Properties

Label 177.12.a.c.1.19
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} -178481. q^{10} -541443. q^{11} +86251.5 q^{12} +289390. q^{13} +2.64531e6 q^{14} +1.05405e6 q^{15} -3.34139e6 q^{16} -5.10994e6 q^{17} +2.42967e6 q^{18} +7.74730e6 q^{19} +1.53963e6 q^{20} -1.56224e7 q^{21} -2.22786e7 q^{22} -1.12741e7 q^{23} +2.40262e7 q^{24} -3.00128e7 q^{25} +1.19075e7 q^{26} -1.43489e7 q^{27} -2.28192e7 q^{28} -1.00038e8 q^{29} +4.33709e7 q^{30} +1.75466e8 q^{31} +6.50052e7 q^{32} +1.31571e8 q^{33} -2.10257e8 q^{34} -2.78867e8 q^{35} -2.09591e7 q^{36} +4.23968e7 q^{37} +3.18776e8 q^{38} -7.03218e7 q^{39} +4.28880e8 q^{40} +9.20980e8 q^{41} -6.42809e8 q^{42} -1.57768e9 q^{43} +1.92182e8 q^{44} -2.56135e8 q^{45} -4.63894e8 q^{46} -3.05940e9 q^{47} +8.11958e8 q^{48} +2.15582e9 q^{49} -1.23493e9 q^{50} +1.24172e9 q^{51} -1.02717e8 q^{52} -2.66837e9 q^{53} -5.90411e8 q^{54} +2.34860e9 q^{55} -6.35652e9 q^{56} -1.88259e9 q^{57} -4.11624e9 q^{58} -7.14924e8 q^{59} -3.74130e8 q^{60} -5.17784e9 q^{61} +7.21984e9 q^{62} +3.79623e9 q^{63} +9.51792e9 q^{64} -1.25528e9 q^{65} +5.41371e9 q^{66} +1.91789e10 q^{67} +1.81374e9 q^{68} +2.73962e9 q^{69} -1.14745e10 q^{70} +1.17361e10 q^{71} -5.83837e9 q^{72} +1.77886e10 q^{73} +1.74449e9 q^{74} +7.29310e9 q^{75} -2.74986e9 q^{76} -3.48091e10 q^{77} -2.89351e9 q^{78} +3.41681e10 q^{79} +1.44939e10 q^{80} +3.48678e9 q^{81} +3.78954e10 q^{82} -1.13758e10 q^{83} +5.54507e9 q^{84} +2.21652e10 q^{85} -6.49162e10 q^{86} +2.43092e10 q^{87} +5.35343e10 q^{88} -5.07069e10 q^{89} -1.05391e10 q^{90} +1.86047e10 q^{91} +4.00169e9 q^{92} -4.26382e10 q^{93} -1.25884e11 q^{94} -3.36052e10 q^{95} -1.57963e10 q^{96} +1.37888e11 q^{97} +8.87049e10 q^{98} -3.19717e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.1468 0.909223 0.454612 0.890690i \(-0.349778\pi\)
0.454612 + 0.890690i \(0.349778\pi\)
\(3\) −243.000 −0.577350
\(4\) −354.944 −0.173313
\(5\) −4337.67 −0.620757 −0.310378 0.950613i \(-0.600456\pi\)
−0.310378 + 0.950613i \(0.600456\pi\)
\(6\) −9998.66 −0.524940
\(7\) 64289.5 1.44578 0.722888 0.690965i \(-0.242814\pi\)
0.722888 + 0.690965i \(0.242814\pi\)
\(8\) −98873.4 −1.06680
\(9\) 59049.0 0.333333
\(10\) −178481. −0.564407
\(11\) −541443. −1.01366 −0.506831 0.862046i \(-0.669183\pi\)
−0.506831 + 0.862046i \(0.669183\pi\)
\(12\) 86251.5 0.100062
\(13\) 289390. 0.216170 0.108085 0.994142i \(-0.465528\pi\)
0.108085 + 0.994142i \(0.465528\pi\)
\(14\) 2.64531e6 1.31453
\(15\) 1.05405e6 0.358394
\(16\) −3.34139e6 −0.796650
\(17\) −5.10994e6 −0.872864 −0.436432 0.899737i \(-0.643758\pi\)
−0.436432 + 0.899737i \(0.643758\pi\)
\(18\) 2.42967e6 0.303074
\(19\) 7.74730e6 0.717803 0.358902 0.933375i \(-0.383151\pi\)
0.358902 + 0.933375i \(0.383151\pi\)
\(20\) 1.53963e6 0.107585
\(21\) −1.56224e7 −0.834719
\(22\) −2.22786e7 −0.921645
\(23\) −1.12741e7 −0.365242 −0.182621 0.983183i \(-0.558458\pi\)
−0.182621 + 0.983183i \(0.558458\pi\)
\(24\) 2.40262e7 0.615919
\(25\) −3.00128e7 −0.614661
\(26\) 1.19075e7 0.196547
\(27\) −1.43489e7 −0.192450
\(28\) −2.28192e7 −0.250571
\(29\) −1.00038e8 −0.905683 −0.452842 0.891591i \(-0.649590\pi\)
−0.452842 + 0.891591i \(0.649590\pi\)
\(30\) 4.33709e7 0.325860
\(31\) 1.75466e8 1.10079 0.550393 0.834906i \(-0.314478\pi\)
0.550393 + 0.834906i \(0.314478\pi\)
\(32\) 6.50052e7 0.342470
\(33\) 1.31571e8 0.585238
\(34\) −2.10257e8 −0.793629
\(35\) −2.78867e8 −0.897475
\(36\) −2.09591e7 −0.0577709
\(37\) 4.23968e7 0.100513 0.0502567 0.998736i \(-0.483996\pi\)
0.0502567 + 0.998736i \(0.483996\pi\)
\(38\) 3.18776e8 0.652644
\(39\) −7.03218e7 −0.124806
\(40\) 4.28880e8 0.662225
\(41\) 9.20980e8 1.24148 0.620739 0.784017i \(-0.286833\pi\)
0.620739 + 0.784017i \(0.286833\pi\)
\(42\) −6.42809e8 −0.758946
\(43\) −1.57768e9 −1.63659 −0.818297 0.574795i \(-0.805082\pi\)
−0.818297 + 0.574795i \(0.805082\pi\)
\(44\) 1.92182e8 0.175680
\(45\) −2.56135e8 −0.206919
\(46\) −4.63894e8 −0.332086
\(47\) −3.05940e9 −1.94580 −0.972898 0.231234i \(-0.925724\pi\)
−0.972898 + 0.231234i \(0.925724\pi\)
\(48\) 8.11958e8 0.459946
\(49\) 2.15582e9 1.09027
\(50\) −1.23493e9 −0.558864
\(51\) 1.24172e9 0.503948
\(52\) −1.02717e8 −0.0374650
\(53\) −2.66837e9 −0.876453 −0.438227 0.898864i \(-0.644393\pi\)
−0.438227 + 0.898864i \(0.644393\pi\)
\(54\) −5.90411e8 −0.174980
\(55\) 2.34860e9 0.629237
\(56\) −6.35652e9 −1.54236
\(57\) −1.88259e9 −0.414424
\(58\) −4.11624e9 −0.823468
\(59\) −7.14924e8 −0.130189
\(60\) −3.74130e8 −0.0621142
\(61\) −5.17784e9 −0.784937 −0.392468 0.919766i \(-0.628379\pi\)
−0.392468 + 0.919766i \(0.628379\pi\)
\(62\) 7.21984e9 1.00086
\(63\) 3.79623e9 0.481925
\(64\) 9.51792e9 1.10803
\(65\) −1.25528e9 −0.134189
\(66\) 5.41371e9 0.532112
\(67\) 1.91789e10 1.73545 0.867726 0.497043i \(-0.165581\pi\)
0.867726 + 0.497043i \(0.165581\pi\)
\(68\) 1.81374e9 0.151278
\(69\) 2.73962e9 0.210872
\(70\) −1.14745e10 −0.816005
\(71\) 1.17361e10 0.771976 0.385988 0.922504i \(-0.373861\pi\)
0.385988 + 0.922504i \(0.373861\pi\)
\(72\) −5.83837e9 −0.355601
\(73\) 1.77886e10 1.00431 0.502153 0.864779i \(-0.332541\pi\)
0.502153 + 0.864779i \(0.332541\pi\)
\(74\) 1.74449e9 0.0913891
\(75\) 7.29310e9 0.354875
\(76\) −2.74986e9 −0.124404
\(77\) −3.48091e10 −1.46553
\(78\) −2.89351e9 −0.113476
\(79\) 3.41681e10 1.24932 0.624658 0.780898i \(-0.285238\pi\)
0.624658 + 0.780898i \(0.285238\pi\)
\(80\) 1.44939e10 0.494526
\(81\) 3.48678e9 0.111111
