Properties

Label 177.12.a.b.1.10
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 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +104646. q^{10} +946706. q^{11} +8710.56 q^{12} +853793. q^{13} -2.52804e6 q^{14} -557052. q^{15} -4.26643e6 q^{16} -1.00374e7 q^{17} -2.69554e6 q^{18} -6.49611e6 q^{19} -82173.0 q^{20} +1.34573e7 q^{21} -4.32163e7 q^{22} -3.83400e7 q^{23} +2.23203e7 q^{24} -4.35730e7 q^{25} -3.89749e7 q^{26} +1.43489e7 q^{27} +1.98514e6 q^{28} +8.96507e7 q^{29} +2.54290e7 q^{30} -1.71742e8 q^{31} +6.64378e6 q^{32} +2.30049e8 q^{33} +4.58198e8 q^{34} -1.26952e8 q^{35} +2.11667e6 q^{36} +4.13912e8 q^{37} +2.96542e8 q^{38} +2.07472e8 q^{39} -2.10564e8 q^{40} -1.94788e8 q^{41} -6.14314e8 q^{42} -4.76784e8 q^{43} +3.39355e7 q^{44} -1.35364e8 q^{45} +1.75019e9 q^{46} -1.06462e9 q^{47} -1.03674e9 q^{48} +1.08959e9 q^{49} +1.98907e9 q^{50} -2.43909e9 q^{51} +3.06050e7 q^{52} -3.74273e8 q^{53} -6.55016e8 q^{54} -2.17022e9 q^{55} +5.08681e9 q^{56} -1.57856e9 q^{57} -4.09248e9 q^{58} -7.14924e8 q^{59} -1.99680e7 q^{60} +8.62006e9 q^{61} +7.83988e9 q^{62} +3.27012e9 q^{63} +8.43437e9 q^{64} -1.95723e9 q^{65} -1.05016e10 q^{66} -2.01539e10 q^{67} -3.59799e8 q^{68} -9.31661e9 q^{69} +5.79527e9 q^{70} -8.96176e9 q^{71} +5.42384e9 q^{72} -1.78559e10 q^{73} -1.88948e10 q^{74} -1.05883e10 q^{75} -2.32859e8 q^{76} +5.24283e10 q^{77} -9.47091e9 q^{78} -1.08063e10 q^{79} +9.78035e9 q^{80} +3.48678e9 q^{81} +8.89193e9 q^{82} -5.12155e10 q^{83} +4.82389e8 q^{84} +2.30097e10 q^{85} +2.17648e10 q^{86} +2.17851e10 q^{87} +8.69579e10 q^{88} +2.09557e9 q^{89} +6.17924e9 q^{90} +4.72829e10 q^{91} -1.37433e9 q^{92} -4.17333e10 q^{93} +4.85992e10 q^{94} +1.48917e10 q^{95} +1.61444e9 q^{96} -8.78726e10 q^{97} -4.97390e10 q^{98} +5.59020e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −45.6492 −1.00871 −0.504357 0.863495i \(-0.668270\pi\)
−0.504357 + 0.863495i \(0.668270\pi\)
\(3\) 243.000 0.577350
\(4\) 35.8459 0.0175029
\(5\) −2292.40 −0.328061 −0.164030 0.986455i \(-0.552450\pi\)
−0.164030 + 0.986455i \(0.552450\pi\)
\(6\) −11092.7 −0.582381
\(7\) 55379.8 1.24541 0.622704 0.782457i \(-0.286034\pi\)
0.622704 + 0.782457i \(0.286034\pi\)
\(8\) 91853.1 0.991058
\(9\) 59049.0 0.333333
\(10\) 104646. 0.330919
\(11\) 946706. 1.77237 0.886187 0.463328i \(-0.153345\pi\)
0.886187 + 0.463328i \(0.153345\pi\)
\(12\) 8710.56 0.0101053
\(13\) 853793. 0.637770 0.318885 0.947793i \(-0.396692\pi\)
0.318885 + 0.947793i \(0.396692\pi\)
\(14\) −2.52804e6 −1.25626
\(15\) −557052. −0.189406
\(16\) −4.26643e6 −1.01720
\(17\) −1.00374e7 −1.71456 −0.857278 0.514854i \(-0.827846\pi\)
−0.857278 + 0.514854i \(0.827846\pi\)
\(18\) −2.69554e6 −0.336238
\(19\) −6.49611e6 −0.601878 −0.300939 0.953643i \(-0.597300\pi\)
−0.300939 + 0.953643i \(0.597300\pi\)
\(20\) −82173.0 −0.00574201
\(21\) 1.34573e7 0.719037
\(22\) −4.32163e7 −1.78782
\(23\) −3.83400e7 −1.24208 −0.621039 0.783780i \(-0.713289\pi\)
−0.621039 + 0.783780i \(0.713289\pi\)
\(24\) 2.23203e7 0.572188
\(25\) −4.35730e7 −0.892376
\(26\) −3.89749e7 −0.643327
\(27\) 1.43489e7 0.192450
\(28\) 1.98514e6 0.0217983
\(29\) 8.96507e7 0.811642 0.405821 0.913953i \(-0.366986\pi\)
0.405821 + 0.913953i \(0.366986\pi\)
\(30\) 2.54290e7 0.191056
\(31\) −1.71742e8 −1.07743 −0.538713 0.842489i \(-0.681089\pi\)
−0.538713 + 0.842489i \(0.681089\pi\)
\(32\) 6.64378e6 0.0350018
\(33\) 2.30049e8 1.02328
\(34\) 4.58198e8 1.72950
\(35\) −1.26952e8 −0.408570
\(36\) 2.11667e6 0.00583430
\(37\) 4.13912e8 0.981294 0.490647 0.871359i \(-0.336761\pi\)
0.490647 + 0.871359i \(0.336761\pi\)
\(38\) 2.96542e8 0.607123
\(39\) 2.07472e8 0.368217
\(40\) −2.10564e8 −0.325127
\(41\) −1.94788e8 −0.262574 −0.131287 0.991344i \(-0.541911\pi\)
−0.131287 + 0.991344i \(0.541911\pi\)
\(42\) −6.14314e8 −0.725303
\(43\) −4.76784e8 −0.494590 −0.247295 0.968940i \(-0.579542\pi\)
−0.247295 + 0.968940i \(0.579542\pi\)
\(44\) 3.39355e7 0.0310216
\(45\) −1.35364e8 −0.109354
\(46\) 1.75019e9 1.25290
\(47\) −1.06462e9 −0.677108 −0.338554 0.940947i \(-0.609938\pi\)
−0.338554 + 0.940947i \(0.609938\pi\)
\(48\) −1.03674e9 −0.587279
\(49\) 1.08959e9 0.551043
\(50\) 1.98907e9 0.900152
\(51\) −2.43909e9 −0.989899
\(52\) 3.06050e7 0.0111628
\(53\) −3.74273e8 −0.122934 −0.0614669 0.998109i \(-0.519578\pi\)
−0.0614669 + 0.998109i \(0.519578\pi\)
\(54\) −6.55016e8 −0.194127
\(55\) −2.17022e9 −0.581446
\(56\) 5.08681e9 1.23427
\(57\) −1.57856e9 −0.347495
\(58\) −4.09248e9 −0.818714
\(59\) −7.14924e8 −0.130189
\(60\) −1.99680e7 −0.00331515
\(61\) 8.62006e9 1.30676 0.653381 0.757029i \(-0.273350\pi\)
0.653381 + 0.757029i \(0.273350\pi\)
\(62\) 7.83988e9 1.08681
\(63\) 3.27012e9 0.415136
\(64\) 8.43437e9 0.981890
\(65\) −1.95723e9 −0.209227
\(66\) −1.05016e10 −1.03220
\(67\) −2.01539e10 −1.82367 −0.911837 0.410552i \(-0.865336\pi\)
−0.911837 + 0.410552i \(0.865336\pi\)
\(68\) −3.59799e8 −0.0300097
\(69\) −9.31661e9 −0.717114
\(70\) 5.79527e9 0.412130
\(71\) −8.96176e9 −0.589485 −0.294742 0.955577i \(-0.595234\pi\)
−0.294742 + 0.955577i \(0.595234\pi\)
\(72\) 5.42384e9 0.330353
\(73\) −1.78559e10 −1.00810 −0.504052 0.863673i \(-0.668158\pi\)
−0.504052 + 0.863673i \(0.668158\pi\)
\(74\) −1.88948e10 −0.989844
\(75\) −1.05883e10 −0.515214
\(76\) −2.32859e8 −0.0105346
\(77\) 5.24283e10 2.20733
\(78\) −9.47091e9 −0.371425
\(79\) −1.08063e10 −0.395120 −0.197560 0.980291i \(-0.563302\pi\)
−0.197560 + 0.980291i \(0.563302\pi\)
