Properties

Label 177.7.c.a.58.15
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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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 58.15
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.46

$q$-expansion

\(f(q)\) \(=\) \(q-8.95127i q^{2} +15.5885 q^{3} -16.1253 q^{4} -71.7905 q^{5} -139.537i q^{6} +97.3010 q^{7} -428.540i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-8.95127i q^{2} +15.5885 q^{3} -16.1253 q^{4} -71.7905 q^{5} -139.537i q^{6} +97.3010 q^{7} -428.540i q^{8} +243.000 q^{9} +642.617i q^{10} +482.035i q^{11} -251.368 q^{12} -2893.78i q^{13} -870.967i q^{14} -1119.10 q^{15} -4867.99 q^{16} +5048.92 q^{17} -2175.16i q^{18} +5538.89 q^{19} +1157.64 q^{20} +1516.77 q^{21} +4314.82 q^{22} -1429.59i q^{23} -6680.27i q^{24} -10471.1 q^{25} -25903.0 q^{26} +3788.00 q^{27} -1569.00 q^{28} -31780.8 q^{29} +10017.4i q^{30} -9649.32i q^{31} +16148.2i q^{32} +7514.18i q^{33} -45194.2i q^{34} -6985.29 q^{35} -3918.44 q^{36} -77149.4i q^{37} -49580.1i q^{38} -45109.6i q^{39} +30765.1i q^{40} -46801.5 q^{41} -13577.0i q^{42} -45083.7i q^{43} -7772.93i q^{44} -17445.1 q^{45} -12796.7 q^{46} -55262.1i q^{47} -75884.5 q^{48} -108182. q^{49} +93729.8i q^{50} +78704.9 q^{51} +46663.0i q^{52} +134801. q^{53} -33907.4i q^{54} -34605.5i q^{55} -41697.3i q^{56} +86342.8 q^{57} +284479. i q^{58} +(-205298. + 5776.52i) q^{59} +18045.8 q^{60} +36516.7i q^{61} -86373.6 q^{62} +23644.1 q^{63} -167005. q^{64} +207746. i q^{65} +67261.4 q^{66} -333094. i q^{67} -81415.1 q^{68} -22285.2i q^{69} +62527.2i q^{70} -32490.0 q^{71} -104135. i q^{72} -18804.5i q^{73} -690585. q^{74} -163229. q^{75} -89316.1 q^{76} +46902.4i q^{77} -403788. q^{78} -294542. q^{79} +349476. q^{80} +59049.0 q^{81} +418933. i q^{82} +1.03667e6i q^{83} -24458.3 q^{84} -362465. q^{85} -403556. q^{86} -495414. q^{87} +206571. q^{88} +449322. i q^{89} +156156. i q^{90} -281568. i q^{91} +23052.6i q^{92} -150418. i q^{93} -494666. q^{94} -397640. q^{95} +251725. i q^{96} +59410.4i q^{97} +968362. i q^{98} +117134. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.95127i 1.11891i −0.828861 0.559454i \(-0.811011\pi\)
0.828861 0.559454i \(-0.188989\pi\)
\(3\) 15.5885 0.577350
\(4\) −16.1253 −0.251957
\(5\) −71.7905 −0.574324 −0.287162 0.957882i \(-0.592712\pi\)
−0.287162 + 0.957882i \(0.592712\pi\)
\(6\) 139.537i 0.646002i
\(7\) 97.3010 0.283676 0.141838 0.989890i \(-0.454699\pi\)
0.141838 + 0.989890i \(0.454699\pi\)
\(8\) 428.540i 0.836992i
\(9\) 243.000 0.333333
\(10\) 642.617i 0.642617i
\(11\) 482.035i 0.362160i 0.983468 + 0.181080i \(0.0579592\pi\)
−0.983468 + 0.181080i \(0.942041\pi\)
\(12\) −251.368 −0.145468
\(13\) 2893.78i 1.31715i −0.752514 0.658576i \(-0.771159\pi\)
0.752514 0.658576i \(-0.228841\pi\)
\(14\) 870.967i 0.317408i
\(15\) −1119.10 −0.331586
\(16\) −4867.99 −1.18847
\(17\) 5048.92 1.02767 0.513833 0.857891i \(-0.328225\pi\)
0.513833 + 0.857891i \(0.328225\pi\)
\(18\) 2175.16i 0.372970i
\(19\) 5538.89 0.807537 0.403768 0.914861i \(-0.367700\pi\)
0.403768 + 0.914861i \(0.367700\pi\)
\(20\) 1157.64 0.144705
\(21\) 1516.77 0.163781
\(22\) 4314.82 0.405224
\(23\) 1429.59i 0.117498i −0.998273 0.0587488i \(-0.981289\pi\)
0.998273 0.0587488i \(-0.0187111\pi\)
\(24\) 6680.27i 0.483237i
\(25\) −10471.1 −0.670152
\(26\) −25903.0 −1.47377
\(27\) 3788.00 0.192450
\(28\) −1569.00 −0.0714743
\(29\) −31780.8 −1.30308 −0.651541 0.758614i \(-0.725877\pi\)
−0.651541 + 0.758614i \(0.725877\pi\)
\(30\) 10017.4i 0.371015i
\(31\) 9649.32i 0.323900i −0.986799 0.161950i \(-0.948222\pi\)
0.986799 0.161950i \(-0.0517784\pi\)
\(32\) 16148.2i 0.492803i
\(33\) 7514.18i 0.209093i
\(34\) 45194.2i 1.14986i
\(35\) −6985.29 −0.162922
\(36\) −3918.44 −0.0839857
\(37\) 77149.4i 1.52310i −0.648108 0.761548i \(-0.724440\pi\)
0.648108 0.761548i \(-0.275560\pi\)
\(38\) 49580.1i 0.903560i
\(39\) 45109.6i 0.760458i
\(40\) 30765.1i 0.480705i
