Properties

Label 177.11.c.a.58.20
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 58.20
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.81

$q$-expansion

\(f(q)\) \(=\) \(q-44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} -6245.94i q^{6} -20369.6 q^{7} -2938.10i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} -6245.94i q^{6} -20369.6 q^{7} -2938.10i q^{8} +19683.0 q^{9} +17992.1i q^{10} +217841. i q^{11} -134404. q^{12} +504544. i q^{13} +906847. i q^{14} -56699.1 q^{15} -1.11180e6 q^{16} +782310. q^{17} -876281. i q^{18} +1.77007e6 q^{19} +387167. q^{20} -2.85777e6 q^{21} +9.69824e6 q^{22} -1.01853e7i q^{23} -412204. i q^{24} -9.60230e6 q^{25} +2.24622e7 q^{26} +2.76145e6 q^{27} +1.95141e7 q^{28} +3.48342e6 q^{29} +2.52423e6i q^{30} -3.18716e7i q^{31} +4.64884e7i q^{32} +3.05623e7i q^{33} -3.48282e7i q^{34} +8.23213e6 q^{35} -1.88564e7 q^{36} +6.84669e7i q^{37} -7.88030e7i q^{38} +7.07856e7i q^{39} +1.18740e6i q^{40} +1.22130e8 q^{41} +1.27227e8i q^{42} +3.24896e7i q^{43} -2.08693e8i q^{44} -7.95466e6 q^{45} -4.53445e8 q^{46} -4.40737e8i q^{47} -1.55981e8 q^{48} +1.32444e8 q^{49} +4.27491e8i q^{50} +1.09755e8 q^{51} -4.83355e8i q^{52} +7.76026e8 q^{53} -1.22939e8i q^{54} -8.80382e7i q^{55} +5.98478e7i q^{56} +2.48334e8 q^{57} -1.55081e8i q^{58} +(-5.68858e8 + 4.33033e8i) q^{59} +5.43180e7 q^{60} -1.05370e9i q^{61} -1.41891e9 q^{62} -4.00934e8 q^{63} +9.31167e8 q^{64} -2.03906e8i q^{65} +1.36063e9 q^{66} +7.80318e8i q^{67} -7.49456e8 q^{68} -1.42895e9i q^{69} -3.66492e8i q^{70} +9.51934e8 q^{71} -5.78306e7i q^{72} -1.89948e9i q^{73} +3.04812e9 q^{74} -1.34716e9 q^{75} -1.69573e9 q^{76} -4.43734e9i q^{77} +3.15135e9 q^{78} -1.34494e9 q^{79} +4.49321e8 q^{80} +3.87420e8 q^{81} -5.43720e9i q^{82} -8.04031e8i q^{83} +2.73776e9 q^{84} -3.16162e8 q^{85} +1.44643e9 q^{86} +4.88711e8 q^{87} +6.40040e8 q^{88} -8.55267e9i q^{89} +3.54139e8i q^{90} -1.02773e10i q^{91} +9.75752e9i q^{92} -4.47146e9i q^{93} -1.96215e10 q^{94} -7.15354e8 q^{95} +6.52214e9i q^{96} -1.17842e10i q^{97} -5.89638e9i q^{98} +4.28777e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 44.5197i 1.39124i −0.718409 0.695620i \(-0.755130\pi\)
0.718409 0.695620i \(-0.244870\pi\)
\(3\) 140.296 0.577350
\(4\) −958.005 −0.935551
\(5\) −404.139 −0.129324 −0.0646622 0.997907i \(-0.520597\pi\)
−0.0646622 + 0.997907i \(0.520597\pi\)
\(6\) 6245.94i 0.803233i
\(7\) −20369.6 −1.21197 −0.605985 0.795476i \(-0.707221\pi\)
−0.605985 + 0.795476i \(0.707221\pi\)
\(8\) 2938.10i 0.0896637i
\(9\) 19683.0 0.333333
\(10\) 17992.1i 0.179921i
\(11\) 217841.i 1.35262i 0.736615 + 0.676312i \(0.236423\pi\)
−0.736615 + 0.676312i \(0.763577\pi\)
\(12\) −134404. −0.540141
\(13\) 504544.i 1.35888i 0.733729 + 0.679442i \(0.237778\pi\)
−0.733729 + 0.679442i \(0.762222\pi\)
\(14\) 906847.i 1.68614i
\(15\) −56699.1 −0.0746655
\(16\) −1.11180e6 −1.06030
\(17\) 782310. 0.550978 0.275489 0.961304i \(-0.411160\pi\)
0.275489 + 0.961304i \(0.411160\pi\)
\(18\) 876281.i 0.463747i
\(19\) 1.77007e6 0.714862 0.357431 0.933940i \(-0.383653\pi\)
0.357431 + 0.933940i \(0.383653\pi\)
\(20\) 387167. 0.120990
\(21\) −2.85777e6 −0.699731
\(22\) 9.69824e6 1.88183
\(23\) 1.01853e7i 1.58246i −0.611518 0.791230i \(-0.709441\pi\)
0.611518 0.791230i \(-0.290559\pi\)
\(24\) 412204.i 0.0517674i
\(25\) −9.60230e6 −0.983275
\(26\) 2.24622e7 1.89053
\(27\) 2.76145e6 0.192450
\(28\) 1.95141e7 1.13386
\(29\) 3.48342e6 0.169831 0.0849154 0.996388i \(-0.472938\pi\)
0.0849154 + 0.996388i \(0.472938\pi\)
\(30\) 2.52423e6i 0.103878i
\(31\) 3.18716e7i 1.11326i −0.830762 0.556628i \(-0.812095\pi\)
0.830762 0.556628i \(-0.187905\pi\)
\(32\) 4.64884e7i 1.38546i
\(33\) 3.05623e7i 0.780938i
\(34\) 3.48282e7i 0.766543i
\(35\) 8.23213e6 0.156737
\(36\) −1.88564e7 −0.311850
\(37\) 6.84669e7i 0.987351i 0.869646 + 0.493676i \(0.164347\pi\)
−0.869646 + 0.493676i \(0.835653\pi\)
\(38\) 7.88030e7i 0.994545i
\(39\) 7.07856e7i 0.784552i
\(40\) 1.18740e6i 0.0115957i
\(41\) 1.22130e8 1.05415 0.527077 0.849818i \(-0.323288\pi\)
0.527077 + 0.849818i \(0.323288\pi\)
\(42\) 1.27227e8i 0.973494i
\(43\) 3.24896e7i 0.221005i 0.993876 + 0.110502i \(0.0352460\pi\)
−0.993876 + 0.110502i \(0.964754\pi\)
\(44\) 2.08693e8i 1.26545i
\(45\) −7.95466e6 −0.0431081
\(46\) −4.53445e8 −2.20158
\(47\) 4.40737e8i 1.92172i −0.277034 0.960860i \(-0.589351\pi\)
0.277034 0.960860i \(-0.410649\pi\)
\(48\) −1.55981e8 −0.612162
