Properties

Label 177.11.c.a.58.6
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 58.6
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.95

$q$-expansion

\(f(q)\) \(=\) \(q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +26424.5i q^{10} +193821. i q^{11} -332756. q^{12} -998.798i q^{13} -935510. i q^{14} -63618.1 q^{15} +2.14819e6 q^{16} +1.44654e6 q^{17} -1.14700e6i q^{18} -1.03387e6 q^{19} +1.07551e6 q^{20} +2.25228e6 q^{21} +1.12947e7 q^{22} +3.69797e6i q^{23} +1.10191e7i q^{24} -9.56000e6 q^{25} -58203.6 q^{26} +2.76145e6 q^{27} -3.80765e7 q^{28} -1.48845e7 q^{29} +3.70726e6i q^{30} -2.62609e7i q^{31} -4.47557e7i q^{32} +2.71924e7i q^{33} -8.42951e7i q^{34} -7.27967e6 q^{35} -4.66844e7 q^{36} -9.93025e7i q^{37} +6.02473e7i q^{38} -140127. i q^{39} -3.56153e7i q^{40} -2.16870e8 q^{41} -1.31248e8i q^{42} +5.20592e7i q^{43} -4.59709e8i q^{44} -8.92538e6 q^{45} +2.15494e8 q^{46} -4.33749e8i q^{47} +3.01383e8 q^{48} -2.47522e7 q^{49} +5.57096e8i q^{50} +2.02944e8 q^{51} +2.36896e6i q^{52} -4.32486e8 q^{53} -1.60920e8i q^{54} -8.78895e7i q^{55} +1.26089e9i q^{56} -1.45048e8 q^{57} +8.67376e8i q^{58} +(-7.62493e7 - 7.10847e8i) q^{59} +1.50890e8 q^{60} +5.30576e8i q^{61} -1.53032e9 q^{62} +3.15986e8 q^{63} -4.08332e8 q^{64} +452911. i q^{65} +1.58460e9 q^{66} -1.25723e9i q^{67} -3.43092e9 q^{68} +5.18810e8i q^{69} +4.24213e8i q^{70} -5.22195e8 q^{71} +1.54594e9i q^{72} -3.99640e8i q^{73} -5.78672e9 q^{74} -1.34123e9 q^{75} +2.45215e9 q^{76} +3.11156e9i q^{77} -8.16573e6 q^{78} -4.13264e9 q^{79} -9.74109e8 q^{80} +3.87420e8 q^{81} +1.26378e10i q^{82} +1.61202e9i q^{83} -5.34199e9 q^{84} -6.55942e8 q^{85} +3.03368e9 q^{86} -2.08824e9 q^{87} -1.52231e10 q^{88} +5.28076e9i q^{89} +5.20114e8i q^{90} -1.60345e7i q^{91} -8.77089e9i q^{92} -3.68430e9i q^{93} -2.52761e10 q^{94} +4.68815e8 q^{95} -6.27905e9i q^{96} -8.89000e9i q^{97} +1.44240e9i q^{98} +3.81499e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 58.2736i 1.82105i −0.413454 0.910525i \(-0.635678\pi\)
0.413454 0.910525i \(-0.364322\pi\)
\(3\) 140.296 0.577350
\(4\) −2371.81 −2.31622
\(5\) −453.456 −0.145106 −0.0725530 0.997365i \(-0.523115\pi\)
−0.0725530 + 0.997365i \(0.523115\pi\)
\(6\) 8175.56i 1.05138i
\(7\) 16053.8 0.955183 0.477591 0.878582i \(-0.341510\pi\)
0.477591 + 0.878582i \(0.341510\pi\)
\(8\) 78542.0i 2.39691i
\(9\) 19683.0 0.333333
\(10\) 26424.5i 0.264245i
\(11\) 193821.i 1.20348i 0.798692 + 0.601739i \(0.205525\pi\)
−0.798692 + 0.601739i \(0.794475\pi\)
\(12\) −332756. −1.33727
\(13\) 998.798i 0.00269005i −0.999999 0.00134503i \(-0.999572\pi\)
0.999999 0.00134503i \(-0.000428135\pi\)
\(14\) 935510.i 1.73944i
\(15\) −63618.1 −0.0837770
\(16\) 2.14819e6 2.04867
\(17\) 1.44654e6 1.01879 0.509396 0.860532i \(-0.329869\pi\)
0.509396 + 0.860532i \(0.329869\pi\)
\(18\) 1.14700e6i 0.607017i
\(19\) −1.03387e6 −0.417540 −0.208770 0.977965i \(-0.566946\pi\)
−0.208770 + 0.977965i \(0.566946\pi\)
\(20\) 1.07551e6 0.336098
\(21\) 2.25228e6 0.551475
\(22\) 1.12947e7 2.19160
\(23\) 3.69797e6i 0.574545i 0.957849 + 0.287272i \(0.0927485\pi\)
−0.957849 + 0.287272i \(0.907252\pi\)
\(24\) 1.10191e7i 1.38386i
\(25\) −9.56000e6 −0.978944
\(26\) −58203.6 −0.00489872
\(27\) 2.76145e6 0.192450
\(28\) −3.80765e7 −2.21242
\(29\) −1.48845e7 −0.725681 −0.362840 0.931851i \(-0.618193\pi\)
−0.362840 + 0.931851i \(0.618193\pi\)
\(30\) 3.70726e6i 0.152562i
\(31\) 2.62609e7i 0.917279i −0.888622 0.458640i \(-0.848337\pi\)
0.888622 0.458640i \(-0.151663\pi\)
\(32\) 4.47557e7i 1.33382i
\(33\) 2.71924e7i 0.694829i
\(34\) 8.42951e7i 1.85527i
\(35\) −7.27967e6 −0.138603
\(36\) −4.66844e7 −0.772075
\(37\) 9.93025e7i 1.43203i −0.698086 0.716014i \(-0.745965\pi\)
0.698086 0.716014i \(-0.254035\pi\)
\(38\) 6.02473e7i 0.760361i
\(39\) 140127.i 0.00155310i
\(40\) 3.56153e7i 0.347806i
\(41\) −2.16870e8 −1.87189 −0.935944 0.352150i \(-0.885451\pi\)
−0.935944 + 0.352150i \(0.885451\pi\)
\(42\) 1.31248e8i 1.00426i
\(43\) 5.20592e7i 0.354124i 0.984200 + 0.177062i \(0.0566593\pi\)
−0.984200 + 0.177062i \(0.943341\pi\)
\(44\) 4.59709e8i 2.78753i
\(45\) −8.92538e6 −0.0483686
\(46\) 2.15494e8 1.04627
\(47\) 4.33749e8i 1.89125i −0.325260 0.945625i \(-0.605452\pi\)
0.325260 0.945625i \(-0.394548\pi\)
\(48\) 3.01383e8 1.18280
\(49\) −2.47522e7 −0.0876260
\(50\) 5.57096e8i 1.78271i
\(51\) 2.02944e8 0.588200
\(52\) 2.36896e6i 0.00623077i
