LMFDB - Embedded newform 531.8.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-14.0604$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.0604 q^{2} +69.6949 q^{4} -153.219 q^{5} -215.221 q^{7} +819.793 q^{8} +O(q^{10})$	\(q-14.0604 q^{2} +69.6949 q^{4} -153.219 q^{5} -215.221 q^{7} +819.793 q^{8} +2154.32 q^{10} -7869.22 q^{11} -14239.1 q^{13} +3026.10 q^{14} -20447.6 q^{16} +14439.7 q^{17} +52274.2 q^{19} -10678.6 q^{20} +110644. q^{22} +20917.2 q^{23} -54648.9 q^{25} +200207. q^{26} -14999.8 q^{28} +136874. q^{29} +9325.59 q^{31} +182567. q^{32} -203028. q^{34} +32976.0 q^{35} -525467. q^{37} -734996. q^{38} -125608. q^{40} -197767. q^{41} +410661. q^{43} -548444. q^{44} -294105. q^{46} +946517. q^{47} -777223. q^{49} +768386. q^{50} -992389. q^{52} +1.55829e6 q^{53} +1.20571e6 q^{55} -176437. q^{56} -1.92450e6 q^{58} -205379. q^{59} -659307. q^{61} -131121. q^{62} +50317.0 q^{64} +2.18169e6 q^{65} -2.30296e6 q^{67} +1.00637e6 q^{68} -463656. q^{70} +1.68822e6 q^{71} +2.53442e6 q^{73} +7.38828e6 q^{74} +3.64324e6 q^{76} +1.69362e6 q^{77} -1.26627e6 q^{79} +3.13296e6 q^{80} +2.78068e6 q^{82} -2.22258e6 q^{83} -2.21243e6 q^{85} -5.77406e6 q^{86} -6.45113e6 q^{88} +1.04798e7 q^{89} +3.06455e6 q^{91} +1.45782e6 q^{92} -1.33084e7 q^{94} -8.00940e6 q^{95} +5.41316e6 q^{97} +1.09281e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) $ 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * 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 $

$2$	−14.0604	−1.24278	−0.621388	−	0.783503i	$-0.713431\pi$
$2$	−14.0604	−1.24278	−0.621388	+	0.783503i	$0.713431\pi$
$3$	0	0
$3$	0	0
$4$	69.6949	0.544491
$5$	−153.219	−0.548173	−0.274087	−	0.961705i	$-0.588375\pi$
$5$	−153.219	−0.548173	−0.274087	+	0.961705i	$0.588375\pi$
$6$	0	0
$7$	−215.221	−0.237160	−0.118580	−	0.992944i	$-0.537834\pi$
$7$	−215.221	−0.237160	−0.118580	+	0.992944i	$0.537834\pi$
$8$	819.793	0.566095
$9$	0	0
$10$	2154.32	0.681256
$11$	−7869.22	−1.78261	−0.891307	−	0.453401i	$-0.850211\pi$
$11$	−7869.22	−1.78261	−0.891307	+	0.453401i	$0.850211\pi$
$12$	0	0
$13$	−14239.1	−1.79754	−0.898772	−	0.438416i	$-0.855540\pi$
$13$	−14239.1	−1.79754	−0.898772	+	0.438416i	$0.855540\pi$
$14$	3026.10	0.294737
$15$	0	0
$16$	−20447.6	−1.24802
$17$	14439.7	0.712830	0.356415	−	0.934328i	$-0.383999\pi$
$17$	14439.7	0.712830	0.356415	+	0.934328i	$0.383999\pi$
$18$	0	0
$19$	52274.2	1.74844	0.874218	−	0.485533i	$-0.161375\pi$
$19$	52274.2	1.74844	0.874218	+	0.485533i	$0.161375\pi$
$20$	−10678.6	−0.298475
$21$	0	0
$22$	110644.	2.21539
$23$	20917.2	0.358473	0.179237	−	0.983806i	$-0.442637\pi$
$23$	20917.2	0.358473	0.179237	+	0.983806i	$0.442637\pi$
$24$	0	0
$25$	−54648.9	−0.699506
$26$	200207.	2.23394
$27$	0	0
$28$	−14999.8	−0.129132
$29$	136874.	1.04214	0.521070	−	0.853514i	$-0.325533\pi$
$29$	136874.	1.04214	0.521070	+	0.853514i	$0.325533\pi$
$30$	0	0
$31$	9325.59	0.0562225	0.0281113	−	0.999605i	$-0.491051\pi$
$31$	9325.59	0.0562225	0.0281113	+	0.999605i	$0.491051\pi$
$32$	182567.	0.984914
$33$	0	0
$34$	−203028.	−0.885888
$35$	32976.0	0.130005
$36$	0	0
$37$	−525467.	−1.70545	−0.852726	−	0.522358i	$-0.825052\pi$
$37$	−525467.	−1.70545	−0.852726	+	0.522358i	$0.825052\pi$
$38$	−734996.	−2.17291
$39$	0	0
$40$	−125608.	−0.310318
$41$	−197767.	−0.448136	−0.224068	−	0.974574i	$-0.571934\pi$
$41$	−197767.	−0.448136	−0.224068	+	0.974574i	$0.571934\pi$
$42$	0	0
$43$	410661.	0.787669	0.393835	−	0.919181i	$-0.371148\pi$
$43$	410661.	0.787669	0.393835	+	0.919181i	$0.371148\pi$
$44$	−548444.	−0.970617
$45$	0	0
$46$	−294105.	−0.445502
$47$	946517.	1.32980	0.664899	−	0.746933i	$-0.268475\pi$
$47$	946517.	1.32980	0.664899	+	0.746933i	$0.268475\pi$
$48$	0	0
$49$	−777223.	−0.943755
$50$	768386.	0.869329
$51$	0	0
$52$	−992389.	−0.978747
$53$	1.55829e6	1.43775	0.718873	−	0.695141i	$-0.244658\pi$
$53$	1.55829e6	1.43775	0.718873	+	0.695141i	$0.244658\pi$
$54$	0	0
$55$	1.20571e6	0.977181
$56$	−176437.	−0.134255
$57$	0	0
$58$	−1.92450e6	−1.29515
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−659307.	−0.371906	−0.185953	−	0.982559i	$-0.559537\pi$
$61$	−659307.	−0.371906	−0.185953	+	0.982559i	$0.559537\pi$
$62$	−131121.	−0.0698720
$63$	0	0
$64$	50317.0	0.0239930
$65$	2.18169e6	0.985365
$66$	0	0
$67$	−2.30296e6	−0.935457	−0.467729	−	0.883872i	$-0.654928\pi$
$67$	−2.30296e6	−0.935457	−0.467729	+	0.883872i	$0.654928\pi$
$68$	1.00637e6	0.388130
$69$	0	0
$70$	−463656.	−0.161567
$71$	1.68822e6	0.559788	0.279894	−	0.960031i	$-0.409701\pi$
$71$	1.68822e6	0.559788	0.279894	+	0.960031i	$0.409701\pi$
$72$	0	0
$73$	2.53442e6	0.762514	0.381257	−	0.924469i	$-0.375491\pi$
$73$	2.53442e6	0.762514	0.381257	+	0.924469i	$0.375491\pi$
$74$	7.38828e6	2.11949
$75$	0	0
$76$	3.64324e6	0.952008
$77$	1.69362e6	0.422765
$78$	0	0
$79$	−1.26627e6	−0.288957	−0.144478	−	0.989508i	$-0.546150\pi$
$79$	−1.26627e6	−0.288957	−0.144478	+	0.989508i	$0.546150\pi$
$80$	3.13296e6	0.684131
$81$	0	0
$82$	2.78068e6	0.556932
$83$	−2.22258e6	−0.426662	−0.213331	−	0.976980i	$-0.568431\pi$
