LMFDB - Embedded newform 261.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,10,Mod(1,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, 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("261.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	261.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:	$134.424353239$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2901 x^{7} - 4592 x^{6} + 2830996 x^{5} + 7409504 x^{4} - 1038861888 x^{3} - 2974719488 x^{2} + \cdots + 456378417152 $ x^9 - 2901x^7 - 4592x^6 + 2830996x^5 + 7409504x^4 - 1038861888x^3 - 2974719488x^2 + 115773751296*x + 456378417152
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-24.3559$ of defining polynomial
Character	$\chi$	$=$	261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-24.3559 q^{2} +81.2084 q^{4} +2213.18 q^{5} -1575.25 q^{7} +10492.3 q^{8} +O(q^{10})$	\(q-24.3559 q^{2} +81.2084 q^{4} +2213.18 q^{5} -1575.25 q^{7} +10492.3 q^{8} -53903.9 q^{10} +60678.9 q^{11} +169843. q^{13} +38366.5 q^{14} -297128. q^{16} -508356. q^{17} -418524. q^{19} +179729. q^{20} -1.47789e6 q^{22} +541114. q^{23} +2.94504e6 q^{25} -4.13668e6 q^{26} -127923. q^{28} +707281. q^{29} -6.62773e6 q^{31} +1.86475e6 q^{32} +1.23815e7 q^{34} -3.48631e6 q^{35} -1.32108e7 q^{37} +1.01935e7 q^{38} +2.32214e7 q^{40} -3.08944e7 q^{41} -2.17269e7 q^{43} +4.92764e6 q^{44} -1.31793e7 q^{46} -5.44016e7 q^{47} -3.78722e7 q^{49} -7.17291e7 q^{50} +1.37927e7 q^{52} +4.58294e6 q^{53} +1.34293e8 q^{55} -1.65280e7 q^{56} -1.72264e7 q^{58} -2.84982e7 q^{59} -6.28415e7 q^{61} +1.61424e8 q^{62} +1.06712e8 q^{64} +3.75894e8 q^{65} -2.22931e8 q^{67} -4.12828e7 q^{68} +8.49120e7 q^{70} +2.72133e8 q^{71} +2.97447e8 q^{73} +3.21760e8 q^{74} -3.39876e7 q^{76} -9.55843e7 q^{77} -1.70482e8 q^{79} -6.57598e8 q^{80} +7.52459e8 q^{82} +3.53366e7 q^{83} -1.12508e9 q^{85} +5.29178e8 q^{86} +6.36662e8 q^{88} -2.52276e7 q^{89} -2.67545e8 q^{91} +4.39429e7 q^{92} +1.32500e9 q^{94} -9.26269e8 q^{95} -7.85122e8 q^{97} +9.22410e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 1194 q^{4} + 738 q^{5} - 7128 q^{7} + 13776 q^{8}+O(q^{10}) $ 9 * q + 1194 * q^4 + 738 * q^5 - 7128 * q^7 + 13776 * q^8	\( 9 q + 1194 q^{4} + 738 q^{5} - 7128 q^{7} + 13776 q^{8} + 37812 q^{10} + 59512 q^{11} - 165758 q^{13} + 406080 q^{14} - 1044958 q^{16} + 394814 q^{17} - 2256606 q^{19} + 2237578 q^{20} - 5311718 q^{22} + 1699500 q^{23} - 983481 q^{25} + 4264740 q^{26} - 8491636 q^{28} + 6365529 q^{29} - 11929632 q^{31} + 1346192 q^{32} + 8655764 q^{34} + 3275324 q^{35} + 14454898 q^{37} - 14709736 q^{38} + 45167060 q^{40} - 52495202 q^{41} + 21819888 q^{43} - 70837004 q^{44} + 20628012 q^{46} - 44968948 q^{47} - 26826775 q^{49} - 155997680 q^{50} + 29562122 q^{52} + 111394302 q^{53} - 173560742 q^{55} - 67419136 q^{56} + 236142720 q^{59} - 241129054 q^{61} - 261343278 q^{62} - 333112958 q^{64} + 625660884 q^{65} - 672046492 q^{67} + 63179948 q^{68} - 366389016 q^{70} + 475841956 q^{71} - 424813822 q^{73} + 532689728 q^{74} - 552478056 q^{76} + 182224776 q^{77} - 170801148 q^{79} - 562655678 q^{80} + 1468192652 q^{82} + 468898296 q^{83} - 271552972 q^{85} - 1462277802 q^{86} + 1176890862 q^{88} + 676036598 q^{89} + 9763884 q^{91} - 2724990708 q^{92} + 2429128614 q^{94} - 69331732 q^{95} + 170708754 q^{97} - 3278517600 q^{98}+O(q^{100}) \) 9 * q + 1194 * q^4 + 738 * q^5 - 7128 * q^7 + 13776 * q^8 + 37812 * q^10 + 59512 * q^11 - 165758 * q^13 + 406080 * q^14 - 1044958 * q^16 + 394814 * q^17 - 2256606 * q^19 + 2237578 * q^20 - 5311718 * q^22 + 1699500 * q^23 - 983481 * q^25 + 4264740 * q^26 - 8491636 * q^28 + 6365529 * q^29 - 11929632 * q^31 + 1346192 * q^32 + 8655764 * q^34 + 3275324 * q^35 + 14454898 * q^37 - 14709736 * q^38 + 45167060 * q^40 - 52495202 * q^41 + 21819888 * q^43 - 70837004 * q^44 + 20628012 * q^46 - 44968948 * q^47 - 26826775 * q^49 - 155997680 * q^50 + 29562122 * q^52 + 111394302 * q^53 - 173560742 * q^55 - 67419136 * q^56 + 236142720 * q^59 - 241129054 * q^61 - 261343278 * q^62 - 333112958 * q^64 + 625660884 * q^65 - 672046492 * q^67 + 63179948 * q^68 - 366389016 * q^70 + 475841956 * q^71 - 424813822 * q^73 + 532689728 * q^74 - 552478056 * q^76 + 182224776 * q^77 - 170801148 * q^79 - 562655678 * q^80 + 1468192652 * q^82 + 468898296 * q^83 - 271552972 * q^85 - 1462277802 * q^86 + 1176890862 * q^88 + 676036598 * q^89 + 9763884 * q^91 - 2724990708 * q^92 + 2429128614 * q^94 - 69331732 * q^95 + 170708754 * q^97 - 3278517600 * 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 $

$2$	−24.3559	−1.07639	−0.538194	−	0.842821i	$-0.680893\pi$
$2$	−24.3559	−1.07639	−0.538194	+	0.842821i	$0.680893\pi$
$3$	0	0
$3$	0	0
$4$	81.2084	0.158610
$5$	2213.18	1.58362	0.791812	−	0.610765i	$-0.209138\pi$
$5$	2213.18	1.58362	0.791812	+	0.610765i	$0.209138\pi$
$6$	0	0
$7$	−1575.25	−0.247975	−0.123987	−	0.992284i	$-0.539568\pi$
$7$	−1575.25	−0.247975	−0.123987	+	0.992284i	$0.539568\pi$
$8$	10492.3	0.905662
$9$	0	0
$10$	−53903.9	−1.70459
$11$	60678.9	1.24960	0.624800	−	0.780785i	$-0.285181\pi$
$11$	60678.9	1.24960	0.624800	+	0.780785i	$0.285181\pi$
$12$	0	0
$13$	169843.	1.64931	0.824656	−	0.565634i	$-0.191369\pi$
$13$	169843.	1.64931	0.824656	+	0.565634i	$0.191369\pi$
$14$	38366.5	0.266917
$15$	0	0
$16$	−297128.	−1.13345
$17$	−508356.	−1.47621	−0.738105	−	0.674686i	$-0.764279\pi$
$17$	−508356.	−1.47621	−0.738105	+	0.674686i	$0.764279\pi$
$18$	0	0
$19$	−418524.	−0.736765	−0.368382	−	0.929674i	$-0.620088\pi$
$19$	−418524.	−0.736765	−0.368382	+	0.929674i	$0.620088\pi$
$20$	179729.	0.251179
$21$	0	0
$22$	−1.47789e6	−1.34505
$23$	541114.	0.403193	0.201597	−	0.979469i	$-0.435387\pi$
$23$	541114.	0.403193	0.201597	+	0.979469i	$0.435387\pi$
$24$	0	0
$25$	2.94504e6	1.50786
$26$	−4.13668e6	−1.77530
$27$	0	0
