Properties

Label 177.12.a.b.1.12
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +118664. q^{10} -623024. q^{11} -412163. q^{12} +528715. q^{13} +1.11924e6 q^{14} -1.53724e6 q^{15} +2.15631e6 q^{16} +8.97468e6 q^{17} -1.10763e6 q^{18} -1.60580e7 q^{19} +1.07300e7 q^{20} -1.44994e7 q^{21} +1.16866e7 q^{22} +2.78241e7 q^{23} +1.70664e7 q^{24} -8.80856e6 q^{25} -9.91753e6 q^{26} +1.43489e7 q^{27} +1.01206e8 q^{28} +1.64181e8 q^{29} +2.88353e7 q^{30} -1.62798e7 q^{31} -1.84283e8 q^{32} -1.51395e8 q^{33} -1.68345e8 q^{34} +3.77467e8 q^{35} -1.00156e8 q^{36} +2.65231e8 q^{37} +3.01212e8 q^{38} +1.28478e8 q^{39} -4.44294e8 q^{40} +8.26019e8 q^{41} +2.71976e8 q^{42} +1.62764e9 q^{43} +1.05674e9 q^{44} -3.73550e8 q^{45} -5.21918e8 q^{46} -7.37241e8 q^{47} +5.23983e8 q^{48} +1.58297e9 q^{49} +1.65229e8 q^{50} +2.18085e9 q^{51} -8.96777e8 q^{52} -5.01219e9 q^{53} -2.69154e8 q^{54} +3.94131e9 q^{55} -4.19061e9 q^{56} -3.90208e9 q^{57} -3.07968e9 q^{58} -7.14924e8 q^{59} +2.60739e9 q^{60} +1.38051e9 q^{61} +3.05374e8 q^{62} -3.52335e9 q^{63} -9.59383e8 q^{64} -3.34470e9 q^{65} +2.83983e9 q^{66} -1.90823e10 q^{67} -1.52224e10 q^{68} +6.76125e9 q^{69} -7.08045e9 q^{70} +1.84853e10 q^{71} +4.14712e9 q^{72} -7.34829e9 q^{73} -4.97515e9 q^{74} -2.14048e9 q^{75} +2.72366e10 q^{76} +3.71747e10 q^{77} -2.40996e9 q^{78} -8.78770e9 q^{79} -1.36410e10 q^{80} +3.48678e9 q^{81} -1.54943e10 q^{82} +4.09401e10 q^{83} +2.45930e10 q^{84} -5.67747e10 q^{85} -3.05310e10 q^{86} +3.98961e10 q^{87} -4.37562e10 q^{88} +3.82223e10 q^{89} +7.00698e9 q^{90} -3.15475e10 q^{91} -4.71937e10 q^{92} -3.95600e9 q^{93} +1.38290e10 q^{94} +1.01584e11 q^{95} -4.47807e10 q^{96} -9.18220e10 q^{97} -2.96930e10 q^{98} -3.67889e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18.7578 −0.414493 −0.207246 0.978289i \(-0.566450\pi\)
−0.207246 + 0.978289i \(0.566450\pi\)
\(3\) 243.000 0.577350
\(4\) −1696.14 −0.828196
\(5\) −6326.10 −0.905318 −0.452659 0.891684i \(-0.649525\pi\)
−0.452659 + 0.891684i \(0.649525\pi\)
\(6\) −4558.15 −0.239308
\(7\) −59668.2 −1.34185 −0.670925 0.741525i \(-0.734103\pi\)
−0.670925 + 0.741525i \(0.734103\pi\)
\(8\) 70231.9 0.757774
\(9\) 59049.0 0.333333
\(10\) 118664. 0.375248
\(11\) −623024. −1.16639 −0.583197 0.812331i \(-0.698198\pi\)
−0.583197 + 0.812331i \(0.698198\pi\)
\(12\) −412163. −0.478159
\(13\) 528715. 0.394942 0.197471 0.980309i \(-0.436727\pi\)
0.197471 + 0.980309i \(0.436727\pi\)
\(14\) 1.11924e6 0.556187
\(15\) −1.53724e6 −0.522686
\(16\) 2.15631e6 0.514104
\(17\) 8.97468e6 1.53303 0.766513 0.642228i \(-0.221990\pi\)
0.766513 + 0.642228i \(0.221990\pi\)
\(18\) −1.10763e6 −0.138164
\(19\) −1.60580e7 −1.48780 −0.743902 0.668289i \(-0.767027\pi\)
−0.743902 + 0.668289i \(0.767027\pi\)
\(20\) 1.07300e7 0.749780
\(21\) −1.44994e7 −0.774717
\(22\) 1.16866e7 0.483462
\(23\) 2.78241e7 0.901400 0.450700 0.892675i \(-0.351174\pi\)
0.450700 + 0.892675i \(0.351174\pi\)
\(24\) 1.70664e7 0.437501
\(25\) −8.80856e6 −0.180399
\(26\) −9.91753e6 −0.163700
\(27\) 1.43489e7 0.192450
\(28\) 1.01206e8 1.11131
\(29\) 1.64181e8 1.48640 0.743199 0.669071i \(-0.233308\pi\)
0.743199 + 0.669071i \(0.233308\pi\)
\(30\) 2.88353e7 0.216649
\(31\) −1.62798e7 −0.102132 −0.0510658 0.998695i \(-0.516262\pi\)
−0.0510658 + 0.998695i \(0.516262\pi\)
\(32\) −1.84283e8 −0.970866
\(33\) −1.51395e8 −0.673418
\(34\) −1.68345e8 −0.635429
\(35\) 3.77467e8 1.21480
\(36\) −1.00156e8 −0.276065
\(37\) 2.65231e8 0.628803 0.314402 0.949290i \(-0.398196\pi\)
0.314402 + 0.949290i \(0.398196\pi\)
\(38\) 3.01212e8 0.616684
\(39\) 1.28478e8 0.228020
\(40\) −4.44294e8 −0.686026
\(41\) 8.26019e8 1.11347 0.556735 0.830690i \(-0.312054\pi\)
0.556735 + 0.830690i \(0.312054\pi\)
\(42\) 2.71976e8 0.321115
\(43\) 1.62764e9 1.68843 0.844214 0.536007i \(-0.180068\pi\)
0.844214 + 0.536007i \(0.180068\pi\)
\(44\) 1.05674e9 0.966002
\(45\) −3.73550e8 −0.301773
\(46\) −5.21918e8 −0.373624
\(47\) −7.37241e8 −0.468891 −0.234445 0.972129i \(-0.575327\pi\)
−0.234445 + 0.972129i \(0.575327\pi\)
\(48\) 5.23983e8 0.296818
\(49\) 1.58297e9 0.800560
\(50\) 1.65229e8 0.0747742
\(51\) 2.18085e9 0.885094
\(52\) −8.96777e8 −0.327089
\(53\) −5.01219e9 −1.64630 −0.823152 0.567821i \(-0.807787\pi\)
−0.823152 + 0.567821i \(0.807787\pi\)
\(54\) −2.69154e8 −0.0797692
\(55\) 3.94131e9 1.05596
\(56\) −4.19061e9 −1.01682
\(57\) −3.90208e9 −0.858983
\(58\) −3.07968e9 −0.616101
\(59\) −7.14924e8 −0.130189
\(60\) 2.60739e9 0.432886
\(61\) 1.38051e9 0.209280 0.104640 0.994510i \(-0.466631\pi\)
0.104640 + 0.994510i \(0.466631\pi\)
\(62\) 3.05374e8 0.0423328
\(63\) −3.52335e9 −0.447283
\(64\) −9.59383e8 −0.111687
\(65\) −3.34470e9 −0.357548
\(66\) 2.83983e9 0.279127
\(67\) −1.90823e10 −1.72671 −0.863356 0.504596i \(-0.831641\pi\)
−0.863356 + 0.504596i \(0.831641\pi\)
\(68\) −1.52224e10 −1.26965
\(69\) 6.76125e9 0.520424
\(70\) −7.08045e9 −0.503526
\(71\) 1.84853e10 1.21592 0.607961 0.793967i \(-0.291988\pi\)
0.607961 + 0.793967i \(0.291988\pi\)
\(72\) 4.14712e9 0.252591
\(73\) −7.34829e9 −0.414869 −0.207434 0.978249i \(-0.566511\pi\)
−0.207434 + 0.978249i \(0.566511\pi\)
\(74\) −4.97515e9 −0.260634
\(75\) −2.14048e9 −0.104154
\(76\) 2.72366e10 1.23219
\(77\) 3.71747e10 1.56512
\(78\) −2.40996e9 −0.0945125
\(79\) −8.78770e9 −0.321312 −0.160656 0.987010i \(-0.551361\pi\)
−0.160656 + 0.987010i \(0.551361\pi\)
\(80\) −1.36410e10 −0.465428
\(81\) 3.48678e9 0.111111
