LMFDB - Embedded newform 342.10.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,10,Mod(1,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, 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("342.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	342.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:	$176.142255968$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-26.2676$ of defining polynomial
Character	$\chi$	$=$	342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +256.000 q^{4} -2126.71 q^{5} +11469.0 q^{7} +4096.00 q^{8} +O(q^{10})$	\(q+16.0000 q^{2} +256.000 q^{4} -2126.71 q^{5} +11469.0 q^{7} +4096.00 q^{8} -34027.4 q^{10} +10430.4 q^{11} +144659. q^{13} +183503. q^{14} +65536.0 q^{16} +654214. q^{17} +130321. q^{19} -544439. q^{20} +166886. q^{22} -1.63517e6 q^{23} +2.56979e6 q^{25} +2.31454e6 q^{26} +2.93605e6 q^{28} -3.60690e6 q^{29} +3.62937e6 q^{31} +1.04858e6 q^{32} +1.04674e7 q^{34} -2.43912e7 q^{35} -1.06553e7 q^{37} +2.08514e6 q^{38} -8.71102e6 q^{40} -1.31851e7 q^{41} -2.73590e6 q^{43} +2.67018e6 q^{44} -2.61627e7 q^{46} +5.26213e7 q^{47} +9.11835e7 q^{49} +4.11167e7 q^{50} +3.70326e7 q^{52} -5.87078e7 q^{53} -2.21825e7 q^{55} +4.69769e7 q^{56} -5.77104e7 q^{58} +7.23340e7 q^{59} -7.46069e7 q^{61} +5.80700e7 q^{62} +1.67772e7 q^{64} -3.07647e8 q^{65} +1.12380e8 q^{67} +1.67479e8 q^{68} -3.90259e8 q^{70} -3.11980e8 q^{71} +3.47317e6 q^{73} -1.70485e8 q^{74} +3.33622e7 q^{76} +1.19626e8 q^{77} +1.96071e8 q^{79} -1.39376e8 q^{80} -2.10961e8 q^{82} +3.30282e8 q^{83} -1.39133e9 q^{85} -4.37745e7 q^{86} +4.27229e7 q^{88} +6.40446e8 q^{89} +1.65908e9 q^{91} -4.18603e8 q^{92} +8.41940e8 q^{94} -2.77156e8 q^{95} +1.56258e9 q^{97} +1.45894e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) $ 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * 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
$5$	−2126.71	−1.52175	−0.760877	−	0.648897i	$-0.775231\pi$
$5$	−2126.71	−1.52175	−0.760877	+	0.648897i	$0.775231\pi$
$6$	0	0
$7$	11469.0	1.80544	0.902720	−	0.430229i	$-0.141567\pi$
$7$	11469.0	1.80544	0.902720	+	0.430229i	$0.141567\pi$
$8$	4096.00	0.353553
$9$	0	0
$10$	−34027.4	−1.07604
$11$	10430.4	0.214800	0.107400	−	0.994216i	$-0.465748\pi$
$11$	10430.4	0.214800	0.107400	+	0.994216i	$0.465748\pi$
$12$	0	0
$13$	144659.	1.40475	0.702375	−	0.711807i	$-0.252123\pi$
$13$	144659.	1.40475	0.702375	+	0.711807i	$0.252123\pi$
$14$	183503.	1.27664
$15$	0	0
$16$	65536.0	0.250000
$17$	654214.	1.89976	0.949882	−	0.312608i	$-0.101203\pi$
$17$	654214.	1.89976	0.949882	+	0.312608i	$0.101203\pi$
$18$	0	0
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−544439.	−0.760877
$21$	0	0
$22$	166886.	0.151886
$23$	−1.63517e6	−1.21839	−0.609196	−	0.793020i	$-0.708508\pi$
$23$	−1.63517e6	−1.21839	−0.609196	+	0.793020i	$0.708508\pi$
$24$	0	0
$25$	2.56979e6	1.31573
$26$	2.31454e6	0.993308
$27$	0	0
$28$	2.93605e6	0.902720
$29$	−3.60690e6	−0.946985	−0.473493	−	0.880798i	$-0.657007\pi$
$29$	−3.60690e6	−0.946985	−0.473493	+	0.880798i	$0.657007\pi$
$30$	0	0
$31$	3.62937e6	0.705836	0.352918	−	0.935654i	$-0.385189\pi$
$31$	3.62937e6	0.705836	0.352918	+	0.935654i	$0.385189\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	1.04674e7	1.34334
$35$	−2.43912e7	−2.74743
$36$	0	0
$37$	−1.06553e7	−0.934668	−0.467334	−	0.884081i	$-0.654785\pi$
$37$	−1.06553e7	−0.934668	−0.467334	+	0.884081i	$0.654785\pi$
$38$	2.08514e6	0.162221
$39$	0	0
$40$	−8.71102e6	−0.538021
$41$	−1.31851e7	−0.728710	−0.364355	−	0.931260i	$-0.618711\pi$
$41$	−1.31851e7	−0.728710	−0.364355	+	0.931260i	$0.618711\pi$
$42$	0	0
$43$	−2.73590e6	−0.122037	−0.0610187	−	0.998137i	$-0.519435\pi$
$43$	−2.73590e6	−0.122037	−0.0610187	+	0.998137i	$0.519435\pi$
$44$	2.67018e6	0.107400
$45$	0	0
$46$	−2.61627e7	−0.861533
$47$	5.26213e7	1.57297	0.786486	−	0.617608i	$-0.211898\pi$
$47$	5.26213e7	1.57297	0.786486	+	0.617608i	$0.211898\pi$
$48$	0	0
$49$	9.11835e7	2.25961
$50$	4.11167e7	0.930364
$51$	0	0
$52$	3.70326e7	0.702375
$53$	−5.87078e7	−1.02201	−0.511004	−	0.859578i	$-0.670726\pi$
$53$	−5.87078e7	−1.02201	−0.511004	+	0.859578i	$0.670726\pi$
$54$	0	0
$55$	−2.21825e7	−0.326872
$56$	4.69769e7	0.638319
$57$	0	0
$58$	−5.77104e7	−0.669620
$59$	7.23340e7	0.777157	0.388578	−	0.921416i	$-0.372966\pi$
$59$	7.23340e7	0.777157	0.388578	+	0.921416i	$0.372966\pi$
$60$	0	0
$61$	−7.46069e7	−0.689914	−0.344957	−	0.938619i	$-0.612106\pi$
$61$	−7.46069e7	−0.689914	−0.344957	+	0.938619i	$0.612106\pi$
$62$	5.80700e7	0.499102
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−3.07647e8	−2.13768
$66$	0	0
$67$	1.12380e8	0.681322	0.340661	−	0.940186i	$-0.389349\pi$
$67$	1.12380e8	0.681322	0.340661	+	0.940186i	$0.389349\pi$
$68$	1.67479e8	0.949882
$69$	0	0
$70$	−3.90259e8	−1.94273
$71$	−3.11980e8	−1.45701	−0.728507	−	0.685038i	$-0.759786\pi$
$71$	−3.11980e8	−1.45701	−0.728507	+	0.685038i	$0.759786\pi$
$72$	0	0
$73$	3.47317e6	0.0143144	0.00715720	−	0.999974i	$-0.497722\pi$
$73$	3.47317e6	0.0143144	0.00715720	+	0.999974i	$0.497722\pi$
$74$	−1.70485e8	−0.660910
$75$	0	0
$76$	3.33622e7	0.114708
$77$	1.19626e8	0.387808
$78$	0	0
$79$	1.96071e8	0.566359	0.283179	−	0.959067i	$-0.408611\pi$
