LMFDB - Embedded newform 98.10.a.k.1.2

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			1.2
Root			$33.7881$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} -102.682 q^{3} +256.000 q^{4} +2094.80 q^{5} +1642.91 q^{6} -4096.00 q^{8} -9139.47 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -102.682 q^{3} +256.000 q^{4} +2094.80 q^{5} +1642.91 q^{6} -4096.00 q^{8} -9139.47 q^{9} -33516.8 q^{10} +56314.4 q^{11} -26286.5 q^{12} -124915. q^{13} -215098. q^{15} +65536.0 q^{16} -388641. q^{17} +146232. q^{18} +246657. q^{19} +536269. q^{20} -901030. q^{22} -1.71777e6 q^{23} +420584. q^{24} +2.43507e6 q^{25} +1.99863e6 q^{26} +2.95954e6 q^{27} +5.75179e6 q^{29} +3.44156e6 q^{30} +5.26785e6 q^{31} -1.04858e6 q^{32} -5.78246e6 q^{33} +6.21825e6 q^{34} -2.33970e6 q^{36} -1.23415e7 q^{37} -3.94651e6 q^{38} +1.28264e7 q^{39} -8.58031e6 q^{40} +5.54285e6 q^{41} -5.78833e6 q^{43} +1.44165e7 q^{44} -1.91454e7 q^{45} +2.74843e7 q^{46} -5.11932e7 q^{47} -6.72935e6 q^{48} -3.89611e7 q^{50} +3.99063e7 q^{51} -3.19782e7 q^{52} -8.14372e7 q^{53} -4.73526e7 q^{54} +1.17967e8 q^{55} -2.53272e7 q^{57} -9.20287e7 q^{58} +7.85852e7 q^{59} -5.50650e7 q^{60} -1.38027e7 q^{61} -8.42856e7 q^{62} +1.67772e7 q^{64} -2.61671e8 q^{65} +9.25193e7 q^{66} -1.01717e8 q^{67} -9.94920e7 q^{68} +1.76384e8 q^{69} -3.75670e8 q^{71} +3.74353e7 q^{72} +4.45945e8 q^{73} +1.97464e8 q^{74} -2.50037e8 q^{75} +6.31442e7 q^{76} -2.05223e8 q^{78} -2.26624e8 q^{79} +1.37285e8 q^{80} -1.23998e8 q^{81} -8.86857e7 q^{82} -5.26823e8 q^{83} -8.14125e8 q^{85} +9.26132e7 q^{86} -5.90604e8 q^{87} -2.30664e8 q^{88} -5.19381e8 q^{89} +3.06326e8 q^{90} -4.39750e8 q^{92} -5.40912e8 q^{93} +8.19091e8 q^{94} +5.16697e8 q^{95} +1.07670e8 q^{96} +8.75899e8 q^{97} -5.14684e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−102.682	−0.731893	−0.365946	−	0.930636i	$-0.619255\pi$
$3$	−102.682	−0.731893	−0.365946	+	0.930636i	$0.619255\pi$
$4$	256.000	0.500000
$5$	2094.80	1.49892	0.749459	−	0.662051i	$-0.230314\pi$
$5$	2094.80	1.49892	0.749459	+	0.662051i	$0.230314\pi$
$6$	1642.91	0.517526
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	−9139.47	−0.464333
$10$	−33516.8	−1.05990
$11$	56314.4	1.15972	0.579859	−	0.814717i	$-0.303108\pi$
$11$	56314.4	1.15972	0.579859	+	0.814717i	$0.303108\pi$
$12$	−26286.5	−0.365946
$13$	−124915.	−1.21302	−0.606510	−	0.795076i	$-0.707431\pi$
$13$	−124915.	−1.21302	−0.606510	+	0.795076i	$0.707431\pi$
$14$	0	0
$15$	−215098.	−1.09705
$16$	65536.0	0.250000
$17$	−388641.	−1.12857	−0.564285	−	0.825580i	$-0.690848\pi$
$17$	−388641.	−1.12857	−0.564285	+	0.825580i	$0.690848\pi$
$18$	146232.	0.328333
$19$	246657.	0.434212	0.217106	−	0.976148i	$-0.430338\pi$
$19$	246657.	0.434212	0.217106	+	0.976148i	$0.430338\pi$
$20$	536269.	0.749459
$21$	0	0
$22$	−901030.	−0.820044
$23$	−1.71777e6	−1.27994	−0.639971	−	0.768399i	$-0.721054\pi$
$23$	−1.71777e6	−1.27994	−0.639971	+	0.768399i	$0.721054\pi$
$24$	420584.	0.258763
$25$	2.43507e6	1.24676
$26$	1.99863e6	0.857735
$27$	2.95954e6	1.07173
$28$	0	0
$29$	5.75179e6	1.51012	0.755061	−	0.655654i	$-0.227607\pi$
$29$	5.75179e6	1.51012	0.755061	+	0.655654i	$0.227607\pi$
$30$	3.44156e6	0.775729
$31$	5.26785e6	1.02449	0.512243	−	0.858841i	$-0.328815\pi$
$31$	5.26785e6	1.02449	0.512243	+	0.858841i	$0.328815\pi$
$32$	−1.04858e6	−0.176777
$33$	−5.78246e6	−0.848789
$34$	6.21825e6	0.798019
$35$	0	0
$36$	−2.33970e6	−0.232167
$37$	−1.23415e7	−1.08258	−0.541290	−	0.840836i	$-0.682064\pi$
$37$	−1.23415e7	−1.08258	−0.541290	+	0.840836i	$0.682064\pi$
$38$	−3.94651e6	−0.307035
$39$	1.28264e7	0.887801
$40$	−8.58031e6	−0.529948
$41$	5.54285e6	0.306342	0.153171	−	0.988200i	$-0.451052\pi$
$41$	5.54285e6	0.306342	0.153171	+	0.988200i	$0.451052\pi$
$42$	0	0
$43$	−5.78833e6	−0.258193	−0.129097	−	0.991632i	$-0.541208\pi$
$43$	−5.78833e6	−0.258193	−0.129097	+	0.991632i	$0.541208\pi$
$44$	1.44165e7	0.579859
$45$	−1.91454e7	−0.695997
$46$	2.74843e7	0.905055
$47$	−5.11932e7	−1.53028	−0.765142	−	0.643861i	$-0.777331\pi$
$47$	−5.11932e7	−1.53028	−0.765142	+	0.643861i	$0.777331\pi$
$48$	−6.72935e6	−0.182973
$49$	0	0
$50$	−3.89611e7	−0.881589
$51$	3.99063e7	0.825991
$52$	−3.19782e7	−0.606510
$53$	−8.14372e7	−1.41769	−0.708845	−	0.705364i	$-0.750783\pi$
$53$	−8.14372e7	−1.41769	−0.708845	+	0.705364i	$0.750783\pi$
$54$	−4.73526e7	−0.757831
$55$	1.17967e8	1.73832
$56$	0	0
$57$	−2.53272e7	−0.317797
$58$	−9.20287e7	−1.06782
$59$	7.85852e7	0.844319	0.422160	−	0.906522i	$-0.361272\pi$
$59$	7.85852e7	0.844319	0.422160	+	0.906522i	$0.361272\pi$
$60$	−5.50650e7	−0.548523
$61$	−1.38027e7	−0.127638	−0.0638188	−	0.997962i	$-0.520328\pi$
$61$	−1.38027e7	−0.127638	−0.0638188	+	0.997962i	$0.520328\pi$
$62$	−8.42856e7	−0.724421
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−2.61671e8	−1.81822
$66$	9.25193e7	0.600184
$67$	−1.01717e8	−0.616678	−0.308339	−	0.951276i	$-0.599773\pi$
$67$	−1.01717e8	−0.616678	−0.308339	+	0.951276i	$0.599773\pi$
$68$	−9.94920e7	−0.564285
$69$	1.76384e8	0.936780
$70$	0	0
$71$	−3.75670e8	−1.75446	−0.877232	−	0.480067i	$-0.840612\pi$
$71$	−3.75670e8	−1.75446	−0.877232	+	0.480067i	$0.840612\pi$
$72$	3.74353e7	0.164167
$73$	4.45945e8	1.83793	0.918964	−	0.394341i	$-0.129027\pi$
$73$	4.45945e8	1.83793	0.918964	+	0.394341i	$0.129027\pi$
$74$	1.97464e8	0.765499
$75$	−2.50037e8	−0.912491
$76$	6.31442e7	0.217106
$77$	0	0
$78$	−2.05223e8	−0.627770
$79$	−2.26624e8	−0.654612	−0.327306	−	0.944918i	$-0.606141\pi$
$79$	−2.26624e8	−0.654612	−0.327306	+	0.944918i	$0.606141\pi$
$80$	1.37285e8	0.374730
$81$	−1.23998e8	−0.320061
$82$	−8.86857e7	−0.216616
$83$	−5.26823e8	−1.21847	−0.609233	−	0.792992i	$-0.708522\pi$
