LMFDB - Embedded newform 98.10.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.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:	$50.4735119441$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{4817})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 2411x^{2} + 2412x + 1444802 $ x^4 - 2x^3 - 2411x^2 + 2412*x + 1444802
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-32.7881$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} -191.777 q^{3} +256.000 q^{4} -33.5898 q^{5} +3068.43 q^{6} -4096.00 q^{8} +17095.5 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -191.777 q^{3} +256.000 q^{4} -33.5898 q^{5} +3068.43 q^{6} -4096.00 q^{8} +17095.5 q^{9} +537.437 q^{10} -51540.4 q^{11} -49094.9 q^{12} -113303. q^{13} +6441.76 q^{15} +65536.0 q^{16} +461667. q^{17} -273528. q^{18} +836657. q^{19} -8598.99 q^{20} +824646. q^{22} +299404. q^{23} +785519. q^{24} -1.95200e6 q^{25} +1.81284e6 q^{26} +496229. q^{27} +2.58319e6 q^{29} -103068. q^{30} +6.84324e6 q^{31} -1.04858e6 q^{32} +9.88427e6 q^{33} -7.38666e6 q^{34} +4.37644e6 q^{36} +1.39547e7 q^{37} -1.33865e7 q^{38} +2.17288e7 q^{39} +137584. q^{40} -2.22245e7 q^{41} -3.24518e7 q^{43} -1.31943e7 q^{44} -574234. q^{45} -4.79046e6 q^{46} +3.18053e6 q^{47} -1.25683e7 q^{48} +3.12319e7 q^{50} -8.85371e7 q^{51} -2.90055e7 q^{52} +8.82912e7 q^{53} -7.93966e6 q^{54} +1.73123e6 q^{55} -1.60452e8 q^{57} -4.13311e7 q^{58} +1.39912e7 q^{59} +1.64909e6 q^{60} +1.13931e8 q^{61} -1.09492e8 q^{62} +1.67772e7 q^{64} +3.80581e6 q^{65} -1.58148e8 q^{66} -3.05493e8 q^{67} +1.18187e8 q^{68} -5.74188e7 q^{69} -2.86664e8 q^{71} -7.00231e7 q^{72} -4.78856e7 q^{73} -2.23275e8 q^{74} +3.74348e8 q^{75} +2.14184e8 q^{76} -3.47661e8 q^{78} -1.07582e8 q^{79} -2.20134e6 q^{80} -4.31656e8 q^{81} +3.55593e8 q^{82} -5.67595e7 q^{83} -1.55073e7 q^{85} +5.19228e8 q^{86} -4.95398e8 q^{87} +2.11109e8 q^{88} +8.48669e8 q^{89} +9.18774e6 q^{90} +7.66474e7 q^{92} -1.31238e9 q^{93} -5.08885e7 q^{94} -2.81032e7 q^{95} +2.01093e8 q^{96} -8.99384e8 q^{97} -8.81107e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 1024 q^{4} - 16384 q^{8} + 15912 q^{9}+O(q^{10}) $ 4 * q - 64 * q^2 + 1024 * q^4 - 16384 * q^8 + 15912 * q^9	$ 4 q - 64 q^{2} + 1024 q^{4} - 16384 q^{8} + 15912 q^{9} + 9548 q^{11} - 417312 q^{15} + 262144 q^{16} - 254592 q^{18} - 152768 q^{22} - 2836736 q^{23} + 966144 q^{25} + 16669972 q^{29} + 6676992 q^{30} - 4194304 q^{32} + 4073472 q^{36} + 3226372 q^{37} + 69110568 q^{39} - 76480204 q^{43} + 2444288 q^{44} + 45387776 q^{46} - 15458304 q^{50} - 97261596 q^{51} + 13708112 q^{53} - 371557692 q^{57} - 266719552 q^{58} - 106831872 q^{60} + 67108864 q^{64} - 515731188 q^{65} - 814420776 q^{67} - 1324668744 q^{71} - 65175552 q^{72} - 51621952 q^{74} - 1105769088 q^{78} - 668411176 q^{79} - 1111307688 q^{81} - 1659264964 q^{85} + 1223683264 q^{86} - 39108608 q^{88} - 726204416 q^{92} - 3706577496 q^{93} + 977188688 q^{95} - 2791581660 q^{99}+O(q^{100}) $ 4 * q - 64 * q^2 + 1024 * q^4 - 16384 * q^8 + 15912 * q^9 + 9548 * q^11 - 417312 * q^15 + 262144 * q^16 - 254592 * q^18 - 152768 * q^22 - 2836736 * q^23 + 966144 * q^25 + 16669972 * q^29 + 6676992 * q^30 - 4194304 * q^32 + 4073472 * q^36 + 3226372 * q^37 + 69110568 * q^39 - 76480204 * q^43 + 2444288 * q^44 + 45387776 * q^46 - 15458304 * q^50 - 97261596 * q^51 + 13708112 * q^53 - 371557692 * q^57 - 266719552 * q^58 - 106831872 * q^60 + 67108864 * q^64 - 515731188 * q^65 - 814420776 * q^67 - 1324668744 * q^71 - 65175552 * q^72 - 51621952 * q^74 - 1105769088 * q^78 - 668411176 * q^79 - 1111307688 * q^81 - 1659264964 * q^85 + 1223683264 * q^86 - 39108608 * q^88 - 726204416 * q^92 - 3706577496 * q^93 + 977188688 * q^95 - 2791581660 * q^99

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
$3$	−191.777	−1.36695	−0.683473	−	0.729976i	$-0.739531\pi$
$3$	−191.777	−1.36695	−0.683473	+	0.729976i	$0.739531\pi$
$4$	256.000	0.500000
$5$	−33.5898	−0.0240349	−0.0120175	−	0.999928i	$-0.503825\pi$
$5$	−33.5898	−0.0240349	−0.0120175	+	0.999928i	$0.503825\pi$
$6$	3068.43	0.966576
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	17095.5	0.868540
$10$	537.437	0.0169953
$11$	−51540.4	−1.06140	−0.530702	−	0.847559i	$-0.678072\pi$
$11$	−51540.4	−1.06140	−0.530702	+	0.847559i	$0.678072\pi$
$12$	−49094.9	−0.683473
$13$	−113303.	−1.10026	−0.550129	−	0.835080i	$-0.685421\pi$
$13$	−113303.	−1.10026	−0.550129	+	0.835080i	$0.685421\pi$
$14$	0	0
$15$	6441.76	0.0328544
$16$	65536.0	0.250000
$17$	461667.	1.34063	0.670314	−	0.742078i	$-0.266159\pi$
$17$	461667.	1.34063	0.670314	+	0.742078i	$0.266159\pi$
$18$	−273528.	−0.614150
$19$	836657.	1.47284	0.736421	−	0.676523i	$-0.236514\pi$
$19$	836657.	1.47284	0.736421	+	0.676523i	$0.236514\pi$
$20$	−8598.99	−0.0120175
$21$	0	0
$22$	824646.	0.750526
$23$	299404.	0.223091	0.111546	−	0.993759i	$-0.464420\pi$
$23$	299404.	0.223091	0.111546	+	0.993759i	$0.464420\pi$
$24$	785519.	0.483288
$25$	−1.95200e6	−0.999422
$26$	1.81284e6	0.778000
$27$	496229.	0.179699
$28$	0	0
$29$	2.58319e6	0.678213	0.339106	−	0.940748i	$-0.389875\pi$
$29$	2.58319e6	0.678213	0.339106	+	0.940748i	$0.389875\pi$
$30$	−103068.	−0.0232316
$31$	6.84324e6	1.33087	0.665433	−	0.746458i	$-0.268247\pi$
$31$	6.84324e6	1.33087	0.665433	+	0.746458i	$0.268247\pi$
$32$	−1.04858e6	−0.176777
$33$	9.88427e6	1.45088
$34$	−7.38666e6	−0.947967
$35$	0	0
$36$	4.37644e6	0.434270
$37$	1.39547e7	1.22409	0.612043	−	0.790825i	$-0.290348\pi$
$37$	1.39547e7	1.22409	0.612043	+	0.790825i	$0.290348\pi$
$38$	−1.33865e7	−1.04146
$39$	2.17288e7	1.50399
$40$	137584.	0.00849763
$41$	−2.22245e7	−1.22830	−0.614151	−	0.789188i	$-0.710502\pi$
$41$	−2.22245e7	−1.22830	−0.614151	+	0.789188i	$0.710502\pi$
$42$	0	0
$43$	−3.24518e7	−1.44754	−0.723770	−	0.690042i	$-0.757592\pi$
$43$	−3.24518e7	−1.44754	−0.723770	+	0.690042i	$0.757592\pi$
$44$	−1.31943e7	−0.530702
$45$	−574234.	−0.0208753
$46$	−4.79046e6	−0.157749
$47$	3.18053e6	0.0950734	0.0475367	−	0.998869i	$-0.484863\pi$
$47$	3.18053e6	0.0950734	0.0475367	+	0.998869i	$0.484863\pi$
$48$	−1.25683e7	−0.341736
$49$	0	0
$50$	3.12319e7	0.706698