\(82\) −1.54943e10 −0.461525
\(83\) 4.09401e10 1.14083 0.570413 0.821358i \(-0.306783\pi\)
0.570413 + 0.821358i \(0.306783\pi\)
\(84\) 2.45930e10 0.641617
\(85\) −5.67747e10 −1.38788
\(86\) −3.05310e10 −0.699841
\(87\) 3.98961e10 0.858172
\(88\) −4.37562e10 −0.883862
\(89\) 3.82223e10 0.725557 0.362779 0.931875i \(-0.381828\pi\)
0.362779 + 0.931875i \(0.381828\pi\)
\(90\) 7.00698e9 0.125083
\(91\) −3.15475e10 −0.529952
\(92\) −4.71937e10 −0.746536
\(93\) −3.95600e9 −0.0589657
\(94\) 1.38290e10 0.194352
\(95\) 1.01584e11 1.34693
\(96\) −4.47807e10 −0.560530
\(97\) −9.18220e10 −1.08568 −0.542840 0.839836i \(-0.682651\pi\)
−0.542840 + 0.839836i \(0.682651\pi\)
\(98\) −2.96930e10 −0.331826
\(99\) −3.67889e10 −0.388798
\(100\) 1.49406e10 0.149406
\(101\) 6.50888e10 0.616224 0.308112 0.951350i \(-0.400303\pi\)
0.308112 + 0.951350i \(0.400303\pi\)
\(102\) −4.09079e10 −0.366865
\(103\) 4.83624e10 0.411058 0.205529 0.978651i \(-0.434109\pi\)
0.205529 + 0.978651i \(0.434109\pi\)
\(104\) 3.71327e10 0.299277
\(105\) 9.17245e10 0.701365
\(106\) 9.40177e10 0.682381
\(107\) −4.20598e10 −0.289905 −0.144953 0.989439i \(-0.546303\pi\)
−0.144953 + 0.989439i \(0.546303\pi\)
\(108\) −2.43378e10 −0.159386
\(109\) 2.20437e10 0.137227 0.0686135 0.997643i \(-0.478142\pi\)
0.0686135 + 0.997643i \(0.478142\pi\)
\(110\) −7.39304e10 −0.437686
\(111\) 6.44511e10 0.363040
\(112\) −1.28663e11 −0.689850
\(113\) 1.79343e11 0.915699 0.457850 0.889030i \(-0.348620\pi\)
0.457850 + 0.889030i \(0.348620\pi\)
\(114\) 7.31945e10 0.356042
\(115\) −1.76018e11 −0.816054
\(116\) −2.78475e11 −1.23103
\(117\) 3.12201e10 0.131647
\(118\) 1.34104e10 0.0539624
\(119\) −5.35503e11 −2.05709
\(120\) −1.07964e11 −0.396077
\(121\) 1.02847e11 0.360474
\(122\) −2.58954e10 −0.0867448
\(123\) 2.00723e11 0.642862
\(124\) 2.76129e10 0.0845850
\(125\) 3.64616e11 1.06864
\(126\) 6.60903e10 0.185396
\(127\) 1.43876e11 0.386427 0.193214 0.981157i \(-0.438109\pi\)
0.193214 + 0.981157i \(0.438109\pi\)
\(128\) 3.95407e11 1.01716
\(129\) 3.95517e11 0.974814
\(130\) 6.27393e10 0.148201
\(131\) −3.73006e10 −0.0844741 −0.0422371 0.999108i \(-0.513448\pi\)
−0.0422371 + 0.999108i \(0.513448\pi\)
\(132\) 2.56788e11 0.557722
\(133\) 9.58149e11 1.99641
\(134\) 3.57942e11 0.715709
\(135\) −9.07726e10 −0.174229
\(136\) 6.30309e11 1.16169
\(137\) −5.11099e11 −0.904777 −0.452389 0.891821i \(-0.649428\pi\)
−0.452389 + 0.891821i \(0.649428\pi\)
\(138\) −1.26826e11 −0.215712
\(139\) −6.28312e9 −0.0102706 −0.00513528 0.999987i \(-0.501635\pi\)
−0.00513528 + 0.999987i \(0.501635\pi\)
\(140\) −6.40239e11 −1.00609
\(141\) −1.79150e11 −0.270714
\(142\) −3.46744e11 −0.503991
\(143\) −3.29402e11 −0.460657
\(144\) 1.27328e11 0.171368
\(145\) −1.03863e12 −1.34566
\(146\) 1.37838e11 0.171960
\(147\) 3.84661e11 0.462203
\(148\) −4.49870e11 −0.520772
\(149\) −1.58987e12 −1.77353 −0.886764 0.462222i \(-0.847052\pi\)
−0.886764 + 0.462222i \(0.847052\pi\)
\(150\) 4.01507e10 0.0431709
\(151\) −1.39363e12 −1.44469 −0.722346 0.691531i \(-0.756936\pi\)
−0.722346 + 0.691531i \(0.756936\pi\)
\(152\) −1.12778e12 −1.12742
\(153\) 5.29946e11 0.511009
\(154\) −6.97316e11 −0.648733
\(155\) 1.02988e11 0.0924616
\(156\) −2.17917e11 −0.188845
\(157\) 8.72531e11 0.730017 0.365008 0.931004i \(-0.381066\pi\)
0.365008 + 0.931004i \(0.381066\pi\)
\(158\) 1.64838e11 0.133181
\(159\) −1.21796e12 −0.950495
\(160\) 1.16579e12 0.878943
\(161\) −1.66021e12 −1.20954
\(162\) −6.54044e10 −0.0460548
\(163\) −9.01074e11 −0.613379 −0.306689 0.951810i \(-0.599221\pi\)
−0.306689 + 0.951810i \(0.599221\pi\)
\(164\) −1.40105e12 −0.922171
\(165\) 9.57739e11 0.609657
\(166\) −7.67946e11 −0.472864
\(167\) 1.09087e12 0.649879 0.324939 0.945735i \(-0.394656\pi\)
0.324939 + 0.945735i \(0.394656\pi\)
\(168\) −1.01832e12 −0.587060
\(169\) −1.51262e12 −0.844021
\(170\) 1.06497e12 0.575265
\(171\) −9.48206e11 −0.495934
\(172\) −2.76072e12 −1.39835
\(173\) −1.06231e12 −0.521194 −0.260597 0.965448i \(-0.583919\pi\)
−0.260597 + 0.965448i \(0.583919\pi\)
\(174\) −7.48363e11 −0.355706
\(175\) 5.25591e11 0.242069
\(176\) −1.34343e12 −0.599647
\(177\) −1.73727e11 −0.0751646
\(178\) −7.16966e11 −0.300738
\(179\) −1.26946e12 −0.516329 −0.258164 0.966101i \(-0.583118\pi\)
−0.258164 + 0.966101i \(0.583118\pi\)
\(180\) 6.33595e11 0.249927
\(181\) 2.39028e12 0.914570 0.457285 0.889320i \(-0.348822\pi\)
0.457285 + 0.889320i \(0.348822\pi\)
\(182\) 5.91761e11 0.219661
\(183\) 3.35465e11 0.120828
\(184\) 1.95414e12 0.683058
\(185\) −1.67788e12 −0.569267
\(186\) 7.42058e10 0.0244409
\(187\) −5.59144e12 −1.78811
\(188\) 1.25047e12 0.388333
\(189\) −8.56174e11 −0.258239
\(190\) −1.90550e12 −0.558295
\(191\) −2.56355e12 −0.729725 −0.364862 0.931061i \(-0.618884\pi\)
−0.364862 + 0.931061i \(0.618884\pi\)
\(192\) −2.33130e11 −0.0644825
\(193\) 2.55408e12 0.686546 0.343273 0.939236i \(-0.388464\pi\)
0.343273 + 0.939236i \(0.388464\pi\)
\(194\) 1.72238e12 0.450007
\(195\) −8.12763e11 −0.206430
\(196\) −2.68494e12 −0.663020
\(197\) 5.14227e12 1.23478 0.617392 0.786656i \(-0.288189\pi\)
0.617392 + 0.786656i \(0.288189\pi\)
\(198\) 6.90080e11 0.161154
\(199\) −5.85424e12 −1.32978 −0.664888 0.746943i \(-0.731521\pi\)
−0.664888 + 0.746943i \(0.731521\pi\)
\(200\) −6.18642e11 −0.136702
\(201\) −4.63700e12 −0.996917
\(202\) −1.22092e12 −0.255420
\(203\) −9.79641e12 −1.99452
\(204\) −3.69903e12 −0.733031
\(205\) −5.22548e12 −1.00804
