LMFDB - Embedded newform 99.8.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, 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("99.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.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:	$30.9261175229$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 382x^{3} + 558x^{2} + 23640x + 53488 $ x^5 - x^4 - 382x^3 + 558x^2 + 23640*x + 53488
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$11.5540$ of defining polynomial
Character	$\chi$	$=$	99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.34840 q^{2} -58.3042 q^{4} -113.711 q^{5} +1428.97 q^{7} -1555.34 q^{8} +O(q^{10})$	\(q+8.34840 q^{2} -58.3042 q^{4} -113.711 q^{5} +1428.97 q^{7} -1555.34 q^{8} -949.305 q^{10} +1331.00 q^{11} -5955.09 q^{13} +11929.7 q^{14} -5521.69 q^{16} +2470.61 q^{17} -16410.2 q^{19} +6629.82 q^{20} +11111.7 q^{22} -88877.0 q^{23} -65194.8 q^{25} -49715.5 q^{26} -83315.1 q^{28} -191729. q^{29} -63943.3 q^{31} +152986. q^{32} +20625.6 q^{34} -162490. q^{35} -112069. q^{37} -136999. q^{38} +176859. q^{40} +65253.9 q^{41} +511782. q^{43} -77602.8 q^{44} -741981. q^{46} -1.35310e6 q^{47} +1.21842e6 q^{49} -544273. q^{50} +347207. q^{52} -795040. q^{53} -151349. q^{55} -2.22254e6 q^{56} -1.60064e6 q^{58} +1.19467e6 q^{59} -464673. q^{61} -533824. q^{62} +1.98397e6 q^{64} +677159. q^{65} +4.43770e6 q^{67} -144047. q^{68} -1.35653e6 q^{70} -4.02780e6 q^{71} +758343. q^{73} -935595. q^{74} +956785. q^{76} +1.90197e6 q^{77} -8.18232e6 q^{79} +627877. q^{80} +544766. q^{82} -7.07133e6 q^{83} -280935. q^{85} +4.27256e6 q^{86} -2.07016e6 q^{88} +7.15790e6 q^{89} -8.50968e6 q^{91} +5.18190e6 q^{92} -1.12963e7 q^{94} +1.86602e6 q^{95} +1.28345e7 q^{97} +1.01719e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8}+O(q^{10}) $ 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8} + 11516 q^{10} + 6655 q^{11} - 16666 q^{13} - 20516 q^{14} + 15010 q^{16} + 1906 q^{17} - 10446 q^{19} - 155572 q^{20} - 10648 q^{22} + 35468 q^{23} + 104239 q^{25} + 136396 q^{26} + 118456 q^{28} - 259062 q^{29} - 44932 q^{31} - 609010 q^{32} - 592888 q^{34} - 963800 q^{35} + 393978 q^{37} - 1319448 q^{38} + 1650684 q^{40} - 1554074 q^{41} + 263118 q^{43} + 220946 q^{44} - 1948268 q^{46} - 2481904 q^{47} + 498177 q^{49} - 5560984 q^{50} - 4530056 q^{52} - 2325840 q^{53} - 665500 q^{55} - 5221992 q^{56} + 2479968 q^{58} - 4613452 q^{59} + 529362 q^{61} - 3077192 q^{62} + 1437674 q^{64} + 2187496 q^{65} - 4612664 q^{67} + 2362916 q^{68} + 7327832 q^{70} - 5583864 q^{71} + 980054 q^{73} - 3387480 q^{74} + 1023396 q^{76} + 593626 q^{77} + 2804758 q^{79} - 10053364 q^{80} - 110080 q^{82} + 2451324 q^{83} - 4240456 q^{85} + 5937408 q^{86} - 3665574 q^{88} - 4025472 q^{89} - 12525436 q^{91} + 44606548 q^{92} + 1592764 q^{94} - 4273320 q^{95} - 234806 q^{97} + 26686536 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8 + 11516 * q^10 + 6655 * q^11 - 16666 * q^13 - 20516 * q^14 + 15010 * q^16 + 1906 * q^17 - 10446 * q^19 - 155572 * q^20 - 10648 * q^22 + 35468 * q^23 + 104239 * q^25 + 136396 * q^26 + 118456 * q^28 - 259062 * q^29 - 44932 * q^31 - 609010 * q^32 - 592888 * q^34 - 963800 * q^35 + 393978 * q^37 - 1319448 * q^38 + 1650684 * q^40 - 1554074 * q^41 + 263118 * q^43 + 220946 * q^44 - 1948268 * q^46 - 2481904 * q^47 + 498177 * q^49 - 5560984 * q^50 - 4530056 * q^52 - 2325840 * q^53 - 665500 * q^55 - 5221992 * q^56 + 2479968 * q^58 - 4613452 * q^59 + 529362 * q^61 - 3077192 * q^62 + 1437674 * q^64 + 2187496 * q^65 - 4612664 * q^67 + 2362916 * q^68 + 7327832 * q^70 - 5583864 * q^71 + 980054 * q^73 - 3387480 * q^74 + 1023396 * q^76 + 593626 * q^77 + 2804758 * q^79 - 10053364 * q^80 - 110080 * q^82 + 2451324 * q^83 - 4240456 * q^85 + 5937408 * q^86 - 3665574 * q^88 - 4025472 * q^89 - 12525436 * q^91 + 44606548 * q^92 + 1592764 * q^94 - 4273320 * q^95 - 234806 * q^97 + 26686536 * 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 $

$2$	8.34840	0.737902	0.368951	−	0.929449i	$-0.379717\pi$
$2$	8.34840	0.737902	0.368951	+	0.929449i	$0.379717\pi$
$3$	0	0
$3$	0	0
$4$	−58.3042	−0.455501
$5$	−113.711	−0.406825	−0.203412	−	0.979093i	$-0.565203\pi$
$5$	−113.711	−0.406825	−0.203412	+	0.979093i	$0.565203\pi$
$6$	0	0
$7$	1428.97	1.57464	0.787320	−	0.616544i	$-0.211468\pi$
$7$	1428.97	1.57464	0.787320	+	0.616544i	$0.211468\pi$
$8$	−1555.34	−1.07402
$9$	0	0
$10$	−949.305	−0.300197
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	−5955.09	−0.751773	−0.375887	−	0.926666i	$-0.622662\pi$
$13$	−5955.09	−0.751773	−0.375887	+	0.926666i	$0.622662\pi$
$14$	11929.7	1.16193
$15$	0	0
$16$	−5521.69	−0.337017
$17$	2470.61	0.121964	0.0609821	−	0.998139i	$-0.480577\pi$
$17$	2470.61	0.121964	0.0609821	+	0.998139i	$0.480577\pi$
$18$	0	0
$19$	−16410.2	−0.548880	−0.274440	−	0.961604i	$-0.588492\pi$
$19$	−16410.2	−0.548880	−0.274440	+	0.961604i	$0.588492\pi$
$20$	6629.82	0.185309
$21$	0	0
$22$	11111.7	0.222486
$23$	−88877.0	−1.52315	−0.761574	−	0.648078i	$-0.775573\pi$
$23$	−88877.0	−1.52315	−0.761574	+	0.648078i	$0.775573\pi$
$24$	0	0
$25$	−65194.8	−0.834494
$26$	−49715.5	−0.554735
$27$	0	0
$28$	−83315.1	−0.717251
$29$	−191729.	−1.45981	−0.729904	−	0.683549i	$-0.760435\pi$
$29$	−191729.	−1.45981	−0.729904	+	0.683549i	$0.760435\pi$
$30$	0	0
$31$	−63943.3	−0.385504	−0.192752	−	0.981248i	$-0.561741\pi$
$31$	−63943.3	−0.385504	−0.192752	+	0.981248i	$0.561741\pi$
$32$	152986.	0.825331
$33$	0	0
$34$	20625.6	0.0899976
$35$	−162490.	−0.640602
$36$	0	0
$37$	−112069.	−0.363729	−0.181865	−	0.983324i	$-0.558213\pi$
$37$	−112069.	−0.363729	−0.181865	+	0.983324i	$0.558213\pi$
