LMFDB - Embedded newform 531.8.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, 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("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.4456 q^{2} +142.458 q^{4} +503.166 q^{5} -880.461 q^{7} -237.762 q^{8} +O(q^{10})$	\(q-16.4456 q^{2} +142.458 q^{4} +503.166 q^{5} -880.461 q^{7} -237.762 q^{8} -8274.86 q^{10} +3650.21 q^{11} -12886.3 q^{13} +14479.7 q^{14} -14324.4 q^{16} +8038.67 q^{17} -12733.9 q^{19} +71679.7 q^{20} -60029.9 q^{22} +87698.9 q^{23} +175051. q^{25} +211923. q^{26} -125428. q^{28} -149709. q^{29} +28047.3 q^{31} +266007. q^{32} -132201. q^{34} -443018. q^{35} -81281.7 q^{37} +209416. q^{38} -119634. q^{40} +174010. q^{41} +381125. q^{43} +520000. q^{44} -1.44226e6 q^{46} -1.29820e6 q^{47} -48332.2 q^{49} -2.87881e6 q^{50} -1.83575e6 q^{52} +1.49870e6 q^{53} +1.83666e6 q^{55} +209340. q^{56} +2.46205e6 q^{58} +205379. q^{59} -642647. q^{61} -461254. q^{62} -2.54112e6 q^{64} -6.48395e6 q^{65} -3.12372e6 q^{67} +1.14517e6 q^{68} +7.28569e6 q^{70} -1.43071e6 q^{71} -4.95647e6 q^{73} +1.33673e6 q^{74} -1.81404e6 q^{76} -3.21387e6 q^{77} -6.63710e6 q^{79} -7.20756e6 q^{80} -2.86170e6 q^{82} -791900. q^{83} +4.04478e6 q^{85} -6.26782e6 q^{86} -867882. q^{88} +1.19247e7 q^{89} +1.13459e7 q^{91} +1.24934e7 q^{92} +2.13497e7 q^{94} -6.40725e6 q^{95} -190733. q^{97} +794851. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) $ 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * 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 $

$2$	−16.4456	−1.45360	−0.726799	−	0.686850i	$-0.758993\pi$
$2$	−16.4456	−1.45360	−0.726799	+	0.686850i	$0.758993\pi$
$3$	0	0
$3$	0	0
$4$	142.458	1.11295
$5$	503.166	1.80018	0.900090	−	0.435704i	$-0.143500\pi$
$5$	503.166	1.80018	0.900090	+	0.435704i	$0.143500\pi$
$6$	0	0
$7$	−880.461	−0.970212	−0.485106	−	0.874455i	$-0.661219\pi$
$7$	−880.461	−0.970212	−0.485106	+	0.874455i	$0.661219\pi$
$8$	−237.762	−0.164183
$9$	0	0
$10$	−8274.86	−2.61674
$11$	3650.21	0.826882	0.413441	−	0.910531i	$-0.364327\pi$
$11$	3650.21	0.826882	0.413441	+	0.910531i	$0.364327\pi$
$12$	0	0
$13$	−12886.3	−1.62677	−0.813386	−	0.581725i	$-0.802378\pi$
$13$	−12886.3	−1.62677	−0.813386	+	0.581725i	$0.802378\pi$
$14$	14479.7	1.41030
$15$	0	0
$16$	−14324.4	−0.874293
$17$	8038.67	0.396838	0.198419	−	0.980117i	$-0.436419\pi$
$17$	8038.67	0.396838	0.198419	+	0.980117i	$0.436419\pi$
$18$	0	0
$19$	−12733.9	−0.425915	−0.212957	−	0.977061i	$-0.568310\pi$
$19$	−12733.9	−0.425915	−0.212957	+	0.977061i	$0.568310\pi$
$20$	71679.7	2.00351
$21$	0	0
$22$	−60029.9	−1.20195
$23$	87698.9	1.50296	0.751479	−	0.659757i	$-0.229341\pi$
$23$	87698.9	1.50296	0.751479	+	0.659757i	$0.229341\pi$
$24$	0	0
$25$	175051.	2.24065
$26$	211923.	2.36467
$27$	0	0
$28$	−125428.	−1.07980
$29$	−149709.	−1.13987	−0.569933	−	0.821691i	$-0.693031\pi$
$29$	−149709.	−1.13987	−0.569933	+	0.821691i	$0.693031\pi$
$30$	0	0
$31$	28047.3	0.169093	0.0845463	−	0.996420i	$-0.473056\pi$
$31$	28047.3	0.169093	0.0845463	+	0.996420i	$0.473056\pi$
$32$	266007.	1.43505
$33$	0	0
$34$	−132201.	−0.576843
$35$	−443018.	−1.74656
$36$	0	0
$37$	−81281.7	−0.263807	−0.131904	−	0.991263i	$-0.542109\pi$
$37$	−81281.7	−0.263807	−0.131904	+	0.991263i	$0.542109\pi$
$38$	209416.	0.619109
$39$	0	0
$40$	−119634.	−0.295559
$41$	174010.	0.394305	0.197152	−	0.980373i	$-0.436831\pi$
$41$	174010.	0.394305	0.197152	+	0.980373i	$0.436831\pi$
$42$	0	0
$43$	381125.	0.731017	0.365509	−	0.930808i	$-0.380895\pi$
$43$	381125.	0.731017	0.365509	+	0.930808i	$0.380895\pi$
$44$	520000.	0.920277
$45$	0	0
$46$	−1.44226e6	−2.18470
$47$	−1.29820e6	−1.82389	−0.911947	−	0.410307i	$-0.865421\pi$
$47$	−1.29820e6	−1.82389	−0.911947	+	0.410307i	$0.865421\pi$
$48$	0	0
$49$	−48332.2	−0.0586881
$50$	−2.87881e6	−3.25701
$51$	0	0
$52$	−1.83575e6	−1.81051
$53$	1.49870e6	1.38277	0.691383	−	0.722488i	$-0.257002\pi$
$53$	1.49870e6	1.38277	0.691383	+	0.722488i	$0.257002\pi$
$54$	0	0
$55$	1.83666e6	1.48854
$56$	209340.	0.159292
$57$	0	0
$58$	2.46205e6	1.65691
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−642647.	−0.362508	−0.181254	−	0.983436i	$-0.558016\pi$
$61$	−642647.	−0.362508	−0.181254	+	0.983436i	$0.558016\pi$
$62$	−461254.	−0.245793
$63$	0	0
$64$	−2.54112e6	−1.21170
$65$	−6.48395e6	−2.92848
$66$	0	0
$67$	−3.12372e6	−1.26885	−0.634426	−	0.772984i	$-0.718763\pi$
$67$	−3.12372e6	−1.26885	−0.634426	+	0.772984i	$0.718763\pi$
$68$	1.14517e6	0.441660
$69$	0	0
$70$	7.28569e6	2.53879
$71$	−1.43071e6	−0.474402	−0.237201	−	0.971461i	$-0.576230\pi$
$71$	−1.43071e6	−0.474402	−0.237201	+	0.971461i	$0.576230\pi$
$72$	0	0
$73$	−4.95647e6	−1.49122	−0.745611	−	0.666381i	$-0.767842\pi$
$73$	−4.95647e6	−1.49122	−0.745611	+	0.666381i	$0.767842\pi$
$74$	1.33673e6	0.383470
$75$	0	0
$76$	−1.81404e6	−0.474022
$77$	−3.21387e6	−0.802251
$78$	0	0
$79$	−6.63710e6	−1.51455	−0.757275	−	0.653096i	$-0.773470\pi$
$79$	−6.63710e6	−1.51455	−0.757275	+	0.653096i	$0.773470\pi$
$80$	−7.20756e6	−1.57389
$81$	0	0
$82$	−2.86170e6	−0.573161
