Properties

Label 177.12.a.a.1.13
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 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.8994 q^{2} -243.000 q^{3} -1929.20 q^{4} +3570.42 q^{5} +2648.56 q^{6} -66491.5 q^{7} +43349.2 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-10.8994 q^{2} -243.000 q^{3} -1929.20 q^{4} +3570.42 q^{5} +2648.56 q^{6} -66491.5 q^{7} +43349.2 q^{8} +59049.0 q^{9} -38915.5 q^{10} -586024. q^{11} +468796. q^{12} -248702. q^{13} +724720. q^{14} -867612. q^{15} +3.47852e6 q^{16} +3.17341e6 q^{17} -643601. q^{18} -8.29582e6 q^{19} -6.88806e6 q^{20} +1.61574e7 q^{21} +6.38733e6 q^{22} +4.26559e7 q^{23} -1.05339e7 q^{24} -3.60802e7 q^{25} +2.71071e6 q^{26} -1.43489e7 q^{27} +1.28276e8 q^{28} -2.96146e7 q^{29} +9.45648e6 q^{30} +7.28074e7 q^{31} -1.26693e8 q^{32} +1.42404e8 q^{33} -3.45884e7 q^{34} -2.37402e8 q^{35} -1.13917e8 q^{36} +4.75313e8 q^{37} +9.04197e7 q^{38} +6.04345e7 q^{39} +1.54775e8 q^{40} +5.12374e7 q^{41} -1.76107e8 q^{42} -1.03154e9 q^{43} +1.13056e9 q^{44} +2.10830e8 q^{45} -4.64925e8 q^{46} +2.14124e9 q^{47} -8.45281e8 q^{48} +2.44379e9 q^{49} +3.93254e8 q^{50} -7.71139e8 q^{51} +4.79796e8 q^{52} +1.08003e9 q^{53} +1.56395e8 q^{54} -2.09235e9 q^{55} -2.88236e9 q^{56} +2.01588e9 q^{57} +3.22783e8 q^{58} +7.14924e8 q^{59} +1.67380e9 q^{60} +8.65057e9 q^{61} -7.93559e8 q^{62} -3.92626e9 q^{63} -5.74313e9 q^{64} -8.87969e8 q^{65} -1.55212e9 q^{66} +1.80367e10 q^{67} -6.12215e9 q^{68} -1.03654e10 q^{69} +2.58755e9 q^{70} -7.45126e9 q^{71} +2.55973e9 q^{72} +2.81179e10 q^{73} -5.18064e9 q^{74} +8.76750e9 q^{75} +1.60043e10 q^{76} +3.89656e10 q^{77} -6.58701e8 q^{78} +1.85738e10 q^{79} +1.24198e10 q^{80} +3.48678e9 q^{81} -5.58459e8 q^{82} -2.72476e10 q^{83} -3.11710e10 q^{84} +1.13304e10 q^{85} +1.12432e10 q^{86} +7.19636e9 q^{87} -2.54037e10 q^{88} -4.76941e10 q^{89} -2.29792e9 q^{90} +1.65365e10 q^{91} -8.22919e10 q^{92} -1.76922e10 q^{93} -2.33383e10 q^{94} -2.96195e10 q^{95} +3.07864e10 q^{96} +4.57032e10 q^{97} -2.66359e10 q^{98} -3.46041e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.8994 −0.240846 −0.120423 0.992723i \(-0.538425\pi\)
−0.120423 + 0.992723i \(0.538425\pi\)
\(3\) −243.000 −0.577350
\(4\) −1929.20 −0.941993
\(5\) 3570.42 0.510957 0.255478 0.966815i \(-0.417767\pi\)
0.255478 + 0.966815i \(0.417767\pi\)
\(6\) 2648.56 0.139052
\(7\) −66491.5 −1.49529 −0.747647 0.664096i \(-0.768817\pi\)
−0.747647 + 0.664096i \(0.768817\pi\)
\(8\) 43349.2 0.467721
\(9\) 59049.0 0.333333
\(10\) −38915.5 −0.123062
\(11\) −586024. −1.09712 −0.548562 0.836110i \(-0.684824\pi\)
−0.548562 + 0.836110i \(0.684824\pi\)
\(12\) 468796. 0.543860
\(13\) −248702. −0.185776 −0.0928881 0.995677i \(-0.529610\pi\)
−0.0928881 + 0.995677i \(0.529610\pi\)
\(14\) 724720. 0.360135
\(15\) −867612. −0.295001
\(16\) 3.47852e6 0.829345
\(17\) 3.17341e6 0.542073 0.271036 0.962569i \(-0.412634\pi\)
0.271036 + 0.962569i \(0.412634\pi\)
\(18\) −643601. −0.0802819
\(19\) −8.29582e6 −0.768625 −0.384312 0.923203i \(-0.625561\pi\)
−0.384312 + 0.923203i \(0.625561\pi\)
\(20\) −6.88806e6 −0.481318
\(21\) 1.61574e7 0.863309
\(22\) 6.38733e6 0.264237
\(23\) 4.26559e7 1.38190 0.690949 0.722903i \(-0.257193\pi\)
0.690949 + 0.722903i \(0.257193\pi\)
\(24\) −1.05339e7 −0.270039
\(25\) −3.60802e7 −0.738923
\(26\) 2.71071e6 0.0447434
\(27\) −1.43489e7 −0.192450
\(28\) 1.28276e8 1.40856
\(29\) −2.96146e7 −0.268113 −0.134056 0.990974i \(-0.542800\pi\)
−0.134056 + 0.990974i \(0.542800\pi\)
\(30\) 9.45648e6 0.0710497
\(31\) 7.28074e7 0.456758 0.228379 0.973572i \(-0.426657\pi\)
0.228379 + 0.973572i \(0.426657\pi\)
\(32\) −1.26693e8 −0.667465
\(33\) 1.42404e8 0.633425
\(34\) −3.45884e7 −0.130556
\(35\) −2.37402e8 −0.764031
\(36\) −1.13917e8 −0.313998
\(37\) 4.75313e8 1.12686 0.563430 0.826164i \(-0.309481\pi\)
0.563430 + 0.826164i \(0.309481\pi\)
\(38\) 9.04197e7 0.185120
\(39\) 6.04345e7 0.107258
\(40\) 1.54775e8 0.238985
\(41\) 5.12374e7 0.0690679 0.0345339 0.999404i \(-0.489005\pi\)
0.0345339 + 0.999404i \(0.489005\pi\)
\(42\) −1.76107e8 −0.207924
\(43\) −1.03154e9 −1.07007 −0.535033 0.844831i \(-0.679701\pi\)
−0.535033 + 0.844831i \(0.679701\pi\)
\(44\) 1.13056e9 1.03348
\(45\) 2.10830e8 0.170319
\(46\) −4.64925e8 −0.332824
\(47\) 2.14124e9 1.36185 0.680923 0.732355i \(-0.261579\pi\)
0.680923 + 0.732355i \(0.261579\pi\)
\(48\) −8.45281e8 −0.478822
\(49\) 2.44379e9 1.23591
\(50\) 3.93254e8 0.177966
\(51\) −7.71139e8 −0.312966
\(52\) 4.79796e8 0.175000
\(53\) 1.08003e9 0.354747 0.177373 0.984144i \(-0.443240\pi\)
0.177373 + 0.984144i \(0.443240\pi\)
\(54\) 1.56395e8 0.0463508
\(55\) −2.09235e9 −0.560583
\(56\) −2.88236e9 −0.699380
\(57\) 2.01588e9 0.443766
\(58\) 3.22783e8 0.0645738
\(59\) 7.14924e8 0.130189
\(60\) 1.67380e9 0.277889
\(61\) 8.65057e9 1.31139 0.655693 0.755027i \(-0.272377\pi\)
0.655693 + 0.755027i \(0.272377\pi\)
\(62\) −7.93559e8 −0.110008
\(63\) −3.92626e9 −0.498432
\(64\) −5.74313e9 −0.668589
\(65\) −8.87969e8 −0.0949236
\(66\) −1.55212e9 −0.152558
\(67\) 1.80367e10 1.63210 0.816048 0.577984i \(-0.196161\pi\)
0.816048 + 0.577984i \(0.196161\pi\)
\(68\) −6.12215e9 −0.510629
\(69\) −1.03654e10 −0.797840
\(70\) 2.58755e9 0.184014
\(71\) −7.45126e9 −0.490127 −0.245063 0.969507i \(-0.578809\pi\)
−0.245063 + 0.969507i \(0.578809\pi\)
\(72\) 2.55973e9 0.155907
\(73\) 2.81179e10 1.58748 0.793738 0.608259i \(-0.208132\pi\)
0.793738 + 0.608259i \(0.208132\pi\)
\(74\) −5.18064e9 −0.271400
