Properties

Label 43.11.b.b.42.1
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.1
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.34

$q$-expansion

\(f(q)\) \(=\) \(q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} +O(q^{10})\) \(q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} -49203.6 q^{10} -30601.5 q^{11} -1.03661e6i q^{12} -11019.9 q^{13} -1.84510e6 q^{14} +349540. q^{15} +2.51904e6 q^{16} +1.14659e6 q^{17} +6.92834e6i q^{18} +4.19962e6i q^{19} +2.05549e6i q^{20} +1.31075e7 q^{21} +1.80859e6i q^{22} -6.78637e6 q^{23} -3.58555e7 q^{24} +9.07252e6 q^{25} +651289. i q^{26} -2.44266e7i q^{27} +7.70793e7i q^{28} +2.48741e7i q^{29} -2.06583e7i q^{30} -3.61300e6 q^{31} -6.14288e7i q^{32} -1.28481e7i q^{33} -6.77651e7i q^{34} -2.59908e7 q^{35} +2.89433e8 q^{36} +1.01376e8i q^{37} +2.48203e8 q^{38} -4.62673e6i q^{39} +7.10980e7 q^{40} -3.57321e7 q^{41} -7.74670e8i q^{42} +(-1.34018e8 + 6.04208e7i) q^{43} +7.55544e7 q^{44} +9.75955e7i q^{45} +4.01084e8i q^{46} +2.71560e8 q^{47} +1.05763e9i q^{48} -6.92160e8 q^{49} -5.36199e8i q^{50} +4.81400e8i q^{51} +2.72078e7 q^{52} +4.96941e8 q^{53} -1.44365e9 q^{54} +2.54766e7i q^{55} +2.66612e9 q^{56} -1.76323e9 q^{57} +1.47010e9 q^{58} -6.47645e8 q^{59} -8.63005e8 q^{60} -5.21284e8i q^{61} +2.13533e8i q^{62} +3.65976e9i q^{63} -1.05104e9 q^{64} +9.17434e6i q^{65} -7.59343e8 q^{66} +1.81540e9 q^{67} -2.83090e9 q^{68} -2.84928e9i q^{69} +1.53609e9i q^{70} -6.55571e8i q^{71} -1.00113e10i q^{72} +2.34267e9i q^{73} +5.99147e9 q^{74} +3.80913e9i q^{75} -1.03688e10i q^{76} +9.55352e8i q^{77} -2.73446e8 q^{78} +3.31775e9 q^{79} -2.09717e9i q^{80} +3.33341e9 q^{81} +2.11182e9i q^{82} -3.83424e9 q^{83} -3.23620e10 q^{84} -9.54568e8i q^{85} +(3.57095e9 + 7.92065e9i) q^{86} -1.04435e10 q^{87} -2.61337e9i q^{88} +7.01136e9i q^{89} +5.76803e9 q^{90} +3.44031e8i q^{91} +1.67554e10 q^{92} -1.51693e9i q^{93} -1.60496e10i q^{94} +3.49630e9 q^{95} +2.57911e10 q^{96} -5.78385e9 q^{97} +4.09076e10i q^{98} +3.58735e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 59.1014i 1.84692i −0.383696 0.923459i \(-0.625349\pi\)
0.383696 0.923459i \(-0.374651\pi\)
\(3\) 419.853i 1.72779i 0.503670 + 0.863896i \(0.331983\pi\)
−0.503670 + 0.863896i \(0.668017\pi\)
\(4\) −2468.98 −2.41111
\(5\) 832.528i 0.266409i −0.991089 0.133204i \(-0.957473\pi\)
0.991089 0.133204i \(-0.0425267\pi\)
\(6\) 24813.9 3.19109
\(7\) 31219.1i 1.85751i −0.370696 0.928754i \(-0.620881\pi\)
0.370696 0.928754i \(-0.379119\pi\)
\(8\) 85400.1i 2.60621i
\(9\) −117228. −1.98527
\(10\) −49203.6 −0.492036
\(11\) −30601.5 −0.190011 −0.0950056 0.995477i \(-0.530287\pi\)
−0.0950056 + 0.995477i \(0.530287\pi\)
\(12\) 1.03661e6i 4.16590i
\(13\) −11019.9 −0.0296797 −0.0148398 0.999890i \(-0.504724\pi\)
−0.0148398 + 0.999890i \(0.504724\pi\)
\(14\) −1.84510e6 −3.43067
\(15\) 349540. 0.460299
\(16\) 2.51904e6 2.40234
\(17\) 1.14659e6 0.807539 0.403769 0.914861i \(-0.367700\pi\)
0.403769 + 0.914861i \(0.367700\pi\)
\(18\) 6.92834e6i 3.66662i
\(19\) 4.19962e6i 1.69606i 0.529946 + 0.848032i \(0.322212\pi\)
−0.529946 + 0.848032i \(0.677788\pi\)
\(20\) 2.05549e6i 0.642341i
\(21\) 1.31075e7 3.20939
\(22\) 1.80859e6i 0.350935i
\(23\) −6.78637e6 −1.05438 −0.527192 0.849746i \(-0.676755\pi\)
−0.527192 + 0.849746i \(0.676755\pi\)
\(24\) −3.58555e7 −4.50298
\(25\) 9.07252e6 0.929026
\(26\) 651289.i 0.0548160i
\(27\) 2.44266e7i 1.70233i
\(28\) 7.70793e7i 4.47866i
\(29\) 2.48741e7i 1.21271i 0.795193 + 0.606356i \(0.207369\pi\)
−0.795193 + 0.606356i \(0.792631\pi\)
\(30\) 2.06583e7i 0.850136i
\(31\) −3.61300e6 −0.126200 −0.0631000 0.998007i \(-0.520099\pi\)
−0.0631000 + 0.998007i \(0.520099\pi\)
\(32\) 6.14288e7i 1.83072i
\(33\) 1.28481e7i 0.328300i
\(34\) 6.77651e7i 1.49146i
\(35\) −2.59908e7 −0.494857
\(36\) 2.89433e8 4.78669
\(37\) 1.01376e8i 1.46193i 0.682414 + 0.730966i \(0.260930\pi\)
−0.682414 + 0.730966i \(0.739070\pi\)
\(38\) 2.48203e8 3.13249
\(39\) 4.62673e6i 0.0512803i
\(40\) 7.10980e7 0.694316
\(41\) −3.57321e7 −0.308418 −0.154209 0.988038i \(-0.549283\pi\)
−0.154209 + 0.988038i \(0.549283\pi\)
\(42\) 7.74670e8i 5.92748i
\(43\) −1.34018e8 + 6.04208e7i −0.911634 + 0.411002i
\(44\) 7.55544e7 0.458138
\(45\) 9.75955e7i 0.528892i
\(46\) 4.01084e8i 1.94736i
\(47\) 2.71560e8 1.18407 0.592034 0.805913i \(-0.298325\pi\)
0.592034 + 0.805913i \(0.298325\pi\)
\(48\) 1.05763e9i 4.15074i
\(49\) −6.92160e8 −2.45034
