Properties

Label 43.10.a.a.1.1
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.1465409550\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(40.4171\) of \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} +O(q^{10})\) \(q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} -11327.5 q^{10} -49756.6 q^{11} +138944. q^{12} +90530.0 q^{13} -45990.0 q^{14} +28825.8 q^{15} +735714. q^{16} +139514. q^{17} +340675. q^{18} -189921. q^{19} +343749. q^{20} +117034. q^{21} +2.11053e6 q^{22} -94945.1 q^{23} -3.54936e6 q^{24} -1.88181e6 q^{25} -3.84002e6 q^{26} -2.99156e6 q^{27} +1.39564e6 q^{28} -4.15457e6 q^{29} -1.22271e6 q^{30} +7.48504e6 q^{31} -1.43712e7 q^{32} -5.37082e6 q^{33} -5.91779e6 q^{34} +289544. q^{35} -1.03383e7 q^{36} +3.13035e6 q^{37} +8.05590e6 q^{38} +9.77197e6 q^{39} -8.78117e6 q^{40} -7.85257e6 q^{41} -4.96425e6 q^{42} -3.41880e6 q^{43} -6.40472e7 q^{44} -2.14482e6 q^{45} +4.02729e6 q^{46} -2.99064e7 q^{47} +7.94143e7 q^{48} -3.91780e7 q^{49} +7.98209e7 q^{50} +1.50594e7 q^{51} +1.16531e8 q^{52} +2.07014e7 q^{53} +1.26893e8 q^{54} -1.32875e7 q^{55} -3.56519e7 q^{56} -2.05004e7 q^{57} +1.76225e8 q^{58} -1.16826e8 q^{59} +3.71049e7 q^{60} -1.04732e8 q^{61} -3.17494e8 q^{62} -8.70808e6 q^{63} +2.32899e8 q^{64} +2.41760e7 q^{65} +2.27815e8 q^{66} -1.64575e8 q^{67} +1.79584e8 q^{68} -1.02485e7 q^{69} -1.22816e7 q^{70} -8.20184e7 q^{71} +2.64095e8 q^{72} -3.51380e8 q^{73} -1.32780e8 q^{74} -2.03126e8 q^{75} -2.44468e8 q^{76} -5.39478e7 q^{77} -4.14499e8 q^{78} +5.29284e8 q^{79} +1.96472e8 q^{80} -1.64829e8 q^{81} +3.33083e8 q^{82} -7.19804e8 q^{83} +1.50648e8 q^{84} +3.72572e7 q^{85} +1.45016e8 q^{86} -4.48452e8 q^{87} +1.63611e9 q^{88} +6.64822e8 q^{89} +9.09772e7 q^{90} +9.81556e7 q^{91} -1.22214e8 q^{92} +8.07950e8 q^{93} +1.26854e9 q^{94} -5.07183e7 q^{95} -1.55125e9 q^{96} +3.05873e8 q^{97} +1.66182e9 q^{98} +3.99623e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.4171 −1.87459 −0.937294 0.348539i \(-0.886678\pi\)
−0.937294 + 0.348539i \(0.886678\pi\)
\(3\) 107.942 0.769386 0.384693 0.923045i \(-0.374307\pi\)
0.384693 + 0.923045i \(0.374307\pi\)
\(4\) 1287.21 2.51408
\(5\) 267.050 0.191085 0.0955426 0.995425i \(-0.469541\pi\)
0.0955426 + 0.995425i \(0.469541\pi\)
\(6\) −4578.58 −1.44228
\(7\) 1084.23 0.170680 0.0853398 0.996352i \(-0.472802\pi\)
0.0853398 + 0.996352i \(0.472802\pi\)
\(8\) −32882.2 −2.83828
\(9\) −8031.56 −0.408045
\(10\) −11327.5 −0.358206
\(11\) −49756.6 −1.02467 −0.512335 0.858786i \(-0.671219\pi\)
−0.512335 + 0.858786i \(0.671219\pi\)
\(12\) 138944. 1.93430
\(13\) 90530.0 0.879118 0.439559 0.898214i \(-0.355135\pi\)
0.439559 + 0.898214i \(0.355135\pi\)
\(14\) −45990.0 −0.319954
\(15\) 28825.8 0.147018
\(16\) 735714. 2.80653
\(17\) 139514. 0.405134 0.202567 0.979268i \(-0.435072\pi\)
0.202567 + 0.979268i \(0.435072\pi\)
\(18\) 340675. 0.764917
\(19\) −189921. −0.334335 −0.167168 0.985929i \(-0.553462\pi\)
−0.167168 + 0.985929i \(0.553462\pi\)
\(20\) 343749. 0.480404
\(21\) 117034. 0.131318
\(22\) 2.11053e6 1.92083
\(23\) −94945.1 −0.0707452 −0.0353726 0.999374i \(-0.511262\pi\)
−0.0353726 + 0.999374i \(0.511262\pi\)
\(24\) −3.54936e6 −2.18373
\(25\) −1.88181e6 −0.963486
\(26\) −3.84002e6 −1.64798
\(27\) −2.99156e6 −1.08333
\(28\) 1.39564e6 0.429103
\(29\) −4.15457e6 −1.09077 −0.545387 0.838184i \(-0.683617\pi\)
−0.545387 + 0.838184i \(0.683617\pi\)
\(30\) −1.22271e6 −0.275599
\(31\) 7.48504e6 1.45568 0.727841 0.685745i \(-0.240524\pi\)
0.727841 + 0.685745i \(0.240524\pi\)
\(32\) −1.43712e7 −2.42280
\(33\) −5.37082e6 −0.788367
\(34\) −5.91779e6 −0.759460
\(35\) 289544. 0.0326143
\(36\) −1.03383e7 −1.02586
\(37\) 3.13035e6 0.274590 0.137295 0.990530i \(-0.456159\pi\)
0.137295 + 0.990530i \(0.456159\pi\)
\(38\) 8.05590e6 0.626741
\(39\) 9.77197e6 0.676381
\(40\) −8.78117e6 −0.542353
\(41\) −7.85257e6 −0.433995 −0.216997 0.976172i \(-0.569626\pi\)
−0.216997 + 0.976172i \(0.569626\pi\)
\(42\) −4.96425e6 −0.246168
\(43\) −3.41880e6 −0.152499
\(44\) −6.40472e7 −2.57610
\(45\) −2.14482e6 −0.0779714
\(46\) 4.02729e6 0.132618
\(47\) −2.99064e7 −0.893973 −0.446986 0.894541i \(-0.647503\pi\)
−0.446986 + 0.894541i \(0.647503\pi\)
\(48\) 7.94143e7 2.15930
\(49\) −3.91780e7 −0.970868
\(50\) 7.98209e7 1.80614
\(51\) 1.50594e7 0.311704
\(52\) 1.16531e8 2.21017
\(53\) 2.07014e7 0.360378 0.180189 0.983632i \(-0.442329\pi\)
0.180189 + 0.983632i \(0.442329\pi\)
\(54\) 1.26893e8 2.03080
\(55\) −1.32875e7 −0.195799
\(56\) −3.56519e7 −0.484437
\(57\) −2.05004e7 −0.257233
\(58\) 1.76225e8 2.04475
\(59\) −1.16826e8 −1.25518 −0.627590 0.778544i \(-0.715959\pi\)
−0.627590 + 0.778544i \(0.715959\pi\)
\(60\) 3.71049e7 0.369616
\(61\) −1.04732e8 −0.968486 −0.484243 0.874934i \(-0.660905\pi\)
−0.484243 + 0.874934i \(0.660905\pi\)
\(62\) −3.17494e8 −2.72881
\(63\) −8.70808e6 −0.0696450
\(64\) 2.32899e8 1.73523
\(65\) 2.41760e7 0.167986
\(66\) 2.27815e8 1.47786
\(67\) −1.64575e8 −0.997764 −0.498882 0.866670i \(-0.666256\pi\)
−0.498882 + 0.866670i \(0.666256\pi\)
\(68\) 1.79584e8 1.01854
\(69\) −1.02485e7 −0.0544304
\(70\) −1.22816e7 −0.0611385
\(71\) −8.20184e7 −0.383044 −0.191522 0.981488i \(-0.561342\pi\)
−0.191522 + 0.981488i \(0.561342\pi\)
\(72\) 2.64095e8 1.15815
\(73\) −3.51380e8 −1.44819 −0.724093 0.689702i \(-0.757741\pi\)
−0.724093 + 0.689702i \(0.757741\pi\)
\(74\) −1.32780e8 −0.514744
\(75\) −2.03126e8 −0.741293
\(76\) −2.44468e8 −0.840546