$28$	−127923.	−0.0393313
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	0	0
$31$	−6.62773e6	−1.28895	−0.644476	−	0.764624i	$-0.722925\pi$
$31$	−6.62773e6	−1.28895	−0.644476	+	0.764624i	$0.722925\pi$
$32$	1.86475e6	0.314373
$33$	0	0
$34$	1.23815e7	1.58897
$35$	−3.48631e6	−0.392698
$36$	0	0
$37$	−1.32108e7	−1.15883	−0.579417	−	0.815032i	$-0.696720\pi$
$37$	−1.32108e7	−1.15883	−0.579417	+	0.815032i	$0.696720\pi$
$38$	1.01935e7	0.793045
$39$	0	0
$40$	2.32214e7	1.43423
$41$	−3.08944e7	−1.70747	−0.853733	−	0.520712i	$-0.825667\pi$
$41$	−3.08944e7	−1.70747	−0.853733	+	0.520712i	$0.825667\pi$
$42$	0	0
$43$	−2.17269e7	−0.969147	−0.484574	−	0.874750i	$-0.661025\pi$
$43$	−2.17269e7	−0.969147	−0.484574	+	0.874750i	$0.661025\pi$
$44$	4.92764e6	0.198199
$45$	0	0
$46$	−1.31793e7	−0.433992
$47$	−5.44016e7	−1.62619	−0.813095	−	0.582131i	$-0.802219\pi$
$47$	−5.44016e7	−1.62619	−0.813095	+	0.582131i	$0.802219\pi$
$48$	0	0
$49$	−3.78722e7	−0.938509
$50$	−7.17291e7	−1.62304
$51$	0	0
$52$	1.37927e7	0.261598
$53$	4.58294e6	0.0797817	0.0398908	−	0.999204i	$-0.487299\pi$
$53$	4.58294e6	0.0797817	0.0398908	+	0.999204i	$0.487299\pi$
$54$	0	0
$55$	1.34293e8	1.97890
$56$	−1.65280e7	−0.224581
$57$	0	0
$58$	−1.72264e7	−0.199880
$59$	−2.84982e7	−0.306184	−0.153092	−	0.988212i	$-0.548923\pi$
$59$	−2.84982e7	−0.306184	−0.153092	+	0.988212i	$0.548923\pi$
$60$	0	0
$61$	−6.28415e7	−0.581115	−0.290558	−	0.956857i	$-0.593841\pi$
$61$	−6.28415e7	−0.581115	−0.290558	+	0.956857i	$0.593841\pi$
$62$	1.61424e8	1.38741
$63$	0	0
$64$	1.06712e8	0.795066
$65$	3.75894e8	2.61189
$66$	0	0
$67$	−2.22931e8	−1.35156	−0.675779	−	0.737104i	$-0.736193\pi$
$67$	−2.22931e8	−1.35156	−0.675779	+	0.737104i	$0.736193\pi$
$68$	−4.12828e7	−0.234142
$69$	0	0
$70$	8.49120e7	0.422696
$71$	2.72133e8	1.27092	0.635460	−	0.772134i	$-0.280810\pi$
$71$	2.72133e8	1.27092	0.635460	+	0.772134i	$0.280810\pi$
$72$	0	0
$73$	2.97447e8	1.22590	0.612952	−	0.790120i	$-0.289982\pi$
$73$	2.97447e8	1.22590	0.612952	+	0.790120i	$0.289982\pi$
$74$	3.21760e8	1.24735
$75$	0	0
$76$	−3.39876e7	−0.116858
$77$	−9.55843e7	−0.309869
$78$	0	0
$79$	−1.70482e8	−0.492445	−0.246223	−	0.969213i	$-0.579189\pi$
$79$	−1.70482e8	−0.492445	−0.246223	+	0.969213i	$0.579189\pi$
$80$	−6.57598e8	−1.79496
$81$	0	0
$82$	7.52459e8	1.83789
$83$	3.53366e7	0.0817286	0.0408643	−	0.999165i	$-0.486989\pi$
$83$	3.53366e7	0.0817286	0.0408643	+	0.999165i	$0.486989\pi$
$84$	0	0
$85$	−1.12508e9	−2.33776
$86$	5.29178e8	1.04318
$87$	0	0
$88$	6.36662e8	1.13171
$89$	−2.52276e7	−0.0426207	−0.0213103	−	0.999773i	$-0.506784\pi$
$89$	−2.52276e7	−0.0426207	−0.0213103	+	0.999773i	$0.506784\pi$
$90$	0	0
$91$	−2.67545e8	−0.408988
$92$	4.39429e7	0.0639505
$93$	0	0
$94$	1.32500e9	1.75041
$95$	−9.26269e8	−1.16676
$96$	0	0
$97$	−7.85122e8	−0.900460	−0.450230	−	0.892913i	$-0.648658\pi$
$97$	−7.85122e8	−0.900460	−0.450230	+	0.892913i	$0.648658\pi$
$98$	9.22410e8	1.01020
$99$	0	0
$100$	2.39162e8	0.239162
$101$	−3.60554e7	−0.0344766	−0.0172383	−	0.999851i	$-0.505487\pi$
$101$	−3.60554e7	−0.0344766	−0.0172383	+	0.999851i	$0.505487\pi$
$102$	0	0
$103$	7.08796e7	0.0620517	0.0310259	−	0.999519i	$-0.490123\pi$
$103$	7.08796e7	0.0620517	0.0310259	+	0.999519i	$0.490123\pi$
$104$	1.78205e9	1.49372
$105$	0	0
$106$	−1.11622e8	−0.0858760
$107$	1.27630e9	0.941297	0.470649	−	0.882321i	$-0.344020\pi$
$107$	1.27630e9	0.941297	0.470649	+	0.882321i	$0.344020\pi$
$108$	0	0
$109$	1.54005e9	1.04500	0.522500	−	0.852639i	$-0.324999\pi$
$109$	1.54005e9	1.04500	0.522500	+	0.852639i	$0.324999\pi$
$110$	−3.27083e9	−2.13006
$111$	0	0
$112$	4.68050e8	0.281068
$113$	1.73234e9	0.999494	0.499747	−	0.866171i	$-0.333426\pi$
$113$	1.73234e9	0.999494	0.499747	+	0.866171i	$0.333426\pi$
$114$	0	0
$115$	1.19758e9	0.638506
$116$	5.74371e7	0.0294532
$117$	0	0
$118$	6.94098e8	0.329573
$119$	8.00786e8	0.366063
$120$	0	0
$121$	1.32399e9	0.561500
$122$	1.53056e9	0.625505
$123$	0	0
$124$	−5.38227e8	−0.204441
$125$	2.19529e9	0.804262
$126$	0	0
$127$	−4.31555e9	−1.47204	−0.736020	−	0.676960i	$-0.763297\pi$
$127$	−4.31555e9	−1.47204	−0.736020	+	0.676960i	$0.763297\pi$
$128$	−3.55381e9	−1.17017
$129$	0	0
$130$	−9.15521e9	−2.81141
$131$	−3.65866e9	−1.08543	−0.542715	−	0.839917i	$-0.682604\pi$
$131$	−3.65866e9	−1.08543	−0.542715	+	0.839917i	$0.682604\pi$
$132$	0	0
$133$	6.59278e8	0.182699
$134$	5.42969e9	1.45480
$135$	0	0
$136$	−5.33383e9	−1.33695
$137$	−4.87699e9	−1.18279	−0.591397	−	0.806381i	$-0.701423\pi$
$137$	−4.87699e9	−1.18279	−0.591397	+	0.806381i	$0.701423\pi$
$138$	0	0
$139$	−3.17975e9	−0.722481	−0.361241	−	0.932473i	$-0.617647\pi$
$139$	−3.17975e9	−0.722481	−0.361241	+	0.932473i	$0.617647\pi$
$140$	−2.83117e8	−0.0622859
$141$	0	0
$142$	−6.62803e9	−1.36800
$143$	1.03059e10	2.06098
$144$	0	0
$145$	1.56534e9	0.294071
$146$	−7.24458e9	−1.31955
$147$	0	0
$148$	−1.07283e9	−0.183803
$149$	1.94311e9	0.322968	0.161484	−	0.986875i	$-0.448372\pi$
$149$	1.94311e9	0.322968	0.161484	+	0.986875i	$0.448372\pi$
$150$	0	0
$151$	2.72664e9	0.426808	0.213404	−	0.976964i	$-0.431545\pi$
$151$	2.72664e9	0.426808	0.213404	+	0.976964i	$0.431545\pi$
$152$	−4.39128e9	−0.667260
$153$	0	0
$154$	2.32804e9	0.333539
$155$	−1.46684e10	−2.04122
$156$	0	0
$157$	3.49578e9	0.459193	0.229596	−	0.973286i	$-0.426259\pi$
$157$	3.49578e9	0.459193	0.229596	+	0.973286i	$0.426259\pi$
$158$	4.15225e9	0.530062
$159$	0	0
$160$	4.12702e9	0.497848
$161$	−8.52387e8	−0.0999817
$162$	0	0
$163$	−5.30051e9	−0.588130	−0.294065	−	0.955785i	$-0.595008\pi$
$163$	−5.30051e9	−0.588130	−0.294065	+	0.955785i	$0.595008\pi$
$164$	−2.50888e9	−0.270821
$165$	0	0
$166$	−8.60655e8	−0.0879716
$167$	−3.77890e9	−0.375959	−0.187980	−	0.982173i	$-0.560194\pi$
$167$	−3.77890e9	−0.375959	−0.187980	+	0.982173i	$0.560194\pi$
$168$	0	0
$169$	1.82422e10	1.72023
