Properties

Label 177.12.a.b.1.20
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +52880.9 q^{10} -336316. q^{11} -199456. q^{12} -1.03704e6 q^{13} +9126.82 q^{14} +366816. q^{15} -1.83957e6 q^{16} +1.09205e7 q^{17} +2.06857e6 q^{18} +1.71468e7 q^{19} -1.23903e6 q^{20} +63309.5 q^{21} -1.17816e7 q^{22} +5.60344e7 q^{23} -2.44210e7 q^{24} -4.65494e7 q^{25} -3.63289e7 q^{26} +1.43489e7 q^{27} -213847. q^{28} -1.56066e8 q^{29} +1.28500e7 q^{30} -1.86762e8 q^{31} +1.41377e8 q^{32} -8.17247e7 q^{33} +3.82561e8 q^{34} +393283. q^{35} -4.84677e7 q^{36} -3.36109e8 q^{37} +6.00675e8 q^{38} -2.52000e8 q^{39} -1.51705e8 q^{40} -7.88676e7 q^{41} +2.21782e6 q^{42} -6.26130e8 q^{43} +2.76050e8 q^{44} +8.91362e7 q^{45} +1.96296e9 q^{46} -1.23527e9 q^{47} -4.47016e8 q^{48} -1.97726e9 q^{49} -1.63069e9 q^{50} +2.65369e9 q^{51} +8.51207e8 q^{52} -4.49700e9 q^{53} +5.02661e8 q^{54} -5.07679e8 q^{55} -2.61831e7 q^{56} +4.16667e9 q^{57} -5.46722e9 q^{58} -7.14924e8 q^{59} -3.01084e8 q^{60} -2.43334e9 q^{61} -6.54252e9 q^{62} +1.53842e7 q^{63} +8.72008e9 q^{64} -1.56544e9 q^{65} -2.86293e9 q^{66} +1.79589e10 q^{67} -8.96364e9 q^{68} +1.36163e10 q^{69} +1.37772e7 q^{70} +2.14587e10 q^{71} -5.93431e9 q^{72} -2.60537e10 q^{73} -1.17743e10 q^{74} -1.13115e10 q^{75} -1.40742e10 q^{76} -8.76214e7 q^{77} -8.82791e9 q^{78} -1.34645e9 q^{79} -2.77689e9 q^{80} +3.48678e9 q^{81} -2.76284e9 q^{82} -4.68213e10 q^{83} -5.19648e7 q^{84} +1.64849e10 q^{85} -2.19342e10 q^{86} -3.79241e10 q^{87} +3.37991e10 q^{88} -4.74741e10 q^{89} +3.12256e9 q^{90} -2.70183e8 q^{91} -4.59933e10 q^{92} -4.53831e10 q^{93} -4.32732e10 q^{94} +2.58836e10 q^{95} +3.43547e10 q^{96} -1.01566e11 q^{97} -6.92660e10 q^{98} -1.98591e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.0313 0.774090 0.387045 0.922061i \(-0.373496\pi\)
0.387045 + 0.922061i \(0.373496\pi\)
\(3\) 243.000 0.577350
\(4\) −820.805 −0.400784
\(5\) 1509.53 0.216026 0.108013 0.994149i \(-0.465551\pi\)
0.108013 + 0.994149i \(0.465551\pi\)
\(6\) 8512.61 0.446921
\(7\) 260.533 0.00585900 0.00292950 0.999996i \(-0.499068\pi\)
0.00292950 + 0.999996i \(0.499068\pi\)
\(8\) −100498. −1.08433
\(9\) 59049.0 0.333333
\(10\) 52880.9 0.167224
\(11\) −336316. −0.629633 −0.314816 0.949153i \(-0.601943\pi\)
−0.314816 + 0.949153i \(0.601943\pi\)
\(12\) −199456. −0.231393
\(13\) −1.03704e6 −0.774652 −0.387326 0.921943i \(-0.626601\pi\)
−0.387326 + 0.921943i \(0.626601\pi\)
\(14\) 9126.82 0.00453540
\(15\) 366816. 0.124723
\(16\) −1.83957e6 −0.438588
\(17\) 1.09205e7 1.86541 0.932707 0.360636i \(-0.117440\pi\)
0.932707 + 0.360636i \(0.117440\pi\)
\(18\) 2.06857e6 0.258030
\(19\) 1.71468e7 1.58869 0.794343 0.607469i \(-0.207815\pi\)
0.794343 + 0.607469i \(0.207815\pi\)
\(20\) −1.23903e6 −0.0865799
\(21\) 63309.5 0.00338270
\(22\) −1.17816e7 −0.487393
\(23\) 5.60344e7 1.81531 0.907656 0.419715i \(-0.137870\pi\)
0.907656 + 0.419715i \(0.137870\pi\)
\(24\) −2.44210e7 −0.626040
\(25\) −4.65494e7 −0.953333
\(26\) −3.63289e7 −0.599651
\(27\) 1.43489e7 0.192450
\(28\) −213847. −0.00234819
\(29\) −1.56066e8 −1.41293 −0.706465 0.707748i \(-0.749711\pi\)
−0.706465 + 0.707748i \(0.749711\pi\)
\(30\) 1.28500e7 0.0965468
\(31\) −1.86762e8 −1.17165 −0.585826 0.810437i \(-0.699230\pi\)
−0.585826 + 0.810437i \(0.699230\pi\)
\(32\) 1.41377e8 0.744826
\(33\) −8.17247e7 −0.363519
\(34\) 3.82561e8 1.44400
\(35\) 393283. 0.00126570
\(36\) −4.84677e7 −0.133595
\(37\) −3.36109e8 −0.796838 −0.398419 0.917203i \(-0.630441\pi\)
−0.398419 + 0.917203i \(0.630441\pi\)
\(38\) 6.00675e8 1.22979
\(39\) −2.52000e8 −0.447246
\(40\) −1.51705e8 −0.234245
\(41\) −7.88676e7 −0.106313 −0.0531566 0.998586i \(-0.516928\pi\)
−0.0531566 + 0.998586i \(0.516928\pi\)
\(42\) 2.21782e6 0.00261851
\(43\) −6.26130e8 −0.649513 −0.324757 0.945798i \(-0.605282\pi\)
−0.324757 + 0.945798i \(0.605282\pi\)
\(44\) 2.76050e8 0.252347
\(45\) 8.91362e7 0.0720088
\(46\) 1.96296e9 1.40522
\(47\) −1.23527e9 −0.785642 −0.392821 0.919615i \(-0.628501\pi\)
−0.392821 + 0.919615i \(0.628501\pi\)
\(48\) −4.47016e8 −0.253219
\(49\) −1.97726e9 −0.999966
\(50\) −1.63069e9 −0.737966
\(51\) 2.65369e9 1.07700
\(52\) 8.51207e8 0.310468
\(53\) −4.49700e9 −1.47708 −0.738542 0.674207i \(-0.764485\pi\)
−0.738542 + 0.674207i \(0.764485\pi\)
\(54\) 5.02661e8 0.148974
\(55\) −5.07679e8 −0.136017
\(56\) −2.61831e7 −0.00635311
\(57\) 4.16667e9 0.917228
\(58\) −5.46722e9 −1.09374
\(59\) −7.14924e8 −0.130189
\(60\) −3.01084e8 −0.0499869
\(61\) −2.43334e9 −0.368884 −0.184442 0.982843i \(-0.559048\pi\)
−0.184442 + 0.982843i \(0.559048\pi\)
\(62\) −6.54252e9 −0.906965
\(63\) 1.53842e7 0.00195300
\(64\) 8.72008e9 1.01515
\(65\) −1.56544e9 −0.167345
\(66\) −2.86293e9 −0.281396
\(67\) 1.79589e10 1.62506 0.812530 0.582920i \(-0.198090\pi\)
0.812530 + 0.582920i \(0.198090\pi\)
\(68\) −8.96364e9 −0.747628
\(69\) 1.36163e10 1.04807
\(70\) 1.37772e7 0.000979766 0
\(71\) 2.14587e10 1.41151 0.705753 0.708458i \(-0.250609\pi\)
0.705753 + 0.708458i \(0.250609\pi\)
\(72\) −5.93431e9 −0.361445
\(73\) −2.60537e10 −1.47094 −0.735469 0.677559i \(-0.763038\pi\)
−0.735469 + 0.677559i \(0.763038\pi\)
\(74\) −1.17743e10 −0.616825
\(75\) −1.13115e10 −0.550407
\(76\) −1.40742e10 −0.636720
\(77\) −8.76214e7 −0.00368902
\(78\) −8.82791e9 −0.346209
\(79\) −1.34645e9 −0.0492313 −0.0246157 0.999697i \(-0.507836\pi\)
−0.0246157 + 0.999697i \(0.507836\pi\)
\(80\) −2.77689e9 −0.0947466
\(81\) 3.48678e9 0.111111
\(82\) −2.76284e9 −0.0822961
