Properties

Label 177.10.a.a.1.19
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+35.2875 q^{2} +81.0000 q^{3} +733.210 q^{4} +388.913 q^{5} +2858.29 q^{6} -2376.48 q^{7} +7805.95 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+35.2875 q^{2} +81.0000 q^{3} +733.210 q^{4} +388.913 q^{5} +2858.29 q^{6} -2376.48 q^{7} +7805.95 q^{8} +6561.00 q^{9} +13723.8 q^{10} -88771.9 q^{11} +59390.0 q^{12} -95019.6 q^{13} -83860.1 q^{14} +31501.9 q^{15} -99950.7 q^{16} +444928. q^{17} +231521. q^{18} -770917. q^{19} +285155. q^{20} -192495. q^{21} -3.13254e6 q^{22} -766183. q^{23} +632282. q^{24} -1.80187e6 q^{25} -3.35301e6 q^{26} +531441. q^{27} -1.74246e6 q^{28} +3.07733e6 q^{29} +1.11163e6 q^{30} -4.59754e6 q^{31} -7.52366e6 q^{32} -7.19053e6 q^{33} +1.57004e7 q^{34} -924243. q^{35} +4.81059e6 q^{36} +8.69434e6 q^{37} -2.72038e7 q^{38} -7.69659e6 q^{39} +3.03583e6 q^{40} +3.69424e6 q^{41} -6.79267e6 q^{42} -1.75003e7 q^{43} -6.50885e7 q^{44} +2.55166e6 q^{45} -2.70367e7 q^{46} +3.58402e7 q^{47} -8.09601e6 q^{48} -3.47060e7 q^{49} -6.35836e7 q^{50} +3.60392e7 q^{51} -6.96693e7 q^{52} +7.15070e7 q^{53} +1.87532e7 q^{54} -3.45245e7 q^{55} -1.85507e7 q^{56} -6.24443e7 q^{57} +1.08591e8 q^{58} +1.21174e7 q^{59} +2.30975e7 q^{60} +1.49133e8 q^{61} -1.62236e8 q^{62} -1.55921e7 q^{63} -2.14317e8 q^{64} -3.69543e7 q^{65} -2.53736e8 q^{66} -1.05475e8 q^{67} +3.26226e8 q^{68} -6.20608e7 q^{69} -3.26143e7 q^{70} -4.67229e7 q^{71} +5.12148e7 q^{72} -4.65823e7 q^{73} +3.06802e8 q^{74} -1.45952e8 q^{75} -5.65244e8 q^{76} +2.10965e8 q^{77} -2.71594e8 q^{78} +2.64195e8 q^{79} -3.88721e7 q^{80} +4.30467e7 q^{81} +1.30361e8 q^{82} -8.34051e8 q^{83} -1.41139e8 q^{84} +1.73038e8 q^{85} -6.17544e8 q^{86} +2.49264e8 q^{87} -6.92949e8 q^{88} +2.19514e8 q^{89} +9.00417e7 q^{90} +2.25812e8 q^{91} -5.61773e8 q^{92} -3.72401e8 q^{93} +1.26471e9 q^{94} -2.99820e8 q^{95} -6.09417e8 q^{96} -6.96003e8 q^{97} -1.22469e9 q^{98} -5.82433e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.2875 1.55950 0.779752 0.626089i \(-0.215345\pi\)
0.779752 + 0.626089i \(0.215345\pi\)
\(3\) 81.0000 0.577350
\(4\) 733.210 1.43205
\(5\) 388.913 0.278283 0.139142 0.990272i \(-0.455566\pi\)
0.139142 + 0.990272i \(0.455566\pi\)
\(6\) 2858.29 0.900380
\(7\) −2376.48 −0.374104 −0.187052 0.982350i \(-0.559893\pi\)
−0.187052 + 0.982350i \(0.559893\pi\)
\(8\) 7805.95 0.673784
\(9\) 6561.00 0.333333
\(10\) 13723.8 0.433984
\(11\) −88771.9 −1.82814 −0.914068 0.405561i \(-0.867076\pi\)
−0.914068 + 0.405561i \(0.867076\pi\)
\(12\) 59390.0 0.826795
\(13\) −95019.6 −0.922716 −0.461358 0.887214i \(-0.652638\pi\)
−0.461358 + 0.887214i \(0.652638\pi\)
\(14\) −83860.1 −0.583417
\(15\) 31501.9 0.160667
\(16\) −99950.7 −0.381282
\(17\) 444928. 1.29202 0.646011 0.763328i \(-0.276436\pi\)
0.646011 + 0.763328i \(0.276436\pi\)
\(18\) 231521. 0.519834
\(19\) −770917. −1.35711 −0.678557 0.734547i \(-0.737395\pi\)
−0.678557 + 0.734547i \(0.737395\pi\)
\(20\) 285155. 0.398516
\(21\) −192495. −0.215989
\(22\) −3.13254e6 −2.85098
\(23\) −766183. −0.570897 −0.285448 0.958394i \(-0.592142\pi\)
−0.285448 + 0.958394i \(0.592142\pi\)
\(24\) 632282. 0.389010
\(25\) −1.80187e6 −0.922558
\(26\) −3.35301e6 −1.43898
\(27\) 531441. 0.192450
\(28\) −1.74246e6 −0.535736
\(29\) 3.07733e6 0.807947 0.403974 0.914771i \(-0.367629\pi\)
0.403974 + 0.914771i \(0.367629\pi\)
\(30\) 1.11163e6 0.250561
\(31\) −4.59754e6 −0.894124 −0.447062 0.894503i \(-0.647530\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(32\) −7.52366e6 −1.26839
\(33\) −7.19053e6 −1.05548
\(34\) 1.57004e7 2.01491
\(35\) −924243. −0.104107
\(36\) 4.81059e6 0.477350
\(37\) 8.69434e6 0.762657 0.381328 0.924440i \(-0.375467\pi\)
0.381328 + 0.924440i \(0.375467\pi\)
\(38\) −2.72038e7 −2.11643
\(39\) −7.69659e6 −0.532731
\(40\) 3.03583e6 0.187503
\(41\) 3.69424e6 0.204173 0.102086 0.994776i \(-0.467448\pi\)
0.102086 + 0.994776i \(0.467448\pi\)
\(42\) −6.79267e6 −0.336836
\(43\) −1.75003e7 −0.780618 −0.390309 0.920684i \(-0.627632\pi\)
−0.390309 + 0.920684i \(0.627632\pi\)
\(44\) −6.50885e7 −2.61798
\(45\) 2.55166e6 0.0927611
\(46\) −2.70367e7 −0.890315
\(47\) 3.58402e7 1.07135 0.535674 0.844425i \(-0.320058\pi\)
0.535674 + 0.844425i \(0.320058\pi\)
\(48\) −8.09601e6 −0.220133
\(49\) −3.47060e7 −0.860046
\(50\) −6.35836e7 −1.43873
\(51\) 3.60392e7 0.745949
\(52\) −6.96693e7 −1.32138
\(53\) 7.15070e7 1.24482 0.622411 0.782690i \(-0.286153\pi\)
0.622411 + 0.782690i \(0.286153\pi\)
\(54\) 1.87532e7 0.300127
\(55\) −3.45245e7 −0.508740
\(56\) −1.85507e7 −0.252066
\(57\) −6.24443e7 −0.783531
\(58\) 1.08591e8 1.26000
\(59\) 1.21174e7 0.130189
\(60\) 2.30975e7 0.230083
\(61\) 1.49133e8 1.37908 0.689542 0.724246i \(-0.257812\pi\)
0.689542 + 0.724246i \(0.257812\pi\)
\(62\) −1.62236e8 −1.39439
\(63\) −1.55921e7 −0.124701
\(64\) −2.14317e8 −1.59678
\(65\) −3.69543e7 −0.256777
\(66\) −2.53736e8 −1.64602
\(67\) −1.05475e8 −0.639459 −0.319730 0.947509i \(-0.603592\pi\)
−0.319730 + 0.947509i \(0.603592\pi\)
\(68\) 3.26226e8 1.85024
\(69\) −6.20608e7 −0.329607
\(70\) −3.26143e7 −0.162355
\(71\) −4.67229e7 −0.218206 −0.109103 0.994030i \(-0.534798\pi\)
−0.109103 + 0.994030i \(0.534798\pi\)
\(72\) 5.12148e7 0.224595
\(73\) −4.65823e7 −0.191985 −0.0959927 0.995382i \(-0.530603\pi\)
−0.0959927 + 0.995382i \(0.530603\pi\)
\(74\) 3.06802e8 1.18937
\(75\) −1.45952e8 −0.532639
\(76\) −5.65244e8 −1.94346
