Properties

Label 177.11.c.a.58.3
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.3
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.98

$q$-expansion

\(f(q)\) \(=\) \(q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} -220965. i q^{10} -108701. i q^{11} -359484. q^{12} +582935. i q^{13} -250832. i q^{14} +517660. q^{15} +2.89309e6 q^{16} +733229. q^{17} -1.17873e6i q^{18} -2.47781e6 q^{19} -9.45436e6 q^{20} +587629. q^{21} -6.50964e6 q^{22} +273388. i q^{23} +1.29246e7i q^{24} +3.84873e6 q^{25} +3.49096e7 q^{26} +2.76145e6 q^{27} -1.07323e7 q^{28} -7.13464e6 q^{29} -3.10005e7i q^{30} +8.58497e6i q^{31} -7.89208e7i q^{32} -1.52503e7i q^{33} -4.39101e7i q^{34} +1.54546e7 q^{35} -5.04341e7 q^{36} +1.12871e8i q^{37} +1.48386e8i q^{38} +8.17835e7i q^{39} +3.39915e8i q^{40} +5.07042e7 q^{41} -3.51907e7i q^{42} +6.60375e7i q^{43} +2.78526e8i q^{44} +7.26256e7 q^{45} +1.63721e7 q^{46} +4.56783e8i q^{47} +4.05890e8 q^{48} -2.64932e8 q^{49} -2.30485e8i q^{50} +1.02869e8 q^{51} -1.49367e9i q^{52} +5.34760e8 q^{53} -1.65372e8i q^{54} -4.01080e8i q^{55} +3.85859e8i q^{56} -3.47628e8 q^{57} +4.27264e8i q^{58} +(3.64006e8 + 6.15318e8i) q^{59} -1.32641e9 q^{60} -5.64631e8i q^{61} +5.14118e8 q^{62} +8.24421e7 q^{63} -1.76372e9 q^{64} +2.15089e9i q^{65} -9.13277e8 q^{66} -3.92311e8i q^{67} -1.87877e9 q^{68} +3.83553e7i q^{69} -9.25510e8i q^{70} +2.57751e9 q^{71} +1.81327e9i q^{72} -1.12186e9i q^{73} +6.75937e9 q^{74} +5.39962e8 q^{75} +6.34895e9 q^{76} -4.55292e8i q^{77} +4.89768e9 q^{78} +2.65793e9 q^{79} +1.06748e10 q^{80} +3.87420e8 q^{81} -3.03647e9i q^{82} -1.54998e8i q^{83} -1.50569e9 q^{84} +2.70544e9 q^{85} +3.95471e9 q^{86} -1.00096e9 q^{87} +1.00139e10 q^{88} +7.28833e9i q^{89} -4.34925e9i q^{90} +2.44162e9i q^{91} -7.00509e8i q^{92} +1.20444e9i q^{93} +2.73549e10 q^{94} -9.14255e9 q^{95} -1.10723e10i q^{96} +3.03929e9i q^{97} +1.58657e10i q^{98} -2.13956e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 59.8859i 1.87143i −0.352751 0.935717i \(-0.614754\pi\)
0.352751 0.935717i \(-0.385246\pi\)
\(3\) 140.296 0.577350
\(4\) −2562.32 −2.50227
\(5\) 3689.76 1.18072 0.590362 0.807138i \(-0.298985\pi\)
0.590362 + 0.807138i \(0.298985\pi\)
\(6\) 8401.76i 1.08047i
\(7\) 4188.49 0.249211 0.124606 0.992206i \(-0.460233\pi\)
0.124606 + 0.992206i \(0.460233\pi\)
\(8\) 92123.7i 2.81139i
\(9\) 19683.0 0.333333
\(10\) 220965.i 2.20965i
\(11\) 108701.i 0.674946i −0.941335 0.337473i \(-0.890428\pi\)
0.941335 0.337473i \(-0.109572\pi\)
\(12\) −359484. −1.44468
\(13\) 582935.i 1.57001i 0.619487 + 0.785007i \(0.287341\pi\)
−0.619487 + 0.785007i \(0.712659\pi\)
\(14\) 250832.i 0.466382i
\(15\) 517660. 0.681692
\(16\) 2.89309e6 2.75907
\(17\) 733229. 0.516410 0.258205 0.966090i \(-0.416869\pi\)
0.258205 + 0.966090i \(0.416869\pi\)
\(18\) 1.17873e6i 0.623811i
\(19\) −2.47781e6 −1.00069 −0.500346 0.865825i \(-0.666794\pi\)
−0.500346 + 0.865825i \(0.666794\pi\)
\(20\) −9.45436e6 −2.95449
\(21\) 587629. 0.143882
\(22\) −6.50964e6 −1.26312
\(23\) 273388.i 0.0424757i 0.999774 + 0.0212379i \(0.00676073\pi\)
−0.999774 + 0.0212379i \(0.993239\pi\)
\(24\) 1.29246e7i 1.62316i
\(25\) 3.84873e6 0.394110
\(26\) 3.49096e7 2.93818
\(27\) 2.76145e6 0.192450
\(28\) −1.07323e7 −0.623593
\(29\) −7.13464e6 −0.347842 −0.173921 0.984760i \(-0.555644\pi\)
−0.173921 + 0.984760i \(0.555644\pi\)
\(30\) 3.10005e7i 1.27574i
\(31\) 8.58497e6i 0.299868i 0.988696 + 0.149934i \(0.0479061\pi\)
−0.988696 + 0.149934i \(0.952094\pi\)
\(32\) 7.89208e7i 2.35202i
\(33\) 1.52503e7i 0.389680i
\(34\) 4.39101e7i 0.966428i
\(35\) 1.54546e7 0.294250
\(36\) −5.04341e7 −0.834089
\(37\) 1.12871e8i 1.62770i 0.581078 + 0.813848i \(0.302631\pi\)
−0.581078 + 0.813848i \(0.697369\pi\)
\(38\) 1.48386e8i 1.87273i
\(39\) 8.17835e7i 0.906448i
\(40\) 3.39915e8i 3.31948i
\(41\) 5.07042e7 0.437648 0.218824 0.975764i \(-0.429778\pi\)
0.218824 + 0.975764i \(0.429778\pi\)
\(42\) 3.51907e7i 0.269266i
\(43\) 6.60375e7i 0.449209i 0.974450 + 0.224604i \(0.0721090\pi\)
−0.974450 + 0.224604i \(0.927891\pi\)
\(44\) 2.78526e8i 1.68889i
\(45\) 7.26256e7 0.393575
\(46\) 1.63721e7 0.0794906
\(47\) 4.56783e8i 1.99169i 0.0910858 + 0.995843i \(0.470966\pi\)
−0.0910858 + 0.995843i \(0.529034\pi\)
\(48\) 4.05890e8 1.59295
\(49\) −2.64932e8 −0.937894
\(50\) 2.30485e8i 0.737551i
\(51\) 1.02869e8 0.298150
\(52\) 1.49367e9i 3.92859i
