Properties

Label 177.14.a.b.1.18
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +O(q^{10})\) \(q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +1.67699e6 q^{10} +7.71041e6 q^{11} +5.22383e6 q^{12} -1.68471e7 q^{13} +1.55596e7 q^{14} -3.81619e7 q^{15} +4.29408e7 q^{16} +1.67050e7 q^{17} +1.70248e7 q^{18} -1.60720e8 q^{19} -3.75114e8 q^{20} -3.54078e8 q^{21} +2.47005e8 q^{22} -7.81810e8 q^{23} +3.58660e8 q^{24} +1.51963e9 q^{25} -5.39701e8 q^{26} -3.87420e8 q^{27} -3.48042e9 q^{28} -4.88831e9 q^{29} -1.22252e9 q^{30} -5.16656e9 q^{31} +5.40599e9 q^{32} -5.62089e9 q^{33} +5.35148e8 q^{34} +2.54257e10 q^{35} -3.80817e9 q^{36} -1.18340e10 q^{37} -5.14870e9 q^{38} +1.22816e10 q^{39} -2.57547e10 q^{40} +3.96298e10 q^{41} -1.13429e10 q^{42} -4.22888e10 q^{43} -5.52509e10 q^{44} +2.78200e10 q^{45} -2.50454e10 q^{46} -1.14604e11 q^{47} -3.13039e10 q^{48} +1.39018e11 q^{49} +4.86818e10 q^{50} -1.21779e10 q^{51} +1.20722e11 q^{52} -1.15968e11 q^{53} -1.24111e10 q^{54} +4.03626e11 q^{55} -2.38960e11 q^{56} +1.17165e11 q^{57} -1.56598e11 q^{58} -4.21805e10 q^{59} +2.73458e11 q^{60} -1.57307e11 q^{61} -1.65512e11 q^{62} +2.58123e11 q^{63} -1.78589e11 q^{64} -8.81918e11 q^{65} -1.80066e11 q^{66} -1.15507e12 q^{67} -1.19704e11 q^{68} +5.69939e11 q^{69} +8.14517e11 q^{70} +1.50486e12 q^{71} -2.61463e11 q^{72} +1.68360e12 q^{73} -3.79106e11 q^{74} -1.10781e12 q^{75} +1.15168e12 q^{76} +3.74497e12 q^{77} +3.93442e11 q^{78} +1.28585e12 q^{79} +2.24788e12 q^{80} +2.82430e11 q^{81} +1.26955e12 q^{82} +3.33442e12 q^{83} +2.53723e12 q^{84} +8.74477e11 q^{85} -1.35473e12 q^{86} +3.56358e12 q^{87} -3.79343e12 q^{88} -6.70262e12 q^{89} +8.91219e11 q^{90} -8.18271e12 q^{91} +5.60225e12 q^{92} +3.76642e12 q^{93} -3.67135e12 q^{94} -8.41341e12 q^{95} -3.94097e12 q^{96} -4.23961e12 q^{97} +4.45348e12 q^{98} +4.09763e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 32.0352 0.353942 0.176971 0.984216i \(-0.443370\pi\)
0.176971 + 0.984216i \(0.443370\pi\)
\(3\) −729.000 −0.577350
\(4\) −7165.75 −0.874725
\(5\) 52348.2 1.49829 0.749147 0.662404i \(-0.230464\pi\)
0.749147 + 0.662404i \(0.230464\pi\)
\(6\) −23353.7 −0.204349
\(7\) 485703. 1.56039 0.780196 0.625535i \(-0.215119\pi\)
0.780196 + 0.625535i \(0.215119\pi\)
\(8\) −491988. −0.663544
\(9\) 531441. 0.333333
\(10\) 1.67699e6 0.530309
\(11\) 7.71041e6 1.31228 0.656138 0.754641i \(-0.272189\pi\)
0.656138 + 0.754641i \(0.272189\pi\)
\(12\) 5.22383e6 0.505023
\(13\) −1.68471e7 −0.968042 −0.484021 0.875056i \(-0.660824\pi\)
−0.484021 + 0.875056i \(0.660824\pi\)
\(14\) 1.55596e7 0.552289
\(15\) −3.81619e7 −0.865040
\(16\) 4.29408e7 0.639868
\(17\) 1.67050e7 0.167853 0.0839264 0.996472i \(-0.473254\pi\)
0.0839264 + 0.996472i \(0.473254\pi\)
\(18\) 1.70248e7 0.117981
\(19\) −1.60720e8 −0.783740 −0.391870 0.920021i \(-0.628172\pi\)
−0.391870 + 0.920021i \(0.628172\pi\)
\(20\) −3.75114e8 −1.31059
\(21\) −3.54078e8 −0.900892
\(22\) 2.47005e8 0.464470
\(23\) −7.81810e8 −1.10121 −0.550605 0.834766i \(-0.685603\pi\)
−0.550605 + 0.834766i \(0.685603\pi\)
\(24\) 3.58660e8 0.383098
\(25\) 1.51963e9 1.24488
\(26\) −5.39701e8 −0.342631
\(27\) −3.87420e8 −0.192450
\(28\) −3.48042e9 −1.36491
\(29\) −4.88831e9 −1.52606 −0.763031 0.646362i \(-0.776289\pi\)
−0.763031 + 0.646362i \(0.776289\pi\)
\(30\) −1.22252e9 −0.306174
\(31\) −5.16656e9 −1.04556 −0.522782 0.852467i \(-0.675106\pi\)
−0.522782 + 0.852467i \(0.675106\pi\)
\(32\) 5.40599e9 0.890021
\(33\) −5.62089e9 −0.757643
\(34\) 5.35148e8 0.0594102
\(35\) 2.54257e10 2.33792
\(36\) −3.80817e9 −0.291575
\(37\) −1.18340e10 −0.758267 −0.379133 0.925342i \(-0.623778\pi\)
−0.379133 + 0.925342i \(0.623778\pi\)
\(38\) −5.14870e9 −0.277399
\(39\) 1.22816e10 0.558899
\(40\) −2.57547e10 −0.994184
\(41\) 3.96298e10 1.30295 0.651473 0.758672i \(-0.274151\pi\)
0.651473 + 0.758672i \(0.274151\pi\)
\(42\) −1.13429e10 −0.318864
\(43\) −4.22888e10 −1.02019 −0.510094 0.860119i \(-0.670389\pi\)
−0.510094 + 0.860119i \(0.670389\pi\)
\(44\) −5.52509e10 −1.14788
\(45\) 2.78200e10 0.499431
\(46\) −2.50454e10 −0.389765
\(47\) −1.14604e11 −1.55083 −0.775413 0.631455i \(-0.782458\pi\)
−0.775413 + 0.631455i \(0.782458\pi\)
\(48\) −3.13039e10 −0.369428
\(49\) 1.39018e11 1.43482
\(50\) 4.86818e10 0.440617
\(51\) −1.21779e10 −0.0969099
\(52\) 1.20722e11 0.846771
\(53\) −1.15968e11 −0.718695 −0.359347 0.933204i \(-0.617001\pi\)
−0.359347 + 0.933204i \(0.617001\pi\)
\(54\) −1.24111e10 −0.0681162
\(55\) 4.03626e11 1.96617
\(56\) −2.38960e11 −1.03539
\(57\) 1.17165e11 0.452492
\(58\) −1.56598e11 −0.540138
\(59\) −4.21805e10 −0.130189
\(60\) 2.73458e11 0.756672
\(61\) −1.57307e11 −0.390934 −0.195467 0.980710i \(-0.562622\pi\)
−0.195467 + 0.980710i \(0.562622\pi\)
\(62\) −1.65512e11 −0.370069
\(63\) 2.58123e11 0.520131
\(64\) −1.78589e11 −0.324852
\(65\) −8.81918e11 −1.45041
\(66\) −1.80066e11 −0.268162
\(67\) −1.15507e12 −1.55999 −0.779996 0.625784i \(-0.784779\pi\)
−0.779996 + 0.625784i \(0.784779\pi\)
\(68\) −1.19704e11 −0.146825
\(69\) 5.69939e11 0.635784
\(70\) 8.14517e11 0.827490
\(71\) 1.50486e12 1.39417 0.697085 0.716988i \(-0.254480\pi\)
0.697085 + 0.716988i \(0.254480\pi\)
\(72\) −2.61463e11 −0.221181
\(73\) 1.68360e12 1.30209 0.651043 0.759041i \(-0.274332\pi\)
0.651043 + 0.759041i \(0.274332\pi\)
\(74\) −3.79106e11 −0.268383
\(75\) −1.10781e12 −0.718734
\(76\) 1.15168e12 0.685557
\(77\) 3.74497e12 2.04766
\(78\) 3.93442e11 0.197818
