Properties

Label 177.14.a.a.1.19
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +O(q^{10})\) \(q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +1.94915e6 q^{10} +1.22717e6 q^{11} -5.23020e6 q^{12} -6.08798e6 q^{13} -7.55091e6 q^{14} +4.45454e7 q^{15} +4.31377e7 q^{16} +1.15524e8 q^{17} +1.69522e7 q^{18} -2.61499e8 q^{19} -4.38395e8 q^{20} -1.72566e8 q^{21} +3.91448e7 q^{22} -1.17829e9 q^{23} -3.57333e8 q^{24} +2.51309e9 q^{25} -1.94198e8 q^{26} +3.87420e8 q^{27} +1.69832e9 q^{28} -1.96230e8 q^{29} +1.42093e9 q^{30} +1.49325e9 q^{31} +5.39149e9 q^{32} +8.94604e8 q^{33} +3.68506e9 q^{34} -1.44645e10 q^{35} -3.81281e9 q^{36} +1.48696e10 q^{37} -8.34144e9 q^{38} -4.43814e9 q^{39} -2.99516e10 q^{40} -1.03207e10 q^{41} -5.50461e9 q^{42} -3.86482e10 q^{43} -8.80428e9 q^{44} +3.24736e10 q^{45} -3.75857e10 q^{46} -1.59891e10 q^{47} +3.14474e10 q^{48} -4.08543e10 q^{49} +8.01640e10 q^{50} +8.42173e10 q^{51} +4.36781e10 q^{52} -3.65459e10 q^{53} +1.23581e10 q^{54} +7.49857e10 q^{55} +1.16031e11 q^{56} -1.90633e11 q^{57} -6.25946e9 q^{58} +4.21805e10 q^{59} -3.19590e11 q^{60} -7.27065e11 q^{61} +4.76325e10 q^{62} -1.25801e11 q^{63} -1.81404e11 q^{64} -3.72005e11 q^{65} +2.85365e10 q^{66} +2.38478e11 q^{67} -8.28828e11 q^{68} -8.58973e11 q^{69} -4.61397e11 q^{70} -4.31528e11 q^{71} -2.60495e11 q^{72} -8.74060e11 q^{73} +4.74317e11 q^{74} +1.83205e12 q^{75} +1.87612e12 q^{76} -2.90491e11 q^{77} -1.41570e11 q^{78} +1.86554e12 q^{79} +2.63592e12 q^{80} +2.82430e11 q^{81} -3.29215e11 q^{82} +2.77153e11 q^{83} +1.23807e12 q^{84} +7.05910e12 q^{85} -1.23282e12 q^{86} -1.43052e11 q^{87} -6.01518e11 q^{88} -1.37556e12 q^{89} +1.03586e12 q^{90} +1.44113e12 q^{91} +8.45362e12 q^{92} +1.08858e12 q^{93} -5.10030e11 q^{94} -1.59789e13 q^{95} +3.93039e12 q^{96} +6.08837e12 q^{97} -1.30319e12 q^{98} +6.52166e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.8985 0.352432 0.176216 0.984352i \(-0.443614\pi\)
0.176216 + 0.984352i \(0.443614\pi\)
\(3\) 729.000 0.577350
\(4\) −7174.48 −0.875792
\(5\) 61104.8 1.74892 0.874461 0.485096i \(-0.161215\pi\)
0.874461 + 0.485096i \(0.161215\pi\)
\(6\) 23254.0 0.203477
\(7\) −236717. −0.760486 −0.380243 0.924887i \(-0.624160\pi\)
−0.380243 + 0.924887i \(0.624160\pi\)
\(8\) −490168. −0.661089
\(9\) 531441. 0.333333
\(10\) 1.94915e6 0.616376
\(11\) 1.22717e6 0.208858 0.104429 0.994532i \(-0.466699\pi\)
0.104429 + 0.994532i \(0.466699\pi\)
\(12\) −5.23020e6 −0.505638
\(13\) −6.08798e6 −0.349818 −0.174909 0.984585i \(-0.555963\pi\)
−0.174909 + 0.984585i \(0.555963\pi\)
\(14\) −7.55091e6 −0.268020
\(15\) 4.45454e7 1.00974
\(16\) 4.31377e7 0.642802
\(17\) 1.15524e8 1.16080 0.580398 0.814333i \(-0.302897\pi\)
0.580398 + 0.814333i \(0.302897\pi\)
\(18\) 1.69522e7 0.117477
\(19\) −2.61499e8 −1.27518 −0.637591 0.770375i \(-0.720069\pi\)
−0.637591 + 0.770375i \(0.720069\pi\)
\(20\) −4.38395e8 −1.53169
\(21\) −1.72566e8 −0.439067
\(22\) 3.91448e7 0.0736082
\(23\) −1.17829e9 −1.65967 −0.829834 0.558010i \(-0.811565\pi\)
−0.829834 + 0.558010i \(0.811565\pi\)
\(24\) −3.57333e8 −0.381680
\(25\) 2.51309e9 2.05873
\(26\) −1.94198e8 −0.123287
\(27\) 3.87420e8 0.192450
\(28\) 1.69832e9 0.666028
\(29\) −1.96230e8 −0.0612603 −0.0306301 0.999531i \(-0.509751\pi\)
−0.0306301 + 0.999531i \(0.509751\pi\)
\(30\) 1.42093e9 0.355865
\(31\) 1.49325e9 0.302191 0.151096 0.988519i \(-0.451720\pi\)
0.151096 + 0.988519i \(0.451720\pi\)
\(32\) 5.39149e9 0.887634
\(33\) 8.94604e8 0.120584
\(34\) 3.68506e9 0.409102
\(35\) −1.44645e10 −1.33003
\(36\) −3.81281e9 −0.291931
\(37\) 1.48696e10 0.952767 0.476383 0.879238i \(-0.341947\pi\)
0.476383 + 0.879238i \(0.341947\pi\)
\(38\) −8.34144e9 −0.449415
\(39\) −4.43814e9 −0.201967
\(40\) −2.99516e10 −1.15619
\(41\) −1.03207e10 −0.339323 −0.169662 0.985502i \(-0.554267\pi\)
−0.169662 + 0.985502i \(0.554267\pi\)
\(42\) −5.50461e9 −0.154741
\(43\) −3.86482e10 −0.932362 −0.466181 0.884689i \(-0.654370\pi\)
−0.466181 + 0.884689i \(0.654370\pi\)
\(44\) −8.80428e9 −0.182916
\(45\) 3.24736e10 0.582974
\(46\) −3.75857e10 −0.584921
\(47\) −1.59891e10 −0.216366 −0.108183 0.994131i \(-0.534503\pi\)
−0.108183 + 0.994131i \(0.534503\pi\)
\(48\) 3.14474e10 0.371122
\(49\) −4.08543e10 −0.421660
\(50\) 8.01640e10 0.725562
\(51\) 8.42173e10 0.670186
\(52\) 4.36781e10 0.306367
\(53\) −3.65459e10 −0.226488 −0.113244 0.993567i \(-0.536124\pi\)
−0.113244 + 0.993567i \(0.536124\pi\)
\(54\) 1.23581e10 0.0678256
\(55\) 7.49857e10 0.365276
\(56\) 1.16031e11 0.502750
\(57\) −1.90633e11 −0.736226
\(58\) −6.25946e9 −0.0215901
\(59\) 4.21805e10 0.130189
\(60\) −3.19590e11 −0.884322
\(61\) −7.27065e11 −1.80688 −0.903440 0.428715i \(-0.858966\pi\)
−0.903440 + 0.428715i \(0.858966\pi\)
\(62\) 4.76325e10 0.106502
\(63\) −1.25801e11 −0.253495
\(64\) −1.81404e11 −0.329972
\(65\) −3.72005e11 −0.611804
\(66\) 2.85365e10 0.0424977
\(67\) 2.38478e11 0.322079 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(68\) −8.28828e11 −1.01662
\(69\) −8.58973e11 −0.958210
\(70\) −4.61397e11 −0.468746
\(71\) −4.31528e11 −0.399788 −0.199894 0.979818i \(-0.564060\pi\)
−0.199894 + 0.979818i \(0.564060\pi\)
\(72\) −2.60495e11 −0.220363
\(73\) −8.74060e11 −0.675994 −0.337997 0.941147i \(-0.609749\pi\)
−0.337997 + 0.941147i \(0.609749\pi\)
\(74\) 4.74317e11 0.335786
\(75\) 1.83205e12 1.18861
\(76\) 1.87612e12 1.11679
\(77\) −2.90491e11 −0.158834
\(78\) −1.41570e11 −0.0711798
\(79\) 1.86554e12 0.863433 0.431717 0.902009i \(-0.357908\pi\)
