LMFDB - Embedded newform 342.10.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,10,Mod(1,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("342.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	342.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:	$176.142255968$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 8016x^{2} - 155839x + 2105804 $ x^4 - 2x^3 - 8016x^2 - 155839*x + 2105804
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$9.19740$ of defining polynomial
Character	$\chi$	$=$	342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} +256.000 q^{4} -745.613 q^{5} -3114.51 q^{7} -4096.00 q^{8} +O(q^{10})$	\(q-16.0000 q^{2} +256.000 q^{4} -745.613 q^{5} -3114.51 q^{7} -4096.00 q^{8} +11929.8 q^{10} +7108.61 q^{11} -6932.19 q^{13} +49832.1 q^{14} +65536.0 q^{16} +327458. q^{17} -130321. q^{19} -190877. q^{20} -113738. q^{22} +955548. q^{23} -1.39719e6 q^{25} +110915. q^{26} -797314. q^{28} -2.95824e6 q^{29} +6.62711e6 q^{31} -1.04858e6 q^{32} -5.23933e6 q^{34} +2.32222e6 q^{35} -1.94520e7 q^{37} +2.08514e6 q^{38} +3.05403e6 q^{40} -2.62428e7 q^{41} +1.75946e7 q^{43} +1.81980e6 q^{44} -1.52888e7 q^{46} +5.09563e7 q^{47} -3.06534e7 q^{49} +2.23550e7 q^{50} -1.77464e6 q^{52} -7.17833e7 q^{53} -5.30027e6 q^{55} +1.27570e7 q^{56} +4.73318e7 q^{58} +1.66365e8 q^{59} -1.58703e8 q^{61} -1.06034e8 q^{62} +1.67772e7 q^{64} +5.16873e6 q^{65} -8.80121e7 q^{67} +8.38293e7 q^{68} -3.71555e7 q^{70} -1.20443e7 q^{71} +1.99123e8 q^{73} +3.11231e8 q^{74} -3.33622e7 q^{76} -2.21398e7 q^{77} +1.03713e8 q^{79} -4.88645e7 q^{80} +4.19884e8 q^{82} -2.63245e8 q^{83} -2.44157e8 q^{85} -2.81514e8 q^{86} -2.91169e7 q^{88} -3.10014e7 q^{89} +2.15904e7 q^{91} +2.44620e8 q^{92} -8.15301e8 q^{94} +9.71691e7 q^{95} +4.04948e8 q^{97} +4.90455e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 1024 q^{4} - 866 q^{5} + 2670 q^{7} - 16384 q^{8}+O(q^{10}) $ 4 * q - 64 * q^2 + 1024 * q^4 - 866 * q^5 + 2670 * q^7 - 16384 * q^8	\( 4 q - 64 q^{2} + 1024 q^{4} - 866 q^{5} + 2670 q^{7} - 16384 q^{8} + 13856 q^{10} - 119234 q^{11} - 6748 q^{13} - 42720 q^{14} + 262144 q^{16} - 678624 q^{17} - 521284 q^{19} - 221696 q^{20} + 1907744 q^{22} - 2911868 q^{23} + 268766 q^{25} + 107968 q^{26} + 683520 q^{28} - 8291104 q^{29} + 3445468 q^{31} - 4194304 q^{32} + 10857984 q^{34} - 7715058 q^{35} - 1005524 q^{37} + 8340544 q^{38} + 3547136 q^{40} - 8514124 q^{41} + 13900726 q^{43} - 30523904 q^{44} + 46589888 q^{46} + 36334954 q^{47} - 30891808 q^{49} - 4300256 q^{50} - 1727488 q^{52} + 113969356 q^{53} - 178140098 q^{55} - 10936320 q^{56} + 132657664 q^{58} + 396773766 q^{59} - 298192066 q^{61} - 55127488 q^{62} + 67108864 q^{64} + 291187676 q^{65} - 113551722 q^{67} - 173727744 q^{68} + 123440928 q^{70} - 4659620 q^{71} + 136198452 q^{73} + 16088384 q^{74} - 133448704 q^{76} - 120551886 q^{77} + 67255424 q^{79} - 56754176 q^{80} + 136225984 q^{82} - 1376505216 q^{83} + 638402178 q^{85} - 222411616 q^{86} + 488382464 q^{88} - 1557211260 q^{89} + 1422773730 q^{91} - 745438208 q^{92} - 581359264 q^{94} + 112857986 q^{95} + 975818188 q^{97} + 494268928 q^{98}+O(q^{100}) \) 4 * q - 64 * q^2 + 1024 * q^4 - 866 * q^5 + 2670 * q^7 - 16384 * q^8 + 13856 * q^10 - 119234 * q^11 - 6748 * q^13 - 42720 * q^14 + 262144 * q^16 - 678624 * q^17 - 521284 * q^19 - 221696 * q^20 + 1907744 * q^22 - 2911868 * q^23 + 268766 * q^25 + 107968 * q^26 + 683520 * q^28 - 8291104 * q^29 + 3445468 * q^31 - 4194304 * q^32 + 10857984 * q^34 - 7715058 * q^35 - 1005524 * q^37 + 8340544 * q^38 + 3547136 * q^40 - 8514124 * q^41 + 13900726 * q^43 - 30523904 * q^44 + 46589888 * q^46 + 36334954 * q^47 - 30891808 * q^49 - 4300256 * q^50 - 1727488 * q^52 + 113969356 * q^53 - 178140098 * q^55 - 10936320 * q^56 + 132657664 * q^58 + 396773766 * q^59 - 298192066 * q^61 - 55127488 * q^62 + 67108864 * q^64 + 291187676 * q^65 - 113551722 * q^67 - 173727744 * q^68 + 123440928 * q^70 - 4659620 * q^71 + 136198452 * q^73 + 16088384 * q^74 - 133448704 * q^76 - 120551886 * q^77 + 67255424 * q^79 - 56754176 * q^80 + 136225984 * q^82 - 1376505216 * q^83 + 638402178 * q^85 - 222411616 * q^86 + 488382464 * q^88 - 1557211260 * q^89 + 1422773730 * q^91 - 745438208 * q^92 - 581359264 * q^94 + 112857986 * q^95 + 975818188 * q^97 + 494268928 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	0	0
$3$	0	0
$4$	256.000	0.500000
$5$	−745.613	−0.533517	−0.266759	−	0.963763i	$-0.585953\pi$
$5$	−745.613	−0.533517	−0.266759	+	0.963763i	$0.585953\pi$
$6$	0	0
$7$	−3114.51	−0.490285	−0.245142	−	0.969487i	$-0.578835\pi$
$7$	−3114.51	−0.490285	−0.245142	+	0.969487i	$0.578835\pi$
$8$	−4096.00	−0.353553
$9$	0	0
$10$	11929.8	0.377254
$11$	7108.61	0.146392	0.0731960	−	0.997318i	$-0.476680\pi$
$11$	7108.61	0.146392	0.0731960	+	0.997318i	$0.476680\pi$
$12$	0	0
$13$	−6932.19	−0.0673171	−0.0336585	−	0.999433i	$-0.510716\pi$
$13$	−6932.19	−0.0673171	−0.0336585	+	0.999433i	$0.510716\pi$
$14$	49832.1	0.346684
$15$	0	0
$16$	65536.0	0.250000
$17$	327458.	0.950902	0.475451	−	0.879742i	$-0.342285\pi$
$17$	327458.	0.950902	0.475451	+	0.879742i	$0.342285\pi$
$18$	0	0
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−190877.	−0.266759
$21$	0	0
$22$	−113738.	−0.103515
$23$	955548.	0.711996	0.355998	−	0.934487i	$-0.384141\pi$
$23$	955548.	0.711996	0.355998	+	0.934487i	$0.384141\pi$
$24$	0	0
$25$	−1.39719e6	−0.715359
$26$	110915.	0.0476004
$27$	0	0
$28$	−797314.	−0.245142
$29$	−2.95824e6	−0.776680	−0.388340	−	0.921516i	$-0.626951\pi$
$29$	−2.95824e6	−0.776680	−0.388340	+	0.921516i	$0.626951\pi$
$30$	0	0
$31$	6.62711e6	1.28883	0.644416	−	0.764675i	$-0.277100\pi$
$31$	6.62711e6	1.28883	0.644416	+	0.764675i	$0.277100\pi$
$32$	−1.04858e6	−0.176777
$33$	0	0
$34$	−5.23933e6	−0.672389
$35$	2.32222e6	0.261575
