LMFDB - Embedded newform 9.28.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,28,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$41.5670017354$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{30001}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 7500 $ x^2 - x - 7500
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$87.1040$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21703.1 q^{2} +3.36807e8 q^{4} +6.93920e8 q^{5} +3.81056e11 q^{7} -4.39681e12 q^{8} +O(q^{10})$	\(q-21703.1 q^{2} +3.36807e8 q^{4} +6.93920e8 q^{5} +3.81056e11 q^{7} -4.39681e12 q^{8} -1.50602e13 q^{10} -1.26337e14 q^{11} -1.31606e15 q^{13} -8.27009e15 q^{14} +5.02190e16 q^{16} +3.53536e16 q^{17} +8.65178e16 q^{19} +2.33717e17 q^{20} +2.74191e18 q^{22} -5.10955e17 q^{23} -6.96906e18 q^{25} +2.85626e19 q^{26} +1.28342e20 q^{28} +2.74961e19 q^{29} -9.77996e19 q^{31} -4.99779e20 q^{32} -7.67282e20 q^{34} +2.64422e20 q^{35} -1.80293e21 q^{37} -1.87770e21 q^{38} -3.05104e21 q^{40} +5.17966e21 q^{41} +8.74613e21 q^{43} -4.25513e22 q^{44} +1.10893e22 q^{46} -2.51817e22 q^{47} +7.94910e22 q^{49} +1.51250e23 q^{50} -4.43258e23 q^{52} -2.11957e23 q^{53} -8.76680e22 q^{55} -1.67543e24 q^{56} -5.96750e23 q^{58} +7.00844e23 q^{59} +1.08505e23 q^{61} +2.12256e24 q^{62} +4.10646e24 q^{64} -9.13240e23 q^{65} +2.46540e24 q^{67} +1.19073e25 q^{68} -5.73878e24 q^{70} -1.29459e25 q^{71} +7.46465e24 q^{73} +3.91291e25 q^{74} +2.91398e25 q^{76} -4.81415e25 q^{77} -4.94644e25 q^{79} +3.48480e25 q^{80} -1.12415e26 q^{82} +5.54332e25 q^{83} +2.45325e25 q^{85} -1.89818e26 q^{86} +5.55481e26 q^{88} +1.32973e26 q^{89} -5.01492e26 q^{91} -1.72093e26 q^{92} +5.46521e26 q^{94} +6.00364e25 q^{95} -1.06222e27 q^{97} -1.72520e27 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 21582 q^{2} + 202603844 q^{4} + 1771946100 q^{5} + 369665199904 q^{7} - 4429319872824 q^{8}+O(q^{10}) $ 2 * q - 21582 * q^2 + 202603844 * q^4 + 1771946100 * q^5 + 369665199904 * q^7 - 4429319872824 * q^8	$ 2 q - 21582 q^{2} + 202603844 q^{4} + 1771946100 q^{5} + 369665199904 q^{7} - 4429319872824 q^{8} - 14929666656300 q^{10} - 75762335668248 q^{11} - 103021079177588 q^{13} - 82\!\cdots\!36 q^{14}+ \cdots - 17\!\cdots\!78 q^{98}+O(q^{100}) $ 2 * q - 21582 * q^2 + 202603844 * q^4 + 1771946100 * q^5 + 369665199904 * q^7 - 4429319872824 * q^8 - 14929666656300 * q^10 - 75762335668248 * q^11 - 103021079177588 * q^13 - 8271467686583136 * q^14 + 68227529433700880 * q^16 - 34691611579147908 * q^17 + 111620476558642216 * q^19 + 89042670767082600 * q^20 + 2748035308851015336 * q^22 + 2892743075819387952 * q^23 - 13257495997920171250 * q^25 + 28709486590882989996 * q^26 + 129870778968981827392 * q^28 - 29959552473322806972 * q^29 + 10367463257055494032 * q^31 - 493234742263884106464 * q^32 - 775764702062031404772 * q^34 + 252142979584030920000 * q^35 - 3703660908819524869316 * q^37 - 1874664150379356981528 * q^38 - 3086079750063749300400 * q^40 - 1481814928479478034772 * q^41 + 9778778623457380249240 * q^43 - 49338574711945832880432 * q^44 + 11501496706538201034672 * q^46 - 89494998518809740323520 * q^47 + 13908377820361409575890 * q^49 + 150488580768890263638750 * q^50 - 606051653487262224622952 * q^52 - 425671275824601813476748 * q^53 - 33146870181194328159600 * q^55 - 1675060131754321848708480 * q^56 - 603708195922408484547804 * q^58 - 369418769643380130292824 * q^59 + 925133397428892745249420 * q^61 + 2135654804561872705821072 * q^62 + 1690192763441891790257216 * q^64 + 394447136075147294825400 * q^65 + 4151706674555213948132968 * q^67 + 21307603540300350668680824 * q^68 - 5740267152557252353752000 * q^70 - 9760455855870867537668784 * q^71 + 28449956347640075157409588 * q^73 + 38898941191404112127623644 * q^74 + 25770925690602426011538256 * q^76 - 48717589762471785388668288 * q^77 - 49553221898675501744231120 * q^79 + 54261621238075868678378400 * q^80 - 113221448313178537381548852 * q^82 + 120473408203228735926347736 * q^83 - 50977978054175038499879400 * q^85 - 189693121470759531169760808 * q^86 + 553837409674913803181095584 * q^88 - 205644052209697133056985556 * q^89 - 515309018103795393250147648 * q^91 - 628879743331458256476717984 * q^92 + 538732610344725656813388864 * q^94 + 87097784513216888583651600 * q^95 - 1478339006400409594836427772 * q^97 - 1733143443943237696043598078 * 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 $

$2$	−21703.1	−1.87334	−0.936671	−	0.350212i	$-0.886110\pi$
$2$	−21703.1	−1.87334	−0.936671	+	0.350212i	$0.886110\pi$
$3$	0	0
$3$	0	0
$4$	3.36807e8	2.50941
$5$	6.93920e8	0.254223	0.127111	−	0.991888i	$-0.459429\pi$
$5$	6.93920e8	0.254223	0.127111	+	0.991888i	$0.459429\pi$
$6$	0	0
$7$	3.81056e11	1.48650	0.743250	−	0.669014i	$-0.233283\pi$
$7$	3.81056e11	1.48650	0.743250	+	0.669014i	$0.233283\pi$
$8$	−4.39681e12	−2.82763
$9$	0	0
$10$	−1.50602e13	−0.476246
$11$	−1.26337e14	−1.10339	−0.551697	−	0.834045i	$-0.686019\pi$
$11$	−1.26337e14	−1.10339	−0.551697	+	0.834045i	$0.686019\pi$
$12$	0	0
$13$	−1.31606e15	−1.20515	−0.602574	−	0.798063i	$-0.705858\pi$
$13$	−1.31606e15	−1.20515	−0.602574	+	0.798063i	$0.705858\pi$
$14$	−8.27009e15	−2.78472
$15$	0	0
$16$	5.02190e16	2.78772
$17$	3.53536e16	0.865711	0.432855	−	0.901463i	$-0.357506\pi$
$17$	3.53536e16	0.865711	0.432855	+	0.901463i	$0.357506\pi$
$18$	0	0
$19$	8.65178e16	0.471989	0.235994	−	0.971754i	$-0.424165\pi$
$19$	8.65178e16	0.471989	0.235994	+	0.971754i	$0.424165\pi$
$20$	2.33717e17	0.637948
$21$	0	0
$22$	2.74191e18	2.06703
$23$	−5.10955e17	−0.211376	−0.105688	−	0.994399i	$-0.533705\pi$
$23$	−5.10955e17	−0.211376	−0.105688	+	0.994399i	$0.533705\pi$
$24$	0	0
$25$	−6.96906e18	−0.935371
$26$	2.85626e19	2.25765
$27$	0	0
$28$	1.28342e20	3.73023
$29$	2.74961e19	0.497620	0.248810	−	0.968552i	$-0.419961\pi$
$29$	2.74961e19	0.497620	0.248810	+	0.968552i	$0.419961\pi$
