Properties

Label 177.12.a.c.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-58.2273 q^{2} -243.000 q^{3} +1342.41 q^{4} +11765.2 q^{5} +14149.2 q^{6} +24587.2 q^{7} +41084.4 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-58.2273 q^{2} -243.000 q^{3} +1342.41 q^{4} +11765.2 q^{5} +14149.2 q^{6} +24587.2 q^{7} +41084.4 q^{8} +59049.0 q^{9} -685053. q^{10} -938997. q^{11} -326206. q^{12} -1.32932e6 q^{13} -1.43164e6 q^{14} -2.85893e6 q^{15} -5.14149e6 q^{16} +500589. q^{17} -3.43826e6 q^{18} -1.82459e7 q^{19} +1.57937e7 q^{20} -5.97469e6 q^{21} +5.46752e7 q^{22} -3.11572e6 q^{23} -9.98350e6 q^{24} +8.95909e7 q^{25} +7.74029e7 q^{26} -1.43489e7 q^{27} +3.30062e7 q^{28} -1.34000e8 q^{29} +1.66468e8 q^{30} +1.46048e8 q^{31} +2.15234e8 q^{32} +2.28176e8 q^{33} -2.91479e7 q^{34} +2.89272e8 q^{35} +7.92682e7 q^{36} -7.84276e8 q^{37} +1.06241e9 q^{38} +3.23026e8 q^{39} +4.83364e8 q^{40} +8.56325e8 q^{41} +3.47890e8 q^{42} -1.12755e9 q^{43} -1.26052e9 q^{44} +6.94721e8 q^{45} +1.81420e8 q^{46} +1.67029e9 q^{47} +1.24938e9 q^{48} -1.37280e9 q^{49} -5.21663e9 q^{50} -1.21643e8 q^{51} -1.78450e9 q^{52} -1.57326e9 q^{53} +8.35497e8 q^{54} -1.10475e10 q^{55} +1.01015e9 q^{56} +4.43375e9 q^{57} +7.80246e9 q^{58} -7.14924e8 q^{59} -3.83787e9 q^{60} +1.01069e10 q^{61} -8.50396e9 q^{62} +1.45185e9 q^{63} -2.00272e9 q^{64} -1.56397e10 q^{65} -1.32861e10 q^{66} +1.64187e10 q^{67} +6.71998e8 q^{68} +7.57121e8 q^{69} -1.68435e10 q^{70} +1.39326e10 q^{71} +2.42599e9 q^{72} -2.39204e10 q^{73} +4.56663e10 q^{74} -2.17706e10 q^{75} -2.44935e10 q^{76} -2.30873e10 q^{77} -1.88089e10 q^{78} -4.32713e9 q^{79} -6.04905e10 q^{80} +3.48678e9 q^{81} -4.98615e10 q^{82} +4.65457e10 q^{83} -8.02050e9 q^{84} +5.88952e9 q^{85} +6.56540e10 q^{86} +3.25620e10 q^{87} -3.85781e10 q^{88} -3.36102e10 q^{89} -4.04517e10 q^{90} -3.26843e10 q^{91} -4.18259e9 q^{92} -3.54896e10 q^{93} -9.72562e10 q^{94} -2.14666e11 q^{95} -5.23019e10 q^{96} +1.01084e11 q^{97} +7.99342e10 q^{98} -5.54468e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −58.2273 −1.28665 −0.643326 0.765592i \(-0.722446\pi\)
−0.643326 + 0.765592i \(0.722446\pi\)
\(3\) −243.000 −0.577350
\(4\) 1342.41 0.655475
\(5\) 11765.2 1.68369 0.841846 0.539717i \(-0.181469\pi\)
0.841846 + 0.539717i \(0.181469\pi\)
\(6\) 14149.2 0.742849
\(7\) 24587.2 0.552929 0.276465 0.961024i \(-0.410837\pi\)
0.276465 + 0.961024i \(0.410837\pi\)
\(8\) 41084.4 0.443284
\(9\) 59049.0 0.333333
\(10\) −685053. −2.16633
\(11\) −938997. −1.75794 −0.878971 0.476875i \(-0.841769\pi\)
−0.878971 + 0.476875i \(0.841769\pi\)
\(12\) −326206. −0.378439
\(13\) −1.32932e6 −0.992984 −0.496492 0.868041i \(-0.665379\pi\)
−0.496492 + 0.868041i \(0.665379\pi\)
\(14\) −1.43164e6 −0.711428
\(15\) −2.85893e6 −0.972081
\(16\) −5.14149e6 −1.22583
\(17\) 500589. 0.0855091 0.0427546 0.999086i \(-0.486387\pi\)
0.0427546 + 0.999086i \(0.486387\pi\)
\(18\) −3.43826e6 −0.428884
\(19\) −1.82459e7 −1.69052 −0.845260 0.534355i \(-0.820555\pi\)
−0.845260 + 0.534355i \(0.820555\pi\)
\(20\) 1.57937e7 1.10362
\(21\) −5.97469e6 −0.319234
\(22\) 5.46752e7 2.26186
\(23\) −3.11572e6 −0.100938 −0.0504691 0.998726i \(-0.516072\pi\)
−0.0504691 + 0.998726i \(0.516072\pi\)
\(24\) −9.98350e6 −0.255930
\(25\) 8.95909e7 1.83482
\(26\) 7.74029e7 1.27763
\(27\) −1.43489e7 −0.192450
\(28\) 3.30062e7 0.362432
\(29\) −1.34000e8 −1.21316 −0.606578 0.795024i \(-0.707458\pi\)
−0.606578 + 0.795024i \(0.707458\pi\)
\(30\) 1.66468e8 1.25073
\(31\) 1.46048e8 0.916232 0.458116 0.888892i \(-0.348524\pi\)
0.458116 + 0.888892i \(0.348524\pi\)
\(32\) 2.15234e8 1.13393
\(33\) 2.28176e8 1.01495
\(34\) −2.91479e7 −0.110021
\(35\) 2.89272e8 0.930963
\(36\) 7.92682e7 0.218492
\(37\) −7.84276e8 −1.85934 −0.929672 0.368389i \(-0.879909\pi\)
−0.929672 + 0.368389i \(0.879909\pi\)
\(38\) 1.06241e9 2.17511
\(39\) 3.23026e8 0.573300
\(40\) 4.83364e8 0.746354
\(41\) 8.56325e8 1.15432 0.577162 0.816630i \(-0.304160\pi\)
0.577162 + 0.816630i \(0.304160\pi\)
\(42\) 3.47890e8 0.410743
\(43\) −1.12755e9 −1.16966 −0.584828 0.811157i \(-0.698838\pi\)
−0.584828 + 0.811157i \(0.698838\pi\)
\(44\) −1.26052e9 −1.15229
\(45\) 6.94721e8 0.561231
\(46\) 1.81420e8 0.129872
\(47\) 1.67029e9 1.06231 0.531157 0.847274i \(-0.321757\pi\)
0.531157 + 0.847274i \(0.321757\pi\)
\(48\) 1.24938e9 0.707732
\(49\) −1.37280e9 −0.694269
\(50\) −5.21663e9 −2.36078
\(51\) −1.21643e8 −0.0493687
\(52\) −1.78450e9 −0.650876
\(53\) −1.57326e9 −0.516753 −0.258377 0.966044i \(-0.583188\pi\)
−0.258377 + 0.966044i \(0.583188\pi\)
\(54\) 8.35497e8 0.247616
\(55\) −1.10475e10 −2.95983
\(56\) 1.01015e9 0.245105
\(57\) 4.43375e9 0.976023
\(58\) 7.80246e9 1.56091
\(59\) −7.14924e8 −0.130189
\(60\) −3.83787e9 −0.637175
\(61\) 1.01069e10 1.53216 0.766082 0.642742i \(-0.222203\pi\)
0.766082 + 0.642742i \(0.222203\pi\)
\(62\) −8.50396e9 −1.17887
\(63\) 1.45185e9 0.184310
\(64\) −2.00272e9 −0.233147
\(65\) −1.56397e10 −1.67188
\(66\) −1.32861e10 −1.30589
\(67\) 1.64187e10 1.48568 0.742842 0.669466i \(-0.233477\pi\)
0.742842 + 0.669466i \(0.233477\pi\)
\(68\) 6.71998e8 0.0560491
\(69\) 7.57121e8 0.0582767
\(70\) −1.68435e10 −1.19783
\(71\) 1.39326e10 0.916454 0.458227 0.888835i \(-0.348485\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(72\) 2.42599e9 0.147761
\(73\) −2.39204e10 −1.35050 −0.675248 0.737591i \(-0.735963\pi\)
−0.675248 + 0.737591i \(0.735963\pi\)
\(74\) 4.56663e10 2.39233