\(75\) 8.76750e9 0.426617
\(76\) 1.60043e10 0.724040
\(77\) 3.89656e10 1.64052
\(78\) −6.58701e8 −0.0258326
\(79\) 1.85738e10 0.679128 0.339564 0.940583i \(-0.389720\pi\)
0.339564 + 0.940583i \(0.389720\pi\)
\(80\) 1.24198e10 0.423759
\(81\) 3.48678e9 0.111111
\(82\) −5.58459e8 −0.0166347
\(83\) −2.72476e10 −0.759273 −0.379637 0.925136i \(-0.623951\pi\)
−0.379637 + 0.925136i \(0.623951\pi\)
\(84\) −3.11710e10 −0.813231
\(85\) 1.13304e10 0.276976
\(86\) 1.12432e10 0.257721
\(87\) 7.19636e9 0.154795
\(88\) −2.54037e10 −0.513147
\(89\) −4.76941e10 −0.905356 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(90\) −2.29792e9 −0.0410206
\(91\) 1.65365e10 0.277790
\(92\) −8.22919e10 −1.30174
\(93\) −1.76922e10 −0.263709
\(94\) −2.33383e10 −0.327995
\(95\) −2.96195e10 −0.392734
\(96\) 3.07864e10 0.385361
\(97\) 4.57032e10 0.540384 0.270192 0.962806i \(-0.412913\pi\)
0.270192 + 0.962806i \(0.412913\pi\)
\(98\) −2.66359e10 −0.297663
\(99\) −3.46041e10 −0.365708
\(100\) 6.96061e10 0.696061
\(101\) −1.05361e11 −0.997499 −0.498750 0.866746i \(-0.666207\pi\)
−0.498750 + 0.866746i \(0.666207\pi\)
\(102\) 8.40498e9 0.0753764
\(103\) 2.07637e10 0.176482 0.0882409 0.996099i \(-0.471875\pi\)
0.0882409 + 0.996099i \(0.471875\pi\)
\(104\) −1.07810e10 −0.0868914
\(105\) 5.76888e10 0.441114
\(106\) −1.17717e10 −0.0854393
\(107\) −1.61325e11 −1.11197 −0.555983 0.831194i \(-0.687658\pi\)
−0.555983 + 0.831194i \(0.687658\pi\)
\(108\) 2.76819e10 0.181287
\(109\) −8.08431e10 −0.503265 −0.251633 0.967823i \(-0.580967\pi\)
−0.251633 + 0.967823i \(0.580967\pi\)
\(110\) 2.28054e10 0.135014
\(111\) −1.15501e11 −0.650593
\(112\) −2.31292e11 −1.24012
\(113\) −1.96639e11 −1.00401 −0.502006 0.864864i \(-0.667405\pi\)
−0.502006 + 0.864864i \(0.667405\pi\)
\(114\) −2.19720e10 −0.106879
\(115\) 1.52299e11 0.706090
\(116\) 5.71326e10 0.252560
\(117\) −1.46856e10 −0.0619254
\(118\) −7.79227e9 −0.0313554
\(119\) −2.11005e11 −0.810558
\(120\) −3.76103e10 −0.137978
\(121\) 5.81123e10 0.203680
\(122\) −9.42863e10 −0.315842
\(123\) −1.24507e10 −0.0398763
\(124\) −1.40460e11 −0.430263
\(125\) −3.03158e11 −0.888515
\(126\) 4.27940e10 0.120045
\(127\) 3.45018e11 0.926662 0.463331 0.886185i \(-0.346654\pi\)
0.463331 + 0.886185i \(0.346654\pi\)
\(128\) 3.22065e11 0.828492
\(129\) 2.50665e11 0.617803
\(130\) 9.67835e9 0.0228619
\(131\) 5.10254e11 1.15556 0.577782 0.816191i \(-0.303918\pi\)
0.577782 + 0.816191i \(0.303918\pi\)
\(132\) −2.74726e11 −0.596682
\(133\) 5.51601e11 1.14932
\(134\) −1.96590e11 −0.393083
\(135\) −5.12316e10 −0.0983337
\(136\) 1.37565e11 0.253539
\(137\) 5.34579e11 0.946344 0.473172 0.880970i \(-0.343109\pi\)
0.473172 + 0.880970i \(0.343109\pi\)
\(138\) 1.12977e11 0.192156
\(139\) 5.71369e11 0.933974 0.466987 0.884264i \(-0.345339\pi\)
0.466987 + 0.884264i \(0.345339\pi\)
\(140\) 4.57997e11 0.719712
\(141\) −5.20322e11 −0.786262
\(142\) 8.12145e10 0.118045
\(143\) 1.45745e11 0.203819
\(144\) 2.05403e11 0.276448
\(145\) −1.05737e11 −0.136994
\(146\) −3.06469e11 −0.382337
\(147\) −5.93841e11 −0.713551
\(148\) −9.16975e11 −1.06150
\(149\) 6.11636e11 0.682289 0.341145 0.940011i \(-0.389185\pi\)
0.341145 + 0.940011i \(0.389185\pi\)
\(150\) −9.55607e10 −0.102749
\(151\) −9.59349e11 −0.994497 −0.497248 0.867608i \(-0.665656\pi\)
−0.497248 + 0.867608i \(0.665656\pi\)
\(152\) −3.59617e11 −0.359502
\(153\) 1.87387e11 0.180691
\(154\) −4.24703e11 −0.395113
\(155\) 2.59953e11 0.233384
\(156\) −1.16590e11 −0.101036
\(157\) −1.46027e12 −1.22175 −0.610877 0.791725i \(-0.709183\pi\)
−0.610877 + 0.791725i \(0.709183\pi\)
\(158\) −2.02444e11 −0.163565
\(159\) −2.62447e11 −0.204813
\(160\) −4.52348e11 −0.341046
\(161\) −2.83626e12 −2.06635
\(162\) −3.80040e10 −0.0267606
\(163\) −2.01632e12 −1.37255 −0.686273 0.727344i \(-0.740755\pi\)
−0.686273 + 0.727344i \(0.740755\pi\)
\(164\) −9.88473e10 −0.0650615
\(165\) 5.08441e11 0.323653
\(166\) 2.96983e11 0.182868
\(167\) −2.14766e12 −1.27946 −0.639728 0.768601i \(-0.720953\pi\)
−0.639728 + 0.768601i \(0.720953\pi\)
\(168\) 7.00413e11 0.403788
\(169\) −1.73031e12 −0.965487
\(170\) −1.23495e11 −0.0667084
\(171\) −4.89860e11 −0.256208
\(172\) 1.99005e12 1.00799
\(173\) 3.00631e12 1.47496 0.737481 0.675368i \(-0.236015\pi\)
0.737481 + 0.675368i \(0.236015\pi\)
\(174\) −7.84362e10 −0.0372817
\(175\) 2.39903e12 1.10491
\(176\) −2.03850e12 −0.909894
\(177\) −1.73727e11 −0.0751646
\(178\) 5.19839e11 0.218051
\(179\) −2.89437e12 −1.17723 −0.588617 0.808412i \(-0.700327\pi\)
−0.588617 + 0.808412i \(0.700327\pi\)
\(180\) −4.06733e11 −0.160439
\(181\) −4.77947e12 −1.82872 −0.914361 0.404899i \(-0.867307\pi\)
−0.914361 + 0.404899i \(0.867307\pi\)
\(182\) −1.80239e11 −0.0669046
\(183\) −2.10209e12 −0.757129
\(184\) 1.84910e12 0.646343
\(185\) 1.69707e12 0.575777
\(186\) 1.92835e11 0.0635133
\(187\) −1.85970e12 −0.594721
\(188\) −4.13089e12 −1.28285
\(189\) 9.54080e11 0.287770
\(190\) 3.22836e11 0.0945883
\(191\) −4.41995e12 −1.25815 −0.629077 0.777343i \(-0.716567\pi\)
−0.629077 + 0.777343i \(0.716567\pi\)
\(192\) 1.39558e12 0.386010
\(193\) 3.26145e12 0.876688 0.438344 0.898807i \(-0.355565\pi\)
0.438344 + 0.898807i \(0.355565\pi\)
\(194\) −4.98139e11 −0.130149
\(195\) 2.15776e11 0.0548042
\(196\) −4.71457e12 −1.16422
\(197\) 1.75273e12 0.420873 0.210437 0.977608i \(-0.432511\pi\)
0.210437 + 0.977608i \(0.432511\pi\)
\(198\) 3.77165e11 0.0880792
\(199\) 1.26489e12 0.287317 0.143658 0.989627i \(-0.454113\pi\)
0.143658 + 0.989627i \(0.454113\pi\)
