Properties

Label 177.10.a.d.1.15
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.4806 q^{2} +81.0000 q^{3} -272.350 q^{4} +2705.59 q^{5} +1253.93 q^{6} +6167.99 q^{7} -12142.2 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+15.4806 q^{2} +81.0000 q^{3} -272.350 q^{4} +2705.59 q^{5} +1253.93 q^{6} +6167.99 q^{7} -12142.2 q^{8} +6561.00 q^{9} +41884.2 q^{10} -32873.7 q^{11} -22060.4 q^{12} +51126.1 q^{13} +95484.4 q^{14} +219153. q^{15} -48525.9 q^{16} +315918. q^{17} +101568. q^{18} -344475. q^{19} -736869. q^{20} +499607. q^{21} -508905. q^{22} +1.91491e6 q^{23} -983521. q^{24} +5.36710e6 q^{25} +791464. q^{26} +531441. q^{27} -1.67986e6 q^{28} +93802.5 q^{29} +3.39262e6 q^{30} -1.74203e6 q^{31} +5.46561e6 q^{32} -2.66277e6 q^{33} +4.89060e6 q^{34} +1.66881e7 q^{35} -1.78689e6 q^{36} +5.42725e6 q^{37} -5.33269e6 q^{38} +4.14122e6 q^{39} -3.28519e7 q^{40} -2.76230e7 q^{41} +7.73423e6 q^{42} -3.64951e7 q^{43} +8.95316e6 q^{44} +1.77514e7 q^{45} +2.96440e7 q^{46} +3.13110e7 q^{47} -3.93060e6 q^{48} -2.30947e6 q^{49} +8.30860e7 q^{50} +2.55893e7 q^{51} -1.39242e7 q^{52} +2.10120e7 q^{53} +8.22704e6 q^{54} -8.89427e7 q^{55} -7.48932e7 q^{56} -2.79025e7 q^{57} +1.45212e6 q^{58} -1.21174e7 q^{59} -5.96864e7 q^{60} -2.14087e7 q^{61} -2.69677e7 q^{62} +4.04682e7 q^{63} +1.09456e8 q^{64} +1.38326e8 q^{65} -4.12213e7 q^{66} +1.80558e8 q^{67} -8.60403e7 q^{68} +1.55108e8 q^{69} +2.58342e8 q^{70} -1.63644e8 q^{71} -7.96652e7 q^{72} +3.32586e8 q^{73} +8.40173e7 q^{74} +4.34735e8 q^{75} +9.38180e7 q^{76} -2.02765e8 q^{77} +6.41086e7 q^{78} +5.93325e8 q^{79} -1.31291e8 q^{80} +4.30467e7 q^{81} -4.27621e8 q^{82} +6.43071e8 q^{83} -1.36068e8 q^{84} +8.54744e8 q^{85} -5.64967e8 q^{86} +7.59801e6 q^{87} +3.99160e8 q^{88} -5.28602e7 q^{89} +2.74802e8 q^{90} +3.15346e8 q^{91} -5.21527e8 q^{92} -1.41105e8 q^{93} +4.84714e8 q^{94} -9.32009e8 q^{95} +4.42715e8 q^{96} -6.12427e8 q^{97} -3.57521e7 q^{98} -2.15684e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.4806 0.684153 0.342077 0.939672i \(-0.388870\pi\)
0.342077 + 0.939672i \(0.388870\pi\)
\(3\) 81.0000 0.577350
\(4\) −272.350 −0.531934
\(5\) 2705.59 1.93596 0.967982 0.251021i \(-0.0807662\pi\)
0.967982 + 0.251021i \(0.0807662\pi\)
\(6\) 1253.93 0.394996
\(7\) 6167.99 0.970963 0.485481 0.874247i \(-0.338644\pi\)
0.485481 + 0.874247i \(0.338644\pi\)
\(8\) −12142.2 −1.04808
\(9\) 6561.00 0.333333
\(10\) 41884.2 1.32450
\(11\) −32873.7 −0.676988 −0.338494 0.940968i \(-0.609918\pi\)
−0.338494 + 0.940968i \(0.609918\pi\)
\(12\) −22060.4 −0.307112
\(13\) 51126.1 0.496475 0.248238 0.968699i \(-0.420149\pi\)
0.248238 + 0.968699i \(0.420149\pi\)
\(14\) 95484.4 0.664287
\(15\) 219153. 1.11773
\(16\) −48525.9 −0.185112
\(17\) 315918. 0.917390 0.458695 0.888594i \(-0.348317\pi\)
0.458695 + 0.888594i \(0.348317\pi\)
\(18\) 101568. 0.228051
\(19\) −344475. −0.606411 −0.303205 0.952925i \(-0.598057\pi\)
−0.303205 + 0.952925i \(0.598057\pi\)
\(20\) −736869. −1.02981
\(21\) 499607. 0.560586
\(22\) −508905. −0.463164
\(23\) 1.91491e6 1.42683 0.713417 0.700740i \(-0.247147\pi\)
0.713417 + 0.700740i \(0.247147\pi\)
\(24\) −983521. −0.605108
\(25\) 5.36710e6 2.74795
\(26\) 791464. 0.339665
\(27\) 531441. 0.192450
\(28\) −1.67986e6 −0.516489
\(29\) 93802.5 0.0246277 0.0123138 0.999924i \(-0.496080\pi\)
0.0123138 + 0.999924i \(0.496080\pi\)
\(30\) 3.39262e6 0.764698
\(31\) −1.74203e6 −0.338788 −0.169394 0.985548i \(-0.554181\pi\)
−0.169394 + 0.985548i \(0.554181\pi\)
\(32\) 5.46561e6 0.921433
\(33\) −2.66277e6 −0.390859
\(34\) 4.89060e6 0.627635
\(35\) 1.66881e7 1.87975
\(36\) −1.78689e6 −0.177311
\(37\) 5.42725e6 0.476072 0.238036 0.971256i \(-0.423496\pi\)
0.238036 + 0.971256i \(0.423496\pi\)
\(38\) −5.33269e6 −0.414878
\(39\) 4.14122e6 0.286640
\(40\) −3.28519e7 −2.02904
\(41\) −2.76230e7 −1.52666 −0.763332 0.646007i \(-0.776438\pi\)
−0.763332 + 0.646007i \(0.776438\pi\)
\(42\) 7.73423e6 0.383527
\(43\) −3.64951e7 −1.62790 −0.813948 0.580938i \(-0.802686\pi\)
−0.813948 + 0.580938i \(0.802686\pi\)
\(44\) 8.95316e6 0.360113
\(45\) 1.77514e7 0.645321
\(46\) 2.96440e7 0.976173
\(47\) 3.13110e7 0.935960 0.467980 0.883739i \(-0.344982\pi\)
0.467980 + 0.883739i \(0.344982\pi\)
\(48\) −3.93060e6 −0.106874
\(49\) −2.30947e6 −0.0572309
\(50\) 8.30860e7 1.88002
\(51\) 2.55893e7 0.529655
\(52\) −1.39242e7 −0.264092
\(53\) 2.10120e7 0.365784 0.182892 0.983133i \(-0.441454\pi\)
0.182892 + 0.983133i \(0.441454\pi\)
\(54\) 8.22704e6 0.131665
\(55\) −8.89427e7 −1.31062
\(56\) −7.48932e7 −1.01764
\(57\) −2.79025e7 −0.350111
\(58\) 1.45212e6 0.0168491
\(59\) −1.21174e7 −0.130189
\(60\) −5.96864e7 −0.594558
\(61\) −2.14087e7 −0.197973 −0.0989867 0.995089i \(-0.531560\pi\)
−0.0989867 + 0.995089i \(0.531560\pi\)
\(62\) −2.69677e7 −0.231783
\(63\) 4.04682e7 0.323654
\(64\) 1.09456e8 0.815513
\(65\) 1.38326e8 0.961158
\(66\) −4.12213e7 −0.267408
\(67\) 1.80558e8 1.09466 0.547332 0.836915i \(-0.315643\pi\)
0.547332 + 0.836915i \(0.315643\pi\)
\(68\) −8.60403e7 −0.487991
\(69\) 1.55108e8 0.823783
\(70\) 2.58342e8 1.28604
\(71\) −1.63644e8 −0.764253 −0.382127 0.924110i \(-0.624808\pi\)
−0.382127 + 0.924110i \(0.624808\pi\)
\(72\) −7.96652e7 −0.349359
\(73\) 3.32586e8 1.37073 0.685364 0.728201i \(-0.259643\pi\)
0.685364 + 0.728201i \(0.259643\pi\)
\(74\) 8.40173e7 0.325706
\(75\) 4.34735e8 1.58653
\(76\) 9.38180e7 0.322571
\(77\) −2.02765e8 −0.657331
\(78\) 6.41086e7 0.196106
