LMFDB - Embedded newform 378.10.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,10,Mod(1,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("378.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	378.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:	$194.683546070$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 22615x^{2} - 631488x + 20384688 $ x^4 - x^3 - 22615x^2 - 631488x + 20384688
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{7} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$19.2354$ of defining polynomial
Character	$\chi$	$=$	378.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +256.000 q^{4} -1105.79 q^{5} -2401.00 q^{7} +4096.00 q^{8} +O(q^{10})$	\(q+16.0000 q^{2} +256.000 q^{4} -1105.79 q^{5} -2401.00 q^{7} +4096.00 q^{8} -17692.7 q^{10} +58260.6 q^{11} +29252.8 q^{13} -38416.0 q^{14} +65536.0 q^{16} -277497. q^{17} -284079. q^{19} -283083. q^{20} +932169. q^{22} +1.24170e6 q^{23} -730351. q^{25} +468044. q^{26} -614656. q^{28} -7.46379e6 q^{29} +4.89151e6 q^{31} +1.04858e6 q^{32} -4.43995e6 q^{34} +2.65500e6 q^{35} +1.45435e7 q^{37} -4.54527e6 q^{38} -4.52932e6 q^{40} -2.07434e7 q^{41} -1.67373e7 q^{43} +1.49147e7 q^{44} +1.98672e7 q^{46} +4.08368e7 q^{47} +5.76480e6 q^{49} -1.16856e7 q^{50} +7.48870e6 q^{52} +8.77551e7 q^{53} -6.44240e7 q^{55} -9.83450e6 q^{56} -1.19421e8 q^{58} +1.46938e8 q^{59} +1.95719e8 q^{61} +7.82641e7 q^{62} +1.67772e7 q^{64} -3.23474e7 q^{65} -3.14844e8 q^{67} -7.10392e7 q^{68} +4.24801e7 q^{70} -3.34578e8 q^{71} -6.07756e7 q^{73} +2.32696e8 q^{74} -7.27243e7 q^{76} -1.39884e8 q^{77} -2.00915e8 q^{79} -7.24691e7 q^{80} -3.31894e8 q^{82} -4.56308e8 q^{83} +3.06854e8 q^{85} -2.67796e8 q^{86} +2.38635e8 q^{88} +8.73425e8 q^{89} -7.02359e7 q^{91} +3.17875e8 q^{92} +6.53388e8 q^{94} +3.14132e8 q^{95} +7.45228e7 q^{97} +9.22368e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 1024 q^{4} - 1649 q^{5} - 9604 q^{7} + 16384 q^{8}+O(q^{10}) $ 4 * q + 64 * q^2 + 1024 * q^4 - 1649 * q^5 - 9604 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} - 1649 q^{5} - 9604 q^{7} + 16384 q^{8} - 26384 q^{10} + 10544 q^{11} - 108585 q^{13} - 153664 q^{14} + 262144 q^{16} + 529388 q^{17} + 467258 q^{19} - 422144 q^{20} + 168704 q^{22} - 1185163 q^{23} + 1267583 q^{25} - 1737360 q^{26} - 2458624 q^{28} - 1945301 q^{29} + 11130777 q^{31} + 4194304 q^{32} + 8470208 q^{34} + 3959249 q^{35} + 6222809 q^{37} + 7476128 q^{38} - 6754304 q^{40} - 35545545 q^{41} - 7202206 q^{43} + 2699264 q^{44} - 18962608 q^{46} + 20761503 q^{47} + 23059204 q^{49} + 20281328 q^{50} - 27797760 q^{52} - 98635821 q^{53} - 235417840 q^{55} - 39337984 q^{56} - 31124816 q^{58} + 33235282 q^{59} + 105743430 q^{61} + 178092432 q^{62} + 67108864 q^{64} + 362384190 q^{65} - 155997695 q^{67} + 135523328 q^{68} + 63347984 q^{70} - 154553551 q^{71} - 696521780 q^{73} + 99564944 q^{74} + 119618048 q^{76} - 25316144 q^{77} - 477454197 q^{79} - 108068864 q^{80} - 568728720 q^{82} - 835952377 q^{83} - 817473505 q^{85} - 115235296 q^{86} + 43188224 q^{88} + 614491047 q^{89} + 260712585 q^{91} - 303401728 q^{92} + 332184048 q^{94} - 1899413188 q^{95} - 1381829600 q^{97} + 368947264 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 - 1649 * q^5 - 9604 * q^7 + 16384 * q^8 - 26384 * q^10 + 10544 * q^11 - 108585 * q^13 - 153664 * q^14 + 262144 * q^16 + 529388 * q^17 + 467258 * q^19 - 422144 * q^20 + 168704 * q^22 - 1185163 * q^23 + 1267583 * q^25 - 1737360 * q^26 - 2458624 * q^28 - 1945301 * q^29 + 11130777 * q^31 + 4194304 * q^32 + 8470208 * q^34 + 3959249 * q^35 + 6222809 * q^37 + 7476128 * q^38 - 6754304 * q^40 - 35545545 * q^41 - 7202206 * q^43 + 2699264 * q^44 - 18962608 * q^46 + 20761503 * q^47 + 23059204 * q^49 + 20281328 * q^50 - 27797760 * q^52 - 98635821 * q^53 - 235417840 * q^55 - 39337984 * q^56 - 31124816 * q^58 + 33235282 * q^59 + 105743430 * q^61 + 178092432 * q^62 + 67108864 * q^64 + 362384190 * q^65 - 155997695 * q^67 + 135523328 * q^68 + 63347984 * q^70 - 154553551 * q^71 - 696521780 * q^73 + 99564944 * q^74 + 119618048 * q^76 - 25316144 * q^77 - 477454197 * q^79 - 108068864 * q^80 - 568728720 * q^82 - 835952377 * q^83 - 817473505 * q^85 - 115235296 * q^86 + 43188224 * q^88 + 614491047 * q^89 + 260712585 * q^91 - 303401728 * q^92 + 332184048 * q^94 - 1899413188 * q^95 - 1381829600 * q^97 + 368947264 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	0	0
$3$	0	0
$4$	256.000	0.500000
$5$	−1105.79	−0.791240	−0.395620	−	0.918414i	$-0.629470\pi$
$5$	−1105.79	−0.791240	−0.395620	+	0.918414i	$0.629470\pi$
$6$	0	0
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	4096.00	0.353553
$9$	0	0
$10$	−17692.7	−0.559491
$11$	58260.6	1.19980	0.599898	−	0.800076i	$-0.295208\pi$
$11$	58260.6	1.19980	0.599898	+	0.800076i	$0.295208\pi$
$12$	0	0
$13$	29252.8	0.284068	0.142034	−	0.989862i	$-0.454636\pi$
$13$	29252.8	0.284068	0.142034	+	0.989862i	$0.454636\pi$
$14$	−38416.0	−0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	−277497.	−0.805820	−0.402910	−	0.915240i	$-0.632001\pi$
$17$	−277497.	−0.805820	−0.402910	+	0.915240i	$0.632001\pi$
$18$	0	0
$19$	−284079.	−0.500090	−0.250045	−	0.968234i	$-0.580445\pi$
$19$	−284079.	−0.500090	−0.250045	+	0.968234i	$0.580445\pi$
$20$	−283083.	−0.395620
$21$	0	0
$22$	932169.	0.848384
$23$	1.24170e6	0.925212	0.462606	−	0.886564i	$-0.346914\pi$
$23$	1.24170e6	0.925212	0.462606	+	0.886564i	$0.346914\pi$
$24$	0	0
$25$	−730351.	−0.373940
$26$	468044.	0.200866
$27$	0	0
$28$	−614656.	−0.188982
$29$	−7.46379e6	−1.95961	−0.979803	−	0.199967i	$-0.935916\pi$
$29$	−7.46379e6	−1.95961	−0.979803	+	0.199967i	$0.935916\pi$
$30$	0	0
$31$	4.89151e6	0.951295	0.475647	−	0.879636i	$-0.342214\pi$
$31$	4.89151e6	0.951295	0.475647	+	0.879636i	$0.342214\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	−4.43995e6	−0.569801
