Properties

Label 177.10.a.d.1.9
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} -2681.84 q^{10} -24455.7 q^{11} -34040.4 q^{12} -4184.11 q^{13} -76178.7 q^{14} +22678.8 q^{15} +129636. q^{16} +164024. q^{17} -62844.7 q^{18} +826643. q^{19} -117664. q^{20} +644198. q^{21} +234249. q^{22} +840452. q^{23} +723298. q^{24} -1.87473e6 q^{25} +40077.6 q^{26} +531441. q^{27} -3.34229e6 q^{28} +6.86036e6 q^{29} -217229. q^{30} -1.00194e7 q^{31} -5.81368e6 q^{32} -1.98091e6 q^{33} -1.57111e6 q^{34} +2.22674e6 q^{35} -2.75727e6 q^{36} +2.02637e6 q^{37} -7.91803e6 q^{38} -338913. q^{39} +2.50015e6 q^{40} -2.68086e7 q^{41} -6.17047e6 q^{42} +3.41186e7 q^{43} +1.02775e7 q^{44} +1.83698e6 q^{45} -8.05029e6 q^{46} -1.02082e7 q^{47} +1.05006e7 q^{48} +2.28976e7 q^{49} +1.79572e7 q^{50} +1.32859e7 q^{51} +1.75838e6 q^{52} -1.18232e7 q^{53} -5.09042e6 q^{54} -6.84722e6 q^{55} +7.10177e7 q^{56} +6.69581e7 q^{57} -6.57122e7 q^{58} -1.21174e7 q^{59} -9.53080e6 q^{60} +2.71179e7 q^{61} +9.59710e7 q^{62} +5.21801e7 q^{63} -1.06874e7 q^{64} -1.17149e6 q^{65} +1.89742e7 q^{66} -5.94366e7 q^{67} -6.89314e7 q^{68} +6.80766e7 q^{69} -2.13289e7 q^{70} -8.70465e7 q^{71} +5.85871e7 q^{72} +5.93796e7 q^{73} -1.94096e7 q^{74} -1.51853e8 q^{75} -3.47398e8 q^{76} -1.94497e8 q^{77} +3.24628e6 q^{78} +4.90761e8 q^{79} +3.62963e7 q^{80} +4.30467e7 q^{81} +2.56787e8 q^{82} -8.27340e7 q^{83} -2.70725e8 q^{84} +4.59243e7 q^{85} -3.26806e8 q^{86} +5.55689e8 q^{87} -2.18379e8 q^{88} +6.23380e8 q^{89} -1.75956e7 q^{90} -3.32765e7 q^{91} -3.53201e8 q^{92} -8.11570e8 q^{93} +9.77792e7 q^{94} +2.31448e8 q^{95} -4.70908e8 q^{96} +1.98677e8 q^{97} -2.19326e8 q^{98} -1.60454e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.57853 −0.423315 −0.211658 0.977344i \(-0.567886\pi\)
−0.211658 + 0.977344i \(0.567886\pi\)
\(3\) 81.0000 0.577350
\(4\) −420.252 −0.820804
\(5\) 279.985 0.200341 0.100170 0.994970i \(-0.468061\pi\)
0.100170 + 0.994970i \(0.468061\pi\)
\(6\) −775.861 −0.244401
\(7\) 7953.06 1.25197 0.625984 0.779836i \(-0.284697\pi\)
0.625984 + 0.779836i \(0.284697\pi\)
\(8\) 8929.60 0.770774
\(9\) 6561.00 0.333333
\(10\) −2681.84 −0.0848074
\(11\) −24455.7 −0.503631 −0.251815 0.967775i \(-0.581028\pi\)
−0.251815 + 0.967775i \(0.581028\pi\)
\(12\) −34040.4 −0.473892
\(13\) −4184.11 −0.0406310 −0.0203155 0.999794i \(-0.506467\pi\)
−0.0203155 + 0.999794i \(0.506467\pi\)
\(14\) −76178.7 −0.529977
\(15\) 22678.8 0.115667
\(16\) 129636. 0.494524
\(17\) 164024. 0.476307 0.238154 0.971227i \(-0.423458\pi\)
0.238154 + 0.971227i \(0.423458\pi\)
\(18\) −62844.7 −0.141105
\(19\) 826643. 1.45521 0.727607 0.685994i \(-0.240632\pi\)
0.727607 + 0.685994i \(0.240632\pi\)
\(20\) −117664. −0.164441
\(21\) 644198. 0.722824
\(22\) 234249. 0.213195
\(23\) 840452. 0.626235 0.313118 0.949714i \(-0.398627\pi\)
0.313118 + 0.949714i \(0.398627\pi\)
\(24\) 723298. 0.445007
\(25\) −1.87473e6 −0.959863
\(26\) 40077.6 0.0171997
\(27\) 531441. 0.192450
\(28\) −3.34229e6 −1.02762
\(29\) 6.86036e6 1.80118 0.900588 0.434674i \(-0.143136\pi\)
0.900588 + 0.434674i \(0.143136\pi\)
\(30\) −217229. −0.0489636
\(31\) −1.00194e7 −1.94856 −0.974279 0.225344i \(-0.927649\pi\)
−0.974279 + 0.225344i \(0.927649\pi\)
\(32\) −5.81368e6 −0.980114
\(33\) −1.98091e6 −0.290771
\(34\) −1.57111e6 −0.201628
\(35\) 2.22674e6 0.250821
\(36\) −2.75727e6 −0.273601
\(37\) 2.02637e6 0.177751 0.0888753 0.996043i \(-0.471673\pi\)
0.0888753 + 0.996043i \(0.471673\pi\)
\(38\) −7.91803e6 −0.616014
\(39\) −338913. −0.0234583
\(40\) 2.50015e6 0.154418
\(41\) −2.68086e7 −1.48165 −0.740827 0.671696i \(-0.765566\pi\)
−0.740827 + 0.671696i \(0.765566\pi\)
\(42\) −6.17047e6 −0.305982
\(43\) 3.41186e7 1.52189 0.760944 0.648818i \(-0.224736\pi\)
0.760944 + 0.648818i \(0.224736\pi\)
\(44\) 1.02775e7 0.413382
\(45\) 1.83698e6 0.0667803
\(46\) −8.05029e6 −0.265095
\(47\) −1.02082e7 −0.305146 −0.152573 0.988292i \(-0.548756\pi\)
−0.152573 + 0.988292i \(0.548756\pi\)
\(48\) 1.05006e7 0.285514
\(49\) 2.28976e7 0.567425
\(50\) 1.79572e7 0.406325
\(51\) 1.32859e7 0.274996
\(52\) 1.75838e6 0.0333501
\(53\) −1.18232e7 −0.205823 −0.102911 0.994691i \(-0.532816\pi\)
−0.102911 + 0.994691i \(0.532816\pi\)
\(54\) −5.09042e6 −0.0814670
\(55\) −6.84722e6 −0.100898
\(56\) 7.10177e7 0.964985
\(57\) 6.69581e7 0.840169
\(58\) −6.57122e7 −0.762465
\(59\) −1.21174e7 −0.130189
\(60\) −9.53080e6 −0.0949399
\(61\) 2.71179e7 0.250768 0.125384 0.992108i \(-0.459984\pi\)
0.125384 + 0.992108i \(0.459984\pi\)
\(62\) 9.59710e7 0.824854
\(63\) 5.21801e7 0.417323
\(64\) −1.06874e7 −0.0796271
\(65\) −1.17149e6 −0.00814006
\(66\) 1.89742e7 0.123088
\(67\) −5.94366e7 −0.360344 −0.180172 0.983635i \(-0.557665\pi\)
−0.180172 + 0.983635i \(0.557665\pi\)
\(68\) −6.89314e7 −0.390955
\(69\) 6.80766e7 0.361557
\(70\) −2.13289e7 −0.106176
\(71\) −8.70465e7 −0.406527 −0.203263 0.979124i \(-0.565155\pi\)
−0.203263 + 0.979124i \(0.565155\pi\)
\(72\) 5.85871e7 0.256925
\(73\) 5.93796e7 0.244728 0.122364 0.992485i \(-0.460952\pi\)
0.122364 + 0.992485i \(0.460952\pi\)
\(74\) −1.94096e7 −0.0752445
\(75\) −1.51853e8 −0.554177
\(76\) −3.47398e8 −1.19445
\(77\) −1.94497e8 −0.630530
\(78\) 3.24628e6 0.00993027
\(79\) 4.90761e8 1.41758 0.708791 0.705418i \(-0.249241\pi\)
0.708791 + 0.705418i \(0.249241\pi\)
\(80\) 3.62963e7 0.0990734
\(81\) 4.30467e7 0.111111
\(82\) 2.56787e8 0.627206
\(83\) −8.27340e7 −0.191352 −0.0956759 0.995413i \(-0.530501\pi\)