\(50\) 5.36199e8i 1.71584i
\(51\) 4.81400e8i 1.39526i
\(52\) 2.72078e7 0.0715610
\(53\) 4.96941e8 1.18830 0.594149 0.804355i \(-0.297489\pi\)
0.594149 + 0.804355i \(0.297489\pi\)
\(54\) −1.44365e9 −3.14407
\(55\) 2.54766e7i 0.0506207i
\(56\) 2.66612e9 4.84105
\(57\) −1.76323e9 −2.93044
\(58\) 1.47010e9 2.23978
\(59\) −6.47645e8 −0.905893 −0.452946 0.891538i \(-0.649627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(60\) −8.63005e8 −1.10983
\(61\) 5.21284e8i 0.617199i −0.951192 0.308599i \(-0.900140\pi\)
0.951192 0.308599i \(-0.0998602\pi\)
\(62\) 2.13533e8i 0.233081i
\(63\) 3.65976e9i 3.68765i
\(64\) −1.05104e9 −0.978855
\(65\) 9.17434e6i 0.00790693i
\(66\) −7.59343e8 −0.606343
\(67\) 1.81540e9 1.34461 0.672307 0.740272i \(-0.265303\pi\)
0.672307 + 0.740272i \(0.265303\pi\)
\(68\) −2.83090e9 −1.94706
\(69\) 2.84928e9i 1.82176i
\(70\) 1.53609e9i 0.913961i
\(71\) 6.55571e8i 0.363353i −0.983358 0.181676i \(-0.941848\pi\)
0.983358 0.181676i \(-0.0581523\pi\)
\(72\) 1.00113e10i 5.17401i
\(73\) 2.34267e9i 1.13005i 0.825074 + 0.565024i \(0.191133\pi\)
−0.825074 + 0.565024i \(0.808867\pi\)
\(74\) 5.99147e9 2.70007
\(75\) 3.80913e9i 1.60516i
\(76\) 1.03688e10i 4.08939i
\(77\) 9.55352e8i 0.352947i
\(78\) −2.73446e8 −0.0947106
\(79\) 3.31775e9 1.07822 0.539110 0.842235i \(-0.318761\pi\)
0.539110 + 0.842235i \(0.318761\pi\)
\(80\) 2.09717e9i 0.640005i
\(81\) 3.33341e9 0.956013
\(82\) 2.11182e9i 0.569622i
\(83\) −3.83424e9 −0.973393 −0.486697 0.873571i \(-0.661798\pi\)
−0.486697 + 0.873571i \(0.661798\pi\)
\(84\) −3.23620e10 −7.73819
\(85\) 9.54568e8i 0.215136i
\(86\) 3.57095e9 + 7.92065e9i 0.759087 + 1.68371i
\(87\) −1.04435e10 −2.09531
\(88\) 2.61337e9i 0.495208i
\(89\) 7.01136e9i 1.25560i 0.778373 + 0.627802i \(0.216045\pi\)
−0.778373 + 0.627802i \(0.783955\pi\)
\(90\) 5.76803e9 0.976822
\(91\) 3.44031e8i 0.0551303i
\(92\) 1.67554e10 2.54223
\(93\) 1.51693e9i 0.218047i
\(94\) 1.60496e10i 2.18688i
\(95\) 3.49630e9 0.451846
\(96\) 2.57911e10 3.16311
\(97\) −5.78385e9 −0.673532 −0.336766 0.941588i \(-0.609333\pi\)
−0.336766 + 0.941588i \(0.609333\pi\)
\(98\) 4.09076e10i 4.52557i
\(99\) 3.58735e9 0.377223
\(100\) −2.23998e10 −2.23998
\(101\) −3.51511e9 −0.334451 −0.167226 0.985919i \(-0.553481\pi\)
−0.167226 + 0.985919i \(0.553481\pi\)
\(102\) 2.84514e10 2.57693
\(103\) 1.15282e10 0.994430 0.497215 0.867627i \(-0.334356\pi\)
0.497215 + 0.867627i \(0.334356\pi\)
\(104\) 9.41097e8i 0.0773513i
\(105\) 1.09123e10i 0.855010i
\(106\) 2.93699e10i 2.19469i
\(107\) 5.33567e9 0.380426 0.190213 0.981743i \(-0.439082\pi\)
0.190213 + 0.981743i \(0.439082\pi\)
\(108\) 6.03088e10i 4.10451i
\(109\) −1.55469e10 −1.01044 −0.505221 0.862990i \(-0.668589\pi\)
−0.505221 + 0.862990i \(0.668589\pi\)
\(110\) 1.50570e9 0.0934923
\(111\) −4.25631e10 −2.52591
\(112\) 7.86421e10i 4.46237i
\(113\) 1.28377e10i 0.696780i −0.937350 0.348390i \(-0.886728\pi\)
0.937350 0.348390i \(-0.113272\pi\)
\(114\) 1.04209e11i 5.41229i
\(115\) 5.64985e9i 0.280897i
\(116\) 6.14136e10i 2.92398i
\(117\) 1.29184e9 0.0589220
\(118\) 3.82767e10i 1.67311i
\(119\) 3.57955e10i 1.50001i
\(120\) 2.98507e10i 1.19963i
\(121\) −2.50010e10 −0.963896
\(122\) −3.08086e10 −1.13992
\(123\) 1.50022e10i 0.532881i
\(124\) 8.92041e9 0.304282
\(125\) 1.56833e10i 0.513910i
\(126\) 2.16297e11 6.81078
\(127\) 2.04030e10 0.617554 0.308777 0.951134i \(-0.400080\pi\)
0.308777 + 0.951134i \(0.400080\pi\)
\(128\) 7.85315e8i 0.0228557i
\(129\) −2.53679e10 5.62679e10i −0.710126 1.57511i
\(130\) 5.42217e8 0.0146035
\(131\) 6.81112e10i 1.76548i 0.469864 + 0.882739i \(0.344303\pi\)
−0.469864 + 0.882739i \(0.655697\pi\)
\(132\) 3.17218e10i 0.791567i
\(133\) 1.31109e11 3.15045
\(134\) 1.07293e11i 2.48339i
\(135\) −2.03358e10 −0.453517
\(136\) 9.79189e10i 2.10461i
\(137\) 1.98461e10i 0.411218i 0.978634 + 0.205609i \(0.0659175\pi\)
−0.978634 + 0.205609i \(0.934083\pi\)
\(138\) −1.68397e11 −3.36464
\(139\) −1.29281e10 −0.249150 −0.124575 0.992210i \(-0.539757\pi\)
−0.124575 + 0.992210i \(0.539757\pi\)
\(140\) 6.41707e10 1.19315
\(141\) 1.14016e11i 2.04582i
\(142\) −3.87452e10 −0.671083
\(143\) 3.37224e8 0.00563947
\(144\) −2.95301e11 −4.76928
\(145\) 2.07084e10 0.323077
\(146\) 1.38455e11 2.08711
\(147\) 2.90606e11i 4.23367i
\(148\) 2.50295e11i 3.52488i
\(149\) 8.07569e10i 1.09963i 0.835285 + 0.549817i \(0.185303\pi\)
−0.835285 + 0.549817i \(0.814697\pi\)
\(150\) 2.25125e11 2.96461