\(80\) 9.78035e9 0.333702
\(81\) 3.48678e9 0.111111
\(82\) 8.89193e9 0.264862
\(83\) −5.12155e10 −1.42716 −0.713579 0.700574i \(-0.752927\pi\)
−0.713579 + 0.700574i \(0.752927\pi\)
\(84\) 4.82389e8 0.0125852
\(85\) 2.30097e10 0.562479
\(86\) 2.17648e10 0.498900
\(87\) 2.17851e10 0.468602
\(88\) 8.69579e10 1.75652
\(89\) 2.09557e9 0.0397792 0.0198896 0.999802i \(-0.493669\pi\)
0.0198896 + 0.999802i \(0.493669\pi\)
\(90\) 6.17924e9 0.110306
\(91\) 4.72829e10 0.794285
\(92\) −1.37433e9 −0.0217399
\(93\) −4.17333e10 −0.622052
\(94\) 4.85992e10 0.683008
\(95\) 1.48917e10 0.197453
\(96\) 1.61444e9 0.0202083
\(97\) −8.78726e10 −1.03898 −0.519492 0.854475i \(-0.673879\pi\)
−0.519492 + 0.854475i \(0.673879\pi\)
\(98\) −4.97390e10 −0.555845
\(99\) 5.59020e10 0.590791
\(100\) −1.56192e9 −0.0156192
\(101\) 7.75387e10 0.734093 0.367046 0.930203i \(-0.380369\pi\)
0.367046 + 0.930203i \(0.380369\pi\)
\(102\) 1.11342e11 0.998525
\(103\) 2.15361e11 1.83047 0.915236 0.402918i \(-0.132004\pi\)
0.915236 + 0.402918i \(0.132004\pi\)
\(104\) 7.84236e10 0.632067
\(105\) −3.08494e10 −0.235888
\(106\) 1.70853e10 0.124005
\(107\) −2.57466e11 −1.77463 −0.887317 0.461160i \(-0.847434\pi\)
−0.887317 + 0.461160i \(0.847434\pi\)
\(108\) 5.14350e8 0.00336843
\(109\) 1.97013e11 1.22645 0.613223 0.789910i \(-0.289873\pi\)
0.613223 + 0.789910i \(0.289873\pi\)
\(110\) 9.90689e10 0.586513
\(111\) 1.00581e11 0.566550
\(112\) −2.36274e11 −1.26683
\(113\) 1.72211e11 0.879286 0.439643 0.898173i \(-0.355105\pi\)
0.439643 + 0.898173i \(0.355105\pi\)
\(114\) 7.20597e10 0.350523
\(115\) 8.78903e10 0.407477
\(116\) 3.21361e9 0.0142061
\(117\) 5.04156e10 0.212590
\(118\) 3.26357e10 0.131323
\(119\) −5.55868e11 −2.13532
\(120\) −5.11670e10 −0.187712
\(121\) 6.10940e11 2.14131
\(122\) −3.93499e11 −1.31815
\(123\) −4.73336e10 −0.151597
\(124\) −6.15625e9 −0.0188581
\(125\) 2.11820e11 0.620815
\(126\) −1.49278e11 −0.418754
\(127\) −3.52150e11 −0.945817 −0.472909 0.881112i \(-0.656796\pi\)
−0.472909 + 0.881112i \(0.656796\pi\)
\(128\) −3.98628e11 −1.02545
\(129\) −1.15859e11 −0.285552
\(130\) 8.93460e10 0.211051
\(131\) 9.90148e9 0.0224237 0.0112119 0.999937i \(-0.496431\pi\)
0.0112119 + 0.999937i \(0.496431\pi\)
\(132\) 8.24633e9 0.0179104
\(133\) −3.59753e11 −0.749585
\(134\) 9.20008e11 1.83956
\(135\) −3.28934e10 −0.0631354
\(136\) −9.21966e11 −1.69922
\(137\) −9.04183e11 −1.60064 −0.800319 0.599575i \(-0.795336\pi\)
−0.800319 + 0.599575i \(0.795336\pi\)
\(138\) 4.25295e11 0.723362
\(139\) −7.81431e11 −1.27735 −0.638674 0.769477i \(-0.720517\pi\)
−0.638674 + 0.769477i \(0.720517\pi\)
\(140\) −4.55072e9 −0.00715115
\(141\) −2.58704e11 −0.390929
\(142\) 4.09097e11 0.594621
\(143\) 8.08291e11 1.13037
\(144\) −2.51929e11 −0.339066
\(145\) −2.05515e11 −0.266268
\(146\) 8.15105e11 1.01689
\(147\) 2.64771e11 0.318145
\(148\) 1.48371e10 0.0171755
\(149\) −5.21209e10 −0.0581417 −0.0290708 0.999577i \(-0.509255\pi\)
−0.0290708 + 0.999577i \(0.509255\pi\)
\(150\) 4.83345e11 0.519703
\(151\) 1.29241e12 1.33976 0.669881 0.742469i \(-0.266345\pi\)
0.669881 + 0.742469i \(0.266345\pi\)
\(152\) −5.96688e11 −0.596497
\(153\) −5.92698e11 −0.571519
\(154\) −2.39331e12 −2.22656
\(155\) 3.93701e11 0.353461
\(156\) 7.43701e9 0.00644486
\(157\) −3.75275e10 −0.0313979 −0.0156990 0.999877i \(-0.504997\pi\)
−0.0156990 + 0.999877i \(0.504997\pi\)
\(158\) 4.93299e11 0.398562
\(159\) −9.09484e10 −0.0709759
\(160\) −1.52302e10 −0.0114827
\(161\) −2.12326e12 −1.54689
\(162\) −1.59169e11 −0.112079
\(163\) −1.37415e12 −0.935412 −0.467706 0.883884i \(-0.654919\pi\)
−0.467706 + 0.883884i \(0.654919\pi\)
\(164\) −6.98237e9 −0.00459581
\(165\) −5.27364e11 −0.335698
\(166\) 2.33795e12 1.43959
\(167\) 1.14860e12 0.684272 0.342136 0.939651i \(-0.388850\pi\)
0.342136 + 0.939651i \(0.388850\pi\)
\(168\) 1.23609e12 0.712608
\(169\) −1.06320e12 −0.593249
\(170\) −1.05037e12 −0.567380
\(171\) −3.83589e11 −0.200626
\(172\) −1.70908e10 −0.00865676
\(173\) −3.02808e12 −1.48564 −0.742819 0.669492i \(-0.766512\pi\)
−0.742819 + 0.669492i \(0.766512\pi\)
\(174\) −9.94472e11 −0.472685
\(175\) −2.41307e12 −1.11137
\(176\) −4.03905e12 −1.80285
\(177\) −1.73727e11 −0.0751646
\(178\) −9.56608e10 −0.0401258
\(179\) −3.88051e12 −1.57833 −0.789164 0.614183i \(-0.789486\pi\)
−0.789164 + 0.614183i \(0.789486\pi\)
\(180\) −4.85223e9 −0.00191400
\(181\) 1.77990e12 0.681027 0.340514 0.940240i \(-0.389399\pi\)
0.340514 + 0.940240i \(0.389399\pi\)
\(182\) −2.15842e12 −0.801206
\(183\) 2.09468e12 0.754459
\(184\) −3.52165e12 −1.23097
\(185\) −9.48851e11 −0.321924
\(186\) 1.90509e12 0.627472
\(187\) −9.50245e12 −3.03883
\(188\) −3.81624e10 −0.0118514
\(189\) 7.94639e11 0.239679
\(190\) −6.79792e11 −0.199173
\(191\) −7.72387e11 −0.219863 −0.109931 0.993939i \(-0.535063\pi\)
−0.109931 + 0.993939i \(0.535063\pi\)
\(192\) 2.04955e12 0.566894
\(193\) −1.25262e12 −0.336709 −0.168355 0.985727i \(-0.553845\pi\)
−0.168355 + 0.985727i \(0.553845\pi\)
\(194\) 4.01131e12 1.04804
\(195\) −4.75607e11 −0.120798
\(196\) 3.90575e10 0.00964485
\(197\) 1.52926e12 0.367211 0.183606 0.983000i \(-0.441223\pi\)
0.183606 + 0.983000i \(0.441223\pi\)
\(198\) −2.55188e12 −0.595939
\(199\) 2.01035e12 0.456646 0.228323 0.973585i \(-0.426676\pi\)
0.228323 + 0.973585i \(0.426676\pi\)
\(200\) −4.00232e12 −0.884396
\(201\) −4.89739e12 −1.05290
\(202\) −3.53958e12 −0.740489
\(203\) 4.96483e12 1.01083
\(204\) −8.74313e10 −0.0173261
