Properties

Label 177.7.c.a.58.2
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.2
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.59

$q$-expansion

\(f(q)\) \(=\) \(q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +1402.29i q^{10} -1188.16i q^{11} -2571.39 q^{12} +1180.06i q^{13} +9015.75i q^{14} -1444.67 q^{15} +12557.0 q^{16} +7501.19 q^{17} -3676.90i q^{18} -6572.73 q^{19} +15287.3 q^{20} -9288.16 q^{21} -17978.3 q^{22} +10020.3i q^{23} +23812.6i q^{24} -7036.28 q^{25} +17855.7 q^{26} +3788.00 q^{27} +98286.1 q^{28} -28197.5 q^{29} +21859.6i q^{30} -24653.7i q^{31} -92238.9i q^{32} -18521.5i q^{33} -113502. i q^{34} +55219.3 q^{35} -40084.1 q^{36} -38798.6i q^{37} +99453.6i q^{38} +18395.2i q^{39} -141569. i q^{40} +61352.8 q^{41} +140542. i q^{42} -19526.7i q^{43} +195993. i q^{44} -22520.1 q^{45} +151620. q^{46} -60661.5i q^{47} +195745. q^{48} +237372. q^{49} +106468. i q^{50} +116932. q^{51} -194656. i q^{52} +128781. q^{53} -57317.1i q^{54} +110113. i q^{55} -910185. i q^{56} -102459. q^{57} +426664. i q^{58} +(65188.5 + 194759. i) q^{59} +238305. q^{60} +200868. i q^{61} -373041. q^{62} -144788. q^{63} -592041. q^{64} -109362. i q^{65} -280254. q^{66} -526100. i q^{67} -1.23736e6 q^{68} +156201. i q^{69} -835538. i q^{70} +123865. q^{71} +371201. i q^{72} +618533. i q^{73} -587072. q^{74} -109685. q^{75} +1.08420e6 q^{76} +707947. i q^{77} +278343. q^{78} +63990.6 q^{79} -1.16373e6 q^{80} +59049.0 q^{81} -928345. i q^{82} -513107. i q^{83} +1.53213e6 q^{84} -695175. q^{85} -295464. q^{86} -439556. q^{87} +1.81500e6 q^{88} -297297. i q^{89} +340758. i q^{90} -703120. i q^{91} -1.65290e6i q^{92} -384313. i q^{93} -917885. q^{94} +609130. q^{95} -1.43786e6i q^{96} +1.39038e6i q^{97} -3.59173e6i q^{98} -288722. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.1313i 1.89141i −0.325030 0.945704i \(-0.605374\pi\)
0.325030 0.945704i \(-0.394626\pi\)
\(3\) 15.5885 0.577350
\(4\) −164.955 −2.57742
\(5\) −92.6753 −0.741403 −0.370701 0.928752i \(-0.620883\pi\)
−0.370701 + 0.928752i \(0.620883\pi\)
\(6\) 235.873i 1.09200i
\(7\) −595.836 −1.73713 −0.868566 0.495574i \(-0.834958\pi\)
−0.868566 + 0.495574i \(0.834958\pi\)
\(8\) 1527.58i 2.98355i
\(9\) 243.000 0.333333
\(10\) 1402.29i 1.40229i
\(11\) 1188.16i 0.892680i −0.894863 0.446340i \(-0.852727\pi\)
0.894863 0.446340i \(-0.147273\pi\)
\(12\) −2571.39 −1.48808
\(13\) 1180.06i 0.537121i 0.963263 + 0.268561i \(0.0865480\pi\)
−0.963263 + 0.268561i \(0.913452\pi\)
\(14\) 9015.75i 3.28562i
\(15\) −1444.67 −0.428049
\(16\) 12557.0 3.06568
\(17\) 7501.19 1.52680 0.763402 0.645924i \(-0.223528\pi\)
0.763402 + 0.645924i \(0.223528\pi\)
\(18\) 3676.90i 0.630469i
\(19\) −6572.73 −0.958263 −0.479132 0.877743i \(-0.659048\pi\)
−0.479132 + 0.877743i \(0.659048\pi\)
\(20\) 15287.3 1.91091
\(21\) −9288.16 −1.00293
\(22\) −17978.3 −1.68842
\(23\) 10020.3i 0.823565i 0.911282 + 0.411782i \(0.135094\pi\)
−0.911282 + 0.411782i \(0.864906\pi\)
\(24\) 23812.6i 1.72255i
\(25\) −7036.28 −0.450322
\(26\) 17855.7 1.01592
\(27\) 3788.00 0.192450
\(28\) 98286.1 4.47732
\(29\) −28197.5 −1.15616 −0.578078 0.815981i \(-0.696197\pi\)
−0.578078 + 0.815981i \(0.696197\pi\)
\(30\) 21859.6i 0.809615i
\(31\) 24653.7i 0.827554i −0.910378 0.413777i \(-0.864209\pi\)
0.910378 0.413777i \(-0.135791\pi\)
\(32\) 92238.9i 2.81491i
\(33\) 18521.5i 0.515389i
\(34\) 113502.i 2.88781i
\(35\) 55219.3 1.28791
\(36\) −40084.1 −0.859141
\(37\) 38798.6i 0.765969i −0.923755 0.382984i \(-0.874896\pi\)
0.923755 0.382984i \(-0.125104\pi\)
\(38\) 99453.6i 1.81247i
\(39\) 18395.2i 0.310107i
\(40\) 141569.i 2.21201i
\(41\) 61352.8 0.890190 0.445095 0.895483i \(-0.353170\pi\)
0.445095 + 0.895483i \(0.353170\pi\)
\(42\) 140542.i 1.89696i
\(43\) 19526.7i 0.245597i −0.992432 0.122799i \(-0.960813\pi\)
0.992432 0.122799i \(-0.0391869\pi\)
\(44\) 195993.i 2.30081i
\(45\) −22520.1 −0.247134
\(46\) 151620. 1.55770
\(47\) 60661.5i 0.584278i −0.956376 0.292139i \(-0.905633\pi\)
0.956376 0.292139i \(-0.0943670\pi\)
\(48\) 195745. 1.76997
\(49\) 237372. 2.01762
\(50\) 106468.i 0.851742i
\(51\) 116932. 0.881501
\(52\) 194656.i 1.38439i
\(53\) 128781. 0.865018 0.432509 0.901630i \(-0.357628\pi\)
0.432509 + 0.901630i \(0.357628\pi\)
\(54\) 57317.1i 0.364002i