$83$	−2.22258e6	−0.426662	−0.213331	+	0.976980i	$0.568431\pi$
$84$	0	0
$85$	−2.21243e6	−0.390754
$86$	−5.77406e6	−0.978896
$87$	0	0
$88$	−6.45113e6	−1.00913
$89$	1.04798e7	1.57575	0.787876	−	0.615834i	$-0.211181\pi$
$89$	1.04798e7	1.57575	0.787876	+	0.615834i	$0.211181\pi$
$90$	0	0
$91$	3.06455e6	0.426306
$92$	1.45782e6	0.195186
$93$	0	0
$94$	−1.33084e7	−1.65264
$95$	−8.00940e6	−0.958446
$96$	0	0
$97$	5.41316e6	0.602212	0.301106	−	0.953591i	$-0.402644\pi$
$97$	5.41316e6	0.602212	0.301106	+	0.953591i	$0.402644\pi$
$98$	1.09281e7	1.17288
$99$	0	0
$100$	−3.80875e6	−0.380875
$101$	8.00726e6	0.773320	0.386660	−	0.922222i	$-0.373629\pi$
$101$	8.00726e6	0.773320	0.386660	+	0.922222i	$0.373629\pi$
$102$	0	0
$103$	2.41569e6	0.217826	0.108913	−	0.994051i	$-0.465263\pi$
$103$	2.41569e6	0.217826	0.108913	+	0.994051i	$0.465263\pi$
$104$	−1.16731e7	−1.01758
$105$	0	0
$106$	−2.19102e7	−1.78680
$107$	−1.50841e7	−1.19035	−0.595175	−	0.803596i	$-0.702917\pi$
$107$	−1.50841e7	−1.19035	−0.595175	+	0.803596i	$0.702917\pi$
$108$	0	0
$109$	1.30931e7	0.968386	0.484193	−	0.874961i	$-0.339113\pi$
$109$	1.30931e7	0.968386	0.484193	+	0.874961i	$0.339113\pi$
$110$	−1.69528e7	−1.21442
$111$	0	0
$112$	4.40075e6	0.295981
$113$	8.64628e6	0.563709	0.281854	−	0.959457i	$-0.409050\pi$
$113$	8.64628e6	0.563709	0.281854	+	0.959457i	$0.409050\pi$
$114$	0	0
$115$	−3.20492e6	−0.196505
$116$	9.53938e6	0.567437
$117$	0	0
$118$	2.88771e6	0.161796
$119$	−3.10772e6	−0.169055
$120$	0	0
$121$	4.24374e7	2.17771
$122$	9.27012e6	0.462196
$123$	0	0
$124$	649946.	0.0306127
$125$	2.03435e7	0.931624
$126$	0	0
$127$	2.77631e7	1.20269	0.601347	−	0.798988i	$-0.294631\pi$
$127$	2.77631e7	1.20269	0.601347	+	0.798988i	$0.294631\pi$
$128$	−2.40761e7	−1.01473
$129$	0	0
$130$	−3.06755e7	−1.22459
$131$	−2.08878e7	−0.811788	−0.405894	−	0.913920i	$-0.633040\pi$
$131$	−2.08878e7	−0.811788	−0.405894	+	0.913920i	$0.633040\pi$
$132$	0	0
$133$	−1.12505e7	−0.414660
$134$	3.23805e7	1.16256
$135$	0	0
$136$	1.18375e7	0.403530
$137$	1.47003e7	0.488432	0.244216	−	0.969721i	$-0.421469\pi$
$137$	1.47003e7	0.488432	0.244216	+	0.969721i	$0.421469\pi$
$138$	0	0
$139$	−3.38613e7	−1.06943	−0.534715	−	0.845033i	$-0.679581\pi$
$139$	−3.38613e7	−1.06943	−0.534715	+	0.845033i	$0.679581\pi$
$140$	2.29826e6	0.0707865
$141$	0	0
$142$	−2.37370e7	−0.695691
$143$	1.12050e8	3.20433
$144$	0	0
$145$	−2.09716e7	−0.571274
$146$	−3.56349e7	−0.947634
$147$	0	0
$148$	−3.66224e7	−0.928604
$149$	3.52382e7	0.872694	0.436347	−	0.899778i	$-0.356272\pi$
$149$	3.52382e7	0.872694	0.436347	+	0.899778i	$0.356272\pi$
$150$	0	0
$151$	4.31481e7	1.01986	0.509932	−	0.860215i	$-0.329671\pi$
$151$	4.31481e7	1.01986	0.509932	+	0.860215i	$0.329671\pi$
$152$	4.28541e7	0.989781
$153$	0	0
$154$	−2.38130e7	−0.525402
$155$	−1.42886e6	−0.0308197
$156$	0	0
$157$	7.00495e6	0.144463	0.0722314	−	0.997388i	$-0.476988\pi$
$157$	7.00495e6	0.144463	0.0722314	+	0.997388i	$0.476988\pi$
$158$	1.78043e7	0.359108
$159$	0	0
$160$	−2.79728e7	−0.539904
$161$	−4.50183e6	−0.0850156
$162$	0	0
$163$	5.15447e7	0.932240	0.466120	−	0.884722i	$-0.345652\pi$
$163$	5.15447e7	0.932240	0.466120	+	0.884722i	$0.345652\pi$
$164$	−1.37833e7	−0.244006
$165$	0	0
$166$	3.12503e7	0.530245
$167$	8.79382e6	0.146107	0.0730533	−	0.997328i	$-0.476726\pi$
$167$	8.79382e6	0.146107	0.0730533	+	0.997328i	$0.476726\pi$
$168$	0	0
$169$	1.40002e8	2.23116
$170$	3.11077e7	0.485620
$171$	0	0
$172$	2.86210e7	0.428879
$173$	−5.52334e7	−0.811037	−0.405518	−	0.914087i	$-0.632909\pi$
$173$	−5.52334e7	−0.811037	−0.405518	+	0.914087i	$0.632909\pi$
$174$	0	0
$175$	1.17616e7	0.165895
$176$	1.60906e8	2.22474
$177$	0	0
$178$	−1.47350e8	−1.95831
$179$	−1.14162e8	−1.48776	−0.743882	−	0.668311i	$-0.767018\pi$
$179$	−1.14162e8	−1.48776	−0.743882	+	0.668311i	$0.767018\pi$
$180$	0	0
$181$	7.45147e6	0.0934044	0.0467022	−	0.998909i	$-0.485129\pi$
$181$	7.45147e6	0.0934044	0.0467022	+	0.998909i	$0.485129\pi$
$182$	−4.30888e7	−0.529803
$183$	0	0
$184$	1.71478e7	0.202930
$185$	8.05116e7	0.934883
$186$	0	0
$187$	−1.13629e8	−1.27070
$188$	6.59674e7	0.724063
$189$	0	0
$190$	1.12615e8	1.19113
$191$	2.65020e7	0.275208	0.137604	−	0.990487i	$-0.456060\pi$
$191$	2.65020e7	0.275208	0.137604	+	0.990487i	$0.456060\pi$
$192$	0	0
$193$	−7.95433e7	−0.796440	−0.398220	−	0.917290i	$-0.630372\pi$
$193$	−7.95433e7	−0.796440	−0.398220	+	0.917290i	$0.630372\pi$
$194$	−7.61112e7	−0.748415
$195$	0	0
$196$	−5.41685e7	−0.513866
$197$	−6.69673e7	−0.624067	−0.312033	−	0.950071i	$-0.601010\pi$
$197$	−6.69673e7	−0.624067	−0.312033	+	0.950071i	$0.601010\pi$
$198$	0	0
$199$	−5.47720e7	−0.492689	−0.246345	−	0.969182i	$-0.579229\pi$
$199$	−5.47720e7	−0.492689	−0.246345	+	0.969182i	$0.579229\pi$
$200$	−4.48008e7	−0.395987
$201$	0	0
$202$	−1.12585e8	−0.961063
$203$	−2.94581e7	−0.247154
$204$	0	0
$205$	3.03016e7	0.245656
$206$	−3.39655e7	−0.270709
$207$	0	0
$208$	2.91154e8	2.24337
$209$	−4.11357e8	−3.11679
$210$	0	0
$211$	−6.45829e7	−0.473292	−0.236646	−	0.971596i	$-0.576048\pi$