$83$	−5.26823e8	−1.21847	−0.609233	+	0.792992i	$0.708522\pi$
$84$	0	0
$85$	−8.14125e8	−1.69163
$86$	9.26132e7	0.182570
$87$	−5.90604e8	−1.10525
$88$	−2.30664e8	−0.410022
$89$	−5.19381e8	−0.877468	−0.438734	−	0.898617i	$-0.644573\pi$
$89$	−5.19381e8	−0.877468	−0.438734	+	0.898617i	$0.644573\pi$
$90$	3.06326e8	0.492145
$91$	0	0
$92$	−4.39750e8	−0.639971
$93$	−5.40912e8	−0.749814
$94$	8.19091e8	1.08207
$95$	5.16697e8	0.650849
$96$	1.07670e8	0.129382
$97$	8.75899e8	1.00457	0.502286	−	0.864701i	$-0.332492\pi$
$97$	8.75899e8	1.00457	0.502286	+	0.864701i	$0.332492\pi$
$98$	0	0
$99$	−5.14684e8	−0.538495
$100$	6.23378e8	0.623378
$101$	8.73621e6	0.00835366	0.00417683	−	0.999991i	$-0.498670\pi$
$101$	8.73621e6	0.00835366	0.00417683	+	0.999991i	$0.498670\pi$
$102$	−6.38501e8	−0.584064
$103$	−9.59029e8	−0.839584	−0.419792	−	0.907620i	$-0.637897\pi$
$103$	−9.59029e8	−0.839584	−0.419792	+	0.907620i	$0.637897\pi$
$104$	5.11650e8	0.428868
$105$	0	0
$106$	1.30299e9	1.00246
$107$	−1.48471e9	−1.09500	−0.547499	−	0.836806i	$-0.684420\pi$
$107$	−1.48471e9	−1.09500	−0.547499	+	0.836806i	$0.684420\pi$
$108$	7.57642e8	0.535867
$109$	−1.53530e9	−1.04178	−0.520888	−	0.853625i	$-0.674399\pi$
$109$	−1.53530e9	−1.04178	−0.520888	+	0.853625i	$0.674399\pi$
$110$	−1.88748e9	−1.22918
$111$	1.26724e9	0.792332
$112$	0	0
$113$	3.29034e9	1.89840	0.949199	−	0.314677i	$-0.101896\pi$
$113$	3.29034e9	1.89840	0.949199	+	0.314677i	$0.101896\pi$
$114$	4.05235e8	0.224716
$115$	−3.59839e9	−1.91853
$116$	1.47246e9	0.755061
$117$	1.14165e9	0.563246
$118$	−1.25736e9	−0.597024
$119$	0	0
$120$	8.81040e8	0.387865
$121$	8.13362e8	0.344945
$122$	2.20843e8	0.0902534
$123$	−5.69150e8	−0.224209
$124$	1.34857e9	0.512243
$125$	1.00958e9	0.369866
$126$	0	0
$127$	−5.41672e9	−1.84765	−0.923826	−	0.382814i	$-0.874955\pi$
$127$	−5.41672e9	−1.84765	−0.923826	+	0.382814i	$0.874955\pi$
$128$	−2.68435e8	−0.0883883
$129$	5.94355e8	0.188970
$130$	4.18674e9	1.28567
$131$	3.38792e9	1.00511	0.502553	−	0.864546i	$-0.332394\pi$
$131$	3.38792e9	1.00511	0.502553	+	0.864546i	$0.332394\pi$
$132$	−1.48031e9	−0.424394
$133$	0	0
$134$	1.62748e9	0.436057
$135$	6.19965e9	1.60644
$136$	1.59187e9	0.399009
$137$	4.74729e9	1.15134	0.575669	−	0.817683i	$-0.304742\pi$
$137$	4.74729e9	1.15134	0.575669	+	0.817683i	$0.304742\pi$
$138$	−2.82214e9	−0.662403
$139$	−2.17838e9	−0.494958	−0.247479	−	0.968893i	$-0.579602\pi$
$139$	−2.17838e9	−0.494958	−0.247479	+	0.968893i	$0.579602\pi$
$140$	0	0
$141$	5.25661e9	1.12000
$142$	6.01073e9	1.24059
$143$	−7.03449e9	−1.40676
$144$	−5.98964e8	−0.116083
$145$	1.20489e10	2.26355
$146$	−7.13512e9	−1.29961
$147$	0	0
$148$	−3.15942e9	−0.541290
$149$	−1.18058e10	−1.96226	−0.981129	−	0.193354i	$-0.938064\pi$
$149$	−1.18058e10	−1.96226	−0.981129	+	0.193354i	$0.938064\pi$
$150$	4.00059e9	0.645228
$151$	−6.31601e9	−0.988660	−0.494330	−	0.869274i	$-0.664586\pi$
$151$	−6.31601e9	−0.988660	−0.494330	+	0.869274i	$0.664586\pi$
$152$	−1.01031e9	−0.153517
$153$	3.55197e9	0.524032
$154$	0	0
$155$	1.10351e10	1.53562
$156$	3.28357e9	0.443900
$157$	1.03026e9	0.135331	0.0676655	−	0.997708i	$-0.478445\pi$
$157$	1.03026e9	0.135331	0.0676655	+	0.997708i	$0.478445\pi$
$158$	3.62598e9	0.462881
$159$	8.36211e9	1.03760
$160$	−2.19656e9	−0.264974
$161$	0	0
$162$	1.98397e9	0.226318
$163$	−3.34930e9	−0.371629	−0.185814	−	0.982585i	$-0.559492\pi$
$163$	−3.34930e9	−0.371629	−0.185814	+	0.982585i	$0.559492\pi$
$164$	1.41897e9	0.153171
$165$	−1.21131e10	−1.27226
$166$	8.42917e9	0.861585
$167$	−1.63487e10	−1.62652	−0.813261	−	0.581899i	$-0.802310\pi$
$167$	−1.63487e10	−1.62652	−0.813261	+	0.581899i	$0.802310\pi$
$168$	0	0
$169$	4.99917e9	0.471420
$170$	1.30260e10	1.19616
$171$	−2.25431e9	−0.201619
$172$	−1.48181e9	−0.129097
$173$	7.47099e9	0.634119	0.317059	−	0.948406i	$-0.397305\pi$
$173$	7.47099e9	0.634119	0.317059	+	0.948406i	$0.397305\pi$
$174$	9.44966e9	0.781528
$175$	0	0
$176$	3.69062e9	0.289929
$177$	−8.06926e9	−0.617951
$178$	8.31010e9	0.620464
$179$	−6.23008e9	−0.453581	−0.226790	−	0.973944i	$-0.572823\pi$
$179$	−6.23008e9	−0.453581	−0.226790	+	0.973944i	$0.572823\pi$
$180$	−4.90122e9	−0.347999
$181$	−5.46976e9	−0.378804	−0.189402	−	0.981900i	$-0.560655\pi$
$181$	−5.46976e9	−0.378804	−0.189402	+	0.981900i	$0.560655\pi$
$182$	0	0
$183$	1.41728e9	0.0934170
$184$	7.03599e9	0.452528
$185$	−2.58530e10	−1.62270
$186$	8.65459e9	0.530198
$187$	−2.18861e10	−1.30882
$188$	−1.31055e10	−0.765142
$189$	0	0
$190$	−8.26716e9	−0.460220
$191$	6.93485e9	0.377039	0.188520	−	0.982069i	$-0.439631\pi$
$191$	6.93485e9	0.377039	0.188520	+	0.982069i	$0.439631\pi$
$192$	−1.72271e9	−0.0914866
$193$	4.17331e9	0.216508	0.108254	−	0.994123i	$-0.465474\pi$
$193$	4.17331e9	0.216508	0.108254	+	0.994123i	$0.465474\pi$
$194$	−1.40144e10	−0.710340
$195$	2.68689e10	1.33074
$196$	0	0
$197$	−3.62569e10	−1.71511	−0.857556	−	0.514391i	$-0.828018\pi$
$197$	−3.62569e10	−1.71511	−0.857556	+	0.514391i	$0.828018\pi$
$198$	8.23494e9	0.380774
$199$	−1.79583e10	−0.811759	−0.405880	−	0.913927i	$-0.633035\pi$
$199$	−1.79583e10	−0.811759	−0.405880	+	0.913927i	$0.633035\pi$
$200$	−9.97404e9	−0.440795
$201$	1.04445e10	0.451342
$202$	−1.39779e8	−0.00590693
$203$	0	0
$204$	1.02160e10	0.412996
$205$	1.16112e10	0.459181
$206$	1.53445e10	0.593675
$207$	1.56995e10	0.594320
$208$	−8.18641e9	−0.303255
$209$	1.38903e10	0.503564
$210$	0	0
$211$	6.33838e9	0.220144	0.110072	−	0.993924i	$-0.464892\pi$
$211$	6.33838e9	0.220144	0.110072	+	0.993924i	$0.464892\pi$
$212$	−2.08479e10	−0.708845
$213$	3.85745e10	1.28408
$214$	2.37553e10	0.774281
$215$	−1.21254e10	−0.387011
$216$	−1.21223e10	−0.378915