\(200\) −1.56405e12 −0.345610
\(201\) −4.38292e12 −0.942291
\(202\) 1.14838e12 0.240243
\(203\) 1.96912e12 0.400908
\(204\) 1.48768e12 0.294812
\(205\) 1.82939e11 0.0352907
\(206\) −2.26313e11 −0.0425049
\(207\) 2.51879e12 0.460633
\(208\) −8.65114e11 −0.154072
\(209\) 4.86155e12 0.843276
\(210\) −6.28775e11 −0.106240
\(211\) −9.77199e12 −1.60853 −0.804266 0.594270i \(-0.797441\pi\)
−0.804266 + 0.594270i \(0.797441\pi\)
\(212\) −2.08360e12 −0.334169
\(213\) 1.81066e12 0.282975
\(214\) 1.75835e12 0.267812
\(215\) −3.68304e12 −0.546757
\(216\) −6.22014e11 −0.0900129
\(217\) −4.84107e12 −0.682988
\(218\) 8.81143e11 0.121209
\(219\) −6.83265e12 −0.916530
\(220\) 4.03657e12 0.528065
\(221\) −7.89232e11 −0.100704
\(222\) 1.25890e12 0.156693
\(223\) 9.61626e11 0.116770 0.0583848 0.998294i \(-0.481405\pi\)
0.0583848 + 0.998294i \(0.481405\pi\)
\(224\) 8.42402e12 0.998057
\(225\) −2.13050e12 −0.246308
\(226\) 2.14326e12 0.241812
\(227\) −1.49335e13 −1.64444 −0.822221 0.569168i \(-0.807265\pi\)
−0.822221 + 0.569168i \(0.807265\pi\)
\(228\) −3.88905e12 −0.418024
\(229\) 3.29995e12 0.346268 0.173134 0.984898i \(-0.444611\pi\)
0.173134 + 0.984898i \(0.444611\pi\)
\(230\) −1.65998e12 −0.170059
\(231\) −9.46864e12 −0.947157
\(232\) −1.28377e12 −0.125402
\(233\) 5.24978e12 0.500822 0.250411 0.968140i \(-0.419434\pi\)
0.250411 + 0.968140i \(0.419434\pi\)
\(234\) 1.60064e11 0.0149145
\(235\) 7.64514e12 0.695844
\(236\) −1.37923e12 −0.122637
\(237\) −4.51343e12 −0.392095
\(238\) 2.29983e12 0.195219
\(239\) −1.06137e13 −0.880400 −0.440200 0.897900i \(-0.645092\pi\)
−0.440200 + 0.897900i \(0.645092\pi\)
\(240\) −3.01801e12 −0.244658
\(241\) 6.93809e12 0.549726 0.274863 0.961483i \(-0.411368\pi\)
0.274863 + 0.961483i \(0.411368\pi\)
\(242\) −6.33391e11 −0.0490555
\(243\) −8.47289e11 −0.0641500
\(244\) −1.66887e13 −1.23532
\(245\) 8.72536e12 0.631495
\(246\) 1.35705e11 0.00960405
\(247\) 2.06318e12 0.142792
\(248\) 3.15615e12 0.213635
\(249\) 6.62116e12 0.438367
\(250\) 3.30425e12 0.213995
\(251\) 1.08474e13 0.687258 0.343629 0.939106i \(-0.388344\pi\)
0.343629 + 0.939106i \(0.388344\pi\)
\(252\) 7.57454e12 0.469519
\(253\) −2.49974e13 −1.51611
\(254\) −3.76050e12 −0.223183
\(255\) −2.75329e12 −0.159912
\(256\) 8.25162e12 0.469050
\(257\) −5.95164e12 −0.331135 −0.165567 0.986198i \(-0.552945\pi\)
−0.165567 + 0.986198i \(0.552945\pi\)
\(258\) −2.73210e12 −0.148795
\(259\) −3.16043e13 −1.68499
\(260\) 1.71307e12 0.0894174
\(261\) −1.74871e12 −0.0893709
\(262\) −5.56148e12 −0.278313
\(263\) −8.89001e12 −0.435658 −0.217829 0.975987i \(-0.569897\pi\)
−0.217829 + 0.975987i \(0.569897\pi\)
\(264\) 6.17310e12 0.296266
\(265\) 3.85616e12 0.181260
\(266\) −6.01214e12 −0.276809
\(267\) 1.15897e13 0.522708
\(268\) −3.47964e13 −1.53742
\(269\) 4.16303e13 1.80207 0.901037 0.433743i \(-0.142807\pi\)
0.901037 + 0.433743i \(0.142807\pi\)
\(270\) 5.58396e11 0.0236832
\(271\) −3.20752e13 −1.33302 −0.666512 0.745494i \(-0.732213\pi\)
−0.666512 + 0.745494i \(0.732213\pi\)
\(272\) 1.10388e13 0.449565
\(273\) −4.01838e12 −0.160382
\(274\) −5.82661e12 −0.227923
\(275\) 2.11439e13 0.810690
\(276\) 1.99969e13 0.751560
\(277\) 3.14801e13 1.15984 0.579919 0.814674i \(-0.303084\pi\)
0.579919 + 0.814674i \(0.303084\pi\)
\(278\) −6.22759e12 −0.224944
\(279\) 4.29920e12 0.152253
\(280\) −1.02912e13 −0.357353
\(281\) −1.35973e13 −0.462987 −0.231493 0.972836i \(-0.574361\pi\)
−0.231493 + 0.972836i \(0.574361\pi\)
\(282\) 5.67122e12 0.189368
\(283\) 2.32657e13 0.761886 0.380943 0.924598i \(-0.375599\pi\)
0.380943 + 0.924598i \(0.375599\pi\)
\(284\) 1.43750e13 0.461696
\(285\) 7.19755e12 0.226745
\(286\) −1.58854e12 −0.0490890
\(287\) −3.40685e12 −0.103277
\(288\) −7.48111e12 −0.222488
\(289\) −2.42014e13 −0.706157
\(290\) 1.15247e12 0.0329944
\(291\) −1.11059e13 −0.311991
\(292\) −5.42451e13 −1.49539
\(293\) 3.24702e13 0.878442 0.439221 0.898379i \(-0.355255\pi\)
0.439221 + 0.898379i \(0.355255\pi\)
\(294\) 6.47253e12 0.171856
\(295\) 2.55258e12 0.0665209
\(296\) 2.06045e13 0.527056
\(297\) 8.40880e12 0.211142
\(298\) −6.66648e12 −0.164326
\(299\) −1.06086e13 −0.256724
\(300\) −1.69143e13 −0.401871
\(301\) 6.85888e13 1.60006
\(302\) 1.04564e13 0.239520
\(303\) 2.56027e13 0.575907
\(304\) −2.88572e13 −0.637455
\(305\) 3.08862e13 0.670062
\(306\) −2.04241e12 −0.0435186
\(307\) 2.27591e13 0.476315 0.238158 0.971226i \(-0.423456\pi\)
0.238158 + 0.971226i \(0.423456\pi\)
\(308\) −7.51725e13 −1.54536
\(309\) −5.04558e12 −0.101892
\(310\) −2.83334e12 −0.0562094
\(311\) 5.49995e13 1.07195 0.535977 0.844233i \(-0.319943\pi\)
0.535977 + 0.844233i \(0.319943\pi\)
\(312\) 2.61979e12 0.0501668
\(313\) −1.78455e13 −0.335765 −0.167882 0.985807i \(-0.553693\pi\)
−0.167882 + 0.985807i \(0.553693\pi\)
\(314\) 1.59161e13 0.294254
\(315\) −1.40184e13 −0.254677
\(316\) −3.58326e13 −0.639734
\(317\) 4.88368e13 0.856882 0.428441 0.903570i \(-0.359063\pi\)
0.428441 + 0.903570i \(0.359063\pi\)
\(318\) 2.86053e12 0.0493284
\(319\) 1.73549e13 0.294153
\(320\) −2.05054e13 −0.341620
\(321\) 3.92020e13 0.641994
\(322\) 3.09136e13 0.497671
\(323\) −2.63261e13 −0.416650
\(324\) −6.72671e12 −0.104666
\(325\) 8.97321e12 0.137274
\(326\) 2.19767e13 0.330572
\(327\) 1.96449e13 0.290560
\(328\) 2.22110e12 0.0323045
\(329\) −1.42374e14 −2.03636
\(330\) −5.54172e12 −0.0779503
\(331\) 1.00303e14 1.38758 0.693791 0.720177i \(-0.255939\pi\)
0.693791 + 0.720177i \(0.255939\pi\)
\(332\) 5.25661e13 0.715230
