Properties

Label 43.11.b.b.42.2
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 42.2
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.33

$q$-expansion

\(f(q)\) \(=\) \(q-58.7853i q^{2} -301.513i q^{3} -2431.72 q^{4} -2781.13i q^{5} -17724.6 q^{6} +4095.06i q^{7} +82753.1i q^{8} -31861.2 q^{9} +O(q^{10})\) \(q-58.7853i q^{2} -301.513i q^{3} -2431.72 q^{4} -2781.13i q^{5} -17724.6 q^{6} +4095.06i q^{7} +82753.1i q^{8} -31861.2 q^{9} -163489. q^{10} -123581. q^{11} +733195. i q^{12} +347183. q^{13} +240730. q^{14} -838546. q^{15} +2.37459e6 q^{16} -82597.3 q^{17} +1.87297e6i q^{18} +1.73289e6i q^{19} +6.76291e6i q^{20} +1.23471e6 q^{21} +7.26474e6i q^{22} -1.02592e7 q^{23} +2.49512e7 q^{24} +2.03096e6 q^{25} -2.04093e7i q^{26} -8.19747e6i q^{27} -9.95803e6i q^{28} -6.06720e6i q^{29} +4.92942e7i q^{30} -4.26574e7 q^{31} -5.48521e7i q^{32} +3.72613e7i q^{33} +4.85551e6i q^{34} +1.13889e7 q^{35} +7.74775e7 q^{36} -1.00476e8i q^{37} +1.01868e8 q^{38} -1.04680e8i q^{39} +2.30147e8 q^{40} +9.51556e7 q^{41} -7.25831e7i q^{42} +(-1.46887e8 - 5.98259e6i) q^{43} +3.00514e8 q^{44} +8.86101e7i q^{45} +6.03091e8i q^{46} +6.18096e6 q^{47} -7.15971e8i q^{48} +2.65706e8 q^{49} -1.19391e8i q^{50} +2.49042e7i q^{51} -8.44251e8 q^{52} -3.72498e8 q^{53} -4.81891e8 q^{54} +3.43694e8i q^{55} -3.38879e8 q^{56} +5.22488e8 q^{57} -3.56662e8 q^{58} +7.30905e8 q^{59} +2.03911e9 q^{60} +5.55615e8i q^{61} +2.50763e9i q^{62} -1.30474e8i q^{63} -7.92916e8 q^{64} -9.65560e8i q^{65} +2.19042e9 q^{66} -1.30656e9 q^{67} +2.00853e8 q^{68} +3.09328e9i q^{69} -6.69499e8i q^{70} +2.26506e9i q^{71} -2.63662e9i q^{72} -1.19629e9i q^{73} -5.90651e9 q^{74} -6.12362e8i q^{75} -4.21389e9i q^{76} -5.06071e8i q^{77} -6.15367e9 q^{78} -5.10251e9 q^{79} -6.60404e9i q^{80} -4.35302e9 q^{81} -5.59375e9i q^{82} +7.51268e9 q^{83} -3.00248e9 q^{84} +2.29714e8i q^{85} +(-3.51689e8 + 8.63478e9i) q^{86} -1.82934e9 q^{87} -1.02267e10i q^{88} +5.82403e9i q^{89} +5.20898e9 q^{90} +1.42174e9i q^{91} +2.49475e10 q^{92} +1.28618e10i q^{93} -3.63350e8i q^{94} +4.81938e9 q^{95} -1.65386e10 q^{96} -8.05991e9 q^{97} -1.56196e10i q^{98} +3.93744e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 58.7853i 1.83704i −0.395372 0.918521i \(-0.629384\pi\)
0.395372 0.918521i \(-0.370616\pi\)
\(3\) 301.513i 1.24080i −0.784287 0.620398i \(-0.786971\pi\)
0.784287 0.620398i \(-0.213029\pi\)
\(4\) −2431.72 −2.37472
\(5\) 2781.13i 0.889960i −0.895540 0.444980i \(-0.853211\pi\)
0.895540 0.444980i \(-0.146789\pi\)
\(6\) −17724.6 −2.27939
\(7\) 4095.06i 0.243652i 0.992551 + 0.121826i \(0.0388750\pi\)
−0.992551 + 0.121826i \(0.961125\pi\)
\(8\) 82753.1i 2.52543i
\(9\) −31861.2 −0.539573
\(10\) −163489. −1.63489
\(11\) −123581. −0.767340 −0.383670 0.923470i \(-0.625340\pi\)
−0.383670 + 0.923470i \(0.625340\pi\)
\(12\) 733195.i 2.94655i
\(13\) 347183. 0.935065 0.467533 0.883976i \(-0.345143\pi\)
0.467533 + 0.883976i \(0.345143\pi\)
\(14\) 240730. 0.447599
\(15\) −838546. −1.10426
\(16\) 2.37459e6 2.26459
\(17\) −82597.3 −0.0581730 −0.0290865 0.999577i \(-0.509260\pi\)
−0.0290865 + 0.999577i \(0.509260\pi\)
\(18\) 1.87297e6i 0.991218i
\(19\) 1.73289e6i 0.699846i 0.936779 + 0.349923i \(0.113792\pi\)
−0.936779 + 0.349923i \(0.886208\pi\)
\(20\) 6.76291e6i 2.11341i
\(21\) 1.23471e6 0.302322
\(22\) 7.26474e6i 1.40964i
\(23\) −1.02592e7 −1.59395 −0.796974 0.604013i \(-0.793567\pi\)
−0.796974 + 0.604013i \(0.793567\pi\)
\(24\) 2.49512e7 3.13354
\(25\) 2.03096e6 0.207970
\(26\) 2.04093e7i 1.71775i
\(27\) 8.19747e6i 0.571296i
\(28\) 9.95803e6i 0.578606i
\(29\) 6.06720e6i 0.295800i −0.989002 0.147900i \(-0.952749\pi\)
0.989002 0.147900i \(-0.0472514\pi\)
\(30\) 4.92942e7i 2.02857i
\(31\) −4.26574e7 −1.49000 −0.745000 0.667064i \(-0.767551\pi\)
−0.745000 + 0.667064i \(0.767551\pi\)
\(32\) 5.48521e7i 1.63472i
\(33\) 3.72613e7i 0.952112i
\(34\) 4.85551e6i 0.106866i
\(35\) 1.13889e7 0.216841
\(36\) 7.74775e7 1.28134
\(37\) 1.00476e8i 1.44895i −0.689301 0.724475i \(-0.742082\pi\)
0.689301 0.724475i \(-0.257918\pi\)
\(38\) 1.01868e8 1.28565
\(39\) 1.04680e8i 1.16022i
\(40\) 2.30147e8 2.24753
\(41\) 9.51556e7 0.821325 0.410662 0.911787i \(-0.365298\pi\)
0.410662 + 0.911787i \(0.365298\pi\)
\(42\) 7.25831e7i 0.555379i
\(43\) −1.46887e8 5.98259e6i −0.999172 0.0406956i
\(44\) 3.00514e8 1.82222
\(45\) 8.86101e7i 0.480198i
\(46\) 6.03091e8i 2.92815i
\(47\) 6.18096e6 0.0269505 0.0134752 0.999909i \(-0.495711\pi\)