\(83\) −4.68213e10 −1.30471 −0.652355 0.757913i \(-0.726219\pi\)
−0.652355 + 0.757913i \(0.726219\pi\)
\(84\) −5.19648e7 −0.00135573
\(85\) 1.64849e10 0.402978
\(86\) −2.19342e10 −0.502782
\(87\) −3.79241e10 −0.815755
\(88\) 3.37991e10 0.682732
\(89\) −4.74741e10 −0.901179 −0.450590 0.892731i \(-0.648786\pi\)
−0.450590 + 0.892731i \(0.648786\pi\)
\(90\) 3.12256e9 0.0557413
\(91\) −2.70183e8 −0.00453869
\(92\) −4.59933e10 −0.727548
\(93\) −4.53831e10 −0.676454
\(94\) −4.32732e10 −0.608158
\(95\) 2.58836e10 0.343198
\(96\) 3.43547e10 0.430026
\(97\) −1.01566e11 −1.20090 −0.600448 0.799663i \(-0.705011\pi\)
−0.600448 + 0.799663i \(0.705011\pi\)
\(98\) −6.92660e10 −0.774064
\(99\) −1.98591e10 −0.209878
\(100\) 3.82080e10 0.382080
\(101\) 1.33164e9 0.0126072 0.00630361 0.999980i \(-0.497993\pi\)
0.00630361 + 0.999980i \(0.497993\pi\)
\(102\) 9.29623e10 0.833693
\(103\) −6.78644e10 −0.576816 −0.288408 0.957508i \(-0.593126\pi\)
−0.288408 + 0.957508i \(0.593126\pi\)
\(104\) 1.04220e11 0.839981
\(105\) 9.55677e7 0.000730752 0
\(106\) −1.57536e11 −1.14340
\(107\) 3.57206e10 0.246211 0.123105 0.992394i \(-0.460715\pi\)
0.123105 + 0.992394i \(0.460715\pi\)
\(108\) −1.17777e10 −0.0771309
\(109\) −2.99734e11 −1.86591 −0.932955 0.359993i \(-0.882779\pi\)
−0.932955 + 0.359993i \(0.882779\pi\)
\(110\) −1.77847e10 −0.105290
\(111\) −8.16744e10 −0.460055
\(112\) −4.79270e8 −0.00256969
\(113\) 2.10528e11 1.07492 0.537462 0.843288i \(-0.319383\pi\)
0.537462 + 0.843288i \(0.319383\pi\)
\(114\) 1.45964e11 0.710018
\(115\) 8.45855e10 0.392155
\(116\) 1.28100e11 0.566279
\(117\) −6.12361e10 −0.258217
\(118\) −2.50448e10 −0.100778
\(119\) 2.84516e9 0.0109295
\(120\) −3.68643e10 −0.135241
\(121\) −1.72203e11 −0.603562
\(122\) −8.52433e10 −0.285549
\(123\) −1.91648e10 −0.0613800
\(124\) 1.53295e11 0.469579
\(125\) −1.43975e11 −0.421971
\(126\) 5.38930e8 0.00151180
\(127\) 4.86852e11 1.30760 0.653802 0.756665i \(-0.273173\pi\)
0.653802 + 0.756665i \(0.273173\pi\)
\(128\) 1.59353e10 0.0409926
\(129\) −1.52150e11 −0.374997
\(130\) −5.48395e10 −0.129540
\(131\) 5.36260e11 1.21446 0.607230 0.794526i \(-0.292281\pi\)
0.607230 + 0.794526i \(0.292281\pi\)
\(132\) 6.70801e10 0.145692
\(133\) 4.46731e9 0.00930812
\(134\) 6.29126e11 1.25794
\(135\) 2.16601e10 0.0415743
\(136\) −1.09749e12 −2.02273
\(137\) −7.55158e11 −1.33683 −0.668413 0.743790i \(-0.733026\pi\)
−0.668413 + 0.743790i \(0.733026\pi\)
\(138\) 4.76999e11 0.811302
\(139\) −4.94454e11 −0.808248 −0.404124 0.914704i \(-0.632424\pi\)
−0.404124 + 0.914704i \(0.632424\pi\)
\(140\) −3.22808e8 −0.000507272 0
\(141\) −3.00171e11 −0.453590
\(142\) 7.51727e11 1.09263
\(143\) 3.48773e11 0.487746
\(144\) −1.08625e11 −0.146196
\(145\) −2.35587e11 −0.305230
\(146\) −9.12697e11 −1.13864
\(147\) −4.80474e11 −0.577330
\(148\) 2.75880e11 0.319360
\(149\) −4.43350e11 −0.494564 −0.247282 0.968944i \(-0.579537\pi\)
−0.247282 + 0.968944i \(0.579537\pi\)
\(150\) −3.96257e11 −0.426065
\(151\) −6.47742e10 −0.0671473 −0.0335737 0.999436i \(-0.510689\pi\)
−0.0335737 + 0.999436i \(0.510689\pi\)
\(152\) −1.72322e12 −1.72267
\(153\) 6.44847e11 0.621804
\(154\) −3.06949e9 −0.00285564
\(155\) −2.81923e11 −0.253108
\(156\) 2.06843e11 0.179249
\(157\) −1.43131e12 −1.19752 −0.598762 0.800927i \(-0.704341\pi\)
−0.598762 + 0.800927i \(0.704341\pi\)
\(158\) −4.71680e10 −0.0381095
\(159\) −1.09277e12 −0.852795
\(160\) 2.13413e11 0.160902
\(161\) 1.45988e10 0.0106359
\(162\) 1.22147e11 0.0860101
\(163\) 1.47004e12 1.00069 0.500343 0.865827i \(-0.333207\pi\)
0.500343 + 0.865827i \(0.333207\pi\)
\(164\) 6.47349e10 0.0426086
\(165\) −1.23366e11 −0.0785296
\(166\) −1.64021e12 −1.00996
\(167\) 2.21102e12 1.31720 0.658602 0.752492i \(-0.271148\pi\)
0.658602 + 0.752492i \(0.271148\pi\)
\(168\) −6.36249e9 −0.00366797
\(169\) −7.16710e11 −0.399914
\(170\) 5.77488e11 0.311942
\(171\) 1.01250e12 0.529562
\(172\) 5.13931e11 0.260315
\(173\) 2.07803e12 1.01952 0.509762 0.860315i \(-0.329733\pi\)
0.509762 + 0.860315i \(0.329733\pi\)
\(174\) −1.32853e12 −0.631468
\(175\) −1.21277e10 −0.00558558
\(176\) 6.18677e11 0.276150
\(177\) −1.73727e11 −0.0751646
\(178\) −1.66308e12 −0.697594
\(179\) −1.83659e12 −0.747001 −0.373501 0.927630i \(-0.621843\pi\)
−0.373501 + 0.927630i \(0.621843\pi\)
\(180\) −7.31635e10 −0.0288600
\(181\) 1.42224e12 0.544179 0.272089 0.962272i \(-0.412285\pi\)
0.272089 + 0.962272i \(0.412285\pi\)
\(182\) −9.46487e9 −0.00351336
\(183\) −5.91302e11 −0.212975
\(184\) −5.63135e12 −1.96840
\(185\) −5.07366e11 −0.172138
\(186\) −1.58983e12 −0.523636
\(187\) −3.67275e12 −1.17453
\(188\) 1.01392e12 0.314873
\(189\) 3.73836e9 0.00112757
\(190\) 9.06737e11 0.265666
\(191\) −1.86729e12 −0.531529 −0.265765 0.964038i \(-0.585624\pi\)
−0.265765 + 0.964038i \(0.585624\pi\)
\(192\) 2.11898e12 0.586098
\(193\) −4.92216e11 −0.132309 −0.0661546 0.997809i \(-0.521073\pi\)
−0.0661546 + 0.997809i \(0.521073\pi\)
\(194\) −3.55801e12 −0.929603
\(195\) −3.80402e11 −0.0966168
\(196\) 1.62294e12 0.400770
\(197\) −2.05476e12 −0.493397 −0.246698 0.969092i \(-0.579346\pi\)
−0.246698 + 0.969092i \(0.579346\pi\)
\(198\) −6.95691e11 −0.162464
\(199\) −4.52000e11 −0.102671 −0.0513353 0.998681i \(-0.516348\pi\)
−0.0513353 + 0.998681i \(0.516348\pi\)
\(200\) 4.67813e12 1.03373
\(201\) 4.36402e12 0.938228
\(202\) 4.66491e10 0.00975913
\(203\) −4.06605e10 −0.00827836
\(204\) −2.17816e12 −0.431643
\(205\) −1.19053e11 −0.0229665
\(206\) −2.37738e12 −0.446508
