Properties

Label 177.10.a.d.1.17
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 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +27000.3 q^{10} -17065.1 q^{11} +17061.8 q^{12} +177208. q^{13} +68293.3 q^{14} +81356.4 q^{15} -325622. q^{16} -49497.6 q^{17} +176373. q^{18} +560689. q^{19} +211566. q^{20} +205779. q^{21} -458742. q^{22} -659184. q^{23} -656194. q^{24} -944305. q^{25} +4.76370e6 q^{26} +531441. q^{27} +535127. q^{28} +4.93430e6 q^{29} +2.18702e6 q^{30} +7.19154e6 q^{31} -4.60558e6 q^{32} -1.38227e6 q^{33} -1.33059e6 q^{34} +2.55167e6 q^{35} +1.38201e6 q^{36} -8.70511e6 q^{37} +1.50724e7 q^{38} +1.43539e7 q^{39} -8.13681e6 q^{40} +3.16641e7 q^{41} +5.53175e6 q^{42} +7.46475e6 q^{43} -3.59458e6 q^{44} +6.58987e6 q^{45} -1.77201e7 q^{46} +9.15962e6 q^{47} -2.63754e7 q^{48} -3.38995e7 q^{49} -2.53848e7 q^{50} -4.00931e6 q^{51} +3.73270e7 q^{52} -2.75118e6 q^{53} +1.42862e7 q^{54} -1.71402e7 q^{55} -2.05809e7 q^{56} +4.54158e7 q^{57} +1.32644e8 q^{58} -1.21174e7 q^{59} +1.71369e7 q^{60} +1.29284e8 q^{61} +1.93323e8 q^{62} +1.66681e7 q^{63} +4.29118e7 q^{64} +1.77988e8 q^{65} -3.71581e7 q^{66} -2.48513e8 q^{67} -1.04262e7 q^{68} -5.33939e7 q^{69} +6.85938e7 q^{70} +2.49769e8 q^{71} -5.31517e7 q^{72} +1.10902e8 q^{73} -2.34010e8 q^{74} -7.64887e7 q^{75} +1.18103e8 q^{76} -4.33536e7 q^{77} +3.85860e8 q^{78} +6.21014e7 q^{79} -3.27055e8 q^{80} +4.30467e7 q^{81} +8.51192e8 q^{82} -1.85488e8 q^{83} +4.33453e7 q^{84} -4.97154e7 q^{85} +2.00667e8 q^{86} +3.99679e8 q^{87} +1.38247e8 q^{88} +3.17916e8 q^{89} +1.77149e8 q^{90} +4.50195e8 q^{91} -1.38850e8 q^{92} +5.82515e8 q^{93} +2.46229e8 q^{94} +5.63157e8 q^{95} -3.73052e8 q^{96} +2.93921e8 q^{97} -9.11286e8 q^{98} -1.11964e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.8820 1.18803 0.594013 0.804455i \(-0.297543\pi\)
0.594013 + 0.804455i \(0.297543\pi\)
\(3\) 81.0000 0.577350
\(4\) 210.640 0.411405
\(5\) 1004.40 0.718691 0.359345 0.933205i \(-0.383000\pi\)
0.359345 + 0.933205i \(0.383000\pi\)
\(6\) 2177.44 0.685907
\(7\) 2540.49 0.399923 0.199961 0.979804i \(-0.435918\pi\)
0.199961 + 0.979804i \(0.435918\pi\)
\(8\) −8101.16 −0.699266
\(9\) 6561.00 0.333333
\(10\) 27000.3 0.853823
\(11\) −17065.1 −0.351431 −0.175716 0.984441i \(-0.556224\pi\)
−0.175716 + 0.984441i \(0.556224\pi\)
\(12\) 17061.8 0.237525
\(13\) 177208. 1.72083 0.860416 0.509593i \(-0.170204\pi\)
0.860416 + 0.509593i \(0.170204\pi\)
\(14\) 68293.3 0.475118
\(15\) 81356.4 0.414936
\(16\) −325622. −1.24215
\(17\) −49497.6 −0.143735 −0.0718677 0.997414i \(-0.522896\pi\)
−0.0718677 + 0.997414i \(0.522896\pi\)
\(18\) 176373. 0.396009
\(19\) 560689. 0.987031 0.493516 0.869737i \(-0.335712\pi\)
0.493516 + 0.869737i \(0.335712\pi\)
\(20\) 211566. 0.295673
\(21\) 205779. 0.230895
\(22\) −458742. −0.417510
\(23\) −659184. −0.491169 −0.245585 0.969375i \(-0.578980\pi\)
−0.245585 + 0.969375i \(0.578980\pi\)
\(24\) −656194. −0.403721
\(25\) −944305. −0.483484
\(26\) 4.76370e6 2.04439
\(27\) 531441. 0.192450
\(28\) 535127. 0.164530
\(29\) 4.93430e6 1.29549 0.647746 0.761856i \(-0.275712\pi\)
0.647746 + 0.761856i \(0.275712\pi\)
\(30\) 2.18702e6 0.492955
\(31\) 7.19154e6 1.39860 0.699301 0.714827i \(-0.253495\pi\)
0.699301 + 0.714827i \(0.253495\pi\)
\(32\) −4.60558e6 −0.776442
\(33\) −1.38227e6 −0.202899
\(34\) −1.33059e6 −0.170761
\(35\) 2.55167e6 0.287421
\(36\) 1.38201e6 0.137135
\(37\) −8.70511e6 −0.763601 −0.381801 0.924245i \(-0.624696\pi\)
−0.381801 + 0.924245i \(0.624696\pi\)
\(38\) 1.50724e7 1.17262
\(39\) 1.43539e7 0.993523
\(40\) −8.13681e6 −0.502556
\(41\) 3.16641e7 1.75001 0.875003 0.484117i \(-0.160859\pi\)
0.875003 + 0.484117i \(0.160859\pi\)
\(42\) 5.53175e6 0.274310
\(43\) 7.46475e6 0.332972 0.166486 0.986044i \(-0.446758\pi\)
0.166486 + 0.986044i \(0.446758\pi\)
\(44\) −3.59458e6 −0.144581
\(45\) 6.58987e6 0.239564
\(46\) −1.77201e7 −0.583522
\(47\) 9.15962e6 0.273802 0.136901 0.990585i \(-0.456286\pi\)
0.136901 + 0.990585i \(0.456286\pi\)
\(48\) −2.63754e7 −0.717156
\(49\) −3.38995e7 −0.840062
\(50\) −2.53848e7 −0.574391
\(51\) −4.00931e6 −0.0829857
\(52\) 3.73270e7 0.707959
\(53\) −2.75118e6 −0.0478935 −0.0239468 0.999713i \(-0.507623\pi\)
−0.0239468 + 0.999713i \(0.507623\pi\)
\(54\) 1.42862e7 0.228636
\(55\) −1.71402e7 −0.252570
\(56\) −2.05809e7 −0.279652
\(57\) 4.54158e7 0.569863
\(58\) 1.32644e8 1.53908
\(59\) −1.21174e7 −0.130189
\(60\) 1.71369e7 0.170707
\(61\) 1.29284e8 1.19553 0.597765 0.801671i \(-0.296055\pi\)
0.597765 + 0.801671i \(0.296055\pi\)
\(62\) 1.93323e8 1.66158
\(63\) 1.66681e7 0.133308
\(64\) 4.29118e7 0.319718
\(65\) 1.77988e8 1.23675
\(66\) −3.71581e7 −0.241049
\(67\) −2.48513e8 −1.50665 −0.753324 0.657650i \(-0.771551\pi\)
−0.753324 + 0.657650i \(0.771551\pi\)
\(68\) −1.04262e7 −0.0591336
\(69\) −5.33939e7 −0.283577
\(70\) 6.85938e7 0.341463
\(71\) 2.49769e8 1.16648 0.583239 0.812301i \(-0.301785\pi\)
0.583239 + 0.812301i \(0.301785\pi\)
\(72\) −5.31517e7 −0.233089
\(73\) 1.10902e8 0.457072 0.228536 0.973535i \(-0.426606\pi\)
0.228536 + 0.973535i \(0.426606\pi\)
\(74\) −2.34010e8 −0.907178
\(75\) −7.64887e7 −0.279140
\(76\) 1.18103e8 0.406070
\(77\) −4.33536e7 −0.140545
\(78\) 3.85860e8 1.18033
\(79\) 6.21014e7 0.179382 0.0896911 0.995970i \(-0.471412\pi\)
0.0896911 + 0.995970i \(0.471412\pi\)
\(80\) −3.27055e8 −0.892722
\(81\) 4.30467e7 0.111111
\(82\) 8.51192e8 2.07905