−0.0956759 + 0.995413i \(0.530501\pi\)
\(84\) −2.70725e8 −0.593297
\(85\) 4.59243e7 0.0954239
\(86\) −3.26806e8 −0.644238
\(87\) 5.55689e8 1.03991
\(88\) −2.18379e8 −0.388185
\(89\) 6.23380e8 1.05317 0.526584 0.850123i \(-0.323473\pi\)
0.526584 + 0.850123i \(0.323473\pi\)
\(90\) −1.75956e7 −0.0282691
\(91\) −3.32765e7 −0.0508687
\(92\) −3.53201e8 −0.514017
\(93\) −8.11570e8 −1.12500
\(94\) 9.77792e7 0.129173
\(95\) 2.31448e8 0.291539
\(96\) −4.70908e8 −0.565869
\(97\) 1.98677e8 0.227864 0.113932 0.993489i \(-0.463655\pi\)
0.113932 + 0.993489i \(0.463655\pi\)
\(98\) −2.19326e8 −0.240199
\(99\) −1.60454e8 −0.167877
\(100\) 7.87860e8 0.787860
\(101\) 3.04753e8 0.291408 0.145704 0.989328i \(-0.453455\pi\)
0.145704 + 0.989328i \(0.453455\pi\)
\(102\) −1.27260e8 −0.116410
\(103\) 3.83311e8 0.335570 0.167785 0.985824i \(-0.446339\pi\)
0.167785 + 0.985824i \(0.446339\pi\)
\(104\) −3.73624e7 −0.0313173
\(105\) 1.80366e8 0.144811
\(106\) 1.13249e8 0.0871280
\(107\) 1.92857e9 1.42236 0.711178 0.703012i \(-0.248162\pi\)
0.711178 + 0.703012i \(0.248162\pi\)
\(108\) −2.23339e8 −0.157964
\(109\) 9.41013e8 0.638523 0.319261 0.947667i \(-0.396565\pi\)
0.319261 + 0.947667i \(0.396565\pi\)
\(110\) 6.55863e7 0.0427116
\(111\) 1.64136e8 0.102624
\(112\) 1.03101e9 0.619128
\(113\) 1.25727e9 0.725398 0.362699 0.931906i \(-0.381855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(114\) −6.41360e8 −0.355656
\(115\) 2.35314e8 0.125461
\(116\) −2.88308e9 −1.47841
\(117\) −2.74519e7 −0.0135437
\(118\) 1.16066e8 0.0551109
\(119\) 1.30449e9 0.596322
\(120\) 2.02513e8 0.0891531
\(121\) −1.75987e9 −0.746356
\(122\) −2.59750e8 −0.106154
\(123\) −2.17150e9 −0.855433
\(124\) 4.21066e9 1.59939
\(125\) −1.07174e9 −0.392641
\(126\) −4.99808e8 −0.176659
\(127\) 2.25881e8 0.0770483 0.0385242 0.999258i \(-0.487734\pi\)
0.0385242 + 0.999258i \(0.487734\pi\)
\(128\) 3.07897e9 1.01382
\(129\) 2.76360e9 0.878662
\(130\) 1.12211e7 0.00344581
\(131\) 8.52863e8 0.253022 0.126511 0.991965i \(-0.459622\pi\)
0.126511 + 0.991965i \(0.459622\pi\)
\(132\) 8.32480e8 0.238666
\(133\) 6.57435e9 1.82188
\(134\) 5.69315e8 0.152539
\(135\) 1.48796e8 0.0385556
\(136\) 1.46467e9 0.367125
\(137\) 4.73702e9 1.14885 0.574424 0.818558i \(-0.305226\pi\)
0.574424 + 0.818558i \(0.305226\pi\)
\(138\) −6.52073e8 −0.153053
\(139\) 8.40208e8 0.190906 0.0954531 0.995434i \(-0.469570\pi\)
0.0954531 + 0.995434i \(0.469570\pi\)
\(140\) −9.35791e8 −0.205875
\(141\) −8.26862e8 −0.176176
\(142\) 8.33778e8 0.172089
\(143\) 1.02325e8 0.0204630
\(144\) 8.50545e8 0.164841
\(145\) 1.92080e9 0.360849
\(146\) −5.68769e8 −0.103597
\(147\) 1.85471e9 0.327603
\(148\) −8.51585e8 −0.145898
\(149\) 4.22892e9 0.702896 0.351448 0.936207i \(-0.385689\pi\)
0.351448 + 0.936207i \(0.385689\pi\)
\(150\) 1.45453e9 0.234592
\(151\) −1.20936e9 −0.189304 −0.0946520 0.995510i \(-0.530174\pi\)
−0.0946520 + 0.995510i \(0.530174\pi\)
\(152\) 7.38160e9 1.12164
\(153\) 1.07616e9 0.158769
\(154\) 1.86300e9 0.266913
\(155\) −2.80528e9 −0.390376
\(156\) 1.42429e8 0.0192547
\(157\) 9.30072e9 1.22171 0.610855 0.791742i \(-0.290826\pi\)
0.610855 + 0.791742i \(0.290826\pi\)
\(158\) −4.70077e9 −0.600084
\(159\) −9.57680e8 −0.118832
\(160\) −1.62774e9 −0.196357
\(161\) 6.68417e9 0.784027
\(162\) −4.12324e8 −0.0470350
\(163\) 1.77937e10 1.97434 0.987169 0.159676i \(-0.0510450\pi\)
0.987169 + 0.159676i \(0.0510450\pi\)
\(164\) 1.12664e10 1.21615
\(165\) −5.54625e8 −0.0582534
\(166\) 7.92470e8 0.0810021
\(167\) 4.36596e9 0.434366 0.217183 0.976131i \(-0.430313\pi\)
0.217183 + 0.976131i \(0.430313\pi\)
\(168\) 5.75243e9 0.557134
\(169\) −1.05870e10 −0.998349
\(170\) −4.39887e8 −0.0403944
\(171\) 5.42361e9 0.485072
\(172\) −1.43384e10 −1.24917
\(173\) 2.07485e10 1.76108 0.880540 0.473971i \(-0.157180\pi\)
0.880540 + 0.473971i \(0.157180\pi\)
\(174\) −5.32269e9 −0.440209
\(175\) −1.49099e10 −1.20172
\(176\) −3.17035e9 −0.249057
\(177\) −9.81506e8 −0.0751646
\(178\) −5.97106e9 −0.445822
\(179\) −1.25662e10 −0.914881 −0.457441 0.889240i \(-0.651234\pi\)
−0.457441 + 0.889240i \(0.651234\pi\)
\(180\) −7.71995e8 −0.0548136
\(181\) −1.09358e8 −0.00757349 −0.00378674 0.999993i \(-0.501205\pi\)
−0.00378674 + 0.999993i \(0.501205\pi\)
\(182\) 3.18740e8 0.0215335
\(183\) 2.19655e9 0.144781
\(184\) 7.50490e9 0.482686
\(185\) 5.67353e8 0.0356107
\(186\) 7.77365e9 0.476230
\(187\) −4.01131e9 −0.239883
\(188\) 4.29000e9 0.250465
\(189\) 4.22658e9 0.240941
\(190\) −2.21693e9 −0.123413
\(191\) 1.10145e10 0.598845 0.299423 0.954121i \(-0.403206\pi\)
0.299423 + 0.954121i \(0.403206\pi\)
\(192\) −8.65677e8 −0.0459727
\(193\) −2.89225e10 −1.50047 −0.750237 0.661169i \(-0.770061\pi\)
−0.750237 + 0.661169i \(0.770061\pi\)
\(194\) −1.90303e9 −0.0964581
\(195\) −9.48905e7 −0.00469966
\(196\) −9.62277e9 −0.465745
\(197\) −1.80535e10 −0.854010 −0.427005 0.904249i \(-0.640431\pi\)
−0.427005 + 0.904249i \(0.640431\pi\)
\(198\) 1.53691e9 0.0710648
\(199\) −2.31277e10 −1.04543 −0.522713 0.852509i \(-0.675080\pi\)
−0.522713 + 0.852509i \(0.675080\pi\)
\(200\) −1.67406e10 −0.739838
\(201\) −4.81436e9 −0.208045
\(202\) −2.91908e9 −0.123357
\(203\) 5.45609e10 2.25501
\(204\) −5.58344e9 −0.225718
\(205\) −7.50600e9 −0.296836
\(206\) −3.67155e9 −0.142052
\(207\) 5.51420e9 0.208745
\(208\) −5.42413e8 −0.0200930
\(209\) −2.02161e10 −0.732891
\(210\) −1.72764e9 −0.0613008