\(206\) −9.07172e11 −0.170381
\(207\) 1.64298e12 0.300467
\(208\) 1.14007e12 0.203041
\(209\) 1.00045e13 1.73536
\(210\) −1.72055e12 −0.290711
\(211\) 1.23214e12 0.202819 0.101409 0.994845i \(-0.467665\pi\)
0.101409 + 0.994845i \(0.467665\pi\)
\(212\) 8.50140e12 1.36346
\(213\) 4.49193e12 0.702013
\(214\) 7.88949e11 0.120164
\(215\) −1.02966e13 −1.52856
\(216\) 1.00775e12 0.145834
\(217\) 9.71388e11 0.137045
\(218\) −4.13492e11 −0.0568796
\(219\) −1.78564e12 −0.239525
\(220\) −6.68504e12 −0.874539
\(221\) 4.74505e12 0.605456
\(222\) −1.20896e12 −0.150477
\(223\) −7.29706e12 −0.886076 −0.443038 0.896503i \(-0.646099\pi\)
−0.443038 + 0.896503i \(0.646099\pi\)
\(224\) 1.09958e13 1.30276
\(225\) −5.20137e11 −0.0601331
\(226\) −3.36408e12 −0.379551
\(227\) −7.25121e12 −0.798488 −0.399244 0.916845i \(-0.630727\pi\)
−0.399244 + 0.916845i \(0.630727\pi\)
\(228\) 6.61850e12 0.711406
\(229\) −1.60900e13 −1.68834 −0.844170 0.536076i \(-0.819906\pi\)
−0.844170 + 0.536076i \(0.819906\pi\)
\(230\) 3.30171e12 0.338248
\(231\) 9.03346e12 0.903625
\(232\) 1.15308e13 1.12635
\(233\) 2.77609e12 0.264835 0.132418 0.991194i \(-0.457726\pi\)
0.132418 + 0.991194i \(0.457726\pi\)
\(234\) −5.85620e11 −0.0545668
\(235\) 4.66386e12 0.424495
\(236\) 1.21262e12 0.107822
\(237\) −2.13541e12 −0.185509
\(238\) 1.00449e13 0.852649
\(239\) −1.58836e13 −1.31753 −0.658767 0.752347i \(-0.728922\pi\)
−0.658767 + 0.752347i \(0.728922\pi\)
\(240\) −3.31477e12 −0.268715
\(241\) 1.69760e13 1.34506 0.672530 0.740070i \(-0.265208\pi\)
0.672530 + 0.740070i \(0.265208\pi\)
\(242\) −1.92919e12 −0.149414
\(243\) 8.47289e11 0.0641500
\(244\) −2.34155e12 −0.173324
\(245\) −1.00140e13 −0.724761
\(246\) −3.76511e12 −0.266462
\(247\) −8.49008e12 −0.587596
\(248\) −1.14336e12 −0.0773927
\(249\) 9.94844e12 0.658656
\(250\) −6.83939e12 −0.442942
\(251\) −1.71441e13 −1.08620 −0.543099 0.839669i \(-0.682749\pi\)
−0.543099 + 0.839669i \(0.682749\pi\)
\(252\) 5.97611e12 0.370438
\(253\) −1.73351e13 −1.05139
\(254\) −2.69880e12 −0.160171
\(255\) −1.37963e13 −0.801291
\(256\) −5.45214e12 −0.309918
\(257\) −1.41542e13 −0.787507 −0.393754 0.919216i \(-0.628824\pi\)
−0.393754 + 0.919216i \(0.628824\pi\)
\(258\) −7.41903e12 −0.404053
\(259\) −1.58259e13 −0.843759
\(260\) 5.67310e12 0.296120
\(261\) 9.69475e12 0.495466
\(262\) 6.99677e11 0.0350139
\(263\) 1.53226e13 0.750887 0.375444 0.926845i \(-0.377490\pi\)
0.375444 + 0.926845i \(0.377490\pi\)
\(264\) −1.06328e13 −0.510298
\(265\) 3.17076e13 1.49043
\(266\) −1.79728e13 −0.827496
\(267\) 9.28802e12 0.418901
\(268\) 3.23664e13 1.43005
\(269\) −2.27171e13 −0.983365 −0.491683 0.870775i \(-0.663618\pi\)
−0.491683 + 0.870775i \(0.663618\pi\)
\(270\) 1.70270e12 0.0722165
\(271\) 1.49874e13 0.622869 0.311434 0.950268i \(-0.399191\pi\)
0.311434 + 0.950268i \(0.399191\pi\)
\(272\) 1.93522e13 0.788135
\(273\) −7.66603e12 −0.305968
\(274\) 9.58709e12 0.375024
\(275\) 5.48795e12 0.210417
\(276\) −1.14681e13 −0.431013
\(277\) 3.51795e13 1.29614 0.648068 0.761583i \(-0.275577\pi\)
0.648068 + 0.761583i \(0.275577\pi\)
\(278\) 1.17858e11 0.00425707
\(279\) −9.61307e11 −0.0340439
\(280\) 2.65102e13 0.920544
\(281\) 8.76473e12 0.298438 0.149219 0.988804i \(-0.452324\pi\)
0.149219 + 0.988804i \(0.452324\pi\)
\(282\) 3.36045e12 0.112209
\(283\) 2.93454e13 0.960981 0.480491 0.877000i \(-0.340459\pi\)
0.480491 + 0.877000i \(0.340459\pi\)
\(284\) −3.13538e13 −1.00702
\(285\) 2.46850e13 0.777653
\(286\) 6.17886e12 0.190939
\(287\) −4.92870e13 −1.49411
\(288\) −1.08817e13 −0.323622
\(289\) 4.62729e13 1.35017
\(290\) 1.94824e13 0.557767
\(291\) −2.23127e13 −0.626818
\(292\) 1.24638e13 0.343593
\(293\) −1.32769e13 −0.359191 −0.179596 0.983741i \(-0.557479\pi\)
−0.179596 + 0.983741i \(0.557479\pi\)
\(294\) −7.21540e12 −0.191580
\(295\) 4.52268e12 0.117862
\(296\) 1.86277e13 0.476491
\(297\) −8.93971e12 −0.224473
\(298\) 2.98225e13 0.735115
\(299\) 1.47110e13 0.356001
\(300\) 3.63057e12 0.0862596
\(301\) −9.71185e13 −2.26562
\(302\) 2.61415e13 0.598815
\(303\) 1.58166e13 0.355777
\(304\) −3.46259e13 −0.764885
\(305\) −8.73327e12 −0.189465
\(306\) −9.94062e12 −0.211810
\(307\) 8.01846e13 1.67815 0.839074 0.544018i \(-0.183098\pi\)
0.839074 + 0.544018i \(0.183098\pi\)
\(308\) −6.30537e13 −1.29623
\(309\) 1.17521e13 0.237324
\(310\) −1.93182e12 −0.0383247
\(311\) −5.11605e13 −0.997132 −0.498566 0.866852i \(-0.666140\pi\)
−0.498566 + 0.866852i \(0.666140\pi\)
\(312\) 9.02324e12 0.172787
\(313\) 1.16380e13 0.218970 0.109485 0.993988i \(-0.465080\pi\)
0.109485 + 0.993988i \(0.465080\pi\)
\(314\) −1.63668e13 −0.302587
\(315\) 2.22891e13 0.404933
\(316\) 1.49052e13 0.266109
\(317\) 3.66542e13 0.643129 0.321565 0.946888i \(-0.395791\pi\)
0.321565 + 0.946888i \(0.395791\pi\)
\(318\) 2.28463e13 0.393973
\(319\) −1.02289e14 −1.73372
\(320\) 6.06916e12 0.101112
\(321\) −1.02205e13 −0.167377
\(322\) 3.11419e13 0.501347
\(323\) −1.44115e14 −2.28084
\(324\) −5.91409e12 −0.0920218
\(325\) −4.65722e12 −0.0712472
\(326\) 1.69022e13 0.254241
\(327\) 5.35663e12 0.0792280
\(328\) 5.80129e13 0.843759
\(329\) 4.39899e13 0.629181
\(330\) −1.79651e13 −0.252698
\(331\) −5.91325e13 −0.818035 −0.409018 0.912526i \(-0.634129\pi\)
−0.409018 + 0.912526i \(0.634129\pi\)
\(332\) −6.94403e13 −0.944827
\(333\) 1.56616e13 0.209601
\(334\) −2.04623e13 −0.269370
\(335\) 1.20717e14 1.56322
\(336\) −3.12651e13 −0.398285