$36$	0	0
$37$	−1.94520e7	−1.70630	−0.853151	−	0.521664i	$-0.825311\pi$
$37$	−1.94520e7	−1.70630	−0.853151	+	0.521664i	$0.825311\pi$
$38$	2.08514e6	0.162221
$39$	0	0
$40$	3.05403e6	0.188627
$41$	−2.62428e7	−1.45038	−0.725191	−	0.688548i	$-0.758249\pi$
$41$	−2.62428e7	−1.45038	−0.725191	+	0.688548i	$0.758249\pi$
$42$	0	0
$43$	1.75946e7	0.784824	0.392412	−	0.919790i	$-0.371641\pi$
$43$	1.75946e7	0.784824	0.392412	+	0.919790i	$0.371641\pi$
$44$	1.81980e6	0.0731960
$45$	0	0
$46$	−1.52888e7	−0.503457
$47$	5.09563e7	1.52320	0.761601	−	0.648046i	$-0.224414\pi$
$47$	5.09563e7	1.52320	0.761601	+	0.648046i	$0.224414\pi$
$48$	0	0
$49$	−3.06534e7	−0.759621
$50$	2.23550e7	0.505835
$51$	0	0
$52$	−1.77464e6	−0.0336585
$53$	−7.17833e7	−1.24963	−0.624816	−	0.780772i	$-0.714826\pi$
$53$	−7.17833e7	−1.24963	−0.624816	+	0.780772i	$0.714826\pi$
$54$	0	0
$55$	−5.30027e6	−0.0781027
$56$	1.27570e7	0.173342
$57$	0	0
$58$	4.73318e7	0.549196
$59$	1.66365e8	1.78742	0.893712	−	0.448641i	$-0.148092\pi$
$59$	1.66365e8	1.78742	0.893712	+	0.448641i	$0.148092\pi$
$60$	0	0
$61$	−1.58703e8	−1.46758	−0.733788	−	0.679379i	$-0.762249\pi$
$61$	−1.58703e8	−1.46758	−0.733788	+	0.679379i	$0.762249\pi$
$62$	−1.06034e8	−0.911342
$63$	0	0
$64$	1.67772e7	0.125000
$65$	5.16873e6	0.0359148
$66$	0	0
$67$	−8.80121e7	−0.533588	−0.266794	−	0.963754i	$-0.585964\pi$
$67$	−8.80121e7	−0.533588	−0.266794	+	0.963754i	$0.585964\pi$
$68$	8.38293e7	0.475451
$69$	0	0
$70$	−3.71555e7	−0.184962
$71$	−1.20443e7	−0.0562495	−0.0281247	−	0.999604i	$-0.508954\pi$
$71$	−1.20443e7	−0.0562495	−0.0281247	+	0.999604i	$0.508954\pi$
$72$	0	0
$73$	1.99123e8	0.820671	0.410335	−	0.911935i	$-0.365412\pi$
$73$	1.99123e8	0.820671	0.410335	+	0.911935i	$0.365412\pi$
$74$	3.11231e8	1.20654
$75$	0	0
$76$	−3.33622e7	−0.114708
$77$	−2.21398e7	−0.0717738
$78$	0	0
$79$	1.03713e8	0.299580	0.149790	−	0.988718i	$-0.452140\pi$
$79$	1.03713e8	0.299580	0.149790	+	0.988718i	$0.452140\pi$
$80$	−4.88645e7	−0.133379
$81$	0	0
$82$	4.19884e8	1.02558
$83$	−2.63245e8	−0.608847	−0.304423	−	0.952537i	$-0.598464\pi$
$83$	−2.63245e8	−0.608847	−0.304423	+	0.952537i	$0.598464\pi$
$84$	0	0
$85$	−2.44157e8	−0.507323
$86$	−2.81514e8	−0.554954
$87$	0	0
$88$	−2.91169e7	−0.0517574
$89$	−3.10014e7	−0.0523753	−0.0261877	−	0.999657i	$-0.508337\pi$
$89$	−3.10014e7	−0.0523753	−0.0261877	+	0.999657i	$0.508337\pi$
$90$	0	0
$91$	2.15904e7	0.0330045
$92$	2.44620e8	0.355998
$93$	0	0
$94$	−8.15301e8	−1.07707
$95$	9.71691e7	0.122397
$96$	0	0
$97$	4.04948e8	0.464436	0.232218	−	0.972664i	$-0.425402\pi$
$97$	4.04948e8	0.464436	0.232218	+	0.972664i	$0.425402\pi$
$98$	4.90455e8	0.537133
$99$	0	0
$100$	−3.57680e8	−0.357680
$101$	1.43648e9	1.37358	0.686790	−	0.726856i	$-0.259019\pi$
$101$	1.43648e9	1.37358	0.686790	+	0.726856i	$0.259019\pi$
$102$	0	0
$103$	−8.82587e8	−0.772663	−0.386331	−	0.922360i	$-0.626258\pi$
$103$	−8.82587e8	−0.772663	−0.386331	+	0.922360i	$0.626258\pi$
$104$	2.83942e7	0.0238002
$105$	0	0
$106$	1.14853e9	0.883623
$107$	−4.30128e8	−0.317228	−0.158614	−	0.987341i	$-0.550703\pi$
$107$	−4.30128e8	−0.317228	−0.158614	+	0.987341i	$0.550703\pi$
$108$	0	0
$109$	−3.22163e8	−0.218603	−0.109302	−	0.994009i	$-0.534861\pi$
$109$	−3.22163e8	−0.218603	−0.109302	+	0.994009i	$0.534861\pi$
$110$	8.48044e7	0.0552270
$111$	0	0
$112$	−2.04112e8	−0.122571
$113$	−3.18937e9	−1.84014	−0.920072	−	0.391750i	$-0.871870\pi$
$113$	−3.18937e9	−1.84014	−0.920072	+	0.391750i	$0.871870\pi$
$114$	0	0
$115$	−7.12469e8	−0.379862
$116$	−7.57309e8	−0.388340
$117$	0	0
$118$	−2.66184e9	−1.26390
$119$	−1.01987e9	−0.466213
$120$	0	0
$121$	−2.30742e9	−0.978569
$122$	2.53924e9	1.03773
$123$	0	0
$124$	1.69654e9	0.644416
$125$	2.49804e9	0.915174
$126$	0	0
$127$	−2.22281e9	−0.758202	−0.379101	−	0.925355i	$-0.623767\pi$
$127$	−2.22281e9	−0.758202	−0.379101	+	0.925355i	$0.623767\pi$
$128$	−2.68435e8	−0.0883883
$129$	0	0
$130$	−8.26997e7	−0.0253956
$131$	−3.24853e9	−0.963753	−0.481877	−	0.876239i	$-0.660045\pi$
$131$	−3.24853e9	−0.963753	−0.481877	+	0.876239i	$0.660045\pi$
$132$	0	0
$133$	4.05886e8	0.112479
$134$	1.40819e9	0.377303
$135$	0	0
$136$	−1.34127e9	−0.336195
$137$	−8.99122e8	−0.218060	−0.109030	−	0.994038i	$-0.534774\pi$
$137$	−8.99122e8	−0.218060	−0.109030	+	0.994038i	$0.534774\pi$
$138$	0	0
$139$	4.25150e9	0.965997	0.482999	−	0.875621i	$-0.339548\pi$
$139$	4.25150e9	0.965997	0.482999	+	0.875621i	$0.339548\pi$
$140$	5.94488e8	0.130788
$141$	0	0
$142$	1.92709e8	0.0397744
$143$	−4.92782e7	−0.00985469
$144$	0	0
$145$	2.20570e9	0.414373
$146$	−3.18597e9	−0.580302
$147$	0	0
$148$	−4.97970e9	−0.853151
$149$	7.82058e9	1.29987	0.649936	−	0.759989i	$-0.274796\pi$
$149$	7.82058e9	1.29987	0.649936	+	0.759989i	$0.274796\pi$
$150$	0	0
$151$	5.43522e8	0.0850787	0.0425393	−	0.999095i	$-0.486455\pi$
$151$	5.43522e8	0.0850787	0.0425393	+	0.999095i	$0.486455\pi$
$152$	5.33795e8	0.0811107
$153$	0	0
$154$	3.54237e8	0.0507518
$155$	−4.94126e9	−0.687615
$156$	0	0
$157$	6.45782e9	0.848276	0.424138	−	0.905598i	$-0.360577\pi$
$157$	6.45782e9	0.848276	0.424138	+	0.905598i	$0.360577\pi$
$158$	−1.65941e9	−0.211835
$159$	0	0
$160$	7.81832e8	0.0943134
$161$	−2.97606e9	−0.349081
$162$	0	0
$163$	1.10714e10	1.22845	0.614224	−	0.789132i	$-0.289469\pi$
$163$	1.10714e10	1.22845	0.614224	+	0.789132i	$0.289469\pi$
$164$	−6.71815e9	−0.725191
$165$	0	0
$166$	4.21191e9	0.430520
$167$	−1.06761e10	−1.06216	−0.531078	−	0.847323i	$-0.678213\pi$
$167$	−1.06761e10	−1.06216	−0.531078	+	0.847323i	$0.678213\pi$
$168$	0	0
$169$	−1.05564e10	−0.995468
$170$	3.90652e9	0.358731
$171$	0	0
$172$	4.50423e9	0.392412
$173$	−1.98302e10	−1.68314	−0.841570	−	0.540148i	$-0.818368\pi$
$173$	−1.98302e10	−1.68314	−0.841570	+	0.540148i	$0.818368\pi$
$174$	0	0
$175$	4.35155e9	0.350730
$176$	4.65870e8	0.0365980
$177$	0	0
