Properties

Label 177.11.c.a.58.10
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 58.10
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.91

$q$-expansion

\(f(q)\) \(=\) \(q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +245660. i q^{10} -21424.0i q^{11} +277891. q^{12} -309118. i q^{13} +1.50037e6i q^{14} +628748. q^{15} +846494. q^{16} +1.91085e6 q^{17} -1.07893e6i q^{18} -675482. q^{19} +8.87686e6 q^{20} +3.84007e6 q^{21} -1.17437e6 q^{22} -4.00666e6i q^{23} -7.35777e6i q^{24} +1.03189e7 q^{25} -1.69445e7 q^{26} -2.76145e6 q^{27} +5.42154e7 q^{28} +1.18366e7 q^{29} -3.44652e7i q^{30} -1.59663e7i q^{31} +7.30219e6i q^{32} +3.00570e6i q^{33} -1.04745e8i q^{34} +1.22666e8 q^{35} -3.89870e7 q^{36} -7.63595e7i q^{37} +3.70269e7i q^{38} +4.33680e7i q^{39} -2.35034e8i q^{40} +4.81846e7 q^{41} -2.10496e8i q^{42} +1.47581e8i q^{43} +4.24354e7i q^{44} -8.82109e7 q^{45} -2.19627e8 q^{46} -8.31364e7i q^{47} -1.18760e8 q^{48} +4.66708e8 q^{49} -5.65637e8i q^{50} -2.68085e8 q^{51} +6.12284e8i q^{52} +5.12608e8 q^{53} +1.51370e8i q^{54} +9.60132e7i q^{55} -1.43547e9i q^{56} +9.47675e7 q^{57} -6.48828e8i q^{58} +(4.98252e8 + 5.12701e8i) q^{59} -1.24539e9 q^{60} +2.96707e8i q^{61} -8.75202e8 q^{62} -5.38747e8 q^{63} +1.26708e9 q^{64} +1.38533e9i q^{65} +1.64759e8 q^{66} +5.57657e8i q^{67} -3.78492e9 q^{68} +5.62119e8i q^{69} -6.72401e9i q^{70} -6.33242e8 q^{71} +1.03227e9i q^{72} -6.09409e8i q^{73} -4.18569e9 q^{74} -1.44770e9 q^{75} +1.33796e9 q^{76} +5.86400e8i q^{77} +2.37724e9 q^{78} -1.56682e9 q^{79} -3.79363e9 q^{80} +3.87420e8 q^{81} -2.64126e9i q^{82} -1.79188e9i q^{83} -7.60621e9 q^{84} -8.56364e9 q^{85} +8.08972e9 q^{86} -1.66062e9 q^{87} +1.12357e9 q^{88} +9.80823e9i q^{89} +4.83533e9i q^{90} +8.46093e9i q^{91} +7.93617e9i q^{92} +2.24001e9i q^{93} -4.55717e9 q^{94} +3.02722e9 q^{95} -1.02447e9i q^{96} -7.87880e9i q^{97} -2.55828e10i q^{98} -4.21688e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 54.8156i 1.71299i −0.516158 0.856493i \(-0.672638\pi\)
0.516158 0.856493i \(-0.327362\pi\)
\(3\) −140.296 −0.577350
\(4\) −1980.75 −1.93432
\(5\) −4481.58 −1.43410 −0.717052 0.697019i \(-0.754509\pi\)
−0.717052 + 0.697019i \(0.754509\pi\)
\(6\) 7690.41i 0.988993i
\(7\) −27371.2 −1.62856 −0.814280 0.580472i \(-0.802868\pi\)
−0.814280 + 0.580472i \(0.802868\pi\)
\(8\) 52444.5i 1.60048i
\(9\) 19683.0 0.333333
\(10\) 245660.i 2.45660i
\(11\) 21424.0i 0.133026i −0.997786 0.0665130i \(-0.978813\pi\)
0.997786 0.0665130i \(-0.0211874\pi\)
\(12\) 277891. 1.11678
\(13\) 309118.i 0.832544i −0.909240 0.416272i \(-0.863336\pi\)
0.909240 0.416272i \(-0.136664\pi\)
\(14\) 1.50037e6i 2.78970i
\(15\) 628748. 0.827981
\(16\) 846494. 0.807279
\(17\) 1.91085e6 1.34581 0.672904 0.739730i \(-0.265047\pi\)
0.672904 + 0.739730i \(0.265047\pi\)
\(18\) 1.07893e6i 0.570995i
\(19\) −675482. −0.272801 −0.136400 0.990654i \(-0.543553\pi\)
−0.136400 + 0.990654i \(0.543553\pi\)
\(20\) 8.87686e6 2.77402
\(21\) 3.84007e6 0.940249
\(22\) −1.17437e6 −0.227872
\(23\) 4.00666e6i 0.622505i −0.950327 0.311253i \(-0.899251\pi\)
0.950327 0.311253i \(-0.100749\pi\)
\(24\) 7.35777e6i 0.924038i
\(25\) 1.03189e7 1.05666
\(26\) −1.69445e7 −1.42614
\(27\) −2.76145e6 −0.192450
\(28\) 5.42154e7 3.15016
\(29\) 1.18366e7 0.577080 0.288540 0.957468i \(-0.406830\pi\)
0.288540 + 0.957468i \(0.406830\pi\)
\(30\) 3.44652e7i 1.41832i
\(31\) 1.59663e7i 0.557694i −0.960336 0.278847i \(-0.910048\pi\)
0.960336 0.278847i \(-0.0899522\pi\)
\(32\) 7.30219e6i 0.217622i
\(33\) 3.00570e6i 0.0768026i
\(34\) 1.04745e8i 2.30535i
\(35\) 1.22666e8 2.33553
\(36\) −3.89870e7 −0.644774
\(37\) 7.63595e7i 1.10117i −0.834779 0.550585i \(-0.814405\pi\)
0.834779 0.550585i \(-0.185595\pi\)
\(38\) 3.70269e7i 0.467304i
\(39\) 4.33680e7i 0.480669i
\(40\) 2.35034e8i 2.29526i
\(41\) 4.81846e7 0.415900 0.207950 0.978139i \(-0.433321\pi\)
0.207950 + 0.978139i \(0.433321\pi\)
\(42\) 2.10496e8i 1.61063i
\(43\) 1.47581e8i 1.00389i 0.864899 + 0.501946i \(0.167383\pi\)
−0.864899 + 0.501946i \(0.832617\pi\)
\(44\) 4.24354e7i 0.257315i
\(45\) −8.82109e7 −0.478035
\(46\) −2.19627e8 −1.06634
\(47\) 8.31364e7i 0.362495i −0.983438 0.181248i \(-0.941986\pi\)
0.983438 0.181248i \(-0.0580135\pi\)
\(48\) −1.18760e8 −0.466083
\(49\) 4.66708e8 1.65221
\(50\) 5.65637e8i 1.81004i
\(51\) −2.68085e8 −0.777002
\(52\) 6.12284e8i 1.61041i
