LMFDB - Embedded newform 531.8.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-11.4478 q^{2} +3.05173 q^{4} -248.349 q^{5} +1066.24 q^{7} +1430.38 q^{8} +O(q^{10})$	\(q-11.4478 q^{2} +3.05173 q^{4} -248.349 q^{5} +1066.24 q^{7} +1430.38 q^{8} +2843.04 q^{10} +5873.38 q^{11} -9754.49 q^{13} -12206.1 q^{14} -16765.3 q^{16} +23228.7 q^{17} +25314.1 q^{19} -757.892 q^{20} -67237.2 q^{22} -71371.9 q^{23} -16447.9 q^{25} +111667. q^{26} +3253.86 q^{28} -214819. q^{29} +153594. q^{31} +8836.87 q^{32} -265917. q^{34} -264799. q^{35} -104296. q^{37} -289790. q^{38} -355233. q^{40} -210689. q^{41} +536151. q^{43} +17923.9 q^{44} +817050. q^{46} -798199. q^{47} +313320. q^{49} +188292. q^{50} -29768.0 q^{52} -51172.0 q^{53} -1.45865e6 q^{55} +1.52513e6 q^{56} +2.45920e6 q^{58} +205379. q^{59} +1.19901e6 q^{61} -1.75832e6 q^{62} +2.04480e6 q^{64} +2.42251e6 q^{65} +2.40742e6 q^{67} +70887.7 q^{68} +3.03136e6 q^{70} -3.05966e6 q^{71} -4.01021e6 q^{73} +1.19396e6 q^{74} +77251.6 q^{76} +6.26242e6 q^{77} +8.12496e6 q^{79} +4.16364e6 q^{80} +2.41193e6 q^{82} +9.00447e6 q^{83} -5.76882e6 q^{85} -6.13774e6 q^{86} +8.40117e6 q^{88} -667911. q^{89} -1.04006e7 q^{91} -217807. q^{92} +9.13761e6 q^{94} -6.28671e6 q^{95} -852924. q^{97} -3.58682e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) $ 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−11.4478	−1.01185	−0.505925	−	0.862577i	$-0.668849\pi$
$2$	−11.4478	−1.01185	−0.505925	+	0.862577i	$0.668849\pi$
$3$	0	0
$3$	0	0
$4$	3.05173	0.0238416
$5$	−248.349	−0.888519	−0.444260	−	0.895898i	$-0.646533\pi$
$5$	−248.349	−0.888519	−0.444260	+	0.895898i	$0.646533\pi$
$6$	0	0
$7$	1066.24	1.17493	0.587463	−	0.809251i	$-0.300127\pi$
$7$	1066.24	1.17493	0.587463	+	0.809251i	$0.300127\pi$
$8$	1430.38	0.987726
$9$	0	0
$10$	2843.04	0.899049
$11$	5873.38	1.33050	0.665248	−	0.746622i	$-0.268326\pi$
$11$	5873.38	1.33050	0.665248	+	0.746622i	$0.268326\pi$
$12$	0	0
$13$	−9754.49	−1.23141	−0.615705	−	0.787977i	$-0.711129\pi$
$13$	−9754.49	−1.23141	−0.615705	+	0.787977i	$0.711129\pi$
$14$	−12206.1	−1.18885
$15$	0	0
$16$	−16765.3	−1.02327
$17$	23228.7	1.14671	0.573355	−	0.819307i	$-0.305641\pi$
$17$	23228.7	1.14671	0.573355	+	0.819307i	$0.305641\pi$
$18$	0	0
$19$	25314.1	0.846689	0.423345	−	0.905969i	$-0.360856\pi$
$19$	25314.1	0.846689	0.423345	+	0.905969i	$0.360856\pi$
$20$	−757.892	−0.0211837
$21$	0	0
$22$	−67237.2	−1.34626
$23$	−71371.9	−1.22315	−0.611575	−	0.791186i	$-0.709464\pi$
$23$	−71371.9	−1.22315	−0.611575	+	0.791186i	$0.709464\pi$
$24$	0	0
$25$	−16447.9	−0.210534
$26$	111667.	1.24600
$27$	0	0
$28$	3253.86	0.0280121
$29$	−214819.	−1.63561	−0.817804	−	0.575497i	$-0.804809\pi$
$29$	−214819.	−1.63561	−0.817804	+	0.575497i	$0.804809\pi$
$30$	0	0
$31$	153594.	0.925997	0.462999	−	0.886359i	$-0.346774\pi$
$31$	153594.	0.925997	0.462999	+	0.886359i	$0.346774\pi$
$32$	8836.87	0.0476731
$33$	0	0
$34$	−265917.	−1.16030
$35$	−264799.	−1.04395
$36$	0	0
$37$	−104296.	−0.338504	−0.169252	−	0.985573i	$-0.554135\pi$
$37$	−104296.	−0.338504	−0.169252	+	0.985573i	$0.554135\pi$
$38$	−289790.	−0.856723
$39$	0	0
$40$	−355233.	−0.877614
$41$	−210689.	−0.477418	−0.238709	−	0.971091i	$-0.576724\pi$
$41$	−210689.	−0.477418	−0.238709	+	0.971091i	$0.576724\pi$
$42$	0	0
$43$	536151.	1.02837	0.514183	−	0.857681i	$-0.328095\pi$
$43$	536151.	1.02837	0.514183	+	0.857681i	$0.328095\pi$
$44$	17923.9	0.0317212
$45$	0	0
$46$	817050.	1.23765
$47$	−798199.	−1.12142	−0.560711	−	0.828012i	$-0.689472\pi$
$47$	−798199.	−1.12142	−0.560711	+	0.828012i	$0.689472\pi$
$48$	0	0
$49$	313320.	0.380453
$50$	188292.	0.213029
$51$	0	0
$52$	−29768.0	−0.0293588
$53$	−51172.0	−0.0472136	−0.0236068	−	0.999721i	$-0.507515\pi$
$53$	−51172.0	−0.0472136	−0.0236068	+	0.999721i	$0.507515\pi$
$54$	0	0
$55$	−1.45865e6	−1.18217
$56$	1.52513e6	1.16051
$57$	0	0
$58$	2.45920e6	1.65499
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	1.19901e6	0.676347	0.338174	−	0.941084i	$-0.390191\pi$
$61$	1.19901e6	0.676347	0.338174	+	0.941084i	$0.390191\pi$
$62$	−1.75832e6	−0.936971
$63$	0	0
$64$	2.04480e6	0.975035
$65$	2.42251e6	1.09413
$66$	0	0
$67$	2.40742e6	0.977890	0.488945	−	0.872315i	$-0.337382\pi$
$67$	2.40742e6	0.977890	0.488945	+	0.872315i	$0.337382\pi$
$68$	70887.7	0.0273394
$69$	0	0
$70$	3.03136e6	1.05632
$71$	−3.05966e6	−1.01454	−0.507270	−	0.861787i	$-0.669345\pi$
$71$	−3.05966e6	−1.01454	−0.507270	+	0.861787i	$0.669345\pi$
$72$	0	0
$73$	−4.01021e6	−1.20653	−0.603263	−	0.797542i	$-0.706133\pi$
$73$	−4.01021e6	−1.20653	−0.603263	+	0.797542i	$0.706133\pi$
$74$	1.19396e6	0.342515
$75$	0	0
$76$	77251.6	0.0201864
$77$	6.26242e6	1.56324
$78$	0	0
$79$	8.12496e6	1.85407	0.927036	−	0.374973i	$-0.122348\pi$
$79$	8.12496e6	1.85407	0.927036	+	0.374973i	$0.122348\pi$
$80$	4.16364e6	0.909198
$81$	0	0
$82$	2.41193e6	0.483076
$83$	9.00447e6	1.72856	0.864281	−	0.503009i	$-0.167774\pi$
$83$	9.00447e6	1.72856	0.864281	+	0.503009i	$0.167774\pi$
$84$	0	0
$85$	−5.76882e6	−1.01887
$86$	−6.13774e6	−1.04055
$87$	0	0