$211$	−6.45829e7	−0.473292	−0.236646	+	0.971596i	$0.576048\pi$
$212$	1.08605e8	0.782840
$213$	0	0
$214$	2.12088e8	1.47934
$215$	−6.29211e7	−0.431779
$216$	0	0
$217$	−2.00706e6	−0.0133337
$218$	−1.84094e8	−1.20349
$219$	0	0
$220$	8.40321e7	0.532066
$221$	−2.05607e8	−1.28134
$222$	0	0
$223$	−2.02022e8	−1.21992	−0.609961	−	0.792431i	$-0.708815\pi$
$223$	−2.02022e8	−1.21992	−0.609961	+	0.792431i	$0.708815\pi$
$224$	−3.92924e7	−0.233583
$225$	0	0
$226$	−1.21570e8	−0.700564
$227$	2.76130e8	1.56683	0.783416	−	0.621497i	$-0.213475\pi$
$227$	2.76130e8	1.56683	0.783416	+	0.621497i	$0.213475\pi$
$228$	0	0
$229$	−1.40164e8	−0.771280	−0.385640	−	0.922649i	$-0.626019\pi$
$229$	−1.40164e8	−0.771280	−0.385640	+	0.922649i	$0.626019\pi$
$230$	4.50624e7	0.244212
$231$	0	0
$232$	1.12208e8	0.589951
$233$	−8.67302e7	−0.449185	−0.224592	−	0.974453i	$-0.572105\pi$
$233$	−8.67302e7	−0.449185	−0.224592	+	0.974453i	$0.572105\pi$
$234$	0	0
$235$	−1.45024e8	−0.728960
$236$	−1.43139e7	−0.0708867
$237$	0	0
$238$	4.36958e7	0.210097
$239$	−2.22648e8	−1.05494	−0.527469	−	0.849574i	$-0.676859\pi$
$239$	−2.22648e8	−1.05494	−0.527469	+	0.849574i	$0.676859\pi$
$240$	0	0
$241$	4.27798e8	1.96870	0.984350	−	0.176226i	$-0.0563888\pi$
$241$	4.27798e8	1.96870	0.984350	+	0.176226i	$0.0563888\pi$
$242$	−5.96687e8	−2.70641
$243$	0	0
$244$	−4.59503e7	−0.202500
$245$	1.19085e8	0.517341
$246$	0	0
$247$	−7.44335e8	−3.14289
$248$	7.64505e6	0.0318273
$249$	0	0
$250$	−2.86038e8	−1.15780
$251$	−4.79689e7	−0.191471	−0.0957353	−	0.995407i	$-0.530520\pi$
$251$	−4.79689e7	−0.191471	−0.0957353	+	0.995407i	$0.530520\pi$
$252$	0	0
$253$	−1.64602e8	−0.639019
$254$	−3.90360e8	−1.49468
$255$	0	0
$256$	3.32079e8	1.23709
$257$	−1.81282e8	−0.666175	−0.333087	−	0.942896i	$-0.608090\pi$
$257$	−1.81282e8	−0.666175	−0.333087	+	0.942896i	$0.608090\pi$
$258$	0	0
$259$	1.13092e8	0.404466
$260$	1.52053e8	0.536523
$261$	0	0
$262$	2.93691e8	1.00887
$263$	2.00422e8	0.679359	0.339680	−	0.940541i	$-0.389681\pi$
$263$	2.00422e8	0.679359	0.339680	+	0.940541i	$0.389681\pi$
$264$	0	0
$265$	−2.38759e8	−0.788134
$266$	1.58187e8	0.515329
$267$	0	0
$268$	−1.60504e8	−0.509348
$269$	−2.62947e8	−0.823637	−0.411819	−	0.911266i	$-0.635106\pi$
$269$	−2.62947e8	−0.823637	−0.411819	+	0.911266i	$0.635106\pi$
$270$	0	0
$271$	3.69328e8	1.12725	0.563625	−	0.826031i	$-0.309406\pi$
$271$	3.69328e8	1.12725	0.563625	+	0.826031i	$0.309406\pi$
$272$	−2.95256e8	−0.889627
$273$	0	0
$274$	−2.06692e8	−0.607011
$275$	4.30044e8	1.24695
$276$	0	0
$277$	−2.94313e8	−0.832014	−0.416007	−	0.909361i	$-0.636571\pi$
$277$	−2.94313e8	−0.832014	−0.416007	+	0.909361i	$0.636571\pi$
$278$	4.76104e8	1.32906
$279$	0	0
$280$	2.70335e7	0.0735951
$281$	−4.33874e8	−1.16652	−0.583258	−	0.812287i	$-0.698223\pi$
$281$	−4.33874e8	−1.16652	−0.583258	+	0.812287i	$0.698223\pi$
$282$	0	0
$283$	−8.12492e7	−0.213092	−0.106546	−	0.994308i	$-0.533979\pi$
$283$	−8.12492e7	−0.213092	−0.106546	+	0.994308i	$0.533979\pi$
$284$	1.17660e8	0.304800
$285$	0	0
$286$	−1.57547e9	−3.98226
$287$	4.25636e7	0.106280
$288$	0	0
$289$	−2.01835e8	−0.491873
$290$	2.94869e8	0.709965
$291$	0	0
$292$	1.76636e8	0.415182
$293$	6.42476e8	1.49218	0.746089	−	0.665847i	$-0.231929\pi$
$293$	6.42476e8	1.49218	0.746089	+	0.665847i	$0.231929\pi$
$294$	0	0
$295$	3.14680e7	0.0713661
$296$	−4.30775e8	−0.965448
$297$	0	0
$298$	−4.95463e8	−1.08456
$299$	−2.97842e8	−0.644372
$300$	0	0
$301$	−8.83829e7	−0.186804
$302$	−6.06679e8	−1.26746
$303$	0	0
$304$	−1.06888e9	−2.18208
$305$	1.01018e8	0.203869
$306$	0	0
$307$	−6.93624e8	−1.36817	−0.684084	−	0.729403i	$-0.739798\pi$
$307$	−6.93624e8	−1.36817	−0.684084	+	0.729403i	$0.739798\pi$
$308$	1.18037e8	0.230192
$309$	0	0
$310$	2.00903e7	0.0383019
$311$	1.86724e8	0.351997	0.175999	−	0.984390i	$-0.443685\pi$
$311$	1.86724e8	0.351997	0.175999	+	0.984390i	$0.443685\pi$
$312$	0	0
$313$	4.50446e8	0.830304	0.415152	−	0.909752i	$-0.363728\pi$
$313$	4.50446e8	0.830304	0.415152	+	0.909752i	$0.363728\pi$
$314$	−9.84924e7	−0.179535
$315$	0	0
$316$	−8.82527e7	−0.157334
$317$	3.97194e8	0.700318	0.350159	−	0.936690i	$-0.386128\pi$
$317$	3.97194e8	0.700318	0.350159	+	0.936690i	$0.386128\pi$
$318$	0	0
$319$	−1.07709e9	−1.85773
$320$	−7.70953e6	−0.0131523
$321$	0	0
$322$	6.32976e7	0.105655
$323$	7.54822e8	1.24634
$324$	0	0
$325$	7.78149e8	1.25739
$326$	−7.24740e8	−1.15856
$327$	0	0
$328$	−1.62128e8	−0.253687
$329$	−2.03710e8	−0.315375
$330$	0	0
$331$	−7.65695e8	−1.16053	−0.580267	−	0.814426i	$-0.697052\pi$
$331$	−7.65695e8	−1.16053	−0.580267	+	0.814426i	$0.697052\pi$
$332$	−1.54902e8	−0.232314
$333$	0	0
$334$	−1.23645e8	−0.181578
$335$	3.52857e8	0.512793
$336$	0	0
$337$	1.34277e8	0.191116	0.0955581	−	0.995424i	$-0.469536\pi$
$337$	1.34277e8	0.191116	0.0955581	+	0.995424i	$0.469536\pi$
$338$	−1.96849e9	−2.77284
$339$	0	0
$340$	−1.54195e8	−0.212762
$341$	−7.33851e7	−0.100223
$342$	0	0
$343$	3.44519e8	0.460981
$344$	3.36657e8	0.445896
$345$	0	0
$346$	7.76604e8	1.00794
$347$	−1.31108e9	−1.68451	−0.842257	−	0.539076i	$-0.818773\pi$
