LMFDB - Embedded newform 18.46.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,46,Mod(1,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 46, names="a")

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

chi := DirichletCharacter("18.1");

S:= CuspForms(chi, 46);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 46 $
Character orbit:	$[\chi]$	$=$	18.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:	$230.860306934$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 163774578 $ x^2 - x - 163774578
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 11 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-12796.9$ of defining polynomial
Character	$\chi$	$=$	18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.19430e6 q^{2} +1.75922e13 q^{4} +5.35098e15 q^{5} -5.31551e18 q^{7} +7.37870e19 q^{8} +O(q^{10})$	\(q+4.19430e6 q^{2} +1.75922e13 q^{4} +5.35098e15 q^{5} -5.31551e18 q^{7} +7.37870e19 q^{8} +2.24436e22 q^{10} -3.01022e23 q^{11} -3.58553e24 q^{13} -2.22949e25 q^{14} +3.09485e26 q^{16} -2.22752e26 q^{17} +4.98355e28 q^{19} +9.41355e28 q^{20} -1.26258e30 q^{22} +4.72970e30 q^{23} +2.11308e29 q^{25} -1.50388e31 q^{26} -9.35114e31 q^{28} -6.15404e32 q^{29} +5.25156e32 q^{31} +1.29807e33 q^{32} -9.34291e32 q^{34} -2.84432e34 q^{35} +2.05864e35 q^{37} +2.09025e35 q^{38} +3.94833e35 q^{40} -1.88067e36 q^{41} -1.70766e36 q^{43} -5.29564e36 q^{44} +1.98378e37 q^{46} -3.61985e37 q^{47} -7.87523e37 q^{49} +8.86290e35 q^{50} -6.30773e37 q^{52} -9.38248e38 q^{53} -1.61077e39 q^{55} -3.92215e38 q^{56} -2.58119e39 q^{58} +4.98073e39 q^{59} +2.73039e39 q^{61} +2.20267e39 q^{62} +5.44452e39 q^{64} -1.91861e40 q^{65} -1.07891e41 q^{67} -3.91870e39 q^{68} -1.19299e41 q^{70} +9.82494e40 q^{71} +2.35740e41 q^{73} +8.63456e41 q^{74} +8.76715e41 q^{76} +1.60009e42 q^{77} -9.11195e42 q^{79} +1.65605e42 q^{80} -7.88811e42 q^{82} +3.78507e42 q^{83} -1.19194e42 q^{85} -7.16245e42 q^{86} -2.22115e43 q^{88} +8.23878e43 q^{89} +1.90589e43 q^{91} +8.32058e43 q^{92} -1.51828e44 q^{94} +2.66669e44 q^{95} -1.69418e44 q^{97} -3.30311e44 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8388608 q^{2} + 35184372088832 q^{4} + 45\!\cdots\!00 q^{5}+ \cdots + 14\!\cdots\!28 q^{8}+O(q^{10}) $ 2 * q + 8388608 * q^2 + 35184372088832 * q^4 + 4502496162681300 * q^5 - 9564351425209104944 * q^7 + 147573952589676412928 * q^8	$ 2 q + 8388608 q^{2} + 35184372088832 q^{4} + 45\!\cdots\!00 q^{5}+ \cdots - 70\!\cdots\!84 q^{98}+O(q^{100}) $ 2 * q + 8388608 * q^2 + 35184372088832 * q^4 + 4502496162681300 * q^5 - 9564351425209104944 * q^7 + 147573952589676412928 * q^8 + 18884837665118827315200 * q^10 - 198786084430704131948664 * q^11 + 11451156052847070865478908 * q^13 - 40115797440160249703038976 * q^14 + 618970019642690137449562112 * q^16 - 1563202963522522223200782756 * q^17 - 38059827532732969070582665400 * q^19 + 79208750158158557883452620800 * q^20 - 833769269072040063448809209856 * q^22 + 3019065536381638234619389053072 * q^23 - 27490471710601873355395547121250 * q^25 + 48029629637080680719361645740032 * q^26 - 168257849666453895970455189192704 * q^28 + 280581379156203770144200953240420 * q^29 - 4189611301991905914902859454659776 * q^31 + 2596148429267413814265248164610048 * q^32 - 6556548442714369050859935916621824 * q^34 - 24838110552152718910556999414853600 * q^35 + 505778201204488215524264884178967916 * q^37 - 159634486859852023104621155817881600 * q^38 + 332225577623365071964796861231923200 * q^40 - 418164031451191405542034507224542484 * q^41 - 3549110943868129840436165872994478152 * q^43 - 3497081780345933926283594264135860224 * q^44 + 12662878655507650774017041982856101888 * q^46 + 12007068225044323361722631178296373024 * q^47 - 167706511209625603483189808428567988046 * q^49 - 115303395457664279822028964872847360000 * q^50 + 201450867705326047463941428173999177728 * q^52 - 1412307165618014181350584692903529779468 * q^53 - 1697512303911992562809549506325502471600 * q^55 - 705724571887406241684464081851715158016 * q^56 + 1176843600920382097930902634980106567680 * q^58 + 14425168975774921208266222088136852713640 * q^59 - 21544742169968151649138784822449267819556 * q^61 - 17572503442389858946500723022117317115904 * q^62 + 10889035741470030830827987437816582766592 * q^64 - 31944525970238170776211660453695076069800 * q^65 - 96479943874272547038464438827275621594584 * q^67 - 27500157359470648967498032654830582890496 * q^68 - 104178586441336357537424864873718113894400 * q^70 - 440739175289788187629870406465468826532944 * q^71 - 346231544919662222196116641714398922459052 * q^73 + 2121387532424789740326286300771381845950464 * q^74 - 669555566774224779915804932331564066406400 * q^76 + 1165701312439316428813861475091700140057408 * q^77 - 627123872043088732794879973354503802534880 * q^79 + 1393455069127990614802235334252500405452800 * q^80 - 1753907069771857917030577501789927438811136 * q^82 - 9625160990874063774180757999996692860808648 * q^83 - 54588720694608839702922500851417883111400 * q^85 - 14886050228309872462260772265764231690846208 * q^86 - 14667824099632072050746984556442095080964096 * q^88 + 125803218506661664646783479200413122083076620 * q^89 - 44829596783932153927475828505081057977500576 * q^91 + 53111962596310361672062775256861279573245952 * q^92 + 50361294284576305653366678841653190560055296 * q^94 + 341246876890106594702844083541175355872770000 * q^95 + 47343316954280034711620535205361321066461636 * q^97 - 703412090792577507191956946251176426533289984 * 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 $

$2$	4.19430e6	0.707107
$2$	4.19430e6	0.707107
$3$	0	0
$3$	0	0
$4$	1.75922e13	0.500000
$5$	5.35098e15	1.00371	0.501855	−	0.864952i	$-0.332651\pi$
$5$	5.35098e15	1.00371	0.501855	+	0.864952i	$0.332651\pi$
$6$	0	0
$7$	−5.31551e18	−0.513853	−0.256927	−	0.966431i	$-0.582710\pi$
$7$	−5.31551e18	−0.513853	−0.256927	+	0.966431i	$0.582710\pi$
$8$	7.37870e19	0.353553
$9$	0	0
$10$	2.24436e22	0.709730
$11$	−3.01022e23	−1.11497	−0.557485	−	0.830187i	$-0.688234\pi$
$11$	−3.01022e23	−1.11497	−0.557485	+	0.830187i	$0.688234\pi$
$12$	0	0