\(333\) 2.80668e13 0.375620
\(334\) 2.34083e13 0.308151
\(335\) 6.43986e13 0.833930
\(336\) 5.62040e13 0.715981
\(337\) 5.21287e12 0.0653299 0.0326650 0.999466i \(-0.489601\pi\)
0.0326650 + 0.999466i \(0.489601\pi\)
\(338\) 1.88594e13 0.232533
\(339\) 4.77834e13 0.579667
\(340\) −2.18587e13 −0.260909
\(341\) −4.26669e13 −0.501120
\(342\) 5.33919e12 0.0617067
\(343\) −3.10160e13 −0.352750
\(344\) −4.47166e13 −0.500492
\(345\) −3.70088e13 −0.407662
\(346\) −3.27671e13 −0.355238
\(347\) −8.57886e12 −0.0915413 −0.0457707 0.998952i \(-0.514574\pi\)
−0.0457707 + 0.998952i \(0.514574\pi\)
\(348\) −1.38832e13 −0.145816
\(349\) 6.67566e13 0.690167 0.345083 0.938572i \(-0.387851\pi\)
0.345083 + 0.938572i \(0.387851\pi\)
\(350\) −2.61480e13 −0.266112
\(351\) 3.56859e12 0.0357526
\(352\) 7.42452e13 0.732291
\(353\) −3.88466e13 −0.377218 −0.188609 0.982052i \(-0.560398\pi\)
−0.188609 + 0.982052i \(0.560398\pi\)
\(354\) 1.89352e12 0.0181031
\(355\) −2.66041e13 −0.250434
\(356\) 9.20116e13 0.852840
\(357\) 5.12742e13 0.467976
\(358\) 3.15470e13 0.283532
\(359\) 1.06909e14 0.946226 0.473113 0.881002i \(-0.343130\pi\)
0.473113 + 0.881002i \(0.343130\pi\)
\(360\) 9.13931e12 0.0796617
\(361\) −4.76697e13 −0.409216
\(362\) 5.20935e13 0.440440
\(363\) −1.41213e13 −0.117595
\(364\) −3.19023e13 −0.261676
\(365\) 1.00393e14 0.811132
\(366\) 2.29116e13 0.182351
\(367\) −1.74287e14 −1.36648 −0.683239 0.730195i \(-0.739429\pi\)
−0.683239 + 0.730195i \(0.739429\pi\)
\(368\) 1.48380e14 1.14607
\(369\) 3.02552e12 0.0230226
\(370\) −1.84971e13 −0.138673
\(371\) −7.18128e13 −0.530451
\(372\) 3.41318e13 0.248412
\(373\) 1.81954e14 1.30486 0.652429 0.757850i \(-0.273750\pi\)
0.652429 + 0.757850i \(0.273750\pi\)
\(374\) 2.02696e13 0.143236
\(375\) 7.36675e13 0.512984
\(376\) 9.28213e13 0.636963
\(377\) 7.36520e12 0.0498089
\(378\) −1.03989e13 −0.0693081
\(379\) −1.00579e14 −0.660678 −0.330339 0.943862i \(-0.607163\pi\)
−0.330339 + 0.943862i \(0.607163\pi\)
\(380\) 5.71421e13 0.369953
\(381\) −8.38394e13 −0.535008
\(382\) 4.81750e13 0.303021
\(383\) −3.59629e13 −0.222978 −0.111489 0.993766i \(-0.535562\pi\)
−0.111489 + 0.993766i \(0.535562\pi\)
\(384\) −7.82617e13 −0.478330
\(385\) 1.39124e14 0.838237
\(386\) −3.55479e13 −0.211147
\(387\) −6.09115e13 −0.356688
\(388\) −8.81708e13 −0.509038
\(389\) 3.31371e14 1.88622 0.943110 0.332482i \(-0.107886\pi\)
0.943110 + 0.332482i \(0.107886\pi\)
\(390\) −2.35184e12 −0.0131993
\(391\) 1.35365e14 0.749089
\(392\) 1.05937e14 0.578059
\(393\) −1.23992e14 −0.667165
\(394\) −1.91038e13 −0.101365
\(395\) 6.63163e13 0.347005
\(396\) 6.67584e13 0.344494
\(397\) 2.27606e14 1.15834 0.579170 0.815207i \(-0.303377\pi\)
0.579170 + 0.815207i \(0.303377\pi\)
\(398\) −1.37866e13 −0.0691990
\(399\) −1.34039e14 −0.663561
\(400\) −1.25506e14 −0.612822
\(401\) −1.66902e14 −0.803838 −0.401919 0.915675i \(-0.631657\pi\)
−0.401919 + 0.915675i \(0.631657\pi\)
\(402\) 4.77713e13 0.226947
\(403\) −1.81073e13 −0.0848547
\(404\) 2.03263e14 0.939638
\(405\) 1.24493e13 0.0567730
\(406\) −2.14623e13 −0.0965569
\(407\) −2.78545e14 −1.23631
\(408\) −3.34283e13 −0.146381
\(409\) 1.21687e14 0.525732 0.262866 0.964832i \(-0.415332\pi\)
0.262866 + 0.964832i \(0.415332\pi\)
\(410\) −1.99393e12 −0.00849961
\(411\) −1.29903e14 −0.546372
\(412\) −4.00574e13 −0.166245
\(413\) −4.75364e13 −0.194671
\(414\) −2.74534e13 −0.110941
\(415\) −9.72852e13 −0.387956
\(416\) 3.15088e13 0.123999
\(417\) −1.38843e14 −0.539230
\(418\) −5.29881e13 −0.203100
\(419\) −4.64645e14 −1.75770 −0.878848 0.477101i \(-0.841688\pi\)
−0.878848 + 0.477101i \(0.841688\pi\)
\(420\) −1.11293e14 −0.415526
\(421\) 3.06553e14 1.12968 0.564838 0.825202i \(-0.308939\pi\)
0.564838 + 0.825202i \(0.308939\pi\)
\(422\) 1.06509e14 0.387408
\(423\) 1.26438e14 0.453948
\(424\) 4.68185e13 0.165922
\(425\) −1.14497e14 −0.400550
\(426\) −1.97351e13 −0.0681533
\(427\) −5.75189e14 −1.96091
\(428\) 3.11229e14 1.04746
\(429\) −3.54160e13 −0.117675
\(430\) 4.01430e13 0.131684
\(431\) −3.15623e14 −1.02222 −0.511109 0.859516i \(-0.670765\pi\)
−0.511109 + 0.859516i \(0.670765\pi\)
\(432\) −4.99130e13 −0.159607
\(433\) −5.21759e13 −0.164735 −0.0823675 0.996602i \(-0.526248\pi\)
−0.0823675 + 0.996602i \(0.526248\pi\)
\(434\) 5.27649e13 0.164495
\(435\) 2.56940e13 0.0790935
\(436\) 1.55963e14 0.474073
\(437\) −3.53866e14 −1.06216
\(438\) 7.44720e13 0.220742
\(439\) −4.75814e14 −1.39278 −0.696390 0.717664i \(-0.745211\pi\)
−0.696390 + 0.717664i \(0.745211\pi\)
\(440\) −9.07018e13 −0.262196
\(441\) 1.44303e14 0.411969
\(442\) 8.60218e12 0.0242542
\(443\) −2.38581e14 −0.664378 −0.332189 0.943213i \(-0.607787\pi\)
−0.332189 + 0.943213i \(0.607787\pi\)
\(444\) 2.22825e14 0.612854
\(445\) −1.70288e14 −0.462598
\(446\) −1.04812e13 −0.0281234
\(447\) −1.48627e14 −0.393920
\(448\) 3.81870e14 0.999737
\(449\) 2.52988e14 0.654251 0.327125 0.944981i \(-0.393920\pi\)
0.327125 + 0.944981i \(0.393920\pi\)
\(450\) 2.32213e13 0.0593222
\(451\) −3.00263e13 −0.0757760
\(452\) 3.79357e14 0.945773
\(453\) 2.33122e14 0.574173
\(454\) 1.62766e14 0.396057
\(455\) 5.90424e13 0.141939
\(456\) 8.73871e13 0.207558
\(457\) −1.80008e14 −0.422428 −0.211214 0.977440i \(-0.567742\pi\)
−0.211214 + 0.977440i \(0.567742\pi\)
\(458\) −3.59676e13 −0.0833972
\(459\) −4.55350e13 −0.104322
\(460\) −2.93817e14 −0.665133
\(461\) 8.67632e14 1.94080 0.970400 0.241504i \(-0.0776407\pi\)
0.970400 + 0.241504i \(0.0776407\pi\)
\(462\) 1.03203e14 0.228119