\(49\) 1.32444e8 0.468870
\(50\) 4.27491e8i 1.36797i
\(51\) 1.09755e8 0.318107
\(52\) 4.83355e8i 1.27131i
\(53\) 7.76026e8 1.85565 0.927827 0.373011i \(-0.121675\pi\)
0.927827 + 0.373011i \(0.121675\pi\)
\(54\) 1.22939e8i 0.267744i
\(55\) 8.80382e7i 0.174927i
\(56\) 5.98478e7i 0.108670i
\(57\) 2.48334e8 0.412726
\(58\) 1.55081e8i 0.236276i
\(59\) −5.68858e8 + 4.33033e8i −0.795689 + 0.605705i
\(60\) 5.43180e7 0.0698534
\(61\) 1.05370e9i 1.24758i −0.781593 0.623788i \(-0.785593\pi\)
0.781593 0.623788i \(-0.214407\pi\)
\(62\) −1.41891e9 −1.54881
\(63\) −4.00934e8 −0.403990
\(64\) 9.31167e8 0.867217
\(65\) 2.03906e8i 0.175737i
\(66\) 1.36063e9 1.08647
\(67\) 7.80318e8i 0.577960i 0.957335 + 0.288980i \(0.0933161\pi\)
−0.957335 + 0.288980i \(0.906684\pi\)
\(68\) −7.49456e8 −0.515468
\(69\) 1.42895e9i 0.913634i
\(70\) 3.66492e8i 0.218059i
\(71\) 9.51934e8 0.527612 0.263806 0.964576i \(-0.415022\pi\)
0.263806 + 0.964576i \(0.415022\pi\)
\(72\) 5.78306e7i 0.0298879i
\(73\) 1.89948e9i 0.916266i −0.888884 0.458133i \(-0.848518\pi\)
0.888884 0.458133i \(-0.151482\pi\)
\(74\) 3.04812e9 1.37364
\(75\) −1.34716e9 −0.567694
\(76\) −1.69573e9 −0.668790
\(77\) 4.43734e9i 1.63934i
\(78\) 3.15135e9 1.09150
\(79\) −1.34494e9 −0.437085 −0.218542 0.975827i \(-0.570130\pi\)
−0.218542 + 0.975827i \(0.570130\pi\)
\(80\) 4.49321e8 0.137122
\(81\) 3.87420e8 0.111111
\(82\) 5.43720e9i 1.46658i
\(83\) 8.04031e8i 0.204119i −0.994778 0.102059i \(-0.967457\pi\)
0.994778 0.102059i \(-0.0325431\pi\)
\(84\) 2.73776e9 0.654634
\(85\) −3.16162e8 −0.0712549
\(86\) 1.44643e9 0.307471
\(87\) 4.88711e8 0.0980519
\(88\) 6.40040e8 0.121281
\(89\) 8.55267e9i 1.53162i −0.643065 0.765811i \(-0.722338\pi\)
0.643065 0.765811i \(-0.277662\pi\)
\(90\) 3.54139e8i 0.0599738i
\(91\) 1.02773e10i 1.64693i
\(92\) 9.75752e9i 1.48047i
\(93\) 4.47146e9i 0.642739i
\(94\) −1.96215e10 −2.67358
\(95\) −7.15354e8 −0.0924491
\(96\) 6.52214e9i 0.799897i
\(97\) 1.17842e10i 1.37227i −0.727474 0.686135i \(-0.759306\pi\)
0.727474 0.686135i \(-0.240694\pi\)
\(98\) 5.89638e9i 0.652311i
\(99\) 4.28777e9i 0.450875i
\(100\) 9.19904e9 0.919904
\(101\) 1.28240e10i 1.22016i 0.792339 + 0.610082i \(0.208863\pi\)
−0.792339 + 0.610082i \(0.791137\pi\)
\(102\) 4.88626e9i 0.442564i
\(103\) 1.49310e10i 1.28796i 0.765040 + 0.643982i \(0.222719\pi\)
−0.765040 + 0.643982i \(0.777281\pi\)
\(104\) 1.48240e9 0.121843
\(105\) 1.15494e9 0.0904923
\(106\) 3.45485e10i 2.58166i
\(107\) 2.44078e10 1.74025 0.870123 0.492835i \(-0.164039\pi\)
0.870123 + 0.492835i \(0.164039\pi\)
\(108\) −2.64548e9 −0.180047
\(109\) 5.84380e9i 0.379807i 0.981803 + 0.189904i \(0.0608175\pi\)
−0.981803 + 0.189904i \(0.939182\pi\)
\(110\) −3.91943e9 −0.243366
\(111\) 9.60563e9i 0.570048i
\(112\) 2.26469e10 1.28505
\(113\) 1.61853e10i 0.878474i −0.898371 0.439237i \(-0.855249\pi\)
0.898371 0.439237i \(-0.144751\pi\)
\(114\) 1.10557e10i 0.574201i
\(115\) 4.11626e9i 0.204651i
\(116\) −3.33714e9 −0.158885
\(117\) 9.93094e9i 0.452961i
\(118\) 1.92785e10 + 2.53254e10i 0.842682 + 1.10700i
\(119\) −1.59353e10 −0.667768
\(120\) 1.66588e8i 0.00669478i
\(121\) −2.15175e10 −0.829592
\(122\) −4.69104e10 −1.73568
\(123\) 1.71344e10 0.608616
\(124\) 3.05331e10i 1.04151i
\(125\) 7.82733e9 0.256486
\(126\) 1.78495e10i 0.562047i
\(127\) 3.67473e10 1.11226 0.556130 0.831095i \(-0.312286\pi\)
0.556130 + 0.831095i \(0.312286\pi\)
\(128\) 6.14885e9i 0.178955i
\(129\) 4.55816e9i 0.127597i
\(130\) −9.07783e9 −0.244492
\(131\) 8.52392e9i 0.220944i −0.993879 0.110472i \(-0.964764\pi\)
0.993879 0.110472i \(-0.0352363\pi\)
\(132\) 2.92788e10i 0.730607i
\(133\) −3.60555e10 −0.866391
\(134\) 3.47395e10 0.804082
\(135\) −1.11601e9 −0.0248885
\(136\) 2.29850e9i 0.0494027i
\(137\) 2.32685e10 0.482132 0.241066 0.970509i \(-0.422503\pi\)
0.241066 + 0.970509i \(0.422503\pi\)
\(138\) −6.36165e10 −1.27108
\(139\) −7.85021e10 −1.51289 −0.756445 0.654057i \(-0.773066\pi\)
−0.756445 + 0.654057i \(0.773066\pi\)
\(140\) −7.88642e9 −0.146636
\(141\) 6.18337e10i 1.10951i
\(142\) 4.23798e10i 0.734036i
\(143\) −1.09911e11 −1.83806
\(144\) −2.18836e10 −0.353432
\(145\) −1.40779e9 −0.0219633
\(146\) −8.45645e10 −1.27475
\(147\) 1.85814e10 0.270702
\(148\) 6.55916e10i 0.923718i
\(149\) 4.42223e10i 0.602157i −0.953599 0.301079i \(-0.902653\pi\)
0.953599 0.301079i \(-0.0973467\pi\)
\(150\) 5.99754e10i 0.789799i
\(151\) 4.09572e10i 0.521729i −0.965375 0.260865i \(-0.915992\pi\)