\(41\) −46801.5 −0.679060 −0.339530 0.940595i \(-0.610268\pi\)
−0.339530 + 0.940595i \(0.610268\pi\)
\(42\) 13577.0i 0.183256i
\(43\) 45083.7i 0.567040i −0.958966 0.283520i \(-0.908498\pi\)
0.958966 0.283520i \(-0.0915023\pi\)
\(44\) 7772.93i 0.0912487i
\(45\) −17445.1 −0.191441
\(46\) −12796.7 −0.131469
\(47\) 55262.1i 0.532272i −0.963935 0.266136i \(-0.914253\pi\)
0.963935 0.266136i \(-0.0857471\pi\)
\(48\) −75884.5 −0.686166
\(49\) −108182. −0.919528
\(50\) 93729.8i 0.749839i
\(51\) 78704.9 0.593323
\(52\) 46663.0i 0.331866i
\(53\) 134801. 0.905453 0.452727 0.891649i \(-0.350451\pi\)
0.452727 + 0.891649i \(0.350451\pi\)
\(54\) 33907.4i 0.215334i
\(55\) 34605.5i 0.207997i
\(56\) 41697.3i 0.237435i
\(57\) 86342.8 0.466231
\(58\) 284479.i 1.45803i
\(59\) −205298. + 5776.52i −0.999604 + 0.0281262i
\(60\) 18045.8 0.0835455
\(61\) 36516.7i 0.160880i 0.996759 + 0.0804399i \(0.0256325\pi\)
−0.996759 + 0.0804399i \(0.974367\pi\)
\(62\) −86373.6 −0.362415
\(63\) 23644.1 0.0945588
\(64\) −167005. −0.637073
\(65\) 207746.i 0.756472i
\(66\) 67261.4 0.233956
\(67\) 333094.i 1.10750i −0.832684 0.553748i \(-0.813197\pi\)
0.832684 0.553748i \(-0.186803\pi\)
\(68\) −81415.1 −0.258928
\(69\) 22285.2i 0.0678373i
\(70\) 62527.2i 0.182295i
\(71\) −32490.0 −0.0907767 −0.0453883 0.998969i \(-0.514453\pi\)
−0.0453883 + 0.998969i \(0.514453\pi\)
\(72\) 104135.i 0.278997i
\(73\) 18804.5i 0.0483386i −0.999708 0.0241693i \(-0.992306\pi\)
0.999708 0.0241693i \(-0.00769407\pi\)
\(74\) −690585. −1.70421
\(75\) −163229. −0.386912
\(76\) −89316.1 −0.203465
\(77\) 46902.4i 0.102736i
\(78\) −403788. −0.850883
\(79\) −294542. −0.597401 −0.298700 0.954347i \(-0.596553\pi\)
−0.298700 + 0.954347i \(0.596553\pi\)
\(80\) 349476. 0.682570
\(81\) 59049.0 0.111111
\(82\) 418933.i 0.759806i
\(83\) 1.03667e6i 1.81304i 0.422168 + 0.906518i \(0.361269\pi\)
−0.422168 + 0.906518i \(0.638731\pi\)
\(84\) −24458.3 −0.0412657
\(85\) −362465. −0.590213
\(86\) −403556. −0.634466
\(87\) −495414. −0.752334
\(88\) 206571. 0.303125
\(89\) 449322.i 0.637365i 0.947862 + 0.318682i \(0.103240\pi\)
−0.947862 + 0.318682i \(0.896760\pi\)
\(90\) 156156.i 0.214206i
\(91\) 281568.i 0.373645i
\(92\) 23052.6i 0.0296044i
\(93\) 150418.i 0.187004i
\(94\) −494666. −0.595564
\(95\) −397640. −0.463788
\(96\) 251725.i 0.284520i
\(97\) 59410.4i 0.0650949i 0.999470 + 0.0325475i \(0.0103620\pi\)
−0.999470 + 0.0325475i \(0.989638\pi\)
\(98\) 968362.i 1.02887i
\(99\) 117134.i 0.120720i
\(100\) 168850. 0.168850
\(101\) 1.37011e6i 1.32981i 0.746927 + 0.664906i \(0.231528\pi\)
−0.746927 + 0.664906i \(0.768472\pi\)
\(102\) 704508.i 0.663874i
\(103\) 1.98724e6i 1.81860i −0.416136 0.909302i \(-0.636616\pi\)
0.416136 0.909302i \(-0.363384\pi\)
\(104\) −1.24010e6 −1.10245
\(105\) −108890. −0.0940632
\(106\) 1.20664e6i 1.01312i
\(107\) 940633. 0.767837 0.383919 0.923367i \(-0.374574\pi\)
0.383919 + 0.923367i \(0.374574\pi\)
\(108\) −61082.4 −0.0484892
\(109\) 200481.i 0.154808i 0.997000 + 0.0774040i \(0.0246631\pi\)
−0.997000 + 0.0774040i \(0.975337\pi\)
\(110\) −309763. −0.232730
\(111\) 1.20264e6i 0.879360i
\(112\) −473660. −0.337142
\(113\) 539176.i 0.373676i −0.982391 0.186838i \(-0.940176\pi\)
0.982391 0.186838i \(-0.0598240\pi\)
\(114\) 772878.i 0.521671i
\(115\) 102631.i 0.0674817i
\(116\) 512474. 0.328321
\(117\) 703189.i 0.439051i
\(118\) 51707.2 + 1.83768e6i 0.0314706 + 1.11847i
\(119\) 491265. 0.291524
\(120\) 479580.i 0.277535i
\(121\) 1.53920e6 0.868840
\(122\) 326871. 0.180010
\(123\) −729563. −0.392055
\(124\) 155598.i 0.0816090i
\(125\) 1.87345e6 0.959209
\(126\) 211645.i 0.105803i
\(127\) 2.49809e6 1.21954 0.609771 0.792578i \(-0.291262\pi\)
0.609771 + 0.792578i \(0.291262\pi\)
\(128\) 2.52839e6i 1.20563i
\(129\) 702785.i 0.327381i
\(130\) 1.85959e6 0.846424
\(131\) 1.66917e6i 0.742483i −0.928536 0.371242i \(-0.878932\pi\)
0.928536 0.371242i \(-0.121068\pi\)
\(132\) 121168.i 0.0526825i
\(133\) 538940. 0.229079
\(134\) −2.98161e6 −1.23919
