Properties

Label 14.10.a.a.1.1
Level $14$
Weight $10$
Character 14.1
Self dual yes
Analytic conductor $7.211$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.21050170629\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 14.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.0000 q^{2} -6.00000 q^{3} +256.000 q^{4} +560.000 q^{5} +96.0000 q^{6} -2401.00 q^{7} -4096.00 q^{8} -19647.0 q^{9} +O(q^{10})\) \(q-16.0000 q^{2} -6.00000 q^{3} +256.000 q^{4} +560.000 q^{5} +96.0000 q^{6} -2401.00 q^{7} -4096.00 q^{8} -19647.0 q^{9} -8960.00 q^{10} -54152.0 q^{11} -1536.00 q^{12} -113172. q^{13} +38416.0 q^{14} -3360.00 q^{15} +65536.0 q^{16} +6262.00 q^{17} +314352. q^{18} +257078. q^{19} +143360. q^{20} +14406.0 q^{21} +866432. q^{22} -266000. q^{23} +24576.0 q^{24} -1.63952e6 q^{25} +1.81075e6 q^{26} +235980. q^{27} -614656. q^{28} +1.57471e6 q^{29} +53760.0 q^{30} -4.63748e6 q^{31} -1.04858e6 q^{32} +324912. q^{33} -100192. q^{34} -1.34456e6 q^{35} -5.02963e6 q^{36} -1.19462e7 q^{37} -4.11325e6 q^{38} +679032. q^{39} -2.29376e6 q^{40} +2.19091e7 q^{41} -230496. q^{42} +2.75206e7 q^{43} -1.38629e7 q^{44} -1.10023e7 q^{45} +4.25600e6 q^{46} +5.29278e7 q^{47} -393216. q^{48} +5.76480e6 q^{49} +2.62324e7 q^{50} -37572.0 q^{51} -2.89720e7 q^{52} +1.62212e7 q^{53} -3.77568e6 q^{54} -3.03251e7 q^{55} +9.83450e6 q^{56} -1.54247e6 q^{57} -2.51954e7 q^{58} -1.40510e8 q^{59} -860160. q^{60} -2.02964e8 q^{61} +7.41997e7 q^{62} +4.71724e7 q^{63} +1.67772e7 q^{64} -6.33763e7 q^{65} -5.19859e6 q^{66} +1.53735e8 q^{67} +1.60307e6 q^{68} +1.59600e6 q^{69} +2.15130e7 q^{70} +2.79656e8 q^{71} +8.04741e7 q^{72} -4.04023e8 q^{73} +1.91140e8 q^{74} +9.83715e6 q^{75} +6.58120e7 q^{76} +1.30019e8 q^{77} -1.08645e7 q^{78} -1.30690e8 q^{79} +3.67002e7 q^{80} +3.85296e8 q^{81} -3.50546e8 q^{82} +4.20134e8 q^{83} +3.68794e6 q^{84} +3.50672e6 q^{85} -4.40329e8 q^{86} -9.44828e6 q^{87} +2.21807e8 q^{88} -4.69542e8 q^{89} +1.76037e8 q^{90} +2.71726e8 q^{91} -6.80960e7 q^{92} +2.78249e7 q^{93} -8.46845e8 q^{94} +1.43964e8 q^{95} +6.29146e6 q^{96} -8.72502e8 q^{97} -9.22368e7 q^{98} +1.06392e9 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 −0.707107
\(3\) −6.00000 −0.0427667 −0.0213833 0.999771i \(-0.506807\pi\)
−0.0213833 + 0.999771i \(0.506807\pi\)
\(4\) 256.000 0.500000
\(5\) 560.000 0.400703 0.200352 0.979724i \(-0.435792\pi\)
0.200352 + 0.979724i \(0.435792\pi\)
\(6\) 96.0000 0.0302406
\(7\) −2401.00 −0.377964
\(8\) −4096.00 −0.353553
\(9\) −19647.0 −0.998171
\(10\) −8960.00 −0.283340
\(11\) −54152.0 −1.11519 −0.557593 0.830114i \(-0.688275\pi\)
−0.557593 + 0.830114i \(0.688275\pi\)
\(12\) −1536.00 −0.0213833
\(13\) −113172. −1.09899 −0.549495 0.835497i \(-0.685180\pi\)
−0.549495 + 0.835497i \(0.685180\pi\)
\(14\) 38416.0 0.267261
\(15\) −3360.00 −0.0171368
\(16\) 65536.0 0.250000
\(17\) 6262.00 0.0181841 0.00909207 0.999959i \(-0.497106\pi\)
0.00909207 + 0.999959i \(0.497106\pi\)
\(18\) 314352. 0.705813
\(19\) 257078. 0.452557 0.226279 0.974063i \(-0.427344\pi\)
0.226279 + 0.974063i \(0.427344\pi\)
\(20\) 143360. 0.200352
\(21\) 14406.0 0.0161643
\(22\) 866432. 0.788556
\(23\) −266000. −0.198201 −0.0991006 0.995077i \(-0.531597\pi\)
−0.0991006 + 0.995077i \(0.531597\pi\)
\(24\) 24576.0 0.0151203
\(25\) −1.63952e6 −0.839437
\(26\) 1.81075e6 0.777104
\(27\) 235980. 0.0854552
\(28\) −614656. −0.188982
\(29\) 1.57471e6 0.413438 0.206719 0.978400i \(-0.433721\pi\)
0.206719 + 0.978400i \(0.433721\pi\)
\(30\) 53760.0 0.0121175
\(31\) −4.63748e6 −0.901893 −0.450946 0.892551i \(-0.648913\pi\)
−0.450946 + 0.892551i \(0.648913\pi\)
\(32\) −1.04858e6 −0.176777
\(33\) 324912. 0.0476928
\(34\) −100192. −0.0128581
\(35\) −1.34456e6 −0.151452
\(36\) −5.02963e6 −0.499086
\(37\) −1.19462e7 −1.04791 −0.523954 0.851746i \(-0.675544\pi\)
−0.523954 + 0.851746i \(0.675544\pi\)
\(38\) −4.11325e6 −0.320006
\(39\) 679032. 0.0470002
\(40\) −2.29376e6 −0.141670
\(41\) 2.19091e7 1.21087 0.605435 0.795895i \(-0.292999\pi\)
0.605435 + 0.795895i \(0.292999\pi\)
\(42\) −230496. −0.0114299
\(43\) 2.75206e7 1.22758 0.613790 0.789469i \(-0.289644\pi\)
0.613790 + 0.789469i \(0.289644\pi\)
\(44\) −1.38629e7 −0.557593
\(45\) −1.10023e7 −0.399970
\(46\) 4.25600e6 0.140149
\(47\) 5.29278e7 1.58214 0.791068 0.611728i \(-0.209525\pi\)
0.791068 + 0.611728i \(0.209525\pi\)
\(48\) −393216. −0.0106917
\(49\) 5.76480e6 0.142857
\(50\) 2.62324e7 0.593571
\(51\) −37572.0 −0.000777676 0
\(52\) −2.89720e7 −0.549495
\(53\) 1.62212e7 0.282385 0.141193 0.989982i \(-0.454906\pi\)
0.141193 + 0.989982i \(0.454906\pi\)
\(54\) −3.77568e6 −0.0604259
\(55\) −3.03251e7 −0.446859
\(56\) 9.83450e6 0.133631
\(57\) −1.54247e6 −0.0193544
\(58\) −2.51954e7 −0.292345
\(59\) −1.40510e8 −1.50964 −0.754818 0.655935i \(-0.772275\pi\)
−0.754818 + 0.655935i \(0.772275\pi\)
\(60\) −860160. −0.00856838
\(61\) −2.02964e8 −1.87687 −0.938434 0.345458i \(-0.887724\pi\)
−0.938434 + 0.345458i \(0.887724\pi\)
\(62\) 7.41997e7 0.637734
\(63\) 4.71724e7 0.377273
\(64\) 1.67772e7 0.125000
\(65\) −6.33763e7 −0.440369
\(66\) −5.19859e6 −0.0337239
\(67\) 1.53735e8 0.932041 0.466020 0.884774i \(-0.345687\pi\)
0.466020 + 0.884774i \(0.345687\pi\)
\(68\) 1.60307e6 0.00909207
\(69\) 1.59600e6 0.00847641
\(70\) 2.15130e7 0.107092
\(71\) 2.79656e8 1.30606 0.653028 0.757334i \(-0.273499\pi\)
0.653028 + 0.757334i \(0.273499\pi\)
\(72\) 8.04741e7 0.352907
\(73\) −4.04023e8 −1.66515 −0.832574 0.553913i \(-0.813134\pi\)
−0.832574 + 0.553913i \(0.813134\pi\)
\(74\) 1.91140e8 0.740983
\(75\) 9.83715e6 0.0358999