0.431717 + 0.902009i \(0.357908\pi\)
\(80\) 2.63592e12 1.12421
\(81\) 2.82430e11 0.111111
\(82\) −3.29215e11 −0.119588
\(83\) 2.77153e11 0.0930491 0.0465245 0.998917i \(-0.485185\pi\)
0.0465245 + 0.998917i \(0.485185\pi\)
\(84\) 1.23807e12 0.384531
\(85\) 7.05910e12 2.03014
\(86\) −1.23282e12 −0.328594
\(87\) −1.43052e11 −0.0353686
\(88\) −6.01518e11 −0.138074
\(89\) −1.37556e12 −0.293389 −0.146695 0.989182i \(-0.546863\pi\)
−0.146695 + 0.989182i \(0.546863\pi\)
\(90\) 1.03586e12 0.205459
\(91\) 1.44113e12 0.266032
\(92\) 8.45362e12 1.45352
\(93\) 1.08858e12 0.174470
\(94\) −5.10030e11 −0.0762544
\(95\) −1.59789e13 −2.23019
\(96\) 3.93039e12 0.512476
\(97\) 6.08837e12 0.742138 0.371069 0.928605i \(-0.378991\pi\)
0.371069 + 0.928605i \(0.378991\pi\)
\(98\) −1.30319e12 −0.148607
\(99\) 6.52166e11 0.0696193
\(100\) −1.80302e13 −1.80302
\(101\) 1.09470e13 1.02614 0.513071 0.858346i \(-0.328508\pi\)
0.513071 + 0.858346i \(0.328508\pi\)
\(102\) 2.68641e12 0.236195
\(103\) −1.90541e13 −1.57234 −0.786168 0.618013i \(-0.787938\pi\)
−0.786168 + 0.618013i \(0.787938\pi\)
\(104\) 2.98414e12 0.231261
\(105\) −1.05446e13 −0.767894
\(106\) −1.16576e12 −0.0798218
\(107\) −1.06552e13 −0.686381 −0.343191 0.939266i \(-0.611508\pi\)
−0.343191 + 0.939266i \(0.611508\pi\)
\(108\) −2.77954e12 −0.168546
\(109\) −8.24908e12 −0.471122 −0.235561 0.971860i \(-0.575693\pi\)
−0.235561 + 0.971860i \(0.575693\pi\)
\(110\) 2.39193e12 0.128735
\(111\) 1.08399e13 0.550080
\(112\) −1.02114e13 −0.488842
\(113\) 3.64270e13 1.64594 0.822969 0.568086i \(-0.192316\pi\)
0.822969 + 0.568086i \(0.192316\pi\)
\(114\) −6.08091e12 −0.259470
\(115\) −7.19992e13 −2.90263
\(116\) 1.40785e12 0.0536512
\(117\) −3.23540e12 −0.116606
\(118\) 1.34550e12 0.0458828
\(119\) −2.73466e13 −0.882770
\(120\) −2.18347e13 −0.667529
\(121\) −3.30168e13 −0.956378
\(122\) −2.31923e13 −0.636803
\(123\) −7.52378e12 −0.195908
\(124\) −1.07133e13 −0.264657
\(125\) 7.89713e13 1.85163
\(126\) −4.01286e12 −0.0893400
\(127\) 4.28928e13 0.907111 0.453556 0.891228i \(-0.350155\pi\)
0.453556 + 0.891228i \(0.350155\pi\)
\(128\) −4.99536e13 −1.00393
\(129\) −2.81745e13 −0.538299
\(130\) −1.18664e13 −0.215619
\(131\) −5.87157e13 −1.01506 −0.507529 0.861635i \(-0.669441\pi\)
−0.507529 + 0.861635i \(0.669441\pi\)
\(132\) −6.41832e12 −0.105607
\(133\) 6.19012e13 0.969758
\(134\) 7.60710e12 0.113511
\(135\) 2.36733e13 0.336580
\(136\) −5.66264e13 −0.767390
\(137\) −3.05025e13 −0.394142 −0.197071 0.980389i \(-0.563143\pi\)
−0.197071 + 0.980389i \(0.563143\pi\)
\(138\) −2.74000e13 −0.337704
\(139\) −8.80908e13 −1.03594 −0.517970 0.855399i \(-0.673312\pi\)
−0.517970 + 0.855399i \(0.673312\pi\)
\(140\) 1.03775e14 1.16483
\(141\) −1.16561e13 −0.124919
\(142\) −1.37651e13 −0.140898
\(143\) −7.47097e12 −0.0730622
\(144\) 2.29252e13 0.214267
\(145\) −1.19906e13 −0.107139
\(146\) −2.78812e13 −0.238242
\(147\) −2.97827e13 −0.243446
\(148\) −1.06681e14 −0.834425
\(149\) 8.99670e13 0.673554 0.336777 0.941584i \(-0.390663\pi\)
0.336777 + 0.941584i \(0.390663\pi\)
\(150\) 5.84395e13 0.418903
\(151\) −2.47335e13 −0.169799 −0.0848995 0.996390i \(-0.527057\pi\)
−0.0848995 + 0.996390i \(0.527057\pi\)
\(152\) 1.28179e14 0.843009
\(153\) 6.13944e13 0.386932
\(154\) −9.26622e12 −0.0559781
\(155\) 9.12448e13 0.528509
\(156\) 3.18414e13 0.176881
\(157\) −1.64598e14 −0.877157 −0.438578 0.898693i \(-0.644518\pi\)
−0.438578 + 0.898693i \(0.644518\pi\)
\(158\) 5.95080e13 0.304302
\(159\) −2.66420e13 −0.130763
\(160\) 3.29446e14 1.55240
\(161\) 2.78921e14 1.26216
\(162\) 9.00909e12 0.0391591
\(163\) −3.36300e14 −1.40446 −0.702228 0.711952i \(-0.747811\pi\)
−0.702228 + 0.711952i \(0.747811\pi\)
\(164\) 7.40456e13 0.297176
\(165\) 5.46646e13 0.210892
\(166\) 8.84078e12 0.0327935
\(167\) 5.17600e14 1.84645 0.923225 0.384261i \(-0.125544\pi\)
0.923225 + 0.384261i \(0.125544\pi\)
\(168\) 8.45866e13 0.290263
\(169\) −2.65812e14 −0.877628
\(170\) 2.25175e14 0.715487
\(171\) −1.38971e14 −0.425061
\(172\) 2.77281e14 0.816554
\(173\) −1.12219e14 −0.318248 −0.159124 0.987259i \(-0.550867\pi\)
−0.159124 + 0.987259i \(0.550867\pi\)
\(174\) −4.56314e12 −0.0124650
\(175\) −5.94891e14 −1.56563
\(176\) 5.29371e13 0.134254
\(177\) 3.07496e13 0.0751646
\(178\) −4.38783e13 −0.103400
\(179\) −5.53289e14 −1.25721 −0.628605 0.777725i \(-0.716374\pi\)
−0.628605 + 0.777725i \(0.716374\pi\)
\(180\) −2.32981e14 −0.510564
\(181\) −6.06513e14 −1.28212 −0.641061 0.767490i \(-0.721505\pi\)
−0.641061 + 0.767490i \(0.721505\pi\)
\(182\) 4.59698e13 0.0937581
\(183\) −5.30030e14 −1.04320
\(184\) 5.77560e14 1.09719
\(185\) 9.08601e14 1.66631
\(186\) 3.47241e13 0.0614889
\(187\) 1.41768e14 0.242441
\(188\) 1.14714e14 0.189492
\(189\) −9.17089e13 −0.146356
\(190\) −5.09702e14 −0.785992
\(191\) 8.16520e14 1.21689 0.608443 0.793597i \(-0.291794\pi\)
0.608443 + 0.793597i \(0.291794\pi\)
\(192\) −1.32243e14 −0.190509
\(193\) 2.28230e14 0.317870 0.158935 0.987289i \(-0.449194\pi\)
0.158935 + 0.987289i \(0.449194\pi\)
\(194\) 1.94210e14 0.261554
\(195\) −2.71192e14 −0.353225
\(196\) 2.93108e14 0.369287
\(197\) −2.72506e14 −0.332158 −0.166079 0.986112i \(-0.553111\pi\)
−0.166079 + 0.986112i \(0.553111\pi\)
\(198\) 2.08031e13 0.0245361
\(199\) −3.44397e14 −0.393110 −0.196555 0.980493i \(-0.562975\pi\)
−0.196555 + 0.980493i \(0.562975\pi\)
\(200\) −1.23184e15 −1.36100
\(201\) 1.73850e14 0.185952
\(202\) 3.49194e14 0.361645