$35$	2.65500e6	0.299061
$36$	0	0
$37$	1.45435e7	1.27574	0.637869	−	0.770145i	$-0.279816\pi$
$37$	1.45435e7	1.27574	0.637869	+	0.770145i	$0.279816\pi$
$38$	−4.54527e6	−0.353617
$39$	0	0
$40$	−4.52932e6	−0.279745
$41$	−2.07434e7	−1.14644	−0.573222	−	0.819400i	$-0.694307\pi$
$41$	−2.07434e7	−1.14644	−0.573222	+	0.819400i	$0.694307\pi$
$42$	0	0
$43$	−1.67373e7	−0.746581	−0.373290	−	0.927715i	$-0.621770\pi$
$43$	−1.67373e7	−0.746581	−0.373290	+	0.927715i	$0.621770\pi$
$44$	1.49147e7	0.599898
$45$	0	0
$46$	1.98672e7	0.654224
$47$	4.08368e7	1.22071	0.610353	−	0.792130i	$-0.291028\pi$
$47$	4.08368e7	1.22071	0.610353	+	0.792130i	$0.291028\pi$
$48$	0	0
$49$	5.76480e6	0.142857
$50$	−1.16856e7	−0.264415
$51$	0	0
$52$	7.48870e6	0.142034
$53$	8.77551e7	1.52767	0.763837	−	0.645409i	$-0.223313\pi$
$53$	8.77551e7	1.52767	0.763837	+	0.645409i	$0.223313\pi$
$54$	0	0
$55$	−6.44240e7	−0.949327
$56$	−9.83450e6	−0.133631
$57$	0	0
$58$	−1.19421e8	−1.38565
$59$	1.46938e8	1.57870	0.789351	−	0.613942i	$-0.210417\pi$
$59$	1.46938e8	1.57870	0.789351	+	0.613942i	$0.210417\pi$
$60$	0	0
$61$	1.95719e8	1.80988	0.904940	−	0.425540i	$-0.139916\pi$
$61$	1.95719e8	1.80988	0.904940	+	0.425540i	$0.139916\pi$
$62$	7.82641e7	0.672667
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−3.23474e7	−0.224766
$66$	0	0
$67$	−3.14844e8	−1.90880	−0.954398	−	0.298539i	$-0.903501\pi$
$67$	−3.14844e8	−1.90880	−0.954398	+	0.298539i	$0.903501\pi$
$68$	−7.10392e7	−0.402910
$69$	0	0
$70$	4.24801e7	0.211468
$71$	−3.34578e8	−1.56255	−0.781276	−	0.624186i	$-0.785431\pi$
$71$	−3.34578e8	−1.56255	−0.781276	+	0.624186i	$0.785431\pi$
$72$	0	0
$73$	−6.07756e7	−0.250482	−0.125241	−	0.992126i	$-0.539970\pi$
$73$	−6.07756e7	−0.250482	−0.125241	+	0.992126i	$0.539970\pi$
$74$	2.32696e8	0.902082
$75$	0	0
$76$	−7.27243e7	−0.250045
$77$	−1.39884e8	−0.453481
$78$	0	0
$79$	−2.00915e8	−0.580349	−0.290175	−	0.956974i	$-0.593713\pi$
$79$	−2.00915e8	−0.580349	−0.290175	+	0.956974i	$0.593713\pi$
$80$	−7.24691e7	−0.197810
$81$	0	0
$82$	−3.31894e8	−0.810658
$83$	−4.56308e8	−1.05537	−0.527687	−	0.849439i	$-0.676941\pi$
$83$	−4.56308e8	−1.05537	−0.527687	+	0.849439i	$0.676941\pi$
$84$	0	0
$85$	3.06854e8	0.637597
$86$	−2.67796e8	−0.527912
$87$	0	0
$88$	2.38635e8	0.424192
$89$	8.73425e8	1.47561	0.737804	−	0.675015i	$-0.235863\pi$
$89$	8.73425e8	1.47561	0.737804	+	0.675015i	$0.235863\pi$
$90$	0	0
$91$	−7.02359e7	−0.107367
$92$	3.17875e8	0.462606
$93$	0	0
$94$	6.53388e8	0.863169
$95$	3.14132e8	0.395691
$96$	0	0
$97$	7.45228e7	0.0854705	0.0427353	−	0.999086i	$-0.486393\pi$
$97$	7.45228e7	0.0854705	0.0427353	+	0.999086i	$0.486393\pi$
$98$	9.22368e7	0.101015
$99$	0	0
$100$	−1.86970e8	−0.186970
$101$	−1.82066e9	−1.74093	−0.870466	−	0.492228i	$-0.836182\pi$
$101$	−1.82066e9	−1.74093	−0.870466	+	0.492228i	$0.836182\pi$
$102$	0	0
$103$	−1.64597e9	−1.44096	−0.720482	−	0.693473i	$-0.756080\pi$
$103$	−1.64597e9	−1.44096	−0.720482	+	0.693473i	$0.756080\pi$
$104$	1.19819e8	0.100433
$105$	0	0
$106$	1.40408e9	1.08023
$107$	−1.21875e9	−0.898850	−0.449425	−	0.893318i	$-0.648371\pi$
$107$	−1.21875e9	−0.898850	−0.449425	+	0.893318i	$0.648371\pi$
$108$	0	0
$109$	−1.47590e9	−1.00147	−0.500733	−	0.865602i	$-0.666936\pi$
$109$	−1.47590e9	−1.00147	−0.500733	+	0.865602i	$0.666936\pi$
$110$	−1.03078e9	−0.671276
$111$	0	0
$112$	−1.57352e8	−0.0944911
$113$	−2.28338e9	−1.31742	−0.658711	−	0.752396i	$-0.728898\pi$
$113$	−2.28338e9	−1.31742	−0.658711	+	0.752396i	$0.728898\pi$
$114$	0	0
$115$	−1.37306e9	−0.732065
$116$	−1.91073e9	−0.979803
$117$	0	0
$118$	2.35101e9	1.11631
$119$	6.66270e8	0.304571
$120$	0	0
$121$	1.03635e9	0.439513
$122$	3.13151e9	1.27978
$123$	0	0
$124$	1.25223e9	0.475647
$125$	2.96736e9	1.08712
$126$	0	0
$127$	−4.67797e9	−1.59566	−0.797830	−	0.602883i	$-0.794019\pi$
$127$	−4.67797e9	−1.59566	−0.797830	+	0.602883i	$0.794019\pi$
$128$	2.68435e8	0.0883883
$129$	0	0
$130$	−5.17559e8	−0.158933
$131$	−2.98420e9	−0.885334	−0.442667	−	0.896686i	$-0.645968\pi$
$131$	−2.98420e9	−0.885334	−0.442667	+	0.896686i	$0.645968\pi$
$132$	0	0
$133$	6.82074e8	0.189016
$134$	−5.03751e9	−1.34972
$135$	0	0
$136$	−1.13663e9	−0.284900
$137$	−5.00908e9	−1.21483	−0.607415	−	0.794385i	$-0.707793\pi$
$137$	−5.00908e9	−1.21483	−0.607415	+	0.794385i	$0.707793\pi$
$138$	0	0
$139$	2.80777e9	0.637961	0.318981	−	0.947761i	$-0.396660\pi$
$139$	2.80777e9	0.637961	0.318981	+	0.947761i	$0.396660\pi$
$140$	6.79681e8	0.149530
$141$	0	0
$142$	−5.35324e9	−1.10489
$143$	1.70428e9	0.340823
$144$	0	0
$145$	8.25340e9	1.55052
$146$	−9.72410e8	−0.177118
$147$	0	0
$148$	3.72314e9	0.637869
$149$	−5.19067e9	−0.862750	−0.431375	−	0.902173i	$-0.641971\pi$
$149$	−5.19067e9	−0.862750	−0.431375	+	0.902173i	$0.641971\pi$
$150$	0	0
$151$	1.00868e10	1.57891	0.789455	−	0.613809i	$-0.210363\pi$
$151$	1.00868e10	1.57891	0.789455	+	0.613809i	$0.210363\pi$
$152$	−1.16359e9	−0.176808
$153$	0	0
$154$	−2.23814e9	−0.320659
$155$	−5.40899e9	−0.752702
$156$	0	0
$157$	−3.48137e9	−0.457300	−0.228650	−	0.973509i	$-0.573431\pi$
$157$	−3.48137e9	−0.457300	−0.228650	+	0.973509i	$0.573431\pi$
$158$	−3.21463e9	−0.410369
$159$	0	0
$160$	−1.15951e9	−0.139873
$161$	−2.98132e9	−0.349697
$162$	0	0
$163$	−1.30096e10	−1.44351	−0.721757	−	0.692147i	$-0.756665\pi$
$163$	−1.30096e10	−1.44351	−0.721757	+	0.692147i	$0.756665\pi$
$164$	−5.31031e9	−0.573222
$165$	0	0
$166$	−7.30092e9	−0.746262
$167$	1.43413e10	1.42681	0.713404	−	0.700753i	$-0.247152\pi$
$167$	1.43413e10	1.42681	0.713404	+	0.700753i	$0.247152\pi$
$168$	0	0
$169$	−9.74878e9	−0.919306
$170$	4.90966e9	0.450849
$171$	0	0
$172$	−4.28474e9	−0.373290
$173$	1.14338e10	0.970472	0.485236	−	0.874383i	$-0.338734\pi$
$173$	1.14338e10	0.970472	0.485236	+	0.874383i	$0.338734\pi$
$174$	0	0