\(82\) 3.78954e10 1.12878
\(83\) −1.13758e10 −0.316995 −0.158498 0.987359i \(-0.550665\pi\)
−0.158498 + 0.987359i \(0.550665\pi\)
\(84\) 5.54507e9 0.144667
\(85\) 2.21652e10 0.541836
\(86\) −6.49162e10 −1.48803
\(87\) 2.43092e10 0.522896
\(88\) 5.35343e10 1.08138
\(89\) −5.07069e10 −0.962547 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(90\) −1.05391e10 −0.188136
\(91\) 1.86047e10 0.312533
\(92\) 4.00169e9 0.0633010
\(93\) −4.26382e10 −0.635539
\(94\) −1.25884e11 −1.76916
\(95\) −3.36052e10 −0.445581
\(96\) −1.57963e10 −0.197725
\(97\) 1.37888e11 1.63035 0.815175 0.579215i \(-0.196641\pi\)
0.815175 + 0.579215i \(0.196641\pi\)
\(98\) 8.87049e10 0.991297
\(99\) −3.19717e10 −0.337887
\(100\) 1.06529e10 0.106529
\(101\) 9.79204e10 0.927055 0.463528 0.886083i \(-0.346584\pi\)
0.463528 + 0.886083i \(0.346584\pi\)
\(102\) 5.10926e10 0.458202
\(103\) 1.22973e11 1.04522 0.522609 0.852573i \(-0.324959\pi\)
0.522609 + 0.852573i \(0.324959\pi\)
\(104\) −2.86130e10 −0.230611
\(105\) 6.77646e10 0.518157
\(106\) −1.09795e11 −0.796892
\(107\) 2.87464e11 1.98140 0.990701 0.136057i \(-0.0434429\pi\)
0.990701 + 0.136057i \(0.0434429\pi\)
\(108\) 5.09306e9 0.0333540
\(109\) 2.82590e11 1.75918 0.879591 0.475730i \(-0.157816\pi\)
0.879591 + 0.475730i \(0.157816\pi\)
\(110\) 9.66373e10 0.572117
\(111\) −1.03024e10 −0.0580314
\(112\) −2.14817e11 −1.15178
\(113\) 3.06089e10 0.156284 0.0781422 0.996942i \(-0.475101\pi\)
0.0781422 + 0.996942i \(0.475101\pi\)
\(114\) −7.74626e10 −0.376804
\(115\) 4.89035e10 0.226726
\(116\) 3.55079e10 0.156966
\(117\) 1.70882e10 0.0720566
\(118\) −2.94168e10 −0.118371
\(119\) −3.28516e11 −1.26197
\(120\) −1.04218e11 −0.382336
\(121\) 7.84883e9 0.0275097
\(122\) −2.13051e11 −0.713683
\(123\) −2.23798e11 −0.716768
\(124\) −6.22805e10 −0.190780
\(125\) 3.41986e11 1.00231
\(126\) 1.56203e11 0.438178
\(127\) 6.43804e10 0.172915 0.0864576 0.996256i \(-0.472445\pi\)
0.0864576 + 0.996256i \(0.472445\pi\)
\(128\) 2.58501e11 0.664979
\(129\) 3.83375e11 0.944888
\(130\) −5.16506e10 −0.122008
\(131\) −2.01111e11 −0.455454 −0.227727 0.973725i \(-0.573129\pi\)
−0.227727 + 0.973725i \(0.573129\pi\)
\(132\) −4.67002e10 −0.101429
\(133\) 4.98070e11 1.03778
\(134\) 7.89150e11 1.57791
\(135\) 6.22408e10 0.119465
\(136\) 5.05237e11 0.931175
\(137\) 1.07444e12 1.90205 0.951023 0.309120i \(-0.100035\pi\)
0.951023 + 0.309120i \(0.100035\pi\)
\(138\) 1.12726e11 0.191730
\(139\) −7.27147e11 −1.18861 −0.594307 0.804238i \(-0.702574\pi\)
−0.594307 + 0.804238i \(0.702574\pi\)
\(140\) 9.89821e10 0.155544
\(141\) 7.43433e11 1.12341
\(142\) 4.82904e11 0.701899
\(143\) −1.56688e11 −0.219123
\(144\) −1.97306e11 −0.265550
\(145\) 4.33932e11 0.562209
\(146\) 7.31943e11 0.913139
\(147\) −5.23863e11 −0.629467
\(148\) −1.50485e10 −0.0174202
\(149\) −7.09274e11 −0.791206 −0.395603 0.918422i \(-0.629464\pi\)
−0.395603 + 0.918422i \(0.629464\pi\)
\(150\) 3.00087e11 0.322661
\(151\) 1.53012e12 1.58618 0.793092 0.609102i \(-0.208470\pi\)
0.793092 + 0.609102i \(0.208470\pi\)
\(152\) −7.66002e11 −0.765755
\(153\) −3.01737e11 −0.290955
\(154\) −1.43228e12 −1.33249
\(155\) −7.61112e11 −0.683320
\(156\) 2.49603e10 0.0216304
\(157\) 6.45190e11 0.539809 0.269904 0.962887i \(-0.413008\pi\)
0.269904 + 0.962887i \(0.413008\pi\)
\(158\) 1.40591e12 1.13591
\(159\) 6.48414e11 0.506021
\(160\) −2.81971e11 −0.212591
\(161\) −7.24809e11 −0.528058
\(162\) 1.43470e11 0.101025
\(163\) −2.28361e12 −1.55450 −0.777248 0.629195i \(-0.783385\pi\)
−0.777248 + 0.629195i \(0.783385\pi\)
\(164\) −3.26897e11 −0.215164
\(165\) −5.70710e11 −0.363290
\(166\) −4.68078e11 −0.288220
\(167\) −1.77082e12 −1.05495 −0.527476 0.849570i \(-0.676862\pi\)
−0.527476 + 0.849570i \(0.676862\pi\)
\(168\) 1.54463e12 0.890481
\(169\) −1.70841e12 −0.953271
\(170\) 9.12027e11 0.492650
\(171\) 4.57470e11 0.239268
\(172\) 5.59987e11 0.283642
\(173\) −1.00215e11 −0.0491676 −0.0245838 0.999698i \(-0.507826\pi\)
−0.0245838 + 0.999698i \(0.507826\pi\)
\(174\) 1.00025e12 0.475430
\(175\) −1.92951e12 −0.888662
\(176\) 1.80917e12 0.807534
\(177\) 1.73727e11 0.0751646
\(178\) −2.08642e12 −0.875171
\(179\) −1.89930e11 −0.0772505 −0.0386252 0.999254i \(-0.512298\pi\)
−0.0386252 + 0.999254i \(0.512298\pi\)
\(180\) 9.09137e10 0.0358617
\(181\) −3.37075e12 −1.28972 −0.644858 0.764303i \(-0.723083\pi\)
−0.644858 + 0.764303i \(0.723083\pi\)
\(182\) 7.65525e11 0.284163
\(183\) 1.25822e12 0.453183
\(184\) 1.11471e12 0.389641
\(185\) −1.83903e11 −0.0623944
\(186\) −1.75442e12 −0.577847
\(187\) 2.76674e12 0.884789
\(188\) 1.08591e12 0.337231
\(189\) −9.22484e11 −0.278240
\(190\) −1.38275e12 −0.405133
\(191\) 5.65554e11 0.160987 0.0804934 0.996755i \(-0.474350\pi\)
0.0804934 + 0.996755i \(0.474350\pi\)
\(192\) −2.31286e12 −0.639723
\(193\) 1.70304e12 0.457782 0.228891 0.973452i \(-0.426490\pi\)
0.228891 + 0.973452i \(0.426490\pi\)
\(194\) 5.67363e12 1.48235
\(195\) 3.05033e11 0.0774740
\(196\) −7.65195e11 −0.188957
\(197\) 4.61776e12 1.10883 0.554417 0.832239i \(-0.312941\pi\)
0.554417 + 0.832239i \(0.312941\pi\)
\(198\) −1.31553e12 −0.307215
\(199\) 5.51998e12 1.25385 0.626925 0.779080i \(-0.284313\pi\)
0.626925 + 0.779080i \(0.284313\pi\)
\(200\) 2.96746e12 0.655723
\(201\) −4.66048e12 −1.00196
\(202\) 4.02911e12 0.842900
\(203\) −6.43140e12 −1.30941
\(204\) −4.40740e11 −0.0873406
\(205\) −3.99491e12 −0.770656
\(206\) 5.05996e12 0.950336