\(83\) −1.85488e8 −0.429008 −0.214504 0.976723i \(-0.568814\pi\)
−0.214504 + 0.976723i \(0.568814\pi\)
\(84\) 4.33453e7 0.0949916
\(85\) −4.97154e7 −0.103301
\(86\) 2.00667e8 0.395579
\(87\) 3.99679e8 0.747953
\(88\) 1.38247e8 0.245744
\(89\) 3.17916e8 0.537103 0.268551 0.963265i \(-0.413455\pi\)
0.268551 + 0.963265i \(0.413455\pi\)
\(90\) 1.77149e8 0.284608
\(91\) 4.50195e8 0.688199
\(92\) −1.38850e8 −0.202070
\(93\) 5.82515e8 0.807484
\(94\) 2.46229e8 0.325284
\(95\) 5.63157e8 0.709370
\(96\) −3.73052e8 −0.448279
\(97\) 2.93921e8 0.337100 0.168550 0.985693i \(-0.446092\pi\)
0.168550 + 0.985693i \(0.446092\pi\)
\(98\) −9.11286e8 −0.998015
\(99\) −1.11964e8 −0.117144
\(100\) −1.98908e8 −0.198908
\(101\) −7.67270e8 −0.733673 −0.366836 0.930286i \(-0.619559\pi\)
−0.366836 + 0.930286i \(0.619559\pi\)
\(102\) −1.07778e8 −0.0985892
\(103\) −9.86745e7 −0.0863848 −0.0431924 0.999067i \(-0.513753\pi\)
−0.0431924 + 0.999067i \(0.513753\pi\)
\(104\) −1.43559e9 −1.20332
\(105\) 2.06685e8 0.165942
\(106\) −7.39570e7 −0.0568988
\(107\) 1.51051e9 1.11403 0.557013 0.830504i \(-0.311947\pi\)
0.557013 + 0.830504i \(0.311947\pi\)
\(108\) 1.11943e8 0.0791750
\(109\) −1.72548e9 −1.17082 −0.585411 0.810736i \(-0.699067\pi\)
−0.585411 + 0.810736i \(0.699067\pi\)
\(110\) −4.60761e8 −0.300060
\(111\) −7.05114e8 −0.440865
\(112\) −8.27240e8 −0.496764
\(113\) 2.29046e9 1.32151 0.660754 0.750603i \(-0.270237\pi\)
0.660754 + 0.750603i \(0.270237\pi\)
\(114\) 1.22087e9 0.677012
\(115\) −6.62084e8 −0.352999
\(116\) 1.03936e9 0.532973
\(117\) 1.16266e9 0.573611
\(118\) −3.25738e8 −0.154668
\(119\) −1.25748e8 −0.0574831
\(120\) −6.59081e8 −0.290151
\(121\) −2.06673e9 −0.876496
\(122\) 3.47541e9 1.42032
\(123\) 2.56479e9 1.01037
\(124\) 1.51482e9 0.575393
\(125\) −2.91018e9 −1.06617
\(126\) 4.48072e8 0.158373
\(127\) 4.13955e9 1.41201 0.706003 0.708209i \(-0.250497\pi\)
0.706003 + 0.708209i \(0.250497\pi\)
\(128\) 3.51161e9 1.15628
\(129\) 6.04645e8 0.192241
\(130\) 4.78466e9 1.46929
\(131\) 4.82605e8 0.143176 0.0715882 0.997434i \(-0.477193\pi\)
0.0715882 + 0.997434i \(0.477193\pi\)
\(132\) −2.91161e8 −0.0834738
\(133\) 1.42442e9 0.394736
\(134\) −6.68050e9 −1.78994
\(135\) 5.33780e8 0.138312
\(136\) 4.00988e8 0.100509
\(137\) −2.53966e9 −0.615932 −0.307966 0.951397i \(-0.599648\pi\)
−0.307966 + 0.951397i \(0.599648\pi\)
\(138\) −1.43533e9 −0.336896
\(139\) −4.54412e9 −1.03248 −0.516242 0.856443i \(-0.672670\pi\)
−0.516242 + 0.856443i \(0.672670\pi\)
\(140\) 5.37482e8 0.118246
\(141\) 7.41930e8 0.158080
\(142\) 6.71429e9 1.38581
\(143\) −3.02407e9 −0.604754
\(144\) −2.13641e9 −0.414050
\(145\) 4.95602e9 0.931058
\(146\) 2.98125e9 0.543014
\(147\) −2.74586e9 −0.485010
\(148\) −1.83364e9 −0.314150
\(149\) −3.49472e9 −0.580863 −0.290432 0.956896i \(-0.593799\pi\)
−0.290432 + 0.956896i \(0.593799\pi\)
\(150\) −2.05617e9 −0.331625
\(151\) −1.55298e8 −0.0243091 −0.0121546 0.999926i \(-0.503869\pi\)
−0.0121546 + 0.999926i \(0.503869\pi\)
\(152\) −4.54223e9 −0.690197
\(153\) −3.24754e8 −0.0479118
\(154\) −1.16543e9 −0.166972
\(155\) 7.22319e9 1.00516
\(156\) 3.02349e9 0.408741
\(157\) 2.17714e8 0.0285981 0.0142991 0.999898i \(-0.495448\pi\)
0.0142991 + 0.999898i \(0.495448\pi\)
\(158\) 1.66941e9 0.213111
\(159\) −2.22845e8 −0.0276513
\(160\) −4.62584e9 −0.558021
\(161\) −1.67465e9 −0.196430
\(162\) 1.15718e9 0.132003
\(163\) −8.72186e9 −0.967754 −0.483877 0.875136i \(-0.660772\pi\)
−0.483877 + 0.875136i \(0.660772\pi\)
\(164\) 6.66971e9 0.719962
\(165\) −1.38835e9 −0.145822
\(166\) −4.98629e9 −0.509673
\(167\) 1.45130e10 1.44389 0.721945 0.691951i \(-0.243249\pi\)
0.721945 + 0.691951i \(0.243249\pi\)
\(168\) −1.66705e9 −0.161457
\(169\) 2.07982e10 1.96126
\(170\) −1.33645e9 −0.122725
\(171\) 3.67868e9 0.329010
\(172\) 1.57237e9 0.136986
\(173\) −1.16705e10 −0.990561 −0.495280 0.868733i \(-0.664935\pi\)
−0.495280 + 0.868733i \(0.664935\pi\)
\(174\) 1.07441e10 0.888587
\(175\) −2.39899e9 −0.193356
\(176\) 5.55677e9 0.436531
\(177\) −9.81506e8 −0.0751646
\(178\) 8.54621e9 0.638092
\(179\) 2.03224e9 0.147957 0.0739787 0.997260i \(-0.476430\pi\)
0.0739787 + 0.997260i \(0.476430\pi\)
\(180\) 1.38809e9 0.0985577
\(181\) −1.11418e10 −0.771616 −0.385808 0.922579i \(-0.626077\pi\)
−0.385808 + 0.922579i \(0.626077\pi\)
\(182\) 1.21021e10 0.817599
\(183\) 1.04720e10 0.690240
\(184\) 5.34015e9 0.343458
\(185\) −8.74342e9 −0.548793
\(186\) 1.56591e10 0.959311
\(187\) 8.44679e8 0.0505132
\(188\) 1.92938e9 0.112644
\(189\) 1.35012e9 0.0769651
\(190\) 1.51387e10 0.842750
\(191\) −1.39384e10 −0.757817 −0.378908 0.925434i \(-0.623700\pi\)
−0.378908 + 0.925434i \(0.623700\pi\)
\(192\) 3.47586e9 0.184589
\(193\) 1.04739e10 0.543374 0.271687 0.962386i \(-0.412418\pi\)
0.271687 + 0.962386i \(0.412418\pi\)
\(194\) 7.90118e9 0.400483
\(195\) 1.44170e10 0.714035
\(196\) −7.14058e9 −0.345606
\(197\) −3.70303e10 −1.75170 −0.875848 0.482587i \(-0.839697\pi\)
−0.875848 + 0.482587i \(0.839697\pi\)
\(198\) −3.00981e9 −0.139170
\(199\) 9.63246e9 0.435410 0.217705 0.976015i \(-0.430143\pi\)
0.217705 + 0.976015i \(0.430143\pi\)
\(200\) 7.64996e9 0.338084
\(201\) −2.01295e10 −0.869863
\(202\) −2.06257e10 −0.871622
\(203\) 1.25355e10 0.518097
\(204\) −8.44518e8 −0.0341408
\(205\) 3.18034e10 1.25771
\(206\) −2.65256e9 −0.102627
\(207\) −4.32490e9 −0.163723
\(208\) −5.77029e10 −2.13753
\(209\) −9.56819e9 −0.346874
\(210\) 5.55610e9 0.197144