\(55\) 110113.i 0.661836i
\(56\) 910185.i 5.18282i
\(57\) −102459. −0.553253
\(58\) 426664.i 2.18676i
\(59\) 65188.5 + 194759.i 0.317406 + 0.948290i
\(60\) 238305. 1.10326
\(61\) 200868.i 0.884955i 0.896780 + 0.442477i \(0.145900\pi\)
−0.896780 + 0.442477i \(0.854100\pi\)
\(62\) −373041. −1.56524
\(63\) −144788. −0.579044
\(64\) −592041. −2.25846
\(65\) 109362.i 0.398223i
\(66\) −280254. −0.974811
\(67\) 526100.i 1.74922i −0.484829 0.874609i \(-0.661118\pi\)
0.484829 0.874609i \(-0.338882\pi\)
\(68\) −1.23736e6 −3.93522
\(69\) 156201.i 0.475485i
\(70\) 835538.i 2.43597i
\(71\) 123865. 0.346079 0.173039 0.984915i \(-0.444641\pi\)
0.173039 + 0.984915i \(0.444641\pi\)
\(72\) 371201.i 0.994516i
\(73\) 618533.i 1.58999i 0.606616 + 0.794995i \(0.292526\pi\)
−0.606616 + 0.794995i \(0.707474\pi\)
\(74\) −587072. −1.44876
\(75\) −109685. −0.259993
\(76\) 1.08420e6 2.46985
\(77\) 707947.i 1.55070i
\(78\) 278343. 0.586539
\(79\) 63990.6 0.129788 0.0648941 0.997892i \(-0.479329\pi\)
0.0648941 + 0.997892i \(0.479329\pi\)
\(80\) −1.16373e6 −2.27291
\(81\) 59049.0 0.111111
\(82\) 928345.i 1.68371i
\(83\) 513107.i 0.897374i −0.893689 0.448687i \(-0.851892\pi\)
0.893689 0.448687i \(-0.148108\pi\)
\(84\) 1.53213e6 2.58498
\(85\) −695175. −1.13198
\(86\) −295464. −0.464525
\(87\) −439556. −0.667508
\(88\) 1.81500e6 2.66336
\(89\) 297297.i 0.421716i −0.977517 0.210858i \(-0.932374\pi\)
0.977517 0.210858i \(-0.0676258\pi\)
\(90\) 340758.i 0.467432i
\(91\) 703120.i 0.933050i
\(92\) 1.65290e6i 2.12267i
\(93\) 384313.i 0.477789i
\(94\) −917885. −1.10511
\(95\) 609130. 0.710459
\(96\) 1.43786e6i 1.62519i
\(97\) 1.39038e6i 1.52341i 0.647924 + 0.761705i \(0.275638\pi\)
−0.647924 + 0.761705i \(0.724362\pi\)
\(98\) 3.59173e6i 3.81615i
\(99\) 288722.i 0.297560i
\(100\) 1.16067e6 1.16067
\(101\) 1.40220e6i 1.36097i 0.732764 + 0.680483i \(0.238230\pi\)
−0.732764 + 0.680483i \(0.761770\pi\)
\(102\) 1.76933e6i 1.66728i
\(103\) 1.73005e6i 1.58324i 0.611014 + 0.791619i \(0.290762\pi\)
−0.611014 + 0.791619i \(0.709238\pi\)
\(104\) −1.80263e6 −1.60253
\(105\) 860784. 0.743577
\(106\) 1.94862e6i 1.63610i
\(107\) 719986. 0.587723 0.293862 0.955848i \(-0.405059\pi\)
0.293862 + 0.955848i \(0.405059\pi\)
\(108\) −624849. −0.496025
\(109\) 1.47588e6i 1.13965i 0.821767 + 0.569823i \(0.192988\pi\)
−0.821767 + 0.569823i \(0.807012\pi\)
\(110\) 1.66615e6 1.25180
\(111\) 604811.i 0.442232i
\(112\) −7.48194e6 −5.32549
\(113\) 130130.i 0.0901868i −0.998983 0.0450934i \(-0.985641\pi\)
0.998983 0.0450934i \(-0.0143585\pi\)
\(114\) 1.55033e6i 1.04643i
\(115\) 928636.i 0.610593i
\(116\) 4.65132e6 2.97990
\(117\) 286754.i 0.179040i
\(118\) 2.94695e6 986384.i 1.79360 0.600344i
\(119\) −4.46948e6 −2.65226
\(120\) 2.20684e6i 1.27711i
\(121\) 359843. 0.203122
\(122\) 3.03939e6 1.67381
\(123\) 956395. 0.513952
\(124\) 4.06675e6i 2.13296i
\(125\) 2.10014e6 1.07527
\(126\) 2.19083e6i 1.09521i
\(127\) 3.38640e6 1.65321 0.826603 0.562785i \(-0.190270\pi\)
0.826603 + 0.562785i \(0.190270\pi\)
\(128\) 3.05503e6i 1.45675i
\(129\) 304391.i 0.141796i
\(130\) −1.65479e6 −0.753203
\(131\) 1.57313e6i 0.699761i 0.936794 + 0.349881i \(0.113778\pi\)
−0.936794 + 0.349881i \(0.886222\pi\)
\(132\) 3.05522e6i 1.32838i
\(133\) 3.91627e6 1.66463
\(134\) −7.96056e6 −3.30848
\(135\) −351054. −0.142683
\(136\) 1.14586e7i 4.55529i
\(137\) −3.59610e6 −1.39853 −0.699263 0.714865i \(-0.746488\pi\)
−0.699263 + 0.714865i \(0.746488\pi\)
\(138\) 2.36352e6 0.899337
\(139\) −3.36752e6 −1.25391 −0.626954 0.779056i \(-0.715699\pi\)
−0.626954 + 0.779056i \(0.715699\pi\)
\(140\) −9.10870e6 −3.31950
\(141\) 945620.i 0.337333i
\(142\) 1.87424e6i 0.654576i
\(143\) 1.40209e6 0.479478
\(144\) 3.05136e6 1.02189
\(145\) 2.61321e6 0.857178
\(146\) 9.35918e6 3.00732
\(147\) 3.70026e6 1.16488
\(148\) 6.40003e6i 1.97423i
\(149\) 3.49052e6i 1.05519i 0.849495 + 0.527596i \(0.176906\pi\)
−0.849495 + 0.527596i \(0.823094\pi\)
\(150\) 1.65967e6i 0.491754i
\(151\) 6.31660e6i 1.83465i 0.398142 + 0.917324i \(0.369655\pi\)
−0.398142 + 0.917324i \(0.630345\pi\)
\(152\) 1.00403e7i 2.85902i
\(153\) 1.82279e6 0.508935
\(154\) 1.07121e7 2.93301
\(155\) 2.28479e6i 0.613551i
\(156\) 3.03439e6i 0.799277i
\(157\) 1.08459e6i 0.280264i −0.990133 0.140132i \(-0.955247\pi\)