\(337\) 6.68543e12 0.0837847 0.0418924 0.999122i \(-0.486661\pi\)
0.0418924 + 0.999122i \(0.486661\pi\)
\(338\) 2.83734e13 0.349841
\(339\) 4.35803e13 0.528679
\(340\) 9.62982e13 1.14943
\(341\) 1.01427e13 0.119126
\(342\) 1.77863e13 0.205561
\(343\) 2.35307e13 0.267619
\(344\) 1.14312e14 1.27945
\(345\) −4.27724e13 −0.471149
\(346\) 1.99267e13 0.216031
\(347\) −4.83060e13 −0.515453 −0.257727 0.966218i \(-0.582973\pi\)
−0.257727 + 0.966218i \(0.582973\pi\)
\(348\) −6.76695e13 −0.710734
\(349\) 4.03826e13 0.417498 0.208749 0.977969i \(-0.433061\pi\)
0.208749 + 0.977969i \(0.433061\pi\)
\(350\) −9.85893e12 −0.100336
\(351\) 7.58648e12 0.0760066
\(352\) 1.14812e14 1.13241
\(353\) −4.44917e13 −0.432034 −0.216017 0.976390i \(-0.569307\pi\)
−0.216017 + 0.976390i \(0.569307\pi\)
\(354\) 3.25873e12 0.0311552
\(355\) −1.16940e14 −1.10080
\(356\) −6.48306e13 −0.600904
\(357\) −1.30127e14 −1.18766
\(358\) 2.38122e13 0.214015
\(359\) 2.44086e13 0.216035 0.108017 0.994149i \(-0.465550\pi\)
0.108017 + 0.994149i \(0.465550\pi\)
\(360\) −2.62351e13 −0.228675
\(361\) 1.41368e14 1.21356
\(362\) −4.48364e13 −0.379083
\(363\) 2.49919e13 0.208119
\(364\) 5.35091e13 0.438904
\(365\) 4.64861e13 0.375588
\(366\) −6.29258e12 −0.0500822
\(367\) −1.78838e14 −1.40215 −0.701077 0.713086i \(-0.747297\pi\)
−0.701077 + 0.713086i \(0.747297\pi\)
\(368\) 5.99973e13 0.463413
\(369\) 4.87756e13 0.371157
\(370\) 3.14733e13 0.235957
\(371\) 2.99068e14 2.20909
\(372\) 6.70994e12 0.0488352
\(373\) 1.62695e14 1.16674 0.583371 0.812206i \(-0.301733\pi\)
0.583371 + 0.812206i \(0.301733\pi\)
\(374\) 1.04883e14 0.741160
\(375\) 8.86016e13 0.616978
\(376\) −5.17779e13 −0.355313
\(377\) 8.68051e13 0.587040
\(378\) 1.60599e13 0.107038
\(379\) 2.00828e14 1.31919 0.659596 0.751620i \(-0.270727\pi\)
0.659596 + 0.751620i \(0.270727\pi\)
\(380\) −1.72302e14 −1.11553
\(381\) 3.49618e13 0.223104
\(382\) 4.80867e13 0.302466
\(383\) 3.29956e13 0.204580 0.102290 0.994755i \(-0.467383\pi\)
0.102290 + 0.994755i \(0.467383\pi\)
\(384\) 9.60838e13 0.587257
\(385\) −2.35171e14 −1.41694
\(386\) −4.79090e13 −0.284568
\(387\) 9.61106e13 0.562809
\(388\) 1.55743e14 0.899156
\(389\) −2.55943e14 −1.45687 −0.728435 0.685114i \(-0.759752\pi\)
−0.728435 + 0.685114i \(0.759752\pi\)
\(390\) 1.52456e13 0.0855639
\(391\) 2.49712e14 1.38187
\(392\) 1.11175e14 0.606643
\(393\) −9.06405e12 −0.0487712
\(394\) −9.64577e13 −0.511809
\(395\) 5.55919e13 0.290889
\(396\) 6.23994e13 0.322001
\(397\) 2.41106e14 1.22704 0.613522 0.789678i \(-0.289752\pi\)
0.613522 + 0.789678i \(0.289752\pi\)
\(398\) 1.09813e14 0.551182
\(399\) 2.32830e14 1.15263
\(400\) −1.89940e13 −0.0927440
\(401\) 2.65952e14 1.28088 0.640441 0.768007i \(-0.278751\pi\)
0.640441 + 0.768007i \(0.278751\pi\)
\(402\) 8.69800e13 0.413215
\(403\) −8.60738e12 −0.0403360
\(404\) −1.10400e14 −0.510354
\(405\) −2.20578e13 −0.100591
\(406\) 1.83759e14 0.826715
\(407\) −1.65245e14 −0.733432
\(408\) 1.53165e14 0.670701
\(409\) −1.75601e14 −0.758665 −0.379332 0.925260i \(-0.623846\pi\)
−0.379332 + 0.925260i \(0.623846\pi\)
\(410\) 9.80185e13 0.417827
\(411\) −1.24197e14 −0.522373
\(412\) −8.20296e13 −0.340436
\(413\) 4.26583e13 0.174694
\(414\) −3.08188e13 −0.124541
\(415\) −2.58991e14 −1.03281
\(416\) −9.74329e13 −0.383436
\(417\) −1.52680e12 −0.00592971
\(418\) −1.87662e14 −0.719296
\(419\) −2.79295e14 −1.05654 −0.528270 0.849076i \(-0.677159\pi\)
−0.528270 + 0.849076i \(0.677159\pi\)
\(420\) −1.55578e14 −0.580868
\(421\) −3.58421e14 −1.32082 −0.660408 0.750907i \(-0.729617\pi\)
−0.660408 + 0.750907i \(0.729617\pi\)
\(422\) −2.31123e13 −0.0840668
\(423\) −4.35334e13 −0.156297
\(424\) −3.52016e14 −1.24753
\(425\) −7.90540e13 −0.276557
\(426\) −8.42588e13 −0.290979
\(427\) −8.23728e13 −0.280822
\(428\) 7.13395e13 0.240098
\(429\) −8.00447e13 −0.265961
\(430\) 1.93142e14 0.633579
\(431\) 5.72779e14 1.85508 0.927539 0.373725i \(-0.121920\pi\)
0.927539 + 0.373725i \(0.121920\pi\)
\(432\) 3.09407e13 0.0989394
\(433\) 3.58056e14 1.13049 0.565246 0.824922i \(-0.308781\pi\)
0.565246 + 0.824922i \(0.308781\pi\)
\(434\) −1.82211e13 −0.0568043
\(435\) −2.52387e14 −0.776919
\(436\) −3.73894e13 −0.113651
\(437\) −4.46798e14 −1.34111
\(438\) 3.34946e13 0.0992812
\(439\) 7.80496e13 0.228463 0.114231 0.993454i \(-0.463559\pi\)
0.114231 + 0.993454i \(0.463559\pi\)
\(440\) 2.76806e14 0.800177
\(441\) 9.34727e13 0.266853
\(442\) −8.90066e13 −0.250957
\(443\) −1.83273e14 −0.510362 −0.255181 0.966893i \(-0.582135\pi\)
−0.255181 + 0.966893i \(0.582135\pi\)
\(444\) −1.09318e14 −0.300668
\(445\) −2.41798e14 −0.656860
\(446\) 1.36877e14 0.367272
\(447\) −3.86339e14 −1.02395
\(448\) 5.72447e13 0.149867
\(449\) 6.91658e13 0.178870 0.0894349 0.995993i \(-0.471494\pi\)
0.0894349 + 0.995993i \(0.471494\pi\)
\(450\) 9.75662e12 0.0249247
\(451\) −5.14629e14 −1.29874
\(452\) −3.04192e14 −0.758378
\(453\) −3.38653e14 −0.834094
\(454\) 1.36017e14 0.330967
\(455\) 1.99572e14 0.479775
\(456\) −2.74051e14 −0.650915
\(457\) −9.59403e12 −0.0225145 −0.0112572 0.999937i \(-0.503583\pi\)
−0.0112572 + 0.999937i \(0.503583\pi\)
\(458\) 3.01812e14 0.699805
\(459\) 1.28777e14 0.295031
\(460\) 2.98552e14 0.675852
\(461\) 3.95833e14 0.885436 0.442718 0.896661i \(-0.354014\pi\)
0.442718 + 0.896661i \(0.354014\pi\)
\(462\) −1.69448e14 −0.374546
\(463\) 6.66262e14 1.45529 0.727645 0.685954i \(-0.240615\pi\)
0.727645 + 0.685954i \(0.240615\pi\)
\(464\) 3.54026e14 0.764163
