LMFDB - Embedded newform 99.8.a.g.1.3

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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 341x^{2} + 1417x - 1412 $ x^4 - x^3 - 341x^2 + 1417x - 1412
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-19.8969$ 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)

$f(q)$	$=$	$q+10.6261 q^{2} -15.0863 q^{4} -512.130 q^{5} +973.904 q^{7} -1520.45 q^{8} +O(q^{10})$	\(q+10.6261 q^{2} -15.0863 q^{4} -512.130 q^{5} +973.904 q^{7} -1520.45 q^{8} -5441.94 q^{10} +1331.00 q^{11} +8638.56 q^{13} +10348.8 q^{14} -14225.4 q^{16} -7207.74 q^{17} +11244.2 q^{19} +7726.14 q^{20} +14143.3 q^{22} +69890.8 q^{23} +184152. q^{25} +91794.1 q^{26} -14692.6 q^{28} +185587. q^{29} +10204.2 q^{31} +43457.3 q^{32} -76590.1 q^{34} -498766. q^{35} -184605. q^{37} +119482. q^{38} +778667. q^{40} -275705. q^{41} -25346.2 q^{43} -20079.8 q^{44} +742665. q^{46} +764328. q^{47} +124946. q^{49} +1.95682e6 q^{50} -130324. q^{52} -1.20360e6 q^{53} -681645. q^{55} -1.48077e6 q^{56} +1.97207e6 q^{58} +2.70756e6 q^{59} +20268.6 q^{61} +108431. q^{62} +2.28263e6 q^{64} -4.42407e6 q^{65} -360405. q^{67} +108738. q^{68} -5.29993e6 q^{70} -1.07417e6 q^{71} +4.32131e6 q^{73} -1.96163e6 q^{74} -169633. q^{76} +1.29627e6 q^{77} -794602. q^{79} +7.28524e6 q^{80} -2.92967e6 q^{82} +6.38583e6 q^{83} +3.69130e6 q^{85} -269331. q^{86} -2.02372e6 q^{88} +1.27059e6 q^{89} +8.41313e6 q^{91} -1.05439e6 q^{92} +8.12182e6 q^{94} -5.75851e6 q^{95} -8.34264e6 q^{97} +1.32768e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 604 q^{4} - 537 q^{5} + 170 q^{7} + 420 q^{8}+O(q^{10}) $ 4 * q + 604 * q^4 - 537 * q^5 + 170 * q^7 + 420 * q^8	\( 4 q + 604 q^{4} - 537 q^{5} + 170 q^{7} + 420 q^{8} + 1470 q^{10} + 5324 q^{11} + 4250 q^{13} + 29988 q^{14} + 52744 q^{16} - 54300 q^{17} + 67844 q^{19} - 15888 q^{20} + 9015 q^{23} + 22531 q^{25} + 311700 q^{26} - 475840 q^{28} - 234078 q^{29} + 189857 q^{31} + 175560 q^{32} + 406536 q^{34} - 154098 q^{35} + 127895 q^{37} + 584760 q^{38} + 2249268 q^{40} - 289842 q^{41} + 704930 q^{43} + 803924 q^{44} + 3519102 q^{46} + 1729080 q^{47} + 139920 q^{49} + 2115918 q^{50} + 2030120 q^{52} - 1098660 q^{53} - 714747 q^{55} + 4311720 q^{56} + 1046100 q^{58} + 4665777 q^{59} + 310610 q^{61} - 4286670 q^{62} + 9539488 q^{64} - 4526160 q^{65} - 3368245 q^{67} - 14958120 q^{68} - 12580596 q^{70} + 3416541 q^{71} + 11466230 q^{73} + 16581438 q^{74} + 2169824 q^{76} + 226270 q^{77} + 566282 q^{79} + 4469544 q^{80} - 11151780 q^{82} + 4220790 q^{83} + 10312902 q^{85} + 5991972 q^{86} + 559020 q^{88} - 18265191 q^{89} - 1133480 q^{91} + 6399240 q^{92} + 8464656 q^{94} + 5662968 q^{95} + 11425325 q^{97} - 36460200 q^{98}+O(q^{100}) \) 4 * q + 604 * q^4 - 537 * q^5 + 170 * q^7 + 420 * q^8 + 1470 * q^10 + 5324 * q^11 + 4250 * q^13 + 29988 * q^14 + 52744 * q^16 - 54300 * q^17 + 67844 * q^19 - 15888 * q^20 + 9015 * q^23 + 22531 * q^25 + 311700 * q^26 - 475840 * q^28 - 234078 * q^29 + 189857 * q^31 + 175560 * q^32 + 406536 * q^34 - 154098 * q^35 + 127895 * q^37 + 584760 * q^38 + 2249268 * q^40 - 289842 * q^41 + 704930 * q^43 + 803924 * q^44 + 3519102 * q^46 + 1729080 * q^47 + 139920 * q^49 + 2115918 * q^50 + 2030120 * q^52 - 1098660 * q^53 - 714747 * q^55 + 4311720 * q^56 + 1046100 * q^58 + 4665777 * q^59 + 310610 * q^61 - 4286670 * q^62 + 9539488 * q^64 - 4526160 * q^65 - 3368245 * q^67 - 14958120 * q^68 - 12580596 * q^70 + 3416541 * q^71 + 11466230 * q^73 + 16581438 * q^74 + 2169824 * q^76 + 226270 * q^77 + 566282 * q^79 + 4469544 * q^80 - 11151780 * q^82 + 4220790 * q^83 + 10312902 * q^85 + 5991972 * q^86 + 559020 * q^88 - 18265191 * q^89 - 1133480 * q^91 + 6399240 * q^92 + 8464656 * q^94 + 5662968 * q^95 + 11425325 * q^97 - 36460200 * 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 $

$2$	10.6261	0.939222	0.469611	−	0.882873i	$-0.344394\pi$
$2$	10.6261	0.939222	0.469611	+	0.882873i	$0.344394\pi$
$3$	0	0
$3$	0	0
$4$	−15.0863	−0.117862
$5$	−512.130	−1.83225	−0.916126	−	0.400890i	$-0.868701\pi$
$5$	−512.130	−1.83225	−0.916126	+	0.400890i	$0.868701\pi$
$6$	0	0
$7$	973.904	1.07318	0.536590	−	0.843843i	$-0.319712\pi$
$7$	973.904	1.07318	0.536590	+	0.843843i	$0.319712\pi$
$8$	−1520.45	−1.04992
$9$	0	0
$10$	−5441.94	−1.72089
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	8638.56	1.09054	0.545268	−	0.838262i	$-0.316428\pi$
$13$	8638.56	1.09054	0.545268	+	0.838262i	$0.316428\pi$
$14$	10348.8	1.00796
$15$	0	0
$16$	−14225.4	−0.868247
$17$	−7207.74	−0.355818	−0.177909	−	0.984047i	$-0.556933\pi$
$17$	−7207.74	−0.355818	−0.177909	+	0.984047i	$0.556933\pi$
$18$	0	0
$19$	11244.2	0.376090	0.188045	−	0.982160i	$-0.439785\pi$
$19$	11244.2	0.376090	0.188045	+	0.982160i	$0.439785\pi$
$20$	7726.14	0.215952
$21$	0	0
$22$	14143.3	0.283186
$23$	69890.8	1.19777	0.598884	−	0.800836i	$-0.295611\pi$
$23$	69890.8	1.19777	0.598884	+	0.800836i	$0.295611\pi$
$24$	0	0
$25$	184152.	2.35715
$26$	91794.1	1.02426
$27$	0	0
$28$	−14692.6	−0.126487
$29$	185587.	1.41304	0.706522	−	0.707691i	$-0.250263\pi$
$29$	185587.	1.41304	0.706522	+	0.707691i	$0.250263\pi$
$30$	0	0
$31$	10204.2	0.0615198	0.0307599	−	0.999527i	$-0.490207\pi$
$31$	10204.2	0.0615198	0.0307599	+	0.999527i	$0.490207\pi$
$32$	43457.3	0.234443
$33$	0	0
$34$	−76590.1	−0.334192
$35$	−498766.	−1.96634
$36$	0	0
$37$	−184605.	−0.599152	−0.299576	−	0.954072i	$-0.596845\pi$
$37$	−184605.	−0.599152	−0.299576	+	0.954072i	$0.596845\pi$
$38$	119482.	0.353232
$39$	0	0
$40$	778667.	1.92372
$41$	−275705.	−0.624744	−0.312372	−	0.949960i	$-0.601123\pi$
$41$	−275705.	−0.624744	−0.312372	+	0.949960i	$0.601123\pi$