$170$	2.74024e10	2.51634
$171$	0	0
$172$	−1.76441e9	−0.153717
$173$	3.15939e9	0.268161	0.134081	−	0.990970i	$-0.457192\pi$
$173$	3.15939e9	0.268161	0.134081	+	0.990970i	$0.457192\pi$
$174$	0	0
$175$	−4.63917e9	−0.373912
$176$	−1.80294e10	−1.41636
$177$	0	0
$178$	6.14440e8	0.0458764
$179$	−5.53361e9	−0.402875	−0.201437	−	0.979501i	$-0.564561\pi$
$179$	−5.53361e9	−0.402875	−0.201437	+	0.979501i	$0.564561\pi$
$180$	0	0
$181$	−2.23326e10	−1.54663	−0.773313	−	0.634025i	$-0.781402\pi$
$181$	−2.23326e10	−1.54663	−0.773313	+	0.634025i	$0.781402\pi$
$182$	6.51629e9	0.440229
$183$	0	0
$184$	5.67753e9	0.365157
$185$	−2.92379e10	−1.83516
$186$	0	0
$187$	−3.08465e10	−1.84467
$188$	−4.41787e9	−0.257930
$189$	0	0
$190$	2.25601e10	1.25588
$191$	2.26102e9	0.122929	0.0614644	−	0.998109i	$-0.480423\pi$
$191$	2.26102e9	0.122929	0.0614644	+	0.998109i	$0.480423\pi$
$192$	0	0
$193$	−2.29730e10	−1.19182	−0.595908	−	0.803053i	$-0.703208\pi$
$193$	−2.29730e10	−1.19182	−0.595908	+	0.803053i	$0.703208\pi$
$194$	1.91223e10	0.969244
$195$	0	0
$196$	−3.07554e9	−0.148857
$197$	−1.92736e10	−0.911728	−0.455864	−	0.890049i	$-0.650670\pi$
$197$	−1.92736e10	−0.911728	−0.455864	+	0.890049i	$0.650670\pi$
$198$	0	0
$199$	2.34419e10	1.05963	0.529815	−	0.848113i	$-0.322261\pi$
$199$	2.34419e10	1.05963	0.529815	+	0.848113i	$0.322261\pi$
$200$	3.09003e10	1.36561
$201$	0	0
$202$	8.78161e8	0.0371102
$203$	−1.11414e9	−0.0460477
$204$	0	0
$205$	−6.83748e10	−2.70398
$206$	−1.72633e9	−0.0667917
$207$	0	0
$208$	−5.04651e10	−1.86942
$209$	−2.53956e10	−0.920661
$210$	0	0
$211$	−9.48128e9	−0.329303	−0.164652	−	0.986352i	$-0.552650\pi$
$211$	−9.48128e9	−0.329303	−0.164652	+	0.986352i	$0.552650\pi$
$212$	3.72173e8	0.0126542
$213$	0	0
$214$	−3.10855e10	−1.01320
$215$	−4.80856e10	−1.53476
$216$	0	0
$217$	1.04403e10	0.319628
$218$	−3.75093e10	−1.12482
$219$	0	0
$220$	1.09058e10	0.313873
$221$	−8.63408e10	−2.43473
$222$	0	0
$223$	6.82860e10	1.84910	0.924548	−	0.381064i	$-0.124442\pi$
$223$	6.82860e10	1.84910	0.924548	+	0.381064i	$0.124442\pi$
$224$	−2.93744e9	−0.0779565
$225$	0	0
$226$	−4.21927e10	−1.07584
$227$	−1.76762e10	−0.441847	−0.220923	−	0.975291i	$-0.570907\pi$
$227$	−1.76762e10	−0.441847	−0.220923	+	0.975291i	$0.570907\pi$
$228$	0	0
$229$	4.44893e10	1.06904	0.534522	−	0.845154i	$-0.320492\pi$
$229$	4.44893e10	1.06904	0.534522	+	0.845154i	$0.320492\pi$
$230$	−2.91682e10	−0.687280
$231$	0	0
$232$	7.42101e9	0.168177
$233$	1.92432e10	0.427736	0.213868	−	0.976863i	$-0.431394\pi$
$233$	1.92432e10	0.427736	0.213868	+	0.976863i	$0.431394\pi$
$234$	0	0
$235$	−1.20401e11	−2.57527
$236$	−2.31429e9	−0.0485639
$237$	0	0
$238$	−1.95038e10	−0.394025
$239$	−4.91269e10	−0.973933	−0.486967	−	0.873421i	$-0.661897\pi$
$239$	−4.91269e10	−0.973933	−0.486967	+	0.873421i	$0.661897\pi$
$240$	0	0
$241$	6.82587e9	0.130341	0.0651706	−	0.997874i	$-0.479241\pi$
$241$	6.82587e9	0.130341	0.0651706	+	0.997874i	$0.479241\pi$
$242$	−3.22469e10	−0.604391
$243$	0	0
$244$	−5.10326e9	−0.0921708
$245$	−8.38180e10	−1.48624
$246$	0	0
$247$	−7.10834e10	−1.21516
$248$	−6.95401e10	−1.16735
$249$	0	0
$250$	−5.34683e10	−0.865698
$251$	1.07483e11	1.70927	0.854633	−	0.519232i	$-0.173782\pi$
$251$	1.07483e11	1.70927	0.854633	+	0.519232i	$0.173782\pi$
$252$	0	0
$253$	3.28342e10	0.503830
$254$	1.05109e11	1.58448
$255$	0	0
$256$	3.19197e10	0.464493
$257$	7.99962e10	1.14385	0.571927	−	0.820305i	$-0.306196\pi$
$257$	7.99962e10	1.14385	0.571927	+	0.820305i	$0.306196\pi$
$258$	0	0
$259$	2.08102e10	0.287361
$260$	3.05257e10	0.414272
$261$	0	0
$262$	8.91099e10	1.16834
$263$	−1.95262e10	−0.251661	−0.125831	−	0.992052i	$-0.540160\pi$
$263$	−1.95262e10	−0.251661	−0.125831	+	0.992052i	$0.540160\pi$
$264$	0	0
$265$	1.01429e10	0.126344
$266$	−1.60573e10	−0.196655
$267$	0	0
$268$	−1.81039e10	−0.214371
$269$	−8.62787e10	−1.00466	−0.502329	−	0.864676i	$-0.667523\pi$
$269$	−8.62787e10	−1.00466	−0.502329	+	0.864676i	$0.667523\pi$
$270$	0	0
$271$	2.21299e10	0.249240	0.124620	−	0.992205i	$-0.460229\pi$
$271$	2.21299e10	0.249240	0.124620	+	0.992205i	$0.460229\pi$
$272$	1.51047e11	1.67321
$273$	0	0
$274$	1.18783e11	1.27314
$275$	1.78702e11	1.88422
$276$	0	0
$277$	−1.59269e10	−0.162544	−0.0812722	−	0.996692i	$-0.525898\pi$
$277$	−1.59269e10	−0.162544	−0.0812722	+	0.996692i	$0.525898\pi$
$278$	7.74456e10	0.777670
$279$	0	0
$280$	−3.65794e10	−0.355652
$281$	8.40158e10	0.803864	0.401932	−	0.915670i	$-0.368339\pi$
$281$	8.40158e10	0.803864	0.401932	+	0.915670i	$0.368339\pi$
$282$	0	0
$283$	−9.71373e10	−0.900217	−0.450108	−	0.892974i	$-0.648615\pi$
$283$	−9.71373e10	−0.900217	−0.450108	+	0.892974i	$0.648615\pi$
$284$	2.20995e10	0.201581
$285$	0	0
$286$	−2.51009e11	−2.21841
$287$	4.86662e10	0.423408
$288$	0	0
$289$	1.39838e11	1.17919
$290$	−3.81252e10	−0.316535
$291$	0	0
$292$	2.41552e10	0.194441
$293$	−6.11579e9	−0.0484784	−0.0242392	−	0.999706i	$-0.507716\pi$
$293$	−6.11579e9	−0.0484784	−0.0242392	+	0.999706i	$0.507716\pi$
$294$	0	0
$295$	−6.30716e10	−0.484881
$296$	−1.38612e11	−1.04951
$297$	0	0
$298$	−4.73261e10	−0.347639
$299$	9.19044e10	0.664992
$300$	0	0
$301$	3.42252e10	0.240324
$302$	−6.64098e10	−0.459411
$303$	0	0
$304$	1.24355e11	0.835088
$305$	−1.39080e11	−0.920268
$306$	0	0
$307$	−1.90822e11	−1.22604	−0.613022	−	0.790065i	$-0.710046\pi$
$307$	−1.90822e11	−1.22604	−0.613022	+	0.790065i	$0.710046\pi$
$308$	−7.76224e9	−0.0491484
$309$	0	0
$310$	3.57261e11	2.19714
$311$	1.27181e11	0.770903	0.385452	−	0.922728i	$-0.374046\pi$
$311$	1.27181e11	0.770903	0.385452	+	0.922728i	$0.374046\pi$
$312$	0	0
$313$	−2.76470e11	−1.62817	−0.814084	−	0.580747i	$-0.802761\pi$
$313$	−2.76470e11	−1.62817	−0.814084	+	0.580747i	$0.802761\pi$
$314$	−8.51427e10	−0.494269
$315$	0	0
$316$	−1.38446e10	−0.0781068
$317$	2.70980e11	1.50720	0.753600	−	0.657333i	$-0.228316\pi$