$83$	−791900.	−0.152019	−0.0760093	−	0.997107i	$-0.524218\pi$
$83$	−791900.	−0.152019	−0.0760093	+	0.997107i	$0.524218\pi$
$84$	0	0
$85$	4.04478e6	0.714380
$86$	−6.26782e6	−1.06261
$87$	0	0
$88$	−867882.	−0.135760
$89$	1.19247e7	1.79301	0.896506	−	0.443031i	$-0.146097\pi$
$89$	1.19247e7	1.79301	0.896506	+	0.443031i	$0.146097\pi$
$90$	0	0
$91$	1.13459e7	1.57831
$92$	1.24934e7	1.67272
$93$	0	0
$94$	2.13497e7	2.65121
$95$	−6.40725e6	−0.766724
$96$	0	0
$97$	−190733.	−0.0212189	−0.0106095	−	0.999944i	$-0.503377\pi$
$97$	−190733.	−0.0212189	−0.0106095	+	0.999944i	$0.503377\pi$
$98$	794851.	0.0853089
$99$	0	0
$100$	2.49373e7	2.49373
$101$	3.70325e6	0.357650	0.178825	−	0.983881i	$-0.442770\pi$
$101$	3.70325e6	0.357650	0.178825	+	0.983881i	$0.442770\pi$
$102$	0	0
$103$	−777286.	−0.0700891	−0.0350445	−	0.999386i	$-0.511157\pi$
$103$	−777286.	−0.0700891	−0.0350445	+	0.999386i	$0.511157\pi$
$104$	3.06388e6	0.267088
$105$	0	0
$106$	−2.46470e7	−2.00999
$107$	2.22278e7	1.75409	0.877047	−	0.480404i	$-0.159510\pi$
$107$	2.22278e7	1.75409	0.877047	+	0.480404i	$0.159510\pi$
$108$	0	0
$109$	1.72711e7	1.27740	0.638701	−	0.769455i	$-0.279472\pi$
$109$	1.72711e7	1.27740	0.638701	+	0.769455i	$0.279472\pi$
$110$	−3.02050e7	−2.16373
$111$	0	0
$112$	1.26121e7	0.848250
$113$	−2.55928e7	−1.66857	−0.834283	−	0.551336i	$-0.814118\pi$
$113$	−2.55928e7	−1.66857	−0.834283	+	0.551336i	$0.814118\pi$
$114$	0	0
$115$	4.41271e7	2.70560
$116$	−2.13271e7	−1.26861
$117$	0	0
$118$	−3.37758e6	−0.189242
$119$	−7.07773e6	−0.385017
$120$	0	0
$121$	−6.16314e6	−0.316267
$122$	1.05687e7	0.526942
$123$	0	0
$124$	3.99554e6	0.188192
$125$	4.87697e7	2.23339
$126$	0	0
$127$	3.99503e7	1.73064	0.865321	−	0.501219i	$-0.167115\pi$
$127$	3.99503e7	1.73064	0.865321	+	0.501219i	$0.167115\pi$
$128$	7.74129e6	0.326271
$129$	0	0
$130$	1.06632e8	4.25684
$131$	−1.11567e7	−0.433599	−0.216799	−	0.976216i	$-0.569562\pi$
$131$	−1.11567e7	−0.433599	−0.216799	+	0.976216i	$0.569562\pi$
$132$	0	0
$133$	1.12117e7	0.413228
$134$	5.13715e7	1.84440
$135$	0	0
$136$	−1.91129e6	−0.0651540
$137$	−3.23399e7	−1.07453	−0.537263	−	0.843415i	$-0.680542\pi$
$137$	−3.23399e7	−1.07453	−0.537263	+	0.843415i	$0.680542\pi$
$138$	0	0
$139$	−3.13650e7	−0.990589	−0.495295	−	0.868725i	$-0.664940\pi$
$139$	−3.13650e7	−0.990589	−0.495295	+	0.868725i	$0.664940\pi$
$140$	−6.31112e7	−1.94383
$141$	0	0
$142$	2.35288e7	0.689590
$143$	−4.70377e7	−1.34515
$144$	0	0
$145$	−7.53282e7	−2.05196
$146$	8.15121e7	2.16764
$147$	0	0
$148$	−1.15792e7	−0.293604
$149$	−6.60578e6	−0.163596	−0.0817979	−	0.996649i	$-0.526066\pi$
$149$	−6.60578e6	−0.163596	−0.0817979	+	0.996649i	$0.526066\pi$
$150$	0	0
$151$	−5.88170e7	−1.39022	−0.695110	−	0.718903i	$-0.744644\pi$
$151$	−5.88170e7	−1.39022	−0.695110	+	0.718903i	$0.744644\pi$
$152$	3.02763e6	0.0699279
$153$	0	0
$154$	5.28539e7	1.16615
$155$	1.41124e7	0.304397
$156$	0	0
$157$	3.78723e7	0.781040	0.390520	−	0.920594i	$-0.372295\pi$
$157$	3.78723e7	0.781040	0.390520	+	0.920594i	$0.372295\pi$
$158$	1.09151e8	2.20155
$159$	0	0
$160$	1.33846e8	2.58336
$161$	−7.72154e7	−1.45819
$162$	0	0
$163$	1.16409e7	0.210537	0.105269	−	0.994444i	$-0.466430\pi$
$163$	1.16409e7	0.210537	0.105269	+	0.994444i	$0.466430\pi$
$164$	2.47891e7	0.438841
$165$	0	0
$166$	1.30233e7	0.220974
$167$	4.63591e7	0.770242	0.385121	−	0.922866i	$-0.374160\pi$
$167$	4.63591e7	0.770242	0.385121	+	0.922866i	$0.374160\pi$
$168$	0	0
$169$	1.03308e8	1.64639
$170$	−6.65189e7	−1.03842
$171$	0	0
$172$	5.42941e7	0.813585
$173$	−1.97847e6	−0.0290515	−0.0145258	−	0.999894i	$-0.504624\pi$
$173$	−1.97847e6	−0.0290515	−0.0145258	+	0.999894i	$0.504624\pi$
$174$	0	0
$175$	−1.54125e8	−2.17391
$176$	−5.22871e7	−0.722937
$177$	0	0
$178$	−1.96109e8	−2.60632
$179$	1.23315e8	1.60706	0.803530	−	0.595265i	$-0.202953\pi$
$179$	1.23315e8	1.60706	0.803530	+	0.595265i	$0.202953\pi$
$180$	0	0
$181$	3.16023e7	0.396135	0.198068	−	0.980188i	$-0.436533\pi$
$181$	3.16023e7	0.396135	0.198068	+	0.980188i	$0.436533\pi$
$182$	−1.86590e8	−2.29424
$183$	0	0
$184$	−2.08515e7	−0.246760
$185$	−4.08982e7	−0.474901
$186$	0	0
$187$	2.93428e7	0.328138
$188$	−1.84939e8	−2.02990
$189$	0	0
$190$	1.05371e8	1.11451
$191$	4.79924e7	0.498374	0.249187	−	0.968455i	$-0.419837\pi$
$191$	4.79924e7	0.498374	0.249187	+	0.968455i	$0.419837\pi$
$192$	0	0
$193$	−1.50921e8	−1.51112	−0.755560	−	0.655079i	$-0.772635\pi$
$193$	−1.50921e8	−1.51112	−0.755560	+	0.655079i	$0.772635\pi$
$194$	3.13671e6	0.0308438
$195$	0	0
$196$	−6.88528e6	−0.0653168
$197$	−9.31739e7	−0.868285	−0.434143	−	0.900844i	$-0.642949\pi$
$197$	−9.31739e7	−0.868285	−0.434143	+	0.900844i	$0.642949\pi$
$198$	0	0
$199$	−1.11446e8	−1.00249	−0.501244	−	0.865306i	$-0.667124\pi$
$199$	−1.11446e8	−1.00249	−0.501244	+	0.865306i	$0.667124\pi$
$200$	−4.16205e7	−0.367876
$201$	0	0
$202$	−6.09021e7	−0.519879
$203$	1.31812e8	1.10591
$204$	0	0
$205$	8.75561e7	0.709819
$206$	1.27829e7	0.101881
$207$	0	0
$208$	1.84589e8	1.42228
$209$	−4.64813e7	−0.352181
$210$	0	0
$211$	3.09247e7	0.226630	0.113315	−	0.993559i	$-0.463853\pi$