\(75\) −2.17706e10 −1.05934
\(76\) −2.44935e10 −1.10809
\(77\) −2.30873e10 −0.972018
\(78\) −1.88089e10 −0.737637
\(79\) −4.32713e9 −0.158216 −0.0791081 0.996866i \(-0.525207\pi\)
−0.0791081 + 0.996866i \(0.525207\pi\)
\(80\) −6.04905e10 −2.06392
\(81\) 3.48678e9 0.111111
\(82\) −4.98615e10 −1.48521
\(83\) 4.65457e10 1.29703 0.648515 0.761202i \(-0.275391\pi\)
0.648515 + 0.761202i \(0.275391\pi\)
\(84\) −8.02050e9 −0.209250
\(85\) 5.88952e9 0.143971
\(86\) 6.56540e10 1.50494
\(87\) 3.25620e10 0.700416
\(88\) −3.85781e10 −0.779267
\(89\) −3.36102e10 −0.638007 −0.319004 0.947754i \(-0.603348\pi\)
−0.319004 + 0.947754i \(0.603348\pi\)
\(90\) −4.04517e10 −0.722109
\(91\) −3.26843e10 −0.549050
\(92\) −4.18259e9 −0.0661625
\(93\) −3.54896e10 −0.528987
\(94\) −9.72562e10 −1.36683
\(95\) −2.14666e11 −2.84632
\(96\) −5.23019e10 −0.654675
\(97\) 1.01084e11 1.19519 0.597596 0.801797i \(-0.296123\pi\)
0.597596 + 0.801797i \(0.296123\pi\)
\(98\) 7.99342e10 0.893283
\(99\) −5.54468e10 −0.585981
\(100\) 1.20268e11 1.20268
\(101\) 9.86051e10 0.933538 0.466769 0.884379i \(-0.345418\pi\)
0.466769 + 0.884379i \(0.345418\pi\)
\(102\) 7.08295e9 0.0635204
\(103\) −2.67202e9 −0.0227110 −0.0113555 0.999936i \(-0.503615\pi\)
−0.0113555 + 0.999936i \(0.503615\pi\)
\(104\) −5.46144e10 −0.440174
\(105\) −7.02932e10 −0.537492
\(106\) 9.16066e10 0.664882
\(107\) 4.78542e10 0.329845 0.164922 0.986307i \(-0.447263\pi\)
0.164922 + 0.986307i \(0.447263\pi\)
\(108\) −1.92622e10 −0.126146
\(109\) −1.86897e10 −0.116347 −0.0581735 0.998306i \(-0.518528\pi\)
−0.0581735 + 0.998306i \(0.518528\pi\)
\(110\) 6.43263e11 3.80828
\(111\) 1.90579e11 1.07349
\(112\) −1.26415e11 −0.677796
\(113\) 4.59970e9 0.0234854 0.0117427 0.999931i \(-0.496262\pi\)
0.0117427 + 0.999931i \(0.496262\pi\)
\(114\) −2.58165e11 −1.25580
\(115\) −3.66570e10 −0.169949
\(116\) −1.79884e11 −0.795193
\(117\) −7.84952e10 −0.330995
\(118\) 4.16281e10 0.167508
\(119\) 1.23081e10 0.0472805
\(120\) −1.17458e11 −0.430908
\(121\) 5.96404e11 2.09036
\(122\) −5.88499e11 −1.97136
\(123\) −2.08087e11 −0.666449
\(124\) 1.96056e11 0.600567
\(125\) 4.79581e11 1.40558
\(126\) −8.45372e10 −0.237143
\(127\) 3.64958e10 0.0980217 0.0490109 0.998798i \(-0.484393\pi\)
0.0490109 + 0.998798i \(0.484393\pi\)
\(128\) −3.24187e11 −0.833951
\(129\) 2.73994e11 0.675301
\(130\) 9.10657e11 2.15113
\(131\) 7.72535e11 1.74955 0.874774 0.484531i \(-0.161010\pi\)
0.874774 + 0.484531i \(0.161010\pi\)
\(132\) 3.06307e11 0.665273
\(133\) −4.48615e11 −0.934739
\(134\) −9.56014e11 −1.91156
\(135\) −1.68817e11 −0.324027
\(136\) 2.05664e10 0.0379048
\(137\) −1.09549e12 −1.93931 −0.969653 0.244484i \(-0.921381\pi\)
−0.969653 + 0.244484i \(0.921381\pi\)
\(138\) −4.40851e10 −0.0749819
\(139\) −1.12823e11 −0.184423 −0.0922114 0.995739i \(-0.529394\pi\)
−0.0922114 + 0.995739i \(0.529394\pi\)
\(140\) 3.88323e11 0.610223
\(141\) −4.05880e11 −0.613327
\(142\) −8.11256e11 −1.17916
\(143\) 1.24823e12 1.74561
\(144\) −3.03600e11 −0.408609
\(145\) −1.57653e12 −2.04258
\(146\) 1.39282e12 1.73762
\(147\) 3.33590e11 0.400836
\(148\) −1.05282e12 −1.21875
\(149\) −9.06159e11 −1.01083 −0.505417 0.862875i \(-0.668661\pi\)
−0.505417 + 0.862875i \(0.668661\pi\)
\(150\) 1.26764e12 1.36300
\(151\) 3.34882e11 0.347151 0.173576 0.984821i \(-0.444468\pi\)
0.173576 + 0.984821i \(0.444468\pi\)
\(152\) −7.49621e11 −0.749380
\(153\) 2.95593e10 0.0285030
\(154\) 1.34431e12 1.25065
\(155\) 1.71827e12 1.54265
\(156\) 4.33634e11 0.375784
\(157\) 1.23760e12 1.03545 0.517727 0.855546i \(-0.326778\pi\)
0.517727 + 0.855546i \(0.326778\pi\)
\(158\) 2.51957e11 0.203569
\(159\) 3.82302e11 0.298348
\(160\) 2.53227e12 1.90919
\(161\) −7.66069e10 −0.0558117
\(162\) −2.03026e11 −0.142961
\(163\) 1.54605e12 1.05243 0.526213 0.850353i \(-0.323612\pi\)
0.526213 + 0.850353i \(0.323612\pi\)
\(164\) 1.14954e12 0.756630
\(165\) 2.68453e12 1.70886
\(166\) −2.71023e12 −1.66883
\(167\) 2.34543e12 1.39728 0.698638 0.715475i \(-0.253790\pi\)
0.698638 + 0.715475i \(0.253790\pi\)
\(168\) −2.45466e11 −0.141511
\(169\) −2.50593e10 −0.0139827
\(170\) −3.42930e11 −0.185241
\(171\) −1.07740e12 −0.563507
\(172\) −1.51363e12 −0.766681
\(173\) −2.18244e12 −1.07075 −0.535376 0.844614i \(-0.679830\pi\)
−0.535376 + 0.844614i \(0.679830\pi\)
\(174\) −1.89600e12 −0.901192
\(175\) 2.20279e12 1.01453
\(176\) 4.82785e12 2.15493
\(177\) 1.73727e11 0.0751646
\(178\) 1.95703e12 0.820894
\(179\) 1.31276e12 0.533940 0.266970 0.963705i \(-0.413977\pi\)
0.266970 + 0.963705i \(0.413977\pi\)
\(180\) 9.32603e11 0.367873
\(181\) −1.55261e11 −0.0594058 −0.0297029 0.999559i \(-0.509456\pi\)
−0.0297029 + 0.999559i \(0.509456\pi\)
\(182\) 1.90312e12 0.706437
\(183\) −2.45599e12 −0.884596
\(184\) −1.28008e11 −0.0447443
\(185\) −9.22714e12 −3.13056
\(186\) 2.06646e12 0.680622
\(187\) −4.70052e11 −0.150320
\(188\) 2.24221e12 0.696320
\(189\) −3.52799e11 −0.106411
\(190\) 1.24994e13 3.66222
\(191\) 1.44276e12 0.410685 0.205343 0.978690i \(-0.434169\pi\)
0.205343 + 0.978690i \(0.434169\pi\)
\(192\) 4.86661e11 0.134608
\(193\) 4.97486e12 1.33726 0.668629 0.743596i \(-0.266881\pi\)
0.668629 + 0.743596i \(0.266881\pi\)
\(194\) −5.88584e12 −1.53780
\(195\) 3.80045e12 0.965261
\(196\) −1.84286e12 −0.455076
\(197\) −3.45348e12 −0.829264 −0.414632 0.909989i \(-0.636090\pi\)
−0.414632 + 0.909989i \(0.636090\pi\)
\(198\) 3.22852e12 0.753954
\(199\) 2.30272e12 0.523057 0.261529 0.965196i \(-0.415773\pi\)
