Properties

Label 177.12.a.a.1.11
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} -328874. q^{10} +524591. q^{11} +329114. q^{12} -36137.3 q^{13} +1.27408e6 q^{14} -3.03441e6 q^{15} +413811. q^{16} +2.33652e6 q^{17} -1.55515e6 q^{18} -1.72596e7 q^{19} -1.69125e7 q^{20} +1.17556e7 q^{21} -1.38160e7 q^{22} -3.09864e7 q^{23} -2.17746e7 q^{24} +1.07104e8 q^{25} +951736. q^{26} -1.43489e7 q^{27} +6.55206e7 q^{28} +2.08422e8 q^{29} +7.99163e7 q^{30} -2.18649e8 q^{31} -1.94414e8 q^{32} -1.27476e8 q^{33} -6.15361e7 q^{34} -6.04096e8 q^{35} -7.99748e7 q^{36} -4.80083e8 q^{37} +4.54559e8 q^{38} +8.78136e6 q^{39} +1.11895e9 q^{40} -2.86197e8 q^{41} -3.09603e8 q^{42} +1.35383e9 q^{43} -7.10496e8 q^{44} +7.37362e8 q^{45} +8.16079e8 q^{46} -2.88733e9 q^{47} -1.00556e8 q^{48} +3.62993e8 q^{49} -2.82077e9 q^{50} -5.67774e8 q^{51} +4.89436e7 q^{52} +2.98644e9 q^{53} +3.77902e8 q^{54} +6.55072e9 q^{55} -4.33492e9 q^{56} +4.19407e9 q^{57} -5.48913e9 q^{58} +7.14924e8 q^{59} +4.10974e9 q^{60} +1.17517e10 q^{61} +5.75848e9 q^{62} -2.85660e9 q^{63} +4.27274e9 q^{64} -4.51257e8 q^{65} +3.35729e9 q^{66} -1.30914e10 q^{67} -3.16453e9 q^{68} +7.52970e9 q^{69} +1.59099e10 q^{70} +4.46502e9 q^{71} +5.29122e9 q^{72} +2.16645e10 q^{73} +1.26438e10 q^{74} -2.60263e10 q^{75} +2.33760e10 q^{76} -2.53781e10 q^{77} -2.31272e8 q^{78} +3.67905e10 q^{79} +5.16738e9 q^{80} +3.48678e9 q^{81} +7.53747e9 q^{82} +1.84426e10 q^{83} -1.59215e10 q^{84} +2.91768e10 q^{85} -3.56554e10 q^{86} -5.06465e10 q^{87} +4.70073e10 q^{88} -2.23424e10 q^{89} -1.94197e10 q^{90} +1.74821e9 q^{91} +4.19674e10 q^{92} +5.31317e10 q^{93} +7.60425e10 q^{94} -2.15525e11 q^{95} +4.72427e10 q^{96} +2.89892e10 q^{97} -9.56002e9 q^{98} +3.09766e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26.3367 −0.581964 −0.290982 0.956729i \(-0.593982\pi\)
−0.290982 + 0.956729i \(0.593982\pi\)
\(3\) −243.000 −0.577350
\(4\) −1354.38 −0.661318
\(5\) 12487.3 1.78703 0.893517 0.449028i \(-0.148230\pi\)
0.893517 + 0.449028i \(0.148230\pi\)
\(6\) 6399.81 0.335997
\(7\) −48376.8 −1.08792 −0.543962 0.839110i \(-0.683076\pi\)
−0.543962 + 0.839110i \(0.683076\pi\)
\(8\) 89607.3 0.966827
\(9\) 59049.0 0.333333
\(10\) −328874. −1.03999
\(11\) 524591. 0.982113 0.491056 0.871128i \(-0.336611\pi\)
0.491056 + 0.871128i \(0.336611\pi\)
\(12\) 329114. 0.381812
\(13\) −36137.3 −0.0269940 −0.0134970 0.999909i \(-0.504296\pi\)
−0.0134970 + 0.999909i \(0.504296\pi\)
\(14\) 1.27408e6 0.633132
\(15\) −3.03441e6 −1.03175
\(16\) 413811. 0.0986603
\(17\) 2.33652e6 0.399117 0.199558 0.979886i \(-0.436049\pi\)
0.199558 + 0.979886i \(0.436049\pi\)
\(18\) −1.55515e6 −0.193988
\(19\) −1.72596e7 −1.59913 −0.799567 0.600577i \(-0.794938\pi\)
−0.799567 + 0.600577i \(0.794938\pi\)
\(20\) −1.69125e7 −1.18180
\(21\) 1.17556e7 0.628113
\(22\) −1.38160e7 −0.571554
\(23\) −3.09864e7 −1.00385 −0.501924 0.864912i \(-0.667374\pi\)
−0.501924 + 0.864912i \(0.667374\pi\)
\(24\) −2.17746e7 −0.558198
\(25\) 1.07104e8 2.19349
\(26\) 951736. 0.0157095
\(27\) −1.43489e7 −0.192450
\(28\) 6.55206e7 0.719464
\(29\) 2.08422e8 1.88692 0.943461 0.331485i \(-0.107550\pi\)
0.943461 + 0.331485i \(0.107550\pi\)
\(30\) 7.99163e7 0.600438
\(31\) −2.18649e8 −1.37170 −0.685848 0.727745i \(-0.740568\pi\)
−0.685848 + 0.727745i \(0.740568\pi\)
\(32\) −1.94414e8 −1.02424
\(33\) −1.27476e8 −0.567023
\(34\) −6.15361e7 −0.232271
\(35\) −6.04096e8 −1.94416
\(36\) −7.99748e7 −0.220439
\(37\) −4.80083e8 −1.13817 −0.569085 0.822279i \(-0.692702\pi\)
−0.569085 + 0.822279i \(0.692702\pi\)
\(38\) 4.54559e8 0.930638
\(39\) 8.78136e6 0.0155850
\(40\) 1.11895e9 1.72775
\(41\) −2.86197e8 −0.385792 −0.192896 0.981219i \(-0.561788\pi\)
−0.192896 + 0.981219i \(0.561788\pi\)
\(42\) −3.09603e8 −0.365539
\(43\) 1.35383e9 1.40439 0.702195 0.711985i \(-0.252204\pi\)
0.702195 + 0.711985i \(0.252204\pi\)
\(44\) −7.10496e8 −0.649489
\(45\) 7.37362e8 0.595678
\(46\) 8.16079e8 0.584203
\(47\) −2.88733e9 −1.83636 −0.918179 0.396165i \(-0.870341\pi\)
−0.918179 + 0.396165i \(0.870341\pi\)
\(48\) −1.00556e8 −0.0569615
\(49\) 3.62993e8 0.183578
\(50\) −2.82077e9 −1.27653
\(51\) −5.67774e8 −0.230430
\(52\) 4.89436e7 0.0178516
\(53\) 2.98644e9 0.980927 0.490464 0.871462i \(-0.336827\pi\)
0.490464 + 0.871462i \(0.336827\pi\)
\(54\) 3.77902e8 0.111999
\(55\) 6.55072e9 1.75507
\(56\) −4.33492e9 −1.05183
\(57\) 4.19407e9 0.923260
\(58\) −5.48913e9 −1.09812
\(59\) 7.14924e8 0.130189
\(60\) 4.10974e9 0.682312
\(61\) 1.17517e10 1.78150 0.890749 0.454495i \(-0.150180\pi\)
0.890749 + 0.454495i \(0.150180\pi\)
\(62\) 5.75848e9 0.798277
\(63\) −2.85660e9 −0.362641
\(64\) 4.27274e9 0.497412
\(65\) −4.51257e8 −0.0482392
\(66\) 3.35729e9 0.329987
\(67\) −1.30914e10 −1.18461 −0.592303 0.805715i \(-0.701781\pi\)
−0.592303 + 0.805715i \(0.701781\pi\)
\(68\) −3.16453e9 −0.263943
\(69\) 7.52970e9 0.579572
\(70\) 1.59099e10 1.13143
\(71\) 4.46502e9 0.293699 0.146850 0.989159i \(-0.453087\pi\)
0.146850 + 0.989159i \(0.453087\pi\)
\(72\) 5.29122e9 0.322276
\(73\) 2.16645e10 1.22313 0.611565 0.791194i \(-0.290540\pi\)
0.611565 + 0.791194i \(0.290540\pi\)
\(74\) 1.26438e10 0.662373
\(75\) −2.60263e10 −1.26641
\(76\) 2.33760e10 1.05754
\(77\) −2.53781e10 −1.06846
\(78\) −2.31272e8 −0.00906990
\(79\) 3.67905e10 1.34520 0.672600 0.740006i \(-0.265177\pi\)
0.672600 + 0.740006i \(0.265177\pi\)
\(80\) 5.16738e9 0.176309
\(81\) 3.48678e9 0.111111
\(82\) 7.53747e9 0.224517