$13$	−3.58553e24	−0.309619	−0.154810	−	0.987944i	$-0.549476\pi$
$13$	−3.58553e24	−0.309619	−0.154810	+	0.987944i	$0.549476\pi$
$14$	−2.22949e25	−0.363349
$15$	0	0
$16$	3.09485e26	0.250000
$17$	−2.22752e26	−0.0459961	−0.0229981	−	0.999736i	$-0.507321\pi$
$17$	−2.22752e26	−0.0459961	−0.0229981	+	0.999736i	$0.507321\pi$
$18$	0	0
$19$	4.98355e28	0.842525	0.421262	−	0.906939i	$-0.361587\pi$
$19$	4.98355e28	0.842525	0.421262	+	0.906939i	$0.361587\pi$
$20$	9.41355e28	0.501855
$21$	0	0
$22$	−1.26258e30	−0.788403
$23$	4.72970e30	1.08632	0.543160	−	0.839629i	$-0.317228\pi$
$23$	4.72970e30	1.08632	0.543160	+	0.839629i	$0.317228\pi$
$24$	0	0
$25$	2.11308e29	0.00743474
$26$	−1.50388e31	−0.218934
$27$	0	0
$28$	−9.35114e31	−0.256927
$29$	−6.15404e32	−0.767725	−0.383862	−	0.923390i	$-0.625406\pi$
$29$	−6.15404e32	−0.767725	−0.383862	+	0.923390i	$0.625406\pi$
$30$	0	0
$31$	5.25156e32	0.146100	0.0730500	−	0.997328i	$-0.476727\pi$
$31$	5.25156e32	0.146100	0.0730500	+	0.997328i	$0.476727\pi$
$32$	1.29807e33	0.176777
$33$	0	0
$34$	−9.34291e32	−0.0325242
$35$	−2.84432e34	−0.515760
$36$	0	0
$37$	2.05864e35	1.06916	0.534579	−	0.845119i	$-0.320470\pi$
$37$	2.05864e35	1.06916	0.534579	+	0.845119i	$0.320470\pi$
$38$	2.09025e35	0.595755
$39$	0	0
$40$	3.94833e35	0.354865
$41$	−1.88067e36	−0.969787	−0.484894	−	0.874573i	$-0.661142\pi$
$41$	−1.88067e36	−0.969787	−0.484894	+	0.874573i	$0.661142\pi$
$42$	0	0
$43$	−1.70766e36	−0.301551	−0.150776	−	0.988568i	$-0.548177\pi$
$43$	−1.70766e36	−0.301551	−0.150776	+	0.988568i	$0.548177\pi$
$44$	−5.29564e36	−0.557485
$45$	0	0
$46$	1.98378e37	0.768144
$47$	−3.61985e37	−0.863951	−0.431976	−	0.901885i	$-0.642183\pi$
$47$	−3.61985e37	−0.863951	−0.431976	+	0.901885i	$0.642183\pi$
$48$	0	0
$49$	−7.87523e37	−0.735955
$50$	8.86290e35	0.00525716
$51$	0	0
$52$	−6.30773e37	−0.154810
$53$	−9.38248e38	−1.50007	−0.750033	−	0.661400i	$-0.769962\pi$
$53$	−9.38248e38	−1.50007	−0.750033	+	0.661400i	$0.769962\pi$
$54$	0	0
$55$	−1.61077e39	−1.11911
$56$	−3.92215e38	−0.181674
$57$	0	0
$58$	−2.58119e39	−0.542863
$59$	4.98073e39	0.713054	0.356527	−	0.934285i	$-0.383961\pi$
$59$	4.98073e39	0.713054	0.356527	+	0.934285i	$0.383961\pi$
$60$	0	0
$61$	2.73039e39	0.184631	0.0923153	−	0.995730i	$-0.470573\pi$
$61$	2.73039e39	0.184631	0.0923153	+	0.995730i	$0.470573\pi$
$62$	2.20267e39	0.103308
$63$	0	0
$64$	5.44452e39	0.125000
$65$	−1.91861e40	−0.310768
$66$	0	0
$67$	−1.07891e41	−0.883698	−0.441849	−	0.897089i	$-0.645677\pi$
$67$	−1.07891e41	−0.883698	−0.441849	+	0.897089i	$0.645677\pi$
$68$	−3.91870e39	−0.0229981
$69$	0	0
$70$	−1.19299e41	−0.364697
$71$	9.82494e40	0.218282	0.109141	−	0.994026i	$-0.465190\pi$
$71$	9.82494e40	0.218282	0.109141	+	0.994026i	$0.465190\pi$
$72$	0	0
$73$	2.35740e41	0.280330	0.140165	−	0.990128i	$-0.455237\pi$
$73$	2.35740e41	0.280330	0.140165	+	0.990128i	$0.455237\pi$
$74$	8.63456e41	0.756008
$75$	0	0
$76$	8.76715e41	0.421262
$77$	1.60009e42	0.572931
$78$	0	0
$79$	−9.11195e42	−1.83232	−0.916161	−	0.400810i	$-0.868729\pi$
$79$	−9.11195e42	−1.83232	−0.916161	+	0.400810i	$0.868729\pi$
$80$	1.65605e42	0.250928
$81$	0	0
$82$	−7.88811e42	−0.685743
$83$	3.78507e42	0.250505	0.125253	−	0.992125i	$-0.460026\pi$
$83$	3.78507e42	0.250505	0.125253	+	0.992125i	$0.460026\pi$
$84$	0	0
$85$	−1.19194e42	−0.0461668
$86$	−7.16245e42	−0.213229
$87$	0	0
$88$	−2.22115e43	−0.394202
$89$	8.23878e43	1.13393	0.566967	−	0.823740i	$-0.308117\pi$
$89$	8.23878e43	1.13393	0.566967	+	0.823740i	$0.308117\pi$
$90$	0	0
$91$	1.90589e43	0.159099
$92$	8.32058e43	0.543160
$93$	0	0
$94$	−1.51828e44	−0.610906
$95$	2.66669e44	0.845651
$96$	0	0
$97$	−1.69418e44	−0.336198	−0.168099	−	0.985770i	$-0.553763\pi$
$97$	−1.69418e44	−0.336198	−0.168099	+	0.985770i	$0.553763\pi$
$98$	−3.30311e44	−0.520399
$99$	0	0
$100$	3.71737e42	0.00371737
$101$	1.33894e45	1.07036	0.535182	−	0.844737i	$-0.320243\pi$
$101$	1.33894e45	1.07036	0.535182	+	0.844737i	$0.320243\pi$
$102$	0	0
$103$	−8.91708e44	−0.458548	−0.229274	−	0.973362i	$-0.573635\pi$
$103$	−8.91708e44	−0.458548	−0.229274	+	0.973362i	$0.573635\pi$
$104$	−2.64565e44	−0.109467
$105$	0	0
$106$	−3.93530e45	−1.06071
$107$	−8.16657e45	−1.78199	−0.890994	−	0.454015i	$-0.849991\pi$
$107$	−8.16657e45	−1.78199	−0.890994	+	0.454015i	$0.849991\pi$
$108$	0	0
$109$	6.73063e45	0.968187	0.484093	−	0.875016i	$-0.339149\pi$
$109$	6.73063e45	0.968187	0.484093	+	0.875016i	$0.339149\pi$
$110$	−6.75604e45	−0.791329
$111$	0	0
$112$	−1.64507e45	−0.128463
$113$	−1.22826e46	−0.785283	−0.392642	−	0.919692i	$-0.628439\pi$
$113$	−1.22826e46	−0.785283	−0.392642	+	0.919692i	$0.628439\pi$
$114$	0	0
$115$	2.53086e46	1.09035
$116$	−1.08263e46	−0.383862
$117$	0	0
$118$	2.08907e46	0.504206
$119$	1.18404e45	0.0236353
$120$	0	0
$121$	1.77240e46	0.243160
$122$	1.14521e46	0.130554
$123$	0	0
$124$	9.23865e45	0.0730500
$125$	−1.50953e47	−0.996248
$126$	0	0
$127$	−3.00310e47	−1.38671	−0.693356	−	0.720595i	$-0.743869\pi$
$127$	−3.00310e47	−1.38671	−0.693356	+	0.720595i	$0.743869\pi$
$128$	2.28360e46	0.0883883
$129$	0	0
$130$	−8.04723e46	−0.219746
$131$	9.92430e45	0.0228085	0.0114042	−	0.999935i	$-0.496370\pi$
$131$	9.92430e45	0.0228085	0.0114042	+	0.999935i	$0.496370\pi$
$132$	0	0
$133$	−2.64901e47	−0.432934
$134$	−4.52529e47	−0.624869
$135$	0	0
$136$	−1.64362e46	−0.0162621
$137$	−8.57379e47	−0.719383	−0.359691	−	0.933071i	$-0.617118\pi$
$137$	−8.57379e47	−0.719383	−0.359691	+	0.933071i	$0.617118\pi$
$138$	0	0
$139$	−2.50782e48	−1.51867	−0.759335	−	0.650699i	$-0.774476\pi$
$139$	−2.50782e48	−1.51867	−0.759335	+	0.650699i	$0.774476\pi$
$140$	−5.00378e47	−0.257880
$141$	0	0
$142$	4.12088e47	0.154348
$143$	1.07932e48	0.345216
$144$	0	0
$145$	−3.29302e48	−0.770574
$146$	9.88766e47	0.198223
$147$	0	0
$148$	3.62160e48	0.534579
$149$	1.24099e48	0.157427	0.0787133	−	0.996897i	$-0.474919\pi$
$149$	1.24099e48	0.157427	0.0787133	+	0.996897i	$0.474919\pi$
$150$	0	0
$151$	6.70853e47	0.0630443	0.0315222	−	0.999503i	$-0.489965\pi$
$151$	6.70853e47	0.0630443	0.0315222	+	0.999503i	$0.489965\pi$
$152$	3.67721e48	0.297878
$153$	0	0
$154$	6.71125e48	0.405124
$155$	2.81010e48	0.146642