\(207\) −6.65727e11 −0.121747
\(208\) −9.66966e11 −0.172212
\(209\) −4.19472e12 −0.727610
\(210\) 2.78829e12 0.471121
\(211\) 1.41210e12 0.232441 0.116221 0.993223i \(-0.462922\pi\)
0.116221 + 0.993223i \(0.462922\pi\)
\(212\) 9.47123e11 0.151900
\(213\) −2.85188e12 −0.445701
\(214\) 1.18282e13 1.80154
\(215\) 6.84343e12 1.01593
\(216\) 1.41872e12 0.205306
\(217\) 1.12806e13 1.59149
\(218\) 1.16277e13 1.59949
\(219\) −4.32263e12 −0.579837
\(220\) −8.33622e11 −0.109055
\(221\) −1.47877e12 −0.188687
\(222\) −4.23912e11 −0.0527635
\(223\) 8.59996e11 0.104429 0.0522143 0.998636i \(-0.483372\pi\)
0.0522143 + 0.998636i \(0.483372\pi\)
\(224\) 4.17915e12 0.495136
\(225\) −1.77222e12 −0.204887
\(226\) 1.25946e12 0.142098
\(227\) −1.38605e13 −1.52629 −0.763145 0.646228i \(-0.776346\pi\)
−0.763145 + 0.646228i \(0.776346\pi\)
\(228\) 6.68216e11 0.0718249
\(229\) 5.84705e12 0.613538 0.306769 0.951784i \(-0.400752\pi\)
0.306769 + 0.951784i \(0.400752\pi\)
\(230\) 2.01222e12 0.206145
\(231\) 8.45861e12 0.846123
\(232\) 9.89110e12 0.966186
\(233\) 9.79197e12 0.934142 0.467071 0.884220i \(-0.345309\pi\)
0.467071 + 0.884220i \(0.345309\pi\)
\(234\) 7.03124e11 0.0655156
\(235\) 1.32706e13 1.20787
\(236\) 2.53758e11 0.0225634
\(237\) −8.30286e12 −0.721293
\(238\) −1.35174e13 −1.14741
\(239\) 1.78247e13 1.47855 0.739273 0.673406i \(-0.235170\pi\)
0.739273 + 0.673406i \(0.235170\pi\)
\(240\) −3.52201e12 −0.285515
\(241\) −1.59589e13 −1.26447 −0.632234 0.774777i \(-0.717862\pi\)
−0.632234 + 0.774777i \(0.717862\pi\)
\(242\) 3.22954e11 0.0250124
\(243\) −8.47289e11 −0.0641500
\(244\) 1.83784e12 0.136039
\(245\) −9.35122e12 −0.676791
\(246\) −9.20857e12 −0.651702
\(247\) 2.24199e12 0.155167
\(248\) −1.73489e13 −1.17432
\(249\) 2.76432e12 0.183017
\(250\) 1.40716e13 0.911325
\(251\) −1.37229e13 −0.869444 −0.434722 0.900565i \(-0.643153\pi\)
−0.434722 + 0.900565i \(0.643153\pi\)
\(252\) −1.34745e12 −0.0835237
\(253\) 6.10431e12 0.370232
\(254\) 2.64904e12 0.157219
\(255\) −5.38615e12 −0.312829
\(256\) −8.85623e12 −0.503418
\(257\) 3.00076e13 1.66955 0.834775 0.550591i \(-0.185598\pi\)
0.834775 + 0.550591i \(0.185598\pi\)
\(258\) 1.57746e13 0.859115
\(259\) 2.72567e12 0.145320
\(260\) 4.45554e11 0.0232566
\(261\) −5.90715e12 −0.301894
\(262\) −8.27508e12 −0.414109
\(263\) 4.69654e12 0.230155 0.115078 0.993356i \(-0.463288\pi\)
0.115078 + 0.993356i \(0.463288\pi\)
\(264\) −1.30088e13 −0.624334
\(265\) 1.15745e13 0.544064
\(266\) 2.04940e13 0.943577
\(267\) 1.23218e13 0.555727
\(268\) −6.80745e12 −0.300776
\(269\) 1.25814e13 0.544618 0.272309 0.962210i \(-0.412213\pi\)
0.272309 + 0.962210i \(0.412213\pi\)
\(270\) 2.56101e12 0.108620
\(271\) −3.84736e13 −1.59894 −0.799469 0.600707i \(-0.794886\pi\)
−0.799469 + 0.600707i \(0.794886\pi\)
\(272\) 1.70743e13 0.695367
\(273\) −4.52095e12 −0.180441
\(274\) 4.42099e13 1.72938
\(275\) 1.62502e13 0.623058
\(276\) −9.72411e11 −0.0365469
\(277\) 3.08447e13 1.13643 0.568213 0.822881i \(-0.307635\pi\)
0.568213 + 0.822881i \(0.307635\pi\)
\(278\) −2.99198e13 −1.08072
\(279\) 1.03611e13 0.366929
\(280\) 2.75725e13 0.957429
\(281\) −8.58731e12 −0.292397 −0.146198 0.989255i \(-0.546704\pi\)
−0.146198 + 0.989255i \(0.546704\pi\)
\(282\) 3.05899e13 1.02143
\(283\) −3.69092e13 −1.20868 −0.604338 0.796728i \(-0.706562\pi\)
−0.604338 + 0.796728i \(0.706562\pi\)
\(284\) −4.16567e12 −0.133793
\(285\) 8.16607e12 0.257256
\(286\) −6.44721e12 −0.199232
\(287\) 5.92094e13 1.79490
\(288\) 3.83849e12 0.114157
\(289\) −8.16041e12 −0.238108
\(290\) 1.78549e13 0.511173
\(291\) −3.35067e13 −0.941283
\(292\) −6.31396e12 −0.174059
\(293\) 5.18707e13 1.40330 0.701649 0.712523i \(-0.252447\pi\)
0.701649 + 0.712523i \(0.252447\pi\)
\(294\) −2.15553e13 −0.572326
\(295\) 3.10110e12 0.0808156
\(296\) −4.19192e12 −0.107228
\(297\) 7.76911e12 0.195079
\(298\) −2.91843e13 −0.719383
\(299\) −3.26262e12 −0.0789543
\(300\) −2.58864e12 −0.0615043
\(301\) −1.01428e14 −2.36615
\(302\) 6.29597e13 1.44220
\(303\) −2.37947e13 −0.535236
\(304\) −2.58868e13 −0.571838
\(305\) 2.24598e13 0.487255
\(306\) −1.24155e13 −0.264543
\(307\) 4.44715e13 0.930724 0.465362 0.885120i \(-0.345924\pi\)
0.465362 + 0.885120i \(0.345924\pi\)
\(308\) 1.23553e13 0.253994
\(309\) −2.98825e13 −0.603456
\(310\) −3.13173e13 −0.621291
\(311\) 1.94368e13 0.378828 0.189414 0.981897i \(-0.439341\pi\)
0.189414 + 0.981897i \(0.439341\pi\)
\(312\) 6.95295e12 0.133143
\(313\) −2.32955e13 −0.438307 −0.219153 0.975690i \(-0.570329\pi\)
−0.219153 + 0.975690i \(0.570329\pi\)
\(314\) 2.65475e13 0.490807
\(315\) −1.64668e13 −0.299158
\(316\) −1.21278e13 −0.216522
\(317\) −1.33535e13 −0.234298 −0.117149 0.993114i \(-0.537376\pi\)
−0.117149 + 0.993114i \(0.537376\pi\)
\(318\) 2.66801e13 0.460086
\(319\) 5.41649e13 0.918056
\(320\) −4.12856e13 −0.687818
\(321\) −6.98537e13 −1.14396
\(322\) −2.98236e13 −0.480123
\(323\) −3.95882e13 −0.626545
\(324\) −1.23761e12 −0.0192570
\(325\) −8.68539e12 −0.132871
\(326\) −9.39630e13 −1.41338
\(327\) −6.86694e13 −1.01566
\(328\) −9.10604e13 −1.32441
\(329\) −1.96687e14 −2.81319
\(330\) −2.34829e13 −0.330312
\(331\) 9.72625e13 1.34552 0.672762 0.739859i \(-0.265108\pi\)
0.672762 + 0.739859i \(0.265108\pi\)
\(332\) 4.03778e12 0.0549393
\(333\) 2.50349e12 0.0335045
\(334\) −7.28634e13 −0.959188
\(335\) −8.31918e13 −1.07729
\(336\) 5.22004e13 0.664979
\(337\) −2.39917e12 −0.0300674 −0.0150337 0.999887i \(-0.504786\pi\)