$38$	−136999.	−0.405019
$39$	0	0
$40$	176859.	0.436936
$41$	65253.9	0.147864	0.0739321	−	0.997263i	$-0.476445\pi$
$41$	65253.9	0.147864	0.0739321	+	0.997263i	$0.476445\pi$
$42$	0	0
$43$	511782.	0.981624	0.490812	−	0.871266i	$-0.336700\pi$
$43$	511782.	0.981624	0.490812	+	0.871266i	$0.336700\pi$
$44$	−77602.8	−0.137339
$45$	0	0
$46$	−741981.	−1.12393
$47$	−1.35310e6	−1.90103	−0.950514	−	0.310682i	$-0.899443\pi$
$47$	−1.35310e6	−1.90103	−0.950514	+	0.310682i	$0.899443\pi$
$48$	0	0
$49$	1.21842e6	1.47949
$50$	−544273.	−0.615774
$51$	0	0
$52$	347207.	0.342434
$53$	−795040.	−0.733539	−0.366770	−	0.930312i	$-0.619536\pi$
$53$	−795040.	−0.733539	−0.366770	+	0.930312i	$0.619536\pi$
$54$	0	0
$55$	−151349.	−0.122662
$56$	−2.22254e6	−1.69119
$57$	0	0
$58$	−1.60064e6	−1.07720
$59$	1.19467e6	0.757294	0.378647	−	0.925541i	$-0.376389\pi$
$59$	1.19467e6	0.757294	0.378647	+	0.925541i	$0.376389\pi$
$60$	0	0
$61$	−464673.	−0.262115	−0.131058	−	0.991375i	$-0.541837\pi$
$61$	−464673.	−0.262115	−0.131058	+	0.991375i	$0.541837\pi$
$62$	−533824.	−0.284464
$63$	0	0
$64$	1.98397e6	0.946030
$65$	677159.	0.305840
$66$	0	0
$67$	4.43770e6	1.80259	0.901294	−	0.433208i	$-0.142618\pi$
$67$	4.43770e6	1.80259	0.901294	+	0.433208i	$0.142618\pi$
$68$	−144047.	−0.0555549
$69$	0	0
$70$	−1.35653e6	−0.472702
$71$	−4.02780e6	−1.33556	−0.667781	−	0.744358i	$-0.732756\pi$
$71$	−4.02780e6	−1.33556	−0.667781	+	0.744358i	$0.732756\pi$
$72$	0	0
$73$	758343.	0.228158	0.114079	−	0.993472i	$-0.463608\pi$
$73$	758343.	0.228158	0.114079	+	0.993472i	$0.463608\pi$
$74$	−935595.	−0.268396
$75$	0	0
$76$	956785.	0.250015
$77$	1.90197e6	0.474772
$78$	0	0
$79$	−8.18232e6	−1.86716	−0.933580	−	0.358369i	$-0.883333\pi$
$79$	−8.18232e6	−1.86716	−0.933580	+	0.358369i	$0.883333\pi$
$80$	627877.	0.137107
$81$	0	0
$82$	544766.	0.109109
$83$	−7.07133e6	−1.35746	−0.678732	−	0.734386i	$-0.737470\pi$
$83$	−7.07133e6	−1.35746	−0.678732	+	0.734386i	$0.737470\pi$
$84$	0	0
$85$	−280935.	−0.0496181
$86$	4.27256e6	0.724342
$87$	0	0
$88$	−2.07016e6	−0.323828
$89$	7.15790e6	1.07627	0.538134	−	0.842859i	$-0.319129\pi$
$89$	7.15790e6	1.07627	0.538134	+	0.842859i	$0.319129\pi$
$90$	0	0
$91$	−8.50968e6	−1.18377
$92$	5.18190e6	0.693796
$93$	0	0
$94$	−1.12963e7	−1.40277
$95$	1.86602e6	0.223298
$96$	0	0
$97$	1.28345e7	1.42784	0.713918	−	0.700230i	$-0.246919\pi$
$97$	1.28345e7	1.42784	0.713918	+	0.700230i	$0.246919\pi$
$98$	1.01719e7	1.09172
$99$	0	0
$100$	3.80113e6	0.380113
$101$	6.28970e6	0.607442	0.303721	−	0.952761i	$-0.401771\pi$
$101$	6.28970e6	0.607442	0.303721	+	0.952761i	$0.401771\pi$
$102$	0	0
$103$	6.50269e6	0.586358	0.293179	−	0.956058i	$-0.405287\pi$
$103$	6.50269e6	0.586358	0.293179	+	0.956058i	$0.405287\pi$
$104$	9.26221e6	0.807417
$105$	0	0
$106$	−6.63731e6	−0.541280
$107$	−1.28937e6	−0.101750	−0.0508748	−	0.998705i	$-0.516201\pi$
$107$	−1.28937e6	−0.101750	−0.0508748	+	0.998705i	$0.516201\pi$
$108$	0	0
$109$	2.18306e6	0.161463	0.0807316	−	0.996736i	$-0.474274\pi$
$109$	2.18306e6	0.161463	0.0807316	+	0.996736i	$0.474274\pi$
$110$	−1.26352e6	−0.0905127
$111$	0	0
$112$	−7.89036e6	−0.530681
$113$	−2.45051e6	−0.159765	−0.0798827	−	0.996804i	$-0.525455\pi$
$113$	−2.45051e6	−0.159765	−0.0798827	+	0.996804i	$0.525455\pi$
$114$	0	0
$115$	1.01063e7	0.619654
$116$	1.11786e7	0.664945
$117$	0	0
$118$	9.97355e6	0.558808
$119$	3.53044e6	0.192050
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	−3.87927e6	−0.193415
$123$	0	0
$124$	3.72816e6	0.175598
$125$	1.62970e7	0.746317
$126$	0	0
$127$	1.49227e7	0.646451	0.323225	−	0.946322i	$-0.395233\pi$
$127$	1.49227e7	0.646451	0.323225	+	0.946322i	$0.395233\pi$
$128$	−3.01929e6	−0.127254
$129$	0	0
$130$	5.65320e6	0.225680
$131$	−3.49929e7	−1.35997	−0.679986	−	0.733225i	$-0.738014\pi$
$131$	−3.49929e7	−1.35997	−0.679986	+	0.733225i	$0.738014\pi$
$132$	0	0
$133$	−2.34498e7	−0.864288
$134$	3.70477e7	1.33013
$135$	0	0
$136$	−3.84264e6	−0.130992
$137$	2.36549e7	0.785956	0.392978	−	0.919548i	$-0.371445\pi$
$137$	2.36549e7	0.785956	0.392978	+	0.919548i	$0.371445\pi$
$138$	0	0
$139$	3.45419e7	1.09093	0.545463	−	0.838135i	$-0.316354\pi$
$139$	3.45419e7	1.09093	0.545463	+	0.838135i	$0.316354\pi$
$140$	9.47384e6	0.291795
$141$	0	0
$142$	−3.36257e7	−0.985514
$143$	−7.92623e6	−0.226668
$144$	0	0
$145$	2.18017e7	0.593886
$146$	6.33095e6	0.168358
$147$	0	0
$148$	6.53407e6	0.165679
$149$	2.43282e7	0.602501	0.301250	−	0.953545i	$-0.402596\pi$
$149$	2.43282e7	0.602501	0.301250	+	0.953545i	$0.402596\pi$
$150$	0	0
$151$	−1.08177e7	−0.255691	−0.127845	−	0.991794i	$-0.540806\pi$
$151$	−1.08177e7	−0.255691	−0.127845	+	0.991794i	$0.540806\pi$
$152$	2.55235e7	0.589506
$153$	0	0
$154$	1.58784e7	0.350335
$155$	7.27105e6	0.156832
$156$	0	0
$157$	5.18103e7	1.06848	0.534241	−	0.845332i	$-0.320597\pi$
$157$	5.18103e7	1.06848	0.534241	+	0.845332i	$0.320597\pi$
$158$	−6.83093e7	−1.37778
$159$	0	0
$160$	−1.73962e7	−0.335765
$161$	−1.27003e8	−2.39841
$162$	0	0
$163$	−3.68086e7	−0.665722	−0.332861	−	0.942976i	$-0.608014\pi$
$163$	−3.68086e7	−0.665722	−0.332861	+	0.942976i	$0.608014\pi$
$164$	−3.80457e6	−0.0673523
$165$	0	0
$166$	−5.90344e7	−1.00167
$167$	−6.63371e7	−1.10217	−0.551085	−	0.834449i	$-0.685786\pi$
$167$	−6.63371e7	−1.10217	−0.551085	+	0.834449i	$0.685786\pi$
$168$	0	0
$169$	−2.72854e7	−0.434837
$170$	−2.34536e6	−0.0366133
$171$	0	0
$172$	−2.98390e7	−0.447131
$173$	−9.01002e7	−1.32301	−0.661507	−	0.749939i	$-0.730083\pi$
$173$	−9.01002e7	−1.32301	−0.661507	+	0.749939i	$0.730083\pi$
$174$	0	0
$175$	−9.31617e7	−1.31403
$176$	−7.34937e6	−0.101615
$177$	0	0
$178$	5.97570e7	0.794180