\(77\) −5.39478e7 −0.174890
\(78\) −4.14499e8 −1.26794
\(79\) 5.29284e8 1.52886 0.764428 0.644709i \(-0.223022\pi\)
0.764428 + 0.644709i \(0.223022\pi\)
\(80\) 1.96472e8 0.536285
\(81\) −1.64829e8 −0.425454
\(82\) 3.33083e8 0.813561
\(83\) −7.19804e8 −1.66480 −0.832402 0.554172i \(-0.813035\pi\)
−0.832402 + 0.554172i \(0.813035\pi\)
\(84\) 1.50648e8 0.330145
\(85\) 3.72572e7 0.0774151
\(86\) 1.45016e8 0.285872
\(87\) −4.48452e8 −0.839226
\(88\) 1.63611e9 2.90830
\(89\) 6.64822e8 1.12318 0.561591 0.827415i \(-0.310189\pi\)
0.561591 + 0.827415i \(0.310189\pi\)
\(90\) 9.09772e7 0.146164
\(91\) 9.81556e7 0.150048
\(92\) −1.22214e8 −0.177859
\(93\) 8.07950e8 1.11998
\(94\) 1.26854e9 1.67583
\(95\) −5.07183e7 −0.0638865
\(96\) −1.55125e9 −1.86407
\(97\) 3.05873e8 0.350807 0.175403 0.984497i \(-0.443877\pi\)
0.175403 + 0.984497i \(0.443877\pi\)
\(98\) 1.66182e9 1.81998
\(99\) 3.99623e8 0.418112
\(100\) −2.42228e9 −2.42228
\(101\) −1.49507e9 −1.42960 −0.714800 0.699328i \(-0.753482\pi\)
−0.714800 + 0.699328i \(0.753482\pi\)
\(102\) −6.38778e8 −0.584317
\(103\) 8.69690e8 0.761372 0.380686 0.924704i \(-0.375688\pi\)
0.380686 + 0.924704i \(0.375688\pi\)
\(104\) −2.97682e9 −2.49518
\(105\) 3.12539e7 0.0250930
\(106\) −8.78094e8 −0.675561
\(107\) −1.70820e9 −1.25983 −0.629915 0.776664i \(-0.716910\pi\)
−0.629915 + 0.776664i \(0.716910\pi\)
\(108\) −3.85077e9 −2.72358
\(109\) 1.88987e9 1.28237 0.641183 0.767388i \(-0.278444\pi\)
0.641183 + 0.767388i \(0.278444\pi\)
\(110\) 5.63617e8 0.367043
\(111\) 3.37896e8 0.211266
\(112\) 7.97686e8 0.479017
\(113\) −1.37931e9 −0.795809 −0.397904 0.917427i \(-0.630262\pi\)
−0.397904 + 0.917427i \(0.630262\pi\)
\(114\) 8.69569e8 0.482205
\(115\) −2.53550e7 −0.0135184
\(116\) −5.34780e9 −2.74230
\(117\) −7.27096e8 −0.358720
\(118\) 4.95543e9 2.35295
\(119\) 1.51266e8 0.0691481
\(120\) −9.47855e8 −0.417279
\(121\) 1.17776e8 0.0499485
\(122\) 4.44241e9 1.81551
\(123\) −8.47621e8 −0.333909
\(124\) 9.63482e9 3.65971
\(125\) −1.02412e9 −0.375193
\(126\) 3.69372e8 0.130556
\(127\) −2.53906e9 −0.866078 −0.433039 0.901375i \(-0.642559\pi\)
−0.433039 + 0.901375i \(0.642559\pi\)
\(128\) −2.52083e9 −0.830039
\(129\) −3.69032e8 −0.117330
\(130\) −1.02548e9 −0.314905
\(131\) 3.77650e9 1.12039 0.560195 0.828361i \(-0.310726\pi\)
0.560195 + 0.828361i \(0.310726\pi\)
\(132\) −6.91338e9 −1.98202
\(133\) −2.05919e8 −0.0570642
\(134\) 6.98080e9 1.87040
\(135\) −7.98895e8 −0.207008
\(136\) −4.58753e9 −1.14988
\(137\) −1.89296e9 −0.459091 −0.229545 0.973298i \(-0.573724\pi\)
−0.229545 + 0.973298i \(0.573724\pi\)
\(138\) 4.34714e8 0.102035
\(139\) 4.91789e9 1.11741 0.558705 0.829367i \(-0.311298\pi\)
0.558705 + 0.829367i \(0.311298\pi\)
\(140\) 3.72704e8 0.0819951
\(141\) −3.22816e9 −0.687810
\(142\) 3.47898e9 0.718050
\(143\) −4.50447e9 −0.900806
\(144\) −5.90893e9 −1.14519
\(145\) −1.10948e9 −0.208431
\(146\) 1.49045e10 2.71475
\(147\) −4.22895e9 −0.746973
\(148\) 4.02942e9 0.690343
\(149\) 1.00447e10 1.66955 0.834773 0.550594i \(-0.185599\pi\)
0.834773 + 0.550594i \(0.185599\pi\)
\(150\) 8.61602e9 1.38962
\(151\) 6.32434e8 0.0989963 0.0494981 0.998774i \(-0.484238\pi\)
0.0494981 + 0.998774i \(0.484238\pi\)
\(152\) 6.24501e9 0.948937
\(153\) −1.12052e9 −0.165313
\(154\) 2.28831e9 0.327847
\(155\) 1.99888e9 0.278159
\(156\) 1.25786e10 1.70048
\(157\) 2.92391e9 0.384075 0.192037 0.981388i \(-0.438490\pi\)
0.192037 + 0.981388i \(0.438490\pi\)
\(158\) −2.24507e10 −2.86598
\(159\) 2.23455e9 0.277270
\(160\) −3.83782e9 −0.462961
\(161\) −1.02943e8 −0.0120748
\(162\) 6.99159e9 0.797550
\(163\) −1.56060e10 −1.73160 −0.865800 0.500389i \(-0.833190\pi\)
−0.865800 + 0.500389i \(0.833190\pi\)
\(164\) −1.01079e10 −1.09110
\(165\) −1.43428e9 −0.150645
\(166\) 3.05320e10 3.12082
\(167\) 1.67291e10 1.66436 0.832182 0.554502i \(-0.187091\pi\)
0.832182 + 0.554502i \(0.187091\pi\)
\(168\) −3.84834e9 −0.372719
\(169\) −2.40883e9 −0.227151
\(170\) −1.58034e9 −0.145121
\(171\) 1.52536e9 0.136424
\(172\) −4.40071e9 −0.383394
\(173\) 1.01069e10 0.857847 0.428924 0.903341i \(-0.358893\pi\)
0.428924 + 0.903341i \(0.358893\pi\)
\(174\) 1.90220e10 1.57320
\(175\) −2.04032e9 −0.164447
\(176\) −3.66067e10 −2.87576
\(177\) −1.26104e10 −0.965718
\(178\) −2.81998e10 −2.10551
\(179\) −1.86270e10 −1.35614 −0.678068 0.734999i \(-0.737183\pi\)
−0.678068 + 0.734999i \(0.737183\pi\)
\(180\) −2.76084e9 −0.196027
\(181\) −1.34573e10 −0.931978 −0.465989 0.884791i \(-0.654301\pi\)
−0.465989 + 0.884791i \(0.654301\pi\)
\(182\) −4.16348e9 −0.281277
\(183\) −1.13049e10 −0.745140
\(184\) 3.12200e9 0.200795
\(185\) 8.35959e8 0.0524701
\(186\) −3.42709e10 −2.09951
\(187\) −6.94176e9 −0.415129
\(188\) −3.84959e10 −2.24752
\(189\) −3.24355e9 −0.184902
\(190\) 2.15132e9 0.119761
\(191\) −2.59444e10 −1.41056 −0.705282 0.708926i \(-0.749180\pi\)
−0.705282 + 0.708926i \(0.749180\pi\)
\(192\) 2.51395e10 1.33506
\(193\) 3.54739e10 1.84035 0.920176 0.391505i \(-0.128045\pi\)
0.920176 + 0.391505i \(0.128045\pi\)
\(194\) −1.29742e10 −0.657618
\(195\) 2.60960e9 0.129246
\(196\) −5.04304e10 −2.44084
\(197\) 1.96576e10 0.929894 0.464947 0.885339i \(-0.346073\pi\)
0.464947 + 0.885339i \(0.346073\pi\)
\(198\) −1.69509e10 −0.783788
\(199\) 1.91082e10 0.863737 0.431869 0.901937i \(-0.357854\pi\)
0.431869 + 0.901937i \(0.357854\pi\)
\(200\) 6.18780e10 2.73465
\(201\) −1.77646e10 −0.767666
\(202\) 6.34164e10 2.67991