$88$	8.40117e6	1.31417
$89$	−667911.	−0.100428	−0.0502138	−	0.998738i	$-0.515990\pi$
$89$	−667911.	−0.100428	−0.0502138	+	0.998738i	$0.515990\pi$
$90$	0	0
$91$	−1.04006e7	−1.44682
$92$	−217807.	−0.0291619
$93$	0	0
$94$	9.13761e6	1.13471
$95$	−6.28671e6	−0.752300
$96$	0	0
$97$	−852924.	−0.0948876	−0.0474438	−	0.998874i	$-0.515107\pi$
$97$	−852924.	−0.0948876	−0.0474438	+	0.998874i	$0.515107\pi$
$98$	−3.58682e6	−0.384962
$99$	0	0
$100$	−50194.6	−0.00501946
$101$	−1.79102e7	−1.72972	−0.864862	−	0.502010i	$-0.832594\pi$
$101$	−1.79102e7	−1.72972	−0.864862	+	0.502010i	$0.832594\pi$
$102$	0	0
$103$	−1.40205e7	−1.26425	−0.632124	−	0.774867i	$-0.717817\pi$
$103$	−1.40205e7	−1.26425	−0.632124	+	0.774867i	$0.717817\pi$
$104$	−1.39526e7	−1.21630
$105$	0	0
$106$	585806.	0.0477731
$107$	−1.76515e7	−1.39296	−0.696478	−	0.717578i	$-0.745251\pi$
$107$	−1.76515e7	−1.39296	−0.696478	+	0.717578i	$0.745251\pi$
$108$	0	0
$109$	−1.06129e7	−0.784948	−0.392474	−	0.919763i	$-0.628381\pi$
$109$	−1.06129e7	−0.784948	−0.392474	+	0.919763i	$0.628381\pi$
$110$	1.66983e7	1.19618
$111$	0	0
$112$	−1.78758e7	−1.20227
$113$	6.98937e6	0.455684	0.227842	−	0.973698i	$-0.426833\pi$
$113$	6.98937e6	0.455684	0.227842	+	0.973698i	$0.426833\pi$
$114$	0	0
$115$	1.77251e7	1.08679
$116$	−655568.	−0.0389955
$117$	0	0
$118$	−2.35113e6	−0.131732
$119$	2.47673e7	1.34730
$120$	0	0
$121$	1.50094e7	0.770220
$122$	−1.37260e7	−0.684362
$123$	0	0
$124$	468728.	0.0220773
$125$	2.34871e7	1.07558
$126$	0	0
$127$	3.42835e7	1.48516	0.742578	−	0.669759i	$-0.233603\pi$
$127$	3.42835e7	1.48516	0.742578	+	0.669759i	$0.233603\pi$
$128$	−2.45395e7	−1.03426
$129$	0	0
$130$	−2.77324e7	−1.10710
$131$	5.07996e6	0.197429	0.0987145	−	0.995116i	$-0.468527\pi$
$131$	5.07996e6	0.197429	0.0987145	+	0.995116i	$0.468527\pi$
$132$	0	0
$133$	2.69908e7	0.994798
$134$	−2.75596e7	−0.989479
$135$	0	0
$136$	3.32259e7	1.13264
$137$	2.08509e7	0.692791	0.346395	−	0.938089i	$-0.387406\pi$
$137$	2.08509e7	0.692791	0.346395	+	0.938089i	$0.387406\pi$
$138$	0	0
$139$	−1.05360e7	−0.332755	−0.166377	−	0.986062i	$-0.553207\pi$
$139$	−1.05360e7	−0.332755	−0.166377	+	0.986062i	$0.553207\pi$
$140$	−808093.	−0.0248893
$141$	0	0
$142$	3.50263e7	1.02656
$143$	−5.72918e7	−1.63839
$144$	0	0
$145$	5.33500e7	1.45327
$146$	4.59080e7	1.22082
$147$	0	0
$148$	−318284.	−0.00807047
$149$	9.41271e6	0.233111	0.116555	−	0.993184i	$-0.462815\pi$
$149$	9.41271e6	0.233111	0.116555	+	0.993184i	$0.462815\pi$
$150$	0	0
$151$	5.33544e7	1.26110	0.630552	−	0.776147i	$-0.282829\pi$
$151$	5.33544e7	1.26110	0.630552	+	0.776147i	$0.282829\pi$
$152$	3.62087e7	0.836298
$153$	0	0
$154$	−7.16908e7	−1.58176
$155$	−3.81450e7	−0.822766
$156$	0	0
$157$	4.42301e7	0.912156	0.456078	−	0.889940i	$-0.349254\pi$
$157$	4.42301e7	0.912156	0.456078	+	0.889940i	$0.349254\pi$
$158$	−9.30128e7	−1.87604
$159$	0	0
$160$	−2.19463e6	−0.0423585
$161$	−7.60994e7	−1.43711
$162$	0	0
$163$	3.86640e7	0.699279	0.349640	−	0.936884i	$-0.386304\pi$
$163$	3.86640e7	0.699279	0.349640	+	0.936884i	$0.386304\pi$
$164$	−642966.	−0.0113824
$165$	0	0
$166$	−1.03081e8	−1.74905
$167$	2.51365e6	0.0417636	0.0208818	−	0.999782i	$-0.493353\pi$
$167$	2.51365e6	0.0417636	0.0208818	+	0.999782i	$0.493353\pi$
$168$	0	0
$169$	3.24015e7	0.516371
$170$	6.60402e7	1.03095
$171$	0	0
$172$	1.63619e6	0.0245179
$173$	−1.01333e7	−0.148795	−0.0743975	−	0.997229i	$-0.523703\pi$
$173$	−1.01333e7	−0.148795	−0.0743975	+	0.997229i	$0.523703\pi$
$174$	0	0
$175$	−1.75374e7	−0.247362
$176$	−9.84690e7	−1.36146
$177$	0	0
$178$	7.64610e6	0.101618
$179$	−1.49278e8	−1.94540	−0.972702	−	0.232058i	$-0.925454\pi$
$179$	−1.49278e8	−1.94540	−0.972702	+	0.232058i	$0.925454\pi$
$180$	0	0
$181$	7.66360e7	0.960634	0.480317	−	0.877095i	$-0.340522\pi$
$181$	7.66360e7	0.960634	0.480317	+	0.877095i	$0.340522\pi$
$182$	1.19064e8	1.46396
$183$	0	0
$184$	−1.02089e8	−1.20814
$185$	2.59019e7	0.300767
$186$	0	0
$187$	1.36431e8	1.52569
$188$	−2.43588e6	−0.0267365
$189$	0	0
$190$	7.19689e7	0.761215
$191$	−6.20858e7	−0.644727	−0.322363	−	0.946616i	$-0.604477\pi$
$191$	−6.20858e7	−0.644727	−0.322363	+	0.946616i	$0.604477\pi$
$192$	0	0
$193$	−1.29748e8	−1.29913	−0.649563	−	0.760308i	$-0.725048\pi$
$193$	−1.29748e8	−1.29913	−0.649563	+	0.760308i	$0.725048\pi$
$194$	9.76409e6	0.0960120
$195$	0	0
$196$	956166.	0.00907062
$197$	5.37725e7	0.501105	0.250552	−	0.968103i	$-0.419388\pi$
$197$	5.37725e7	0.501105	0.250552	+	0.968103i	$0.419388\pi$
$198$	0	0
$199$	−1.70742e8	−1.53587	−0.767936	−	0.640527i	$-0.778716\pi$
$199$	−1.70742e8	−1.53587	−0.767936	+	0.640527i	$0.778716\pi$
$200$	−2.35268e7	−0.207950
$201$	0	0
$202$	2.05033e8	1.75022
$203$	−2.29048e8	−1.92172
$204$	0	0
$205$	5.23244e7	0.424195
$206$	1.60503e8	1.27923
$207$	0	0
$208$	1.63537e8	1.26007
$209$	1.48679e8	1.12652
$210$	0	0
$211$	2.39474e8	1.75497	0.877485	−	0.479603i	$-0.159219\pi$
$211$	2.39474e8	1.75497	0.877485	+	0.479603i	$0.159219\pi$
$212$	−156163.	−0.00112565
$213$	0	0
$214$	2.02070e8	1.40946
$215$	−1.33152e8	−0.913723
$216$	0	0