\(79\) 1.28585e12 0.595135 0.297568 0.954701i \(-0.403825\pi\)
0.297568 + 0.954701i \(0.403825\pi\)
\(80\) 2.24788e12 0.958711
\(81\) 2.82430e11 0.111111
\(82\) 1.26955e12 0.461168
\(83\) 3.33442e12 1.11947 0.559736 0.828671i \(-0.310903\pi\)
0.559736 + 0.828671i \(0.310903\pi\)
\(84\) 2.53723e12 0.788033
\(85\) 8.74477e11 0.251493
\(86\) −1.35473e12 −0.361087
\(87\) 3.56358e12 0.881072
\(88\) −3.79343e12 −0.870753
\(89\) −6.70262e12 −1.42958 −0.714792 0.699337i \(-0.753479\pi\)
−0.714792 + 0.699337i \(0.753479\pi\)
\(90\) 8.91219e11 0.176770
\(91\) −8.18271e12 −1.51052
\(92\) 5.60225e12 0.963256
\(93\) 3.76642e12 0.603656
\(94\) −3.67135e12 −0.548903
\(95\) −8.41341e12 −1.17427
\(96\) −3.94097e12 −0.513854
\(97\) −4.23961e12 −0.516784 −0.258392 0.966040i \(-0.583193\pi\)
−0.258392 + 0.966040i \(0.583193\pi\)
\(98\) 4.45348e12 0.507844
\(99\) 4.09763e12 0.437425
\(100\) −1.08893e13 −1.08893
\(101\) 1.56745e13 1.46928 0.734642 0.678455i \(-0.237350\pi\)
0.734642 + 0.678455i \(0.237350\pi\)
\(102\) −3.90123e11 −0.0343005
\(103\) 1.97494e13 1.62971 0.814856 0.579663i \(-0.196816\pi\)
0.814856 + 0.579663i \(0.196816\pi\)
\(104\) 8.28860e12 0.642339
\(105\) −1.85353e13 −1.34980
\(106\) −3.71505e12 −0.254376
\(107\) −2.33565e13 −1.50457 −0.752286 0.658836i \(-0.771049\pi\)
−0.752286 + 0.658836i \(0.771049\pi\)
\(108\) 2.77616e12 0.168341
\(109\) −2.58309e13 −1.47525 −0.737627 0.675209i \(-0.764053\pi\)
−0.737627 + 0.675209i \(0.764053\pi\)
\(110\) 1.29303e13 0.695912
\(111\) 8.62702e12 0.437786
\(112\) 2.08565e13 0.998445
\(113\) −4.19797e13 −1.89683 −0.948417 0.317027i \(-0.897315\pi\)
−0.948417 + 0.317027i \(0.897315\pi\)
\(114\) 3.75340e12 0.160156
\(115\) −4.09264e13 −1.64994
\(116\) 3.50284e13 1.33488
\(117\) −8.95326e12 −0.322681
\(118\) −1.35126e12 −0.0460794
\(119\) 8.11367e12 0.261916
\(120\) 1.87752e13 0.573993
\(121\) 2.49278e13 0.722068
\(122\) −5.03935e12 −0.138368
\(123\) −2.88901e13 −0.752256
\(124\) 3.70222e13 0.914580
\(125\) 1.56484e13 0.366907
\(126\) 8.26901e12 0.184096
\(127\) −8.77420e13 −1.85560 −0.927798 0.373083i \(-0.878301\pi\)
−0.927798 + 0.373083i \(0.878301\pi\)
\(128\) −5.00070e13 −1.00500
\(129\) 3.08285e13 0.589005
\(130\) −2.82524e13 −0.513362
\(131\) 3.42417e13 0.591960 0.295980 0.955194i \(-0.404354\pi\)
0.295980 + 0.955194i \(0.404354\pi\)
\(132\) 4.02779e13 0.662729
\(133\) −7.80623e13 −1.22294
\(134\) −3.70029e13 −0.552147
\(135\) −2.02808e13 −0.288347
\(136\) −8.21867e12 −0.111378
\(137\) −2.06259e13 −0.266520 −0.133260 0.991081i \(-0.542544\pi\)
−0.133260 + 0.991081i \(0.542544\pi\)
\(138\) 1.82581e13 0.225031
\(139\) 9.83229e13 1.15627 0.578134 0.815942i \(-0.303781\pi\)
0.578134 + 0.815942i \(0.303781\pi\)
\(140\) −1.82194e14 −2.04504
\(141\) 8.35461e13 0.895369
\(142\) 4.82084e13 0.493456
\(143\) −1.29898e14 −1.27034
\(144\) 2.28205e13 0.213289
\(145\) −2.55894e14 −2.28649
\(146\) 5.39344e13 0.460863
\(147\) −1.01344e14 −0.828395
\(148\) 8.47998e13 0.663275
\(149\) −9.26359e13 −0.693535 −0.346768 0.937951i \(-0.612721\pi\)
−0.346768 + 0.937951i \(0.612721\pi\)
\(150\) −3.54890e13 −0.254390
\(151\) 3.43768e13 0.236002 0.118001 0.993013i \(-0.462351\pi\)
0.118001 + 0.993013i \(0.462351\pi\)
\(152\) 7.90725e13 0.520046
\(153\) 8.87772e12 0.0559509
\(154\) 1.19971e14 0.724755
\(155\) −2.70460e14 −1.56656
\(156\) −8.80066e13 −0.488883
\(157\) 3.42941e13 0.182756 0.0913779 0.995816i \(-0.470873\pi\)
0.0913779 + 0.995816i \(0.470873\pi\)
\(158\) 4.11926e13 0.210643
\(159\) 8.45406e13 0.414939
\(160\) 2.82994e14 1.33351
\(161\) −3.79727e14 −1.71832
\(162\) 9.04769e12 0.0393269
\(163\) −3.18781e13 −0.133129 −0.0665645 0.997782i \(-0.521204\pi\)
−0.0665645 + 0.997782i \(0.521204\pi\)
\(164\) −2.83977e14 −1.13972
\(165\) −2.94244e14 −1.13517
\(166\) 1.06819e14 0.396229
\(167\) 1.46800e14 0.523684 0.261842 0.965111i \(-0.415670\pi\)
0.261842 + 0.965111i \(0.415670\pi\)
\(168\) 1.74202e14 0.597782
\(169\) −1.90491e13 −0.0628941
\(170\) 2.80141e13 0.0890139
\(171\) −8.54133e13 −0.261247
\(172\) 3.03030e14 0.892383
\(173\) −2.52855e14 −0.717087 −0.358543 0.933513i \(-0.616727\pi\)
−0.358543 + 0.933513i \(0.616727\pi\)
\(174\) 1.14160e14 0.311849
\(175\) 7.38090e14 1.94251
\(176\) 3.31092e14 0.839684
\(177\) 3.07496e13 0.0751646
\(178\) −2.14720e14 −0.505990
\(179\) −8.22155e14 −1.86814 −0.934069 0.357092i \(-0.883768\pi\)
−0.934069 + 0.357092i \(0.883768\pi\)
\(180\) −1.99351e14 −0.436865
\(181\) 8.34518e14 1.76411 0.882054 0.471148i \(-0.156160\pi\)
0.882054 + 0.471148i \(0.156160\pi\)
\(182\) −2.62135e14 −0.534639
\(183\) 1.14677e14 0.225706
\(184\) 3.84641e14 0.730702
\(185\) −6.19491e14 −1.13611
\(186\) 1.20658e14 0.213660
\(187\) 1.28802e14 0.220269
\(188\) 8.21221e14 1.35655
\(189\) −1.88171e14 −0.300297
\(190\) −2.69525e14 −0.415625
\(191\) −5.01005e14 −0.746664 −0.373332 0.927698i \(-0.621785\pi\)
−0.373332 + 0.927698i \(0.621785\pi\)
\(192\) 1.30192e14 0.187554
\(193\) −1.51823e14 −0.211454 −0.105727 0.994395i \(-0.533717\pi\)
−0.105727 + 0.994395i \(0.533717\pi\)
\(194\) −1.35817e14 −0.182912
\(195\) 6.42918e14 0.837395
\(196\) −9.96171e14 −1.25507
\(197\) 1.40464e15 1.71212 0.856062 0.516873i \(-0.172904\pi\)
0.856062 + 0.516873i \(0.172904\pi\)
\(198\) 1.31268e14 0.154823
\(199\) 3.32481e14 0.379508 0.189754 0.981832i \(-0.439231\pi\)
0.189754 + 0.981832i \(0.439231\pi\)
\(200\) −7.47642e14 −0.826035
\(201\) 8.42047e14 0.900662