\(463\) 6.99011e14 1.52682 0.763411 0.645913i \(-0.223523\pi\)
0.763411 + 0.645913i \(0.223523\pi\)
\(464\) −1.03015e14 −0.222358
\(465\) −6.31685e13 −0.134744
\(466\) −5.72196e13 −0.120621
\(467\) −3.20026e14 −0.666718 −0.333359 0.942800i \(-0.608182\pi\)
−0.333359 + 0.942800i \(0.608182\pi\)
\(468\) 2.83314e13 0.0583333
\(469\) −1.19929e15 −2.44046
\(470\) −8.33276e13 −0.167591
\(471\) 3.54845e14 0.705380
\(472\) 3.09914e13 0.0608921
\(473\) 6.04508e14 1.17399
\(474\) 4.91939e13 0.0944344
\(475\) 2.99315e14 0.567955
\(476\) 4.07071e14 0.763541
\(477\) 6.37747e13 0.118249
\(478\) 1.15684e14 0.212040
\(479\) −2.51037e14 −0.454875 −0.227438 0.973793i \(-0.573035\pi\)
−0.227438 + 0.973793i \(0.573035\pi\)
\(480\) 1.09921e14 0.196903
\(481\) −1.18211e14 −0.209344
\(482\) −7.56212e13 −0.132399
\(483\) 6.89210e14 1.19301
\(484\) −1.12110e14 −0.191865
\(485\) 1.63180e14 0.276113
\(486\) 9.23496e12 0.0154503
\(487\) −2.64352e14 −0.437294 −0.218647 0.975804i \(-0.570164\pi\)
−0.218647 + 0.975804i \(0.570164\pi\)
\(488\) 3.74996e14 0.613363
\(489\) 4.89965e14 0.792440
\(490\) −9.51015e13 −0.152093
\(491\) −1.63858e14 −0.259132 −0.129566 0.991571i \(-0.541358\pi\)
−0.129566 + 0.991571i \(0.541358\pi\)
\(492\) 2.40199e13 0.0375633
\(493\) −9.39794e13 −0.145337
\(494\) −2.24875e13 −0.0343909
\(495\) −1.23551e14 −0.186861
\(496\) 2.53262e14 0.378810
\(497\) 4.95445e14 0.732884
\(498\) −7.21669e13 −0.105579
\(499\) −1.30857e13 −0.0189340 −0.00946701 0.999955i \(-0.503013\pi\)
−0.00946701 + 0.999955i \(0.503013\pi\)
\(500\) 5.84854e14 0.836975
\(501\) 5.21882e14 0.738694
\(502\) −1.18230e14 −0.165523
\(503\) 6.57715e14 0.910781 0.455390 0.890292i \(-0.349500\pi\)
0.455390 + 0.890292i \(0.349500\pi\)
\(504\) −1.70200e14 −0.233127
\(505\) −3.76183e14 −0.509679
\(506\) 2.72457e14 0.365149
\(507\) 4.20465e14 0.557424
\(508\) −6.65609e14 −0.872909
\(509\) 4.66671e14 0.605429 0.302714 0.953081i \(-0.402107\pi\)
0.302714 + 0.953081i \(0.402107\pi\)
\(510\) 3.00093e13 0.0385141
\(511\) −1.86960e15 −2.37375
\(512\) −7.49526e14 −0.941460
\(513\) 1.19036e14 0.147922
\(514\) 6.48695e13 0.0797523
\(515\) 7.41351e13 0.0901746
\(516\) −4.83583e14 −0.581966
\(517\) −1.25482e15 −1.49411
\(518\) 3.44469e14 0.405822
\(519\) −7.30534e14 −0.851570
\(520\) −3.84928e13 −0.0443977
\(521\) −1.66453e15 −1.89970 −0.949849 0.312709i \(-0.898764\pi\)
−0.949849 + 0.312709i \(0.898764\pi\)
\(522\) 1.90600e13 0.0215246
\(523\) −1.49774e15 −1.67369 −0.836847 0.547436i \(-0.815604\pi\)
−0.836847 + 0.547436i \(0.815604\pi\)
\(524\) −9.84383e14 −1.08853
\(525\) −5.82964e14 −0.637919
\(526\) 9.68960e13 0.104926
\(527\) 2.31048e14 0.247596
\(528\) 4.95355e14 0.525327
\(529\) 8.66717e14 0.909644
\(530\) −4.20300e13 −0.0436558
\(531\) 4.22156e13 0.0433963
\(532\) −1.06415e15 −1.08265
\(533\) −1.27428e13 −0.0128312
\(534\) −1.26321e14 −0.125892
\(535\) −5.75999e14 −0.568166
\(536\) 7.81877e14 0.763365
\(537\) 7.03333e14 0.679677
\(538\) −4.53747e14 −0.434022
\(539\) −1.43212e15 −1.35594
\(540\) 9.88361e13 0.0926297
\(541\) 3.51108e14 0.325729 0.162864 0.986648i \(-0.447927\pi\)
0.162864 + 0.986648i \(0.447927\pi\)
\(542\) 3.49601e14 0.321053
\(543\) 1.16141e15 1.05581
\(544\) −4.02050e14 −0.361814
\(545\) −2.88644e14 −0.257147
\(546\) 4.37980e13 0.0386274
\(547\) −8.72037e14 −0.761385 −0.380693 0.924702i \(-0.624314\pi\)
−0.380693 + 0.924702i \(0.624314\pi\)
\(548\) −1.03131e15 −0.891449
\(549\) 5.10808e14 0.437129
\(550\) −2.30456e14 −0.195251
\(551\) 2.45678e14 0.206078
\(552\) −4.49332e14 −0.373166
\(553\) −1.23500e15 −1.01550
\(554\) −3.43115e14 −0.279342
\(555\) −4.12387e14 −0.332425
\(556\) −1.10229e15 −0.879798
\(557\) −1.24034e15 −0.980248 −0.490124 0.871653i \(-0.663048\pi\)
−0.490124 + 0.871653i \(0.663048\pi\)
\(558\) −4.68589e13 −0.0366694
\(559\) 2.56546e14 0.198793
\(560\) −8.25810e14 −0.633645
\(561\) 4.51906e14 0.343362
\(562\) 1.48203e14 0.111508
\(563\) −3.60595e13 −0.0268673 −0.0134336 0.999910i \(-0.504276\pi\)
−0.0134336 + 0.999910i \(0.504276\pi\)
\(564\) 1.00381e15 0.740653
\(565\) −7.02085e14 −0.513007
\(566\) −2.53583e14 −0.183497
\(567\) −2.31841e14 −0.166144
\(568\) −3.23006e14 −0.229243
\(569\) 1.14019e15 0.801421 0.400710 0.916205i \(-0.368763\pi\)
0.400710 + 0.916205i \(0.368763\pi\)
\(570\) −7.84492e13 −0.0546106
\(571\) 7.03830e14 0.485254 0.242627 0.970120i \(-0.421991\pi\)
0.242627 + 0.970120i \(0.421991\pi\)
\(572\) −2.81172e14 −0.191997
\(573\) 1.07405e15 0.726396
\(574\) 3.71328e13 0.0248738
\(575\) −1.53904e15 −1.02112
\(576\) −3.39126e14 −0.222863
\(577\) −1.63485e15 −1.06417 −0.532086 0.846690i \(-0.678592\pi\)
−0.532086 + 0.846690i \(0.678592\pi\)
\(578\) 2.63781e14 0.170075
\(579\) −7.92532e14 −0.506156
\(580\) 2.03987e14 0.129047
\(581\) 1.81173e15 1.13534
\(582\) 1.21048e14 0.0751417
\(583\) −6.32923e14 −0.389201
\(584\) 1.21889e15 0.742496
\(585\) −5.24337e13 −0.0316412
\(586\) −3.53907e14 −0.211569
\(587\) −2.17586e14 −0.128861 −0.0644305 0.997922i \(-0.520523\pi\)
−0.0644305 + 0.997922i \(0.520523\pi\)
\(588\) 1.14564e15 0.672160
\(589\) −6.03997e14 −0.351076
\(590\) −2.78217e13 −0.0160213
\(591\) −4.25914e14 −0.242991
\(592\) 1.65339e15 0.934556
\(593\) −2.13126e15 −1.19354 −0.596769 0.802413i \(-0.703549\pi\)
−0.596769 + 0.802413i \(0.703549\pi\)
\(594\) −9.16512e13 −0.0508525
\(595\) −7.53376e14 −0.414160
\(596\) −1.17997e15 −0.642712
\(597\) −3.07368e14 −0.165882
\(598\) 1.15628e14 0.0618308
