LMFDB - Embedded newform 45.24.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,24,Mod(1,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("45.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	45.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:	$150.841816805$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5761014x^{2} - 3205061410x + 2143006857425 $ x^4 - 2x^3 - 5761014x^2 - 3205061410*x + 2143006857425
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1838.47$ of defining polynomial
Character	$\chi$	$=$	45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3482.94 q^{2} +3.74229e6 q^{4} +4.88281e7 q^{5} +8.64758e9 q^{7} +1.61829e10 q^{8} +O(q^{10})$	\(q-3482.94 q^{2} +3.74229e6 q^{4} +4.88281e7 q^{5} +8.64758e9 q^{7} +1.61829e10 q^{8} -1.70066e11 q^{10} -4.59523e11 q^{11} -2.79244e12 q^{13} -3.01190e13 q^{14} -8.77566e13 q^{16} +1.40467e14 q^{17} +7.82480e14 q^{19} +1.82729e14 q^{20} +1.60049e15 q^{22} +3.06806e15 q^{23} +2.38419e15 q^{25} +9.72592e15 q^{26} +3.23617e16 q^{28} +9.69499e16 q^{29} +1.54585e16 q^{31} +1.69899e17 q^{32} -4.89240e17 q^{34} +4.22245e17 q^{35} -4.47673e17 q^{37} -2.72533e18 q^{38} +7.90180e17 q^{40} +4.27946e18 q^{41} +3.50056e18 q^{43} -1.71967e18 q^{44} -1.06859e19 q^{46} +1.79769e19 q^{47} +4.74120e19 q^{49} -8.30398e18 q^{50} -1.04501e19 q^{52} -4.84476e19 q^{53} -2.24376e19 q^{55} +1.39943e20 q^{56} -3.37671e20 q^{58} +1.49550e20 q^{59} -1.86216e20 q^{61} -5.38410e19 q^{62} +1.44406e20 q^{64} -1.36350e20 q^{65} -1.62625e21 q^{67} +5.25669e20 q^{68} -1.47066e21 q^{70} -1.03230e21 q^{71} +4.50707e20 q^{73} +1.55922e21 q^{74} +2.92826e21 q^{76} -3.97376e21 q^{77} +7.76563e21 q^{79} -4.28499e21 q^{80} -1.49051e22 q^{82} -6.10977e21 q^{83} +6.85876e21 q^{85} -1.21923e22 q^{86} -7.43640e21 q^{88} -4.80129e22 q^{89} -2.41479e22 q^{91} +1.14815e22 q^{92} -6.26124e22 q^{94} +3.82070e22 q^{95} +1.13004e23 q^{97} -1.65133e23 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 780 q^{2} + 12685792 q^{4} + 195312500 q^{5} - 1010710600 q^{7} + 90964721760 q^{8}+O(q^{10}) $ 4 * q + 780 * q^2 + 12685792 * q^4 + 195312500 * q^5 - 1010710600 * q^7 + 90964721760 * q^8	$ 4 q + 780 q^{2} + 12685792 q^{4} + 195312500 q^{5} - 1010710600 q^{7} + 90964721760 q^{8} + 38085937500 q^{10} - 510770963328 q^{11} - 14153856943960 q^{13} - 64982579554584 q^{14} + 113436824881024 q^{16} - 15332090016360 q^{17} + 11\!\cdots\!40 q^{19}+ \cdots + 80\!\cdots\!40 q^{98}+O(q^{100}) $ 4 * q + 780 * q^2 + 12685792 * q^4 + 195312500 * q^5 - 1010710600 * q^7 + 90964721760 * q^8 + 38085937500 * q^10 - 510770963328 * q^11 - 14153856943960 * q^13 - 64982579554584 * q^14 + 113436824881024 * q^16 - 15332090016360 * q^17 + 1111809672255440 * q^19 + 619423437500000 * q^20 + 10708927083459840 * q^22 + 3998020505342040 * q^23 + 9536743164062500 * q^25 + 877714925108472 * q^26 - 113078857801120960 * q^28 + 170274795551093640 * q^29 - 172942006080462832 * q^31 + 567511045488564480 * q^32 + 207151653136271304 * q^34 - 49351103515625000 * q^35 + 461695977491285480 * q^37 - 2127655695829602960 * q^38 + 4441636804687500000 * q^40 - 1746066900841990488 * q^41 + 13231308551430609800 * q^43 + 21011535794344429056 * q^44 + 22929884441616610248 * q^46 + 25463181064945728360 * q^47 + 27752501816433355572 * q^49 + 1859664916992187500 * q^50 - 155108839850940462400 * q^52 - 19153511824499883720 * q^53 - 24939988443750000000 * q^55 - 411860605716761453760 * q^56 + 221034899302314393240 * q^58 - 217218038347313160720 * q^59 + 152379678911827122728 * q^61 + 363203697269394525360 * q^62 + 1121074796200062441472 * q^64 - 691106296091796875000 * q^65 - 2317407910895557756840 * q^67 + 3800878923901661494080 * q^68 - 3172977517313671875000 * q^70 - 1453247054528140867248 * q^71 + 2601821824581282121160 * q^73 + 3991697886987492208056 * q^74 - 514198358053038321280 * q^76 - 7444709512703076153600 * q^77 + 22817266427547282683360 * q^79 + 5538907464893750000000 * q^80 - 25020293761756353578760 * q^82 - 49081293110242175251080 * q^83 - 748637207830078125000 * q^85 + 37195944193834827943512 * q^86 + 7962508551211096903680 * q^88 - 50023669870473477290280 * q^89 + 55881722079510765798448 * q^91 + 239405355986426422923840 * q^92 - 34668831477450377120136 * q^94 + 54287581653097656250000 * q^95 - 141223261544238546490360 * q^97 + 8062497360198964195740 * 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 $

$2$	−3482.94	−1.20255	−0.601273	−	0.799044i	$-0.705339\pi$
$2$	−3482.94	−1.20255	−0.601273	+	0.799044i	$0.705339\pi$
$3$	0	0
$3$	0	0
$4$	3.74229e6	0.446115
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	0	0
$7$	8.64758e9	1.65298	0.826489	−	0.562952i	$-0.190334\pi$
$7$	8.64758e9	1.65298	0.826489	+	0.562952i	$0.190334\pi$
$8$	1.61829e10	0.666072
$9$	0	0
$10$	−1.70066e11	−0.537795
$11$	−4.59523e11	−0.485614	−0.242807	−	0.970075i	$-0.578068\pi$
$11$	−4.59523e11	−0.485614	−0.242807	+	0.970075i	$0.578068\pi$
$12$	0	0
$13$	−2.79244e12	−0.432151	−0.216076	−	0.976377i	$-0.569326\pi$
$13$	−2.79244e12	−0.432151	−0.216076	+	0.976377i	$0.569326\pi$
$14$	−3.01190e13	−1.98778
$15$	0	0
$16$	−8.77566e13	−1.24710
$17$	1.40467e14	0.994060	0.497030	−	0.867733i	$-0.334424\pi$
$17$	1.40467e14	0.994060	0.497030	+	0.867733i	$0.334424\pi$
$18$	0	0
$19$	7.82480e14	1.54101	0.770507	−	0.637431i	$-0.220003\pi$
$19$	7.82480e14	1.54101	0.770507	+	0.637431i	$0.220003\pi$
$20$	1.82729e14	0.199509
$21$	0	0
$22$	1.60049e15	0.583973
$23$	3.06806e15	0.671418	0.335709	−	0.941966i	$-0.391024\pi$
$23$	3.06806e15	0.671418	0.335709	+	0.941966i	$0.391024\pi$
$24$	0	0
$25$	2.38419e15	0.200000
$26$	9.72592e15	0.519681
$27$	0	0
$28$	3.23617e16	0.737419
$29$	9.69499e16	1.47561	0.737803	−	0.675016i	$-0.235863\pi$
$29$	9.69499e16	1.47561	0.737803	+	0.675016i	$0.235863\pi$
$30$	0	0