\(207\) 3.30877e12 0.605104
\(208\) 1.90771e12 0.339753
\(209\) −5.76674e12 −1.00029
\(210\) 3.34786e9 0.000565668 0
\(211\) −5.87467e12 −0.967007 −0.483504 0.875342i \(-0.660636\pi\)
−0.483504 + 0.875342i \(0.660636\pi\)
\(212\) 3.69116e12 0.591992
\(213\) 5.21447e12 0.814933
\(214\) 1.25134e12 0.190590
\(215\) −9.45162e11 −0.140312
\(216\) −1.44204e12 −0.208680
\(217\) −4.86576e10 −0.00686471
\(218\) −1.05001e13 −1.44438
\(219\) −6.33106e12 −0.849246
\(220\) 4.16706e11 0.0545136
\(221\) −1.13250e13 −1.44505
\(222\) −2.86116e12 −0.356124
\(223\) −6.67176e12 −0.810146 −0.405073 0.914284i \(-0.632754\pi\)
−0.405073 + 0.914284i \(0.632754\pi\)
\(224\) 3.68335e10 0.00436394
\(225\) −2.74870e12 −0.317778
\(226\) 7.37507e12 0.832089
\(227\) −8.01220e12 −0.882286 −0.441143 0.897437i \(-0.645427\pi\)
−0.441143 + 0.897437i \(0.645427\pi\)
\(228\) −3.42003e12 −0.367610
\(229\) −2.34900e12 −0.246484 −0.123242 0.992377i \(-0.539329\pi\)
−0.123242 + 0.992377i \(0.539329\pi\)
\(230\) 2.96314e12 0.303564
\(231\) −2.12920e10 −0.00212986
\(232\) 1.56844e13 1.53209
\(233\) 2.08431e13 1.98840 0.994201 0.107536i \(-0.0342962\pi\)
0.994201 + 0.107536i \(0.0342962\pi\)
\(234\) −2.14518e12 −0.199884
\(235\) −1.86468e12 −0.169719
\(236\) 5.86814e11 0.0521776
\(237\) −3.27188e11 −0.0284237
\(238\) 9.96698e10 0.00846039
\(239\) −1.45584e13 −1.20760 −0.603801 0.797135i \(-0.706348\pi\)
−0.603801 + 0.797135i \(0.706348\pi\)
\(240\) −6.74784e11 −0.0547020
\(241\) 4.94274e12 0.391628 0.195814 0.980641i \(-0.437265\pi\)
0.195814 + 0.980641i \(0.437265\pi\)
\(242\) −6.03251e12 −0.467212
\(243\) 8.47289e11 0.0641500
\(244\) 1.99730e12 0.147843
\(245\) −2.98473e12 −0.216019
\(246\) −6.71369e11 −0.0475137
\(247\) −1.77819e13 −1.23068
\(248\) 1.87692e13 1.27046
\(249\) −1.13776e13 −0.753275
\(250\) −5.04365e12 −0.326644
\(251\) 3.01994e13 1.91334 0.956672 0.291167i \(-0.0940435\pi\)
0.956672 + 0.291167i \(0.0940435\pi\)
\(252\) −1.26275e10 −0.000782731 0
\(253\) −1.88452e13 −1.14298
\(254\) 1.70551e13 1.01220
\(255\) 4.00583e12 0.232660
\(256\) −1.73005e13 −0.983419
\(257\) 1.73748e13 0.966688 0.483344 0.875430i \(-0.339422\pi\)
0.483344 + 0.875430i \(0.339422\pi\)
\(258\) −5.33000e12 −0.290281
\(259\) −8.75674e10 −0.00466868
\(260\) 1.28492e12 0.0670693
\(261\) −9.21557e12 −0.470977
\(262\) 1.87859e13 0.940102
\(263\) −2.89941e13 −1.42087 −0.710434 0.703764i \(-0.751501\pi\)
−0.710434 + 0.703764i \(0.751501\pi\)
\(264\) 8.21318e12 0.394176
\(265\) −6.78835e12 −0.319089
\(266\) 1.56496e11 0.00720532
\(267\) −1.15362e13 −0.520296
\(268\) −1.47408e13 −0.651298
\(269\) 3.67415e13 1.59045 0.795224 0.606316i \(-0.207353\pi\)
0.795224 + 0.606316i \(0.207353\pi\)
\(270\) 7.58783e11 0.0321823
\(271\) −2.77787e13 −1.15446 −0.577232 0.816580i \(-0.695867\pi\)
−0.577232 + 0.816580i \(0.695867\pi\)
\(272\) −2.00891e13 −0.818148
\(273\) −6.56545e10 −0.00262041
\(274\) −2.64542e13 −1.03482
\(275\) 1.56553e13 0.600250
\(276\) −1.11764e13 −0.420050
\(277\) −3.35056e12 −0.123447 −0.0617233 0.998093i \(-0.519660\pi\)
−0.0617233 + 0.998093i \(0.519660\pi\)
\(278\) −1.73214e13 −0.625657
\(279\) −1.10281e13 −0.390551
\(280\) −3.95241e10 −0.00137244
\(281\) −2.49018e13 −0.847903 −0.423951 0.905685i \(-0.639357\pi\)
−0.423951 + 0.905685i \(0.639357\pi\)
\(282\) −1.05154e13 −0.351120
\(283\) 1.77230e13 0.580378 0.290189 0.956969i \(-0.406282\pi\)
0.290189 + 0.956969i \(0.406282\pi\)
\(284\) −1.76134e13 −0.565709
\(285\) 6.28971e12 0.198146
\(286\) 1.22180e13 0.377560
\(287\) −2.05476e10 −0.000622889 0
\(288\) 8.34819e12 0.248275
\(289\) 8.49863e13 2.47977
\(290\) −8.25293e12 −0.236276
\(291\) −2.46806e13 −0.693338
\(292\) 2.13850e13 0.589528
\(293\) −3.45104e13 −0.933636 −0.466818 0.884353i \(-0.654600\pi\)
−0.466818 + 0.884353i \(0.654600\pi\)
\(294\) −1.68316e13 −0.446906
\(295\) −1.07920e12 −0.0281242
\(296\) 3.37783e13 0.864038
\(297\) −4.82576e12 −0.121173
\(298\) −1.55311e13 −0.382837
\(299\) −5.81098e13 −1.40624
\(300\) 9.28455e12 0.220594
\(301\) −1.63128e11 −0.00380550
\(302\) −2.26913e12 −0.0519781
\(303\) 3.23588e11 0.00727878
\(304\) −3.15428e13 −0.696779
\(305\) −3.67321e12 −0.0796886
\(306\) 2.25899e13 0.481333
\(307\) 1.44189e12 0.0301767 0.0150883 0.999886i \(-0.495197\pi\)
0.0150883 + 0.999886i \(0.495197\pi\)
\(308\) 7.19201e10 0.00147850
\(309\) −1.64911e13 −0.333025
\(310\) −9.87613e12 −0.195928
\(311\) 8.31693e13 1.62099 0.810496 0.585744i \(-0.199198\pi\)
0.810496 + 0.585744i \(0.199198\pi\)
\(312\) 2.53256e13 0.484963
\(313\) −7.11877e13 −1.33940 −0.669701 0.742631i \(-0.733578\pi\)
−0.669701 + 0.742631i \(0.733578\pi\)
\(314\) −5.01406e13 −0.926993
\(315\) 2.32229e10 0.000421900 0
\(316\) 1.10517e12 0.0197311
\(317\) −3.80953e13 −0.668413 −0.334207 0.942500i \(-0.608468\pi\)
−0.334207 + 0.942500i \(0.608468\pi\)
\(318\) −3.82812e13 −0.660141
\(319\) 5.24876e13 0.889627
\(320\) 1.31632e13 0.219299
\(321\) 8.68009e12 0.142150
\(322\) 5.11416e11 0.00823316
\(323\) 1.87252e14 2.96356
\(324\) −2.86197e12 −0.0445315
\(325\) 4.82736e13 0.738501
\(326\) 5.14975e13 0.774622
\(327\) −7.28354e13 −1.07728
\(328\) 7.92604e12 0.115279
\(329\) −3.21829e11 −0.00460308
\(330\) −4.32167e12 −0.0607890
\(331\) 3.71033e13 0.513285 0.256642 0.966506i \(-0.417384\pi\)
0.256642 + 0.966506i \(0.417384\pi\)
\(332\) 3.84312e13 0.522907
\(333\) −1.98469e13 −0.265613
\(334\) 7.74551e13 1.01963
\(335\) 2.71096e13 0.351056
\(336\) −1.16463e11 −0.00148361