$317$	2.70980e11	1.50720	0.753600	+	0.657333i	$0.228316\pi$
$318$	0	0
$319$	4.29171e10	0.232045
$320$	2.36173e11	1.25908
$321$	0	0
$322$	2.07606e10	0.107619
$323$	2.12759e11	1.08762
$324$	0	0
$325$	5.00195e11	2.48694
$326$	1.29098e11	0.633056
$327$	0	0
$328$	−3.24153e11	−1.54639
$329$	8.56959e10	0.403254
$330$	0	0
$331$	−5.53815e10	−0.253594	−0.126797	−	0.991929i	$-0.540470\pi$
$331$	−5.53815e10	−0.253594	−0.126797	+	0.991929i	$0.540470\pi$
$332$	2.86963e9	0.0129630
$333$	0	0
$334$	9.20383e10	0.404678
$335$	−4.93387e11	−2.14036
$336$	0	0
$337$	3.48911e11	1.47360	0.736802	−	0.676109i	$-0.236335\pi$
$337$	3.48911e11	1.47360	0.736802	+	0.676109i	$0.236335\pi$
$338$	−4.44305e11	−1.85164
$339$	0	0
$340$	−9.13662e10	−0.370792
$341$	−4.02163e11	−1.61067
$342$	0	0
$343$	1.23225e11	0.480701
$344$	−2.27965e11	−0.877720
$345$	0	0
$346$	−7.69497e10	−0.288645
$347$	2.61067e11	0.966652	0.483326	−	0.875440i	$-0.339429\pi$
$347$	2.61067e11	0.966652	0.483326	+	0.875440i	$0.339429\pi$
$348$	0	0
$349$	−6.20656e10	−0.223942	−0.111971	−	0.993711i	$-0.535716\pi$
$349$	−6.20656e10	−0.223942	−0.111971	+	0.993711i	$0.535716\pi$
$350$	1.12991e11	0.402474
$351$	0	0
$352$	1.13151e11	0.392840
$353$	−1.63816e11	−0.561526	−0.280763	−	0.959777i	$-0.590588\pi$
$353$	−1.63816e11	−0.561526	−0.280763	+	0.959777i	$0.590588\pi$
$354$	0	0
$355$	6.02279e11	2.01266
$356$	−2.04869e9	−0.00676007
$357$	0	0
$358$	1.34776e11	0.433649
$359$	−2.44825e11	−0.777912	−0.388956	−	0.921256i	$-0.627164\pi$
$359$	−2.44825e11	−0.777912	−0.388956	+	0.921256i	$0.627164\pi$
$360$	0	0
$361$	−1.47526e11	−0.457177
$362$	5.43929e11	1.66477
$363$	0	0
$364$	−2.17269e10	−0.0648696
$365$	6.58304e11	1.94137
$366$	0	0
$367$	−4.19390e11	−1.20676	−0.603380	−	0.797454i	$-0.706180\pi$
$367$	−4.19390e11	−1.20676	−0.603380	+	0.797454i	$0.706180\pi$
$368$	−1.60780e11	−0.457000
$369$	0	0
$370$	7.12113e11	1.97534
$371$	−7.21927e9	−0.0197838
$372$	0	0
$373$	2.68648e11	0.718611	0.359305	−	0.933220i	$-0.383014\pi$
$373$	2.68648e11	0.718611	0.359305	+	0.933220i	$0.383014\pi$
$374$	7.51294e11	1.98558
$375$	0	0
$376$	−5.70798e11	−1.47278
$377$	1.20127e11	0.306270
$378$	0	0
$379$	4.18554e11	1.04202	0.521009	−	0.853551i	$-0.325556\pi$
$379$	4.18554e11	1.04202	0.521009	+	0.853551i	$0.325556\pi$
$380$	−7.52208e10	−0.185060
$381$	0	0
$382$	−5.50690e10	−0.132319
$383$	2.61122e11	0.620083	0.310041	−	0.950723i	$-0.399657\pi$
$383$	2.61122e11	0.620083	0.310041	+	0.950723i	$0.399657\pi$
$384$	0	0
$385$	−2.11545e11	−0.490716
$386$	5.59527e11	1.28286
$387$	0	0
$388$	−6.37585e10	−0.142822
$389$	−3.59930e11	−0.796974	−0.398487	−	0.917174i	$-0.630465\pi$
$389$	−3.59930e11	−0.796974	−0.398487	+	0.917174i	$0.630465\pi$
$390$	0	0
$391$	−2.75078e11	−0.595198
$392$	−3.97367e11	−0.849971
$393$	0	0
$394$	4.69426e11	0.981372
$395$	−3.77309e11	−0.779847
$396$	0	0
$397$	5.61304e11	1.13407	0.567037	−	0.823693i	$-0.308090\pi$
$397$	5.61304e11	1.13407	0.567037	+	0.823693i	$0.308090\pi$
$398$	−5.70948e11	−1.14057
$399$	0	0
$400$	−8.75055e11	−1.70909
$401$	−2.69326e11	−0.520149	−0.260075	−	0.965589i	$-0.583747\pi$
$401$	−2.69326e11	−0.520149	−0.260075	+	0.965589i	$0.583747\pi$
$402$	0	0
$403$	−1.12567e12	−2.12589
$404$	−2.92800e9	−0.00546833
$405$	0	0
$406$	2.71359e10	0.0495652
$407$	−8.01617e11	−1.44808
$408$	0	0
$409$	1.43250e11	0.253128	0.126564	−	0.991958i	$-0.459605\pi$
$409$	1.43250e11	0.253128	0.126564	+	0.991958i	$0.459605\pi$
$410$	1.66533e12	2.91053
$411$	0	0
$412$	5.75602e9	0.00984203
$413$	4.48917e10	0.0759260
$414$	0	0
$415$	7.82064e10	0.129427
$416$	3.16715e11	0.518499
$417$	0	0
$418$	6.18532e11	0.990988
$419$	−9.83015e11	−1.55811	−0.779053	−	0.626958i	$-0.784300\pi$
$419$	−9.83015e11	−1.55811	−0.779053	+	0.626958i	$0.784300\pi$
$420$	0	0
$421$	4.46349e11	0.692477	0.346238	−	0.938147i	$-0.387459\pi$
$421$	4.46349e11	0.692477	0.346238	+	0.938147i	$0.387459\pi$
$422$	2.30925e11	0.354458
$423$	0	0
$424$	4.80856e10	0.0722552
$425$	−1.49713e12	−2.22592
$426$	0	0
$427$	9.89909e10	0.144102
$428$	1.03646e11	0.149299
$429$	0	0
$430$	1.17117e12	1.65200
$431$	−5.92430e11	−0.826969	−0.413485	−	0.910511i	$-0.635688\pi$
$431$	−5.92430e11	−0.826969	−0.413485	+	0.910511i	$0.635688\pi$
$432$	0	0
$433$	6.25587e11	0.855248	0.427624	−	0.903957i	$-0.359351\pi$
$433$	6.25587e11	0.855248	0.427624	+	0.903957i	$0.359351\pi$
$434$	−2.54283e11	−0.344043
$435$	0	0
$436$	1.25065e11	0.165748
$437$	−2.26469e11	−0.297059
$438$	0	0
$439$	−7.82327e10	−0.100530	−0.0502652	−	0.998736i	$-0.516007\pi$
$439$	−7.82327e10	−0.100530	−0.0502652	+	0.998736i	$0.516007\pi$
$440$	1.40905e12	1.79221
$441$	0	0
$442$	2.10291e12	2.62071
$443$	1.09899e12	1.35575	0.677873	−	0.735179i	$-0.262902\pi$
$443$	1.09899e12	1.35575	0.677873	+	0.735179i	$0.262902\pi$
$444$	0	0
$445$	−5.58332e10	−0.0674951
$446$	−1.66316e12	−1.99034
$447$	0	0
$448$	−1.68098e11	−0.197156
$449$	1.05130e12	1.22073	0.610363	−	0.792122i	$-0.291024\pi$
$449$	1.05130e12	1.22073	0.610363	+	0.792122i	$0.291024\pi$
$450$	0	0
$451$	−1.87464e12	−2.13365
$452$	1.40681e11	0.158530
$453$	0	0
$454$	4.30518e11	0.475598
$455$	−5.92125e11	−0.647682
$456$	0	0
$457$	−6.09881e11	−0.654067	−0.327034	−	0.945013i	$-0.606049\pi$
$457$	−6.09881e11	−0.654067	−0.327034	+	0.945013i	$0.606049\pi$
$458$	−1.08358e12	−1.15071
$459$	0	0
$460$	9.72537e10	0.101273
$461$	1.33133e12	1.37288	0.686438	−	0.727189i	$-0.259173\pi$
$461$	1.33133e12	1.37288	0.686438	+	0.727189i	$0.259173\pi$
$462$	0	0
$463$	1.44868e12	1.46507	0.732535	−	0.680730i	$-0.238337\pi$
$463$	1.44868e12	1.46507	0.732535	+	0.680730i	$0.238337\pi$
$464$	−2.10153e11	−0.210477
$465$	0	0
$466$	−4.68685e11	−0.460410
$467$	−1.85556e11	−0.180530	−0.0902652	−	0.995918i	$-0.528771\pi$
$467$	−1.85556e11	−0.180530	−0.0902652	+	0.995918i	$0.528771\pi$