\(202\) 5.02137e14 0.520042
\(203\) −2.37427e15 −2.38125
\(204\) 8.72641e13 0.0847695
\(205\) 2.07455e15 1.95220
\(206\) 6.32675e14 0.576824
\(207\) −4.15486e14 −0.367070
\(208\) −7.23430e14 −0.619420
\(209\) −1.23922e15 −1.02848
\(210\) −5.93783e14 −0.477752
\(211\) −1.06679e14 −0.0832230 −0.0416115 0.999134i \(-0.513249\pi\)
−0.0416115 + 0.999134i \(0.513249\pi\)
\(212\) 8.30996e14 0.628660
\(213\) −1.09704e15 −0.804924
\(214\) −7.48230e14 −0.532532
\(215\) −2.21374e15 −1.52854
\(216\) 1.90606e14 0.127699
\(217\) −2.50941e15 −1.63149
\(218\) −8.27497e14 −0.522155
\(219\) −1.22734e15 −0.751760
\(220\) −2.89228e15 −1.71986
\(221\) −2.81432e14 −0.162489
\(222\) 2.76368e14 0.154951
\(223\) 5.46831e14 0.297764 0.148882 0.988855i \(-0.452433\pi\)
0.148882 + 0.988855i \(0.452433\pi\)
\(224\) 2.62571e15 1.38878
\(225\) 8.07595e14 0.414961
\(226\) −1.34483e15 −0.671369
\(227\) −3.30107e14 −0.160135 −0.0800675 0.996789i \(-0.525514\pi\)
−0.0800675 + 0.996789i \(0.525514\pi\)
\(228\) −8.39575e14 −0.395806
\(229\) 3.25892e15 1.49329 0.746644 0.665224i \(-0.231664\pi\)
0.746644 + 0.665224i \(0.231664\pi\)
\(230\) −1.31108e15 −0.583982
\(231\) −2.73008e15 −1.18222
\(232\) 2.40499e15 1.01261
\(233\) −1.08294e15 −0.443396 −0.221698 0.975115i \(-0.571160\pi\)
−0.221698 + 0.975115i \(0.571160\pi\)
\(234\) −2.86819e14 −0.114210
\(235\) −5.99930e15 −2.32359
\(236\) 3.02255e14 0.113879
\(237\) −9.37388e14 −0.343601
\(238\) 2.59923e14 0.0927032
\(239\) −2.83994e15 −0.985650 −0.492825 0.870129i \(-0.664036\pi\)
−0.492825 + 0.870129i \(0.664036\pi\)
\(240\) −1.63870e15 −0.553512
\(241\) 1.55768e15 0.512114 0.256057 0.966662i \(-0.417577\pi\)
0.256057 + 0.966662i \(0.417577\pi\)
\(242\) 7.98566e14 0.255571
\(243\) −2.05891e14 −0.0641500
\(244\) 1.12722e15 0.341960
\(245\) 7.27737e15 2.14978
\(246\) −9.25500e14 −0.266255
\(247\) 2.70767e15 0.758693
\(248\) 2.54189e15 0.693778
\(249\) −2.43080e15 −0.646327
\(250\) 5.01301e14 0.129864
\(251\) 1.40586e15 0.354865 0.177433 0.984133i \(-0.443221\pi\)
0.177433 + 0.984133i \(0.443221\pi\)
\(252\) −1.84964e15 −0.454971
\(253\) −6.02808e15 −1.44509
\(254\) −2.81083e15 −0.656774
\(255\) −6.37494e14 −0.145199
\(256\) −1.38980e14 −0.0308597
\(257\) −6.93421e15 −1.50118 −0.750588 0.660771i \(-0.770230\pi\)
−0.750588 + 0.660771i \(0.770230\pi\)
\(258\) 9.87597e14 0.208474
\(259\) −5.74783e15 −1.18319
\(260\) 6.31960e15 1.26871
\(261\) −2.59785e15 −0.508687
\(262\) 1.09694e15 0.209520
\(263\) −8.75842e15 −1.63197 −0.815987 0.578070i \(-0.803806\pi\)
−0.815987 + 0.578070i \(0.803806\pi\)
\(264\) 2.76541e15 0.502730
\(265\) −6.07071e15 −1.07682
\(266\) −2.50074e15 −0.432851
\(267\) 4.88621e15 0.825371
\(268\) 8.27695e15 1.36456
\(269\) 1.04083e15 0.167490 0.0837450 0.996487i \(-0.473312\pi\)
0.0837450 + 0.996487i \(0.473312\pi\)
\(270\) −6.49699e14 −0.102058
\(271\) 3.55084e15 0.544541 0.272270 0.962221i \(-0.412225\pi\)
0.272270 + 0.962221i \(0.412225\pi\)
\(272\) 7.17327e14 0.107404
\(273\) 5.96519e15 0.872102
\(274\) −6.60755e14 −0.0943325
\(275\) 1.17170e16 1.63363
\(276\) −4.08404e15 −0.556136
\(277\) 4.83555e15 0.643172 0.321586 0.946880i \(-0.395784\pi\)
0.321586 + 0.946880i \(0.395784\pi\)
\(278\) 3.14979e15 0.409252
\(279\) −2.74572e15 −0.348521
\(280\) −1.25091e16 −1.55132
\(281\) 7.71208e15 0.934502 0.467251 0.884125i \(-0.345244\pi\)
0.467251 + 0.884125i \(0.345244\pi\)
\(282\) 2.67642e15 0.316909
\(283\) 1.30634e16 1.51163 0.755815 0.654785i \(-0.227241\pi\)
0.755815 + 0.654785i \(0.227241\pi\)
\(284\) −1.07834e16 −1.21952
\(285\) 6.13338e15 0.677966
\(286\) −4.16132e15 −0.449627
\(287\) 1.92483e16 2.03311
\(288\) 2.87296e15 0.296674
\(289\) −9.62552e15 −0.971825
\(290\) −8.19763e15 −0.809285
\(291\) 3.09067e15 0.298365
\(292\) −1.20642e16 −1.13897
\(293\) −1.22226e16 −1.12856 −0.564278 0.825585i \(-0.690845\pi\)
−0.564278 + 0.825585i \(0.690845\pi\)
\(294\) −3.24659e15 −0.293204
\(295\) −2.20808e15 −0.195061
\(296\) 5.82221e15 0.503144
\(297\) −2.98717e15 −0.252548
\(298\) −2.96761e15 −0.245471
\(299\) 1.31713e16 1.06602
\(300\) 7.93830e15 0.628694
\(301\) −2.05398e16 −1.59189
\(302\) 1.10127e15 0.0835310
\(303\) −1.14267e16 −0.848292
\(304\) −6.90146e15 −0.501490
\(305\) −8.23472e15 −0.585734
\(306\) 2.84400e14 0.0198034
\(307\) 1.24361e16 0.847780 0.423890 0.905714i \(-0.360664\pi\)
0.423890 + 0.905714i \(0.360664\pi\)
\(308\) −2.68355e16 −1.79114
\(309\) −1.43973e16 −0.940915
\(310\) −8.66425e15 −0.554472
\(311\) 1.87158e16 1.17291 0.586456 0.809981i \(-0.300523\pi\)
0.586456 + 0.809981i \(0.300523\pi\)
\(312\) −6.04239e15 −0.370855
\(313\) −1.73461e16 −1.04271 −0.521355 0.853340i \(-0.674573\pi\)
−0.521355 + 0.853340i \(0.674573\pi\)
\(314\) 1.09862e15 0.0646850
\(315\) 1.35123e16 0.779308
\(316\) −9.21410e15 −0.520579
\(317\) −9.81312e15 −0.543153 −0.271576 0.962417i \(-0.587545\pi\)
−0.271576 + 0.962417i \(0.587545\pi\)
\(318\) 2.70827e15 0.146864
\(319\) −3.76909e16 −2.00261
\(320\) −9.34884e15 −0.486724
\(321\) 1.70269e16 0.868665
\(322\) −1.21646e16 −0.608186
\(323\) −2.68483e15 −0.131553
\(324\) −2.02382e15 −0.0971916
\(325\) −2.56015e16 −1.20510
\(326\) −1.02122e15 −0.0471200
\(327\) 1.88307e16 0.851738
\(328\) −1.94974e16 −0.864563
\(329\) −5.56634e16 −2.41989
\(330\) −9.42615e15 −0.401785
\(331\) 9.73826e15 0.407005 0.203502 0.979074i \(-0.434768\pi\)
0.203502 + 0.979074i \(0.434768\pi\)
\(332\) −2.38936e16 −0.979230
\(333\) −6.28910e15 −0.252756