0.0134752 + 0.999909i \(0.495711\pi\)
\(48\) 7.15971e8i 2.80989i
\(49\) 2.65706e8 0.940634
\(50\) 1.19391e8i 0.382050i
\(51\) 2.49042e7i 0.0721808i
\(52\) −8.44251e8 −2.22052
\(53\) −3.72498e8 −0.890726 −0.445363 0.895350i \(-0.646925\pi\)
−0.445363 + 0.895350i \(0.646925\pi\)
\(54\) −4.81891e8 −1.04949
\(55\) 3.43694e8i 0.682902i
\(56\) −3.38879e8 −0.615325
\(57\) 5.22488e8 0.868365
\(58\) −3.56662e8 −0.543397
\(59\) 7.30905e8 1.02235 0.511177 0.859476i \(-0.329210\pi\)
0.511177 + 0.859476i \(0.329210\pi\)
\(60\) 2.03911e9 2.62231
\(61\) 5.55615e8i 0.657847i 0.944357 + 0.328924i \(0.106686\pi\)
−0.944357 + 0.328924i \(0.893314\pi\)
\(62\) 2.50763e9i 2.73719i
\(63\) 1.30474e8i 0.131468i
\(64\) −7.92916e8 −0.738460
\(65\) 9.65560e8i 0.832171i
\(66\) 2.19042e9 1.74907
\(67\) −1.30656e9 −0.967734 −0.483867 0.875142i \(-0.660768\pi\)
−0.483867 + 0.875142i \(0.660768\pi\)
\(68\) 2.00853e8 0.138145
\(69\) 3.09328e9i 1.97776i
\(70\) 6.69499e8i 0.398345i
\(71\) 2.26506e9i 1.25541i 0.778449 + 0.627707i \(0.216007\pi\)
−0.778449 + 0.627707i \(0.783993\pi\)
\(72\) 2.63662e9i 1.36265i
\(73\) 1.19629e9i 0.577062i −0.957471 0.288531i \(-0.906833\pi\)
0.957471 0.288531i \(-0.0931668\pi\)
\(74\) −5.90651e9 −2.66178
\(75\) 6.12362e8i 0.258049i
\(76\) 4.21389e9i 1.66194i
\(77\) 5.06071e8i 0.186964i
\(78\) −6.15367e9 −2.13138
\(79\) −5.10251e9 −1.65824 −0.829122 0.559067i \(-0.811159\pi\)
−0.829122 + 0.559067i \(0.811159\pi\)
\(80\) 6.60404e9i 2.01539i
\(81\) −4.35302e9 −1.24843
\(82\) 5.59375e9i 1.50881i
\(83\) 7.51268e9 1.90724 0.953618 0.301020i \(-0.0973272\pi\)
0.953618 + 0.301020i \(0.0973272\pi\)
\(84\) −3.00248e9 −0.717932
\(85\) 2.29714e8i 0.0517716i
\(86\) −3.51689e8 + 8.63478e9i −0.0747595 + 1.83552i
\(87\) −1.82934e9 −0.367027
\(88\) 1.02267e10i 1.93786i
\(89\) 5.82403e9i 1.04297i 0.853259 + 0.521487i \(0.174623\pi\)
−0.853259 + 0.521487i \(0.825377\pi\)
\(90\) 5.20898e9 0.882145
\(91\) 1.42174e9i 0.227831i
\(92\) 2.49475e10 3.78519
\(93\) 1.28618e10i 1.84879i
\(94\) 3.63350e8i 0.0495092i
\(95\) 4.81938e9 0.622835
\(96\) −1.65386e10 −2.02835
\(97\) −8.05991e9 −0.938580 −0.469290 0.883044i \(-0.655490\pi\)
−0.469290 + 0.883044i \(0.655490\pi\)
\(98\) 1.56196e10i 1.72798i
\(99\) 3.93744e9 0.414036
\(100\) −4.93872e9 −0.493872
\(101\) 4.21055e8 0.0400620 0.0200310 0.999799i \(-0.493624\pi\)
0.0200310 + 0.999799i \(0.493624\pi\)
\(102\) 1.46400e9 0.132599
\(103\) 2.05118e9 0.176936 0.0884682 0.996079i \(-0.471803\pi\)
0.0884682 + 0.996079i \(0.471803\pi\)
\(104\) 2.87305e10i 2.36144i
\(105\) 3.43390e9i 0.269055i
\(106\) 2.18974e10i 1.63630i
\(107\) 1.77156e10 1.26309 0.631547 0.775337i \(-0.282420\pi\)
0.631547 + 0.775337i \(0.282420\pi\)
\(108\) 1.99339e10i 1.35667i
\(109\) 1.07286e10 0.697288 0.348644 0.937255i \(-0.386642\pi\)
0.348644 + 0.937255i \(0.386642\pi\)
\(110\) 2.02042e10 1.25452
\(111\) −3.02948e10 −1.79785
\(112\) 9.72410e9i 0.551772i
\(113\) 2.05731e10i 1.11663i 0.829630 + 0.558314i \(0.188551\pi\)
−0.829630 + 0.558314i \(0.811449\pi\)
\(114\) 3.07147e10i 1.59522i
\(115\) 2.85321e10i 1.41855i
\(116\) 1.47537e10i 0.702443i
\(117\) −1.10617e10 −0.504536
\(118\) 4.29665e10i 1.87811i
\(119\) 3.38241e8i 0.0141740i
\(120\) 6.93923e10i 2.78872i
\(121\) −1.06652e10 −0.411190
\(122\) 3.26620e10 1.20849
\(123\) 2.86907e10i 1.01910i
\(124\) 1.03731e11 3.53834
\(125\) 3.28078e10i 1.07505i
\(126\) −7.66994e9 −0.241512
\(127\) −1.51740e10 −0.459283 −0.229641 0.973275i \(-0.573755\pi\)
−0.229641 + 0.973275i \(0.573755\pi\)
\(128\) 9.55672e9i 0.278137i
\(129\) −1.80383e9 + 4.42883e10i −0.0504949 + 1.23977i
\(130\) −5.67608e10 −1.52873
\(131\) 1.12052e10i 0.290443i −0.989399 0.145222i \(-0.953610\pi\)
0.989399 0.145222i \(-0.0463895\pi\)
\(132\) 9.06088e10i 2.26100i
\(133\) −7.09628e9 −0.170519
\(134\) 7.68067e10i 1.77777i
\(135\) −2.27982e10 −0.508431
\(136\) 6.83519e9i 0.146912i
\(137\) 7.63190e10i 1.58136i −0.612231 0.790679i \(-0.709728\pi\)
0.612231 0.790679i \(-0.290272\pi\)
\(138\) 1.81840e11 3.63324
\(139\) −7.87273e10 −1.51723 −0.758615 0.651539i \(-0.774123\pi\)
−0.758615 + 0.651539i \(0.774123\pi\)
\(140\) −2.76945e10 −0.514937
\(141\) 1.86364e9i 0.0334400i
\(142\) 1.33152e11 2.30625
\(143\) −4.29052e10 −0.717513
\(144\) −7.56575e10 −1.22191
\(145\) −1.68736e10 −0.263250
\(146\) −7.03244e10 −1.06009
\(147\) 8.01138e10i 1.16713i
\(148\) 2.44329e11i 3.44086i
\(149\) 3.16960e10i 0.431592i −0.976438 0.215796i \(-0.930765\pi\)