\(337\) 2.84418e13 0.356445 0.178223 0.983990i \(-0.442965\pi\)
0.178223 + 0.983990i \(0.442965\pi\)
\(338\) −2.51073e13 −0.309570
\(339\) 5.11583e13 0.620608
\(340\) −1.35309e13 −0.161507
\(341\) 6.28109e13 0.737711
\(342\) 3.54693e13 0.409929
\(343\) −1.03030e12 −0.0117178
\(344\) 6.29249e13 0.704289
\(345\) 2.05543e13 0.226411
\(346\) 7.27961e13 0.789205
\(347\) 9.79399e13 1.04507 0.522537 0.852616i \(-0.324985\pi\)
0.522537 + 0.852616i \(0.324985\pi\)
\(348\) 3.11283e13 0.326942
\(349\) −1.19120e14 −1.23153 −0.615766 0.787929i \(-0.711153\pi\)
−0.615766 + 0.787929i \(0.711153\pi\)
\(350\) −4.24848e11 −0.00432374
\(351\) −1.48804e13 −0.149082
\(352\) −4.75474e13 −0.468967
\(353\) 1.20545e14 1.17054 0.585272 0.810837i \(-0.300988\pi\)
0.585272 + 0.810837i \(0.300988\pi\)
\(354\) −6.08588e12 −0.0581842
\(355\) 3.23926e13 0.304922
\(356\) 3.89670e13 0.361178
\(357\) 6.91374e11 0.00631013
\(358\) −6.43383e13 −0.578246
\(359\) −5.83637e13 −0.516563 −0.258281 0.966070i \(-0.583156\pi\)
−0.258281 + 0.966070i \(0.583156\pi\)
\(360\) −8.95802e12 −0.0780815
\(361\) 1.77522e14 1.52392
\(362\) 4.98231e13 0.421244
\(363\) −4.18454e13 −0.348467
\(364\) 2.21768e11 0.00181903
\(365\) −3.93289e13 −0.317761
\(366\) −2.07141e13 −0.164862
\(367\) −3.93716e13 −0.308688 −0.154344 0.988017i \(-0.549326\pi\)
−0.154344 + 0.988017i \(0.549326\pi\)
\(368\) −1.03079e14 −0.796175
\(369\) −4.65705e12 −0.0354377
\(370\) −1.77737e13 −0.133250
\(371\) −1.17162e12 −0.00865424
\(372\) 3.72507e13 0.271112
\(373\) 1.32550e14 0.950567 0.475283 0.879833i \(-0.342346\pi\)
0.475283 + 0.879833i \(0.342346\pi\)
\(374\) −1.28661e14 −0.909189
\(375\) −3.49860e13 −0.243625
\(376\) 1.24143e14 0.851898
\(377\) 1.61847e14 1.09453
\(378\) 1.30960e11 0.000872838 0
\(379\) 1.76578e13 0.115990 0.0579952 0.998317i \(-0.481529\pi\)
0.0579952 + 0.998317i \(0.481529\pi\)
\(380\) −2.12454e13 −0.137548
\(381\) 1.18305e14 0.754946
\(382\) −6.54135e13 −0.411452
\(383\) −4.09907e13 −0.254151 −0.127075 0.991893i \(-0.540559\pi\)
−0.127075 + 0.991893i \(0.540559\pi\)
\(384\) 3.87228e12 0.0236671
\(385\) −1.32267e11 −0.000796926 0
\(386\) −1.72430e13 −0.102419
\(387\) −3.69724e13 −0.216504
\(388\) 8.33663e13 0.481300
\(389\) 3.53527e13 0.201233 0.100617 0.994925i \(-0.467918\pi\)
0.100617 + 0.994925i \(0.467918\pi\)
\(390\) −1.33260e13 −0.0747902
\(391\) 6.11925e14 3.38631
\(392\) 1.98711e14 1.08430
\(393\) 1.30311e14 0.701169
\(394\) −7.19809e13 −0.381934
\(395\) −2.03251e12 −0.0106353
\(396\) 1.63005e13 0.0841156
\(397\) 5.79838e13 0.295093 0.147546 0.989055i \(-0.452862\pi\)
0.147546 + 0.989055i \(0.452862\pi\)
\(398\) −1.58342e13 −0.0794764
\(399\) 1.08556e12 0.00537404
\(400\) 8.56311e13 0.418121
\(401\) 1.33258e14 0.641801 0.320900 0.947113i \(-0.396015\pi\)
0.320900 + 0.947113i \(0.396015\pi\)
\(402\) 1.52878e14 0.726274
\(403\) 1.93679e14 0.907623
\(404\) −1.09302e12 −0.00505277
\(405\) 5.26341e12 0.0240029
\(406\) −1.42439e12 −0.00640820
\(407\) 1.13039e14 0.501716
\(408\) −2.66691e14 −1.16782
\(409\) −2.38767e14 −1.03156 −0.515782 0.856720i \(-0.672499\pi\)
−0.515782 + 0.856720i \(0.672499\pi\)
\(410\) −4.17059e12 −0.0177781
\(411\) −1.83503e14 −0.771817
\(412\) 5.57035e13 0.231179
\(413\) −1.86261e11 −0.000762777 0
\(414\) 1.15911e14 0.468405
\(415\) −7.06782e13 −0.281852
\(416\) −1.46614e14 −0.576981
\(417\) −1.20152e14 −0.466642
\(418\) −2.02016e14 −0.774314
\(419\) −2.05161e14 −0.776102 −0.388051 0.921638i \(-0.626852\pi\)
−0.388051 + 0.921638i \(0.626852\pi\)
\(420\) −7.84425e10 −0.000292874 0
\(421\) −5.23103e13 −0.192768 −0.0963842 0.995344i \(-0.530728\pi\)
−0.0963842 + 0.995344i \(0.530728\pi\)
\(422\) −2.05797e14 −0.748551
\(423\) −7.29416e13 −0.261881
\(424\) 4.51940e14 1.60165
\(425\) −5.08345e14 −1.77836
\(426\) 1.82670e14 0.630832
\(427\) −6.33966e11 −0.00216129
\(428\) −2.93196e13 −0.0986774
\(429\) 8.47517e13 0.281601
\(430\) −3.31103e13 −0.108614
\(431\) −1.30800e14 −0.423625 −0.211813 0.977310i \(-0.567937\pi\)
−0.211813 + 0.977310i \(0.567937\pi\)
\(432\) −2.63959e13 −0.0844064
\(433\) −4.07842e14 −1.28768 −0.643841 0.765160i \(-0.722660\pi\)
−0.643841 + 0.765160i \(0.722660\pi\)
\(434\) −1.70454e12 −0.00531391
\(435\) −5.72476e13 −0.176225
\(436\) 2.46024e14 0.747827
\(437\) 9.60809e14 2.88396
\(438\) −2.21785e14 −0.657393
\(439\) 1.90268e14 0.556943 0.278471 0.960445i \(-0.410172\pi\)
0.278471 + 0.960445i \(0.410172\pi\)
\(440\) 5.10207e13 0.147488
\(441\) −1.16755e14 −0.333322
\(442\) −3.96731e14 −1.11860
\(443\) 4.99000e14 1.38957 0.694784 0.719218i \(-0.255500\pi\)
0.694784 + 0.719218i \(0.255500\pi\)
\(444\) 6.70388e13 0.184383
\(445\) −7.16635e13 −0.194679
\(446\) −2.33721e14 −0.627127
\(447\) −1.07734e14 −0.285537
\(448\) 2.27187e12 0.00594777
\(449\) −7.64726e14 −1.97766 −0.988829 0.149054i \(-0.952377\pi\)
−0.988829 + 0.149054i \(0.952377\pi\)
\(450\) −9.62906e13 −0.245989
\(451\) 2.65244e13 0.0669383
\(452\) −1.72802e14 −0.430813
\(453\) −1.57401e13 −0.0387675
\(454\) −2.80678e14 −0.682969
\(455\) −4.07849e11 −0.000980476 0
\(456\) −4.18742e14 −0.994581
\(457\) 5.37215e14 1.26069 0.630346 0.776314i \(-0.282913\pi\)
0.630346 + 0.776314i \(0.282913\pi\)
\(458\) −8.22886e13 −0.190801
\(459\) 1.56698e14 0.358999
\(460\) −6.94283e13 −0.157170
\(461\) −3.46322e14 −0.774684 −0.387342 0.921936i \(-0.626607\pi\)
−0.387342 + 0.921936i \(0.626607\pi\)
\(462\) −7.45887e11 −0.00164870
\(463\) −4.09490e14 −0.894434 −0.447217 0.894426i \(-0.647585\pi\)
−0.447217 + 0.894426i \(0.647585\pi\)