\(77\) 2.10965e8 0.683914
\(78\) −2.71594e8 −0.830795
\(79\) 2.64195e8 0.763137 0.381568 0.924341i \(-0.375384\pi\)
0.381568 + 0.924341i \(0.375384\pi\)
\(80\) −3.88721e7 −0.106104
\(81\) 4.30467e7 0.111111
\(82\) 1.30361e8 0.318408
\(83\) −8.34051e8 −1.92904 −0.964520 0.264011i \(-0.914954\pi\)
−0.964520 + 0.264011i \(0.914954\pi\)
\(84\) −1.41139e8 −0.309308
\(85\) 1.73038e8 0.359548
\(86\) −6.17544e8 −1.21738
\(87\) 2.49264e8 0.466469
\(88\) −6.92949e8 −1.23177
\(89\) 2.19514e8 0.370858 0.185429 0.982658i \(-0.440633\pi\)
0.185429 + 0.982658i \(0.440633\pi\)
\(90\) 9.00417e7 0.144661
\(91\) 2.25812e8 0.345192
\(92\) −5.61773e8 −0.817553
\(93\) −3.72401e8 −0.516223
\(94\) 1.26471e9 1.67077
\(95\) −2.99820e8 −0.377662
\(96\) −6.09417e8 −0.732308
\(97\) −6.96003e8 −0.798249 −0.399124 0.916897i \(-0.630686\pi\)
−0.399124 + 0.916897i \(0.630686\pi\)
\(98\) −1.22469e9 −1.34124
\(99\) −5.82433e8 −0.609379
\(100\) −1.32115e9 −1.32115
\(101\) 1.26703e9 1.21155 0.605776 0.795635i \(-0.292863\pi\)
0.605776 + 0.795635i \(0.292863\pi\)
\(102\) 1.27173e9 1.16331
\(103\) −3.05984e8 −0.267875 −0.133937 0.990990i \(-0.542762\pi\)
−0.133937 + 0.990990i \(0.542762\pi\)
\(104\) −7.41718e8 −0.621712
\(105\) −7.48637e7 −0.0601062
\(106\) 2.52331e9 1.94130
\(107\) −1.88673e9 −1.39150 −0.695748 0.718286i \(-0.744927\pi\)
−0.695748 + 0.718286i \(0.744927\pi\)
\(108\) 3.89658e8 0.275598
\(109\) −4.53422e8 −0.307669 −0.153834 0.988097i \(-0.549162\pi\)
−0.153834 + 0.988097i \(0.549162\pi\)
\(110\) −1.21829e9 −0.793382
\(111\) 7.04242e8 0.440320
\(112\) 2.37531e8 0.142639
\(113\) −1.03901e9 −0.599470 −0.299735 0.954022i \(-0.596898\pi\)
−0.299735 + 0.954022i \(0.596898\pi\)
\(114\) −2.20351e9 −1.22192
\(115\) −2.97978e8 −0.158871
\(116\) 2.25633e9 1.15702
\(117\) −6.23424e8 −0.307572
\(118\) 4.27592e8 0.203030
\(119\) −1.05736e9 −0.483351
\(120\) 2.45903e8 0.108255
\(121\) 5.52251e9 2.34208
\(122\) 5.26255e9 2.15068
\(123\) 2.99234e8 0.117879
\(124\) −3.37096e9 −1.28043
\(125\) −1.46037e9 −0.535016
\(126\) −5.50206e8 −0.194472
\(127\) −1.27717e9 −0.435644 −0.217822 0.975989i \(-0.569895\pi\)
−0.217822 + 0.975989i \(0.569895\pi\)
\(128\) −3.71059e9 −1.22179
\(129\) −1.41753e9 −0.450690
\(130\) −1.30403e9 −0.400444
\(131\) 4.28850e9 1.27229 0.636143 0.771571i \(-0.280529\pi\)
0.636143 + 0.771571i \(0.280529\pi\)
\(132\) −5.27217e9 −1.51149
\(133\) 1.83207e9 0.507703
\(134\) −3.72195e9 −0.997238
\(135\) 2.06684e8 0.0535557
\(136\) 3.47309e9 0.870544
\(137\) −2.80697e9 −0.680763 −0.340381 0.940287i \(-0.610556\pi\)
−0.340381 + 0.940287i \(0.610556\pi\)
\(138\) −2.18997e9 −0.514024
\(139\) −5.88780e9 −1.33778 −0.668892 0.743359i \(-0.733231\pi\)
−0.668892 + 0.743359i \(0.733231\pi\)
\(140\) −6.77664e8 −0.149086
\(141\) 2.90306e9 0.618543
\(142\) −1.64873e9 −0.340293
\(143\) 8.43508e9 1.68685
\(144\) −6.55777e8 −0.127094
\(145\) 1.19681e9 0.224838
\(146\) −1.64377e9 −0.299402
\(147\) −2.81118e9 −0.496548
\(148\) 6.37478e9 1.09216
\(149\) 7.38986e9 1.22828 0.614141 0.789196i \(-0.289503\pi\)
0.614141 + 0.789196i \(0.289503\pi\)
\(150\) −5.15027e9 −0.830653
\(151\) −3.01188e8 −0.0471456 −0.0235728 0.999722i \(-0.507504\pi\)
−0.0235728 + 0.999722i \(0.507504\pi\)
\(152\) −6.01774e9 −0.914403
\(153\) 2.91918e9 0.430674
\(154\) 7.44442e9 1.06657
\(155\) −1.78804e9 −0.248820
\(156\) −5.64322e9 −0.762897
\(157\) 5.43841e9 0.714370 0.357185 0.934034i \(-0.383737\pi\)
0.357185 + 0.934034i \(0.383737\pi\)
\(158\) 9.32278e9 1.19011
\(159\) 5.79207e9 0.718699
\(160\) −2.92605e9 −0.352973
\(161\) 1.82082e9 0.213575
\(162\) 1.51901e9 0.173278
\(163\) −1.08869e10 −1.20798 −0.603988 0.796993i \(-0.706423\pi\)
−0.603988 + 0.796993i \(0.706423\pi\)
\(164\) 2.70865e9 0.292386
\(165\) −2.79649e9 −0.293721
\(166\) −2.94316e10 −3.00834
\(167\) 1.30636e10 1.29969 0.649845 0.760066i \(-0.274834\pi\)
0.649845 + 0.760066i \(0.274834\pi\)
\(168\) −1.50260e9 −0.145530
\(169\) −1.57577e9 −0.148595
\(170\) 6.10610e9 0.560717
\(171\) −5.05799e9 −0.452372
\(172\) −1.28314e10 −1.11788
\(173\) 1.81666e10 1.54193 0.770967 0.636875i \(-0.219773\pi\)
0.770967 + 0.636875i \(0.219773\pi\)
\(174\) 8.79590e9 0.727459
\(175\) 4.28211e9 0.345133
\(176\) 8.87282e9 0.697035
\(177\) 9.81506e8 0.0751646
\(178\) 7.74612e9 0.578354
\(179\) −2.07402e10 −1.50999 −0.754995 0.655731i \(-0.772361\pi\)
−0.754995 + 0.655731i \(0.772361\pi\)
\(180\) 1.87090e9 0.132839
\(181\) −5.49313e9 −0.380422 −0.190211 0.981743i \(-0.560917\pi\)
−0.190211 + 0.981743i \(0.560917\pi\)
\(182\) 7.96835e9 0.538328
\(183\) 1.20798e10 0.796214
\(184\) −5.98079e9 −0.384661
\(185\) 3.38134e9 0.212235
\(186\) −1.31411e10 −0.805051
\(187\) −3.94972e10 −2.36199
\(188\) 2.62784e10 1.53422
\(189\) −1.26296e9 −0.0719964
\(190\) −1.05799e10 −0.588966
\(191\) −2.67154e10 −1.45248 −0.726242 0.687439i \(-0.758735\pi\)
−0.726242 + 0.687439i \(0.758735\pi\)
\(192\) −1.73596e10 −0.921903
\(193\) −2.33288e10 −1.21027 −0.605137 0.796121i \(-0.706882\pi\)
−0.605137 + 0.796121i \(0.706882\pi\)
\(194\) −2.45602e10 −1.24487
\(195\) −2.99330e9 −0.148250
\(196\) −2.54468e10 −1.23163
\(197\) −3.67488e10 −1.73838 −0.869190 0.494478i \(-0.835359\pi\)
−0.869190 + 0.494478i \(0.835359\pi\)
\(198\) −2.05526e10 −0.950328
\(199\) −1.48780e10 −0.672522 −0.336261 0.941769i \(-0.609162\pi\)
−0.336261 + 0.941769i \(0.609162\pi\)
\(200\) −1.40653e10 −0.621605
\(201\) −8.54347e9 −0.369192
\(202\) 4.47105e10 1.88942