$30$	0	0
$31$	−9.77996e19	−0.719373	−0.359687	−	0.933073i	$-0.617116\pi$
$31$	−9.77996e19	−0.719373	−0.359687	+	0.933073i	$0.617116\pi$
$32$	−4.99779e20	−2.39471
$33$	0	0
$34$	−7.67282e20	−1.62177
$35$	2.64422e20	0.377902
$36$	0	0
$37$	−1.80293e21	−1.21690	−0.608450	−	0.793592i	$-0.708208\pi$
$37$	−1.80293e21	−1.21690	−0.608450	+	0.793592i	$0.708208\pi$
$38$	−1.87770e21	−0.884196
$39$	0	0
$40$	−3.05104e21	−0.718849
$41$	5.17966e21	0.874419	0.437209	−	0.899360i	$-0.355967\pi$
$41$	5.17966e21	0.874419	0.437209	+	0.899360i	$0.355967\pi$
$42$	0	0
$43$	8.74613e21	0.776233	0.388116	−	0.921610i	$-0.373126\pi$
$43$	8.74613e21	0.776233	0.388116	+	0.921610i	$0.373126\pi$
$44$	−4.25513e22	−2.76886
$45$	0	0
$46$	1.10893e22	0.395980
$47$	−2.51817e22	−0.672611	−0.336306	−	0.941753i	$-0.609177\pi$
$47$	−2.51817e22	−0.672611	−0.336306	+	0.941753i	$0.609177\pi$
$48$	0	0
$49$	7.94910e22	1.20968
$50$	1.51250e23	1.75227
$51$	0	0
$52$	−4.43258e23	−3.02421
$53$	−2.11957e23	−1.11821	−0.559106	−	0.829096i	$-0.688856\pi$
$53$	−2.11957e23	−1.11821	−0.559106	+	0.829096i	$0.688856\pi$
$54$	0	0
$55$	−8.76680e22	−0.280508
$56$	−1.67543e24	−4.20328
$57$	0	0
$58$	−5.96750e23	−0.932212
$59$	7.00844e23	0.869199	0.434600	−	0.900624i	$-0.356890\pi$
$59$	7.00844e23	0.869199	0.434600	+	0.900624i	$0.356890\pi$
$60$	0	0
$61$	1.08505e23	0.0858020	0.0429010	−	0.999079i	$-0.486340\pi$
$61$	1.08505e23	0.0858020	0.0429010	+	0.999079i	$0.486340\pi$
$62$	2.12256e24	1.34763
$63$	0	0
$64$	4.10646e24	1.69839
$65$	−9.13240e23	−0.306376
$66$	0	0
$67$	2.46540e24	0.549387	0.274693	−	0.961532i	$-0.411424\pi$
$67$	2.46540e24	0.549387	0.274693	+	0.961532i	$0.411424\pi$
$68$	1.19073e25	2.17242
$69$	0	0
$70$	−5.73878e24	−0.707939
$71$	−1.29459e25	−1.31870	−0.659349	−	0.751837i	$-0.729168\pi$
$71$	−1.29459e25	−1.31870	−0.659349	+	0.751837i	$0.729168\pi$
$72$	0	0
$73$	7.46465e24	0.522577	0.261289	−	0.965261i	$-0.415853\pi$
$73$	7.46465e24	0.522577	0.261289	+	0.965261i	$0.415853\pi$
$74$	3.91291e25	2.27967
$75$	0	0
$76$	2.91398e25	1.18441
$77$	−4.81415e25	−1.64019
$78$	0	0
$79$	−4.94644e25	−1.19214	−0.596070	−	0.802933i	$-0.703272\pi$
$79$	−4.94644e25	−1.19214	−0.596070	+	0.802933i	$0.703272\pi$
$80$	3.48480e25	0.708701
$81$	0	0
$82$	−1.12415e26	−1.63808
$83$	5.54332e25	0.685828	0.342914	−	0.939367i	$-0.388586\pi$
$83$	5.54332e25	0.685828	0.342914	+	0.939367i	$0.388586\pi$
$84$	0	0
$85$	2.45325e25	0.220083
$86$	−1.89818e26	−1.45415
$87$	0	0
$88$	5.55481e26	3.11999
$89$	1.32973e26	0.641206	0.320603	−	0.947214i	$-0.396114\pi$
$89$	1.32973e26	0.641206	0.320603	+	0.947214i	$0.396114\pi$
$90$	0	0
$91$	−5.01492e26	−1.79145
$92$	−1.72093e26	−0.530430
$93$	0	0
$94$	5.46521e26	1.26003
$95$	6.00364e25	0.119990
$96$	0	0
$97$	−1.06222e27	−1.60249	−0.801243	−	0.598339i	$-0.795827\pi$
$97$	−1.06222e27	−1.60249	−0.801243	+	0.598339i	$0.795827\pi$
$98$	−1.72520e27	−2.26615
$99$	0	0
$100$	−2.34723e27	−2.34723
$101$	−1.74011e27	−1.52138	−0.760691	−	0.649114i	$-0.775140\pi$
$101$	−1.74011e27	−1.52138	−0.760691	+	0.649114i	$0.775140\pi$
$102$	0	0
$103$	4.99563e26	0.335187	0.167594	−	0.985856i	$-0.446400\pi$
$103$	4.99563e26	0.335187	0.167594	+	0.985856i	$0.446400\pi$
$104$	5.78647e27	3.40772
$105$	0	0
$106$	4.60013e27	2.09479
$107$	1.30395e27	0.523096	0.261548	−	0.965190i	$-0.415767\pi$
$107$	1.30395e27	0.523096	0.261548	+	0.965190i	$0.415767\pi$
$108$	0	0
$109$	−5.74920e27	−1.79618	−0.898089	−	0.439814i	$-0.855044\pi$
$109$	−5.74920e27	−1.79618	−0.898089	+	0.439814i	$0.855044\pi$
$110$	1.90267e27	0.525486
$111$	0	0
$112$	1.91362e28	4.14394
$113$	−8.29240e27	−1.59265	−0.796326	−	0.604867i	$-0.793226\pi$
$113$	−8.29240e27	−1.59265	−0.796326	+	0.604867i	$0.793226\pi$
$114$	0	0
$115$	−3.54562e26	−0.0537367
$116$	9.26087e27	1.24873
$117$	0	0
$118$	−1.52105e28	−1.62831
$119$	1.34717e28	1.28688
$120$	0	0
$121$	2.85111e27	0.217476
$122$	−2.35490e27	−0.160736
$123$	0	0
$124$	−3.29396e28	−1.80520
$125$	−1.00061e28	−0.492015
$126$	0	0
$127$	2.16098e27	0.0857631	0.0428815	−	0.999080i	$-0.486346\pi$
$127$	2.16098e27	0.0857631	0.0428815	+	0.999080i	$0.486346\pi$
$128$	−2.20438e28	−0.786957
$129$	0	0
$130$	1.98202e28	0.573947
$131$	−7.19824e28	−1.87959	−0.939797	−	0.341734i	$-0.888986\pi$
$131$	−7.19824e28	−1.87959	−0.939797	+	0.341734i	$0.888986\pi$
$132$	0	0
$133$	3.29681e28	0.701611
$134$	−5.35069e28	−1.02919
$135$	0	0
$136$	−1.55443e29	−2.44791
$137$	8.23477e28	1.17469	0.587346	−	0.809336i	$-0.300173\pi$
$137$	8.23477e28	1.17469	0.587346	+	0.809336i	$0.300173\pi$
$138$	0	0
$139$	1.17233e29	1.37515	0.687574	−	0.726114i	$-0.258676\pi$
$139$	1.17233e29	1.37515	0.687574	+	0.726114i	$0.258676\pi$
$140$	8.90592e28	0.948310
$141$	0	0
$142$	2.80967e29	2.47037
$143$	1.66267e29	1.32975
$144$	0	0
$145$	1.90801e28	0.126506
$146$	−1.62006e29	−0.978966
$147$	0	0
$148$	−6.07239e29	−3.05370
$149$	2.66795e28	0.122508	0.0612538	−	0.998122i	$-0.480490\pi$
$149$	2.66795e28	0.122508	0.0612538	+	0.998122i	$0.480490\pi$
$150$	0	0
$151$	−4.49422e29	−1.72372	−0.861859	−	0.507149i	$-0.830699\pi$
$151$	−4.49422e29	−1.72372	−0.861859	+	0.507149i	$0.830699\pi$
$152$	−3.80403e29	−1.33461
$153$	0	0
$154$	1.04482e30	3.07264
$155$	−6.78651e28	−0.182881
$156$	0	0
$157$	2.00427e29	0.454268	0.227134	−	0.973864i	$-0.427065\pi$
$157$	2.00427e29	0.454268	0.227134	+	0.973864i	$0.427065\pi$
$158$	1.07353e30	2.23328
$159$	0	0
$160$	−3.46806e29	−0.608790
$161$	−1.94702e29	−0.314211
$162$	0	0
$163$	6.62774e29	0.905384	0.452692	−	0.891667i	$-0.350464\pi$
$163$	6.62774e29	0.905384	0.452692	+	0.891667i	$0.350464\pi$
$164$	1.74455e30	2.19427
$165$	0	0
$166$	−1.20307e30	−1.28479
$167$	−1.07500e30	−1.05861	−0.529307	−	0.848431i	$-0.677548\pi$
$167$	−1.07500e30	−1.05861	−0.529307	+	0.848431i	$0.677548\pi$
$168$	0	0
$169$	5.39481e29	0.452382