$217$	0	0
$218$	2.45648e10	0.736647
$219$	−4.57904e10	−1.34517
$220$	3.01997e10	0.869161
$221$	4.85469e10	1.36898
$222$	−2.02759e10	−0.560263
$223$	4.34746e10	1.17724	0.588619	−	0.808411i	$-0.299672\pi$
$223$	4.34746e10	1.17724	0.588619	+	0.808411i	$0.299672\pi$
$224$	0	0
$225$	−2.22552e10	−0.578910
$226$	−5.26454e10	−1.34237
$227$	1.89487e10	0.473657	0.236828	−	0.971552i	$-0.423892\pi$
$227$	1.89487e10	0.473657	0.236828	+	0.971552i	$0.423892\pi$
$228$	−6.48375e9	−0.158898
$229$	−3.72378e10	−0.894796	−0.447398	−	0.894335i	$-0.647649\pi$
$229$	−3.72378e10	−0.894796	−0.447398	+	0.894335i	$0.647649\pi$
$230$	5.75743e10	1.35660
$231$	0	0
$232$	−2.35593e10	−0.533909
$233$	1.83837e10	0.408632	0.204316	−	0.978905i	$-0.434503\pi$
$233$	1.83837e10	0.408632	0.204316	+	0.978905i	$0.434503\pi$
$234$	−1.82665e10	−0.398275
$235$	−1.07240e11	−2.29377
$236$	2.01178e10	0.422160
$237$	2.32701e10	0.479106
$238$	0	0
$239$	−3.65476e10	−0.724550	−0.362275	−	0.932071i	$-0.618000\pi$
$239$	−3.65476e10	−0.724550	−0.362275	+	0.932071i	$0.618000\pi$
$240$	−1.40966e10	−0.274262
$241$	−2.85905e10	−0.545941	−0.272970	−	0.962022i	$-0.588006\pi$
$241$	−2.85905e10	−0.545941	−0.272970	+	0.962022i	$0.588006\pi$
$242$	−1.30138e10	−0.243913
$243$	−4.55203e10	−0.837484
$244$	−3.53348e9	−0.0638188
$245$	0	0
$246$	9.10639e9	0.158540
$247$	−3.08111e10	−0.526709
$248$	−2.15771e10	−0.362210
$249$	5.40951e10	0.891786
$250$	−1.61532e10	−0.261535
$251$	1.00172e10	0.159300	0.0796499	−	0.996823i	$-0.474620\pi$
$251$	1.00172e10	0.159300	0.0796499	+	0.996823i	$0.474620\pi$
$252$	0	0
$253$	−9.67353e10	−1.48437
$254$	8.66676e10	1.30649
$255$	8.35957e10	1.23809
$256$	4.29497e9	0.0625000
$257$	1.69681e10	0.242625	0.121312	−	0.992614i	$-0.461290\pi$
$257$	1.69681e10	0.242625	0.121312	+	0.992614i	$0.461290\pi$
$258$	−9.50968e9	−0.133622
$259$	0	0
$260$	−6.69879e10	−0.909109
$261$	−5.25683e10	−0.701200
$262$	−5.42067e10	−0.710717
$263$	7.07192e9	0.0911458	0.0455729	−	0.998961i	$-0.485489\pi$
$263$	7.07192e9	0.0911458	0.0455729	+	0.998961i	$0.485489\pi$
$264$	2.36849e10	0.300092
$265$	−1.70595e11	−2.12500
$266$	0	0
$267$	5.33310e10	0.642212
$268$	−2.60397e10	−0.308339
$269$	3.69954e8	0.00430787	0.00215393	−	0.999998i	$-0.499314\pi$
$269$	3.69954e8	0.00430787	0.00215393	+	0.999998i	$0.499314\pi$
$270$	−9.91944e10	−1.13593
$271$	−1.24288e11	−1.39981	−0.699904	−	0.714237i	$-0.746774\pi$
$271$	−1.24288e11	−1.39981	−0.699904	+	0.714237i	$0.746774\pi$
$272$	−2.54700e10	−0.282142
$273$	0	0
$274$	−7.59566e10	−0.814119
$275$	1.37129e11	1.44588
$276$	4.51542e10	0.468390
$277$	1.69613e10	0.173101	0.0865506	−	0.996247i	$-0.472416\pi$
$277$	1.69613e10	0.173101	0.0865506	+	0.996247i	$0.472416\pi$
$278$	3.48542e10	0.349988
$279$	−4.81454e10	−0.475703
$280$	0	0
$281$	1.16441e11	1.11411	0.557053	−	0.830477i	$-0.311932\pi$
$281$	1.16441e11	1.11411	0.557053	+	0.830477i	$0.311932\pi$
$282$	−8.41057e10	−0.791962
$283$	2.65533e10	0.246082	0.123041	−	0.992402i	$-0.460735\pi$
$283$	2.65533e10	0.246082	0.123041	+	0.992402i	$0.460735\pi$
$284$	−9.61716e10	−0.877232
$285$	−5.30554e10	−0.476351
$286$	1.12552e11	0.994731
$287$	0	0
$288$	9.58343e9	0.0820833
$289$	3.24537e10	0.273668
$290$	−1.92782e11	−1.60057
$291$	−8.99388e10	−0.735239
$292$	1.14162e11	0.918964
$293$	9.43424e8	0.00747829	0.00373915	−	0.999993i	$-0.498810\pi$
$293$	9.43424e8	0.00747829	0.00373915	+	0.999993i	$0.498810\pi$
$294$	0	0
$295$	1.64620e11	1.26557
$296$	5.05507e10	0.382750
$297$	1.66665e11	1.24291
$298$	1.88892e11	1.38753
$299$	2.14575e11	1.55260
$300$	−6.40095e10	−0.456245
$301$	0	0
$302$	1.01056e11	0.699088
$303$	−8.97049e8	−0.00611398
$304$	1.61649e10	0.108553
$305$	−2.89139e10	−0.191318
$306$	−5.68315e10	−0.370547
$307$	−2.20668e10	−0.141780	−0.0708902	−	0.997484i	$-0.522584\pi$
$307$	−2.20668e10	−0.141780	−0.0708902	+	0.997484i	$0.522584\pi$
$308$	0	0
$309$	9.84747e10	0.614485
$310$	−1.76562e11	−1.08585
$311$	2.30243e11	1.39561	0.697805	−	0.716288i	$-0.254160\pi$
$311$	2.30243e11	1.39561	0.697805	+	0.716288i	$0.254160\pi$
$312$	−5.25371e10	−0.313885
$313$	1.57588e11	0.928055	0.464027	−	0.885821i	$-0.346404\pi$
$313$	1.57588e11	0.928055	0.464027	+	0.885821i	$0.346404\pi$
$314$	−1.64841e10	−0.0956935
$315$	0	0
$316$	−5.80158e10	−0.327306
$317$	2.41500e11	1.34323	0.671614	−	0.740901i	$-0.265601\pi$
$317$	2.41500e11	1.34323	0.671614	+	0.740901i	$0.265601\pi$
$318$	−1.33794e11	−0.733692
$319$	3.23909e11	1.75132
$320$	3.51449e10	0.187365
$321$	1.52452e11	0.801422
$322$	0	0
$323$	−9.58610e10	−0.490039
$324$	−3.17436e10	−0.160031
$325$	−3.04176e11	−1.51234
$326$	5.35887e10	0.262781
$327$	1.57647e11	0.762468
$328$	−2.27035e10	−0.108308
$329$	0	0
$330$	1.93810e11	0.899627
$331$	1.43537e11	0.657259	0.328630	−	0.944459i	$-0.393413\pi$
$331$	1.43537e11	0.657259	0.328630	+	0.944459i	$0.393413\pi$
$332$	−1.34867e11	−0.609233
$333$	1.12795e11	0.502678
$334$	2.61580e11	1.15012
$335$	−2.13078e11	−0.924350
$336$	0	0
$337$	1.35343e11	0.571612	0.285806	−	0.958288i	$-0.407739\pi$
$337$	1.35343e11	0.571612	0.285806	+	0.958288i	$0.407739\pi$
$338$	−7.99867e10	−0.333344
$339$	−3.37857e11	−1.38942
$340$	−2.08416e11	−0.845816
$341$	2.96656e11	1.18811
$342$	3.60690e10	0.142566
$343$	0	0
$344$	2.37090e10	0.0912851
$345$	3.69489e11	1.40416
$346$	−1.19536e11	−0.448390
$347$	3.87493e11	1.43477	0.717383	−	0.696679i	$-0.245340\pi$
$347$	3.87493e11	1.43477	0.717383	+	0.696679i	$0.245340\pi$
$348$	−1.51195e11	−0.552624
$349$	1.02561e11	0.370056	0.185028	−	0.982733i	$-0.440762\pi$
$349$	1.02561e11	0.370056	0.185028	+	0.982733i	$0.440762\pi$
$350$	0	0
$351$	−3.69690e11	−1.30004
$352$	−5.90499e10	−0.205011