\(135\) −271942. −0.110529
\(136\) 2.16366e6i 0.860147i
\(137\) −2.25194e6 −0.875779 −0.437889 0.899029i \(-0.644274\pi\)
−0.437889 + 0.899029i \(0.644274\pi\)
\(138\) −199480. −0.0759037
\(139\) 4.53055e6 1.68697 0.843484 0.537155i \(-0.180501\pi\)
0.843484 + 0.537155i \(0.180501\pi\)
\(140\) 112640. 0.0410494
\(141\) 861451.i 0.307308i
\(142\) 290827.i 0.101571i
\(143\) 1.39490e6 0.477019
\(144\) −1.18292e6 −0.396158
\(145\) 2.28156e6 0.748391
\(146\) −168324. −0.0540864
\(147\) −1.68638e6 −0.530890
\(148\) 1.24405e6i 0.383755i
\(149\) 4.52796e6i 1.36881i −0.729101 0.684406i \(-0.760062\pi\)
0.729101 0.684406i \(-0.239938\pi\)
\(150\) 1.46110e6i 0.432920i
\(151\) 2.85686e6i 0.829771i −0.909874 0.414885i \(-0.863822\pi\)
0.909874 0.414885i \(-0.136178\pi\)
\(152\) 2.37364e6i 0.675902i
\(153\) 1.22689e6 0.342555
\(154\) 419836. 0.114952
\(155\) 692730.i 0.186024i
\(156\) 727404.i 0.191603i
\(157\) 2.72732e6i 0.704754i −0.935858 0.352377i \(-0.885374\pi\)
0.935858 0.352377i \(-0.114626\pi\)
\(158\) 2.63652e6i 0.668437i
\(159\) 2.10134e6 0.522764
\(160\) 1.15929e6i 0.283029i
\(161\) 139101.i 0.0333313i
\(162\) 528564.i 0.124323i
\(163\) 1.21774e6 0.281184 0.140592 0.990068i \(-0.455099\pi\)
0.140592 + 0.990068i \(0.455099\pi\)
\(164\) 754686. 0.171094
\(165\) 539447.i 0.120087i
\(166\) 9.27952e6 2.02862
\(167\) 4.35007e6 0.934000 0.467000 0.884257i \(-0.345335\pi\)
0.467000 + 0.884257i \(0.345335\pi\)
\(168\) 649997.i 0.137083i
\(169\) −3.54717e6 −0.734889
\(170\) 3.24452e6i 0.660395i
\(171\) 1.34595e6 0.269179
\(172\) 726986.i 0.142870i
\(173\) 459316.i 0.0887101i 0.999016 + 0.0443550i \(0.0141233\pi\)
−0.999016 + 0.0443550i \(0.985877\pi\)
\(174\) 4.43459e6i 0.841794i
\(175\) −1.01885e6 −0.190106
\(176\) 2.34654e6i 0.430418i
\(177\) −3.20028e6 + 90047.1i −0.577122 + 0.0162386i
\(178\) 4.02201e6 0.713153
\(179\) 2.92311e6i 0.509667i −0.966985 0.254833i \(-0.917979\pi\)
0.966985 0.254833i \(-0.0820206\pi\)
\(180\) 281307. 0.0482350
\(181\) −185853. −0.0313425 −0.0156713 0.999877i \(-0.504989\pi\)
−0.0156713 + 0.999877i \(0.504989\pi\)
\(182\) −2.52039e6 −0.418074
\(183\) 569238.i 0.0928840i
\(184\) −612638. −0.0983445
\(185\) 5.53860e6i 0.874751i
\(186\) −1.34643e6 −0.209240
\(187\) 2.43375e6i 0.372179i
\(188\) 891116.i 0.134110i
\(189\) 368576. 0.0545935
\(190\) 3.55938e6i 0.518936i
\(191\) 2.84725e6i 0.408626i 0.978906 + 0.204313i \(0.0654960\pi\)
−0.978906 + 0.204313i \(0.934504\pi\)
\(192\) −2.60335e6 −0.367814
\(193\) −9.28519e6 −1.29157 −0.645786 0.763518i \(-0.723470\pi\)
−0.645786 + 0.763518i \(0.723470\pi\)
\(194\) 531799. 0.0728353
\(195\) 3.23844e6i 0.436749i
\(196\) 1.74446e6 0.231682
\(197\) 3.45147e6 0.451446 0.225723 0.974192i \(-0.427526\pi\)
0.225723 + 0.974192i \(0.427526\pi\)
\(198\) 1.04850e6 0.135075
\(199\) 1.47009e7 1.86546 0.932730 0.360576i \(-0.117420\pi\)
0.932730 + 0.360576i \(0.117420\pi\)
\(200\) 4.48729e6i 0.560911i
\(201\) 5.19242e6i 0.639413i
\(202\) 1.22642e7 1.48794
\(203\) −3.09231e6 −0.369653
\(204\) −1.26914e6 −0.149492
\(205\) 3.35990e6 0.390000
\(206\) −1.77883e7 −2.03485
\(207\) 347391.i 0.0391659i
\(208\) 1.40869e7i 1.56540i
\(209\) 2.66994e6i 0.292457i
\(210\) 974703.i 0.105248i
\(211\) 1.19188e7i 1.26878i 0.773014 + 0.634389i \(0.218748\pi\)
−0.773014 + 0.634389i \(0.781252\pi\)
\(212\) −2.17370e6 −0.228135
\(213\) −506469. −0.0524099
\(214\) 8.41987e6i 0.859140i
\(215\) 3.23658e6i 0.325665i
\(216\) 1.62331e6i 0.161079i
\(217\) 938888.i 0.0918828i
\(218\) 1.79456e6 0.173216
\(219\) 293133.i 0.0279083i
\(220\) 558023.i 0.0524064i
\(221\) 1.46105e7i 1.35359i
\(222\) −1.07652e7 −0.983924
\(223\) 1.02240e7 0.921945 0.460973 0.887414i \(-0.347501\pi\)
0.460973 + 0.887414i \(0.347501\pi\)
\(224\) 1.57123e6i 0.139797i
\(225\) −2.54448e6 −0.223384
\(226\) −4.82631e6 −0.418110
\(227\) 1.76067e6i 0.150522i 0.997164 + 0.0752610i \(0.0239790\pi\)
−0.997164 + 0.0752610i \(0.976021\pi\)
\(228\) −1.39230e6 −0.117470