0.990133 0.140132i \(-0.0447528\pi\)
\(158\) 968259.i 0.245482i
\(159\) 2.00750e6 0.499418
\(160\) 8.54827e6i 2.08698i
\(161\) 5.97046e6i 1.43064i
\(162\) 893486.i 0.210156i
\(163\) 3.99116e6 0.921588 0.460794 0.887507i \(-0.347565\pi\)
0.460794 + 0.887507i \(0.347565\pi\)
\(164\) −1.01205e7 −2.29440
\(165\) 1.71649e6i 0.382111i
\(166\) −7.76395e6 −1.69730
\(167\) −119449. −0.0256469 −0.0128234 0.999918i \(-0.504082\pi\)
−0.0128234 + 0.999918i \(0.504082\pi\)
\(168\) 1.41884e7i 2.99230i
\(169\) 3.43428e6 0.711501
\(170\) 1.05189e7i 2.14103i
\(171\) −1.59717e6 −0.319421
\(172\) 3.22103e6i 0.633008i
\(173\) 4.96046e6i 0.958040i −0.877804 0.479020i \(-0.840992\pi\)
0.877804 0.479020i \(-0.159008\pi\)
\(174\) 6.65103e6i 1.26253i
\(175\) 4.19247e6 0.782268
\(176\) 1.49197e7i 2.73668i
\(177\) 1.01619e6 + 3.03599e6i 0.183254 + 0.547495i
\(178\) −4.49847e6 −0.797637
\(179\) 9.53711e6i 1.66287i −0.555624 0.831434i \(-0.687520\pi\)
0.555624 0.831434i \(-0.312480\pi\)
\(180\) 3.71481e6 0.636969
\(181\) −6.69436e6 −1.12895 −0.564473 0.825452i \(-0.690921\pi\)
−0.564473 + 0.825452i \(0.690921\pi\)
\(182\) −1.06391e7 −1.76478
\(183\) 3.13122e6i 0.510929i
\(184\) −1.53068e7 −2.45715
\(185\) 3.59568e6i 0.567892i
\(186\) −5.81513e6 −0.903693
\(187\) 8.91259e6i 1.36295i
\(188\) 1.00064e7i 1.50593i
\(189\) −2.25702e6 −0.334311
\(190\) 9.21690e6i 1.34377i
\(191\) 8.32841e6i 1.19526i 0.801773 + 0.597629i \(0.203891\pi\)
−0.801773 + 0.597629i \(0.796109\pi\)
\(192\) −9.22900e6 −1.30392
\(193\) 9.49958e6 1.32140 0.660698 0.750652i \(-0.270261\pi\)
0.660698 + 0.750652i \(0.270261\pi\)
\(194\) 2.10381e7 2.88139
\(195\) 1.70479e6i 0.229914i
\(196\) −3.91556e7 −5.20027
\(197\) 2.34210e6 0.306342 0.153171 0.988200i \(-0.451051\pi\)
0.153171 + 0.988200i \(0.451051\pi\)
\(198\) −4.36873e6 −0.562807
\(199\) −7.24381e6 −0.919196 −0.459598 0.888127i \(-0.652006\pi\)
−0.459598 + 0.888127i \(0.652006\pi\)
\(200\) 1.07485e7i 1.34356i
\(201\) 8.20109e6i 1.00991i
\(202\) 2.12171e7 2.57414
\(203\) 1.68011e7 2.00840
\(204\) −1.92885e7 −2.27200
\(205\) −5.68589e6 −0.659990
\(206\) 2.61778e7 2.99455
\(207\) 2.43494e6i 0.274522i
\(208\) 1.48180e7i 1.64664i
\(209\) 7.80944e6i 0.855423i
\(210\) 1.30247e7i 1.40641i
\(211\) 8.80392e6i 0.937192i −0.883413 0.468596i \(-0.844760\pi\)
0.883413 0.468596i \(-0.155240\pi\)
\(212\) −2.12431e7 −2.22952
\(213\) 1.93087e6 0.199809
\(214\) 1.08943e7i 1.11162i
\(215\) 1.80964e6i 0.182087i
\(216\) 5.78645e6i 0.574184i
\(217\) 1.46895e7i 1.43757i
\(218\) 2.23319e7 2.15554
\(219\) 9.64197e6i 0.917981i
\(220\) 1.81637e7i 1.70583i
\(221\) 8.85182e6i 0.820079i
\(222\) −9.15155e6 −0.836442
\(223\) −5.42731e6 −0.489407 −0.244703 0.969598i \(-0.578691\pi\)
−0.244703 + 0.969598i \(0.578691\pi\)
\(224\) 5.49593e7i 4.88987i
\(225\) −1.70982e6 −0.150107
\(226\) −1.96903e6 −0.170580
\(227\) 3.67832e6i 0.314464i 0.987562 + 0.157232i \(0.0502571\pi\)
−0.987562 + 0.157232i \(0.949743\pi\)
\(228\) 1.69011e7 1.42597
\(229\) 1.67437e7i 1.39426i −0.716943 0.697132i \(-0.754459\pi\)
0.716943 0.697132i \(-0.245541\pi\)
\(230\) −1.40514e7 −1.15488
\(231\) 1.10358e7i 0.895299i
\(232\) 4.30739e7i 3.44945i
\(233\) 1.79137e7i 1.41618i 0.706124 + 0.708088i \(0.250442\pi\)
−0.706124 + 0.708088i \(0.749558\pi\)
\(234\) 4.33894e6 0.338638
\(235\) 5.62183e6i 0.433186i
\(236\) −1.07532e7 3.21264e7i −0.818089 2.44414i
\(237\) 997515. 0.0749332
\(238\) 6.76288e7i 5.01650i
\(239\) 7.08766e6 0.519170 0.259585 0.965720i \(-0.416414\pi\)
0.259585 + 0.965720i \(0.416414\pi\)
\(240\) −1.81407e7 −1.31226
\(241\) −1.91122e7 −1.36540 −0.682699 0.730700i \(-0.739194\pi\)
−0.682699 + 0.730700i \(0.739194\pi\)
\(242\) 5.44487e6i 0.384186i
\(243\) 920483. 0.0641500
\(244\) 3.31342e7i 2.28090i
\(245\) −2.19985e7 −1.49587
\(246\) 1.44715e7i 0.972092i
\(247\) 7.75618e6i 0.514704i
\(248\) 3.76604e7 2.46905
\(249\) 7.99854e6i 0.518099i
\(250\) 3.17778e7i 2.03378i
\(251\) −1.00728e7 −0.636984 −0.318492 0.947926i \(-0.603176\pi\)
−0.318492 + 0.947926i \(0.603176\pi\)
\(252\) 2.38835e7 1.49244
\(253\) 1.19057e7 0.735180
\(254\) 5.12405e7i 3.12689i
\(255\) −1.08367e7 −0.653547
\(256\) 8.33583e6 0.496854
\(257\) −2.64289e7 −1.55697 −0.778483 0.627666i \(-0.784011\pi\)
−0.778483 + 0.627666i \(0.784011\pi\)