$353$	1.30016e10	0.0445667	0.0222834	−	0.999752i	$-0.492906\pi$
$353$	1.30016e10	0.0445667	0.0222834	+	0.999752i	$0.492906\pi$
$354$	1.29108e11	0.436957
$355$	−7.86955e11	−2.62980
$356$	−1.32962e11	−0.438734
$357$	0	0
$358$	9.96812e10	0.320730
$359$	−8.55526e10	−0.271837	−0.135918	−	0.990720i	$-0.543398\pi$
$359$	−8.55526e10	−0.271837	−0.135918	+	0.990720i	$0.543398\pi$
$360$	7.84195e10	0.246072
$361$	−2.61848e11	−0.811460
$362$	8.75161e10	0.267855
$363$	−8.35174e10	−0.252463
$364$	0	0
$365$	9.34166e11	2.75490
$366$	−2.26765e10	−0.0660558
$367$	1.13117e11	0.325484	0.162742	−	0.986669i	$-0.447966\pi$
$367$	1.13117e11	0.325484	0.162742	+	0.986669i	$0.447966\pi$
$368$	−1.12576e11	−0.319985
$369$	−5.06588e10	−0.142245
$370$	4.13647e11	1.14742
$371$	0	0
$372$	−1.38473e11	−0.374907
$373$	−1.94719e11	−0.520857	−0.260428	−	0.965493i	$-0.583864\pi$
$373$	−1.94719e11	−0.520857	−0.260428	+	0.965493i	$0.583864\pi$
$374$	3.50177e11	0.925477
$375$	−1.03665e11	−0.270702
$376$	2.09687e11	0.541037
$377$	−7.18483e11	−1.83181
$378$	0	0
$379$	−2.22727e11	−0.554493	−0.277247	−	0.960799i	$-0.589422\pi$
$379$	−2.22727e11	−0.554493	−0.277247	+	0.960799i	$0.589422\pi$
$380$	1.32275e11	0.325424
$381$	5.56198e11	1.35228
$382$	−1.10958e11	−0.266607
$383$	3.36594e11	0.799305	0.399652	−	0.916667i	$-0.369131\pi$
$383$	3.36594e11	0.799305	0.399652	+	0.916667i	$0.369131\pi$
$384$	2.75634e10	0.0646908
$385$	0	0
$386$	−6.67730e10	−0.153094
$387$	5.29023e10	0.119888
$388$	2.24230e11	0.502286
$389$	−3.47900e11	−0.770338	−0.385169	−	0.922846i	$-0.625857\pi$
$389$	−3.47900e11	−0.770338	−0.385169	+	0.922846i	$0.625857\pi$
$390$	−4.29902e11	−0.940976
$391$	6.67596e11	1.44450
$392$	0	0
$393$	−3.47877e11	−0.735630
$394$	5.80110e11	1.21277
$395$	−4.74732e11	−0.981210
$396$	−1.31759e11	−0.269248
$397$	−2.75509e10	−0.0556645	−0.0278323	−	0.999613i	$-0.508860\pi$
$397$	−2.75509e10	−0.0556645	−0.0278323	+	0.999613i	$0.508860\pi$
$398$	2.87333e11	0.574001
$399$	0	0
$400$	1.59585e11	0.311689
$401$	−6.21170e11	−1.19967	−0.599834	−	0.800124i	$-0.704767\pi$
$401$	−6.21170e11	−1.19967	−0.599834	+	0.800124i	$0.704767\pi$
$402$	−1.67112e11	−0.319147
$403$	−6.58032e11	−1.24272
$404$	2.23647e9	0.00417683
$405$	−2.59752e11	−0.479746
$406$	0	0
$407$	−6.95003e11	−1.25549
$408$	−1.63456e11	−0.292032
$409$	−1.46395e10	−0.0258686	−0.0129343	−	0.999916i	$-0.504117\pi$
$409$	−1.46395e10	−0.0258686	−0.0129343	+	0.999916i	$0.504117\pi$
$410$	−1.85779e11	−0.324690
$411$	−4.87459e11	−0.842656
$412$	−2.45511e11	−0.419792
$413$	0	0
$414$	−2.51192e11	−0.420247
$415$	−1.10359e12	−1.82638
$416$	1.30983e11	0.214434
$417$	2.23680e11	0.362256
$418$	−2.22245e11	−0.356073
$419$	−1.21505e11	−0.192589	−0.0962946	−	0.995353i	$-0.530699\pi$
$419$	−1.21505e11	−0.192589	−0.0962946	+	0.995353i	$0.530699\pi$
$420$	0	0
$421$	−5.61016e11	−0.870373	−0.435187	−	0.900340i	$-0.643318\pi$
$421$	−5.61016e11	−0.870373	−0.435187	+	0.900340i	$0.643318\pi$
$422$	−1.01414e11	−0.155666
$423$	4.67879e11	0.710562
$424$	3.33567e11	0.501229
$425$	−9.46367e11	−1.40705
$426$	−6.17192e11	−0.907981
$427$	0	0
$428$	−3.80085e11	−0.547499
$429$	7.22313e11	1.02960
$430$	1.94006e11	0.273658
$431$	1.04432e12	1.45776	0.728878	−	0.684644i	$-0.240042\pi$
$431$	1.04432e12	1.45776	0.728878	+	0.684644i	$0.240042\pi$
$432$	1.93956e11	0.267934
$433$	1.05446e12	1.44156	0.720781	−	0.693163i	$-0.243784\pi$
$433$	1.05446e12	1.44156	0.720781	+	0.693163i	$0.243784\pi$
$434$	0	0
$435$	−1.23720e12	−1.65668
$436$	−3.93037e11	−0.520888
$437$	−4.23700e11	−0.555767
$438$	7.32646e11	0.951176
$439$	1.17037e12	1.50395	0.751973	−	0.659194i	$-0.229103\pi$
$439$	1.17037e12	1.50395	0.751973	+	0.659194i	$0.229103\pi$
$440$	−4.83195e11	−0.614589
$441$	0	0
$442$	−7.76751e11	−0.968014
$443$	−7.10660e11	−0.876688	−0.438344	−	0.898807i	$-0.644435\pi$
$443$	−7.10660e11	−0.876688	−0.438344	+	0.898807i	$0.644435\pi$
$444$	3.24415e11	0.396166
$445$	−1.08800e12	−1.31525
$446$	−6.95594e11	−0.832433
$447$	1.21224e12	1.43616
$448$	0	0
$449$	9.40485e11	1.09205	0.546026	−	0.837768i	$-0.316140\pi$
$449$	9.40485e11	1.09205	0.546026	+	0.837768i	$0.316140\pi$
$450$	3.56084e11	0.409351
$451$	3.12142e11	0.355270
$452$	8.42326e11	0.949199
$453$	6.48539e11	0.723593
$454$	−3.03180e11	−0.334926
$455$	0	0
$456$	1.03740e11	0.112358
$457$	−1.15083e12	−1.23420	−0.617102	−	0.786883i	$-0.711693\pi$
$457$	−1.15083e12	−1.23420	−0.617102	+	0.786883i	$0.711693\pi$
$458$	5.95805e11	0.632716
$459$	−1.15020e12	−1.20953
$460$	−9.21188e11	−0.959264
$461$	2.66471e11	0.274786	0.137393	−	0.990517i	$-0.456128\pi$
$461$	2.66471e11	0.274786	0.137393	+	0.990517i	$0.456128\pi$
$462$	0	0
$463$	−4.48766e11	−0.453843	−0.226921	−	0.973913i	$-0.572866\pi$
$463$	−4.48766e11	−0.453843	−0.226921	+	0.973913i	$0.572866\pi$
$464$	3.76949e11	0.377531
$465$	−1.13310e12	−1.12391
$466$	−2.94140e11	−0.288946
$467$	−1.77815e12	−1.72999	−0.864993	−	0.501783i	$-0.832677\pi$
$467$	−1.77815e12	−1.72999	−0.864993	+	0.501783i	$0.832677\pi$
$468$	2.92263e11	0.281623
$469$	0	0
$470$	1.71583e12	1.62194
$471$	−1.05789e11	−0.0990478
$472$	−3.21885e11	−0.298512
$473$	−3.25966e11	−0.299431
$474$	−3.72322e11	−0.338779
$475$	6.00627e11	0.541357
$476$	0	0
$477$	7.44293e11	0.658281
$478$	5.84762e11	0.512334
$479$	1.98906e12	1.72639	0.863194	−	0.504872i	$-0.168460\pi$
$479$	1.98906e12	1.72639	0.863194	+	0.504872i	$0.168460\pi$
$480$	2.25546e11	0.193932
$481$	1.54163e12	1.31319
$482$	4.57448e11	0.386038
$483$	0	0
$484$	2.08221e11	0.172472
$485$	1.83484e12	1.50577
$486$	7.28324e11	0.592191
$487$	6.88592e11	0.554730	0.277365	−	0.960765i	$-0.410539\pi$
$487$	6.88592e11	0.554730	0.277365	+	0.960765i	$0.410539\pi$