\(599\) 7.51937e14 0.398413 0.199207 0.979958i \(-0.436164\pi\)
0.199207 + 0.979958i \(0.436164\pi\)
\(600\) 3.80064e14 0.199538
\(601\) −1.89694e14 −0.0986833 −0.0493416 0.998782i \(-0.515712\pi\)
−0.0493416 + 0.998782i \(0.515712\pi\)
\(602\) −7.47579e14 −0.385368
\(603\) 1.06505e15 0.544032
\(604\) 1.85078e15 0.936809
\(605\) 2.07485e14 0.104072
\(606\) −2.79055e14 −0.138705
\(607\) 6.99157e14 0.344379 0.172190 0.985064i \(-0.444916\pi\)
0.172190 + 0.985064i \(0.444916\pi\)
\(608\) 1.05102e15 0.513030
\(609\) −4.78496e14 −0.231464
\(610\) −3.36642e14 −0.161381
\(611\) −5.32530e14 −0.252998
\(612\) −3.61507e14 −0.170210
\(613\) −3.50244e15 −1.63432 −0.817162 0.576408i \(-0.804454\pi\)
−0.817162 + 0.576408i \(0.804454\pi\)
\(614\) −2.48062e14 −0.114719
\(615\) −4.44542e13 −0.0203751
\(616\) 1.68913e15 0.767307
\(617\) −1.88470e15 −0.848542 −0.424271 0.905535i \(-0.639470\pi\)
−0.424271 + 0.905535i \(0.639470\pi\)
\(618\) 5.49939e13 0.0245402
\(619\) −1.49500e15 −0.661215 −0.330607 0.943768i \(-0.607254\pi\)
−0.330607 + 0.943768i \(0.607254\pi\)
\(620\) −5.01502e14 −0.219846
\(621\) −6.12066e14 −0.265947
\(622\) −5.99463e14 −0.258176
\(623\) 3.17125e15 1.35377
\(624\) 2.10223e14 0.0889538
\(625\) 6.79327e14 0.284931
\(626\) 1.94506e14 0.0808675
\(627\) −1.18136e15 −0.486866
\(628\) 2.81715e15 1.15088
\(629\) 1.50836e15 0.610840
\(630\) 1.52792e14 0.0613379
\(631\) −2.92460e15 −1.16387 −0.581937 0.813234i \(-0.697705\pi\)
−0.581937 + 0.813234i \(0.697705\pi\)
\(632\) 8.05160e14 0.317642
\(633\) 2.37459e15 0.928686
\(634\) −5.32293e14 −0.206376
\(635\) 1.23186e15 0.473484
\(636\) 5.06314e14 0.192933
\(637\) −6.07775e14 −0.229602
\(638\) −1.89158e14 −0.0708454
\(639\) −4.39989e14 −0.163376
\(640\) 1.14991e15 0.423323
\(641\) −3.97230e15 −1.44985 −0.724925 0.688828i \(-0.758126\pi\)
−0.724925 + 0.688828i \(0.758126\pi\)
\(642\) −4.27280e14 −0.154621
\(643\) 2.53653e15 0.910081 0.455040 0.890471i \(-0.349625\pi\)
0.455040 + 0.890471i \(0.349625\pi\)
\(644\) 5.47171e15 1.94648
\(645\) 8.94978e14 0.315670
\(646\) 2.86939e14 0.100348
\(647\) 1.99270e15 0.690985 0.345493 0.938421i \(-0.387712\pi\)
0.345493 + 0.938421i \(0.387712\pi\)
\(648\) 1.51149e14 0.0519690
\(649\) −4.18963e14 −0.142833
\(650\) −9.78029e13 −0.0330619
\(651\) 1.17638e15 0.394323
\(652\) 3.88988e15 1.29293
\(653\) 3.16053e15 1.04169 0.520844 0.853652i \(-0.325618\pi\)
0.520844 + 0.853652i \(0.325618\pi\)
\(654\) −2.14118e14 −0.0699802
\(655\) 1.82182e15 0.590444
\(656\) 1.78231e14 0.0572811
\(657\) 1.66033e15 0.529159
\(658\) 1.55180e15 0.490449
\(659\) 2.29959e15 0.720744 0.360372 0.932809i \(-0.382650\pi\)
0.360372 + 0.932809i \(0.382650\pi\)
\(660\) −9.80886e14 −0.304879
\(661\) 3.49964e14 0.107874 0.0539368 0.998544i \(-0.482823\pi\)
0.0539368 + 0.998544i \(0.482823\pi\)
\(662\) −1.09324e15 −0.334193
\(663\) 1.91783e14 0.0581416
\(664\) −1.18116e15 −0.355128
\(665\) 1.96945e15 0.587253
\(666\) −3.05912e14 −0.0904665
\(667\) −1.26324e15 −0.370505
\(668\) 4.14327e15 1.20524
\(669\) −2.33675e14 −0.0674169
\(670\) −7.01908e14 −0.200849
\(671\) −5.06944e15 −1.43875
\(672\) −2.04704e15 −0.576228
\(673\) −5.14921e15 −1.43766 −0.718832 0.695184i \(-0.755323\pi\)
−0.718832 + 0.695184i \(0.755323\pi\)
\(674\) −5.68173e13 −0.0157344
\(675\) 5.17712e14 0.142206
\(676\) 3.33811e15 0.909483
\(677\) −2.04118e15 −0.551626 −0.275813 0.961211i \(-0.588947\pi\)
−0.275813 + 0.961211i \(0.588947\pi\)
\(678\) −5.20812e14 −0.139610
\(679\) −3.03888e15 −0.808033
\(680\) 4.91165e14 0.129547
\(681\) 3.62883e15 0.949419
\(682\) 4.65045e14 0.120693
\(683\) 2.53084e15 0.651554 0.325777 0.945447i \(-0.394374\pi\)
0.325777 + 0.945447i \(0.394374\pi\)
\(684\) 9.45039e14 0.241347
\(685\) 1.90867e15 0.483541
\(686\) 3.38056e14 0.0849584
\(687\) −8.01889e14 −0.199918
\(688\) −3.58824e15 −0.887453
\(689\) −2.68605e14 −0.0659035
\(690\) 4.03375e14 0.0981835
\(691\) −2.87994e15 −0.695430 −0.347715 0.937600i \(-0.613042\pi\)
−0.347715 + 0.937600i \(0.613042\pi\)
\(692\) −5.79979e15 −1.38940
\(693\) 2.30088e15 0.546841
\(694\) 9.35047e13 0.0220473
\(695\) 2.04003e15 0.477221
\(696\) 3.11957e14 0.0724008
\(697\) 1.62597e14 0.0374398
\(698\) −7.27609e14 −0.166224
\(699\) −1.27570e15 −0.289150
\(700\) −4.62821e15 −1.04082
\(701\) 8.64233e14 0.192833 0.0964166 0.995341i \(-0.469262\pi\)
0.0964166 + 0.995341i \(0.469262\pi\)
\(702\) −3.88957e13 −0.00861087
\(703\) −3.94311e15 −0.866133
\(704\) 3.36561e15 0.733524
\(705\) −1.85777e15 −0.401746
\(706\) 4.23406e14 0.0908512
\(707\) 7.00561e15 1.49156
\(708\) 3.35154e14 0.0708046
\(709\) 5.64182e15 1.18267 0.591337 0.806424i \(-0.298600\pi\)
0.591337 + 0.806424i \(0.298600\pi\)
\(710\) 2.89970e14 0.0603159
\(711\) 1.09676e15 0.226376
\(712\) −2.06750e15 −0.423454
\(713\) 3.10567e15 0.631193
\(714\) −5.58860e14 −0.112710
\(715\) 5.20371e14 0.104143
\(716\) 5.58383e15 1.10895
\(717\) 2.57914e15 0.508299
\(718\) −1.16525e15 −0.227894
\(719\) 8.02417e15 1.55737 0.778684 0.627416i \(-0.215888\pi\)
0.778684 + 0.627416i \(0.215888\pi\)
\(720\) 7.33376e14 0.141253
\(721\) −1.38061e15 −0.263892
\(722\) 5.19572e14 0.0985579
\(723\) −1.68596e15 −0.317384
\(724\) 9.22057e15 1.72264
\(725\) 1.06850e15 0.198115
\(726\) 1.53914e14 0.0283222
\(727\) 4.28976e15 0.783419 0.391710 0.920089i \(-0.371884\pi\)
0.391710 + 0.920089i \(0.371884\pi\)
\(728\) 7.16846e14 0.129928
\(729\) 2.05891e14 0.0370370
\(730\) −1.09422e15 −0.195358
\(731\) −3.27351e15 −0.580053
\(732\) 4.05535e15 0.713211
