Properties

Label 177.10.a.c.1.18
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +61733.3 q^{10} -79089.2 q^{11} -39190.4 q^{12} -1847.31 q^{13} -154715. q^{14} -158457. q^{15} -275773. q^{16} +459823. q^{17} +207044. q^{18} +1.08468e6 q^{19} +946500. q^{20} +397123. q^{21} -2.49580e6 q^{22} +2.20622e6 q^{23} +72001.0 q^{24} +1.87383e6 q^{25} -58295.3 q^{26} -531441. q^{27} -2.37210e6 q^{28} -4.56225e6 q^{29} -5.00040e6 q^{30} +6.82675e6 q^{31} -8.24739e6 q^{32} +6.40623e6 q^{33} +1.45105e7 q^{34} -9.59105e6 q^{35} +3.17442e6 q^{36} +1.05656e7 q^{37} +3.42292e7 q^{38} +149632. q^{39} -1.73892e6 q^{40} -1.66901e7 q^{41} +1.25319e7 q^{42} +3.40809e7 q^{43} -3.82659e7 q^{44} +1.28350e7 q^{45} +6.96214e7 q^{46} +3.70501e6 q^{47} +2.23376e7 q^{48} -1.63167e7 q^{49} +5.91319e7 q^{50} -3.72456e7 q^{51} -893789. q^{52} -2.35435e7 q^{53} -1.67706e7 q^{54} -1.54719e8 q^{55} +4.35806e6 q^{56} -8.78594e7 q^{57} -1.43970e8 q^{58} +1.21174e7 q^{59} -7.66665e7 q^{60} +1.59558e8 q^{61} +2.15430e8 q^{62} -3.21669e7 q^{63} -1.19066e8 q^{64} -3.61383e6 q^{65} +2.02160e8 q^{66} +1.14987e8 q^{67} +2.22477e8 q^{68} -1.78704e8 q^{69} -3.02663e8 q^{70} +1.06400e8 q^{71} -5.83208e6 q^{72} +2.12864e7 q^{73} +3.33415e8 q^{74} -1.51780e8 q^{75} +5.24805e8 q^{76} +3.87755e8 q^{77} +4.72192e6 q^{78} +3.40239e8 q^{79} -5.39483e8 q^{80} +4.30467e7 q^{81} -5.26685e8 q^{82} -9.07182e7 q^{83} +1.92140e8 q^{84} +8.99532e8 q^{85} +1.07548e9 q^{86} +3.69542e8 q^{87} +7.03025e7 q^{88} +7.56249e8 q^{89} +4.05032e8 q^{90} +9.05692e6 q^{91} +1.06744e9 q^{92} -5.52966e8 q^{93} +1.16918e8 q^{94} +2.12192e9 q^{95} +6.68038e8 q^{96} +3.71927e8 q^{97} -5.14902e8 q^{98} -5.18904e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.5568 1.39463 0.697313 0.716766i \(-0.254379\pi\)
0.697313 + 0.716766i \(0.254379\pi\)
\(3\) −81.0000 −0.577350
\(4\) 483.832 0.944984
\(5\) 1956.26 1.39979 0.699893 0.714248i \(-0.253231\pi\)
0.699893 + 0.714248i \(0.253231\pi\)
\(6\) −2556.10 −0.805188
\(7\) −4902.75 −0.771789 −0.385894 0.922543i \(-0.626107\pi\)
−0.385894 + 0.922543i \(0.626107\pi\)
\(8\) −888.901 −0.0767271
\(9\) 6561.00 0.333333
\(10\) 61733.3 1.95218
\(11\) −79089.2 −1.62873 −0.814367 0.580350i \(-0.802916\pi\)
−0.814367 + 0.580350i \(0.802916\pi\)
\(12\) −39190.4 −0.545587
\(13\) −1847.31 −0.0179389 −0.00896945 0.999960i \(-0.502855\pi\)
−0.00896945 + 0.999960i \(0.502855\pi\)
\(14\) −154715. −1.07636
\(15\) −158457. −0.808166
\(16\) −275773. −1.05199
\(17\) 459823. 1.33527 0.667637 0.744487i \(-0.267306\pi\)
0.667637 + 0.744487i \(0.267306\pi\)
\(18\) 207044. 0.464876
\(19\) 1.08468e6 1.90947 0.954734 0.297462i \(-0.0961402\pi\)
0.954734 + 0.297462i \(0.0961402\pi\)
\(20\) 946500. 1.32277
\(21\) 397123. 0.445592
\(22\) −2.49580e6 −2.27148
\(23\) 2.20622e6 1.64390 0.821948 0.569563i \(-0.192887\pi\)
0.821948 + 0.569563i \(0.192887\pi\)
\(24\) 72001.0 0.0442984
\(25\) 1.87383e6 0.959399
\(26\) −58295.3 −0.0250181
\(27\) −531441. −0.192450
\(28\) −2.37210e6 −0.729328
\(29\) −4.56225e6 −1.19781 −0.598905 0.800820i \(-0.704397\pi\)
−0.598905 + 0.800820i \(0.704397\pi\)
\(30\) −5.00040e6 −1.12709
\(31\) 6.82675e6 1.32766 0.663829 0.747885i \(-0.268930\pi\)
0.663829 + 0.747885i \(0.268930\pi\)
\(32\) −8.24739e6 −1.39041
\(33\) 6.40623e6 0.940350
\(34\) 1.45105e7 1.86221
\(35\) −9.59105e6 −1.08034
\(36\) 3.17442e6 0.314995
\(37\) 1.05656e7 0.926797 0.463399 0.886150i \(-0.346630\pi\)
0.463399 + 0.886150i \(0.346630\pi\)
\(38\) 3.42292e7 2.66299
\(39\) 149632. 0.0103570
\(40\) −1.73892e6 −0.107401
\(41\) −1.66901e7 −0.922424 −0.461212 0.887290i \(-0.652585\pi\)
−0.461212 + 0.887290i \(0.652585\pi\)
\(42\) 1.25319e7 0.621435
\(43\) 3.40809e7 1.52021 0.760103 0.649802i \(-0.225148\pi\)
0.760103 + 0.649802i \(0.225148\pi\)
\(44\) −3.82659e7 −1.53913
\(45\) 1.28350e7 0.466595
\(46\) 6.96214e7 2.29262
\(47\) 3.70501e6 0.110751 0.0553757 0.998466i \(-0.482364\pi\)
0.0553757 + 0.998466i \(0.482364\pi\)
\(48\) 2.23376e7 0.607366
\(49\) −1.63167e7 −0.404342
\(50\) 5.91319e7 1.33800
\(51\) −3.72456e7 −0.770921
\(52\) −893789. −0.0169520
\(53\) −2.35435e7 −0.409855 −0.204928 0.978777i \(-0.565696\pi\)
−0.204928 + 0.978777i \(0.565696\pi\)
\(54\) −1.67706e7 −0.268396
\(55\) −1.54719e8 −2.27988
\(56\) 4.35806e6 0.0592171
\(57\) −8.78594e7 −1.10243
\(58\) −1.43970e8 −1.67050
\(59\) 1.21174e7 0.130189
\(60\) −7.66665e7 −0.763704
\(61\) 1.59558e8 1.47548 0.737741 0.675083i \(-0.235892\pi\)
0.737741 + 0.675083i \(0.235892\pi\)
\(62\) 2.15430e8 1.85159
\(63\) −3.21669e7 −0.257263
\(64\) −1.19066e8 −0.887107
\(65\) −3.61383e6 −0.0251106
\(66\) 2.02160e8 1.31144
\(67\) 1.14987e8 0.697125 0.348563 0.937285i \(-0.386670\pi\)
0.348563 + 0.937285i \(0.386670\pi\)
\(68\) 2.22477e8 1.26181
\(69\) −1.78704e8 −0.949104
\(70\) −3.02663e8 −1.50667
\(71\) 1.06400e8 0.496911 0.248456 0.968643i \(-0.420077\pi\)
0.248456 + 0.968643i \(0.420077\pi\)
\(72\) −5.83208e6 −0.0255757
\(73\) 2.12864e7 0.0877303 0.0438651 0.999037i \(-0.486033\pi\)
0.0438651 + 0.999037i \(0.486033\pi\)
\(74\) 3.33415e8 1.29254
\(75\) −1.51780e8 −0.553909
\(76\) 5.24805e8 1.80442
\(77\) 3.87755e8 1.25704
\(78\) 4.72192e6 0.0144442
\(79\) 3.40239e8 0.982794 0.491397 0.870936i \(-0.336486\pi\)
0.491397 + 0.870936i \(0.336486\pi\)
\(80\) −5.39483e8 −1.47256
\(81\) 4.30467e7 0.111111
\(82\) −5.26685e8 −1.28644
\(83\) −9.07182e7 −0.209818 −0.104909 0.994482i \(-0.533455\pi\)