\(76\) 6.58120e7 0.226279
\(77\) 1.30019e8 0.421501
\(78\) −1.08645e7 −0.0332341
\(79\) −1.30690e8 −0.377503 −0.188751 0.982025i \(-0.560444\pi\)
−0.188751 + 0.982025i \(0.560444\pi\)
\(80\) 3.67002e7 0.100176
\(81\) 3.85296e8 0.994516
\(82\) −3.50546e8 −0.856215
\(83\) 4.20134e8 0.971709 0.485855 0.874040i \(-0.338508\pi\)
0.485855 + 0.874040i \(0.338508\pi\)
\(84\) 3.68794e6 0.00808214
\(85\) 3.50672e6 0.00728645
\(86\) −4.40329e8 −0.868030
\(87\) −9.44828e6 −0.0176814
\(88\) 2.21807e8 0.394278
\(89\) −4.69542e8 −0.793268 −0.396634 0.917977i \(-0.629822\pi\)
−0.396634 + 0.917977i \(0.629822\pi\)
\(90\) 1.76037e8 0.282822
\(91\) 2.71726e8 0.415379
\(92\) −6.80960e7 −0.0991006
\(93\) 2.78249e7 0.0385710
\(94\) −8.46845e8 −1.11874
\(95\) 1.43964e8 0.181341
\(96\) 6.29146e6 0.00756015
\(97\) −8.72502e8 −1.00068 −0.500338 0.865830i \(-0.666791\pi\)
−0.500338 + 0.865830i \(0.666791\pi\)
\(98\) −9.22368e7 −0.101015
\(99\) 1.06392e9 1.11315
\(100\) −4.19718e8 −0.419718
\(101\) −1.20901e9 −1.15607 −0.578037 0.816011i \(-0.696181\pi\)
−0.578037 + 0.816011i \(0.696181\pi\)
\(102\) 601152. 0.000549900 0
\(103\) 6.90563e8 0.604555 0.302277 0.953220i \(-0.402253\pi\)
0.302277 + 0.953220i \(0.402253\pi\)
\(104\) 4.63553e8 0.388552
\(105\) 8.06736e6 0.00647708
\(106\) −2.59540e8 −0.199677
\(107\) 1.79499e8 0.132384 0.0661921 0.997807i \(-0.478915\pi\)
0.0661921 + 0.997807i \(0.478915\pi\)
\(108\) 6.04109e7 0.0427276
\(109\) −1.60361e9 −1.08813 −0.544063 0.839044i \(-0.683115\pi\)
−0.544063 + 0.839044i \(0.683115\pi\)
\(110\) 4.85202e8 0.315977
\(111\) 7.16774e7 0.0448156
\(112\) −1.57352e8 −0.0944911
\(113\) 1.42785e9 0.823815 0.411908 0.911226i \(-0.364863\pi\)
0.411908 + 0.911226i \(0.364863\pi\)
\(114\) 2.46795e7 0.0136856
\(115\) −1.48960e8 −0.0794199
\(116\) 4.03127e8 0.206719
\(117\) 2.22349e9 1.09698
\(118\) 2.24815e9 1.06747
\(119\) −1.50351e7 −0.00687296
\(120\) 1.37626e7 0.00605876
\(121\) 5.74491e8 0.243640
\(122\) 3.24742e9 1.32715
\(123\) −1.31455e8 −0.0517849
\(124\) −1.18720e9 −0.450946
\(125\) −2.01188e9 −0.737069
\(126\) −7.54759e8 −0.266772
\(127\) −2.35873e9 −0.804565 −0.402282 0.915516i \(-0.631783\pi\)
−0.402282 + 0.915516i \(0.631783\pi\)
\(128\) −2.68435e8 −0.0883883
\(129\) −1.65124e8 −0.0524995
\(130\) 1.01402e9 0.311388
\(131\) 6.01665e8 0.178498 0.0892492 0.996009i \(-0.471553\pi\)
0.0892492 + 0.996009i \(0.471553\pi\)
\(132\) 8.31775e7 0.0238464
\(133\) −6.17244e8 −0.171051
\(134\) −2.45975e9 −0.659052
\(135\) 1.32149e8 0.0342422
\(136\) −2.56492e7 −0.00642907
\(137\) −5.16009e9 −1.25145 −0.625726 0.780043i \(-0.715197\pi\)
−0.625726 + 0.780043i \(0.715197\pi\)
\(138\) −2.55360e7 −0.00599373
\(139\) −7.14356e9 −1.62311 −0.811556 0.584275i \(-0.801379\pi\)
−0.811556 + 0.584275i \(0.801379\pi\)
\(140\) −3.44207e8 −0.0757258
\(141\) −3.17567e8 −0.0676627
\(142\) −4.47449e9 −0.923520
\(143\) 6.12849e9 1.22558
\(144\) −1.28759e9 −0.249543
\(145\) 8.81840e8 0.165666
\(146\) 6.46437e9 1.17744
\(147\) −3.45888e7 −0.00610953
\(148\) −3.05824e9 −0.523954
\(149\) 9.10424e9 1.51323 0.756616 0.653859i \(-0.226851\pi\)
0.756616 + 0.653859i \(0.226851\pi\)
\(150\) −1.57394e8 −0.0253851
\(151\) −2.89432e8 −0.0453054 −0.0226527 0.999743i \(-0.507211\pi\)
−0.0226527 + 0.999743i \(0.507211\pi\)
\(152\) −1.05299e9 −0.160003
\(153\) −1.23030e8 −0.0181509
\(154\) −2.08030e9 −0.298046
\(155\) −2.59699e9 −0.361391
\(156\) 1.73832e8 0.0235001
\(157\) 1.39068e10 1.82675 0.913373 0.407124i \(-0.133468\pi\)
0.913373 + 0.407124i \(0.133468\pi\)
\(158\) 2.09104e9 0.266935
\(159\) −9.73273e7 −0.0120767
\(160\) −5.87203e8 −0.0708350
\(161\) 6.38666e8 0.0749130
\(162\) −6.16474e9 −0.703229
\(163\) 1.66232e10 1.84447 0.922235 0.386629i \(-0.126361\pi\)
0.922235 + 0.386629i \(0.126361\pi\)
\(164\) 5.60874e9 0.605435
\(165\) 1.81951e8 0.0191107
\(166\) −6.72214e9 −0.687102
\(167\) −1.58019e10 −1.57212 −0.786061 0.618149i \(-0.787883\pi\)
−0.786061 + 0.618149i \(0.787883\pi\)
\(168\) −5.90070e7 −0.00571494
\(169\) 2.20340e9 0.207780
\(170\) −5.61075e7 −0.00515230
\(171\) −5.05081e9 −0.451730
\(172\) 7.04527e9 0.613790
\(173\) 3.23125e9 0.274260 0.137130 0.990553i \(-0.456212\pi\)
0.137130 + 0.990553i \(0.456212\pi\)
\(174\) 1.51173e8 0.0125026
\(175\) 3.93650e9 0.317277
\(176\) −3.54891e9 −0.278797
\(177\) 8.43058e8 0.0645621
\(178\) 7.51268e9 0.560925
\(179\) −2.41408e10 −1.75757 −0.878785 0.477218i \(-0.841645\pi\)
−0.878785 + 0.477218i \(0.841645\pi\)
\(180\) −2.81659e9 −0.199985
\(181\) −3.89332e9 −0.269629 −0.134814 0.990871i \(-0.543044\pi\)
−0.134814 + 0.990871i \(0.543044\pi\)
\(182\) −4.34762e9 −0.293718
\(183\) 1.21778e9 0.0802674
\(184\) 1.08954e9 0.0700747
\(185\) −6.68989e9 −0.419901
\(186\) −4.45198e8 −0.0272738
\(187\) −3.39100e8 −0.0202787
\(188\) 1.35495e10 0.791068
\(189\) −5.66588e8 −0.0322990
\(190\) −2.30342e9 −0.128228
\(191\) −2.58988e10 −1.40809 −0.704043 0.710157i \(-0.748624\pi\)
−0.704043 + 0.710157i \(0.748624\pi\)
\(192\) −1.00663e8 −0.00534584
\(193\) 1.59367e10 0.826783 0.413391 0.910553i \(-0.364344\pi\)
0.413391 + 0.910553i \(0.364344\pi\)
\(194\) 1.39600e10 0.707585
\(195\) 3.80258e8 0.0188331
\(196\) 1.47579e9 0.0714286
\(197\) −3.34685e9 −0.158321 −0.0791604 0.996862i \(-0.525224\pi\)
−0.0791604 + 0.996862i \(0.525224\pi\)
\(198\) −1.70228e10 −0.787114
\(199\) −1.34261e10 −0.606891 −0.303445 0.952849i \(-0.598137\pi\)
−0.303445 + 0.952849i \(0.598137\pi\)
\(200\) 6.71549e9 0.296786
\(201\) −9.22407e8 −0.0398603
\(202\) 1.93442e10 0.817467
\(203\) −3.78089e9 −0.156265
\(204\) −9.61843e6 −0.000388838 0