\(229\) 9.14750e6i 0.761721i 0.924632 + 0.380861i \(0.124372\pi\)
−0.924632 + 0.380861i \(0.875628\pi\)
\(230\) 918680. 0.0755059
\(231\) 731136.i 0.0593147i
\(232\) 1.36194e7i 1.09067i
\(233\) 1.95132e7i 1.54263i −0.636456 0.771313i \(-0.719600\pi\)
0.636456 0.771313i \(-0.280400\pi\)
\(234\) −6.29444e6 −0.491258
\(235\) 3.96730e6i 0.305697i
\(236\) 3.31048e6 93147.9i 0.251857 0.00708659i
\(237\) −4.59145e6 −0.344909
\(238\) 4.39744e6i 0.326189i
\(239\) −234850. −0.0172027 −0.00860135 0.999963i \(-0.502738\pi\)
−0.00860135 + 0.999963i \(0.502738\pi\)
\(240\) 5.44779e6 0.394082
\(241\) −1.22084e6 −0.0872180 −0.0436090 0.999049i \(-0.513886\pi\)
−0.0436090 + 0.999049i \(0.513886\pi\)
\(242\) 1.37778e7i 0.972153i
\(243\) 920483. 0.0641500
\(244\) 588841.i 0.0405348i
\(245\) 7.76641e6 0.528107
\(246\) 6.53051e6i 0.438674i
\(247\) 1.60284e7i 1.06365i
\(248\) −4.13512e6 −0.271102
\(249\) 1.61601e7i 1.04676i
\(250\) 1.67698e7i 1.07327i
\(251\) −2.47884e7 −1.56757 −0.783786 0.621031i \(-0.786714\pi\)
−0.783786 + 0.621031i \(0.786714\pi\)
\(252\) −381268. −0.0238248
\(253\) 689113. 0.0425529
\(254\) 2.23611e7i 1.36456i
\(255\) −5.65026e6 −0.340760
\(256\) 1.19440e7 0.711917
\(257\) 2.03723e7 1.20017 0.600083 0.799938i \(-0.295134\pi\)
0.600083 + 0.799938i \(0.295134\pi\)
\(258\) −6.29082e6 −0.366309
\(259\) 7.50671e6i 0.432066i
\(260\) 3.34996e6i 0.190599i
\(261\) −7.72275e6 −0.434360
\(262\) −1.49412e7 −0.830771
\(263\) 8.00692e6 0.440148 0.220074 0.975483i \(-0.429370\pi\)
0.220074 + 0.975483i \(0.429370\pi\)
\(264\) 3.22012e6 0.175009
\(265\) −9.67745e6 −0.520024
\(266\) 4.82419e6i 0.256318i
\(267\) 7.00424e6i 0.367983i
\(268\) 5.37122e6i 0.279042i
\(269\) 3.55017e7i 1.82387i 0.410339 + 0.911933i \(0.365410\pi\)
−0.410339 + 0.911933i \(0.634590\pi\)
\(270\) 2.43423e6i 0.123672i
\(271\) −30019.5 −0.00150833 −0.000754163 1.00000i \(-0.500240\pi\)
−0.000754163 1.00000i \(0.500240\pi\)
\(272\) −2.45781e7 −1.22135
\(273\) 4.38921e6i 0.215724i
\(274\) 2.01577e7i 0.979917i
\(275\) 5.04744e6i 0.242702i
\(276\) 359354.i 0.0170921i
\(277\) 2.16758e7 1.01985 0.509924 0.860219i \(-0.329673\pi\)
0.509924 + 0.860219i \(0.329673\pi\)
\(278\) 4.05542e7i 1.88756i
\(279\) 2.34478e6i 0.107967i
\(280\) 2.99347e6i 0.136365i
\(281\) −1.70271e7 −0.767399 −0.383700 0.923458i \(-0.625350\pi\)
−0.383700 + 0.923458i \(0.625350\pi\)
\(282\) −7.71108e6 −0.343849
\(283\) 4.09677e6i 0.180751i −0.995908 0.0903757i \(-0.971193\pi\)
0.995908 0.0903757i \(-0.0288068\pi\)
\(284\) 523909. 0.0228718
\(285\) −6.19860e6 −0.267768
\(286\) 1.24862e7i 0.533741i
\(287\) −4.55383e6 −0.192633
\(288\) 3.92401e6i 0.164268i
\(289\) 1.35401e6 0.0560955
\(290\) 2.04229e7i 0.837382i
\(291\) 926116.i 0.0375826i
\(292\) 303228.i 0.0121792i
\(293\) −2.19280e7 −0.871757 −0.435879 0.900005i \(-0.643562\pi\)
−0.435879 + 0.900005i \(0.643562\pi\)
\(294\) 1.50953e7i 0.594017i
\(295\) 1.47384e7 414700.i 0.574097 0.0161535i
\(296\) −3.30616e7 −1.27482
\(297\) 1.82594e6i 0.0696977i
\(298\) −4.05310e7 −1.53158
\(299\) −4.13693e6 −0.154762
\(300\) 2.63210e6 0.0974853
\(301\) 4.38668e6i 0.160856i
\(302\) −2.55725e7 −0.928438
\(303\) 2.13578e7i 0.767767i
\(304\) −2.69633e7 −0.959737
\(305\) 2.62155e6i 0.0923972i
\(306\) 1.09822e7i 0.383288i
\(307\) 4.69803e7 1.62368 0.811841 0.583879i \(-0.198466\pi\)
0.811841 + 0.583879i \(0.198466\pi\)
\(308\) 756314.i 0.0258851i
\(309\) 3.09780e7i 1.04997i
\(310\) 6.20081e6 0.208144
\(311\) 2.31630e7 0.770040 0.385020 0.922908i \(-0.374195\pi\)
0.385020 + 0.922908i \(0.374195\pi\)
\(312\) −1.93313e7 −0.636497
\(313\) 2.47358e7i 0.806663i −0.915054 0.403332i \(-0.867852\pi\)
0.915054 0.403332i \(-0.132148\pi\)
\(314\) −2.44130e7 −0.788555
\(315\) −1.69742e6 −0.0543074
\(316\) 4.74956e6 0.150519
\(317\) −8.60613e6 −0.270166 −0.135083 0.990834i \(-0.543130\pi\)
−0.135083 + 0.990834i \(0.543130\pi\)
\(318\) 1.88097e7i 0.584925i
\(319\) 1.53195e7i 0.471923i
\(320\) 1.19894e7 0.365886
\(321\) 1.46630e7 0.443311