\(53\) 5.12608e8 1.22576 0.612881 0.790176i \(-0.290011\pi\)
0.612881 + 0.790176i \(0.290011\pi\)
\(54\) 1.51370e8i 0.329664i
\(55\) 9.60132e7i 0.190773i
\(56\) 1.43547e9i 2.60648i
\(57\) 9.47675e7 0.157502
\(58\) 6.48828e8i 0.988529i
\(59\) 4.98252e8 + 5.12701e8i 0.696929 + 0.717140i
\(60\) −1.24539e9 −1.60158
\(61\) 2.96707e8i 0.351301i 0.984453 + 0.175650i \(0.0562028\pi\)
−0.984453 + 0.175650i \(0.943797\pi\)
\(62\) −8.75202e8 −0.955322
\(63\) −5.38747e8 −0.542853
\(64\) 1.26708e9 1.18006
\(65\) 1.38533e9i 1.19396i
\(66\) 1.64759e8 0.131562
\(67\) 5.57657e8i 0.413041i 0.978442 + 0.206520i \(0.0662140\pi\)
−0.978442 + 0.206520i \(0.933786\pi\)
\(68\) −3.78492e9 −2.60322
\(69\) 5.62119e8i 0.359404i
\(70\) 6.72401e9i 4.00072i
\(71\) −6.33242e8 −0.350976 −0.175488 0.984482i \(-0.556150\pi\)
−0.175488 + 0.984482i \(0.556150\pi\)
\(72\) 1.03227e9i 0.533493i
\(73\) 6.09409e8i 0.293964i −0.989139 0.146982i \(-0.953044\pi\)
0.989139 0.146982i \(-0.0469560\pi\)
\(74\) −4.18569e9 −1.88629
\(75\) −1.44770e9 −0.610061
\(76\) 1.33796e9 0.527685
\(77\) 5.86400e8i 0.216641i
\(78\) 2.37724e9 0.823380
\(79\) −1.56682e9 −0.509196 −0.254598 0.967047i \(-0.581943\pi\)
−0.254598 + 0.967047i \(0.581943\pi\)
\(80\) −3.79363e9 −1.15772
\(81\) 3.87420e8 0.111111
\(82\) 2.64126e9i 0.712431i
\(83\) 1.79188e9i 0.454903i −0.973789 0.227451i \(-0.926961\pi\)
0.973789 0.227451i \(-0.0730393\pi\)
\(84\) −7.60621e9 −1.81875
\(85\) −8.56364e9 −1.93003
\(86\) 8.08972e9 1.71965
\(87\) −1.66062e9 −0.333177
\(88\) 1.12357e9 0.212906
\(89\) 9.80823e9i 1.75647i 0.478230 + 0.878235i \(0.341279\pi\)
−0.478230 + 0.878235i \(0.658721\pi\)
\(90\) 4.83533e9i 0.818867i
\(91\) 8.46093e9i 1.35585i
\(92\) 7.93617e9i 1.20413i
\(93\) 2.24001e9i 0.321985i
\(94\) −4.55717e9 −0.620949
\(95\) 3.02722e9 0.391225
\(96\) 1.02447e9i 0.125644i
\(97\) 7.87880e9i 0.917490i −0.888568 0.458745i \(-0.848299\pi\)
0.888568 0.458745i \(-0.151701\pi\)
\(98\) 2.55828e10i 2.83021i
\(99\) 4.21688e8i 0.0443420i
\(100\) −2.04391e10 −2.04391
\(101\) 1.38657e10i 1.31927i −0.751584 0.659637i \(-0.770710\pi\)
0.751584 0.659637i \(-0.229290\pi\)
\(102\) 1.46952e10i 1.33099i
\(103\) 7.33673e9i 0.632872i −0.948614 0.316436i \(-0.897514\pi\)
0.948614 0.316436i \(-0.102486\pi\)
\(104\) 1.62115e10 1.33247
\(105\) −1.72096e10 −1.34842
\(106\) 2.80989e10i 2.09971i
\(107\) −1.43613e10 −1.02394 −0.511971 0.859003i \(-0.671085\pi\)
−0.511971 + 0.859003i \(0.671085\pi\)
\(108\) 5.46973e9 0.372260
\(109\) 1.28408e10i 0.834562i −0.908777 0.417281i \(-0.862983\pi\)
0.908777 0.417281i \(-0.137017\pi\)
\(110\) 5.26302e9 0.326792
\(111\) 1.07129e10i 0.635761i
\(112\) −2.31696e10 −1.31470
\(113\) 4.19928e9i 0.227920i 0.993485 + 0.113960i \(0.0363536\pi\)
−0.993485 + 0.113960i \(0.963646\pi\)
\(114\) 5.19473e9i 0.269798i
\(115\) 1.79561e10i 0.892738i
\(116\) −2.34452e10 −1.11626
\(117\) 6.08436e9i 0.277515i
\(118\) 2.81040e10 2.73119e10i 1.22845 1.19383i
\(119\) −5.23024e10 −2.19173
\(120\) 3.29744e10i 1.32517i
\(121\) 2.54784e10 0.982304
\(122\) 1.62642e10 0.601773
\(123\) −6.76011e9 −0.240120
\(124\) 3.16252e10i 1.07876i
\(125\) −2.47957e9 −0.0812505
\(126\) 2.95317e10i 0.929900i
\(127\) 4.28326e10 1.29645 0.648225 0.761449i \(-0.275511\pi\)
0.648225 + 0.761449i \(0.275511\pi\)
\(128\) 6.19784e10i 1.80381i
\(129\) 2.07050e10i 0.579598i
\(130\) 7.59379e10 2.04523
\(131\) 7.08750e10i 1.83712i 0.395285 + 0.918558i \(0.370646\pi\)
−0.395285 + 0.918558i \(0.629354\pi\)
\(132\) 5.95353e9i 0.148561i
\(133\) 1.84888e10 0.444272
\(134\) 3.05683e10 0.707534
\(135\) 1.23756e10 0.275994
\(136\) 1.00214e11i 2.15394i
\(137\) 6.98990e10 1.44833 0.724166 0.689625i \(-0.242225\pi\)
0.724166 + 0.689625i \(0.242225\pi\)
\(138\) 3.08128e10 0.615654
\(139\) 1.83568e7 0.000353771 0.000176886 1.00000i \(-0.499944\pi\)
0.000176886 1.00000i \(0.499944\pi\)
\(140\) −2.42970e11 −4.51766
\(141\) 1.16637e10i 0.209287i
\(142\) 3.47115e10i 0.601218i
\(143\) −6.62253e9 −0.110750
\(144\) 1.66615e10 0.269093
\(145\) −5.30465e10 −0.827593
\(146\) −3.34051e10 −0.503556
\(147\) −6.54773e10 −0.953902
\(148\) 1.51249e11i 2.13002i
\(149\) 6.81370e10i 0.927795i −0.885889 0.463897i \(-0.846451\pi\)
0.885889 0.463897i \(-0.153549\pi\)
\(150\) 7.93566e10i 1.04503i
\(151\) 1.12413e11i 1.43196i 0.698119 + 0.715981i \(0.254020\pi\)
−0.698119 + 0.715981i \(0.745980\pi\)
\(152\) 3.54253e10i 0.436612i
\(153\) 3.76113e10 0.448602