$156$	0	0
$157$	2.27753e49	0.890682	0.445341	−	0.895361i	$-0.353082\pi$
$157$	2.27753e49	0.890682	0.445341	+	0.895361i	$0.353082\pi$
$158$	−3.82183e49	−1.29565
$159$	0	0
$160$	6.94597e48	0.177433
$161$	−2.51408e49	−0.558209
$162$	0	0
$163$	2.89919e49	0.487590	0.243795	−	0.969827i	$-0.421608\pi$
$163$	2.89919e49	0.487590	0.243795	+	0.969827i	$0.421608\pi$
$164$	−3.30852e49	−0.484894
$165$	0	0
$166$	1.58757e49	0.177134
$167$	7.10968e49	0.692994	0.346497	−	0.938051i	$-0.387371\pi$
$167$	7.10968e49	0.692994	0.346497	+	0.938051i	$0.387371\pi$
$168$	0	0
$169$	−1.21251e50	−0.904136
$170$	−4.99937e48	−0.0326449
$171$	0	0
$172$	−3.00415e49	−0.150776
$173$	4.08899e50	1.80127	0.900634	−	0.434578i	$-0.143103\pi$
$173$	4.08899e50	1.80127	0.900634	+	0.434578i	$0.143103\pi$
$174$	0	0
$175$	−1.12321e48	−0.00382036
$176$	−9.31619e49	−0.278743
$177$	0	0
$178$	3.45560e50	0.801813
$179$	4.98693e50	1.02009	0.510047	−	0.860147i	$-0.329628\pi$
$179$	4.98693e50	1.02009	0.510047	+	0.860147i	$0.329628\pi$
$180$	0	0
$181$	−8.16176e50	−1.30022	−0.650109	−	0.759841i	$-0.725277\pi$
$181$	−8.16176e50	−1.30022	−0.650109	+	0.759841i	$0.725277\pi$
$182$	7.99388e49	0.112500
$183$	0	0
$184$	3.48991e50	0.384072
$185$	1.10157e51	1.07312
$186$	0	0
$187$	6.70534e49	0.0512843
$188$	−6.36812e50	−0.431976
$189$	0	0
$190$	1.11849e51	0.597966
$191$	−1.24243e51	−0.590229	−0.295114	−	0.955462i	$-0.595358\pi$
$191$	−1.24243e51	−0.590229	−0.295114	+	0.955462i	$0.595358\pi$
$192$	0	0
$193$	−1.67929e51	−0.631082	−0.315541	−	0.948912i	$-0.602186\pi$
$193$	−1.67929e51	−0.631082	−0.315541	+	0.948912i	$0.602186\pi$
$194$	−7.10590e50	−0.237728
$195$	0	0
$196$	−1.38542e51	−0.367978
$197$	−6.97671e51	−1.65257	−0.826287	−	0.563250i	$-0.809551\pi$
$197$	−6.97671e51	−1.65257	−0.826287	+	0.563250i	$0.809551\pi$
$198$	0	0
$199$	−3.27895e51	−0.618785	−0.309393	−	0.950934i	$-0.600126\pi$
$199$	−3.27895e51	−0.618785	−0.309393	+	0.950934i	$0.600126\pi$
$200$	1.55918e49	0.00262858
$201$	0	0
$202$	5.61594e51	0.756862
$203$	3.27119e51	0.394498
$204$	0	0
$205$	−1.00634e52	−0.973386
$206$	−3.74009e51	−0.324242
$207$	0	0
$208$	−1.10967e51	−0.0774048
$209$	−1.50016e52	−0.939391
$210$	0	0
$211$	3.10810e52	1.57087	0.785434	−	0.618946i	$-0.212440\pi$
$211$	3.10810e52	1.57087	0.785434	+	0.618946i	$0.212440\pi$
$212$	−1.65058e52	−0.750033
$213$	0	0
$214$	−3.42531e52	−1.26006
$215$	−9.13767e51	−0.302670
$216$	0	0
$217$	−2.79147e51	−0.0750740
$218$	2.82303e52	0.684612
$219$	0	0
$220$	−2.83369e52	−0.559554
$221$	7.98684e50	0.0142413
$222$	0	0
$223$	−9.83175e52	−1.43143	−0.715717	−	0.698390i	$-0.753900\pi$
$223$	−9.83175e52	−1.43143	−0.715717	+	0.698390i	$0.753900\pi$
$224$	−6.89993e51	−0.0908372
$225$	0	0
$226$	−5.15171e52	−0.555279
$227$	−6.71123e51	−0.0654969	−0.0327484	−	0.999464i	$-0.510426\pi$
$227$	−6.71123e51	−0.0654969	−0.0327484	+	0.999464i	$0.510426\pi$
$228$	0	0
$229$	3.17367e51	0.0254251	0.0127126	−	0.999919i	$-0.495953\pi$
$229$	3.17367e51	0.0254251	0.0127126	+	0.999919i	$0.495953\pi$
$230$	1.06152e53	0.770994
$231$	0	0
$232$	−4.54088e52	−0.271432
$233$	−5.76404e52	−0.312766	−0.156383	−	0.987697i	$-0.549983\pi$
$233$	−5.76404e52	−0.312766	−0.156383	+	0.987697i	$0.549983\pi$
$234$	0	0
$235$	−1.93698e53	−0.867157
$236$	8.76219e52	0.356527
$237$	0	0
$238$	4.96623e51	0.0167126
$239$	−3.11836e52	−0.0954934	−0.0477467	−	0.998859i	$-0.515204\pi$
$239$	−3.11836e52	−0.0954934	−0.0477467	+	0.998859i	$0.515204\pi$
$240$	0	0
$241$	1.25122e53	0.317652	0.158826	−	0.987307i	$-0.449229\pi$
$241$	1.25122e53	0.317652	0.158826	+	0.987307i	$0.449229\pi$
$242$	7.43400e52	0.171940
$243$	0	0
$244$	4.80336e52	0.0923153
$245$	−4.21402e53	−0.738686
$246$	0	0
$247$	−1.78687e53	−0.260862
$248$	3.87497e52	0.0516542
$249$	0	0
$250$	−6.33144e53	−0.704454
$251$	−1.51663e54	−1.54249	−0.771245	−	0.636539i	$-0.780366\pi$
$251$	−1.51663e54	−1.54249	−0.771245	+	0.636539i	$0.780366\pi$
$252$	0	0
$253$	−1.42375e54	−1.21121
$254$	−1.25959e54	−0.980554
$255$	0	0
$256$	9.57810e52	0.0625000
$257$	5.72779e53	0.342367	0.171183	−	0.985239i	$-0.445241\pi$
$257$	5.72779e53	0.342367	0.171183	+	0.985239i	$0.445241\pi$
$258$	0	0
$259$	−1.09427e54	−0.549390
$260$	−3.37525e53	−0.155384
$261$	0	0
$262$	4.16255e52	0.0161280
$263$	2.41909e53	0.0860295	0.0430147	−	0.999074i	$-0.486304\pi$
$263$	2.41909e53	0.0860295	0.0430147	+	0.999074i	$0.486304\pi$
$264$	0	0
$265$	−5.02055e54	−1.50563
$266$	−1.11108e54	−0.306131
$267$	0	0
$268$	−1.89805e54	−0.441849
$269$	−2.64339e54	−0.565894	−0.282947	−	0.959136i	$-0.591312\pi$
$269$	−2.64339e54	−0.565894	−0.282947	+	0.959136i	$0.591312\pi$
$270$	0	0
$271$	−8.54630e54	−1.54871	−0.774353	−	0.632754i	$-0.781924\pi$
$271$	−8.54630e54	−1.54871	−0.774353	+	0.632754i	$0.781924\pi$
$272$	−6.89385e52	−0.0114990
$273$	0	0
$274$	−3.59611e54	−0.508681
$275$	−6.36085e52	−0.00828952
$276$	0	0
$277$	−5.04059e54	−0.558067	−0.279033	−	0.960281i	$-0.590014\pi$
$277$	−5.04059e54	−0.558067	−0.279033	+	0.960281i	$0.590014\pi$
$278$	−1.05186e55	−1.07386
$279$	0	0
$280$	−2.09874e54	−0.182349
$281$	−4.09835e54	−0.328637	−0.164318	−	0.986407i	$-0.552542\pi$
$281$	−4.09835e54	−0.328637	−0.164318	+	0.986407i	$0.552542\pi$
$282$	0	0
$283$	−2.06696e55	−1.41298	−0.706491	−	0.707722i	$-0.749723\pi$
$283$	−2.06696e55	−1.41298	−0.706491	+	0.707722i	$0.749723\pi$
$284$	1.72842e54	0.109141
$285$	0	0
$286$	4.52702e54	0.244105
$287$	9.99673e54	0.498328
$288$	0	0
$289$	−2.34035e55	−0.997884
$290$	−1.38119e55	−0.544878
$291$	0	0
$292$	4.14719e54	0.140165
$293$	−4.39999e55	−1.37699	−0.688494	−	0.725242i	$-0.741728\pi$
$293$	−4.39999e55	−1.37699	−0.688494	+	0.725242i	$0.741728\pi$
$294$	0	0
$295$	2.66518e55	0.715700
$296$	1.51901e55	0.378004
$297$	0	0
$298$	5.20510e54	0.111317
$299$	−1.69585e55	−0.336345
$300$	0	0
$301$	9.07709e54	0.154953
$302$	2.81376e54	0.0445791
$303$	0	0
$304$	1.54233e55	0.210631
$305$	1.46103e55	0.185316
$306$	0	0
$307$	8.99516e55	0.984907	0.492453	−	0.870339i	$-0.336100\pi$
$307$	8.99516e55	0.984907	0.492453	+	0.870339i	$0.336100\pi$
$308$	2.81490e55	0.286466
$309$	0	0
$310$	1.17864e55	0.103692
