LMFDB - Embedded newform 54.8.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(1,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("54.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.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:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{329}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 82 $ x^2 - x - 82
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.56918$ of defining polynomial
Character	$\chi$	$=$	54.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +64.0000 q^{4} -465.736 q^{5} -49.7356 q^{7} -512.000 q^{8} +O(q^{10})$	\(q-8.00000 q^{2} +64.0000 q^{4} -465.736 q^{5} -49.7356 q^{7} -512.000 q^{8} +3725.89 q^{10} +302.885 q^{11} -5514.71 q^{13} +397.885 q^{14} +4096.00 q^{16} -22646.7 q^{17} +52805.5 q^{19} -29807.1 q^{20} -2423.08 q^{22} +20019.3 q^{23} +138785. q^{25} +44117.7 q^{26} -3183.08 q^{28} +250279. q^{29} +262367. q^{31} -32768.0 q^{32} +181174. q^{34} +23163.7 q^{35} -460621. q^{37} -422444. q^{38} +238457. q^{40} -240404. q^{41} +568376. q^{43} +19384.6 q^{44} -160154. q^{46} +875232. q^{47} -821069. q^{49} -1.11028e6 q^{50} -352942. q^{52} +811041. q^{53} -141064. q^{55} +25464.6 q^{56} -2.00223e6 q^{58} -1.29203e6 q^{59} -1.62852e6 q^{61} -2.09893e6 q^{62} +262144. q^{64} +2.56840e6 q^{65} -1.84317e6 q^{67} -1.44939e6 q^{68} -185309. q^{70} +4.56707e6 q^{71} -1.91494e6 q^{73} +3.68496e6 q^{74} +3.37955e6 q^{76} -15064.2 q^{77} -1.81088e6 q^{79} -1.90765e6 q^{80} +1.92323e6 q^{82} +3.08928e6 q^{83} +1.05474e7 q^{85} -4.54701e6 q^{86} -155077. q^{88} -4.10492e6 q^{89} +274278. q^{91} +1.28123e6 q^{92} -7.00186e6 q^{94} -2.45934e7 q^{95} +7.91623e6 q^{97} +6.56855e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} + 128 q^{4} + 48 q^{5} + 880 q^{7} - 1024 q^{8}+O(q^{10}) $ 2 * q - 16 * q^2 + 128 * q^4 + 48 * q^5 + 880 * q^7 - 1024 * q^8	\( 2 q - 16 q^{2} + 128 q^{4} + 48 q^{5} + 880 q^{7} - 1024 q^{8} - 384 q^{10} - 7230 q^{11} + 8560 q^{13} - 7040 q^{14} + 8192 q^{16} - 25704 q^{17} + 37048 q^{19} + 3072 q^{20} + 57840 q^{22} + 59628 q^{23} + 324584 q^{25} - 68480 q^{26} + 56320 q^{28} + 275280 q^{29} + 245584 q^{31} - 65536 q^{32} + 205632 q^{34} + 500802 q^{35} - 71060 q^{37} - 296384 q^{38} - 24576 q^{40} - 494520 q^{41} + 825280 q^{43} - 462720 q^{44} - 477024 q^{46} + 927708 q^{47} - 780204 q^{49} - 2596672 q^{50} + 547840 q^{52} + 1382112 q^{53} - 4010976 q^{55} - 450560 q^{56} - 2202240 q^{58} - 1588920 q^{59} - 3021968 q^{61} - 1964672 q^{62} + 524288 q^{64} + 9799080 q^{65} - 1882160 q^{67} - 1645056 q^{68} - 4006416 q^{70} + 3394440 q^{71} + 895090 q^{73} + 568480 q^{74} + 2371072 q^{76} - 7018656 q^{77} - 369920 q^{79} + 196608 q^{80} + 3956160 q^{82} + 9352050 q^{83} + 8976744 q^{85} - 6602240 q^{86} + 3701760 q^{88} + 912960 q^{89} + 13360040 q^{91} + 3816192 q^{92} - 7421664 q^{94} - 32688588 q^{95} + 1359790 q^{97} + 6241632 q^{98}+O(q^{100}) \) 2 * q - 16 * q^2 + 128 * q^4 + 48 * q^5 + 880 * q^7 - 1024 * q^8 - 384 * q^10 - 7230 * q^11 + 8560 * q^13 - 7040 * q^14 + 8192 * q^16 - 25704 * q^17 + 37048 * q^19 + 3072 * q^20 + 57840 * q^22 + 59628 * q^23 + 324584 * q^25 - 68480 * q^26 + 56320 * q^28 + 275280 * q^29 + 245584 * q^31 - 65536 * q^32 + 205632 * q^34 + 500802 * q^35 - 71060 * q^37 - 296384 * q^38 - 24576 * q^40 - 494520 * q^41 + 825280 * q^43 - 462720 * q^44 - 477024 * q^46 + 927708 * q^47 - 780204 * q^49 - 2596672 * q^50 + 547840 * q^52 + 1382112 * q^53 - 4010976 * q^55 - 450560 * q^56 - 2202240 * q^58 - 1588920 * q^59 - 3021968 * q^61 - 1964672 * q^62 + 524288 * q^64 + 9799080 * q^65 - 1882160 * q^67 - 1645056 * q^68 - 4006416 * q^70 + 3394440 * q^71 + 895090 * q^73 + 568480 * q^74 + 2371072 * q^76 - 7018656 * q^77 - 369920 * q^79 + 196608 * q^80 + 3956160 * q^82 + 9352050 * q^83 + 8976744 * q^85 - 6602240 * q^86 + 3701760 * q^88 + 912960 * q^89 + 13360040 * q^91 + 3816192 * q^92 - 7421664 * q^94 - 32688588 * q^95 + 1359790 * q^97 + 6241632 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	64.0000	0.500000
$5$	−465.736	−1.66627	−0.833133	−	0.553072i	$-0.813455\pi$
$5$	−465.736	−1.66627	−0.833133	+	0.553072i	$0.813455\pi$
$6$	0	0
$7$	−49.7356	−0.0548056	−0.0274028	−	0.999624i	$-0.508724\pi$
$7$	−49.7356	−0.0548056	−0.0274028	+	0.999624i	$0.508724\pi$
$8$	−512.000	−0.353553
$9$	0	0
$10$	3725.89	1.17823
$11$	302.885	0.0686126	0.0343063	−	0.999411i	$-0.489078\pi$
$11$	302.885	0.0686126	0.0343063	+	0.999411i	$0.489078\pi$
$12$	0	0
$13$	−5514.71	−0.696179	−0.348090	−	0.937461i	$-0.613170\pi$
$13$	−5514.71	−0.696179	−0.348090	+	0.937461i	$0.613170\pi$
$14$	397.885	0.0387534
$15$	0	0
$16$	4096.00	0.250000
$17$	−22646.7	−1.11798	−0.558990	−	0.829174i	$-0.688811\pi$
$17$	−22646.7	−1.11798	−0.558990	+	0.829174i	$0.688811\pi$
$18$	0	0
$19$	52805.5	1.76621	0.883103	−	0.469179i	$-0.155450\pi$
$19$	52805.5	1.76621	0.883103	+	0.469179i	$0.155450\pi$
$20$	−29807.1	−0.833133
$21$	0	0
$22$	−2423.08	−0.0485164
$23$	20019.3	0.343085	0.171542	−	0.985177i	$-0.445125\pi$
$23$	20019.3	0.343085	0.171542	+	0.985177i	$0.445125\pi$
$24$	0	0
$25$	138785.	1.77644
$26$	44117.7	0.492273
$27$	0	0
$28$	−3183.08	−0.0274028
$29$	250279.	1.90560	0.952800	−	0.303599i	$-0.0981882\pi$
$29$	250279.	1.90560	0.952800	+	0.303599i	$0.0981882\pi$
$30$	0	0
$31$	262367.	1.58177	0.790884	−	0.611966i	$-0.209621\pi$
$31$	262367.	1.58177	0.790884	+	0.611966i	$0.209621\pi$
$32$	−32768.0	−0.176777
$33$	0	0
$34$	181174.	0.790531
$35$	23163.7	0.0913207
$36$	0	0
$37$	−460621.	−1.49499	−0.747493	−	0.664269i	$-0.768743\pi$
$37$	−460621.	−1.49499	−0.747493	+	0.664269i	$0.768743\pi$
$38$	−422444.	−1.24890
$39$	0	0