$42$	0	0
$43$	−25346.2	−0.0486154	−0.0243077	−	0.999705i	$-0.507738\pi$
$43$	−25346.2	−0.0486154	−0.0243077	+	0.999705i	$0.507738\pi$
$44$	−20079.8	−0.0355366
$45$	0	0
$46$	742665.	1.12497
$47$	764328.	1.07383	0.536917	−	0.843635i	$-0.319589\pi$
$47$	764328.	1.07383	0.536917	+	0.843635i	$0.319589\pi$
$48$	0	0
$49$	124946.	0.151717
$50$	1.95682e6	2.21389
$51$	0	0
$52$	−130324.	−0.128532
$53$	−1.20360e6	−1.11050	−0.555249	−	0.831684i	$-0.687377\pi$
$53$	−1.20360e6	−1.11050	−0.555249	+	0.831684i	$0.687377\pi$
$54$	0	0
$55$	−681645.	−0.552445
$56$	−1.48077e6	−1.12675
$57$	0	0
$58$	1.97207e6	1.32716
$59$	2.70756e6	1.71631	0.858155	−	0.513391i	$-0.171611\pi$
$59$	2.70756e6	1.71631	0.858155	+	0.513391i	$0.171611\pi$
$60$	0	0
$61$	20268.6	0.0114332	0.00571661	−	0.999984i	$-0.498180\pi$
$61$	20268.6	0.0114332	0.00571661	+	0.999984i	$0.498180\pi$
$62$	108431.	0.0577807
$63$	0	0
$64$	2.28263e6	1.08844
$65$	−4.42407e6	−1.99814
$66$	0	0
$67$	−360405.	−0.146396	−0.0731980	−	0.997317i	$-0.523321\pi$
$67$	−360405.	−0.146396	−0.0731980	+	0.997317i	$0.523321\pi$
$68$	108738.	0.0419373
$69$	0	0
$70$	−5.29993e6	−1.84683
$71$	−1.07417e6	−0.356179	−0.178090	−	0.984014i	$-0.556992\pi$
$71$	−1.07417e6	−0.356179	−0.178090	+	0.984014i	$0.556992\pi$
$72$	0	0
$73$	4.32131e6	1.30013	0.650063	−	0.759880i	$-0.274743\pi$
$73$	4.32131e6	1.30013	0.650063	+	0.759880i	$0.274743\pi$
$74$	−1.96163e6	−0.562737
$75$	0	0
$76$	−169633.	−0.0443266
$77$	1.29627e6	0.323576
$78$	0	0
$79$	−794602.	−0.181324	−0.0906619	−	0.995882i	$-0.528898\pi$
$79$	−794602.	−0.181324	−0.0906619	+	0.995882i	$0.528898\pi$
$80$	7.28524e6	1.59085
$81$	0	0
$82$	−2.92967e6	−0.586773
$83$	6.38583e6	1.22587	0.612934	−	0.790134i	$-0.289989\pi$
$83$	6.38583e6	1.22587	0.612934	+	0.790134i	$0.289989\pi$
$84$	0	0
$85$	3.69130e6	0.651949
$86$	−269331.	−0.0456607
$87$	0	0
$88$	−2.02372e6	−0.316563
$89$	1.27059e6	0.191047	0.0955237	−	0.995427i	$-0.469547\pi$
$89$	1.27059e6	0.191047	0.0955237	+	0.995427i	$0.469547\pi$
$90$	0	0
$91$	8.41313e6	1.17034
$92$	−1.05439e6	−0.141171
$93$	0	0
$94$	8.12182e6	1.00857
$95$	−5.75851e6	−0.689092
$96$	0	0
$97$	−8.34264e6	−0.928116	−0.464058	−	0.885805i	$-0.653607\pi$
$97$	−8.34264e6	−0.928116	−0.464058	+	0.885805i	$0.653607\pi$
$98$	1.32768e6	0.142496
$99$	0	0
$100$	−2.77817e6	−0.277817
$101$	−442553.	−0.0427406	−0.0213703	−	0.999772i	$-0.506803\pi$
$101$	−442553.	−0.0427406	−0.0213703	+	0.999772i	$0.506803\pi$
$102$	0	0
$103$	−6.11290e6	−0.551210	−0.275605	−	0.961271i	$-0.588878\pi$
$103$	−6.11290e6	−0.551210	−0.275605	+	0.961271i	$0.588878\pi$
$104$	−1.31345e7	−1.14498
$105$	0	0
$106$	−1.27896e7	−1.04301
$107$	2.22580e7	1.75648	0.878241	−	0.478219i	$-0.158717\pi$
$107$	2.22580e7	1.75648	0.878241	+	0.478219i	$0.158717\pi$
$108$	0	0
$109$	−7.83386e6	−0.579406	−0.289703	−	0.957117i	$-0.593557\pi$
$109$	−7.83386e6	−0.579406	−0.289703	+	0.957117i	$0.593557\pi$
$110$	−7.24322e6	−0.518869
$111$	0	0
$112$	−1.38541e7	−0.931786
$113$	−1.96933e7	−1.28394	−0.641968	−	0.766731i	$-0.721882\pi$
$113$	−1.96933e7	−1.28394	−0.641968	+	0.766731i	$0.721882\pi$
$114$	0	0
$115$	−3.57932e7	−2.19461
$116$	−2.79982e6	−0.166544
$117$	0	0
$118$	2.87707e7	1.61200
$119$	−7.01965e6	−0.381857
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	215375.	0.0107383
$123$	0	0
$124$	−153944.	−0.00725082
$125$	−5.42998e7	−2.48664
$126$	0	0
$127$	1.81856e7	0.787800	0.393900	−	0.919153i	$-0.371126\pi$
$127$	1.81856e7	0.787800	0.393900	+	0.919153i	$0.371126\pi$
$128$	1.86929e7	0.787845
$129$	0	0
$130$	−4.70105e7	−1.87669
$131$	2.97514e7	1.15627	0.578134	−	0.815942i	$-0.303781\pi$
$131$	2.97514e7	1.15627	0.578134	+	0.815942i	$0.303781\pi$
$132$	0	0
$133$	1.09508e7	0.403613
$134$	−3.82970e6	−0.137498
$135$	0	0
$136$	1.09590e7	0.373581
$137$	−1.70380e7	−0.566103	−0.283051	−	0.959105i	$-0.591347\pi$
$137$	−1.70380e7	−0.566103	−0.283051	+	0.959105i	$0.591347\pi$
$138$	0	0
$139$	5.96399e7	1.88359	0.941793	−	0.336194i	$-0.109140\pi$
$139$	5.96399e7	1.88359	0.941793	+	0.336194i	$0.109140\pi$
$140$	7.52452e6	0.231756
$141$	0	0
$142$	−1.14142e7	−0.334531
$143$	1.14979e7	0.328809
$144$	0	0
$145$	−9.50449e7	−2.58905
$146$	4.59186e7	1.22111
$147$	0	0
$148$	2.78500e6	0.0706170
$149$	−4.37684e7	−1.08395	−0.541974	−	0.840395i	$-0.682323\pi$
$149$	−4.37684e7	−1.08395	−0.541974	+	0.840395i	$0.682323\pi$
$150$	0	0
$151$	1.83916e7	0.434711	0.217356	−	0.976092i	$-0.430257\pi$
$151$	1.83916e7	0.434711	0.217356	+	0.976092i	$0.430257\pi$
$152$	−1.70962e7	−0.394865
$153$	0	0
$154$	1.37742e7	0.303910
$155$	−5.22590e6	−0.112720
$156$	0	0
$157$	1.03509e7	0.213467	0.106733	−	0.994288i	$-0.465961\pi$
$157$	1.03509e7	0.213467	0.106733	+	0.994288i	$0.465961\pi$
$158$	−8.44351e6	−0.170303
$159$	0	0
$160$	−2.22558e7	−0.429560
$161$	6.80669e7	1.28542
$162$	0	0
$163$	5.17108e7	0.935243	0.467621	−	0.883929i	$-0.345111\pi$
$163$	5.17108e7	0.935243	0.467621	+	0.883929i	$0.345111\pi$
$164$	4.15937e6	0.0736332
$165$	0	0
$166$	6.78564e7	1.15136
$167$	2.59367e7	0.430931	0.215465	−	0.976511i	$-0.430873\pi$
$167$	2.59367e7	0.430931	0.215465	+	0.976511i	$0.430873\pi$
$168$	0	0
$169$	1.18763e7	0.189267
$170$	3.92241e7	0.612325
$171$	0	0
$172$	382380.	0.00572989
$173$	−4.52289e7	−0.664132	−0.332066	−	0.943256i	$-0.607746\pi$
$173$	−4.52289e7	−0.664132	−0.332066	+	0.943256i	$0.607746\pi$
$174$	0	0
$175$	1.79347e8	2.52965
$176$	−1.89340e7	−0.261786
$177$	0	0
$178$	1.35014e7	0.179436
$179$	−5.70702e7	−0.743744	−0.371872	−	0.928284i	$-0.621284\pi$
$179$	−5.70702e7	−0.743744	−0.371872	+	0.928284i	$0.621284\pi$
$180$	0	0
$181$	5.34641e7	0.670173	0.335087	−	0.942187i	$-0.391234\pi$