\(53\) −4.32486e8 −1.03417 −0.517086 0.855934i \(-0.672983\pi\)
−0.517086 + 0.855934i \(0.672983\pi\)
\(54\) 1.60920e8i 0.350461i
\(55\) 8.78895e7i 0.174632i
\(56\) 1.26089e9i 2.28949i
\(57\) −1.45048e8 −0.241067
\(58\) 8.67376e8i 1.32150i
\(59\) −7.62493e7 7.10847e8i −0.106654 0.994296i
\(60\) 1.50890e8 0.194046
\(61\) 5.30576e8i 0.628201i 0.949390 + 0.314100i \(0.101703\pi\)
−0.949390 + 0.314100i \(0.898297\pi\)
\(62\) −1.53032e9 −1.67041
\(63\) 3.15986e8 0.318394
\(64\) −4.08332e8 −0.380288
\(65\) 452911.i 0.000390343i
\(66\) 1.58460e9 1.26532
\(67\) 1.25723e9i 0.931196i −0.884996 0.465598i \(-0.845839\pi\)
0.884996 0.465598i \(-0.154161\pi\)
\(68\) −3.43092e9 −2.35975
\(69\) 5.18810e8i 0.331714i
\(70\) 4.24213e8i 0.252403i
\(71\) −5.22195e8 −0.289428 −0.144714 0.989474i \(-0.546226\pi\)
−0.144714 + 0.989474i \(0.546226\pi\)
\(72\) 1.54594e9i 0.798971i
\(73\) 3.99640e8i 0.192777i −0.995344 0.0963885i \(-0.969271\pi\)
0.995344 0.0963885i \(-0.0307291\pi\)
\(74\) −5.78672e9 −2.60780
\(75\) −1.34123e9 −0.565194
\(76\) 2.45215e9 0.967116
\(77\) 3.11156e9i 1.14954i
\(78\) −8.16573e6 −0.00282828
\(79\) −4.13264e9 −1.34305 −0.671526 0.740981i \(-0.734361\pi\)
−0.671526 + 0.740981i \(0.734361\pi\)
\(80\) −9.74109e8 −0.297275
\(81\) 3.87420e8 0.111111
\(82\) 1.26378e10i 3.40880i
\(83\) 1.61202e9i 0.409243i 0.978841 + 0.204621i \(0.0655963\pi\)
−0.978841 + 0.204621i \(0.934404\pi\)
\(84\) −5.34199e9 −1.27734
\(85\) −6.55942e8 −0.147833
\(86\) 3.03368e9 0.644878
\(87\) −2.08824e9 −0.418972
\(88\) −1.52231e10 −2.88463
\(89\) 5.28076e9i 0.945685i 0.881147 + 0.472842i \(0.156772\pi\)
−0.881147 + 0.472842i \(0.843228\pi\)
\(90\) 5.20114e8i 0.0880818i
\(91\) 1.60345e7i 0.00256949i
\(92\) 8.77089e9i 1.33077i
\(93\) 3.68430e9i 0.529591i
\(94\) −2.52761e10 −3.44406
\(95\) 4.68815e8 0.0605875
\(96\) 6.27905e9i 0.770084i
\(97\) 8.89000e9i 1.03525i −0.855609 0.517623i \(-0.826817\pi\)
0.855609 0.517623i \(-0.173183\pi\)
\(98\) 1.44240e9i 0.159571i
\(99\) 3.81499e9i 0.401160i
\(100\) 2.26745e10 2.26745
\(101\) 1.39205e10i 1.32449i −0.749288 0.662245i \(-0.769604\pi\)
0.749288 0.662245i \(-0.230396\pi\)
\(102\) 1.18263e10i 1.07114i
\(103\) 3.01374e9i 0.259968i 0.991516 + 0.129984i \(0.0414925\pi\)
−0.991516 + 0.129984i \(0.958507\pi\)
\(104\) 7.84476e7 0.00644782
\(105\) −1.02131e9 −0.0800223
\(106\) 2.52025e10i 1.88328i
\(107\) 1.02881e10 0.733526 0.366763 0.930314i \(-0.380466\pi\)
0.366763 + 0.930314i \(0.380466\pi\)
\(108\) −6.54964e9 −0.445758
\(109\) 7.35418e9i 0.477971i −0.971023 0.238986i \(-0.923185\pi\)
0.971023 0.238986i \(-0.0768149\pi\)
\(110\) −5.12164e9 −0.318014
\(111\) 1.39318e10i 0.826782i
\(112\) 3.44865e10 1.95686
\(113\) 5.92428e9i 0.321546i −0.986991 0.160773i \(-0.948601\pi\)
0.986991 0.160773i \(-0.0513987\pi\)
\(114\) 8.45247e9i 0.438995i
\(115\) 1.67687e9i 0.0833699i
\(116\) 3.53034e10 1.68084
\(117\) 1.96593e7i 0.000896684i
\(118\) −4.14236e10 + 4.44332e9i −1.81066 + 0.194222i
\(119\) 2.32224e10 0.973133
\(120\) 4.99670e9i 0.200806i
\(121\) −1.16293e10 −0.448362
\(122\) 3.09186e10 1.14399
\(123\) −3.04260e10 −1.08073
\(124\) 6.22860e10i 2.12462i
\(125\) 8.76332e9 0.287157
\(126\) 1.84137e10i 0.579812i
\(127\) −3.03560e10 −0.918809 −0.459405 0.888227i \(-0.651937\pi\)
−0.459405 + 0.888227i \(0.651937\pi\)
\(128\) 2.20349e10i 0.641300i
\(129\) 7.30371e9i 0.204454i
\(130\) 2.63928e7 0.000710834
\(131\) 2.23580e10i 0.579531i −0.957098 0.289766i \(-0.906423\pi\)
0.957098 0.289766i \(-0.0935773\pi\)
\(132\) 6.44953e10i 1.60938i
\(133\) −1.65975e10 −0.398827
\(134\) −7.32634e10 −1.69575
\(135\) −1.25220e9 −0.0279257
\(136\) 1.13614e11i 2.44196i
\(137\) −1.67018e9 −0.0346068 −0.0173034 0.999850i \(-0.505508\pi\)
−0.0173034 + 0.999850i \(0.505508\pi\)
\(138\) 3.02330e10 0.604067
\(139\) −2.92344e10 −0.563404 −0.281702 0.959502i \(-0.590899\pi\)
−0.281702 + 0.959502i \(0.590899\pi\)
\(140\) 1.72660e10 0.321035
\(141\) 6.08532e10i 1.09191i
\(142\) 3.04302e10i 0.527063i
\(143\) 1.93588e8 0.00323742
\(144\) 4.22828e10 0.682891
\(145\) 6.74949e9 0.105301
\(146\) −2.32885e10 −0.351057
\(147\) −3.47263e9 −0.0505909
\(148\) 2.35527e11i 3.31690i
\(149\) 3.42814e10i 0.466796i 0.972381 + 0.233398i \(0.0749845\pi\)
−0.972381 + 0.233398i \(0.925015\pi\)
\(150\) 7.81584e10i 1.02925i
\(151\) 1.37379e11i 1.75000i 0.484127 + 0.874998i \(0.339137\pi\)
−0.484127 + 0.874998i \(0.660863\pi\)
\(152\) 8.12022e10i 1.00081i
\(153\) 2.84722e10 0.339598