−0.0150337 + 0.999887i \(0.504786\pi\)
\(338\) −7.02957e13 −0.866736
\(339\) −7.43796e12 −0.0902309
\(340\) −7.86742e12 −0.0939071
\(341\) −9.50046e13 −1.11582
\(342\) 1.88234e13 0.217548
\(343\) 1.14750e13 0.130507
\(344\) 1.55990e14 1.74592
\(345\) −1.18836e13 −0.130900
\(346\) −4.12352e12 −0.0447043
\(347\) −1.29189e14 −1.37852 −0.689261 0.724513i \(-0.742065\pi\)
−0.689261 + 0.724513i \(0.742065\pi\)
\(348\) −8.62843e12 −0.0906246
\(349\) 6.60836e13 0.683210 0.341605 0.939844i \(-0.389030\pi\)
0.341605 + 0.939844i \(0.389030\pi\)
\(350\) −7.93929e13 −0.807993
\(351\) −4.15243e12 −0.0416019
\(352\) −3.51966e13 −0.347149
\(353\) 9.77591e13 0.949285 0.474642 0.880179i \(-0.342577\pi\)
0.474642 + 0.880179i \(0.342577\pi\)
\(354\) 7.14829e12 0.0683414
\(355\) −5.09074e13 −0.479209
\(356\) 1.79981e13 0.166822
\(357\) 7.98293e13 0.728596
\(358\) −7.81499e12 −0.0702379
\(359\) 1.93981e14 1.71688 0.858441 0.512913i \(-0.171434\pi\)
0.858441 + 0.512913i \(0.171434\pi\)
\(360\) 2.53249e13 0.220742
\(361\) −5.64696e13 −0.484758
\(362\) −1.38695e14 −1.17264
\(363\) −1.90727e12 −0.0158827
\(364\) −6.60365e12 −0.0541660
\(365\) −7.71611e13 −0.623430
\(366\) 5.17715e13 0.412045
\(367\) −8.64895e13 −0.678110 −0.339055 0.940767i \(-0.610107\pi\)
−0.339055 + 0.940767i \(0.610107\pi\)
\(368\) 3.76713e13 0.290970
\(369\) 5.43830e13 0.413826
\(370\) −7.56703e12 −0.0567304
\(371\) −1.71548e14 −1.26716
\(372\) 1.51342e13 0.110147
\(373\) −2.14662e14 −1.53942 −0.769708 0.638396i \(-0.779598\pi\)
−0.769708 + 0.638396i \(0.779598\pi\)
\(374\) 1.13842e14 0.804471
\(375\) −8.31025e13 −0.578685
\(376\) 3.02493e14 2.07578
\(377\) −2.89500e13 −0.195781
\(378\) −3.79572e13 −0.252982
\(379\) 1.65130e14 1.08470 0.542352 0.840151i \(-0.317534\pi\)
0.542352 + 0.840151i \(0.317534\pi\)
\(380\) 1.19280e13 0.0772249
\(381\) −1.56444e13 −0.0998326
\(382\) 2.32707e13 0.146373
\(383\) −6.64821e13 −0.412203 −0.206102 0.978531i \(-0.566078\pi\)
−0.206102 + 0.978531i \(0.566078\pi\)
\(384\) −6.28158e13 −0.383926
\(385\) 1.50990e14 0.909736
\(386\) 7.00745e13 0.416227
\(387\) −9.31601e13 −0.545531
\(388\) −4.89424e13 −0.282560
\(389\) −1.50018e14 −0.853927 −0.426964 0.904269i \(-0.640417\pi\)
−0.426964 + 0.904269i \(0.640417\pi\)
\(390\) 1.25511e13 0.0704412
\(391\) 5.76102e13 0.318806
\(392\) −2.13153e14 −1.16310
\(393\) 4.88701e13 0.262956
\(394\) 1.90006e14 1.00818
\(395\) −1.48210e14 −0.775521
\(396\) 1.13482e13 0.0585601
\(397\) −1.82934e14 −0.930994 −0.465497 0.885050i \(-0.654124\pi\)
−0.465497 + 0.885050i \(0.654124\pi\)
\(398\) 2.27129e14 1.14003
\(399\) −1.21031e14 −0.599164
\(400\) 1.00284e14 0.489670
\(401\) 2.93556e14 1.41383 0.706914 0.707299i \(-0.250087\pi\)
0.706914 + 0.707299i \(0.250087\pi\)
\(402\) −1.91763e14 −0.911009
\(403\) 5.07780e13 0.237957
\(404\) −3.47563e13 −0.160670
\(405\) −1.51245e13 −0.0689730
\(406\) −2.64631e14 −1.19055
\(407\) −2.29555e13 −0.101887
\(408\) −1.22773e14 −0.537614
\(409\) 2.59552e13 0.112136 0.0560682 0.998427i \(-0.482144\pi\)
0.0560682 + 0.998427i \(0.482144\pi\)
\(410\) −1.64378e14 −0.700699
\(411\) −2.61090e14 −1.09815
\(412\) −4.36487e13 −0.181149
\(413\) −4.59621e13 −0.188224
\(414\) −2.73925e13 −0.110695
\(415\) 4.93445e13 0.196777
\(416\) 1.88119e13 0.0740318
\(417\) 1.76697e14 0.686247
\(418\) −1.72599e14 −0.661560
\(419\) 1.79032e14 0.677257 0.338629 0.940920i \(-0.390037\pi\)
0.338629 + 0.940920i \(0.390037\pi\)
\(420\) −2.40527e13 −0.0898032
\(421\) −2.82305e14 −1.04032 −0.520160 0.854069i \(-0.674128\pi\)
−0.520160 + 0.854069i \(0.674128\pi\)
\(422\) 5.81035e13 0.211341
\(423\) −1.80654e14 −0.648599
\(424\) 2.63831e14 0.935004
\(425\) 1.53363e14 0.536516
\(426\) −1.17346e14 −0.405241
\(427\) −3.32881e14 −1.13484
\(428\) −1.02034e14 −0.343402
\(429\) 3.80752e13 0.126511
\(430\) 2.81585e14 0.923705
\(431\) −1.29967e14 −0.420929 −0.210464 0.977602i \(-0.567498\pi\)
−0.210464 + 0.977602i \(0.567498\pi\)
\(432\) 4.79453e13 0.153315
\(433\) 4.10611e14 1.29642 0.648212 0.761460i \(-0.275517\pi\)
0.648212 + 0.761460i \(0.275517\pi\)
\(434\) 4.64160e14 1.44702
\(435\) −1.05445e14 −0.324591
\(436\) −1.00304e14 −0.304889
\(437\) −8.73442e13 −0.262172
\(438\) −1.77862e14 −0.527201
\(439\) 7.71968e13 0.225967 0.112983 0.993597i \(-0.463959\pi\)
0.112983 + 0.993597i \(0.463959\pi\)
\(440\) −2.32214e14 −0.671272
\(441\) 1.27299e14 0.363423
\(442\) −6.08464e13 −0.171559
\(443\) −2.80872e14 −0.782147 −0.391073 0.920359i \(-0.627896\pi\)
−0.391073 + 0.920359i \(0.627896\pi\)
\(444\) 3.65679e12 0.0100576
\(445\) 2.19950e14 0.597508
\(446\) 3.53860e13 0.0949490
\(447\) 1.72354e14 0.456803
\(448\) 6.11903e14 1.60197
\(449\) −6.51039e14 −1.68365 −0.841825 0.539750i \(-0.818519\pi\)
−0.841825 + 0.539750i \(0.818519\pi\)
\(450\) −7.29212e13 −0.186288
\(451\) −4.98658e14 −1.25844
\(452\) −1.08644e13 −0.0270861
\(453\) −3.71820e14 −0.915784
\(454\) −5.70315e14 −1.38774
\(455\) −8.07012e13 −0.194007
\(456\) 1.86138e14 0.442109
\(457\) 1.31023e14 0.307474 0.153737 0.988112i \(-0.450869\pi\)
0.153737 + 0.988112i \(0.450869\pi\)
\(458\) 2.40587e14 0.557844
\(459\) 7.33220e13 0.167983
\(460\) −1.73580e13 −0.0392945
\(461\) 4.27698e14 0.956713 0.478357 0.878166i \(-0.341233\pi\)
0.478357 + 0.878166i \(0.341233\pi\)
\(462\) 3.48045e14 0.769315
\(463\) −2.53709e13 −0.0554167 −0.0277084 0.999616i \(-0.508821\pi\)
−0.0277084 + 0.999616i \(0.508821\pi\)