\(79\) 5.93325e8 1.71384 0.856920 0.515449i \(-0.172375\pi\)
0.856920 + 0.515449i \(0.172375\pi\)
\(80\) −1.31291e8 −0.358369
\(81\) 4.30467e7 0.111111
\(82\) −4.27621e8 −1.04447
\(83\) 6.43071e8 1.48733 0.743666 0.668552i \(-0.233085\pi\)
0.743666 + 0.668552i \(0.233085\pi\)
\(84\) −1.36068e8 −0.298195
\(85\) 8.54744e8 1.77603
\(86\) −5.64967e8 −1.11373
\(87\) 7.59801e6 0.0142188
\(88\) 3.99160e8 0.709537
\(89\) −5.28602e7 −0.0893045 −0.0446523 0.999003i \(-0.514218\pi\)
−0.0446523 + 0.999003i \(0.514218\pi\)
\(90\) 2.74802e8 0.441499
\(91\) 3.15346e8 0.482059
\(92\) −5.21527e8 −0.758982
\(93\) −1.41105e8 −0.195599
\(94\) 4.84714e8 0.640340
\(95\) −9.32009e8 −1.17399
\(96\) 4.42715e8 0.531990
\(97\) −6.12427e8 −0.702395 −0.351198 0.936301i \(-0.614225\pi\)
−0.351198 + 0.936301i \(0.614225\pi\)
\(98\) −3.57521e7 −0.0391547
\(99\) −2.15684e8 −0.225663
\(100\) −1.46173e9 −1.46173
\(101\) −4.75399e7 −0.0454581 −0.0227291 0.999742i \(-0.507236\pi\)
−0.0227291 + 0.999742i \(0.507236\pi\)
\(102\) 3.96139e8 0.362365
\(103\) 1.44103e9 1.26155 0.630775 0.775966i \(-0.282737\pi\)
0.630775 + 0.775966i \(0.282737\pi\)
\(104\) −6.20785e8 −0.520345
\(105\) 1.35173e9 1.08527
\(106\) 3.25278e8 0.250252
\(107\) −1.16043e9 −0.855841 −0.427921 0.903816i \(-0.640754\pi\)
−0.427921 + 0.903816i \(0.640754\pi\)
\(108\) −1.44738e8 −0.102371
\(109\) −1.35745e9 −0.921092 −0.460546 0.887636i \(-0.652346\pi\)
−0.460546 + 0.887636i \(0.652346\pi\)
\(110\) −1.37689e9 −0.896668
\(111\) 4.39608e8 0.274860
\(112\) −2.99307e8 −0.179736
\(113\) −1.97565e9 −1.13987 −0.569937 0.821688i \(-0.693033\pi\)
−0.569937 + 0.821688i \(0.693033\pi\)
\(114\) −4.31948e8 −0.239530
\(115\) 5.18097e9 2.76230
\(116\) −2.55472e7 −0.0131003
\(117\) 3.35438e8 0.165492
\(118\) −1.87584e8 −0.0890692
\(119\) 1.94858e9 0.890751
\(120\) −2.66101e9 −1.17147
\(121\) −1.27727e9 −0.541687
\(122\) −3.31421e8 −0.135444
\(123\) −2.23746e9 −0.881419
\(124\) 4.74443e8 0.180213
\(125\) 9.23682e9 3.38398
\(126\) 6.26473e8 0.221429
\(127\) 5.68693e9 1.93982 0.969909 0.243468i \(-0.0782849\pi\)
0.969909 + 0.243468i \(0.0782849\pi\)
\(128\) −1.10394e9 −0.363497
\(129\) −2.95610e9 −0.939866
\(130\) 2.14138e9 0.657580
\(131\) 2.31518e9 0.686852 0.343426 0.939180i \(-0.388413\pi\)
0.343426 + 0.939180i \(0.388413\pi\)
\(132\) 7.25206e8 0.207912
\(133\) −2.12472e9 −0.588802
\(134\) 2.79516e9 0.748919
\(135\) 1.43786e9 0.372576
\(136\) −3.83595e9 −0.961496
\(137\) −1.96670e9 −0.476975 −0.238488 0.971146i \(-0.576652\pi\)
−0.238488 + 0.971146i \(0.576652\pi\)
\(138\) 2.40116e9 0.563594
\(139\) 4.29465e9 0.975800 0.487900 0.872900i \(-0.337763\pi\)
0.487900 + 0.872900i \(0.337763\pi\)
\(140\) −4.54500e9 −0.999903
\(141\) 2.53619e9 0.540377
\(142\) −2.53331e9 −0.522866
\(143\) −1.68070e9 −0.336108
\(144\) −3.18378e8 −0.0617039
\(145\) 2.53791e8 0.0476783
\(146\) 5.14864e9 0.937788
\(147\) −1.87067e8 −0.0330423
\(148\) −1.47811e9 −0.253239
\(149\) −9.65567e8 −0.160489 −0.0802443 0.996775i \(-0.525570\pi\)
−0.0802443 + 0.996775i \(0.525570\pi\)
\(150\) 6.72997e9 1.08543
\(151\) −4.21969e9 −0.660518 −0.330259 0.943890i \(-0.607136\pi\)
−0.330259 + 0.943890i \(0.607136\pi\)
\(152\) 4.18270e9 0.635566
\(153\) 2.07274e9 0.305797
\(154\) −3.13892e9 −0.449715
\(155\) −4.71322e9 −0.655882
\(156\) −1.12786e9 −0.152474
\(157\) 1.50283e9 0.197407 0.0987033 0.995117i \(-0.468531\pi\)
0.0987033 + 0.995117i \(0.468531\pi\)
\(158\) 9.18503e9 1.17253
\(159\) 1.70197e9 0.211186
\(160\) 1.47877e10 1.78386
\(161\) 1.18112e10 1.38540
\(162\) 6.66390e8 0.0760170
\(163\) −1.21636e10 −1.34964 −0.674818 0.737984i \(-0.735778\pi\)
−0.674818 + 0.737984i \(0.735778\pi\)
\(164\) 7.52313e9 0.812085
\(165\) −7.20436e9 −0.756690
\(166\) 9.95514e9 1.01756
\(167\) −1.76101e10 −1.75201 −0.876007 0.482299i \(-0.839802\pi\)
−0.876007 + 0.482299i \(0.839802\pi\)
\(168\) −6.06635e9 −0.587537
\(169\) −7.99062e9 −0.753512
\(170\) 1.32320e10 1.21508
\(171\) −2.26010e9 −0.202137
\(172\) 9.93946e9 0.865934
\(173\) 4.59312e9 0.389852 0.194926 0.980818i \(-0.437553\pi\)
0.194926 + 0.980818i \(0.437553\pi\)
\(174\) 1.17622e8 0.00972784
\(175\) 3.31042e10 2.66816
\(176\) 1.59522e9 0.125318
\(177\) −9.81506e8 −0.0751646
\(178\) −8.18308e8 −0.0610980
\(179\) 2.09551e10 1.52564 0.762818 0.646613i \(-0.223815\pi\)
0.762818 + 0.646613i \(0.223815\pi\)
\(180\) −4.83460e9 −0.343268
\(181\) 5.51548e9 0.381970 0.190985 0.981593i \(-0.438832\pi\)
0.190985 + 0.981593i \(0.438832\pi\)
\(182\) 4.88174e9 0.329802
\(183\) −1.73411e9 −0.114300
\(184\) −2.32513e10 −1.49543
\(185\) 1.46839e10 0.921658
\(186\) −2.18439e9 −0.133820
\(187\) −1.03854e10 −0.621062
\(188\) −8.52757e9 −0.497869
\(189\) 3.27792e9 0.186862
\(190\) −1.44281e10 −0.803188
\(191\) −1.13676e9 −0.0618042 −0.0309021 0.999522i \(-0.509838\pi\)
−0.0309021 + 0.999522i \(0.509838\pi\)
\(192\) 8.86596e9 0.470837
\(193\) −1.22673e8 −0.00636414 −0.00318207 0.999995i \(-0.501013\pi\)
−0.00318207 + 0.999995i \(0.501013\pi\)
\(194\) −9.48075e9 −0.480546
\(195\) 1.12044e10 0.554925
\(196\) 6.28986e8 0.0304431
\(197\) 1.43712e10 0.679820 0.339910 0.940458i \(-0.389603\pi\)
0.339910 + 0.940458i \(0.389603\pi\)
\(198\) −3.33893e9 −0.154388
\(199\) −3.95837e10 −1.78928 −0.894639 0.446790i \(-0.852567\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(200\) −6.51686e10 −2.88007
\(201\) 1.46252e10 0.632005
\(202\) −7.35946e8 −0.0311003
\(203\) 5.78573e8 0.0239126