$488$	5.65357e10	0.0451267
$489$	3.43911e11	0.271992
$490$	0	0
$491$	1.86881e12	1.45111	0.725553	−	0.688166i	$-0.241584\pi$
$491$	1.86881e12	1.45111	0.725553	+	0.688166i	$0.241584\pi$
$492$	−1.45702e11	−0.112105
$493$	−2.23538e12	−1.70428
$494$	4.92977e11	0.372439
$495$	−1.07816e12	−0.807161
$496$	3.45234e11	0.256121
$497$	0	0
$498$	−8.65521e11	−0.630588
$499$	−8.77411e11	−0.633506	−0.316753	−	0.948508i	$-0.602593\pi$
$499$	−8.77411e11	−0.633506	−0.316753	+	0.948508i	$0.602593\pi$
$500$	2.58452e11	0.184933
$501$	1.67872e12	1.19044
$502$	−1.60275e11	−0.112642
$503$	2.12177e11	0.147789	0.0738945	−	0.997266i	$-0.476457\pi$
$503$	2.12177e11	0.147789	0.0738945	+	0.997266i	$0.476457\pi$
$504$	0	0
$505$	1.83006e10	0.0125215
$506$	1.54776e12	1.04961
$507$	−5.13323e11	−0.345029
$508$	−1.38668e12	−0.923826
$509$	1.82871e12	1.20758	0.603790	−	0.797144i	$-0.293657\pi$
$509$	1.82871e12	1.20758	0.603790	+	0.797144i	$0.293657\pi$
$510$	−1.33753e12	−0.875464
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	7.29991e11	0.465361
$514$	−2.71490e11	−0.171561
$515$	−2.00897e12	−1.25847
$516$	1.52155e11	0.0944849
$517$	−2.88291e12	−1.77470
$518$	0	0
$519$	−7.67134e11	−0.464107
$520$	1.07181e12	0.642837
$521$	−2.68357e12	−1.59567	−0.797834	−	0.602877i	$-0.794021\pi$
$521$	−2.68357e12	−1.59567	−0.797834	+	0.602877i	$0.794021\pi$
$522$	8.41093e11	0.495823
$523$	−9.07444e11	−0.530349	−0.265175	−	0.964200i	$-0.585430\pi$
$523$	−9.07444e11	−0.530349	−0.265175	+	0.964200i	$0.585430\pi$
$524$	8.67307e11	0.502553
$525$	0	0
$526$	−1.13151e11	−0.0644498
$527$	−2.04730e12	−1.15620
$528$	−3.78959e11	−0.212197
$529$	1.14959e12	0.638251
$530$	2.72952e12	1.50260
$531$	−7.18227e11	−0.392046
$532$	0	0
$533$	−6.92384e11	−0.371599
$534$	−8.53295e11	−0.454113
$535$	−3.11017e12	−1.64131
$536$	4.16635e11	0.218029
$537$	6.39715e11	0.331972
$538$	−5.91926e9	−0.00304612
$539$	0	0
$540$	1.58711e12	0.803221
$541$	−4.83134e11	−0.242482	−0.121241	−	0.992623i	$-0.538687\pi$
$541$	−4.83134e11	−0.242482	−0.121241	+	0.992623i	$0.538687\pi$
$542$	1.98861e12	0.989814
$543$	5.61644e11	0.277244
$544$	4.07519e11	0.199505
$545$	−3.21615e12	−1.56154
$546$	0	0
$547$	2.24340e12	1.07143	0.535716	−	0.844398i	$-0.320042\pi$
$547$	2.24340e12	1.07143	0.535716	+	0.844398i	$0.320042\pi$
$548$	1.21531e12	0.575669
$549$	1.26149e11	0.0592664
$550$	−2.19407e12	−1.02239
$551$	1.41872e12	0.655714
$552$	−7.22468e11	−0.331202
$553$	0	0
$554$	−2.71381e11	−0.122401
$555$	2.65463e12	1.18764
$556$	−5.57666e11	−0.247479
$557$	7.24610e11	0.318974	0.159487	−	0.987200i	$-0.449016\pi$
$557$	7.24610e11	0.318974	0.159487	+	0.987200i	$0.449016\pi$
$558$	7.70326e11	0.336373
$559$	7.23047e11	0.313194
$560$	0	0
$561$	2.24730e12	0.957917
$562$	−1.86305e12	−0.787792
$563$	4.21854e12	1.76960	0.884799	−	0.465973i	$-0.154296\pi$
$563$	4.21854e12	1.76960	0.884799	+	0.465973i	$0.154296\pi$
$564$	1.34569e12	0.560002
$565$	6.89260e12	2.84554
$566$	−4.24852e11	−0.174006
$567$	0	0
$568$	1.53875e12	0.620297
$569$	4.34809e12	1.73898	0.869488	−	0.493954i	$-0.164449\pi$
$569$	4.34809e12	1.73898	0.869488	+	0.493954i	$0.164449\pi$
$570$	8.48886e11	0.336831
$571$	−2.24603e12	−0.884206	−0.442103	−	0.896964i	$-0.645767\pi$
$571$	−2.24603e12	−0.884206	−0.442103	+	0.896964i	$0.645767\pi$
$572$	−1.80083e12	−0.703381
$573$	−7.12082e11	−0.275952
$574$	0	0
$575$	−4.18289e12	−1.59577
$576$	−1.53335e11	−0.0580417
$577$	2.64828e12	0.994655	0.497328	−	0.867563i	$-0.334315\pi$
$577$	2.64828e12	0.994655	0.497328	+	0.867563i	$0.334315\pi$
$578$	−5.19260e11	−0.193513
$579$	−4.28523e11	−0.158460
$580$	3.08451e12	1.13177
$581$	0	0
$582$	1.43902e12	0.519893
$583$	−4.58608e12	−1.64412
$584$	−1.82659e12	−0.649806
$585$	2.39154e12	0.844259
$586$	−1.50948e10	−0.00528795
$587$	2.72201e12	0.946276	0.473138	−	0.880988i	$-0.343121\pi$
$587$	2.72201e12	0.946276	0.473138	+	0.880988i	$0.343121\pi$
$588$	0	0
$589$	1.29935e12	0.444845
$590$	−2.63393e12	−0.894890
$591$	3.72292e12	1.25528
$592$	−8.08812e11	−0.270645
$593$	−2.15619e11	−0.0716046	−0.0358023	−	0.999359i	$-0.511399\pi$
$593$	−2.15619e11	−0.0716046	−0.0358023	+	0.999359i	$0.511399\pi$
$594$	−2.66663e12	−0.878870
$595$	0	0
$596$	−3.02228e12	−0.981129
$597$	1.84399e12	0.594121
$598$	−3.43320e12	−1.09785
$599$	−1.11903e12	−0.355156	−0.177578	−	0.984107i	$-0.556826\pi$
$599$	−1.11903e12	−0.355156	−0.177578	+	0.984107i	$0.556826\pi$
$600$	1.02415e12	0.322614
$601$	−2.89926e12	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$601$	−2.89926e12	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$602$	0	0
$603$	9.29643e11	0.286344
$604$	−1.61690e12	−0.494330
$605$	1.70383e12	0.517044
$606$	1.43528e10	0.00432324
$607$	−1.76725e12	−0.528384	−0.264192	−	0.964470i	$-0.585105\pi$
$607$	−1.76725e12	−0.528384	−0.264192	+	0.964470i	$0.585105\pi$
$608$	−2.58639e11	−0.0767586
$609$	0	0
$610$	4.62622e11	0.135283
$611$	6.39478e12	1.85627
$612$	9.09305e11	0.262016
$613$	−7.94293e11	−0.227200	−0.113600	−	0.993527i	$-0.536238\pi$
$613$	−7.94293e11	−0.227200	−0.113600	+	0.993527i	$0.536238\pi$
$614$	3.53068e11	0.100254
$615$	−1.19226e12	−0.336071
$616$	0	0
$617$	3.17799e12	0.882815	0.441407	−	0.897307i	$-0.354479\pi$
$617$	3.17799e12	0.882815	0.441407	+	0.897307i	$0.354479\pi$
$618$	−1.57559e12	−0.434507
$619$	−6.59526e12	−1.80561	−0.902804	−	0.430051i	$-0.858495\pi$
$619$	−6.59526e12	−1.80561	−0.902804	+	0.430051i	$0.858495\pi$
$620$	2.82499e12	0.767810
$621$	−5.08381e12	−1.37176
$622$	−3.68388e12	−0.986845
$623$	0	0
$624$	8.40594e11	0.221950
$625$	−2.64113e12	−0.692357
$626$	−2.52141e12	−0.656234
$627$	−1.42628e12	−0.368555
$628$	2.63746e11	0.0676655