0.965375 0.260865i \(-0.0840077\pi\)
\(152\) 5.20064e9i 0.0640972i
\(153\) 1.53982e10 0.183659
\(154\) −1.97549e11 −2.28072
\(155\) 1.28805e10i 0.143971i
\(156\) 6.78129e10i 0.733988i
\(157\) 7.64414e10i 0.801365i −0.916217 0.400682i \(-0.868773\pi\)
0.916217 0.400682i \(-0.131227\pi\)
\(158\) 5.98761e10i 0.608090i
\(159\) 1.08873e11 1.07136
\(160\) 1.87878e10i 0.179174i
\(161\) 2.07469e11i 1.91789i
\(162\) 1.72478e10i 0.154582i
\(163\) −1.37094e11 −1.19146 −0.595731 0.803184i \(-0.703137\pi\)
−0.595731 + 0.803184i \(0.703137\pi\)
\(164\) −1.17001e11 −0.986215
\(165\) 1.23514e10i 0.100994i
\(166\) −3.57952e10 −0.283978
\(167\) −1.91516e11 −1.47443 −0.737213 0.675660i \(-0.763859\pi\)
−0.737213 + 0.675660i \(0.763859\pi\)
\(168\) 8.39642e9i 0.0627405i
\(169\) −1.16706e11 −0.846565
\(170\) 1.40754e10i 0.0991327i
\(171\) 3.48403e10 0.238287
\(172\) 3.11252e10i 0.206761i
\(173\) 4.21931e10i 0.272277i −0.990690 0.136139i \(-0.956531\pi\)
0.990690 0.136139i \(-0.0434692\pi\)
\(174\) 2.17573e10i 0.136414i
\(175\) 1.95595e11 1.19170
\(176\) 2.42196e11i 1.43418i
\(177\) −7.98085e10 + 6.07529e10i −0.459391 + 0.349704i
\(178\) −3.80763e11 −2.13086
\(179\) 2.23288e11i 1.21507i 0.794294 + 0.607534i \(0.207841\pi\)
−0.794294 + 0.607534i \(0.792159\pi\)
\(180\) 7.62060e9 0.0403299
\(181\) 1.43418e11 0.738265 0.369132 0.929377i \(-0.379655\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(182\) −4.57544e11 −2.29127
\(183\) 1.47830e11i 0.720289i
\(184\) −2.99253e10 −0.141889
\(185\) 2.76701e10i 0.127689i
\(186\) −1.99068e11 −0.894205
\(187\) 1.70420e11i 0.745266i
\(188\) 4.22228e11i 1.79787i
\(189\) −5.62495e10 −0.233244
\(190\) 3.18473e10i 0.128619i
\(191\) 2.93853e11i 1.15602i −0.816031 0.578008i \(-0.803830\pi\)
0.816031 0.578008i \(-0.196170\pi\)
\(192\) 1.30639e11 0.500688
\(193\) 1.32219e11 0.493751 0.246876 0.969047i \(-0.420596\pi\)
0.246876 + 0.969047i \(0.420596\pi\)
\(194\) −5.24627e11 −1.90916
\(195\) 2.86072e10i 0.101462i
\(196\) −1.26882e11 −0.438652
\(197\) 4.33826e11 1.46213 0.731063 0.682310i \(-0.239024\pi\)
0.731063 + 0.682310i \(0.239024\pi\)
\(198\) 1.90890e11 0.627275
\(199\) 5.60523e11 1.79609 0.898045 0.439904i \(-0.144988\pi\)
0.898045 + 0.439904i \(0.144988\pi\)
\(200\) 2.82125e10i 0.0881641i
\(201\) 1.09476e11i 0.333685i
\(202\) 5.70922e11 1.69754
\(203\) −7.09559e10 −0.205830
\(204\) −1.05146e11 −0.297606
\(205\) −4.93576e10 −0.136328
\(206\) 6.64725e11 1.79187
\(207\) 2.00476e11i 0.527487i
\(208\) 5.60952e11i 1.44082i
\(209\) 3.85594e11i 0.966939i
\(210\) 5.14174e10i 0.125897i
\(211\) 4.46975e11i 1.06874i −0.845252 0.534368i \(-0.820550\pi\)
0.845252 0.534368i \(-0.179450\pi\)
\(212\) −7.43436e11 −1.73606
\(213\) 1.33553e11 0.304617
\(214\) 1.08663e12i 2.42110i
\(215\) 1.31303e10i 0.0285813i
\(216\) 8.11341e9i 0.0172558i
\(217\) 6.49211e11i 1.34923i
\(218\) 2.60164e11 0.528403
\(219\) 2.66490e11i 0.529006i
\(220\) 8.43410e10i 0.163653i
\(221\) 3.94710e11i 0.748715i
\(222\) 4.27640e11 0.793074
\(223\) −1.83058e11 −0.331944 −0.165972 0.986130i \(-0.553076\pi\)
−0.165972 + 0.986130i \(0.553076\pi\)
\(224\) 9.46949e11i 1.67914i
\(225\) −1.89002e11 −0.327758
\(226\) −7.20566e11 −1.22217
\(227\) 5.28624e11i 0.877037i 0.898722 + 0.438518i \(0.144497\pi\)
−0.898722 + 0.438518i \(0.855503\pi\)
\(228\) −2.37905e11 −0.386126
\(229\) 1.02826e12i 1.63277i −0.577509 0.816384i \(-0.695975\pi\)
0.577509 0.816384i \(-0.304025\pi\)
\(230\) 1.83255e11 0.284718
\(231\) 6.22541e11i 0.946473i
\(232\) 1.02347e10i 0.0152277i
\(233\) 5.29944e10i 0.0771703i 0.999255 + 0.0385852i \(0.0122851\pi\)
−0.999255 + 0.0385852i \(0.987715\pi\)
\(234\) 4.42123e11 0.630178
\(235\) 1.78119e11i 0.248525i
\(236\) 5.44968e11 4.14848e11i 0.744408 0.566668i
\(237\) −1.88689e11 −0.252351
\(238\) 7.09436e11i 0.929027i
\(239\) −7.56160e11 −0.969670 −0.484835 0.874606i \(-0.661120\pi\)
−0.484835 + 0.874606i \(0.661120\pi\)
\(240\) 6.30381e10 0.0791674
\(241\) 1.24623e12 1.53290 0.766451 0.642302i \(-0.222021\pi\)
0.766451 + 0.642302i \(0.222021\pi\)
\(242\) 9.57952e11i 1.15416i
\(243\) 5.43536e10 0.0641500
\(244\) 1.00945e12i 1.16717i
\(245\) −5.35258e10 −0.0606363
\(246\) 7.62819e11i 0.846732i
\(247\) 8.93078e11i 0.971414i
\(248\) −9.36419e10 −0.0998187
\(249\) 1.12802e11i 0.117848i
\(250\) 3.48470e11i 0.356834i
\(251\) −6.99905e11 −0.702539 −0.351270 0.936274i \(-0.614250\pi\)
−0.351270 + 0.936274i \(0.614250\pi\)