$178$	4.96023e8	0.0370350
$179$	−2.15446e10	−1.56855	−0.784276	−	0.620412i	$-0.786965\pi$
$179$	−2.15446e10	−1.56855	−0.784276	+	0.620412i	$0.786965\pi$
$180$	0	0
$181$	2.32047e10	1.60702	0.803512	−	0.595288i	$-0.202962\pi$
$181$	2.32047e10	1.60702	0.803512	+	0.595288i	$0.202962\pi$
$182$	−3.45446e8	−0.0233377
$183$	0	0
$184$	−3.91392e9	−0.251728
$185$	1.45036e10	0.910342
$186$	0	0
$187$	2.32777e9	0.139205
$188$	1.30448e10	0.761601
$189$	0	0
$190$	−1.55471e9	−0.0865480
$191$	2.12441e10	1.15501	0.577507	−	0.816386i	$-0.304026\pi$
$191$	2.12441e10	1.15501	0.577507	+	0.816386i	$0.304026\pi$
$192$	0	0
$193$	2.75033e10	1.42684	0.713422	−	0.700735i	$-0.247144\pi$
$193$	2.75033e10	1.42684	0.713422	+	0.700735i	$0.247144\pi$
$194$	−6.47916e9	−0.328406
$195$	0	0
$196$	−7.84728e9	−0.379810
$197$	−9.83478e9	−0.465229	−0.232614	−	0.972569i	$-0.574728\pi$
$197$	−9.83478e9	−0.465229	−0.232614	+	0.972569i	$0.574728\pi$
$198$	0	0
$199$	1.42117e10	0.642402	0.321201	−	0.947011i	$-0.395914\pi$
$199$	1.42117e10	0.642402	0.321201	+	0.947011i	$0.395914\pi$
$200$	5.72287e9	0.252918
$201$	0	0
$202$	−2.29837e10	−0.971267
$203$	9.21346e9	0.380795
$204$	0	0
$205$	1.95670e10	0.773804
$206$	1.41214e10	0.546355
$207$	0	0
$208$	−4.54308e8	−0.0168293
$209$	−9.26401e8	−0.0335846
$210$	0	0
$211$	5.10522e10	1.77314	0.886570	−	0.462594i	$-0.153081\pi$
$211$	5.10522e10	1.77314	0.886570	+	0.462594i	$0.153081\pi$
$212$	−1.83765e10	−0.624816
$213$	0	0
$214$	6.88206e9	0.224314
$215$	−1.31188e10	−0.418717
$216$	0	0
$217$	−2.06402e10	−0.631895
$218$	5.15461e9	0.154576
$219$	0	0
$220$	−1.35687e9	−0.0390514
$221$	−2.27000e9	−0.0640119
$222$	0	0
$223$	3.39299e10	0.918778	0.459389	−	0.888235i	$-0.348068\pi$
$223$	3.39299e10	0.918778	0.459389	+	0.888235i	$0.348068\pi$
$224$	3.26580e9	0.0866709
$225$	0	0
$226$	5.10299e10	1.30118
$227$	6.89446e10	1.72339	0.861695	−	0.507426i	$-0.169403\pi$
$227$	6.89446e10	1.72339	0.861695	+	0.507426i	$0.169403\pi$
$228$	0	0
$229$	−2.33816e10	−0.561843	−0.280921	−	0.959731i	$-0.590640\pi$
$229$	−2.33816e10	−0.561843	−0.280921	+	0.959731i	$0.590640\pi$
$230$	1.13995e10	0.268603
$231$	0	0
$232$	1.21170e10	0.274598
$233$	1.93703e10	0.430561	0.215280	−	0.976552i	$-0.430933\pi$
$233$	1.93703e10	0.430561	0.215280	+	0.976552i	$0.430933\pi$
$234$	0	0
$235$	−3.79937e10	−0.812655
$236$	4.25894e10	0.893712
$237$	0	0
$238$	1.63179e10	0.329662
$239$	2.36983e9	0.0469814	0.0234907	−	0.999724i	$-0.492522\pi$
$239$	2.36983e9	0.0469814	0.0234907	+	0.999724i	$0.492522\pi$
$240$	0	0
$241$	6.11488e10	1.16765	0.583823	−	0.811881i	$-0.301556\pi$
$241$	6.11488e10	1.16765	0.583823	+	0.811881i	$0.301556\pi$
$242$	3.69186e10	0.691953
$243$	0	0
$244$	−4.06279e10	−0.733788
$245$	2.28556e10	0.405271
$246$	0	0
$247$	9.03410e8	0.0154436
$248$	−2.71446e10	−0.455671
$249$	0	0
$250$	−3.99686e10	−0.647126
$251$	5.87525e10	0.934318	0.467159	−	0.884173i	$-0.345278\pi$
$251$	5.87525e10	0.934318	0.467159	+	0.884173i	$0.345278\pi$
$252$	0	0
$253$	6.79262e9	0.104231
$254$	3.55649e10	0.536130
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	3.95191e10	0.565078	0.282539	−	0.959256i	$-0.408823\pi$
$257$	3.95191e10	0.565078	0.282539	+	0.959256i	$0.408823\pi$
$258$	0	0
$259$	6.05833e10	0.836574
$260$	1.32320e9	0.0179574
$261$	0	0
$262$	5.19765e10	0.681477
$263$	5.22430e10	0.673329	0.336664	−	0.941625i	$-0.390701\pi$
$263$	5.22430e10	0.673329	0.336664	+	0.941625i	$0.390701\pi$
$264$	0	0
$265$	5.35226e10	0.666700
$266$	−6.49417e9	−0.0795347
$267$	0	0
$268$	−2.25311e10	−0.266794
$269$	1.25553e11	1.46198	0.730992	−	0.682386i	$-0.239058\pi$
$269$	1.25553e11	1.46198	0.730992	+	0.682386i	$0.239058\pi$
$270$	0	0
$271$	−5.75589e10	−0.648262	−0.324131	−	0.946012i	$-0.605072\pi$
$271$	−5.75589e10	−0.648262	−0.324131	+	0.946012i	$0.605072\pi$
$272$	2.14603e10	0.237726
$273$	0	0
$274$	1.43860e10	0.154192
$275$	−9.93205e9	−0.104723
$276$	0	0
$277$	−1.34940e9	−0.0137715	−0.00688575	−	0.999976i	$-0.502192\pi$
$277$	−1.34940e9	−0.0137715	−0.00688575	+	0.999976i	$0.502192\pi$
$278$	−6.80241e10	−0.683063
$279$	0	0
$280$	−9.51181e9	−0.0924809
$281$	−5.25143e10	−0.502457	−0.251229	−	0.967928i	$-0.580835\pi$
$281$	−5.25143e10	−0.502457	−0.251229	+	0.967928i	$0.580835\pi$
$282$	0	0
$283$	1.73137e11	1.60454	0.802269	−	0.596962i	$-0.203626\pi$
$283$	1.73137e11	1.60454	0.802269	+	0.596962i	$0.203626\pi$
$284$	−3.08334e9	−0.0281247
$285$	0	0
$286$	7.88451e8	0.00696832
$287$	8.17334e10	0.711100
$288$	0	0
$289$	−1.13589e10	−0.0957851
$290$	−3.52912e10	−0.293006
$291$	0	0
$292$	5.09755e10	0.410335
$293$	2.84362e10	0.225407	0.112703	−	0.993629i	$-0.464049\pi$
$293$	2.84362e10	0.225407	0.112703	+	0.993629i	$0.464049\pi$
$294$	0	0
$295$	−1.24044e11	−0.953622
$296$	7.96753e10	0.603269
$297$	0	0
$298$	−1.25129e11	−0.919149
$299$	−6.62404e9	−0.0479294
$300$	0	0
$301$	−5.47986e10	−0.384787
$302$	−8.69635e9	−0.0601597
$303$	0	0
$304$	−8.54072e9	−0.0573539
$305$	1.18331e11	0.782977
$306$	0	0
$307$	1.99656e11	1.28280	0.641400	−	0.767206i	$-0.278354\pi$
$307$	1.99656e11	1.28280	0.641400	+	0.767206i	$0.278354\pi$
$308$	−5.66780e9	−0.0358869
$309$	0	0
$310$	7.90602e10	0.486217
$311$	8.35290e9	0.0506309	0.0253154	−	0.999680i	$-0.491941\pi$
$311$	8.35290e9	0.0506309	0.0253154	+	0.999680i	$0.491941\pi$
$312$	0	0
$313$	−7.40232e10	−0.435932	−0.217966	−	0.975956i	$-0.569942\pi$
$313$	−7.40232e10	−0.435932	−0.217966	+	0.975956i	$0.569942\pi$
$314$	−1.03325e11	−0.599822
$315$	0	0
$316$	2.65506e10	0.149790
$317$	1.73358e11	0.964223	0.482111	−	0.876110i	$-0.339870\pi$
$317$	1.73358e11	0.964223	0.482111	+	0.876110i	$0.339870\pi$
$318$	0	0
$319$	−2.10290e10	−0.113700
$320$	−1.25093e10	−0.0666897
$321$	0	0
$322$	4.76170e10	0.246837
$323$	−4.26747e10	−0.218152
$324$	0	0
$325$	9.68555e9	0.0481559
$326$	−1.77142e11	−0.868644
