Properties

Label 177.10.a.d.1.6
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 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} -52560.7 q^{10} +94387.2 q^{11} -8869.24 q^{12} +101912. q^{13} +93148.8 q^{14} +212208. q^{15} -194092. q^{16} -174668. q^{17} -131630. q^{18} +598100. q^{19} -286865. q^{20} -376078. q^{21} -1.89364e6 q^{22} -811615. q^{23} +1.00997e6 q^{24} +4.91050e6 q^{25} -2.04461e6 q^{26} +531441. q^{27} +508387. q^{28} +7.22901e6 q^{29} -4.25742e6 q^{30} +7.32811e6 q^{31} -2.49004e6 q^{32} +7.64536e6 q^{33} +3.50427e6 q^{34} -1.21638e7 q^{35} -718409. q^{36} +715607. q^{37} -1.19994e7 q^{38} +8.25488e6 q^{39} +3.26663e7 q^{40} -2.55171e7 q^{41} +7.54505e6 q^{42} -8.78795e6 q^{43} -1.03351e7 q^{44} +1.71888e7 q^{45} +1.62830e7 q^{46} +7.96566e6 q^{47} -1.57215e7 q^{48} -1.87968e7 q^{49} -9.85168e7 q^{50} -1.41481e7 q^{51} -1.11590e7 q^{52} -1.41564e7 q^{53} -1.06620e7 q^{54} +2.47281e8 q^{55} -5.78917e7 q^{56} +4.84461e7 q^{57} -1.45032e8 q^{58} -1.21174e7 q^{59} -2.32361e7 q^{60} -1.20131e8 q^{61} -1.47020e8 q^{62} -3.04623e7 q^{63} +1.49332e8 q^{64} +2.66994e8 q^{65} -1.53385e8 q^{66} -1.23118e8 q^{67} +1.91255e7 q^{68} -6.57408e7 q^{69} +2.44036e8 q^{70} -3.13097e8 q^{71} +8.18076e7 q^{72} -1.28195e8 q^{73} -1.43569e7 q^{74} +3.97750e8 q^{75} -6.54901e7 q^{76} -4.38234e8 q^{77} -1.65613e8 q^{78} -3.90227e8 q^{79} -5.08492e8 q^{80} +4.30467e7 q^{81} +5.11936e8 q^{82} +5.79282e8 q^{83} +4.11793e7 q^{84} -4.57603e8 q^{85} +1.76308e8 q^{86} +5.85550e8 q^{87} +1.17689e9 q^{88} +1.25314e8 q^{89} -3.44851e8 q^{90} -4.73171e8 q^{91} +8.88693e7 q^{92} +5.93577e8 q^{93} -1.59811e8 q^{94} +1.56693e9 q^{95} -2.01693e8 q^{96} +5.54861e8 q^{97} +3.77110e8 q^{98} +6.19275e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −20.0625 −0.886645 −0.443322 0.896362i \(-0.646200\pi\)
−0.443322 + 0.896362i \(0.646200\pi\)
\(3\) 81.0000 0.577350
\(4\) −109.497 −0.213861
\(5\) 2619.85 1.87461 0.937307 0.348506i \(-0.113311\pi\)
0.937307 + 0.348506i \(0.113311\pi\)
\(6\) −1625.06 −0.511905
\(7\) −4642.93 −0.730889 −0.365444 0.930833i \(-0.619083\pi\)
−0.365444 + 0.930833i \(0.619083\pi\)
\(8\) 12468.8 1.07626
\(9\) 6561.00 0.333333
\(10\) −52560.7 −1.66212
\(11\) 94387.2 1.94378 0.971888 0.235445i \(-0.0756546\pi\)
0.971888 + 0.235445i \(0.0756546\pi\)
\(12\) −8869.24 −0.123473
\(13\) 101912. 0.989647 0.494824 0.868993i \(-0.335233\pi\)
0.494824 + 0.868993i \(0.335233\pi\)
\(14\) 93148.8 0.648039
\(15\) 212208. 1.08231
\(16\) −194092. −0.740402
\(17\) −174668. −0.507215 −0.253608 0.967307i \(-0.581617\pi\)
−0.253608 + 0.967307i \(0.581617\pi\)
\(18\) −131630. −0.295548
\(19\) 598100. 1.05289 0.526445 0.850209i \(-0.323525\pi\)
0.526445 + 0.850209i \(0.323525\pi\)
\(20\) −286865. −0.400907
\(21\) −376078. −0.421979
\(22\) −1.89364e6 −1.72344
\(23\) −811615. −0.604749 −0.302374 0.953189i \(-0.597779\pi\)
−0.302374 + 0.953189i \(0.597779\pi\)
\(24\) 1.00997e6 0.621381
\(25\) 4.91050e6 2.51418
\(26\) −2.04461e6 −0.877466
\(27\) 531441. 0.192450
\(28\) 508387. 0.156309
\(29\) 7.22901e6 1.89796 0.948982 0.315331i \(-0.102116\pi\)
0.948982 + 0.315331i \(0.102116\pi\)
\(30\) −4.25742e6 −0.959623
\(31\) 7.32811e6 1.42516 0.712581 0.701590i \(-0.247526\pi\)
0.712581 + 0.701590i \(0.247526\pi\)
\(32\) −2.49004e6 −0.419790
\(33\) 7.64536e6 1.12224
\(34\) 3.50427e6 0.449720
\(35\) −1.21638e7 −1.37013
\(36\) −718409. −0.0712870
\(37\) 715607. 0.0627721 0.0313861 0.999507i \(-0.490008\pi\)
0.0313861 + 0.999507i \(0.490008\pi\)
\(38\) −1.19994e7 −0.933539
\(39\) 8.25488e6 0.571373
\(40\) 3.26663e7 2.01758
\(41\) −2.55171e7 −1.41027 −0.705137 0.709071i \(-0.749115\pi\)
−0.705137 + 0.709071i \(0.749115\pi\)
\(42\) 7.54505e6 0.374145
\(43\) −8.78795e6 −0.391994 −0.195997 0.980604i \(-0.562794\pi\)
−0.195997 + 0.980604i \(0.562794\pi\)
\(44\) −1.03351e7 −0.415698
\(45\) 1.71888e7 0.624871
\(46\) 1.62830e7 0.536197
\(47\) 7.96566e6 0.238112 0.119056 0.992888i \(-0.462013\pi\)
0.119056 + 0.992888i \(0.462013\pi\)
\(48\) −1.57215e7 −0.427472
\(49\) −1.87968e7 −0.465801
\(50\) −9.85168e7 −2.22918
\(51\) −1.41481e7 −0.292841
\(52\) −1.11590e7 −0.211647
\(53\) −1.41564e7 −0.246441 −0.123220 0.992379i \(-0.539322\pi\)
−0.123220 + 0.992379i \(0.539322\pi\)
\(54\) −1.06620e7 −0.170635
\(55\) 2.47281e8 3.64383
\(56\) −5.78917e7 −0.786629
\(57\) 4.84461e7 0.607886
\(58\) −1.45032e8 −1.68282
\(59\) −1.21174e7 −0.130189
\(60\) −2.32361e7 −0.231464
\(61\) −1.20131e8 −1.11089 −0.555444 0.831554i \(-0.687452\pi\)
−0.555444 + 0.831554i \(0.687452\pi\)
\(62\) −1.47020e8 −1.26361
\(63\) −3.04623e7 −0.243630
\(64\) 1.49332e8 1.11261
\(65\) 2.66994e8 1.85521
\(66\) −1.53385e8 −0.995028
\(67\) −1.23118e8 −0.746423 −0.373212 0.927746i \(-0.621743\pi\)
−0.373212 + 0.927746i \(0.621743\pi\)
\(68\) 1.91255e7 0.108474
\(69\) −6.57408e7 −0.349152
\(70\) 2.44036e8 1.21482
\(71\) −3.13097e8 −1.46223 −0.731115 0.682254i \(-0.761000\pi\)
−0.731115 + 0.682254i \(0.761000\pi\)
\(72\) 8.18076e7 0.358755
\(73\) −1.28195e8 −0.528348 −0.264174 0.964475i \(-0.585099\pi\)
−0.264174 + 0.964475i \(0.585099\pi\)
\(74\) −1.43569e7 −0.0556566
\(75\) 3.97750e8 1.45156
\(76\) −6.54901e7 −0.225172
\(77\) −4.38234e8 −1.42068
\(78\) −1.65613e8 −0.506605
\(79\) −3.90227e8 −1.12718 −0.563592 0.826053i \(-0.690581\pi\)
−0.563592 + 0.826053i \(0.690581\pi\)
\(80\) −5.08492e8 −1.38797
\(81\) 4.30467e7 0.111111