$311$	1.48938e56	1.21870	0.609350	−	0.792901i	$-0.291430\pi$
$311$	1.48938e56	1.21870	0.609350	+	0.792901i	$0.291430\pi$
$312$	0	0
$313$	−9.05220e55	−0.641220	−0.320610	−	0.947211i	$-0.603888\pi$
$313$	−9.05220e55	−0.641220	−0.320610	+	0.947211i	$0.603888\pi$
$314$	9.55267e55	0.629807
$315$	0	0
$316$	−1.60299e56	−0.916161
$317$	−5.63393e55	−0.299901	−0.149951	−	0.988693i	$-0.547911\pi$
$317$	−5.63393e55	−0.299901	−0.149951	+	0.988693i	$0.547911\pi$
$318$	0	0
$319$	1.85251e56	0.855991
$320$	2.91335e55	0.125464
$321$	0	0
$322$	−1.05448e56	−0.394713
$323$	−1.11010e55	−0.0387529
$324$	0	0
$325$	−7.57651e53	−0.00230194
$326$	1.21601e56	0.344779
$327$	0	0
$328$	−1.38769e56	−0.342872
$329$	1.92414e56	0.443944
$330$	0	0
$331$	3.85197e55	0.0775448	0.0387724	−	0.999248i	$-0.487655\pi$
$331$	3.85197e55	0.0775448	0.0387724	+	0.999248i	$0.487655\pi$
$332$	6.65877e55	0.125253
$333$	0	0
$334$	2.98202e56	0.490021
$335$	−5.77325e56	−0.886977
$336$	0	0
$337$	1.10153e57	1.48021	0.740104	−	0.672492i	$-0.234776\pi$
$337$	1.10153e57	1.48021	0.740104	+	0.672492i	$0.234776\pi$
$338$	−5.08563e56	−0.639321
$339$	0	0
$340$	−2.09689e55	−0.0230834
$341$	−1.58084e56	−0.162897
$342$	0	0
$343$	9.87405e56	0.892026
$344$	−1.26003e56	−0.106615
$345$	0	0
$346$	1.71505e57	1.27369
$347$	1.58911e57	1.10596	0.552981	−	0.833194i	$-0.313490\pi$
$347$	1.58911e57	1.10596	0.552981	+	0.833194i	$0.313490\pi$
$348$	0	0
$349$	1.31112e57	0.801806	0.400903	−	0.916121i	$-0.368696\pi$
$349$	1.31112e57	0.801806	0.400903	+	0.916121i	$0.368696\pi$
$350$	−4.71108e54	−0.00270141
$351$	0	0
$352$	−3.90750e56	−0.197101
$353$	8.53713e56	0.404000	0.202000	−	0.979386i	$-0.435256\pi$
$353$	8.53713e56	0.404000	0.202000	+	0.979386i	$0.435256\pi$
$354$	0	0
$355$	5.25731e56	0.219092
$356$	1.44938e57	0.566967
$357$	0	0
$358$	2.09167e57	0.721315
$359$	2.26719e56	0.0734281	0.0367141	−	0.999326i	$-0.488311\pi$
$359$	2.26719e56	0.0734281	0.0367141	+	0.999326i	$0.488311\pi$
$360$	0	0
$361$	−1.01517e57	−0.290152
$362$	−3.42329e57	−0.919392
$363$	0	0
$364$	3.35288e56	0.0795494
$365$	1.26144e57	0.281370
$366$	0	0
$367$	−3.47667e57	−0.685768	−0.342884	−	0.939378i	$-0.611404\pi$
$367$	−3.47667e57	−0.685768	−0.342884	+	0.939378i	$0.611404\pi$
$368$	1.46377e57	0.271580
$369$	0	0
$370$	4.62034e57	0.758814
$371$	4.98726e57	0.770814
$372$	0	0
$373$	−7.80953e57	−1.06949	−0.534744	−	0.845014i	$-0.679592\pi$
$373$	−7.80953e57	−1.06949	−0.534744	+	0.845014i	$0.679592\pi$
$374$	2.81242e56	0.0362635
$375$	0	0
$376$	−2.67098e57	−0.305453
$377$	2.20655e57	0.237702
$378$	0	0
$379$	1.79759e58	1.71913	0.859565	−	0.511026i	$-0.170735\pi$
$379$	1.79759e58	1.71913	0.859565	+	0.511026i	$0.170735\pi$
$380$	4.69129e57	0.422826
$381$	0	0
$382$	−5.21112e57	−0.417355
$383$	2.20965e58	1.66859	0.834297	−	0.551315i	$-0.185874\pi$
$383$	2.20965e58	1.66859	0.834297	+	0.551315i	$0.185874\pi$
$384$	0	0
$385$	8.56204e57	0.575057
$386$	−7.04344e57	−0.446242
$387$	0	0
$388$	−2.98043e57	−0.168099
$389$	5.18043e57	0.275740	0.137870	−	0.990450i	$-0.455974\pi$
$389$	5.18043e57	0.275740	0.137870	+	0.990450i	$0.455974\pi$
$390$	0	0
$391$	−1.05355e57	−0.0499665
$392$	−5.81089e57	−0.260199
$393$	0	0
$394$	−2.92624e58	−1.16855
$395$	−4.87579e58	−1.83912
$396$	0	0
$397$	−2.60130e58	−0.875797	−0.437898	−	0.899024i	$-0.644277\pi$
$397$	−2.60130e58	−0.875797	−0.437898	+	0.899024i	$0.644277\pi$
$398$	−1.37529e58	−0.437547
$399$	0	0
$400$	6.53967e55	0.00185869
$401$	−5.24055e58	−1.40808	−0.704042	−	0.710159i	$-0.748623\pi$
$401$	−5.24055e58	−1.40808	−0.704042	+	0.710159i	$0.748623\pi$
$402$	0	0
$403$	−1.88296e57	−0.0452354
$404$	2.35550e58	0.535182
$405$	0	0
$406$	1.37204e58	0.278952
$407$	−6.19697e58	−1.19208
$408$	0	0
$409$	−5.81978e58	−1.00261	−0.501305	−	0.865270i	$-0.667147\pi$
$409$	−5.81978e58	−1.00261	−0.501305	+	0.865270i	$0.667147\pi$
$410$	−4.22092e58	−0.688288
$411$	0	0
$412$	−1.56871e58	−0.229274
$413$	−2.64751e58	−0.366405
$414$	0	0
$415$	2.02538e58	0.251435
$416$	−4.65428e57	−0.0547334
$417$	0	0
$418$	−6.29213e58	−0.664250
$419$	1.08479e58	0.108525	0.0542623	−	0.998527i	$-0.482719\pi$
$419$	1.08479e58	0.108525	0.0542623	+	0.998527i	$0.482719\pi$
$420$	0	0
$421$	−1.99082e59	−1.78930	−0.894652	−	0.446763i	$-0.852577\pi$
$421$	−1.99082e59	−1.78930	−0.894652	+	0.446763i	$0.852577\pi$
$422$	1.30363e59	1.11077
$423$	0	0
$424$	−6.92305e58	−0.530354
$425$	−4.70693e55	−0.000341969 0
$426$	0	0
$427$	−1.45134e58	−0.0948730
$428$	−1.43668e59	−0.890994
$429$	0	0
$430$	−3.83261e58	−0.214020
$431$	2.82963e59	1.49965	0.749826	−	0.661635i	$-0.230137\pi$
$431$	2.82963e59	1.49965	0.749826	+	0.661635i	$0.230137\pi$
$432$	0	0
$433$	7.60858e58	0.363350	0.181675	−	0.983359i	$-0.441848\pi$
$433$	7.60858e58	0.363350	0.181675	+	0.983359i	$0.441848\pi$
$434$	−1.17083e58	−0.0530853
$435$	0	0
$436$	1.18406e59	0.484093
$437$	2.35707e59	0.915251
$438$	0	0
$439$	−2.36220e59	−0.827685	−0.413843	−	0.910348i	$-0.635814\pi$
$439$	−2.36220e59	−0.827685	−0.413843	+	0.910348i	$0.635814\pi$
$440$	−1.18854e59	−0.395664
$441$	0	0
$442$	3.34993e57	0.0100701
$443$	2.46091e59	0.703091	0.351546	−	0.936171i	$-0.385656\pi$
$443$	2.46091e59	0.703091	0.351546	+	0.936171i	$0.385656\pi$
$444$	0	0
$445$	4.40856e59	1.13814
$446$	−4.12374e59	−1.01218
$447$	0	0
$448$	−2.89404e58	−0.0642316
$449$	−4.92131e59	−1.03881	−0.519407	−	0.854527i	$-0.673847\pi$
$449$	−4.92131e59	−1.03881	−0.519407	+	0.854527i	$0.673847\pi$
$450$	0	0
$451$	5.66125e59	1.08128
$452$	−2.16078e59	−0.392642
$453$	0	0
$454$	−2.81490e58	−0.0463133
$455$	1.01984e59	0.159689
$456$	0	0
$457$	−6.04235e59	−0.857218	−0.428609	−	0.903490i	$-0.640996\pi$
$457$	−6.04235e59	−0.857218	−0.428609	+	0.903490i	$0.640996\pi$
$458$	1.33113e58	0.0179783
$459$	0	0
$460$	4.45233e59	0.545175
$461$	1.23009e60	1.43439	0.717195	−	0.696873i	$-0.245426\pi$
$461$	1.23009e60	1.43439	0.717195	+	0.696873i	$0.245426\pi$
$462$	0	0
$463$	1.58815e60	1.68004	0.840020	−	0.542556i	$-0.182543\pi$
$463$	1.58815e60	1.68004	0.840020	+	0.542556i	$0.182543\pi$
$464$	−1.90458e59	−0.191931
$465$	0	0
$466$	−2.41762e59	−0.221159
$467$	1.01307e60	0.883103	0.441551	−	0.897236i	$-0.354428\pi$