\(465\) 2.50260e13 0.0533827
\(466\) −5.20733e13 −0.109772
\(467\) −5.46946e14 −1.13947 −0.569733 0.821830i \(-0.692953\pi\)
−0.569733 + 0.821830i \(0.692953\pi\)
\(468\) −5.29538e13 −0.109030
\(469\) 1.13861e15 2.31699
\(470\) −8.74838e13 −0.175950
\(471\) 2.12025e14 0.421475
\(472\) −5.02105e13 −0.0986538
\(473\) −1.01406e15 −1.96937
\(474\) 4.00556e13 0.0768923
\(475\) 1.41448e14 0.268399
\(476\) 9.08291e14 1.70367
\(477\) −2.95965e14 −0.548768
\(478\) 2.97942e14 0.546108
\(479\) −6.19015e14 −1.12165 −0.560823 0.827936i \(-0.689515\pi\)
−0.560823 + 0.827936i \(0.689515\pi\)
\(480\) 2.83287e14 0.507458
\(481\) 1.40232e14 0.248341
\(482\) −3.18433e14 −0.557518
\(483\) −4.03432e14 −0.698330
\(484\) −1.74444e14 −0.298543
\(485\) 5.80875e14 0.982886
\(486\) −1.58933e13 −0.0265897
\(487\) −7.04223e14 −1.16493 −0.582467 0.812855i \(-0.697912\pi\)
−0.582467 + 0.812855i \(0.697912\pi\)
\(488\) 9.69562e13 0.158587
\(489\) −2.18961e14 −0.354135
\(490\) 1.87841e14 0.300408
\(491\) −7.66078e14 −1.21150 −0.605752 0.795653i \(-0.707128\pi\)
−0.605752 + 0.795653i \(0.707128\pi\)
\(492\) −3.40454e14 −0.532416
\(493\) 1.47348e15 2.27869
\(494\) 1.59255e14 0.243554
\(495\) 2.32731e14 0.351986
\(496\) −3.51043e13 −0.0525063
\(497\) −1.10299e15 −1.63159
\(498\) −1.86611e14 −0.273008
\(499\) −6.43649e13 −0.0931314 −0.0465657 0.998915i \(-0.514828\pi\)
−0.0465657 + 0.998915i \(0.514828\pi\)
\(500\) −6.18441e14 −0.885040
\(501\) 2.65081e14 0.375208
\(502\) 3.21585e14 0.450221
\(503\) −1.10390e14 −0.152864 −0.0764322 0.997075i \(-0.524353\pi\)
−0.0764322 + 0.997075i \(0.524353\pi\)
\(504\) −2.47452e14 −0.338939
\(505\) −4.11758e14 −0.557879
\(506\) 3.25168e14 0.435792
\(507\) −3.67567e14 −0.487296
\(508\) −2.44034e14 −0.320037
\(509\) 1.83785e14 0.238430 0.119215 0.992868i \(-0.461962\pi\)
0.119215 + 0.992868i \(0.461962\pi\)
\(510\) 2.58787e14 0.332129
\(511\) 4.38459e14 0.556691
\(512\) −7.07523e14 −0.888701
\(513\) −2.30414e14 −0.286328
\(514\) 2.65503e14 0.326416
\(515\) −3.05945e14 −0.372138
\(516\) −6.70854e14 −0.807337
\(517\) 4.59319e14 0.546911
\(518\) 2.96858e14 0.349732
\(519\) −2.58142e14 −0.300912
\(520\) −2.34905e14 −0.270940
\(521\) 1.42304e15 1.62409 0.812043 0.583597i \(-0.198355\pi\)
0.812043 + 0.583597i \(0.198355\pi\)
\(522\) −1.81852e14 −0.205367
\(523\) 1.72810e15 1.93112 0.965558 0.260188i \(-0.0837844\pi\)
0.965558 + 0.260188i \(0.0837844\pi\)
\(524\) 6.32672e13 0.0699611
\(525\) 1.27719e14 0.139758
\(526\) −2.87417e14 −0.311237
\(527\) −1.46106e14 −0.156571
\(528\) −3.26454e14 −0.346207
\(529\) −1.78631e14 −0.187478
\(530\) −5.94765e14 −0.617772
\(531\) −4.22156e13 −0.0433963
\(532\) −1.62516e15 −1.65342
\(533\) 4.36728e14 0.439756
\(534\) −1.74223e14 −0.173631
\(535\) 2.66075e14 0.262457
\(536\) −1.34019e15 −1.30846
\(537\) −3.08478e14 −0.298103
\(538\) 4.26122e14 0.407598
\(539\) −9.86227e14 −0.933768
\(540\) 1.53964e14 0.144295
\(541\) 1.38184e15 1.28195 0.640977 0.767560i \(-0.278529\pi\)
0.640977 + 0.767560i \(0.278529\pi\)
\(542\) −2.81132e14 −0.258175
\(543\) 5.80839e14 0.528027
\(544\) −1.65388e15 −1.48836
\(545\) −1.39451e14 −0.124234
\(546\) 1.43798e14 0.126822
\(547\) −1.56163e15 −1.36348 −0.681738 0.731596i \(-0.738776\pi\)
−0.681738 + 0.731596i \(0.738776\pi\)
\(548\) 8.66898e14 0.749333
\(549\) 8.15180e13 0.0697598
\(550\) −1.02942e14 −0.0872162
\(551\) −2.63642e15 −2.21147
\(552\) 4.74856e14 0.394363
\(553\) 5.24347e14 0.431152
\(554\) −6.59889e14 −0.537239
\(555\) −4.07724e14 −0.328666
\(556\) 1.06571e13 0.00850604
\(557\) 8.19309e13 0.0647507 0.0323753 0.999476i \(-0.489693\pi\)
0.0323753 + 0.999476i \(0.489693\pi\)
\(558\) 1.80320e13 0.0141109
\(559\) 8.60558e14 0.666830
\(560\) 8.13936e14 0.624534
\(561\) −1.35872e15 −1.03237
\(562\) −1.64407e14 −0.123700
\(563\) 1.44215e15 1.07452 0.537260 0.843417i \(-0.319459\pi\)
0.537260 + 0.843417i \(0.319459\pi\)
\(564\) 3.03864e14 0.224204
\(565\) −1.13454e15 −0.828999
\(566\) −5.50456e14 −0.398320
\(567\) −2.08050e14 −0.149094
\(568\) 1.29826e15 0.921395
\(569\) −1.65138e15 −1.16073 −0.580364 0.814357i \(-0.697090\pi\)
−0.580364 + 0.814357i \(0.697090\pi\)
\(570\) −4.63036e14 −0.322332
\(571\) −3.40796e14 −0.234961 −0.117481 0.993075i \(-0.537482\pi\)
−0.117481 + 0.993075i \(0.537482\pi\)
\(572\) 5.58714e14 0.381515
\(573\) −6.22944e14 −0.421307
\(574\) 9.24517e14 0.619297
\(575\) −2.45090e14 −0.162612
\(576\) −5.66506e13 −0.0372290
\(577\) −1.73380e15 −1.12858 −0.564290 0.825577i \(-0.690850\pi\)
−0.564290 + 0.825577i \(0.690850\pi\)
\(578\) −8.67979e14 −0.559636
\(579\) 6.20642e14 0.396378
\(580\) 1.76166e15 1.11447
\(581\) −2.44282e15 −1.53082
\(582\) 4.18538e14 0.259812
\(583\) 3.12271e15 1.92024
\(584\) −5.16085e14 −0.314377
\(585\) −1.97501e14 −0.119183
\(586\) 2.49046e14 0.148882
\(587\) 1.20999e14 0.0716590 0.0358295 0.999358i \(-0.488593\pi\)
0.0358295 + 0.999358i \(0.488593\pi\)
\(588\) −6.52441e14 −0.382795
\(589\) 2.61421e14 0.151952
\(590\) −8.48356e13 −0.0488531
\(591\) 1.24957e15 0.712903
\(592\) 5.71920e14 0.323270
\(593\) −1.87568e15 −1.05041 −0.525205 0.850976i \(-0.676011\pi\)
−0.525205 + 0.850976i \(0.676011\pi\)
\(594\) 1.67689e14 0.0930422
\(595\) 3.38765e15 1.86232
\(596\) 2.69666e15 1.46883
\(597\) −1.42258e15 −0.767746
\(598\) −2.75946e14 −0.147560
\(599\) −2.77141e15 −1.46843 −0.734215 0.678917i \(-0.762449\pi\)
−0.734215 + 0.678917i \(0.762449\pi\)
\(600\) −1.50330e14 −0.0789249