\(154\) 3.21438e10 0.371103
\(155\) 7.15542e10i 0.799791i
\(156\) 8.59010e10i 0.929769i
\(157\) 1.54822e11i 1.62306i 0.584313 + 0.811528i \(0.301364\pi\)
−0.584313 + 0.811528i \(0.698636\pi\)
\(158\) 8.58864e10i 0.872246i
\(159\) −7.19169e10 −0.707693
\(160\) 3.27253e10i 0.312093i
\(161\) 1.09667e11i 1.01379i
\(162\) 2.12367e10i 0.190332i
\(163\) 2.52617e10 0.219545 0.109773 0.993957i \(-0.464988\pi\)
0.109773 + 0.993957i \(0.464988\pi\)
\(164\) −9.54414e10 −0.804484
\(165\) 1.34703e10i 0.110143i
\(166\) −9.82229e10 −0.779242
\(167\) −8.02086e9 −0.0617502 −0.0308751 0.999523i \(-0.509829\pi\)
−0.0308751 + 0.999523i \(0.509829\pi\)
\(168\) 2.01391e11i 1.50485i
\(169\) 4.23047e10 0.306871
\(170\) 4.69421e11i 3.30611i
\(171\) −1.32955e10 −0.0909336
\(172\) 2.92320e11i 1.94185i
\(173\) 2.51337e11i 1.62190i −0.585113 0.810952i \(-0.698950\pi\)
0.585113 0.810952i \(-0.301050\pi\)
\(174\) 9.10280e10i 0.570728i
\(175\) −2.82441e11 −1.72083
\(176\) 1.81353e10i 0.107389i
\(177\) −6.99028e10 7.19299e10i −0.402372 0.414041i
\(178\) 5.37644e11 3.00881
\(179\) 1.16008e11i 0.631283i 0.948878 + 0.315642i \(0.102220\pi\)
−0.948878 + 0.315642i \(0.897780\pi\)
\(180\) 1.74723e11 0.924673
\(181\) 1.96522e11 1.01162 0.505811 0.862644i \(-0.331193\pi\)
0.505811 + 0.862644i \(0.331193\pi\)
\(182\) 4.63790e11 2.32255
\(183\) 4.16269e10i 0.202824i
\(184\) 2.10127e11 0.996308
\(185\) 3.42211e11i 1.57919i
\(186\) 1.22787e11 0.551555
\(187\) 4.09381e10i 0.179027i
\(188\) 1.64672e11i 0.701182i
\(189\) 7.55842e10 0.313416
\(190\) 1.65939e11i 0.670163i
\(191\) 4.12495e11i 1.62275i −0.584524 0.811376i \(-0.698719\pi\)
0.584524 0.811376i \(-0.301281\pi\)
\(192\) −1.77767e11 −0.681310
\(193\) −2.45939e11 −0.918418 −0.459209 0.888328i \(-0.651867\pi\)
−0.459209 + 0.888328i \(0.651867\pi\)
\(194\) −4.31881e11 −1.57165
\(195\) 1.94357e11i 0.689330i
\(196\) −9.24429e11 −3.19590
\(197\) −3.72976e10 −0.125704 −0.0628521 0.998023i \(-0.520020\pi\)
−0.0628521 + 0.998023i \(0.520020\pi\)
\(198\) −2.31151e10 −0.0759573
\(199\) 4.63716e11 1.48589 0.742946 0.669352i \(-0.233428\pi\)
0.742946 + 0.669352i \(0.233428\pi\)
\(200\) 5.41170e11i 1.69116i
\(201\) 7.82371e10i 0.238469i
\(202\) −7.60056e11 −2.25990
\(203\) −3.23981e11 −0.939809
\(204\) 5.31009e11 1.50297
\(205\) −2.15943e11 −0.596444
\(206\) −4.02167e11 −1.08410
\(207\) 7.88631e10i 0.207502i
\(208\) 2.61666e11i 0.672095i
\(209\) 1.44715e10i 0.0362896i
\(210\) 9.43353e11i 2.30982i
\(211\) 7.10941e11i 1.69989i −0.526871 0.849946i \(-0.676635\pi\)
0.526871 0.849946i \(-0.323365\pi\)
\(212\) −1.01535e12 −2.37102
\(213\) 8.88414e10 0.202636
\(214\) 7.87224e11i 1.75400i
\(215\) 6.61394e11i 1.43969i
\(216\) 1.44823e11i 0.308013i
\(217\) 4.37017e11i 0.908238i
\(218\) −7.03874e11 −1.42959
\(219\) 8.54977e10i 0.169720i
\(220\) 1.90178e11i 0.369017i
\(221\) 5.90679e11i 1.12044i
\(222\) 5.87236e11 1.08905
\(223\) 8.81026e11 1.59759 0.798794 0.601605i \(-0.205472\pi\)
0.798794 + 0.601605i \(0.205472\pi\)
\(224\) 1.99870e11i 0.354411i
\(225\) 2.03107e11 0.352219
\(226\) 2.30186e11 0.390424
\(227\) 5.30184e11i 0.879625i −0.898090 0.439813i \(-0.855045\pi\)
0.898090 0.439813i \(-0.144955\pi\)
\(228\) −1.87710e11 −0.304659
\(229\) 5.38590e11i 0.855226i 0.903962 + 0.427613i \(0.140645\pi\)
−0.903962 + 0.427613i \(0.859355\pi\)
\(230\) 9.84276e11 1.52925
\(231\) 8.22697e10i 0.125078i
\(232\) 6.20763e11i 0.923605i
\(233\) 3.84999e11i 0.560635i −0.959907 0.280318i \(-0.909560\pi\)
0.959907 0.280318i \(-0.0904398\pi\)
\(234\) −3.33518e11 −0.475379
\(235\) 3.72582e11i 0.519856i
\(236\) −9.86910e11 1.01553e12i −1.34809 1.38718i
\(237\) 2.19819e11 0.293984
\(238\) 2.86698e12i 3.75440i
\(239\) −1.14818e12 −1.47238 −0.736190 0.676775i \(-0.763377\pi\)
−0.736190 + 0.676775i \(0.763377\pi\)
\(240\) 5.32231e11 0.668412
\(241\) −4.12541e11 −0.507436 −0.253718 0.967278i \(-0.581654\pi\)
−0.253718 + 0.967278i \(0.581654\pi\)
\(242\) 1.39661e12i 1.68267i
\(243\) −5.43536e10 −0.0641500
\(244\) 5.87702e11i 0.679529i
\(245\) −2.09159e12 −2.36944
\(246\) 3.70559e11i 0.411322i
\(247\) 2.08803e11i 0.227119i
\(248\) 8.37345e11 0.892578
\(249\) 2.51394e11i 0.262638i
\(250\) 1.35919e11i 0.139181i
\(251\) −7.38749e11 −0.741530 −0.370765 0.928727i \(-0.620904\pi\)
−0.370765 + 0.928727i \(0.620904\pi\)
\(252\) 1.06712e12 1.05005
\(253\) −8.58386e10 −0.0828094
\(254\) 2.34789e12i 2.22080i
\(255\) 1.20145e12 1.11430