\(334\) 4.70277e15 0.185354
\(335\) −6.04659e16 −2.33733
\(336\) −1.52044e16 −0.576453
\(337\) 7.79523e15 0.289891 0.144945 0.989440i \(-0.453699\pi\)
0.144945 + 0.989440i \(0.453699\pi\)
\(338\) −6.10241e14 −0.0222609
\(339\) 3.06032e16 1.09514
\(340\) −6.26628e15 −0.219987
\(341\) −3.98363e16 −1.37207
\(342\) −2.73623e15 −0.0924662
\(343\) 2.04624e16 0.678492
\(344\) 2.08056e16 0.676940
\(345\) 2.98353e16 0.952591
\(346\) −8.10026e15 −0.253807
\(347\) −9.26264e15 −0.284835 −0.142418 0.989807i \(-0.545488\pi\)
−0.142418 + 0.989807i \(0.545488\pi\)
\(348\) −2.55357e16 −0.770695
\(349\) −3.21933e16 −0.953675 −0.476837 0.878992i \(-0.658217\pi\)
−0.476837 + 0.878992i \(0.658217\pi\)
\(350\) 2.36449e16 0.687535
\(351\) 6.52693e15 0.186300
\(352\) 4.16824e16 1.16795
\(353\) −1.62281e16 −0.446407 −0.223204 0.974772i \(-0.571651\pi\)
−0.223204 + 0.974772i \(0.571651\pi\)
\(354\) 9.85070e14 0.0266039
\(355\) 7.87766e16 2.08888
\(356\) 4.80293e16 1.25049
\(357\) −5.91487e15 −0.151217
\(358\) −2.63379e16 −0.661213
\(359\) 3.32964e16 0.820887 0.410444 0.911886i \(-0.365374\pi\)
0.410444 + 0.911886i \(0.365374\pi\)
\(360\) −1.36871e16 −0.331395
\(361\) −1.62220e16 −0.385752
\(362\) 2.67340e16 0.624392
\(363\) −1.81723e16 −0.416886
\(364\) 5.86352e16 1.32129
\(365\) 8.81333e16 1.95091
\(366\) 3.67369e15 0.0798868
\(367\) −7.77449e16 −1.66090 −0.830448 0.557097i \(-0.811915\pi\)
−0.830448 + 0.557097i \(0.811915\pi\)
\(368\) −3.35716e16 −0.704630
\(369\) 2.10609e16 0.434315
\(370\) −1.98455e16 −0.402116
\(371\) −5.63259e16 −1.12145
\(372\) −2.69892e16 −0.528033
\(373\) 6.08101e16 1.16915 0.584573 0.811341i \(-0.301262\pi\)
0.584573 + 0.811341i \(0.301262\pi\)
\(374\) 4.12621e15 0.0779626
\(375\) −1.14077e16 −0.211834
\(376\) 5.63837e16 1.02904
\(377\) 8.23541e16 1.47729
\(378\) −6.02811e15 −0.106288
\(379\) 8.97513e16 1.55556 0.777778 0.628539i \(-0.216347\pi\)
0.777778 + 0.628539i \(0.216347\pi\)
\(380\) 6.02884e16 1.02717
\(381\) 6.39639e16 1.07133
\(382\) −1.60498e16 −0.264276
\(383\) −6.99155e16 −1.13183 −0.565915 0.824464i \(-0.691477\pi\)
−0.565915 + 0.824464i \(0.691477\pi\)
\(384\) 3.64551e16 0.580237
\(385\) 1.96043e17 3.06800
\(386\) −4.86369e15 −0.0748426
\(387\) −2.24740e16 −0.340062
\(388\) 3.03799e16 0.452044
\(389\) 4.80283e16 0.702788 0.351394 0.936228i \(-0.385708\pi\)
0.351394 + 0.936228i \(0.385708\pi\)
\(390\) 2.05960e16 0.296390
\(391\) −1.30601e16 −0.184841
\(392\) −6.83955e16 −0.952068
\(393\) −2.49622e16 −0.341768
\(394\) 4.49980e16 0.605993
\(395\) 6.73122e16 0.891687
\(396\) −2.93626e16 −0.382627
\(397\) −2.88338e16 −0.369626 −0.184813 0.982774i \(-0.559168\pi\)
−0.184813 + 0.982774i \(0.559168\pi\)
\(398\) 1.06511e16 0.134324
\(399\) 5.69074e16 0.706065
\(400\) 6.52543e16 0.796561
\(401\) −5.84467e16 −0.701975 −0.350988 0.936380i \(-0.614154\pi\)
−0.350988 + 0.936380i \(0.614154\pi\)
\(402\) 2.69751e16 0.318782
\(403\) 8.70417e16 1.01215
\(404\) −1.12320e17 −1.28522
\(405\) 1.47847e16 0.166477
\(406\) −7.60602e16 −0.842826
\(407\) −9.12454e16 −0.995055
\(408\) 5.99141e15 0.0643040
\(409\) −1.86398e16 −0.196897 −0.0984486 0.995142i \(-0.531388\pi\)
−0.0984486 + 0.995142i \(0.531388\pi\)
\(410\) 6.64586e16 0.690965
\(411\) 1.50363e16 0.153875
\(412\) −1.41519e17 −1.42555
\(413\) −2.04872e16 −0.203146
\(414\) −1.33102e16 −0.129922
\(415\) 1.74551e17 1.67730
\(416\) −9.10754e16 −0.861578
\(417\) −7.16774e16 −0.667572
\(418\) −3.96986e16 −0.364024
\(419\) 2.92711e16 0.264270 0.132135 0.991232i \(-0.457817\pi\)
0.132135 + 0.991232i \(0.457817\pi\)
\(420\) 1.32819e17 1.18070
\(421\) −1.93762e17 −1.69603 −0.848017 0.529969i \(-0.822204\pi\)
−0.848017 + 0.529969i \(0.822204\pi\)
\(422\) −3.41749e15 −0.0294561
\(423\) −6.09051e16 −0.516942
\(424\) 5.70548e16 0.476886
\(425\) 2.53855e16 0.208957
\(426\) −3.51439e16 −0.284897
\(427\) −7.64043e16 −0.610010
\(428\) 1.67367e17 1.31609
\(429\) 9.46959e16 0.733430
\(430\) −7.09176e16 −0.541015
\(431\) 3.77201e16 0.283446 0.141723 0.989906i \(-0.454736\pi\)
0.141723 + 0.989906i \(0.454736\pi\)
\(432\) −1.66362e16 −0.123143
\(433\) −2.20311e17 −1.60644 −0.803221 0.595682i \(-0.796882\pi\)
−0.803221 + 0.595682i \(0.796882\pi\)
\(434\) −8.03896e16 −0.577453
\(435\) 1.86547e17 1.32010
\(436\) 1.85097e17 1.29044
\(437\) 1.25653e17 0.863062
\(438\) −3.93182e16 −0.266080
\(439\) 2.31477e17 1.54344 0.771718 0.635965i \(-0.219398\pi\)
0.771718 + 0.635965i \(0.219398\pi\)
\(440\) −1.98580e17 −1.30464
\(441\) 7.38801e16 0.478274
\(442\) −9.01572e15 −0.0575116
\(443\) −5.29852e16 −0.333066 −0.166533 0.986036i \(-0.553257\pi\)
−0.166533 + 0.986036i \(0.553257\pi\)
\(444\) −6.18190e16 −0.382942
\(445\) −3.50870e17 −2.14194
\(446\) 1.75178e16 0.105391
\(447\) 6.75315e16 0.400413
\(448\) −8.67414e16 −0.506897
\(449\) 2.43564e17 1.40285 0.701427 0.712741i \(-0.252547\pi\)
0.701427 + 0.712741i \(0.252547\pi\)
\(450\) 2.58715e16 0.146872
\(451\) 3.05562e17 1.70982
\(452\) 3.00816e17 1.65921
\(453\) −2.50607e16 −0.136256
\(454\) −1.05750e16 −0.0566785
\(455\) −4.28350e17 −2.26321
\(456\) −5.76438e16 −0.300249
\(457\) 1.71174e17 0.878988 0.439494 0.898245i \(-0.355158\pi\)
0.439494 + 0.898245i \(0.355158\pi\)
\(458\) 1.04400e17 0.528538
\(459\) −6.47186e15 −0.0323033
\(460\) 2.93268e17 1.44324
\(461\) 2.62111e17 1.27183 0.635916 0.771759i \(-0.280623\pi\)
0.635916 + 0.771759i \(0.280623\pi\)
\(462\) −8.74588e16 −0.418438