$31$	1.54585e16	0.109272	0.0546358	−	0.998506i	$-0.482600\pi$
$31$	1.54585e16	0.109272	0.0546358	+	0.998506i	$0.482600\pi$
$32$	1.69899e17	0.833618
$33$	0	0
$34$	−4.89240e17	−1.19540
$35$	4.22245e17	0.739235
$36$	0	0
$37$	−4.47673e17	−0.413658	−0.206829	−	0.978377i	$-0.566314\pi$
$37$	−4.47673e17	−0.413658	−0.206829	+	0.978377i	$0.566314\pi$
$38$	−2.72533e18	−1.85314
$39$	0	0
$40$	7.90180e17	0.297876
$41$	4.27946e18	1.21444	0.607218	−	0.794535i	$-0.292286\pi$
$41$	4.27946e18	1.21444	0.607218	+	0.794535i	$0.292286\pi$
$42$	0	0
$43$	3.50056e18	0.574448	0.287224	−	0.957863i	$-0.407268\pi$
$43$	3.50056e18	0.574448	0.287224	+	0.957863i	$0.407268\pi$
$44$	−1.71967e18	−0.216640
$45$	0	0
$46$	−1.06859e19	−0.807411
$47$	1.79769e19	1.06069	0.530345	−	0.847782i	$-0.322062\pi$
$47$	1.79769e19	1.06069	0.530345	+	0.847782i	$0.322062\pi$
$48$	0	0
$49$	4.74120e19	1.73234
$50$	−8.30398e18	−0.240509
$51$	0	0
$52$	−1.04501e19	−0.192789
$53$	−4.84476e19	−0.717959	−0.358980	−	0.933345i	$-0.616875\pi$
$53$	−4.84476e19	−0.717959	−0.358980	+	0.933345i	$0.616875\pi$
$54$	0	0
$55$	−2.24376e19	−0.217173
$56$	1.39943e20	1.10100
$57$	0	0
$58$	−3.37671e20	−1.77448
$59$	1.49550e20	0.645639	0.322819	−	0.946461i	$-0.395369\pi$
$59$	1.49550e20	0.645639	0.322819	+	0.946461i	$0.395369\pi$
$60$	0	0
$61$	−1.86216e20	−0.547929	−0.273965	−	0.961740i	$-0.588335\pi$
$61$	−1.86216e20	−0.547929	−0.273965	+	0.961740i	$0.588335\pi$
$62$	−5.38410e19	−0.131404
$63$	0	0
$64$	1.44406e20	0.244632
$65$	−1.36350e20	−0.193264
$66$	0	0
$67$	−1.62625e21	−1.62677	−0.813386	−	0.581725i	$-0.802378\pi$
$67$	−1.62625e21	−1.62677	−0.813386	+	0.581725i	$0.802378\pi$
$68$	5.25669e20	0.443465
$69$	0	0
$70$	−1.47066e21	−0.888963
$71$	−1.03230e21	−0.530073	−0.265037	−	0.964238i	$-0.585384\pi$
$71$	−1.03230e21	−0.530073	−0.265037	+	0.964238i	$0.585384\pi$
$72$	0	0
$73$	4.50707e20	0.168144	0.0840721	−	0.996460i	$-0.473207\pi$
$73$	4.50707e20	0.168144	0.0840721	+	0.996460i	$0.473207\pi$
$74$	1.55922e21	0.497443
$75$	0	0
$76$	2.92826e21	0.687470
$77$	−3.97376e21	−0.802710
$78$	0	0
$79$	7.76563e21	1.16806	0.584030	−	0.811732i	$-0.301475\pi$
$79$	7.76563e21	1.16806	0.584030	+	0.811732i	$0.301475\pi$
$80$	−4.28499e21	−0.557718
$81$	0	0
$82$	−1.49051e22	−1.46041
$83$	−6.10977e21	−0.520747	−0.260374	−	0.965508i	$-0.583846\pi$
$83$	−6.10977e21	−0.520747	−0.260374	+	0.965508i	$0.583846\pi$
$84$	0	0
$85$	6.85876e21	0.444557
$86$	−1.21923e22	−0.690799
$87$	0	0
$88$	−7.43640e21	−0.323454
$89$	−4.80129e22	−1.83389	−0.916943	−	0.399017i	$-0.869351\pi$
$89$	−4.80129e22	−1.83389	−0.916943	+	0.399017i	$0.869351\pi$
$90$	0	0
$91$	−2.41479e22	−0.714337
$92$	1.14815e22	0.299530
$93$	0	0
$94$	−6.26124e22	−1.27553
$95$	3.82070e22	0.689162
$96$	0	0
$97$	1.13004e23	1.60405	0.802025	−	0.597291i	$-0.203756\pi$
$97$	1.13004e23	1.60405	0.802025	+	0.597291i	$0.203756\pi$
$98$	−1.65133e23	−2.08322
$99$	0	0
$100$	8.92230e21	0.0892230
$101$	−6.96717e22	−0.621385	−0.310692	−	0.950510i	$-0.600561\pi$
$101$	−6.96717e22	−0.621385	−0.310692	+	0.950510i	$0.600561\pi$
$102$	0	0
$103$	−4.66657e22	−0.332177	−0.166088	−	0.986111i	$-0.553114\pi$
$103$	−4.66657e22	−0.332177	−0.166088	+	0.986111i	$0.553114\pi$
$104$	−4.51898e22	−0.287844
$105$	0	0
$106$	1.68740e23	0.863379
$107$	−1.36060e23	−0.624909	−0.312454	−	0.949933i	$-0.601151\pi$
$107$	−1.36060e23	−0.624909	−0.312454	+	0.949933i	$0.601151\pi$
$108$	0	0
$109$	2.92750e23	1.08665	0.543327	−	0.839521i	$-0.317164\pi$
$109$	2.92750e23	1.08665	0.543327	+	0.839521i	$0.317164\pi$
$110$	7.81490e22	0.261161
$111$	0	0
$112$	−7.58883e23	−2.06142
$113$	−3.58585e23	−0.879407	−0.439704	−	0.898143i	$-0.644916\pi$
$113$	−3.58585e23	−0.879407	−0.439704	+	0.898143i	$0.644916\pi$
$114$	0	0
$115$	1.49807e23	0.300267
$116$	3.62814e23	0.658290
$117$	0	0
$118$	−5.20876e23	−0.776410
$119$	1.21470e24	1.64316
$120$	0	0
$121$	−6.84269e23	−0.764179
$122$	6.48581e23	0.658910
$123$	0	0
$124$	5.78501e22	0.0487477
$125$	1.16415e23	0.0894427
$126$	0	0
$127$	−1.35565e24	−0.867773	−0.433887	−	0.900967i	$-0.642858\pi$
$127$	−1.35565e24	−0.867773	−0.433887	+	0.900967i	$0.642858\pi$
$128$	−1.92818e24	−1.12780
$129$	0	0
$130$	4.74899e23	0.232409
$131$	1.30032e24	0.582682	0.291341	−	0.956619i	$-0.405899\pi$
$131$	1.30032e24	0.582682	0.291341	+	0.956619i	$0.405899\pi$
$132$	0	0
$133$	6.76656e24	2.54726
$134$	5.66413e24	1.95627
$135$	0	0
$136$	2.27317e24	0.662115
$137$	−1.67618e23	−0.0448780	−0.0224390	−	0.999748i	$-0.507143\pi$
$137$	−1.67618e23	−0.0448780	−0.0224390	+	0.999748i	$0.507143\pi$
$138$	0	0
$139$	4.85141e24	1.09951	0.549753	−	0.835327i	$-0.314722\pi$
$139$	4.85141e24	1.09951	0.549753	+	0.835327i	$0.314722\pi$
$140$	1.58016e24	0.329784
$141$	0	0
$142$	3.59545e24	0.637437
$143$	1.28319e24	0.209859
$144$	0	0
$145$	4.73388e24	0.659911
$146$	−1.56979e24	−0.202201
$147$	0	0
$148$	−1.67532e24	−0.184539
$149$	3.22578e24	0.328846	0.164423	−	0.986390i	$-0.447424\pi$
$149$	3.22578e24	0.328846	0.164423	+	0.986390i	$0.447424\pi$
$150$	0	0
$151$	−1.29362e25	−1.13128	−0.565640	−	0.824652i	$-0.691371\pi$
$151$	−1.29362e25	−1.13128	−0.565640	+	0.824652i	$0.691371\pi$
$152$	1.26628e25	1.02643
$153$	0	0
$154$	1.38404e25	0.965295
$155$	7.54809e23	0.0488678
$156$	0	0
$157$	2.60805e25	1.45704	0.728518	−	0.685027i	$-0.240209\pi$
$157$	2.60805e25	1.45704	0.728518	+	0.685027i	$0.240209\pi$
$158$	−2.70472e25	−1.40464
$159$	0	0
$160$	8.29587e24	0.372806
$161$	2.65313e25	1.10984
$162$	0	0
$163$	−1.16248e25	−0.421919	−0.210959	−	0.977495i	$-0.567659\pi$
$163$	−1.16248e25	−0.421919	−0.210959	+	0.977495i	$0.567659\pi$
$164$	1.60150e25	0.541778
$165$	0	0
$166$	2.12800e25	0.626222
$167$	−5.88853e24	−0.161721	−0.0808607	−	0.996725i	$-0.525767\pi$
$167$	−5.88853e24	−0.161721	−0.0808607	+	0.996725i	$0.525767\pi$
$168$	0	0
$169$	−3.39562e25	−0.813245
$170$	−2.38887e25	−0.534600