\(256\) −2.09989e12 −1.90984
\(257\) 1.59405e12 1.42180 0.710898 0.703296i \(-0.248289\pi\)
0.710898 + 0.703296i \(0.248289\pi\)
\(258\) −1.13496e12 −0.992843
\(259\) 2.09005e12i 1.79332i
\(260\) 2.74400e12i 2.30949i
\(261\) 2.32979e11 0.192360
\(262\) 3.88505e12 3.14696
\(263\) −1.52501e12 −1.21197 −0.605987 0.795475i \(-0.707222\pi\)
−0.605987 + 0.795475i \(0.707222\pi\)
\(264\) −1.57633e11 −0.122921
\(265\) −2.29729e12 −1.75787
\(266\) 1.01347e12i 0.761033i
\(267\) 1.37606e12i 1.01410i
\(268\) 1.10458e12i 0.798954i
\(269\) 2.61925e12i 1.85959i −0.368083 0.929793i \(-0.619986\pi\)
0.368083 0.929793i \(-0.380014\pi\)
\(270\) 6.78378e11i 0.472773i
\(271\) −2.22168e12 −1.51997 −0.759984 0.649942i \(-0.774793\pi\)
−0.759984 + 0.649942i \(0.774793\pi\)
\(272\) 1.61753e12 1.08644
\(273\) 1.18703e12i 0.782799i
\(274\) 3.83155e12i 2.48097i
\(275\) 2.21072e11i 0.140563i
\(276\) 1.11341e12i 0.695202i
\(277\) 1.07104e12 0.656758 0.328379 0.944546i \(-0.393498\pi\)
0.328379 + 0.944546i \(0.393498\pi\)
\(278\) 1.00624e9i 0.000606006i
\(279\) 3.14265e11i 0.185898i
\(280\) 6.43317e12i 3.73796i
\(281\) −9.21119e11 −0.525756 −0.262878 0.964829i \(-0.584672\pi\)
−0.262878 + 0.964829i \(0.584672\pi\)
\(282\) 6.39353e11 0.358505
\(283\) 1.71565e12i 0.945142i 0.881293 + 0.472571i \(0.156674\pi\)
−0.881293 + 0.472571i \(0.843326\pi\)
\(284\) 1.25429e12 0.678901
\(285\) −4.24708e11 −0.225874
\(286\) 3.63018e11i 0.189713i
\(287\) −1.31887e12 −0.677318
\(288\) 1.43729e11i 0.0725408i
\(289\) 1.63537e12 0.811197
\(290\) 2.90777e12i 1.41765i
\(291\) 1.10536e12i 0.529713i
\(292\) 1.20708e12i 0.568621i
\(293\) 9.31552e10 0.0431389 0.0215694 0.999767i \(-0.493134\pi\)
0.0215694 + 0.999767i \(0.493134\pi\)
\(294\) 3.58917e12i 1.63402i
\(295\) −2.23295e12 2.29771e12i −0.999470 1.02845i
\(296\) 4.00464e12 1.76240
\(297\) 5.91612e10i 0.0256009i
\(298\) −3.73497e12 −1.58930
\(299\) −1.23853e12 −0.518263
\(300\) 2.86753e12 1.18005
\(301\) 4.03946e12i 1.63490i
\(302\) 6.16198e12 2.45293
\(303\) 1.94530e12i 0.761683i
\(304\) −5.71791e11 −0.220226
\(305\) 1.32972e12i 0.503802i
\(306\) 2.06169e12i 0.768450i
\(307\) −1.27727e12 −0.468374 −0.234187 0.972192i \(-0.575243\pi\)
−0.234187 + 0.972192i \(0.575243\pi\)
\(308\) 1.16151e12i 0.419053i
\(309\) 1.02931e12i 0.365389i
\(310\) 3.92228e12 1.37003
\(311\) 2.75148e12 0.945723 0.472862 0.881137i \(-0.343221\pi\)
0.472862 + 0.881137i \(0.343221\pi\)
\(312\) −2.27442e12 −0.769302
\(313\) 2.13941e12i 0.712151i 0.934457 + 0.356075i \(0.115885\pi\)
−0.934457 + 0.356075i \(0.884115\pi\)
\(314\) 8.48664e12 2.78027
\(315\) 2.41444e12 0.778508
\(316\) 3.10348e12 0.984949
\(317\) 1.34809e12 0.421137 0.210568 0.977579i \(-0.432469\pi\)
0.210568 + 0.977579i \(0.432469\pi\)
\(318\) 3.94216e12i 1.21227i
\(319\) 2.53586e11i 0.0767666i
\(320\) −5.67853e12 −1.69233
\(321\) 2.01484e12 0.591174
\(322\) 6.01146e12 1.73660
\(323\) −1.29075e12 −0.367137
\(324\) −7.67381e11 −0.214925
\(325\) 3.18976e12i 0.879712i
\(326\) 1.38473e12i 0.376078i
\(327\) 1.80151e12i 0.481835i
\(328\) 2.52702e12i 0.665639i
\(329\) 2.27554e12i 0.590345i
\(330\) −7.38381e11 −0.188673
\(331\) 5.34528e12 1.34534 0.672668 0.739944i \(-0.265148\pi\)
0.672668 + 0.739944i \(0.265148\pi\)
\(332\) 3.54926e12i 0.879928i
\(333\) 1.50298e12i 0.367057i
\(334\) 4.39668e11i 0.105777i
\(335\) 2.49918e12i 0.592344i
\(336\) 3.25060e12 0.759044
\(337\) 5.65028e11i 0.129993i 0.997885 + 0.0649965i \(0.0207036\pi\)
−0.997885 + 0.0649965i \(0.979296\pi\)
\(338\) 2.31896e12i 0.525665i
\(339\) 5.89143e11i 0.131590i
\(340\) 1.69624e13 3.73330
\(341\) −3.42062e11 −0.0741878
\(342\) 7.28801e11i 0.155768i
\(343\) −5.04266e12 −1.06216
\(344\) −7.73980e12 −1.60671
\(345\) 2.51918e12i 0.515422i
\(346\) −1.37772e13 −2.77830
\(347\) 3.89130e12i 0.773476i 0.922190 + 0.386738i \(0.126398\pi\)
−0.922190 + 0.386738i \(0.873602\pi\)
\(348\) 3.28927e12 0.644472
\(349\) 1.06678e12i 0.206039i −0.994679 0.103020i \(-0.967150\pi\)
0.994679 0.103020i \(-0.0328504\pi\)
\(350\) 1.54822e13i 2.94775i
\(351\) 8.53613e11i 0.160223i
\(352\) 1.56442e11 0.0289494
\(353\) 4.84504e11i 0.0883942i −0.999023 0.0441971i \(-0.985927\pi\)
0.999023 0.0441971i \(-0.0140730\pi\)
\(354\) −3.94288e12 + 3.83176e12i −0.709246 + 0.689258i
\(355\) 2.83792e12 0.503337
\(356\) 1.94276e13i 3.39758i
\(357\) 7.33782e12 1.26539
\(358\) 6.35907e12 1.08138