−0.104909 + 0.994482i \(0.533455\pi\)
\(84\) 1.92140e8 0.421078
\(85\) 8.99532e8 1.86910
\(86\) 1.07548e9 2.12012
\(87\) 3.69542e8 0.691556
\(88\) 7.03025e7 0.124968
\(89\) 7.56249e8 1.27764 0.638822 0.769355i \(-0.279422\pi\)
0.638822 + 0.769355i \(0.279422\pi\)
\(90\) 4.05032e8 0.650726
\(91\) 9.05692e6 0.0138450
\(92\) 1.06744e9 1.55345
\(93\) −5.52966e8 −0.766523
\(94\) 1.16918e8 0.154457
\(95\) 2.12192e9 2.67284
\(96\) 6.68038e8 0.802751
\(97\) 3.71927e8 0.426564 0.213282 0.976991i \(-0.431585\pi\)
0.213282 + 0.976991i \(0.431585\pi\)
\(98\) −5.14902e8 −0.563907
\(99\) −5.18904e8 −0.542911
\(100\) 9.06616e8 0.906616
\(101\) 1.46160e8 0.139760 0.0698798 0.997555i \(-0.477738\pi\)
0.0698798 + 0.997555i \(0.477738\pi\)
\(102\) −1.17535e9 −1.07515
\(103\) −1.24880e9 −1.09326 −0.546632 0.837373i \(-0.684090\pi\)
−0.546632 + 0.837373i \(0.684090\pi\)
\(104\) 1.64208e6 0.00137640
\(105\) 7.76875e8 0.623734
\(106\) −7.42959e8 −0.571595
\(107\) 1.73100e9 1.27664 0.638322 0.769770i \(-0.279629\pi\)
0.638322 + 0.769770i \(0.279629\pi\)
\(108\) −2.57128e8 −0.181862
\(109\) −1.34909e6 −0.000915426 0 −0.000457713 1.00000i \(-0.500146\pi\)
−0.000457713 1.00000i \(0.500146\pi\)
\(110\) −4.88244e9 −3.17958
\(111\) −8.55810e8 −0.535087
\(112\) 1.35204e9 0.811913
\(113\) −1.90229e9 −1.09755 −0.548775 0.835970i \(-0.684905\pi\)
−0.548775 + 0.835970i \(0.684905\pi\)
\(114\) −2.77256e9 −1.53748
\(115\) 4.31595e9 2.30110
\(116\) −2.20736e9 −1.13191
\(117\) −1.21202e7 −0.00597963
\(118\) 3.82385e8 0.181565
\(119\) −2.25439e9 −1.03055
\(120\) 1.40853e8 0.0620082
\(121\) 3.89716e9 1.65278
\(122\) 5.03514e9 2.05775
\(123\) 1.35189e9 0.532562
\(124\) 3.30300e9 1.25461
\(125\) −1.55131e8 −0.0568333
\(126\) −1.01509e9 −0.358786
\(127\) −1.62957e9 −0.555848 −0.277924 0.960603i \(-0.589646\pi\)
−0.277924 + 0.960603i \(0.589646\pi\)
\(128\) 4.65335e8 0.153222
\(129\) −2.76055e9 −0.877692
\(130\) −1.14041e8 −0.0350199
\(131\) −2.05451e9 −0.609519 −0.304760 0.952429i \(-0.598576\pi\)
−0.304760 + 0.952429i \(0.598576\pi\)
\(132\) 3.09954e9 0.888616
\(133\) −5.31793e9 −1.47371
\(134\) 3.62861e9 0.972230
\(135\) −1.03964e9 −0.269389
\(136\) −4.08737e8 −0.102452
\(137\) 4.37780e9 1.06173 0.530865 0.847457i \(-0.321867\pi\)
0.530865 + 0.847457i \(0.321867\pi\)
\(138\) −5.63933e9 −1.32365
\(139\) −1.23302e9 −0.280157 −0.140079 0.990140i \(-0.544736\pi\)
−0.140079 + 0.990140i \(0.544736\pi\)
\(140\) −4.64045e9 −1.02090
\(141\) −3.00106e8 −0.0639423
\(142\) 3.35764e9 0.693005
\(143\) 1.46103e8 0.0292177
\(144\) −1.80934e9 −0.350663
\(145\) −8.92495e9 −1.67668
\(146\) 6.71731e8 0.122351
\(147\) 1.32165e9 0.233447
\(148\) 5.11195e9 0.875809
\(149\) −6.18776e9 −1.02848 −0.514239 0.857647i \(-0.671926\pi\)
−0.514239 + 0.857647i \(0.671926\pi\)
\(150\) −4.78969e9 −0.772496
\(151\) 1.21679e9 0.190467 0.0952335 0.995455i \(-0.469640\pi\)
0.0952335 + 0.995455i \(0.469640\pi\)
\(152\) −9.64177e8 −0.146508
\(153\) 3.01690e9 0.445091
\(154\) 1.22363e10 1.75310
\(155\) 1.33549e10 1.85844
\(156\) 7.23969e7 0.00978722
\(157\) −5.87350e9 −0.771522 −0.385761 0.922599i \(-0.626061\pi\)
−0.385761 + 0.922599i \(0.626061\pi\)
\(158\) 1.07369e10 1.37063
\(159\) 1.90703e9 0.236630
\(160\) −1.61340e10 −1.94627
\(161\) −1.08166e10 −1.26874
\(162\) 1.35842e9 0.154959
\(163\) −2.41860e9 −0.268361 −0.134181 0.990957i \(-0.542840\pi\)
−0.134181 + 0.990957i \(0.542840\pi\)
\(164\) −8.07518e9 −0.871676
\(165\) 1.25322e10 1.31629
\(166\) −2.86278e9 −0.292618
\(167\) −2.02117e9 −0.201085 −0.100543 0.994933i \(-0.532058\pi\)
−0.100543 + 0.994933i \(0.532058\pi\)
\(168\) −3.53003e8 −0.0341890
\(169\) −1.06011e10 −0.999678
\(170\) 2.83864e10 2.60669
\(171\) 7.11661e9 0.636489
\(172\) 1.64894e10 1.43657
\(173\) −1.02328e10 −0.868538 −0.434269 0.900783i \(-0.642993\pi\)
−0.434269 + 0.900783i \(0.642993\pi\)
\(174\) 1.16616e10 0.964463
\(175\) −9.18689e9 −0.740453
\(176\) 2.18107e10 1.71341
\(177\) −9.81506e8 −0.0751646
\(178\) 2.38648e10 1.78184
\(179\) 1.40447e10 1.02252 0.511262 0.859425i \(-0.329178\pi\)
0.511262 + 0.859425i \(0.329178\pi\)
\(180\) 6.20999e9 0.440925
\(181\) −1.33959e10 −0.927723 −0.463862 0.885908i \(-0.653536\pi\)
−0.463862 + 0.885908i \(0.653536\pi\)
\(182\) 2.85807e8 0.0193087
\(183\) −1.29242e10 −0.851870
\(184\) −1.96111e9 −0.126131
\(185\) 2.06690e10 1.29732
\(186\) −1.74498e10 −1.06901
\(187\) −3.63670e10 −2.17481
\(188\) 1.79260e9 0.104658
\(189\) 2.60552e9 0.148531
\(190\) 6.69611e10 3.72762
\(191\) 8.66978e9 0.471366 0.235683 0.971830i \(-0.424267\pi\)
0.235683 + 0.971830i \(0.424267\pi\)
\(192\) 9.64431e9 0.512172
\(193\) −2.95756e10 −1.53436 −0.767178 0.641435i \(-0.778340\pi\)
−0.767178 + 0.641435i \(0.778340\pi\)
\(194\) 1.17368e10 0.594898
\(195\) 2.92720e8 0.0144976
\(196\) −7.89452e9 −0.382097
\(197\) 2.56328e10 1.21255 0.606273 0.795257i \(-0.292664\pi\)
0.606273 + 0.795257i \(0.292664\pi\)
\(198\) −1.63750e10 −0.757159
\(199\) 3.76194e10 1.70048 0.850242 0.526392i \(-0.176456\pi\)
0.850242 + 0.526392i \(0.176456\pi\)
\(200\) −1.66565e9 −0.0736118
\(201\) −9.31392e9 −0.402486
\(202\) 4.61233e9 0.194912
\(203\) 2.23676e10 0.924457
\(204\) −1.80206e10 −0.728507
\(205\) −3.26501e10 −1.29120
\(206\) −3.94081e10 −1.52469
\(207\) 1.44750e10 0.547965
\(208\) 5.09439e8 0.0188715
\(209\) −8.57868e10 −3.11001
\(210\) 2.45157e10 0.869876