$79$	1.96071e8	0.566359	0.283179	+	0.959067i	$0.408611\pi$
$80$	−1.39376e8	−0.380438
$81$	0	0
$82$	−2.10961e8	−0.515276
$83$	3.30282e8	0.763895	0.381948	−	0.924184i	$-0.375253\pi$
$83$	3.30282e8	0.763895	0.381948	+	0.924184i	$0.375253\pi$
$84$	0	0
$85$	−1.39133e9	−2.89097
$86$	−4.37745e7	−0.0862934
$87$	0	0
$88$	4.27229e7	0.0759431
$89$	6.40446e8	1.08200	0.541000	−	0.841023i	$-0.318046\pi$
$89$	6.40446e8	1.08200	0.541000	+	0.841023i	$0.318046\pi$
$90$	0	0
$91$	1.65908e9	2.53619
$92$	−4.18603e8	−0.609196
$93$	0	0
$94$	8.41940e8	1.11226
$95$	−2.77156e8	−0.349114
$96$	0	0
$97$	1.56258e9	1.79213	0.896064	−	0.443925i	$-0.146414\pi$
$97$	1.56258e9	1.79213	0.896064	+	0.443925i	$0.146414\pi$
$98$	1.45894e9	1.59779
$99$	0	0
$100$	6.57866e8	0.657866
$101$	−2.55498e8	−0.244310	−0.122155	−	0.992511i	$-0.538981\pi$
$101$	−2.55498e8	−0.244310	−0.122155	+	0.992511i	$0.538981\pi$
$102$	0	0
$103$	−9.05731e8	−0.792925	−0.396462	−	0.918051i	$-0.629762\pi$
$103$	−9.05731e8	−0.792925	−0.396462	+	0.918051i	$0.629762\pi$
$104$	5.92521e8	0.496654
$105$	0	0
$106$	−9.39325e8	−0.722669
$107$	3.97489e8	0.293155	0.146578	−	0.989199i	$-0.453174\pi$
$107$	3.97489e8	0.293155	0.146578	+	0.989199i	$0.453174\pi$
$108$	0	0
$109$	5.91761e8	0.401538	0.200769	−	0.979639i	$-0.435656\pi$
$109$	5.91761e8	0.401538	0.200769	+	0.979639i	$0.435656\pi$
$110$	−3.54919e8	−0.231133
$111$	0	0
$112$	7.51630e8	0.451360
$113$	2.57125e9	1.48351	0.741757	−	0.670668i	$-0.233993\pi$
$113$	2.57125e9	1.48351	0.741757	+	0.670668i	$0.233993\pi$
$114$	0	0
$115$	3.47753e9	1.85409
$116$	−9.23367e8	−0.473493
$117$	0	0
$118$	1.15734e9	0.549533
$119$	7.50316e9	3.42991
$120$	0	0
$121$	−2.24915e9	−0.953861
$122$	−1.19371e9	−0.487843
$123$	0	0
$124$	9.29120e8	0.352918
$125$	−1.31147e9	−0.480468
$126$	0	0
$127$	1.47739e9	0.503938	0.251969	−	0.967735i	$-0.418922\pi$
$127$	1.47739e9	0.503938	0.251969	+	0.967735i	$0.418922\pi$
$128$	2.68435e8	0.0883883
$129$	0	0
$130$	−4.92236e9	−1.51157
$131$	5.81972e9	1.72656	0.863279	−	0.504726i	$-0.168407\pi$
$131$	5.81972e9	1.72656	0.863279	+	0.504726i	$0.168407\pi$
$132$	0	0
$133$	1.49465e9	0.414196
$134$	1.79808e9	0.481768
$135$	0	0
$136$	2.67966e9	0.671668
$137$	2.81502e8	0.0682715	0.0341358	−	0.999417i	$-0.489132\pi$
$137$	2.81502e8	0.0682715	0.0341358	+	0.999417i	$0.489132\pi$
$138$	0	0
$139$	−3.71990e9	−0.845210	−0.422605	−	0.906314i	$-0.638884\pi$
$139$	−3.71990e9	−0.845210	−0.422605	+	0.906314i	$0.638884\pi$
$140$	−6.24415e9	−1.37372
$141$	0	0
$142$	−4.99168e9	−1.03027
$143$	1.50884e9	0.301740
$144$	0	0
$145$	7.67085e9	1.44108
$146$	5.55707e7	0.0101218
$147$	0	0
$148$	−2.72775e9	−0.467334
$149$	−2.98264e9	−0.495750	−0.247875	−	0.968792i	$-0.579732\pi$
$149$	−2.98264e9	−0.495750	−0.247875	+	0.968792i	$0.579732\pi$
$150$	0	0
$151$	−1.07704e10	−1.68592	−0.842960	−	0.537977i	$-0.819189\pi$
$151$	−1.07704e10	−1.68592	−0.842960	+	0.537977i	$0.819189\pi$
$152$	5.33795e8	0.0811107
$153$	0	0
$154$	1.91401e9	0.274221
$155$	−7.71864e9	−1.07411
$156$	0	0
$157$	4.65738e8	0.0611777	0.0305889	−	0.999532i	$-0.490262\pi$
$157$	4.65738e8	0.0611777	0.0305889	+	0.999532i	$0.490262\pi$
$158$	3.13714e9	0.400476
$159$	0	0
$160$	−2.23002e9	−0.269011
$161$	−1.87537e10	−2.19973
$162$	0	0
$163$	−3.04519e9	−0.337885	−0.168943	−	0.985626i	$-0.554035\pi$
$163$	−3.04519e9	−0.337885	−0.168943	+	0.985626i	$0.554035\pi$
$164$	−3.37538e9	−0.364355
$165$	0	0
$166$	5.28452e9	0.540155
$167$	5.43187e9	0.540413	0.270206	−	0.962802i	$-0.412908\pi$
$167$	5.43187e9	0.540413	0.270206	+	0.962802i	$0.412908\pi$
$168$	0	0
$169$	1.03216e10	0.973322
$170$	−2.22612e10	−2.04423
$171$	0	0
$172$	−7.00391e8	−0.0610187
$173$	5.67736e8	0.0481880	0.0240940	−	0.999710i	$-0.492330\pi$
$173$	5.67736e8	0.0481880	0.0240940	+	0.999710i	$0.492330\pi$
$174$	0	0
$175$	2.94728e10	2.37548
$176$	6.83566e8	0.0536999
$177$	0	0
$178$	1.02471e10	0.765089
$179$	1.14816e9	0.0835920	0.0417960	−	0.999126i	$-0.486692\pi$
$179$	1.14816e9	0.0835920	0.0417960	+	0.999126i	$0.486692\pi$
$180$	0	0
$181$	−1.40584e10	−0.973606	−0.486803	−	0.873512i	$-0.661837\pi$
$181$	−1.40584e10	−0.973606	−0.486803	+	0.873512i	$0.661837\pi$
$182$	2.65453e10	1.79336
$183$	0	0
$184$	−6.69765e9	−0.430767
$185$	2.26608e10	1.42233
$186$	0	0
$187$	6.82370e9	0.408068
$188$	1.34710e10	0.786486
$189$	0	0
$190$	−4.43449e9	−0.246861
$191$	1.97985e10	1.07642	0.538209	−	0.842811i	$-0.319101\pi$
$191$	1.97985e10	1.07642	0.538209	+	0.842811i	$0.319101\pi$
$192$	0	0
$193$	2.34501e10	1.21657	0.608284	−	0.793719i	$-0.291858\pi$
$193$	2.34501e10	1.21657	0.608284	+	0.793719i	$0.291858\pi$
$194$	2.50013e10	1.26723
$195$	0	0
$196$	2.33430e10	1.12981
$197$	−6.29979e8	−0.0298008	−0.0149004	−	0.999889i	$-0.504743\pi$
$197$	−6.29979e8	−0.0298008	−0.0149004	+	0.999889i	$0.504743\pi$
$198$	0	0
$199$	−6.30124e9	−0.284831	−0.142416	−	0.989807i	$-0.545487\pi$
$199$	−6.30124e9	−0.284831	−0.142416	+	0.989807i	$0.545487\pi$
$200$	1.05259e10	0.465182
$201$	0	0
$202$	−4.08797e9	−0.172753
$203$	−4.13674e10	−1.70973
$204$	0	0
$205$	2.80409e10	1.10892
$206$	−1.44917e10	−0.560682
$207$	0	0
$208$	9.48034e9	0.351187