\(204\) −6.96926e9 −0.281742
\(205\) −7.47365e10 −2.95556
\(206\) 2.23080e10 0.863093
\(207\) 1.25637e10 0.475611
\(208\) −2.48094e9 −0.0919033
\(209\) 1.13242e10 0.410533
\(210\) 2.09257e10 0.742493
\(211\) 4.12016e10 1.43101 0.715505 0.698607i \(-0.246197\pi\)
0.715505 + 0.698607i \(0.246197\pi\)
\(212\) −5.72261e9 −0.194573
\(213\) −1.32552e10 −0.441242
\(214\) −1.79642e10 −0.585527
\(215\) −9.87408e10 −3.15155
\(216\) −6.45288e9 −0.201703
\(217\) −1.07448e10 −0.328951
\(218\) −2.10141e10 −0.630168
\(219\) 2.69395e10 0.791390
\(220\) 2.42236e10 0.697166
\(221\) 1.61516e10 0.455461
\(222\) 6.80540e9 0.188046
\(223\) 6.42284e10 1.73922 0.869611 0.493738i \(-0.164370\pi\)
0.869611 + 0.493738i \(0.164370\pi\)
\(224\) 3.37119e10 0.894677
\(225\) 3.52135e10 0.915985
\(226\) −3.05843e10 −0.779849
\(227\) −3.01980e10 −0.754851 −0.377426 0.926040i \(-0.623191\pi\)
−0.377426 + 0.926040i \(0.623191\pi\)
\(228\) 7.59925e9 0.186236
\(229\) 3.09811e10 0.744454 0.372227 0.928142i \(-0.378594\pi\)
0.372227 + 0.928142i \(0.378594\pi\)
\(230\) 8.02046e10 1.88984
\(231\) −1.64239e10 −0.379510
\(232\) −1.13897e9 −0.0258117
\(233\) −6.21511e10 −1.38149 −0.690744 0.723099i \(-0.742717\pi\)
−0.690744 + 0.723099i \(0.742717\pi\)
\(234\) 5.19280e9 0.113222
\(235\) 8.47149e10 1.81198
\(236\) 3.30017e9 0.0692519
\(237\) 4.80593e10 0.989487
\(238\) 3.01652e10 0.609410
\(239\) −4.77594e10 −0.946822 −0.473411 0.880842i \(-0.656978\pi\)
−0.473411 + 0.880842i \(0.656978\pi\)
\(240\) −1.06346e10 −0.206905
\(241\) −5.41525e10 −1.03405 −0.517026 0.855970i \(-0.672961\pi\)
−0.517026 + 0.855970i \(0.672961\pi\)
\(242\) −1.97729e10 −0.370597
\(243\) 3.48678e9 0.0641500
\(244\) 5.83068e9 0.105309
\(245\) −6.24849e9 −0.110797
\(246\) −3.46373e10 −0.603026
\(247\) −1.76117e10 −0.301068
\(248\) 2.11521e10 0.355076
\(249\) 5.20888e10 0.858711
\(250\) 1.42992e11 2.31516
\(251\) −6.90249e10 −1.09768 −0.548838 0.835929i \(-0.684930\pi\)
−0.548838 + 0.835929i \(0.684930\pi\)
\(252\) −1.10215e10 −0.172163
\(253\) −6.29502e10 −0.965950
\(254\) 8.80372e10 1.32713
\(255\) 6.92343e10 1.02539
\(256\) −7.31313e10 −1.06420
\(257\) −8.85275e9 −0.126584 −0.0632921 0.997995i \(-0.520160\pi\)
−0.0632921 + 0.997995i \(0.520160\pi\)
\(258\) −4.57623e10 −0.643012
\(259\) 3.34753e10 0.462248
\(260\) −3.76732e10 −0.511273
\(261\) 6.15438e8 0.00820923
\(262\) 3.58404e10 0.469912
\(263\) 1.29348e11 1.66709 0.833544 0.552453i \(-0.186308\pi\)
0.833544 + 0.552453i \(0.186308\pi\)
\(264\) 3.23319e10 0.409651
\(265\) 5.68498e10 0.708145
\(266\) −3.28920e10 −0.402831
\(267\) −4.28167e9 −0.0515600
\(268\) −4.91752e10 −0.582290
\(269\) −1.38394e11 −1.61151 −0.805755 0.592249i \(-0.798240\pi\)
−0.805755 + 0.592249i \(0.798240\pi\)
\(270\) 2.22590e10 0.254899
\(271\) 3.54688e10 0.399470 0.199735 0.979850i \(-0.435992\pi\)
0.199735 + 0.979850i \(0.435992\pi\)
\(272\) −1.53302e10 −0.169819
\(273\) 2.55430e10 0.278317
\(274\) −3.04457e10 −0.326324
\(275\) −1.76436e11 −1.86033
\(276\) −4.22437e10 −0.438198
\(277\) −9.61581e10 −0.981357 −0.490679 0.871341i \(-0.663251\pi\)
−0.490679 + 0.871341i \(0.663251\pi\)
\(278\) 6.64838e10 0.667597
\(279\) −1.14295e10 −0.112929
\(280\) −2.02630e11 −1.97012
\(281\) −1.28466e11 −1.22916 −0.614580 0.788855i \(-0.710674\pi\)
−0.614580 + 0.788855i \(0.710674\pi\)
\(282\) 3.92619e10 0.369700
\(283\) −1.14423e11 −1.06041 −0.530204 0.847870i \(-0.677885\pi\)
−0.530204 + 0.847870i \(0.677885\pi\)
\(284\) 4.45685e10 0.406532
\(285\) −7.54927e10 −0.677803
\(286\) −2.60183e10 −0.229949
\(287\) −1.70378e11 −1.48233
\(288\) 3.58599e10 0.307144
\(289\) −1.87839e10 −0.158396
\(290\) 3.92885e9 0.0326193
\(291\) −4.96066e10 −0.405528
\(292\) −9.05800e10 −0.729137
\(293\) −1.69874e11 −1.34655 −0.673275 0.739392i \(-0.735113\pi\)
−0.673275 + 0.739392i \(0.735113\pi\)
\(294\) −2.89592e9 −0.0226060
\(295\) −3.27846e10 −0.252041
\(296\) −6.58990e10 −0.498960
\(297\) −1.74704e10 −0.130286
\(298\) −1.49476e10 −0.109799
\(299\) 9.79020e10 0.708388
\(300\) −1.18400e11 −0.843931
\(301\) −2.25102e11 −1.58063
\(302\) −6.53234e10 −0.451895
\(303\) −3.85073e9 −0.0262453
\(304\) 1.67160e10 0.112254
\(305\) −5.79233e10 −0.383269
\(306\) 3.20872e10 0.209212
\(307\) 5.43889e10 0.349452 0.174726 0.984617i \(-0.444096\pi\)
0.174726 + 0.984617i \(0.444096\pi\)
\(308\) 5.52230e10 0.349657
\(309\) 1.16723e11 0.728356
\(310\) −7.29636e10 −0.448724
\(311\) 1.19316e11 0.723230 0.361615 0.932327i \(-0.382225\pi\)
0.361615 + 0.932327i \(0.382225\pi\)
\(312\) −5.02836e10 −0.300421
\(313\) −1.91719e11 −1.12906 −0.564528 0.825414i \(-0.690942\pi\)
−0.564528 + 0.825414i \(0.690942\pi\)
\(314\) 2.32648e10 0.135056
\(315\) 1.09490e11 0.626583
\(316\) −1.61592e11 −0.911651
\(317\) −7.25862e10 −0.403727 −0.201863 0.979414i \(-0.564700\pi\)
−0.201863 + 0.979414i \(0.564700\pi\)
\(318\) 2.63475e10 0.144483
\(319\) −3.08363e9 −0.0166727
\(320\) 2.96144e11 1.57880
\(321\) −9.39951e10 −0.494120
\(322\) 1.82844e11 0.947828
\(323\) −1.08826e11 −0.556315
\(324\) −1.17238e10 −0.0591038
\(325\) 2.74399e11 1.36429
\(326\) −1.88300e11 −0.923359
\(327\) −1.09953e11 −0.531793
\(328\) 3.35405e11 1.60006
\(329\) 1.93126e11 0.908782
\(330\) −1.11528e11 −0.517692
\(331\) −2.21274e11 −1.01322 −0.506611 0.862174i \(-0.669102\pi\)
−0.506611 + 0.862174i \(0.669102\pi\)
\(332\) −1.75141e11 −0.791163
\(333\) 3.56082e10 0.158691
\(334\) −2.72615e11 −1.19865
\(335\) 4.88517e11 2.11923