\(322\) −1.24513e6 −0.0372947
\(323\) 2.79654e7 0.829877
\(324\) −952180. −0.0279952
\(325\) 3.03011e7i 0.882691i
\(326\) 1.09003e7i 0.314620i
\(327\) 3.12519e6i 0.0893784i
\(328\) 2.00563e7i 0.568367i
\(329\) 5.37706e6i 0.150993i
\(330\) −4.82873e6 −0.134367
\(331\) 7.29798e6 0.201242 0.100621 0.994925i \(-0.467917\pi\)
0.100621 + 0.994925i \(0.467917\pi\)
\(332\) 1.67166e7i 0.456807i
\(333\) 1.87473e7i 0.507699i
\(334\) 3.89386e7i 1.04506i
\(335\) 2.39130e7i 0.636062i
\(336\) −7.38363e6 −0.194649
\(337\) 4.46800e7i 1.16741i 0.811966 + 0.583705i \(0.198397\pi\)
−0.811966 + 0.583705i \(0.801603\pi\)
\(338\) 3.17517e7i 0.822273i
\(339\) 8.40493e6i 0.215742i
\(340\) 5.84484e6 0.148708
\(341\) 4.65130e6 0.117304
\(342\) 1.20480e7i 0.301187i
\(343\) −2.19735e7 −0.544524
\(344\) −1.93201e7 −0.474608
\(345\) 1.59986e6i 0.0389606i
\(346\) 4.11146e6 0.0992585
\(347\) 4.71309e7i 1.12802i 0.825767 + 0.564011i \(0.190743\pi\)
−0.825767 + 0.564011i \(0.809257\pi\)
\(348\) 7.98869e6 0.189556
\(349\) 4.38597e7i 1.03178i 0.856654 + 0.515892i \(0.172539\pi\)
−0.856654 + 0.515892i \(0.827461\pi\)
\(350\) 9.12000e6i 0.212711i
\(351\) 1.09616e7i 0.253486i
\(352\) −7.78398e6 −0.178473
\(353\) 3.37708e7i 0.767746i 0.923386 + 0.383873i \(0.125410\pi\)
−0.923386 + 0.383873i \(0.874590\pi\)
\(354\) 806036. + 2.86465e7i 0.0181696 + 0.645747i
\(355\) 2.33247e6 0.0521352
\(356\) 7.24544e6i 0.160589i
\(357\) 7.65806e6 0.168312
\(358\) −2.61656e7 −0.570271
\(359\) 3.64347e7 0.787466 0.393733 0.919225i \(-0.371183\pi\)
0.393733 + 0.919225i \(0.371183\pi\)
\(360\) 7.47592e6i 0.160235i
\(361\) −1.63665e7 −0.347885
\(362\) 1.66362e6i 0.0350694i
\(363\) 2.39938e7 0.501625
\(364\) 4.54035e6i 0.0941425i
\(365\) 1.34999e6i 0.0277620i
\(366\) 5.09541e6 0.103929
\(367\) 1.35223e7i 0.273560i −0.990601 0.136780i \(-0.956325\pi\)
0.990601 0.136780i \(-0.0436754\pi\)
\(368\) 6.95925e6i 0.139643i
\(369\) −1.13728e7 −0.226353
\(370\) 4.95775e7 0.978767
\(371\) 1.31163e7 0.256856
\(372\) 2.42553e6i 0.0471170i
\(373\) 7.26776e7 1.40047 0.700236 0.713912i \(-0.253078\pi\)
0.700236 + 0.713912i \(0.253078\pi\)
\(374\) 2.17852e7 0.416434
\(375\) 2.92043e7 0.553799
\(376\) −2.36820e7 −0.445508
\(377\) 9.19669e7i 1.71636i
\(378\) 3.29922e6i 0.0610852i
\(379\) −2.79400e7 −0.513227 −0.256613 0.966514i \(-0.582607\pi\)
−0.256613 + 0.966514i \(0.582607\pi\)
\(380\) 6.41205e6 0.116855
\(381\) 3.89413e7 0.704102
\(382\) 2.54865e7 0.457215
\(383\) 4.89699e7 0.871631 0.435815 0.900036i \(-0.356460\pi\)
0.435815 + 0.900036i \(0.356460\pi\)
\(384\) 3.94137e7i 0.696071i
\(385\) 3.36715e6i 0.0590038i
\(386\) 8.31142e7i 1.44515i
\(387\) 1.09553e7i 0.189013i
\(388\) 958008.i 0.0164011i
\(389\) 3.12900e7 0.531566 0.265783 0.964033i \(-0.414369\pi\)
0.265783 + 0.964033i \(0.414369\pi\)
\(390\) 2.89882e7 0.488683
\(391\) 7.21790e6i 0.120748i
\(392\) 4.63601e7i 0.769637i
\(393\) 2.60198e7i 0.428673i
\(394\) 3.08951e7i 0.505127i
\(395\) 2.11453e7 0.343102
\(396\) 1.88882e6i 0.0304162i
\(397\) 6.06000e7i 0.968503i −0.874929 0.484252i \(-0.839092\pi\)
0.874929 0.484252i \(-0.160908\pi\)
\(398\) 1.31592e8i 2.08728i
\(399\) 8.40124e6 0.132259
\(400\) 5.09733e7 0.796458
\(401\) 6.28406e7i 0.974557i 0.873247 + 0.487278i \(0.162010\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(402\) −4.64788e7 −0.715445
\(403\) −2.79230e7 −0.426626
\(404\) 2.20933e7i 0.335056i
\(405\) −4.23916e6 −0.0638138
\(406\) 2.76801e7i 0.413608i
\(407\) 3.71887e7 0.551604
\(408\) 3.37282e7i 0.496606i
\(409\) 1.24482e7i 0.181943i −0.995853 0.0909717i \(-0.971003\pi\)
0.995853 0.0909717i \(-0.0289973\pi\)
\(410\) 3.00754e7i 0.436375i
\(411\) −3.51042e7 −0.505631
\(412\) 3.20447e7i 0.458210i
\(413\) −1.99757e7 + 562061.i −0.283564 + 0.00797872i
\(414\) −3.10959e6 −0.0438230
\(415\) 7.44231e7i 1.04127i
\(416\) 4.67293e7 0.649097
\(417\) 7.06243e7 0.973971
\(418\) 2.38993e7 0.327233
\(419\) 1.32473e8i 1.80089i 0.434974 + 0.900443i \(0.356758\pi\)