$40$	238457.	0.589114
$41$	−240404.	−0.544751	−0.272375	−	0.962191i	$-0.587809\pi$
$41$	−240404.	−0.544751	−0.272375	+	0.962191i	$0.587809\pi$
$42$	0	0
$43$	568376.	1.09017	0.545087	−	0.838379i	$-0.316496\pi$
$43$	568376.	1.09017	0.545087	+	0.838379i	$0.316496\pi$
$44$	19384.6	0.0343063
$45$	0	0
$46$	−160154.	−0.242597
$47$	875232.	1.22965	0.614824	−	0.788665i	$-0.289227\pi$
$47$	875232.	1.22965	0.614824	+	0.788665i	$0.289227\pi$
$48$	0	0
$49$	−821069.	−0.996996
$50$	−1.11028e6	−1.25614
$51$	0	0
$52$	−352942.	−0.348090
$53$	811041.	0.748303	0.374151	−	0.927368i	$-0.377934\pi$
$53$	811041.	0.748303	0.374151	+	0.927368i	$0.377934\pi$
$54$	0	0
$55$	−141064.	−0.114327
$56$	25464.6	0.0193767
$57$	0	0
$58$	−2.00223e6	−1.34746
$59$	−1.29203e6	−0.819013	−0.409507	−	0.912307i	$-0.634299\pi$
$59$	−1.29203e6	−0.819013	−0.409507	+	0.912307i	$0.634299\pi$
$60$	0	0
$61$	−1.62852e6	−0.918626	−0.459313	−	0.888274i	$-0.651904\pi$
$61$	−1.62852e6	−0.918626	−0.459313	+	0.888274i	$0.651904\pi$
$62$	−2.09893e6	−1.11848
$63$	0	0
$64$	262144.	0.125000
$65$	2.56840e6	1.16002
$66$	0	0
$67$	−1.84317e6	−0.748694	−0.374347	−	0.927289i	$-0.622133\pi$
$67$	−1.84317e6	−0.748694	−0.374347	+	0.927289i	$0.622133\pi$
$68$	−1.44939e6	−0.558990
$69$	0	0
$70$	−185309.	−0.0645735
$71$	4.56707e6	1.51438	0.757188	−	0.653197i	$-0.226573\pi$
$71$	4.56707e6	1.51438	0.757188	+	0.653197i	$0.226573\pi$
$72$	0	0
$73$	−1.91494e6	−0.576136	−0.288068	−	0.957610i	$-0.593013\pi$
$73$	−1.91494e6	−0.576136	−0.288068	+	0.957610i	$0.593013\pi$
$74$	3.68496e6	1.05712
$75$	0	0
$76$	3.37955e6	0.883103
$77$	−15064.2	−0.00376035
$78$	0	0
$79$	−1.81088e6	−0.413233	−0.206617	−	0.978422i	$-0.566245\pi$
$79$	−1.81088e6	−0.413233	−0.206617	+	0.978422i	$0.566245\pi$
$80$	−1.90765e6	−0.416567
$81$	0	0
$82$	1.92323e6	0.385197
$83$	3.08928e6	0.593040	0.296520	−	0.955027i	$-0.404174\pi$
$83$	3.08928e6	0.593040	0.296520	+	0.955027i	$0.404174\pi$
$84$	0	0
$85$	1.05474e7	1.86285
$86$	−4.54701e6	−0.770870
$87$	0	0
$88$	−155077.	−0.0242582
$89$	−4.10492e6	−0.617219	−0.308610	−	0.951189i	$-0.599864\pi$
$89$	−4.10492e6	−0.617219	−0.308610	+	0.951189i	$0.599864\pi$
$90$	0	0
$91$	274278.	0.0381545
$92$	1.28123e6	0.171542
$93$	0	0
$94$	−7.00186e6	−0.869492
$95$	−2.45934e7	−2.94297
$96$	0	0
$97$	7.91623e6	0.880678	0.440339	−	0.897832i	$-0.354858\pi$
$97$	7.91623e6	0.880678	0.440339	+	0.897832i	$0.354858\pi$
$98$	6.56855e6	0.704983
$99$	0	0
$100$	8.88222e6	0.888222
$101$	9.63259e6	0.930290	0.465145	−	0.885235i	$-0.346002\pi$
$101$	9.63259e6	0.930290	0.465145	+	0.885235i	$0.346002\pi$
$102$	0	0
$103$	9.18015e6	0.827789	0.413894	−	0.910325i	$-0.364168\pi$
$103$	9.18015e6	0.827789	0.413894	+	0.910325i	$0.364168\pi$
$104$	2.82353e6	0.246137
$105$	0	0
$106$	−6.48833e6	−0.529130
$107$	3.82175e6	0.301591	0.150796	−	0.988565i	$-0.451816\pi$
$107$	3.82175e6	0.301591	0.150796	+	0.988565i	$0.451816\pi$
$108$	0	0
$109$	1.90995e7	1.41264	0.706318	−	0.707895i	$-0.250355\pi$
$109$	1.90995e7	1.41264	0.706318	+	0.707895i	$0.250355\pi$
$110$	1.12852e6	0.0808413
$111$	0	0
$112$	−203717.	−0.0137014
$113$	230270.	0.0150129	0.00750643	−	0.999972i	$-0.497611\pi$
$113$	230270.	0.0150129	0.00750643	+	0.999972i	$0.497611\pi$
$114$	0	0
$115$	−9.32370e6	−0.571670
$116$	1.60179e7	0.952800
$117$	0	0
$118$	1.03363e7	0.579130
$119$	1.12635e6	0.0612715
$120$	0	0
$121$	−1.93954e7	−0.995292
$122$	1.30282e7	0.649567
$123$	0	0
$124$	1.67915e7	0.790884
$125$	−2.82514e7	−1.29376
$126$	0	0
$127$	−3.92443e7	−1.70006	−0.850028	−	0.526737i	$-0.823415\pi$
$127$	−3.92443e7	−1.70006	−0.850028	+	0.526737i	$0.823415\pi$
$128$	−2.09715e6	−0.0883883
$129$	0	0
$130$	−2.05472e7	−0.820258
$131$	−2.12776e7	−0.826940	−0.413470	−	0.910518i	$-0.635683\pi$
$131$	−2.12776e7	−0.826940	−0.413470	+	0.910518i	$0.635683\pi$
$132$	0	0
$133$	−2.62632e6	−0.0967979
$134$	1.47454e7	0.529407
$135$	0	0
$136$	1.15951e7	0.395266
$137$	1.82304e7	0.605723	0.302862	−	0.953035i	$-0.402058\pi$
$137$	1.82304e7	0.605723	0.302862	+	0.953035i	$0.402058\pi$
$138$	0	0
$139$	2.16169e7	0.682720	0.341360	−	0.939933i	$-0.389113\pi$
$139$	2.16169e7	0.682720	0.341360	+	0.939933i	$0.389113\pi$
$140$	1.48247e6	0.0456603
$141$	0	0
$142$	−3.65366e7	−1.07083
$143$	−1.67032e6	−0.0477666
$144$	0	0
$145$	−1.16564e8	−3.17524
$146$	1.53195e7	0.407390
$147$	0	0
$148$	−2.94797e7	−0.747493
$149$	7.00600e7	1.73508	0.867538	−	0.497372i	$-0.165701\pi$
$149$	7.00600e7	1.73508	0.867538	+	0.497372i	$0.165701\pi$
$150$	0	0
$151$	6.21546e7	1.46911	0.734555	−	0.678549i	$-0.237391\pi$
$151$	6.21546e7	1.46911	0.734555	+	0.678549i	$0.237391\pi$
$152$	−2.70364e7	−0.624448
$153$	0	0
$154$	120513.	0.00265897
$155$	−1.22194e8	−2.63565
$156$	0	0
$157$	5.33254e7	1.09973	0.549864	−	0.835254i	$-0.314680\pi$
$157$	5.33254e7	1.09973	0.549864	+	0.835254i	$0.314680\pi$
$158$	1.44871e7	0.292200
$159$	0	0
$160$	1.52612e7	0.294557
$161$	−995672.	−0.0188029
$162$	0	0
$163$	8.41147e6	0.152130	0.0760650	−	0.997103i	$-0.475764\pi$
$163$	8.41147e6	0.152130	0.0760650	+	0.997103i	$0.475764\pi$
$164$	−1.53858e7	−0.272375
$165$	0	0
$166$	−2.47143e7	−0.419343
$167$	2.87845e6	0.0478245	0.0239122	−	0.999714i	$-0.492388\pi$
$167$	2.87845e6	0.0478245	0.0239122	+	0.999714i	$0.492388\pi$
$168$	0	0
$169$	−3.23365e7	−0.515334
$170$	−8.43791e7	−1.31724
$171$	0	0
$172$	3.63761e7	0.545087
$173$	−2.45088e7	−0.359883	−0.179941	−	0.983677i	$-0.557591\pi$
$173$	−2.45088e7	−0.359883	−0.179941	+	0.983677i	$0.557591\pi$
$174$	0	0
$175$	−6.90255e6	−0.0973590
$176$	1.24062e6	0.0171531
$177$	0	0
$178$	3.28393e7	0.436440
$179$	8.25306e7	1.07555	0.537773	−	0.843089i	$-0.319266\pi$
$179$	8.25306e7	1.07555	0.537773	+	0.843089i	$0.319266\pi$