\(211\) 2.93108e9 0.101802 0.0509010 0.998704i \(-0.483791\pi\)
0.0509010 + 0.998704i \(0.483791\pi\)
\(212\) 4.96872e9 0.168940
\(213\) −7.05077e9 −0.234708
\(214\) −1.84729e10 −0.602105
\(215\) 9.55269e9 0.304897
\(216\) 4.74556e9 0.148336
\(217\) −7.96848e10 −2.43953
\(218\) −9.01352e9 −0.270296
\(219\) 4.80975e9 0.141294
\(220\) 2.87756e9 0.0828174
\(221\) −6.86294e8 −0.0193529
\(222\) −1.57218e9 −0.0434424
\(223\) −3.19223e10 −0.864414 −0.432207 0.901774i \(-0.642265\pi\)
−0.432207 + 0.901774i \(0.642265\pi\)
\(224\) −4.62366e10 −1.22707
\(225\) −1.23001e10 −0.319954
\(226\) −1.20428e10 −0.307072
\(227\) 4.18184e10 1.04532 0.522662 0.852540i \(-0.324939\pi\)
0.522662 + 0.852540i \(0.324939\pi\)
\(228\) −2.81393e10 −0.689614
\(229\) 7.18309e10 1.72604 0.863022 0.505167i \(-0.168569\pi\)
0.863022 + 0.505167i \(0.168569\pi\)
\(230\) −2.25396e9 −0.0531094
\(231\) −1.57543e10 −0.364036
\(232\) 6.12603e10 1.38830
\(233\) 2.46588e10 0.548113 0.274057 0.961714i \(-0.411634\pi\)
0.274057 + 0.961714i \(0.411634\pi\)
\(234\) 2.62949e8 0.00573324
\(235\) −2.85813e9 −0.0611332
\(236\) 5.09234e9 0.106860
\(237\) 3.97517e10 0.818442
\(238\) −1.24951e10 −0.252432
\(239\) 3.63090e10 0.719820 0.359910 0.932987i \(-0.382807\pi\)
0.359910 + 0.932987i \(0.382807\pi\)
\(240\) 2.94000e9 0.0572001
\(241\) 2.69176e10 0.513996 0.256998 0.966412i \(-0.417267\pi\)
0.256998 + 0.966412i \(0.417267\pi\)
\(242\) 1.68570e10 0.315944
\(243\) 3.48678e9 0.0641500
\(244\) −1.13964e10 −0.205832
\(245\) 6.41099e9 0.113678
\(246\) 2.07997e10 0.362118
\(247\) −3.45876e9 −0.0591268
\(248\) −8.94691e10 −1.50190
\(249\) −6.70146e9 −0.110477
\(250\) 1.02657e10 0.166211
\(251\) 8.57174e10 1.36313 0.681565 0.731758i \(-0.261300\pi\)
0.681565 + 0.731758i \(0.261300\pi\)
\(252\) −2.19288e10 −0.342540
\(253\) −2.05538e10 −0.315391
\(254\) −2.16361e9 −0.0326157
\(255\) 3.71987e9 0.0550930
\(256\) −2.40201e10 −0.349539
\(257\) −5.60139e10 −0.800934 −0.400467 0.916311i \(-0.631152\pi\)
−0.400467 + 0.916311i \(0.631152\pi\)
\(258\) −2.64713e10 −0.371951
\(259\) 1.61158e10 0.222538
\(260\) 4.92320e8 0.00668139
\(261\) 4.50108e10 0.600392
\(262\) −8.16917e9 −0.107108
\(263\) −5.53871e10 −0.713852 −0.356926 0.934133i \(-0.616175\pi\)
−0.356926 + 0.934133i \(0.616175\pi\)
\(264\) −1.76887e10 −0.224119
\(265\) −3.31032e9 −0.0412348
\(266\) −6.29726e10 −0.771230
\(267\) 5.04937e10 0.608047
\(268\) 2.49783e10 0.295772
\(269\) 1.29810e11 1.51155 0.755777 0.654829i \(-0.227259\pi\)
0.755777 + 0.654829i \(0.227259\pi\)
\(270\) −1.42524e9 −0.0163212
\(271\) −3.87526e10 −0.436455 −0.218227 0.975898i \(-0.570027\pi\)
−0.218227 + 0.975898i \(0.570027\pi\)
\(272\) 2.12635e10 0.235545
\(273\) −2.69539e9 −0.0293691
\(274\) −4.53736e10 −0.486324
\(275\) 4.58478e10 0.483417
\(276\) −2.86093e10 −0.296768
\(277\) −7.14595e10 −0.729292 −0.364646 0.931146i \(-0.618810\pi\)
−0.364646 + 0.931146i \(0.618810\pi\)
\(278\) −8.04796e9 −0.0808135
\(279\) −6.57372e10 −0.649519
\(280\) 1.98839e10 0.193326
\(281\) −1.06795e10 −0.102182 −0.0510910 0.998694i \(-0.516270\pi\)
−0.0510910 + 0.998694i \(0.516270\pi\)
\(282\) 7.92012e9 0.0745780
\(283\) −1.74567e11 −1.61779 −0.808895 0.587953i \(-0.799934\pi\)
−0.808895 + 0.587953i \(0.799934\pi\)
\(284\) 3.65815e10 0.333679
\(285\) 1.87473e10 0.168320
\(286\) −9.80124e8 −0.00866231
\(287\) −2.13210e11 −1.85498
\(288\) −3.81436e10 −0.326705
\(289\) −9.16840e10 −0.773131
\(290\) −1.83984e10 −0.152753
\(291\) 1.60928e10 0.131557
\(292\) −2.49544e10 −0.200874
\(293\) −8.31117e10 −0.658806 −0.329403 0.944189i \(-0.606848\pi\)
−0.329403 + 0.944189i \(0.606848\pi\)
\(294\) −1.77654e10 −0.138679
\(295\) −3.39268e9 −0.0260822
\(296\) 1.80947e10 0.137005
\(297\) −1.29967e10 −0.0969238
\(298\) −4.05068e10 −0.297547
\(299\) −3.51654e9 −0.0254446
\(300\) 6.38167e10 0.454871
\(301\) 2.71347e11 1.90536
\(302\) 1.15839e10 0.0801353
\(303\) 2.46850e10 0.168244
\(304\) 1.07163e11 0.719638
\(305\) 7.59262e9 0.0502391
\(306\) −1.03080e10 −0.0672094
\(307\) −2.41303e11 −1.55039 −0.775194 0.631724i \(-0.782348\pi\)
−0.775194 + 0.631724i \(0.782348\pi\)
\(308\) 8.17379e10 0.517541
\(309\) 3.10482e10 0.193742
\(310\) 2.68704e10 0.165252
\(311\) −3.16050e11 −1.91573 −0.957864 0.287224i \(-0.907268\pi\)
−0.957864 + 0.287224i \(0.907268\pi\)
\(312\) −3.02635e9 −0.0180811
\(313\) 2.18895e11 1.28910 0.644550 0.764562i \(-0.277045\pi\)
0.644550 + 0.764562i \(0.277045\pi\)
\(314\) −8.90872e10 −0.517168
\(315\) 1.46096e10 0.0836069
\(316\) −2.06243e11 −1.16356
\(317\) −4.19690e10 −0.233433 −0.116716 0.993165i \(-0.537237\pi\)
−0.116716 + 0.993165i \(0.537237\pi\)
\(318\) 9.17316e9 0.0503034
\(319\) −1.67775e11 −0.907127
\(320\) −2.99230e9 −0.0159526
\(321\) 1.56214e11 0.821198
\(322\) −6.40245e10 −0.331890
\(323\) 1.35589e11 0.693129
\(324\) −1.80905e10 −0.0912005
\(325\) 7.84408e9 0.0390002
\(326\) −1.70437e11 −0.835768
\(327\) 7.62221e10 0.368651
\(328\) −2.39390e11 −1.14202
\(329\) −8.11862e10 −0.382033
\(330\) 5.31249e9 0.0246596
\(331\) −6.43346e9 −0.0294590 −0.0147295 0.999892i \(-0.504689\pi\)
−0.0147295 + 0.999892i \(0.504689\pi\)
\(332\) 3.47691e10 0.157062
\(333\) 1.32950e10 0.0592502
\(334\) −4.18195e10 −0.183874
\(335\) −1.66414e10 −0.0721917
\(336\) 8.35116e10 0.357454
\(337\) −1.98819e11 −0.839698 −0.419849 0.907594i \(-0.637917\pi\)
−0.419849 + 0.907594i \(0.637917\pi\)
\(338\) 1.01408e11 0.422616
\(339\) 1.01839e11 0.418809