\(464\) 3.34266e14 0.721513
\(465\) 1.84950e14 0.394515
\(466\) 4.02908e14 0.849344
\(467\) 5.75188e14 1.19830 0.599152 0.800635i \(-0.295504\pi\)
0.599152 + 0.800635i \(0.295504\pi\)
\(468\) −6.06536e12 −0.0124883
\(469\) 1.23300e15 2.50907
\(470\) 5.46044e14 1.09822
\(471\) −1.56781e14 −0.311659
\(472\) 7.06870e13 0.138886
\(473\) 8.54221e14 1.65895
\(474\) −3.41636e14 −0.655817
\(475\) −2.32518e14 −0.441206
\(476\) 1.16605e14 0.218715
\(477\) −1.57565e14 −0.292151
\(478\) 7.33430e14 1.34433
\(479\) −5.96075e14 −1.08008 −0.540039 0.841640i \(-0.681591\pi\)
−0.540039 + 0.841640i \(0.681591\pi\)
\(480\) 6.85189e13 0.122739
\(481\) 1.22692e13 0.0217280
\(482\) −6.56655e14 −1.14968
\(483\) 1.76129e14 0.304874
\(484\) −2.78590e12 −0.00476777
\(485\) −5.98111e14 −1.01205
\(486\) −3.48632e13 −0.0583267
\(487\) 2.82223e14 0.466857 0.233428 0.972374i \(-0.425006\pi\)
0.233428 + 0.972374i \(0.425006\pi\)
\(488\) 5.11950e14 0.837373
\(489\) 5.54916e14 0.897488
\(490\) −3.84772e14 −0.615354
\(491\) −1.58749e14 −0.251051 −0.125526 0.992090i \(-0.540062\pi\)
−0.125526 + 0.992090i \(0.540062\pi\)
\(492\) 7.94359e13 0.124225
\(493\) 5.11188e14 0.790538
\(494\) 9.22507e13 0.141082
\(495\) 1.38683e14 0.209746
\(496\) −5.86300e14 −0.876941
\(497\) 7.54510e14 1.11610
\(498\) 1.13743e14 0.166404
\(499\) 6.43076e14 0.930484 0.465242 0.885183i \(-0.345967\pi\)
0.465242 + 0.885183i \(0.345967\pi\)
\(500\) −1.21386e14 −0.173713
\(501\) 4.30309e14 0.609077
\(502\) −5.64654e14 −0.790519
\(503\) −9.67165e14 −1.33930 −0.669648 0.742679i \(-0.733555\pi\)
−0.669648 + 0.742679i \(0.733555\pi\)
\(504\) −3.75346e14 −0.514120
\(505\) −4.24746e14 −0.575476
\(506\) 2.51172e14 0.336623
\(507\) 4.15145e14 0.550371
\(508\) −2.28515e13 −0.0299684
\(509\) 5.42613e14 0.703951 0.351975 0.936009i \(-0.385510\pi\)
0.351975 + 0.936009i \(0.385510\pi\)
\(510\) −2.21623e14 −0.284432
\(511\) 1.14362e15 1.45200
\(512\) −8.93815e14 −1.12270
\(513\) −1.11165e14 −0.138141
\(514\) 1.23472e15 1.51799
\(515\) −5.33418e14 −0.648826
\(516\) −1.36077e14 −0.163761
\(517\) 1.65649e15 1.97238
\(518\) 1.12153e14 0.132128
\(519\) 2.43522e13 0.0283869
\(520\) 1.24114e14 0.143153
\(521\) −6.72659e14 −0.767693 −0.383846 0.923397i \(-0.625401\pi\)
−0.383846 + 0.923397i \(0.625401\pi\)
\(522\) −2.43060e14 −0.274489
\(523\) 1.57267e15 1.75743 0.878717 0.477343i \(-0.158400\pi\)
0.878717 + 0.477343i \(0.158400\pi\)
\(524\) 7.13833e13 0.0789359
\(525\) 4.68870e14 0.513069
\(526\) 1.93247e14 0.209263
\(527\) −8.96619e14 −0.960836
\(528\) −4.39629e14 −0.466230
\(529\) −8.25703e14 −0.866598
\(530\) 4.76253e14 0.494676
\(531\) −4.22156e13 −0.0433963
\(532\) −1.76787e14 −0.179861
\(533\) 2.66523e14 0.268370
\(534\) 5.07001e14 0.505280
\(535\) −1.24692e15 −1.22997
\(536\) −1.89628e15 −1.85139
\(537\) 4.61529e13 0.0446006
\(538\) 5.17684e14 0.495179
\(539\) −1.16725e15 −1.10516
\(540\) −2.20920e13 −0.0207047
\(541\) 1.82845e15 1.69628 0.848141 0.529770i \(-0.177722\pi\)
0.848141 + 0.529770i \(0.177722\pi\)
\(542\) −1.58306e15 −1.45379
\(543\) 8.19091e14 0.744618
\(544\) −3.32173e14 −0.298930
\(545\) −1.22578e15 −1.09202
\(546\) −1.86023e14 −0.164061
\(547\) −1.38114e15 −1.20589 −0.602946 0.797782i \(-0.706007\pi\)
−0.602946 + 0.797782i \(0.706007\pi\)
\(548\) −3.81368e14 −0.329649
\(549\) −3.05746e14 −0.261646
\(550\) 6.68643e14 0.566499
\(551\) −7.75025e14 −0.650102
\(552\) −2.70875e14 −0.224959
\(553\) 2.19665e15 1.80623
\(554\) 1.26916e15 1.03327
\(555\) 4.46885e13 0.0360234
\(556\) 2.58097e14 0.206002
\(557\) 6.87300e13 0.0543179 0.0271589 0.999631i \(-0.491354\pi\)
0.0271589 + 0.999631i \(0.491354\pi\)
\(558\) 4.26324e14 0.333620
\(559\) −4.56563e14 −0.353782
\(560\) 9.31803e14 0.714974
\(561\) −6.72318e14 −0.510833
\(562\) −3.53340e14 −0.265854
\(563\) −4.13813e14 −0.308324 −0.154162 0.988046i \(-0.549268\pi\)
−0.154162 + 0.988046i \(0.549268\pi\)
\(564\) −2.63877e14 −0.194700
\(565\) −1.32771e14 −0.0970146
\(566\) −1.51870e15 −1.09896
\(567\) 2.24164e14 0.160642
\(568\) −1.16039e15 −0.823547
\(569\) 1.44956e15 1.01887 0.509433 0.860510i \(-0.329855\pi\)
0.509433 + 0.860510i \(0.329855\pi\)
\(570\) 3.36007e14 0.233904
\(571\) 1.93283e14 0.133258 0.0666291 0.997778i \(-0.478776\pi\)
0.0666291 + 0.997778i \(0.478776\pi\)
\(572\) 5.56156e13 0.0379768
\(573\) −1.37430e14 −0.0929458
\(574\) 2.43627e15 1.63196
\(575\) 3.38368e14 0.224500
\(576\) 5.62024e14 0.369344
\(577\) 1.92752e15 1.25468 0.627339 0.778746i \(-0.284144\pi\)
0.627339 + 0.778746i \(0.284144\pi\)
\(578\) −3.35775e14 −0.216493
\(579\) −4.13838e14 −0.264301
\(580\) −1.54022e14 −0.0974379
\(581\) −7.31346e14 −0.458304
\(582\) −1.37869e15 −0.855836
\(583\) 1.44477e15 0.888427
\(584\) −1.75882e15 −1.07140
\(585\) −7.41229e13 −0.0447296
\(586\) 2.13431e15 1.27591
\(587\) 2.27708e15 1.34856 0.674278 0.738478i \(-0.264455\pi\)
0.674278 + 0.738478i \(0.264455\pi\)
\(588\) 1.85942e14 0.109095
\(589\) 1.35938e15 0.790148
\(590\) 1.27600e14 0.0734795
\(591\) −1.12211e15 −0.640186
\(592\) −1.41664e14 −0.0800740
\(593\) 9.08968e14 0.509035 0.254518 0.967068i \(-0.418083\pi\)
0.254518 + 0.967068i \(0.418083\pi\)
\(594\) 3.19674e14 0.177371
\(595\) 1.42499e15 0.783374
\(596\) 2.51753e14 0.137126
\(597\) −1.34135e15 −0.723910
\(598\) −1.34246e14 −0.0717871
\(599\) 3.31252e15 1.75514 0.877569 0.479450i \(-0.159164\pi\)
0.877569 + 0.479450i \(0.159164\pi\)
\(600\) −7.21093e14 −0.378582