\(203\) −7.31321e9 −0.302257
\(204\) 2.64243e10 1.06824
\(205\) 1.43674e9 0.0568179
\(206\) −1.07974e10 −0.417751
\(207\) −5.02693e9 −0.190299
\(208\) 9.49728e9 0.351815
\(209\) 6.84358e10 2.48099
\(210\) −2.64175e9 −0.0937358
\(211\) 4.69174e10 1.62953 0.814766 0.579790i \(-0.196865\pi\)
0.814766 + 0.579790i \(0.196865\pi\)
\(212\) 5.24297e10 1.78265
\(213\) −3.78455e9 −0.125981
\(214\) −6.65779e10 −2.17004
\(215\) −6.80610e9 −0.217233
\(216\) 4.14840e9 0.129670
\(217\) 1.09259e10 0.334496
\(218\) −1.60001e10 −0.479810
\(219\) −3.77317e9 −0.110843
\(220\) −2.53137e10 −0.728541
\(221\) −4.22769e10 −1.19217
\(222\) 2.48510e10 0.686681
\(223\) 1.08667e10 0.294256 0.147128 0.989117i \(-0.452997\pi\)
0.147128 + 0.989117i \(0.452997\pi\)
\(224\) 1.78798e10 0.474512
\(225\) −1.18221e10 −0.307519
\(226\) −3.66642e10 −0.934876
\(227\) −1.18817e10 −0.297005 −0.148502 0.988912i \(-0.547445\pi\)
−0.148502 + 0.988912i \(0.547445\pi\)
\(228\) −4.57848e10 −1.12206
\(229\) −3.31356e10 −0.796223 −0.398111 0.917337i \(-0.630334\pi\)
−0.398111 + 0.917337i \(0.630334\pi\)
\(230\) −1.05149e10 −0.247760
\(231\) 1.70881e10 0.394858
\(232\) 2.40215e10 0.544382
\(233\) 7.33018e10 1.62934 0.814672 0.579922i \(-0.196917\pi\)
0.814672 + 0.579922i \(0.196917\pi\)
\(234\) −2.19991e10 −0.479660
\(235\) 1.39387e10 0.298138
\(236\) 8.88457e9 0.186437
\(237\) 2.13998e10 0.440597
\(238\) −3.73117e10 −0.753788
\(239\) −4.41464e10 −0.875195 −0.437597 0.899171i \(-0.644170\pi\)
−0.437597 + 0.899171i \(0.644170\pi\)
\(240\) −3.14864e9 −0.0612594
\(241\) −2.28274e10 −0.435893 −0.217946 0.975961i \(-0.569936\pi\)
−0.217946 + 0.975961i \(0.569936\pi\)
\(242\) 1.94876e11 3.65249
\(243\) 3.48678e9 0.0641500
\(244\) 1.09346e11 1.97492
\(245\) −1.34976e10 −0.239336
\(246\) 1.05592e10 0.183833
\(247\) 7.32523e10 1.25223
\(248\) −3.58882e10 −0.602447
\(249\) −6.75581e10 −1.11373
\(250\) −5.15327e10 −0.834359
\(251\) 9.73729e9 0.154848 0.0774242 0.996998i \(-0.475330\pi\)
0.0774242 + 0.996998i \(0.475330\pi\)
\(252\) −1.14323e10 −0.178579
\(253\) 6.80156e10 1.04368
\(254\) −4.50681e10 −0.679388
\(255\) 1.40161e10 0.207585
\(256\) −2.12075e10 −0.308609
\(257\) 1.33586e11 1.91012 0.955061 0.296410i \(-0.0957896\pi\)
0.955061 + 0.296410i \(0.0957896\pi\)
\(258\) −5.00210e10 −0.702852
\(259\) −2.06619e10 −0.285313
\(260\) −2.70953e10 −0.367717
\(261\) 2.01904e10 0.269316
\(262\) 1.51331e11 1.98413
\(263\) 1.31485e11 1.69463 0.847314 0.531092i \(-0.178218\pi\)
0.847314 + 0.531092i \(0.178218\pi\)
\(264\) −5.61289e10 −0.711162
\(265\) 2.78100e10 0.346413
\(266\) 6.46492e10 0.791764
\(267\) 1.77807e10 0.214115
\(268\) −7.73353e10 −0.915738
\(269\) 1.01003e11 1.17612 0.588058 0.808819i \(-0.299893\pi\)
0.588058 + 0.808819i \(0.299893\pi\)
\(270\) 7.29338e9 0.0835202
\(271\) 7.61574e10 0.857730 0.428865 0.903369i \(-0.358914\pi\)
0.428865 + 0.903369i \(0.358914\pi\)
\(272\) −4.44709e10 −0.492625
\(273\) 1.82908e10 0.199297
\(274\) −9.90512e10 −1.06165
\(275\) 1.59956e11 1.68656
\(276\) −4.55036e10 −0.472014
\(277\) 3.71033e10 0.378664 0.189332 0.981913i \(-0.439368\pi\)
0.189332 + 0.981913i \(0.439368\pi\)
\(278\) −2.07766e11 −2.08628
\(279\) −3.01644e10 −0.298041
\(280\) −7.21459e9 −0.0701457
\(281\) −8.14367e10 −0.779187 −0.389593 0.920987i \(-0.627384\pi\)
−0.389593 + 0.920987i \(0.627384\pi\)
\(282\) 1.02442e11 0.964619
\(283\) −3.03484e9 −0.0281253 −0.0140627 0.999901i \(-0.504476\pi\)
−0.0140627 + 0.999901i \(0.504476\pi\)
\(284\) −3.42577e10 −0.312482
\(285\) −2.42854e10 −0.218044
\(286\) 2.97653e11 2.63065
\(287\) −8.77929e9 −0.0763819
\(288\) −4.93627e10 −0.422798
\(289\) 7.93734e10 0.669321
\(290\) 4.22326e10 0.350636
\(291\) −5.63762e10 −0.460869
\(292\) −3.41546e10 −0.274933
\(293\) 1.24746e11 0.988835 0.494417 0.869225i \(-0.335381\pi\)
0.494417 + 0.869225i \(0.335381\pi\)
\(294\) −9.91997e10 −0.774368
\(295\) 4.71260e9 0.0362294
\(296\) 6.78676e10 0.513866
\(297\) −4.71770e10 −0.351825
\(298\) 2.60770e11 1.91551
\(299\) 7.28024e10 0.526776
\(300\) −1.07013e11 −0.762766
\(301\) 4.15892e10 0.292032
\(302\) −1.06282e10 −0.0735237
\(303\) 1.02630e11 0.699490
\(304\) 7.70538e10 0.517443
\(305\) 5.79999e10 0.383776
\(306\) 1.03010e11 0.671638
\(307\) −2.13327e11 −1.37064 −0.685318 0.728244i \(-0.740337\pi\)
−0.685318 + 0.728244i \(0.740337\pi\)
\(308\) 1.54681e11 0.979399
\(309\) −2.47847e10 −0.154658
\(310\) −6.30956e10 −0.388035
\(311\) −3.12533e10 −0.189441 −0.0947205 0.995504i \(-0.530196\pi\)
−0.0947205 + 0.995504i \(0.530196\pi\)
\(312\) −6.00792e10 −0.358945
\(313\) −1.74897e11 −1.02999 −0.514995 0.857193i \(-0.672206\pi\)
−0.514995 + 0.857193i \(0.672206\pi\)
\(314\) 1.91908e11 1.11406
\(315\) −6.06396e9 −0.0347023
\(316\) 1.93710e11 1.09285
\(317\) 1.30476e11 0.725709 0.362855 0.931846i \(-0.381802\pi\)
0.362855 + 0.931846i \(0.381802\pi\)
\(318\) 2.04388e11 1.12081
\(319\) −2.73181e11 −1.47704
\(320\) −8.33505e10 −0.444358
\(321\) −1.52825e11 −0.803380
\(322\) 6.42522e10 0.333071
\(323\) −3.43003e11 −1.75342
\(324\) 3.15623e10 0.159117
\(325\) 1.71213e11 0.851260
\(326\) −3.84171e11 −1.88384
\(327\) −3.67272e10 −0.177632
\(328\) 2.88371e10 0.137568
\(329\) −8.51735e10 −0.400796
\(330\) −9.86811e10 −0.458059
\(331\) 3.15453e11 1.44447 0.722236 0.691647i \(-0.243114\pi\)
0.722236 + 0.691647i \(0.243114\pi\)
\(332\) −6.11534e11 −2.76248
\(333\) 5.70436e10 0.254219
\(334\) 4.60984e11 2.02687
\(335\) −4.10206e10 −0.177951