$180$	0	0
$181$	4.49477e7	0.563420	0.281710	−	0.959500i	$-0.409098\pi$
$181$	4.49477e7	0.563420	0.281710	+	0.959500i	$0.409098\pi$
$182$	−2.19422e6	−0.0269793
$183$	0	0
$184$	−1.02499e7	−0.121299
$185$	2.14527e8	2.49105
$186$	0	0
$187$	−6.85935e6	−0.0767074
$188$	5.60148e7	0.614824
$189$	0	0
$190$	1.96747e8	2.08099
$191$	4.45002e6	0.0462110	0.0231055	−	0.999733i	$-0.492645\pi$
$191$	4.45002e6	0.0462110	0.0231055	+	0.999733i	$0.492645\pi$
$192$	0	0
$193$	6.70317e7	0.671166	0.335583	−	0.942011i	$-0.391067\pi$
$193$	6.70317e7	0.671166	0.335583	+	0.942011i	$0.391067\pi$
$194$	−6.33298e7	−0.622734
$195$	0	0
$196$	−5.25484e7	−0.498498
$197$	9.80246e7	0.913489	0.456745	−	0.889598i	$-0.349015\pi$
$197$	9.80246e7	0.913489	0.456745	+	0.889598i	$0.349015\pi$
$198$	0	0
$199$	5.48349e7	0.493254	0.246627	−	0.969110i	$-0.420678\pi$
$199$	5.48349e7	0.493254	0.246627	+	0.969110i	$0.420678\pi$
$200$	−7.10578e7	−0.628068
$201$	0	0
$202$	−7.70607e7	−0.657814
$203$	−1.24478e7	−0.104437
$204$	0	0
$205$	1.11965e8	0.907700
$206$	−7.34412e7	−0.585335
$207$	0	0
$208$	−2.25883e7	−0.174045
$209$	1.59940e7	0.121184
$210$	0	0
$211$	1.16275e8	0.852117	0.426058	−	0.904696i	$-0.359902\pi$
$211$	1.16275e8	0.852117	0.426058	+	0.904696i	$0.359902\pi$
$212$	5.19066e7	0.374151
$213$	0	0
$214$	−3.05740e7	−0.213257
$215$	−2.64713e8	−1.81652
$216$	0	0
$217$	−1.30490e7	−0.0866897
$218$	−1.52796e8	−0.998884
$219$	0	0
$220$	−9.02812e6	−0.0571634
$221$	1.24890e8	0.778314
$222$	0	0
$223$	−1.32149e8	−0.797988	−0.398994	−	0.916953i	$-0.630641\pi$
$223$	−1.32149e8	−0.797988	−0.398994	+	0.916953i	$0.630641\pi$
$224$	1.62974e6	0.00968835
$225$	0	0
$226$	−1.84216e6	−0.0106157
$227$	−5.64612e7	−0.320376	−0.160188	−	0.987087i	$-0.551210\pi$
$227$	−5.64612e7	−0.320376	−0.160188	+	0.987087i	$0.551210\pi$
$228$	0	0
$229$	1.77874e8	0.978786	0.489393	−	0.872063i	$-0.337218\pi$
$229$	1.77874e8	0.978786	0.489393	+	0.872063i	$0.337218\pi$
$230$	7.45896e7	0.404232
$231$	0	0
$232$	−1.28143e8	−0.673731
$233$	1.00997e8	0.523076	0.261538	−	0.965193i	$-0.415770\pi$
$233$	1.00997e8	0.523076	0.261538	+	0.965193i	$0.415770\pi$
$234$	0	0
$235$	−4.07627e8	−2.04892
$236$	−8.26900e7	−0.409507
$237$	0	0
$238$	−9.01079e6	−0.0433255
$239$	−1.21426e8	−0.575334	−0.287667	−	0.957731i	$-0.592880\pi$
$239$	−1.21426e8	−0.575334	−0.287667	+	0.957731i	$0.592880\pi$
$240$	0	0
$241$	−2.28248e8	−1.05038	−0.525191	−	0.850984i	$-0.676006\pi$
$241$	−2.28248e8	−1.05038	−0.525191	+	0.850984i	$0.676006\pi$
$242$	1.55163e8	0.703778
$243$	0	0
$244$	−1.04225e8	−0.459313
$245$	3.82401e8	1.66126
$246$	0	0
$247$	−2.91207e8	−1.22960
$248$	−1.34332e8	−0.559239
$249$	0	0
$250$	2.26011e8	0.914828
$251$	−3.32724e8	−1.32808	−0.664042	−	0.747695i	$-0.731160\pi$
$251$	−3.32724e8	−1.32808	−0.664042	+	0.747695i	$0.731160\pi$
$252$	0	0
$253$	6.06354e6	0.0235399
$254$	3.13954e8	1.20212
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	−4.62423e8	−1.69931	−0.849657	−	0.527336i	$-0.823191\pi$
$257$	−4.62423e8	−1.69931	−0.849657	+	0.527336i	$0.823191\pi$
$258$	0	0
$259$	2.29093e7	0.0819336
$260$	1.64377e8	0.580010
$261$	0	0
$262$	1.70221e8	0.584735
$263$	−1.33063e8	−0.451037	−0.225519	−	0.974239i	$-0.572408\pi$
$263$	−1.33063e8	−0.451037	−0.225519	+	0.974239i	$0.572408\pi$
$264$	0	0
$265$	−3.77731e8	−1.24687
$266$	2.10105e7	0.0684465
$267$	0	0
$268$	−1.17963e8	−0.374347
$269$	3.65232e8	1.14403	0.572013	−	0.820245i	$-0.306163\pi$
$269$	3.65232e8	1.14403	0.572013	+	0.820245i	$0.306163\pi$
$270$	0	0
$271$	1.75400e8	0.535348	0.267674	−	0.963510i	$-0.413745\pi$
$271$	1.75400e8	0.535348	0.267674	+	0.963510i	$0.413745\pi$
$272$	−9.27609e7	−0.279495
$273$	0	0
$274$	−1.45843e8	−0.428311
$275$	4.20358e7	0.121886
$276$	0	0
$277$	1.84284e8	0.520965	0.260483	−	0.965479i	$-0.416118\pi$
$277$	1.84284e8	0.520965	0.260483	+	0.965479i	$0.416118\pi$
$278$	−1.72936e8	−0.482756
$279$	0	0
$280$	−1.18598e7	−0.0322867
$281$	8.72612e7	0.234611	0.117306	−	0.993096i	$-0.462574\pi$
$281$	8.72612e7	0.234611	0.117306	+	0.993096i	$0.462574\pi$
$282$	0	0
$283$	1.87621e8	0.492071	0.246036	−	0.969261i	$-0.420872\pi$
$283$	1.87621e8	0.492071	0.246036	+	0.969261i	$0.420872\pi$
$284$	2.92293e8	0.757188
$285$	0	0
$286$	1.33626e7	0.0337761
$287$	1.19566e7	0.0298554
$288$	0	0
$289$	1.02535e8	0.249879
$290$	9.32512e8	2.24523
$291$	0	0
$292$	−1.22556e8	−0.288068
$293$	−6.10145e8	−1.41709	−0.708543	−	0.705667i	$-0.750647\pi$
$293$	−6.10145e8	−1.41709	−0.708543	+	0.705667i	$0.750647\pi$
$294$	0	0
$295$	6.01745e8	1.36469
$296$	2.35838e8	0.528558
$297$	0	0
$298$	−5.60480e8	−1.22688
$299$	−1.10401e8	−0.238848
$300$	0	0
$301$	−2.82685e7	−0.0597476
$302$	−4.97237e8	−1.03882
$303$	0	0
$304$	2.16291e8	0.441552
$305$	7.58460e8	1.53068
$306$	0	0
$307$	7.70231e8	1.51928	0.759638	−	0.650346i	$-0.225376\pi$
$307$	7.70231e8	1.51928	0.759638	+	0.650346i	$0.225376\pi$
$308$	−964108.	−0.00188017
$309$	0	0
$310$	9.77548e8	1.86368
$311$	−8.72713e8	−1.64517	−0.822584	−	0.568644i	$-0.807468\pi$
$311$	−8.72713e8	−1.64517	−0.822584	+	0.568644i	$0.807468\pi$
$312$	0	0
$313$	−1.54391e7	−0.0284587	−0.0142294	−	0.999899i	$-0.504530\pi$
$313$	−1.54391e7	−0.0284587	−0.0142294	+	0.999899i	$0.504530\pi$
$314$	−4.26603e8	−0.777625
$315$	0	0
$316$	−1.15896e8	−0.206617
$317$	−2.55887e8	−0.451171	−0.225586	−	0.974223i	$-0.572430\pi$
$317$	−2.55887e8	−0.451171	−0.225586	+	0.974223i	$0.572430\pi$
$318$	0	0
$319$	7.58059e7	0.130748
$320$	−1.22090e8	−0.208283
$321$	0	0
$322$	7.96538e6	0.0132957
$323$	−1.19587e9	−1.97458
$324$	0	0
$325$	−7.65358e8	−1.23672
$326$	−6.72917e7	−0.107572
$327$	0	0
$328$	1.23087e8	0.192598
$329$	−4.35302e7	−0.0673915
$330$	0	0