\(336\) −2.42439e10 −0.103771
\(337\) 1.16167e11 0.490622 0.245311 0.969444i \(-0.421110\pi\)
0.245311 + 0.969444i \(0.421110\pi\)
\(338\) −1.23700e11 −0.515518
\(339\) −1.60028e11 −0.658107
\(340\) −2.32790e11 −0.944733
\(341\) 5.72670e10 0.229356
\(342\) −3.49878e10 −0.138293
\(343\) −2.63146e11 −1.02653
\(344\) 4.43132e11 1.70616
\(345\) 4.19658e11 1.59481
\(346\) 7.11043e10 0.266719
\(347\) 2.20270e11 0.815591 0.407795 0.913073i \(-0.366298\pi\)
0.407795 + 0.913073i \(0.366298\pi\)
\(348\) −2.06932e9 −0.00756347
\(349\) −1.49592e11 −0.539751 −0.269875 0.962895i \(-0.586982\pi\)
−0.269875 + 0.962895i \(0.586982\pi\)
\(350\) 5.12474e11 1.82543
\(351\) 2.71705e10 0.0955467
\(352\) −1.79675e11 −0.623800
\(353\) 1.18625e11 0.406621 0.203310 0.979114i \(-0.434830\pi\)
0.203310 + 0.979114i \(0.434830\pi\)
\(354\) −1.51943e10 −0.0514241
\(355\) −4.42753e11 −1.47957
\(356\) 1.43965e10 0.0475042
\(357\) 1.57835e11 0.514276
\(358\) 3.24398e11 1.04377
\(359\) 1.65103e11 0.524602 0.262301 0.964986i \(-0.415519\pi\)
0.262301 + 0.964986i \(0.415519\pi\)
\(360\) −2.15541e11 −0.676347
\(361\) −2.04025e11 −0.632266
\(362\) 8.53830e10 0.261326
\(363\) −1.03459e11 −0.312743
\(364\) −8.58845e10 −0.256424
\(365\) 8.99842e11 2.65368
\(366\) −2.68451e10 −0.0781987
\(367\) −1.12315e11 −0.323176 −0.161588 0.986858i \(-0.551662\pi\)
−0.161588 + 0.986858i \(0.551662\pi\)
\(368\) −9.29228e10 −0.264123
\(369\) −1.81234e11 −0.508888
\(370\) 2.27316e11 0.630555
\(371\) 1.29602e11 0.355163
\(372\) 3.84299e10 0.104046
\(373\) 1.30882e11 0.350098 0.175049 0.984560i \(-0.443992\pi\)
0.175049 + 0.984560i \(0.443992\pi\)
\(374\) −1.60772e11 −0.424902
\(375\) 7.48182e11 1.95374
\(376\) −3.80186e11 −0.980959
\(377\) 4.79576e9 0.0122270
\(378\) 5.07443e10 0.127842
\(379\) −1.99756e11 −0.497305 −0.248652 0.968593i \(-0.579988\pi\)
−0.248652 + 0.968593i \(0.579988\pi\)
\(380\) 2.53833e11 0.624485
\(381\) 4.60641e11 1.11995
\(382\) −1.75977e10 −0.0422836
\(383\) 2.82553e11 0.670973 0.335487 0.942045i \(-0.391099\pi\)
0.335487 + 0.942045i \(0.391099\pi\)
\(384\) −8.94192e10 −0.209865
\(385\) −5.48598e11 −1.27257
\(386\) −1.89905e9 −0.00435404
\(387\) −2.39444e11 −0.542632
\(388\) 1.66795e11 0.373628
\(389\) −4.69799e11 −1.04025 −0.520126 0.854089i \(-0.674115\pi\)
−0.520126 + 0.854089i \(0.674115\pi\)
\(390\) 1.73452e11 0.379654
\(391\) 6.04954e11 1.30896
\(392\) 2.80422e10 0.0599825
\(393\) 1.87529e11 0.396554
\(394\) 2.22475e11 0.465101
\(395\) 1.60529e12 3.31793
\(396\) 5.87417e10 0.120038
\(397\) −3.74008e11 −0.755655 −0.377828 0.925876i \(-0.623329\pi\)
−0.377828 + 0.925876i \(0.623329\pi\)
\(398\) −6.12780e11 −1.22414
\(399\) −1.72102e11 −0.339945
\(400\) −2.60443e11 −0.508678
\(401\) −3.55173e11 −0.685946 −0.342973 0.939345i \(-0.611434\pi\)
−0.342973 + 0.939345i \(0.611434\pi\)
\(402\) 2.26408e11 0.432388
\(403\) −8.90633e10 −0.168200
\(404\) 1.29475e10 0.0241807
\(405\) 1.16467e11 0.215107
\(406\) 8.95668e9 0.0163599
\(407\) −1.78414e11 −0.322295
\(408\) −3.10712e11 −0.555120
\(409\) 1.11660e12 1.97308 0.986538 0.163530i \(-0.0522882\pi\)
0.986538 + 0.163530i \(0.0522882\pi\)
\(410\) −1.15697e12 −2.02206
\(411\) −1.59303e11 −0.275382
\(412\) −3.92464e11 −0.671062
\(413\) −7.47398e10 −0.126409
\(414\) 1.94494e11 0.325391
\(415\) 1.73989e12 2.87942
\(416\) 2.79435e11 0.457469
\(417\) 3.47866e11 0.563378
\(418\) 1.75305e11 0.280867
\(419\) −1.16246e12 −1.84253 −0.921265 0.388935i \(-0.872843\pi\)
−0.921265 + 0.388935i \(0.872843\pi\)
\(420\) −3.68145e11 −0.577294
\(421\) −9.54242e11 −1.48043 −0.740217 0.672368i \(-0.765277\pi\)
−0.740217 + 0.672368i \(0.765277\pi\)
\(422\) 6.37826e11 0.979030
\(423\) 2.05432e11 0.311987
\(424\) −2.55132e11 −0.383370
\(425\) 1.69556e12 2.52095
\(426\) −2.05198e11 −0.301877
\(427\) −1.32049e11 −0.192225
\(428\) 3.16045e11 0.455251
\(429\) −1.36137e11 −0.194052
\(430\) −1.52857e12 −2.15614
\(431\) −1.34099e11 −0.187187 −0.0935937 0.995610i \(-0.529835\pi\)
−0.0935937 + 0.995610i \(0.529835\pi\)
\(432\) −2.57886e10 −0.0356247
\(433\) 5.84817e11 0.799511 0.399756 0.916622i \(-0.369095\pi\)
0.399756 + 0.916622i \(0.369095\pi\)
\(434\) −1.66337e11 −0.225053
\(435\) 2.05571e10 0.0275271
\(436\) 3.69701e11 0.489961
\(437\) −6.59639e11 −0.865247
\(438\) 4.17040e11 0.541432
\(439\) −3.43004e11 −0.440766 −0.220383 0.975413i \(-0.570731\pi\)
−0.220383 + 0.975413i \(0.570731\pi\)
\(440\) 1.07996e12 1.37364
\(441\) −1.51525e10 −0.0190770
\(442\) 2.50038e11 0.311605
\(443\) 8.20374e10 0.101203 0.0506017 0.998719i \(-0.483886\pi\)
0.0506017 + 0.998719i \(0.483886\pi\)
\(444\) −1.19727e11 −0.146208
\(445\) −1.43018e11 −0.172890
\(446\) 9.94295e11 1.18989
\(447\) −7.82110e10 −0.0926582
\(448\) 6.75126e11 0.791833
\(449\) 3.17617e11 0.368803 0.184402 0.982851i \(-0.440965\pi\)
0.184402 + 0.982851i \(0.440965\pi\)
\(450\) 5.45127e11 0.626674
\(451\) 9.08069e11 1.03353
\(452\) 5.38069e11 0.606339
\(453\) −3.41795e11 −0.381350
\(454\) −4.67483e11 −0.516434
\(455\) 8.53196e11 0.933249
\(456\) 3.38799e11 0.366944
\(457\) −1.18051e12 −1.26604 −0.633018 0.774137i \(-0.718184\pi\)
−0.633018 + 0.774137i \(0.718184\pi\)
\(458\) 4.79607e11 0.509320
\(459\) 1.67892e11 0.176552
\(460\) −1.41104e12 −1.46936
\(461\) −6.23259e11 −0.642709 −0.321354 0.946959i \(-0.604138\pi\)
−0.321354 + 0.946959i \(0.604138\pi\)
\(462\) −2.54253e11 −0.259643
\(463\) 5.71370e11 0.577834 0.288917 0.957354i \(-0.406705\pi\)