$179$	−1.61245e7	−0.210136	−0.105068	−	0.994465i	$-0.533506\pi$
$179$	−1.61245e7	−0.210136	−0.105068	+	0.994465i	$0.533506\pi$
$180$	0	0
$181$	−6.85391e7	−0.859139	−0.429570	−	0.903034i	$-0.641335\pi$
$181$	−6.85391e7	−0.859139	−0.429570	+	0.903034i	$0.641335\pi$
$182$	−7.10422e7	−0.873507
$183$	0	0
$184$	1.38234e8	1.63589
$185$	1.27434e7	0.147974
$186$	0	0
$187$	3.28838e6	0.0367736
$188$	7.88915e7	0.865920
$189$	0	0
$190$	1.55783e7	0.164772
$191$	4.43836e7	0.460899	0.230450	−	0.973084i	$-0.425980\pi$
$191$	4.43836e7	0.460899	0.230450	+	0.973084i	$0.425980\pi$
$192$	0	0
$193$	6.03569e7	0.604333	0.302167	−	0.953255i	$-0.402290\pi$
$193$	6.03569e7	0.604333	0.302167	+	0.953255i	$0.402290\pi$
$194$	1.07148e8	1.05360
$195$	0	0
$196$	−7.10392e7	−0.673910
$197$	−1.43901e8	−1.34101	−0.670504	−	0.741906i	$-0.733922\pi$
$197$	−1.43901e8	−1.34101	−0.670504	+	0.741906i	$0.733922\pi$
$198$	0	0
$199$	−1.26448e8	−1.13743	−0.568717	−	0.822533i	$-0.692560\pi$
$199$	−1.26448e8	−1.13743	−0.568717	+	0.822533i	$0.692560\pi$
$200$	1.01400e8	0.896260
$201$	0	0
$202$	5.25089e7	0.448232
$203$	−2.73977e8	−2.29867
$204$	0	0
$205$	−7.42008e6	−0.0601548
$206$	5.42871e7	0.432674
$207$	0	0
$208$	3.28822e7	0.253361
$209$	−2.18420e7	−0.165493
$210$	0	0
$211$	9.15276e7	0.670754	0.335377	−	0.942084i	$-0.391136\pi$
$211$	9.15276e7	0.670754	0.335377	+	0.942084i	$0.391136\pi$
$212$	4.63541e7	0.334128
$213$	0	0
$214$	−1.07641e7	−0.0750812
$215$	−5.81952e7	−0.399349
$216$	0	0
$217$	−9.13733e7	−0.607030
$218$	1.82251e7	0.119144
$219$	0	0
$220$	8.82429e6	0.0558728
$221$	−1.47127e7	−0.0916895
$222$	0	0
$223$	−1.00011e8	−0.603924	−0.301962	−	0.953320i	$-0.597642\pi$
$223$	−1.00011e8	−0.603924	−0.301962	+	0.953320i	$0.597642\pi$
$224$	2.18614e8	1.29960
$225$	0	0
$226$	−2.04579e7	−0.117891
$227$	−2.04849e8	−1.16237	−0.581183	−	0.813773i	$-0.697410\pi$
$227$	−2.04849e8	−1.16237	−0.581183	+	0.813773i	$0.697410\pi$
$228$	0	0
$229$	2.34263e8	1.28908	0.644538	−	0.764572i	$-0.277050\pi$
$229$	2.34263e8	1.28908	0.644538	+	0.764572i	$0.277050\pi$
$230$	8.43714e7	0.457244
$231$	0	0
$232$	2.98205e8	1.56786
$233$	1.07149e8	0.554936	0.277468	−	0.960735i	$-0.410505\pi$
$233$	1.07149e8	0.554936	0.277468	+	0.960735i	$0.410505\pi$
$234$	0	0
$235$	1.53863e8	0.773385
$236$	−6.96540e7	−0.344948
$237$	0	0
$238$	2.94735e7	0.141714
$239$	3.55647e8	1.68510	0.842550	−	0.538617i	$-0.181053\pi$
$239$	3.55647e8	1.68510	0.842550	+	0.538617i	$0.181053\pi$
$240$	0	0
$241$	−9.22417e7	−0.424490	−0.212245	−	0.977216i	$-0.568078\pi$
$241$	−9.22417e7	−0.424490	−0.212245	+	0.977216i	$0.568078\pi$
$242$	1.47897e7	0.0670820
$243$	0	0
$244$	2.70923e7	0.119394
$245$	−1.38548e8	−0.601894
$246$	0	0
$247$	9.77245e7	0.412633
$248$	9.94536e7	0.414038
$249$	0	0
$250$	1.36054e8	0.550709
$251$	4.32276e8	1.72545	0.862727	−	0.505670i	$-0.168755\pi$
$251$	4.32276e8	1.72545	0.862727	+	0.505670i	$0.168755\pi$
$252$	0	0
$253$	−1.18295e8	−0.459246
$254$	1.24581e8	0.477017
$255$	0	0
$256$	−2.79154e8	−1.03993
$257$	1.71468e8	0.630111	0.315055	−	0.949073i	$-0.397977\pi$
$257$	1.71468e8	0.630111	0.315055	+	0.949073i	$0.397977\pi$
$258$	0	0
$259$	−1.60143e8	−0.572743
$260$	−3.94812e7	−0.139310
$261$	0	0
$262$	−2.92135e8	−1.00353
$263$	3.32214e8	1.12609	0.563044	−	0.826427i	$-0.309630\pi$
$263$	3.32214e8	1.12609	0.563044	+	0.826427i	$0.309630\pi$
$264$	0	0
$265$	9.04047e7	0.298422
$266$	−1.95768e8	−0.637760
$267$	0	0
$268$	−2.58737e8	−0.821081
$269$	−3.28368e8	−1.02856	−0.514278	−	0.857623i	$-0.671940\pi$
$269$	−3.28368e8	−1.02856	−0.514278	+	0.857623i	$0.671940\pi$
$270$	0	0
$271$	4.13362e8	1.26165	0.630824	−	0.775926i	$-0.282717\pi$
$271$	4.13362e8	1.26165	0.630824	+	0.775926i	$0.282717\pi$
$272$	−1.36419e7	−0.0411041
$273$	0	0
$274$	1.97480e8	0.579958
$275$	−8.67743e7	−0.251609
$276$	0	0
$277$	−5.62537e8	−1.59027	−0.795137	−	0.606430i	$-0.792601\pi$
$277$	−5.62537e8	−1.59027	−0.795137	+	0.606430i	$0.792601\pi$
$278$	2.88370e8	0.804995
$279$	0	0
$280$	2.52728e8	0.688018
$281$	3.44952e7	0.0927443	0.0463721	−	0.998924i	$-0.485234\pi$
$281$	3.44952e7	0.0927443	0.0463721	+	0.998924i	$0.485234\pi$
$282$	0	0
$283$	−4.92967e8	−1.29290	−0.646451	−	0.762956i	$-0.723747\pi$
$283$	−4.92967e8	−1.29290	−0.646451	+	0.762956i	$0.723747\pi$
$284$	2.34838e8	0.608350
$285$	0	0
$286$	−6.61714e7	−0.167259
$287$	9.32461e7	0.232833
$288$	0	0
$289$	−4.04235e8	−0.985125
$290$	1.82010e8	0.438230
$291$	0	0
$292$	−4.42145e7	−0.103926
$293$	−6.80257e8	−1.57992	−0.789962	−	0.613155i	$-0.789900\pi$
$293$	−6.80257e8	−1.57992	−0.789962	+	0.613155i	$0.789900\pi$
$294$	0	0
$295$	−1.35847e8	−0.308086
$296$	1.74305e8	0.390651
$297$	0	0
$298$	2.03101e8	0.444586
$299$	5.29271e8	1.14506
$300$	0	0
$301$	7.31323e8	1.54570
$302$	−9.03104e7	−0.188675
$303$	0	0
$304$	9.06123e7	0.184982
$305$	5.28384e7	0.106635
$306$	0	0
$307$	8.57248e7	0.169092	0.0845458	−	0.996420i	$-0.473056\pi$
$307$	8.57248e7	0.169092	0.0845458	+	0.996420i	$0.473056\pi$
$308$	−1.10892e8	−0.216259
$309$	0	0
$310$	6.07016e7	0.115727
$311$	−6.37786e7	−0.120230	−0.0601151	−	0.998191i	$-0.519147\pi$
$311$	−6.37786e7	−0.120230	−0.0601151	+	0.998191i	$0.519147\pi$
$312$	0	0
$313$	1.82766e8	0.336891	0.168446	−	0.985711i	$-0.446125\pi$
$313$	1.82766e8	0.336891	0.168446	+	0.985711i	$0.446125\pi$
$314$	4.32533e8	0.788435
$315$	0	0
$316$	4.77063e8	0.850494
$317$	2.77863e8	0.489918	0.244959	−	0.969533i	$-0.421225\pi$
$317$	2.77863e8	0.489918	0.244959	+	0.969533i	$0.421225\pi$
$318$	0	0
$319$	−2.55192e8	−0.440149
$320$	−2.25599e8	−0.384869
$321$	0	0
$322$	−1.06027e9	−1.76979
$323$	−4.05433e7	−0.0669437
$324$	0	0
$325$	3.88241e8	0.627350