$467$	1.01307e60	0.883103	0.441551	+	0.897236i	$0.354428\pi$
$468$	0	0
$469$	5.73498e59	0.454091
$470$	−8.12427e59	−0.613173
$471$	0	0
$472$	3.67513e59	0.252103
$473$	5.14044e59	0.336221
$474$	0	0
$475$	1.05306e58	0.00626395
$476$	2.08299e58	0.0118176
$477$	0	0
$478$	−1.30794e59	−0.0675241
$479$	2.68469e59	0.132234	0.0661172	−	0.997812i	$-0.478939\pi$
$479$	2.68469e59	0.132234	0.0661172	+	0.997812i	$0.478939\pi$
$480$	0	0
$481$	−7.38131e59	−0.331031
$482$	5.24801e59	0.224614
$483$	0	0
$484$	3.11805e59	0.121580
$485$	−9.06552e59	−0.337446
$486$	0	0
$487$	4.16113e60	1.41192	0.705960	−	0.708252i	$-0.250516\pi$
$487$	4.16113e60	1.41192	0.705960	+	0.708252i	$0.250516\pi$
$488$	2.01467e59	0.0652768
$489$	0	0
$490$	−1.76749e60	−0.522330
$491$	2.11553e60	0.597154	0.298577	−	0.954386i	$-0.403488\pi$
$491$	2.11553e60	0.597154	0.298577	+	0.954386i	$0.403488\pi$
$492$	0	0
$493$	1.37083e59	0.0353124
$494$	−7.49466e59	−0.184457
$495$	0	0
$496$	1.62528e59	0.0365250
$497$	−5.22246e59	−0.112165
$498$	0	0
$499$	1.98362e60	0.389222	0.194611	−	0.980881i	$-0.437656\pi$
$499$	1.98362e60	0.389222	0.194611	+	0.980881i	$0.437656\pi$
$500$	−2.65560e60	−0.498124
$501$	0	0
$502$	−6.36123e60	−1.09070
$503$	5.05113e60	0.828150	0.414075	−	0.910243i	$-0.364105\pi$
$503$	5.05113e60	0.828150	0.414075	+	0.910243i	$0.364105\pi$
$504$	0	0
$505$	7.16467e60	1.07434
$506$	−5.97163e60	−0.856458
$507$	0	0
$508$	−5.28311e60	−0.693356
$509$	1.02093e61	1.28188	0.640939	−	0.767592i	$-0.278545\pi$
$509$	1.02093e61	1.28188	0.640939	+	0.767592i	$0.278545\pi$
$510$	0	0
$511$	−1.25308e60	−0.144048
$512$	4.01735e59	0.0441942
$513$	0	0
$514$	2.40241e60	0.242090
$515$	−4.77151e60	−0.460250
$516$	0	0
$517$	1.08966e61	0.963281
$518$	−4.58971e60	−0.388477
$519$	0	0
$520$	−1.41568e60	−0.109873
$521$	3.62888e60	0.269727	0.134863	−	0.990864i	$-0.456940\pi$
$521$	3.62888e60	0.269727	0.134863	+	0.990864i	$0.456940\pi$
$522$	0	0
$523$	9.71059e60	0.662152	0.331076	−	0.943604i	$-0.392588\pi$
$523$	9.71059e60	0.662152	0.331076	+	0.943604i	$0.392588\pi$
$524$	1.74590e59	0.0114042
$525$	0	0
$526$	1.01464e60	0.0608320
$527$	−1.16980e59	−0.00672004
$528$	0	0
$529$	3.41384e60	0.180090
$530$	−2.10577e61	−1.06464
$531$	0	0
$532$	−4.66019e60	−0.216467
$533$	6.74321e60	0.300265
$534$	0	0
$535$	−4.36992e61	−1.78860
$536$	−7.96098e60	−0.312434
$537$	0	0
$538$	−1.10872e61	−0.400148
$539$	2.37062e61	0.820568
$540$	0	0
$541$	−5.23091e61	−1.66586	−0.832931	−	0.553377i	$-0.813339\pi$
$541$	−5.23091e61	−1.66586	−0.832931	+	0.553377i	$0.813339\pi$
$542$	−3.58458e61	−1.09510
$543$	0	0
$544$	−2.89149e59	−0.00813104
$545$	3.60155e61	0.971779
$546$	0	0
$547$	−5.85485e61	−1.45479	−0.727396	−	0.686218i	$-0.759270\pi$
$547$	−5.85485e61	−1.45479	−0.727396	+	0.686218i	$0.759270\pi$
$548$	−1.50832e61	−0.359691
$549$	0	0
$550$	−2.66793e59	−0.00586158
$551$	−3.06690e61	−0.646827
$552$	0	0
$553$	4.84347e61	0.941544
$554$	−2.11418e61	−0.394613
$555$	0	0
$556$	−4.41181e61	−0.759335
$557$	1.16829e62	1.93111	0.965556	−	0.260196i	$-0.0837873\pi$
$557$	1.16829e62	1.93111	0.965556	+	0.260196i	$0.0837873\pi$
$558$	0	0
$559$	6.12287e60	0.0933661
$560$	−8.80274e60	−0.128940
$561$	0	0
$562$	−1.71897e61	−0.232381
$563$	−1.02917e62	−1.33675	−0.668374	−	0.743825i	$-0.733009\pi$
$563$	−1.02917e62	−1.33675	−0.668374	+	0.743825i	$0.733009\pi$
$564$	0	0
$565$	−6.57242e61	−0.788197
$566$	−8.66944e61	−0.999129
$567$	0	0
$568$	7.24953e60	0.0771742
$569$	−7.76715e61	−0.794760	−0.397380	−	0.917654i	$-0.630080\pi$
$569$	−7.76715e61	−0.794760	−0.397380	+	0.917654i	$0.630080\pi$
$570$	0	0
$571$	3.25317e61	0.307606	0.153803	−	0.988102i	$-0.450848\pi$
$571$	3.25317e61	0.307606	0.153803	+	0.988102i	$0.450848\pi$
$572$	1.89877e61	0.172608
$573$	0	0
$574$	4.19293e61	0.352371
$575$	9.99424e59	0.00807650
$576$	0	0
$577$	1.39990e62	1.04626	0.523131	−	0.852252i	$-0.324764\pi$
$577$	1.39990e62	1.04626	0.523131	+	0.852252i	$0.324764\pi$
$578$	−9.81616e61	−0.705611
$579$	0	0
$580$	−5.79314e61	−0.385287
$581$	−2.01196e61	−0.128723
$582$	0	0
$583$	2.82434e62	1.67253
$584$	1.73946e61	0.0991116
$585$	0	0
$586$	−1.84549e62	−0.973677
$587$	1.67424e62	0.850083	0.425042	−	0.905174i	$-0.360259\pi$
$587$	1.67424e62	0.850083	0.425042	+	0.905174i	$0.360259\pi$
$588$	0	0
$589$	2.61714e61	0.123093
$590$	1.11786e62	0.506076
$591$	0	0
$592$	6.37118e61	0.267289
$593$	2.09278e62	0.845266	0.422633	−	0.906301i	$-0.361106\pi$
$593$	2.09278e62	0.845266	0.422633	+	0.906301i	$0.361106\pi$
$594$	0	0
$595$	6.33579e60	0.0237230
$596$	2.18318e61	0.0787133
$597$	0	0
$598$	−7.11290e61	−0.237832
$599$	2.68603e62	0.864983	0.432492	−	0.901638i	$-0.357634\pi$
$599$	2.68603e62	0.864983	0.432492	+	0.901638i	$0.357634\pi$
$600$	0	0
$601$	5.99608e62	1.79140	0.895699	−	0.444661i	$-0.146676\pi$
$601$	5.99608e62	1.79140	0.895699	+	0.444661i	$0.146676\pi$
$602$	3.80721e61	0.109568
$603$	0	0
$604$	1.18018e61	0.0315222
$605$	9.48411e61	0.244062
$606$	0	0
$607$	3.35261e62	0.801009	0.400504	−	0.916295i	$-0.368835\pi$
$607$	3.35261e62	0.801009	0.400504	+	0.916295i	$0.368835\pi$
$608$	6.46902e61	0.148939
$609$	0	0
$610$	6.12800e61	0.131038
$611$	1.29791e62	0.267496
$612$	0	0
$613$	−8.00170e62	−1.53222	−0.766111	−	0.642708i	$-0.777811\pi$
$613$	−8.00170e62	−1.53222	−0.766111	+	0.642708i	$0.777811\pi$
$614$	3.77284e62	0.696434
$615$	0	0
$616$	1.18066e62	0.202562
$617$	6.47534e62	1.07114	0.535570	−	0.844491i	$-0.320097\pi$
$617$	6.47534e62	1.07114	0.535570	+	0.844491i	$0.320097\pi$
$618$	0	0
$619$	6.57187e62	1.01076	0.505382	−	0.862896i	$-0.331352\pi$
$619$	6.57187e62	1.01076	0.505382	+	0.862896i	$0.331352\pi$
$620$	4.94358e61	0.0733211
$621$	0	0
$622$	6.24691e62	0.861751
$623$	−4.37933e62	−0.582676
$624$	0	0
$625$	−8.13755e62	−1.00738
$626$	−3.79677e62	−0.453411
$627$	0	0
$628$	4.00668e62	0.445341
$629$	−4.58567e61	−0.0491771
$630$	0	0
$631$	−3.17698e62	−0.317216	−0.158608	−	0.987342i	$-0.550701\pi$
$631$	−3.17698e62	−0.317216	−0.158608	+	0.987342i	$0.550701\pi$
$632$	−6.72343e62	−0.647824
$633$	0	0
$634$	−2.36304e62	−0.212062
$635$	−1.60696e63	−1.39186
$636$	0	0
$637$	2.82368e62	0.227866
$638$	7.76997e62	0.605277
