LMFDB - Embedded newform 99.8.a.g.1.2

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			1.2
Root			$1.64802$ 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)

$f(q)$	$=$	$q-11.0598 q^{2} -5.68000 q^{4} +60.1766 q^{5} +698.069 q^{7} +1478.48 q^{8} +O(q^{10})$	\(q-11.0598 q^{2} -5.68000 q^{4} +60.1766 q^{5} +698.069 q^{7} +1478.48 q^{8} -665.544 q^{10} +1331.00 q^{11} -10970.2 q^{13} -7720.53 q^{14} -15624.7 q^{16} +1820.14 q^{17} +49614.4 q^{19} -341.803 q^{20} -14720.6 q^{22} -80659.2 q^{23} -74503.8 q^{25} +121329. q^{26} -3965.03 q^{28} -88686.8 q^{29} +176260. q^{31} -16438.7 q^{32} -20130.5 q^{34} +42007.4 q^{35} +106270. q^{37} -548728. q^{38} +88969.9 q^{40} +464715. q^{41} +837231. q^{43} -7560.08 q^{44} +892077. q^{46} +679973. q^{47} -336243. q^{49} +824000. q^{50} +62310.8 q^{52} +177071. q^{53} +80095.1 q^{55} +1.03208e6 q^{56} +980861. q^{58} +2.54327e6 q^{59} -23420.1 q^{61} -1.94941e6 q^{62} +2.18177e6 q^{64} -660150. q^{65} -1.88677e6 q^{67} -10338.4 q^{68} -464595. q^{70} +4.49270e6 q^{71} +3.15445e6 q^{73} -1.17533e6 q^{74} -281810. q^{76} +929130. q^{77} +4.45391e6 q^{79} -940241. q^{80} -5.13968e6 q^{82} -2.74298e6 q^{83} +109530. q^{85} -9.25964e6 q^{86} +1.96786e6 q^{88} -1.10880e7 q^{89} -7.65796e6 q^{91} +458144. q^{92} -7.52039e6 q^{94} +2.98563e6 q^{95} -3.95601e6 q^{97} +3.71879e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.0598	−0.977561	−0.488780	−	0.872407i	$-0.662558\pi$
$2$	−11.0598	−0.977561	−0.488780	+	0.872407i	$0.662558\pi$
$3$	0	0
$3$	0	0
$4$	−5.68000	−0.0443750
$5$	60.1766	0.215294	0.107647	−	0.994189i	$-0.465668\pi$
$5$	60.1766	0.215294	0.107647	+	0.994189i	$0.465668\pi$
$6$	0	0
$7$	698.069	0.769228	0.384614	−	0.923077i	$-0.374335\pi$
$7$	698.069	0.769228	0.384614	+	0.923077i	$0.374335\pi$
$8$	1478.48	1.02094
$9$	0	0
$10$	−665.544	−0.210463
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	−10970.2	−1.38488	−0.692441	−	0.721474i	$-0.743465\pi$
$13$	−10970.2	−1.38488	−0.692441	+	0.721474i	$0.743465\pi$
$14$	−7720.53	−0.751967
$15$	0	0
$16$	−15624.7	−0.953656
$17$	1820.14	0.0898533	0.0449266	−	0.998990i	$-0.485695\pi$
$17$	1820.14	0.0898533	0.0449266	+	0.998990i	$0.485695\pi$
$18$	0	0
$19$	49614.4	1.65947	0.829737	−	0.558154i	$-0.188490\pi$
$19$	49614.4	1.65947	0.829737	+	0.558154i	$0.188490\pi$
$20$	−341.803	−0.00955369
$21$	0	0
$22$	−14720.6	−0.294746
$23$	−80659.2	−1.38231	−0.691157	−	0.722705i	$-0.742898\pi$
$23$	−80659.2	−1.38231	−0.691157	+	0.722705i	$0.742898\pi$
$24$	0	0
$25$	−74503.8	−0.953648
$26$	121329.	1.35381
$27$	0	0
$28$	−3965.03	−0.0341345
$29$	−88686.8	−0.675252	−0.337626	−	0.941280i	$-0.609624\pi$
$29$	−88686.8	−0.675252	−0.337626	+	0.941280i	$0.609624\pi$
$30$	0	0
$31$	176260.	1.06265	0.531323	−	0.847170i	$-0.321695\pi$
$31$	176260.	1.06265	0.531323	+	0.847170i	$0.321695\pi$
$32$	−16438.7	−0.0886835
$33$	0	0
$34$	−20130.5	−0.0878370
$35$	42007.4	0.165611
$36$	0	0
$37$	106270.	0.344909	0.172454	−	0.985017i	$-0.444830\pi$
$37$	106270.	0.344909	0.172454	+	0.985017i	$0.444830\pi$
$38$	−548728.	−1.62224
$39$	0	0
$40$	88969.9	0.219803
$41$	464715.	1.05304	0.526519	−	0.850164i	$-0.323497\pi$
$41$	464715.	1.05304	0.526519	+	0.850164i	$0.323497\pi$
$42$	0	0
$43$	837231.	1.60585	0.802927	−	0.596078i	$-0.203275\pi$
$43$	837231.	1.60585	0.802927	+	0.596078i	$0.203275\pi$
$44$	−7560.08	−0.0133796
$45$	0	0
$46$	892077.	1.35129
$47$	679973.	0.955321	0.477661	−	0.878544i	$-0.341485\pi$
$47$	679973.	0.955321	0.477661	+	0.878544i	$0.341485\pi$
$48$	0	0
$49$	−336243.	−0.408288
$50$	824000.	0.932249
$51$	0	0
$52$	62310.8	0.0614542
$53$	177071.	0.163374	0.0816868	−	0.996658i	$-0.473969\pi$
$53$	177071.	0.163374	0.0816868	+	0.996658i	$0.473969\pi$
$54$	0	0
$55$	80095.1	0.0649137
$56$	1.03208e6	0.785336
$57$	0	0
$58$	980861.	0.660100
$59$	2.54327e6	1.61217	0.806083	−	0.591803i	$-0.201583\pi$
$59$	2.54327e6	1.61217	0.806083	+	0.591803i	$0.201583\pi$
$60$	0	0
$61$	−23420.1	−0.0132110	−0.00660548	−	0.999978i	$-0.502103\pi$
$61$	−23420.1	−0.0132110	−0.00660548	+	0.999978i	$0.502103\pi$
$62$	−1.94941e6	−1.03880
$63$	0	0
$64$	2.18177e6	1.04035
$65$	−660150.	−0.298158
$66$	0	0
$67$	−1.88677e6	−0.766404	−0.383202	−	0.923665i	$-0.625179\pi$
$67$	−1.88677e6	−0.766404	−0.383202	+	0.923665i	$0.625179\pi$
$68$	−10338.4	−0.00398724
$69$	0	0
$70$	−464595.	−0.161894
$71$	4.49270e6	1.48971	0.744857	−	0.667224i	$-0.232517\pi$
$71$	4.49270e6	1.48971	0.744857	+	0.667224i	$0.232517\pi$
$72$	0	0
$73$	3.15445e6	0.949058	0.474529	−	0.880240i	$-0.342618\pi$
$73$	3.15445e6	0.949058	0.474529	+	0.880240i	$0.342618\pi$
$74$	−1.17533e6	−0.337169
$75$	0	0
$76$	−281810.	−0.0736392
$77$	929130.	0.231931
$78$	0	0
$79$	4.45391e6	1.01636	0.508178	−	0.861252i	$-0.330319\pi$
$79$	4.45391e6	1.01636	0.508178	+	0.861252i	$0.330319\pi$
$80$	−940241.	−0.205317
$81$	0	0
$82$	−5.13968e6	−1.02941
$83$	−2.74298e6	−0.526562	−0.263281	−	0.964719i	$-0.584805\pi$
$83$	−2.74298e6	−0.526562	−0.263281	+	0.964719i	$0.584805\pi$
$84$	0	0
$85$	109530.	0.0193449