\(203\) −4.50452e9 −0.186173
\(204\) 1.93847e10 0.783650
\(205\) −2.09702e9 −0.0829299
\(206\) −3.68897e10 −1.42726
\(207\) 7.62557e8 0.0288673
\(208\) 6.66042e10 2.46727
\(209\) 9.44983e9 0.342583
\(210\) −1.32570e9 −0.0470391
\(211\) −2.94149e9 −0.102164 −0.0510818 0.998694i \(-0.516267\pi\)
−0.0510818 + 0.998694i \(0.516267\pi\)
\(212\) 2.66471e10 0.906020
\(213\) −8.85322e9 −0.294709
\(214\) 7.24570e10 2.36166
\(215\) −9.12989e8 −0.0291402
\(216\) 9.83690e10 3.07480
\(217\) 8.11554e9 0.248455
\(218\) −8.01627e10 −2.40391
\(219\) −3.79286e10 −1.11421
\(220\) −1.71038e10 −0.492255
\(221\) 1.26302e10 0.356161
\(222\) −1.43326e10 −0.396037
\(223\) −4.30635e7 −0.00116610 −0.000583052 1.00000i \(-0.500186\pi\)
−0.000583052 1.00000i \(0.500186\pi\)
\(224\) −1.55817e10 −0.413523
\(225\) 1.51139e10 0.393146
\(226\) 5.85063e10 1.49181
\(227\) −5.87731e10 −1.46914 −0.734569 0.678534i \(-0.762615\pi\)
−0.734569 + 0.678534i \(0.762615\pi\)
\(228\) −2.63884e10 −0.646704
\(229\) −4.67848e9 −0.112420 −0.0562101 0.998419i \(-0.517902\pi\)
−0.0562101 + 0.998419i \(0.517902\pi\)
\(230\) 1.07549e9 0.0253414
\(231\) −5.82323e9 −0.134558
\(232\) 1.36611e11 3.09592
\(233\) −6.22080e10 −1.38275 −0.691377 0.722494i \(-0.742996\pi\)
−0.691377 + 0.722494i \(0.742996\pi\)
\(234\) 3.08413e10 0.672452
\(235\) −7.98650e9 −0.170825
\(236\) −1.50380e11 −3.15563
\(237\) 5.71318e10 1.17628
\(238\) −6.41627e9 −0.129624
\(239\) 8.17154e10 1.61999 0.809997 0.586434i \(-0.199469\pi\)
0.809997 + 0.586434i \(0.199469\pi\)
\(240\) 2.12076e10 0.412610
\(241\) −7.26673e9 −0.138759 −0.0693796 0.997590i \(-0.522102\pi\)
−0.0693796 + 0.997590i \(0.522102\pi\)
\(242\) −4.99571e9 −0.0936328
\(243\) 4.10909e10 0.755992
\(244\) −1.34812e11 −2.43485
\(245\) −1.04625e10 −0.185519
\(246\) 3.59536e10 0.625942
\(247\) −1.71935e10 −0.293920
\(248\) −2.46124e11 −4.13164
\(249\) −7.76970e10 −1.28088
\(250\) 4.34401e10 0.703333
\(251\) 6.85052e10 1.08941 0.544706 0.838627i \(-0.316641\pi\)
0.544706 + 0.838627i \(0.316641\pi\)
\(252\) −1.12091e10 −0.175093
\(253\) 4.72415e9 0.0724905
\(254\) 1.07700e11 1.62354
\(255\) 4.02162e9 0.0595621
\(256\) −1.23178e10 −0.179247
\(257\) 1.40768e10 0.201281 0.100641 0.994923i \(-0.467911\pi\)
0.100641 + 0.994923i \(0.467911\pi\)
\(258\) 1.56533e10 0.219946
\(259\) 3.39403e9 0.0468670
\(260\) 3.11196e10 0.422332
\(261\) 3.33676e10 0.445085
\(262\) −1.60188e11 −2.10027
\(263\) 4.75236e10 0.612503 0.306252 0.951951i \(-0.400925\pi\)
0.306252 + 0.951951i \(0.400925\pi\)
\(264\) 1.76604e11 2.23761
\(265\) 5.52830e9 0.0688629
\(266\) 8.73448e9 0.106972
\(267\) 7.17621e10 0.864161
\(268\) −2.11843e11 −2.50846
\(269\) 3.74937e10 0.436589 0.218294 0.975883i \(-0.429951\pi\)
0.218294 + 0.975883i \(0.429951\pi\)
\(270\) 3.38868e10 0.388055
\(271\) 9.32440e10 1.05017 0.525084 0.851050i \(-0.324034\pi\)
0.525084 + 0.851050i \(0.324034\pi\)
\(272\) 1.02643e11 1.13702
\(273\) 1.05951e10 0.115444
\(274\) 8.02938e10 0.860606
\(275\) 9.36325e10 0.987256
\(276\) −1.31920e10 −0.136842
\(277\) −1.14756e11 −1.17116 −0.585582 0.810614i \(-0.699134\pi\)
−0.585582 + 0.810614i \(0.699134\pi\)
\(278\) −2.08603e11 −2.09468
\(279\) −6.01166e10 −0.593985
\(280\) −9.52084e9 −0.0925686
\(281\) 1.15044e11 1.10074 0.550372 0.834920i \(-0.314486\pi\)
0.550372 + 0.834920i \(0.314486\pi\)
\(282\) 1.36929e11 1.28936
\(283\) −3.96421e10 −0.367382 −0.183691 0.982984i \(-0.558805\pi\)
−0.183691 + 0.982984i \(0.558805\pi\)
\(284\) −1.05575e11 −0.963004
\(285\) −5.47463e9 −0.0491533
\(286\) 1.91066e11 1.68864
\(287\) −8.51402e9 −0.0740740
\(288\) 1.15423e11 0.988613
\(289\) −9.91236e10 −0.835866
\(290\) 4.70607e10 0.390722
\(291\) 3.30164e10 0.269906
\(292\) −4.52300e11 −3.64086
\(293\) 1.46620e11 1.16222 0.581109 0.813825i \(-0.302619\pi\)
0.581109 + 0.813825i \(0.302619\pi\)
\(294\) 1.79380e11 1.40027
\(295\) −3.11984e10 −0.239846
\(296\) −1.02933e11 −0.779364
\(297\) 1.48850e11 1.11006
\(298\) −4.26067e11 −3.12971
\(299\) −8.59537e9 −0.0621934
\(300\) −2.61466e11 −1.86367
\(301\) −3.70678e9 −0.0260284
\(302\) −2.68260e10 −0.185577
\(303\) −1.61380e11 −1.09991
\(304\) −1.39728e11 −0.938320
\(305\) −2.79685e10 −0.185063
\(306\) 4.75291e10 0.309894
\(307\) 2.04547e11 1.31423 0.657114 0.753792i \(-0.271777\pi\)
0.657114 + 0.753792i \(0.271777\pi\)
\(308\) −6.94422e10 −0.439688
\(309\) 9.38760e10 0.585789
\(310\) −8.47866e10 −0.521434
\(311\) 2.05452e11 1.24534 0.622671 0.782483i \(-0.286047\pi\)
0.622671 + 0.782483i \(0.286047\pi\)
\(312\) −3.21323e11 −1.91976
\(313\) 2.06361e11 1.21528 0.607642 0.794211i \(-0.292116\pi\)
0.607642 + 0.794211i \(0.292116\pi\)
\(314\) −1.24024e11 −0.719982
\(315\) −2.32549e9 −0.0133081
\(316\) 6.81299e11 3.84367
\(317\) −2.13970e10 −0.119011 −0.0595053 0.998228i \(-0.518952\pi\)
−0.0595053 + 0.998228i \(0.518952\pi\)
\(318\) −9.47831e10 −0.519767
\(319\) 2.06717e11 1.11768
\(320\) 6.21955e10 0.331577
\(321\) −1.84386e11 −0.969296
\(322\) 4.36653e9 0.0226352
\(323\) −2.64967e10 −0.135450
\(324\) −2.12170e11 −1.06963
\(325\) −1.70360e11 −0.847018
\(326\) 6.61962e11 3.24604
\(327\) 2.03996e11 0.986634
\(328\) 2.58209e11 1.23180
\(329\) −3.24256e10 −0.152583
\(330\) 6.08378e10 0.282398
\(331\) 1.60601e11 0.735396 0.367698 0.929945i \(-0.380146\pi\)
0.367698 + 0.929945i \(0.380146\pi\)
\(332\) −9.26539e11 −4.18545
\(333\) −2.51416e10 −0.112045
\(334\) −7.09600e11 −3.12000
\(335\) −4.39498e10 −0.190658
