Properties

Label 177.10.a.c.1.11
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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

$q$-expansion

\(f(q)\) \(=\) \(q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +2748.88 q^{10} +58546.2 q^{11} +40719.7 q^{12} -16581.3 q^{13} -4008.42 q^{14} +73060.1 q^{15} +247964. q^{16} -314209. q^{17} -19995.4 q^{18} -530644. q^{19} +453435. q^{20} -106537. q^{21} -178426. q^{22} -1.77605e6 q^{23} -250489. q^{24} -1.13956e6 q^{25} +50533.4 q^{26} -531441. q^{27} -661200. q^{28} -969983. q^{29} -222659. q^{30} -1.85049e6 q^{31} -2.33903e6 q^{32} -4.74224e6 q^{33} +957589. q^{34} -1.18634e6 q^{35} -3.29829e6 q^{36} -1.58532e7 q^{37} +1.61720e6 q^{38} +1.34309e6 q^{39} -2.78932e6 q^{40} +1.46562e7 q^{41} +324682. q^{42} +8.74387e6 q^{43} -2.94319e7 q^{44} -5.91787e6 q^{45} +5.41271e6 q^{46} +9.62436e6 q^{47} -2.00851e7 q^{48} -3.86237e7 q^{49} +3.47295e6 q^{50} +2.54510e7 q^{51} +8.33562e6 q^{52} +1.35914e7 q^{53} +1.61963e6 q^{54} -5.28073e7 q^{55} +4.06740e6 q^{56} +4.29821e7 q^{57} +2.95614e6 q^{58} +1.21174e7 q^{59} -3.67282e7 q^{60} +2.10664e8 q^{61} +5.63958e6 q^{62} +8.62946e6 q^{63} -1.19829e8 q^{64} +1.49560e7 q^{65} +1.44525e7 q^{66} -7.42783e7 q^{67} +1.57957e8 q^{68} +1.43860e8 q^{69} +3.61551e6 q^{70} -2.60132e8 q^{71} +2.02896e7 q^{72} +1.75339e8 q^{73} +4.83144e7 q^{74} +9.23046e7 q^{75} +2.66761e8 q^{76} +7.70038e7 q^{77} -4.09321e6 q^{78} +5.38457e6 q^{79} -2.23658e8 q^{80} +4.30467e7 q^{81} -4.46665e7 q^{82} +1.20469e8 q^{83} +5.35572e7 q^{84} +2.83410e8 q^{85} -2.66479e7 q^{86} +7.85687e7 q^{87} +1.81051e8 q^{88} -1.11762e9 q^{89} +1.80354e7 q^{90} -2.18088e7 q^{91} +8.92841e8 q^{92} +1.49890e8 q^{93} -2.93313e7 q^{94} +4.78628e8 q^{95} +1.89462e8 q^{96} -1.55196e9 q^{97} +1.17710e8 q^{98} +3.84122e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.04761 −0.134687 −0.0673434 0.997730i \(-0.521452\pi\)
−0.0673434 + 0.997730i \(0.521452\pi\)
\(3\) −81.0000 −0.577350
\(4\) −502.712 −0.981859
\(5\) −901.977 −0.645402 −0.322701 0.946501i \(-0.604591\pi\)
−0.322701 + 0.946501i \(0.604591\pi\)
\(6\) 246.857 0.0777615
\(7\) 1315.27 0.207049 0.103524 0.994627i \(-0.466988\pi\)
0.103524 + 0.994627i \(0.466988\pi\)
\(8\) 3092.45 0.266930
\(9\) 6561.00 0.333333
\(10\) 2748.88 0.0869272
\(11\) 58546.2 1.20568 0.602839 0.797863i \(-0.294036\pi\)
0.602839 + 0.797863i \(0.294036\pi\)
\(12\) 40719.7 0.566877
\(13\) −16581.3 −0.161018 −0.0805088 0.996754i \(-0.525655\pi\)
−0.0805088 + 0.996754i \(0.525655\pi\)
\(14\) −4008.42 −0.0278867
\(15\) 73060.1 0.372623
\(16\) 247964. 0.945907
\(17\) −314209. −0.912429 −0.456214 0.889870i \(-0.650795\pi\)
−0.456214 + 0.889870i \(0.650795\pi\)
\(18\) −19995.4 −0.0448956
\(19\) −530644. −0.934139 −0.467070 0.884220i \(-0.654690\pi\)
−0.467070 + 0.884220i \(0.654690\pi\)
\(20\) 453435. 0.633694
\(21\) −106537. −0.119540
\(22\) −178426. −0.162389
\(23\) −1.77605e6 −1.32337 −0.661683 0.749784i \(-0.730157\pi\)
−0.661683 + 0.749784i \(0.730157\pi\)
\(24\) −250489. −0.154112
\(25\) −1.13956e6 −0.583456
\(26\) 50533.4 0.0216870
\(27\) −531441. −0.192450
\(28\) −661200. −0.203293
\(29\) −969983. −0.254667 −0.127334 0.991860i \(-0.540642\pi\)
−0.127334 + 0.991860i \(0.540642\pi\)
\(30\) −222659. −0.0501874
\(31\) −1.85049e6 −0.359881 −0.179941 0.983677i \(-0.557591\pi\)
−0.179941 + 0.983677i \(0.557591\pi\)
\(32\) −2.33903e6 −0.394332
\(33\) −4.74224e6 −0.696099
\(34\) 957589. 0.122892
\(35\) −1.18634e6 −0.133630
\(36\) −3.29829e6 −0.327286
\(37\) −1.58532e7 −1.39062 −0.695311 0.718709i \(-0.744733\pi\)
−0.695311 + 0.718709i \(0.744733\pi\)
\(38\) 1.61720e6 0.125816
\(39\) 1.34309e6 0.0929636
\(40\) −2.78932e6 −0.172277
\(41\) 1.46562e7 0.810018 0.405009 0.914313i \(-0.367268\pi\)
0.405009 + 0.914313i \(0.367268\pi\)
\(42\) 324682. 0.0161004
\(43\) 8.74387e6 0.390028 0.195014 0.980800i \(-0.437525\pi\)
0.195014 + 0.980800i \(0.437525\pi\)
\(44\) −2.94319e7 −1.18381
\(45\) −5.91787e6 −0.215134
\(46\) 5.41271e6 0.178240
\(47\) 9.62436e6 0.287694 0.143847 0.989600i \(-0.454053\pi\)
0.143847 + 0.989600i \(0.454053\pi\)
\(48\) −2.00851e7 −0.546120
\(49\) −3.86237e7 −0.957131
\(50\) 3.47295e6 0.0785838
\(51\) 2.54510e7 0.526791
\(52\) 8.33562e6 0.158097
\(53\) 1.35914e7 0.236604 0.118302 0.992978i \(-0.462255\pi\)
0.118302 + 0.992978i \(0.462255\pi\)
\(54\) 1.61963e6 0.0259205
\(55\) −5.28073e7 −0.778148
\(56\) 4.06740e6 0.0552676
\(57\) 4.29821e7 0.539326
\(58\) 2.95614e6 0.0343003
\(59\) 1.21174e7 0.130189
\(60\) −3.67282e7 −0.365864
\(61\) 2.10664e8 1.94807 0.974036 0.226393i \(-0.0726933\pi\)
0.974036 + 0.226393i \(0.0726933\pi\)
\(62\) 5.63958e6 0.0484712
\(63\) 8.62946e6 0.0690162
\(64\) −1.19829e8 −0.892796
\(65\) 1.49560e7 0.103921
\(66\) 1.44525e7 0.0937553
\(67\) −7.42783e7 −0.450324 −0.225162 0.974321i \(-0.572291\pi\)
−0.225162 + 0.974321i \(0.572291\pi\)
\(68\) 1.57957e8 0.895877
\(69\) 1.43860e8 0.764045
\(70\) 3.61551e6 0.0179982
\(71\) −2.60132e8 −1.21487 −0.607436 0.794369i \(-0.707802\pi\)
−0.607436 + 0.794369i \(0.707802\pi\)
\(72\) 2.02896e7 0.0889768
\(73\) 1.75339e8 0.722648 0.361324 0.932440i \(-0.382325\pi\)
0.361324 + 0.932440i \(0.382325\pi\)
\(74\) 4.83144e7 0.187298
\(75\) 9.23046e7 0.336858
\(76\) 2.66761e8 0.917194
\(77\) 7.70038e7 0.249634
\(78\) −4.09321e6 −0.0125210
\(79\) 5.38457e6 0.0155535 0.00777676 0.999970i \(-0.497525\pi\)
0.00777676 + 0.999970i \(0.497525\pi\)