\(211\) 4.47769e10 1.55519 0.777594 0.628767i \(-0.216440\pi\)
0.777594 + 0.628767i \(0.216440\pi\)
\(212\) −1.13911e10 −0.387306
\(213\) −8.61839e9 −0.286892
\(214\) 5.46248e10 1.78044
\(215\) 6.66710e10 2.12796
\(216\) 4.72399e8 0.0147661
\(217\) −3.34698e10 −1.02467
\(218\) −4.25731e7 −0.00127668
\(219\) −1.72420e9 −0.0506511
\(220\) −7.48580e10 −2.15445
\(221\) −8.49437e8 −0.0239533
\(222\) −2.70066e10 −0.746246
\(223\) −1.95185e9 −0.0528536 −0.0264268 0.999651i \(-0.508413\pi\)
−0.0264268 + 0.999651i \(0.508413\pi\)
\(224\) 4.04349e10 1.07310
\(225\) 1.22942e10 0.319800
\(226\) −6.00302e10 −1.53067
\(227\) −3.36446e9 −0.0841007 −0.0420503 0.999115i \(-0.513389\pi\)
−0.0420503 + 0.999115i \(0.513389\pi\)
\(228\) −4.25092e10 −1.04178
\(229\) 7.32608e10 1.76040 0.880202 0.474600i \(-0.157407\pi\)
0.880202 + 0.474600i \(0.157407\pi\)
\(230\) 1.36197e11 3.20918
\(231\) −3.14081e10 −0.725752
\(232\) 4.05539e9 0.0919045
\(233\) 5.46189e10 1.21406 0.607032 0.794677i \(-0.292360\pi\)
0.607032 + 0.794677i \(0.292360\pi\)
\(234\) −3.82476e8 −0.00833935
\(235\) 7.24796e9 0.155028
\(236\) 5.86276e9 0.123026
\(237\) −2.75594e10 −0.567416
\(238\) −7.11415e10 −1.43723
\(239\) −1.09256e10 −0.216599 −0.108299 0.994118i \(-0.534541\pi\)
−0.108299 + 0.994118i \(0.534541\pi\)
\(240\) 4.36981e10 0.850182
\(241\) −1.81118e10 −0.345847 −0.172924 0.984935i \(-0.555321\pi\)
−0.172924 + 0.984935i \(0.555321\pi\)
\(242\) 1.22982e11 2.30500
\(243\) −3.48678e9 −0.0641500
\(244\) 7.71992e10 1.39431
\(245\) −3.19196e10 −0.565992
\(246\) 4.26615e10 0.742725
\(247\) −2.00375e9 −0.0342537
\(248\) −6.06830e9 −0.101867
\(249\) 7.34817e9 0.121139
\(250\) −4.89543e9 −0.0792613
\(251\) 3.71772e10 0.591214 0.295607 0.955310i \(-0.404478\pi\)
0.295607 + 0.955310i \(0.404478\pi\)
\(252\) −1.55634e10 −0.243109
\(253\) −1.74489e11 −2.67747
\(254\) −5.14240e10 −0.775201
\(255\) −7.28621e10 −1.07912
\(256\) 7.56460e10 1.10079
\(257\) −8.72339e10 −1.24734 −0.623672 0.781686i \(-0.714360\pi\)
−0.623672 + 0.781686i \(0.714360\pi\)
\(258\) −8.71142e10 −1.22405
\(259\) −5.18003e10 −0.715292
\(260\) −1.74848e9 −0.0237291
\(261\) −2.99329e10 −0.399270
\(262\) −6.48338e10 −0.850052
\(263\) −8.87644e10 −1.14403 −0.572016 0.820243i \(-0.693838\pi\)
−0.572016 + 0.820243i \(0.693838\pi\)
\(264\) −5.69450e9 −0.0721503
\(265\) −4.60573e10 −0.573709
\(266\) −1.67817e11 −2.05527
\(267\) −6.12561e10 −0.737648
\(268\) 5.56342e10 0.658772
\(269\) 5.60043e9 0.0652133 0.0326067 0.999468i \(-0.489619\pi\)
0.0326067 + 0.999468i \(0.489619\pi\)
\(270\) −3.28076e10 −0.375697
\(271\) 1.21138e11 1.36433 0.682163 0.731200i \(-0.261039\pi\)
0.682163 + 0.731200i \(0.261039\pi\)
\(272\) −1.26807e11 −1.40469
\(273\) −7.33610e8 −0.00799343
\(274\) 1.38149e11 1.48072
\(275\) −1.48199e11 −1.56261
\(276\) −8.64627e10 −0.896888
\(277\) −6.77355e10 −0.691286 −0.345643 0.938366i \(-0.612339\pi\)
−0.345643 + 0.938366i \(0.612339\pi\)
\(278\) −3.89100e10 −0.390715
\(279\) 4.47903e10 0.442553
\(280\) 8.52549e9 0.0828912
\(281\) 1.42849e11 1.36678 0.683390 0.730053i \(-0.260505\pi\)
0.683390 + 0.730053i \(0.260505\pi\)
\(282\) −9.47038e9 −0.0891757
\(283\) −2.08907e11 −1.93604 −0.968020 0.250874i \(-0.919282\pi\)
−0.968020 + 0.250874i \(0.919282\pi\)
\(284\) 5.14796e10 0.469573
\(285\) −1.71876e11 −1.54317
\(286\) 4.61053e9 0.0407478
\(287\) 8.18271e10 0.711916
\(288\) −5.41111e10 −0.463469
\(289\) 9.28490e10 0.782956
\(290\) −2.81643e11 −2.33834
\(291\) −3.01261e10 −0.246277
\(292\) 1.02990e10 0.0829037
\(293\) 1.16872e11 0.926419 0.463209 0.886249i \(-0.346698\pi\)
0.463209 + 0.886249i \(0.346698\pi\)
\(294\) 4.17071e10 0.325572
\(295\) 2.37047e10 0.182237
\(296\) −9.39174e9 −0.0711104
\(297\) 4.20313e10 0.313450
\(298\) −1.95266e11 −1.43434
\(299\) −4.07559e9 −0.0294897
\(300\) −7.34359e10 −0.523435
\(301\) −1.67090e11 −1.17328
\(302\) 3.83980e10 0.265630
\(303\) −1.18389e10 −0.0806902
\(304\) −2.99126e11 −2.00874
\(305\) 3.12137e11 2.06536
\(306\) 9.52036e10 0.620736
\(307\) −8.34907e10 −0.536433 −0.268216 0.963359i \(-0.586434\pi\)
−0.268216 + 0.963359i \(0.586434\pi\)
\(308\) 1.87608e11 1.18788
\(309\) 1.01153e11 0.631196
\(310\) 4.21437e11 2.59182
\(311\) −2.23495e11 −1.35471 −0.677356 0.735656i \(-0.736874\pi\)
−0.677356 + 0.735656i \(0.736874\pi\)
\(312\) −1.33008e8 −0.000794664 0
\(313\) −9.88835e10 −0.582337 −0.291168 0.956672i \(-0.594044\pi\)
−0.291168 + 0.956672i \(0.594044\pi\)
\(314\) −1.85349e11 −1.07598
\(315\) −6.29269e10 −0.360113
\(316\) 1.64619e11 0.928724
\(317\) −3.06064e11 −1.70233 −0.851167 0.524894i \(-0.824105\pi\)
−0.851167 + 0.524894i \(0.824105\pi\)
\(318\) 6.01797e10 0.330010
\(319\) 3.60825e11 1.95092
\(320\) −2.32923e11 −1.24176
\(321\) −1.40211e11 −0.737070
\(322\) −3.41336e11 −1.76942
\(323\) 4.98763e11 2.54966
\(324\) 2.08274e10 0.104998
\(325\) −3.46154e9 −0.0172106
\(326\) −7.63233e10 −0.374264
\(327\) 1.09277e8 0.000528521 0
\(328\) 1.48358e10 0.0707749
\(329\) −1.81647e10 −0.0854766
\(330\) 3.95477e11 1.83573
\(331\) −1.87985e11 −0.860788 −0.430394 0.902641i \(-0.641625\pi\)
−0.430394 + 0.902641i \(0.641625\pi\)
\(332\) −4.38923e10 −0.198275
\(333\) 6.93206e10 0.308932
\(334\) −6.37818e10 −0.280439
\(335\) 2.24944e11 0.975826
\(336\) −1.09516e11 −0.468758
\(337\) 3.42393e11 1.44607 0.723037 0.690810i \(-0.242746\pi\)
0.723037 + 0.690810i \(0.242746\pi\)
\(338\) −3.34536e11 −1.39418
