Properties

Label 177.10.a.d.1.19
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} -101247. q^{10} -29647.1 q^{11} +73729.6 q^{12} -62958.6 q^{13} +328806. q^{14} -217461. q^{15} +100353. q^{16} +515394. q^{17} +247433. q^{18} +165208. q^{19} -2.44373e6 q^{20} +706217. q^{21} -1.11807e6 q^{22} +2.59310e6 q^{23} +1.21652e6 q^{24} +5.25451e6 q^{25} -2.37434e6 q^{26} +531441. q^{27} +7.93616e6 q^{28} +5.90158e6 q^{29} -8.20103e6 q^{30} +6.31829e6 q^{31} -3.90503e6 q^{32} -2.40141e6 q^{33} +1.94369e7 q^{34} -2.34072e7 q^{35} +5.97210e6 q^{36} -1.29343e7 q^{37} +6.23042e6 q^{38} -5.09965e6 q^{39} -4.03209e7 q^{40} +406055. q^{41} +2.66333e7 q^{42} -8.02029e6 q^{43} -2.69860e7 q^{44} -1.76143e7 q^{45} +9.77926e7 q^{46} +1.31877e7 q^{47} +8.12859e6 q^{48} +3.56627e7 q^{49} +1.98161e8 q^{50} +4.17469e7 q^{51} -5.73076e7 q^{52} -5.16715e7 q^{53} +2.00420e7 q^{54} +7.95936e7 q^{55} +1.30945e8 q^{56} +1.33818e7 q^{57} +2.22564e8 q^{58} -1.21174e7 q^{59} -1.97942e8 q^{60} +1.69831e7 q^{61} +2.38279e8 q^{62} +5.72036e7 q^{63} -1.98650e8 q^{64} +1.69025e8 q^{65} -9.05635e7 q^{66} +2.43696e8 q^{67} +4.69133e8 q^{68} +2.10041e8 q^{69} -8.82748e8 q^{70} +3.15773e8 q^{71} +9.85381e7 q^{72} -3.21356e8 q^{73} -4.87786e8 q^{74} +4.25615e8 q^{75} +1.50379e8 q^{76} -2.58485e8 q^{77} -1.92321e8 q^{78} -5.46294e8 q^{79} -2.69418e8 q^{80} +4.30467e7 q^{81} +1.53134e7 q^{82} +2.03715e8 q^{83} +6.42829e8 q^{84} -1.38368e9 q^{85} -3.02466e8 q^{86} +4.78028e8 q^{87} -4.45262e8 q^{88} +2.89913e8 q^{89} -6.64283e8 q^{90} -5.48920e8 q^{91} +2.36035e9 q^{92} +5.11781e8 q^{93} +4.97344e8 q^{94} -4.43534e8 q^{95} -3.16308e8 q^{96} +7.57382e8 q^{97} +1.34493e9 q^{98} -1.94514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 37.7126 1.66668 0.833339 0.552762i \(-0.186426\pi\)
0.833339 + 0.552762i \(0.186426\pi\)
\(3\) 81.0000 0.577350
\(4\) 910.242 1.77782
\(5\) −2684.70 −1.92102 −0.960509 0.278249i \(-0.910246\pi\)
−0.960509 + 0.278249i \(0.910246\pi\)
\(6\) 3054.72 0.962257
\(7\) 8718.73 1.37250 0.686250 0.727366i \(-0.259256\pi\)
0.686250 + 0.727366i \(0.259256\pi\)
\(8\) 15018.8 1.29637
\(9\) 6561.00 0.333333
\(10\) −101247. −3.20172
\(11\) −29647.1 −0.610540 −0.305270 0.952266i \(-0.598747\pi\)
−0.305270 + 0.952266i \(0.598747\pi\)
\(12\) 73729.6 1.02642
\(13\) −62958.6 −0.611379 −0.305689 0.952131i \(-0.598887\pi\)
−0.305689 + 0.952131i \(0.598887\pi\)
\(14\) 328806. 2.28752
\(15\) −217461. −1.10910
\(16\) 100353. 0.382816
\(17\) 515394. 1.49665 0.748323 0.663334i \(-0.230859\pi\)
0.748323 + 0.663334i \(0.230859\pi\)
\(18\) 247433. 0.555559
\(19\) 165208. 0.290830 0.145415 0.989371i \(-0.453548\pi\)
0.145415 + 0.989371i \(0.453548\pi\)
\(20\) −2.44373e6 −3.41522
\(21\) 706217. 0.792413
\(22\) −1.11807e6 −1.01757
\(23\) 2.59310e6 1.93216 0.966081 0.258237i \(-0.0831417\pi\)
0.966081 + 0.258237i \(0.0831417\pi\)
\(24\) 1.21652e6 0.748460
\(25\) 5.25451e6 2.69031
\(26\) −2.37434e6 −1.01897
\(27\) 531441. 0.192450
\(28\) 7.93616e6 2.44005
\(29\) 5.90158e6 1.54945 0.774724 0.632299i \(-0.217889\pi\)
0.774724 + 0.632299i \(0.217889\pi\)
\(30\) −8.20103e6 −1.84851
\(31\) 6.31829e6 1.22877 0.614387 0.789005i \(-0.289403\pi\)
0.614387 + 0.789005i \(0.289403\pi\)
\(32\) −3.90503e6 −0.658339
\(33\) −2.40141e6 −0.352496
\(34\) 1.94369e7 2.49443
\(35\) −2.34072e7 −2.63660
\(36\) 5.97210e6 0.592606
\(37\) −1.29343e7 −1.13458 −0.567289 0.823519i \(-0.692008\pi\)
−0.567289 + 0.823519i \(0.692008\pi\)
\(38\) 6.23042e6 0.484720
\(39\) −5.09965e6 −0.352980
\(40\) −4.03209e7 −2.49035
\(41\) 406055. 0.0224418 0.0112209 0.999937i \(-0.496428\pi\)
0.0112209 + 0.999937i \(0.496428\pi\)
\(42\) 2.66333e7 1.32070
\(43\) −8.02029e6 −0.357752 −0.178876 0.983872i \(-0.557246\pi\)
−0.178876 + 0.983872i \(0.557246\pi\)
\(44\) −2.69860e7 −1.08543
\(45\) −1.76143e7 −0.640339
\(46\) 9.77926e7 3.22029
\(47\) 1.31877e7 0.394212 0.197106 0.980382i \(-0.436846\pi\)
0.197106 + 0.980382i \(0.436846\pi\)
\(48\) 8.12859e6 0.221019
\(49\) 3.56627e7 0.883755
\(50\) 1.98161e8 4.48388
\(51\) 4.17469e7 0.864089
\(52\) −5.73076e7 −1.08692
\(53\) −5.16715e7 −0.899517 −0.449759 0.893150i \(-0.648490\pi\)
−0.449759 + 0.893150i \(0.648490\pi\)
\(54\) 2.00420e7 0.320752
\(55\) 7.95936e7 1.17286
\(56\) 1.30945e8 1.77927
\(57\) 1.33818e7 0.167911
\(58\) 2.22564e8 2.58243
\(59\) −1.21174e7 −0.130189
\(60\) −1.97942e8 −1.97178
\(61\) 1.69831e7 0.157048 0.0785242 0.996912i \(-0.474979\pi\)
0.0785242 + 0.996912i \(0.474979\pi\)
\(62\) 2.38279e8 2.04797
\(63\) 5.72036e7 0.457500
\(64\) −1.98650e8 −1.48006
\(65\) 1.69025e8 1.17447
\(66\) −9.05635e7 −0.587497
\(67\) 2.43696e8 1.47745 0.738724 0.674008i \(-0.235429\pi\)
0.738724 + 0.674008i \(0.235429\pi\)
\(68\) 4.69133e8 2.66076
\(69\) 2.10041e8 1.11553
\(70\) −8.82748e8 −4.39436
\(71\) 3.15773e8 1.47473 0.737364 0.675495i \(-0.236070\pi\)
0.737364 + 0.675495i \(0.236070\pi\)
\(72\) 9.85381e7 0.432124
\(73\) −3.21356e8 −1.32444 −0.662221 0.749308i \(-0.730386\pi\)
−0.662221 + 0.749308i \(0.730386\pi\)
\(74\) −4.87786e8 −1.89098
\(75\) 4.25615e8 1.55325
\(76\) 1.50379e8 0.517042
\(77\) −2.58485e8 −0.837967
\(78\) −1.92321e8 −0.588304
\(79\) −5.46294e8 −1.57799 −0.788995 0.614400i \(-0.789398\pi\)
−0.788995 + 0.614400i \(0.789398\pi\)
\(80\) −2.69418e8 −0.735397
\(81\) 4.30467e7 0.111111
\(82\) 1.53134e7 0.0374033