\(601\) −4.32128e14 −0.224803 −0.112402 0.993663i \(-0.535854\pi\)
−0.112402 + 0.993663i \(0.535854\pi\)
\(602\) −4.17343e15 −2.15136
\(603\) 1.13250e15 0.578484
\(604\) −5.43109e14 −0.274906
\(605\) −3.40456e13 −0.0170768
\(606\) −9.79073e14 −0.486649
\(607\) −1.58856e15 −0.782464 −0.391232 0.920292i \(-0.627951\pi\)
−0.391232 + 0.920292i \(0.627951\pi\)
\(608\) 5.03615e14 0.245826
\(609\) 1.56283e15 0.755991
\(610\) 9.24146e14 0.443023
\(611\) −8.85359e14 −0.420623
\(612\) 1.07100e14 0.0504261
\(613\) 1.44900e15 0.676138 0.338069 0.941121i \(-0.390226\pi\)
0.338069 + 0.941121i \(0.390226\pi\)
\(614\) 1.82986e15 0.846236
\(615\) 9.70763e14 0.444938
\(616\) 3.44169e15 1.56343
\(617\) 7.43149e14 0.334586 0.167293 0.985907i \(-0.446497\pi\)
0.167293 + 0.985907i \(0.446497\pi\)
\(618\) −1.22957e15 −0.548677
\(619\) 2.27293e15 1.00528 0.502641 0.864495i \(-0.332362\pi\)
0.502641 + 0.864495i \(0.332362\pi\)
\(620\) 2.70152e14 0.118428
\(621\) 1.61772e14 0.0702908
\(622\) 7.99761e14 0.344440
\(623\) −3.25992e15 −1.39163
\(624\) 2.34973e14 0.0994265
\(625\) −1.79540e13 −0.00753046
\(626\) −9.58534e14 −0.398519
\(627\) 1.01932e15 0.420086
\(628\) −2.29007e14 −0.0935557
\(629\) −2.16645e14 −0.0877345
\(630\) −6.77555e14 −0.272002
\(631\) −3.65257e15 −1.45357 −0.726786 0.686864i \(-0.758987\pi\)
−0.726786 + 0.686864i \(0.758987\pi\)
\(632\) −3.37832e15 −1.33277
\(633\) −3.43141e14 −0.134200
\(634\) −5.49454e14 −0.213030
\(635\) −2.79261e14 −0.107338
\(636\) −2.30151e14 −0.0876998
\(637\) 6.23872e14 0.235683
\(638\) 2.22871e15 0.834718
\(639\) 6.93007e14 0.257325
\(640\) −1.12129e15 −0.412790
\(641\) −4.59570e15 −1.67738 −0.838691 0.544607i \(-0.816679\pi\)
−0.838691 + 0.544607i \(0.816679\pi\)
\(642\) −2.87426e15 −1.04012
\(643\) 1.49893e15 0.537801 0.268900 0.963168i \(-0.413340\pi\)
0.268900 + 0.963168i \(0.413340\pi\)
\(644\) 2.57267e14 0.0915191
\(645\) −1.66295e15 −0.586546
\(646\) −1.62893e15 −0.569669
\(647\) −1.85166e15 −0.642077 −0.321039 0.947066i \(-0.604032\pi\)
−0.321039 + 0.947066i \(0.604032\pi\)
\(648\) −3.44750e14 −0.118534
\(649\) 3.87091e14 0.131967
\(650\) −3.57376e14 −0.120810
\(651\) −2.74119e15 −0.918847
\(652\) 8.10553e14 0.269414
\(653\) 4.48071e15 1.47681 0.738404 0.674358i \(-0.235580\pi\)
0.738404 + 0.674358i \(0.235580\pi\)
\(654\) −2.82552e15 −0.923466
\(655\) 8.72355e14 0.282726
\(656\) −3.07736e15 −0.989024
\(657\) 1.05040e15 0.334769
\(658\) −8.09304e15 −2.55781
\(659\) −2.57359e15 −0.806623 −0.403311 0.915063i \(-0.632141\pi\)
−0.403311 + 0.915063i \(0.632141\pi\)
\(660\) 2.02570e14 0.0629628
\(661\) 2.69950e15 0.832100 0.416050 0.909342i \(-0.363414\pi\)
0.416050 + 0.909342i \(0.363414\pi\)
\(662\) 4.00204e15 1.22338
\(663\) 3.59340e14 0.108938
\(664\) 1.12477e15 0.338172
\(665\) −2.16046e15 −0.644211
\(666\) 1.03011e14 0.0304630
\(667\) 1.12784e15 0.330793
\(668\) 6.28541e14 0.182837
\(669\) −2.08979e14 −0.0602919
\(670\) −3.42307e15 −0.979500
\(671\) 2.80351e15 0.795660
\(672\) −1.01553e15 −0.285867
\(673\) −4.85570e15 −1.35572 −0.677858 0.735193i \(-0.737091\pi\)
−0.677858 + 0.735193i \(0.737091\pi\)
\(674\) −9.87179e13 −0.0273380
\(675\) 4.30650e14 0.118292
\(676\) 6.06392e14 0.165214
\(677\) −2.83566e15 −0.766332 −0.383166 0.923680i \(-0.625166\pi\)
−0.383166 + 0.923680i \(0.625166\pi\)
\(678\) −3.06048e14 −0.0820400
\(679\) 8.86473e15 2.35712
\(680\) −2.19155e15 −0.578033
\(681\) 3.36810e15 0.881204
\(682\) −3.90913e15 −1.01453
\(683\) −4.40038e15 −1.13286 −0.566430 0.824110i \(-0.691676\pi\)
−0.566430 + 0.824110i \(0.691676\pi\)
\(684\) −1.62376e14 −0.0414681
\(685\) −4.66059e15 −1.18071
\(686\) 4.72159e14 0.118660
\(687\) −1.42083e15 −0.354227
\(688\) 5.27163e15 1.30379
\(689\) −7.72200e14 −0.189463
\(690\) −4.88970e14 −0.119018
\(691\) 2.97282e15 0.717859 0.358930 0.933365i \(-0.383142\pi\)
0.358930 + 0.933365i \(0.383142\pi\)
\(692\) 3.55707e13 0.00852137
\(693\) −2.05544e15 −0.488509
\(694\) −5.31571e15 −1.25338
\(695\) 3.15413e15 0.737840
\(696\) −2.40354e15 −0.557828
\(697\) −4.70615e15 −1.08364
\(698\) 2.71913e15 0.621190
\(699\) −2.37945e15 −0.539327
\(700\) 6.84867e14 0.154016
\(701\) 6.40626e15 1.42940 0.714702 0.699429i \(-0.246562\pi\)
0.714702 + 0.699429i \(0.246562\pi\)
\(702\) −1.70859e14 −0.0378254
\(703\) 3.28461e14 0.0721489
\(704\) −5.15341e15 −1.12317
\(705\) −3.22477e15 −0.697362
\(706\) 4.02247e15 0.863112
\(707\) 6.29525e15 1.34031
\(708\) −6.16633e13 −0.0130270
\(709\) −4.50543e15 −0.944457 −0.472228 0.881476i \(-0.656550\pi\)
−0.472228 + 0.881476i \(0.656550\pi\)
\(710\) −2.09468e15 −0.435708
\(711\) 2.01759e15 0.416439
\(712\) 5.01356e15 1.02685
\(713\) −1.97822e15 −0.402053
\(714\) 3.28472e15 0.662457
\(715\) 6.79662e14 0.136022
\(716\) 6.74144e13 0.0133885
\(717\) −4.33141e15 −0.853638
\(718\) 7.98170e15 1.56103
\(719\) 2.98746e15 0.579821 0.289910 0.957054i \(-0.406374\pi\)
0.289910 + 0.957054i \(0.406374\pi\)
\(720\) 8.55848e14 0.164842
\(721\) 7.90590e15 1.51115
\(722\) −2.32354e15 −0.440754
\(723\) 3.87800e15 0.730041
\(724\) 1.19643e15 0.223524
\(725\) 3.00242e15 0.556688
\(726\) −7.84778e13 −0.0144409
\(727\) −1.50136e15 −0.274185 −0.137093 0.990558i \(-0.543776\pi\)
−0.137093 + 0.990558i \(0.543776\pi\)
\(728\) −1.83951e15 −0.333411
\(729\) 2.05891e14 0.0370370
\(730\) −3.17493e15 −0.566837
\(731\) 8.06182e15 1.42852
\(732\) −4.46596e14 −0.0785424
\(733\) 2.64632e15 0.461923 0.230962 0.972963i \(-0.425813\pi\)