$327$	0	0
$328$	1.07490e11	0.512788
$329$	−1.58704e11	−0.746803
$330$	0	0
$331$	1.47158e11	0.673841	0.336921	−	0.941533i	$-0.390615\pi$
$331$	1.47158e11	0.673841	0.336921	+	0.941533i	$0.390615\pi$
$332$	−6.73906e10	−0.304423
$333$	0	0
$334$	1.70817e11	0.751058
$335$	6.56230e10	0.284678
$336$	0	0
$337$	−1.47260e11	−0.621943	−0.310972	−	0.950419i	$-0.600654\pi$
$337$	−1.47260e11	−0.621943	−0.310972	+	0.950419i	$0.600654\pi$
$338$	1.68903e11	0.703902
$339$	0	0
$340$	−6.25043e10	−0.253661
$341$	4.71095e10	0.188675
$342$	0	0
$343$	2.21152e11	0.862715
$344$	−7.20676e10	−0.277477
$345$	0	0
$346$	3.17284e11	1.19016
$347$	−1.23328e11	−0.456645	−0.228322	−	0.973586i	$-0.573324\pi$
$347$	−1.23328e11	−0.456645	−0.228322	+	0.973586i	$0.573324\pi$
$348$	0	0
$349$	4.35449e11	1.57117	0.785584	−	0.618754i	$-0.212362\pi$
$349$	4.35449e11	1.57117	0.785584	+	0.618754i	$0.212362\pi$
$350$	−6.96248e10	−0.248003
$351$	0	0
$352$	−7.45392e9	−0.0258787
$353$	5.33542e11	1.82887	0.914435	−	0.404734i	$-0.132636\pi$
$353$	5.33542e11	1.82887	0.914435	+	0.404734i	$0.132636\pi$
$354$	0	0
$355$	8.98038e9	0.0300101
$356$	−7.93637e9	−0.0261877
$357$	0	0
$358$	3.44713e11	1.10913
$359$	−1.60183e11	−0.508968	−0.254484	−	0.967077i	$-0.581906\pi$
$359$	−1.60183e11	−0.508968	−0.254484	+	0.967077i	$0.581906\pi$
$360$	0	0
$361$	1.69836e10	0.0526316
$362$	−3.71275e11	−1.13634
$363$	0	0
$364$	5.52713e9	0.0165023
$365$	−1.48469e11	−0.437842
$366$	0	0
$367$	−4.05680e11	−1.16731	−0.583655	−	0.812002i	$-0.698378\pi$
$367$	−4.05680e11	−1.16731	−0.583655	+	0.812002i	$0.698378\pi$
$368$	6.26228e10	0.177999
$369$	0	0
$370$	−2.32058e11	−0.643709
$371$	2.23570e11	0.612675
$372$	0	0
$373$	6.58883e10	0.176246	0.0881228	−	0.996110i	$-0.471913\pi$
$373$	6.58883e10	0.176246	0.0881228	+	0.996110i	$0.471913\pi$
$374$	−3.72444e10	−0.0984325
$375$	0	0
$376$	−2.08717e11	−0.538533
$377$	2.05071e10	0.0522839
$378$	0	0
$379$	−1.93504e11	−0.481741	−0.240871	−	0.970557i	$-0.577433\pi$
$379$	−1.93504e11	−0.481741	−0.240871	+	0.970557i	$0.577433\pi$
$380$	2.48753e10	0.0611986
$381$	0	0
$382$	−3.39905e11	−0.816718
$383$	−2.46085e11	−0.584374	−0.292187	−	0.956361i	$-0.594383\pi$
$383$	−2.46085e11	−0.584374	−0.292187	+	0.956361i	$0.594383\pi$
$384$	0	0
$385$	1.65078e10	0.0382926
$386$	−4.40052e11	−1.00893
$387$	0	0
$388$	1.03667e11	0.232218
$389$	5.67775e11	1.25720	0.628598	−	0.777730i	$-0.283629\pi$
$389$	5.67775e11	1.25720	0.628598	+	0.777730i	$0.283629\pi$
$390$	0	0
$391$	3.12902e11	0.677038
$392$	1.25556e11	0.268567
$393$	0	0
$394$	1.57356e11	0.328966
$395$	−7.73300e10	−0.159831
$396$	0	0
$397$	8.60827e11	1.73924	0.869618	−	0.493725i	$-0.164365\pi$
$397$	8.60827e11	1.73924	0.869618	+	0.493725i	$0.164365\pi$
$398$	−2.27387e11	−0.454247
$399$	0	0
$400$	−9.15660e10	−0.178840
$401$	5.53713e10	0.106939	0.0534694	−	0.998569i	$-0.482972\pi$
$401$	5.53713e10	0.106939	0.0534694	+	0.998569i	$0.482972\pi$
$402$	0	0
$403$	−4.59404e10	−0.0867604
$404$	3.67739e11	0.686790
$405$	0	0
$406$	−1.47415e11	−0.269262
$407$	−1.38276e11	−0.249789
$408$	0	0
$409$	−2.89036e11	−0.510737	−0.255369	−	0.966844i	$-0.582197\pi$
$409$	−2.89036e11	−0.510737	−0.255369	+	0.966844i	$0.582197\pi$
$410$	−3.13071e11	−0.547162
$411$	0	0
$412$	−2.25942e11	−0.386331
$413$	−5.18145e11	−0.876347
$414$	0	0
$415$	1.96279e11	0.324830
$416$	7.26892e9	0.0119001
$417$	0	0
$418$	1.48224e10	0.0237479
$419$	5.63685e11	0.893457	0.446728	−	0.894670i	$-0.352589\pi$
$419$	5.63685e11	0.893457	0.446728	+	0.894670i	$0.352589\pi$
$420$	0	0
$421$	−8.51738e11	−1.32141	−0.660703	−	0.750647i	$-0.729742\pi$
$421$	−8.51738e11	−1.32141	−0.660703	+	0.750647i	$0.729742\pi$
$422$	−8.16835e11	−1.25380
$423$	0	0
$424$	2.94024e11	0.441811
$425$	−4.57520e11	−0.680237
$426$	0	0
$427$	4.94281e11	0.719530
$428$	−1.10113e11	−0.158614
$429$	0	0
$430$	2.09901e11	0.296078
$431$	2.10629e11	0.294015	0.147008	−	0.989135i	$-0.453036\pi$
$431$	2.10629e11	0.294015	0.147008	+	0.989135i	$0.453036\pi$
$432$	0	0
$433$	−5.28248e11	−0.722175	−0.361088	−	0.932532i	$-0.617594\pi$
$433$	−5.28248e11	−0.722175	−0.361088	+	0.932532i	$0.617594\pi$
$434$	3.30243e11	0.446817
$435$	0	0
$436$	−8.24737e10	−0.109302
$437$	−1.24528e11	−0.163343
$438$	0	0
$439$	3.30605e11	0.424834	0.212417	−	0.977179i	$-0.431867\pi$
$439$	3.30605e11	0.424834	0.212417	+	0.977179i	$0.431867\pi$
$440$	2.17099e10	0.0276135
$441$	0	0
$442$	3.63200e10	0.0452633
$443$	−1.22589e11	−0.151229	−0.0756145	−	0.997137i	$-0.524092\pi$
$443$	−1.22589e11	−0.151229	−0.0756145	+	0.997137i	$0.524092\pi$
$444$	0	0
$445$	2.31151e10	0.0279432
$446$	−5.42878e11	−0.649674
$447$	0	0
$448$	−5.22528e10	−0.0612856
$449$	6.36510e11	0.739089	0.369545	−	0.929213i	$-0.379514\pi$
$449$	6.36510e11	0.739089	0.369545	+	0.929213i	$0.379514\pi$
$450$	0	0
$451$	−1.86550e11	−0.212324
$452$	−8.16478e11	−0.920072
$453$	0	0
$454$	−1.10311e12	−1.21862
$455$	−1.60981e10	−0.0176085
$456$	0	0
$457$	−9.93014e11	−1.06496	−0.532479	−	0.846443i	$-0.678739\pi$
$457$	−9.93014e11	−1.06496	−0.532479	+	0.846443i	$0.678739\pi$
$458$	3.74106e11	0.397283
$459$	0	0
$460$	−1.82392e11	−0.189931
$461$	−5.66503e11	−0.584182	−0.292091	−	0.956390i	$-0.594351\pi$
$461$	−5.66503e11	−0.584182	−0.292091	+	0.956390i	$0.594351\pi$
$462$	0	0
$463$	−1.07970e12	−1.09192	−0.545959	−	0.837812i	$-0.683834\pi$
$463$	−1.07970e12	−1.09192	−0.545959	+	0.837812i	$0.683834\pi$
$464$	−1.93871e11	−0.194170
$465$	0	0
$466$	−3.09925e11	−0.304452
$467$	−1.72029e12	−1.67369	−0.836847	−	0.547437i	$-0.815604\pi$
$467$	−1.72029e12	−1.67369	−0.836847	+	0.547437i	$0.815604\pi$
$468$	0	0
$469$	2.74114e11	0.261610
$470$	6.07899e11	0.574634
$471$	0	0
$472$	−6.81430e11	−0.631950
$473$	1.25073e11	0.114892
$474$	0	0
$475$	1.82083e11	0.164115
$476$	−2.61087e11	−0.233106
$477$	0	0