\(80\) −2.23658e8 −0.610491
\(81\) 4.30467e7 0.111111
\(82\) −4.46665e7 −0.109099
\(83\) 1.20469e8 0.278627 0.139314 0.990248i \(-0.455510\pi\)
0.139314 + 0.990248i \(0.455510\pi\)
\(84\) 5.35572e7 0.117371
\(85\) 2.83410e8 0.588883
\(86\) −2.66479e7 −0.0525316
\(87\) 7.85687e7 0.147032
\(88\) 1.81051e8 0.321832
\(89\) −1.11762e9 −1.88816 −0.944080 0.329717i \(-0.893047\pi\)
−0.944080 + 0.329717i \(0.893047\pi\)
\(90\) 1.80354e7 0.0289757
\(91\) −2.18088e7 −0.0333385
\(92\) 8.92841e8 1.29936
\(93\) 1.49890e8 0.207777
\(94\) −2.93313e7 −0.0387486
\(95\) 4.78628e8 0.602896
\(96\) 1.89462e8 0.227667
\(97\) −1.55196e9 −1.77996 −0.889978 0.456004i \(-0.849280\pi\)
−0.889978 + 0.456004i \(0.849280\pi\)
\(98\) 1.17710e8 0.128913
\(99\) 3.84122e8 0.401893
\(100\) 5.72872e8 0.572872
\(101\) −6.59584e8 −0.630702 −0.315351 0.948975i \(-0.602122\pi\)
−0.315351 + 0.948975i \(0.602122\pi\)
\(102\) −7.75647e7 −0.0709518
\(103\) −5.65496e8 −0.495065 −0.247532 0.968880i \(-0.579620\pi\)
−0.247532 + 0.968880i \(0.579620\pi\)
\(104\) −5.12769e7 −0.0429805
\(105\) 9.60935e7 0.0771511
\(106\) −4.14212e7 −0.0318674
\(107\) 2.46996e9 1.82164 0.910819 0.412805i \(-0.135451\pi\)
0.910819 + 0.412805i \(0.135451\pi\)
\(108\) 2.67162e8 0.188959
\(109\) 1.07908e7 0.00732205 0.00366103 0.999993i \(-0.498835\pi\)
0.00366103 + 0.999993i \(0.498835\pi\)
\(110\) 1.60936e8 0.104806
\(111\) 1.28411e9 0.802875
\(112\) 3.26139e8 0.195849
\(113\) 2.28566e9 1.31874 0.659370 0.751819i \(-0.270823\pi\)
0.659370 + 0.751819i \(0.270823\pi\)
\(114\) −1.30993e8 −0.0726400
\(115\) 1.60196e9 0.854103
\(116\) 4.87622e8 0.250048
\(117\) −1.08790e8 −0.0536726
\(118\) −3.69290e7 −0.0175347
\(119\) −4.13269e8 −0.188917
\(120\) 2.25935e8 0.0994644
\(121\) 1.06971e9 0.453661
\(122\) −6.42021e8 −0.262380
\(123\) −1.18715e9 −0.467664
\(124\) 9.30263e8 0.353353
\(125\) 2.78953e9 1.02197
\(126\) −2.62993e7 −0.00929557
\(127\) −4.78876e9 −1.63345 −0.816726 0.577026i \(-0.804213\pi\)
−0.816726 + 0.577026i \(0.804213\pi\)
\(128\) 1.56278e9 0.514579
\(129\) −7.08253e8 −0.225183
\(130\) −4.55800e7 −0.0139968
\(131\) −3.74607e9 −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(132\) 2.38398e9 0.683471
\(133\) −6.97937e8 −0.193412
\(134\) 2.26372e8 0.0606528
\(135\) 4.79348e8 0.124208
\(136\) −9.71677e8 −0.243555
\(137\) 6.96038e9 1.68807 0.844035 0.536288i \(-0.180174\pi\)
0.844035 + 0.536288i \(0.180174\pi\)
\(138\) −4.38430e8 −0.102907
\(139\) 2.25010e9 0.511251 0.255626 0.966776i \(-0.417719\pi\)
0.255626 + 0.966776i \(0.417719\pi\)
\(140\) 5.96387e8 0.131206
\(141\) −7.79573e8 −0.166100
\(142\) 7.92781e8 0.163627
\(143\) −9.70772e8 −0.194136
\(144\) 1.62689e9 0.315302
\(145\) 8.74903e8 0.164363
\(146\) −5.34367e8 −0.0973312
\(147\) 3.12852e9 0.552600
\(148\) 7.96959e9 1.36539
\(149\) 3.86787e9 0.642885 0.321443 0.946929i \(-0.395832\pi\)
0.321443 + 0.946929i \(0.395832\pi\)
\(150\) −2.81309e8 −0.0453704
\(151\) 6.03451e9 0.944596 0.472298 0.881439i \(-0.343425\pi\)
0.472298 + 0.881439i \(0.343425\pi\)
\(152\) −1.64099e9 −0.249350
\(153\) −2.06153e9 −0.304143
\(154\) −2.34678e8 −0.0336224
\(155\) 1.66910e9 0.232268
\(156\) −6.75185e8 −0.0912772
\(157\) 1.04664e10 1.37483 0.687414 0.726266i \(-0.258746\pi\)
0.687414 + 0.726266i \(0.258746\pi\)
\(158\) −1.64101e7 −0.00209485
\(159\) −1.10090e9 −0.136603
\(160\) 2.10975e9 0.254502
\(161\) −2.33598e9 −0.274001
\(162\) −1.31190e8 −0.0149652
\(163\) 9.62382e9 1.06783 0.533916 0.845537i \(-0.320720\pi\)
0.533916 + 0.845537i \(0.320720\pi\)
\(164\) −7.36786e9 −0.795324
\(165\) 4.27739e9 0.449264
\(166\) −3.67143e8 −0.0375274
\(167\) −7.42318e9 −0.738526 −0.369263 0.929325i \(-0.620390\pi\)
−0.369263 + 0.929325i \(0.620390\pi\)
\(168\) −3.29459e8 −0.0319087
\(169\) −1.03296e10 −0.974073
\(170\) −8.63723e8 −0.0793148
\(171\) −3.48155e9 −0.311380
\(172\) −4.39565e9 −0.382952
\(173\) 1.62267e10 1.37728 0.688642 0.725102i \(-0.258207\pi\)
0.688642 + 0.725102i \(0.258207\pi\)
\(174\) −2.39447e8 −0.0198033
\(175\) −1.49883e9 −0.120804
\(176\) 1.45173e10 1.14046
\(177\) −9.81506e8 −0.0751646
\(178\) 3.40607e9 0.254310
\(179\) −5.30261e9 −0.386057 −0.193028 0.981193i \(-0.561831\pi\)
−0.193028 + 0.981193i \(0.561831\pi\)
\(180\) 2.97499e9 0.211231
\(181\) −5.17037e9 −0.358070 −0.179035 0.983843i \(-0.557298\pi\)
−0.179035 + 0.983843i \(0.557298\pi\)
\(182\) 6.64649e7 0.00449025
\(183\) −1.70637e10 −1.12472
\(184\) −5.49235e9 −0.353246
\(185\) 1.42992e10 0.897510
\(186\) −4.56806e8 −0.0279849
\(187\) −1.83958e10 −1.10010
\(188\) −4.83828e9 −0.282475
\(189\) −6.98986e8 −0.0398465
\(190\) −1.45867e9 −0.0812021
\(191\) 1.32702e10 0.721484 0.360742 0.932666i \(-0.382523\pi\)
0.360742 + 0.932666i \(0.382523\pi\)
\(192\) 9.70616e9 0.515456
\(193\) 3.53079e10 1.83174 0.915871 0.401473i \(-0.131502\pi\)
0.915871 + 0.401473i \(0.131502\pi\)
\(194\) 4.72979e9 0.239736
\(195\) −1.21143e9 −0.0599989
\(196\) 1.94166e10 0.939768
\(197\) −5.84038e9 −0.276276 −0.138138 0.990413i \(-0.544112\pi\)
−0.138138 + 0.990413i \(0.544112\pi\)
\(198\) −1.17065e9 −0.0541297
\(199\) 2.30703e10 1.04283 0.521417 0.853302i \(-0.325404\pi\)
0.521417 + 0.853302i \(0.325404\pi\)
\(200\) −3.52404e9 −0.155742
\(201\) 6.01654e9 0.259995
\(202\) 2.01016e9 0.0849472
\(203\) −1.27579e9 −0.0527285
\(204\) −1.27945e10 −0.517235
\(205\) −1.32196e10 −0.522787
\(206\) 1.72341e9 0.0666787
\(207\) −1.16527e10 −0.441122
\(208\) −4.11157e9 −0.152308