\(258\) −4.60582e6 −0.268193
\(259\) 2.31176e7i 1.33059i
\(260\) 1.80398e7i 1.02639i
\(261\) −6.85200e6 −0.385386
\(262\) 2.38034e7 1.32353
\(263\) −9.07873e6 −0.499066 −0.249533 0.968366i \(-0.580277\pi\)
−0.249533 + 0.968366i \(0.580277\pi\)
\(264\) 2.82931e7 1.53769
\(265\) −1.19349e7 −0.641327
\(266\) 5.92581e7i 3.14849i
\(267\) 4.63440e6i 0.243478i
\(268\) 8.67828e7i 4.50847i
\(269\) 3.68828e6i 0.189482i −0.995502 0.0947409i \(-0.969798\pi\)
0.995502 0.0947409i \(-0.0302023\pi\)
\(270\) 5.31189e6i 0.269872i
\(271\) 2.96429e7 1.48941 0.744703 0.667396i \(-0.232591\pi\)
0.744703 + 0.667396i \(0.232591\pi\)
\(272\) 9.41927e7 4.68070
\(273\) 1.09606e7i 0.538697i
\(274\) 5.44136e7i 2.64518i
\(275\) 8.36021e6i 0.401994i
\(276\) 2.57662e7i 1.22553i
\(277\) −3.08538e7 −1.45167 −0.725837 0.687867i \(-0.758547\pi\)
−0.725837 + 0.687867i \(0.758547\pi\)
\(278\) 5.09548e7i 2.37165i
\(279\) 5.99084e6i 0.275851i
\(280\) 8.43517e7i 3.84255i
\(281\) 3.94507e7 1.77802 0.889008 0.457892i \(-0.151396\pi\)
0.889008 + 0.457892i \(0.151396\pi\)
\(282\) −1.43084e7 −0.638035
\(283\) 2.68048e7i 1.18264i −0.806436 0.591322i \(-0.798606\pi\)
0.806436 0.591322i \(-0.201394\pi\)
\(284\) −2.04322e7 −0.891991
\(285\) 9.49539e6 0.410184
\(286\) 2.12154e7i 0.906888i
\(287\) −3.65562e7 −1.54638
\(288\) 2.24141e7i 0.938303i
\(289\) 3.21302e7 1.33113
\(290\) 3.95412e7i 1.62127i
\(291\) 2.16738e7i 0.879542i
\(292\) 1.02030e8i 4.09807i
\(293\) 1.18646e7 0.471683 0.235842 0.971792i \(-0.424215\pi\)
0.235842 + 0.971792i \(0.424215\pi\)
\(294\) 5.59895e7i 2.20326i
\(295\) −6.04137e6 1.80493e7i −0.235326 0.703065i
\(296\) 5.92679e7 2.28531
\(297\) 4.50074e6i 0.171796i
\(298\) 5.28160e7 1.99580
\(299\) −1.18245e7 −0.442354
\(300\) 1.80931e7 0.670113
\(301\) 1.16347e7i 0.426635i
\(302\) 9.55781e7 3.47007
\(303\) 2.18582e7i 0.785754i
\(304\) −8.25340e7 −2.93773
\(305\) 1.86155e7i 0.656108i
\(306\) 2.75811e7i 0.962603i
\(307\) 2.24412e7 0.775587 0.387793 0.921746i \(-0.373237\pi\)
0.387793 + 0.921746i \(0.373237\pi\)
\(308\) 1.16779e8i 3.99682i
\(309\) 2.69688e7i 0.914083i
\(310\) 3.45717e7 1.16047
\(311\) −4.88319e7 −1.62339 −0.811695 0.584082i \(-0.801455\pi\)
−0.811695 + 0.584082i \(0.801455\pi\)
\(312\) −2.81002e7 −0.925220
\(313\) 3.07669e7i 1.00335i −0.865057 0.501674i \(-0.832718\pi\)
0.865057 0.501674i \(-0.167282\pi\)
\(314\) −1.64113e7 −0.530094
\(315\) 1.34183e7 0.429305
\(316\) −1.05556e7 −0.334519
\(317\) 5.20357e6 0.163352 0.0816759 0.996659i \(-0.473973\pi\)
0.0816759 + 0.996659i \(0.473973\pi\)
\(318\) 3.03760e7i 0.944604i
\(319\) 3.35031e7i 1.03208i
\(320\) 5.48676e7 1.67443
\(321\) 1.12235e7 0.339322
\(322\) −9.03406e7 −2.70592
\(323\) −4.93033e7 −1.46308
\(324\) −9.74043e6 −0.286380
\(325\) 8.30320e6i 0.241878i
\(326\) 6.03914e7i 1.74310i
\(327\) 2.30066e7i 0.657975i
\(328\) 9.37211e7i 2.65593i
\(329\) 3.61443e7i 1.01497i
\(330\) 2.59727e7 0.722728
\(331\) 7.01782e6 0.193517 0.0967583 0.995308i \(-0.469153\pi\)
0.0967583 + 0.995308i \(0.469153\pi\)
\(332\) 8.46395e7i 2.31291i
\(333\) 9.42807e6i 0.255323i
\(334\) 1.80742e6i 0.0485087i
\(335\) 4.87565e7i 1.29687i
\(336\) −1.16632e8 −3.07468
\(337\) 5.80128e7i 1.51577i 0.652387 + 0.757886i \(0.273768\pi\)
−0.652387 + 0.757886i \(0.726232\pi\)
\(338\) 5.19649e7i 1.34574i
\(339\) 2.02853e6i 0.0520694i
\(340\) 1.14673e8 2.91758
\(341\) −2.92924e7 −0.738741
\(342\) 2.41672e7i 0.604155i
\(343\) −7.13350e7 −1.76775
\(344\) 2.98285e7 0.732751
\(345\) 1.44760e7i 0.352526i
\(346\) −7.50580e7 −1.81204
\(347\) 1.15980e7i 0.277585i 0.990322 + 0.138792i \(0.0443220\pi\)
−0.990322 + 0.138792i \(0.955678\pi\)
\(348\) 7.25069e7 1.72045
\(349\) 536779.i 0.0126275i 0.999980 + 0.00631377i \(0.00200975\pi\)
−0.999980 + 0.00631377i \(0.997990\pi\)
\(350\) 6.34373e7i 1.47959i
\(351\) 4.47005e6i 0.103369i
\(352\) −1.09594e8 −2.51281
\(353\) 6.84752e7i 1.55672i −0.627821 0.778358i \(-0.716053\pi\)
0.627821 0.778358i \(-0.283947\pi\)
\(354\) 4.59383e7 1.53762e7i 1.03554 0.346609i
\(355\) −1.14793e7 −0.256584
\(356\) 4.90406e7i 1.08694i
\(357\) −6.96723e7 −1.53128
\(358\) −1.44309e8 −3.14516
\(359\) −1.42567e6 −0.0308131 −0.0154066 0.999881i \(-0.504904\pi\)
−0.0154066 + 0.999881i \(0.504904\pi\)
\(360\) 3.44012e7i 0.737337i
\(361\) −3.84514e6 −0.0817317