\(339\) 1.54086e11 0.633670
\(340\) 4.35222e11 1.76627
\(341\) −5.39922e11 −2.16240
\(342\) 2.24578e11 0.887665
\(343\) 2.77840e11 1.08386
\(344\) −3.02945e10 −0.116641
\(345\) −3.49592e11 −1.32854
\(346\) −3.22916e11 −1.21129
\(347\) −1.69656e11 −0.628182 −0.314091 0.949393i \(-0.601700\pi\)
−0.314091 + 0.949393i \(0.601700\pi\)
\(348\) 1.78796e11 0.653510
\(349\) −1.32210e11 −0.477035 −0.238517 0.971138i \(-0.576661\pi\)
−0.238517 + 0.971138i \(0.576661\pi\)
\(350\) −2.89909e11 −1.03266
\(351\) 9.81739e8 0.00345234
\(352\) 6.52279e11 2.26460
\(353\) −2.27467e11 −0.779709 −0.389855 0.920876i \(-0.627475\pi\)
−0.389855 + 0.920876i \(0.627475\pi\)
\(354\) −3.09732e10 −0.104827
\(355\) 2.08146e11 0.695569
\(356\) 3.65897e11 1.20735
\(357\) 1.82606e11 0.594988
\(358\) 4.43205e11 1.42604
\(359\) 2.94417e10 0.0935487 0.0467744 0.998905i \(-0.485106\pi\)
0.0467744 + 0.998905i \(0.485106\pi\)
\(360\) −1.14091e10 −0.0358005
\(361\) 8.53853e11 2.64606
\(362\) −4.22732e11 −1.29383
\(363\) −3.15670e11 −0.954230
\(364\) 4.38202e9 0.0130833
\(365\) 4.16417e10 0.122804
\(366\) −4.07846e11 −1.18804
\(367\) 3.66167e11 1.05361 0.526807 0.849985i \(-0.323389\pi\)
0.526807 + 0.849985i \(0.323389\pi\)
\(368\) −6.08416e11 −1.72936
\(369\) −1.09503e11 −0.307475
\(370\) 6.52247e11 1.80927
\(371\) 1.15428e11 0.316321
\(372\) −2.67543e11 −0.724352
\(373\) −5.10926e11 −1.36668 −0.683342 0.730098i \(-0.739474\pi\)
−0.683342 + 0.730098i \(0.739474\pi\)
\(374\) −1.14763e12 −3.03304
\(375\) 1.25656e10 0.0328127
\(376\) −3.29339e9 −0.00849763
\(377\) 8.42791e9 0.0214874
\(378\) 8.22219e10 0.207145
\(379\) 5.37042e10 0.133700 0.0668501 0.997763i \(-0.478705\pi\)
0.0668501 + 0.997763i \(0.478705\pi\)
\(380\) 1.02665e12 2.52579
\(381\) 1.31995e11 0.320919
\(382\) 2.73590e11 0.657379
\(383\) 3.89219e11 0.924271 0.462136 0.886809i \(-0.347083\pi\)
0.462136 + 0.886809i \(0.347083\pi\)
\(384\) −3.76921e10 −0.0884627
\(385\) 7.58548e11 1.75958
\(386\) −9.33312e11 −2.13985
\(387\) 2.23605e11 0.506736
\(388\) 1.79950e11 0.403096
\(389\) 1.53424e11 0.339719 0.169860 0.985468i \(-0.445669\pi\)
0.169860 + 0.985468i \(0.445669\pi\)
\(390\) 9.23730e9 0.0202188
\(391\) 1.01447e12 2.19505
\(392\) 1.45039e10 0.0310240
\(393\) 1.66415e11 0.351906
\(394\) 8.08889e11 1.69105
\(395\) 6.65596e11 1.37570
\(396\) −2.51062e11 −0.513043
\(397\) 6.24737e11 1.26223 0.631117 0.775687i \(-0.282597\pi\)
0.631117 + 0.775687i \(0.282597\pi\)
\(398\) 1.18715e12 2.37154
\(399\) 4.30753e11 0.850844
\(400\) −5.16750e11 −1.00928
\(401\) −2.72742e11 −0.526747 −0.263374 0.964694i \(-0.584835\pi\)
−0.263374 + 0.964694i \(0.584835\pi\)
\(402\) −2.93918e11 −0.561317
\(403\) −1.26111e10 −0.0238167
\(404\) 7.07167e10 0.132070
\(405\) 8.42105e10 0.155532
\(406\) 7.05849e11 1.28927
\(407\) −8.35622e11 −1.50951
\(408\) 3.31077e10 0.0591505
\(409\) −8.30315e11 −1.46720 −0.733598 0.679583i \(-0.762161\pi\)
−0.733598 + 0.679583i \(0.762161\pi\)
\(410\) −1.03033e12 −1.80074
\(411\) −3.54602e11 −0.612990
\(412\) −6.04208e11 −1.03312
\(413\) −5.94084e10 −0.100478
\(414\) 4.56786e11 0.764207
\(415\) −1.77468e11 −0.293700
\(416\) 1.52355e10 0.0249423
\(417\) 9.98742e10 0.161749
\(418\) −2.70716e12 −4.33731
\(419\) −9.27538e11 −1.47017 −0.735087 0.677973i \(-0.762859\pi\)
−0.735087 + 0.677973i \(0.762859\pi\)
\(420\) 3.75877e11 0.589418
\(421\) −7.16269e11 −1.11124 −0.555619 0.831437i \(-0.687519\pi\)
−0.555619 + 0.831437i \(0.687519\pi\)
\(422\) 1.41302e12 2.16891
\(423\) 2.43086e10 0.0369171
\(424\) 2.09279e10 0.0314470
\(425\) 8.61627e11 1.28106
\(426\) −2.71969e11 −0.400107
\(427\) −7.82272e11 −1.13876
\(428\) 8.37512e11 1.20641
\(429\) −1.18343e10 −0.0168688
\(430\) 2.10392e12 2.96771
\(431\) 1.24444e11 0.173711 0.0868556 0.996221i \(-0.472318\pi\)
0.0868556 + 0.996221i \(0.472318\pi\)
\(432\) 1.46557e11 0.202455
\(433\) −1.33355e12 −1.82312 −0.911560 0.411167i \(-0.865121\pi\)
−0.911560 + 0.411167i \(0.865121\pi\)
\(434\) −1.05620e12 −1.42903
\(435\) 7.22921e11 0.968030
\(436\) −6.52735e8 −0.000865063 0
\(437\) 2.39306e12 3.13896
\(438\) −5.44102e10 −0.0706394
\(439\) 5.63941e11 0.724676 0.362338 0.932047i \(-0.381979\pi\)
0.362338 + 0.932047i \(0.381979\pi\)
\(440\) 1.37530e11 0.174928
\(441\) −1.07054e11 −0.134781
\(442\) −2.68055e10 −0.0334060
\(443\) −1.49448e12 −1.84363 −0.921815 0.387630i \(-0.873294\pi\)
−0.921815 + 0.387630i \(0.873294\pi\)
\(444\) −4.14068e11 −0.505648
\(445\) 1.47942e12 1.78843
\(446\) −6.15941e10 −0.0737110
\(447\) 5.01208e11 0.593792
\(448\) 5.83748e11 0.684659
\(449\) −3.74619e11 −0.434992 −0.217496 0.976061i \(-0.569789\pi\)
−0.217496 + 0.976061i \(0.569789\pi\)
\(450\) 3.87965e11 0.446001
\(451\) 1.32000e12 1.50238
\(452\) −9.20389e11 −1.03717
\(453\) −9.85601e10 −0.109966
\(454\) −1.06172e11 −0.117289
\(455\) 1.77177e10 0.0193801
\(456\) 7.80984e10 0.0845863
\(457\) −1.43898e12 −1.54323 −0.771617 0.636087i \(-0.780552\pi\)
−0.771617 + 0.636087i \(0.780552\pi\)
\(458\) 2.31188e12 2.45511
\(459\) −2.44369e11 −0.256974
\(460\) 2.08819e12 2.17450
\(461\) −4.45857e10 −0.0459771 −0.0229885 0.999736i \(-0.507318\pi\)
−0.0229885 + 0.999736i \(0.507318\pi\)
\(462\) −9.91140e11 −1.01215
\(463\) 5.37437e11 0.543517 0.271759 0.962365i \(-0.412395\pi\)
0.271759 + 0.962365i \(0.412395\pi\)
\(464\) 1.25814e12 1.26008
\(465\) −1.08175e12 −1.07297
\(466\) 1.72360e12 1.69317