\(209\) −3.10672e10 −1.12627
\(210\) −2.92856e8 −0.0103912
\(211\) −9.86647e9 −0.342682 −0.171341 0.985212i \(-0.554810\pi\)
−0.171341 + 0.985212i \(0.554810\pi\)
\(212\) −6.83254e9 −0.232312
\(213\) 2.10707e10 0.701407
\(214\) −7.52747e9 −0.245351
\(215\) −7.88677e9 −0.251725
\(216\) −1.64346e9 −0.0513708
\(217\) −2.43389e9 −0.0745129
\(218\) −3.28861e7 −0.000986184 0
\(219\) −1.42025e10 −0.417221
\(220\) 2.65469e10 0.764032
\(221\) 5.21000e9 0.146917
\(222\) −3.91347e9 −0.108137
\(223\) 6.98728e10 1.89207 0.946033 0.324072i \(-0.105052\pi\)
0.946033 + 0.324072i \(0.105052\pi\)
\(224\) −3.07645e9 −0.0816458
\(225\) −7.47667e9 −0.194485
\(226\) −6.96582e9 −0.177617
\(227\) −5.38083e10 −1.34503 −0.672517 0.740082i \(-0.734787\pi\)
−0.672517 + 0.740082i \(0.734787\pi\)
\(228\) −2.16076e10 −0.529542
\(229\) 3.90912e10 0.939333 0.469666 0.882844i \(-0.344374\pi\)
0.469666 + 0.882844i \(0.344374\pi\)
\(230\) −4.88214e9 −0.115036
\(231\) −6.23731e9 −0.144126
\(232\) −2.99963e9 −0.0679784
\(233\) −5.08792e10 −1.13094 −0.565469 0.824769i \(-0.691305\pi\)
−0.565469 + 0.824769i \(0.691305\pi\)
\(234\) 3.31550e8 0.00722898
\(235\) −8.68095e9 −0.185679
\(236\) −6.09154e9 −0.127827
\(237\) −4.36150e8 −0.00897983
\(238\) 1.25948e9 0.0254446
\(239\) −6.86409e10 −1.36079 −0.680397 0.732843i \(-0.738193\pi\)
−0.680397 + 0.732843i \(0.738193\pi\)
\(240\) 1.81163e10 0.352467
\(241\) 6.40754e10 1.22353 0.611765 0.791040i \(-0.290460\pi\)
0.611765 + 0.791040i \(0.290460\pi\)
\(242\) −3.26006e9 −0.0611021
\(243\) −3.48678e9 −0.0641500
\(244\) −1.05903e11 −1.91273
\(245\) 3.48377e10 0.617734
\(246\) 3.61799e9 0.0629882
\(247\) 8.79876e9 0.150413
\(248\) −5.72255e9 −0.0960632
\(249\) −9.75798e9 −0.160865
\(250\) −8.50142e9 −0.137645
\(251\) −3.82370e10 −0.608067 −0.304034 0.952661i \(-0.598334\pi\)
−0.304034 + 0.952661i \(0.598334\pi\)
\(252\) −4.33813e9 −0.0677642
\(253\) −1.03981e11 −1.59555
\(254\) 1.45943e10 0.220004
\(255\) −2.29562e10 −0.339992
\(256\) 5.65897e10 0.823489
\(257\) 2.41008e10 0.344613 0.172307 0.985043i \(-0.444878\pi\)
0.172307 + 0.985043i \(0.444878\pi\)
\(258\) 2.15848e9 0.0303291
\(259\) −2.08512e10 −0.287926
\(260\) −7.51854e9 −0.102036
\(261\) −6.36406e9 −0.0848891
\(262\) 1.14166e10 0.149686
\(263\) 3.70783e10 0.477881 0.238940 0.971034i \(-0.423200\pi\)
0.238940 + 0.971034i \(0.423200\pi\)
\(264\) −1.46651e10 −0.185810
\(265\) −1.22591e10 −0.152705
\(266\) 2.12704e9 0.0260501
\(267\) 9.05271e10 1.09013
\(268\) 3.73406e10 0.442155
\(269\) −9.07848e10 −1.05713 −0.528565 0.848893i \(-0.677270\pi\)
−0.528565 + 0.848893i \(0.677270\pi\)
\(270\) −1.46087e9 −0.0167291
\(271\) −1.00447e10 −0.113129 −0.0565647 0.998399i \(-0.518015\pi\)
−0.0565647 + 0.998399i \(0.518015\pi\)
\(272\) −7.79126e10 −0.863073
\(273\) 1.76651e9 0.0192480
\(274\) −2.12126e10 −0.227361
\(275\) −6.67170e10 −0.703460
\(276\) −7.23202e10 −0.750185
\(277\) 8.59336e10 0.877009 0.438505 0.898729i \(-0.355508\pi\)
0.438505 + 0.898729i \(0.355508\pi\)
\(278\) −6.85742e9 −0.0688588
\(279\) −1.21411e10 −0.119960
\(280\) −3.66870e9 −0.0356698
\(281\) −7.17150e10 −0.686169 −0.343085 0.939304i \(-0.611472\pi\)
−0.343085 + 0.939304i \(0.611472\pi\)
\(282\) 2.37584e9 0.0223715
\(283\) −1.35746e11 −1.25803 −0.629013 0.777395i \(-0.716541\pi\)
−0.629013 + 0.777395i \(0.716541\pi\)
\(284\) 1.30771e11 1.19283
\(285\) −3.87689e10 −0.348082
\(286\) 2.95854e9 0.0261475
\(287\) 1.92768e10 0.167713
\(288\) −1.53464e10 −0.131444
\(289\) −1.98604e10 −0.167474
\(290\) −2.66637e9 −0.0221375
\(291\) 1.25709e11 1.02766
\(292\) −8.81453e10 −0.709539
\(293\) 1.62874e10 0.129107 0.0645533 0.997914i \(-0.479438\pi\)
0.0645533 + 0.997914i \(0.479438\pi\)
\(294\) −9.53452e9 −0.0744279
\(295\) −1.09296e10 −0.0840242
\(296\) −4.90252e10 −0.371199
\(297\) −3.11138e10 −0.232033
\(298\) −1.17878e10 −0.0865882
\(299\) 2.94492e10 0.213085
\(300\) −4.64026e10 −0.330748
\(301\) 1.15005e10 0.0807547
\(302\) −1.83909e10 −0.127225
\(303\) 5.34263e10 0.364136
\(304\) −1.31580e11 −0.883610
\(305\) −1.90014e11 −1.25729
\(306\) 6.28274e9 0.0409640
\(307\) 1.47734e11 0.949199 0.474600 0.880202i \(-0.342593\pi\)
0.474600 + 0.880202i \(0.342593\pi\)
\(308\) −3.87107e10 −0.245106
\(309\) 4.58052e10 0.285826
\(310\) −5.08677e9 −0.0312834
\(311\) −1.58619e11 −0.961466 −0.480733 0.876867i \(-0.659629\pi\)
−0.480733 + 0.876867i \(0.659629\pi\)
\(312\) 4.15343e9 0.0248148
\(313\) 1.25095e11 0.736699 0.368350 0.929687i \(-0.379923\pi\)
0.368350 + 0.929687i \(0.379923\pi\)
\(314\) −3.18975e10 −0.185171
\(315\) −7.78357e9 −0.0445432
\(316\) −2.70689e9 −0.0152714
\(317\) −6.32118e10 −0.351586 −0.175793 0.984427i \(-0.556249\pi\)
−0.175793 + 0.984427i \(0.556249\pi\)
\(318\) 3.35512e9 0.0183987
\(319\) −5.67888e10 −0.307047
\(320\) 1.08083e11 0.576213
\(321\) −2.00066e11 −1.05172
\(322\) 7.11916e9 0.0369043
\(323\) 1.66733e11 0.852336
\(324\) −2.16401e10 −0.109095
\(325\) 1.88954e10 0.0939467
\(326\) −2.93297e10 −0.143823
\(327\) −8.74052e8 −0.00422739
\(328\) 4.53237e10 0.216218
\(329\) 1.26586e10 0.0595667
\(330\) −1.30358e10 −0.0605099
\(331\) 2.23089e11 1.02153 0.510767 0.859719i \(-0.329361\pi\)
0.510767 + 0.859719i \(0.329361\pi\)
\(332\) −6.05611e10 −0.273573
\(333\) −1.04013e11 −0.463540
\(334\) 2.26230e10 0.0994697
\(335\) 6.69973e10 0.290640
\(336\) −2.64172e10 −0.113073
\(337\) 3.34285e11 1.41183 0.705914 0.708297i \(-0.250536\pi\)
0.705914 + 0.708297i \(0.250536\pi\)