$326$	−3.07293e8	−0.491237
$327$	0	0
$328$	−1.01492e8	−0.158809
$329$	−1.93355e9	−2.99343
$330$	0	0
$331$	−1.98774e8	−0.301274	−0.150637	−	0.988589i	$-0.548132\pi$
$331$	−1.98774e8	−0.301274	−0.150637	+	0.988589i	$0.548132\pi$
$332$	4.12288e8	0.618326
$333$	0	0
$334$	−5.53809e8	−0.813293
$335$	−5.04615e8	−0.733337
$336$	0	0
$337$	9.21576e8	1.31168	0.655838	−	0.754902i	$-0.272316\pi$
$337$	9.21576e8	1.31168	0.655838	+	0.754902i	$0.272316\pi$
$338$	−2.27789e8	−0.320867
$339$	0	0
$340$	1.63797e7	0.0226011
$341$	−8.51085e7	−0.116234
$342$	0	0
$343$	5.64276e8	0.755027
$344$	−7.95996e8	−1.05428
$345$	0	0
$346$	−7.52193e8	−0.976255
$347$	−1.40696e9	−1.80771	−0.903855	−	0.427839i	$-0.859275\pi$
$347$	−1.40696e9	−1.80771	−0.903855	+	0.427839i	$0.859275\pi$
$348$	0	0
$349$	4.71866e8	0.594195	0.297098	−	0.954847i	$-0.403981\pi$
$349$	4.71866e8	0.594195	0.297098	+	0.954847i	$0.403981\pi$
$350$	−7.77752e8	−0.969623
$351$	0	0
$352$	2.03625e8	0.248847
$353$	1.34122e9	1.62289	0.811447	−	0.584426i	$-0.198680\pi$
$353$	1.34122e9	1.62289	0.811447	+	0.584426i	$0.198680\pi$
$354$	0	0
$355$	4.58005e8	0.543340
$356$	−4.17335e8	−0.490241
$357$	0	0
$358$	−1.34614e8	−0.155060
$359$	2.88844e8	0.329482	0.164741	−	0.986337i	$-0.447321\pi$
$359$	2.88844e8	0.329482	0.164741	+	0.986337i	$0.447321\pi$
$360$	0	0
$361$	−6.24576e8	−0.698731
$362$	−5.72192e8	−0.633960
$363$	0	0
$364$	4.96149e8	0.539210
$365$	−8.62319e7	−0.0928203
$366$	0	0
$367$	1.54823e9	1.63494	0.817472	−	0.575968i	$-0.195375\pi$
$367$	1.54823e9	1.63494	0.817472	+	0.575968i	$0.195375\pi$
$368$	4.90752e8	0.513327
$369$	0	0
$370$	1.06387e8	0.109190
$371$	−1.13609e9	−1.15506
$372$	0	0
$373$	−1.74462e9	−1.74069	−0.870343	−	0.492446i	$-0.836103\pi$
$373$	−1.74462e9	−1.74069	−0.870343	+	0.492446i	$0.836103\pi$
$374$	2.74527e7	0.0271353
$375$	0	0
$376$	2.10454e9	2.04174
$377$	1.14177e9	1.09744
$378$	0	0
$379$	3.06631e8	0.289320	0.144660	−	0.989481i	$-0.453791\pi$
$379$	3.06631e8	0.289320	0.144660	+	0.989481i	$0.453791\pi$
$380$	−1.08797e8	−0.101712
$381$	0	0
$382$	3.70532e8	0.340098
$383$	1.87405e9	1.70445	0.852227	−	0.523172i	$-0.175251\pi$
$383$	1.87405e9	1.70445	0.852227	+	0.523172i	$0.175251\pi$
$384$	0	0
$385$	−2.16274e8	−0.193149
$386$	5.03884e8	0.445939
$387$	0	0
$388$	−7.48305e8	−0.650381
$389$	8.34994e7	0.0719217	0.0359609	−	0.999353i	$-0.488551\pi$
$389$	8.34994e7	0.0719217	0.0359609	+	0.999353i	$0.488551\pi$
$390$	0	0
$391$	−2.19580e8	−0.185770
$392$	−1.89507e9	−1.58900
$393$	0	0
$394$	−1.20134e9	−0.989532
$395$	9.30419e8	0.759607
$396$	0	0
$397$	−1.93236e9	−1.54996	−0.774980	−	0.631986i	$-0.782240\pi$
$397$	−1.93236e9	−1.54996	−0.774980	+	0.631986i	$0.782240\pi$
$398$	−1.05564e9	−0.839314
$399$	0	0
$400$	3.59986e8	0.281239
$401$	4.85986e8	0.376373	0.188187	−	0.982133i	$-0.439739\pi$
$401$	4.85986e8	0.376373	0.188187	+	0.982133i	$0.439739\pi$
$402$	0	0
$403$	3.80788e8	0.289811
$404$	−3.66715e8	−0.276691
$405$	0	0
$406$	−2.28727e9	−1.69619
$407$	−1.49163e8	−0.109669
$408$	0	0
$409$	1.79333e9	1.29607	0.648036	−	0.761610i	$-0.275591\pi$
$409$	1.79333e9	1.29607	0.648036	+	0.761610i	$0.275591\pi$
$410$	−6.19458e7	−0.0443883
$411$	0	0
$412$	−3.79134e8	−0.267087
$413$	1.70715e9	1.19247
$414$	0	0
$415$	8.04088e8	0.552249
$416$	−9.11049e8	−0.620462
$417$	0	0
$418$	−1.82346e8	−0.122118
$419$	−1.65555e9	−1.09949	−0.549747	−	0.835331i	$-0.685276\pi$
$419$	−1.65555e9	−1.09949	−0.549747	+	0.835331i	$0.685276\pi$
$420$	0	0
$421$	−8.47769e8	−0.553720	−0.276860	−	0.960910i	$-0.589294\pi$
$421$	−8.47769e8	−0.553720	−0.276860	+	0.960910i	$0.589294\pi$
$422$	7.64109e8	0.494951
$423$	0	0
$424$	1.23656e9	0.787834
$425$	−1.61071e8	−0.101778
$426$	0	0
$427$	−6.64005e8	−0.412737
$428$	7.51754e7	0.0463471
$429$	0	0
$430$	−4.85837e8	−0.294680
$431$	3.04758e9	1.83352	0.916758	−	0.399444i	$-0.130797\pi$
$431$	3.04758e9	1.83352	0.916758	+	0.399444i	$0.130797\pi$
$432$	0	0
$433$	−1.20109e7	−0.00710997	−0.00355499	−	0.999994i	$-0.501132\pi$
$433$	−1.20109e7	−0.00710997	−0.00355499	+	0.999994i	$0.501132\pi$
$434$	−7.62821e8	−0.447928
$435$	0	0
$436$	−1.27282e8	−0.0735466
$437$	1.45849e9	0.836025
$438$	0	0
$439$	−1.73781e9	−0.980340	−0.490170	−	0.871627i	$-0.663065\pi$
$439$	−1.73781e9	−0.980340	−0.490170	+	0.871627i	$0.663065\pi$
$440$	2.35400e8	0.131741
$441$	0	0
$442$	−1.22828e8	−0.0676578
$443$	−8.52762e8	−0.466031	−0.233015	−	0.972473i	$-0.574859\pi$
$443$	−8.52762e8	−0.466031	−0.233015	+	0.972473i	$0.574859\pi$
$444$	0	0
$445$	−8.13931e8	−0.437852
$446$	−8.34935e8	−0.445636
$447$	0	0
$448$	2.83504e9	1.48966
$449$	7.98275e8	0.416189	0.208094	−	0.978109i	$-0.433274\pi$
$449$	7.98275e8	0.416189	0.208094	+	0.978109i	$0.433274\pi$
$450$	0	0
$451$	8.68529e7	0.0445827
$452$	1.42875e8	0.0727733
$453$	0	0
$454$	−1.71016e9	−0.857712
$455$	9.67643e8	0.481588
$456$	0	0
$457$	−2.14046e8	−0.104906	−0.0524531	−	0.998623i	$-0.516704\pi$
$457$	−2.14046e8	−0.104906	−0.0524531	+	0.998623i	$0.516704\pi$
$458$	1.95572e9	0.951211
$459$	0	0
$460$	−5.89239e8	−0.282253
$461$	2.91313e9	1.38486	0.692431	−	0.721484i	$-0.256540\pi$
$461$	2.91313e9	1.38486	0.692431	+	0.721484i	$0.256540\pi$
$462$	0	0
$463$	−2.53358e9	−1.18632	−0.593158	−	0.805086i	$-0.702119\pi$
$463$	−2.53358e9	−1.18632	−0.593158	+	0.805086i	$0.702119\pi$
$464$	1.05867e9	0.491981
$465$	0	0
$466$	8.94524e8	0.409488
$467$	1.90713e9	0.866507	0.433254	−	0.901272i	$-0.357365\pi$
$467$	1.90713e9	0.866507	0.433254	+	0.901272i	$0.357365\pi$
$468$	0	0
$469$	6.34136e9	2.83843
$470$	1.28451e9	0.570682
$471$	0	0
$472$	−1.85811e9	−0.813346
$473$	6.81181e8	0.295971
$474$	0	0
$475$	1.06986e9	0.458037