\(203\) 4.64510e13 0.0465876
\(204\) −6.04216e14 −0.586943
\(205\) −6.30644e14 −0.593450
\(206\) −6.07796e14 −0.554142
\(207\) −6.26192e14 −0.553223
\(208\) −2.62622e14 −0.224864
\(209\) −3.20903e14 −0.266332
\(210\) −3.36358e14 −0.270631
\(211\) −9.27119e14 −0.723268 −0.361634 0.932320i \(-0.617781\pi\)
−0.361634 + 0.932320i \(0.617781\pi\)
\(212\) 2.62198e14 0.198356
\(213\) −3.14584e14 −0.230818
\(214\) −3.39884e14 −0.241903
\(215\) −2.36159e15 −1.63063
\(216\) −1.89901e14 −0.127227
\(217\) −3.53477e14 −0.229812
\(218\) −2.63134e14 −0.166039
\(219\) −6.37190e14 −0.390285
\(220\) −5.37984e14 −0.319906
\(221\) −7.03311e14 −0.406067
\(222\) 3.45777e14 0.193866
\(223\) −3.07542e15 −1.67465 −0.837324 0.546708i \(-0.815881\pi\)
−0.837324 + 0.546708i \(0.815881\pi\)
\(224\) −1.27625e15 −0.675033
\(225\) 1.33556e15 0.686242
\(226\) 1.16197e15 0.580082
\(227\) 6.53264e14 0.316899 0.158449 0.987367i \(-0.449351\pi\)
0.158449 + 0.987367i \(0.449351\pi\)
\(228\) 1.36769e15 0.644781
\(229\) −3.20867e15 −1.47026 −0.735131 0.677926i \(-0.762879\pi\)
−0.735131 + 0.677926i \(0.762879\pi\)
\(230\) −2.29667e15 −1.02298
\(231\) −2.11768e14 −0.0917026
\(232\) 9.61858e13 0.0404985
\(233\) 5.16607e14 0.211518 0.105759 0.994392i \(-0.466273\pi\)
0.105759 + 0.994392i \(0.466273\pi\)
\(234\) −1.03205e14 −0.0410957
\(235\) −9.77014e14 −0.378407
\(236\) −3.02624e14 −0.114018
\(237\) 1.35998e15 0.498503
\(238\) −8.72315e14 −0.311117
\(239\) −1.95374e15 −0.678080 −0.339040 0.940772i \(-0.610102\pi\)
−0.339040 + 0.940772i \(0.610102\pi\)
\(240\) 1.92159e15 0.649063
\(241\) −2.51478e15 −0.826779 −0.413389 0.910554i \(-0.635655\pi\)
−0.413389 + 0.910554i \(0.635655\pi\)
\(242\) −1.05319e15 −0.337059
\(243\) 2.05891e14 0.0641500
\(244\) 5.21632e15 1.58245
\(245\) −2.49639e15 −0.737451
\(246\) −2.39998e14 −0.0690444
\(247\) 1.59200e15 0.446081
\(248\) −7.31944e14 −0.199775
\(249\) 2.02045e14 0.0537219
\(250\) 2.51907e15 0.652574
\(251\) −5.01551e15 −1.26601 −0.633004 0.774149i \(-0.718178\pi\)
−0.633004 + 0.774149i \(0.718178\pi\)
\(252\) 9.02557e14 0.222009
\(253\) −1.44596e15 −0.346635
\(254\) 1.36822e15 0.319695
\(255\) 5.14608e15 1.17210
\(256\) −1.07386e14 −0.0238445
\(257\) −2.61044e14 −0.0565130 −0.0282565 0.999601i \(-0.508996\pi\)
−0.0282565 + 0.999601i \(0.508996\pi\)
\(258\) −8.98726e14 −0.189714
\(259\) −3.51987e15 −0.724566
\(260\) 2.66894e15 0.535812
\(261\) −1.04285e14 −0.0204201
\(262\) −1.87294e15 −0.357739
\(263\) −6.79659e15 −1.26642 −0.633211 0.773979i \(-0.718264\pi\)
−0.633211 + 0.773979i \(0.718264\pi\)
\(264\) −4.38506e14 −0.0797169
\(265\) −2.23313e15 −0.396110
\(266\) 1.97456e15 0.341774
\(267\) −1.00278e15 −0.169388
\(268\) −1.71096e15 −0.282074
\(269\) 1.47692e15 0.237666 0.118833 0.992914i \(-0.462085\pi\)
0.118833 + 0.992914i \(0.462085\pi\)
\(270\) 7.55142e14 0.118622
\(271\) −6.15043e15 −0.943203 −0.471601 0.881812i \(-0.656324\pi\)
−0.471601 + 0.881812i \(0.656324\pi\)
\(272\) 4.98346e15 0.746162
\(273\) 1.05058e15 0.153593
\(274\) −9.72986e14 −0.138908
\(275\) 3.08398e15 0.429981
\(276\) 6.16269e15 0.839192
\(277\) 1.55873e15 0.207326 0.103663 0.994613i \(-0.466944\pi\)
0.103663 + 0.994613i \(0.466944\pi\)
\(278\) −2.80997e15 −0.365098
\(279\) 7.93575e14 0.100730
\(280\) 7.09005e15 0.879270
\(281\) 1.02028e15 0.123631 0.0618157 0.998088i \(-0.480311\pi\)
0.0618157 + 0.998088i \(0.480311\pi\)
\(282\) −3.71812e14 −0.0440255
\(283\) −3.55832e15 −0.411750 −0.205875 0.978578i \(-0.566004\pi\)
−0.205875 + 0.978578i \(0.566004\pi\)
\(284\) 3.09599e15 0.350131
\(285\) −1.16486e16 −1.28760
\(286\) −2.38313e14 −0.0257495
\(287\) 2.44308e15 0.258051
\(288\) 2.86526e15 0.295878
\(289\) 3.44133e15 0.347448
\(290\) −3.82483e14 −0.0377594
\(291\) 4.43842e15 0.428474
\(292\) 6.27093e15 0.592029
\(293\) 9.91796e15 0.915763 0.457881 0.889013i \(-0.348608\pi\)
0.457881 + 0.889013i \(0.348608\pi\)
\(294\) −9.50026e14 −0.0857981
\(295\) 2.57743e15 0.227690
\(296\) −7.28858e15 −0.629864
\(297\) 4.75429e14 0.0401947
\(298\) 2.86981e15 0.237382
\(299\) 7.17341e15 0.580581
\(300\) −1.31440e16 −1.04097
\(301\) 9.14867e15 0.709048
\(302\) −7.88961e14 −0.0598426
\(303\) 7.98038e15 0.592443
\(304\) −1.12805e16 −0.819690
\(305\) −4.44272e16 −3.16009
\(306\) 1.95839e15 0.136367
\(307\) 2.05391e15 0.140017 0.0700087 0.997546i \(-0.477697\pi\)
0.0700087 + 0.997546i \(0.477697\pi\)
\(308\) 2.08412e15 0.139105
\(309\) −1.38904e16 −0.907789
\(310\) 2.91058e15 0.186264
\(311\) −1.23258e16 −0.772452 −0.386226 0.922404i \(-0.626222\pi\)
−0.386226 + 0.922404i \(0.626222\pi\)
\(312\) 2.17544e15 0.133518
\(313\) −1.78783e16 −1.07470 −0.537352 0.843358i \(-0.680575\pi\)
−0.537352 + 0.843358i \(0.680575\pi\)
\(314\) −5.25044e15 −0.309138
\(315\) −7.68704e15 −0.443344
\(316\) −1.33843e16 −0.756188
\(317\) −1.45191e15 −0.0803628 −0.0401814 0.999192i \(-0.512794\pi\)
−0.0401814 + 0.999192i \(0.512794\pi\)
\(318\) −8.49840e14 −0.0460851
\(319\) −2.40807e14 −0.0127947
\(320\) −1.10846e16 −0.577094
\(321\) −7.76761e15 −0.396283
\(322\) 8.89716e15 0.444824
\(323\) −3.02096e16 −1.48023
\(324\) −2.02629e15 −0.0973102
\(325\) −1.52997e16 −0.720179
\(326\) −1.07275e16 −0.494975
\(327\) −6.01358e15 −0.272002
\(328\) 5.05887e15 0.224323
\(329\) 3.78490e15 0.164544
\(330\) 1.74372e15 0.0743252
\(331\) −1.14585e16 −0.478901 −0.239450 0.970909i \(-0.576967\pi\)
−0.239450 + 0.970909i \(0.576967\pi\)
\(332\) −1.98843e15 −0.0814916