$170$	−5.32432e29	−0.412291
$171$	0	0
$172$	2.94576e30	1.94788
$173$	−8.13189e29	−0.497244	−0.248622	−	0.968601i	$-0.579978\pi$
$173$	−8.13189e29	−0.497244	−0.248622	+	0.968601i	$0.579978\pi$
$174$	0	0
$175$	−2.65560e30	−1.39043
$176$	−6.34454e30	−3.07595
$177$	0	0
$178$	−2.88592e30	−1.20120
$179$	−1.37936e30	−0.532305	−0.266152	−	0.963931i	$-0.585752\pi$
$179$	−1.37936e30	−0.532305	−0.266152	+	0.963931i	$0.585752\pi$
$180$	0	0
$181$	−1.97778e30	−0.656927	−0.328464	−	0.944517i	$-0.606531\pi$
$181$	−1.97778e30	−0.656927	−0.328464	+	0.944517i	$0.606531\pi$
$182$	1.08839e31	3.35600
$183$	0	0
$184$	2.24657e30	0.597695
$185$	−1.25109e30	−0.309364
$186$	0	0
$187$	−4.46647e30	−0.955219
$188$	−8.48137e30	−1.68785
$189$	0	0
$190$	−1.30298e30	−0.224783
$191$	−8.23146e30	−1.32290	−0.661449	−	0.749990i	$-0.730058\pi$
$191$	−8.23146e30	−1.32290	−0.661449	+	0.749990i	$0.730058\pi$
$192$	0	0
$193$	−2.63632e30	−0.368107	−0.184054	−	0.982916i	$-0.558922\pi$
$193$	−2.63632e30	−0.368107	−0.184054	+	0.982916i	$0.558922\pi$
$194$	2.30534e31	3.00200
$195$	0	0
$196$	2.67731e31	3.03558
$197$	−9.66937e30	−1.02354	−0.511769	−	0.859123i	$-0.671010\pi$
$197$	−9.66937e30	−1.02354	−0.511769	+	0.859123i	$0.671010\pi$
$198$	0	0
$199$	−8.33709e30	−0.770012	−0.385006	−	0.922914i	$-0.625801\pi$
$199$	−8.33709e30	−0.770012	−0.385006	+	0.922914i	$0.625801\pi$
$200$	3.06416e31	2.64489
$201$	0	0
$202$	3.77658e31	2.85007
$203$	1.04775e31	0.739712
$204$	0	0
$205$	3.59427e30	0.222297
$206$	−1.08421e31	−0.627920
$207$	0	0
$208$	−6.60913e31	−3.35961
$209$	−1.09304e31	−0.520789
$210$	0	0
$211$	1.34579e31	0.563850	0.281925	−	0.959437i	$-0.409027\pi$
$211$	1.34579e31	0.563850	0.281925	+	0.959437i	$0.409027\pi$
$212$	−7.13887e31	−2.80605
$213$	0	0
$214$	−2.82998e31	−0.979937
$215$	6.06912e30	0.197336
$216$	0	0
$217$	−3.72671e31	−1.06935
$218$	1.24775e32	3.36485
$219$	0	0
$220$	−2.95272e31	−0.703908
$221$	−4.65274e31	−1.04331
$222$	0	0
$223$	7.20166e30	0.142994	0.0714969	−	0.997441i	$-0.477222\pi$
$223$	7.20166e30	0.142994	0.0714969	+	0.997441i	$0.477222\pi$
$224$	−1.90443e32	−3.55974
$225$	0	0
$226$	1.79971e32	2.98358
$227$	1.24397e32	1.94294	0.971472	−	0.237153i	$-0.0762144\pi$
$227$	1.24397e32	1.94294	0.971472	+	0.237153i	$0.0762144\pi$
$228$	0	0
$229$	1.14944e32	1.59481	0.797403	−	0.603447i	$-0.206206\pi$
$229$	1.14944e32	1.59481	0.797403	+	0.603447i	$0.206206\pi$
$230$	7.69509e30	0.100667
$231$	0	0
$232$	−1.20895e32	−1.40709
$233$	−1.39267e32	−1.52948	−0.764741	−	0.644337i	$-0.777133\pi$
$233$	−1.39267e32	−1.52948	−0.764741	+	0.644337i	$0.777133\pi$
$234$	0	0
$235$	−1.74741e31	−0.170993
$236$	2.36049e32	2.18117
$237$	0	0
$238$	−2.92377e32	−2.41076
$239$	−1.18142e32	−0.920517	−0.460259	−	0.887785i	$-0.652243\pi$
$239$	−1.18142e32	−0.920517	−0.460259	+	0.887785i	$0.652243\pi$
$240$	0	0
$241$	1.39602e32	0.971991	0.485996	−	0.873961i	$-0.338457\pi$
$241$	1.39602e32	0.971991	0.485996	+	0.873961i	$0.338457\pi$
$242$	−6.18779e31	−0.407407
$243$	0	0
$244$	3.65453e31	0.215312
$245$	5.51604e31	0.307528
$246$	0	0
$247$	−1.13863e32	−0.568817
$248$	4.30007e32	2.03412
$249$	0	0
$250$	2.17163e32	0.921712
$251$	−9.88006e31	−0.397342	−0.198671	−	0.980066i	$-0.563662\pi$
$251$	−9.88006e31	−0.397342	−0.198671	+	0.980066i	$0.563662\pi$
$252$	0	0
$253$	6.45526e31	0.233231
$254$	−4.69000e31	−0.160664
$255$	0	0
$256$	−7.27415e31	−0.224152
$257$	8.60649e31	0.251611	0.125805	−	0.992055i	$-0.459849\pi$
$257$	8.60649e31	0.251611	0.125805	+	0.992055i	$0.459849\pi$
$258$	0	0
$259$	−6.87016e32	−1.80892
$260$	−3.07586e32	−0.768822
$261$	0	0
$262$	1.56224e33	3.52112
$263$	2.80912e32	0.601405	0.300703	−	0.953718i	$-0.402779\pi$
$263$	2.80912e32	0.601405	0.300703	+	0.953718i	$0.402779\pi$
$264$	0	0
$265$	−1.47081e32	−0.284275
$266$	−7.15510e32	−1.31436
$267$	0	0
$268$	8.30365e32	1.37864
$269$	1.02703e32	0.162153	0.0810767	−	0.996708i	$-0.474164\pi$
$269$	1.02703e32	0.162153	0.0810767	+	0.996708i	$0.474164\pi$
$270$	0	0
$271$	−1.27505e33	−1.82155	−0.910775	−	0.412903i	$-0.864515\pi$
$271$	−1.27505e33	−1.82155	−0.910775	+	0.412903i	$0.864515\pi$
$272$	1.77542e33	2.41336
$273$	0	0
$274$	−1.78720e33	−2.20060
$275$	8.80451e32	1.03208
$276$	0	0
$277$	1.09712e33	1.16621	0.583107	−	0.812396i	$-0.301837\pi$
$277$	1.09712e33	1.16621	0.583107	+	0.812396i	$0.301837\pi$
$278$	−2.54432e33	−2.57612
$279$	0	0
$280$	−1.16261e33	−1.06857
$281$	−1.35684e33	−1.18849	−0.594244	−	0.804285i	$-0.702549\pi$
$281$	−1.35684e33	−1.18849	−0.594244	+	0.804285i	$0.702549\pi$
$282$	0	0
$283$	2.13864e33	1.70224	0.851120	−	0.524972i	$-0.175924\pi$
$283$	2.13864e33	1.70224	0.851120	+	0.524972i	$0.175924\pi$
$284$	−4.36028e33	−3.30915
$285$	0	0
$286$	−3.60852e33	−2.49108
$287$	1.97374e33	1.29982
$288$	0	0
$289$	−4.17837e32	−0.250545
$290$	−4.14097e32	−0.236989
$291$	0	0
$292$	2.51414e33	1.31136
$293$	−4.30088e32	−0.214212	−0.107106	−	0.994248i	$-0.534158\pi$
$293$	−4.30088e32	−0.214212	−0.107106	+	0.994248i	$0.534158\pi$
$294$	0	0
$295$	4.86330e32	0.220970
$296$	7.92714e33	3.44095
$297$	0	0
$298$	−5.79028e32	−0.229499
$299$	6.72447e32	0.254740
$300$	0	0
$301$	3.33276e33	1.15387
$302$	9.75386e33	3.22911
$303$	0	0
$304$	4.34484e33	1.31577
$305$	7.52938e31	0.0218128
$306$	0	0
$307$	−5.70033e32	−0.151193	−0.0755966	−	0.997138i	$-0.524086\pi$
$307$	−5.70033e32	−0.151193	−0.0755966	+	0.997138i	$0.524086\pi$
$308$	−1.62144e34	−4.11591
$309$	0	0
$310$	1.47288e33	0.342599
$311$	4.65284e33	1.03622	0.518111	−	0.855313i	$-0.326635\pi$
$311$	4.65284e33	1.03622	0.518111	+	0.855313i	$0.326635\pi$
$312$	0	0
$313$	4.33109e33	0.884604	0.442302	−	0.896866i	$-0.354162\pi$
$313$	4.33109e33	0.884604	0.442302	+	0.896866i	$0.354162\pi$
$314$	−4.34990e33	−0.850998
$315$	0	0
$316$	−1.66600e34	−2.99156
$317$	2.47386e33	0.425671	0.212836	−	0.977088i	$-0.431730\pi$