\(359\) 1.04808e13 1.75762 0.878808 0.477175i \(-0.158339\pi\)
0.878808 + 0.477175i \(0.158339\pi\)
\(360\) 4.62618e12i 0.765085i
\(361\) −5.67479e12 −0.925580
\(362\) 1.07725e13i 1.73290i
\(363\) −3.57453e12 −0.567134
\(364\) 1.67589e13i 2.62265i
\(365\) 2.73111e12i 0.421575i
\(366\) −2.28180e12 −0.347434
\(367\) 8.72911e12i 1.31111i −0.755147 0.655555i \(-0.772435\pi\)
0.755147 0.655555i \(-0.227565\pi\)
\(368\) 3.39161e12i 0.502536i
\(369\) 9.48417e11 0.138633
\(370\) 1.87585e13 2.70514
\(371\) −1.40307e13 −1.99623
\(372\) 4.43689e12i 0.622822i
\(373\) 7.39620e12 1.02439 0.512194 0.858870i \(-0.328833\pi\)
0.512194 + 0.858870i \(0.328833\pi\)
\(374\) −2.24404e12 −0.306671
\(375\) 3.47874e11 0.0469100
\(376\) 4.36005e12 0.580166
\(377\) 3.65889e12i 0.480444i
\(378\) 4.14319e12i 0.536878i
\(379\) −2.11206e12 −0.270091 −0.135045 0.990839i \(-0.543118\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(380\) −5.99616e12 −0.756755
\(381\) −6.00925e12 −0.748506
\(382\) −2.26112e13 −2.77975
\(383\) −1.52770e12 −0.185372 −0.0926862 0.995695i \(-0.529545\pi\)
−0.0926862 + 0.995695i \(0.529545\pi\)
\(384\) 8.69533e12i 1.04143i
\(385\) 2.62800e12i 0.310686i
\(386\) 1.34813e13i 1.57324i
\(387\) 2.90483e12i 0.334631i
\(388\) 1.56059e13i 1.77472i
\(389\) −6.15791e12 −0.691329 −0.345665 0.938358i \(-0.612347\pi\)
−0.345665 + 0.938358i \(0.612347\pi\)
\(390\) −1.06538e13 −1.18081
\(391\) 7.65614e12i 0.837772i
\(392\) 2.44763e13i 2.64433i
\(393\) 9.94349e12i 1.06066i
\(394\) 2.04449e12i 0.215330i
\(395\) 7.02185e12 0.730240
\(396\) 8.35257e11i 0.0857717i
\(397\) 2.95400e12i 0.299543i 0.988721 + 0.149771i \(0.0478537\pi\)
−0.988721 + 0.149771i \(0.952146\pi\)
\(398\) 2.54189e13i 2.54531i
\(399\) −2.59390e12 −0.256501
\(400\) 8.73489e12 0.853016
\(401\) 1.10122e13i 1.06206i 0.847352 + 0.531032i \(0.178196\pi\)
−0.847352 + 0.531032i \(0.821804\pi\)
\(402\) −4.28861e12 −0.408495
\(403\) −4.93547e12 −0.464305
\(404\) 2.74644e13i 2.55190i
\(405\) −1.73625e12 −0.159345
\(406\) 1.77592e13i 1.60988i
\(407\) −1.63592e12 −0.146484
\(408\) 1.40596e13i 1.24358i
\(409\) 1.11556e13i 0.974708i −0.873204 0.487354i \(-0.837962\pi\)
0.873204 0.487354i \(-0.162038\pi\)
\(410\) 1.18370e13i 1.02170i
\(411\) −9.80656e12 −0.836195
\(412\) 1.45322e13i 1.22418i
\(413\) −1.36378e13 1.40332e13i −1.13499 1.16791i
\(414\) −4.32292e12 −0.355448
\(415\) 8.03045e12i 0.652378i
\(416\) 2.25724e12 0.181180
\(417\) −2.57539e9 −0.000204250
\(418\) 7.93264e11 0.0621636
\(419\) 5.63550e12i 0.436377i 0.975907 + 0.218189i \(0.0700148\pi\)
−0.975907 + 0.218189i \(0.929985\pi\)
\(420\) 3.40878e13 2.60827
\(421\) 1.37108e12i 0.103670i 0.998656 + 0.0518349i \(0.0165070\pi\)
−0.998656 + 0.0518349i \(0.983493\pi\)
\(422\) −3.89706e13 −2.91189
\(423\) 1.63637e12i 0.120832i
\(424\) 2.68835e13i 1.96181i
\(425\) 1.97179e13 1.42206
\(426\) 4.86989e12i 0.347113i
\(427\) 8.12124e12i 0.572114i
\(428\) 2.84461e13 1.98063
\(429\) 9.29115e11 0.0639416
\(430\) −3.62547e13 −2.46616
\(431\) 2.81455e13i 1.89244i 0.323525 + 0.946219i \(0.395132\pi\)
−0.323525 + 0.946219i \(0.604868\pi\)
\(432\) −2.33755e12 −0.155361
\(433\) −1.64021e13 −1.07760 −0.538802 0.842432i \(-0.681123\pi\)
−0.538802 + 0.842432i \(0.681123\pi\)
\(434\) 2.39553e13 1.55580
\(435\) 7.44221e12 0.477811
\(436\) 2.54343e13i 1.61431i
\(437\) 2.70642e12i 0.169820i
\(438\) 4.68660e12 0.290728
\(439\) −2.05239e13 −1.25875 −0.629373 0.777103i \(-0.716688\pi\)
−0.629373 + 0.777103i \(0.716688\pi\)
\(440\) −5.03537e12 −0.305329
\(441\) 9.18621e12 0.550736
\(442\) −3.23784e13 −1.91930
\(443\) 3.21792e13i 1.88606i −0.332704 0.943031i \(-0.607961\pi\)
0.332704 0.943031i \(-0.392039\pi\)
\(444\) 2.12196e13i 1.22977i
\(445\) 4.39563e13i 2.51896i
\(446\) 4.82940e13i 2.73665i
\(447\) 9.55936e12i 0.535662i
\(448\) −3.46816e13 −1.92180
\(449\) −2.00652e13 −1.09954 −0.549772 0.835315i \(-0.685285\pi\)
−0.549772 + 0.835315i \(0.685285\pi\)
\(450\) 1.11334e13i 0.603346i
\(451\) 1.03231e12i 0.0553255i
\(452\) 8.31771e12i 0.440871i
\(453\) 1.57711e13i 0.826744i
\(454\) −2.90624e13 −1.50679
\(455\) 3.79183e13i 1.94443i
\(456\) 4.97004e12i 0.252078i
\(457\) 1.86358e13i 0.934905i −0.884018 0.467453i \(-0.845172\pi\)
0.884018 0.467453i \(-0.154828\pi\)
\(458\) 2.95231e13 1.46499
\(459\) −5.27672e12 −0.259001
\(460\) 3.55666e13i 1.72684i
\(461\) −1.98467e13 −0.953201 −0.476601 0.879120i \(-0.658131\pi\)