\(82\) 5.11936e8 1.25041
\(83\) 5.79282e8 1.33980 0.669898 0.742453i \(-0.266338\pi\)
0.669898 + 0.742453i \(0.266338\pi\)
\(84\) 4.11793e7 0.0902448
\(85\) −4.57603e8 −0.950832
\(86\) 1.76308e8 0.347560
\(87\) 5.85550e8 1.09579
\(88\) 1.17689e9 2.09201
\(89\) 1.25314e8 0.211712 0.105856 0.994381i \(-0.466242\pi\)
0.105856 + 0.994381i \(0.466242\pi\)
\(90\) −3.44851e8 −0.554039
\(91\) −4.73171e8 −0.723322
\(92\) 8.88693e7 0.129332
\(93\) 5.93577e8 0.822818
\(94\) −1.59811e8 −0.211121
\(95\) 1.56693e9 1.97376
\(96\) −2.01693e8 −0.242366
\(97\) 5.54861e8 0.636373 0.318186 0.948028i \(-0.396926\pi\)
0.318186 + 0.948028i \(0.396926\pi\)
\(98\) 3.77110e8 0.413000
\(99\) 6.19275e8 0.647925
\(100\) −5.37684e8 −0.537684
\(101\) −9.65044e8 −0.922785 −0.461393 0.887196i \(-0.652650\pi\)
−0.461393 + 0.887196i \(0.652650\pi\)
\(102\) 2.83846e8 0.259646
\(103\) −4.46300e8 −0.390715 −0.195357 0.980732i \(-0.562587\pi\)
−0.195357 + 0.980732i \(0.562587\pi\)
\(104\) 1.27072e9 1.06512
\(105\) −9.85268e8 −0.791047
\(106\) 2.84013e8 0.218506
\(107\) 8.14950e8 0.601040 0.300520 0.953775i \(-0.402840\pi\)
0.300520 + 0.953775i \(0.402840\pi\)
\(108\) −5.81911e7 −0.0411576
\(109\) 9.99145e8 0.677968 0.338984 0.940792i \(-0.389917\pi\)
0.338984 + 0.940792i \(0.389917\pi\)
\(110\) −4.96106e9 −3.23078
\(111\) 5.79642e7 0.0362415
\(112\) 9.01157e8 0.541152
\(113\) −2.39006e9 −1.37897 −0.689487 0.724298i \(-0.742164\pi\)
−0.689487 + 0.724298i \(0.742164\pi\)
\(114\) −9.71949e8 −0.538979
\(115\) −2.12631e9 −1.13367
\(116\) −7.91554e8 −0.405900
\(117\) 6.68645e8 0.329882
\(118\) 2.43104e8 0.115431
\(119\) 8.10970e8 0.370718
\(120\) 2.64597e9 1.16485
\(121\) 6.55100e9 2.77826
\(122\) 2.41012e9 0.984964
\(123\) −2.06688e9 −0.814222
\(124\) −8.02405e8 −0.304787
\(125\) 7.74788e9 2.83849
\(126\) 6.11149e8 0.216013
\(127\) 3.72987e9 1.27226 0.636131 0.771581i \(-0.280534\pi\)
0.636131 + 0.771581i \(0.280534\pi\)
\(128\) −1.72106e9 −0.566697
\(129\) −7.11824e8 −0.226318
\(130\) −5.35657e9 −1.64491
\(131\) −5.89914e9 −1.75012 −0.875060 0.484014i \(-0.839179\pi\)
−0.875060 + 0.484014i \(0.839179\pi\)
\(132\) −8.37143e8 −0.240003
\(133\) −2.77694e9 −0.769545
\(134\) 2.47005e9 0.661812
\(135\) 1.39230e9 0.360770
\(136\) −2.17789e9 −0.545897
\(137\) 6.38085e9 1.54752 0.773760 0.633479i \(-0.218374\pi\)
0.773760 + 0.633479i \(0.218374\pi\)
\(138\) 1.31892e9 0.309574
\(139\) −2.76211e9 −0.627588 −0.313794 0.949491i \(-0.601600\pi\)
−0.313794 + 0.949491i \(0.601600\pi\)
\(140\) 1.33190e9 0.293018
\(141\) 6.45218e8 0.137474
\(142\) 6.28149e9 1.29648
\(143\) 9.61919e9 1.92365
\(144\) −1.27344e9 −0.246801
\(145\) 1.89389e10 3.55795
\(146\) 2.57192e9 0.468457
\(147\) −1.52254e9 −0.268931
\(148\) −7.83567e7 −0.0134245
\(149\) 6.08916e9 1.01209 0.506045 0.862507i \(-0.331107\pi\)
0.506045 + 0.862507i \(0.331107\pi\)
\(150\) −7.97986e9 −1.28702
\(151\) −2.28550e9 −0.357755 −0.178877 0.983871i \(-0.557247\pi\)
−0.178877 + 0.983871i \(0.557247\pi\)
\(152\) 7.45757e9 1.13319
\(153\) −1.14599e9 −0.169072
\(154\) 8.79206e9 1.25964
\(155\) 1.91986e10 2.67163
\(156\) −9.03883e8 −0.122194
\(157\) 1.20766e10 1.58635 0.793173 0.608996i \(-0.208428\pi\)
0.793173 + 0.608996i \(0.208428\pi\)
\(158\) 7.82891e9 0.999412
\(159\) −1.14667e9 −0.142283
\(160\) −6.52354e9 −0.786943
\(161\) 3.76828e9 0.442004
\(162\) −8.63624e8 −0.0985161
\(163\) 7.24899e9 0.804328 0.402164 0.915568i \(-0.368258\pi\)
0.402164 + 0.915568i \(0.368258\pi\)
\(164\) 2.79404e9 0.301603
\(165\) 2.00297e10 2.10376
\(166\) −1.16218e10 −1.18792
\(167\) 7.99480e9 0.795396 0.397698 0.917516i \(-0.369809\pi\)
0.397698 + 0.917516i \(0.369809\pi\)
\(168\) −4.68923e9 −0.454161
\(169\) −2.18435e8 −0.0205983
\(170\) 9.18066e9 0.843050
\(171\) 3.92414e9 0.350963
\(172\) 9.62253e8 0.0838322
\(173\) −1.17866e10 −1.00041 −0.500207 0.865906i \(-0.666743\pi\)
−0.500207 + 0.865906i \(0.666743\pi\)
\(174\) −1.17476e10 −0.971576
\(175\) −2.27991e10 −1.83758
\(176\) −1.83198e10 −1.43918
\(177\) −9.81506e8 −0.0751646
\(178\) −2.51411e9 −0.187713
\(179\) −1.07231e10 −0.780694 −0.390347 0.920668i \(-0.627645\pi\)
−0.390347 + 0.920668i \(0.627645\pi\)
\(180\) −1.88212e9 −0.133636
\(181\) −2.63189e10 −1.82270 −0.911348 0.411637i \(-0.864957\pi\)
−0.911348 + 0.411637i \(0.864957\pi\)
\(182\) 9.49298e9 0.641330
\(183\) −9.73060e9 −0.641372
\(184\) −1.01198e10 −0.650869
\(185\) 1.87478e9 0.117673
\(186\) −1.19086e10 −0.729547
\(187\) −1.64864e10 −0.985912
\(188\) −8.72214e8 −0.0509229
\(189\) −2.46745e9 −0.140660
\(190\) −3.14366e10 −1.75002
\(191\) 4.47796e9 0.243461 0.121731 0.992563i \(-0.461156\pi\)
0.121731 + 0.992563i \(0.461156\pi\)
\(192\) 1.20959e10 0.642364
\(193\) 2.23390e10 1.15893 0.579464 0.814998i \(-0.303262\pi\)
0.579464 + 0.814998i \(0.303262\pi\)
\(194\) −1.11319e10 −0.564236
\(195\) 2.16266e10 1.07110
\(196\) 2.05819e9 0.0996167
\(197\) −1.08202e10 −0.511843 −0.255921 0.966698i \(-0.582379\pi\)
−0.255921 + 0.966698i \(0.582379\pi\)
\(198\) −1.24242e10 −0.574480
\(199\) 6.34469e9 0.286795 0.143398 0.989665i \(-0.454197\pi\)
0.143398 + 0.989665i \(0.454197\pi\)
\(200\) 6.12279e10 2.70591
\(201\) −9.97256e9 −0.430948
\(202\) 1.93612e10 0.818183
\(203\) −3.35638e10 −1.38720
\(204\) 1.54917e9 0.0626272
\(205\) −6.68510e10 −2.64372
\(206\) 8.95389e9 0.346425
\(207\) −5.32501e9 −0.201583
\(208\) −1.97803e10 −0.732737
\(209\) 5.64530e10 2.04658