\(338\) 3.14805e10 0.131195
\(339\) −1.85139e11 −0.761375
\(340\) −1.42473e11 −0.578201
\(341\) −1.08339e11 −0.433901
\(342\) 1.06104e10 0.0419388
\(343\) −1.03876e11 −0.405221
\(344\) 2.70400e10 0.104110
\(345\) −1.29758e11 −0.493117
\(346\) −4.94528e10 −0.185502
\(347\) −6.46893e10 −0.239524 −0.119762 0.992803i \(-0.538213\pi\)
−0.119762 + 0.992803i \(0.538213\pi\)
\(348\) −3.94974e10 −0.144365
\(349\) 8.16421e10 0.294578 0.147289 0.989094i \(-0.452945\pi\)
0.147289 + 0.989094i \(0.452945\pi\)
\(350\) 4.56785e9 0.0162707
\(351\) 8.81198e9 0.0309879
\(352\) −1.36941e11 −0.475437
\(353\) 4.09816e11 1.40476 0.702381 0.711802i \(-0.252120\pi\)
0.702381 + 0.711802i \(0.252120\pi\)
\(354\) 2.99125e9 0.0101237
\(355\) 2.34633e11 0.784081
\(356\) 5.61841e11 1.85391
\(357\) 3.34748e10 0.109071
\(358\) 1.61603e10 0.0519967
\(359\) 5.01343e11 1.59298 0.796490 0.604652i \(-0.206688\pi\)
0.796490 + 0.604652i \(0.206688\pi\)
\(360\) −1.83007e10 −0.0574258
\(361\) −4.11051e10 −0.127383
\(362\) 1.57573e10 0.0482273
\(363\) −8.66464e10 −0.261921
\(364\) 1.09636e10 0.0327337
\(365\) −1.58152e11 −0.466399
\(366\) 5.20037e10 0.151485
\(367\) −3.40745e11 −0.980465 −0.490233 0.871592i \(-0.663088\pi\)
−0.490233 + 0.871592i \(0.663088\pi\)
\(368\) −4.40396e11 −1.25178
\(369\) 9.61595e10 0.270006
\(370\) −4.35785e10 −0.120883
\(371\) 1.78763e10 0.0489885
\(372\) −7.53513e10 −0.204008
\(373\) 3.56680e11 0.954088 0.477044 0.878879i \(-0.341708\pi\)
0.477044 + 0.878879i \(0.341708\pi\)
\(374\) 5.60632e10 0.148168
\(375\) −2.25952e11 −0.590032
\(376\) 2.97629e10 0.0767944
\(377\) 1.60836e10 0.0410059
\(378\) 2.13024e9 0.00536680
\(379\) 1.35033e11 0.336174 0.168087 0.985772i \(-0.446241\pi\)
0.168087 + 0.985772i \(0.446241\pi\)
\(380\) −2.40612e11 −0.591959
\(381\) 3.87889e11 0.943073
\(382\) −4.04424e10 −0.0971744
\(383\) 3.10673e11 0.737749 0.368874 0.929479i \(-0.379743\pi\)
0.368874 + 0.929479i \(0.379743\pi\)
\(384\) −1.26585e11 −0.297093
\(385\) −6.94557e10 −0.161114
\(386\) −1.07605e11 −0.246711
\(387\) 5.73685e10 0.130009
\(388\) 7.80191e11 1.74767
\(389\) −2.90209e11 −0.642596 −0.321298 0.946978i \(-0.604119\pi\)
−0.321298 + 0.946978i \(0.604119\pi\)
\(390\) 3.69198e9 0.00808106
\(391\) 5.58051e11 1.20748
\(392\) −1.19442e11 −0.255487
\(393\) 3.03432e11 0.641644
\(394\) 1.77992e10 0.0372107
\(395\) −4.85675e9 −0.0100383
\(396\) −1.93103e11 −0.394602
\(397\) 4.88071e11 0.986110 0.493055 0.869998i \(-0.335880\pi\)
0.493055 + 0.869998i \(0.335880\pi\)
\(398\) −7.03095e10 −0.140456
\(399\) 5.65329e10 0.111667
\(400\) −2.82570e11 −0.551895
\(401\) −9.52691e11 −1.83993 −0.919967 0.391996i \(-0.871785\pi\)
−0.919967 + 0.391996i \(0.871785\pi\)
\(402\) −1.83361e10 −0.0350179
\(403\) 3.06835e10 0.0579472
\(404\) 3.31581e11 0.619261
\(405\) −3.88272e10 −0.0717114
\(406\) 3.88810e9 0.00710184
\(407\) −9.28144e11 −1.67664
\(408\) 7.87058e10 0.140616
\(409\) 9.64628e11 1.70453 0.852265 0.523110i \(-0.175228\pi\)
0.852265 + 0.523110i \(0.175228\pi\)
\(410\) 4.02882e10 0.0704126
\(411\) −5.63791e11 −0.974608
\(412\) 2.84282e11 0.486084
\(413\) 1.59376e10 0.0269554
\(414\) 3.55128e10 0.0594133
\(415\) −1.08660e11 −0.179827
\(416\) 3.87842e10 0.0634943
\(417\) −1.82258e11 −0.295171
\(418\) 9.46807e10 0.151694
\(419\) 4.13312e11 0.655111 0.327556 0.944832i \(-0.393775\pi\)
0.327556 + 0.944832i \(0.393775\pi\)
\(420\) −4.83074e10 −0.0757516
\(421\) 8.80319e10 0.136575 0.0682874 0.997666i \(-0.478247\pi\)
0.0682874 + 0.997666i \(0.478247\pi\)
\(422\) 3.00692e10 0.0461547
\(423\) 6.31454e10 0.0958981
\(424\) 4.20306e10 0.0631567
\(425\) 3.58061e11 0.532362
\(426\) −6.42152e10 −0.0944702
\(427\) 2.77079e11 0.403346
\(428\) −1.24168e12 −1.78859
\(429\) 7.86325e10 0.112084
\(430\) 2.40358e10 0.0339040
\(431\) 1.23323e12 1.72146 0.860730 0.509062i \(-0.170008\pi\)
0.860730 + 0.509062i \(0.170008\pi\)
\(432\) −1.31778e11 −0.182040
\(433\) 1.16757e12 1.59620 0.798098 0.602528i \(-0.205840\pi\)
0.798098 + 0.602528i \(0.205840\pi\)
\(434\) 7.41755e9 0.0100359
\(435\) −7.08671e10 −0.0948950
\(436\) −5.42465e9 −0.00718923
\(437\) 9.42449e11 1.23621
\(438\) 4.32837e10 0.0561942
\(439\) 8.59317e11 1.10424 0.552119 0.833765i \(-0.313819\pi\)
0.552119 + 0.833765i \(0.313819\pi\)
\(440\) −1.63304e11 −0.207711
\(441\) −2.53410e11 −0.319044
\(442\) −1.58781e10 −0.0197878
\(443\) −9.24505e11 −1.14049 −0.570246 0.821474i \(-0.693152\pi\)
−0.570246 + 0.821474i \(0.693152\pi\)
\(444\) −6.45537e11 −0.788311
\(445\) 1.00807e12 1.21862
\(446\) −2.12945e11 −0.254836
\(447\) −3.13297e11 −0.371170
\(448\) −1.57607e11 −0.184852
\(449\) −2.10652e11 −0.244600 −0.122300 0.992493i \(-0.539027\pi\)
−0.122300 + 0.992493i \(0.539027\pi\)
\(450\) 2.27860e10 0.0261946
\(451\) 8.58066e11 0.976622
\(452\) −1.14903e12 −1.29482
\(453\) −4.88795e11 −0.545362
\(454\) 1.63987e11 0.181158
\(455\) 1.96711e10 0.0215167
\(456\) 1.32920e11 0.143962
\(457\) −6.63413e11 −0.711477 −0.355738 0.934586i \(-0.615771\pi\)
−0.355738 + 0.934586i \(0.615771\pi\)
\(458\) −1.19135e11 −0.126516
\(459\) 1.66984e11 0.175597
\(460\) −8.05322e11 −0.838609
\(461\) 2.75456e11 0.284052 0.142026 0.989863i \(-0.454638\pi\)
0.142026 + 0.989863i \(0.454638\pi\)
\(462\) 1.90089e10 0.0194119
\(463\) −1.19847e11 −0.121203 −0.0606015 0.998162i \(-0.519302\pi\)
−0.0606015 + 0.998162i \(0.519302\pi\)
\(464\) −2.40521e11 −0.240892
\(465\) −1.35197e11 −0.134100
\(466\) 1.55060e11 0.152322