\(336\) 8.61037e10 0.368549
\(337\) −3.08563e11 −1.30320 −0.651598 0.758564i \(-0.725901\pi\)
−0.651598 + 0.758564i \(0.725901\pi\)
\(338\) 1.02175e11 0.425815
\(339\) −1.48885e11 −0.612284
\(340\) 4.79579e10 0.194628
\(341\) −3.72431e11 −1.49159
\(342\) −6.47014e10 −0.255739
\(343\) −8.62309e10 −0.336387
\(344\) 1.12418e11 0.432834
\(345\) −2.73687e9 −0.0104008
\(346\) −4.28705e11 −1.60811
\(347\) 1.34264e11 0.497138 0.248569 0.968614i \(-0.420040\pi\)
0.248569 + 0.968614i \(0.420040\pi\)
\(348\) −5.77251e11 −2.10988
\(349\) 2.70503e11 0.976016 0.488008 0.872839i \(-0.337724\pi\)
0.488008 + 0.872839i \(0.337724\pi\)
\(350\) 8.65445e10 0.308271
\(351\) −2.70826e11 −0.952375
\(352\) 7.15062e11 2.48257
\(353\) 1.67866e10 0.0575408 0.0287704 0.999586i \(-0.490841\pi\)
0.0287704 + 0.999586i \(0.490841\pi\)
\(354\) 5.34898e11 1.81032
\(355\) −2.19030e10 −0.0731940
\(356\) 8.55766e11 2.82377
\(357\) 1.63279e10 0.0532016
\(358\) 7.90102e11 2.54220
\(359\) 4.80875e11 1.52794 0.763972 0.645250i \(-0.223247\pi\)
0.763972 + 0.645250i \(0.223247\pi\)
\(360\) 7.05264e10 0.221305
\(361\) −2.86618e11 −0.888220
\(362\) 5.70821e11 1.74707
\(363\) 1.27129e10 0.0384296
\(364\) 1.26347e11 0.377232
\(365\) −9.38359e10 −0.276727
\(366\) 4.79522e11 1.39683
\(367\) −5.91797e11 −1.70285 −0.851424 0.524479i \(-0.824260\pi\)
−0.851424 + 0.524479i \(0.824260\pi\)
\(368\) −6.98524e10 −0.198548
\(369\) 6.30683e10 0.177089
\(370\) −3.54589e10 −0.0983599
\(371\) 2.24452e10 0.0615092
\(372\) 1.04000e12 2.81573
\(373\) −5.20908e11 −1.39338 −0.696692 0.717370i \(-0.745346\pi\)
−0.696692 + 0.717370i \(0.745346\pi\)
\(374\) 2.94450e11 0.778195
\(375\) −1.10545e11 −0.288668
\(376\) 9.83388e11 2.53735
\(377\) −3.76113e11 −0.958919
\(378\) 1.37582e11 0.346616
\(379\) −9.96613e10 −0.248113 −0.124057 0.992275i \(-0.539590\pi\)
−0.124057 + 0.992275i \(0.539590\pi\)
\(380\) −6.52852e10 −0.160616
\(381\) −2.74071e11 −0.666348
\(382\) 1.10049e12 2.64423
\(383\) −3.57401e11 −0.848714 −0.424357 0.905495i \(-0.639500\pi\)
−0.424357 + 0.905495i \(0.639500\pi\)
\(384\) −2.72103e11 −0.638621
\(385\) −1.44067e10 −0.0334189
\(386\) −1.50470e12 −3.44990
\(387\) 2.74583e10 0.0622263
\(388\) 3.93722e11 0.881956
\(389\) −4.67526e11 −1.03522 −0.517610 0.855617i \(-0.673178\pi\)
−0.517610 + 0.855617i \(0.673178\pi\)
\(390\) −1.10692e11 −0.242284
\(391\) −1.32462e10 −0.0286613
\(392\) 1.28826e12 2.75560
\(393\) 4.07643e11 0.862012
\(394\) −8.33820e11 −1.74317
\(395\) 1.41345e11 0.292142
\(396\) 5.14399e11 1.05117
\(397\) −9.97116e10 −0.201460 −0.100730 0.994914i \(-0.532118\pi\)
−0.100730 + 0.994914i \(0.532118\pi\)
\(398\) −8.10516e11 −1.61915
\(399\) −2.22273e10 −0.0439044
\(400\) −1.38447e12 −2.70405
\(401\) −4.32588e11 −0.835459 −0.417729 0.908572i \(-0.637174\pi\)
−0.417729 + 0.908572i \(0.637174\pi\)
\(402\) 7.53521e11 1.43906
\(403\) 6.77621e11 1.27972
\(404\) −1.92447e12 −3.59413
\(405\) −4.40176e10 −0.0812979
\(406\) 1.91069e11 0.348998
\(407\) −1.55756e11 −0.281364
\(408\) −4.95187e11 −0.884705
\(409\) −8.08953e11 −1.42945 −0.714724 0.699406i \(-0.753448\pi\)
−0.714724 + 0.699406i \(0.753448\pi\)
\(410\) 8.89497e10 0.155459
\(411\) −2.04329e11 −0.353218
\(412\) 1.11947e12 1.91415
\(413\) −1.26667e11 −0.214234
\(414\) −3.23454e10 −0.0541142
\(415\) −1.92223e11 −0.318119
\(416\) −1.30102e12 −2.12993
\(417\) 5.30846e11 0.859719
\(418\) −4.00835e11 −0.642202
\(419\) 7.28742e11 1.15508 0.577538 0.816364i \(-0.304014\pi\)
0.577538 + 0.816364i \(0.304014\pi\)
\(420\) 4.02304e10 0.0630859
\(421\) −6.26279e11 −0.971625 −0.485812 0.874063i \(-0.661476\pi\)
−0.485812 + 0.874063i \(0.661476\pi\)
\(422\) 1.24769e11 0.191515
\(423\) 2.40195e11 0.364781
\(424\) −6.80707e11 −1.02285
\(425\) −2.62539e11 −0.390341
\(426\) 3.75528e11 0.552457
\(427\) −1.13553e11 −0.165301
\(428\) −2.19881e12 −3.16732
\(429\) −4.86220e11 −0.693067
\(430\) 3.87264e10 0.0546259
\(431\) 9.36909e11 1.30782 0.653912 0.756570i \(-0.273127\pi\)
0.653912 + 0.756570i \(0.273127\pi\)
\(432\) −2.20093e12 −3.04039
\(433\) −2.08675e11 −0.285282 −0.142641 0.989774i \(-0.545560\pi\)
−0.142641 + 0.989774i \(0.545560\pi\)
\(434\) −3.44237e11 −0.465752
\(435\) −1.19759e11 −0.160364
\(436\) 2.43266e12 3.22397
\(437\) 1.80321e10 0.0236526
\(438\) 1.60882e12 2.08869
\(439\) 4.01235e10 0.0515594 0.0257797 0.999668i \(-0.491793\pi\)
0.0257797 + 0.999668i \(0.491793\pi\)
\(440\) 4.36921e11 0.555733
\(441\) 3.14661e11 0.396158
\(442\) −5.35738e11 −0.667655
\(443\) −4.49679e11 −0.554735 −0.277367 0.960764i \(-0.589462\pi\)
−0.277367 + 0.960764i \(0.589462\pi\)
\(444\) 4.34943e11 0.531140
\(445\) 1.77540e11 0.214624
\(446\) 1.82663e9 0.00218597
\(447\) 1.08424e12 1.28453
\(448\) 2.52516e11 0.296168
\(449\) 2.85367e11 0.331357 0.165678 0.986180i \(-0.447019\pi\)
0.165678 + 0.986180i \(0.447019\pi\)
\(450\) −6.41086e11 −0.736987
\(451\) 3.90717e11 0.444701
\(452\) −1.77546e12 −2.00073
\(453\) 6.82661e10 0.0761663
\(454\) 2.49299e12 2.75403
\(455\) 2.62124e10 0.0286719
\(456\) 6.74098e11 0.730099
\(457\) 3.04646e11 0.326718 0.163359 0.986567i \(-0.447767\pi\)
0.163359 + 0.986567i \(0.447767\pi\)
\(458\) 1.98447e11 0.210742
\(459\) −4.17366e11 −0.438894
\(460\) −3.26373e10 −0.0339863
\(461\) 6.14100e11 0.633265 0.316632 0.948548i \(-0.397448\pi\)
0.316632 + 0.948548i \(0.397448\pi\)
\(462\) 2.47004e11 0.252241
\(463\) −1.91905e11 −0.194076 −0.0970382 0.995281i \(-0.530937\pi\)