$639$	0	0
$640$	1.22195e62	0.0887163
$641$	−8.07272e62	−0.565867	−0.282933	−	0.959140i	$-0.591308\pi$
$641$	−8.07272e62	−0.565867	−0.282933	+	0.959140i	$0.591308\pi$
$642$	0	0
$643$	1.81867e63	1.18852	0.594261	−	0.804273i	$-0.297445\pi$
$643$	1.81867e63	1.18852	0.594261	+	0.804273i	$0.297445\pi$
$644$	−4.42281e62	−0.279104
$645$	0	0
$646$	−4.65608e61	−0.0274024
$647$	6.55772e62	0.372741	0.186370	−	0.982480i	$-0.440328\pi$
$647$	6.55772e62	0.372741	0.186370	+	0.982480i	$0.440328\pi$
$648$	0	0
$649$	−1.49931e63	−0.795035
$650$	−3.17782e60	−0.00162772
$651$	0	0
$652$	5.10030e62	0.243795
$653$	5.28862e62	0.244228	0.122114	−	0.992516i	$-0.461033\pi$
$653$	5.28862e62	0.244228	0.122114	+	0.992516i	$0.461033\pi$
$654$	0	0
$655$	5.31048e61	0.0228931
$656$	−5.82040e62	−0.242447
$657$	0	0
$658$	8.07042e62	0.313916
$659$	−1.82135e63	−0.684653	−0.342327	−	0.939581i	$-0.611215\pi$
$659$	−1.82135e63	−0.684653	−0.342327	+	0.939581i	$0.611215\pi$
$660$	0	0
$661$	−2.93115e63	−1.02921	−0.514607	−	0.857426i	$-0.672062\pi$
$661$	−2.93115e63	−1.02921	−0.514607	+	0.857426i	$0.672062\pi$
$662$	1.61563e62	0.0548324
$663$	0	0
$664$	2.79289e62	0.0885670
$665$	−1.41748e63	−0.434540
$666$	0	0
$667$	−2.91068e63	−0.833995
$668$	1.25075e63	0.346497
$669$	0	0
$670$	−2.42148e63	−0.627187
$671$	−8.21910e62	−0.205858
$672$	0	0
$673$	−7.82685e63	−1.83336	−0.916681	−	0.399620i	$-0.869142\pi$
$673$	−7.82685e63	−1.83336	−0.916681	+	0.399620i	$0.869142\pi$
$674$	4.62014e63	1.04667
$675$	0	0
$676$	−2.13307e63	−0.452068
$677$	7.03892e62	0.144298	0.0721491	−	0.997394i	$-0.477014\pi$
$677$	7.03892e62	0.144298	0.0721491	+	0.997394i	$0.477014\pi$
$678$	0	0
$679$	9.00543e62	0.172756
$680$	−8.79499e61	−0.0163224
$681$	0	0
$682$	−6.63052e62	−0.115186
$683$	−5.76408e63	−0.968866	−0.484433	−	0.874828i	$-0.660974\pi$
$683$	−5.76408e63	−0.968866	−0.484433	+	0.874828i	$0.660974\pi$
$684$	0	0
$685$	−4.58782e63	−0.722052
$686$	4.14147e63	0.630757
$687$	0	0
$688$	−5.28496e62	−0.0753879
$689$	3.36411e63	0.464449
$690$	0	0
$691$	2.79477e63	0.361485	0.180742	−	0.983530i	$-0.442150\pi$
$691$	2.79477e63	0.361485	0.180742	+	0.983530i	$0.442150\pi$
$692$	7.19342e63	0.900634
$693$	0	0
$694$	6.66520e63	0.782033
$695$	−1.34193e64	−1.52431
$696$	0	0
$697$	4.18924e62	0.0446065
$698$	5.49922e63	0.566962
$699$	0	0
$700$	−1.97597e61	−0.00191018
$701$	−6.93963e63	−0.649652	−0.324826	−	0.945774i	$-0.605306\pi$
$701$	−6.93963e63	−0.649652	−0.324826	+	0.945774i	$0.605306\pi$
$702$	0	0
$703$	1.02593e64	0.900792
$704$	−1.63892e63	−0.139371
$705$	0	0
$706$	3.58073e63	0.285671
$707$	−7.11717e63	−0.550010
$708$	0	0
$709$	−1.01767e64	−0.738019	−0.369009	−	0.929426i	$-0.620303\pi$
$709$	−1.01767e64	−0.738019	−0.369009	+	0.929426i	$0.620303\pi$
$710$	2.20508e63	0.154921
$711$	0	0
$712$	6.07915e63	0.400906
$713$	2.48383e63	0.158711
$714$	0	0
$715$	5.77545e63	0.346497
$716$	8.77310e63	0.510047
$717$	0	0
$718$	9.50928e62	0.0519215
$719$	−1.82743e64	−0.967031	−0.483516	−	0.875336i	$-0.660640\pi$
$719$	−1.82743e64	−0.967031	−0.483516	+	0.875336i	$0.660640\pi$
$720$	0	0
$721$	4.73988e63	0.235626
$722$	−4.25792e63	−0.205168
$723$	0	0
$724$	−1.43583e64	−0.650109
$725$	−1.30040e62	−0.00570784
$726$	0	0
$727$	6.92061e63	0.285509	0.142755	−	0.989758i	$-0.454404\pi$
$727$	6.92061e63	0.285509	0.142755	+	0.989758i	$0.454404\pi$
$728$	1.40630e63	0.0562499
$729$	0	0
$730$	5.29087e63	0.198959
$731$	3.80385e62	0.0138702
$732$	0	0
$733$	−2.71099e64	−0.929585	−0.464793	−	0.885420i	$-0.653871\pi$
$733$	−2.71099e64	−0.929585	−0.464793	+	0.885420i	$0.653871\pi$
$734$	−1.45822e64	−0.484911
$735$	0	0
$736$	6.13951e63	0.192036
$737$	3.24777e64	0.985298
$738$	0	0
$739$	1.02173e64	0.291632	0.145816	−	0.989312i	$-0.453419\pi$
$739$	1.02173e64	0.291632	0.145816	+	0.989312i	$0.453419\pi$
$740$	1.93791e64	0.536562
$741$	0	0
$742$	2.09181e64	0.545048
$743$	5.09461e63	0.128784	0.0643921	−	0.997925i	$-0.479489\pi$
$743$	5.09461e63	0.128784	0.0643921	+	0.997925i	$0.479489\pi$
$744$	0	0
$745$	6.64053e63	0.158011
$746$	−3.27555e64	−0.756243
$747$	0	0
$748$	1.17962e63	0.0256422
$749$	4.34095e64	0.915680
$750$	0	0
$751$	2.78830e64	0.553911	0.276956	−	0.960883i	$-0.410674\pi$
$751$	2.78830e64	0.553911	0.276956	+	0.960883i	$0.410674\pi$
$752$	−1.12029e64	−0.215988
$753$	0	0
$754$	9.25494e63	0.168081
$755$	3.58972e63	0.0632782
$756$	0	0
$757$	2.39252e64	0.397372	0.198686	−	0.980063i	$-0.436333\pi$
$757$	2.39252e64	0.397372	0.198686	+	0.980063i	$0.436333\pi$
$758$	7.53964e64	1.21561
$759$	0	0
$760$	1.96767e64	0.298983
$761$	9.78797e64	1.44390	0.721951	−	0.691944i	$-0.243245\pi$
$761$	9.78797e64	1.44390	0.721951	+	0.691944i	$0.243245\pi$
$762$	0	0
$763$	−3.57767e64	−0.497506
$764$	−2.18570e64	−0.295114
$765$	0	0
$766$	9.26794e64	1.17987
$767$	−1.78585e64	−0.220775
$768$	0	0
$769$	1.03162e65	1.20276	0.601380	−	0.798963i	$-0.294618\pi$
$769$	1.03162e65	1.20276	0.601380	+	0.798963i	$0.294618\pi$
$770$	3.59118e64	0.406627
$771$	0	0
$772$	−2.95423e64	−0.315541
$773$	−5.42578e64	−0.562891	−0.281445	−	0.959577i	$-0.590814\pi$
$773$	−5.42578e64	−0.562891	−0.281445	+	0.959577i	$0.590814\pi$
$774$	0	0
$775$	1.10970e62	0.00108622
$776$	−1.25008e64	−0.118864
$777$	0	0
$778$	2.17283e64	0.194978
$779$	−9.37243e64	−0.817070
$780$	0	0
$781$	−2.95753e64	−0.243378
$782$	−4.41892e63	−0.0353316
$783$	0	0
$784$	−2.43726e64	−0.183989
$785$	1.21870e65	0.893987
$786$	0	0
$787$	6.58146e64	0.455922	0.227961	−	0.973670i	$-0.426794\pi$
$787$	6.58146e64	0.455922	0.227961	+	0.973670i	$0.426794\pi$
$788$	−1.22736e65	−0.826287
$789$	0	0
$790$	−2.04505e65	−1.30045
$791$	6.52884e64	0.403520
$792$	0	0
$793$	−9.78990e63	−0.0571652
$794$	−1.09106e65	−0.619282
$795$	0	0
$796$	−5.76838e64	−0.309393
$797$	−2.53956e65	−1.32418	−0.662089	−	0.749425i	$-0.730330\pi$
$797$	−2.53956e65	−1.32418	−0.662089	+	0.749425i	$0.730330\pi$
$798$	0	0
$799$	8.06331e63	0.0397384
$800$	2.74294e62	0.00131429
$801$	0	0
$802$	−2.19805e65	−0.995665
$803$	−7.09631e64	−0.312560
$804$	0	0
$805$	−1.34528e65	−0.560280
$806$	−7.89772e63	−0.0319862
$807$	0	0
$808$	9.87967e64	0.378431
$809$	6.75007e64	0.251459	0.125729	−	0.992065i	$-0.459873\pi$