$211$	3.09247e7	0.226630	0.113315	+	0.993559i	$0.463853\pi$
$212$	2.13501e8	1.53895
$213$	0	0
$214$	−3.65549e8	−2.54975
$215$	1.91769e8	1.31596
$216$	0	0
$217$	−2.46945e7	−0.164056
$218$	−2.84034e8	−1.85683
$219$	0	0
$220$	2.61646e8	1.65667
$221$	−1.03589e8	−0.645564
$222$	0	0
$223$	−2.08972e8	−1.26189	−0.630945	−	0.775828i	$-0.717333\pi$
$223$	−2.08972e8	−1.26189	−0.630945	+	0.775828i	$0.717333\pi$
$224$	−2.34209e8	−1.39231
$225$	0	0
$226$	4.20889e8	2.42543
$227$	−3.39143e8	−1.92438	−0.962192	−	0.272372i	$-0.912192\pi$
$227$	−3.39143e8	−1.92438	−0.962192	+	0.272372i	$0.912192\pi$
$228$	0	0
$229$	−1.60117e7	−0.0881073	−0.0440537	−	0.999029i	$-0.514027\pi$
$229$	−1.60117e7	−0.0881073	−0.0440537	+	0.999029i	$0.514027\pi$
$230$	−7.25696e8	−3.93285
$231$	0	0
$232$	3.55950e7	0.187146
$233$	3.55157e8	1.83939	0.919697	−	0.392628i	$-0.128434\pi$
$233$	3.55157e8	1.83939	0.919697	+	0.392628i	$0.128434\pi$
$234$	0	0
$235$	−6.53211e8	−3.28334
$236$	2.92578e7	0.144894
$237$	0	0
$238$	1.16397e8	0.559660
$239$	−2.06526e8	−0.978550	−0.489275	−	0.872130i	$-0.662738\pi$
$239$	−2.06526e8	−0.978550	−0.489275	+	0.872130i	$0.662738\pi$
$240$	0	0
$241$	−5.76212e7	−0.265169	−0.132585	−	0.991172i	$-0.542328\pi$
$241$	−5.76212e7	−0.265169	−0.132585	+	0.991172i	$0.542328\pi$
$242$	1.01357e8	0.459725
$243$	0	0
$244$	−9.15499e7	−0.403453
$245$	−2.43191e7	−0.105649
$246$	0	0
$247$	1.64092e8	0.692866
$248$	−6.66858e6	−0.0277621
$249$	0	0
$250$	−8.02047e8	−3.24646
$251$	−2.09133e8	−0.834767	−0.417384	−	0.908730i	$-0.637053\pi$
$251$	−2.09133e8	−0.834767	−0.417384	+	0.908730i	$0.637053\pi$
$252$	0	0
$253$	3.20119e8	1.24277
$254$	−6.57006e8	−2.51566
$255$	0	0
$256$	1.97953e8	0.737433
$257$	−2.23832e6	−0.00822540	−0.00411270	−	0.999992i	$-0.501309\pi$
$257$	−2.23832e6	−0.00822540	−0.00411270	+	0.999992i	$0.501309\pi$
$258$	0	0
$259$	7.15653e7	0.255949
$260$	−9.23687e8	−3.25925
$261$	0	0
$262$	1.83479e8	0.630278
$263$	−2.38990e7	−0.0810093	−0.0405046	−	0.999179i	$-0.512897\pi$
$263$	−2.38990e7	−0.0810093	−0.0405046	+	0.999179i	$0.512897\pi$
$264$	0	0
$265$	7.54094e8	2.48923
$266$	−1.84383e8	−0.600667
$267$	0	0
$268$	−4.44998e8	−1.41217
$269$	1.06664e8	0.334108	0.167054	−	0.985948i	$-0.446575\pi$
$269$	1.06664e8	0.334108	0.167054	+	0.985948i	$0.446575\pi$
$270$	0	0
$271$	−2.87451e8	−0.877347	−0.438674	−	0.898646i	$-0.644552\pi$
$271$	−2.87451e8	−0.877347	−0.438674	+	0.898646i	$0.644552\pi$
$272$	−1.15149e8	−0.346953
$273$	0	0
$274$	5.31849e8	1.56193
$275$	6.38972e8	1.85275
$276$	0	0
$277$	−2.49921e8	−0.706519	−0.353259	−	0.935525i	$-0.614927\pi$
$277$	−2.49921e8	−0.706519	−0.353259	+	0.935525i	$0.614927\pi$
$278$	5.15816e8	1.43992
$279$	0	0
$280$	1.05333e8	0.286755
$281$	−4.63280e8	−1.24558	−0.622790	−	0.782389i	$-0.714001\pi$
$281$	−4.63280e8	−1.24558	−0.622790	+	0.782389i	$0.714001\pi$
$282$	0	0
$283$	−1.53501e8	−0.402586	−0.201293	−	0.979531i	$-0.564514\pi$
$283$	−1.53501e8	−0.402586	−0.201293	+	0.979531i	$0.564514\pi$
$284$	−2.03815e8	−0.527985
$285$	0	0
$286$	7.73563e8	1.95531
$287$	−1.53209e8	−0.382559
$288$	0	0
$289$	−3.45718e8	−0.842520
$290$	1.23882e9	2.98273
$291$	0	0
$292$	−7.06086e8	−1.65965
$293$	5.66633e8	1.31603	0.658014	−	0.753005i	$-0.271397\pi$
$293$	5.66633e8	1.31603	0.658014	+	0.753005i	$0.271397\pi$
$294$	0	0
$295$	1.03340e8	0.234364
$296$	1.93257e7	0.0433126
$297$	0	0
$298$	1.08636e8	0.237803
$299$	−1.13011e9	−2.44497
$300$	0	0
$301$	−3.35565e8	−0.709242
$302$	9.67280e8	2.02082
$303$	0	0
$304$	1.82405e8	0.372374
$305$	−3.23358e8	−0.652580
$306$	0	0
$307$	9.68734e7	0.191082	0.0955411	−	0.995425i	$-0.469542\pi$
$307$	9.68734e7	0.191082	0.0955411	+	0.995425i	$0.469542\pi$
$308$	−4.57839e8	−0.892864
$309$	0	0
$310$	−2.32087e8	−0.442472
$311$	7.92556e8	1.49406	0.747031	−	0.664789i	$-0.231479\pi$
$311$	7.92556e8	1.49406	0.747031	+	0.664789i	$0.231479\pi$
$312$	0	0
$313$	−9.31754e8	−1.71750	−0.858749	−	0.512397i	$-0.828758\pi$
$313$	−9.31754e8	−1.71750	−0.858749	+	0.512397i	$0.828758\pi$
$314$	−6.22833e8	−1.13532
$315$	0	0
$316$	−9.45505e8	−1.68562
$317$	1.05607e8	0.186203	0.0931013	−	0.995657i	$-0.470322\pi$
$317$	1.05607e8	0.186203	0.0931013	+	0.995657i	$0.470322\pi$
$318$	0	0
$319$	−5.46468e8	−0.942534
$320$	−1.27860e9	−2.18128
$321$	0	0
$322$	1.26985e9	2.11962
$323$	−1.02363e8	−0.169019
$324$	0	0
$325$	−2.25576e9	−3.64503
$326$	−1.91441e8	−0.306036
$327$	0	0
$328$	−4.13731e7	−0.0647381
$329$	1.14302e9	1.76956
$330$	0	0
$331$	4.98311e8	0.755270	0.377635	−	0.925955i	$-0.376737\pi$
$331$	4.98311e8	0.755270	0.377635	+	0.925955i	$0.376737\pi$
$332$	−1.12812e8	−0.169189
$333$	0	0
$334$	−7.62403e8	−1.11962
$335$	−1.57175e9	−2.28416
$336$	0	0
$337$	−3.58052e8	−0.509614	−0.254807	−	0.966992i	$-0.582012\pi$
$337$	−3.58052e8	−0.509614	−0.254807	+	0.966992i	$0.582012\pi$
$338$	−1.69897e9	−2.39318
$339$	0	0
$340$	5.76210e8	0.795068
$341$	1.02378e8	0.139820
$342$	0	0
$343$	7.67652e8	1.02715
$344$	−9.06171e7	−0.120021
$345$	0	0
$346$	3.25372e7	0.0422293
$347$	3.32014e8	0.426582	0.213291	−	0.976989i	$-0.431582\pi$