−0.434974 + 0.900443i \(0.643242\pi\)
\(420\) 1.75588e6 0.0236999
\(421\) 7.59498e7i 1.01784i 0.860813 + 0.508921i \(0.169955\pi\)
−0.860813 + 0.508921i \(0.830045\pi\)
\(422\) 1.06689e8 1.41965
\(423\) 1.34287e7i 0.177424i
\(424\) 5.77677e7i 0.757857i
\(425\) −5.28678e7 −0.688691
\(426\) 4.53354e6i 0.0586419i
\(427\) 3.55311e6i 0.0456378i
\(428\) −1.51680e7 −0.193462
\(429\) 2.17444e7 0.275407
\(430\) 2.89715e7 0.364389
\(431\) 6.64451e7i 0.829910i −0.909842 0.414955i \(-0.863797\pi\)
0.909842 0.414955i \(-0.136203\pi\)
\(432\) −1.84399e7 −0.228722
\(433\) 7.41056e7 0.912824 0.456412 0.889769i \(-0.349134\pi\)
0.456412 + 0.889769i \(0.349134\pi\)
\(434\) −8.40424e6 −0.102809
\(435\) 3.55661e7 0.432084
\(436\) 3.23281e6i 0.0390050i
\(437\) 7.91837e6i 0.0948836i
\(438\) −2.62392e6 −0.0312268
\(439\) −1.46356e8 −1.72988 −0.864939 0.501876i \(-0.832643\pi\)
−0.864939 + 0.501876i \(0.832643\pi\)
\(440\) −1.48298e7 −0.174092
\(441\) −2.62881e7 −0.306509
\(442\) −1.30782e8 −1.51454
\(443\) 2.28018e7i 0.262275i −0.991364 0.131138i \(-0.958137\pi\)
0.991364 0.131138i \(-0.0418630\pi\)
\(444\) 1.93929e7i 0.221561i
\(445\) 3.22571e7i 0.366054i
\(446\) 9.15176e7i 1.03157i
\(447\) 7.05839e7i 0.790284i
\(448\) −1.62497e7 −0.180722
\(449\) 8.21601e7 0.907657 0.453829 0.891089i \(-0.350058\pi\)
0.453829 + 0.891089i \(0.350058\pi\)
\(450\) 2.27763e7i 0.249946i
\(451\) 2.25599e7i 0.245928i
\(452\) 8.69436e6i 0.0941504i
\(453\) 4.45340e7i 0.479068i
\(454\) 1.57602e7 0.168420
\(455\) 2.02139e7i 0.214593i
\(456\) 3.70013e7i 0.390232i
\(457\) 1.81968e8i 1.90654i −0.302119 0.953270i \(-0.597694\pi\)
0.302119 0.953270i \(-0.402306\pi\)
\(458\) 8.18818e7 0.852297
\(459\) 1.91253e7 0.197774
\(460\) 1.65496e6i 0.0170025i
\(461\) −1.01124e8 −1.03217 −0.516083 0.856538i \(-0.672611\pi\)
−0.516083 + 0.856538i \(0.672611\pi\)
\(462\) 6.54460e6 0.0663678
\(463\) 9.24206e7i 0.931163i 0.885005 + 0.465582i \(0.154155\pi\)
−0.885005 + 0.465582i \(0.845845\pi\)
\(464\) 1.54709e8 1.54868
\(465\) 1.07986e7i 0.107401i
\(466\) −1.74668e8 −1.72606
\(467\) 2.84588e7i 0.279426i 0.990192 + 0.139713i \(0.0446179\pi\)
−0.990192 + 0.139713i \(0.955382\pi\)
\(468\) 1.13391e7i 0.110622i
\(469\) 3.24103e7i 0.314170i
\(470\) 3.55123e7 0.342047
\(471\) 4.25147e7i 0.406890i
\(472\) 2.47547e6 + 8.79783e7i 0.0235414 + 0.836661i
\(473\) 2.17319e7 0.205359
\(474\) 4.10993e7i 0.385922i
\(475\) −5.79984e7 −0.541172
\(476\) −7.92177e6 −0.0734516
\(477\) 3.27567e7 0.301818
\(478\) 2.10221e6i 0.0192483i
\(479\) −2.24562e7 −0.204329 −0.102164 0.994768i \(-0.532577\pi\)
−0.102164 + 0.994768i \(0.532577\pi\)
\(480\) 1.80715e7i 0.163407i
\(481\) −2.23254e8 −2.00615
\(482\) 1.09280e7i 0.0975890i
\(483\) 2.16837e6i 0.0192438i
\(484\) −2.48201e7 −0.218911
\(485\) 4.26510e6i 0.0373856i
\(486\) 8.23949e6i 0.0717780i
\(487\) 2.12849e8 1.84283 0.921415 0.388581i \(-0.127035\pi\)
0.921415 + 0.388581i \(0.127035\pi\)
\(488\) 1.56488e7 0.134655
\(489\) 1.89827e7 0.162342
\(490\) 6.95192e7i 0.590904i
\(491\) 2.40452e7 0.203135 0.101568 0.994829i \(-0.467614\pi\)
0.101568 + 0.994829i \(0.467614\pi\)
\(492\) 1.17644e7 0.0987811
\(493\) −1.60459e8 −1.33913
\(494\) −1.43474e8 −1.19013
\(495\) 8.40914e6i 0.0693324i
\(496\) 4.69728e7i 0.384947i
\(497\) −3.16131e6 −0.0257512
\(498\) 1.44653e8 1.17123
\(499\) −1.09742e8 −0.883225 −0.441613 0.897206i \(-0.645593\pi\)
−0.441613 + 0.897206i \(0.645593\pi\)
\(500\) −3.02099e7 −0.241679
\(501\) 6.78109e7 0.539245
\(502\) 2.21888e8i 1.75397i
\(503\) 2.81469e7i 0.221171i −0.993867 0.110585i \(-0.964727\pi\)
0.993867 0.110585i \(-0.0352725\pi\)
\(504\) 1.01325e7i 0.0791449i
\(505\) 9.83607e7i 0.763743i
\(506\) 6.16844e6i 0.0476128i
\(507\) −5.52949e7 −0.424288
\(508\) −4.02823e7 −0.307272
\(509\) 2.06631e8i 1.56690i −0.621455 0.783450i \(-0.713458\pi\)
0.621455 0.783450i \(-0.286542\pi\)
\(510\) 5.05770e7i 0.381279i
\(511\) 1.82970e6i 0.0137125i
\(512\) 5.49030e7i 0.409059i
\(513\) 2.09813e7 0.155410