\(463\) 1.98787e17 0.937801 0.468900 0.883251i \(-0.344650\pi\)
0.468900 + 0.883251i \(0.344650\pi\)
\(464\) −2.09908e17 −0.976478
\(465\) 1.97165e17 0.904454
\(466\) −3.46923e16 −0.156937
\(467\) 3.01014e17 1.34285 0.671425 0.741073i \(-0.265683\pi\)
0.671425 + 0.741073i \(0.265683\pi\)
\(468\) 6.41568e16 0.282257
\(469\) −5.61022e17 −2.43420
\(470\) −1.92189e17 −0.822417
\(471\) −2.50004e16 −0.105514
\(472\) 2.07523e16 0.0863861
\(473\) −3.26064e17 −1.33877
\(474\) −3.00294e16 −0.121615
\(475\) −2.44236e17 −0.975665
\(476\) −5.81405e16 −0.229105
\(477\) −6.16301e16 −0.239565
\(478\) −9.09780e16 −0.348863
\(479\) 2.50277e17 0.946759 0.473379 0.880859i \(-0.343034\pi\)
0.473379 + 0.880859i \(0.343034\pi\)
\(480\) −2.06303e17 −0.769904
\(481\) 1.99370e17 0.734034
\(482\) 4.99005e16 0.181259
\(483\) 2.76821e17 0.992072
\(484\) −1.78626e17 −0.631611
\(485\) −2.21936e17 −0.774294
\(486\) −6.59576e15 −0.0227054
\(487\) 4.96787e16 0.168745 0.0843727 0.996434i \(-0.473111\pi\)
0.0843727 + 0.996434i \(0.473111\pi\)
\(488\) 7.73931e16 0.259402
\(489\) 2.32391e16 0.0768620
\(490\) 2.33132e17 0.760900
\(491\) 7.49828e16 0.241508 0.120754 0.992682i \(-0.461469\pi\)
0.120754 + 0.992682i \(0.461469\pi\)
\(492\) 2.07019e17 0.658017
\(493\) −8.16593e16 −0.256154
\(494\) 8.67409e16 0.268534
\(495\) 2.14504e17 0.655392
\(496\) −2.21856e17 −0.669023
\(497\) 7.30913e17 2.17545
\(498\) −7.78710e16 −0.228763
\(499\) −2.43010e17 −0.704646 −0.352323 0.935879i \(-0.614608\pi\)
−0.352323 + 0.935879i \(0.614608\pi\)
\(500\) −1.12133e17 −0.320943
\(501\) −1.07017e17 −0.302349
\(502\) 4.50371e16 0.125602
\(503\) −4.48131e17 −1.23371 −0.616855 0.787077i \(-0.711594\pi\)
−0.616855 + 0.787077i \(0.711594\pi\)
\(504\) −1.26993e17 −0.345130
\(505\) 8.20534e17 2.20142
\(506\) −1.93111e17 −0.511479
\(507\) 1.38868e16 0.0363119
\(508\) 6.28737e17 1.62314
\(509\) 4.56958e17 1.16469 0.582345 0.812941i \(-0.302135\pi\)
0.582345 + 0.812941i \(0.302135\pi\)
\(510\) −2.04222e16 −0.0513922
\(511\) 8.17728e17 2.03176
\(512\) 4.05205e17 0.994077
\(513\) 6.22663e16 0.150831
\(514\) −2.22139e17 −0.531330
\(515\) 1.03384e18 2.44179
\(516\) −2.20909e17 −0.515218
\(517\) −8.83642e17 −2.03511
\(518\) −1.84133e17 −0.418782
\(519\) 1.84331e17 0.414010
\(520\) 4.33893e17 0.962412
\(521\) 9.57048e16 0.209647 0.104823 0.994491i \(-0.466572\pi\)
0.104823 + 0.994491i \(0.466572\pi\)
\(522\) −8.32226e16 −0.180046
\(523\) −6.12717e17 −1.30918 −0.654589 0.755985i \(-0.727158\pi\)
−0.654589 + 0.755985i \(0.727158\pi\)
\(524\) −2.45368e17 −0.517802
\(525\) −5.38068e17 −1.12151
\(526\) −2.80578e17 −0.577625
\(527\) −8.63074e16 −0.175501
\(528\) −2.41366e17 −0.484792
\(529\) 1.07190e17 0.212664
\(530\) −1.94476e17 −0.381131
\(531\) −2.24165e16 −0.0433963
\(532\) 5.59374e17 1.06974
\(533\) −6.67648e17 −1.26131
\(534\) 1.56531e17 0.292134
\(535\) −1.22267e18 −2.25429
\(536\) 5.68282e17 1.03512
\(537\) 5.99351e17 1.07857
\(538\) 3.33431e16 0.0592818
\(539\) 1.07189e18 1.88288
\(540\) 1.45327e17 0.252224
\(541\) 2.14986e16 0.0368661 0.0184331 0.999830i \(-0.494132\pi\)
0.0184331 + 0.999830i \(0.494132\pi\)
\(542\) 1.13752e17 0.192736
\(543\) −6.08364e17 −1.01851
\(544\) 9.03071e16 0.149393
\(545\) −1.35220e18 −2.21036
\(546\) 1.91096e17 0.308674
\(547\) −3.63252e17 −0.579816 −0.289908 0.957054i \(-0.593625\pi\)
−0.289908 + 0.957054i \(0.593625\pi\)
\(548\) 1.47800e17 0.233131
\(549\) −8.35992e16 −0.130311
\(550\) 3.75356e17 0.578211
\(551\) 7.85650e17 1.19604
\(552\) −2.80404e17 −0.421871
\(553\) 6.24543e17 0.928644
\(554\) 1.54908e17 0.227646
\(555\) 4.51609e17 0.655931
\(556\) −7.04557e17 −1.01142
\(557\) −2.48805e17 −0.353021 −0.176511 0.984299i \(-0.556481\pi\)
−0.176511 + 0.984299i \(0.556481\pi\)
\(558\) −8.79597e16 −0.123356
\(559\) 7.12444e17 0.987585
\(560\) 1.09180e18 1.49596
\(561\) −9.38970e16 −0.127172
\(562\) 2.47058e17 0.330760
\(563\) −4.54008e17 −0.600840 −0.300420 0.953807i \(-0.597127\pi\)
−0.300420 + 0.953807i \(0.597127\pi\)
\(564\) −5.98670e17 −0.783202
\(565\) −2.19756e18 −2.84201
\(566\) 4.18490e17 0.535030
\(567\) 1.37177e17 0.173377
\(568\) −7.40372e17 −0.925094
\(569\) −4.33355e17 −0.535321 −0.267660 0.963513i \(-0.586251\pi\)
−0.267660 + 0.963513i \(0.586251\pi\)
\(570\) 1.96484e17 0.239961
\(571\) −7.27408e17 −0.878301 −0.439151 0.898413i \(-0.644721\pi\)
−0.439151 + 0.898413i \(0.644721\pi\)
\(572\) 9.30819e17 1.11120
\(573\) 3.65233e17 0.431087
\(574\) 6.16623e17 0.719602
\(575\) −1.18806e18 −1.37088
\(576\) −9.49097e16 −0.108284
\(577\) −1.52093e17 −0.171579 −0.0857897 0.996313i \(-0.527341\pi\)
−0.0857897 + 0.996313i \(0.527341\pi\)
\(578\) −3.08356e17 −0.343970
\(579\) 1.10679e17 0.122083
\(580\) 1.83367e18 2.00005
\(581\) 1.61954e18 1.74681
\(582\) 9.90103e16 0.105604
\(583\) −8.94160e17 −0.943126
\(584\) −8.28310e17 −0.863992
\(585\) −4.68687e17 −0.483470
\(586\) −3.91552e17 −0.399443
\(587\) −2.29539e17 −0.231584 −0.115792 0.993273i \(-0.536941\pi\)
−0.115792 + 0.993273i \(0.536941\pi\)
\(588\) 7.26209e17 0.724617
\(589\) 8.30370e17 0.819450
\(590\) −7.07362e16 −0.0690404
\(591\) −1.02398e18 −0.988495
\(592\) −5.08164e17 −0.485191
\(593\) 2.48505e17 0.234682 0.117341 0.993092i \(-0.462563\pi\)
0.117341 + 0.993092i \(0.462563\pi\)
\(594\) −9.56947e16 −0.0893873
\(595\) 4.24736e17 0.392427
\(596\) 6.63805e17 0.606652
\(597\) −2.42378e17 −0.219109
\(598\) 4.21944e17 0.377309
\(599\) −1.43267e18 −1.26728 −0.633638 0.773630i \(-0.718439\pi\)