$331$	3.98365e8	0.603787	0.301893	−	0.953342i	$-0.402381\pi$
$331$	3.98365e8	0.603787	0.301893	+	0.953342i	$0.402381\pi$
$332$	1.97714e8	0.296520
$333$	0	0
$334$	−2.30276e7	−0.0338170
$335$	8.58431e8	1.24752
$336$	0	0
$337$	1.16261e9	1.65474	0.827368	−	0.561660i	$-0.189837\pi$
$337$	1.16261e9	1.65474	0.827368	+	0.561660i	$0.189837\pi$
$338$	2.58692e8	0.364396
$339$	0	0
$340$	6.75032e8	0.931426
$341$	7.94670e7	0.108529
$342$	0	0
$343$	8.17959e7	0.109446
$344$	−2.91008e8	−0.385435
$345$	0	0
$346$	1.96071e8	0.254476
$347$	1.14802e9	1.47501	0.737507	−	0.675340i	$-0.236003\pi$
$347$	1.14802e9	1.47501	0.737507	+	0.675340i	$0.236003\pi$
$348$	0	0
$349$	−1.37598e9	−1.73270	−0.866351	−	0.499436i	$-0.833541\pi$
$349$	−1.37598e9	−1.73270	−0.866351	+	0.499436i	$0.833541\pi$
$350$	5.52204e7	0.0688432
$351$	0	0
$352$	−9.92494e6	−0.0121291
$353$	4.44990e8	0.538442	0.269221	−	0.963078i	$-0.413234\pi$
$353$	4.44990e8	0.538442	0.269221	+	0.963078i	$0.413234\pi$
$354$	0	0
$355$	−2.12705e9	−2.52335
$356$	−2.62715e8	−0.308610
$357$	0	0
$358$	−6.60245e8	−0.760526
$359$	1.14314e9	1.30397	0.651984	−	0.758233i	$-0.273937\pi$
$359$	1.14314e9	1.30397	0.651984	+	0.758233i	$0.273937\pi$
$360$	0	0
$361$	1.89455e9	2.11949
$362$	−3.59582e8	−0.398398
$363$	0	0
$364$	1.75538e7	0.0190773
$365$	8.91856e8	0.959996
$366$	0	0
$367$	−7.51043e8	−0.793111	−0.396555	−	0.918011i	$-0.629794\pi$
$367$	−7.51043e8	−0.793111	−0.396555	+	0.918011i	$0.629794\pi$
$368$	8.19990e7	0.0857711
$369$	0	0
$370$	−1.71622e9	−1.76144
$371$	−4.03377e7	−0.0410112
$372$	0	0
$373$	−1.33035e9	−1.32734	−0.663672	−	0.748024i	$-0.731003\pi$
$373$	−1.33035e9	−1.32734	−0.663672	+	0.748024i	$0.731003\pi$
$374$	5.48748e7	0.0542404
$375$	0	0
$376$	−4.48119e8	−0.434746
$377$	−1.38022e9	−1.32664
$378$	0	0
$379$	1.06374e9	1.00369	0.501845	−	0.864958i	$-0.332655\pi$
$379$	1.06374e9	1.00369	0.501845	+	0.864958i	$0.332655\pi$
$380$	−1.57398e9	−1.47149
$381$	0	0
$382$	−3.56002e7	−0.0326761
$383$	−2.10175e8	−0.191155	−0.0955774	−	0.995422i	$-0.530470\pi$
$383$	−2.10175e8	−0.191155	−0.0955774	+	0.995422i	$0.530470\pi$
$384$	0	0
$385$	7.01593e6	0.00626574
$386$	−5.36254e8	−0.474586
$387$	0	0
$388$	5.06639e8	0.440339
$389$	3.95462e8	0.340628	0.170314	−	0.985390i	$-0.445522\pi$
$389$	3.95462e8	0.340628	0.170314	+	0.985390i	$0.445522\pi$
$390$	0	0
$391$	−4.53371e8	−0.383562
$392$	4.20388e8	0.352491
$393$	0	0
$394$	−7.84197e8	−0.645934
$395$	8.43392e8	0.688557
$396$	0	0
$397$	1.60421e8	0.128675	0.0643375	−	0.997928i	$-0.479507\pi$
$397$	1.60421e8	0.128675	0.0643375	+	0.997928i	$0.479507\pi$
$398$	−4.38679e8	−0.348784
$399$	0	0
$400$	5.68462e8	0.444111
$401$	2.81287e8	0.217843	0.108922	−	0.994050i	$-0.465260\pi$
$401$	2.81287e8	0.217843	0.108922	+	0.994050i	$0.465260\pi$
$402$	0	0
$403$	−1.44688e9	−1.10119
$404$	6.16486e8	0.465145
$405$	0	0
$406$	9.95824e7	0.0738484
$407$	−1.39515e8	−0.102575
$408$	0	0
$409$	4.14549e8	0.299602	0.149801	−	0.988716i	$-0.452137\pi$
$409$	4.14549e8	0.299602	0.149801	+	0.988716i	$0.452137\pi$
$410$	−8.95717e8	−0.641840
$411$	0	0
$412$	5.87530e8	0.413894
$413$	6.42600e7	0.0448865
$414$	0	0
$415$	−1.43879e9	−0.988163
$416$	1.80706e8	0.123068
$417$	0	0
$418$	−1.27952e8	−0.0856900
$419$	2.59925e9	1.72623	0.863114	−	0.505008i	$-0.168511\pi$
$419$	2.59925e9	1.72623	0.863114	+	0.505008i	$0.168511\pi$
$420$	0	0
$421$	5.78564e8	0.377889	0.188944	−	0.981988i	$-0.439493\pi$
$421$	5.78564e8	0.377889	0.188944	+	0.981988i	$0.439493\pi$
$422$	−9.30203e8	−0.602538
$423$	0	0
$424$	−4.15253e8	−0.264565
$425$	−3.14302e9	−1.98603
$426$	0	0
$427$	8.09955e7	0.0503458
$428$	2.44592e8	0.150796
$429$	0	0
$430$	2.11770e9	1.28447
$431$	7.69740e7	0.0463099	0.0231549	−	0.999732i	$-0.492629\pi$
$431$	7.69740e7	0.0463099	0.0231549	+	0.999732i	$0.492629\pi$
$432$	0	0
$433$	−2.75020e8	−0.162801	−0.0814005	−	0.996681i	$-0.525939\pi$
$433$	−2.75020e8	−0.162801	−0.0814005	+	0.996681i	$0.525939\pi$
$434$	1.04392e8	0.0612988
$435$	0	0
$436$	1.22237e9	0.706318
$437$	1.05713e9	0.605958
$438$	0	0
$439$	1.52299e9	0.859157	0.429579	−	0.903029i	$-0.358662\pi$
$439$	1.52299e9	0.859157	0.429579	+	0.903029i	$0.358662\pi$
$440$	7.22250e7	0.0404206
$441$	0	0
$442$	−9.99121e8	−0.550351
$443$	−2.08057e9	−1.13702	−0.568512	−	0.822675i	$-0.692481\pi$
$443$	−2.08057e9	−1.13702	−0.568512	+	0.822675i	$0.692481\pi$
$444$	0	0
$445$	1.91181e9	1.02845
$446$	1.05719e9	0.564263
$447$	0	0
$448$	−1.30379e7	−0.00685069
$449$	−1.89838e9	−0.989741	−0.494870	−	0.868967i	$-0.664784\pi$
$449$	−1.89838e9	−0.989741	−0.494870	+	0.868967i	$0.664784\pi$
$450$	0	0
$451$	−7.28147e7	−0.0373767
$452$	1.47373e7	0.00750643
$453$	0	0
$454$	4.51690e8	0.226540
$455$	−1.27741e8	−0.0635756
$456$	0	0
$457$	6.86064e8	0.336246	0.168123	−	0.985766i	$-0.446229\pi$
$457$	6.86064e8	0.336246	0.168123	+	0.985766i	$0.446229\pi$
$458$	−1.42299e9	−0.692107
$459$	0	0
$460$	−5.96717e8	−0.285835
$461$	−1.52097e9	−0.723047	−0.361523	−	0.932363i	$-0.617743\pi$
$461$	−1.52097e9	−0.723047	−0.361523	+	0.932363i	$0.617743\pi$
$462$	0	0
$463$	−5.00286e8	−0.234253	−0.117126	−	0.993117i	$-0.537368\pi$
$463$	−5.00286e8	−0.234253	−0.117126	+	0.993117i	$0.537368\pi$
$464$	1.02514e9	0.476400
$465$	0	0
$466$	−8.07979e8	−0.369870
$467$	4.03333e9	1.83255	0.916274	−	0.400553i	$-0.131182\pi$
$467$	4.03333e9	1.83255	0.916274	+	0.400553i	$0.131182\pi$
$468$	0	0
$469$	9.16714e7	0.0410326
$470$	3.26101e9	1.44881
$471$	0	0
$472$	6.61520e8	0.289565
$473$	1.72153e8	0.0747997
$474$	0	0
$475$	7.32859e9	3.13757
$476$	7.20863e7	0.0306358
$477$	0	0
$478$	9.71410e8	0.406822
$479$	2.60262e9	1.08202	0.541012	−	0.841015i	$-0.318042\pi$
$479$	2.60262e9	1.08202	0.541012	+	0.841015i	$0.318042\pi$
$480$	0	0