\(252\) 3.84097e11 0.377953
\(253\) 2.21877e12 2.14047
\(254\) 1.63598e12i 1.54742i
\(255\) −4.43563e10 −0.0411390
\(256\) 1.22726e12 1.11619
\(257\) −1.71467e12 −1.52938 −0.764688 0.644401i \(-0.777107\pi\)
−0.764688 + 0.644401i \(0.777107\pi\)
\(258\) 2.02928e11 0.177519
\(259\) 1.39464e12i 1.19664i
\(260\) 1.95343e11i 0.164411i
\(261\) 6.85643e10 0.0566103
\(262\) −3.79483e11 −0.307387
\(263\) 1.23966e11 0.0985200 0.0492600 0.998786i \(-0.484314\pi\)
0.0492600 + 0.998786i \(0.484314\pi\)
\(264\) 8.97951e10 0.0700218
\(265\) −3.13622e11 −0.239981
\(266\) 1.60518e12i 1.20536i
\(267\) 1.19991e12i 0.884283i
\(268\) 7.47549e11i 0.540711i
\(269\) 2.34489e10i 0.0166479i −0.999965 0.00832397i \(-0.997350\pi\)
0.999965 0.00832397i \(-0.00264963\pi\)
\(270\) 4.96844e10i 0.0346259i
\(271\) 1.77300e12 1.21300 0.606501 0.795083i \(-0.292573\pi\)
0.606501 + 0.795083i \(0.292573\pi\)
\(272\) −8.69772e11 −0.584199
\(273\) 1.44187e12i 0.950853i
\(274\) 1.03591e12i 0.670761i
\(275\) 2.09178e12i 1.33000i
\(276\) 1.36894e12i 0.854751i
\(277\) 2.94048e12 1.80310 0.901549 0.432677i \(-0.142431\pi\)
0.901549 + 0.432677i \(0.142431\pi\)
\(278\) 3.49489e12i 2.10480i
\(279\) 6.27329e11i 0.371086i
\(280\) 2.41868e10i 0.0140536i
\(281\) 7.51601e11 0.428999 0.214499 0.976724i \(-0.431188\pi\)
0.214499 + 0.976724i \(0.431188\pi\)
\(282\) −2.75282e12 −1.54359
\(283\) 8.77176e11i 0.483231i 0.970372 + 0.241615i \(0.0776772\pi\)
−0.970372 + 0.241615i \(0.922323\pi\)
\(284\) −9.11957e11 −0.493608
\(285\) −1.00361e11 −0.0533755
\(286\) 4.89319e12i 2.55718i
\(287\) −2.48774e12 −1.27760
\(288\) 9.15031e11i 0.461821i
\(289\) −1.40399e12 −0.696423
\(290\) 6.26743e10i 0.0305562i
\(291\) 1.65327e12i 0.792281i
\(292\) 1.81971e12i 0.857214i
\(293\) 4.81109e11 0.222795 0.111398 0.993776i \(-0.464467\pi\)
0.111398 + 0.993776i \(0.464467\pi\)
\(294\) 8.27239e11i 0.376612i
\(295\) 2.29897e11 1.75006e11i 0.102902 0.0783325i
\(296\) 2.01162e11 0.0885296
\(297\) 6.01558e11i 0.260313i
\(298\) −1.96876e12 −0.837746
\(299\) 5.13891e12 2.15038
\(300\) 1.29059e12 0.531107
\(301\) 6.61799e11i 0.267851i
\(302\) −1.82340e12 −0.725851
\(303\) 1.79916e12i 0.704461i
\(304\) −1.96796e12 −0.757965
\(305\) 4.25841e11i 0.161342i
\(306\) 6.85524e11i 0.255514i
\(307\) 2.86946e12 1.05222 0.526112 0.850415i \(-0.323649\pi\)
0.526112 + 0.850415i \(0.323649\pi\)
\(308\) 4.25099e12i 1.53369i
\(309\) 2.09477e12i 0.743607i
\(310\) 5.73438e11 0.200299
\(311\) −3.23107e12 −1.11057 −0.555284 0.831661i \(-0.687390\pi\)
−0.555284 + 0.831661i \(0.687390\pi\)
\(312\) 2.07975e11 0.0703458
\(313\) 4.31323e12i 1.43576i −0.696168 0.717879i \(-0.745113\pi\)
0.696168 0.717879i \(-0.254887\pi\)
\(314\) −3.40315e12 −1.11489
\(315\) 1.62033e11 0.0522457
\(316\) 1.28845e12 0.408915
\(317\) −3.32947e12 −1.04011 −0.520054 0.854133i \(-0.674088\pi\)
−0.520054 + 0.854133i \(0.674088\pi\)
\(318\) 4.84701e12i 1.49052i
\(319\) 7.58834e11i 0.229717i
\(320\) −3.76321e11 −0.112152
\(321\) 3.42433e12 1.00473
\(322\) 9.23647e12 2.66825
\(323\) 1.38474e12 0.393873
\(324\) −3.71151e11 −0.103950
\(325\) 4.84478e12i 1.33616i
\(326\) 6.10338e12i 1.65761i
\(327\) 8.19863e11i 0.219282i
\(328\) 3.58831e11i 0.0945193i
\(329\) 8.97762e12i 2.32907i
\(330\) −5.49881e11 −0.140507
\(331\) 6.08638e11 0.153186 0.0765929 0.997062i \(-0.475596\pi\)
0.0765929 + 0.997062i \(0.475596\pi\)
\(332\) 7.70266e11i 0.190963i
\(333\) 1.34763e12i 0.329117i
\(334\) 8.52625e12i 2.05128i
\(335\) 3.15357e11i 0.0747443i
\(336\) 3.17727e12 0.741921
\(337\) 3.59578e12i 0.827264i 0.910444 + 0.413632i \(0.135740\pi\)
−0.910444 + 0.413632i \(0.864260\pi\)
\(338\) 5.19572e12i 1.17778i
\(339\) 2.27074e12i 0.507187i
\(340\) 3.02884e11 0.0666626
\(341\) 6.94295e12 1.50582
\(342\) 1.55108e12i 0.331515i
\(343\) 3.05607e12 0.643713
\(344\) 9.54577e10 0.0198161
\(345\) 5.77495e11i 0.118155i
\(346\) −1.87843e12 −0.378803
\(347\) 9.14707e11i 0.181817i −0.995859 0.0909085i \(-0.971023\pi\)
0.995859 0.0909085i \(-0.0289771\pi\)
\(348\) −4.68187e11 −0.0917325
\(349\) 9.57475e12i 1.84927i 0.380854 + 0.924635i \(0.375630\pi\)
−0.380854 + 0.924635i \(0.624370\pi\)
\(350\) 8.70782e12i 1.65794i
\(351\) 1.39327e12i 0.261517i
\(352\) −1.01271e13 −1.87401
\(353\) 6.77934e12i 1.23684i −0.785847 0.618420i \(-0.787773\pi\)
0.785847 0.618420i \(-0.212227\pi\)
\(354\) 2.70470e12 + 3.55305e12i 0.486523 + 0.639124i
\(355\) −3.84713e11 −0.0682331
\(356\) 8.19350e12i 1.43291i