$468$	0	0
$469$	3.51172e11	0.335152
$470$	2.93246e12	2.77199
$471$	0	0
$472$	−2.99012e11	−0.277300
$473$	−1.31837e12	−1.21105
$474$	0	0
$475$	−1.23257e12	−1.11094
$476$	6.50305e10	0.0580612
$477$	0	0
$478$	1.19653e12	1.04833
$479$	1.56593e12	1.35914	0.679569	−	0.733612i	$-0.262167\pi$
$479$	1.56593e12	1.35914	0.679569	+	0.733612i	$0.262167\pi$
$480$	0	0
$481$	−2.24376e12	−1.91128
$482$	−1.66250e11	−0.140298
$483$	0	0
$484$	1.07519e11	0.0890595
$485$	−1.73762e12	−1.42599
$486$	0	0
$487$	−2.10160e12	−1.69305	−0.846524	−	0.532350i	$-0.821309\pi$
$487$	−2.10160e12	−1.69305	−0.846524	+	0.532350i	$0.821309\pi$
$488$	−6.59352e11	−0.526294
$489$	0	0
$490$	2.04146e12	1.59977
$491$	1.86653e12	1.44933	0.724667	−	0.689099i	$-0.241993\pi$
$491$	1.86653e12	1.44933	0.724667	+	0.689099i	$0.241993\pi$
$492$	0	0
$493$	−3.59551e11	−0.274125
$494$	1.73130e12	1.30798
$495$	0	0
$496$	1.96928e12	1.46097
$497$	−4.28676e11	−0.315156
$498$	0	0
$499$	3.38151e11	0.244151	0.122075	−	0.992521i	$-0.461045\pi$
$499$	3.38151e11	0.244151	0.122075	+	0.992521i	$0.461045\pi$
$500$	1.78276e11	0.127564
$501$	0	0
$502$	−2.61785e12	−1.83983
$503$	−1.30064e12	−0.905947	−0.452973	−	0.891524i	$-0.649637\pi$
$503$	−1.30064e12	−0.905947	−0.452973	+	0.891524i	$0.649637\pi$
$504$	0	0
$505$	−7.97971e10	−0.0545979
$506$	−7.99706e11	−0.542316
$507$	0	0
$508$	−3.50459e11	−0.233480
$509$	−2.79225e12	−1.84384	−0.921921	−	0.387379i	$-0.873381\pi$
$509$	−2.79225e12	−1.84384	−0.921921	+	0.387379i	$0.873381\pi$
$510$	0	0
$511$	−4.68552e11	−0.303993
$512$	1.04212e12	0.670198
$513$	0	0
$514$	−1.94838e12	−1.23123
$515$	1.56869e11	0.0982665
$516$	0	0
$517$	−3.30103e12	−2.03209
$518$	−5.06852e11	−0.309312
$519$	0	0
$520$	3.94399e12	2.36549
$521$	3.11544e12	1.85246	0.926231	−	0.376956i	$-0.123029\pi$
$521$	3.11544e12	1.85246	0.926231	+	0.376956i	$0.123029\pi$
$522$	0	0
$523$	−7.97590e11	−0.466146	−0.233073	−	0.972459i	$-0.574878\pi$
$523$	−7.97590e11	−0.466146	−0.233073	+	0.972459i	$0.574878\pi$
$524$	−2.97114e11	−0.172160
$525$	0	0
$526$	4.75577e11	0.270885
$527$	3.36925e12	1.90276
$528$	0	0
$529$	−1.50835e12	−0.837435
$530$	−2.47039e11	−0.135995
$531$	0	0
$532$	5.35389e10	0.0289779
$533$	−5.24720e12	−2.81614
$534$	0	0
$535$	2.82469e12	1.49066
$536$	−2.33906e12	−1.22405
$537$	0	0
$538$	2.10139e12	1.08140
$539$	−2.29805e12	−1.17276
$540$	0	0
$541$	2.66102e12	1.33555	0.667776	−	0.744362i	$-0.267246\pi$
$541$	2.66102e12	1.33555	0.667776	+	0.744362i	$0.267246\pi$
$542$	−5.38994e11	−0.268279
$543$	0	0
$544$	−9.47956e11	−0.464080
$545$	3.40841e12	1.65489
$546$	0	0
$547$	−2.32575e12	−1.11076	−0.555379	−	0.831597i	$-0.687427\pi$
$547$	−2.32575e12	−1.11076	−0.555379	+	0.831597i	$0.687427\pi$
$548$	−3.96052e11	−0.187603
$549$	0	0
$550$	−4.35245e12	−2.02816
$551$	−2.96014e11	−0.136814
$552$	0	0
$553$	2.68552e11	0.122114
$554$	3.87913e11	0.174961
$555$	0	0
$556$	−2.58222e11	−0.114593
$557$	8.52834e11	0.375419	0.187709	−	0.982225i	$-0.439894\pi$
$557$	8.52834e11	0.375419	0.187709	+	0.982225i	$0.439894\pi$
$558$	0	0
$559$	−3.69017e12	−1.59843
$560$	1.03588e12	0.445105
$561$	0	0
$562$	−2.04628e12	−0.865269
$563$	−4.06061e12	−1.70335	−0.851675	−	0.524070i	$-0.824413\pi$
$563$	−4.06061e12	−1.70335	−0.851675	+	0.524070i	$0.824413\pi$
$564$	0	0
$565$	3.83398e12	1.58282
$566$	2.36586e12	0.968982
$567$	0	0
$568$	2.85530e12	1.15102
$569$	2.57557e12	1.03007	0.515037	−	0.857168i	$-0.327778\pi$
$569$	2.57557e12	1.03007	0.515037	+	0.857168i	$0.327778\pi$
$570$	0	0
$571$	1.16025e12	0.456760	0.228380	−	0.973572i	$-0.426657\pi$
$571$	1.16025e12	0.456760	0.228380	+	0.973572i	$0.426657\pi$
$572$	8.36926e11	0.326892
$573$	0	0
$574$	−1.18531e12	−0.455751
$575$	1.59360e12	0.607960
$576$	0	0
$577$	4.68066e12	1.75799	0.878993	−	0.476834i	$-0.158216\pi$
$577$	4.68066e12	1.75799	0.878993	+	0.476834i	$0.158216\pi$
$578$	−3.40588e12	−1.26927
$579$	0	0
$580$	1.27119e11	0.0466427
$581$	−5.56639e10	−0.0202666
$582$	0	0
$583$	2.78088e11	0.0996952
$584$	3.12090e12	1.11025
$585$	0	0
$586$	1.48955e11	0.0521816
$587$	2.02367e12	0.703506	0.351753	−	0.936093i	$-0.385586\pi$
$587$	2.02367e12	0.703506	0.351753	+	0.936093i	$0.385586\pi$
$588$	0	0
$589$	2.77386e12	0.949655
$590$	1.53616e12	0.521920
$591$	0	0
$592$	3.92529e12	1.31348
$593$	2.18835e12	0.726727	0.363363	−	0.931647i	$-0.381628\pi$
$593$	2.18835e12	0.726727	0.363363	+	0.931647i	$0.381628\pi$
$594$	0	0
$595$	1.77228e12	0.579705
$596$	1.57797e11	0.0512260
$597$	0	0
$598$	−2.23841e12	−0.715789
$599$	−3.95151e12	−1.25413	−0.627064	−	0.778968i	$-0.715744\pi$
$599$	−3.95151e12	−1.25413	−0.627064	+	0.778968i	$0.715744\pi$
$600$	0	0
$601$	−4.59686e12	−1.43723	−0.718614	−	0.695409i	$-0.755223\pi$
$601$	−4.59686e12	−1.43723	−0.718614	+	0.695409i	$0.755223\pi$
$602$	−8.33585e11	−0.258682
$603$	0	0
$604$	2.21426e11	0.0676960
$605$	2.93022e12	0.889204
$606$	0	0
$607$	−6.36094e11	−0.190183	−0.0950916	−	0.995469i	$-0.530314\pi$
$607$	−6.36094e11	−0.190183	−0.0950916	+	0.995469i	$0.530314\pi$
$608$	−7.80441e11	−0.231619
$609$	0	0
$610$	3.38741e12	0.990565
$611$	−9.23974e12	−2.68210
$612$	0	0
$613$	1.20615e12	0.345008	0.172504	−	0.985009i	$-0.444814\pi$
$613$	1.20615e12	0.345008	0.172504	+	0.985009i	$0.444814\pi$
$614$	4.64764e12	1.31970
$615$	0	0
$616$	−1.00290e12	−0.280637
$617$	3.39703e11	0.0943662	0.0471831	−	0.998886i	$-0.484976\pi$
$617$	3.39703e11	0.0943662	0.0471831	+	0.998886i	$0.484976\pi$
$618$	0	0
$619$	3.36814e12	0.922110	0.461055	−	0.887372i	$-0.347471\pi$
$619$	3.36814e12	0.922110	0.461055	+	0.887372i	$0.347471\pi$
$620$	−1.19119e12	−0.323757
$621$	0	0
$622$	−3.09760e12	−0.829791
$623$	3.97397e10	0.0105689
$624$	0	0
$625$	−8.93454e11	−0.234214
$626$	6.73368e12	1.75254
$627$	0	0
$628$	2.83886e11	0.0728326
$629$	6.71579e12	1.71068
$630$	0	0