\(205\) 4.46532e11 0.0861403
\(206\) −9.83107e12 −1.84642
\(207\) −2.26394e12 −0.414026
\(208\) −3.64265e12 −0.648738
\(209\) −6.14991e12 −1.06675
\(210\) 1.40825e12 0.237943
\(211\) 1.15333e13 1.89845 0.949226 0.314596i \(-0.101869\pi\)
0.949226 + 0.314596i \(0.101869\pi\)
\(212\) −1.34162e10 −0.00215170
\(213\) −2.17771e12 −0.340339
\(214\) 1.17531e13 1.79010
\(215\) 1.09298e12 0.162256
\(216\) 1.31799e12 0.190729
\(217\) −9.51104e12 −1.34184
\(218\) −8.99346e12 −1.23713
\(219\) −4.33897e12 −0.582029
\(220\) −7.77936e10 −0.0101770
\(221\) −8.56985e12 −1.09349
\(222\) −4.59143e12 −0.571487
\(223\) −3.82932e12 −0.464992 −0.232496 0.972597i \(-0.574689\pi\)
−0.232496 + 0.972597i \(0.574689\pi\)
\(224\) 3.67931e11 0.0435915
\(225\) −2.57294e12 −0.297459
\(226\) −7.86130e12 −0.886948
\(227\) 3.99728e12 0.440171 0.220086 0.975481i \(-0.429366\pi\)
0.220086 + 0.975481i \(0.429366\pi\)
\(228\) −5.65848e10 −0.00608216
\(229\) 1.28159e13 1.34479 0.672395 0.740192i \(-0.265265\pi\)
0.672395 + 0.740192i \(0.265265\pi\)
\(230\) −4.01212e12 −0.411028
\(231\) 1.27401e13 1.27440
\(232\) 8.23470e12 0.804384
\(233\) 1.68344e13 1.60598 0.802990 0.595993i \(-0.203241\pi\)
0.802990 + 0.595993i \(0.203241\pi\)
\(234\) −2.30143e12 −0.214442
\(235\) 2.44054e12 0.222133
\(236\) −2.56271e10 −0.00227868
\(237\) −2.62593e12 −0.228122
\(238\) 2.53749e13 2.15393
\(239\) 1.59953e13 1.32679 0.663396 0.748269i \(-0.269115\pi\)
0.663396 + 0.748269i \(0.269115\pi\)
\(240\) 2.37662e12 0.192663
\(241\) 4.50987e12 0.357331 0.178666 0.983910i \(-0.442822\pi\)
0.178666 + 0.983910i \(0.442822\pi\)
\(242\) −2.78889e13 −2.15997
\(243\) 8.47289e11 0.0641500
\(244\) 3.08994e11 0.0228721
\(245\) −2.49778e12 −0.180776
\(246\) 2.16074e12 0.152918
\(247\) −5.54634e12 −0.383860
\(248\) −1.57751e13 −1.06779
\(249\) −1.24454e13 −0.823971
\(250\) −9.66941e12 −0.626224
\(251\) −4.00229e12 −0.253573 −0.126786 0.991930i \(-0.540466\pi\)
−0.126786 + 0.991930i \(0.540466\pi\)
\(252\) 1.17220e11 0.00726608
\(253\) −3.62967e13 −2.20142
\(254\) 1.60753e13 0.954058
\(255\) 5.59135e12 0.324747
\(256\) 9.23461e11 0.0524927
\(257\) 4.14560e12 0.230651 0.115325 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(258\) 5.28885e12 0.288040
\(259\) 2.29224e13 1.22211
\(260\) −7.01587e10 −0.00366208
\(261\) 5.29378e12 0.270547
\(262\) −4.51994e11 −0.0226191
\(263\) −2.60341e13 −1.27581 −0.637904 0.770116i \(-0.720198\pi\)
−0.637904 + 0.770116i \(0.720198\pi\)
\(264\) 2.11308e13 1.01413
\(265\) 8.57982e11 0.0403298
\(266\) 1.64224e13 0.756116
\(267\) 5.09222e11 0.0229665
\(268\) −7.22434e11 −0.0319196
\(269\) 2.33894e12 0.101247 0.0506234 0.998718i \(-0.483879\pi\)
0.0506234 + 0.998718i \(0.483879\pi\)
\(270\) 1.50155e12 0.0636855
\(271\) −7.38151e12 −0.306771 −0.153385 0.988166i \(-0.549018\pi\)
−0.153385 + 0.988166i \(0.549018\pi\)
\(272\) 4.28238e13 1.74404
\(273\) 1.14897e13 0.458580
\(274\) 4.12752e13 1.61458
\(275\) −4.12508e13 −1.58162
\(276\) −3.33962e11 −0.0125516
\(277\) −8.75117e9 −0.000322424 0 −0.000161212 1.00000i \(-0.500051\pi\)
−0.000161212 1.00000i \(0.500051\pi\)
\(278\) 3.56717e13 1.28848
\(279\) −1.01412e13 −0.359142
\(280\) −1.16610e13 −0.404917
\(281\) −3.35223e13 −1.14143 −0.570714 0.821149i \(-0.693334\pi\)
−0.570714 + 0.821149i \(0.693334\pi\)
\(282\) 1.18096e13 0.394335
\(283\) 8.53267e12 0.279421 0.139711 0.990192i \(-0.455383\pi\)
0.139711 + 0.990192i \(0.455383\pi\)
\(284\) −3.21243e11 −0.0103177
\(285\) 3.61867e12 0.113999
\(286\) −3.68978e13 −1.14022
\(287\) −1.07873e13 −0.327012
\(288\) 3.92308e11 0.0116673
\(289\) 6.64773e13 1.93970
\(290\) 9.38158e12 0.268588
\(291\) −2.13530e13 −0.599858
\(292\) −6.40060e11 −0.0176447
\(293\) −5.45014e13 −1.47447 −0.737235 0.675636i \(-0.763869\pi\)
−0.737235 + 0.675636i \(0.763869\pi\)
\(294\) −1.20866e13 −0.320917
\(295\) 1.63889e12 0.0427099
\(296\) 3.80192e13 0.972519
\(297\) 1.35842e13 0.341093
\(298\) 2.37928e12 0.0586483
\(299\) −3.27344e13 −0.792160
\(300\) −3.79546e11 −0.00901772
\(301\) −2.64042e13 −0.615967
\(302\) −5.89975e13 −1.35144
\(303\) 1.88419e13 0.423829
\(304\) 2.77152e13 0.612229
\(305\) −1.97606e13 −0.428697
\(306\) 2.70562e13 0.576499
\(307\) 7.80827e13 1.63416 0.817078 0.576527i \(-0.195592\pi\)
0.817078 + 0.576527i \(0.195592\pi\)
\(308\) 1.87934e12 0.0386346
\(309\) 5.23328e13 1.05682
\(310\) −1.79721e13 −0.356541
\(311\) −4.62993e13 −0.902386 −0.451193 0.892427i \(-0.649001\pi\)
−0.451193 + 0.892427i \(0.649001\pi\)
\(312\) 1.90569e13 0.364924
\(313\) −2.52505e13 −0.475090 −0.237545 0.971376i \(-0.576343\pi\)
−0.237545 + 0.971376i \(0.576343\pi\)
\(314\) 1.71310e12 0.0316715
\(315\) −7.49641e12 −0.136190
\(316\) −3.87362e11 −0.00691573
\(317\) −4.06043e13 −0.712436 −0.356218 0.934403i \(-0.615934\pi\)
−0.356218 + 0.934403i \(0.615934\pi\)
\(318\) 4.15172e12 0.0715943
\(319\) 8.48728e13 1.43853
\(320\) −1.93349e13 −0.322120
\(321\) −6.25642e13 −1.02459
\(322\) 9.69250e13 1.56037
\(323\) 6.52040e13 1.03195
\(324\) 1.24987e11 0.00194477
\(325\) −3.72024e13 −0.569131
\(326\) 6.27289e13 0.943562
\(327\) 4.78741e13 0.708089
\(328\) −1.78919e13 −0.260226
\(329\) −5.89587e13 −0.843277
\(330\) 2.40737e13 0.338623
\(331\) −2.51913e13 −0.348494 −0.174247 0.984702i \(-0.555749\pi\)
−0.174247 + 0.984702i \(0.555749\pi\)
\(332\) −1.83587e12 −0.0249794
\(333\) 2.44411e13 0.327098
\(334\) −5.24327e13 −0.690234
\(335\) 4.62007e13 0.598276
\(336\) −5.74146e13 −0.731402