\(83\) 2.03715e8 0.471163 0.235581 0.971855i \(-0.424301\pi\)
0.235581 + 0.971855i \(0.424301\pi\)
\(84\) 6.42829e8 1.40877
\(85\) −1.38368e9 −2.87508
\(86\) −3.02466e8 −0.596258
\(87\) 4.78028e8 0.894575
\(88\) −4.45262e8 −0.791487
\(89\) 2.89913e8 0.489793 0.244897 0.969549i \(-0.421246\pi\)
0.244897 + 0.969549i \(0.421246\pi\)
\(90\) −6.64283e8 −1.06724
\(91\) −5.48920e8 −0.839117
\(92\) 2.36035e9 3.43503
\(93\) 5.11781e8 0.709433
\(94\) 4.97344e8 0.657025
\(95\) −4.43534e8 −0.558689
\(96\) −3.16308e8 −0.380092
\(97\) 7.57382e8 0.868645 0.434322 0.900758i \(-0.356988\pi\)
0.434322 + 0.900758i \(0.356988\pi\)
\(98\) 1.34493e9 1.47294
\(99\) −1.94514e8 −0.203513
\(100\) 4.78288e9 4.78288
\(101\) 1.04159e9 0.995976 0.497988 0.867184i \(-0.334072\pi\)
0.497988 + 0.867184i \(0.334072\pi\)
\(102\) 1.57439e9 1.44016
\(103\) 1.02405e9 0.896509 0.448255 0.893906i \(-0.352046\pi\)
0.448255 + 0.893906i \(0.352046\pi\)
\(104\) −9.45561e8 −0.792573
\(105\) −1.89598e9 −1.52224
\(106\) −1.94867e9 −1.49921
\(107\) 1.59574e9 1.17689 0.588444 0.808538i \(-0.299741\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(108\) 4.83740e8 0.342141
\(109\) 1.72861e8 0.117295 0.0586473 0.998279i \(-0.481321\pi\)
0.0586473 + 0.998279i \(0.481321\pi\)
\(110\) 3.00168e9 1.95478
\(111\) −1.04768e9 −0.655049
\(112\) 8.74951e8 0.525415
\(113\) −2.58205e9 −1.48974 −0.744872 0.667207i \(-0.767490\pi\)
−0.744872 + 0.667207i \(0.767490\pi\)
\(114\) 5.04664e8 0.279853
\(115\) −6.96170e9 −3.71172
\(116\) 5.37187e9 2.75464
\(117\) −4.13072e8 −0.203793
\(118\) −4.56978e8 −0.216983
\(119\) 4.49358e9 2.05415
\(120\) −3.26600e9 −1.43781
\(121\) −1.47900e9 −0.627240
\(122\) 6.40479e8 0.261749
\(123\) 3.28905e7 0.0129568
\(124\) 5.75117e9 2.18453
\(125\) −8.86324e9 −3.24711
\(126\) 2.15730e9 0.762505
\(127\) −1.44051e9 −0.491361 −0.245681 0.969351i \(-0.579011\pi\)
−0.245681 + 0.969351i \(0.579011\pi\)
\(128\) −5.49223e9 −1.80844
\(129\) −6.49644e8 −0.206548
\(130\) 6.37439e9 1.95746
\(131\) −9.89228e8 −0.293478 −0.146739 0.989175i \(-0.546878\pi\)
−0.146739 + 0.989175i \(0.546878\pi\)
\(132\) −2.18587e9 −0.626673
\(133\) 1.44040e9 0.399164
\(134\) 9.19042e9 2.46243
\(135\) −1.42676e9 −0.369700
\(136\) 7.74058e9 1.94021
\(137\) 4.29261e9 1.04107 0.520534 0.853841i \(-0.325733\pi\)
0.520534 + 0.853841i \(0.325733\pi\)
\(138\) 7.92120e9 1.85924
\(139\) 1.77464e9 0.403222 0.201611 0.979466i \(-0.435382\pi\)
0.201611 + 0.979466i \(0.435382\pi\)
\(140\) −2.13062e10 −4.68739
\(141\) 1.06821e9 0.227598
\(142\) 1.19086e10 2.45790
\(143\) 1.86654e9 0.373271
\(144\) 6.58416e8 0.127605
\(145\) −1.58440e10 −2.97652
\(146\) −1.21192e10 −2.20742
\(147\) 2.88868e9 0.510236
\(148\) −1.17733e10 −2.01707
\(149\) −2.93967e9 −0.488609 −0.244304 0.969699i \(-0.578560\pi\)
−0.244304 + 0.969699i \(0.578560\pi\)
\(150\) 1.60511e10 2.58877
\(151\) −1.11610e10 −1.74706 −0.873532 0.486767i \(-0.838176\pi\)
−0.873532 + 0.486767i \(0.838176\pi\)
\(152\) 2.48122e9 0.377023
\(153\) 3.38150e9 0.498882
\(154\) −9.74814e9 −1.39662
\(155\) −1.69627e10 −2.36050
\(156\) −4.64192e9 −0.627533
\(157\) 1.33277e10 1.75068 0.875338 0.483511i \(-0.160639\pi\)
0.875338 + 0.483511i \(0.160639\pi\)
\(158\) −2.06022e10 −2.63000
\(159\) −4.18539e9 −0.519337
\(160\) 1.04839e10 1.26468
\(161\) 2.26085e10 2.65189
\(162\) 1.62340e9 0.185186
\(163\) 1.67599e8 0.0185964 0.00929819 0.999957i \(-0.497040\pi\)
0.00929819 + 0.999957i \(0.497040\pi\)
\(164\) 3.69609e8 0.0398974
\(165\) 6.44708e9 0.677151
\(166\) 7.68262e9 0.785277
\(167\) 1.54656e10 1.53866 0.769330 0.638851i \(-0.220590\pi\)
0.769330 + 0.638851i \(0.220590\pi\)
\(168\) 1.06065e10 1.02726
\(169\) −6.64071e9 −0.626216
\(170\) −5.21822e10 −4.79184
\(171\) 1.08393e9 0.0969433
\(172\) −7.30041e9 −0.636018
\(173\) −1.88972e10 −1.60395 −0.801973 0.597360i \(-0.796216\pi\)
−0.801973 + 0.597360i \(0.796216\pi\)
\(174\) 1.80277e10 1.49097
\(175\) 4.58127e10 3.69245
\(176\) −2.97517e9 −0.233725
\(177\) −9.81506e8 −0.0751646
\(178\) 1.09334e10 0.816328
\(179\) 7.91689e9 0.576389 0.288195 0.957572i \(-0.406945\pi\)
0.288195 + 0.957572i \(0.406945\pi\)
\(180\) −1.60333e10 −1.13841
\(181\) −9.67084e9 −0.669747 −0.334873 0.942263i \(-0.608694\pi\)
−0.334873 + 0.942263i \(0.608694\pi\)
\(182\) −2.07012e10 −1.39854
\(183\) 1.37563e9 0.0906719
\(184\) 3.89451e10 2.50480
\(185\) 3.47247e10 2.17955
\(186\) 1.93006e10 1.18240
\(187\) −1.52799e10 −0.913763
\(188\) 1.20040e10 0.700837
\(189\) 4.63349e9 0.264138
\(190\) −1.67268e10 −0.931156
\(191\) −8.34529e9 −0.453723 −0.226862 0.973927i \(-0.572847\pi\)
−0.226862 + 0.973927i \(0.572847\pi\)
\(192\) −1.60906e10 −0.854511
\(193\) −1.47147e10 −0.763383 −0.381691 0.924290i \(-0.624658\pi\)
−0.381691 + 0.924290i \(0.624658\pi\)
\(194\) 2.85629e10 1.44775
\(195\) 1.36911e10 0.678080
\(196\) 3.24617e10 1.57115
\(197\) −1.93698e10 −0.916279 −0.458140 0.888880i \(-0.651484\pi\)
−0.458140 + 0.888880i \(0.651484\pi\)
\(198\) −7.33565e9 −0.339192
\(199\) −2.78962e10 −1.26098 −0.630488 0.776199i \(-0.717145\pi\)
−0.630488 + 0.776199i \(0.717145\pi\)
\(200\) 7.89162e10 3.48764
\(201\) 1.97394e10 0.853005
\(202\) 3.92809e10 1.65997
\(203\) 5.14543e10 2.12662
\(204\) 3.79998e10 1.53619
\(205\) −1.09014e9 −0.0431111
\(206\) 3.86197e10 1.49419
\(207\) 1.70133e10 0.644054
\(208\) −6.31809e9 −0.234046
\(209\) −4.89792e9 −0.177563