\(83\) 1.84426e10 0.513917 0.256958 0.966422i \(-0.417280\pi\)
0.256958 + 0.966422i \(0.417280\pi\)
\(84\) −1.59215e10 −0.415383
\(85\) 2.91768e10 0.713235
\(86\) −3.56554e10 −0.817304
\(87\) −5.06465e10 −1.08941
\(88\) 4.70073e10 0.949533
\(89\) −2.23424e10 −0.424117 −0.212058 0.977257i \(-0.568017\pi\)
−0.212058 + 0.977257i \(0.568017\pi\)
\(90\) −1.94197e10 −0.346663
\(91\) 1.74821e9 0.0293674
\(92\) 4.19674e10 0.663863
\(93\) 5.31317e10 0.791949
\(94\) 7.60425e10 1.06869
\(95\) −2.15525e11 −2.85771
\(96\) 4.72427e10 0.591347
\(97\) 2.89892e10 0.342761 0.171381 0.985205i \(-0.445177\pi\)
0.171381 + 0.985205i \(0.445177\pi\)
\(98\) −9.56002e9 −0.106835
\(99\) 3.09766e10 0.327371
\(100\) −1.45060e11 −1.45060
\(101\) −9.13004e9 −0.0864380 −0.0432190 0.999066i \(-0.513761\pi\)
−0.0432190 + 0.999066i \(0.513761\pi\)
\(102\) 1.49533e10 0.134102
\(103\) −5.62201e10 −0.477845 −0.238923 0.971039i \(-0.576794\pi\)
−0.238923 + 0.971039i \(0.576794\pi\)
\(104\) −3.23817e9 −0.0260985
\(105\) 1.46795e11 1.12246
\(106\) −7.86529e10 −0.570864
\(107\) −1.76188e11 −1.21441 −0.607204 0.794546i \(-0.707709\pi\)
−0.607204 + 0.794546i \(0.707709\pi\)
\(108\) 1.94339e10 0.127271
\(109\) −4.75790e9 −0.0296189 −0.0148095 0.999890i \(-0.504714\pi\)
−0.0148095 + 0.999890i \(0.504714\pi\)
\(110\) −1.72524e11 −1.02139
\(111\) 1.16660e11 0.657122
\(112\) −2.00189e10 −0.107335
\(113\) 8.06303e10 0.411687 0.205843 0.978585i \(-0.434006\pi\)
0.205843 + 0.978585i \(0.434006\pi\)
\(114\) −1.10458e11 −0.537304
\(115\) −3.86936e11 −1.79391
\(116\) −2.82282e11 −1.24786
\(117\) −2.13387e9 −0.00899800
\(118\) −1.88287e10 −0.0757652
\(119\) −1.13033e11 −0.434208
\(120\) −2.71905e11 −0.997519
\(121\) −1.01155e10 −0.0354541
\(122\) −3.09500e11 −1.03677
\(123\) 6.95458e10 0.222737
\(124\) 2.96134e11 0.907127
\(125\) 7.27710e11 2.13282
\(126\) 7.52334e10 0.211044
\(127\) 7.84337e10 0.210660 0.105330 0.994437i \(-0.466410\pi\)
0.105330 + 0.994437i \(0.466410\pi\)
\(128\) 2.85631e11 0.734768
\(129\) −3.28981e11 −0.810825
\(130\) 1.18846e10 0.0280735
\(131\) −3.75789e11 −0.851043 −0.425521 0.904948i \(-0.639909\pi\)
−0.425521 + 0.904948i \(0.639909\pi\)
\(132\) 1.72651e11 0.374983
\(133\) 8.34963e11 1.73974
\(134\) 3.44783e11 0.689397
\(135\) −1.79179e11 −0.343915
\(136\) 2.09369e11 0.385877
\(137\) −5.28340e11 −0.935299 −0.467649 0.883914i \(-0.654899\pi\)
−0.467649 + 0.883914i \(0.654899\pi\)
\(138\) −1.98307e11 −0.337290
\(139\) −6.91093e11 −1.12968 −0.564840 0.825201i \(-0.691062\pi\)
−0.564840 + 0.825201i \(0.691062\pi\)
\(140\) 8.18175e11 1.28571
\(141\) 7.01620e11 1.06022
\(142\) −1.17594e11 −0.170922
\(143\) −1.89573e10 −0.0265112
\(144\) 2.44351e10 0.0328868
\(145\) 2.60262e12 3.37199
\(146\) −5.70570e11 −0.711817
\(147\) −8.82072e10 −0.105989
\(148\) 6.50215e11 0.752692
\(149\) 3.32192e11 0.370565 0.185283 0.982685i \(-0.440680\pi\)
0.185283 + 0.982685i \(0.440680\pi\)
\(150\) 6.85447e11 0.737007
\(151\) −6.81029e11 −0.705980 −0.352990 0.935627i \(-0.614835\pi\)
−0.352990 + 0.935627i \(0.614835\pi\)
\(152\) −1.54658e12 −1.54609
\(153\) 1.37969e11 0.133039
\(154\) 6.68374e11 0.621807
\(155\) −2.73033e12 −2.45127
\(156\) −1.18933e10 −0.0103066
\(157\) −1.09900e12 −0.919497 −0.459749 0.888049i \(-0.652061\pi\)
−0.459749 + 0.888049i \(0.652061\pi\)
\(158\) −9.68940e11 −0.782858
\(159\) −7.25705e11 −0.566339
\(160\) −2.42771e12 −1.83036
\(161\) 1.49902e12 1.09211
\(162\) −9.18303e10 −0.0646626
\(163\) 5.96889e11 0.406314 0.203157 0.979146i \(-0.434880\pi\)
0.203157 + 0.979146i \(0.434880\pi\)
\(164\) 3.87619e11 0.255132
\(165\) −1.59183e12 −1.01329
\(166\) −4.85717e11 −0.299081
\(167\) 1.69444e11 0.100945 0.0504725 0.998725i \(-0.483927\pi\)
0.0504725 + 0.998725i \(0.483927\pi\)
\(168\) 1.05339e12 0.607276
\(169\) −1.79085e12 −0.999271
\(170\) −7.68419e11 −0.415077
\(171\) −1.01916e12 −0.533045
\(172\) −1.83360e12 −0.928749
\(173\) −2.02888e12 −0.995412 −0.497706 0.867346i \(-0.665824\pi\)
−0.497706 + 0.867346i \(0.665824\pi\)
\(174\) 1.33386e12 0.634000
\(175\) −5.18136e12 −2.38635
\(176\) 2.17082e11 0.0968955
\(177\) −1.73727e11 −0.0751646
\(178\) 5.88425e11 0.246820
\(179\) 1.76691e12 0.718660 0.359330 0.933211i \(-0.383005\pi\)
0.359330 + 0.933211i \(0.383005\pi\)
\(180\) −9.98668e11 −0.393933
\(181\) −1.48789e12 −0.569295 −0.284647 0.958632i \(-0.591877\pi\)
−0.284647 + 0.958632i \(0.591877\pi\)
\(182\) −4.60420e10 −0.0170908
\(183\) −2.85566e12 −1.02855
\(184\) −2.77661e12 −0.970547
\(185\) −5.99493e12 −2.03395
\(186\) −1.39931e12 −0.460885
\(187\) 1.22572e12 0.391978
\(188\) 3.91054e12 1.21442
\(189\) 6.94155e11 0.209371
\(190\) 5.67621e12 1.66308
\(191\) 2.18296e10 0.00621386 0.00310693 0.999995i \(-0.499011\pi\)
0.00310693 + 0.999995i \(0.499011\pi\)
\(192\) −1.03828e12 −0.287181
\(193\) −6.17050e12 −1.65865 −0.829325 0.558766i \(-0.811275\pi\)
−0.829325 + 0.558766i \(0.811275\pi\)
\(194\) −7.63479e11 −0.199475
\(195\) 1.09655e11 0.0278509
\(196\) −4.91630e11 −0.121403
\(197\) −3.05266e12 −0.733018 −0.366509 0.930414i \(-0.619447\pi\)
−0.366509 + 0.930414i \(0.619447\pi\)
\(198\) −8.15820e11 −0.190518
\(199\) −2.46535e12 −0.559998 −0.279999 0.960000i \(-0.590334\pi\)
−0.279999 + 0.960000i \(0.590334\pi\)
\(200\) 9.59732e12 2.12073
\(201\) 3.18120e12 0.683932
\(202\) 2.40455e11 0.0503038
\(203\) −1.00828e13 −2.05283
\(204\) 7.68981e11 0.152388
\(205\) −3.57382e12 −0.689424