$51$	−8.85371e7	−1.83257
$52$	−2.90055e7	−0.550129
$53$	8.82912e7	1.53701	0.768504	−	0.639845i	$-0.221001\pi$
$53$	8.82912e7	1.53701	0.768504	+	0.639845i	$0.221001\pi$
$54$	−7.93966e6	−0.127066
$55$	1.73123e6	0.0255107
$56$	0	0
$57$	−1.60452e8	−2.01330
$58$	−4.13311e7	−0.479569
$59$	1.39912e7	0.150321	0.0751606	−	0.997171i	$-0.476053\pi$
$59$	1.39912e7	0.150321	0.0751606	+	0.997171i	$0.476053\pi$
$60$	1.64909e6	0.0164272
$61$	1.13931e8	1.05355	0.526777	−	0.850004i	$-0.323400\pi$
$61$	1.13931e8	1.05355	0.526777	+	0.850004i	$0.323400\pi$
$62$	−1.09492e8	−0.941064
$63$	0	0
$64$	1.67772e7	0.125000
$65$	3.80581e6	0.0264446
$66$	−1.58148e8	−1.02593
$67$	−3.05493e8	−1.85210	−0.926050	−	0.377400i	$-0.876818\pi$
$67$	−3.05493e8	−1.85210	−0.926050	+	0.377400i	$0.876818\pi$
$68$	1.18187e8	0.670314
$69$	−5.74188e7	−0.304953
$70$	0	0
$71$	−2.86664e8	−1.33878	−0.669392	−	0.742909i	$-0.733445\pi$
$71$	−2.86664e8	−1.33878	−0.669392	+	0.742909i	$0.733445\pi$
$72$	−7.00231e7	−0.307075
$73$	−4.78856e7	−0.197357	−0.0986785	−	0.995119i	$-0.531462\pi$
$73$	−4.78856e7	−0.197357	−0.0986785	+	0.995119i	$0.531462\pi$
$74$	−2.23275e8	−0.865559
$75$	3.74348e8	1.36616
$76$	2.14184e8	0.736421
$77$	0	0
$78$	−3.47661e8	−1.06348
$79$	−1.07582e8	−0.310753	−0.155377	−	0.987855i	$-0.549659\pi$
$79$	−1.07582e8	−0.310753	−0.155377	+	0.987855i	$0.549659\pi$
$80$	−2.20134e6	−0.00600873
$81$	−4.31656e8	−1.11418
$82$	3.55593e8	0.868541
$83$	−5.67595e7	−0.131277	−0.0656383	−	0.997843i	$-0.520908\pi$
$83$	−5.67595e7	−0.131277	−0.0656383	+	0.997843i	$0.520908\pi$
$84$	0	0
$85$	−1.55073e7	−0.0322219
$86$	5.19228e8	1.02356
$87$	−4.95398e8	−0.927080
$88$	2.11109e8	0.375263
$89$	8.48669e8	1.43378	0.716891	−	0.697185i	$-0.245564\pi$
$89$	8.48669e8	1.43378	0.716891	+	0.697185i	$0.245564\pi$
$90$	9.18774e6	0.0147611
$91$	0	0
$92$	7.66474e7	0.111546
$93$	−1.31238e9	−1.81922
$94$	−5.08885e7	−0.0672270
$95$	−2.81032e7	−0.0353996
$96$	2.01093e8	0.241644
$97$	−8.99384e8	−1.03151	−0.515754	−	0.856737i	$-0.672488\pi$
$97$	−8.99384e8	−1.03151	−0.515754	+	0.856737i	$0.672488\pi$
$98$	0	0
$99$	−8.81107e8	−0.921871
$100$	−4.99711e8	−0.499711
$101$	−6.32202e7	−0.0604519	−0.0302259	−	0.999543i	$-0.509623\pi$
$101$	−6.32202e7	−0.0604519	−0.0302259	+	0.999543i	$0.509623\pi$
$102$	1.41659e9	1.29582
$103$	−1.21580e9	−1.06437	−0.532185	−	0.846628i	$-0.678629\pi$
$103$	−1.21580e9	−1.06437	−0.532185	+	0.846628i	$0.678629\pi$
$104$	4.64087e8	0.389000
$105$	0	0
$106$	−1.41266e9	−1.08683
$107$	−1.28242e9	−0.945811	−0.472906	−	0.881113i	$-0.656795\pi$
$107$	−1.28242e9	−0.945811	−0.472906	+	0.881113i	$0.656795\pi$
$108$	1.27035e8	0.0898494
$109$	−5.06567e8	−0.343730	−0.171865	−	0.985120i	$-0.554979\pi$
$109$	−5.06567e8	−0.343730	−0.171865	+	0.985120i	$0.554979\pi$
$110$	−2.76997e7	−0.0180388
$111$	−2.67619e9	−1.67326
$112$	0	0
$113$	1.15512e9	0.666462	0.333231	−	0.942845i	$-0.391861\pi$
$113$	1.15512e9	0.666462	0.333231	+	0.942845i	$0.391861\pi$
$114$	2.56723e9	1.42361
$115$	−1.00569e7	−0.00536197
$116$	6.61298e8	0.339106
$117$	−1.93696e9	−0.955618
$118$	−2.23859e8	−0.106293
$119$	0	0
$120$	−2.63854e7	−0.0116158
$121$	2.98463e8	0.126578
$122$	−1.82289e9	−0.744975
$123$	4.26216e9	1.67902
$124$	1.75187e9	0.665433
$125$	1.31172e8	0.0480559
$126$	0	0
$127$	3.41280e9	1.16411	0.582055	−	0.813150i	$-0.302249\pi$
$127$	3.41280e9	1.16411	0.582055	+	0.813150i	$0.302249\pi$
$128$	−2.68435e8	−0.0883883
$129$	6.22351e9	1.97871
$130$	−6.08930e7	−0.0186992
$131$	−7.17987e8	−0.213008	−0.106504	−	0.994312i	$-0.533966\pi$
$131$	−7.17987e8	−0.213008	−0.106504	+	0.994312i	$0.533966\pi$
$132$	2.53037e9	0.725440
$133$	0	0
$134$	4.88789e9	1.30963
$135$	−1.66682e7	−0.00431904
$136$	−1.89099e9	−0.473984
$137$	−7.31370e9	−1.77376	−0.886880	−	0.462000i	$-0.847132\pi$
$137$	−7.31370e9	−1.77376	−0.886880	+	0.462000i	$0.847132\pi$
$138$	9.18701e8	0.215634
$139$	4.88666e9	1.11031	0.555157	−	0.831746i	$-0.312658\pi$
$139$	4.88666e9	1.11031	0.555157	+	0.831746i	$0.312658\pi$
$140$	0	0
$141$	−6.09953e8	−0.129960
$142$	4.58662e9	0.946663
$143$	5.83966e9	1.16782
$144$	1.12037e9	0.217135
$145$	−8.67690e7	−0.0163008
$146$	7.66170e8	0.139552
$147$	0	0
$148$	3.57240e9	0.612043
$149$	6.90289e9	1.14734	0.573671	−	0.819086i	$-0.305519\pi$
$149$	6.90289e9	1.14734	0.573671	+	0.819086i	$0.305519\pi$
$150$	−5.98957e9	−0.966018
$151$	−5.65547e9	−0.885263	−0.442632	−	0.896704i	$-0.645955\pi$
$151$	−5.65547e9	−0.885263	−0.442632	+	0.896704i	$0.645955\pi$
$152$	−3.42695e9	−0.520728
$153$	7.89241e9	1.16439
$154$	0	0
$155$	−2.29863e8	−0.0319872
$156$	5.56258e9	0.751996
$157$	6.59975e9	0.866920	0.433460	−	0.901173i	$-0.357293\pi$
$157$	6.59975e9	0.866920	0.433460	+	0.901173i	$0.357293\pi$
$158$	1.72130e9	0.219736
$159$	−1.69322e10	−2.10101
$160$	3.52215e7	0.00424881
$161$	0	0
$162$	6.90649e9	0.787843
$163$	−7.98797e9	−0.886323	−0.443162	−	0.896442i	$-0.646143\pi$
$163$	−7.98797e9	−0.886323	−0.443162	+	0.896442i	$0.646143\pi$
$164$	−5.68948e9	−0.614151
$165$	−3.32011e8	−0.0348718
$166$	9.08152e8	0.0928266
$167$	−4.34905e9	−0.432683	−0.216342	−	0.976318i	$-0.569412\pi$
$167$	−4.34905e9	−0.432683	−0.216342	+	0.976318i	$0.569412\pi$
$168$	0	0
$169$	2.23297e9	0.210568
$170$	2.48117e8	0.0227843
$171$	1.43030e10	1.27922
$172$	−8.30765e9	−0.723770
$173$	−1.38491e10	−1.17548	−0.587739	−	0.809051i	$-0.699982\pi$
$173$	−1.38491e10	−1.17548	−0.587739	+	0.809051i	$0.699982\pi$
$174$	7.92636e9	0.655545
$175$	0	0
$176$	−3.37775e9	−0.265351
$177$	−2.68319e9	−0.205481
$178$	−1.35787e10	−1.01384
$179$	1.99542e10	1.45277	0.726384	−	0.687289i	$-0.241199\pi$
$179$	1.99542e10	1.45277	0.726384	+	0.687289i	$0.241199\pi$
$180$	−1.47004e8	−0.0104376
$181$	3.33705e9	0.231105	0.115552	−	0.993301i	$-0.463136\pi$
$181$	3.33705e9	0.231105	0.115552	+	0.993301i	$0.463136\pi$
$182$	0	0
$183$	−2.18493e10	−1.44015
$184$	−1.22636e9	−0.0788746
$185$	−4.68735e8	−0.0294208
$186$	2.09980e10	1.28638
$187$	−2.37945e10	−1.42295
$188$	8.14216e8	0.0475367
$189$	0	0
$190$	4.49650e8	0.0250313
$191$	−2.45891e10	−1.33688	−0.668441	−	0.743765i	$-0.733038\pi$