$629$	4.79640e12	1.22177
$630$	0	0
$631$	−5.22143e12	−1.31117	−0.655583	−	0.755123i	$-0.727577\pi$
$631$	−5.22143e12	−1.31117	−0.655583	+	0.755123i	$0.727577\pi$
$632$	9.28252e11	0.231440
$633$	−6.50836e11	−0.161122
$634$	−3.86399e12	−0.949806
$635$	−1.13470e13	−2.76948
$636$	2.14070e12	0.518798
$637$	0	0
$638$	−5.18254e12	−1.23837
$639$	3.43343e12	0.814656
$640$	−5.62319e11	−0.132487
$641$	3.69727e12	0.865008	0.432504	−	0.901632i	$-0.357630\pi$
$641$	3.69727e12	0.865008	0.432504	+	0.901632i	$0.357630\pi$
$642$	−2.43923e12	−0.566691
$643$	5.23082e12	1.20676	0.603379	−	0.797455i	$-0.293821\pi$
$643$	5.23082e12	1.20676	0.603379	+	0.797455i	$0.293821\pi$
$644$	0	0
$645$	1.24506e12	0.283250
$646$	1.53378e12	0.346510
$647$	2.92473e12	0.656170	0.328085	−	0.944648i	$-0.393597\pi$
$647$	2.92473e12	0.656170	0.328085	+	0.944648i	$0.393597\pi$
$648$	5.07897e11	0.113159
$649$	4.42548e12	0.979172
$650$	4.86681e12	1.06939
$651$	0	0
$652$	−8.57420e11	−0.185814
$653$	−4.32042e11	−0.0929859	−0.0464930	−	0.998919i	$-0.514805\pi$
$653$	−4.32042e11	−0.0929859	−0.0464930	+	0.998919i	$0.514805\pi$
$654$	−2.52236e12	−0.539146
$655$	7.09701e12	1.50657
$656$	3.63257e11	0.0765854
$657$	−4.07570e12	−0.853411
$658$	0	0
$659$	−6.16777e12	−1.27393	−0.636963	−	0.770894i	$-0.719810\pi$
$659$	−6.16777e12	−1.27393	−0.636963	+	0.770894i	$0.719810\pi$
$660$	−3.10095e12	−0.636132
$661$	2.25373e12	0.459193	0.229596	−	0.973286i	$-0.426259\pi$
$661$	2.25373e12	0.459193	0.229596	+	0.973286i	$0.426259\pi$
$662$	−2.29659e12	−0.464752
$663$	−4.98488e12	−1.00194
$664$	2.15787e12	0.430793
$665$	0	0
$666$	−1.80471e12	−0.355447
$667$	−9.88027e12	−1.93287
$668$	−4.18528e12	−0.813261
$669$	−4.46405e12	−0.861611
$670$	3.40925e12	0.653614
$671$	−7.77289e11	−0.148024
$672$	0	0
$673$	4.91498e12	0.923536	0.461768	−	0.887001i	$-0.347215\pi$
$673$	4.91498e12	0.923536	0.461768	+	0.887001i	$0.347215\pi$
$674$	−2.16549e12	−0.404191
$675$	7.20668e12	1.33619
$676$	1.27979e12	0.235710
$677$	−1.00923e12	−0.184647	−0.0923233	−	0.995729i	$-0.529429\pi$
$677$	−1.00923e12	−0.184647	−0.0923233	+	0.995729i	$0.529429\pi$
$678$	5.40571e12	0.982470
$679$	0	0
$680$	3.33466e12	0.598082
$681$	−1.94569e12	−0.346666
$682$	−4.74649e12	−0.840124
$683$	−2.33611e12	−0.410772	−0.205386	−	0.978681i	$-0.565845\pi$
$683$	−2.33611e12	−0.410772	−0.205386	+	0.978681i	$0.565845\pi$
$684$	−5.77105e11	−0.100810
$685$	9.94462e12	1.72576
$686$	0	0
$687$	3.82364e12	0.654895
$688$	−3.79344e11	−0.0645483
$689$	1.01727e13	1.71969
$690$	−5.91182e12	−0.992888
$691$	−1.10788e13	−1.84860	−0.924300	−	0.381666i	$-0.875350\pi$
$691$	−1.10788e13	−1.84860	−0.924300	+	0.381666i	$0.875350\pi$
$692$	1.91257e12	0.317059
$693$	0	0
$694$	−6.19989e12	−1.01453
$695$	−4.56328e12	−0.741901
$696$	2.41911e12	0.390764
$697$	−2.15418e12	−0.345728
$698$	−1.64098e12	−0.261669
$699$	−1.88767e12	−0.299075
$700$	0	0
$701$	8.11682e11	0.126956	0.0634782	−	0.997983i	$-0.479781\pi$
$701$	8.11682e11	0.126956	0.0634782	+	0.997983i	$0.479781\pi$
$702$	5.91504e12	0.919265
$703$	−3.04411e12	−0.470069
$704$	9.44799e11	0.144965
$705$	1.10115e13	1.67879
$706$	−2.08026e11	−0.0315134
$707$	0	0
$708$	−2.06573e12	−0.308976
$709$	8.96980e12	1.33314	0.666568	−	0.745444i	$-0.267762\pi$
$709$	8.96980e12	1.33314	0.666568	+	0.745444i	$0.267762\pi$
$710$	1.25913e13	1.85955
$711$	2.07122e12	0.303958
$712$	2.12739e12	0.310232
$713$	−9.04897e12	−1.31128
$714$	0	0
$715$	−1.47359e13	−2.10862
$716$	−1.59490e12	−0.226790
$717$	3.75277e12	0.530293
$718$	1.36884e12	0.192218
$719$	−1.05576e13	−1.47328	−0.736638	−	0.676287i	$-0.763588\pi$
$719$	−1.05576e13	−1.47328	−0.736638	+	0.676287i	$0.763588\pi$
$720$	−1.25471e12	−0.173999
$721$	0	0
$722$	4.18957e12	0.573789
$723$	2.93572e12	0.399570
$724$	−1.40026e12	−0.189402
$725$	1.40060e13	1.88275
$726$	1.33628e12	0.178518
$727$	−2.48043e12	−0.329323	−0.164661	−	0.986350i	$-0.552653\pi$
$727$	−2.48043e12	−0.329323	−0.164661	+	0.986350i	$0.552653\pi$
$728$	0	0
$729$	7.11476e12	0.933010
$730$	−1.49467e13	−1.94801
$731$	2.24958e12	0.291389
$732$	3.62824e11	0.0467085
$733$	9.95078e12	1.27318	0.636589	−	0.771203i	$-0.280345\pi$
$733$	9.95078e12	1.27318	0.636589	+	0.771203i	$0.280345\pi$
$734$	−1.80987e12	−0.230152
$735$	0	0
$736$	1.80121e12	0.226264
$737$	−5.72815e12	−0.715173
$738$	8.10540e11	0.100582
$739$	−3.52201e12	−0.434401	−0.217200	−	0.976127i	$-0.569692\pi$
$739$	−3.52201e12	−0.434401	−0.217200	+	0.976127i	$0.569692\pi$
$740$	−6.61836e12	−0.811349
$741$	3.16373e12	0.385494
$742$	0	0
$743$	−1.25259e13	−1.50786	−0.753930	−	0.656955i	$-0.771844\pi$
$743$	−1.25259e13	−1.50786	−0.753930	+	0.656955i	$0.771844\pi$
$744$	2.21558e12	0.265099
$745$	−2.47307e13	−2.94126
$746$	3.11550e12	0.368301
$747$	4.81488e12	0.565774
$748$	−5.60283e12	−0.654411
$749$	0	0
$750$	1.65864e12	0.191415
$751$	6.91859e12	0.793666	0.396833	−	0.917891i	$-0.370109\pi$
$751$	6.91859e12	0.793666	0.396833	+	0.917891i	$0.370109\pi$
$752$	−3.35500e12	−0.382571
$753$	−1.02858e12	−0.116590
$754$	1.14957e13	1.29529
$755$	−1.32308e13	−1.48192
$756$	0	0
$757$	−2.68669e12	−0.297362	−0.148681	−	0.988885i	$-0.547503\pi$
$757$	−2.68669e12	−0.297362	−0.148681	+	0.988885i	$0.547503\pi$
$758$	3.56363e12	0.392086
$759$	9.93294e12	1.08640
$760$	−2.11639e12	−0.230110
$761$	−4.54213e12	−0.490940	−0.245470	−	0.969404i	$-0.578942\pi$
$761$	−4.54213e12	−0.490940	−0.245470	+	0.969404i	$0.578942\pi$
$762$	−8.89917e12	−0.956208
$763$	0	0
$764$	1.77532e12	0.188520
$765$	7.44067e12	0.785481
$766$	−5.38551e12	−0.565194
$767$	−9.81644e12	−1.02418
$768$	−4.41014e11	−0.0457433
$769$	2.34852e12	0.242173	0.121087	−	0.992642i	$-0.461362\pi$