$86$	−9.25964e6	−1.56982
$87$	0	0
$88$	1.96786e6	0.307825
$89$	−1.10880e7	−1.66721	−0.833603	−	0.552365i	$-0.813726\pi$
$89$	−1.10880e7	−1.66721	−0.833603	+	0.552365i	$0.813726\pi$
$90$	0	0
$91$	−7.65796e6	−1.06529
$92$	458144.	0.0613402
$93$	0	0
$94$	−7.52039e6	−0.933884
$95$	2.98563e6	0.357276
$96$	0	0
$97$	−3.95601e6	−0.440105	−0.220053	−	0.975488i	$-0.570623\pi$
$97$	−3.95601e6	−0.440105	−0.220053	+	0.975488i	$0.570623\pi$
$98$	3.71879e6	0.399126
$99$	0	0
$100$	423182.	0.0423182
$101$	818011.	0.0790013	0.0395007	−	0.999220i	$-0.487423\pi$
$101$	818011.	0.0790013	0.0395007	+	0.999220i	$0.487423\pi$
$102$	0	0
$103$	750708.	0.0676925	0.0338463	−	0.999427i	$-0.489224\pi$
$103$	750708.	0.0676925	0.0338463	+	0.999427i	$0.489224\pi$
$104$	−1.62192e7	−1.41388
$105$	0	0
$106$	−1.95838e6	−0.159708
$107$	9.70597e6	0.765942	0.382971	−	0.923760i	$-0.374901\pi$
$107$	9.70597e6	0.765942	0.382971	+	0.923760i	$0.374901\pi$
$108$	0	0
$109$	65223.6	0.00482406	0.00241203	−	0.999997i	$-0.499232\pi$
$109$	65223.6	0.00482406	0.00241203	+	0.999997i	$0.499232\pi$
$110$	−885839.	−0.0634571
$111$	0	0
$112$	−1.09071e7	−0.733579
$113$	1.58160e7	1.03115	0.515574	−	0.856845i	$-0.327579\pi$
$113$	1.58160e7	1.03115	0.515574	+	0.856845i	$0.327579\pi$
$114$	0	0
$115$	−4.85380e6	−0.297604
$116$	503741.	0.0299643
$117$	0	0
$118$	−2.81281e7	−1.57599
$119$	1.27058e6	0.0691177
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	259023.	0.0129145
$123$	0	0
$124$	−1.00116e6	−0.0471549
$125$	−9.18468e6	−0.420610
$126$	0	0
$127$	2.14149e7	0.927690	0.463845	−	0.885916i	$-0.346469\pi$
$127$	2.14149e7	0.927690	0.463845	+	0.885916i	$0.346469\pi$
$128$	−2.20259e7	−0.928321
$129$	0	0
$130$	7.30115e6	0.291467
$131$	5.41196e6	0.210332	0.105166	−	0.994455i	$-0.466463\pi$
$131$	5.41196e6	0.210332	0.105166	+	0.994455i	$0.466463\pi$
$132$	0	0
$133$	3.46343e7	1.27651
$134$	2.08674e7	0.749206
$135$	0	0
$136$	2.69104e6	0.0917348
$137$	4.18596e7	1.39083	0.695413	−	0.718610i	$-0.255221\pi$
$137$	4.18596e7	1.39083	0.695413	+	0.718610i	$0.255221\pi$
$138$	0	0
$139$	−2.86132e7	−0.903681	−0.451840	−	0.892099i	$-0.649232\pi$
$139$	−2.86132e7	−0.903681	−0.451840	+	0.892099i	$0.649232\pi$
$140$	−238602.	−0.00734897
$141$	0	0
$142$	−4.96885e7	−1.45629
$143$	−1.46013e7	−0.417558
$144$	0	0
$145$	−5.33687e6	−0.145378
$146$	−3.48877e7	−0.927762
$147$	0	0
$148$	−603614.	−0.0153053
$149$	−4.55561e6	−0.112822	−0.0564111	−	0.998408i	$-0.517966\pi$
$149$	−4.55561e6	−0.112822	−0.0564111	+	0.998408i	$0.517966\pi$
$150$	0	0
$151$	5.18767e7	1.22618	0.613089	−	0.790014i	$-0.289927\pi$
$151$	5.18767e7	1.22618	0.613089	+	0.790014i	$0.289927\pi$
$152$	7.33539e7	1.69422
$153$	0	0
$154$	−1.02760e7	−0.226727
$155$	1.06067e7	0.228782
$156$	0	0
$157$	5.01985e7	1.03524	0.517621	−	0.855610i	$-0.326818\pi$
$157$	5.01985e7	1.03524	0.517621	+	0.855610i	$0.326818\pi$
$158$	−4.92595e7	−0.993551
$159$	0	0
$160$	−989226.	−0.0190931
$161$	−5.63057e7	−1.06331
$162$	0	0
$163$	3.13082e7	0.566242	0.283121	−	0.959084i	$-0.408630\pi$
$163$	3.13082e7	0.566242	0.283121	+	0.959084i	$0.408630\pi$
$164$	−2.63958e6	−0.0467285
$165$	0	0
$166$	3.03369e7	0.514747
$167$	−3.30269e6	−0.0548731	−0.0274366	−	0.999624i	$-0.508734\pi$
$167$	−3.30269e6	−0.0548731	−0.0274366	+	0.999624i	$0.508734\pi$
$168$	0	0
$169$	5.75969e7	0.917901
$170$	−1.21138e6	−0.0189108
$171$	0	0
$172$	−4.75547e6	−0.0712598
$173$	−1.76609e7	−0.259329	−0.129664	−	0.991558i	$-0.541390\pi$
$173$	−1.76609e7	−0.259329	−0.129664	+	0.991558i	$0.541390\pi$
$174$	0	0
$175$	−5.20088e7	−0.733573
$176$	−2.07965e7	−0.287538
$177$	0	0
$178$	1.22632e8	1.62979
$179$	−2.48730e7	−0.324148	−0.162074	−	0.986779i	$-0.551818\pi$
$179$	−2.48730e7	−0.324148	−0.162074	+	0.986779i	$0.551818\pi$
$180$	0	0
$181$	−1.60151e6	−0.0200749	−0.0100374	−	0.999950i	$-0.503195\pi$
$181$	−1.60151e6	−0.0200749	−0.0100374	+	0.999950i	$0.503195\pi$
$182$	8.46958e7	1.04139
$183$	0	0
$184$	−1.19253e8	−1.41126
$185$	6.39497e6	0.0742570
$186$	0	0
$187$	2.42261e6	0.0270918
$188$	−3.86225e6	−0.0423924
$189$	0	0
$190$	−3.30206e7	−0.349259
$191$	1.34327e8	1.39491	0.697454	−	0.716630i	$-0.254316\pi$
$191$	1.34327e8	1.39491	0.697454	+	0.716630i	$0.254316\pi$
$192$	0	0
$193$	−1.67372e8	−1.67584	−0.837919	−	0.545795i	$-0.816228\pi$
$193$	−1.67372e8	−1.67584	−0.837919	+	0.545795i	$0.816228\pi$
$194$	4.37529e7	0.430230
$195$	0	0
$196$	1.90986e6	0.0181178
$197$	8.17612e7	0.761930	0.380965	−	0.924589i	$-0.375592\pi$
$197$	8.17612e7	0.761930	0.380965	+	0.924589i	$0.375592\pi$
$198$	0	0
$199$	2.04375e8	1.83841	0.919206	−	0.393778i	$-0.128832\pi$
$199$	2.04375e8	1.83841	0.919206	+	0.393778i	$0.128832\pi$
$200$	−1.10152e8	−0.973618
$201$	0	0
$202$	−9.04707e6	−0.0772286
$203$	−6.19095e7	−0.519423
$204$	0	0
$205$	2.79650e7	0.226713
$206$	−8.30271e6	−0.0661735
$207$	0	0
$208$	1.71406e8	1.32070
$209$	6.60368e7	0.500350
$210$	0	0
$211$	−1.14120e8	−0.836319	−0.418159	−	0.908374i	$-0.637325\pi$
$211$	−1.14120e8	−0.836319	−0.418159	+	0.908374i	$0.637325\pi$
$212$	−1.00576e6	−0.00724970