\(154\) 1.81322e11 2.09337
\(155\) 1.19082e10i 0.133103i
\(156\) 3.32356e8i 0.00359734i
\(157\) 2.67147e10i 0.280060i 0.990147 + 0.140030i \(0.0447199\pi\)
−0.990147 + 0.140030i \(0.955280\pi\)
\(158\) 2.40824e11i 2.44576i
\(159\) −6.06761e10 −0.597079
\(160\) 2.02947e10i 0.193546i
\(161\) 5.93663e10i 0.548795i
\(162\) 2.25764e10i 0.202339i
\(163\) −3.14499e10 −0.273326 −0.136663 0.990618i \(-0.543638\pi\)
−0.136663 + 0.990618i \(0.543638\pi\)
\(164\) 5.14375e11 4.33571
\(165\) 1.23306e10i 0.100824i
\(166\) 9.39384e10 0.745251
\(167\) 1.78444e11 1.37379 0.686894 0.726757i \(-0.258974\pi\)
0.686894 + 0.726757i \(0.258974\pi\)
\(168\) 1.76899e11i 1.32184i
\(169\) 1.37857e11 0.999993
\(170\) 3.82241e10i 0.269211i
\(171\) −2.03497e10 −0.139180
\(172\) 1.23475e11i 0.820231i
\(173\) 1.88237e11i 1.21472i −0.794428 0.607358i \(-0.792229\pi\)
0.794428 0.607358i \(-0.207771\pi\)
\(174\) 1.21689e11i 0.762969i
\(175\) −1.53474e11 −0.935071
\(176\) 4.16365e11i 2.46553i
\(177\) −1.06975e10 9.97290e10i −0.0615765 0.574057i
\(178\) 3.07729e11 1.72214
\(179\) 1.10184e11i 0.599588i 0.954004 + 0.299794i \(0.0969179\pi\)
−0.954004 + 0.299794i \(0.903082\pi\)
\(180\) 2.11693e10 0.112033
\(181\) −1.39727e11 −0.719265 −0.359632 0.933094i \(-0.617098\pi\)
−0.359632 + 0.933094i \(0.617098\pi\)
\(182\) −9.34386e8 −0.00467917
\(183\) 7.44378e10i 0.362692i
\(184\) −2.90446e11 −1.37713
\(185\) 4.50293e10i 0.207796i
\(186\) −2.14698e11 −0.964412
\(187\) 2.80371e11i 1.22610i
\(188\) 1.02877e12i 4.38056i
\(189\) 4.43316e10 0.183825
\(190\) 2.73195e10i 0.110333i
\(191\) 3.88976e11i 1.53023i −0.643896 0.765113i \(-0.722683\pi\)
0.643896 0.765113i \(-0.277317\pi\)
\(192\) −5.72873e10 −0.219560
\(193\) 1.03390e11 0.386092 0.193046 0.981190i \(-0.438163\pi\)
0.193046 + 0.981190i \(0.438163\pi\)
\(194\) −5.18053e11 −1.88523
\(195\) 6.35416e7i 0.000225364i
\(196\) 5.87075e10 0.202961
\(197\) 3.84746e11 1.29671 0.648355 0.761338i \(-0.275457\pi\)
0.648355 + 0.761338i \(0.275457\pi\)
\(198\) 2.22313e11 0.730532
\(199\) −2.30471e10 −0.0738499 −0.0369250 0.999318i \(-0.511756\pi\)
−0.0369250 + 0.999318i \(0.511756\pi\)
\(200\) 7.50862e11i 2.34644i
\(201\) 1.76385e11i 0.537626i
\(202\) −8.11199e11 −2.41196
\(203\) −2.38953e11 −0.693158
\(204\) −4.81345e11 −1.36240
\(205\) 9.83409e10 0.271622
\(206\) 1.75621e11 0.473414
\(207\) 7.27871e10i 0.191515i
\(208\) 2.14561e9i 0.00551104i
\(209\) 2.00386e11i 0.502500i
\(210\) 5.95154e10i 0.145725i
\(211\) 7.28762e11i 1.74250i −0.490838 0.871251i \(-0.663309\pi\)
0.490838 0.871251i \(-0.336691\pi\)
\(212\) 1.02578e12 2.39537
\(213\) −7.32619e10 −0.167101
\(214\) 5.99524e11i 1.33579i
\(215\) 2.36066e10i 0.0513855i
\(216\) 2.16890e11i 0.461286i
\(217\) 4.21586e11i 0.876169i
\(218\) −4.28555e11 −0.870410
\(219\) 5.60680e10i 0.111300i
\(220\) 2.08458e11i 0.404487i
\(221\) 1.44480e9i 0.00274061i
\(222\) −8.11854e11 −1.50561
\(223\) −8.96759e11 −1.62612 −0.813058 0.582183i \(-0.802199\pi\)
−0.813058 + 0.582183i \(0.802199\pi\)
\(224\) 7.18497e11i 1.27405i
\(225\) −1.88170e11 −0.326315
\(226\) −3.45229e11 −0.585551
\(227\) 2.55999e11i 0.424726i −0.977191 0.212363i \(-0.931884\pi\)
0.977191 0.212363i \(-0.0681160\pi\)
\(228\) 3.44027e11 0.558365
\(229\) 3.03874e10i 0.0482521i 0.999709 + 0.0241260i \(0.00768030\pi\)
−0.999709 + 0.0241260i \(0.992320\pi\)
\(230\) −9.77170e10 −0.151821
\(231\) 4.36540e11i 0.663689i
\(232\) 1.16906e12i 1.73939i
\(233\) 5.98615e11i 0.871702i 0.900019 + 0.435851i \(0.143552\pi\)
−0.900019 + 0.435851i \(0.856448\pi\)
\(234\) −1.14562e9 −0.00163291
\(235\) 1.96686e11i 0.274432i
\(236\) 1.80849e11 + 1.68600e12i 0.247034 + 2.30301i
\(237\) −5.79794e11 −0.775411
\(238\) 1.35325e12i 1.77212i
\(239\) −1.31673e10 −0.0168852 −0.00844262 0.999964i \(-0.502687\pi\)
−0.00844262 + 0.999964i \(0.502687\pi\)
\(240\) −1.36664e11 −0.171632
\(241\) 1.79766e11 0.221118 0.110559 0.993870i \(-0.464736\pi\)
0.110559 + 0.993870i \(0.464736\pi\)
\(242\) 6.77684e11i 0.816489i
\(243\) 5.43536e10 0.0641500
\(244\) 1.25843e12i 1.45505i
\(245\) 1.12240e10 0.0127150
\(246\) 1.77303e12i 1.96807i
\(247\) 1.03263e9i 0.00112320i
\(248\) 2.06259e12 2.19864
\(249\) 2.26161e11i 0.236276i
\(250\) 5.10671e11i 0.522927i
\(251\) 8.07379e11 0.810418 0.405209 0.914224i \(-0.367199\pi\)
0.405209 + 0.914224i \(0.367199\pi\)
\(252\) −7.49460e11 −0.737473
\(253\) −7.16746e11 −0.691453
\(254\) 1.76895e12i 1.67320i