−0.476601 + 0.879120i \(0.658131\pi\)
\(462\) −4.50966e12 −0.214256
\(463\) 9.83106e12i 0.462057i −0.972947 0.231028i \(-0.925791\pi\)
0.972947 0.231028i \(-0.0742090\pi\)
\(464\) 1.00196e13 0.465864
\(465\) 1.00388e13i 0.461760i
\(466\) −2.11040e13 −0.960361
\(467\) 7.05766e12i 0.317743i 0.987299 + 0.158872i \(0.0507856\pi\)
−0.987299 + 0.158872i \(0.949214\pi\)
\(468\) 1.20516e13i 0.536803i
\(469\) 1.52637e13i 0.672662i
\(470\) 2.04233e13 0.890506
\(471\) 2.17209e13i 0.937072i
\(472\) −2.68884e13 + 2.61306e13i −1.14777 + 1.11542i
\(473\) 3.16177e12 0.133544
\(474\) 1.20495e13i 0.503591i
\(475\) −6.97023e12 −0.288257
\(476\) 1.03598e14 4.23951
\(477\) 1.00897e13 0.408587
\(478\) 6.29380e13i 2.52217i
\(479\) −1.57057e13 −0.622844 −0.311422 0.950272i \(-0.600805\pi\)
−0.311422 + 0.950272i \(0.600805\pi\)
\(480\) 4.59124e12i 0.180187i
\(481\) −2.36041e13 −0.916773
\(482\) 2.26136e13i 0.869231i
\(483\) 1.53859e13i 0.585310i
\(484\) −5.04663e13 −1.90009
\(485\) 3.53094e13i 1.31578i
\(486\) 2.97942e12i 0.109888i
\(487\) 3.55340e13 1.29718 0.648589 0.761139i \(-0.275359\pi\)
0.648589 + 0.761139i \(0.275359\pi\)
\(488\) −1.55607e13 −0.562250
\(489\) −3.54412e12 −0.126755
\(490\) 1.14651e14i 4.05881i
\(491\) 4.49539e13 1.57529 0.787644 0.616131i \(-0.211301\pi\)
0.787644 + 0.616131i \(0.211301\pi\)
\(492\) 1.33901e13 0.464469
\(493\) 2.26179e13 0.776638
\(494\) 1.14457e13 0.389051
\(495\) 1.88983e12i 0.0635911i
\(496\) 1.35154e13i 0.450215i
\(497\) 1.73326e13 0.571586
\(498\) 1.37803e13 0.449896
\(499\) 5.61991e13 1.81646 0.908232 0.418467i \(-0.137432\pi\)
0.908232 + 0.418467i \(0.137432\pi\)
\(500\) 4.91139e12 0.157165
\(501\) 1.12529e12 0.0356515
\(502\) 4.04950e13i 1.27023i
\(503\) 1.85153e12i 0.0575030i 0.999587 + 0.0287515i \(0.00915316\pi\)
−0.999587 + 0.0287515i \(0.990847\pi\)
\(504\) 2.82544e13i 0.868826i
\(505\) 6.21402e13i 1.89198i
\(506\) 4.70529e12i 0.141851i
\(507\) −5.93519e12 −0.177172
\(508\) −8.48405e13 −2.50775
\(509\) 6.65068e13i 1.94660i 0.229530 + 0.973302i \(0.426281\pi\)
−0.229530 + 0.973302i \(0.573719\pi\)
\(510\) 6.58579e13i 1.90878i
\(511\) 1.66802e13i 0.478738i
\(512\) 5.16407e13i 1.46772i
\(513\) 1.86531e12 0.0525005
\(514\) 8.73789e13i 2.43552i
\(515\) 3.28801e13i 0.907605i
\(516\) 4.10113e13i 1.12113i
\(517\) −1.78111e12 −0.0482213
\(518\) 1.14567e14 3.07193
\(519\) 3.52615e13i 0.936407i
\(520\) −7.26533e13 −1.91090
\(521\) 7.49443e13 1.95232 0.976158 0.217060i \(-0.0696467\pi\)
0.976158 + 0.217060i \(0.0696467\pi\)
\(522\) 1.27709e13i 0.329510i
\(523\) −2.65517e13 −0.678554 −0.339277 0.940686i \(-0.610182\pi\)
−0.339277 + 0.940686i \(0.610182\pi\)
\(524\) 1.40385e14i 3.55358i
\(525\) 3.96254e13 0.993520
\(526\) 8.35941e13i 2.07609i
\(527\) 3.05093e13i 0.750548i
\(528\) 2.54431e12i 0.0620012i
\(529\) 2.53732e13 0.612487
\(530\) 1.25927e14i 3.01121i
\(531\) 9.80709e12 + 1.00915e13i 0.232310 + 0.239047i
\(532\) −3.66215e13 −0.859366
\(533\) 1.48947e13i 0.346255i
\(534\) −7.54293e13 −1.73714
\(535\) 6.43614e13 1.46844
\(536\) −2.92461e13 −0.661064
\(537\) 1.62755e13i 0.364472i
\(538\) −1.43576e14 −3.18544
\(539\) 9.99873e12i 0.219787i
\(540\) −2.45130e13 −0.533860
\(541\) 8.54421e13i 1.84368i 0.387570 + 0.921840i \(0.373315\pi\)
−0.387570 + 0.921840i \(0.626685\pi\)
\(542\) 1.21782e14i 2.60368i
\(543\) −2.75713e13 −0.584061
\(544\) 1.39534e13i 0.292878i
\(545\) 5.75469e13i 1.19685i
\(546\) −6.50680e13 −1.34092
\(547\) −3.36039e13 −0.686205 −0.343102 0.939298i \(-0.611478\pi\)
−0.343102 + 0.939298i \(0.611478\pi\)
\(548\) −1.38452e14 −2.80154
\(549\) 5.84009e12i 0.117100i
\(550\) −1.21182e13 −0.240782
\(551\) −7.99539e12 −0.157428
\(552\) −2.94801e13 −0.575219
\(553\) 4.28859e13 0.829256
\(554\) 5.87095e13i 1.12502i
\(555\) 4.80109e13i 0.911748i
\(556\) −3.63601e10 −0.000684308
\(557\) −6.37800e13 −1.18962 −0.594810 0.803866i \(-0.702773\pi\)
−0.594810 + 0.803866i \(0.702773\pi\)
\(558\) −1.72266e13 −0.318441
\(559\) 4.56198e13 0.835785
\(560\) 1.03836e14 1.88542
\(561\) 5.74345e12i 0.103362i
\(562\) 5.04917e13i 0.900613i
\(563\) 5.16188e13i 0.912570i −0.889834 0.456285i \(-0.849180\pi\)
0.889834 0.456285i \(-0.150820\pi\)
\(564\) 2.31029e13i 0.404828i
\(565\) 1.88194e13i 0.326862i
\(566\) 9.40445e13 1.61902
\(567\) −1.06042e13 −0.180951
\(568\) 3.32101e13i 0.561731i
\(569\) 1.06813e14i 1.79087i −0.445190 0.895436i \(-0.646864\pi\)
0.445190 0.895436i \(-0.353136\pi\)
