Properties

Label 1.98.a.a.1.6
Level $1$
Weight $98$
Character 1.1
Self dual yes
Analytic conductor $59.585$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1,98,Mod(1,1)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1, base_ring=CyclotomicField(1))
 
chi = DirichletCharacter(H, H._module([]))
 
N = Newforms(chi, 98, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1.1");
 
S:= CuspForms(chi, 98);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 98 \)
Character orbit: \([\chi]\) \(=\) 1.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: \(59.5852992940\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} + \cdots - 60\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.16497e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.56799e14 q^{2} -1.35917e23 q^{3} +1.51568e29 q^{4} +4.66064e33 q^{5} -7.56782e37 q^{6} +2.73237e40 q^{7} -3.83521e42 q^{8} -6.14732e44 q^{9} +O(q^{10})\) \(q+5.56799e14 q^{2} -1.35917e23 q^{3} +1.51568e29 q^{4} +4.66064e33 q^{5} -7.56782e37 q^{6} +2.73237e40 q^{7} -3.83521e42 q^{8} -6.14732e44 q^{9} +2.59504e48 q^{10} +3.91912e50 q^{11} -2.06007e52 q^{12} -1.22584e54 q^{13} +1.52138e55 q^{14} -6.33459e56 q^{15} -2.61524e58 q^{16} -1.30833e59 q^{17} -3.42282e59 q^{18} +1.63455e62 q^{19} +7.06406e62 q^{20} -3.71374e63 q^{21} +2.18216e65 q^{22} +5.04020e64 q^{23} +5.21269e65 q^{24} -4.13873e67 q^{25} -6.82546e68 q^{26} +2.67794e69 q^{27} +4.14140e69 q^{28} -9.43257e70 q^{29} -3.52709e71 q^{30} -3.22328e72 q^{31} -1.39539e73 q^{32} -5.32674e73 q^{33} -7.28475e73 q^{34} +1.27346e74 q^{35} -9.31739e73 q^{36} -5.50816e75 q^{37} +9.10113e76 q^{38} +1.66612e77 q^{39} -1.78746e76 q^{40} -2.31752e78 q^{41} -2.06780e78 q^{42} -2.39827e79 q^{43} +5.94015e79 q^{44} -2.86505e78 q^{45} +2.80637e79 q^{46} +8.89362e80 q^{47} +3.55455e81 q^{48} -8.68338e81 q^{49} -2.30444e82 q^{50} +1.77823e82 q^{51} -1.85798e83 q^{52} -1.93323e83 q^{53} +1.49107e84 q^{54} +1.82656e84 q^{55} -1.04792e83 q^{56} -2.22162e85 q^{57} -5.25204e85 q^{58} -4.61663e85 q^{59} -9.60123e85 q^{60} +3.65079e86 q^{61} -1.79472e87 q^{62} -1.67967e85 q^{63} -3.62550e87 q^{64} -5.71320e87 q^{65} -2.96592e88 q^{66} -6.07665e88 q^{67} -1.98301e88 q^{68} -6.85047e87 q^{69} +7.09060e88 q^{70} +6.82951e89 q^{71} +2.35763e87 q^{72} -2.98123e89 q^{73} -3.06694e90 q^{74} +5.62522e90 q^{75} +2.47745e91 q^{76} +1.07085e91 q^{77} +9.27693e91 q^{78} +1.13407e92 q^{79} -1.21887e92 q^{80} -3.52242e92 q^{81} -1.29039e93 q^{82} +1.13702e93 q^{83} -5.62885e92 q^{84} -6.09765e92 q^{85} -1.33535e94 q^{86} +1.28204e94 q^{87} -1.50307e93 q^{88} -9.49289e93 q^{89} -1.59525e93 q^{90} -3.34944e94 q^{91} +7.63934e93 q^{92} +4.38098e95 q^{93} +4.95196e95 q^{94} +7.61803e95 q^{95} +1.89657e96 q^{96} -4.30104e96 q^{97} -4.83489e96 q^{98} -2.40921e95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.56799e14 1.39876 0.699380 0.714750i \(-0.253459\pi\)
0.699380 + 0.714750i \(0.253459\pi\)
\(3\) −1.35917e23 −0.983766 −0.491883 0.870661i \(-0.663691\pi\)
−0.491883 + 0.870661i \(0.663691\pi\)
\(4\) 1.51568e29 0.956531
\(5\) 4.66064e33 0.586679 0.293340 0.956008i \(-0.405233\pi\)
0.293340 + 0.956008i \(0.405233\pi\)
\(6\) −7.56782e37 −1.37605
\(7\) 2.73237e40 0.281374 0.140687 0.990054i \(-0.455069\pi\)
0.140687 + 0.990054i \(0.455069\pi\)
\(8\) −3.83521e42 −0.0608030
\(9\) −6.14732e44 −0.0322050
\(10\) 2.59504e48 0.820624
\(11\) 3.91912e50 1.21799 0.608995 0.793174i \(-0.291573\pi\)
0.608995 + 0.793174i \(0.291573\pi\)
\(12\) −2.06007e52 −0.941002
\(13\) −1.22584e54 −1.15393 −0.576967 0.816767i \(-0.695764\pi\)
−0.576967 + 0.816767i \(0.695764\pi\)
\(14\) 1.52138e55 0.393575
\(15\) −6.33459e56 −0.577155
\(16\) −2.61524e58 −1.04158
\(17\) −1.30833e59 −0.275387 −0.137694 0.990475i \(-0.543969\pi\)
−0.137694 + 0.990475i \(0.543969\pi\)
\(18\) −3.42282e59 −0.0450471
\(19\) 1.63455e62 1.56260 0.781299 0.624157i \(-0.214557\pi\)
0.781299 + 0.624157i \(0.214557\pi\)
\(20\) 7.06406e62 0.561177
\(21\) −3.71374e63 −0.276806
\(22\) 2.18216e65 1.70368
\(23\) 5.04020e64 0.0455667 0.0227833 0.999740i \(-0.492747\pi\)
0.0227833 + 0.999740i \(0.492747\pi\)
\(24\) 5.21269e65 0.0598159
\(25\) −4.13873e67 −0.655808
\(26\) −6.82546e68 −1.61408
\(27\) 2.67794e69 1.01545
\(28\) 4.14140e69 0.269143
\(29\) −9.43257e70 −1.11771 −0.558853 0.829267i \(-0.688758\pi\)
−0.558853 + 0.829267i \(0.688758\pi\)
\(30\) −3.52709e71 −0.807301
\(31\) −3.22328e72 −1.50403 −0.752015 0.659146i \(-0.770918\pi\)
−0.752015 + 0.659146i \(0.770918\pi\)
\(32\) −1.39539e73 −1.39612
\(33\) −5.32674e73 −1.19822
\(34\) −7.28475e73 −0.385201
\(35\) 1.27346e74 0.165076
\(36\) −9.31739e73 −0.0308051
\(37\) −5.50816e75 −0.482195 −0.241098 0.970501i \(-0.577507\pi\)
−0.241098 + 0.970501i \(0.577507\pi\)
\(38\) 9.10113e76 2.18570
\(39\) 1.66612e77 1.13520
\(40\) −1.78746e76 −0.0356719
\(41\) −2.31752e78 −1.39639 −0.698196 0.715907i \(-0.746014\pi\)
−0.698196 + 0.715907i \(0.746014\pi\)
\(42\) −2.06780e78 −0.387185
\(43\) −2.39827e79 −1.43442 −0.717212 0.696856i \(-0.754582\pi\)
−0.717212 + 0.696856i \(0.754582\pi\)
\(44\) 5.94015e79 1.16505
\(45\) −2.86505e78 −0.0188940
\(46\) 2.80637e79 0.0637369
\(47\) 8.89362e80 0.711758 0.355879 0.934532i \(-0.384181\pi\)
0.355879 + 0.934532i \(0.384181\pi\)
\(48\) 3.55455e81 1.02467
\(49\) −8.68338e81 −0.920829
\(50\) −2.30444e82 −0.917318
\(51\) 1.77823e82 0.270916
\(52\) −1.85798e83 −1.10377
\(53\) −1.93323e83 −0.455936 −0.227968 0.973669i \(-0.573208\pi\)
−0.227968 + 0.973669i \(0.573208\pi\)
\(54\) 1.49107e84 1.42037
\(55\) 1.82656e84 0.714570
\(56\) −1.04792e83 −0.0171084
\(57\) −2.22162e85 −1.53723
\(58\) −5.25204e85 −1.56340
\(59\) −4.61663e85 −0.599795 −0.299898 0.953971i \(-0.596952\pi\)