$171$	0	0
$172$	1.31001e25	0.256270
$173$	−4.10418e25	−0.751097	−0.375548	−	0.926803i	$-0.622546\pi$
$173$	−4.10418e25	−0.751097	−0.375548	+	0.926803i	$0.622546\pi$
$174$	0	0
$175$	2.06174e25	0.330596
$176$	4.03262e25	0.605607
$177$	0	0
$178$	1.67226e26	2.20533
$179$	3.35956e25	0.415406	0.207703	−	0.978192i	$-0.433401\pi$
$179$	3.35956e25	0.415406	0.207703	+	0.978192i	$0.433401\pi$
$180$	0	0
$181$	−5.14467e25	−0.559827	−0.279913	−	0.960025i	$-0.590306\pi$
$181$	−5.14467e25	−0.559827	−0.279913	+	0.960025i	$0.590306\pi$
$182$	8.41057e25	0.859023
$183$	0	0
$184$	4.96500e25	0.447213
$185$	−2.18591e25	−0.184993
$186$	0	0
$187$	−6.45479e25	−0.482729
$188$	6.72746e25	0.473190
$189$	0	0
$190$	−1.33073e26	−0.828749
$191$	−8.94888e25	−0.524669	−0.262334	−	0.964977i	$-0.584492\pi$
$191$	−8.94888e25	−0.524669	−0.262334	+	0.964977i	$0.584492\pi$
$192$	0	0
$193$	1.00398e26	0.522173	0.261087	−	0.965315i	$-0.415919\pi$
$193$	1.00398e26	0.522173	0.261087	+	0.965315i	$0.415919\pi$
$194$	−3.93586e26	−1.92894
$195$	0	0
$196$	1.77429e26	0.772823
$197$	2.28398e26	0.938277	0.469138	−	0.883125i	$-0.344565\pi$
$197$	2.28398e26	0.938277	0.469138	+	0.883125i	$0.344565\pi$
$198$	0	0
$199$	3.01704e25	0.110350	0.0551748	−	0.998477i	$-0.482428\pi$
$199$	3.01704e25	0.110350	0.0551748	+	0.998477i	$0.482428\pi$
$200$	3.85830e25	0.133214
$201$	0	0
$202$	2.42663e26	0.747243
$203$	8.38382e26	2.43914
$204$	0	0
$205$	2.08958e26	0.543112
$206$	1.62534e26	0.399458
$207$	0	0
$208$	2.45055e26	0.538934
$209$	−3.59567e26	−0.748338
$210$	0	0
$211$	6.35486e26	1.18538	0.592690	−	0.805430i	$-0.298066\pi$
$211$	6.35486e26	1.18538	0.592690	+	0.805430i	$0.298066\pi$
$212$	−1.81305e26	−0.320293
$213$	0	0
$214$	4.73889e26	0.751481
$215$	1.70926e26	0.256901
$216$	0	0
$217$	1.33679e26	0.180624
$218$	−1.01963e27	−1.30675
$219$	0	0
$220$	−8.39680e25	−0.0968843
$221$	−3.92247e26	−0.429584
$222$	0	0
$223$	2.33487e26	0.230546	0.115273	−	0.993334i	$-0.463226\pi$
$223$	2.33487e26	0.230546	0.115273	+	0.993334i	$0.463226\pi$
$224$	1.46922e27	1.37795
$225$	0	0
$226$	1.24893e27	1.05753
$227$	1.62098e27	1.30461	0.652305	−	0.757956i	$-0.273802\pi$
$227$	1.62098e27	1.30461	0.652305	+	0.757956i	$0.273802\pi$
$228$	0	0
$229$	−1.18775e27	−0.864203	−0.432102	−	0.901825i	$-0.642228\pi$
$229$	−1.18775e27	−0.864203	−0.432102	+	0.901825i	$0.642228\pi$
$230$	−5.21771e26	−0.361085
$231$	0	0
$232$	1.56893e27	0.982859
$233$	2.57303e27	1.53409	0.767046	−	0.641592i	$-0.221726\pi$
$233$	2.57303e27	1.53409	0.767046	+	0.641592i	$0.221726\pi$
$234$	0	0
$235$	8.77777e26	0.474355
$236$	5.59661e26	0.288029
$237$	0	0
$238$	−4.23074e27	−1.97597
$239$	−2.57120e27	−1.14435	−0.572177	−	0.820130i	$-0.693901\pi$
$239$	−2.57120e27	−1.14435	−0.572177	+	0.820130i	$0.693901\pi$
$240$	0	0
$241$	9.02690e26	0.365042	0.182521	−	0.983202i	$-0.441574\pi$
$241$	9.02690e26	0.365042	0.182521	+	0.983202i	$0.441574\pi$
$242$	2.38327e27	0.918960
$243$	0	0
$244$	−6.96874e26	−0.244440
$245$	2.31504e27	0.774726
$246$	0	0
$247$	−2.18503e27	−0.665951
$248$	2.50163e26	0.0727827
$249$	0	0
$250$	−4.05468e26	−0.107559
$251$	−1.83880e27	−0.465894	−0.232947	−	0.972489i	$-0.574837\pi$
$251$	−1.83880e27	−0.465894	−0.232947	+	0.972489i	$0.574837\pi$
$252$	0	0
$253$	−1.40984e27	−0.326050
$254$	4.72167e27	1.04354
$255$	0	0
$256$	5.50437e27	1.11160
$257$	−4.62113e27	−0.892313	−0.446157	−	0.894955i	$-0.647208\pi$
$257$	−4.62113e27	−0.892313	−0.446157	+	0.894955i	$0.647208\pi$
$258$	0	0
$259$	−3.87129e27	−0.683768
$260$	−5.10260e26	−0.0862180
$261$	0	0
$262$	−4.52896e27	−0.700702
$263$	−8.97869e27	−1.32960	−0.664801	−	0.747020i	$-0.731484\pi$
$263$	−8.97869e27	−1.32960	−0.664801	+	0.747020i	$0.731484\pi$
$264$	0	0
$265$	−2.36561e27	−0.321081
$266$	−2.35675e28	−3.06320
$267$	0	0
$268$	−6.08588e27	−0.725728
$269$	4.19862e27	0.479684	0.239842	−	0.970812i	$-0.422904\pi$
$269$	4.19862e27	0.479684	0.239842	+	0.970812i	$0.422904\pi$
$270$	0	0
$271$	−1.79741e28	−1.88582	−0.942910	−	0.333048i	$-0.891923\pi$
$271$	−1.79741e28	−1.88582	−0.942910	+	0.333048i	$0.891923\pi$
$272$	−1.23269e28	−1.23969
$273$	0	0
$274$	5.83804e26	0.0539679
$275$	−1.09559e27	−0.0971228
$276$	0	0
$277$	−1.68639e28	−1.37543	−0.687717	−	0.725979i	$-0.741387\pi$
$277$	−1.68639e28	−1.37543	−0.687717	+	0.725979i	$0.741387\pi$
$278$	−1.68972e28	−1.32221
$279$	0	0
$280$	6.83314e27	0.492383
$281$	3.68206e27	0.254665	0.127332	−	0.991860i	$-0.459359\pi$
$281$	3.68206e27	0.254665	0.127332	+	0.991860i	$0.459359\pi$
$282$	0	0
$283$	1.38319e28	0.881733	0.440867	−	0.897573i	$-0.354671\pi$
$283$	1.38319e28	0.881733	0.440867	+	0.897573i	$0.354671\pi$
$284$	−3.86317e27	−0.236474
$285$	0	0
$286$	−4.46928e27	−0.252365
$287$	3.70070e28	2.00744
$288$	0	0
$289$	−2.36505e26	−0.0118445
$290$	−1.64878e28	−0.793573
$291$	0	0
$292$	1.68668e27	0.0750117
$293$	1.22393e28	0.523333	0.261667	−	0.965158i	$-0.415728\pi$
$293$	1.22393e28	0.523333	0.261667	+	0.965158i	$0.415728\pi$
$294$	0	0
$295$	7.30227e27	0.288738
$296$	−7.24464e27	−0.275526
$297$	0	0
$298$	−1.12352e28	−0.395452
$299$	−8.56737e27	−0.290154
$300$	0	0
$301$	3.02714e28	0.949550
$302$	4.50559e28	1.36042
$303$	0	0
$304$	−6.86678e28	−1.92179
$305$	−9.09259e27	−0.245041
$306$	0	0
$307$	−1.17607e28	−0.293997	−0.146998	−	0.989137i	$-0.546961\pi$
$307$	−1.17607e28	−0.293997	−0.146998	+	0.989137i	$0.546961\pi$
$308$	−1.48710e28	−0.358101
$309$	0	0
$310$	−2.62896e27	−0.0587657
$311$	1.40025e28	0.301622	0.150811	−	0.988563i	$-0.451812\pi$
$311$	1.40025e28	0.301622	0.150811	+	0.988563i	$0.451812\pi$
$312$	0	0
$313$	2.95636e28	0.591559	0.295780	−	0.955256i	$-0.404421\pi$
$313$	2.95636e28	0.591559	0.295780	+	0.955256i	$0.404421\pi$
$314$	−9.08370e28	−1.75215
$315$	0	0
$316$	2.90612e28	0.521089
$317$	3.09352e28	0.534898	0.267449	−	0.963572i	$-0.413819\pi$
$317$	3.09352e28	0.534898	0.267449	+	0.963572i	$0.413819\pi$