$347$	−1.31108e9	−1.68451	−0.842257	+	0.539076i	$0.818773\pi$
$348$	0	0
$349$	−1.04850e9	−1.32032	−0.660160	−	0.751125i	$-0.729511\pi$
$349$	−1.04850e9	−1.32032	−0.660160	+	0.751125i	$0.729511\pi$
$350$	−1.65373e8	−0.206170
$351$	0	0
$352$	−1.43666e9	−1.75572
$353$	1.06498e9	1.28863	0.644317	−	0.764758i	$-0.277142\pi$
$353$	1.06498e9	1.28863	0.644317	+	0.764758i	$0.277142\pi$
$354$	0	0
$355$	−2.58667e8	−0.306861
$356$	7.30388e8	0.857983
$357$	0	0
$358$	1.60516e9	1.84896
$359$	8.86207e8	1.01089	0.505446	−	0.862858i	$-0.331328\pi$
$359$	8.86207e8	1.01089	0.505446	+	0.862858i	$0.331328\pi$
$360$	0	0
$361$	1.83872e9	2.05703
$362$	−1.04771e8	−0.116081
$363$	0	0
$364$	2.13583e8	0.232120
$365$	−3.88321e8	−0.417990
$366$	0	0
$367$	−9.92035e8	−1.04760	−0.523801	−	0.851841i	$-0.675486\pi$
$367$	−9.92035e8	−1.04760	−0.523801	+	0.851841i	$0.675486\pi$
$368$	−4.27707e8	−0.447382
$369$	0	0
$370$	−1.13203e9	−1.16185
$371$	−3.35377e8	−0.340976
$372$	0	0
$373$	9.84405e8	0.982184	0.491092	−	0.871108i	$-0.336598\pi$
$373$	9.84405e8	0.982184	0.491092	+	0.871108i	$0.336598\pi$
$374$	1.59767e9	1.57920
$375$	0	0
$376$	7.75948e8	0.752792
$377$	−1.94895e9	−1.87329
$378$	0	0
$379$	−1.03216e9	−0.973888	−0.486944	−	0.873433i	$-0.661888\pi$
$379$	−1.03216e9	−0.973888	−0.486944	+	0.873433i	$0.661888\pi$
$380$	−5.58214e8	−0.521865
$381$	0	0
$382$	−3.72629e8	−0.342022
$383$	−1.11996e9	−1.01861	−0.509303	−	0.860587i	$-0.670097\pi$
$383$	−1.11996e9	−1.01861	−0.509303	+	0.860587i	$0.670097\pi$
$384$	0	0
$385$	−2.59495e8	−0.231748
$386$	1.11841e9	0.989796
$387$	0	0
$388$	3.77269e8	0.327899
$389$	2.19361e9	1.88945	0.944725	−	0.327865i	$-0.106329\pi$
$389$	2.19361e9	1.88945	0.944725	+	0.327865i	$0.106329\pi$
$390$	0	0
$391$	3.02038e8	0.255531
$392$	−6.37162e8	−0.534255
$393$	0	0
$394$	9.41587e8	0.775575
$395$	1.94017e8	0.158398
$396$	0	0
$397$	−1.87970e9	−1.50772	−0.753862	−	0.657033i	$-0.771811\pi$
$397$	−1.87970e9	−1.50772	−0.753862	+	0.657033i	$0.771811\pi$
$398$	7.70117e8	0.612302
$399$	0	0
$400$	1.11744e9	0.872998
$401$	−1.82808e9	−1.41576	−0.707881	−	0.706332i	$-0.750349\pi$
$401$	−1.82808e9	−1.41576	−0.707881	+	0.706332i	$0.750349\pi$
$402$	0	0
$403$	−1.32788e8	−0.101062
$404$	5.58065e8	0.421066
$405$	0	0
$406$	4.14192e8	0.307157
$407$	4.13502e9	3.04016
$408$	0	0
$409$	−2.05110e9	−1.48237	−0.741183	−	0.671303i	$-0.765735\pi$
$409$	−2.05110e9	−1.48237	−0.741183	+	0.671303i	$0.765735\pi$
$410$	−4.26053e8	−0.305295
$411$	0	0
$412$	1.68361e8	0.118604
$413$	4.42019e7	0.0308756
$414$	0	0
$415$	3.40541e8	0.233884
$416$	−2.59959e9	−1.77043
$417$	0	0
$418$	5.78385e9	3.87347
$419$	1.07209e8	0.0712005	0.0356002	−	0.999366i	$-0.488666\pi$
$419$	1.07209e8	0.0712005	0.0356002	+	0.999366i	$0.488666\pi$
$420$	0	0
$421$	−2.81280e9	−1.83718	−0.918589	−	0.395213i	$-0.870671\pi$
$421$	−2.81280e9	−1.83718	−0.918589	+	0.395213i	$0.870671\pi$
$422$	9.08061e8	0.588195
$423$	0	0
$424$	1.27747e9	0.813901
$425$	−7.89113e8	−0.498629
$426$	0	0
$427$	1.41897e8	0.0882013
$428$	−1.05128e9	−0.648135
$429$	0	0
$430$	8.84696e8	0.536604
$431$	−1.62988e9	−0.980583	−0.490292	−	0.871558i	$-0.663110\pi$
$431$	−1.62988e9	−0.980583	−0.490292	+	0.871558i	$0.663110\pi$
$432$	0	0
$433$	−8.30649e8	−0.491711	−0.245856	−	0.969306i	$-0.579069\pi$
$433$	−8.30649e8	−0.491711	−0.245856	+	0.969306i	$0.579069\pi$
$434$	2.82201e7	0.0165709
$435$	0	0
$436$	9.12520e8	0.527278
$437$	1.09343e9	0.626768
$438$	0	0
$439$	2.22387e9	1.25454	0.627270	−	0.778802i	$-0.284172\pi$
$439$	2.22387e9	1.25454	0.627270	+	0.778802i	$0.284172\pi$
$440$	9.88436e8	0.553177
$441$	0	0
$442$	2.89092e9	1.59242
$443$	−1.30013e9	−0.710516	−0.355258	−	0.934768i	$-0.615607\pi$
$443$	−1.30013e9	−0.710516	−0.355258	+	0.934768i	$0.615607\pi$
$444$	0	0
$445$	−1.60570e9	−0.863785
$446$	2.84052e9	1.51609
$447$	0	0
$448$	−1.08293e7	−0.00569019
$449$	−1.41883e9	−0.739720	−0.369860	−	0.929088i	$-0.620594\pi$
$449$	−1.41883e9	−0.739720	−0.369860	+	0.929088i	$0.620594\pi$
$450$	0	0
$451$	1.55627e9	0.798852
$452$	6.02602e8	0.306935
$453$	0	0
$454$	−3.88249e9	−1.94722
$455$	−4.69547e8	−0.233689
$456$	0	0
$457$	−2.30832e9	−1.13133	−0.565664	−	0.824636i	$-0.691380\pi$
$457$	−2.30832e9	−1.13133	−0.565664	+	0.824636i	$0.691380\pi$
$458$	1.97076e9	0.958528
$459$	0	0
$460$	−2.23366e8	−0.106995
$461$	2.65874e8	0.126393	0.0631965	−	0.998001i	$-0.479871\pi$
$461$	2.65874e8	0.126393	0.0631965	+	0.998001i	$0.479871\pi$
$462$	0	0
$463$	−1.76799e9	−0.827840	−0.413920	−	0.910313i	$-0.635841\pi$
$463$	−1.76799e9	−0.827840	−0.413920	+	0.910313i	$0.635841\pi$
$464$	−2.79873e9	−1.30061
$465$	0	0
$466$	1.21946e9	0.558236
$467$	−3.74007e9	−1.69930	−0.849652	−	0.527344i	$-0.823188\pi$
$467$	−3.74007e9	−1.69930	−0.849652	+	0.527344i	$0.823188\pi$
$468$	0	0
$469$	4.95645e8	0.221853
$470$	2.03910e9	0.905933
$471$	0	0
$472$	−1.68368e8	−0.0736993
$473$	−3.23158e9	−1.40411
$474$	0	0
$475$	−2.85673e9	−1.22304
$476$	−2.16592e8	−0.0920490
$477$	0	0
$478$	3.13052e9	1.31105