$181$	5.34641e7	0.670173	0.335087	+	0.942187i	$0.391234\pi$
$182$	8.93986e7	1.09921
$183$	0	0
$184$	−1.06265e8	−1.25756
$185$	9.45417e7	1.09780
$186$	0	0
$187$	−9.59351e6	−0.107283
$188$	−1.15309e7	−0.126564
$189$	0	0
$190$	−6.11904e7	−0.647210
$191$	1.63924e8	1.70226	0.851128	−	0.524957i	$-0.175919\pi$
$191$	1.63924e8	1.70226	0.851128	+	0.524957i	$0.175919\pi$
$192$	0	0
$193$	5.15672e7	0.516324	0.258162	−	0.966102i	$-0.416883\pi$
$193$	5.15672e7	0.516324	0.258162	+	0.966102i	$0.416883\pi$
$194$	−8.86496e7	−0.871707
$195$	0	0
$196$	−1.88496e6	−0.0178816
$197$	1.82052e8	1.69654	0.848269	−	0.529566i	$-0.177645\pi$
$197$	1.82052e8	1.69654	0.848269	+	0.529566i	$0.177645\pi$
$198$	0	0
$199$	−1.82846e8	−1.64475	−0.822376	−	0.568945i	$-0.807352\pi$
$199$	−1.82846e8	−1.64475	−0.822376	+	0.568945i	$0.807352\pi$
$200$	−2.79994e8	−2.47482
$201$	0	0
$202$	−4.70261e6	−0.0401429
$203$	1.80744e8	1.51645
$204$	0	0
$205$	1.41197e8	1.14469
$206$	−6.49562e7	−0.517708
$207$	0	0
$208$	−1.22887e8	−0.946854
$209$	1.49661e7	0.113395
$210$	0	0
$211$	2.55859e8	1.87505	0.937524	−	0.347921i	$-0.113112\pi$
$211$	2.55859e8	1.87505	0.937524	+	0.347921i	$0.113112\pi$
$212$	1.81579e7	0.130885
$213$	0	0
$214$	2.36516e8	1.64973
$215$	1.29806e7	0.0890757
$216$	0	0
$217$	9.93795e6	0.0660219
$218$	−8.32433e7	−0.544191
$219$	0	0
$220$	1.02835e7	0.0651120
$221$	−6.22645e7	−0.388032
$222$	0	0
$223$	1.32058e8	0.797438	0.398719	−	0.917073i	$-0.369455\pi$
$223$	1.32058e8	0.797438	0.398719	+	0.917073i	$0.369455\pi$
$224$	4.23233e7	0.251600
$225$	0	0
$226$	−2.09262e8	−1.20590
$227$	−1.36717e8	−0.775767	−0.387883	−	0.921708i	$-0.626794\pi$
$227$	−1.36717e8	−0.775767	−0.387883	+	0.921708i	$0.626794\pi$
$228$	0	0
$229$	−1.80217e8	−0.991678	−0.495839	−	0.868414i	$-0.665139\pi$
$229$	−1.80217e8	−0.991678	−0.495839	+	0.868414i	$0.665139\pi$
$230$	−3.80341e8	−2.06123
$231$	0	0
$232$	−2.82176e8	−1.48358
$233$	1.02560e8	0.531168	0.265584	−	0.964088i	$-0.414435\pi$
$233$	1.02560e8	0.531168	0.265584	+	0.964088i	$0.414435\pi$
$234$	0	0
$235$	−3.91436e8	−1.96754
$236$	−4.08470e7	−0.202287
$237$	0	0
$238$	−7.45914e7	−0.358649
$239$	−1.74905e8	−0.828722	−0.414361	−	0.910113i	$-0.635995\pi$
$239$	−1.74905e8	−0.828722	−0.414361	+	0.910113i	$0.635995\pi$
$240$	0	0
$241$	7.30848e7	0.336331	0.168166	−	0.985759i	$-0.446216\pi$
$241$	7.30848e7	0.336331	0.168166	+	0.985759i	$0.446216\pi$
$242$	1.88248e7	0.0853838
$243$	0	0
$244$	−305777.	−0.00134754
$245$	−6.39884e7	−0.277984
$246$	0	0
$247$	9.71339e7	0.410139
$248$	−1.55150e7	−0.0645909
$249$	0	0
$250$	−5.76994e8	−2.33551
$251$	−2.48021e8	−0.989988	−0.494994	−	0.868896i	$-0.664830\pi$
$251$	−2.48021e8	−0.989988	−0.494994	+	0.868896i	$0.664830\pi$
$252$	0	0
$253$	9.30246e7	0.361140
$254$	1.93242e8	0.739919
$255$	0	0
$256$	−9.35444e7	−0.348480
$257$	−1.37536e8	−0.505417	−0.252708	−	0.967543i	$-0.581321\pi$
$257$	−1.37536e8	−0.505417	−0.252708	+	0.967543i	$0.581321\pi$
$258$	0	0
$259$	−1.79787e8	−0.642999
$260$	6.67427e7	0.235503
$261$	0	0
$262$	3.16141e8	1.08599
$263$	2.19671e8	0.744609	0.372305	−	0.928111i	$-0.378568\pi$
$263$	2.19671e8	0.744609	0.372305	+	0.928111i	$0.378568\pi$
$264$	0	0
$265$	6.16402e8	2.03471
$266$	1.16364e8	0.379082
$267$	0	0
$268$	5.43718e6	0.0172545
$269$	1.39454e8	0.436816	0.218408	−	0.975858i	$-0.429914\pi$
$269$	1.39454e8	0.436816	0.218408	+	0.975858i	$0.429914\pi$
$270$	0	0
$271$	1.73191e8	0.528606	0.264303	−	0.964440i	$-0.414858\pi$
$271$	1.73191e8	0.528606	0.264303	+	0.964440i	$0.414858\pi$
$272$	1.02533e8	0.308938
$273$	0	0
$274$	−1.81047e8	−0.531696
$275$	2.45107e8	0.710707
$276$	0	0
$277$	−3.67865e8	−1.03994	−0.519972	−	0.854184i	$-0.674058\pi$
$277$	−3.67865e8	−1.03994	−0.519972	+	0.854184i	$0.674058\pi$
$278$	6.33739e8	1.76911
$279$	0	0
$280$	7.58347e8	2.06450
$281$	−3.79512e7	−0.102036	−0.0510180	−	0.998698i	$-0.516247\pi$
$281$	−3.79512e7	−0.102036	−0.0510180	+	0.998698i	$0.516247\pi$
$282$	0	0
$283$	1.19413e8	0.313183	0.156591	−	0.987663i	$-0.449949\pi$
$283$	1.19413e8	0.313183	0.156591	+	0.987663i	$0.449949\pi$
$284$	1.62052e7	0.0419798
$285$	0	0
$286$	1.22178e8	0.308825
$287$	−2.68511e8	−0.670463
$288$	0	0
$289$	−3.58387e8	−0.873393
$290$	−1.00996e9	−2.43170
$291$	0	0
$292$	−6.51925e7	−0.153235
$293$	−1.56012e8	−0.362344	−0.181172	−	0.983451i	$-0.557989\pi$
$293$	−1.56012e8	−0.362344	−0.181172	+	0.983451i	$0.557989\pi$
$294$	0	0
$295$	−1.38662e9	−3.14471
$296$	2.80682e8	0.629062
$297$	0	0
$298$	−4.65087e8	−1.01807
$299$	6.03756e8	1.30621
$300$	0	0
$301$	−2.46848e7	−0.0521731
$302$	1.95431e8	0.408290
$303$	0	0
$304$	−1.59953e8	−0.326539
$305$	−1.03801e7	−0.0209485
$306$	0	0
$307$	6.18409e8	1.21981	0.609904	−	0.792475i	$-0.291208\pi$
$307$	6.18409e8	1.21981	0.609904	+	0.792475i	$0.291208\pi$
$308$	−1.95558e7	−0.0381372
$309$	0	0
$310$	−5.55309e7	−0.105869
$311$	−2.24098e8	−0.422452	−0.211226	−	0.977437i	$-0.567746\pi$
$311$	−2.24098e8	−0.422452	−0.211226	+	0.977437i	$0.567746\pi$
$312$	0	0
$313$	2.98737e7	0.0550660	0.0275330	−	0.999621i	$-0.491235\pi$
$313$	2.98737e7	0.0550660	0.0275330	+	0.999621i	$0.491235\pi$
$314$	1.09990e8	0.200493
$315$	0	0
$316$	1.19876e7	0.0213711
$317$	−5.29451e8	−0.933509	−0.466754	−	0.884387i	$-0.654577\pi$
$317$	−5.29451e8	−0.933509	−0.466754	+	0.884387i	$0.654577\pi$
$318$	0	0
$319$	2.47017e8	0.426049
$320$	−1.16900e9	−1.99430
$321$	0	0
$322$	7.23285e8	1.20730
$323$	−8.10455e7	−0.133820
$324$	0	0
$325$	1.59081e9	2.57056
$326$	5.49483e8	0.878401
$327$	0	0
$328$	4.19195e8	0.655931
$329$	7.44382e8	1.15242
$330$	0	0
$331$	−4.68831e8	−0.710588	−0.355294	−	0.934755i	$-0.615619\pi$