0.261529 + 0.965196i \(0.415773\pi\)
\(200\) 3.68079e12 0.813347
\(201\) −3.98974e12 −0.857760
\(202\) −5.74151e12 −1.20114
\(203\) −3.29469e12 −0.670789
\(204\) −1.63295e11 −0.0323600
\(205\) 1.00748e13 1.94353
\(206\) 1.55585e11 0.0292211
\(207\) −1.83980e11 −0.0336461
\(208\) 6.83471e12 1.21723
\(209\) 1.71329e13 2.97184
\(210\) 4.09298e12 0.691565
\(211\) 1.12022e13 1.84395 0.921976 0.387247i \(-0.126574\pi\)
0.921976 + 0.387247i \(0.126574\pi\)
\(212\) −2.11197e12 −0.338719
\(213\) −3.38562e12 −0.529115
\(214\) −2.78642e12 −0.424396
\(215\) −1.32658e13 −1.96934
\(216\) −5.89516e11 −0.0853100
\(217\) 3.59090e12 0.506612
\(218\) 1.08825e12 0.149698
\(219\) 5.81266e12 0.779709
\(220\) −1.48303e13 −1.94010
\(221\) −6.65445e11 −0.0849092
\(222\) −1.10969e13 −1.38121
\(223\) −5.12284e12 −0.622063 −0.311031 0.950400i \(-0.600674\pi\)
−0.311031 + 0.950400i \(0.600674\pi\)
\(224\) 5.29200e12 0.626983
\(225\) 5.29025e12 0.611607
\(226\) −2.67828e11 −0.0302176
\(227\) −3.87426e12 −0.426625 −0.213313 0.976984i \(-0.568425\pi\)
−0.213313 + 0.976984i \(0.568425\pi\)
\(228\) 5.95193e12 0.639759
\(229\) 6.67895e12 0.700831 0.350415 0.936594i \(-0.386040\pi\)
0.350415 + 0.936594i \(0.386040\pi\)
\(230\) 2.13444e12 0.218665
\(231\) 5.61021e12 0.561195
\(232\) −5.50531e12 −0.537772
\(233\) 1.77552e12 0.169383 0.0846913 0.996407i \(-0.473010\pi\)
0.0846913 + 0.996407i \(0.473010\pi\)
\(234\) 4.57056e12 0.425875
\(235\) 1.96512e13 1.78861
\(236\) −9.59724e11 −0.0853356
\(237\) 1.05149e12 0.0913462
\(238\) −7.16666e11 −0.0608336
\(239\) 7.31609e12 0.606863 0.303432 0.952853i \(-0.401868\pi\)
0.303432 + 0.952853i \(0.401868\pi\)
\(240\) 1.46992e13 1.19160
\(241\) 1.82714e13 1.44770 0.723848 0.689959i \(-0.242372\pi\)
0.723848 + 0.689959i \(0.242372\pi\)
\(242\) −3.47270e13 −2.68957
\(243\) −8.47289e11 −0.0641500
\(244\) 1.35677e13 1.00430
\(245\) −1.61512e13 −1.16894
\(246\) 1.21163e13 0.857488
\(247\) 2.42547e13 1.67866
\(248\) 6.00028e12 0.406151
\(249\) −1.13106e13 −0.748840
\(250\) −2.79247e13 −1.80850
\(251\) −9.76997e12 −0.618996 −0.309498 0.950900i \(-0.600161\pi\)
−0.309498 + 0.950900i \(0.600161\pi\)
\(252\) 1.94898e12 0.120811
\(253\) 2.92566e12 0.177444
\(254\) −2.12505e12 −0.126120
\(255\) −1.43115e12 −0.0831218
\(256\) 2.29781e13 1.30615
\(257\) −3.48937e13 −1.94140 −0.970699 0.240298i \(-0.922755\pi\)
−0.970699 + 0.240298i \(0.922755\pi\)
\(258\) −1.59539e13 −0.868878
\(259\) −1.92831e13 −1.02809
\(260\) −2.09950e13 −1.09588
\(261\) −7.91258e12 −0.404385
\(262\) −4.49826e13 −2.25106
\(263\) 1.57851e13 0.773556 0.386778 0.922173i \(-0.373588\pi\)
0.386778 + 0.922173i \(0.373588\pi\)
\(264\) 9.37448e12 0.449910
\(265\) −1.85097e13 −0.870054
\(266\) 2.61216e13 1.20268
\(267\) 8.16727e12 0.368354
\(268\) 2.20406e13 0.973829
\(269\) −2.10203e13 −0.909916 −0.454958 0.890513i \(-0.650346\pi\)
−0.454958 + 0.890513i \(0.650346\pi\)
\(270\) 9.82976e12 0.416910
\(271\) 9.01121e12 0.374500 0.187250 0.982312i \(-0.440043\pi\)
0.187250 + 0.982312i \(0.440043\pi\)
\(272\) −2.57378e12 −0.104819
\(273\) 7.94229e12 0.316994
\(274\) 6.37875e13 2.49521
\(275\) −8.41256e13 −3.22551
\(276\) 1.01637e12 0.0381989
\(277\) −1.25993e12 −0.0464203 −0.0232102 0.999731i \(-0.507389\pi\)
−0.0232102 + 0.999731i \(0.507389\pi\)
\(278\) 6.56935e12 0.237288
\(279\) 8.62397e12 0.305411
\(280\) 1.18846e13 0.412681
\(281\) −2.75168e13 −0.936944 −0.468472 0.883478i \(-0.655195\pi\)
−0.468472 + 0.883478i \(0.655195\pi\)
\(282\) 2.36333e13 0.789139
\(283\) −4.14144e13 −1.35621 −0.678104 0.734966i \(-0.737198\pi\)
−0.678104 + 0.734966i \(0.737198\pi\)
\(284\) 1.87033e13 0.600713
\(285\) 5.21638e13 1.64332
\(286\) −7.26811e13 −2.24599
\(287\) 2.10546e13 0.638259
\(288\) 1.27094e13 0.377977
\(289\) −3.40213e13 −0.992688
\(290\) 9.17972e13 2.62809
\(291\) −2.45634e13 −0.690045
\(292\) −3.21111e13 −0.885216
\(293\) 2.32467e12 0.0628912 0.0314456 0.999505i \(-0.489989\pi\)
0.0314456 + 0.999505i \(0.489989\pi\)
\(294\) −1.94240e13 −0.515737
\(295\) −8.41120e12 −0.219198
\(296\) −3.22215e13 −0.824217
\(297\) 1.34736e13 0.338316
\(298\) 5.27632e13 1.30059
\(299\) 4.14180e12 0.100230
\(300\) −2.92251e13 −0.694368
\(301\) −2.77232e13 −0.646737
\(302\) −1.94993e13 −0.446663
\(303\) −2.39610e13 −0.538978
\(304\) 9.38112e13 2.07229
\(305\) 1.18910e14 2.57970
\(306\) −1.72116e12 −0.0366735
\(307\) −6.10687e13 −1.27808 −0.639039 0.769174i \(-0.720668\pi\)
−0.639039 + 0.769174i \(0.720668\pi\)
\(308\) −3.09927e13 −0.637134
\(309\) 6.49301e11 0.0131122
\(310\) −1.00050e14 −1.98486
\(311\) −2.82075e13 −0.549772 −0.274886 0.961477i \(-0.588640\pi\)
−0.274886 + 0.961477i \(0.588640\pi\)
\(312\) 1.32713e13 0.254134
\(313\) −4.99330e13 −0.939493 −0.469746 0.882801i \(-0.655655\pi\)
−0.469746 + 0.882801i \(0.655655\pi\)
\(314\) −7.20618e13 −1.33227
\(315\) 1.70812e13 0.310321
\(316\) −5.80880e12 −0.103707
\(317\) −2.26238e13 −0.396953 −0.198476 0.980106i \(-0.563599\pi\)
−0.198476 + 0.980106i \(0.563599\pi\)
\(318\) −2.22604e13 −0.383870
\(319\) 1.25826e14 2.13266
\(320\) −2.35623e13 −0.392549
\(321\) −1.16286e13 −0.190436
\(322\) 4.46061e12 0.0718103
\(323\) −9.13370e12 −0.144555
\(324\) 4.68071e12 0.0728306
\(325\) −1.19095e14 −1.82195
\(326\) −9.00222e13 −1.35411
\(327\) 4.54159e12 0.0671730
\(328\) 3.51816e13 0.511693
\(329\) 4.10677e13 0.587384
\(330\) −1.56313e14 −2.19871
\(331\) 2.60340e13 0.360153 0.180077 0.983653i \(-0.442365\pi\)