$479$	4.49040e8	0.186686	0.0933428	−	0.995634i	$-0.470245\pi$
$479$	4.49040e8	0.186686	0.0933428	+	0.995634i	$0.470245\pi$
$480$	0	0
$481$	7.48216e9	3.06563
$482$	−6.01502e9	−2.44665
$483$	0	0
$484$	2.95767e9	1.18574
$485$	−8.29399e8	−0.330117
$486$	0	0
$487$	−3.09706e9	−1.21506	−0.607531	−	0.794296i	$-0.707840\pi$
$487$	−3.09706e9	−1.21506	−0.607531	+	0.794296i	$0.707840\pi$
$488$	−5.40495e8	−0.210534
$489$	0	0
$490$	−1.67439e9	−0.642939
$491$	2.15480e9	0.821527	0.410763	−	0.911742i	$-0.365262\pi$
$491$	2.15480e9	0.821527	0.410763	+	0.911742i	$0.365262\pi$
$492$	0	0
$493$	1.97641e9	0.742869
$494$	1.04657e10	3.90591
$495$	0	0
$496$	−1.90686e8	−0.0701669
$497$	−3.63340e8	−0.132759
$498$	0	0
$499$	5.11219e9	1.84185	0.920926	−	0.389738i	$-0.127434\pi$
$499$	5.11219e9	1.84185	0.920926	+	0.389738i	$0.127434\pi$
$500$	1.41784e9	0.507261
$501$	0	0
$502$	6.74462e8	0.237955
$503$	3.11720e9	1.09214	0.546069	−	0.837740i	$-0.316124\pi$
$503$	3.11720e9	1.09214	0.546069	+	0.837740i	$0.316124\pi$
$504$	0	0
$505$	−1.22687e9	−0.423913
$506$	2.31437e9	0.794158
$507$	0	0
$508$	1.93495e9	0.654856
$509$	3.33182e9	1.11988	0.559938	−	0.828535i	$-0.310825\pi$
$509$	3.33182e9	1.11988	0.559938	+	0.828535i	$0.310825\pi$
$510$	0	0
$511$	−5.45460e8	−0.180838
$512$	−1.58742e9	−0.522695
$513$	0	0
$514$	2.54889e9	0.827905
$515$	−3.70129e8	−0.119406
$516$	0	0
$517$	−7.44834e9	−2.37052
$518$	−1.59011e9	−0.502660
$519$	0	0
$520$	1.78854e9	0.557811
$521$	1.20322e8	0.0372745	0.0186373	−	0.999826i	$-0.494067\pi$
$521$	1.20322e8	0.0372745	0.0186373	+	0.999826i	$0.494067\pi$
$522$	0	0
$523$	1.56158e9	0.477318	0.238659	−	0.971103i	$-0.423292\pi$
$523$	1.56158e9	0.477318	0.238659	+	0.971103i	$0.423292\pi$
$524$	−1.45577e9	−0.442012
$525$	0	0
$526$	−2.81801e9	−0.844291
$527$	1.34658e8	0.0400771
$528$	0	0
$529$	−2.96729e9	−0.871497
$530$	3.35705e9	0.979473
$531$	0	0
$532$	−7.84103e8	−0.225779
$533$	2.81601e9	0.805543
$534$	0	0
$535$	2.31116e9	0.652518
$536$	−1.88795e9	−0.529558
$537$	0	0
$538$	3.69715e9	1.02360
$539$	6.11614e9	1.68235
$540$	0	0
$541$	2.94601e9	0.799914	0.399957	−	0.916534i	$-0.369025\pi$
$541$	2.94601e9	0.799914	0.399957	+	0.916534i	$0.369025\pi$
$542$	−5.19290e9	−1.40092
$543$	0	0
$544$	2.63621e9	0.702077
$545$	−2.00611e9	−0.530843
$546$	0	0
$547$	5.07000e9	1.32450	0.662251	−	0.749282i	$-0.269601\pi$
$547$	5.07000e9	1.32450	0.662251	+	0.749282i	$0.269601\pi$
$548$	1.02453e9	0.265947
$549$	0	0
$550$	−6.04659e9	−1.54968
$551$	7.15495e9	1.82212
$552$	0	0
$553$	2.72529e8	0.0685290
$554$	4.13816e9	1.03401
$555$	0	0
$556$	−2.35996e9	−0.582295
$557$	−7.03628e9	−1.72524	−0.862621	−	0.505851i	$-0.831179\pi$
$557$	−7.03628e9	−1.72524	−0.862621	+	0.505851i	$0.831179\pi$
$558$	0	0
$559$	−5.84742e9	−1.41587
$560$	−6.74279e8	−0.162249
$561$	0	0
$562$	6.10044e9	1.44972
$563$	4.94078e9	1.16685	0.583426	−	0.812166i	$-0.301712\pi$
$563$	4.94078e9	1.16685	0.583426	+	0.812166i	$0.301712\pi$
$564$	0	0
$565$	−1.32478e9	−0.309010
$566$	1.14240e9	0.264825
$567$	0	0
$568$	1.38399e9	0.316893
$569$	−2.66776e9	−0.607090	−0.303545	−	0.952817i	$-0.598170\pi$
$569$	−2.66776e9	−0.607090	−0.303545	+	0.952817i	$0.598170\pi$
$570$	0	0
$571$	6.77696e9	1.52338	0.761690	−	0.647941i	$-0.224370\pi$
$571$	6.77696e9	1.52338	0.761690	+	0.647941i	$0.224370\pi$
$572$	7.80933e9	1.74473
$573$	0	0
$574$	−5.98461e8	−0.132082
$575$	−1.14310e9	−0.250754
$576$	0	0
$577$	−5.53458e9	−1.19941	−0.599707	−	0.800219i	$-0.704716\pi$
$577$	−5.53458e9	−1.19941	−0.599707	+	0.800219i	$0.704716\pi$
$578$	2.83787e9	0.611288
$579$	0	0
$580$	−1.46162e9	−0.311053
$581$	4.78346e8	0.101187
$582$	0	0
$583$	−1.22625e10	−2.56294
$584$	2.07770e9	0.431655
$585$	0	0
$586$	−9.03347e9	−1.85444
$587$	−5.22919e9	−1.06709	−0.533545	−	0.845771i	$-0.679141\pi$
$587$	−5.22919e9	−1.06709	−0.533545	+	0.845771i	$0.679141\pi$
$588$	0	0
$589$	4.87488e8	0.0983015
$590$	−4.42452e8	−0.0886920
$591$	0	0
$592$	1.07445e10	2.12844
$593$	−8.33930e8	−0.164224	−0.0821122	−	0.996623i	$-0.526167\pi$
$593$	−8.33930e8	−0.164224	−0.0821122	+	0.996623i	$0.526167\pi$
$594$	0	0
$595$	4.76162e8	0.0926714
$596$	2.45592e9	0.475174
$597$	0	0
$598$	4.18777e9	0.800809
$599$	−3.80759e9	−0.723863	−0.361931	−	0.932205i	$-0.617883\pi$
$599$	−3.80759e9	−0.723863	−0.361931	+	0.932205i	$0.617883\pi$
$600$	0	0
$601$	8.81584e9	1.65654	0.828272	−	0.560326i	$-0.189324\pi$
$601$	8.81584e9	1.65654	0.828272	+	0.560326i	$0.189324\pi$
$602$	1.24270e9	0.232155
$603$	0	0
$604$	3.00720e9	0.555307
$605$	−6.50222e9	−1.19376
$606$	0	0
$607$	3.12869e9	0.567809	0.283904	−	0.958853i	$-0.408370\pi$
$607$	3.12869e9	0.567809	0.283904	+	0.958853i	$0.408370\pi$
$608$	9.54357e9	1.72206
$609$	0	0
$610$	−1.42036e9	−0.253363
$611$	−1.34775e10	−2.39037
$612$	0	0
$613$	6.07990e9	1.06607	0.533034	−	0.846094i	$-0.321052\pi$
$613$	6.07990e9	1.06607	0.533034	+	0.846094i	$0.321052\pi$
$614$	9.75263e9	1.70033
$615$	0	0
$616$	1.38842e9	0.239325
$617$	1.45081e9	0.248664	0.124332	−	0.992241i	$-0.460321\pi$
$617$	1.45081e9	0.248664	0.124332	+	0.992241i	$0.460321\pi$