$631$	−9.61309e11	−0.241397	−0.120698	−	0.992689i	$-0.538513\pi$
$631$	−9.61309e11	−0.241397	−0.120698	+	0.992689i	$0.538513\pi$
$632$	−1.78875e12	−0.445989
$633$	0	0
$634$	−6.59996e12	−1.62233
$635$	−9.55109e12	−2.33116
$636$	0	0
$637$	−6.43233e12	−1.54789
$638$	−1.04528e12	−0.249770
$639$	0	0
$640$	−7.86523e12	−1.85311
$641$	2.11380e11	0.0494542	0.0247271	−	0.999694i	$-0.492128\pi$
$641$	2.11380e11	0.0494542	0.0247271	+	0.999694i	$0.492128\pi$
$642$	0	0
$643$	−1.04548e12	−0.241194	−0.120597	−	0.992702i	$-0.538481\pi$
$643$	−1.04548e12	−0.241194	−0.120597	+	0.992702i	$0.538481\pi$
$644$	−6.92210e10	−0.0158581
$645$	0	0
$646$	−5.18193e12	−1.17070
$647$	−5.91760e11	−0.132763	−0.0663813	−	0.997794i	$-0.521145\pi$
$647$	−5.91760e11	−0.132763	−0.0663813	+	0.997794i	$0.521145\pi$
$648$	0	0
$649$	−1.72924e12	−0.382608
$650$	−1.21827e13	−2.67691
$651$	0	0
$652$	−4.30446e11	−0.0932833
$653$	6.95010e12	1.49583	0.747914	−	0.663796i	$-0.231055\pi$
$653$	6.95010e12	1.49583	0.747914	+	0.663796i	$0.231055\pi$
$654$	0	0
$655$	−8.09728e12	−1.71891
$656$	9.17958e12	1.93533
$657$	0	0
$658$	−2.08720e12	−0.434058
$659$	4.88531e12	1.00904	0.504519	−	0.863401i	$-0.331670\pi$
$659$	4.88531e12	1.00904	0.504519	+	0.863401i	$0.331670\pi$
$660$	0	0
$661$	−5.32521e12	−1.08500	−0.542500	−	0.840056i	$-0.682522\pi$
$661$	−5.32521e12	−1.08500	−0.542500	+	0.840056i	$0.682522\pi$
$662$	1.34886e12	0.272965
$663$	0	0
$664$	3.70763e11	0.0740184
$665$	1.45910e12	0.289326
$666$	0	0
$667$	3.82719e11	0.0748711
$668$	−3.06878e11	−0.0596309
$669$	0	0
$670$	1.20169e13	2.30386
$671$	−3.81316e12	−0.726162
$672$	0	0
$673$	−2.69464e12	−0.506328	−0.253164	−	0.967423i	$-0.581471\pi$
$673$	−2.69464e12	−0.506328	−0.253164	+	0.967423i	$0.581471\pi$
$674$	−8.49804e12	−1.58617
$675$	0	0
$676$	1.48142e12	0.272846
$677$	5.90009e12	1.07947	0.539734	−	0.841836i	$-0.318525\pi$
$677$	5.90009e12	1.07947	0.539734	+	0.841836i	$0.318525\pi$
$678$	0	0
$679$	1.23676e12	0.223291
$680$	−1.18047e13	−2.11722
$681$	0	0
$682$	9.79504e12	1.73371
$683$	−7.67339e12	−1.34925	−0.674627	−	0.738158i	$-0.735696\pi$
$683$	−7.67339e12	−1.34925	−0.674627	+	0.738158i	$0.735696\pi$
$684$	0	0
$685$	−1.07937e13	−1.87310
$686$	−3.00125e12	−0.517421
$687$	0	0
$688$	6.45567e12	1.09848
$689$	7.78382e11	0.131585
$690$	0	0
$691$	−8.36632e12	−1.39599	−0.697997	−	0.716101i	$-0.745925\pi$
$691$	−8.36632e12	−1.39599	−0.697997	+	0.716101i	$0.745925\pi$
$692$	2.56569e11	0.0425331
$693$	0	0
$694$	−6.35852e12	−1.04049
$695$	−7.03736e12	−1.14414
$696$	0	0
$697$	1.57053e13	2.52058
$698$	1.51166e12	0.241049
$699$	0	0
$700$	−3.76739e11	−0.0593062
$701$	7.10717e11	0.111164	0.0555822	−	0.998454i	$-0.482299\pi$
$701$	7.10717e11	0.111164	0.0555822	+	0.998454i	$0.482299\pi$
$702$	0	0
$703$	5.52903e12	0.853788
$704$	6.47517e12	0.993514
$705$	0	0
$706$	3.98988e12	0.604420
$707$	5.67961e10	0.00854932
$708$	0	0
$709$	−5.96922e12	−0.887176	−0.443588	−	0.896231i	$-0.646295\pi$
$709$	−5.96922e12	−0.887176	−0.443588	+	0.896231i	$0.646295\pi$
$710$	−1.46690e13	−2.16640
$711$	0	0
$712$	−2.64695e11	−0.0385999
$713$	−3.58635e12	−0.519697
$714$	0	0
$715$	2.28088e13	3.26382
$716$	−4.49375e11	−0.0639000
$717$	0	0
$718$	5.96292e12	0.837334
$719$	−9.68339e12	−1.35129	−0.675643	−	0.737229i	$-0.736134\pi$
$719$	−9.68339e12	−1.35129	−0.675643	+	0.737229i	$0.736134\pi$
$720$	0	0
$721$	−1.11653e11	−0.0153873
$722$	3.59311e12	0.492100
$723$	0	0
$724$	−1.81359e12	−0.245310
$725$	2.08297e12	0.280003
$726$	0	0
$727$	−1.29591e13	−1.72056	−0.860282	−	0.509819i	$-0.829712\pi$
$727$	−1.29591e13	−1.72056	−0.860282	+	0.509819i	$0.829712\pi$
$728$	−2.80716e12	−0.370405
$729$	0	0
$730$	−1.60336e13	−2.08967
$731$	1.10450e13	1.43066
$732$	0	0
$733$	−3.93613e12	−0.503618	−0.251809	−	0.967777i	$-0.581025\pi$
$733$	−3.93613e12	−0.503618	−0.251809	+	0.967777i	$0.581025\pi$
$734$	1.02146e13	1.29894
$735$	0	0
$736$	1.00904e12	0.126753
$737$	−1.35272e13	−1.68891
$738$	0	0
$739$	−8.82704e12	−1.08872	−0.544359	−	0.838853i	$-0.683227\pi$
$739$	−8.82704e12	−1.08872	−0.544359	+	0.838853i	$0.683227\pi$
$740$	−2.37436e12	−0.291074
$741$	0	0
$742$	1.75832e11	0.0212951
$743$	−5.32733e12	−0.641299	−0.320649	−	0.947198i	$-0.603901\pi$
$743$	−5.32733e12	−0.641299	−0.320649	+	0.947198i	$0.603901\pi$
$744$	0	0
$745$	4.30045e12	0.511459
$746$	−6.54315e12	−0.773504
$747$	0	0
$748$	−2.50500e12	−0.292583
$749$	−2.01049e12	−0.233418
$750$	0	0
$751$	−4.52905e12	−0.519550	−0.259775	−	0.965669i	$-0.583648\pi$
$751$	−4.52905e12	−0.519550	−0.259775	+	0.965669i	$0.583648\pi$
$752$	1.61642e13	1.84321
$753$	0	0
$754$	−2.92579e12	−0.329665
$755$	6.03456e12	0.675903
$756$	0	0
$757$	−6.14985e12	−0.680664	−0.340332	−	0.940305i	$-0.610539\pi$
$757$	−6.14985e12	−0.680664	−0.340332	+	0.940305i	$0.610539\pi$
$758$	−1.01943e13	−1.12162
$759$	0	0
$760$	−9.71869e12	−1.05669
$761$	6.25614e12	0.676201	0.338100	−	0.941110i	$-0.390216\pi$
$761$	6.25614e12	0.676201	0.338100	+	0.941110i	$0.390216\pi$
$762$	0	0
$763$	−2.42596e12	−0.259134
$764$	1.83613e11	0.0194977
$765$	0	0
$766$	−6.35986e12	−0.667449
$767$	−4.84022e12	−0.504994
$768$	0	0
$769$	5.75533e12	0.593474	0.296737	−	0.954959i	$-0.404101\pi$
$769$	5.75533e12	0.593474	0.296737	+	0.954959i	$0.404101\pi$
$770$	5.15237e12	0.528201
$771$	0	0
$772$	−1.86560e12	−0.189034
$773$	4.67836e11	0.0471288	0.0235644	−	0.999722i	$-0.492499\pi$
$773$	4.67836e11	0.0471288	0.0235644	+	0.999722i	$0.492499\pi$
$774$	0	0
$775$	−1.95189e13	−1.94356
$776$	−8.23774e12	−0.815512
$777$	0	0
$778$	8.76640e12	0.857853
$779$	1.29300e13	1.25800
$780$	0	0
$781$	1.65127e13	1.58814
$782$	6.69977e12	0.640663
$783$	0	0
$784$	1.12529e13	1.06376
$785$	7.73678e12	0.727188
$786$	0	0
$787$	−3.26611e12	−0.303490	−0.151745	−	0.988420i	$-0.548489\pi$
$787$	−3.26611e12	−0.303490	−0.151745	+	0.988420i	$0.548489\pi$