\(211\) 1.24880e10 0.433732 0.216866 0.976201i \(-0.430416\pi\)
0.216866 + 0.976201i \(0.430416\pi\)
\(212\) −5.79507e8 −0.0197037
\(213\) 2.02313e10 0.673466
\(214\) 4.06054e10 1.32349
\(215\) 7.49760e9 0.239304
\(216\) −4.30529e9 −0.134574
\(217\) 1.82700e10 0.559333
\(218\) −4.63843e10 −1.39097
\(219\) 8.98303e9 0.263891
\(220\) −3.61039e9 −0.103909
\(221\) −8.77137e9 −0.247345
\(222\) −1.89548e10 −0.523759
\(223\) −3.24581e10 −0.878923 −0.439462 0.898261i \(-0.644831\pi\)
−0.439462 + 0.898261i \(0.644831\pi\)
\(224\) −1.17004e10 −0.310517
\(225\) −6.19558e9 −0.161161
\(226\) 6.15720e10 1.56998
\(227\) 4.82276e10 1.20553 0.602766 0.797918i \(-0.294065\pi\)
0.602766 + 0.797918i \(0.294065\pi\)
\(228\) 9.56637e9 0.234445
\(229\) 6.50235e10 1.56247 0.781233 0.624240i \(-0.214591\pi\)
0.781233 + 0.624240i \(0.214591\pi\)
\(230\) −1.77981e10 −0.419372
\(231\) −3.51164e9 −0.0811439
\(232\) −3.99736e10 −0.905893
\(233\) −2.95164e10 −0.656087 −0.328043 0.944663i \(-0.606389\pi\)
−0.328043 + 0.944663i \(0.606389\pi\)
\(234\) 3.12546e10 0.681464
\(235\) 9.19993e9 0.196779
\(236\) −2.55240e9 −0.0535604
\(237\) 5.03021e9 0.103566
\(238\) −3.38035e9 −0.0682914
\(239\) 7.31519e9 0.145022 0.0725112 0.997368i \(-0.476899\pi\)
0.0725112 + 0.997368i \(0.476899\pi\)
\(240\) −2.64915e10 −0.515413
\(241\) −6.99742e10 −1.33617 −0.668085 0.744085i \(-0.732886\pi\)
−0.668085 + 0.744085i \(0.732886\pi\)
\(242\) −5.55578e10 −1.04130
\(243\) 3.48678e9 0.0641500
\(244\) 2.72323e10 0.491848
\(245\) −3.40487e10 −0.603745
\(246\) 6.89466e10 1.20034
\(247\) 9.93586e10 1.69851
\(248\) −5.82598e10 −0.977995
\(249\) −1.50246e10 −0.247688
\(250\) −7.82313e10 −1.26663
\(251\) −9.97303e10 −1.58597 −0.792985 0.609241i \(-0.791474\pi\)
−0.792985 + 0.609241i \(0.791474\pi\)
\(252\) 3.51097e9 0.0548434
\(253\) 1.12490e10 0.172612
\(254\) 1.11279e11 1.67750
\(255\) −4.02695e9 −0.0596410
\(256\) 7.24280e10 1.05397
\(257\) 2.72429e9 0.0389542 0.0194771 0.999810i \(-0.493800\pi\)
0.0194771 + 0.999810i \(0.493800\pi\)
\(258\) 1.62540e10 0.228388
\(259\) −2.21152e10 −0.305381
\(260\) 3.74913e10 0.508804
\(261\) 3.23740e10 0.431831
\(262\) 1.29734e10 0.170097
\(263\) −1.08091e11 −1.39312 −0.696559 0.717500i \(-0.745287\pi\)
−0.696559 + 0.717500i \(0.745287\pi\)
\(264\) 1.11980e10 0.141880
\(265\) −2.76328e9 −0.0344206
\(266\) 3.82913e10 0.468957
\(267\) 2.57512e10 0.310097
\(268\) −5.23466e10 −0.619843
\(269\) −1.39793e11 −1.62780 −0.813901 0.581004i \(-0.802660\pi\)
−0.813901 + 0.581004i \(0.802660\pi\)
\(270\) 1.43490e10 0.164318
\(271\) −1.32949e11 −1.49735 −0.748675 0.662938i \(-0.769309\pi\)
−0.748675 + 0.662938i \(0.769309\pi\)
\(272\) 1.61175e10 0.178541
\(273\) 3.64658e10 0.397332
\(274\) −6.82710e10 −0.731743
\(275\) 1.61146e10 0.169911
\(276\) −1.12469e10 −0.116665
\(277\) −1.69080e11 −1.72558 −0.862789 0.505565i \(-0.831284\pi\)
−0.862789 + 0.505565i \(0.831284\pi\)
\(278\) −1.22155e11 −1.22662
\(279\) 4.71837e10 0.466201
\(280\) −2.06715e10 −0.200983
\(281\) −1.57003e11 −1.50221 −0.751104 0.660184i \(-0.770478\pi\)
−0.751104 + 0.660184i \(0.770478\pi\)
\(282\) 1.99445e10 0.187803
\(283\) −1.41256e11 −1.30908 −0.654541 0.756026i \(-0.727138\pi\)
−0.654541 + 0.756026i \(0.727138\pi\)
\(284\) 5.26113e10 0.479895
\(285\) 4.56157e10 0.409555
\(286\) −8.12928e10 −0.718464
\(287\) 8.04422e10 0.699867
\(288\) −3.02172e10 −0.258814
\(289\) −1.16138e11 −0.979340
\(290\) 1.33227e11 1.10612
\(291\) 2.38076e10 0.194625
\(292\) 2.33603e10 0.188042
\(293\) −7.72906e10 −0.612664 −0.306332 0.951925i \(-0.599102\pi\)
−0.306332 + 0.951925i \(0.599102\pi\)
\(294\) −7.38141e10 −0.576204
\(295\) −1.21707e10 −0.0935655
\(296\) 7.05215e10 0.533960
\(297\) −9.06907e9 −0.0676330
\(298\) −9.39448e10 −0.690080
\(299\) −1.16813e11 −0.845220
\(300\) −1.61115e10 −0.114840
\(301\) 1.89641e10 0.133163
\(302\) −4.17471e9 −0.0288799
\(303\) −6.21489e10 −0.423586
\(304\) −1.82573e11 −1.22604
\(305\) 1.29853e11 0.859216
\(306\) −8.73002e9 −0.0569205
\(307\) 1.33175e10 0.0855656 0.0427828 0.999084i \(-0.486378\pi\)
0.0427828 + 0.999084i \(0.486378\pi\)
\(308\) −9.13198e9 −0.0578211
\(309\) −7.99263e9 −0.0498743
\(310\) 1.94173e11 1.19416
\(311\) 3.71351e10 0.225093 0.112547 0.993646i \(-0.464099\pi\)
0.112547 + 0.993646i \(0.464099\pi\)
\(312\) −1.16283e11 −0.694736
\(313\) −2.77950e10 −0.163688 −0.0818440 0.996645i \(-0.526081\pi\)
−0.0818440 + 0.996645i \(0.526081\pi\)
\(314\) 5.85258e9 0.0339753
\(315\) 1.67415e10 0.0958068
\(316\) 1.30810e10 0.0737988
\(317\) 9.28132e10 0.516230 0.258115 0.966114i \(-0.416899\pi\)
0.258115 + 0.966114i \(0.416899\pi\)
\(318\) −5.99052e9 −0.0328505
\(319\) −8.42042e10 −0.455277
\(320\) 4.31006e10 0.229778
\(321\) 1.22351e11 0.643184
\(322\) −4.50178e10 −0.233364
\(323\) −2.77528e10 −0.141871
\(324\) 9.06734e9 0.0457117
\(325\) −1.67338e11 −0.831994
\(326\) −2.34461e11 −1.14972
\(327\) −1.39764e11 −0.675975
\(328\) −2.56516e11 −1.22372
\(329\) 2.32699e10 0.109500
\(330\) −3.73216e10 −0.173240
\(331\) −1.33057e10 −0.0609271 −0.0304636 0.999536i \(-0.509698\pi\)
−0.0304636 + 0.999536i \(0.509698\pi\)
\(332\) −3.90712e10 −0.176496
\(333\) −5.71142e10 −0.254534
\(334\) 3.90138e11 1.71538
\(335\) −2.49606e11 −1.08281
\(336\) −6.70064e10 −0.286807
\(337\) −2.49443e11 −1.05351 −0.526754 0.850018i \(-0.676591\pi\)
−0.526754 + 0.850018i \(0.676591\pi\)
\(338\) 5.59096e11 2.33003