$481$	2.54019e9	1.04078
$482$	1.82598e9	0.742732
$483$	0	0
$484$	−1.24131e9	−0.497646
$485$	−3.68687e9	−1.46744
$486$	0	0
$487$	4.35516e9	1.70865	0.854325	−	0.519739i	$-0.173971\pi$
$487$	4.35516e9	1.70865	0.854325	+	0.519739i	$0.173971\pi$
$488$	8.33803e8	0.324783
$489$	0	0
$490$	−3.05921e9	−1.17469
$491$	−4.16655e8	−0.158852	−0.0794258	−	0.996841i	$-0.525309\pi$
$491$	−4.16655e8	−0.158852	−0.0794258	+	0.996841i	$0.525309\pi$
$492$	0	0
$493$	−5.66800e9	−2.13042
$494$	2.32966e9	0.869456
$495$	0	0
$496$	1.07465e9	0.395442
$497$	−2.27146e8	−0.0829962
$498$	0	0
$499$	−3.34270e9	−1.20433	−0.602164	−	0.798372i	$-0.705695\pi$
$499$	−3.34270e9	−1.20433	−0.602164	+	0.798372i	$0.705695\pi$
$500$	−1.80809e9	−0.646881
$501$	0	0
$502$	2.66179e9	0.939097
$503$	1.48681e9	0.520915	0.260458	−	0.965485i	$-0.416127\pi$
$503$	1.48681e9	0.520915	0.260458	+	0.965485i	$0.416127\pi$
$504$	0	0
$505$	−4.48624e9	−1.55011
$506$	−4.85084e7	−0.0166452
$507$	0	0
$508$	−2.51163e9	−0.850028
$509$	6.34341e8	0.213212	0.106606	−	0.994301i	$-0.466002\pi$
$509$	6.34341e8	0.213212	0.106606	+	0.994301i	$0.466002\pi$
$510$	0	0
$511$	9.52408e7	0.0315755
$512$	−1.34218e8	−0.0441942
$513$	0	0
$514$	3.69939e9	1.20160
$515$	−4.27552e9	−1.37932
$516$	0	0
$517$	2.65095e8	0.0843693
$518$	−1.83274e8	−0.0579358
$519$	0	0
$520$	−1.31502e9	−0.410129
$521$	−5.00649e9	−1.55096	−0.775481	−	0.631371i	$-0.782493\pi$
$521$	−5.00649e9	−1.55096	−0.775481	+	0.631371i	$0.782493\pi$
$522$	0	0
$523$	−4.06385e9	−1.24217	−0.621086	−	0.783743i	$-0.713308\pi$
$523$	−4.06385e9	−1.24217	−0.621086	+	0.783743i	$0.713308\pi$
$524$	−1.36177e9	−0.413470
$525$	0	0
$526$	1.06450e9	0.318931
$527$	−5.94174e9	−1.76838
$528$	0	0
$529$	−3.00405e9	−0.882293
$530$	3.02185e9	0.881672
$531$	0	0
$532$	−1.68084e8	−0.0483990
$533$	1.32576e9	0.379244
$534$	0	0
$535$	−1.77992e9	−0.502531
$536$	9.43705e8	0.264703
$537$	0	0
$538$	−2.92185e9	−0.808948
$539$	−2.48690e8	−0.0684065
$540$	0	0
$541$	6.36182e8	0.172739	0.0863696	−	0.996263i	$-0.472473\pi$
$541$	6.36182e8	0.172739	0.0863696	+	0.996263i	$0.472473\pi$
$542$	−1.40320e9	−0.378548
$543$	0	0
$544$	7.42087e8	0.197633
$545$	−8.89533e9	−2.35383
$546$	0	0
$547$	−2.54847e9	−0.665769	−0.332884	−	0.942968i	$-0.608022\pi$
$547$	−2.54847e9	−0.665769	−0.332884	+	0.942968i	$0.608022\pi$
$548$	1.16675e9	0.302862
$549$	0	0
$550$	−3.36287e8	−0.0861867
$551$	1.32161e10	3.36568
$552$	0	0
$553$	9.00654e7	0.0226475
$554$	−1.47427e9	−0.368378
$555$	0	0
$556$	1.38348e9	0.341360
$557$	3.06157e9	0.750673	0.375337	−	0.926889i	$-0.377527\pi$
$557$	3.06157e9	0.750673	0.375337	+	0.926889i	$0.377527\pi$
$558$	0	0
$559$	−3.13443e9	−0.758957
$560$	9.48784e7	0.0228302
$561$	0	0
$562$	−6.98089e8	−0.165895
$563$	4.24700e9	1.00300	0.501502	−	0.865156i	$-0.332781\pi$
$563$	4.24700e9	1.00300	0.501502	+	0.865156i	$0.332781\pi$
$564$	0	0
$565$	−1.07245e8	−0.0250154
$566$	−1.50096e9	−0.347947
$567$	0	0
$568$	−2.33834e9	−0.535413
$569$	5.47492e6	0.00124590	0.000622952	−	1.00000i	$-0.499802\pi$
$569$	5.47492e6	0.00124590	0.000622952		1.00000i	$0.499802\pi$
$570$	0	0
$571$	4.95114e9	1.11296	0.556479	−	0.830861i	$-0.312152\pi$
$571$	4.95114e9	1.11296	0.556479	+	0.830861i	$0.312152\pi$
$572$	−1.06901e8	−0.0238833
$573$	0	0
$574$	−9.56531e7	−0.0211109
$575$	2.77837e9	0.609471
$576$	0	0
$577$	−3.55867e9	−0.771210	−0.385605	−	0.922664i	$-0.626007\pi$
$577$	−3.55867e9	−0.771210	−0.385605	+	0.922664i	$0.626007\pi$
$578$	−8.20279e8	−0.176691
$579$	0	0
$580$	−7.46009e9	−1.58762
$581$	−1.53647e8	−0.0325019
$582$	0	0
$583$	2.45652e8	0.0513430
$584$	9.80449e8	0.203695
$585$	0	0
$586$	4.88116e9	1.00203
$587$	−4.34853e7	−0.00887379	−0.00443690	−	0.999990i	$-0.501412\pi$
$587$	−4.34853e7	−0.00887379	−0.00443690	+	0.999990i	$0.501412\pi$
$588$	0	0
$589$	1.38544e10	2.79373
$590$	−4.81396e9	−0.964985
$591$	0	0
$592$	−1.88670e9	−0.373747
$593$	2.06982e9	0.407607	0.203804	−	0.979012i	$-0.434670\pi$
$593$	2.06982e9	0.407607	0.203804	+	0.979012i	$0.434670\pi$
$594$	0	0
$595$	−5.24581e8	−0.102095
$596$	4.48384e9	0.867538
$597$	0	0
$598$	8.83205e8	0.168891
$599$	−9.07889e9	−1.72599	−0.862996	−	0.505210i	$-0.831415\pi$
$599$	−9.07889e9	−1.72599	−0.862996	+	0.505210i	$0.831415\pi$
$600$	0	0
$601$	3.03970e8	0.0571176	0.0285588	−	0.999592i	$-0.490908\pi$
$601$	3.03970e8	0.0571176	0.0285588	+	0.999592i	$0.490908\pi$
$602$	2.26148e8	0.0422480
$603$	0	0
$604$	3.97790e9	0.734555
$605$	9.03314e9	1.65842
$606$	0	0
$607$	−6.50286e9	−1.18017	−0.590084	−	0.807342i	$-0.700905\pi$
$607$	−6.50286e9	−1.18017	−0.590084	+	0.807342i	$0.700905\pi$
$608$	−1.73033e9	−0.312224
$609$	0	0
$610$	−6.06768e9	−1.08235
$611$	−4.82665e9	−0.856055
$612$	0	0
$613$	2.20282e9	0.386249	0.193124	−	0.981174i	$-0.438138\pi$
$613$	2.20282e9	0.386249	0.193124	+	0.981174i	$0.438138\pi$
$614$	−6.16185e9	−1.07429
$615$	0	0
$616$	7.71286e6	0.00132948
$617$	3.98619e9	0.683219	0.341610	−	0.939842i	$-0.389028\pi$
$617$	3.98619e9	0.683219	0.341610	+	0.939842i	$0.389028\pi$
$618$	0	0
$619$	1.50832e9	0.255610	0.127805	−	0.991799i	$-0.459207\pi$
$619$	1.50832e9	0.255610	0.127805	+	0.991799i	$0.459207\pi$
$620$	−7.82038e9	−1.31782
$621$	0	0
$622$	6.98171e9	1.16331
$623$	2.04161e8	0.0338270
$624$	0	0
$625$	2.31512e9	0.379309
$626$	1.23512e8	0.0201234
$627$	0	0
$628$	3.41282e9	0.549864
$629$	1.04315e10	1.67136
$630$	0	0
$631$	5.99394e9	0.949751	0.474875	−	0.880053i	$-0.342493\pi$
$631$	5.99394e9	0.949751	0.474875	+	0.880053i	$0.342493\pi$
$632$	9.27172e8	0.146100
$633$	0	0
$634$	2.04710e9	0.319026
$635$	1.82775e10	2.83275
$636$	0	0
$637$	4.52796e9	0.694088
$638$	−6.06447e8	−0.0924529
$639$	0	0
$640$	9.76718e8	0.147279