−0.0970382 + 0.995281i \(0.530937\pi\)
\(464\) −3.05657e12 −3.06129
\(465\) 2.15763e11 0.214012
\(466\) 2.63868e12 2.59209
\(467\) 3.82929e11 0.372556 0.186278 0.982497i \(-0.440357\pi\)
0.186278 + 0.982497i \(0.440357\pi\)
\(468\) −9.35926e11 −0.901852
\(469\) −1.78438e11 −0.170298
\(470\) 3.38764e11 0.320226
\(471\) 3.15613e11 0.295502
\(472\) 3.84150e12 3.56255
\(473\) 1.70108e11 0.156261
\(474\) −2.42337e12 −2.20504
\(475\) 3.57395e11 0.322127
\(476\) 1.94711e11 0.173844
\(477\) −1.66265e11 −0.147051
\(478\) −3.46613e12 −3.03682
\(479\) −1.69714e11 −0.147302 −0.0736510 0.997284i \(-0.523465\pi\)
−0.0736510 + 0.997284i \(0.523465\pi\)
\(480\) −4.14261e11 −0.356196
\(481\) 2.83391e11 0.241397
\(482\) 3.08233e11 0.260117
\(483\) −1.11118e10 −0.00929016
\(484\) 1.51602e11 0.125575
\(485\) 8.16831e10 0.0670339
\(486\) −1.74296e12 −1.41717
\(487\) 2.46356e11 0.198465 0.0992324 0.995064i \(-0.468361\pi\)
0.0992324 + 0.995064i \(0.468361\pi\)
\(488\) 3.44380e12 2.74884
\(489\) −1.68454e12 −1.33227
\(490\) 4.43788e11 0.347771
\(491\) 1.01928e12 0.791458 0.395729 0.918367i \(-0.370492\pi\)
0.395729 + 0.918367i \(0.370492\pi\)
\(492\) −1.09107e12 −0.839475
\(493\) −5.79622e11 −0.441910
\(494\) 7.29300e11 0.550979
\(495\) 1.06719e11 0.0798950
\(496\) 5.50685e12 4.08541
\(497\) −8.89271e10 −0.0653778
\(498\) 3.29568e12 2.40112
\(499\) 1.06244e12 0.767101 0.383550 0.923520i \(-0.374701\pi\)
0.383550 + 0.923520i \(0.374701\pi\)
\(500\) −1.31825e12 −0.943266
\(501\) 1.80577e12 1.28054
\(502\) −2.90579e12 −2.04220
\(503\) −2.56713e12 −1.78810 −0.894051 0.447965i \(-0.852149\pi\)
−0.894051 + 0.447965i \(0.852149\pi\)
\(504\) 2.86341e11 0.197672
\(505\) −3.99257e11 −0.273175
\(506\) −2.00385e11 −0.135890
\(507\) −2.60013e11 −0.174767
\(508\) −3.26831e12 −2.17739
\(509\) 2.54412e12 1.67999 0.839997 0.542590i \(-0.182556\pi\)
0.839997 + 0.542590i \(0.182556\pi\)
\(510\) −1.70585e11 −0.111654
\(511\) −3.80978e11 −0.247176
\(512\) 1.81315e12 1.16605
\(513\) 5.68160e11 0.362195
\(514\) −5.97095e11 −0.377320
\(515\) 2.32250e11 0.145487
\(516\) −4.75021e11 −0.294978
\(517\) 1.48804e12 0.916027
\(518\) −1.43965e11 −0.0878563
\(519\) 1.09096e12 0.660015
\(520\) −7.94959e11 −0.476793
\(521\) −1.73418e12 −1.03116 −0.515579 0.856842i \(-0.672423\pi\)
−0.515579 + 0.856842i \(0.672423\pi\)
\(522\) −1.41536e12 −0.834352
\(523\) 1.03596e12 0.605457 0.302729 0.953077i \(-0.402102\pi\)
0.302729 + 0.953077i \(0.402102\pi\)
\(524\) 4.86115e12 2.81675
\(525\) −2.20236e11 −0.126524
\(526\) −2.01581e12 −1.14819
\(527\) 1.04427e12 0.589747
\(528\) −3.95139e12 −2.21257
\(529\) −1.79214e12 −0.994995
\(530\) −2.34495e11 −0.129090
\(531\) 9.38296e11 0.512170
\(532\) −2.65061e11 −0.143464
\(533\) −7.10892e11 −0.381532
\(534\) −3.04394e12 −1.61995
\(535\) −4.56175e11 −0.240735
\(536\) 5.41159e12 2.83194
\(537\) −2.01063e12 −1.04339
\(538\) −1.59037e12 −0.818424
\(539\) 1.94937e12 0.994820
\(540\) −1.02835e12 −0.520436
\(541\) −2.94842e12 −1.47980 −0.739898 0.672719i \(-0.765126\pi\)
−0.739898 + 0.672719i \(0.765126\pi\)
\(542\) −3.95514e12 −1.96863
\(543\) −1.45261e12 −0.717050
\(544\) −2.00499e12 −0.981559
\(545\) 5.04688e11 0.245041
\(546\) −4.49413e11 −0.216411
\(547\) 2.32179e12 1.10887 0.554435 0.832227i \(-0.312935\pi\)
0.554435 + 0.832227i \(0.312935\pi\)
\(548\) −2.43663e12 −1.15419
\(549\) 8.41158e11 0.395186
\(550\) −3.97162e12 −1.85070
\(551\) 7.89040e11 0.364684
\(552\) 3.36994e11 0.154489
\(553\) 5.73867e11 0.260944
\(554\) 4.86763e12 2.19545
\(555\) 9.02350e10 0.0403698
\(556\) 6.33036e12 2.80926
\(557\) 2.16532e12 0.953176 0.476588 0.879127i \(-0.341873\pi\)
0.476588 + 0.879127i \(0.341873\pi\)
\(558\) 2.54997e12 1.11348
\(559\) −3.09504e11 −0.134064
\(560\) 2.13022e11 0.0915330
\(561\) −7.49307e11 −0.319394
\(562\) −4.87984e12 −2.06344
\(563\) −1.91225e12 −0.802154 −0.401077 0.916044i \(-0.631364\pi\)
−0.401077 + 0.916044i \(0.631364\pi\)
\(564\) −4.15531e12 −1.72921
\(565\) −3.68344e11 −0.152067
\(566\) 1.68150e12 0.688690
\(567\) −1.78714e11 −0.0726163
\(568\) 2.69694e12 1.08719
\(569\) 2.85153e12 1.14044 0.570220 0.821492i \(-0.306858\pi\)
0.570220 + 0.821492i \(0.306858\pi\)
\(570\) 2.32218e11 0.0921423
\(571\) −2.16577e12 −0.852608 −0.426304 0.904580i \(-0.640185\pi\)
−0.426304 + 0.904580i \(0.640185\pi\)
\(572\) −5.79819e12 −2.26470
\(573\) −2.80048e12 −1.08527
\(574\) 3.61140e11 0.138858
\(575\) 1.78669e11 0.0681621
\(576\) −1.87054e12 −0.708052
\(577\) −2.81611e12 −1.05769 −0.528845 0.848718i \(-0.677375\pi\)
−0.528845 + 0.848718i \(0.677375\pi\)
\(578\) 4.20454e12 1.56691
\(579\) 3.82912e12 1.41594
\(580\) −1.42813e12 −0.524012
\(581\) −7.80436e11 −0.284148
\(582\) −1.40046e12 −0.505962
\(583\) −1.03003e12 −0.369269
\(584\) 1.15541e13 4.11036
\(585\) −1.94171e11 −0.0685461
\(586\) −6.21918e12 −2.17868
\(587\) −1.61735e12 −0.562255 −0.281128 0.959670i \(-0.590708\pi\)
−0.281128 + 0.959670i \(0.590708\pi\)
\(588\) −5.44355e12 −1.87795
\(589\) −1.42157e12 −0.486686
\(590\) 1.32334e12 0.449613
\(591\) 2.12188e12 0.715447
\(592\) 2.30304e12 0.770645
\(593\) 2.81752e12 0.935665 0.467833 0.883817i \(-0.345035\pi\)
0.467833 + 0.883817i \(0.345035\pi\)
\(594\) −6.31379e12 −2.08090
\(595\) 4.03956e10 0.0132132
\(596\) 1.29296e13 4.19738
\(597\) 2.06258e12 0.664547
\(598\) 3.64591e11 0.116587
\(599\) 1.84733e12 0.586305 0.293152 0.956066i \(-0.405296\pi\)
0.293152 + 0.956066i \(0.405296\pi\)
\(600\) 6.67922e12 2.10400