$175$	1.75357e9	0.141336
$176$	3.81817e9	0.299949
$177$	0	0
$178$	1.39748e10	1.04341
$179$	−6.67757e9	−0.486161	−0.243080	−	0.970006i	$-0.578158\pi$
$179$	−6.67757e9	−0.486161	−0.243080	+	0.970006i	$0.578158\pi$
$180$	0	0
$181$	−6.54148e9	−0.453026	−0.226513	−	0.974008i	$-0.572733\pi$
$181$	−6.54148e9	−0.453026	−0.226513	+	0.974008i	$0.572733\pi$
$182$	−1.12377e9	−0.0759203
$183$	0	0
$184$	5.08600e9	0.327112
$185$	−1.60821e10	−1.00941
$186$	0	0
$187$	−1.61671e10	−0.966820
$188$	1.04542e10	0.610353
$189$	0	0
$190$	5.02611e9	0.279796
$191$	6.68484e9	0.363447	0.181723	−	0.983350i	$-0.441832\pi$
$191$	6.68484e9	0.363447	0.181723	+	0.983350i	$0.441832\pi$
$192$	0	0
$193$	9.21052e9	0.477833	0.238917	−	0.971040i	$-0.423208\pi$
$193$	9.21052e9	0.477833	0.238917	+	0.971040i	$0.423208\pi$
$194$	1.19236e9	0.0604368
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	1.21568e9	0.0575069	0.0287535	−	0.999587i	$-0.490846\pi$
$197$	1.21568e9	0.0575069	0.0287535	+	0.999587i	$0.490846\pi$
$198$	0	0
$199$	−2.68467e10	−1.21354	−0.606768	−	0.794879i	$-0.707534\pi$
$199$	−2.68467e10	−1.21354	−0.606768	+	0.794879i	$0.707534\pi$
$200$	−2.99152e9	−0.132208
$201$	0	0
$202$	−2.91305e10	−1.23102
$203$	1.79206e10	0.740661
$204$	0	0
$205$	2.29379e10	0.907111
$206$	−2.63355e10	−1.01892
$207$	0	0
$208$	1.91711e9	0.0710169
$209$	−1.65506e10	−0.600006
$210$	0	0
$211$	−4.56558e10	−1.58571	−0.792857	−	0.609408i	$-0.791407\pi$
$211$	−4.56558e10	−1.58571	−0.792857	+	0.609408i	$0.791407\pi$
$212$	2.24653e10	0.763837
$213$	0	0
$214$	−1.95000e10	−0.635583
$215$	1.85079e10	0.590724
$216$	0	0
$217$	−1.17445e10	−0.359556
$218$	−2.36143e10	−0.708144
$219$	0	0
$220$	−1.64926e10	−0.474663
$221$	−8.11755e9	−0.228907
$222$	0	0
$223$	2.97386e10	0.805284	0.402642	−	0.915357i	$-0.368092\pi$
$223$	2.97386e10	0.805284	0.402642	+	0.915357i	$0.368092\pi$
$224$	−2.51763e9	−0.0668153
$225$	0	0
$226$	−3.65341e10	−0.931558
$227$	−4.05356e10	−1.01326	−0.506629	−	0.862164i	$-0.669109\pi$
$227$	−4.05356e10	−1.01326	−0.506629	+	0.862164i	$0.669109\pi$
$228$	0	0
$229$	−6.16278e10	−1.48087	−0.740435	−	0.672128i	$-0.765381\pi$
$229$	−6.16278e10	−1.48087	−0.740435	+	0.672128i	$0.765381\pi$
$230$	−2.19690e10	−0.517648
$231$	0	0
$232$	−3.05717e10	−0.692825
$233$	1.63334e10	0.363057	0.181528	−	0.983386i	$-0.441896\pi$
$233$	1.63334e10	0.363057	0.181528	+	0.983386i	$0.441896\pi$
$234$	0	0
$235$	−4.51569e10	−0.965871
$236$	3.76161e10	0.789351
$237$	0	0
$238$	1.06603e10	0.215364
$239$	−5.16156e10	−1.02327	−0.511635	−	0.859203i	$-0.670960\pi$
$239$	−5.16156e10	−1.02327	−0.511635	+	0.859203i	$0.670960\pi$
$240$	0	0
$241$	−1.46221e10	−0.279211	−0.139606	−	0.990207i	$-0.544584\pi$
$241$	−1.46221e10	−0.279211	−0.139606	+	0.990207i	$0.544584\pi$
$242$	1.65816e10	0.310782
$243$	0	0
$244$	5.01042e10	0.904940
$245$	−6.37467e9	−0.113034
$246$	0	0
$247$	−8.31010e9	−0.142059
$248$	2.00356e10	0.336334
$249$	0	0
$250$	4.74778e10	0.768707
$251$	3.29015e10	0.523219	0.261610	−	0.965174i	$-0.415747\pi$
$251$	3.29015e10	0.523219	0.261610	+	0.965174i	$0.415747\pi$
$252$	0	0
$253$	7.23422e10	1.11007
$254$	−7.48474e10	−1.12830
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	5.56154e9	0.0795236	0.0397618	−	0.999209i	$-0.487340\pi$
$257$	5.56154e9	0.0795236	0.0397618	+	0.999209i	$0.487340\pi$
$258$	0	0
$259$	−3.49189e10	−0.482183
$260$	−8.28094e9	−0.112383
$261$	0	0
$262$	−4.77472e10	−0.626025
$263$	7.92647e9	0.102160	0.0510798	−	0.998695i	$-0.483734\pi$
$263$	7.92647e9	0.102160	0.0510798	+	0.998695i	$0.483734\pi$
$264$	0	0
$265$	−9.70388e10	−1.20876
$266$	1.09132e10	0.133655
$267$	0	0
$268$	−8.06002e10	−0.954398
$269$	8.25299e10	0.961006	0.480503	−	0.876993i	$-0.340454\pi$
$269$	8.25299e10	0.961006	0.480503	+	0.876993i	$0.340454\pi$
$270$	0	0
$271$	−1.18435e11	−1.33389	−0.666944	−	0.745108i	$-0.732398\pi$
$271$	−1.18435e11	−1.33389	−0.666944	+	0.745108i	$0.732398\pi$
$272$	−1.81860e10	−0.201455
$273$	0	0
$274$	−8.01452e10	−0.859014
$275$	−4.25507e10	−0.448652
$276$	0	0
$277$	7.10126e10	0.724730	0.362365	−	0.932036i	$-0.381969\pi$
$277$	7.10126e10	0.724730	0.362365	+	0.932036i	$0.381969\pi$
$278$	4.49243e10	0.451107
$279$	0	0
$280$	1.08749e10	0.105734
$281$	1.92181e11	1.83879	0.919394	−	0.393339i	$-0.128680\pi$
$281$	1.92181e11	1.83879	0.919394	+	0.393339i	$0.128680\pi$
$282$	0	0
$283$	1.31859e10	0.122199	0.0610997	−	0.998132i	$-0.480539\pi$
$283$	1.31859e10	0.122199	0.0610997	+	0.998132i	$0.480539\pi$
$284$	−8.56519e10	−0.781276
$285$	0	0
$286$	2.72685e10	0.240999
$287$	4.98049e10	0.433315
$288$	0	0
$289$	−4.15834e10	−0.350655
$290$	1.32054e11	1.09638
$291$	0	0
$292$	−1.55586e10	−0.125241
$293$	6.63145e10	0.525659	0.262830	−	0.964842i	$-0.415344\pi$
$293$	6.63145e10	0.525659	0.262830	+	0.964842i	$0.415344\pi$
$294$	0	0
$295$	−1.62483e11	−1.24913
$296$	5.95702e10	0.451041
$297$	0	0
$298$	−8.30507e10	−0.610056
$299$	3.63231e10	0.262823
$300$	0	0
$301$	4.01862e10	0.282181
$302$	1.61389e11	1.11646
$303$	0	0
$304$	−1.86174e10	−0.125022
$305$	−2.16425e11	−1.43205
$306$	0	0
$307$	6.91990e10	0.444608	0.222304	−	0.974977i	$-0.428642\pi$
$307$	6.91990e10	0.444608	0.222304	+	0.974977i	$0.428642\pi$
$308$	−3.58102e10	−0.226740
$309$	0	0
$310$	−8.65438e10	−0.532241
$311$	1.81610e11	1.10083	0.550413	−	0.834892i	$-0.314470\pi$
$311$	1.81610e11	1.10083	0.550413	+	0.834892i	$0.314470\pi$
$312$	0	0
$313$	−1.61096e11	−0.948715	−0.474357	−	0.880332i	$-0.657320\pi$
$313$	−1.61096e11	−0.948715	−0.474357	+	0.880332i	$0.657320\pi$
$314$	−5.57019e10	−0.323360
$315$	0	0
$316$	−5.14341e10	−0.290175
$317$	−3.77197e10	−0.209798	−0.104899	−	0.994483i	$-0.533452\pi$
$317$	−3.77197e10	−0.209798	−0.104899	+	0.994483i	$0.533452\pi$
$318$	0	0
$319$	−4.34845e11	−2.35113
$320$	−1.85521e10	−0.0989050
$321$	0	0
$322$	−4.77012e10	−0.247273