$213$	0	0
$214$	−1.07346e8	−0.748754
$215$	5.03817e7	0.345731
$216$	0	0
$217$	1.23042e8	0.817417
$218$	−721363.	−0.00471581
$219$	0	0
$220$	−454940.	−0.00288055
$221$	−1.99673e7	−0.124436
$222$	0	0
$223$	2.10742e8	1.27258	0.636288	−	0.771452i	$-0.280469\pi$
$223$	2.10742e8	1.27258	0.636288	+	0.771452i	$0.280469\pi$
$224$	−1.14754e7	−0.0682178
$225$	0	0
$226$	−1.74922e8	−1.00801
$227$	−2.75513e8	−1.56334	−0.781668	−	0.623695i	$-0.785631\pi$
$227$	−2.75513e8	−1.56334	−0.781668	+	0.623695i	$0.785631\pi$
$228$	0	0
$229$	2.46934e8	1.35880	0.679402	−	0.733767i	$-0.262239\pi$
$229$	2.46934e8	1.35880	0.679402	+	0.733767i	$0.262239\pi$
$230$	5.36822e7	0.290926
$231$	0	0
$232$	−1.31122e8	−0.689392
$233$	1.43817e8	0.744841	0.372421	−	0.928064i	$-0.378528\pi$
$233$	1.43817e8	0.744841	0.372421	+	0.928064i	$0.378528\pi$
$234$	0	0
$235$	4.09185e7	0.205675
$236$	−1.44458e7	−0.0715399
$237$	0	0
$238$	−1.40525e7	−0.0675667
$239$	1.04920e8	0.497123	0.248561	−	0.968616i	$-0.420042\pi$
$239$	1.04920e8	0.497123	0.248561	+	0.968616i	$0.420042\pi$
$240$	0	0
$241$	−7.87388e7	−0.362351	−0.181175	−	0.983451i	$-0.557990\pi$
$241$	−7.87388e7	−0.362351	−0.181175	+	0.983451i	$0.557990\pi$
$242$	−1.95932e7	−0.0888692
$243$	0	0
$244$	133026.	0.000586237 0
$245$	−2.02339e7	−0.0879021
$246$	0	0
$247$	−5.44281e8	−2.29818
$248$	2.60597e8	1.08490
$249$	0	0
$250$	1.01581e8	0.411171
$251$	1.47720e8	0.589634	0.294817	−	0.955554i	$-0.404741\pi$
$251$	1.47720e8	0.589634	0.294817	+	0.955554i	$0.404741\pi$
$252$	0	0
$253$	−1.07357e8	−0.416783
$254$	−2.36845e8	−0.906873
$255$	0	0
$256$	−3.56641e7	−0.132859
$257$	−1.68032e8	−0.617484	−0.308742	−	0.951146i	$-0.599908\pi$
$257$	−1.68032e8	−0.617484	−0.308742	+	0.951146i	$0.599908\pi$
$258$	0	0
$259$	7.41838e7	0.265314
$260$	3.74965e6	0.0132307
$261$	0	0
$262$	−5.98554e7	−0.205612
$263$	−2.11675e8	−0.717503	−0.358751	−	0.933433i	$-0.616797\pi$
$263$	−2.11675e8	−0.717503	−0.358751	+	0.933433i	$0.616797\pi$
$264$	0	0
$265$	1.06555e7	0.0351734
$266$	−3.83050e8	−1.24787
$267$	0	0
$268$	1.07169e7	0.0340092
$269$	−9.94546e7	−0.311524	−0.155762	−	0.987795i	$-0.549783\pi$
$269$	−9.94546e7	−0.311524	−0.155762	+	0.987795i	$0.549783\pi$
$270$	0	0
$271$	−5.89823e8	−1.80023	−0.900117	−	0.435648i	$-0.856519\pi$
$271$	−5.89823e8	−1.80023	−0.900117	+	0.435648i	$0.856519\pi$
$272$	−2.84392e7	−0.0856891
$273$	0	0
$274$	−4.62960e8	−1.35962
$275$	−9.91645e7	−0.287536
$276$	0	0
$277$	5.73183e8	1.62037	0.810185	−	0.586174i	$-0.199367\pi$
$277$	5.73183e8	1.62037	0.810185	+	0.586174i	$0.199367\pi$
$278$	3.16458e8	0.883403
$279$	0	0
$280$	6.21071e7	0.169078
$281$	−2.95626e8	−0.794824	−0.397412	−	0.917640i	$-0.630092\pi$
$281$	−2.95626e8	−0.794824	−0.397412	+	0.917640i	$0.630092\pi$
$282$	0	0
$283$	−3.02985e8	−0.794636	−0.397318	−	0.917681i	$-0.630059\pi$
$283$	−3.02985e8	−0.794636	−0.397318	+	0.917681i	$0.630059\pi$
$284$	−2.55185e7	−0.0661061
$285$	0	0
$286$	1.61488e8	0.408188
$287$	3.24403e8	0.810026
$288$	0	0
$289$	−4.07026e8	−0.991926
$290$	5.90249e7	0.142116
$291$	0	0
$292$	−1.79173e7	−0.0421145
$293$	−7.64795e8	−1.77627	−0.888133	−	0.459586i	$-0.847998\pi$
$293$	−7.64795e8	−1.77627	−0.888133	+	0.459586i	$0.847998\pi$
$294$	0	0
$295$	1.53045e8	0.347090
$296$	1.57118e8	0.352131
$297$	0	0
$298$	5.03843e7	0.110291
$299$	8.84848e8	1.91434
$300$	0	0
$301$	5.84445e8	1.23527
$302$	−5.73748e8	−1.19866
$303$	0	0
$304$	−7.75211e8	−1.58257
$305$	−1.40934e6	−0.00284425
$306$	0	0
$307$	2.50216e8	0.493550	0.246775	−	0.969073i	$-0.420629\pi$
$307$	2.50216e8	0.493550	0.246775	+	0.969073i	$0.420629\pi$
$308$	−5.27746e6	−0.0102919
$309$	0	0
$310$	−1.17309e8	−0.223648
$311$	1.10731e8	0.208741	0.104370	−	0.994538i	$-0.466717\pi$
$311$	1.10731e8	0.208741	0.104370	+	0.994538i	$0.466717\pi$
$312$	0	0
$313$	−5.21969e8	−0.962143	−0.481071	−	0.876681i	$-0.659752\pi$
$313$	−5.21969e8	−0.962143	−0.481071	+	0.876681i	$0.659752\pi$
$314$	−5.55187e8	−1.01201
$315$	0	0
$316$	−2.52982e7	−0.0451008
$317$	6.18490e8	1.09050	0.545250	−	0.838274i	$-0.316435\pi$
$317$	6.18490e8	1.09050	0.545250	+	0.838274i	$0.316435\pi$
$318$	0	0
$319$	−1.18042e8	−0.203596
$320$	1.31292e8	0.223981
$321$	0	0
$322$	6.22732e8	1.03945
$323$	9.03053e7	0.149109
$324$	0	0
$325$	8.17322e8	1.32069
$326$	−3.46264e8	−0.553535
$327$	0	0
$328$	6.87072e8	1.07509
$329$	4.74668e8	0.734860
$330$	0	0
$331$	9.84142e8	1.49163	0.745813	−	0.666156i	$-0.232061\pi$
$331$	9.84142e8	1.49163	0.745813	+	0.666156i	$0.232061\pi$
$332$	1.55801e7	0.0233662
$333$	0	0
$334$	3.65272e7	0.0536418
$335$	−1.13540e8	−0.165002
$336$	0	0
$337$	8.42573e6	0.0119923	0.00599616	−	0.999982i	$-0.498091\pi$
$337$	8.42573e6	0.0119923	0.00599616	+	0.999982i	$0.498091\pi$
$338$	−6.37012e8	−0.897303
$339$	0	0
$340$	−622130.	−0.000858430 0
$341$	2.34602e8	0.320400
$342$	0	0
$343$	−8.09610e8	−1.08329
$344$	1.23783e9	1.63948
$345$	0	0
$346$	1.95326e8	0.253509
$347$	−3.48322e8	−0.447536	−0.223768	−	0.974642i	$-0.571836\pi$
$347$	−3.48322e8	−0.447536	−0.223768	+	0.974642i	$0.571836\pi$