−0.299898 + 0.953971i \(0.596952\pi\)
\(60\) −9.60123e85 −0.552066
\(61\) 3.65079e86 0.941652 0.470826 0.882226i \(-0.343956\pi\)
0.470826 + 0.882226i \(0.343956\pi\)
\(62\) −1.79472e87 −2.10378
\(63\) −1.67967e85 −0.00906166
\(64\) −3.62550e87 −0.911254
\(65\) −5.71320e87 −0.676989
\(66\) −2.96592e88 −1.67602
\(67\) −6.07665e88 −1.65591 −0.827955 0.560795i \(-0.810496\pi\)
−0.827955 + 0.560795i \(0.810496\pi\)
\(68\) −1.98301e88 −0.263416
\(69\) −6.85047e87 −0.0448269
\(70\) 7.09060e88 0.230902
\(71\) 6.82951e89 1.11779 0.558894 0.829239i \(-0.311226\pi\)
0.558894 + 0.829239i \(0.311226\pi\)
\(72\) 2.35763e87 0.00195816
\(73\) −2.98123e89 −0.126834 −0.0634171 0.997987i \(-0.520200\pi\)
−0.0634171 + 0.997987i \(0.520200\pi\)
\(74\) −3.06694e90 −0.674476
\(75\) 5.62522e90 0.645161
\(76\) 2.47745e91 1.49467
\(77\) 1.07085e91 0.342711
\(78\) 9.27693e91 1.58787
\(79\) 1.13407e92 1.04647 0.523236 0.852188i \(-0.324725\pi\)
0.523236 + 0.852188i \(0.324725\pi\)
\(80\) −1.21887e92 −0.611073
\(81\) −3.52242e92 −0.966758
\(82\) −1.29039e93 −1.95322
\(83\) 1.13702e93 0.956054 0.478027 0.878345i \(-0.341352\pi\)
0.478027 + 0.878345i \(0.341352\pi\)
\(84\) −5.62885e92 −0.264774
\(85\) −6.09765e92 −0.161564
\(86\) −1.33535e94 −2.00641
\(87\) 1.28204e94 1.09956
\(88\) −1.50307e93 −0.0740575
\(89\) −9.49289e93 −0.270385 −0.135193 0.990819i \(-0.543165\pi\)
−0.135193 + 0.990819i \(0.543165\pi\)
\(90\) −1.59525e93 −0.0264282
\(91\) −3.34944e94 −0.324687
\(92\) 7.63934e93 0.0435859
\(93\) 4.38098e95 1.47961
\(94\) 4.95196e95 0.995579
\(95\) 7.61803e95 0.916744
\(96\) 1.89657e96 1.37345
\(97\) −4.30104e96 −1.88427 −0.942137 0.335228i \(-0.891187\pi\)
−0.942137 + 0.335228i \(0.891187\pi\)
\(98\) −4.83489e96 −1.28802
\(99\) −2.40921e95 −0.0392254
\(100\) −6.27300e96 −0.627300
\(101\) −6.37462e96 −0.393430 −0.196715 0.980461i \(-0.563027\pi\)
−0.196715 + 0.980461i \(0.563027\pi\)
\(102\) 9.90118e96 0.378947
\(103\) 6.76626e94 0.00161340 0.000806702 1.00000i \(-0.499743\pi\)
0.000806702 1.00000i \(0.499743\pi\)
\(104\) 4.70135e96 0.0701627
\(105\) −1.73084e97 −0.162396
\(106\) −1.07642e98 −0.637746
\(107\) −9.38861e97 −0.352767 −0.176384 0.984321i \(-0.556440\pi\)
−0.176384 + 0.984321i \(0.556440\pi\)
\(108\) 4.05890e98 0.971307
\(109\) 5.07226e98 0.776276 0.388138 0.921601i \(-0.373118\pi\)
0.388138 + 0.921601i \(0.373118\pi\)
\(110\) 1.01703e99 0.999512
\(111\) 7.48650e98 0.474367
\(112\) −7.14579e98 −0.293073
\(113\) 4.60425e99 1.22703 0.613514 0.789684i \(-0.289755\pi\)
0.613514 + 0.789684i \(0.289755\pi\)
\(114\) −1.23699e100 −2.15022
\(115\) 2.34906e98 0.0267330
\(116\) −1.42968e100 −1.06912
\(117\) 7.53562e98 0.0371625
\(118\) −2.57054e100 −0.838970
\(119\) −3.57483e99 −0.0774868
\(120\) 2.42945e99 0.0350928
\(121\) 5.00596e100 0.483500
\(122\) 2.03276e101 1.31715
\(123\) 3.14990e101 1.37372
\(124\) −4.88548e101 −1.43865
\(125\) −4.87019e101 −0.971428
\(126\) −9.35239e99 −0.0126751
\(127\) 1.73469e102 1.60229 0.801146 0.598469i \(-0.204224\pi\)
0.801146 + 0.598469i \(0.204224\pi\)
\(128\) 1.92410e101 0.121491
\(129\) 3.25964e102 1.41114
\(130\) −3.18110e102 −0.946945
\(131\) −4.26262e102 −0.875022 −0.437511 0.899213i \(-0.644140\pi\)
−0.437511 + 0.899213i \(0.644140\pi\)
\(132\) −8.07365e102 −1.14613
\(133\) 4.46618e102 0.439674
\(134\) −3.38347e103 −2.31622
\(135\) 1.24809e103 0.595742
\(136\) 5.01771e101 0.0167444
\(137\) 6.31336e103 1.47677 0.738386 0.674379i \(-0.235588\pi\)
0.738386 + 0.674379i \(0.235588\pi\)
\(138\) −3.81433e102 −0.0627022
\(139\) 1.17407e104 1.35981 0.679904 0.733301i \(-0.262021\pi\)
0.679904 + 0.733301i \(0.262021\pi\)
\(140\) 1.93016e103 0.157901
\(141\) −1.20879e104 −0.700203
\(142\) 3.80266e104 1.56352
\(143\) −4.80422e104 −1.40548
\(144\) 1.60767e103 0.0335441
\(145\) −4.39619e104 −0.655734
\(146\) −1.65994e104 −0.177411
\(147\) 1.18022e105 0.905880
\(148\) −8.34863e104 −0.461235
\(149\) −3.69564e105 −1.47284 −0.736421 0.676524i \(-0.763486\pi\)
−0.736421 + 0.676524i \(0.763486\pi\)
\(150\) 3.13211e105 0.902426
\(151\) −1.91877e105 −0.400536 −0.200268 0.979741i \(-0.564181\pi\)
−0.200268 + 0.979741i \(0.564181\pi\)
\(152\) −6.26883e104 −0.0950107
\(153\) 8.04270e103 0.00886886
\(154\) 5.96247e105 0.479370
\(155\) −1.50226e106 −0.882383
\(156\) 2.52531e106 1.08585
\(157\) 2.05563e106 0.648355 0.324177 0.945996i \(-0.394913\pi\)
0.324177 + 0.945996i \(0.394913\pi\)
\(158\) 6.31451e106 1.46376
\(159\) 2.62758e106 0.448535
\(160\) −6.50342e106 −0.819073
\(161\) 1.37717e105 0.0128213
\(162\) −1.96128e107 −1.35226
\(163\) −1.65361e107 −0.845932 −0.422966 0.906146i \(-0.639011\pi\)
−0.422966 + 0.906146i \(0.639011\pi\)
\(164\) −3.51263e107 −1.33569
\(165\) −2.48260e107 −0.702969
\(166\) 6.33094e107 1.33729
\(167\) 8.88372e107 1.40232 0.701158 0.713006i \(-0.252667\pi\)
0.701158 + 0.713006i \(0.252667\pi\)
\(168\) 1.42430e106 0.0168306
\(169\) 3.74173e107 0.331564
\(170\) −3.39516e107 −0.225989
\(171\) −1.00481e107 −0.0503235
\(172\) −3.63501e108 −1.37207
\(173\) 4.51855e108 1.28755 0.643773 0.765216i \(-0.277368\pi\)
0.643773 + 0.765216i \(0.277368\pi\)
\(174\) 7.13840e108 1.53802
\(175\) −1.13085e108 −0.184527
\(176\) −1.02495e109 −1.26863
\(177\) 6.27477e108 0.590058
\(178\) −5.28563e108 −0.378204
\(179\) 3.66503e108 0.199851 0.0999254 0.994995i \(-0.468140\pi\)
0.0999254 + 0.994995i \(0.468140\pi\)
\(180\) −4.34250e107 −0.0180727
\(181\) −2.82368e109 −0.898265 −0.449132 0.893465i \(-0.648267\pi\)
−0.449132 + 0.893465i \(0.648267\pi\)
\(182\) −1.86496e109 −0.454159
\(183\) −4.96203e109 −0.926365
\(184\) −1.93302e107 −0.00277059
\(185\) −2.56716e109 −0.282894
\(186\) 2.43932e110 2.06962
\(187\) −5.12750e109 −0.335419