\(337\) −8.31760e13 −1.04240 −0.521199 0.853435i \(-0.674515\pi\)
−0.521199 + 0.853435i \(0.674515\pi\)
\(338\) 4.85341e13 0.598418
\(339\) 4.18473e13 0.507656
\(340\) 8.24802e11 0.00984500
\(341\) −1.62589e14 −1.90960
\(342\) 1.75105e13 0.202374
\(343\) −4.91625e13 −0.559135
\(344\) −4.37942e13 −0.490168
\(345\) 2.13574e13 0.235257
\(346\) 1.38229e14 1.49858
\(347\) −1.29687e14 −1.38383 −0.691915 0.721979i \(-0.743233\pi\)
−0.691915 + 0.721979i \(0.743233\pi\)
\(348\) 7.80907e11 0.00820188
\(349\) 1.52157e14 1.57308 0.786541 0.617538i \(-0.211870\pi\)
0.786541 + 0.617538i \(0.211870\pi\)
\(350\) 1.10154e14 1.12106
\(351\) 1.22510e13 0.122739
\(352\) 6.28970e12 0.0620362
\(353\) 7.62557e13 0.740477 0.370238 0.928937i \(-0.379276\pi\)
0.370238 + 0.928937i \(0.379276\pi\)
\(354\) 7.93047e12 0.0758195
\(355\) 2.05439e13 0.193387
\(356\) 7.51175e10 0.000696251 0
\(357\) −1.35076e14 −1.23283
\(358\) 1.77142e14 1.59208
\(359\) −1.21029e14 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(360\) −1.24336e13 −0.108376
\(361\) −7.42908e13 −0.637742
\(362\) −8.12511e13 −0.686961
\(363\) 1.48458e14 1.23628
\(364\) 1.69490e12 0.0139023
\(365\) 4.09327e13 0.330719
\(366\) −9.56202e13 −0.761033
\(367\) 9.61873e12 0.0754144 0.0377072 0.999289i \(-0.487995\pi\)
0.0377072 + 0.999289i \(0.487995\pi\)
\(368\) 1.63575e14 1.26344
\(369\) −1.15021e13 −0.0875247
\(370\) 4.33143e13 0.324729
\(371\) −2.07272e13 −0.153103
\(372\) −1.49597e12 −0.0108877
\(373\) 6.11511e13 0.438537 0.219268 0.975665i \(-0.429633\pi\)
0.219268 + 0.975665i \(0.429633\pi\)
\(374\) 4.33779e14 3.06531
\(375\) 5.14723e13 0.358427
\(376\) −9.77891e13 −0.671054
\(377\) 7.65431e13 0.517641
\(378\) −3.62746e13 −0.241768
\(379\) −2.49856e14 −1.64124 −0.820622 0.571471i \(-0.806373\pi\)
−0.820622 + 0.571471i \(0.806373\pi\)
\(380\) 5.33805e11 0.00345599
\(381\) −8.55724e13 −0.546068
\(382\) 3.52588e13 0.221778
\(383\) −1.81282e14 −1.12399 −0.561995 0.827141i \(-0.689966\pi\)
−0.561995 + 0.827141i \(0.689966\pi\)
\(384\) −9.68667e13 −0.592042
\(385\) −1.20186e14 −0.724139
\(386\) 5.71811e13 0.339643
\(387\) −2.81536e13 −0.164863
\(388\) −3.14987e12 −0.0181852
\(389\) −3.10316e14 −1.76637 −0.883185 0.469025i \(-0.844605\pi\)
−0.883185 + 0.469025i \(0.844605\pi\)
\(390\) 2.17111e13 0.121850
\(391\) 3.84833e14 2.12961
\(392\) 1.00083e14 0.546116
\(393\) 2.40606e12 0.0129463
\(394\) −6.98092e13 −0.370411
\(395\) 2.47723e13 0.129623
\(396\) 2.00386e12 0.0103405
\(397\) 1.60268e14 0.815642 0.407821 0.913062i \(-0.366289\pi\)
0.407821 + 0.913062i \(0.366289\pi\)
\(398\) −9.17708e13 −0.460625
\(399\) −8.74201e13 −0.432773
\(400\) 1.85901e14 0.907722
\(401\) −2.08875e14 −1.00599 −0.502993 0.864291i \(-0.667768\pi\)
−0.502993 + 0.864291i \(0.667768\pi\)
\(402\) 2.23562e14 1.06207
\(403\) −1.46632e14 −0.687150
\(404\) 2.77945e12 0.0128487
\(405\) −7.99309e12 −0.0364512
\(406\) −2.26641e14 −1.01963
\(407\) 3.91853e14 1.73922
\(408\) −2.24038e14 −0.981048
\(409\) 2.18943e14 0.945917 0.472958 0.881085i \(-0.343186\pi\)
0.472958 + 0.881085i \(0.343186\pi\)
\(410\) −2.03838e13 −0.0868909
\(411\) −2.19716e14 −0.924129
\(412\) 7.71983e12 0.0320386
\(413\) −3.95923e13 −0.162138
\(414\) 1.03347e14 0.417633
\(415\) 1.17406e14 0.468195
\(416\) 5.67241e12 0.0223231
\(417\) −1.89888e14 −0.737478
\(418\) 2.80738e14 1.07605
\(419\) −9.83765e13 −0.372147 −0.186073 0.982536i \(-0.559576\pi\)
−0.186073 + 0.982536i \(0.559576\pi\)
\(420\) −1.10583e12 −0.00412872
\(421\) −9.72533e13 −0.358387 −0.179194 0.983814i \(-0.557349\pi\)
−0.179194 + 0.983814i \(0.557349\pi\)
\(422\) −5.26485e14 −1.91499
\(423\) −6.28650e13 −0.225703
\(424\) −3.43782e13 −0.121835
\(425\) 4.37360e14 1.53003
\(426\) 9.94105e13 0.343305
\(427\) 4.77377e14 1.62745
\(428\) −9.22910e12 −0.0310612
\(429\) 1.96415e14 0.652618
\(430\) −4.98936e13 −0.163670
\(431\) 2.09361e14 0.678063 0.339031 0.940775i \(-0.389901\pi\)
0.339031 + 0.940775i \(0.389901\pi\)
\(432\) −6.12186e13 −0.195760
\(433\) 5.48395e14 1.73145 0.865726 0.500519i \(-0.166857\pi\)
0.865726 + 0.500519i \(0.166857\pi\)
\(434\) 4.34171e14 1.35353
\(435\) −4.99401e13 −0.153730
\(436\) 7.06210e12 0.0214663
\(437\) 2.49061e14 0.747580
\(438\) 1.98071e14 0.587100
\(439\) 3.87623e14 1.13463 0.567315 0.823501i \(-0.307982\pi\)
0.567315 + 0.823501i \(0.307982\pi\)
\(440\) −1.99342e14 −0.576247
\(441\) 6.43394e13 0.183681
\(442\) 3.91207e14 1.10302
\(443\) −1.78451e14 −0.496934 −0.248467 0.968640i \(-0.579927\pi\)
−0.248467 + 0.968640i \(0.579927\pi\)
\(444\) 3.60541e12 0.00991626
\(445\) −4.80387e12 −0.0130500
\(446\) 1.74805e14 0.469043
\(447\) −1.26654e13 −0.0335681
\(448\) 4.67093e14 1.22285
\(449\) −4.36198e14 −1.12805 −0.564025 0.825758i \(-0.690748\pi\)
−0.564025 + 0.825758i \(0.690748\pi\)
\(450\) 1.17453e14 0.300051
\(451\) −1.84407e14 −0.465379
\(452\) 6.17307e12 0.0153900
\(453\) 3.14056e14 0.773512
\(454\) −1.82472e14 −0.444007
\(455\) −1.08391e14 −0.260574
\(456\) −1.44995e14 −0.344387
\(457\) 8.18828e14 1.92156 0.960779 0.277315i \(-0.0894446\pi\)
0.960779 + 0.277315i \(0.0894446\pi\)
\(458\) −5.85036e14 −1.35651
\(459\) −1.44026e14 −0.329966
\(460\) 3.15051e12 0.00713202
\(461\) −7.92188e14 −1.77204 −0.886019 0.463648i \(-0.846540\pi\)
−0.886019 + 0.463648i \(0.846540\pi\)
\(462\) −5.81574e14 −1.28551
\(463\) 3.66634e14 0.800825 0.400412 0.916335i \(-0.368867\pi\)
0.400412 + 0.916335i \(0.368867\pi\)
\(464\) −3.82488e14 −0.825600
\(465\) 9.56693e13 0.204071