$641$	−8.25615e9	−1.23815	−0.619076	−	0.785331i	$-0.712493\pi$
$641$	−8.25615e9	−1.23815	−0.619076	+	0.785331i	$0.712493\pi$
$642$	0	0
$643$	−1.09680e10	−1.62701	−0.813505	−	0.581558i	$-0.802443\pi$
$643$	−1.09680e10	−1.62701	−0.813505	+	0.581558i	$0.802443\pi$
$644$	−6.37230e7	−0.00940147
$645$	0	0
$646$	9.56697e9	1.39624
$647$	−2.91111e9	−0.422565	−0.211283	−	0.977425i	$-0.567764\pi$
$647$	−2.91111e9	−0.422565	−0.211283	+	0.977425i	$0.567764\pi$
$648$	0	0
$649$	−3.91337e8	−0.0561946
$650$	6.12286e9	0.874496
$651$	0	0
$652$	5.38334e8	0.0760650
$653$	−1.06135e10	−1.49163	−0.745816	−	0.666152i	$-0.767940\pi$
$653$	−1.06135e10	−1.49163	−0.745816	+	0.666152i	$0.767940\pi$
$654$	0	0
$655$	9.90975e9	1.37790
$656$	−9.84694e8	−0.136188
$657$	0	0
$658$	3.48242e8	0.0476530
$659$	−3.22866e9	−0.439464	−0.219732	−	0.975560i	$-0.570518\pi$
$659$	−3.22866e9	−0.439464	−0.219732	+	0.975560i	$0.570518\pi$
$660$	0	0
$661$	1.01147e10	1.36222	0.681112	−	0.732179i	$-0.261497\pi$
$661$	1.01147e10	1.36222	0.681112	+	0.732179i	$0.261497\pi$
$662$	−3.18692e9	−0.426942
$663$	0	0
$664$	−1.58171e9	−0.209671
$665$	1.22317e9	0.161291
$666$	0	0
$667$	5.01041e9	0.653782
$668$	1.84221e8	0.0239122
$669$	0	0
$670$	−6.86745e9	−0.882132
$671$	−4.93255e8	−0.0630293
$672$	0	0
$673$	−1.27338e10	−1.61029	−0.805146	−	0.593076i	$-0.797913\pi$
$673$	−1.27338e10	−1.61029	−0.805146	+	0.593076i	$0.797913\pi$
$674$	−9.30086e9	−1.17007
$675$	0	0
$676$	−2.06953e9	−0.257667
$677$	−4.60677e8	−0.0570606	−0.0285303	−	0.999593i	$-0.509083\pi$
$677$	−4.60677e8	−0.0570606	−0.0285303	+	0.999593i	$0.509083\pi$
$678$	0	0
$679$	−3.93719e8	−0.0482661
$680$	−5.40026e9	−0.658618
$681$	0	0
$682$	−6.35736e8	−0.0767417
$683$	−1.53853e9	−0.184771	−0.0923856	−	0.995723i	$-0.529449\pi$
$683$	−1.53853e9	−0.184771	−0.0923856	+	0.995723i	$0.529449\pi$
$684$	0	0
$685$	−8.49055e9	−1.00930
$686$	−6.54367e8	−0.0773904
$687$	0	0
$688$	2.32807e9	0.272544
$689$	−4.47266e9	−0.520953
$690$	0	0
$691$	9.06481e9	1.04517	0.522583	−	0.852588i	$-0.324968\pi$
$691$	9.06481e9	1.04517	0.522583	+	0.852588i	$0.324968\pi$
$692$	−1.56857e9	−0.179941
$693$	0	0
$694$	−9.18415e9	−1.04299
$695$	−1.00678e10	−1.13759
$696$	0	0
$697$	5.44435e9	0.609020
$698$	1.10079e10	1.22521
$699$	0	0
$700$	−4.41763e8	−0.0486795
$701$	9.14932e9	1.00317	0.501586	−	0.865108i	$-0.332750\pi$
$701$	9.14932e9	1.00317	0.501586	+	0.865108i	$0.332750\pi$
$702$	0	0
$703$	−2.43233e10	−2.64046
$704$	7.93995e7	0.00857657
$705$	0	0
$706$	−3.55992e9	−0.380736
$707$	−4.79083e8	−0.0509850
$708$	0	0
$709$	2.13810e8	0.0225303	0.0112651	−	0.999937i	$-0.496414\pi$
$709$	2.13810e8	0.0225303	0.0112651	+	0.999937i	$0.496414\pi$
$710$	1.70164e10	1.78428
$711$	0	0
$712$	2.10172e9	0.218220
$713$	5.25239e9	0.542680
$714$	0	0
$715$	7.77930e8	0.0795920
$716$	5.28196e9	0.537773
$717$	0	0
$718$	−9.14508e9	−0.922045
$719$	−8.06712e9	−0.809408	−0.404704	−	0.914448i	$-0.632625\pi$
$719$	−8.06712e9	−0.809408	−0.404704	+	0.914448i	$0.632625\pi$
$720$	0	0
$721$	−4.56581e8	−0.0453674
$722$	−1.51564e10	−1.49870
$723$	0	0
$724$	2.87665e9	0.281710
$725$	3.47349e10	3.38519
$726$	0	0
$727$	1.56449e10	1.51009	0.755043	−	0.655675i	$-0.227616\pi$
$727$	1.56449e10	1.51009	0.755043	+	0.655675i	$0.227616\pi$
$728$	−1.40430e8	−0.0134897
$729$	0	0
$730$	−7.13485e9	−0.678820
$731$	−1.28718e10	−1.21879
$732$	0	0
$733$	−9.81566e9	−0.920567	−0.460283	−	0.887772i	$-0.652252\pi$
$733$	−9.81566e9	−0.920567	−0.460283	+	0.887772i	$0.652252\pi$
$734$	6.00835e9	0.560814
$735$	0	0
$736$	−6.55992e8	−0.0606494
$737$	−5.58270e8	−0.0513698
$738$	0	0
$739$	−3.29280e8	−0.0300131	−0.0150065	−	0.999887i	$-0.504777\pi$
$739$	−3.29280e8	−0.0300131	−0.0150065	+	0.999887i	$0.504777\pi$
$740$	1.37298e10	1.24552
$741$	0	0
$742$	3.22701e8	0.0289993
$743$	6.07649e9	0.543490	0.271745	−	0.962369i	$-0.412399\pi$
$743$	6.07649e9	0.543490	0.271745	+	0.962369i	$0.412399\pi$
$744$	0	0
$745$	−3.26294e10	−2.89110
$746$	1.06428e10	0.938574
$747$	0	0
$748$	−4.38999e8	−0.0383537
$749$	−1.90077e8	−0.0165289
$750$	0	0
$751$	−8.99081e9	−0.774567	−0.387283	−	0.921961i	$-0.626586\pi$
$751$	−8.99081e9	−0.774567	−0.387283	+	0.921961i	$0.626586\pi$
$752$	3.58495e9	0.307412
$753$	0	0
$754$	1.10417e10	0.938076
$755$	−2.89476e10	−2.44793
$756$	0	0
$757$	−4.08451e9	−0.342219	−0.171109	−	0.985252i	$-0.554735\pi$
$757$	−4.08451e9	−0.342219	−0.171109	+	0.985252i	$0.554735\pi$
$758$	−8.50994e9	−0.709715
$759$	0	0
$760$	1.25918e10	1.04050
$761$	−1.81552e10	−1.49333	−0.746663	−	0.665203i	$-0.768345\pi$
$761$	−1.81552e10	−1.49333	−0.746663	+	0.665203i	$0.768345\pi$
$762$	0	0
$763$	−9.49928e8	−0.0774203
$764$	2.84801e8	0.0231055
$765$	0	0
$766$	1.68140e9	0.135167
$767$	7.12518e9	0.570180
$768$	0	0
$769$	−3.86911e9	−0.306810	−0.153405	−	0.988163i	$-0.549024\pi$
$769$	−3.86911e9	−0.306810	−0.153405	+	0.988163i	$0.549024\pi$
$770$	−5.61274e7	−0.00443055
$771$	0	0
$772$	4.29003e9	0.335583
$773$	5.34479e9	0.416201	0.208100	−	0.978107i	$-0.433272\pi$
$773$	5.34479e9	0.416201	0.208100	+	0.978107i	$0.433272\pi$
$774$	0	0
$775$	3.64125e10	2.80992
$776$	−4.05311e9	−0.311367
$777$	0	0
$778$	−3.16369e9	−0.240861
$779$	−1.26946e10	−0.962142
$780$	0	0
$781$	1.38330e9	0.103905
$782$	3.62697e9	0.271219
$783$	0	0
$784$	−3.36310e9	−0.249249
$785$	−2.48355e10	−1.83244
$786$	0	0
$787$	−1.82027e10	−1.33114	−0.665570	−	0.746335i	$-0.731812\pi$
$787$	−1.82027e10	−1.33114	−0.665570	+	0.746335i	$0.731812\pi$
$788$	6.27358e9	0.456745
$789$	0	0
$790$	−6.74714e9	−0.486883
$791$	−1.14526e7	−0.000822788 0
$792$	0	0
$793$	8.98082e9	0.639529
$794$	−1.28337e9	−0.0909869
$795$	0	0
$796$	3.50943e9	0.246627
$797$	1.56933e10	1.09802	0.549009	−	0.835817i	$-0.315005\pi$