\(188\) 1.34799e110 0.680819
\(189\) 7.31710e109 0.285721
\(190\) 4.24171e110 1.28231
\(191\) −3.19030e110 −0.747675 −0.373837 0.927494i \(-0.621958\pi\)
−0.373837 + 0.927494i \(0.621958\pi\)
\(192\) 4.92766e110 0.896461
\(193\) −2.94804e110 −0.416873 −0.208436 0.978036i \(-0.566837\pi\)
−0.208436 + 0.978036i \(0.566837\pi\)
\(194\) −2.39481e111 −2.63565
\(195\) 7.76519e110 0.665999
\(196\) −1.31613e111 −0.880801
\(197\) 2.89772e110 0.151511 0.0757554 0.997126i \(-0.475863\pi\)
0.0757554 + 0.997126i \(0.475863\pi\)
\(198\) −1.34144e110 −0.0548670
\(199\) 4.51636e110 0.144682 0.0723409 0.997380i \(-0.476953\pi\)
0.0723409 + 0.997380i \(0.476953\pi\)
\(200\) 1.58729e110 0.0398751
\(201\) 8.25918e111 1.62903
\(202\) −3.54938e111 −0.550315
\(203\) −2.57732e111 −0.314493
\(204\) 2.69524e111 0.259140
\(205\) −1.08012e112 −0.819234
\(206\) 3.76744e109 0.00225677
\(207\) −3.09837e109 −0.00146748
\(208\) 3.20586e112 1.20191
\(209\) 6.40599e112 1.90323
\(210\) −9.63730e111 −0.227154
\(211\) −4.76566e112 −0.892122 −0.446061 0.895003i \(-0.647174\pi\)
−0.446061 + 0.895003i \(0.647174\pi\)
\(212\) −2.93017e112 −0.436117
\(213\) −9.28244e112 −1.09964
\(214\) −5.22757e112 −0.493437
\(215\) −1.11775e113 −0.841546
\(216\) −1.02705e112 −0.0617423
\(217\) −8.80719e112 −0.423195
\(218\) 2.82423e113 1.08582
\(219\) 4.05198e112 0.124775
\(220\) 2.76849e113 0.683508
\(221\) 1.60380e113 0.317779
\(222\) 4.16848e113 0.663526
\(223\) 1.96663e113 0.251731 0.125865 0.992047i \(-0.459829\pi\)
0.125865 + 0.992047i \(0.459829\pi\)
\(224\) −3.81272e113 −0.392831
\(225\) 2.54421e112 0.0211203
\(226\) 2.56364e114 1.71632
\(227\) −1.82708e114 −0.987423 −0.493712 0.869626i \(-0.664360\pi\)
−0.493712 + 0.869626i \(0.664360\pi\)
\(228\) −3.36727e114 −1.47041
\(229\) −2.36794e114 −0.836277 −0.418138 0.908383i \(-0.637317\pi\)
−0.418138 + 0.908383i \(0.637317\pi\)
\(230\) 1.30795e113 0.0373931
\(231\) −1.45546e114 −0.337147
\(232\) 3.61759e113 0.0679598
\(233\) 6.68027e114 1.01867 0.509333 0.860570i \(-0.329892\pi\)
0.509333 + 0.860570i \(0.329892\pi\)
\(234\) 4.19582e113 0.0519814
\(235\) 4.14500e114 0.417574
\(236\) −6.99736e114 −0.573722
\(237\) −1.54139e115 −1.02948
\(238\) −1.99046e114 −0.108385
\(239\) 2.80228e115 1.24513 0.622563 0.782570i \(-0.286091\pi\)
0.622563 + 0.782570i \(0.286091\pi\)
\(240\) 1.65665e115 0.601153
\(241\) −2.46032e115 −0.729735 −0.364868 0.931059i \(-0.618886\pi\)
−0.364868 + 0.931059i \(0.618886\pi\)
\(242\) 2.78731e115 0.676301
\(243\) −3.24106e114 −0.0643848
\(244\) 5.53345e115 0.900719
\(245\) −4.04701e115 −0.540231
\(246\) 1.75386e116 1.92151
\(247\) −2.00369e116 −1.80314
\(248\) 1.23620e115 0.0914495
\(249\) −1.54541e116 −0.940533
\(250\) −2.71172e116 −1.35879
\(251\) −3.13517e116 −1.29445 −0.647225 0.762299i \(-0.724070\pi\)
−0.647225 + 0.762299i \(0.724070\pi\)
\(252\) −2.54585e114 −0.00866776
\(253\) 1.97532e115 0.0554998
\(254\) 9.65873e116 2.24122
\(255\) 8.28772e115 0.158941
\(256\) 6.81618e116 1.08119
\(257\) −8.27239e116 −1.08611 −0.543056 0.839697i \(-0.682733\pi\)
−0.543056 + 0.839697i \(0.682733\pi\)
\(258\) 1.81496e117 1.97384
\(259\) −1.50503e116 −0.135677
\(260\) −8.65940e116 −0.647561
\(261\) 5.79850e115 0.0359957
\(262\) −2.37342e117 −1.22395
\(263\) 3.71022e116 0.159055 0.0795273 0.996833i \(-0.474659\pi\)
0.0795273 + 0.996833i \(0.474659\pi\)
\(264\) 2.04292e116 0.0728552
\(265\) −9.01010e116 −0.267488
\(266\) 2.48676e117 0.614999
\(267\) 1.29024e117 0.265996
\(268\) −9.21029e117 −1.58393
\(269\) 1.31056e117 0.188135 0.0940676 0.995566i \(-0.470013\pi\)
0.0940676 + 0.995566i \(0.470013\pi\)
\(270\) 6.94935e117 0.833301
\(271\) −1.76170e118 −1.76571 −0.882857 0.469643i \(-0.844383\pi\)
−0.882857 + 0.469643i \(0.844383\pi\)
\(272\) 3.42159e117 0.286838
\(273\) 4.55245e117 0.319416
\(274\) 3.51527e118 2.06565
\(275\) −1.62202e118 −0.798767
\(276\) −1.03831e117 −0.0428784
\(277\) −4.94686e118 −1.71420 −0.857099 0.515152i \(-0.827736\pi\)
−0.857099 + 0.515152i \(0.827736\pi\)
\(278\) 6.53723e118 1.90205
\(279\) 1.98145e117 0.0484373
\(280\) −4.88398e116 −0.0100371
\(281\) 1.08158e119 1.86983 0.934914 0.354874i \(-0.115476\pi\)
0.934914 + 0.354874i \(0.115476\pi\)
\(282\) −6.73053e118 −0.979417
\(283\) −3.09182e118 −0.378941 −0.189471 0.981886i \(-0.560677\pi\)
−0.189471 + 0.981886i \(0.560677\pi\)
\(284\) 1.03514e119 1.06920
\(285\) −1.03542e119 −0.901861
\(286\) −2.67498e119 −1.96593
\(287\) −6.33232e118 −0.392908
\(288\) 8.57791e117 0.0449620
\(289\) −2.08590e119 −0.924162
\(290\) −2.44779e119 −0.917215
\(291\) 5.84582e119 1.85368
\(292\) −4.51860e118 −0.121321
\(293\) 6.68329e119 1.52023 0.760117 0.649786i \(-0.225141\pi\)
0.760117 + 0.649786i \(0.225141\pi\)
\(294\) 6.57142e119 1.26711
\(295\) −2.15165e119 −0.351887
\(296\) 2.11250e118 0.0293189
\(297\) 1.04952e120 1.23681
\(298\) −2.05773e120 −2.06015
\(299\) −6.17847e118 −0.0525810
\(300\) 8.52605e119 0.617116
\(301\) −6.55294e119 −0.403609
\(302\) −1.06837e120 −0.560253
\(303\) 8.66417e119 0.387043
\(304\) −4.27473e120 −1.62757
\(305\) 1.70150e120 0.552447
\(306\) 4.47817e118 0.0124054
\(307\) 4.55957e120 1.07823 0.539117 0.842231i \(-0.318758\pi\)
0.539117 + 0.842231i \(0.318758\pi\)
\(308\) 1.62307e120 0.327813
\(309\) −9.19647e117 −0.00158721
\(310\) −8.36455e120 −1.23424
\(311\) −4.75642e120 −0.600346 −0.300173 0.953885i \(-0.597044\pi\)
−0.300173 + 0.953885i \(0.597044\pi\)
\(312\) −6.38992e119 −0.0690236
\(313\) −4.80816e120 −0.444712 −0.222356 0.974966i \(-0.571375\pi\)
−0.222356 + 0.974966i \(0.571375\pi\)
\(314\) 1.14457e121 0.906893
\(315\) −7.82835e118 −0.00531629
\(316\) 1.71890e121 1.00098
\(317\) 3.46333e121 1.73029 0.865145 0.501521i \(-0.167226\pi\)