\(210\) 1.97669e10 0.701378
\(211\) 2.33646e10 0.811498 0.405749 0.913985i \(-0.367011\pi\)
0.405749 + 0.913985i \(0.367011\pi\)
\(212\) 1.55009e9 0.0527041
\(213\) −2.53608e10 −0.844219
\(214\) −1.63499e10 −0.532909
\(215\) −2.30231e10 −0.734837
\(216\) 6.62641e9 0.207127
\(217\) −3.40239e10 −1.04164
\(218\) −2.00453e10 −0.601117
\(219\) −1.03838e10 −0.305042
\(220\) −2.70764e10 −0.779273
\(221\) −1.78007e10 −0.501964
\(222\) −1.16291e9 −0.0321333
\(223\) 4.97717e10 1.34775 0.673877 0.738844i \(-0.264628\pi\)
0.673877 + 0.738844i \(0.264628\pi\)
\(224\) 1.15611e10 0.306820
\(225\) 3.22178e10 0.838058
\(226\) 4.79506e10 1.22266
\(227\) −2.07221e10 −0.517985 −0.258992 0.965879i \(-0.583390\pi\)
−0.258992 + 0.965879i \(0.583390\pi\)
\(228\) −5.30470e9 −0.130003
\(229\) −6.32264e10 −1.51928 −0.759641 0.650342i \(-0.774626\pi\)
−0.759641 + 0.650342i \(0.774626\pi\)
\(230\) 4.26591e10 1.00516
\(231\) −3.54969e10 −0.820232
\(232\) 9.01368e10 2.04271
\(233\) 5.89052e9 0.130934 0.0654669 0.997855i \(-0.479146\pi\)
0.0654669 + 0.997855i \(0.479146\pi\)
\(234\) −1.34147e10 −0.292489
\(235\) 2.08688e10 0.446368
\(236\) 1.32681e9 0.0278423
\(237\) −3.16084e10 −0.650780
\(238\) −1.62701e10 −0.328695
\(239\) −5.30021e10 −1.05076 −0.525379 0.850868i \(-0.676076\pi\)
−0.525379 + 0.850868i \(0.676076\pi\)
\(240\) −4.11879e10 −0.801344
\(241\) 8.88739e10 1.69706 0.848531 0.529146i \(-0.177488\pi\)
0.848531 + 0.529146i \(0.177488\pi\)
\(242\) −1.31429e11 −2.46333
\(243\) 3.48678e9 0.0641500
\(244\) 1.31540e10 0.237576
\(245\) −4.92447e10 −0.873197
\(246\) 4.14668e10 0.721926
\(247\) 6.09536e10 1.04199
\(248\) 9.13725e10 1.53385
\(249\) 4.69218e10 0.773531
\(250\) −1.55442e11 −2.51673
\(251\) 5.90117e10 0.938440 0.469220 0.883081i \(-0.344535\pi\)
0.469220 + 0.883081i \(0.344535\pi\)
\(252\) 3.33552e9 0.0521029
\(253\) −7.66061e10 −1.17550
\(254\) −7.48304e10 −1.12804
\(255\) −3.70659e10 −0.548963
\(256\) −4.19290e10 −0.610147
\(257\) −8.45554e10 −1.20904 −0.604522 0.796588i \(-0.706636\pi\)
−0.604522 + 0.796588i \(0.706636\pi\)
\(258\) 1.42810e10 0.200664
\(259\) −3.32252e9 −0.0458795
\(260\) −2.92350e10 −0.396756
\(261\) 4.74295e10 0.632654
\(262\) 1.18351e11 1.55174
\(263\) 3.27803e10 0.422485 0.211243 0.977434i \(-0.432249\pi\)
0.211243 + 0.977434i \(0.432249\pi\)
\(264\) 9.53283e10 1.20783
\(265\) −3.70878e10 −0.461981
\(266\) 5.57123e10 0.682313
\(267\) 1.01504e10 0.122232
\(268\) 1.34810e10 0.159631
\(269\) −4.94973e9 −0.0576363 −0.0288182 0.999585i \(-0.509174\pi\)
−0.0288182 + 0.999585i \(0.509174\pi\)
\(270\) −2.79329e10 −0.319874
\(271\) −1.06262e11 −1.19679 −0.598393 0.801203i \(-0.704194\pi\)
−0.598393 + 0.801203i \(0.704194\pi\)
\(272\) 3.39016e10 0.375543
\(273\) −3.83268e10 −0.417610
\(274\) −1.28016e11 −1.37210
\(275\) 4.63488e11 4.88699
\(276\) 7.19841e9 0.0746699
\(277\) 2.17004e10 0.221467 0.110733 0.993850i \(-0.464680\pi\)
0.110733 + 0.993850i \(0.464680\pi\)
\(278\) 5.54148e10 0.556448
\(279\) 4.80797e10 0.475054
\(280\) −1.51668e11 −1.47463
\(281\) −6.09824e10 −0.583481 −0.291740 0.956498i \(-0.594234\pi\)
−0.291740 + 0.956498i \(0.594234\pi\)
\(282\) −1.29447e10 −0.121891
\(283\) −2.24580e10 −0.208129 −0.104065 0.994571i \(-0.533185\pi\)
−0.104065 + 0.994571i \(0.533185\pi\)
\(284\) 3.42831e10 0.312714
\(285\) 1.26922e11 1.13955
\(286\) −1.92985e11 −1.70560
\(287\) 1.18474e11 1.03075
\(288\) −1.63372e10 −0.139930
\(289\) −8.80791e10 −0.742733
\(290\) −3.79962e11 −3.15464
\(291\) 4.49437e10 0.367410
\(292\) 1.40370e10 0.112993
\(293\) 5.49774e10 0.435793 0.217896 0.975972i \(-0.430081\pi\)
0.217896 + 0.975972i \(0.430081\pi\)
\(294\) 3.05459e10 0.238446
\(295\) −3.17457e10 −0.244054
\(296\) 8.92274e9 0.0675594
\(297\) 5.01612e10 0.374080
\(298\) −1.22164e11 −0.897365
\(299\) −8.27133e10 −0.598488
\(300\) −4.35524e10 −0.310432
\(301\) 4.08019e10 0.286504
\(302\) 4.58529e10 0.317202
\(303\) −7.81685e10 −0.532770
\(304\) −1.16087e11 −0.779562
\(305\) −3.14725e11 −2.08249
\(306\) 2.29915e10 0.149907
\(307\) 1.69953e11 1.09196 0.545979 0.837799i \(-0.316158\pi\)
0.545979 + 0.837799i \(0.316158\pi\)
\(308\) 4.79852e10 0.303829
\(309\) −3.61503e10 −0.225579
\(310\) −3.85171e11 −2.36879
\(311\) 7.45434e10 0.451843 0.225922 0.974145i \(-0.427461\pi\)
0.225922 + 0.974145i \(0.427461\pi\)
\(312\) 1.02928e11 0.614948
\(313\) −1.89734e11 −1.11737 −0.558683 0.829381i \(-0.688693\pi\)
−0.558683 + 0.829381i \(0.688693\pi\)
\(314\) −2.42288e11 −1.40653
\(315\) −7.98067e10 −0.456711
\(316\) 4.27286e10 0.241061
\(317\) −3.01500e11 −1.67695 −0.838475 0.544940i \(-0.816552\pi\)
−0.838475 + 0.544940i \(0.816552\pi\)
\(318\) 2.30051e10 0.126154
\(319\) 6.82326e11 3.68921
\(320\) 3.91227e11 2.08571
\(321\) 6.60109e10 0.347011
\(322\) −7.56010e10 −0.391901
\(323\) −1.04469e11 −0.534041
\(324\) −4.71348e9 −0.0237623
\(325\) 5.00439e11 2.48815
\(326\) −1.45433e11 −0.713153
\(327\) 8.09308e10 0.391425
\(328\) −3.18167e11 −1.51783
\(329\) −3.69840e10 −0.174033
\(330\) −4.01846e11 −1.86529
\(331\) 6.12456e10 0.280446 0.140223 0.990120i \(-0.455218\pi\)
0.140223 + 0.990120i \(0.455218\pi\)
\(332\) −6.34295e10 −0.286530
\(333\) 4.69510e9 0.0209240
\(334\) −1.60395e11 −0.705234
\(335\) −3.22551e11 −1.39925
\(336\) 7.29937e10 0.312434
\(337\) 3.11346e11 1.31495 0.657473 0.753478i \(-0.271625\pi\)
0.657473 + 0.753478i \(0.271625\pi\)
\(338\) 4.38234e9 0.0182634