\(464\) 2.87096e14 0.619694
\(465\) −6.85072e13 −0.146132
\(466\) 7.30161e14 1.53920
\(467\) −2.72786e14 −0.568302 −0.284151 0.958779i \(-0.591712\pi\)
−0.284151 + 0.958779i \(0.591712\pi\)
\(468\) 5.02629e13 0.103489
\(469\) 4.67890e12 0.00952123
\(470\) −6.53223e13 −0.131378
\(471\) −3.47807e14 −0.691391
\(472\) 7.18485e13 0.141168
\(473\) 2.10577e14 0.408955
\(474\) −1.14618e13 −0.0220025
\(475\) −7.98174e14 −1.51455
\(476\) −2.33532e12 −0.00438035
\(477\) −2.65543e14 −0.492362
\(478\) −5.09999e14 −0.934793
\(479\) 1.26905e14 0.229950 0.114975 0.993368i \(-0.463321\pi\)
0.114975 + 0.993368i \(0.463321\pi\)
\(480\) 5.18595e13 0.0928969
\(481\) 3.48558e14 0.617272
\(482\) 1.73151e14 0.303156
\(483\) 3.54751e12 0.00614065
\(484\) 1.41345e14 0.241898
\(485\) −1.53318e14 −0.259425
\(486\) 2.96817e13 0.0496579
\(487\) 5.80668e14 0.960547 0.480274 0.877119i \(-0.340537\pi\)
0.480274 + 0.877119i \(0.340537\pi\)
\(488\) 2.44546e14 0.399993
\(489\) 3.57220e14 0.577747
\(490\) −1.04559e14 −0.167218
\(491\) −1.06280e15 −1.68076 −0.840378 0.542001i \(-0.817667\pi\)
−0.840378 + 0.542001i \(0.817667\pi\)
\(492\) 1.57306e13 0.0246001
\(493\) −1.70433e15 −2.63570
\(494\) −6.22923e14 −0.952657
\(495\) −2.99779e13 −0.0453391
\(496\) 3.43562e14 0.513873
\(497\) 5.59070e12 0.00827001
\(498\) −3.98572e14 −0.583103
\(499\) −7.69931e14 −1.11403 −0.557017 0.830501i \(-0.688054\pi\)
−0.557017 + 0.830501i \(0.688054\pi\)
\(500\) 1.18176e14 0.169119
\(501\) 5.37279e14 0.760488
\(502\) 1.05793e15 1.48110
\(503\) −1.25577e15 −1.73895 −0.869473 0.493980i \(-0.835542\pi\)
−0.869473 + 0.493980i \(0.835542\pi\)
\(504\) −1.54608e12 −0.00211770
\(505\) 2.01015e12 0.00272349
\(506\) −6.60174e14 −0.884770
\(507\) −1.74161e14 −0.230891
\(508\) −3.99611e14 −0.524067
\(509\) 2.94090e14 0.381534 0.190767 0.981635i \(-0.438903\pi\)
0.190767 + 0.981635i \(0.438903\pi\)
\(510\) 1.40329e14 0.180100
\(511\) −6.78786e12 −0.00861823
\(512\) −6.38695e14 −0.802248
\(513\) 2.46038e14 0.305743
\(514\) 6.08661e14 0.748304
\(515\) −1.02443e14 −0.124608
\(516\) 1.24885e14 0.150293
\(517\) 4.15442e14 0.494666
\(518\) −3.06760e12 −0.00361398
\(519\) 5.04961e14 0.588623
\(520\) 1.57324e14 0.181458
\(521\) 4.38782e14 0.500773 0.250387 0.968146i \(-0.419442\pi\)
0.250387 + 0.968146i \(0.419442\pi\)
\(522\) −3.22834e14 −0.364578
\(523\) 1.10640e15 1.23639 0.618193 0.786027i \(-0.287865\pi\)
0.618193 + 0.786027i \(0.287865\pi\)
\(524\) −4.40165e14 −0.486736
\(525\) −2.94702e12 −0.00322483
\(526\) −1.01570e15 −1.09988
\(527\) −2.03954e15 −2.18562
\(528\) 1.50339e14 0.159435
\(529\) 2.18704e15 2.29536
\(530\) −2.37805e14 −0.247004
\(531\) −4.22156e13 −0.0433963
\(532\) −3.66679e12 −0.00373054
\(533\) 8.17888e13 0.0823558
\(534\) −4.04128e14 −0.402756
\(535\) 5.39213e13 0.0531881
\(536\) −1.80484e15 −1.76211
\(537\) −4.46292e14 −0.431281
\(538\) 1.28710e15 1.23115
\(539\) 6.64983e14 0.629611
\(540\) −1.77787e13 −0.0166623
\(541\) 1.86406e15 1.72931 0.864657 0.502363i \(-0.167536\pi\)
0.864657 + 0.502363i \(0.167536\pi\)
\(542\) −9.73123e14 −0.893659
\(543\) 3.45605e14 0.314182
\(544\) 1.54392e15 1.38941
\(545\) −4.52458e14 −0.403086
\(546\) −2.29996e12 −0.00202844
\(547\) 1.53114e15 1.33686 0.668429 0.743776i \(-0.266967\pi\)
0.668429 + 0.743776i \(0.266967\pi\)
\(548\) 6.19838e14 0.535778
\(549\) −1.43686e14 −0.122961
\(550\) 5.48426e14 0.464648
\(551\) −2.67604e15 −2.24470
\(552\) −1.36842e15 −1.13646
\(553\) −3.50795e11 −0.000288446 0
\(554\) −1.17375e14 −0.0955588
\(555\) −1.23290e14 −0.0993840
\(556\) 4.05851e14 0.323933
\(557\) −1.89472e13 −0.0149742 −0.00748708 0.999972i \(-0.502383\pi\)
−0.00748708 + 0.999972i \(0.502383\pi\)
\(558\) −3.86329e14 −0.302322
\(559\) 6.49321e14 0.503147
\(560\) −7.23472e11 −0.000555121 0
\(561\) −8.92478e14 −0.678113
\(562\) −8.72343e14 −0.656353
\(563\) 5.31050e14 0.395675 0.197838 0.980235i \(-0.436608\pi\)
0.197838 + 0.980235i \(0.436608\pi\)
\(564\) 2.46382e14 0.181792
\(565\) 3.17798e14 0.232212
\(566\) 6.20859e14 0.449265
\(567\) 9.08423e11 0.000651000 0
\(568\) −2.15656e15 −1.53054
\(569\) −1.05670e15 −0.742734 −0.371367 0.928486i \(-0.621111\pi\)
−0.371367 + 0.928486i \(0.621111\pi\)
\(570\) 2.20337e14 0.153383
\(571\) 2.39861e15 1.65372 0.826859 0.562409i \(-0.190125\pi\)
0.826859 + 0.562409i \(0.190125\pi\)
\(572\) −2.86274e14 −0.195481
\(573\) −4.53750e14 −0.306879
\(574\) −7.19810e11 −0.000482173 0
\(575\) −2.60837e15 −1.73060
\(576\) 5.14912e14 0.338384
\(577\) −2.64391e15 −1.72100 −0.860498 0.509455i \(-0.829847\pi\)
−0.860498 + 0.509455i \(0.829847\pi\)
\(578\) 2.97718e15 1.91956
\(579\) −1.19608e14 −0.0763888
\(580\) 1.93371e14 0.122331
\(581\) −1.21985e13 −0.00764430
\(582\) −8.64596e14 −0.536706
\(583\) 1.51241e15 0.930021
\(584\) 2.61835e15 1.59499
\(585\) −9.24378e13 −0.0557818
\(586\) −1.20894e15 −0.722719
\(587\) −9.10850e14 −0.539433 −0.269716 0.962940i \(-0.586930\pi\)
−0.269716 + 0.962940i \(0.586930\pi\)
\(588\) 3.94376e14 0.231385
\(589\) −3.20237e15 −1.86139
\(590\) −3.78058e13 −0.0217707
\(591\) −4.99306e14 −0.284863
\(592\) 6.18296e14 0.349484
\(593\) 2.44368e15 1.36850 0.684248 0.729249i \(-0.260130\pi\)
0.684248 + 0.729249i \(0.260130\pi\)
\(594\) −1.69053e14 −0.0937988
\(595\) 4.29486e12 0.00236105
\(596\) 3.63904e14 0.198213
\(597\) −1.09836e14 −0.0592769
\(598\) −2.03566e15 −1.08855
\(599\) −2.57542e15 −1.36458 −0.682292 0.731080i \(-0.739017\pi\)
−0.682292 + 0.731080i \(0.739017\pi\)