\(357\) −2.23566e12 −0.385536
\(358\) 9.94072e12 1.69045
\(359\) 1.09240e13 1.83193 0.915963 0.401263i \(-0.131429\pi\)
0.915963 + 0.401263i \(0.131429\pi\)
\(360\) 2.33716e10i 0.00386523i
\(361\) −2.99792e12 −0.488972
\(362\) 6.38495e12i 1.02710i
\(363\) −3.01882e12 −0.478965
\(364\) 9.84574e12i 1.54078i
\(365\) 7.67655e11i 0.118496i
\(366\) −6.58134e12 −1.00210
\(367\) 5.47292e12i 0.822032i −0.911628 0.411016i \(-0.865174\pi\)
0.911628 0.411016i \(-0.134826\pi\)
\(368\) 1.13240e13i 1.67787i
\(369\) 2.40389e12 0.351385
\(370\) −1.23187e12 −0.177646
\(371\) −1.58073e13 −2.24900
\(372\) 4.28368e12i 0.601315i
\(373\) −4.26707e12 −0.590997 −0.295499 0.955343i \(-0.595486\pi\)
−0.295499 + 0.955343i \(0.595486\pi\)
\(374\) 7.58703e12 1.03684
\(375\) 1.09814e12 0.148082
\(376\) −1.29493e12 −0.172309
\(377\) 1.75754e12i 0.230780i
\(378\) 2.50421e12i 0.324498i
\(379\) −7.08379e12 −0.905877 −0.452939 0.891542i \(-0.649624\pi\)
−0.452939 + 0.891542i \(0.649624\pi\)
\(380\) 6.85312e11 0.0864909
\(381\) 5.15550e12 0.642164
\(382\) −1.30823e13 −1.60830
\(383\) 1.13036e13 1.37158 0.685791 0.727799i \(-0.259456\pi\)
0.685791 + 0.727799i \(0.259456\pi\)
\(384\) 8.62659e11i 0.103320i
\(385\) 1.79330e12i 0.212007i
\(386\) 5.88636e12i 0.686927i
\(387\) 6.39493e11i 0.0736683i
\(388\) 1.12893e13i 1.28383i
\(389\) 1.56295e13 1.75467 0.877337 0.479874i \(-0.159318\pi\)
0.877337 + 0.479874i \(0.159318\pi\)
\(390\) −1.27358e12 −0.141158
\(391\) 7.96803e12i 0.871901i
\(392\) 3.89134e11i 0.0420406i
\(393\) 1.19587e12i 0.127562i
\(394\) 1.93138e13i 2.03417i
\(395\) 5.43540e11 0.0565258
\(396\) 4.10771e12i 0.421816i
\(397\) 3.48262e12i 0.353145i −0.984288 0.176573i \(-0.943499\pi\)
0.984288 0.176573i \(-0.0565011\pi\)
\(398\) 2.49543e13i 2.49879i
\(399\) −5.05845e12 −0.500211
\(400\) 1.06758e13 1.04256
\(401\) 6.73309e12i 0.649370i −0.945822 0.324685i \(-0.894742\pi\)
0.945822 0.324685i \(-0.105258\pi\)
\(402\) 4.87382e12 0.464237
\(403\) 1.60806e13 1.51279
\(404\) 1.22855e13i 1.14153i
\(405\) −1.56572e11 −0.0143694
\(406\) 3.15893e12i 0.286359i
\(407\) −1.49149e13 −1.33552
\(408\) 3.22471e11i 0.0285227i
\(409\) 5.82257e12i 0.508742i 0.967107 + 0.254371i \(0.0818685\pi\)
−0.967107 + 0.254371i \(0.918131\pi\)
\(410\) 2.19739e12i 0.189665i
\(411\) 3.26448e12 0.278359
\(412\) 1.43040e13i 1.20496i
\(413\) 1.15874e13 8.82070e12i 0.964351 0.734096i
\(414\) −8.92515e12 −0.733861
\(415\) 3.24940e11i 0.0263975i
\(416\) −2.34554e13 −1.88268
\(417\) −1.10135e13 −0.873468
\(418\) 1.71666e13 1.34525
\(419\) 1.84198e13i 1.42632i −0.701004 0.713158i \(-0.747264\pi\)
0.701004 0.713158i \(-0.252736\pi\)
\(420\) −1.10643e12 −0.0846602
\(421\) 1.05826e13i 0.800170i −0.916478 0.400085i \(-0.868981\pi\)
0.916478 0.400085i \(-0.131019\pi\)
\(422\) −1.98992e13 −1.48687
\(423\) 8.67503e12i 0.640573i
\(424\) 2.28004e12i 0.166385i
\(425\) −7.51197e12 −0.541763
\(426\) 5.94572e12i 0.423796i
\(427\) 2.14634e13i 1.51203i
\(428\) −2.33828e13 −1.62809
\(429\) −1.54200e13 −1.06120
\(430\) −5.84557e11 −0.0397635
\(431\) 4.63964e12i 0.311959i 0.987760 + 0.155980i \(0.0498535\pi\)
−0.987760 + 0.155980i \(0.950147\pi\)
\(432\) −3.07018e12 −0.204054
\(433\) 2.71254e13 1.78212 0.891058 0.453889i \(-0.149964\pi\)
0.891058 + 0.453889i \(0.149964\pi\)
\(434\) 2.89027e13 1.87711
\(435\) −1.97507e11 −0.0126805
\(436\) 5.59839e12i 0.355329i
\(437\) 1.80286e13i 1.13124i
\(438\) −1.18641e13 −0.735975
\(439\) 9.17569e11 0.0562751 0.0281375 0.999604i \(-0.491042\pi\)
0.0281375 + 0.999604i \(0.491042\pi\)
\(440\) −2.58665e11 −0.0156846
\(441\) 2.60690e12 0.156290
\(442\) 1.75724e13 1.04164
\(443\) 1.91563e13i 1.12278i −0.827552 0.561389i \(-0.810267\pi\)
0.827552 0.561389i \(-0.189733\pi\)
\(444\) 9.20224e12i 0.533309i
\(445\) 3.45647e12i 0.198076i
\(446\) 8.14969e12i 0.461814i
\(447\) 6.20422e12i 0.347656i
\(448\) −1.89675e13 −1.05104
\(449\) 2.20311e13 1.20727 0.603634 0.797262i \(-0.293719\pi\)
0.603634 + 0.797262i \(0.293719\pi\)
\(450\) 8.41431e12i 0.455991i
\(451\) 2.66050e13i 1.42587i
\(452\) 1.55056e13i 0.821858i
\(453\) 5.74613e12i 0.301221i
\(454\) 2.35342e13 1.22017
\(455\) 4.15347e12i 0.212988i
\(456\) 7.29630e11i 0.0370065i
\(457\) 2.51973e13i 1.26408i 0.774938 + 0.632038i \(0.217781\pi\)
−0.774938 + 0.632038i \(0.782219\pi\)
\(458\) −4.57777e13 −2.27157
\(459\) 2.16031e12 0.106036
\(460\) 3.94339e12i 0.191461i
\(461\) 2.32158e13 1.11501 0.557504 0.830174i \(-0.311759\pi\)