\(339\) 1.85527e11 0.762972
\(340\) −1.04720e10 −0.0424987
\(341\) −1.22724e11 −0.491513
\(342\) 9.88902e10 0.390873
\(343\) −1.88639e11 −0.735882
\(344\) −6.04731e10 −0.232836
\(345\) −5.36288e10 −0.203804
\(346\) −3.13725e11 −1.17681
\(347\) 3.58966e11 1.32914 0.664570 0.747226i \(-0.268615\pi\)
0.664570 + 0.747226i \(0.268615\pi\)
\(348\) 8.41881e10 0.307712
\(349\) 1.63254e11 0.589045 0.294522 0.955645i \(-0.404839\pi\)
0.294522 + 0.955645i \(0.404839\pi\)
\(350\) −6.44896e10 −0.229712
\(351\) 9.41756e10 0.331174
\(352\) 7.85944e10 0.272866
\(353\) 4.68374e11 1.60549 0.802744 0.596324i \(-0.203373\pi\)
0.802744 + 0.596324i \(0.203373\pi\)
\(354\) −2.63848e10 −0.0892975
\(355\) 2.50868e11 0.838336
\(356\) 6.69657e10 0.220967
\(357\) −1.01856e10 −0.0331879
\(358\) 5.46306e10 0.175777
\(359\) −1.51162e10 −0.0480307 −0.0240153 0.999712i \(-0.507645\pi\)
−0.0240153 + 0.999712i \(0.507645\pi\)
\(360\) −5.33856e10 −0.167519
\(361\) −8.31533e9 −0.0257690
\(362\) −2.99513e11 −0.916700
\(363\) −1.67405e11 −0.506045
\(364\) 9.48288e10 0.283129
\(365\) 1.11390e11 0.328493
\(366\) 2.81508e11 0.820023
\(367\) −5.96213e11 −1.71555 −0.857776 0.514024i \(-0.828154\pi\)
−0.857776 + 0.514024i \(0.828154\pi\)
\(368\) 2.14645e11 0.610106
\(369\) 2.07748e11 0.583335
\(370\) −2.35040e11 −0.651980
\(371\) −6.98933e9 −0.0191537
\(372\) 1.22701e11 0.332203
\(373\) 3.43289e11 0.918270 0.459135 0.888367i \(-0.348160\pi\)
0.459135 + 0.888367i \(0.348160\pi\)
\(374\) 2.27066e10 0.0600110
\(375\) −2.35725e11 −0.615551
\(376\) −7.42036e10 −0.191461
\(377\) 8.74398e11 2.22932
\(378\) 3.62938e10 0.0914366
\(379\) −3.16105e11 −0.786965 −0.393482 0.919332i \(-0.628730\pi\)
−0.393482 + 0.919332i \(0.628730\pi\)
\(380\) 1.18623e11 0.291839
\(381\) 3.35304e11 0.815222
\(382\) −3.74693e11 −0.900306
\(383\) 1.76185e11 0.418383 0.209192 0.977875i \(-0.432917\pi\)
0.209192 + 0.977875i \(0.432917\pi\)
\(384\) 2.84440e11 0.667576
\(385\) −4.35443e10 −0.101009
\(386\) 2.81558e11 0.645542
\(387\) 4.89762e10 0.110991
\(388\) 6.19115e10 0.138685
\(389\) 8.21100e11 1.81812 0.909061 0.416664i \(-0.136801\pi\)
0.909061 + 0.416664i \(0.136801\pi\)
\(390\) 3.87558e11 0.848292
\(391\) 3.26280e10 0.0705985
\(392\) 2.74625e11 0.587426
\(393\) 3.90910e10 0.0826629
\(394\) −9.95446e11 −2.08106
\(395\) 6.23746e10 0.128920
\(396\) −2.35840e10 −0.0481936
\(397\) −2.79061e11 −0.563821 −0.281911 0.959441i \(-0.590968\pi\)
−0.281911 + 0.959441i \(0.590968\pi\)
\(398\) 2.58939e11 0.517278
\(399\) 1.15378e11 0.227901
\(400\) 3.07487e11 0.600560
\(401\) 7.21122e11 1.39270 0.696352 0.717700i \(-0.254805\pi\)
0.696352 + 0.717700i \(0.254805\pi\)
\(402\) −5.41121e11 −1.03342
\(403\) 1.27440e12 2.40676
\(404\) −1.61618e11 −0.301837
\(405\) 4.32361e10 0.0798545
\(406\) 3.36980e11 0.615512
\(407\) 1.48553e11 0.268353
\(408\) 3.24800e10 0.0580291
\(409\) −5.40997e11 −0.955960 −0.477980 0.878371i \(-0.658631\pi\)
−0.477980 + 0.878371i \(0.658631\pi\)
\(410\) 8.54938e11 1.49420
\(411\) −2.05712e11 −0.355609
\(412\) −2.07847e10 −0.0355392
\(413\) −3.07840e10 −0.0520655
\(414\) −1.16262e11 −0.194507
\(415\) −1.86305e11 −0.308324
\(416\) −8.16145e11 −1.33613
\(417\) −3.68074e11 −0.596105
\(418\) −2.57212e11 −0.412095
\(419\) −4.35766e11 −0.690701 −0.345350 0.938474i \(-0.612240\pi\)
−0.345350 + 0.938474i \(0.612240\pi\)
\(420\) 4.35360e10 0.0682696
\(421\) 5.04248e11 0.782303 0.391151 0.920326i \(-0.372077\pi\)
0.391151 + 0.920326i \(0.372077\pi\)
\(422\) 3.35702e11 0.515285
\(423\) 6.00963e10 0.0912675
\(424\) 2.22877e10 0.0334903
\(425\) 4.67408e10 0.0694938
\(426\) 5.43857e11 0.800095
\(427\) 3.28444e11 0.478120
\(428\) 3.18172e11 0.458317
\(429\) −2.44949e11 −0.349155
\(430\) 2.01550e11 0.284299
\(431\) 8.09773e11 1.13036 0.565179 0.824969i \(-0.308807\pi\)
0.565179 + 0.824969i \(0.308807\pi\)
\(432\) −1.73049e11 −0.239052
\(433\) 5.81362e11 0.794787 0.397394 0.917648i \(-0.369915\pi\)
0.397394 + 0.917648i \(0.369915\pi\)
\(434\) 4.91134e11 0.664502
\(435\) 4.01437e11 0.537547
\(436\) −3.63455e11 −0.481683
\(437\) −3.69597e11 −0.484800
\(438\) 2.41481e11 0.313509
\(439\) 4.32577e11 0.555870 0.277935 0.960600i \(-0.410350\pi\)
0.277935 + 0.960600i \(0.410350\pi\)
\(440\) 1.38855e11 0.176614
\(441\) −2.22415e11 −0.280021
\(442\) −2.35792e11 −0.293852
\(443\) 1.47115e12 1.81484 0.907422 0.420220i \(-0.138047\pi\)
0.907422 + 0.420220i \(0.138047\pi\)
\(444\) −1.48525e11 −0.181374
\(445\) 3.19315e11 0.386011
\(446\) −8.72537e11 −1.04418
\(447\) −2.83072e11 −0.335361
\(448\) 1.09017e11 0.127862
\(449\) −1.70596e12 −1.98089 −0.990444 0.137916i \(-0.955960\pi\)
−0.990444 + 0.137916i \(0.955960\pi\)
\(450\) −1.66549e11 −0.191464
\(451\) −5.40349e11 −0.615007
\(452\) 4.82461e11 0.543675
\(453\) −1.25791e10 −0.0140349
\(454\) 1.29645e12 1.43220
\(455\) 4.52176e11 0.494602
\(456\) −3.67921e11 −0.398485
\(457\) −6.16875e10 −0.0661568 −0.0330784 0.999453i \(-0.510531\pi\)
−0.0330784 + 0.999453i \(0.510531\pi\)
\(458\) 1.74796e12 1.85625
\(459\) −2.63051e10 −0.0276619
\(460\) −1.39461e11 −0.145226
\(461\) 6.66518e11 0.687318 0.343659 0.939094i \(-0.388334\pi\)
0.343659 + 0.939094i \(0.388334\pi\)
\(462\) −9.43997e10 −0.0964011
\(463\) −6.86095e11 −0.693857 −0.346928 0.937892i \(-0.612775\pi\)
−0.346928 + 0.937892i \(0.612775\pi\)
\(464\) −1.60672e12 −1.60920
\(465\) 5.85078e11 0.580331
\(466\) −7.93458e11 −0.779448