$618$	0	0
$619$	−3.93245e9	−0.666416	−0.333208	−	0.942853i	$-0.608131\pi$
$619$	−3.93245e9	−0.666416	−0.333208	+	0.942853i	$0.608131\pi$
$620$	−9.95841e7	−0.0167810
$621$	0	0
$622$	−2.62542e9	−0.437454
$623$	−2.25547e9	−0.373706
$624$	0	0
$625$	1.15244e9	0.188815
$626$	−6.33345e9	−1.03188
$627$	0	0
$628$	4.88209e8	0.0786588
$629$	−7.58757e9	−1.21570
$630$	0	0
$631$	9.82173e9	1.55627	0.778135	−	0.628097i	$-0.216166\pi$
$631$	9.82173e9	1.55627	0.778135	+	0.628097i	$0.216166\pi$
$632$	−1.03808e9	−0.163577
$633$	0	0
$634$	−5.58470e9	−0.870338
$635$	−4.25383e9	−0.659284
$636$	0	0
$637$	1.10669e10	1.69644
$638$	1.51443e10	2.30875
$639$	0	0
$640$	3.68892e9	0.556249
$641$	7.96630e9	1.19469	0.597343	−	0.801986i	$-0.296223\pi$
$641$	7.96630e9	1.19469	0.597343	+	0.801986i	$0.296223\pi$
$642$	0	0
$643$	7.54836e9	1.11973	0.559866	−	0.828583i	$-0.310852\pi$
$643$	7.54836e9	1.11973	0.559866	+	0.828583i	$0.310852\pi$
$644$	−3.13755e8	−0.0462903
$645$	0	0
$646$	−1.06131e10	−1.54892
$647$	−1.12209e10	−1.62878	−0.814388	−	0.580321i	$-0.802927\pi$
$647$	−1.12209e10	−1.62878	−0.814388	+	0.580321i	$0.802927\pi$
$648$	0	0
$649$	1.61617e9	0.232076
$650$	−1.09411e10	−1.56266
$651$	0	0
$652$	3.59240e9	0.507596
$653$	6.06010e9	0.851694	0.425847	−	0.904795i	$-0.359976\pi$
$653$	6.06010e9	0.851694	0.425847	+	0.904795i	$0.359976\pi$
$654$	0	0
$655$	3.20041e9	0.445001
$656$	4.04385e9	0.559282
$657$	0	0
$658$	2.86425e9	0.391941
$659$	1.39437e10	1.89792	0.948960	−	0.315398i	$-0.102138\pi$
$659$	1.39437e10	1.89792	0.948960	+	0.315398i	$0.102138\pi$
$660$	0	0
$661$	−8.46218e9	−1.13966	−0.569832	−	0.821761i	$-0.692992\pi$
$661$	−8.46218e9	−1.13966	−0.569832	+	0.821761i	$0.692992\pi$
$662$	1.07660e10	1.44228
$663$	0	0
$664$	−1.82205e9	−0.241531
$665$	1.72379e9	0.227305
$666$	0	0
$667$	2.86302e9	0.373580
$668$	6.12884e8	0.0795538
$669$	0	0
$670$	−4.96131e9	−0.637286
$671$	5.18823e9	0.662965
$672$	0	0
$673$	2.59986e9	0.328773	0.164387	−	0.986396i	$-0.447436\pi$
$673$	2.59986e9	0.328773	0.164387	+	0.986396i	$0.447436\pi$
$674$	−1.88799e9	−0.237514
$675$	0	0
$676$	9.75744e9	1.21485
$677$	−2.24286e8	−0.0277807	−0.0138903	−	0.999904i	$-0.504422\pi$
$677$	−2.24286e8	−0.0277807	−0.0138903	+	0.999904i	$0.504422\pi$
$678$	0	0
$679$	−1.16503e9	−0.142821
$680$	−1.81374e9	−0.221204
$681$	0	0
$682$	1.03182e9	0.124555
$683$	1.29921e9	0.156029	0.0780146	−	0.996952i	$-0.475142\pi$
$683$	1.29921e9	0.156029	0.0780146	+	0.996952i	$0.475142\pi$
$684$	0	0
$685$	−2.25236e9	−0.267745
$686$	−4.84407e9	−0.572896
$687$	0	0
$688$	−8.39702e9	−0.983027
$689$	−2.21886e10	−2.58441
$690$	0	0
$691$	−1.09890e10	−1.26703	−0.633514	−	0.773732i	$-0.718388\pi$
$691$	−1.09890e10	−1.26703	−0.633514	+	0.773732i	$0.718388\pi$
$692$	−3.84949e9	−0.441602
$693$	0	0
$694$	1.84342e10	2.09347
$695$	5.18820e9	0.586232
$696$	0	0
$697$	−2.85568e9	−0.319445
$698$	1.47423e10	1.64086
$699$	0	0
$700$	8.19724e8	0.0903284
$701$	−1.12676e10	−1.23543	−0.617715	−	0.786402i	$-0.711941\pi$
$701$	−1.12676e10	−1.23543	−0.617715	+	0.786402i	$0.711941\pi$
$702$	0	0
$703$	−2.74684e10	−2.98188
$704$	−3.95956e8	−0.0427703
$705$	0	0
$706$	−1.49740e10	−1.60148
$707$	−1.72333e9	−0.183401
$708$	0	0
$709$	−8.10979e9	−0.854571	−0.427285	−	0.904117i	$-0.640530\pi$
$709$	−8.10979e9	−0.854571	−0.427285	+	0.904117i	$0.640530\pi$
$710$	3.63696e9	0.381359
$711$	0	0
$712$	8.59127e9	0.892026
$713$	1.95065e8	0.0201543
$714$	0	0
$715$	−1.71682e10	−1.75653
$716$	−7.95647e9	−0.810075
$717$	0	0
$718$	−1.24604e10	−1.25631
$719$	−1.37914e10	−1.38375	−0.691873	−	0.722019i	$-0.743214\pi$
$719$	−1.37914e10	−1.38375	−0.691873	+	0.722019i	$0.743214\pi$
$720$	0	0
$721$	−5.19907e8	−0.0516597
$722$	−2.58532e10	−2.55643
$723$	0	0
$724$	5.19330e8	0.0508579
$725$	−7.47999e9	−0.728984
$726$	0	0
$727$	−8.25616e9	−0.796907	−0.398454	−	0.917189i	$-0.630453\pi$
$727$	−8.25616e9	−0.796907	−0.398454	+	0.917189i	$0.630453\pi$
$728$	2.51230e9	0.241330
$729$	0	0
$730$	5.45994e9	0.519467
$731$	5.92981e9	0.561474
$732$	0	0
$733$	1.14387e10	1.07279	0.536395	−	0.843967i	$-0.319786\pi$
$733$	1.14387e10	1.07279	0.536395	+	0.843967i	$0.319786\pi$
$734$	1.39484e10	1.30193
$735$	0	0
$736$	3.81881e9	0.353065
$737$	1.81225e10	1.66756
$738$	0	0
$739$	1.48024e10	1.34920	0.674598	−	0.738185i	$-0.264317\pi$
$739$	1.48024e10	1.34920	0.674598	+	0.738185i	$0.264317\pi$
$740$	5.61125e9	0.509036
$741$	0	0
$742$	4.71553e9	0.423757
$743$	−1.21140e10	−1.08349	−0.541746	−	0.840542i	$-0.682236\pi$
$743$	−1.21140e10	−1.08349	−0.541746	+	0.840542i	$0.682236\pi$
$744$	0	0
$745$	−5.39917e9	−0.478387
$746$	−1.38411e10	−1.22063
$747$	0	0
$748$	−7.91935e9	−0.691885
$749$	3.24641e9	0.282304
$750$	0	0
$751$	−3.71223e9	−0.319812	−0.159906	−	0.987132i	$-0.551119\pi$
$751$	−3.71223e9	−0.319812	−0.159906	+	0.987132i	$0.551119\pi$
$752$	−1.93540e10	−1.65962
$753$	0	0
$754$	2.74030e10	2.32808
$755$	−6.61111e9	−0.559062
$756$	0	0
$757$	2.68089e9	0.224617	0.112309	−	0.993673i	$-0.464175\pi$
$757$	2.68089e9	0.224617	0.112309	+	0.993673i	$0.464175\pi$