\(467\) 1.61766e12 1.57384 0.786922 0.617052i \(-0.211673\pi\)
0.786922 + 0.617052i \(0.211673\pi\)
\(468\) 5.46900e10 0.0526989
\(469\) −9.76958e10 −0.0932391
\(470\) 2.64562e10 0.0250085
\(471\) −8.47777e11 −0.793757
\(472\) 3.74723e10 0.0347514
\(473\) 5.11920e11 0.470248
\(474\) 1.32922e9 0.00120946
\(475\) 6.04702e11 0.545029
\(476\) 2.07755e11 0.185490
\(477\) 8.91729e10 0.0788679
\(478\) 2.09191e11 0.183281
\(479\) −1.35413e12 −1.17531 −0.587653 0.809113i \(-0.699948\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(480\) −1.70890e11 −0.146937
\(481\) 2.62866e11 0.223915
\(482\) −1.95277e11 −0.164793
\(483\) 1.89214e11 0.158195
\(484\) −5.37755e11 −0.445431
\(485\) 1.39984e12 1.14879
\(486\) 1.06264e10 0.00864016
\(487\) −3.58121e10 −0.0288502 −0.0144251 0.999896i \(-0.504592\pi\)
−0.0144251 + 0.999896i \(0.504592\pi\)
\(488\) 6.51467e11 0.519999
\(489\) −7.79529e11 −0.616514
\(490\) −1.06172e11 −0.0832007
\(491\) 1.75049e12 1.35923 0.679616 0.733568i \(-0.262146\pi\)
0.679616 + 0.733568i \(0.262146\pi\)
\(492\) 5.96797e11 0.459181
\(493\) 3.04778e11 0.232366
\(494\) −2.68152e10 −0.0202586
\(495\) −3.46469e11 −0.259383
\(496\) −4.58855e11 −0.340414
\(497\) −3.42142e11 −0.251538
\(498\) 2.97385e10 0.0216664
\(499\) 2.12252e12 1.53250 0.766248 0.642545i \(-0.222121\pi\)
0.766248 + 0.642545i \(0.222121\pi\)
\(500\) −1.40233e12 −1.00343
\(501\) 6.01277e11 0.426388
\(502\) 1.16532e11 0.0818987
\(503\) −1.34616e12 −0.937651 −0.468826 0.883291i \(-0.655323\pi\)
−0.468826 + 0.883291i \(0.655323\pi\)
\(504\) 2.66862e10 0.0184225
\(505\) 5.94930e11 0.407056
\(506\) 3.16894e11 0.214900
\(507\) 8.36694e11 0.562381
\(508\) 2.40737e12 1.60382
\(509\) −1.19438e12 −0.788704 −0.394352 0.918959i \(-0.629031\pi\)
−0.394352 + 0.918959i \(0.629031\pi\)
\(510\) 6.99616e10 0.0457924
\(511\) 2.30618e11 0.149623
\(512\) −9.72606e11 −0.625493
\(513\) 2.82006e11 0.179775
\(514\) −7.34499e10 −0.0464149
\(515\) 5.10064e11 0.319516
\(516\) 3.56047e11 0.221098
\(517\) 5.63469e11 0.346867
\(518\) 6.35463e10 0.0387799
\(519\) −1.31436e12 −0.795175
\(520\) 4.62505e10 0.0277397
\(521\) −2.86170e11 −0.170159 −0.0850795 0.996374i \(-0.527114\pi\)
−0.0850795 + 0.996374i \(0.527114\pi\)
\(522\) 1.93952e10 0.0114334
\(523\) 7.15569e11 0.418210 0.209105 0.977893i \(-0.432945\pi\)
0.209105 + 0.977893i \(0.432945\pi\)
\(524\) 1.88319e12 1.09120
\(525\) 1.21405e11 0.0697461
\(526\) −1.13001e11 −0.0643642
\(527\) 5.81441e11 0.328366
\(528\) −1.17590e12 −0.658445
\(529\) 1.35320e12 0.751296
\(530\) 3.73610e10 0.0205673
\(531\) 7.95020e10 0.0433963
\(532\) 3.50862e11 0.189904
\(533\) −2.43019e11 −0.130427
\(534\) −2.75892e11 −0.146826
\(535\) −2.22784e12 −1.17569
\(536\) −2.29702e11 −0.120205
\(537\) 4.29511e11 0.222890
\(538\) 2.76677e11 0.142381
\(539\) −2.26127e12 −1.15399
\(540\) −2.40974e11 −0.121955
\(541\) −1.19257e12 −0.598546 −0.299273 0.954168i \(-0.596744\pi\)
−0.299273 + 0.954168i \(0.596744\pi\)
\(542\) 3.06124e10 0.0152370
\(543\) 4.18800e11 0.206732
\(544\) 7.34946e11 0.359799
\(545\) −9.73302e9 −0.00472567
\(546\) −5.38366e9 −0.00259245
\(547\) −1.17324e12 −0.560329 −0.280164 0.959952i \(-0.590389\pi\)
−0.280164 + 0.959952i \(0.590389\pi\)
\(548\) −3.49907e12 −1.65745
\(549\) 1.38216e12 0.649357
\(550\) 2.03328e11 0.0947468
\(551\) 5.14715e11 0.237895
\(552\) 4.44880e11 0.203947
\(553\) 7.08214e9 0.00322034
\(554\) −2.61893e11 −0.118122
\(555\) −1.15824e12 −0.518178
\(556\) −1.13115e12 −0.501977
\(557\) −3.52276e12 −1.55072 −0.775362 0.631517i \(-0.782433\pi\)
−0.775362 + 0.631517i \(0.782433\pi\)
\(558\) 3.70013e10 0.0161571
\(559\) −1.44985e11 −0.0628014
\(560\) −2.94170e11 −0.126401
\(561\) 1.49006e12 0.635141
\(562\) 2.18560e11 0.0924180
\(563\) −2.82214e11 −0.118383 −0.0591917 0.998247i \(-0.518852\pi\)
−0.0591917 + 0.998247i \(0.518852\pi\)
\(564\) 3.91901e11 0.163087
\(565\) −2.06161e12 −0.851117
\(566\) 4.13703e11 0.169439
\(567\) 5.66179e10 0.0230054
\(568\) −8.04444e11 −0.324286
\(569\) 7.84903e11 0.313914 0.156957 0.987605i \(-0.449832\pi\)
0.156957 + 0.987605i \(0.449832\pi\)
\(570\) 1.18153e11 0.0468820
\(571\) −4.58710e12 −1.80583 −0.902913 0.429824i \(-0.858575\pi\)
−0.902913 + 0.429824i \(0.858575\pi\)
\(572\) 4.88019e11 0.190614
\(573\) −1.07488e12 −0.416549
\(574\) −5.87484e10 −0.0225887
\(575\) 2.02392e12 0.772125
\(576\) −7.86199e11 −0.297599
\(577\) 5.80964e11 0.218202 0.109101 0.994031i \(-0.465203\pi\)
0.109101 + 0.994031i \(0.465203\pi\)
\(578\) 6.05267e10 0.0225565
\(579\) −2.85994e12 −1.05756
\(580\) −4.39824e11 −0.161381
\(581\) 1.58449e11 0.0576894
\(582\) −3.83113e11 −0.138412
\(583\) 7.95722e11 0.285268
\(584\) 5.42229e11 0.192897
\(585\) 9.81260e10 0.0346404
\(586\) −4.96378e10 −0.0173890
\(587\) 1.82522e12 0.634518 0.317259 0.948339i \(-0.397238\pi\)
0.317259 + 0.948339i \(0.397238\pi\)
\(588\) −1.57274e12 −0.542575
\(589\) 9.81950e11 0.336179
\(590\) 3.33091e10 0.0113170
\(591\) 4.73071e11 0.159508
\(592\) −3.93102e12 −1.31540
\(593\) −5.13878e12 −1.70653 −0.853265 0.521478i \(-0.825381\pi\)
−0.853265 + 0.521478i \(0.825381\pi\)
\(594\) 9.48230e10 0.0312518
\(595\) 3.72759e11 0.121928
\(596\) −1.94442e12 −0.631223
\(597\) −1.86870e12 −0.602080
\(598\) −8.97498e10 −0.0286998
\(599\) −1.31947e12 −0.418774 −0.209387 0.977833i \(-0.567147\pi\)
−0.209387 + 0.977833i \(0.567147\pi\)
\(600\) 2.85447e11 0.0899177
\(601\) −1.88238e12 −0.588535 −0.294267 0.955723i \(-0.595076\pi\)