$318$	0	0
$319$	−4.45507e28	−0.716575
$320$	7.05105e27	0.109403
$321$	0	0
$322$	−9.24069e28	−1.33463
$323$	1.09913e29	1.53186
$324$	0	0
$325$	−6.65770e27	−0.0864303
$326$	4.04886e28	0.507377
$327$	0	0
$328$	6.92540e28	0.808901
$329$	1.55457e29	1.75330
$330$	0	0
$331$	8.94811e28	0.941260	0.470630	−	0.882331i	$-0.344027\pi$
$331$	8.94811e28	0.941260	0.470630	+	0.882331i	$0.344027\pi$
$332$	−2.28645e28	−0.232313
$333$	0	0
$334$	2.05094e28	0.194477
$335$	−7.94066e28	−0.727514
$336$	0	0
$337$	−1.88248e28	−0.161059	−0.0805297	−	0.996752i	$-0.525661\pi$
$337$	−1.88248e28	−0.161059	−0.0805297	+	0.996752i	$0.525661\pi$
$338$	1.18267e29	0.977964
$339$	0	0
$340$	2.56674e28	0.198324
$341$	−7.10353e27	−0.0530638
$342$	0	0
$343$	1.73325e29	1.21054
$344$	5.66492e28	0.382623
$345$	0	0
$346$	1.42946e29	0.903228
$347$	−1.45249e29	−0.887818	−0.443909	−	0.896072i	$-0.646409\pi$
$347$	−1.45249e29	−0.887818	−0.443909	+	0.896072i	$0.646409\pi$
$348$	0	0
$349$	5.82508e28	0.333280	0.166640	−	0.986018i	$-0.446708\pi$
$349$	5.82508e28	0.333280	0.166640	+	0.986018i	$0.446708\pi$
$350$	−7.18094e28	−0.397556
$351$	0	0
$352$	−7.80727e28	−0.404817
$353$	6.95395e27	0.0348998	0.0174499	−	0.999848i	$-0.494445\pi$
$353$	6.95395e27	0.0348998	0.0174499	+	0.999848i	$0.494445\pi$
$354$	0	0
$355$	−5.04054e28	−0.237056
$356$	−1.79678e29	−0.818125
$357$	0	0
$358$	−1.17012e29	−0.499545
$359$	−1.54223e29	−0.637623	−0.318812	−	0.947818i	$-0.603284\pi$
$359$	−1.54223e29	−0.637623	−0.318812	+	0.947818i	$0.603284\pi$
$360$	0	0
$361$	3.54445e29	1.37472
$362$	1.79186e29	0.673217
$363$	0	0
$364$	−9.03683e28	−0.318677
$365$	2.20072e28	0.0751964
$366$	0	0
$367$	3.30752e29	1.06131	0.530656	−	0.847587i	$-0.321946\pi$
$367$	3.30752e29	1.06131	0.530656	+	0.847587i	$0.321946\pi$
$368$	−2.69242e29	−0.837323
$369$	0	0
$370$	7.61338e28	0.222463
$371$	−4.18955e29	−1.18677
$372$	0	0
$373$	−1.41877e29	−0.377799	−0.188899	−	0.981996i	$-0.560492\pi$
$373$	−1.41877e29	−0.377799	−0.188899	+	0.981996i	$0.560492\pi$
$374$	2.24817e29	0.580504
$375$	0	0
$376$	2.90918e29	0.706496
$377$	−2.70727e29	−0.637685
$378$	0	0
$379$	−3.35326e29	−0.743219	−0.371610	−	0.928389i	$-0.621194\pi$
$379$	−3.35326e29	−0.743219	−0.371610	+	0.928389i	$0.621194\pi$
$380$	1.42982e29	0.307446
$381$	0	0
$382$	3.11684e29	0.630938
$383$	6.42876e29	1.26282	0.631410	−	0.775449i	$-0.282477\pi$
$383$	6.42876e29	1.26282	0.631410	+	0.775449i	$0.282477\pi$
$384$	0	0
$385$	−1.94031e29	−0.358983
$386$	−3.49679e29	−0.627937
$387$	0	0
$388$	4.22892e29	0.715591
$389$	1.65277e29	0.271515	0.135757	−	0.990742i	$-0.456653\pi$
$389$	1.65277e29	0.271515	0.135757	+	0.990742i	$0.456653\pi$
$390$	0	0
$391$	4.30962e29	0.667430
$392$	7.67262e29	1.15386
$393$	0	0
$394$	−7.95498e29	−1.12832
$395$	3.79181e29	0.522372
$396$	0	0
$397$	8.33502e28	0.108347	0.0541734	−	0.998532i	$-0.482748\pi$
$397$	8.33502e28	0.108347	0.0541734	+	0.998532i	$0.482748\pi$
$398$	−1.05082e29	−0.132700
$399$	0	0
$400$	−2.09228e29	−0.249419
$401$	1.27732e30	1.47958	0.739789	−	0.672839i	$-0.234925\pi$
$401$	1.27732e30	1.47958	0.739789	+	0.672839i	$0.234925\pi$
$402$	0	0
$403$	−4.31669e28	−0.0472219
$404$	−2.60731e29	−0.277209
$405$	0	0
$406$	−2.92004e30	−2.93318
$407$	2.05716e29	0.200878
$408$	0	0
$409$	1.55049e30	1.43104	0.715519	−	0.698594i	$-0.246191\pi$
$409$	1.55049e30	1.43104	0.715519	+	0.698594i	$0.246191\pi$
$410$	−7.27789e29	−0.653117
$411$	0	0
$412$	−1.74636e29	−0.148189
$413$	1.29325e30	1.06723
$414$	0	0
$415$	−2.98329e29	−0.232885
$416$	−4.74435e29	−0.360249
$417$	0	0
$418$	1.25235e30	0.899910
$419$	−8.47546e29	−0.592518	−0.296259	−	0.955108i	$-0.595739\pi$
$419$	−8.47546e29	−0.592518	−0.296259	+	0.955108i	$0.595739\pi$
$420$	0	0
$421$	2.82495e30	1.86968	0.934839	−	0.355072i	$-0.115544\pi$
$421$	2.82495e30	1.86968	0.934839	+	0.355072i	$0.115544\pi$
$422$	−2.21336e30	−1.42547
$423$	0	0
$424$	−7.84022e29	−0.478212
$425$	3.34900e29	0.198812
$426$	0	0
$427$	−1.61032e30	−0.905716
$428$	−5.09175e29	−0.278781
$429$	0	0
$430$	−5.95325e29	−0.308935
$431$	3.23923e30	1.63664	0.818321	−	0.574762i	$-0.194905\pi$
$431$	3.23923e30	1.63664	0.818321	+	0.574762i	$0.194905\pi$
$432$	0	0
$433$	3.92656e30	1.88105	0.940527	−	0.339719i	$-0.110332\pi$
$433$	3.92656e30	1.88105	0.940527	+	0.339719i	$0.110332\pi$
$434$	−4.65595e29	−0.217208
$435$	0	0
$436$	1.09555e30	0.484773
$437$	2.40069e30	1.03467
$438$	0	0
$439$	−4.50231e30	−1.84117	−0.920585	−	0.390543i	$-0.872287\pi$
$439$	−4.50231e30	−1.84117	−0.920585	+	0.390543i	$0.872287\pi$
$440$	−3.63105e29	−0.144653
$441$	0	0
$442$	1.36617e30	0.516595
$443$	−2.44230e30	−0.899820	−0.449910	−	0.893074i	$-0.648544\pi$
$443$	−2.44230e30	−0.899820	−0.449910	+	0.893074i	$0.648544\pi$
$444$	0	0
$445$	−2.34438e30	−0.820139
$446$	−8.13222e29	−0.277241
$447$	0	0
$448$	1.24876e30	0.404372
$449$	−5.34123e30	−1.68581	−0.842904	−	0.538064i	$-0.819156\pi$
$449$	−5.34123e30	−1.68581	−0.842904	+	0.538064i	$0.819156\pi$
$450$	0	0
$451$	−1.96651e30	−0.589747
$452$	−1.34193e30	−0.392317
$453$	0	0
$454$	−5.64579e30	−1.56885
$455$	−1.17910e30	−0.319461
$456$	0	0
$457$	4.09268e30	1.05432	0.527159	−	0.849767i	$-0.323257\pi$
$457$	4.09268e30	1.05432	0.527159	+	0.849767i	$0.323257\pi$
$458$	4.13686e30	1.03924
$459$	0	0
$460$	5.60622e29	0.133954
$461$	4.79456e30	1.11735	0.558674	−	0.829388i	$-0.311310\pi$
$461$	4.79456e30	1.11735	0.558674	+	0.829388i	$0.311310\pi$
$462$	0	0
$463$	−4.18755e30	−0.928493	−0.464247	−	0.885706i	$-0.653675\pi$
$463$	−4.18755e30	−0.928493	−0.464247	+	0.885706i	$0.653675\pi$
$464$	−8.50799e30	−1.84022
$465$	0	0
$466$	−8.96171e30	−1.84482
$467$	−3.38764e29	−0.0680382	−0.0340191	−	0.999421i	$-0.510831\pi$
$467$	−3.38764e29	−0.0680382	−0.0340191	+	0.999421i	$0.510831\pi$
$468$	0	0
$469$	−1.40631e31	−2.68902
$470$	−3.05725e30	−0.570434
$471$	0	0