$217$	1.63768e8	1.08798
$218$	1.21494e8	0.794250
$219$	0	0
$220$	−4.45139e6	−0.0281849
$221$	−2.26584e8	−1.41207
$222$	0	0
$223$	−8.96080e6	−0.0541103	−0.0270551	−	0.999634i	$-0.508613\pi$
$223$	−8.96080e6	−0.0541103	−0.0270551	+	0.999634i	$0.508613\pi$
$224$	9.42221e6	0.0560124
$225$	0	0
$226$	−8.00128e7	−0.461084
$227$	−1.08726e7	−0.0616938	−0.0308469	−	0.999524i	$-0.509820\pi$
$227$	−1.08726e7	−0.0616938	−0.0308469	+	0.999524i	$0.509820\pi$
$228$	0	0
$229$	−1.97522e8	−1.08690	−0.543452	−	0.839440i	$-0.682883\pi$
$229$	−1.97522e8	−1.08690	−0.543452	+	0.839440i	$0.682883\pi$
$230$	−2.02913e8	−1.09967
$231$	0	0
$232$	−3.07273e8	−1.61553
$233$	−1.17148e8	−0.606720	−0.303360	−	0.952876i	$-0.598108\pi$
$233$	−1.17148e8	−0.606720	−0.303360	+	0.952876i	$0.598108\pi$
$234$	0	0
$235$	1.98232e8	0.996404
$236$	626760.	0.00310391
$237$	0	0
$238$	−2.83531e8	−1.36327
$239$	−8.30954e7	−0.393717	−0.196858	−	0.980432i	$-0.563074\pi$
$239$	−8.30954e7	−0.393717	−0.196858	+	0.980432i	$0.563074\pi$
$240$	0	0
$241$	−1.15750e8	−0.532675	−0.266338	−	0.963880i	$-0.585814\pi$
$241$	−1.15750e8	−0.532675	−0.266338	+	0.963880i	$0.585814\pi$
$242$	−1.71824e8	−0.779347
$243$	0	0
$244$	3.65906e6	0.0161252
$245$	−7.78125e7	−0.338040
$246$	0	0
$247$	−2.46926e8	−1.04262
$248$	2.19699e8	0.914632
$249$	0	0
$250$	−2.68875e8	−1.08833
$251$	6.57578e6	0.0262476	0.0131238	−	0.999914i	$-0.495822\pi$
$251$	6.57578e6	0.0262476	0.0131238	+	0.999914i	$0.495822\pi$
$252$	0	0
$253$	−4.19194e8	−1.62740
$254$	−3.92470e8	−1.50276
$255$	0	0
$256$	1.91890e7	0.0714845
$257$	1.93111e8	0.709646	0.354823	−	0.934933i	$-0.384541\pi$
$257$	1.93111e8	0.709646	0.354823	+	0.934933i	$0.384541\pi$
$258$	0	0
$259$	−1.11205e8	−0.397717
$260$	7.39285e6	0.0260859
$261$	0	0
$262$	−5.81543e7	−0.199769
$263$	−2.30313e8	−0.780682	−0.390341	−	0.920670i	$-0.627643\pi$
$263$	−2.30313e8	−0.780682	−0.390341	+	0.920670i	$0.627643\pi$
$264$	0	0
$265$	1.27085e7	0.0419502
$266$	−3.08985e8	−1.00659
$267$	0	0
$268$	7.34679e6	0.0233145
$269$	−1.30078e8	−0.407448	−0.203724	−	0.979028i	$-0.565305\pi$
$269$	−1.30078e8	−0.407448	−0.203724	+	0.979028i	$0.565305\pi$
$270$	0	0
$271$	2.28844e8	0.698469	0.349235	−	0.937035i	$-0.386442\pi$
$271$	2.28844e8	0.698469	0.349235	+	0.937035i	$0.386442\pi$
$272$	−3.89437e8	−1.17340
$273$	0	0
$274$	−2.38696e8	−0.701001
$275$	−9.66050e7	−0.280114
$276$	0	0
$277$	−5.75948e8	−1.62819	−0.814093	−	0.580734i	$-0.802766\pi$
$277$	−5.75948e8	−1.62819	−0.814093	+	0.580734i	$0.802766\pi$
$278$	1.20614e8	0.336698
$279$	0	0
$280$	−3.78763e8	−1.03113
$281$	−3.98213e8	−1.07064	−0.535319	−	0.844650i	$-0.679809\pi$
$281$	−3.98213e8	−1.07064	−0.535319	+	0.844650i	$0.679809\pi$
$282$	0	0
$283$	−6.07354e8	−1.59290	−0.796451	−	0.604703i	$-0.793292\pi$
$283$	−6.07354e8	−1.59290	−0.796451	+	0.604703i	$0.793292\pi$
$284$	−9.33724e6	−0.0241882
$285$	0	0
$286$	6.55864e8	1.65780
$287$	−2.24645e8	−0.560932
$288$	0	0
$289$	1.29235e8	0.314946
$290$	−6.10739e8	−1.47049
$291$	0	0
$292$	−1.22381e7	−0.0287655
$293$	6.30951e8	1.46541	0.732705	−	0.680547i	$-0.238258\pi$
$293$	6.30951e8	1.46541	0.732705	+	0.680547i	$0.238258\pi$
$294$	0	0
$295$	−5.10056e7	−0.115675
$296$	−1.49184e8	−0.334349
$297$	0	0
$298$	−1.07755e8	−0.235873
$299$	6.96196e8	1.50620
$300$	0	0
$301$	5.71664e8	1.20825
$302$	−6.10790e8	−1.27605
$303$	0	0
$304$	−4.24398e8	−0.866395
$305$	−2.97773e8	−0.600948
$306$	0	0
$307$	−5.01869e8	−0.989933	−0.494966	−	0.868912i	$-0.664820\pi$
$307$	−5.01869e8	−0.989933	−0.494966	+	0.868912i	$0.664820\pi$
$308$	1.91112e7	0.0372701
$309$	0	0
$310$	4.36675e8	0.832516
$311$	−3.11092e8	−0.586446	−0.293223	−	0.956044i	$-0.594728\pi$
$311$	−3.11092e8	−0.586446	−0.293223	+	0.956044i	$0.594728\pi$
$312$	0	0
$313$	−2.26588e8	−0.417669	−0.208834	−	0.977951i	$-0.566967\pi$
$313$	−2.26588e8	−0.417669	−0.208834	+	0.977951i	$0.566967\pi$
$314$	−5.06336e8	−0.922965
$315$	0	0
$316$	2.47952e7	0.0442040
$317$	−4.69611e8	−0.828001	−0.414000	−	0.910277i	$-0.635869\pi$
$317$	−4.69611e8	−0.828001	−0.414000	+	0.910277i	$0.635869\pi$
$318$	0	0
$319$	−1.26171e9	−2.17617
$320$	−5.07823e8	−0.866337
$321$	0	0
$322$	8.71170e8	1.45414
$323$	5.88013e8	0.970908
$324$	0	0
$325$	1.60441e8	0.259253
$326$	−4.42618e8	−0.707566
$327$	0	0
$328$	−3.01366e8	−0.471559
$329$	−8.51070e8	−1.31759
$330$	0	0
$331$	1.05164e9	1.59394	0.796968	−	0.604021i	$-0.206436\pi$
$331$	1.05164e9	1.59394	0.796968	+	0.604021i	$0.206436\pi$
$332$	2.74792e7	0.0412117
$333$	0	0
$334$	−2.87757e7	−0.0422585
$335$	−5.97880e8	−0.868874
$336$	0	0
$337$	1.53200e8	0.218049	0.109025	−	0.994039i	$-0.465227\pi$
$337$	1.53200e8	0.218049	0.109025	+	0.994039i	$0.465227\pi$
$338$	−3.70925e8	−0.522490
$339$	0	0
$340$	−1.76049e7	−0.0242916
$341$	9.02118e8	1.23204
$342$	0	0
$343$	−5.44019e8	−0.727922
$344$	7.66900e8	1.01574
$345$	0	0
$346$	1.16003e8	0.150558
$347$	1.35085e8	0.173561	0.0867807	−	0.996227i	$-0.472342\pi$
$347$	1.35085e8	0.173561	0.0867807	+	0.996227i	$0.472342\pi$
$348$	0	0
$349$	−4.38527e7	−0.0552214	−0.0276107	−	0.999619i	$-0.508790\pi$