\(205\) 1.22691e10 0.485200
\(206\) −1.10490e10 −0.427485
\(207\) 5.22610e9 0.197839
\(208\) −7.41684e9 −0.274748
\(209\) −1.39213e10 −0.504686
\(210\) −1.29078e8 −0.00457999
\(211\) 3.01702e10 1.04787 0.523935 0.851759i \(-0.324464\pi\)
0.523935 + 0.851759i \(0.324464\pi\)
\(212\) 4.15263e9 0.141193
\(213\) −1.67794e9 −0.0558556
\(214\) −2.87199e9 −0.0936097
\(215\) 1.54115e10 0.491895
\(216\) −9.66574e8 −0.0302130
\(217\) 1.11346e10 0.340883
\(218\) 2.56577e10 0.769421
\(219\) 2.42414e9 0.0712129
\(220\) −7.76323e9 −0.223429
\(221\) −7.08683e8 −0.0199842
\(222\) −1.14684e9 −0.0316894
\(223\) 5.35030e10 1.44879 0.724396 0.689384i \(-0.242119\pi\)
0.724396 + 0.689384i \(0.242119\pi\)
\(224\) 2.51763e9 0.0668153
\(225\) 3.22117e10 0.837901
\(226\) −2.28456e10 −0.582525
\(227\) −4.02704e10 −1.00663 −0.503315 0.864103i \(-0.667886\pi\)
−0.503315 + 0.864103i \(0.667886\pi\)
\(228\) −3.94872e8 −0.00967719
\(229\) 1.90247e10 0.457150 0.228575 0.973526i \(-0.426593\pi\)
0.228575 + 0.973526i \(0.426593\pi\)
\(230\) 2.38336e9 0.0561584
\(231\) −7.80114e8 −0.0180262
\(232\) −6.45003e9 −0.146173
\(233\) −3.67748e10 −0.817426 −0.408713 0.912663i \(-0.634022\pi\)
−0.408713 + 0.912663i \(0.634022\pi\)
\(234\) −3.55758e10 −0.775682
\(235\) 2.96396e10 0.633967
\(236\) −3.59705e10 −0.754818
\(237\) 7.84139e8 0.0161445
\(238\) 2.40561e8 0.00485992
\(239\) 6.56110e9 0.130073 0.0650363 0.997883i \(-0.479284\pi\)
0.0650363 + 0.997883i \(0.479284\pi\)
\(240\) −2.20201e8 −0.00428419
\(241\) −8.96818e10 −1.71249 −0.856244 0.516572i \(-0.827208\pi\)
−0.856244 + 0.516572i \(0.827208\pi\)
\(242\) −9.19186e9 −0.172280
\(243\) −6.95657e9 −0.127987
\(244\) −5.19587e10 −0.938434
\(245\) 3.22829e9 0.0572433
\(246\) 2.10328e9 0.0366175
\(247\) −2.90940e10 −0.497356
\(248\) 1.89951e10 0.318867
\(249\) −2.52080e9 −0.0415568
\(250\) 3.21901e10 0.521186
\(251\) 5.33703e9 0.0848727 0.0424363 0.999099i \(-0.486488\pi\)
0.0424363 + 0.999099i \(0.486488\pi\)
\(252\) 1.20761e10 0.188637
\(253\) 1.44044e10 0.221031
\(254\) 3.77396e10 0.568913
\(255\) −2.10403e7 −0.000311617 0
\(256\) 4.29497e9 0.0625000
\(257\) −8.35575e10 −1.19478 −0.597388 0.801952i \(-0.703795\pi\)
−0.597388 + 0.801952i \(0.703795\pi\)
\(258\) 2.64198e9 0.0371228
\(259\) 2.86829e10 0.396072
\(260\) −1.62243e10 −0.220185
\(261\) −3.09384e10 −0.412682
\(262\) −9.62665e9 −0.126217
\(263\) 1.08635e11 1.40013 0.700065 0.714079i \(-0.253154\pi\)
0.700065 + 0.714079i \(0.253154\pi\)
\(264\) −1.33084e9 −0.0168620
\(265\) 9.08388e9 0.113153
\(266\) 9.87591e9 0.120951
\(267\) 2.81725e9 0.0339254
\(268\) 3.93561e10 0.466020
\(269\) 1.41401e11 1.64652 0.823258 0.567668i \(-0.192154\pi\)
0.823258 + 0.567668i \(0.192154\pi\)
\(270\) −2.11438e9 −0.0242129
\(271\) −9.08353e10 −1.02304 −0.511520 0.859271i \(-0.670917\pi\)
−0.511520 + 0.859271i \(0.670917\pi\)
\(272\) 4.10386e8 0.00454604
\(273\) −1.63036e9 −0.0177644
\(274\) 8.25614e10 0.884911
\(275\) 8.87836e10 0.936128
\(276\) 4.08576e8 0.00423821
\(277\) −2.65075e10 −0.270527 −0.135263 0.990810i \(-0.543188\pi\)
−0.135263 + 0.990810i \(0.543188\pi\)
\(278\) 1.14297e11 1.14771
\(279\) 9.11126e10 0.900243
\(280\) 5.50732e9 0.0535462
\(281\) −1.86968e11 −1.78891 −0.894455 0.447158i \(-0.852436\pi\)
−0.894455 + 0.447158i \(0.852436\pi\)
\(282\) 5.08107e9 0.0478448
\(283\) −5.33413e9 −0.0494338 −0.0247169 0.999694i \(-0.507868\pi\)
−0.0247169 + 0.999694i \(0.507868\pi\)
\(284\) 7.15919e10 0.653028
\(285\) −8.63782e8 −0.00775537
\(286\) −9.80558e10 −0.866615
\(287\) −5.26038e10 −0.457666
\(288\) 2.06014e10 0.176453
\(289\) −1.18549e11 −0.999669
\(290\) −1.41094e10 −0.117144
\(291\) 5.23501e9 0.0427956
\(292\) −1.03430e11 −0.832574
\(293\) 7.65433e10 0.606741 0.303370 0.952873i \(-0.401888\pi\)
0.303370 + 0.952873i \(0.401888\pi\)
\(294\) 5.53421e8 0.00432009
\(295\) −7.86854e10 −0.604916
\(296\) 4.89318e10 0.370492
\(297\) −1.27788e10 −0.0952984
\(298\) −1.45668e11 −1.07002
\(299\) 3.01038e10 0.217821
\(300\) 2.51831e9 0.0179500
\(301\) −6.60769e10 −0.463982
\(302\) 4.63091e9 0.0320358
\(303\) 7.25409e9 0.0494414
\(304\) 1.68479e10 0.113139
\(305\) −1.13660e11 −0.752068
\(306\) 1.96847e9 0.0128346
\(307\) −7.51944e10 −0.483128 −0.241564 0.970385i \(-0.577660\pi\)
−0.241564 + 0.970385i \(0.577660\pi\)
\(308\) 3.32849e10 0.210750
\(309\) −4.14338e9 −0.0258548
\(310\) 4.15519e10 0.255542
\(311\) 2.15134e11 1.30403 0.652014 0.758207i \(-0.273924\pi\)
0.652014 + 0.758207i \(0.273924\pi\)
\(312\) −2.78132e9 −0.0166171
\(313\) 9.59075e10 0.564811 0.282405 0.959295i \(-0.408868\pi\)
0.282405 + 0.959295i \(0.408868\pi\)
\(314\) −2.22508e11 −1.29170
\(315\) 2.64166e10 0.151175
\(316\) −3.34566e10 −0.188751
\(317\) 1.70586e11 0.948807 0.474403 0.880308i \(-0.342664\pi\)
0.474403 + 0.880308i \(0.342664\pi\)
\(318\) 1.55724e9 0.00853951
\(319\) −8.52739e10 −0.461061
\(320\) 9.39524e9 0.0500879
\(321\) −1.07700e9 −0.00566163
\(322\) −1.02187e10 −0.0529715
\(323\) 1.60982e9 0.00822937
\(324\) 9.86358e10 0.497258
\(325\) 1.85548e11 0.922533
\(326\) −2.65972e11 −1.30424
\(327\) 9.62165e9 0.0465355
\(328\) −8.97398e10 −0.428107
\(329\) −1.27080e11 −0.597991
\(330\) −2.91121e9 −0.0135133
\(331\) −1.23992e11 −0.567762 −0.283881 0.958859i \(-0.591622\pi\)
−0.283881 + 0.958859i \(0.591622\pi\)
\(332\) 1.07554e11 0.485855
\(333\) 2.34708e11 1.04599
\(334\) 2.52831e11 1.11166
\(335\) 8.60914e10 0.373472
\(336\) 9.44112e8 0.00404107
\(337\) −7.29335e10 −0.308030 −0.154015 0.988069i \(-0.549220\pi\)
−0.154015 + 0.988069i \(0.549220\pi\)
\(338\) −3.52544e10 −0.146923