\(206\) 1.48065e12 0.278088
\(207\) −1.82972e12 −0.334616
\(208\) −1.49540e10 −0.00266324
\(209\) −9.05421e12 −1.57053
\(210\) −3.86610e12 −0.653231
\(211\) 4.65591e12 0.766392 0.383196 0.923667i \(-0.374823\pi\)
0.383196 + 0.923667i \(0.374823\pi\)
\(212\) −4.04478e12 −0.648705
\(213\) −1.08500e12 −0.169567
\(214\) 4.64019e12 0.706741
\(215\) 1.69057e13 2.50969
\(216\) −1.28577e12 −0.186066
\(217\) 1.05775e13 1.49230
\(218\) 1.25307e11 0.0172371
\(219\) −5.26447e12 −0.706174
\(220\) −8.87217e12 −1.16066
\(221\) −8.44354e10 −0.0107738
\(222\) −3.07244e12 −0.382421
\(223\) −1.14935e13 −1.39565 −0.697823 0.716271i \(-0.745848\pi\)
−0.697823 + 0.716271i \(0.745848\pi\)
\(224\) 9.40515e12 1.11430
\(225\) 6.32440e12 0.731165
\(226\) −2.12353e12 −0.239587
\(227\) 1.45997e13 1.60769 0.803844 0.594840i \(-0.202785\pi\)
0.803844 + 0.594840i \(0.202785\pi\)
\(228\) −5.68037e12 −0.610569
\(229\) 6.11729e12 0.641895 0.320947 0.947097i \(-0.395999\pi\)
0.320947 + 0.947097i \(0.395999\pi\)
\(230\) 1.01906e13 1.04399
\(231\) 6.16687e12 0.616878
\(232\) 1.86761e13 1.82433
\(233\) −1.11247e13 −1.06128 −0.530641 0.847597i \(-0.678049\pi\)
−0.530641 + 0.847597i \(0.678049\pi\)
\(234\) 5.61991e10 0.00523651
\(235\) −3.60549e13 −3.28164
\(236\) −9.68279e11 −0.0860963
\(237\) −8.94010e12 −0.776652
\(238\) 2.97692e12 0.252694
\(239\) 2.31592e12 0.192104 0.0960518 0.995376i \(-0.469379\pi\)
0.0960518 + 0.995376i \(0.469379\pi\)
\(240\) −1.25567e12 −0.101792
\(241\) −1.59364e13 −1.26269 −0.631343 0.775504i \(-0.717496\pi\)
−0.631343 + 0.775504i \(0.717496\pi\)
\(242\) 2.66408e11 0.0206330
\(243\) −8.47289e11 −0.0641500
\(244\) −1.59162e13 −1.17814
\(245\) 4.53279e12 0.328059
\(246\) −1.83161e12 −0.129625
\(247\) 6.23714e11 0.0431670
\(248\) −1.95925e13 −1.32619
\(249\) −4.48155e12 −0.296710
\(250\) −1.91655e13 −1.24122
\(251\) −3.67863e12 −0.233067 −0.116533 0.993187i \(-0.537178\pi\)
−0.116533 + 0.993187i \(0.537178\pi\)
\(252\) 3.86893e12 0.239821
\(253\) −1.62552e13 −0.985892
\(254\) −2.06568e12 −0.122596
\(255\) −7.08995e12 −0.411787
\(256\) −1.62731e13 −0.925020
\(257\) −1.35585e13 −0.754364 −0.377182 0.926139i \(-0.623107\pi\)
−0.377182 + 0.926139i \(0.623107\pi\)
\(258\) 8.66425e12 0.471871
\(259\) 2.32249e13 1.23824
\(260\) 6.11173e11 0.0319015
\(261\) 1.23071e13 0.628974
\(262\) 9.89702e12 0.495276
\(263\) 3.83441e13 1.87907 0.939533 0.342459i \(-0.111260\pi\)
0.939533 + 0.342459i \(0.111260\pi\)
\(264\) −1.14228e13 −0.548213
\(265\) 3.72926e13 1.75295
\(266\) −2.19901e13 −1.01246
\(267\) 5.42921e12 0.244864
\(268\) 1.77307e13 0.783401
\(269\) 2.94324e13 1.27405 0.637027 0.770841i \(-0.280164\pi\)
0.637027 + 0.770841i \(0.280164\pi\)
\(270\) 4.71898e12 0.200146
\(271\) 1.59914e13 0.664591 0.332295 0.943175i \(-0.392177\pi\)
0.332295 + 0.943175i \(0.392177\pi\)
\(272\) 9.66877e11 0.0393770
\(273\) −4.24815e11 −0.0169553
\(274\) 1.39147e13 0.544310
\(275\) 5.61859e13 2.15426
\(276\) −1.01981e13 −0.383282
\(277\) 4.56572e13 1.68217 0.841087 0.540900i \(-0.181916\pi\)
0.841087 + 0.540900i \(0.181916\pi\)
\(278\) 1.82011e13 0.657432
\(279\) −1.29110e13 −0.457232
\(280\) −5.41314e13 −1.87966
\(281\) −2.99031e13 −1.01820 −0.509098 0.860708i \(-0.670021\pi\)
−0.509098 + 0.860708i \(0.670021\pi\)
\(282\) −1.84783e13 −0.617011
\(283\) −3.77834e13 −1.23730 −0.618651 0.785666i \(-0.712321\pi\)
−0.618651 + 0.785666i \(0.712321\pi\)
\(284\) −6.04734e12 −0.194229
\(285\) 5.23726e13 1.64990
\(286\) 4.99273e11 0.0154285
\(287\) 1.38453e13 0.419713
\(288\) −1.14800e13 −0.341415
\(289\) −2.88126e13 −0.840706
\(290\) −6.85443e13 −1.96238
\(291\) −7.04438e12 −0.197893
\(292\) −2.93419e13 −0.808878
\(293\) −2.20547e13 −0.596664 −0.298332 0.954462i \(-0.596430\pi\)
−0.298332 + 0.954462i \(0.596430\pi\)
\(294\) 2.32308e12 0.0616815
\(295\) 8.92746e12 0.232652
\(296\) −4.30190e13 −1.10041
\(297\) −7.52731e12 −0.189008
\(298\) −8.74883e12 −0.215655
\(299\) 1.11976e12 0.0270979
\(300\) 3.52495e13 0.837503
\(301\) −6.54940e13 −1.52787
\(302\) 1.79360e13 0.410855
\(303\) 2.21860e12 0.0499050
\(304\) −7.14220e12 −0.157771
\(305\) 1.46746e14 3.18360
\(306\) −3.63364e12 −0.0774238
\(307\) −4.50168e13 −0.942136 −0.471068 0.882097i \(-0.656131\pi\)
−0.471068 + 0.882097i \(0.656131\pi\)
\(308\) 3.43716e13 0.706595
\(309\) 1.36615e13 0.275884
\(310\) 7.19078e13 1.42655
\(311\) 2.82077e12 0.0549776 0.0274888 0.999622i \(-0.491249\pi\)
0.0274888 + 0.999622i \(0.491249\pi\)
\(312\) 7.86875e11 0.0150680
\(313\) −1.18762e12 −0.0223451 −0.0111726 0.999938i \(-0.503556\pi\)
−0.0111726 + 0.999938i \(0.503556\pi\)
\(314\) 2.89441e13 0.535114
\(315\) −3.56712e13 −0.648052
\(316\) −4.98284e13 −0.889606
\(317\) −5.05554e13 −0.887037 −0.443518 0.896265i \(-0.646270\pi\)
−0.443518 + 0.896265i \(0.646270\pi\)
\(318\) 1.91127e13 0.329588
\(319\) 1.09336e14 1.85317
\(320\) 5.33549e13 0.888893
\(321\) 4.28136e13 0.701138
\(322\) −3.94793e13 −0.635568
\(323\) −4.03272e13 −0.638241
\(324\) −4.72243e12 −0.0734798
\(325\) −3.87046e12 −0.0592112
\(326\) −1.57201e13 −0.236460
\(327\) 1.15617e12 0.0171005
\(328\) −2.56453e13 −0.372994
\(329\) 1.39680e14 1.99782
\(330\) 4.19234e13 0.589698
\(331\) 8.19340e13 1.13347 0.566735 0.823900i \(-0.308206\pi\)
0.566735 + 0.823900i \(0.308206\pi\)
\(332\) −2.49783e13 −0.339862
\(333\) −2.83484e13 −0.379390
\(334\) −4.46258e12 −0.0587463
\(335\) −1.63476e14 −2.11693
\(336\) 4.86459e12 0.0619698