0.976438 0.215796i \(-0.0692346\pi\)
\(150\) −3.59979e10 −0.474046
\(151\) 1.06479e11i 1.35638i −0.734888 0.678188i \(-0.762766\pi\)
0.734888 0.678188i \(-0.237234\pi\)
\(152\) −1.43402e11 −1.76741
\(153\) 2.63165e9 0.0313886
\(154\) −2.97496e10 −0.343461
\(155\) 1.18636e11i 1.32604i
\(156\) 2.54553e11i 2.75521i
\(157\) 1.03422e11i 1.08421i −0.840311 0.542105i \(-0.817628\pi\)
0.840311 0.542105i \(-0.182372\pi\)
\(158\) 2.99953e11i 3.04626i
\(159\) 1.12313e11i 1.10521i
\(160\) −1.52551e11 −1.45484
\(161\) 4.20120e10i 0.388369i
\(162\) 2.55894e11i 2.29343i
\(163\) 1.65963e11i 1.44236i −0.692748 0.721180i \(-0.743600\pi\)
0.692748 0.721180i \(-0.256400\pi\)
\(164\) −2.31391e11 −1.95042
\(165\) 1.03628e11 0.847342
\(166\) 4.41635e11i 3.50367i
\(167\) −1.88099e10 −0.144812 −0.0724061 0.997375i \(-0.523068\pi\)
−0.0724061 + 0.997375i \(0.523068\pi\)
\(168\) 1.02177e11i 0.763492i
\(169\) −1.73223e10 −0.125653
\(170\) 1.35038e10 0.0951067
\(171\) 5.52119e10i 0.377618i
\(172\) 3.57187e11 + 1.45480e10i 2.37276 + 0.0966408i
\(173\) 3.76642e10 0.243052 0.121526 0.992588i \(-0.461221\pi\)
0.121526 + 0.992588i \(0.461221\pi\)
\(174\) 1.07538e11i 0.674245i
\(175\) 8.31691e9i 0.0506724i
\(176\) −2.93454e11 −1.73771
\(177\) 2.20378e11i 1.26853i
\(178\) 3.42368e11 1.91599
\(179\) 1.05319e11i 0.573116i 0.958063 + 0.286558i \(0.0925111\pi\)
−0.958063 + 0.286558i \(0.907489\pi\)
\(180\) 2.15475e11i 1.14034i
\(181\) −9.42249e10 −0.485035 −0.242517 0.970147i \(-0.577973\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(182\) 8.35773e10 0.418534
\(183\) 1.67525e11 0.816254
\(184\) 8.48981e11i 4.02540i
\(185\) −2.79436e11 −1.28951
\(186\) 7.56084e11 3.39630
\(187\) 1.02074e10 0.0446384
\(188\) −1.50303e10 −0.0639999
\(189\) 3.35691e10 0.139197
\(190\) 2.83309e11i 1.14417i
\(191\) 2.21542e10i 0.0871542i 0.999050 + 0.0435771i \(0.0138754\pi\)
−0.999050 + 0.0435771i \(0.986125\pi\)
\(192\) 2.39075e11i 0.916278i
\(193\) −3.99665e11 −1.49248 −0.746241 0.665676i \(-0.768143\pi\)
−0.746241 + 0.665676i \(0.768143\pi\)
\(194\) 4.73804e11i 1.72421i
\(195\) −2.91129e11 −1.03255
\(196\) −6.46121e11 −2.23375
\(197\) −2.90810e11 −0.980117 −0.490059 0.871689i \(-0.663025\pi\)
−0.490059 + 0.871689i \(0.663025\pi\)
\(198\) 2.31464e11i 0.760601i
\(199\) 4.67310e11i 1.49741i 0.662904 + 0.748704i \(0.269324\pi\)
−0.662904 + 0.748704i \(0.730676\pi\)
\(200\) 1.68068e11i 0.525214i
\(201\) 3.93946e11i 1.20076i
\(202\) 2.47519e10i 0.0735955i
\(203\) 2.48455e10 0.0720723
\(204\) 6.05599e10i 0.171409i
\(205\) 2.64640e11i 0.730946i
\(206\) 1.20579e11i 0.325040i
\(207\) 3.26871e11 0.860051
\(208\) 8.24419e11 2.11754
\(209\) 2.14152e11i 0.537019i
\(210\) −2.01863e11 −0.494265
\(211\) 6.62830e11i 1.58486i 0.609965 + 0.792428i \(0.291183\pi\)
−0.609965 + 0.792428i \(0.708817\pi\)
\(212\) 9.05809e11 2.11523
\(213\) 6.82944e11 1.55771
\(214\) 1.04141e12i 2.32036i
\(215\) −1.66384e10 + 4.08510e11i −0.0362175 + 0.889223i
\(216\) 6.78367e11 1.44277
\(217\) 1.74685e11i 0.363042i
\(218\) 6.30687e11i 1.28095i
\(219\) −3.60697e11 −0.716016
\(220\) 8.35766e11i 1.62170i
\(221\) −2.86764e10 −0.0543955
\(222\) 1.78089e12i 3.30273i
\(223\) 2.54463e11i 0.461424i 0.973022 + 0.230712i \(0.0741056\pi\)
−0.973022 + 0.230712i \(0.925894\pi\)
\(224\) 2.24623e11 0.398303
\(225\) −6.47089e10 −0.112215
\(226\) 1.20940e12 2.05129
\(227\) 8.55296e11i 1.41902i 0.704698 + 0.709508i \(0.251083\pi\)
−0.704698 + 0.709508i \(0.748917\pi\)
\(228\) −1.27054e12 −2.06213
\(229\) −1.39540e11 −0.221575 −0.110787 0.993844i \(-0.535337\pi\)
−0.110787 + 0.993844i \(0.535337\pi\)
\(230\) 1.67727e12 2.60594
\(231\) −1.52587e11 −0.231984
\(232\) 5.02080e11 0.747021
\(233\) 4.38920e11i 0.639154i −0.947560 0.319577i \(-0.896459\pi\)
0.947560 0.319577i \(-0.103541\pi\)
\(234\) 6.50265e11i 0.926854i
\(235\) 1.71900e10i 0.0239849i
\(236\) −1.77735e12 −2.42781
\(237\) 1.53847e12i 2.05754i
\(238\) −1.98836e10 −0.0260382
\(239\) −1.22437e12 −1.57008 −0.785041 0.619444i \(-0.787358\pi\)
−0.785041 + 0.619444i \(0.787358\pi\)
\(240\) −1.99121e12 −2.50069
\(241\) 1.20039e11i 0.147652i 0.997271 + 0.0738259i \(0.0235209\pi\)
−0.997271 + 0.0738259i \(0.976479\pi\)
\(242\) 6.26958e11i 0.755373i
\(243\) 8.28441e11i 0.977755i
\(244\) 1.35110e12i 1.56221i
\(245\) 7.38961e11i 0.837127i
\(246\) −1.68659e12 −1.87212
\(247\) 6.01629e11i 0.654401i
\(248\) 3.53004e12i 3.76288i
\(249\) 2.26517e12i 2.36649i
\(250\) −1.92862e12 −1.97490