$797$	1.56933e10	1.09802	0.549009	+	0.835817i	$0.315005\pi$
$798$	0	0
$799$	−1.98211e10	−1.37472
$800$	−4.54770e9	−0.314034
$801$	0	0
$802$	−2.25029e9	−0.154038
$803$	−5.80007e8	−0.0395302
$804$	0	0
$805$	4.63720e8	0.0313307
$806$	1.15750e10	0.778662
$807$	0	0
$808$	−4.93188e9	−0.328907
$809$	−1.94092e10	−1.28880	−0.644402	−	0.764687i	$-0.722894\pi$
$809$	−1.94092e10	−1.28880	−0.644402	+	0.764687i	$0.722894\pi$
$810$	0	0
$811$	2.10932e10	1.38858	0.694288	−	0.719698i	$-0.255720\pi$
$811$	2.10932e10	1.38858	0.694288	+	0.719698i	$0.255720\pi$
$812$	−7.96659e8	−0.0522187
$813$	0	0
$814$	1.11612e9	0.0725314
$815$	−3.91752e9	−0.253489
$816$	0	0
$817$	3.00134e10	1.92547
$818$	−3.31639e9	−0.211850
$819$	0	0
$820$	7.16573e9	0.453850
$821$	2.18482e10	1.37789	0.688945	−	0.724813i	$-0.258074\pi$
$821$	2.18482e10	1.37789	0.688945	+	0.724813i	$0.258074\pi$
$822$	0	0
$823$	−4.35990e9	−0.272632	−0.136316	−	0.990665i	$-0.543526\pi$
$823$	−4.35990e9	−0.272632	−0.136316	+	0.990665i	$0.543526\pi$
$824$	−4.70024e9	−0.292668
$825$	0	0
$826$	−5.14080e8	−0.0317395
$827$	8.96887e9	0.551402	0.275701	−	0.961243i	$-0.411090\pi$
$827$	8.96887e9	0.551402	0.275701	+	0.961243i	$0.411090\pi$
$828$	0	0
$829$	1.87500e10	1.14304	0.571518	−	0.820590i	$-0.306355\pi$
$829$	1.87500e10	1.14304	0.571518	+	0.820590i	$0.306355\pi$
$830$	1.15103e10	0.698737
$831$	0	0
$832$	−1.44565e9	−0.0870224
$833$	1.85945e10	1.11462
$834$	0	0
$835$	−1.34059e9	−0.0796884
$836$	1.02362e9	0.0605920
$837$	0	0
$838$	−2.07940e10	−1.22063
$839$	−2.51063e10	−1.46763	−0.733814	−	0.679351i	$-0.762261\pi$
$839$	−2.51063e10	−1.46763	−0.733814	+	0.679351i	$0.762261\pi$
$840$	0	0
$841$	4.53898e10	2.63131
$842$	−4.62851e9	−0.267208
$843$	0	0
$844$	7.44162e9	0.426058
$845$	1.50602e10	0.858684
$846$	0	0
$847$	9.64644e8	0.0545475
$848$	3.32202e9	0.187076
$849$	0	0
$850$	2.51441e10	1.40433
$851$	−9.22129e9	−0.512907
$852$	0	0
$853$	−1.76584e10	−0.974159	−0.487079	−	0.873358i	$-0.661938\pi$
$853$	−1.76584e10	−0.974159	−0.487079	+	0.873358i	$0.661938\pi$
$854$	−6.47964e8	−0.0355999
$855$	0	0
$856$	−1.95673e9	−0.106629
$857$	2.43968e9	0.132404	0.0662019	−	0.997806i	$-0.478912\pi$
$857$	2.43968e9	0.132404	0.0662019	+	0.997806i	$0.478912\pi$
$858$	0	0
$859$	5.91397e9	0.318348	0.159174	−	0.987251i	$-0.449117\pi$
$859$	5.91397e9	0.318348	0.159174	+	0.987251i	$0.449117\pi$
$860$	−1.69416e10	−0.908261
$861$	0	0
$862$	−6.15792e8	−0.0327460
$863$	2.02665e9	0.107335	0.0536673	−	0.998559i	$-0.482909\pi$
$863$	2.02665e9	0.107335	0.0536673	+	0.998559i	$0.482909\pi$
$864$	0	0
$865$	1.14146e10	0.599661
$866$	2.20016e9	0.115118
$867$	0	0
$868$	−8.35134e8	−0.0433448
$869$	−5.48489e8	−0.0283530
$870$	0	0
$871$	1.01646e10	0.521225
$872$	−9.77896e9	−0.499442
$873$	0	0
$874$	−8.45703e9	−0.428477
$875$	1.40510e9	0.0709054
$876$	0	0
$877$	−1.06789e10	−0.534599	−0.267299	−	0.963614i	$-0.586131\pi$
$877$	−1.06789e10	−0.534599	−0.267299	+	0.963614i	$0.586131\pi$
$878$	−1.21840e10	−0.607516
$879$	0	0
$880$	−5.77800e8	−0.0285817
$881$	4.67496e9	0.230336	0.115168	−	0.993346i	$-0.463259\pi$
$881$	4.67496e9	0.230336	0.115168	+	0.993346i	$0.463259\pi$
$882$	0	0
$883$	−2.97465e10	−1.45403	−0.727015	−	0.686622i	$-0.759093\pi$
$883$	−2.97465e10	−1.45403	−0.727015	+	0.686622i	$0.759093\pi$
$884$	7.99297e9	0.389157
$885$	0	0
$886$	1.66446e10	0.803997
$887$	−1.45442e10	−0.699774	−0.349887	−	0.936792i	$-0.613780\pi$
$887$	−1.45442e10	−0.699774	−0.349887	+	0.936792i	$0.613780\pi$
$888$	0	0
$889$	1.95184e9	0.0931725
$890$	−1.52945e10	−0.727225
$891$	0	0
$892$	−8.45753e9	−0.398994
$893$	4.62171e10	2.17181
$894$	0	0
$895$	−3.84374e10	−1.79215
$896$	1.04303e8	0.00484417
$897$	0	0
$898$	1.51871e10	0.699852
$899$	6.56649e10	3.01422
$900$	0	0
$901$	−1.83674e10	−0.836587
$902$	5.82518e8	0.0264293
$903$	0	0
$904$	−1.17898e8	−0.00530785
$905$	−2.09337e10	−0.938808
$906$	0	0
$907$	3.57735e10	1.59197	0.795987	−	0.605314i	$-0.206952\pi$
$907$	3.57735e10	1.59197	0.795987	+	0.605314i	$0.206952\pi$
$908$	−3.61352e9	−0.160188
$909$	0	0
$910$	1.02193e9	0.0449547
$911$	−2.65125e9	−0.116182	−0.0580908	−	0.998311i	$-0.518501\pi$
$911$	−2.65125e9	−0.116182	−0.0580908	+	0.998311i	$0.518501\pi$
$912$	0	0
$913$	9.35697e8	0.0406900
$914$	−5.48851e9	−0.237762
$915$	0	0
$916$	1.13839e10	0.489393
$917$	1.05826e9	0.0453209
$918$	0	0
$919$	−2.21012e9	−0.0939317	−0.0469659	−	0.998896i	$-0.514955\pi$
$919$	−2.21012e9	−0.0939317	−0.0469659	+	0.998896i	$0.514955\pi$
$920$	4.77373e9	0.202116
$921$	0	0
$922$	1.21677e10	0.511271
$923$	−2.51861e10	−1.05428
$924$	0	0
$925$	−6.39271e10	−2.65576
$926$	4.00229e9	0.165642
$927$	0	0
$928$	−8.20115e9	−0.336866
$929$	1.65364e10	0.676684	0.338342	−	0.941023i	$-0.390134\pi$
$929$	1.65364e10	0.676684	0.338342	+	0.941023i	$0.390134\pi$
$930$	0	0
$931$	−4.33570e10	−1.76090
$932$	6.46383e9	0.261538
$933$	0	0
$934$	−3.22667e10	−1.29581
$935$	3.19465e9	0.127815
$936$	0	0
$937$	1.52847e10	0.606973	0.303487	−	0.952836i	$-0.401849\pi$
$937$	1.52847e10	0.606973	0.303487	+	0.952836i	$0.401849\pi$
$938$	−7.33371e8	−0.0290144
$939$	0	0
$940$	−2.60881e10	−1.02446
$941$	1.62545e10	0.635929	0.317965	−	0.948103i	$-0.397001\pi$
$941$	1.62545e10	0.635929	0.317965	+	0.948103i	$0.397001\pi$
$942$	0	0
$943$	−4.81271e9	−0.186895
$944$	−5.29216e9	−0.204753
$945$	0	0
$946$	−1.37722e9	−0.0528914
$947$	2.77329e10	1.06113	0.530567	−	0.847643i	$-0.321979\pi$
$947$	2.77329e10	1.06113	0.530567	+	0.847643i	$0.321979\pi$
$948$	0	0
$949$	1.05603e10	0.401094
$950$	−5.86288e10	−2.21860
$951$	0	0
$952$	−5.76691e8	−0.0216627
$953$	−3.88172e10	−1.45278	−0.726388	−	0.687285i	$-0.758802\pi$
$953$	−3.88172e10	−1.45278	−0.726388	+	0.687285i	$0.758802\pi$