$348$	0	0
$349$	7.40547e8	0.932532	0.466266	−	0.884645i	$-0.345599\pi$
$349$	7.40547e8	0.932532	0.466266	+	0.884645i	$0.345599\pi$
$350$	5.75209e8	0.717112
$351$	0	0
$352$	−2.18799e7	−0.0267391
$353$	−2.96936e8	−0.359295	−0.179647	−	0.983731i	$-0.557496\pi$
$353$	−2.96936e8	−0.359295	−0.179647	+	0.983731i	$0.557496\pi$
$354$	0	0
$355$	2.70355e8	0.320727
$356$	6.29800e7	0.0739823
$357$	0	0
$358$	2.75092e8	0.316874
$359$	4.98228e8	0.568326	0.284163	−	0.958776i	$-0.408284\pi$
$359$	4.98228e8	0.568326	0.284163	+	0.958776i	$0.408284\pi$
$360$	0	0
$361$	1.56772e9	1.75386
$362$	1.77124e7	0.0196244
$363$	0	0
$364$	4.34972e7	0.0472723
$365$	1.89824e8	0.204327
$366$	0	0
$367$	−1.05029e9	−1.10911	−0.554557	−	0.832146i	$-0.687112\pi$
$367$	−1.05029e9	−1.10911	−0.554557	+	0.832146i	$0.687112\pi$
$368$	1.26028e9	1.31825
$369$	0	0
$370$	−7.07273e7	−0.0725907
$371$	1.23608e8	0.125672
$372$	0	0
$373$	−2.53790e8	−0.253217	−0.126609	−	0.991953i	$-0.540409\pi$
$373$	−2.53790e8	−0.253217	−0.126609	+	0.991953i	$0.540409\pi$
$374$	−2.67936e7	−0.0264839
$375$	0	0
$376$	1.00533e9	0.975326
$377$	9.72912e8	0.935145
$378$	0	0
$379$	9.42700e8	0.889480	0.444740	−	0.895660i	$-0.353296\pi$
$379$	9.42700e8	0.889480	0.444740	+	0.895660i	$0.353296\pi$
$380$	−1.69584e7	−0.0158541
$381$	0	0
$382$	−1.48563e9	−1.36361
$383$	−9.93096e8	−0.903224	−0.451612	−	0.892214i	$-0.649151\pi$
$383$	−9.93096e8	−0.903224	−0.451612	+	0.892214i	$0.649151\pi$
$384$	0	0
$385$	5.59119e7	0.0499335
$386$	1.85111e9	1.63823
$387$	0	0
$388$	2.24702e7	0.0195297
$389$	−1.85245e9	−1.59559	−0.797797	−	0.602926i	$-0.794002\pi$
$389$	−1.85245e9	−1.59559	−0.797797	+	0.602926i	$0.794002\pi$
$390$	0	0
$391$	−1.46811e8	−0.124205
$392$	−4.97128e8	−0.416838
$393$	0	0
$394$	−9.04265e8	−0.744833
$395$	2.68021e8	0.218816
$396$	0	0
$397$	−9.21943e8	−0.739499	−0.369749	−	0.929132i	$-0.620556\pi$
$397$	−9.21943e8	−0.739499	−0.369749	+	0.929132i	$0.620556\pi$
$398$	−2.26036e9	−1.79716
$399$	0	0
$400$	1.16410e9	0.909452
$401$	−8.72543e8	−0.675743	−0.337872	−	0.941192i	$-0.609707\pi$
$401$	−8.72543e8	−0.675743	−0.337872	+	0.941192i	$0.609707\pi$
$402$	0	0
$403$	−1.93361e9	−1.47164
$404$	−4.64631e6	−0.00350569
$405$	0	0
$406$	6.84709e8	0.507767
$407$	1.41445e8	0.103994
$408$	0	0
$409$	3.83123e8	0.276890	0.138445	−	0.990370i	$-0.455790\pi$
$409$	3.83123e8	0.276890	0.138445	+	0.990370i	$0.455790\pi$
$410$	−3.09288e8	−0.221626
$411$	0	0
$412$	−4.26402e6	−0.00300386
$413$	1.77538e9	1.24012
$414$	0	0
$415$	−1.65063e8	−0.113366
$416$	1.80336e8	0.122816
$417$	0	0
$418$	−7.30357e8	−0.489123
$419$	1.25662e9	0.834552	0.417276	−	0.908780i	$-0.362985\pi$
$419$	1.25662e9	0.834552	0.417276	+	0.908780i	$0.362985\pi$
$420$	0	0
$421$	−1.19966e9	−0.783560	−0.391780	−	0.920059i	$-0.628141\pi$
$421$	−1.19966e9	−0.783560	−0.391780	+	0.920059i	$0.628141\pi$
$422$	1.26214e9	0.817552
$423$	0	0
$424$	2.61796e8	0.166795
$425$	−1.35607e8	−0.0856884
$426$	0	0
$427$	−1.63489e7	−0.0101622
$428$	−5.51299e7	−0.0339887
$429$	0	0
$430$	−5.57214e8	−0.337973
$431$	−3.22074e9	−1.93770	−0.968848	−	0.247655i	$-0.920340\pi$
$431$	−3.22074e9	−1.93770	−0.968848	+	0.247655i	$0.920340\pi$
$432$	0	0
$433$	−2.53616e9	−1.50130	−0.750652	−	0.660697i	$-0.770261\pi$
$433$	−2.53616e9	−1.50130	−0.750652	+	0.660697i	$0.770261\pi$
$434$	−1.36082e9	−0.799074
$435$	0	0
$436$	−370470.	−0.000214068 0
$437$	−4.00186e9	−2.29391
$438$	0	0
$439$	1.18782e9	0.670079	0.335039	−	0.942204i	$-0.391250\pi$
$439$	1.18782e9	0.670079	0.335039	+	0.942204i	$0.391250\pi$
$440$	1.18419e8	0.0662730
$441$	0	0
$442$	2.20835e8	0.121644
$443$	9.76489e8	0.533647	0.266824	−	0.963745i	$-0.414026\pi$
$443$	9.76489e8	0.533647	0.266824	+	0.963745i	$0.414026\pi$
$444$	0	0
$445$	−6.67240e8	−0.358940
$446$	−2.33077e9	−1.24402
$447$	0	0
$448$	1.52303e9	0.800266
$449$	2.52186e9	1.31480	0.657398	−	0.753543i	$-0.271657\pi$
$449$	2.52186e9	1.31480	0.657398	+	0.753543i	$0.271657\pi$
$450$	0	0
$451$	6.18536e8	0.317503
$452$	−8.98347e7	−0.0457572
$453$	0	0
$454$	3.04713e9	1.52826
$455$	−4.60830e8	−0.229351
$456$	0	0
$457$	−2.36676e9	−1.15997	−0.579987	−	0.814626i	$-0.696942\pi$
$457$	−2.36676e9	−1.15997	−0.579987	+	0.814626i	$0.696942\pi$
$458$	−2.73105e9	−1.32831
$459$	0	0
$460$	2.75696e7	0.0132062
$461$	4.52148e8	0.214945	0.107472	−	0.994208i	$-0.465724\pi$
$461$	4.52148e8	0.214945	0.107472	+	0.994208i	$0.465724\pi$
$462$	0	0
$463$	−1.36961e9	−0.641302	−0.320651	−	0.947197i	$-0.603902\pi$
$463$	−1.36961e9	−0.641302	−0.320651	+	0.947197i	$0.603902\pi$
$464$	1.38570e9	0.643958
$465$	0	0
$466$	−1.59059e9	−0.728128
$467$	1.76054e7	0.00799902	0.00399951	−	0.999992i	$-0.498727\pi$
$467$	1.76054e7	0.00799902	0.00399951	+	0.999992i	$0.498727\pi$
$468$	0	0
$469$	−1.31710e9	−0.589539
$470$	−4.52552e8	−0.201060
$471$	0	0
$472$	3.76017e9	1.64592
$473$	1.11435e9	0.484183
$474$	0	0
$475$	−3.69646e9	−1.58255
$476$	−7.21692e6	−0.00306710
$477$	0	0
$478$	−1.16039e9	−0.485968
$479$	−1.20785e9	−0.502154	−0.251077	−	0.967967i	$-0.580785\pi$