0.557504 + 0.830174i \(0.311759\pi\)
\(462\) −2.77154e13 −1.31677
\(463\) 1.16250e13i 0.546371i −0.961961 0.273186i \(-0.911923\pi\)
0.961961 0.273186i \(-0.0880773\pi\)
\(464\) −3.87287e12 −0.180071
\(465\) 1.80709e12i 0.0831218i
\(466\) 2.35929e12 0.107362
\(467\) 3.39054e13i 1.52645i −0.646130 0.763227i \(-0.723614\pi\)
0.646130 0.763227i \(-0.276386\pi\)
\(468\) 9.51388e12i 0.423768i
\(469\) 1.58948e13i 0.700470i
\(470\) 7.92980e12 0.345759
\(471\) 1.07244e13i 0.462668i
\(472\) 1.27230e12 + 1.67136e12i 0.0543098 + 0.0713444i
\(473\) −7.07758e12 −0.298937
\(474\) 8.40039e12i 0.351081i
\(475\) −1.69967e13 −0.702906
\(476\) 1.52661e13 0.624732
\(477\) 1.52745e13 0.618551
\(478\) 3.36640e13i 1.34905i
\(479\) −1.20587e13 −0.478213 −0.239106 0.970993i \(-0.576854\pi\)
−0.239106 + 0.970993i \(0.576854\pi\)
\(480\) 2.63585e12i 0.103446i
\(481\) −3.45445e13 −1.34170
\(482\) 5.54820e13i 2.13264i
\(483\) 2.91071e13i 1.10730i
\(484\) 2.06138e13 0.776126
\(485\) 4.76243e12i 0.177468i
\(486\) 2.41981e12i 0.0892481i
\(487\) −2.37666e13 −0.867606 −0.433803 0.901008i \(-0.642829\pi\)
−0.433803 + 0.901008i \(0.642829\pi\)
\(488\) −3.09587e12 −0.111862
\(489\) −1.92337e13 −0.687891
\(490\) 2.38295e12i 0.0843598i
\(491\) −6.53918e12 −0.229148 −0.114574 0.993415i \(-0.536550\pi\)
−0.114574 + 0.993415i \(0.536550\pi\)
\(492\) −1.64148e13 −0.569392
\(493\) 2.72512e12 0.0935730
\(494\) 3.97596e13 1.35147
\(495\) 1.73286e12i 0.0583091i
\(496\) 3.54348e13i 1.18038i
\(497\) −1.93905e13 −0.639450
\(498\) −5.02193e12 −0.163955
\(499\) 4.86138e13 1.57129 0.785646 0.618676i \(-0.212331\pi\)
0.785646 + 0.618676i \(0.212331\pi\)
\(500\) −7.49862e12 −0.239956
\(501\) −2.68690e13 −0.851261
\(502\) 3.11596e13i 0.977401i
\(503\) 1.05896e13i 0.328883i 0.986387 + 0.164441i \(0.0525821\pi\)
−0.986387 + 0.164441i \(0.947418\pi\)
\(504\) 1.17799e12i 0.0362232i
\(505\) 5.18269e12i 0.157797i
\(506\) 9.87790e13i 2.97791i
\(507\) −1.63734e13 −0.488764
\(508\) −3.52040e13 −1.04058
\(509\) 2.81554e13i 0.824087i 0.911164 + 0.412044i \(0.135185\pi\)
−0.911164 + 0.412044i \(0.864815\pi\)
\(510\) 1.97473e12i 0.0572343i
\(511\) 3.86917e13i 1.11049i
\(512\) 4.83408e13i 1.37393i
\(513\) 4.88795e12 0.137575
\(514\) 7.63365e13i 2.12773i
\(515\) 6.03421e12i 0.166565i
\(516\) 4.36674e12i 0.119374i
\(517\) 9.60108e13 2.59936
\(518\) −6.20890e13 −1.66481
\(519\) 5.91953e12i 0.157199i
\(520\) −5.99096e11 −0.0157572
\(521\) −3.10161e13 −0.807975 −0.403987 0.914765i \(-0.632376\pi\)
−0.403987 + 0.914765i \(0.632376\pi\)
\(522\) 3.05246e12i 0.0787585i
\(523\) −2.84566e13 −0.727235 −0.363617 0.931548i \(-0.618458\pi\)
−0.363617 + 0.931548i \(0.618458\pi\)
\(524\) 8.16596e12i 0.206705i
\(525\) 2.74412e13 0.688028
\(526\) 5.51894e12i 0.137065i
\(527\) 2.49335e13i 0.613380i
\(528\) 3.39792e13i 0.828025i
\(529\) −6.23130e13 −1.50418
\(530\) 1.39624e13i 0.333872i
\(531\) −1.11968e13 + 8.52339e12i −0.265230 + 0.201902i
\(532\) 3.45414e13 0.810553
\(533\) 6.16201e13i 1.43247i
\(534\) −5.34195e13 −1.23025
\(535\) −9.86416e12 −0.225056
\(536\) 2.29265e12 0.0518220
\(537\) 3.13264e13i 0.701519i
\(538\) −1.04394e12 −0.0231613
\(539\) 2.88518e13i 0.634205i
\(540\) 1.06914e12 0.0232845
\(541\) 4.88003e12i 0.105302i 0.998613 + 0.0526509i \(0.0167671\pi\)
−0.998613 + 0.0526509i \(0.983233\pi\)
\(542\) 7.89333e13i 1.68758i
\(543\) 2.01211e13 0.426237
\(544\) 3.63683e13i 0.763359i
\(545\) 2.36171e12i 0.0491183i
\(546\) −6.41917e13 −1.32287
\(547\) 7.70756e12 0.157391 0.0786955 0.996899i \(-0.474925\pi\)
0.0786955 + 0.996899i \(0.474925\pi\)
\(548\) −2.22913e13 −0.451059
\(549\) 2.07400e13i 0.415859i
\(550\) −9.31254e13 −1.85035
\(551\) 6.16590e12 0.121406
\(552\) −4.19840e12 −0.0819198
\(553\) 2.73958e13 0.529734
\(554\) 1.30909e14i 2.50854i
\(555\) 3.88201e12i 0.0737211i
\(556\) 7.52054e13 1.41539
\(557\) −8.10191e13 −1.51116 −0.755582 0.655054i \(-0.772646\pi\)
−0.755582 + 0.655054i \(0.772646\pi\)
\(558\) −2.79285e13 −0.516269
\(559\) −1.63924e13 −0.300320
\(560\) −9.15249e12 −0.166188
\(561\) 2.39092e13i 0.430279i
\(562\) 3.34611e13i 0.596840i
\(563\) 1.43723e13i 0.254089i 0.991897 + 0.127044i \(0.0405491\pi\)
−0.991897 + 0.127044i \(0.959451\pi\)
\(564\) 5.92369e13i 1.03800i
\(565\) 6.54111e12i 0.113608i
\(566\) 3.90516e13 0.672290
\(567\) −7.89159e12 −0.134663
\(568\) 2.79688e12i 0.0473077i
\(569\) 3.15550e13i 0.529063i 0.964377 + 0.264532i \(0.0852173\pi\)