$769$	2.34852e12	0.242173	0.121087	+	0.992642i	$0.461362\pi$
$770$	0	0
$771$	−1.74232e12	−0.177575
$772$	1.06837e12	0.108254
$773$	−3.78193e11	−0.0380983	−0.0190492	−	0.999819i	$-0.506064\pi$
$773$	−3.78193e11	−0.0380983	−0.0190492	+	0.999819i	$0.506064\pi$
$774$	−8.46436e11	−0.0847734
$775$	1.28276e13	1.27728
$776$	−3.58768e12	−0.355170
$777$	0	0
$778$	5.56640e12	0.544711
$779$	1.36718e12	0.133017
$780$	6.87843e12	0.665370
$781$	−2.11556e13	−2.03468
$782$	−1.06815e13	−1.02142
$783$	1.70227e13	1.61845
$784$	0	0
$785$	2.15818e12	0.202850
$786$	5.56603e12	0.520169
$787$	−1.21085e13	−1.12514	−0.562568	−	0.826751i	$-0.690186\pi$
$787$	−1.21085e13	−1.12514	−0.562568	+	0.826751i	$0.690186\pi$
$788$	−9.28176e12	−0.857556
$789$	−7.26157e11	−0.0667089
$790$	7.59572e12	0.693820
$791$	0	0
$792$	2.10814e12	0.190387
$793$	1.72416e12	0.154827
$794$	4.40815e11	0.0393608
$795$	1.75170e13	1.55527
$796$	−4.59733e12	−0.405880
$797$	−2.16394e13	−1.89969	−0.949846	−	0.312719i	$-0.898760\pi$
$797$	−2.16394e13	−1.89969	−0.949846	+	0.312719i	$0.898760\pi$
$798$	0	0
$799$	1.98958e13	1.72703
$800$	−2.55335e12	−0.220397
$801$	4.74687e12	0.407438
$802$	9.93873e12	0.848293
$803$	2.51131e13	2.13148
$804$	2.67380e12	0.225671
$805$	0	0
$806$	1.05285e13	0.878738
$807$	−3.79875e10	−0.00315289
$808$	−3.57835e10	−0.00295347
$809$	−4.36869e12	−0.358578	−0.179289	−	0.983796i	$-0.557380\pi$
$809$	−4.36869e12	−0.358578	−0.179289	+	0.983796i	$0.557380\pi$
$810$	4.15603e12	0.339231
$811$	1.39017e13	1.12843	0.564215	−	0.825628i	$-0.309179\pi$
$811$	1.39017e13	1.12843	0.564215	+	0.825628i	$0.309179\pi$
$812$	0	0
$813$	1.27621e13	1.02451
$814$	1.11201e13	0.887763
$815$	−7.01611e12	−0.557041
$816$	2.61530e12	0.206498
$817$	−1.42773e12	−0.112111
$818$	2.34233e11	0.0182919
$819$	0	0
$820$	2.97246e12	0.229591
$821$	8.03927e12	0.617551	0.308775	−	0.951135i	$-0.400081\pi$
$821$	8.03927e12	0.617551	0.308775	+	0.951135i	$0.400081\pi$
$822$	7.79935e12	0.595848
$823$	−1.95539e13	−1.48571	−0.742854	−	0.669454i	$-0.766528\pi$
$823$	−1.95539e13	−1.48571	−0.742854	+	0.669454i	$0.766528\pi$
$824$	3.92818e12	0.296838
$825$	−1.40807e13	−1.05823
$826$	0	0
$827$	1.31390e13	0.976760	0.488380	−	0.872631i	$-0.337588\pi$
$827$	1.31390e13	0.976760	0.488380	+	0.872631i	$0.337588\pi$
$828$	4.01908e12	0.297160
$829$	−2.18347e13	−1.60565	−0.802827	−	0.596211i	$-0.796672\pi$
$829$	−2.18347e13	−1.60565	−0.802827	+	0.596211i	$0.796672\pi$
$830$	1.76574e13	1.29145
$831$	−1.74161e12	−0.126692
$832$	−2.09572e12	−0.151628
$833$	0	0
$834$	−3.57888e12	−0.256154
$835$	−3.42474e13	−2.43802
$836$	3.55593e12	0.251782
$837$	1.55904e13	1.09798
$838$	1.94408e12	0.136181
$839$	1.23225e13	0.858561	0.429281	−	0.903171i	$-0.358767\pi$
$839$	1.23225e13	0.858561	0.429281	+	0.903171i	$0.358767\pi$
$840$	0	0
$841$	1.85760e13	1.28047
$842$	8.97625e12	0.615447
$843$	−1.19563e13	−0.815406
$844$	1.62263e12	0.110072
$845$	1.04723e13	0.706620
$846$	−7.48606e12	−0.502443
$847$	0	0
$848$	−5.33707e12	−0.354423
$849$	−2.72654e12	−0.180105
$850$	1.51419e13	0.994934
$851$	2.11999e13	1.38564
$852$	9.87506e12	0.642040
$853$	9.07085e12	0.586647	0.293324	−	0.956013i	$-0.405239\pi$
$853$	9.07085e12	0.586647	0.293324	+	0.956013i	$0.405239\pi$
$854$	0	0
$855$	−4.72234e12	−0.302211
$856$	6.08136e12	0.387141
$857$	1.66440e12	0.105401	0.0527003	−	0.998610i	$-0.483217\pi$
$857$	1.66440e12	0.105401	0.0527003	+	0.998610i	$0.483217\pi$
$858$	−1.15570e13	−0.728036
$859$	−1.40232e12	−0.0878775	−0.0439388	−	0.999034i	$-0.513991\pi$
$859$	−1.40232e12	−0.0878775	−0.0439388	+	0.999034i	$0.513991\pi$
$860$	−3.10410e12	−0.193505
$861$	0	0
$862$	−1.67091e13	−1.03079
$863$	−2.05982e12	−0.126410	−0.0632049	−	0.998001i	$-0.520132\pi$
$863$	−2.05982e12	−0.126410	−0.0632049	+	0.998001i	$0.520132\pi$
$864$	−3.10330e12	−0.189458
$865$	1.56502e13	0.950492
$866$	−1.68713e13	−1.01934
$867$	−3.33240e12	−0.200296
$868$	0	0
$869$	−1.27622e13	−0.759165
$870$	1.97952e13	1.17145
$871$	1.27060e13	0.748044
$872$	6.28859e12	0.368323
$873$	−8.00526e12	−0.466457
$874$	6.77921e12	0.392986
$875$	0	0
$876$	−1.17223e13	−0.672583
$877$	1.74285e13	0.994859	0.497429	−	0.867504i	$-0.334277\pi$
$877$	1.74285e13	0.994859	0.497429	+	0.867504i	$0.334277\pi$
$878$	−1.87259e13	−1.06345
$879$	−9.68723e10	−0.00547331
$880$	7.73112e12	0.434580
$881$	−1.33834e11	−0.00748471	−0.00374235	−	0.999993i	$-0.501191\pi$
$881$	−1.33834e11	−0.00748471	−0.00374235	+	0.999993i	$0.501191\pi$
$882$	0	0
$883$	2.44009e12	0.135077	0.0675386	−	0.997717i	$-0.478485\pi$
$883$	2.44009e12	0.135077	0.0675386	+	0.997717i	$0.478485\pi$
$884$	1.24280e13	0.684489
$885$	−1.69035e13	−0.926258
$886$	1.13706e13	0.619912
$887$	−1.36032e13	−0.737877	−0.368939	−	0.929454i	$-0.620279\pi$
$887$	−1.36032e13	−0.737877	−0.368939	+	0.929454i	$0.620279\pi$
$888$	−5.19063e12	−0.280132
$889$	0	0
$890$	1.74080e13	0.930024
$891$	−6.98289e12	−0.371181
$892$	1.11295e13	0.588619
$893$	−1.26272e13	−0.664468
$894$	−1.93958e13	−1.01552
$895$	−1.30508e13	−0.679880
$896$	0	0
$897$	−2.20329e13	−1.13633
$898$	−1.50478e13	−0.772197
$899$	3.02996e13	1.54710
$900$	−5.69734e12	−0.289455
$901$	3.16498e13	1.59996
$902$	−4.99428e12	−0.251214
$903$	0	0
$904$	−1.34772e13	−0.671185
$905$	−1.14581e13	−0.567796
$906$	−1.03766e13	−0.511657
$907$	−6.73549e12	−0.330473	−0.165237	−	0.986254i	$-0.552839\pi$
$907$	−6.73549e12	−0.330473	−0.165237	+	0.986254i	$0.552839\pi$
$908$	4.85087e12	0.236828
$909$	−7.98443e10	−0.00387888
$910$	0	0
$911$	6.74134e12	0.324275	0.162137	−	0.986768i	$-0.448161\pi$
$911$	6.74134e12	0.324275	0.162137	+	0.986768i	$0.448161\pi$
$912$	−1.65984e12	−0.0794492