$191$	−2.45891e10	−1.33688	−0.668441	+	0.743765i	$0.733038\pi$
$192$	−3.21749e9	−0.170868
$193$	−1.80119e10	−0.934438	−0.467219	−	0.884142i	$-0.654744\pi$
$193$	−1.80119e10	−0.934438	−0.467219	+	0.884142i	$0.654744\pi$
$194$	1.43901e10	0.729386
$195$	−7.29868e8	−0.0361483
$196$	0	0
$197$	4.02716e10	1.90503	0.952514	−	0.304496i	$-0.0984880\pi$
$197$	4.02716e10	1.90503	0.952514	+	0.304496i	$0.0984880\pi$
$198$	1.40977e10	0.651862
$199$	−3.76852e10	−1.70346	−0.851730	−	0.523981i	$-0.824446\pi$
$199$	−3.76852e10	−1.70346	−0.851730	+	0.523981i	$0.824446\pi$
$200$	7.99538e9	0.353349
$201$	5.85866e10	2.53172
$202$	1.01152e9	0.0427459
$203$	0	0
$204$	−2.26655e10	−0.916283
$205$	7.46518e8	0.0295221
$206$	1.94527e10	0.752624
$207$	5.11845e9	0.193763
$208$	−7.42540e9	−0.275065
$209$	−4.31216e10	−1.56328
$210$	0	0
$211$	−1.57268e10	−0.546223	−0.273111	−	0.961982i	$-0.588053\pi$
$211$	−1.57268e10	−0.546223	−0.273111	+	0.961982i	$0.588053\pi$
$212$	2.26026e10	0.768504
$213$	5.49756e10	1.83004
$214$	2.05188e10	0.668790
$215$	1.09005e9	0.0347915
$216$	−2.03255e9	−0.0635331
$217$	0	0
$218$	8.10508e9	0.243054
$219$	9.18337e9	0.269776
$220$	4.43195e8	0.0127554
$221$	−5.23080e10	−1.47504
$222$	4.28190e10	1.18317
$223$	−6.29667e10	−1.70506	−0.852528	−	0.522681i	$-0.824932\pi$
$223$	−6.29667e10	−1.70506	−0.852528	+	0.522681i	$0.824932\pi$
$224$	0	0
$225$	−3.33703e10	−0.868038
$226$	−1.84820e10	−0.471260
$227$	−5.48011e10	−1.36985	−0.684925	−	0.728614i	$-0.740165\pi$
$227$	−5.48011e10	−1.36985	−0.684925	+	0.728614i	$0.740165\pi$
$228$	−4.10756e10	−1.00665
$229$	6.14118e10	1.47568	0.737840	−	0.674976i	$-0.235846\pi$
$229$	6.14118e10	1.47568	0.737840	+	0.674976i	$0.235846\pi$
$230$	1.60911e8	0.00379149
$231$	0	0
$232$	−1.05808e10	−0.239784
$233$	−8.42910e9	−0.187361	−0.0936806	−	0.995602i	$-0.529863\pi$
$233$	−8.42910e9	−0.187361	−0.0936806	+	0.995602i	$0.529863\pi$
$234$	3.09914e10	0.675724
$235$	−1.06833e8	−0.00228508
$236$	3.58174e9	0.0751606
$237$	2.06317e10	0.424783
$238$	0	0
$239$	3.13951e10	0.622402	0.311201	−	0.950344i	$-0.399269\pi$
$239$	3.13951e10	0.622402	0.311201	+	0.950344i	$0.399269\pi$
$240$	4.22167e8	0.00821360
$241$	−1.45866e10	−0.278533	−0.139267	−	0.990255i	$-0.544475\pi$
$241$	−1.45866e10	−0.278533	−0.139267	+	0.990255i	$0.544475\pi$
$242$	−4.77541e9	−0.0895039
$243$	7.30144e10	1.34332
$244$	2.91663e10	0.526777
$245$	0	0
$246$	−6.81945e10	−1.18725
$247$	−9.47954e10	−1.62051
$248$	−2.80299e10	−0.470532
$249$	1.08852e10	0.179448
$250$	−2.09876e9	−0.0339807
$251$	3.56389e10	0.566752	0.283376	−	0.959009i	$-0.408546\pi$
$251$	3.56389e10	0.566752	0.283376	+	0.959009i	$0.408546\pi$
$252$	0	0
$253$	−1.54314e10	−0.236790
$254$	−5.46048e10	−0.823150
$255$	2.97394e9	0.0440455
$256$	4.29497e9	0.0625000
$257$	−6.94569e10	−0.993154	−0.496577	−	0.867993i	$-0.665410\pi$
$257$	−6.94569e10	−0.993154	−0.496577	+	0.867993i	$0.665410\pi$
$258$	−9.95761e10	−1.39916
$259$	0	0
$260$	9.74288e8	0.0132223
$261$	4.41609e10	0.589055
$262$	1.14878e10	0.150619
$263$	7.23020e10	0.931857	0.465929	−	0.884822i	$-0.345720\pi$
$263$	7.23020e10	0.931857	0.465929	+	0.884822i	$0.345720\pi$
$264$	−4.04860e10	−0.512964
$265$	−2.96569e9	−0.0369419
$266$	0	0
$267$	−1.62755e11	−1.95990
$268$	−7.82062e10	−0.926050
$269$	−9.03066e10	−1.05156	−0.525780	−	0.850621i	$-0.676226\pi$
$269$	−9.03066e10	−1.05156	−0.525780	+	0.850621i	$0.676226\pi$
$270$	2.66692e8	0.00305403
$271$	−4.02229e10	−0.453014	−0.226507	−	0.974010i	$-0.572731\pi$
$271$	−4.02229e10	−0.453014	−0.226507	+	0.974010i	$0.572731\pi$
$272$	3.02558e10	0.335157
$273$	0	0
$274$	1.17019e11	1.25424
$275$	1.00607e11	1.06079
$276$	−1.46992e10	−0.152477
$277$	−2.06717e10	−0.210968	−0.105484	−	0.994421i	$-0.533639\pi$
$277$	−2.06717e10	−0.210968	−0.105484	+	0.994421i	$0.533639\pi$
$278$	−7.81866e10	−0.785110
$279$	1.16988e11	1.15591
$280$	0	0
$281$	−3.46833e10	−0.331850	−0.165925	−	0.986138i	$-0.553061\pi$
$281$	−3.46833e10	−0.331850	−0.165925	+	0.986138i	$0.553061\pi$
$282$	9.75925e9	0.0918957
$283$	−1.04639e11	−0.969741	−0.484870	−	0.874586i	$-0.661133\pi$
$283$	−1.04639e11	−0.969741	−0.484870	+	0.874586i	$0.661133\pi$
$284$	−7.33860e10	−0.669392
$285$	5.38954e9	0.0483894
$286$	−9.34345e10	−0.825772
$287$	0	0
$288$	−1.79259e10	−0.153538
$289$	9.45481e10	0.797283
$290$	1.38830e9	0.0115264
$291$	1.72481e11	1.41001
$292$	−1.22587e10	−0.0986785
$293$	1.60760e11	1.27431	0.637153	−	0.770737i	$-0.280112\pi$
$293$	1.60760e11	1.27431	0.637153	+	0.770737i	$0.280112\pi$
$294$	0	0
$295$	−4.69961e8	−0.00361296
$296$	−5.71583e10	−0.432780
$297$	−2.55758e10	−0.190733
$298$	−1.10446e11	−0.811293
$299$	−3.39232e10	−0.245458
$300$	9.58332e10	0.683078
$301$	0	0
$302$	9.04875e10	0.625976
$303$	1.21242e10	0.0826344
$304$	5.48312e10	0.368211
$305$	−3.82691e9	−0.0253221
$306$	−1.26279e11	−0.823347
$307$	−1.45170e11	−0.932725	−0.466362	−	0.884594i	$-0.654436\pi$
$307$	−1.45170e11	−0.932725	−0.466362	+	0.884594i	$0.654436\pi$
$308$	0	0
$309$	2.33162e11	1.45494
$310$	3.67781e9	0.0226184
$311$	2.63090e11	1.59471	0.797356	−	0.603510i	$-0.206232\pi$
$311$	2.63090e11	1.59471	0.797356	+	0.603510i	$0.206232\pi$
$312$	−8.90013e10	−0.531742
$313$	8.38203e10	0.493628	0.246814	−	0.969063i	$-0.420616\pi$
$313$	8.38203e10	0.493628	0.246814	+	0.969063i	$0.420616\pi$
$314$	−1.05596e11	−0.613005
$315$	0	0
$316$	−2.75409e10	−0.155377
$317$	2.70716e11	1.50573	0.752865	−	0.658175i	$-0.228671\pi$
$317$	2.70716e11	1.50573	0.752865	+	0.658175i	$0.228671\pi$
$318$	2.70916e11	1.48564
$319$	−1.33139e11	−0.719858
$320$	−5.63544e8	−0.00300436
$321$	2.45940e11	1.29287
$322$	0	0
$323$	3.86257e11	1.97453
$324$	−1.10504e11	−0.557089
$325$	2.21166e11	1.09962
$326$	1.27807e11	0.626725
$327$	9.71480e10	0.469861
$328$	9.10317e10	0.434271
$329$	0	0
$330$	5.31217e9	0.0246581
$331$	1.93741e11	0.887146	0.443573	−	0.896238i	$-0.353711\pi$
$331$	1.93741e11	0.887146	0.443573	+	0.896238i	$0.353711\pi$
$332$	−1.45304e10	−0.0656383
$333$	2.38562e11	1.06317
$334$	6.95847e10	0.305953
$335$	1.02615e10	0.0445151
$336$	0	0
$337$	2.23909e11	0.945665	0.472832	−	0.881152i	$-0.343232\pi$