$349$	−4.38527e7	−0.0552214	−0.0276107	+	0.999619i	$0.508790\pi$
$350$	2.00764e8	0.250293
$351$	0	0
$352$	5.19023e7	0.0634289
$353$	7.46292e8	0.903020	0.451510	−	0.892266i	$-0.350886\pi$
$353$	7.46292e8	0.903020	0.451510	+	0.892266i	$0.350886\pi$
$354$	0	0
$355$	7.59862e8	0.901437
$356$	−2.03828e6	−0.00239436
$357$	0	0
$358$	1.70890e9	1.96846
$359$	−3.50916e8	−0.400287	−0.200144	−	0.979767i	$-0.564141\pi$
$359$	−3.50916e8	−0.400287	−0.200144	+	0.979767i	$0.564141\pi$
$360$	0	0
$361$	−2.53070e8	−0.283117
$362$	−8.77312e8	−0.972018
$363$	0	0
$364$	−3.17398e7	−0.0344944
$365$	9.95930e8	1.07202
$366$	0	0
$367$	1.26801e9	1.33903	0.669515	−	0.742799i	$-0.266502\pi$
$367$	1.26801e9	1.33903	0.669515	+	0.742799i	$0.266502\pi$
$368$	1.19657e9	1.25162
$369$	0	0
$370$	−2.96519e8	−0.304331
$371$	−5.45615e7	−0.0554725
$372$	0	0
$373$	−4.91443e8	−0.490334	−0.245167	−	0.969481i	$-0.578843\pi$
$373$	−4.91443e8	−0.490334	−0.245167	+	0.969481i	$0.578843\pi$
$374$	−1.56183e9	−1.54377
$375$	0	0
$376$	−1.14173e9	−1.10766
$377$	2.09545e9	2.01410
$378$	0	0
$379$	−1.56154e9	−1.47339	−0.736693	−	0.676228i	$-0.763614\pi$
$379$	−1.56154e9	−1.47339	−0.736693	+	0.676228i	$0.763614\pi$
$380$	−1.91853e7	−0.0179360
$381$	0	0
$382$	7.10745e8	0.652367
$383$	−1.14067e9	−1.03745	−0.518723	−	0.854942i	$-0.673593\pi$
$383$	−1.14067e9	−1.03745	−0.518723	+	0.854942i	$0.673593\pi$
$384$	0	0
$385$	−1.55526e9	−1.38896
$386$	1.48533e9	1.31452
$387$	0	0
$388$	−2.60289e6	−0.00226227
$389$	1.32750e9	1.14343	0.571717	−	0.820451i	$-0.306277\pi$
$389$	1.32750e9	1.14343	0.571717	+	0.820451i	$0.306277\pi$
$390$	0	0
$391$	−1.65788e9	−1.40260
$392$	4.48166e8	0.375784
$393$	0	0
$394$	−6.15576e8	−0.507043
$395$	−2.01782e9	−1.64738
$396$	0	0
$397$	−4.99363e8	−0.400544	−0.200272	−	0.979740i	$-0.564183\pi$
$397$	−4.99363e8	−0.400544	−0.200272	+	0.979740i	$0.564183\pi$
$398$	1.95462e9	1.55407
$399$	0	0
$400$	2.75755e8	0.215433
$401$	−1.52012e9	−1.17726	−0.588630	−	0.808403i	$-0.700332\pi$
$401$	−1.52012e9	−1.17726	−0.588630	+	0.808403i	$0.700332\pi$
$402$	0	0
$403$	−1.49824e9	−1.14028
$404$	−5.46572e7	−0.0412394
$405$	0	0
$406$	2.62209e9	1.94449
$407$	−6.12573e8	−0.450378
$408$	0	0
$409$	1.45554e9	1.05194	0.525972	−	0.850502i	$-0.323702\pi$
$409$	1.45554e9	1.05194	0.525972	+	0.850502i	$0.323702\pi$
$410$	−5.98999e8	−0.429222
$411$	0	0
$412$	−4.27866e7	−0.0301417
$413$	2.18983e8	0.152962
$414$	0	0
$415$	−2.23625e9	−1.53586
$416$	−8.61992e7	−0.0587052
$417$	0	0
$418$	−1.70205e9	−1.13987
$419$	−2.27897e9	−1.51353	−0.756763	−	0.653690i	$-0.773220\pi$
$419$	−2.27897e9	−1.51353	−0.756763	+	0.653690i	$0.773220\pi$
$420$	0	0
$421$	2.32187e9	1.51653	0.758265	−	0.651946i	$-0.226047\pi$
$421$	2.32187e9	1.51653	0.758265	+	0.651946i	$0.226047\pi$
$422$	−2.74145e9	−1.77577
$423$	0	0
$424$	−7.31955e7	−0.0466341
$425$	−3.82065e8	−0.241421
$426$	0	0
$427$	1.27843e9	0.794659
$428$	−5.38674e7	−0.0332103
$429$	0	0
$430$	1.52430e9	0.924551
$431$	−2.19733e9	−1.32198	−0.660991	−	0.750394i	$-0.729864\pi$
$431$	−2.19733e9	−1.32198	−0.660991	+	0.750394i	$0.729864\pi$
$432$	0	0
$433$	6.23438e8	0.369050	0.184525	−	0.982828i	$-0.440925\pi$
$433$	6.23438e8	0.369050	0.184525	+	0.982828i	$0.440925\pi$
$434$	−1.87478e9	−1.10087
$435$	0	0
$436$	−3.23876e7	−0.0187144
$437$	−1.80671e9	−1.03563
$438$	0	0
$439$	1.99502e9	1.12544	0.562719	−	0.826648i	$-0.309755\pi$
$439$	1.99502e9	1.12544	0.562719	+	0.826648i	$0.309755\pi$
$440$	−2.08642e9	−1.16766
$441$	0	0
$442$	2.59389e9	1.42881
$443$	−1.12206e9	−0.613199	−0.306600	−	0.951839i	$-0.599191\pi$
$443$	−1.12206e9	−0.613199	−0.306600	+	0.951839i	$0.599191\pi$
$444$	0	0
$445$	1.65875e8	0.0892319
$446$	1.02581e8	0.0547515
$447$	0	0
$448$	2.18024e9	1.14560
$449$	3.82800e9	1.99577	0.997883	−	0.0650332i	$-0.0207153\pi$
$449$	3.82800e9	1.99577	0.997883	+	0.0650332i	$0.0207153\pi$
$450$	0	0
$451$	−1.23746e9	−0.635203
$452$	2.13296e7	0.0108642
$453$	0	0
$454$	1.24467e8	0.0624249
$455$	2.58298e9	1.28552
$456$	0	0
$457$	2.06705e9	1.01308	0.506540	−	0.862217i	$-0.330924\pi$
$457$	2.06705e9	1.01308	0.506540	+	0.862217i	$0.330924\pi$
$458$	2.26119e9	1.09979
$459$	0	0
$460$	5.40922e7	0.0259109
$461$	−1.10058e9	−0.523202	−0.261601	−	0.965176i	$-0.584250\pi$
$461$	−1.10058e9	−0.523202	−0.261601	+	0.965176i	$0.584250\pi$
$462$	0	0
$463$	1.49291e8	0.0699038	0.0349519	−	0.999389i	$-0.488872\pi$
$463$	1.49291e8	0.0699038	0.0349519	+	0.999389i	$0.488872\pi$
$464$	3.60150e9	1.67367
$465$	0	0
$466$	1.34108e9	0.613910
$467$	3.94611e8	0.179292	0.0896459	−	0.995974i	$-0.471426\pi$
$467$	3.94611e8	0.179292	0.0896459	+	0.995974i	$0.471426\pi$
$468$	0	0
$469$	2.56688e9	1.14895
$470$	−2.26931e9	−1.00821
$471$	0	0
$472$	2.93770e8	0.128591
$473$	3.14902e9	1.36824
$474$	0	0
$475$	−4.16364e8	−0.178257
$476$	7.55831e7	0.0321218
$477$	0	0
$478$	9.51258e8	0.398383
$479$	1.15689e8	0.0480972	0.0240486	−	0.999711i	$-0.492344\pi$
$479$	1.15689e8	0.0480972	0.0240486	+	0.999711i	$0.492344\pi$
$480$	0	0
$481$	1.01736e9	0.416837