\(601\) 1.93095e12 0.603720 0.301860 0.953352i \(-0.402392\pi\)
0.301860 + 0.953352i \(0.402392\pi\)
\(602\) 1.57231e11 0.0487925
\(603\) 1.32180e12 0.407133
\(604\) 8.14075e11 0.248885
\(605\) 3.14520e10 0.00954441
\(606\) 6.84529e12 2.06189
\(607\) 2.77322e12 0.829155 0.414578 0.910014i \(-0.363929\pi\)
0.414578 + 0.910014i \(0.363929\pi\)
\(608\) 2.72939e12 0.810027
\(609\) −4.86226e11 −0.143239
\(610\) 1.18634e12 0.346918
\(611\) −2.70743e12 −0.785908
\(612\) −1.44234e12 −0.415611
\(613\) −6.12373e12 −1.75164 −0.875819 0.482640i \(-0.839678\pi\)
−0.875819 + 0.482640i \(0.839678\pi\)
\(614\) −8.67629e12 −2.46364
\(615\) −2.26357e11 −0.0638051
\(616\) 1.77392e12 0.496388
\(617\) −5.57842e12 −1.54963 −0.774815 0.632188i \(-0.782157\pi\)
−0.774815 + 0.632188i \(0.782157\pi\)
\(618\) −3.98195e12 −1.09811
\(619\) −1.98413e12 −0.543203 −0.271602 0.962410i \(-0.587553\pi\)
−0.271602 + 0.962410i \(0.587553\pi\)
\(620\) 2.57298e12 0.699315
\(621\) 2.84034e11 0.0766404
\(622\) −8.71468e12 −2.33451
\(623\) 7.20822e11 0.191704
\(624\) 7.18938e12 1.89828
\(625\) 3.40192e12 0.891793
\(626\) −8.75322e12 −2.27816
\(627\) 1.02003e12 0.263579
\(628\) 3.76369e12 0.965596
\(629\) 4.36729e11 0.111246
\(630\) 9.86405e10 0.0249473
\(631\) −5.57032e12 −1.39878 −0.699388 0.714743i \(-0.746544\pi\)
−0.699388 + 0.714743i \(0.746544\pi\)
\(632\) −1.74040e13 −4.33932
\(633\) −3.17510e11 −0.0786033
\(634\) 9.07598e11 0.223096
\(635\) −6.78056e11 −0.165495
\(636\) 2.87633e12 0.697079
\(637\) −3.54679e12 −0.853508
\(638\) −8.76835e12 −2.09520
\(639\) 6.58735e11 0.156299
\(640\) −6.73187e11 −0.158608
\(641\) −5.38235e12 −1.25925 −0.629623 0.776901i \(-0.716791\pi\)
−0.629623 + 0.776901i \(0.716791\pi\)
\(642\) 7.82114e12 1.81703
\(643\) 7.27179e11 0.167761 0.0838807 0.996476i \(-0.473269\pi\)
0.0838807 + 0.996476i \(0.473269\pi\)
\(644\) −1.32509e11 −0.0303570
\(645\) −9.85498e10 −0.0224201
\(646\) 1.12391e12 0.253914
\(647\) 1.81068e12 0.406231 0.203116 0.979155i \(-0.434893\pi\)
0.203116 + 0.979155i \(0.434893\pi\)
\(648\) 5.41995e12 1.20756
\(649\) 5.81288e12 1.28615
\(650\) 7.22618e12 1.58781
\(651\) 8.76006e11 0.191158
\(652\) −2.00882e13 −4.35339
\(653\) −3.82339e12 −0.822886 −0.411443 0.911435i \(-0.634975\pi\)
−0.411443 + 0.911435i \(0.634975\pi\)
\(654\) −8.65291e12 −1.84953
\(655\) 1.00851e12 0.214090
\(656\) −5.77724e12 −1.21802
\(657\) 2.82213e12 0.590926
\(658\) 1.37540e12 0.286030
\(659\) 3.40517e12 0.703323 0.351661 0.936127i \(-0.385617\pi\)
0.351661 + 0.936127i \(0.385617\pi\)
\(660\) −1.84621e12 −0.378734
\(661\) 1.30545e12 0.265982 0.132991 0.991117i \(-0.457542\pi\)
0.132991 + 0.991117i \(0.457542\pi\)
\(662\) −6.81221e12 −1.37857
\(663\) 1.36333e12 0.274025
\(664\) 2.36687e13 4.72518
\(665\) −5.49905e10 −0.0109041
\(666\) 1.06643e12 0.210039
\(667\) 3.94456e11 0.0771671
\(668\) 2.15339e13 4.18435
\(669\) −4.64836e9 −0.000897185 0
\(670\) 1.86422e12 0.357405
\(671\) 5.21109e12 0.992379
\(672\) −1.68192e12 −0.318159
\(673\) −1.13952e12 −0.214119 −0.107059 0.994253i \(-0.534143\pi\)
−0.107059 + 0.994253i \(0.534143\pi\)
\(674\) 1.30884e13 2.44296
\(675\) 5.62955e12 1.04377
\(676\) −3.10067e12 −0.571077
\(677\) −2.85019e12 −0.521464 −0.260732 0.965411i \(-0.583964\pi\)
−0.260732 + 0.965411i \(0.583964\pi\)
\(678\) 6.31528e12 1.14778
\(679\) 3.31637e11 0.0598755
\(680\) −1.22510e12 −0.219726
\(681\) −6.34408e12 −1.13033
\(682\) 1.57974e13 2.79613
\(683\) 6.16518e12 1.08406 0.542029 0.840360i \(-0.317656\pi\)
0.542029 + 0.840360i \(0.317656\pi\)
\(684\) 1.96346e12 0.342981
\(685\) −5.05514e11 −0.0877254
\(686\) 3.65766e12 0.630587
\(687\) −5.05003e11 −0.0864946
\(688\) −2.51526e12 −0.427991
\(689\) 1.87410e12 0.316815
\(690\) 1.16090e11 0.0194973
\(691\) 9.71088e12 1.62034 0.810172 0.586192i \(-0.199374\pi\)
0.810172 + 0.586192i \(0.199374\pi\)
\(692\) 1.30097e13 2.15670
\(693\) 4.33285e11 0.0713632
\(694\) −5.69509e12 −0.931929
\(695\) 1.31332e12 0.213520
\(696\) 1.47461e13 2.38196
\(697\) −1.09555e12 −0.175826
\(698\) −1.14739e13 −1.82963
\(699\) −6.71485e12 −1.06387
\(700\) −2.62632e12 −0.413435
\(701\) 3.33352e12 0.521402 0.260701 0.965420i \(-0.416046\pi\)
0.260701 + 0.965420i \(0.416046\pi\)
\(702\) 1.14876e13 1.78531
\(703\) −5.94520e11 −0.0918052
\(704\) −1.15882e13 −1.77804
\(705\) −8.62078e11 −0.131430
\(706\) −7.12037e11 −0.107865
\(707\) −1.62100e12 −0.244004
\(708\) −1.62323e13 −2.42789
\(709\) −6.12092e12 −0.909723 −0.454861 0.890562i \(-0.650311\pi\)
−0.454861 + 0.890562i \(0.650311\pi\)
\(710\) 9.29061e11 0.137209
\(711\) −4.25097e12 −0.623842
\(712\) −2.18608e13 −3.18791
\(713\) −7.10668e11 −0.102983
\(714\) −6.92584e11 −0.0997311
\(715\) −1.20292e12 −0.172131
\(716\) −2.39768e13 −3.40944
\(717\) 8.82051e12 1.24640
\(718\) −2.03973e13 −2.86427
\(719\) 2.16423e12 0.302012 0.151006 0.988533i \(-0.451749\pi\)
0.151006 + 0.988533i \(0.451749\pi\)
\(720\) −1.57798e12 −0.218829
\(721\) 9.42947e11 0.129951
\(722\) 1.21575e13 1.66505
\(723\) −7.84384e11 −0.106759
\(724\) −1.73224e13 −2.34307
\(725\) 7.81810e12 1.05095
\(726\) −5.39246e11 −0.0720398
\(727\) 1.22681e13 1.62882 0.814412 0.580287i \(-0.197060\pi\)
0.814412 + 0.580287i \(0.197060\pi\)
\(728\) −3.22757e12 −0.425877
\(729\) 7.67976e12 1.00710
\(730\) 3.98025e12 0.518749
\(731\) −4.76972e11 −0.0617824
\(732\) −1.45518e13 −1.87334
\(733\) −1.22993e13 −1.57367 −0.786833 0.617166i \(-0.788281\pi\)