\(339\) −8.56710e9 −0.0352318
\(340\) 8.97720e8 0.00364322
\(341\) 2.51129e11 1.00578
\(342\) 8.08130e10 0.319421
\(343\) −1.38413e10 −0.0539949
\(344\) −1.12724e11 −0.434015
\(345\) 8.93760e8 0.00339653
\(346\) −5.17000e10 −0.193931
\(347\) −1.55720e11 −0.576584 −0.288292 0.957542i \(-0.593087\pi\)
−0.288292 + 0.957542i \(0.593087\pi\)
\(348\) −2.41876e9 −0.00884069
\(349\) 1.08728e11 0.392310 0.196155 0.980573i \(-0.437154\pi\)
0.196155 + 0.980573i \(0.437154\pi\)
\(350\) −6.29840e10 −0.224349
\(351\) −2.67063e10 −0.0939144
\(352\) 5.67825e10 0.197139
\(353\) 3.25585e11 1.11604 0.558018 0.829829i \(-0.311562\pi\)
0.558018 + 0.829829i \(0.311562\pi\)
\(354\) −1.34889e10 −0.0456523
\(355\) 1.56607e11 0.523341
\(356\) −1.20203e11 −0.396634
\(357\) 9.02104e7 0.000293934 0
\(358\) 3.86252e11 1.24279
\(359\) −2.27550e11 −0.723022 −0.361511 0.932368i \(-0.617739\pi\)
−0.361511 + 0.932368i \(0.617739\pi\)
\(360\) 4.50655e10 0.141411
\(361\) −2.56599e11 −0.795192
\(362\) 6.22931e10 0.190656
\(363\) −3.44695e9 −0.0104197
\(364\) 6.95618e10 0.207690
\(365\) −2.26253e11 −0.667231
\(366\) −1.94845e10 −0.0567577
\(367\) −4.21993e11 −1.21425 −0.607125 0.794607i \(-0.707677\pi\)
−0.607125 + 0.794607i \(0.707677\pi\)
\(368\) −1.74326e10 −0.0495503
\(369\) −4.30449e11 −1.20866
\(370\) 1.07038e11 0.296915
\(371\) −3.89472e10 −0.106732
\(372\) 7.12318e9 0.0192855
\(373\) 3.83283e11 1.02525 0.512625 0.858613i \(-0.328673\pi\)
0.512625 + 0.858613i \(0.328673\pi\)
\(374\) 5.42560e9 0.0143392
\(375\) 1.20713e10 0.0315220
\(376\) −2.16792e11 −0.559370
\(377\) −1.78214e11 −0.454365
\(378\) 9.06541e9 0.0228389
\(379\) −1.21462e11 −0.302386 −0.151193 0.988504i \(-0.548312\pi\)
−0.151193 + 0.988504i \(0.548312\pi\)
\(380\) 3.68547e10 0.0906706
\(381\) 1.41524e10 0.0344086
\(382\) 4.14381e11 0.995667
\(383\) −3.97721e11 −0.944461 −0.472230 0.881475i \(-0.656551\pi\)
−0.472230 + 0.881475i \(0.656551\pi\)
\(384\) 1.61061e9 0.00378008
\(385\) 7.28106e10 0.168897
\(386\) −2.54988e11 −0.584624
\(387\) −5.40697e11 −1.22533
\(388\) −2.23360e11 −0.500338
\(389\) 6.75462e10 0.149564 0.0747821 0.997200i \(-0.476174\pi\)
0.0747821 + 0.997200i \(0.476174\pi\)
\(390\) −6.08413e9 −0.0133170
\(391\) −1.66569e9 −0.00360412
\(392\) −2.36126e10 −0.0505076
\(393\) −3.60999e9 −0.00763378
\(394\) 5.35495e10 0.111950
\(395\) −7.31863e10 −0.151267
\(396\) 2.72365e11 0.556573
\(397\) 1.24656e11 0.251857 0.125929 0.992039i \(-0.459809\pi\)
0.125929 + 0.992039i \(0.459809\pi\)
\(398\) 2.14817e11 0.429136
\(399\) 3.70347e9 0.00731527
\(400\) −1.07448e11 −0.209859
\(401\) 3.51196e11 0.678265 0.339133 0.940739i \(-0.389866\pi\)
0.339133 + 0.940739i \(0.389866\pi\)
\(402\) 1.47585e10 0.0281855
\(403\) 5.24833e11 0.991171
\(404\) −3.09508e11 −0.578037
\(405\) 2.15766e11 0.398506
\(406\) 6.04942e10 0.110496
\(407\) 6.46913e11 1.16861
\(408\) 1.53895e8 0.000274950 0
\(409\) −3.81956e10 −0.0674930 −0.0337465 0.999430i \(-0.510744\pi\)
−0.0337465 + 0.999430i \(0.510744\pi\)
\(410\) −1.96306e11 −0.343088
\(411\) 3.09605e10 0.0535205
\(412\) 1.76784e11 0.302277
\(413\) 3.37364e11 0.570588
\(414\) −8.36176e10 −0.139893
\(415\) 2.35275e11 0.389367
\(416\) 1.18669e11 0.194276
\(417\) 4.28614e10 0.0694151
\(418\) 2.22741e11 0.356867
\(419\) 2.15268e11 0.341205 0.170603 0.985340i \(-0.445429\pi\)
0.170603 + 0.985340i \(0.445429\pi\)
\(420\) 2.06524e9 0.00323854
\(421\) 1.19933e12 1.86066 0.930332 0.366718i \(-0.119519\pi\)
0.930332 + 0.366718i \(0.119519\pi\)
\(422\) −4.82723e11 −0.740955
\(423\) −1.03987e12 −1.57924
\(424\) −6.64421e10 −0.0998383
\(425\) −1.02667e10 −0.0152644
\(426\) 2.68470e10 0.0394959
\(427\) 4.87316e11 0.709390
\(428\) 4.59518e10 0.0661921
\(429\) −3.67709e10 −0.0524140
\(430\) −2.46585e11 −0.347823
\(431\) 7.91117e11 1.10432 0.552158 0.833740i \(-0.313805\pi\)
0.552158 + 0.833740i \(0.313805\pi\)
\(432\) 1.54652e10 0.0213638
\(433\) −1.15451e12 −1.57834 −0.789170 0.614174i \(-0.789489\pi\)
−0.789170 + 0.614174i \(0.789489\pi\)
\(434\) −1.78154e11 −0.241041
\(435\) −5.29104e9 −0.00708499
\(436\) −4.10524e11 −0.544063
\(437\) −6.83827e10 −0.0896974
\(438\) −3.87862e10 −0.0503551
\(439\) −2.12728e11 −0.273360 −0.136680 0.990615i \(-0.543643\pi\)
−0.136680 + 0.990615i \(0.543643\pi\)
\(440\) 1.24212e11 0.157988
\(441\) −1.13261e11 −0.142596
\(442\) 1.13389e10 0.0141310
\(443\) −6.48300e10 −0.0799759 −0.0399880 0.999200i \(-0.512732\pi\)
−0.0399880 + 0.999200i \(0.512732\pi\)
\(444\) 1.83494e10 0.0224078
\(445\) −2.62944e11 −0.317865
\(446\) −8.56047e11 −1.02445
\(447\) −5.46255e10 −0.0647159
\(448\) −4.02821e10 −0.0472456
\(449\) −1.08031e12 −1.25441 −0.627207 0.778853i \(-0.715802\pi\)
−0.627207 + 0.778853i \(0.715802\pi\)
\(450\) −5.15388e11 −0.592486
\(451\) −1.18642e12 −1.35035
\(452\) 3.65530e11 0.411908
\(453\) 1.73659e9 0.00193756
\(454\) 6.44326e11 0.711794
\(455\) 1.52167e11 0.166444
\(456\) 6.31795e9 0.00684281
\(457\) −6.46725e10 −0.0693581 −0.0346790 0.999399i \(-0.511041\pi\)
−0.0346790 + 0.999399i \(0.511041\pi\)
\(458\) −3.04395e11 −0.323254
\(459\) 1.47771e9 0.00155393
\(460\) −3.81338e10 −0.0397100
\(461\) 4.29254e11 0.442649 0.221325 0.975200i \(-0.428962\pi\)
0.221325 + 0.975200i \(0.428962\pi\)
\(462\) 1.24818e10 0.0127464
\(463\) 1.61883e12 1.63715 0.818574 0.574401i \(-0.194765\pi\)
0.818574 + 0.574401i \(0.194765\pi\)
\(464\) 1.03200e11 0.103360
\(465\) 1.55819e10 0.0154555
\(466\) 5.88396e11 0.578007
\(467\) 3.27321e11 0.318455 0.159228 0.987242i \(-0.449100\pi\)
0.159228 + 0.987242i \(0.449100\pi\)
\(468\) 5.69214e11 0.548490