$482$	1.32508e9	0.538988
$483$	0	0
$484$	4.58046e7	0.0183633
$485$	2.11823e8	0.0843094
$486$	0	0
$487$	−8.74534e8	−0.343103	−0.171552	−	0.985175i	$-0.554878\pi$
$487$	−8.74534e8	−0.343103	−0.171552	+	0.985175i	$0.554878\pi$
$488$	1.71505e9	0.668046
$489$	0	0
$490$	8.90781e8	0.342046
$491$	8.49527e8	0.323886	0.161943	−	0.986800i	$-0.448224\pi$
$491$	8.49527e8	0.323886	0.161943	+	0.986800i	$0.448224\pi$
$492$	0	0
$493$	−4.98996e9	−1.87557
$494$	2.82675e9	1.05498
$495$	0	0
$496$	−2.57506e9	−0.947548
$497$	−3.26232e9	−1.19201
$498$	0	0
$499$	−2.05277e9	−0.739584	−0.369792	−	0.929115i	$-0.620571\pi$
$499$	−2.05277e9	−0.739584	−0.369792	+	0.929115i	$0.620571\pi$
$500$	7.16761e7	0.0256436
$501$	0	0
$502$	−7.52781e7	−0.0265586
$503$	−2.40965e8	−0.0844239	−0.0422120	−	0.999109i	$-0.513440\pi$
$503$	−2.40965e8	−0.0844239	−0.0422120	+	0.999109i	$0.513440\pi$
$504$	0	0
$505$	4.44798e9	1.53689
$506$	4.79884e9	1.64668
$507$	0	0
$508$	1.04624e8	0.0354085
$509$	−4.25842e9	−1.43132	−0.715660	−	0.698449i	$-0.753874\pi$
$509$	−4.25842e9	−1.43132	−0.715660	+	0.698449i	$0.753874\pi$
$510$	0	0
$511$	−4.27583e9	−1.41758
$512$	2.92139e9	0.961931
$513$	0	0
$514$	−2.21070e9	−0.718056
$515$	3.48196e9	1.12331
$516$	0	0
$517$	−4.68813e9	−1.49205
$518$	1.27305e9	0.402430
$519$	0	0
$520$	3.46512e9	1.08070
$521$	−9.31078e8	−0.288439	−0.144219	−	0.989546i	$-0.546067\pi$
$521$	−9.31078e8	−0.288439	−0.144219	+	0.989546i	$0.546067\pi$
$522$	0	0
$523$	−4.81473e9	−1.47169	−0.735844	−	0.677151i	$-0.763214\pi$
$523$	−4.81473e9	−1.47169	−0.735844	+	0.677151i	$0.763214\pi$
$524$	1.55027e7	0.00470703
$525$	0	0
$526$	2.63658e9	0.789934
$527$	3.56780e9	1.06185
$528$	0	0
$529$	1.68912e9	0.496097
$530$	−1.45484e8	−0.0424473
$531$	0	0
$532$	8.23685e7	0.0237176
$533$	2.05517e9	0.587898
$534$	0	0
$535$	4.38372e9	1.23767
$536$	3.44353e9	0.965888
$537$	0	0
$538$	1.48911e9	0.412276
$539$	1.84025e9	0.506192
$540$	0	0
$541$	5.71741e9	1.55242	0.776209	−	0.630476i	$-0.217140\pi$
$541$	5.71741e9	1.55242	0.776209	+	0.630476i	$0.217140\pi$
$542$	−2.61976e9	−0.706747
$543$	0	0
$544$	2.05269e8	0.0546673
$545$	2.63570e9	0.697441
$546$	0	0
$547$	−3.34146e7	−0.00872932	−0.00436466	−	0.999990i	$-0.501389\pi$
$547$	−3.34146e7	−0.00872932	−0.00436466	+	0.999990i	$0.501389\pi$
$548$	6.36311e7	0.0165172
$549$	0	0
$550$	1.10591e9	0.283434
$551$	−5.43794e9	−1.38485
$552$	0	0
$553$	8.66314e9	2.17840
$554$	6.59333e9	1.64748
$555$	0	0
$556$	−3.21530e7	−0.00793341
$557$	−7.64789e9	−1.87520	−0.937601	−	0.347712i	$-0.886959\pi$
$557$	−7.64789e9	−1.87520	−0.937601	+	0.347712i	$0.886959\pi$
$558$	0	0
$559$	−5.22988e9	−1.26634
$560$	4.43943e9	1.06824
$561$	0	0
$562$	4.55865e9	1.08333
$563$	1.29632e9	0.306148	0.153074	−	0.988215i	$-0.451083\pi$
$563$	1.29632e9	0.306148	0.153074	+	0.988215i	$0.451083\pi$
$564$	0	0
$565$	−1.73580e9	−0.404884
$566$	6.95285e9	1.61178
$567$	0	0
$568$	−4.37648e9	−1.00209
$569$	−6.14994e8	−0.139952	−0.0699758	−	0.997549i	$-0.522292\pi$
$569$	−6.14994e8	−0.139952	−0.0699758	+	0.997549i	$0.522292\pi$
$570$	0	0
$571$	−4.67486e9	−1.05085	−0.525427	−	0.850839i	$-0.676094\pi$
$571$	−4.67486e9	−1.05085	−0.525427	+	0.850839i	$0.676094\pi$
$572$	−1.74839e8	−0.0390618
$573$	0	0
$574$	2.57169e9	0.567579
$575$	1.17392e9	0.257514
$576$	0	0
$577$	−4.50172e9	−0.975581	−0.487790	−	0.872961i	$-0.662197\pi$
$577$	−4.50172e9	−0.975581	−0.487790	+	0.872961i	$0.662197\pi$
$578$	−1.47945e9	−0.318678
$579$	0	0
$580$	1.62809e8	0.0346483
$581$	9.60091e9	2.03093
$582$	0	0
$583$	−3.00553e8	−0.0628175
$584$	−5.73612e9	−1.19172
$585$	0	0
$586$	−7.22299e9	−1.48278
$587$	5.85435e8	0.119466	0.0597331	−	0.998214i	$-0.480975\pi$
$587$	5.85435e8	0.119466	0.0597331	+	0.998214i	$0.480975\pi$
$588$	0	0
$589$	3.88810e9	0.784032
$590$	5.83901e8	0.117046
$591$	0	0
$592$	1.74856e9	0.346382
$593$	2.83176e9	0.557655	0.278827	−	0.960341i	$-0.410054\pi$
$593$	2.83176e9	0.557655	0.278827	+	0.960341i	$0.410054\pi$
$594$	0	0
$595$	−6.15093e9	−1.19710
$596$	2.87250e7	0.00555774
$597$	0	0
$598$	−7.96990e9	−1.52405
$599$	−9.58087e9	−1.82142	−0.910712	−	0.413041i	$-0.864467\pi$
$599$	−9.58087e9	−1.82142	−0.910712	+	0.413041i	$0.864467\pi$
$600$	0	0
$601$	9.28624e9	1.74493	0.872467	−	0.488673i	$-0.162519\pi$
$601$	9.28624e9	1.74493	0.872467	+	0.488673i	$0.162519\pi$
$602$	−6.54429e9	−1.22257
$603$	0	0
$604$	1.62823e8	0.0300668
$605$	−3.72757e9	−0.684355
$606$	0	0
$607$	−9.57911e9	−1.73846	−0.869230	−	0.494408i	$-0.835385\pi$
$607$	−9.57911e9	−1.73846	−0.869230	+	0.494408i	$0.835385\pi$
$608$	2.23697e8	0.0403643
$609$	0	0
$610$	3.40885e9	0.608069
$611$	7.78602e9	1.38093
$612$	0	0
$613$	−6.04849e9	−1.06056	−0.530280	−	0.847822i	$-0.677913\pi$
$613$	−6.04849e9	−1.06056	−0.530280	+	0.847822i	$0.677913\pi$
$614$	5.74528e9	1.00166
$615$	0	0
$616$	8.95764e9	1.54405
$617$	7.35409e9	1.26046	0.630232	−	0.776407i	$-0.282960\pi$
$617$	7.35409e9	1.26046	0.630232	+	0.776407i	$0.282960\pi$
$618$	0	0
$619$	2.47023e9	0.418620	0.209310	−	0.977849i	$-0.432878\pi$