\(467\) −2.57366e11 −0.250395 −0.125197 0.992132i \(-0.539956\pi\)
−0.125197 + 0.992132i \(0.539956\pi\)
\(468\) −5.86415e9 −0.00565066
\(469\) −5.63751e11 −0.538033
\(470\) 2.28722e11 0.216206
\(471\) 4.75753e11 0.445438
\(472\) −1.07711e10 −0.00998901
\(473\) −2.69543e12 −2.47601
\(474\) −8.69686e11 −0.791334
\(475\) 2.03251e12 1.83194
\(476\) −1.09075e12 −0.973852
\(477\) −1.54469e11 −0.136618
\(478\) −3.44778e11 −0.302074
\(479\) −3.26878e11 −0.283711 −0.141855 0.989887i \(-0.545307\pi\)
−0.141855 + 0.989887i \(0.545307\pi\)
\(480\) 1.30686e12 1.12368
\(481\) −1.95179e10 −0.0166257
\(482\) −5.71549e11 −0.482328
\(483\) 8.76141e11 0.732507
\(484\) 1.88557e12 1.56185
\(485\) 7.27585e11 0.597098
\(486\) −1.10032e11 −0.0894653
\(487\) 2.01920e12 1.62667 0.813333 0.581799i \(-0.197651\pi\)
0.813333 + 0.581799i \(0.197651\pi\)
\(488\) −1.41831e11 −0.113209
\(489\) 1.95907e11 0.154938
\(490\) −1.00728e12 −0.789348
\(491\) 1.19020e11 0.0924170 0.0462085 0.998932i \(-0.485286\pi\)
0.0462085 + 0.998932i \(0.485286\pi\)
\(492\) 6.54090e11 0.503262
\(493\) −2.09783e12 −1.59941
\(494\) −6.32320e10 −0.0477712
\(495\) −1.01511e12 −0.759959
\(496\) −1.88263e12 −1.39668
\(497\) −5.21652e11 −0.383510
\(498\) 2.31885e11 0.168943
\(499\) −3.24580e11 −0.234352 −0.117176 0.993111i \(-0.537384\pi\)
−0.117176 + 0.993111i \(0.537384\pi\)
\(500\) −7.50572e10 −0.0537066
\(501\) 1.63715e11 0.116096
\(502\) 1.17319e12 0.824523
\(503\) −2.26643e12 −1.57865 −0.789325 0.613976i \(-0.789569\pi\)
−0.789325 + 0.613976i \(0.789569\pi\)
\(504\) 2.85932e10 0.0197390
\(505\) 2.85926e11 0.195633
\(506\) −5.50630e12 −3.73407
\(507\) 8.58688e11 0.577164
\(508\) −7.88438e11 −0.525268
\(509\) 1.77037e12 1.16905 0.584527 0.811374i \(-0.301280\pi\)
0.584527 + 0.811374i \(0.301280\pi\)
\(510\) −2.29930e12 −1.50497
\(511\) −1.04362e11 −0.0677092
\(512\) 2.14890e12 1.38198
\(513\) −5.76446e11 −0.367477
\(514\) −2.75282e12 −1.73958
\(515\) −2.44297e12 −1.53033
\(516\) −1.33564e12 −0.829405
\(517\) −2.93026e11 −0.180385
\(518\) −1.63465e12 −0.997565
\(519\) 8.28860e11 0.501451
\(520\) 3.21233e9 0.00192666
\(521\) 1.14290e11 0.0679576 0.0339788 0.999423i \(-0.489182\pi\)
0.0339788 + 0.999423i \(0.489182\pi\)
\(522\) −9.44588e11 −0.556833
\(523\) 5.11463e11 0.298921 0.149461 0.988768i \(-0.452246\pi\)
0.149461 + 0.988768i \(0.452246\pi\)
\(524\) −9.94037e11 −0.575986
\(525\) 7.44138e11 0.427501
\(526\) −2.80112e12 −1.59550
\(527\) 3.13909e12 1.77279
\(528\) −1.76666e12 −0.989238
\(529\) 3.06627e12 1.70239
\(530\) −1.45342e12 −0.800110
\(531\) 7.95020e10 0.0433963
\(532\) −2.57299e12 −1.39263
\(533\) 3.08318e10 0.0165473
\(534\) −1.93305e12 −1.02874
\(535\) 3.38628e12 1.78703
\(536\) −1.02212e11 −0.0534884
\(537\) −1.13762e12 −0.590354
\(538\) 1.76732e11 0.0909482
\(539\) 1.29047e12 0.658566
\(540\) −5.03009e11 −0.254568
\(541\) −1.19821e12 −0.601377 −0.300688 0.953722i \(-0.597216\pi\)
−0.300688 + 0.953722i \(0.597216\pi\)
\(542\) 3.82273e12 1.90273
\(543\) 1.08507e12 0.535621
\(544\) −3.79234e12 −1.85657
\(545\) −2.63918e9 −0.00128140
\(546\) −2.31504e10 −0.0111479
\(547\) 2.72863e12 1.30317 0.651587 0.758574i \(-0.274104\pi\)
0.651587 + 0.758574i \(0.274104\pi\)
\(548\) 2.11812e12 1.00332
\(549\) 1.04686e12 0.491828
\(550\) −4.67670e12 −2.17925
\(551\) −4.94860e12 −2.28718
\(552\) 1.58850e11 0.0728219
\(553\) −1.66811e12 −0.758509
\(554\) −2.13752e12 −0.964086
\(555\) −1.67419e12 −0.749006
\(556\) −5.96572e11 −0.264744
\(557\) −3.14208e12 −1.38315 −0.691573 0.722306i \(-0.743082\pi\)
−0.691573 + 0.722306i \(0.743082\pi\)
\(558\) 1.41344e12 0.617196
\(559\) −6.29581e10 −0.0272708
\(560\) 2.64495e12 1.13650
\(561\) 2.94573e12 1.25562
\(562\) 4.50786e12 1.90615
\(563\) 3.69947e12 1.55186 0.775929 0.630820i \(-0.217281\pi\)
0.775929 + 0.630820i \(0.217281\pi\)
\(564\) −1.45201e11 −0.0604245
\(565\) −3.72137e12 −1.53633
\(566\) −6.59244e12 −2.70005
\(567\) −2.11047e11 −0.0857543
\(568\) −9.45790e10 −0.0381265
\(569\) 1.93401e12 0.773489 0.386744 0.922187i \(-0.373600\pi\)
0.386744 + 0.922187i \(0.373600\pi\)
\(570\) −5.42385e12 −2.15214
\(571\) 3.78514e12 1.49012 0.745058 0.667000i \(-0.232422\pi\)
0.745058 + 0.667000i \(0.232422\pi\)
\(572\) 7.06891e10 0.0276102
\(573\) −7.02252e11 −0.272143
\(574\) 2.58220e12 0.992857
\(575\) 4.13408e12 1.57715
\(576\) −7.81189e11 −0.295702
\(577\) 4.23047e12 1.58890 0.794452 0.607328i \(-0.207758\pi\)
0.794452 + 0.607328i \(0.207758\pi\)
\(578\) 2.93002e12 1.09193
\(579\) 2.39562e12 0.885860
\(580\) −4.31817e12 −1.58443
\(581\) 4.44769e11 0.161935
\(582\) −9.50682e11 −0.343465
\(583\) 1.86204e12 0.667545
\(584\) −1.89215e10 −0.00673129
\(585\) −2.37103e10 −0.00837020
\(586\) 3.68812e12 1.29201
\(587\) 1.98842e12 0.691254 0.345627 0.938372i \(-0.387666\pi\)
0.345627 + 0.938372i \(0.387666\pi\)
\(588\) 6.39456e11 0.220604
\(589\) 7.40486e12 2.53512
\(590\) 7.48044e11 0.254152
\(591\) −2.07626e12 −0.700064
\(592\) −2.91369e12 −0.974981
\(593\) 1.52171e12 0.505344 0.252672 0.967552i \(-0.418691\pi\)
0.252672 + 0.967552i \(0.418691\pi\)
\(594\) 1.32637e12 0.437146
\(595\) −4.41018e12 −1.44255
\(596\) −2.99383e12 −0.971895
\(597\) −3.04717e12 −0.981775
\(598\) −1.28613e11 −0.0411271
\(599\) 8.87750e11 0.281754 0.140877 0.990027i \(-0.455008\pi\)
0.140877 + 0.990027i \(0.455008\pi\)
\(600\) 1.34917e11 0.0424998
\(601\) −4.01927e12 −1.25664 −0.628322 0.777954i \(-0.716258\pi\)