\(340\) −1.92998e10 −0.0783243
\(341\) 2.45031e11 0.981354
\(342\) −5.19502e10 −0.205338
\(343\) −1.38829e11 −0.541571
\(344\) 3.04665e11 1.17303
\(345\) 1.90604e10 0.0724347
\(346\) −1.98740e11 −0.745492
\(347\) 3.33397e11 1.23447 0.617233 0.786780i \(-0.288254\pi\)
0.617233 + 0.786780i \(0.288254\pi\)
\(348\) −2.33529e11 −0.853562
\(349\) 2.25022e10 0.0811916 0.0405958 0.999176i \(-0.487074\pi\)
0.0405958 + 0.999176i \(0.487074\pi\)
\(350\) 1.42815e11 0.508706
\(351\) −2.22361e9 −0.00781944
\(352\) 1.42177e11 0.493615
\(353\) 3.24247e11 1.11145 0.555725 0.831366i \(-0.312441\pi\)
0.555725 + 0.831366i \(0.312441\pi\)
\(354\) 9.40139e9 0.0318183
\(355\) −2.43717e10 −0.0814439
\(356\) −2.61976e11 −0.864445
\(357\) 1.05664e11 0.344286
\(358\) 1.20366e11 0.387283
\(359\) 5.14941e11 1.63618 0.818092 0.575087i \(-0.195032\pi\)
0.818092 + 0.575087i \(0.195032\pi\)
\(360\) 1.64035e10 0.0514725
\(361\) 3.60652e11 1.11765
\(362\) 1.04749e9 0.00320597
\(363\) −1.42549e11 −0.430909
\(364\) 1.39845e10 0.0417533
\(365\) 1.66254e10 0.0490291
\(366\) −2.10397e10 −0.0612880
\(367\) −4.75270e11 −1.36755 −0.683775 0.729693i \(-0.739663\pi\)
−0.683775 + 0.729693i \(0.739663\pi\)
\(368\) 1.08953e11 0.309688
\(369\) −1.75891e11 −0.493884
\(370\) −5.43441e9 −0.0150746
\(371\) −9.40307e10 −0.257684
\(372\) 3.41064e11 0.923405
\(373\) −3.17239e11 −0.848587 −0.424294 0.905525i \(-0.639478\pi\)
−0.424294 + 0.905525i \(0.639478\pi\)
\(374\) 3.84225e10 0.101546
\(375\) −8.68112e10 −0.226691
\(376\) −9.11549e10 −0.235199
\(377\) −2.87045e10 −0.0731836
\(378\) −4.04845e10 −0.101994
\(379\) 2.91888e11 0.726674 0.363337 0.931658i \(-0.381637\pi\)
0.363337 + 0.931658i \(0.381637\pi\)
\(380\) −9.72664e10 −0.239297
\(381\) 1.82964e10 0.0444839
\(382\) −1.05503e11 −0.253500
\(383\) −1.63564e11 −0.388413 −0.194207 0.980961i \(-0.562213\pi\)
−0.194207 + 0.980961i \(0.562213\pi\)
\(384\) 2.49397e11 0.585330
\(385\) −5.44564e10 −0.126321
\(386\) 2.77035e11 0.635173
\(387\) 2.23852e11 0.507296
\(388\) −8.34944e10 −0.187031
\(389\) −4.14721e11 −0.918297 −0.459148 0.888360i \(-0.651845\pi\)
−0.459148 + 0.888360i \(0.651845\pi\)
\(390\) 9.08911e8 0.00198944
\(391\) 1.37854e11 0.298280
\(392\) 2.04467e11 0.437356
\(393\) 6.90819e10 0.146082
\(394\) 1.72926e11 0.361515
\(395\) 1.37406e11 0.284000
\(396\) 6.74309e10 0.137794
\(397\) −4.15700e10 −0.0839890 −0.0419945 0.999118i \(-0.513371\pi\)
−0.0419945 + 0.999118i \(0.513371\pi\)
\(398\) 2.21529e11 0.442545
\(399\) 5.32522e11 1.05186
\(400\) −2.43034e11 −0.474676
\(401\) −4.54725e11 −0.878212 −0.439106 0.898435i \(-0.644705\pi\)
−0.439106 + 0.898435i \(0.644705\pi\)
\(402\) 4.61145e10 0.0880685
\(403\) 4.19222e10 0.0791719
\(404\) −1.28073e11 −0.239189
\(405\) 1.20524e10 0.0222601
\(406\) −5.22613e11 −0.954582
\(407\) −4.95562e10 −0.0895206
\(408\) 1.18638e11 0.211960
\(409\) 6.69144e11 1.18240 0.591200 0.806525i \(-0.298654\pi\)
0.591200 + 0.806525i \(0.298654\pi\)
\(410\) 7.18965e10 0.125655
\(411\) 3.83698e11 0.663287
\(412\) −1.61087e11 −0.275438
\(413\) −9.63702e10 −0.162992
\(414\) −5.28180e10 −0.0883649
\(415\) −2.31643e10 −0.0383356
\(416\) 2.43251e10 0.0398230
\(417\) 6.80568e10 0.110220
\(418\) 1.93641e11 0.310244
\(419\) 4.40416e11 0.698071 0.349036 0.937109i \(-0.386509\pi\)
0.349036 + 0.937109i \(0.386509\pi\)
\(420\) −7.57991e10 −0.118862
\(421\) 6.33252e11 0.982442 0.491221 0.871035i \(-0.336551\pi\)
0.491221 + 0.871035i \(0.336551\pi\)
\(422\) −2.80754e10 −0.0430943
\(423\) −6.69758e10 −0.101715
\(424\) −1.05576e11 −0.158643
\(425\) −3.07501e11 −0.457190
\(426\) 6.75360e10 0.0993555
\(427\) 2.15671e11 0.313954
\(428\) −8.10485e11 −1.16748
\(429\) 8.28833e9 0.0118143
\(430\) −9.15007e10 −0.129067
\(431\) 9.74440e11 1.36021 0.680107 0.733113i \(-0.261933\pi\)
0.680107 + 0.733113i \(0.261933\pi\)
\(432\) 6.88941e10 0.0951712
\(433\) 1.90387e11 0.260281 0.130141 0.991496i \(-0.458457\pi\)
0.130141 + 0.991496i \(0.458457\pi\)
\(434\) 7.63263e11 1.03269
\(435\) 1.55585e11 0.208336
\(436\) −3.95463e11 −0.524102
\(437\) 6.94754e11 0.911307
\(438\) −4.60703e10 −0.0598119
\(439\) −1.27826e12 −1.64259 −0.821297 0.570501i \(-0.806749\pi\)
−0.821297 + 0.570501i \(0.806749\pi\)
\(440\) −6.11429e10 −0.0777695
\(441\) 1.50231e11 0.189142
\(442\) 6.57369e9 0.00819236
\(443\) −1.09736e12 −1.35374 −0.676868 0.736105i \(-0.736663\pi\)
−0.676868 + 0.736105i \(0.736663\pi\)
\(444\) −6.89784e10 −0.0842345
\(445\) 1.74537e11 0.210993
\(446\) 3.05768e11 0.365920
\(447\) 3.42542e11 0.405817
\(448\) −8.49973e10 −0.0996906
\(449\) 1.35831e12 1.57722 0.788609 0.614895i \(-0.210802\pi\)
0.788609 + 0.614895i \(0.210802\pi\)
\(450\) 1.17817e11 0.135442
\(451\) 6.55622e11 0.746206
\(452\) −5.28371e11 −0.595410
\(453\) −9.79583e10 −0.109295
\(454\) −4.00558e11 −0.442501
\(455\) −9.31691e9 −0.0101911
\(456\) 5.97909e11 0.647580
\(457\) 4.51819e11 0.484554 0.242277 0.970207i \(-0.422106\pi\)
0.242277 + 0.970207i \(0.422106\pi\)
\(458\) −6.88035e11 −0.730660
\(459\) 8.71691e10 0.0916654
\(460\) −9.88911e10 −0.102979
\(461\) 1.06027e12 1.09336 0.546678 0.837343i \(-0.315892\pi\)
0.546678 + 0.837343i \(0.315892\pi\)
\(462\) 1.50903e11 0.154102
\(463\) 7.93160e11 0.802133 0.401067 0.916049i \(-0.368640\pi\)
0.401067 + 0.916049i \(0.368640\pi\)
\(464\) 8.89353e11 0.890725
\(465\) −2.27228e11 −0.225384
\(466\) −2.36195e11 −0.232025
\(467\) 1.10323e12 1.07335 0.536675 0.843789i \(-0.319680\pi\)