0.230962 + 0.972963i \(0.425813\pi\)
\(734\) −3.55876e15 −0.616553
\(735\) 2.27235e15 0.390746
\(736\) −7.32878e14 −0.125085
\(737\) −1.03843e16 −1.75916
\(738\) 2.23768e15 0.376260
\(739\) −1.18888e16 −1.98423 −0.992117 0.125313i \(-0.960006\pi\)
−0.992117 + 0.125313i \(0.960006\pi\)
\(740\) 6.52755e13 0.0108137
\(741\) −5.44804e14 −0.0895860
\(742\) −7.05866e15 −1.15213
\(743\) −8.52748e15 −1.38160 −0.690800 0.723046i \(-0.742741\pi\)
−0.690800 + 0.723046i \(0.742741\pi\)
\(744\) 4.21578e15 0.677995
\(745\) 3.07659e15 0.491146
\(746\) −8.83263e15 −1.39967
\(747\) −6.71730e14 −0.105665
\(748\) −9.82039e14 −0.153345
\(749\) 1.84809e16 2.86466
\(750\) −3.41940e15 −0.526154
\(751\) −5.33920e15 −0.815561 −0.407781 0.913080i \(-0.633697\pi\)
−0.407781 + 0.913080i \(0.633697\pi\)
\(752\) 1.02226e16 1.55012
\(753\) 3.33467e15 0.501974
\(754\) −1.19120e15 −0.178009
\(755\) −6.63717e15 −0.984634
\(756\) 3.27431e14 0.0482225
\(757\) −9.52636e15 −1.39283 −0.696417 0.717637i \(-0.745224\pi\)
−0.696417 + 0.717637i \(0.745224\pi\)
\(758\) 6.79458e15 0.986238
\(759\) −1.48335e15 −0.213753
\(760\) 3.32266e15 0.475348
\(761\) 2.96485e15 0.421102 0.210551 0.977583i \(-0.432474\pi\)
0.210551 + 0.977583i \(0.432474\pi\)
\(762\) −6.43718e14 −0.0907702
\(763\) 1.81676e16 2.54338
\(764\) −2.00740e14 −0.0279010
\(765\) 1.30883e15 0.180612
\(766\) −2.73552e15 −0.374785
\(767\) −2.06892e14 −0.0281429
\(768\) 2.15206e15 0.290649
\(769\) 9.49392e15 1.27307 0.636533 0.771250i \(-0.280368\pi\)
0.636533 + 0.771250i \(0.280368\pi\)
\(770\) 6.21277e15 0.827153
\(771\) −7.29185e15 −0.963915
\(772\) −6.04484e14 −0.0793395
\(773\) −2.48526e15 −0.323880 −0.161940 0.986801i \(-0.551775\pi\)
−0.161940 + 0.986801i \(0.551775\pi\)
\(774\) −3.83324e15 −0.496010
\(775\) −5.26621e15 −0.676610
\(776\) −1.36334e16 −1.73926
\(777\) −6.62338e14 −0.0839004
\(778\) −6.17276e15 −0.776411
\(779\) 7.13511e15 0.891137
\(780\) −1.08270e14 −0.0134272
\(781\) −6.35444e15 −0.782522
\(782\) 2.37047e15 0.289866
\(783\) 1.43544e15 0.174299
\(784\) −7.20343e15 −0.868562
\(785\) −2.79862e15 −0.335090
\(786\) 2.01084e15 0.239086
\(787\) 6.76231e15 0.798425 0.399212 0.916859i \(-0.369284\pi\)
0.399212 + 0.916859i \(0.369284\pi\)
\(788\) −1.63905e15 −0.192175
\(789\) −1.14126e15 −0.132880
\(790\) −6.09837e15 −0.705122
\(791\) 1.96783e15 0.225952
\(792\) 3.16115e15 0.360459
\(793\) −1.49842e15 −0.169680
\(794\) −7.52714e15 −0.846481
\(795\) −2.81261e15 −0.314116
\(796\) −1.95928e15 −0.217308
\(797\) −7.96991e15 −0.877875 −0.438937 0.898518i \(-0.644645\pi\)
−0.438937 + 0.898518i \(0.644645\pi\)
\(798\) −4.98004e15 −0.544774
\(799\) 1.56333e16 1.69842
\(800\) −1.95098e15 −0.210503
\(801\) −2.99419e15 −0.320849
\(802\) 1.20789e16 1.28549
\(803\) −9.63152e15 −1.01803
\(804\) 1.65421e15 0.173653
\(805\) 3.14398e15 0.327795
\(806\) 2.08935e15 0.216356
\(807\) −3.05728e15 −0.314435
\(808\) −9.68172e15 −0.988986
\(809\) 1.52337e16 1.54557 0.772787 0.634665i \(-0.218862\pi\)
0.772787 + 0.634665i \(0.218862\pi\)
\(810\) −6.22325e14 −0.0627118
\(811\) 6.78720e15 0.679323 0.339661 0.940548i \(-0.389688\pi\)
0.339661 + 0.940548i \(0.389688\pi\)
\(812\) 2.28279e15 0.226938
\(813\) 9.34908e15 0.923148
\(814\) −9.44543e14 −0.0926376
\(815\) 9.90553e15 0.964963
\(816\) −4.14906e15 −0.401471
\(817\) −1.22227e16 −1.17475
\(818\) 1.06797e15 0.101957
\(819\) 1.09859e15 0.104178
\(820\) 1.41797e15 0.133564
\(821\) 9.39770e15 0.879294 0.439647 0.898171i \(-0.355104\pi\)
0.439647 + 0.898171i \(0.355104\pi\)
\(822\) −1.07430e16 −0.998461
\(823\) −5.61268e15 −0.518169 −0.259084 0.965855i \(-0.583421\pi\)
−0.259084 + 0.965855i \(0.583421\pi\)
\(824\) −1.21588e16 −1.11504
\(825\) −3.94880e15 −0.359723
\(826\) −1.89119e15 −0.171138
\(827\) 2.83293e15 0.254657 0.127328 0.991861i \(-0.459360\pi\)
0.127328 + 0.991861i \(0.459360\pi\)
\(828\) 2.36296e14 0.0211003
\(829\) −7.31651e15 −0.649014 −0.324507 0.945883i \(-0.605198\pi\)
−0.324507 + 0.945883i \(0.605198\pi\)
\(830\) 2.03037e15 0.178914
\(831\) −7.49525e15 −0.656116
\(832\) 2.75439e15 0.239523
\(833\) −1.10161e16 −0.951656
\(834\) 7.27050e15 0.623952
\(835\) 7.68122e15 0.654869
\(836\) 1.48889e15 0.126104
\(837\) −2.51774e15 −0.211846
\(838\) 7.36659e15 0.615778
\(839\) −1.05461e15 −0.0875793 −0.0437896 0.999041i \(-0.513943\pi\)
−0.0437896 + 0.999041i \(0.513943\pi\)
\(840\) −6.70011e15 −0.552772
\(841\) −2.19290e15 −0.179738
\(842\) −1.16159e16 −0.945883
\(843\) 2.08672e15 0.168815
\(844\) −5.01218e14 −0.0402850
\(845\) 7.41053e15 0.591749
\(846\) −7.43334e15 −0.589721
\(847\) 5.04597e14 0.0397728
\(848\) 8.91607e15 0.698227
\(849\) 8.96894e15 0.697829
\(850\) 6.31040e15 0.487813
\(851\) −4.77988e14 −0.0367117
\(852\) 1.01226e15 0.0772455
\(853\) 6.21804e15 0.471448 0.235724 0.971820i \(-0.424254\pi\)
0.235724 + 0.971820i \(0.424254\pi\)
\(854\) −1.36970e16 −1.03183
\(855\) −1.98435e15 −0.148527
\(856\) −2.84225e16 −2.11377
\(857\) −1.23315e16 −0.911213 −0.455606 0.890181i \(-0.650578\pi\)
−0.455606 + 0.890181i \(0.650578\pi\)
\(858\) 1.56667e15 0.115027
\(859\) −5.58613e15 −0.407520 −0.203760 0.979021i \(-0.565316\pi\)
−0.203760 + 0.979021i \(0.565316\pi\)
\(860\) −2.42904e15 −0.176073
\(861\) −1.43879e16 −1.03629
\(862\) −5.34773e15 −0.382718
\(863\) 1.14764e16 0.816106 0.408053 0.912958i \(-0.366208\pi\)
0.408053 + 0.912958i \(0.366208\pi\)
\(864\) −9.32753e14 −0.0659085