\(601\) −2.64870e15 −1.37792 −0.688958 0.724801i \(-0.741932\pi\)
−0.688958 + 0.724801i \(0.741932\pi\)
\(602\) 1.82173e15 0.939081
\(603\) −1.12679e15 −0.575570
\(604\) 2.36381e15 1.19649
\(605\) −6.50623e14 −0.326343
\(606\) −2.96684e14 −0.147467
\(607\) −3.55601e15 −1.75156 −0.875780 0.482710i \(-0.839652\pi\)
−0.875780 + 0.482710i \(0.839652\pi\)
\(608\) 2.95920e15 1.44446
\(609\) −2.38053e15 −1.15154
\(610\) 1.63817e14 0.0785317
\(611\) −3.89790e14 −0.185184
\(612\) −8.98865e14 −0.423215
\(613\) 1.55534e14 0.0725761 0.0362881 0.999341i \(-0.488447\pi\)
0.0362881 + 0.999341i \(0.488447\pi\)
\(614\) −1.50409e15 −0.695580
\(615\) −1.26979e15 −0.581995
\(616\) 2.61085e15 1.18601
\(617\) 6.40049e14 0.288167 0.144084 0.989566i \(-0.453977\pi\)
0.144084 + 0.989566i \(0.453977\pi\)
\(618\) −2.20443e14 −0.0983692
\(619\) −9.15332e14 −0.404837 −0.202418 0.979299i \(-0.564880\pi\)
−0.202418 + 0.979299i \(0.564880\pi\)
\(620\) −1.74682e14 −0.0765763
\(621\) 3.99245e14 0.173475
\(622\) 9.59659e14 0.413304
\(623\) −2.28066e15 −0.973589
\(624\) 2.77038e14 0.117226
\(625\) −1.87649e15 −0.787057
\(626\) −2.18303e14 −0.0907615
\(627\) 2.43109e15 1.00191
\(628\) −1.47994e15 −0.604597
\(629\) 2.38036e15 0.963972
\(630\) −4.18094e14 −0.167842
\(631\) −4.83096e15 −1.92252 −0.961262 0.275637i \(-0.911111\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(632\) −6.17177e14 −0.243482
\(633\) 2.99411e14 0.117097
\(634\) −6.87553e14 −0.266572
\(635\) −9.10174e14 −0.349839
\(636\) 2.06584e15 0.787196
\(637\) 8.36939e14 0.316174
\(638\) 1.91872e15 0.718616
\(639\) 1.09154e15 0.405308
\(640\) −2.50138e15 −0.920853
\(641\) −4.80211e15 −1.75272 −0.876361 0.481656i \(-0.840036\pi\)
−0.876361 + 0.481656i \(0.840036\pi\)
\(642\) 1.91715e14 0.0693765
\(643\) 2.91474e15 1.04578 0.522889 0.852401i \(-0.324854\pi\)
0.522889 + 0.852401i \(0.324854\pi\)
\(644\) 2.81596e15 1.00174
\(645\) −2.50208e15 −0.882517
\(646\) 2.70328e15 0.945393
\(647\) 4.69134e15 1.62676 0.813380 0.581732i \(-0.197625\pi\)
0.813380 + 0.581732i \(0.197625\pi\)
\(648\) 2.44884e14 0.0841971
\(649\) 4.45415e14 0.151851
\(650\) 8.73592e13 0.0295315
\(651\) 2.36047e14 0.0791231
\(652\) 1.52835e15 0.507998
\(653\) 1.45232e15 0.478675 0.239338 0.970936i \(-0.423070\pi\)
0.239338 + 0.970936i \(0.423070\pi\)
\(654\) −1.00479e14 −0.0328394
\(655\) 2.35967e14 0.0764759
\(656\) 1.78115e15 0.572439
\(657\) −4.33909e14 −0.138290
\(658\) −8.25153e14 −0.260791
\(659\) 5.40645e15 1.69450 0.847252 0.531191i \(-0.178255\pi\)
0.847252 + 0.531191i \(0.178255\pi\)
\(660\) −1.62446e15 −0.504915
\(661\) −5.16445e15 −1.59190 −0.795950 0.605363i \(-0.793028\pi\)
−0.795950 + 0.605363i \(0.793028\pi\)
\(662\) 1.10920e15 0.339070
\(663\) 1.15305e15 0.349560
\(664\) 2.87530e15 0.864488
\(665\) −6.06135e15 −1.80738
\(666\) −2.93778e14 −0.0868781
\(667\) 4.56820e15 1.33984
\(668\) −1.85027e15 −0.538227
\(669\) −1.77319e15 −0.511576
\(670\) −2.26438e15 −0.647944
\(671\) −8.60093e14 −0.244102
\(672\) 2.67198e15 0.752147
\(673\) 1.36310e15 0.380580 0.190290 0.981728i \(-0.439057\pi\)
0.190290 + 0.981728i \(0.439057\pi\)
\(674\) −1.25404e14 −0.0347282
\(675\) −1.26393e14 −0.0347179
\(676\) 2.56562e15 0.699015
\(677\) 3.81268e15 1.03037 0.515184 0.857080i \(-0.327724\pi\)
0.515184 + 0.857080i \(0.327724\pi\)
\(678\) −8.17471e14 −0.219134
\(679\) 5.47885e15 1.45682
\(680\) −3.98740e15 −1.05170
\(681\) −1.76204e15 −0.461007
\(682\) −1.90255e14 −0.0493767
\(683\) 5.05328e14 0.130095 0.0650474 0.997882i \(-0.479280\pi\)
0.0650474 + 0.997882i \(0.479280\pi\)
\(684\) 1.60830e15 0.410731
\(685\) 3.23326e15 0.819111
\(686\) −4.41383e14 −0.110926
\(687\) −3.90986e15 −0.974764
\(688\) 3.50970e15 0.868027
\(689\) −2.65002e15 −0.650194
\(690\) 8.02315e14 0.195288
\(691\) 4.43928e15 1.07197 0.535986 0.844227i \(-0.319940\pi\)
0.535986 + 0.844227i \(0.319940\pi\)
\(692\) 1.80184e15 0.431651
\(693\) 2.19513e15 0.521708
\(694\) 9.06115e14 0.213652
\(695\) 3.97477e13 0.00929813
\(696\) 2.80198e15 0.650300
\(697\) 7.41325e15 1.70698
\(698\) −7.57489e14 −0.173050
\(699\) 6.74590e14 0.152903
\(700\) −8.91479e14 −0.200480
\(701\) −1.42493e15 −0.317940 −0.158970 0.987283i \(-0.550817\pi\)
−0.158970 + 0.987283i \(0.550817\pi\)
\(702\) −1.42306e14 −0.0315042
\(703\) −4.25907e15 −0.935535
\(704\) 5.97719e14 0.130271
\(705\) 1.13332e15 0.245082
\(706\) 8.34566e14 0.179075
\(707\) −3.88373e15 −0.826880
\(708\) 2.94665e14 0.0622510
\(709\) −4.12853e14 −0.0865449 −0.0432725 0.999063i \(-0.513778\pi\)
−0.0432725 + 0.999063i \(0.513778\pi\)
\(710\) 2.19354e15 0.456272
\(711\) −5.18905e14 −0.107104
\(712\) 2.68443e15 0.549808
\(713\) −4.52971e14 −0.0920615
\(714\) 2.44090e15 0.492277
\(715\) 2.08383e15 0.417041
\(716\) 2.15318e15 0.427621
\(717\) −3.85973e15 −0.760678
\(718\) −4.57852e14 −0.0895448
\(719\) 7.07599e15 1.37334 0.686670 0.726969i \(-0.259072\pi\)
0.686670 + 0.726969i \(0.259072\pi\)
\(720\) −8.05489e14 −0.155143
\(721\) −2.88570e15 −0.551578
\(722\) −2.65175e15 −0.503011
\(723\) 4.12517e15 0.776571
\(724\) −4.05427e15 −0.757443
\(725\) −1.44620e15 −0.268145
\(726\) −4.68793e14 −0.0862640
\(727\) −9.41983e15 −1.72030 −0.860149 0.510042i \(-0.829630\pi\)
−0.860149 + 0.510042i \(0.829630\pi\)
\(728\) −2.21564e15 −0.401584
\(729\) 2.05891e14 0.0370370
\(730\) −8.71976e14 −0.155679
\(731\) 1.46076e16 2.58840
\(732\) −5.68997e14 −0.100069
\(733\) 1.10606e15 0.193066 0.0965329 0.995330i \(-0.469225\pi\)