0.536675 + 0.843789i \(0.319680\pi\)
\(468\) 1.15367e10 0.0111167
\(469\) −4.72703e11 −0.451139
\(470\) 2.73767e10 0.0258786
\(471\) 7.53358e11 0.705355
\(472\) −1.08203e11 −0.100346
\(473\) −8.34392e11 −0.766469
\(474\) −3.80762e11 −0.346459
\(475\) −1.54974e12 −1.39681
\(476\) −5.48216e11 −0.489463
\(477\) −7.75720e10 −0.0686076
\(478\) −3.47787e11 −0.304711
\(479\) −6.09570e11 −0.529071 −0.264535 0.964376i \(-0.585219\pi\)
−0.264535 + 0.964376i \(0.585219\pi\)
\(480\) −1.31847e11 −0.113367
\(481\) −8.47855e9 −0.00722218
\(482\) −2.57831e11 −0.217582
\(483\) 5.41417e11 0.452658
\(484\) 7.39588e11 0.612612
\(485\) 5.56266e10 0.0456504
\(486\) −3.33983e10 −0.0271557
\(487\) −2.37201e12 −1.91090 −0.955448 0.295161i \(-0.904627\pi\)
−0.955448 + 0.295161i \(0.904627\pi\)
\(488\) 2.42152e11 0.193286
\(489\) 1.44129e12 1.13989
\(490\) −6.14079e10 −0.0481218
\(491\) −4.27405e11 −0.331874 −0.165937 0.986136i \(-0.553065\pi\)
−0.165937 + 0.986136i \(0.553065\pi\)
\(492\) 9.12575e11 0.702143
\(493\) 1.12526e12 0.857913
\(494\) 3.31299e10 0.0250293
\(495\) −4.49246e10 −0.0336326
\(496\) −1.29888e12 −0.963609
\(497\) −6.92287e11 −0.508958
\(498\) 6.41901e10 0.0467666
\(499\) −9.86003e11 −0.711911 −0.355956 0.934503i \(-0.615845\pi\)
−0.355956 + 0.934503i \(0.615845\pi\)
\(500\) 4.50402e11 0.322281
\(501\) 3.53643e11 0.250781
\(502\) −8.21046e11 −0.577033
\(503\) 2.34755e12 1.63516 0.817579 0.575817i \(-0.195316\pi\)
0.817579 + 0.575817i \(0.195316\pi\)
\(504\) 4.65947e11 0.321662
\(505\) 8.53262e10 0.0583810
\(506\) 1.96875e11 0.133510
\(507\) −8.57546e11 −0.576397
\(508\) −9.49269e10 −0.0632416
\(509\) 2.11552e12 1.39697 0.698483 0.715626i \(-0.253859\pi\)
0.698483 + 0.715626i \(0.253859\pi\)
\(510\) −3.56308e10 −0.0233217
\(511\) 4.72250e11 0.306392
\(512\) −1.34636e12 −0.865856
\(513\) 4.39312e11 0.280056
\(514\) 5.36531e11 0.339048
\(515\) 1.07321e11 0.0672285
\(516\) −1.16141e12 −0.721210
\(517\) 2.49647e11 0.153681
\(518\) −1.54366e11 −0.0942037
\(519\) 1.68063e12 1.01676
\(520\) −1.04609e10 −0.00627415
\(521\) 1.32436e12 0.787474 0.393737 0.919223i \(-0.371182\pi\)
0.393737 + 0.919223i \(0.371182\pi\)
\(522\) −4.31138e11 −0.254155
\(523\) −2.18959e11 −0.127969 −0.0639845 0.997951i \(-0.520381\pi\)
−0.0639845 + 0.997951i \(0.520381\pi\)
\(524\) −3.58417e11 −0.207682
\(525\) −1.20770e12 −0.693813
\(526\) 5.30527e11 0.302184
\(527\) −1.64342e12 −0.928113
\(528\) −2.56798e11 −0.143793
\(529\) −1.09479e12 −0.607830
\(530\) 3.17080e10 0.0174553
\(531\) −7.95020e10 −0.0433963
\(532\) −2.76288e12 −1.49541
\(533\) 1.12170e11 0.0602011
\(534\) −4.83656e11 −0.257395
\(535\) 5.39971e11 0.284956
\(536\) −5.30745e11 −0.277744
\(537\) −1.01786e12 −0.528207
\(538\) −1.24339e12 −0.639864
\(539\) −5.59977e11 −0.285772
\(540\) −6.25316e10 −0.0316466
\(541\) −1.87971e12 −0.943416 −0.471708 0.881755i \(-0.656362\pi\)
−0.471708 + 0.881755i \(0.656362\pi\)
\(542\) 3.71193e11 0.184758
\(543\) −8.85798e9 −0.00437256
\(544\) −9.53583e11 −0.466835
\(545\) 2.63470e11 0.127922
\(546\) 2.58179e10 0.0124324
\(547\) 1.45627e12 0.695502 0.347751 0.937587i \(-0.386946\pi\)
0.347751 + 0.937587i \(0.386946\pi\)
\(548\) −1.99074e12 −0.942979
\(549\) 1.77921e11 0.0835894
\(550\) −4.39155e11 −0.204638
\(551\) 5.67107e12 2.62110
\(552\) 6.07897e11 0.278679
\(553\) 3.90306e12 1.77477
\(554\) 6.84477e11 0.308720
\(555\) 4.59556e10 0.0205599
\(556\) −3.53099e11 −0.156697
\(557\) 1.34465e11 0.0591919 0.0295959 0.999562i \(-0.490578\pi\)
0.0295959 + 0.999562i \(0.490578\pi\)
\(558\) 6.29665e11 0.274951
\(559\) −1.42756e11 −0.0618358
\(560\) 2.88667e11 0.124037
\(561\) −3.24916e11 −0.138497
\(562\) 1.02294e11 0.0432552
\(563\) −3.82201e12 −1.60326 −0.801630 0.597820i \(-0.796034\pi\)
−0.801630 + 0.597820i \(0.796034\pi\)
\(564\) 3.47490e11 0.144606
\(565\) 3.52018e11 0.145327
\(566\) 1.67209e12 0.684835
\(567\) 3.42353e11 0.139108
\(568\) −7.77291e11 −0.313340
\(569\) −2.55907e12 −1.02348 −0.511738 0.859142i \(-0.670998\pi\)
−0.511738 + 0.859142i \(0.670998\pi\)
\(570\) −1.79571e11 −0.0712525
\(571\) 3.38712e11 0.133342 0.0666712 0.997775i \(-0.478762\pi\)
0.0666712 + 0.997775i \(0.478762\pi\)
\(572\) −4.30023e10 −0.0167961
\(573\) 8.92175e11 0.345744
\(574\) 2.04224e12 0.785242
\(575\) −1.57562e12 −0.601100
\(576\) −7.01198e10 −0.0265424
\(577\) −1.31031e12 −0.492134 −0.246067 0.969253i \(-0.579138\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(578\) 8.78198e11 0.327278
\(579\) −2.34272e12 −0.866299
\(580\) −8.07219e11 −0.296187
\(581\) −6.57989e11 −0.239566
\(582\) −1.54146e11 −0.0556901
\(583\) 2.89144e11 0.103659
\(584\) 5.30236e11 0.188630
\(585\) −7.68613e9 −0.00271335
\(586\) 7.96088e11 0.278883
\(587\) −1.73713e12 −0.603893 −0.301946 0.953325i \(-0.597636\pi\)
−0.301946 + 0.953325i \(0.597636\pi\)
\(588\) −7.79444e11 −0.268898
\(589\) −8.28246e12 −2.83557
\(590\) 3.24969e10 0.0110410
\(591\) −1.46233e12 −0.493063
\(592\) 2.62691e11 0.0879019
\(593\) 1.03177e11 0.0342640 0.0171320 0.999853i \(-0.494546\pi\)
0.0171320 + 0.999853i \(0.494546\pi\)
\(594\) 1.24490e11 0.0410293
\(595\) 3.65239e11 0.119468
\(596\) −1.77721e12 −0.576940
\(597\) −1.87334e12 −0.603577
\(598\) 3.36833e10 0.0107711
\(599\) 2.06669e11 0.0655926 0.0327963 0.999462i \(-0.489559\pi\)
0.0327963 + 0.999462i \(0.489559\pi\)
\(600\) −1.35599e12 −0.427146
\(601\) −4.41366e12 −1.37995 −0.689975 0.723833i \(-0.742379\pi\)