\(255\) −9.20262e10 −0.0853513
\(256\) −1.70218e12 −1.54813
\(257\) −7.25110e11 −0.646753 −0.323377 0.946270i \(-0.604818\pi\)
−0.323377 + 0.946270i \(0.604818\pi\)
\(258\) 4.25614e11 0.372320
\(259\) 1.59418e12i 1.36785i
\(260\) 1.07422e9i 0.000904121i
\(261\) −2.92972e11 −0.241894
\(262\) −1.30288e12 −1.05536
\(263\) 4.72240e10 0.0375305 0.0187652 0.999824i \(-0.494026\pi\)
0.0187652 + 0.999824i \(0.494026\pi\)
\(264\) −2.13575e12 −1.66544
\(265\) 1.96113e11 0.150064
\(266\) 9.67196e11i 0.726284i
\(267\) 7.40870e11i 0.545991i
\(268\) 2.98192e12i 2.15686i
\(269\) 7.51336e11i 0.533424i 0.963776 + 0.266712i \(0.0859373\pi\)
−0.963776 + 0.266712i \(0.914063\pi\)
\(270\) 7.29700e10i 0.0508540i
\(271\) −1.14249e12 −0.781640 −0.390820 0.920467i \(-0.627809\pi\)
−0.390820 + 0.920467i \(0.627809\pi\)
\(272\) 3.10744e12 2.08717
\(273\) 2.24957e9i 0.00148350i
\(274\) 9.73277e10i 0.0630208i
\(275\) 1.85293e12i 1.17814i
\(276\) 1.23052e12i 0.768323i
\(277\) −2.06781e12 −1.26798 −0.633990 0.773341i \(-0.718584\pi\)
−0.633990 + 0.773341i \(0.718584\pi\)
\(278\) 1.70359e12i 1.02599i
\(279\) 5.16894e11i 0.305760i
\(280\) 5.71760e11i 0.332218i
\(281\) 3.12787e12 1.78533 0.892663 0.450724i \(-0.148834\pi\)
0.892663 + 0.450724i \(0.148834\pi\)
\(282\) −3.54614e12 −1.98843
\(283\) 4.01605e11i 0.221242i −0.993863 0.110621i \(-0.964716\pi\)
0.993863 0.110621i \(-0.0352839\pi\)
\(284\) 1.23855e12 0.670381
\(285\) 6.57729e10 0.0349802
\(286\) 1.12811e10i 0.00589551i
\(287\) −3.48157e12 −1.78799
\(288\) 8.80927e11i 0.444608i
\(289\) 7.64837e10 0.0379384
\(290\) 3.93317e11i 0.191758i
\(291\) 1.24723e12i 0.597699i
\(292\) 9.47873e11i 0.446515i
\(293\) −3.65208e12 −1.69123 −0.845615 0.533793i \(-0.820766\pi\)
−0.845615 + 0.533793i \(0.820766\pi\)
\(294\) 2.02363e11i 0.0921285i
\(295\) 3.45757e10 + 3.22338e11i 0.0154761 + 0.144278i
\(296\) 7.79942e12 3.43244
\(297\) 5.35228e11i 0.231610i
\(298\) 1.99770e12 0.850059
\(299\) 3.69352e9 0.00154556
\(300\) 3.18115e12 1.30912
\(301\) 8.35746e11i 0.338253i
\(302\) 8.00560e12 3.18683
\(303\) 1.95299e12i 0.764694i
\(304\) −2.22095e12 −0.855402
\(305\) 2.40593e11i 0.0911557i
\(306\) 1.65918e12i 0.618424i
\(307\) −9.35620e11 −0.343090 −0.171545 0.985176i \(-0.554876\pi\)
−0.171545 + 0.985176i \(0.554876\pi\)
\(308\) 7.38005e12i 2.66260i
\(309\) 4.22815e11i 0.150092i
\(310\) 6.93932e11 0.242387
\(311\) −3.68900e12 −1.26797 −0.633983 0.773347i \(-0.718581\pi\)
−0.633983 + 0.773347i \(0.718581\pi\)
\(312\) 1.10059e10 0.00372265
\(313\) 4.34246e12i 1.44549i 0.691116 + 0.722744i \(0.257119\pi\)
−0.691116 + 0.722744i \(0.742881\pi\)
\(314\) 1.55676e12 0.510004
\(315\) −1.43286e11 −0.0462009
\(316\) 9.80186e12 3.11081
\(317\) −2.26865e12 −0.708714 −0.354357 0.935110i \(-0.615300\pi\)
−0.354357 + 0.935110i \(0.615300\pi\)
\(318\) 3.53581e12i 1.08731i
\(319\) 2.88494e12i 0.873341i
\(320\) 1.85160e11 0.0551821
\(321\) 1.44338e12 0.423502
\(322\) 3.45949e12 0.999384
\(323\) −1.49553e12 −0.425386
\(324\) −9.18889e11 −0.257358
\(325\) 9.54851e9i 0.00263341i
\(326\) 1.83270e12i 0.497741i
\(327\) 1.03176e12i 0.275957i
\(328\) 1.70334e13i 4.48675i
\(329\) 6.96329e12i 1.80649i
\(330\) −7.18546e11 −0.183605
\(331\) 7.43069e12 1.87021 0.935103 0.354376i \(-0.115307\pi\)
0.935103 + 0.354376i \(0.115307\pi\)
\(332\) 3.82342e12i 0.947898i
\(333\) 1.95457e12i 0.477343i
\(334\) 1.03986e13i 2.50174i
\(335\) 5.70099e11i 0.135122i
\(336\) 4.83832e12 1.12979
\(337\) 4.75034e12i 1.09289i 0.837496 + 0.546443i \(0.184019\pi\)
−0.837496 + 0.546443i \(0.815981\pi\)
\(338\) 8.03345e12i 1.82104i
\(339\) 8.31153e11i 0.185645i
\(340\) 1.55577e12 0.342414
\(341\) 5.08993e12 1.10393
\(342\) 1.18585e12i 0.253454i
\(343\) −4.93215e12 −1.03888
\(344\) −4.08884e12 −0.848804
\(345\) 2.35258e11i 0.0481336i
\(346\) −1.09693e13 −2.21206
\(347\) 2.93340e12i 0.583074i −0.956560 0.291537i \(-0.905833\pi\)
0.956560 0.291537i \(-0.0941667\pi\)
\(348\) 4.95293e12 0.970433
\(349\) 9.46228e11i 0.182755i 0.995816 + 0.0913774i \(0.0291270\pi\)
−0.995816 + 0.0913774i \(0.970873\pi\)
\(350\) 8.94348e12i 1.70281i
\(351\) 2.75813e9i 0.000517701i
\(352\) 8.67462e12 1.60523
\(353\) 7.08157e12i 1.29198i 0.763346 + 0.645990i \(0.223555\pi\)
−0.763346 + 0.645990i \(0.776445\pi\)
\(354\) −5.81157e12 + 6.23381e11i −1.04539 + 0.112134i
\(355\) 2.36792e11 0.0419978
\(356\) 1.25250e13i 2.19042i
\(357\) 3.25801e12 0.561839
\(358\) 6.42081e12 1.09188