$331$	−4.68831e8	−0.710588	−0.355294	+	0.934755i	$0.615619\pi$
$332$	−9.63384e7	−0.144483
$333$	0	0
$334$	2.75606e8	0.404740
$335$	1.84574e8	0.268235
$336$	0	0
$337$	2.51716e8	0.358267	0.179134	−	0.983825i	$-0.442671\pi$
$337$	2.51716e8	0.358267	0.179134	+	0.983825i	$0.442671\pi$
$338$	1.26198e8	0.177764
$339$	0	0
$340$	−5.56880e7	−0.0768397
$341$	1.35818e7	0.0185489
$342$	0	0
$343$	−6.80367e8	−0.910361
$344$	3.85376e7	0.0510423
$345$	0	0
$346$	−4.80606e8	−0.623768
$347$	−8.97428e8	−1.15305	−0.576523	−	0.817081i	$-0.695591\pi$
$347$	−8.97428e8	−1.15305	−0.576523	+	0.817081i	$0.695591\pi$
$348$	0	0
$349$	6.22863e8	0.784338	0.392169	−	0.919893i	$-0.371725\pi$
$349$	6.22863e8	0.784338	0.392169	+	0.919893i	$0.371725\pi$
$350$	1.90575e9	2.37590
$351$	0	0
$352$	5.78417e7	0.0706874
$353$	1.40520e9	1.70030	0.850151	−	0.526538i	$-0.176510\pi$
$353$	1.40520e9	1.70030	0.850151	+	0.526538i	$0.176510\pi$
$354$	0	0
$355$	5.50114e8	0.652610
$356$	−1.91685e7	−0.0225171
$357$	0	0
$358$	−6.06433e8	−0.698541
$359$	−8.07630e7	−0.0921259	−0.0460630	−	0.998939i	$-0.514667\pi$
$359$	−8.07630e7	−0.0921259	−0.0460630	+	0.998939i	$0.514667\pi$
$360$	0	0
$361$	−7.67439e8	−0.858556
$362$	5.68114e8	0.629441
$363$	0	0
$364$	−1.26923e8	−0.137938
$365$	−2.21307e9	−2.38216
$366$	0	0
$367$	8.06769e8	0.851958	0.425979	−	0.904733i	$-0.359930\pi$
$367$	8.06769e8	0.851958	0.425979	+	0.904733i	$0.359930\pi$
$368$	−9.94221e8	−1.03996
$369$	0	0
$370$	1.00461e9	1.03108
$371$	−1.17219e9	−1.19177
$372$	0	0
$373$	7.72466e8	0.770723	0.385362	−	0.922766i	$-0.374077\pi$
$373$	7.72466e8	0.770723	0.385362	+	0.922766i	$0.374077\pi$
$374$	−1.01941e8	−0.100763
$375$	0	0
$376$	−1.16212e9	−1.12744
$377$	1.60321e9	1.54097
$378$	0	0
$379$	−1.16144e9	−1.09587	−0.547934	−	0.836522i	$-0.684585\pi$
$379$	−1.16144e9	−1.09587	−0.547934	+	0.836522i	$0.684585\pi$
$380$	8.68744e7	0.0812174
$381$	0	0
$382$	1.74187e9	1.59880
$383$	−2.45239e8	−0.223046	−0.111523	−	0.993762i	$-0.535573\pi$
$383$	−2.45239e8	−0.223046	−0.111523	+	0.993762i	$0.535573\pi$
$384$	0	0
$385$	−6.63857e8	−0.592873
$386$	5.47957e8	0.484943
$387$	0	0
$388$	1.25859e8	0.109389
$389$	−3.20778e8	−0.276300	−0.138150	−	0.990411i	$-0.544116\pi$
$389$	−3.20778e8	−0.276300	−0.138150	+	0.990411i	$0.544116\pi$
$390$	0	0
$391$	−5.03755e8	−0.426187
$392$	−1.89973e8	−0.159291
$393$	0	0
$394$	1.93450e9	1.59343
$395$	4.06940e8	0.332231
$396$	0	0
$397$	−7.88876e6	−0.00632764	−0.00316382	−	0.999995i	$-0.501007\pi$
$397$	−7.88876e6	−0.00632764	−0.00316382	+	0.999995i	$0.501007\pi$
$398$	−1.94294e9	−1.54479
$399$	0	0
$400$	−2.61963e9	−2.04659
$401$	−9.15449e8	−0.708972	−0.354486	−	0.935061i	$-0.615344\pi$
$401$	−9.15449e8	−0.708972	−0.354486	+	0.935061i	$0.615344\pi$
$402$	0	0
$403$	8.81500e7	0.0670895
$404$	6.67648e6	0.00503747
$405$	0	0
$406$	1.92060e9	1.42428
$407$	−2.45709e8	−0.180651
$408$	0	0
$409$	−1.03380e9	−0.747144	−0.373572	−	0.927601i	$-0.621867\pi$
$409$	−1.03380e9	−0.747144	−0.373572	+	0.927601i	$0.621867\pi$
$410$	1.50037e9	1.07512
$411$	0	0
$412$	9.22209e7	0.0649664
$413$	2.63690e9	1.84191
$414$	0	0
$415$	−3.27038e9	−2.24610
$416$	3.75409e8	0.255669
$417$	0	0
$418$	1.59031e8	0.106503
$419$	−6.02583e8	−0.400191	−0.200096	−	0.979776i	$-0.564125\pi$
$419$	−6.02583e8	−0.400191	−0.200096	+	0.979776i	$0.564125\pi$
$420$	0	0
$421$	2.65450e9	1.73379	0.866894	−	0.498492i	$-0.166113\pi$
$421$	2.65450e9	1.73379	0.866894	+	0.498492i	$0.166113\pi$
$422$	2.71878e9	1.76109
$423$	0	0
$424$	1.83002e9	1.16594
$425$	−1.32732e9	−0.838717
$426$	0	0
$427$	1.97396e7	0.0122699
$428$	−3.35791e8	−0.207022
$429$	0	0
$430$	1.37933e8	0.0836619
$431$	6.31002e8	0.379630	0.189815	−	0.981820i	$-0.439211\pi$
$431$	6.31002e8	0.379630	0.189815	+	0.981820i	$0.439211\pi$
$432$	0	0
$433$	−3.17507e9	−1.87952	−0.939758	−	0.341840i	$-0.888950\pi$
$433$	−3.17507e9	−1.87952	−0.939758	+	0.341840i	$0.888950\pi$
$434$	1.05602e8	0.0620092
$435$	0	0
$436$	1.18184e8	0.0682897
$437$	7.85867e8	0.450468
$438$	0	0
$439$	9.74824e8	0.549921	0.274960	−	0.961456i	$-0.411335\pi$
$439$	9.74824e8	0.549921	0.274960	+	0.961456i	$0.411335\pi$
$440$	1.03641e9	0.580023
$441$	0	0
$442$	−6.61628e8	−0.364449
$443$	9.30289e8	0.508399	0.254200	−	0.967152i	$-0.418188\pi$
$443$	9.30289e8	0.508399	0.254200	+	0.967152i	$0.418188\pi$
$444$	0	0
$445$	−6.50709e8	−0.350047
$446$	1.40326e9	0.748971
$447$	0	0
$448$	2.22306e9	1.16809
$449$	−2.18935e9	−1.14144	−0.570719	−	0.821145i	$-0.693335\pi$
$449$	−2.18935e9	−1.14144	−0.570719	+	0.821145i	$0.693335\pi$
$450$	0	0
$451$	−3.66964e8	−0.188367
$452$	2.97098e8	0.151327
$453$	0	0
$454$	−1.45276e9	−0.728617
$455$	−4.30862e9	−2.14436
$456$	0	0
$457$	−2.98855e9	−1.46472	−0.732358	−	0.680920i	$-0.761580\pi$
$457$	−2.98855e9	−1.46472	−0.732358	+	0.680920i	$0.761580\pi$
$458$	−1.91500e9	−0.931406
$459$	0	0
$460$	5.39986e8	0.258660
$461$	1.73041e9	0.822614	0.411307	−	0.911497i	$-0.365072\pi$
$461$	1.73041e9	0.822614	0.411307	+	0.911497i	$0.365072\pi$
$462$	0	0
$463$	1.17219e9	0.548866	0.274433	−	0.961606i	$-0.411510\pi$
$463$	1.17219e9	0.548866	0.274433	+	0.961606i	$0.411510\pi$
$464$	−2.64005e9	−1.22687
$465$	0	0
$466$	1.08981e9	0.498885
$467$	1.16283e9	0.528334	0.264167	−	0.964477i	$-0.414903\pi$
$467$	1.16283e9	0.528334	0.264167	+	0.964477i	$0.414903\pi$
$468$	0	0
$469$	−3.51000e8	−0.157109
$470$	−4.15943e9	−1.84795
$471$	0	0
$472$	−4.11670e9	−1.80199
$473$	−3.37358e7	−0.0146581
$474$	0	0
$475$	2.07065e9	0.886500
$476$	1.05900e8	0.0450063
$477$	0	0
$478$	−1.85855e9	−0.778354
$479$	−3.65352e9	−1.51893	−0.759464	−	0.650550i	$-0.774539\pi$
$479$	−3.65352e9	−1.51893	−0.759464	+	0.650550i	$0.774539\pi$
$480$	0	0