$317$	2.47386e33	0.425671	0.212836	+	0.977088i	$0.431730\pi$
$318$	0	0
$319$	−3.47378e33	−0.549070
$320$	2.84955e33	0.431770
$321$	0	0
$322$	4.22564e33	0.588624
$323$	3.05871e33	0.408606
$324$	0	0
$325$	9.17170e33	1.12726
$326$	−1.43842e34	−1.69609
$327$	0	0
$328$	−2.27740e34	−2.47254
$329$	−9.59563e33	−0.999836
$330$	0	0
$331$	−2.93911e33	−0.282188	−0.141094	−	0.989996i	$-0.545062\pi$
$331$	−2.93911e33	−0.282188	−0.141094	+	0.989996i	$0.545062\pi$
$332$	1.86703e34	1.72102
$333$	0	0
$334$	2.33309e34	1.98314
$335$	1.71079e33	0.139667
$336$	0	0
$337$	−1.57199e34	−1.18426	−0.592128	−	0.805844i	$-0.701712\pi$
$337$	−1.57199e34	−1.18426	−0.592128	+	0.805844i	$0.701712\pi$
$338$	−1.17084e34	−0.847466
$339$	0	0
$340$	8.26273e33	0.552279
$341$	1.23557e34	0.793752
$342$	0	0
$343$	5.25043e33	0.311691
$344$	−3.84551e34	−2.19490
$345$	0	0
$346$	1.76487e34	0.931507
$347$	−2.55505e34	−1.29703	−0.648516	−	0.761201i	$-0.724610\pi$
$347$	−2.55505e34	−1.29703	−0.648516	+	0.761201i	$0.724610\pi$
$348$	0	0
$349$	−3.50116e34	−1.64463	−0.822316	−	0.569031i	$-0.807319\pi$
$349$	−3.50116e34	−1.64463	−0.822316	+	0.569031i	$0.807319\pi$
$350$	5.76347e34	2.60475
$351$	0	0
$352$	6.31407e34	2.64231
$353$	6.64200e33	0.267510	0.133755	−	0.991014i	$-0.457296\pi$
$353$	6.64200e33	0.267510	0.133755	+	0.991014i	$0.457296\pi$
$354$	0	0
$355$	−8.98343e33	−0.335243
$356$	4.47861e34	1.60905
$357$	0	0
$358$	2.99363e34	0.997188
$359$	−4.11061e34	−1.31865	−0.659327	−	0.751856i	$-0.729159\pi$
$359$	−4.11061e34	−1.31865	−0.659327	+	0.751856i	$0.729159\pi$
$360$	0	0
$361$	−2.61153e34	−0.777227
$362$	4.29240e34	1.23065
$363$	0	0
$364$	−1.68906e35	−4.49548
$365$	5.17987e33	0.132851
$366$	0	0
$367$	−3.04370e33	−0.0725121	−0.0362560	−	0.999343i	$-0.511543\pi$
$367$	−3.04370e33	−0.0725121	−0.0362560	+	0.999343i	$0.511543\pi$
$368$	−2.56597e34	−0.589258
$369$	0	0
$370$	2.71525e34	0.579544
$371$	−8.07675e34	−1.66222
$372$	0	0
$373$	4.11966e34	0.788483	0.394242	−	0.919007i	$-0.371007\pi$
$373$	4.11966e34	0.788483	0.394242	+	0.919007i	$0.371007\pi$
$374$	9.69363e34	1.78945
$375$	0	0
$376$	1.10719e35	1.90190
$377$	−3.61865e34	−0.599706
$378$	0	0
$379$	8.35010e34	1.28843	0.644217	−	0.764842i	$-0.277183\pi$
$379$	8.35010e34	1.28843	0.644217	+	0.764842i	$0.277183\pi$
$380$	2.02207e34	0.301104
$381$	0	0
$382$	1.78648e35	2.47824
$383$	5.20579e34	0.697113	0.348557	−	0.937288i	$-0.386672\pi$
$383$	5.20579e34	0.697113	0.348557	+	0.937288i	$0.386672\pi$
$384$	0	0
$385$	−3.34064e34	−0.416974
$386$	5.72163e34	0.689591
$387$	0	0
$388$	−3.57761e35	−4.02129
$389$	3.57703e34	0.388332	0.194166	−	0.980969i	$-0.437800\pi$
$389$	3.57703e34	0.388332	0.194166	+	0.980969i	$0.437800\pi$
$390$	0	0
$391$	−1.80641e34	−0.182991
$392$	−3.49507e35	−3.42054
$393$	0	0
$394$	2.09855e35	1.91744
$395$	−3.43243e34	−0.303069
$396$	0	0
$397$	−7.79828e34	−0.643172	−0.321586	−	0.946880i	$-0.604216\pi$
$397$	−7.79828e34	−0.643172	−0.321586	+	0.946880i	$0.604216\pi$
$398$	1.80941e35	1.44250
$399$	0	0
$400$	−3.49979e35	−2.60755
$401$	2.28761e34	0.164791	0.0823955	−	0.996600i	$-0.473743\pi$
$401$	2.28761e34	0.164791	0.0823955	+	0.996600i	$0.473743\pi$
$402$	0	0
$403$	1.28710e35	0.866952
$404$	−5.86081e35	−3.81777
$405$	0	0
$406$	−2.27395e35	−1.38573
$407$	2.27777e35	1.34272
$408$	0	0
$409$	−1.15859e34	−0.0639243	−0.0319621	−	0.999489i	$-0.510176\pi$
$409$	−1.15859e34	−0.0639243	−0.0319621	+	0.999489i	$0.510176\pi$
$410$	−7.80068e34	−0.416438
$411$	0	0
$412$	1.68256e35	0.841121
$413$	2.67061e35	1.29206
$414$	0	0
$415$	3.84662e34	0.174353
$416$	6.57739e35	2.88598
$417$	0	0
$418$	2.37224e35	0.975616
$419$	−6.19060e34	−0.246515	−0.123258	−	0.992375i	$-0.539334\pi$
$419$	−6.19060e34	−0.246515	−0.123258	+	0.992375i	$0.539334\pi$
$420$	0	0
$421$	−8.53227e33	−0.0318608	−0.0159304	−	0.999873i	$-0.505071\pi$
$421$	−8.53227e33	−0.0318608	−0.0159304	+	0.999873i	$0.505071\pi$
$422$	−2.92078e35	−1.05628
$423$	0	0
$424$	9.31937e35	3.16190
$425$	−2.46381e35	−0.809761
$426$	0	0
$427$	4.13465e34	0.127545
$428$	4.39181e35	1.31266
$429$	0	0
$430$	−1.31719e35	−0.369678
$431$	−4.08719e35	−1.11169	−0.555843	−	0.831288i	$-0.687604\pi$
$431$	−4.08719e35	−1.11169	−0.555843	+	0.831288i	$0.687604\pi$
$432$	0	0
$433$	1.44666e35	0.369642	0.184821	−	0.982772i	$-0.440830\pi$
$433$	1.44666e35	0.369642	0.184821	+	0.982772i	$0.440830\pi$
$434$	8.08812e35	2.00325
$435$	0	0
$436$	−1.93637e36	−4.50734
$437$	−4.42067e34	−0.0997673
$438$	0	0
$439$	2.97115e34	0.0630454	0.0315227	−	0.999503i	$-0.489964\pi$
$439$	2.97115e34	0.0630454	0.0315227	+	0.999503i	$0.489964\pi$
$440$	3.85460e35	0.793173
$441$	0	0
$442$	1.00979e36	1.95448
$443$	1.94735e35	0.365589	0.182795	−	0.983151i	$-0.441486\pi$
$443$	1.94735e35	0.365589	0.182795	+	0.983151i	$0.441486\pi$
$444$	0	0
$445$	9.22725e34	0.163009
$446$	−1.56298e35	−0.267876
$447$	0	0
$448$	1.56479e36	2.52466
$449$	3.89051e35	0.609089	0.304544	−	0.952498i	$-0.401496\pi$
$449$	3.89051e35	0.609089	0.304544	+	0.952498i	$0.401496\pi$
$450$	0	0
$451$	−6.54384e35	−0.964827
$452$	−2.79294e36	−3.99661
$453$	0	0
$454$	−2.69980e36	−3.63980
$455$	−3.47995e35	−0.455428
$456$	0	0
$457$	−7.79952e35	−0.962053	−0.481027	−	0.876706i	$-0.659736\pi$
$457$	−7.79952e35	−0.962053	−0.481027	+	0.876706i	$0.659736\pi$
$458$	−2.49465e36	−2.98762
$459$	0	0
$460$	−1.19419e35	−0.134847
$461$	1.33828e36	1.46752	0.733760	−	0.679408i	$-0.237764\pi$
$461$	1.33828e36	1.46752	0.733760	+	0.679408i	$0.237764\pi$
$462$	0	0
$463$	3.79932e35	0.392973	0.196486	−	0.980507i	$-0.437047\pi$
$463$	3.79932e35	0.392973	0.196486	+	0.980507i	$0.437047\pi$
$464$	1.38083e36	1.38722
$465$	0	0
$466$	3.02253e36	2.86524
$467$	7.20473e35	0.663499	0.331749	−	0.943368i	$-0.392361\pi$
$467$	7.20473e35	0.663499	0.331749	+	0.943368i	$0.392361\pi$
$468$	0	0
$469$	9.39456e35	0.816664
$470$	3.79242e35	0.320328
$471$	0	0