\(359\) −9.87389e12 −1.65583 −0.827916 0.560852i \(-0.810474\pi\)
−0.827916 + 0.560852i \(0.810474\pi\)
\(360\) 7.01017e11i 0.115935i
\(361\) −5.06218e12 −0.825661
\(362\) 8.14242e12i 1.30982i
\(363\) −1.63155e12 −0.258862
\(364\) 3.80308e10i 0.00595152i
\(365\) 1.81219e11i 0.0279731i
\(366\) 4.33776e12 0.660480
\(367\) 5.63992e12i 0.847115i 0.905869 + 0.423557i \(0.139219\pi\)
−0.905869 + 0.423557i \(0.860781\pi\)
\(368\) 7.94393e12i 1.17705i
\(369\) −4.26865e12 −0.623962
\(370\) 2.62402e12 0.378407
\(371\) −6.94302e12 −0.987822
\(372\) 8.73849e12i 1.22665i
\(373\) −1.28318e13 −1.77724 −0.888618 0.458648i \(-0.848334\pi\)
−0.888618 + 0.458648i \(0.848334\pi\)
\(374\) 1.63382e13 2.23278
\(375\) 1.22946e12 0.165790
\(376\) 3.40675e13 4.53316
\(377\) 1.48666e10i 0.00195212i
\(378\) 2.58336e12i 0.334755i
\(379\) −5.10730e12 −0.653124 −0.326562 0.945176i \(-0.605890\pi\)
−0.326562 + 0.945176i \(0.605890\pi\)
\(380\) −1.11194e12 −0.140334
\(381\) −4.25882e12 −0.530475
\(382\) −2.26670e13 −2.78662
\(383\) −2.03408e12 −0.246816 −0.123408 0.992356i \(-0.539382\pi\)
−0.123408 + 0.992356i \(0.539382\pi\)
\(384\) 3.09141e12i 0.370254i
\(385\) 1.41096e12i 0.166805i
\(386\) 6.02490e12i 0.703094i
\(387\) 1.02468e12i 0.118041i
\(388\) 2.10854e13i 2.39786i
\(389\) 1.38866e13 1.55900 0.779502 0.626399i \(-0.215472\pi\)
0.779502 + 0.626399i \(0.215472\pi\)
\(390\) 3.70280e9 0.000410400
\(391\) 5.34926e12i 0.585342i
\(392\) 1.94408e12i 0.210032i
\(393\) 3.13674e12i 0.334592i
\(394\) 2.24205e13i 2.36137i
\(395\) 1.87397e12 0.194885
\(396\) 9.04844e12i 0.929176i
\(397\) 5.08486e12i 0.515616i 0.966196 + 0.257808i \(0.0830002\pi\)
−0.966196 + 0.257808i \(0.917000\pi\)
\(398\) 1.34303e12i 0.134484i
\(399\) −2.32856e12 −0.230263
\(400\) −2.05367e13 −2.00554
\(401\) 9.39192e12i 0.905800i −0.891561 0.452900i \(-0.850389\pi\)
0.891561 0.452900i \(-0.149611\pi\)
\(402\) −1.02786e13 −0.979044
\(403\) −2.62293e10 −0.00246753
\(404\) 3.30169e13i 3.06781i
\(405\) −1.75678e11 −0.0161229
\(406\) 1.39246e13i 1.26227i
\(407\) 1.92470e13 1.72342
\(408\) 1.59396e13i 1.40986i
\(409\) 2.20792e12i 0.192916i 0.995337 + 0.0964578i \(0.0307513\pi\)
−0.995337 + 0.0964578i \(0.969249\pi\)
\(410\) 5.73068e12i 0.494637i
\(411\) −2.34320e11 −0.0199803
\(412\) 7.14802e12i 0.602143i
\(413\) −1.22409e12 1.14118e13i −0.101874 0.949735i
\(414\) 4.24157e12 0.348758
\(415\) 7.30982e11i 0.0593835i
\(416\) −4.47019e10 −0.00358806
\(417\) −4.10147e12 −0.325281
\(418\) −1.16772e13 −0.915079
\(419\) 1.34513e13i 1.04158i 0.853684 + 0.520792i \(0.174363\pi\)
−0.853684 + 0.520792i \(0.825637\pi\)
\(420\) 2.42236e12 0.185350
\(421\) 9.57556e12i 0.724025i 0.932173 + 0.362013i \(0.117910\pi\)
−0.932173 + 0.362013i \(0.882090\pi\)
\(422\) −4.24676e13 −3.17318
\(423\) 8.53747e12i 0.630417i
\(424\) 3.39683e13i 2.47882i
\(425\) −1.38289e13 −0.997341
\(426\) 4.26924e12i 0.304300i
\(427\) 8.51774e12i 0.600047i
\(428\) −2.44014e13 −1.69901
\(429\) 2.71597e10 0.00186913
\(430\) −1.37564e12 −0.0935756
\(431\) 3.96460e12i 0.266571i 0.991078 + 0.133285i \(0.0425527\pi\)
−0.991078 + 0.133285i \(0.957447\pi\)
\(432\) 5.93211e12 0.394267
\(433\) −1.24379e13 −0.817162 −0.408581 0.912722i \(-0.633976\pi\)
−0.408581 + 0.912722i \(0.633976\pi\)
\(434\) −2.45674e13 −1.59555
\(435\) 9.46927e11 0.0607953
\(436\) 1.74427e13i 1.10709i
\(437\) 3.82322e12i 0.239895i
\(438\) −3.26728e12 −0.202683
\(439\) 1.48417e13 0.910252 0.455126 0.890427i \(-0.349594\pi\)
0.455126 + 0.890427i \(0.349594\pi\)
\(440\) 6.90302e12 0.418577
\(441\) −4.87197e11 −0.0292087
\(442\) −8.41938e10 −0.00499078
\(443\) 6.54734e12i 0.383748i −0.981420 0.191874i \(-0.938543\pi\)
0.981420 0.191874i \(-0.0614565\pi\)
\(444\) 3.30435e13i 1.91501i
\(445\) 2.39459e12i 0.137224i
\(446\) 5.22574e13i 2.96124i
\(447\) 4.80955e12i 0.269505i
\(448\) −6.55526e12 −0.363245
\(449\) −6.92776e12 −0.379631 −0.189815 0.981820i \(-0.560789\pi\)
−0.189815 + 0.981820i \(0.560789\pi\)
\(450\) 1.09653e13i 0.594236i
\(451\) 4.20340e13i 2.25278i
\(452\) 1.40513e13i 0.744773i
\(453\) 1.92738e13i 1.01036i
\(454\) −1.49180e13 −0.773448
\(455\) 7.27092e9i 0.000372849i
\(456\) 1.13924e13i 0.577816i
\(457\) 2.41663e13i 1.21235i −0.795330 0.606176i \(-0.792703\pi\)
0.795330 0.606176i \(-0.207297\pi\)
\(458\) 1.77078e12 0.0878695
\(459\) 3.99455e12 0.196067
\(460\) 3.97721e12i 0.193103i
\(461\) −2.45000e13 −1.17669 −0.588345 0.808610i \(-0.700220\pi\)