−0.633638 + 0.773630i \(0.718439\pi\)
\(600\) 5.45031e17 0.476912
\(601\) 4.76099e17 0.412110 0.206055 0.978540i \(-0.433937\pi\)
0.206055 + 0.978540i \(0.433937\pi\)
\(602\) −6.57996e17 −0.563438
\(603\) −6.13852e17 −0.519997
\(604\) −2.46335e17 −0.206437
\(605\) 1.30492e18 1.08187
\(606\) −3.66058e17 −0.300246
\(607\) −2.45086e16 −0.0198880 −0.00994401 0.999951i \(-0.503165\pi\)
−0.00994401 + 0.999951i \(0.503165\pi\)
\(608\) −8.68851e17 −0.697545
\(609\) 1.73084e18 1.37482
\(610\) −2.63801e17 −0.207316
\(611\) 1.93075e18 1.50126
\(612\) −6.36155e16 −0.0489417
\(613\) 1.78818e18 1.36119 0.680593 0.732662i \(-0.261722\pi\)
0.680593 + 0.732662i \(0.261722\pi\)
\(614\) 3.98391e17 0.300065
\(615\) −1.51235e18 −1.12710
\(616\) −1.84248e18 −1.35872
\(617\) −2.36700e18 −1.72721 −0.863603 0.504173i \(-0.831797\pi\)
−0.863603 + 0.504173i \(0.831797\pi\)
\(618\) −4.61220e17 −0.333030
\(619\) −1.72699e18 −1.23396 −0.616978 0.786981i \(-0.711643\pi\)
−0.616978 + 0.786981i \(0.711643\pi\)
\(620\) 1.93805e18 1.37031
\(621\) 3.02889e17 0.211928
\(622\) 5.99564e17 0.415143
\(623\) −3.25549e18 −2.23071
\(624\) 5.27381e17 0.357622
\(625\) −1.03585e18 −0.695149
\(626\) −5.55685e17 −0.369059
\(627\) 9.03391e17 0.593795
\(628\) −2.45743e17 −0.159861
\(629\) −1.97688e17 −0.127277
\(630\) 4.32868e17 0.275830
\(631\) −1.39038e18 −0.876884 −0.438442 0.898759i \(-0.644470\pi\)
−0.438442 + 0.898759i \(0.644470\pi\)
\(632\) −6.32625e17 −0.394899
\(633\) 7.77691e16 0.0480488
\(634\) −3.14365e17 −0.192245
\(635\) −4.59314e18 −2.78023
\(636\) −6.05796e17 −0.362957
\(637\) −2.34206e18 −1.38897
\(638\) −1.20744e18 −0.708810
\(639\) 7.99742e17 0.464723
\(640\) −2.61778e18 −1.50578
\(641\) −2.31193e17 −0.131643 −0.0658214 0.997831i \(-0.520967\pi\)
−0.0658214 + 0.997831i \(0.520967\pi\)
\(642\) 5.45460e17 0.307457
\(643\) −2.50596e18 −1.39831 −0.699155 0.714971i \(-0.746440\pi\)
−0.699155 + 0.714971i \(0.746440\pi\)
\(644\) 2.72103e18 1.50306
\(645\) 1.61382e18 0.882503
\(646\) −8.60091e16 −0.0465622
\(647\) 9.43881e17 0.505871 0.252935 0.967483i \(-0.418604\pi\)
0.252935 + 0.967483i \(0.418604\pi\)
\(648\) −1.38952e17 −0.0737272
\(649\) −3.25229e17 −0.170844
\(650\) −8.20148e17 −0.426536
\(651\) 1.82936e18 0.941940
\(652\) 2.28430e17 0.116451
\(653\) −1.51419e18 −0.764266 −0.382133 0.924107i \(-0.624810\pi\)
−0.382133 + 0.924107i \(0.624810\pi\)
\(654\) 6.03245e17 0.301466
\(655\) 1.79249e18 0.886930
\(656\) 1.70174e18 0.833714
\(657\) 8.94733e17 0.434029
\(658\) −1.78319e18 −0.856503
\(659\) 6.65290e17 0.316414 0.158207 0.987406i \(-0.449429\pi\)
0.158207 + 0.987406i \(0.449429\pi\)
\(660\) 2.10848e18 0.992963
\(661\) −1.48382e17 −0.0691945 −0.0345973 0.999401i \(-0.511015\pi\)
−0.0345973 + 0.999401i \(0.511015\pi\)
\(662\) 3.11967e17 0.144056
\(663\) 2.05164e17 0.0938128
\(664\) −1.64050e18 −0.742819
\(665\) −4.08642e18 −1.83232
\(666\) −2.01472e17 −0.0894609
\(667\) 3.82173e18 1.68051
\(668\) −1.05193e18 −0.458079
\(669\) −3.98640e17 −0.171914
\(670\) −1.93704e18 −0.827279
\(671\) −1.21290e18 −0.513013
\(672\) −1.91414e18 −0.801813
\(673\) −4.26382e18 −1.76889 −0.884446 0.466643i \(-0.845463\pi\)
−0.884446 + 0.466643i \(0.845463\pi\)
\(674\) 2.49722e17 0.102605
\(675\) −5.88737e17 −0.239578
\(676\) 1.36501e17 0.0550150
\(677\) 3.08939e18 1.23324 0.616618 0.787263i \(-0.288502\pi\)
0.616618 + 0.787263i \(0.288502\pi\)
\(678\) 9.80379e17 0.387615
\(679\) −2.05919e18 −0.806386
\(680\) −4.30233e17 −0.166877
\(681\) 2.40648e17 0.0924539
\(682\) −1.27616e18 −0.485633
\(683\) 7.57376e17 0.285481 0.142740 0.989760i \(-0.454409\pi\)
0.142740 + 0.989760i \(0.454409\pi\)
\(684\) 6.12050e17 0.228519
\(685\) −1.07973e18 −0.399324
\(686\) 6.55517e17 0.240147
\(687\) −2.37575e18 −0.862150
\(688\) −1.81591e18 −0.652786
\(689\) 1.95373e18 0.695727
\(690\) 9.55780e17 0.337162
\(691\) −2.28803e18 −0.799564 −0.399782 0.916610i \(-0.630914\pi\)
−0.399782 + 0.916610i \(0.630914\pi\)
\(692\) 1.81189e18 0.627254
\(693\) 1.99023e18 0.682555
\(694\) −2.96731e17 −0.100815
\(695\) 5.14703e18 1.73243
\(696\) −1.75324e18 −0.584630
\(697\) 6.62015e17 0.218703
\(698\) −1.03132e18 −0.337546
\(699\) 7.89465e17 0.255995
\(700\) −5.28897e18 −1.69916
\(701\) 2.55032e18 0.811761 0.405881 0.913926i \(-0.366965\pi\)
0.405881 + 0.913926i \(0.366965\pi\)
\(702\) 2.09091e17 0.0659394
\(703\) 1.90197e18 0.594284
\(704\) −1.37700e18 −0.426296
\(705\) 4.37349e18 1.34153
\(706\) −5.19869e17 −0.158002
\(707\) 7.61317e18 2.29266
\(708\) −2.20344e17 −0.0657483
\(709\) 1.33695e18 0.395288 0.197644 0.980274i \(-0.436671\pi\)
0.197644 + 0.980274i \(0.436671\pi\)
\(710\) 2.52362e18 0.739342
\(711\) 6.83356e17 0.198378
\(712\) 3.29761e18 0.948593
\(713\) 4.03927e18 1.15139
\(714\) −1.89484e17 −0.0535222
\(715\) −6.79995e18 −1.90334
\(716\) 5.89135e18 1.63411
\(717\) 2.07031e18 0.569065
\(718\) 1.06666e18 0.290547
\(719\) −2.11011e18 −0.569595 −0.284798 0.958588i \(-0.591926\pi\)
−0.284798 + 0.958588i \(0.591926\pi\)
\(720\) 1.19461e18 0.319570
\(721\) 9.59232e18 2.54299
\(722\) −5.19675e17 −0.136534
\(723\) −1.13555e18 −0.295669
\(724\) −5.97995e18 −1.54311
\(725\) −7.42844e18 −1.89977
\(726\) −5.82154e17 −0.147554
\(727\) −1.12546e18 −0.282720 −0.141360 0.989958i \(-0.545148\pi\)
−0.141360 + 0.989958i \(0.545148\pi\)
\(728\) 4.02580e18 1.00230
\(729\) 1.50095e17 0.0370370
\(730\) 2.82337e18 0.690508
\(731\) −7.06434e17 −0.171241
\(732\) −8.21743e17 −0.197430