$472$	−3.08148e36	−2.45778
$473$	−1.10496e36	−0.856490
$474$	0	0
$475$	−6.02947e35	−0.441485
$476$	4.53735e36	3.22930
$477$	0	0
$478$	2.56404e36	1.72444
$479$	4.56900e34	0.0298739	0.0149370	−	0.999888i	$-0.495245\pi$
$479$	4.56900e34	0.0298739	0.0149370	+	0.999888i	$0.495245\pi$
$480$	0	0
$481$	2.37276e36	1.46655
$482$	−3.02980e36	−1.82087
$483$	0	0
$484$	9.60274e35	0.545736
$485$	−7.37092e35	−0.407388
$486$	0	0
$487$	−2.25055e36	−1.17665	−0.588326	−	0.808624i	$-0.700213\pi$
$487$	−2.25055e36	−1.17665	−0.588326	+	0.808624i	$0.700213\pi$
$488$	−4.77077e35	−0.242617
$489$	0	0
$490$	−1.19715e36	−0.576106
$491$	3.36099e36	1.57350	0.786751	−	0.617271i	$-0.211762\pi$
$491$	3.36099e36	1.57350	0.786751	+	0.617271i	$0.211762\pi$
$492$	0	0
$493$	9.72085e35	0.430795
$494$	2.47117e36	1.06559
$495$	0	0
$496$	−4.91140e36	−2.00541
$497$	−4.93312e36	−1.96024
$498$	0	0
$499$	1.11121e35	0.0418253	0.0209127	−	0.999781i	$-0.493343\pi$
$499$	1.11121e35	0.0418253	0.0209127	+	0.999781i	$0.493343\pi$
$500$	−3.37012e36	−1.23467
$501$	0	0
$502$	2.14428e36	0.744357
$503$	1.49384e36	0.504818	0.252409	−	0.967621i	$-0.418777\pi$
$503$	1.49384e36	0.504818	0.252409	+	0.967621i	$0.418777\pi$
$504$	0	0
$505$	−1.20750e36	−0.386770
$506$	−1.40099e36	−0.436922
$507$	0	0
$508$	7.27833e35	0.215215
$509$	5.00593e36	1.44143	0.720717	−	0.693230i	$-0.243813\pi$
$509$	5.00593e36	1.44143	0.720717	+	0.693230i	$0.243813\pi$
$510$	0	0
$511$	2.84445e36	0.776811
$512$	4.53738e36	1.20687
$513$	0	0
$514$	−1.86788e36	−0.471352
$515$	3.46657e35	0.0852122
$516$	0	0
$517$	3.18139e36	0.742154
$518$	1.49104e37	3.38873
$519$	0	0
$520$	4.01535e36	0.866319
$521$	−3.77205e36	−0.792990	−0.396495	−	0.918037i	$-0.629774\pi$
$521$	−3.77205e36	−0.792990	−0.396495	+	0.918037i	$0.629774\pi$
$522$	0	0
$523$	−7.85298e35	−0.156770	−0.0783848	−	0.996923i	$-0.524976\pi$
$523$	−7.85298e35	−0.156770	−0.0783848	+	0.996923i	$0.524976\pi$
$524$	−2.42442e37	−4.71666
$525$	0	0
$526$	−6.09666e36	−1.12664
$527$	−3.45757e36	−0.622769
$528$	0	0
$529$	−5.58214e36	−0.955320
$530$	3.19212e36	0.532544
$531$	0	0
$532$	1.11039e37	1.76063
$533$	−6.81675e36	−1.05380
$534$	0	0
$535$	9.04840e35	0.132983
$536$	−1.08399e37	−1.55347
$537$	0	0
$538$	−2.22897e36	−0.303769
$539$	−1.00427e37	−1.33475
$540$	0	0
$541$	6.90432e36	0.872887	0.436444	−	0.899732i	$-0.356238\pi$
$541$	6.90432e36	0.872887	0.436444	+	0.899732i	$0.356238\pi$
$542$	2.76725e37	3.41238
$543$	0	0
$544$	−1.76690e37	−2.07313
$545$	−3.98948e36	−0.456629
$546$	0	0
$547$	−4.90777e36	−0.534632	−0.267316	−	0.963609i	$-0.586137\pi$
$547$	−4.90777e36	−0.534632	−0.267316	+	0.963609i	$0.586137\pi$
$548$	2.77353e37	2.94778
$549$	0	0
$550$	−1.91085e37	−1.93344
$551$	2.37890e36	0.234871
$552$	0	0
$553$	−1.88487e37	−1.77211
$554$	−2.38109e37	−2.18471
$555$	0	0
$556$	3.94848e37	3.45081
$557$	8.37169e36	0.714115	0.357058	−	0.934082i	$-0.383780\pi$
$557$	8.37169e36	0.714115	0.357058	+	0.934082i	$0.383780\pi$
$558$	0	0
$559$	−1.15104e37	−0.935475
$560$	1.32790e37	1.05348
$561$	0	0
$562$	2.94477e37	2.22644
$563$	−1.53607e37	−1.13383	−0.566913	−	0.823778i	$-0.691862\pi$
$563$	−1.53607e37	−1.13383	−0.566913	+	0.823778i	$0.691862\pi$
$564$	0	0
$565$	−5.75426e36	−0.404889
$566$	−4.64151e37	−3.18887
$567$	0	0
$568$	5.69208e37	3.72879
$569$	2.56048e37	1.63797	0.818986	−	0.573814i	$-0.194537\pi$
$569$	2.56048e37	1.63797	0.818986	+	0.573814i	$0.194537\pi$
$570$	0	0
$571$	−1.84375e37	−1.12490	−0.562450	−	0.826831i	$-0.690141\pi$
$571$	−1.84375e37	−1.12490	−0.562450	+	0.826831i	$0.690141\pi$
$572$	5.60000e37	3.33689
$573$	0	0
$574$	−4.28363e37	−2.43501
$575$	3.56087e36	0.197715
$576$	0	0
$577$	2.60648e37	1.38096	0.690479	−	0.723352i	$-0.257400\pi$
$577$	2.60648e37	1.38096	0.690479	+	0.723352i	$0.257400\pi$
$578$	9.06835e36	0.469356
$579$	0	0
$580$	6.42630e36	0.317456
$581$	2.11231e37	1.01948
$582$	0	0
$583$	2.67781e37	1.23383
$584$	−3.28207e37	−1.47766
$585$	0	0
$586$	9.33423e36	0.401292
$587$	−1.64116e37	−0.689505	−0.344752	−	0.938694i	$-0.612037\pi$
$587$	−1.64116e37	−0.689505	−0.344752	+	0.938694i	$0.612037\pi$
$588$	0	0
$589$	−8.46141e36	−0.339536
$590$	−1.05549e37	−0.413953
$591$	0	0
$592$	−9.05413e37	−3.39237
$593$	−6.39232e35	−0.0234110	−0.0117055	−	0.999931i	$-0.503726\pi$
$593$	−6.39232e35	−0.0234110	−0.0117055	+	0.999931i	$0.503726\pi$
$594$	0	0
$595$	9.34827e36	0.327154
$596$	8.98584e36	0.307421
$597$	0	0
$598$	−1.45942e37	−0.477215
$599$	−3.67500e37	−1.17488	−0.587442	−	0.809266i	$-0.699865\pi$
$599$	−3.67500e37	−1.17488	−0.587442	+	0.809266i	$0.699865\pi$
$600$	0	0
$601$	4.35901e36	0.133224	0.0666120	−	0.997779i	$-0.478781\pi$
$601$	4.35901e36	0.133224	0.0666120	+	0.997779i	$0.478781\pi$
$602$	−7.23313e37	−2.16159
$603$	0	0
$604$	−1.51369e38	−4.32551
$605$	1.97844e36	0.0552874
$606$	0	0
$607$	4.98438e37	1.33218	0.666092	−	0.745870i	$-0.267966\pi$
$607$	4.98438e37	1.33218	0.666092	+	0.745870i	$0.267966\pi$
$608$	−4.32397e37	−1.13028
$609$	0	0
$610$	−1.63411e36	−0.0408628
$611$	3.31406e37	0.810596
$612$	0	0
$613$	2.09778e37	0.490958	0.245479	−	0.969402i	$-0.421055\pi$
$613$	2.09778e37	0.490958	0.245479	+	0.969402i	$0.421055\pi$
$614$	1.23715e37	0.283236
$615$	0	0
$616$	2.11669e38	4.63787
$617$	9.28596e37	1.99057	0.995284	−	0.0970039i	$-0.0309259\pi$
$617$	9.28596e37	1.99057	0.995284	+	0.0970039i	$0.0309259\pi$
$618$	0	0
$619$	4.21148e37	0.864194	0.432097	−	0.901827i	$-0.357774\pi$
$619$	4.21148e37	0.864194	0.432097	+	0.901827i	$0.357774\pi$
$620$	−2.28574e37	−0.458923
$621$	0	0
$622$	−1.00981e38	−1.94120
$623$	5.06700e37	0.953153
$624$	0	0
$625$	4.49801e37	0.810289
$626$	−9.39981e37	−1.65716
$627$	0	0
$628$	6.75053e37	1.13994
$629$	−6.37399e37	−1.05348
$630$	0	0
$631$	−1.60405e37	−0.253993	−0.126997	−	0.991903i	$-0.540534\pi$
$631$	−1.60405e37	−0.253993	−0.126997	+	0.991903i	$0.540534\pi$
$632$	2.17486e38	3.37093