−0.628322 + 0.777954i \(0.716258\pi\)
\(602\) −5.27282e12 −1.63629
\(603\) 7.54428e11 0.232375
\(604\) 5.88722e11 0.179988
\(605\) 7.62385e12 2.31353
\(606\) −3.73599e11 −0.112533
\(607\) 6.00721e12 1.79607 0.898035 0.439923i \(-0.144994\pi\)
0.898035 + 0.439923i \(0.144994\pi\)
\(608\) −8.94581e12 −2.65493
\(609\) −1.81177e12 −0.533735
\(610\) 9.85004e12 2.88040
\(611\) −6.84432e9 −0.00198676
\(612\) 1.45967e12 0.420604
\(613\) 4.90828e12 1.40397 0.701984 0.712193i \(-0.252298\pi\)
0.701984 + 0.712193i \(0.252298\pi\)
\(614\) −2.63470e12 −0.748124
\(615\) 2.64466e12 0.745472
\(616\) −3.44675e11 −0.0964489
\(617\) 4.52149e12 1.25603 0.628013 0.778203i \(-0.283868\pi\)
0.628013 + 0.778203i \(0.283868\pi\)
\(618\) 3.19206e12 0.880283
\(619\) −5.02565e12 −1.37589 −0.687946 0.725762i \(-0.741487\pi\)
−0.687946 + 0.725762i \(0.741487\pi\)
\(620\) 6.46152e12 1.75619
\(621\) −1.17248e12 −0.316368
\(622\) −7.05280e12 −1.88932
\(623\) −3.70770e12 −0.986070
\(624\) −4.12645e10 −0.0108955
\(625\) −3.96329e12 −1.03895
\(626\) −3.12045e12 −0.812143
\(627\) 6.94873e12 1.79557
\(628\) −2.84178e12 −0.729076
\(629\) 4.85828e12 1.23753
\(630\) −1.98577e12 −0.502223
\(631\) −3.67636e12 −0.923178 −0.461589 0.887094i \(-0.652721\pi\)
−0.461589 + 0.887094i \(0.652721\pi\)
\(632\) −3.02439e11 −0.0754069
\(633\) −3.62693e12 −0.897888
\(634\) −9.65839e12 −2.37412
\(635\) −3.18786e12 −0.778068
\(636\) 9.22680e11 0.223611
\(637\) 3.01420e10 0.00725345
\(638\) 1.13865e13 2.72080
\(639\) 6.98090e11 0.165637
\(640\) 9.10316e11 0.214478
\(641\) −1.04966e12 −0.245576 −0.122788 0.992433i \(-0.539184\pi\)
−0.122788 + 0.992433i \(0.539184\pi\)
\(642\) −4.42461e12 −1.02794
\(643\) −2.71624e12 −0.626642 −0.313321 0.949647i \(-0.601442\pi\)
−0.313321 + 0.949647i \(0.601442\pi\)
\(644\) −5.23339e12 −1.19894
\(645\) −5.40035e12 −1.22858
\(646\) 1.57393e13 3.55583
\(647\) 1.92188e12 0.431179 0.215590 0.976484i \(-0.430833\pi\)
0.215590 + 0.976484i \(0.430833\pi\)
\(648\) −3.82643e10 −0.00852523
\(649\) −9.58353e11 −0.212043
\(650\) −1.09235e11 −0.0240023
\(651\) 2.71105e12 0.591594
\(652\) −1.17019e12 −0.253597
\(653\) 9.02523e11 0.194245 0.0971223 0.995272i \(-0.469036\pi\)
0.0971223 + 0.995272i \(0.469036\pi\)
\(654\) 3.44842e9 0.000737090 0
\(655\) −4.01915e12 −0.853196
\(656\) 4.60266e12 0.970380
\(657\) 1.39660e11 0.0292434
\(658\) −5.73221e11 −0.119208
\(659\) 2.16361e12 0.446884 0.223442 0.974717i \(-0.428271\pi\)
0.223442 + 0.974717i \(0.428271\pi\)
\(660\) 6.06350e12 1.24387
\(661\) 9.09841e12 1.85378 0.926891 0.375330i \(-0.122470\pi\)
0.926891 + 0.375330i \(0.122470\pi\)
\(662\) −5.93219e12 −1.20048
\(663\) 6.88044e10 0.0138295
\(664\) 8.06395e10 0.0160987
\(665\) −1.04033e13 −2.06287
\(666\) 2.18754e12 0.430845
\(667\) −1.00653e13 −1.96908
\(668\) −9.77908e11 −0.190022
\(669\) 1.58100e11 0.0305150
\(670\) 7.09851e12 1.36091
\(671\) −1.26193e13 −2.40317
\(672\) −3.27522e12 −0.619554
\(673\) 9.38452e12 1.76337 0.881687 0.471835i \(-0.156408\pi\)
0.881687 + 0.471835i \(0.156408\pi\)
\(674\) 1.08048e13 2.01673
\(675\) −9.95828e11 −0.184636
\(676\) −5.12914e12 −0.944680
\(677\) −4.25164e12 −0.777871 −0.388935 0.921265i \(-0.627157\pi\)
−0.388935 + 0.921265i \(0.627157\pi\)
\(678\) 4.86245e12 0.883734
\(679\) −1.82346e12 −0.329217
\(680\) −7.99596e11 −0.143410
\(681\) 2.72522e11 0.0485555
\(682\) −1.70382e13 −3.01574
\(683\) 7.18700e12 1.26373 0.631866 0.775078i \(-0.282289\pi\)
0.631866 + 0.775078i \(0.282289\pi\)
\(684\) 3.44324e12 0.601472
\(685\) 8.56412e12 1.48619
\(686\) 8.76774e12 1.51157
\(687\) −5.93413e12 −1.01637
\(688\) −9.39857e12 −1.59924
\(689\) 4.34923e10 0.00735235
\(690\) −1.10320e13 −1.85282
\(691\) 5.15669e12 0.860438 0.430219 0.902725i \(-0.358436\pi\)
0.430219 + 0.902725i \(0.358436\pi\)
\(692\) −4.95097e12 −0.820754
\(693\) 2.54406e12 0.419013
\(694\) −5.35379e12 −0.876080
\(695\) −2.41210e12 −0.392160
\(696\) −3.28487e11 −0.0530611
\(697\) −7.67447e12 −1.23169
\(698\) −4.17212e12 −0.665285
\(699\) −4.42413e12 −0.700940
\(700\) −4.44491e12 −0.699716
\(701\) −2.57658e12 −0.403007 −0.201503 0.979488i \(-0.564583\pi\)
−0.201503 + 0.979488i \(0.564583\pi\)
\(702\) 3.09805e10 0.00481473
\(703\) 1.14603e13 1.76969
\(704\) 9.41680e12 1.44486
\(705\) −5.87085e11 −0.0895055
\(706\) −7.17814e12 −1.08740
\(707\) −7.16584e11 −0.107865
\(708\) −4.74884e11 −0.0710293
\(709\) −6.76459e12 −1.00539 −0.502694 0.864465i \(-0.667658\pi\)
−0.502694 + 0.864465i \(0.667658\pi\)
\(710\) 6.56841e12 0.970059
\(711\) 2.23231e12 0.327598
\(712\) −6.72230e11 −0.0980298
\(713\) 1.50613e13 2.18253
\(714\) 5.76246e12 0.829786
\(715\) 2.85815e11 0.0408985
\(716\) 6.79527e12 0.966268
\(717\) 8.84976e11 0.125053
\(718\) 9.29086e11 0.130466
\(719\) 5.26570e10 0.00734812 0.00367406 0.999993i \(-0.498831\pi\)
0.00367406 + 0.999993i \(0.498831\pi\)
\(720\) −3.53955e12 −0.490853
\(721\) 6.12255e12 0.843769
\(722\) 2.69449e13 3.69027
\(723\) 1.46705e12 0.199675
\(724\) −6.48136e12 −0.876683
\(725\) −8.54886e12 −1.14918
\(726\) −9.96153e12 −1.33080
\(727\) −1.51266e12 −0.200834 −0.100417 0.994945i \(-0.532018\pi\)
−0.100417 + 0.994945i \(0.532018\pi\)
\(728\) −8.05070e9 −0.00106229
\(729\) 2.82430e11 0.0370370
\(730\) 1.31408e12 0.171265
\(731\) 1.56712e13 2.02989
\(732\) −6.25313e12 −0.805004
\(733\) −8.43668e12 −1.07945 −0.539726 0.841841i \(-0.681472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(734\) 1.15551e13 1.46940