\(251\) 8.36159e11 0.839306 0.419653 0.907685i \(-0.362152\pi\)
0.419653 + 0.907685i \(0.362152\pi\)
\(252\) 3.17275e11i 0.312200i
\(253\) 1.26784e12 1.22310
\(254\) 8.92006e11i 0.843722i
\(255\) 6.92617e10 0.0642380
\(256\) −1.37374e12 −1.24941
\(257\) 5.72904e10i 0.0510994i 0.999674 + 0.0255497i \(0.00813361\pi\)
−0.999674 + 0.0255497i \(0.991866\pi\)
\(258\) 2.60350e12 + 1.06039e11i 2.27750 + 0.0927612i
\(259\) 4.11455e11 0.353040
\(260\) 2.34797e12i 1.97618i
\(261\) 1.93308e11i 0.159606i
\(262\) −6.58699e11 −0.533557
\(263\) 1.94524e12i 1.54594i −0.634441 0.772971i \(-0.718770\pi\)
0.634441 0.772971i \(-0.281230\pi\)
\(264\) −3.08349e12 −2.40449
\(265\) 1.03596e12i 0.792711i
\(266\) 4.17157e11i 0.313250i
\(267\) 1.75602e12 1.29412
\(268\) 3.17719e12 2.29810
\(269\) −2.22693e11 −0.158105 −0.0790525 0.996870i \(-0.525189\pi\)
−0.0790525 + 0.996870i \(0.525189\pi\)
\(270\) 1.34020e12i 0.934009i
\(271\) 1.96371e12 1.34348 0.671741 0.740786i \(-0.265547\pi\)
0.671741 + 0.740786i \(0.265547\pi\)
\(272\) −1.96135e11 −0.131738
\(273\) 4.28672e11 0.282691
\(274\) −4.48644e12 −2.90502
\(275\) −2.50988e11 −0.159584
\(276\) 7.52199e12i 4.69664i
\(277\) 2.96481e12i 1.81802i −0.416774 0.909010i \(-0.636840\pi\)
0.416774 0.909010i \(-0.363160\pi\)
\(278\) 4.62801e12i 2.78721i
\(279\) 1.35912e12 0.803963
\(280\) 9.42466e11i 0.547615i
\(281\) 1.19276e12 0.680803 0.340401 0.940280i \(-0.389437\pi\)
0.340401 + 0.940280i \(0.389437\pi\)
\(282\) −1.09555e11 −0.0614307
\(283\) −1.85174e12 −1.02011 −0.510056 0.860141i \(-0.670375\pi\)
−0.510056 + 0.860141i \(0.670375\pi\)
\(284\) 5.50798e12i 2.98126i
\(285\) 1.45311e12i 0.772810i
\(286\) 2.52220e12i 1.31810i
\(287\) 3.89668e11i 0.200117i
\(288\) 1.74766e12i 0.882050i
\(289\) −2.00917e12 −0.996616
\(290\) 9.91923e11i 0.483602i
\(291\) 2.43017e12i 1.16459i
\(292\) 2.90904e12i 1.37036i
\(293\) 1.59940e12 0.740662 0.370331 0.928900i \(-0.379244\pi\)
0.370331 + 0.928900i \(0.379244\pi\)
\(294\) −4.70952e12 −2.14407
\(295\) 2.03274e12i 0.909854i
\(296\) 8.31470e12 3.65921
\(297\) 1.01305e12i 0.438378i
\(298\) −1.86326e12 −0.792853
\(299\) −3.56182e12 −1.49045
\(300\) 1.48909e12i 0.612794i
\(301\) 2.44991e10 6.01510e11i 0.00991556 0.243450i
\(302\) −6.25942e12 −2.49172
\(303\) 1.26954e11i 0.0497087i
\(304\) 4.11490e12i 1.58486i
\(305\) 1.54524e12 0.585458
\(306\) 1.54703e11i 0.0576621i
\(307\) −4.23749e12 −1.55388 −0.776938 0.629577i \(-0.783228\pi\)
−0.776938 + 0.629577i \(0.783228\pi\)
\(308\) 1.23062e12i 0.443988i
\(309\) 6.18457e11i 0.219542i
\(310\) 6.97404e12 2.43599
\(311\) 1.81080e12 0.622400 0.311200 0.950345i \(-0.399269\pi\)
0.311200 + 0.950345i \(0.399269\pi\)
\(312\) 8.66263e12 2.93006
\(313\) 2.35705e12i 0.784597i 0.919838 + 0.392299i \(0.128320\pi\)
−0.919838 + 0.392299i \(0.871680\pi\)
\(314\) −6.07968e12 −1.99174
\(315\) −3.62864e11 −0.117001
\(316\) 1.24079e13 3.93787
\(317\) −2.44343e11 −0.0763315 −0.0381657 0.999271i \(-0.512151\pi\)
−0.0381657 + 0.999271i \(0.512151\pi\)
\(318\) 6.60236e12 2.03032
\(319\) 7.49789e11i 0.226979i
\(320\) 2.20520e12i 0.657201i
\(321\) 5.34147e12i 1.56724i
\(322\) −2.46969e12 −0.713450
\(323\) 1.43132e11i 0.0407121i
\(324\) 1.05853e13 2.96469
\(325\) 7.05116e11 0.194466
\(326\) −9.75620e12 −2.64968
\(327\) 3.23483e12i 0.865192i
\(328\) 7.87442e12i 2.07419i
\(329\) 2.53114e10i 0.00656654i
\(330\) 6.09182e12i 1.55660i
\(331\) 4.84332e12i 1.21900i −0.792787 0.609499i \(-0.791371\pi\)
0.792787 0.609499i \(-0.208629\pi\)
\(332\) −1.82687e13 −4.52916
\(333\) 3.20129e12i 0.781814i
\(334\) 1.10575e12i 0.266026i
\(335\) 3.63371e12i 0.861245i
\(336\) 2.93195e12 0.684636
\(337\) 1.12548e12 0.258934 0.129467 0.991584i \(-0.458673\pi\)
0.129467 + 0.991584i \(0.458673\pi\)
\(338\) 1.01830e12i 0.230829i
\(339\) 6.20307e12 1.38551
\(340\) 5.58598e11i 0.122943i
\(341\) 5.27164e12 1.14334
\(342\) −3.24565e12 −0.693699
\(343\) 2.24483e12i 0.472839i
\(344\) 4.95078e11 1.21553e13i 0.102774 2.52333i
\(345\) 8.60282e12 1.76013
\(346\) 2.21410e12i 0.446496i
\(347\) 7.96450e12i 1.58311i −0.611098 0.791555i \(-0.709272\pi\)
0.611098 0.791555i \(-0.290728\pi\)
\(348\) 4.44844e12 0.871588
\(349\) 6.88437e12i 1.32965i 0.747000 + 0.664825i \(0.231494\pi\)
−0.747000 + 0.664825i \(0.768506\pi\)
\(350\) 4.88912e11 0.0930874
\(351\) 2.84602e12i 0.534199i
\(352\) 6.77867e12i 1.25439i
\(353\) −7.60397e12 −1.38729 −0.693644 0.720318i \(-0.743996\pi\)
−0.693644 + 0.720318i \(0.743996\pi\)