\(514\) 1.82358e8i 1.34288i
\(515\) 1.42665e8i 1.04447i
\(516\) 1.13326e7i 0.0824860i
\(517\) 2.66382e7 0.192768
\(518\) −6.71946e7 −0.483443
\(519\) 7.16002e6i 0.0512168i
\(520\) 8.90275e7 0.633161
\(521\) 2.50237e8 1.76945 0.884726 0.466112i \(-0.154346\pi\)
0.884726 + 0.466112i \(0.154346\pi\)
\(522\) 6.91284e7i 0.486010i
\(523\) −1.01073e8 −0.706529 −0.353265 0.935523i \(-0.614928\pi\)
−0.353265 + 0.935523i \(0.614928\pi\)
\(524\) 2.69158e7i 0.187074i
\(525\) −1.58823e7 −0.109758
\(526\) 7.16721e7i 0.492485i
\(527\) 4.87186e7i 0.332861i
\(528\) 3.65789e7i 0.248502i
\(529\) 1.45992e8 0.986194
\(530\) 8.66255e7i 0.581859i
\(531\) −4.98874e7 + 1.40370e6i −0.333201 + 0.00937539i
\(532\) −8.69054e6 −0.0577181
\(533\) 1.35433e8i 0.894424i
\(534\) 6.26969e7 0.411739
\(535\) −6.75286e7 −0.440988
\(536\) −1.42744e8 −0.926965
\(537\) 4.55668e7i 0.294256i
\(538\) 3.17786e8 2.04074
\(539\) 5.21472e7i 0.333016i
\(540\) 4.38514e6 0.0278485
\(541\) 8.03359e7i 0.507362i −0.967288 0.253681i \(-0.918359\pi\)
0.967288 0.253681i \(-0.0816413\pi\)
\(542\) 268712.i 0.00168768i
\(543\) −2.89716e6 −0.0180956
\(544\) 8.15308e7i 0.506437i
\(545\) 1.43926e7i 0.0889100i
\(546\) −3.92890e7 −0.241375
\(547\) −2.50417e8 −1.53003 −0.765017 0.644010i \(-0.777269\pi\)
−0.765017 + 0.644010i \(0.777269\pi\)
\(548\) 3.63131e7 0.220659
\(549\) 8.87355e6i 0.0536266i
\(550\) −4.51810e7 −0.271561
\(551\) −1.76031e8 −1.05229
\(552\) −9.55008e6 −0.0567792
\(553\) −2.86592e7 −0.169468
\(554\) 1.94026e8i 1.14112i
\(555\) 8.63382e7i 0.505038i
\(556\) −7.30563e7 −0.425044
\(557\) −3.09319e8 −1.78995 −0.894975 0.446117i \(-0.852807\pi\)
−0.894975 + 0.446117i \(0.852807\pi\)
\(558\) −2.09888e7 −0.120805
\(559\) −1.30462e8 −0.746878
\(560\) 3.40043e7 0.193629
\(561\) 3.79385e7i 0.214878i
\(562\) 1.52414e8i 0.858650i
\(563\) 1.14334e8i 0.640695i −0.947300 0.320348i \(-0.896200\pi\)
0.947300 0.320348i \(-0.103800\pi\)
\(564\) 1.38911e7i 0.0774283i
\(565\) 3.87078e7i 0.214611i
\(566\) −3.66713e7 −0.202244
\(567\) 5.74552e6 0.0315196
\(568\) 1.39232e7i 0.0759793i
\(569\) 1.51192e8i 0.820716i 0.911925 + 0.410358i \(0.134596\pi\)
−0.911925 + 0.410358i \(0.865404\pi\)
\(570\) 5.54853e7i 0.299608i
\(571\) 7.77405e7i 0.417580i 0.977961 + 0.208790i \(0.0669524\pi\)
−0.977961 + 0.208790i \(0.933048\pi\)
\(572\) −2.24932e7 −0.120188
\(573\) 4.43843e7i 0.235920i
\(574\) 4.07625e7i 0.215539i
\(575\) 1.49694e7i 0.0787412i
\(576\) −4.05822e7 −0.212358
\(577\) −2.90410e8 −1.51176 −0.755882 0.654708i \(-0.772792\pi\)
−0.755882 + 0.654708i \(0.772792\pi\)
\(578\) 1.21201e7i 0.0627658i
\(579\) −1.44742e8 −0.745690
\(580\) −3.67908e7 −0.188563
\(581\) 1.00869e8i 0.514315i
\(582\) 8.28992e6 0.0420515
\(583\) 6.49788e7i 0.327919i
\(584\) −8.05849e6 −0.0404590
\(585\) 5.04823e7i 0.252157i
\(586\) 1.96283e8i 0.975417i
\(587\) 4.68864e7i 0.231810i −0.993260 0.115905i \(-0.963023\pi\)
0.993260 0.115905i \(-0.0369769\pi\)
\(588\) 2.71934e7 0.133761
\(589\) 5.34465e7i 0.261561i
\(590\) −3.71209e6 1.31928e8i −0.0180743 0.642362i
\(591\) 5.38031e7 0.260642
\(592\) 3.75563e8i 1.81016i
\(593\) 1.47717e8 0.708381 0.354191 0.935173i \(-0.384756\pi\)
0.354191 + 0.935173i \(0.384756\pi\)
\(594\) 1.63445e7 0.0779853
\(595\) −3.52681e7 −0.167429
\(596\) 7.30145e7i 0.344882i
\(597\) 2.29165e8 1.07702
\(598\) 3.70308e7i 0.173165i
\(599\) 2.75154e8 1.28025 0.640125 0.768271i \(-0.278883\pi\)
0.640125 + 0.768271i \(0.278883\pi\)
\(600\) 6.99499e7i 0.323842i
\(601\) 6.29253e6i 0.0289869i 0.999895 + 0.0144935i \(0.00461357\pi\)
−0.999895 + 0.0144935i \(0.995386\pi\)
\(602\) −3.92664e7 −0.179983
\(603\) 8.09418e7i 0.369165i
\(604\) 4.60676e7i 0.209067i
\(605\) −1.10500e8 −0.498996
\(606\) 1.91180e8 0.859061
\(607\) −4.87706e7 −0.218068 −0.109034 0.994038i \(-0.534776\pi\)
−0.109034 + 0.994038i \(0.534776\pi\)
\(608\) 8.94430e7i 0.397957i
\(609\) −4.82043e7 −0.213419
\(610\) −2.34662e7 −0.103384
\(611\) −1.59916e8 −0.701083