\(210\) −7.15026e10 −2.53708
\(211\) −1.95764e10 −0.679927 −0.339964 0.940439i \(-0.610415\pi\)
−0.339964 + 0.940439i \(0.610415\pi\)
\(212\) −4.70336e10 −1.59918
\(213\) 2.55776e10 0.851435
\(214\) 6.01796e10 1.96149
\(215\) 2.15321e10 0.687248
\(216\) 7.98159e9 0.249487
\(217\) 5.50875e10 1.68649
\(218\) 6.51904e9 0.195492
\(219\) −2.60298e10 −0.764667
\(220\) 7.24494e10 2.08513
\(221\) −3.24485e10 −0.915017
\(222\) −3.95107e10 −1.09176
\(223\) 2.64641e9 0.0716614 0.0358307 0.999358i \(-0.488592\pi\)
0.0358307 + 0.999358i \(0.488592\pi\)
\(224\) −3.40469e10 −0.903570
\(225\) 3.44748e10 0.896770
\(226\) −9.73759e10 −2.48292
\(227\) −1.39185e10 −0.347918 −0.173959 0.984753i \(-0.555656\pi\)
−0.173959 + 0.984753i \(0.555656\pi\)
\(228\) 1.21807e10 0.298515
\(229\) 2.39412e10 0.575290 0.287645 0.957737i \(-0.407128\pi\)
0.287645 + 0.957737i \(0.407128\pi\)
\(230\) −2.62544e11 −6.18624
\(231\) −2.09373e10 −0.483800
\(232\) 8.86344e10 2.00866
\(233\) −1.94275e10 −0.431832 −0.215916 0.976412i \(-0.569274\pi\)
−0.215916 + 0.976412i \(0.569274\pi\)
\(234\) −1.55780e10 −0.339657
\(235\) −3.54052e10 −0.757288
\(236\) −1.10297e10 −0.231452
\(237\) −4.42498e10 −0.911053
\(238\) 1.69465e11 3.42360
\(239\) −3.65784e10 −0.725160 −0.362580 0.931953i \(-0.618104\pi\)
−0.362580 + 0.931953i \(0.618104\pi\)
\(240\) −2.18229e10 −0.424582
\(241\) 2.75986e10 0.527000 0.263500 0.964659i \(-0.415123\pi\)
0.263500 + 0.964659i \(0.415123\pi\)
\(242\) −5.57770e10 −1.04541
\(243\) 3.48678e9 0.0641500
\(244\) 1.54588e10 0.279203
\(245\) −9.57438e10 −1.69771
\(246\) 1.24039e9 0.0215948
\(247\) −1.04013e10 −0.177807
\(248\) 9.48929e10 1.59295
\(249\) 1.65009e10 0.272026
\(250\) −3.34256e11 −5.41189
\(251\) −7.68115e10 −1.22150 −0.610751 0.791823i \(-0.709132\pi\)
−0.610751 + 0.791823i \(0.709132\pi\)
\(252\) 5.20691e10 0.813351
\(253\) −7.68777e10 −1.17966
\(254\) −5.43256e10 −0.818941
\(255\) −1.12078e11 −1.65993
\(256\) −1.05418e11 −1.53403
\(257\) 2.41025e10 0.344638 0.172319 0.985041i \(-0.444874\pi\)
0.172319 + 0.985041i \(0.444874\pi\)
\(258\) −2.44998e10 −0.344250
\(259\) −1.12771e11 −1.55721
\(260\) 1.53854e11 2.08799
\(261\) 3.87203e10 0.516483
\(262\) −3.73064e10 −0.489134
\(263\) 9.54317e10 1.22996 0.614981 0.788542i \(-0.289164\pi\)
0.614981 + 0.788542i \(0.289164\pi\)
\(264\) −3.60662e10 −0.456965
\(265\) 1.38723e11 1.72799
\(266\) 5.43213e10 0.665278
\(267\) 2.34830e10 0.282782
\(268\) 2.21823e11 2.62663
\(269\) 8.71165e10 1.01441 0.507207 0.861824i \(-0.330678\pi\)
0.507207 + 0.861824i \(0.330678\pi\)
\(270\) −5.38069e10 −0.616171
\(271\) −1.29398e11 −1.45735 −0.728677 0.684858i \(-0.759864\pi\)
−0.728677 + 0.684858i \(0.759864\pi\)
\(272\) 5.17213e10 0.572941
\(273\) −4.44625e10 −0.484464
\(274\) 1.61886e11 1.73513
\(275\) −1.55781e11 −1.64254
\(276\) 1.91188e11 1.98322
\(277\) −1.54712e11 −1.57894 −0.789470 0.613789i \(-0.789645\pi\)
−0.789470 + 0.613789i \(0.789645\pi\)
\(278\) 6.69264e10 0.672042
\(279\) 4.14543e10 0.409591
\(280\) −3.51547e11 −3.41801
\(281\) 1.50279e11 1.43787 0.718934 0.695078i \(-0.244630\pi\)
0.718934 + 0.695078i \(0.244630\pi\)
\(282\) 4.02849e10 0.379333
\(283\) 4.34423e10 0.402601 0.201300 0.979530i \(-0.435483\pi\)
0.201300 + 0.979530i \(0.435483\pi\)
\(284\) 2.87430e11 2.62180
\(285\) −3.59262e10 −0.322560
\(286\) 7.03921e10 0.622123
\(287\) 3.54029e9 0.0308014
\(288\) −2.56209e10 −0.219446
\(289\) 1.47043e11 1.23995
\(290\) −5.97519e11 −4.96090
\(291\) 6.13479e10 0.501512
\(292\) −2.92512e11 −2.35462
\(293\) 5.89544e10 0.467317 0.233659 0.972319i \(-0.424930\pi\)
0.233659 + 0.972319i \(0.424930\pi\)
\(294\) 1.08940e11 0.850400
\(295\) 3.25315e10 0.250095
\(296\) −1.94257e11 −1.47083
\(297\) −1.57557e10 −0.117499
\(298\) −1.10863e11 −0.814353
\(299\) −1.63258e11 −1.18128
\(300\) 3.87413e11 2.76140
\(301\) −6.99268e10 −0.491015
\(302\) −4.20912e11 −2.91179
\(303\) 8.43684e10 0.575027
\(304\) 1.65791e10 0.111334
\(305\) −4.55947e10 −0.301693
\(306\) 1.27525e11 0.831476
\(307\) 7.67544e10 0.493152 0.246576 0.969123i \(-0.420694\pi\)
0.246576 + 0.969123i \(0.420694\pi\)
\(308\) −2.35284e11 −1.48975
\(309\) 8.29483e10 0.517600
\(310\) −6.39709e11 −3.93419
\(311\) 6.02515e10 0.365213 0.182607 0.983186i \(-0.441547\pi\)
0.182607 + 0.983186i \(0.441547\pi\)
\(312\) −7.65904e10 −0.457593
\(313\) −1.71527e11 −1.01015 −0.505073 0.863077i \(-0.668534\pi\)
−0.505073 + 0.863077i \(0.668534\pi\)
\(314\) 5.02622e11 2.91782
\(315\) −1.53575e11 −0.878865
\(316\) −4.97260e11 −2.80538
\(317\) 2.11191e11 1.17465 0.587324 0.809352i \(-0.300181\pi\)
0.587324 + 0.809352i \(0.300181\pi\)
\(318\) −1.57842e11 −0.865567
\(319\) −1.74964e11 −0.946001
\(320\) 5.33316e11 2.84321
\(321\) 1.29255e11 0.679477
\(322\) 8.52627e11 4.41985
\(323\) 8.51470e10 0.435269
\(324\) 3.91829e10 0.197535
\(325\) −3.30817e11 −1.64480
\(326\) 6.32062e9 0.0309942
\(327\) 1.40017e10 0.0677200
\(328\) 6.09845e9 0.0290929
\(329\) 1.14980e11 0.541056
\(330\) 2.43136e11 1.12859
\(331\) −2.30634e10 −0.105608 −0.0528041 0.998605i \(-0.516816\pi\)
−0.0528041 + 0.998605i \(0.516816\pi\)
\(332\) 1.85430e11 0.837641
\(333\) −8.48618e10 −0.378193
\(334\) 5.83249e11 2.56445
\(335\) −6.54252e11 −2.83820
\(336\) 7.08710e10 0.303349
\(337\) 4.02987e11 1.70199 0.850994 0.525175i \(-0.176000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(338\) −2.50439e11 −1.04370