\(339\) −1.93595e11 −0.796151
\(340\) 5.01061e10 0.203346
\(341\) 6.91680e11 2.77020
\(342\) −7.87279e10 −0.311180
\(343\) 2.74631e11 1.07134
\(344\) −1.09575e11 −0.421889
\(345\) −1.72231e11 −0.654524
\(346\) 2.36468e11 0.887012
\(347\) 9.84171e10 0.364408 0.182204 0.983261i \(-0.441677\pi\)
0.182204 + 0.983261i \(0.441677\pi\)
\(348\) −6.41158e10 −0.234347
\(349\) −1.25695e11 −0.453529 −0.226765 0.973950i \(-0.572815\pi\)
−0.226765 + 0.973950i \(0.572815\pi\)
\(350\) 4.57407e11 1.62928
\(351\) 5.41602e10 0.190458
\(352\) −2.35028e11 −0.815977
\(353\) 3.19345e11 1.09465 0.547324 0.836921i \(-0.315647\pi\)
0.547324 + 0.836921i \(0.315647\pi\)
\(354\) 1.96915e10 0.0666443
\(355\) −8.20266e11 −2.74112
\(356\) −1.37215e10 −0.0452768
\(357\) 6.56886e10 0.214034
\(358\) 2.15132e11 0.692198
\(359\) 2.19489e10 0.0697410 0.0348705 0.999392i \(-0.488898\pi\)
0.0348705 + 0.999392i \(0.488898\pi\)
\(360\) 2.14324e11 0.672526
\(361\) 3.50362e10 0.108576
\(362\) 5.28022e11 1.61608
\(363\) 5.30631e11 1.60403
\(364\) 5.18107e10 0.154690
\(365\) −3.35853e11 −0.990448
\(366\) 1.95220e11 0.568669
\(367\) −2.12729e11 −0.612110 −0.306055 0.952014i \(-0.599009\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(368\) 1.57528e11 0.447757
\(369\) −1.67418e11 −0.470091
\(370\) −3.76128e10 −0.104335
\(371\) 6.57275e10 0.180121
\(372\) −6.49948e10 −0.175969
\(373\) −2.24274e11 −0.599914 −0.299957 0.953953i \(-0.596972\pi\)
−0.299957 + 0.953953i \(0.596972\pi\)
\(374\) 3.30758e11 0.874154
\(375\) 6.27578e11 1.63880
\(376\) 9.93219e10 0.256271
\(377\) 7.36723e11 1.87831
\(378\) 4.95031e10 0.124715
\(379\) −4.97926e11 −1.23962 −0.619809 0.784752i \(-0.712790\pi\)
−0.619809 + 0.784752i \(0.712790\pi\)
\(380\) −1.71574e11 −0.422110
\(381\) 3.02119e11 0.734541
\(382\) −8.98390e10 −0.215864
\(383\) 3.98168e11 0.945521 0.472761 0.881191i \(-0.343257\pi\)
0.472761 + 0.881191i \(0.343257\pi\)
\(384\) −1.39406e11 −0.327183
\(385\) −1.14811e12 −2.66323
\(386\) −4.48177e11 −1.02756
\(387\) −5.76577e10 −0.130665
\(388\) −6.07555e10 −0.136095
\(389\) −4.13365e11 −0.915293 −0.457647 0.889134i \(-0.651308\pi\)
−0.457647 + 0.889134i \(0.651308\pi\)
\(390\) −4.33882e11 −0.949688
\(391\) 1.41763e11 0.306738
\(392\) −2.34372e11 −0.501325
\(393\) −4.77831e11 −1.01043
\(394\) 2.17080e11 0.453823
\(395\) −1.02234e12 −2.11303
\(396\) −6.78086e10 −0.138566
\(397\) 6.21335e10 0.125536 0.0627680 0.998028i \(-0.480007\pi\)
0.0627680 + 0.998028i \(0.480007\pi\)
\(398\) −1.27290e11 −0.254285
\(399\) −2.24932e11 −0.444297
\(400\) −9.53089e11 −1.86150
\(401\) 3.10487e11 0.599645 0.299823 0.953995i \(-0.403072\pi\)
0.299823 + 0.953995i \(0.403072\pi\)
\(402\) 2.00074e11 0.382098
\(403\) 7.46823e11 1.41041
\(404\) 1.05669e11 0.197348
\(405\) 1.12776e11 0.208290
\(406\) 6.73373e11 1.22995
\(407\) 6.75442e10 0.122015
\(408\) −1.76409e11 −0.315174
\(409\) −7.93556e11 −1.40224 −0.701121 0.713043i \(-0.747317\pi\)
−0.701121 + 0.713043i \(0.747317\pi\)
\(410\) 1.34120e12 2.34404
\(411\) 5.16849e11 0.893461
\(412\) 4.88685e10 0.0835586
\(413\) 5.62601e10 0.0951536
\(414\) 1.06833e11 0.178732
\(415\) 1.51763e12 2.51160
\(416\) −2.53765e11 −0.415444
\(417\) −2.23731e11 −0.362338
\(418\) −1.13259e12 −1.81459
\(419\) 6.60242e10 0.104650 0.0523251 0.998630i \(-0.483337\pi\)
0.0523251 + 0.998630i \(0.483337\pi\)
\(420\) 1.07884e11 0.169174
\(421\) −3.88291e11 −0.602404 −0.301202 0.953560i \(-0.597388\pi\)
−0.301202 + 0.953560i \(0.597388\pi\)
\(422\) −4.68752e11 −0.719510
\(423\) 5.22627e10 0.0793707
\(424\) −1.76513e11 −0.265235
\(425\) −8.57705e11 −1.27523
\(426\) 5.08801e11 0.748522
\(427\) 5.57760e11 0.811936
\(428\) −8.92344e10 −0.128539
\(429\) 7.79155e11 1.11062
\(430\) 4.61901e11 0.651540
\(431\) 9.04844e10 0.126307 0.0631533 0.998004i \(-0.479884\pi\)
0.0631533 + 0.998004i \(0.479884\pi\)
\(432\) −1.03148e11 −0.142491
\(433\) −9.10222e11 −1.24438 −0.622188 0.782868i \(-0.713756\pi\)
−0.622188 + 0.782868i \(0.713756\pi\)
\(434\) 6.82605e11 0.923561
\(435\) 1.53405e12 2.05418
\(436\) −1.09403e11 −0.144991
\(437\) −4.85427e11 −0.636733
\(438\) 2.08326e11 0.270464
\(439\) 5.83572e11 0.749901 0.374951 0.927045i \(-0.377660\pi\)
0.374951 + 0.927045i \(0.377660\pi\)
\(440\) 3.08328e12 3.92172
\(441\) −1.23326e11 −0.155267
\(442\) 3.57127e11 0.445064
\(443\) −2.48193e11 −0.306177 −0.153088 0.988213i \(-0.548922\pi\)
−0.153088 + 0.988213i \(0.548922\pi\)
\(444\) −6.34689e9 −0.00775065
\(445\) 3.28304e11 0.396877
\(446\) −9.98543e11 −1.19498
\(447\) 4.93222e11 0.584331
\(448\) −6.93337e11 −0.813192
\(449\) 3.24622e11 0.376938 0.188469 0.982079i \(-0.439648\pi\)
0.188469 + 0.982079i \(0.439648\pi\)
\(450\) −6.46369e11 −0.743060
\(451\) −2.40849e12 −2.74126
\(452\) 2.61704e11 0.294909
\(453\) −1.85126e11 −0.206550
\(454\) 4.15736e11 0.459268
\(455\) −1.23964e12 −1.35595
\(456\) 6.04063e11 0.654246
\(457\) 4.72129e11 0.506335 0.253167 0.967423i \(-0.418528\pi\)
0.253167 + 0.967423i \(0.418528\pi\)
\(458\) 1.26848e12 1.34706
\(459\) −9.28255e10 −0.0976136
\(460\) 2.32824e11 0.242448
\(461\) −3.91642e11 −0.403864 −0.201932 0.979400i \(-0.564722\pi\)
−0.201932 + 0.979400i \(0.564722\pi\)
\(462\) 7.12157e11 0.727255
\(463\) 3.19127e11 0.322738 0.161369 0.986894i \(-0.448409\pi\)
0.161369 + 0.986894i \(0.448409\pi\)
\(464\) −1.40309e12 −1.40526
\(465\) 1.55508e12 1.54247
\(466\) −1.18178e11 −0.116092