−0.588345 + 0.808610i \(0.700220\pi\)
\(462\) 2.54388e13 1.20861
\(463\) 2.87034e13i 1.34905i −0.738252 0.674525i \(-0.764348\pi\)
0.738252 0.674525i \(-0.235652\pi\)
\(464\) −3.19748e13 −1.48668
\(465\) 1.67067e12i 0.0768468i
\(466\) 3.48834e13 1.58741
\(467\) 4.39060e11i 0.0197669i 0.999951 + 0.00988347i \(0.00314606\pi\)
−0.999951 + 0.00988347i \(0.996854\pi\)
\(468\) 4.66283e10i 0.00207692i
\(469\) 2.01833e13i 0.889462i
\(470\) 1.14616e13 0.499754
\(471\) 3.74796e12i 0.161693i
\(472\) 5.58313e13 5.98877e12i 2.38324 0.255639i
\(473\) −1.00902e13 −0.426181
\(474\) 3.37867e13i 1.41206i
\(475\) 9.88380e12 0.408748
\(476\) −5.50792e13 −2.25400
\(477\) −8.51262e12 −0.344724
\(478\) 7.67306e11i 0.0307489i
\(479\) 3.31370e13 1.31412 0.657062 0.753837i \(-0.271799\pi\)
0.657062 + 0.753837i \(0.271799\pi\)
\(480\) 2.84727e12i 0.111744i
\(481\) −9.91831e10 −0.00385223
\(482\) 1.04756e13i 0.402666i
\(483\) 8.32886e12i 0.316847i
\(484\) 2.75827e13 1.03851
\(485\) 4.03123e12i 0.150220i
\(486\) 3.16738e12i 0.116820i
\(487\) 2.45975e12 0.0897939 0.0448970 0.998992i \(-0.485704\pi\)
0.0448970 + 0.998992i \(0.485704\pi\)
\(488\) −4.16725e13 −1.50574
\(489\) −4.41230e12 −0.157805
\(490\) 6.54064e11i 0.0231547i
\(491\) −1.84615e13 −0.646933 −0.323467 0.946240i \(-0.604848\pi\)
−0.323467 + 0.946240i \(0.604848\pi\)
\(492\) 7.21648e13 2.50322
\(493\) −2.15311e13 −0.739318
\(494\) 6.01749e10 0.00204541
\(495\) 1.72993e12i 0.0582107i
\(496\) 5.64134e13i 1.87920i
\(497\) −8.38319e12 −0.276457
\(498\) 1.31792e13 0.430271
\(499\) 3.38598e13 1.09441 0.547206 0.836998i \(-0.315691\pi\)
0.547206 + 0.836998i \(0.315691\pi\)
\(500\) −2.07850e13 −0.665119
\(501\) 2.50350e13 0.793157
\(502\) 4.70489e13i 1.47581i
\(503\) 2.88342e13i 0.895504i −0.894158 0.447752i \(-0.852225\pi\)
0.894158 0.447752i \(-0.147775\pi\)
\(504\) 2.48182e13i 0.763163i
\(505\) 6.31234e12i 0.192191i
\(506\) 4.17674e13i 1.25917i
\(507\) 1.93409e13 0.577346
\(508\) 7.19987e13 2.12817
\(509\) 3.13949e13i 0.918905i 0.888202 + 0.459452i \(0.151954\pi\)
−0.888202 + 0.459452i \(0.848046\pi\)
\(510\) 5.36270e12i 0.155429i
\(511\) 6.41573e12i 0.184137i
\(512\) 7.66287e13i 2.17792i
\(513\) −2.85498e12 −0.0803556
\(514\) 4.22548e13i 1.17777i
\(515\) 1.36660e12i 0.0377228i
\(516\) 1.73230e13i 0.473561i
\(517\) 8.40698e13 2.27608
\(518\) −9.28985e13 −2.49092
\(519\) 2.64090e13i 0.701317i
\(520\) −3.55725e10 −0.000935617
\(521\) 4.01429e13 1.04573 0.522865 0.852415i \(-0.324863\pi\)
0.522865 + 0.852415i \(0.324863\pi\)
\(522\) 1.70726e13i 0.440500i
\(523\) −4.64938e13 −1.18819 −0.594095 0.804395i \(-0.702490\pi\)
−0.594095 + 0.804395i \(0.702490\pi\)
\(524\) 5.30291e13i 1.34232i
\(525\) −2.15318e13 −0.539863
\(526\) 2.75191e12i 0.0683448i
\(527\) 3.79875e13i 0.934517i
\(528\) 5.84144e13i 1.42348i
\(529\) 2.77516e13 0.669898
\(530\) 1.14282e13i 0.273275i
\(531\) −1.50081e12 1.39916e13i −0.0355512 0.331432i
\(532\) 3.93662e13 0.923772
\(533\) 2.16609e11i 0.00503548i
\(534\) 4.31732e13 0.994278
\(535\) −4.66519e12 −0.106439
\(536\) 9.87454e13 2.23199
\(537\) 1.54584e13i 0.346172i
\(538\) 4.37831e13 0.971393
\(539\) 4.79750e12i 0.105456i
\(540\) 2.96998e12 0.0646821
\(541\) 3.31324e13i 0.714934i 0.933926 + 0.357467i \(0.116360\pi\)
−0.933926 + 0.357467i \(0.883640\pi\)
\(542\) 6.65772e13i 1.42341i
\(543\) −1.96032e13 −0.415268
\(544\) 6.47409e13i 1.35889i
\(545\) 3.33480e12i 0.0693565i
\(546\) −1.31091e11 −0.00270152
\(547\) −5.13121e13 −1.04781 −0.523906 0.851776i \(-0.675526\pi\)
−0.523906 + 0.851776i \(0.675526\pi\)
\(548\) 3.96137e12 0.0801572
\(549\) 1.04433e13i 0.209400i
\(550\) −1.07977e14 −2.14545
\(551\) 1.53887e13 0.303001
\(552\) −4.07484e13 −0.795088
\(553\) −6.63445e13 −1.28286
\(554\) 1.20499e14i 2.30906i
\(555\) 6.31744e12i 0.119971i
\(556\) 6.93385e13 1.30497
\(557\) 7.43485e13 1.38674 0.693372 0.720580i \(-0.256124\pi\)
0.693372 + 0.720580i \(0.256124\pi\)
\(558\) −3.01213e13 −0.556804
\(559\) 5.19967e10 0.000952613
\(560\) −1.56381e13 −0.283952
\(561\) 3.93349e13i 0.707887i
\(562\) 1.82273e14i 3.25117i
\(563\) 8.25542e12i 0.145948i −0.997334 0.0729738i \(-0.976751\pi\)
0.997334 0.0729738i \(-0.0232490\pi\)
\(564\) 1.44333e14i 2.52912i
\(565\) 2.68640e12i 0.0466582i
\(566\) −2.34030e13 −0.402893
\(567\) 6.21955e12 0.106131
\(568\) 4.10142e13i 0.693734i
\(569\) 2.89565e13i 0.485495i −0.970089 0.242748i \(-0.921951\pi\)
0.970089 0.242748i \(-0.0780487\pi\)