$479$	−1.20785e9	−0.502154	−0.251077	+	0.967967i	$0.580785\pi$
$480$	0	0
$481$	−1.16580e9	−0.477659
$482$	8.70838e8	0.354220
$483$	0	0
$484$	−1.00625e7	−0.00403409
$485$	−2.38059e8	−0.0947522
$486$	0	0
$487$	1.01854e7	0.00399600	0.00199800	−	0.999998i	$-0.499364\pi$
$487$	1.01854e7	0.00399600	0.00199800	+	0.999998i	$0.499364\pi$
$488$	−3.46262e7	−0.0134876
$489$	0	0
$490$	2.23784e8	0.0859297
$491$	−2.93964e9	−1.12075	−0.560375	−	0.828239i	$-0.689343\pi$
$491$	−2.93964e9	−1.12075	−0.560375	+	0.828239i	$0.689343\pi$
$492$	0	0
$493$	−1.61422e8	−0.0606736
$494$	6.01966e9	2.24661
$495$	0	0
$496$	−2.75401e9	−1.01340
$497$	3.13621e9	1.14593
$498$	0	0
$499$	3.42779e9	1.23499	0.617493	−	0.786576i	$-0.288148\pi$
$499$	3.42779e9	1.23499	0.617493	+	0.786576i	$0.288148\pi$
$500$	5.21690e7	0.0186646
$501$	0	0
$502$	−1.63376e9	−0.576403
$503$	1.81978e9	0.637573	0.318786	−	0.947827i	$-0.396725\pi$
$503$	1.81978e9	0.637573	0.318786	+	0.947827i	$0.396725\pi$
$504$	0	0
$505$	4.92252e7	0.0170085
$506$	1.18736e9	0.407431
$507$	0	0
$508$	−1.21637e8	−0.0411663
$509$	2.42087e9	0.813691	0.406846	−	0.913497i	$-0.366629\pi$
$509$	2.42087e9	0.813691	0.406846	+	0.913497i	$0.366629\pi$
$510$	0	0
$511$	2.20202e9	0.730043
$512$	3.21375e9	1.05820
$513$	0	0
$514$	1.85841e9	0.603628
$515$	4.51751e7	0.0145738
$516$	0	0
$517$	9.05045e8	0.288040
$518$	−8.20460e8	−0.259360
$519$	0	0
$520$	−9.76018e8	−0.304401
$521$	−2.08008e9	−0.644390	−0.322195	−	0.946673i	$-0.604421\pi$
$521$	−2.08008e9	−0.644390	−0.322195	+	0.946673i	$0.604421\pi$
$522$	0	0
$523$	3.00947e8	0.0919887	0.0459944	−	0.998942i	$-0.485354\pi$
$523$	3.00947e8	0.0919887	0.0459944	+	0.998942i	$0.485354\pi$
$524$	−3.07399e7	−0.00933347
$525$	0	0
$526$	2.34109e9	0.701403
$527$	3.20818e8	0.0954821
$528$	0	0
$529$	3.10108e9	0.910789
$530$	−1.17848e8	−0.0343841
$531$	0	0
$532$	−1.96723e8	−0.0566453
$533$	−5.09802e9	−1.45833
$534$	0	0
$535$	5.84072e8	0.164903
$536$	−2.78955e9	−0.782452
$537$	0	0
$538$	1.09995e9	0.304534
$539$	−4.47539e8	−0.123103
$540$	0	0
$541$	−5.12243e8	−0.139087	−0.0695433	−	0.997579i	$-0.522154\pi$
$541$	−5.12243e8	−0.139087	−0.0695433	+	0.997579i	$0.522154\pi$
$542$	6.52334e9	1.75984
$543$	0	0
$544$	−2.99208e7	−0.00796850
$545$	3.92494e6	0.00103859
$546$	0	0
$547$	−4.24814e9	−1.10979	−0.554897	−	0.831919i	$-0.687243\pi$
$547$	−4.24814e9	−1.10979	−0.554897	+	0.831919i	$0.687243\pi$
$548$	−2.37762e8	−0.0617179
$549$	0	0
$550$	1.09674e9	0.281084
$551$	−4.40015e9	−1.12056
$552$	0	0
$553$	3.10913e9	0.781810
$554$	−6.33931e9	−1.58401
$555$	0	0
$556$	1.62523e8	0.0401009
$557$	4.61753e9	1.13218	0.566091	−	0.824343i	$-0.308455\pi$
$557$	4.61753e9	1.13218	0.566091	+	0.824343i	$0.308455\pi$
$558$	0	0
$559$	−9.18460e9	−2.22392
$560$	−6.56353e8	−0.157935
$561$	0	0
$562$	3.26958e9	0.776988
$563$	−7.29234e9	−1.72222	−0.861108	−	0.508422i	$-0.830229\pi$
$563$	−7.29234e9	−1.72222	−0.861108	+	0.508422i	$0.830229\pi$
$564$	0	0
$565$	9.51751e8	0.222000
$566$	3.35096e9	0.776805
$567$	0	0
$568$	6.64236e9	1.52091
$569$	8.21738e8	0.186999	0.0934997	−	0.995619i	$-0.470195\pi$
$569$	8.21738e8	0.186999	0.0934997	+	0.995619i	$0.470195\pi$
$570$	0	0
$571$	−1.38125e9	−0.310490	−0.155245	−	0.987876i	$-0.549617\pi$
$571$	−1.38125e9	−0.310490	−0.155245	+	0.987876i	$0.549617\pi$
$572$	8.29357e7	0.0185291
$573$	0	0
$574$	−3.58785e9	−0.791849
$575$	6.00941e9	1.31824
$576$	0	0
$577$	4.15413e9	0.900254	0.450127	−	0.892965i	$-0.351379\pi$
$577$	4.15413e9	0.900254	0.450127	+	0.892965i	$0.351379\pi$
$578$	4.50164e9	0.969668
$579$	0	0
$580$	3.03134e7	0.00645115
$581$	−1.91479e9	−0.405046
$582$	0	0
$583$	2.35681e8	0.0492590
$584$	4.66378e9	0.968932
$585$	0	0
$586$	8.45850e9	1.73641
$587$	−7.46108e9	−1.52254	−0.761269	−	0.648436i	$-0.775423\pi$
$587$	−7.46108e9	−1.52254	−0.761269	+	0.648436i	$0.775423\pi$
$588$	0	0
$589$	8.74505e9	1.76343
$590$	−1.69265e9	−0.339302
$591$	0	0
$592$	−1.66044e9	−0.328924
$593$	5.81111e9	1.14437	0.572187	−	0.820123i	$-0.306095\pi$
$593$	5.81111e9	1.14437	0.572187	+	0.820123i	$0.306095\pi$
$594$	0	0
$595$	7.64595e7	0.0148806
$596$	2.58759e7	0.00500649
$597$	0	0
$598$	−9.78627e9	−1.87139
$599$	6.11327e9	1.16220	0.581099	−	0.813833i	$-0.302623\pi$
$599$	6.11327e9	1.16220	0.581099	+	0.813833i	$0.302623\pi$
$600$	0	0
$601$	5.94867e9	1.11779	0.558893	−	0.829240i	$-0.311226\pi$
$601$	5.94867e9	1.11779	0.558893	+	0.829240i	$0.311226\pi$
$602$	−6.46387e9	−1.20755
$603$	0	0
$604$	−2.94660e8	−0.0544116
$605$	1.06607e8	0.0195722
$606$	0	0
$607$	−1.95313e9	−0.354463	−0.177232	−	0.984169i	$-0.556714\pi$
$607$	−1.95313e9	−0.354463	−0.177232	+	0.984169i	$0.556714\pi$
$608$	−8.15597e8	−0.147168
$609$	0	0
$610$	1.55871e7	0.00278042
$611$	−7.45945e9	−1.32301
$612$	0	0
$613$	−3.31869e9	−0.581908	−0.290954	−	0.956737i	$-0.593973\pi$
$613$	−3.31869e9	−0.581908	−0.290954	+	0.956737i	$0.593973\pi$
$614$	−2.76735e9	−0.482475
$615$	0	0
$616$	1.37370e9	0.236788
$617$	−2.71103e9	−0.464661	−0.232330	−	0.972637i	$-0.574635\pi$
$617$	−2.71103e9	−0.464661	−0.232330	+	0.972637i	$0.574635\pi$