\(362\) 1.01294e8i 2.13530i
\(363\) 5.60939e6 0.117272
\(364\) 1.15983e8i 2.40486i
\(365\) 5.73228e7i 1.17882i
\(366\) 4.73793e7 0.966375
\(367\) 5.92009e7i 1.19765i 0.800880 + 0.598826i \(0.204366\pi\)
−0.800880 + 0.598826i \(0.795634\pi\)
\(368\) 1.25825e8i 2.52479i
\(369\) 1.49087e7 0.296730
\(370\) 5.44071e7 1.07411
\(371\) −7.67325e7 −1.50265
\(372\) 6.33943e7i 1.23146i
\(373\) 4.76153e7 0.917530 0.458765 0.888558i \(-0.348292\pi\)
0.458765 + 0.888558i \(0.348292\pi\)
\(374\) −1.34859e8 −2.57789
\(375\) 3.27380e7 0.620809
\(376\) 9.26651e7 1.74322
\(377\) 3.32746e7i 0.620997i
\(378\) 3.41516e7i 0.632318i
\(379\) 4.30636e7 0.791029 0.395515 0.918460i \(-0.370566\pi\)
0.395515 + 0.918460i \(0.370566\pi\)
\(380\) −1.00479e8 −1.83115
\(381\) 5.27888e7 0.954479
\(382\) 1.26019e8 2.26072
\(383\) −5.11356e7 −0.910180 −0.455090 0.890446i \(-0.650393\pi\)
−0.455090 + 0.890446i \(0.650393\pi\)
\(384\) 4.76232e7i 0.841056i
\(385\) 6.56092e7i 1.14970i
\(386\) 1.43741e8i 2.49930i
\(387\) 4.74499e6i 0.0818658i
\(388\) 2.29349e8i 3.92647i
\(389\) −8.81530e7 −1.49757 −0.748787 0.662811i \(-0.769363\pi\)
−0.748787 + 0.662811i \(0.769363\pi\)
\(390\) −2.57956e7 −0.434862
\(391\) 7.51642e7i 1.25742i
\(392\) 3.62603e8i 6.01968i
\(393\) 2.45226e7i 0.404007i
\(394\) 3.54389e7i 0.579418i
\(395\) −5.93035e6 −0.0962253
\(396\) 4.76262e7i 0.766938i
\(397\) 1.55026e7i 0.247762i 0.992297 + 0.123881i \(0.0395341\pi\)
−0.992297 + 0.123881i \(0.960466\pi\)
\(398\) 1.09608e8i 1.73857i
\(399\) 6.10486e7 0.961074
\(400\) −8.83548e7 −1.38054
\(401\) 2.07907e7i 0.322430i −0.986919 0.161215i \(-0.948459\pi\)
0.986919 0.161215i \(-0.0515413\pi\)
\(402\) −1.24093e8 −1.91015
\(403\) 2.90927e7 0.444497
\(404\) 2.31301e8i 3.50778i
\(405\) −5.47239e6 −0.0823781
\(406\) 2.54222e8i 3.79870i
\(407\) −4.60989e7 −0.683765
\(408\) 1.78623e8i 2.63000i
\(409\) 6.42981e7i 0.939784i −0.882724 0.469892i \(-0.844293\pi\)
0.882724 0.469892i \(-0.155707\pi\)
\(410\) 8.60347e7i 1.24831i
\(411\) −5.60577e7 −0.807439
\(412\) 2.85380e8i 4.08068i
\(413\) −3.88416e7 1.16044e8i −0.551376 1.64730i
\(414\) 3.68436e7 0.519232
\(415\) 4.75523e7i 0.665315i
\(416\) 1.08847e8 1.51195
\(417\) −5.24945e7 −0.723945
\(418\) 1.18167e8 1.61795
\(419\) 1.31802e8i 1.79176i 0.444293 + 0.895882i \(0.353455\pi\)
−0.444293 + 0.895882i \(0.646545\pi\)
\(420\) −1.41991e8 −1.91651
\(421\) 1.19244e8i 1.59805i 0.601297 + 0.799026i \(0.294651\pi\)
−0.601297 + 0.799026i \(0.705349\pi\)
\(422\) −1.33214e8 −1.77261
\(423\) 1.47408e7i 0.194759i
\(424\) 1.96723e8i 2.58082i
\(425\) −5.27804e7 −0.687553
\(426\) 2.92165e7i 0.377920i
\(427\) 1.19684e8i 1.53728i
\(428\) −1.18765e8 −1.51481
\(429\) 2.18565e7 0.276827
\(430\) 2.73822e7 0.344400
\(431\) 3.54230e7i 0.442439i −0.975224 0.221219i \(-0.928996\pi\)
0.975224 0.221219i \(-0.0710037\pi\)
\(432\) 4.75660e7 0.589991
\(433\) 7.84185e7 0.965950 0.482975 0.875634i \(-0.339556\pi\)
0.482975 + 0.875634i \(0.339556\pi\)
\(434\) 2.22271e8 2.71903
\(435\) 4.07360e7 0.494892
\(436\) 2.43453e8i 2.93735i
\(437\) 6.58608e7i 0.789192i
\(438\) 1.45895e8 1.73628
\(439\) −2.27293e7 −0.268654 −0.134327 0.990937i \(-0.542887\pi\)
−0.134327 + 0.990937i \(0.542887\pi\)
\(440\) −1.68206e8 −1.97462
\(441\) 5.76813e7 0.672542
\(442\) 1.33939e8 1.55110
\(443\) 2.48221e7i 0.285514i −0.989758 0.142757i \(-0.954403\pi\)
0.989758 0.142757i \(-0.0455968\pi\)
\(444\) 9.97666e7i 1.13982i
\(445\) 2.75521e7i 0.312662i
\(446\) 8.21221e7i 0.925668i
\(447\) 5.44118e7i 0.609215i
\(448\) 3.52759e8 3.92323
\(449\) 1.38674e8 1.53199 0.765995 0.642846i \(-0.222247\pi\)
0.765995 + 0.642846i \(0.222247\pi\)
\(450\) 2.58717e7i 0.283914i
\(451\) 7.28968e7i 0.794655i
\(452\) 2.14656e7i 0.232449i
\(453\) 9.84661e7i 1.05923i
\(454\) 5.56576e7 0.594780
\(455\) 6.51619e7i 0.691766i
\(456\) 1.56513e8i 1.65066i
\(457\) 3.89150e7i 0.407726i 0.978999 + 0.203863i \(0.0653498\pi\)
−0.978999 + 0.203863i \(0.934650\pi\)
\(458\) −2.53353e8 −2.63712
\(459\) 2.84145e7 0.293834
\(460\) 1.53183e8i 1.57376i
\(461\) 1.46047e8 1.49070 0.745349 0.666675i \(-0.232283\pi\)
0.745349 + 0.666675i \(0.232283\pi\)
\(462\) 1.66986e8 1.69337
\(463\) 8.54558e7i 0.860991i −0.902593 0.430496i \(-0.858339\pi\)
0.902593 0.430496i \(-0.141661\pi\)
\(464\) −3.54077e8 −3.54441