\(467\) 3.42865e11 0.333578 0.166789 0.985993i \(-0.446660\pi\)
0.166789 + 0.985993i \(0.446660\pi\)
\(468\) −7.32145e10 −0.0705490
\(469\) 5.71629e11 0.545553
\(470\) −4.18681e11 −0.395770
\(471\) 9.78209e11 0.915878
\(472\) −1.51089e11 −0.140118
\(473\) −8.29470e11 −0.761949
\(474\) 6.34142e11 0.577011
\(475\) 2.93697e12 2.64715
\(476\) −8.87987e10 −0.0792821
\(477\) −9.28804e10 −0.0821470
\(478\) 1.06335e12 0.931649
\(479\) −1.63372e12 −1.41797 −0.708987 0.705222i \(-0.750848\pi\)
−0.708987 + 0.705222i \(0.750848\pi\)
\(480\) −5.28407e11 −0.454342
\(481\) 7.29290e10 0.0621223
\(482\) −1.78303e12 −1.50469
\(483\) 3.05230e11 0.255191
\(484\) −7.17314e11 −0.594162
\(485\) 1.45365e12 1.19295
\(486\) −6.99535e10 −0.0568783
\(487\) 6.17831e11 0.497725 0.248862 0.968539i \(-0.419943\pi\)
0.248862 + 0.968539i \(0.419943\pi\)
\(488\) −1.49788e12 −1.19561
\(489\) 5.87168e11 0.464379
\(490\) 9.87972e11 0.774216
\(491\) 1.56189e12 1.21279 0.606393 0.795165i \(-0.292616\pi\)
0.606393 + 0.795165i \(0.292616\pi\)
\(492\) 2.26317e11 0.174130
\(493\) −1.26267e12 −0.962676
\(494\) −1.22288e12 −0.923874
\(495\) 1.62241e12 1.21461
\(496\) −1.42233e12 −1.05519
\(497\) 1.45369e12 1.06873
\(498\) −9.41368e11 −0.685847
\(499\) 4.28815e11 0.309612 0.154806 0.987945i \(-0.450525\pi\)
0.154806 + 0.987945i \(0.450525\pi\)
\(500\) −8.48368e11 −0.607043
\(501\) 6.47579e11 0.459222
\(502\) −1.18392e12 −0.832063
\(503\) −2.85102e11 −0.198584 −0.0992920 0.995058i \(-0.531658\pi\)
−0.0992920 + 0.995058i \(0.531658\pi\)
\(504\) −3.79827e11 −0.262210
\(505\) −2.52827e12 −1.72987
\(506\) 1.53691e12 1.04225
\(507\) −1.76932e10 −0.0118924
\(508\) −4.08408e11 −0.272087
\(509\) 2.89839e12 1.91394 0.956968 0.290195i \(-0.0937201\pi\)
0.956968 + 0.290195i \(0.0937201\pi\)
\(510\) 7.43633e11 0.486735
\(511\) 5.95203e11 0.386164
\(512\) 1.72238e12 1.10768
\(513\) 3.17855e11 0.202629
\(514\) 1.69639e12 1.07199
\(515\) −1.16924e12 −0.732439
\(516\) 7.79425e10 0.0484006
\(517\) 7.51856e11 0.462836
\(518\) 6.66579e10 0.0406788
\(519\) −9.54712e11 −0.577589
\(520\) 3.32909e12 1.99669
\(521\) −2.83708e12 −1.68695 −0.843473 0.537172i \(-0.819493\pi\)
−0.843473 + 0.537172i \(0.819493\pi\)
\(522\) −9.51554e11 −0.560940
\(523\) 2.70892e12 1.58321 0.791606 0.611032i \(-0.209245\pi\)
0.791606 + 0.611032i \(0.209245\pi\)
\(524\) 6.45937e11 0.374283
\(525\) −1.84673e12 −1.06093
\(526\) −6.57654e11 −0.374595
\(527\) −1.27998e12 −0.722864
\(528\) −1.48390e12 −0.830909
\(529\) −1.14243e12 −0.634279
\(530\) 7.44073e11 0.409613
\(531\) −7.95020e10 −0.0433963
\(532\) 3.04066e11 0.164576
\(533\) −2.60050e12 −1.39567
\(534\) −2.03643e11 −0.108376
\(535\) 2.13505e12 1.12672
\(536\) −1.53513e12 −0.803348
\(537\) −8.68569e11 −0.450734
\(538\) 9.93039e10 0.0511030
\(539\) −1.77417e12 −0.905413
\(540\) −1.52452e11 −0.0771545
\(541\) −2.37196e12 −1.19047 −0.595236 0.803551i \(-0.702941\pi\)
−0.595236 + 0.803551i \(0.702941\pi\)
\(542\) 2.13188e12 1.06112
\(543\) −2.13183e12 −1.05233
\(544\) 4.34929e11 0.212924
\(545\) 2.61761e12 1.27093
\(546\) 7.68932e11 0.370272
\(547\) −3.31592e12 −1.58365 −0.791827 0.610745i \(-0.790870\pi\)
−0.791827 + 0.610745i \(0.790870\pi\)
\(548\) −6.98683e11 −0.330954
\(549\) −7.88179e11 −0.370296
\(550\) −9.29873e12 −4.33303
\(551\) 4.32367e12 1.99835
\(552\) −8.19707e11 −0.375779
\(553\) 1.81180e12 0.823847
\(554\) −4.35364e11 −0.196363
\(555\) 1.51858e11 0.0679388
\(556\) 3.02442e11 0.134217
\(557\) 2.66734e12 1.17417 0.587084 0.809526i \(-0.300276\pi\)
0.587084 + 0.809526i \(0.300276\pi\)
\(558\) −9.64599e11 −0.421204
\(559\) −8.95598e11 −0.387936
\(560\) 2.36090e12 1.01445
\(561\) −1.33540e12 −0.569217
\(562\) 1.22346e12 0.517340
\(563\) 1.91035e12 0.801356 0.400678 0.916219i \(-0.368775\pi\)
0.400678 + 0.916219i \(0.368775\pi\)
\(564\) −7.06494e10 −0.0294003
\(565\) −6.26161e12 −2.58504
\(566\) 4.50564e11 0.184537
\(567\) −1.99863e11 −0.0812099
\(568\) −3.90393e12 −1.57374
\(569\) 9.95402e11 0.398101 0.199051 0.979989i \(-0.436214\pi\)
0.199051 + 0.979989i \(0.436214\pi\)
\(570\) −2.54636e12 −1.01038
\(571\) −4.29714e12 −1.69168 −0.845838 0.533439i \(-0.820899\pi\)
−0.845838 + 0.533439i \(0.820899\pi\)
\(572\) −1.05327e12 −0.411394
\(573\) 3.62715e11 0.140562
\(574\) −2.37689e12 −0.913913
\(575\) −3.98543e12 −1.52044
\(576\) 9.79764e11 0.370869
\(577\) −4.74470e12 −1.78204 −0.891021 0.453962i \(-0.850010\pi\)
−0.891021 + 0.453962i \(0.850010\pi\)
\(578\) 1.76709e12 0.658540
\(579\) 1.80946e12 0.669108
\(580\) −2.07375e12 −0.760906
\(581\) −2.68957e12 −0.979242
\(582\) −9.01683e11 −0.325762
\(583\) −1.33619e12 −0.479026
\(584\) −1.59844e12 −0.568641
\(585\) 1.75175e12 0.618402
\(586\) −1.10298e12 −0.386393
\(587\) 5.62007e12 1.95376 0.976879 0.213794i \(-0.0685822\pi\)
0.976879 + 0.213794i \(0.0685822\pi\)
\(588\) 1.66713e11 0.0575137
\(589\) 4.38294e12 1.50054
\(590\) 6.36897e11 0.216389
\(591\) −8.76435e11 −0.295513
\(592\) −1.38894e11 −0.0464766
\(593\) −2.19578e12 −0.729193 −0.364597 0.931166i \(-0.618793\pi\)
−0.364597 + 0.931166i \(0.618793\pi\)
\(594\) −1.00636e12 −0.331676
\(595\) 2.12462e12 0.694953
\(596\) −6.66744e11 −0.216447
\(597\) 5.13920e11 0.165581
\(598\) 1.65944e12 0.530646
\(599\) 1.86738e12 0.592667 0.296334 0.955085i \(-0.404236\pi\)
0.296334 + 0.955085i \(0.404236\pi\)
\(600\) 4.95946e12 1.56226
\(601\) 4.35928e12 1.36295 0.681475 0.731842i \(-0.261339\pi\)