\(466\) −7.68476e14 −1.61997
\(467\) −1.80916e13 −0.0376906 −0.0188453 0.999822i \(-0.505999\pi\)
−0.0188453 + 0.999822i \(0.505999\pi\)
\(468\) 1.80719e12 0.00372094
\(469\) −1.11612e15 −2.27122
\(470\) −1.11409e14 −0.224068
\(471\) −9.11917e12 −0.0181276
\(472\) −6.56680e13 −0.129025
\(473\) −4.51375e14 −0.876599
\(474\) 1.19872e14 0.230110
\(475\) 2.83055e14 0.537102
\(476\) −1.99256e13 −0.0373743
\(477\) −2.21005e13 −0.0409779
\(478\) −7.30170e14 −1.33835
\(479\) −1.42483e14 −0.258178 −0.129089 0.991633i \(-0.541205\pi\)
−0.129089 + 0.991633i \(0.541205\pi\)
\(480\) −3.70093e12 −0.00662955
\(481\) 3.53396e14 0.625840
\(482\) −2.05872e14 −0.360445
\(483\) −5.15952e14 −0.893100
\(484\) 2.18997e13 0.0374791
\(485\) 2.01439e14 0.340850
\(486\) −3.86780e13 −0.0647090
\(487\) −5.62723e13 −0.0930862 −0.0465431 0.998916i \(-0.514820\pi\)
−0.0465431 + 0.998916i \(0.514820\pi\)
\(488\) 7.91780e14 1.29508
\(489\) −3.33919e14 −0.540060
\(490\) 1.14021e14 0.182351
\(491\) 3.83123e14 0.605885 0.302942 0.953009i \(-0.402031\pi\)
0.302942 + 0.953009i \(0.402031\pi\)
\(492\) −1.69672e12 −0.00265339
\(493\) −8.99859e14 −1.39161
\(494\) 2.53186e14 0.387205
\(495\) −1.28150e14 −0.193815
\(496\) 7.32726e14 1.09595
\(497\) −4.96300e14 −0.734149
\(498\) 5.68121e14 0.831150
\(499\) −8.22669e14 −1.19034 −0.595172 0.803598i \(-0.702916\pi\)
−0.595172 + 0.803598i \(0.702916\pi\)
\(500\) 7.59288e12 0.0108660
\(501\) 2.79110e14 0.395064
\(502\) 1.82701e14 0.255782
\(503\) 9.04428e14 1.25242 0.626210 0.779654i \(-0.284605\pi\)
0.626210 + 0.779654i \(0.284605\pi\)
\(504\) 3.00371e14 0.411424
\(505\) −1.77749e14 −0.240827
\(506\) 1.65691e15 2.22061
\(507\) −2.58357e14 −0.342513
\(508\) −1.26231e13 −0.0165545
\(509\) 9.07252e14 1.17701 0.588505 0.808494i \(-0.299717\pi\)
0.588505 + 0.808494i \(0.299717\pi\)
\(510\) −2.55240e14 −0.327577
\(511\) −9.88854e14 −1.25550
\(512\) 7.74236e14 0.972497
\(513\) −9.32121e13 −0.115832
\(514\) −1.89243e14 −0.232661
\(515\) −4.93694e14 −0.600507
\(516\) −4.15306e12 −0.00499798
\(517\) −1.00789e15 −1.20009
\(518\) −1.04639e15 −1.23276
\(519\) −7.35822e14 −0.857734
\(520\) −1.79778e14 −0.207357
\(521\) −3.79217e14 −0.432793 −0.216396 0.976306i \(-0.569430\pi\)
−0.216396 + 0.976306i \(0.569430\pi\)
\(522\) −2.41657e14 −0.272905
\(523\) −5.94956e14 −0.664853 −0.332426 0.943129i \(-0.607867\pi\)
−0.332426 + 0.943129i \(0.607867\pi\)
\(524\) 3.54927e11 0.000392480 0
\(525\) −5.86375e14 −0.641652
\(526\) 1.18843e15 1.28692
\(527\) 1.72384e15 1.84731
\(528\) −9.81490e14 −1.04088
\(529\) 5.17143e14 0.542756
\(530\) −3.91662e13 −0.0406812
\(531\) −4.22156e13 −0.0433963
\(532\) −1.28957e13 −0.0131199
\(533\) −1.66309e14 −0.167462
\(534\) −2.32456e13 −0.0231667
\(535\) 5.90214e14 0.582188
\(536\) −1.85120e15 −1.80737
\(537\) −9.42964e14 −0.911248
\(538\) −1.06771e14 −0.102129
\(539\) 1.03152e15 0.976655
\(540\) −1.17909e12 −0.00110505
\(541\) −1.96976e14 −0.182738 −0.0913688 0.995817i \(-0.529124\pi\)
−0.0913688 + 0.995817i \(0.529124\pi\)
\(542\) 3.36960e14 0.309444
\(543\) 4.32517e14 0.393191
\(544\) −6.66862e13 −0.0600125
\(545\) −4.51631e14 −0.402349
\(546\) −5.24497e14 −0.462576
\(547\) −1.09754e15 −0.958271 −0.479135 0.877741i \(-0.659050\pi\)
−0.479135 + 0.877741i \(0.659050\pi\)
\(548\) −3.24113e13 −0.0280158
\(549\) 5.09006e14 0.435587
\(550\) 1.88307e15 1.59540
\(551\) −5.82381e14 −0.488510
\(552\) −8.55760e14 −0.710701
\(553\) −5.98451e14 −0.492086
\(554\) 3.99484e11 0.000325233 0
\(555\) −2.30571e14 −0.185863
\(556\) −2.80111e13 −0.0223573
\(557\) −1.50745e15 −1.19135 −0.595675 0.803226i \(-0.703115\pi\)
−0.595675 + 0.803226i \(0.703115\pi\)
\(558\) 4.62937e14 0.362271
\(559\) −4.07075e14 −0.315435
\(560\) 5.41633e14 0.415596
\(561\) −2.30910e15 −1.75447
\(562\) 1.53026e15 1.15137
\(563\) 4.37573e14 0.326028 0.163014 0.986624i \(-0.447878\pi\)
0.163014 + 0.986624i \(0.447878\pi\)
\(564\) −9.27347e12 −0.00684238
\(565\) −3.94776e14 −0.288459
\(566\) −3.89509e14 −0.281856
\(567\) 1.93097e14 0.138379
\(568\) −8.23166e14 −0.584213
\(569\) 1.56835e15 1.10236 0.551182 0.834385i \(-0.314177\pi\)
0.551182 + 0.834385i \(0.314177\pi\)
\(570\) −1.65189e14 −0.114993
\(571\) 5.15698e14 0.355547 0.177773 0.984071i \(-0.443111\pi\)
0.177773 + 0.984071i \(0.443111\pi\)
\(572\) 2.89739e13 0.0197847
\(573\) −1.87690e14 −0.126938
\(574\) 4.92433e14 0.329862
\(575\) 1.67059e15 1.10840
\(576\) 4.98041e14 0.327297
\(577\) −4.83873e13 −0.0314967 −0.0157483 0.999876i \(-0.505013\pi\)
−0.0157483 + 0.999876i \(0.505013\pi\)
\(578\) −3.03463e15 −1.95660
\(579\) −3.04387e14 −0.194399
\(580\) −7.36686e12 −0.00466046
\(581\) −2.83631e15 −1.77740
\(582\) 9.74748e14 0.605084
\(583\) −3.54326e14 −0.217885
\(584\) −1.64012e15 −0.999089
\(585\) −1.15573e14 −0.0697425
\(586\) 2.48795e15 1.48732
\(587\) −2.20013e15 −1.30298 −0.651492 0.758655i \(-0.725857\pi\)
−0.651492 + 0.758655i \(0.725857\pi\)
\(588\) 9.49096e12 0.00556846
\(589\) 1.11566e15 0.648480
\(590\) −7.48139e13 −0.0430820
\(591\) 3.71609e14 0.212009
\(592\) −1.76593e15 −0.998169
\(593\) −7.70185e14 −0.431315 −0.215657 0.976469i \(-0.569189\pi\)
−0.215657 + 0.976469i \(0.569189\pi\)
\(594\) −6.20107e14 −0.344065
\(595\) 1.27427e15 0.700516
\(596\) −1.86832e12 −0.00101765
\(597\) 4.88515e14 0.263645
\(598\) 1.49430e15 0.799062
\(599\) 2.28431e15 1.21034 0.605171 0.796096i \(-0.293105\pi\)
0.605171 + 0.796096i \(0.293105\pi\)
\(600\) −9.72564e14 −0.510607