$481$	−1.59472e9	−0.653397
$482$	7.76605e8	0.315890
$483$	0	0
$484$	−2.67263e7	−0.0107147
$485$	4.27252e9	1.70054
$486$	0	0
$487$	−2.10390e9	−0.825417	−0.412709	−	0.910863i	$-0.635417\pi$
$487$	−2.10390e9	−0.825417	−0.412709	+	0.910863i	$0.635417\pi$
$488$	−3.08173e7	−0.0120040
$489$	0	0
$490$	−6.79946e8	−0.261089
$491$	−3.49825e9	−1.33372	−0.666861	−	0.745182i	$-0.732363\pi$
$491$	−3.49825e9	−1.33372	−0.666861	+	0.745182i	$0.732363\pi$
$492$	0	0
$493$	−1.33767e9	−0.502787
$494$	1.03215e9	0.385212
$495$	0	0
$496$	−1.45159e8	−0.0534144
$497$	−1.04614e9	−0.382245
$498$	0	0
$499$	−1.02908e9	−0.370763	−0.185381	−	0.982667i	$-0.559352\pi$
$499$	−1.02908e9	−0.370763	−0.185381	+	0.982667i	$0.559352\pi$
$500$	8.19182e8	0.293079
$501$	0	0
$502$	−2.63549e9	−0.929819
$503$	1.38834e9	0.486417	0.243209	−	0.969974i	$-0.421800\pi$
$503$	1.38834e9	0.486417	0.243209	+	0.969974i	$0.421800\pi$
$504$	0	0
$505$	2.26645e8	0.0783116
$506$	9.88488e8	0.339191
$507$	0	0
$508$	−2.74354e8	−0.0928513
$509$	9.79884e8	0.329354	0.164677	−	0.986348i	$-0.447342\pi$
$509$	9.79884e8	0.329354	0.164677	+	0.986348i	$0.447342\pi$
$510$	0	0
$511$	4.20854e9	1.39527
$512$	−3.38670e9	−1.11515
$513$	0	0
$514$	−1.46147e9	−0.474699
$515$	3.13060e9	1.00996
$516$	0	0
$517$	1.01732e9	0.323773
$518$	−1.91044e9	−0.603919
$519$	0	0
$520$	6.72656e9	2.09788
$521$	−4.61670e9	−1.43021	−0.715105	−	0.699017i	$-0.753621\pi$
$521$	−4.61670e9	−1.43021	−0.715105	+	0.699017i	$0.753621\pi$
$522$	0	0
$523$	5.19545e9	1.58806	0.794030	−	0.607878i	$-0.207979\pi$
$523$	5.19545e9	1.58806	0.794030	+	0.607878i	$0.207979\pi$
$524$	−4.48838e8	−0.136279
$525$	0	0
$526$	2.33425e9	0.699354
$527$	−7.35495e7	−0.0218899
$528$	0	0
$529$	1.47989e9	0.434646
$530$	6.54994e9	1.91105
$531$	0	0
$532$	−1.65207e8	−0.0475704
$533$	−2.38170e9	−0.681305
$534$	0	0
$535$	−1.13990e10	−3.21832
$536$	5.47977e8	0.153704
$537$	0	0
$538$	1.48185e9	0.410267
$539$	1.66303e8	0.0457444
$540$	0	0
$541$	5.44614e9	1.47876	0.739381	−	0.673288i	$-0.235118\pi$
$541$	5.44614e9	1.47876	0.739381	+	0.673288i	$0.235118\pi$
$542$	1.84034e9	0.496479
$543$	0	0
$544$	−3.13229e8	−0.0834192
$545$	4.01196e9	1.06162
$546$	0	0
$547$	−3.98073e9	−1.03994	−0.519969	−	0.854185i	$-0.674056\pi$
$547$	−3.98073e9	−1.03994	−0.519969	+	0.854185i	$0.674056\pi$
$548$	2.57039e8	0.0667218
$549$	0	0
$550$	2.60453e9	0.667512
$551$	2.08679e9	0.531432
$552$	0	0
$553$	−7.73866e8	−0.194593
$554$	−3.90897e9	−0.976738
$555$	0	0
$556$	−8.99745e8	−0.222002
$557$	−8.72453e8	−0.213919	−0.106959	−	0.994263i	$-0.534111\pi$
$557$	−8.72453e8	−0.213919	−0.106959	+	0.994263i	$0.534111\pi$
$558$	0	0
$559$	−2.18955e8	−0.0530168
$560$	7.09512e9	1.70727
$561$	0	0
$562$	−4.03273e8	−0.0958346
$563$	3.28829e9	0.776588	0.388294	−	0.921536i	$-0.373065\pi$
$563$	3.28829e9	0.776588	0.388294	+	0.921536i	$0.373065\pi$
$564$	0	0
$565$	1.00855e10	2.35250
$566$	1.26889e9	0.294148
$567$	0	0
$568$	1.63322e9	0.373960
$569$	−5.26548e9	−1.19824	−0.599121	−	0.800658i	$-0.704483\pi$
$569$	−5.26548e9	−1.19824	−0.599121	+	0.800658i	$0.704483\pi$
$570$	0	0
$571$	2.64249e9	0.594000	0.297000	−	0.954877i	$-0.404014\pi$
$571$	2.64249e9	0.594000	0.297000	+	0.954877i	$0.404014\pi$
$572$	−1.73461e8	−0.0387539
$573$	0	0
$574$	−2.85322e9	−0.629714
$575$	1.28705e10	2.82332
$576$	0	0
$577$	2.19983e9	0.476732	0.238366	−	0.971175i	$-0.423388\pi$
$577$	2.19983e9	0.476732	0.238366	+	0.971175i	$0.423388\pi$
$578$	−3.80825e9	−0.820311
$579$	0	0
$580$	1.43387e9	0.305150
$581$	6.21918e9	1.31558
$582$	0	0
$583$	−1.60200e9	−0.334828
$584$	−6.57032e9	−1.36503
$585$	0	0
$586$	−1.65779e9	−0.340321
$587$	4.39678e9	0.897225	0.448612	−	0.893726i	$-0.351918\pi$
$587$	4.39678e9	0.897225	0.448612	+	0.893726i	$0.351918\pi$
$588$	0	0
$589$	1.14739e8	0.0231370
$590$	−1.47344e10	−2.95358
$591$	0	0
$592$	2.62607e9	0.520212
$593$	3.88011e9	0.764104	0.382052	−	0.924141i	$-0.375218\pi$
$593$	3.88011e9	0.764104	0.382052	+	0.924141i	$0.375218\pi$
$594$	0	0
$595$	3.59497e9	0.699659
$596$	6.60302e8	0.127756
$597$	0	0
$598$	6.41556e9	1.22682
$599$	−5.84811e9	−1.11179	−0.555894	−	0.831253i	$-0.687624\pi$
$599$	−5.84811e9	−1.11179	−0.555894	+	0.831253i	$0.687624\pi$
$600$	0	0
$601$	−8.91798e9	−1.67574	−0.837868	−	0.545872i	$-0.816198\pi$
$601$	−8.91798e9	−1.67574	−0.837868	+	0.545872i	$0.816198\pi$
$602$	−2.62303e8	−0.0490022
$603$	0	0
$604$	−2.77461e8	−0.0512357
$605$	−9.07270e8	−0.166568
$606$	0	0
$607$	7.78861e9	1.41351	0.706756	−	0.707458i	$-0.250158\pi$
$607$	7.78861e9	1.41351	0.706756	+	0.707458i	$0.250158\pi$
$608$	4.88644e8	0.0881718
$609$	0	0
$610$	−1.10300e8	−0.0196753
$611$	6.60270e9	1.17105
$612$	0	0
$613$	−2.74753e9	−0.481761	−0.240880	−	0.970555i	$-0.577436\pi$
$613$	−2.74753e9	−0.481761	−0.240880	+	0.970555i	$0.577436\pi$
$614$	6.57127e9	1.14567
$615$	0	0
$616$	−1.97090e9	−0.339729
$617$	−9.83844e9	−1.68627	−0.843137	−	0.537699i	$-0.819294\pi$
$617$	−9.83844e9	−1.68627	−0.843137	+	0.537699i	$0.819294\pi$
$618$	0	0
$619$	−1.40412e8	−0.0237951	−0.0118976	−	0.999929i	$-0.503787\pi$
$619$	−1.40412e8	−0.0237951	−0.0118976	+	0.999929i	$0.503787\pi$
$620$	7.88394e7	0.0132853
$621$	0	0
$622$	−2.38129e9	−0.396776
$623$	1.23743e9	0.205028
$624$	0	0
$625$	1.34217e10	2.19901
$626$	3.17440e8	0.0517192
$627$	0	0
$628$	−1.56157e8	−0.0251595
$629$	1.33058e9	0.213189
$630$	0	0
$631$	6.82477e8	0.108140	0.0540699	−	0.998537i	$-0.482781\pi$
$631$	6.82477e8	0.108140	0.0540699	+	0.998537i	$0.482781\pi$
$632$	1.20815e9	0.190376
$633$	0	0
$634$	−5.62599e9	−0.876772
$635$	−9.31342e9	−1.44345
$636$	0	0
$637$	1.07935e9	0.165453
$638$	2.62482e9	0.400154
$639$	0	0
$640$	−9.57318e9	−1.44353