−0.964377 + 0.264532i \(0.914783\pi\)
\(570\) 4.46806e12i 0.0742582i
\(571\) 6.11208e13i 1.00695i −0.864010 0.503475i \(-0.832054\pi\)
0.864010 0.503475i \(-0.167946\pi\)
\(572\) 1.05295e14 1.71960
\(573\) 4.12265e13i 0.667426i
\(574\) 1.10754e14i 1.77745i
\(575\) 9.78019e13i 1.55599i
\(576\) 1.83282e13 0.289072
\(577\) 7.26221e13 1.13551 0.567754 0.823199i \(-0.307813\pi\)
0.567754 + 0.823199i \(0.307813\pi\)
\(578\) 6.25050e13i 0.968893i
\(579\) 1.85499e13 0.285067
\(580\) 1.34867e12 0.0205478
\(581\) 1.63778e13i 0.247385i
\(582\) −7.36032e13 −1.10225
\(583\) 1.69051e14i 2.51000i
\(584\) −5.58088e12 −0.0821558
\(585\) 4.01348e12i 0.0585789i
\(586\) 2.14189e13i 0.309962i
\(587\) 1.17608e14i 1.68750i 0.536733 + 0.843752i \(0.319658\pi\)
−0.536733 + 0.843752i \(0.680342\pi\)
\(588\) −1.78011e13 −0.253256
\(589\) 5.64149e13i 0.795825i
\(590\) −7.79120e12 1.02350e13i −0.108979 0.143162i
\(591\) 6.08642e13 0.844159
\(592\) 7.61214e13i 1.04688i
\(593\) 5.71849e13 0.779845 0.389922 0.920848i \(-0.372502\pi\)
0.389922 + 0.920848i \(0.372502\pi\)
\(594\) 2.67812e13 0.362158
\(595\) 6.44008e12 0.0863588
\(596\) 4.23652e13i 0.563349i
\(597\) 7.86392e13 1.03697
\(598\) 2.28783e14i 2.99170i
\(599\) −1.04476e13 −0.135482 −0.0677412 0.997703i \(-0.521579\pi\)
−0.0677412 + 0.997703i \(0.521579\pi\)
\(600\) 3.95811e12i 0.0509016i
\(601\) 3.38326e13i 0.431483i −0.976451 0.215741i \(-0.930783\pi\)
0.976451 0.215741i \(-0.0692168\pi\)
\(602\) −2.94631e13 −0.372646
\(603\) 1.53590e13i 0.192653i
\(604\) 3.92372e13i 0.488105i
\(605\) 8.69604e12 0.107286
\(606\) 8.00982e13 0.980076
\(607\) 8.28195e12 0.100505 0.0502526 0.998737i \(-0.483997\pi\)
0.0502526 + 0.998737i \(0.483997\pi\)
\(608\) 8.22877e13i 0.990414i
\(609\) −9.95483e12 −0.118836
\(610\) 1.89583e13 0.224466
\(611\) 2.22371e14 2.61139
\(612\) −1.47515e13 −0.171823
\(613\) 1.35326e14i 1.56343i −0.623636 0.781715i \(-0.714345\pi\)
0.623636 0.781715i \(-0.285655\pi\)
\(614\) 1.27748e14i 1.46390i
\(615\) −6.92468e12 −0.0787089
\(616\) −1.30373e13 −0.146989
\(617\) −1.17189e14 −1.31058 −0.655289 0.755379i \(-0.727453\pi\)
−0.655289 + 0.755379i \(0.727453\pi\)
\(618\) 9.32584e13 1.03454
\(619\) −3.39180e13 −0.373231 −0.186615 0.982433i \(-0.559752\pi\)
−0.186615 + 0.982433i \(0.559752\pi\)
\(620\) 1.23396e13i 0.134692i
\(621\) 2.81261e13i 0.304545i
\(622\) 1.43847e14i 1.54507i
\(623\) 1.74214e14i 1.85628i
\(624\) 7.86994e13i 0.831856i
\(625\) 9.06091e13 0.950105
\(626\) −1.92024e14 −1.99749
\(627\) 5.40974e13i 0.558263i
\(628\) 7.32312e13i 0.749718i
\(629\) 5.35623e13i 0.544009i
\(630\) 7.21367e12i 0.0726864i
\(631\) −1.41485e13 −0.141437 −0.0707186 0.997496i \(-0.522529\pi\)
−0.0707186 + 0.997496i \(0.522529\pi\)
\(632\) 3.95155e12i 0.0391907i
\(633\) 6.27088e13i 0.617035i
\(634\) 1.48227e14i 1.44704i
\(635\) −1.48510e13 −0.143842
\(636\) −1.04301e14 −1.00231
\(637\) 6.68239e13i 0.637140i
\(638\) 3.37831e13 0.319592
\(639\) 1.87369e13 0.175871
\(640\) 2.48499e12i 0.0231432i
\(641\) −7.49349e13 −0.692459 −0.346229 0.938150i \(-0.612538\pi\)
−0.346229 + 0.938150i \(0.612538\pi\)
\(642\) 1.52450e14i 1.39782i
\(643\) 7.12517e13 0.648247 0.324123 0.946015i \(-0.394931\pi\)
0.324123 + 0.946015i \(0.394931\pi\)
\(644\) 1.98757e14i 1.79429i
\(645\) 1.84213e12i 0.0165014i
\(646\) 6.16483e13i 0.547972i
\(647\) 1.07039e14 0.944105 0.472052 0.881571i \(-0.343513\pi\)
0.472052 + 0.881571i \(0.343513\pi\)
\(648\) 1.13828e12i 0.00996263i
\(649\) −9.43326e13 1.23921e14i −0.819291 1.07627i
\(650\) −2.15688e14 −1.85892
\(651\) 9.10817e13i 0.778980i
\(652\) 1.31337e14 1.11467
\(653\) 4.66881e12 0.0393224 0.0196612 0.999807i \(-0.493741\pi\)
0.0196612 + 0.999807i \(0.493741\pi\)
\(654\) 3.65001e13 0.305074
\(655\) 3.44485e12i 0.0285735i
\(656\) −1.35784e14 −1.11771
\(657\) 3.73876e13i 0.305422i
\(658\) 3.99681e14 3.24029
\(659\) 1.26192e14i 1.01533i −0.861556 0.507663i \(-0.830509\pi\)
0.861556 0.507663i \(-0.169491\pi\)
\(660\) 1.18327e13i 0.0944854i
\(661\) 2.02053e14 1.60125 0.800624 0.599167i \(-0.204501\pi\)
0.800624 + 0.599167i \(0.204501\pi\)
\(662\) 2.70964e13i 0.213118i
\(663\) 5.53762e13i 0.432271i
\(664\) −2.36232e12 −0.0183020
\(665\) 1.45714e13 0.112045
\(666\) 5.99962e13 0.457881
\(667\) 3.54796e13i 0.268751i
\(668\) 1.83473e14 1.37940
\(669\) −2.56823e13 −0.191648
\(670\) −1.40396e13 −0.103987
\(671\) 2.29539e14 1.68750
\(672\) 1.32853e14i 0.969451i