\(735\) 2.58549e12 0.326776
\(736\) −1.81956e13 −2.28568
\(737\) −9.09421e12 −1.13543
\(738\) −3.45558e12 −0.428812
\(739\) 6.45681e12 0.796376 0.398188 0.917304i \(-0.369639\pi\)
0.398188 + 0.917304i \(0.369639\pi\)
\(740\) 1.00003e13 1.22594
\(741\) 1.62304e11 0.0197764
\(742\) 3.64254e12 0.441150
\(743\) −7.53304e12 −0.906819 −0.453410 0.891302i \(-0.649793\pi\)
−0.453410 + 0.891302i \(0.649793\pi\)
\(744\) 4.91532e11 0.0588131
\(745\) −1.21049e13 −1.43965
\(746\) −1.61232e13 −1.90602
\(747\) −5.95202e11 −0.0699394
\(748\) −1.75955e13 −2.05516
\(749\) −8.48665e12 −0.985299
\(750\) 3.96530e11 0.0457615
\(751\) −1.64730e12 −0.188970 −0.0944851 0.995526i \(-0.530120\pi\)
−0.0944851 + 0.995526i \(0.530120\pi\)
\(752\) −1.02174e12 −0.116509
\(753\) −3.01135e12 −0.341338
\(754\) 2.65958e11 0.0299669
\(755\) 2.38036e12 0.266613
\(756\) 1.26063e12 0.140359
\(757\) 4.40812e12 0.487890 0.243945 0.969789i \(-0.421558\pi\)
0.243945 + 0.969789i \(0.421558\pi\)
\(758\) 1.69473e12 0.186462
\(759\) 1.41336e13 1.54584
\(760\) −1.88618e12 −0.205079
\(761\) −9.40473e12 −1.01652 −0.508259 0.861204i \(-0.669711\pi\)
−0.508259 + 0.861204i \(0.669711\pi\)
\(762\) 4.16535e12 0.447563
\(763\) 6.61427e9 0.000706515 0
\(764\) 4.19471e12 0.445433
\(765\) 5.90183e12 0.623032
\(766\) 1.22825e13 1.28901
\(767\) −2.23846e10 −0.00233545
\(768\) −6.12733e12 −0.635544
\(769\) 4.11650e12 0.424482 0.212241 0.977217i \(-0.431924\pi\)
0.212241 + 0.977217i \(0.431924\pi\)
\(770\) 2.39374e13 2.45396
\(771\) 7.06594e12 0.720154
\(772\) −1.43096e13 −1.44994
\(773\) 5.85547e12 0.589867 0.294933 0.955518i \(-0.404703\pi\)
0.294933 + 0.955518i \(0.404703\pi\)
\(774\) 7.05625e12 0.706707
\(775\) 1.27921e13 1.27375
\(776\) −3.30606e11 −0.0327290
\(777\) 4.19582e12 0.412974
\(778\) 4.84157e12 0.473782
\(779\) −1.81034e13 −1.76134
\(780\) 1.41627e11 0.0137000
\(781\) −8.41508e12 −0.809336
\(782\) 3.20135e13 3.06128
\(783\) 2.42457e12 0.230519
\(784\) 4.49969e12 0.425364
\(785\) −1.14901e13 −1.07996
\(786\) 5.25153e12 0.490778
\(787\) 7.07362e12 0.657288 0.328644 0.944454i \(-0.393408\pi\)
0.328644 + 0.944454i \(0.393408\pi\)
\(788\) 1.24020e13 1.14584
\(789\) 7.18991e12 0.660507
\(790\) 2.10041e13 1.91859
\(791\) 9.32645e12 0.847076
\(792\) 4.61255e11 0.0416560
\(793\) −2.94754e11 −0.0264685
\(794\) 1.97147e13 1.76035
\(795\) 3.73064e12 0.331231
\(796\) 1.82014e13 1.60693
\(797\) −1.28079e13 −1.12439 −0.562193 0.827006i \(-0.690042\pi\)
−0.562193 + 0.827006i \(0.690042\pi\)
\(798\) 1.35932e13 1.18661
\(799\) 1.70365e12 0.147883
\(800\) −1.54542e13 −1.33395
\(801\) 4.96175e12 0.425881
\(802\) −8.60686e12 −0.734616
\(803\) −1.68353e12 −0.142889
\(804\) −4.50637e12 −0.380342
\(805\) −2.11600e13 −1.77596
\(806\) −3.97967e11 −0.0332154
\(807\) −4.53635e11 −0.0376509
\(808\) −1.29922e11 −0.0107233
\(809\) −1.83179e12 −0.150352 −0.0751758 0.997170i \(-0.523952\pi\)
−0.0751758 + 0.997170i \(0.523952\pi\)
\(810\) 2.65742e12 0.216909
\(811\) −2.04629e13 −1.66102 −0.830509 0.557005i \(-0.811950\pi\)
−0.830509 + 0.557005i \(0.811950\pi\)
\(812\) 1.08221e13 0.873597
\(813\) −9.81217e12 −0.787694
\(814\) −2.63696e13 −2.10520
\(815\) −4.73141e12 −0.375648
\(816\) 1.02713e13 0.811000
\(817\) 3.69670e13 2.90278
\(818\) −2.62021e13 −2.04619
\(819\) 5.94224e10 0.00461501
\(820\) −1.57971e13 −1.22016
\(821\) 1.08327e13 0.832133 0.416066 0.909334i \(-0.363408\pi\)
0.416066 + 0.909334i \(0.363408\pi\)
\(822\) −1.11901e13 −0.854892
\(823\) 2.52645e12 0.191960 0.0959802 0.995383i \(-0.469401\pi\)
0.0959802 + 0.995383i \(0.469401\pi\)
\(824\) 1.11006e12 0.0838829
\(825\) 1.20042e13 0.902171
\(826\) −1.87474e12 −0.140130
\(827\) −1.26388e13 −0.939571 −0.469785 0.882781i \(-0.655669\pi\)
−0.469785 + 0.882781i \(0.655669\pi\)
\(828\) 7.00348e12 0.517818
\(829\) −2.40266e12 −0.176684 −0.0883419 0.996090i \(-0.528157\pi\)
−0.0883419 + 0.996090i \(0.528157\pi\)
\(830\) −5.60033e12 −0.409602
\(831\) 5.48658e12 0.399114
\(832\) 2.19951e11 0.0159137
\(833\) −7.50278e12 −0.539908
\(834\) 3.15171e12 0.225579
\(835\) −3.95394e12 −0.281476
\(836\) −4.15064e13 −2.93891
\(837\) −3.62801e12 −0.255508
\(838\) −2.92701e13 −2.05034
\(839\) 1.42527e13 0.993045 0.496523 0.868024i \(-0.334610\pi\)
0.496523 + 0.868024i \(0.334610\pi\)
\(840\) −6.90565e11 −0.0478572
\(841\) 6.30699e12 0.434751
\(842\) −2.26032e13 −1.54976
\(843\) −1.15708e13 −0.789111
\(844\) 2.16645e13 1.46963
\(845\) −2.07385e13 −1.39933
\(846\) 7.67101e11 0.0514856
\(847\) −1.91068e13 −1.27559
\(848\) 6.49267e12 0.431163
\(849\) 1.69215e13 1.11777
\(850\) 2.71902e13 1.78660
\(851\) 2.33100e13 1.52356
\(852\) −4.16985e12 −0.271108
\(853\) 3.62046e12 0.234149 0.117075 0.993123i \(-0.462648\pi\)
0.117075 + 0.993123i \(0.462648\pi\)
\(854\) −2.46860e13 −1.58815
\(855\) 1.39219e13 0.890948
\(856\) −1.53869e12 −0.0979531
\(857\) 2.03191e13 1.28674 0.643371 0.765555i \(-0.277535\pi\)
0.643371 + 0.765555i \(0.277535\pi\)
\(858\) −3.73453e11 −0.0235257
\(859\) −1.37685e13 −0.862814 −0.431407 0.902157i \(-0.641983\pi\)
−0.431407 + 0.902157i \(0.641983\pi\)
\(860\) 3.22576e13 2.01089
\(861\) −6.62800e12 −0.411025
\(862\) 3.92707e12 0.242262
\(863\) −1.23986e13 −0.760894 −0.380447 0.924803i \(-0.624230\pi\)
−0.380447 + 0.924803i \(0.624230\pi\)
\(864\) 4.38300e12 0.267584
\(865\) −2.00181e13 −1.21577
\(866\) −4.20827e13 −2.54257