−0.689975 + 0.723833i \(0.742379\pi\)
\(602\) −2.59911e12 −0.806566
\(603\) −3.89964e11 −0.120115
\(604\) 5.08236e11 0.155382
\(605\) −4.92737e11 −0.149526
\(606\) −2.36446e11 −0.0712204
\(607\) 3.52761e12 1.05471 0.527354 0.849646i \(-0.323184\pi\)
0.527354 + 0.849646i \(0.323184\pi\)
\(608\) −4.80584e12 −1.42628
\(609\) 4.41943e12 1.30193
\(610\) −7.27261e10 −0.0212670
\(611\) 4.27121e10 0.0123984
\(612\) −4.52259e11 −0.130318
\(613\) −1.61053e11 −0.0460677 −0.0230339 0.999735i \(-0.507333\pi\)
−0.0230339 + 0.999735i \(0.507333\pi\)
\(614\) 2.31133e12 0.656303
\(615\) −6.07986e11 −0.171378
\(616\) −1.73678e12 −0.485996
\(617\) −4.10818e12 −1.14121 −0.570606 0.821224i \(-0.693292\pi\)
−0.570606 + 0.821224i \(0.693292\pi\)
\(618\) −2.97396e11 −0.0820138
\(619\) 3.36299e12 0.920698 0.460349 0.887738i \(-0.347724\pi\)
0.460349 + 0.887738i \(0.347724\pi\)
\(620\) 1.17892e12 0.320422
\(621\) 4.46650e11 0.120519
\(622\) 3.02729e12 0.810956
\(623\) 4.95778e12 1.31853
\(624\) −4.39354e10 −0.0116007
\(625\) 3.36152e12 0.881201
\(626\) −2.09669e12 −0.545696
\(627\) −1.63750e12 −0.423135
\(628\) −3.90864e12 −1.00278
\(629\) 3.32373e11 0.0846639
\(630\) −1.39939e11 −0.0353920
\(631\) −4.90415e12 −1.23149 −0.615747 0.787944i \(-0.711145\pi\)
−0.615747 + 0.787944i \(0.711145\pi\)
\(632\) 4.38230e12 1.09264
\(633\) 2.37417e11 0.0587754
\(634\) 4.02001e11 0.0988156
\(635\) 6.32433e10 0.0154359
\(636\) 4.02467e11 0.0975378
\(637\) −9.58061e10 −0.0230550
\(638\) 1.60703e12 0.384001
\(639\) −5.71112e11 −0.135509
\(640\) 8.62067e11 0.203110
\(641\) 9.35863e11 0.218953 0.109477 0.993989i \(-0.465083\pi\)
0.109477 + 0.993989i \(0.465083\pi\)
\(642\) −1.49630e12 −0.347625
\(643\) 7.78616e11 0.179628 0.0898140 0.995959i \(-0.471373\pi\)
0.0898140 + 0.995959i \(0.471373\pi\)
\(644\) −2.80903e12 −0.643532
\(645\) 7.73768e11 0.176032
\(646\) −1.29875e12 −0.293412
\(647\) 1.37091e12 0.307568 0.153784 0.988104i \(-0.450854\pi\)
0.153784 + 0.988104i \(0.450854\pi\)
\(648\) 3.84390e11 0.0856416
\(649\) 2.96338e11 0.0655671
\(650\) −7.51348e10 −0.0165094
\(651\) −6.45447e12 −1.40847
\(652\) −7.47783e12 −1.62055
\(653\) −7.64528e12 −1.64545 −0.822724 0.568441i \(-0.807547\pi\)
−0.822724 + 0.568441i \(0.807547\pi\)
\(654\) −7.30095e11 −0.156056
\(655\) 2.38789e11 0.0506907
\(656\) −3.47537e12 −0.732713
\(657\) 3.89589e11 0.0815761
\(658\) 7.77645e11 0.161720
\(659\) 1.26763e12 0.261823 0.130911 0.991394i \(-0.458210\pi\)
0.130911 + 0.991394i \(0.458210\pi\)
\(660\) 2.33082e11 0.0478147
\(661\) 5.08848e12 1.03677 0.518384 0.855148i \(-0.326534\pi\)
0.518384 + 0.855148i \(0.326534\pi\)
\(662\) 6.16231e10 0.0124705
\(663\) −5.55898e10 −0.0111734
\(664\) −7.38782e11 −0.147489
\(665\) 1.84072e12 0.364998
\(666\) −1.27347e11 −0.0250815
\(667\) 5.76580e12 1.12796
\(668\) −1.83480e12 −0.356529
\(669\) −2.58570e12 −0.499070
\(670\) 1.59400e11 0.0305598
\(671\) −6.63187e11 −0.126295
\(672\) −3.74516e12 −0.708450
\(673\) 1.67350e12 0.314455 0.157227 0.987562i \(-0.449744\pi\)
0.157227 + 0.987562i \(0.449744\pi\)
\(674\) 1.90439e12 0.355457
\(675\) −9.96310e11 −0.184726
\(676\) 4.44920e12 0.819449
\(677\) −1.45172e12 −0.265603 −0.132802 0.991143i \(-0.542397\pi\)
−0.132802 + 0.991143i \(0.542397\pi\)
\(678\) −9.75469e11 −0.177288
\(679\) 1.58009e12 0.285278
\(680\) 4.10085e11 0.0735503
\(681\) 3.38729e12 0.603518
\(682\) −2.34703e12 −0.415422
\(683\) 5.62955e12 0.989876 0.494938 0.868928i \(-0.335191\pi\)
0.494938 + 0.868928i \(0.335191\pi\)
\(684\) −2.27928e12 −0.398149
\(685\) 1.32629e12 0.230161
\(686\) 1.32977e12 0.229255
\(687\) 5.81830e12 0.996532
\(688\) 4.42301e12 0.752610
\(689\) 4.94695e10 0.00836280
\(690\) −1.82571e11 −0.0306627
\(691\) 7.22348e12 1.20530 0.602650 0.798005i \(-0.294111\pi\)
0.602650 + 0.798005i \(0.294111\pi\)
\(692\) −8.71960e12 −1.44550
\(693\) −1.27610e12 −0.210177
\(694\) −3.19345e12 −0.522568
\(695\) 2.35246e11 0.0382464
\(696\) 4.96208e12 0.801535
\(697\) −4.39725e12 −0.705722
\(698\) −2.15538e11 −0.0343696
\(699\) 1.99736e12 0.316453
\(700\) 6.26590e12 0.986376
\(701\) 1.16867e13 1.82793 0.913967 0.405789i \(-0.133003\pi\)
0.913967 + 0.405789i \(0.133003\pi\)
\(702\) 2.12989e10 0.00331009
\(703\) 1.67509e12 0.258665
\(704\) 2.61367e11 0.0401026
\(705\) −2.31509e11 −0.0352953
\(706\) −3.10581e12 −0.470493
\(707\) 2.42372e12 0.364834
\(708\) 4.12480e11 0.0616954
\(709\) 1.02089e13 1.51730 0.758652 0.651496i \(-0.225858\pi\)
0.758652 + 0.651496i \(0.225858\pi\)
\(710\) 2.33445e11 0.0344764
\(711\) 3.21988e12 0.472528
\(712\) 5.56653e12 0.811754
\(713\) −8.42081e12 −1.22026
\(714\) −1.01211e12 −0.145742
\(715\) 2.86495e10 0.00409958
\(716\) 5.28096e12 0.750938
\(717\) 2.94103e12 0.415588
\(718\) −4.93237e12 −0.692622
\(719\) 8.61256e12 1.20186 0.600928 0.799303i \(-0.294798\pi\)
0.600928 + 0.799303i \(0.294798\pi\)
\(720\) 2.38140e11 0.0330245
\(721\) 3.04850e12 0.420123
\(722\) −3.45451e12 −0.473118
\(723\) 2.18032e12 0.296756
\(724\) 4.59578e10 0.00621635
\(725\) −1.28613e13 −1.72888
\(726\) 1.36541e12 0.182410
\(727\) −1.13796e13 −1.51086 −0.755428 0.655231i \(-0.772571\pi\)
−0.755428 + 0.655231i \(0.772571\pi\)
\(728\) −2.97146e11 −0.0392083
\(729\) 2.82430e11 0.0370370
\(730\) −1.59247e11 −0.0207548
\(731\) 5.59626e12 0.724886
\(732\) −9.23105e11 −0.118837
\(733\) −1.07252e12 −0.137226 −0.0686131 0.997643i \(-0.521857\pi\)
−0.0686131 + 0.997643i \(0.521857\pi\)