\(570\) 3.83282e12i 0.0637007i
\(571\) 8.69719e12i 0.143284i 0.997430 + 0.0716421i \(0.0228240\pi\)
−0.997430 + 0.0716421i \(0.977176\pi\)
\(572\) −4.59156e11 −0.00749860
\(573\) 5.45718e13i 0.883476i
\(574\) 2.02884e14i 3.25603i
\(575\) 3.53526e13i 0.562447i
\(576\) −8.03719e12 −0.126763
\(577\) 6.26532e12 0.0979635 0.0489818 0.998800i \(-0.484402\pi\)
0.0489818 + 0.998800i \(0.484402\pi\)
\(578\) 4.45698e12i 0.0690878i
\(579\) 1.45052e13 0.222911
\(580\) −1.60085e13 −0.243900
\(581\) 2.58790e13i 0.390901i
\(582\) −7.26808e13 −1.08844
\(583\) 8.38250e13i 1.24460i
\(584\) 3.13886e13 0.462069
\(585\) 8.91465e9i 0.000130114i
\(586\) 2.12820e14i 3.07982i
\(587\) 3.89264e13i 0.558539i −0.960213 0.279270i \(-0.909908\pi\)
0.960213 0.279270i \(-0.0900923\pi\)
\(588\) 8.23644e12 0.117180
\(589\) 2.71504e13i 0.383000i
\(590\) 1.87838e13 2.01485e12i 0.262738 0.0281827i
\(591\) 5.39784e13 0.748656
\(592\) 2.13320e14i 2.93376i
\(593\) 3.62556e13 0.494426 0.247213 0.968961i \(-0.420485\pi\)
0.247213 + 0.968961i \(0.420485\pi\)
\(594\) 3.11897e13 0.421773
\(595\) −1.05303e13 −0.141207
\(596\) 8.13091e13i 1.08120i
\(597\) −3.23341e12 −0.0426373
\(598\) 2.15235e11i 0.00281454i
\(599\) −8.15328e12 −0.105730 −0.0528650 0.998602i \(-0.516835\pi\)
−0.0528650 + 0.998602i \(0.516835\pi\)
\(600\) 1.05343e14i 1.35472i
\(601\) 7.92561e12i 0.101079i 0.998722 + 0.0505394i \(0.0160941\pi\)
−0.998722 + 0.0505394i \(0.983906\pi\)
\(602\) 4.87020e13 0.615976
\(603\) 2.47461e13i 0.310399i
\(604\) 3.25839e14i 4.05338i
\(605\) 5.27340e12 0.0650600
\(606\) −1.13808e14 −1.39255
\(607\) 3.53230e13 0.428661 0.214331 0.976761i \(-0.431243\pi\)
0.214331 + 0.976761i \(0.431243\pi\)
\(608\) 4.62716e13i 0.556925i
\(609\) −3.35242e13 −0.400195
\(610\) −1.40202e13 −0.165999
\(611\) −4.33227e11 −0.00508756
\(612\) −6.75309e13 −0.786584
\(613\) 7.66908e13i 0.886015i −0.896518 0.443007i \(-0.853912\pi\)
0.896518 0.443007i \(-0.146088\pi\)
\(614\) 5.45220e13i 0.624784i
\(615\) 1.37968e13 0.156821
\(616\) −2.44388e14 −2.75535
\(617\) 7.45415e13 0.833628 0.416814 0.908992i \(-0.363147\pi\)
0.416814 + 0.908992i \(0.363147\pi\)
\(618\) 2.46390e13 0.273326
\(619\) 1.57891e14 1.73741 0.868707 0.495327i \(-0.164952\pi\)
0.868707 + 0.495327i \(0.164952\pi\)
\(620\) 2.82440e13i 0.308296i
\(621\) 1.02117e13i 0.110571i
\(622\) 2.14972e14i 2.30903i
\(623\) 8.47760e13i 0.903302i
\(624\) 3.01020e11i 0.00318180i
\(625\) 8.93856e13 0.937276
\(626\) 2.53051e14 2.63231
\(627\) 2.81134e13i 0.290119i
\(628\) 6.33622e13i 0.648682i
\(629\) 1.43645e14i 1.45894i
\(630\) 8.34978e12i 0.0841342i
\(631\) −1.06377e13 −0.106341 −0.0531703 0.998585i \(-0.516933\pi\)
−0.0531703 + 0.998585i \(0.516933\pi\)
\(632\) 3.24586e14i 3.21918i
\(633\) 1.02242e14i 1.00603i
\(634\) 1.32202e14i 1.29060i
\(635\) 1.37651e13 0.133325
\(636\) 1.43912e14 1.38297
\(637\) 2.47224e10i 0.000235718i
\(638\) −1.68116e14 −1.59040
\(639\) −1.02784e13 −0.0964761
\(640\) 9.99185e12i 0.0930564i
\(641\) 1.97871e14 1.82849 0.914245 0.405163i \(-0.132785\pi\)
0.914245 + 0.405163i \(0.132785\pi\)
\(642\) 8.41109e13i 0.771218i
\(643\) −6.34533e13 −0.577297 −0.288648 0.957435i \(-0.593206\pi\)
−0.288648 + 0.957435i \(0.593206\pi\)
\(644\) 1.40806e14i 1.27113i
\(645\) 3.31191e12i 0.0296674i
\(646\) 8.71502e13i 0.774650i
\(647\) 1.30597e14 1.15189 0.575947 0.817487i \(-0.304633\pi\)
0.575947 + 0.817487i \(0.304633\pi\)
\(648\) 3.04288e13i 0.266324i
\(649\) 1.37777e14 1.47787e13i 1.19661 0.128355i
\(650\) 5.56426e11 0.00479558
\(651\) 5.91469e13i 0.505856i
\(652\) 7.45934e13 0.633085
\(653\) −1.54474e14 −1.30104 −0.650519 0.759490i \(-0.725449\pi\)
−0.650519 + 0.759490i \(0.725449\pi\)
\(654\) −6.01245e13 −0.502531
\(655\) 1.01384e13i 0.0840934i
\(656\) −4.65877e14 −3.83488
\(657\) 7.86612e12i 0.0642590i
\(658\) −4.05776e14 −3.28971
\(659\) 1.03024e14i 0.828915i 0.910069 + 0.414458i \(0.136029\pi\)
−0.910069 + 0.414458i \(0.863971\pi\)
\(660\) 2.92458e13i 0.233531i
\(661\) −8.55031e13 −0.677602 −0.338801 0.940858i \(-0.610021\pi\)
−0.338801 + 0.940858i \(0.610021\pi\)
\(662\) 4.33013e14i 3.40574i
\(663\) 2.02700e11i 0.00158229i
\(664\) −1.26612e14 −0.980918
\(665\) 7.52623e12 0.0578721
\(666\) −1.13900e14 −0.869265
\(667\) 5.50425e13i 0.416936i
\(668\) −4.23236e14 −3.18200
\(669\) −1.25812e14 −0.938838
\(670\) 3.32217e13 0.246064
\(671\) −1.02837e14 −0.756027
\(672\) 1.00802e14i 0.735571i