$478$	−3.79172e10	−0.0332209
$479$	1.20425e12	1.04522	0.522611	−	0.852571i	$-0.324958\pi$
$479$	1.20425e12	1.04522	0.522611	+	0.852571i	$0.324958\pi$
$480$	0	0
$481$	1.34845e11	0.114863
$482$	−9.78381e11	−0.825651
$483$	0	0
$484$	−5.90698e11	−0.489285
$485$	−3.01934e11	−0.247785
$486$	0	0
$487$	6.45510e11	0.520023	0.260011	−	0.965606i	$-0.416274\pi$
$487$	6.45510e11	0.520023	0.260011	+	0.965606i	$0.416274\pi$
$488$	6.50047e11	0.518866
$489$	0	0
$490$	−3.65690e11	−0.286570
$491$	−1.33254e11	−0.103469	−0.0517347	−	0.998661i	$-0.516475\pi$
$491$	−1.33254e11	−0.103469	−0.0517347	+	0.998661i	$0.516475\pi$
$492$	0	0
$493$	−9.68700e11	−0.738547
$494$	−1.44546e10	−0.0109203
$495$	0	0
$496$	4.34314e11	0.322208
$497$	3.75120e10	0.0275783
$498$	0	0
$499$	−6.97799e11	−0.503823	−0.251912	−	0.967750i	$-0.581059\pi$
$499$	−6.97799e11	−0.503823	−0.251912	+	0.967750i	$0.581059\pi$
$500$	6.39497e11	0.457587
$501$	0	0
$502$	−9.40040e11	−0.660662
$503$	2.59285e11	0.180601	0.0903006	−	0.995915i	$-0.471217\pi$
$503$	2.59285e11	0.180601	0.0903006	+	0.995915i	$0.471217\pi$
$504$	0	0
$505$	−1.07106e12	−0.732829
$506$	−1.08682e11	−0.0737021
$507$	0	0
$508$	−5.69039e11	−0.379101
$509$	2.51001e11	0.165747	0.0828734	−	0.996560i	$-0.473590\pi$
$509$	2.51001e11	0.165747	0.0828734	+	0.996560i	$0.473590\pi$
$510$	0	0
$511$	−6.20171e11	−0.402362
$512$	−6.87195e10	−0.0441942
$513$	0	0
$514$	−6.32306e11	−0.399571
$515$	6.58069e11	0.412229
$516$	0	0
$517$	3.62229e11	0.222985
$518$	−9.69333e11	−0.591547
$519$	0	0
$520$	−2.11711e10	−0.0126978
$521$	6.85917e11	0.407851	0.203926	−	0.978986i	$-0.434630\pi$
$521$	6.85917e11	0.407851	0.203926	+	0.978986i	$0.434630\pi$
$522$	0	0
$523$	6.83211e11	0.399298	0.199649	−	0.979867i	$-0.436020\pi$
$523$	6.83211e11	0.399298	0.199649	+	0.979867i	$0.436020\pi$
$524$	−8.31623e11	−0.481877
$525$	0	0
$526$	−8.35888e11	−0.476115
$527$	2.17010e12	1.22555
$528$	0	0
$529$	−8.88081e11	−0.493062
$530$	−8.56361e11	−0.471428
$531$	0	0
$532$	1.03907e11	0.0562395
$533$	1.81920e11	0.0976355
$534$	0	0
$535$	3.20710e11	0.169247
$536$	3.60498e11	0.188652
$537$	0	0
$538$	−2.00885e12	−1.03378
$539$	−2.17903e11	−0.111202
$540$	0	0
$541$	−3.22569e12	−1.61896	−0.809479	−	0.587149i	$-0.800250\pi$
$541$	−3.22569e12	−1.61896	−0.809479	+	0.587149i	$0.800250\pi$
$542$	9.20943e11	0.458391
$543$	0	0
$544$	−3.43365e11	−0.168097
$545$	2.40209e11	0.116629
$546$	0	0
$547$	3.66670e12	1.75118	0.875592	−	0.483051i	$-0.160471\pi$
$547$	3.66670e12	1.75118	0.875592	+	0.483051i	$0.160471\pi$
$548$	−2.30175e11	−0.109030
$549$	0	0
$550$	1.58913e11	0.0740503
$551$	3.85521e11	0.178183
$552$	0	0
$553$	−3.23016e11	−0.146879
$554$	2.15904e10	0.00973792
$555$	0	0
$556$	1.08839e12	0.482999
$557$	3.37245e12	1.48456	0.742279	−	0.670091i	$-0.233745\pi$
$557$	3.37245e12	1.48456	0.742279	+	0.670091i	$0.233745\pi$
$558$	0	0
$559$	−1.21969e11	−0.0528320
$560$	1.52189e11	0.0653939
$561$	0	0
$562$	8.40229e11	0.355291
$563$	7.60757e11	0.319123	0.159562	−	0.987188i	$-0.448992\pi$
$563$	7.60757e11	0.319123	0.159562	+	0.987188i	$0.448992\pi$
$564$	0	0
$565$	2.37803e12	0.981748
$566$	−2.77019e12	−1.13458
$567$	0	0
$568$	4.93334e10	0.0198872
$569$	−1.64729e11	−0.0658816	−0.0329408	−	0.999457i	$-0.510487\pi$
$569$	−1.64729e11	−0.0658816	−0.0329408	+	0.999457i	$0.510487\pi$
$570$	0	0
$571$	4.41784e11	0.173919	0.0869596	−	0.996212i	$-0.472285\pi$
$571$	4.41784e11	0.173919	0.0869596	+	0.996212i	$0.472285\pi$
$572$	−1.26152e10	−0.00492734
$573$	0	0
$574$	−1.30773e12	−0.502824
$575$	−1.33508e12	−0.509333
$576$	0	0
$577$	1.98878e12	0.746958	0.373479	−	0.927639i	$-0.378165\pi$
$577$	1.98878e12	0.746958	0.373479	+	0.927639i	$0.378165\pi$
$578$	1.81743e11	0.0677303
$579$	0	0
$580$	5.64660e11	0.207186
$581$	8.19878e11	0.298508
$582$	0	0
$583$	−5.10279e11	−0.182936
$584$	−8.15608e11	−0.290151
$585$	0	0
$586$	−4.54979e11	−0.159387
$587$	−7.69057e11	−0.267354	−0.133677	−	0.991025i	$-0.542679\pi$
$587$	−7.69057e11	−0.267354	−0.133677	+	0.991025i	$0.542679\pi$
$588$	0	0
$589$	−8.63651e11	−0.295678
$590$	1.98470e12	0.674312
$591$	0	0
$592$	−1.27480e12	−0.426575
$593$	3.94755e12	1.31093	0.655467	−	0.755223i	$-0.272472\pi$
$593$	3.94755e12	1.31093	0.655467	+	0.755223i	$0.272472\pi$
$594$	0	0
$595$	7.60430e11	0.248733
$596$	2.00207e12	0.649936
$597$	0	0
$598$	1.05985e11	0.0338912
$599$	−4.13671e12	−1.31291	−0.656455	−	0.754366i	$-0.727945\pi$
$599$	−4.13671e12	−1.31291	−0.656455	+	0.754366i	$0.727945\pi$
$600$	0	0
$601$	−3.78750e12	−1.18418	−0.592089	−	0.805872i	$-0.701697\pi$
$601$	−3.78750e12	−1.18418	−0.592089	+	0.805872i	$0.701697\pi$
$602$	8.76778e11	0.272086
$603$	0	0
$604$	1.39142e11	0.0425393
$605$	1.72044e12	0.522084
$606$	0	0
$607$	3.01015e12	0.899992	0.449996	−	0.893030i	$-0.351425\pi$
$607$	3.01015e12	0.899992	0.449996	+	0.893030i	$0.351425\pi$
$608$	1.36651e11	0.0405554
$609$	0	0
$610$	−1.89329e12	−0.553648
$611$	−3.53239e11	−0.102538
$612$	0	0
$613$	−3.97481e12	−1.13696	−0.568479	−	0.822698i	$-0.692468\pi$
$613$	−3.97481e12	−1.13696	−0.568479	+	0.822698i	$0.692468\pi$
$614$	−3.19449e12	−0.907077
$615$	0	0
$616$	9.06847e10	0.0253759
$617$	−5.13703e12	−1.42702	−0.713508	−	0.700647i	$-0.752895\pi$
$617$	−5.13703e12	−1.42702	−0.713508	+	0.700647i	$0.752895\pi$
$618$	0	0
$619$	3.34739e12	0.916429	0.458215	−	0.888842i	$-0.348489\pi$
$619$	3.34739e12	0.916429	0.458215	+	0.888842i	$0.348489\pi$
$620$	−1.26496e12	−0.343807
$621$	0	0
$622$	−1.33646e11	−0.0358014
$623$	9.65543e10	0.0256788
$624$	0	0
$625$	8.66310e11	0.227098
$626$	1.18437e12	0.308250
$627$	0	0
$628$	1.65320e12	0.424138
$629$	−6.36971e12	−1.62253
$630$	0	0
$631$	3.65721e12	0.918371	0.459185	−	0.888340i	$-0.348141\pi$
$631$	3.65721e12	0.918371	0.459185	+	0.888340i	$0.348141\pi$
$632$	−4.24810e11	−0.105917
$633$	0	0