\(53\) 5.34760e8 1.27873 0.639366 0.768902i \(-0.279197\pi\)
0.639366 + 0.768902i \(0.279197\pi\)
\(54\) 1.65372e8i 0.360158i
\(55\) 4.01080e8i 0.796925i
\(56\) 3.85859e8i 0.700630i
\(57\) −3.47628e8 −0.577750
\(58\) 4.27264e8i 0.650963i
\(59\) 3.64006e8 + 6.15318e8i 0.509153 + 0.860676i
\(60\) −1.32641e9 −1.70577
\(61\) 5.64631e8i 0.668522i −0.942481 0.334261i \(-0.891513\pi\)
0.942481 0.334261i \(-0.108487\pi\)
\(62\) 5.14118e8 0.561183
\(63\) 8.24421e7 0.0830704
\(64\) −1.76372e9 −1.64259
\(65\) 2.15089e9i 1.85375i
\(66\) −9.13277e8 −0.729261
\(67\) 3.92311e8i 0.290574i −0.989390 0.145287i \(-0.953589\pi\)
0.989390 0.145287i \(-0.0464106\pi\)
\(68\) −1.87877e9 −1.29220
\(69\) 3.83553e7i 0.0245234i
\(70\) 9.25510e8i 0.550669i
\(71\) 2.57751e9 1.42860 0.714298 0.699842i \(-0.246746\pi\)
0.714298 + 0.699842i \(0.246746\pi\)
\(72\) 1.81327e9i 0.937131i
\(73\) 1.12186e9i 0.541159i −0.962698 0.270579i \(-0.912785\pi\)
0.962698 0.270579i \(-0.0872152\pi\)
\(74\) 6.75937e9 3.04613
\(75\) 5.39962e8 0.227540
\(76\) 6.34895e9 2.50400
\(77\) 4.55292e8i 0.168204i
\(78\) 4.89768e9 1.69636
\(79\) 2.65793e9 0.863791 0.431895 0.901924i \(-0.357845\pi\)
0.431895 + 0.901924i \(0.357845\pi\)
\(80\) 1.06748e10 3.25770
\(81\) 3.87420e8 0.111111
\(82\) 3.03647e9i 0.819029i
\(83\) 1.54998e8i 0.0393492i −0.999806 0.0196746i \(-0.993737\pi\)
0.999806 0.0196746i \(-0.00626302\pi\)
\(84\) −1.50569e9 −0.360031
\(85\) 2.70544e9 0.609738
\(86\) 3.95471e9 0.840665
\(87\) −1.00096e9 −0.200827
\(88\) 1.00139e10 1.89754
\(89\) 7.28833e9i 1.30520i 0.757701 + 0.652602i \(0.226322\pi\)
−0.757701 + 0.652602i \(0.773678\pi\)
\(90\) 4.34925e9i 0.736549i
\(91\) 2.44162e9i 0.391265i
\(92\) 7.00509e8i 0.106286i
\(93\) 1.20444e9i 0.173129i
\(94\) 2.73549e10 3.72731
\(95\) −9.14255e9 −1.18154
\(96\) 1.10723e10i 1.35794i
\(97\) 3.03929e9i 0.353927i 0.984217 + 0.176963i \(0.0566274\pi\)
−0.984217 + 0.176963i \(0.943373\pi\)
\(98\) 1.58657e10i 1.75521i
\(99\) 2.13956e9i 0.224982i
\(100\) −9.86168e9 −0.986168
\(101\) 2.69242e9i 0.256174i −0.991763 0.128087i \(-0.959116\pi\)
0.991763 0.128087i \(-0.0408837\pi\)
\(102\) 6.16041e9i 0.557968i
\(103\) 4.44428e7i 0.00383368i 0.999998 + 0.00191684i \(0.000610149\pi\)
−0.999998 + 0.00191684i \(0.999390\pi\)
\(104\) −5.37021e10 −4.41392
\(105\) 2.16821e9 0.169885
\(106\) 3.20246e10i 2.39306i
\(107\) −9.08377e9 −0.647660 −0.323830 0.946115i \(-0.604971\pi\)
−0.323830 + 0.946115i \(0.604971\pi\)
\(108\) −7.07572e9 −0.481561
\(109\) 5.38541e9i 0.350015i 0.984567 + 0.175007i \(0.0559949\pi\)
−0.984567 + 0.175007i \(0.944005\pi\)
\(110\) −2.40190e10 −1.49139
\(111\) 1.58353e10i 0.939751i
\(112\) 1.21177e10 0.687591
\(113\) 3.54688e9i 0.192510i 0.995357 + 0.0962552i \(0.0306865\pi\)
−0.995357 + 0.0962552i \(0.969313\pi\)
\(114\) 2.08180e10i 1.08122i
\(115\) 1.00874e9i 0.0501521i
\(116\) 1.82812e10 0.870393
\(117\) 1.14739e10i 0.523338i
\(118\) 3.68489e10 2.17988e10i 1.61070 0.952847i
\(119\) 3.07112e9 0.128695
\(120\) 4.76887e10i 1.91650i
\(121\) 1.41216e10 0.544448
\(122\) −3.38134e10 −1.25109
\(123\) 7.11360e9 0.252676
\(124\) 2.19974e10i 0.750350i
\(125\) −2.18319e10 −0.715389
\(126\) 4.93712e9i 0.155461i
\(127\) −1.69243e10 −0.512262 −0.256131 0.966642i \(-0.582448\pi\)
−0.256131 + 0.966642i \(0.582448\pi\)
\(128\) 2.48068e10i 0.721973i
\(129\) 9.26480e9i 0.259351i
\(130\) 1.28808e11 3.46918
\(131\) 5.73326e9i 0.148609i −0.997236 0.0743045i \(-0.976326\pi\)
0.997236 0.0743045i \(-0.0236737\pi\)
\(132\) 3.90761e10i 0.975083i
\(133\) −1.03783e10 −0.249384
\(134\) −2.34939e10 −0.543790
\(135\) 1.01891e10 0.227231
\(136\) 6.75478e10i 1.45183i
\(137\) 3.13369e10 0.649313 0.324656 0.945832i \(-0.394751\pi\)
0.324656 + 0.945832i \(0.394751\pi\)
\(138\) 2.29694e9 0.0458939
\(139\) −4.94543e10 −0.953082 −0.476541 0.879152i \(-0.658110\pi\)
−0.476541 + 0.879152i \(0.658110\pi\)
\(140\) −3.95995e10 −0.736291
\(141\) 6.40849e10i 1.14990i
\(142\) 1.54357e11i 2.67352i
\(143\) 6.33654e10 1.05967
\(144\) 5.69448e10 0.919690
\(145\) −2.63251e10 −0.410706
\(146\) −6.71836e10 −1.01274
\(147\) −3.71689e10 −0.541493
\(148\) 2.89211e11i 4.07293i
\(149\) 1.08170e11i 1.47290i 0.676490 + 0.736452i \(0.263500\pi\)
−0.676490 + 0.736452i \(0.736500\pi\)
\(150\) 3.23361e10i 0.425825i
\(151\) 8.13371e10i 1.03611i −0.855349 0.518053i \(-0.826657\pi\)
0.855349 0.518053i \(-0.173343\pi\)
\(152\) 2.28265e11i 2.81334i