0.681475 + 0.731842i \(0.261339\pi\)
\(602\) −8.18587e11 −0.254027
\(603\) −8.07778e11 −0.248808
\(604\) 2.50255e11 0.0765098
\(605\) 1.71626e13 5.20817
\(606\) 1.56825e12 0.472378
\(607\) 2.75537e12 0.823817 0.411908 0.911225i \(-0.364862\pi\)
0.411908 + 0.911225i \(0.364862\pi\)
\(608\) −1.48929e12 −0.441992
\(609\) −2.71867e12 −0.800900
\(610\) 6.31417e12 1.84643
\(611\) 8.11796e11 0.235647
\(612\) 1.25483e11 0.0361578
\(613\) −3.60906e12 −1.03234 −0.516169 0.856487i \(-0.672642\pi\)
−0.516169 + 0.856487i \(0.672642\pi\)
\(614\) −3.40968e12 −0.968178
\(615\) −5.41493e12 −1.52635
\(616\) −5.46423e12 −1.52903
\(617\) −2.90935e12 −0.808189 −0.404095 0.914717i \(-0.632413\pi\)
−0.404095 + 0.914717i \(0.632413\pi\)
\(618\) 7.25265e11 0.200009
\(619\) −2.61466e10 −0.00715825 −0.00357912 0.999994i \(-0.501139\pi\)
−0.00357912 + 0.999994i \(0.501139\pi\)
\(620\) −2.10218e12 −0.571357
\(621\) −4.31326e11 −0.116384
\(622\) −1.49553e12 −0.400624
\(623\) −5.81825e11 −0.154738
\(624\) −1.60221e12 −0.423046
\(625\) 1.07075e13 2.80690
\(626\) 3.80654e12 0.990707
\(627\) 4.57269e12 1.18159
\(628\) −1.32235e12 −0.339258
\(629\) −1.24993e11 −0.0318390
\(630\) 1.60112e12 0.404941
\(631\) −2.64461e12 −0.664093 −0.332047 0.943263i \(-0.607739\pi\)
−0.332047 + 0.943263i \(0.607739\pi\)
\(632\) −4.86564e12 −1.21315
\(633\) 1.89253e12 0.468518
\(634\) 6.04883e12 1.48686
\(635\) 9.77169e12 2.38500
\(636\) 1.25557e11 0.0304287
\(637\) −1.91562e12 −0.460979
\(638\) −1.36892e13 −3.27102
\(639\) −2.05423e12 −0.487410
\(640\) −4.50892e12 −1.06234
\(641\) 4.50041e11 0.105291 0.0526455 0.998613i \(-0.483235\pi\)
0.0526455 + 0.998613i \(0.483235\pi\)
\(642\) −1.32434e12 −0.307675
\(643\) −7.34415e12 −1.69431 −0.847153 0.531349i \(-0.821685\pi\)
−0.847153 + 0.531349i \(0.821685\pi\)
\(644\) −4.12614e11 −0.0945274
\(645\) −1.86487e12 −0.424259
\(646\) 2.09590e12 0.473505
\(647\) 5.31477e12 1.19238 0.596190 0.802843i \(-0.296680\pi\)
0.596190 + 0.802843i \(0.296680\pi\)
\(648\) 5.36740e11 0.119585
\(649\) −1.14372e12 −0.253058
\(650\) −1.00400e13 −2.20610
\(651\) −2.75594e12 −0.601388
\(652\) −7.93741e11 −0.172014
\(653\) 3.21840e12 0.692678 0.346339 0.938109i \(-0.387425\pi\)
0.346339 + 0.938109i \(0.387425\pi\)
\(654\) −1.62367e12 −0.347055
\(655\) −1.54549e13 −3.28080
\(656\) 4.95266e12 1.04417
\(657\) −8.41091e11 −0.176116
\(658\) 7.41991e11 0.154306
\(659\) −4.67442e12 −0.965479 −0.482740 0.875764i \(-0.660358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(660\) −2.19319e12 −0.449913
\(661\) 4.37429e12 0.891252 0.445626 0.895219i \(-0.352981\pi\)
0.445626 + 0.895219i \(0.352981\pi\)
\(662\) −1.22874e12 −0.248656
\(663\) −1.44186e12 −0.289809
\(664\) 7.22293e12 1.44197
\(665\) −7.27517e12 −1.44260
\(666\) −9.41953e10 −0.0185522
\(667\) −5.86717e12 −1.14779
\(668\) −8.75405e11 −0.170104
\(669\) 4.03151e12 0.778126
\(670\) 6.47117e12 1.24064
\(671\) −1.13388e13 −2.15932
\(672\) 9.36449e11 0.177142
\(673\) −5.15555e12 −0.968741 −0.484370 0.874863i \(-0.660951\pi\)
−0.484370 + 0.874863i \(0.660951\pi\)
\(674\) −6.24636e12 −1.16589
\(675\) 2.60964e12 0.483853
\(676\) 2.39179e10 0.00440517
\(677\) 9.72694e12 1.77962 0.889810 0.456331i \(-0.150837\pi\)
0.889810 + 0.456331i \(0.150837\pi\)
\(678\) 3.88400e12 0.705903
\(679\) −2.57618e12 −0.465118
\(680\) −5.70575e12 −1.02335
\(681\) −1.67849e12 −0.299059
\(682\) −1.38768e13 −2.45618
\(683\) −6.89717e12 −1.21277 −0.606384 0.795172i \(-0.707381\pi\)
−0.606384 + 0.795172i \(0.707381\pi\)
\(684\) −4.29680e11 −0.0750573
\(685\) 1.67169e13 2.90100
\(686\) −5.50979e12 −0.949896
\(687\) −5.12134e12 −0.877158
\(688\) 1.70567e12 0.290233
\(689\) −1.44271e12 −0.243890
\(690\) 3.45539e12 0.580331
\(691\) −1.93434e12 −0.322762 −0.161381 0.986892i \(-0.551595\pi\)
−0.161381 + 0.986892i \(0.551595\pi\)
\(692\) 1.29059e12 0.213950
\(693\) −2.87525e12 −0.473561
\(694\) −1.97449e12 −0.323100
\(695\) −7.23632e12 −1.17648
\(696\) 7.30108e12 1.17936
\(697\) 4.45701e12 0.715313
\(698\) 2.52176e12 0.402119
\(699\) 4.77132e11 0.0755947
\(700\) 2.49643e12 0.392987
\(701\) −1.76848e12 −0.276611 −0.138306 0.990390i \(-0.544166\pi\)
−0.138306 + 0.990390i \(0.544166\pi\)
\(702\) −1.08659e12 −0.168868
\(703\) 4.28005e11 0.0660921
\(704\) 1.40950e13 2.16266
\(705\) 1.69038e12 0.257711
\(706\) −6.40686e12 −0.970564
\(707\) 4.48063e12 0.674454
\(708\) 1.07472e11 0.0160748
\(709\) 7.22441e12 1.07373 0.536864 0.843669i \(-0.319609\pi\)
0.536864 + 0.843669i \(0.319609\pi\)
\(710\) 1.64566e13 2.43040
\(711\) −2.56028e12 −0.375728
\(712\) 1.56251e12 0.227857
\(713\) −5.94760e12 −0.861865
\(714\) −1.31788e12 −0.189772
\(715\) 2.52009e13 3.60610
\(716\) 1.17414e12 0.166960
\(717\) −4.29317e12 −0.606655
\(718\) −4.40350e11 −0.0618355
\(719\) 3.55344e12 0.495871 0.247936 0.968777i \(-0.420248\pi\)
0.247936 + 0.968777i \(0.420248\pi\)
\(720\) −3.33622e12 −0.462656
\(721\) 2.07214e12 0.285569
\(722\) −7.02913e11 −0.0962684
\(723\) 7.19879e12 0.979799
\(724\) 2.88184e12 0.389803
\(725\) 3.54980e13 4.77181
\(726\) −1.06458e13 −1.42221
\(727\) 6.89027e12 0.914811 0.457405 0.889258i \(-0.348779\pi\)
0.457405 + 0.889258i \(0.348779\pi\)
\(728\) −5.89986e12 −0.778485
\(729\) 2.82430e11 0.0370370
\(730\) 6.73805e12 0.878175
\(731\) 1.53497e12 0.198825
\(732\) 1.06547e12 0.137164
\(733\) −3.14265e12 −0.402094 −0.201047 0.979582i \(-0.564434\pi\)
−0.201047 + 0.979582i \(0.564434\pi\)