\(733\) −2.41198e18 −0.574378 −0.287189 0.957874i \(-0.592721\pi\)
−0.287189 + 0.957874i \(0.592721\pi\)
\(734\) −2.49057e18 −0.587861
\(735\) −5.30520e18 −1.24118
\(736\) −4.22646e18 −0.980100
\(737\) −8.90608e18 −2.04714
\(738\) 6.74690e17 0.153723
\(739\) 4.14722e17 0.0936631 0.0468315 0.998903i \(-0.485088\pi\)
0.0468315 + 0.998903i \(0.485088\pi\)
\(740\) 4.43912e18 0.993780
\(741\) −1.97389e18 −0.438032
\(742\) −1.80441e18 −0.396927
\(743\) 3.39730e18 0.740809 0.370405 0.928871i \(-0.379219\pi\)
0.370405 + 0.928871i \(0.379219\pi\)
\(744\) −1.85304e18 −0.400553
\(745\) −4.84932e18 −1.03912
\(746\) 1.94806e18 0.413810
\(747\) 1.77205e18 0.373157
\(748\) −9.22966e17 −0.192675
\(749\) −1.13443e19 −2.34772
\(750\) −3.65449e17 −0.0749770
\(751\) −1.32835e18 −0.270181 −0.135090 0.990833i \(-0.543132\pi\)
−0.135090 + 0.990833i \(0.543132\pi\)
\(752\) −4.92118e18 −0.992324
\(753\) −1.02487e18 −0.204882
\(754\) 2.63823e18 0.522876
\(755\) 1.79956e18 0.353600
\(756\) 1.34839e18 0.262678
\(757\) 1.99577e16 0.00385467 0.00192733 0.999998i \(-0.499387\pi\)
0.00192733 + 0.999998i \(0.499387\pi\)
\(758\) 2.87520e18 0.550577
\(759\) 4.39447e18 0.834324
\(760\) 4.13930e18 0.779182
\(761\) 4.42416e18 0.825715 0.412858 0.910796i \(-0.364531\pi\)
0.412858 + 0.910796i \(0.364531\pi\)
\(762\) 2.04910e18 0.379189
\(763\) −1.25461e19 −2.30197
\(764\) 3.59008e18 0.653126
\(765\) 4.64733e17 0.0838309
\(766\) −2.23976e18 −0.400602
\(767\) 7.10621e17 0.126028
\(768\) 1.01316e17 0.0178169
\(769\) 5.45929e18 0.951951 0.475976 0.879458i \(-0.342095\pi\)
0.475976 + 0.879458i \(0.342095\pi\)
\(770\) 6.28026e18 1.08590
\(771\) 5.05504e18 0.866704
\(772\) 1.08793e18 0.184964
\(773\) 5.23841e18 0.883147 0.441573 0.897225i \(-0.354420\pi\)
0.441573 + 0.897225i \(0.354420\pi\)
\(774\) −7.19958e17 −0.120362
\(775\) −7.85127e18 −1.30160
\(776\) 2.08584e18 0.342909
\(777\) 4.19017e18 0.683117
\(778\) 1.53860e18 0.248747
\(779\) −6.36930e18 −1.02117
\(780\) −4.60699e18 −0.732491
\(781\) 1.16031e19 1.82954
\(782\) −4.18384e17 −0.0654231
\(783\) 1.89383e18 0.293691
\(784\) 5.96957e18 0.918097
\(785\) 1.79523e18 0.273822
\(786\) −7.99670e17 −0.120966
\(787\) 1.09536e19 1.64331 0.821656 0.569984i \(-0.193050\pi\)
0.821656 + 0.569984i \(0.193050\pi\)
\(788\) −1.00653e19 −1.49764
\(789\) 6.38489e18 0.942221
\(790\) 2.15636e18 0.315606
\(791\) −2.03897e19 −2.95980
\(792\) −2.01599e18 −0.290251
\(793\) 2.65017e18 0.378440
\(794\) −9.23695e17 −0.130826
\(795\) 4.42555e18 0.621700
\(796\) −2.38247e18 −0.331965
\(797\) 1.74637e18 0.241355 0.120678 0.992692i \(-0.461493\pi\)
0.120678 + 0.992692i \(0.461493\pi\)
\(798\) 1.82304e18 0.249906
\(799\) −1.91446e18 −0.260310
\(800\) 8.21512e18 1.10797
\(801\) −3.56205e18 −0.476528
\(802\) −1.87235e18 −0.248459
\(803\) 1.29812e19 1.70870
\(804\) −6.03389e18 −0.787831
\(805\) −1.98781e19 −2.57455
\(806\) 2.78840e18 0.358243
\(807\) −7.58763e17 −0.0967004
\(808\) −7.71169e18 −0.974935
\(809\) 1.32134e19 1.65710 0.828549 0.559916i \(-0.189167\pi\)
0.828549 + 0.559916i \(0.189167\pi\)
\(810\) 4.73630e17 0.0589233
\(811\) −3.58558e18 −0.442510 −0.221255 0.975216i \(-0.571015\pi\)
−0.221255 + 0.975216i \(0.571015\pi\)
\(812\) 1.70134e19 2.08294
\(813\) −2.58856e18 −0.314391
\(814\) −2.92306e18 −0.352192
\(815\) −1.66876e18 −0.199466
\(816\) −5.22931e17 −0.0620096
\(817\) 6.79666e18 0.799562
\(818\) −5.97129e17 −0.0696902
\(819\) −4.34863e18 −0.503508
\(820\) −1.48657e19 −1.70763
\(821\) 1.45956e18 0.166338 0.0831688 0.996535i \(-0.473496\pi\)
0.0831688 + 0.996535i \(0.473496\pi\)
\(822\) 4.81690e17 0.0544629
\(823\) −8.13681e18 −0.912757 −0.456379 0.889786i \(-0.650854\pi\)
−0.456379 + 0.889786i \(0.650854\pi\)
\(824\) −9.71646e18 −1.08139
\(825\) −8.54169e18 −0.943177
\(826\) −6.56312e17 −0.0719019
\(827\) 4.53647e18 0.493097 0.246548 0.969130i \(-0.420704\pi\)
0.246548 + 0.969130i \(0.420704\pi\)
\(828\) 2.97727e18 0.321085
\(829\) −2.08028e18 −0.222596 −0.111298 0.993787i \(-0.535501\pi\)
−0.111298 + 0.993787i \(0.535501\pi\)
\(830\) 5.59178e18 0.593667
\(831\) −3.52511e18 −0.371335
\(832\) 3.00872e18 0.314471
\(833\) 2.32230e18 0.240839
\(834\) −2.29620e18 −0.236282
\(835\) 7.68472e18 0.784632
\(836\) 8.87993e18 0.899640
\(837\) 2.00163e18 0.201219
\(838\) 9.37706e17 0.0935364
\(839\) −1.65818e19 −1.64126 −0.820632 0.571457i \(-0.806378\pi\)
−0.820632 + 0.571457i \(0.806378\pi\)
\(840\) 9.11917e18 0.895653
\(841\) 1.36350e19 1.32886
\(842\) −6.20720e18 −0.600298
\(843\) −5.62211e18 −0.539535
\(844\) 7.64435e17 0.0727972
\(845\) −9.97184e17 −0.0942338
\(846\) −1.95111e18 −0.182968
\(847\) 1.21075e19 1.12671
\(848\) −4.97976e18 −0.459870
\(849\) −9.52324e18 −0.872740
\(850\) 8.13229e17 0.0739588
\(851\) 9.25197e18 0.835011
\(852\) 7.86111e18 0.704087
\(853\) 1.58201e19 1.40617 0.703087 0.711103i \(-0.251804\pi\)
0.703087 + 0.711103i \(0.251804\pi\)
\(854\) −2.44763e18 −0.215908
\(855\) −4.47123e18 −0.391424
\(856\) 1.14911e19 0.998351
\(857\) −1.07971e19 −0.930960 −0.465480 0.885059i \(-0.654118\pi\)
−0.465480 + 0.885059i \(0.654118\pi\)
\(858\) 3.03360e18 0.259592
\(859\) −1.35604e19 −1.15164 −0.575821 0.817576i \(-0.695317\pi\)
−0.575821 + 0.817576i \(0.695317\pi\)
\(860\) 1.58631e19 1.33705
\(861\) −1.40320e19 −1.17381
\(862\) 1.20837e18 0.100324
\(863\) 3.42847e18 0.282507 0.141254 0.989973i \(-0.454887\pi\)
0.141254 + 0.989973i \(0.454887\pi\)
\(864\) −2.09439e18 −0.171285