$323$	7.88311e10	0.402982
$324$	0	0
$325$	−2.13648e10	−0.106224
$326$	−2.08154e11	−1.02072
$327$	0	0
$328$	−8.49649e10	−0.405329
$329$	−9.80491e10	−0.461383
$330$	0	0
$331$	4.60949e10	0.211070	0.105535	−	0.994416i	$-0.466344\pi$
$331$	4.60949e10	0.211070	0.105535	+	0.994416i	$0.466344\pi$
$332$	−1.16815e11	−0.527687
$333$	0	0
$334$	2.29462e11	1.00891
$335$	3.48152e11	1.51031
$336$	0	0
$337$	−3.14854e10	−0.132976	−0.0664882	−	0.997787i	$-0.521179\pi$
$337$	−3.14854e10	−0.132976	−0.0664882	+	0.997787i	$0.521179\pi$
$338$	−1.55980e11	−0.650047
$339$	0	0
$340$	7.85545e10	0.318798
$341$	2.84982e11	1.14136
$342$	0	0
$343$	−1.38413e10	−0.0539949
$344$	−6.85559e10	−0.263956
$345$	0	0
$346$	1.82941e11	0.686227
$347$	3.34449e11	1.23836	0.619180	−	0.785249i	$-0.287465\pi$
$347$	3.34449e11	1.23836	0.619180	+	0.785249i	$0.287465\pi$
$348$	0	0
$349$	−1.38558e11	−0.499939	−0.249970	−	0.968254i	$-0.580421\pi$
$349$	−1.38558e11	−0.499939	−0.249970	+	0.968254i	$0.580421\pi$
$350$	2.80572e10	0.0999396
$351$	0	0
$352$	6.10906e10	0.212096
$353$	−1.83319e11	−0.628378	−0.314189	−	0.949361i	$-0.601732\pi$
$353$	−1.83319e11	−0.628378	−0.314189	+	0.949361i	$0.601732\pi$
$354$	0	0
$355$	3.69973e11	1.23635
$356$	2.23597e11	0.737804
$357$	0	0
$358$	−1.06841e11	−0.343768
$359$	−2.39769e11	−0.761847	−0.380924	−	0.924607i	$-0.624394\pi$
$359$	−2.39769e11	−0.761847	−0.380924	+	0.924607i	$0.624394\pi$
$360$	0	0
$361$	−2.41987e11	−0.749910
$362$	−1.04664e11	−0.320337
$363$	0	0
$364$	−1.79804e10	−0.0536837
$365$	6.72051e10	0.198191
$366$	0	0
$367$	−5.66841e11	−1.63104	−0.815518	−	0.578731i	$-0.803548\pi$
$367$	−5.66841e11	−1.63104	−0.815518	+	0.578731i	$0.803548\pi$
$368$	8.13761e10	0.231303
$369$	0	0
$370$	−2.57313e11	−0.713763
$371$	−2.10700e11	−0.577407
$372$	0	0
$373$	−9.61902e10	−0.257301	−0.128650	−	0.991690i	$-0.541065\pi$
$373$	−9.61902e10	−0.257301	−0.128650	+	0.991690i	$0.541065\pi$
$374$	−2.58674e11	−0.683645
$375$	0	0
$376$	1.67267e11	0.431585
$377$	−2.18336e11	−0.556660
$378$	0	0
$379$	−2.15943e11	−0.537604	−0.268802	−	0.963196i	$-0.586628\pi$
$379$	−2.15943e11	−0.537604	−0.268802	+	0.963196i	$0.586628\pi$
$380$	8.04178e10	0.197846
$381$	0	0
$382$	1.06957e11	0.256996
$383$	5.72972e10	0.136063	0.0680314	−	0.997683i	$-0.478328\pi$
$383$	5.72972e10	0.136063	0.0680314	+	0.997683i	$0.478328\pi$
$384$	0	0
$385$	1.54682e11	0.358812
$386$	1.47368e11	0.337879
$387$	0	0
$388$	1.90778e10	0.0427353
$389$	3.82287e11	0.846480	0.423240	−	0.906018i	$-0.360893\pi$
$389$	3.82287e11	0.846480	0.423240	+	0.906018i	$0.360893\pi$
$390$	0	0
$391$	−3.44568e11	−0.745554
$392$	2.36126e10	0.0505076
$393$	0	0
$394$	1.94508e10	0.0406635
$395$	2.22169e11	0.459195
$396$	0	0
$397$	−7.08917e11	−1.43231	−0.716157	−	0.697940i	$-0.754100\pi$
$397$	−7.08917e11	−1.43231	−0.716157	+	0.697940i	$0.754100\pi$
$398$	−4.29548e11	−0.858099
$399$	0	0
$400$	−4.78643e10	−0.0934849
$401$	2.45144e11	0.473448	0.236724	−	0.971577i	$-0.423926\pi$
$401$	2.45144e11	0.473448	0.236724	+	0.971577i	$0.423926\pi$
$402$	0	0
$403$	1.43090e11	0.270232
$404$	−4.66088e11	−0.870466
$405$	0	0
$406$	2.86729e11	0.523727
$407$	8.47313e11	1.53063
$408$	0	0
$409$	−7.42460e11	−1.31195	−0.655977	−	0.754781i	$-0.727743\pi$
$409$	−7.42460e11	−1.31195	−0.655977	+	0.754781i	$0.727743\pi$
$410$	3.67006e11	0.641425
$411$	0	0
$412$	−4.21367e11	−0.720482
$413$	−3.52798e11	−0.596693
$414$	0	0
$415$	5.04581e11	0.835054
$416$	3.06737e10	0.0502165
$417$	0	0
$418$	−2.64810e11	−0.424269
$419$	−5.79723e11	−0.918878	−0.459439	−	0.888209i	$-0.651949\pi$
$419$	−5.79723e11	−0.918878	−0.459439	+	0.888209i	$0.651949\pi$
$420$	0	0
$421$	6.09805e10	0.0946066	0.0473033	−	0.998881i	$-0.484937\pi$
$421$	6.09805e10	0.0946066	0.0473033	+	0.998881i	$0.484937\pi$
$422$	−7.30492e11	−1.12127
$423$	0	0
$424$	3.59445e11	0.540115
$425$	2.02670e11	0.301328
$426$	0	0
$427$	−4.69922e11	−0.684070
$428$	−3.12000e11	−0.449425
$429$	0	0
$430$	2.96127e11	0.417705
$431$	−1.04601e12	−1.46011	−0.730057	−	0.683386i	$-0.760507\pi$
$431$	−1.04601e12	−1.46011	−0.730057	+	0.683386i	$0.760507\pi$
$432$	0	0
$433$	1.17773e12	1.61010	0.805048	−	0.593210i	$-0.202140\pi$
$433$	1.17773e12	1.61010	0.805048	+	0.593210i	$0.202140\pi$
$434$	−1.87912e11	−0.254244
$435$	0	0
$436$	−3.77829e11	−0.500733
$437$	−3.52741e11	−0.462689
$438$	0	0
$439$	8.48573e11	1.09043	0.545216	−	0.838295i	$-0.316448\pi$
$439$	8.48573e11	1.09043	0.545216	+	0.838295i	$0.316448\pi$
$440$	−2.63881e11	−0.335638
$441$	0	0
$442$	−1.29881e11	−0.161862
$443$	−1.07512e12	−1.32629	−0.663147	−	0.748490i	$-0.730779\pi$
$443$	−1.07512e12	−1.32629	−0.663147	+	0.748490i	$0.730779\pi$
$444$	0	0
$445$	−9.65826e11	−1.16756
$446$	4.75818e11	0.569422
$447$	0	0
$448$	−4.02821e10	−0.0472456
$449$	−6.13145e10	−0.0711958	−0.0355979	−	0.999366i	$-0.511334\pi$
$449$	−6.13145e10	−0.0711958	−0.0355979	+	0.999366i	$0.511334\pi$
$450$	0	0
$451$	−1.20852e12	−1.37550
$452$	−5.84545e11	−0.658711
$453$	0	0
$454$	−6.48569e11	−0.716481
$455$	7.76662e10	0.0849534
$456$	0	0
$457$	9.95050e11	1.06714	0.533571	−	0.845755i	$-0.320850\pi$
$457$	9.95050e11	1.06714	0.533571	+	0.845755i	$0.320850\pi$
$458$	−9.86045e11	−1.04713
$459$	0	0
$460$	−3.51504e11	−0.366032
$461$	2.30259e11	0.237445	0.118722	−	0.992927i	$-0.462120\pi$
$461$	2.30259e11	0.237445	0.118722	+	0.992927i	$0.462120\pi$
$462$	0	0
$463$	−1.42783e12	−1.44398	−0.721990	−	0.691903i	$-0.756773\pi$
$463$	−1.42783e12	−1.44398	−0.721990	+	0.691903i	$0.756773\pi$
$464$	−4.89147e11	−0.489901
$465$	0	0
$466$	2.61334e11	0.256720
$467$	7.28765e11	0.709025	0.354512	−	0.935051i	$-0.384647\pi$
$467$	7.28765e11	0.709025	0.354512	+	0.935051i	$0.384647\pi$
$468$	0	0
$469$	7.55941e11	0.721457
$470$	−7.22511e11	−0.682974
$471$	0	0
$472$	6.01858e11	0.558156
$473$	−9.75123e11	−0.895745