$337$	2.23909e11	0.945665	0.472832	+	0.881152i	$0.343232\pi$
$338$	−3.57275e10	−0.148894
$339$	−2.21526e11	−0.911017
$340$	−3.96987e9	−0.0161109
$341$	−3.52703e11	−1.41259
$342$	−2.28849e11	−0.904547
$343$	0	0
$344$	1.32922e11	0.511782
$345$	1.92869e9	0.00732953
$346$	2.21586e11	0.831188
$347$	−2.57729e11	−0.954289	−0.477145	−	0.878825i	$-0.658328\pi$
$347$	−2.57729e11	−0.954289	−0.477145	+	0.878825i	$0.658328\pi$
$348$	−1.26822e11	−0.463540
$349$	−1.38744e11	−0.500609	−0.250304	−	0.968167i	$-0.580531\pi$
$349$	−1.38744e11	−0.500609	−0.250304	+	0.968167i	$0.580531\pi$
$350$	0	0
$351$	−5.62240e10	−0.197715
$352$	5.40440e10	0.187631
$353$	−1.86980e11	−0.640929	−0.320464	−	0.947261i	$-0.603839\pi$
$353$	−1.86980e11	−0.640929	−0.320464	+	0.947261i	$0.603839\pi$
$354$	4.29310e10	0.145297
$355$	9.62899e9	0.0321776
$356$	2.17259e11	0.716891
$357$	0	0
$358$	−3.19268e11	−1.02726
$359$	2.07563e11	0.659516	0.329758	−	0.944066i	$-0.393033\pi$
$359$	2.07563e11	0.659516	0.329758	+	0.944066i	$0.393033\pi$
$360$	2.35206e9	0.00738053
$361$	3.77307e11	1.16926
$362$	−5.33928e10	−0.163416
$363$	−5.72384e10	−0.173025
$364$	0	0
$365$	1.60847e9	0.00474346
$366$	3.49589e11	1.01834
$367$	−1.79331e11	−0.516009	−0.258004	−	0.966144i	$-0.583065\pi$
$367$	−1.79331e11	−0.516009	−0.258004	+	0.966144i	$0.583065\pi$
$368$	1.96217e10	0.0557728
$369$	−3.79939e11	−1.06683
$370$	7.49976e9	0.0208036
$371$	0	0
$372$	−3.35968e11	−0.909610
$373$	−5.44836e11	−1.45739	−0.728696	−	0.684837i	$-0.759873\pi$
$373$	−5.44836e11	−1.45739	−0.728696	+	0.684837i	$0.759873\pi$
$374$	3.80711e11	1.00618
$375$	−2.51559e10	−0.0656899
$376$	−1.30274e10	−0.0336135
$377$	−2.92682e11	−0.746209
$378$	0	0
$379$	−1.24662e11	−0.310353	−0.155177	−	0.987887i	$-0.549595\pi$
$379$	−1.24662e11	−0.310353	−0.155177	+	0.987887i	$0.549595\pi$
$380$	−7.19441e9	−0.0176998
$381$	−6.54497e11	−1.59127
$382$	3.93426e11	0.945319
$383$	4.08245e11	0.969453	0.484726	−	0.874666i	$-0.338919\pi$
$383$	4.08245e11	0.969453	0.484726	+	0.874666i	$0.338919\pi$
$384$	5.14798e10	0.120822
$385$	0	0
$386$	2.88190e11	0.660748
$387$	−5.54778e11	−1.25725
$388$	−2.30242e11	−0.515754
$389$	5.13640e11	1.13733	0.568663	−	0.822570i	$-0.307461\pi$
$389$	5.13640e11	1.13733	0.568663	+	0.822570i	$0.307461\pi$
$390$	1.16779e10	0.0255607
$391$	1.38225e11	0.299082
$392$	0	0
$393$	1.37694e11	0.291170
$394$	−6.44346e11	−1.34706
$395$	3.61364e9	0.00746893
$396$	−2.25563e11	−0.460936
$397$	−3.60814e11	−0.728998	−0.364499	−	0.931204i	$-0.618760\pi$
$397$	−3.60814e11	−0.728998	−0.364499	+	0.931204i	$0.618760\pi$
$398$	6.02963e11	1.20453
$399$	0	0
$400$	−1.27926e11	−0.249856
$401$	2.38594e11	0.460797	0.230399	−	0.973096i	$-0.425997\pi$
$401$	2.38594e11	0.460797	0.230399	+	0.973096i	$0.425997\pi$
$402$	−9.37385e11	−1.79020
$403$	−7.75356e11	−1.46430
$404$	−1.61844e10	−0.0302259
$405$	1.44992e10	0.0267792
$406$	0	0
$407$	−7.19229e11	−1.29925
$408$	3.62648e11	0.647910
$409$	7.74690e11	1.36890	0.684452	−	0.729058i	$-0.260041\pi$
$409$	7.74690e11	1.36890	0.684452	+	0.729058i	$0.260041\pi$
$410$	−1.19443e10	−0.0208753
$411$	1.40260e12	2.42463
$412$	−3.11244e11	−0.532185
$413$	0	0
$414$	−8.18952e10	−0.137011
$415$	1.90654e9	0.00315522
$416$	1.18806e11	0.194500
$417$	−9.37150e11	−1.51774
$418$	6.89946e11	1.10541
$419$	5.87231e11	0.930777	0.465389	−	0.885106i	$-0.345915\pi$
$419$	5.87231e11	0.930777	0.465389	+	0.885106i	$0.345915\pi$
$420$	0	0
$421$	−1.12541e12	−1.74599	−0.872993	−	0.487733i	$-0.837824\pi$
$421$	−1.12541e12	−1.74599	−0.872993	+	0.487733i	$0.837824\pi$
$422$	2.51629e11	0.386238
$423$	5.43726e10	0.0825750
$424$	−3.61641e11	−0.543414
$425$	−9.01172e11	−1.33985
$426$	−8.79610e11	−1.29404
$427$	0	0
$428$	−3.28300e11	−0.472906
$429$	−1.11991e12	−1.59634
$430$	−1.74408e10	−0.0246013
$431$	−6.77668e11	−0.945952	−0.472976	−	0.881075i	$-0.656820\pi$
$431$	−6.77668e11	−0.945952	−0.472976	+	0.881075i	$0.656820\pi$
$432$	3.25209e10	0.0449247
$433$	−5.66584e11	−0.774585	−0.387292	−	0.921957i	$-0.626590\pi$
$433$	−5.66584e11	−0.774585	−0.387292	+	0.921957i	$0.626590\pi$
$434$	0	0
$435$	1.66403e10	0.0222823
$436$	−1.29681e11	−0.171865
$437$	2.50498e11	0.328578
$438$	−1.46934e11	−0.190761
$439$	7.41236e11	0.952503	0.476252	−	0.879309i	$-0.341995\pi$
$439$	7.41236e11	0.952503	0.476252	+	0.879309i	$0.341995\pi$
$440$	−7.09113e9	−0.00901941
$441$	0	0
$442$	8.36928e11	1.04301
$443$	9.25207e10	0.114136	0.0570679	−	0.998370i	$-0.481825\pi$
$443$	9.25207e10	0.114136	0.0570679	+	0.998370i	$0.481825\pi$
$444$	−6.85104e11	−0.836629
$445$	−2.85066e10	−0.0344608
$446$	1.00747e12	1.20566
$447$	−1.32382e12	−1.56835
$448$	0	0
$449$	−1.26884e11	−0.147333	−0.0736664	−	0.997283i	$-0.523470\pi$
$449$	−1.26884e11	−0.147333	−0.0736664	+	0.997283i	$0.523470\pi$
$450$	5.33925e11	0.613796
$451$	1.14546e12	1.30372
$452$	2.95711e11	0.333231
$453$	1.08459e12	1.21011
$454$	8.76817e11	0.968630
$455$	0	0
$456$	6.57210e11	0.711807
$457$	1.02815e12	1.10264	0.551321	−	0.834293i	$-0.314124\pi$
$457$	1.02815e12	1.10264	0.551321	+	0.834293i	$0.314124\pi$
$458$	−9.82588e11	−1.04346
$459$	2.29092e11	0.240909
$460$	−2.57457e9	−0.00268099
$461$	8.10233e11	0.835518	0.417759	−	0.908558i	$-0.362816\pi$
$461$	8.10233e11	0.835518	0.417759	+	0.908558i	$0.362816\pi$
$462$	0	0
$463$	−1.44793e12	−1.46431	−0.732155	−	0.681139i	$-0.761485\pi$
$463$	−1.44793e12	−1.46431	−0.732155	+	0.681139i	$0.761485\pi$
$464$	1.69292e11	0.169553
$465$	4.40825e10	0.0437248
$466$	1.34866e11	0.132484
$467$	4.47034e11	0.434926	0.217463	−	0.976069i	$-0.430222\pi$
$467$	4.47034e11	0.434926	0.217463	+	0.976069i	$0.430222\pi$
$468$	−4.95862e11	−0.477809
$469$	0	0
$470$	1.70933e9	0.00161580
$471$	−1.26568e12	−1.18503
$472$	−5.73079e10	−0.0531466
$473$	1.67258e12	1.53642
$474$	−3.30107e11	−0.300367
$475$	−1.63315e12	−1.47199
$476$	0	0
$477$	1.50938e12	1.33495
$478$	−5.02321e11	−0.440105
$479$	8.69551e10	0.0754719	0.0377360	−	0.999288i	$-0.487985\pi$
$479$	8.69551e10	0.0754719	0.0377360	+	0.999288i	$0.487985\pi$
$480$	−6.75467e9	−0.00580790
$481$	−1.58110e12	−1.34681
$482$	2.33386e11	0.196953
$483$	0	0
$484$	7.64066e10	0.0632888