0.180077 + 0.983653i \(0.442365\pi\)
\(332\) 6.24835e13 0.850171
\(333\) −4.63107e13 −0.619781
\(334\) −1.36568e14 −1.79781
\(335\) 1.93168e14 2.50144
\(336\) 3.07188e13 0.391326
\(337\) 7.39619e13 0.926923 0.463462 0.886117i \(-0.346607\pi\)
0.463462 + 0.886117i \(0.346607\pi\)
\(338\) 1.45913e12 0.0179909
\(339\) −1.11773e12 −0.0135593
\(340\) 7.90616e12 0.0943695
\(341\) −1.37138e14 −1.61068
\(342\) 6.27342e13 0.725038
\(343\) −8.23701e13 −0.936811
\(344\) −4.63246e13 −0.518490
\(345\) 8.90765e12 0.0981201
\(346\) 1.27078e14 1.37769
\(347\) −5.03244e13 −0.536991 −0.268495 0.963281i \(-0.586526\pi\)
−0.268495 + 0.963281i \(0.586526\pi\)
\(348\) 4.37117e13 0.459105
\(349\) 1.23412e14 1.27591 0.637954 0.770075i \(-0.279781\pi\)
0.637954 + 0.770075i \(0.279781\pi\)
\(350\) −1.28262e14 −1.30534
\(351\) 1.90743e13 0.191100
\(352\) −2.02104e14 −1.99338
\(353\) −1.29551e14 −1.25800 −0.629000 0.777405i \(-0.716536\pi\)
−0.629000 + 0.777405i \(0.716536\pi\)
\(354\) −1.01156e13 −0.0967107
\(355\) 1.63919e14 1.54303
\(356\) −4.51187e13 −0.418198
\(357\) −2.99086e12 −0.0272974
\(358\) −7.64382e13 −0.686996
\(359\) 1.45803e14 1.29047 0.645235 0.763984i \(-0.276760\pi\)
0.645235 + 0.763984i \(0.276760\pi\)
\(360\) 2.85422e13 0.248785
\(361\) 2.16423e14 1.85786
\(362\) 9.04040e12 0.0764347
\(363\) −1.44926e14 −1.20687
\(364\) −4.38759e13 −0.359889
\(365\) −2.81428e14 −2.27382
\(366\) 1.43005e14 1.13817
\(367\) 1.94975e14 1.52868 0.764338 0.644816i \(-0.223066\pi\)
0.764338 + 0.644816i \(0.223066\pi\)
\(368\) 1.60195e13 0.123733
\(369\) 5.05651e13 0.384774
\(370\) 5.37271e14 4.02795
\(371\) −3.86820e13 −0.285728
\(372\) −4.76417e13 −0.346738
\(373\) 1.89658e14 1.36011 0.680053 0.733163i \(-0.261957\pi\)
0.680053 + 0.733163i \(0.261957\pi\)
\(374\) 2.73698e13 0.193410
\(375\) −1.16538e14 −0.811514
\(376\) 6.86227e13 0.470906
\(377\) 1.78130e14 1.20464
\(378\) 2.05425e13 0.136914
\(379\) −9.21260e13 −0.605155 −0.302578 0.953125i \(-0.597847\pi\)
−0.302578 + 0.953125i \(0.597847\pi\)
\(380\) −2.88170e14 −1.86569
\(381\) −8.86848e12 −0.0565929
\(382\) −8.40077e13 −0.528409
\(383\) 3.06491e14 1.90031 0.950155 0.311779i \(-0.100925\pi\)
0.950155 + 0.311779i \(0.100925\pi\)
\(384\) 7.87774e13 0.481482
\(385\) −2.71626e14 −1.63658
\(386\) −2.89672e14 −1.72059
\(387\) −6.65806e13 −0.389885
\(388\) 1.35697e14 0.783419
\(389\) 1.21080e14 0.689206 0.344603 0.938748i \(-0.388014\pi\)
0.344603 + 0.938748i \(0.388014\pi\)
\(390\) −2.21290e14 −1.24196
\(391\) −1.55970e12 −0.00863114
\(392\) −5.64005e13 −0.307758
\(393\) −1.87726e14 −1.01010
\(394\) 2.01087e14 1.06697
\(395\) −5.09094e13 −0.266388
\(396\) −7.44326e13 −0.384096
\(397\) 2.58359e14 1.31485 0.657424 0.753521i \(-0.271646\pi\)
0.657424 + 0.753521i \(0.271646\pi\)
\(398\) −1.34081e14 −0.672993
\(399\) 1.09014e14 0.539672
\(400\) −4.60631e14 −2.24918
\(401\) 1.57462e14 0.758372 0.379186 0.925321i \(-0.376204\pi\)
0.379186 + 0.925321i \(0.376204\pi\)
\(402\) 2.32311e14 1.10364
\(403\) −1.94145e14 −0.909804
\(404\) 1.32369e14 0.611911
\(405\) 4.10226e13 0.187077
\(406\) 1.91841e14 0.863073
\(407\) 7.36433e14 3.26862
\(408\) −4.99764e12 −0.0218844
\(409\) 8.32952e12 0.0359867 0.0179933 0.999838i \(-0.494272\pi\)
0.0179933 + 0.999838i \(0.494272\pi\)
\(410\) −5.86628e14 −2.50064
\(411\) 2.66205e14 1.11966
\(412\) −3.58696e12 −0.0148865
\(413\) −1.75780e13 −0.0719853
\(414\) 1.07127e13 0.0432908
\(415\) 5.47617e14 2.18380
\(416\) −2.86116e14 −1.12597
\(417\) 2.74159e13 0.106477
\(418\) −9.97599e14 −3.82372
\(419\) −4.35102e14 −1.64594 −0.822970 0.568085i \(-0.807684\pi\)
−0.822970 + 0.568085i \(0.807684\pi\)
\(420\) −9.43625e13 −0.352313
\(421\) −1.03075e14 −0.379841 −0.189921 0.981799i \(-0.560823\pi\)
−0.189921 + 0.981799i \(0.560823\pi\)
\(422\) −6.52273e14 −2.37253
\(423\) 9.86288e13 0.354105
\(424\) −6.46364e13 −0.229068
\(425\) 4.48483e13 0.156894
\(426\) 1.97135e14 0.680787
\(427\) 2.48501e14 0.847179
\(428\) 6.42401e13 0.216205
\(429\) −3.03320e14 −1.00783
\(430\) 7.72430e14 2.53386
\(431\) −2.78201e14 −0.901019 −0.450509 0.892772i \(-0.648758\pi\)
−0.450509 + 0.892772i \(0.648758\pi\)
\(432\) 7.37748e13 0.235911
\(433\) 6.07379e14 1.91768 0.958841 0.283943i \(-0.0916428\pi\)
0.958841 + 0.283943i \(0.0916428\pi\)
\(434\) −2.09088e14 −0.651833
\(435\) 3.83098e14 1.17928
\(436\) −2.50892e13 −0.0762626
\(437\) 5.68492e13 0.170638
\(438\) −3.38455e14 −1.00321
\(439\) −1.94149e14 −0.568304 −0.284152 0.958779i \(-0.591712\pi\)
−0.284152 + 0.958779i \(0.591712\pi\)
\(440\) −4.53878e14 −1.31205
\(441\) −8.10623e13 −0.231423
\(442\) 3.87471e13 0.109249
\(443\) 3.04022e14 0.846611 0.423305 0.905987i \(-0.360870\pi\)
0.423305 + 0.905987i \(0.360870\pi\)
\(444\) 2.55836e14 0.703648
\(445\) −3.95429e14 −1.07421
\(446\) 2.98289e14 0.800378
\(447\) 2.20197e14 0.583605
\(448\) −4.92413e13 −0.128914
\(449\) −3.59382e14 −0.929399 −0.464699 0.885469i \(-0.653838\pi\)
−0.464699 + 0.885469i \(0.653838\pi\)
\(450\) −3.08037e14 −0.786926
\(451\) −8.04087e14 −2.02923
\(452\) 6.17470e12 0.0153941
\(453\) −8.13763e13 −0.200428
\(454\) 2.25587e14 0.548918
\(455\) −3.84536e14 −0.924432
\(456\) 1.82158e14 0.432655
\(457\) 3.82052e13 0.0896569 0.0448284 0.998995i \(-0.485726\pi\)
0.0448284 + 0.998995i \(0.485726\pi\)
\(458\) −3.88897e14 −0.901726
\(459\) −7.18291e12 −0.0164562
\(460\) −4.92088e13 −0.111397
\(461\) −2.71731e14 −0.607833 −0.303916 0.952699i \(-0.598294\pi\)