$618$	0	0
$619$	1.20094e9	0.203519	0.101759	−	0.994809i	$-0.467553\pi$
$619$	1.20094e9	0.203519	0.101759	+	0.994809i	$0.467553\pi$
$620$	−6.02463e7	−0.0101522
$621$	0	0
$622$	−1.22467e9	−0.204057
$623$	−7.74020e9	−1.28246
$624$	0	0
$625$	5.26790e9	0.863093
$626$	5.77289e9	0.940553
$627$	0	0
$628$	−2.85127e8	−0.0459388
$629$	1.93426e8	0.0309912
$630$	0	0
$631$	−6.09708e9	−0.966093	−0.483047	−	0.875595i	$-0.660470\pi$
$631$	−6.09708e9	−0.966093	−0.483047	+	0.875595i	$0.660470\pi$
$632$	6.58501e9	1.03764
$633$	0	0
$634$	−6.84040e9	−1.06603
$635$	1.28868e9	0.199726
$636$	0	0
$637$	3.68865e9	0.565431
$638$	1.30553e9	0.199028
$639$	0	0
$640$	−1.32544e9	−0.199862
$641$	7.99109e9	1.19840	0.599201	−	0.800598i	$-0.295485\pi$
$641$	7.99109e9	1.19840	0.599201	+	0.800598i	$0.295485\pi$
$642$	0	0
$643$	−7.57666e7	−0.0112393	−0.00561966	−	0.999984i	$-0.501789\pi$
$643$	−7.57666e7	−0.0112393	−0.00561966	+	0.999984i	$0.501789\pi$
$644$	3.19816e8	0.0471846
$645$	0	0
$646$	−9.98762e8	−0.145763
$647$	1.01975e10	1.48023	0.740116	−	0.672479i	$-0.234771\pi$
$647$	1.01975e10	1.48023	0.740116	+	0.672479i	$0.234771\pi$
$648$	0	0
$649$	3.38509e9	0.486086
$650$	−9.03945e9	−1.29106
$651$	0	0
$652$	−1.77831e8	−0.0251270
$653$	1.53376e9	0.215556	0.107778	−	0.994175i	$-0.465626\pi$
$653$	1.53376e9	0.215556	0.107778	+	0.994175i	$0.465626\pi$
$654$	0	0
$655$	3.25673e8	0.0452832
$656$	−7.26104e9	−1.00423
$657$	0	0
$658$	−5.24975e9	−0.718370
$659$	7.32323e9	0.996790	0.498395	−	0.866950i	$-0.333923\pi$
$659$	7.32323e9	0.996790	0.498395	+	0.866950i	$0.333923\pi$
$660$	0	0
$661$	−7.01205e9	−0.944365	−0.472183	−	0.881501i	$-0.656534\pi$
$661$	−7.01205e9	−0.944365	−0.472183	+	0.881501i	$0.656534\pi$
$662$	−1.08844e10	−1.45815
$663$	0	0
$664$	−4.05544e9	−0.537588
$665$	2.08418e9	0.274826
$666$	0	0
$667$	7.15340e9	0.933410
$668$	1.87593e7	0.00243500
$669$	0	0
$670$	1.25573e9	0.161300
$671$	−3.11722e7	−0.00398326
$672$	0	0
$673$	−4.37758e9	−0.553582	−0.276791	−	0.960930i	$-0.589271\pi$
$673$	−4.37758e9	−0.553582	−0.276791	+	0.960930i	$0.589271\pi$
$674$	−9.31872e7	−0.0117232
$675$	0	0
$676$	−3.27150e8	−0.0407318
$677$	1.42594e10	1.76620	0.883099	−	0.469186i	$-0.155453\pi$
$677$	1.42594e10	1.76620	0.883099	+	0.469186i	$0.155453\pi$
$678$	0	0
$679$	−2.76157e9	−0.338541
$680$	1.61938e8	0.0197500
$681$	0	0
$682$	−2.59466e9	−0.313210
$683$	4.51198e9	0.541870	0.270935	−	0.962598i	$-0.412667\pi$
$683$	4.51198e9	0.541870	0.270935	+	0.962598i	$0.412667\pi$
$684$	0	0
$685$	2.51897e9	0.299437
$686$	8.95416e9	1.05899
$687$	0	0
$688$	−1.30815e10	−1.53143
$689$	−1.94250e9	−0.226253
$690$	0	0
$691$	9.24446e9	1.06588	0.532940	−	0.846153i	$-0.321087\pi$
$691$	9.24446e9	1.06588	0.532940	+	0.846153i	$0.321087\pi$
$692$	1.00314e8	0.0115077
$693$	0	0
$694$	3.85238e9	0.437493
$695$	−1.72185e9	−0.194557
$696$	0	0
$697$	8.45848e8	0.0946188
$698$	−8.19033e9	−0.911606
$699$	0	0
$700$	2.95410e8	0.0325523
$701$	−1.80992e9	−0.198448	−0.0992238	−	0.995065i	$-0.531636\pi$
$701$	−1.80992e9	−0.198448	−0.0992238	+	0.995065i	$0.531636\pi$
$702$	0	0
$703$	5.27253e9	0.572368
$704$	2.90394e9	0.313677
$705$	0	0
$706$	3.28406e9	0.351233
$707$	5.71028e8	0.0607701
$708$	0	0
$709$	5.14612e9	0.542273	0.271137	−	0.962541i	$-0.412600\pi$
$709$	5.14612e9	0.542273	0.271137	+	0.962541i	$0.412600\pi$
$710$	−2.99009e9	−0.313530
$711$	0	0
$712$	−1.63934e10	−1.70212
$713$	−1.42170e10	−1.46891
$714$	0	0
$715$	−8.78660e8	−0.0898979
$716$	1.41279e8	0.0143841
$717$	0	0
$718$	−5.51032e9	−0.555573
$719$	−6.56632e9	−0.658827	−0.329413	−	0.944186i	$-0.606851\pi$
$719$	−6.56632e9	−0.658827	−0.329413	+	0.944186i	$0.606851\pi$
$720$	0	0
$721$	5.24046e8	0.0520710
$722$	−1.73387e10	−1.71450
$723$	0	0
$724$	9.09655e6	0.000890824 0
$725$	6.60750e9	0.643953
$726$	0	0
$727$	4.82284e9	0.465514	0.232757	−	0.972535i	$-0.425225\pi$
$727$	4.82284e9	0.465514	0.232757	+	0.972535i	$0.425225\pi$
$728$	−1.13221e10	−1.08760
$729$	0	0
$730$	−2.09942e9	−0.199742
$731$	1.52388e9	0.144291
$732$	0	0
$733$	−6.22780e9	−0.584078	−0.292039	−	0.956406i	$-0.594334\pi$
$733$	−6.22780e9	−0.584078	−0.292039	+	0.956406i	$0.594334\pi$
$734$	1.16160e10	1.08423
$735$	0	0
$736$	1.32593e9	0.122588
$737$	−2.51129e9	−0.231079
$738$	0	0
$739$	−2.50070e9	−0.227932	−0.113966	−	0.993485i	$-0.536355\pi$
$739$	−2.50070e9	−0.227932	−0.113966	+	0.993485i	$0.536355\pi$
$740$	−3.63234e7	−0.00329515
$741$	0	0
$742$	−1.36708e9	−0.122852
$743$	−3.39408e9	−0.303571	−0.151786	−	0.988413i	$-0.548502\pi$
$743$	−3.39408e9	−0.303571	−0.151786	+	0.988413i	$0.548502\pi$
$744$	0	0
$745$	−2.74141e8	−0.0242900
$746$	2.80687e9	0.247535
$747$	0	0
$748$	−1.37604e7	−0.00120220
$749$	6.77544e9	0.589184
$750$	0	0
$751$	−1.15314e10	−0.993438	−0.496719	−	0.867911i	$-0.665462\pi$
$751$	−1.15314e10	−0.993438	−0.496719	+	0.867911i	$0.665462\pi$
$752$	−1.06244e10	−0.911048
$753$	0	0
$754$	−1.07603e10	−0.914161
$755$	3.12177e9	0.263989
$756$	0	0
$757$	−3.22313e9	−0.270049	−0.135024	−	0.990842i	$-0.543111\pi$
$757$	−3.22313e9	−0.270049	−0.135024	+	0.990842i	$0.543111\pi$