\(354\) −1.29550e13 −2.33035
\(355\) 6.29941e12 1.11727
\(356\) 1.41624e13i 2.47678i
\(357\) −1.01984e11 −0.0175870
\(358\) 6.19123e12 1.05284
\(359\) 1.16452e12 0.195287 0.0976434 0.995221i \(-0.468870\pi\)
0.0976434 + 0.995221i \(0.468870\pi\)
\(360\) −7.33276e12 −1.21271
\(361\) 3.12817e12 0.510216
\(362\) 5.53904e12i 0.891029i
\(363\) 3.21570e12i 0.510202i
\(364\) 3.45726e12i 0.541035i
\(365\) −3.32704e12 −0.513562
\(366\) 9.84804e12i 1.49949i
\(367\) −2.37467e11 −0.0356675 −0.0178338 0.999841i \(-0.505677\pi\)
−0.0178338 + 0.999841i \(0.505677\pi\)
\(368\) −2.43614e13 −3.60964
\(369\) −3.03177e12 −0.443164
\(370\) 1.64268e13i 2.36888i
\(371\) 1.52540e12i 0.217027i
\(372\) 3.12762e13i 4.39035i
\(373\) 7.65200e12i 1.05982i 0.848055 + 0.529908i \(0.177774\pi\)
−0.848055 + 0.529908i \(0.822226\pi\)
\(374\) 6.00048e11i 0.0820027i
\(375\) −9.89199e12 −1.33391
\(376\) 5.11494e11i 0.0680614i
\(377\) 2.10643e12i 0.276592i
\(378\) 1.97337e12i 0.255712i
\(379\) 2.37829e12 0.304136 0.152068 0.988370i \(-0.451407\pi\)
0.152068 + 0.988370i \(0.451407\pi\)
\(380\) −1.17194e13 −1.47906
\(381\) 4.57515e12i 0.569876i
\(382\) 1.30234e12 0.160106
\(383\) 1.19635e13i 1.45166i −0.687876 0.725829i \(-0.741457\pi\)
0.687876 0.725829i \(-0.258543\pi\)
\(384\) −2.88148e12 −0.345111
\(385\) −1.40745e12 −0.166390
\(386\) 2.34944e13i 2.74175i
\(387\) 4.67999e12 + 1.90613e11i 0.539126 + 0.0219582i
\(388\) 1.95994e13 2.22887
\(389\) 3.01793e12i 0.338814i 0.985546 + 0.169407i \(0.0541853\pi\)
−0.985546 + 0.169407i \(0.945815\pi\)
\(390\) 1.71141e13i 1.89685i
\(391\) 8.47382e11 0.0927247
\(392\) 2.19880e13i 2.37550i
\(393\) −3.37850e12 −0.360381
\(394\) 1.70954e13i 1.80052i
\(395\) 1.41907e13i 1.47577i
\(396\) −9.57473e12 −0.983220
\(397\) −3.39287e12 −0.344045 −0.172022 0.985093i \(-0.555030\pi\)
−0.172022 + 0.985093i \(0.555030\pi\)
\(398\) 2.74710e13 2.75080
\(399\) 2.13962e12i 0.211579i
\(400\) 4.82271e12 0.470968
\(401\) 1.35236e13 1.30428 0.652141 0.758098i \(-0.273871\pi\)
0.652141 + 0.758098i \(0.273871\pi\)
\(402\) 2.31582e13 2.20585
\(403\) −1.48099e13 −1.39325
\(404\) −1.02389e12 −0.0951361
\(405\) 1.21063e13i 1.11106i
\(406\) 1.46055e12i 0.132400i
\(407\) 1.24169e13i 1.11184i
\(408\) −2.06090e12 −0.182287
\(409\) 8.00571e12i 0.699493i −0.936844 0.349746i \(-0.886268\pi\)
0.936844 0.349746i \(-0.113732\pi\)
\(410\) −1.55569e13 −1.34278
\(411\) −2.30112e13 −1.96214
\(412\) −4.98789e12 −0.420175
\(413\) 2.99310e12i 0.249099i
\(414\) 1.92152e13i 1.57995i
\(415\) 2.08937e13i 1.69736i
\(416\) 1.90437e13i 1.52857i
\(417\) 2.37373e13i 1.88257i
\(418\) −1.25890e13 −0.986527
\(419\) 2.17731e13i 1.68597i −0.537936 0.842986i \(-0.680796\pi\)
0.537936 0.842986i \(-0.319204\pi\)
\(420\) 8.35027e12i 0.638931i
\(421\) 3.22439e11i 0.0243802i 0.999926 + 0.0121901i \(0.00388033\pi\)
−0.999926 + 0.0121901i \(0.996120\pi\)
\(422\) 3.89647e13 2.91145
\(423\) −1.96933e11 −0.0145417
\(424\) 3.08254e13i 2.24946i
\(425\) −1.67752e11 −0.0120983
\(426\) 4.01471e13i 2.86158i
\(427\) −2.27528e12 −0.160286
\(428\) −4.30792e13 −2.99950
\(429\) 1.29365e13i 0.890287i
\(430\) 2.40144e13 + 9.78091e11i 1.63354 + 0.0665330i
\(431\) −1.35035e13 −0.907947 −0.453974 0.891015i \(-0.649994\pi\)
−0.453974 + 0.891015i \(0.649994\pi\)
\(432\) 1.94657e13i 1.29375i
\(433\) 8.25814e12i 0.542554i 0.962501 + 0.271277i \(0.0874459\pi\)
−0.962501 + 0.271277i \(0.912554\pi\)
\(434\) −1.02689e13 −0.666923
\(435\) 5.08763e12i 0.326640i
\(436\) −2.60890e13 −1.65587
\(437\) 1.77780e13i 1.11552i
\(438\) 2.12037e13i 1.31535i
\(439\) 7.62272e12 0.467506 0.233753 0.972296i \(-0.424899\pi\)
0.233753 + 0.972296i \(0.424899\pi\)
\(440\) −2.84418e13 −1.72462
\(441\) −8.46571e12 −0.507540
\(442\) 1.68575e12i 0.0999269i
\(443\) 2.83041e13 1.65894 0.829469 0.558553i \(-0.188643\pi\)
0.829469 + 0.558553i \(0.188643\pi\)
\(444\) 7.36684e13 4.26940
\(445\) 1.61974e13 0.928206
\(446\) 1.49587e13 0.847656
\(447\) −9.55677e12 −0.535518
\(448\) 3.24704e12i 0.179927i
\(449\) 1.76773e13i 0.968690i 0.874877 + 0.484345i \(0.160942\pi\)
−0.874877 + 0.484345i \(0.839058\pi\)
\(450\) 3.80394e12i 0.206144i
\(451\) −1.17594e13 −0.630235
\(452\) 5.00280e13i 2.65168i
\(453\) −3.21049e13 −1.68298
\(454\) 5.02789e13 2.60679
\(455\) 3.95403e12 0.202760
\(456\) 4.32375e13i 2.19299i
\(457\) 3.19607e13i 1.60338i −0.597742 0.801689i \(-0.703935\pi\)
0.597742 0.801689i \(-0.296065\pi\)
\(458\) 8.20289e12i 0.407042i