\(734\) 4.55239e12 0.578905
\(735\) 5.19291e11 0.0656323
\(736\) −4.88612e12 −0.613782
\(737\) 1.45356e12 0.181480
\(738\) 1.68478e12 0.209069
\(739\) −1.10892e13 −1.36773 −0.683865 0.729609i \(-0.739702\pi\)
−0.683865 + 0.729609i \(0.739702\pi\)
\(740\) −2.38431e11 −0.0292294
\(741\) −2.80160e11 −0.0341369
\(742\) 9.00676e11 0.109081
\(743\) −5.45647e12 −0.656843 −0.328422 0.944531i \(-0.606517\pi\)
−0.328422 + 0.944531i \(0.606517\pi\)
\(744\) −7.24700e12 −0.867121
\(745\) 1.18403e12 0.140819
\(746\) 3.03868e12 0.359220
\(747\) −5.42818e11 −0.0637840
\(748\) 1.68576e12 0.196897
\(749\) 1.53380e13 1.78074
\(750\) 8.31523e11 0.0959619
\(751\) −1.27661e13 −1.46447 −0.732234 0.681053i \(-0.761522\pi\)
−0.732234 + 0.681053i \(0.761522\pi\)
\(752\) −1.32335e12 −0.150902
\(753\) 6.94311e12 0.787003
\(754\) 2.74947e11 0.0309797
\(755\) −3.38603e11 −0.0379254
\(756\) −1.77623e12 −0.197766
\(757\) −5.42850e12 −0.600826 −0.300413 0.953809i \(-0.597124\pi\)
−0.300413 + 0.953809i \(0.597124\pi\)
\(758\) −2.79586e12 −0.307612
\(759\) −1.66486e12 −0.182091
\(760\) 2.06674e12 0.224711
\(761\) 1.16683e13 1.26118 0.630591 0.776116i \(-0.282813\pi\)
0.630591 + 0.776116i \(0.282813\pi\)
\(762\) −1.75252e11 −0.0188307
\(763\) 7.48394e12 0.799411
\(764\) −4.62886e12 −0.491535
\(765\) 3.01309e11 0.0318080
\(766\) 1.56671e12 0.164421
\(767\) 5.07003e10 0.00528971
\(768\) −1.94563e12 −0.201806
\(769\) 7.33122e11 0.0755976 0.0377988 0.999285i \(-0.487965\pi\)
0.0377988 + 0.999285i \(0.487965\pi\)
\(770\) 5.21612e11 0.0534736
\(771\) −4.53713e12 −0.462420
\(772\) 1.21547e13 1.23160
\(773\) 1.97291e13 1.98746 0.993732 0.111789i \(-0.0356580\pi\)
0.993732 + 0.111789i \(0.0356580\pi\)
\(774\) −2.14417e12 −0.214746
\(775\) 1.87837e13 1.87035
\(776\) 1.77411e12 0.175631
\(777\) 1.30538e12 0.128482
\(778\) 3.97242e12 0.388729
\(779\) −2.21611e13 −2.15612
\(780\) 3.98779e10 0.00385750
\(781\) 2.12878e12 0.204739
\(782\) −1.32044e12 −0.126267
\(783\) 3.64588e12 0.346636
\(784\) 2.96837e12 0.280605
\(785\) 2.60406e12 0.244759
\(786\) −6.61703e11 −0.0618389
\(787\) −7.76348e12 −0.721390 −0.360695 0.932684i \(-0.617460\pi\)
−0.360695 + 0.932684i \(0.617460\pi\)
\(788\) 7.58701e12 0.700975
\(789\) −4.48636e12 −0.412143
\(790\) −1.31615e12 −0.120221
\(791\) 9.99917e12 0.908176
\(792\) −1.43279e12 −0.129395
\(793\) −1.13464e11 −0.0101890
\(794\) 3.98179e11 0.0355538
\(795\) −2.68136e11 −0.0238069
\(796\) 9.71945e12 0.858090
\(797\) −9.48983e12 −0.833098 −0.416549 0.909113i \(-0.636761\pi\)
−0.416549 + 0.909113i \(0.636761\pi\)
\(798\) −5.10078e12 −0.445270
\(799\) −1.67438e12 −0.145343
\(800\) 1.08991e13 0.940775
\(801\) 4.08999e12 0.351056
\(802\) 4.35560e12 0.371760
\(803\) −1.45217e12 −0.123253
\(804\) 2.02325e12 0.170764
\(805\) 1.87147e12 0.157073
\(806\) −4.01553e11 −0.0335147
\(807\) 1.05146e13 0.872697
\(808\) 2.72132e12 0.224610
\(809\) −2.02032e13 −1.65826 −0.829128 0.559059i \(-0.811163\pi\)
−0.829128 + 0.559059i \(0.811163\pi\)
\(810\) −1.15445e11 −0.00942304
\(811\) 1.33725e13 1.08547 0.542735 0.839904i \(-0.317389\pi\)
0.542735 + 0.839904i \(0.317389\pi\)
\(812\) −2.29293e13 −1.85093
\(813\) −3.13896e12 −0.251987
\(814\) 4.74675e11 0.0378954
\(815\) 4.98197e12 0.395541
\(816\) 1.72234e12 0.135992
\(817\) 2.82039e13 2.21467
\(818\) −6.40941e12 −0.500528
\(819\) −2.18327e11 −0.0169562
\(820\) 3.15441e12 0.243644
\(821\) −6.30233e12 −0.484124 −0.242062 0.970261i \(-0.577824\pi\)
−0.242062 + 0.970261i \(0.577824\pi\)
\(822\) −3.67526e12 −0.280780
\(823\) −1.10580e13 −0.840190 −0.420095 0.907480i \(-0.638003\pi\)
−0.420095 + 0.907480i \(0.638003\pi\)
\(824\) 3.42281e12 0.258649
\(825\) 3.71367e12 0.279101
\(826\) 9.23084e11 0.0689971
\(827\) 9.48648e12 0.705229 0.352614 0.935769i \(-0.385293\pi\)
0.352614 + 0.935769i \(0.385293\pi\)
\(828\) −2.31735e12 −0.171339
\(829\) 1.42896e13 1.05081 0.525406 0.850852i \(-0.323913\pi\)
0.525406 + 0.850852i \(0.323913\pi\)
\(830\) 2.21880e11 0.0162280
\(831\) −5.78822e12 −0.421057
\(832\) 4.47171e10 0.00323533
\(833\) 3.75576e12 0.270269
\(834\) −6.51884e11 −0.0466577
\(835\) 1.22240e12 0.0870213
\(836\) 8.49586e12 0.601560
\(837\) −5.32471e12 −0.375000
\(838\) −4.21854e12 −0.295504
\(839\) 2.21256e13 1.54158 0.770789 0.637091i \(-0.219862\pi\)
0.770789 + 0.637091i \(0.219862\pi\)
\(840\) 1.61060e12 0.111617
\(841\) 3.25574e13 2.24423
\(842\) −6.06562e12 −0.415883
\(843\) −8.65043e11 −0.0589948
\(844\) −1.23179e12 −0.0835595
\(845\) −2.96420e12 −0.200010
\(846\) 6.41530e11 0.0430576
\(847\) −1.39963e13 −0.934414
\(848\) −1.53272e12 −0.101784
\(849\) −1.41399e13 −0.934031
\(850\) 2.94541e12 0.193535
\(851\) 1.70307e12 0.111314
\(852\) 2.96310e12 0.192650
\(853\) −2.45669e13 −1.58884 −0.794418 0.607371i \(-0.792224\pi\)
−0.794418 + 0.607371i \(0.792224\pi\)
\(854\) −2.06581e12 −0.132901
\(855\) 1.51853e12 0.0971797
\(856\) 1.72214e13 1.09631
\(857\) 1.18349e12 0.0749467 0.0374734 0.999298i \(-0.488069\pi\)
0.0374734 + 0.999298i \(0.488069\pi\)
\(858\) −7.93900e10 −0.00500119
\(859\) −7.80900e12 −0.489357 −0.244679 0.969604i \(-0.578682\pi\)
−0.244679 + 0.969604i \(0.578682\pi\)
\(860\) −4.01453e12 −0.250260
\(861\) −1.72700e13 −1.07097
\(862\) −9.33370e12 −0.575799
\(863\) −2.60230e13 −1.59701 −0.798507 0.601986i \(-0.794376\pi\)
−0.798507 + 0.601986i \(0.794376\pi\)
\(864\) −3.08963e12 −0.188623
\(865\) 5.80927e12 0.352817
\(866\) −1.82363e12 −0.110181