\(337\) 1.18757e14 1.48832 0.744158 0.668003i \(-0.232851\pi\)
0.744158 + 0.668003i \(0.232851\pi\)
\(338\) 4.71651e13 0.581540
\(339\) −1.95932e13 −0.237687
\(340\) −3.95164e13 −0.471676
\(341\) −1.14701e14 −1.34716
\(342\) 2.68413e13 0.310213
\(343\) 7.80964e13 0.888205
\(344\) 1.21313e14 1.35780
\(345\) 9.40255e13 1.03572
\(346\) 5.34339e13 0.579293
\(347\) 3.64520e13 0.388964 0.194482 0.980906i \(-0.437697\pi\)
0.194482 + 0.980906i \(0.437697\pi\)
\(348\) 6.85945e13 0.720450
\(349\) −1.03842e14 −1.07358 −0.536789 0.843717i \(-0.680363\pi\)
−0.536789 + 0.843717i \(0.680363\pi\)
\(350\) 1.36460e14 1.38877
\(351\) 5.18531e11 0.00519500
\(352\) −1.01988e14 −1.00592
\(353\) −1.35379e14 −1.31459 −0.657297 0.753632i \(-0.728300\pi\)
−0.657297 + 0.753632i \(0.728300\pi\)
\(354\) 4.57538e12 0.0437431
\(355\) 5.57560e13 0.524851
\(356\) 3.02601e13 0.280476
\(357\) 2.74671e13 0.250690
\(358\) −4.65346e13 −0.418234
\(359\) −1.06092e14 −0.938998 −0.469499 0.882933i \(-0.655565\pi\)
−0.469499 + 0.882933i \(0.655565\pi\)
\(360\) 6.60730e13 0.575918
\(361\) 1.81402e14 1.55723
\(362\) 3.91859e13 0.331309
\(363\) 2.45806e12 0.0204694
\(364\) −2.36774e12 −0.0194212
\(365\) 2.70531e14 2.18578
\(366\) 7.52085e13 0.598578
\(367\) 1.60911e14 1.26160 0.630801 0.775945i \(-0.282727\pi\)
0.630801 + 0.775945i \(0.282727\pi\)
\(368\) −1.28225e13 −0.0990399
\(369\) −1.68996e13 −0.128597
\(370\) 1.57887e14 1.18368
\(371\) −1.44475e14 −1.06717
\(372\) −7.19604e13 −0.523730
\(373\) −4.09228e13 −0.293472 −0.146736 0.989176i \(-0.546877\pi\)
−0.146736 + 0.989176i \(0.546877\pi\)
\(374\) −3.22813e13 −0.228117
\(375\) −1.76834e14 −1.23138
\(376\) −2.58726e14 −1.77544
\(377\) −7.53179e12 −0.0509356
\(378\) −1.82817e13 −0.121846
\(379\) 1.53430e13 0.100785 0.0503924 0.998729i \(-0.483953\pi\)
0.0503924 + 0.998729i \(0.483953\pi\)
\(380\) 2.91903e14 1.88985
\(381\) −1.90594e13 −0.121625
\(382\) −5.74918e11 −0.00361624
\(383\) −1.76593e14 −1.09492 −0.547458 0.836833i \(-0.684404\pi\)
−0.547458 + 0.836833i \(0.684404\pi\)
\(384\) −6.94083e13 −0.424218
\(385\) −3.16903e14 −1.90938
\(386\) 1.62510e14 0.965274
\(387\) 7.99423e13 0.468130
\(388\) −3.92624e13 −0.226674
\(389\) −3.21024e14 −1.82732 −0.913660 0.406480i \(-0.866756\pi\)
−0.913660 + 0.406480i \(0.866756\pi\)
\(390\) −2.88796e12 −0.0162082
\(391\) −7.24003e13 −0.400653
\(392\) 3.25268e13 0.177488
\(393\) 9.13166e13 0.491350
\(394\) 8.03970e13 0.426590
\(395\) 4.59414e14 2.40392
\(396\) −4.19541e13 −0.216496
\(397\) −3.26179e14 −1.66000 −0.830001 0.557762i \(-0.811660\pi\)
−0.830001 + 0.557762i \(0.811660\pi\)
\(398\) 6.49290e13 0.325898
\(399\) −2.02896e14 −1.00444
\(400\) 4.43209e13 0.216411
\(401\) −1.49182e14 −0.718494 −0.359247 0.933243i \(-0.616966\pi\)
−0.359247 + 0.933243i \(0.616966\pi\)
\(402\) −8.37823e13 −0.398024
\(403\) 7.90138e12 0.0370276
\(404\) 1.23655e13 0.0571631
\(405\) 4.35405e13 0.198559
\(406\) 2.65547e14 1.19467
\(407\) −2.51847e14 −1.11781
\(408\) −5.08767e13 −0.222786
\(409\) −1.06632e14 −0.460689 −0.230344 0.973109i \(-0.573985\pi\)
−0.230344 + 0.973109i \(0.573985\pi\)
\(410\) 9.41226e13 0.401220
\(411\) 1.28387e14 0.539995
\(412\) 7.61434e13 0.316008
\(413\) −3.45858e13 −0.141636
\(414\) 4.81886e13 0.194734
\(415\) 2.30298e14 0.918387
\(416\) 7.02561e12 0.0276484
\(417\) 1.67936e14 0.652221
\(418\) 2.38458e14 0.913991
\(419\) −2.41998e14 −0.915451 −0.457726 0.889093i \(-0.651336\pi\)
−0.457726 + 0.889093i \(0.651336\pi\)
\(420\) −1.98817e14 −0.742303
\(421\) 3.95612e14 1.45787 0.728934 0.684584i \(-0.240016\pi\)
0.728934 + 0.684584i \(0.240016\pi\)
\(422\) −1.22621e14 −0.446012
\(423\) −1.70494e14 −0.612119
\(424\) 2.67607e14 0.948387
\(425\) 2.50251e14 0.875460
\(426\) 2.85753e13 0.0986820
\(427\) −5.68509e14 −1.93813
\(428\) 2.38625e14 0.803110
\(429\) 4.60663e12 0.0153062
\(430\) −4.45239e14 −1.46055
\(431\) −4.83344e14 −1.56542 −0.782711 0.622385i \(-0.786164\pi\)
−0.782711 + 0.622385i \(0.786164\pi\)
\(432\) −5.93774e12 −0.0189872
\(433\) −3.08341e14 −0.973526 −0.486763 0.873534i \(-0.661822\pi\)
−0.486763 + 0.873534i \(0.661822\pi\)
\(434\) −2.78577e14 −0.868464
\(435\) −6.32437e14 −1.94682
\(436\) 6.44400e12 0.0195875
\(437\) 5.34811e14 1.60529
\(438\) 1.38649e14 0.410968
\(439\) 5.22632e14 1.52982 0.764912 0.644135i \(-0.222782\pi\)
0.764912 + 0.644135i \(0.222782\pi\)
\(440\) 5.86993e14 1.69685
\(441\) 2.14344e13 0.0611925
\(442\) 2.22375e12 0.00626993
\(443\) 5.54397e14 1.54383 0.771916 0.635724i \(-0.219298\pi\)
0.771916 + 0.635724i \(0.219298\pi\)
\(444\) −1.58002e14 −0.434567
\(445\) −2.78996e14 −0.757911
\(446\) 3.02700e14 0.812215
\(447\) −8.07226e13 −0.213946
\(448\) −2.06702e14 −0.541146
\(449\) −2.36672e14 −0.612057 −0.306028 0.952022i \(-0.599000\pi\)
−0.306028 + 0.952022i \(0.599000\pi\)
\(450\) −1.66564e14 −0.425511
\(451\) −1.50136e14 −0.378892
\(452\) −1.09204e14 −0.272256
\(453\) 1.65490e14 0.407598
\(454\) −3.84507e14 −0.935616
\(455\) 2.18304e13 0.0524806
\(456\) 3.75820e14 0.892633
\(457\) −2.39897e14 −0.562970 −0.281485 0.959566i \(-0.590827\pi\)
−0.281485 + 0.959566i \(0.590827\pi\)
\(458\) −1.61109e14 −0.373559
\(459\) −3.35265e13 −0.0768100
\(460\) 5.24058e14 1.18635
\(461\) 6.67770e14 1.49373 0.746864 0.664977i \(-0.231559\pi\)
0.746864 + 0.664977i \(0.231559\pi\)
\(462\) −1.62415e14 −0.359000
\(463\) −1.98612e14 −0.433821 −0.216910 0.976192i \(-0.569598\pi\)
−0.216910 + 0.976192i \(0.569598\pi\)