\(469\) −3.69117e11 −0.352278
\(470\) −4.74233e11 −0.448283
\(471\) −8.34407e10 −0.0781239
\(472\) 5.75527e11 0.533737
\(473\) −1.49030e12 −1.36898
\(474\) −1.25462e10 −0.0114159
\(475\) −4.21486e11 −0.379893
\(476\) −3.84898e9 −0.00343648
\(477\) −3.18698e11 −0.281869
\(478\) −1.04978e11 −0.0919752
\(479\) 2.84811e11 0.247199 0.123600 0.992332i \(-0.460556\pi\)
0.123600 + 0.992332i \(0.460556\pi\)
\(480\) 3.52322e9 0.00302938
\(481\) 1.35198e12 1.15164
\(482\) 1.43491e12 1.21091
\(483\) −3.83200e9 −0.00320378
\(484\) 1.47070e11 0.121820
\(485\) −4.88601e11 −0.400974
\(486\) 1.11305e11 0.0905007
\(487\) −7.14776e11 −0.575824 −0.287912 0.957657i \(-0.592961\pi\)
−0.287912 + 0.957657i \(0.592961\pi\)
\(488\) 8.31339e11 0.663573
\(489\) −9.97395e10 −0.0788819
\(490\) −5.16526e10 −0.0404772
\(491\) 1.01506e12 0.788176 0.394088 0.919073i \(-0.371061\pi\)
0.394088 + 0.919073i \(0.371061\pi\)
\(492\) −3.36524e10 −0.0258925
\(493\) 9.86086e9 0.00751802
\(494\) 4.65505e11 0.351684
\(495\) 5.95798e11 0.446042
\(496\) −3.03922e11 −0.225473
\(497\) −6.71454e11 −0.493642
\(498\) 4.03329e10 0.0293851
\(499\) 1.33412e12 0.963260 0.481630 0.876375i \(-0.340045\pi\)
0.481630 + 0.876375i \(0.340045\pi\)
\(500\) −5.15042e11 −0.368534
\(501\) 9.48116e10 0.0672345
\(502\) −8.53925e10 −0.0600140
\(503\) −5.68445e11 −0.395943 −0.197971 0.980208i \(-0.563435\pi\)
−0.197971 + 0.980208i \(0.563435\pi\)
\(504\) −1.93218e11 −0.133386
\(505\) −6.77048e11 −0.463243
\(506\) −2.30471e11 −0.156293
\(507\) −1.32204e10 −0.00888606
\(508\) −6.03834e11 −0.402282
\(509\) 3.57173e11 0.235857 0.117928 0.993022i \(-0.462375\pi\)
0.117928 + 0.993022i \(0.462375\pi\)
\(510\) 3.36645e8 0.000220347 0
\(511\) 9.70059e11 0.629367
\(512\) −6.87195e10 −0.0441942
\(513\) 6.06653e10 0.0386734
\(514\) 1.33692e12 0.844834
\(515\) 3.86715e11 0.242247
\(516\) −4.22716e10 −0.0262498
\(517\) −2.86615e12 −1.76438
\(518\) −4.58927e11 −0.280065
\(519\) −1.93875e10 −0.0117292
\(520\) 2.59589e11 0.155694
\(521\) 2.17972e12 1.29608 0.648040 0.761606i \(-0.275589\pi\)
0.648040 + 0.761606i \(0.275589\pi\)
\(522\) 4.95014e11 0.291810
\(523\) −1.57081e12 −0.918048 −0.459024 0.888424i \(-0.651801\pi\)
−0.459024 + 0.888424i \(0.651801\pi\)
\(524\) 1.54026e11 0.0892492
\(525\) −2.36190e10 −0.0135689
\(526\) −1.73816e12 −0.990042
\(527\) −2.90399e10 −0.0164001
\(528\) 2.12934e10 0.0119232
\(529\) −1.73040e12 −0.960716
\(530\) −1.45342e11 −0.0800111
\(531\) 2.76059e12 1.50687
\(532\) −1.58015e11 −0.0855253
\(533\) −2.47950e12 −1.33074
\(534\) −4.50761e10 −0.0239889
\(535\) 1.00520e11 0.0530468
\(536\) −6.29697e11 −0.329526
\(537\) 1.44845e11 0.0751655
\(538\) −2.26241e12 −1.16426
\(539\) −3.12176e11 −0.159312
\(540\) 3.38301e10 0.0171211
\(541\) 2.24544e12 1.12697 0.563486 0.826126i \(-0.309460\pi\)
0.563486 + 0.826126i \(0.309460\pi\)
\(542\) 1.45336e12 0.723399
\(543\) 2.33599e10 0.0115311
\(544\) −6.56618e9 −0.00321453
\(545\) −8.98021e11 −0.436016
\(546\) 2.60857e10 0.0125613
\(547\) −3.86062e11 −0.184380 −0.0921899 0.995741i \(-0.529387\pi\)
−0.0921899 + 0.995741i \(0.529387\pi\)
\(548\) −1.32098e12 −0.625726
\(549\) 3.98763e12 1.87344
\(550\) −1.42054e12 −0.661943
\(551\) 4.04824e11 0.187105
\(552\) −6.53722e9 −0.00299686
\(553\) 3.13786e11 0.142683
\(554\) 4.24120e11 0.191291
\(555\) 4.01394e10 0.0179578
\(556\) −1.82875e12 −0.811556
\(557\) −7.95102e11 −0.350005 −0.175003 0.984568i \(-0.555993\pi\)
−0.175003 + 0.984568i \(0.555993\pi\)
\(558\) −1.45780e12 −0.636568
\(559\) −3.11456e12 −1.34910
\(560\) −8.81171e10 −0.0378629
\(561\) 2.03460e9 0.000867253 0
\(562\) 2.99149e12 1.26495
\(563\) −2.13667e12 −0.896292 −0.448146 0.893960i \(-0.647916\pi\)
−0.448146 + 0.893960i \(0.647916\pi\)
\(564\) −8.12972e10 −0.0338314
\(565\) 7.99596e11 0.330105
\(566\) 8.53460e10 0.0349550
\(567\) −9.25096e11 −0.375892
\(568\) −1.14547e12 −0.461760
\(569\) 2.17461e12 0.869714 0.434857 0.900500i \(-0.356799\pi\)
0.434857 + 0.900500i \(0.356799\pi\)
\(570\) 1.38205e10 0.00548387
\(571\) 9.95075e11 0.391736 0.195868 0.980630i \(-0.437248\pi\)
0.195868 + 0.980630i \(0.437248\pi\)
\(572\) 1.56889e12 0.612790
\(573\) 1.55393e11 0.0602192
\(574\) 8.41661e11 0.323619
\(575\) 4.36114e11 0.166377
\(576\) −3.29622e11 −0.124771
\(577\) 4.30588e12 1.61723 0.808614 0.588340i \(-0.200218\pi\)
0.808614 + 0.588340i \(0.200218\pi\)
\(578\) 1.89678e12 0.706873
\(579\) −9.56204e10 −0.0353588
\(580\) 2.25751e11 0.0828331
\(581\) −1.00874e12 −0.367272
\(582\) −8.37602e10 −0.0302611
\(583\) −8.78412e11 −0.314912
\(584\) 1.65488e12 0.588719
\(585\) 1.24515e12 0.439564
\(586\) −1.22469e12 −0.429030
\(587\) 5.05762e12 1.75822 0.879112 0.476615i \(-0.158136\pi\)
0.879112 + 0.476615i \(0.158136\pi\)
\(588\) −8.85473e9 −0.00305476
\(589\) −1.19220e12 −0.408158
\(590\) 1.25897e12 0.427740
\(591\) 2.00811e10 0.00677085
\(592\) −7.82909e11 −0.261977
\(593\) −2.80300e12 −0.930844 −0.465422 0.885089i \(-0.654097\pi\)
−0.465422 + 0.885089i \(0.654097\pi\)
\(594\) 2.04461e11 0.0673862
\(595\) −8.41963e9 −0.00275402
\(596\) 2.33069e12 0.756616
\(597\) 8.05565e10 0.0259547
\(598\) −4.81660e11 −0.154023
\(599\) 3.20907e12 1.01849 0.509247 0.860620i \(-0.329924\pi\)
0.509247 + 0.860620i \(0.329924\pi\)
\(600\) −4.02930e10 −0.0126925
\(601\) 7.49502e11 0.234335 0.117168 0.993112i \(-0.462619\pi\)
0.117168 + 0.993112i \(0.462619\pi\)
\(602\) 1.05723e12 0.328084
\(603\) −3.02042e12 −0.930336
\(604\) −7.40946e10 −0.0226527
\(605\) 3.21715e11 0.0976275
\(606\) −1.16065e11 −0.0349604
\(607\) −1.74097e12 −0.520526 −0.260263 0.965538i \(-0.583809\pi\)