$634$	−2.77373e12	−0.681808
$635$	1.65735e12	0.404514
$636$	0	0
$637$	2.12495e11	0.0511354
$638$	3.36464e11	0.0803980
$639$	0	0
$640$	2.00149e11	0.0471567
$641$	3.19721e11	0.0748015	0.0374008	−	0.999300i	$-0.488092\pi$
$641$	3.19721e11	0.0748015	0.0374008	+	0.999300i	$0.488092\pi$
$642$	0	0
$643$	−3.18003e12	−0.733637	−0.366819	−	0.930293i	$-0.619553\pi$
$643$	−3.18003e12	−0.733637	−0.366819	+	0.930293i	$0.619553\pi$
$644$	−7.61872e11	−0.174540
$645$	0	0
$646$	6.82795e11	0.154257
$647$	2.76643e12	0.620655	0.310327	−	0.950630i	$-0.399561\pi$
$647$	2.76643e12	0.620655	0.310327	+	0.950630i	$0.399561\pi$
$648$	0	0
$649$	1.18262e12	0.261665
$650$	−1.54969e11	−0.0340513
$651$	0	0
$652$	2.83427e12	0.614224
$653$	2.44398e12	0.526003	0.263001	−	0.964795i	$-0.415288\pi$
$653$	2.44398e12	0.526003	0.263001	+	0.964795i	$0.415288\pi$
$654$	0	0
$655$	2.42215e12	0.514179
$656$	−1.71985e12	−0.362596
$657$	0	0
$658$	2.53926e12	0.528070
$659$	−1.74003e12	−0.359394	−0.179697	−	0.983722i	$-0.557512\pi$
$659$	−1.74003e12	−0.359394	−0.179697	+	0.983722i	$0.557512\pi$
$660$	0	0
$661$	4.85977e12	0.990168	0.495084	−	0.868845i	$-0.335137\pi$
$661$	4.85977e12	0.990168	0.495084	+	0.868845i	$0.335137\pi$
$662$	−2.35453e12	−0.476478
$663$	0	0
$664$	1.07825e12	0.215260
$665$	−3.02634e11	−0.0600095
$666$	0	0
$667$	−2.82674e12	−0.552993
$668$	−2.73308e12	−0.531078
$669$	0	0
$670$	−1.04997e12	−0.201298
$671$	−1.12816e12	−0.214841
$672$	0	0
$673$	1.05381e13	1.98013	0.990065	−	0.140610i	$-0.0449064\pi$
$673$	1.05381e13	1.98013	0.990065	+	0.140610i	$0.0449064\pi$
$674$	2.35616e12	0.439780
$675$	0	0
$676$	−2.70245e12	−0.497734
$677$	3.80947e12	0.696972	0.348486	−	0.937314i	$-0.386696\pi$
$677$	3.80947e12	0.696972	0.348486	+	0.937314i	$0.386696\pi$
$678$	0	0
$679$	−1.26121e12	−0.227706
$680$	1.00007e12	0.179366
$681$	0	0
$682$	−7.53753e11	−0.133413
$683$	−3.27230e12	−0.575386	−0.287693	−	0.957723i	$-0.592888\pi$
$683$	−3.27230e12	−0.575386	−0.287693	+	0.957723i	$0.592888\pi$
$684$	0	0
$685$	6.70397e11	0.116339
$686$	−3.53843e12	−0.610032
$687$	0	0
$688$	1.15308e12	0.196206
$689$	4.97615e11	0.0841215
$690$	0	0
$691$	−9.51135e12	−1.58705	−0.793526	−	0.608537i	$-0.791757\pi$
$691$	−9.51135e12	−1.58705	−0.793526	+	0.608537i	$0.791757\pi$
$692$	−5.07654e12	−0.841570
$693$	0	0
$694$	1.97324e12	0.322897
$695$	−3.16998e12	−0.515376
$696$	0	0
$697$	−8.59342e12	−1.37917
$698$	−6.96718e12	−1.11098
$699$	0	0
$700$	1.11400e12	0.175365
$701$	1.65914e12	0.259508	0.129754	−	0.991546i	$-0.458581\pi$
$701$	1.65914e12	0.259508	0.129754	+	0.991546i	$0.458581\pi$
$702$	0	0
$703$	2.53500e12	0.391452
$704$	1.19263e11	0.0182990
$705$	0	0
$706$	−8.53668e12	−1.29321
$707$	−4.47393e12	−0.673445
$708$	0	0
$709$	−1.06842e13	−1.58795	−0.793973	−	0.607953i	$-0.791991\pi$
$709$	−1.06842e13	−1.58795	−0.793973	+	0.607953i	$0.791991\pi$
$710$	−1.43686e11	−0.0212203
$711$	0	0
$712$	1.26982e11	0.0185175
$713$	6.33252e12	0.917643
$714$	0	0
$715$	3.67425e10	0.00525765
$716$	−5.51541e12	−0.784276
$717$	0	0
$718$	2.56292e12	0.359895
$719$	−6.05478e12	−0.844926	−0.422463	−	0.906380i	$-0.638834\pi$
$719$	−6.05478e12	−0.844926	−0.422463	+	0.906380i	$0.638834\pi$
$720$	0	0
$721$	2.74882e12	0.378825
$722$	−2.71737e11	−0.0372161
$723$	0	0
$724$	5.94041e12	0.803512
$725$	4.13321e12	0.555605
$726$	0	0
$727$	2.04756e12	0.271852	0.135926	−	0.990719i	$-0.456599\pi$
$727$	2.04756e12	0.271852	0.135926	+	0.990719i	$0.456599\pi$
$728$	−8.84341e10	−0.0116689
$729$	0	0
$730$	2.37550e12	0.309601
$731$	5.76151e12	0.746291
$732$	0	0
$733$	6.16018e12	0.788181	0.394090	−	0.919072i	$-0.371060\pi$
$733$	6.16018e12	0.788181	0.394090	+	0.919072i	$0.371060\pi$
$734$	6.49087e12	0.825412
$735$	0	0
$736$	−1.00196e12	−0.125864
$737$	−6.25644e11	−0.0781130
$738$	0	0
$739$	4.77375e12	0.588789	0.294394	−	0.955684i	$-0.404882\pi$
$739$	4.77375e12	0.588789	0.294394	+	0.955684i	$0.404882\pi$
$740$	3.71293e12	0.455171
$741$	0	0
$742$	−3.57712e12	−0.433227
$743$	1.33263e13	1.60420	0.802102	−	0.597187i	$-0.203715\pi$
$743$	1.33263e13	1.60420	0.802102	+	0.597187i	$0.203715\pi$
$744$	0	0
$745$	−5.83113e12	−0.693505
$746$	−1.05421e12	−0.124625
$747$	0	0
$748$	5.95910e11	0.0696023
$749$	1.33964e12	0.155532
$750$	0	0
$751$	3.53427e12	0.405434	0.202717	−	0.979237i	$-0.435023\pi$
$751$	3.53427e12	0.405434	0.202717	+	0.979237i	$0.435023\pi$
$752$	3.33947e12	0.380801
$753$	0	0
$754$	−3.28113e11	−0.0369703
$755$	−4.05257e11	−0.0453910
$756$	0	0
$757$	7.93100e12	0.877802	0.438901	−	0.898535i	$-0.355368\pi$
$757$	7.93100e12	0.877802	0.438901	+	0.898535i	$0.355368\pi$
$758$	3.09607e12	0.340643
$759$	0	0
$760$	−3.98005e11	−0.0432740
$761$	7.15667e11	0.0773535	0.0386767	−	0.999252i	$-0.487686\pi$
$761$	7.15667e11	0.0773535	0.0386767	+	0.999252i	$0.487686\pi$
$762$	0	0
$763$	1.00338e12	0.107178
$764$	5.43848e12	0.577507
$765$	0	0
$766$	3.93736e12	0.413215
$767$	−1.15327e12	−0.120324
$768$	0	0
$769$	−1.10683e13	−1.14133	−0.570666	−	0.821182i	$-0.693315\pi$
$769$	−1.10683e13	−1.14133	−0.570666	+	0.821182i	$0.693315\pi$
$770$	−2.64124e11	−0.0270769
$771$	0	0
$772$	7.04084e12	0.713422
$773$	1.47552e13	1.48641	0.743203	−	0.669065i	$-0.233305\pi$
$773$	1.47552e13	1.48641	0.743203	+	0.669065i	$0.233305\pi$
$774$	0	0
$775$	−9.25930e12	−0.921978
$776$	−1.65867e12	−0.164203
$777$	0	0
$778$	−9.08440e12	−0.888972
$779$	3.41999e12	0.332741
$780$	0	0
$781$	−8.56181e10	−0.00823448
$782$	−5.00643e12	−0.478738
$783$	0	0
$784$	−2.00890e12	−0.189905
$785$	−4.81503e12	−0.452570
$786$	0	0
$787$	−1.04208e13	−0.968313	−0.484157	−	0.874981i	$-0.660874\pi$
$787$	−1.04208e13	−0.968313	−0.484157	+	0.874981i	$0.660874\pi$
$788$	−2.51770e12	−0.232614
$789$	0	0
$790$	1.23728e12	0.113018
$791$	9.93331e12	0.902194
$792$	0	0
$793$	1.10016e12	0.0987929
$794$	−1.37732e13	−1.22983