\(467\) 8.37390e11 0.814707 0.407354 0.913271i \(-0.366452\pi\)
0.407354 + 0.913271i \(0.366452\pi\)
\(468\) 2.44903e11 0.235986
\(469\) −6.31343e11 −0.602542
\(470\) 2.47312e11 0.233779
\(471\) 1.76348e10 0.0165111
\(472\) 9.81647e10 0.0910366
\(473\) −1.27386e11 −0.117017
\(474\) 1.35222e11 0.123039
\(475\) −5.29461e11 −0.477214
\(476\) −2.64875e10 −0.0236488
\(477\) −1.80505e10 −0.0159645
\(478\) 1.96647e11 0.172290
\(479\) −6.38652e11 −0.554313 −0.277156 0.960825i \(-0.589392\pi\)
−0.277156 + 0.960825i \(0.589392\pi\)
\(480\) −3.74693e11 −0.322174
\(481\) −1.54262e12 −1.31403
\(482\) −1.88104e12 −1.58740
\(483\) −1.35646e11 −0.113409
\(484\) −4.35335e11 −0.360595
\(485\) 2.95215e11 0.242270
\(486\) 9.37316e10 0.0762119
\(487\) 4.45800e11 0.359137 0.179568 0.983745i \(-0.442530\pi\)
0.179568 + 0.983745i \(0.442530\pi\)
\(488\) −1.04735e12 −0.835993
\(489\) −7.06471e11 −0.558733
\(490\) −9.15296e11 −0.717264
\(491\) 7.33856e10 0.0569829 0.0284914 0.999594i \(-0.490930\pi\)
0.0284914 + 0.999594i \(0.490930\pi\)
\(492\) 5.40246e11 0.415670
\(493\) −2.44236e11 −0.186208
\(494\) 2.67095e12 2.01788
\(495\) −1.12457e11 −0.0841902
\(496\) −2.34173e12 −1.73728
\(497\) 6.34536e11 0.466501
\(498\) −4.03890e11 −0.294260
\(499\) 9.92890e11 0.716884 0.358442 0.933552i \(-0.383308\pi\)
0.358442 + 0.933552i \(0.383308\pi\)
\(500\) −6.12999e11 −0.438626
\(501\) 1.17556e12 0.833630
\(502\) −2.68094e12 −1.88417
\(503\) −2.24824e12 −1.56598 −0.782989 0.622035i \(-0.786306\pi\)
−0.782989 + 0.622035i \(0.786306\pi\)
\(504\) −1.35031e11 −0.0932173
\(505\) −7.70647e11 −0.527283
\(506\) 3.02395e11 0.205068
\(507\) 1.68465e12 1.13233
\(508\) 8.71953e11 0.580907
\(509\) −1.49442e12 −0.986829 −0.493414 0.869794i \(-0.664251\pi\)
−0.493414 + 0.869794i \(0.664251\pi\)
\(510\) −1.08252e11 −0.0708551
\(511\) 2.81744e11 0.182793
\(512\) 1.49064e11 0.0958647
\(513\) 2.97973e11 0.189954
\(514\) 7.32342e10 0.0462786
\(515\) −9.91087e10 −0.0620839
\(516\) 1.27362e11 0.0790891
\(517\) −1.56310e11 −0.0962228
\(518\) −5.94500e11 −0.362801
\(519\) −9.45309e11 −0.571901
\(520\) −1.44191e12 −0.864813
\(521\) 3.29635e10 0.0196003 0.00980017 0.999952i \(-0.496880\pi\)
0.00980017 + 0.999952i \(0.496880\pi\)
\(522\) 8.70276e11 0.513026
\(523\) 2.00057e12 1.16922 0.584609 0.811315i \(-0.301248\pi\)
0.584609 + 0.811315i \(0.301248\pi\)
\(524\) 1.01656e11 0.0589035
\(525\) −1.94319e11 −0.111634
\(526\) −2.90569e12 −1.65506
\(527\) −3.55964e11 −0.201029
\(528\) 4.50098e11 0.252031
\(529\) −1.36663e12 −0.758753
\(530\) −7.42824e10 −0.0408926
\(531\) −7.95020e10 −0.0433963
\(532\) 3.00040e11 0.162397
\(533\) 5.61113e12 3.01147
\(534\) 6.92243e11 0.368403
\(535\) 1.51715e12 0.800640
\(536\) 2.01324e12 1.05355
\(537\) 1.64612e11 0.0854232
\(538\) −3.75792e12 −1.93387
\(539\) 5.78497e11 0.295224
\(540\) 1.12435e11 0.0569023
\(541\) −1.86300e12 −0.935028 −0.467514 0.883986i \(-0.654850\pi\)
−0.467514 + 0.883986i \(0.654850\pi\)
\(542\) −3.57393e12 −1.77889
\(543\) −9.02485e11 −0.445493
\(544\) 2.27965e11 0.111602
\(545\) −1.73308e12 −0.841459
\(546\) 9.80272e11 0.472041
\(547\) −3.94348e11 −0.188338 −0.0941688 0.995556i \(-0.530019\pi\)
−0.0941688 + 0.995556i \(0.530019\pi\)
\(548\) −5.34953e11 −0.253398
\(549\) 8.48233e11 0.398510
\(550\) 4.33192e11 0.201859
\(551\) 2.76661e12 1.27869
\(552\) 4.32552e11 0.198295
\(553\) 1.57768e11 0.0717390
\(554\) −4.54521e12 −2.05003
\(555\) −7.08217e11 −0.316846
\(556\) −9.57172e11 −0.424770
\(557\) −8.18991e11 −0.360521 −0.180261 0.983619i \(-0.557694\pi\)
−0.180261 + 0.983619i \(0.557694\pi\)
\(558\) 1.26839e12 0.553859
\(559\) 1.32281e12 0.572988
\(560\) −8.30880e11 −0.357020
\(561\) 6.84190e10 0.0291638
\(562\) −4.22055e12 −1.78466
\(563\) 2.58923e12 1.08613 0.543066 0.839690i \(-0.317264\pi\)
0.543066 + 0.839690i \(0.317264\pi\)
\(564\) 1.56280e11 0.0650349
\(565\) 2.30054e12 0.949755
\(566\) −3.79723e12 −1.55522
\(567\) 1.09360e11 0.0444358
\(568\) −2.02342e12 −0.815678
\(569\) 4.71689e11 0.188647 0.0943237 0.995542i \(-0.469931\pi\)
0.0943237 + 0.995542i \(0.469931\pi\)
\(570\) 1.22624e12 0.486562
\(571\) 3.68890e12 1.45223 0.726113 0.687576i \(-0.241325\pi\)
0.726113 + 0.687576i \(0.241325\pi\)
\(572\) −6.36988e11 −0.248799
\(573\) −1.12901e12 −0.437526
\(574\) 2.16244e12 0.831460
\(575\) 6.22470e11 0.237472
\(576\) 2.81544e11 0.106573
\(577\) 2.54528e12 0.955969 0.477985 0.878368i \(-0.341368\pi\)
0.477985 + 0.878368i \(0.341368\pi\)
\(578\) −3.12201e12 −1.16348
\(579\) 8.48382e11 0.313717
\(580\) 1.04393e12 0.383042
\(581\) −4.71231e11 −0.171570
\(582\) 6.39996e11 0.231219
\(583\) 4.69490e10 0.0168313
\(584\) −8.98431e11 −0.319615
\(585\) 1.16778e12 0.412248
\(586\) −2.07772e12 −0.727861
\(587\) 6.08590e11 0.211570 0.105785 0.994389i \(-0.466265\pi\)
0.105785 + 0.994389i \(0.466265\pi\)
\(588\) −5.78387e11 −0.199536
\(589\) 4.03222e12 1.38046
\(590\) −3.27172e11 −0.111158
\(591\) −2.99945e12 −1.01134
\(592\) 2.83458e12 0.948508
\(593\) 5.29940e12 1.75987 0.879936 0.475093i \(-0.157585\pi\)
0.879936 + 0.475093i \(0.157585\pi\)
\(594\) −2.43794e11 −0.0803498
\(595\) −1.26301e11 −0.0413125
\(596\) −7.36126e11 −0.238970
\(597\) 7.80229e11 0.251384
\(598\) −3.14015e12 −1.00414
\(599\) −1.40023e12 −0.444404 −0.222202 0.975001i \(-0.571324\pi\)
−0.222202 + 0.975001i \(0.571324\pi\)
\(600\) 6.19647e11 0.195193
\(601\) −5.15838e12 −1.61279 −0.806396 0.591376i \(-0.798585\pi\)