−0.260263 + 0.965538i \(0.583809\pi\)
\(608\) −2.69566e11 −0.0800016
\(609\) 2.26853e10 0.00668294
\(610\) 1.81855e12 0.531792
\(611\) −5.98995e12 −1.73875
\(612\) −3.14956e10 −0.00907544
\(613\) −4.03977e12 −1.15554 −0.577770 0.816200i \(-0.696077\pi\)
−0.577770 + 0.816200i \(0.696077\pi\)
\(614\) 1.20311e12 0.341623
\(615\) −7.36147e10 −0.0207504
\(616\) −5.32558e11 −0.149023
\(617\) −2.93367e12 −0.814945 −0.407472 0.913218i \(-0.633590\pi\)
−0.407472 + 0.913218i \(0.633590\pi\)
\(618\) 6.62940e10 0.0182821
\(619\) −5.77691e12 −1.58157 −0.790784 0.612095i \(-0.790327\pi\)
−0.790784 + 0.612095i \(0.790327\pi\)
\(620\) −6.64830e11 −0.180696
\(621\) −6.27707e10 −0.0169373
\(622\) −3.44214e12 −0.922088
\(623\) 1.12737e12 0.299827
\(624\) 4.45010e10 0.0117500
\(625\) 2.07554e12 0.544091
\(626\) −1.53452e12 −0.399381
\(627\) 8.35277e10 0.0215837
\(628\) 3.56014e12 0.913373
\(629\) −7.48073e10 −0.0190553
\(630\) −4.22665e11 −0.106897
\(631\) 3.99985e12 1.00441 0.502206 0.864748i \(-0.332522\pi\)
0.502206 + 0.864748i \(0.332522\pi\)
\(632\) 5.35305e11 0.133467
\(633\) −1.81021e11 −0.0448139
\(634\) −2.72938e12 −0.670908
\(635\) −1.32089e12 −0.322392
\(636\) −2.49158e10 −0.00603834
\(637\) −6.52414e11 −0.156999
\(638\) 1.36438e12 0.326019
\(639\) −5.49440e12 −1.30367
\(640\) −1.50324e11 −0.0354175
\(641\) 4.68328e12 1.09569 0.547846 0.836579i \(-0.315448\pi\)
0.547846 + 0.836579i \(0.315448\pi\)
\(642\) 1.72319e10 0.00400338
\(643\) −1.54877e12 −0.357304 −0.178652 0.983912i \(-0.557174\pi\)
−0.178652 + 0.983912i \(0.557174\pi\)
\(644\) 1.63498e11 0.0374565
\(645\) −9.24692e10 −0.0210367
\(646\) −2.57572e10 −0.00581904
\(647\) −8.14493e12 −1.82733 −0.913667 0.406463i \(-0.866762\pi\)
−0.913667 + 0.406463i \(0.866762\pi\)
\(648\) −1.57817e12 −0.351615
\(649\) 7.60888e12 1.68352
\(650\) −2.96877e12 −0.652329
\(651\) −6.68076e10 −0.0145785
\(652\) 4.25555e12 0.922235
\(653\) −2.88925e12 −0.621836 −0.310918 0.950437i \(-0.600636\pi\)
−0.310918 + 0.950437i \(0.600636\pi\)
\(654\) −1.53946e11 −0.0329056
\(655\) 3.36933e11 0.0715249
\(656\) 1.43584e12 0.302718
\(657\) 7.93784e12 1.66210
\(658\) 2.03328e12 0.422844
\(659\) 5.20255e12 1.07456 0.537281 0.843403i \(-0.319451\pi\)
0.537281 + 0.843403i \(0.319451\pi\)
\(660\) 4.65794e10 0.00955534
\(661\) 2.88973e12 0.588777 0.294388 0.955686i \(-0.404884\pi\)
0.294388 + 0.955686i \(0.404884\pi\)
\(662\) 1.98387e12 0.401469
\(663\) 4.25210e9 0.000854658 0
\(664\) −1.72087e12 −0.343551
\(665\) −3.45657e11 −0.0685406
\(666\) −3.75532e12 −0.739628
\(667\) −4.18874e11 −0.0819440
\(668\) −4.04530e12 −0.786061
\(669\) −3.21018e11 −0.0619600
\(670\) −1.37746e12 −0.264085
\(671\) 1.09909e13 2.09306
\(672\) −1.51058e10 −0.00285747
\(673\) 9.46362e12 1.77824 0.889119 0.457677i \(-0.151318\pi\)
0.889119 + 0.457677i \(0.151318\pi\)
\(674\) 1.16694e12 0.217810
\(675\) −3.86895e11 −0.0717342
\(676\) 5.64071e11 0.103890
\(677\) −6.52268e12 −1.19338 −0.596688 0.802474i \(-0.703517\pi\)
−0.596688 + 0.802474i \(0.703517\pi\)
\(678\) 1.37074e11 0.0249127
\(679\) 2.09488e12 0.378220
\(680\) −1.43635e10 −0.00257615
\(681\) 2.41622e11 0.0430502
\(682\) −4.01806e12 −0.711193
\(683\) 5.37240e12 0.944660 0.472330 0.881422i \(-0.343413\pi\)
0.472330 + 0.881422i \(0.343413\pi\)
\(684\) −1.29301e12 −0.225865
\(685\) −2.88965e12 −0.501461
\(686\) 2.21461e11 0.0381802
\(687\) −1.14148e11 −0.0195508
\(688\) 1.80359e12 0.306895
\(689\) −1.83579e12 −0.310339
\(690\) −1.43002e10 −0.00240171
\(691\) 2.01563e12 0.336325 0.168163 0.985759i \(-0.446217\pi\)
0.168163 + 0.985759i \(0.446217\pi\)
\(692\) 8.27200e11 0.137130
\(693\) −2.55448e12 −0.420730
\(694\) 2.49153e12 0.407707
\(695\) −4.00040e12 −0.650386
\(696\) 3.87002e10 0.00625131
\(697\) 1.37195e11 0.0220186
\(698\) −1.73966e12 −0.277405
\(699\) 2.20649e11 0.0349586
\(700\) 1.00774e12 0.158639
\(701\) −1.06523e13 −1.66614 −0.833068 0.553171i \(-0.813418\pi\)
−0.833068 + 0.553171i \(0.813418\pi\)
\(702\) 4.27301e11 0.0664075
\(703\) −3.07111e12 −0.474239
\(704\) −9.08520e11 −0.139398
\(705\) −1.77838e11 −0.0271127
\(706\) −5.20936e12 −0.789157
\(707\) 2.90284e12 0.436955
\(708\) 2.15823e11 0.0322810
\(709\) 3.46187e12 0.514520 0.257260 0.966342i \(-0.417180\pi\)
0.257260 + 0.966342i \(0.417180\pi\)
\(710\) −2.50572e12 −0.370058
\(711\) 2.56766e12 0.376812
\(712\) 1.92325e12 0.280462
\(713\) 1.23357e12 0.178756
\(714\) −1.44337e9 −0.000207843 0
\(715\) 3.43195e12 0.491094
\(716\) −6.18004e12 −0.878785
\(717\) −3.93666e10 −0.00556277
\(718\) 3.64080e12 0.511253
\(719\) −9.62025e12 −1.34248 −0.671238 0.741242i \(-0.734237\pi\)
−0.671238 + 0.741242i \(0.734237\pi\)
\(720\) −7.21048e11 −0.0999926
\(721\) −1.65804e12 −0.228500
\(722\) 4.10558e12 0.562285
\(723\) 5.38091e11 0.0732374
\(724\) −9.96689e11 −0.134814
\(725\) −2.58178e12 −0.347055
\(726\) 5.51512e10 0.00736784
\(727\) −3.13479e12 −0.416202 −0.208101 0.978107i \(-0.566728\pi\)
−0.208101 + 0.978107i \(0.566728\pi\)
\(728\) −1.11299e12 −0.146859
\(729\) −7.54204e12 −0.989043
\(730\) 3.62004e12 0.471803
\(731\) 1.72334e11 0.0223225
\(732\) 3.11752e11 0.0401337
\(733\) 6.47775e12 0.828812 0.414406 0.910092i \(-0.363989\pi\)
0.414406 + 0.910092i \(0.363989\pi\)
\(734\) 6.75189e12 0.858604
\(735\) −1.93697e10 −0.00244811
\(736\) 2.78921e11 0.0350374
\(737\) −8.32503e12 −1.03940
\(738\) 6.88718e12 0.854649
\(739\) −1.12510e12 −0.138769 −0.0693843 0.997590i \(-0.522103\pi\)
−0.0693843 + 0.997590i \(0.522103\pi\)
\(740\) −1.71261e12 −0.209950
\(741\) 1.74564e11 0.0212703
\(742\) 6.23154e11 0.0754707