$476$	−2.05839e8	−0.0874789
$477$	0	0
$478$	2.96908e9	1.24344
$479$	1.08003e9	0.449016	0.224508	−	0.974472i	$-0.427922\pi$
$479$	1.08003e9	0.449016	0.224508	+	0.974472i	$0.427922\pi$
$480$	0	0
$481$	6.67380e8	0.273442
$482$	−7.70071e8	−0.313232
$483$	0	0
$484$	−1.03289e8	−0.0414092
$485$	−1.45942e9	−0.580879
$486$	0	0
$487$	−4.22859e9	−1.65899	−0.829496	−	0.558513i	$-0.811372\pi$
$487$	−4.22859e9	−1.65899	−0.829496	+	0.558513i	$0.811372\pi$
$488$	7.22725e8	0.281516
$489$	0	0
$490$	−1.15666e9	−0.444138
$491$	1.89651e9	0.723054	0.361527	−	0.932362i	$-0.382256\pi$
$491$	1.89651e9	0.723054	0.361527	+	0.932362i	$0.382256\pi$
$492$	0	0
$493$	−4.73688e8	−0.178045
$494$	8.15843e8	0.304483
$495$	0	0
$496$	3.53075e8	0.129922
$497$	−5.75563e9	−2.10303
$498$	0	0
$499$	4.04770e9	1.45833	0.729166	−	0.684337i	$-0.239908\pi$
$499$	4.04770e9	1.45833	0.729166	+	0.684337i	$0.239908\pi$
$500$	−9.50185e8	−0.339948
$501$	0	0
$502$	3.60882e9	1.27322
$503$	3.61417e9	1.26625	0.633126	−	0.774048i	$-0.281771\pi$
$503$	3.61417e9	1.26625	0.633126	+	0.774048i	$0.281771\pi$
$504$	0	0
$505$	−7.15207e8	−0.247122
$506$	−9.87577e8	−0.338879
$507$	0	0
$508$	−8.70057e8	−0.294459
$509$	−2.70662e9	−0.909734	−0.454867	−	0.890559i	$-0.650313\pi$
$509$	−2.70662e9	−0.909734	−0.454867	+	0.890559i	$0.650313\pi$
$510$	0	0
$511$	1.08365e9	0.359267
$512$	−1.94402e9	−0.640113
$513$	0	0
$514$	1.43148e9	0.464960
$515$	−7.39427e8	−0.238545
$516$	0	0
$517$	−1.80098e9	−0.573181
$518$	−1.33694e9	−0.422628
$519$	0	0
$520$	−1.05321e9	−0.328477
$521$	2.38145e8	0.0737752	0.0368876	−	0.999319i	$-0.488256\pi$
$521$	2.38145e8	0.0737752	0.0368876	+	0.999319i	$0.488256\pi$
$522$	0	0
$523$	−2.20640e9	−0.674416	−0.337208	−	0.941430i	$-0.609483\pi$
$523$	−2.20640e9	−0.674416	−0.337208	+	0.941430i	$0.609483\pi$
$524$	2.04023e9	0.619469
$525$	0	0
$526$	2.77345e9	0.830942
$527$	−1.57979e8	−0.0470177
$528$	0	0
$529$	4.49430e9	1.31998
$530$	7.54735e8	0.220206
$531$	0	0
$532$	1.36722e9	0.393684
$533$	−3.88593e8	−0.111160
$534$	0	0
$535$	1.46615e8	0.0413942
$536$	−6.90215e9	−1.93601
$537$	0	0
$538$	−2.74135e9	−0.758973
$539$	1.62172e9	0.446084
$540$	0	0
$541$	−3.78571e9	−1.02791	−0.513957	−	0.857816i	$-0.671821\pi$
$541$	−3.78571e9	−1.02791	−0.513957	+	0.857816i	$0.671821\pi$
$542$	3.45091e9	0.930972
$543$	0	0
$544$	3.77970e8	0.100661
$545$	−2.48238e8	−0.0656872
$546$	0	0
$547$	4.64093e9	1.21241	0.606204	−	0.795309i	$-0.292691\pi$
$547$	4.64093e9	1.21241	0.606204	+	0.795309i	$0.292691\pi$
$548$	−1.37918e9	−0.358004
$549$	0	0
$550$	−7.24427e8	−0.185663
$551$	3.14633e9	0.801259
$552$	0	0
$553$	−1.16923e10	−2.94010
$554$	−4.69629e9	−1.17347
$555$	0	0
$556$	−2.01394e9	−0.496918
$557$	1.15036e9	0.282059	0.141029	−	0.990005i	$-0.454959\pi$
$557$	1.15036e9	0.282059	0.141029	+	0.990005i	$0.454959\pi$
$558$	0	0
$559$	−3.04771e9	−0.737959
$560$	8.97220e8	0.215894
$561$	0	0
$562$	2.87980e8	0.0684361
$563$	−4.10000e9	−0.968288	−0.484144	−	0.874988i	$-0.660869\pi$
$563$	−4.10000e9	−0.968288	−0.484144	+	0.874988i	$0.660869\pi$
$564$	0	0
$565$	2.78650e8	0.0649965
$566$	−4.11549e9	−0.954034
$567$	0	0
$568$	6.26461e9	1.43442
$569$	−3.24571e9	−0.738613	−0.369307	−	0.929308i	$-0.620405\pi$
$569$	−3.24571e9	−0.738613	−0.369307	+	0.929308i	$0.620405\pi$
$570$	0	0
$571$	−6.25977e9	−1.40712	−0.703561	−	0.710635i	$-0.748408\pi$
$571$	−6.25977e9	−1.40712	−0.703561	+	0.710635i	$0.748408\pi$
$572$	4.62132e8	0.103248
$573$	0	0
$574$	7.78456e8	0.171808
$575$	5.79432e9	1.27106
$576$	0	0
$577$	5.21950e9	1.13113	0.565567	−	0.824702i	$-0.308657\pi$
$577$	5.21950e9	1.13113	0.565567	+	0.824702i	$0.308657\pi$
$578$	−3.37472e9	−0.726925
$579$	0	0
$580$	−1.27113e9	−0.270516
$581$	−1.01048e10	−2.13752
$582$	0	0
$583$	−1.05820e9	−0.221170
$584$	−1.17948e9	−0.245045
$585$	0	0
$586$	−5.67906e9	−1.16583
$587$	−6.89364e9	−1.40675	−0.703373	−	0.710821i	$-0.748324\pi$
$587$	−6.89364e9	−1.40675	−0.703373	+	0.710821i	$0.748324\pi$
$588$	0	0
$589$	1.04932e9	0.211595
$590$	−1.13410e9	−0.227337
$591$	0	0
$592$	6.18809e8	0.122583
$593$	−6.33127e9	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$593$	−6.33127e9	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$594$	0	0
$595$	−4.01449e8	−0.0781306
$596$	−1.41843e9	−0.274440
$597$	0	0
$598$	4.41857e9	0.844943
$599$	4.99599e9	0.949791	0.474895	−	0.880042i	$-0.342486\pi$
$599$	4.99599e9	0.949791	0.474895	+	0.880042i	$0.342486\pi$
$600$	0	0
$601$	−1.60151e9	−0.300933	−0.150466	−	0.988615i	$-0.548078\pi$
$601$	−1.60151e9	−0.300933	−0.150466	+	0.988615i	$0.548078\pi$
$602$	6.10538e9	1.14058
$603$	0	0
$604$	6.30716e8	0.116467
$605$	−2.01446e8	−0.0369841
$606$	0	0
$607$	8.95652e9	1.62547	0.812735	−	0.582633i	$-0.197978\pi$
$607$	8.95652e9	1.62547	0.812735	+	0.582633i	$0.197978\pi$
$608$	−2.51054e9	−0.453007
$609$	0	0
$610$	4.41116e8	0.0786861
$611$	8.05786e9	1.42914
$612$	0	0
$613$	4.08877e9	0.716937	0.358469	−	0.933542i	$-0.383299\pi$
$613$	4.08877e9	0.716937	0.358469	+	0.933542i	$0.383299\pi$
$614$	7.15665e8	0.124773
$615$	0	0
$616$	−2.95821e9	−0.509913
$617$	−7.03716e9	−1.20614	−0.603072	−	0.797686i	$-0.706057\pi$
$617$	−7.03716e9	−1.20614	−0.603072	+	0.797686i	$0.706057\pi$
$618$	0	0
$619$	−8.32185e9	−1.41027	−0.705136	−	0.709072i	$-0.749114\pi$
$619$	−8.32185e9	−1.41027	−0.705136	+	0.709072i	$0.749114\pi$
$620$	−4.23932e8	−0.0714374
$621$	0	0
$622$	−5.32450e8	−0.0887181
$623$	1.02285e10	1.69474
$624$	0	0
$625$	3.24019e9	0.530873
$626$	1.52580e9	0.248593
$627$	0	0
$628$	−3.02076e9	−0.486695
$629$	−2.76878e8	−0.0443620
$630$	0	0
$631$	−2.08999e8	−0.0331163	−0.0165581	−	0.999863i	$-0.505271\pi$