\(865\) −1.32365e19 −1.07441
\(866\) −7.05771e18 −0.568588
\(867\) 7.01700e18 0.561084
\(868\) 1.79818e19 1.42710
\(869\) 9.91447e18 0.780982
\(870\) 5.97607e18 0.467241
\(871\) 1.94596e19 1.51014
\(872\) 1.27085e19 0.978896
\(873\) −2.25310e18 −0.172261
\(874\) 4.02531e18 0.305474
\(875\) 7.60050e18 0.572519
\(876\) 8.79482e18 0.657583
\(877\) −1.50516e19 −1.11708 −0.558541 0.829477i \(-0.688639\pi\)
−0.558541 + 0.829477i \(0.688639\pi\)
\(878\) 7.41541e18 0.546287
\(879\) 8.91025e18 0.651572
\(880\) 1.73321e19 1.25809
\(881\) −5.85836e18 −0.422117 −0.211058 0.977473i \(-0.567691\pi\)
−0.211058 + 0.977473i \(0.567691\pi\)
\(882\) 2.36676e18 0.169281
\(883\) 1.29408e19 0.918790 0.459395 0.888232i \(-0.348066\pi\)
0.459395 + 0.888232i \(0.348066\pi\)
\(884\) 2.01667e18 0.142133
\(885\) 1.60969e18 0.112619
\(886\) −1.69739e18 −0.117886
\(887\) −5.97829e18 −0.412167 −0.206083 0.978534i \(-0.566072\pi\)
−0.206083 + 0.978534i \(0.566072\pi\)
\(888\) −4.24439e18 −0.290490
\(889\) −4.26166e19 −2.89546
\(890\) −1.12402e19 −0.758122
\(891\) 2.17765e18 0.145808
\(892\) −3.91845e18 −0.260461
\(893\) 1.84191e19 1.21544
\(894\) 2.16339e18 0.141723
\(895\) −4.30384e19 −2.79902
\(896\) −2.42886e19 −1.56819
\(897\) −9.60185e18 −0.615466
\(898\) 7.80263e18 0.496529
\(899\) 2.52558e19 1.59559
\(900\) −5.78702e18 −0.362977
\(901\) −1.93724e18 −0.120635
\(902\) 9.78874e18 0.605179
\(903\) 1.49735e19 0.919079
\(904\) 2.06535e19 1.25863
\(905\) 4.36856e19 2.64315
\(906\) −8.02824e17 −0.0482266
\(907\) 8.69133e18 0.518369 0.259185 0.965828i \(-0.416546\pi\)
0.259185 + 0.965828i \(0.416546\pi\)
\(908\) 2.36546e18 0.140074
\(909\) 8.33009e18 0.489761
\(910\) −1.37223e19 −0.801046
\(911\) −3.39930e19 −1.97024 −0.985122 0.171858i \(-0.945023\pi\)
−0.985122 + 0.171858i \(0.945023\pi\)
\(912\) 5.03116e18 0.289536
\(913\) 2.57098e19 1.46906
\(914\) 5.48360e18 0.311111
\(915\) 6.00311e18 0.338173
\(916\) −2.33526e19 −1.30622
\(917\) 1.66313e19 0.923689
\(918\) −2.07327e17 −0.0114335
\(919\) −9.37352e18 −0.513277 −0.256639 0.966507i \(-0.582615\pi\)
−0.256639 + 0.966507i \(0.582615\pi\)
\(920\) 2.01353e19 1.09481
\(921\) −9.06588e18 −0.489466
\(922\) 8.39678e18 0.450155
\(923\) −2.53525e19 −1.34962
\(924\) 1.95631e19 1.03412
\(925\) −1.79834e19 −0.943954
\(926\) 6.36817e18 0.331927
\(927\) 1.04956e19 0.543238
\(928\) −2.64262e19 −1.35823
\(929\) −5.54495e18 −0.283006 −0.141503 0.989938i \(-0.545194\pi\)
−0.141503 + 0.989938i \(0.545194\pi\)
\(930\) 6.31624e18 0.320125
\(931\) −2.23431e19 −1.12453
\(932\) 7.76009e18 0.387849
\(933\) −1.36438e19 −0.677181
\(934\) 9.64306e18 0.475291
\(935\) 6.74258e18 0.330028
\(936\) 4.40490e18 0.214113
\(937\) −1.72390e19 −0.832157 −0.416079 0.909329i \(-0.636596\pi\)
−0.416079 + 0.909329i \(0.636596\pi\)
\(938\) −1.79724e19 −0.861566
\(939\) 1.26453e19 0.602008
\(940\) 4.29895e19 2.03250
\(941\) −2.51439e18 −0.118060 −0.0590298 0.998256i \(-0.518801\pi\)
−0.0590298 + 0.998256i \(0.518801\pi\)
\(942\) −8.00892e17 −0.0373459
\(943\) −3.09829e19 −1.43482
\(944\) −1.81127e18 −0.0833038
\(945\) −9.85043e18 −0.449934
\(946\) −1.04455e19 −0.473846
\(947\) −1.89103e19 −0.851969 −0.425985 0.904730i \(-0.640072\pi\)
−0.425985 + 0.904730i \(0.640072\pi\)
\(948\) 6.71708e18 0.300557
\(949\) −2.83638e19 −1.26047
\(950\) −7.82414e18 −0.345329
\(951\) 7.15376e18 0.313589
\(952\) −3.99183e18 −0.173793
\(953\) 2.77370e18 0.119938 0.0599688 0.998200i \(-0.480900\pi\)
0.0599688 + 0.998200i \(0.480900\pi\)
\(954\) −1.97433e18 −0.0847921
\(955\) −2.62267e19 −1.11872
\(956\) 2.03503e19 0.862172
\(957\) 2.74767e19 1.15621
\(958\) 8.01766e18 0.335098
\(959\) −1.00181e19 −0.415875
\(960\) 6.81530e18 0.281010
\(961\) 2.27579e18 0.0932029
\(962\) 6.38685e18 0.259806
\(963\) −1.24126e19 −0.501524
\(964\) −1.11619e19 −0.447959
\(965\) −7.94769e18 −0.316820
\(966\) 8.86803e18 0.351136
\(967\) 4.35158e19 1.71149 0.855747 0.517395i \(-0.173098\pi\)
0.855747 + 0.517395i \(0.173098\pi\)
\(968\) −1.22642e19 −0.479124
\(969\) 1.95724e18 0.0759521
\(970\) −7.10976e18 −0.274056
\(971\) 1.11305e19 0.426175 0.213088 0.977033i \(-0.431648\pi\)
0.213088 + 0.977033i \(0.431648\pi\)
\(972\) 1.47536e18 0.0561136
\(973\) 4.77557e19 1.80423
\(974\) 1.59147e18 0.0597261
\(975\) 1.86635e19 0.695765
\(976\) −6.75488e18 −0.250146
\(977\) 1.68696e19 0.620568 0.310284 0.950644i \(-0.399576\pi\)
0.310284 + 0.950644i \(0.399576\pi\)
\(978\) 7.44470e17 0.0272047
\(979\) −5.16800e19 −1.87601
\(980\) −5.21478e19 −1.88047
\(981\) −1.37276e19 −0.491751
\(982\) 2.40209e18 0.0854800
\(983\) 2.33001e18 0.0823681 0.0411841 0.999152i \(-0.486887\pi\)
0.0411841 + 0.999152i \(0.486887\pi\)
\(984\) 1.42136e19 0.499155
\(985\) 7.35305e19 2.56526
\(986\) −2.61597e18 −0.0906636
\(987\) 4.05786e19 1.39713
\(988\) −1.94025e19 −0.663648
\(989\) 3.30618e19 1.12344
\(990\) 6.87167e18 0.231971
\(991\) 3.77599e19 1.26635 0.633173 0.774010i \(-0.281752\pi\)
0.633173 + 0.774010i \(0.281752\pi\)
\(992\) −2.79304e19 −0.930573
\(993\) −7.09919e18 −0.234984
\(994\) 2.34150e19 0.769984
\(995\) 1.74048e19 0.568615
\(996\) 1.74185e19 0.565359
\(997\) 6.10950e19 1.97009 0.985047 0.172287i \(-0.0551158\pi\)
0.985047 + 0.172287i \(0.0551158\pi\)
\(998\) −7.78488e18 −0.249404
\(999\) 4.58475e18 0.145929
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 177.14.a.b.1.18 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.18 31 1.1 even 1 trivial