$209$	1.35930e9	0.0492784
$210$	0	0
$211$	−4.85098e10	−1.68484	−0.842419	−	0.538823i	$-0.818869\pi$
$211$	−4.85098e10	−1.68484	−0.842419	+	0.538823i	$0.818869\pi$
$212$	−1.50292e10	−0.511004
$213$	0	0
$214$	6.35982e9	0.207292
$215$	5.81849e9	0.185711
$216$	0	0
$217$	4.16252e10	1.27435
$218$	9.46818e9	0.283931
$219$	0	0
$220$	−5.67871e9	−0.163436
$221$	9.46377e10	2.66869
$222$	0	0
$223$	2.29208e10	0.620666	0.310333	−	0.950628i	$-0.399560\pi$
$223$	2.29208e10	0.620666	0.310333	+	0.950628i	$0.399560\pi$
$224$	1.20261e10	0.319160
$225$	0	0
$226$	4.11401e10	1.04900
$227$	2.40728e10	0.601742	0.300871	−	0.953665i	$-0.402723\pi$
$227$	2.40728e10	0.601742	0.300871	+	0.953665i	$0.402723\pi$
$228$	0	0
$229$	1.31840e10	0.316801	0.158400	−	0.987375i	$-0.449366\pi$
$229$	1.31840e10	0.316801	0.158400	+	0.987375i	$0.449366\pi$
$230$	5.56406e10	1.31104
$231$	0	0
$232$	−1.47739e10	−0.334810
$233$	−1.64719e10	−0.366135	−0.183068	−	0.983100i	$-0.558603\pi$
$233$	−1.64719e10	−0.366135	−0.183068	+	0.983100i	$0.558603\pi$
$234$	0	0
$235$	−1.11910e11	−2.39367
$236$	1.85175e10	0.388578
$237$	0	0
$238$	1.20051e11	2.42531
$239$	−6.84337e9	−0.135669	−0.0678343	−	0.997697i	$-0.521609\pi$
$239$	−6.84337e9	−0.135669	−0.0678343	+	0.997697i	$0.521609\pi$
$240$	0	0
$241$	6.99690e10	1.33607	0.668034	−	0.744130i	$-0.267136\pi$
$241$	6.99690e10	1.33607	0.668034	+	0.744130i	$0.267136\pi$
$242$	−3.59865e10	−0.674482
$243$	0	0
$244$	−1.90994e10	−0.344957
$245$	−1.93921e11	−3.43857
$246$	0	0
$247$	1.88520e10	0.322272
$248$	1.48659e10	0.249551
$249$	0	0
$250$	−2.09836e10	−0.339742
$251$	6.10283e10	0.970509	0.485254	−	0.874373i	$-0.338727\pi$
$251$	6.10283e10	0.970509	0.485254	+	0.874373i	$0.338727\pi$
$252$	0	0
$253$	−1.70554e10	−0.261710
$254$	2.36382e10	0.356338
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	5.46978e10	0.782115	0.391058	−	0.920366i	$-0.372109\pi$
$257$	5.46978e10	0.782115	0.391058	+	0.920366i	$0.372109\pi$
$258$	0	0
$259$	−1.22205e11	−1.68749
$260$	−7.87578e10	−1.06884
$261$	0	0
$262$	9.31155e10	1.22086
$263$	−6.53058e9	−0.0841688	−0.0420844	−	0.999114i	$-0.513400\pi$
$263$	−6.53058e9	−0.0841688	−0.0420844	+	0.999114i	$0.513400\pi$
$264$	0	0
$265$	1.24855e11	1.55524
$266$	2.39143e10	0.292881
$267$	0	0
$268$	2.87693e10	0.340661
$269$	−1.22877e11	−1.43082	−0.715409	−	0.698706i	$-0.753759\pi$
$269$	−1.22877e11	−1.43082	−0.715409	+	0.698706i	$0.753759\pi$
$270$	0	0
$271$	3.90560e10	0.439872	0.219936	−	0.975514i	$-0.429415\pi$
$271$	3.90560e10	0.439872	0.219936	+	0.975514i	$0.429415\pi$
$272$	4.28746e10	0.474941
$273$	0	0
$274$	4.50404e9	0.0482752
$275$	2.68039e10	0.282619
$276$	0	0
$277$	−2.55807e10	−0.261068	−0.130534	−	0.991444i	$-0.541669\pi$
$277$	−2.55807e10	−0.261068	−0.130534	+	0.991444i	$0.541669\pi$
$278$	−5.95184e10	−0.597654
$279$	0	0
$280$	−9.99064e10	−0.971365
$281$	1.33338e10	0.127578	0.0637888	−	0.997963i	$-0.479682\pi$
$281$	1.33338e10	0.127578	0.0637888	+	0.997963i	$0.479682\pi$
$282$	0	0
$283$	−1.04221e11	−0.965862	−0.482931	−	0.875658i	$-0.660428\pi$
$283$	−1.04221e11	−0.965862	−0.482931	+	0.875658i	$0.660428\pi$
$284$	−7.98668e10	−0.728507
$285$	0	0
$286$	2.41415e10	0.213362
$287$	−1.51219e11	−1.31564
$288$	0	0
$289$	3.09408e11	2.60910
$290$	1.22734e11	1.01900
$291$	0	0
$292$	8.89132e8	0.00715720
$293$	2.48589e11	1.97050	0.985251	−	0.171114i	$-0.0547368\pi$
$293$	2.48589e11	1.97050	0.985251	+	0.171114i	$0.0547368\pi$
$294$	0	0
$295$	−1.53834e11	−1.18264
$296$	−4.36440e10	−0.330455
$297$	0	0
$298$	−4.77222e10	−0.350548
$299$	−2.36541e11	−1.71154
$300$	0	0
$301$	−3.13780e10	−0.220331
$302$	−1.72327e11	−1.19213
$303$	0	0
$304$	8.54072e9	0.0573539
$305$	1.58668e11	1.04988
$306$	0	0
$307$	3.35661e10	0.215664	0.107832	−	0.994169i	$-0.465609\pi$
$307$	3.35661e10	0.215664	0.107832	+	0.994169i	$0.465609\pi$
$308$	3.06242e10	0.193904
$309$	0	0
$310$	−1.23498e11	−0.759510
$311$	−6.13779e10	−0.372041	−0.186020	−	0.982546i	$-0.559559\pi$
$311$	−6.13779e10	−0.372041	−0.186020	+	0.982546i	$0.559559\pi$
$312$	0	0
$313$	−1.45987e11	−0.859738	−0.429869	−	0.902891i	$-0.641440\pi$
$313$	−1.45987e11	−0.859738	−0.429869	+	0.902891i	$0.641440\pi$
$314$	7.45181e9	0.0432592
$315$	0	0
$316$	5.01942e10	0.283179
$317$	−2.34017e10	−0.130161	−0.0650806	−	0.997880i	$-0.520730\pi$
$317$	−2.34017e10	−0.130161	−0.0650806	+	0.997880i	$0.520730\pi$
$318$	0	0
$319$	−3.76214e10	−0.203412
$320$	−3.56804e10	−0.190219
$321$	0	0
$322$	−3.00059e11	−1.55545
$323$	8.52578e10	0.435836
$324$	0	0
$325$	3.71742e11	1.84828
$326$	−4.87230e10	−0.238921
$327$	0	0
$328$	−5.40060e10	−0.257638
$329$	6.03511e11	2.83991
$330$	0	0
$331$	1.52176e11	0.696818	0.348409	−	0.937343i	$-0.386722\pi$
$331$	1.52176e11	0.696818	0.348409	+	0.937343i	$0.386722\pi$
$332$	8.45522e10	0.381948
$333$	0	0
$334$	8.69100e10	0.382129
$335$	−2.39000e11	−1.03680
$336$	0	0
$337$	1.05261e11	0.444565	0.222282	−	0.974982i	$-0.428649\pi$
$337$	1.05261e11	0.444565	0.222282	+	0.974982i	$0.428649\pi$
$338$	1.65146e11	0.688243
$339$	0	0
$340$	−3.56180e11	−1.44549
$341$	3.78558e10	0.151613
$342$	0	0
$343$	5.82967e11	2.27416
$344$	−1.12063e10	−0.0431467
$345$	0	0
$346$	9.08377e9	0.0340740