$633$	0	0
$634$	−5.36903e37	−0.797427
$635$	1.49955e36	0.0218029
$636$	0	0
$637$	−1.04615e38	−1.45784
$638$	7.53918e37	1.02860
$639$	0	0
$640$	−1.52966e37	−0.200062
$641$	4.27881e37	0.547948	0.273974	−	0.961737i	$-0.411662\pi$
$641$	4.27881e37	0.547948	0.273974	+	0.961737i	$0.411662\pi$
$642$	0	0
$643$	6.44875e36	0.0791821	0.0395911	−	0.999216i	$-0.487394\pi$
$643$	6.44875e36	0.0791821	0.0395911	+	0.999216i	$0.487394\pi$
$644$	−6.55770e37	−0.788483
$645$	0	0
$646$	−6.63835e37	−0.765458
$647$	−1.16912e38	−1.32024	−0.660118	−	0.751162i	$-0.729494\pi$
$647$	−1.16912e38	−1.32024	−0.660118	+	0.751162i	$0.729494\pi$
$648$	0	0
$649$	−8.85427e37	−0.959068
$650$	−1.99054e38	−2.11174
$651$	0	0
$652$	2.23227e38	2.27198
$653$	7.34409e37	0.732167	0.366083	−	0.930582i	$-0.380699\pi$
$653$	7.34409e37	0.732167	0.366083	+	0.930582i	$0.380699\pi$
$654$	0	0
$655$	−4.99500e37	−0.477835
$656$	2.60118e38	2.43763
$657$	0	0
$658$	2.08255e38	1.87303
$659$	−3.42254e37	−0.301575	−0.150788	−	0.988566i	$-0.548181\pi$
$659$	−3.42254e37	−0.301575	−0.150788	+	0.988566i	$0.548181\pi$
$660$	0	0
$661$	−1.89312e37	−0.160125	−0.0800625	−	0.996790i	$-0.525512\pi$
$661$	−1.89312e37	−0.160125	−0.0800625	+	0.996790i	$0.525512\pi$
$662$	6.37878e37	0.528634
$663$	0	0
$664$	−2.43729e38	−1.93927
$665$	2.28772e37	0.178366
$666$	0	0
$667$	−1.40493e37	−0.105185
$668$	−3.62068e38	−2.65649
$669$	0	0
$670$	−3.71295e37	−0.261643
$671$	−1.37082e37	−0.0946733
$672$	0	0
$673$	2.43532e38	1.61567	0.807835	−	0.589409i	$-0.200639\pi$
$673$	2.43532e38	1.61567	0.807835	+	0.589409i	$0.200639\pi$
$674$	3.41170e38	2.21852
$675$	0	0
$676$	1.81701e38	1.13521
$677$	−2.58654e38	−1.58406	−0.792032	−	0.610479i	$-0.790977\pi$
$677$	−2.58654e38	−1.58406	−0.792032	+	0.610479i	$0.790977\pi$
$678$	0	0
$679$	−4.04763e38	−2.38209
$680$	−1.07865e38	−0.622315
$681$	0	0
$682$	−2.68158e38	−1.48697
$683$	−5.72592e37	−0.311290	−0.155645	−	0.987813i	$-0.549746\pi$
$683$	−5.72592e37	−0.311290	−0.155645	+	0.987813i	$0.549746\pi$
$684$	0	0
$685$	5.71427e37	0.298633
$686$	−1.13951e38	−0.583903
$687$	0	0
$688$	4.39222e38	2.16392
$689$	2.78949e38	1.34761
$690$	0	0
$691$	−1.45765e38	−0.677175	−0.338588	−	0.940935i	$-0.609949\pi$
$691$	−1.45765e38	−0.677175	−0.338588	+	0.940935i	$0.609949\pi$
$692$	−2.73888e38	−1.24779
$693$	0	0
$694$	5.54524e38	2.42978
$695$	8.13502e37	0.349594
$696$	0	0
$697$	1.83120e38	0.756994
$698$	7.59861e38	3.08096
$699$	0	0
$700$	−8.94424e38	−3.48915
$701$	5.69328e37	0.217856	0.108928	−	0.994050i	$-0.465258\pi$
$701$	5.69328e37	0.217856	0.108928	+	0.994050i	$0.465258\pi$
$702$	0	0
$703$	−1.55985e38	−0.574363
$704$	−5.18799e38	−1.87399
$705$	0	0
$706$	−1.44152e38	−0.501138
$707$	−6.63079e38	−2.26153
$708$	0	0
$709$	2.15586e38	0.707776	0.353888	−	0.935288i	$-0.384859\pi$
$709$	2.15586e38	0.707776	0.353888	+	0.935288i	$0.384859\pi$
$710$	1.94968e38	0.628024
$711$	0	0
$712$	−5.84656e38	−1.81310
$713$	4.99712e37	0.152059
$714$	0	0
$715$	1.15376e38	0.338053
$716$	−4.64577e38	−1.33577
$717$	0	0
$718$	8.92129e38	2.47029
$719$	−2.25632e38	−0.613141	−0.306571	−	0.951848i	$-0.599182\pi$
$719$	−2.25632e38	−0.613141	−0.306571	+	0.951848i	$0.599182\pi$
$720$	0	0
$721$	1.90361e38	0.498256
$722$	5.66783e38	1.45601
$723$	0	0
$724$	−6.66130e38	−1.64850
$725$	−1.91622e38	−0.465459
$726$	0	0
$727$	3.26448e38	0.764010	0.382005	−	0.924160i	$-0.375234\pi$
$727$	3.26448e38	0.764010	0.382005	+	0.924160i	$0.375234\pi$
$728$	2.20497e39	5.06557
$729$	0	0
$730$	−1.12419e38	−0.248875
$731$	3.09207e38	0.671993
$732$	0	0
$733$	3.51091e38	0.735387	0.367694	−	0.929947i	$-0.380147\pi$
$733$	3.51091e38	0.735387	0.367694	+	0.929947i	$0.380147\pi$
$734$	6.60578e37	0.135840
$735$	0	0
$736$	2.55364e38	0.506185
$737$	−3.11472e38	−0.606190
$738$	0	0
$739$	−5.12467e38	−0.961537	−0.480768	−	0.876848i	$-0.659642\pi$
$739$	−5.12467e38	−0.961537	−0.480768	+	0.876848i	$0.659642\pi$
$740$	−4.21375e38	−0.776320
$741$	0	0
$742$	1.75291e39	3.11391
$743$	6.94450e38	1.21141	0.605706	−	0.795688i	$-0.292891\pi$
$743$	6.94450e38	1.21141	0.605706	+	0.795688i	$0.292891\pi$
$744$	0	0
$745$	1.85134e37	0.0311442
$746$	−8.94095e38	−1.47710
$747$	0	0
$748$	−1.50434e39	−2.39703
$749$	4.96879e38	0.777582
$750$	0	0
$751$	5.87337e38	0.886642	0.443321	−	0.896363i	$-0.353800\pi$
$751$	5.87337e38	0.886642	0.443321	+	0.896363i	$0.353800\pi$
$752$	−1.26460e39	−1.87505
$753$	0	0
$754$	7.85359e38	1.12345
$755$	−3.11863e38	−0.438208
$756$	0	0
$757$	1.01202e38	0.137212	0.0686062	−	0.997644i	$-0.478145\pi$
$757$	1.01202e38	0.137212	0.0686062	+	0.997644i	$0.478145\pi$
$758$	−1.81223e39	−2.41368
$759$	0	0
$760$	−2.63969e38	−0.339289
$761$	1.48838e39	1.87941	0.939705	−	0.341987i	$-0.111100\pi$
$761$	1.48838e39	1.87941	0.939705	+	0.341987i	$0.111100\pi$
$762$	0	0
$763$	−2.19076e39	−2.67002
$764$	−2.77241e39	−3.31969
$765$	0	0
$766$	−1.12982e39	−1.30593
$767$	−9.22353e38	−1.04751
$768$	0	0
$769$	−1.63286e39	−1.79037	−0.895186	−	0.445692i	$-0.852958\pi$
$769$	−1.63286e39	−1.79037	−0.895186	+	0.445692i	$0.852958\pi$
$770$	7.25022e38	0.781135
$771$	0	0
$772$	−8.87931e38	−0.923731
$773$	−9.47969e36	−0.00969105	−0.00484552	−	0.999988i	$-0.501542\pi$
$773$	−9.47969e36	−0.00969105	−0.00484552	+	0.999988i	$0.501542\pi$
$774$	0	0
$775$	6.81571e38	0.672881
$776$	4.67036e39	4.53124
$777$	0	0
$778$	−7.76327e38	−0.727479
$779$	4.48133e38	0.412716
$780$	0	0
$781$	1.63555e39	1.45504
$782$	3.92046e38	0.342804
$783$	0	0
$784$	3.99196e39	3.37225
$785$	1.39081e38	0.115485
$786$	0	0
$787$	1.01258e39	0.812401	0.406201	−	0.913784i	$-0.366853\pi$
$787$	1.01258e39	0.812401	0.406201	+	0.913784i	$0.366853\pi$
$788$	−3.25671e39	−2.56847
$789$	0	0
$790$	7.44945e38	0.567752
$791$	−3.15986e39	−2.36748
$792$	0	0
$793$	−1.42799e38	−0.103404
$794$	1.69247e39	1.20488
$795$	0	0
$796$	−2.80799e39	−1.93227