−0.303916 + 0.952699i \(0.598294\pi\)
\(462\) −3.26667e14 −0.722063
\(463\) −2.18845e14 −0.478016 −0.239008 0.971018i \(-0.576822\pi\)
−0.239008 + 0.971018i \(0.576822\pi\)
\(464\) 6.88961e14 1.48712
\(465\) −4.17541e14 −0.890651
\(466\) −1.03384e14 −0.217937
\(467\) 2.84426e14 0.592551 0.296276 0.955103i \(-0.404255\pi\)
0.296276 + 0.955103i \(0.404255\pi\)
\(468\) −1.05373e14 −0.216959
\(469\) 4.03689e14 0.821479
\(470\) −1.14424e15 −2.30132
\(471\) −3.00736e14 −0.597819
\(472\) −2.93722e13 −0.0577106
\(473\) 1.05876e15 2.05619
\(474\) −6.12255e13 −0.117531
\(475\) −1.63467e15 −3.10180
\(476\) 1.65225e13 0.0309912
\(477\) −9.28994e13 −0.172251
\(478\) −4.25996e14 −0.780822
\(479\) 4.43363e14 0.803366 0.401683 0.915779i \(-0.368425\pi\)
0.401683 + 0.915779i \(0.368425\pi\)
\(480\) −6.15341e14 −1.10227
\(481\) 1.04256e15 1.84630
\(482\) −1.06389e15 −1.86268
\(483\) 1.86155e13 0.0322229
\(484\) 8.00621e14 1.37018
\(485\) 1.18927e15 2.01234
\(486\) 4.93353e13 0.0825388
\(487\) 9.07514e14 1.50122 0.750609 0.660746i \(-0.229760\pi\)
0.750609 + 0.660746i \(0.229760\pi\)
\(488\) 4.15237e14 0.679184
\(489\) −3.75690e14 −0.607618
\(490\) 9.40439e14 1.50401
\(491\) 5.96037e14 0.942594 0.471297 0.881975i \(-0.343786\pi\)
0.471297 + 0.881975i \(0.343786\pi\)
\(492\) −2.79339e14 −0.436841
\(493\) −6.70791e13 −0.103736
\(494\) −1.41228e15 −2.15985
\(495\) −6.52341e14 −0.986612
\(496\) −7.50903e14 −1.12314
\(497\) 3.42563e14 0.506735
\(498\) 6.58585e14 0.963497
\(499\) −6.54341e14 −0.946785 −0.473393 0.880852i \(-0.656971\pi\)
−0.473393 + 0.880852i \(0.656971\pi\)
\(500\) 6.43796e14 0.921326
\(501\) −5.69940e14 −0.806718
\(502\) 5.68878e14 0.796432
\(503\) 1.33214e15 1.84470 0.922348 0.386360i \(-0.126268\pi\)
0.922348 + 0.386360i \(0.126268\pi\)
\(504\) 5.96483e13 0.0817015
\(505\) 1.16011e15 1.57179
\(506\) −1.70353e14 −0.228308
\(507\) 6.08940e12 0.00807292
\(508\) 4.89924e13 0.0642508
\(509\) 1.04814e15 1.35979 0.679894 0.733311i \(-0.262026\pi\)
0.679894 + 0.733311i \(0.262026\pi\)
\(510\) 8.33321e13 0.106949
\(511\) −5.88136e14 −0.746729
\(512\) −6.74016e14 −0.846614
\(513\) 2.61809e14 0.325341
\(514\) 2.03176e15 2.49791
\(515\) −3.14368e13 −0.0382383
\(516\) 3.67813e14 0.442643
\(517\) −1.56839e15 −1.86749
\(518\) 1.12280e15 1.32279
\(519\) 5.30333e14 0.618199
\(520\) −6.42548e14 −0.741117
\(521\) −8.97945e14 −1.02481 −0.512403 0.858745i \(-0.671245\pi\)
−0.512403 + 0.858745i \(0.671245\pi\)
\(522\) 4.60728e14 0.520303
\(523\) 5.23369e14 0.584855 0.292428 0.956288i \(-0.405537\pi\)
0.292428 + 0.956288i \(0.405537\pi\)
\(524\) 1.03706e15 1.14679
\(525\) −5.35278e14 −0.585737
\(526\) −9.19125e14 −0.995298
\(527\) 7.31099e13 0.0783462
\(528\) −1.17317e15 −1.24415
\(529\) −9.43102e14 −0.989811
\(530\) 1.07777e15 1.11946
\(531\) −4.22156e13 −0.0433963
\(532\) −6.02227e14 −0.612698
\(533\) −1.13833e15 −1.14622
\(534\) −4.75558e14 −0.473943
\(535\) 5.63013e14 0.555357
\(536\) 6.74551e14 0.658580
\(537\) −3.19000e14 −0.308271
\(538\) 1.22395e15 1.17075
\(539\) 1.28905e15 1.22048
\(540\) −2.26622e14 −0.212392
\(541\) 5.56840e14 0.516589 0.258295 0.966066i \(-0.416839\pi\)
0.258295 + 0.966066i \(0.416839\pi\)
\(542\) −5.24698e14 −0.481852
\(543\) 3.77283e13 0.0342980
\(544\) 1.07744e14 0.0969614
\(545\) −2.19887e14 −0.195893
\(546\) −4.62458e14 −0.407861
\(547\) 6.40584e14 0.559301 0.279651 0.960102i \(-0.409781\pi\)
0.279651 + 0.960102i \(0.409781\pi\)
\(548\) −1.47060e15 −1.27117
\(549\) 5.96805e14 0.510722
\(550\) 4.89840e15 4.15011
\(551\) 2.44495e15 2.05086
\(552\) 3.11058e13 0.0258331
\(553\) −1.06392e14 −0.0874824
\(554\) 7.33623e13 0.0597268
\(555\) 2.24219e15 1.80743
\(556\) −1.51455e14 −0.120885
\(557\) 4.05693e14 0.320623 0.160311 0.987067i \(-0.448750\pi\)
0.160311 + 0.987067i \(0.448750\pi\)
\(558\) −5.02150e14 −0.392957
\(559\) 1.49888e15 1.16145
\(560\) −1.48729e15 −1.14120
\(561\) 1.14223e14 0.0867874
\(562\) 1.60223e15 1.20552
\(563\) 2.20951e15 1.64627 0.823134 0.567847i \(-0.192223\pi\)
0.823134 + 0.567847i \(0.192223\pi\)
\(564\) −5.44858e14 −0.402021
\(565\) 5.41162e13 0.0395422
\(566\) 2.41145e15 1.74497
\(567\) 8.57302e13 0.0614366
\(568\) 5.72412e14 0.406249
\(569\) 8.35343e14 0.587148 0.293574 0.955936i \(-0.405155\pi\)
0.293574 + 0.955936i \(0.405155\pi\)
\(570\) −3.03736e15 −2.11439
\(571\) 6.77122e14 0.466840 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(572\) 1.67564e15 1.14420
\(573\) −3.50589e14 −0.237109
\(574\) −1.22595e15 −0.821218
\(575\) −2.79141e14 −0.185204
\(576\) −1.18259e14 −0.0777158
\(577\) −1.07648e15 −0.700711 −0.350356 0.936617i \(-0.613939\pi\)
−0.350356 + 0.936617i \(0.613939\pi\)
\(578\) 1.98097e15 1.27724
\(579\) −1.20889e15 −0.772066
\(580\) −2.11636e15 −1.33886
\(581\) 1.14443e15 0.717166
\(582\) 1.43026e15 0.887848
\(583\) 1.47729e15 0.908422
\(584\) −9.82756e14 −0.598653
\(585\) −9.23509e14 −0.557293
\(586\) −1.35359e14 −0.0809192
\(587\) −1.69997e15 −1.00677 −0.503385 0.864062i \(-0.667912\pi\)
−0.503385 + 0.864062i \(0.667912\pi\)
\(588\) 4.47815e14 0.262738
\(589\) −2.66477e15 −1.54891
\(590\) 4.89761e14 0.282032
\(591\) 8.39196e14 0.478776
\(592\) 4.03235e15 2.27923
\(593\) −1.76484e15 −0.988333 −0.494167 0.869367i \(-0.664527\pi\)
−0.494167 + 0.869367i \(0.664527\pi\)
\(594\) −7.84530e14 −0.435295
\(595\) 1.44807e14 0.0796059
\(596\) −1.21644e15 −0.662577
\(597\) −5.59561e14 −0.301987