0.288917 + 0.957354i \(0.406705\pi\)
\(464\) −4.55185e9 −0.00455887
\(465\) −3.81771e11 −0.378673
\(466\) −9.62138e11 −0.945150
\(467\) −6.04506e11 −0.588132 −0.294066 0.955785i \(-0.595008\pi\)
−0.294066 + 0.955785i \(0.595008\pi\)
\(468\) −9.13568e10 −0.0880308
\(469\) 1.11368e12 1.06288
\(470\) 1.31144e12 1.23967
\(471\) 1.21729e11 0.113973
\(472\) 1.47132e11 0.136448
\(473\) 1.19973e12 1.10207
\(474\) 7.43988e11 0.676960
\(475\) −1.84883e12 −1.66639
\(476\) −5.30696e11 −0.473821
\(477\) 1.37859e11 0.121928
\(478\) −7.39346e11 −0.647772
\(479\) 1.66001e12 1.44079 0.720396 0.693563i \(-0.243960\pi\)
0.720396 + 0.693563i \(0.243960\pi\)
\(480\) 1.19780e12 1.02991
\(481\) 2.77474e11 0.236358
\(482\) −8.38315e11 −0.707450
\(483\) 9.56704e11 0.799863
\(484\) 3.47865e11 0.288142
\(485\) −1.65698e12 −1.35981
\(486\) 5.39776e10 0.0438885
\(487\) 1.61282e11 0.129929 0.0649643 0.997888i \(-0.479307\pi\)
0.0649643 + 0.997888i \(0.479307\pi\)
\(488\) 2.59950e11 0.207491
\(489\) −9.85249e11 −0.779213
\(490\) −9.67306e10 −0.0758021
\(491\) −2.97845e11 −0.231272 −0.115636 0.993292i \(-0.536891\pi\)
−0.115636 + 0.993292i \(0.536891\pi\)
\(492\) 6.09374e11 0.468857
\(493\) 2.96339e10 0.0225932
\(494\) −2.72640e11 −0.205977
\(495\) −5.83553e11 −0.436875
\(496\) 8.45336e10 0.0627136
\(497\) −1.00935e12 −0.742061
\(498\) 8.06367e11 0.587490
\(499\) −9.01997e11 −0.651257 −0.325629 0.945498i \(-0.605576\pi\)
−0.325629 + 0.945498i \(0.605576\pi\)
\(500\) −2.51565e12 −1.80005
\(501\) −1.42642e12 −1.01153
\(502\) −1.06855e12 −0.750978
\(503\) −8.18016e11 −0.569778 −0.284889 0.958560i \(-0.591957\pi\)
−0.284889 + 0.958560i \(0.591957\pi\)
\(504\) −4.91374e11 −0.339215
\(505\) −1.28623e11 −0.0880053
\(506\) −9.74508e11 −0.660858
\(507\) −6.47240e11 −0.435040
\(508\) −1.54884e12 −1.03186
\(509\) −1.65125e12 −1.09039 −0.545196 0.838309i \(-0.683545\pi\)
−0.545196 + 0.838309i \(0.683545\pi\)
\(510\) 1.07179e12 0.701526
\(511\) 2.05139e12 1.33093
\(512\) −5.66900e11 −0.364579
\(513\) −1.83068e11 −0.116704
\(514\) −1.37046e11 −0.0866030
\(515\) 3.89883e12 2.44231
\(516\) 8.05096e11 0.499947
\(517\) −1.02931e12 −0.633634
\(518\) 5.18218e11 0.316249
\(519\) 3.72042e11 0.225081
\(520\) −1.67959e12 −1.00737
\(521\) 2.10756e12 1.25317 0.626587 0.779352i \(-0.284451\pi\)
0.626587 + 0.779352i \(0.284451\pi\)
\(522\) 9.52737e9 0.00561637
\(523\) −2.54069e12 −1.48489 −0.742445 0.669907i \(-0.766334\pi\)
−0.742445 + 0.669907i \(0.766334\pi\)
\(524\) −6.30539e11 −0.365360
\(525\) 2.68144e12 1.54046
\(526\) 2.00239e12 1.14054
\(527\) −5.50339e11 −0.310801
\(528\) 1.29213e11 0.0723526
\(529\) 1.86573e12 1.03585
\(530\) 8.80070e11 0.484480
\(531\) −7.95020e10 −0.0433963
\(532\) 5.78668e11 0.313204
\(533\) −1.41226e12 −0.757951
\(534\) −6.62830e10 −0.0352749
\(535\) −3.13966e12 −1.65688
\(536\) −2.19238e12 −1.14729
\(537\) 1.69736e12 0.880827
\(538\) −2.14243e12 −1.10252
\(539\) 7.59209e10 0.0387447
\(540\) −3.91602e11 −0.198186
\(541\) −9.01442e11 −0.452429 −0.226214 0.974078i \(-0.572635\pi\)
−0.226214 + 0.974078i \(0.572635\pi\)
\(542\) 5.49078e11 0.273299
\(543\) 4.46754e11 0.220531
\(544\) 1.72668e12 0.845313
\(545\) −3.67269e12 −1.78320
\(546\) 3.95421e11 0.190411
\(547\) 1.22878e12 0.586854 0.293427 0.955982i \(-0.405204\pi\)
0.293427 + 0.955982i \(0.405204\pi\)
\(548\) 5.35632e11 0.253719
\(549\) −1.40463e11 −0.0659911
\(550\) −2.73134e12 −1.27275
\(551\) −3.23127e10 −0.0149345
\(552\) −1.88335e12 −0.863388
\(553\) 3.65962e12 1.66408
\(554\) −1.48859e12 −0.671399
\(555\) 1.18940e12 0.532119
\(556\) −1.16965e12 −0.519061
\(557\) 1.23203e12 0.542342 0.271171 0.962531i \(-0.412589\pi\)
0.271171 + 0.962531i \(0.412589\pi\)
\(558\) −1.76935e11 −0.0772610
\(559\) −1.86585e12 −0.808210
\(560\) −8.09803e11 −0.347963
\(561\) −8.41216e11 −0.358570
\(562\) −1.98873e12 −0.840933
\(563\) 9.73419e11 0.408331 0.204165 0.978936i \(-0.434552\pi\)
0.204165 + 0.978936i \(0.434552\pi\)
\(564\) −6.90734e11 −0.287445
\(565\) −5.34530e12 −2.20676
\(566\) −1.77134e12 −0.725482
\(567\) 2.65512e11 0.107885
\(568\) 1.98700e12 0.800997
\(569\) 2.21746e12 0.886850 0.443425 0.896311i \(-0.353763\pi\)
0.443425 + 0.896311i \(0.353763\pi\)
\(570\) −1.16867e12 −0.463721
\(571\) 1.58521e12 0.624056 0.312028 0.950073i \(-0.398992\pi\)
0.312028 + 0.950073i \(0.398992\pi\)
\(572\) 4.57740e11 0.178787
\(573\) −9.20775e10 −0.0356827
\(574\) −2.63756e12 −1.01414
\(575\) 1.02775e13 3.92087
\(576\) 7.18143e11 0.271838
\(577\) 1.15220e12 0.432750 0.216375 0.976310i \(-0.430577\pi\)
0.216375 + 0.976310i \(0.430577\pi\)
\(578\) −2.90786e11 −0.108367
\(579\) −9.93648e9 −0.00367434
\(580\) −6.91202e10 −0.0253617
\(581\) 3.96646e12 1.44414
\(582\) −7.67941e11 −0.277443
\(583\) −6.90740e11 −0.247632
\(584\) −4.03834e12 −1.43663
\(585\) 9.07559e11 0.320386
\(586\) −2.62975e12 −0.921246
\(587\) −3.59138e12 −1.24850 −0.624251 0.781224i \(-0.714596\pi\)
−0.624251 + 0.781224i \(0.714596\pi\)
\(588\) 5.09479e10 0.0175763
\(589\) 6.00087e11 0.205445
\(590\) −5.07526e11 −0.172435
\(591\) 1.16406e12 0.392494
\(592\) −2.63362e11 −0.0881264
\(593\) 2.18885e12 0.726891 0.363446 0.931615i \(-0.381600\pi\)
0.363446 + 0.931615i \(0.381600\pi\)
\(594\) −2.70453e11 −0.0891359
\(595\) 5.27206e12 1.72446
\(596\) 2.62973e11 0.0853694
\(597\) −3.20628e12 −1.03304
\(598\) 1.51558e12 0.484646
\(599\) −4.07824e11 −0.129435 −0.0647175 0.997904i \(-0.520615\pi\)
−0.0647175 + 0.997904i \(0.520615\pi\)