$347$	2.81412e11	1.04198	0.520992	−	0.853562i	$-0.325562\pi$
$347$	2.81412e11	1.04198	0.520992	+	0.853562i	$0.325562\pi$
$348$	0	0
$349$	3.55958e11	1.28435	0.642176	−	0.766557i	$-0.278032\pi$
$349$	3.55958e11	1.28435	0.642176	+	0.766557i	$0.278032\pi$
$350$	4.71565e11	1.67972
$351$	0	0
$352$	1.09371e10	0.0379715
$353$	−1.35601e11	−0.464813	−0.232406	−	0.972619i	$-0.574660\pi$
$353$	−1.35601e11	−0.464813	−0.232406	+	0.972619i	$0.574660\pi$
$354$	0	0
$355$	6.63492e11	2.21722
$356$	1.63954e11	0.541000
$357$	0	0
$358$	1.83706e10	0.0591085
$359$	2.12047e11	0.673764	0.336882	−	0.941547i	$-0.390628\pi$
$359$	2.12047e11	0.673764	0.336882	+	0.941547i	$0.390628\pi$
$360$	0	0
$361$	1.69836e10	0.0526316
$362$	−2.24935e11	−0.688443
$363$	0	0
$364$	4.24725e11	1.26810
$365$	−7.38644e9	−0.0217830
$366$	0	0
$367$	−4.48163e11	−1.28955	−0.644775	−	0.764372i	$-0.723049\pi$
$367$	−4.48163e11	−1.28955	−0.644775	+	0.764372i	$0.723049\pi$
$368$	−1.07162e11	−0.304598
$369$	0	0
$370$	3.62572e11	1.00574
$371$	−6.73318e11	−1.84517
$372$	0	0
$373$	1.86916e11	0.499985	0.249993	−	0.968248i	$-0.419572\pi$
$373$	1.86916e11	0.499985	0.249993	+	0.968248i	$0.419572\pi$
$374$	1.09179e11	0.288548
$375$	0	0
$376$	2.15537e11	0.556129
$377$	−5.21769e11	−1.33028
$378$	0	0
$379$	−3.54895e11	−0.883535	−0.441768	−	0.897130i	$-0.645648\pi$
$379$	−3.54895e11	−0.883535	−0.441768	+	0.897130i	$0.645648\pi$
$380$	−7.09518e10	−0.174557
$381$	0	0
$382$	3.16775e11	0.761143
$383$	−6.87668e10	−0.163299	−0.0816497	−	0.996661i	$-0.526019\pi$
$383$	−6.87668e10	−0.163299	−0.0816497	+	0.996661i	$0.526019\pi$
$384$	0	0
$385$	−2.54410e11	−0.590147
$386$	3.75201e11	0.860244
$387$	0	0
$388$	4.00020e11	0.896064
$389$	−7.25930e10	−0.160739	−0.0803696	−	0.996765i	$-0.525610\pi$
$389$	−7.25930e10	−0.160739	−0.0803696	+	0.996765i	$0.525610\pi$
$390$	0	0
$391$	−1.06975e12	−2.31466
$392$	3.73488e11	0.798894
$393$	0	0
$394$	−1.00797e10	−0.0210724
$395$	−4.16987e11	−0.861858
$396$	0	0
$397$	2.87651e11	0.581178	0.290589	−	0.956848i	$-0.406149\pi$
$397$	2.87651e11	0.581178	0.290589	+	0.956848i	$0.406149\pi$
$398$	−1.00820e11	−0.201406
$399$	0	0
$400$	1.68414e11	0.328933
$401$	4.88308e11	0.943071	0.471535	−	0.881847i	$-0.343700\pi$
$401$	4.88308e11	0.943071	0.471535	+	0.881847i	$0.343700\pi$
$402$	0	0
$403$	5.25020e11	0.991524
$404$	−6.54076e10	−0.122155
$405$	0	0
$406$	−6.61879e11	−1.20896
$407$	−1.11139e11	−0.200766
$408$	0	0
$409$	5.83827e11	1.03164	0.515821	−	0.856696i	$-0.327487\pi$
$409$	5.83827e11	1.03164	0.515821	+	0.856696i	$0.327487\pi$
$410$	4.48654e11	0.784123
$411$	0	0
$412$	−2.31867e11	−0.396462
$413$	8.29596e11	1.40311
$414$	0	0
$415$	−7.02416e11	−1.16246
$416$	1.51685e11	0.248327
$417$	0	0
$418$	2.17488e10	0.0348451
$419$	2.09427e11	0.331947	0.165974	−	0.986130i	$-0.446923\pi$
$419$	2.09427e11	0.331947	0.165974	+	0.986130i	$0.446923\pi$
$420$	0	0
$421$	−4.21346e11	−0.653687	−0.326844	−	0.945078i	$-0.605985\pi$
$421$	−4.21346e11	−0.653687	−0.326844	+	0.945078i	$0.605985\pi$
$422$	−7.76157e11	−1.19136
$423$	0	0
$424$	−2.40467e11	−0.361335
$425$	1.68119e12	2.49958
$426$	0	0
$427$	−8.55664e11	−1.24560
$428$	1.01757e11	0.146578
$429$	0	0
$430$	9.30958e10	0.131317
$431$	3.62152e11	0.505525	0.252763	−	0.967528i	$-0.418661\pi$
$431$	3.62152e11	0.505525	0.252763	+	0.967528i	$0.418661\pi$
$432$	0	0
$433$	−8.27434e10	−0.113120	−0.0565598	−	0.998399i	$-0.518013\pi$
$433$	−8.27434e10	−0.113120	−0.0565598	+	0.998399i	$0.518013\pi$
$434$	6.66002e11	0.901098
$435$	0	0
$436$	1.51491e11	0.200769
$437$	−2.13097e11	−0.279518
$438$	0	0
$439$	−6.69663e11	−0.860530	−0.430265	−	0.902703i	$-0.641580\pi$
$439$	−6.69663e11	−0.860530	−0.430265	+	0.902703i	$0.641580\pi$
$440$	−9.08593e10	−0.115567
$441$	0	0
$442$	1.51420e12	1.88705
$443$	−5.66791e11	−0.699208	−0.349604	−	0.936898i	$-0.613684\pi$
$443$	−5.66791e11	−0.699208	−0.349604	+	0.936898i	$0.613684\pi$
$444$	0	0
$445$	−1.36205e12	−1.64654
$446$	3.66733e11	0.438877
$447$	0	0
$448$	1.92417e11	0.225680
$449$	−3.81051e11	−0.442461	−0.221230	−	0.975222i	$-0.571007\pi$
$449$	−3.81051e11	−0.442461	−0.221230	+	0.975222i	$0.571007\pi$
$450$	0	0
$451$	−1.37525e11	−0.156527
$452$	6.58241e11	0.741757
$453$	0	0
$454$	3.85165e11	0.425496
$455$	−3.52840e12	−3.85946
$456$	0	0
$457$	−1.09800e12	−1.17755	−0.588775	−	0.808297i	$-0.700390\pi$
$457$	−1.09800e12	−1.17755	−0.588775	+	0.808297i	$0.700390\pi$
$458$	2.10943e11	0.224012
$459$	0	0
$460$	8.90249e11	0.927046
$461$	−6.53157e11	−0.673540	−0.336770	−	0.941587i	$-0.609335\pi$
$461$	−6.53157e11	−0.673540	−0.336770	+	0.941587i	$0.609335\pi$
$462$	0	0
$463$	−9.03119e11	−0.913336	−0.456668	−	0.889637i	$-0.650957\pi$
$463$	−9.03119e11	−0.913336	−0.456668	+	0.889637i	$0.650957\pi$
$464$	−2.36382e11	−0.236746
$465$	0	0
$466$	−2.63550e11	−0.258897
$467$	1.07789e12	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$467$	1.07789e12	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$468$	0	0
$469$	1.28888e12	1.23009
$470$	−1.79057e12	−1.69258
$471$	0	0
$472$	2.96280e11	0.274766
$473$	−2.85365e10	−0.0262136
$474$	0	0
$475$	3.34898e11	0.301850
$476$	1.92081e12	1.71495
$477$	0	0