\(339\) −2.09146e11 −0.860104
\(340\) −1.25948e12 −5.11137
\(341\) −1.87319e11 −0.750216
\(342\) 4.08778e10 0.161573
\(343\) −4.08987e10 −0.159546
\(344\) −1.20455e11 −0.463779
\(345\) −5.63898e11 −2.14296
\(346\) −7.12663e11 −2.67326
\(347\) −3.14698e11 −1.16523 −0.582615 0.812748i \(-0.697971\pi\)
−0.582615 + 0.812748i \(0.697971\pi\)
\(348\) 4.35121e11 1.59039
\(349\) 1.07454e11 0.387711 0.193856 0.981030i \(-0.437901\pi\)
0.193856 + 0.981030i \(0.437901\pi\)
\(350\) 1.72772e12 6.15412
\(351\) −3.34588e10 −0.117660
\(352\) 1.15773e11 0.401943
\(353\) 1.24803e11 0.427800 0.213900 0.976856i \(-0.431383\pi\)
0.213900 + 0.976856i \(0.431383\pi\)
\(354\) −3.70152e10 −0.125275
\(355\) −8.47757e11 −2.83298
\(356\) 2.63891e11 0.870763
\(357\) 3.63980e11 1.18596
\(358\) 2.98567e11 0.960656
\(359\) 2.55234e11 0.810988 0.405494 0.914098i \(-0.367100\pi\)
0.405494 + 0.914098i \(0.367100\pi\)
\(360\) −2.64546e11 −0.830117
\(361\) −2.95394e11 −0.915418
\(362\) −3.64713e11 −1.11625
\(363\) −1.19799e11 −0.362137
\(364\) −4.99650e11 −1.49180
\(365\) 8.62745e11 2.54428
\(366\) 5.18788e10 0.151121
\(367\) −4.01666e11 −1.15576 −0.577880 0.816122i \(-0.696120\pi\)
−0.577880 + 0.816122i \(0.696120\pi\)
\(368\) 2.60225e11 0.739664
\(369\) 2.66413e9 0.00748060
\(370\) 1.30956e12 3.63260
\(371\) −4.50510e11 −1.23459
\(372\) 4.65845e11 1.26124
\(373\) −2.60275e11 −0.696214 −0.348107 0.937455i \(-0.613175\pi\)
−0.348107 + 0.937455i \(0.613175\pi\)
\(374\) −5.76246e11 −1.52295
\(375\) −7.17923e11 −1.87472
\(376\) 1.98063e11 0.511045
\(377\) −3.71555e11 −0.947300
\(378\) 1.74741e11 0.440233
\(379\) 1.10582e11 0.275301 0.137651 0.990481i \(-0.456045\pi\)
0.137651 + 0.990481i \(0.456045\pi\)
\(380\) −4.03723e11 −0.993248
\(381\) −1.16682e11 −0.283687
\(382\) −3.14723e11 −0.756211
\(383\) −1.02360e11 −0.243072 −0.121536 0.992587i \(-0.538782\pi\)
−0.121536 + 0.992587i \(0.538782\pi\)
\(384\) −4.44870e11 −1.04410
\(385\) 6.93955e11 1.60975
\(386\) −5.54928e11 −1.27231
\(387\) −5.26211e10 −0.119251
\(388\) 6.89401e11 1.54429
\(389\) 4.50698e11 0.997958 0.498979 0.866614i \(-0.333708\pi\)
0.498979 + 0.866614i \(0.333708\pi\)
\(390\) 5.16325e11 1.13014
\(391\) 1.33647e12 2.89176
\(392\) 5.35610e11 1.14567
\(393\) −8.01275e10 −0.169440
\(394\) −7.30487e11 −1.52714
\(395\) 1.46664e12 3.03135
\(396\) −1.77055e11 −0.361810
\(397\) −2.59155e10 −0.0523604 −0.0261802 0.999657i \(-0.508334\pi\)
−0.0261802 + 0.999657i \(0.508334\pi\)
\(398\) −1.05204e12 −2.10164
\(399\) 1.16673e11 0.230457
\(400\) 5.27306e11 1.02989
\(401\) 5.09445e10 0.0983893 0.0491947 0.998789i \(-0.484335\pi\)
0.0491947 + 0.998789i \(0.484335\pi\)
\(402\) 7.44424e11 1.42168
\(403\) −3.97791e11 −0.751246
\(404\) 9.48095e11 1.77066
\(405\) −1.15568e11 −0.213446
\(406\) 1.94048e12 3.54439
\(407\) 3.83463e11 0.692706
\(408\) 6.26987e11 1.12018
\(409\) 3.18061e11 0.562025 0.281013 0.959704i \(-0.409330\pi\)
0.281013 + 0.959704i \(0.409330\pi\)
\(410\) −4.11120e10 −0.0718524
\(411\) 3.47702e11 0.601061
\(412\) 9.32136e11 1.59383
\(413\) −1.05648e11 −0.178684
\(414\) 6.41617e11 1.07343
\(415\) −5.46914e11 −0.905112
\(416\) 2.45855e11 0.402494
\(417\) 1.43746e11 0.232800
\(418\) −1.84714e11 −0.295941
\(419\) 3.49468e11 0.553916 0.276958 0.960882i \(-0.410674\pi\)
0.276958 + 0.960882i \(0.410674\pi\)
\(420\) −1.72581e12 −2.70626
\(421\) 4.66258e11 0.723364 0.361682 0.932302i \(-0.382203\pi\)
0.361682 + 0.932302i \(0.382203\pi\)
\(422\) −7.38278e11 −1.13322
\(423\) 8.65247e10 0.131404
\(424\) −7.76042e11 −1.16611
\(425\) 2.70814e12 4.02644
\(426\) 9.64599e11 1.41907
\(427\) 1.48071e11 0.215549
\(428\) 1.45251e12 2.09229
\(429\) 1.51190e11 0.215508
\(430\) 8.12032e11 1.14542
\(431\) 2.23331e11 0.311746 0.155873 0.987777i \(-0.450181\pi\)
0.155873 + 0.987777i \(0.450181\pi\)
\(432\) 5.33317e10 0.0736730
\(433\) 2.87584e11 0.393160 0.196580 0.980488i \(-0.437016\pi\)
0.196580 + 0.980488i \(0.437016\pi\)
\(434\) 2.07749e12 2.81084
\(435\) −1.28336e12 −1.71849
\(436\) 1.57345e11 0.208528
\(437\) 4.28400e11 0.561931
\(438\) −9.81653e11 −1.27445
\(439\) 3.84850e9 0.00494539 0.00247270 0.999997i \(-0.499213\pi\)
0.00247270 + 0.999997i \(0.499213\pi\)
\(440\) 1.19540e12 1.52046
\(441\) 2.33983e11 0.294585
\(442\) −1.22372e12 −1.52504
\(443\) −4.55745e11 −0.562218 −0.281109 0.959676i \(-0.590702\pi\)
−0.281109 + 0.959676i \(0.590702\pi\)
\(444\) −9.53640e11 −1.16456
\(445\) −7.78331e11 −0.940901
\(446\) 9.98031e10 0.119437
\(447\) −2.38114e11 −0.282098
\(448\) −1.73197e12 −2.03138
\(449\) −2.12096e11 −0.246277 −0.123139 0.992389i \(-0.539296\pi\)
−0.123139 + 0.992389i \(0.539296\pi\)
\(450\) 1.30014e12 1.49463
\(451\) −1.20383e10 −0.0137016
\(452\) −2.35029e12 −2.64849
\(453\) −9.04045e11 −1.00867
\(454\) −5.24904e11 −0.579867
\(455\) 1.47369e12 1.61196
\(456\) 2.00978e11 0.217675
\(457\) 4.71276e11 0.505420 0.252710 0.967542i \(-0.418678\pi\)
0.252710 + 0.967542i \(0.418678\pi\)
\(458\) 9.02887e11 0.958823
\(459\) 2.73901e11 0.288030
\(460\) −6.33684e12 −6.59876
\(461\) 4.29257e11 0.442653 0.221326 0.975200i \(-0.428961\pi\)
0.221326 + 0.975200i \(0.428961\pi\)
\(462\) −7.89599e11 −0.806339
\(463\) −1.66714e12 −1.68600 −0.843001 0.537912i \(-0.819213\pi\)
−0.843001 + 0.537912i \(0.819213\pi\)
\(464\) 5.92241e11 0.593154
\(465\) −1.37398e12 −1.36283