\(459\) 6.77089e11i 0.0332340i
\(460\) 6.93821e13i 3.36867i
\(461\) 2.66536e13 1.28012 0.640061 0.768324i \(-0.278909\pi\)
0.640061 + 0.768324i \(0.278909\pi\)
\(462\) 8.96989e12i 0.426164i
\(463\) 8.75833e12i 0.411639i −0.978590 0.205820i \(-0.934014\pi\)
0.978590 0.205820i \(-0.0659860\pi\)
\(464\) 1.44071e13i 0.669865i
\(465\) 3.57702e13 1.64535
\(466\) −2.58021e13 −1.17415
\(467\) 2.30755e13i 1.03889i 0.854505 + 0.519443i \(0.173860\pi\)
−0.854505 + 0.519443i \(0.826140\pi\)
\(468\) 2.68989e13 1.19813
\(469\) 5.35045e12i 0.235790i
\(470\) −1.01052e12 −0.0440612
\(471\) −3.11830e13 −1.34528
\(472\) 6.04847e13i 2.58188i
\(473\) 1.81524e13 + 7.39334e11i 0.766704 + 0.0312273i
\(474\) 9.04398e13 3.77979
\(475\) 3.51943e12i 0.145547i
\(476\) 8.22506e11i 0.0336593i
\(477\) 1.18682e13 0.480612
\(478\) 7.19749e13i 2.88431i
\(479\) −2.26972e13 −0.900110 −0.450055 0.893001i \(-0.648596\pi\)
−0.450055 + 0.893001i \(0.648596\pi\)
\(480\) 4.59960e13i 1.80515i
\(481\) 3.48836e13i 1.35486i
\(482\) 7.05656e12 0.271242
\(483\) −1.26672e13 −0.481886
\(484\) 2.59348e13 0.976462
\(485\) 2.24156e13i 0.835299i
\(486\) 4.87002e13 1.79618
\(487\) −3.49809e13 −1.27698 −0.638492 0.769628i \(-0.720442\pi\)
−0.638492 + 0.769628i \(0.720442\pi\)
\(488\) −4.59789e13 −1.66134
\(489\) −5.00401e13 −1.78967
\(490\) −4.34401e13 −1.53784
\(491\) 1.18333e13i 0.414666i 0.978270 + 0.207333i \(0.0664784\pi\)
−0.978270 + 0.207333i \(0.933522\pi\)
\(492\) 6.97676e13i 2.42007i
\(493\) 5.01134e11i 0.0172076i
\(494\) 3.53670e13 1.20216
\(495\) 1.09505e13i 0.368475i
\(496\) −1.01294e14 −3.37424
\(497\) −9.27554e12 −0.305884
\(498\) −1.33159e14 −4.34734
\(499\) 2.21676e13i 0.716501i −0.933625 0.358251i \(-0.883373\pi\)
0.933625 0.358251i \(-0.116627\pi\)
\(500\) 7.97793e13i 2.55294i
\(501\) 5.67145e12i 0.179682i
\(502\) 4.91539e13i 1.54184i
\(503\) 4.12286e12i 0.128044i −0.997948 0.0640220i \(-0.979607\pi\)
0.997948 0.0640220i \(-0.0203928\pi\)
\(504\) 1.07971e13 0.332013
\(505\) 1.17101e12i 0.0356536i
\(506\) 7.45305e13i 2.24689i
\(507\) 5.22290e12i 0.155909i
\(508\) 3.68988e13 1.09067
\(509\) −2.25492e13 −0.659997 −0.329999 0.943981i \(-0.607048\pi\)
−0.329999 + 0.943981i \(0.607048\pi\)
\(510\) 4.07157e12i 0.118008i
\(511\) 4.89888e12 0.140602
\(512\) 7.09697e13i 2.01708i
\(513\) 1.42053e13 0.399819
\(514\) 3.36783e12 0.0938718
\(515\) 5.70459e12i 0.157466i
\(516\) 4.38641e12 1.07697e14i 0.119911 2.94410i
\(517\) −7.63848e11 −0.0206802
\(518\) 2.41875e13i 0.648549i
\(519\) 1.13563e13i 0.301577i
\(520\) 7.99032e13 2.10159
\(521\) 2.68827e13i 0.700299i −0.936694 0.350150i \(-0.886131\pi\)
0.936694 0.350150i \(-0.113869\pi\)
\(522\) 1.13637e13 0.293202
\(523\) 2.93357e13i 0.749700i 0.927085 + 0.374850i \(0.122306\pi\)
−0.927085 + 0.374850i \(0.877694\pi\)
\(524\) 2.72478e13i 0.689723i
\(525\) 2.50766e12 0.0628741
\(526\) −1.14351e14 −2.83996
\(527\) 3.52339e12 0.0866777
\(528\) 8.84803e13i 2.15614i
\(529\) 6.38247e13 1.54067
\(530\) 6.08995e13 1.45624
\(531\) −2.32875e13 −0.551634
\(532\) 1.72561e13 0.404935
\(533\) 3.30364e13 0.767992
\(534\) 1.03228e14i 2.37735i
\(535\) 4.92692e13i 1.12410i
\(536\) 1.08122e14i 2.44394i
\(537\) 3.17552e13 0.711120
\(538\) 1.30911e13i 0.290445i
\(539\) −3.28361e13 −0.721786
\(540\) 5.54388e13 1.20738
\(541\) 1.04143e13 0.224722 0.112361 0.993667i \(-0.464159\pi\)
0.112361 + 0.993667i \(0.464159\pi\)
\(542\) 1.15438e14i 2.46803i
\(543\) 2.84101e13i 0.601829i
\(544\) 4.53064e12i 0.0950965i
\(545\) 2.98377e13i 0.620559i
\(546\) 2.51997e13i 0.519316i
\(547\) −2.26544e13 −0.462611 −0.231306 0.972881i \(-0.574300\pi\)
−0.231306 + 0.972881i \(0.574300\pi\)
\(548\) 1.85586e14i 3.75529i
\(549\) 1.77026e13i 0.354957i
\(550\) 1.47544e13i 0.293163i
\(551\) 1.05138e13 0.207014
\(552\) −2.55979e14 −4.99470
\(553\) 2.08951e13i 0.404035i
\(554\) −1.74288e14 −3.33978
\(555\) 8.42537e13i 1.60002i
\(556\) 1.91442e14 3.60300
\(557\) −7.42359e13 −1.38464 −0.692322 0.721589i \(-0.743412\pi\)
−0.692322 + 0.721589i \(0.743412\pi\)
\(558\) 7.98963e13i 1.47691i
\(559\) −5.09966e13 2.07706e12i −0.934291 0.0380530i
\(560\) 2.70440e13 0.491055
\(561\) 3.07768e12i 0.0553872i
\(562\) 7.01168e13i 1.25066i
\(563\) 6.40693e13 1.13268 0.566341 0.824171i \(-0.308359\pi\)
0.566341 + 0.824171i \(0.308359\pi\)
\(564\) 4.53185e12i 0.0794108i
\(565\) 5.72165e13 0.993754
\(566\) 1.08855e14i 1.87399i
\(567\) 1.78259e13i 0.304184i
\(568\) −1.87441e14 −3.17046