0.0965329 + 0.995330i \(0.469225\pi\)
\(734\) 3.35460e15 0.581183
\(735\) −2.43341e15 −0.418441
\(736\) −5.12749e15 −0.875139
\(737\) 1.18887e16 2.01402
\(738\) −9.14922e14 −0.153842
\(739\) 1.02129e16 1.70454 0.852269 0.523104i \(-0.175226\pi\)
0.852269 + 0.523104i \(0.175226\pi\)
\(740\) 2.84592e15 0.471464
\(741\) −2.06309e15 −0.339248
\(742\) −5.60987e15 −0.915653
\(743\) −9.97555e15 −1.61621 −0.808106 0.589037i \(-0.799507\pi\)
−0.808106 + 0.589037i \(0.799507\pi\)
\(744\) −2.77837e14 −0.0446827
\(745\) 1.00577e16 1.60561
\(746\) −3.05180e15 −0.483606
\(747\) 2.41747e15 0.380275
\(748\) 9.48389e15 1.48091
\(749\) 2.50963e15 0.389009
\(750\) −1.66197e15 −0.255733
\(751\) 1.28086e16 1.95650 0.978252 0.207418i \(-0.0665061\pi\)
0.978252 + 0.207418i \(0.0665061\pi\)
\(752\) −1.58972e15 −0.241059
\(753\) −4.16601e15 −0.627116
\(754\) −1.62827e15 −0.243324
\(755\) 8.81627e15 1.30791
\(756\) 1.45219e15 0.213872
\(757\) −2.95980e15 −0.432748 −0.216374 0.976311i \(-0.569423\pi\)
−0.216374 + 0.976311i \(0.569423\pi\)
\(758\) −3.76709e15 −0.546796
\(759\) −4.21242e15 −0.607019
\(760\) 7.13446e15 1.02067
\(761\) −3.46860e15 −0.492650 −0.246325 0.969187i \(-0.579223\pi\)
−0.246325 + 0.969187i \(0.579223\pi\)
\(762\) −6.55807e14 −0.0924749
\(763\) −1.31531e15 −0.184138
\(764\) 4.34816e15 0.604355
\(765\) −3.35249e15 −0.462626
\(766\) −6.18925e14 −0.0847969
\(767\) −3.77991e14 −0.0514170
\(768\) −1.32487e15 −0.178931
\(769\) 1.31193e15 0.175920 0.0879599 0.996124i \(-0.471965\pi\)
0.0879599 + 0.996124i \(0.471965\pi\)
\(770\) 4.41129e15 0.587309
\(771\) −3.43948e15 −0.454668
\(772\) −4.33210e15 −0.568595
\(773\) 5.62151e15 0.732598 0.366299 0.930497i \(-0.380625\pi\)
0.366299 + 0.930497i \(0.380625\pi\)
\(774\) −1.80282e15 −0.233280
\(775\) 1.43402e14 0.0184245
\(776\) −6.44884e15 −0.822701
\(777\) −3.84568e15 −0.487145
\(778\) 4.80093e15 0.603862
\(779\) −1.32642e16 −1.65662
\(780\) 1.37856e15 0.170965
\(781\) −1.15168e16 −1.41824
\(782\) −4.68405e15 −0.572775
\(783\) 2.35582e15 0.286057
\(784\) 3.41337e15 0.411571
\(785\) −5.51972e15 −0.660897
\(786\) 1.70022e14 0.0202153
\(787\) 1.18717e16 1.40169 0.700847 0.713312i \(-0.252806\pi\)
0.700847 + 0.713312i \(0.252806\pi\)
\(788\) −8.72204e15 −1.02264
\(789\) 3.72338e15 0.433525
\(790\) −1.04278e15 −0.120571
\(791\) −1.07011e16 −1.22873
\(792\) −2.58376e15 −0.294621
\(793\) 7.29898e14 0.0826532
\(794\) −4.52262e15 −0.508601
\(795\) 7.70495e15 0.860500
\(796\) 9.92963e15 1.10131
\(797\) −2.99495e15 −0.329890 −0.164945 0.986303i \(-0.552745\pi\)
−0.164945 + 0.986303i \(0.552745\pi\)
\(798\) −4.36738e15 −0.477755
\(799\) −6.61650e15 −0.718822
\(800\) 1.62326e15 0.175144
\(801\) 2.25699e15 0.241852
\(802\) −4.98868e15 −0.530917
\(803\) 4.57816e15 0.483900
\(804\) 7.86503e15 0.825643
\(805\) 1.05027e16 1.09502
\(806\) 1.61456e14 0.0167190
\(807\) −5.52025e15 −0.567746
\(808\) 4.57131e15 0.466959
\(809\) −6.24312e15 −0.633410 −0.316705 0.948524i \(-0.602577\pi\)
−0.316705 + 0.948524i \(0.602577\pi\)
\(810\) 4.13755e14 0.0416942
\(811\) −1.60844e16 −1.60987 −0.804934 0.593364i \(-0.797799\pi\)
−0.804934 + 0.593364i \(0.797799\pi\)
\(812\) 1.66161e16 1.65185
\(813\) 3.64195e15 0.359613
\(814\) 3.09964e15 0.304002
\(815\) 5.70029e15 0.555303
\(816\) 4.70258e15 0.455030
\(817\) −2.61366e16 −2.51205
\(818\) 3.29390e15 0.314461
\(819\) −1.86285e15 −0.176651
\(820\) 8.86317e15 0.834858
\(821\) −1.49902e16 −1.40255 −0.701275 0.712890i \(-0.747386\pi\)
−0.701275 + 0.712890i \(0.747386\pi\)
\(822\) 2.32966e15 0.216520
\(823\) −9.82787e13 −0.00907320 −0.00453660 0.999990i \(-0.501444\pi\)
−0.00453660 + 0.999990i \(0.501444\pi\)
\(824\) 3.39658e15 0.311489
\(825\) 1.33357e15 0.121484
\(826\) −8.00175e14 −0.0724094
\(827\) −1.33337e16 −1.19859 −0.599297 0.800527i \(-0.704553\pi\)
−0.599297 + 0.800527i \(0.704553\pi\)
\(828\) −2.78674e15 −0.248845
\(829\) 6.17427e15 0.547691 0.273845 0.961774i \(-0.411704\pi\)
0.273845 + 0.961774i \(0.411704\pi\)
\(830\) 4.85810e15 0.428092
\(831\) 8.54861e15 0.748324
\(832\) −5.07240e14 −0.0441098
\(833\) 1.42066e16 1.22728
\(834\) 2.86394e13 0.00245782
\(835\) −6.90095e15 −0.588347
\(836\) −1.69691e16 −1.43722
\(837\) −2.33598e14 −0.0196552
\(838\) 5.23896e15 0.437928
\(839\) −5.50384e15 −0.457062 −0.228531 0.973537i \(-0.573392\pi\)
−0.228531 + 0.973537i \(0.573392\pi\)
\(840\) 6.44199e15 0.531476
\(841\) 1.47550e16 1.20938
\(842\) 6.72320e15 0.547469
\(843\) 2.12983e15 0.172303
\(844\) −2.08989e15 −0.167973
\(845\) 9.56899e15 0.764107
\(846\) 8.16590e14 0.0647839
\(847\) −6.13671e15 −0.483701
\(848\) −1.08078e16 −0.846372
\(849\) 7.13094e15 0.554823
\(850\) 1.48288e15 0.114631
\(851\) 7.37981e15 0.566803
\(852\) −7.61897e15 −0.581405
\(853\) −4.69851e15 −0.356238 −0.178119 0.984009i \(-0.557001\pi\)
−0.178119 + 0.984009i \(0.557001\pi\)
\(854\) 1.54513e15 0.116399
\(855\) 5.99845e15 0.448978
\(856\) −2.95394e15 −0.219683
\(857\) 3.62402e15 0.267791 0.133896 0.990995i \(-0.457251\pi\)
0.133896 + 0.990995i \(0.457251\pi\)
\(858\) 1.50146e15 0.110239
\(859\) 4.53693e15 0.330978 0.165489 0.986212i \(-0.447080\pi\)
0.165489 + 0.986212i \(0.447080\pi\)
\(860\) 1.74646e16 1.26595
\(861\) −1.19768e16 −0.862624
\(862\) −1.07441e16 −0.768917
\(863\) −2.51827e16 −1.79078 −0.895392 0.445278i \(-0.853105\pi\)
−0.895392 + 0.445278i \(0.853105\pi\)
\(864\) −2.64425e15 −0.186843
\(865\) 6.72031e15 0.471846