\(466\) −7.32662e11 −0.719725
\(467\) −1.03665e12 −1.00857 −0.504286 0.863537i \(-0.668244\pi\)
−0.504286 + 0.863537i \(0.668244\pi\)
\(468\) −3.75995e11 −0.362306
\(469\) 2.12472e12 2.02780
\(470\) −1.33522e12 −1.26216
\(471\) 1.07954e12 1.01075
\(472\) −1.81988e11 −0.168773
\(473\) 2.37778e11 0.218422
\(474\) −1.66878e12 −1.51843
\(475\) 8.68086e11 0.782422
\(476\) 4.09025e12 3.65190
\(477\) −3.39017e11 −0.299839
\(478\) −1.37947e12 −1.20861
\(479\) 8.90476e10 0.0772881 0.0386440 0.999253i \(-0.487696\pi\)
0.0386440 + 0.999253i \(0.487696\pi\)
\(480\) 8.49192e11 0.730164
\(481\) 8.14325e11 0.693657
\(482\) 1.04082e12 0.878340
\(483\) 1.83129e12 1.53107
\(484\) −1.34625e12 −1.11512
\(485\) −2.03335e12 −1.66868
\(486\) 1.31496e11 0.106917
\(487\) 1.54005e12 1.24067 0.620334 0.784338i \(-0.286997\pi\)
0.620334 + 0.784338i \(0.286997\pi\)
\(488\) 2.55066e11 0.203593
\(489\) 1.35756e10 0.0107366
\(490\) −3.61075e12 −2.82954
\(491\) −1.44485e12 −1.12191 −0.560953 0.827848i \(-0.689565\pi\)
−0.560953 + 0.827848i \(0.689565\pi\)
\(492\) 2.99383e10 0.0230348
\(493\) 3.04164e12 2.31898
\(494\) −3.92259e11 −0.296347
\(495\) 5.22213e11 0.390953
\(496\) 6.34059e11 0.470395
\(497\) 2.75314e12 2.02406
\(498\) 6.22292e11 0.453380
\(499\) 2.36049e12 1.70431 0.852157 0.523286i \(-0.175294\pi\)
0.852157 + 0.523286i \(0.175294\pi\)
\(500\) −8.06770e12 −5.77277
\(501\) 1.25271e12 0.888346
\(502\) −2.89676e12 −2.03585
\(503\) 1.34281e12 0.935315 0.467658 0.883910i \(-0.345098\pi\)
0.467658 + 0.883910i \(0.345098\pi\)
\(504\) 8.59128e11 0.593089
\(505\) −2.79635e12 −1.91329
\(506\) −2.89926e12 −1.96612
\(507\) −5.37897e11 −0.361546
\(508\) −1.31122e12 −0.873550
\(509\) −1.80032e11 −0.118883 −0.0594414 0.998232i \(-0.518932\pi\)
−0.0594414 + 0.998232i \(0.518932\pi\)
\(510\) −4.22676e12 −2.76657
\(511\) −2.80181e12 −1.81780
\(512\) −1.16356e12 −0.748295
\(513\) 8.77982e10 0.0559702
\(514\) 9.08970e11 0.574401
\(515\) −2.74928e12 −1.72221
\(516\) −5.91333e11 −0.367205
\(517\) −3.90977e11 −0.240682
\(518\) −4.25288e12 −2.59537
\(519\) −1.53067e12 −0.926039
\(520\) 2.53855e12 1.52255
\(521\) −1.65240e11 −0.0982529 −0.0491265 0.998793i \(-0.515644\pi\)
−0.0491265 + 0.998793i \(0.515644\pi\)
\(522\) 1.46024e12 0.860811
\(523\) −2.42593e12 −1.41782 −0.708908 0.705301i \(-0.750812\pi\)
−0.708908 + 0.705301i \(0.750812\pi\)
\(524\) −9.00437e11 −0.521750
\(525\) 3.71083e12 2.13184
\(526\) 3.59898e12 2.04995
\(527\) 3.25641e12 1.83904
\(528\) −2.40989e11 −0.134941
\(529\) 4.92301e12 2.73325
\(530\) 5.23160e12 2.88000
\(531\) −7.95020e10 −0.0433963
\(532\) 1.31111e12 0.709640
\(533\) −2.55647e10 −0.0137204
\(534\) 8.85604e11 0.471307
\(535\) −4.28409e12 −2.26082
\(536\) 3.66001e12 1.91532
\(537\) 6.41268e11 0.332779
\(538\) 3.28539e12 1.69070
\(539\) −1.05729e12 −0.539568
\(540\) −1.29870e12 −0.657259
\(541\) 4.55520e11 0.228623 0.114311 0.993445i \(-0.463534\pi\)
0.114311 + 0.993445i \(0.463534\pi\)
\(542\) −4.87993e12 −2.42894
\(543\) −7.83338e11 −0.386678
\(544\) −2.01263e12 −0.985301
\(545\) −4.64081e11 −0.225325
\(546\) −1.67680e12 −0.807446
\(547\) −9.68091e11 −0.462352 −0.231176 0.972912i \(-0.574257\pi\)
−0.231176 + 0.972912i \(0.574257\pi\)
\(548\) 3.90732e12 1.85083
\(549\) 1.11426e11 0.0523495
\(550\) −5.87490e12 −2.73759
\(551\) 9.74986e11 0.450626
\(552\) 3.15456e12 1.44615
\(553\) −4.76299e12 −2.16579
\(554\) −5.83461e12 −2.63159
\(555\) 2.81270e12 1.25836
\(556\) 1.61535e12 0.716855
\(557\) 1.60833e12 0.707991 0.353996 0.935247i \(-0.384823\pi\)
0.353996 + 0.935247i \(0.384823\pi\)
\(558\) 1.56335e12 0.682657
\(559\) 5.04947e11 0.218722
\(560\) −2.34898e12 −1.00933
\(561\) −1.23767e12 −0.527561
\(562\) 5.66740e12 2.39646
\(563\) 2.03919e12 0.855403 0.427702 0.903920i \(-0.359323\pi\)
0.427702 + 0.903920i \(0.359323\pi\)
\(564\) 9.72327e11 0.404628
\(565\) 6.93204e12 2.86183
\(566\) 1.63833e12 0.671006
\(567\) 3.75313e11 0.152500
\(568\) 4.74252e12 1.91180
\(569\) −3.82797e12 −1.53096 −0.765479 0.643461i \(-0.777498\pi\)
−0.765479 + 0.643461i \(0.777498\pi\)
\(570\) −1.35487e12 −0.537603
\(571\) −3.15952e12 −1.24382 −0.621912 0.783087i \(-0.713644\pi\)
−0.621912 + 0.783087i \(0.713644\pi\)
\(572\) 1.69900e12 0.663608
\(573\) −6.75968e11 −0.261957
\(574\) 1.33514e11 0.0513360
\(575\) 1.36255e13 5.19812
\(576\) −1.30334e12 −0.493352
\(577\) 3.80747e11 0.143003 0.0715015 0.997440i \(-0.477221\pi\)
0.0715015 + 0.997440i \(0.477221\pi\)
\(578\) 5.54538e12 2.06660
\(579\) −1.19189e12 −0.440739
\(580\) −1.44219e13 −5.29170
\(581\) 1.77613e12 0.646671
\(582\) 2.31359e12 0.835860
\(583\) 1.53191e12 0.549192
\(584\) −4.82637e12 −1.71697
\(585\) 1.10898e12 0.391490
\(586\) 2.22332e12 0.778867
\(587\) −1.87272e12 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(588\) 2.62940e12 0.907107
\(589\) 1.04383e12 0.357364
\(590\) 1.22685e12 0.416828
\(591\) −1.56896e12 −0.529014
\(592\) −1.29799e12 −0.434335
\(593\) −2.65121e12 −0.880436 −0.440218 0.897891i \(-0.645099\pi\)
−0.440218 + 0.897891i \(0.645099\pi\)
\(594\) −5.94187e11 −0.195832
\(595\) −1.20639e13 −3.94605
\(596\) −2.67582e12 −0.868657
\(597\) −2.25959e12 −0.728024
\(598\) −6.15689e12 −1.96882
\(599\) 1.09816e12 0.348533 0.174267 0.984698i \(-0.444245\pi\)
0.174267 + 0.984698i \(0.444245\pi\)
\(600\) 6.39222e12 2.01359
\(601\) 3.22983e12 1.00982 0.504911 0.863171i \(-0.331525\pi\)