\(569\) −3.19302e13 −0.535352 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(570\) −8.54213e13 −1.41969
\(571\) 9.43273e13i 1.55402i −0.629488 0.777011i \(-0.716735\pi\)
0.629488 0.777011i \(-0.283265\pi\)
\(572\) 1.04333e14 1.70389
\(573\) 6.67977e12 0.108141
\(574\) 2.29068e13 0.367624
\(575\) −2.08360e13 −0.331494
\(576\) 2.52633e13 0.398453
\(577\) 6.67376e13i 1.04350i −0.853099 0.521749i \(-0.825280\pi\)
0.853099 0.521749i \(-0.174720\pi\)
\(578\) 1.18110e14i 1.83083i
\(579\) 1.20504e14i 1.85186i
\(580\) 4.10319e13 0.625147
\(581\) 3.07649e13i 0.464702i
\(582\) 1.42858e14 2.13939
\(583\) 4.60336e13 0.683490
\(584\) 9.89968e13 1.45733
\(585\) 3.07639e13i 0.449017i
\(586\) 9.40215e13i 1.36063i
\(587\) 3.87372e13i 0.555825i 0.960606 + 0.277912i \(0.0896425\pi\)
−0.960606 + 0.277912i \(0.910357\pi\)
\(588\) 1.94814e14i 2.77162i
\(589\) 7.39205e13i 1.04277i
\(590\) −1.19495e14 −1.67144
\(591\) 8.76830e13i 1.21612i
\(592\) 2.38589e14i 3.28128i
\(593\) 2.58904e13i 0.353073i −0.984294 0.176537i \(-0.943511\pi\)
0.984294 0.176537i \(-0.0564894\pi\)
\(594\) 5.95525e13 0.805319
\(595\) −9.40691e11 −0.0126143
\(596\) 7.70758e13i 1.02491i
\(597\) 1.40900e14 1.85798
\(598\) 2.09383e14i 2.73801i
\(599\) 3.67692e12 0.0476815 0.0238407 0.999716i \(-0.492411\pi\)
0.0238407 + 0.999716i \(0.492411\pi\)
\(600\) 5.06749e13 0.651683
\(601\) 1.31596e14i 1.67830i −0.543902 0.839148i \(-0.683054\pi\)
0.543902 0.839148i \(-0.316946\pi\)
\(602\) −3.53600e13 1.44019e12i −0.447228 0.0182153i
\(603\) 4.16287e13 0.522163
\(604\) 2.58927e14i 3.22102i
\(605\) 2.96613e13i 0.365943i
\(606\) −7.46302e12 −0.0913170
\(607\) 9.60688e12i 0.116584i 0.998300 + 0.0582920i \(0.0185654\pi\)
−0.998300 + 0.0582920i \(0.981435\pi\)
\(608\) 9.50525e13 1.14405
\(609\) 7.49126e12i 0.0894269i
\(610\) 9.08373e13i 1.07551i
\(611\) 2.14593e12 0.0252005
\(612\) −6.39943e12 −0.0745391
\(613\) 5.67285e12 0.0655388 0.0327694 0.999463i \(-0.489567\pi\)
0.0327694 + 0.999463i \(0.489567\pi\)
\(614\) 2.49102e14i 2.85454i
\(615\) −7.97924e13 −0.906955
\(616\) 4.18790e13 0.472163
\(617\) 6.89629e13 0.771240 0.385620 0.922658i \(-0.373988\pi\)
0.385620 + 0.922658i \(0.373988\pi\)
\(618\) −3.63562e13 −0.403308
\(619\) 8.35140e13 0.918980 0.459490 0.888183i \(-0.348032\pi\)
0.459490 + 0.888183i \(0.348032\pi\)
\(620\) 2.88489e14i 3.14898i
\(621\) 8.40995e13i 0.910616i
\(622\) 1.06449e14i 1.14337i
\(623\) −2.38498e13 −0.254123
\(624\) 2.48573e14i 2.62743i
\(625\) −7.14090e13 −0.748778
\(626\) 1.38560e14 1.44134
\(627\) −6.45695e13 −0.666331
\(628\) 2.51492e14i 2.57470i
\(629\) 8.29904e12i 0.0842897i
\(630\) 2.13311e13i 0.214936i
\(631\) 1.17694e13i 0.117654i 0.998268 + 0.0588271i \(0.0187361\pi\)
−0.998268 + 0.0588271i \(0.981264\pi\)
\(632\) 4.22249e14i 4.18777i
\(633\) 1.99852e14 1.96648
\(634\) 1.43638e13i 0.140224i
\(635\) 4.22007e13i 0.408743i
\(636\) 2.73113e14i 2.62457i
\(637\) 9.22486e13 0.879554
\(638\) 4.40766e13 0.416970
\(639\) 7.21675e13i 0.677388i
\(640\) −2.65784e13 −0.247531
\(641\) 1.39288e14i 1.28713i 0.765392 + 0.643565i \(0.222545\pi\)
−0.765392 + 0.643565i \(0.777455\pi\)
\(642\) −3.14000e14 −2.87909
\(643\) −8.45328e13 −0.769078 −0.384539 0.923109i \(-0.625640\pi\)
−0.384539 + 0.923109i \(0.625640\pi\)
\(644\) 1.02161e14i 0.922269i
\(645\) 1.23171e14 + 5.01668e12i 1.10334 + 0.0449385i
\(646\) −8.41405e12 −0.0747898
\(647\) 7.54213e13i 0.665231i −0.943063 0.332615i \(-0.892069\pi\)
0.943063 0.332615i \(-0.107931\pi\)
\(648\) 3.60226e14i 3.15283i
\(649\) −9.03259e13 −0.784492
\(650\) 4.14505e13i 0.357242i
\(651\) −5.26698e13 −0.450460
\(652\) 4.03575e14i 3.42521i
\(653\) 5.99341e13i 0.504787i 0.967625 + 0.252393i \(0.0812177\pi\)
−0.967625 + 0.252393i \(0.918782\pi\)
\(654\) −1.90161e14 −1.58939
\(655\) −3.11630e13 −0.258483
\(656\) 2.25956e14 1.85996
\(657\) 3.81153e13i 0.311367i
\(658\) 1.48794e12 0.0120630
\(659\) −2.14727e14 −1.72766 −0.863832 0.503781i \(-0.831942\pi\)
−0.863832 + 0.503781i \(0.831942\pi\)
\(660\) −2.51995e14 −2.01220
\(661\) 4.43828e13 0.351728 0.175864 0.984414i \(-0.443728\pi\)
0.175864 + 0.984414i \(0.443728\pi\)
\(662\) −2.84716e14 −2.23935
\(663\) 8.64632e12i 0.0674937i
\(664\) 6.21698e14i 4.81658i
\(665\) 1.97356e13i 0.151755i
\(666\) 1.88189e14 1.43622
\(667\) 6.22446e13i 0.471490i
\(668\) 4.57404e13 0.343889
\(669\) 7.67240e13 0.572533
\(670\) 2.13609e14 1.58214
\(671\) 6.86634e13i 0.504792i
\(672\) 6.77267e13i 0.494212i