\(333\) 7.90229e15 0.317589
\(334\) 1.65107e16 0.650748
\(335\) 1.45722e16 0.563290
\(336\) −7.44412e15 −0.282233
\(337\) 2.20633e16 0.820497 0.410248 0.911974i \(-0.365442\pi\)
0.410248 + 0.911974i \(0.365442\pi\)
\(338\) −8.47900e15 −0.309304
\(339\) 2.65553e16 0.950283
\(340\) −5.06454e16 −1.77798
\(341\) 1.83247e15 0.0631150
\(342\) −4.43298e15 −0.149805
\(343\) 3.26061e16 1.08115
\(344\) 1.89441e16 0.616374
\(345\) −5.24874e16 −1.67583
\(346\) −3.57961e15 −0.112161
\(347\) 3.06253e16 0.941756 0.470878 0.882198i \(-0.343937\pi\)
0.470878 + 0.882198i \(0.343937\pi\)
\(348\) 1.02632e15 0.0309756
\(349\) −2.42759e16 −0.719136 −0.359568 0.933119i \(-0.617076\pi\)
−0.359568 + 0.933119i \(0.617076\pi\)
\(350\) −1.89761e16 −0.551780
\(351\) −2.35861e15 −0.0673224
\(352\) 6.61625e15 0.185389
\(353\) −2.83637e16 −0.780238 −0.390119 0.920765i \(-0.627566\pi\)
−0.390119 + 0.920765i \(0.627566\pi\)
\(354\) 9.80867e14 0.0264904
\(355\) −2.63684e16 −0.699197
\(356\) 9.86892e15 0.256948
\(357\) −1.99356e16 −0.509667
\(358\) −1.76491e16 −0.443081
\(359\) 2.74348e16 0.676375 0.338187 0.941079i \(-0.390186\pi\)
0.338187 + 0.941079i \(0.390186\pi\)
\(360\) −1.59175e16 −0.385398
\(361\) 2.63289e16 0.626088
\(362\) −1.93469e16 −0.451861
\(363\) −2.40692e16 −0.552165
\(364\) −1.03393e16 −0.232988
\(365\) −5.34093e16 −1.18226
\(366\) −1.69072e16 −0.367658
\(367\) −4.88581e16 −1.04377 −0.521887 0.853014i \(-0.674772\pi\)
−0.521887 + 0.853014i \(0.674772\pi\)
\(368\) −5.08288e16 −1.06684
\(369\) −5.48484e15 −0.113108
\(370\) 2.89830e16 0.587263
\(371\) 8.65102e15 0.172241
\(372\) −7.81000e15 −0.152800
\(373\) 4.30144e16 0.827001 0.413500 0.910504i \(-0.364306\pi\)
0.413500 + 0.910504i \(0.364306\pi\)
\(374\) 4.52218e15 0.0854442
\(375\) 5.75701e16 1.06904
\(376\) 7.83737e15 0.143037
\(377\) 1.19465e15 0.0214299
\(378\) −2.92538e15 −0.0515805
\(379\) 8.99296e16 1.55865 0.779323 0.626622i \(-0.215563\pi\)
0.779323 + 0.626622i \(0.215563\pi\)
\(380\) 1.14640e17 1.95318
\(381\) 3.12689e16 0.523721
\(382\) 2.60458e16 0.428870
\(383\) 5.93851e16 0.961359 0.480680 0.876896i \(-0.340390\pi\)
0.480680 + 0.876896i \(0.340390\pi\)
\(384\) −3.64162e16 −0.579617
\(385\) −1.77504e16 −0.277787
\(386\) 7.28020e15 0.112028
\(387\) −2.05392e16 −0.310787
\(388\) −4.36809e16 −0.649958
\(389\) 1.12825e17 1.65094 0.825471 0.564445i \(-0.190910\pi\)
0.825471 + 0.564445i \(0.190910\pi\)
\(390\) −8.65062e15 −0.124488
\(391\) −1.36121e17 −1.92654
\(392\) 2.00255e16 0.278755
\(393\) −4.28038e16 −0.586044
\(394\) −8.69253e15 −0.117063
\(395\) 1.13994e17 1.51008
\(396\) −4.67896e15 −0.0609720
\(397\) 1.47653e17 1.89280 0.946400 0.322996i \(-0.104690\pi\)
0.946400 + 0.322996i \(0.104690\pi\)
\(398\) −1.09858e16 −0.138545
\(399\) 4.51260e16 0.559890
\(400\) 1.08409e17 1.32335
\(401\) 1.58877e17 1.90819 0.954096 0.299501i \(-0.0968201\pi\)
0.954096 + 0.299501i \(0.0968201\pi\)
\(402\) 5.54557e15 0.0655356
\(403\) −9.09089e15 −0.105712
\(404\) −7.85392e16 −0.898686
\(405\) 1.72578e16 0.194325
\(406\) 1.48172e15 0.0164190
\(407\) 1.82474e16 0.198993
\(408\) −4.12807e16 −0.443053
\(409\) −4.33141e16 −0.457539 −0.228769 0.973481i \(-0.573470\pi\)
−0.228769 + 0.973481i \(0.573470\pi\)
\(410\) −2.01166e16 −0.209151
\(411\) −2.22364e16 −0.227558
\(412\) 1.36703e17 1.37704
\(413\) −9.98483e15 −0.0990069
\(414\) −1.99746e16 −0.194974
\(415\) 1.69354e16 0.162736
\(416\) −3.28233e16 −0.310510
\(417\) −6.42182e16 −0.598100
\(418\) −1.02363e16 −0.0938639
\(419\) −1.14548e17 −1.03418 −0.517088 0.855932i \(-0.672984\pi\)
−0.517088 + 0.855932i \(0.672984\pi\)
\(420\) 7.56523e16 0.672515
\(421\) 1.28806e16 0.112746 0.0563732 0.998410i \(-0.482046\pi\)
0.0563732 + 0.998410i \(0.482046\pi\)
\(422\) −2.95737e16 −0.254903
\(423\) −8.49729e15 −0.0721220
\(424\) 1.79136e16 0.149729
\(425\) 2.90324e17 2.38976
\(426\) −1.00348e16 −0.0813475
\(427\) 1.72108e17 1.37411
\(428\) 7.64453e16 0.601127
\(429\) −5.44633e15 −0.0421825
\(430\) −7.53313e16 −0.574686
\(431\) 1.00330e17 0.753923 0.376962 0.926229i \(-0.376969\pi\)
0.376962 + 0.926229i \(0.376969\pi\)
\(432\) 1.67124e16 0.123707
\(433\) −1.36706e17 −0.996820 −0.498410 0.866941i \(-0.666083\pi\)
−0.498410 + 0.866941i \(0.666083\pi\)
\(434\) −1.12754e16 −0.0809933
\(435\) −8.74115e15 −0.0618570
\(436\) 5.91829e16 0.412605
\(437\) 3.08122e17 2.11638
\(438\) −2.03254e16 −0.137549
\(439\) −2.05821e17 −1.37236 −0.686182 0.727430i \(-0.740715\pi\)
−0.686182 + 0.727430i \(0.740715\pi\)
\(440\) −3.67556e16 −0.241480
\(441\) −2.17116e16 −0.140553
\(442\) −2.24346e16 −0.143111
\(443\) 5.17244e16 0.325141 0.162570 0.986697i \(-0.448022\pi\)
0.162570 + 0.986697i \(0.448022\pi\)
\(444\) −7.77707e16 −0.481756
\(445\) −8.40532e16 −0.513115
\(446\) −9.81015e16 −0.590200
\(447\) 6.55859e16 0.388877
\(448\) 4.29413e16 0.250939
\(449\) 1.72646e17 0.994384 0.497192 0.867640i \(-0.334364\pi\)
0.497192 + 0.867640i \(0.334364\pi\)
\(450\) 4.26024e16 0.241854
\(451\) −1.26652e16 −0.0708703
\(452\) −2.61345e17 −1.44150
\(453\) −1.80307e16 −0.0980335
\(454\) 2.08382e16 0.111685
\(455\) 8.80598e16 0.465268
\(456\) 9.34422e16 0.486712
\(457\) 2.70189e17 1.38744 0.693718 0.720247i \(-0.255972\pi\)
0.693718 + 0.720247i \(0.255972\pi\)
\(458\) −1.02352e17 −0.518167
\(459\) 4.47565e16 0.223395
\(460\) 5.16557e17 2.54210
\(461\) −2.84833e17 −1.38209 −0.691043 0.722814i \(-0.742848\pi\)
−0.691043 + 0.722814i \(0.742848\pi\)
\(462\) −6.75507e15 −0.0323190