\(153\) 1.44321e10 0.172137
\(154\) −2.72656e10 −0.314783
\(155\) 3.16765e10i 0.354062i
\(156\) 2.09556e11i 2.26817i
\(157\) 7.35807e10i 0.771375i 0.922630 + 0.385687i \(0.126036\pi\)
−0.922630 + 0.385687i \(0.873964\pi\)
\(158\) 1.59173e11i 1.61653i
\(159\) 7.50248e10 0.738276
\(160\) 2.91199e11i 2.77709i
\(161\) 1.14509e9i 0.0105854i
\(162\) 2.32010e10i 0.207937i
\(163\) −1.86149e11 −1.61779 −0.808894 0.587954i \(-0.799934\pi\)
−0.808894 + 0.587954i \(0.799934\pi\)
\(164\) −1.29920e11 −1.09511
\(165\) 5.62699e10i 0.460105i
\(166\) −9.28219e9 −0.0736394
\(167\) 1.29426e11 0.996413 0.498206 0.867059i \(-0.333992\pi\)
0.498206 + 0.867059i \(0.333992\pi\)
\(168\) 5.41346e10i 0.404509i
\(169\) −2.01955e11 −1.46494
\(170\) 1.62018e11i 1.14109i
\(171\) −4.87708e10 −0.333564
\(172\) 1.69209e11i 1.12404i
\(173\) 2.96176e11i 1.91126i −0.294574 0.955629i \(-0.595178\pi\)
0.294574 0.955629i \(-0.404822\pi\)
\(174\) 5.99435e10i 0.375834i
\(175\) 1.61204e10 0.0982167
\(176\) 3.14481e11i 1.86222i
\(177\) 5.10686e10 + 8.63267e10i 0.293960 + 0.496911i
\(178\) 4.36468e11 2.44260
\(179\) 1.75062e11i 0.952635i 0.879273 + 0.476318i \(0.158029\pi\)
−0.879273 + 0.476318i \(0.841971\pi\)
\(180\) −1.86090e11 −0.984829
\(181\) 1.31742e11 0.678158 0.339079 0.940758i \(-0.389885\pi\)
0.339079 + 0.940758i \(0.389885\pi\)
\(182\) 1.46219e11 0.732227
\(183\) 7.92156e10i 0.385971i
\(184\) −2.51856e10 −0.119416
\(185\) 4.16467e11i 1.92186i
\(186\) 7.21288e10 0.323999
\(187\) 7.97025e10i 0.348549i
\(188\) 1.17042e12i 4.98373i
\(189\) 1.15663e10 0.0479607
\(190\) 5.47510e11i 2.21118i
\(191\) 1.80546e11i 0.710266i −0.934816 0.355133i \(-0.884436\pi\)
0.934816 0.355133i \(-0.115564\pi\)
\(192\) −2.47443e11 −0.948349
\(193\) 3.40553e11 1.27174 0.635870 0.771796i \(-0.280641\pi\)
0.635870 + 0.771796i \(0.280641\pi\)
\(194\) 1.82011e11 0.662351
\(195\) 3.01762e11i 1.07026i
\(196\) 6.78840e11 2.34686
\(197\) 2.99654e10 0.100993 0.0504963 0.998724i \(-0.483920\pi\)
0.0504963 + 0.998724i \(0.483920\pi\)
\(198\) −1.28129e11 −0.421039
\(199\) −3.92538e11 −1.25781 −0.628906 0.777481i \(-0.716497\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(200\) 3.54559e11i 1.10800i
\(201\) 5.50398e10i 0.167763i
\(202\) −1.61238e11 −0.479414
\(203\) −2.98834e10 −0.0866861
\(204\) −2.63584e11 −0.746050
\(205\) 1.87086e11 0.516741
\(206\) 2.66150e9 0.00717447
\(207\) 5.38110e9i 0.0141586i
\(208\) 1.68649e12i 4.33177i
\(209\) 2.69340e11i 0.675413i
\(210\) 1.29845e11i 0.317929i
\(211\) 6.00627e11i 1.43613i −0.695978 0.718063i \(-0.745029\pi\)
0.695978 0.718063i \(-0.254971\pi\)
\(212\) −1.37023e12 −3.19973
\(213\) 3.61615e11 0.824800
\(214\) 5.43989e11i 1.21205i
\(215\) 2.43663e11i 0.530392i
\(216\) 2.54395e11i 0.541053i
\(217\) 3.59581e10i 0.0747305i
\(218\) 3.22510e11 0.655029
\(219\) 1.57393e11i 0.312438i
\(220\) 1.02770e12i 1.99412i
\(221\) 4.27425e11i 0.810771i
\(222\) 9.48314e11 1.75868
\(223\) −5.76487e11 −1.04536 −0.522679 0.852529i \(-0.675067\pi\)
−0.522679 + 0.852529i \(0.675067\pi\)
\(224\) 3.30559e11i 0.586151i
\(225\) 7.57546e10 0.131370
\(226\) 2.12408e11 0.360271
\(227\) 4.22740e9i 0.00701366i −0.999994 0.00350683i \(-0.998884\pi\)
0.999994 0.00350683i \(-0.00111626\pi\)
\(228\) 8.90734e11 1.44568
\(229\) 8.05126e11i 1.27846i 0.769016 + 0.639229i \(0.220746\pi\)
−0.769016 + 0.639229i \(0.779254\pi\)
\(230\) 6.04092e10 0.0938564
\(231\) 6.38757e10i 0.0971127i
\(232\) 6.57269e11i 0.977920i
\(233\) 3.62083e11i 0.527264i −0.964623 0.263632i \(-0.915080\pi\)
0.964623 0.263632i \(-0.0849205\pi\)
\(234\) 6.87125e11 0.979392
\(235\) 1.68542e12i 2.35163i
\(236\) −9.32700e11 1.57664e12i −1.27404 2.15364i
\(237\) 3.72898e11 0.498710
\(238\) 1.83917e11i 0.240845i
\(239\) −1.53434e12 −1.96758 −0.983791 0.179319i \(-0.942611\pi\)
−0.983791 + 0.179319i \(0.942611\pi\)
\(240\) 1.49764e12 1.88083
\(241\) 6.63824e11 0.816522 0.408261 0.912865i \(-0.366135\pi\)
0.408261 + 0.912865i \(0.366135\pi\)
\(242\) 8.45684e11i 1.01890i
\(243\) 5.43536e10 0.0641500
\(244\) 1.44677e12i 1.67282i
\(245\) −9.77536e11 −1.10739
\(246\) 4.26004e11i 0.472866i
\(247\) 1.44440e12i 1.57110i
\(248\) −7.90879e11 −0.843047
\(249\) 2.17456e10i 0.0227182i
\(250\) 1.30743e12i 1.33880i
\(251\) 1.52621e12 1.53195 0.765977 0.642868i \(-0.222256\pi\)
0.765977 + 0.642868i \(0.222256\pi\)
\(252\) −2.11243e11 −0.207864
\(253\) 2.97175e10 0.0286688
\(254\) 1.01353e12i 0.958664i