\(734\) 4.26787e12 0.542724
\(735\) −3.98882e12 −0.504141
\(736\) 2.02095e12 0.253867
\(737\) −1.16208e13 −1.45088
\(738\) 3.35881e12 0.416804
\(739\) 1.41697e13 1.74768 0.873840 0.486214i \(-0.161623\pi\)
0.873840 + 0.486214i \(0.161623\pi\)
\(740\) −2.05283e11 −0.0251658
\(741\) 4.93724e12 0.601593
\(742\) −1.31866e12 −0.159703
\(743\) −1.25170e13 −1.50678 −0.753392 0.657572i \(-0.771584\pi\)
−0.753392 + 0.657572i \(0.771584\pi\)
\(744\) 7.40117e12 0.885569
\(745\) 1.59527e13 1.89728
\(746\) 4.49949e12 0.531911
\(747\) 3.80067e12 0.446598
\(748\) 1.80521e12 0.210848
\(749\) −3.78376e12 −0.439294
\(750\) −1.25908e13 −1.45304
\(751\) 9.03491e12 1.03644 0.518220 0.855248i \(-0.326595\pi\)
0.518220 + 0.855248i \(0.326595\pi\)
\(752\) −1.54607e12 −0.176299
\(753\) 4.77995e12 0.541808
\(754\) −1.47805e13 −1.66540
\(755\) −5.98768e12 −0.670652
\(756\) 2.70177e11 0.0300816
\(757\) −1.39440e13 −1.54331 −0.771657 0.636039i \(-0.780572\pi\)
−0.771657 + 0.636039i \(0.780572\pi\)
\(758\) 9.98963e12 1.09910
\(759\) −6.20509e12 −0.678673
\(760\) 1.95377e13 2.12429
\(761\) −1.41470e13 −1.52909 −0.764547 0.644568i \(-0.777037\pi\)
−0.764547 + 0.644568i \(0.777037\pi\)
\(762\) −6.06126e12 −0.651277
\(763\) −4.63897e12 −0.495520
\(764\) −4.90322e11 −0.0520669
\(765\) −3.00233e12 −0.316944
\(766\) −7.98823e12 −0.838342
\(767\) −1.23491e12 −0.128841
\(768\) −3.39625e12 −0.352269
\(769\) 7.29078e12 0.751805 0.375903 0.926659i \(-0.377333\pi\)
0.375903 + 0.926659i \(0.377333\pi\)
\(770\) 2.30339e13 2.36134
\(771\) −6.84898e12 −0.698042
\(772\) −2.44605e12 −0.247850
\(773\) −1.14023e12 −0.114864 −0.0574320 0.998349i \(-0.518291\pi\)
−0.0574320 + 0.998349i \(0.518291\pi\)
\(774\) 1.15676e12 0.115853
\(775\) 3.59847e13 3.58311
\(776\) 6.91843e12 0.684905
\(777\) −2.69124e11 −0.0264885
\(778\) 8.29312e12 0.811540
\(779\) −1.52618e13 −1.48486
\(780\) −2.36804e12 −0.229067
\(781\) −2.95523e13 −2.84225
\(782\) −2.84411e12 −0.271967
\(783\) 3.84179e12 0.365263
\(784\) 3.64830e12 0.344880
\(785\) 3.16390e13 2.97379
\(786\) 9.58647e12 0.895895
\(787\) −7.37896e11 −0.0685660 −0.0342830 0.999412i \(-0.510915\pi\)
−0.0342830 + 0.999412i \(0.510915\pi\)
\(788\) 1.18478e12 0.109463
\(789\) 2.65520e12 0.243922
\(790\) 2.05106e13 1.87351
\(791\) 1.10969e13 1.00788
\(792\) 7.72159e12 0.697338
\(793\) −1.22428e13 −1.09939
\(794\) −1.24655e12 −0.111306
\(795\) −3.00411e12 −0.266725
\(796\) −6.94724e11 −0.0613343
\(797\) −4.78686e12 −0.420231 −0.210116 0.977677i \(-0.567384\pi\)
−0.210116 + 0.977677i \(0.567384\pi\)
\(798\) 4.51270e12 0.393934
\(799\) −1.39134e12 −0.120774
\(800\) −1.22273e13 −1.05542
\(801\) 8.22185e11 0.0705705
\(802\) −6.22915e12 −0.531672
\(803\) −1.21000e13 −1.02699
\(804\) 1.09196e12 0.0921629
\(805\) 9.87232e12 0.828587
\(806\) −1.49831e13 −1.25053
\(807\) −4.00928e11 −0.0332764
\(808\) −1.20329e13 −0.993160
\(809\) −1.29881e13 −1.06605 −0.533025 0.846100i \(-0.678945\pi\)
−0.533025 + 0.846100i \(0.678945\pi\)
\(810\) −2.26257e12 −0.184680
\(811\) 6.81318e12 0.553039 0.276520 0.961008i \(-0.410819\pi\)
0.276520 + 0.961008i \(0.410819\pi\)
\(812\) 3.67513e12 0.296668
\(813\) −8.60723e12 −0.690965
\(814\) −1.35510e12 −0.108184
\(815\) 1.89913e13 1.50780
\(816\) 2.74603e12 0.216820
\(817\) −5.25607e12 −0.412726
\(818\) 1.59207e13 1.24329
\(819\) −3.10447e12 −0.241107
\(820\) 7.31997e12 0.565388
\(821\) −1.67652e13 −1.28784 −0.643922 0.765091i \(-0.722694\pi\)
−0.643922 + 0.765091i \(0.722694\pi\)
\(822\) −1.03693e13 −0.792183
\(823\) −3.68616e12 −0.280075 −0.140038 0.990146i \(-0.544722\pi\)
−0.140038 + 0.990146i \(0.544722\pi\)
\(824\) −5.56482e12 −0.420512
\(825\) 3.75426e13 2.82151
\(826\) −1.12872e12 −0.0843675
\(827\) −8.35656e12 −0.621231 −0.310615 0.950536i \(-0.600535\pi\)
−0.310615 + 0.950536i \(0.600535\pi\)
\(828\) 5.83071e11 0.0431107
\(829\) −1.32045e13 −0.971013 −0.485507 0.874233i \(-0.661365\pi\)
−0.485507 + 0.874233i \(0.661365\pi\)
\(830\) −3.04475e13 −2.22690
\(831\) 1.75773e12 0.127864
\(832\) 1.52187e13 1.10109
\(833\) 3.28319e12 0.236261
\(834\) 4.48860e12 0.321265
\(835\) 2.09452e13 1.49106
\(836\) −6.18143e12 −0.437684
\(837\) 3.89446e12 0.274273
\(838\) −1.32461e12 −0.0927876
\(839\) 2.94279e11 0.0205036 0.0102518 0.999947i \(-0.496737\pi\)
0.0102518 + 0.999947i \(0.496737\pi\)
\(840\) −1.22851e13 −0.851375
\(841\) 3.77514e13 2.60226
\(842\) 7.79009e12 0.534119
\(843\) −4.93958e12 −0.336873
\(844\) −2.55835e12 −0.173548
\(845\) −5.72266e11 −0.0386138
\(846\) −1.04852e12 −0.0703736
\(847\) −3.04159e13 −2.03060
\(848\) 2.74765e12 0.182465
\(849\) −1.81910e12 −0.120163
\(850\) 1.72077e13 1.13067
\(851\) −5.80798e11 −0.0379614
\(852\) 2.77693e12 0.180545
\(853\) 1.03099e13 0.666782 0.333391 0.942789i \(-0.391807\pi\)
0.333391 + 0.942789i \(0.391807\pi\)
\(854\) −1.11900e13 −0.719899
\(855\) 1.02807e13 0.657920
\(856\) 1.01614e13 0.646878
\(857\) −1.79877e12 −0.113910 −0.0569549 0.998377i \(-0.518139\pi\)
−0.0569549 + 0.998377i \(0.518139\pi\)
\(858\) −1.56318e13 −0.984726
\(859\) 1.54668e13 0.969240 0.484620 0.874725i \(-0.338958\pi\)
0.484620 + 0.874725i \(0.338958\pi\)
\(860\) 2.52096e12 0.157153
\(861\) 9.59641e12 0.595106
\(862\) −1.81534e12 −0.111989
\(863\) −2.07216e13 −1.27167 −0.635836 0.771825i \(-0.719344\pi\)
−0.635836 + 0.771825i \(0.719344\pi\)
\(864\) −1.32331e12 −0.0807885
\(865\) −3.08791e13 −1.87539