\(465\) 3.56163e7i 0.354234i
\(466\) 2.71057e8 2.67857
\(467\) 1.88192e8i 1.84778i 0.382656 + 0.923891i \(0.375009\pi\)
−0.382656 + 0.923891i \(0.624991\pi\)
\(468\) 4.73014e7i 0.461463i
\(469\) 3.13469e8i 3.03862i
\(470\) 8.50653e7 0.819330
\(471\) 1.69071e7i 0.161811i
\(472\) −2.97509e8 + 9.95804e7i −2.82927 + 0.946996i
\(473\) −2.32008e7 −0.219240
\(474\) 1.50937e7i 0.141729i
\(475\) 4.62475e7 0.431527
\(476\) 7.37263e8 6.83599
\(477\) 3.12939e7 0.288339
\(478\) 1.07245e8i 0.981962i
\(479\) 1.84353e8 1.67743 0.838713 0.544573i \(-0.183308\pi\)
0.838713 + 0.544573i \(0.183308\pi\)
\(480\) 1.33254e8i 1.20492i
\(481\) 4.57845e7 0.411418
\(482\) 2.89191e8i 2.58252i
\(483\) 9.30703e7i 0.825980i
\(484\) −5.93578e7 −0.523531
\(485\) 1.28854e8i 1.12946i
\(486\) 1.39281e7i 0.121334i
\(487\) 4.40439e6 0.0381328 0.0190664 0.999818i \(-0.493931\pi\)
0.0190664 + 0.999818i \(0.493931\pi\)
\(488\) −3.06841e8 −2.64031
\(489\) 6.22161e7 0.532079
\(490\) 3.32865e8i 2.82931i
\(491\) −1.86538e8 −1.57588 −0.787941 0.615751i \(-0.788853\pi\)
−0.787941 + 0.615751i \(0.788853\pi\)
\(492\) −1.57762e8 −1.32467
\(493\) −2.11515e8 −1.76522
\(494\) −1.17361e8 −0.973514
\(495\) 2.67574e7i 0.220612i
\(496\) 3.09577e8i 2.53702i
\(497\) −7.38034e7 −0.601184
\(498\) −1.21028e8 −0.979936
\(499\) 1.68862e8 1.35904 0.679518 0.733659i \(-0.262189\pi\)
0.679518 + 0.733659i \(0.262189\pi\)
\(500\) −3.46429e8 −2.77143
\(501\) −1.86203e6 −0.0148072
\(502\) 1.52414e8i 1.20480i
\(503\) 5.98804e7i 0.470523i 0.971932 + 0.235262i \(0.0755947\pi\)
−0.971932 + 0.235262i \(0.924405\pi\)
\(504\) 2.21175e8i 1.72761i
\(505\) 1.29950e8i 1.00902i
\(506\) 1.80148e8i 1.39053i
\(507\) 5.35351e7 0.410785
\(508\) −5.58604e8 −4.26101
\(509\) 9.59701e7i 0.727751i 0.931448 + 0.363875i \(0.118547\pi\)
−0.931448 + 0.363875i \(0.881453\pi\)
\(510\) 1.63973e8i 1.23612i
\(511\) 3.68544e8i 2.76202i
\(512\) 6.93902e7i 0.516997i
\(513\) −2.48975e7 −0.184418
\(514\) 3.99902e8i 2.94486i
\(515\) 1.60333e8i 1.17382i
\(516\) 5.02109e7i 0.365467i
\(517\) −7.20755e7 −0.521574
\(518\) 3.49799e8 2.51669
\(519\) 7.73259e7i 0.553125i
\(520\) 1.67059e8 1.18812
\(521\) 4.20956e7 0.297662 0.148831 0.988863i \(-0.452449\pi\)
0.148831 + 0.988863i \(0.452449\pi\)
\(522\) 1.03679e8i 0.728921i
\(523\) −7.93657e7 −0.554789 −0.277395 0.960756i \(-0.589471\pi\)
−0.277395 + 0.960756i \(0.589471\pi\)
\(524\) 2.59495e8i 1.80358i
\(525\) 6.53541e7 0.451643
\(526\) 1.37373e8i 0.943936i
\(527\) 1.84932e8i 1.26351i
\(528\) 2.32576e8i 1.58002i
\(529\) 4.76292e7 0.321741
\(530\) 1.80589e8i 1.21301i
\(531\) 1.58408e7 + 4.73264e7i 0.105802 + 0.316097i
\(532\) −6.46008e8 −4.29045
\(533\) 7.23997e7i 0.478140i
\(534\) −7.01243e7 −0.460516
\(535\) −6.67250e7 −0.435740
\(536\) 8.03658e8 5.21888
\(537\) 1.48669e8i 0.960057i
\(538\) −5.58084e7 −0.358387
\(539\) 2.82035e8i 1.80109i
\(540\) 5.79081e7 0.367754
\(541\) 9.87052e7i 0.623373i 0.950185 + 0.311687i \(0.100894\pi\)
−0.950185 + 0.311687i \(0.899106\pi\)
\(542\) 4.48535e8i 2.81707i
\(543\) −1.04355e8 −0.651797
\(544\) 6.91901e8i 4.29781i
\(545\) 1.36777e8i 0.844937i
\(546\) −1.65847e8 −1.01890
\(547\) 2.02839e8 1.23934 0.619670 0.784863i \(-0.287267\pi\)
0.619670 + 0.784863i \(0.287267\pi\)
\(548\) 5.93195e8 3.60459
\(549\) 4.88109e7i 0.294985i
\(550\) 1.26500e8 0.760334
\(551\) 1.85335e8 1.10790
\(552\) −2.38609e8 −1.41863
\(553\) −3.81279e7 −0.225459
\(554\) 4.66857e8i 2.74571i
\(555\) 5.60510e7i 0.327872i
\(556\) 5.55490e8 3.23185
\(557\) −1.45125e8 −0.839799 −0.419900 0.907571i \(-0.637935\pi\)
−0.419900 + 0.907571i \(0.637935\pi\)
\(558\) −9.06490e7 −0.521747
\(559\) 2.30426e7 0.131916
\(560\) 6.93391e8 3.94834
\(561\) 1.38934e8i 0.786898i
\(562\) 5.96938e8i 3.36295i
\(563\) 5.96255e7i 0.334123i 0.985946 + 0.167062i \(0.0534279\pi\)
−0.985946 + 0.167062i \(0.946572\pi\)
\(564\) 1.55985e8i 0.869450i
\(565\) 1.20599e7i 0.0668647i
\(566\) −4.05591e8 −2.23686
\(567\) −3.51835e7 −0.193015
\(568\) 1.89214e8i 1.03254i
\(569\) 1.89340e8i 1.02779i 0.857853 + 0.513895i \(0.171798\pi\)
−0.857853 + 0.513895i \(0.828202\pi\)
\(570\) 1.43677e8i 0.775825i
\(571\) 1.06328e8i 0.571134i −0.958359 0.285567i \(-0.907818\pi\)
0.958359 0.285567i \(-0.0921819\pi\)
\(572\) −2.31282e8 −1.23582
\(573\) 1.29827e8i 0.690083i