−0.786833 + 0.617166i \(0.788281\pi\)
\(734\) 2.51023e13 3.19214
\(735\) −1.12934e12 −0.142735
\(736\) 1.36447e12 0.171402
\(737\) 8.18871e12 1.02238
\(738\) −2.67518e12 −0.331970
\(739\) 2.39881e12 0.295867 0.147933 0.988997i \(-0.452738\pi\)
0.147933 + 0.988997i \(0.452738\pi\)
\(740\) 1.07605e12 0.131914
\(741\) −1.85590e12 −0.226138
\(742\) −9.52059e11 −0.115304
\(743\) −9.39278e12 −1.13069 −0.565346 0.824854i \(-0.691258\pi\)
−0.565346 + 0.824854i \(0.691258\pi\)
\(744\) −2.65671e13 −3.17882
\(745\) 2.68243e12 0.319026
\(746\) 2.20954e13 2.61202
\(747\) 5.78115e12 0.679316
\(748\) −8.93551e12 −1.04367
\(749\) −1.85209e12 −0.215027
\(750\) 4.68900e12 0.541134
\(751\) −1.66561e13 −1.91070 −0.955352 0.295469i \(-0.904524\pi\)
−0.955352 + 0.295469i \(0.904524\pi\)
\(752\) −2.20026e13 −2.50896
\(753\) 7.39458e12 0.838178
\(754\) 1.59536e13 1.79758
\(755\) 1.68891e11 0.0189167
\(756\) −4.17513e12 −0.464860
\(757\) −1.58067e13 −1.74949 −0.874743 0.484587i \(-0.838970\pi\)
−0.874743 + 0.484587i \(0.838970\pi\)
\(758\) 4.22734e12 0.465111
\(759\) 5.09933e11 0.0557732
\(760\) 1.66773e12 0.181328
\(761\) −1.76096e13 −1.90335 −0.951673 0.307112i \(-0.900637\pi\)
−0.951673 + 0.307112i \(0.900637\pi\)
\(762\) 1.16253e13 1.24913
\(763\) 2.04906e12 0.218874
\(764\) −3.33959e13 −3.54628
\(765\) −2.99234e11 −0.0315889
\(766\) 1.51599e13 1.59099
\(767\) −1.05763e13 −1.10345
\(768\) −1.32960e12 −0.137910
\(769\) −1.26882e13 −1.30838 −0.654188 0.756332i \(-0.726989\pi\)
−0.654188 + 0.756332i \(0.726989\pi\)
\(770\) 6.11092e11 0.0626467
\(771\) 1.51947e12 0.154863
\(772\) 4.56623e13 4.62680
\(773\) 1.57233e12 0.158393 0.0791965 0.996859i \(-0.474765\pi\)
0.0791965 + 0.996859i \(0.474765\pi\)
\(774\) −1.16470e12 −0.116649
\(775\) −1.40854e13 −1.40253
\(776\) −1.00577e13 −0.995687
\(777\) 3.66358e11 0.0360588
\(778\) 1.98311e13 1.94061
\(779\) 1.49137e12 0.145100
\(780\) 3.35910e12 0.324936
\(781\) 4.08096e12 0.392494
\(782\) 5.61865e11 0.0537281
\(783\) 1.24286e13 1.18167
\(784\) −2.88238e13 −2.72477
\(785\) 7.80830e11 0.0733910
\(786\) −1.72910e13 −1.61592
\(787\) −7.00350e12 −0.650772 −0.325386 0.945581i \(-0.605494\pi\)
−0.325386 + 0.945581i \(0.605494\pi\)
\(788\) 2.53035e13 2.33783
\(789\) 5.12978e12 0.471251
\(790\) −5.99544e12 −0.547645
\(791\) −1.49549e12 −0.135828
\(792\) −1.31405e13 −1.18672
\(793\) −9.48135e12 −0.851414
\(794\) 4.22948e12 0.377654
\(795\) 5.96735e11 0.0529822
\(796\) 2.45963e13 2.17151
\(797\) 6.34176e12 0.556734 0.278367 0.960475i \(-0.410207\pi\)
0.278367 + 0.960475i \(0.410207\pi\)
\(798\) 9.42816e11 0.0823026
\(799\) −4.17238e12 −0.362179
\(800\) 2.70438e13 2.33434
\(801\) −5.33956e12 −0.458309
\(802\) 1.83491e13 1.56614
\(803\) 1.74835e13 1.48391
\(804\) −2.28667e13 −1.92997
\(805\) −2.74908e10 −0.00230731
\(806\) −2.87427e13 −2.39894
\(807\) 4.04713e12 0.335905
\(808\) 4.91611e13 4.05761
\(809\) −1.84767e13 −1.51654 −0.758272 0.651938i \(-0.773956\pi\)
−0.758272 + 0.651938i \(0.773956\pi\)
\(810\) 1.86710e12 0.152400
\(811\) 9.90436e12 0.803956 0.401978 0.915649i \(-0.368323\pi\)
0.401978 + 0.915649i \(0.368323\pi\)
\(812\) −5.79826e12 −0.468054
\(813\) 1.00649e13 0.807985
\(814\) 6.60671e12 0.527443
\(815\) −4.16758e12 −0.330883
\(816\) 1.10794e13 0.874807
\(817\) 6.49302e11 0.0509856
\(818\) 3.43135e13 2.67963
\(819\) −7.88342e11 −0.0612262
\(820\) −2.69931e12 −0.208493
\(821\) −6.67366e12 −0.512649 −0.256324 0.966591i \(-0.582512\pi\)
−0.256324 + 0.966591i \(0.582512\pi\)
\(822\) 8.66706e12 0.662138
\(823\) −1.21283e13 −0.921512 −0.460756 0.887527i \(-0.652422\pi\)
−0.460756 + 0.887527i \(0.652422\pi\)
\(824\) −2.85973e13 −2.16099
\(825\) 1.01069e13 0.759581
\(826\) 5.37284e12 0.401600
\(827\) −1.18283e13 −0.879318 −0.439659 0.898165i \(-0.644901\pi\)
−0.439659 + 0.898165i \(0.644901\pi\)
\(828\) 9.81571e11 0.0725747
\(829\) 7.07948e12 0.520602 0.260301 0.965527i \(-0.416178\pi\)
0.260301 + 0.965527i \(0.416178\pi\)
\(830\) 8.15356e12 0.596343
\(831\) −1.23870e13 −0.901076
\(832\) 2.10843e13 1.52547
\(833\) −5.46590e12 −0.393332
\(834\) −2.25170e13 −1.61162
\(835\) 4.46750e12 0.318035
\(836\) 1.21639e13 0.861282
\(837\) −2.23920e13 −1.57699
\(838\) −3.09111e13 −2.16529
\(839\) −2.29506e12 −0.159906 −0.0799532 0.996799i \(-0.525477\pi\)
−0.0799532 + 0.996799i \(0.525477\pi\)
\(840\) −1.02770e12 −0.0712210
\(841\) 2.75328e12 0.189788
\(842\) 2.65649e13 1.82140
\(843\) 1.24181e13 0.846897
\(844\) −3.78632e12 −0.256848
\(845\) −6.43276e11 −0.0434053
\(846\) −1.01884e13 −0.683815
\(847\) 1.27697e11 0.00852519
\(848\) 1.52303e13 1.01141
\(849\) −4.27904e12 −0.282659
\(850\) 1.11362e13 0.731729
\(851\) −2.97211e11 −0.0194260
\(852\) −1.13960e13 −0.740922
\(853\) 1.07725e13 0.696700 0.348350 0.937365i \(-0.386742\pi\)
0.348350 + 0.937365i \(0.386742\pi\)
\(854\) 4.81661e12 0.309871
\(855\) 4.07347e11 0.0260686
\(856\) 5.61694e13 3.57575
\(857\) 1.70306e13 1.07849 0.539246 0.842148i \(-0.318709\pi\)
0.539246 + 0.842148i \(0.318709\pi\)
\(858\) 2.06241e13 1.29922
\(859\) 1.68432e13 1.05549 0.527747 0.849402i \(-0.323037\pi\)
0.527747 + 0.849402i \(0.323037\pi\)
\(860\) −1.17521e12 −0.0732609
\(861\) −9.19019e11 −0.0569915
\(862\) −3.97409e13 −2.45163
\(863\) 2.85773e13 1.75377 0.876886 0.480699i \(-0.159617\pi\)
0.876886 + 0.480699i \(0.159617\pi\)
\(864\) 4.29923e13 2.62469
\(865\) 2.69904e12 0.163922
\(866\) 8.85139e12 0.534787
\(867\) −1.06996e13 −0.643104