\(601\) −2.38115e15 −1.23873 −0.619366 0.785102i \(-0.712610\pi\)
−0.619366 + 0.785102i \(0.712610\pi\)
\(602\) 1.20533e15 0.621334
\(603\) −1.19007e15 −0.607891
\(604\) 4.63277e13 0.0234497
\(605\) −1.40052e15 −0.702479
\(606\) −8.60117e14 −0.427522
\(607\) 6.17573e13 0.0304194 0.0152097 0.999884i \(-0.495158\pi\)
0.0152097 + 0.999884i \(0.495158\pi\)
\(608\) −4.31587e13 −0.0210668
\(609\) 1.20645e15 0.583601
\(610\) 9.02054e14 0.432433
\(611\) −9.08969e14 −0.431840
\(612\) −2.12458e13 −0.0100032
\(613\) −1.42374e15 −0.664350 −0.332175 0.943218i \(-0.607782\pi\)
−0.332175 + 0.943218i \(0.607782\pi\)
\(614\) −3.56441e15 −1.64840
\(615\) 1.08507e14 0.0497331
\(616\) 4.81571e15 2.18759
\(617\) 2.11352e15 0.951563 0.475781 0.879564i \(-0.342165\pi\)
0.475781 + 0.879564i \(0.342165\pi\)
\(618\) −2.38895e15 −1.06603
\(619\) −1.87457e15 −0.829095 −0.414547 0.910028i \(-0.636060\pi\)
−0.414547 + 0.910028i \(0.636060\pi\)
\(620\) 1.41126e13 0.00618659
\(621\) −5.50137e14 −0.239038
\(622\) 2.11352e15 0.910248
\(623\) 1.16052e14 0.0495414
\(624\) −8.85164e14 −0.374549
\(625\) 1.64202e15 0.688711
\(626\) 1.15266e15 0.479230
\(627\) −1.49443e15 −0.615890
\(628\) −1.34521e12 −0.000549555 0
\(629\) −4.15460e15 −1.68248
\(630\) 3.42205e14 0.137377
\(631\) 3.36702e15 1.33994 0.669968 0.742390i \(-0.266308\pi\)
0.669968 + 0.742390i \(0.266308\pi\)
\(632\) −9.92594e14 −0.391586
\(633\) 2.80259e15 1.09607
\(634\) 1.85355e15 0.718644
\(635\) 8.07267e14 0.310286
\(636\) −3.26013e12 −0.00124228
\(637\) 9.30287e14 0.351439
\(638\) −3.87437e15 −1.45107
\(639\) −5.29183e14 −0.196495
\(640\) 9.13814e14 0.336409
\(641\) −4.16406e15 −1.51984 −0.759920 0.650017i \(-0.774762\pi\)
−0.759920 + 0.650017i \(0.774762\pi\)
\(642\) 2.85600e15 1.03351
\(643\) −2.00066e15 −0.717816 −0.358908 0.933373i \(-0.616851\pi\)
−0.358908 + 0.933373i \(0.616851\pi\)
\(644\) −7.61101e13 −0.0270751
\(645\) 2.65594e14 0.0936784
\(646\) −2.97651e15 −1.04095
\(647\) −4.89568e15 −1.69762 −0.848809 0.528700i \(-0.822680\pi\)
−0.848809 + 0.528700i \(0.822680\pi\)
\(648\) 3.20272e14 0.110118
\(649\) −6.76823e14 −0.230743
\(650\) 1.69826e15 0.574090
\(651\) −2.31118e15 −0.774709
\(652\) −4.92577e13 −0.0163724
\(653\) 4.83871e15 1.59480 0.797402 0.603449i \(-0.206207\pi\)
0.797402 + 0.603449i \(0.206207\pi\)
\(654\) −2.18541e15 −0.714258
\(655\) −2.26981e13 −0.00735635
\(656\) 8.31052e14 0.267090
\(657\) −1.05437e15 −0.336034
\(658\) 2.69141e15 0.850625
\(659\) −1.44327e15 −0.452352 −0.226176 0.974086i \(-0.572622\pi\)
−0.226176 + 0.974086i \(0.572622\pi\)
\(660\) −1.89039e13 −0.00587569
\(661\) 4.10129e15 1.26419 0.632095 0.774891i \(-0.282195\pi\)
0.632095 + 0.774891i \(0.282195\pi\)
\(662\) 1.14996e15 0.351531
\(663\) −2.08247e15 −0.631328
\(664\) −4.70431e15 −1.41440
\(665\) 8.24697e14 0.245909
\(666\) −1.11572e15 −0.329948
\(667\) −3.43720e15 −1.00812
\(668\) 4.11726e13 0.0119767
\(669\) −9.30525e14 −0.268463
\(670\) −2.10902e15 −0.603489
\(671\) 8.16066e15 2.31607
\(672\) 8.94072e13 0.0251676
\(673\) 6.68396e15 1.86617 0.933085 0.359656i \(-0.117106\pi\)
0.933085 + 0.359656i \(0.117106\pi\)
\(674\) 3.79692e15 1.05148
\(675\) −6.25226e14 −0.171738
\(676\) −3.81113e13 −0.0103836
\(677\) 1.83931e15 0.497071 0.248535 0.968623i \(-0.420051\pi\)
0.248535 + 0.968623i \(0.420051\pi\)
\(678\) −1.91030e15 −0.512080
\(679\) −4.86636e15 −1.29396
\(680\) 2.11351e15 0.557449
\(681\) 9.71338e14 0.254133
\(682\) 7.42206e15 1.92624
\(683\) 1.20792e15 0.310975 0.155487 0.987838i \(-0.450305\pi\)
0.155487 + 0.987838i \(0.450305\pi\)
\(684\) −1.37501e13 −0.00351154
\(685\) 2.07274e15 0.525107
\(686\) 2.24423e15 0.564007
\(687\) 3.11427e15 0.776415
\(688\) 2.03417e15 0.503096
\(689\) −3.19552e14 −0.0784035
\(690\) −9.74945e14 −0.237307
\(691\) 1.74426e15 0.421193 0.210597 0.977573i \(-0.432459\pi\)
0.210597 + 0.977573i \(0.432459\pi\)
\(692\) −1.08544e14 −0.0260030
\(693\) 3.09584e15 0.735776
\(694\) 5.92008e15 1.39589
\(695\) 1.79135e15 0.419048
\(696\) 2.00103e15 0.464412
\(697\) 1.95517e15 0.450198
\(698\) −6.94583e15 −1.58679
\(699\) 4.09076e15 0.927213
\(700\) −8.64985e13 −0.0194522
\(701\) −4.82894e15 −1.07746 −0.538732 0.842477i \(-0.681096\pi\)
−0.538732 + 0.842477i \(0.681096\pi\)
\(702\) −5.59248e14 −0.123808
\(703\) −2.68882e15 −0.590620
\(704\) 7.98486e15 1.74028
\(705\) 5.93051e14 0.128248
\(706\) −3.48101e15 −0.746929
\(707\) 4.29408e15 0.914246
\(708\) −6.22739e12 −0.00131560
\(709\) −1.00902e15 −0.211518 −0.105759 0.994392i \(-0.533727\pi\)
−0.105759 + 0.994392i \(0.533727\pi\)
\(710\) −9.37812e14 −0.195072
\(711\) −6.38102e14 −0.131707
\(712\) 1.92484e14 0.0394235
\(713\) 6.58459e15 1.33825
\(714\) 6.16611e15 1.24357
\(715\) −1.85292e15 −0.370829
\(716\) −1.39100e14 −0.0276253
\(717\) 3.88685e15 0.766023
\(718\) 5.52485e15 1.08053
\(719\) 5.37134e15 1.04250 0.521248 0.853405i \(-0.325467\pi\)
0.521248 + 0.853405i \(0.325467\pi\)
\(720\) 5.77520e14 0.111234
\(721\) 1.19267e16 2.27969
\(722\) 3.39131e15 0.643299
\(723\) 1.09590e15 0.206305
\(724\) 6.38023e13 0.0119199
\(725\) −3.90635e15 −0.724290
\(726\) −6.77700e15 −1.24706
\(727\) −1.01159e15 −0.184742 −0.0923712 0.995725i \(-0.529445\pi\)
−0.0923712 + 0.995725i \(0.529445\pi\)
\(728\) 4.34308e15 0.787182
\(729\) 2.05891e14 0.0370370
\(730\) −1.86854e15 −0.333601
\(731\) 4.78567e15 0.848003
\(732\) 7.50855e13 0.0132052
\(733\) 9.27668e15 1.61928 0.809638 0.586929i \(-0.199663\pi\)