\(463\) 2.36098e17 1.11382 0.556912 0.830571i \(-0.311986\pi\)
0.556912 + 0.830571i \(0.311986\pi\)
\(464\) −8.46493e15 −0.0393782
\(465\) 6.65175e16 0.305135
\(466\) 1.64790e16 0.0745457
\(467\) −2.54803e17 −1.13670 −0.568348 0.822788i \(-0.692417\pi\)
−0.568348 + 0.822788i \(0.692417\pi\)
\(468\) 2.32124e16 0.102122
\(469\) −5.64517e16 −0.244937
\(470\) −3.11653e16 −0.133363
\(471\) −1.19992e17 −0.506427
\(472\) −2.06756e16 −0.0860665
\(473\) −4.74278e16 −0.194731
\(474\) 4.33813e16 0.175689
\(475\) −6.57172e17 −2.62525
\(476\) 1.96197e17 0.773122
\(477\) −1.94220e16 −0.0754961
\(478\) −6.23215e16 −0.238977
\(479\) 5.00063e16 0.189166 0.0945831 0.995517i \(-0.469848\pi\)
0.0945831 + 0.995517i \(0.469848\pi\)
\(480\) 2.40166e17 0.896279
\(481\) −9.05256e16 −0.333295
\(482\) −8.02178e16 −0.291384
\(483\) 2.03333e17 0.728706
\(484\) 2.36878e17 0.837588
\(485\) 3.72029e17 1.29794
\(486\) 6.56762e15 0.0226085
\(487\) −5.46060e17 −1.85482 −0.927410 0.374046i \(-0.877970\pi\)
−0.927410 + 0.374046i \(0.877970\pi\)
\(488\) 3.56384e17 1.19451
\(489\) −2.45163e17 −0.810863
\(490\) −7.96312e16 −0.259901
\(491\) −4.51729e16 −0.145495 −0.0727476 0.997350i \(-0.523177\pi\)
−0.0727476 + 0.997350i \(0.523177\pi\)
\(492\) 5.39793e16 0.171575
\(493\) −2.26694e16 −0.0711107
\(494\) 5.07826e16 0.157213
\(495\) 3.98505e16 0.121759
\(496\) 6.44155e16 0.194249
\(497\) 1.02150e17 0.304033
\(498\) 6.44493e15 0.0189333
\(499\) 3.26679e17 0.947256 0.473628 0.880725i \(-0.342944\pi\)
0.473628 + 0.880725i \(0.342944\pi\)
\(500\) −5.66578e17 −1.62164
\(501\) 3.77331e17 1.06605
\(502\) −1.59987e17 −0.446182
\(503\) 3.73415e17 1.02802 0.514008 0.857786i \(-0.328160\pi\)
0.514008 + 0.857786i \(0.328160\pi\)
\(504\) 6.16636e16 0.167583
\(505\) 6.68916e17 1.79464
\(506\) −4.61239e16 −0.122165
\(507\) −1.93777e17 −0.506699
\(508\) −3.07734e17 −0.794440
\(509\) 4.39988e17 1.12144 0.560719 0.828006i \(-0.310525\pi\)
0.560719 + 0.828006i \(0.310525\pi\)
\(510\) 1.64152e17 0.413087
\(511\) 2.06904e17 0.514084
\(512\) 4.05794e17 0.995523
\(513\) −1.01310e17 −0.245409
\(514\) −8.32691e15 −0.0199170
\(515\) −1.16429e18 −2.74989
\(516\) 2.02138e17 0.471438
\(517\) −1.96213e16 −0.0451898
\(518\) −1.12279e17 −0.255361
\(519\) −8.18074e16 −0.183740
\(520\) 1.82345e17 0.404457
\(521\) 1.37202e17 0.300549 0.150275 0.988644i \(-0.451984\pi\)
0.150275 + 0.988644i \(0.451984\pi\)
\(522\) −3.32653e15 −0.00719670
\(523\) 4.14693e17 0.886065 0.443032 0.896506i \(-0.353903\pi\)
0.443032 + 0.896506i \(0.353903\pi\)
\(524\) 4.21255e17 0.888979
\(525\) −4.33676e17 −0.903919
\(526\) −2.16801e17 −0.446328
\(527\) 1.72507e17 0.350782
\(528\) 3.85912e16 0.0775118
\(529\) 8.84331e17 1.75450
\(530\) −7.12336e16 −0.139602
\(531\) 2.24165e16 0.0433963
\(532\) −4.44109e17 −0.849306
\(533\) 6.28322e16 0.118701
\(534\) −3.19873e16 −0.0596979
\(535\) −6.51082e17 −1.20043
\(536\) −1.16894e17 −0.212923
\(537\) −4.03348e17 −0.725850
\(538\) 4.71116e16 0.0837613
\(539\) −5.01349e16 −0.0880671
\(540\) −1.69843e17 −0.294774
\(541\) −1.38315e17 −0.237186 −0.118593 0.992943i \(-0.537838\pi\)
−0.118593 + 0.992943i \(0.537838\pi\)
\(542\) −1.96190e17 −0.332415
\(543\) −4.42148e17 −0.740233
\(544\) 6.22849e17 1.03036
\(545\) −5.04058e17 −0.823955
\(546\) 3.35120e16 0.0541313
\(547\) 2.79562e17 0.446232 0.223116 0.974792i \(-0.428377\pi\)
0.223116 + 0.974792i \(0.428377\pi\)
\(548\) 2.18840e17 0.345186
\(549\) −3.86392e17 −0.602293
\(550\) 9.83745e16 0.151539
\(551\) 5.13141e16 0.0781180
\(552\) 4.21041e17 0.633462
\(553\) −4.41605e17 −0.656629
\(554\) 4.97212e16 0.0730682
\(555\) 6.62370e17 0.962047
\(556\) 6.32006e17 0.907267
\(557\) 6.12643e17 0.869259 0.434629 0.900609i \(-0.356879\pi\)
0.434629 + 0.900609i \(0.356879\pi\)
\(558\) 2.53139e16 0.0355006
\(559\) 2.35290e17 0.326157
\(560\) −6.23967e17 −0.854947
\(561\) 1.03349e17 0.139974
\(562\) 3.25455e16 0.0435717
\(563\) −4.57103e17 −0.604935 −0.302468 0.953160i \(-0.597810\pi\)
−0.302468 + 0.953160i \(0.597810\pi\)
\(564\) 8.36264e16 0.109403
\(565\) 2.22586e18 2.87862
\(566\) −1.13505e17 −0.145114
\(567\) −6.68558e16 −0.0844985
\(568\) 2.11521e17 0.264295
\(569\) −3.02816e17 −0.374067 −0.187033 0.982354i \(-0.559887\pi\)
−0.187033 + 0.982354i \(0.559887\pi\)
\(570\) −3.71573e17 −0.453793
\(571\) 4.55065e17 0.549463 0.274732 0.961521i \(-0.411411\pi\)
0.274732 + 0.961521i \(0.411411\pi\)
\(572\) 5.36003e16 0.0639872
\(573\) 5.95243e17 0.702570
\(574\) 7.79306e16 0.0909454
\(575\) −2.96115e18 −3.41680
\(576\) −9.64054e16 −0.109991
\(577\) −1.34983e18 −1.52278 −0.761391 0.648293i \(-0.775483\pi\)
−0.761391 + 0.648293i \(0.775483\pi\)
\(578\) 1.09773e17 0.122452
\(579\) 1.66380e17 0.183522
\(580\) 8.60264e16 0.0938318
\(581\) −6.56067e16 −0.0707626
\(582\) 1.41579e17 0.151008
\(583\) −4.48479e16 −0.0473038
\(584\) 4.28436e17 0.446892
\(585\) −1.97699e17 −0.203935
\(586\) 3.16368e17 0.322744
\(587\) −3.09629e17 −0.312388 −0.156194 0.987726i \(-0.549923\pi\)
−0.156194 + 0.987726i \(0.549923\pi\)
\(588\) 2.13676e17 0.213208
\(589\) −3.90484e17 −0.385349
\(590\) 8.22163e16 0.0802454
\(591\) −1.98657e17 −0.191772
\(592\) 6.41439e17 0.612441
\(593\) −1.77955e18 −1.68056 −0.840282 0.542149i \(-0.817611\pi\)
−0.840282 + 0.542149i \(0.817611\pi\)
\(594\) 1.51655e16 0.0141659
\(595\) −1.67101e18 −1.54390
\(596\) −6.45467e17 −0.589893
\(597\) −2.51065e17 −0.226962
\(598\) 2.28821e17 0.204616
\(599\) 1.80860e17 0.159981 0.0799906 0.996796i \(-0.474511\pi\)