\(866\) 1.82613e13 1.10332
\(867\) −7.13441e12 −0.428817
\(868\) 3.72551e12 0.222765
\(869\) −3.68324e13 −2.19099
\(870\) −3.07769e13 −1.82133
\(871\) −1.25472e13 −0.738696
\(872\) 1.24581e13 0.729673
\(873\) 3.64044e12 0.212124
\(874\) 9.73887e12 0.564556
\(875\) −3.59729e13 −2.07462
\(876\) 1.13700e12 0.0652365
\(877\) −1.00413e11 −0.00573182 −0.00286591 0.999996i \(-0.500912\pi\)
−0.00286591 + 0.999996i \(0.500912\pi\)
\(878\) −1.17079e13 −0.664896
\(879\) 4.45317e12 0.251605
\(880\) −4.79952e13 −2.69790
\(881\) 3.37574e13 1.88789 0.943946 0.330100i \(-0.107082\pi\)
0.943946 + 0.330100i \(0.107082\pi\)
\(882\) 2.47422e12 0.137667
\(883\) 1.65265e13 0.914864 0.457432 0.889245i \(-0.348769\pi\)
0.457432 + 0.889245i \(0.348769\pi\)
\(884\) 1.94912e12 0.107351
\(885\) −2.57140e12 −0.140905
\(886\) 4.97936e12 0.271470
\(887\) 2.28789e13 1.24102 0.620510 0.784198i \(-0.286926\pi\)
0.620510 + 0.784198i \(0.286926\pi\)
\(888\) 7.22742e11 0.0390054
\(889\) −1.73175e13 −0.929882
\(890\) −6.58659e12 −0.351889
\(891\) 4.06306e12 0.215975
\(892\) −5.44984e12 −0.288232
\(893\) 4.76426e12 0.250706
\(894\) −9.89526e12 −0.518094
\(895\) −2.80929e13 −1.46350
\(896\) 7.99077e12 0.414193
\(897\) −6.69978e12 −0.345537
\(898\) −6.51273e12 −0.334210
\(899\) 5.29750e13 2.70491
\(900\) −3.52774e12 −0.179228
\(901\) 2.47267e12 0.124999
\(902\) 4.83202e13 2.43052
\(903\) 3.30495e12 0.165413
\(904\) −2.98011e13 −1.48414
\(905\) −6.89516e13 −3.41685
\(906\) 3.71408e12 0.183136
\(907\) −5.90929e12 −0.289936 −0.144968 0.989436i \(-0.546308\pi\)
−0.144968 + 0.989436i \(0.546308\pi\)
\(908\) 2.26900e12 0.110777
\(909\) −6.33165e12 −0.307595
\(910\) 2.48702e13 1.20225
\(911\) −1.93776e13 −0.932110 −0.466055 0.884756i \(-0.654325\pi\)
−0.466055 + 0.884756i \(0.654325\pi\)
\(912\) −9.40301e12 −0.450080
\(913\) 5.46768e13 2.60426
\(914\) −9.47208e12 −0.448939
\(915\) −2.54927e13 −1.20232
\(916\) 6.92309e12 0.324915
\(917\) 2.73893e13 1.27914
\(918\) 1.86231e12 0.0865486
\(919\) −1.84541e12 −0.0853439 −0.0426720 0.999089i \(-0.513587\pi\)
−0.0426720 + 0.999089i \(0.513587\pi\)
\(920\) −2.65125e13 −1.22013
\(921\) 1.37662e13 0.630442
\(922\) 7.85731e12 0.358084
\(923\) −3.19083e13 −1.44709
\(924\) 3.88680e12 0.175416
\(925\) 3.51399e12 0.157820
\(926\) −6.40249e12 −0.286154
\(927\) −2.92818e12 −0.130238
\(928\) −1.80005e13 −0.796745
\(929\) −3.06785e13 −1.35134 −0.675668 0.737206i \(-0.736145\pi\)
−0.675668 + 0.737206i \(0.736145\pi\)
\(930\) −3.11988e13 −1.36762
\(931\) −1.12423e13 −0.490437
\(932\) −6.44993e11 −0.0280016
\(933\) 6.03802e12 0.260872
\(934\) −6.87873e12 −0.295765
\(935\) −4.31919e13 −1.84820
\(936\) 8.33718e12 0.355040
\(937\) 8.12349e12 0.344282 0.172141 0.985072i \(-0.444931\pi\)
0.172141 + 0.985072i \(0.444931\pi\)
\(938\) −1.14683e13 −0.483711
\(939\) −1.53685e13 −0.645112
\(940\) −2.28507e12 −0.0954607
\(941\) −2.62020e13 −1.08939 −0.544693 0.838635i \(-0.683354\pi\)
−0.544693 + 0.838635i \(0.683354\pi\)
\(942\) −1.96253e13 −0.812058
\(943\) 2.07100e13 0.852861
\(944\) 2.35188e12 0.0963922
\(945\) −6.46434e12 −0.263682
\(946\) 1.66412e13 0.675578
\(947\) 1.74982e13 0.706998 0.353499 0.935435i \(-0.384992\pi\)
0.353499 + 0.935435i \(0.384992\pi\)
\(948\) 3.46101e12 0.139176
\(949\) −1.30647e13 −0.522878
\(950\) −5.89229e13 −2.34708
\(951\) −2.44215e13 −0.968187
\(952\) 1.01118e13 0.398990
\(953\) 3.99984e13 1.57081 0.785407 0.618980i \(-0.212454\pi\)
0.785407 + 0.618980i \(0.212454\pi\)
\(954\) 1.86341e12 0.0728352
\(955\) 1.17316e13 0.456396
\(956\) 5.80356e12 0.224716
\(957\) 5.52684e13 2.12997
\(958\) 3.27765e13 1.25724
\(959\) −2.96259e13 −1.13107
\(960\) 3.16893e13 1.20418
\(961\) 2.72616e13 1.03109
\(962\) −1.46314e12 −0.0550804
\(963\) 5.34688e12 0.200347
\(964\) −9.73141e12 −0.362935
\(965\) 5.85250e13 2.17254
\(966\) −6.12368e12 −0.226264
\(967\) 6.64062e12 0.244225 0.122112 0.992516i \(-0.461033\pi\)
0.122112 + 0.992516i \(0.461033\pi\)
\(968\) 8.16829e13 2.99014
\(969\) −8.46197e12 −0.308329
\(970\) −2.91639e13 −1.05773
\(971\) 2.22077e13 0.801708 0.400854 0.916142i \(-0.368713\pi\)
0.400854 + 0.916142i \(0.368713\pi\)
\(972\) −3.81792e11 −0.0137192
\(973\) 1.28243e13 0.458697
\(974\) −1.23952e13 −0.441305
\(975\) 4.05356e13 1.43653
\(976\) 2.33165e13 0.822505
\(977\) −1.67680e13 −0.588785 −0.294392 0.955685i \(-0.595117\pi\)
−0.294392 + 0.955685i \(0.595117\pi\)
\(978\) −1.17800e13 −0.411739
\(979\) 1.18280e13 0.411520
\(980\) 5.39214e12 0.186743
\(981\) 6.55539e12 0.225989
\(982\) −3.13354e13 −1.07531
\(983\) −1.63039e13 −0.556930 −0.278465 0.960446i \(-0.589826\pi\)
−0.278465 + 0.960446i \(0.589826\pi\)
\(984\) −2.57715e13 −0.876318
\(985\) −2.83473e13 −0.959508
\(986\) 2.53324e13 0.853551
\(987\) −2.99571e12 −0.100478
\(988\) −6.67423e12 −0.222841
\(989\) 7.13243e12 0.237058
\(990\) −3.25495e13 −1.07693
\(991\) 3.73024e13 1.22859 0.614293 0.789078i \(-0.289441\pi\)
0.614293 + 0.789078i \(0.289441\pi\)
\(992\) −1.82473e13 −0.598268
\(993\) 4.96089e12 0.161915
\(994\) −2.91646e13 −0.947582
\(995\) 1.66222e13 0.537630
\(996\) −5.13779e12 −0.165428
\(997\) −4.09992e12 −0.131416 −0.0657078 0.997839i \(-0.520931\pi\)
−0.0657078 + 0.997839i \(0.520931\pi\)
\(998\) −8.60309e12 −0.274516
\(999\) 3.80303e11 0.0120805
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.1.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.6 22 1.1 even 1 trivial