$472$	2.42016e30	0.430042
$473$	−1.60859e30	−0.278960
$474$	0	0
$475$	1.86558e30	0.308203
$476$	4.54577e30	0.733039
$477$	0	0
$478$	8.95535e30	1.37614
$479$	−1.01289e31	−1.51950	−0.759752	−	0.650212i	$-0.774680\pi$
$479$	−1.01289e31	−1.51950	−0.759752	+	0.650212i	$0.774680\pi$
$480$	0	0
$481$	1.25010e30	0.178763
$482$	−3.14402e30	−0.438979
$483$	0	0
$484$	−2.56073e30	−0.340912
$485$	5.51776e30	0.717353
$486$	0	0
$487$	−4.51035e30	−0.559277	−0.279638	−	0.960105i	$-0.590215\pi$
$487$	−4.51035e30	−0.559277	−0.279638	+	0.960105i	$0.590215\pi$
$488$	−3.01351e30	−0.364960
$489$	0	0
$490$	−8.06314e30	−0.931643
$491$	−9.02388e29	−0.101849	−0.0509244	−	0.998703i	$-0.516217\pi$
$491$	−9.02388e29	−0.101849	−0.0509244	+	0.998703i	$0.516217\pi$
$492$	0	0
$493$	1.36183e31	1.46684
$494$	7.61034e30	0.800837
$495$	0	0
$496$	−1.35658e30	−0.136272
$497$	−8.92692e30	−0.876200
$498$	0	0
$499$	5.96674e30	0.559217	0.279609	−	0.960114i	$-0.409795\pi$
$499$	5.96674e30	0.559217	0.279609	+	0.960114i	$0.409795\pi$
$500$	4.35659e29	0.0399018
$501$	0	0
$502$	6.40445e30	0.560259
$503$	1.74710e31	1.49378	0.746889	−	0.664948i	$-0.231546\pi$
$503$	1.74710e31	1.49378	0.746889	+	0.664948i	$0.231546\pi$
$504$	0	0
$505$	−3.40194e30	−0.277892
$506$	4.91040e30	0.392090
$507$	0	0
$508$	−5.07325e30	−0.387127
$509$	1.04409e31	0.778901	0.389451	−	0.921047i	$-0.372665\pi$
$509$	1.04409e31	0.778901	0.389451	+	0.921047i	$0.372665\pi$
$510$	0	0
$511$	3.89753e30	0.277939
$512$	−2.99668e30	−0.208947
$513$	0	0
$514$	1.60951e31	1.07305
$515$	−2.27860e30	−0.148554
$516$	0	0
$517$	−8.26078e30	−0.515086
$518$	1.34835e31	0.822262
$519$	0	0
$520$	−2.20653e30	−0.128728
$521$	−1.37614e31	−0.785289	−0.392645	−	0.919690i	$-0.628440\pi$
$521$	−1.37614e31	−0.785289	−0.392645	+	0.919690i	$0.628440\pi$
$522$	0	0
$523$	8.72908e30	0.476649	0.238325	−	0.971186i	$-0.423402\pi$
$523$	8.72908e30	0.476649	0.238325	+	0.971186i	$0.423402\pi$
$524$	4.86619e30	0.259943
$525$	0	0
$526$	3.12723e31	1.59891
$527$	2.17141e30	0.108623
$528$	0	0
$529$	−1.14675e31	−0.549197
$530$	8.23927e30	0.386115
$531$	0	0
$532$	2.53224e31	1.13637
$533$	−1.19501e31	−0.524820
$534$	0	0
$535$	−6.64355e30	−0.279468
$536$	−2.63174e31	−1.08355
$537$	0	0
$538$	−1.46235e31	−0.576842
$539$	−2.17869e31	−0.841248
$540$	0	0
$541$	1.86887e31	0.691529	0.345765	−	0.938321i	$-0.387620\pi$
$541$	1.86887e31	0.691529	0.345765	+	0.938321i	$0.387620\pi$
$542$	6.26028e31	2.26778
$543$	0	0
$544$	2.38653e31	0.828667
$545$	1.42944e31	0.485967
$546$	0	0
$547$	4.47901e31	1.45992	0.729958	−	0.683492i	$-0.239540\pi$
$547$	4.47901e31	1.45992	0.729958	+	0.683492i	$0.239540\pi$
$548$	−6.27274e29	−0.0200208
$549$	0	0
$550$	3.81587e30	0.116795
$551$	7.58613e31	2.27393
$552$	0	0
$553$	6.71539e31	1.93078
$554$	5.87359e31	1.65402
$555$	0	0
$556$	1.81553e31	0.490506
$557$	−5.47014e31	−1.44765	−0.723825	−	0.689984i	$-0.757618\pi$
$557$	−5.47014e31	−1.44765	−0.723825	+	0.689984i	$0.757618\pi$
$558$	0	0
$559$	−9.77512e30	−0.248248
$560$	−3.70548e31	−0.921897
$561$	0	0
$562$	−1.28244e31	−0.306246
$563$	4.68187e31	1.09540	0.547700	−	0.836675i	$-0.315503\pi$
$563$	4.68187e31	1.09540	0.547700	+	0.836675i	$0.315503\pi$
$564$	0	0
$565$	−1.75090e31	−0.393283
$566$	−4.81757e31	−1.06032
$567$	0	0
$568$	−1.67056e31	−0.353067
$569$	−2.97676e31	−0.616528	−0.308264	−	0.951301i	$-0.599748\pi$
$569$	−2.97676e31	−0.616528	−0.308264	+	0.951301i	$0.599748\pi$
$570$	0	0
$571$	−1.67432e31	−0.333061	−0.166531	−	0.986036i	$-0.553256\pi$
$571$	−1.67432e31	−0.333061	−0.166531	+	0.986036i	$0.553256\pi$
$572$	4.80207e30	0.0936212
$573$	0	0
$574$	−1.28893e32	−2.41403
$575$	7.31482e30	0.134284
$576$	0	0
$577$	−1.06853e32	−1.88481	−0.942403	−	0.334480i	$-0.891439\pi$
$577$	−1.06853e32	−1.88481	−0.942403	+	0.334480i	$0.891439\pi$
$578$	8.23734e29	0.0142435
$579$	0	0
$580$	1.77155e31	0.294396
$581$	−5.28348e31	−0.860784
$582$	0	0
$583$	2.22628e31	0.348651
$584$	7.29374e30	0.111996
$585$	0	0
$586$	−4.26287e31	−0.629332
$587$	2.57743e31	0.373121	0.186560	−	0.982444i	$-0.440266\pi$
$587$	2.57743e31	0.373121	0.186560	+	0.982444i	$0.440266\pi$
$588$	0	0
$589$	1.20959e31	0.168389
$590$	−2.54334e31	−0.347221
$591$	0	0
$592$	3.92863e31	0.515871
$593$	5.96138e31	0.767747	0.383874	−	0.923386i	$-0.374590\pi$
$593$	5.96138e31	0.767747	0.383874	+	0.923386i	$0.374590\pi$
$594$	0	0
$595$	5.93117e31	0.734844
$596$	1.20718e31	0.146703
$597$	0	0
$598$	2.98397e31	0.348924
$599$	−1.18951e32	−1.36446	−0.682230	−	0.731138i	$-0.738990\pi$
$599$	−1.18951e32	−1.36446	−0.682230	+	0.731138i	$0.738990\pi$
$600$	0	0
$601$	1.20295e32	1.32798	0.663988	−	0.747743i	$-0.268863\pi$
$601$	1.20295e32	1.32798	0.663988	+	0.747743i	$0.268863\pi$
$602$	−1.05434e32	−1.14188
$603$	0	0
$604$	−4.84108e31	−0.504682
$605$	−3.34116e31	−0.341751
$606$	0	0
$607$	−1.66513e32	−1.63976	−0.819878	−	0.572538i	$-0.805959\pi$
$607$	−1.66513e32	−1.63976	−0.819878	+	0.572538i	$0.805959\pi$
$608$	1.32943e32	1.28462
$609$	0	0
$610$	3.16690e31	0.294673
$611$	−5.01994e31	−0.458379
$612$	0	0
$613$	−1.62167e32	−1.42615	−0.713077	−	0.701086i	$-0.752699\pi$
$613$	−1.62167e32	−1.42615	−0.713077	+	0.701086i	$0.752699\pi$
$614$	4.09619e31	0.353544
$615$	0	0
$616$	−6.43069e31	−0.534662
$617$	9.13641e30	0.0745583	0.0372792	−	0.999305i	$-0.488131\pi$
$617$	9.13641e30	0.0745583	0.0372792	+	0.999305i	$0.488131\pi$
$618$	0	0
$619$	2.00611e32	1.57729	0.788645	−	0.614849i	$-0.210783\pi$
$619$	2.00611e32	1.57729	0.788645	+	0.614849i	$0.210783\pi$
$620$	2.82471e30	0.0218007
$621$	0	0
$622$	−4.87701e31	−0.362714
$623$	−4.15195e32	−3.03138
$624$	0	0
$625$	5.68434e30	0.0400000
$626$	−1.02968e32	−0.711377
$627$	0	0
$628$	9.76008e31	0.650006
$629$	−6.28835e31	−0.411201
$630$	0	0
$631$	4.21641e31	0.265831	0.132915	−	0.991127i	$-0.457566\pi$
$631$	4.21641e31	0.265831	0.132915	+	0.991127i	$0.457566\pi$