$474$	0	0
$475$	2.07477e11	0.187003
$476$	1.70565e11	0.152286
$477$	0	0
$478$	−8.25849e11	−0.723561
$479$	3.71663e11	0.322582	0.161291	−	0.986907i	$-0.448434\pi$
$479$	3.71663e11	0.322582	0.161291	+	0.986907i	$0.448434\pi$
$480$	0	0
$481$	4.25437e11	0.362396
$482$	−2.33954e11	−0.197432
$483$	0	0
$484$	2.65305e11	0.219756
$485$	−8.24067e10	−0.0676277
$486$	0	0
$487$	1.77531e12	1.43019	0.715095	−	0.699028i	$-0.246384\pi$
$487$	1.77531e12	1.43019	0.715095	+	0.699028i	$0.246384\pi$
$488$	8.01667e11	0.639889
$489$	0	0
$490$	−1.01995e11	−0.0799273
$491$	2.90478e11	0.225552	0.112776	−	0.993620i	$-0.464026\pi$
$491$	2.90478e11	0.225552	0.112776	+	0.993620i	$0.464026\pi$
$492$	0	0
$493$	2.07118e12	1.57909
$494$	−1.32962e11	−0.100451
$495$	0	0
$496$	3.20570e11	0.237824
$497$	8.03321e11	0.590589
$498$	0	0
$499$	2.67145e11	0.192883	0.0964417	−	0.995339i	$-0.469254\pi$
$499$	2.67145e11	0.192883	0.0964417	+	0.995339i	$0.469254\pi$
$500$	7.59645e11	0.543558
$501$	0	0
$502$	5.26424e11	0.369972
$503$	1.16670e12	0.812650	0.406325	−	0.913729i	$-0.366810\pi$
$503$	1.16670e12	0.812650	0.406325	+	0.913729i	$0.366810\pi$
$504$	0	0
$505$	2.01327e12	1.37749
$506$	1.15747e12	0.784936
$507$	0	0
$508$	−1.19756e12	−0.797830
$509$	2.22126e12	1.46679	0.733397	−	0.679800i	$-0.237934\pi$
$509$	2.22126e12	1.46679	0.733397	+	0.679800i	$0.237934\pi$
$510$	0	0
$511$	1.45922e11	0.0946733
$512$	6.87195e10	0.0441942
$513$	0	0
$514$	8.89846e10	0.0562317
$515$	1.82009e12	1.14015
$516$	0	0
$517$	2.37917e12	1.46460
$518$	−5.58703e11	−0.340955
$519$	0	0
$520$	−1.32495e11	−0.0794666
$521$	−4.88960e11	−0.290739	−0.145370	−	0.989377i	$-0.546437\pi$
$521$	−4.88960e11	−0.290739	−0.145370	+	0.989377i	$0.546437\pi$
$522$	0	0
$523$	8.15361e11	0.476532	0.238266	−	0.971200i	$-0.423421\pi$
$523$	8.15361e11	0.476532	0.238266	+	0.971200i	$0.423421\pi$
$524$	−7.63955e11	−0.442667
$525$	0	0
$526$	1.26824e11	0.0722377
$527$	−1.35738e12	−0.766572
$528$	0	0
$529$	−2.59333e11	−0.143982
$530$	−1.55262e12	−0.854720
$531$	0	0
$532$	1.74611e11	0.0945081
$533$	−6.06801e11	−0.325667
$534$	0	0
$535$	1.34768e12	0.711206
$536$	−1.28960e12	−0.674861
$537$	0	0
$538$	1.32048e12	0.679534
$539$	3.35861e11	0.171400
$540$	0	0
$541$	−1.22419e12	−0.614412	−0.307206	−	0.951643i	$-0.599394\pi$
$541$	−1.22419e12	−0.614412	−0.307206	+	0.951643i	$0.599394\pi$
$542$	−1.89496e12	−0.943201
$543$	0	0
$544$	−2.90977e11	−0.142450
$545$	1.63203e12	0.792400
$546$	0	0
$547$	6.47839e11	0.309403	0.154701	−	0.987961i	$-0.450558\pi$
$547$	6.47839e11	0.309403	0.154701	+	0.987961i	$0.450558\pi$
$548$	−1.28232e12	−0.607415
$549$	0	0
$550$	−6.80811e11	−0.317245
$551$	2.12031e12	0.979979
$552$	0	0
$553$	4.82396e11	0.219351
$554$	1.13620e12	0.512462
$555$	0	0
$556$	7.18788e11	0.318981
$557$	−4.03854e11	−0.177777	−0.0888886	−	0.996042i	$-0.528332\pi$
$557$	−4.03854e11	−0.177777	−0.0888886	+	0.996042i	$0.528332\pi$
$558$	0	0
$559$	−4.89611e11	−0.212079
$560$	1.73998e11	0.0747651
$561$	0	0
$562$	3.07489e12	1.30022
$563$	3.19283e12	1.33933	0.669666	−	0.742662i	$-0.266437\pi$
$563$	3.19283e12	1.33933	0.669666	+	0.742662i	$0.266437\pi$
$564$	0	0
$565$	2.52494e12	1.04240
$566$	2.10974e11	0.0864081
$567$	0	0
$568$	−1.37043e12	−0.552445
$569$	3.78630e12	1.51429	0.757146	−	0.653245i	$-0.226593\pi$
$569$	3.78630e12	1.51429	0.757146	+	0.653245i	$0.226593\pi$
$570$	0	0
$571$	1.12645e12	0.443456	0.221728	−	0.975109i	$-0.428830\pi$
$571$	1.12645e12	0.443456	0.221728	+	0.975109i	$0.428830\pi$
$572$	4.36296e11	0.170412
$573$	0	0
$574$	7.96878e11	0.306400
$575$	−9.06877e11	−0.345974
$576$	0	0
$577$	−3.66585e12	−1.37684	−0.688420	−	0.725312i	$-0.741696\pi$
$577$	−3.66585e12	−1.37684	−0.688420	+	0.725312i	$0.741696\pi$
$578$	−6.65334e11	−0.247950
$579$	0	0
$580$	2.11287e12	0.775259
$581$	1.09560e12	0.398894
$582$	0	0
$583$	5.11266e12	1.83290
$584$	−2.48937e11	−0.0885588
$585$	0	0
$586$	1.06103e12	0.371697
$587$	−2.45741e12	−0.854292	−0.427146	−	0.904183i	$-0.640481\pi$
$587$	−2.45741e12	−0.854292	−0.427146	+	0.904183i	$0.640481\pi$
$588$	0	0
$589$	−1.38958e12	−0.475733
$590$	−2.59972e12	−0.883270
$591$	0	0
$592$	9.53123e11	0.318934
$593$	1.94025e12	0.644336	0.322168	−	0.946683i	$-0.395588\pi$
$593$	1.94025e12	0.644336	0.322168	+	0.946683i	$0.395588\pi$
$594$	0	0
$595$	−7.36755e11	−0.240989
$596$	−1.32881e12	−0.431375
$597$	0	0
$598$	5.81170e11	0.185844
$599$	2.85436e12	0.905915	0.452957	−	0.891532i	$-0.350369\pi$
$599$	2.85436e12	0.905915	0.452957	+	0.891532i	$0.350369\pi$
$600$	0	0
$601$	2.69023e12	0.841113	0.420557	−	0.907266i	$-0.361835\pi$
$601$	2.69023e12	0.841113	0.420557	+	0.907266i	$0.361835\pi$
$602$	6.42979e11	0.199532
$603$	0	0
$604$	2.58222e12	0.789455
$605$	−1.14598e12	−0.347760
$606$	0	0
$607$	−2.05866e12	−0.615512	−0.307756	−	0.951465i	$-0.599578\pi$
$607$	−2.05866e12	−0.615512	−0.307756	+	0.951465i	$0.599578\pi$
$608$	−2.97879e11	−0.0884042
$609$	0	0
$610$	−3.46280e12	−1.01261
$611$	1.19459e12	0.346763
$612$	0	0
$613$	−1.35290e11	−0.0386984	−0.0193492	−	0.999813i	$-0.506159\pi$
$613$	−1.35290e11	−0.0386984	−0.0193492	+	0.999813i	$0.506159\pi$
$614$	1.10718e12	0.314385
$615$	0	0
$616$	−5.72963e11	−0.160330
$617$	−2.31268e11	−0.0642440	−0.0321220	−	0.999484i	$-0.510227\pi$
$617$	−2.31268e11	−0.0642440	−0.0321220	+	0.999484i	$0.510227\pi$
$618$	0	0
$619$	−3.91258e12	−1.07116	−0.535581	−	0.844484i	$-0.679907\pi$
$619$	−3.91258e12	−1.07116	−0.535581	+	0.844484i	$0.679907\pi$
$620$	−1.38470e12	−0.376351
$621$	0	0
$622$	2.90577e12	0.778402
$623$	−2.09709e12	−0.557727
$624$	0	0
$625$	−1.85482e12	−0.486229
$626$	−2.57754e12	−0.670843
$627$	0	0
$628$	−8.91230e11	−0.228650
$629$	−4.03578e12	−1.02801
$630$	0	0
$631$	5.25922e12	1.32065	0.660327	−	0.750978i	$-0.270418\pi$
$631$	5.25922e12	1.32065	0.660327	+	0.750978i	$0.270418\pi$