0.809638 + 0.586929i \(0.199663\pi\)
\(734\) −4.39087e14 −0.0760716
\(735\) −6.06960e14 −0.104371
\(736\) −2.54722e14 −0.0434749
\(737\) −1.90798e16 −3.23223
\(738\) 5.25059e14 0.0882874
\(739\) −5.39464e15 −0.900365 −0.450182 0.892937i \(-0.648641\pi\)
−0.450182 + 0.892937i \(0.648641\pi\)
\(740\) −3.40124e13 −0.00563460
\(741\) −1.34776e15 −0.221622
\(742\) 9.46177e14 0.154437
\(743\) 5.12721e15 0.830697 0.415349 0.909662i \(-0.363660\pi\)
0.415349 + 0.909662i \(0.363660\pi\)
\(744\) −3.83334e15 −0.616490
\(745\) 1.19482e14 0.0190740
\(746\) −2.79150e15 −0.442358
\(747\) −3.02423e15 −0.475720
\(748\) −3.40624e14 −0.0531884
\(749\) −1.42584e16 −2.21015
\(750\) −2.34967e15 −0.361551
\(751\) −5.16172e15 −0.788451 −0.394225 0.919014i \(-0.628987\pi\)
−0.394225 + 0.919014i \(0.628987\pi\)
\(752\) 4.54215e15 0.688752
\(753\) −9.72556e14 −0.146400
\(754\) −3.49413e15 −0.522152
\(755\) −2.96272e15 −0.439523
\(756\) 2.84846e13 0.00419508
\(757\) 1.03746e15 0.151685 0.0758426 0.997120i \(-0.475835\pi\)
0.0758426 + 0.997120i \(0.475835\pi\)
\(758\) 1.14057e16 1.65555
\(759\) −8.82009e15 −1.27099
\(760\) 1.36785e15 0.195687
\(761\) 9.01004e15 1.27971 0.639855 0.768496i \(-0.278995\pi\)
0.639855 + 0.768496i \(0.278995\pi\)
\(762\) 3.90631e15 0.550826
\(763\) 1.09105e16 1.52743
\(764\) −2.76869e13 −0.00384823
\(765\) 1.35870e15 0.187493
\(766\) 8.27539e15 1.13378
\(767\) −6.10397e14 −0.0830306
\(768\) 2.24401e14 0.0303067
\(769\) −1.31431e16 −1.76239 −0.881196 0.472751i \(-0.843261\pi\)
−0.881196 + 0.472751i \(0.843261\pi\)
\(770\) 5.48641e15 0.730448
\(771\) 1.00738e15 0.133166
\(772\) −4.49014e13 −0.00589338
\(773\) −3.73422e15 −0.486646 −0.243323 0.969945i \(-0.578237\pi\)
−0.243323 + 0.969945i \(0.578237\pi\)
\(774\) 1.28519e15 0.166300
\(775\) 7.48333e15 0.961469
\(776\) −8.07137e15 −1.02969
\(777\) 5.57014e15 0.705587
\(778\) 1.41657e16 1.78176
\(779\) 1.26537e15 0.158038
\(780\) −1.70486e13 −0.00211431
\(781\) −8.48415e15 −1.04479
\(782\) −1.75673e16 −2.14817
\(783\) 1.28639e15 0.156201
\(784\) −4.64867e15 −0.560519
\(785\) 8.60278e13 0.0103004
\(786\) −1.09835e14 −0.0130592
\(787\) −6.18378e15 −0.730118 −0.365059 0.930984i \(-0.618951\pi\)
−0.365059 + 0.930984i \(0.618951\pi\)
\(788\) 5.48176e13 0.00642725
\(789\) −6.32627e15 −0.736588
\(790\) −1.13084e15 −0.130753
\(791\) 9.53702e15 1.09507
\(792\) 5.13478e15 0.585508
\(793\) 7.35975e15 0.833414
\(794\) −7.31611e15 −0.822749
\(795\) 2.08490e14 0.0232844
\(796\) 7.20628e13 0.00799263
\(797\) −7.49422e15 −0.825478 −0.412739 0.910849i \(-0.635428\pi\)
−0.412739 + 0.910849i \(0.635428\pi\)
\(798\) 3.99065e15 0.436544
\(799\) 1.06861e16 1.16094
\(800\) −2.89490e14 −0.0312347
\(801\) 1.23741e14 0.0132597
\(802\) 9.53496e15 1.01475
\(803\) −1.69042e16 −1.78674
\(804\) −1.75552e14 −0.0184288
\(805\) 4.86735e15 0.507475
\(806\) 6.69364e15 0.693138
\(807\) 5.68363e14 0.0584549
\(808\) 7.12218e15 0.727529
\(809\) −5.07971e15 −0.515374 −0.257687 0.966228i \(-0.582960\pi\)
−0.257687 + 0.966228i \(0.582960\pi\)
\(810\) 3.64878e14 0.0367688
\(811\) 4.13943e15 0.414311 0.207155 0.978308i \(-0.433579\pi\)
0.207155 + 0.978308i \(0.433579\pi\)
\(812\) 1.77969e14 0.0176924
\(813\) −1.79371e15 −0.177114
\(814\) −1.78878e16 −1.75437
\(815\) 3.15010e15 0.306872
\(816\) 1.04062e16 1.00692
\(817\) 3.09725e15 0.297683
\(818\) −9.99457e15 −0.954159
\(819\) 2.79201e15 0.264762
\(820\) 1.60064e13 0.00150770
\(821\) 1.31830e16 1.23347 0.616735 0.787171i \(-0.288455\pi\)
0.616735 + 0.787171i \(0.288455\pi\)
\(822\) 1.00299e16 0.932181
\(823\) −3.65311e15 −0.337259 −0.168630 0.985679i \(-0.553934\pi\)
−0.168630 + 0.985679i \(0.553934\pi\)
\(824\) 1.97816e16 1.81410
\(825\) −1.00240e16 −0.913151
\(826\) 1.80736e15 0.163551
\(827\) −4.28535e15 −0.385217 −0.192609 0.981276i \(-0.561695\pi\)
−0.192609 + 0.981276i \(0.561695\pi\)
\(828\) −8.11529e13 −0.00724665
\(829\) −9.68218e14 −0.0858862 −0.0429431 0.999078i \(-0.513673\pi\)
−0.0429431 + 0.999078i \(0.513673\pi\)
\(830\) −5.35950e15 −0.472275
\(831\) −2.12653e12 −0.000186152 0
\(832\) 7.20121e15 0.626220
\(833\) −1.09367e16 −0.944795
\(834\) 8.66822e15 0.743904
\(835\) −2.63305e15 −0.224483
\(836\) −2.20449e14 −0.0186713
\(837\) −2.46431e15 −0.207351
\(838\) 4.49080e15 0.375389
\(839\) −6.92947e15 −0.575452 −0.287726 0.957713i \(-0.592899\pi\)
−0.287726 + 0.957713i \(0.592899\pi\)
\(840\) −2.83362e15 −0.233779
\(841\) −4.16327e15 −0.341237
\(842\) 4.43953e15 0.361510
\(843\) −8.14591e15 −0.659004
\(844\) 4.13421e14 0.0332284
\(845\) 2.43727e15 0.194622
\(846\) 2.86974e15 0.227669
\(847\) 3.38337e16 2.66680
\(848\) 1.59681e15 0.125048
\(849\) 2.07344e15 0.161324
\(850\) −1.99651e16 −1.54336
\(851\) −1.58694e16 −1.21884
\(852\) −7.80619e13 −0.00595692
\(853\) −8.53570e14 −0.0647172 −0.0323586 0.999476i \(-0.510302\pi\)
−0.0323586 + 0.999476i \(0.510302\pi\)
\(854\) −2.17919e16 −1.64163
\(855\) 8.79338e14 0.0658176
\(856\) −2.36491e16 −1.75877
\(857\) −1.33844e16 −0.989019 −0.494510 0.869172i \(-0.664652\pi\)
−0.494510 + 0.869172i \(0.664652\pi\)
\(858\) −8.96616e15 −0.658304
\(859\) −8.83485e15 −0.644520 −0.322260 0.946651i \(-0.604443\pi\)
−0.322260 + 0.946651i \(0.604443\pi\)
\(860\) 3.91788e13 0.00283994
\(861\) −2.62132e15 −0.188801
\(862\) −9.55714e15 −0.683971
\(863\) 2.00425e16 1.42525 0.712626 0.701544i \(-0.247506\pi\)
0.712626 + 0.701544i \(0.247506\pi\)
\(864\) 9.53309e13 0.00673610
\(865\) 6.94155e15 0.487380