\(867\) −7.52077e12 −0.452040
\(868\) −1.61938e13 −0.968297
\(869\) −2.69093e13 −1.60071
\(870\) 2.28131e13 1.35004
\(871\) −2.12417e11 −0.0125057
\(872\) 1.19921e9 7.02379e−5 0
\(873\) 2.44021e12 0.142188
\(874\) 7.55172e13 4.37768
\(875\) 7.60567e11 0.0438633
\(876\) −8.34222e11 −0.0478645
\(877\) 3.04802e13 1.73988 0.869939 0.493159i \(-0.164158\pi\)
0.869939 + 0.493159i \(0.164158\pi\)
\(878\) 1.77962e13 1.01065
\(879\) −9.46666e12 −0.534868
\(880\) 4.26673e13 2.39841
\(881\) 2.94577e13 1.64743 0.823715 0.567004i \(-0.191898\pi\)
0.823715 + 0.567004i \(0.191898\pi\)
\(882\) −3.37827e12 −0.187969
\(883\) 1.79573e13 0.994073 0.497036 0.867730i \(-0.334422\pi\)
0.497036 + 0.867730i \(0.334422\pi\)
\(884\) −4.10985e11 −0.0226355
\(885\) −1.92008e12 −0.105214
\(886\) −4.71611e13 −2.57118
\(887\) 1.85718e12 0.100739 0.0503696 0.998731i \(-0.483960\pi\)
0.0503696 + 0.998731i \(0.483960\pi\)
\(888\) 7.60731e11 0.0410556
\(889\) 7.98937e12 0.428998
\(890\) 4.66857e13 2.49419
\(891\) −3.40453e12 −0.180970
\(892\) −9.44367e11 −0.0499458
\(893\) 4.01877e12 0.211476
\(894\) 1.58165e13 0.828118
\(895\) 2.74751e13 1.43131
\(896\) −2.28142e12 −0.118255
\(897\) 3.30123e11 0.0170259
\(898\) −1.18218e13 −0.606651
\(899\) −3.11453e13 −1.59028
\(900\) 5.94831e12 0.302205
\(901\) −1.08259e13 −0.547269
\(902\) 4.16551e13 2.09526
\(903\) 1.35343e13 0.677393
\(904\) 1.69095e12 0.0842117
\(905\) −2.62059e13 −1.29861
\(906\) −3.11024e12 −0.153362
\(907\) 2.61442e13 1.28275 0.641377 0.767226i \(-0.278364\pi\)
0.641377 + 0.767226i \(0.278364\pi\)
\(908\) −1.62783e12 −0.0794738
\(909\) 9.58954e11 0.0465865
\(910\) 5.59113e11 0.0270280
\(911\) −4.33892e12 −0.208713 −0.104356 0.994540i \(-0.533278\pi\)
−0.104356 + 0.994540i \(0.533278\pi\)
\(912\) 2.42292e13 1.15975
\(913\) 7.17483e12 0.341738
\(914\) −4.54096e13 −2.15224
\(915\) −2.52831e13 −1.19244
\(916\) 3.54459e13 1.66355
\(917\) 1.00727e13 0.470420
\(918\) −7.71149e12 −0.358382
\(919\) −3.66087e13 −1.69303 −0.846514 0.532366i \(-0.821303\pi\)
−0.846514 + 0.532366i \(0.821303\pi\)
\(920\) −3.83645e12 −0.176557
\(921\) 6.76275e12 0.309710
\(922\) −1.40698e12 −0.0641208
\(923\) −1.96554e11 −0.00891403
\(924\) −1.51962e13 −0.685823
\(925\) 1.97980e13 0.889168
\(926\) 1.69598e13 0.758004
\(927\) −8.19337e12 −0.364421
\(928\) 3.76267e13 1.66544
\(929\) −2.26411e13 −0.997304 −0.498652 0.866802i \(-0.666171\pi\)
−0.498652 + 0.866802i \(0.666171\pi\)
\(930\) −3.41364e13 −1.49639
\(931\) −1.76984e13 −0.772078
\(932\) 2.64264e13 1.14727
\(933\) 1.81031e13 0.782143
\(934\) −8.12164e12 −0.349207
\(935\) −7.11433e13 −3.04426
\(936\) 1.07737e10 0.000458800 0
\(937\) 4.17920e13 1.77119 0.885595 0.464459i \(-0.153751\pi\)
0.885595 + 0.464459i \(0.153751\pi\)
\(938\) −1.77902e13 −0.750356
\(939\) 8.00956e12 0.336212
\(940\) 3.50679e12 0.146499
\(941\) −1.33777e13 −0.556196 −0.278098 0.960553i \(-0.589704\pi\)
−0.278098 + 0.960553i \(0.589704\pi\)
\(942\) 1.50132e13 0.621220
\(943\) −3.68220e13 −1.51637
\(944\) −3.34164e12 −0.136957
\(945\) 5.09707e12 0.207911
\(946\) −8.50591e13 −3.45311
\(947\) −2.53638e13 −1.02480 −0.512401 0.858746i \(-0.671244\pi\)
−0.512401 + 0.858746i \(0.671244\pi\)
\(948\) −1.33341e13 −0.536199
\(949\) −3.93227e10 −0.00157378
\(950\) 6.41395e13 2.55487
\(951\) 2.47912e13 0.982844
\(952\) 2.00393e12 0.0790710
\(953\) 3.42985e13 1.34697 0.673483 0.739203i \(-0.264797\pi\)
0.673483 + 0.739203i \(0.264797\pi\)
\(954\) −4.87455e12 −0.190532
\(955\) 1.69603e13 0.659810
\(956\) −5.28617e12 −0.204682
\(957\) −2.92268e13 −1.12636
\(958\) −1.03152e13 −0.395670
\(959\) −2.14633e13 −0.819430
\(960\) 1.88668e13 0.716930
\(961\) 2.01648e13 0.762675
\(962\) −6.15923e11 −0.0231867
\(963\) 1.13571e13 0.425548
\(964\) −8.76305e12 −0.326820
\(965\) −5.78576e13 −2.14777
\(966\) 2.76482e13 1.02157
\(967\) −4.25219e13 −1.56384 −0.781922 0.623376i \(-0.785760\pi\)
−0.781922 + 0.623376i \(0.785760\pi\)
\(968\) −3.46419e12 −0.126813
\(969\) −4.03998e13 −1.47205
\(970\) 2.29603e13 0.832729
\(971\) 4.34846e12 0.156982 0.0784908 0.996915i \(-0.474990\pi\)
0.0784908 + 0.996915i \(0.474990\pi\)
\(972\) −1.68702e12 −0.0606207
\(973\) 6.04516e12 0.216222
\(974\) 6.37194e13 2.26859
\(975\) 2.80385e11 0.00993652
\(976\) −4.40017e13 −1.55219
\(977\) −3.55468e13 −1.24817 −0.624087 0.781355i \(-0.714529\pi\)
−0.624087 + 0.781355i \(0.714529\pi\)
\(978\) 6.18218e12 0.216081
\(979\) −5.98111e13 −2.08094
\(980\) −1.54437e13 −0.534854
\(981\) −8.85141e9 −0.000305142 0
\(982\) 3.75588e12 0.128887
\(983\) −2.05160e13 −0.700813 −0.350407 0.936598i \(-0.613957\pi\)
−0.350407 + 0.936598i \(0.613957\pi\)
\(984\) −1.20170e12 −0.0408619
\(985\) 5.01444e13 1.69730
\(986\) −6.62007e13 −2.23057
\(987\) 1.47134e12 0.0493500
\(988\) −9.69479e11 −0.0323692
\(989\) 7.51900e13 2.49906
\(990\) −3.20337e13 −1.05986
\(991\) 1.78616e13 0.588286 0.294143 0.955761i \(-0.404966\pi\)
0.294143 + 0.955761i \(0.404966\pi\)
\(992\) −5.63028e13 −1.84598
\(993\) 1.52268e13 0.496976
\(994\) −1.64617e13 −0.534854
\(995\) 7.35932e13 2.38031
\(996\) 3.55528e12 0.114474
\(997\) −5.83450e12 −0.187015 −0.0935073 0.995619i \(-0.529808\pi\)
−0.0935073 + 0.995619i \(0.529808\pi\)
\(998\) −1.02427e13 −0.326834
\(999\) −5.61497e12 −0.178362
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.c.1.18 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.18 22 1.1 even 1 trivial