$485$	3.02101e10	0.0247922
$486$	−1.16823e12	−0.949872
$487$	−4.81935e8	−0.000388247 0	−0.000194124	−	1.00000i	$-0.500062\pi$
$487$	−4.81935e8	−0.000388247 0	−0.000194124		1.00000i	$0.500062\pi$
$488$	−4.66660e11	−0.372487
$489$	1.53191e12	1.21156
$490$	0	0
$491$	−5.88640e11	−0.457070	−0.228535	−	0.973536i	$-0.573394\pi$
$491$	−5.88640e11	−0.457070	−0.228535	+	0.973536i	$0.573394\pi$
$492$	1.09111e12	0.839511
$493$	1.19257e12	0.909231
$494$	1.51673e12	1.14587
$495$	2.95962e10	0.0221571
$496$	4.48478e11	0.332716
$497$	0	0
$498$	−1.74163e11	−0.126889
$499$	−2.47946e12	−1.79021	−0.895107	−	0.445852i	$-0.852901\pi$
$499$	−2.47946e12	−1.79021	−0.895107	+	0.445852i	$0.852901\pi$
$500$	3.35801e10	0.0240280
$501$	8.34048e11	0.591454
$502$	−5.70223e11	−0.400754
$503$	−1.35604e12	−0.944530	−0.472265	−	0.881457i	$-0.656563\pi$
$503$	−1.35604e12	−0.944530	−0.472265	+	0.881457i	$0.656563\pi$
$504$	0	0
$505$	2.12356e9	0.00145296
$506$	2.46902e11	0.167436
$507$	−4.28232e11	−0.287835
$508$	8.73676e11	0.582055
$509$	−1.68824e12	−1.11482	−0.557409	−	0.830238i	$-0.688205\pi$
$509$	−1.68824e12	−1.11482	−0.557409	+	0.830238i	$0.688205\pi$
$510$	−4.75831e10	−0.0311449
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	4.15173e11	0.264668
$514$	1.11131e12	0.702266
$515$	4.08383e10	0.0255821
$516$	1.59322e12	0.989354
$517$	−1.63926e11	−0.100911
$518$	0	0
$519$	2.65594e12	1.60681
$520$	−1.55886e10	−0.00934958
$521$	−9.42135e11	−0.560200	−0.280100	−	0.959971i	$-0.590368\pi$
$521$	−9.42135e11	−0.560200	−0.280100	+	0.959971i	$0.590368\pi$
$522$	−7.06575e11	−0.416525
$523$	−2.44405e12	−1.42841	−0.714206	−	0.699936i	$-0.753212\pi$
$523$	−2.44405e12	−1.42841	−0.714206	+	0.699936i	$0.753212\pi$
$524$	−1.83805e11	−0.106504
$525$	0	0
$526$	−1.15683e12	−0.658923
$527$	3.15929e12	1.78419
$528$	6.47775e11	0.362720
$529$	−1.71151e12	−0.950230
$530$	4.74510e10	0.0261218
$531$	2.39186e11	0.130560
$532$	0	0
$533$	2.51810e12	1.35145
$534$	2.60408e12	1.38586
$535$	4.30764e10	0.0227325
$536$	1.25130e12	0.654816
$537$	−3.82677e12	−1.98586
$538$	1.44490e12	0.743565
$539$	0	0
$540$	−4.26707e9	−0.00215952
$541$	−6.58195e11	−0.330344	−0.165172	−	0.986265i	$-0.552818\pi$
$541$	−6.58195e11	−0.330344	−0.165172	+	0.986265i	$0.552818\pi$
$542$	6.43566e11	0.320329
$543$	−6.39970e11	−0.315908
$544$	−4.84092e11	−0.236992
$545$	1.70155e10	0.00826153
$546$	0	0
$547$	−2.50775e12	−1.19768	−0.598840	−	0.800869i	$-0.704372\pi$
$547$	−2.50775e12	−1.19768	−0.598840	+	0.800869i	$0.704372\pi$
$548$	−1.87231e12	−0.886880
$549$	1.94770e12	0.915053
$550$	−1.60971e12	−0.750092
$551$	2.16125e12	0.998901
$552$	2.35187e11	0.107817
$553$	0	0
$554$	3.30747e11	0.149177
$555$	8.98926e10	0.0402166
$556$	1.25099e12	0.555157
$557$	−2.60505e12	−1.14675	−0.573375	−	0.819293i	$-0.694366\pi$
$557$	−2.60505e12	−1.14675	−0.573375	+	0.819293i	$0.694366\pi$
$558$	−1.87181e12	−0.817351
$559$	3.67687e12	1.59267
$560$	0	0
$561$	4.56324e12	1.94509
$562$	5.54933e11	0.234654
$563$	−2.59402e11	−0.108814	−0.0544071	−	0.998519i	$-0.517327\pi$
$563$	−2.59402e11	−0.108814	−0.0544071	+	0.998519i	$0.517327\pi$
$564$	−1.56148e11	−0.0649801
$565$	−3.88004e10	−0.0160183
$566$	1.67423e12	0.685710
$567$	0	0
$568$	1.17418e12	0.473332
$569$	2.64332e12	1.05717	0.528585	−	0.848880i	$-0.322723\pi$
$569$	2.64332e12	1.05717	0.528585	+	0.848880i	$0.322723\pi$
$570$	−8.62327e10	−0.0342165
$571$	−2.06794e12	−0.814098	−0.407049	−	0.913406i	$-0.633442\pi$
$571$	−2.06794e12	−0.814098	−0.407049	+	0.913406i	$0.633442\pi$
$572$	1.49495e12	0.583909
$573$	4.71564e12	1.82745
$574$	0	0
$575$	−5.84435e11	−0.222962
$576$	2.86814e11	0.108567
$577$	2.56500e12	0.963377	0.481688	−	0.876343i	$-0.340024\pi$
$577$	2.56500e12	0.963377	0.481688	+	0.876343i	$0.340024\pi$
$578$	−1.51277e12	−0.563764
$579$	3.45426e12	1.27733
$580$	−2.22129e10	−0.00815039
$581$	0	0
$582$	−2.75970e12	−0.997030
$583$	−4.55056e12	−1.63139
$584$	1.96140e11	0.0697762
$585$	6.50621e10	0.0229682
$586$	−2.57216e12	−0.901071
$587$	−1.59591e12	−0.554800	−0.277400	−	0.960755i	$-0.589473\pi$
$587$	−1.59591e12	−0.554800	−0.277400	+	0.960755i	$0.589473\pi$
$588$	0	0
$589$	5.72544e12	1.96015
$590$	7.51938e9	0.00255475
$591$	−7.72318e12	−2.60407
$592$	9.14533e11	0.306021
$593$	1.97116e12	0.654600	0.327300	−	0.944920i	$-0.393861\pi$
$593$	1.97116e12	0.654600	0.327300	+	0.944920i	$0.393861\pi$
$594$	4.09213e11	0.134869
$595$	0	0
$596$	1.76714e12	0.573671
$597$	7.22716e12	2.32854
$598$	5.42771e11	0.173565
$599$	4.97079e12	1.57763	0.788814	−	0.614632i	$-0.210696\pi$
$599$	4.97079e12	1.57763	0.788814	+	0.614632i	$0.210696\pi$
$600$	−1.53333e12	−0.483009
$601$	−4.73669e12	−1.48095	−0.740475	−	0.672084i	$-0.765399\pi$
$601$	−4.73669e12	−1.48095	−0.740475	+	0.672084i	$0.765399\pi$
$602$	0	0
$603$	−5.22255e12	−1.60862
$604$	−1.44780e12	−0.442632
$605$	−1.00253e10	−0.00304228
$606$	−1.93987e11	−0.0584314
$607$	−3.26903e12	−0.977395	−0.488697	−	0.872453i	$-0.662528\pi$
$607$	−3.26903e12	−0.977395	−0.488697	+	0.872453i	$0.662528\pi$
$608$	−8.77298e11	−0.260364
$609$	0	0
$610$	6.12306e10	0.0179054
$611$	−3.60362e11	−0.104605
$612$	2.02046e12	0.582194
$613$	−6.53577e11	−0.186950	−0.0934748	−	0.995622i	$-0.529797\pi$
$613$	−6.53577e11	−0.186950	−0.0934748	+	0.995622i	$0.529797\pi$
$614$	2.32272e12	0.659536
$615$	−1.43165e11	−0.0403552
$616$	0	0
$617$	−6.63823e12	−1.84404	−0.922018	−	0.387148i	$-0.873460\pi$
$617$	−6.63823e12	−1.84404	−0.922018	+	0.387148i	$0.873460\pi$
$618$	−3.73059e12	−1.02880
$619$	−7.25374e10	−0.0198589	−0.00992943	−	0.999951i	$-0.503161\pi$
$619$	−7.25374e10	−0.0198589	−0.00992943	+	0.999951i	$0.503161\pi$
$620$	−5.88450e10	−0.0159936
$621$	1.48573e11	0.0400892
$622$	−4.20943e12	−1.12763
$623$	0	0
$624$	1.42402e12	0.375998
$625$	3.80809e12	0.998267
$626$	−1.34113e12	−0.349048
$627$	8.26974e12	2.13692
$628$	1.68954e12	0.433460
$629$	6.44240e12	1.64104
$630$	0	0
$631$	−2.35325e12	−0.590930	−0.295465	−	0.955354i	$-0.595475\pi$
$631$	−2.35325e12	−0.590930	−0.295465	+	0.955354i	$0.595475\pi$
$632$	4.40654e11	0.109868
$633$	3.01604e12	0.746657
$634$	−4.33145e12	−1.06471
$635$	−1.14635e11	−0.0279793