$347$	3.32014e8	0.426582	0.213291	+	0.976989i	$0.431582\pi$
$348$	0	0
$349$	−7.26470e8	−0.914806	−0.457403	−	0.889260i	$-0.651220\pi$
$349$	−7.26470e8	−0.914806	−0.457403	+	0.889260i	$0.651220\pi$
$350$	2.53468e9	3.15999
$351$	0	0
$352$	9.70982e8	1.18662
$353$	4.26013e8	0.515479	0.257740	−	0.966214i	$-0.417022\pi$
$353$	4.26013e8	0.515479	0.257740	+	0.966214i	$0.417022\pi$
$354$	0	0
$355$	−7.19882e8	−0.854009
$356$	1.69877e9	1.99553
$357$	0	0
$358$	−2.02800e9	−2.33602
$359$	−2.06872e8	−0.235978	−0.117989	−	0.993015i	$-0.537645\pi$
$359$	−2.06872e8	−0.235978	−0.117989	+	0.993015i	$0.537645\pi$
$360$	0	0
$361$	−7.31720e8	−0.818597
$362$	−5.19718e8	−0.575822
$363$	0	0
$364$	1.61631e9	1.75658
$365$	−2.49392e9	−2.68447
$366$	0	0
$367$	6.43290e8	0.679322	0.339661	−	0.940548i	$-0.389688\pi$
$367$	6.43290e8	0.679322	0.339661	+	0.940548i	$0.389688\pi$
$368$	−1.25624e9	−1.31403
$369$	0	0
$370$	6.72594e8	0.690315
$371$	−1.31955e9	−1.34158
$372$	0	0
$373$	1.96256e9	1.95813	0.979066	−	0.203541i	$-0.0652451\pi$
$373$	1.96256e9	1.95813	0.979066	+	0.203541i	$0.0652451\pi$
$374$	−4.82560e8	−0.476981
$375$	0	0
$376$	3.08663e8	0.299452
$377$	1.92919e9	1.85430
$378$	0	0
$379$	−3.20733e7	−0.0302626	−0.0151313	−	0.999886i	$-0.504817\pi$
$379$	−3.20733e7	−0.0302626	−0.0151313	+	0.999886i	$0.504817\pi$
$380$	−9.12760e8	−0.853324
$381$	0	0
$382$	−7.89263e8	−0.724436
$383$	1.15327e8	0.104890	0.0524451	−	0.998624i	$-0.483299\pi$
$383$	1.15327e8	0.104890	0.0524451	+	0.998624i	$0.483299\pi$
$384$	0	0
$385$	−1.61711e9	−1.44420
$386$	2.48199e9	2.19656
$387$	0	0
$388$	−2.71713e7	−0.0236156
$389$	1.76561e8	0.152080	0.0760400	−	0.997105i	$-0.475772\pi$
$389$	1.76561e8	0.152080	0.0760400	+	0.997105i	$0.475772\pi$
$390$	0	0
$391$	7.04983e8	0.596430
$392$	1.14916e7	0.00963558
$393$	0	0
$394$	1.53230e9	1.26214
$395$	−3.33956e9	−2.72646
$396$	0	0
$397$	−5.74255e8	−0.460615	−0.230307	−	0.973118i	$-0.573973\pi$
$397$	−5.74255e8	−0.460615	−0.230307	+	0.973118i	$0.573973\pi$
$398$	1.83280e9	1.45722
$399$	0	0
$400$	−2.50750e9	−1.95898
$401$	−1.53794e9	−1.19106	−0.595531	−	0.803332i	$-0.703058\pi$
$401$	−1.53794e9	−1.19106	−0.595531	+	0.803332i	$0.703058\pi$
$402$	0	0
$403$	−3.61426e8	−0.275075
$404$	5.27555e8	0.398046
$405$	0	0
$406$	−2.16773e9	−1.60755
$407$	−2.96695e8	−0.218137
$408$	0	0
$409$	−2.47197e9	−1.78654	−0.893269	−	0.449522i	$-0.851594\pi$
$409$	−2.47197e9	−1.78654	−0.893269	+	0.449522i	$0.851594\pi$
$410$	−1.43991e9	−1.03179
$411$	0	0
$412$	−1.10730e8	−0.0780056
$413$	−1.80828e8	−0.126311
$414$	0	0
$415$	−3.98457e8	−0.273661
$416$	−3.42785e9	−2.33451
$417$	0	0
$418$	7.64412e8	0.511930
$419$	6.90685e8	0.458702	0.229351	−	0.973344i	$-0.426340\pi$
$419$	6.90685e8	0.458702	0.229351	+	0.973344i	$0.426340\pi$
$420$	0	0
$421$	−1.12202e8	−0.0732848	−0.0366424	−	0.999328i	$-0.511666\pi$
$421$	−1.12202e8	−0.0732848	−0.0366424	+	0.999328i	$0.511666\pi$
$422$	−5.08576e8	−0.329429
$423$	0	0
$424$	−3.56334e8	−0.227027
$425$	1.40718e9	0.889174
$426$	0	0
$427$	5.65825e8	0.351710
$428$	3.16651e9	1.95222
$429$	0	0
$430$	−3.15375e9	−1.91288
$431$	−2.64480e9	−1.59119	−0.795595	−	0.605828i	$-0.792842\pi$
$431$	−2.64480e9	−1.59119	−0.795595	+	0.605828i	$0.792842\pi$
$432$	0	0
$433$	2.00053e9	1.18424	0.592118	−	0.805851i	$-0.298292\pi$
$433$	2.00053e9	1.18424	0.592118	+	0.805851i	$0.298292\pi$
$434$	4.06116e8	0.238471
$435$	0	0
$436$	2.46040e9	1.42168
$437$	−1.11675e9	−0.640132
$438$	0	0
$439$	−2.43012e8	−0.137089	−0.0685444	−	0.997648i	$-0.521835\pi$
$439$	−2.43012e8	−0.137089	−0.0685444	+	0.997648i	$0.521835\pi$
$440$	−4.36688e8	−0.244392
$441$	0	0
$442$	1.70358e9	0.938392
$443$	2.02048e9	1.10418	0.552092	−	0.833784i	$-0.313830\pi$
$443$	2.02048e9	1.10418	0.552092	+	0.833784i	$0.313830\pi$
$444$	0	0
$445$	6.00011e9	3.22775
$446$	3.43667e9	1.83428
$447$	0	0
$448$	2.23736e9	1.17561
$449$	−5.42877e8	−0.283035	−0.141517	−	0.989936i	$-0.545198\pi$
$449$	−5.42877e8	−0.283035	−0.141517	+	0.989936i	$0.545198\pi$
$450$	0	0
$451$	6.35175e8	0.326043
$452$	−3.64589e9	−1.85703
$453$	0	0
$454$	5.57740e9	2.79728
$455$	5.70886e9	2.84125
$456$	0	0
$457$	4.73514e8	0.232074	0.116037	−	0.993245i	$-0.462981\pi$
$457$	4.73514e8	0.232074	0.116037	+	0.993245i	$0.462981\pi$
$458$	2.63321e8	0.128073
$459$	0	0
$460$	6.28624e9	3.01119
$461$	−4.33013e8	−0.205849	−0.102924	−	0.994689i	$-0.532820\pi$
$461$	−4.33013e8	−0.205849	−0.102924	+	0.994689i	$0.532820\pi$
$462$	0	0
$463$	−7.80956e8	−0.365673	−0.182837	−	0.983143i	$-0.558528\pi$
$463$	−7.80956e8	−0.365673	−0.182837	+	0.983143i	$0.558528\pi$
$464$	2.14449e9	0.996577
$465$	0	0
$466$	−5.84077e9	−2.67374
$467$	−2.81340e9	−1.27827	−0.639134	−	0.769095i	$-0.720707\pi$
$467$	−2.81340e9	−1.27827	−0.639134	+	0.769095i	$0.720707\pi$
$468$	0	0
$469$	2.75032e9	1.23106
$470$	1.07424e10	4.77266
$471$	0	0
$472$	−4.88314e7	−0.0213748
$473$	1.39119e9	0.604465
$474$	0	0
$475$	−2.22907e9	−0.954326
$476$	−1.00828e9	−0.428504
$477$	0	0
$478$	3.39645e9	1.42242
$479$	1.32364e9	0.550297	0.275149	−	0.961402i	$-0.411273\pi$