$631$	−2.08999e8	−0.0331163	−0.0165581	+	0.999863i	$0.505271\pi$
$632$	1.27263e10	2.00536
$633$	0	0
$634$	2.31971e9	0.361512
$635$	−1.69688e9	−0.262992
$636$	0	0
$637$	−7.25583e9	−1.11224
$638$	−2.13045e9	−0.324787
$639$	0	0
$640$	3.43326e8	0.0517699
$641$	−1.01510e10	−1.52233	−0.761163	−	0.648561i	$-0.775371\pi$
$641$	−1.01510e10	−1.52233	−0.761163	+	0.648561i	$0.775371\pi$
$642$	0	0
$643$	−9.54144e9	−1.41539	−0.707694	−	0.706519i	$-0.750265\pi$
$643$	−9.54144e9	−1.41539	−0.707694	+	0.706519i	$0.750265\pi$
$644$	7.40480e9	1.09248
$645$	0	0
$646$	−3.38472e8	−0.0493979
$647$	3.81503e8	0.0553775	0.0276887	−	0.999617i	$-0.491185\pi$
$647$	3.81503e8	0.0553775	0.0276887	+	0.999617i	$0.491185\pi$
$648$	0	0
$649$	1.59010e9	0.228333
$650$	3.24119e9	0.462923
$651$	0	0
$652$	2.14610e9	0.303237
$653$	−5.38710e9	−0.757110	−0.378555	−	0.925579i	$-0.623579\pi$
$653$	−5.38710e9	−0.757110	−0.378555	+	0.925579i	$0.623579\pi$
$654$	0	0
$655$	3.97907e9	0.553270
$656$	−3.60312e8	−0.0498328
$657$	0	0
$658$	−1.61421e10	−2.20886
$659$	−5.97181e8	−0.0812844	−0.0406422	−	0.999174i	$-0.512940\pi$
$659$	−5.97181e8	−0.0812844	−0.0406422	+	0.999174i	$0.512940\pi$
$660$	0	0
$661$	8.12004e9	1.09359	0.546793	−	0.837268i	$-0.315848\pi$
$661$	8.12004e9	1.09359	0.546793	+	0.837268i	$0.315848\pi$
$662$	−1.65944e9	−0.222310
$663$	0	0
$664$	1.09983e10	1.45794
$665$	2.66650e9	0.351614
$666$	0	0
$667$	1.70403e10	2.22350
$668$	3.86773e9	0.502040
$669$	0	0
$670$	−4.21273e9	−0.541131
$671$	−6.18479e8	−0.0790308
$672$	0	0
$673$	1.01545e10	1.28412	0.642058	−	0.766656i	$-0.278081\pi$
$673$	1.01545e10	1.28412	0.642058	+	0.766656i	$0.278081\pi$
$674$	7.69369e9	0.967887
$675$	0	0
$676$	1.59085e9	0.198069
$677$	−6.25953e9	−0.775321	−0.387660	−	0.921802i	$-0.626717\pi$
$677$	−6.25953e9	−0.775321	−0.387660	+	0.921802i	$0.626717\pi$
$678$	0	0
$679$	1.83402e10	2.24833
$680$	4.36950e8	0.0532906
$681$	0	0
$682$	−7.10520e8	−0.0857691
$683$	−1.54207e9	−0.185196	−0.0925980	−	0.995704i	$-0.529517\pi$
$683$	−1.54207e9	−0.185196	−0.0925980	+	0.995704i	$0.529517\pi$
$684$	0	0
$685$	−2.68982e9	−0.319746
$686$	4.71081e9	0.557136
$687$	0	0
$688$	−2.82590e9	−0.330824
$689$	4.73454e9	0.551455
$690$	0	0
$691$	−1.47663e10	−1.70255	−0.851275	−	0.524720i	$-0.824170\pi$
$691$	−1.47663e10	−1.70255	−0.851275	+	0.524720i	$0.824170\pi$
$692$	5.25322e9	0.602635
$693$	0	0
$694$	−1.17459e10	−1.33391
$695$	−3.92780e9	−0.443815
$696$	0	0
$697$	1.61217e8	0.0180341
$698$	3.93932e9	0.438458
$699$	0	0
$700$	5.43172e9	0.598541
$701$	−1.02379e10	−1.12254	−0.561268	−	0.827634i	$-0.689686\pi$
$701$	−1.02379e10	−1.12254	−0.561268	+	0.827634i	$0.689686\pi$
$702$	0	0
$703$	1.83907e9	0.199644
$704$	2.64066e9	0.285239
$705$	0	0
$706$	1.11971e10	1.19754
$707$	8.98781e9	0.956503
$708$	0	0
$709$	4.34652e9	0.458016	0.229008	−	0.973425i	$-0.426452\pi$
$709$	4.34652e9	0.458016	0.229008	+	0.973425i	$0.426452\pi$
$710$	3.82361e9	0.400931
$711$	0	0
$712$	−1.11330e10	−1.15593
$713$	5.68309e9	0.587179
$714$	0	0
$715$	9.01299e8	0.0922142
$716$	9.40126e8	0.0957173
$717$	0	0
$718$	2.41138e9	0.243125
$719$	1.72551e9	0.173128	0.0865640	−	0.996246i	$-0.472411\pi$
$719$	1.72551e9	0.173128	0.0865640	+	0.996246i	$0.472411\pi$
$720$	0	0
$721$	9.29218e9	0.923302
$722$	−5.21421e9	−0.515595
$723$	0	0
$724$	3.99612e9	0.391339
$725$	1.24998e10	1.21820
$726$	0	0
$727$	−1.47195e10	−1.42077	−0.710385	−	0.703814i	$-0.751479\pi$
$727$	−1.47195e10	−1.42077	−0.710385	+	0.703814i	$0.751479\pi$
$728$	1.32355e10	1.27139
$729$	0	0
$730$	−7.19898e8	−0.0684922
$731$	1.26441e9	0.119723
$732$	0	0
$733$	−7.46118e9	−0.699751	−0.349876	−	0.936796i	$-0.613776\pi$
$733$	−7.46118e9	−0.699751	−0.349876	+	0.936796i	$0.613776\pi$
$734$	1.29252e10	1.20643
$735$	0	0
$736$	−1.35970e10	−1.25710
$737$	5.90658e9	0.543501
$738$	0	0
$739$	8.86866e9	0.808355	0.404178	−	0.914680i	$-0.367558\pi$
$739$	8.86866e9	0.808355	0.404178	+	0.914680i	$0.367558\pi$
$740$	−7.42995e8	−0.0674024
$741$	0	0
$742$	−9.48455e9	−0.852321
$743$	7.70003e9	0.688702	0.344351	−	0.938841i	$-0.388099\pi$
$743$	7.70003e9	0.688702	0.344351	+	0.938841i	$0.388099\pi$
$744$	0	0
$745$	−2.76638e9	−0.245112
$746$	−1.45648e10	−1.28445
$747$	0	0
$748$	−1.91726e8	−0.0167504
$749$	−1.84247e9	−0.160219
$750$	0	0
$751$	−5.25287e9	−0.452540	−0.226270	−	0.974065i	$-0.572653\pi$
$751$	−5.25287e9	−0.452540	−0.226270	+	0.974065i	$0.572653\pi$
$752$	7.47142e9	0.640680
$753$	0	0
$754$	9.53193e9	0.809806
$755$	1.23009e9	0.104021
$756$	0	0
$757$	−1.86825e10	−1.56531	−0.782654	−	0.622457i	$-0.786135\pi$
$757$	−1.86825e10	−1.56531	−0.782654	+	0.622457i	$0.786135\pi$
$758$	2.55988e9	0.213490
$759$	0	0
$760$	−2.90231e9	−0.239826
$761$	3.18263e9	0.261782	0.130891	−	0.991397i	$-0.458216\pi$
$761$	3.18263e9	0.261782	0.130891	+	0.991397i	$0.458216\pi$
$762$	0	0
$763$	3.11954e9	0.254246
$764$	−2.58775e9	−0.209940
$765$	0	0
$766$	1.56453e10	1.25772
$767$	−7.11435e9	−0.569313
$768$	0	0
$769$	−1.06228e10	−0.842360	−0.421180	−	0.906977i	$-0.638384\pi$
$769$	−1.06228e10	−0.842360	−0.421180	+	0.906977i	$0.638384\pi$
$770$	−1.80554e9	−0.142525
$771$	0	0
$772$	−3.51906e9	−0.275275
$773$	−1.10774e10	−0.862600	−0.431300	−	0.902208i	$-0.641945\pi$
$773$	−1.10774e10	−0.862600	−0.431300	+	0.902208i	$0.641945\pi$
$774$	0	0
$775$	4.16877e9	0.321701
$776$	−1.99621e10	−1.53352
$777$	0	0
$778$	6.97087e8	0.0530711
$779$	−1.07083e9	−0.0811596
$780$	0	0
$781$	−5.36101e9	−0.402687
$782$	−1.83314e9	−0.137080
$783$	0	0
$784$	−6.72777e9	−0.498614
$785$	−5.89140e9	−0.434685
$786$	0	0
$787$	−7.13350e9	−0.521664	−0.260832	−	0.965384i	$-0.583997\pi$