$619$	2.47023e9	0.418620	0.209310	+	0.977849i	$0.432878\pi$
$620$	−1.16408e8	−0.0196161
$621$	0	0
$622$	3.56132e9	0.593396
$623$	−7.12151e8	−0.117995
$624$	0	0
$625$	−4.54799e9	−0.745142
$626$	2.59393e9	0.422618
$627$	0	0
$628$	1.34978e8	0.0217473
$629$	−2.42267e9	−0.388166
$630$	0	0
$631$	8.10020e9	1.28349	0.641746	−	0.766917i	$-0.278210\pi$
$631$	8.10020e9	1.28349	0.641746	+	0.766917i	$0.278210\pi$
$632$	1.16218e10	1.83132
$633$	0	0
$634$	5.37600e9	0.837813
$635$	−8.51426e9	−1.31959
$636$	0	0
$637$	−3.05627e9	−0.468494
$638$	1.44438e10	2.20196
$639$	0	0
$640$	6.09435e9	0.918963
$641$	1.99053e9	0.298515	0.149258	−	0.988798i	$-0.452312\pi$
$641$	1.99053e9	0.298515	0.149258	+	0.988798i	$0.452312\pi$
$642$	0	0
$643$	−1.08481e10	−1.60922	−0.804608	−	0.593807i	$-0.797624\pi$
$643$	−1.08481e10	−1.60922	−0.804608	+	0.593807i	$0.797624\pi$
$644$	−2.32235e8	−0.0342631
$645$	0	0
$646$	−6.73145e9	−0.982414
$647$	−1.50715e9	−0.218772	−0.109386	−	0.993999i	$-0.534888\pi$
$647$	−1.50715e9	−0.218772	−0.109386	+	0.993999i	$0.534888\pi$
$648$	0	0
$649$	1.20627e9	0.173216
$650$	−1.83670e9	−0.262326
$651$	0	0
$652$	1.17992e8	0.0166719
$653$	1.60880e9	0.226103	0.113052	−	0.993589i	$-0.463937\pi$
$653$	1.60880e9	0.226103	0.113052	+	0.993589i	$0.463937\pi$
$654$	0	0
$655$	−1.26160e9	−0.175419
$656$	3.53227e9	0.488529
$657$	0	0
$658$	9.74286e9	1.33320
$659$	−1.03783e10	−1.41263	−0.706316	−	0.707897i	$-0.749644\pi$
$659$	−1.03783e10	−1.41263	−0.706316	+	0.707897i	$0.749644\pi$
$660$	0	0
$661$	−1.21282e10	−1.63340	−0.816698	−	0.577065i	$-0.804198\pi$
$661$	−1.21282e10	−1.63340	−0.816698	+	0.577065i	$0.804198\pi$
$662$	−1.20390e10	−1.61283
$663$	0	0
$664$	1.28798e10	1.70735
$665$	−6.70313e9	−0.883897
$666$	0	0
$667$	1.53320e10	2.00060
$668$	7.67098e6	0.000995710 0
$669$	0	0
$670$	6.84440e9	0.879171
$671$	7.04226e9	0.899877
$672$	0	0
$673$	8.64750e8	0.109355	0.0546774	−	0.998504i	$-0.482587\pi$
$673$	8.64750e8	0.109355	0.0546774	+	0.998504i	$0.482587\pi$
$674$	−1.75380e9	−0.220633
$675$	0	0
$676$	9.88805e7	0.0123111
$677$	1.49687e10	1.85406	0.927032	−	0.374983i	$-0.122351\pi$
$677$	1.49687e10	1.85406	0.927032	+	0.374983i	$0.122351\pi$
$678$	0	0
$679$	−9.09420e8	−0.111486
$680$	−8.25161e9	−1.00637
$681$	0	0
$682$	−1.03273e10	−1.24664
$683$	1.62541e9	0.195204	0.0976021	−	0.995226i	$-0.468883\pi$
$683$	1.62541e9	0.195204	0.0976021	+	0.995226i	$0.468883\pi$
$684$	0	0
$685$	−5.17828e9	−0.615558
$686$	6.22781e9	0.736548
$687$	0	0
$688$	−8.98874e9	−1.05230
$689$	4.99157e8	0.0581393
$690$	0	0
$691$	−2.95082e9	−0.340228	−0.170114	−	0.985424i	$-0.554414\pi$
$691$	−2.95082e9	−0.340228	−0.170114	+	0.985424i	$0.554414\pi$
$692$	−3.09240e7	−0.00354751
$693$	0	0
$694$	−1.54642e9	−0.175618
$695$	2.61660e9	0.295659
$696$	0	0
$697$	−4.89404e9	−0.547461
$698$	5.02016e8	0.0558758
$699$	0	0
$700$	−5.35194e7	−0.00589750
$701$	8.14206e9	0.892732	0.446366	−	0.894851i	$-0.352718\pi$
$701$	8.14206e9	0.892732	0.446366	+	0.894851i	$0.352718\pi$
$702$	0	0
$703$	−2.64017e9	−0.286608
$704$	1.20099e10	1.29728
$705$	0	0
$706$	−8.54339e9	−0.913721
$707$	−1.90966e10	−2.03230
$708$	0	0
$709$	−2.09539e9	−0.220802	−0.110401	−	0.993887i	$-0.535213\pi$
$709$	−2.09539e9	−0.220802	−0.110401	+	0.993887i	$0.535213\pi$
$710$	−8.69874e9	−0.912120
$711$	0	0
$712$	−9.55366e8	−0.0991951
$713$	−1.09623e10	−1.13263
$714$	0	0
$715$	1.42283e10	1.45574
$716$	−4.55555e8	−0.0463816
$717$	0	0
$718$	4.01720e9	0.405031
$719$	1.55761e10	1.56281	0.781406	−	0.624023i	$-0.214503\pi$
$719$	1.55761e10	1.56281	0.781406	+	0.624023i	$0.214503\pi$
$720$	0	0
$721$	−1.49491e10	−1.48540
$722$	2.89709e9	0.286472
$723$	0	0
$724$	2.33872e8	0.0229031
$725$	3.53333e9	0.344351
$726$	0	0
$727$	−4.43489e9	−0.428067	−0.214034	−	0.976826i	$-0.568660\pi$
$727$	−4.43489e9	−0.428067	−0.214034	+	0.976826i	$0.568660\pi$
$728$	−1.48768e10	−1.42906
$729$	0	0
$730$	−1.14012e10	−1.08473
$731$	1.24541e10	1.17924
$732$	0	0
$733$	−1.22887e10	−1.15250	−0.576250	−	0.817274i	$-0.695484\pi$
$733$	−1.22887e10	−1.15250	−0.576250	+	0.817274i	$0.695484\pi$
$734$	−1.45159e10	−1.35490
$735$	0	0
$736$	−6.30704e8	−0.0583114
$737$	1.41397e10	1.30108
$738$	0	0
$739$	−5.31950e9	−0.484859	−0.242429	−	0.970169i	$-0.577944\pi$
$739$	−5.31950e9	−0.484859	−0.242429	+	0.970169i	$0.577944\pi$
$740$	7.90455e7	0.00717077
$741$	0	0
$742$	6.24609e8	0.0561299
$743$	1.43754e10	1.28575	0.642877	−	0.765970i	$-0.277741\pi$
$743$	1.43754e10	1.28575	0.642877	+	0.765970i	$0.277741\pi$
$744$	0	0
$745$	−2.33763e9	−0.207124
$746$	5.62593e9	0.496145
$747$	0	0
$748$	4.16350e8	0.0363750
$749$	−1.88207e10	−1.63662
$750$	0	0
$751$	−9.41966e9	−0.811513	−0.405756	−	0.913981i	$-0.632992\pi$
$751$	−9.41966e9	−0.811513	−0.405756	+	0.913981i	$0.632992\pi$
$752$	1.33821e10	1.14752
$753$	0	0
$754$	−2.39882e10	−2.03797
$755$	−1.32505e10	−1.12052
$756$	0	0
$757$	1.47359e10	1.23464	0.617321	−	0.786711i	$-0.288218\pi$
$757$	1.47359e10	1.23464	0.617321	+	0.786711i	$0.288218\pi$
$758$	1.78762e10	1.49085
$759$	0	0
$760$	−8.99239e9	−0.743066