\(673\) 2.10395e13i 0.152392i −0.997093 0.0761958i \(-0.975723\pi\)
0.997093 0.0761958i \(-0.0242774\pi\)
\(674\) 6.61617e13i 0.475672i
\(675\) 1.66487e13i 0.118813i
\(676\) 4.21229e13 0.298390
\(677\) 1.41079e14i 0.992018i −0.868317 0.496009i \(-0.834798\pi\)
0.868317 0.496009i \(-0.165202\pi\)
\(678\) 3.64650e14i 2.54523i
\(679\) 3.30058e13i 0.228687i
\(680\) −1.90095e13 −0.130745
\(681\) 2.57883e14 1.76071
\(682\) 3.09895e14i 2.10036i
\(683\) −9.61331e13 −0.646799 −0.323400 0.946263i \(-0.604826\pi\)
−0.323400 + 0.946263i \(0.604826\pi\)
\(684\) 1.34260e14i 0.896737i
\(685\) −2.12253e14 −1.40735
\(686\) 1.31963e14 0.868626
\(687\) 4.20731e13i 0.274929i
\(688\) −3.48796e14 1.42062e13i −2.26271 0.0921588i
\(689\) −1.29325e14 −0.832887
\(690\) 5.05720e14i 3.23344i
\(691\) 2.58847e14i 1.64306i 0.570168 + 0.821528i \(0.306878\pi\)
−0.570168 + 0.821528i \(0.693122\pi\)
\(692\) −9.15887e13 −0.577180
\(693\) 1.61240e13i 0.100881i
\(694\) −4.68196e14 −2.90824
\(695\) 2.18951e14i 1.35027i
\(696\) 1.51384e14i 0.926900i
\(697\) −7.85959e12 −0.0477789
\(698\) 4.04700e14 2.44262
\(699\) −1.32340e14 −0.793060
\(700\) 2.02244e13i 0.120333i
\(701\) 2.64616e14 1.56324 0.781621 0.623753i \(-0.214393\pi\)
0.781621 + 0.623753i \(0.214393\pi\)
\(702\) −1.67305e14 −0.981346
\(703\) 1.74113e14 1.01404
\(704\) 9.79892e13 0.566650
\(705\) −5.18302e12 −0.0297603
\(706\) 4.47002e14i 2.54851i
\(707\) 1.72425e12i 0.00976118i
\(708\) 5.35896e14i 3.01241i
\(709\) −1.70519e14 −0.951790 −0.475895 0.879502i \(-0.657876\pi\)
−0.475895 + 0.879502i \(0.657876\pi\)
\(710\) 3.70313e14i 2.05247i
\(711\) 1.62572e14 0.894744
\(712\) −4.81957e14 −2.63395
\(713\) 4.37631e14 2.37498
\(714\) 5.99517e12i 0.0323080i
\(715\) 1.19325e14i 0.638558i
\(716\) 2.56107e14i 1.36099i
\(717\) 3.69163e14i 1.94815i
\(718\) 6.84564e13i 0.358750i
\(719\) 5.08876e13 0.264830 0.132415 0.991194i \(-0.457727\pi\)
0.132415 + 0.991194i \(0.457727\pi\)
\(720\) 2.10413e14i 1.08745i
\(721\) 8.39970e12i 0.0431109i
\(722\) 1.83891e14i 0.937289i
\(723\) 3.61935e13 0.183206
\(724\) 2.29128e14 1.15182
\(725\) 1.23222e13i 0.0615177i
\(726\) 1.89036e14 0.937263
\(727\) 1.03917e14i 0.511700i −0.966716 0.255850i \(-0.917645\pi\)
0.966716 0.255850i \(-0.0823554\pi\)
\(728\) −1.17653e14 −0.575369
\(729\) −7.25565e12 −0.0352402
\(730\) 1.95581e14i 0.943435i
\(731\) 1.21324e13 + 4.94146e11i 0.0581248 + 0.00236738i
\(732\) −4.07374e14 −1.93838
\(733\) 3.08035e14i 1.45573i −0.685722 0.727863i \(-0.740514\pi\)
0.685722 0.727863i \(-0.259486\pi\)
\(734\) 1.39596e13i 0.0655227i
\(735\) −2.22807e14 −1.03870
\(736\) 5.62739e14i 2.60566i
\(737\) 1.61466e14 0.742581
\(738\) 1.78224e14i 0.814112i
\(739\) 2.65696e14i 1.20549i −0.797934 0.602744i \(-0.794074\pi\)
0.797934 0.602744i \(-0.205926\pi\)
\(740\) 6.79510e14 3.06222
\(741\) 1.81399e14 0.811978
\(742\) −8.96712e13 −0.398688
\(743\) 4.04479e13i 0.178629i −0.996003 0.0893145i \(-0.971532\pi\)
0.996003 0.0893145i \(-0.0284676\pi\)
\(744\) −1.06435e15 −4.66897
\(745\) −8.81507e13 −0.384100
\(746\) 4.49826e14 1.94693
\(747\) −2.39363e14 −1.02909
\(748\) −2.48216e13 −0.106004
\(749\) 7.25462e13i 0.307756i
\(750\) 5.81504e14i 2.45045i
\(751\) 4.55885e14i 1.90834i −0.299267 0.954169i \(-0.596742\pi\)
0.299267 0.954169i \(-0.403258\pi\)
\(752\) 1.46773e13 0.0610318
\(753\) 2.52113e14i 1.04141i
\(754\) −1.23827e14 −0.508112
\(755\) −2.96132e14 −1.20712
\(756\) −8.16307e13 −0.330555
\(757\) 1.68937e14i 0.679589i 0.940500 + 0.339794i \(0.110357\pi\)
−0.940500 + 0.339794i \(0.889643\pi\)
\(758\) 1.39808e14i 0.558711i
\(759\) 3.82271e14i 1.51762i
\(760\) 3.98819e14i 1.57292i
\(761\) 1.58991e14i 0.622944i 0.950255 + 0.311472i \(0.100822\pi\)
−0.950255 + 0.311472i \(0.899178\pi\)
\(762\) 2.68952e14 1.04689
\(763\) 4.39345e13i 0.169896i
\(764\) 5.38726e13i 0.206967i
\(765\) 7.31896e12i 0.0279346i
\(766\) −7.03278e14 −2.66676
\(767\) 2.53758e14 0.955967
\(768\) 4.14201e14i 1.55026i
\(769\) −5.15268e13 −0.191603 −0.0958013 0.995400i \(-0.530541\pi\)
−0.0958013 + 0.995400i \(0.530541\pi\)
\(770\) 8.27373e13i 0.305666i
\(771\) 1.72738e13 0.0634039
\(772\) 9.71871e14 3.54423
\(773\) 1.55645e14i 0.563944i −0.959423 0.281972i \(-0.909011\pi\)
0.959423 0.281972i \(-0.0909886\pi\)
\(774\) 1.12052e13 2.75115e14i 0.0403382 0.990397i
\(775\) −8.66356e13 −0.309876
\(776\) 6.66983e14i 2.37031i
\(777\) 1.24059e14i 0.438050i
\(778\) 1.77410e14 0.622416
\(779\) 1.64894e14i 0.574800i
\(780\) 7.07944e14 2.45203