\(743\) 1.65266e12 0.198945 0.0994725 0.995040i \(-0.468284\pi\)
0.0994725 + 0.995040i \(0.468284\pi\)
\(744\) −1.13971e11 −0.0136369
\(745\) 5.09838e12 0.606357
\(746\) −6.13253e12 −0.724961
\(747\) −8.25437e12 −0.969932
\(748\) −8.68096e10 −0.0101394
\(749\) −4.30978e11 −0.0500365
\(750\) −1.93141e11 −0.0222894
\(751\) 6.03299e12 0.692074 0.346037 0.938221i \(-0.387527\pi\)
0.346037 + 0.938221i \(0.387527\pi\)
\(752\) 3.46868e12 0.395534
\(753\) −3.20222e10 −0.00362972
\(754\) 2.85142e12 0.321284
\(755\) −1.62082e11 −0.0181540
\(756\) −1.45047e11 −0.0161495
\(757\) −8.02798e12 −0.888535 −0.444268 0.895894i \(-0.646536\pi\)
−0.444268 + 0.895894i \(0.646536\pi\)
\(758\) 1.94338e12 0.213820
\(759\) −8.64266e10 −0.00945278
\(760\) −5.89675e11 −0.0641138
\(761\) −6.51923e12 −0.704637 −0.352318 0.935880i \(-0.614607\pi\)
−0.352318 + 0.935880i \(0.614607\pi\)
\(762\) −2.26438e11 −0.0243305
\(763\) 3.85026e12 0.411273
\(764\) −6.63009e12 −0.704043
\(765\) −6.88965e10 −0.00727312
\(766\) 6.36354e12 0.667835
\(767\) 1.59018e13 1.65907
\(768\) −2.57698e10 −0.00267292
\(769\) −1.34250e13 −1.38435 −0.692175 0.721730i \(-0.743347\pi\)
−0.692175 + 0.721730i \(0.743347\pi\)
\(770\) −1.16497e12 −0.119428
\(771\) 5.01345e11 0.0510966
\(772\) 4.07980e12 0.413391
\(773\) 7.85934e12 0.791733 0.395866 0.918308i \(-0.370444\pi\)
0.395866 + 0.918308i \(0.370444\pi\)
\(774\) 8.65115e12 0.866442
\(775\) 7.60327e12 0.757082
\(776\) 3.57377e12 0.353792
\(777\) −1.72098e11 −0.0169387
\(778\) −1.08074e12 −0.105758
\(779\) 5.63235e12 0.547988
\(780\) 9.73460e10 0.00941657
\(781\) −1.51439e13 −1.45649
\(782\) 2.66511e10 0.00254850
\(783\) 3.71601e11 0.0353304
\(784\) 3.77802e11 0.0357143
\(785\) 7.78780e12 0.731983
\(786\) 5.77599e10 0.00539790
\(787\) −1.47720e12 −0.137263 −0.0686316 0.997642i \(-0.521863\pi\)
−0.0686316 + 0.997642i \(0.521863\pi\)
\(788\) −8.56793e11 −0.0791604
\(789\) −6.51809e11 −0.0598789
\(790\) 1.17098e12 0.106962
\(791\) −3.42827e12 −0.311373
\(792\) −4.35783e12 −0.393557
\(793\) 2.29698e13 2.06266
\(794\) −1.99449e12 −0.178090
\(795\) −5.45033e10 −0.00483917
\(796\) −3.43708e12 −0.303445
\(797\) −6.47327e12 −0.568278 −0.284139 0.958783i \(-0.591708\pi\)
−0.284139 + 0.958783i \(0.591708\pi\)
\(798\) −5.92555e10 −0.00517268
\(799\) 3.31434e11 0.0287698
\(800\) 1.71917e12 0.148393
\(801\) 9.22510e12 0.791817
\(802\) −5.61913e12 −0.479606
\(803\) 2.18786e13 1.85695
\(804\) −2.36136e11 −0.0199301
\(805\) 3.57653e11 0.0300179
\(806\) −8.39733e12 −0.700864
\(807\) −8.48403e11 −0.0704160
\(808\) 4.95212e12 0.408734
\(809\) −1.53631e13 −1.26099 −0.630493 0.776195i \(-0.717147\pi\)
−0.630493 + 0.776195i \(0.717147\pi\)
\(810\) −3.45225e12 −0.281786
\(811\) −1.29056e13 −1.04757 −0.523787 0.851849i \(-0.675481\pi\)
−0.523787 + 0.851849i \(0.675481\pi\)
\(812\) −9.67907e11 −0.0781325
\(813\) 5.45012e11 0.0437520
\(814\) −1.03506e13 −0.826334
\(815\) 9.30902e12 0.739085
\(816\) −2.46232e9 −0.000194419 0
\(817\) 7.07494e12 0.555550
\(818\) 6.11130e11 0.0477247
\(819\) −5.33860e12 −0.414620
\(820\) 3.14089e12 0.242600
\(821\) 8.93771e11 0.0686566 0.0343283 0.999411i \(-0.489071\pi\)
0.0343283 + 0.999411i \(0.489071\pi\)
\(822\) −4.95368e11 −0.0378447
\(823\) −2.29844e13 −1.74636 −0.873182 0.487394i \(-0.837947\pi\)
−0.873182 + 0.487394i \(0.837947\pi\)
\(824\) −2.82854e12 −0.213742
\(825\) −5.32701e11 −0.0400351
\(826\) −5.39782e12 −0.403467
\(827\) −2.75618e12 −0.204896 −0.102448 0.994738i \(-0.532667\pi\)
−0.102448 + 0.994738i \(0.532667\pi\)
\(828\) 1.33788e12 0.0989194
\(829\) −3.15925e12 −0.232321 −0.116160 0.993230i \(-0.537059\pi\)
−0.116160 + 0.993230i \(0.537059\pi\)
\(830\) −3.76440e12 −0.275324
\(831\) 1.59045e11 0.0115695
\(832\) −1.89871e12 −0.137374
\(833\) 3.60992e10 0.00259774
\(834\) −6.85782e11 −0.0490839
\(835\) −8.84909e12 −0.629955
\(836\) −3.56385e12 −0.252343
\(837\) −1.09435e12 −0.0770714
\(838\) −3.44428e12 −0.241269
\(839\) 1.92403e13 1.34055 0.670277 0.742111i \(-0.266175\pi\)
0.670277 + 0.742111i \(0.266175\pi\)
\(840\) −3.30439e10 −0.00229000
\(841\) −1.20274e13 −0.829069
\(842\) −1.91892e13 −1.31569
\(843\) 1.12181e12 0.0765058
\(844\) 7.72357e12 0.523935
\(845\) 1.23391e12 0.0832581
\(846\) 1.66380e13 1.11669
\(847\) −1.37935e12 −0.0920874
\(848\) 1.06307e12 0.0705963
\(849\) 3.20048e10 0.00211412
\(850\) 1.64267e11 0.0107936
\(851\) 3.17770e12 0.207697
\(852\) −4.29552e11 −0.0279278
\(853\) −2.60804e13 −1.68672 −0.843362 0.537345i \(-0.819427\pi\)
−0.843362 + 0.537345i \(0.819427\pi\)
\(854\) −7.79705e12 −0.501614
\(855\) −2.82845e12 −0.181010
\(856\) −7.35229e11 −0.0468049
\(857\) 2.19177e13 1.38797 0.693986 0.719988i \(-0.255853\pi\)
0.693986 + 0.719988i \(0.255853\pi\)
\(858\) 5.88335e11 0.0370623
\(859\) −3.55588e12 −0.222832 −0.111416 0.993774i \(-0.535539\pi\)
−0.111416 + 0.993774i \(0.535539\pi\)
\(860\) 3.94535e12 0.245948
\(861\) 3.15623e11 0.0195729
\(862\) −1.26579e13 −0.780869
\(863\) 2.22084e13 1.36292 0.681458 0.731858i \(-0.261346\pi\)
0.681458 + 0.731858i \(0.261346\pi\)
\(864\) −2.47443e11 −0.0151065
\(865\) 1.80950e12 0.109897
\(866\) 1.84721e13 1.11606
\(867\) 7.11292e11 0.0427525
\(868\) 2.85046e12 0.170442
\(869\) 7.07711e12 0.420986
\(870\) 8.46566e10 0.00500985
\(871\) −1.73984e13 −1.02430
\(872\) 6.56838e12 0.384711
\(873\) 1.71420e13 0.998846
\(874\) 1.09412e12 0.0634257
\(875\) 4.83053e12 0.278586
\(876\) 6.20579e11 0.0356064
\(877\) 3.38004e12 0.192941 0.0964703 0.995336i \(-0.469245\pi\)
0.0964703 + 0.995336i \(0.469245\pi\)
\(878\) 3.40365e12 0.193295
\(879\) −4.59260e11 −0.0259483