0.0799906 + 0.996796i \(0.474511\pi\)
\(600\) −8.98010e17 −0.785775
\(601\) −5.00295e17 −0.433054 −0.216527 0.976277i \(-0.569473\pi\)
−0.216527 + 0.976277i \(0.569473\pi\)
\(602\) 2.91829e17 0.249892
\(603\) 1.26737e17 0.107360
\(604\) 1.77450e17 0.148708
\(605\) −2.01748e18 −1.67263
\(606\) 2.54562e17 0.208796
\(607\) −1.91470e18 −1.55373 −0.776864 0.629668i \(-0.783191\pi\)
−0.776864 + 0.629668i \(0.783191\pi\)
\(608\) −1.40987e18 −1.13189
\(609\) 3.38627e16 0.0268974
\(610\) −1.41716e18 −1.11372
\(611\) 9.73417e16 0.0756887
\(612\) −4.40473e17 −0.338872
\(613\) 4.62799e17 0.352290 0.176145 0.984364i \(-0.443637\pi\)
0.176145 + 0.984364i \(0.443637\pi\)
\(614\) 6.55167e16 0.0493467
\(615\) −4.59739e17 −0.342628
\(616\) 1.42389e17 0.105003
\(617\) 2.13534e18 1.55817 0.779083 0.626921i \(-0.215685\pi\)
0.779083 + 0.626921i \(0.215685\pi\)
\(618\) −4.43083e17 −0.319934
\(619\) −7.96416e16 −0.0569051 −0.0284525 0.999595i \(-0.509058\pi\)
−0.0284525 + 0.999595i \(0.509058\pi\)
\(620\) −6.54634e17 −0.462863
\(621\) −4.56494e17 −0.319403
\(622\) −3.93174e17 −0.272237
\(623\) 3.25618e17 0.223118
\(624\) −1.91451e17 −0.129825
\(625\) 1.75778e18 1.17963
\(626\) −5.70293e17 −0.378760
\(627\) −2.33938e17 −0.153767
\(628\) 1.18091e18 0.768207
\(629\) 1.71780e18 1.10597
\(630\) −2.45205e17 −0.156249
\(631\) 1.92195e18 1.21213 0.606067 0.795414i \(-0.292746\pi\)
0.606067 + 0.795414i \(0.292746\pi\)
\(632\) −9.14429e17 −0.570807
\(633\) −6.75869e17 −0.417579
\(634\) −4.63139e16 −0.0283224
\(635\) 2.62096e18 1.58647
\(636\) 1.91142e17 0.114521
\(637\) 2.48720e17 0.147504
\(638\) −7.68139e15 −0.00450926
\(639\) −2.29332e17 −0.133263
\(640\) −3.05240e18 −1.75579
\(641\) 1.47841e18 0.841819 0.420909 0.907103i \(-0.361711\pi\)
0.420909 + 0.907103i \(0.361711\pi\)
\(642\) −2.47775e17 −0.139663
\(643\) 3.10088e18 1.73027 0.865135 0.501539i \(-0.167233\pi\)
0.865135 + 0.501539i \(0.167233\pi\)
\(644\) −2.00111e18 −1.10538
\(645\) −1.72160e18 −0.941443
\(646\) −9.63641e17 −0.521679
\(647\) −2.73452e18 −1.46556 −0.732780 0.680465i \(-0.761778\pi\)
−0.732780 + 0.680465i \(0.761778\pi\)
\(648\) −1.38438e17 −0.0734544
\(649\) 5.17625e16 0.0271910
\(650\) −4.88037e17 −0.253814
\(651\) −2.57685e17 −0.132682
\(652\) 2.41278e18 1.23001
\(653\) 1.21786e18 0.614696 0.307348 0.951597i \(-0.400558\pi\)
0.307348 + 0.951597i \(0.400558\pi\)
\(654\) −1.91824e17 −0.0958624
\(655\) −3.58781e18 −1.77526
\(656\) −4.45211e17 −0.218118
\(657\) −4.64511e17 −0.225331
\(658\) 1.20733e17 0.0579904
\(659\) 1.74676e18 0.830766 0.415383 0.909647i \(-0.363648\pi\)
0.415383 + 0.909647i \(0.363648\pi\)
\(660\) −3.92190e17 −0.184698
\(661\) 4.20821e18 1.96240 0.981201 0.192989i \(-0.0618181\pi\)
0.981201 + 0.192989i \(0.0618181\pi\)
\(662\) −3.65509e17 −0.168780
\(663\) −5.12714e17 −0.234443
\(664\) −1.35852e17 −0.0615138
\(665\) 3.78246e18 1.69603
\(666\) 2.52071e17 0.111929
\(667\) 2.31216e17 0.101672
\(668\) −3.71351e18 −1.61710
\(669\) −2.24198e18 −0.966858
\(670\) 4.64830e17 0.198522
\(671\) −8.92229e17 −0.377381
\(672\) −9.30390e17 −0.389731
\(673\) 4.24735e18 1.76206 0.881030 0.473061i \(-0.156851\pi\)
0.881030 + 0.473061i \(0.156851\pi\)
\(674\) 7.03788e17 0.289170
\(675\) 9.73624e17 0.396202
\(676\) 1.90706e18 0.768619
\(677\) −8.79869e17 −0.351230 −0.175615 0.984459i \(-0.556191\pi\)
−0.175615 + 0.984459i \(0.556191\pi\)
\(678\) 8.47074e17 0.334910
\(679\) −1.44122e18 −0.564386
\(680\) −3.46015e18 −1.34211
\(681\) 4.76229e17 0.182962
\(682\) 5.84530e16 0.0222438
\(683\) 5.01079e18 1.88874 0.944369 0.328887i \(-0.106673\pi\)
0.944369 + 0.328887i \(0.106673\pi\)
\(684\) 9.97048e17 0.372264
\(685\) −1.86385e18 −0.689323
\(686\) 1.04009e18 0.381033
\(687\) −2.33912e18 −0.848856
\(688\) −1.66720e18 −0.599324
\(689\) 2.22491e17 0.0792296
\(690\) −1.67427e18 −0.590618
\(691\) 3.55620e18 1.24274 0.621368 0.783519i \(-0.286577\pi\)
0.621368 + 0.783519i \(0.286577\pi\)
\(692\) 8.05111e17 0.278719
\(693\) −1.54379e17 −0.0529445
\(694\) 9.76901e17 0.331905
\(695\) −5.38277e18 −1.81178
\(696\) 7.01195e16 0.0233818
\(697\) −1.19229e18 −0.393885
\(698\) −7.74367e17 −0.253447
\(699\) 3.76607e17 0.122120
\(700\) 4.26804e18 1.37117
\(701\) 8.46551e17 0.269455 0.134727 0.990883i \(-0.456984\pi\)
0.134727 + 0.990883i \(0.456984\pi\)
\(702\) −7.52362e16 −0.0237266
\(703\) −3.88838e18 −1.21495
\(704\) −2.22612e17 −0.0689171
\(705\) −7.12243e17 −0.218474
\(706\) −9.04759e17 −0.274981
\(707\) −2.59134e18 −0.780366
\(708\) −2.20613e17 −0.0658285
\(709\) 3.28062e18 0.969963 0.484982 0.874524i \(-0.338826\pi\)
0.484982 + 0.874524i \(0.338826\pi\)
\(710\) −8.41114e17 −0.246420
\(711\) 9.91425e17 0.287811
\(712\) 6.74255e17 0.193956
\(713\) −1.75948e18 −0.501537
\(714\) −6.35918e17 −0.179623
\(715\) −4.56512e17 −0.127780
\(716\) 3.96957e18 1.10105
\(717\) −1.42428e18 −0.391489
\(718\) 8.75128e17 0.238376
\(719\) 4.73928e18 1.27931 0.639653 0.768664i \(-0.279078\pi\)
0.639653 + 0.768664i \(0.279078\pi\)
\(720\) 1.40084e18 0.374737
\(721\) 4.51041e18 1.19574
\(722\) 8.39852e17 0.220654
\(723\) −1.83328e18 −0.477341
\(724\) 4.35142e18 1.12287
\(725\) −4.93145e17 −0.126118
\(726\) −7.67773e17 −0.194601
\(727\) −4.27803e18 −1.07466 −0.537329 0.843373i \(-0.680567\pi\)
−0.537329 + 0.843373i \(0.680567\pi\)
\(728\) −7.06395e17 −0.175871
\(729\) 1.50095e17 0.0370370
\(730\) −1.70368e18 −0.416666
\(731\) −4.46481e18 −1.08228
\(732\) 3.80269e18 0.913628