$632$	−8.22946e11	−0.205184
$633$	0	0
$634$	−6.03515e11	−0.148350
$635$	5.17285e12	1.26255
$636$	0	0
$637$	1.68636e11	0.0405811
$638$	−6.95752e12	−1.66250
$639$	0	0
$640$	−2.96834e11	−0.0699364
$641$	5.03824e12	1.17874	0.589370	−	0.807863i	$-0.299376\pi$
$641$	5.03824e12	1.17874	0.589370	+	0.807863i	$0.299376\pi$
$642$	0	0
$643$	−2.87046e12	−0.662221	−0.331110	−	0.943592i	$-0.607423\pi$
$643$	−2.87046e12	−0.662221	−0.331110	+	0.943592i	$0.607423\pi$
$644$	−7.63218e11	−0.174849
$645$	0	0
$646$	1.26130e12	0.284952
$647$	−7.47217e11	−0.167640	−0.0838200	−	0.996481i	$-0.526712\pi$
$647$	−7.47217e11	−0.167640	−0.0838200	+	0.996481i	$0.526712\pi$
$648$	0	0
$649$	8.56070e12	1.89412
$650$	−3.41836e11	−0.0751118
$651$	0	0
$652$	−3.33047e12	−0.721757
$653$	4.85314e12	1.04451	0.522257	−	0.852788i	$-0.325090\pi$
$653$	4.85314e12	1.04451	0.522257	+	0.852788i	$0.325090\pi$
$654$	0	0
$655$	3.29990e12	0.700511
$656$	−1.35944e12	−0.286611
$657$	0	0
$658$	−1.56879e12	−0.326247
$659$	−4.07773e12	−0.842236	−0.421118	−	0.907006i	$-0.638362\pi$
$659$	−4.07773e12	−0.842236	−0.421118	+	0.907006i	$0.638362\pi$
$660$	0	0
$661$	9.28686e12	1.89218	0.946090	−	0.323904i	$-0.104995\pi$
$661$	9.28686e12	1.89218	0.946090	+	0.323904i	$0.104995\pi$
$662$	7.37519e11	0.149249
$663$	0	0
$664$	−1.86904e12	−0.373131
$665$	−7.54231e11	−0.149557
$666$	0	0
$667$	−9.26779e12	−1.81305
$668$	3.67138e12	0.713404
$669$	0	0
$670$	5.57043e12	1.06795
$671$	1.14027e13	2.17149
$672$	0	0
$673$	−6.32833e11	−0.118911	−0.0594554	−	0.998231i	$-0.518936\pi$
$673$	−6.32833e11	−0.118911	−0.0594554	+	0.998231i	$0.518936\pi$
$674$	−5.03766e11	−0.0940284
$675$	0	0
$676$	−2.49569e12	−0.459653
$677$	−7.33969e11	−0.134285	−0.0671427	−	0.997743i	$-0.521388\pi$
$677$	−7.33969e11	−0.134285	−0.0671427	+	0.997743i	$0.521388\pi$
$678$	0	0
$679$	−1.78929e11	−0.0323048
$680$	1.25687e12	0.225424
$681$	0	0
$682$	4.55971e12	0.807064
$683$	1.70656e11	0.0300074	0.0150037	−	0.999887i	$-0.495224\pi$
$683$	1.70656e11	0.0300074	0.0150037	+	0.999887i	$0.495224\pi$
$684$	0	0
$685$	5.53899e12	0.961221
$686$	−2.21461e11	−0.0381802
$687$	0	0
$688$	−1.09689e12	−0.186645
$689$	2.56708e12	0.433963
$690$	0	0
$691$	−8.48021e12	−1.41500	−0.707498	−	0.706715i	$-0.750176\pi$
$691$	−8.48021e12	−1.41500	−0.707498	+	0.706715i	$0.750176\pi$
$692$	2.92705e12	0.485236
$693$	0	0
$694$	5.35118e12	0.875652
$695$	−3.10480e12	−0.504780
$696$	0	0
$697$	5.75623e12	0.923826
$698$	−2.21693e12	−0.353511
$699$	0	0
$700$	4.48915e11	0.0706680
$701$	9.50392e12	1.48652	0.743261	−	0.669001i	$-0.233278\pi$
$701$	9.50392e12	1.48652	0.743261	+	0.669001i	$0.233278\pi$
$702$	0	0
$703$	−4.13150e12	−0.637983
$704$	9.77450e11	0.149975
$705$	0	0
$706$	−2.93310e12	−0.444330
$707$	4.37140e12	0.658010
$708$	0	0
$709$	−4.73328e12	−0.703485	−0.351742	−	0.936097i	$-0.614411\pi$
$709$	−4.73328e12	−0.703485	−0.351742	+	0.936097i	$0.614411\pi$
$710$	5.91957e12	0.874234
$711$	0	0
$712$	3.57755e12	0.521706
$713$	6.07379e12	0.880150
$714$	0	0
$715$	−1.88458e12	−0.269673
$716$	−1.70946e12	−0.243080
$717$	0	0
$718$	−3.83630e12	−0.538707
$719$	−1.26848e13	−1.77012	−0.885062	−	0.465472i	$-0.845885\pi$
$719$	−1.26848e13	−1.77012	−0.885062	+	0.465472i	$0.845885\pi$
$720$	0	0
$721$	3.95196e12	0.544634
$722$	−3.87179e12	−0.530267
$723$	0	0
$724$	−1.67462e12	−0.226513
$725$	5.45119e12	0.732774
$726$	0	0
$727$	8.67932e12	1.15234	0.576170	−	0.817330i	$-0.304546\pi$
$727$	8.67932e12	1.15234	0.576170	+	0.817330i	$0.304546\pi$
$728$	−2.87686e11	−0.0379601
$729$	0	0
$730$	1.07528e12	0.140142
$731$	4.64454e12	0.601609
$732$	0	0
$733$	−4.76159e12	−0.609234	−0.304617	−	0.952475i	$-0.598528\pi$
$733$	−4.76159e12	−0.609234	−0.304617	+	0.952475i	$0.598528\pi$
$734$	−9.06945e12	−1.15332
$735$	0	0
$736$	1.30202e12	0.163556
$737$	−1.83430e13	−2.29017
$738$	0	0
$739$	9.22702e12	1.13805	0.569025	−	0.822320i	$-0.307321\pi$
$739$	9.22702e12	1.13805	0.569025	+	0.822320i	$0.307321\pi$
$740$	−4.11701e12	−0.504707
$741$	0	0
$742$	−3.37120e12	−0.408288
$743$	9.84233e12	1.18481	0.592405	−	0.805641i	$-0.298179\pi$
$743$	9.84233e12	1.18481	0.592405	+	0.805641i	$0.298179\pi$
$744$	0	0
$745$	5.73979e12	0.682642
$746$	−1.53904e12	−0.181939
$747$	0	0
$748$	−4.13878e12	−0.483410
$749$	2.92622e12	0.339733
$750$	0	0
$751$	7.08669e12	0.812949	0.406475	−	0.913662i	$-0.366758\pi$
$751$	7.08669e12	0.812949	0.406475	+	0.913662i	$0.366758\pi$
$752$	2.67628e12	0.305176
$753$	0	0
$754$	−3.49338e12	−0.393618
$755$	−1.11539e13	−1.24930
$756$	0	0
$757$	−1.77650e13	−1.96623	−0.983114	−	0.182996i	$-0.941420\pi$
$757$	−1.77650e13	−1.96623	−0.983114	+	0.182996i	$0.941420\pi$
$758$	−3.45508e12	−0.380143
$759$	0	0
$760$	1.28669e12	0.139898
$761$	−1.62372e12	−0.175501	−0.0877507	−	0.996142i	$-0.527968\pi$
$761$	−1.62372e12	−0.175501	−0.0877507	+	0.996142i	$0.527968\pi$
$762$	0	0
$763$	3.54362e12	0.378519
$764$	1.71132e12	0.181723
$765$	0	0
$766$	9.16756e11	0.0962109
$767$	4.29834e12	0.448458
$768$	0	0
$769$	−9.75735e12	−1.00615	−0.503076	−	0.864242i	$-0.667798\pi$
$769$	−9.75735e12	−1.00615	−0.503076	+	0.864242i	$0.667798\pi$
$770$	2.47491e12	0.253718
$771$	0	0
$772$	2.35789e12	0.238917
$773$	1.21097e13	1.21991	0.609954	−	0.792437i	$-0.291188\pi$
$773$	1.21097e13	1.21991	0.609954	+	0.792437i	$0.291188\pi$
$774$	0	0
$775$	−3.57252e12	−0.355727
$776$	3.05245e11	0.0302184
$777$	0	0
$778$	6.11660e12	0.598552
$779$	5.89277e12	0.573325
$780$	0	0
$781$	−1.94927e13	−1.87474
$782$	−5.51309e12	−0.527187
$783$	0	0
$784$	3.77802e11	0.0357143
$785$	3.84967e12	0.361834
$786$	0	0
$787$	3.45575e12	0.321112	0.160556	−	0.987027i	$-0.448671\pi$
$787$	3.45575e12	0.321112	0.160556	+	0.987027i	$0.448671\pi$
$788$	3.11213e11	0.0287535
$789$	0	0
$790$	3.55471e12	0.324700
$791$	5.48239e12	0.497939
$792$	0	0