$632$	1.25670e32	0.778011
$633$	0	0
$634$	−1.07745e32	−0.643239
$635$	−6.61941e31	−0.388080
$636$	0	0
$637$	−1.32395e32	−0.748633
$638$	1.55167e32	0.861713
$639$	0	0
$640$	−9.41492e31	−0.504368
$641$	1.52885e32	0.804448	0.402224	−	0.915541i	$-0.368237\pi$
$641$	1.52885e32	0.804448	0.402224	+	0.915541i	$0.368237\pi$
$642$	0	0
$643$	2.75547e32	1.39884	0.699422	−	0.714709i	$-0.253441\pi$
$643$	2.75547e32	1.39884	0.699422	+	0.714709i	$0.253441\pi$
$644$	9.92876e31	0.495117
$645$	0	0
$646$	−3.82820e32	−1.84213
$647$	2.72847e32	1.28979	0.644896	−	0.764270i	$-0.276901\pi$
$647$	2.72847e32	1.28979	0.644896	+	0.764270i	$0.276901\pi$
$648$	0	0
$649$	−6.87218e31	−0.313531
$650$	2.31884e31	0.103936
$651$	0	0
$652$	−4.35034e31	−0.188224
$653$	−1.77887e32	−0.756209	−0.378105	−	0.925763i	$-0.623424\pi$
$653$	−1.77887e32	−0.756209	−0.378105	+	0.925763i	$0.623424\pi$
$654$	0	0
$655$	6.34924e31	0.260583
$656$	−3.75551e32	−1.51452
$657$	0	0
$658$	−5.41446e32	−2.10842
$659$	3.66864e32	1.40386	0.701928	−	0.712248i	$-0.252323\pi$
$659$	3.66864e32	1.40386	0.701928	+	0.712248i	$0.252323\pi$
$660$	0	0
$661$	1.42358e32	0.526094	0.263047	−	0.964783i	$-0.415273\pi$
$661$	1.42358e32	0.526094	0.263047	+	0.964783i	$0.415273\pi$
$662$	−3.11658e32	−1.13191
$663$	0	0
$664$	−9.88737e31	−0.346855
$665$	3.30398e32	1.13917
$666$	0	0
$667$	2.97448e32	0.990748
$668$	−2.20366e31	−0.0721464
$669$	0	0
$670$	2.76569e32	0.874869
$671$	8.55706e31	0.266082
$672$	0	0
$673$	−4.30783e32	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$673$	−4.30783e32	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$674$	6.55656e31	0.193681
$675$	0	0
$676$	−1.27074e32	−0.362801
$677$	4.18262e32	1.17403	0.587015	−	0.809576i	$-0.300303\pi$
$677$	4.18262e32	1.17403	0.587015	+	0.809576i	$0.300303\pi$
$678$	0	0
$679$	9.77209e32	2.65146
$680$	1.10994e32	0.296107
$681$	0	0
$682$	2.47412e31	0.0638117
$683$	6.21337e32	1.57576	0.787878	−	0.615832i	$-0.211180\pi$
$683$	6.21337e32	1.57576	0.787878	+	0.615832i	$0.211180\pi$
$684$	0	0
$685$	−8.18447e30	−0.0200701
$686$	−6.03683e32	−1.45573
$687$	0	0
$688$	−3.07197e32	−0.716392
$689$	1.35287e32	0.310267
$690$	0	0
$691$	−3.22727e32	−0.715876	−0.357938	−	0.933745i	$-0.616520\pi$
$691$	−3.22727e32	−0.715876	−0.357938	+	0.933745i	$0.616520\pi$
$692$	−1.53590e32	−0.335076
$693$	0	0
$694$	5.05894e32	1.06764
$695$	2.36885e32	0.491714
$696$	0	0
$697$	6.01124e32	1.20722
$698$	−2.02884e32	−0.400785
$699$	0	0
$700$	7.71564e31	0.147484
$701$	−6.04008e32	−1.13576	−0.567879	−	0.823112i	$-0.692236\pi$
$701$	−6.04008e32	−1.13576	−0.567879	+	0.823112i	$0.692236\pi$
$702$	0	0
$703$	−3.50295e32	−0.637453
$704$	−6.63576e31	−0.118797
$705$	0	0
$706$	−2.42202e31	−0.0419685
$707$	−6.02492e32	−1.02714
$708$	0	0
$709$	1.41695e32	0.233842	0.116921	−	0.993141i	$-0.462698\pi$
$709$	1.41695e32	0.233842	0.116921	+	0.993141i	$0.462698\pi$
$710$	1.75559e32	0.285071
$711$	0	0
$712$	−7.76986e32	−1.22150
$713$	4.74275e31	0.0733670
$714$	0	0
$715$	6.26558e31	0.0938517
$716$	1.25724e32	0.185319
$717$	0	0
$718$	5.37151e32	0.766771
$719$	7.99309e32	1.12288	0.561439	−	0.827518i	$-0.310248\pi$
$719$	7.99309e32	1.12288	0.561439	+	0.827518i	$0.310248\pi$
$720$	0	0
$721$	−4.03545e32	−0.549081
$722$	−1.23451e33	−1.65317
$723$	0	0
$724$	−1.92528e32	−0.249747
$725$	2.31146e32	0.295121
$726$	0	0
$727$	−5.38025e32	−0.665514	−0.332757	−	0.943013i	$-0.607979\pi$
$727$	−5.38025e32	−0.665514	−0.332757	+	0.943013i	$0.607979\pi$
$728$	−3.90782e32	−0.475800
$729$	0	0
$730$	−7.66498e31	−0.0904270
$731$	4.91714e32	0.571036
$732$	0	0
$733$	2.14429e32	0.241317	0.120658	−	0.992694i	$-0.461499\pi$
$733$	2.14429e32	0.241317	0.120658	+	0.992694i	$0.461499\pi$
$734$	−1.15199e33	−1.27628
$735$	0	0
$736$	5.21261e32	0.559707
$737$	7.47298e32	0.789983
$738$	0	0
$739$	1.13335e33	1.16132	0.580660	−	0.814146i	$-0.302795\pi$
$739$	1.13335e33	1.16132	0.580660	+	0.814146i	$0.302795\pi$
$740$	−8.18028e31	−0.0825284
$741$	0	0
$742$	1.45920e33	1.42715
$743$	6.51220e32	0.627128	0.313564	−	0.949567i	$-0.398477\pi$
$743$	6.51220e32	0.627128	0.313564	+	0.949567i	$0.398477\pi$
$744$	0	0
$745$	1.57509e32	0.147064
$746$	4.94150e32	0.454320
$747$	0	0
$748$	−2.41557e32	−0.215353
$749$	−1.17659e33	−1.03296
$750$	0	0
$751$	−3.51591e32	−0.299349	−0.149675	−	0.988735i	$-0.547823\pi$
$751$	−3.51591e32	−0.299349	−0.149675	+	0.988735i	$0.547823\pi$
$752$	−1.57759e33	−1.32278
$753$	0	0
$754$	9.42927e32	0.766845
$755$	−6.31648e32	−0.505924
$756$	0	0
$757$	6.99863e32	0.543764	0.271882	−	0.962331i	$-0.412354\pi$
$757$	6.99863e32	0.543764	0.271882	+	0.962331i	$0.412354\pi$
$758$	1.16792e33	0.893755
$759$	0	0
$760$	6.18299e32	0.459031
$761$	4.14558e32	0.303153	0.151576	−	0.988446i	$-0.451565\pi$
$761$	4.14558e32	0.303153	0.151576	+	0.988446i	$0.451565\pi$
$762$	0	0
$763$	2.53158e33	1.79622
$764$	−3.34893e32	−0.234063
$765$	0	0
$766$	−2.23910e33	−1.51860
$767$	−4.17611e32	−0.279014
$768$	0	0
$769$	9.81121e32	0.636165	0.318082	−	0.948063i	$-0.396961\pi$
$769$	9.81121e32	0.636165	0.318082	+	0.948063i	$0.396961\pi$
$770$	6.75800e32	0.431693
$771$	0	0
$772$	3.75717e32	0.232949
$773$	2.80480e33	1.71332	0.856659	−	0.515883i	$-0.172536\pi$
$773$	2.80480e33	1.71332	0.856659	+	0.515883i	$0.172536\pi$
$774$	0	0
$775$	3.68559e31	0.0218543
$776$	1.82873e33	1.06841
$777$	0	0
$778$	−5.75652e32	−0.326509
$779$	3.34859e33	1.87146
$780$	0	0
$781$	4.74367e32	0.257411
$782$	−1.50101e33	−0.802615
$783$	0	0
$784$	−4.16071e33	−2.16039
$785$	1.27346e33	0.651606
$786$	0	0
$787$	1.29475e31	0.00643395	0.00321697	−	0.999995i	$-0.498976\pi$
$787$	1.29475e31	0.00643395	0.00321697	+	0.999995i	$0.498976\pi$
$788$	8.54731e32	0.418580
$789$	0	0
$790$	−1.32067e33	−0.628176
$791$	−3.10089e33	−1.45364
$792$	0	0
$793$	5.19998e32	0.236788
$794$	−2.90304e32	−0.130292
$795$	0	0