$761$	2.03933e10	1.67742	0.838709	−	0.544580i	$-0.183311\pi$
$761$	2.03933e10	1.67742	0.838709	+	0.544580i	$0.183311\pi$
$762$	0	0
$763$	−1.13159e10	−0.922257
$764$	−1.89469e8	−0.0153713
$765$	0	0
$766$	1.30582e10	1.04974
$767$	−2.00337e9	−0.160316
$768$	0	0
$769$	−2.70875e9	−0.214796	−0.107398	−	0.994216i	$-0.534252\pi$
$769$	−2.70875e9	−0.214796	−0.107398	+	0.994216i	$0.534252\pi$
$770$	1.78043e10	1.40543
$771$	0	0
$772$	−3.95957e8	−0.0309733
$773$	−1.87226e10	−1.45793	−0.728967	−	0.684548i	$-0.759999\pi$
$773$	−1.87226e10	−1.45793	−0.728967	+	0.684548i	$0.759999\pi$
$774$	0	0
$775$	−2.52631e9	−0.194954
$776$	−1.22001e9	−0.0937230
$777$	0	0
$778$	−1.51969e10	−1.15698
$779$	−5.33340e9	−0.404225
$780$	0	0
$781$	−1.79705e10	−1.34984
$782$	1.89790e10	1.41922
$783$	0	0
$784$	−5.25290e9	−0.389308
$785$	−1.09845e10	−0.810468
$786$	0	0
$787$	2.19811e10	1.60745	0.803726	−	0.595000i	$-0.202848\pi$
$787$	2.19811e10	1.60745	0.803726	+	0.595000i	$0.202848\pi$
$788$	1.64099e8	0.0119471
$789$	0	0
$790$	2.30996e10	1.66690
$791$	7.45233e9	0.535395
$792$	0	0
$793$	−1.16958e10	−0.832861
$794$	5.71660e9	0.405290
$795$	0	0
$796$	−5.21058e8	−0.0366176
$797$	−1.48772e10	−1.04092	−0.520459	−	0.853886i	$-0.674239\pi$
$797$	−1.48772e10	−1.04092	−0.520459	+	0.853886i	$0.674239\pi$
$798$	0	0
$799$	−1.85411e10	−1.28595
$800$	−1.45348e8	−0.0100368
$801$	0	0
$802$	1.74020e10	1.19121
$803$	−2.35535e10	−1.60528
$804$	0	0
$805$	1.88992e10	1.27690
$806$	1.71515e10	1.15380
$807$	0	0
$808$	−2.56185e10	−1.70849
$809$	−1.26415e10	−0.839419	−0.419709	−	0.907659i	$-0.637868\pi$
$809$	−1.26415e10	−0.839419	−0.419709	+	0.907659i	$0.637868\pi$
$810$	0	0
$811$	1.80433e10	1.18780	0.593899	−	0.804540i	$-0.297588\pi$
$811$	1.80433e10	1.18780	0.593899	+	0.804540i	$0.297588\pi$
$812$	−6.98991e8	−0.0458169
$813$	0	0
$814$	7.01260e9	0.455715
$815$	−9.60216e9	−0.621323
$816$	0	0
$817$	1.35722e10	0.870706
$818$	−1.66627e10	−1.06441
$819$	0	0
$820$	1.59680e8	0.0101135
$821$	5.97739e8	0.0376973	0.0188487	−	0.999822i	$-0.494000\pi$
$821$	5.97739e8	0.0376973	0.0188487	+	0.999822i	$0.494000\pi$
$822$	0	0
$823$	−1.68006e10	−1.05057	−0.525287	−	0.850925i	$-0.676042\pi$
$823$	−1.68006e10	−1.05057	−0.525287	+	0.850925i	$0.676042\pi$
$824$	−2.00546e10	−1.24873
$825$	0	0
$826$	−2.50687e9	−0.154775
$827$	−1.81137e10	−1.11362	−0.556810	−	0.830640i	$-0.687975\pi$
$827$	−1.81137e10	−1.11362	−0.556810	+	0.830640i	$0.687975\pi$
$828$	0	0
$829$	−6.09499e9	−0.371563	−0.185781	−	0.982591i	$-0.559482\pi$
$829$	−6.09499e9	−0.371563	−0.185781	+	0.982591i	$0.559482\pi$
$830$	2.56001e10	1.55406
$831$	0	0
$832$	−1.99459e10	−1.20067
$833$	7.27801e9	0.436270
$834$	0	0
$835$	−6.24262e8	−0.0371077
$836$	4.53728e8	0.0268580
$837$	0	0
$838$	2.60892e10	1.53146
$839$	2.06089e10	1.20472	0.602362	−	0.798223i	$-0.294226\pi$
$839$	2.06089e10	1.20472	0.602362	+	0.798223i	$0.294226\pi$
$840$	0	0
$841$	2.88972e10	1.67521
$842$	−2.65803e10	−1.53450
$843$	0	0
$844$	7.30809e8	0.0418413
$845$	−8.04687e9	−0.458805
$846$	0	0
$847$	1.60036e10	0.904952
$848$	8.57915e8	0.0483124
$849$	0	0
$850$	4.37379e9	0.244282
$851$	7.44384e9	0.414041
$852$	0	0
$853$	−1.89472e10	−1.04526	−0.522628	−	0.852561i	$-0.675048\pi$
$853$	−1.89472e10	−1.04526	−0.522628	+	0.852561i	$0.675048\pi$
$854$	−1.46352e10	−0.804076
$855$	0	0
$856$	−2.52483e10	−1.37586
$857$	−1.39113e9	−0.0754980	−0.0377490	−	0.999287i	$-0.512019\pi$
$857$	−1.39113e9	−0.0754980	−0.0377490	+	0.999287i	$0.512019\pi$
$858$	0	0
$859$	3.00645e10	1.61837	0.809184	−	0.587555i	$-0.199910\pi$
$859$	3.00645e10	1.61837	0.809184	+	0.587555i	$0.199910\pi$
$860$	−4.06345e8	−0.0217846
$861$	0	0
$862$	2.51546e10	1.33765
$863$	−2.01007e10	−1.06457	−0.532284	−	0.846566i	$-0.678666\pi$
$863$	−2.01007e10	−1.06457	−0.532284	+	0.846566i	$0.678666\pi$
$864$	0	0
$865$	2.51658e9	0.132207
$866$	−7.13698e9	−0.373424
$867$	0	0
$868$	4.99776e8	0.0259392
$869$	4.77210e10	2.46683
$870$	0	0
$871$	−2.34832e10	−1.20418
$872$	−1.51805e10	−0.775314
$873$	0	0
$874$	2.06829e10	1.04790
$875$	2.50428e10	1.26373
$876$	0	0
$877$	1.59271e7	0.000797329 0	0.000398665	−	1.00000i	$-0.499873\pi$
$877$	1.59271e7	0.000797329 0	0.000398665		1.00000i	$0.499873\pi$
$878$	−2.28386e10	−1.13878
$879$	0	0
$880$	2.44546e10	1.20968
$881$	−2.54639e10	−1.25461	−0.627306	−	0.778773i	$-0.715843\pi$
$881$	−2.54639e10	−1.25461	−0.627306	+	0.778773i	$0.715843\pi$
$882$	0	0
$883$	1.07111e10	0.523565	0.261782	−	0.965127i	$-0.415690\pi$
$883$	1.07111e10	0.523565	0.261782	+	0.965127i	$0.415690\pi$
$884$	−6.91473e8	−0.0336661
$885$	0	0
$886$	1.28451e10	0.620466
$887$	−1.80502e10	−0.868461	−0.434231	−	0.900802i	$-0.642980\pi$
$887$	−1.80502e10	−0.868461	−0.434231	+	0.900802i	$0.642980\pi$
$888$	0	0
$889$	3.65544e10	1.74495
$890$	−1.89890e9	−0.0902894
$891$	0	0
$892$	−2.73459e7	−0.00129008
$893$	−2.02057e10	−0.949496
$894$	0	0
$895$	3.70730e10	1.72853
$896$	−2.61649e10	−1.21518
$897$	0	0
$898$	−4.38221e10	−2.01942
$899$	−3.29950e10	−1.51457
$900$	0	0
$901$	−1.18866e9	−0.0541403
$902$	1.41662e10	0.642731
$903$	0	0