\(151\) 2.06213e10i 0.262682i −0.991337 0.131341i \(-0.958072\pi\)
0.991337 0.131341i \(-0.0419283\pi\)
\(152\) −3.58648e11 −4.42029
\(153\) −1.34412e11 −1.60318
\(154\) 5.64627e10 0.651865
\(155\) 3.00792e9i 0.0336208i
\(156\) 1.14233e10i 0.123642i
\(157\) 5.75822e10i 0.603656i 0.953362 + 0.301828i \(0.0975969\pi\)
−0.953362 + 0.301828i \(0.902403\pi\)
\(158\) 1.96083e11i 1.99139i
\(159\) 2.08642e11i 2.05313i
\(160\) −5.11412e10 −0.487721
\(161\) 2.11865e11i 1.95853i
\(162\) 1.97009e11i 1.76568i
\(163\) 1.01222e11i 0.879707i −0.898070 0.439853i \(-0.855030\pi\)
0.898070 0.439853i \(-0.144970\pi\)
\(164\) 8.82217e10 0.743629
\(165\) −1.06964e10 −0.0874620
\(166\) 2.26609e11i 1.79778i
\(167\) −1.61243e11 −1.24136 −0.620681 0.784063i \(-0.713144\pi\)
−0.620681 + 0.784063i \(0.713144\pi\)
\(168\) 1.11938e12i 8.36432i
\(169\) −1.37737e11 −0.999119
\(170\) −5.64163e10 −0.397338
\(171\) 4.92313e11i 3.36714i
\(172\) 3.30887e11 1.49177e11i 2.19805 0.990971i
\(173\) −5.74774e10 −0.370908 −0.185454 0.982653i \(-0.559376\pi\)
−0.185454 + 0.982653i \(0.559376\pi\)
\(174\) 6.17225e11i 3.86988i
\(175\) 2.83236e11i 1.72567i
\(176\) −7.70863e10 −0.456472
\(177\) 2.71916e11i 1.56519i
\(178\) 4.14381e11 2.31900
\(179\) 4.14002e10i 0.225288i −0.993635 0.112644i \(-0.964068\pi\)
0.993635 0.112644i \(-0.0359319\pi\)
\(180\) 2.40961e11i 1.27522i
\(181\) 1.16160e10 0.0597947 0.0298973 0.999553i \(-0.490482\pi\)
0.0298973 + 0.999553i \(0.490482\pi\)
\(182\) 2.03327e10 0.101821
\(183\) 2.18863e11 1.06639
\(184\) 5.79557e11i 2.74794i
\(185\) 8.43985e10 0.389472
\(186\) −8.96527e10 −0.402716
\(187\) −3.50874e10 −0.153441
\(188\) −6.70476e11 −2.85492
\(189\) −7.62578e11 −3.16210
\(190\) 2.06636e11i 0.834524i
\(191\) 1.75795e11i 0.691575i 0.938313 + 0.345787i \(0.112388\pi\)
−0.938313 + 0.345787i \(0.887612\pi\)
\(192\) 4.41282e11i 1.69126i
\(193\) −8.33306e10 −0.311184 −0.155592 0.987821i \(-0.549729\pi\)
−0.155592 + 0.987821i \(0.549729\pi\)
\(194\) 3.41834e11i 1.24396i
\(195\) −3.85188e9 −0.0136615
\(196\) 1.70893e12 5.90803
\(197\) 4.38324e10 0.147728 0.0738641 0.997268i \(-0.476467\pi\)
0.0738641 + 0.997268i \(0.476467\pi\)
\(198\) 2.12017e11i 0.696700i
\(199\) 3.35527e11i 1.07513i −0.843221 0.537566i \(-0.819344\pi\)
0.843221 0.537566i \(-0.180656\pi\)
\(200\) 7.74795e11i 2.42123i
\(201\) 7.62201e11i 2.32321i
\(202\) 2.07748e11i 0.617704i
\(203\) 7.76549e11 2.25262
\(204\) 1.18856e12i 3.36412i
\(205\) 2.97480e10i 0.0821652i
\(206\) 6.81331e11i 1.83663i
\(207\) 7.95553e11 2.09323
\(208\) −2.77594e10 −0.0713007
\(209\) 1.28515e11i 0.322271i
\(210\) −6.44934e11 −1.57913
\(211\) 3.28767e11i 0.786097i 0.919518 + 0.393048i \(0.128580\pi\)
−0.919518 + 0.393048i \(0.871420\pi\)
\(212\) −1.22693e12 −2.86512
\(213\) 2.75244e11 0.627798
\(214\) 3.15346e11i 0.702616i
\(215\) 5.03020e10 + 1.11574e11i 0.109495 + 0.242868i
\(216\) 2.08604e12 4.43663
\(217\) 1.12795e11i 0.234417i
\(218\) 9.18844e11i 1.86621i
\(219\) −9.83579e11 −1.95249
\(220\) 6.29011e10i 0.122052i
\(221\) −1.26353e10 −0.0239675
\(222\) 2.51554e12i 4.66516i
\(223\) 2.39669e11i 0.434599i −0.976105 0.217299i \(-0.930275\pi\)
0.976105 0.217299i \(-0.0697248\pi\)
\(224\) −1.91776e12 −3.40058
\(225\) −1.06355e12 −1.84436
\(226\) −7.58728e11 −1.28690
\(227\) 1.85715e11i 0.308118i −0.988062 0.154059i \(-0.950765\pi\)
0.988062 0.154059i \(-0.0492346\pi\)
\(228\) 4.35336e12 7.06562
\(229\) 1.47897e11 0.234846 0.117423 0.993082i \(-0.462537\pi\)
0.117423 + 0.993082i \(0.462537\pi\)
\(230\) 3.33914e11 0.518795
\(231\) −4.01108e11 −0.609820
\(232\) −2.12425e12 −3.16058
\(233\) 2.30728e11i 0.335985i −0.985788 0.167992i \(-0.946272\pi\)
0.985788 0.167992i \(-0.0537284\pi\)
\(234\) 7.63493e10i 0.108824i
\(235\) 2.26082e11i 0.315447i
\(236\) 1.59902e12 2.18421
\(237\) 1.39297e12i 1.86294i
\(238\) −2.11557e12 −2.77040
\(239\) −4.08458e11 −0.523791 −0.261895 0.965096i \(-0.584348\pi\)
−0.261895 + 0.965096i \(0.584348\pi\)
\(240\) 8.80503e11 1.10580
\(241\) 8.99974e11i 1.10699i 0.832851 + 0.553497i \(0.186707\pi\)
−0.832851 + 0.553497i \(0.813293\pi\)
\(242\) 1.47759e12i 1.78024i
\(243\) 4.28238e10i 0.0505421i
\(244\) 1.28704e12i 1.48813i
\(245\) 5.76242e11i 0.652792i
\(246\) −8.86654e11 −0.984189
\(247\) 4.62792e10i 0.0503386i
\(248\) 3.08550e11i 0.328903i
\(249\) 1.60982e12i 1.68182i
\(250\) −9.26904e11 −0.949150
\(251\) −1.12564e12 −1.12988 −0.564939 0.825133i \(-0.691100\pi\)