$787$	−7.13350e9	−0.521664	−0.260832	+	0.965384i	$0.583997\pi$
$788$	8.39002e9	0.610831
$789$	0	0
$790$	7.76751e9	0.560515
$791$	−3.50172e9	−0.251573
$792$	0	0
$793$	2.76717e9	0.197051
$794$	−1.61321e10	−1.14372
$795$	0	0
$796$	7.37244e9	0.518103
$797$	−2.49431e10	−1.74520	−0.872601	−	0.488434i	$-0.837568\pi$
$797$	−2.49431e10	−1.74520	−0.872601	+	0.488434i	$0.837568\pi$
$798$	0	0
$799$	−3.34299e9	−0.231858
$800$	−9.97393e9	−0.688734
$801$	0	0
$802$	4.05721e9	0.277726
$803$	1.00935e9	0.0687922
$804$	0	0
$805$	1.44416e10	0.975732
$806$	3.17897e9	0.213852
$807$	0	0
$808$	−9.78263e9	−0.652403
$809$	−2.35458e10	−1.56348	−0.781742	−	0.623602i	$-0.785668\pi$
$809$	−2.35458e10	−1.56348	−0.781742	+	0.623602i	$0.785668\pi$
$810$	0	0
$811$	5.05892e9	0.333031	0.166516	−	0.986039i	$-0.446748\pi$
$811$	5.05892e9	0.333031	0.166516	+	0.986039i	$0.446748\pi$
$812$	1.59740e10	1.04705
$813$	0	0
$814$	−1.24528e9	−0.0809246
$815$	4.18554e9	0.270832
$816$	0	0
$817$	−8.39846e9	−0.538794
$818$	1.49715e10	0.956373
$819$	0	0
$820$	4.32621e8	0.0274006
$821$	−2.76919e9	−0.174643	−0.0873216	−	0.996180i	$-0.527831\pi$
$821$	−2.76919e9	−0.174643	−0.0873216	+	0.996180i	$0.527831\pi$
$822$	0	0
$823$	1.01522e10	0.634835	0.317418	−	0.948286i	$-0.397184\pi$
$823$	1.01522e10	0.634835	0.317418	+	0.948286i	$0.397184\pi$
$824$	−1.01139e10	−0.629758
$825$	0	0
$826$	1.42520e10	0.879922
$827$	3.25613e9	0.200185	0.100093	−	0.994978i	$-0.468086\pi$
$827$	3.25613e9	0.200185	0.100093	+	0.994978i	$0.468086\pi$
$828$	0	0
$829$	−1.11649e10	−0.680632	−0.340316	−	0.940311i	$-0.610534\pi$
$829$	−1.11649e10	−0.680632	−0.340316	+	0.940311i	$0.610534\pi$
$830$	6.71285e9	0.407506
$831$	0	0
$832$	−1.18147e10	−0.711200
$833$	3.01025e9	0.180445
$834$	0	0
$835$	7.54325e9	0.448390
$836$	1.27348e9	0.0753825
$837$	0	0
$838$	−1.38212e10	−0.811318
$839$	−2.90154e10	−1.69614	−0.848071	−	0.529882i	$-0.822236\pi$
$839$	−2.90154e10	−1.69614	−0.848071	+	0.529882i	$0.822236\pi$
$840$	0	0
$841$	1.95103e10	1.13104
$842$	−7.07752e9	−0.408591
$843$	0	0
$844$	−5.33644e9	−0.305529
$845$	3.10265e9	0.176902
$846$	0	0
$847$	2.53152e9	0.143149
$848$	4.38997e9	0.247216
$849$	0	0
$850$	−1.34468e9	−0.0751025
$851$	9.96033e9	0.554013
$852$	0	0
$853$	−1.88958e10	−1.04242	−0.521210	−	0.853428i	$-0.674519\pi$
$853$	−1.88958e10	−1.04242	−0.521210	+	0.853428i	$0.674519\pi$
$854$	−5.54338e9	−0.304560
$855$	0	0
$856$	2.00540e9	0.109281
$857$	−7.43007e9	−0.403237	−0.201618	−	0.979464i	$-0.564620\pi$
$857$	−7.43007e9	−0.403237	−0.201618	+	0.979464i	$0.564620\pi$
$858$	0	0
$859$	1.69236e10	0.910996	0.455498	−	0.890237i	$-0.349461\pi$
$859$	1.69236e10	0.910996	0.455498	+	0.890237i	$0.349461\pi$
$860$	3.39302e9	0.181904
$861$	0	0
$862$	2.54424e10	1.35295
$863$	−2.98403e9	−0.158039	−0.0790196	−	0.996873i	$-0.525179\pi$
$863$	−2.98403e9	−0.158039	−0.0790196	+	0.996873i	$0.525179\pi$
$864$	0	0
$865$	1.02454e10	0.538235
$866$	−1.00272e8	−0.00524646
$867$	0	0
$868$	5.32744e9	0.276503
$869$	−1.08907e10	−0.562970
$870$	0	0
$871$	−2.64269e10	−1.35514
$872$	−3.39541e9	−0.173414
$873$	0	0
$874$	1.21761e10	0.616904
$875$	2.32880e10	1.17518
$876$	0	0
$877$	9.83575e9	0.492390	0.246195	−	0.969220i	$-0.420820\pi$
$877$	9.83575e9	0.492390	0.246195	+	0.969220i	$0.420820\pi$
$878$	−1.45080e10	−0.723395
$879$	0	0
$880$	8.35704e8	0.0413393
$881$	−2.62064e10	−1.29120	−0.645598	−	0.763677i	$-0.723392\pi$
$881$	−2.62064e10	−1.29120	−0.645598	+	0.763677i	$0.723392\pi$
$882$	0	0
$883$	−6.25320e8	−0.0305661	−0.0152831	−	0.999883i	$-0.504865\pi$
$883$	−6.25320e8	−0.0305661	−0.0152831	+	0.999883i	$0.504865\pi$
$884$	8.57812e8	0.0417647
$885$	0	0
$886$	−7.11920e9	−0.343885
$887$	−3.69171e10	−1.77621	−0.888107	−	0.459637i	$-0.847980\pi$
$887$	−3.69171e10	−1.77621	−0.888107	+	0.459637i	$0.847980\pi$
$888$	0	0
$889$	2.13242e10	1.01793
$890$	−6.79503e9	−0.323092
$891$	0	0
$892$	5.83108e9	0.275088
$893$	2.22047e10	1.04344
$894$	0	0
$895$	1.83353e9	0.0854886
$896$	−4.31449e9	−0.200379
$897$	0	0
$898$	6.66432e9	0.307106
$899$	1.22598e10	0.562762
$900$	0	0
$901$	−1.96423e9	−0.0894656
$902$	7.25083e8	0.0328977
$903$	0	0
$904$	3.81139e9	0.171591
$905$	7.79365e9	0.349519
$906$	0	0
$907$	−1.98518e10	−0.883433	−0.441717	−	0.897155i	$-0.645630\pi$
$907$	−1.98518e10	−0.883433	−0.441717	+	0.897155i	$0.645630\pi$
$908$	1.19435e10	0.529459
$909$	0	0
$910$	8.07828e9	0.355364
$911$	2.59898e10	1.13891	0.569453	−	0.822024i	$-0.307155\pi$
$911$	2.59898e10	1.13891	0.569453	+	0.822024i	$0.307155\pi$
$912$	0	0
$913$	−9.41195e9	−0.409291
$914$	−1.78694e9	−0.0774104
$915$	0	0
$916$	−1.36585e10	−0.587176
$917$	−5.00039e10	−2.14147
$918$	0	0
$919$	1.95805e9	0.0832186	0.0416093	−	0.999134i	$-0.486752\pi$
$919$	1.95805e9	0.0832186	0.0416093	+	0.999134i	$0.486752\pi$
$920$	−1.57187e10	−0.665519
$921$	0	0
$922$	2.43200e10	1.02189
$923$	2.39860e10	1.00404
$924$	0	0
$925$	7.30630e9	0.303530
$926$	−2.11513e10	−0.875385
$927$	0	0
$928$	−2.93320e10	−1.20483
$929$	−1.18676e10	−0.485633	−0.242816	−	0.970072i	$-0.578071\pi$
$929$	−1.18676e10	−0.485633	−0.242816	+	0.970072i	$0.578071\pi$
$930$	0	0
$931$	−1.99946e10	−0.812063
$932$	−6.24724e9	−0.252774
$933$	0	0
$934$	1.59215e10	0.639397
$935$	−3.73925e8	−0.0149604
$936$	0	0
$937$	−4.62869e10	−1.83810	−0.919050	−	0.394141i	$-0.871042\pi$
$937$	−4.62869e10	−1.83810	−0.919050	+	0.394141i	$0.871042\pi$
$938$	5.29403e10	2.09448
$939$	0	0
$940$	−8.97083e9	−0.352278
$941$	4.08305e10	1.59743	0.798714	−	0.601710i	$-0.205514\pi$
$941$	4.08305e10	1.59743	0.798714	+	0.601710i	$0.205514\pi$
$942$	0	0
$943$	−5.79957e9	−0.225219
$944$	−6.59658e9	−0.255221
$945$	0	0
$946$	5.68678e9	0.218397