$641$	−1.23429e9	−0.185103	−0.0925517	−	0.995708i	$-0.529502\pi$
$641$	−1.23429e9	−0.185103	−0.0925517	+	0.995708i	$0.529502\pi$
$642$	0	0
$643$	−1.23695e10	−1.83491	−0.917454	−	0.397842i	$-0.869759\pi$
$643$	−1.23695e10	−1.83491	−0.917454	+	0.397842i	$0.869759\pi$
$644$	−1.02688e9	−0.151502
$645$	0	0
$646$	−8.61196e8	−0.125686
$647$	2.52538e9	0.366573	0.183287	−	0.983059i	$-0.441326\pi$
$647$	2.52538e9	0.366573	0.183287	+	0.983059i	$0.441326\pi$
$648$	0	0
$649$	3.60376e9	0.517487
$650$	1.69041e10	2.41432
$651$	0	0
$652$	−7.80123e8	−0.110229
$653$	1.19528e10	1.67986	0.839928	−	0.542699i	$-0.182597\pi$
$653$	1.19528e10	1.67986	0.839928	+	0.542699i	$0.182597\pi$
$654$	0	0
$655$	−1.52366e10	−2.11857
$656$	3.92201e9	0.542432
$657$	0	0
$658$	7.90987e9	1.08238
$659$	−8.29954e9	−1.12968	−0.564840	−	0.825201i	$-0.691062\pi$
$659$	−8.29954e9	−1.12968	−0.564840	+	0.825201i	$0.691062\pi$
$660$	0	0
$661$	4.49916e9	0.605935	0.302967	−	0.953001i	$-0.402023\pi$
$661$	4.49916e9	0.605935	0.302967	+	0.953001i	$0.402023\pi$
$662$	−4.98183e9	−0.667400
$663$	0	0
$664$	−9.70931e9	−1.28706
$665$	−5.60823e9	−0.739520
$666$	0	0
$667$	1.29708e10	1.69250
$668$	−3.91289e8	−0.0507902
$669$	0	0
$670$	1.96130e9	0.251932
$671$	2.69775e7	0.00344724
$672$	0	0
$673$	−6.55115e8	−0.0828447	−0.0414224	−	0.999142i	$-0.513189\pi$
$673$	−6.55115e8	−0.0828447	−0.0414224	+	0.999142i	$0.513189\pi$
$674$	2.67476e9	0.336492
$675$	0	0
$676$	−1.79168e8	−0.0223074
$677$	−1.18054e10	−1.46224	−0.731121	−	0.682248i	$-0.761002\pi$
$677$	−1.18054e10	−1.46224	−0.731121	+	0.682248i	$0.761002\pi$
$678$	0	0
$679$	−8.12492e9	−0.996036
$680$	−5.61243e9	−0.684494
$681$	0	0
$682$	1.44322e8	0.0174216
$683$	4.27330e8	0.0513205	0.0256602	−	0.999671i	$-0.491831\pi$
$683$	4.27330e8	0.0513205	0.0256602	+	0.999671i	$0.491831\pi$
$684$	0	0
$685$	8.72565e9	1.03724
$686$	−7.22964e9	−0.855031
$687$	0	0
$688$	3.60559e8	0.0422102
$689$	−1.03974e10	−1.21104
$690$	0	0
$691$	−1.47238e10	−1.69764	−0.848820	−	0.528681i	$-0.822687\pi$
$691$	−1.47238e10	−1.69764	−0.848820	+	0.528681i	$0.822687\pi$
$692$	6.82336e8	0.0782757
$693$	0	0
$694$	−9.53615e9	−1.08297
$695$	−3.05434e10	−3.45121
$696$	0	0
$697$	1.98721e9	0.222295
$698$	6.61859e9	0.736668
$699$	0	0
$700$	−2.70567e9	−0.298148
$701$	−1.04804e10	−1.14912	−0.574561	−	0.818461i	$-0.694827\pi$
$701$	−1.04804e10	−1.14912	−0.574561	+	0.818461i	$0.694827\pi$
$702$	0	0
$703$	−2.07574e9	−0.225335
$704$	3.03818e9	0.328177
$705$	0	0
$706$	1.49318e10	1.59696
$707$	−4.31004e8	−0.0458684
$708$	0	0
$709$	−5.07005e9	−0.534258	−0.267129	−	0.963661i	$-0.586075\pi$
$709$	−5.07005e9	−0.534258	−0.267129	+	0.963661i	$0.586075\pi$
$710$	5.84556e9	0.612946
$711$	0	0
$712$	−1.93187e9	−0.200585
$713$	7.13182e8	0.0736864
$714$	0	0
$715$	−5.88844e9	−0.602461
$716$	8.60977e8	0.0876589
$717$	0	0
$718$	−8.58195e8	−0.0865267
$719$	−4.77437e9	−0.479032	−0.239516	−	0.970892i	$-0.576989\pi$
$719$	−4.77437e9	−0.479032	−0.239516	+	0.970892i	$0.576989\pi$
$720$	0	0
$721$	−5.95337e9	−0.591548
$722$	−8.15488e9	−0.806375
$723$	0	0
$724$	−8.06574e8	−0.0789876
$725$	3.41764e10	3.33076
$726$	0	0
$727$	1.51188e9	0.145931	0.0729655	−	0.997334i	$-0.476754\pi$
$727$	1.51188e9	0.145931	0.0729655	+	0.997334i	$0.476754\pi$
$728$	−1.27917e10	−1.22877
$729$	0	0
$730$	−2.35163e10	−2.23738
$731$	1.82689e8	0.0172982
$732$	0	0
$733$	−8.39271e9	−0.787115	−0.393558	−	0.919300i	$-0.628756\pi$
$733$	−8.39271e9	−0.787115	−0.393558	+	0.919300i	$0.628756\pi$
$734$	8.57280e9	0.800177
$735$	0	0
$736$	3.03727e9	0.280809
$737$	−4.79700e8	−0.0441401
$738$	0	0
$739$	−1.05843e10	−0.964732	−0.482366	−	0.875970i	$-0.660222\pi$
$739$	−1.05843e10	−0.964732	−0.482366	+	0.875970i	$0.660222\pi$
$740$	−1.42628e9	−0.129388
$741$	0	0
$742$	−1.24558e10	−1.11933
$743$	1.40718e10	1.25860	0.629302	−	0.777161i	$-0.283341\pi$
$743$	1.40718e10	1.25860	0.629302	+	0.777161i	$0.283341\pi$
$744$	0	0
$745$	2.24151e10	1.98607
$746$	8.20829e9	0.723881
$747$	0	0
$748$	1.44730e8	0.0126446
$749$	2.16772e10	1.88502
$750$	0	0
$751$	1.84768e10	1.59180	0.795899	−	0.605430i	$-0.206999\pi$
$751$	1.84768e10	1.59180	0.795899	+	0.605430i	$0.206999\pi$
$752$	−1.08728e10	−0.932354
$753$	0	0
$754$	1.70358e10	1.44732
$755$	−9.41891e9	−0.796501
$756$	0	0
$757$	1.20946e10	1.01334	0.506671	−	0.862139i	$-0.330876\pi$
$757$	1.20946e10	1.01334	0.506671	+	0.862139i	$0.330876\pi$
$758$	−1.23415e10	−1.02926
$759$	0	0
$760$	8.75550e9	0.723492
$761$	1.65085e10	1.35788	0.678942	−	0.734192i	$-0.262439\pi$
$761$	1.65085e10	1.35788	0.678942	+	0.734192i	$0.262439\pi$
$762$	0	0
$763$	−7.62943e9	−0.621808
$764$	−2.47300e9	−0.200631
$765$	0	0
$766$	−2.60594e9	−0.209490
$767$	2.33894e10	1.87170
$768$	0	0
$769$	1.02708e10	0.814444	0.407222	−	0.913329i	$-0.366498\pi$
$769$	1.02708e10	0.814444	0.407222	+	0.913329i	$0.366498\pi$
$770$	−7.05420e9	−0.556840
$771$	0	0
$772$	−7.77957e8	−0.0608548
$773$	8.57433e9	0.667686	0.333843	−	0.942629i	$-0.391655\pi$
$773$	8.57433e9	0.667686	0.333843	+	0.942629i	$0.391655\pi$
$774$	0	0
$775$	1.87913e9	0.145011
$776$	1.26845e10	0.974448
$777$	0	0
$778$	−3.40861e9	−0.259507
$779$	−3.10009e9	−0.234960
$780$	0	0
$781$	−1.42972e9	−0.107392
$782$	−5.35294e9	−0.400285
$783$	0	0
$784$	−1.77740e9	−0.131728
$785$	−5.30101e9	−0.391125
$786$	0	0
$787$	2.36365e10	1.72851	0.864256	−	0.503052i	$-0.167790\pi$
$787$	2.36365e10	1.72851	0.864256	+	0.503052i	$0.167790\pi$
$788$	−2.74649e9	−0.199957
$789$	0	0
$790$	4.32418e9	0.312039
$791$	−1.91794e10	−1.37790
$792$	0	0
$793$	1.75091e8	0.0124683
$794$	−8.38267e7	−0.00594306
$795$	0	0
$796$	2.75847e9	0.193853
$797$	1.44253e10	1.00930	0.504650	−	0.863324i	$-0.331622\pi$