\(570\) 2.32806e13i 0.386919i
\(571\) 5.47878e13i 0.902616i 0.892368 + 0.451308i \(0.149042\pi\)
−0.892368 + 0.451308i \(0.850958\pi\)
\(572\) 1.31175e13 0.214226
\(573\) 5.78715e13i 0.936896i
\(574\) 7.22946e13i 1.16024i
\(575\) 4.13443e13i 0.657774i
\(576\) 2.49400e13 0.393354
\(577\) 7.67946e13 1.20075 0.600373 0.799720i \(-0.295019\pi\)
0.600373 + 0.799720i \(0.295019\pi\)
\(578\) 8.96436e13i 1.38957i
\(579\) 3.45042e13 0.530249
\(580\) 1.05072e14 1.60083
\(581\) 4.90459e13i 0.740836i
\(582\) 6.05912e13 0.907391
\(583\) 1.09821e13i 0.163058i
\(584\) 3.19602e13 0.470484
\(585\) 2.72675e13i 0.397985i
\(586\) 5.10635e12i 0.0738963i
\(587\) 2.35646e13i 0.338119i −0.985606 0.169059i \(-0.945927\pi\)
0.985606 0.169059i \(-0.0540729\pi\)
\(588\) 1.29694e14 1.84515
\(589\) 1.07849e13i 0.152139i
\(590\) −1.25950e14 + 1.22401e14i −1.76173 + 1.71208i
\(591\) 5.23271e12 0.0725754
\(592\) 6.46378e13i 0.888952i
\(593\) −3.97416e12 −0.0541966 −0.0270983 0.999633i \(-0.508627\pi\)
−0.0270983 + 0.999633i \(0.508627\pi\)
\(594\) 3.24295e12 0.0438539
\(595\) 2.34397e14 3.14317
\(596\) 1.34962e14i 1.79465i
\(597\) −6.50576e13 −0.857880
\(598\) 6.78907e13i 0.887778i
\(599\) 9.56501e13 1.24037 0.620185 0.784455i \(-0.287057\pi\)
0.620185 + 0.784455i \(0.287057\pi\)
\(600\) 7.59241e13i 0.976390i
\(601\) 1.19763e14i 1.52739i −0.645578 0.763694i \(-0.723384\pi\)
0.645578 0.763694i \(-0.276616\pi\)
\(602\) −2.21425e14 −2.80056
\(603\) 1.09764e13i 0.137680i
\(604\) 2.22662e14i 2.76988i
\(605\) −1.14184e14 −1.40873
\(606\) 1.06633e14 1.30475
\(607\) 9.12510e13 1.10737 0.553687 0.832725i \(-0.313221\pi\)
0.553687 + 0.832725i \(0.313221\pi\)
\(608\) 4.93250e12i 0.0593675i
\(609\) 4.54533e13 0.542599
\(610\) −7.28892e13 −0.863006
\(611\) −2.56989e13 −0.301793
\(612\) −7.44985e13 −0.867741
\(613\) 1.62743e14i 1.88018i 0.340928 + 0.940089i \(0.389259\pi\)
−0.340928 + 0.940089i \(0.610741\pi\)
\(614\) 7.00145e13i 0.802317i
\(615\) 3.02959e13 0.344357
\(616\) −3.07535e13 −0.346729
\(617\) −1.37883e13 −0.154200 −0.0771002 0.997023i \(-0.524566\pi\)
−0.0771002 + 0.997023i \(0.524566\pi\)
\(618\) 5.64224e13 0.625906
\(619\) 2.94466e13 0.324028 0.162014 0.986788i \(-0.448201\pi\)
0.162014 + 0.986788i \(0.448201\pi\)
\(620\) 1.41731e14i 1.54705i
\(621\) 1.10642e13i 0.119801i
\(622\) 1.50824e14i 1.62001i
\(623\) 2.68463e14i 2.86052i
\(624\) 3.67108e13i 0.388034i
\(625\) −8.96582e13 −0.940134
\(626\) 1.17273e14 1.21990
\(627\) 2.03030e12i 0.0209518i
\(628\) 3.06662e14i 3.13951i
\(629\) 1.45912e14i 1.48196i
\(630\) 1.32349e14i 1.33357i
\(631\) 5.81855e13 0.581658 0.290829 0.956775i \(-0.406069\pi\)
0.290829 + 0.956775i \(0.406069\pi\)
\(632\) 8.21714e13i 0.814958i
\(633\) 9.97422e13i 0.981433i
\(634\) 7.38964e13i 0.721402i
\(635\) −1.91958e14 −1.85925
\(636\) 1.42449e14 1.36891
\(637\) 1.44268e14i 1.37554i
\(638\) −1.39005e13 −0.131500
\(639\) −1.24641e13 −0.116992
\(640\) 2.77761e14i 2.58685i
\(641\) 7.38506e13 0.682439 0.341219 0.939984i \(-0.389160\pi\)
0.341219 + 0.939984i \(0.389160\pi\)
\(642\) 1.10444e14i 1.01267i
\(643\) −8.30666e13 −0.755739 −0.377869 0.925859i \(-0.623343\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(644\) 2.17223e14i 1.96099i
\(645\) 9.27910e13i 0.831204i
\(646\) 7.07530e13i 0.628901i
\(647\) 1.99383e14 1.75860 0.879300 0.476268i \(-0.158011\pi\)
0.879300 + 0.476268i \(0.158011\pi\)
\(648\) 2.03181e13i 0.177831i
\(649\) 1.09841e13 1.06745e13i 0.0953983 0.0927097i
\(650\) −1.74848e14 −1.50694
\(651\) 6.13118e13i 0.524371i
\(652\) −5.00370e13 −0.424671
\(653\) 4.42893e13 0.373021 0.186510 0.982453i \(-0.440282\pi\)
0.186510 + 0.982453i \(0.440282\pi\)
\(654\) 9.87508e13 0.825376
\(655\) 3.17632e14i 2.63462i
\(656\) 4.07879e13 0.335747
\(657\) 1.19950e13i 0.0979880i
\(658\) 1.24735e14 1.01125
\(659\) 9.75611e13i 0.784964i 0.919760 + 0.392482i \(0.128383\pi\)
−0.919760 + 0.392482i \(0.871617\pi\)
\(660\) 2.66812e13i 0.213052i
\(661\) 6.45464e12 0.0511523 0.0255761 0.999673i \(-0.491858\pi\)
0.0255761 + 0.999673i \(0.491858\pi\)
\(662\) 2.93005e14i 2.30454i
\(663\) 8.28699e13i 0.646888i
\(664\) 9.39743e13 0.728063
\(665\) −8.28588e13 −0.637133
\(666\) −8.23869e13 −0.628763
\(667\) 4.74251e13i 0.359235i
\(668\) 1.58873e13 0.119445
\(669\) −1.23605e14 −0.922367
\(670\) −1.36994e14 −1.01468
\(671\) 6.35665e12 0.0467322
\(672\) 2.80410e13i 0.204619i