0.504911 + 0.863171i \(0.331525\pi\)
\(602\) −2.63712e12 −0.818363
\(603\) 1.59889e12 0.492482
\(604\) −1.01593e13 −3.10596
\(605\) 3.97068e12 1.20494
\(606\) 3.18176e12 0.958385
\(607\) 5.65303e12 1.69018 0.845089 0.534626i \(-0.179548\pi\)
0.845089 + 0.534626i \(0.179548\pi\)
\(608\) −6.45141e11 −0.191465
\(609\) 4.16780e12 1.22780
\(610\) −1.71950e12 −0.502825
\(611\) −8.30282e11 −0.241013
\(612\) 3.07798e12 0.886921
\(613\) 6.24408e12 1.78606 0.893031 0.449996i \(-0.148574\pi\)
0.893031 + 0.449996i \(0.148574\pi\)
\(614\) 2.89461e12 0.821926
\(615\) −8.83012e10 −0.0248902
\(616\) −3.88212e12 −1.08632
\(617\) −2.50075e12 −0.694683 −0.347341 0.937739i \(-0.612916\pi\)
−0.347341 + 0.937739i \(0.612916\pi\)
\(618\) 3.12820e12 0.862672
\(619\) −4.57288e12 −1.25194 −0.625968 0.779849i \(-0.715296\pi\)
−0.625968 + 0.779849i \(0.715296\pi\)
\(620\) −1.54402e13 −4.19653
\(621\) 1.37808e12 0.371845
\(622\) 2.27224e12 0.608693
\(623\) 2.52767e12 0.672241
\(624\) −5.11765e11 −0.135126
\(625\) 1.35325e13 3.54745
\(626\) −6.46875e12 −1.68359
\(627\) −3.96732e11 −0.102516
\(628\) 1.21314e13 3.11238
\(629\) −6.66625e12 −1.69806
\(630\) −5.79171e12 −1.46479
\(631\) −7.23797e12 −1.81754 −0.908771 0.417295i \(-0.862978\pi\)
−0.908771 + 0.417295i \(0.862978\pi\)
\(632\) −8.20466e12 −2.04566
\(633\) −1.58569e12 −0.392556
\(634\) 7.96455e12 1.95776
\(635\) 3.86735e12 0.943913
\(636\) −3.80972e12 −0.923286
\(637\) −2.24528e12 −0.540309
\(638\) −6.59837e12 −1.57668
\(639\) 2.07179e12 0.491576
\(640\) 1.47450e13 3.47404
\(641\) −5.23968e12 −1.22587 −0.612934 0.790134i \(-0.710011\pi\)
−0.612934 + 0.790134i \(0.710011\pi\)
\(642\) 4.87454e12 1.13247
\(643\) 3.47830e11 0.0802450 0.0401225 0.999195i \(-0.487225\pi\)
0.0401225 + 0.999195i \(0.487225\pi\)
\(644\) 2.05792e13 4.71458
\(645\) 1.74410e12 0.396783
\(646\) 3.21112e12 0.725454
\(647\) −6.78788e11 −0.152288 −0.0761439 0.997097i \(-0.524261\pi\)
−0.0761439 + 0.997097i \(0.524261\pi\)
\(648\) 6.46509e11 0.144041
\(649\) 3.59244e11 0.0794856
\(650\) −1.24760e13 −2.74135
\(651\) 4.46209e12 0.973696
\(652\) 1.52556e11 0.0330610
\(653\) −4.84386e12 −1.04252 −0.521258 0.853399i \(-0.674537\pi\)
−0.521258 + 0.853399i \(0.674537\pi\)
\(654\) 5.28042e11 0.112868
\(655\) 2.65578e12 0.563777
\(656\) 4.07489e10 0.00859109
\(657\) −2.10841e12 −0.441481
\(658\) 4.33621e12 0.901766
\(659\) −7.06815e12 −1.45989 −0.729947 0.683504i \(-0.760455\pi\)
−0.729947 + 0.683504i \(0.760455\pi\)
\(660\) 5.86840e12 1.20385
\(661\) 2.76923e12 0.564225 0.282112 0.959381i \(-0.408965\pi\)
0.282112 + 0.959381i \(0.408965\pi\)
\(662\) −8.69781e11 −0.176015
\(663\) −2.62833e12 −0.528286
\(664\) 3.05954e12 0.610802
\(665\) −3.86705e12 −0.766801
\(666\) −3.20036e12 −0.630326
\(667\) 1.53034e13 2.99379
\(668\) 1.40775e13 2.73546
\(669\) 2.14359e11 0.0413737
\(670\) −2.46736e13 −4.73037
\(671\) −5.03500e11 −0.0958844
\(672\) −2.75780e12 −0.521676
\(673\) −5.79571e12 −1.08903 −0.544513 0.838752i \(-0.683286\pi\)
−0.544513 + 0.838752i \(0.683286\pi\)
\(674\) 1.51977e13 2.83667
\(675\) 2.79246e12 0.517750
\(676\) −6.04465e12 −1.11330
\(677\) −4.41498e12 −0.807755 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(678\) −7.88745e12 −1.43352
\(679\) 6.60341e12 1.19221
\(680\) −2.07812e13 −3.72717
\(681\) −1.12740e12 −0.200871
\(682\) −7.06428e12 −1.25037
\(683\) −2.14581e12 −0.377310 −0.188655 0.982043i \(-0.560413\pi\)
−0.188655 + 0.982043i \(0.560413\pi\)
\(684\) 9.86637e11 0.172347
\(685\) −1.15244e13 −1.99991
\(686\) −1.54240e12 −0.265912
\(687\) 1.93924e12 0.332144
\(688\) −8.04861e11 −0.136953
\(689\) 3.25317e12 0.549946
\(690\) −2.12661e13 −3.57163
\(691\) −1.21012e12 −0.201920 −0.100960 0.994890i \(-0.532191\pi\)
−0.100960 + 0.994890i \(0.532191\pi\)
\(692\) −1.72010e13 −2.85152
\(693\) −1.69592e12 −0.279322
\(694\) −1.18681e13 −1.94207
\(695\) −4.76439e12 −0.774597
\(696\) 7.17939e12 1.15970
\(697\) 2.09278e11 0.0335874
\(698\) 4.05237e12 0.646190
\(699\) −1.57363e12 −0.249318
\(700\) 4.17006e13 6.56450
\(701\) 4.58684e12 0.717435 0.358717 0.933446i \(-0.383214\pi\)
0.358717 + 0.933446i \(0.383214\pi\)
\(702\) −1.26182e12 −0.196101
\(703\) −2.13684e12 −0.329969
\(704\) 5.88938e12 0.903634
\(705\) −2.86782e12 −0.437221
\(706\) 4.70667e12 0.713005
\(707\) 9.08131e12 1.36698
\(708\) −8.93409e11 −0.133629
\(709\) −1.21012e13 −1.79854 −0.899271 0.437393i \(-0.855902\pi\)
−0.899271 + 0.437393i \(0.855902\pi\)
\(710\) −3.19711e13 −4.72167
\(711\) −3.58423e12 −0.525997
\(712\) 4.35414e12 0.634954
\(713\) 1.63839e13 2.37419
\(714\) 1.37266e13 1.97662
\(715\) −5.01110e12 −0.717061
\(716\) 7.20629e12 1.02472
\(717\) −2.96285e12 −0.418671
\(718\) 9.62556e12 1.35166
\(719\) 3.23141e12 0.450933 0.225467 0.974251i \(-0.427609\pi\)
0.225467 + 0.974251i \(0.427609\pi\)
\(720\) −1.76765e12 −0.245132
\(721\) 8.92844e12 1.23046
\(722\) −1.11401e13 −1.52571
\(723\) 2.23549e12 0.304264
\(724\) −8.80281e12 −1.19069
\(725\) 3.10099e13 4.16850
\(726\) −4.51793e12 −0.603567
\(727\) 1.39712e13 1.85494 0.927468 0.373902i \(-0.121980\pi\)
0.927468 + 0.373902i \(0.121980\pi\)
\(728\) −8.24409e12 −1.08781
\(729\) 2.82430e11 0.0370370
\(730\) 3.25364e13 4.24049
\(731\) −4.13361e12 −0.535428
\(732\) 1.25216e12 0.161198
\(733\) −6.76655e12 −0.865764 −0.432882 0.901451i \(-0.642503\pi\)
−0.432882 + 0.901451i \(0.642503\pi\)