\(574\) 5.53141e8i 2.92483i
\(575\) 7.05057e7i 0.370869i
\(576\) −1.43866e8 −0.752818
\(577\) 5.19980e7 0.270682 0.135341 0.990799i \(-0.456787\pi\)
0.135341 + 0.990799i \(0.456787\pi\)
\(578\) 4.86171e8i 2.51771i
\(579\) 1.48084e8 0.762908
\(580\) −4.31063e8 −2.20931
\(581\) 3.05727e8i 1.55886i
\(582\) 3.27952e8 1.66357
\(583\) 1.53012e8i 0.772185i
\(584\) −9.44857e8 −4.74381
\(585\) 2.65750e7i 0.132741i
\(586\) 1.79526e8i 0.892145i
\(587\) 1.55758e8i 0.770079i 0.922900 + 0.385040i \(0.125812\pi\)
−0.922900 + 0.385040i \(0.874188\pi\)
\(588\) −6.10376e8 −3.00238
\(589\) 1.62042e8i 0.793015i
\(590\) −2.73109e8 + 9.14135e7i −1.32978 + 0.445096i
\(591\) 3.65097e7 0.176867
\(592\) 4.87196e8i 2.34822i
\(593\) −2.00518e8 −0.961590 −0.480795 0.876833i \(-0.659652\pi\)
−0.480795 + 0.876833i \(0.659652\pi\)
\(594\) −6.81018e7 −0.324937
\(595\) 4.14210e8 1.96639
\(596\) 5.75779e8i 2.71967i
\(597\) −1.12920e8 −0.530698
\(598\) 1.78920e8i 0.836672i
\(599\) 1.37449e8 0.639532 0.319766 0.947497i \(-0.396396\pi\)
0.319766 + 0.947497i \(0.396396\pi\)
\(600\) 1.67552e8i 0.775703i
\(601\) 8.17326e7i 0.376506i 0.982121 + 0.188253i \(0.0602825\pi\)
−0.982121 + 0.188253i \(0.939717\pi\)
\(602\) 1.76048e8 0.806940
\(603\) 1.27842e8i 0.583073i
\(604\) 1.04196e9i 4.72866i
\(605\) −3.33485e7 −0.150595
\(606\) 3.30742e8 1.48618
\(607\) 2.19240e8 0.980287 0.490144 0.871642i \(-0.336944\pi\)
0.490144 + 0.871642i \(0.336944\pi\)
\(608\) 6.06261e8i 2.69742i
\(609\) 2.61903e8 1.15955
\(610\) −2.81676e8 −1.24097
\(611\) 7.15840e7 0.313828
\(612\) −3.00678e8 −1.31174
\(613\) 2.72141e8i 1.18144i 0.806875 + 0.590722i \(0.201157\pi\)
−0.806875 + 0.590722i \(0.798843\pi\)
\(614\) 3.39563e8i 1.46695i
\(615\) −8.86343e7 −0.381045
\(616\) −1.08144e9 −4.62660
\(617\) 2.19651e8 0.935141 0.467570 0.883956i \(-0.345129\pi\)
0.467570 + 0.883956i \(0.345129\pi\)
\(618\) 4.08072e8 1.72890
\(619\) −1.55922e7 −0.0657407 −0.0328703 0.999460i \(-0.510465\pi\)
−0.0328703 + 0.999460i \(0.510465\pi\)
\(620\) 3.76887e8i 1.58138i
\(621\) 3.79569e7i 0.158495i
\(622\) 7.38889e8i 3.07049i
\(623\) 1.77140e8i 0.732576i
\(624\) 2.30990e8i 0.950690i
\(625\) −8.46895e7 −0.346888
\(626\) −4.65543e8 −1.89774
\(627\) 1.21737e8i 0.493879i
\(628\) 1.78909e8i 0.722360i
\(629\) 2.91036e8i 1.16948i
\(630\) 2.03036e8i 0.811990i
\(631\) 2.72913e8 1.08627 0.543133 0.839647i \(-0.317238\pi\)
0.543133 + 0.839647i \(0.317238\pi\)
\(632\) 9.77506e7i 0.387229i
\(633\) 1.37239e8i 0.541088i
\(634\) 7.87366e7i 0.308965i
\(635\) −3.13836e8 −1.22569
\(636\) −3.31148e8 −1.28721
\(637\) 2.80112e8i 1.08371i
\(638\) 5.06944e8 1.95208
\(639\) 3.00993e7 0.115360
\(640\) 2.83126e8i 1.08004i
\(641\) −1.14939e8 −0.436408 −0.218204 0.975903i \(-0.570020\pi\)
−0.218204 + 0.975903i \(0.570020\pi\)
\(642\) 1.69825e8i 0.641797i
\(643\) 6.33589e7 0.238328 0.119164 0.992875i \(-0.461979\pi\)
0.119164 + 0.992875i \(0.461979\pi\)
\(644\) 9.84858e8i 3.68736i
\(645\) 2.82096e7i 0.105128i
\(646\) 7.46020e8i 2.76728i
\(647\) −1.82038e8 −0.672124 −0.336062 0.941840i \(-0.609095\pi\)
−0.336062 + 0.941840i \(0.609095\pi\)
\(648\) 9.02019e7i 0.331505i
\(649\) 2.31404e8 7.74542e7i 0.846520 0.283342i
\(650\) −1.25638e8 −0.457489
\(651\) 2.28987e8i 0.829981i
\(652\) −6.58363e8 −2.37532
\(653\) 1.02226e8 0.367133 0.183567 0.983007i \(-0.441236\pi\)
0.183567 + 0.983007i \(0.441236\pi\)
\(654\) 3.48119e8 1.24450
\(655\) 1.45790e8i 0.518805i
\(656\) 7.70410e8 2.72904
\(657\) 1.50304e8i 0.529997i
\(658\) 5.46909e8 1.91972
\(659\) 1.72924e8i 0.604224i −0.953272 0.302112i \(-0.902308\pi\)
0.953272 0.302112i \(-0.0976917\pi\)
\(660\) 2.83144e8i 0.984862i
\(661\) −3.09634e8 −1.07212 −0.536061 0.844179i \(-0.680088\pi\)
−0.536061 + 0.844179i \(0.680088\pi\)
\(662\) 1.06188e8i 0.366019i
\(663\) 1.37986e8i 0.473473i
\(664\) 7.83810e8 2.67736
\(665\) −3.62941e8 −1.23416
\(666\) −1.42659e8 −0.482920
\(667\) 2.82548e8i 0.952170i
\(668\) 1.97038e7 0.0661028
\(669\) −8.46034e7 −0.282559
\(670\) 7.37747e8 2.45292
\(671\) 2.38663e8 0.789982
\(672\) 8.56730e8i 2.82317i
\(673\) 1.81697e7i 0.0596077i 0.999556 + 0.0298039i \(0.00948827\pi\)
−0.999556 + 0.0298039i \(0.990512\pi\)
\(674\) 8.77806e8 2.86694
\(675\) −2.66534e7 −0.0866645
\(676\) −5.66501e8 −1.83384