$788$	−1.56518e12	−0.144609
$789$	0	0
$790$	9.18968e12	0.839418
$791$	−2.72886e12	−0.247849
$792$	0	0
$793$	−1.06732e13	−0.958441
$794$	−1.36711e13	−1.22070
$795$	0	0
$796$	1.90368e12	0.168068
$797$	−7.21893e12	−0.633739	−0.316869	−	0.948469i	$-0.602632\pi$
$797$	−7.21893e12	−0.633739	−0.316869	+	0.948469i	$0.602632\pi$
$798$	0	0
$799$	2.76554e13	2.40060
$800$	5.49176e12	0.474031
$801$	0	0
$802$	6.55966e12	0.559882
$803$	1.80488e13	1.53189
$804$	0	0
$805$	−1.88649e12	−0.158333
$806$	2.74168e13	2.28828
$807$	0	0
$808$	−3.78304e11	−0.0312241
$809$	5.31395e12	0.436163	0.218082	−	0.975931i	$-0.430020\pi$
$809$	5.31395e12	0.436163	0.218082	+	0.975931i	$0.430020\pi$
$810$	0	0
$811$	2.47114e12	0.200588	0.100294	−	0.994958i	$-0.468022\pi$
$811$	2.47114e12	0.200588	0.100294	+	0.994958i	$0.468022\pi$
$812$	−9.04776e10	−0.00730364
$813$	0	0
$814$	1.95241e13	1.55869
$815$	−1.17310e13	−0.931376
$816$	0	0
$817$	9.09323e12	0.714034
$818$	−3.48899e12	−0.272464
$819$	0	0
$820$	−5.55261e12	−0.428879
$821$	1.31768e13	1.01220	0.506100	−	0.862475i	$-0.331086\pi$
$821$	1.31768e13	1.01220	0.506100	+	0.862475i	$0.331086\pi$
$822$	0	0
$823$	3.25277e12	0.247147	0.123573	−	0.992335i	$-0.460565\pi$
$823$	3.25277e12	0.247147	0.123573	+	0.992335i	$0.460565\pi$
$824$	7.43690e11	0.0561979
$825$	0	0
$826$	−1.09338e12	−0.0817258
$827$	2.49083e13	1.85169	0.925847	−	0.377899i	$-0.123353\pi$
$827$	2.49083e13	1.85169	0.925847	+	0.377899i	$0.123353\pi$
$828$	0	0
$829$	−5.37114e12	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$829$	−5.37114e12	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$830$	−1.90478e12	−0.139314
$831$	0	0
$832$	1.81243e13	1.31131
$833$	1.92526e13	1.38544
$834$	0	0
$835$	−8.36338e12	−0.595378
$836$	−2.06233e12	−0.146026
$837$	0	0
$838$	2.39422e13	1.67713
$839$	−1.73928e13	−1.21183	−0.605915	−	0.795530i	$-0.707193\pi$
$839$	−1.73928e13	−1.21183	−0.605915	+	0.795530i	$0.707193\pi$
$840$	0	0
$841$	5.00246e11	0.0344828
$842$	−1.08712e13	−0.745373
$843$	0	0
$844$	−7.69960e11	−0.0522308
$845$	4.03733e13	2.72420
$846$	0	0
$847$	−2.08561e12	−0.139238
$848$	−1.36172e12	−0.0904288
$849$	0	0
$850$	3.64639e13	2.39595
$851$	−7.14854e12	−0.467234
$852$	0	0
$853$	2.55914e13	1.65510	0.827548	−	0.561395i	$-0.189735\pi$
$853$	2.55914e13	1.65510	0.827548	+	0.561395i	$0.189735\pi$
$854$	−2.41101e12	−0.155110
$855$	0	0
$856$	1.33914e13	0.852497
$857$	−9.16963e12	−0.580682	−0.290341	−	0.956923i	$-0.593769\pi$
$857$	−9.16963e12	−0.580682	−0.290341	+	0.956923i	$0.593769\pi$
$858$	0	0
$859$	−2.27442e12	−0.142528	−0.0712641	−	0.997457i	$-0.522703\pi$
$859$	−2.27442e12	−0.142528	−0.0712641	+	0.997457i	$0.522703\pi$
$860$	−3.90495e12	−0.243429
$861$	0	0
$862$	1.44291e13	0.890139
$863$	−2.09452e13	−1.28540	−0.642698	−	0.766120i	$-0.722185\pi$
$863$	−2.09452e13	−1.28540	−0.642698	+	0.766120i	$0.722185\pi$
$864$	0	0
$865$	6.99231e12	0.424666
$866$	−1.52367e13	−0.920579
$867$	0	0
$868$	8.47840e11	0.0506962
$869$	−1.03447e13	−0.615359
$870$	0	0
$871$	−3.78634e13	−2.22914
$872$	1.61587e13	0.946416
$873$	0	0
$874$	5.51585e12	0.319750
$875$	−3.45813e12	−0.199437
$876$	0	0
$877$	−8.04577e12	−0.459272	−0.229636	−	0.973277i	$-0.573754\pi$
$877$	−8.04577e12	−0.459272	−0.229636	+	0.973277i	$0.573754\pi$
$878$	1.90542e12	0.108210
$879$	0	0
$880$	−3.99023e13	−2.24298
$881$	−1.56243e13	−0.873794	−0.436897	−	0.899512i	$-0.643922\pi$
$881$	−1.56243e13	−0.873794	−0.436897	+	0.899512i	$0.643922\pi$
$882$	0	0
$883$	1.21770e13	0.674087	0.337044	−	0.941489i	$-0.390573\pi$
$883$	1.21770e13	0.674087	0.337044	+	0.941489i	$0.390573\pi$
$884$	−7.01160e12	−0.386173
$885$	0	0
$886$	−2.67669e13	−1.45931
$887$	−2.50236e13	−1.35735	−0.678676	−	0.734438i	$-0.737446\pi$
$887$	−2.50236e13	−1.35735	−0.678676	+	0.734438i	$0.737446\pi$
$888$	0	0
$889$	6.79805e12	0.365028
$890$	1.35987e12	0.0726509
$891$	0	0
$892$	5.54539e12	0.293285
$893$	2.27684e13	1.19812
$894$	0	0
$895$	−1.22469e13	−0.638002
$896$	5.59813e12	0.290173
$897$	0	0
$898$	−2.56053e13	−1.31397
$899$	−4.68766e12	−0.239352
$900$	0	0
$901$	−2.32977e12	−0.117774
$902$	4.56584e13	2.29663
$903$	0	0
$904$	1.81762e13	0.905204
$905$	−4.94260e13	−2.44927
$906$	0	0
$907$	1.42304e13	0.698207	0.349103	−	0.937084i	$-0.386486\pi$
$907$	1.42304e13	0.698207	0.349103	+	0.937084i	$0.386486\pi$
$908$	−1.43545e12	−0.0700814
$909$	0	0
$910$	1.44217e13	0.697157
$911$	3.22836e13	1.55292	0.776460	−	0.630167i	$-0.217014\pi$
$911$	3.22836e13	1.55292	0.776460	+	0.630167i	$0.217014\pi$
$912$	0	0
$913$	2.14419e12	0.102128
$914$	1.48542e13	0.704030
$915$	0	0
$916$	3.61290e12	0.169561
$917$	5.76330e12	0.269159
$918$	0	0
$919$	7.65321e12	0.353935	0.176968	−	0.984217i	$-0.443371\pi$
$919$	7.65321e12	0.353935	0.176968	+	0.984217i	$0.443371\pi$
$920$	1.25654e13	0.578270
$921$	0	0
$922$	−3.24257e13	−1.47775
$923$	4.62199e13	2.09614
$924$	0	0
$925$	−3.89063e13	−1.74736
$926$	−3.52839e13	−1.57698
$927$	0	0
$928$	1.31890e12	0.0583776
$929$	−1.59043e13	−0.700558	−0.350279	−	0.936645i	$-0.613913\pi$
$929$	−1.59043e13	−0.700558	−0.350279	+	0.936645i	$0.613913\pi$
$930$	0	0
$931$	1.58504e13	0.691460
$932$	1.56271e12	0.0678432
$933$	0	0
$934$	4.51939e12	0.194321
$935$	−6.82689e13	−2.92126
$936$	0	0
$937$	2.24799e13	0.952722	0.476361	−	0.879250i	$-0.341956\pi$
$937$	2.24799e13	0.952722	0.476361	+	0.879250i	$0.341956\pi$
$938$	−8.55310e12	−0.360754
$939$	0	0
$940$	−9.77753e12	−0.408464
$941$	5.26818e12	0.219032	0.109516	−	0.993985i	$-0.465070\pi$
$941$	5.26818e12	0.219032	0.109516	+	0.993985i	$0.465070\pi$
$942$	0	0
$943$	−1.67174e13	−0.688438
$944$	8.46761e12	0.347046
$945$	0	0
$946$	3.21099e13	1.30356
$947$	5.63863e12	0.227823	0.113912	−	0.993491i	$-0.463662\pi$
$947$	5.63863e12	0.227823	0.113912	+	0.993491i	$0.463662\pi$
$948$	0	0
$949$	5.05193e13	2.02190