\(336\) 1.92400e10 0.0823528
\(337\) 3.13163e11 1.32262 0.661311 0.750112i \(-0.270000\pi\)
0.661311 + 0.750112i \(0.270000\pi\)
\(338\) −5.56051e10 −0.231734
\(339\) −8.41600e10 −0.346104
\(340\) 1.26873e11 0.514891
\(341\) 4.08132e11 1.63458
\(342\) −1.78484e11 −0.705475
\(343\) 1.78377e11 0.695851
\(344\) −1.36607e11 −0.525968
\(345\) −2.41363e10 −0.0917242
\(346\) 6.41054e11 2.40465
\(347\) −1.66053e11 −0.614844 −0.307422 0.951573i \(-0.599466\pi\)
−0.307422 + 0.951573i \(0.599466\pi\)
\(348\) 1.82763e11 0.668007
\(349\) −2.49063e11 −0.898659 −0.449329 0.893366i \(-0.648337\pi\)
−0.449329 + 0.893366i \(0.648337\pi\)
\(350\) 1.51105e11 0.538236
\(351\) −5.04973e10 −0.177577
\(352\) 6.67890e11 2.31880
\(353\) 2.16105e11 0.740762 0.370381 0.928880i \(-0.379227\pi\)
0.370381 + 0.928880i \(0.379227\pi\)
\(354\) 3.46349e10 0.117219
\(355\) −1.81711e10 −0.0607231
\(356\) 1.60950e11 0.531087
\(357\) −8.56464e10 −0.279063
\(358\) −7.31870e11 −2.35483
\(359\) −3.36268e11 −1.06846 −0.534232 0.845338i \(-0.679399\pi\)
−0.534232 + 0.845338i \(0.679399\pi\)
\(360\) 1.99181e10 0.0625010
\(361\) 2.71626e11 0.841761
\(362\) −1.93839e11 −0.593270
\(363\) 4.47323e11 1.35220
\(364\) 1.65568e11 0.494333
\(365\) −1.81165e10 −0.0534263
\(366\) 4.26266e11 1.24170
\(367\) 4.49802e11 1.29427 0.647134 0.762377i \(-0.275968\pi\)
0.647134 + 0.762377i \(0.275968\pi\)
\(368\) 7.65806e10 0.217672
\(369\) 2.42379e10 0.0680576
\(370\) 1.19319e11 0.330981
\(371\) −1.69935e11 −0.465693
\(372\) −2.73048e11 −0.739257
\(373\) −1.71165e11 −0.457852 −0.228926 0.973444i \(-0.573521\pi\)
−0.228926 + 0.973444i \(0.573521\pi\)
\(374\) −1.39376e12 −3.68354
\(375\) −1.18290e11 −0.308892
\(376\) 2.79767e11 0.721857
\(377\) −2.92407e11 −0.745506
\(378\) −4.45667e10 −0.112279
\(379\) 2.37121e11 0.590329 0.295164 0.955447i \(-0.404626\pi\)
0.295164 + 0.955447i \(0.404626\pi\)
\(380\) −2.19831e11 −0.540832
\(381\) −1.03451e11 −0.251519
\(382\) −9.42720e11 −2.26515
\(383\) −4.26137e11 −1.01194 −0.505970 0.862551i \(-0.668865\pi\)
−0.505970 + 0.862551i \(0.668865\pi\)
\(384\) −3.00558e11 −0.705404
\(385\) 8.20468e10 0.190322
\(386\) −8.23214e11 −1.88743
\(387\) −1.14820e11 −0.260206
\(388\) −5.10316e11 −1.14313
\(389\) −4.49580e11 −0.995484 −0.497742 0.867325i \(-0.665837\pi\)
−0.497742 + 0.867325i \(0.665837\pi\)
\(390\) −1.05626e11 −0.231196
\(391\) −3.40897e11 −0.737611
\(392\) −2.70913e11 −0.579485
\(393\) 3.47368e11 0.734554
\(394\) −1.29677e12 −2.71101
\(395\) 1.02749e11 0.212368
\(396\) −4.27045e11 −0.872661
\(397\) −4.70283e11 −0.950172 −0.475086 0.879939i \(-0.657583\pi\)
−0.475086 + 0.879939i \(0.657583\pi\)
\(398\) −5.25009e11 −1.04880
\(399\) 1.48398e11 0.293122
\(400\) 1.80098e11 0.351755
\(401\) −2.57893e10 −0.0498070 −0.0249035 0.999690i \(-0.507928\pi\)
−0.0249035 + 0.999690i \(0.507928\pi\)
\(402\) −3.01478e11 −0.575756
\(403\) 4.36856e11 0.825023
\(404\) 9.29002e11 1.73500
\(405\) 1.67414e10 0.0309204
\(406\) −2.58065e11 −0.471370
\(407\) −7.71814e11 −1.39424
\(408\) 2.81320e11 0.502609
\(409\) −6.37794e11 −1.12700 −0.563502 0.826115i \(-0.690546\pi\)
−0.563502 + 0.826115i \(0.690546\pi\)
\(410\) 5.06989e10 0.0886077
\(411\) −2.27365e11 −0.393039
\(412\) −2.24351e11 −0.383610
\(413\) −2.87966e10 −0.0487042
\(414\) −1.77388e11 −0.296772
\(415\) −3.24373e11 −0.536819
\(416\) 7.14895e11 1.17037
\(417\) −4.76912e11 −0.772370
\(418\) 2.41493e12 3.86911
\(419\) 4.40211e11 0.697746 0.348873 0.937170i \(-0.386564\pi\)
0.348873 + 0.937170i \(0.386564\pi\)
\(420\) −5.48908e10 −0.0860751
\(421\) −8.51162e11 −1.32051 −0.660257 0.751040i \(-0.729553\pi\)
−0.660257 + 0.751040i \(0.729553\pi\)
\(422\) 1.65560e12 2.54126
\(423\) 2.35148e11 0.357116
\(424\) 5.58180e11 0.838742
\(425\) −8.01704e11 −1.19197
\(426\) −1.33547e11 −0.196468
\(427\) −3.54412e11 −0.515921
\(428\) −1.38337e12 −1.99269
\(429\) 6.83241e11 0.973904
\(430\) −2.40171e11 −0.338775
\(431\) −6.20060e11 −0.865538 −0.432769 0.901505i \(-0.642463\pi\)
−0.432769 + 0.901505i \(0.642463\pi\)
\(432\) −5.31179e10 −0.0733777
\(433\) 8.37180e11 1.14452 0.572260 0.820072i \(-0.306067\pi\)
0.572260 + 0.820072i \(0.306067\pi\)
\(434\) 3.85550e11 0.521647
\(435\) 9.69419e10 0.129810
\(436\) −3.32453e11 −0.440597
\(437\) 5.90664e11 0.774772
\(438\) −1.33146e11 −0.172860
\(439\) 7.66484e11 0.984947 0.492474 0.870327i \(-0.336093\pi\)
0.492474 + 0.870327i \(0.336093\pi\)
\(440\) −2.69497e11 −0.342781
\(441\) −2.27706e11 −0.286682
\(442\) −1.49185e12 −1.85919
\(443\) −1.30219e12 −1.60642 −0.803209 0.595698i \(-0.796876\pi\)
−0.803209 + 0.595698i \(0.796876\pi\)
\(444\) 5.16357e11 0.630561
\(445\) 8.53719e10 0.103204
\(446\) 3.83459e11 0.458894
\(447\) 5.98579e11 0.709149
\(448\) 5.09319e11 0.597364
\(449\) −1.53372e12 −1.78089 −0.890446 0.455089i \(-0.849608\pi\)
−0.890446 + 0.455089i \(0.849608\pi\)
\(450\) −4.17172e11 −0.479578
\(451\) −3.27945e11 −0.373256
\(452\) −7.61814e11 −0.858471
\(453\) −2.43962e10 −0.0272195
\(454\) −4.19277e11 −0.463180
\(455\) 8.78212e10 0.0960612
\(456\) −4.87437e11 −0.527931
\(457\) −4.73372e11 −0.507668 −0.253834 0.967248i \(-0.581692\pi\)
−0.253834 + 0.967248i \(0.581692\pi\)
\(458\) −1.16927e12 −1.24171
\(459\) 2.36453e11 0.248650
\(460\) −2.18481e11 −0.227511
\(461\) −5.55441e11 −0.572774 −0.286387 0.958114i \(-0.592454\pi\)
−0.286387 + 0.958114i \(0.592454\pi\)
\(462\) 6.02998e11 0.615782
\(463\) 1.00553e12 1.01690 0.508452 0.861090i \(-0.330218\pi\)