$797$	1.64542e39	1.11324	0.556620	−	0.830767i	$-0.312098\pi$
$797$	1.64542e39	1.11324	0.556620	+	0.830767i	$0.312098\pi$
$798$	0	0
$799$	−8.90263e38	−0.582287
$800$	3.48298e39	2.23994
$801$	0	0
$802$	−4.96483e38	−0.308710
$803$	−9.43063e38	−0.576608
$804$	0	0
$805$	−1.35108e38	−0.0798796
$806$	−2.79341e39	−1.62410
$807$	0	0
$808$	7.65094e39	4.30191
$809$	3.76453e38	0.208164	0.104082	−	0.994569i	$-0.466810\pi$
$809$	3.76453e38	0.208164	0.104082	+	0.994569i	$0.466810\pi$
$810$	0	0
$811$	1.84807e39	0.988408	0.494204	−	0.869346i	$-0.335460\pi$
$811$	1.84807e39	0.988408	0.494204	+	0.869346i	$0.335460\pi$
$812$	3.52891e39	1.85624
$813$	0	0
$814$	−4.94347e39	−2.51537
$815$	4.59912e38	0.230169
$816$	0	0
$817$	7.56696e38	0.366373
$818$	2.51450e38	0.119752
$819$	0	0
$820$	1.21058e39	0.557834
$821$	4.29041e39	1.94476	0.972380	−	0.233401i	$-0.0749856\pi$
$821$	4.29041e39	1.94476	0.972380	+	0.233401i	$0.0749856\pi$
$822$	0	0
$823$	−1.74258e39	−0.764355	−0.382177	−	0.924089i	$-0.624826\pi$
$823$	−1.74258e39	−0.764355	−0.382177	+	0.924089i	$0.624826\pi$
$824$	−2.19648e39	−0.947787
$825$	0	0
$826$	−5.79604e39	−2.42048
$827$	−3.90760e39	−1.60541	−0.802704	−	0.596378i	$-0.796606\pi$
$827$	−3.90760e39	−1.60541	−0.802704	+	0.596378i	$0.796606\pi$
$828$	0	0
$829$	1.05175e39	0.418243	0.209121	−	0.977890i	$-0.432940\pi$
$829$	1.05175e39	0.418243	0.209121	+	0.977890i	$0.432940\pi$
$830$	−8.34836e38	−0.326623
$831$	0	0
$832$	−5.40435e39	−2.04681
$833$	2.81029e39	1.04723
$834$	0	0
$835$	−7.45966e38	−0.269124
$836$	−3.68144e39	−1.30687
$837$	0	0
$838$	1.34355e39	0.461807
$839$	9.84534e38	0.333000	0.166500	−	0.986041i	$-0.446753\pi$
$839$	9.84534e38	0.333000	0.166500	+	0.986041i	$0.446753\pi$
$840$	0	0
$841$	−2.29710e39	−0.752374
$842$	1.85177e38	0.0596861
$843$	0	0
$844$	4.53270e39	1.41493
$845$	3.74357e38	0.115006
$846$	0	0
$847$	1.08643e39	0.323278
$848$	−1.06443e40	−3.11726
$849$	0	0
$850$	5.34723e39	1.51696
$851$	9.21214e38	0.257224
$852$	0	0
$853$	2.30350e39	0.623125	0.311563	−	0.950226i	$-0.399148\pi$
$853$	2.30350e39	0.623125	0.311563	+	0.950226i	$0.399148\pi$
$854$	−8.97347e38	−0.238935
$855$	0	0
$856$	−5.73324e39	−1.47912
$857$	1.77038e39	0.449600	0.224800	−	0.974405i	$-0.427827\pi$
$857$	1.77038e39	0.449600	0.224800	+	0.974405i	$0.427827\pi$
$858$	0	0
$859$	5.46881e39	1.34581	0.672907	−	0.739727i	$-0.265046\pi$
$859$	5.46881e39	1.34581	0.672907	+	0.739727i	$0.265046\pi$
$860$	2.04412e39	0.495196
$861$	0	0
$862$	8.87047e39	2.08257
$863$	−5.53394e39	−1.27905	−0.639526	−	0.768769i	$-0.720870\pi$
$863$	−5.53394e39	−1.27905	−0.639526	+	0.768769i	$0.720870\pi$
$864$	0	0
$865$	−5.64288e38	−0.126411
$866$	−3.13971e39	−0.692465
$867$	0	0
$868$	−1.25518e40	−2.68343
$869$	6.24920e39	1.31540
$870$	0	0
$871$	−3.24462e39	−0.662093
$872$	2.52781e40	5.07893
$873$	0	0
$874$	9.59422e38	0.186898
$875$	−3.81287e39	−0.731380
$876$	0	0
$877$	7.58578e39	1.41093	0.705466	−	0.708744i	$-0.250738\pi$
$877$	7.58578e39	1.41093	0.705466	+	0.708744i	$0.250738\pi$
$878$	−6.44831e38	−0.118106
$879$	0	0
$880$	−4.40260e39	−0.781976
$881$	5.97063e38	0.104435	0.0522174	−	0.998636i	$-0.483371\pi$
$881$	5.97063e38	0.104435	0.0522174	+	0.998636i	$0.483371\pi$
$882$	0	0
$883$	−7.85839e39	−1.33310	−0.666552	−	0.745459i	$-0.732230\pi$
$883$	−7.85839e39	−1.33310	−0.666552	+	0.745459i	$0.732230\pi$
$884$	−1.56708e40	−2.61809
$885$	0	0
$886$	−4.22635e39	−0.684874
$887$	−5.04306e39	−0.804869	−0.402434	−	0.915449i	$-0.631836\pi$
$887$	−5.04306e39	−0.804869	−0.402434	+	0.915449i	$0.631836\pi$
$888$	0	0
$889$	8.23453e38	0.127487
$890$	−2.00260e39	−0.305372
$891$	0	0
$892$	2.42557e39	0.358829
$893$	−2.17866e39	−0.317465
$894$	0	0
$895$	−9.57163e38	−0.135324
$896$	−8.39990e39	−1.16981
$897$	0	0
$898$	−8.44360e39	−1.14103
$899$	−2.68911e39	−0.357975
$900$	0	0
$901$	−7.49345e39	−0.968048
$902$	1.42022e40	1.80745
$903$	0	0
$904$	3.64601e40	4.50344
$905$	−1.37242e39	−0.167006
$906$	0	0
$907$	−7.33863e39	−0.866796	−0.433398	−	0.901203i	$-0.642686\pi$
$907$	−7.33863e39	−0.866796	−0.433398	+	0.901203i	$0.642686\pi$
$908$	4.18977e40	4.87564
$909$	0	0
$910$	7.55258e39	0.853172
$911$	−7.23054e39	−0.804771	−0.402386	−	0.915470i	$-0.631819\pi$
$911$	−7.23054e39	−0.804771	−0.402386	+	0.915470i	$0.631819\pi$
$912$	0	0
$913$	−7.00327e39	−0.756738
$914$	1.69274e40	1.80225
$915$	0	0
$916$	3.87140e40	4.00202
$917$	−2.74293e40	−2.79401
$918$	0	0
$919$	−1.06263e40	−1.05105	−0.525523	−	0.850780i	$-0.676130\pi$
$919$	−1.06263e40	−1.05105	−0.525523	+	0.850780i	$0.676130\pi$
$920$	1.55894e39	0.151948
$921$	0	0
$922$	−2.90448e40	−2.74917
$923$	1.70376e40	1.58923
$924$	0	0
$925$	1.25647e40	1.13825
$926$	−8.24570e39	−0.736172
$927$	0	0
$928$	−1.37419e40	−1.19166
$929$	9.62717e39	0.822785	0.411392	−	0.911458i	$-0.365043\pi$
$929$	9.62717e39	0.822785	0.411392	+	0.911458i	$0.365043\pi$
$930$	0	0
$931$	6.87738e39	0.570956
$932$	−4.69062e40	−3.83809
$933$	0	0
$934$	−1.56365e40	−1.24296
$935$	−3.09938e39	−0.242838
$936$	0	0
$937$	1.21318e40	0.923509	0.461755	−	0.887008i	$-0.347220\pi$
$937$	1.21318e40	0.923509	0.461755	+	0.887008i	$0.347220\pi$
$938$	−2.03891e40	−1.52989
$939$	0	0
$940$	−5.88539e39	−0.429091
$941$	5.05393e38	0.0363219	0.0181610	−	0.999835i	$-0.494219\pi$
$941$	5.05393e38	0.0363219	0.0181610	+	0.999835i	$0.494219\pi$
$942$	0	0
$943$	−2.64657e39	−0.184831
$944$	3.51957e40	2.42308
$945$	0	0
$946$	2.39811e40	1.60450
$947$	−8.58094e39	−0.565992	−0.282996	−	0.959121i	$-0.591328\pi$
$947$	−8.58094e39	−0.565992	−0.282996	+	0.959121i	$0.591328\pi$
$948$	0	0
$949$	−9.82392e39	−0.629783
$950$	1.30858e40	0.827051
$951$	0	0
$952$	−5.92324e40	−3.63882
$953$	2.53482e39	0.153530	0.0767649	−	0.997049i	$-0.475541\pi$
$953$	2.53482e39	0.153530	0.0767649	+	0.997049i	$0.475541\pi$
$954$	0	0
$955$	−5.71197e39	−0.336311
$956$	−3.97910e40	−2.30995
$957$	0	0