$797$	1.44253e10	1.00930	0.504650	+	0.863324i	$0.331622\pi$
$798$	0	0
$799$	−5.50908e9	−0.382090
$800$	8.00277e9	0.552618
$801$	0	0
$802$	−9.72764e9	−0.665882
$803$	5.75166e9	0.392003
$804$	0	0
$805$	−3.48591e10	−2.35522
$806$	9.36689e8	0.0630120
$807$	0	0
$808$	6.72878e8	0.0448742
$809$	−2.54447e10	−1.68957	−0.844787	−	0.535103i	$-0.820273\pi$
$809$	−2.54447e10	−1.68957	−0.844787	+	0.535103i	$0.820273\pi$
$810$	0	0
$811$	2.37251e10	1.56184	0.780918	−	0.624633i	$-0.214751\pi$
$811$	2.37251e10	1.56184	0.780918	+	0.624633i	$0.214751\pi$
$812$	−2.72676e9	−0.178731
$813$	0	0
$814$	−2.61093e9	−0.169672
$815$	−2.64826e10	−1.71360
$816$	0	0
$817$	−2.84999e8	−0.0182838
$818$	−1.09852e10	−0.701735
$819$	0	0
$820$	−2.13014e9	−0.134915
$821$	2.21648e10	1.39786	0.698928	−	0.715192i	$-0.253661\pi$
$821$	2.21648e10	1.39786	0.698928	+	0.715192i	$0.253661\pi$
$822$	0	0
$823$	−5.65346e9	−0.353521	−0.176760	−	0.984254i	$-0.556562\pi$
$823$	−5.65346e9	−0.353521	−0.176760	+	0.984254i	$0.556562\pi$
$824$	9.29434e9	0.578726
$825$	0	0
$826$	2.80199e10	1.72996
$827$	2.09164e10	1.28593	0.642967	−	0.765894i	$-0.277703\pi$
$827$	2.09164e10	1.28593	0.642967	+	0.765894i	$0.277703\pi$
$828$	0	0
$829$	5.12905e9	0.312677	0.156339	−	0.987704i	$-0.450031\pi$
$829$	5.12905e9	0.312677	0.156339	+	0.987704i	$0.450031\pi$
$830$	−3.47513e10	−2.10959
$831$	0	0
$832$	1.97186e10	1.18698
$833$	−9.00576e8	−0.0539837
$834$	0	0
$835$	−1.32830e10	−0.789574
$836$	−2.25782e8	−0.0133650
$837$	0	0
$838$	−6.40310e9	−0.375869
$839$	2.82987e10	1.65425	0.827123	−	0.562021i	$-0.189976\pi$
$839$	2.82987e10	1.65425	0.827123	+	0.562021i	$0.189976\pi$
$840$	0	0
$841$	1.71928e10	0.996692
$842$	2.82070e10	1.62841
$843$	0	0
$844$	−3.85996e9	−0.220996
$845$	−6.08219e9	−0.346786
$846$	0	0
$847$	1.72533e9	0.0975619
$848$	1.71217e10	0.964187
$849$	0	0
$850$	−1.41042e10	−0.787741
$851$	−1.29022e10	−0.717645
$852$	0	0
$853$	2.96443e9	0.163538	0.0817692	−	0.996651i	$-0.473943\pi$
$853$	2.96443e9	0.163538	0.0817692	+	0.996651i	$0.473943\pi$
$854$	2.09755e8	0.0115242
$855$	0	0
$856$	−3.38422e10	−1.84417
$857$	1.61651e10	0.877295	0.438648	−	0.898659i	$-0.355458\pi$
$857$	1.61651e10	0.877295	0.438648	+	0.898659i	$0.355458\pi$
$858$	0	0
$859$	−1.23861e10	−0.666744	−0.333372	−	0.942795i	$-0.608187\pi$
$859$	−1.23861e10	−0.666744	−0.333372	+	0.942795i	$0.608187\pi$
$860$	−1.95829e8	−0.0104986
$861$	0	0
$862$	6.70509e9	0.356557
$863$	−1.43200e10	−0.758414	−0.379207	−	0.925312i	$-0.623803\pi$
$863$	−1.43200e10	−0.758414	−0.379207	+	0.925312i	$0.623803\pi$
$864$	0	0
$865$	2.31631e10	1.21686
$866$	−3.37386e10	−1.76528
$867$	0	0
$868$	−1.49927e8	−0.00778144
$869$	−1.05762e9	−0.0546712
$870$	0	0
$871$	−3.11338e9	−0.159650
$872$	1.19110e10	0.608331
$873$	0	0
$874$	8.35069e9	0.423090
$875$	−5.28828e10	−2.66862
$876$	0	0
$877$	2.50398e9	0.125352	0.0626762	−	0.998034i	$-0.480036\pi$
$877$	2.50398e9	0.125352	0.0626762	+	0.998034i	$0.480036\pi$
$878$	1.03586e10	0.516498
$879$	0	0
$880$	9.69665e9	0.479659
$881$	5.20849e9	0.256623	0.128312	−	0.991734i	$-0.459044\pi$
$881$	5.20849e9	0.256623	0.128312	+	0.991734i	$0.459044\pi$
$882$	0	0
$883$	1.04253e10	0.509596	0.254798	−	0.966994i	$-0.417991\pi$
$883$	1.04253e10	0.509596	0.254798	+	0.966994i	$0.417991\pi$
$884$	9.39340e8	0.0457341
$885$	0	0
$886$	9.88533e9	0.477500
$887$	−6.11702e9	−0.294312	−0.147156	−	0.989113i	$-0.547012\pi$
$887$	−6.11702e9	−0.294312	−0.147156	+	0.989113i	$0.547012\pi$
$888$	0	0
$889$	1.77111e10	0.845452
$890$	−6.91449e9	−0.328772
$891$	0	0
$892$	−1.99226e9	−0.0939872
$893$	8.59428e9	0.403858
$894$	0	0
$895$	2.92274e10	1.36273
$896$	1.82050e10	0.845500
$897$	0	0
$898$	−2.32642e10	−1.07206
$899$	1.89378e9	0.0869301
$900$	0	0
$901$	8.67527e9	0.395136
$902$	−3.89939e9	−0.176919
$903$	0	0
$904$	2.99426e10	1.34803
$905$	−2.73806e10	−1.22793
$906$	0	0
$907$	−2.62413e10	−1.16778	−0.583889	−	0.811833i	$-0.698470\pi$
$907$	−2.62413e10	−1.16778	−0.583889	+	0.811833i	$0.698470\pi$
$908$	2.06255e9	0.0914331
$909$	0	0
$910$	−4.57837e10	−2.01403
$911$	2.13178e10	0.934173	0.467086	−	0.884212i	$-0.345304\pi$
$911$	2.13178e10	0.934173	0.467086	+	0.884212i	$0.345304\pi$
$912$	0	0
$913$	8.49954e9	0.369613
$914$	−3.17565e10	−1.37569
$915$	0	0
$916$	2.71880e9	0.116881
$917$	2.89750e10	1.24088
$918$	0	0
$919$	1.10481e9	0.0469551	0.0234775	−	0.999724i	$-0.492526\pi$
$919$	1.10481e9	0.0469551	0.0234775	+	0.999724i	$0.492526\pi$
$920$	5.44216e10	2.30417
$921$	0	0
$922$	1.83875e10	0.772617
$923$	−9.27928e9	−0.388426
$924$	0	0
$925$	−3.39954e10	−1.41229
$926$	1.24558e10	0.515507
$927$	0	0
$928$	8.06513e9	0.331279
$929$	2.03974e10	0.834679	0.417339	−	0.908751i	$-0.362963\pi$
$929$	2.03974e10	0.834679	0.417339	+	0.908751i	$0.362963\pi$
$930$	0	0
$931$	1.40492e9	0.0570593
$932$	−1.54725e9	−0.0626043
$933$	0	0
$934$	1.23564e10	0.496223
$935$	4.91312e9	0.196570
$936$	0	0
$937$	−7.48258e9	−0.297141	−0.148571	−	0.988902i	$-0.547467\pi$
$937$	−7.48258e9	−0.297141	−0.148571	+	0.988902i	$0.547467\pi$
$938$	−3.72976e9	−0.147561
$939$	0	0
$940$	5.90531e9	0.231897
$941$	3.93036e10	1.53769	0.768845	−	0.639435i	$-0.220832\pi$
$941$	3.93036e10	1.53769	0.768845	+	0.639435i	$0.220832\pi$
$942$	0	0
$943$	−1.92693e10	−0.748297
$944$	−3.85160e10	−1.49018
$945$	0	0
$946$	−3.58480e8	−0.0137672
$947$	−2.90226e10	−1.11048	−0.555241	−	0.831690i	$-0.687374\pi$
$947$	−2.90226e10	−1.11048	−0.555241	+	0.831690i	$0.687374\pi$
$948$	0	0
$949$	3.73299e10	1.41783
$950$	2.20029e10	0.832621
$951$	0	0
$952$	1.06730e10	0.400920
$953$	−1.70185e10	−0.636937	−0.318468	−	0.947934i	$-0.603168\pi$
$953$	−1.70185e10	−0.636937	−0.318468	+	0.947934i	$0.603168\pi$