\(600\) −5.27865e12 −1.66281
\(601\) 2.45187e12 0.766587 0.383294 0.923627i \(-0.374790\pi\)
0.383294 + 0.923627i \(0.374790\pi\)
\(602\) −3.48471e12 −1.08139
\(603\) 1.18464e12 0.364888
\(604\) 1.14923e12 0.351352
\(605\) −3.45577e12 −1.04869
\(606\) −5.96117e10 −0.0179558
\(607\) −3.23935e12 −0.968520 −0.484260 0.874924i \(-0.660911\pi\)
−0.484260 + 0.874924i \(0.660911\pi\)
\(608\) −1.88277e12 −0.558767
\(609\) 4.68644e10 0.0138059
\(610\) −8.96688e11 −0.262215
\(611\) 1.60081e12 0.464681
\(612\) −5.64510e11 −0.162664
\(613\) −1.68344e12 −0.481531 −0.240766 0.970583i \(-0.577399\pi\)
−0.240766 + 0.970583i \(0.577399\pi\)
\(614\) 8.41974e11 0.239079
\(615\) −6.05366e12 −1.70640
\(616\) 2.46201e12 0.688934
\(617\) −3.21030e12 −0.891789 −0.445895 0.895085i \(-0.647114\pi\)
−0.445895 + 0.895085i \(0.647114\pi\)
\(618\) 1.80695e12 0.498307
\(619\) 5.01363e12 1.37260 0.686300 0.727318i \(-0.259234\pi\)
0.686300 + 0.727318i \(0.259234\pi\)
\(620\) 1.28365e12 0.348886
\(621\) 1.01766e12 0.274594
\(622\) 1.84708e12 0.494800
\(623\) −3.26041e11 −0.0867114
\(624\) −2.00956e11 −0.0530604
\(625\) 1.45084e13 3.80330
\(626\) −2.96793e12 −0.772448
\(627\) 9.17258e11 0.237021
\(628\) −4.09296e11 −0.105007
\(629\) 1.71457e12 0.436743
\(630\) 1.69498e12 0.428679
\(631\) −7.69257e12 −1.93170 −0.965850 0.259103i \(-0.916573\pi\)
−0.965850 + 0.259103i \(0.916573\pi\)
\(632\) −7.20429e12 −1.79624
\(633\) 3.33733e12 0.826194
\(634\) −1.12368e12 −0.276211
\(635\) 1.53865e13 3.75542
\(636\) −4.63532e11 −0.112337
\(637\) −1.18074e11 −0.0284137
\(638\) −4.77366e10 −0.0114067
\(639\) −1.07367e12 −0.254751
\(640\) −2.98681e12 −0.703717
\(641\) −4.04028e12 −0.945258 −0.472629 0.881262i \(-0.656695\pi\)
−0.472629 + 0.881262i \(0.656695\pi\)
\(642\) −1.45510e12 −0.338054
\(643\) 3.64890e12 0.841807 0.420904 0.907105i \(-0.361713\pi\)
0.420904 + 0.907105i \(0.361713\pi\)
\(644\) −3.21677e12 −0.736943
\(645\) −7.99801e12 −1.81955
\(646\) −1.68469e12 −0.380605
\(647\) −5.28484e12 −1.18567 −0.592834 0.805325i \(-0.701991\pi\)
−0.592834 + 0.805325i \(0.701991\pi\)
\(648\) −5.22683e11 −0.116453
\(649\) 3.98342e11 0.0881364
\(650\) 4.24787e12 0.933385
\(651\) −8.70332e11 −0.189920
\(652\) 3.31275e12 0.717918
\(653\) 1.54335e12 0.332166 0.166083 0.986112i \(-0.446888\pi\)
0.166083 + 0.986112i \(0.446888\pi\)
\(654\) −1.70214e12 −0.363828
\(655\) 6.26392e12 1.32972
\(656\) 1.34043e12 0.282603
\(657\) 2.18210e12 0.456909
\(658\) 2.98971e12 0.621746
\(659\) 4.58152e12 0.946292 0.473146 0.880984i \(-0.343118\pi\)
0.473146 + 0.880984i \(0.343118\pi\)
\(660\) 1.96211e12 0.402509
\(661\) 1.22952e11 0.0250513 0.0125257 0.999922i \(-0.496013\pi\)
0.0125257 + 0.999922i \(0.496013\pi\)
\(662\) −3.42546e12 −0.693200
\(663\) 1.30828e12 0.262961
\(664\) −7.80832e12 −1.55884
\(665\) −5.74863e12 −1.13990
\(666\) 5.51237e11 0.108569
\(667\) 1.79624e11 0.0351396
\(668\) 4.79611e12 0.931956
\(669\) 5.20250e12 1.00414
\(670\) 7.56255e12 1.44988
\(671\) 7.03784e11 0.134026
\(672\) 2.73066e12 0.516542
\(673\) −5.20612e12 −0.978242 −0.489121 0.872216i \(-0.662682\pi\)
−0.489121 + 0.872216i \(0.662682\pi\)
\(674\) 1.79833e12 0.335660
\(675\) 2.85230e12 0.528844
\(676\) 2.17625e12 0.400819
\(677\) −4.77789e12 −0.874152 −0.437076 0.899425i \(-0.643986\pi\)
−0.437076 + 0.899425i \(0.643986\pi\)
\(678\) −2.47733e12 −0.450246
\(679\) −3.77745e12 −0.682000
\(680\) −1.03785e13 −1.86142
\(681\) −2.44604e12 −0.435814
\(682\) 8.86528e11 0.156914
\(683\) −9.92427e11 −0.174504 −0.0872520 0.996186i \(-0.527809\pi\)
−0.0872520 + 0.996186i \(0.527809\pi\)
\(684\) 6.15540e11 0.107524
\(685\) −5.32109e12 −0.923406
\(686\) −4.07366e12 −0.702305
\(687\) 2.50947e12 0.429811
\(688\) 1.77096e12 0.301342
\(689\) 1.07426e12 0.181603
\(690\) 6.49657e12 1.09110
\(691\) −7.80881e12 −1.30297 −0.651483 0.758663i \(-0.725853\pi\)
−0.651483 + 0.758663i \(0.725853\pi\)
\(692\) −1.25094e12 −0.207376
\(693\) −1.33034e12 −0.219110
\(694\) 3.40991e12 0.557989
\(695\) 1.16196e13 1.88911
\(696\) −9.22567e10 −0.0149024
\(697\) −8.72659e12 −1.40055
\(698\) −2.31577e12 −0.369272
\(699\) −5.03424e12 −0.797603
\(700\) −9.01595e12 −1.41929
\(701\) 1.08389e13 1.69532 0.847662 0.530536i \(-0.178009\pi\)
0.847662 + 0.530536i \(0.178009\pi\)
\(702\) 4.20616e11 0.0653686
\(703\) −1.86955e12 −0.288695
\(704\) −3.59823e12 −0.552093
\(705\) 6.86191e12 1.04615
\(706\) 1.83639e12 0.278191
\(707\) −2.93225e11 −0.0441382
\(708\) 2.67314e11 0.0399826
\(709\) −6.00507e12 −0.892503 −0.446252 0.894908i \(-0.647241\pi\)
−0.446252 + 0.894908i \(0.647241\pi\)
\(710\) −6.85410e12 −1.01225
\(711\) 3.89280e12 0.571280
\(712\) 6.41840e11 0.0935981
\(713\) −3.33583e12 −0.483394
\(714\) 2.44338e12 0.351843
\(715\) −4.54730e12 −0.650693
\(716\) −5.70713e12 −0.811538
\(717\) −3.86851e12 −0.546648
\(718\) 2.55590e12 0.358908
\(719\) −1.67277e12 −0.233430 −0.116715 0.993165i \(-0.537236\pi\)
−0.116715 + 0.993165i \(0.537236\pi\)
\(720\) −8.61402e11 −0.119456
\(721\) 8.88824e12 1.22492
\(722\) −3.15843e12 −0.432567
\(723\) −4.38636e12 −0.597010
\(724\) −1.50214e12 −0.203183
\(725\) 5.03448e11 0.0676758
\(726\) −1.60161e12 −0.213964
\(727\) 2.70647e12 0.359334 0.179667 0.983727i \(-0.442498\pi\)
0.179667 + 0.983727i \(0.442498\pi\)
\(728\) −3.82900e12 −0.505236
\(729\) 2.82430e11 0.0370370
\(730\) 1.39301e13 1.81552
\(731\) −1.15294e13 −1.49341
\(732\) 4.72285e11 0.0608001