\(733\) 8.93218e15 1.55914 0.779571 0.626314i \(-0.215437\pi\)
0.779571 + 0.626314i \(0.215437\pi\)
\(734\) 1.89963e15 0.329110
\(735\) −2.12026e15 −0.364594
\(736\) −5.40421e15 −0.922369
\(737\) −1.05699e16 −1.79061
\(738\) −3.29764e13 −0.00554490
\(739\) −2.28468e15 −0.381313 −0.190657 0.981657i \(-0.561062\pi\)
−0.190657 + 0.981657i \(0.561062\pi\)
\(740\) −3.27398e15 −0.542378
\(741\) −5.01353e14 −0.0824411
\(742\) 7.82719e14 0.127757
\(743\) −1.52362e15 −0.246853 −0.123427 0.992354i \(-0.539388\pi\)
−0.123427 + 0.992354i \(0.539388\pi\)
\(744\) −7.66943e14 −0.123342
\(745\) 2.18380e15 0.348620
\(746\) −1.98320e15 −0.314270
\(747\) −1.60894e15 −0.253091
\(748\) 3.58773e15 0.560223
\(749\) 1.07268e16 1.66272
\(750\) −8.02934e14 −0.123550
\(751\) −6.85472e15 −1.04706 −0.523528 0.852008i \(-0.675385\pi\)
−0.523528 + 0.852008i \(0.675385\pi\)
\(752\) 7.44837e15 1.12944
\(753\) −2.63591e15 −0.396788
\(754\) −8.02765e13 −0.0119963
\(755\) −3.42528e15 −0.508145
\(756\) −1.84061e15 −0.271077
\(757\) −1.54090e15 −0.225293 −0.112647 0.993635i \(-0.535933\pi\)
−0.112647 + 0.993635i \(0.535933\pi\)
\(758\) 1.09625e15 0.159122
\(759\) 6.07436e15 0.875329
\(760\) −1.28399e15 −0.183690
\(761\) 1.02518e16 1.45607 0.728037 0.685538i \(-0.240433\pi\)
0.728037 + 0.685538i \(0.240433\pi\)
\(762\) 9.13801e14 0.128854
\(763\) 5.37538e15 0.752530
\(764\) 8.52698e15 1.18517
\(765\) 6.69049e14 0.0923252
\(766\) 3.91975e14 0.0537032
\(767\) −1.77803e14 −0.0241860
\(768\) −2.00514e15 −0.270806
\(769\) −1.26692e16 −1.69884 −0.849421 0.527715i \(-0.823049\pi\)
−0.849421 + 0.527715i \(0.823049\pi\)
\(770\) −1.51637e15 −0.201886
\(771\) 1.44625e15 0.191181
\(772\) −6.29199e15 −0.825834
\(773\) −9.49478e15 −1.23736 −0.618682 0.785641i \(-0.712333\pi\)
−0.618682 + 0.785641i \(0.712333\pi\)
\(774\) 6.63901e14 0.0859069
\(775\) −2.62691e15 −0.337509
\(776\) 1.98120e15 0.252749
\(777\) 7.67984e15 0.972829
\(778\) −3.61176e15 −0.454288
\(779\) −4.25056e14 −0.0530873
\(780\) −4.16276e14 −0.0516252
\(781\) 4.36661e15 0.537730
\(782\) −1.47540e15 −0.180415
\(783\) 4.24938e14 0.0515983
\(784\) 8.50079e15 1.02499
\(785\) −5.21376e15 −0.624264
\(786\) 1.35144e15 0.160684
\(787\) −8.98457e15 −1.06081 −0.530403 0.847745i \(-0.677960\pi\)
−0.530403 + 0.847745i \(0.677960\pi\)
\(788\) −3.38137e15 −0.396460
\(789\) 2.16027e15 0.251527
\(790\) −7.22810e14 −0.0835747
\(791\) 1.30748e16 1.50129
\(792\) −1.50006e15 −0.171049
\(793\) −2.15141e15 −0.243624
\(794\) −2.48078e15 −0.278981
\(795\) −9.37047e14 −0.104651
\(796\) −2.44023e15 −0.270650
\(797\) −6.11982e15 −0.674090 −0.337045 0.941488i \(-0.609428\pi\)
−0.337045 + 0.941488i \(0.609428\pi\)
\(798\) 1.46095e15 0.159816
\(799\) 6.79505e15 0.738219
\(800\) 4.57112e15 0.493205
\(801\) −2.81629e15 −0.301785
\(802\) 1.81914e15 0.193601
\(803\) −1.64778e16 −1.74166
\(804\) 8.45554e15 0.887632
\(805\) −1.01266e16 −1.05581
\(806\) 1.97359e14 0.0204369
\(807\) −1.01162e16 −1.04043
\(808\) −4.56732e15 −0.466551
\(809\) 2.16381e15 0.219534 0.109767 0.993957i \(-0.464990\pi\)
0.109767 + 0.993957i \(0.464990\pi\)
\(810\) −1.35690e14 −0.0136735
\(811\) 6.81862e15 0.682467 0.341233 0.939979i \(-0.389155\pi\)
0.341233 + 0.939979i \(0.389155\pi\)
\(812\) −3.79883e15 −0.377652
\(813\) 7.79427e15 0.769622
\(814\) 3.03598e15 0.297759
\(815\) −7.19910e15 −0.701312
\(816\) −2.68243e15 −0.259556
\(817\) 8.55748e15 0.822479
\(818\) −1.32632e15 −0.126620
\(819\) 9.76466e14 0.0925967
\(820\) −3.52926e14 −0.0332436
\(821\) −1.02535e16 −0.959370 −0.479685 0.877441i \(-0.659249\pi\)
−0.479685 + 0.877441i \(0.659249\pi\)
\(822\) 1.41587e15 0.131591
\(823\) −1.50827e16 −1.39245 −0.696227 0.717822i \(-0.745139\pi\)
−0.696227 + 0.717822i \(0.745139\pi\)
\(824\) 9.00091e14 0.0825442
\(825\) −5.13796e15 −0.468052
\(826\) 5.18120e14 0.0468856
\(827\) −1.09528e16 −0.984562 −0.492281 0.870436i \(-0.663837\pi\)
−0.492281 + 0.870436i \(0.663837\pi\)
\(828\) −4.85925e15 −0.433913
\(829\) 1.00515e15 0.0891620 0.0445810 0.999006i \(-0.485805\pi\)
0.0445810 + 0.999006i \(0.485805\pi\)
\(830\) 1.06035e15 0.0934375
\(831\) −7.64966e15 −0.669633
\(832\) 1.42833e15 0.124208
\(833\) 7.75516e15 0.669951
\(834\) 1.51331e15 0.129871
\(835\) −7.66805e15 −0.653747
\(836\) −9.37891e15 −0.794361
\(837\) −1.04471e15 −0.0879031
\(838\) 5.06436e15 0.423334
\(839\) 1.23063e16 1.02196 0.510982 0.859591i \(-0.329282\pi\)
0.510982 + 0.859591i \(0.329282\pi\)
\(840\) 2.50077e15 0.206318
\(841\) −1.13235e16 −0.928116
\(842\) −3.34125e15 −0.272077
\(843\) 3.30415e15 0.267306
\(844\) 1.88522e16 1.51523
\(845\) −6.17792e15 −0.493322
\(846\) −1.37811e15 −0.109332
\(847\) −3.86397e15 −0.304562
\(848\) 3.75691e15 0.294207
\(849\) −5.65356e15 −0.439875
\(850\) 1.24796e15 0.0964707
\(851\) 2.02749e16 1.55721
\(852\) −3.49312e15 −0.266560
\(853\) 1.92488e16 1.45943 0.729716 0.683750i \(-0.239652\pi\)
0.729716 + 0.683750i \(0.239652\pi\)
\(854\) 6.26924e15 0.472277
\(855\) −1.74900e15 −0.130911
\(856\) −6.99333e15 −0.520089
\(857\) 1.82821e13 0.00135093 0.000675463 1.00000i \(-0.499785\pi\)
0.000675463 1.00000i \(0.499785\pi\)
\(858\) 3.86015e14 0.0283416
\(859\) 8.50521e15 0.620472 0.310236 0.950660i \(-0.399592\pi\)
0.310236 + 0.950660i \(0.399592\pi\)
\(860\) 7.10532e15 0.515042
\(861\) 8.27865e14 0.0596269
\(862\) 3.44011e15 0.246197
\(863\) −1.21922e16 −0.867005 −0.433502 0.901152i \(-0.642722\pi\)
−0.433502 + 0.901152i \(0.642722\pi\)
\(864\) 1.81791e15 0.128454