$636$	−4.33465e12	−1.05050
$637$	0	0
$638$	2.13022e12	0.509016
$639$	−4.90066e12	−1.16279
$640$	9.01670e9	0.00212441
$641$	−7.52887e11	−0.176144	−0.0880722	−	0.996114i	$-0.528071\pi$
$641$	−7.52887e11	−0.176144	−0.0880722	+	0.996114i	$0.528071\pi$
$642$	−3.93503e12	−0.914199
$643$	−4.82355e12	−1.11280	−0.556400	−	0.830915i	$-0.687818\pi$
$643$	−4.82355e12	−1.11280	−0.556400	+	0.830915i	$0.687818\pi$
$644$	0	0
$645$	−2.09047e11	−0.0475581
$646$	−6.18010e12	−1.39621
$647$	−8.19172e12	−1.83783	−0.918916	−	0.394454i	$-0.870934\pi$
$647$	−8.19172e12	−1.83783	−0.918916	+	0.394454i	$0.870934\pi$
$648$	1.76806e12	0.393922
$649$	−7.21111e11	−0.159552
$650$	−3.53866e12	−0.777551
$651$	0	0
$652$	−2.04492e12	−0.443162
$653$	−5.81217e12	−1.25092	−0.625460	−	0.780257i	$-0.715088\pi$
$653$	−5.81217e12	−1.25092	−0.625460	+	0.780257i	$0.715088\pi$
$654$	−1.55437e12	−0.332242
$655$	2.41171e10	0.00511963
$656$	−1.45651e12	−0.307076
$657$	−8.18628e11	−0.171412
$658$	0	0
$659$	−3.45418e12	−0.713446	−0.356723	−	0.934210i	$-0.616106\pi$
$659$	−3.45418e12	−0.713446	−0.356723	+	0.934210i	$0.616106\pi$
$660$	−8.49947e10	−0.0174359
$661$	5.45581e12	1.11161	0.555805	−	0.831313i	$-0.312410\pi$
$661$	5.45581e12	1.11161	0.555805	+	0.831313i	$0.312410\pi$
$662$	−3.09985e12	−0.627307
$663$	1.00315e13	2.01629
$664$	2.32487e11	0.0464133
$665$	0	0
$666$	−3.81699e12	−0.751773
$667$	7.73418e11	0.151303
$668$	−1.11336e12	−0.216342
$669$	1.20756e13	2.33072
$670$	−1.64183e11	−0.0314769
$671$	−5.87203e12	−1.11825
$672$	0	0
$673$	4.93782e12	0.927828	0.463914	−	0.885880i	$-0.346445\pi$
$673$	4.93782e12	0.927828	0.463914	+	0.885880i	$0.346445\pi$
$674$	−3.58255e12	−0.668686
$675$	−9.68637e11	−0.179595
$676$	5.71639e11	0.105284
$677$	9.07898e12	1.66107	0.830535	−	0.556967i	$-0.188035\pi$
$677$	9.07898e12	1.66107	0.830535	+	0.556967i	$0.188035\pi$
$678$	3.54442e12	0.644186
$679$	0	0
$680$	6.35179e10	0.0113922
$681$	1.05096e13	1.87251
$682$	5.64325e12	0.998848
$683$	−5.09917e12	−0.896615	−0.448308	−	0.893879i	$-0.647973\pi$
$683$	−5.09917e12	−0.896615	−0.448308	+	0.893879i	$0.647973\pi$
$684$	3.66158e12	0.639611
$685$	2.45666e11	0.0426322
$686$	0	0
$687$	−1.17774e13	−2.01717
$688$	−2.12676e12	−0.361885
$689$	−1.00036e13	−1.69111
$690$	−3.08590e10	−0.00518276
$691$	6.84110e12	1.14150	0.570748	−	0.821125i	$-0.306653\pi$
$691$	6.84110e12	1.14150	0.570748	+	0.821125i	$0.306653\pi$
$692$	−3.54537e12	−0.587739
$693$	0	0
$694$	4.12366e12	0.674785
$695$	−1.64142e11	−0.0266863
$696$	2.02915e12	0.327772
$697$	−1.02603e13	−1.64670
$698$	2.21990e12	0.353984
$699$	1.61651e12	0.256112
$700$	0	0
$701$	9.89108e12	1.54708	0.773539	−	0.633748i	$-0.218484\pi$
$701$	9.89108e12	1.54708	0.773539	+	0.633748i	$0.218484\pi$
$702$	8.99584e11	0.139806
$703$	1.16753e13	1.80289
$704$	−8.64704e11	−0.132675
$705$	2.04882e10	0.00312358
$706$	2.99169e12	0.453205
$707$	0	0
$708$	−6.86896e11	−0.102740
$709$	−1.14431e13	−1.70074	−0.850368	−	0.526189i	$-0.823620\pi$
$709$	−1.14431e13	−1.70074	−0.850368	+	0.526189i	$0.823620\pi$
$710$	−1.54064e11	−0.0227530
$711$	−1.83916e12	−0.269902
$712$	−3.47615e12	−0.506919
$713$	2.04889e12	0.296904
$714$	0	0
$715$	−1.96153e11	−0.0280684
$716$	5.10828e12	0.726384
$717$	−6.02086e12	−0.850790
$718$	−3.32101e12	−0.466348
$719$	7.20450e12	1.00537	0.502683	−	0.864471i	$-0.332346\pi$
$719$	7.20450e12	1.00537	0.502683	+	0.864471i	$0.332346\pi$
$720$	−3.76330e10	−0.00521882
$721$	0	0
$722$	−6.03692e12	−0.826795
$723$	2.79738e12	0.380740
$724$	8.54285e11	0.115552
$725$	−5.04239e12	−0.677821
$726$	9.15815e11	0.122347
$727$	−7.27861e12	−0.966371	−0.483185	−	0.875518i	$-0.660520\pi$
$727$	−7.27861e12	−0.966371	−0.483185	+	0.875518i	$0.660520\pi$
$728$	0	0
$729$	−5.50621e12	−0.722070
$730$	−2.57355e10	−0.00335413
$731$	−1.49819e13	−1.94061
$732$	−5.59342e12	−0.720075
$733$	−1.36945e13	−1.75218	−0.876092	−	0.482144i	$-0.839858\pi$
$733$	−1.36945e13	−1.75218	−0.876092	+	0.482144i	$0.839858\pi$
$734$	2.86929e12	0.364873
$735$	0	0
$736$	−3.13948e11	−0.0394373
$737$	1.57452e13	1.96583
$738$	6.07902e12	0.754363
$739$	−1.65987e12	−0.204726	−0.102363	−	0.994747i	$-0.532640\pi$
$739$	−1.65987e12	−0.204726	−0.102363	+	0.994747i	$0.532640\pi$
$740$	−1.19996e11	−0.0147104
$741$	1.81796e13	2.21514
$742$	0	0
$743$	−4.66431e11	−0.0561484	−0.0280742	−	0.999606i	$-0.508937\pi$
$743$	−4.66431e11	−0.0561484	−0.0280742	+	0.999606i	$0.508937\pi$
$744$	5.37550e12	0.643191
$745$	−2.31867e11	−0.0275763
$746$	8.71738e12	1.03053
$747$	−9.70331e11	−0.114019
$748$	−6.09138e12	−0.711474
$749$	0	0
$750$	4.02494e11	0.0464497
$751$	−5.33602e12	−0.612122	−0.306061	−	0.952012i	$-0.599011\pi$
$751$	−5.33602e12	−0.612122	−0.306061	+	0.952012i	$0.599011\pi$
$752$	2.08439e11	0.0237684
$753$	−6.83473e12	−0.774719
$754$	4.68292e12	0.527650
$755$	1.89966e11	0.0212772
$756$	0	0
$757$	8.40938e12	0.930748	0.465374	−	0.885114i	$-0.345920\pi$
$757$	8.40938e12	0.930748	0.465374	+	0.885114i	$0.345920\pi$
$758$	1.99458e12	0.219453
$759$	2.95939e12	0.323678
$760$	1.15111e11	0.0125157
$761$	−6.16386e12	−0.666227	−0.333113	−	0.942887i	$-0.608099\pi$
$761$	−6.16386e12	−0.666227	−0.333113	+	0.942887i	$0.608099\pi$
$762$	1.04719e13	1.12520
$763$	0	0
$764$	−6.29482e12	−0.668441
$765$	−2.65104e11	−0.0279860
$766$	−6.53192e12	−0.685507
$767$	−1.58524e12	−0.165392
$768$	−8.23677e11	−0.0854341
$769$	−9.39193e12	−0.968470	−0.484235	−	0.874938i	$-0.660902\pi$
$769$	−9.39193e12	−0.968470	−0.484235	+	0.874938i	$0.660902\pi$
$770$	0	0
$771$	1.33203e13	1.35759
$772$	−4.61104e12	−0.467219
$773$	4.22637e12	0.425755	0.212877	−	0.977079i	$-0.431717\pi$
$773$	4.22637e12	0.425755	0.212877	+	0.977079i	$0.431717\pi$
$774$	8.87645e12	0.889007
$775$	−1.33580e13	−1.33010
$776$	3.68388e12	0.364693
$777$	0	0
$778$	−8.21823e12	−0.804212
$779$	−1.85943e13	−1.80910
$780$	−1.86846e11	−0.0180742
$781$	1.47748e13	1.42099
$782$	−2.21160e12	−0.211483
$783$	1.28186e12	0.121874
$784$	0	0
$785$	−2.21684e11	−0.0208363
$786$	−2.20310e12	−0.205889
$787$	5.89826e11	0.0548072	0.0274036	−	0.999624i	$-0.491276\pi$
$787$	5.89826e11	0.0548072	0.0274036	+	0.999624i	$0.491276\pi$