$793$	5.72533e12	0.514128
$794$	−1.13427e13	−1.01280
$795$	0	0
$796$	−6.87276e12	−0.606768
$797$	−1.12359e13	−0.986383	−0.493192	−	0.869921i	$-0.664170\pi$
$797$	−1.12359e13	−0.986383	−0.493192	+	0.869921i	$0.664170\pi$
$798$	0	0
$799$	−1.13321e13	−0.983669
$800$	−7.65828e11	−0.0661038
$801$	0	0
$802$	3.92231e12	0.334778
$803$	−3.54082e12	−0.300528
$804$	0	0
$805$	3.29672e12	0.276695
$806$	2.28944e12	0.191083
$807$	0	0
$808$	−7.45741e12	−0.615512
$809$	−1.67149e13	−1.37195	−0.685973	−	0.727627i	$-0.740623\pi$
$809$	−1.67149e13	−1.37195	−0.685973	+	0.727627i	$0.740623\pi$
$810$	0	0
$811$	4.93940e12	0.400941	0.200470	−	0.979700i	$-0.435753\pi$
$811$	4.93940e12	0.400941	0.200470	+	0.979700i	$0.435753\pi$
$812$	4.58766e12	0.370331
$813$	0	0
$814$	1.35570e13	1.08232
$815$	1.43859e13	1.14217
$816$	0	0
$817$	4.75471e12	0.373357
$818$	−1.18794e13	−0.927691
$819$	0	0
$820$	5.87209e12	0.453556
$821$	−1.88939e13	−1.45137	−0.725685	−	0.688027i	$-0.758477\pi$
$821$	−1.88939e13	−1.45137	−0.725685	+	0.688027i	$0.758477\pi$
$822$	0	0
$823$	−1.11277e13	−0.845486	−0.422743	−	0.906250i	$-0.638933\pi$
$823$	−1.11277e13	−0.845486	−0.422743	+	0.906250i	$0.638933\pi$
$824$	−6.74188e12	−0.509458
$825$	0	0
$826$	−5.64477e12	−0.421926
$827$	−1.87228e13	−1.39186	−0.695931	−	0.718109i	$-0.745008\pi$
$827$	−1.87228e13	−1.39186	−0.695931	+	0.718109i	$0.745008\pi$
$828$	0	0
$829$	−1.16382e13	−0.855836	−0.427918	−	0.903818i	$-0.640753\pi$
$829$	−1.16382e13	−0.855836	−0.427918	+	0.903818i	$0.640753\pi$
$830$	8.07330e12	0.590472
$831$	0	0
$832$	4.90780e11	0.0355084
$833$	−1.59971e12	−0.115117
$834$	0	0
$835$	−1.58585e13	−1.12895
$836$	−4.23696e12	−0.300003
$837$	0	0
$838$	−9.27557e12	−0.649745
$839$	−1.32059e13	−0.920111	−0.460055	−	0.887890i	$-0.652170\pi$
$839$	−1.32059e13	−0.920111	−0.460055	+	0.887890i	$0.652170\pi$
$840$	0	0
$841$	4.12011e13	2.84005
$842$	9.75688e11	0.0668970
$843$	0	0
$844$	−1.16879e13	−0.792857
$845$	1.07801e13	0.727391
$846$	0	0
$847$	−2.48827e12	−0.166120
$848$	5.75112e12	0.381919
$849$	0	0
$850$	3.24272e12	0.213071
$851$	1.80587e13	1.18033
$852$	0	0
$853$	−2.41724e13	−1.56332	−0.781662	−	0.623702i	$-0.785628\pi$
$853$	−2.41724e13	−1.56332	−0.781662	+	0.623702i	$0.785628\pi$
$854$	−7.51876e12	−0.483711
$855$	0	0
$856$	−4.99199e12	−0.317791
$857$	3.02390e13	1.91494	0.957468	−	0.288541i	$-0.0931701\pi$
$857$	3.02390e13	1.91494	0.957468	+	0.288541i	$0.0931701\pi$
$858$	0	0
$859$	1.00419e13	0.629286	0.314643	−	0.949210i	$-0.398115\pi$
$859$	1.00419e13	0.629286	0.314643	+	0.949210i	$0.398115\pi$
$860$	4.73803e12	0.295362
$861$	0	0
$862$	−1.67361e13	−1.03246
$863$	−8.61217e12	−0.528523	−0.264262	−	0.964451i	$-0.585128\pi$
$863$	−8.61217e12	−0.528523	−0.264262	+	0.964451i	$0.585128\pi$
$864$	0	0
$865$	−1.26434e13	−0.767876
$866$	1.88437e13	1.13851
$867$	0	0
$868$	−3.00660e12	−0.179778
$869$	−1.17054e13	−0.696301
$870$	0	0
$871$	−9.21006e12	−0.542227
$872$	−6.04527e12	−0.354072
$873$	0	0
$874$	−5.64386e12	−0.327171
$875$	−7.12464e12	−0.410891
$876$	0	0
$877$	−2.33231e13	−1.33134	−0.665670	−	0.746246i	$-0.731854\pi$
$877$	−2.33231e13	−1.33134	−0.665670	+	0.746246i	$0.731854\pi$
$878$	1.35772e13	0.771052
$879$	0	0
$880$	−4.22209e12	−0.237332
$881$	−6.95838e12	−0.389150	−0.194575	−	0.980888i	$-0.562333\pi$
$881$	−6.95838e12	−0.389150	−0.194575	+	0.980888i	$0.562333\pi$
$882$	0	0
$883$	1.86054e13	1.02995	0.514975	−	0.857205i	$-0.327801\pi$
$883$	1.86054e13	1.02995	0.514975	+	0.857205i	$0.327801\pi$
$884$	−2.07809e12	−0.114454
$885$	0	0
$886$	−1.72019e13	−0.937831
$887$	−8.33576e12	−0.452157	−0.226078	−	0.974109i	$-0.572591\pi$
$887$	−8.33576e12	−0.452157	−0.226078	+	0.974109i	$0.572591\pi$
$888$	0	0
$889$	1.12318e13	0.603103
$890$	−1.54532e13	−0.825589
$891$	0	0
$892$	7.61309e12	0.402642
$893$	−1.16009e13	−0.610463
$894$	0	0
$895$	7.38400e12	0.384670
$896$	−6.44514e11	−0.0334077
$897$	0	0
$898$	−9.81032e11	−0.0503431
$899$	−3.65092e13	−1.86416
$900$	0	0
$901$	−2.43518e13	−1.23103
$902$	−1.93364e13	−0.972625
$903$	0	0
$904$	−9.35272e12	−0.465779
$905$	7.23352e12	0.358452
$906$	0	0
$907$	2.23958e13	1.09884	0.549419	−	0.835547i	$-0.314849\pi$
$907$	2.23958e13	1.09884	0.549419	+	0.835547i	$0.314849\pi$
$908$	−1.03771e13	−0.506629
$909$	0	0
$910$	1.24266e12	0.0600711
$911$	2.22361e12	0.106961	0.0534806	−	0.998569i	$-0.482968\pi$
$911$	2.22361e12	0.106961	0.0534806	+	0.998569i	$0.482968\pi$
$912$	0	0
$913$	−2.65848e13	−1.26623
$914$	1.59208e13	0.754583
$915$	0	0
$916$	−1.57767e13	−0.740435
$917$	7.16506e12	0.334625
$918$	0	0
$919$	−2.22073e12	−0.102701	−0.0513507	−	0.998681i	$-0.516353\pi$
$919$	−2.22073e12	−0.102701	−0.0513507	+	0.998681i	$0.516353\pi$
$920$	−5.62406e12	−0.258824
$921$	0	0
$922$	3.68415e12	0.167899
$923$	−9.78732e12	−0.443870
$924$	0	0
$925$	−1.06219e13	−0.477049
$926$	−2.28452e13	−1.02105
$927$	0	0
$928$	−7.82635e12	−0.346413
$929$	3.22932e12	0.142246	0.0711230	−	0.997468i	$-0.477342\pi$
$929$	3.22932e12	0.142246	0.0711230	+	0.997468i	$0.477342\pi$
$930$	0	0
$931$	−1.63766e12	−0.0714414
$932$	4.18135e12	0.181528
$933$	0	0
$934$	1.16602e13	0.501356
$935$	1.78775e13	0.764986
$936$	0	0
$937$	−3.42947e13	−1.45344	−0.726722	−	0.686931i	$-0.758957\pi$
$937$	−3.42947e13	−1.45344	−0.726722	+	0.686931i	$0.758957\pi$
$938$	1.20951e13	0.510147
$939$	0	0
$940$	−1.15602e13	−0.482936
$941$	−1.66895e13	−0.693891	−0.346945	−	0.937885i	$-0.612781\pi$
$941$	−1.66895e13	−0.693891	−0.346945	+	0.937885i	$0.612781\pi$
$942$	0	0
$943$	−2.57571e13	−1.06070
$944$	9.62973e12	0.394676
$945$	0	0
$946$	−1.56020e13	−0.633387
$947$	3.77613e13	1.52571	0.762856	−	0.646569i	$-0.223797\pi$
$947$	3.77613e13	1.52571	0.762856	+	0.646569i	$0.223797\pi$
$948$	0	0
$949$	−1.77785e12	−0.0711538
$950$	3.31964e12	0.132231
$951$	0	0
$952$	2.72904e12	0.107682