\(734\) −1.51479e13 −1.92628
\(735\) −7.75525e12 −0.980173
\(736\) −1.01261e13 −1.27202
\(737\) −7.22487e12 −0.902041
\(738\) 1.00471e11 0.0124678
\(739\) 1.34500e13 1.65891 0.829456 0.558572i \(-0.188650\pi\)
0.829456 + 0.558572i \(0.188650\pi\)
\(740\) 3.16079e13 3.87483
\(741\) −8.42502e11 −0.102657
\(742\) −1.69899e13 −2.05766
\(743\) −1.48305e13 −1.78528 −0.892641 0.450769i \(-0.851150\pi\)
−0.892641 + 0.450769i \(0.851150\pi\)
\(744\) 7.68632e12 0.919688
\(745\) 7.89216e12 0.938626
\(746\) −9.81565e12 −1.16036
\(747\) 1.33657e12 0.157054
\(748\) −1.39084e13 −1.62450
\(749\) 1.39128e13 1.61528
\(750\) −2.70747e13 −3.12456
\(751\) −2.98445e12 −0.342362 −0.171181 0.985240i \(-0.554758\pi\)
−0.171181 + 0.985240i \(0.554758\pi\)
\(752\) 1.32343e12 0.150911
\(753\) −6.22173e12 −0.705235
\(754\) −1.40123e13 −1.57884
\(755\) 2.99641e13 3.35614
\(756\) 4.21760e12 0.469588
\(757\) 7.48619e12 0.828570 0.414285 0.910147i \(-0.364032\pi\)
0.414285 + 0.910147i \(0.364032\pi\)
\(758\) 4.17034e12 0.458838
\(759\) −6.22710e12 −0.681079
\(760\) −6.66133e12 −0.724269
\(761\) −6.74085e12 −0.728590 −0.364295 0.931284i \(-0.618690\pi\)
−0.364295 + 0.931284i \(0.618690\pi\)
\(762\) −4.40037e12 −0.472816
\(763\) 1.50713e12 0.160987
\(764\) −7.59624e12 −0.806637
\(765\) −9.07832e12 −0.958361
\(766\) −3.86026e12 −0.405123
\(767\) 7.62893e11 0.0795947
\(768\) −8.53883e12 −0.885672
\(769\) −1.61315e13 −1.66343 −0.831716 0.555202i \(-0.812641\pi\)
−0.831716 + 0.555202i \(0.812641\pi\)
\(770\) 2.61709e13 2.68293
\(771\) 1.95231e12 0.198977
\(772\) −1.33939e13 −1.35715
\(773\) −5.10799e12 −0.514568 −0.257284 0.966336i \(-0.582828\pi\)
−0.257284 + 0.966336i \(0.582828\pi\)
\(774\) −1.98448e12 −0.198753
\(775\) 3.31995e13 3.30578
\(776\) 1.13749e13 1.12609
\(777\) −9.13442e12 −0.899055
\(778\) 1.69970e13 1.66328
\(779\) 6.70835e10 0.00652675
\(780\) 1.24622e13 1.20550
\(781\) −9.36173e12 −0.900382
\(782\) 5.04017e13 4.81964
\(783\) 3.13634e12 0.298192
\(784\) 3.57886e12 0.338316
\(785\) −3.57809e13 −3.36308
\(786\) −3.02182e12 −0.282401
\(787\) 3.10210e12 0.288250 0.144125 0.989559i \(-0.453963\pi\)
0.144125 + 0.989559i \(0.453963\pi\)
\(788\) −1.76312e13 −1.62898
\(789\) 7.72997e12 0.710119
\(790\) 5.53107e13 5.05228
\(791\) −2.25122e13 −2.04467
\(792\) −2.92136e12 −0.263829
\(793\) −1.06924e12 −0.0960160
\(794\) −9.77343e11 −0.0872679
\(795\) 1.12365e13 0.997655
\(796\) −2.53923e13 −2.24178
\(797\) −6.73763e12 −0.591486 −0.295743 0.955268i \(-0.595567\pi\)
−0.295743 + 0.955268i \(0.595567\pi\)
\(798\) 4.40003e12 0.384098
\(799\) 6.79688e12 0.589996
\(800\) −2.05190e13 −1.77114
\(801\) 1.90212e12 0.163264
\(802\) 1.92125e12 0.163983
\(803\) 9.52725e12 0.808626
\(804\) 1.79676e13 1.51649
\(805\) −6.06972e13 −5.09433
\(806\) −1.50017e13 −1.25209
\(807\) 7.05644e12 0.585672
\(808\) 1.56433e13 1.29115
\(809\) −3.96895e12 −0.325767 −0.162884 0.986645i \(-0.552080\pi\)
−0.162884 + 0.986645i \(0.552080\pi\)
\(810\) −4.35836e12 −0.355747
\(811\) 4.77001e12 0.387191 0.193596 0.981081i \(-0.437985\pi\)
0.193596 + 0.981081i \(0.437985\pi\)
\(812\) 4.68359e13 3.78074
\(813\) −1.04812e13 −0.841404
\(814\) 1.44614e13 1.15452
\(815\) −4.49955e11 −0.0357240
\(816\) 4.18943e12 0.330787
\(817\) −1.32501e12 −0.104045
\(818\) 1.19949e13 0.936715
\(819\) −3.60146e12 −0.279706
\(820\) −9.92290e11 −0.0766437
\(821\) 3.01276e12 0.231430 0.115715 0.993282i \(-0.463084\pi\)
0.115715 + 0.993282i \(0.463084\pi\)
\(822\) 1.31127e13 1.00178
\(823\) −9.94134e12 −0.755346 −0.377673 0.925939i \(-0.623276\pi\)
−0.377673 + 0.925939i \(0.623276\pi\)
\(824\) 1.53800e13 1.16221
\(825\) −1.26182e13 −0.948322
\(826\) −3.98427e12 −0.297809
\(827\) −1.66093e13 −1.23475 −0.617373 0.786671i \(-0.711803\pi\)
−0.617373 + 0.786671i \(0.711803\pi\)
\(828\) 1.54862e13 1.14501
\(829\) −8.34298e12 −0.613516 −0.306758 0.951788i \(-0.599244\pi\)
−0.306758 + 0.951788i \(0.599244\pi\)
\(830\) −2.06255e13 −1.50853
\(831\) −1.25317e13 −0.911602
\(832\) 1.25067e13 0.904875
\(833\) 1.83803e13 1.32267
\(834\) 5.42104e12 0.388003
\(835\) −4.15206e13 −2.95579
\(836\) −4.45830e12 −0.315675
\(837\) 3.35780e12 0.236478
\(838\) 1.31793e13 0.923200
\(839\) 2.62298e13 1.82754 0.913770 0.406233i \(-0.133158\pi\)
0.913770 + 0.406233i \(0.133158\pi\)
\(840\) −2.84753e13 −1.97339
\(841\) 2.03215e13 1.40079
\(842\) 1.75838e13 1.20561
\(843\) 1.21726e13 0.830153
\(844\) −1.78193e13 −1.20879
\(845\) 1.78283e13 1.20297
\(846\) 3.26307e12 0.219008
\(847\) −1.28950e13 −0.860887
\(848\) −5.18539e12 −0.344350
\(849\) 3.51883e12 0.232442
\(850\) 1.02131e14 6.71078
\(851\) −3.35399e13 −2.19219
\(852\) 2.32818e13 1.51370
\(853\) −1.91183e13 −1.23646 −0.618229 0.785998i \(-0.712150\pi\)
−0.618229 + 0.785998i \(0.712150\pi\)
\(854\) 5.58416e12 0.359251
\(855\) −2.91003e12 −0.186230
\(856\) 2.39660e13 1.52568
\(857\) 2.55437e13 1.61760 0.808799 0.588086i \(-0.200118\pi\)
0.808799 + 0.588086i \(0.200118\pi\)
\(858\) 5.70176e12 0.359183
\(859\) −1.63534e13 −1.02480 −0.512398 0.858748i \(-0.671243\pi\)
−0.512398 + 0.858748i \(0.671243\pi\)
\(860\) 1.95994e13 1.22180
\(861\) 2.86763e11 0.0177832
\(862\) 8.42238e12 0.519580
\(863\) 4.89259e12 0.300255 0.150127 0.988667i \(-0.452032\pi\)
0.150127 + 0.988667i \(0.452032\pi\)
\(864\) −2.07529e12 −0.126697
\(865\) 5.07334e13 3.08121
\(866\) 1.08455e13 0.655271