−0.564939 + 0.825133i \(0.691100\pi\)
\(252\) 9.03585e12i 8.89132i
\(253\) 2.07673e11 0.200345
\(254\) 1.20584e12i 1.14057i
\(255\) 4.00779e11 0.371710
\(256\) −1.12268e12 −1.02107
\(257\) 2.02956e12i 1.81024i 0.425154 + 0.905121i \(0.360220\pi\)
−0.425154 + 0.905121i \(0.639780\pi\)
\(258\) −3.32551e12 + 1.49928e12i −2.90911 + 1.31155i
\(259\) 3.16488e12 2.71555
\(260\) 2.26512e10i 0.0190645i
\(261\) 2.91594e12i 2.40756i
\(262\) 4.02547e12 3.26069
\(263\) 1.35423e12i 1.07625i 0.842866 + 0.538124i \(0.180867\pi\)
−0.842866 + 0.538124i \(0.819133\pi\)
\(264\) 1.09723e12 0.855617
\(265\) 4.13717e11i 0.316573i
\(266\) 7.74870e12i 5.81863i
\(267\) −2.94375e12 −2.16942
\(268\) −4.48218e12 −3.24201
\(269\) 1.52798e12 1.08482 0.542408 0.840115i \(-0.317513\pi\)
0.542408 + 0.840115i \(0.317513\pi\)
\(270\) 1.20188e12i 0.837609i
\(271\) −1.08870e12 −0.744839 −0.372420 0.928064i \(-0.621472\pi\)
−0.372420 + 0.928064i \(0.621472\pi\)
\(272\) 2.88830e12 1.93998
\(273\) −1.44442e11 −0.0952536
\(274\) 1.17293e12 0.759486
\(275\) −2.77633e11 −0.176525
\(276\) 7.03481e12i 4.39245i
\(277\) 1.26133e12i 0.773448i 0.922196 + 0.386724i \(0.126393\pi\)
−0.922196 + 0.386724i \(0.873607\pi\)
\(278\) 7.64070e11i 0.460160i
\(279\) 4.23544e11 0.250540
\(280\) 2.21962e12i 1.28970i
\(281\) 9.77086e11 0.557701 0.278850 0.960335i \(-0.410047\pi\)
0.278850 + 0.960335i \(0.410047\pi\)
\(282\) 6.73848e12 3.77847
\(283\) 1.67181e12 0.920989 0.460494 0.887663i \(-0.347672\pi\)
0.460494 + 0.887663i \(0.347672\pi\)
\(284\) 1.61859e12i 0.876083i
\(285\) 1.46793e12i 0.780697i
\(286\) 1.99304e10i 0.0104156i
\(287\) 1.11553e12i 0.572888i
\(288\) 7.20118e12i 3.63447i
\(289\) −7.01326e11 −0.347881
\(290\) 1.22390e12i 0.596698i
\(291\) 2.42837e12i 1.16372i
\(292\) 5.78400e12i 2.72467i
\(293\) 2.94397e12 1.36331 0.681656 0.731673i \(-0.261260\pi\)
0.681656 + 0.731673i \(0.261260\pi\)
\(294\) −1.71752e13 −7.81925
\(295\) 5.39182e11i 0.241338i
\(296\) −8.65753e12 −3.81009
\(297\) 7.47491e11i 0.323462i
\(298\) 4.77285e12 2.03094
\(299\) 7.47849e10 0.0312938
\(300\) 9.40465e12i 3.87023i
\(301\) 1.88628e12 + 4.18393e12i 0.763440 + 1.69337i
\(302\) −1.21875e12 −0.485152
\(303\) 1.47583e12i 0.577862i
\(304\) 1.05790e13i 4.07452i
\(305\) −4.33983e11 −0.164427
\(306\) 7.94396e12i 2.96094i
\(307\) −1.62167e11 −0.0594661 −0.0297330 0.999558i \(-0.509466\pi\)
−0.0297330 + 0.999558i \(0.509466\pi\)
\(308\) 2.35874e12i 0.850995i
\(309\) 4.84014e12i 1.71817i
\(310\) 1.77772e11 0.0620949
\(311\) −1.80279e12 −0.619646 −0.309823 0.950794i \(-0.600270\pi\)
−0.309823 + 0.950794i \(0.600270\pi\)
\(312\) 3.95123e11 0.133647
\(313\) 4.74297e12i 1.57881i −0.613876 0.789403i \(-0.710390\pi\)
0.613876 0.789403i \(-0.289610\pi\)
\(314\) 3.40319e12 1.11490
\(315\) 3.04685e12 0.982422
\(316\) −8.19144e12 −2.59971
\(317\) 3.23655e12 1.01108 0.505541 0.862803i \(-0.331293\pi\)
0.505541 + 0.862803i \(0.331293\pi\)
\(318\) 1.23310e13 3.79197
\(319\) 7.61185e11i 0.230429i
\(320\) 8.75018e11i 0.260776i
\(321\) 2.24020e12i 0.657297i
\(322\) 1.25215e13 3.61724
\(323\) 4.81524e12i 1.36964i
\(324\) −8.23011e12 −2.30505
\(325\) −9.99779e10 −0.0275732
\(326\) −5.98238e12 −1.62475
\(327\) 6.52742e12i 1.74583i
\(328\) 3.05153e12i 0.803799i
\(329\) 8.47788e12i 2.19942i
\(330\) 6.32175e11i 0.161535i
\(331\) 5.02102e12i 1.26372i −0.775081 0.631862i \(-0.782291\pi\)
0.775081 0.631862i \(-0.217709\pi\)
\(332\) 9.46664e12 2.34696
\(333\) 1.18841e13i 2.90232i
\(334\) 9.52969e12i 2.29270i
\(335\) 1.51137e12i 0.358217i
\(336\) 3.30182e13 7.71004
\(337\) 3.22069e12 0.740967 0.370483 0.928839i \(-0.379192\pi\)
0.370483 + 0.928839i \(0.379192\pi\)
\(338\) 8.14045e12i 1.84529i
\(339\) 5.38996e12 1.20389
\(340\) 2.35681e12i 0.518716i
\(341\) 1.10563e11 0.0239794
\(342\) −2.90964e13 −6.21883
\(343\) 1.27900e13i 2.69401i
\(344\) −5.15994e12 1.14452e13i −1.07116 2.37591i
\(345\) −2.37211e12 −0.485332
\(346\) 3.39699e12i 0.685037i
\(347\) 1.79363e12i 0.356521i −0.983983 0.178260i \(-0.942953\pi\)
0.983983 0.178260i \(-0.0570469\pi\)
\(348\) 2.57847e13 5.05203
\(349\) 1.98981e12i 0.384312i 0.981364 + 0.192156i \(0.0615480\pi\)
−0.981364 + 0.192156i \(0.938452\pi\)
\(350\) −1.67397e13 −3.18718
\(351\) 2.69178e11i 0.0505247i
\(352\) 1.87981e12i 0.347858i
\(353\) −6.67536e12 −1.21787 −0.608935 0.793220i \(-0.708403\pi\)
−0.608935 + 0.793220i \(0.708403\pi\)
\(354\) −1.60706e13 −2.89079
\(355\) −5.45782e11 −0.0968004