\(255\) 3.79563e11 0.352033
\(256\) −3.20468e11 −0.291464
\(257\) 1.83131e12 1.63342 0.816709 0.577050i \(-0.195796\pi\)
0.816709 + 0.577050i \(0.195796\pi\)
\(258\) 5.54831e11 0.485358
\(259\) 4.72759e11i 0.405640i
\(260\) 5.51128e12i 4.63858i
\(261\) −1.40431e11 −0.115947
\(262\) −3.43341e11 −0.278112
\(263\) 5.40085e11 0.429223 0.214612 0.976699i \(-0.431151\pi\)
0.214612 + 0.976699i \(0.431151\pi\)
\(264\) 1.40491e12 1.09554
\(265\) 1.97314e12 1.50983
\(266\) 6.21514e11i 0.466706i
\(267\) 1.02252e12i 0.753559i
\(268\) 1.00523e12i 0.727094i
\(269\) 1.39002e12i 0.986868i −0.869783 0.493434i \(-0.835741\pi\)
0.869783 0.493434i \(-0.164259\pi\)
\(270\) 6.10183e11i 0.425247i
\(271\) 5.54735e11 0.379524 0.189762 0.981830i \(-0.439228\pi\)
0.189762 + 0.981830i \(0.439228\pi\)
\(272\) 2.12130e12 1.42481
\(273\) 3.42550e11i 0.225897i
\(274\) 1.87664e12i 1.21515i
\(275\) 4.18360e11i 0.266003i
\(276\) 9.82787e10i 0.0613640i
\(277\) −1.21573e12 −0.745484 −0.372742 0.927935i \(-0.621582\pi\)
−0.372742 + 0.927935i \(0.621582\pi\)
\(278\) 2.96162e12i 1.78363i
\(279\) 1.68978e11i 0.0999560i
\(280\) 1.42373e12i 0.827251i
\(281\) 2.31227e12 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(282\) 3.83778e12 2.15196
\(283\) 2.17126e12i 1.19613i −0.801447 0.598065i \(-0.795936\pi\)
0.801447 0.598065i \(-0.204064\pi\)
\(284\) −6.60441e12 −3.57472
\(285\) −1.28266e12 −0.682164
\(286\) 3.79470e12i 1.98311i
\(287\) 2.12374e11 0.109067
\(288\) 1.55340e12i 0.784008i
\(289\) −1.47837e12 −0.733320
\(290\) 1.57650e12i 0.768608i
\(291\) 4.26401e11i 0.204340i
\(292\) 2.87457e12i 1.35412i
\(293\) 1.50545e12 0.697155 0.348578 0.937280i \(-0.386665\pi\)
0.348578 + 0.937280i \(0.386665\pi\)
\(294\) 2.22589e12i 1.01337i
\(295\) 1.34310e12 + 2.27038e12i 0.601170 + 1.01622i
\(296\) −1.03981e13 −4.57609
\(297\) 3.00171e11i 0.129893i
\(298\) 6.47784e12 2.75644
\(299\) −1.59368e11 −0.0666875
\(300\) −1.38356e12 −0.569365
\(301\) 2.76598e11i 0.111948i
\(302\) −4.87095e12 −1.93900
\(303\) 3.77736e11i 0.147902i
\(304\) −7.16855e12 −2.76098
\(305\) 2.08336e12i 0.789340i
\(306\) 8.64282e11i 0.322143i
\(307\) 3.98881e12 1.46269 0.731344 0.682009i \(-0.238894\pi\)
0.731344 + 0.682009i \(0.238894\pi\)
\(308\) 1.16660e12i 0.420891i
\(309\) 6.23515e9i 0.00221337i
\(310\) 1.89698e12 0.662603
\(311\) −8.53242e11 −0.293272 −0.146636 0.989191i \(-0.546845\pi\)
−0.146636 + 0.989191i \(0.546845\pi\)
\(312\) −7.53420e12 −2.54838
\(313\) 2.21559e12i 0.737510i 0.929527 + 0.368755i \(0.120216\pi\)
−0.929527 + 0.368755i \(0.879784\pi\)
\(314\) 4.40644e12 1.44358
\(315\) 3.04192e11 0.0980833
\(316\) −6.81048e12 −2.16143
\(317\) 8.88746e11 0.277639 0.138820 0.990318i \(-0.455669\pi\)
0.138820 + 0.990318i \(0.455669\pi\)
\(318\) 4.49292e12i 1.38164i
\(319\) 7.75540e11i 0.234774i
\(320\) −6.50770e12 −1.93944
\(321\) −1.27442e12 −0.373927
\(322\) 6.85745e10 0.0198099
\(323\) −1.81681e12 −0.516768
\(324\) −9.92695e11 −0.278030
\(325\) 2.24356e12i 0.618758i
\(326\) 1.11477e13i 3.02758i
\(327\) 7.55552e11i 0.202081i
\(328\) 4.67106e12i 1.23040i
\(329\) 1.91323e12i 0.496351i
\(330\) −3.36978e12 −0.861056
\(331\) 2.15439e12 0.542232 0.271116 0.962547i \(-0.412607\pi\)
0.271116 + 0.962547i \(0.412607\pi\)
\(332\) 3.97154e11i 0.0984621i
\(333\) 2.22164e12i 0.542565i
\(334\) 7.75079e12i 1.86472i
\(335\) 1.44754e12i 0.343088i
\(336\) 1.70007e12 0.396981
\(337\) 6.35856e12i 1.46288i 0.681905 + 0.731441i \(0.261152\pi\)
−0.681905 + 0.731441i \(0.738848\pi\)
\(338\) 1.20942e13i 2.74154i
\(339\) 4.97614e11i 0.111146i
\(340\) −6.93221e12 −1.52573
\(341\) 9.33192e11 0.202395
\(342\) 2.92068e12i 0.624244i
\(343\) −2.29281e12 −0.482945
\(344\) −6.08362e12 −1.26290
\(345\) 1.41522e11i 0.0289554i
\(346\) −1.77368e13 −3.57679
\(347\) 2.39510e12i 0.476076i 0.971256 + 0.238038i \(0.0765043\pi\)
−0.971256 + 0.238038i \(0.923496\pi\)
\(348\) 2.56479e12 0.502522
\(349\) 5.67456e12i 1.09599i 0.836483 + 0.547993i \(0.184608\pi\)
−0.836483 + 0.547993i \(0.815392\pi\)
\(350\) 9.65384e11i 0.183806i
\(351\) 1.60974e12i 0.302149i
\(352\) −8.57875e12 −1.58749
\(353\) 6.15338e12i 1.12264i 0.827599 + 0.561320i \(0.189706\pi\)
−0.827599 + 0.561320i \(0.810294\pi\)
\(354\) 5.16975e12 3.05829e12i 0.929937 0.550126i
\(355\) 9.51041e12 1.68678
\(356\) 1.86750e13i 3.26597i
\(357\) 4.30867e11 0.0743023
\(358\) 1.04837e13 1.78279