\(598\) −2.41166e14 −0.128961
\(599\) −3.07963e15 −1.63174 −0.815869 0.578237i \(-0.803741\pi\)
−0.815869 + 0.578237i \(0.803741\pi\)
\(600\) −8.94431e14 −0.469586
\(601\) −8.80163e14 −0.457882 −0.228941 0.973440i \(-0.573526\pi\)
−0.228941 + 0.973440i \(0.573526\pi\)
\(602\) 1.61425e15 0.832126
\(603\) 9.69506e14 0.495228
\(604\) 4.49550e14 0.227549
\(605\) 7.01679e15 3.51952
\(606\) 1.39519e15 0.693478
\(607\) −7.46375e14 −0.367637 −0.183819 0.982960i \(-0.558846\pi\)
−0.183819 + 0.982960i \(0.558846\pi\)
\(608\) −3.92714e15 −1.91693
\(609\) 8.00609e14 0.387280
\(610\) −6.92379e15 −3.31917
\(611\) −2.22035e15 −1.05486
\(612\) 3.96808e13 0.0186830
\(613\) 9.96720e14 0.465094 0.232547 0.972585i \(-0.425294\pi\)
0.232547 + 0.972585i \(0.425294\pi\)
\(614\) 3.55586e15 1.64444
\(615\) −2.44818e15 −1.12210
\(616\) −9.48528e14 −0.430880
\(617\) 1.97496e15 0.889180 0.444590 0.895734i \(-0.353349\pi\)
0.444590 + 0.895734i \(0.353349\pi\)
\(618\) −3.78070e13 −0.0168708
\(619\) 1.46186e15 0.646556 0.323278 0.946304i \(-0.395215\pi\)
0.323278 + 0.946304i \(0.395215\pi\)
\(620\) 2.30663e15 1.01117
\(621\) 4.47072e13 0.0194256
\(622\) 1.64245e15 0.707365
\(623\) −8.26379e14 −0.352773
\(624\) −1.66083e15 −0.702766
\(625\) 1.26779e15 0.531750
\(626\) 2.90746e15 1.20880
\(627\) −4.16328e15 −1.71579
\(628\) 1.66136e15 0.678714
\(629\) −3.92600e14 −0.158991
\(630\) −9.94594e14 −0.399276
\(631\) −1.71105e15 −0.680929 −0.340464 0.940257i \(-0.610584\pi\)
−0.340464 + 0.940257i \(0.610584\pi\)
\(632\) −1.77778e14 −0.0701347
\(633\) −2.72213e15 −1.06461
\(634\) 1.31732e15 0.510740
\(635\) 4.29379e14 0.165038
\(636\) 5.13208e14 0.195560
\(637\) 1.82489e15 0.689398
\(638\) −7.32649e15 −2.74399
\(639\) 8.22705e14 0.305485
\(640\) −3.81411e15 −1.40412
\(641\) 1.88928e15 0.689570 0.344785 0.938682i \(-0.387952\pi\)
0.344785 + 0.938682i \(0.387952\pi\)
\(642\) 6.77100e14 0.245025
\(643\) 7.12649e14 0.255691 0.127845 0.991794i \(-0.459194\pi\)
0.127845 + 0.991794i \(0.459194\pi\)
\(644\) −1.02838e14 −0.0365832
\(645\) 3.22358e15 1.13700
\(646\) 5.31831e14 0.185992
\(647\) −4.01542e15 −1.39238 −0.696189 0.717858i \(-0.745122\pi\)
−0.696189 + 0.717858i \(0.745122\pi\)
\(648\) 1.43252e14 0.0492537
\(649\) 6.71312e14 0.228865
\(650\) 6.93459e15 2.34422
\(651\) −8.72589e14 −0.292492
\(652\) 2.07544e15 0.689839
\(653\) −4.19924e15 −1.38404 −0.692019 0.721879i \(-0.743279\pi\)
−0.692019 + 0.721879i \(0.743279\pi\)
\(654\) −2.64444e14 −0.0864284
\(655\) 9.08899e15 2.94570
\(656\) −4.40279e15 −1.41500
\(657\) −1.41248e15 −0.450165
\(658\) −2.39126e15 −0.755760
\(659\) 2.44602e14 0.0766638 0.0383319 0.999265i \(-0.487796\pi\)
0.0383319 + 0.999265i \(0.487796\pi\)
\(660\) 3.60375e15 1.12012
\(661\) −5.05315e15 −1.55759 −0.778797 0.627276i \(-0.784170\pi\)
−0.778797 + 0.627276i \(0.784170\pi\)
\(662\) −1.51589e15 −0.463392
\(663\) 1.61703e14 0.0490224
\(664\) 1.91230e15 0.574952
\(665\) −5.27803e15 −1.57381
\(666\) 2.69655e15 0.797443
\(667\) 4.17507e14 0.122454
\(668\) 3.14854e15 0.915880
\(669\) 1.24485e15 0.359148
\(670\) −1.12477e16 −3.21848
\(671\) −9.49039e15 −2.69346
\(672\) −1.28596e15 −0.361989
\(673\) 4.82571e15 1.34734 0.673672 0.739031i \(-0.264716\pi\)
0.673672 + 0.739031i \(0.264716\pi\)
\(674\) −4.30660e15 −1.19263
\(675\) −1.28553e15 −0.353112
\(676\) −3.36399e13 −0.00916532
\(677\) 6.51006e14 0.175933 0.0879664 0.996123i \(-0.471963\pi\)
0.0879664 + 0.996123i \(0.471963\pi\)
\(678\) 6.50822e13 0.0174461
\(679\) 2.48537e15 0.660857
\(680\) 2.41967e14 0.0638201
\(681\) 9.41445e14 0.246312
\(682\) 7.98519e15 2.07239
\(683\) 1.40170e14 0.0360863 0.0180432 0.999837i \(-0.494256\pi\)
0.0180432 + 0.999837i \(0.494256\pi\)
\(684\) −1.44632e15 −0.369365
\(685\) −1.28887e16 −3.26520
\(686\) 4.79619e15 1.20535
\(687\) −1.62299e15 −0.404625
\(688\) 5.79728e15 1.43380
\(689\) 2.09137e15 0.513128
\(690\) −5.18668e14 −0.126247
\(691\) −3.29282e15 −0.795131 −0.397566 0.917574i \(-0.630145\pi\)
−0.397566 + 0.917574i \(0.630145\pi\)
\(692\) −2.92974e15 −0.701852
\(693\) −1.36328e15 −0.324006
\(694\) 2.93025e15 0.690920
\(695\) −1.32738e15 −0.310511
\(696\) 1.33779e15 0.310483
\(697\) 4.28667e14 0.0987052
\(698\) −7.18597e15 −1.64165
\(699\) −4.31452e14 −0.0977931
\(700\) 2.95705e15 0.664997
\(701\) −1.08970e15 −0.243140 −0.121570 0.992583i \(-0.538793\pi\)
−0.121570 + 0.992583i \(0.538793\pi\)
\(702\) −1.11065e15 −0.245879
\(703\) 1.43098e16 3.14326
\(704\) 1.88055e15 0.409859
\(705\) −4.77524e15 −1.03265
\(706\) 7.54342e15 1.61861
\(707\) 2.42442e15 0.516181
\(708\) 2.33213e14 0.0492685
\(709\) 2.16098e15 0.452998 0.226499 0.974011i \(-0.427272\pi\)
0.226499 + 0.974011i \(0.427272\pi\)
\(710\) −9.54456e15 −1.98534
\(711\) −2.55513e14 −0.0527387
\(712\) −1.38085e15 −0.282818
\(713\) −4.55044e14 −0.0924828
\(714\) 1.74150e14 0.0351223
\(715\) 1.46856e16 2.93907
\(716\) 1.76226e15 0.349985
\(717\) −1.77781e15 −0.350373
\(718\) −8.48972e15 −1.66039
\(719\) 2.61328e15 0.507197 0.253598 0.967310i \(-0.418386\pi\)
0.253598 + 0.967310i \(0.418386\pi\)
\(720\) −3.57190e15 −0.687972
\(721\) −6.56975e13 −0.0125576
\(722\) −1.26017e16 −2.39042
\(723\) −4.43994e15 −0.835828
\(724\) −2.08424e14 −0.0389390
\(725\) −1.20052e16 −2.22592
\(726\) 8.43866e15 1.55282
\(727\) −2.19187e15 −0.400291 −0.200145 0.979766i \(-0.564141\pi\)
−0.200145 + 0.979766i \(0.564141\pi\)
\(728\) −1.34282e15 −0.243385
\(729\) 2.05891e14 0.0370370