0.865145 + 0.501521i \(0.167226\pi\)
\(318\) 1.46303e121 0.627392
\(319\) −3.69674e121 −1.36135
\(320\) −1.68972e121 −0.534614
\(321\) 1.27607e121 0.347040
\(322\) 7.66804e119 0.0179339
\(323\) −2.13852e121 −0.430320
\(324\) −5.33887e121 −0.924734
\(325\) 5.07341e121 0.756759
\(326\) −9.20730e121 −1.18326
\(327\) −6.89404e121 −0.763674
\(328\) 8.88820e120 0.0849048
\(329\) 2.43006e121 0.200270
\(330\) −1.38231e122 −0.983285
\(331\) 1.29740e122 0.796924 0.398462 0.917185i \(-0.369544\pi\)
0.398462 + 0.917185i \(0.369544\pi\)
\(332\) 1.72337e122 0.914495
\(333\) 3.38604e120 0.0155291
\(334\) 4.94644e122 1.96150
\(335\) −2.83211e122 −0.971488
\(336\) 9.71232e121 0.288316
\(337\) 5.17092e122 1.32898 0.664489 0.747298i \(-0.268649\pi\)
0.664489 + 0.747298i \(0.268649\pi\)
\(338\) 2.08339e122 0.463778
\(339\) −6.25794e122 −1.20711
\(340\) −9.24210e121 −0.154541
\(341\) −1.26324e123 −1.83189
\(342\) −5.59475e121 −0.0703906
\(343\) −4.94923e122 −0.540471
\(344\) 9.19786e121 0.0872172
\(345\) −3.19276e121 −0.0262990
\(346\) 2.51592e123 1.80097
\(347\) −1.84097e123 −1.14569 −0.572845 0.819664i \(-0.694160\pi\)
−0.572845 + 0.819664i \(0.694160\pi\)
\(348\) 1.94317e123 1.05176
\(349\) 3.57643e122 0.168429 0.0842145 0.996448i \(-0.473162\pi\)
0.0842145 + 0.996448i \(0.473162\pi\)
\(350\) −6.29657e122 −0.258109
\(351\) −3.28272e123 −1.17176
\(352\) −5.46871e123 −1.70046
\(353\) 4.06742e123 1.10216 0.551081 0.834452i \(-0.314216\pi\)
0.551081 + 0.834452i \(0.314216\pi\)
\(354\) 3.49378e123 0.825349
\(355\) 3.18299e123 0.655783
\(356\) −1.43882e123 −0.258632
\(357\) 4.85879e122 0.0762288
\(358\) 2.04068e123 0.279543
\(359\) 8.70448e123 1.04151 0.520754 0.853707i \(-0.325651\pi\)
0.520754 + 0.853707i \(0.325651\pi\)
\(360\) 1.09881e121 0.00114881
\(361\) 1.57753e124 1.44171
\(362\) −1.57222e124 −1.25646
\(363\) −6.80393e123 −0.475651
\(364\) −5.07669e123 −0.310573
\(365\) −1.38944e123 −0.0744110
\(366\) −2.76285e124 −1.29576
\(367\) −2.33190e124 −0.958089 −0.479045 0.877791i \(-0.659017\pi\)
−0.479045 + 0.877791i \(0.659017\pi\)
\(368\) −1.31813e123 −0.0474613
\(369\) 1.42466e123 0.0449709
\(370\) −1.42939e124 −0.395701
\(371\) −5.28230e123 −0.128289
\(372\) 6.64018e124 1.41530
\(373\) 4.36469e124 0.816724 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(374\) −2.85498e124 −0.469171
\(375\) 6.61940e124 0.955657
\(376\) −3.41089e123 −0.0432770
\(377\) 1.15628e125 1.28976
\(378\) 4.07415e124 0.399655
\(379\) −1.60339e125 −1.38368 −0.691842 0.722049i \(-0.743201\pi\)
−0.691842 + 0.722049i \(0.743201\pi\)
\(380\) 1.15465e125 0.876894
\(381\) −2.35773e125 −1.57628
\(382\) −1.77635e125 −1.04582
\(383\) 2.86390e125 1.48531 0.742654 0.669675i \(-0.233567\pi\)
0.742654 + 0.669675i \(0.233567\pi\)
\(384\) −2.61517e124 −0.119519
\(385\) 4.99084e124 0.201061
\(386\) −1.64146e125 −0.583105
\(387\) 1.47429e124 0.0461957
\(388\) −6.51901e125 −1.80237
\(389\) −3.30470e124 −0.0806448 −0.0403224 0.999187i \(-0.512838\pi\)
−0.0403224 + 0.999187i \(0.512838\pi\)
\(390\) 4.32365e125 0.931572
\(391\) −6.59423e123 −0.0125485
\(392\) 3.33026e124 0.0559892
\(393\) 5.79361e125 0.860817
\(394\) 1.61344e125 0.211927
\(395\) 5.28551e125 0.613943
\(396\) −3.65160e124 −0.0375203
\(397\) −1.73042e126 −1.57330 −0.786649 0.617400i \(-0.788186\pi\)
−0.786649 + 0.617400i \(0.788186\pi\)
\(398\) 2.51470e125 0.202375
\(399\) −6.07027e125 −0.432537
\(400\) 1.08238e126 0.683076
\(401\) −1.93417e126 −1.08142 −0.540708 0.841210i \(-0.681844\pi\)
−0.540708 + 0.841210i \(0.681844\pi\)
\(402\) 4.59870e126 2.27862
\(403\) 3.95123e126 1.73555
\(404\) −9.66191e125 −0.376328
\(405\) −1.64167e126 −0.567177
\(406\) −1.43505e126 −0.439900
\(407\) −2.15872e126 −0.587309
\(408\) −6.81991e124 −0.0164725
\(409\) −1.45137e126 −0.311313 −0.155656 0.987811i \(-0.549749\pi\)
−0.155656 + 0.987811i \(0.549749\pi\)
\(410\) −6.01407e126 −1.14591
\(411\) −8.58091e126 −1.45280
\(412\) 1.02555e124 0.00154327
\(413\) −1.26143e126 −0.168767
\(414\) −1.72517e124 −0.00205265
\(415\) 5.29927e126 0.560897
\(416\) 1.71052e127 1.61103
\(417\) −1.59576e127 −1.33773
\(418\) 3.56684e127 2.66216
\(419\) 1.52094e127 1.01095 0.505477 0.862840i \(-0.331316\pi\)
0.505477 + 0.862840i \(0.331316\pi\)
\(420\) −2.62341e126 −0.155337
\(421\) 4.18467e126 0.220790 0.110395 0.993888i \(-0.464788\pi\)
0.110395 + 0.993888i \(0.464788\pi\)
\(422\) −2.65351e127 −1.24786
\(423\) −5.46719e125 −0.0229222
\(424\) 7.41435e125 0.0277223
\(425\) 5.41481e126 0.180601
\(426\) −5.16845e127 −1.53814
\(427\) 9.97530e126 0.264956
\(428\) −1.42302e127 −0.337433
\(429\) 6.52973e127 1.38266
\(430\) −6.22360e127 −1.17712
\(431\) −1.47635e127 −0.249484 −0.124742 0.992189i \(-0.539810\pi\)
−0.124742 + 0.992189i \(0.539810\pi\)
\(432\) −7.00345e127 −1.05767
\(433\) 6.61951e127 0.893641 0.446821 0.894624i \(-0.352556\pi\)
0.446821 + 0.894624i \(0.352556\pi\)
\(434\) −4.90383e127 −0.591948
\(435\) 5.97515e127 0.645089
\(436\) 7.68794e127 0.742532
\(437\) 8.23843e126 0.0712024
\(438\) 2.25614e127 0.174531
\(439\) −1.19115e128 −0.824965 −0.412483 0.910965i \(-0.635338\pi\)
−0.412483 + 0.910965i \(0.635338\pi\)
\(440\) −7.00526e126 −0.0434480
\(441\) 5.33795e126 0.0296553
\(442\) 8.92993e127 0.444496
\(443\) −1.78349e127 −0.0795590 −0.0397795 0.999208i \(-0.512666\pi\)
−0.0397795 + 0.999208i \(0.512666\pi\)
\(444\) 1.13472e128 0.453747
\(445\) −4.42430e127 −0.158629
\(446\) 1.09502e128 0.352111
\(447\) 5.02299e128 1.44893
\(448\) −9.90620e127 −0.256403
\(449\) −2.61967e128 −0.608555 −0.304277 0.952583i \(-0.598415\pi\)
−0.304277 + 0.952583i \(0.598415\pi\)
\(450\) 1.41661e127 0.0295423
\(451\) −9.08267e128 −1.70079
\(452\) 6.97859e128 1.17369
\(453\) 2.60793e128 0.394033