\(356\) 1.73109e13i 3.02740i
\(357\) 1.50289e13 2.59171
\(358\) −2.44681e12 −0.416088
\(359\) −4.33742e12 −0.727376 −0.363688 0.931521i \(-0.618483\pi\)
−0.363688 + 0.931521i \(0.618483\pi\)
\(360\) −8.33467e12 −1.37840
\(361\) −1.15057e13 −1.87663
\(362\) 6.86520e11i 0.110436i
\(363\) 1.04967e13i 1.66541i
\(364\) 8.49403e11i 0.132925i
\(365\) 1.95034e12 0.301055
\(366\) 1.29351e13i 1.96954i
\(367\) −6.86650e12 −1.03135 −0.515674 0.856785i \(-0.672458\pi\)
−0.515674 + 0.856785i \(0.672458\pi\)
\(368\) −1.70951e13 −2.53299
\(369\) 4.18880e12 0.612291
\(370\) 4.98807e12i 0.719323i
\(371\) 1.55141e13i 2.20727i
\(372\) 3.74526e12i 0.525736i
\(373\) 3.72115e12i 0.515386i 0.966227 + 0.257693i \(0.0829623\pi\)
−0.966227 + 0.257693i \(0.917038\pi\)
\(374\) 2.07371e12i 0.283394i
\(375\) 6.58468e12 0.887929
\(376\) 2.31913e13i 3.08593i
\(377\) 2.74109e11i 0.0359929i
\(378\) 4.50694e13i 5.84014i
\(379\) 7.27747e12 0.930646 0.465323 0.885141i \(-0.345938\pi\)
0.465323 + 0.885141i \(0.345938\pi\)
\(380\) −8.63229e12 −1.08945
\(381\) 8.56626e12i 1.06700i
\(382\) 1.03897e13 1.27728
\(383\) 1.39131e13i 1.68822i 0.536168 + 0.844112i \(0.319872\pi\)
−0.536168 + 0.844112i \(0.680128\pi\)
\(384\) 3.29717e11 0.0394899
\(385\) 7.95358e11 0.0940284
\(386\) 4.92496e12i 0.574732i
\(387\) 1.57106e13 7.08300e12i 1.80984 0.815948i
\(388\) 1.42802e13 1.62396
\(389\) 5.23131e12i 0.587303i 0.955912 + 0.293652i \(0.0948706\pi\)
−0.955912 + 0.293652i \(0.905129\pi\)
\(390\) 2.27651e11i 0.0252318i
\(391\) −7.78119e12 −0.851456
\(392\) 5.91105e13i 6.38608i
\(393\) −2.85967e13 −3.05038
\(394\) 2.59055e12i 0.272842i
\(395\) 2.76212e12i 0.287248i
\(396\) −8.85708e12 −0.909525
\(397\) −3.23534e12 −0.328071 −0.164035 0.986454i \(-0.552451\pi\)
−0.164035 + 0.986454i \(0.552451\pi\)
\(398\) −1.98301e13 −1.98568
\(399\) 5.50464e13i 5.44333i
\(400\) 2.28540e13 2.23184
\(401\) 6.71315e12 0.647448 0.323724 0.946152i \(-0.395065\pi\)
0.323724 + 0.946152i \(0.395065\pi\)
\(402\) 4.50472e13 4.29079
\(403\) 3.98147e10 0.00374558
\(404\) 8.67873e12 0.806398
\(405\) 2.77516e12i 0.254690i
\(406\) 4.58951e13i 4.16041i
\(407\) 3.10226e12i 0.277783i
\(408\) −4.11116e13 −3.63633
\(409\) 3.76964e12i 0.329369i −0.986346 0.164685i \(-0.947339\pi\)
0.986346 0.164685i \(-0.0526606\pi\)
\(410\) 1.75815e12 0.151752
\(411\) −8.33244e12 −0.710499
\(412\) −2.84628e13 −2.39768
\(413\) 2.02189e13i 1.68270i
\(414\) 4.70183e13i 3.86603i
\(415\) 3.19211e12i 0.259321i
\(416\) 6.76937e11i 0.0543353i
\(417\) 5.42792e12i 0.430480i
\(418\) −7.59540e12 −0.595208
\(419\) 5.70342e12i 0.441636i 0.975315 + 0.220818i \(0.0708728\pi\)
−0.975315 + 0.220818i \(0.929127\pi\)
\(420\) 2.69423e13i 2.06152i
\(421\) 6.78163e12i 0.512771i −0.966575 0.256386i \(-0.917468\pi\)
0.966575 0.256386i \(-0.0825317\pi\)
\(422\) 1.94306e13 1.45186
\(423\) −3.18345e13 −2.35069
\(424\) 4.24388e13i 3.09695i
\(425\) 1.04025e13 0.750225
\(426\) 1.62673e13i 1.15949i
\(427\) −1.62740e13 −1.14645
\(428\) −1.31736e13 −0.917249
\(429\) 1.41585e11i 0.00974384i
\(430\) 6.59416e12 2.97292e12i 0.448557 0.202228i
\(431\) 1.47502e13 0.991769 0.495884 0.868389i \(-0.334844\pi\)
0.495884 + 0.868389i \(0.334844\pi\)
\(432\) 6.15315e13i 4.08958i
\(433\) 4.40794e12i 0.289598i 0.989461 + 0.144799i \(0.0462536\pi\)
−0.989461 + 0.144799i \(0.953746\pi\)
\(434\) 6.66632e12 0.432950
\(435\) 8.69450e12i 0.558211i
\(436\) 3.83850e13 2.43629
\(437\) 2.85002e13i 1.78830i
\(438\) 5.81309e13i 3.60609i
\(439\) −2.34447e13 −1.43788 −0.718938 0.695074i \(-0.755371\pi\)
−0.718938 + 0.695074i \(0.755371\pi\)
\(440\) −2.17571e12 −0.131928
\(441\) 8.11404e13 4.86457
\(442\) 7.46761e11i 0.0442660i
\(443\) −2.81507e13 −1.64995 −0.824975 0.565169i \(-0.808811\pi\)
−0.824975 + 0.565169i \(0.808811\pi\)
\(444\) 1.05087e14 6.09026
\(445\) 5.83716e12 0.334504
\(446\) −1.41648e13 −0.802669
\(447\) −3.39061e13 −1.89994
\(448\) 3.28125e13i 1.81823i
\(449\) 1.80546e13i 0.989363i 0.869074 + 0.494681i \(0.164715\pi\)
−0.869074 + 0.494681i \(0.835285\pi\)
\(450\) 6.28575e13i 3.40639i
\(451\) 1.09346e12 0.0586028
\(452\) 3.16960e13i 1.68001i
\(453\) 8.65791e12 0.453860
\(454\) −1.09760e13 −0.569069
\(455\) 2.86415e11 0.0146872
\(456\) 1.50580e14i 7.63734i
\(457\) 1.63525e13i 0.820357i −0.912005 0.410179i \(-0.865466\pi\)
0.912005 0.410179i \(-0.134534\pi\)
\(458\) 8.74093e12i 0.433741i
\(459\) 2.80073e13i 1.37470i
\(460\) 1.39493e13i 0.677274i