$788$	1.03095e13	0.952514
$789$	−1.38659e13	−1.27380
$790$	−5.78183e10	−0.00528133
$791$	0	0
$792$	3.60901e12	0.325931
$793$	−1.29086e13	−1.15918
$794$	5.77303e12	0.515480
$795$	5.68751e11	0.0504975
$796$	−9.64741e12	−0.851730
$797$	2.83029e12	0.248467	0.124233	−	0.992253i	$-0.460353\pi$
$797$	2.83029e12	0.248467	0.124233	+	0.992253i	$0.460353\pi$
$798$	0	0
$799$	1.46834e12	0.127458
$800$	2.04682e12	0.176675
$801$	1.45084e13	1.24530
$802$	−3.81751e12	−0.325833
$803$	2.46804e12	0.209475
$804$	1.49982e13	1.26586
$805$	0	0
$806$	1.24057e13	1.03541
$807$	1.73187e13	1.43743
$808$	2.58950e11	0.0213730
$809$	1.16033e13	0.952388	0.476194	−	0.879340i	$-0.342016\pi$
$809$	1.16033e13	0.952388	0.476194	+	0.879340i	$0.342016\pi$
$810$	−2.31988e11	−0.0189357
$811$	4.13817e12	0.335903	0.167952	−	0.985795i	$-0.446285\pi$
$811$	4.13817e12	0.335903	0.167952	+	0.985795i	$0.446285\pi$
$812$	0	0
$813$	7.71383e12	0.619245
$814$	1.15077e13	0.918708
$815$	2.68314e11	0.0213027
$816$	−5.80237e12	−0.458141
$817$	−2.71510e13	−2.13200
$818$	−1.23950e13	−0.967961
$819$	0	0
$820$	1.91109e11	0.0147611
$821$	−1.95703e11	−0.0150332	−0.00751662	−	0.999972i	$-0.502393\pi$
$821$	−1.95703e11	−0.0150332	−0.00751662	+	0.999972i	$0.502393\pi$
$822$	−2.24416e13	−1.71447
$823$	−8.51398e12	−0.646895	−0.323447	−	0.946246i	$-0.604842\pi$
$823$	−8.51398e12	−0.646895	−0.323447	+	0.946246i	$0.604842\pi$
$824$	4.97990e12	0.376312
$825$	−1.92941e13	−1.45004
$826$	0	0
$827$	−1.19931e12	−0.0891576	−0.0445788	−	0.999006i	$-0.514195\pi$
$827$	−1.19931e12	−0.0891576	−0.0445788	+	0.999006i	$0.514195\pi$
$828$	1.31032e12	0.0968817
$829$	1.64084e13	1.20662	0.603311	−	0.797506i	$-0.293848\pi$
$829$	1.64084e13	1.20662	0.603311	+	0.797506i	$0.293848\pi$
$830$	−3.05047e10	−0.00223108
$831$	3.96436e12	0.288382
$832$	−1.90090e12	−0.137532
$833$	0	0
$834$	1.49944e13	1.07320
$835$	1.46084e11	0.0103995
$836$	−1.10391e13	−0.781640
$837$	3.39581e12	0.239155
$838$	−9.39570e12	−0.658159
$839$	1.67670e13	1.16822	0.584111	−	0.811674i	$-0.301443\pi$
$839$	1.67670e13	1.16822	0.584111	+	0.811674i	$0.301443\pi$
$840$	0	0
$841$	−7.83425e12	−0.540027
$842$	1.80065e13	1.23460
$843$	6.65147e12	0.453622
$844$	−4.02607e12	−0.273111
$845$	−7.50049e10	−0.00506098
$846$	−8.69962e11	−0.0583894
$847$	0	0
$848$	5.78625e12	0.384252
$849$	2.00674e13	1.32558
$850$	1.44187e13	0.947419
$851$	4.17808e12	0.273083
$852$	1.40738e13	0.915022
$853$	6.93277e12	0.448370	0.224185	−	0.974547i	$-0.428028\pi$
$853$	6.93277e12	0.448370	0.224185	+	0.974547i	$0.428028\pi$
$854$	0	0
$855$	−4.80437e11	−0.0307460
$856$	5.25281e12	0.334395
$857$	2.60920e11	0.0165232	0.00826158	−	0.999966i	$-0.497370\pi$
$857$	2.60920e11	0.0165232	0.00826158	+	0.999966i	$0.497370\pi$
$858$	1.79186e13	1.12879
$859$	2.54206e13	1.59300	0.796502	−	0.604636i	$-0.206681\pi$
$859$	2.54206e13	1.59300	0.796502	+	0.604636i	$0.206681\pi$
$860$	2.79053e11	0.0173957
$861$	0	0
$862$	1.08427e13	0.668889
$863$	7.18619e12	0.441012	0.220506	−	0.975386i	$-0.429229\pi$
$863$	7.18619e12	0.441012	0.220506	+	0.975386i	$0.429229\pi$
$864$	−5.20334e11	−0.0317666
$865$	4.65189e11	0.0282525
$866$	9.06535e12	0.547714
$867$	−1.81322e13	−1.08984
$868$	0	0
$869$	5.54479e12	0.329835
$870$	−2.66245e11	−0.0157560
$871$	3.46131e13	2.03779
$872$	2.07490e12	0.121527
$873$	−1.53754e13	−0.895905
$874$	−4.00797e12	−0.232340
$875$	0	0
$876$	2.35094e12	0.134888
$877$	−2.68806e13	−1.53441	−0.767205	−	0.641402i	$-0.778353\pi$
$877$	−2.68806e13	−1.53441	−0.767205	+	0.641402i	$0.778353\pi$
$878$	−1.18598e13	−0.673521
$879$	−3.08301e13	−1.74191
$880$	1.13458e11	0.00637769
$881$	−5.33553e11	−0.0298391	−0.0149195	−	0.999889i	$-0.504749\pi$
$881$	−5.33553e11	−0.0298391	−0.0149195	+	0.999889i	$0.504749\pi$
$882$	0	0
$883$	6.42561e12	0.355706	0.177853	−	0.984057i	$-0.443085\pi$
$883$	6.42561e12	0.355706	0.177853	+	0.984057i	$0.443085\pi$
$884$	−1.33908e13	−0.737518
$885$	9.01278e10	0.00493872
$886$	−1.48033e12	−0.0807062
$887$	2.88437e12	0.156457	0.0782285	−	0.996935i	$-0.475074\pi$
$887$	2.88437e12	0.156457	0.0782285	+	0.996935i	$0.475074\pi$
$888$	1.09617e13	0.591586
$889$	0	0
$890$	4.56106e11	0.0243675
$891$	2.22477e13	1.18259
$892$	−1.61195e13	−0.852528
$893$	2.66101e12	0.140028
$894$	2.11811e13	1.10899
$895$	−6.70259e11	−0.0349172
$896$	0	0
$897$	6.50570e12	0.335527
$898$	2.03015e12	0.104180
$899$	1.76774e13	0.902610
$900$	−8.54280e12	−0.434019
$901$	4.07611e13	2.06056
$902$	−1.83274e13	−0.921873
$903$	0	0
$904$	−4.73138e12	−0.235630
$905$	−1.12091e11	−0.00555459
$906$	−1.73534e13	−0.855675
$907$	−1.74881e13	−0.858044	−0.429022	−	0.903294i	$-0.641142\pi$
$907$	−1.74881e13	−0.858044	−0.429022	+	0.903294i	$0.641142\pi$
$908$	−1.40291e13	−0.684925
$909$	−1.08078e12	−0.0525049
$910$	0	0
$911$	−1.68088e13	−0.808543	−0.404271	−	0.914639i	$-0.632475\pi$
$911$	−1.68088e13	−0.808543	−0.404271	+	0.914639i	$0.632475\pi$
$912$	−1.05154e13	−0.503324
$913$	2.92541e12	0.139337
$914$	−1.64504e13	−0.779686
$915$	7.33914e11	0.0346139
$916$	1.57214e13	0.737840
$917$	0	0
$918$	−3.66548e12	−0.170348
$919$	−2.48947e13	−1.15130	−0.575648	−	0.817698i	$-0.695250\pi$
$919$	−2.48947e13	−1.15130	−0.575648	+	0.817698i	$0.695250\pi$
$920$	4.11931e10	0.00189574
$921$	2.78403e13	1.27498
$922$	−1.29637e13	−0.590800
$923$	3.24798e13	1.47301
$924$	0	0
$925$	−2.72395e13	−1.22338
$926$	2.31669e13	1.03542
$927$	−2.07846e13	−0.924449
$928$	−2.70868e12	−0.119892
$929$	−3.84486e13	−1.69360	−0.846799	−	0.531914i	$-0.821473\pi$
$929$	−3.84486e13	−1.69360	−0.846799	+	0.531914i	$0.821473\pi$
$930$	−7.05320e11	−0.0309181
$931$	0	0
$932$	−2.15785e12	−0.0936806
$933$	−5.04546e13	−2.17988
$934$	−7.15255e12	−0.307539
$935$	7.99252e11	0.0342004
$936$	7.93379e12	0.337862
$937$	4.89574e11	0.0207486	0.0103743	−	0.999946i	$-0.496698\pi$
$937$	4.89574e11	0.0207486	0.0103743	+	0.999946i	$0.496698\pi$
$938$	0	0
$939$	−1.60748e13	−0.674763
$940$	−2.73493e10	−0.00114254
$941$	−2.20721e13	−0.917679	−0.458840	−	0.888519i	$-0.651735\pi$
$941$	−2.20721e13	−0.917679	−0.458840	+	0.888519i	$0.651735\pi$
$942$	2.02509e13	0.837944