−0.294267 + 0.955723i \(0.595076\pi\)
\(602\) −3.50491e10 −0.0108766
\(603\) −4.87340e11 −0.150108
\(604\) −3.03362e12 −0.927460
\(605\) −9.64853e11 −0.292794
\(606\) −1.62823e11 −0.0490443
\(607\) 1.29228e12 0.386372 0.193186 0.981162i \(-0.438118\pi\)
0.193186 + 0.981162i \(0.438118\pi\)
\(608\) 1.24119e12 0.368361
\(609\) 1.03339e11 0.0304428
\(610\) 5.79088e11 0.169340
\(611\) −1.59584e11 −0.0463239
\(612\) 1.03635e12 0.298626
\(613\) −2.00466e12 −0.573415 −0.286707 0.958018i \(-0.592561\pi\)
−0.286707 + 0.958018i \(0.592561\pi\)
\(614\) −4.50236e11 −0.127845
\(615\) 1.07079e12 0.301832
\(616\) 2.38131e11 0.0666349
\(617\) −2.59273e12 −0.720235 −0.360118 0.932907i \(-0.617263\pi\)
−0.360118 + 0.932907i \(0.617263\pi\)
\(618\) −1.39596e11 −0.0384969
\(619\) −6.08895e12 −1.66700 −0.833498 0.552522i \(-0.813665\pi\)
−0.833498 + 0.552522i \(0.813665\pi\)
\(620\) −8.39076e11 −0.228055
\(621\) 9.43865e11 0.254682
\(622\) 4.83410e11 0.129497
\(623\) −1.46997e12 −0.390941
\(624\) 3.33037e11 0.0879350
\(625\) −2.90387e11 −0.0761231
\(626\) −3.81241e11 −0.0992237
\(627\) 2.51644e12 0.650253
\(628\) −5.26158e12 −1.34989
\(629\) 4.98122e12 1.26884
\(630\) 2.37213e10 0.00599938
\(631\) 2.63247e12 0.661046 0.330523 0.943798i \(-0.392775\pi\)
0.330523 + 0.943798i \(0.392775\pi\)
\(632\) 1.66515e10 0.00415171
\(633\) 7.99184e11 0.197847
\(634\) 1.92645e11 0.0473540
\(635\) 4.31935e12 1.05423
\(636\) 5.53436e11 0.134125
\(637\) 6.40431e11 0.154115
\(638\) 1.73070e11 0.0413552
\(639\) −1.70672e12 −0.404957
\(640\) −1.40959e12 −0.332111
\(641\) −3.27779e12 −0.766867 −0.383434 0.923568i \(-0.625259\pi\)
−0.383434 + 0.923568i \(0.625259\pi\)
\(642\) 6.09725e11 0.141653
\(643\) −1.69121e12 −0.390166 −0.195083 0.980787i \(-0.562498\pi\)
−0.195083 + 0.980787i \(0.562498\pi\)
\(644\) 1.17432e12 0.269031
\(645\) 6.38828e11 0.145333
\(646\) −5.08138e11 −0.114798
\(647\) −5.65660e11 −0.126907 −0.0634535 0.997985i \(-0.520211\pi\)
−0.0634535 + 0.997985i \(0.520211\pi\)
\(648\) 1.33120e11 0.0296589
\(649\) 7.09425e11 0.156966
\(650\) −5.75860e10 −0.0126534
\(651\) 1.97145e11 0.0430200
\(652\) −4.83801e12 −1.04846
\(653\) −6.06730e10 −0.0130583 −0.00652914 0.999979i \(-0.502078\pi\)
−0.00652914 + 0.999979i \(0.502078\pi\)
\(654\) 2.66377e9 0.000569374 0
\(655\) 3.37887e12 0.717274
\(656\) 3.63422e12 0.766202
\(657\) 1.15040e12 0.240883
\(658\) −3.85785e10 −0.00802285
\(659\) 1.77971e12 0.367590 0.183795 0.982965i \(-0.441162\pi\)
0.183795 + 0.982965i \(0.441162\pi\)
\(660\) −2.15030e12 −0.441114
\(661\) 4.30203e12 0.876530 0.438265 0.898846i \(-0.355593\pi\)
0.438265 + 0.898846i \(0.355593\pi\)
\(662\) −6.79890e11 −0.137587
\(663\) −4.22010e11 −0.0848226
\(664\) 3.72544e11 0.0743740
\(665\) 6.29524e11 0.124829
\(666\) 3.16991e11 0.0624328
\(667\) 1.72274e12 0.337018
\(668\) 3.73172e12 0.725128
\(669\) −5.65969e12 −1.09238
\(670\) −2.04182e11 −0.0391454
\(671\) 1.23335e13 2.34875
\(672\) 2.49193e11 0.0471382
\(673\) 4.39676e12 0.826162 0.413081 0.910694i \(-0.364453\pi\)
0.413081 + 0.910694i \(0.364453\pi\)
\(674\) −1.01877e12 −0.190155
\(675\) 6.05610e11 0.112286
\(676\) 5.19279e12 0.956403
\(677\) −1.43011e12 −0.261650 −0.130825 0.991405i \(-0.541763\pi\)
−0.130825 + 0.991405i \(0.541763\pi\)
\(678\) 5.64231e11 0.102547
\(679\) −2.04125e12 −0.368537
\(680\) 8.76430e11 0.157191
\(681\) 4.35847e12 0.776555
\(682\) 3.30176e11 0.0584407
\(683\) 3.56294e12 0.626492 0.313246 0.949672i \(-0.398584\pi\)
0.313246 + 0.949672i \(0.398584\pi\)
\(684\) 1.75022e12 0.305731
\(685\) −6.27811e12 −1.08948
\(686\) 3.16574e11 0.0545780
\(687\) −3.16639e12 −0.542324
\(688\) 2.16816e12 0.368930
\(689\) −2.25362e11 −0.0380974
\(690\) 3.95454e11 0.0664163
\(691\) 6.12100e12 1.02134 0.510671 0.859776i \(-0.329397\pi\)
0.510671 + 0.859776i \(0.329397\pi\)
\(692\) −8.15737e12 −1.35230
\(693\) 5.05222e11 0.0832114
\(694\) 1.97148e11 0.0322608
\(695\) −2.02953e12 −0.329963
\(696\) 2.42970e11 0.0392474
\(697\) −4.60512e12 −0.739084
\(698\) −2.48814e11 −0.0396757
\(699\) 4.12122e12 0.652948
\(700\) 7.53479e11 0.118612
\(701\) −2.36726e12 −0.370266 −0.185133 0.982713i \(-0.559272\pi\)
−0.185133 + 0.982713i \(0.559272\pi\)
\(702\) −2.68555e10 −0.00417366
\(703\) 8.41239e12 1.29903
\(704\) −7.01554e12 −1.07643
\(705\) 7.03157e11 0.107202
\(706\) −1.24896e12 −0.189203
\(707\) −8.67529e11 −0.130586
\(708\) 4.93415e11 0.0738011
\(709\) 1.21948e13 1.81245 0.906224 0.422798i \(-0.138952\pi\)
0.906224 + 0.422798i \(0.138952\pi\)
\(710\) −7.15070e11 −0.105605
\(711\) 3.53281e10 0.00518451
\(712\) −3.45618e12 −0.504007
\(713\) 3.28656e12 0.476254
\(714\) −1.02018e11 −0.0146905
\(715\) 8.75614e11 0.125296
\(716\) 2.66569e12 0.379053
\(717\) 5.55992e12 0.785655
\(718\) −1.52790e12 −0.214553
\(719\) 2.87521e12 0.401226 0.200613 0.979671i \(-0.435707\pi\)
0.200613 + 0.979671i \(0.435707\pi\)
\(720\) −1.46742e12 −0.203497
\(721\) −7.43777e11 −0.102502
\(722\) 1.25272e11 0.0171569
\(723\) −5.19010e12 −0.706405
\(724\) 2.59921e12 0.351574
\(725\) 1.10536e12 0.148587
\(726\) 2.64065e11 0.0352773
\(727\) 6.04263e12 0.802272 0.401136 0.916019i \(-0.368616\pi\)
0.401136 + 0.916019i \(0.368616\pi\)
\(728\) −6.74427e10 −0.00889905
\(729\) 2.82430e11 0.0370370
\(730\) 4.81987e11 0.0628177
\(731\) −2.74740e12 −0.355873
\(732\) 8.57815e12 1.10432
\(733\) −3.93902e12 −0.503988 −0.251994 0.967729i \(-0.581086\pi\)
−0.251994 + 0.967729i \(0.581086\pi\)