$758$	1.45126e10	1.21032
$759$	0	0
$760$	−6.56606e9	−0.542572
$761$	8.48234e9	0.697701	0.348850	−	0.937178i	$-0.386572\pi$
$761$	8.48234e9	0.697701	0.348850	+	0.937178i	$0.386572\pi$
$762$	0	0
$763$	−2.81791e9	−0.229663
$764$	1.84705e9	0.149849
$765$	0	0
$766$	1.57471e10	1.26590
$767$	2.92440e9	0.234020
$768$	0	0
$769$	4.34767e9	0.344758	0.172379	−	0.985031i	$-0.444855\pi$
$769$	4.34767e9	0.344758	0.172379	+	0.985031i	$0.444855\pi$
$770$	3.64861e9	0.288011
$771$	0	0
$772$	−5.54376e9	−0.433655
$773$	1.06536e10	0.829601	0.414800	−	0.909912i	$-0.363851\pi$
$773$	1.06536e10	0.829601	0.414800	+	0.909912i	$0.363851\pi$
$774$	0	0
$775$	−5.09633e8	−0.0393280
$776$	4.43767e9	0.340910
$777$	0	0
$778$	−3.08430e10	−2.34816
$779$	−1.03381e10	−0.783537
$780$	0	0
$781$	−1.32849e10	−0.997886
$782$	−4.24678e9	−0.317567
$783$	0	0
$784$	1.58923e10	1.17783
$785$	−1.07329e9	−0.0791907
$786$	0	0
$787$	2.49085e9	0.182153	0.0910763	−	0.995844i	$-0.470969\pi$
$787$	2.49085e9	0.182153	0.0910763	+	0.995844i	$0.470969\pi$
$788$	−4.66728e9	−0.339799
$789$	0	0
$790$	−2.72796e9	−0.196853
$791$	−1.86086e9	−0.133689
$792$	0	0
$793$	9.38791e9	0.668517
$794$	2.64293e10	1.87376
$795$	0	0
$796$	−3.81733e9	−0.268265
$797$	−6.71594e9	−0.469897	−0.234949	−	0.972008i	$-0.575492\pi$
$797$	−6.71594e9	−0.469897	−0.234949	+	0.972008i	$0.575492\pi$
$798$	0	0
$799$	1.36674e10	0.947920
$800$	−9.97712e9	−0.688954
$801$	0	0
$802$	2.57036e10	1.75947
$803$	−1.99439e10	−1.35927
$804$	0	0
$805$	6.89766e8	0.0466033
$806$	1.86705e9	0.125598
$807$	0	0
$808$	6.56430e9	0.437773
$809$	5.26318e9	0.349485	0.174743	−	0.984614i	$-0.444091\pi$
$809$	5.26318e9	0.349485	0.174743	+	0.984614i	$0.444091\pi$
$810$	0	0
$811$	1.05418e10	0.693971	0.346985	−	0.937870i	$-0.387205\pi$
$811$	1.05418e10	0.693971	0.346985	+	0.937870i	$0.387205\pi$
$812$	−2.05308e9	−0.134573
$813$	0	0
$814$	−5.81400e10	−3.77824
$815$	−7.89763e9	−0.511029
$816$	0	0
$817$	2.14670e10	1.37719
$818$	2.88393e10	1.84225
$819$	0	0
$820$	2.11187e9	0.133757
$821$	−2.59089e10	−1.63399	−0.816994	−	0.576646i	$-0.804361\pi$
$821$	−2.59089e10	−1.63399	−0.816994	+	0.576646i	$0.804361\pi$
$822$	0	0
$823$	−8.31491e9	−0.519946	−0.259973	−	0.965616i	$-0.583714\pi$
$823$	−8.31491e9	−0.519946	−0.259973	+	0.965616i	$0.583714\pi$
$824$	1.98036e9	0.123310
$825$	0	0
$826$	−6.21497e8	−0.0383715
$827$	6.36168e9	0.391113	0.195557	−	0.980692i	$-0.437349\pi$
$827$	6.36168e9	0.391113	0.195557	+	0.980692i	$0.437349\pi$
$828$	0	0
$829$	−2.31191e10	−1.40938	−0.704692	−	0.709513i	$-0.748915\pi$
$829$	−2.31191e10	−1.40938	−0.704692	+	0.709513i	$0.748915\pi$
$830$	−4.78815e9	−0.290666
$831$	0	0
$832$	−7.16467e8	−0.0431285
$833$	−1.12228e10	−0.672737
$834$	0	0
$835$	−1.34738e9	−0.0800918
$836$	−2.86695e10	−1.69706
$837$	0	0
$838$	−1.50740e9	−0.0884862
$839$	−1.96736e10	−1.15005	−0.575026	−	0.818135i	$-0.695008\pi$
$839$	−1.96736e10	−1.15005	−0.575026	+	0.818135i	$0.695008\pi$
$840$	0	0
$841$	1.48448e9	0.0860574
$842$	3.95491e10	2.28320
$843$	0	0
$844$	−4.50110e9	−0.257703
$845$	−2.14510e10	−1.22306
$846$	0	0
$847$	−9.13343e9	−0.516466
$848$	−3.18632e10	−1.79434
$849$	0	0
$850$	1.10952e10	0.619684
$851$	−1.09913e10	−0.611359
$852$	0	0
$853$	−2.05583e10	−1.13413	−0.567067	−	0.823671i	$-0.691922\pi$
$853$	−2.05583e10	−1.13413	−0.567067	+	0.823671i	$0.691922\pi$
$854$	−1.99513e9	−0.109614
$855$	0	0
$856$	−1.23658e10	−0.673852
$857$	1.22990e10	0.667476	0.333738	−	0.942666i	$-0.391690\pi$
$857$	1.22990e10	0.667476	0.333738	+	0.942666i	$0.391690\pi$
$858$	0	0
$859$	6.11395e9	0.329114	0.164557	−	0.986368i	$-0.447381\pi$
$859$	6.11395e9	0.329114	0.164557	+	0.986368i	$0.447381\pi$
$860$	−4.38528e9	−0.235100
$861$	0	0
$862$	2.29167e10	1.21864
$863$	5.85317e9	0.309994	0.154997	−	0.987915i	$-0.450463\pi$
$863$	5.85317e9	0.309994	0.154997	+	0.987915i	$0.450463\pi$
$864$	0	0
$865$	8.46281e9	0.444589
$866$	1.16793e10	0.611087
$867$	0	0
$868$	−1.39882e8	−0.00726011
$869$	9.96458e9	0.515098
$870$	0	0
$871$	3.27919e10	1.68153
$872$	1.07336e10	0.548199
$873$	0	0
$874$	−1.53741e10	−0.778932
$875$	−4.37835e9	−0.220944
$876$	0	0
$877$	−5.35250e9	−0.267953	−0.133976	−	0.990985i	$-0.542775\pi$
$877$	−5.35250e9	−0.267953	−0.133976	+	0.990985i	$0.542775\pi$
$878$	−3.12686e10	−1.55911
$879$	0	0
$880$	−2.46539e10	−1.21954
$881$	9.28115e9	0.457284	0.228642	−	0.973511i	$-0.426571\pi$
$881$	9.28115e9	0.457284	0.228642	+	0.973511i	$0.426571\pi$
$882$	0	0
$883$	−1.19702e10	−0.585114	−0.292557	−	0.956248i	$-0.594506\pi$
$883$	−1.19702e10	−0.585114	−0.292557	+	0.956248i	$0.594506\pi$
$884$	−1.43298e10	−0.697680
$885$	0	0
$886$	1.82804e10	0.883012
$887$	−2.48052e10	−1.19347	−0.596734	−	0.802439i	$-0.703535\pi$
$887$	−2.48052e10	−1.19347	−0.596734	+	0.802439i	$0.703535\pi$
$888$	0	0
$889$	−5.97521e9	−0.285231
$890$	2.25769e10	1.07349
$891$	0	0
$892$	−1.40799e10	−0.664237
$893$	4.94784e10	2.32507
$894$	0	0
$895$	1.74917e10	0.815552
$896$	5.18169e9	0.240654
$897$	0	0
$898$	1.99493e10	0.919306
$899$	1.27643e9	0.0585918
$900$	0	0