−0.806396 + 0.591376i \(0.798585\pi\)
\(602\) 5.09792e11 0.158201
\(603\) −1.63049e12 −0.502216
\(604\) −3.27119e10 −0.0100009
\(605\) −2.07583e12 −0.629929
\(606\) −1.67068e12 −0.503231
\(607\) −1.84609e11 −0.0551954 −0.0275977 0.999619i \(-0.508786\pi\)
−0.0275977 + 0.999619i \(0.508786\pi\)
\(608\) −2.58230e12 −0.766373
\(609\) 1.01538e12 0.299123
\(610\) 3.49070e12 1.02077
\(611\) 1.62316e12 0.471168
\(612\) −6.84060e10 −0.0197112
\(613\) 2.95650e12 0.845678 0.422839 0.906205i \(-0.361033\pi\)
0.422839 + 0.906205i \(0.361033\pi\)
\(614\) 3.58000e11 0.101654
\(615\) 2.57608e12 0.726141
\(616\) 3.51214e11 0.0982785
\(617\) 5.12873e12 1.42471 0.712355 0.701819i \(-0.247629\pi\)
0.712355 + 0.701819i \(0.247629\pi\)
\(618\) −2.14858e11 −0.0592519
\(619\) −3.52031e12 −0.963769 −0.481884 0.876235i \(-0.660047\pi\)
−0.481884 + 0.876235i \(0.660047\pi\)
\(620\) 1.52149e12 0.413529
\(621\) −3.50317e11 −0.0945256
\(622\) 9.98264e11 0.267417
\(623\) 8.07662e11 0.214800
\(624\) −4.67394e12 −1.23411
\(625\) −1.07864e12 −0.282759
\(626\) −7.47183e11 −0.194466
\(627\) −7.75024e11 −0.200268
\(628\) 4.58592e10 0.0117654
\(629\) 4.30882e11 0.109757
\(630\) 4.50044e11 0.113821
\(631\) 7.39205e12 1.85624 0.928118 0.372287i \(-0.121426\pi\)
0.928118 + 0.372287i \(0.121426\pi\)
\(632\) −5.03093e11 −0.125436
\(633\) 1.01153e12 0.250415
\(634\) 2.49500e12 0.613295
\(635\) 4.15777e12 1.01479
\(636\) −4.69400e10 −0.0113759
\(637\) −6.00727e12 −1.44561
\(638\) −2.26357e12 −0.540881
\(639\) 1.63874e12 0.388826
\(640\) 3.52706e12 0.831004
\(641\) −4.35042e11 −0.101782 −0.0508908 0.998704i \(-0.516206\pi\)
−0.0508908 + 0.998704i \(0.516206\pi\)
\(642\) 3.28903e12 0.764119
\(643\) 4.15366e12 0.958256 0.479128 0.877745i \(-0.340953\pi\)
0.479128 + 0.877745i \(0.340953\pi\)
\(644\) −3.52747e11 −0.0808122
\(645\) 6.07306e11 0.138162
\(646\) −7.46049e11 −0.168547
\(647\) 6.51804e11 0.146234 0.0731169 0.997323i \(-0.476705\pi\)
0.0731169 + 0.997323i \(0.476705\pi\)
\(648\) −3.48728e11 −0.0776962
\(649\) 2.06783e11 0.0457525
\(650\) −4.49838e12 −0.988431
\(651\) 1.47987e12 0.322931
\(652\) −1.83717e12 −0.398139
\(653\) −3.91543e12 −0.842695 −0.421347 0.906899i \(-0.638443\pi\)
−0.421347 + 0.906899i \(0.638443\pi\)
\(654\) −3.75713e12 −0.803076
\(655\) 4.84729e11 0.102899
\(656\) −1.03105e13 −2.17377
\(657\) 7.27625e11 0.152357
\(658\) 6.25541e11 0.130089
\(659\) 1.01878e12 0.210425 0.105212 0.994450i \(-0.466448\pi\)
0.105212 + 0.994450i \(0.466448\pi\)
\(660\) −2.92442e11 −0.0599918
\(661\) 9.61179e11 0.195838 0.0979192 0.995194i \(-0.468781\pi\)
0.0979192 + 0.995194i \(0.468781\pi\)
\(662\) −3.57682e11 −0.0723830
\(663\) −7.10481e11 −0.142804
\(664\) 1.50267e12 0.299991
\(665\) 1.43069e12 0.283693
\(666\) −1.53534e12 −0.302393
\(667\) −3.25261e12 −0.636306
\(668\) 3.05702e12 0.594024
\(669\) −2.62911e12 −0.507447
\(670\) −6.70990e12 −1.28641
\(671\) −2.20624e12 −0.420147
\(672\) −9.47733e11 −0.179277
\(673\) 5.32563e12 1.00070 0.500350 0.865823i \(-0.333205\pi\)
0.500350 + 0.865823i \(0.333205\pi\)
\(674\) −6.70553e12 −1.25159
\(675\) −5.01842e11 −0.0930465
\(676\) 4.38092e12 0.806874
\(677\) 1.50186e12 0.274777 0.137388 0.990517i \(-0.456129\pi\)
0.137388 + 0.990517i \(0.456129\pi\)
\(678\) 4.98733e12 0.906431
\(679\) 7.46704e11 0.134814
\(680\) 4.02752e11 0.0722351
\(681\) 3.90643e12 0.696015
\(682\) −3.29906e12 −0.583930
\(683\) −2.94350e12 −0.517572 −0.258786 0.965935i \(-0.583323\pi\)
−0.258786 + 0.965935i \(0.583323\pi\)
\(684\) 7.74876e11 0.135357
\(685\) −2.55084e12 −0.442665
\(686\) −5.07099e12 −0.874247
\(687\) 5.26690e12 0.902090
\(688\) −2.43069e12 −0.413601
\(689\) −4.87531e11 −0.0824167
\(690\) −1.44165e12 −0.242124
\(691\) −5.59771e12 −0.934026 −0.467013 0.884250i \(-0.654670\pi\)
−0.467013 + 0.884250i \(0.654670\pi\)
\(692\) −2.45826e12 −0.407522
\(693\) −2.84443e11 −0.0468485
\(694\) 9.64971e12 1.57905
\(695\) −4.56412e12 −0.742037
\(696\) −3.23786e12 −0.523018
\(697\) −1.56730e12 −0.251538
\(698\) 4.38858e12 0.699800
\(699\) −2.39083e12 −0.378792
\(700\) −5.05323e11 −0.0795478
\(701\) −1.22684e12 −0.191892 −0.0959459 0.995387i \(-0.530588\pi\)
−0.0959459 + 0.995387i \(0.530588\pi\)
\(702\) 2.53163e12 0.393444
\(703\) −4.88086e12 −0.753698
\(704\) −7.32293e11 −0.112359
\(705\) 7.45194e11 0.113611
\(706\) 1.25908e13 1.90736
\(707\) −1.94924e12 −0.293412
\(708\) −2.06744e11 −0.0309231
\(709\) 1.14374e13 1.69989 0.849943 0.526875i \(-0.176637\pi\)
0.849943 + 0.526875i \(0.176637\pi\)
\(710\) 6.74383e12 0.995965
\(711\) 4.07447e11 0.0597941
\(712\) −2.57549e12 −0.375578
\(713\) −4.74055e12 −0.686951
\(714\) −2.73809e11 −0.0394280
\(715\) −3.03737e12 −0.434631
\(716\) 4.28070e11 0.0608705
\(717\) 5.92530e11 0.0837287
\(718\) −4.06354e11 −0.0570617
\(719\) −5.07223e10 −0.00707813 −0.00353907 0.999994i \(-0.501127\pi\)
−0.00353907 + 0.999994i \(0.501127\pi\)
\(720\) −2.14581e12 −0.297574
\(721\) −2.50681e11 −0.0345472
\(722\) −2.23532e11 −0.0306142
\(723\) −5.66791e12 −0.771438
\(724\) −2.34690e12 −0.317447
\(725\) −4.65949e12 −0.626350
\(726\) −4.50018e12 −0.601195
\(727\) −1.25047e13 −1.66024 −0.830118 0.557588i \(-0.811727\pi\)
−0.830118 + 0.557588i \(0.811727\pi\)
\(728\) −3.64710e12 −0.481234
\(729\) 2.82430e11 0.0370370
\(730\) 2.99437e12 0.390259
\(731\) −3.69487e11 −0.0478598
\(732\) 2.20582e12 0.283968
\(733\) −4.88939e12 −0.625586 −0.312793 0.949821i \(-0.601265\pi\)