\(600\) 1.13679e15 0.596825
\(601\) −1.67024e15 −0.868900 −0.434450 0.900696i \(-0.643057\pi\)
−0.434450 + 0.900696i \(0.643057\pi\)
\(602\) −5.71458e12 −0.00294580
\(603\) 1.06046e15 0.541686
\(604\) 5.31670e13 0.0269116
\(605\) −2.59946e14 −0.130385
\(606\) 1.13357e13 0.00563443
\(607\) 3.23790e15 1.59487 0.797436 0.603403i \(-0.206189\pi\)
0.797436 + 0.603403i \(0.206189\pi\)
\(608\) 2.42417e15 1.18330
\(609\) −9.88049e12 −0.00477951
\(610\) −1.28677e14 −0.0616862
\(611\) 1.28103e15 0.608599
\(612\) −5.29294e14 −0.249209
\(613\) −3.65672e15 −1.70631 −0.853157 0.521655i \(-0.825315\pi\)
−0.853157 + 0.521655i \(0.825315\pi\)
\(614\) 5.05113e13 0.0233595
\(615\) −2.89299e13 −0.0132597
\(616\) 8.80578e12 0.00400013
\(617\) −1.42899e15 −0.643369 −0.321685 0.946847i \(-0.604249\pi\)
−0.321685 + 0.946847i \(0.604249\pi\)
\(618\) −5.77704e14 −0.257791
\(619\) 4.16060e15 1.84017 0.920085 0.391719i \(-0.128120\pi\)
0.920085 + 0.391719i \(0.128120\pi\)
\(620\) 2.31404e14 0.101442
\(621\) 8.04032e14 0.349357
\(622\) 2.91353e15 1.25479
\(623\) −1.23686e13 −0.00528001
\(624\) 4.63573e14 0.196157
\(625\) 2.05559e15 0.862176
\(626\) −2.49380e15 −1.03682
\(627\) −1.40132e15 −0.577517
\(628\) 1.17482e15 0.479949
\(629\) −3.67049e15 −1.48643
\(630\) 8.13531e11 0.000326589 0
\(631\) 2.74324e15 1.09170 0.545849 0.837883i \(-0.316207\pi\)
0.545849 + 0.837883i \(0.316207\pi\)
\(632\) 1.35316e14 0.0533832
\(633\) −1.42754e15 −0.558302
\(634\) −1.33453e15 −0.517412
\(635\) 7.34918e14 0.282477
\(636\) 8.96952e14 0.341787
\(637\) 2.05049e15 0.774625
\(638\) 1.83871e15 0.688652
\(639\) 1.26712e15 0.470502
\(640\) 2.40548e13 0.00885548
\(641\) 7.55048e14 0.275585 0.137793 0.990461i \(-0.455999\pi\)
0.137793 + 0.990461i \(0.455999\pi\)
\(642\) 3.04075e14 0.110037
\(643\) 1.51360e15 0.543064 0.271532 0.962429i \(-0.412470\pi\)
0.271532 + 0.962429i \(0.412470\pi\)
\(644\) −1.19828e13 −0.00426270
\(645\) −2.29674e14 −0.0810092
\(646\) 6.55970e15 2.29406
\(647\) −2.58593e15 −0.896691 −0.448345 0.893860i \(-0.647987\pi\)
−0.448345 + 0.893860i \(0.647987\pi\)
\(648\) −3.50415e14 −0.120482
\(649\) 2.40440e14 0.0819712
\(650\) 1.69109e15 0.571667
\(651\) −1.18238e13 −0.00396334
\(652\) −1.20662e15 −0.401059
\(653\) −1.26468e14 −0.0416829 −0.0208415 0.999783i \(-0.506635\pi\)
−0.0208415 + 0.999783i \(0.506635\pi\)
\(654\) −2.55152e15 −0.833915
\(655\) 8.09501e14 0.262355
\(656\) 1.45083e14 0.0466277
\(657\) −1.53845e15 −0.490313
\(658\) −1.12741e13 −0.00356320
\(659\) 5.47257e14 0.171523 0.0857613 0.996316i \(-0.472668\pi\)
0.0857613 + 0.996316i \(0.472668\pi\)
\(660\) 1.01259e14 0.0314734
\(661\) −1.94531e15 −0.599627 −0.299814 0.953998i \(-0.596924\pi\)
−0.299814 + 0.953998i \(0.596924\pi\)
\(662\) 1.29978e15 0.397329
\(663\) −2.75198e15 −0.834298
\(664\) 4.70545e15 1.41474
\(665\) 6.74353e12 0.00201080
\(666\) −6.95263e14 −0.205608
\(667\) −8.74508e15 −2.56491
\(668\) −1.81482e15 −0.527914
\(669\) −1.62124e15 −0.467738
\(670\) 9.49684e14 0.271749
\(671\) 8.18372e14 0.232261
\(672\) 8.95054e12 0.00251952
\(673\) −4.53850e15 −1.26715 −0.633577 0.773679i \(-0.718414\pi\)
−0.633577 + 0.773679i \(0.718414\pi\)
\(674\) 9.96354e14 0.275921
\(675\) −6.67934e14 −0.183469
\(676\) 5.88280e14 0.160279
\(677\) 7.30525e15 1.97423 0.987114 0.160017i \(-0.0511548\pi\)
0.987114 + 0.160017i \(0.0511548\pi\)
\(678\) 1.79214e15 0.480407
\(679\) −2.64614e13 −0.00703606
\(680\) −1.65670e15 −0.436963
\(681\) −1.94696e15 −0.509388
\(682\) 2.20035e15 0.571055
\(683\) −4.57455e15 −1.17770 −0.588850 0.808243i \(-0.700419\pi\)
−0.588850 + 0.808243i \(0.700419\pi\)
\(684\) −8.31066e14 −0.212240
\(685\) −1.13993e15 −0.288790
\(686\) −3.60928e13 −0.00907064
\(687\) −5.70807e14 −0.142307
\(688\) 1.15181e15 0.284869
\(689\) 4.66356e15 1.14423
\(690\) 7.20044e14 0.175263
\(691\) 6.68207e15 1.61355 0.806774 0.590860i \(-0.201212\pi\)
0.806774 + 0.590860i \(0.201212\pi\)
\(692\) −1.70566e15 −0.408609
\(693\) −5.17396e12 −0.00122967
\(694\) 3.43096e15 0.808982
\(695\) −7.46393e14 −0.174603
\(696\) 3.81130e15 0.884551
\(697\) −8.61277e14 −0.198318
\(698\) −4.17294e15 −0.953317
\(699\) 5.06487e15 1.14800
\(700\) 9.95446e12 0.00223861
\(701\) −3.24290e15 −0.723576 −0.361788 0.932260i \(-0.617834\pi\)
−0.361788 + 0.932260i \(0.617834\pi\)
\(702\) −5.21279e14 −0.115403
\(703\) −5.76319e15 −1.26593
\(704\) −2.93270e15 −0.639173
\(705\) −4.53117e14 −0.0979875
\(706\) 4.22285e15 0.906107
\(707\) 3.46936e11 7.38657e−5 0
\(708\) 1.42596e14 0.0301248
\(709\) −4.82624e15 −1.01171 −0.505854 0.862619i \(-0.668822\pi\)
−0.505854 + 0.862619i \(0.668822\pi\)
\(710\) 1.13475e15 0.236038
\(711\) −7.95066e13 −0.0164104
\(712\) 4.77105e15 0.977179
\(713\) −1.04651e16 −2.12691
\(714\) 2.42198e13 0.00488461
\(715\) 5.26483e14 0.105366
\(716\) 1.50749e15 0.299386
\(717\) −3.53768e15 −0.697209
\(718\) −2.04456e15 −0.399866
\(719\) −2.42863e14 −0.0471360 −0.0235680 0.999722i \(-0.507503\pi\)
−0.0235680 + 0.999722i \(0.507503\pi\)
\(720\) −1.63973e14 −0.0315822
\(721\) −1.76809e13 −0.00337957
\(722\) 6.21884e15 1.17965
\(723\) 1.20109e15 0.226107
\(724\) −1.16738e15 −0.218098
\(725\) 7.26481e15 1.34699
\(726\) −1.46590e15 −0.269745
\(727\) 6.24008e14 0.113960 0.0569798 0.998375i \(-0.481853\pi\)
0.0569798 + 0.998375i \(0.481853\pi\)
\(728\) 2.71529e13 0.00492145
\(729\) 2.05891e14 0.0370370
\(730\) −1.37774e15 −0.245976
\(731\) −6.83768e15 −1.21161
\(732\) 4.85344e14 0.0853570
\(733\) 8.38297e15 1.46327 0.731637 0.681694i \(-0.238757\pi\)