$901$	2.25012e10	1.02487
$902$	−2.18818e10	−0.992794
$903$	0	0
$904$	7.08816e9	0.319113
$905$	−1.14171e9	−0.0512018
$906$	0	0
$907$	9.90452e9	0.440766	0.220383	−	0.975413i	$-0.429269\pi$
$907$	9.90452e9	0.440766	0.220383	+	0.975413i	$0.429269\pi$
$908$	1.92448e10	0.853127
$909$	0	0
$910$	6.60202e9	0.290424
$911$	8.15910e8	0.0357543	0.0178771	−	0.999840i	$-0.494309\pi$
$911$	8.15910e8	0.0357543	0.0178771	+	0.999840i	$0.494309\pi$
$912$	0	0
$913$	1.74899e10	0.760573
$914$	3.24559e10	1.40599
$915$	0	0
$916$	−9.76871e9	−0.419955
$917$	4.49549e9	0.192524
$918$	0	0
$919$	−3.65375e9	−0.155287	−0.0776434	−	0.996981i	$-0.524740\pi$
$919$	−3.65375e9	−0.155287	−0.0776434	+	0.996981i	$0.524740\pi$
$920$	−2.62737e9	−0.111241
$921$	0	0
$922$	−3.73830e9	−0.157078
$923$	−2.40386e10	−1.00624
$924$	0	0
$925$	2.87162e10	1.19297
$926$	2.48587e10	1.02882
$927$	0	0
$928$	2.49886e10	1.02642
$929$	−3.46180e10	−1.41660	−0.708299	−	0.705913i	$-0.750537\pi$
$929$	−3.46180e10	−1.41660	−0.708299	+	0.705913i	$0.750537\pi$
$930$	0	0
$931$	−4.06287e10	−1.65010
$932$	−6.04465e9	−0.244577
$933$	0	0
$934$	5.25869e10	2.11185
$935$	1.74101e10	0.696564
$936$	0	0
$937$	−1.64978e10	−0.655143	−0.327572	−	0.944826i	$-0.606230\pi$
$937$	−1.64978e10	−0.655143	−0.327572	+	0.944826i	$0.606230\pi$
$938$	−6.96897e9	−0.275714
$939$	0	0
$940$	−1.01075e10	−0.396912
$941$	2.07806e10	0.813009	0.406504	−	0.913649i	$-0.366748\pi$
$941$	2.07806e10	0.813009	0.406504	+	0.913649i	$0.366748\pi$
$942$	0	0
$943$	−4.13673e9	−0.160645
$944$	4.19950e9	0.162478
$945$	0	0
$946$	4.54373e10	1.74499
$947$	3.39662e10	1.29964	0.649818	−	0.760090i	$-0.274845\pi$
$947$	3.39662e10	1.29964	0.649818	+	0.760090i	$0.274845\pi$
$948$	0	0
$949$	−3.60877e10	−1.37065
$950$	4.01668e10	1.51997
$951$	0	0
$952$	−2.54769e9	−0.0957012
$953$	−1.25066e9	−0.0468074	−0.0234037	−	0.999726i	$-0.507450\pi$
$953$	−1.25066e9	−0.0468074	−0.0234037	+	0.999726i	$0.507450\pi$
$954$	0	0
$955$	−4.06061e9	−0.150862
$956$	−1.55174e10	−0.574404
$957$	0	0
$958$	−6.31369e9	−0.232008
$959$	−3.16381e9	−0.115837
$960$	0	0
$961$	−2.74256e10	−0.996839
$962$	−1.05202e11	−3.80989
$963$	0	0
$964$	2.98154e10	1.07194
$965$	1.21876e10	0.436587
$966$	0	0
$967$	1.99659e10	0.710063	0.355032	−	0.934854i	$-0.384470\pi$
$967$	1.99659e10	0.710063	0.355032	+	0.934854i	$0.384470\pi$
$968$	3.47899e10	1.23279
$969$	0	0
$970$	1.16617e10	0.410261
$971$	5.02413e10	1.76114	0.880569	−	0.473919i	$-0.157161\pi$
$971$	5.02413e10	1.76114	0.880569	+	0.473919i	$0.157161\pi$
$972$	0	0
$973$	7.28767e9	0.253626
$974$	4.35459e10	1.51005
$975$	0	0
$976$	1.34812e10	0.464146
$977$	5.76202e10	1.97671	0.988357	−	0.152155i	$-0.0486213\pi$
$977$	5.76202e10	1.97671	0.988357	+	0.152155i	$0.0486213\pi$
$978$	0	0
$979$	−8.24678e10	−2.80896
$980$	8.29964e9	0.281688
$981$	0	0
$982$	−3.02974e10	−1.02097
$983$	−1.60520e10	−0.539003	−0.269502	−	0.963000i	$-0.586859\pi$
$983$	−1.60520e10	−0.539003	−0.269502	+	0.963000i	$0.586859\pi$
$984$	0	0
$985$	1.02607e10	0.342096
$986$	−2.77891e10	−0.923220
$987$	0	0
$988$	−5.18764e10	−1.71128
$989$	8.58989e9	0.282358
$990$	0	0
$991$	−8.99460e9	−0.293578	−0.146789	−	0.989168i	$-0.546894\pi$
$991$	−8.99460e9	−0.293578	−0.146789	+	0.989168i	$0.546894\pi$
$992$	1.70255e9	0.0553744
$993$	0	0
$994$	5.10870e9	0.164990
$995$	8.39212e9	0.270079
$996$	0	0
$997$	1.62638e9	0.0519744	0.0259872	−	0.999662i	$-0.491727\pi$
$997$	1.62638e9	0.0519744	0.0259872	+	0.999662i	$0.491727\pi$
$998$	−7.18794e10	−2.28901
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.4		16
3.2	odd	2		177.8.a.a.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.13	✓	16	3.2	odd	2
531.8.a.b.1.4		16	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-14.0604 q^{2} +69.6949 q^{4} -153.219 q^{5} -215.221 q^{7} +819.793 q^{8} +O(q^{10})\)	\(q-14.0604 q^{2} +69.6949 q^{4} -153.219 q^{5} -215.221 q^{7} +819.793 q^{8} +2154.32 q^{10} -7869.22 q^{11} -14239.1 q^{13} +3026.10 q^{14} -20447.6 q^{16} +14439.7 q^{17} +52274.2 q^{19} -10678.6 q^{20} +110644. q^{22} +20917.2 q^{23} -54648.9 q^{25} +200207. q^{26} -14999.8 q^{28} +136874. q^{29} +9325.59 q^{31} +182567. q^{32} -203028. q^{34} +32976.0 q^{35} -525467. q^{37} -734996. q^{38} -125608. q^{40} -197767. q^{41} +410661. q^{43} -548444. q^{44} -294105. q^{46} +946517. q^{47} -777223. q^{49} +768386. q^{50} -992389. q^{52} +1.55829e6 q^{53} +1.20571e6 q^{55} -176437. q^{56} -1.92450e6 q^{58} -205379. q^{59} -659307. q^{61} -131121. q^{62} +50317.0 q^{64} +2.18169e6 q^{65} -2.30296e6 q^{67} +1.00637e6 q^{68} -463656. q^{70} +1.68822e6 q^{71} +2.53442e6 q^{73} +7.38828e6 q^{74} +3.64324e6 q^{76} +1.69362e6 q^{77} -1.26627e6 q^{79} +3.13296e6 q^{80} +2.78068e6 q^{82} -2.22258e6 q^{83} -2.21243e6 q^{85} -5.77406e6 q^{86} -6.45113e6 q^{88} +1.04798e7 q^{89} +3.06455e6 q^{91} +1.45782e6 q^{92} -1.33084e7 q^{94} -8.00940e6 q^{95} +5.41316e6 q^{97} +1.09281e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Introduction

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