\(865\) 1.07338e16 0.753642
\(866\) 5.68687e14 0.0396757
\(867\) 5.88093e15 0.407700
\(868\) 9.33941e15 0.643370
\(869\) −1.08847e16 −0.745088
\(870\) −2.80050e14 −0.0190493
\(871\) −4.48575e15 −0.303204
\(872\) −3.50449e15 −0.235388
\(873\) 2.69873e15 0.180128
\(874\) 3.85694e15 0.255817
\(875\) 2.01575e16 1.32859
\(876\) 1.31816e16 0.863365
\(877\) 1.97025e16 1.28240 0.641202 0.767373i \(-0.278436\pi\)
0.641202 + 0.767373i \(0.278436\pi\)
\(878\) 5.18610e15 0.335445
\(879\) −7.89026e15 −0.507169
\(880\) −7.27829e15 −0.464916
\(881\) 1.51238e16 0.960047 0.480023 0.877256i \(-0.340628\pi\)
0.480023 + 0.877256i \(0.340628\pi\)
\(882\) −1.57283e15 −0.0992210
\(883\) −7.01193e15 −0.439596 −0.219798 0.975545i \(-0.570540\pi\)
−0.219798 + 0.975545i \(0.570540\pi\)
\(884\) 1.52259e15 0.0948626
\(885\) −6.20277e14 −0.0384059
\(886\) 2.60040e15 0.160013
\(887\) −1.24879e15 −0.0763677 −0.0381839 0.999271i \(-0.512157\pi\)
−0.0381839 + 0.999271i \(0.512157\pi\)
\(888\) −5.00688e15 −0.304296
\(889\) −2.29408e16 −1.38563
\(890\) 1.85604e15 0.111415
\(891\) −2.04334e15 −0.121903
\(892\) −1.85517e15 −0.109996
\(893\) −1.77634e16 −1.04675
\(894\) 1.61996e15 0.0948739
\(895\) −1.03341e16 −0.601516
\(896\) −2.14146e16 −1.23884
\(897\) 2.57789e15 0.148220
\(898\) −2.75742e15 −0.157574
\(899\) −2.15616e15 −0.122463
\(900\) 4.11017e15 0.232020
\(901\) 3.42738e15 0.192299
\(902\) 3.27270e14 0.0182503
\(903\) −1.66671e16 −0.923797
\(904\) −8.52417e15 −0.469598
\(905\) −1.70647e16 −0.934398
\(906\) −2.54089e15 −0.138287
\(907\) 9.02571e15 0.488249 0.244124 0.969744i \(-0.421499\pi\)
0.244124 + 0.969744i \(0.421499\pi\)
\(908\) 2.88097e16 1.54905
\(909\) −6.22147e15 −0.332500
\(910\) −6.43528e14 −0.0341853
\(911\) −1.08368e16 −0.572201 −0.286101 0.958200i \(-0.592359\pi\)
−0.286101 + 0.958200i \(0.592359\pi\)
\(912\) 7.01230e15 0.368035
\(913\) 1.59677e16 0.833017
\(914\) 1.96198e15 0.101740
\(915\) −7.50534e15 −0.386860
\(916\) −6.36628e15 −0.326182
\(917\) −3.39275e16 −1.72791
\(918\) 4.96306e14 0.0251255
\(919\) −1.63964e16 −0.825112 −0.412556 0.910932i \(-0.635364\pi\)
−0.412556 + 0.910932i \(0.635364\pi\)
\(920\) 6.60207e15 0.330253
\(921\) −5.53047e15 −0.275001
\(922\) −9.45670e15 −0.467433
\(923\) 1.85314e15 0.0910539
\(924\) 1.82669e16 0.892215
\(925\) −1.71494e16 −0.832663
\(926\) −7.61882e15 −0.367729
\(927\) 1.22608e15 0.0588273
\(928\) 3.75197e15 0.178956
\(929\) 3.91452e16 1.85606 0.928031 0.372504i \(-0.121501\pi\)
0.928031 + 0.372504i \(0.121501\pi\)
\(930\) 6.88501e14 0.0324525
\(931\) −2.02733e16 −0.949949
\(932\) −1.01279e16 −0.471771
\(933\) −1.33649e16 −0.618893
\(934\) 3.48810e15 0.160576
\(935\) −6.63989e15 −0.303876
\(936\) −6.36609e14 −0.0289638
\(937\) −1.21357e15 −0.0548906 −0.0274453 0.999623i \(-0.508737\pi\)
−0.0274453 + 0.999623i \(0.508737\pi\)
\(938\) 1.30715e16 0.587775
\(939\) 4.33646e15 0.193854
\(940\) −1.47490e16 −0.655481
\(941\) −9.02660e15 −0.398824 −0.199412 0.979916i \(-0.563903\pi\)
−0.199412 + 0.979916i \(0.563903\pi\)
\(942\) −3.86761e15 −0.169888
\(943\) 2.18558e15 0.0954448
\(944\) 2.48688e15 0.107971
\(945\) 3.40647e15 0.147038
\(946\) −6.58880e15 −0.282751
\(947\) −3.18898e15 −0.136059 −0.0680295 0.997683i \(-0.521671\pi\)
−0.0680295 + 0.997683i \(0.521671\pi\)
\(948\) 8.70733e15 0.369351
\(949\) −6.99297e15 −0.294915
\(950\) −3.26236e15 −0.136789
\(951\) −1.18673e16 −0.494721
\(952\) −9.14690e15 −0.379115
\(953\) −2.20951e16 −0.910510 −0.455255 0.890361i \(-0.650452\pi\)
−0.455255 + 0.890361i \(0.650452\pi\)
\(954\) −6.95108e14 −0.0284798
\(955\) −1.57811e16 −0.642863
\(956\) 2.04760e16 0.829330
\(957\) −4.21724e15 −0.169829
\(958\) 2.73616e15 0.109555
\(959\) −3.55450e16 −1.41506
\(960\) 4.98281e15 0.197234
\(961\) −2.01076e16 −0.791372
\(962\) 1.28843e15 0.0504196
\(963\) −9.52609e15 −0.370655
\(964\) −1.33850e16 −0.517838
\(965\) 1.16447e16 0.447950
\(966\) −7.51200e15 −0.287330
\(967\) 2.73879e16 1.04163 0.520814 0.853670i \(-0.325629\pi\)
0.520814 + 0.853670i \(0.325629\pi\)
\(968\) 2.51912e15 0.0952654
\(969\) 6.39723e15 0.240553
\(970\) −1.77857e15 −0.0665006
\(971\) −4.51755e16 −1.67957 −0.839784 0.542921i \(-0.817318\pi\)
−0.839784 + 0.542921i \(0.817318\pi\)
\(972\) 1.63459e15 0.0604289
\(973\) −3.79911e16 −1.39657
\(974\) 2.88129e15 0.105320
\(975\) −2.18049e15 −0.0792554
\(976\) 3.00912e16 1.08759
\(977\) −2.54411e16 −0.914356 −0.457178 0.889375i \(-0.651140\pi\)
−0.457178 + 0.889375i \(0.651140\pi\)
\(978\) −5.34034e15 −0.190856
\(979\) 2.79499e16 0.993288
\(980\) −1.68330e16 −0.594864
\(981\) −4.77370e15 −0.167755
\(982\) 1.78596e15 0.0624107
\(983\) 2.71225e16 0.942508 0.471254 0.881997i \(-0.343801\pi\)
0.471254 + 0.881997i \(0.343801\pi\)
\(984\) −5.39728e14 −0.0186510
\(985\) 6.25799e15 0.215048
\(986\) 1.02432e15 0.0350037
\(987\) 3.45970e16 1.17569
\(988\) −3.98030e15 −0.134509
\(989\) −4.40014e16 −1.47872
\(990\) 1.34664e15 0.0450046
\(991\) 5.91660e16 1.96638 0.983189 0.182591i \(-0.0584483\pi\)
0.983189 + 0.182591i \(0.0584483\pi\)
\(992\) −9.22420e15 −0.304870
\(993\) −2.43735e16 −0.801121
\(994\) −5.40007e15 −0.176512
\(995\) 4.51619e15 0.146806
\(996\) −1.27736e16 −0.412938
\(997\) 1.87920e16 0.604158 0.302079 0.953283i \(-0.402319\pi\)
0.302079 + 0.953283i \(0.402319\pi\)
\(998\) 1.42626e14 0.00456018
\(999\) −6.82022e15 −0.216864
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.1.13 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.13 26 1.1 even 1 trivial