$796$	1.12906e32	0.0492287
$797$	4.31035e33	1.85243	0.926214	−	0.376998i	$-0.123044\pi$
$797$	4.31035e33	1.85243	0.926214	+	0.376998i	$0.123044\pi$
$798$	0	0
$799$	2.52516e33	1.05439
$800$	4.05072e32	0.166724
$801$	0	0
$802$	−4.44882e33	−1.77926
$803$	−2.07110e32	−0.0816532
$804$	0	0
$805$	1.29547e33	0.496336
$806$	1.50348e32	0.0567864
$807$	0	0
$808$	−1.12749e33	−0.413887
$809$	−1.38091e33	−0.499754	−0.249877	−	0.968278i	$-0.580390\pi$
$809$	−1.38091e33	−0.499754	−0.249877	+	0.968278i	$0.580390\pi$
$810$	0	0
$811$	−5.31082e33	−1.86819	−0.934097	−	0.357019i	$-0.883793\pi$
$811$	−5.31082e33	−1.86819	−0.934097	+	0.357019i	$0.883793\pi$
$812$	3.13747e33	1.08814
$813$	0	0
$814$	−7.16498e32	−0.241565
$815$	−5.67618e32	−0.188688
$816$	0	0
$817$	2.73912e33	0.885232
$818$	−5.40027e33	−1.72089
$819$	0	0
$820$	7.81980e32	0.242291
$821$	−3.74336e33	−1.14371	−0.571854	−	0.820355i	$-0.693776\pi$
$821$	−3.74336e33	−1.14371	−0.571854	+	0.820355i	$0.693776\pi$
$822$	0	0
$823$	5.42555e33	1.61193	0.805965	−	0.591964i	$-0.201647\pi$
$823$	5.42555e33	1.61193	0.805965	+	0.591964i	$0.201647\pi$
$824$	−7.55185e32	−0.221254
$825$	0	0
$826$	−4.50432e33	−1.28339
$827$	−4.40624e33	−1.23810	−0.619049	−	0.785352i	$-0.712482\pi$
$827$	−4.40624e33	−1.23810	−0.619049	+	0.785352i	$0.712482\pi$
$828$	0	0
$829$	−2.97522e32	−0.0813098	−0.0406549	−	0.999173i	$-0.512944\pi$
$829$	−2.97522e32	−0.0813098	−0.0406549	+	0.999173i	$0.512944\pi$
$830$	1.03906e33	0.280055
$831$	0	0
$832$	−4.03244e32	−0.105718
$833$	6.65983e33	1.72205
$834$	0	0
$835$	−2.87526e32	−0.0723240
$836$	−1.34560e33	−0.333845
$837$	0	0
$838$	2.95195e33	0.712530
$839$	−3.05689e33	−0.727809	−0.363904	−	0.931436i	$-0.618557\pi$
$839$	−3.05689e33	−0.727809	−0.363904	+	0.931436i	$0.618557\pi$
$840$	0	0
$841$	5.08255e33	1.17741
$842$	−9.83914e33	−2.24837
$843$	0	0
$844$	2.37817e33	0.528816
$845$	−1.65802e33	−0.363694
$846$	0	0
$847$	−5.91727e33	−1.26317
$848$	4.25160e33	0.895365
$849$	0	0
$850$	−1.16644e33	−0.239080
$851$	−1.37349e33	−0.277738
$852$	0	0
$853$	−2.74815e33	−0.540911	−0.270456	−	0.962732i	$-0.587174\pi$
$853$	−2.74815e33	−0.540911	−0.270456	+	0.962732i	$0.587174\pi$
$854$	5.60866e33	1.08916
$855$	0	0
$856$	−2.20184e33	−0.416234
$857$	−7.03785e33	−1.31269	−0.656343	−	0.754463i	$-0.727897\pi$
$857$	−7.03785e33	−1.31269	−0.656343	+	0.754463i	$0.727897\pi$
$858$	0	0
$859$	−5.19873e33	−0.944009	−0.472005	−	0.881596i	$-0.656469\pi$
$859$	−5.19873e33	−0.944009	−0.472005	+	0.881596i	$0.656469\pi$
$860$	6.39653e32	0.114607
$861$	0	0
$862$	−1.12821e34	−1.96814
$863$	−4.99662e33	−0.860107	−0.430054	−	0.902803i	$-0.641505\pi$
$863$	−4.99662e33	−0.860107	−0.430054	+	0.902803i	$0.641505\pi$
$864$	0	0
$865$	−2.00399e33	−0.335901
$866$	−1.36760e34	−2.26205
$867$	0	0
$868$	5.00263e32	0.0805790
$869$	−3.56848e33	−0.567226
$870$	0	0
$871$	4.54121e33	0.703011
$872$	4.73753e33	0.723790
$873$	0	0
$874$	−8.36147e33	−1.24423
$875$	1.00671e33	0.147847
$876$	0	0
$877$	8.71040e33	1.24607	0.623035	−	0.782194i	$-0.285899\pi$
$877$	8.71040e33	1.24607	0.623035	+	0.782194i	$0.285899\pi$
$878$	1.56813e34	2.21409
$879$	0	0
$880$	1.96905e33	0.270836
$881$	−1.34397e33	−0.182460	−0.0912301	−	0.995830i	$-0.529080\pi$
$881$	−1.34397e33	−0.182460	−0.0912301	+	0.995830i	$0.529080\pi$
$882$	0	0
$883$	−9.50375e33	−1.25703	−0.628517	−	0.777796i	$-0.716338\pi$
$883$	−9.50375e33	−1.25703	−0.628517	+	0.777796i	$0.716338\pi$
$884$	−1.46790e33	−0.191644
$885$	0	0
$886$	8.50639e33	1.08207
$887$	1.82994e33	0.229782	0.114891	−	0.993378i	$-0.463348\pi$
$887$	1.82994e33	0.229782	0.114891	+	0.993378i	$0.463348\pi$
$888$	0	0
$889$	−1.17231e34	−1.43441
$890$	8.16534e33	0.986254
$891$	0	0
$892$	8.73775e32	0.102850
$893$	1.40665e34	1.63454
$894$	0	0
$895$	1.64041e33	0.185775
$896$	−1.66741e34	−1.86423
$897$	0	0
$898$	1.86032e34	2.02726
$899$	1.49870e33	0.161242
$900$	0	0
$901$	−6.80531e33	−0.713695
$902$	6.84924e33	0.709197
$903$	0	0
$904$	−5.80294e33	−0.585748
$905$	−2.51204e33	−0.250362
$906$	0	0
$907$	1.77973e34	1.72930	0.864650	−	0.502375i	$-0.167540\pi$
$907$	1.77973e34	1.72930	0.864650	+	0.502375i	$0.167540\pi$
$908$	6.06618e33	0.582007
$909$	0	0
$910$	4.10672e33	0.384167
$911$	−1.74322e34	−1.61024	−0.805119	−	0.593114i	$-0.797898\pi$
$911$	−1.74322e34	−1.61024	−0.805119	+	0.593114i	$0.797898\pi$
$912$	0	0
$913$	2.80758e33	0.252882
$914$	−1.42546e34	−1.26787
$915$	0	0
$916$	−4.44489e33	−0.385534
$917$	1.12447e34	0.963162
$918$	0	0
$919$	−1.47114e34	−1.22893	−0.614464	−	0.788945i	$-0.710628\pi$
$919$	−1.47114e34	−1.22893	−0.614464	+	0.788945i	$0.710628\pi$
$920$	2.42431e33	0.200000
$921$	0	0
$922$	−1.66992e34	−1.34366
$923$	2.88265e33	0.229072
$924$	0	0
$925$	−1.06734e33	−0.0827316
$926$	1.45850e34	1.11656
$927$	0	0
$928$	1.64717e34	1.23009
$929$	−8.36002e33	−0.616633	−0.308317	−	0.951284i	$-0.599766\pi$
$929$	−8.36002e33	−0.616633	−0.308317	+	0.951284i	$0.599766\pi$
$930$	0	0
$931$	3.70989e34	2.66956
$932$	9.62901e33	0.684382
$933$	0	0
$934$	1.17990e33	0.0818191
$935$	−3.15175e33	−0.215883
$936$	0	0
$937$	−1.67822e34	−1.12161	−0.560807	−	0.827947i	$-0.689509\pi$
$937$	−1.67822e34	−1.12161	−0.560807	+	0.827947i	$0.689509\pi$
$938$	4.89810e34	3.23367
$939$	0	0
$940$	3.28489e33	0.211617
$941$	2.19130e34	1.39451	0.697254	−	0.716824i	$-0.254405\pi$
$941$	2.19130e34	1.39451	0.697254	+	0.716824i	$0.254405\pi$
$942$	0	0
$943$	1.31296e34	0.815394
$944$	−1.31240e34	−0.805174
$945$	0	0
$946$	5.60262e33	0.335462
$947$	−1.41902e34	−0.839388	−0.419694	−	0.907666i	$-0.637863\pi$
$947$	−1.41902e34	−0.839388	−0.419694	+	0.907666i	$0.637863\pi$
$948$	0	0
$949$	−1.25857e33	−0.0726637
$950$	−6.49770e33	−0.370628
$951$	0	0
$952$	1.96574e34	1.09446
$953$	9.37154e33	0.515517	0.257758	−	0.966209i	$-0.417016\pi$
$953$	9.37154e33	0.515517	0.257758	+	0.966209i	$0.417016\pi$
$954$	0	0