\(673\) 1.94663e14i 1.40997i 0.709223 + 0.704984i \(0.249046\pi\)
−0.709223 + 0.704984i \(0.750954\pi\)
\(674\) 1.60083e14 1.15092
\(675\) −2.65162e13 −0.189231
\(676\) 1.11805e14 0.792005
\(677\) 4.09581e13 0.288003 0.144001 0.989577i \(-0.454003\pi\)
0.144001 + 0.989577i \(0.454003\pi\)
\(678\) −1.01093e14 −0.705620
\(679\) 2.40038e14i 1.66315i
\(680\) 9.28915e11i 0.00638898i
\(681\) 7.41639e13i 0.506357i
\(682\) 3.09098e14i 2.09496i
\(683\) 2.42465e14i 1.63135i −0.578513 0.815673i \(-0.696367\pi\)
0.578513 0.815673i \(-0.303633\pi\)
\(684\) −3.33771e13 −0.222930
\(685\) −9.40371e12 −0.0623514
\(686\) 1.36055e14i 0.895560i
\(687\) 1.44261e14i 0.942680i
\(688\) 3.61219e13i 0.234330i
\(689\) 3.91539e14i 2.52162i
\(690\) 2.57099e13 0.164382
\(691\) 1.97068e14i 1.25091i 0.780259 + 0.625456i \(0.215087\pi\)
−0.780259 + 0.625456i \(0.784913\pi\)
\(692\) 4.04212e13i 0.254729i
\(693\) 8.73401e13i 0.546446i
\(694\) −4.07225e13 −0.252951
\(695\) 3.17258e13 0.195654
\(696\) 1.43588e12i 0.00879169i
\(697\) 9.55437e13 0.580816
\(698\) 4.26265e14 2.57278
\(699\) 7.43491e12i 0.0445543i
\(700\) −1.87381e14 −1.11490
\(701\) 2.17248e14i 1.28341i 0.766952 + 0.641705i \(0.221773\pi\)
−0.766952 + 0.641705i \(0.778227\pi\)
\(702\) 6.20281e13 0.363834
\(703\) 1.21191e14i 0.705820i
\(704\) 2.02847e14i 1.17302i
\(705\) 2.49894e13i 0.143486i
\(706\) −3.01814e14 −1.72074
\(707\) 2.61220e14i 1.47880i
\(708\) 7.64569e13 5.82015e13i 0.429784 0.327166i
\(709\) 6.87942e13 0.383991 0.191995 0.981396i \(-0.438504\pi\)
0.191995 + 0.981396i \(0.438504\pi\)
\(710\) 1.71273e13i 0.0949287i
\(711\) −2.64724e13 −0.145695
\(712\) −2.51286e13 −0.137331
\(713\) −3.24620e14 −1.76168
\(714\) 9.95311e13i 0.536374i
\(715\) 4.44191e13 0.237706
\(716\) 2.13911e14i 1.13676i
\(717\) −1.06086e14 −0.559839
\(718\) 4.86332e14i 2.54865i
\(719\) 1.36484e14i 0.710291i 0.934811 + 0.355145i \(0.115569\pi\)
−0.934811 + 0.355145i \(0.884431\pi\)
\(720\) 8.84399e12 0.0457073
\(721\) 3.04139e14i 1.56097i
\(722\) 1.33467e14i 0.680278i
\(723\) 1.74842e14 0.885022
\(724\) −1.37396e14 −0.690685
\(725\) −3.34489e13 −0.166990
\(726\) 1.34397e14i 0.666356i
\(727\) 1.12919e14 0.556028 0.278014 0.960577i \(-0.410324\pi\)
0.278014 + 0.960577i \(0.410324\pi\)
\(728\) −3.01959e13 −0.147669
\(729\) 7.62560e12 0.0370370
\(730\) 3.41758e13 0.164856
\(731\) 2.54169e13i 0.121769i
\(732\) 1.41622e14i 0.673867i
\(733\) −1.55631e14 −0.735488 −0.367744 0.929927i \(-0.619870\pi\)
−0.367744 + 0.929927i \(0.619870\pi\)
\(734\) −2.43653e14 −1.14365
\(735\) −7.50947e12 −0.0350084
\(736\) 4.73496e14 2.19244
\(737\) −1.69986e14 −0.781763
\(738\) 1.07020e14i 0.488861i
\(739\) 3.63072e13i 0.164729i 0.996602 + 0.0823646i \(0.0262472\pi\)
−0.996602 + 0.0823646i \(0.973753\pi\)
\(740\) 2.65081e13i 0.119459i
\(741\) 1.25295e14i 0.560846i
\(742\) 7.03737e14i 3.12889i
\(743\) 6.28873e13 0.277728 0.138864 0.990311i \(-0.455655\pi\)
0.138864 + 0.990311i \(0.455655\pi\)
\(744\) −1.31376e13 −0.0576304
\(745\) 1.78719e13i 0.0778736i
\(746\) 1.89969e14i 0.822220i
\(747\) 1.58257e13i 0.0680395i
\(748\) 1.63263e14i 0.697235i
\(749\) −4.97177e14 −2.10912
\(750\) 4.88890e13i 0.206018i
\(751\) 1.72446e13i 0.0721863i −0.999348 0.0360931i \(-0.988509\pi\)
0.999348 0.0360931i \(-0.0114913\pi\)
\(752\) 4.90011e14i 2.03759i
\(753\) −9.81940e13 −0.405611
\(754\) 7.82452e13 0.321071
\(755\) 1.65524e13i 0.0674723i
\(756\) 5.38873e13 0.218211
\(757\) −1.41562e13 −0.0569466 −0.0284733 0.999595i \(-0.509065\pi\)
−0.0284733 + 0.999595i \(0.509065\pi\)
\(758\) 3.15368e14i 1.26029i
\(759\) 3.11285e14 1.23580
\(760\) 2.10178e12i 0.00828933i
\(761\) −3.21252e14 −1.25870 −0.629350 0.777122i \(-0.716679\pi\)
−0.629350 + 0.777122i \(0.716679\pi\)
\(762\) 2.29521e14i 0.893404i
\(763\) 1.19036e14i 0.460315i
\(764\) 2.81513e14i 1.08151i
\(765\) −6.22301e12 −0.0237516
\(766\) 5.03232e14i 1.90820i
\(767\) −2.18484e14 2.87014e14i −0.823083 1.08125i
\(768\) 1.72180e14 0.644430
\(769\) 1.72173e14i 0.640225i 0.947380 + 0.320113i \(0.103721\pi\)
−0.947380 + 0.320113i \(0.896279\pi\)
\(770\) 7.98372e13 0.294952
\(771\) −2.40561e14 −0.882985
\(772\) −1.26667e14 −0.461930
\(773\) 3.04500e14i 1.10329i 0.834079 + 0.551644i \(0.185999\pi\)
−0.834079 + 0.551644i \(0.814001\pi\)
\(774\) 2.84700e13 0.102490
\(775\) 3.06040e14i 1.09464i
\(776\) −3.46230e13 −0.123043
\(777\) 1.95663e14i 0.690880i
\(778\) 6.95820e14i 2.44118i
\(779\) 2.16179e14 0.753575