$947$	4.89438e10	1.87272	0.936360	−	0.351041i	$-0.114172\pi$
$947$	4.89438e10	1.87272	0.936360	+	0.351041i	$0.114172\pi$
$948$	0	0
$949$	−4.51600e9	−0.171523
$950$	8.93164e9	0.337986
$951$	0	0
$952$	−5.49104e9	−0.206265
$953$	−1.57392e10	−0.589057	−0.294529	−	0.955643i	$-0.595163\pi$
$953$	−1.57392e10	−0.589057	−0.294529	+	0.955643i	$0.595163\pi$
$954$	0	0
$955$	−5.04690e9	−0.187505
$956$	−2.07357e10	−0.767566
$957$	0	0
$958$	9.01654e9	0.331330
$959$	3.38022e10	1.23760
$960$	0	0
$961$	−2.34239e10	−0.851387
$962$	5.57155e9	0.201773
$963$	0	0
$964$	5.37807e9	0.193356
$965$	−6.86324e9	−0.245858
$966$	0	0
$967$	3.69812e10	1.31519	0.657596	−	0.753371i	$-0.271574\pi$
$967$	3.69812e10	1.31519	0.657596	+	0.753371i	$0.271574\pi$
$968$	−2.75538e9	−0.0976379
$969$	0	0
$970$	−1.21839e10	−0.428631
$971$	9.25697e9	0.324490	0.162245	−	0.986750i	$-0.448126\pi$
$971$	9.25697e9	0.324490	0.162245	+	0.986750i	$0.448126\pi$
$972$	0	0
$973$	4.93596e10	1.71781
$974$	−3.53020e10	−1.22417
$975$	0	0
$976$	2.56578e9	0.0883375
$977$	4.79231e10	1.64404	0.822022	−	0.569455i	$-0.192846\pi$
$977$	4.79231e10	1.64404	0.822022	+	0.569455i	$0.192846\pi$
$978$	0	0
$979$	9.52716e9	0.324507
$980$	8.07794e9	0.274163
$981$	0	0
$982$	1.58329e10	0.533543
$983$	5.66633e10	1.90267	0.951337	−	0.308151i	$-0.0997102\pi$
$983$	5.66633e10	1.90267	0.951337	+	0.308151i	$0.0997102\pi$
$984$	0	0
$985$	1.63631e10	0.545555
$986$	−3.95454e9	−0.131379
$987$	0	0
$988$	−5.69774e9	−0.187955
$989$	−4.54856e10	−1.49516
$990$	0	0
$991$	−4.97633e10	−1.62425	−0.812123	−	0.583487i	$-0.801688\pi$
$991$	−4.97633e10	−1.62425	−0.812123	+	0.583487i	$0.801688\pi$
$992$	−9.78245e9	−0.318168
$993$	0	0
$994$	−4.80503e10	−1.55183
$995$	1.43785e10	0.462736
$996$	0	0
$997$	−2.80585e10	−0.896669	−0.448334	−	0.893866i	$-0.647983\pi$
$997$	−2.80585e10	−0.896669	−0.448334	+	0.893866i	$0.647983\pi$
$998$	3.37918e10	1.07611
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.h.1.4	✓	5
3.2	odd	2		99.8.a.i.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.a.h.1.4	✓	5	1.1	even	1	trivial
99.8.a.i.1.2	yes	5	3.2	odd	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

\(f(q)\)	\(=\)	\(q+8.34840 q^{2} -58.3042 q^{4} -113.711 q^{5} +1428.97 q^{7} -1555.34 q^{8} +O(q^{10})\)	\(q+8.34840 q^{2} -58.3042 q^{4} -113.711 q^{5} +1428.97 q^{7} -1555.34 q^{8} -949.305 q^{10} +1331.00 q^{11} -5955.09 q^{13} +11929.7 q^{14} -5521.69 q^{16} +2470.61 q^{17} -16410.2 q^{19} +6629.82 q^{20} +11111.7 q^{22} -88877.0 q^{23} -65194.8 q^{25} -49715.5 q^{26} -83315.1 q^{28} -191729. q^{29} -63943.3 q^{31} +152986. q^{32} +20625.6 q^{34} -162490. q^{35} -112069. q^{37} -136999. q^{38} +176859. q^{40} +65253.9 q^{41} +511782. q^{43} -77602.8 q^{44} -741981. q^{46} -1.35310e6 q^{47} +1.21842e6 q^{49} -544273. q^{50} +347207. q^{52} -795040. q^{53} -151349. q^{55} -2.22254e6 q^{56} -1.60064e6 q^{58} +1.19467e6 q^{59} -464673. q^{61} -533824. q^{62} +1.98397e6 q^{64} +677159. q^{65} +4.43770e6 q^{67} -144047. q^{68} -1.35653e6 q^{70} -4.02780e6 q^{71} +758343. q^{73} -935595. q^{74} +956785. q^{76} +1.90197e6 q^{77} -8.18232e6 q^{79} +627877. q^{80} +544766. q^{82} -7.07133e6 q^{83} -280935. q^{85} +4.27256e6 q^{86} -2.07016e6 q^{88} +7.15790e6 q^{89} -8.50968e6 q^{91} +5.18190e6 q^{92} -1.12963e7 q^{94} +1.86602e6 q^{95} +1.28345e7 q^{97} +1.01719e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8}+O(q^{10}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8} + 11516 q^{10} + 6655 q^{11} - 16666 q^{13} - 20516 q^{14} + 15010 q^{16} + 1906 q^{17} - 10446 q^{19} - 155572 q^{20} - 10648 q^{22} + 35468 q^{23} + 104239 q^{25} + 136396 q^{26} + 118456 q^{28} - 259062 q^{29} - 44932 q^{31} - 609010 q^{32} - 592888 q^{34} - 963800 q^{35} + 393978 q^{37} - 1319448 q^{38} + 1650684 q^{40} - 1554074 q^{41} + 263118 q^{43} + 220946 q^{44} - 1948268 q^{46} - 2481904 q^{47} + 498177 q^{49} - 5560984 q^{50} - 4530056 q^{52} - 2325840 q^{53} - 665500 q^{55} - 5221992 q^{56} + 2479968 q^{58} - 4613452 q^{59} + 529362 q^{61} - 3077192 q^{62} + 1437674 q^{64} + 2187496 q^{65} - 4612664 q^{67} + 2362916 q^{68} + 7327832 q^{70} - 5583864 q^{71} + 980054 q^{73} - 3387480 q^{74} + 1023396 q^{76} + 593626 q^{77} + 2804758 q^{79} - 10053364 q^{80} - 110080 q^{82} + 2451324 q^{83} - 4240456 q^{85} + 5937408 q^{86} - 3665574 q^{88} - 4025472 q^{89} - 12525436 q^{91} + 44606548 q^{92} + 1592764 q^{94} - 4273320 q^{95} - 234806 q^{97} + 26686536 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8 + 11516 * q^10 + 6655 * q^11 - 16666 * q^13 - 20516 * q^14 + 15010 * q^16 + 1906 * q^17 - 10446 * q^19 - 155572 * q^20 - 10648 * q^22 + 35468 * q^23 + 104239 * q^25 + 136396 * q^26 + 118456 * q^28 - 259062 * q^29 - 44932 * q^31 - 609010 * q^32 - 592888 * q^34 - 963800 * q^35 + 393978 * q^37 - 1319448 * q^38 + 1650684 * q^40 - 1554074 * q^41 + 263118 * q^43 + 220946 * q^44 - 1948268 * q^46 - 2481904 * q^47 + 498177 * q^49 - 5560984 * q^50 - 4530056 * q^52 - 2325840 * q^53 - 665500 * q^55 - 5221992 * q^56 + 2479968 * q^58 - 4613452 * q^59 + 529362 * q^61 - 3077192 * q^62 + 1437674 * q^64 + 2187496 * q^65 - 4612664 * q^67 + 2362916 * q^68 + 7327832 * q^70 - 5583864 * q^71 + 980054 * q^73 - 3387480 * q^74 + 1023396 * q^76 + 593626 * q^77 + 2804758 * q^79 - 10053364 * q^80 - 110080 * q^82 + 2451324 * q^83 - 4240456 * q^85 + 5937408 * q^86 - 3665574 * q^88 - 4025472 * q^89 - 12525436 * q^91 + 44606548 * q^92 + 1592764 * q^94 - 4273320 * q^95 - 234806 * q^97 + 26686536 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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