$809$	6.75007e64	0.251459	0.125729	+	0.992065i	$0.459873\pi$
$810$	0	0
$811$	1.13300e65	0.399266	0.199633	−	0.979871i	$-0.436025\pi$
$811$	1.13300e65	0.399266	0.199633	+	0.979871i	$0.436025\pi$
$812$	5.75473e64	0.197249
$813$	0	0
$814$	−2.59920e65	−0.842927
$815$	1.55135e65	0.489400
$816$	0	0
$817$	−8.51021e64	−0.254065
$818$	−2.44099e65	−0.708953
$819$	0	0
$820$	−1.77038e65	−0.486693
$821$	3.62842e65	0.970502	0.485251	−	0.874375i	$-0.338728\pi$
$821$	3.62842e65	0.970502	0.485251	+	0.874375i	$0.338728\pi$
$822$	0	0
$823$	−3.21071e65	−0.813025	−0.406513	−	0.913645i	$-0.633255\pi$
$823$	−3.21071e65	−0.813025	−0.406513	+	0.913645i	$0.633255\pi$
$824$	−6.57964e64	−0.162121
$825$	0	0
$826$	−1.11045e65	−0.259088
$827$	2.23466e65	0.507386	0.253693	−	0.967285i	$-0.418355\pi$
$827$	2.23466e65	0.507386	0.253693	+	0.967285i	$0.418355\pi$
$828$	0	0
$829$	−6.35722e65	−1.36707	−0.683535	−	0.729918i	$-0.739558\pi$
$829$	−6.35722e65	−1.36707	−0.683535	+	0.729918i	$0.739558\pi$
$830$	8.49508e64	0.177791
$831$	0	0
$832$	−1.95215e64	−0.0387024
$833$	1.75422e64	0.0338511
$834$	0	0
$835$	3.80438e65	0.695565
$836$	−2.63911e65	−0.469695
$837$	0	0
$838$	4.54992e64	0.0767385
$839$	−7.86587e65	−1.29152	−0.645762	−	0.763538i	$-0.723460\pi$
$839$	−7.86587e65	−1.29152	−0.645762	+	0.763538i	$0.723460\pi$
$840$	0	0
$841$	−2.63832e65	−0.410599
$842$	−8.35009e65	−1.26523
$843$	0	0
$844$	5.46782e65	0.785434
$845$	−6.48811e65	−0.907491
$846$	0	0
$847$	−9.42123e64	−0.124948
$848$	−2.90374e65	−0.375017
$849$	0	0
$850$	−1.97423e62	−0.000241809 0
$851$	9.73676e65	1.16145
$852$	0	0
$853$	7.20063e65	0.814736	0.407368	−	0.913264i	$-0.366447\pi$
$853$	7.20063e65	0.814736	0.407368	+	0.913264i	$0.366447\pi$
$854$	−6.08737e64	−0.0670854
$855$	0	0
$856$	−6.02587e65	−0.630028
$857$	3.35470e64	0.0341653	0.0170826	−	0.999854i	$-0.494562\pi$
$857$	3.35470e64	0.0341653	0.0170826	+	0.999854i	$0.494562\pi$
$858$	0	0
$859$	−3.58672e65	−0.346619	−0.173309	−	0.984867i	$-0.555446\pi$
$859$	−3.58672e65	−0.346619	−0.173309	+	0.984867i	$0.555446\pi$
$860$	−1.60752e65	−0.151335
$861$	0	0
$862$	1.18683e66	1.06041
$863$	8.48055e65	0.738212	0.369106	−	0.929387i	$-0.379664\pi$
$863$	8.48055e65	0.738212	0.369106	+	0.929387i	$0.379664\pi$
$864$	0	0
$865$	2.18801e66	1.80795
$866$	3.19127e65	0.256928
$867$	0	0
$868$	−4.91081e64	−0.0375370
$869$	2.74290e66	2.04299
$870$	0	0
$871$	3.86848e65	0.273610
$872$	4.96633e65	0.342306
$873$	0	0
$874$	9.88627e65	0.647180
$875$	8.02394e65	0.511925
$876$	0	0
$877$	−8.34705e64	−0.0505874	−0.0252937	−	0.999680i	$-0.508052\pi$
$877$	−8.34705e64	−0.0505874	−0.0252937	+	0.999680i	$0.508052\pi$
$878$	−9.90779e65	−0.585262
$879$	0	0
$880$	−4.98508e65	−0.279777
$881$	−1.29862e66	−0.710432	−0.355216	−	0.934784i	$-0.615593\pi$
$881$	−1.29862e66	−0.710432	−0.355216	+	0.934784i	$0.615593\pi$
$882$	0	0
$883$	−1.41183e66	−0.733950	−0.366975	−	0.930231i	$-0.619607\pi$
$883$	−1.41183e66	−0.733950	−0.366975	+	0.930231i	$0.619607\pi$
$884$	1.40506e64	0.00712064
$885$	0	0
$886$	1.03218e66	0.497161
$887$	3.71572e66	1.74487	0.872433	−	0.488735i	$-0.162541\pi$
$887$	3.71572e66	1.74487	0.872433	+	0.488735i	$0.162541\pi$
$888$	0	0
$889$	1.59630e66	0.712567
$890$	1.84908e66	0.804788
$891$	0	0
$892$	−1.72962e66	−0.715717
$893$	−1.80397e66	−0.727901
$894$	0	0
$895$	2.66850e66	1.02388
$896$	−1.21385e65	−0.0454186
$897$	0	0
$898$	−2.06415e66	−0.734553
$899$	−3.23183e65	−0.112165
$900$	0	0
$901$	2.08997e65	0.0689972
$902$	2.37450e66	0.764584
$903$	0	0
$904$	−9.06298e65	−0.277640
$905$	−4.36734e66	−1.30504
$906$	0	0
$907$	2.68518e66	0.763500	0.381750	−	0.924266i	$-0.375322\pi$
$907$	2.68518e66	0.763500	0.381750	+	0.924266i	$0.375322\pi$
$908$	−1.18065e65	−0.0327484
$909$	0	0
$910$	4.27751e65	0.112917
$911$	−3.66119e66	−0.942886	−0.471443	−	0.881897i	$-0.656267\pi$
$911$	−3.66119e66	−0.942886	−0.471443	+	0.881897i	$0.656267\pi$
$912$	0	0
$913$	−1.13939e66	−0.279306
$914$	−2.53435e66	−0.606145
$915$	0	0
$916$	5.58318e64	0.0127126
$917$	−5.27527e64	−0.0117202
$918$	0	0
$919$	−2.41366e66	−0.510595	−0.255298	−	0.966863i	$-0.582173\pi$
$919$	−2.41366e66	−0.510595	−0.255298	+	0.966863i	$0.582173\pi$
$920$	1.86744e66	0.385497
$921$	0	0
$922$	5.15938e66	1.01427
$923$	−3.52276e65	−0.0675841
$924$	0	0
$925$	4.35007e64	0.00794891
$926$	6.66119e66	1.18797
$927$	0	0
$928$	−7.98841e65	−0.135716
$929$	−5.90852e66	−0.979772	−0.489886	−	0.871786i	$-0.662962\pi$
$929$	−5.90852e66	−0.979772	−0.489886	+	0.871786i	$0.662962\pi$
$930$	0	0
$931$	−3.92466e66	−0.620060
$932$	−1.01402e66	−0.156383
$933$	0	0
$934$	4.24914e66	0.624448
$935$	3.58802e65	0.0514746
$936$	0	0
$937$	5.01170e66	0.685243	0.342621	−	0.939474i	$-0.388685\pi$
$937$	5.01170e66	0.685243	0.342621	+	0.939474i	$0.388685\pi$
$938$	2.40542e66	0.321091
$939$	0	0
$940$	−3.40757e66	−0.433579
$941$	−4.09627e66	−0.508888	−0.254444	−	0.967088i	$-0.581892\pi$
$941$	−4.09627e66	−0.508888	−0.254444	+	0.967088i	$0.581892\pi$
$942$	0	0
$943$	−8.89503e66	−1.05350
$944$	1.54146e66	0.178264
$945$	0	0
$946$	2.15606e66	0.237744
$947$	−4.36909e66	−0.470453	−0.235226	−	0.971941i	$-0.575583\pi$
$947$	−4.36909e66	−0.470453	−0.235226	+	0.971941i	$0.575583\pi$
$948$	0	0
$949$	−8.45253e65	−0.0867955
$950$	4.41687e64	0.00442928
$951$	0	0
$952$	8.73668e64	0.00835632
$953$	−3.02105e66	−0.282207	−0.141104	−	0.989995i	$-0.545065\pi$
$953$	−3.02105e66	−0.282207	−0.141104	+	0.989995i	$0.545065\pi$
$954$	0	0
$955$	−6.64821e66	−0.592419
$956$	−5.48588e65	−0.0477467
$957$	0	0
$958$	1.12604e66	0.0935039
$959$	4.55741e66	0.369657
$960$	0	0
$961$	−1.26446e67	−0.978655
$962$	−3.09595e66	−0.234075
$963$	0	0
$964$	2.20118e66	0.158826
$965$	−8.98584e66	−0.633424
$966$	0	0
$967$	−1.34618e67	−0.905749	−0.452875	−	0.891574i	$-0.649601\pi$
$967$	−1.34618e67	−0.905749	−0.452875	+	0.891574i	$0.649601\pi$
$968$	1.30780e66	0.0859700
$969$	0	0
$970$	−3.80236e66	−0.238610
$971$	1.81545e67	1.11315	0.556573	−	0.830799i	$-0.312116\pi$
$971$	1.81545e67	1.11315	0.556573	+	0.830799i	$0.312116\pi$
$972$	0	0
$973$	1.33303e67	0.780374
$974$	1.74531e67	0.998378
$975$	0	0