\(734\) 1.03846e12 0.132056
\(735\) −2.82185e12 −0.356649
\(736\) 4.15424e12 0.521845
\(737\) −4.34871e12 −0.542946
\(738\) −2.93057e11 −0.0363662
\(739\) −1.10501e13 −1.36290 −0.681451 0.731863i \(-0.738651\pi\)
−0.681451 + 0.731863i \(0.738651\pi\)
\(740\) −7.18839e12 −0.881229
\(741\) −7.12700e11 −0.0868410
\(742\) −5.44799e10 −0.00659810
\(743\) 1.30929e13 1.57611 0.788054 0.615606i \(-0.211089\pi\)
0.788054 + 0.615606i \(0.211089\pi\)
\(744\) 4.63526e11 0.0554621
\(745\) −3.48873e12 −0.414920
\(746\) −1.08702e12 −0.128503
\(747\) 7.90396e11 0.0928757
\(748\) 9.24777e12 1.08014
\(749\) 3.24865e12 0.377168
\(750\) 6.88615e11 0.0794696
\(751\) −1.04795e12 −0.120216 −0.0601080 0.998192i \(-0.519145\pi\)
−0.0601080 + 0.998192i \(0.519145\pi\)
\(752\) 2.38649e12 0.272132
\(753\) 3.09719e12 0.351068
\(754\) −4.90166e10 −0.00552296
\(755\) −5.44299e12 −0.609644
\(756\) 3.51389e11 0.0391237
\(757\) 1.14401e13 1.26619 0.633094 0.774075i \(-0.281785\pi\)
0.633094 + 0.774075i \(0.281785\pi\)
\(758\) −4.11529e11 −0.0452781
\(759\) 8.42245e12 0.921193
\(760\) 1.48013e12 0.160931
\(761\) 1.01121e13 1.09297 0.546485 0.837469i \(-0.315966\pi\)
0.546485 + 0.837469i \(0.315966\pi\)
\(762\) −1.18214e12 −0.127020
\(763\) 1.41927e10 0.00151602
\(764\) −6.67108e12 −0.708396
\(765\) 1.85945e12 0.196294
\(766\) −9.46810e11 −0.0993650
\(767\) −2.00922e11 −0.0209627
\(768\) −4.58377e12 −0.475442
\(769\) −5.58480e11 −0.0575890 −0.0287945 0.999585i \(-0.509167\pi\)
−0.0287945 + 0.999585i \(0.509167\pi\)
\(770\) 2.11674e11 0.0217000
\(771\) −1.95216e12 −0.198963
\(772\) −1.77497e13 −1.79851
\(773\) 5.41948e11 0.0545946 0.0272973 0.999627i \(-0.491310\pi\)
0.0272973 + 0.999627i \(0.491310\pi\)
\(774\) −1.74837e11 −0.0175105
\(775\) 2.10875e12 0.209975
\(776\) −4.79937e12 −0.475124
\(777\) 1.68894e12 0.166234
\(778\) 8.84445e11 0.0865491
\(779\) −7.77723e12 −0.756670
\(780\) 6.09002e11 0.0589105
\(781\) −1.52297e13 −1.46475
\(782\) −1.70073e12 −0.162631
\(783\) 5.15489e11 0.0490108
\(784\) −9.57728e12 −0.905357
\(785\) −9.44044e12 −0.887317
\(786\) −9.24742e11 −0.0864210
\(787\) 4.03856e12 0.375267 0.187633 0.982239i \(-0.439918\pi\)
0.187633 + 0.982239i \(0.439918\pi\)
\(788\) 2.93603e12 0.271264
\(789\) −3.00335e12 −0.275905
\(790\) 1.48015e10 0.00135202
\(791\) 3.00625e12 0.273043
\(792\) 1.18788e12 0.107277
\(793\) −3.49307e12 −0.313674
\(794\) −1.48745e12 −0.132816
\(795\) 9.92987e11 0.0881640
\(796\) −1.15977e13 −1.02392
\(797\) 2.35759e12 0.206969 0.103485 0.994631i \(-0.467001\pi\)
0.103485 + 0.994631i \(0.467001\pi\)
\(798\) −1.72291e11 −0.0150400
\(799\) −3.02406e12 −0.262501
\(800\) 2.66547e12 0.230075
\(801\) −7.33270e12 −0.629387
\(802\) 2.90343e12 0.247815
\(803\) 1.02655e13 0.871281
\(804\) −3.02459e12 −0.255278
\(805\) 2.10700e12 0.176841
\(806\) −9.35115e10 −0.00780472
\(807\) 7.35357e12 0.610334
\(808\) −2.03973e12 −0.168353
\(809\) 1.93887e13 1.59140 0.795702 0.605689i \(-0.207102\pi\)
0.795702 + 0.605689i \(0.207102\pi\)
\(810\) 1.18330e11 0.00965857
\(811\) 6.28461e12 0.510134 0.255067 0.966923i \(-0.417902\pi\)
0.255067 + 0.966923i \(0.417902\pi\)
\(812\) 6.41353e11 0.0517720
\(813\) 8.13621e11 0.0653152
\(814\) 2.82862e12 0.225822
\(815\) −8.68046e12 −0.689182
\(816\) 6.31092e12 0.498296
\(817\) −4.63988e12 −0.364340
\(818\) −2.93981e12 −0.229578
\(819\) −1.43088e11 −0.0111128
\(820\) 6.64564e12 0.513304
\(821\) 1.17775e13 0.904709 0.452355 0.891838i \(-0.350584\pi\)
0.452355 + 0.891838i \(0.350584\pi\)
\(822\) 1.71822e12 0.131267
\(823\) 7.43728e11 0.0565087 0.0282543 0.999601i \(-0.491005\pi\)
0.0282543 + 0.999601i \(0.491005\pi\)
\(824\) −1.74877e12 −0.132148
\(825\) 5.40408e12 0.406143
\(826\) −4.85715e10 −0.00363054
\(827\) −2.94757e10 −0.00219124 −0.00109562 0.999999i \(-0.500349\pi\)
−0.00109562 + 0.999999i \(0.500349\pi\)
\(828\) 5.85793e12 0.433120
\(829\) −1.09813e12 −0.0807526 −0.0403763 0.999185i \(-0.512856\pi\)
−0.0403763 + 0.999185i \(0.512856\pi\)
\(830\) 3.31154e11 0.0242203
\(831\) −6.96062e12 −0.506342
\(832\) 1.98692e12 0.143756
\(833\) 1.21359e13 0.873314
\(834\) 5.55451e11 0.0397556
\(835\) 6.69553e12 0.476646
\(836\) 1.56178e13 1.10584
\(837\) 9.83426e11 0.0692591
\(838\) −1.25962e12 −0.0882348
\(839\) 1.55564e13 1.08388 0.541940 0.840417i \(-0.317690\pi\)
0.541940 + 0.840417i \(0.317690\pi\)
\(840\) 2.97164e11 0.0205940
\(841\) −1.35663e13 −0.935145
\(842\) −2.68287e11 −0.0183948
\(843\) 5.80891e12 0.396160
\(844\) 4.95999e12 0.336465
\(845\) 9.31703e12 0.628669
\(846\) −1.92443e11 −0.0129162
\(847\) 1.40695e12 0.0939299
\(848\) 3.37017e12 0.223805
\(849\) 1.09955e13 0.726322
\(850\) −1.09123e12 −0.0717021
\(851\) 2.81560e13 1.84030
\(852\) −1.05925e13 −0.688683
\(853\) −2.03753e13 −1.31775 −0.658876 0.752251i \(-0.728968\pi\)
−0.658876 + 0.752251i \(0.728968\pi\)
\(854\) −8.44429e11 −0.0543253
\(855\) 3.14028e12 0.200965
\(856\) 7.63822e12 0.486251
\(857\) −5.18994e12 −0.328661 −0.164331 0.986405i \(-0.552546\pi\)
−0.164331 + 0.986405i \(0.552546\pi\)
\(858\) −2.39642e11 −0.0150963
\(859\) 1.77656e13 1.11330 0.556648 0.830749i \(-0.312087\pi\)
0.556648 + 0.830749i \(0.312087\pi\)
\(860\) 3.96477e12 0.247158
\(861\) −1.56142e12 −0.0968292
\(862\) −3.75841e12 −0.231858
\(863\) 1.87710e13 1.15197 0.575983 0.817461i \(-0.304619\pi\)
0.575983 + 0.817461i \(0.304619\pi\)
\(864\) 1.24306e12 0.0758891
\(865\) −1.46361e13 −0.888902
\(866\) −3.55829e12 −0.214987