$478$	−1.09494e11	−0.0959322
$479$	1.13640e12	0.986329	0.493165	−	0.869936i	$-0.335840\pi$
$479$	1.13640e12	0.986329	0.493165	+	0.869936i	$0.335840\pi$
$480$	0	0
$481$	−1.54138e12	−1.31297
$482$	1.11950e12	0.944743
$483$	0	0
$484$	−5.75784e11	−0.476931
$485$	−3.32316e12	−2.72718
$486$	0	0
$487$	2.14926e11	0.173144	0.0865721	−	0.996246i	$-0.472409\pi$
$487$	2.14926e11	0.173144	0.0865721	+	0.996246i	$0.472409\pi$
$488$	−3.05590e11	−0.243921
$489$	0	0
$490$	−3.10274e12	−2.43144
$491$	−1.98317e12	−1.53991	−0.769953	−	0.638100i	$-0.779720\pi$
$491$	−1.98317e12	−1.53991	−0.769953	+	0.638100i	$0.779720\pi$
$492$	0	0
$493$	−2.35969e12	−1.79905
$494$	3.01633e11	0.227881
$495$	0	0
$496$	2.37855e11	0.176459
$497$	−3.57809e12	−2.63055
$498$	0	0
$499$	1.66297e12	1.20070	0.600348	−	0.799739i	$-0.295029\pi$
$499$	1.66297e12	1.20070	0.600348	+	0.799739i	$0.295029\pi$
$500$	−3.35737e11	−0.240234
$501$	0	0
$502$	9.76453e11	0.686253
$503$	−2.73936e12	−1.90806	−0.954031	−	0.299707i	$-0.903111\pi$
$503$	−2.73936e12	−1.90806	−0.954031	+	0.299707i	$0.903111\pi$
$504$	0	0
$505$	5.43372e11	0.371780
$506$	−2.72887e11	−0.185057
$507$	0	0
$508$	3.78211e11	0.251969
$509$	1.41595e12	0.935016	0.467508	−	0.883989i	$-0.345152\pi$
$509$	1.41595e12	0.935016	0.467508	+	0.883989i	$0.345152\pi$
$510$	0	0
$511$	3.98337e10	0.0258438
$512$	6.87195e10	0.0441942
$513$	0	0
$514$	8.75165e11	0.553039
$515$	1.92623e12	1.20664
$516$	0	0
$517$	5.48860e11	0.337874
$518$	−1.95528e12	−1.19323
$519$	0	0
$520$	−1.26012e12	−0.755785
$521$	2.76092e12	1.64166	0.820832	−	0.571170i	$-0.193510\pi$
$521$	2.76092e12	1.64166	0.820832	+	0.571170i	$0.193510\pi$
$522$	0	0
$523$	5.34558e11	0.312419	0.156209	−	0.987724i	$-0.450073\pi$
$523$	5.34558e11	0.312419	0.156209	+	0.987724i	$0.450073\pi$
$524$	1.48985e12	0.863279
$525$	0	0
$526$	−1.04489e11	−0.0595163
$527$	2.37439e12	1.34092
$528$	0	0
$529$	8.72619e11	0.484478
$530$	1.99768e12	1.09972
$531$	0	0
$532$	3.82630e11	0.207098
$533$	−1.90733e12	−1.02366
$534$	0	0
$535$	−8.45346e11	−0.446110
$536$	4.60309e11	0.240884
$537$	0	0
$538$	−1.96603e12	−1.01174
$539$	9.51079e11	0.485364
$540$	0	0
$541$	−3.40287e12	−1.70788	−0.853941	−	0.520369i	$-0.825794\pi$
$541$	−3.40287e12	−1.70788	−0.853941	+	0.520369i	$0.825794\pi$
$542$	6.24896e11	0.311036
$543$	0	0
$544$	6.85993e11	0.335834
$545$	−1.25851e12	−0.611042
$546$	0	0
$547$	−1.07691e12	−0.514321	−0.257161	−	0.966369i	$-0.582787\pi$
$547$	−1.07691e12	−0.514321	−0.257161	+	0.966369i	$0.582787\pi$
$548$	7.20646e10	0.0341358
$549$	0	0
$550$	4.28863e11	0.199842
$551$	−4.70055e11	−0.217253
$552$	0	0
$553$	2.24873e12	1.02253
$554$	−4.09292e11	−0.184603
$555$	0	0
$556$	−9.52295e11	−0.422605
$557$	−3.44597e12	−1.51692	−0.758460	−	0.651720i	$-0.774048\pi$
$557$	−3.44597e12	−1.51692	−0.758460	+	0.651720i	$0.774048\pi$
$558$	0	0
$559$	−3.95772e11	−0.171432
$560$	−1.59850e12	−0.686858
$561$	0	0
$562$	2.13340e11	0.0902110
$563$	−3.12894e12	−1.31253	−0.656266	−	0.754530i	$-0.727865\pi$
$563$	−3.12894e12	−1.31253	−0.656266	+	0.754530i	$0.727865\pi$
$564$	0	0
$565$	−5.46832e12	−2.25754
$566$	−1.66753e12	−0.682968
$567$	0	0
$568$	−1.27787e12	−0.515133
$569$	3.86048e12	1.54396	0.771980	−	0.635647i	$-0.219266\pi$
$569$	3.86048e12	1.54396	0.771980	+	0.635647i	$0.219266\pi$
$570$	0	0
$571$	4.04984e12	1.59432	0.797160	−	0.603768i	$-0.206335\pi$
$571$	4.04984e12	1.59432	0.797160	+	0.603768i	$0.206335\pi$
$572$	3.86264e11	0.150870
$573$	0	0
$574$	−2.41951e12	−0.930300
$575$	−4.20204e12	−1.60308
$576$	0	0
$577$	1.81317e11	0.0681001	0.0340500	−	0.999420i	$-0.489159\pi$
$577$	1.81317e11	0.0681001	0.0340500	+	0.999420i	$0.489159\pi$
$578$	4.95053e12	1.84492
$579$	0	0
$580$	1.96374e12	0.720539
$581$	3.78799e12	1.37917
$582$	0	0
$583$	−6.12345e11	−0.219527
$584$	1.42261e10	0.00506091
$585$	0	0
$586$	3.97742e12	1.39336
$587$	−4.63066e11	−0.160980	−0.0804900	−	0.996755i	$-0.525649\pi$
$587$	−4.63066e11	−0.160980	−0.0804900	+	0.996755i	$0.525649\pi$
$588$	0	0
$589$	4.72984e11	0.161930
$590$	−2.46134e12	−0.836253
$591$	0	0
$592$	−6.98305e11	−0.233667
$593$	−3.90685e12	−1.29742	−0.648711	−	0.761035i	$-0.724692\pi$
$593$	−3.90685e12	−1.29742	−0.648711	+	0.761035i	$0.724692\pi$
$594$	0	0
$595$	−1.59571e13	−5.21948
$596$	−7.63555e11	−0.247875
$597$	0	0
$598$	−3.78465e12	−1.21024
$599$	4.47991e11	0.142183	0.0710916	−	0.997470i	$-0.477352\pi$
$599$	4.47991e11	0.142183	0.0710916	+	0.997470i	$0.477352\pi$
$600$	0	0
$601$	2.01818e12	0.630994	0.315497	−	0.948927i	$-0.397829\pi$
$601$	2.01818e12	0.630994	0.315497	+	0.948927i	$0.397829\pi$
$602$	−5.02048e11	−0.155798
$603$	0	0
$604$	−2.75723e12	−0.842960
$605$	4.78331e12	1.45154
$606$	0	0
$607$	6.23030e12	1.86277	0.931387	−	0.364032i	$-0.118600\pi$
$607$	6.23030e12	1.86277	0.931387	+	0.364032i	$0.118600\pi$
$608$	1.36651e11	0.0405554
$609$	0	0
$610$	2.53868e12	0.742376
$611$	7.61212e12	2.20963
$612$	0	0
$613$	3.59461e11	0.102820	0.0514102	−	0.998678i	$-0.483628\pi$
$613$	3.59461e11	0.102820	0.0514102	+	0.998678i	$0.483628\pi$
$614$	5.37058e11	0.152498
$615$	0	0
$616$	4.89987e11	0.137111
$617$	−4.00051e12	−1.11130	−0.555650	−	0.831416i	$-0.687531\pi$