−0.312793 + 0.949821i \(0.601265\pi\)
\(734\) −1.60274e13 −2.03812
\(735\) −2.75795e12 −0.348572
\(736\) 3.03592e12 0.381364
\(737\) 4.24088e12 0.529483
\(738\) 5.58467e12 0.693017
\(739\) −1.41341e13 −1.74328 −0.871641 0.490146i \(-0.836944\pi\)
−0.871641 + 0.490146i \(0.836944\pi\)
\(740\) −1.84171e12 −0.225776
\(741\) 8.04805e12 0.980638
\(742\) −1.87887e11 −0.0227551
\(743\) 6.49246e12 0.781555 0.390778 0.920485i \(-0.372206\pi\)
0.390778 + 0.920485i \(0.372206\pi\)
\(744\) −4.71904e12 −0.564646
\(745\) −3.51009e12 −0.417461
\(746\) 9.22828e12 1.09093
\(747\) −1.21699e12 −0.143003
\(748\) 1.77923e11 0.0207814
\(749\) 3.83742e12 0.445524
\(750\) −6.33674e12 −0.731291
\(751\) 1.27660e13 1.46445 0.732227 0.681060i \(-0.238481\pi\)
0.732227 + 0.681060i \(0.238481\pi\)
\(752\) −2.98258e12 −0.340104
\(753\) −8.07815e12 −0.915661
\(754\) 2.35055e13 2.64849
\(755\) −1.55981e11 −0.0174707
\(756\) 2.84389e11 0.0316639
\(757\) 1.98458e12 0.219653 0.109827 0.993951i \(-0.464970\pi\)
0.109827 + 0.993951i \(0.464970\pi\)
\(758\) −8.49753e12 −0.934934
\(759\) 9.11170e11 0.0996578
\(760\) −4.56222e12 −0.496038
\(761\) 1.71578e13 1.85451 0.927257 0.374426i \(-0.122160\pi\)
0.927257 + 0.374426i \(0.122160\pi\)
\(762\) 9.01362e12 0.968504
\(763\) −4.38357e12 −0.468238
\(764\) −2.93599e12 −0.311770
\(765\) −3.26183e11 −0.0344338
\(766\) 4.73620e12 0.497050
\(767\) −2.14729e12 −0.224033
\(768\) 5.86667e12 0.608508
\(769\) 1.34721e13 1.38921 0.694606 0.719391i \(-0.255579\pi\)
0.694606 + 0.719391i \(0.255579\pi\)
\(770\) −1.17056e12 −0.120001
\(771\) 2.20667e11 0.0224902
\(772\) 2.20621e12 0.223547
\(773\) −9.26209e12 −0.933042 −0.466521 0.884510i \(-0.654493\pi\)
−0.466521 + 0.884510i \(0.654493\pi\)
\(774\) 1.31658e12 0.131860
\(775\) −6.79101e12 −0.676202
\(776\) −2.38110e12 −0.235722
\(777\) −1.79133e12 −0.176312
\(778\) 2.20728e13 2.15998
\(779\) 1.77537e13 1.72731
\(780\) 3.03679e12 0.293758
\(781\) −4.26233e12 −0.409937
\(782\) 8.77105e11 0.0838728
\(783\) 2.62229e12 0.249318
\(784\) 1.10384e13 1.04348
\(785\) 2.18672e11 0.0205532
\(786\) 1.05084e12 0.0982057
\(787\) 1.57166e13 1.46040 0.730201 0.683232i \(-0.239426\pi\)
0.730201 + 0.683232i \(0.239426\pi\)
\(788\) −7.80004e12 −0.720657
\(789\) −8.75535e12 −0.804317
\(790\) 1.67675e12 0.153161
\(791\) 5.81888e12 0.528500
\(792\) 9.07037e11 0.0819146
\(793\) 2.29102e13 2.05731
\(794\) −7.50170e12 −0.669834
\(795\) −2.23826e11 −0.0198728
\(796\) 2.02898e12 0.179130
\(797\) 1.84624e13 1.62078 0.810391 0.585890i \(-0.199255\pi\)
0.810391 + 0.585890i \(0.199255\pi\)
\(798\) 3.10160e12 0.270752
\(799\) −4.53379e11 −0.0393551
\(800\) 4.34907e12 0.375397
\(801\) 2.08585e12 0.179034
\(802\) 1.93852e13 1.65457
\(803\) −1.89254e12 −0.160630
\(804\) −4.24007e12 −0.357867
\(805\) −1.68202e12 −0.141172
\(806\) 3.42583e13 2.85929
\(807\) −1.13233e13 −0.939812
\(808\) 6.21578e12 0.513032
\(809\) 4.37858e12 0.359389 0.179695 0.983722i \(-0.442489\pi\)
0.179695 + 0.983722i \(0.442489\pi\)
\(810\) 1.16227e12 0.0948692
\(811\) −3.85768e11 −0.0313135 −0.0156568 0.999877i \(-0.504984\pi\)
−0.0156568 + 0.999877i \(0.504984\pi\)
\(812\) 2.64048e12 0.213148
\(813\) −1.07689e13 −0.864495
\(814\) 3.99340e12 0.318811
\(815\) −8.76024e12 −0.695516
\(816\) 1.30552e12 0.103081
\(817\) 4.18541e12 0.328654
\(818\) −1.45430e13 −1.13570
\(819\) 2.95373e12 0.229400
\(820\) 6.69906e12 0.517430
\(821\) −1.46865e13 −1.12817 −0.564083 0.825718i \(-0.690770\pi\)
−0.564083 + 0.825718i \(0.690770\pi\)
\(822\) −5.52995e12 −0.422472
\(823\) −1.51766e13 −1.15313 −0.576563 0.817053i \(-0.695606\pi\)
−0.576563 + 0.817053i \(0.695606\pi\)
\(824\) 7.99377e11 0.0604059
\(825\) 1.30528e12 0.0980984
\(826\) −8.27534e11 −0.0618551
\(827\) −1.74238e13 −1.29529 −0.647646 0.761941i \(-0.724246\pi\)
−0.647646 + 0.761941i \(0.724246\pi\)
\(828\) −9.10996e11 −0.0673566
\(829\) −1.91002e13 −1.40457 −0.702284 0.711897i \(-0.747836\pi\)
−0.702284 + 0.711897i \(0.747836\pi\)
\(830\) −5.00823e12 −0.366297
\(831\) −1.36955e13 −0.996263
\(832\) 7.60432e12 0.550181
\(833\) 1.67795e12 0.120747
\(834\) −9.89455e12 −0.708188
\(835\) 1.45769e13 1.03771
\(836\) −2.01544e12 −0.142706
\(837\) 3.82188e12 0.269161
\(838\) −1.17142e13 −0.820570
\(839\) −5.97560e12 −0.416345 −0.208172 0.978092i \(-0.566751\pi\)
−0.208172 + 0.978092i \(0.566751\pi\)
\(840\) −1.67439e12 −0.116038
\(841\) 9.84020e12 0.678301
\(842\) 1.35552e13 0.929396
\(843\) −1.27173e13 −0.867300
\(844\) 2.63047e12 0.178440
\(845\) 2.08897e13 1.40954
\(846\) 1.61551e12 0.108428
\(847\) −5.25051e12 −0.350530
\(848\) 8.95845e11 0.0594910
\(849\) −1.14417e13 −0.755799
\(850\) 1.25648e12 0.0825604
\(851\) 5.73827e12 0.375057
\(852\) 4.26151e12 0.277068
\(853\) −9.12291e12 −0.590014 −0.295007 0.955495i \(-0.595322\pi\)
−0.295007 + 0.955495i \(0.595322\pi\)
\(854\) 8.82923e12 0.568018
\(855\) 3.69487e12 0.236457
\(856\) −1.22369e13 −0.779001
\(857\) −4.11601e12 −0.260653 −0.130326 0.991471i \(-0.541603\pi\)
−0.130326 + 0.991471i \(0.541603\pi\)
\(858\) −6.58472e12 −0.414805
\(859\) 4.94399e11 0.0309819 0.0154910 0.999880i \(-0.495069\pi\)
0.0154910 + 0.999880i \(0.495069\pi\)
\(860\) 1.57929e12 0.0984508
\(861\) 6.51582e12 0.404068
\(862\) 2.17683e13 1.34289
\(863\) 1.22015e13 0.748797 0.374398 0.927268i \(-0.377849\pi\)
0.374398 + 0.927268i \(0.377849\pi\)
\(864\) −2.44759e12 −0.149426
\(865\) −1.17218e13 −0.711907
\(866\) 1.56281e13 0.944228
