941889224 * q^68 - 2235006928450834744320 * q^70 + 383942598581649272976 * q^71 - 2812202351440561692428 * q^73 - 5219558875357315020756 * q^74 + 1238138884710050927056 * q^76 - 4569917579124061519872 * q^77 + 21069388575313284880 * q^79 - 12235121810092022582880 * q^80 + 13416177399661303790652 * q^82 + 14817262080324402696024 * q^83 - 4164778183840982876520 * q^85 + 43019621516128896935352 * q^86 - 12182478384106427357664 * q^88 + 43449805260884456557164 * q^89 + 44146945026523904417792 * q^91 + 31310234209098260658144 * q^92 - 22713687421447503614976 * q^94 - 106687644602844474428400 * q^95 + 107136573045242168450692 * q^97 + 52061241480597067368618 * q^98

Introduction

L-functions

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Database

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