\(454\) −1.01732e129 −1.38117
\(455\) −1.56106e128 −0.190487
\(456\) 8.52038e127 0.0934683
\(457\) −2.50980e128 −0.247573 −0.123787 0.992309i \(-0.539504\pi\)
−0.123787 + 0.992309i \(0.539504\pi\)
\(458\) −1.31847e129 −1.16975
\(459\) −3.50362e128 −0.279641
\(460\) 3.56043e127 0.0255710
\(461\) 2.49750e129 1.61440 0.807198 0.590280i \(-0.200983\pi\)
0.807198 + 0.590280i \(0.200983\pi\)
\(462\) −8.10398e128 −0.471588
\(463\) −8.35396e128 −0.437738 −0.218869 0.975754i \(-0.570237\pi\)
−0.218869 + 0.975754i \(0.570237\pi\)
\(464\) 2.46684e129 1.16418
\(465\) 2.04182e129 0.868058
\(466\) 3.71956e129 1.42487
\(467\) 6.68430e128 0.230774 0.115387 0.993321i \(-0.463189\pi\)
0.115387 + 0.993321i \(0.463189\pi\)
\(468\) 1.14216e128 0.0355471
\(469\) −1.66036e129 −0.465930
\(470\) 2.30793e129 0.584086
\(471\) −2.79395e129 −0.637829
\(472\) 1.77058e128 0.0364693
\(473\) −9.39910e129 −1.74711
\(474\) −8.58246e129 −1.44000
\(475\) −6.76494e129 −1.02476
\(476\) −5.41831e128 −0.0741185
\(477\) 1.18842e128 0.0146834
\(478\) 1.56031e130 1.74163
\(479\) 3.95123e129 0.398529 0.199265 0.979946i \(-0.436145\pi\)
0.199265 + 0.979946i \(0.436145\pi\)
\(480\) 8.83923e129 0.805776
\(481\) 6.75212e129 0.556422
\(482\) −1.36990e130 −1.02072
\(483\) −1.87180e128 −0.0126131
\(484\) 7.58745e129 0.462483
\(485\) −2.00456e130 −1.10546
\(486\) −1.80462e129 −0.0900589
\(487\) 3.95586e129 0.178684 0.0893420 0.996001i \(-0.471524\pi\)
0.0893420 + 0.996001i \(0.471524\pi\)
\(488\) −1.40016e129 −0.0572553
\(489\) 2.24754e130 0.832199
\(490\) −2.25337e130 −0.755654
\(491\) 3.72426e130 1.13133 0.565663 0.824637i \(-0.308620\pi\)
0.565663 + 0.824637i \(0.308620\pi\)
\(492\) 4.77425e130 1.31401
\(493\) 1.23409e130 0.307802
\(494\) −1.11565e131 −2.52215
\(495\) −1.12285e129 −0.0230127
\(496\) 8.42966e130 1.56657
\(497\) 1.86607e130 0.314517
\(498\) −8.60479e130 −1.31558
\(499\) 1.22476e131 1.69893 0.849463 0.527648i \(-0.176926\pi\)
0.849463 + 0.527648i \(0.176926\pi\)
\(500\) −7.38167e130 −0.929201
\(501\) −1.20744e131 −1.37955
\(502\) −1.74566e131 −1.81062
\(503\) 1.00764e131 0.948980 0.474490 0.880261i \(-0.342632\pi\)
0.474490 + 0.880261i \(0.342632\pi\)
\(504\) 6.44190e127 0.000550976 0
\(505\) −2.97098e130 −0.230817
\(506\) 1.09985e130 0.0776309
\(507\) −5.08563e130 −0.326181
\(508\) 2.62924e131 1.53264
\(509\) −1.64486e131 −0.871598 −0.435799 0.900044i \(-0.643534\pi\)
−0.435799 + 0.900044i \(0.643534\pi\)
\(510\) 4.61459e130 0.222320
\(511\) −8.14581e129 −0.0356879
\(512\) 3.49035e131 1.39084
\(513\) 4.37721e131 1.58674
\(514\) −4.60606e131 −1.51921
\(515\) 3.15351e128 0.000946551 0
\(516\) 4.94059e131 1.34980
\(517\) 3.48552e131 0.866915
\(518\) −8.37999e130 −0.189780
\(519\) −6.14146e131 −1.26664
\(520\) 2.19113e130 0.0411630
\(521\) −9.86220e131 −1.68789 −0.843945 0.536430i \(-0.819773\pi\)
−0.843945 + 0.536430i \(0.819773\pi\)
\(522\) 3.22860e130 0.0503494
\(523\) −6.15255e131 −0.874426 −0.437213 0.899358i \(-0.644034\pi\)
−0.437213 + 0.899358i \(0.644034\pi\)
\(524\) −6.46078e131 −0.836985
\(525\) 1.53702e131 0.181531
\(526\) 2.06585e131 0.222479
\(527\) 4.21711e131 0.414191
\(528\) 1.39307e132 1.24804
\(529\) −1.22095e132 −0.997924
\(530\) −5.01681e131 −0.374152
\(531\) 2.83799e130 0.0193164
\(532\) 6.76931e131 0.420562
\(533\) 2.84091e132 1.61134
\(534\) 7.18405e131 0.372064
\(535\) −4.37570e131 −0.206961
\(536\) 2.33053e131 0.100684
\(537\) −4.98139e131 −0.196606
\(538\) 7.29716e131 0.263156
\(539\) −3.40312e132 −1.12156
\(540\) 1.89171e132 0.569846
\(541\) 1.62318e132 0.446992 0.223496 0.974705i \(-0.428253\pi\)
0.223496 + 0.974705i \(0.428253\pi\)
\(542\) −9.80909e132 −2.46981
\(543\) 3.83785e132 0.883682
\(544\) 1.82563e132 0.384473
\(545\) 2.36400e132 0.455425
\(546\) 2.53480e132 0.446786
\(547\) −8.11601e130 −0.0130905 −0.00654526 0.999979i \(-0.502083\pi\)
−0.00654526 + 0.999979i \(0.502083\pi\)
\(548\) 9.56906e132 1.41258
\(549\) −2.24426e131 −0.0303259
\(550\) −9.03138e132 −1.11728
\(551\) −1.54180e133 −1.74652
\(552\) 2.62730e130 0.00272561
\(553\) 3.09870e132 0.294450
\(554\) −2.75441e133 −2.39775
\(555\) 3.48919e132 0.278301
\(556\) 1.77952e133 1.30070
\(557\) −1.26292e133 −0.846054 −0.423027 0.906117i \(-0.639033\pi\)
−0.423027 + 0.906117i \(0.639033\pi\)
\(558\) 1.10327e132 0.0677522
\(559\) 2.93989e133 1.65523
\(560\) −3.33040e132 −0.171940
\(561\) 6.96912e132 0.329974
\(562\) 6.02222e133 2.61544
\(563\) 3.25814e130 0.00129811 0.000649056 1.00000i \(-0.499793\pi\)
0.000649056 1.00000i \(0.499793\pi\)
\(564\) −1.83214e133 −0.669766
\(565\) 2.14588e133 0.719872
\(566\) −1.72152e133 −0.530048
\(567\) −9.62454e132 −0.272020
\(568\) −2.61926e132 −0.0679649
\(569\) −3.87831e133 −0.924054 −0.462027 0.886866i \(-0.652878\pi\)
−0.462027 + 0.886866i \(0.652878\pi\)
\(570\) −5.76519e133 −1.26149
\(571\) 5.41263e133 1.08782 0.543910 0.839144i \(-0.316943\pi\)
0.543910 + 0.839144i \(0.316943\pi\)
\(572\) −7.28167e133 −1.34439
\(573\) 4.33614e133 0.735537
\(574\) −3.52583e133 −0.549585
\(575\) −2.08600e132 −0.0298830
\(576\) 2.22871e132 0.0293470
\(577\) 1.44687e132 0.0175147 0.00875734 0.999962i \(-0.497212\pi\)
0.00875734 + 0.999962i \(0.497212\pi\)
\(578\) −1.16143e134 −1.29268
\(579\) 4.00687e133 0.410105
\(580\) −6.66323e133 −0.627230
\(581\) 3.10677e133 0.269009
\(582\) 3.25495e134 2.59286
\(583\) −7.57657e133 −0.555326
\(584\) 1.14336e132 0.00771190
\(585\) 3.51208e132 0.0218025
\(586\) 3.72125e134 2.12644
\(587\) −7.76480e133 −0.408491 −0.204245 0.978920i \(-0.565474\pi\)
−0.204245 + 0.978920i \(0.565474\pi\)
\(588\) 1.78883e134 0.866502
\(589\) −5.26860e134 −2.35019
\(590\) −1.19803e134 −0.492206
\(591\) −3.93848e133 −0.149051
\(592\) 1.44052e134 0.502245