$479$	1.32364e9	0.550297	0.275149	+	0.961402i	$0.411273\pi$
$480$	0	0
$481$	1.04742e9	0.429154
$482$	9.47615e8	0.385449
$483$	0	0
$484$	−8.77986e8	−0.351989
$485$	−9.59701e7	−0.0381979
$486$	0	0
$487$	−7.45478e8	−0.292472	−0.146236	−	0.989250i	$-0.546716\pi$
$487$	−7.45478e8	−0.292472	−0.146236	+	0.989250i	$0.546716\pi$
$488$	1.52797e8	0.0595177
$489$	0	0
$490$	3.99942e8	0.153571
$491$	−2.42096e9	−0.923000	−0.461500	−	0.887140i	$-0.652689\pi$
$491$	−2.42096e9	−0.923000	−0.461500	+	0.887140i	$0.652689\pi$
$492$	0	0
$493$	−1.20346e9	−0.452342
$494$	−2.69860e9	−1.00715
$495$	0	0
$496$	−4.01761e8	−0.147837
$497$	1.25968e9	0.460270
$498$	0	0
$499$	−2.55957e9	−0.922180	−0.461090	−	0.887353i	$-0.652541\pi$
$499$	−2.55957e9	−0.922180	−0.461090	+	0.887353i	$0.652541\pi$
$500$	6.94761e9	2.48565
$501$	0	0
$502$	3.43932e9	1.21342
$503$	−3.11936e9	−1.09289	−0.546446	−	0.837495i	$-0.684019\pi$
$503$	−3.11936e9	−1.09289	−0.546446	+	0.837495i	$0.684019\pi$
$504$	0	0
$505$	1.86335e9	0.643834
$506$	−5.26455e9	−1.80649
$507$	0	0
$508$	5.69122e9	1.92612
$509$	−8.95837e8	−0.301104	−0.150552	−	0.988602i	$-0.548105\pi$
$509$	−8.95837e8	−0.301104	−0.150552	+	0.988602i	$0.548105\pi$
$510$	0	0
$511$	4.36397e9	1.44680
$512$	−4.24634e9	−1.39820
$513$	0	0
$514$	3.68106e7	0.0119564
$515$	−3.91104e8	−0.126173
$516$	0	0
$517$	−4.73871e9	−1.50815
$518$	−1.17693e9	−0.372047
$519$	0	0
$520$	1.54164e9	0.480807
$521$	−4.55174e9	−1.41009	−0.705043	−	0.709164i	$-0.749073\pi$
$521$	−4.55174e9	−1.41009	−0.705043	+	0.709164i	$0.749073\pi$
$522$	0	0
$523$	3.42336e9	1.04640	0.523199	−	0.852211i	$-0.324739\pi$
$523$	3.42336e9	1.04640	0.523199	+	0.852211i	$0.324739\pi$
$524$	−1.58936e9	−0.482573
$525$	0	0
$526$	3.93033e8	0.117755
$527$	2.25463e8	0.0671023
$528$	0	0
$529$	4.28628e9	1.25888
$530$	−1.24015e10	−3.61834
$531$	0	0
$532$	1.59719e9	0.459902
$533$	−2.24235e9	−0.641443
$534$	0	0
$535$	1.11843e10	3.15769
$536$	7.42704e8	0.208324
$537$	0	0
$538$	−1.75416e9	−0.485659
$539$	−1.76422e8	−0.0485281
$540$	0	0
$541$	−1.67371e9	−0.454455	−0.227227	−	0.973842i	$-0.572966\pi$
$541$	−1.67371e9	−0.454455	−0.227227	+	0.973842i	$0.572966\pi$
$542$	4.72730e9	1.27531
$543$	0	0
$544$	2.13834e9	0.569484
$545$	8.69023e9	2.29955
$546$	0	0
$547$	3.46139e9	0.904265	0.452132	−	0.891951i	$-0.350664\pi$
$547$	3.46139e9	0.904265	0.452132	+	0.891951i	$0.350664\pi$
$548$	−4.60706e9	−1.19589
$549$	0	0
$550$	−1.05083e10	−2.69316
$551$	1.90637e9	0.485486
$552$	0	0
$553$	5.84371e9	1.46944
$554$	4.11010e9	1.02699
$555$	0	0
$556$	−4.46818e9	−1.10248
$557$	−4.02826e9	−0.987698	−0.493849	−	0.869548i	$-0.664410\pi$
$557$	−4.02826e9	−0.987698	−0.493849	+	0.869548i	$0.664410\pi$
$558$	0	0
$559$	−4.91129e9	−1.18920
$560$	6.34597e9	1.52700
$561$	0	0
$562$	7.61892e9	1.81057
$563$	4.59603e9	1.08544	0.542718	−	0.839915i	$-0.317395\pi$
$563$	4.59603e9	1.08544	0.542718	+	0.839915i	$0.317395\pi$
$564$	0	0
$565$	−1.28774e10	−3.00372
$566$	2.52441e9	0.585198
$567$	0	0
$568$	3.40168e8	0.0778887
$569$	−3.61693e9	−0.823089	−0.411544	−	0.911390i	$-0.635011\pi$
$569$	−3.61693e9	−0.823089	−0.411544	+	0.911390i	$0.635011\pi$
$570$	0	0
$571$	−5.26683e9	−1.18392	−0.591961	−	0.805966i	$-0.701646\pi$
$571$	−5.26683e9	−1.18392	−0.591961	+	0.805966i	$0.701646\pi$
$572$	−6.70087e9	−1.49708
$573$	0	0
$574$	2.51962e9	0.556087
$575$	1.53518e10	3.36760
$576$	0	0
$577$	−4.68999e9	−1.01638	−0.508191	−	0.861244i	$-0.669686\pi$
$577$	−4.68999e9	−1.01638	−0.508191	+	0.861244i	$0.669686\pi$
$578$	5.68554e9	1.22469
$579$	0	0
$580$	−1.07311e10	−2.28373
$581$	6.97236e8	0.147490
$582$	0	0
$583$	5.47057e9	1.14338
$584$	1.17846e9	0.244833
$585$	0	0
$586$	−9.31862e9	−1.91298
$587$	3.85707e9	0.787090	0.393545	−	0.919305i	$-0.371249\pi$
$587$	3.85707e9	0.787090	0.393545	+	0.919305i	$0.371249\pi$
$588$	0	0
$589$	−3.57150e8	−0.0720191
$590$	−1.69948e9	−0.340671
$591$	0	0
$592$	1.16431e9	0.230645
$593$	1.00785e10	1.98475	0.992373	−	0.123269i	$-0.0393378\pi$
$593$	1.00785e10	1.98475	0.992373	+	0.123269i	$0.0393378\pi$
$594$	0	0
$595$	−3.56127e9	−0.693100
$596$	−9.41043e8	−0.182074
$597$	0	0
$598$	1.85854e10	3.55400
$599$	−5.11362e9	−0.972153	−0.486076	−	0.873916i	$-0.661572\pi$
$599$	−5.11362e9	−0.972153	−0.486076	+	0.873916i	$0.661572\pi$
$600$	0	0
$601$	−9.02170e9	−1.69523	−0.847613	−	0.530615i	$-0.821961\pi$
$601$	−9.02170e9	−1.69523	−0.847613	+	0.530615i	$0.821961\pi$
$602$	5.51857e9	1.03095
$603$	0	0
$604$	−8.37892e9	−1.54724
$605$	−3.10108e9	−0.569337
$606$	0	0
$607$	−8.87849e9	−1.61131	−0.805654	−	0.592386i	$-0.798186\pi$
$607$	−8.87849e9	−1.61131	−0.805654	+	0.592386i	$0.798186\pi$
$608$	−3.38730e9	−0.611211
$609$	0	0
$610$	5.31781e9	0.948590
$611$	1.67290e10	2.96706
$612$	0	0
$613$	−1.05857e10	−1.85613	−0.928067	−	0.372414i	$-0.878530\pi$
$613$	−1.05857e10	−1.85613	−0.928067	+	0.372414i	$0.878530\pi$
$614$	−1.59314e9	−0.277757
$615$	0	0
$616$	7.64136e8	0.131716
$617$	1.54747e9	0.265231	0.132616	−	0.991168i	$-0.457662\pi$
$617$	1.54747e9	0.265231	0.132616	+	0.991168i	$0.457662\pi$