\(359\) −1.09396e11 −0.0183454 −0.00917271 0.999958i \(-0.502920\pi\)
−0.00917271 + 0.999958i \(0.502920\pi\)
\(360\) 6.69054e12i 1.10649i
\(361\) 8.49956e9 0.00138631
\(362\) 7.88948e12i 1.26913i
\(363\) 1.98120e12 0.314337
\(364\) 6.25621e12i 0.979049i
\(365\) 4.13940e12i 0.638959i
\(366\) −4.74389e12 −0.722320
\(367\) 3.95385e12i 0.593868i −0.954898 0.296934i \(-0.904036\pi\)
0.954898 0.296934i \(-0.0959641\pi\)
\(368\) 7.90938e11i 0.117193i
\(369\) 9.98011e11 0.145883
\(370\) 2.49405e13 3.59664
\(371\) 2.23984e12 0.318674
\(372\) 3.08616e12i 0.433215i
\(373\) 9.57607e12 1.32630 0.663152 0.748485i \(-0.269218\pi\)
0.663152 + 0.748485i \(0.269218\pi\)
\(374\) −4.77306e12 −0.652287
\(375\) −3.06294e12 −0.413030
\(376\) −4.20806e13 −5.59941
\(377\) 4.15903e12i 0.546117i
\(378\) 6.92659e11i 0.0897553i
\(379\) 1.54106e13 1.97071 0.985356 0.170509i \(-0.0545412\pi\)
0.985356 + 0.170509i \(0.0545412\pi\)
\(380\) 2.34261e13 2.95653
\(381\) −2.37441e12 −0.295754
\(382\) −1.08122e13 −1.32922
\(383\) −3.03341e12 −0.368076 −0.184038 0.982919i \(-0.558917\pi\)
−0.184038 + 0.982919i \(0.558917\pi\)
\(384\) 3.48030e12i 0.416831i
\(385\) 1.67992e12i 0.198603i
\(386\) 2.03943e13i 2.37998i
\(387\) 1.29982e12i 0.149736i
\(388\) 7.78764e12i 0.885619i
\(389\) −1.30546e13 −1.46560 −0.732799 0.680446i \(-0.761786\pi\)
−0.732799 + 0.680446i \(0.761786\pi\)
\(390\) 1.80713e13 2.00293
\(391\) 2.00456e11i 0.0219349i
\(392\) 2.44065e13i 2.63679i
\(393\) 8.04354e11i 0.0857994i
\(394\) 1.79451e12i 0.189001i
\(395\) 9.80715e12 1.01990
\(396\) 5.48223e12i 0.562965i
\(397\) 1.07348e13i 1.08853i −0.838914 0.544264i \(-0.816809\pi\)
0.838914 0.544264i \(-0.183191\pi\)
\(398\) 2.35075e13i 2.35391i
\(399\) −1.45604e12 −0.143982
\(400\) 1.11347e13 1.08738
\(401\) 1.62822e13i 1.57033i 0.619286 + 0.785166i \(0.287422\pi\)
−0.619286 + 0.785166i \(0.712578\pi\)
\(402\) −3.29611e12 −0.313957
\(403\) −5.00448e12 −0.470797
\(404\) 6.89884e12i 0.641016i
\(405\) 1.42949e12 0.131192
\(406\) 1.78959e12i 0.162227i
\(407\) 1.22691e13 1.09861
\(408\) 9.47669e12i 0.838216i
\(409\) 6.46721e12i 0.565068i 0.959257 + 0.282534i \(0.0911750\pi\)
−0.959257 + 0.282534i \(0.908825\pi\)
\(410\) 1.12038e13i 0.967047i
\(411\) 4.39645e12 0.374881
\(412\) 1.13877e11i 0.00959288i
\(413\) 1.52464e12 + 2.57726e12i 0.126887 + 0.214490i
\(414\) 3.22252e11 0.0264969
\(415\) 5.71906e11i 0.0464605i
\(416\) 4.60057e13 3.69271
\(417\) −6.93825e12 −0.550262
\(418\) 1.61297e13 1.26399
\(419\) 6.56873e12i 0.508641i −0.967120 0.254320i \(-0.918148\pi\)
0.967120 0.254320i \(-0.0818518\pi\)
\(420\) −5.55566e12 −0.425098
\(421\) 5.80550e12i 0.438964i −0.975617 0.219482i \(-0.929563\pi\)
0.975617 0.219482i \(-0.0704367\pi\)
\(422\) −3.59691e13 −2.68762
\(423\) 8.99086e12i 0.663895i
\(424\) 4.92641e13i 3.59502i
\(425\) 2.82200e12 0.203523
\(426\) 2.16556e13i 1.54356i
\(427\) 2.36495e12i 0.166603i
\(428\) 2.32755e13 1.62062
\(429\) 8.88992e12 0.611803
\(430\) 1.45920e13 0.992593
\(431\) 1.22660e13i 0.824737i 0.911017 + 0.412369i \(0.135298\pi\)
−0.911017 + 0.412369i \(0.864702\pi\)
\(432\) 7.98913e12 0.530983
\(433\) −4.42984e12 −0.291037 −0.145518 0.989356i \(-0.546485\pi\)
−0.145518 + 0.989356i \(0.546485\pi\)
\(434\) 2.15338e12 0.139853
\(435\) −3.69331e12 −0.237121
\(436\) 1.37991e13i 0.875830i
\(437\) 6.77406e11i 0.0425052i
\(438\) −9.42560e12 −0.584707
\(439\) −9.48510e12 −0.581727 −0.290864 0.956765i \(-0.593943\pi\)
−0.290864 + 0.956765i \(0.593943\pi\)
\(440\) 3.69490e13 2.24047
\(441\) −5.21465e12 −0.312631
\(442\) 2.55967e13 1.51731
\(443\) 1.92750e13i 1.12973i −0.825182 0.564867i \(-0.808928\pi\)
0.825182 0.564867i \(-0.191072\pi\)
\(444\) 4.05752e13i 2.35151i
\(445\) 2.68922e13i 1.54109i
\(446\) 3.45234e13i 1.95632i
\(447\) 1.51758e13i 0.850382i
\(448\) −7.38731e12 −0.409352
\(449\) −1.18642e13 −0.650139 −0.325069 0.945690i \(-0.605388\pi\)
−0.325069 + 0.945690i \(0.605388\pi\)
\(450\) 4.53663e12i 0.245850i
\(451\) 5.51158e12i 0.295388i
\(452\) 9.08824e12i 0.481712i
\(453\) 1.14113e13i 0.598196i
\(454\) −2.53162e11 −0.0131256
\(455\) 9.00900e12i 0.461976i
\(456\) 3.20248e13i 1.62428i
\(457\) 1.68398e12i 0.0844804i −0.999107 0.0422402i \(-0.986551\pi\)
0.999107 0.0422402i \(-0.0134495\pi\)
\(458\) 4.82157e13 2.39255
\(459\) 2.02477e12 0.0993832
\(460\) 2.58471e12i 0.125494i
\(461\) −3.27427e13 −1.57257 −0.786286 0.617863i \(-0.787999\pi\)
−0.786286 + 0.617863i \(0.787999\pi\)