\(461\) −2.03281e13 −0.976321 −0.488161 0.872754i \(-0.662332\pi\)
−0.488161 + 0.872754i \(0.662332\pi\)
\(462\) 2.37060e13i 1.12629i
\(463\) 1.17169e13i 0.550689i −0.961346 0.275345i \(-0.911208\pi\)
0.961346 0.275345i \(-0.0887919\pi\)
\(464\) 6.26588e13i 2.91335i
\(465\) −1.26289e12 −0.0580898
\(466\) −1.36363e13 −0.620537
\(467\) 2.71597e13i 1.22276i 0.791337 + 0.611380i \(0.209385\pi\)
−0.791337 + 0.611380i \(0.790615\pi\)
\(468\) −3.18951e12 −0.142068
\(469\) 5.66752e13i 2.49763i
\(470\) −1.33617e13 −0.582604
\(471\) −2.41761e13 −1.04299
\(472\) 5.53089e13i 2.36094i
\(473\) 4.10115e12 1.84897e12i 0.173221 0.0780950i
\(474\) 8.23263e13 3.44070
\(475\) 3.81012e13i 1.57569i
\(476\) 8.83784e13i 3.61669i
\(477\) −5.82553e13 −2.35909
\(478\) 2.41404e13i 0.967399i
\(479\) 3.61505e13 1.43363 0.716815 0.697263i \(-0.245599\pi\)
0.716815 + 0.697263i \(0.245599\pi\)
\(480\) 2.14718e13i 0.842680i
\(481\) 1.11715e12i 0.0433897i
\(482\) 5.31897e13 2.04453
\(483\) −8.89522e13 −3.38393
\(484\) 6.17268e13 2.32406
\(485\) 4.81522e12i 0.179435i
\(486\) −2.53095e12 −0.0933472
\(487\) −1.13607e13 −0.414727 −0.207363 0.978264i \(-0.566488\pi\)
−0.207363 + 0.978264i \(0.566488\pi\)
\(488\) 4.45177e13 1.60855
\(489\) 4.24985e13 1.51995
\(490\) 3.40567e13 1.20565
\(491\) 3.37611e13i 1.18307i −0.806280 0.591534i \(-0.798523\pi\)
0.806280 0.591534i \(-0.201477\pi\)
\(492\) 3.70402e13i 1.28484i
\(493\) 2.85204e13i 0.979312i
\(494\) −2.73517e12 −0.0929714
\(495\) 2.98657e12i 0.100496i
\(496\) −9.10127e12 −0.303175
\(497\) −2.04664e13 −0.674931
\(498\) −9.51425e13 −3.10619
\(499\) 1.56284e13i 0.505142i −0.967578 0.252571i \(-0.918724\pi\)
0.967578 0.252571i \(-0.0812761\pi\)
\(500\) 3.87217e13i 1.23909i
\(501\) 6.76985e13i 2.14482i
\(502\) 6.65269e13i 2.08679i
\(503\) 1.88419e13i 0.585172i 0.956239 + 0.292586i \(0.0945158\pi\)
−0.956239 + 0.292586i \(0.905484\pi\)
\(504\) −3.12544e14 −9.61076
\(505\) 2.92643e12i 0.0891008i
\(506\) 1.22738e13i 0.370020i
\(507\) 5.78294e13i 1.72627i
\(508\) −5.03744e13 −1.48899
\(509\) −3.67101e13 −1.07448 −0.537238 0.843431i \(-0.680532\pi\)
−0.537238 + 0.843431i \(0.680532\pi\)
\(510\) 2.36866e13i 0.686517i
\(511\) 7.31362e13 2.09907
\(512\) 6.55476e13i 1.86297i
\(513\) 1.02583e14 2.88727
\(514\) 1.19950e14 3.34337
\(515\) 9.59752e12i 0.264925i
\(516\) 6.26327e13 + 1.38924e14i 1.71219 + 3.79777i
\(517\) −8.31015e12 −0.224986
\(518\) 1.87049e14i 5.01540i
\(519\) 2.41321e13i 0.640852i
\(520\) −7.83490e11 −0.0206071
\(521\) 5.47337e13i 1.42583i 0.701253 + 0.712913i \(0.252624\pi\)
−0.701253 + 0.712913i \(0.747376\pi\)
\(522\) −1.72336e14 −4.44656
\(523\) 8.36353e12i 0.213738i −0.994273 0.106869i \(-0.965917\pi\)
0.994273 0.106869i \(-0.0340825\pi\)
\(524\) 1.68165e14i 4.25676i
\(525\) 1.18918e14 2.98161
\(526\) 8.00367e13 1.98774
\(527\) −4.14263e12 −0.101911
\(528\) 3.23649e13i 0.788688i
\(529\) 4.62837e12 0.111725
\(530\) −2.44513e13 −0.584685
\(531\) 7.59220e13 1.79844
\(532\) −3.23704e14 −7.59608
\(533\) 3.93763e11 0.00915374
\(534\) 1.73980e14i 4.00675i
\(535\) 4.44210e12i 0.101349i
\(536\) 1.55035e14i 3.50434i
\(537\) 1.73820e13 0.389251
\(538\) 9.03058e13i 2.00357i
\(539\) 2.11811e13 0.465592
\(540\) 5.02087e13 1.09348
\(541\) −3.55836e13 −0.767828 −0.383914 0.923369i \(-0.625424\pi\)
−0.383914 + 0.923369i \(0.625424\pi\)
\(542\) 6.43438e13i 1.37566i
\(543\) 4.87700e12i 0.103313i
\(544\) 7.04337e13i 1.47838i
\(545\) 1.29432e13i 0.269191i
\(546\) 8.53675e12i 0.175926i
\(547\) 7.88966e13 1.61110 0.805548 0.592530i \(-0.201871\pi\)
0.805548 + 0.592530i \(0.201871\pi\)
\(548\) 4.89995e13i 0.991491i
\(549\) 6.11090e13i 1.22530i
\(550\) 1.64085e13i 0.326028i
\(551\) −1.04462e14 −2.05684
\(552\) 2.43329e14 4.74787
\(553\) 1.03577e14i 2.00280i
\(554\) 7.45466e13 1.42850
\(555\) 3.54350e13i 0.672926i
\(556\) 3.19192e13 0.600729
\(557\) −8.83010e13 −1.64699 −0.823493 0.567327i \(-0.807978\pi\)
−0.823493 + 0.567327i \(0.807978\pi\)
\(558\) 2.50321e13i 0.462728i
\(559\) 1.47686e12 6.65828e11i 0.0270570 0.0121984i
\(560\) −6.54718e13 −1.18881
\(561\) 1.47315e13i 0.265115i
\(562\) 5.77472e13i 1.03003i
\(563\) 3.50978e13 0.620495 0.310247 0.950656i \(-0.399588\pi\)
0.310247 + 0.950656i \(0.399588\pi\)
\(564\) 2.81502e14i 4.93271i
\(565\) −1.06878e13 −0.185629
\(566\) 9.88063e13i 1.70099i
\(567\) 1.04066e14i 1.77580i
\(568\) 5.59859e13 0.946971
\(569\) −3.13808e13 −0.526141 −0.263071 0.964777i \(-0.584735\pi\)