\(868\) 1.04464e13 0.624637
\(869\) −2.63354e13 −1.56657
\(870\) 5.07982e12 0.300616
\(871\) −1.48990e13 −0.877153
\(872\) −6.21429e13 −3.63971
\(873\) −2.45663e12 −0.143145
\(874\) −7.64868e11 −0.0443389
\(875\) −1.11038e12 −0.0640378
\(876\) −4.88221e13 −2.80123
\(877\) −1.62714e12 −0.0928807 −0.0464404 0.998921i \(-0.514788\pi\)
−0.0464404 + 0.998921i \(0.514788\pi\)
\(878\) −1.70192e12 −0.0966527
\(879\) 1.58264e13 0.894195
\(880\) −9.77579e12 −0.549516
\(881\) 9.31457e12 0.520920 0.260460 0.965485i \(-0.416126\pi\)
0.260460 + 0.965485i \(0.416126\pi\)
\(882\) −1.33470e13 −0.742634
\(883\) −1.11738e12 −0.0618553 −0.0309277 0.999522i \(-0.509846\pi\)
−0.0309277 + 0.999522i \(0.509846\pi\)
\(884\) 1.62578e13 0.895417
\(885\) −3.36761e12 −0.184534
\(886\) 1.90741e13 1.03990
\(887\) −1.85575e13 −1.00661 −0.503307 0.864108i \(-0.667884\pi\)
−0.503307 + 0.864108i \(0.667884\pi\)
\(888\) −1.11107e13 −0.599632
\(889\) −2.75294e12 −0.147822
\(890\) −7.53075e12 −0.402331
\(891\) 8.20136e12 0.435950
\(892\) −5.54318e10 −0.00293168
\(893\) 5.67986e12 0.298886
\(894\) −4.59904e13 −2.40796
\(895\) −4.97432e12 −0.259138
\(896\) −2.73317e12 −0.141671
\(897\) −9.27800e11 −0.0478507
\(898\) −1.21045e13 −0.621158
\(899\) −3.10971e13 −1.58782
\(900\) 1.94547e13 0.988402
\(901\) 2.88814e12 0.146001
\(902\) −1.65731e13 −0.833632
\(903\) −4.00117e11 −0.0200259
\(904\) 4.53547e13 2.25873
\(905\) −3.59378e12 −0.178087
\(906\) −2.89565e12 −0.142781
\(907\) −1.49318e13 −0.732620 −0.366310 0.930493i \(-0.619379\pi\)
−0.366310 + 0.930493i \(0.619379\pi\)
\(908\) −7.56533e13 −3.69353
\(909\) 1.20077e13 0.583342
\(910\) −1.11185e12 −0.0537479
\(911\) −2.77113e13 −1.33298 −0.666490 0.745514i \(-0.732204\pi\)
−0.666490 + 0.745514i \(0.732204\pi\)
\(912\) −1.50825e13 −0.721930
\(913\) 3.58151e13 1.70587
\(914\) −1.29222e13 −0.612462
\(915\) −3.01897e12 −0.142385
\(916\) −6.02218e12 −0.282634
\(917\) 4.09461e12 0.191228
\(918\) 1.77034e13 0.822745
\(919\) 2.32626e13 1.07582 0.537909 0.843003i \(-0.319214\pi\)
0.537909 + 0.843003i \(0.319214\pi\)
\(920\) 8.33728e11 0.0383689
\(921\) 2.20792e13 1.01115
\(922\) −2.60484e13 −1.18711
\(923\) −7.42512e12 −0.336741
\(924\) −7.49572e12 −0.338290
\(925\) −5.89072e12 −0.264564
\(926\) 8.14007e12 0.363813
\(927\) −6.98497e12 −0.310674
\(928\) 5.97061e13 2.64273
\(929\) −2.61747e13 −1.15295 −0.576476 0.817114i \(-0.695572\pi\)
−0.576476 + 0.817114i \(0.695572\pi\)
\(930\) −9.15202e12 −0.401184
\(931\) 7.44074e12 0.324595
\(932\) −8.00748e13 −3.47636
\(933\) 2.21769e13 0.958149
\(934\) −1.62427e13 −0.698390
\(935\) −1.85380e12 −0.0793249
\(936\) 2.39085e13 1.01815
\(937\) 1.82019e12 0.0771417 0.0385709 0.999256i \(-0.487719\pi\)
0.0385709 + 0.999256i \(0.487719\pi\)
\(938\) 7.56882e12 0.319239
\(939\) 2.22750e13 0.935022
\(940\) −1.02803e13 −0.429468
\(941\) 3.78437e13 1.57340 0.786702 0.617332i \(-0.211787\pi\)
0.786702 + 0.617332i \(0.211787\pi\)
\(942\) −1.33874e13 −0.553944
\(943\) 7.45562e11 0.0307030
\(944\) −8.59507e13 −3.52270
\(945\) −8.66189e11 −0.0353321
\(946\) −7.21549e12 −0.292925
\(947\) 1.25246e13 0.506045 0.253022 0.967460i \(-0.418575\pi\)
0.253022 + 0.967460i \(0.418575\pi\)
\(948\) 7.35407e13 2.95726
\(949\) −3.18104e13 −1.27313
\(950\) −1.51597e13 −0.603856
\(951\) −2.30963e12 −0.0915652
\(952\) −4.97396e12 −0.196262
\(953\) 6.72806e12 0.264224 0.132112 0.991235i \(-0.457824\pi\)
0.132112 + 0.991235i \(0.457824\pi\)
\(954\) 7.05246e12 0.275659
\(955\) −6.92844e12 −0.269538
\(956\) 1.05185e14 4.07280
\(957\) 2.23135e13 0.859930
\(958\) 7.19879e12 0.276131
\(959\) −2.05241e12 −0.0783574
\(960\) 6.71349e12 0.255110
\(961\) 2.95863e13 1.11901
\(962\) −1.20206e13 −0.452521
\(963\) 1.37195e13 0.514068
\(964\) −9.35380e12 −0.348852
\(965\) 9.47329e12 0.351664
\(966\) 4.71331e11 0.0174152
\(967\) 4.50859e13 1.65814 0.829071 0.559143i \(-0.188870\pi\)
0.829071 + 0.559143i \(0.188870\pi\)
\(968\) −3.87272e12 −0.141768
\(969\) −2.86010e12 −0.104214
\(970\) −3.46476e12 −0.125661
\(971\) 6.75879e12 0.243996 0.121998 0.992530i \(-0.461070\pi\)
0.121998 + 0.992530i \(0.461070\pi\)
\(972\) 5.28926e13 1.90063
\(973\) 5.33214e12 0.190719
\(974\) −1.04497e13 −0.372040
\(975\) −1.83890e13 −0.651684
\(976\) −7.70525e13 −2.71808
\(977\) 2.58525e13 0.907772 0.453886 0.891060i \(-0.350037\pi\)
0.453886 + 0.891060i \(0.350037\pi\)
\(978\) 7.14534e13 2.49746
\(979\) −3.30793e13 −1.15089
\(980\) −1.34674e13 −0.466409
\(981\) −1.51786e13 −0.523263
\(982\) −4.32350e13 −1.48366
\(983\) 1.85340e13 0.633109 0.316554 0.948574i \(-0.397474\pi\)
0.316554 + 0.948574i \(0.397474\pi\)
\(984\) 2.78716e13 0.947728
\(985\) 5.24957e12 0.177689
\(986\) 2.45859e13 0.828399
\(987\) −3.50007e12 −0.117395
\(988\) −2.21317e13 −0.738939
\(989\) 3.24598e11 0.0107885
\(990\) −4.52672e12 −0.149770
\(991\) −4.66998e12 −0.153809 −0.0769047 0.997038i \(-0.524504\pi\)
−0.0769047 + 0.997038i \(0.524504\pi\)
\(992\) −1.07569e14 −3.52683
\(993\) 1.73355e13 0.565803
\(994\) 3.77203e12 0.122556
\(995\) 5.10285e12 0.165047
\(996\) −1.00012e14 −3.22023
\(997\) 3.66040e13 1.17328 0.586639 0.809849i \(-0.300451\pi\)
0.586639 + 0.809849i \(0.300451\pi\)
\(998\) −4.50657e13 −1.43800
\(999\) −9.36463e12 −0.297472
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 43.10.a.a.1.1 15
3.2 odd 2 387.10.a.c.1.15 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.1 15 1.1 even 1 trivial
387.10.a.c.1.15 15 3.2 odd 2