0.508452 + 0.861090i \(0.330218\pi\)
\(464\) −3.07581e11 −0.308056
\(465\) −1.44831e11 −0.143656
\(466\) 2.58664e12 2.54097
\(467\) 9.53952e11 0.928112 0.464056 0.885806i \(-0.346394\pi\)
0.464056 + 0.885806i \(0.346394\pi\)
\(468\) −4.57100e11 −0.440459
\(469\) 2.50659e11 0.239224
\(470\) 4.91863e11 0.464947
\(471\) 4.40511e11 0.412442
\(472\) 9.45875e10 0.0877192
\(473\) 1.55354e12 1.42708
\(474\) 7.55145e11 0.687113
\(475\) 1.38909e12 1.25202
\(476\) −7.75269e11 −0.692183
\(477\) 4.69158e11 0.414941
\(478\) −1.55782e12 −1.36487
\(479\) −1.56392e12 −1.35739 −0.678696 0.734419i \(-0.737455\pi\)
−0.678696 + 0.734419i \(0.737455\pi\)
\(480\) −2.37010e11 −0.203789
\(481\) −8.26133e11 −0.703716
\(482\) −8.05522e11 −0.679776
\(483\) 1.47486e11 0.123308
\(484\) 4.04916e12 3.35398
\(485\) −2.70684e11 −0.222139
\(486\) 1.23040e11 0.100042
\(487\) −1.90185e12 −1.53213 −0.766065 0.642763i \(-0.777788\pi\)
−0.766065 + 0.642763i \(0.777788\pi\)
\(488\) 1.16413e12 0.929205
\(489\) −8.81836e11 −0.697426
\(490\) −4.76297e11 −0.373246
\(491\) −1.22015e12 −0.947428 −0.473714 0.880679i \(-0.657087\pi\)
−0.473714 + 0.880679i \(0.657087\pi\)
\(492\) 2.19401e11 0.168809
\(493\) 1.36919e12 1.04389
\(494\) 2.58489e12 1.95286
\(495\) −2.26516e11 −0.169580
\(496\) 4.59527e11 0.340913
\(497\) 1.11036e11 0.0816318
\(498\) −2.38396e12 −1.73687
\(499\) 6.90463e11 0.498526 0.249263 0.968436i \(-0.419812\pi\)
0.249263 + 0.968436i \(0.419812\pi\)
\(500\) −1.07076e12 −0.766170
\(501\) 1.05815e12 0.750377
\(502\) 3.43605e11 0.241486
\(503\) 2.00172e12 1.39427 0.697135 0.716940i \(-0.254458\pi\)
0.697135 + 0.716940i \(0.254458\pi\)
\(504\) −1.21711e11 −0.0840219
\(505\) 4.92766e11 0.337155
\(506\) 2.40010e12 1.62762
\(507\) −1.27637e11 −0.0857911
\(508\) −9.36433e11 −0.623864
\(509\) −4.83312e11 −0.319152 −0.159576 0.987186i \(-0.551013\pi\)
−0.159576 + 0.987186i \(0.551013\pi\)
\(510\) 4.94594e11 0.323730
\(511\) 1.10702e11 0.0718225
\(512\) 1.15146e12 0.740517
\(513\) −4.09697e11 −0.261177
\(514\) 4.71391e12 2.97884
\(515\) −1.19001e11 −0.0745451
\(516\) −1.03935e12 −0.645411
\(517\) −3.18161e12 −1.95857
\(518\) −7.29108e11 −0.444947
\(519\) 1.47149e12 0.890236
\(520\) −2.88464e11 −0.173012
\(521\) −1.07336e12 −0.638230 −0.319115 0.947716i \(-0.603386\pi\)
−0.319115 + 0.947716i \(0.603386\pi\)
\(522\) 7.12468e11 0.419999
\(523\) 2.32758e12 1.36034 0.680169 0.733056i \(-0.261907\pi\)
0.680169 + 0.733056i \(0.261907\pi\)
\(524\) 3.14437e12 1.82198
\(525\) 3.46851e11 0.199263
\(526\) 4.63977e12 2.64278
\(527\) −2.04558e12 −1.15523
\(528\) 7.18698e11 0.402433
\(529\) −1.21412e12 −0.674077
\(530\) 9.81346e11 0.540233
\(531\) 7.95020e10 0.0433963
\(532\) 1.34329e12 0.727056
\(533\) −3.51025e11 −0.188394
\(534\) 6.27435e11 0.333913
\(535\) −7.33772e11 −0.387230
\(536\) −8.23332e11 −0.430857
\(537\) −1.67995e12 −0.871793
\(538\) 3.56416e12 1.83416
\(539\) 3.08091e12 1.57228
\(540\) 1.51543e11 0.0766944
\(541\) −2.13813e11 −0.107312 −0.0536558 0.998559i \(-0.517087\pi\)
−0.0536558 + 0.998559i \(0.517087\pi\)
\(542\) 2.68741e12 1.33763
\(543\) −4.44943e11 −0.219637
\(544\) −3.34749e12 −1.63879
\(545\) −1.76341e11 −0.0856190
\(546\) 6.45436e11 0.310804
\(547\) −2.35000e12 −1.12234 −0.561170 0.827701i \(-0.689649\pi\)
−0.561170 + 0.827701i \(0.689649\pi\)
\(548\) −2.05810e12 −0.974887
\(549\) 9.78464e11 0.459694
\(550\) 5.64444e12 2.63020
\(551\) −2.37237e12 −1.09648
\(552\) −4.84444e11 −0.222084
\(553\) −6.27853e11 −0.285493
\(554\) 1.30928e12 0.590528
\(555\) 2.73889e11 0.122534
\(556\) −4.31699e12 −1.91578
\(557\) −3.02608e12 −1.33209 −0.666044 0.745913i \(-0.732014\pi\)
−0.666044 + 0.745913i \(0.732014\pi\)
\(558\) −1.06443e12 −0.464796
\(559\) 1.66288e12 0.720289
\(560\) 9.23788e10 0.0396941
\(561\) −3.19927e12 −1.36370
\(562\) −2.87370e12 −1.21514
\(563\) −1.05199e12 −0.441291 −0.220645 0.975354i \(-0.570816\pi\)
−0.220645 + 0.975354i \(0.570816\pi\)
\(564\) 2.12855e12 0.885785
\(565\) −4.04085e11 −0.166823
\(566\) −1.07092e11 −0.0438615
\(567\) −1.02300e11 −0.0415671
\(568\) −3.64716e11 −0.147024
\(569\) −2.24721e12 −0.898751 −0.449375 0.893343i \(-0.648353\pi\)
−0.449375 + 0.893343i \(0.648353\pi\)
\(570\) −8.56971e11 −0.340040
\(571\) 3.88739e12 1.53037 0.765183 0.643813i \(-0.222649\pi\)
0.765183 + 0.643813i \(0.222649\pi\)
\(572\) 6.18468e12 2.41566
\(573\) −2.16395e12 −0.838592
\(574\) −3.09799e11 −0.119118
\(575\) 1.38056e12 0.526685
\(576\) −1.40613e12 −0.532261
\(577\) −5.00381e12 −1.87936 −0.939679 0.342057i \(-0.888876\pi\)
−0.939679 + 0.342057i \(0.888876\pi\)
\(578\) 2.80089e12 1.04381
\(579\) −1.88963e12 −0.698752
\(580\) 8.77515e11 0.321980
\(581\) 1.98210e12 0.721662
\(582\) −1.98938e12 −0.718727
\(583\) −6.34782e12 −2.27570
\(584\) −3.63619e11 −0.129357
\(585\) −2.42457e11 −0.0855922
\(586\) 4.40199e12 1.54209
\(587\) −1.72176e12 −0.598552 −0.299276 0.954167i \(-0.596745\pi\)
−0.299276 + 0.954167i \(0.596745\pi\)
\(588\) −2.06119e12 −0.711081
\(589\) 3.54432e12 1.21343
\(590\) 1.66296e11 0.0564999
\(591\) −2.97665e12 −1.00365
\(592\) −8.69006e11 −0.290787
\(593\) −3.09332e12 −1.02726 −0.513628 0.858013i \(-0.671699\pi\)
−0.513628 + 0.858013i \(0.671699\pi\)
\(594\) −1.66476e12 −0.548672
\(595\) −4.11222e11 −0.134509
\(596\) 5.41832e12 1.75896
\(597\) −1.20512e12 −0.388281
\(598\) 2.56902e12 0.821508
\(599\) −5.51356e12 −1.74989 −0.874947 0.484219i \(-0.839104\pi\)