$795$	0	0
$796$	3.63819e12	0.321201
$797$	1.61644e13	1.41905	0.709525	−	0.704680i	$-0.248909\pi$
$797$	1.61644e13	1.41905	0.709525	+	0.704680i	$0.248909\pi$
$798$	0	0
$799$	1.66861e13	1.44842
$800$	1.46506e12	0.126459
$801$	0	0
$802$	−8.85941e11	−0.0756171
$803$	1.41549e12	0.120140
$804$	0	0
$805$	2.21899e12	0.186241
$806$	7.35046e11	0.0613489
$807$	0	0
$808$	−5.88383e12	−0.485634
$809$	−1.95464e12	−0.160435	−0.0802175	−	0.996777i	$-0.525561\pi$
$809$	−1.95464e12	−0.160435	−0.0802175	+	0.996777i	$0.525561\pi$
$810$	0	0
$811$	5.06971e12	0.411519	0.205759	−	0.978603i	$-0.434034\pi$
$811$	5.06971e12	0.411519	0.205759	+	0.978603i	$0.434034\pi$
$812$	2.35865e12	0.190397
$813$	0	0
$814$	2.21242e12	0.176628
$815$	−8.25495e12	−0.655398
$816$	0	0
$817$	−2.29295e12	−0.180051
$818$	4.62458e12	0.361146
$819$	0	0
$820$	5.00914e12	0.386902
$821$	1.41159e13	1.08434	0.542170	−	0.840269i	$-0.317603\pi$
$821$	1.41159e13	1.08434	0.542170	+	0.840269i	$0.317603\pi$
$822$	0	0
$823$	1.28449e13	0.975957	0.487978	−	0.872856i	$-0.337734\pi$
$823$	1.28449e13	0.975957	0.487978	+	0.872856i	$0.337734\pi$
$824$	3.61508e12	0.273178
$825$	0	0
$826$	8.29032e12	0.619671
$827$	−1.23760e12	−0.0920038	−0.0460019	−	0.998941i	$-0.514648\pi$
$827$	−1.23760e12	−0.0920038	−0.0460019	+	0.998941i	$0.514648\pi$
$828$	0	0
$829$	−2.44412e12	−0.179733	−0.0898665	−	0.995954i	$-0.528644\pi$
$829$	−2.44412e12	−0.179733	−0.0898665	+	0.995954i	$0.528644\pi$
$830$	−3.14046e12	−0.229690
$831$	0	0
$832$	−1.16303e11	−0.00841463
$833$	−1.00377e13	−0.722325
$834$	0	0
$835$	7.96024e12	0.566679
$836$	−2.37159e11	−0.0167923
$837$	0	0
$838$	−9.01896e12	−0.631769
$839$	−7.02405e10	−0.00489394	−0.00244697	−	0.999997i	$-0.500779\pi$
$839$	−7.02405e10	−0.00489394	−0.00244697	+	0.999997i	$0.500779\pi$
$840$	0	0
$841$	−5.75596e12	−0.396767
$842$	1.36278e13	0.934375
$843$	0	0
$844$	1.30694e13	0.886570
$845$	7.87103e12	0.531100
$846$	0	0
$847$	7.18647e12	0.479778
$848$	−4.70439e12	−0.312408
$849$	0	0
$850$	7.32032e12	0.481000
$851$	−1.85873e13	−1.21488
$852$	0	0
$853$	9.22335e12	0.596511	0.298255	−	0.954486i	$-0.403595\pi$
$853$	9.22335e12	0.596511	0.298255	+	0.954486i	$0.403595\pi$
$854$	−7.90850e12	−0.508784
$855$	0	0
$856$	1.76181e12	0.112157
$857$	1.79256e13	1.13517	0.567583	−	0.823316i	$-0.307879\pi$
$857$	1.79256e13	1.13517	0.567583	+	0.823316i	$0.307879\pi$
$858$	0	0
$859$	1.46624e13	0.918831	0.459415	−	0.888222i	$-0.348059\pi$
$859$	1.46624e13	0.918831	0.459415	+	0.888222i	$0.348059\pi$
$860$	−3.35841e12	−0.209359
$861$	0	0
$862$	−3.37006e12	−0.207900
$863$	−2.49772e13	−1.53283	−0.766416	−	0.642344i	$-0.777962\pi$
$863$	−2.49772e13	−1.53283	−0.766416	+	0.642344i	$0.777962\pi$
$864$	0	0
$865$	1.47857e13	0.897984
$866$	8.45197e12	0.510655
$867$	0	0
$868$	−5.28389e12	−0.315947
$869$	7.37257e11	0.0438561
$870$	0	0
$871$	6.10116e11	0.0359196
$872$	1.31958e12	0.0772879
$873$	0	0
$874$	1.99245e12	0.115501
$875$	−7.78016e12	−0.448696
$876$	0	0
$877$	−1.49317e13	−0.852334	−0.426167	−	0.904644i	$-0.640136\pi$
$877$	−1.49317e13	−0.852334	−0.426167	+	0.904644i	$0.640136\pi$
$878$	−5.28968e12	−0.300403
$879$	0	0
$880$	−3.47359e11	−0.0195257
$881$	3.19747e13	1.78819	0.894096	−	0.447875i	$-0.147819\pi$
$881$	3.19747e13	1.78819	0.894096	+	0.447875i	$0.147819\pi$
$882$	0	0
$883$	−2.24320e13	−1.24178	−0.620890	−	0.783897i	$-0.713229\pi$
$883$	−2.24320e13	−1.24178	−0.620890	+	0.783897i	$0.713229\pi$
$884$	−5.81121e11	−0.0320060
$885$	0	0
$886$	1.96142e12	0.106935
$887$	4.07823e11	0.0221216	0.0110608	−	0.999939i	$-0.496479\pi$
$887$	4.07823e11	0.0221216	0.0110608	+	0.999939i	$0.496479\pi$
$888$	0	0
$889$	6.92295e12	0.371735
$890$	−3.69841e11	−0.0197588
$891$	0	0
$892$	8.68605e12	0.459389
$893$	−6.64068e12	−0.349447
$894$	0	0
$895$	1.60639e13	0.836850
$896$	8.36045e11	0.0433355
$897$	0	0
$898$	−1.01842e13	−0.522615
$899$	−1.96046e13	−1.00101
$900$	0	0
$901$	−2.35060e13	−1.18828
$902$	2.98480e12	0.150136
$903$	0	0
$904$	1.30637e13	0.650589
$905$	−1.73017e13	−0.857376
$906$	0	0
$907$	3.79333e13	1.86118	0.930588	−	0.366068i	$-0.119296\pi$
$907$	3.79333e13	1.86118	0.930588	+	0.366068i	$0.119296\pi$
$908$	1.76498e13	0.861695
$909$	0	0
$910$	2.57569e11	0.0124511
$911$	1.22581e13	0.589643	0.294821	−	0.955552i	$-0.404740\pi$
$911$	1.22581e13	0.589643	0.294821	+	0.955552i	$0.404740\pi$
$912$	0	0
$913$	−1.87130e12	−0.0891303
$914$	1.58882e13	0.753039
$915$	0	0
$916$	−5.98569e12	−0.280921
$917$	1.01176e13	0.472514
$918$	0	0
$919$	−5.56990e12	−0.257589	−0.128795	−	0.991671i	$-0.541111\pi$
$919$	−5.56990e12	−0.257589	−0.128795	+	0.991671i	$0.541111\pi$
$920$	2.91827e12	0.134302
$921$	0	0
$922$	9.06405e12	0.413079
$923$	8.34932e10	0.00378655
$924$	0	0
$925$	2.71780e13	1.22062
$926$	1.72752e13	0.772102
$927$	0	0
$928$	3.10194e12	0.137299
$929$	1.06041e12	0.0467095	0.0233547	−	0.999727i	$-0.492565\pi$
$929$	1.06041e12	0.0467095	0.0233547	+	0.999727i	$0.492565\pi$
$930$	0	0
$931$	3.99479e12	0.174269
$932$	4.95879e12	0.215280
$933$	0	0
$934$	2.75247e13	1.18348
$935$	−1.73562e12	−0.0742681
$936$	0	0
$937$	2.18020e13	0.923993	0.461997	−	0.886882i	$-0.347133\pi$
$937$	2.18020e13	0.923993	0.461997	+	0.886882i	$0.347133\pi$
$938$	−4.38583e12	−0.184986
$939$	0	0
$940$	−9.72639e12	−0.406328
$941$	−4.21269e13	−1.75149	−0.875743	−	0.482778i	$-0.839628\pi$
$941$	−4.21269e13	−1.75149	−0.875743	+	0.482778i	$0.839628\pi$
$942$	0	0
$943$	−2.50762e13	−1.03267
$944$	1.09029e13	0.446856
$945$	0	0
$946$	−2.00117e12	−0.0812409
$947$	6.94154e12	0.280467	0.140233	−	0.990118i	$-0.455215\pi$
$947$	6.94154e12	0.280467	0.140233	+	0.990118i	$0.455215\pi$
$948$	0	0
$949$	−1.38036e12	−0.0552451
$950$	−2.91332e12	−0.116047
$951$	0	0
$952$	4.17739e12	0.164831
$953$	−4.19327e13	−1.64678	−0.823389	−	0.567478i	$-0.807919\pi$