\(462\) −3.82525e12 −0.181740
\(463\) 2.15339e13i 1.01208i 0.862509 + 0.506042i \(0.168892\pi\)
−0.862509 + 0.506042i \(0.831108\pi\)
\(464\) −2.06412e13 −0.959720
\(465\) 4.44409e12i 0.204418i
\(466\) −2.16837e13 −0.986740
\(467\) 6.68552e11i 0.0300989i −0.999887 0.0150495i \(-0.995209\pi\)
0.999887 0.0150495i \(-0.00479057\pi\)
\(468\) 2.93998e13i 1.30953i
\(469\) 1.64319e12i 0.0724143i
\(470\) 1.00933e14 4.40093
\(471\) 1.03231e13i 0.445353i
\(472\) −5.66854e13 + 3.35336e13i −2.41970 + 1.43143i
\(473\) 7.17832e12 0.303192
\(474\) 2.23313e13i 0.933303i
\(475\) −9.53645e12 −0.394383
\(476\) −7.86921e12 −0.322030
\(477\) 1.05257e13 0.426244
\(478\) 9.18855e13i 3.68220i
\(479\) 1.30537e13 0.517673 0.258836 0.965921i \(-0.416661\pi\)
0.258836 + 0.965921i \(0.416661\pi\)
\(480\) 4.08541e13i 1.60335i
\(481\) −6.57964e13 −2.55550
\(482\) 3.97537e13i 1.52807i
\(483\) 1.60651e11i 0.00611150i
\(484\) −3.61840e13 −1.36235
\(485\) 1.12143e13i 0.417890i
\(486\) 3.25501e12i 0.120053i
\(487\) 2.60567e13 0.951206 0.475603 0.879660i \(-0.342230\pi\)
0.475603 + 0.879660i \(0.342230\pi\)
\(488\) 5.20159e13 1.87948
\(489\) −2.61159e13 −0.934031
\(490\) 5.85406e13i 2.07242i
\(491\) 3.68761e13 1.29222 0.646112 0.763243i \(-0.276394\pi\)
0.646112 + 0.763243i \(0.276394\pi\)
\(492\) −1.82273e13 −0.632262
\(493\) −5.23132e12 −0.179629
\(494\) −8.64995e13 −2.94021
\(495\) 7.89445e12i 0.265642i
\(496\) 2.48371e13i 0.827357i
\(497\) 1.07959e13 0.356022
\(498\) −1.30226e12 −0.0425157
\(499\) −6.15494e13 −1.98939 −0.994697 0.102849i \(-0.967204\pi\)
−0.994697 + 0.102849i \(0.967204\pi\)
\(500\) 5.59404e13 1.79009
\(501\) 1.81580e13 0.575279
\(502\) 9.13984e13i 2.86695i
\(503\) 2.81370e13i 0.873852i −0.899497 0.436926i \(-0.856067\pi\)
0.899497 0.436926i \(-0.143933\pi\)
\(504\) 7.59487e12i 0.233543i
\(505\) 9.93439e12i 0.302471i
\(506\) 1.77966e12i 0.0536518i
\(507\) −2.83335e13 −0.845785
\(508\) 4.33654e13 1.28181
\(509\) 6.37637e13i 1.86631i −0.359469 0.933157i \(-0.617042\pi\)
0.359469 0.933157i \(-0.382958\pi\)
\(510\) 2.27305e13i 0.658806i
\(511\) 4.69891e12i 0.134863i
\(512\) 4.45937e13i 1.26743i
\(513\) −6.84236e12 −0.192583
\(514\) 1.09670e14i 3.05683i
\(515\) 1.63983e11i 0.00452651i
\(516\) 2.37394e13i 0.648965i
\(517\) 4.96527e13 1.34428
\(518\) 2.83116e13 0.759129
\(519\) 4.15523e13i 1.10346i
\(520\) −1.98148e14 −5.21163
\(521\) 7.61660e12 0.198414 0.0992070 0.995067i \(-0.468369\pi\)
0.0992070 + 0.995067i \(0.468369\pi\)
\(522\) 8.40984e12i 0.216988i
\(523\) 3.85918e13 0.986248 0.493124 0.869959i \(-0.335855\pi\)
0.493124 + 0.869959i \(0.335855\pi\)
\(524\) 1.46904e13i 0.371859i
\(525\) 2.26163e12 0.0567054
\(526\) 3.23434e13i 0.803263i
\(527\) 6.29475e12i 0.154855i
\(528\) 4.41205e13i 1.07515i
\(529\) 4.13518e13 0.998196
\(530\) 1.18163e14i 2.82555i
\(531\) 7.16473e12 + 1.21113e13i 0.169718 + 0.286892i
\(532\) 2.65926e13 0.624025
\(533\) 2.95572e13i 0.687113i
\(534\) 6.12348e13 1.41024
\(535\) −3.35169e13 −0.764708
\(536\) 3.61412e13 0.816918
\(537\) 2.45605e13i 0.550004i
\(538\) −8.32425e13 −1.84686
\(539\) 2.87983e13i 0.633027i
\(540\) −2.61077e13 −0.568591
\(541\) 4.17389e13i 0.900646i 0.892866 + 0.450323i \(0.148691\pi\)
−0.892866 + 0.450323i \(0.851309\pi\)
\(542\) 3.32208e13i 0.710254i
\(543\) 1.84829e13 0.391535
\(544\) 5.78670e13i 1.21461i
\(545\) 1.98709e13i 0.413271i
\(546\) 2.05139e13 0.422751
\(547\) −5.05567e13 −1.03239 −0.516193 0.856472i \(-0.672651\pi\)
−0.516193 + 0.856472i \(0.672651\pi\)
\(548\) −8.02953e13 −1.62475
\(549\) 1.11136e13i 0.222841i
\(550\) −2.50539e13 −0.497807
\(551\) 1.76783e13 0.348083
\(552\) −3.53343e12 −0.0689448
\(553\) 1.11327e13 0.215266
\(554\) 7.28051e13i 1.39512i
\(555\) 5.84287e13i 1.10959i
\(556\) 1.26718e14 2.38486
\(557\) −1.34896e12 −0.0251607 −0.0125803 0.999921i \(-0.504005\pi\)
−0.0125803 + 0.999921i \(0.504005\pi\)
\(558\) 1.01194e13 0.187061
\(559\) −3.84956e13 −0.705264
\(560\) 4.47115e13 0.811855
\(561\) 1.11820e13i 0.201235i
\(562\) 1.38472e14i 2.46991i
\(563\) 8.53764e11i 0.0150937i −0.999972 0.00754685i \(-0.997598\pi\)
0.999972 0.00754685i \(-0.00240226\pi\)
\(564\) 1.64206e14i 2.87736i
\(565\) 1.30872e13i 0.227302i
\(566\) −1.30028e14 −2.23848
\(567\) 1.62271e12 0.0276901
\(568\) 2.37450e14i 4.01634i
\(569\) 3.89773e13i 0.653507i 0.945110 + 0.326754i \(0.105955\pi\)
−0.945110 + 0.326754i \(0.894045\pi\)