\(866\) −2.50338e16 −1.74654
\(867\) 1.61540e16 1.11989
\(868\) −3.40932e14 −0.0234860
\(869\) −1.02304e16 −0.700299
\(870\) 2.27972e15 0.155069
\(871\) −1.72072e16 −1.16308
\(872\) 1.80962e16 1.21548
\(873\) −5.18879e15 −0.346328
\(874\) −1.13694e16 −0.754094
\(875\) 1.17305e16 0.773168
\(876\) −1.55534e14 −0.0101872
\(877\) −4.19319e15 −0.272927 −0.136463 0.990645i \(-0.543574\pi\)
−0.136463 + 0.990645i \(0.543574\pi\)
\(878\) −1.76946e16 −1.14452
\(879\) −1.32439e16 −0.851286
\(880\) 9.25911e15 0.591445
\(881\) −2.40393e16 −1.52600 −0.763000 0.646399i \(-0.776274\pi\)
−0.763000 + 0.646399i \(0.776274\pi\)
\(882\) −2.93704e15 −0.185282
\(883\) −6.12735e15 −0.384139 −0.192070 0.981381i \(-0.561520\pi\)
−0.192070 + 0.981381i \(0.561520\pi\)
\(884\) −3.07194e14 −0.0191393
\(885\) 3.98250e14 0.0246586
\(886\) 8.14614e15 0.501264
\(887\) −1.15893e16 −0.708724 −0.354362 0.935108i \(-0.615302\pi\)
−0.354362 + 0.935108i \(0.615302\pi\)
\(888\) 9.23866e15 0.561484
\(889\) −1.95020e16 −1.17793
\(890\) 2.19292e14 0.0131637
\(891\) 3.30096e15 0.196930
\(892\) −1.37266e14 −0.00813870
\(893\) 6.91592e15 0.407537
\(894\) 5.78164e14 0.0338606
\(895\) 8.89566e15 0.517788
\(896\) −2.20759e16 −1.27710
\(897\) −7.95446e15 −0.457354
\(898\) 1.99121e16 1.13788
\(899\) −1.53968e16 −0.874484
\(900\) −9.22296e13 −0.00520639
\(901\) 3.75672e15 0.210777
\(902\) 8.41804e15 0.469434
\(903\) −6.41623e15 −0.355629
\(904\) 1.58181e16 0.871424
\(905\) −4.08024e15 −0.223418
\(906\) −1.43364e16 −0.780252
\(907\) 3.52662e15 0.190774 0.0953868 0.995440i \(-0.469591\pi\)
0.0953868 + 0.995440i \(0.469591\pi\)
\(908\) 1.43286e14 0.00770427
\(909\) 4.57858e15 0.244698
\(910\) 4.94796e15 0.262844
\(911\) −4.46644e14 −0.0235836 −0.0117918 0.999930i \(-0.503754\pi\)
−0.0117918 + 0.999930i \(0.503754\pi\)
\(912\) 6.73480e15 0.353470
\(913\) −4.84860e16 −2.52946
\(914\) −3.73788e16 −1.93830
\(915\) −4.80182e15 −0.247509
\(916\) 4.59398e14 0.0235377
\(917\) 5.48342e14 0.0279267
\(918\) 6.57465e15 0.332842
\(919\) −2.41299e16 −1.21429 −0.607143 0.794593i \(-0.707684\pi\)
−0.607143 + 0.794593i \(0.707684\pi\)
\(920\) 8.07300e15 0.403833
\(921\) 1.89741e16 0.943480
\(922\) 3.61627e16 1.78748
\(923\) −7.65149e15 −0.375956
\(924\) 4.56680e14 0.0223057
\(925\) −1.80354e16 −0.875683
\(926\) −1.67365e16 −0.807803
\(927\) 1.27169e16 0.610158
\(928\) 5.95619e14 0.0284089
\(929\) −5.21221e15 −0.247136 −0.123568 0.992336i \(-0.539434\pi\)
−0.123568 + 0.992336i \(0.539434\pi\)
\(930\) −4.36722e15 −0.205849
\(931\) −7.07812e15 −0.331661
\(932\) 6.03444e14 0.0281093
\(933\) −1.12507e16 −0.520993
\(934\) 8.25865e14 0.0380191
\(935\) 2.17834e16 0.996922
\(936\) 4.63083e15 0.210689
\(937\) −3.76736e16 −1.70400 −0.852000 0.523541i \(-0.824611\pi\)
−0.852000 + 0.523541i \(0.824611\pi\)
\(938\) 5.09498e16 2.29101
\(939\) −6.13587e15 −0.274294
\(940\) 8.74834e13 0.00388797
\(941\) 2.55617e16 1.12940 0.564698 0.825298i \(-0.308993\pi\)
0.564698 + 0.825298i \(0.308993\pi\)
\(942\) 4.16283e14 0.0182856
\(943\) 7.46818e15 0.326137
\(944\) 3.05018e15 0.132428
\(945\) −1.82163e15 −0.0786293
\(946\) 2.06049e16 0.884237
\(947\) 1.81337e13 0.000773681 0 0.000386840 1.00000i \(-0.499877\pi\)
0.000386840 1.00000i \(0.499877\pi\)
\(948\) −9.41290e13 −0.00399280
\(949\) −1.52452e16 −0.642938
\(950\) −1.29212e16 −0.541782
\(951\) −9.86684e15 −0.411325
\(952\) −5.10583e16 −2.11623
\(953\) 4.71702e16 1.94382 0.971912 0.235344i \(-0.0756218\pi\)
0.971912 + 0.235344i \(0.0756218\pi\)
\(954\) 1.00887e15 0.0413350
\(955\) 1.77062e15 0.0721284
\(956\) 5.73364e14 0.0232227
\(957\) 2.06241e16 0.830537
\(958\) 6.50424e15 0.260427
\(959\) −5.00734e16 −1.99345
\(960\) −4.69838e15 −0.185976
\(961\) 4.08687e15 0.160847
\(962\) −1.61322e16 −0.631293
\(963\) −1.52031e16 −0.591545
\(964\) 1.61661e14 0.00625432
\(965\) 2.87150e15 0.110461
\(966\) 2.35528e16 0.900882
\(967\) 7.07719e15 0.269163 0.134581 0.990903i \(-0.457031\pi\)
0.134581 + 0.990903i \(0.457031\pi\)
\(968\) 5.61167e16 2.12216
\(969\) 1.58446e16 0.595799
\(970\) −9.19551e15 −0.343820
\(971\) 2.78049e16 1.03375 0.516875 0.856061i \(-0.327095\pi\)
0.516875 + 0.856061i \(0.327095\pi\)
\(972\) 3.03718e13 0.00112281
\(973\) −4.32755e16 −1.59082
\(974\) 2.56878e15 0.0938973
\(975\) −9.04018e15 −0.328588
\(976\) −3.67769e16 −1.32923
\(977\) 3.67508e14 0.0132083 0.00660415 0.999978i \(-0.497898\pi\)
0.00660415 + 0.999978i \(0.497898\pi\)
\(978\) 1.52431e16 0.544766
\(979\) 1.98388e15 0.0705036
\(980\) −8.95351e13 −0.00316410
\(981\) 1.16334e16 0.408815
\(982\) −1.74892e16 −0.611164
\(983\) 1.64787e16 0.572635 0.286317 0.958135i \(-0.407569\pi\)
0.286317 + 0.958135i \(0.407569\pi\)
\(984\) −4.34774e15 −0.150242
\(985\) −3.50566e15 −0.120468
\(986\) 4.10778e16 1.40373
\(987\) −1.43270e16 −0.486866
\(988\) −1.98814e14 −0.00671866
\(989\) 1.82799e16 0.614319
\(990\) 5.84992e15 0.195504
\(991\) −7.53912e15 −0.250562 −0.125281 0.992121i \(-0.539983\pi\)
−0.125281 + 0.992121i \(0.539983\pi\)
\(992\) −1.14102e15 −0.0377118
\(993\) −6.12147e15 −0.201203
\(994\) 2.26557e16 0.740546
\(995\) −4.60852e15 −0.149808
\(996\) −4.46116e14 −0.0144219
\(997\) 9.66084e15 0.310593 0.155296 0.987868i \(-0.450367\pi\)
0.155296 + 0.987868i \(0.450367\pi\)
\(998\) 3.75542e16 1.20072
\(999\) 5.93919e15 0.188850
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.1.10 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.10 27 1.1 even 1 trivial