\(865\) 4.34699e14 0.0305211
\(866\) 1.68953e16 1.17874
\(867\) 1.98298e15 0.137472
\(868\) −4.00399e15 −0.275825
\(869\) −1.85001e16 −1.26638
\(870\) −4.33874e15 −0.295126
\(871\) 5.55019e15 0.375152
\(872\) −2.79406e16 −1.87670
\(873\) 8.14213e15 0.543450
\(874\) −3.59393e15 −0.238373
\(875\) 2.19861e16 1.44912
\(876\) 1.53429e15 0.100493
\(877\) 8.06301e15 0.524807 0.262403 0.964958i \(-0.415485\pi\)
0.262403 + 0.964958i \(0.415485\pi\)
\(878\) 3.17640e15 0.205454
\(879\) −1.26046e16 −0.810195
\(880\) −7.84760e15 −0.501282
\(881\) 2.43541e16 1.54598 0.772991 0.634417i \(-0.218760\pi\)
0.772991 + 0.634417i \(0.218760\pi\)
\(882\) 5.23793e15 0.330432
\(883\) 2.72747e16 1.70992 0.854960 0.518694i \(-0.173581\pi\)
0.854960 + 0.518694i \(0.173581\pi\)
\(884\) 5.24879e14 0.0327018
\(885\) −7.53569e14 −0.0466589
\(886\) −1.15570e16 −0.711146
\(887\) 2.52449e16 1.54381 0.771904 0.635739i \(-0.219305\pi\)
0.771904 + 0.635739i \(0.219305\pi\)
\(888\) 1.01864e15 0.0619081
\(889\) 4.13899e15 0.249997
\(890\) 9.05022e15 0.543268
\(891\) −1.88789e15 −0.112629
\(892\) −3.05251e14 −0.0180988
\(893\) −2.37021e16 −1.39670
\(894\) 7.09179e15 0.415336
\(895\) 8.23852e14 0.0479537
\(896\) 1.66189e16 0.961410
\(897\) 7.92818e14 0.0455843
\(898\) −2.67881e16 −1.53081
\(899\) −1.75532e16 −0.996963
\(900\) 6.29040e14 0.0355095
\(901\) 1.36352e16 0.765025
\(902\) −2.05182e16 −1.14420
\(903\) 2.46470e16 1.36610
\(904\) −3.02640e15 −0.166725
\(905\) 1.46212e16 0.800600
\(906\) −1.52992e16 −0.832652
\(907\) 1.39982e16 0.757235 0.378618 0.925553i \(-0.376400\pi\)
0.378618 + 0.925553i \(0.376400\pi\)
\(908\) 4.91971e15 0.264525
\(909\) 5.78210e15 0.309018
\(910\) −3.32059e15 −0.176396
\(911\) 2.63670e16 1.39223 0.696113 0.717933i \(-0.254911\pi\)
0.696113 + 0.717933i \(0.254911\pi\)
\(912\) 6.29048e15 0.330151
\(913\) 6.15936e15 0.321326
\(914\) 5.39117e15 0.279563
\(915\) −5.45772e15 −0.281317
\(916\) −2.07538e15 −0.106334
\(917\) −1.29294e16 −0.658484
\(918\) 3.01696e15 0.152734
\(919\) −1.07900e16 −0.542982 −0.271491 0.962441i \(-0.587517\pi\)
−0.271491 + 0.962441i \(0.587517\pi\)
\(920\) −4.83525e15 −0.241872
\(921\) −1.08066e16 −0.537354
\(922\) 1.75984e16 0.869866
\(923\) 3.39632e15 0.166878
\(924\) −3.00234e15 −0.146644
\(925\) −1.27245e15 −0.0617817
\(926\) −1.04393e15 −0.0503862
\(927\) 7.26146e15 0.348406
\(928\) −6.50299e15 −0.310170
\(929\) 1.47613e16 0.699903 0.349952 0.936768i \(-0.386198\pi\)
0.349952 + 0.936768i \(0.386198\pi\)
\(930\) 7.61010e15 0.358702
\(931\) 1.67018e16 0.782598
\(932\) −3.47561e15 −0.161899
\(933\) −4.72314e15 −0.218717
\(934\) 2.36671e16 1.08953
\(935\) −1.20012e16 −0.549239
\(936\) −1.68957e15 −0.0768703
\(937\) 1.11966e15 0.0506428 0.0253214 0.999679i \(-0.491939\pi\)
0.0253214 + 0.999679i \(0.491939\pi\)
\(938\) 5.07341e16 2.28131
\(939\) 5.66081e15 0.253056
\(940\) −4.71034e15 −0.209338
\(941\) −2.41753e16 −1.06814 −0.534072 0.845439i \(-0.679339\pi\)
−0.534072 + 0.845439i \(0.679339\pi\)
\(942\) −6.45104e15 −0.283367
\(943\) −1.03833e16 −0.453440
\(944\) 2.38884e15 0.103715
\(945\) 4.00143e15 0.172719
\(946\) 3.51484e16 1.50836
\(947\) −3.69952e16 −1.57841 −0.789206 0.614129i \(-0.789508\pi\)
−0.789206 + 0.614129i \(0.789508\pi\)
\(948\) 2.94705e15 0.125009
\(949\) 5.14785e15 0.217101
\(950\) −9.56735e15 −0.401155
\(951\) 3.24490e15 0.135272
\(952\) 3.24814e16 1.34627
\(953\) 4.76843e15 0.196501 0.0982505 0.995162i \(-0.468675\pi\)
0.0982505 + 0.995162i \(0.468675\pi\)
\(954\) −6.48327e15 −0.265631
\(955\) −2.45318e15 −0.0999336
\(956\) −6.32679e15 −0.256251
\(957\) −1.31621e16 −0.530040
\(958\) −2.45265e16 −0.982033
\(959\) 6.90756e16 2.74993
\(960\) 1.00324e16 0.397112
\(961\) 5.37972e15 0.211729
\(962\) 5.04839e14 0.0197556
\(963\) 1.69745e16 0.660467
\(964\) 5.66451e15 0.219148
\(965\) −7.38722e15 −0.284172
\(966\) 7.24712e15 0.277199
\(967\) 1.44949e16 0.551276 0.275638 0.961261i \(-0.411111\pi\)
0.275638 + 0.961261i \(0.411111\pi\)
\(968\) −7.76040e14 −0.0293474
\(969\) 9.61994e15 0.361736
\(970\) −2.46103e16 −0.920180
\(971\) 2.89022e16 1.07455 0.537273 0.843409i \(-0.319455\pi\)
0.537273 + 0.843409i \(0.319455\pi\)
\(972\) 3.00740e14 0.0111180
\(973\) −4.67480e16 −1.71847
\(974\) 1.16126e16 0.424477
\(975\) 2.11055e15 0.0767132
\(976\) 1.73012e16 0.625320
\(977\) 3.86502e16 1.38909 0.694546 0.719448i \(-0.255605\pi\)
0.694546 + 0.719448i \(0.255605\pi\)
\(978\) 2.28330e16 0.816017
\(979\) 2.74549e16 0.975697
\(980\) 3.31916e15 0.117296
\(981\) 1.66867e16 0.586394
\(982\) −6.53200e15 −0.228262
\(983\) −5.15943e16 −1.79290 −0.896452 0.443140i \(-0.853864\pi\)
−0.896452 + 0.443140i \(0.853864\pi\)
\(984\) 2.21277e16 0.764650
\(985\) −2.00303e16 −0.688316
\(986\) 2.10337e16 0.718776
\(987\) 4.77950e16 1.62419
\(988\) −7.95782e14 −0.0268925
\(989\) 1.77869e16 0.597753
\(990\) 5.70634e15 0.190706
\(991\) −3.25115e16 −1.08052 −0.540259 0.841499i \(-0.681674\pi\)
−0.540259 + 0.841499i \(0.681674\pi\)
\(992\) 1.14062e16 0.376987
\(993\) −2.36348e16 −0.776839
\(994\) 3.10456e16 1.01479
\(995\) −2.39438e16 −0.778335
\(996\) −9.81181e14 −0.0317192
\(997\) −1.73387e16 −0.557434 −0.278717 0.960373i \(-0.589909\pi\)
−0.278717 + 0.960373i \(0.589909\pi\)
\(998\) 2.64605e16 0.846018
\(999\) −6.08348e14 −0.0193438
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 177.12.a.c.1.19 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.19 27 1.1 even 1 trivial