\(464\) 8.62472e13 0.186164
\(465\) 6.63470e14 1.41524
\(466\) 2.92988e14 0.617628
\(467\) −8.55770e14 −1.78285 −0.891424 0.453170i \(-0.850293\pi\)
−0.891424 + 0.453170i \(0.850293\pi\)
\(468\) 2.89007e12 0.00595054
\(469\) 6.33319e14 1.28876
\(470\) 9.49565e14 1.90979
\(471\) 2.67058e14 0.530872
\(472\) 6.40625e13 0.125870
\(473\) 7.10208e14 1.37927
\(474\) 2.35452e14 0.451983
\(475\) −1.84857e15 −3.50769
\(476\) 1.53090e14 0.287150
\(477\) 1.76346e14 0.326976
\(478\) −6.09937e13 −0.111797
\(479\) −1.35120e14 −0.244835 −0.122417 0.992479i \(-0.539065\pi\)
−0.122417 + 0.992479i \(0.539065\pi\)
\(480\) 5.89933e14 1.05676
\(481\) 1.73489e13 0.0307237
\(482\) 4.19711e14 0.734837
\(483\) −3.64263e14 −0.630530
\(484\) 1.37002e13 0.0234464
\(485\) 3.61997e14 0.612527
\(486\) 2.23148e13 0.0373330
\(487\) −7.97829e14 −1.31978 −0.659889 0.751363i \(-0.729397\pi\)
−0.659889 + 0.751363i \(0.729397\pi\)
\(488\) 1.05304e15 1.72240
\(489\) −1.45044e14 −0.234585
\(490\) −1.19379e14 −0.190919
\(491\) −1.65399e14 −0.261568 −0.130784 0.991411i \(-0.541750\pi\)
−0.130784 + 0.991411i \(0.541750\pi\)
\(492\) −9.41915e13 −0.147300
\(493\) 4.86981e14 0.753102
\(494\) −1.64265e13 −0.0251216
\(495\) 3.86814e14 0.585023
\(496\) −9.04793e13 −0.135332
\(497\) −2.16004e14 −0.319522
\(498\) 1.18029e14 0.172674
\(499\) 1.35908e15 1.96649 0.983246 0.182285i \(-0.0583492\pi\)
0.983246 + 0.182285i \(0.0583492\pi\)
\(500\) −9.85596e14 −1.41047
\(501\) −4.11748e13 −0.0582806
\(502\) 9.68827e13 0.135636
\(503\) −1.17264e14 −0.162383 −0.0811913 0.996699i \(-0.525872\pi\)
−0.0811913 + 0.996699i \(0.525872\pi\)
\(504\) −2.55973e14 −0.350611
\(505\) −1.14009e14 −0.154468
\(506\) 4.28108e14 0.573754
\(507\) 4.35178e14 0.576930
\(508\) −1.06229e14 −0.139313
\(509\) −6.28883e12 −0.00815872 −0.00407936 0.999992i \(-0.501299\pi\)
−0.00407936 + 0.999992i \(0.501299\pi\)
\(510\) 1.86726e14 0.239645
\(511\) −1.04806e15 −1.33067
\(512\) −1.56392e14 −0.196440
\(513\) 2.47656e14 0.307753
\(514\) 3.57087e14 0.439012
\(515\) −7.02037e14 −0.853926
\(516\) 4.45565e14 0.536213
\(517\) −1.51467e15 −1.80351
\(518\) −6.11667e14 −0.720611
\(519\) 4.93018e14 0.574701
\(520\) −4.04359e13 −0.0466390
\(521\) −5.25502e14 −0.599746 −0.299873 0.953979i \(-0.596944\pi\)
−0.299873 + 0.953979i \(0.596944\pi\)
\(522\) −3.24128e14 −0.366040
\(523\) −1.36794e15 −1.52865 −0.764326 0.644830i \(-0.776928\pi\)
−0.764326 + 0.644830i \(0.776928\pi\)
\(524\) 5.08960e14 0.562810
\(525\) 1.25907e15 1.37776
\(526\) −1.00986e15 −1.09355
\(527\) −5.10877e14 −0.547467
\(528\) −5.27509e13 −0.0559427
\(529\) 7.34736e12 0.00771126
\(530\) −9.82162e14 −1.02015
\(531\) 4.22156e13 0.0433963
\(532\) −1.13086e15 −1.15052
\(533\) 1.03424e13 0.0104141
\(534\) −1.42987e14 −0.142502
\(535\) −2.20010e15 −2.17019
\(536\) −1.17308e15 −1.14531
\(537\) −4.29360e14 −0.414918
\(538\) −7.75151e14 −0.741453
\(539\) 1.90423e14 0.180294
\(540\) 2.42676e14 0.227437
\(541\) 5.35959e14 0.497217 0.248609 0.968604i \(-0.420027\pi\)
0.248609 + 0.968604i \(0.420027\pi\)
\(542\) −4.21159e14 −0.386768
\(543\) 3.61556e14 0.328683
\(544\) −4.54252e14 −0.408793
\(545\) −5.94132e13 −0.0529301
\(546\) 1.11882e13 0.00986736
\(547\) 1.04435e15 0.911836 0.455918 0.890022i \(-0.349311\pi\)
0.455918 + 0.890022i \(0.349311\pi\)
\(548\) 7.15573e14 0.618530
\(549\) 6.93924e14 0.593833
\(550\) −1.47975e15 −1.25370
\(551\) −3.59726e15 −3.01744
\(552\) 6.74716e14 0.560346
\(553\) −1.77981e15 −1.46348
\(554\) −1.20246e15 −0.978964
\(555\) 1.45677e15 1.17430
\(556\) 9.36003e14 0.747078
\(557\) −1.96163e15 −1.55029 −0.775145 0.631783i \(-0.782323\pi\)
−0.775145 + 0.631783i \(0.782323\pi\)
\(558\) 3.40033e14 0.266092
\(559\) −4.89238e13 −0.0379101
\(560\) −2.49981e14 −0.191811
\(561\) −2.97849e14 −0.226308
\(562\) 7.87548e14 0.592553
\(563\) −1.43165e15 −1.06670 −0.533348 0.845896i \(-0.679066\pi\)
−0.533348 + 0.845896i \(0.679066\pi\)
\(564\) −9.50260e14 −0.701144
\(565\) 1.00685e15 0.735699
\(566\) 9.95089e14 0.720065
\(567\) −1.68680e14 −0.120880
\(568\) 4.00099e14 0.283956
\(569\) −1.48396e15 −1.04305 −0.521524 0.853237i \(-0.674636\pi\)
−0.521524 + 0.853237i \(0.674636\pi\)
\(570\) −1.37932e15 −0.960181
\(571\) −5.40035e12 −0.00372326 −0.00186163 0.999998i \(-0.500593\pi\)
−0.00186163 + 0.999998i \(0.500593\pi\)
\(572\) 2.56754e13 0.0175323
\(573\) −5.30458e12 −0.00358757
\(574\) −3.64639e14 −0.244257
\(575\) −3.31877e15 −2.20194
\(576\) 2.52301e14 0.165804
\(577\) 2.11173e15 1.37458 0.687291 0.726382i \(-0.258800\pi\)
0.687291 + 0.726382i \(0.258800\pi\)
\(578\) 7.58827e14 0.489260
\(579\) 1.49943e15 0.957622
\(580\) −3.52494e15 −2.22996
\(581\) −8.92195e14 −0.559102
\(582\) 1.85525e14 0.115167
\(583\) 1.56666e15 0.963381
\(584\) 1.94130e15 1.18255
\(585\) −2.66463e13 −0.0160797
\(586\) 5.80848e14 0.347237
\(587\) −2.44871e15 −1.45020 −0.725099 0.688644i \(-0.758206\pi\)
−0.725099 + 0.688644i \(0.758206\pi\)
\(588\) 1.19466e14 0.0700922
\(589\) 3.77378e15 2.19352
\(590\) −2.35120e14 −0.135395
\(591\) 7.41797e14 0.423208
\(592\) −1.98664e14 −0.112292
\(593\) 2.23333e15 1.25070 0.625350 0.780345i \(-0.284956\pi\)
0.625350 + 0.780345i \(0.284956\pi\)
\(594\) 1.98244e14 0.109996
\(595\) −1.41148e15 −0.775946
\(596\) −4.49914e14 −0.245061
\(597\) 5.99079e14 0.323315
\(598\) −2.94909e13 −0.0157700
\(599\) 8.49048e14 0.449868 0.224934 0.974374i \(-0.427783\pi\)
0.224934 + 0.974374i \(0.427783\pi\)