\(677\) 1.33288e8 0.429560 0.214780 0.976662i \(-0.431096\pi\)
0.214780 + 0.976662i \(0.431096\pi\)
\(678\) −3.06942e7 −0.0984844
\(679\) 8.28436e8i 2.64636i
\(680\) 1.06193e9i 3.37731i
\(681\) 5.73393e7i 0.181556i
\(682\) 4.43231e8i 1.39726i
\(683\) 6.18392e8i 1.94089i 0.241314 + 0.970447i \(0.422422\pi\)
−0.241314 + 0.970447i \(0.577578\pi\)
\(684\) 2.63462e8 0.823283
\(685\) 3.33270e8 1.03687
\(686\) 1.07939e9i 3.34353i
\(687\) 2.61008e8i 0.804979i
\(688\) 2.45198e8i 0.752924i
\(689\) 1.51969e8i 0.464620i
\(690\) −2.19040e8 −0.666771
\(691\) 3.88370e8i 1.17709i −0.808463 0.588547i \(-0.799700\pi\)
0.808463 0.588547i \(-0.200300\pi\)
\(692\) 8.18253e8i 2.46927i
\(693\) 1.72031e8i 0.516901i
\(694\) 1.75493e8 0.525026
\(695\) 3.12086e8 0.929651
\(696\) 6.71455e8i 1.99154i
\(697\) 4.60219e8 1.35915
\(698\) 8.12214e6 0.0238838
\(699\) 2.79247e8i 0.817630i
\(700\) −6.91569e8 −2.01624
\(701\) 1.30199e8i 0.377968i −0.981980 0.188984i \(-0.939481\pi\)
0.981980 0.188984i \(-0.0605194\pi\)
\(702\) 6.76374e7 0.195513
\(703\) 2.55013e8i 0.734000i
\(704\) 7.03437e8i 2.01608i
\(705\) 8.76356e7i 0.250100i
\(706\) −1.03612e9 −2.94438
\(707\) 8.35484e8i 2.36418i
\(708\) −1.67625e8 5.00802e8i −0.472324 1.41113i
\(709\) 3.25855e8 0.914292 0.457146 0.889392i \(-0.348872\pi\)
0.457146 + 0.889392i \(0.348872\pi\)
\(710\) 1.73696e8i 0.485304i
\(711\) 1.55497e7 0.0432627
\(712\) 4.54144e8 1.25821
\(713\) 2.47037e8 0.681544
\(714\) 1.05423e9i 2.89628i
\(715\) −1.29939e8 −0.355486
\(716\) 1.57319e9i 4.28591i
\(717\) 1.10486e8 0.299743
\(718\) 2.15722e7i 0.0582801i
\(719\) 6.80856e8i 1.83176i 0.401453 + 0.915880i \(0.368505\pi\)
−0.401453 + 0.915880i \(0.631495\pi\)
\(720\) −2.82786e8 −0.757635
\(721\) 1.03082e9i 2.75029i
\(722\) 5.81818e7i 0.154588i
\(723\) −2.97929e8 −0.788313
\(724\) 1.10427e9 2.90977
\(725\) 1.98406e8 0.520643
\(726\) 8.48771e7i 0.221810i
\(727\) −5.81108e8 −1.51236 −0.756178 0.654367i \(-0.772935\pi\)
−0.756178 + 0.654367i \(0.772935\pi\)
\(728\) 1.07407e9 2.78380
\(729\) 1.43489e7 0.0370370
\(730\) −8.67366e8 −2.22963
\(731\) 1.46473e8i 0.374979i
\(732\) 5.16511e8i 1.31688i
\(733\) −6.55023e8 −1.66320 −0.831601 0.555374i \(-0.812575\pi\)
−0.831601 + 0.555374i \(0.812575\pi\)
\(734\) 8.95785e8 2.26525
\(735\) −3.42923e8 −0.863643
\(736\) 9.24263e8 2.31826
\(737\) −6.25090e8 −1.56149
\(738\) 2.25588e8i 0.561237i
\(739\) 9.21054e7i 0.228219i 0.993468 + 0.114109i \(0.0364015\pi\)
−0.993468 + 0.114109i \(0.963599\pi\)
\(740\) 5.93125e8i 1.46370i
\(741\) 1.20907e8i 0.297164i
\(742\) 1.16106e9i 2.84212i
\(743\) −1.08383e8 −0.264237 −0.132118 0.991234i \(-0.542178\pi\)
−0.132118 + 0.991234i \(0.542178\pi\)
\(744\) 5.87067e8 1.42551
\(745\) 3.23485e8i 0.782322i
\(746\) 7.20480e8i 1.73542i
\(747\) 1.24685e8i 0.299125i
\(748\) 1.47018e9i 3.51289i
\(749\) −4.28994e8 −1.02095
\(750\) 4.95367e8i 1.17420i
\(751\) 2.13766e8i 0.504684i −0.967638 0.252342i \(-0.918799\pi\)
0.967638 0.252342i \(-0.0812008\pi\)
\(752\) 7.61729e8i 1.79121i
\(753\) −1.57019e8 −0.367763
\(754\) −5.03487e8 −1.17456
\(755\) 5.85393e8i 1.36021i
\(756\) 3.72307e8 0.861661
\(757\) 1.56480e7 0.0360721 0.0180360 0.999837i \(-0.494259\pi\)
0.0180360 + 0.999837i \(0.494259\pi\)
\(758\) 6.51606e8i 1.49616i
\(759\) 1.85592e8 0.424456
\(760\) 9.30493e8i 2.11969i
\(761\) −3.91353e8 −0.888005 −0.444002 0.896026i \(-0.646442\pi\)
−0.444002 + 0.896026i \(0.646442\pi\)
\(762\) 7.98761e8i 1.80531i
\(763\) 8.79380e8i 1.97972i
\(764\) 1.37381e9i 3.08069i
\(765\) −1.68928e8 −0.377326
\(766\) 7.73746e8i 1.72152i
\(767\) −2.29826e8 + 7.69260e7i −0.509347 + 0.170485i
\(768\) 1.29943e8 0.286859
\(769\) 4.26822e8i 0.938573i −0.883046 0.469286i \(-0.844511\pi\)
0.883046 0.469286i \(-0.155489\pi\)
\(770\) −9.92751e8 −2.17454
\(771\) −4.11985e8 −0.898915
\(772\) −1.56700e9 −3.40579
\(773\) 4.13804e8i 0.895892i 0.894061 + 0.447946i \(0.147844\pi\)
−0.894061 + 0.447946i \(0.852156\pi\)
\(774\) −7.17977e7 −0.154842
\(775\) 1.73470e8i 0.372666i
\(776\) −2.12391e9 −4.54517
\(777\) 3.60368e8i 0.768216i
\(778\) 1.33387e9i 2.83252i
\(779\) −4.03255e8 −0.853036
\(780\) 2.81213e8i 0.592586i
\(781\) 1.47172e8i 0.308938i
\(782\) 1.13733e9 2.37830
\(783\) −1.06812e8 −0.222503
\(784\) 2.98068e9 6.18540
\(785\) 1.00515e8i 0.207789i
\(786\) 3.71058e8