$958$	−9.91616e38	−0.0559640
$959$	3.13791e40	1.74618
$960$	0	0
$961$	−8.91794e39	−0.482502
$962$	−5.14963e40	−2.74734
$963$	0	0
$964$	4.70190e40	2.43912
$965$	−1.82940e39	−0.0935813
$966$	0	0
$967$	−2.17064e39	−0.107977	−0.0539884	−	0.998542i	$-0.517193\pi$
$967$	−2.17064e39	−0.107977	−0.0539884	+	0.998542i	$0.517193\pi$
$968$	−1.25358e40	−0.614943
$969$	0	0
$970$	1.59972e40	0.763177
$971$	−2.71062e40	−1.27529	−0.637645	−	0.770330i	$-0.720091\pi$
$971$	−2.71062e40	−1.27529	−0.637645	+	0.770330i	$0.720091\pi$
$972$	0	0
$973$	4.46722e40	2.04416
$974$	4.88440e40	2.20427
$975$	0	0
$976$	5.44902e39	0.239192
$977$	4.41710e40	1.91232	0.956161	−	0.292841i	$-0.0946007\pi$
$977$	4.41710e40	1.91232	0.956161	+	0.292841i	$0.0946007\pi$
$978$	0	0
$979$	−1.67994e40	−0.707502
$980$	1.85784e40	0.771714
$981$	0	0
$982$	−7.29439e40	−2.94770
$983$	2.40915e40	0.960266	0.480133	−	0.877196i	$-0.340588\pi$
$983$	2.40915e40	0.960266	0.480133	+	0.877196i	$0.340588\pi$
$984$	0	0
$985$	−6.70977e39	−0.260207
$986$	−2.10972e40	−0.807026
$987$	0	0
$988$	−3.83497e40	−1.42739
$989$	−4.46888e39	−0.164077
$990$	0	0
$991$	−1.16541e39	−0.0416376	−0.0208188	−	0.999783i	$-0.506627\pi$
$991$	−1.16541e39	−0.0416376	−0.0208188	+	0.999783i	$0.506627\pi$
$992$	4.88782e40	1.72269
$993$	0	0
$994$	1.07064e41	3.67221
$995$	−5.78527e39	−0.195755
$996$	0	0
$997$	5.76017e40	1.89693	0.948463	−	0.316888i	$-0.102638\pi$
$997$	5.76017e40	1.89693	0.948463	+	0.316888i	$0.102638\pi$
$998$	−2.41167e39	−0.0783531
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.28.a.b.1.1		2
3.2	odd	2		3.28.a.b.1.2	✓	2
12.11	even	2		48.28.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.28.a.b.1.2	✓	2	3.2	odd	2
9.28.a.b.1.1		2	1.1	even	1	trivial
48.28.a.e.1.2		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-21703.1 q^{2} +3.36807e8 q^{4} +6.93920e8 q^{5} +3.81056e11 q^{7} -4.39681e12 q^{8} +O(q^{10})\)	\(q-21703.1 q^{2} +3.36807e8 q^{4} +6.93920e8 q^{5} +3.81056e11 q^{7} -4.39681e12 q^{8} -1.50602e13 q^{10} -1.26337e14 q^{11} -1.31606e15 q^{13} -8.27009e15 q^{14} +5.02190e16 q^{16} +3.53536e16 q^{17} +8.65178e16 q^{19} +2.33717e17 q^{20} +2.74191e18 q^{22} -5.10955e17 q^{23} -6.96906e18 q^{25} +2.85626e19 q^{26} +1.28342e20 q^{28} +2.74961e19 q^{29} -9.77996e19 q^{31} -4.99779e20 q^{32} -7.67282e20 q^{34} +2.64422e20 q^{35} -1.80293e21 q^{37} -1.87770e21 q^{38} -3.05104e21 q^{40} +5.17966e21 q^{41} +8.74613e21 q^{43} -4.25513e22 q^{44} +1.10893e22 q^{46} -2.51817e22 q^{47} +7.94910e22 q^{49} +1.51250e23 q^{50} -4.43258e23 q^{52} -2.11957e23 q^{53} -8.76680e22 q^{55} -1.67543e24 q^{56} -5.96750e23 q^{58} +7.00844e23 q^{59} +1.08505e23 q^{61} +2.12256e24 q^{62} +4.10646e24 q^{64} -9.13240e23 q^{65} +2.46540e24 q^{67} +1.19073e25 q^{68} -5.73878e24 q^{70} -1.29459e25 q^{71} +7.46465e24 q^{73} +3.91291e25 q^{74} +2.91398e25 q^{76} -4.81415e25 q^{77} -4.94644e25 q^{79} +3.48480e25 q^{80} -1.12415e26 q^{82} +5.54332e25 q^{83} +2.45325e25 q^{85} -1.89818e26 q^{86} +5.55481e26 q^{88} +1.32973e26 q^{89} -5.01492e26 q^{91} -1.72093e26 q^{92} +5.46521e26 q^{94} +6.00364e25 q^{95} -1.06222e27 q^{97} -1.72520e27 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 21582 q^{2} + 202603844 q^{4} + 1771946100 q^{5} + 369665199904 q^{7} - 4429319872824 q^{8}+O(q^{10}) \) 2 * q - 21582 * q^2 + 202603844 * q^4 + 1771946100 * q^5 + 369665199904 * q^7 - 4429319872824 * q^8	\( 2 q - 21582 q^{2} + 202603844 q^{4} + 1771946100 q^{5} + 369665199904 q^{7} - 4429319872824 q^{8} - 14929666656300 q^{10} - 75762335668248 q^{11} - 103021079177588 q^{13} - 82\!\cdots\!36 q^{14}+ \cdots - 17\!\cdots\!78 q^{98}+O(q^{100}) \) 2 * q - 21582 * q^2 + 202603844 * q^4 + 1771946100 * q^5 + 369665199904 * q^7 - 4429319872824 * q^8 - 14929666656300 * q^10 - 75762335668248 * q^11 - 103021079177588 * q^13 - 8271467686583136 * q^14 + 68227529433700880 * q^16 - 34691611579147908 * q^17 + 111620476558642216 * q^19 + 89042670767082600 * q^20 + 2748035308851015336 * q^22 + 2892743075819387952 * q^23 - 13257495997920171250 * q^25 + 28709486590882989996 * q^26 + 129870778968981827392 * q^28 - 29959552473322806972 * q^29 + 10367463257055494032 * q^31 - 493234742263884106464 * q^32 - 775764702062031404772 * q^34 + 252142979584030920000 * q^35 - 3703660908819524869316 * q^37 - 1874664150379356981528 * q^38 - 3086079750063749300400 * q^40 - 1481814928479478034772 * q^41 + 9778778623457380249240 * q^43 - 49338574711945832880432 * q^44 + 11501496706538201034672 * q^46 - 89494998518809740323520 * q^47 + 13908377820361409575890 * q^49 + 150488580768890263638750 * q^50 - 606051653487262224622952 * q^52 - 425671275824601813476748 * q^53 - 33146870181194328159600 * q^55 - 1675060131754321848708480 * q^56 - 603708195922408484547804 * q^58 - 369418769643380130292824 * q^59 + 925133397428892745249420 * q^61 + 2135654804561872705821072 * q^62 + 1690192763441891790257216 * q^64 + 394447136075147294825400 * q^65 + 4151706674555213948132968 * q^67 + 21307603540300350668680824 * q^68 - 5740267152557252353752000 * q^70 - 9760455855870867537668784 * q^71 + 28449956347640075157409588 * q^73 + 38898941191404112127623644 * q^74 + 25770925690602426011538256 * q^76 - 48717589762471785388668288 * q^77 - 49553221898675501744231120 * q^79 + 54261621238075868678378400 * q^80 - 113221448313178537381548852 * q^82 + 120473408203228735926347736 * q^83 - 50977978054175038499879400 * q^85 - 189693121470759531169760808 * q^86 + 553837409674913803181095584 * q^88 - 205644052209697133056985556 * q^89 - 515309018103795393250147648 * q^91 - 628879743331458256476717984 * q^92 + 538732610344725656813388864 * q^94 + 87097784513216888583651600 * q^95 - 1478339006400409594836427772 * q^97 - 1733143443943237696043598078 * q^98

Introduction

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