$758$	−1.04261e10	−0.869521
$759$	0	0
$760$	4.41419e9	0.364757
$761$	6.00476e9	0.493911	0.246956	−	0.969027i	$-0.420570\pi$
$761$	6.00476e9	0.493911	0.246956	+	0.969027i	$0.420570\pi$
$762$	0	0
$763$	4.55306e7	0.00371080
$764$	−7.62975e8	−0.0618990
$765$	0	0
$766$	1.09835e10	0.882956
$767$	−2.79002e10	−2.23266
$768$	0	0
$769$	−2.67592e9	−0.212193	−0.106097	−	0.994356i	$-0.533835\pi$
$769$	−2.67592e9	−0.212193	−0.106097	+	0.994356i	$0.533835\pi$
$770$	−6.18376e8	−0.0488130
$771$	0	0
$772$	9.50672e8	0.0743653
$773$	−8.00647e9	−0.623466	−0.311733	−	0.950170i	$-0.600909\pi$
$773$	−8.00647e9	−0.623466	−0.311733	+	0.950170i	$0.600909\pi$
$774$	0	0
$775$	−1.31320e10	−1.01339
$776$	−5.84888e9	−0.449321
$777$	0	0
$778$	2.04878e10	1.55979
$779$	2.30566e10	1.74749
$780$	0	0
$781$	5.97978e9	0.449166
$782$	1.62371e9	0.121418
$783$	0	0
$784$	5.25369e9	0.389366
$785$	3.02077e9	0.222882
$786$	0	0
$787$	1.09870e9	0.0803465	0.0401733	−	0.999193i	$-0.487209\pi$
$787$	1.09870e9	0.0803465	0.0401733	+	0.999193i	$0.487209\pi$
$788$	−4.64404e8	−0.0338107
$789$	0	0
$790$	−2.96427e9	−0.213906
$791$	1.10406e10	0.793188
$792$	0	0
$793$	2.56923e8	0.0182956
$794$	1.01965e10	0.722905
$795$	0	0
$796$	−1.16085e9	−0.0815795
$797$	−4.45517e8	−0.0311717	−0.0155858	−	0.999879i	$-0.504961\pi$
$797$	−4.45517e8	−0.0311717	−0.0155858	+	0.999879i	$0.504961\pi$
$798$	0	0
$799$	1.23765e9	0.0858387
$800$	1.22475e9	0.0845729
$801$	0	0
$802$	9.65019e9	0.660580
$803$	4.19857e9	0.286152
$804$	0	0
$805$	−3.38829e9	−0.228926
$806$	2.13854e10	1.43862
$807$	0	0
$808$	1.20941e9	0.0806556
$809$	−1.72932e8	−0.0114830	−0.00574150	−	0.999984i	$-0.501828\pi$
$809$	−1.72932e8	−0.0114830	−0.00574150	+	0.999984i	$0.501828\pi$
$810$	0	0
$811$	−1.88310e9	−0.123965	−0.0619826	−	0.998077i	$-0.519742\pi$
$811$	−1.88310e9	−0.123965	−0.0619826	+	0.998077i	$0.519742\pi$
$812$	3.51646e8	0.0230494
$813$	0	0
$814$	−1.56436e9	−0.101660
$815$	1.88402e9	0.121909
$816$	0	0
$817$	4.15388e10	2.66487
$818$	−4.23728e9	−0.270677
$819$	0	0
$820$	−1.58841e8	−0.0100604
$821$	1.81880e10	1.14706	0.573529	−	0.819186i	$-0.305574\pi$
$821$	1.81880e10	1.14706	0.573529	+	0.819186i	$0.305574\pi$
$822$	0	0
$823$	−1.31757e10	−0.823899	−0.411949	−	0.911207i	$-0.635152\pi$
$823$	−1.31757e10	−0.823899	−0.411949	+	0.911207i	$0.635152\pi$
$824$	1.10991e9	0.0691100
$825$	0	0
$826$	−1.96354e10	−1.21230
$827$	−1.60104e10	−0.984313	−0.492157	−	0.870507i	$-0.663791\pi$
$827$	−1.60104e10	−0.984313	−0.492157	+	0.870507i	$0.663791\pi$
$828$	0	0
$829$	8.99595e9	0.548411	0.274206	−	0.961671i	$-0.411585\pi$
$829$	8.99595e9	0.548411	0.274206	+	0.961671i	$0.411585\pi$
$830$	1.82557e9	0.110822
$831$	0	0
$832$	−2.39345e10	−1.44076
$833$	−6.12009e8	−0.0366860
$834$	0	0
$835$	−1.98744e8	−0.0118139
$836$	−3.75089e8	−0.0222031
$837$	0	0
$838$	−1.38980e10	−0.815825
$839$	−7.43957e9	−0.434892	−0.217446	−	0.976072i	$-0.569773\pi$
$839$	−7.43957e9	−0.434892	−0.217446	+	0.976072i	$0.569773\pi$
$840$	0	0
$841$	−9.38453e9	−0.544035
$842$	1.32681e10	0.765977
$843$	0	0
$844$	6.48200e8	0.0371117
$845$	3.46599e9	0.197619
$846$	0	0
$847$	1.23667e9	0.0699298
$848$	−2.76668e9	−0.155802
$849$	0	0
$850$	1.49980e9	0.0837656
$851$	−8.57165e9	−0.476772
$852$	0	0
$853$	2.81819e10	1.55471	0.777353	−	0.629064i	$-0.216562\pi$
$853$	2.81819e10	1.55471	0.777353	+	0.629064i	$0.216562\pi$
$854$	1.80816e8	0.00993422
$855$	0	0
$856$	1.43501e10	0.781980
$857$	1.63183e10	0.885608	0.442804	−	0.896618i	$-0.353984\pi$
$857$	1.63183e10	0.885608	0.442804	+	0.896618i	$0.353984\pi$
$858$	0	0
$859$	1.52511e10	0.820964	0.410482	−	0.911869i	$-0.365360\pi$
$859$	1.52511e10	0.820964	0.410482	+	0.911869i	$0.365360\pi$
$860$	−2.86168e8	−0.0153418
$861$	0	0
$862$	3.56209e10	1.89422
$863$	−3.50608e9	−0.185688	−0.0928440	−	0.995681i	$-0.529596\pi$
$863$	−3.50608e9	−0.185688	−0.0928440	+	0.995681i	$0.529596\pi$
$864$	0	0
$865$	−1.06277e9	−0.0558320
$866$	2.80495e10	1.46762
$867$	0	0
$868$	−6.98877e8	−0.0362729
$869$	5.92815e9	0.306443
$870$	0	0
$871$	2.06983e10	1.06138
$872$	9.64318e7	0.00492507
$873$	0	0
$874$	4.42599e10	2.24244
$875$	−6.41154e9	−0.323545
$876$	0	0
$877$	1.83413e10	0.918190	0.459095	−	0.888387i	$-0.348174\pi$
$877$	1.83413e10	0.918190	0.459095	+	0.888387i	$0.348174\pi$
$878$	−1.31371e10	−0.655043
$879$	0	0
$880$	−1.25146e9	−0.0619053
$881$	−2.35342e10	−1.15953	−0.579766	−	0.814783i	$-0.696856\pi$
$881$	−2.35342e10	−1.15953	−0.579766	+	0.814783i	$0.696856\pi$
$882$	0	0
$883$	−3.39126e10	−1.65767	−0.828837	−	0.559490i	$-0.810997\pi$
$883$	−3.39126e10	−1.65767	−0.828837	+	0.559490i	$0.810997\pi$
$884$	1.13414e8	0.00552186
$885$	0	0
$886$	−1.07998e10	−0.521673
$887$	1.88887e10	0.908800	0.454400	−	0.890798i	$-0.349854\pi$
$887$	1.88887e10	0.908800	0.454400	+	0.890798i	$0.349854\pi$
$888$	0	0
$889$	1.49491e10	0.713605
$890$	7.37956e9	0.350886
$891$	0	0
$892$	−1.19701e9	−0.0564706
$893$	3.37365e10	1.58533
$894$	0	0
$895$	−1.49677e9	−0.0697872
$896$	−1.53756e10	−0.714091
$897$	0	0
$898$	−2.78913e10	−1.28529