−0.263071 + 0.964777i \(0.584735\pi\)
\(570\) 8.67570e13 1.44188
\(571\) 8.66236e13i 1.42710i −0.700602 0.713552i \(-0.747085\pi\)
0.700602 0.713552i \(-0.252915\pi\)
\(572\) −8.32598e11 −0.0135974
\(573\) −7.38081e13 −1.19490
\(574\) 6.59291e13 1.05808
\(575\) −6.15695e13 −0.979550
\(576\) 1.23211e14 1.94329
\(577\) 4.60046e13i 0.719321i 0.933083 + 0.359660i \(0.117107\pi\)
−0.933083 + 0.359660i \(0.882893\pi\)
\(578\) 4.14494e13i 0.642508i
\(579\) 3.49866e13i 0.537662i
\(580\) −5.11286e13 −0.778975
\(581\) 1.19702e14i 1.80809i
\(582\) −1.43520e14 −2.14930
\(583\) −1.52071e13 −0.225790
\(584\) −2.00064e14 −2.94514
\(585\) 1.07549e12i 0.0156974i
\(586\) 1.73993e14i 2.51793i
\(587\) 1.77739e12i 0.0255031i 0.999919 + 0.0127515i \(0.00405905\pi\)
−0.999919 + 0.0127515i \(0.995941\pi\)
\(588\) 7.17498e14i 10.2079i
\(589\) 1.51732e13i 0.214043i
\(590\) 3.18664e13 0.445732
\(591\) 1.84032e13i 0.255244i
\(592\) 2.55370e14i 3.51206i
\(593\) 8.29707e12i 0.113149i 0.998398 + 0.0565746i \(0.0180179\pi\)
−0.998398 + 0.0565746i \(0.981982\pi\)
\(594\) 4.41778e13 0.597409
\(595\) −2.98008e13 −0.399616
\(596\) 1.99387e14i 2.65134i
\(597\) 1.40872e14 1.85761
\(598\) 4.41989e12i 0.0577971i
\(599\) −6.78681e13 −0.880100 −0.440050 0.897973i \(-0.645039\pi\)
−0.440050 + 0.897973i \(0.645039\pi\)
\(600\) −3.25300e14 −4.18339
\(601\) 1.16255e13i 0.148265i 0.997248 + 0.0741325i \(0.0236188\pi\)
−0.997248 + 0.0741325i \(0.976381\pi\)
\(602\) 2.47276e14 1.11482e14i 3.12751 1.41001i
\(603\) −2.12815e14 −2.66942
\(604\) 5.09134e13i 0.633355i
\(605\) 2.08140e13i 0.256790i
\(606\) −8.72238e13 −1.06726
\(607\) 3.16649e13i 0.384269i −0.981369 0.192134i \(-0.938459\pi\)
0.981369 0.192134i \(-0.0615409\pi\)
\(608\) 2.57978e14 3.10502
\(609\) 3.26037e14i 3.89206i
\(610\) 2.56490e13i 0.303684i
\(611\) −2.99256e12 −0.0351428
\(612\) 3.31861e14 3.86544
\(613\) 8.80871e13 1.01768 0.508839 0.860862i \(-0.330075\pi\)
0.508839 + 0.860862i \(0.330075\pi\)
\(614\) 9.58427e12i 0.109829i
\(615\) −1.24898e13 −0.141964
\(616\) −8.15872e13 −0.919853
\(617\) −8.82304e12 −0.0986717 −0.0493358 0.998782i \(-0.515710\pi\)
−0.0493358 + 0.998782i \(0.515710\pi\)
\(618\) 2.86059e14 3.17332
\(619\) 5.83774e13 0.642380 0.321190 0.947015i \(-0.395917\pi\)
0.321190 + 0.947015i \(0.395917\pi\)
\(620\) 7.42649e12i 0.0810634i
\(621\) 1.65768e14i 1.79491i
\(622\) 1.06548e14i 1.14444i
\(623\) 2.18889e14 2.33229
\(624\) 1.16549e13i 0.123193i
\(625\) 7.55421e13 0.792116
\(626\) −2.80316e14 −2.91593
\(627\) 5.39573e13 0.556817
\(628\) 1.42169e14i 1.45548i
\(629\) 1.16237e14i 1.18057i
\(630\) 1.80073e14i 1.81445i
\(631\) 6.00578e13i 0.600375i 0.953880 + 0.300188i \(0.0970493\pi\)
−0.953880 + 0.300188i \(0.902951\pi\)
\(632\) 2.83336e14i 2.81006i
\(633\) −1.38034e14 −1.35821
\(634\) 1.91285e14i 1.86739i
\(635\) 1.69860e13i 0.164522i
\(636\) 5.15133e14i 4.95032i
\(637\) 7.62750e12 0.0727252
\(638\) −4.49871e13 −0.425584
\(639\) 7.68513e13i 0.721351i
\(640\) −6.53797e11 −0.00608896
\(641\) 1.93396e14i 1.78713i 0.448933 + 0.893565i \(0.351804\pi\)
−0.448933 + 0.893565i \(0.648196\pi\)
\(642\) 1.32399e14 1.21397
\(643\) −9.91593e13 −0.902150 −0.451075 0.892486i \(-0.648959\pi\)
−0.451075 + 0.892486i \(0.648959\pi\)
\(644\) 5.23089e14i 4.72222i
\(645\) −4.68446e13 + 2.11195e13i −0.419625 + 0.189184i
\(646\) 2.84588e14 2.52961
\(647\) 1.71080e14i 1.50896i −0.656324 0.754479i \(-0.727889\pi\)
0.656324 0.754479i \(-0.272111\pi\)
\(648\) 2.84674e14i 2.49157i
\(649\) 1.98189e13 0.172130
\(650\) 5.90884e12i 0.0509255i
\(651\) −4.73572e13 −0.405025
\(652\) 2.49915e14i 2.12107i
\(653\) 8.58206e13i 0.722813i 0.932408 + 0.361406i \(0.117703\pi\)
−0.932408 + 0.361406i \(0.882297\pi\)
\(654\) −3.85780e14 −3.22441
\(655\) 5.67045e13 0.470339
\(656\) −9.00104e13 −0.740924
\(657\) 2.74626e14i 2.24345i
\(658\) −5.01055e14 −4.06215
\(659\) 1.56412e14 1.25847 0.629235 0.777215i \(-0.283368\pi\)
0.629235 + 0.777215i \(0.283368\pi\)
\(660\) 2.64093e13 0.210881
\(661\) 1.56927e14 1.24363 0.621814 0.783165i \(-0.286396\pi\)
0.621814 + 0.783165i \(0.286396\pi\)
\(662\) −2.96749e14 −2.33400
\(663\) 5.30496e12i 0.0414109i
\(664\) 3.27444e14i 2.53686i
\(665\) 1.09152e14i 0.839309i
\(666\) −7.02368e14 −5.36035
\(667\) 1.68805e14i 1.27866i
\(668\) 3.98105e14 2.99306
\(669\) 1.00626e14 0.750896
\(670\) −8.93241e13 −0.661599
\(671\) 1.59521e13i 0.117275i
\(672\) 8.05176e14i 5.87550i