$913$	−2.96677e13	−1.41308
$914$	1.84132e13	0.872714
$915$	2.96892e12	0.140024
$916$	−9.53287e12	−0.447398
$917$	0	0
$918$	1.84032e13	0.855264
$919$	−2.79444e13	−1.29233	−0.646167	−	0.763196i	$-0.723629\pi$
$919$	−2.79444e13	−1.29233	−0.646167	+	0.763196i	$0.723629\pi$
$920$	1.47390e13	0.678302
$921$	2.26585e12	0.103768
$922$	−4.26353e12	−0.194303
$923$	4.69267e13	2.12820
$924$	0	0
$925$	−3.00524e13	−1.34971
$926$	7.18025e12	0.320915
$927$	8.76501e12	0.389847
$928$	−6.03119e12	−0.266954
$929$	−1.03095e13	−0.454118	−0.227059	−	0.973881i	$-0.572911\pi$
$929$	−1.03095e13	−0.454118	−0.227059	+	0.973881i	$0.572911\pi$
$930$	1.81297e13	0.794724
$931$	0	0
$932$	4.70624e12	0.204316
$933$	−2.36417e13	−1.02144
$934$	2.84504e13	1.22329
$935$	−4.58470e13	−1.96182
$936$	−4.67621e12	−0.199138
$937$	2.54975e13	1.08061	0.540306	−	0.841468i	$-0.318308\pi$
$937$	2.54975e13	1.08061	0.540306	+	0.841468i	$0.318308\pi$
$938$	0	0
$939$	−1.61814e13	−0.679236
$940$	−2.74533e13	−1.14689
$941$	1.65839e13	0.689498	0.344749	−	0.938695i	$-0.387964\pi$
$941$	1.65839e13	0.689498	0.344749	+	0.938695i	$0.387964\pi$
$942$	1.69262e12	0.0700373
$943$	−9.52136e12	−0.392100
$944$	5.15016e12	0.211080
$945$	0	0
$946$	5.21546e12	0.211730
$947$	2.26232e13	0.914067	0.457034	−	0.889449i	$-0.348912\pi$
$947$	2.26232e13	0.914067	0.457034	+	0.889449i	$0.348912\pi$
$948$	5.95716e12	0.239553
$949$	−5.57051e13	−2.22945
$950$	−9.61003e12	−0.382797
$951$	−2.47976e13	−0.983099
$952$	0	0
$953$	−3.02695e11	−0.0118874	−0.00594370	−	0.999982i	$-0.501892\pi$
$953$	−3.02695e11	−0.0118874	−0.00594370	+	0.999982i	$0.501892\pi$
$954$	−1.19087e13	−0.465475
$955$	1.45271e13	0.565151
$956$	−9.35618e12	−0.362275
$957$	−3.32595e13	−1.28177
$958$	−3.18250e13	−1.22074
$959$	0	0
$960$	−3.60874e12	−0.137131
$961$	1.31065e12	0.0495715
$962$	−2.46661e13	−0.928566
$963$	1.35694e13	0.508444
$964$	−7.31918e12	−0.272970
$965$	8.74227e12	0.324527
$966$	0	0
$967$	3.03988e12	0.111799	0.0558994	−	0.998436i	$-0.482197\pi$
$967$	3.03988e12	0.111799	0.0558994	+	0.998436i	$0.482197\pi$
$968$	−3.33153e12	−0.121956
$969$	9.84316e12	0.358656
$970$	−2.93574e13	−1.06474
$971$	2.15206e13	0.776906	0.388453	−	0.921468i	$-0.373010\pi$
$971$	2.15206e13	0.776906	0.388453	+	0.921468i	$0.373010\pi$
$972$	−1.16532e13	−0.418742
$973$	0	0
$974$	−1.10175e13	−0.392254
$975$	3.12333e13	1.10687
$976$	−9.04572e11	−0.0319094
$977$	−1.56454e13	−0.549364	−0.274682	−	0.961535i	$-0.588573\pi$
$977$	−1.56454e13	−0.549364	−0.274682	+	0.961535i	$0.588573\pi$
$978$	−5.50258e12	−0.192328
$979$	−2.92486e13	−1.01762
$980$	0	0
$981$	1.40318e13	0.483731
$982$	−2.99010e13	−1.02609
$983$	−2.28763e13	−0.781437	−0.390719	−	0.920510i	$-0.627773\pi$
$983$	−2.28763e13	−0.781437	−0.390719	+	0.920510i	$0.627773\pi$
$984$	2.33124e12	0.0792699
$985$	−7.59510e13	−2.57081
$986$	3.57661e13	1.20511
$987$	0	0
$988$	−7.88763e12	−0.263354
$989$	9.94303e12	0.330472
$990$	1.72506e13	0.570749
$991$	4.47356e13	1.47340	0.736701	−	0.676218i	$-0.236382\pi$
$991$	4.47356e13	1.47340	0.736701	+	0.676218i	$0.236382\pi$
$992$	−5.52374e12	−0.181105
$993$	−1.47386e13	−0.481043
$994$	0	0
$995$	−3.76192e13	−1.21676
$996$	1.38483e13	0.445893
$997$	3.24564e13	1.04033	0.520166	−	0.854065i	$-0.325870\pi$
$997$	3.24564e13	1.04033	0.520166	+	0.854065i	$0.325870\pi$
$998$	1.40386e13	0.447956
$999$	−3.65251e13	−1.16024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.k.1.2	✓	4
7.2	even	3		98.10.c.m.67.3		8
7.3	odd	6		98.10.c.m.79.2		8
7.4	even	3		98.10.c.m.79.3		8
7.5	odd	6		98.10.c.m.67.2		8
7.6	odd	2	inner	98.10.a.k.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.k.1.2	✓	4	1.1	even	1	trivial
98.10.a.k.1.3	yes	4	7.6	odd	2	inner
98.10.c.m.67.2		8	7.5	odd	6
98.10.c.m.67.3		8	7.2	even	3
98.10.c.m.79.2		8	7.3	odd	6
98.10.c.m.79.3		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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -102.682 q^{3} +256.000 q^{4} +2094.80 q^{5} +1642.91 q^{6} -4096.00 q^{8} -9139.47 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -102.682 q^{3} +256.000 q^{4} +2094.80 q^{5} +1642.91 q^{6} -4096.00 q^{8} -9139.47 q^{9} -33516.8 q^{10} +56314.4 q^{11} -26286.5 q^{12} -124915. q^{13} -215098. q^{15} +65536.0 q^{16} -388641. q^{17} +146232. q^{18} +246657. q^{19} +536269. q^{20} -901030. q^{22} -1.71777e6 q^{23} +420584. q^{24} +2.43507e6 q^{25} +1.99863e6 q^{26} +2.95954e6 q^{27} +5.75179e6 q^{29} +3.44156e6 q^{30} +5.26785e6 q^{31} -1.04858e6 q^{32} -5.78246e6 q^{33} +6.21825e6 q^{34} -2.33970e6 q^{36} -1.23415e7 q^{37} -3.94651e6 q^{38} +1.28264e7 q^{39} -8.58031e6 q^{40} +5.54285e6 q^{41} -5.78833e6 q^{43} +1.44165e7 q^{44} -1.91454e7 q^{45} +2.74843e7 q^{46} -5.11932e7 q^{47} -6.72935e6 q^{48} -3.89611e7 q^{50} +3.99063e7 q^{51} -3.19782e7 q^{52} -8.14372e7 q^{53} -4.73526e7 q^{54} +1.17967e8 q^{55} -2.53272e7 q^{57} -9.20287e7 q^{58} +7.85852e7 q^{59} -5.50650e7 q^{60} -1.38027e7 q^{61} -8.42856e7 q^{62} +1.67772e7 q^{64} -2.61671e8 q^{65} +9.25193e7 q^{66} -1.01717e8 q^{67} -9.94920e7 q^{68} +1.76384e8 q^{69} -3.75670e8 q^{71} +3.74353e7 q^{72} +4.45945e8 q^{73} +1.97464e8 q^{74} -2.50037e8 q^{75} +6.31442e7 q^{76} -2.05223e8 q^{78} -2.26624e8 q^{79} +1.37285e8 q^{80} -1.23998e8 q^{81} -8.86857e7 q^{82} -5.26823e8 q^{83} -8.14125e8 q^{85} +9.26132e7 q^{86} -5.90604e8 q^{87} -2.30664e8 q^{88} -5.19381e8 q^{89} +3.06326e8 q^{90} -4.39750e8 q^{92} -5.40912e8 q^{93} +8.19091e8 q^{94} +5.16697e8 q^{95} +1.07670e8 q^{96} +8.75899e8 q^{97} -5.14684e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 1024 q^{4} - 16384 q^{8} + 15912 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more