\(733\) −1.08195e13 −1.38433 −0.692163 0.721741i \(-0.743342\pi\)
−0.692163 + 0.721741i \(0.743342\pi\)
\(734\) −1.73870e12 −0.221102
\(735\) −5.06128e11 −0.0639687
\(736\) 1.04662e13 1.31473
\(737\) −5.93562e12 −0.741075
\(738\) −2.80562e12 −0.348157
\(739\) 7.60283e12 0.937725 0.468863 0.883271i \(-0.344664\pi\)
0.468863 + 0.883271i \(0.344664\pi\)
\(740\) −3.99917e12 −0.490261
\(741\) −1.42655e12 −0.173822
\(742\) 2.00631e12 0.242986
\(743\) 1.12698e13 1.35665 0.678324 0.734763i \(-0.262707\pi\)
0.678324 + 0.734763i \(0.262707\pi\)
\(744\) 1.71332e12 0.205003
\(745\) −2.61243e12 −0.310700
\(746\) 2.02613e12 0.239521
\(747\) 4.21919e12 0.495777
\(748\) 2.82846e12 0.330364
\(749\) −7.15755e12 −0.830990
\(750\) 1.15823e13 1.33666
\(751\) 2.12477e12 0.243743 0.121872 0.992546i \(-0.461110\pi\)
0.121872 + 0.992546i \(0.461110\pi\)
\(752\) −1.51940e12 −0.173257
\(753\) −5.59102e12 −0.633743
\(754\) 7.42413e10 0.00836517
\(755\) −1.14168e13 −1.27874
\(756\) −8.92744e11 −0.0993983
\(757\) 1.03037e13 1.14041 0.570204 0.821503i \(-0.306864\pi\)
0.570204 + 0.821503i \(0.306864\pi\)
\(758\) −3.09234e12 −0.340233
\(759\) −5.09896e12 −0.557691
\(760\) 1.13167e13 1.23043
\(761\) 9.29234e12 1.00437 0.502185 0.864760i \(-0.332530\pi\)
0.502185 + 0.864760i \(0.332530\pi\)
\(762\) 7.13101e12 0.766221
\(763\) −8.37271e12 −0.894347
\(764\) 3.09597e11 0.0328758
\(765\) 5.60798e12 0.592011
\(766\) 4.37409e12 0.459048
\(767\) −6.19514e11 −0.0646356
\(768\) −5.92364e12 −0.614417
\(769\) 1.44633e13 1.49142 0.745710 0.666270i \(-0.232110\pi\)
0.745710 + 0.666270i \(0.232110\pi\)
\(770\) −8.49264e12 −0.870632
\(771\) −7.17073e11 −0.0730834
\(772\) 3.34099e10 0.00338530
\(773\) 1.46485e13 1.47566 0.737829 0.674988i \(-0.235851\pi\)
0.737829 + 0.674988i \(0.235851\pi\)
\(774\) −3.70675e12 −0.371243
\(775\) −9.34965e12 −0.930975
\(776\) 7.43623e12 0.736165
\(777\) 2.71150e12 0.266879
\(778\) −7.27278e12 −0.711692
\(779\) 9.51543e12 0.925785
\(780\) −3.05153e12 −0.295184
\(781\) 5.37958e12 0.517390
\(782\) 9.36507e12 0.895531
\(783\) 4.98505e10 0.00473960
\(784\) 1.12069e11 0.0105941
\(785\) 4.06605e12 0.382172
\(786\) 2.90307e12 0.271304
\(787\) 1.19309e13 1.10863 0.554316 0.832307i \(-0.312980\pi\)
0.554316 + 0.832307i \(0.312980\pi\)
\(788\) −3.91399e12 −0.361620
\(789\) 1.04772e13 0.962493
\(790\) 2.48510e13 2.26998
\(791\) −1.21858e13 −1.10678
\(792\) 2.61889e12 0.236512
\(793\) −1.09455e12 −0.0982889
\(794\) −5.78988e12 −0.516984
\(795\) 4.60483e12 0.408848
\(796\) 1.07806e13 0.951778
\(797\) 1.87900e13 1.64955 0.824774 0.565463i \(-0.191302\pi\)
0.824774 + 0.565463i \(0.191302\pi\)
\(798\) −2.66425e12 −0.232575
\(799\) 9.89171e12 0.858640
\(800\) 2.93345e13 2.53206
\(801\) −3.46816e11 −0.0297682
\(802\) −5.49830e12 −0.469292
\(803\) −1.09333e13 −0.927967
\(804\) −3.98319e12 −0.336185
\(805\) 3.19562e13 2.68209
\(806\) −1.37876e12 −0.115075
\(807\) −1.12099e13 −0.930406
\(808\) 5.77240e11 0.0476437
\(809\) 8.88894e12 0.729594 0.364797 0.931087i \(-0.381138\pi\)
0.364797 + 0.931087i \(0.381138\pi\)
\(810\) 1.80298e12 0.147166
\(811\) 9.54487e12 0.774776 0.387388 0.921917i \(-0.373377\pi\)
0.387388 + 0.921917i \(0.373377\pi\)
\(812\) −1.57575e11 −0.0127199
\(813\) 2.87297e12 0.230634
\(814\) −2.76196e12 −0.220499
\(815\) −3.29097e13 −2.61285
\(816\) −1.24175e12 −0.0980453
\(817\) 1.25717e13 0.987173
\(818\) 1.72857e13 1.34989
\(819\) 2.06898e12 0.160686
\(820\) 2.03545e13 1.57217
\(821\) 2.35485e13 1.80892 0.904460 0.426559i \(-0.140274\pi\)
0.904460 + 0.426559i \(0.140274\pi\)
\(822\) −2.46611e12 −0.188403
\(823\) −1.90283e13 −1.44577 −0.722887 0.690966i \(-0.757185\pi\)
−0.722887 + 0.690966i \(0.757185\pi\)
\(824\) −1.74973e13 −1.32220
\(825\) −1.42913e13 −1.07406
\(826\) −1.15702e12 −0.0864829
\(827\) 1.75869e13 1.30741 0.653707 0.756748i \(-0.273213\pi\)
0.653707 + 0.756748i \(0.273213\pi\)
\(828\) −3.42174e12 −0.252994
\(829\) −1.83668e13 −1.35063 −0.675317 0.737528i \(-0.735993\pi\)
−0.675317 + 0.737528i \(0.735993\pi\)
\(830\) 2.69345e13 1.96996
\(831\) −7.78881e12 −0.566587
\(832\) 5.59608e12 0.404882
\(833\) −7.29604e11 −0.0525031
\(834\) 5.38519e12 0.385437
\(835\) −4.76457e13 −3.39183
\(836\) −3.08414e12 −0.218377
\(837\) −9.25787e11 −0.0651998
\(838\) −1.79956e13 −1.26057
\(839\) −1.31008e13 −0.912788 −0.456394 0.889778i \(-0.650859\pi\)
−0.456394 + 0.889778i \(0.650859\pi\)
\(840\) −1.64131e13 −1.13745
\(841\) −1.44983e13 −0.999393
\(842\) −1.47723e13 −1.01284
\(843\) −1.04057e13 −0.709655
\(844\) −1.12213e13 −0.761204
\(845\) −2.16194e13 −1.45877
\(846\) 3.18021e12 0.213447
\(847\) −7.87819e12 −0.525958
\(848\) −1.01962e12 −0.0677109
\(849\) −9.26824e12 −0.612227
\(850\) 2.62483e13 1.72471
\(851\) 1.03927e13 0.679275
\(852\) 3.61005e12 0.234712
\(853\) −5.39668e12 −0.349025 −0.174512 0.984655i \(-0.555835\pi\)
−0.174512 + 0.984655i \(0.555835\pi\)
\(854\) −2.04420e12 −0.131511
\(855\) −6.11491e12 −0.391330
\(856\) 1.40903e13 0.896988
\(857\) −3.03714e13 −1.92332 −0.961659 0.274250i \(-0.911571\pi\)
−0.961659 + 0.274250i \(0.911571\pi\)
\(858\) −2.10749e12 −0.132761
\(859\) −5.28273e12 −0.331047 −0.165523 0.986206i \(-0.552931\pi\)
−0.165523 + 0.986206i \(0.552931\pi\)
\(860\) 2.68921e13 1.67642
\(861\) −1.38006e13 −0.855826
\(862\) −2.07593e12 −0.128065
\(863\) −1.50779e13 −0.925323 −0.462661 0.886535i \(-0.653105\pi\)
−0.462661 + 0.886535i \(0.653105\pi\)
\(864\) 2.90465e12 0.177330
\(865\) 1.24271e13 0.754739