\(880\) −1.98739e12 −0.111715
\(881\) 5.25103e11 0.0293665 0.0146833 0.999892i \(-0.495326\pi\)
0.0146833 + 0.999892i \(0.495326\pi\)
\(882\) 1.81218e12 0.100830
\(883\) 3.33972e13 1.84879 0.924393 0.381441i \(-0.124572\pi\)
0.924393 + 0.381441i \(0.124572\pi\)
\(884\) −1.81423e11 −0.00999210
\(885\) 4.72112e11 0.0258702
\(886\) 1.03728e12 0.0565515
\(887\) −9.61964e12 −0.521798 −0.260899 0.965366i \(-0.584019\pi\)
−0.260899 + 0.965366i \(0.584019\pi\)
\(888\) −2.93591e11 −0.0158447
\(889\) 5.66331e12 0.304097
\(890\) 4.20710e12 0.224765
\(891\) −2.08646e13 −1.10907
\(892\) 1.36968e13 0.724396
\(893\) 1.36066e13 0.716007
\(894\) 8.74007e11 0.0457611
\(895\) −1.35188e13 −0.704264
\(896\) 6.44514e11 0.0334077
\(897\) −1.80623e11 −0.00931549
\(898\) 1.72850e13 0.887004
\(899\) −7.30271e12 −0.372877
\(900\) 8.24621e12 0.418951
\(901\) 1.01577e11 0.00513494
\(902\) 1.89828e13 0.954839
\(903\) 3.96462e11 0.0198430
\(904\) −5.84848e12 −0.291263
\(905\) −2.18026e12 −0.108041
\(906\) −2.77855e10 −0.00137006
\(907\) −2.08341e13 −1.02221 −0.511107 0.859517i \(-0.670764\pi\)
−0.511107 + 0.859517i \(0.670764\pi\)
\(908\) −1.03092e13 −0.503315
\(909\) 2.37535e13 1.15396
\(910\) −2.43466e12 −0.117694
\(911\) −1.33789e13 −0.643560 −0.321780 0.946814i \(-0.604281\pi\)
−0.321780 + 0.946814i \(0.604281\pi\)
\(912\) −1.01087e11 −0.00483860
\(913\) −2.27511e13 −1.08364
\(914\) 1.03476e12 0.0490436
\(915\) 6.81958e11 0.0321634
\(916\) 4.87033e12 0.228575
\(917\) −1.44460e12 −0.0674660
\(918\) −2.36433e10 −0.00109879
\(919\) −1.38352e13 −0.639830 −0.319915 0.947446i \(-0.603654\pi\)
−0.319915 + 0.947446i \(0.603654\pi\)
\(920\) 6.10140e11 0.0280792
\(921\) 4.51166e11 0.0206618
\(922\) −6.86806e12 −0.313000
\(923\) −3.16492e13 −1.43534
\(924\) −1.99709e11 −0.00901310
\(925\) 1.95862e13 0.879653
\(926\) −2.59013e13 −1.15764
\(927\) −1.35675e13 −0.603449
\(928\) −1.65121e12 −0.0730863
\(929\) −1.74073e13 −0.766761 −0.383380 0.923591i \(-0.625240\pi\)
−0.383380 + 0.923591i \(0.625240\pi\)
\(930\) −2.49311e11 −0.0109287
\(931\) 1.48200e12 0.0646511
\(932\) −9.41434e12 −0.408713
\(933\) −1.29080e12 −0.0557690
\(934\) −5.23714e12 −0.225182
\(935\) −1.89896e11 −0.00812575
\(936\) −9.10742e12 −0.387841
\(937\) 1.98361e12 0.0840676 0.0420338 0.999116i \(-0.486616\pi\)
0.0420338 + 0.999116i \(0.486616\pi\)
\(938\) 5.90587e12 0.249098
\(939\) −5.75445e11 −0.0241551
\(940\) 7.58773e12 0.316984
\(941\) −2.33533e13 −0.970946 −0.485473 0.874252i \(-0.661353\pi\)
−0.485473 + 0.874252i \(0.661353\pi\)
\(942\) 1.33505e12 0.0552419
\(943\) −5.82783e12 −0.239996
\(944\) −9.20844e12 −0.377409
\(945\) −3.17289e11 −0.0129423
\(946\) 2.38447e13 0.968015
\(947\) 3.59882e13 1.45407 0.727035 0.686600i \(-0.240898\pi\)
0.727035 + 0.686600i \(0.240898\pi\)
\(948\) 2.00740e11 0.00807227
\(949\) 4.57241e13 1.82998
\(950\) 6.74377e12 0.268625
\(951\) −1.02352e12 −0.0405773
\(952\) 6.15836e10 0.00242996
\(953\) −1.37662e13 −0.540624 −0.270312 0.962773i \(-0.587127\pi\)
−0.270312 + 0.962773i \(0.587127\pi\)
\(954\) 5.09917e12 0.199311
\(955\) −1.45033e13 −0.564225
\(956\) 1.67964e12 0.0650363
\(957\) 5.11643e11 0.0197180
\(958\) −4.55698e12 −0.174796
\(959\) 1.23894e13 0.473005
\(960\) −5.63714e10 −0.00214209
\(961\) −4.93336e12 −0.186590
\(962\) −2.16317e13 −0.814334
\(963\) −3.52662e12 −0.132142
\(964\) −2.29585e13 −0.856244
\(965\) 8.92457e12 0.331295
\(966\) 6.13119e10 0.00226542
\(967\) −3.02718e12 −0.111332 −0.0556659 0.998449i \(-0.517728\pi\)
−0.0556659 + 0.998449i \(0.517728\pi\)
\(968\) −2.35312e12 −0.0861399
\(969\) −9.65893e9 −0.000351943 0
\(970\) 7.81762e12 0.283532
\(971\) −2.53183e13 −0.914003 −0.457002 0.889466i \(-0.651077\pi\)
−0.457002 + 0.889466i \(0.651077\pi\)
\(972\) −1.78088e12 −0.0639937
\(973\) 1.71517e13 0.613478
\(974\) 1.14364e13 0.407169
\(975\) −1.11329e12 −0.0394537
\(976\) −1.33014e13 −0.469217
\(977\) 9.90729e12 0.347880 0.173940 0.984756i \(-0.444350\pi\)
0.173940 + 0.984756i \(0.444350\pi\)
\(978\) 1.59583e12 0.0557779
\(979\) 2.54267e13 0.884641
\(980\) 8.26442e11 0.0286217
\(981\) 3.15061e13 1.08614
\(982\) −1.62409e13 −0.557325
\(983\) 2.40523e13 0.821610 0.410805 0.911723i \(-0.365248\pi\)
0.410805 + 0.911723i \(0.365248\pi\)
\(984\) 5.38439e11 0.0183087
\(985\) −1.87423e12 −0.0634397
\(986\) −1.57774e11 −0.00531604
\(987\) 7.62478e11 0.0255741
\(988\) −7.44807e12 −0.248678
\(989\) −7.32048e12 −0.243308
\(990\) −9.53276e12 −0.315399
\(991\) 3.15782e13 1.04005 0.520027 0.854150i \(-0.325922\pi\)
0.520027 + 0.854150i \(0.325922\pi\)
\(992\) 4.86275e12 0.159434
\(993\) 7.43950e11 0.0242813
\(994\) 1.07433e13 0.349058
\(995\) −7.51860e12 −0.243183
\(996\) −6.45326e11 −0.0207784
\(997\) 9.32241e12 0.298813 0.149407 0.988776i \(-0.452264\pi\)
0.149407 + 0.988776i \(0.452264\pi\)
\(998\) −2.13460e13 −0.681128
\(999\) −2.81907e12 −0.0895492
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 14.10.a.a.1.1 1
3.2 odd 2 126.10.a.e.1.1 1
4.3 odd 2 112.10.a.b.1.1 1
5.2 odd 4 350.10.c.b.99.1 2
5.3 odd 4 350.10.c.b.99.2 2
5.4 even 2 350.10.a.c.1.1 1
7.2 even 3 98.10.c.f.67.1 2
7.3 odd 6 98.10.c.e.79.1 2
7.4 even 3 98.10.c.f.79.1 2
7.5 odd 6 98.10.c.e.67.1 2
7.6 odd 2 98.10.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.10.a.a.1.1 1 1.1 even 1 trivial
98.10.a.a.1.1 1 7.6 odd 2
98.10.c.e.67.1 2 7.5 odd 6
98.10.c.e.79.1 2 7.3 odd 6
98.10.c.f.67.1 2 7.2 even 3
98.10.c.f.79.1 2 7.4 even 3
112.10.a.b.1.1 1 4.3 odd 2
126.10.a.e.1.1 1 3.2 odd 2
350.10.a.c.1.1 1 5.4 even 2
350.10.c.b.99.1 2 5.2 odd 4
350.10.c.b.99.2 2 5.3 odd 4