$618$	0	0
$619$	−8.22537e9	−1.39392	−0.696961	−	0.717109i	$-0.745465\pi$
$619$	−8.22537e9	−1.39392	−0.696961	+	0.717109i	$0.745465\pi$
$620$	2.01042e9	0.338779
$621$	0	0
$622$	−1.30341e10	−2.17177
$623$	−1.04992e10	−1.73960
$624$	0	0
$625$	1.08634e10	1.77986
$626$	1.53232e10	2.49655
$627$	0	0
$628$	5.39520e9	0.869258
$629$	−6.53397e8	−0.104689
$630$	0	0
$631$	8.41980e8	0.133413	0.0667066	−	0.997773i	$-0.478751\pi$
$631$	8.41980e8	0.133413	0.0667066	+	0.997773i	$0.478751\pi$
$632$	1.57805e9	0.248663
$633$	0	0
$634$	−1.73677e9	−0.270664
$635$	2.01016e10	3.11547
$636$	0	0
$637$	6.22823e8	0.0954721
$638$	8.98698e9	1.37007
$639$	0	0
$640$	3.89515e9	0.587347
$641$	7.50261e8	0.112515	0.0562574	−	0.998416i	$-0.482083\pi$
$641$	7.50261e8	0.112515	0.0562574	+	0.998416i	$0.482083\pi$
$642$	0	0
$643$	2.28515e9	0.338981	0.169491	−	0.985532i	$-0.445788\pi$
$643$	2.28515e9	0.338981	0.169491	+	0.985532i	$0.445788\pi$
$644$	−1.09999e10	−1.62289
$645$	0	0
$646$	1.68343e9	0.245686
$647$	5.47871e9	0.795268	0.397634	−	0.917544i	$-0.369831\pi$
$647$	5.47871e9	0.795268	0.397634	+	0.917544i	$0.369831\pi$
$648$	0	0
$649$	7.49676e8	0.107651
$650$	3.70973e10	5.29840
$651$	0	0
$652$	1.65833e9	0.234317
$653$	−1.99751e8	−0.0280733	−0.0140366	−	0.999901i	$-0.504468\pi$
$653$	−1.99751e8	−0.0280733	−0.0140366	+	0.999901i	$0.504468\pi$
$654$	0	0
$655$	−5.61369e9	−0.780556
$656$	−2.49260e9	−0.344738
$657$	0	0
$658$	−1.87976e10	−2.57224
$659$	9.51418e9	1.29501	0.647504	−	0.762062i	$-0.275813\pi$
$659$	9.51418e9	1.29501	0.647504	+	0.762062i	$0.275813\pi$
$660$	0	0
$661$	1.01921e9	0.137265	0.0686324	−	0.997642i	$-0.478136\pi$
$661$	1.01921e9	0.137265	0.0686324	+	0.997642i	$0.478136\pi$
$662$	−8.19502e9	−1.09786
$663$	0	0
$664$	1.88284e8	0.0249589
$665$	5.64133e9	0.743885
$666$	0	0
$667$	−1.31293e10	−1.71317
$668$	6.60420e9	0.857240
$669$	0	0
$670$	2.58484e10	3.32026
$671$	−2.34580e9	−0.299751
$672$	0	0
$673$	−1.62094e9	−0.204982	−0.102491	−	0.994734i	$-0.532681\pi$
$673$	−1.62094e9	−0.204982	−0.102491	+	0.994734i	$0.532681\pi$
$674$	5.88838e9	0.740775
$675$	0	0
$676$	1.47170e10	1.83234
$677$	−1.19208e10	−1.47653	−0.738267	−	0.674508i	$-0.764356\pi$
$677$	−1.19208e10	−1.47653	−0.738267	+	0.674508i	$0.764356\pi$
$678$	0	0
$679$	1.67932e8	0.0205869
$680$	−9.61697e8	−0.117289
$681$	0	0
$682$	−1.68367e9	−0.203242
$683$	−2.19627e9	−0.263763	−0.131881	−	0.991265i	$-0.542102\pi$
$683$	−2.19627e9	−0.263763	−0.131881	+	0.991265i	$0.542102\pi$
$684$	0	0
$685$	−1.62723e10	−1.93434
$686$	−1.26245e10	−1.49307
$687$	0	0
$688$	−5.45939e9	−0.639123
$689$	−1.93127e10	−2.24945
$690$	0	0
$691$	6.06217e9	0.698964	0.349482	−	0.936943i	$-0.386358\pi$
$691$	6.06217e9	0.698964	0.349482	+	0.936943i	$0.386358\pi$
$692$	−2.81848e8	−0.0323329
$693$	0	0
$694$	−5.46016e9	−0.620079
$695$	−1.57818e10	−1.78324
$696$	0	0
$697$	1.39881e9	0.156475
$698$	1.19472e10	1.32976
$699$	0	0
$700$	−2.19563e10	−2.41945
$701$	−1.56309e10	−1.71385	−0.856924	−	0.515444i	$-0.827627\pi$
$701$	−1.56309e10	−1.71385	−0.856924	+	0.515444i	$0.827627\pi$
$702$	0	0
$703$	1.03503e9	0.112359
$704$	−9.27562e9	−1.00193
$705$	0	0
$706$	−7.00603e9	−0.749300
$707$	−3.26056e9	−0.346996
$708$	0	0
$709$	−1.23867e10	−1.30526	−0.652628	−	0.757679i	$-0.726333\pi$
$709$	−1.23867e10	−1.30526	−0.652628	+	0.757679i	$0.726333\pi$
$710$	1.18389e10	1.24139
$711$	0	0
$712$	−2.83525e9	−0.294382
$713$	2.45972e9	0.254139
$714$	0	0
$715$	−2.36678e10	−2.42151
$716$	1.75672e10	1.78858
$717$	0	0
$718$	3.40213e9	0.343017
$719$	8.62174e9	0.865055	0.432528	−	0.901621i	$-0.357622\pi$
$719$	8.62174e9	0.865055	0.432528	+	0.901621i	$0.357622\pi$
$720$	0	0
$721$	6.84370e8	0.0680013
$722$	1.20336e10	1.18991
$723$	0	0
$724$	4.50198e9	0.440879
$725$	−2.62066e10	−2.55404
$726$	0	0
$727$	4.13776e9	0.399388	0.199694	−	0.979858i	$-0.436005\pi$
$727$	4.13776e9	0.399388	0.199694	+	0.979858i	$0.436005\pi$
$728$	−2.69762e9	−0.259132
$729$	0	0
$730$	4.10141e10	3.90214
$731$	3.06374e9	0.290095
$732$	0	0
$733$	−1.53664e10	−1.44115	−0.720575	−	0.693377i	$-0.756122\pi$
$733$	−1.53664e10	−1.44115	−0.720575	+	0.693377i	$0.756122\pi$
$734$	−1.05793e10	−0.987462
$735$	0	0
$736$	2.33285e10	2.15683
$737$	−1.14023e10	−1.04919
$738$	0	0
$739$	1.34234e10	1.22351	0.611756	−	0.791046i	$-0.290463\pi$
$739$	1.34234e10	1.22351	0.611756	+	0.791046i	$0.290463\pi$
$740$	−5.82625e9	−0.528540
$741$	0	0
$742$	2.17007e10	1.95012
$743$	−1.81636e10	−1.62458	−0.812289	−	0.583255i	$-0.801779\pi$
$743$	−1.81636e10	−1.62458	−0.812289	+	0.583255i	$0.801779\pi$
$744$	0	0
$745$	−3.32380e9	−0.294502
$746$	−3.22755e10	−2.84634
$747$	0	0
$748$	4.18011e9	0.365201
$749$	−1.95707e10	−1.70184
$750$	0	0
$751$	1.88209e10	1.62144	0.810719	−	0.585435i	$-0.199076\pi$
$751$	1.88209e10	1.62144	0.810719	+	0.585435i	$0.199076\pi$
$752$	1.85960e10	1.59462
$753$	0	0
$754$	−3.17267e10	−2.69541
$755$	−2.95947e10	−2.50265
$756$	0	0
$757$	−6.17064e9	−0.517005	−0.258503	−	0.966011i	$-0.583229\pi$
$757$	−6.17064e9	−0.517005	−0.258503	+	0.966011i	$0.583229\pi$