−0.874947 + 0.484219i \(0.839104\pi\)
\(600\) −1.13929e12 −0.358884
\(601\) −2.07713e12 −0.649424 −0.324712 0.945813i \(-0.605267\pi\)
−0.324712 + 0.945813i \(0.605267\pi\)
\(602\) 1.46758e12 0.455426
\(603\) −6.92021e11 −0.213153
\(604\) −2.20834e11 −0.0675149
\(605\) 2.14777e12 0.651763
\(606\) 3.62155e12 1.09086
\(607\) −3.23861e12 −0.968299 −0.484149 0.874985i \(-0.660871\pi\)
−0.484149 + 0.874985i \(0.660871\pi\)
\(608\) 5.80012e12 1.72136
\(609\) −5.92370e11 −0.174508
\(610\) 2.04667e12 0.598500
\(611\) −3.40552e12 −0.988550
\(612\) 2.14037e12 0.616747
\(613\) −4.38376e11 −0.125393 −0.0626967 0.998033i \(-0.519970\pi\)
−0.0626967 + 0.998033i \(0.519970\pi\)
\(614\) −7.52777e12 −2.13751
\(615\) 1.16376e11 0.0328038
\(616\) 1.64678e12 0.460810
\(617\) −1.81189e12 −0.503324 −0.251662 0.967815i \(-0.580977\pi\)
−0.251662 + 0.967815i \(0.580977\pi\)
\(618\) −8.74592e11 −0.241189
\(619\) −1.52091e12 −0.416386 −0.208193 0.978088i \(-0.566758\pi\)
−0.208193 + 0.978088i \(0.566758\pi\)
\(620\) −1.31101e12 −0.356322
\(621\) −4.07181e11 −0.109869
\(622\) −1.10285e12 −0.295434
\(623\) −5.21671e11 −0.138740
\(624\) 7.69280e11 0.203120
\(625\) 2.95133e12 0.773672
\(626\) −6.17169e12 −1.60627
\(627\) 5.54330e12 1.43240
\(628\) 3.98749e12 1.02301
\(629\) 3.86836e12 0.985369
\(630\) −2.13982e11 −0.0541184
\(631\) −1.89271e12 −0.475283 −0.237641 0.971353i \(-0.576374\pi\)
−0.237641 + 0.971353i \(0.576374\pi\)
\(632\) 2.06229e12 0.514189
\(633\) 3.80031e12 0.940811
\(634\) 4.60416e12 1.13175
\(635\) −4.96707e11 −0.121232
\(636\) 4.24680e12 1.02921
\(637\) 3.29775e12 0.793578
\(638\) −9.63987e12 −2.30345
\(639\) −3.06549e11 −0.0727354
\(640\) −1.44310e12 −0.340005
\(641\) −1.16060e12 −0.271533 −0.135767 0.990741i \(-0.543350\pi\)
−0.135767 + 0.990741i \(0.543350\pi\)
\(642\) −5.39281e12 −1.25287
\(643\) 6.78316e12 1.56488 0.782442 0.622723i \(-0.213974\pi\)
0.782442 + 0.622723i \(0.213974\pi\)
\(644\) 1.33504e12 0.305850
\(645\) −5.51294e11 −0.125419
\(646\) −1.21037e13 −2.73447
\(647\) −1.40949e12 −0.316223 −0.158112 0.987421i \(-0.550541\pi\)
−0.158112 + 0.987421i \(0.550541\pi\)
\(648\) 3.36021e11 0.0748649
\(649\) −1.07568e12 −0.238003
\(650\) 6.04169e12 1.32754
\(651\) 8.85002e11 0.193121
\(652\) −7.98236e12 −1.72988
\(653\) 4.47782e12 0.963735 0.481868 0.876244i \(-0.339959\pi\)
0.481868 + 0.876244i \(0.339959\pi\)
\(654\) −1.29601e12 −0.277018
\(655\) 1.66785e12 0.354056
\(656\) −3.69242e11 −0.0778474
\(657\) −3.05626e11 −0.0639951
\(658\) −3.00556e12 −0.625042
\(659\) 3.08721e12 0.637650 0.318825 0.947814i \(-0.396712\pi\)
0.318825 + 0.947814i \(0.396712\pi\)
\(660\) −2.05041e12 −0.420623
\(661\) 4.08659e12 0.832636 0.416318 0.909219i \(-0.363320\pi\)
0.416318 + 0.909219i \(0.363320\pi\)
\(662\) 1.11316e13 2.25266
\(663\) −3.42443e12 −0.688300
\(664\) −6.51056e12 −1.29976
\(665\) 7.12515e11 0.141285
\(666\) 2.01293e12 0.396455
\(667\) −2.35780e12 −0.461254
\(668\) 9.57839e12 1.86122
\(669\) 8.80203e11 0.169889
\(670\) −1.44751e12 −0.277515
\(671\) −1.32389e13 −2.52115
\(672\) 1.44827e12 0.273960
\(673\) −7.17605e12 −1.34840 −0.674198 0.738550i \(-0.735511\pi\)
−0.674198 + 0.738550i \(0.735511\pi\)
\(674\) 1.10507e13 2.06263
\(675\) −9.57589e11 −0.177546
\(676\) −1.15537e12 −0.212795
\(677\) 4.40269e12 0.805507 0.402753 0.915309i \(-0.368053\pi\)
0.402753 + 0.915309i \(0.368053\pi\)
\(678\) −2.96980e12 −0.539751
\(679\) 1.65404e12 0.298628
\(680\) 1.35073e12 0.242258
\(681\) −9.62421e11 −0.171476
\(682\) 1.44020e13 2.54913
\(683\) 8.67012e12 1.52452 0.762258 0.647274i \(-0.224091\pi\)
0.762258 + 0.647274i \(0.224091\pi\)
\(684\) −3.70857e12 −0.647819
\(685\) −1.09167e12 −0.189445
\(686\) 6.29450e12 1.08518
\(687\) −2.68398e12 −0.459700
\(688\) 1.74917e12 0.297635
\(689\) −6.79457e12 −1.14862
\(690\) −8.51709e11 −0.143044
\(691\) 1.93668e11 0.0323151 0.0161576 0.999869i \(-0.494857\pi\)
0.0161576 + 0.999869i \(0.494857\pi\)
\(692\) 1.33199e13 2.20813
\(693\) 1.38414e12 0.227971
\(694\) −5.85961e12 −0.958852
\(695\) −2.28984e12 −0.372283
\(696\) 1.94574e12 0.314299
\(697\) 1.64367e12 0.263796
\(698\) −8.78882e12 −1.40146
\(699\) 5.93744e12 0.940702
\(700\) 3.13969e12 0.494248
\(701\) 1.12033e13 1.75232 0.876162 0.482017i \(-0.160096\pi\)
0.876162 + 0.482017i \(0.160096\pi\)
\(702\) −1.78193e12 −0.276932
\(703\) −6.70262e12 −1.03501
\(704\) 1.90253e13 2.91914
\(705\) 1.12904e12 0.172130
\(706\) 7.62582e12 1.15522
\(707\) −3.01108e12 −0.453247
\(708\) 7.19650e11 0.107640
\(709\) 3.44393e12 0.511854 0.255927 0.966696i \(-0.417619\pi\)
0.255927 + 0.966696i \(0.417619\pi\)
\(710\) −6.41214e11 −0.0946979
\(711\) 1.73338e12 0.254379
\(712\) 1.71352e12 0.249878
\(713\) 3.52256e12 0.510452
\(714\) −3.02225e12 −0.435200
\(715\) 3.28051e12 0.469423
\(716\) −1.52069e13 −2.16238
\(717\) −3.57586e12 −0.505294
\(718\) −1.18661e13 −1.66627
\(719\) −1.08645e13 −1.51610 −0.758050 0.652197i \(-0.773848\pi\)
−0.758050 + 0.652197i \(0.773848\pi\)
\(720\) −2.55040e11 −0.0353681
\(721\) 7.27165e11 0.100213
\(722\) 9.58501e12 1.31273
\(723\) −1.84902e12 −0.251663
\(724\) −4.02761e12 −0.544784
\(725\) −5.54495e12 −0.745379
\(726\) 1.57849e13 2.10876
\(727\) 3.05328e12 0.405380 0.202690 0.979243i \(-0.435032\pi\)
0.202690 + 0.979243i \(0.435032\pi\)
\(728\) 1.76268e12 0.232585
\(729\) 2.82430e11 0.0370370
\(730\) −6.39285e11 −0.0833185
\(731\) −7.78640e12 −1.00858
\(732\) 8.85703e12 1.14022