$617$	−4.00051e12	−1.11130	−0.555650	+	0.831416i	$0.687531\pi$
$618$	0	0
$619$	−3.72631e12	−1.02017	−0.510084	−	0.860125i	$-0.670386\pi$
$619$	−3.72631e12	−1.02017	−0.510084	+	0.860125i	$0.670386\pi$
$620$	−1.97597e12	−0.537054
$621$	0	0
$622$	−9.82046e11	−0.263072
$623$	7.34525e12	1.95349
$624$	0	0
$625$	−2.22999e12	−0.584580
$626$	−2.33580e12	−0.607926
$627$	0	0
$628$	1.19229e11	0.0305889
$629$	−6.97084e12	−1.77565
$630$	0	0
$631$	5.38677e11	0.135268	0.0676342	−	0.997710i	$-0.478455\pi$
$631$	5.38677e11	0.135268	0.0676342	+	0.997710i	$0.478455\pi$
$632$	8.03107e11	0.200238
$633$	0	0
$634$	−3.74428e11	−0.0920378
$635$	−3.14198e12	−0.766869
$636$	0	0
$637$	1.31905e13	3.17419
$638$	−6.01942e11	−0.143834
$639$	0	0
$640$	−5.70886e11	−0.134505
$641$	−5.87686e12	−1.37494	−0.687471	−	0.726212i	$-0.741279\pi$
$641$	−5.87686e12	−1.37494	−0.687471	+	0.726212i	$0.741279\pi$
$642$	0	0
$643$	3.03822e12	0.700923	0.350462	−	0.936577i	$-0.386025\pi$
$643$	3.03822e12	0.700923	0.350462	+	0.936577i	$0.386025\pi$
$644$	−4.80094e12	−1.09987
$645$	0	0
$646$	1.36413e12	0.308182
$647$	−1.92485e12	−0.431844	−0.215922	−	0.976411i	$-0.569276\pi$
$647$	−1.92485e12	−0.431844	−0.215922	+	0.976411i	$0.569276\pi$
$648$	0	0
$649$	7.54472e11	0.166933
$650$	5.94788e12	1.30693
$651$	0	0
$652$	−7.79567e11	−0.168943
$653$	4.80531e12	1.03422	0.517109	−	0.855920i	$-0.327008\pi$
$653$	4.80531e12	1.03422	0.517109	+	0.855920i	$0.327008\pi$
$654$	0	0
$655$	−1.23769e13	−2.62740
$656$	−8.64097e11	−0.182178
$657$	0	0
$658$	9.65618e12	2.00812
$659$	−7.75087e12	−1.60091	−0.800454	−	0.599394i	$-0.795408\pi$
$659$	−7.75087e12	−1.60091	−0.800454	+	0.599394i	$0.795408\pi$
$660$	0	0
$661$	4.58458e12	0.934100	0.467050	−	0.884231i	$-0.345317\pi$
$661$	4.58458e12	0.934100	0.467050	+	0.884231i	$0.345317\pi$
$662$	2.43481e12	0.492725
$663$	0	0
$664$	1.35284e12	0.270078
$665$	−3.17869e12	−0.630305
$666$	0	0
$667$	5.89789e12	1.15380
$668$	1.39056e12	0.270206
$669$	0	0
$670$	−3.82400e12	−0.733131
$671$	−7.78179e11	−0.148193
$672$	0	0
$673$	−7.38830e12	−1.38828	−0.694139	−	0.719841i	$-0.744215\pi$
$673$	−7.38830e12	−1.38828	−0.694139	+	0.719841i	$0.744215\pi$
$674$	1.68418e12	0.314355
$675$	0	0
$676$	2.64233e12	0.486661
$677$	3.48101e12	0.636878	0.318439	−	0.947943i	$-0.396841\pi$
$677$	3.48101e12	0.636878	0.318439	+	0.947943i	$0.396841\pi$
$678$	0	0
$679$	1.79212e13	3.23558
$680$	−5.69887e12	−1.02211
$681$	0	0
$682$	6.05692e11	0.107207
$683$	−6.60095e12	−1.16068	−0.580341	−	0.814373i	$-0.697081\pi$
$683$	−6.60095e12	−1.16068	−0.580341	+	0.814373i	$0.697081\pi$
$684$	0	0
$685$	−5.98675e11	−0.103892
$686$	9.32746e12	1.60807
$687$	0	0
$688$	−1.79300e11	−0.0305093
$689$	−8.49259e12	−1.43567
$690$	0	0
$691$	−8.94184e12	−1.49202	−0.746012	−	0.665933i	$-0.768034\pi$
$691$	−8.94184e12	−1.49202	−0.746012	+	0.665933i	$0.768034\pi$
$692$	1.45340e11	0.0240940
$693$	0	0
$694$	4.50260e12	0.736793
$695$	7.91117e12	1.28620
$696$	0	0
$697$	−8.62586e12	−1.38438
$698$	5.69532e12	0.908174
$699$	0	0
$700$	7.54505e12	1.18774
$701$	9.13468e11	0.142877	0.0714385	−	0.997445i	$-0.477241\pi$
$701$	9.13468e11	0.142877	0.0714385	+	0.997445i	$0.477241\pi$
$702$	0	0
$703$	−1.38861e12	−0.214428
$704$	1.74993e11	0.0268499
$705$	0	0
$706$	−2.16962e12	−0.328672
$707$	−2.93030e12	−0.441088
$708$	0	0
$709$	2.22286e12	0.330372	0.165186	−	0.986262i	$-0.447178\pi$
$709$	2.22286e12	0.330372	0.165186	+	0.986262i	$0.447178\pi$
$710$	1.06159e13	1.56781
$711$	0	0
$712$	2.62327e12	0.382545
$713$	−5.93463e12	−0.859985
$714$	0	0
$715$	−3.20888e12	−0.459173
$716$	2.93930e11	0.0417960
$717$	0	0
$718$	3.39276e12	0.476423
$719$	1.38107e12	0.192724	0.0963622	−	0.995346i	$-0.469279\pi$
$719$	1.38107e12	0.192724	0.0963622	+	0.995346i	$0.469279\pi$
$720$	0	0
$721$	−1.03878e13	−1.43158
$722$	2.71737e11	0.0372161
$723$	0	0
$724$	−3.59896e12	−0.486803
$725$	−9.26898e12	−1.24598
$726$	0	0
$727$	−1.01054e13	−1.34168	−0.670838	−	0.741604i	$-0.734065\pi$
$727$	−1.01054e13	−1.34168	−0.670838	+	0.741604i	$0.734065\pi$
$728$	6.79561e12	0.896679
$729$	0	0
$730$	−1.18183e11	−0.0154029
$731$	−1.78987e12	−0.231842
$732$	0	0
$733$	−2.46166e12	−0.314964	−0.157482	−	0.987522i	$-0.550338\pi$
$733$	−2.46166e12	−0.314964	−0.157482	+	0.987522i	$0.550338\pi$
$734$	−7.17060e12	−0.911850
$735$	0	0
$736$	−1.71460e12	−0.215383
$737$	1.17217e12	0.146348
$738$	0	0
$739$	8.80833e12	1.08641	0.543205	−	0.839600i	$-0.317211\pi$
$739$	8.80833e12	1.08641	0.543205	+	0.839600i	$0.317211\pi$
$740$	5.80115e12	0.711167
$741$	0	0
$742$	−1.07731e13	−1.30474
$743$	2.35539e11	0.0283539	0.0141770	−	0.999900i	$-0.495487\pi$
$743$	2.35539e11	0.0283539	0.0141770	+	0.999900i	$0.495487\pi$
$744$	0	0
$745$	6.34322e12	0.754409
$746$	2.99066e12	0.353543
$747$	0	0
$748$	1.74687e12	0.204034
$749$	4.55879e12	0.529275
$750$	0	0
$751$	−6.15738e12	−0.706344	−0.353172	−	0.935558i	$-0.614897\pi$
$751$	−6.15738e12	−0.706344	−0.353172	+	0.935558i	$0.614897\pi$
$752$	3.44859e12	0.393243
$753$	0	0
$754$	−8.34831e12	−0.940648
$755$	2.29056e13	2.56555
$756$	0	0
$757$	1.74954e12	0.193639	0.0968195	−	0.995302i	$-0.469133\pi$
$757$	1.74954e12	0.193639	0.0968195	+	0.995302i	$0.469133\pi$