0.731637 + 0.681694i \(0.238757\pi\)
\(734\) −1.37924e15 −0.238952
\(735\) −7.25290e14 −0.124719
\(736\) 7.92199e15 1.35209
\(737\) −6.03987e15 −1.02319
\(738\) −1.63143e14 −0.0274320
\(739\) −4.89206e15 −0.816483 −0.408242 0.912874i \(-0.633858\pi\)
−0.408242 + 0.912874i \(0.633858\pi\)
\(740\) 4.16449e14 0.0689902
\(741\) −4.32100e15 −0.710533
\(742\) −4.10433e13 −0.00669917
\(743\) 1.60463e15 0.259978 0.129989 0.991515i \(-0.458506\pi\)
0.129989 + 0.991515i \(0.458506\pi\)
\(744\) 4.56092e15 0.733502
\(745\) −6.69250e14 −0.106839
\(746\) 4.64342e15 0.735825
\(747\) −2.76475e15 −0.434904
\(748\) 3.01461e15 0.470731
\(749\) 9.30639e12 0.00144255
\(750\) −1.22561e15 −0.188588
\(751\) −6.10570e15 −0.932643 −0.466322 0.884615i \(-0.654421\pi\)
−0.466322 + 0.884615i \(0.654421\pi\)
\(752\) 2.27237e15 0.344573
\(753\) 7.33846e15 1.10467
\(754\) 5.66972e15 0.847264
\(755\) −9.77786e13 −0.0145056
\(756\) −3.06847e12 −0.000451910 0
\(757\) −4.37120e14 −0.0639107 −0.0319553 0.999489i \(-0.510173\pi\)
−0.0319553 + 0.999489i \(0.510173\pi\)
\(758\) 6.18578e14 0.0897871
\(759\) −4.57939e15 −0.659900
\(760\) −2.60125e15 −0.372141
\(761\) 2.99517e15 0.425409 0.212704 0.977117i \(-0.431773\pi\)
0.212704 + 0.977117i \(0.431773\pi\)
\(762\) 4.14438e15 0.584397
\(763\) −7.80907e13 −0.0109324
\(764\) 1.53268e15 0.213028
\(765\) 9.73416e14 0.134326
\(766\) −1.43596e15 −0.196736
\(767\) 7.41404e14 0.100851
\(768\) −4.20402e15 −0.567777
\(769\) 4.32927e15 0.580524 0.290262 0.956947i \(-0.406258\pi\)
0.290262 + 0.956947i \(0.406258\pi\)
\(770\) −4.63349e12 −0.000616893 0
\(771\) 4.22207e15 0.558118
\(772\) 4.04013e14 0.0530274
\(773\) 7.12088e14 0.0927997 0.0463998 0.998923i \(-0.485225\pi\)
0.0463998 + 0.998923i \(0.485225\pi\)
\(774\) −1.29519e15 −0.167594
\(775\) 8.69366e15 1.11697
\(776\) 1.02072e16 1.30217
\(777\) −2.12789e13 −0.00269546
\(778\) 1.23845e15 0.155773
\(779\) −1.35233e15 −0.168898
\(780\) 3.12236e14 0.0387225
\(781\) −7.21690e15 −0.888730
\(782\) 2.14366e16 2.62131
\(783\) −2.23938e15 −0.271918
\(784\) 3.63731e15 0.438573
\(785\) −2.16060e15 −0.258697
\(786\) 4.56498e15 0.542768
\(787\) 1.24106e16 1.46531 0.732656 0.680599i \(-0.238280\pi\)
0.732656 + 0.680599i \(0.238280\pi\)
\(788\) 1.68656e15 0.197746
\(789\) −7.04558e15 −0.820338
\(790\) −7.12015e13 −0.00823266
\(791\) 5.48495e13 0.00629799
\(792\) 1.99580e15 0.227577
\(793\) 2.52347e15 0.285756
\(794\) 2.03125e15 0.228429
\(795\) −1.64957e15 −0.184226
\(796\) 3.71004e14 0.0411487
\(797\) 1.39035e16 1.53145 0.765724 0.643170i \(-0.222381\pi\)
0.765724 + 0.643170i \(0.222381\pi\)
\(798\) 3.80285e13 0.00416000
\(799\) −1.34898e16 −1.46555
\(800\) −6.58104e15 −0.710067
\(801\) −2.80330e15 −0.300393
\(802\) 4.66822e15 0.496812
\(803\) 8.76228e15 0.926151
\(804\) −3.58201e15 −0.376027
\(805\) 2.20373e13 0.00229764
\(806\) 6.78484e15 0.702582
\(807\) 8.92819e15 0.918245
\(808\) −1.33827e14 −0.0136704
\(809\) 8.18105e14 0.0830027 0.0415013 0.999138i \(-0.486786\pi\)
0.0415013 + 0.999138i \(0.486786\pi\)
\(810\) 1.84384e14 0.0185804
\(811\) 7.48413e15 0.749077 0.374538 0.927211i \(-0.377801\pi\)
0.374538 + 0.927211i \(0.377801\pi\)
\(812\) 3.33743e13 0.00331783
\(813\) −6.75021e15 −0.666530
\(814\) 3.95989e15 0.388373
\(815\) 2.21907e15 0.216175
\(816\) −4.88166e15 −0.472358
\(817\) −1.07361e16 −1.03187
\(818\) −8.36434e15 −0.798525
\(819\) −1.59540e13 −0.00151290
\(820\) 9.77194e13 0.00920459
\(821\) −3.87011e15 −0.362106 −0.181053 0.983473i \(-0.557951\pi\)
−0.181053 + 0.983473i \(0.557951\pi\)
\(822\) −6.42837e15 −0.597456
\(823\) −1.03561e16 −0.956086 −0.478043 0.878336i \(-0.658654\pi\)
−0.478043 + 0.878336i \(0.658654\pi\)
\(824\) 6.82025e15 0.625461
\(825\) 3.80424e15 0.346554
\(826\) −6.52499e12 −0.000590459 0
\(827\) −7.27159e15 −0.653656 −0.326828 0.945084i \(-0.605980\pi\)
−0.326828 + 0.945084i \(0.605980\pi\)
\(828\) −2.71586e15 −0.242516
\(829\) 5.68645e15 0.504419 0.252209 0.967673i \(-0.418843\pi\)
0.252209 + 0.967673i \(0.418843\pi\)
\(830\) −2.47595e15 −0.218179
\(831\) −8.14187e14 −0.0712719
\(832\) −9.04307e15 −0.786389
\(833\) −2.15927e16 −1.86535
\(834\) −4.20910e15 −0.361223
\(835\) 3.33761e15 0.284551
\(836\) 4.73337e15 0.400900
\(837\) −2.67983e15 −0.225485
\(838\) −7.18708e15 −0.600773
\(839\) −2.22324e16 −1.84627 −0.923134 0.384478i \(-0.874382\pi\)
−0.923134 + 0.384478i \(0.874382\pi\)
\(840\) −9.60437e12 −0.000792378 0
\(841\) 1.21562e16 0.996370
\(842\) −1.83250e15 −0.149220
\(843\) −6.05114e15 −0.489537
\(844\) 4.82196e15 0.387561
\(845\) −1.08190e15 −0.0863920
\(846\) −2.55524e15 −0.202719
\(847\) −4.48647e13 −0.00353627
\(848\) 8.27255e15 0.647832
\(849\) 4.30668e15 0.335081
\(850\) −1.78080e16 −1.37661
\(851\) −1.88336e16 −1.44651
\(852\) −4.28006e15 −0.326612
\(853\) 1.52570e15 0.115678 0.0578388 0.998326i \(-0.481579\pi\)
0.0578388 + 0.998326i \(0.481579\pi\)
\(854\) −2.22087e13 −0.00167303
\(855\) 1.52840e15 0.114399
\(856\) −3.58985e15 −0.266975
\(857\) 1.81734e16 1.34290 0.671449 0.741051i \(-0.265672\pi\)
0.671449 + 0.741051i \(0.265672\pi\)
\(858\) 2.96897e15 0.217984
\(859\) −8.59917e15 −0.627327 −0.313664 0.949534i \(-0.601556\pi\)
−0.313664 + 0.949534i \(0.601556\pi\)
\(860\) 7.75794e14 0.0562348
\(861\) −4.99307e12 −0.000359625 0
\(862\) −4.58209e15 −0.327924
\(863\) 2.56137e16 1.82143 0.910717 0.413031i \(-0.135530\pi\)
0.910717 + 0.413031i \(0.135530\pi\)
\(864\) 2.02861e15 0.143342
\(865\) 3.13685e15 0.220244