\(673\) 3.05917e13i 0.221579i −0.993844 0.110790i \(-0.964662\pi\)
0.993844 0.110790i \(-0.0353379\pi\)
\(674\) 2.76819e14 1.99020
\(675\) −2.63995e13 −0.188398
\(676\) −3.26972e14 −2.31621
\(677\) 8.09365e13 0.569116 0.284558 0.958659i \(-0.408153\pi\)
0.284558 + 0.958659i \(0.408153\pi\)
\(678\) −4.84343e13 −0.338068
\(679\) 1.42718e14i 0.988848i
\(680\) 5.15190e13i 0.354342i
\(681\) 3.59157e13i 0.245216i
\(682\) 2.96609e14i 2.01031i
\(683\) 4.74853e13i 0.319489i 0.987158 + 0.159744i \(0.0510670\pi\)
−0.987158 + 0.159744i \(0.948933\pi\)
\(684\) 4.82656e13 0.322372
\(685\) 7.57355e11 0.00502166
\(686\) 2.87414e14i 1.89186i
\(687\) 4.26323e12i 0.0278584i
\(688\) 1.11833e14i 0.725484i
\(689\) 4.31966e11i 0.00278197i
\(690\) −1.37093e13 −0.0876537
\(691\) 2.57228e14i 1.63278i 0.577500 + 0.816391i \(0.304028\pi\)
−0.577500 + 0.816391i \(0.695972\pi\)
\(692\) 4.46464e14i 2.81356i
\(693\) 6.12449e13i 0.383181i
\(694\) −1.70940e14 −1.06181
\(695\) 1.32565e13 0.0817533
\(696\) 1.64015e14i 1.00424i
\(697\) −3.13711e14 −1.90706
\(698\) 5.51401e13 0.332806
\(699\) 8.39833e13i 0.503277i
\(700\) 3.64012e14 2.16583
\(701\) 4.15156e13i 0.245257i −0.992453 0.122628i \(-0.960868\pi\)
0.992453 0.122628i \(-0.0391323\pi\)
\(702\) −1.60726e11 −0.000942759
\(703\) 1.02666e14i 0.597929i
\(704\) 7.91434e13i 0.457669i
\(705\) 2.75943e13i 0.158443i
\(706\) 4.12668e14 2.35276
\(707\) 2.23477e14i 1.26513i
\(708\) 2.53724e13 + 2.36539e14i 0.142625 + 1.32965i
\(709\) −2.09515e14 −1.16946 −0.584729 0.811229i \(-0.698799\pi\)
−0.584729 + 0.811229i \(0.698799\pi\)
\(710\) 1.37988e13i 0.0764800i
\(711\) −8.13428e13 −0.447684
\(712\) −4.14761e14 −2.26672
\(713\) 9.71120e13 0.527018
\(714\) 1.89856e14i 1.02314i
\(715\) −8.77839e10 −0.000469769
\(716\) 2.61336e14i 1.38878i
\(717\) −1.84732e12 −0.00974869
\(718\) 5.75387e14i 3.01535i
\(719\) 1.97557e14i 1.02813i −0.857752 0.514064i \(-0.828139\pi\)
0.857752 0.514064i \(-0.171861\pi\)
\(720\) −1.91734e13 −0.0990915
\(721\) 4.83818e13i 0.248317i
\(722\) 2.94991e14i 1.50357i
\(723\) 2.52205e13 0.127662
\(724\) 3.31408e14 1.66598
\(725\) 1.42296e14 0.710401
\(726\) 9.50765e13i 0.471400i
\(727\) 2.12601e14 1.04687 0.523435 0.852066i \(-0.324650\pi\)
0.523435 + 0.852066i \(0.324650\pi\)
\(728\) 1.25938e12 0.00615885
\(729\) 7.62560e12 0.0370370
\(730\) 1.05603e13 0.0509404
\(731\) 7.53058e13i 0.360779i
\(732\) 1.76553e14i 0.840076i
\(733\) 2.62897e14 1.24241 0.621207 0.783646i \(-0.286642\pi\)
0.621207 + 0.783646i \(0.286642\pi\)
\(734\) 3.28658e14 1.54264
\(735\) 1.57469e12 0.00734104
\(736\) 1.65505e14 0.766342
\(737\) 2.43678e14 1.12067
\(738\) 2.48749e14i 1.13627i
\(739\) 4.13594e14i 1.87651i −0.345939 0.938257i \(-0.612440\pi\)
0.345939 0.938257i \(-0.387560\pi\)
\(740\) 1.06801e14i 0.481302i
\(741\) 1.44874e11i 0.000648482i
\(742\) 4.04595e14i 1.79887i
\(743\) 1.23128e14 0.543768 0.271884 0.962330i \(-0.412353\pi\)
0.271884 + 0.962330i \(0.412353\pi\)
\(744\) 2.89373e14 1.26938
\(745\) 1.55451e13i 0.0677349i
\(746\) 7.47758e14i 3.23644i
\(747\) 3.17295e13i 0.136414i
\(748\) 6.64987e14i 2.83991i
\(749\) 1.65162e14 0.700652
\(750\) 7.16451e13i 0.301912i
\(751\) 8.48640e13i 0.355241i 0.984099 + 0.177621i \(0.0568400\pi\)
−0.984099 + 0.177621i \(0.943160\pi\)
\(752\) 9.31774e14i 3.87455i
\(753\) 1.13272e14 0.467895
\(754\) 8.66333e11 0.00355491
\(755\) 6.22955e13i 0.253935i
\(756\) −1.05146e14 −0.425780
\(757\) 8.05195e13 0.323908 0.161954 0.986798i \(-0.448220\pi\)
0.161954 + 0.986798i \(0.448220\pi\)
\(758\) 2.97621e14i 1.18937i
\(759\) −1.00557e14 −0.399210
\(760\) 3.68216e13i 0.145223i
\(761\) 4.06457e14 1.59254 0.796272 0.604938i \(-0.206802\pi\)
0.796272 + 0.604938i \(0.206802\pi\)
\(762\) 2.48177e14i 0.966021i
\(763\) 1.18062e14i 0.456550i
\(764\) 9.22578e14i 3.54435i
\(765\) −1.29109e13 −0.0492776
\(766\) 1.18533e14i 0.449464i
\(767\) −7.09992e11 + 7.61576e10i −0.00267471 + 0.000286904i
\(768\) −2.38810e14 −0.893812
\(769\) 4.75763e13i 0.176913i −0.996080 0.0884563i \(-0.971807\pi\)
0.996080 0.0884563i \(-0.0281934\pi\)
\(770\) −8.22216e13 −0.303761
\(771\) −1.01730e14 −0.373403
\(772\) −2.45221e14 −0.894277
\(773\) 3.40471e13i 0.123362i 0.998096 + 0.0616811i \(0.0196462\pi\)
−0.998096 + 0.0616811i \(0.980354\pi\)
\(774\) 5.97119e13 0.214959
\(775\) 2.51054e14i 0.897965i
\(776\) 6.98239e14 2.48139
\(777\) 2.23657e14i 0.789728i
\(778\) 8.09222e14i 2.83903i
\(779\) 2.24215e14 0.781587