$758$	5.27465e8	0.0439897
$759$	0	0
$760$	1.52340e9	0.125883
$761$	−2.31155e10	−1.90133	−0.950665	−	0.310219i	$-0.899598\pi$
$761$	−2.31155e10	−1.90133	−0.950665	+	0.310219i	$0.899598\pi$
$762$	0	0
$763$	−1.52065e10	−1.23935
$764$	6.83687e9	0.554665
$765$	0	0
$766$	−1.89662e9	−0.152468
$767$	−2.64658e9	−0.211788
$768$	0	0
$769$	−1.75289e10	−1.38999	−0.694996	−	0.719014i	$-0.744594\pi$
$769$	−1.75289e10	−1.38999	−0.694996	+	0.719014i	$0.744594\pi$
$770$	2.65943e10	2.09928
$771$	0	0
$772$	−2.14998e10	−1.68180
$773$	−7.06814e9	−0.550398	−0.275199	−	0.961387i	$-0.588744\pi$
$773$	−7.06814e9	−0.550398	−0.275199	+	0.961387i	$0.588744\pi$
$774$	0	0
$775$	4.90970e9	0.378877
$776$	4.53490e7	0.00348379
$777$	0	0
$778$	−2.90366e9	−0.221063
$779$	−2.21583e9	−0.167940
$780$	0	0
$781$	−5.22238e9	−0.392274
$782$	−1.15939e10	−0.866971
$783$	0	0
$784$	6.92330e8	0.0513106
$785$	1.90561e10	1.40601
$786$	0	0
$787$	−6.40732e9	−0.468559	−0.234280	−	0.972169i	$-0.575273\pi$
$787$	−6.40732e9	−0.468559	−0.234280	+	0.972169i	$0.575273\pi$
$788$	−1.32733e10	−0.966357
$789$	0	0
$790$	5.49211e10	3.96318
$791$	2.25335e10	1.61886
$792$	0	0
$793$	8.28134e9	0.589718
$794$	9.44396e9	0.669549
$795$	0	0
$796$	−1.58763e10	−1.11572
$797$	−9.49012e9	−0.663999	−0.332000	−	0.943279i	$-0.607723\pi$
$797$	−9.49012e9	−0.663999	−0.332000	+	0.943279i	$0.607723\pi$
$798$	0	0
$799$	−1.04358e10	−0.723790
$800$	4.65647e10	3.21545
$801$	0	0
$802$	2.52924e10	1.73133
$803$	−1.80921e10	−1.23306
$804$	0	0
$805$	−3.88522e10	−2.62500
$806$	5.94386e9	0.399849
$807$	0	0
$808$	−8.80492e8	−0.0587200
$809$	6.90815e9	0.458714	0.229357	−	0.973342i	$-0.426338\pi$
$809$	6.90815e9	0.458714	0.229357	+	0.973342i	$0.426338\pi$
$810$	0	0
$811$	1.33817e9	0.0880925	0.0440462	−	0.999029i	$-0.485975\pi$
$811$	1.33817e9	0.0880925	0.0440462	+	0.999029i	$0.485975\pi$
$812$	1.87777e10	1.23082
$813$	0	0
$814$	4.87933e9	0.317084
$815$	5.85728e9	0.379005
$816$	0	0
$817$	−4.85319e9	−0.311351
$818$	4.06531e10	2.59691
$819$	0	0
$820$	1.24730e10	0.789993
$821$	−2.36075e10	−1.48884	−0.744420	−	0.667711i	$-0.767274\pi$
$821$	−2.36075e10	−1.48884	−0.744420	+	0.667711i	$0.767274\pi$
$822$	0	0
$823$	8.76462e9	0.548067	0.274033	−	0.961720i	$-0.411642\pi$
$823$	8.76462e9	0.548067	0.274033	+	0.961720i	$0.411642\pi$
$824$	1.84809e8	0.0115074
$825$	0	0
$826$	2.97383e9	0.183605
$827$	6.51503e9	0.400541	0.200271	−	0.979741i	$-0.435818\pi$
$827$	6.51503e9	0.400541	0.200271	+	0.979741i	$0.435818\pi$
$828$	0	0
$829$	−1.98528e10	−1.21026	−0.605132	−	0.796125i	$-0.706880\pi$
$829$	−1.98528e10	−1.21026	−0.605132	+	0.796125i	$0.706880\pi$
$830$	6.55286e9	0.397793
$831$	0	0
$832$	3.27456e10	1.97116
$833$	−3.88526e8	−0.0232896
$834$	0	0
$835$	2.33263e10	1.38657
$836$	−6.62161e9	−0.391960
$837$	0	0
$838$	−1.13587e10	−0.666769
$839$	−2.67640e10	−1.56453	−0.782265	−	0.622945i	$-0.785936\pi$
$839$	−2.67640e10	−1.56453	−0.782265	+	0.622945i	$0.785936\pi$
$840$	0	0
$841$	5.16278e9	0.299293
$842$	1.84523e9	0.106527
$843$	0	0
$844$	4.40546e9	0.252228
$845$	5.19812e10	2.96379
$846$	0	0
$847$	5.42640e9	0.306846
$848$	−2.14680e10	−1.20894
$849$	0	0
$850$	−2.31418e10	−1.29250
$851$	−7.12832e9	−0.396491
$852$	0	0
$853$	−1.30910e10	−0.722191	−0.361095	−	0.932529i	$-0.617597\pi$
$853$	−1.30910e10	−0.722191	−0.361095	+	0.932529i	$0.617597\pi$
$854$	−9.30533e9	−0.511245
$855$	0	0
$856$	−5.28493e9	−0.287992
$857$	7.58570e9	0.411683	0.205841	−	0.978585i	$-0.434007\pi$
$857$	7.58570e9	0.411683	0.205841	+	0.978585i	$0.434007\pi$
$858$	0	0
$859$	1.73685e10	0.934945	0.467473	−	0.884008i	$-0.345165\pi$
$859$	1.73685e10	0.934945	0.467473	+	0.884008i	$0.345165\pi$
$860$	2.73189e10	1.46460
$861$	0	0
$862$	4.34953e10	2.31295
$863$	2.94182e10	1.55804	0.779020	−	0.626999i	$-0.215717\pi$
$863$	2.94182e10	1.55804	0.779020	+	0.626999i	$0.215717\pi$
$864$	0	0
$865$	−9.95500e8	−0.0522980
$866$	−3.29000e10	−1.72140
$867$	0	0
$868$	−3.51792e9	−0.182586
$869$	−2.42268e10	−1.25235
$870$	0	0
$871$	4.02533e10	2.06413
$872$	−4.10642e9	−0.209728
$873$	0	0
$874$	1.83656e10	0.930495
$875$	−4.29398e10	−2.16687
$876$	0	0
$877$	2.34419e10	1.17353	0.586766	−	0.809757i	$-0.300401\pi$
$877$	2.34419e10	1.17353	0.586766	+	0.809757i	$0.300401\pi$
$878$	3.99648e9	0.199272
$879$	0	0
$880$	−2.63091e10	−1.30142
$881$	−1.05992e10	−0.522223	−0.261112	−	0.965309i	$-0.584089\pi$
$881$	−1.05992e10	−0.522223	−0.261112	+	0.965309i	$0.584089\pi$
$882$	0	0
$883$	5.42116e9	0.264990	0.132495	−	0.991184i	$-0.457701\pi$
$883$	5.42116e9	0.264990	0.132495	+	0.991184i	$0.457701\pi$
$884$	−1.47570e10	−0.718480
$885$	0	0
$886$	−3.32280e10	−1.60504
$887$	2.94607e10	1.41746	0.708729	−	0.705481i	$-0.249269\pi$
$887$	2.94607e10	1.41746	0.708729	+	0.705481i	$0.249269\pi$
$888$	0	0
$889$	−3.51747e10	−1.67909
$890$	−9.86754e10	−4.69185
$891$	0	0
$892$	−2.97697e10	−1.40442
$893$	1.65311e10	0.776824
$894$	0	0
$895$	6.20481e10	2.89300
$896$	−6.81590e9	−0.316552
$897$	0	0
$898$	8.92794e9	0.411419
$899$	−4.19892e9	−0.192743
$900$	0	0
$901$	1.20475e10	0.548734