$758$	−5.67833e12	−0.624754
$759$	0	0
$760$	−1.13523e12	−0.123430
$761$	1.52097e13	1.64395	0.821976	−	0.569522i	$-0.192872\pi$
$761$	1.52097e13	1.64395	0.821976	+	0.569522i	$0.192872\pi$
$762$	0	0
$763$	6.78688e12	0.724953
$764$	5.06840e12	0.538209
$765$	0	0
$766$	−1.10027e12	−0.115470
$767$	1.04637e13	1.09171
$768$	0	0
$769$	−9.63035e12	−0.993055	−0.496528	−	0.868021i	$-0.665392\pi$
$769$	−9.63035e12	−0.993055	−0.496528	+	0.868021i	$0.665392\pi$
$770$	−4.07056e12	−0.417297
$771$	0	0
$772$	6.00322e12	0.608284
$773$	−1.49129e13	−1.50230	−0.751148	−	0.660134i	$-0.770499\pi$
$773$	−1.49129e13	−1.50230	−0.751148	+	0.660134i	$0.770499\pi$
$774$	0	0
$775$	9.32673e12	0.928692
$776$	6.40032e12	0.633613
$777$	0	0
$778$	−1.16149e12	−0.113660
$779$	−1.71829e12	−0.167178
$780$	0	0
$781$	−3.25407e12	−0.312966
$782$	−1.71160e13	−1.63671
$783$	0	0
$784$	5.97580e12	0.564903
$785$	−9.90492e11	−0.0930974
$786$	0	0
$787$	1.51917e13	1.41163	0.705816	−	0.708396i	$-0.250581\pi$
$787$	1.51917e13	1.41163	0.705816	+	0.708396i	$0.250581\pi$
$788$	−1.61275e11	−0.0149004
$789$	0	0
$790$	−6.67180e12	−0.609426
$791$	2.94896e13	2.67840
$792$	0	0
$793$	−1.07925e13	−0.969157
$794$	4.60242e12	0.410955
$795$	0	0
$796$	−1.61312e12	−0.142416
$797$	−1.37336e13	−1.20565	−0.602827	−	0.797872i	$-0.705959\pi$
$797$	−1.37336e13	−1.20565	−0.602827	+	0.797872i	$0.705959\pi$
$798$	0	0
$799$	3.44256e13	2.98828
$800$	2.69462e12	0.232591
$801$	0	0
$802$	7.81293e12	0.666852
$803$	3.62265e10	0.00307473
$804$	0	0
$805$	3.98837e13	3.34745
$806$	8.40032e12	0.701113
$807$	0	0
$808$	−1.04652e12	−0.0863767
$809$	1.54605e12	0.126898	0.0634491	−	0.997985i	$-0.479790\pi$
$809$	1.54605e12	0.126898	0.0634491	+	0.997985i	$0.479790\pi$
$810$	0	0
$811$	1.50745e13	1.22363	0.611814	−	0.791002i	$-0.290440\pi$
$811$	1.50745e13	1.22363	0.611814	+	0.791002i	$0.290440\pi$
$812$	−1.05901e13	−0.854863
$813$	0	0
$814$	−1.77822e12	−0.141963
$815$	6.47624e12	0.514178
$816$	0	0
$817$	−3.56546e11	−0.0279973
$818$	9.34123e12	0.729482
$819$	0	0
$820$	7.17846e12	0.554459
$821$	−7.55550e12	−0.580389	−0.290194	−	0.956968i	$-0.593720\pi$
$821$	−7.55550e12	−0.580389	−0.290194	+	0.956968i	$0.593720\pi$
$822$	0	0
$823$	3.21334e12	0.244150	0.122075	−	0.992521i	$-0.461045\pi$
$823$	3.21334e12	0.244150	0.122075	+	0.992521i	$0.461045\pi$
$824$	−3.70988e12	−0.280341
$825$	0	0
$826$	1.32735e13	0.992148
$827$	−8.79853e12	−0.654087	−0.327043	−	0.945009i	$-0.606052\pi$
$827$	−8.79853e12	−0.654087	−0.327043	+	0.945009i	$0.606052\pi$
$828$	0	0
$829$	2.39558e13	1.76163	0.880816	−	0.473459i	$-0.156995\pi$
$829$	2.39558e13	1.76163	0.880816	+	0.473459i	$0.156995\pi$
$830$	−1.12387e13	−0.821983
$831$	0	0
$832$	2.42697e12	0.175594
$833$	5.96535e13	4.29273
$834$	0	0
$835$	−1.15520e13	−0.822375
$836$	3.47980e11	0.0246392
$837$	0	0
$838$	3.35083e12	0.234722
$839$	2.38372e13	1.66083	0.830417	−	0.557143i	$-0.188103\pi$
$839$	2.38372e13	1.66083	0.830417	+	0.557143i	$0.188103\pi$
$840$	0	0
$841$	−1.49741e12	−0.103219
$842$	−6.74154e12	−0.462227
$843$	0	0
$844$	−1.24185e13	−0.842419
$845$	−2.19511e13	−1.48116
$846$	0	0
$847$	−2.57955e13	−1.72214
$848$	−3.84747e12	−0.255502
$849$	0	0
$850$	2.68991e13	1.76747
$851$	1.74232e13	1.13879
$852$	0	0
$853$	1.15908e13	0.749621	0.374811	−	0.927101i	$-0.377708\pi$
$853$	1.15908e13	0.749621	0.374811	+	0.927101i	$0.377708\pi$
$854$	−1.36906e13	−0.880771
$855$	0	0
$856$	1.62811e12	0.103646
$857$	−2.40055e13	−1.52019	−0.760093	−	0.649815i	$-0.774846\pi$
$857$	−2.40055e13	−1.52019	−0.760093	+	0.649815i	$0.774846\pi$
$858$	0	0
$859$	−1.28254e13	−0.803712	−0.401856	−	0.915703i	$-0.631635\pi$
$859$	−1.28254e13	−0.803712	−0.401856	+	0.915703i	$0.631635\pi$
$860$	1.48953e12	0.0928553
$861$	0	0
$862$	5.79443e12	0.357460
$863$	−1.10966e13	−0.680994	−0.340497	−	0.940246i	$-0.610595\pi$
$863$	−1.10966e13	−0.680994	−0.340497	+	0.940246i	$0.610595\pi$
$864$	0	0
$865$	−1.20741e12	−0.0733302
$866$	−1.32390e12	−0.0799877
$867$	0	0
$868$	1.06560e13	0.637173
$869$	2.04510e12	0.121654
$870$	0	0
$871$	1.62567e13	0.957087
$872$	2.42385e12	0.141965
$873$	0	0
$874$	−3.40955e12	−0.197649
$875$	−1.50412e13	−0.867455
$876$	0	0
$877$	2.34043e12	0.133597	0.0667986	−	0.997766i	$-0.478721\pi$
$877$	2.34043e12	0.133597	0.0667986	+	0.997766i	$0.478721\pi$
$878$	−1.07146e13	−0.608486
$879$	0	0
$880$	−1.45375e12	−0.0817180
$881$	1.38455e12	0.0774315	0.0387158	−	0.999250i	$-0.487673\pi$
$881$	1.38455e12	0.0774315	0.0387158	+	0.999250i	$0.487673\pi$
$882$	0	0
$883$	−6.13771e12	−0.339769	−0.169884	−	0.985464i	$-0.554339\pi$
$883$	−6.13771e12	−0.339769	−0.169884	+	0.985464i	$0.554339\pi$
$884$	2.42272e13	1.33435
$885$	0	0
$886$	−9.06866e12	−0.494415
$887$	−8.64012e12	−0.468666	−0.234333	−	0.972156i	$-0.575291\pi$
$887$	−8.64012e12	−0.468666	−0.234333	+	0.972156i	$0.575291\pi$
$888$	0	0
$889$	1.69441e13	0.909830
$890$	−2.17927e13	−1.16428
$891$	0	0
$892$	5.86772e12	0.310333
$893$	6.85766e12	0.360864
$894$	0	0
$895$	−2.44181e12	−0.127206
$896$	3.07868e12	0.159580
$897$	0	0
$898$	−6.09682e12	−0.312867
$899$	−1.30908e13	−0.668417
$900$	0	0
$901$	−3.84075e13	−1.94157
$902$	−2.20041e12	−0.110681