\(867\) 1.19105e13 0.715885
\(868\) 5.01430e13 2.99827
\(869\) 1.61960e13 0.963427
\(870\) −4.83990e13 −2.86418
\(871\) −1.53428e13 −0.903280
\(872\) 2.59616e12 0.152057
\(873\) 4.96918e12 0.289548
\(874\) 1.61561e13 0.936558
\(875\) −7.72762e13 −4.45666
\(876\) −2.36934e13 −1.35944
\(877\) −1.26114e13 −0.719887 −0.359943 0.932974i \(-0.617204\pi\)
−0.359943 + 0.932974i \(0.617204\pi\)
\(878\) 1.45137e11 0.00824238
\(879\) 4.77530e12 0.269806
\(880\) 7.98745e12 0.448990
\(881\) 3.04432e13 1.70255 0.851273 0.524722i \(-0.175831\pi\)
0.851273 + 0.524722i \(0.175831\pi\)
\(882\) 8.82411e12 0.490978
\(883\) −8.12469e12 −0.449763 −0.224881 0.974386i \(-0.572199\pi\)
−0.224881 + 0.974386i \(0.572199\pi\)
\(884\) −2.95360e13 −1.62673
\(885\) 2.63505e12 0.144393
\(886\) −1.71873e13 −0.937037
\(887\) 1.35980e13 0.737596 0.368798 0.929510i \(-0.379769\pi\)
0.368798 + 0.929510i \(0.379769\pi\)
\(888\) −1.57348e13 −0.849187
\(889\) −1.25595e13 −0.674393
\(890\) −2.93529e13 −1.56818
\(891\) −1.27621e12 −0.0678378
\(892\) 2.40888e12 0.127401
\(893\) 2.17872e12 0.114649
\(894\) −8.97989e12 −0.470167
\(895\) −2.12545e13 −1.10725
\(896\) −4.78853e13 −2.48208
\(897\) −1.32239e13 −0.682014
\(898\) −7.99871e12 −0.410465
\(899\) 3.72879e13 1.90392
\(900\) 3.13805e13 1.59429
\(901\) −2.66312e13 −1.34626
\(902\) −4.53998e11 −0.0228362
\(903\) −5.66407e12 −0.283487
\(904\) −3.87792e13 −1.93126
\(905\) 2.59633e13 1.28660
\(906\) −3.40939e13 −1.68112
\(907\) −1.34500e13 −0.659917 −0.329959 0.943995i \(-0.607035\pi\)
−0.329959 + 0.943995i \(0.607035\pi\)
\(908\) −1.26692e13 −0.618534
\(909\) 6.83384e12 0.331992
\(910\) 5.55766e13 2.68662
\(911\) −1.49411e13 −0.718702 −0.359351 0.933202i \(-0.617002\pi\)
−0.359351 + 0.933202i \(0.617002\pi\)
\(912\) 1.34291e12 0.0642790
\(913\) −6.03954e12 −0.287664
\(914\) 1.77730e13 0.842372
\(915\) −3.69317e12 −0.174182
\(916\) 2.17923e13 1.02276
\(917\) −8.62482e12 −0.402799
\(918\) 1.03295e13 0.480053
\(919\) 1.87777e13 0.868405 0.434203 0.900815i \(-0.357030\pi\)
0.434203 + 0.900815i \(0.357030\pi\)
\(920\) −1.04556e14 −4.81176
\(921\) 6.21711e12 0.284721
\(922\) 1.61884e13 0.737760
\(923\) −1.98806e13 −0.901618
\(924\) −1.90580e13 −0.860108
\(925\) −6.79633e13 −3.05237
\(926\) −6.28723e13 −2.81002
\(927\) 6.71881e12 0.298836
\(928\) −2.30458e13 −1.02006
\(929\) −1.45957e13 −0.642918 −0.321459 0.946923i \(-0.604173\pi\)
−0.321459 + 0.946923i \(0.604173\pi\)
\(930\) −5.18165e13 −2.27140
\(931\) 5.89175e12 0.257022
\(932\) −1.76837e13 −0.767719
\(933\) 4.88038e12 0.210856
\(934\) −3.90948e13 −1.68096
\(935\) 4.10220e13 1.75535
\(936\) −6.20383e12 −0.264191
\(937\) −2.50294e13 −1.06077 −0.530386 0.847757i \(-0.677953\pi\)
−0.530386 + 0.847757i \(0.677953\pi\)
\(938\) 8.01288e13 3.37968
\(939\) −1.38937e13 −0.583208
\(940\) −3.22273e13 −1.34632
\(941\) 3.34102e13 1.38907 0.694537 0.719457i \(-0.255609\pi\)
0.694537 + 0.719457i \(0.255609\pi\)
\(942\) 4.07124e13 1.68460
\(943\) 1.05294e12 0.0433612
\(944\) −1.21601e12 −0.0498384
\(945\) −1.24396e13 −0.507413
\(946\) 8.96723e12 0.364039
\(947\) −3.09383e13 −1.25003 −0.625016 0.780612i \(-0.714908\pi\)
−0.625016 + 0.780612i \(0.714908\pi\)
\(948\) −4.02780e13 −1.61969
\(949\) 2.02321e13 0.809736
\(950\) 3.27378e13 1.30405
\(951\) 1.71064e13 0.678183
\(952\) 6.74880e13 2.66294
\(953\) 8.22593e12 0.323048 0.161524 0.986869i \(-0.448359\pi\)
0.161524 + 0.986869i \(0.448359\pi\)
\(954\) −1.27852e13 −0.499735
\(955\) 2.24046e13 0.871611
\(956\) −3.32952e13 −1.28920
\(957\) −1.41721e13 −0.546174
\(958\) 3.35822e12 0.128814
\(959\) 3.74261e13 1.42887
\(960\) 4.31986e13 1.64153
\(961\) 1.34812e13 0.509885
\(962\) 3.07103e13 1.15610
\(963\) 1.04697e13 0.392296
\(964\) 2.51214e13 0.936910
\(965\) 3.95045e13 1.46647
\(966\) 6.90628e13 2.55180
\(967\) 4.11299e13 1.51265 0.756326 0.654195i \(-0.226993\pi\)
0.756326 + 0.654195i \(0.226993\pi\)
\(968\) −2.22128e13 −0.813136
\(969\) 6.89691e12 0.251303
\(970\) −7.66828e13 −2.78116
\(971\) 8.74724e12 0.315780 0.157890 0.987457i \(-0.449531\pi\)
0.157890 + 0.987457i \(0.449531\pi\)
\(972\) 3.17382e12 0.114047
\(973\) 1.54726e13 0.553422
\(974\) 5.80795e13 2.06779
\(975\) −2.67962e13 −0.949624
\(976\) 1.70431e12 0.0601207
\(977\) 1.00439e13 0.352676 0.176338 0.984330i \(-0.443575\pi\)
0.176338 + 0.984330i \(0.443575\pi\)
\(978\) 5.11970e11 0.0178945
\(979\) −8.59507e12 −0.299039
\(980\) −8.71501e13 −3.01822
\(981\) 1.13414e12 0.0390982
\(982\) −5.44891e13 −1.86986
\(983\) 5.44392e12 0.185961 0.0929803 0.995668i \(-0.470361\pi\)
0.0929803 + 0.995668i \(0.470361\pi\)
\(984\) 4.93974e11 0.0167968
\(985\) 5.20023e13 1.76019
\(986\) 1.14708e14 3.86499
\(987\) 9.31341e12 0.312379
\(988\) −9.46766e12 −0.316109
\(989\) −2.07974e13 −0.691235
\(990\) 1.96940e13 0.651593
\(991\) −5.35928e13 −1.76512 −0.882561 0.470197i \(-0.844183\pi\)
−0.882561 + 0.470197i \(0.844183\pi\)
\(992\) −2.46731e13 −0.808950
\(993\) −1.86814e12 −0.0609729
\(994\) 1.03828e14 3.37347
\(995\) 7.48931e13 2.42236
\(996\) 1.50198e13 0.483612
\(997\) −3.42583e12 −0.109809 −0.0549044 0.998492i \(-0.517485\pi\)
−0.0549044 + 0.998492i \(0.517485\pi\)
\(998\) 8.90203e13 2.84054
\(999\) −6.87381e12 −0.218350
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 177.10.a.d.1.19 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.19 22 1.1 even 1 trivial