$902$	−1.04458e10	−0.473936
$903$	0	0
$904$	6.08500e9	0.273950
$905$	1.59012e10	0.713115
$906$	0	0
$907$	−2.61053e9	−0.116172	−0.0580862	−	0.998312i	$-0.518500\pi$
$907$	−2.61053e9	−0.116172	−0.0580862	+	0.998312i	$0.518500\pi$
$908$	−4.83134e10	−2.14174
$909$	0	0
$910$	−9.38856e10	−4.13004
$911$	−2.85634e10	−1.25169	−0.625844	−	0.779948i	$-0.715245\pi$
$911$	−2.85634e10	−1.25169	−0.625844	+	0.779948i	$0.715245\pi$
$912$	0	0
$913$	−2.89060e9	−0.125701
$914$	−7.78721e9	−0.337342
$915$	0	0
$916$	−2.28098e9	−0.0980590
$917$	9.82307e9	0.420683
$918$	0	0
$919$	2.32191e10	0.986827	0.493413	−	0.869795i	$-0.335749\pi$
$919$	2.32191e10	0.986827	0.493413	+	0.869795i	$0.335749\pi$
$920$	−1.04918e10	−0.444212
$921$	0	0
$922$	7.12116e9	0.299221
$923$	1.84365e10	0.771743
$924$	0	0
$925$	−1.42284e10	−0.591099
$926$	1.28433e10	0.531542
$927$	0	0
$928$	−3.98235e10	−1.63577
$929$	1.58034e10	0.646691	0.323346	−	0.946281i	$-0.395192\pi$
$929$	1.58034e10	0.646691	0.323346	+	0.946281i	$0.395192\pi$
$930$	0	0
$931$	6.15455e8	0.0249961
$932$	5.05948e10	2.04715
$933$	0	0
$934$	4.62680e10	1.85809
$935$	1.47643e10	0.590707
$936$	0	0
$937$	4.20742e9	0.167081	0.0835406	−	0.996504i	$-0.473377\pi$
$937$	4.20742e9	0.167081	0.0835406	+	0.996504i	$0.473377\pi$
$938$	−4.52306e10	−1.78946
$939$	0	0
$940$	−9.30548e10	−3.65419
$941$	−2.44794e10	−0.957719	−0.478859	−	0.877892i	$-0.658950\pi$
$941$	−2.44794e10	−0.957719	−0.478859	+	0.877892i	$0.658950\pi$
$942$	0	0
$943$	1.52605e10	0.592623
$944$	−2.94194e9	−0.113823
$945$	0	0
$946$	−2.28789e10	−0.878649
$947$	4.06567e9	0.155563	0.0777817	−	0.996970i	$-0.475216\pi$
$947$	4.06567e9	0.155563	0.0777817	+	0.996970i	$0.475216\pi$
$948$	0	0
$949$	6.38705e10	2.42588
$950$	3.66584e10	1.38721
$951$	0	0
$952$	1.68282e9	0.0632132
$953$	1.54604e9	0.0578623	0.0289312	−	0.999581i	$-0.490790\pi$
$953$	1.54604e9	0.0578623	0.0289312	+	0.999581i	$0.490790\pi$
$954$	0	0
$955$	2.41481e10	0.897163
$956$	−2.94212e10	−1.08908
$957$	0	0
$958$	−2.17681e10	−0.799911
$959$	2.84740e10	1.04252
$960$	0	0
$961$	−2.67260e10	−0.971408
$962$	−1.72254e10	−0.623818
$963$	0	0
$964$	−8.20858e9	−0.295120
$965$	−7.59383e10	−2.72029
$966$	0	0
$967$	−3.00507e10	−1.06872	−0.534358	−	0.845258i	$-0.679446\pi$
$967$	−3.00507e10	−1.06872	−0.534358	+	0.845258i	$0.679446\pi$
$968$	1.46536e9	0.0519256
$969$	0	0
$970$	1.57828e9	0.0555245
$971$	−1.87536e9	−0.0657380	−0.0328690	−	0.999460i	$-0.510464\pi$
$971$	−1.87536e9	−0.0657380	−0.0328690	+	0.999460i	$0.510464\pi$
$972$	0	0
$973$	2.76157e10	0.961082
$974$	1.22598e10	0.425136
$975$	0	0
$976$	9.20554e9	0.316939
$977$	−2.34050e10	−0.802931	−0.401465	−	0.915874i	$-0.631499\pi$
$977$	−2.34050e10	−0.802931	−0.401465	+	0.915874i	$0.631499\pi$
$978$	0	0
$979$	4.35277e10	1.48261
$980$	−3.46444e9	−0.117582
$981$	0	0
$982$	3.98141e10	1.34167
$983$	3.41979e10	1.14832	0.574160	−	0.818743i	$-0.305329\pi$
$983$	3.41979e10	1.14832	0.574160	+	0.818743i	$0.305329\pi$
$984$	0	0
$985$	−4.68819e10	−1.56307
$986$	1.97916e10	0.657523
$987$	0	0
$988$	2.33762e10	0.771125
$989$	3.34242e10	1.09869
$990$	0	0
$991$	2.02941e10	0.662386	0.331193	−	0.943563i	$-0.392549\pi$
$991$	2.02941e10	0.662386	0.331193	+	0.943563i	$0.392549\pi$
$992$	7.46078e9	0.242657
$993$	0	0
$994$	−2.07162e10	−0.669049
$995$	−5.60759e10	−1.80466
$996$	0	0
$997$	1.19326e10	0.381332	0.190666	−	0.981655i	$-0.438935\pi$
$997$	1.19326e10	0.381332	0.190666	+	0.981655i	$0.438935\pi$
$998$	4.20937e10	1.34048
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.g.1.5	✓	33
3.2	odd	2		531.8.a.h.1.29	yes	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.5	✓	33	1.1	even	1	trivial
531.8.a.h.1.29	yes	33	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-16.4456 q^{2} +142.458 q^{4} +503.166 q^{5} -880.461 q^{7} -237.762 q^{8} +O(q^{10})\)	\(q-16.4456 q^{2} +142.458 q^{4} +503.166 q^{5} -880.461 q^{7} -237.762 q^{8} -8274.86 q^{10} +3650.21 q^{11} -12886.3 q^{13} +14479.7 q^{14} -14324.4 q^{16} +8038.67 q^{17} -12733.9 q^{19} +71679.7 q^{20} -60029.9 q^{22} +87698.9 q^{23} +175051. q^{25} +211923. q^{26} -125428. q^{28} -149709. q^{29} +28047.3 q^{31} +266007. q^{32} -132201. q^{34} -443018. q^{35} -81281.7 q^{37} +209416. q^{38} -119634. q^{40} +174010. q^{41} +381125. q^{43} +520000. q^{44} -1.44226e6 q^{46} -1.29820e6 q^{47} -48332.2 q^{49} -2.87881e6 q^{50} -1.83575e6 q^{52} +1.49870e6 q^{53} +1.83666e6 q^{55} +209340. q^{56} +2.46205e6 q^{58} +205379. q^{59} -642647. q^{61} -461254. q^{62} -2.54112e6 q^{64} -6.48395e6 q^{65} -3.12372e6 q^{67} +1.14517e6 q^{68} +7.28569e6 q^{70} -1.43071e6 q^{71} -4.95647e6 q^{73} +1.33673e6 q^{74} -1.81404e6 q^{76} -3.21387e6 q^{77} -6.63710e6 q^{79} -7.20756e6 q^{80} -2.86170e6 q^{82} -791900. q^{83} +4.04478e6 q^{85} -6.26782e6 q^{86} -867882. q^{88} +1.19247e7 q^{89} +1.13459e7 q^{91} +1.24934e7 q^{92} +2.13497e7 q^{94} -6.40725e6 q^{95} -190733. q^{97} +794851. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * q^98

Introduction

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