\(733\) −6.99073e18 −1.66474 −0.832371 0.554219i \(-0.813017\pi\)
−0.832371 + 0.554219i \(0.813017\pi\)
\(734\) −1.55850e18 −0.367860
\(735\) −1.81987e18 −0.425767
\(736\) −6.35274e18 −1.47318
\(737\) 2.92652e17 0.0672687
\(738\) −1.74958e17 −0.0398628
\(739\) −3.99272e18 −0.901736 −0.450868 0.892591i \(-0.648886\pi\)
−0.450868 + 0.892591i \(0.648886\pi\)
\(740\) −6.51874e18 −1.45934
\(741\) 1.16057e18 0.257545
\(742\) 2.75955e17 0.0607034
\(743\) −8.47400e18 −1.84783 −0.923913 0.382603i \(-0.875028\pi\)
−0.923913 + 0.382603i \(0.875028\pi\)
\(744\) −5.33587e17 −0.115340
\(745\) 5.49741e18 1.17799
\(746\) 1.37209e18 0.291462
\(747\) 1.47291e17 0.0310164
\(748\) −1.01711e18 −0.212328
\(749\) 2.52225e18 0.521984
\(750\) 1.83640e18 0.376764
\(751\) 1.30595e18 0.265624 0.132812 0.991141i \(-0.457599\pi\)
0.132812 + 0.991141i \(0.457599\pi\)
\(752\) −6.89736e17 −0.139081
\(753\) −3.65631e18 −0.730930
\(754\) 3.81075e16 0.00755260
\(755\) −1.51133e18 −0.296965
\(756\) 6.57964e17 0.128177
\(757\) −3.49982e18 −0.675963 −0.337982 0.941153i \(-0.609744\pi\)
−0.337982 + 0.941153i \(0.609744\pi\)
\(758\) 2.86862e18 0.549317
\(759\) −1.05410e18 −0.200130
\(760\) 7.83233e18 1.47436
\(761\) 7.28338e18 1.35935 0.679677 0.733511i \(-0.262120\pi\)
0.679677 + 0.733511i \(0.262120\pi\)
\(762\) 9.97431e17 0.184576
\(763\) 1.95269e18 0.358282
\(764\) −5.85811e18 −1.06574
\(765\) 3.75150e18 0.676714
\(766\) 1.89430e18 0.338814
\(767\) −2.56794e17 −0.0455424
\(768\) −7.82845e16 −0.0137666
\(769\) −2.42836e18 −0.423440 −0.211720 0.977330i \(-0.567907\pi\)
−0.211720 + 0.977330i \(0.567907\pi\)
\(770\) −5.66211e17 −0.0979013
\(771\) −1.90301e17 −0.0326278
\(772\) −1.63743e18 −0.278388
\(773\) −9.57989e18 −1.61508 −0.807539 0.589814i \(-0.799201\pi\)
−0.807539 + 0.589814i \(0.799201\pi\)
\(774\) −6.55172e17 −0.109531
\(775\) 3.75268e18 0.622129
\(776\) −2.98433e18 −0.490620
\(777\) −2.56599e18 −0.418329
\(778\) 3.59894e18 0.581845
\(779\) 2.69885e18 0.432699
\(780\) 1.94566e18 0.309351
\(781\) −5.29556e17 −0.0834988
\(782\) −4.34207e18 −0.678974
\(783\) −7.60236e16 −0.0117895
\(784\) −1.76236e18 −0.271044
\(785\) −1.00577e19 −1.53408
\(786\) −1.36538e18 −0.206541
\(787\) −7.50361e18 −1.12573 −0.562865 0.826549i \(-0.690301\pi\)
−0.562865 + 0.826549i \(0.690301\pi\)
\(788\) 1.95509e18 0.290901
\(789\) −4.95471e18 −0.731169
\(790\) 3.63623e18 0.532200
\(791\) −8.62288e18 −1.25171
\(792\) −3.19671e17 −0.0460246
\(793\) 4.42636e18 0.632078
\(794\) 4.70992e18 0.667084
\(795\) −1.62795e18 −0.228694
\(796\) 2.47087e18 0.344283
\(797\) 1.11566e19 1.54189 0.770944 0.636903i \(-0.219785\pi\)
0.770944 + 0.636903i \(0.219785\pi\)
\(798\) 1.43945e18 0.197323
\(799\) −1.84714e18 −0.251157
\(800\) 1.35493e19 1.82739
\(801\) −7.31028e17 −0.0977964
\(802\) 5.06794e18 0.672508
\(803\) −1.07262e18 −0.141187
\(804\) −1.24729e18 −0.162855
\(805\) 1.70434e19 2.20741
\(806\) −2.89986e17 −0.0372563
\(807\) 1.07668e18 0.137217
\(808\) −5.36588e18 −0.678371
\(809\) 6.68924e17 0.0838902 0.0419451 0.999120i \(-0.486645\pi\)
0.0419451 + 0.999120i \(0.486645\pi\)
\(810\) 5.50498e17 0.0684863
\(811\) −7.52813e17 −0.0929077 −0.0464539 0.998920i \(-0.514792\pi\)
−0.0464539 + 0.998920i \(0.514792\pi\)
\(812\) −3.33262e17 −0.0408010
\(813\) −4.48366e18 −0.544558
\(814\) 5.82065e17 0.0701315
\(815\) −2.05496e19 −2.45628
\(816\) 3.63294e18 0.430797
\(817\) 1.01065e19 1.18893
\(818\) −1.38166e18 −0.161251
\(819\) 7.65874e17 0.0886772
\(820\) 4.52454e18 0.519738
\(821\) −4.89736e18 −0.558125 −0.279062 0.960273i \(-0.590024\pi\)
−0.279062 + 0.960273i \(0.590024\pi\)
\(822\) −7.09307e17 −0.0801987
\(823\) 1.48706e19 1.66813 0.834065 0.551666i \(-0.186008\pi\)
0.834065 + 0.551666i \(0.186008\pi\)
\(824\) 9.33969e18 1.03945
\(825\) 2.24822e18 0.248250
\(826\) −3.18501e17 −0.0348932
\(827\) 9.49478e18 1.03205 0.516023 0.856575i \(-0.327412\pi\)
0.516023 + 0.856575i \(0.327412\pi\)
\(828\) 4.49260e18 0.484508
\(829\) −9.27501e18 −0.992453 −0.496227 0.868193i \(-0.665282\pi\)
−0.496227 + 0.868193i \(0.665282\pi\)
\(830\) 5.40214e17 0.0573533
\(831\) 1.13632e18 0.119699
\(832\) 1.10438e18 0.115430
\(833\) −4.71967e18 −0.489462
\(834\) −2.04847e18 −0.210790
\(835\) 3.16279e19 3.22929
\(836\) 2.30231e18 0.233251
\(837\) 5.78516e17 0.0581567
\(838\) −3.65390e18 −0.364477
\(839\) 1.10658e19 1.09529 0.547646 0.836710i \(-0.315524\pi\)
0.547646 + 0.836710i \(0.315524\pi\)
\(840\) 5.16865e18 0.507647
\(841\) −1.02221e19 −0.996247
\(842\) 4.10873e17 0.0397355
\(843\) 7.43785e17 0.0713787
\(844\) 6.65160e18 0.633432
\(845\) −1.62424e19 −1.53490
\(846\) −2.71051e17 −0.0254181
\(847\) 7.81562e18 0.727313
\(848\) −1.57651e18 −0.145587
\(849\) −2.59402e18 −0.237724
\(850\) 9.26090e18 0.842229
\(851\) −1.75206e19 −1.58128
\(852\) 2.25698e18 0.202148
\(853\) 1.96256e19 1.74443 0.872217 0.489119i \(-0.162682\pi\)
0.872217 + 0.489119i \(0.162682\pi\)
\(854\) 5.49000e18 0.484280
\(855\) −8.49182e18 −0.743398
\(856\) 5.22282e18 0.453760
\(857\) −5.45242e18 −0.470126 −0.235063 0.971980i \(-0.575530\pi\)
−0.235063 + 0.971980i \(0.575530\pi\)
\(858\) −1.73730e17 −0.0148665
\(859\) −5.00600e18 −0.425144 −0.212572 0.977145i \(-0.568184\pi\)
−0.212572 + 0.977145i \(0.568184\pi\)
\(860\) 1.69432e19 1.42809
\(861\) 1.78100e18 0.148986
\(862\) 3.20037e18 0.265707
\(863\) 9.36860e18 0.771977 0.385989 0.922503i \(-0.373860\pi\)
0.385989 + 0.922503i \(0.373860\pi\)
\(864\) 2.08877e18 0.170825