\(733\) −6.43109e12 −0.822842 −0.411421 0.911445i \(-0.634967\pi\)
−0.411421 + 0.911445i \(0.634967\pi\)
\(734\) 1.58724e13 2.01841
\(735\) −1.09330e12 −0.138181
\(736\) 5.76450e12 0.724122
\(737\) 9.36322e12 1.16902
\(738\) 8.55296e11 0.106136
\(739\) −4.53850e12 −0.559774 −0.279887 0.960033i \(-0.590297\pi\)
−0.279887 + 0.960033i \(0.590297\pi\)
\(740\) 2.47923e12 0.303931
\(741\) 5.93343e12 0.722977
\(742\) −5.99658e12 −0.726250
\(743\) 1.04874e13 1.26247 0.631234 0.775593i \(-0.282549\pi\)
0.631234 + 0.775593i \(0.282549\pi\)
\(744\) −2.90694e12 −0.347823
\(745\) 2.87401e12 0.341810
\(746\) −6.03999e12 −0.714021
\(747\) −5.47221e12 −0.643013
\(748\) −2.89597e13 −3.38249
\(749\) 4.48376e12 0.520564
\(750\) −4.17415e12 −0.481717
\(751\) 5.78172e12 0.663250 0.331625 0.943411i \(-0.392403\pi\)
0.331625 + 0.943411i \(0.392403\pi\)
\(752\) −3.58226e12 −0.408485
\(753\) 7.88721e11 0.0894017
\(754\) −1.03183e13 −1.16262
\(755\) −1.17136e11 −0.0131198
\(756\) −9.26013e11 −0.103103
\(757\) −1.49716e13 −1.65706 −0.828528 0.559948i \(-0.810821\pi\)
−0.828528 + 0.559948i \(0.810821\pi\)
\(758\) 8.36742e12 0.920619
\(759\) 5.50926e12 0.602567
\(760\) −2.34038e12 −0.254463
\(761\) −4.47071e12 −0.483221 −0.241611 0.970373i \(-0.577676\pi\)
−0.241611 + 0.970373i \(0.577676\pi\)
\(762\) −3.65052e12 −0.392245
\(763\) 1.07755e12 0.115100
\(764\) −1.95880e13 −2.08003
\(765\) 1.13530e12 0.119849
\(766\) −1.50373e13 −1.57812
\(767\) −1.15139e12 −0.120127
\(768\) −1.71781e12 −0.178176
\(769\) −1.16212e13 −1.19835 −0.599175 0.800618i \(-0.704505\pi\)
−0.599175 + 0.800618i \(0.704505\pi\)
\(770\) 2.89523e12 0.296807
\(771\) 1.08204e13 1.10281
\(772\) −1.71049e13 −1.73317
\(773\) 3.55448e12 0.358070 0.179035 0.983843i \(-0.442702\pi\)
0.179035 + 0.983843i \(0.442702\pi\)
\(774\) −4.05170e12 −0.405792
\(775\) 8.28417e12 0.824881
\(776\) −5.43297e12 −0.537848
\(777\) −1.67362e12 −0.164726
\(778\) −1.58646e13 −1.55246
\(779\) −2.84796e12 −0.277086
\(780\) −2.19472e12 −0.212302
\(781\) 4.14768e12 0.398910
\(782\) −1.20294e13 −1.15031
\(783\) 1.63542e12 0.155490
\(784\) 3.46889e12 0.327920
\(785\) 2.11507e12 0.198797
\(786\) 1.22578e13 1.14554
\(787\) 3.33602e12 0.309986 0.154993 0.987916i \(-0.450464\pi\)
0.154993 + 0.987916i \(0.450464\pi\)
\(788\) −2.69446e13 −2.48945
\(789\) 1.06503e13 0.978394
\(790\) 3.62575e12 0.331189
\(791\) 2.46919e12 0.224264
\(792\) −4.54644e12 −0.410590
\(793\) −1.41706e13 −1.27250
\(794\) −1.65951e13 −1.48180
\(795\) 2.25261e12 0.200002
\(796\) −1.09087e13 −0.963086
\(797\) −1.81568e13 −1.59396 −0.796979 0.604007i \(-0.793570\pi\)
−0.796979 + 0.604007i \(0.793570\pi\)
\(798\) 5.23658e12 0.457125
\(799\) 1.59463e13 1.38420
\(800\) 1.35567e13 1.17017
\(801\) 1.44023e12 0.123619
\(802\) −9.10042e11 −0.0776742
\(803\) 4.13520e12 0.350975
\(804\) −6.26416e12 −0.528701
\(805\) 7.08140e11 0.0594343
\(806\) 1.54156e13 1.28663
\(807\) 8.18126e12 0.679031
\(808\) 9.89041e12 0.816325
\(809\) −6.19366e12 −0.508369 −0.254184 0.967156i \(-0.581807\pi\)
−0.254184 + 0.967156i \(0.581807\pi\)
\(810\) 5.90763e11 0.0482204
\(811\) 1.44878e13 1.17600 0.588000 0.808861i \(-0.299915\pi\)
0.588000 + 0.808861i \(0.299915\pi\)
\(812\) −5.36212e12 −0.432847
\(813\) 6.16875e12 0.495211
\(814\) −2.72354e13 −2.17432
\(815\) −4.23404e12 −0.336160
\(816\) −3.60214e12 −0.284417
\(817\) 1.34913e13 1.05939
\(818\) −2.25062e13 −1.75757
\(819\) 1.48155e12 0.115064
\(820\) 1.05343e12 0.0813661
\(821\) −5.08820e12 −0.390859 −0.195429 0.980718i \(-0.562610\pi\)
−0.195429 + 0.980718i \(0.562610\pi\)
\(822\) −8.02314e12 −0.612945
\(823\) 1.62319e13 1.23330 0.616650 0.787237i \(-0.288489\pi\)
0.616650 + 0.787237i \(0.288489\pi\)
\(824\) −2.38850e12 −0.180490
\(825\) 1.29564e13 0.973737
\(826\) −1.01616e12 −0.0759544
\(827\) 1.70769e12 0.126950 0.0634752 0.997983i \(-0.479782\pi\)
0.0634752 + 0.997983i \(0.479782\pi\)
\(828\) −3.68579e12 −0.272518
\(829\) −7.13685e12 −0.524821 −0.262411 0.964956i \(-0.584517\pi\)
−0.262411 + 0.964956i \(0.584517\pi\)
\(830\) −1.14463e13 −0.837172
\(831\) 3.00537e12 0.218622
\(832\) 2.03643e13 1.47338
\(833\) −1.54417e13 −1.11120
\(834\) −1.68290e13 −1.20451
\(835\) 5.08062e12 0.361682
\(836\) 5.01778e13 3.55290
\(837\) −2.44332e12 −0.172074
\(838\) 1.55340e13 1.08814
\(839\) 2.19459e13 1.52906 0.764529 0.644590i \(-0.222972\pi\)
0.764529 + 0.644590i \(0.222972\pi\)
\(840\) −5.84382e11 −0.0404986
\(841\) −5.03719e12 −0.347221
\(842\) −3.00354e13 −2.05935
\(843\) −6.59637e12 −0.449864
\(844\) 3.44003e13 2.33357
\(845\) −6.12838e11 −0.0413514
\(846\) 8.29778e12 0.556923
\(847\) −1.31241e13 −0.876183
\(848\) −7.14718e12 −0.474628
\(849\) −2.45822e11 −0.0162382
\(850\) −2.82902e13 −1.85887
\(851\) −6.66146e12 −0.435398
\(852\) −2.77487e12 −0.180412
\(853\) −1.48939e13 −0.963249 −0.481624 0.876378i \(-0.659953\pi\)
−0.481624 + 0.876378i \(0.659953\pi\)
\(854\) −1.25063e13 −0.804580
\(855\) −1.96712e12 −0.125887
\(856\) −1.47277e13 −0.937568
\(857\) −1.35869e13 −0.860415 −0.430208 0.902730i \(-0.641560\pi\)
−0.430208 + 0.902730i \(0.641560\pi\)
\(858\) 2.41099e13 1.51881
\(859\) 7.93178e12 0.497052 0.248526 0.968625i \(-0.420054\pi\)
0.248526 + 0.968625i \(0.420054\pi\)
\(860\) −4.99030e12 −0.311088
\(861\) −7.11122e11 −0.0440991
\(862\) −2.18804e13 −1.34981
\(863\) 2.41151e13 1.47993 0.739963 0.672648i \(-0.234843\pi\)
0.739963 + 0.672648i \(0.234843\pi\)
\(864\) −3.99838e12 −0.244103