\(570\) 7.68135e13i 1.27662i
\(571\) 2.89747e13i 0.477351i −0.971099 0.238676i \(-0.923287\pi\)
0.971099 0.238676i \(-0.0767133\pi\)
\(572\) −1.62363e14 −2.65159
\(573\) 2.53299e13i 0.410072i
\(574\) 1.27182e13i 0.204111i
\(575\) 1.05220e12i 0.0167401i
\(576\) −3.47152e13 −0.547530
\(577\) 3.30742e13 0.517142 0.258571 0.965992i \(-0.416748\pi\)
0.258571 + 0.965992i \(0.416748\pi\)
\(578\) 8.85335e13i 1.37236i
\(579\) 4.77783e13 0.734240
\(580\) 6.74534e13 1.02769
\(581\) 6.49208e11i 0.00980625i
\(582\) 2.55354e13 0.382408
\(583\) 5.81288e13i 0.863075i
\(584\) 1.03350e14 1.52141
\(585\) 4.23360e13i 0.617918i
\(586\) 9.01555e13i 1.30468i
\(587\) 3.07500e13i 0.441219i −0.975362 0.220609i \(-0.929195\pi\)
0.975362 0.220609i \(-0.0708046\pi\)
\(588\) 9.52386e13 1.35496
\(589\) 2.12720e13i 0.300076i
\(590\) 1.35964e14 8.04325e13i 1.90179 1.12505i
\(591\) 4.20403e12 0.0583081
\(592\) 3.26546e14i 4.49092i
\(593\) 6.88754e13 0.939271 0.469635 0.882860i \(-0.344385\pi\)
0.469635 + 0.882860i \(0.344385\pi\)
\(594\) −1.79760e13 −0.243087
\(595\) 1.13317e13 0.151954
\(596\) 2.77166e14i 3.68560i
\(597\) −5.50715e13 −0.726198
\(598\) 9.54388e12i 0.124801i
\(599\) −9.66992e13 −1.25398 −0.626988 0.779029i \(-0.715712\pi\)
−0.626988 + 0.779029i \(0.715712\pi\)
\(600\) 4.97433e13i 0.639703i
\(601\) 9.80497e13i 1.25047i 0.780436 + 0.625236i \(0.214997\pi\)
−0.780436 + 0.625236i \(0.785003\pi\)
\(602\) 1.65643e13 0.209503
\(603\) 7.72187e12i 0.0968580i
\(604\) 2.08412e14i 2.59261i
\(605\) 5.21053e13 0.642843
\(606\) −2.26211e13 −0.276790
\(607\) −1.27930e14 −1.55248 −0.776242 0.630435i \(-0.782877\pi\)
−0.776242 + 0.630435i \(0.782877\pi\)
\(608\) 1.95551e14i 2.35365i
\(609\) −4.19252e12 −0.0500483
\(610\) −1.24764e14 −1.47720
\(611\) −2.66275e14 −3.12697
\(612\) −3.69798e13 −0.430732
\(613\) 1.02278e14i 1.18162i 0.806810 + 0.590811i \(0.201192\pi\)
−0.806810 + 0.590811i \(0.798808\pi\)
\(614\) 2.38873e14i 2.73732i
\(615\) 2.62475e13 0.298341
\(616\) 4.19432e13 0.472888
\(617\) −1.44309e14 −1.61387 −0.806936 0.590639i \(-0.798876\pi\)
−0.806936 + 0.590639i \(0.798876\pi\)
\(618\) 3.73398e11 0.00414218
\(619\) −6.82218e13 −0.750706 −0.375353 0.926882i \(-0.622479\pi\)
−0.375353 + 0.926882i \(0.622479\pi\)
\(620\) 8.11653e13i 0.885956i
\(621\) 7.54948e11i 0.00817446i
\(622\) 5.10971e13i 0.548839i
\(623\) 3.05271e13i 0.325271i
\(624\) 2.36607e14i 2.50095i
\(625\) −1.18140e14 −1.23879
\(626\) 1.32683e14 1.38020
\(627\) 3.77874e13i 0.389950i
\(628\) 1.88537e14i 1.93019i
\(629\) 8.27602e13i 0.840559i
\(630\) 1.82168e13i 0.183556i
\(631\) −5.13267e13 −0.513093 −0.256547 0.966532i \(-0.582585\pi\)
−0.256547 + 0.966532i \(0.582585\pi\)
\(632\) 2.44859e14i 2.42845i
\(633\) 8.42656e13i 0.829148i
\(634\) 5.32233e13i 0.519584i
\(635\) −6.24466e13 −0.604840
\(636\) −1.92237e14 −1.84736
\(637\) 1.54438e14i 1.47251i
\(638\) 4.64439e13 0.439365
\(639\) 5.07332e13 0.476198
\(640\) 9.15312e13i 0.852451i
\(641\) −1.34940e14 −1.24696 −0.623478 0.781841i \(-0.714281\pi\)
−0.623478 + 0.781841i \(0.714281\pi\)
\(642\) 7.63196e13i 0.699779i
\(643\) 1.94621e14 1.77066 0.885328 0.464966i \(-0.153934\pi\)
0.885328 + 0.464966i \(0.153934\pi\)
\(644\) 2.93408e12i 0.0264876i
\(645\) 3.41849e13i 0.306222i
\(646\) 1.08801e14i 0.967098i
\(647\) 4.61702e13 0.407230 0.203615 0.979051i \(-0.434731\pi\)
0.203615 + 0.979051i \(0.434731\pi\)
\(648\) 3.56906e13i 0.312377i
\(649\) 6.68855e13 3.95677e13i 0.580910 0.343651i
\(650\) 1.34358e14 1.15797
\(651\) 5.04478e12i 0.0431457i
\(652\) 4.76972e14 4.04814
\(653\) −1.65374e14 −1.39284 −0.696420 0.717635i \(-0.745225\pi\)
−0.696420 + 0.717635i \(0.745225\pi\)
\(654\) 4.52469e13 0.378181
\(655\) 2.11544e13i 0.175466i
\(656\) 1.46692e14 1.20750
\(657\) 2.20816e13i 0.180386i
\(658\) 1.14576e14 0.928887
\(659\) 1.51824e14i 1.22156i −0.791801 0.610779i \(-0.790856\pi\)
0.791801 0.610779i \(-0.209144\pi\)
\(660\) 1.44182e14i 1.15130i
\(661\) −1.09780e13 −0.0869994 −0.0434997 0.999053i \(-0.513851\pi\)
−0.0434997 + 0.999053i \(0.513851\pi\)
\(662\) 1.29018e14i 1.01475i
\(663\) 5.99660e13i 0.468099i
\(664\) 1.42790e13 0.110626
\(665\) −3.82935e13 −0.294454
\(666\) 1.33045e14 1.01538
\(667\) 1.95053e12i 0.0147748i
\(668\) −3.31631e14 −2.49329
\(669\) −8.08789e13 −0.603538
\(670\) −8.66870e13 −0.642067
\(671\) −6.13758e13 −0.451216
\(672\) 4.63762e13i 0.338414i