\(600\) −2.33215e15 −1.22440
\(601\) −1.56134e15 −0.812246 −0.406123 0.913818i \(-0.633120\pi\)
−0.406123 + 0.913818i \(0.633120\pi\)
\(602\) 1.72489e15 0.889164
\(603\) −7.73033e14 −0.394869
\(604\) 9.22372e14 0.466878
\(605\) −1.26315e14 −0.0633577
\(606\) −5.84305e13 −0.0290429
\(607\) 1.26588e15 0.623526 0.311763 0.950160i \(-0.399080\pi\)
0.311763 + 0.950160i \(0.399080\pi\)
\(608\) 3.35550e15 1.63790
\(609\) 2.45012e15 1.18520
\(610\) −3.86481e15 −1.85274
\(611\) 1.04340e14 0.0495707
\(612\) −1.86862e14 −0.0879811
\(613\) −3.11063e15 −1.45149 −0.725747 0.687961i \(-0.758506\pi\)
−0.725747 + 0.687961i \(0.758506\pi\)
\(614\) 1.18559e15 0.548289
\(615\) 8.68439e14 0.398039
\(616\) −2.27406e15 −1.03302
\(617\) 1.28911e15 0.580394 0.290197 0.956967i \(-0.406279\pi\)
0.290197 + 0.956967i \(0.406279\pi\)
\(618\) −3.59798e14 −0.160554
\(619\) −4.72039e14 −0.208775 −0.104388 0.994537i \(-0.533288\pi\)
−0.104388 + 0.994537i \(0.533288\pi\)
\(620\) 3.69790e15 1.62107
\(621\) 4.44621e14 0.193191
\(622\) −7.42897e13 −0.0319950
\(623\) 1.08086e15 0.461406
\(624\) 3.63383e12 0.00153762
\(625\) 3.85743e15 1.61792
\(626\) 3.12779e13 0.0130040
\(627\) 2.20017e15 0.906746
\(628\) 1.48847e15 0.608080
\(629\) −1.12172e15 −0.454262
\(630\) 9.39462e14 0.377143
\(631\) −2.79261e15 −1.11134 −0.555672 0.831401i \(-0.687539\pi\)
−0.555672 + 0.831401i \(0.687539\pi\)
\(632\) 3.29670e15 1.30058
\(633\) −1.13139e15 −0.442476
\(634\) 1.33146e15 0.516223
\(635\) 9.79424e14 0.376457
\(636\) 9.82881e14 0.374530
\(637\) −1.31176e13 −0.00495549
\(638\) −2.87955e15 −1.07848
\(639\) 2.63655e14 0.0978998
\(640\) 3.56675e15 1.31306
\(641\) −5.70990e13 −0.0208406 −0.0104203 0.999946i \(-0.503317\pi\)
−0.0104203 + 0.999946i \(0.503317\pi\)
\(642\) −1.12757e15 −0.408037
\(643\) −3.74924e14 −0.134519 −0.0672593 0.997736i \(-0.521425\pi\)
−0.0672593 + 0.997736i \(0.521425\pi\)
\(644\) −2.03025e15 −0.722232
\(645\) −4.10808e15 −1.44897
\(646\) 1.06209e15 0.371433
\(647\) −6.23178e14 −0.216092 −0.108046 0.994146i \(-0.534459\pi\)
−0.108046 + 0.994146i \(0.534459\pi\)
\(648\) 3.12442e14 0.107425
\(649\) 3.75043e14 0.127860
\(650\) 1.01935e14 0.0344588
\(651\) −2.57034e15 −0.861580
\(652\) −8.08414e14 −0.268703
\(653\) 5.00096e15 1.64828 0.824140 0.566387i \(-0.191659\pi\)
0.824140 + 0.566387i \(0.191659\pi\)
\(654\) −3.04496e13 −0.00995187
\(655\) −4.69258e15 −1.52084
\(656\) −1.18431e14 −0.0380624
\(657\) 1.27927e15 0.407710
\(658\) −3.67870e15 −1.16266
\(659\) 1.57034e15 0.492181 0.246091 0.969247i \(-0.420854\pi\)
0.246091 + 0.969247i \(0.420854\pi\)
\(660\) 2.15594e15 0.670107
\(661\) −1.30021e15 −0.400780 −0.200390 0.979716i \(-0.564221\pi\)
−0.200390 + 0.979716i \(0.564221\pi\)
\(662\) −2.15787e15 −0.659639
\(663\) 2.05178e13 0.00622023
\(664\) 1.65259e15 0.496868
\(665\) 1.04264e16 3.10897
\(666\) 7.46603e14 0.220791
\(667\) −6.45824e15 −1.89418
\(668\) −2.29491e14 −0.0667568
\(669\) 2.79292e15 0.805776
\(670\) 4.30541e15 1.23198
\(671\) 6.16483e15 1.74963
\(672\) −2.28545e15 −0.643341
\(673\) −1.61815e15 −0.451790 −0.225895 0.974152i \(-0.572531\pi\)
−0.225895 + 0.974152i \(0.572531\pi\)
\(674\) −3.12767e15 −0.866146
\(675\) −1.53683e15 −0.422138
\(676\) 2.42550e15 0.660836
\(677\) −2.27778e15 −0.615564 −0.307782 0.951457i \(-0.599587\pi\)
−0.307782 + 0.951457i \(0.599587\pi\)
\(678\) 5.16019e14 0.138325
\(679\) −1.40241e15 −0.372898
\(680\) 2.61445e15 0.689575
\(681\) −3.54773e15 −0.928199
\(682\) 3.02085e15 0.783998
\(683\) −3.00858e14 −0.0774548 −0.0387274 0.999250i \(-0.512330\pi\)
−0.0387274 + 0.999250i \(0.512330\pi\)
\(684\) 1.38033e15 0.352512
\(685\) −6.59753e15 −1.67141
\(686\) −2.05680e15 −0.516903
\(687\) −1.48650e15 −0.370598
\(688\) 5.60230e14 0.138557
\(689\) −1.07922e14 −0.0264791
\(690\) −2.47632e15 −0.602749
\(691\) −4.82000e15 −1.16391 −0.581953 0.813223i \(-0.697711\pi\)
−0.581953 + 0.813223i \(0.697711\pi\)
\(692\) 2.74787e15 0.658284
\(693\) −1.49855e15 −0.356155
\(694\) −9.60024e14 −0.226363
\(695\) −8.62988e15 −2.01878
\(696\) −4.53829e15 −1.05328
\(697\) −6.68704e14 −0.153976
\(698\) 2.73485e15 0.624783
\(699\) 2.70330e15 0.612732
\(700\) 7.01754e15 1.57814
\(701\) 4.76905e14 0.106410 0.0532051 0.998584i \(-0.483056\pi\)
0.0532051 + 0.998584i \(0.483056\pi\)
\(702\) −1.36564e13 −0.00302330
\(703\) 8.28602e15 1.82008
\(704\) 2.24144e15 0.488515
\(705\) 8.76133e15 1.89465
\(706\) 3.56544e15 0.765045
\(707\) 4.41682e14 0.0940380
\(708\) 2.35292e14 0.0497077
\(709\) −9.36719e15 −1.96361 −0.981804 0.189897i \(-0.939185\pi\)
−0.981804 + 0.189897i \(0.939185\pi\)
\(710\) −1.46843e15 −0.305444
\(711\) 2.17244e15 0.448400
\(712\) −2.00205e15 −0.410047
\(713\) 6.77514e15 1.37697
\(714\) −7.23392e14 −0.145893
\(715\) −2.36725e14 −0.0473764
\(716\) −2.39307e15 −0.475263
\(717\) −5.62769e14 −0.110911
\(718\) 2.79412e15 0.546462
\(719\) 7.76886e15 1.50782 0.753908 0.656980i \(-0.228166\pi\)
0.753908 + 0.656980i \(0.228166\pi\)
\(720\) 3.05129e14 0.0587698
\(721\) 2.71975e15 0.519859
\(722\) −4.77752e15 −0.906250
\(723\) 3.87254e15 0.729012
\(724\) 2.01516e15 0.376485
\(725\) 2.23228e16 4.13895
\(726\) −6.47371e13 −0.0119125
\(727\) 6.75552e15 1.23373 0.616864 0.787070i \(-0.288403\pi\)
0.616864 + 0.787070i \(0.288403\pi\)
\(728\) 1.56652e14 0.0283932
\(729\) 2.05891e14 0.0370370
\(730\) −7.12488e15 −1.27204
\(731\) 3.16325e15 0.560515
\(732\) 3.86764e15 0.680198