\(866\) 9.05333e12 0.546988
\(867\) −1.52149e12 −0.0914501
\(868\) 2.92636e12 0.174980
\(869\) −1.95048e13 −1.16025
\(870\) 3.18237e11 0.0188327
\(871\) 9.23125e12 0.543474
\(872\) 1.64824e13 0.965376
\(873\) −4.01813e12 −0.234132
\(874\) −1.02116e13 −0.591962
\(875\) 5.69726e13 3.28572
\(876\) −7.33698e12 −0.420968
\(877\) 1.69113e13 0.965336 0.482668 0.875804i \(-0.339668\pi\)
0.482668 + 0.875804i \(0.339668\pi\)
\(878\) −5.30991e12 −0.301552
\(879\) −1.37598e13 −0.777431
\(880\) 4.31603e12 0.242612
\(881\) 1.01161e13 0.565748 0.282874 0.959157i \(-0.408712\pi\)
0.282874 + 0.959157i \(0.408712\pi\)
\(882\) −2.34569e11 −0.0130516
\(883\) −1.98105e13 −1.09666 −0.548331 0.836261i \(-0.684737\pi\)
−0.548331 + 0.836261i \(0.684737\pi\)
\(884\) −4.39891e12 −0.242276
\(885\) −2.65555e12 −0.145516
\(886\) 1.26999e12 0.0692386
\(887\) 2.64125e11 0.0143270 0.00716348 0.999974i \(-0.497720\pi\)
0.00716348 + 0.999974i \(0.497720\pi\)
\(888\) −5.33782e12 −0.288075
\(889\) 3.50769e13 1.88349
\(890\) −2.21401e12 −0.118283
\(891\) −1.41510e12 −0.0752209
\(892\) −1.74926e13 −0.925152
\(893\) −1.07859e13 −0.567576
\(894\) −1.21075e12 −0.0633924
\(895\) 5.66959e13 2.95358
\(896\) −6.80910e12 −0.352942
\(897\) 7.93006e12 0.408988
\(898\) 4.91691e12 0.252318
\(899\) −1.63407e11 −0.00834357
\(900\) −9.59042e12 −0.487244
\(901\) 6.63805e12 0.335567
\(902\) 1.40575e13 0.707095
\(903\) −1.82332e13 −0.912575
\(904\) 2.39888e13 1.19468
\(905\) 1.49226e13 0.739481
\(906\) −5.29120e12 −0.260902
\(907\) −2.74744e13 −1.34802 −0.674008 0.738724i \(-0.735429\pi\)
−0.674008 + 0.738724i \(0.735429\pi\)
\(908\) 8.22443e12 0.401531
\(909\) −3.11909e11 −0.0151527
\(910\) 1.32080e13 0.638485
\(911\) 1.80257e13 0.867081 0.433541 0.901134i \(-0.357264\pi\)
0.433541 + 0.901134i \(0.357264\pi\)
\(912\) 1.35399e12 0.0648097
\(913\) −2.11401e13 −1.00691
\(914\) −1.82750e13 −0.866162
\(915\) −4.69179e12 −0.221281
\(916\) −8.43773e12 −0.396001
\(917\) 1.42800e13 0.666908
\(918\) 2.59907e12 0.120788
\(919\) −3.60174e13 −1.66568 −0.832842 0.553511i \(-0.813288\pi\)
−0.832842 + 0.553511i \(0.813288\pi\)
\(920\) −6.29085e13 −2.89510
\(921\) 4.40550e12 0.201756
\(922\) −9.64844e12 −0.439711
\(923\) −8.36648e12 −0.379433
\(924\) 4.47306e12 0.201874
\(925\) 2.91286e13 1.30822
\(926\) 8.84517e12 0.395327
\(927\) 9.45457e12 0.420517
\(928\) 5.12688e11 0.0226928
\(929\) 2.58775e13 1.13986 0.569931 0.821693i \(-0.306970\pi\)
0.569931 + 0.821693i \(0.306970\pi\)
\(930\) −5.91006e12 −0.259071
\(931\) 7.95557e11 0.0347054
\(932\) 1.69269e13 0.734861
\(933\) 9.66459e12 0.417557
\(934\) −9.35812e12 −0.402372
\(935\) −2.80986e13 −1.20235
\(936\) −4.07297e12 −0.173448
\(937\) −2.81864e13 −1.19457 −0.597284 0.802030i \(-0.703753\pi\)
−0.597284 + 0.802030i \(0.703753\pi\)
\(938\) 1.72405e13 0.727172
\(939\) −1.55292e13 −0.651861
\(940\) −2.30721e13 −0.963857
\(941\) 4.32208e13 1.79697 0.898483 0.439009i \(-0.144670\pi\)
0.898483 + 0.439009i \(0.144670\pi\)
\(942\) 1.88444e12 0.0779748
\(943\) −5.28956e13 −2.17829
\(944\) 5.88006e11 0.0240995
\(945\) 8.86872e12 0.361758
\(946\) 1.85725e13 0.753982
\(947\) −2.25984e13 −0.913067 −0.456533 0.889706i \(-0.650909\pi\)
−0.456533 + 0.889706i \(0.650909\pi\)
\(948\) −1.30890e13 −0.526342
\(949\) 1.70038e13 0.680533
\(950\) −2.86211e13 −1.14007
\(951\) −5.87948e12 −0.233092
\(952\) −2.36601e13 −0.933577
\(953\) 3.52469e13 1.38421 0.692107 0.721795i \(-0.256683\pi\)
0.692107 + 0.721795i \(0.256683\pi\)
\(954\) 2.13415e12 0.0834175
\(955\) −3.07561e12 −0.119651
\(956\) 1.30073e13 0.503647
\(957\) −2.49774e11 −0.00962596
\(958\) 2.56980e13 0.985722
\(959\) −1.21306e13 −0.463125
\(960\) 2.39877e13 0.911523
\(961\) −2.34049e13 −0.885223
\(962\) 4.29548e12 0.161705
\(963\) −7.61360e12 −0.285280
\(964\) 1.47485e13 0.550047
\(965\) −3.31902e11 −0.0123207
\(966\) 1.48104e13 0.547229
\(967\) 2.49854e13 0.918897 0.459448 0.888205i \(-0.348047\pi\)
0.459448 + 0.888205i \(0.348047\pi\)
\(968\) 1.55089e13 0.567730
\(969\) −8.81489e12 −0.321189
\(970\) −2.56510e13 −0.930320
\(971\) 2.88425e12 0.104123 0.0520615 0.998644i \(-0.483421\pi\)
0.0520615 + 0.998644i \(0.483421\pi\)
\(972\) −9.49627e11 −0.0341236
\(973\) 2.64893e13 0.947466
\(974\) 2.49674e12 0.0888911
\(975\) 2.22263e13 0.787674
\(976\) 1.03888e12 0.0366472
\(977\) 2.74797e13 0.964908 0.482454 0.875921i \(-0.339746\pi\)
0.482454 + 0.875921i \(0.339746\pi\)
\(978\) −1.52523e13 −0.533101
\(979\) 1.73771e12 0.0604581
\(980\) 1.70178e12 0.0589367
\(981\) −8.90620e12 −0.307031
\(982\) −4.61083e12 −0.158226
\(983\) −1.15701e13 −0.395225 −0.197613 0.980280i \(-0.563319\pi\)
−0.197613 + 0.980280i \(0.563319\pi\)
\(984\) 2.71678e13 0.923796
\(985\) 3.88825e13 1.31611
\(986\) 4.58751e11 0.0154572
\(987\) 1.56432e13 0.524686
\(988\) 4.79655e12 0.160148
\(989\) −6.98849e13 −2.32274
\(990\) −9.03377e12 −0.298889
\(991\) 2.09240e13 0.689148 0.344574 0.938759i \(-0.388023\pi\)
0.344574 + 0.938759i \(0.388023\pi\)
\(992\) −9.52127e12 −0.312171
\(993\) −1.79232e13 −0.584984
\(994\) −1.56254e13 −0.507684
\(995\) −1.07097e14 −3.46398
\(996\) −1.41864e13 −0.456778
\(997\) −2.69160e13 −0.862744 −0.431372 0.902174i \(-0.641970\pi\)
−0.431372 + 0.902174i \(0.641970\pi\)
\(998\) −1.39635e13 −0.445560
\(999\) 2.88427e12 0.0916201
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.d.1.15 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.15 22 1.1 even 1 trivial