\(673\) 4.61819e13i 0.334500i 0.985914 + 0.167250i \(0.0534887\pi\)
−0.985914 + 0.167250i \(0.946511\pi\)
\(674\) 3.09723e13 0.222676
\(675\) −2.84951e13 −0.203354
\(676\) −8.37949e13 −0.593586
\(677\) 8.77618e13 0.617110 0.308555 0.951207i \(-0.400155\pi\)
0.308555 + 0.951207i \(0.400155\pi\)
\(678\) −3.22942e13 −0.225412
\(679\) 2.15652e14i 1.49419i
\(680\) 4.49116e14i 3.08897i
\(681\) 7.43828e13i 0.507852i
\(682\) 1.87503e13i 0.127083i
\(683\) 2.02710e14i 1.36387i 0.731414 + 0.681933i \(0.238861\pi\)
−0.731414 + 0.681933i \(0.761139\pi\)
\(684\) 2.63350e13 0.175895
\(685\) −3.13258e14 −2.07706
\(686\) 2.76416e14i 1.81946i
\(687\) 7.55621e13i 0.493765i
\(688\) 1.24926e14i 0.810422i
\(689\) 1.58456e14i 1.02050i
\(690\) −1.38090e14 −0.882912
\(691\) 2.19696e14i 1.39454i −0.716806 0.697272i \(-0.754397\pi\)
0.716806 0.697272i \(-0.245603\pi\)
\(692\) 4.97834e14i 3.13728i
\(693\) 1.15421e13i 0.0722136i
\(694\) 2.13304e14 1.32495
\(695\) −8.22674e10 −0.000507345
\(696\) 8.70907e13i 0.533243i
\(697\) 9.20737e13 0.559721
\(698\) −5.84764e13 −0.352942
\(699\) 5.40139e13i 0.323683i
\(700\) 5.59444e14 3.32863
\(701\) 3.01975e14i 1.78394i 0.452091 + 0.891972i \(0.350678\pi\)
−0.452091 + 0.891972i \(0.649322\pi\)
\(702\) 4.67913e13 0.274460
\(703\) 5.15794e13i 0.300400i
\(704\) 2.71460e13i 0.156979i
\(705\) 5.22718e13i 0.300139i
\(706\) −2.65583e13 −0.151418
\(707\) 3.79521e14i 2.14852i
\(708\) 1.38460e14 + 1.42475e14i 0.778318 + 0.800888i
\(709\) −7.73009e13 −0.431473 −0.215736 0.976452i \(-0.569215\pi\)
−0.215736 + 0.976452i \(0.569215\pi\)
\(710\) 1.55562e14i 0.862209i
\(711\) −3.08398e13 −0.169732
\(712\) −5.14388e14 −2.81120
\(713\) −6.39715e13 −0.347167
\(714\) 4.02227e14i 2.16760i
\(715\) 2.96794e13 0.158827
\(716\) 2.29783e14i 1.22111i
\(717\) 1.61085e14 0.850079
\(718\) 5.74514e14i 3.01077i
\(719\) 2.62216e14i 1.36463i −0.731059 0.682314i \(-0.760974\pi\)
0.731059 0.682314i \(-0.239026\pi\)
\(720\) −7.46699e13 −0.385908
\(721\) 2.00815e14i 1.03067i
\(722\) 3.11067e14i 1.58551i
\(723\) 5.78778e13 0.292968
\(724\) −3.89260e14 −1.95680
\(725\) 1.22140e14 0.609775
\(726\) 1.95940e14i 0.971492i
\(727\) −1.80737e14 −0.889970 −0.444985 0.895538i \(-0.646791\pi\)
−0.444985 + 0.895538i \(0.646791\pi\)
\(728\) −4.43729e14 −2.17001
\(729\) 7.62560e12 0.0370370
\(730\) 1.49707e14 0.722153
\(731\) 2.82005e14i 1.35105i
\(732\) 8.24523e13i 0.392326i
\(733\) 3.23004e14 1.52647 0.763236 0.646120i \(-0.223610\pi\)
0.763236 + 0.646120i \(0.223610\pi\)
\(734\) −4.78491e14 −2.24591
\(735\) 2.93441e14 1.36800
\(736\) 2.92574e13 0.135471
\(737\) 1.19472e13 0.0549452
\(738\) 5.19880e13i 0.237477i
\(739\) 7.65366e13i 0.347254i 0.984812 + 0.173627i \(0.0555486\pi\)
−0.984812 + 0.173627i \(0.944451\pi\)
\(740\) 6.77833e14i 3.05467i
\(741\) 2.92943e13i 0.131127i
\(742\) 7.69100e14i 3.41951i
\(743\) −2.02718e14 −0.895257 −0.447629 0.894220i \(-0.647731\pi\)
−0.447629 + 0.894220i \(0.647731\pi\)
\(744\) −1.17476e14 −0.515330
\(745\) 3.05361e14i 1.33055i
\(746\) 4.05427e14i 1.75476i
\(747\) 3.52696e13i 0.151634i
\(748\) 8.10879e13i 0.346297i
\(749\) 3.93087e14 1.66755
\(750\) 1.90689e13i 0.0803562i
\(751\) 4.55437e14i 1.90647i 0.302238 + 0.953233i \(0.402266\pi\)
−0.302238 + 0.953233i \(0.597734\pi\)
\(752\) 7.03745e13i 0.292635i
\(753\) 1.03644e14 0.428122
\(754\) −2.00564e14 −0.822994
\(755\) 5.03787e14i 2.05358i
\(756\) −1.49713e14 −0.606248
\(757\) 1.19767e14 0.481788 0.240894 0.970551i \(-0.422559\pi\)
0.240894 + 0.970551i \(0.422559\pi\)
\(758\) 1.15774e14i 0.462662i
\(759\) 1.20428e13 0.0478100
\(760\) 1.58761e14i 0.626148i
\(761\) −3.20270e14 −1.25485 −0.627427 0.778676i \(-0.715892\pi\)
−0.627427 + 0.778676i \(0.715892\pi\)
\(762\) 3.29400e14i 1.28218i
\(763\) 3.51468e14i 1.35913i
\(764\) 8.17048e14i 3.13893i
\(765\) −1.68558e14 −0.643343
\(766\) 8.37419e13i 0.317540i
\(767\) 1.58485e14 1.54018e14i 0.597050 0.580224i
\(768\) 2.94606e14 1.10265
\(769\) 1.47981e14i 0.550268i 0.961406 + 0.275134i \(0.0887223\pi\)
−0.961406 + 0.275134i \(0.911278\pi\)
\(770\) −1.44055e14 −0.532200
\(771\) −2.23639e14 −0.820874
\(772\) 4.87142e14 1.77652
\(773\) 4.29167e13i 0.155500i −0.996973 0.0777498i \(-0.975226\pi\)
0.996973 0.0777498i \(-0.0247735\pi\)
\(774\) 1.59230e14 0.573218
\(775\) 1.64755e14i 0.589290i
\(776\) 4.13200e14 1.46842
\(777\) 2.93226e14i 1.03537i
\(778\) 3.37549e14i 1.18424i
\(779\) −3.25478e13 −0.113458