$955$	−4.36957e33	−0.234639
$956$	−9.62217e33	−0.510513
$957$	0	0
$958$	3.52782e34	1.82727
$959$	−1.44949e33	−0.0741825
$960$	0	0
$961$	−1.97743e34	−0.988060
$962$	−4.35404e33	−0.214970
$963$	0	0
$964$	3.37812e33	0.162851
$965$	4.90223e33	0.233523
$966$	0	0
$967$	−4.30462e33	−0.200231	−0.100115	−	0.994976i	$-0.531921\pi$
$967$	−4.30462e33	−0.200231	−0.100115	+	0.994976i	$0.531921\pi$
$968$	−1.10734e34	−0.508998
$969$	0	0
$970$	−1.92180e34	−0.862649
$971$	−3.14085e33	−0.139324	−0.0696619	−	0.997571i	$-0.522192\pi$
$971$	−3.14085e33	−0.139324	−0.0696619	+	0.997571i	$0.522192\pi$
$972$	0	0
$973$	4.19529e34	1.81746
$974$	1.57093e34	0.672556
$975$	0	0
$976$	1.63417e34	0.683321
$977$	−1.88718e33	−0.0779877	−0.0389939	−	0.999239i	$-0.512415\pi$
$977$	−1.88718e33	−0.0779877	−0.0389939	+	0.999239i	$0.512415\pi$
$978$	0	0
$979$	2.20630e34	0.890561
$980$	8.66353e33	0.345617
$981$	0	0
$982$	3.14297e33	0.122478
$983$	3.74187e34	1.44120	0.720599	−	0.693352i	$-0.243867\pi$
$983$	3.74187e34	1.44120	0.720599	+	0.693352i	$0.243867\pi$
$984$	0	0
$985$	1.11523e34	0.419610
$986$	−4.74317e34	−1.76394
$987$	0	0
$988$	−8.17701e33	−0.297091
$989$	1.07399e34	0.385695
$990$	0	0
$991$	−3.57254e34	−1.25352	−0.626759	−	0.779213i	$-0.715619\pi$
$991$	−3.57254e34	−1.25352	−0.626759	+	0.779213i	$0.715619\pi$
$992$	2.62639e33	0.0910909
$993$	0	0
$994$	3.10920e34	1.05367
$995$	1.47317e33	0.0493499
$996$	0	0
$997$	−7.47285e33	−0.244620	−0.122310	−	0.992492i	$-0.539030\pi$
$997$	−7.47285e33	−0.244620	−0.122310	+	0.992492i	$0.539030\pi$
$998$	−2.07818e34	−0.672484
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.24.a.d.1.1		4
3.2	odd	2		5.24.a.b.1.4	✓	4
15.2	even	4		25.24.b.c.24.7		8
15.8	even	4		25.24.b.c.24.2		8
15.14	odd	2		25.24.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.a.b.1.4	✓	4	3.2	odd	2
25.24.a.c.1.1		4	15.14	odd	2
25.24.b.c.24.2		8	15.8	even	4
25.24.b.c.24.7		8	15.2	even	4
45.24.a.d.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q-3482.94 q^{2} +3.74229e6 q^{4} +4.88281e7 q^{5} +8.64758e9 q^{7} +1.61829e10 q^{8} +O(q^{10})\)	\(q-3482.94 q^{2} +3.74229e6 q^{4} +4.88281e7 q^{5} +8.64758e9 q^{7} +1.61829e10 q^{8} -1.70066e11 q^{10} -4.59523e11 q^{11} -2.79244e12 q^{13} -3.01190e13 q^{14} -8.77566e13 q^{16} +1.40467e14 q^{17} +7.82480e14 q^{19} +1.82729e14 q^{20} +1.60049e15 q^{22} +3.06806e15 q^{23} +2.38419e15 q^{25} +9.72592e15 q^{26} +3.23617e16 q^{28} +9.69499e16 q^{29} +1.54585e16 q^{31} +1.69899e17 q^{32} -4.89240e17 q^{34} +4.22245e17 q^{35} -4.47673e17 q^{37} -2.72533e18 q^{38} +7.90180e17 q^{40} +4.27946e18 q^{41} +3.50056e18 q^{43} -1.71967e18 q^{44} -1.06859e19 q^{46} +1.79769e19 q^{47} +4.74120e19 q^{49} -8.30398e18 q^{50} -1.04501e19 q^{52} -4.84476e19 q^{53} -2.24376e19 q^{55} +1.39943e20 q^{56} -3.37671e20 q^{58} +1.49550e20 q^{59} -1.86216e20 q^{61} -5.38410e19 q^{62} +1.44406e20 q^{64} -1.36350e20 q^{65} -1.62625e21 q^{67} +5.25669e20 q^{68} -1.47066e21 q^{70} -1.03230e21 q^{71} +4.50707e20 q^{73} +1.55922e21 q^{74} +2.92826e21 q^{76} -3.97376e21 q^{77} +7.76563e21 q^{79} -4.28499e21 q^{80} -1.49051e22 q^{82} -6.10977e21 q^{83} +6.85876e21 q^{85} -1.21923e22 q^{86} -7.43640e21 q^{88} -4.80129e22 q^{89} -2.41479e22 q^{91} +1.14815e22 q^{92} -6.26124e22 q^{94} +3.82070e22 q^{95} +1.13004e23 q^{97} -1.65133e23 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 780 q^{2} + 12685792 q^{4} + 195312500 q^{5} - 1010710600 q^{7} + 90964721760 q^{8}+O(q^{10}) \) 4 * q + 780 * q^2 + 12685792 * q^4 + 195312500 * q^5 - 1010710600 * q^7 + 90964721760 * q^8	\( 4 q + 780 q^{2} + 12685792 q^{4} + 195312500 q^{5} - 1010710600 q^{7} + 90964721760 q^{8} + 38085937500 q^{10} - 510770963328 q^{11} - 14153856943960 q^{13} - 64982579554584 q^{14} + 113436824881024 q^{16} - 15332090016360 q^{17} + 11\!\cdots\!40 q^{19}+ \cdots + 80\!\cdots\!40 q^{98}+O(q^{100}) \) 4 * q + 780 * q^2 + 12685792 * q^4 + 195312500 * q^5 - 1010710600 * q^7 + 90964721760 * q^8 + 38085937500 * q^10 - 510770963328 * q^11 - 14153856943960 * q^13 - 64982579554584 * q^14 + 113436824881024 * q^16 - 15332090016360 * q^17 + 1111809672255440 * q^19 + 619423437500000 * q^20 + 10708927083459840 * q^22 + 3998020505342040 * q^23 + 9536743164062500 * q^25 + 877714925108472 * q^26 - 113078857801120960 * q^28 + 170274795551093640 * q^29 - 172942006080462832 * q^31 + 567511045488564480 * q^32 + 207151653136271304 * q^34 - 49351103515625000 * q^35 + 461695977491285480 * q^37 - 2127655695829602960 * q^38 + 4441636804687500000 * q^40 - 1746066900841990488 * q^41 + 13231308551430609800 * q^43 + 21011535794344429056 * q^44 + 22929884441616610248 * q^46 + 25463181064945728360 * q^47 + 27752501816433355572 * q^49 + 1859664916992187500 * q^50 - 155108839850940462400 * q^52 - 19153511824499883720 * q^53 - 24939988443750000000 * q^55 - 411860605716761453760 * q^56 + 221034899302314393240 * q^58 - 217218038347313160720 * q^59 + 152379678911827122728 * q^61 + 363203697269394525360 * q^62 + 1121074796200062441472 * q^64 - 691106296091796875000 * q^65 - 2317407910895557756840 * q^67 + 3800878923901661494080 * q^68 - 3172977517313671875000 * q^70 - 1453247054528140867248 * q^71 + 2601821824581282121160 * q^73 + 3991697886987492208056 * q^74 - 514198358053038321280 * q^76 - 7444709512703076153600 * q^77 + 22817266427547282683360 * q^79 + 5538907464893750000000 * q^80 - 25020293761756353578760 * q^82 - 49081293110242175251080 * q^83 - 748637207830078125000 * q^85 + 37195944193834827943512 * q^86 + 7962508551211096903680 * q^88 - 50023669870473477290280 * q^89 + 55881722079510765798448 * q^91 + 239405355986426422923840 * q^92 - 34668831477450377120136 * q^94 + 54287581653097656250000 * q^95 - 141223261544238546490360 * q^97 + 8062497360198964195740 * q^98

Introduction

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