$950$	3.00203e13	1.19580
$951$	0	0
$952$	8.40210e12	0.331529
$953$	5.07222e13	1.99196	0.995979	−	0.0895917i	$-0.0285562\pi$
$953$	5.07222e13	1.99196	0.995979	+	0.0895917i	$0.0285562\pi$
$954$	0	0
$955$	5.00404e12	0.194673
$956$	−3.98952e12	−0.154476
$957$	0	0
$958$	−3.81397e13	−1.46296
$959$	7.68246e12	0.293303
$960$	0	0
$961$	1.74871e13	0.661399
$962$	5.46488e13	2.05728
$963$	0	0
$964$	5.54318e11	0.0206734
$965$	−5.08433e13	−1.88739
$966$	0	0
$967$	−4.27613e12	−0.157265	−0.0786324	−	0.996904i	$-0.525055\pi$
$967$	−4.27613e12	−0.157265	−0.0786324	+	0.996904i	$0.525055\pi$
$968$	1.38917e13	0.508529
$969$	0	0
$970$	4.23212e13	1.53492
$971$	1.12150e13	0.404868	0.202434	−	0.979296i	$-0.435115\pi$
$971$	1.12150e13	0.404868	0.202434	+	0.979296i	$0.435115\pi$
$972$	0	0
$973$	5.00889e12	0.179157
$974$	5.11863e13	1.82238
$975$	0	0
$976$	1.86720e13	0.658667
$977$	−4.98842e13	−1.75161	−0.875806	−	0.482664i	$-0.839669\pi$
$977$	−4.98842e13	−1.75161	−0.875806	+	0.482664i	$0.839669\pi$
$978$	0	0
$979$	−1.53078e12	−0.0532588
$980$	−6.80672e12	−0.235733
$981$	0	0
$982$	−4.54610e13	−1.56005
$983$	4.09483e13	1.39877	0.699383	−	0.714748i	$-0.253458\pi$
$983$	4.09483e13	1.39877	0.699383	+	0.714748i	$0.253458\pi$
$984$	0	0
$985$	−4.26560e13	−1.44383
$986$	8.75717e12	0.295065
$987$	0	0
$988$	−5.77257e12	−0.192736
$989$	−1.17567e13	−0.390754
$990$	0	0
$991$	2.36513e13	0.778975	0.389488	−	0.921032i	$-0.372652\pi$
$991$	2.36513e13	0.778975	0.389488	+	0.921032i	$0.372652\pi$
$992$	−1.23590e13	−0.405212
$993$	0	0
$994$	1.04408e13	0.339230
$995$	5.18812e13	1.67805
$996$	0	0
$997$	−2.65134e13	−0.849841	−0.424920	−	0.905231i	$-0.639698\pi$
$997$	−2.65134e13	−0.849841	−0.424920	+	0.905231i	$0.639698\pi$
$998$	−8.23596e12	−0.262801
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.10.a.b.1.3		9
3.2	odd	2		29.10.a.a.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.7	✓	9	3.2	odd	2
261.10.a.b.1.3		9	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	261.a (trivial)

\(f(q)\)	\(=\)	\(q-24.3559 q^{2} +81.2084 q^{4} +2213.18 q^{5} -1575.25 q^{7} +10492.3 q^{8} +O(q^{10})\)	\(q-24.3559 q^{2} +81.2084 q^{4} +2213.18 q^{5} -1575.25 q^{7} +10492.3 q^{8} -53903.9 q^{10} +60678.9 q^{11} +169843. q^{13} +38366.5 q^{14} -297128. q^{16} -508356. q^{17} -418524. q^{19} +179729. q^{20} -1.47789e6 q^{22} +541114. q^{23} +2.94504e6 q^{25} -4.13668e6 q^{26} -127923. q^{28} +707281. q^{29} -6.62773e6 q^{31} +1.86475e6 q^{32} +1.23815e7 q^{34} -3.48631e6 q^{35} -1.32108e7 q^{37} +1.01935e7 q^{38} +2.32214e7 q^{40} -3.08944e7 q^{41} -2.17269e7 q^{43} +4.92764e6 q^{44} -1.31793e7 q^{46} -5.44016e7 q^{47} -3.78722e7 q^{49} -7.17291e7 q^{50} +1.37927e7 q^{52} +4.58294e6 q^{53} +1.34293e8 q^{55} -1.65280e7 q^{56} -1.72264e7 q^{58} -2.84982e7 q^{59} -6.28415e7 q^{61} +1.61424e8 q^{62} +1.06712e8 q^{64} +3.75894e8 q^{65} -2.22931e8 q^{67} -4.12828e7 q^{68} +8.49120e7 q^{70} +2.72133e8 q^{71} +2.97447e8 q^{73} +3.21760e8 q^{74} -3.39876e7 q^{76} -9.55843e7 q^{77} -1.70482e8 q^{79} -6.57598e8 q^{80} +7.52459e8 q^{82} +3.53366e7 q^{83} -1.12508e9 q^{85} +5.29178e8 q^{86} +6.36662e8 q^{88} -2.52276e7 q^{89} -2.67545e8 q^{91} +4.39429e7 q^{92} +1.32500e9 q^{94} -9.26269e8 q^{95} -7.85122e8 q^{97} +9.22410e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 1194 q^{4} + 738 q^{5} - 7128 q^{7} + 13776 q^{8}+O(q^{10}) \) 9 * q + 1194 * q^4 + 738 * q^5 - 7128 * q^7 + 13776 * q^8	\( 9 q + 1194 q^{4} + 738 q^{5} - 7128 q^{7} + 13776 q^{8} + 37812 q^{10} + 59512 q^{11} - 165758 q^{13} + 406080 q^{14} - 1044958 q^{16} + 394814 q^{17} - 2256606 q^{19} + 2237578 q^{20} - 5311718 q^{22} + 1699500 q^{23} - 983481 q^{25} + 4264740 q^{26} - 8491636 q^{28} + 6365529 q^{29} - 11929632 q^{31} + 1346192 q^{32} + 8655764 q^{34} + 3275324 q^{35} + 14454898 q^{37} - 14709736 q^{38} + 45167060 q^{40} - 52495202 q^{41} + 21819888 q^{43} - 70837004 q^{44} + 20628012 q^{46} - 44968948 q^{47} - 26826775 q^{49} - 155997680 q^{50} + 29562122 q^{52} + 111394302 q^{53} - 173560742 q^{55} - 67419136 q^{56} + 236142720 q^{59} - 241129054 q^{61} - 261343278 q^{62} - 333112958 q^{64} + 625660884 q^{65} - 672046492 q^{67} + 63179948 q^{68} - 366389016 q^{70} + 475841956 q^{71} - 424813822 q^{73} + 532689728 q^{74} - 552478056 q^{76} + 182224776 q^{77} - 170801148 q^{79} - 562655678 q^{80} + 1468192652 q^{82} + 468898296 q^{83} - 271552972 q^{85} - 1462277802 q^{86} + 1176890862 q^{88} + 676036598 q^{89} + 9763884 q^{91} - 2724990708 q^{92} + 2429128614 q^{94} - 69331732 q^{95} + 170708754 q^{97} - 3278517600 q^{98}+O(q^{100}) \) 9 * q + 1194 * q^4 + 738 * q^5 - 7128 * q^7 + 13776 * q^8 + 37812 * q^10 + 59512 * q^11 - 165758 * q^13 + 406080 * q^14 - 1044958 * q^16 + 394814 * q^17 - 2256606 * q^19 + 2237578 * q^20 - 5311718 * q^22 + 1699500 * q^23 - 983481 * q^25 + 4264740 * q^26 - 8491636 * q^28 + 6365529 * q^29 - 11929632 * q^31 + 1346192 * q^32 + 8655764 * q^34 + 3275324 * q^35 + 14454898 * q^37 - 14709736 * q^38 + 45167060 * q^40 - 52495202 * q^41 + 21819888 * q^43 - 70837004 * q^44 + 20628012 * q^46 - 44968948 * q^47 - 26826775 * q^49 - 155997680 * q^50 + 29562122 * q^52 + 111394302 * q^53 - 173560742 * q^55 - 67419136 * q^56 + 236142720 * q^59 - 241129054 * q^61 - 261343278 * q^62 - 333112958 * q^64 + 625660884 * q^65 - 672046492 * q^67 + 63179948 * q^68 - 366389016 * q^70 + 475841956 * q^71 - 424813822 * q^73 + 532689728 * q^74 - 552478056 * q^76 + 182224776 * q^77 - 170801148 * q^79 - 562655678 * q^80 + 1468192652 * q^82 + 468898296 * q^83 - 271552972 * q^85 - 1462277802 * q^86 + 1176890862 * q^88 + 676036598 * q^89 + 9763884 * q^91 - 2724990708 * q^92 + 2429128614 * q^94 - 69331732 * q^95 + 170708754 * q^97 - 3278517600 * q^98

Introduction

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