\(673\) 1.83915e13i 0.133211i −0.997779 0.0666057i \(-0.978783\pi\)
0.997779 0.0666057i \(-0.0212170\pi\)
\(674\) 3.80788e14 2.73769
\(675\) 1.06281e13 0.0758465
\(676\) 5.17473e14 3.66567
\(677\) −8.09994e13 −0.569559 −0.284779 0.958593i \(-0.591920\pi\)
−0.284779 + 0.958593i \(0.591920\pi\)
\(678\) 2.98000e13 0.208002
\(679\) 1.27301e13i 0.0882026i
\(680\) 2.49235e14i 1.71421i
\(681\) 5.93088e11i 0.00404934i
\(682\) 5.58850e13i 0.378768i
\(683\) 2.28666e14i 1.53850i 0.638947 + 0.769251i \(0.279370\pi\)
−0.638947 + 0.769251i \(0.720630\pi\)
\(684\) 1.24966e14 0.834667
\(685\) 1.15626e14 0.766659
\(686\) 1.37307e14i 0.903800i
\(687\) 1.12956e14i 0.738118i
\(688\) 1.91053e14i 1.23940i
\(689\) 3.11730e14i 2.00763i
\(690\) 8.47518e12 0.0541880
\(691\) 1.24377e14i 0.789497i 0.918789 + 0.394749i \(0.129168\pi\)
−0.918789 + 0.394749i \(0.870832\pi\)
\(692\) 7.58897e14i 4.78247i
\(693\) 8.96151e12i 0.0560680i
\(694\) 1.43433e14 0.890946
\(695\) −1.82475e14 −1.12533
\(696\) 9.22123e13i 0.564602i
\(697\) 3.71778e13 0.226006
\(698\) 3.39826e14 2.05107
\(699\) 5.07988e13i 0.304416i
\(700\) −4.13056e13 −0.245764
\(701\) 2.12939e14i 1.25796i −0.777423 0.628978i \(-0.783473\pi\)
0.777423 0.628978i \(-0.216527\pi\)
\(702\) 9.64010e13 0.565452
\(703\) 2.79673e14i 1.62882i
\(704\) 1.91717e14i 1.10866i
\(705\) 2.36458e14i 1.35772i
\(706\) 3.68501e14 2.10095
\(707\) 1.12772e13i 0.0638415i
\(708\) −1.30854e14 2.21197e14i −0.735565 1.24340i
\(709\) −1.03181e14 −0.575930 −0.287965 0.957641i \(-0.592979\pi\)
−0.287965 + 0.957641i \(0.592979\pi\)
\(710\) 5.69540e14i 3.15669i
\(711\) 5.23161e13 0.287930
\(712\) −6.71428e14 −3.66944
\(713\) −2.34703e12 −0.0127371
\(714\) 2.58028e13i 0.139052i
\(715\) 2.33803e14 1.25118
\(716\) 4.48565e14i 2.38375i
\(717\) −2.15262e14 −1.13598
\(718\) 6.55126e12i 0.0343323i
\(719\) 2.82697e14i 1.47122i −0.677408 0.735608i \(-0.736897\pi\)
0.677408 0.735608i \(-0.263103\pi\)
\(720\) 2.10113e14 1.08590
\(721\) 1.86148e11i 0.000955395i
\(722\) 5.09004e11i 0.00259439i
\(723\) 9.31319e13 0.471419
\(724\) −3.37565e14 −1.69693
\(725\) −2.74593e13 −0.137088
\(726\) 1.18646e14i 0.588262i
\(727\) −3.94443e14 −1.94228 −0.971140 0.238510i \(-0.923341\pi\)
−0.971140 + 0.238510i \(0.923341\pi\)
\(728\) −2.24931e14 −1.10000
\(729\) 7.62560e12 0.0370370
\(730\) −2.47892e14 −1.19577
\(731\) 4.84206e13i 0.231976i
\(732\) 2.02976e14i 0.965803i
\(733\) −1.37662e14 −0.650572 −0.325286 0.945616i \(-0.605461\pi\)
−0.325286 + 0.945616i \(0.605461\pi\)
\(734\) −2.36780e14 −1.11138
\(735\) −1.37144e14 −0.639354
\(736\) 2.15760e13 0.0999039
\(737\) −4.26445e13 −0.196122
\(738\) 5.97668e13i 0.273010i
\(739\) 1.66109e14i 0.753654i 0.926284 + 0.376827i \(0.122985\pi\)
−0.926284 + 0.376827i \(0.877015\pi\)
\(740\) 1.06712e15i 4.80901i
\(741\) 2.02644e14i 0.907076i
\(742\) 1.34135e14i 0.596378i
\(743\) 2.91675e14 1.28812 0.644058 0.764976i \(-0.277249\pi\)
0.644058 + 0.764976i \(0.277249\pi\)
\(744\) −1.10957e14 −0.486733
\(745\) 3.99121e14i 1.73909i
\(746\) 5.73471e14i 2.48209i
\(747\) 3.05082e12i 0.0131164i
\(748\) 2.04223e14i 0.872162i
\(749\) −3.80473e13 −0.161404
\(750\) 1.83427e14i 0.772958i
\(751\) 2.42985e13i 0.101714i −0.998706 0.0508569i \(-0.983805\pi\)
0.998706 0.0508569i \(-0.0161952\pi\)
\(752\) 1.32152e15i 5.49520i
\(753\) 2.14121e14 0.884474
\(754\) −2.49067e14 −1.02202
\(755\) 3.00115e14i 1.22336i
\(756\) −2.96366e13 −0.120010
\(757\) 3.15140e14 1.26772 0.633861 0.773447i \(-0.281469\pi\)
0.633861 + 0.773447i \(0.281469\pi\)
\(758\) 9.22877e14i 3.68806i
\(759\) 4.16925e12 0.0165520
\(760\) 8.42245e14i 3.32178i
\(761\) −2.69468e14 −1.05581 −0.527903 0.849305i \(-0.677022\pi\)
−0.527903 + 0.849305i \(0.677022\pi\)
\(762\) 1.42194e14i 0.553485i
\(763\) 2.25568e13i 0.0872276i
\(764\) 4.62617e14i 1.77727i
\(765\) 5.32512e13 0.203246
\(766\) 1.81658e14i 0.688829i
\(767\) −3.58690e14 + 2.12192e14i −1.35127 + 0.799377i
\(768\) −4.49604e13 −0.168277
\(769\) 4.26168e14i 1.58471i 0.610063 + 0.792353i \(0.291144\pi\)
−0.610063 + 0.792353i \(0.708856\pi\)
\(770\) −1.00604e14 −0.371672
\(771\) 2.56926e14 0.943054
\(772\) −8.72607e14 −3.18223
\(773\) 4.02297e14i 1.45764i −0.684707 0.728818i \(-0.740070\pi\)
0.684707 0.728818i \(-0.259930\pi\)
\(774\) 7.78406e13 0.280222
\(775\) 3.30412e13i 0.118181i
\(776\) −2.79991e14 −0.995027
\(777\) 6.63262e13i 0.234196i
\(778\) 7.81785e14i 2.74277i
\(779\) −1.25636e14 −0.437951