$954$	0	0
$955$	−2.07253e9	−0.0769998
$956$	−7.77128e9	−0.287667
$957$	0	0
$958$	−2.08210e10	−0.765106
$959$	−9.06701e8	−0.0331970
$960$	0	0
$961$	4.13236e10	1.50199
$962$	−2.03215e10	−0.735942
$963$	0	0
$964$	−1.46079e10	−0.525191
$965$	−3.12191e10	−1.11834
$966$	0	0
$967$	1.27521e10	0.453513	0.226756	−	0.973952i	$-0.427188\pi$
$967$	1.27521e10	0.453513	0.226756	+	0.973952i	$0.427188\pi$
$968$	9.93046e9	0.351889
$969$	0	0
$970$	2.94950e10	1.03764
$971$	−4.92971e10	−1.72804	−0.864021	−	0.503456i	$-0.832062\pi$
$971$	−4.92971e10	−1.72804	−0.864021	+	0.503456i	$0.832062\pi$
$972$	0	0
$973$	−1.07513e9	−0.0374168
$974$	−3.48413e10	−1.20820
$975$	0	0
$976$	−6.67042e9	−0.229657
$977$	−1.45743e10	−0.499984	−0.249992	−	0.968248i	$-0.580428\pi$
$977$	−1.45743e10	−0.499984	−0.249992	+	0.968248i	$0.580428\pi$
$978$	0	0
$979$	−1.24332e9	−0.0423490
$980$	2.44737e10	0.830631
$981$	0	0
$982$	3.33324e9	0.112325
$983$	3.76159e10	1.26309	0.631546	−	0.775339i	$-0.282421\pi$
$983$	3.76159e10	1.26309	0.631546	+	0.775339i	$0.282421\pi$
$984$	0	0
$985$	−4.56536e10	−1.52212
$986$	4.53440e10	1.50644
$987$	0	0
$988$	−1.86373e10	−0.614798
$989$	1.13785e10	0.374022
$990$	0	0
$991$	3.09606e10	1.01054	0.505268	−	0.862962i	$-0.331394\pi$
$991$	3.09606e10	1.01054	0.505268	+	0.862962i	$0.331394\pi$
$992$	−8.59723e9	−0.279620
$993$	0	0
$994$	1.81717e9	0.0586872
$995$	−2.55385e10	−0.821893
$996$	0	0
$997$	−7.82917e9	−0.250197	−0.125099	−	0.992144i	$-0.539925\pi$
$997$	−7.82917e9	−0.250197	−0.125099	+	0.992144i	$0.539925\pi$
$998$	2.67416e10	0.851589
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.a.g.1.1	✓	2
3.2	odd	2		54.8.a.h.1.2	yes	2
4.3	odd	2		432.8.a.p.1.1		2
9.2	odd	6		162.8.c.m.109.1		4
9.4	even	3		162.8.c.p.55.2		4
9.5	odd	6		162.8.c.m.55.1		4
9.7	even	3		162.8.c.p.109.2		4
12.11	even	2		432.8.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.a.g.1.1	✓	2	1.1	even	1	trivial
54.8.a.h.1.2	yes	2	3.2	odd	2
162.8.c.m.55.1		4	9.5	odd	6
162.8.c.m.109.1		4	9.2	odd	6
162.8.c.p.55.2		4	9.4	even	3
162.8.c.p.109.2		4	9.7	even	3
432.8.a.k.1.2		2	12.11	even	2
432.8.a.p.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +64.0000 q^{4} -465.736 q^{5} -49.7356 q^{7} -512.000 q^{8} +O(q^{10})\)	\(q-8.00000 q^{2} +64.0000 q^{4} -465.736 q^{5} -49.7356 q^{7} -512.000 q^{8} +3725.89 q^{10} +302.885 q^{11} -5514.71 q^{13} +397.885 q^{14} +4096.00 q^{16} -22646.7 q^{17} +52805.5 q^{19} -29807.1 q^{20} -2423.08 q^{22} +20019.3 q^{23} +138785. q^{25} +44117.7 q^{26} -3183.08 q^{28} +250279. q^{29} +262367. q^{31} -32768.0 q^{32} +181174. q^{34} +23163.7 q^{35} -460621. q^{37} -422444. q^{38} +238457. q^{40} -240404. q^{41} +568376. q^{43} +19384.6 q^{44} -160154. q^{46} +875232. q^{47} -821069. q^{49} -1.11028e6 q^{50} -352942. q^{52} +811041. q^{53} -141064. q^{55} +25464.6 q^{56} -2.00223e6 q^{58} -1.29203e6 q^{59} -1.62852e6 q^{61} -2.09893e6 q^{62} +262144. q^{64} +2.56840e6 q^{65} -1.84317e6 q^{67} -1.44939e6 q^{68} -185309. q^{70} +4.56707e6 q^{71} -1.91494e6 q^{73} +3.68496e6 q^{74} +3.37955e6 q^{76} -15064.2 q^{77} -1.81088e6 q^{79} -1.90765e6 q^{80} +1.92323e6 q^{82} +3.08928e6 q^{83} +1.05474e7 q^{85} -4.54701e6 q^{86} -155077. q^{88} -4.10492e6 q^{89} +274278. q^{91} +1.28123e6 q^{92} -7.00186e6 q^{94} -2.45934e7 q^{95} +7.91623e6 q^{97} +6.56855e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} + 128 q^{4} + 48 q^{5} + 880 q^{7} - 1024 q^{8}+O(q^{10}) \) 2 * q - 16 * q^2 + 128 * q^4 + 48 * q^5 + 880 * q^7 - 1024 * q^8	\( 2 q - 16 q^{2} + 128 q^{4} + 48 q^{5} + 880 q^{7} - 1024 q^{8} - 384 q^{10} - 7230 q^{11} + 8560 q^{13} - 7040 q^{14} + 8192 q^{16} - 25704 q^{17} + 37048 q^{19} + 3072 q^{20} + 57840 q^{22} + 59628 q^{23} + 324584 q^{25} - 68480 q^{26} + 56320 q^{28} + 275280 q^{29} + 245584 q^{31} - 65536 q^{32} + 205632 q^{34} + 500802 q^{35} - 71060 q^{37} - 296384 q^{38} - 24576 q^{40} - 494520 q^{41} + 825280 q^{43} - 462720 q^{44} - 477024 q^{46} + 927708 q^{47} - 780204 q^{49} - 2596672 q^{50} + 547840 q^{52} + 1382112 q^{53} - 4010976 q^{55} - 450560 q^{56} - 2202240 q^{58} - 1588920 q^{59} - 3021968 q^{61} - 1964672 q^{62} + 524288 q^{64} + 9799080 q^{65} - 1882160 q^{67} - 1645056 q^{68} - 4006416 q^{70} + 3394440 q^{71} + 895090 q^{73} + 568480 q^{74} + 2371072 q^{76} - 7018656 q^{77} - 369920 q^{79} + 196608 q^{80} + 3956160 q^{82} + 9352050 q^{83} + 8976744 q^{85} - 6602240 q^{86} + 3701760 q^{88} + 912960 q^{89} + 13360040 q^{91} + 3816192 q^{92} - 7421664 q^{94} - 32688588 q^{95} + 1359790 q^{97} + 6241632 q^{98}+O(q^{100}) \) 2 * q - 16 * q^2 + 128 * q^4 + 48 * q^5 + 880 * q^7 - 1024 * q^8 - 384 * q^10 - 7230 * q^11 + 8560 * q^13 - 7040 * q^14 + 8192 * q^16 - 25704 * q^17 + 37048 * q^19 + 3072 * q^20 + 57840 * q^22 + 59628 * q^23 + 324584 * q^25 - 68480 * q^26 + 56320 * q^28 + 275280 * q^29 + 245584 * q^31 - 65536 * q^32 + 205632 * q^34 + 500802 * q^35 - 71060 * q^37 - 296384 * q^38 - 24576 * q^40 - 494520 * q^41 + 825280 * q^43 - 462720 * q^44 - 477024 * q^46 + 927708 * q^47 - 780204 * q^49 - 2596672 * q^50 + 547840 * q^52 + 1382112 * q^53 - 4010976 * q^55 - 450560 * q^56 - 2202240 * q^58 - 1588920 * q^59 - 3021968 * q^61 - 1964672 * q^62 + 524288 * q^64 + 9799080 * q^65 - 1882160 * q^67 - 1645056 * q^68 - 4006416 * q^70 + 3394440 * q^71 + 895090 * q^73 + 568480 * q^74 + 2371072 * q^76 - 7018656 * q^77 - 369920 * q^79 + 196608 * q^80 + 3956160 * q^82 + 9352050 * q^83 + 8976744 * q^85 - 6602240 * q^86 + 3701760 * q^88 + 912960 * q^89 + 13360040 * q^91 + 3816192 * q^92 - 7421664 * q^94 - 32688588 * q^95 + 1359790 * q^97 + 6241632 * q^98

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