$953$	−3.09215e13	−1.21435	−0.607173	−	0.794570i	$-0.707696\pi$
$953$	−3.09215e13	−1.21435	−0.607173	+	0.794570i	$0.707696\pi$
$954$	0	0
$955$	−7.39204e12	−0.287574
$956$	−1.32136e13	−0.511635
$957$	0	0
$958$	5.94661e12	0.228100
$959$	1.20268e13	0.459162
$960$	0	0
$961$	−2.51276e12	−0.0950378
$962$	6.80700e12	0.256252
$963$	0	0
$964$	−3.74326e12	−0.139606
$965$	−1.01849e13	−0.378081
$966$	0	0
$967$	1.38467e13	0.509245	0.254623	−	0.967041i	$-0.418049\pi$
$967$	1.38467e13	0.509245	0.254623	+	0.967041i	$0.418049\pi$
$968$	4.24488e12	0.155391
$969$	0	0
$970$	−1.31851e12	−0.0478200
$971$	−3.78953e13	−1.36804	−0.684020	−	0.729463i	$-0.739770\pi$
$971$	−3.78953e13	−1.36804	−0.684020	+	0.729463i	$0.739770\pi$
$972$	0	0
$973$	−6.74145e12	−0.241127
$974$	2.84049e13	1.01130
$975$	0	0
$976$	1.28267e13	0.452470
$977$	4.73587e13	1.66293	0.831465	−	0.555577i	$-0.187503\pi$
$977$	4.73587e13	1.66293	0.831465	+	0.555577i	$0.187503\pi$
$978$	0	0
$979$	5.08863e13	1.77043
$980$	−1.63191e12	−0.0565171
$981$	0	0
$982$	4.64765e12	0.159489
$983$	5.15941e13	1.76242	0.881209	−	0.472726i	$-0.156730\pi$
$983$	5.15941e13	1.76242	0.881209	+	0.472726i	$0.156730\pi$
$984$	0	0
$985$	−1.34428e12	−0.0455018
$986$	3.31389e13	1.11658
$987$	0	0
$988$	−2.12738e12	−0.0710297
$989$	−2.07827e13	−0.690746
$990$	0	0
$991$	−3.59499e13	−1.18404	−0.592021	−	0.805923i	$-0.701670\pi$
$991$	−3.59499e13	−1.18404	−0.592021	+	0.805923i	$0.701670\pi$
$992$	5.12912e12	0.168167
$993$	0	0
$994$	1.28531e13	0.417609
$995$	2.96869e13	0.960198
$996$	0	0
$997$	−3.22710e13	−1.03439	−0.517195	−	0.855868i	$-0.673024\pi$
$997$	−3.22710e13	−1.03439	−0.517195	+	0.855868i	$0.673024\pi$
$998$	4.27432e12	0.136389
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.10.a.f.1.2	yes	4
3.2	odd	2		378.10.a.c.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.10.a.c.1.3	✓	4	3.2	odd	2
378.10.a.f.1.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	378.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +256.000 q^{4} -1105.79 q^{5} -2401.00 q^{7} +4096.00 q^{8} +O(q^{10})\)	\(q+16.0000 q^{2} +256.000 q^{4} -1105.79 q^{5} -2401.00 q^{7} +4096.00 q^{8} -17692.7 q^{10} +58260.6 q^{11} +29252.8 q^{13} -38416.0 q^{14} +65536.0 q^{16} -277497. q^{17} -284079. q^{19} -283083. q^{20} +932169. q^{22} +1.24170e6 q^{23} -730351. q^{25} +468044. q^{26} -614656. q^{28} -7.46379e6 q^{29} +4.89151e6 q^{31} +1.04858e6 q^{32} -4.43995e6 q^{34} +2.65500e6 q^{35} +1.45435e7 q^{37} -4.54527e6 q^{38} -4.52932e6 q^{40} -2.07434e7 q^{41} -1.67373e7 q^{43} +1.49147e7 q^{44} +1.98672e7 q^{46} +4.08368e7 q^{47} +5.76480e6 q^{49} -1.16856e7 q^{50} +7.48870e6 q^{52} +8.77551e7 q^{53} -6.44240e7 q^{55} -9.83450e6 q^{56} -1.19421e8 q^{58} +1.46938e8 q^{59} +1.95719e8 q^{61} +7.82641e7 q^{62} +1.67772e7 q^{64} -3.23474e7 q^{65} -3.14844e8 q^{67} -7.10392e7 q^{68} +4.24801e7 q^{70} -3.34578e8 q^{71} -6.07756e7 q^{73} +2.32696e8 q^{74} -7.27243e7 q^{76} -1.39884e8 q^{77} -2.00915e8 q^{79} -7.24691e7 q^{80} -3.31894e8 q^{82} -4.56308e8 q^{83} +3.06854e8 q^{85} -2.67796e8 q^{86} +2.38635e8 q^{88} +8.73425e8 q^{89} -7.02359e7 q^{91} +3.17875e8 q^{92} +6.53388e8 q^{94} +3.14132e8 q^{95} +7.45228e7 q^{97} +9.22368e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 1024 q^{4} - 1649 q^{5} - 9604 q^{7} + 16384 q^{8}+O(q^{10}) \) 4 * q + 64 * q^2 + 1024 * q^4 - 1649 * q^5 - 9604 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} - 1649 q^{5} - 9604 q^{7} + 16384 q^{8} - 26384 q^{10} + 10544 q^{11} - 108585 q^{13} - 153664 q^{14} + 262144 q^{16} + 529388 q^{17} + 467258 q^{19} - 422144 q^{20} + 168704 q^{22} - 1185163 q^{23} + 1267583 q^{25} - 1737360 q^{26} - 2458624 q^{28} - 1945301 q^{29} + 11130777 q^{31} + 4194304 q^{32} + 8470208 q^{34} + 3959249 q^{35} + 6222809 q^{37} + 7476128 q^{38} - 6754304 q^{40} - 35545545 q^{41} - 7202206 q^{43} + 2699264 q^{44} - 18962608 q^{46} + 20761503 q^{47} + 23059204 q^{49} + 20281328 q^{50} - 27797760 q^{52} - 98635821 q^{53} - 235417840 q^{55} - 39337984 q^{56} - 31124816 q^{58} + 33235282 q^{59} + 105743430 q^{61} + 178092432 q^{62} + 67108864 q^{64} + 362384190 q^{65} - 155997695 q^{67} + 135523328 q^{68} + 63347984 q^{70} - 154553551 q^{71} - 696521780 q^{73} + 99564944 q^{74} + 119618048 q^{76} - 25316144 q^{77} - 477454197 q^{79} - 108068864 q^{80} - 568728720 q^{82} - 835952377 q^{83} - 817473505 q^{85} - 115235296 q^{86} + 43188224 q^{88} + 614491047 q^{89} + 260712585 q^{91} - 303401728 q^{92} + 332184048 q^{94} - 1899413188 q^{95} - 1381829600 q^{97} + 368947264 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 - 1649 * q^5 - 9604 * q^7 + 16384 * q^8 - 26384 * q^10 + 10544 * q^11 - 108585 * q^13 - 153664 * q^14 + 262144 * q^16 + 529388 * q^17 + 467258 * q^19 - 422144 * q^20 + 168704 * q^22 - 1185163 * q^23 + 1267583 * q^25 - 1737360 * q^26 - 2458624 * q^28 - 1945301 * q^29 + 11130777 * q^31 + 4194304 * q^32 + 8470208 * q^34 + 3959249 * q^35 + 6222809 * q^37 + 7476128 * q^38 - 6754304 * q^40 - 35545545 * q^41 - 7202206 * q^43 + 2699264 * q^44 - 18962608 * q^46 + 20761503 * q^47 + 23059204 * q^49 + 20281328 * q^50 - 27797760 * q^52 - 98635821 * q^53 - 235417840 * q^55 - 39337984 * q^56 - 31124816 * q^58 + 33235282 * q^59 + 105743430 * q^61 + 178092432 * q^62 + 67108864 * q^64 + 362384190 * q^65 - 155997695 * q^67 + 135523328 * q^68 + 63347984 * q^70 - 154553551 * q^71 - 696521780 * q^73 + 99564944 * q^74 + 119618048 * q^76 - 25316144 * q^77 - 477454197 * q^79 - 108068864 * q^80 - 568728720 * q^82 - 835952377 * q^83 - 817473505 * q^85 - 115235296 * q^86 + 43188224 * q^88 + 614491047 * q^89 + 260712585 * q^91 - 303401728 * q^92 + 332184048 * q^94 - 1899413188 * q^95 - 1381829600 * q^97 + 368947264 * q^98

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