\(730\) 1.63868e16 2.92562
\(731\) −5.64438e14 −0.100016
\(732\) −3.29695e15 −0.579831
\(733\) 4.76089e15 0.831029 0.415514 0.909587i \(-0.363602\pi\)
0.415514 + 0.909587i \(0.363602\pi\)
\(734\) −1.13529e16 −1.96687
\(735\) 3.92474e15 0.674886
\(736\) −6.70610e14 −0.114457
\(737\) −1.54171e16 −2.61175
\(738\) −2.94427e15 −0.495071
\(739\) −6.71737e15 −1.12113 −0.560563 0.828112i \(-0.689415\pi\)
−0.560563 + 0.828112i \(0.689415\pi\)
\(740\) −1.23866e16 −2.05201
\(741\) −5.89389e15 −0.969175
\(742\) 2.25235e15 0.367633
\(743\) −1.05977e16 −1.71702 −0.858508 0.512801i \(-0.828608\pi\)
−0.858508 + 0.512801i \(0.828608\pi\)
\(744\) −1.45807e15 −0.234491
\(745\) −1.06611e16 −1.70193
\(746\) −1.10433e16 −1.74998
\(747\) 2.74848e15 0.432343
\(748\) −6.31004e14 −0.0985311
\(749\) 1.17660e15 0.182381
\(750\) 6.78570e15 1.04414
\(751\) 6.75467e15 1.03177 0.515887 0.856657i \(-0.327462\pi\)
0.515887 + 0.856657i \(0.327462\pi\)
\(752\) −8.58777e15 −1.30221
\(753\) 2.37410e15 0.357377
\(754\) −1.03720e16 −1.54996
\(755\) 3.93994e15 0.584496
\(756\) −4.73602e14 −0.0697500
\(757\) −1.32539e16 −1.93783 −0.968915 0.247395i \(-0.920426\pi\)
−0.968915 + 0.247395i \(0.920426\pi\)
\(758\) 5.36425e15 0.778625
\(759\) −7.10934e14 −0.102447
\(760\) −8.81942e15 −1.26173
\(761\) 9.80400e15 1.39248 0.696238 0.717811i \(-0.254856\pi\)
0.696238 + 0.717811i \(0.254856\pi\)
\(762\) 5.16387e14 0.0728154
\(763\) −4.59526e14 −0.0643317
\(764\) 1.93677e15 0.269194
\(765\) 3.47770e14 0.0479904
\(766\) −1.78461e16 −2.44504
\(767\) 9.50366e14 0.129276
\(768\) −5.58367e15 −0.754107
\(769\) 4.16517e15 0.558519 0.279259 0.960216i \(-0.409911\pi\)
0.279259 + 0.960216i \(0.409911\pi\)
\(770\) 1.58160e16 2.10571
\(771\) 8.47917e15 1.12087
\(772\) 6.67831e15 0.876540
\(773\) 1.20746e16 1.57357 0.786784 0.617228i \(-0.211745\pi\)
0.786784 + 0.617228i \(0.211745\pi\)
\(774\) 3.87680e15 0.501647
\(775\) 1.30845e16 1.68112
\(776\) 4.15297e15 0.529809
\(777\) 4.68581e15 0.593565
\(778\) −7.05015e15 −0.886769
\(779\) −1.56244e16 −1.95141
\(780\) 5.10177e15 0.632704
\(781\) −1.30827e16 −1.61107
\(782\) 9.08169e13 0.0111053
\(783\) 1.92276e15 0.233472
\(784\) 7.05823e15 0.851054
\(785\) 1.45605e16 1.74339
\(786\) 1.09308e16 1.29965
\(787\) −9.66403e15 −1.14103 −0.570515 0.821287i \(-0.693257\pi\)
−0.570515 + 0.821287i \(0.693257\pi\)
\(788\) −4.63600e15 −0.543562
\(789\) −3.83579e15 −0.446613
\(790\) 2.96431e15 0.342748
\(791\) 1.13094e14 0.0129858
\(792\) −2.27800e15 −0.259756
\(793\) −1.34354e16 −1.52142
\(794\) −1.50435e16 −1.69175
\(795\) 4.49785e15 0.502326
\(796\) 3.09120e15 0.342851
\(797\) −5.54146e15 −0.610385 −0.305192 0.952291i \(-0.598721\pi\)
−0.305192 + 0.952291i \(0.598721\pi\)
\(798\) −6.34756e15 −0.694370
\(799\) 8.36128e14 0.0908375
\(800\) 1.92830e16 2.08056
\(801\) −1.98465e15 −0.212669
\(802\) −9.16859e15 −0.975761
\(803\) 2.24612e16 2.37409
\(804\) −5.35588e15 −0.562241
\(805\) −9.01292e14 −0.0939698
\(806\) 1.13045e16 1.17060
\(807\) 5.10793e15 0.525340
\(808\) 4.05113e15 0.413822
\(809\) 1.54128e16 1.56374 0.781871 0.623440i \(-0.214265\pi\)
0.781871 + 0.623440i \(0.214265\pi\)
\(810\) −2.38863e15 −0.240703
\(811\) 5.36186e15 0.536662 0.268331 0.963327i \(-0.413528\pi\)
0.268331 + 0.963327i \(0.413528\pi\)
\(812\) −4.42283e15 −0.439686
\(813\) −2.18972e15 −0.216218
\(814\) −4.28805e16 −4.20558
\(815\) 1.81895e16 1.77196
\(816\) 6.25428e14 0.0605175
\(817\) 2.05731e16 1.97733
\(818\) −4.85005e14 −0.0463023
\(819\) −1.92998e15 −0.183017
\(820\) 1.35245e16 1.27393
\(821\) −6.85834e15 −0.641699 −0.320850 0.947130i \(-0.603968\pi\)
−0.320850 + 0.947130i \(0.603968\pi\)
\(822\) −1.55004e16 −1.44061
\(823\) −1.33875e16 −1.23595 −0.617973 0.786200i \(-0.712046\pi\)
−0.617973 + 0.786200i \(0.712046\pi\)
\(824\) −1.09778e14 −0.0100674
\(825\) 2.04425e16 1.86225
\(826\) 1.02352e15 0.0926200
\(827\) 1.11449e16 1.00183 0.500915 0.865496i \(-0.332997\pi\)
0.500915 + 0.865496i \(0.332997\pi\)
\(828\) −2.46978e14 −0.0220542
\(829\) −4.45261e15 −0.394971 −0.197485 0.980306i \(-0.563277\pi\)
−0.197485 + 0.980306i \(0.563277\pi\)
\(830\) −3.18863e16 −2.80979
\(831\) 3.06163e14 0.0268008
\(832\) 2.66226e15 0.231512
\(833\) −6.87208e14 −0.0593664
\(834\) −1.59635e15 −0.136998
\(835\) 2.75944e16 2.35258
\(836\) 2.29994e16 1.94797
\(837\) −2.09562e15 −0.176329
\(838\) 2.53348e16 2.11775
\(839\) 9.72331e15 0.807465 0.403732 0.914877i \(-0.367713\pi\)
0.403732 + 0.914877i \(0.367713\pi\)
\(840\) −2.88795e15 −0.238261
\(841\) 5.75554e15 0.471746
\(842\) 6.00178e15 0.488724
\(843\) 6.68659e15 0.540945
\(844\) 1.50380e16 1.20866
\(845\) −2.94826e14 −0.0235426
\(846\) −5.74288e15 −0.455610
\(847\) 1.46639e16 1.15582
\(848\) 8.08891e15 0.633450
\(849\) 1.00637e16 0.783007
\(850\) −2.61139e15 −0.201868
\(851\) 2.44359e15 0.187679
\(852\) −4.54490e15 −0.346822
\(853\) 1.55174e16 1.17652 0.588259 0.808672i \(-0.299813\pi\)
0.588259 + 0.808672i \(0.299813\pi\)
\(854\) −1.44695e16 −1.09003
\(855\) −1.26758e16 −0.948773
\(856\) 1.96606e15 0.146215
\(857\) −6.29204e15 −0.464940 −0.232470 0.972604i \(-0.574681\pi\)
−0.232470 + 0.972604i \(0.574681\pi\)
\(858\) 1.76615e16 1.29672
\(859\) −1.13138e16 −0.825365 −0.412683 0.910875i \(-0.635408\pi\)
−0.412683 + 0.910875i \(0.635408\pi\)
\(860\) −1.78082e16 −1.29086
\(861\) −5.11627e15 −0.368499
\(862\) 1.61989e16 1.15930
\(863\) 2.82180e15 0.200663 0.100331 0.994954i \(-0.468010\pi\)