\(866\) −1.42872e16 −0.996782
\(867\) 2.06517e16 1.43169
\(868\) 3.99385e13 0.00275127
\(869\) 4.52833e14 0.0309977
\(870\) −2.00546e15 −0.136414
\(871\) −1.86241e16 −1.25886
\(872\) 3.01227e16 2.02327
\(873\) −5.99740e15 −0.400299
\(874\) 3.36584e16 2.23245
\(875\) −3.75103e13 −0.00247233
\(876\) 5.19657e15 0.340364
\(877\) 1.07443e16 0.699327 0.349664 0.936875i \(-0.386296\pi\)
0.349664 + 0.936875i \(0.386296\pi\)
\(878\) 6.66534e15 0.431124
\(879\) −8.38602e15 −0.539035
\(880\) 9.33912e14 0.0596556
\(881\) −6.60441e15 −0.419244 −0.209622 0.977783i \(-0.567223\pi\)
−0.209622 + 0.977783i \(0.567223\pi\)
\(882\) −4.09009e15 −0.258021
\(883\) 6.53384e15 0.409623 0.204812 0.978801i \(-0.434342\pi\)
0.204812 + 0.978801i \(0.434342\pi\)
\(884\) 9.29564e15 0.579151
\(885\) −2.62246e14 −0.0162375
\(886\) 1.74806e16 1.07565
\(887\) 1.44562e15 0.0884044 0.0442022 0.999023i \(-0.485925\pi\)
0.0442022 + 0.999023i \(0.485925\pi\)
\(888\) 8.20812e15 0.498853
\(889\) 1.26841e14 0.00766126
\(890\) −2.51047e15 −0.150699
\(891\) −1.17266e15 −0.0699592
\(892\) 5.47621e15 0.324694
\(893\) −2.11810e16 −1.24814
\(894\) −3.77407e15 −0.221031
\(895\) −2.77239e15 −0.161372
\(896\) 4.15167e12 0.000240176 0
\(897\) −1.41207e16 −0.811890
\(898\) −2.67894e16 −1.53089
\(899\) 2.91473e16 1.65546
\(900\) 2.25615e15 0.127360
\(901\) −4.91096e16 −2.75537
\(902\) 9.29186e14 0.0518163
\(903\) −3.96400e13 −0.00219711
\(904\) −2.11576e16 −1.16558
\(905\) 2.14692e15 0.117557
\(906\) −5.51398e14 −0.0300096
\(907\) 3.18040e15 0.172045 0.0860223 0.996293i \(-0.472584\pi\)
0.0860223 + 0.996293i \(0.472584\pi\)
\(908\) 6.57646e15 0.353606
\(909\) 7.86320e13 0.00420241
\(910\) −1.42875e13 −0.000758977 0
\(911\) −2.72796e16 −1.44041 −0.720207 0.693759i \(-0.755953\pi\)
−0.720207 + 0.693759i \(0.755953\pi\)
\(912\) −7.66489e15 −0.402286
\(913\) 1.57468e16 0.821489
\(914\) 1.88194e16 0.975890
\(915\) −8.92589e14 −0.0460082
\(916\) 1.92807e15 0.0987867
\(917\) 1.39713e14 0.00711553
\(918\) 5.48933e15 0.277898
\(919\) −1.45843e16 −0.733924 −0.366962 0.930236i \(-0.619602\pi\)
−0.366962 + 0.930236i \(0.619602\pi\)
\(920\) −8.50069e15 −0.425227
\(921\) 3.50379e14 0.0174225
\(922\) −1.21321e16 −0.599675
\(923\) −2.22535e16 −1.09343
\(924\) 1.74766e13 0.000853613 0
\(925\) 1.56457e16 0.759652
\(926\) −1.43450e16 −0.692373
\(927\) −4.00733e15 −0.192272
\(928\) −2.20643e16 −1.05239
\(929\) −2.40579e16 −1.14070 −0.570349 0.821403i \(-0.693192\pi\)
−0.570349 + 0.821403i \(0.693192\pi\)
\(930\) −2.39990e15 −0.113119
\(931\) −3.39036e16 −1.58863
\(932\) −1.71081e16 −0.796920
\(933\) 2.02101e16 0.935880
\(934\) −9.55606e15 −0.439918
\(935\) −5.54413e15 −0.253729
\(936\) 6.15411e15 0.279994
\(937\) −2.42969e16 −1.09896 −0.549482 0.835506i \(-0.685175\pi\)
−0.549482 + 0.835506i \(0.685175\pi\)
\(938\) 1.63908e14 0.00737029
\(939\) −1.72986e16 −0.773304
\(940\) 1.53054e15 0.0680208
\(941\) 1.97378e16 0.872081 0.436040 0.899927i \(-0.356380\pi\)
0.436040 + 0.899927i \(0.356380\pi\)
\(942\) −1.21842e16 −0.535199
\(943\) −4.41929e15 −0.192992
\(944\) 1.31516e15 0.0570993
\(945\) 5.64317e12 0.000243584 0
\(946\) 7.37681e15 0.316568
\(947\) 4.26802e16 1.82097 0.910483 0.413546i \(-0.135710\pi\)
0.910483 + 0.413546i \(0.135710\pi\)
\(948\) 2.68557e14 0.0113918
\(949\) 2.70187e16 1.13946
\(950\) −2.79611e16 −1.17240
\(951\) −9.25715e15 −0.385908
\(952\) −2.85933e14 −0.0118512
\(953\) −9.01467e15 −0.371483 −0.185741 0.982599i \(-0.559469\pi\)
−0.185741 + 0.982599i \(0.559469\pi\)
\(954\) −9.30233e15 −0.381132
\(955\) −2.81872e15 −0.114824
\(956\) 1.19496e16 0.483988
\(957\) 1.27545e16 0.513626
\(958\) 4.44566e15 0.178002
\(959\) −1.96744e14 −0.00783247
\(960\) 3.19866e15 0.126613
\(961\) 9.47150e15 0.372769
\(962\) 1.22104e16 0.477825
\(963\) 2.10926e15 0.0820703
\(964\) −4.05703e15 −0.156958
\(965\) −7.43014e14 −0.0285823
\(966\) 1.24274e14 0.00475342
\(967\) −6.16835e15 −0.234597 −0.117299 0.993097i \(-0.537423\pi\)
−0.117299 + 0.993097i \(0.537423\pi\)
\(968\) 1.73061e16 0.654463
\(969\) 4.55023e16 1.71101
\(970\) −5.37092e15 −0.200819
\(971\) −3.34244e16 −1.24267 −0.621337 0.783543i \(-0.713410\pi\)
−0.621337 + 0.783543i \(0.713410\pi\)
\(972\) −6.95459e14 −0.0257103
\(973\) −1.28822e14 −0.00473553
\(974\) 2.03416e16 0.743551
\(975\) 1.17305e16 0.426374
\(976\) 4.47631e15 0.161788
\(977\) −1.05518e16 −0.379233 −0.189617 0.981858i \(-0.560724\pi\)
−0.189617 + 0.981858i \(0.560724\pi\)
\(978\) 1.25139e16 0.447228
\(979\) 1.59663e16 0.567412
\(980\) 2.44988e15 0.0865769
\(981\) −1.76990e16 −0.621970
\(982\) −3.72314e16 −1.30106
\(983\) 3.82164e16 1.32802 0.664012 0.747722i \(-0.268853\pi\)
0.664012 + 0.747722i \(0.268853\pi\)
\(984\) 1.92603e15 0.0665564
\(985\) −3.10172e15 −0.106587
\(986\) −5.97049e16 −2.04027
\(987\) −7.82045e13 −0.00265759
\(988\) 1.45955e16 0.493236
\(989\) −3.50848e16 −1.17907
\(990\) −1.05017e15 −0.0350966
\(991\) −2.62516e16 −0.872470 −0.436235 0.899833i \(-0.643688\pi\)
−0.436235 + 0.899833i \(0.643688\pi\)
\(992\) −2.64039e16 −0.872678
\(993\) 9.01609e15 0.296345
\(994\) 1.95850e14 0.00640174
\(995\) −6.82307e14 −0.0221796
\(996\) 9.33878e15 0.301901
\(997\) −3.88199e16 −1.24805 −0.624024 0.781405i \(-0.714503\pi\)
−0.624024 + 0.781405i \(0.714503\pi\)
\(998\) −2.69717e16 −0.862364
\(999\) −4.82279e15 −0.153352
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.b.1.20 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.20 27 1.1 even 1 trivial