$943$	−6.65411e12	−0.274023
$944$	9.16926e11	0.0375803
$945$	0	0
$946$	−2.67612e13	−1.08642
$947$	4.86143e11	0.0196422	0.00982108	−	0.999952i	$-0.496874\pi$
$947$	4.86143e11	0.0196422	0.00982108	+	0.999952i	$0.496874\pi$
$948$	5.28171e12	0.212391
$949$	5.42556e12	0.217144
$950$	2.61304e13	1.04086
$951$	−5.19171e13	−2.05825
$952$	0	0
$953$	−2.77682e13	−1.09051	−0.545254	−	0.838271i	$-0.683567\pi$
$953$	−2.77682e13	−1.09051	−0.545254	+	0.838271i	$0.683567\pi$
$954$	−2.41501e13	−0.943954
$955$	8.25945e11	0.0321319
$956$	8.03714e12	0.311201
$957$	2.55330e13	0.984006
$958$	−1.39128e12	−0.0533667
$959$	0	0
$960$	1.08075e11	0.00410680
$961$	2.03903e13	0.771202
$962$	2.52976e13	0.952339
$963$	−2.19236e13	−0.821475
$964$	−3.73417e12	−0.139267
$965$	6.05015e11	0.0224591
$966$	0	0
$967$	−2.53282e12	−0.0931505	−0.0465752	−	0.998915i	$-0.514831\pi$
$967$	−2.53282e12	−0.0931505	−0.0465752	+	0.998915i	$0.514831\pi$
$968$	−1.22251e12	−0.0447519
$969$	−7.40752e13	−2.69908
$970$	−4.83362e11	−0.0175307
$971$	−8.52422e12	−0.307729	−0.153864	−	0.988092i	$-0.549172\pi$
$971$	−8.52422e12	−0.307729	−0.153864	+	0.988092i	$0.549172\pi$
$972$	1.86917e13	0.671661
$973$	0	0
$974$	7.71096e9	0.000274532 0
$975$	−4.24146e13	−1.50312
$976$	7.46657e12	0.263388
$977$	−3.37176e13	−1.18394	−0.591972	−	0.805958i	$-0.701651\pi$
$977$	−3.37176e13	−1.18394	−0.591972	+	0.805958i	$0.701651\pi$
$978$	−2.45106e13	−0.856699
$979$	−4.37407e13	−1.52182
$980$	0	0
$981$	−8.66001e12	−0.298544
$982$	9.41824e12	0.323197
$983$	−3.27904e12	−0.112010	−0.0560049	−	0.998430i	$-0.517836\pi$
$983$	−3.27904e12	−0.112010	−0.0560049	+	0.998430i	$0.517836\pi$
$984$	−1.74578e13	−0.593624
$985$	−1.35272e12	−0.0457872
$986$	−1.90812e13	−0.642923
$987$	0	0
$988$	−2.42676e13	−0.810253
$989$	−9.71618e12	−0.322933
$990$	−4.73540e11	−0.0156674
$991$	2.29294e13	0.755200	0.377600	−	0.925969i	$-0.376749\pi$
$991$	2.29294e13	0.755200	0.377600	+	0.925969i	$0.376749\pi$
$992$	−7.17566e12	−0.235266
$993$	−3.71550e13	−1.21268
$994$	0	0
$995$	1.26584e12	0.0409425
$996$	2.78661e12	0.0897240
$997$	−1.25509e13	−0.402297	−0.201148	−	0.979561i	$-0.564467\pi$
$997$	−1.25509e13	−0.402297	−0.201148	+	0.979561i	$0.564467\pi$
$998$	3.96714e13	1.26587
$999$	6.92471e12	0.219967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.k.1.1	✓	4
7.2	even	3		98.10.c.m.67.4		8
7.3	odd	6		98.10.c.m.79.1		8
7.4	even	3		98.10.c.m.79.4		8
7.5	odd	6		98.10.c.m.67.1		8
7.6	odd	2	inner	98.10.a.k.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.k.1.1	✓	4	1.1	even	1	trivial
98.10.a.k.1.4	yes	4	7.6	odd	2	inner
98.10.c.m.67.1		8	7.5	odd	6
98.10.c.m.67.4		8	7.2	even	3
98.10.c.m.79.1		8	7.3	odd	6
98.10.c.m.79.4		8	7.4	even	3

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -191.777 q^{3} +256.000 q^{4} -33.5898 q^{5} +3068.43 q^{6} -4096.00 q^{8} +17095.5 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -191.777 q^{3} +256.000 q^{4} -33.5898 q^{5} +3068.43 q^{6} -4096.00 q^{8} +17095.5 q^{9} +537.437 q^{10} -51540.4 q^{11} -49094.9 q^{12} -113303. q^{13} +6441.76 q^{15} +65536.0 q^{16} +461667. q^{17} -273528. q^{18} +836657. q^{19} -8598.99 q^{20} +824646. q^{22} +299404. q^{23} +785519. q^{24} -1.95200e6 q^{25} +1.81284e6 q^{26} +496229. q^{27} +2.58319e6 q^{29} -103068. q^{30} +6.84324e6 q^{31} -1.04858e6 q^{32} +9.88427e6 q^{33} -7.38666e6 q^{34} +4.37644e6 q^{36} +1.39547e7 q^{37} -1.33865e7 q^{38} +2.17288e7 q^{39} +137584. q^{40} -2.22245e7 q^{41} -3.24518e7 q^{43} -1.31943e7 q^{44} -574234. q^{45} -4.79046e6 q^{46} +3.18053e6 q^{47} -1.25683e7 q^{48} +3.12319e7 q^{50} -8.85371e7 q^{51} -2.90055e7 q^{52} +8.82912e7 q^{53} -7.93966e6 q^{54} +1.73123e6 q^{55} -1.60452e8 q^{57} -4.13311e7 q^{58} +1.39912e7 q^{59} +1.64909e6 q^{60} +1.13931e8 q^{61} -1.09492e8 q^{62} +1.67772e7 q^{64} +3.80581e6 q^{65} -1.58148e8 q^{66} -3.05493e8 q^{67} +1.18187e8 q^{68} -5.74188e7 q^{69} -2.86664e8 q^{71} -7.00231e7 q^{72} -4.78856e7 q^{73} -2.23275e8 q^{74} +3.74348e8 q^{75} +2.14184e8 q^{76} -3.47661e8 q^{78} -1.07582e8 q^{79} -2.20134e6 q^{80} -4.31656e8 q^{81} +3.55593e8 q^{82} -5.67595e7 q^{83} -1.55073e7 q^{85} +5.19228e8 q^{86} -4.95398e8 q^{87} +2.11109e8 q^{88} +8.48669e8 q^{89} +9.18774e6 q^{90} +7.66474e7 q^{92} -1.31238e9 q^{93} -5.08885e7 q^{94} -2.81032e7 q^{95} +2.01093e8 q^{96} -8.99384e8 q^{97} -8.81107e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 1024 q^{4} - 16384 q^{8} + 15912 q^{9}+O(q^{10}) \) 4 * q - 64 * q^2 + 1024 * q^4 - 16384 * q^8 + 15912 * q^9	\( 4 q - 64 q^{2} + 1024 q^{4} - 16384 q^{8} + 15912 q^{9} + 9548 q^{11} - 417312 q^{15} + 262144 q^{16} - 254592 q^{18} - 152768 q^{22} - 2836736 q^{23} + 966144 q^{25} + 16669972 q^{29} + 6676992 q^{30} - 4194304 q^{32} + 4073472 q^{36} + 3226372 q^{37} + 69110568 q^{39} - 76480204 q^{43} + 2444288 q^{44} + 45387776 q^{46} - 15458304 q^{50} - 97261596 q^{51} + 13708112 q^{53} - 371557692 q^{57} - 266719552 q^{58} - 106831872 q^{60} + 67108864 q^{64} - 515731188 q^{65} - 814420776 q^{67} - 1324668744 q^{71} - 65175552 q^{72} - 51621952 q^{74} - 1105769088 q^{78} - 668411176 q^{79} - 1111307688 q^{81} - 1659264964 q^{85} + 1223683264 q^{86} - 39108608 q^{88} - 726204416 q^{92} - 3706577496 q^{93} + 977188688 q^{95} - 2791581660 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 1024 * q^4 - 16384 * q^8 + 15912 * q^9 + 9548 * q^11 - 417312 * q^15 + 262144 * q^16 - 254592 * q^18 - 152768 * q^22 - 2836736 * q^23 + 966144 * q^25 + 16669972 * q^29 + 6676992 * q^30 - 4194304 * q^32 + 4073472 * q^36 + 3226372 * q^37 + 69110568 * q^39 - 76480204 * q^43 + 2444288 * q^44 + 45387776 * q^46 - 15458304 * q^50 - 97261596 * q^51 + 13708112 * q^53 - 371557692 * q^57 - 266719552 * q^58 - 106831872 * q^60 + 67108864 * q^64 - 515731188 * q^65 - 814420776 * q^67 - 1324668744 * q^71 - 65175552 * q^72 - 51621952 * q^74 - 1105769088 * q^78 - 668411176 * q^79 - 1111307688 * q^81 - 1659264964 * q^85 + 1223683264 * q^86 - 39108608 * q^88 - 726204416 * q^92 - 3706577496 * q^93 + 977188688 * q^95 - 2791581660 * q^99

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