$904$	9.99746e9	0.450091
$905$	−1.90325e10	−0.853542
$906$	0	0
$907$	4.30944e10	1.91777	0.958883	−	0.283801i	$-0.0915955\pi$
$907$	4.30944e10	1.91777	0.958883	+	0.283801i	$0.0915955\pi$
$908$	−3.31801e7	−0.00147088
$909$	0	0
$910$	−2.95693e10	−1.30076
$911$	−2.99740e10	−1.31350	−0.656750	−	0.754108i	$-0.728069\pi$
$911$	−2.99740e10	−1.31350	−0.656750	+	0.754108i	$0.728069\pi$
$912$	0	0
$913$	5.28867e10	2.29985
$914$	−2.36631e10	−1.02508
$915$	0	0
$916$	−6.02783e8	−0.0259136
$917$	5.41645e9	0.231965
$918$	0	0
$919$	−2.87791e10	−1.22313	−0.611565	−	0.791194i	$-0.709460\pi$
$919$	−2.87791e10	−1.22313	−0.611565	+	0.791194i	$0.709460\pi$
$920$	2.53537e10	1.07345
$921$	0	0
$922$	1.25992e10	0.529402
$923$	2.98454e10	1.24931
$924$	0	0
$925$	1.71546e9	0.0712664
$926$	−1.70905e9	−0.0707322
$927$	0	0
$928$	−1.89833e9	−0.0779746
$929$	−3.70327e9	−0.151541	−0.0757705	−	0.997125i	$-0.524142\pi$
$929$	−3.70327e9	−0.151541	−0.0757705	+	0.997125i	$0.524142\pi$
$930$	0	0
$931$	7.93139e9	0.322126
$932$	−3.57503e8	−0.0144652
$933$	0	0
$934$	−4.51742e9	−0.181416
$935$	−3.38825e10	−1.35561
$936$	0	0
$937$	−3.73687e10	−1.48395	−0.741974	−	0.670428i	$-0.766110\pi$
$937$	−3.73687e10	−1.48395	−0.741974	+	0.670428i	$0.766110\pi$
$938$	−2.93851e10	−1.16257
$939$	0	0
$940$	6.04949e8	0.0237559
$941$	−2.34846e10	−0.918797	−0.459399	−	0.888230i	$-0.651935\pi$
$941$	−2.34846e10	−0.918797	−0.459399	+	0.888230i	$0.651935\pi$
$942$	0	0
$943$	1.50373e10	0.583955
$944$	−3.44324e9	−0.133219
$945$	0	0
$946$	−3.60493e10	−1.38445
$947$	−2.26967e10	−0.868435	−0.434218	−	0.900808i	$-0.642975\pi$
$947$	−2.26967e10	−0.868435	−0.434218	+	0.900808i	$0.642975\pi$
$948$	0	0
$949$	3.91175e10	1.48573
$950$	4.76645e9	0.180369
$951$	0	0
$952$	3.54267e10	1.33077
$953$	1.47239e10	0.551060	0.275530	−	0.961293i	$-0.411147\pi$
$953$	1.47239e10	0.551060	0.275530	+	0.961293i	$0.411147\pi$
$954$	0	0
$955$	1.54189e10	0.572852
$956$	−2.53584e8	−0.00938684
$957$	0	0
$958$	−1.32439e9	−0.0486672
$959$	2.22320e10	0.813978
$960$	0	0
$961$	−3.92136e9	−0.142529
$962$	−1.16465e10	−0.421777
$963$	0	0
$964$	−3.53238e8	−0.0126998
$965$	3.22228e10	1.15430
$966$	0	0
$967$	1.53302e10	0.545201	0.272600	−	0.962127i	$-0.412116\pi$
$967$	1.53302e10	0.545201	0.272600	+	0.962127i	$0.412116\pi$
$968$	2.14692e10	0.760767
$969$	0	0
$970$	−2.42490e9	−0.0853085
$971$	6.17192e9	0.216348	0.108174	−	0.994132i	$-0.465500\pi$
$971$	6.17192e9	0.216348	0.108174	+	0.994132i	$0.465500\pi$
$972$	0	0
$973$	−1.12339e10	−0.390963
$974$	1.00115e10	0.347169
$975$	0	0
$976$	−2.01018e10	−0.692088
$977$	1.42966e10	0.490458	0.245229	−	0.969465i	$-0.421137\pi$
$977$	1.42966e10	0.490458	0.245229	+	0.969465i	$0.421137\pi$
$978$	0	0
$979$	−3.92289e9	−0.133619
$980$	−2.37462e8	−0.00805942
$981$	0	0
$982$	−9.72520e9	−0.327724
$983$	−1.77363e10	−0.595560	−0.297780	−	0.954634i	$-0.596246\pi$
$983$	−1.77363e10	−0.595560	−0.297780	+	0.954634i	$0.596246\pi$
$984$	0	0
$985$	−1.33543e10	−0.445241
$986$	5.71240e10	1.89780
$987$	0	0
$988$	−7.53549e8	−0.0248578
$989$	−3.82661e10	−1.25785
$990$	0	0
$991$	−5.82498e10	−1.90124	−0.950620	−	0.310358i	$-0.899551\pi$
$991$	−5.82498e10	−1.90124	−0.950620	+	0.310358i	$0.899551\pi$
$992$	1.35729e9	0.0441452
$993$	0	0
$994$	3.73464e10	1.20614
$995$	4.24036e10	1.36465
$996$	0	0
$997$	−1.43646e10	−0.459052	−0.229526	−	0.973303i	$-0.573718\pi$
$997$	−1.43646e10	−0.459052	−0.229526	+	0.973303i	$0.573718\pi$
$998$	2.34996e10	0.748349
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.g.1.9	✓	33
3.2	odd	2		531.8.a.h.1.25	yes	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.9	✓	33	1.1	even	1	trivial
531.8.a.h.1.25	yes	33	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-11.4478 q^{2} +3.05173 q^{4} -248.349 q^{5} +1066.24 q^{7} +1430.38 q^{8} +O(q^{10})\)	\(q-11.4478 q^{2} +3.05173 q^{4} -248.349 q^{5} +1066.24 q^{7} +1430.38 q^{8} +2843.04 q^{10} +5873.38 q^{11} -9754.49 q^{13} -12206.1 q^{14} -16765.3 q^{16} +23228.7 q^{17} +25314.1 q^{19} -757.892 q^{20} -67237.2 q^{22} -71371.9 q^{23} -16447.9 q^{25} +111667. q^{26} +3253.86 q^{28} -214819. q^{29} +153594. q^{31} +8836.87 q^{32} -265917. q^{34} -264799. q^{35} -104296. q^{37} -289790. q^{38} -355233. q^{40} -210689. q^{41} +536151. q^{43} +17923.9 q^{44} +817050. q^{46} -798199. q^{47} +313320. q^{49} +188292. q^{50} -29768.0 q^{52} -51172.0 q^{53} -1.45865e6 q^{55} +1.52513e6 q^{56} +2.45920e6 q^{58} +205379. q^{59} +1.19901e6 q^{61} -1.75832e6 q^{62} +2.04480e6 q^{64} +2.42251e6 q^{65} +2.40742e6 q^{67} +70887.7 q^{68} +3.03136e6 q^{70} -3.05966e6 q^{71} -4.01021e6 q^{73} +1.19396e6 q^{74} +77251.6 q^{76} +6.26242e6 q^{77} +8.12496e6 q^{79} +4.16364e6 q^{80} +2.41193e6 q^{82} +9.00447e6 q^{83} -5.76882e6 q^{85} -6.13774e6 q^{86} +8.40117e6 q^{88} -667911. q^{89} -1.04006e7 q^{91} -217807. q^{92} +9.13761e6 q^{94} -6.28671e6 q^{95} -852924. q^{97} -3.58682e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * q^98

Introduction

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