\(867\) 1.60869e12 0.0966911
\(868\) 1.22354e12 0.0731612
\(869\) 3.15246e11 0.0187526
\(870\) 2.15976e11 0.0127811
\(871\) 1.23163e12 0.0725102
\(872\) 3.33699e10 0.00195448
\(873\) −1.01824e13 −0.593318
\(874\) −2.87222e12 −0.166501
\(875\) 3.66898e12 0.211597
\(876\) 7.13977e12 0.409652
\(877\) −2.65144e13 −1.51350 −0.756752 0.653702i \(-0.773215\pi\)
−0.756752 + 0.653702i \(0.773215\pi\)
\(878\) −2.61887e12 −0.148726
\(879\) −1.31928e12 −0.0745397
\(880\) −1.30943e13 −0.736056
\(881\) −7.93722e12 −0.443892 −0.221946 0.975059i \(-0.571241\pi\)
−0.221946 + 0.975059i \(0.571241\pi\)
\(882\) 7.72296e11 0.0429710
\(883\) 6.81888e12 0.377476 0.188738 0.982027i \(-0.439560\pi\)
0.188738 + 0.982027i \(0.439560\pi\)
\(884\) −2.61913e12 −0.144252
\(885\) 8.85296e11 0.0485114
\(886\) 2.81753e12 0.153609
\(887\) −9.06171e12 −0.491534 −0.245767 0.969329i \(-0.579040\pi\)
−0.245767 + 0.969329i \(0.579040\pi\)
\(888\) 3.97104e12 0.214312
\(889\) −6.29849e12 −0.338204
\(890\) −3.07220e12 −0.164132
\(891\) 2.52022e12 0.133964
\(892\) −3.51259e13 −1.85774
\(893\) −5.10710e12 −0.268747
\(894\) 9.54810e11 0.0499917
\(895\) 4.78283e12 0.249162
\(896\) 2.05547e12 0.106543
\(897\) −2.38539e12 −0.123025
\(898\) 6.41986e11 0.0329444
\(899\) 1.79494e12 0.0916500
\(900\) 3.75861e12 0.190957
\(901\) −4.27053e12 −0.215884
\(902\) −2.61505e12 −0.131538
\(903\) −9.31541e11 −0.0466238
\(904\) 7.06830e12 0.352012
\(905\) 4.66355e12 0.231099
\(906\) 1.48966e12 0.0734531
\(907\) −3.11139e12 −0.152659 −0.0763294 0.997083i \(-0.524320\pi\)
−0.0763294 + 0.997083i \(0.524320\pi\)
\(908\) 2.70501e13 1.32063
\(909\) −4.32753e12 −0.210234
\(910\) −5.99498e10 −0.00289802
\(911\) −2.08740e13 −1.00409 −0.502046 0.864841i \(-0.667419\pi\)
−0.502046 + 0.864841i \(0.667419\pi\)
\(912\) 1.06580e13 0.510152
\(913\) 7.05299e12 0.335935
\(914\) 2.02183e12 0.0958265
\(915\) 1.53911e13 0.725897
\(916\) −1.96516e13 −0.922293
\(917\) −4.92708e12 −0.230106
\(918\) −5.08902e11 −0.0236506
\(919\) −1.30825e13 −0.605020 −0.302510 0.953146i \(-0.597825\pi\)
−0.302510 + 0.953146i \(0.597825\pi\)
\(920\) 4.95397e12 0.227986
\(921\) −1.19664e13 −0.548020
\(922\) −8.39484e11 −0.0382581
\(923\) 4.31332e12 0.195616
\(924\) 3.13557e12 0.141512
\(925\) 1.80657e13 0.811366
\(926\) 3.65248e11 0.0163244
\(927\) −3.71022e12 −0.165022
\(928\) 2.26882e12 0.100423
\(929\) −3.66290e13 −1.61345 −0.806723 0.590929i \(-0.798761\pi\)
−0.806723 + 0.590929i \(0.798761\pi\)
\(930\) 4.12028e11 0.0180615
\(931\) 2.04954e13 0.894094
\(932\) 2.55776e13 1.11042
\(933\) 1.28482e13 0.555103
\(934\) −4.93001e12 −0.211976
\(935\) 1.65926e13 0.710004
\(936\) −3.36427e11 −0.0143268
\(937\) −4.16405e13 −1.76477 −0.882384 0.470530i \(-0.844063\pi\)
−0.882384 + 0.470530i \(0.844063\pi\)
\(938\) 2.97739e11 0.0125581
\(939\) −1.01327e13 −0.425334
\(940\) 4.36402e12 0.182310
\(941\) −1.28257e13 −0.533248 −0.266624 0.963801i \(-0.585908\pi\)
−0.266624 + 0.963801i \(0.585908\pi\)
\(942\) 2.58370e12 0.106909
\(943\) −2.60302e13 −1.07195
\(944\) 3.00467e12 0.123147
\(945\) 6.30470e11 0.0257170
\(946\) −1.56013e12 −0.0633362
\(947\) −2.34295e13 −0.946648 −0.473324 0.880889i \(-0.656946\pi\)
−0.473324 + 0.880889i \(0.656946\pi\)
\(948\) 2.19258e11 0.00881693
\(949\) −2.90736e12 −0.116359
\(950\) −1.84290e12 −0.0734082
\(951\) 5.12016e12 0.202988
\(952\) −1.27801e12 −0.0504277
\(953\) −6.35831e12 −0.249703 −0.124852 0.992175i \(-0.539845\pi\)
−0.124852 + 0.992175i \(0.539845\pi\)
\(954\) −2.71765e11 −0.0106225
\(955\) −1.19694e13 −0.465647
\(956\) 3.45066e13 1.33611
\(957\) 4.59990e12 0.177274
\(958\) 4.12687e12 0.158298
\(959\) 9.15476e12 0.349513
\(960\) −8.75473e12 −0.332677
\(961\) −2.30153e13 −0.870486
\(962\) −8.01116e11 −0.0301583
\(963\) 1.62054e13 0.607213
\(964\) −3.22115e13 −1.20133
\(965\) −3.18469e13 −1.18221
\(966\) −5.76652e11 −0.0213067
\(967\) −4.99997e13 −1.83886 −0.919430 0.393254i \(-0.871349\pi\)
−0.919430 + 0.393254i \(0.871349\pi\)
\(968\) 3.30802e12 0.121096
\(969\) −1.35054e13 −0.492096
\(970\) −4.26616e12 −0.154726
\(971\) −3.43173e13 −1.23887 −0.619437 0.785046i \(-0.712639\pi\)
−0.619437 + 0.785046i \(0.712639\pi\)
\(972\) 1.75285e12 0.0629863
\(973\) 2.95947e12 0.105854
\(974\) 1.09141e11 0.00388574
\(975\) −1.53053e12 −0.0542402
\(976\) 5.22370e13 1.84270
\(977\) −2.71239e13 −0.952416 −0.476208 0.879333i \(-0.657989\pi\)
−0.476208 + 0.879333i \(0.657989\pi\)
\(978\) 2.37571e12 0.0830362
\(979\) −6.54323e13 −2.27651
\(980\) −1.75133e13 −0.606528
\(981\) 7.07982e10 0.00244068
\(982\) −5.33483e12 −0.183071
\(983\) 6.56996e12 0.224425 0.112213 0.993684i \(-0.464206\pi\)
0.112213 + 0.993684i \(0.464206\pi\)
\(984\) −3.67122e12 −0.124834
\(985\) 5.26789e12 0.178309
\(986\) −9.28845e11 −0.0312966
\(987\) −1.02535e12 −0.0343909
\(988\) −4.42324e12 −0.147684
\(989\) −1.55295e13 −0.516149
\(990\) 1.05590e12 0.0349354
\(991\) 2.02868e13 0.668162 0.334081 0.942544i \(-0.391574\pi\)
0.334081 + 0.942544i \(0.391574\pi\)
\(992\) 4.32836e12 0.141912
\(993\) −1.80702e13 −0.589783
\(994\) 1.04272e12 0.0338788
\(995\) −2.08089e13 −0.673047
\(996\) 4.90545e12 0.157947
\(997\) 4.84876e13 1.55418 0.777091 0.629388i \(-0.216694\pi\)
0.777091 + 0.629388i \(0.216694\pi\)
\(998\) −6.46862e12 −0.206407
\(999\) 8.42503e12 0.267625
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.c.1.11 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.11 22 1.1 even 1 trivial