\(866\) −6.71635e15 −0.468581
\(867\) 1.12443e16 0.779522
\(868\) −1.64761e15 −0.113500
\(869\) 5.47495e15 0.374776
\(870\) 4.73422e15 0.322027
\(871\) −1.00891e16 −0.681950
\(872\) 1.54817e15 0.103987
\(873\) −5.42200e15 −0.361894
\(874\) 8.38094e15 0.555879
\(875\) −2.17560e16 −1.43395
\(876\) 3.02870e15 0.198373
\(877\) 1.39459e16 0.907713 0.453857 0.891075i \(-0.350048\pi\)
0.453857 + 0.891075i \(0.350048\pi\)
\(878\) −1.46404e15 −0.0946962
\(879\) −3.22629e15 −0.207379
\(880\) 8.49869e15 0.542872
\(881\) −1.04395e16 −0.662690 −0.331345 0.943510i \(-0.607502\pi\)
−0.331345 + 0.943510i \(0.607502\pi\)
\(882\) −1.75334e15 −0.110609
\(883\) −8.98179e15 −0.563092 −0.281546 0.959548i \(-0.590847\pi\)
−0.281546 + 0.959548i \(0.590847\pi\)
\(884\) −8.04828e15 −0.501436
\(885\) 1.09901e15 0.0680479
\(886\) 3.43780e15 0.211541
\(887\) −3.94709e15 −0.241378 −0.120689 0.992690i \(-0.538510\pi\)
−0.120689 + 0.992690i \(0.538510\pi\)
\(888\) 4.52653e15 0.275102
\(889\) −8.58482e15 −0.518527
\(890\) 4.53560e15 0.272264
\(891\) −2.17235e15 −0.129599
\(892\) 1.23769e16 0.733845
\(893\) 1.18386e16 0.697617
\(894\) 7.24687e15 0.424419
\(895\) 8.03072e15 0.467442
\(896\) −2.35932e16 −1.36488
\(897\) 3.57477e15 0.205537
\(898\) −1.29740e15 −0.0741402
\(899\) −2.67284e15 −0.151808
\(900\) 8.82227e14 0.0498020
\(901\) −4.49828e16 −2.52383
\(902\) 9.65332e15 0.538320
\(903\) −2.35998e16 −1.30805
\(904\) 1.25956e16 0.693893
\(905\) −1.51212e16 −0.827977
\(906\) 6.35239e15 0.345726
\(907\) 1.05811e16 0.572389 0.286194 0.958172i \(-0.407610\pi\)
0.286194 + 0.958172i \(0.407610\pi\)
\(908\) 1.22991e16 0.661304
\(909\) 3.84343e15 0.205408
\(910\) −3.74354e15 −0.198863
\(911\) 1.66134e16 0.877218 0.438609 0.898678i \(-0.355471\pi\)
0.438609 + 0.898678i \(0.355471\pi\)
\(912\) −8.41409e15 −0.441607
\(913\) −2.55067e16 −1.33065
\(914\) 1.79963e14 0.00933209
\(915\) −2.12219e15 −0.109387
\(916\) 2.72909e16 1.39828
\(917\) 2.22566e15 0.113352
\(918\) −2.41557e15 −0.122288
\(919\) −2.03950e16 −1.02633 −0.513167 0.858289i \(-0.671528\pi\)
−0.513167 + 0.858289i \(0.671528\pi\)
\(920\) −1.23621e16 −0.618384
\(921\) 1.94849e16 0.968879
\(922\) −7.42496e15 −0.367007
\(923\) 9.77346e15 0.480219
\(924\) −1.53221e16 −0.748378
\(925\) −2.33630e15 −0.113436
\(926\) −1.24976e16 −0.603207
\(927\) 2.85575e15 0.137019
\(928\) −3.02558e16 −1.44309
\(929\) −3.59026e16 −1.70231 −0.851156 0.524912i \(-0.824098\pi\)
−0.851156 + 0.524912i \(0.824098\pi\)
\(930\) −4.69433e14 −0.0221268
\(931\) −2.54192e16 −1.19108
\(932\) −4.70865e15 −0.219335
\(933\) −1.24320e16 −0.575695
\(934\) 1.02595e16 0.472301
\(935\) 3.53720e16 1.61881
\(936\) 2.19265e15 0.0997588
\(937\) −3.02293e16 −1.36729 −0.683645 0.729815i \(-0.739606\pi\)
−0.683645 + 0.729815i \(0.739606\pi\)
\(938\) −2.13578e16 −0.960374
\(939\) 2.82804e15 0.126422
\(940\) −7.91059e15 −0.351565
\(941\) −2.08747e16 −0.922313 −0.461157 0.887319i \(-0.652565\pi\)
−0.461157 + 0.887319i \(0.652565\pi\)
\(942\) −3.97712e15 −0.174699
\(943\) 2.29832e16 1.00368
\(944\) −1.54160e15 −0.0669306
\(945\) 5.41624e15 0.233788
\(946\) 1.90215e16 0.816290
\(947\) −1.68268e16 −0.717920 −0.358960 0.933353i \(-0.616869\pi\)
−0.358960 + 0.933353i \(0.616869\pi\)
\(948\) 3.62197e15 0.153638
\(949\) −3.88515e15 −0.163849
\(950\) −2.65324e15 −0.111249
\(951\) 8.90698e15 0.371311
\(952\) −3.76094e16 −1.55881
\(953\) −1.46538e16 −0.603866 −0.301933 0.953329i \(-0.597632\pi\)
−0.301933 + 0.953329i \(0.597632\pi\)
\(954\) 5.55165e15 0.227460
\(955\) 1.62173e16 0.660633
\(956\) 2.69410e16 1.09118
\(957\) −2.48562e16 −1.00097
\(958\) 1.16114e16 0.464914
\(959\) 3.04963e16 1.21407
\(960\) 1.47480e15 0.0583771
\(961\) −2.51434e16 −0.989569
\(962\) −2.63044e15 −0.102935
\(963\) −2.48359e15 −0.0966351
\(964\) −2.87938e16 −1.11397
\(965\) −1.61574e16 −0.621543
\(966\) 7.56749e15 0.289453
\(967\) −4.43380e16 −1.68628 −0.843141 0.537693i \(-0.819296\pi\)
−0.843141 + 0.537693i \(0.819296\pi\)
\(968\) 7.22316e15 0.273157
\(969\) −3.50199e16 −1.31684
\(970\) −1.08959e16 −0.407399
\(971\) −2.70153e16 −1.00439 −0.502196 0.864754i \(-0.667475\pi\)
−0.502196 + 0.864754i \(0.667475\pi\)
\(972\) −1.43712e15 −0.0531288
\(973\) 3.74903e14 0.0137815
\(974\) 1.32097e16 0.482856
\(975\) −1.13170e15 −0.0411346
\(976\) 2.97681e15 0.107591
\(977\) −1.90954e16 −0.686292 −0.343146 0.939282i \(-0.611493\pi\)
−0.343146 + 0.939282i \(0.611493\pi\)
\(978\) 4.10723e15 0.146786
\(979\) −2.38134e16 −0.846285
\(980\) 1.69852e16 0.600244
\(981\) 1.30166e15 0.0457423
\(982\) 1.43699e16 0.502160
\(983\) −2.94931e16 −1.02489 −0.512443 0.858721i \(-0.671259\pi\)
−0.512443 + 0.858721i \(0.671259\pi\)
\(984\) 1.40971e16 0.487144
\(985\) −3.25305e16 −1.11787
\(986\) −2.76392e16 −0.944500
\(987\) 1.06895e16 0.363258
\(988\) 1.44004e16 0.486644
\(989\) 4.52876e16 1.52195
\(990\) −4.36551e15 −0.145895
\(991\) 5.85273e16 1.94515 0.972575 0.232587i \(-0.0747192\pi\)
0.972575 + 0.232587i \(0.0747192\pi\)
\(992\) 3.00009e15 0.0991562
\(993\) −1.43692e16 −0.472293
\(994\) 2.06896e16 0.676280
\(995\) 3.70345e16 1.20387
\(996\) −1.68740e16 −0.545496
\(997\) −3.07013e16 −0.987038 −0.493519 0.869735i \(-0.664290\pi\)
−0.493519 + 0.869735i \(0.664290\pi\)
\(998\) 1.20734e15 0.0386023
\(999\) 3.80577e15 0.121013
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.1.12 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.12 27 1.1 even 1 trivial