\(865\) 7.06521e12 0.429094
\(866\) 2.95420e13 1.78488
\(867\) 6.42925e12 0.386433
\(868\) 8.01101e12 0.479015
\(869\) −2.34531e13 −1.39512
\(870\) 3.42084e12 0.202440
\(871\) 1.00222e13 0.590039
\(872\) −3.53939e12 −0.207302
\(873\) −4.56648e12 −0.266083
\(874\) 2.08431e13 1.20826
\(875\) 3.47053e12 0.200152
\(876\) −2.76652e12 −0.158732
\(877\) 1.78340e13 1.01801 0.509005 0.860764i \(-0.330014\pi\)
0.509005 + 0.860764i \(0.330014\pi\)
\(878\) 2.70473e13 1.53603
\(879\) 1.01045e13 0.570904
\(880\) 3.45075e12 0.193973
\(881\) 1.07118e13 0.599059 0.299529 0.954087i \(-0.403170\pi\)
0.299529 + 0.954087i \(0.403170\pi\)
\(882\) −8.03517e12 −0.447082
\(883\) −6.53602e12 −0.361818 −0.180909 0.983500i \(-0.557904\pi\)
−0.180909 + 0.983500i \(0.557904\pi\)
\(884\) −3.09979e13 −1.70725
\(885\) 3.81720e11 0.0209171
\(886\) −4.59512e13 −2.50521
\(887\) −2.36595e13 −1.28336 −0.641681 0.766972i \(-0.721763\pi\)
−0.641681 + 0.766972i \(0.721763\pi\)
\(888\) 5.49728e12 0.296681
\(889\) 3.03516e12 0.162976
\(890\) 3.01256e12 0.160946
\(891\) −3.82134e12 −0.203126
\(892\) 7.96757e12 0.421390
\(893\) −2.76299e13 −1.45394
\(894\) 2.11224e13 1.10592
\(895\) −8.06612e12 −0.420205
\(896\) 8.81814e12 0.457079
\(897\) 5.89700e12 0.304134
\(898\) −5.41212e13 −2.77731
\(899\) −1.41481e13 −0.722405
\(900\) −8.66807e12 −0.440383
\(901\) 3.18155e13 1.60834
\(902\) −1.15724e13 −0.582094
\(903\) 3.36872e12 0.168605
\(904\) −8.11048e12 −0.403913
\(905\) −2.13635e12 −0.105865
\(906\) −8.60882e11 −0.0424489
\(907\) 2.65879e12 0.130452 0.0652261 0.997871i \(-0.479223\pi\)
0.0652261 + 0.997871i \(0.479223\pi\)
\(908\) −8.71181e12 −0.425326
\(909\) 8.31301e12 0.403851
\(910\) 3.09899e12 0.149808
\(911\) −1.64923e13 −0.793322 −0.396661 0.917965i \(-0.629831\pi\)
−0.396661 + 0.917965i \(0.629831\pi\)
\(912\) 6.24135e12 0.298746
\(913\) 7.40403e13 3.52655
\(914\) −1.67041e13 −0.791710
\(915\) 4.69799e12 0.221573
\(916\) −2.42953e13 −1.14023
\(917\) −1.01915e13 −0.475968
\(918\) 8.34385e12 0.387770
\(919\) 3.80293e12 0.175873 0.0879365 0.996126i \(-0.471973\pi\)
0.0879365 + 0.996126i \(0.471973\pi\)
\(920\) −2.32601e12 −0.107045
\(921\) −1.72795e13 −0.791338
\(922\) −1.96001e13 −0.893243
\(923\) 4.43959e12 0.201342
\(924\) 1.25292e13 0.565456
\(925\) −1.56661e13 −0.703595
\(926\) 3.54826e13 1.58586
\(927\) −2.00756e12 −0.0892916
\(928\) −2.31528e13 −1.02480
\(929\) −6.89689e12 −0.303796 −0.151898 0.988396i \(-0.548539\pi\)
−0.151898 + 0.988396i \(0.548539\pi\)
\(930\) −5.11074e12 −0.224032
\(931\) 2.67554e13 1.16718
\(932\) 5.37456e13 2.33330
\(933\) −2.53152e12 −0.109374
\(934\) 3.36626e13 1.44739
\(935\) −1.53609e13 −0.657303
\(936\) −4.86641e12 −0.207237
\(937\) 2.21460e13 0.938571 0.469286 0.883046i \(-0.344511\pi\)
0.469286 + 0.883046i \(0.344511\pi\)
\(938\) 8.84514e12 0.373071
\(939\) −1.41667e13 −0.594665
\(940\) 1.02200e13 0.426949
\(941\) 1.85240e13 0.770159 0.385080 0.922883i \(-0.374174\pi\)
0.385080 + 0.922883i \(0.374174\pi\)
\(942\) 1.55445e13 0.643204
\(943\) −2.83047e12 −0.116562
\(944\) −1.21114e12 −0.0496387
\(945\) −4.91181e11 −0.0200354
\(946\) 5.48205e13 2.22553
\(947\) 4.78860e13 1.93479 0.967394 0.253277i \(-0.0815083\pi\)
0.967394 + 0.253277i \(0.0815083\pi\)
\(948\) 1.56905e13 0.630957
\(949\) 4.42623e12 0.177148
\(950\) 4.90177e13 1.95253
\(951\) 1.05685e13 0.418988
\(952\) −8.25372e12 −0.325674
\(953\) −1.27910e13 −0.502327 −0.251163 0.967945i \(-0.580813\pi\)
−0.251163 + 0.967945i \(0.580813\pi\)
\(954\) 1.65554e13 0.647102
\(955\) −1.03900e13 −0.404202
\(956\) −3.23686e13 −1.25332
\(957\) −2.21276e13 −0.852768
\(958\) −5.51869e13 −2.11686
\(959\) 6.67071e12 0.254676
\(960\) −6.75139e12 −0.256550
\(961\) −5.30227e12 −0.200543
\(962\) −2.91522e13 −1.09745
\(963\) −1.23788e13 −0.463832
\(964\) −1.67373e13 −0.624220
\(965\) −9.07285e12 −0.336799
\(966\) 5.20443e12 0.192298
\(967\) 3.54914e13 1.30528 0.652640 0.757668i \(-0.273661\pi\)
0.652640 + 0.757668i \(0.273661\pi\)
\(968\) 4.31084e13 1.57806
\(969\) −2.77832e13 −1.01234
\(970\) −9.55179e12 −0.346427
\(971\) −1.76220e13 −0.636163 −0.318081 0.948063i \(-0.603039\pi\)
−0.318081 + 0.948063i \(0.603039\pi\)
\(972\) 2.55654e12 0.0918661
\(973\) 1.39922e13 0.500471
\(974\) −6.71116e13 −2.38936
\(975\) 1.38683e13 0.491475
\(976\) −1.49060e13 −0.525819
\(977\) −3.75917e13 −1.31998 −0.659988 0.751276i \(-0.729439\pi\)
−0.659988 + 0.751276i \(0.729439\pi\)
\(978\) −3.11178e13 −1.08764
\(979\) −1.94867e13 −0.677979
\(980\) −9.89657e12 −0.342742
\(981\) −2.97490e12 −0.102556
\(982\) −4.30560e13 −1.47752
\(983\) 4.15795e13 1.42033 0.710164 0.704037i \(-0.248621\pi\)
0.710164 + 0.704037i \(0.248621\pi\)
\(984\) 2.33580e12 0.0794252
\(985\) −1.42921e13 −0.483762
\(986\) 4.83154e13 1.62794
\(987\) −6.89906e12 −0.231400
\(988\) 5.37093e13 1.79326
\(989\) 1.34085e13 0.445652
\(990\) −7.99317e12 −0.264461
\(991\) 4.43558e11 0.0146089 0.00730447 0.999973i \(-0.497675\pi\)
0.00730447 + 0.999973i \(0.497675\pi\)
\(992\) 3.45903e13 1.13410
\(993\) 2.55517e13 0.833967
\(994\) 3.91818e12 0.127305
\(995\) −5.78626e12 −0.187152
\(996\) −4.95343e13 −1.59492
\(997\) 4.97398e13 1.59432 0.797161 0.603767i \(-0.206334\pi\)
0.797161 + 0.603767i \(0.206334\pi\)
\(998\) 2.43647e13 0.777454
\(999\) 4.62053e12 0.146773
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.a.1.19 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.19 21 1.1 even 1 trivial