$899$	−1.56319e10	−0.717553
$900$	0	0
$901$	3.22294e8	0.0146796
$902$	−6.84091e9	−0.310378
$903$	0	0
$904$	2.33836e10	1.05274
$905$	−9.63732e7	−0.00432201
$906$	0	0
$907$	−2.28453e10	−1.01665	−0.508324	−	0.861166i	$-0.669735\pi$
$907$	−2.28453e10	−1.01665	−0.508324	+	0.861166i	$0.669735\pi$
$908$	1.56492e9	0.0693730
$909$	0	0
$910$	5.09671e9	0.224205
$911$	2.64329e10	1.15832	0.579162	−	0.815212i	$-0.303380\pi$
$911$	2.64329e10	1.15832	0.579162	+	0.815212i	$0.303380\pi$
$912$	0	0
$913$	−3.65091e9	−0.158764
$914$	2.61760e10	1.13394
$915$	0	0
$916$	−1.40259e9	−0.0602969
$917$	3.77792e9	0.161793
$918$	0	0
$919$	1.26026e10	0.535620	0.267810	−	0.963472i	$-0.413700\pi$
$919$	1.26026e10	0.535620	0.267810	+	0.963472i	$0.413700\pi$
$920$	−7.17624e9	−0.303836
$921$	0	0
$922$	−5.00068e9	−0.210122
$923$	−4.92858e10	−2.06308
$924$	0	0
$925$	−7.91751e9	−0.328922
$926$	1.51476e10	0.626912
$927$	0	0
$928$	1.45790e9	0.0598837
$929$	−3.04525e10	−1.24614	−0.623072	−	0.782164i	$-0.714116\pi$
$929$	−3.04525e10	−1.24614	−0.623072	+	0.782164i	$0.714116\pi$
$930$	0	0
$931$	−1.66825e10	−0.677543
$932$	−8.16879e8	−0.0330523
$933$	0	0
$934$	−1.94713e8	−0.00781952
$935$	1.45784e8	0.00583271
$936$	0	0
$937$	−9.24061e9	−0.366954	−0.183477	−	0.983024i	$-0.558735\pi$
$937$	−9.24061e9	−0.366954	−0.183477	+	0.983024i	$0.558735\pi$
$938$	1.45669e10	0.576311
$939$	0	0
$940$	−2.32417e8	−0.00912684
$941$	−3.02061e10	−1.18177	−0.590883	−	0.806757i	$-0.701220\pi$
$941$	−3.02061e10	−1.18177	−0.590883	+	0.806757i	$0.701220\pi$
$942$	0	0
$943$	−3.74836e10	−1.45563
$944$	−3.97378e10	−1.53745
$945$	0	0
$946$	−1.23246e10	−0.473318
$947$	−1.81462e9	−0.0694322	−0.0347161	−	0.999397i	$-0.511053\pi$
$947$	−1.81462e9	−0.0694322	−0.0347161	+	0.999397i	$0.511053\pi$
$948$	0	0
$949$	−3.46049e10	−1.31433
$950$	4.08823e10	1.54704
$951$	0	0
$952$	1.87853e9	0.0705650
$953$	−2.33932e10	−0.875517	−0.437758	−	0.899093i	$-0.644227\pi$
$953$	−2.33932e10	−0.875517	−0.437758	+	0.899093i	$0.644227\pi$
$954$	0	0
$955$	8.08332e9	0.300316
$956$	−5.95943e8	−0.0220598
$957$	0	0
$958$	1.33586e10	0.490886
$959$	2.92209e10	1.06986
$960$	0	0
$961$	3.55504e9	0.129215
$962$	1.28936e10	0.466940
$963$	0	0
$964$	4.47236e8	0.0160793
$965$	−1.00719e10	−0.360798
$966$	0	0
$967$	−3.73590e10	−1.32863	−0.664314	−	0.747454i	$-0.731276\pi$
$967$	−3.73590e10	−1.32863	−0.664314	+	0.747454i	$0.731276\pi$
$968$	2.61922e9	0.0928127
$969$	0	0
$970$	2.63290e9	0.0926261
$971$	−2.54149e10	−0.890883	−0.445442	−	0.895311i	$-0.646953\pi$
$971$	−2.54149e10	−0.890883	−0.445442	+	0.895311i	$0.646953\pi$
$972$	0	0
$973$	−1.99740e10	−0.695137
$974$	−1.12649e8	−0.00390633
$975$	0	0
$976$	3.65932e8	0.0125987
$977$	1.70188e10	0.583844	0.291922	−	0.956442i	$-0.405705\pi$
$977$	1.70188e10	0.583844	0.291922	+	0.956442i	$0.405705\pi$
$978$	0	0
$979$	−1.47582e10	−0.502681
$980$	1.14929e8	0.00390066
$981$	0	0
$982$	3.25119e10	1.09560
$983$	−2.17173e10	−0.729237	−0.364619	−	0.931157i	$-0.618801\pi$
$983$	−2.17173e10	−0.729237	−0.364619	+	0.931157i	$0.618801\pi$
$984$	0	0
$985$	4.92011e9	0.164039
$986$	1.78531e9	0.0593121
$987$	0	0
$988$	3.09152e9	0.101982
$989$	−6.75304e10	−2.21979
$990$	0	0
$991$	−4.06405e9	−0.132648	−0.0663240	−	0.997798i	$-0.521127\pi$
$991$	−4.06405e9	−0.132648	−0.0663240	+	0.997798i	$0.521127\pi$
$992$	−2.89749e9	−0.0942391
$993$	0	0
$994$	−3.46860e10	−1.12022
$995$	1.22986e10	0.395800
$996$	0	0
$997$	−4.73391e9	−0.151282	−0.0756410	−	0.997135i	$-0.524100\pi$
$997$	−4.73391e9	−0.151282	−0.0756410	+	0.997135i	$0.524100\pi$
$998$	−3.79108e10	−1.20727
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q-11.0598 q^{2} -5.68000 q^{4} +60.1766 q^{5} +698.069 q^{7} +1478.48 q^{8} +O(q^{10})\)	\(q-11.0598 q^{2} -5.68000 q^{4} +60.1766 q^{5} +698.069 q^{7} +1478.48 q^{8} -665.544 q^{10} +1331.00 q^{11} -10970.2 q^{13} -7720.53 q^{14} -15624.7 q^{16} +1820.14 q^{17} +49614.4 q^{19} -341.803 q^{20} -14720.6 q^{22} -80659.2 q^{23} -74503.8 q^{25} +121329. q^{26} -3965.03 q^{28} -88686.8 q^{29} +176260. q^{31} -16438.7 q^{32} -20130.5 q^{34} +42007.4 q^{35} +106270. q^{37} -548728. q^{38} +88969.9 q^{40} +464715. q^{41} +837231. q^{43} -7560.08 q^{44} +892077. q^{46} +679973. q^{47} -336243. q^{49} +824000. q^{50} +62310.8 q^{52} +177071. q^{53} +80095.1 q^{55} +1.03208e6 q^{56} +980861. q^{58} +2.54327e6 q^{59} -23420.1 q^{61} -1.94941e6 q^{62} +2.18177e6 q^{64} -660150. q^{65} -1.88677e6 q^{67} -10338.4 q^{68} -464595. q^{70} +4.49270e6 q^{71} +3.15445e6 q^{73} -1.17533e6 q^{74} -281810. q^{76} +929130. q^{77} +4.45391e6 q^{79} -940241. q^{80} -5.13968e6 q^{82} -2.74298e6 q^{83} +109530. q^{85} -9.25964e6 q^{86} +1.96786e6 q^{88} -1.10880e7 q^{89} -7.65796e6 q^{91} +458144. q^{92} -7.52039e6 q^{94} +2.98563e6 q^{95} -3.95601e6 q^{97} +3.71879e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 604 q^{4} - 537 q^{5} + 170 q^{7} + 420 q^{8}+O(q^{10}) \) 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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