0.100331 + 0.994954i \(0.468010\pi\)
\(864\) −3.08838e15 −0.218225
\(865\) −2.56768e16 −1.80282
\(866\) −3.53660e16 −2.46739
\(867\) 8.26718e15 0.573129
\(868\) 4.82047e15 0.332071
\(869\) 4.06316e15 0.278135
\(870\) −2.23067e16 −1.51733
\(871\) −2.18257e16 −1.47526
\(872\) −7.67853e14 −0.0515748
\(873\) 5.96891e15 0.398398
\(874\) −3.31017e15 −0.219552
\(875\) 1.17915e16 0.777189
\(876\) 7.80300e15 0.511080
\(877\) 1.46198e16 0.951574 0.475787 0.879561i \(-0.342163\pi\)
0.475787 + 0.879561i \(0.342163\pi\)
\(878\) 1.13048e16 0.731211
\(879\) −5.64896e14 −0.0363103
\(880\) 5.68004e16 3.62825
\(881\) 2.16330e16 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(882\) 4.72003e15 0.297761
\(883\) 2.11487e16 1.32587 0.662933 0.748679i \(-0.269311\pi\)
0.662933 + 0.748679i \(0.269311\pi\)
\(884\) −8.93303e14 −0.0556559
\(885\) 2.04392e15 0.126554
\(886\) −1.77023e16 −1.08929
\(887\) 1.97250e16 1.20625 0.603124 0.797648i \(-0.293923\pi\)
0.603124 + 0.797648i \(0.293923\pi\)
\(888\) 7.82982e15 0.475862
\(889\) 8.97329e14 0.0541991
\(890\) 2.30247e16 1.38213
\(891\) −3.27408e15 −0.195327
\(892\) −6.87697e15 −0.407747
\(893\) −3.04759e16 −1.79586
\(894\) −1.28214e16 −0.750898
\(895\) 1.54448e16 0.898992
\(896\) −7.97084e15 −0.461116
\(897\) −1.00646e15 −0.0578679
\(898\) 2.09259e16 1.19581
\(899\) −1.95704e16 −1.11153
\(900\) 7.10171e15 0.400893
\(901\) −7.87557e14 −0.0441871
\(902\) 4.68198e16 2.61092
\(903\) 6.73674e15 0.373394
\(904\) 1.88976e14 0.0104107
\(905\) −1.82667e15 −0.100021
\(906\) 4.73832e15 0.257881
\(907\) 3.73802e15 0.202209 0.101105 0.994876i \(-0.467762\pi\)
0.101105 + 0.994876i \(0.467762\pi\)
\(908\) −5.20086e15 −0.279642
\(909\) 5.82253e15 0.311179
\(910\) 2.23905e16 1.18942
\(911\) −1.90655e16 −1.00669 −0.503346 0.864085i \(-0.667898\pi\)
−0.503346 + 0.864085i \(0.667898\pi\)
\(912\) −2.27961e16 −1.19644
\(913\) −4.37063e16 −2.28010
\(914\) −2.22459e15 −0.115357
\(915\) −2.88951e16 −1.48939
\(916\) 8.96591e15 0.459377
\(917\) 1.89945e16 0.967376
\(918\) 4.18241e14 0.0211735
\(919\) 9.20979e15 0.463462 0.231731 0.972780i \(-0.425561\pi\)
0.231731 + 0.972780i \(0.425561\pi\)
\(920\) −1.50603e15 −0.0753356
\(921\) 1.48397e16 0.737899
\(922\) 1.58222e16 0.782070
\(923\) −1.85209e16 −0.910025
\(924\) 7.53123e15 0.367849
\(925\) −7.02640e16 −3.41156
\(926\) 1.27428e16 0.615040
\(927\) −1.57780e14 −0.00757032
\(928\) −2.88414e16 −1.37563
\(929\) −3.45766e16 −1.63944 −0.819721 0.572762i \(-0.805872\pi\)
−0.819721 + 0.572762i \(0.805872\pi\)
\(930\) 2.43123e16 1.14596
\(931\) 2.50479e16 1.17368
\(932\) 2.38349e15 0.111026
\(933\) 6.85442e15 0.317411
\(934\) −1.65613e16 −0.762407
\(935\) −5.53024e15 −0.253093
\(936\) −3.22493e15 −0.146725
\(937\) −1.44218e16 −0.652309 −0.326154 0.945317i \(-0.605753\pi\)
−0.326154 + 0.945317i \(0.605753\pi\)
\(938\) −2.35057e16 −1.05696
\(939\) 1.21337e16 0.542416
\(940\) 2.63800e16 1.17239
\(941\) −2.61042e16 −1.15337 −0.576684 0.816967i \(-0.695654\pi\)
−0.576684 + 0.816967i \(0.695654\pi\)
\(942\) 1.75110e16 0.769186
\(943\) −2.66807e15 −0.116515
\(944\) 3.67578e15 0.159589
\(945\) −4.15074e15 −0.179164
\(946\) −6.16489e16 −2.64560
\(947\) −6.66470e15 −0.284352 −0.142176 0.989841i \(-0.545410\pi\)
−0.142176 + 0.989841i \(0.545410\pi\)
\(948\) 1.41154e15 0.0598752
\(949\) 3.17980e16 1.34102
\(950\) 9.51822e16 3.99095
\(951\) 5.49757e15 0.229181
\(952\) 5.05670e14 0.0209587
\(953\) 9.43610e15 0.388849 0.194425 0.980917i \(-0.437716\pi\)
0.194425 + 0.980917i \(0.437716\pi\)
\(954\) 5.40928e15 0.221627
\(955\) 1.69742e16 0.691468
\(956\) 9.82122e15 0.397784
\(957\) −3.05757e16 −1.23129
\(958\) −2.58158e16 −1.03365
\(959\) −2.69351e16 −1.07230
\(960\) 5.72565e15 0.226638
\(961\) −4.07855e15 −0.160519
\(962\) −6.07052e16 −2.37554
\(963\) 2.82574e15 0.109948
\(964\) 2.45277e16 0.948929
\(965\) 5.85300e16 2.25153
\(966\) −1.08393e15 −0.0414597
\(967\) −1.99274e16 −0.757889 −0.378945 0.925419i \(-0.623713\pi\)
−0.378945 + 0.925419i \(0.623713\pi\)
\(968\) 2.45029e16 0.926623
\(969\) 2.21949e15 0.0834589
\(970\) −6.92479e16 −2.58918
\(971\) −2.18003e16 −0.810506 −0.405253 0.914205i \(-0.632817\pi\)
−0.405253 + 0.914205i \(0.632817\pi\)
\(972\) −1.13741e15 −0.0420488
\(973\) −2.77399e15 −0.101973
\(974\) −5.28420e16 −1.93155
\(975\) 2.89402e16 1.05190
\(976\) −5.19647e16 −1.87817
\(977\) −1.26115e16 −0.453259 −0.226630 0.973981i \(-0.572771\pi\)
−0.226630 + 0.973981i \(0.572771\pi\)
\(978\) 2.18754e16 0.781794
\(979\) 3.15598e16 1.12158
\(980\) −2.16816e16 −0.766209
\(981\) −1.10361e15 −0.0387824
\(982\) −3.47056e16 −1.21279
\(983\) 2.69450e16 0.936342 0.468171 0.883638i \(-0.344913\pi\)
0.468171 + 0.883638i \(0.344913\pi\)
\(984\) −8.54912e15 −0.295426
\(985\) −4.06307e16 −1.39623
\(986\) 3.90583e15 0.133472
\(987\) −9.97944e15 −0.339127
\(988\) 3.25598e16 1.10032
\(989\) 3.51313e15 0.118063
\(990\) 3.79840e16 1.26943
\(991\) 3.48894e16 1.15955 0.579774 0.814777i \(-0.303141\pi\)
0.579774 + 0.814777i \(0.303141\pi\)
\(992\) 3.14345e16 1.03894
\(993\) −6.32626e15 −0.207934
\(994\) −1.99465e16 −0.651991
\(995\) 2.70919e16 0.880667
\(996\) −1.51835e16 −0.490846
\(997\) −4.49354e15 −0.144466 −0.0722329 0.997388i \(-0.523013\pi\)
−0.0722329 + 0.997388i \(0.523013\pi\)
\(998\) 3.81005e16 1.21818
\(999\) 1.12535e16 0.357831
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.1.7 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.7 27 1.1 even 1 trivial