\(673\) 2.20542e14i 1.59741i 0.601725 + 0.798703i \(0.294480\pi\)
−0.601725 + 0.798703i \(0.705520\pi\)
\(674\) 1.90347e14i 1.36851i
\(675\) 2.21611e14i 1.58151i
\(676\) 3.40070e14 2.40899
\(677\) 1.53249e14i 1.07759i 0.842436 + 0.538796i \(0.181121\pi\)
−0.842436 + 0.538796i \(0.818879\pi\)
\(678\) 3.18554e14i 2.22349i
\(679\) 1.80567e14i 1.25109i
\(680\) 8.15202e13 0.560687
\(681\) 7.79729e13 0.532363
\(682\) 6.53444e12i 0.0442880i
\(683\) 5.29142e13 0.356015 0.178008 0.984029i \(-0.443035\pi\)
0.178008 + 0.984029i \(0.443035\pi\)
\(684\) 1.21551e15i 8.11853i
\(685\) 1.65224e13 0.109552
\(686\) 7.55907e14 4.97562
\(687\) 6.20952e13i 0.405765i
\(688\) −3.37596e14 + 1.52202e14i −2.19006 + 0.987366i
\(689\) −5.47622e12 −0.0352683
\(690\) 1.40195e14i 0.896369i
\(691\) 2.26934e14i 1.44049i −0.693720 0.720245i \(-0.744029\pi\)
0.693720 0.720245i \(-0.255971\pi\)
\(692\) 1.41910e14 0.894300
\(693\) 1.11994e14i 0.700694i
\(694\) −1.06006e14 −0.658465
\(695\) 1.07630e13i 0.0663759i
\(696\) 8.91875e14i 5.46082i
\(697\) −4.09700e13 −0.249059
\(698\) 1.17601e14 0.709794
\(699\) 9.68718e13 0.580512
\(700\) 6.99304e14i 4.16079i
\(701\) 2.48822e14 1.46994 0.734968 0.678102i \(-0.237197\pi\)
0.734968 + 0.678102i \(0.237197\pi\)
\(702\) 1.59088e13 0.0933151
\(703\) −4.25741e14 −2.47953
\(704\) 3.21633e13 0.185993
\(705\) 9.49211e13 0.545026
\(706\) 3.94523e14i 2.24931i
\(707\) 1.09739e14i 0.621246i
\(708\) 6.71354e14i 3.77385i
\(709\) 1.36841e14 0.763811 0.381906 0.924201i \(-0.375268\pi\)
0.381906 + 0.924201i \(0.375268\pi\)
\(710\) 3.22565e13i 0.178783i
\(711\) −3.88933e14 −2.14055
\(712\) −5.98771e14 −3.27236
\(713\) 2.45192e13 0.133063
\(714\) 8.88228e14i 4.78667i
\(715\) 2.80749e11i 0.00150241i
\(716\) 1.02216e14i 0.543194i
\(717\) 1.71493e14i 0.905002i
\(718\) 2.56347e14i 1.34340i
\(719\) 1.12409e14 0.585001 0.292500 0.956265i \(-0.405513\pi\)
0.292500 + 0.956265i \(0.405513\pi\)
\(720\) 2.45847e14i 1.27058i
\(721\) 3.59900e14i 1.84716i
\(722\) 6.80006e14i 3.46598i
\(723\) −3.77857e14 −1.91265
\(724\) −2.86795e13 −0.144172
\(725\) 2.25671e14i 1.12664i
\(726\) −6.20372e14 −3.07588
\(727\) 3.16879e13i 0.156035i −0.996952 0.0780173i \(-0.975141\pi\)
0.996952 0.0780173i \(-0.0248589\pi\)
\(728\) −2.93803e13 −0.143681
\(729\) 2.14814e14 1.04334
\(730\) 1.15268e14i 0.556024i
\(731\) −1.53664e14 + 6.92778e13i −0.736180 + 0.331900i
\(732\) −5.40367e14 −2.57119
\(733\) 1.08536e14i 0.512924i −0.966554 0.256462i \(-0.917443\pi\)
0.966554 0.256462i \(-0.0825568\pi\)
\(734\) 4.05820e14i 1.90482i
\(735\) −2.41937e14 −1.12789
\(736\) 4.16879e14i 1.93028i
\(737\) −5.55539e13 −0.255492
\(738\) 2.47564e14i 1.13085i
\(739\) 1.36188e14i 0.617898i −0.951079 0.308949i \(-0.900023\pi\)
0.951079 0.308949i \(-0.0999773\pi\)
\(740\) −2.08378e14 −0.939059
\(741\) 1.94305e13 0.0869747
\(742\) −9.16903e14 −4.07665
\(743\) 3.99392e13i 0.176383i −0.996104 0.0881913i \(-0.971891\pi\)
0.996104 0.0881913i \(-0.0281087\pi\)
\(744\) 1.29546e14 0.568276
\(745\) 6.72324e13 0.292952
\(746\) 2.19925e14 0.951876
\(747\) 4.49480e14 1.93244
\(748\) 8.66299e13 0.369964
\(749\) 1.66575e14i 0.706644i
\(750\) 3.89164e14i 1.63993i
\(751\) 1.85094e14i 0.774806i −0.921910 0.387403i \(-0.873372\pi\)
0.921910 0.387403i \(-0.126628\pi\)
\(752\) 6.84070e14 2.84454
\(753\) 4.72604e14i 1.95219i
\(754\) −1.62002e13 −0.0664760
\(755\) −1.71678e13 −0.0699809
\(756\) 1.88279e15 7.62417
\(757\) 4.67882e14i 1.88216i −0.338183 0.941080i \(-0.609812\pi\)
0.338183 0.941080i \(-0.390188\pi\)
\(758\) 4.30109e14i 1.71883i
\(759\) 8.71923e13i 0.346154i
\(760\) 2.98585e14i 1.17760i
\(761\) 6.00935e13i 0.235453i 0.993046 + 0.117726i \(0.0375606\pi\)
−0.993046 + 0.117726i \(0.962439\pi\)
\(762\) 5.06278e14 1.97067
\(763\) 4.85361e14i 1.87691i
\(764\) 4.34033e14i 1.66746i
\(765\) 1.11902e14i 0.427101i
\(766\) 8.22283e14 3.11801
\(767\) 7.13695e12 0.0268866
\(768\) 4.71359e14i 1.76419i
\(769\) 4.69428e14 1.74557 0.872785 0.488104i \(-0.162311\pi\)
0.872785 + 0.488104i \(0.162311\pi\)
\(770\) 4.70068e13i 0.173663i
\(771\) −8.52118e14 −3.12772
\(772\) 2.05741e14 0.750300
\(773\) 1.61620e14i 0.585595i −0.956174 0.292798i \(-0.905414\pi\)
0.956174 0.292798i \(-0.0945862\pi\)
\(774\) −4.18615e14 9.28521e14i −1.50699 3.34262i
\(775\) −3.27790e13 −0.117243
\(776\) 4.93942e14i 1.75536i
\(777\) 1.32878e15i 4.69191i
\(778\) 3.09178e14 1.08470
\(779\) 1.50061e14i 0.523096i
\(780\) 9.51020e12 0.0329395