$976$	8.45016e65	0.0461577
$977$	7.06118e66	0.376920	0.188460	−	0.982081i	$-0.439650\pi$
$977$	7.06118e66	0.376920	0.188460	+	0.982081i	$0.439650\pi$
$978$	0	0
$979$	−2.48006e67	−1.26430
$980$	−7.41338e66	−0.369343
$981$	0	0
$982$	8.87319e66	0.422252
$983$	−5.04041e66	−0.234429	−0.117215	−	0.993107i	$-0.537397\pi$
$983$	−5.04041e66	−0.234429	−0.117215	+	0.993107i	$0.537397\pi$
$984$	0	0
$985$	−3.73323e67	−1.65870
$986$	5.74966e65	0.0249696
$987$	0	0
$988$	−3.14349e66	−0.130431
$989$	−8.07673e66	−0.327581
$990$	0	0
$991$	−1.58623e67	−0.614763	−0.307381	−	0.951586i	$-0.599453\pi$
$991$	−1.58623e67	−0.614763	−0.307381	+	0.951586i	$0.599453\pi$
$992$	6.81692e65	0.0258271
$993$	0	0
$994$	−2.19046e66	−0.0793124
$995$	−1.75456e67	−0.621081
$996$	0	0
$997$	5.10990e67	1.72890	0.864452	−	0.502715i	$-0.167665\pi$
$997$	5.10990e67	1.72890	0.864452	+	0.502715i	$0.167665\pi$
$998$	8.31992e66	0.275221
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.46.a.f.1.2		2
3.2	odd	2		2.46.a.a.1.1	✓	2
12.11	even	2		16.46.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.46.a.a.1.1	✓	2	3.2	odd	2
16.46.a.b.1.2		2	12.11	even	2
18.46.a.f.1.2		2	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 46 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)

\(f(q)\)	\(=\)	\(q+4.19430e6 q^{2} +1.75922e13 q^{4} +5.35098e15 q^{5} -5.31551e18 q^{7} +7.37870e19 q^{8} +O(q^{10})\)	\(q+4.19430e6 q^{2} +1.75922e13 q^{4} +5.35098e15 q^{5} -5.31551e18 q^{7} +7.37870e19 q^{8} +2.24436e22 q^{10} -3.01022e23 q^{11} -3.58553e24 q^{13} -2.22949e25 q^{14} +3.09485e26 q^{16} -2.22752e26 q^{17} +4.98355e28 q^{19} +9.41355e28 q^{20} -1.26258e30 q^{22} +4.72970e30 q^{23} +2.11308e29 q^{25} -1.50388e31 q^{26} -9.35114e31 q^{28} -6.15404e32 q^{29} +5.25156e32 q^{31} +1.29807e33 q^{32} -9.34291e32 q^{34} -2.84432e34 q^{35} +2.05864e35 q^{37} +2.09025e35 q^{38} +3.94833e35 q^{40} -1.88067e36 q^{41} -1.70766e36 q^{43} -5.29564e36 q^{44} +1.98378e37 q^{46} -3.61985e37 q^{47} -7.87523e37 q^{49} +8.86290e35 q^{50} -6.30773e37 q^{52} -9.38248e38 q^{53} -1.61077e39 q^{55} -3.92215e38 q^{56} -2.58119e39 q^{58} +4.98073e39 q^{59} +2.73039e39 q^{61} +2.20267e39 q^{62} +5.44452e39 q^{64} -1.91861e40 q^{65} -1.07891e41 q^{67} -3.91870e39 q^{68} -1.19299e41 q^{70} +9.82494e40 q^{71} +2.35740e41 q^{73} +8.63456e41 q^{74} +8.76715e41 q^{76} +1.60009e42 q^{77} -9.11195e42 q^{79} +1.65605e42 q^{80} -7.88811e42 q^{82} +3.78507e42 q^{83} -1.19194e42 q^{85} -7.16245e42 q^{86} -2.22115e43 q^{88} +8.23878e43 q^{89} +1.90589e43 q^{91} +8.32058e43 q^{92} -1.51828e44 q^{94} +2.66669e44 q^{95} -1.69418e44 q^{97} -3.30311e44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8388608 q^{2} + 35184372088832 q^{4} + 45\!\cdots\!00 q^{5}+ \cdots + 14\!\cdots\!28 q^{8}+O(q^{10}) \) 2 * q + 8388608 * q^2 + 35184372088832 * q^4 + 4502496162681300 * q^5 - 9564351425209104944 * q^7 + 147573952589676412928 * q^8	\( 2 q + 8388608 q^{2} + 35184372088832 q^{4} + 45\!\cdots\!00 q^{5}+ \cdots - 70\!\cdots\!84 q^{98}+O(q^{100}) \) 2 * q + 8388608 * q^2 + 35184372088832 * q^4 + 4502496162681300 * q^5 - 9564351425209104944 * q^7 + 147573952589676412928 * q^8 + 18884837665118827315200 * q^10 - 198786084430704131948664 * q^11 + 11451156052847070865478908 * q^13 - 40115797440160249703038976 * q^14 + 618970019642690137449562112 * q^16 - 1563202963522522223200782756 * q^17 - 38059827532732969070582665400 * q^19 + 79208750158158557883452620800 * q^20 - 833769269072040063448809209856 * q^22 + 3019065536381638234619389053072 * q^23 - 27490471710601873355395547121250 * q^25 + 48029629637080680719361645740032 * q^26 - 168257849666453895970455189192704 * q^28 + 280581379156203770144200953240420 * q^29 - 4189611301991905914902859454659776 * q^31 + 2596148429267413814265248164610048 * q^32 - 6556548442714369050859935916621824 * q^34 - 24838110552152718910556999414853600 * q^35 + 505778201204488215524264884178967916 * q^37 - 159634486859852023104621155817881600 * q^38 + 332225577623365071964796861231923200 * q^40 - 418164031451191405542034507224542484 * q^41 - 3549110943868129840436165872994478152 * q^43 - 3497081780345933926283594264135860224 * q^44 + 12662878655507650774017041982856101888 * q^46 + 12007068225044323361722631178296373024 * q^47 - 167706511209625603483189808428567988046 * q^49 - 115303395457664279822028964872847360000 * q^50 + 201450867705326047463941428173999177728 * q^52 - 1412307165618014181350584692903529779468 * q^53 - 1697512303911992562809549506325502471600 * q^55 - 705724571887406241684464081851715158016 * q^56 + 1176843600920382097930902634980106567680 * q^58 + 14425168975774921208266222088136852713640 * q^59 - 21544742169968151649138784822449267819556 * q^61 - 17572503442389858946500723022117317115904 * q^62 + 10889035741470030830827987437816582766592 * q^64 - 31944525970238170776211660453695076069800 * q^65 - 96479943874272547038464438827275621594584 * q^67 - 27500157359470648967498032654830582890496 * q^68 - 104178586441336357537424864873718113894400 * q^70 - 440739175289788187629870406465468826532944 * q^71 - 346231544919662222196116641714398922459052 * q^73 + 2121387532424789740326286300771381845950464 * q^74 - 669555566774224779915804932331564066406400 * q^76 + 1165701312439316428813861475091700140057408 * q^77 - 627123872043088732794879973354503802534880 * q^79 + 1393455069127990614802235334252500405452800 * q^80 - 1753907069771857917030577501789927438811136 * q^82 - 9625160990874063774180757999996692860808648 * q^83 - 54588720694608839702922500851417883111400 * q^85 - 14886050228309872462260772265764231690846208 * q^86 - 14667824099632072050746984556442095080964096 * q^88 + 125803218506661664646783479200413122083076620 * q^89 - 44829596783932153927475828505081057977500576 * q^91 + 53111962596310361672062775256861279573245952 * q^92 + 50361294284576305653366678841653190560055296 * q^94 + 341246876890106594702844083541175355872770000 * q^95 + 47343316954280034711620535205361321066461636 * q^97 - 703412090792577507191956946251176426533289984 * q^98

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