\(593\) −2.11462e134 −0.679330 −0.339665 0.940547i \(-0.610314\pi\)
−0.339665 + 0.940547i \(0.610314\pi\)
\(594\) 5.84369e134 1.72999
\(595\) −1.66610e133 −0.0454599
\(596\) −5.60143e134 −1.40882
\(597\) −6.13848e133 −0.142333
\(598\) −3.44016e133 −0.0735482
\(599\) 2.23758e134 0.441141 0.220571 0.975371i \(-0.429208\pi\)
0.220571 + 0.975371i \(0.429208\pi\)
\(600\) −2.15739e133 −0.0392277
\(601\) 1.32563e134 0.222337 0.111168 0.993802i \(-0.464541\pi\)
0.111168 + 0.993802i \(0.464541\pi\)
\(602\) −3.64867e134 −0.564553
\(603\) 3.73551e133 0.0533286
\(604\) −2.90825e134 −0.383125
\(605\) 2.33310e134 0.283660
\(606\) 4.82420e134 0.541381
\(607\) −1.06946e133 −0.0110793 −0.00553964 0.999985i \(-0.501763\pi\)
−0.00553964 + 0.999985i \(0.501763\pi\)
\(608\) −2.28083e135 −2.18157
\(609\) 3.50301e134 0.309388
\(610\) 9.47396e134 0.772742
\(611\) −1.09021e135 −0.821322
\(612\) 1.21902e133 0.00848333
\(613\) 2.12784e135 1.36806 0.684032 0.729452i \(-0.260225\pi\)
0.684032 + 0.729452i \(0.260225\pi\)
\(614\) 2.53876e135 1.50819
\(615\) 1.46806e135 0.805934
\(616\) −4.10693e133 −0.0208378
\(617\) −2.66046e134 −0.124774 −0.0623872 0.998052i \(-0.519871\pi\)
−0.0623872 + 0.998052i \(0.519871\pi\)
\(618\) −5.12058e132 −0.00222013
\(619\) 2.14756e135 0.860892 0.430446 0.902616i \(-0.358356\pi\)
0.430446 + 0.902616i \(0.358356\pi\)
\(620\) −2.27695e135 −0.844026
\(621\) 1.34973e134 0.0462706
\(622\) −2.64837e135 −0.839740
\(623\) −2.59380e134 −0.0760794
\(624\) −4.35730e135 −1.18240
\(625\) 3.42081e134 0.0858910
\(626\) −2.67718e135 −0.622046
\(627\) −8.70680e135 −1.87233
\(628\) 3.11569e135 0.620171
\(629\) 7.20648e134 0.132790
\(630\) −4.35882e133 −0.00743621
\(631\) −4.79344e135 −0.757222 −0.378611 0.925556i \(-0.623598\pi\)
−0.378611 + 0.925556i \(0.623598\pi\)
\(632\) −4.34941e134 −0.0636286
\(633\) 6.47733e135 0.877639
\(634\) 1.92837e136 2.42026
\(635\) 8.08477e135 0.940031
\(636\) 3.98258e135 0.429037
\(637\) 1.06444e136 1.06258
\(638\) −2.05834e136 −1.90421
\(639\) −4.19832e134 −0.0359984
\(640\) 8.96755e134 0.0712763
\(641\) −1.80663e136 −1.33124 −0.665619 0.746291i \(-0.731833\pi\)
−0.665619 + 0.746291i \(0.731833\pi\)
\(642\) 7.10513e135 0.485426
\(643\) −3.51510e135 −0.222693 −0.111346 0.993782i \(-0.535516\pi\)
−0.111346 + 0.993782i \(0.535516\pi\)
\(644\) 2.08735e134 0.0122639
\(645\) 1.51920e136 0.827884
\(646\) −1.19073e136 −0.601914
\(647\) 4.19654e135 0.196804 0.0984019 0.995147i \(-0.468627\pi\)
0.0984019 + 0.995147i \(0.468627\pi\)
\(648\) 1.35092e135 0.0587818
\(649\) −1.80932e136 −0.730544
\(650\) 2.82487e136 1.05852
\(651\) 1.19704e136 0.416324
\(652\) −2.50636e136 −0.809160
\(653\) −3.81194e136 −1.14250 −0.571250 0.820776i \(-0.693541\pi\)
−0.571250 + 0.820776i \(0.693541\pi\)
\(654\) −3.83859e136 −1.06820
\(655\) −1.98666e136 −0.513357
\(656\) 6.06088e136 1.45445
\(657\) 1.83266e134 0.00408470
\(658\) 1.35306e136 0.280130
\(659\) 5.46387e136 1.05089 0.525445 0.850827i \(-0.323899\pi\)
0.525445 + 0.850827i \(0.323899\pi\)
\(660\) −3.76284e136 −0.672411
\(661\) −6.27330e136 −1.04166 −0.520830 0.853661i \(-0.674377\pi\)
−0.520830 + 0.853661i \(0.674377\pi\)
\(662\) 7.22392e136 1.11471
\(663\) −2.17983e136 −0.312620
\(664\) −4.36073e135 −0.0581310
\(665\) 2.08153e136 0.257948
\(666\) 1.88534e135 0.0217215
\(667\) −4.75420e135 −0.0509301
\(668\) 1.34649e137 1.34136
\(669\) −2.67298e136 −0.247644
\(670\) −1.57692e137 −1.35888
\(671\) 1.43079e137 1.14692
\(672\) 5.18212e136 0.386454
\(673\) −1.67353e136 −0.116119 −0.0580594 0.998313i \(-0.518491\pi\)
−0.0580594 + 0.998313i \(0.518491\pi\)
\(674\) 2.87916e137 1.85892
\(675\) −1.10832e137 −0.665938
\(676\) 5.67127e136 0.317151
\(677\) −1.69999e137 −0.884901 −0.442451 0.896793i \(-0.645891\pi\)
−0.442451 + 0.896793i \(0.645891\pi\)
\(678\) −3.48441e137 −1.68846
\(679\) −1.17520e137 −0.530186
\(680\) 2.33858e135 0.00982358
\(681\) 2.48330e137 0.971393
\(682\) −7.03373e137 −2.56238
\(683\) −2.06049e137 −0.699143 −0.349572 0.936910i \(-0.613673\pi\)
−0.349572 + 0.936910i \(0.613673\pi\)
\(684\) −1.52297e136 −0.0481360
\(685\) 2.94243e137 0.866391
\(686\) −2.75572e137 −0.755990
\(687\) 3.21843e137 0.822701
\(688\) 6.27204e137 1.49407
\(689\) 2.36983e137 0.526120
\(690\) −1.77772e136 −0.0367861
\(691\) 5.67605e137 1.09487 0.547433 0.836850i \(-0.315605\pi\)
0.547433 + 0.836850i \(0.315605\pi\)
\(692\) 6.84869e137 1.23158
\(693\) −6.58284e135 −0.0110370
\(694\) −1.02505e138 −1.60255
\(695\) 5.47194e137 0.797771
\(696\) −4.91691e136 −0.0668566
\(697\) 3.03208e137 0.384548
\(698\) 1.99135e137 0.235592
\(699\) −9.07959e137 −1.00213
\(700\) −1.71401e137 −0.176506
\(701\) 7.43944e137 0.714852 0.357426 0.933941i \(-0.383654\pi\)
0.357426 + 0.933941i \(0.383654\pi\)
\(702\) −1.82781e138 −1.63901
\(703\) −9.00334e137 −0.753478
\(704\) −1.42088e138 −1.10990
\(705\) −5.63374e137 −0.410795
\(706\) 2.26473e138 1.54166
\(707\) −1.74178e137 −0.110701
\(708\) 9.51057e137 0.564408
\(709\) −4.02698e137 −0.223171 −0.111585 0.993755i \(-0.535593\pi\)
−0.111585 + 0.993755i \(0.535593\pi\)
\(710\) 1.77229e138 0.917284
\(711\) −6.97151e136 −0.0337017
\(712\) 3.64073e136 0.0164402
\(713\) −1.62460e137 −0.0685337
\(714\) 2.70537e137 0.106626
\(715\) −2.23907e138 −0.824566
\(716\) 5.55503e137 0.191163
\(717\) −3.80877e138 −1.22491
\(718\) 4.84664e138 1.45682
\(719\) −4.27047e138 −1.19984 −0.599921 0.800059i \(-0.704801\pi\)
−0.599921 + 0.800059i \(0.704801\pi\)
\(720\) 7.49278e136 0.0196796
\(721\) 1.84879e135 0.000453970 0
\(722\) 8.78368e138 2.01661
\(723\) 3.34399e138 0.717888
\(724\) −4.27980e138 −0.859218
\(725\) 3.90388e138 0.732999
\(726\) −3.78842e138 −0.665322
\(727\) 5.97013e137 0.0980765 0.0490383 0.998797i \(-0.484384\pi\)