\(733\) −5.62650e15 −0.982124 −0.491062 0.871125i \(-0.663391\pi\)
−0.491062 + 0.871125i \(0.663391\pi\)
\(734\) −4.23786e15 −0.734206
\(735\) −1.10147e15 −0.189405
\(736\) 6.02420e15 1.02819
\(737\) −6.86762e15 −1.16342
\(738\) 4.45080e14 0.0748390
\(739\) 3.13907e15 0.523909 0.261955 0.965080i \(-0.415633\pi\)
0.261955 + 0.965080i \(0.415633\pi\)
\(740\) 8.11942e15 1.34509
\(741\) −1.51562e14 −0.0249225
\(742\) 3.80498e15 0.621056
\(743\) 6.84927e15 1.10970 0.554850 0.831950i \(-0.312776\pi\)
0.554850 + 0.831950i \(0.312776\pi\)
\(744\) 4.76099e15 0.765677
\(745\) 4.14817e15 0.662213
\(746\) 1.07777e15 0.170790
\(747\) 1.08902e15 0.171306
\(748\) −1.66009e15 −0.259222
\(749\) 8.52340e15 1.32118
\(750\) 4.65721e15 0.716619
\(751\) −7.39272e15 −1.12924 −0.564618 0.825352i \(-0.690977\pi\)
−0.564618 + 0.825352i \(0.690977\pi\)
\(752\) −1.19481e15 −0.181176
\(753\) 8.93906e14 0.134561
\(754\) 1.98362e14 0.0296426
\(755\) −8.50421e15 −1.26161
\(756\) −9.40149e14 −0.138461
\(757\) −8.61752e15 −1.25995 −0.629977 0.776614i \(-0.716936\pi\)
−0.629977 + 0.776614i \(0.716936\pi\)
\(758\) −4.04084e14 −0.0586531
\(759\) 3.95001e15 0.569205
\(760\) −1.93126e16 −2.76291
\(761\) −1.03952e16 −1.47645 −0.738225 0.674554i \(-0.764336\pi\)
−0.738225 + 0.674554i \(0.764336\pi\)
\(762\) 5.01961e14 0.0707811
\(763\) 2.30172e14 0.0322231
\(764\) −2.95655e13 −0.00410934
\(765\) 1.72286e15 0.237745
\(766\) 4.65088e15 0.637201
\(767\) −2.58354e13 −0.00351432
\(768\) 3.95437e15 0.534061
\(769\) 1.31344e16 1.76122 0.880611 0.473839i \(-0.157132\pi\)
0.880611 + 0.473839i \(0.157132\pi\)
\(770\) 8.34618e15 1.11119
\(771\) 3.29473e15 0.435532
\(772\) 8.35720e15 1.09690
\(773\) −6.94848e15 −0.905530 −0.452765 0.891630i \(-0.649562\pi\)
−0.452765 + 0.891630i \(0.649562\pi\)
\(774\) −2.10541e15 −0.272435
\(775\) −2.34182e16 −3.00881
\(776\) 2.59765e15 0.331391
\(777\) −5.64365e15 −0.714899
\(778\) 8.45470e15 1.06343
\(779\) 4.93963e15 0.616933
\(780\) −1.48515e14 −0.0184183
\(781\) 2.34231e15 0.288446
\(782\) 1.90678e15 0.233165
\(783\) −2.99062e15 −0.363138
\(784\) 1.50210e14 0.0181118
\(785\) −1.37236e16 −1.64317
\(786\) −2.40498e15 −0.285948
\(787\) 8.13204e15 0.960149 0.480075 0.877228i \(-0.340610\pi\)
0.480075 + 0.877228i \(0.340610\pi\)
\(788\) 4.13447e15 0.484758
\(789\) −9.31762e15 −1.08488
\(790\) −1.20994e16 −1.39899
\(791\) −3.90064e15 −0.447884
\(792\) 2.77573e15 0.316511
\(793\) −4.24674e14 −0.0480898
\(794\) 8.59047e15 0.966061
\(795\) −9.06209e15 −1.01207
\(796\) 3.33902e15 0.370337
\(797\) −1.08942e16 −1.19999 −0.599993 0.800005i \(-0.704830\pi\)
−0.599993 + 0.800005i \(0.704830\pi\)
\(798\) 5.34360e15 0.584546
\(799\) −6.74628e15 −0.732921
\(800\) −2.08226e16 −2.24667
\(801\) −1.31930e15 −0.141372
\(802\) 3.92896e15 0.418137
\(803\) 1.13650e16 1.20125
\(804\) −4.30856e15 −0.452297
\(805\) 1.87187e16 1.95164
\(806\) −2.08096e14 −0.0215487
\(807\) −7.15207e15 −0.735575
\(808\) −8.18118e14 −0.0835706
\(809\) −6.93189e15 −0.703290 −0.351645 0.936133i \(-0.614378\pi\)
−0.351645 + 0.936133i \(0.614378\pi\)
\(810\) −1.14671e15 −0.115554
\(811\) −2.04337e15 −0.204518 −0.102259 0.994758i \(-0.532607\pi\)
−0.102259 + 0.994758i \(0.532607\pi\)
\(812\) 1.36559e16 1.35757
\(813\) −3.88590e15 −0.383702
\(814\) 6.63282e15 0.650525
\(815\) 7.45352e15 0.726097
\(816\) −2.34951e14 −0.0227343
\(817\) −2.33665e16 −2.24581
\(818\) 2.80832e15 0.268104
\(819\) 1.03230e14 0.00978914
\(820\) 4.84031e15 0.455929
\(821\) 1.84447e15 0.172578 0.0862889 0.996270i \(-0.472499\pi\)
0.0862889 + 0.996270i \(0.472499\pi\)
\(822\) −3.38128e15 −0.314257
\(823\) −1.78380e15 −0.164682 −0.0823411 0.996604i \(-0.526240\pi\)
−0.0823411 + 0.996604i \(0.526240\pi\)
\(824\) −5.03774e15 −0.461993
\(825\) −1.36532e16 −1.24376
\(826\) 9.10874e14 0.0824268
\(827\) 1.54315e16 1.38717 0.693584 0.720376i \(-0.256031\pi\)
0.693584 + 0.720376i \(0.256031\pi\)
\(828\) 2.47813e15 0.221288
\(829\) 2.03589e15 0.180594 0.0902971 0.995915i \(-0.471218\pi\)
0.0902971 + 0.995915i \(0.471218\pi\)
\(830\) −6.06528e15 −0.534468
\(831\) −1.10947e16 −0.971203
\(832\) −1.54405e14 −0.0134271
\(833\) 8.48139e14 0.0732689
\(834\) −4.42287e15 −0.379569
\(835\) 2.11589e15 0.180392
\(836\) 1.22628e16 1.03862
\(837\) 3.13737e15 0.263983
\(838\) 6.37343e15 0.532759
\(839\) −1.88602e16 −1.56623 −0.783116 0.621876i \(-0.786371\pi\)
−0.783116 + 0.621876i \(0.786371\pi\)
\(840\) 1.31539e16 1.08522
\(841\) 3.12391e16 2.56047
\(842\) −1.04191e16 −0.848426
\(843\) 7.26646e15 0.587856
\(844\) −6.30587e15 −0.506829
\(845\) −2.23629e16 −1.78573
\(846\) 4.49023e15 0.356231
\(847\) 4.89354e14 0.0385713
\(848\) 1.23582e15 0.0967785
\(849\) 9.18137e15 0.714357
\(850\) −6.59077e15 −0.509486
\(851\) 1.48760e16 1.14255
\(852\) 1.46950e15 0.112138
\(853\) −8.85786e15 −0.671598 −0.335799 0.941934i \(-0.609006\pi\)
−0.335799 + 0.941934i \(0.609006\pi\)
\(854\) 1.49726e16 1.12792
\(855\) −1.27265e16 −0.952569
\(856\) −1.57877e16 −1.17412
\(857\) 9.83544e15 0.726774 0.363387 0.931638i \(-0.381620\pi\)
0.363387 + 0.931638i \(0.381620\pi\)
\(858\) −1.21323e14 −0.00890767
\(859\) 4.25863e15 0.310676 0.155338 0.987861i \(-0.450353\pi\)
0.155338 + 0.987861i \(0.450353\pi\)
\(860\) −2.28967e16 −1.65971
\(861\) −3.36441e15 −0.242321
\(862\) 1.27297e16 0.911019
\(863\) −8.53353e15 −0.606833 −0.303417 0.952858i \(-0.598127\pi\)
−0.303417 + 0.952858i \(0.598127\pi\)
\(864\) 2.78963e15 0.197116
\(865\) −2.53352e16 −1.77884