$953$	−4.19327e13	−1.64678	−0.823389	+	0.567478i	$0.807919\pi$
$954$	0	0
$955$	−1.58398e13	−0.616220
$956$	6.06676e11	0.0234907
$957$	0	0
$958$	−1.92681e13	−0.739083
$959$	2.80032e12	0.106912
$960$	0	0
$961$	1.74789e13	0.661089
$962$	−2.15751e12	−0.0812206
$963$	0	0
$964$	1.56541e13	0.583823
$965$	−2.05068e13	−0.761246
$966$	0	0
$967$	−3.44588e13	−1.26730	−0.633652	−	0.773618i	$-0.718445\pi$
$967$	−3.44588e13	−1.26730	−0.633652	+	0.773618i	$0.718445\pi$
$968$	9.45117e12	0.345977
$969$	0	0
$970$	4.83095e12	0.175210
$971$	−2.24294e13	−0.809712	−0.404856	−	0.914380i	$-0.632678\pi$
$971$	−2.24294e13	−0.809712	−0.404856	+	0.914380i	$0.632678\pi$
$972$	0	0
$973$	−1.32413e13	−0.473614
$974$	−1.03282e13	−0.367712
$975$	0	0
$976$	−1.04007e13	−0.366894
$977$	7.81859e12	0.274538	0.137269	−	0.990534i	$-0.456167\pi$
$977$	7.81859e12	0.274538	0.137269	+	0.990534i	$0.456167\pi$
$978$	0	0
$979$	−2.20377e11	−0.00766734
$980$	5.85104e12	0.202635
$981$	0	0
$982$	2.13206e12	0.0731640
$983$	5.19974e12	0.177620	0.0888099	−	0.996049i	$-0.471694\pi$
$983$	5.19974e12	0.177620	0.0888099	+	0.996049i	$0.471694\pi$
$984$	0	0
$985$	7.33294e12	0.248208
$986$	1.54992e13	0.522232
$987$	0	0
$988$	2.31273e11	0.00772180
$989$	1.68125e13	0.558791
$990$	0	0
$991$	−5.54452e12	−0.182613	−0.0913067	−	0.995823i	$-0.529104\pi$
$991$	−5.54452e12	−0.182613	−0.0913067	+	0.995823i	$0.529104\pi$
$992$	−6.94903e12	−0.227836
$993$	0	0
$994$	−6.00192e11	−0.0195008
$995$	−1.05964e13	−0.342733
$996$	0	0
$997$	5.26130e13	1.68642	0.843208	−	0.537587i	$-0.180664\pi$
$997$	5.26130e13	1.68642	0.843208	+	0.537587i	$0.180664\pi$
$998$	1.11648e13	0.356257
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.10.a.i.1.2		4
3.2	odd	2		38.10.a.e.1.4	✓	4
12.11	even	2		304.10.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.e.1.4	✓	4	3.2	odd	2
304.10.a.d.1.1		4	12.11	even	2
342.10.a.i.1.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	342.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +256.000 q^{4} -745.613 q^{5} -3114.51 q^{7} -4096.00 q^{8} +O(q^{10})\)	\(q-16.0000 q^{2} +256.000 q^{4} -745.613 q^{5} -3114.51 q^{7} -4096.00 q^{8} +11929.8 q^{10} +7108.61 q^{11} -6932.19 q^{13} +49832.1 q^{14} +65536.0 q^{16} +327458. q^{17} -130321. q^{19} -190877. q^{20} -113738. q^{22} +955548. q^{23} -1.39719e6 q^{25} +110915. q^{26} -797314. q^{28} -2.95824e6 q^{29} +6.62711e6 q^{31} -1.04858e6 q^{32} -5.23933e6 q^{34} +2.32222e6 q^{35} -1.94520e7 q^{37} +2.08514e6 q^{38} +3.05403e6 q^{40} -2.62428e7 q^{41} +1.75946e7 q^{43} +1.81980e6 q^{44} -1.52888e7 q^{46} +5.09563e7 q^{47} -3.06534e7 q^{49} +2.23550e7 q^{50} -1.77464e6 q^{52} -7.17833e7 q^{53} -5.30027e6 q^{55} +1.27570e7 q^{56} +4.73318e7 q^{58} +1.66365e8 q^{59} -1.58703e8 q^{61} -1.06034e8 q^{62} +1.67772e7 q^{64} +5.16873e6 q^{65} -8.80121e7 q^{67} +8.38293e7 q^{68} -3.71555e7 q^{70} -1.20443e7 q^{71} +1.99123e8 q^{73} +3.11231e8 q^{74} -3.33622e7 q^{76} -2.21398e7 q^{77} +1.03713e8 q^{79} -4.88645e7 q^{80} +4.19884e8 q^{82} -2.63245e8 q^{83} -2.44157e8 q^{85} -2.81514e8 q^{86} -2.91169e7 q^{88} -3.10014e7 q^{89} +2.15904e7 q^{91} +2.44620e8 q^{92} -8.15301e8 q^{94} +9.71691e7 q^{95} +4.04948e8 q^{97} +4.90455e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 1024 q^{4} - 866 q^{5} + 2670 q^{7} - 16384 q^{8}+O(q^{10}) \) 4 * q - 64 * q^2 + 1024 * q^4 - 866 * q^5 + 2670 * q^7 - 16384 * q^8	\( 4 q - 64 q^{2} + 1024 q^{4} - 866 q^{5} + 2670 q^{7} - 16384 q^{8} + 13856 q^{10} - 119234 q^{11} - 6748 q^{13} - 42720 q^{14} + 262144 q^{16} - 678624 q^{17} - 521284 q^{19} - 221696 q^{20} + 1907744 q^{22} - 2911868 q^{23} + 268766 q^{25} + 107968 q^{26} + 683520 q^{28} - 8291104 q^{29} + 3445468 q^{31} - 4194304 q^{32} + 10857984 q^{34} - 7715058 q^{35} - 1005524 q^{37} + 8340544 q^{38} + 3547136 q^{40} - 8514124 q^{41} + 13900726 q^{43} - 30523904 q^{44} + 46589888 q^{46} + 36334954 q^{47} - 30891808 q^{49} - 4300256 q^{50} - 1727488 q^{52} + 113969356 q^{53} - 178140098 q^{55} - 10936320 q^{56} + 132657664 q^{58} + 396773766 q^{59} - 298192066 q^{61} - 55127488 q^{62} + 67108864 q^{64} + 291187676 q^{65} - 113551722 q^{67} - 173727744 q^{68} + 123440928 q^{70} - 4659620 q^{71} + 136198452 q^{73} + 16088384 q^{74} - 133448704 q^{76} - 120551886 q^{77} + 67255424 q^{79} - 56754176 q^{80} + 136225984 q^{82} - 1376505216 q^{83} + 638402178 q^{85} - 222411616 q^{86} + 488382464 q^{88} - 1557211260 q^{89} + 1422773730 q^{91} - 745438208 q^{92} - 581359264 q^{94} + 112857986 q^{95} + 975818188 q^{97} + 494268928 q^{98}+O(q^{100}) \) 4 * q - 64 * q^2 + 1024 * q^4 - 866 * q^5 + 2670 * q^7 - 16384 * q^8 + 13856 * q^10 - 119234 * q^11 - 6748 * q^13 - 42720 * q^14 + 262144 * q^16 - 678624 * q^17 - 521284 * q^19 - 221696 * q^20 + 1907744 * q^22 - 2911868 * q^23 + 268766 * q^25 + 107968 * q^26 + 683520 * q^28 - 8291104 * q^29 + 3445468 * q^31 - 4194304 * q^32 + 10857984 * q^34 - 7715058 * q^35 - 1005524 * q^37 + 8340544 * q^38 + 3547136 * q^40 - 8514124 * q^41 + 13900726 * q^43 - 30523904 * q^44 + 46589888 * q^46 + 36334954 * q^47 - 30891808 * q^49 - 4300256 * q^50 - 1727488 * q^52 + 113969356 * q^53 - 178140098 * q^55 - 10936320 * q^56 + 132657664 * q^58 + 396773766 * q^59 - 298192066 * q^61 - 55127488 * q^62 + 67108864 * q^64 + 291187676 * q^65 - 113551722 * q^67 - 173727744 * q^68 + 123440928 * q^70 - 4659620 * q^71 + 136198452 * q^73 + 16088384 * q^74 - 133448704 * q^76 - 120551886 * q^77 + 67255424 * q^79 - 56754176 * q^80 + 136225984 * q^82 - 1376505216 * q^83 + 638402178 * q^85 - 222411616 * q^86 + 488382464 * q^88 - 1557211260 * q^89 + 1422773730 * q^91 - 745438208 * q^92 - 581359264 * q^94 + 112857986 * q^95 + 975818188 * q^97 + 494268928 * q^98

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