$903$	0	0
$904$	1.05319e13	0.524502
$905$	2.98983e13	1.48159
$906$	0	0
$907$	−3.36715e13	−1.65207	−0.826037	−	0.563616i	$-0.809410\pi$
$907$	−3.36715e13	−1.65207	−0.826037	+	0.563616i	$0.809410\pi$
$908$	6.16263e12	0.300871
$909$	0	0
$910$	−5.64544e13	−2.72905
$911$	−2.03568e13	−0.979211	−0.489606	−	0.871944i	$-0.662859\pi$
$911$	−2.03568e13	−0.979211	−0.489606	+	0.871944i	$0.662859\pi$
$912$	0	0
$913$	3.44497e12	0.164084
$914$	−1.75680e13	−0.832654
$915$	0	0
$916$	3.37509e12	0.158400
$917$	6.67462e13	3.11720
$918$	0	0
$919$	2.44953e13	1.13282	0.566412	−	0.824122i	$-0.308331\pi$
$919$	2.44953e13	1.13282	0.566412	+	0.824122i	$0.308331\pi$
$920$	1.42440e13	0.655520
$921$	0	0
$922$	−1.04505e13	−0.476265
$923$	−4.51306e13	−2.04674
$924$	0	0
$925$	−2.73819e13	−1.22977
$926$	−1.44499e13	−0.645826
$927$	0	0
$928$	−3.78211e12	−0.167405
$929$	−2.79588e13	−1.23154	−0.615768	−	0.787928i	$-0.711154\pi$
$929$	−2.79588e13	−1.23154	−0.615768	+	0.787928i	$0.711154\pi$
$930$	0	0
$931$	1.18831e13	0.518391
$932$	−4.21680e12	−0.183068
$933$	0	0
$934$	1.72462e13	0.741536
$935$	−1.45121e13	−0.620979
$936$	0	0
$937$	−8.07789e12	−0.342349	−0.171175	−	0.985241i	$-0.554756\pi$
$937$	−8.07789e12	−0.342349	−0.171175	+	0.985241i	$0.554756\pi$
$938$	2.06221e13	0.869802
$939$	0	0
$940$	−2.86491e13	−1.19684
$941$	−1.80335e12	−0.0749768	−0.0374884	−	0.999297i	$-0.511936\pi$
$941$	−1.80335e12	−0.0749768	−0.0374884	+	0.999297i	$0.511936\pi$
$942$	0	0
$943$	2.15598e13	0.887855
$944$	4.74048e12	0.194289
$945$	0	0
$946$	−4.56584e11	−0.0185358
$947$	−1.33152e13	−0.537989	−0.268995	−	0.963142i	$-0.586691\pi$
$947$	−1.33152e13	−0.537989	−0.268995	+	0.963142i	$0.586691\pi$
$948$	0	0
$949$	5.02424e11	0.0201082
$950$	5.35836e12	0.213440
$951$	0	0
$952$	3.07329e13	1.21266
$953$	3.50858e13	1.37789	0.688943	−	0.724815i	$-0.258075\pi$
$953$	3.50858e13	1.37789	0.688943	+	0.724815i	$0.258075\pi$
$954$	0	0
$955$	−4.21057e13	−1.63804
$956$	−1.75190e12	−0.0678343
$957$	0	0
$958$	1.81824e13	0.697440
$959$	3.22854e12	0.123260
$960$	0	0
$961$	−1.32673e13	−0.501795
$962$	−2.46620e13	−0.928413
$963$	0	0
$964$	1.79121e13	0.668034
$965$	−4.98716e13	−1.85132
$966$	0	0
$967$	3.33371e13	1.22605	0.613026	−	0.790063i	$-0.289952\pi$
$967$	3.33371e13	1.22605	0.613026	+	0.790063i	$0.289952\pi$
$968$	−9.21254e12	−0.337241
$969$	0	0
$970$	−5.31705e13	−1.92840
$971$	3.31130e13	1.19540	0.597698	−	0.801722i	$-0.296082\pi$
$971$	3.31130e13	1.19540	0.597698	+	0.801722i	$0.296082\pi$
$972$	0	0
$973$	−4.26634e13	−1.52598
$974$	3.43881e12	0.122431
$975$	0	0
$976$	−4.88944e12	−0.172478
$977$	1.28147e12	0.0449969	0.0224984	−	0.999747i	$-0.492838\pi$
$977$	1.28147e12	0.0449969	0.0224984	+	0.999747i	$0.492838\pi$
$978$	0	0
$979$	6.68009e12	0.232413
$980$	−4.96439e13	−1.71929
$981$	0	0
$982$	−3.17308e13	−1.08888
$983$	−3.93077e13	−1.34272	−0.671362	−	0.741130i	$-0.734290\pi$
$983$	−3.93077e13	−1.34272	−0.671362	+	0.741130i	$0.734290\pi$
$984$	0	0
$985$	1.33979e12	0.0453495
$986$	−3.77550e13	−1.27212
$987$	0	0
$988$	4.82612e12	0.161136
$989$	4.47366e12	0.148689
$990$	0	0
$991$	−3.13171e13	−1.03145	−0.515727	−	0.856753i	$-0.672478\pi$
$991$	−3.13171e13	−1.03145	−0.515727	+	0.856753i	$0.672478\pi$
$992$	3.80567e12	0.124775
$993$	0	0
$994$	−5.72494e13	−1.86008
$995$	1.34010e13	0.433443
$996$	0	0
$997$	−8.04007e12	−0.257710	−0.128855	−	0.991663i	$-0.541130\pi$
$997$	−8.04007e12	−0.257710	−0.128855	+	0.991663i	$0.541130\pi$
$998$	2.66076e13	0.849021
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.10.a.l.1.1		4
3.2	odd	2		38.10.a.d.1.3	✓	4
12.11	even	2		304.10.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.3	✓	4	3.2	odd	2
304.10.a.e.1.2		4	12.11	even	2
342.10.a.l.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	342.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +256.000 q^{4} -2126.71 q^{5} +11469.0 q^{7} +4096.00 q^{8} +O(q^{10})\)	\(q+16.0000 q^{2} +256.000 q^{4} -2126.71 q^{5} +11469.0 q^{7} +4096.00 q^{8} -34027.4 q^{10} +10430.4 q^{11} +144659. q^{13} +183503. q^{14} +65536.0 q^{16} +654214. q^{17} +130321. q^{19} -544439. q^{20} +166886. q^{22} -1.63517e6 q^{23} +2.56979e6 q^{25} +2.31454e6 q^{26} +2.93605e6 q^{28} -3.60690e6 q^{29} +3.62937e6 q^{31} +1.04858e6 q^{32} +1.04674e7 q^{34} -2.43912e7 q^{35} -1.06553e7 q^{37} +2.08514e6 q^{38} -8.71102e6 q^{40} -1.31851e7 q^{41} -2.73590e6 q^{43} +2.67018e6 q^{44} -2.61627e7 q^{46} +5.26213e7 q^{47} +9.11835e7 q^{49} +4.11167e7 q^{50} +3.70326e7 q^{52} -5.87078e7 q^{53} -2.21825e7 q^{55} +4.69769e7 q^{56} -5.77104e7 q^{58} +7.23340e7 q^{59} -7.46069e7 q^{61} +5.80700e7 q^{62} +1.67772e7 q^{64} -3.07647e8 q^{65} +1.12380e8 q^{67} +1.67479e8 q^{68} -3.90259e8 q^{70} -3.11980e8 q^{71} +3.47317e6 q^{73} -1.70485e8 q^{74} +3.33622e7 q^{76} +1.19626e8 q^{77} +1.96071e8 q^{79} -1.39376e8 q^{80} -2.10961e8 q^{82} +3.30282e8 q^{83} -1.39133e9 q^{85} -4.37745e7 q^{86} +4.27229e7 q^{88} +6.40446e8 q^{89} +1.65908e9 q^{91} -4.18603e8 q^{92} +8.41940e8 q^{94} -2.77156e8 q^{95} +1.56258e9 q^{97} +1.45894e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * q^98

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