\(865\) −6.85710e18 −0.556591
\(866\) −4.36073e18 −0.351312
\(867\) 2.50873e18 0.200599
\(868\) 2.53602e18 0.201268
\(869\) 2.28933e18 0.180335
\(870\) −2.78830e17 −0.0218004
\(871\) −1.45185e18 −0.112669
\(872\) 4.04344e18 0.311454
\(873\) 3.23561e18 0.247379
\(874\) 9.82864e18 0.745880
\(875\) −1.86938e19 −1.40814
\(876\) 4.57151e18 0.341808
\(877\) −1.78464e19 −1.32450 −0.662252 0.749281i \(-0.730399\pi\)
−0.662252 + 0.749281i \(0.730399\pi\)
\(878\) −6.56537e18 −0.483666
\(879\) 7.23020e18 0.528716
\(880\) 3.23471e18 0.234800
\(881\) 1.66487e19 1.19960 0.599801 0.800149i \(-0.295246\pi\)
0.599801 + 0.800149i \(0.295246\pi\)
\(882\) −6.92569e17 −0.0495356
\(883\) 9.29562e18 0.659985 0.329992 0.943984i \(-0.392954\pi\)
0.329992 + 0.943984i \(0.392954\pi\)
\(884\) 5.04590e18 0.355630
\(885\) 1.87895e18 0.131457
\(886\) 1.64993e18 0.114590
\(887\) −2.31206e19 −1.59403 −0.797013 0.603962i \(-0.793588\pi\)
−0.797013 + 0.603962i \(0.793588\pi\)
\(888\) −5.31338e18 −0.363652
\(889\) −1.01534e19 −0.689846
\(890\) −2.68117e18 −0.180838
\(891\) 3.46588e17 0.0232064
\(892\) 2.20646e19 1.46664
\(893\) 4.18115e18 0.275906
\(894\) 2.09209e18 0.137053
\(895\) −3.38086e19 −2.19876
\(896\) 1.18248e19 0.763472
\(897\) 5.22942e18 0.335199
\(898\) 5.50714e18 0.350453
\(899\) −2.93021e17 −0.0185123
\(900\) −9.58196e18 −0.601005
\(901\) −4.22195e18 −0.262907
\(902\) −4.04001e17 −0.0249770
\(903\) 6.66938e18 0.409369
\(904\) −1.78554e19 −1.08811
\(905\) −3.70608e19 −2.24233
\(906\) −5.75153e17 −0.0345502
\(907\) 5.63564e18 0.336121 0.168061 0.985777i \(-0.446250\pi\)
0.168061 + 0.985777i \(0.446250\pi\)
\(908\) −4.68683e18 −0.277537
\(909\) 5.81770e18 0.342047
\(910\) 2.80898e18 0.163976
\(911\) 4.33976e18 0.251534 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(912\) −8.22347e18 −0.473248
\(913\) 3.40113e17 0.0194340
\(914\) 8.61864e18 0.488977
\(915\) −3.23874e19 −1.82448
\(916\) 2.30206e19 1.28764
\(917\) 1.38990e19 0.771938
\(918\) 1.42767e18 0.0787317
\(919\) −1.11553e19 −0.610844 −0.305422 0.952217i \(-0.598798\pi\)
−0.305422 + 0.952217i \(0.598798\pi\)
\(920\) 3.52917e19 1.91890
\(921\) 1.49730e18 0.0808391
\(922\) −9.08577e18 −0.487091
\(923\) 2.62713e18 0.139853
\(924\) 1.51932e18 0.0803124
\(925\) 3.73686e19 1.96149
\(926\) 7.53119e18 0.392548
\(927\) −1.01261e19 −0.524112
\(928\) −1.05797e18 −0.0543767
\(929\) 1.47329e19 0.751944 0.375972 0.926631i \(-0.377309\pi\)
0.375972 + 0.926631i \(0.377309\pi\)
\(930\) 2.12181e18 0.107539
\(931\) 1.06834e19 0.537693
\(932\) −3.70639e18 −0.185246
\(933\) −8.98549e18 −0.445975
\(934\) −8.12784e18 −0.400609
\(935\) 8.66269e18 0.424011
\(936\) 1.58589e18 0.0770869
\(937\) −8.83941e18 −0.426694 −0.213347 0.976977i \(-0.568436\pi\)
−0.213347 + 0.976977i \(0.568436\pi\)
\(938\) −1.80073e18 −0.0863235
\(939\) −1.30333e19 −0.620481
\(940\) 7.00957e18 0.331406
\(941\) −1.84886e19 −0.868102 −0.434051 0.900888i \(-0.642916\pi\)
−0.434051 + 0.900888i \(0.642916\pi\)
\(942\) −3.82757e18 −0.178481
\(943\) 1.21608e19 0.563164
\(944\) 1.81957e18 0.0836857
\(945\) −5.60385e18 −0.255965
\(946\) −1.51288e18 −0.0686295
\(947\) 3.98813e19 1.79678 0.898389 0.439200i \(-0.144738\pi\)
0.898389 + 0.439200i \(0.144738\pi\)
\(948\) −9.75715e18 −0.436585
\(949\) 5.32126e18 0.236475
\(950\) −2.09628e19 −0.925223
\(951\) −1.05844e18 −0.0463975
\(952\) 1.34044e19 0.583590
\(953\) 1.34098e19 0.579852 0.289926 0.957049i \(-0.406369\pi\)
0.289926 + 0.957049i \(0.406369\pi\)
\(954\) −6.19533e17 −0.0266073
\(955\) 4.98933e19 2.12824
\(956\) 1.40171e19 0.593856
\(957\) −1.75548e17 −0.00738702
\(958\) 1.59513e18 0.0666683
\(959\) 7.22046e18 0.299739
\(960\) −8.08070e18 −0.333186
\(961\) −2.21877e19 −0.908680
\(962\) −2.88763e18 −0.117464
\(963\) −5.66259e18 −0.228794
\(964\) 1.80423e19 0.724086
\(965\) 1.39459e19 0.555930
\(966\) 6.48603e18 0.256819
\(967\) −4.28033e19 −1.68347 −0.841734 0.539892i \(-0.818465\pi\)
−0.841734 + 0.539892i \(0.818465\pi\)
\(968\) 1.61838e19 0.632252
\(969\) −2.20228e19 −0.854609
\(970\) 1.18672e19 0.457437
\(971\) −3.07681e19 −1.17808 −0.589041 0.808103i \(-0.700495\pi\)
−0.589041 + 0.808103i \(0.700495\pi\)
\(972\) −1.47716e18 −0.0561821
\(973\) 2.08526e19 0.787818
\(974\) −1.74185e19 −0.653698
\(975\) −1.11535e19 −0.415795
\(976\) −3.13639e19 −1.16147
\(977\) 3.07179e19 1.13000 0.564998 0.825093i \(-0.308877\pi\)
0.564998 + 0.825093i \(0.308877\pi\)
\(978\) −7.82034e18 −0.285774
\(979\) −1.68804e18 −0.0612766
\(980\) 1.79103e19 0.645853
\(981\) −4.38390e18 −0.157041
\(982\) −1.44095e18 −0.0512772
\(983\) 1.53784e18 0.0543641 0.0271820 0.999631i \(-0.491347\pi\)
0.0271820 + 0.999631i \(0.491347\pi\)
\(984\) 3.68792e18 0.129513
\(985\) −1.66514e19 −0.580919
\(986\) −7.23120e17 −0.0250617
\(987\) 2.75919e18 0.0949992
\(988\) −1.14218e19 −0.390674
\(989\) 4.55388e19 1.54741
\(990\) 1.27117e18 0.0429117
\(991\) −1.73780e18 −0.0582803 −0.0291401 0.999575i \(-0.509277\pi\)
−0.0291401 + 0.999575i \(0.509277\pi\)
\(992\) 8.05085e18 0.268235
\(993\) −8.35324e18 −0.276493
\(994\) 3.25843e18 0.107151
\(995\) −2.10443e19 −0.687519
\(996\) −1.44957e18 −0.0470492
\(997\) −2.74038e19 −0.883675 −0.441837 0.897095i \(-0.645673\pi\)
−0.441837 + 0.897095i \(0.645673\pi\)
\(998\) 1.04206e19 0.333843
\(999\) 5.76077e18 0.183360
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 177.14.a.a.1.19 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.19 30 1.1 even 1 trivial