0.0490383 + 0.998797i \(0.484384\pi\)
\(728\) 1.28458e137 0.0197419
\(729\) 7.16413e138 1.03010
\(730\) −7.73641e137 −0.104083
\(731\) 3.13772e138 0.395022
\(732\) −7.52087e138 −0.886096
\(733\) −3.84503e138 −0.423992 −0.211996 0.977271i \(-0.567996\pi\)
−0.211996 + 0.977271i \(0.567996\pi\)
\(734\) −1.29840e139 −1.34014
\(735\) 5.50056e138 0.531461
\(736\) −7.03305e137 −0.0636164
\(737\) −2.38152e139 −2.01688
\(738\) 7.93246e137 0.0629035
\(739\) −6.16139e138 −0.457534 −0.228767 0.973481i \(-0.573469\pi\)
−0.228767 + 0.973481i \(0.573469\pi\)
\(740\) −3.89100e138 −0.270597
\(741\) 2.72335e139 1.77386
\(742\) −2.94117e138 −0.179445
\(743\) 1.66865e139 0.953691 0.476846 0.878987i \(-0.341780\pi\)
0.476846 + 0.878987i \(0.341780\pi\)
\(744\) −1.68020e138 −0.0899649
\(745\) −1.72241e139 −0.864086
\(746\) 2.43025e139 1.14240
\(747\) −6.98965e137 −0.0307898
\(748\) −7.77166e138 −0.320839
\(749\) −2.56531e138 −0.0992595
\(750\) 3.68567e139 1.33674
\(751\) 3.06018e138 0.104042 0.0520211 0.998646i \(-0.483434\pi\)
0.0520211 + 0.998646i \(0.483434\pi\)
\(752\) −2.32590e139 −0.741353
\(753\) 4.26121e139 1.27344
\(754\) 6.43816e139 1.80406
\(755\) −8.94271e138 −0.234986
\(756\) 1.10904e139 0.273301
\(757\) −4.50908e139 −1.04217 −0.521084 0.853505i \(-0.674472\pi\)
−0.521084 + 0.853505i \(0.674472\pi\)
\(758\) −8.92764e139 −1.93544
\(759\) −2.68478e138 −0.0545988
\(760\) −2.92168e138 −0.0557408
\(761\) −3.68505e139 −0.659610 −0.329805 0.944049i \(-0.606983\pi\)
−0.329805 + 0.944049i \(0.606983\pi\)
\(762\) −1.31278e140 −2.20484
\(763\) 1.38593e139 0.218424
\(764\) −4.83548e139 −0.715174
\(765\) 3.74842e137 0.00520317
\(766\) 1.59461e140 2.07759
\(767\) 5.65925e139 0.692124
\(768\) −9.26432e139 −1.06364
\(769\) 1.27976e140 1.37943 0.689715 0.724081i \(-0.257736\pi\)
0.689715 + 0.724081i \(0.257736\pi\)
\(770\) 2.77889e139 0.281237
\(771\) 1.12436e140 1.06848
\(772\) −4.46829e139 −0.398752
\(773\) −1.66967e140 −1.39935 −0.699674 0.714462i \(-0.746671\pi\)
−0.699674 + 0.714462i \(0.746671\pi\)
\(774\) 8.20883e138 0.0646167
\(775\) 1.33403e140 0.986354
\(776\) 1.64954e139 0.114570
\(777\) 2.04559e139 0.133475
\(778\) −1.84005e139 −0.112803
\(779\) −3.78810e140 −2.18200
\(780\) 1.17696e140 0.637048
\(781\) 2.67657e140 1.36146
\(782\) −3.67166e138 −0.0175523
\(783\) −2.52598e140 −1.13497
\(784\) 2.27091e140 0.959116
\(785\) 9.58058e139 0.380376
\(786\) 3.22587e140 1.20408
\(787\) −3.94973e140 −1.38609 −0.693047 0.720893i \(-0.743732\pi\)
−0.693047 + 0.720893i \(0.743732\pi\)
\(788\) 4.39202e139 0.144925
\(789\) −5.04281e139 −0.156472
\(790\) 2.94297e140 0.858759
\(791\) 1.25805e140 0.345254
\(792\) 9.23983e137 0.00238502
\(793\) −4.47529e140 −1.08660
\(794\) −9.63494e140 −2.20067
\(795\) 1.22462e140 0.263146
\(796\) 6.84537e139 0.138393
\(797\) −1.74076e139 −0.0331140 −0.0165570 0.999863i \(-0.505270\pi\)
−0.0165570 + 0.999863i \(0.505270\pi\)
\(798\) −3.37992e140 −0.605015
\(799\) −1.16358e140 −0.196009
\(800\) 5.77514e140 0.915584
\(801\) 5.83558e138 0.00870777
\(802\) −1.07694e141 −1.51264
\(803\) −1.16838e140 −0.154483
\(804\) 1.25183e141 1.55821
\(805\) 6.41848e138 0.00752198
\(806\) 2.20004e141 2.42762
\(807\) −1.78126e140 −0.185081
\(808\) 2.44480e139 0.0239217
\(809\) 9.54940e140 0.879980 0.439990 0.898003i \(-0.354982\pi\)
0.439990 + 0.898003i \(0.354982\pi\)
\(810\) −9.14082e140 −0.793344
\(811\) 9.09885e140 0.743832 0.371916 0.928266i \(-0.378701\pi\)
0.371916 + 0.928266i \(0.378701\pi\)
\(812\) −3.90641e140 −0.300822
\(813\) 2.39444e141 1.73705
\(814\) −1.20197e141 −0.821505
\(815\) −7.70691e140 −0.496291
\(816\) −4.65051e140 −0.282181
\(817\) −3.92007e141 −2.24143
\(818\) −8.08119e140 −0.435452
\(819\) 2.05901e139 0.0104566
\(820\) −1.63711e141 −0.783623
\(821\) 2.89041e141 1.30412 0.652059 0.758168i \(-0.273905\pi\)
0.652059 + 0.758168i \(0.273905\pi\)
\(822\) −4.77784e141 −2.03212
\(823\) 3.60875e141 1.44699 0.723495 0.690330i \(-0.242535\pi\)
0.723495 + 0.690330i \(0.242535\pi\)
\(824\) −2.59501e137 −9.80999e−5 0
\(825\) 2.20459e141 0.785800
\(826\) −7.02364e140 −0.236064
\(827\) −2.12752e141 −0.674305 −0.337153 0.941450i \(-0.609464\pi\)
−0.337153 + 0.941450i \(0.609464\pi\)
\(828\) −4.69615e138 −0.00140369
\(829\) −6.01564e141 −1.69585 −0.847925 0.530116i \(-0.822148\pi\)
−0.847925 + 0.530116i \(0.822148\pi\)
\(830\) 2.95062e141 0.784560
\(831\) 6.72361e141 1.68637
\(832\) 4.44428e141 1.05153
\(833\) 1.13607e141 0.253584
\(834\) −8.88518e141 −1.87117
\(835\) 4.14038e141 0.822710
\(836\) 9.70945e141 1.82050
\(837\) −8.63175e141 −1.52726
\(838\) 8.46857e141 1.41408
\(839\) −1.64061e141 −0.258553 −0.129277 0.991609i \(-0.541266\pi\)
−0.129277 + 0.991609i \(0.541266\pi\)
\(840\) 6.63815e139 0.00987419
\(841\) 1.77528e141 0.249265
\(842\) 2.33002e141 0.308833
\(843\) −1.47005e142 −1.83947
\(844\) −7.22323e141 −0.853342
\(845\) 1.74388e141 0.194521
\(846\) −3.04412e140 −0.0320627
\(847\) 1.36781e141 0.136044
\(848\) 5.05587e141 0.474894
\(849\) 4.20229e141 0.372789
\(850\) 3.01496e141 0.252618
\(851\) −2.77622e140 −0.0219720
\(852\) −1.40692e142 −1.05184
\(853\) −5.34434e141 −0.377456 −0.188728 0.982029i \(-0.560436\pi\)
−0.188728 + 0.982029i \(0.560436\pi\)
\(854\) 5.55424e141 0.370610
\(855\) −4.68305e140 −0.0295238
\(856\) 3.60073e140 0.0214493
\(857\) 4.63866e140 0.0261109 0.0130555 0.999915i \(-0.495844\pi\)
0.0130555 + 0.999915i \(0.495844\pi\)
\(858\) 3.63574e142 1.93401
\(859\) −3.09056e142 −1.55370 −0.776852 0.629683i \(-0.783185\pi\)
−0.776852 + 0.629683i \(0.783185\pi\)
\(860\) −1.69415e142 −0.804965
\(861\) 8.60668e141 0.386530
\(862\) −8.22031e141 −0.348968
\(863\) −3.22288e142 −1.29336 −0.646681 0.762760i \(-0.723844\pi\)