\(867\) −9.40717e12 −0.565422
\(868\) 3.84839e12 0.230113
\(869\) −1.05976e12 −0.0630405
\(870\) 1.07914e13 0.638619
\(871\) −4.40384e13 −2.59269
\(872\) 1.39784e13 0.818716
\(873\) 1.92842e12 0.112367
\(874\) −9.93550e12 −0.575954
\(875\) −7.39327e12 −0.426384
\(876\) 1.89218e12 0.108566
\(877\) −2.66821e13 −1.52308 −0.761539 0.648120i \(-0.775556\pi\)
−0.761539 + 0.648120i \(0.775556\pi\)
\(878\) 1.16285e13 0.660388
\(879\) −6.26054e12 −0.353722
\(880\) 5.58122e12 0.313731
\(881\) −4.84046e12 −0.270704 −0.135352 0.990798i \(-0.543217\pi\)
−0.135352 + 0.990798i \(0.543217\pi\)
\(882\) −5.97895e12 −0.332672
\(883\) −9.59584e12 −0.531202 −0.265601 0.964083i \(-0.585570\pi\)
−0.265601 + 0.964083i \(0.585570\pi\)
\(884\) −1.84760e12 −0.101759
\(885\) −9.85825e11 −0.0540201
\(886\) 3.95473e13 2.15608
\(887\) −1.61306e13 −0.874973 −0.437486 0.899225i \(-0.644131\pi\)
−0.437486 + 0.899225i \(0.644131\pi\)
\(888\) 5.71224e12 0.308282
\(889\) 1.05165e13 0.564693
\(890\) 8.58381e12 0.458591
\(891\) −7.34595e11 −0.0390479
\(892\) −6.83696e12 −0.361594
\(893\) 5.13570e12 0.270252
\(894\) −7.60953e12 −0.398418
\(895\) 2.04118e12 0.106336
\(896\) 8.92120e12 0.462420
\(897\) −9.46183e12 −0.487988
\(898\) −4.58595e13 −2.35335
\(899\) 3.54852e13 1.81188
\(900\) −1.30503e12 −0.0663026
\(901\) 1.36177e11 0.00688400
\(902\) −1.45256e13 −0.730644
\(903\) 1.53609e12 0.0768816
\(904\) −1.85554e13 −0.924084
\(905\) −1.11908e13 −0.554553
\(906\) −3.38151e11 −0.0166738
\(907\) 1.76304e13 0.865029 0.432514 0.901627i \(-0.357626\pi\)
0.432514 + 0.901627i \(0.357626\pi\)
\(908\) 1.01586e13 0.495963
\(909\) −5.03406e12 −0.244558
\(910\) 1.21554e13 0.587600
\(911\) 1.71264e13 0.823824 0.411912 0.911224i \(-0.364861\pi\)
0.411912 + 0.911224i \(0.364861\pi\)
\(912\) −1.47884e13 −0.707856
\(913\) 3.16537e12 0.150767
\(914\) −1.65828e12 −0.0785959
\(915\) 1.05181e13 0.496069
\(916\) 1.36965e13 0.642807
\(917\) 1.22605e12 0.0572595
\(918\) −7.07131e11 −0.0328631
\(919\) 2.33347e13 1.07915 0.539576 0.841937i \(-0.318584\pi\)
0.539576 + 0.841937i \(0.318584\pi\)
\(920\) 5.36365e12 0.246840
\(921\) 1.07872e12 0.0494013
\(922\) 1.79173e13 0.816552
\(923\) 4.42611e13 2.00731
\(924\) −7.39690e11 −0.0333830
\(925\) 8.22028e12 0.369189
\(926\) −1.84436e13 −0.824319
\(927\) −6.47403e11 −0.0287949
\(928\) −2.27253e13 −1.00587
\(929\) 4.53635e12 0.199819 0.0999094 0.994997i \(-0.468145\pi\)
0.0999094 + 0.994997i \(0.468145\pi\)
\(930\) 1.57280e13 0.689448
\(931\) −1.90071e13 −0.829168
\(932\) −6.21731e12 −0.269918
\(933\) 3.00794e12 0.129958
\(934\) 2.25107e13 0.967893
\(935\) 8.48396e11 0.0363033
\(936\) −9.41891e12 −0.401106
\(937\) 5.78059e12 0.244987 0.122494 0.992469i \(-0.460911\pi\)
0.122494 + 0.992469i \(0.460911\pi\)
\(938\) −1.69717e13 −0.715836
\(939\) −2.25139e12 −0.0945053
\(940\) 1.93787e12 0.0809560
\(941\) −4.12365e13 −1.71446 −0.857231 0.514932i \(-0.827817\pi\)
−0.857231 + 0.514932i \(0.827817\pi\)
\(942\) 4.74059e11 0.0196157
\(943\) −2.08724e13 −0.859549
\(944\) 3.94568e12 0.161714
\(945\) 1.35606e12 0.0553141
\(946\) −3.42440e12 −0.139019
\(947\) 5.25224e12 0.212212 0.106106 0.994355i \(-0.466162\pi\)
0.106106 + 0.994355i \(0.466162\pi\)
\(948\) 1.05956e12 0.0426078
\(949\) 1.96526e13 0.786544
\(950\) −1.42330e13 −0.566942
\(951\) 7.51787e12 0.298046
\(952\) 1.01870e12 0.0401959
\(953\) −3.07823e13 −1.20888 −0.604440 0.796651i \(-0.706603\pi\)
−0.604440 + 0.796651i \(0.706603\pi\)
\(954\) −4.85232e11 −0.0189663
\(955\) −1.39998e13 −0.544636
\(956\) 1.54087e12 0.0596630
\(957\) −6.82054e12 −0.262854
\(958\) −1.71682e13 −0.658538
\(959\) −6.45197e12 −0.246325
\(960\) 3.49115e12 0.132663
\(961\) 2.52786e13 0.956089
\(962\) −4.14685e13 −1.56110
\(963\) 9.91043e12 0.371342
\(964\) −1.47393e13 −0.549707
\(965\) 1.05199e13 0.390518
\(966\) −3.64644e12 −0.134732
\(967\) −4.21928e13 −1.55174 −0.775871 0.630892i \(-0.782689\pi\)
−0.775871 + 0.630892i \(0.782689\pi\)
\(968\) 1.67429e13 0.612903
\(969\) −2.24797e12 −0.0819095
\(970\) 7.93595e12 0.287823
\(971\) 1.49247e13 0.538791 0.269395 0.963030i \(-0.413176\pi\)
0.269395 + 0.963030i \(0.413176\pi\)
\(972\) 7.34455e11 0.0263917
\(973\) −1.15443e13 −0.412914
\(974\) 1.19840e13 0.426664
\(975\) −1.35544e13 −0.480352
\(976\) −4.20978e13 −1.48503
\(977\) 1.00619e13 0.353309 0.176654 0.984273i \(-0.443473\pi\)
0.176654 + 0.984273i \(0.443473\pi\)
\(978\) −1.89913e13 −0.663789
\(979\) −5.42526e12 −0.188755
\(980\) −7.17201e12 −0.248384
\(981\) −1.13209e13 −0.390274
\(982\) 1.97275e12 0.0676971
\(983\) −1.70566e13 −0.582641 −0.291321 0.956626i \(-0.594095\pi\)
−0.291321 + 0.956626i \(0.594095\pi\)
\(984\) −2.07778e13 −0.706514
\(985\) −3.71932e13 −1.25893
\(986\) −6.56555e12 −0.221220
\(987\) 1.88486e12 0.0632197
\(988\) 2.09289e13 0.698778
\(989\) −4.92064e12 −0.163545
\(990\) −3.02305e12 −0.100020
\(991\) 4.73012e13 1.55791 0.778953 0.627083i \(-0.215751\pi\)
0.778953 + 0.627083i \(0.215751\pi\)
\(992\) −3.31212e13 −1.08593
\(993\) −1.07776e12 −0.0351763
\(994\) 1.70576e13 0.554215
\(995\) 9.67484e12 0.312925
\(996\) −3.16477e12 −0.101900
\(997\) 3.88932e13 1.24665 0.623326 0.781962i \(-0.285781\pi\)
0.623326 + 0.781962i \(0.285781\pi\)
\(998\) 2.66908e13 0.851676
\(999\) −4.62625e12 −0.146955
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.1.17 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.17 22 1.1 even 1 trivial