$954$	0	0
$955$	−8.39503e10	−3.11896
$956$	2.63866e9	0.0976744
$957$	0	0
$958$	−3.88226e10	−1.42661
$959$	−1.65933e10	−0.607531
$960$	0	0
$961$	−2.74085e10	−0.996215
$962$	−1.69456e10	−0.613685
$963$	0	0
$964$	−1.10258e9	−0.0396405
$965$	−2.64091e10	−0.946037
$966$	0	0
$967$	−2.36228e10	−0.840117	−0.420058	−	0.907497i	$-0.637990\pi$
$967$	−2.36228e10	−0.840117	−0.420058	+	0.907497i	$0.637990\pi$
$968$	−2.69357e9	−0.0954473
$969$	0	0
$970$	4.54001e10	1.59719
$971$	−2.51769e10	−0.882541	−0.441270	−	0.897374i	$-0.645472\pi$
$971$	−2.51769e10	−0.882541	−0.441270	+	0.897374i	$0.645472\pi$
$972$	0	0
$973$	5.80836e10	2.02143
$974$	−2.23562e10	−0.775250
$975$	0	0
$976$	−2.88328e8	−0.00992686
$977$	−2.40625e10	−0.825487	−0.412743	−	0.910847i	$-0.635429\pi$
$977$	−2.40625e10	−0.825487	−0.412743	+	0.910847i	$0.635429\pi$
$978$	0	0
$979$	1.69116e9	0.0576030
$980$	9.65347e8	0.0327636
$981$	0	0
$982$	−3.71727e10	−1.25266
$983$	1.58590e10	0.532522	0.266261	−	0.963901i	$-0.414212\pi$
$983$	1.58590e10	0.532522	0.266261	+	0.963901i	$0.414212\pi$
$984$	0	0
$985$	−9.32343e10	−3.10849
$986$	−1.42142e10	−0.472228
$987$	0	0
$988$	−1.46539e9	−0.0483397
$989$	−1.77147e9	−0.0582299
$990$	0	0
$991$	−1.43183e10	−0.467340	−0.233670	−	0.972316i	$-0.575074\pi$
$991$	−1.43183e10	−0.467340	−0.233670	+	0.972316i	$0.575074\pi$
$992$	4.43449e8	0.0144229
$993$	0	0
$994$	−1.11163e10	−0.359013
$995$	9.36411e10	3.01360
$996$	0	0
$997$	5.74847e10	1.83704	0.918521	−	0.395373i	$-0.129385\pi$
$997$	5.74847e10	1.83704	0.918521	+	0.395373i	$0.129385\pi$
$998$	−1.09351e10	−0.348229
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.g.1.3		4
3.2	odd	2		11.8.a.b.1.2	✓	4
12.11	even	2		176.8.a.j.1.2		4
15.14	odd	2		275.8.a.b.1.3		4
21.20	even	2		539.8.a.b.1.2		4
33.32	even	2		121.8.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.a.b.1.2	✓	4	3.2	odd	2
99.8.a.g.1.3		4	1.1	even	1	trivial
121.8.a.c.1.3		4	33.32	even	2
176.8.a.j.1.2		4	12.11	even	2
275.8.a.b.1.3		4	15.14	odd	2
539.8.a.b.1.2		4	21.20	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

\(f(q)\)	\(=\)	\(q+10.6261 q^{2} -15.0863 q^{4} -512.130 q^{5} +973.904 q^{7} -1520.45 q^{8} +O(q^{10})\)	\(q+10.6261 q^{2} -15.0863 q^{4} -512.130 q^{5} +973.904 q^{7} -1520.45 q^{8} -5441.94 q^{10} +1331.00 q^{11} +8638.56 q^{13} +10348.8 q^{14} -14225.4 q^{16} -7207.74 q^{17} +11244.2 q^{19} +7726.14 q^{20} +14143.3 q^{22} +69890.8 q^{23} +184152. q^{25} +91794.1 q^{26} -14692.6 q^{28} +185587. q^{29} +10204.2 q^{31} +43457.3 q^{32} -76590.1 q^{34} -498766. q^{35} -184605. q^{37} +119482. q^{38} +778667. q^{40} -275705. q^{41} -25346.2 q^{43} -20079.8 q^{44} +742665. q^{46} +764328. q^{47} +124946. q^{49} +1.95682e6 q^{50} -130324. q^{52} -1.20360e6 q^{53} -681645. q^{55} -1.48077e6 q^{56} +1.97207e6 q^{58} +2.70756e6 q^{59} +20268.6 q^{61} +108431. q^{62} +2.28263e6 q^{64} -4.42407e6 q^{65} -360405. q^{67} +108738. q^{68} -5.29993e6 q^{70} -1.07417e6 q^{71} +4.32131e6 q^{73} -1.96163e6 q^{74} -169633. q^{76} +1.29627e6 q^{77} -794602. q^{79} +7.28524e6 q^{80} -2.92967e6 q^{82} +6.38583e6 q^{83} +3.69130e6 q^{85} -269331. q^{86} -2.02372e6 q^{88} +1.27059e6 q^{89} +8.41313e6 q^{91} -1.05439e6 q^{92} +8.12182e6 q^{94} -5.75851e6 q^{95} -8.34264e6 q^{97} +1.32768e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 604 q^{4} - 537 q^{5} + 170 q^{7} + 420 q^{8}+O(q^{10}) \) 4 * q + 604 * q^4 - 537 * q^5 + 170 * q^7 + 420 * q^8	\( 4 q + 604 q^{4} - 537 q^{5} + 170 q^{7} + 420 q^{8} + 1470 q^{10} + 5324 q^{11} + 4250 q^{13} + 29988 q^{14} + 52744 q^{16} - 54300 q^{17} + 67844 q^{19} - 15888 q^{20} + 9015 q^{23} + 22531 q^{25} + 311700 q^{26} - 475840 q^{28} - 234078 q^{29} + 189857 q^{31} + 175560 q^{32} + 406536 q^{34} - 154098 q^{35} + 127895 q^{37} + 584760 q^{38} + 2249268 q^{40} - 289842 q^{41} + 704930 q^{43} + 803924 q^{44} + 3519102 q^{46} + 1729080 q^{47} + 139920 q^{49} + 2115918 q^{50} + 2030120 q^{52} - 1098660 q^{53} - 714747 q^{55} + 4311720 q^{56} + 1046100 q^{58} + 4665777 q^{59} + 310610 q^{61} - 4286670 q^{62} + 9539488 q^{64} - 4526160 q^{65} - 3368245 q^{67} - 14958120 q^{68} - 12580596 q^{70} + 3416541 q^{71} + 11466230 q^{73} + 16581438 q^{74} + 2169824 q^{76} + 226270 q^{77} + 566282 q^{79} + 4469544 q^{80} - 11151780 q^{82} + 4220790 q^{83} + 10312902 q^{85} + 5991972 q^{86} + 559020 q^{88} - 18265191 q^{89} - 1133480 q^{91} + 6399240 q^{92} + 8464656 q^{94} + 5662968 q^{95} + 11425325 q^{97} - 36460200 q^{98}+O(q^{100}) \) 4 * q + 604 * q^4 - 537 * q^5 + 170 * q^7 + 420 * q^8 + 1470 * q^10 + 5324 * q^11 + 4250 * q^13 + 29988 * q^14 + 52744 * q^16 - 54300 * q^17 + 67844 * q^19 - 15888 * q^20 + 9015 * q^23 + 22531 * q^25 + 311700 * q^26 - 475840 * q^28 - 234078 * q^29 + 189857 * q^31 + 175560 * q^32 + 406536 * q^34 - 154098 * q^35 + 127895 * q^37 + 584760 * q^38 + 2249268 * q^40 - 289842 * q^41 + 704930 * q^43 + 803924 * q^44 + 3519102 * q^46 + 1729080 * q^47 + 139920 * q^49 + 2115918 * q^50 + 2030120 * q^52 - 1098660 * q^53 - 714747 * q^55 + 4311720 * q^56 + 1046100 * q^58 + 4665777 * q^59 + 310610 * q^61 - 4286670 * q^62 + 9539488 * q^64 - 4526160 * q^65 - 3368245 * q^67 - 14958120 * q^68 - 12580596 * q^70 + 3416541 * q^71 + 11466230 * q^73 + 16581438 * q^74 + 2169824 * q^76 + 226270 * q^77 + 566282 * q^79 + 4469544 * q^80 - 11151780 * q^82 + 4220790 * q^83 + 10312902 * q^85 + 5991972 * q^86 + 559020 * q^88 - 18265191 * q^89 - 1133480 * q^91 + 6399240 * q^92 + 8464656 * q^94 + 5662968 * q^95 + 11425325 * q^97 - 36460200 * q^98

Introduction

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