\(866\) 8.12067e15 0.566557
\(867\) 7.00146e15 0.485382
\(868\) −1.43260e16 −0.986885
\(869\) 1.93000e16 1.32114
\(870\) 1.66563e16 1.13298
\(871\) 4.73087e14 0.0319772
\(872\) −4.26343e14 −0.0286364
\(873\) 1.71178e15 0.114254
\(874\) −1.40852e16 −0.934219
\(875\) −3.52043e16 −2.32034
\(876\) 7.13009e15 0.467006
\(877\) −5.44470e15 −0.354386 −0.177193 0.984176i \(-0.556702\pi\)
−0.177193 + 0.984176i \(0.556702\pi\)
\(878\) −1.37644e16 −0.890302
\(879\) 5.35930e15 0.344484
\(880\) 2.71076e15 0.173156
\(881\) −2.95851e15 −0.187805 −0.0939023 0.995581i \(-0.529934\pi\)
−0.0939023 + 0.995581i \(0.529934\pi\)
\(882\) −5.64510e14 −0.0356118
\(883\) 8.77592e15 0.550185 0.275092 0.961418i \(-0.411292\pi\)
0.275092 + 0.961418i \(0.411292\pi\)
\(884\) 1.14358e14 0.00712488
\(885\) −2.16937e15 −0.134322
\(886\) −1.46010e16 −0.898454
\(887\) −2.94302e16 −1.79976 −0.899878 0.436142i \(-0.856344\pi\)
−0.899878 + 0.436142i \(0.856344\pi\)
\(888\) 1.04536e16 0.635324
\(889\) −3.79437e15 −0.229182
\(890\) 7.34783e15 0.441077
\(891\) 1.82914e15 0.109124
\(892\) 1.55665e16 0.922966
\(893\) 4.98339e16 2.93658
\(894\) 2.12596e15 0.124509
\(895\) 2.20639e16 1.28427
\(896\) −1.38179e16 −0.799371
\(897\) −2.72103e14 −0.0156450
\(898\) 6.23315e15 0.356195
\(899\) −4.55711e16 −2.58828
\(900\) −8.56564e15 −0.483533
\(901\) 6.97787e15 0.391504
\(902\) 3.95409e15 0.220501
\(903\) 1.59150e16 0.882115
\(904\) 7.22507e15 0.398030
\(905\) −1.85797e16 −1.01735
\(906\) −4.35846e15 −0.237207
\(907\) 7.61735e14 0.0412063 0.0206032 0.999788i \(-0.493441\pi\)
0.0206032 + 0.999788i \(0.493441\pi\)
\(908\) −1.97735e16 −1.06319
\(909\) −5.39119e14 −0.0288127
\(910\) −5.74940e14 −0.0305418
\(911\) 1.78047e16 0.940122 0.470061 0.882634i \(-0.344232\pi\)
0.470061 + 0.882634i \(0.344232\pi\)
\(912\) 1.73555e15 0.0910891
\(913\) 9.67483e15 0.504724
\(914\) 6.31808e15 0.327628
\(915\) −3.56594e16 −1.83805
\(916\) −8.28513e15 −0.424497
\(917\) 1.81795e16 0.925870
\(918\) 8.82975e14 0.0447006
\(919\) −2.59175e16 −1.30424 −0.652121 0.758115i \(-0.726121\pi\)
−0.652121 + 0.758115i \(0.726121\pi\)
\(920\) −3.46723e16 −1.73440
\(921\) 1.09391e16 0.543942
\(922\) −1.75868e16 −0.869296
\(923\) −1.61354e14 −0.00792812
\(924\) −8.35229e15 −0.407953
\(925\) −5.14189e16 −2.49657
\(926\) 5.23078e15 0.252468
\(927\) −3.31974e15 −0.159282
\(928\) −4.05201e16 −1.93267
\(929\) 1.93663e16 0.918247 0.459124 0.888372i \(-0.348164\pi\)
0.459124 + 0.888372i \(0.348164\pi\)
\(930\) −1.74736e16 −0.823618
\(931\) −6.26509e15 −0.293565
\(932\) 1.50671e16 0.701845
\(933\) −6.85448e14 −0.0317413
\(934\) 2.25381e16 1.03755
\(935\) 1.53059e16 0.700478
\(936\) −1.91211e14 −0.00869951
\(937\) 1.94280e16 0.878738 0.439369 0.898307i \(-0.355202\pi\)
0.439369 + 0.898307i \(0.355202\pi\)
\(938\) −1.66795e16 −0.750012
\(939\) 2.88591e14 0.0129010
\(940\) 4.88320e16 2.17021
\(941\) −6.94877e15 −0.307019 −0.153510 0.988147i \(-0.549058\pi\)
−0.153510 + 0.988147i \(0.549058\pi\)
\(942\) −7.03341e15 −0.308948
\(943\) 8.86821e15 0.387277
\(944\) 2.95844e14 0.0128445
\(945\) 8.66811e15 0.374153
\(946\) −1.87045e16 −0.802685
\(947\) 2.18006e16 0.930131 0.465066 0.885276i \(-0.346031\pi\)
0.465066 + 0.885276i \(0.346031\pi\)
\(948\) 1.21083e16 0.513614
\(949\) −7.82896e14 −0.0330172
\(950\) 4.86852e16 2.04135
\(951\) 1.22850e16 0.512131
\(952\) −1.01286e16 −0.419804
\(953\) 2.38204e16 0.981608 0.490804 0.871270i \(-0.336703\pi\)
0.490804 + 0.871270i \(0.336703\pi\)
\(954\) −4.64438e15 −0.190288
\(955\) 2.72592e14 0.0111044
\(956\) −3.13664e15 −0.127042
\(957\) −2.65687e16 −1.06993
\(958\) 3.55860e15 0.142485
\(959\) 2.55594e16 1.01753
\(960\) −1.29652e16 −0.513203
\(961\) 2.23988e16 0.881549
\(962\) −4.56912e14 −0.0178801
\(963\) −1.04037e16 −0.404802
\(964\) 2.15839e16 0.835037
\(965\) −7.70528e16 −2.96407
\(966\) 9.59347e15 0.366946
\(967\) 4.40469e16 1.67521 0.837606 0.546275i \(-0.183954\pi\)
0.837606 + 0.546275i \(0.183954\pi\)
\(968\) −9.06420e14 −0.0342780
\(969\) 9.79952e15 0.368489
\(970\) −9.53378e15 −0.356468
\(971\) −3.21209e16 −1.19421 −0.597106 0.802162i \(-0.703683\pi\)
−0.597106 + 0.802162i \(0.703683\pi\)
\(972\) 1.14755e15 0.0424236
\(973\) 3.34329e16 1.22900
\(974\) 2.10122e16 0.768062
\(975\) 9.40521e14 0.0341856
\(976\) 4.86297e15 0.175763
\(977\) −8.06446e15 −0.289838 −0.144919 0.989444i \(-0.546292\pi\)
−0.144919 + 0.989444i \(0.546292\pi\)
\(978\) 3.81998e15 0.136520
\(979\) −1.17206e16 −0.416530
\(980\) −6.13913e15 −0.216952
\(981\) −2.80949e14 −0.00987298
\(982\) 4.35607e15 0.152223
\(983\) 2.83361e15 0.0984681 0.0492340 0.998787i \(-0.484322\pi\)
0.0492340 + 0.998787i \(0.484322\pi\)
\(984\) 6.23182e15 0.215348
\(985\) −3.81195e16 −1.30993
\(986\) −1.28254e16 −0.438278
\(987\) −3.39422e16 −1.15344
\(988\) −8.44745e14 −0.0285471
\(989\) −4.19503e16 −1.40979
\(990\) −1.01874e16 −0.340462
\(991\) 4.17181e15 0.138650 0.0693250 0.997594i \(-0.477915\pi\)
0.0693250 + 0.997594i \(0.477915\pi\)
\(992\) 4.25084e16 1.40495
\(993\) −1.99100e16 −0.654409
\(994\) 5.68882e15 0.185950
\(995\) −3.07855e16 −1.00074
\(996\) 6.06972e15 0.196220
\(997\) −5.18055e16 −1.66553 −0.832765 0.553627i \(-0.813243\pi\)
−0.832765 + 0.553627i \(0.813243\pi\)
\(998\) −3.57936e16 −1.14443
\(999\) 6.88867e15 0.219041
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.a.1.11 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.11 26 1.1 even 1 trivial