\(867\) −7.42640e12 −0.446368
\(868\) 3.34877e13 2.00238
\(869\) −1.20019e13 −0.713938
\(870\) −1.49027e12 −0.0881920
\(871\) 2.48689e11 0.0146411
\(872\) 8.40287e12 0.492157
\(873\) 1.30352e12 0.0759546
\(874\) −6.65472e12 −0.385770
\(875\) −8.52364e12 −0.491574
\(876\) −2.02130e12 −0.115975
\(877\) 2.23145e13 1.27377 0.636883 0.770961i \(-0.280224\pi\)
0.636883 + 0.770961i \(0.280224\pi\)
\(878\) 1.22439e13 0.695335
\(879\) −6.73205e12 −0.380362
\(880\) −8.87649e11 −0.0498964
\(881\) −4.12977e12 −0.230958 −0.115479 0.993310i \(-0.536840\pi\)
−0.115479 + 0.993310i \(0.536840\pi\)
\(882\) −1.43900e12 −0.0800665
\(883\) 1.42470e13 0.788682 0.394341 0.918964i \(-0.370973\pi\)
0.394341 + 0.918964i \(0.370973\pi\)
\(884\) 2.88416e11 0.0158849
\(885\) −2.74807e11 −0.0150586
\(886\) 1.05111e13 0.573057
\(887\) −1.91200e13 −1.03712 −0.518562 0.855040i \(-0.673532\pi\)
−0.518562 + 0.855040i \(0.673532\pi\)
\(888\) 1.46567e12 0.0791002
\(889\) 1.79645e12 0.0964620
\(890\) −1.67181e12 −0.0893164
\(891\) −1.05274e12 −0.0559590
\(892\) 1.34154e13 0.709515
\(893\) −8.43852e12 −0.444053
\(894\) −3.28105e12 −0.171789
\(895\) −3.51834e12 −0.183288
\(896\) 2.44873e13 1.26927
\(897\) −2.84840e11 −0.0146904
\(898\) −1.30106e13 −0.667660
\(899\) −6.87366e13 −3.50970
\(900\) 5.16915e12 0.262620
\(901\) −1.93929e12 −0.0980350
\(902\) −6.27989e12 −0.315880
\(903\) 2.19791e13 1.10006
\(904\) 1.12269e13 0.559118
\(905\) −3.06185e10 −0.00151728
\(906\) 9.38296e11 0.0462661
\(907\) 2.51088e12 0.123195 0.0615974 0.998101i \(-0.480381\pi\)
0.0615974 + 0.998101i \(0.480381\pi\)
\(908\) −1.75742e13 −0.858006
\(909\) 1.99948e12 0.0971360
\(910\) 8.92423e10 0.00431404
\(911\) −9.38760e12 −0.451567 −0.225783 0.974178i \(-0.572494\pi\)
−0.225783 + 0.974178i \(0.572494\pi\)
\(912\) 8.68022e12 0.415483
\(913\) 2.02331e12 0.0963707
\(914\) −4.32777e12 −0.205119
\(915\) 6.15002e11 0.0290056
\(916\) −3.01871e13 −1.41674
\(917\) 6.78288e12 0.316776
\(918\) −8.34952e11 −0.0388033
\(919\) −1.67433e13 −0.774320 −0.387160 0.922013i \(-0.626544\pi\)
−0.387160 + 0.922013i \(0.626544\pi\)
\(920\) 2.10126e12 0.0967018
\(921\) −1.95456e13 −0.895117
\(922\) −1.01558e13 −0.462834
\(923\) 3.64212e11 0.0165176
\(924\) 6.62077e12 0.298803
\(925\) −3.79890e12 −0.170616
\(926\) −7.59731e12 −0.339555
\(927\) 2.51490e12 0.111857
\(928\) −3.98840e13 −1.76536
\(929\) −2.28909e13 −1.00830 −0.504152 0.863615i \(-0.668195\pi\)
−0.504152 + 0.863615i \(0.668195\pi\)
\(930\) 2.17651e12 0.0954084
\(931\) 1.89282e13 0.825725
\(932\) −1.03629e13 −0.449894
\(933\) −2.56000e13 −1.10605
\(934\) −1.05673e13 −0.454365
\(935\) −1.12311e12 −0.0480584
\(936\) −2.45135e11 −0.0104391
\(937\) 1.00934e13 0.427770 0.213885 0.976859i \(-0.431388\pi\)
0.213885 + 0.976859i \(0.431388\pi\)
\(938\) 4.52780e12 0.190974
\(939\) 1.77305e13 0.744263
\(940\) 1.20114e12 0.0501784
\(941\) −1.00404e13 −0.417444 −0.208722 0.977975i \(-0.566930\pi\)
−0.208722 + 0.977975i \(0.566930\pi\)
\(942\) −7.21606e12 −0.298587
\(943\) −2.25313e13 −0.927863
\(944\) −1.57085e12 −0.0643815
\(945\) 1.18338e12 0.0482704
\(946\) 7.99224e12 0.324458
\(947\) 1.08513e13 0.438438 0.219219 0.975676i \(-0.429649\pi\)
0.219219 + 0.975676i \(0.429649\pi\)
\(948\) −1.67057e13 −0.671781
\(949\) −2.48450e11 −0.00994356
\(950\) 1.48442e13 0.591290
\(951\) −3.39949e12 −0.134773
\(952\) 1.16486e13 0.459629
\(953\) −4.63187e13 −1.81902 −0.909511 0.415680i \(-0.863544\pi\)
−0.909511 + 0.415680i \(0.863544\pi\)
\(954\) 7.43026e11 0.0290427
\(955\) 3.08390e12 0.119973
\(956\) −1.52589e13 −0.590831
\(957\) −1.35897e13 −0.523730
\(958\) 5.83878e12 0.223964
\(959\) 3.76738e13 1.43832
\(960\) −2.42377e11 −0.00921022
\(961\) 7.39485e13 2.79688
\(962\) 8.12120e10 0.00305726
\(963\) 1.26533e13 0.474119
\(964\) −1.13122e13 −0.421890
\(965\) −8.09788e12 −0.300606
\(966\) −5.18598e12 −0.191617
\(967\) 1.75311e13 0.644748 0.322374 0.946612i \(-0.395519\pi\)
0.322374 + 0.946612i \(0.395519\pi\)
\(968\) −1.57149e13 −0.575272
\(969\) 1.09827e13 0.400178
\(970\) −5.32821e11 −0.0193245
\(971\) −5.17404e13 −1.86786 −0.933928 0.357462i \(-0.883642\pi\)
−0.933928 + 0.357462i \(0.883642\pi\)
\(972\) −1.46533e12 −0.0526546
\(973\) 6.68223e12 0.239009
\(974\) 2.27204e13 0.808911
\(975\) 6.35371e11 0.0225168
\(976\) 3.51547e12 0.124011
\(977\) 3.99723e13 1.40357 0.701785 0.712389i \(-0.252387\pi\)
0.701785 + 0.712389i \(0.252387\pi\)
\(978\) −1.38054e13 −0.482531
\(979\) −1.52452e13 −0.530408
\(980\) −2.69423e12 −0.0933077
\(981\) 6.17399e12 0.212841
\(982\) 4.09391e12 0.140487
\(983\) 8.61081e12 0.294140 0.147070 0.989126i \(-0.453016\pi\)
0.147070 + 0.989126i \(0.453016\pi\)
\(984\) −1.93906e13 −0.659345
\(985\) −5.05470e12 −0.171093
\(986\) −1.07784e13 −0.363168
\(987\) −6.57608e12 −0.220567
\(988\) 1.45355e12 0.0485316
\(989\) 2.86750e13 0.953060
\(990\) 4.30311e11 0.0142372
\(991\) −3.90846e13 −1.28728 −0.643642 0.765326i \(-0.722578\pi\)
−0.643642 + 0.765326i \(0.722578\pi\)
\(992\) 5.82495e13 1.90981
\(993\) −5.21110e11 −0.0170082
\(994\) 6.63109e12 0.215450
\(995\) −6.47541e12 −0.209442
\(996\) 2.81630e12 0.0906800
\(997\) 4.21821e12 0.135207 0.0676037 0.997712i \(-0.478465\pi\)
0.0676037 + 0.997712i \(0.478465\pi\)
\(998\) 9.44446e12 0.301363
\(999\) 1.07690e12 0.0342081
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 177.10.a.d.1.9 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.9 22 1.1 even 1 trivial