−0.646681 + 0.762760i \(0.723844\pi\)
\(864\) −3.73677e142 −1.41768
\(865\) 2.10593e142 0.755377
\(866\) 3.68574e142 1.24999
\(867\) 2.83508e142 0.909159
\(868\) −1.33489e142 −0.404799
\(869\) 4.44458e142 1.27459
\(870\) 3.32695e142 0.902325
\(871\) 7.44900e142 1.91081
\(872\) −1.94532e141 −0.0471999
\(873\) 2.64398e141 0.0606831
\(874\) 4.58715e141 0.0995951
\(875\) −1.33071e142 −0.273334
\(876\) 6.14153e141 0.119351
\(877\) −6.11498e142 −1.12438 −0.562192 0.827007i \(-0.690042\pi\)
−0.562192 + 0.827007i \(0.690042\pi\)
\(878\) −6.63228e142 −1.15393
\(879\) −9.08370e142 −1.49555
\(880\) −4.77690e142 −0.744281
\(881\) −4.39442e141 −0.0647992 −0.0323996 0.999475i \(-0.510315\pi\)
−0.0323996 + 0.999475i \(0.510315\pi\)
\(882\) 2.97216e141 0.0414807
\(883\) −4.34742e142 −0.574298 −0.287149 0.957886i \(-0.592707\pi\)
−0.287149 + 0.957886i \(0.592707\pi\)
\(884\) 2.43085e142 0.303965
\(885\) 2.92445e142 0.346175
\(886\) −9.93043e141 −0.111284
\(887\) 2.29243e142 0.243221 0.121610 0.992578i \(-0.461194\pi\)
0.121610 + 0.992578i \(0.461194\pi\)
\(888\) −2.87123e141 −0.0288430
\(889\) 4.73981e142 0.450843
\(890\) −2.46344e142 −0.221885
\(891\) −1.38048e143 −1.17750
\(892\) 2.98079e142 0.240788
\(893\) 1.45370e143 1.11219
\(894\) 2.79680e143 2.02671
\(895\) 1.70814e142 0.117248
\(896\) 5.25735e141 0.0341844
\(897\) 8.39757e141 0.0517273
\(898\) −1.45863e143 −0.851222
\(899\) 3.04039e143 1.68106
\(900\) 3.85621e141 0.0202022
\(901\) 2.52930e142 0.125559
\(902\) −5.05722e143 −2.37900
\(903\) 8.90653e142 0.397057
\(904\) −1.76583e142 −0.0746070
\(905\) −1.31602e143 −0.526993
\(906\) 1.45209e143 0.551158
\(907\) 2.02374e143 0.728117 0.364058 0.931376i \(-0.381391\pi\)
0.364058 + 0.931376i \(0.381391\pi\)
\(908\) −2.76927e143 −0.944501
\(909\) 3.91868e141 0.0126704
\(910\) −8.69193e142 −0.266446
\(911\) −5.57500e143 −1.62033 −0.810166 0.586201i \(-0.800623\pi\)
−0.810166 + 0.586201i \(0.800623\pi\)
\(912\) 5.81007e143 1.60115
\(913\) 4.45614e143 1.16446
\(914\) −1.39745e143 −0.346296
\(915\) −2.31263e143 −0.543479
\(916\) −3.58905e143 −0.799925
\(917\) −1.16470e143 −0.246208
\(918\) −1.95081e143 −0.391151
\(919\) 4.43056e143 0.842669 0.421334 0.906905i \(-0.361562\pi\)
0.421334 + 0.906905i \(0.361562\pi\)
\(920\) −9.00913e140 −0.00162545
\(921\) −6.19721e143 −1.06073
\(922\) 1.39060e144 2.25815
\(923\) −8.37188e143 −1.28985
\(924\) −2.20602e143 −0.322492
\(925\) 2.27968e143 0.316227
\(926\) −4.65147e143 −0.612291
\(927\) −4.15943e139 −5.19598e−5 0
\(928\) 1.31621e144 1.56045
\(929\) −5.20440e143 −0.585610 −0.292805 0.956172i \(-0.594589\pi\)
−0.292805 + 0.956172i \(0.594589\pi\)
\(930\) 1.13688e144 1.21421
\(931\) −1.41934e144 −1.43889
\(932\) 1.01252e144 0.974385
\(933\) 6.46477e143 0.590599
\(934\) 3.72181e143 0.322798
\(935\) −2.38974e143 −0.196783
\(936\) −2.89007e141 −0.00225959
\(937\) 1.99216e143 0.147895 0.0739477 0.997262i \(-0.476440\pi\)
0.0739477 + 0.997262i \(0.476440\pi\)
\(938\) −9.24489e143 −0.651724
\(939\) 6.53509e143 0.437493
\(940\) 6.28251e143 0.399422
\(941\) −1.36308e143 −0.0823049 −0.0411524 0.999153i \(-0.513103\pi\)
−0.0411524 + 0.999153i \(0.513103\pi\)
\(942\) −1.55567e144 −0.892170
\(943\) −1.16808e143 −0.0636290
\(944\) 1.20736e144 0.624734
\(945\) 3.41024e143 0.167626
\(946\) −5.23341e144 −2.44379
\(947\) 2.79634e144 1.24055 0.620277 0.784383i \(-0.287020\pi\)
0.620277 + 0.784383i \(0.287020\pi\)
\(948\) −2.33627e144 −0.984732
\(949\) 3.65451e143 0.146358
\(950\) −3.76671e144 −1.43340
\(951\) −4.70723e144 −1.70220
\(952\) 1.37102e142 0.00471143
\(953\) 4.62054e144 1.50899 0.754496 0.656305i \(-0.227882\pi\)
0.754496 + 0.656305i \(0.227882\pi\)
\(954\) 6.61710e142 0.0205386
\(955\) −1.48688e144 −0.438645
\(956\) 4.24737e144 1.19100
\(957\) 5.02449e144 1.33925
\(958\) 2.20004e144 0.557447
\(959\) 1.72504e144 0.415525
\(960\) 2.29661e144 0.525935
\(961\) 5.79669e144 1.26211
\(962\) 3.75957e144 0.778300
\(963\) 5.77148e142 0.0113609
\(964\) −3.72907e144 −0.698014
\(965\) −1.37398e144 −0.244571
\(966\) −1.04221e143 −0.0176428
\(967\) −1.02299e145 −1.64697 −0.823487 0.567335i \(-0.807974\pi\)
−0.823487 + 0.567335i \(0.807974\pi\)
\(968\) −1.91989e143 −0.0293983
\(969\) 2.90660e144 0.423334
\(970\) −1.11614e145 −1.54628
\(971\) −4.08826e144 −0.538773 −0.269386 0.963032i \(-0.586821\pi\)
−0.269386 + 0.963032i \(0.586821\pi\)
\(972\) −4.91242e143 −0.0615860
\(973\) 3.20800e144 0.382614
\(974\) 2.20261e144 0.249936
\(975\) −6.89561e144 −0.744473
\(976\) −9.54770e144 −0.980805
\(977\) 1.04203e145 1.01858 0.509288 0.860596i \(-0.329909\pi\)
0.509288 + 0.860596i \(0.329909\pi\)
\(978\) 1.25143e145 1.16405
\(979\) −3.72038e144 −0.329327
\(980\) −6.13399e144 −0.516748
\(981\) −3.11808e143 −0.0250000
\(982\) 2.07366e145 1.58245
\(983\) −8.25221e144 −0.599411 −0.299706 0.954032i \(-0.596888\pi\)
−0.299706 + 0.954032i \(0.596888\pi\)
\(984\) −1.20805e144 −0.0835265
\(985\) 1.35052e144 0.0888883
\(986\) 6.87139e144 0.430541
\(987\) −3.30286e144 −0.197019
\(988\) −3.03696e145 −1.72475
\(989\) −1.20877e144 −0.0653619
\(990\) −6.25200e143 −0.0321893
\(991\) −5.52515e144 −0.270877 −0.135438 0.990786i \(-0.543244\pi\)
−0.135438 + 0.990786i \(0.543244\pi\)
\(992\) 4.49774e145 2.09980
\(993\) −1.76339e145 −0.783987
\(994\) 1.03903e145 0.439933
\(995\) 2.10491e144 0.0848818
\(996\) −2.34234e145 −0.899649
\(997\) 3.50363e145 1.28175 0.640875 0.767645i \(-0.278571\pi\)
0.640875 + 0.767645i \(0.278571\pi\)
\(998\) 6.81945e145 2.37639
\(999\) −1.47505e145 −0.489644
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.98.a.a.1.6 7
3.2 odd 2 9.98.a.a.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.98.a.a.1.6 7 1.1 even 1 trivial
9.98.a.a.1.2 7 3.2 odd 2