\(612\) −1.97839e7 −0.0863092
\(613\) 8.11274e7i 0.352197i −0.984373 0.176099i \(-0.943652\pi\)
0.984373 0.176099i \(-0.0563478\pi\)
\(614\) 4.20533e8i 1.81675i
\(615\) 5.23757e7 0.225167
\(616\) 2.00996e7 0.0859893
\(617\) 6.11368e7 0.260284 0.130142 0.991495i \(-0.458457\pi\)
0.130142 + 0.991495i \(0.458457\pi\)
\(618\) −2.77292e8 −1.17482
\(619\) 3.43981e7 0.145031 0.0725157 0.997367i \(-0.476897\pi\)
0.0725157 + 0.997367i \(0.476897\pi\)
\(620\) 1.11704e7i 0.0468700i
\(621\) 5.41529e6i 0.0226124i
\(622\) 2.07338e8i 0.861604i
\(623\) 4.37195e7i 0.180805i
\(624\) 2.19593e8i 0.903785i
\(625\) 2.91149e7 0.119255
\(626\) −2.21417e8 −0.902583
\(627\) 4.16202e7i 0.168850i
\(628\) 4.39788e7i 0.177568i
\(629\) 3.89521e8i 1.56523i
\(630\) 1.51941e7i 0.0607650i
\(631\) −4.09893e8 −1.63148 −0.815742 0.578416i \(-0.803671\pi\)
−0.815742 + 0.578416i \(0.803671\pi\)
\(632\) 1.26223e8i 0.500019i
\(633\) 1.85796e8i 0.732529i
\(634\) 7.70358e7i 0.302291i
\(635\) −1.79339e8 −0.700412
\(636\) −3.38847e7 −0.131714
\(637\) 3.13054e8i 1.21116i
\(638\) −1.37129e8 −0.528039
\(639\) −7.89506e6 −0.0302589
\(640\) 1.81514e8i 0.692422i
\(641\) 2.74486e8 1.04219 0.521094 0.853499i \(-0.325524\pi\)
0.521094 + 0.853499i \(0.325524\pi\)
\(642\) 1.31253e8i 0.496025i
\(643\) 1.65161e8 0.621260 0.310630 0.950531i \(-0.399460\pi\)
0.310630 + 0.950531i \(0.399460\pi\)
\(644\) 2.24304e6i 0.00839806i
\(645\) 5.04533e7i 0.188023i
\(646\) 2.50326e8i 0.928557i
\(647\) 3.83011e7 0.141416 0.0707080 0.997497i \(-0.477474\pi\)
0.0707080 + 0.997497i \(0.477474\pi\)
\(648\) 2.53048e7i 0.0929991i
\(649\) −2.78448e6 9.89606e7i −0.0101862 0.362016i
\(650\) 2.71234e8 0.987651
\(651\) 1.46358e7i 0.0530486i
\(652\) −1.96363e7 −0.0708464
\(653\) −6.65856e7 −0.239134 −0.119567 0.992826i \(-0.538151\pi\)
−0.119567 + 0.992826i \(0.538151\pi\)
\(654\) 2.79744e7 0.100006
\(655\) 1.19831e8i 0.426426i
\(656\) 2.27829e8 0.807045
\(657\) 4.56950e6i 0.0161129i
\(658\) −4.81315e7 −0.168947
\(659\) 5.53332e8i 1.93344i −0.255843 0.966718i \(-0.582353\pi\)
0.255843 0.966718i \(-0.417647\pi\)
\(660\) 8.69872e6i 0.0302568i
\(661\) 4.89443e7 0.169472 0.0847360 0.996403i \(-0.472995\pi\)
0.0847360 + 0.996403i \(0.472995\pi\)
\(662\) 6.53262e7i 0.225171i
\(663\) 2.27755e8i 0.781496i
\(664\) 4.44254e8 1.51750
\(665\) −3.86908e7 −0.131566
\(666\) −1.67812e8 −0.568069
\(667\) 4.54337e7i 0.153109i
\(668\) −7.01460e7 −0.235328
\(669\) 1.59376e8 0.532285
\(670\) 2.14052e8 0.711695
\(671\) −1.76023e7 −0.0582642
\(672\) 2.44931e7i 0.0807116i
\(673\) 1.64019e8i 0.538082i −0.963129 0.269041i \(-0.913293\pi\)
0.963129 0.269041i \(-0.0867067\pi\)
\(674\) 3.99943e8 1.30622
\(675\) −3.96645e7 −0.128971
\(676\) 5.71990e7 0.185160
\(677\) −1.58965e8 −0.512313 −0.256156 0.966635i \(-0.582456\pi\)
−0.256156 + 0.966635i \(0.582456\pi\)
\(678\) −7.52348e7 −0.241396
\(679\) 5.78069e6i 0.0184659i
\(680\) 1.55330e8i 0.494003i
\(681\) 2.74461e7i 0.0869039i
\(682\) 4.16351e7i 0.131252i
\(683\) 7.60272e7i 0.238620i −0.992857 0.119310i \(-0.961932\pi\)
0.992857 0.119310i \(-0.0380682\pi\)
\(684\) −2.17038e7 −0.0678215
\(685\) 1.61668e8 0.502981
\(686\) 1.96691e8i 0.609273i
\(687\) 1.42595e8i 0.439780i
\(688\) 2.19467e8i 0.673913i
\(689\) 3.90085e8i 1.19262i
\(690\) 1.43208e7 0.0435934
\(691\) 4.52482e7i 0.137141i −0.997646 0.0685704i \(-0.978156\pi\)
0.997646 0.0685704i \(-0.0218438\pi\)
\(692\) 7.40658e6i 0.0223511i
\(693\) 1.13973e7i 0.0342454i
\(694\) 4.21882e8 1.26215
\(695\) −3.25251e8 −0.968866
\(696\) 2.12305e8i 0.629698i
\(697\) −2.36297e8 −0.697846
\(698\) 3.92600e8 1.15447
\(699\) 3.04181e8i 0.890636i
\(700\) 1.64292e7 0.0478986
\(701\) 1.05088e8i 0.305069i 0.988298 + 0.152534i \(0.0487435\pi\)
−0.988298 + 0.152534i \(0.951257\pi\)
\(702\) −9.81206e7 −0.283628
\(703\) 4.27322e8i 1.22996i
\(704\) 8.05021e7i 0.230722i
\(705\) 6.18440e7i 0.176494i
\(706\) 3.02292e8 0.859037
\(707\) 1.33313e8i 0.377236i
\(708\) 5.16053e7 1.45203e6i 0.145410 0.00409144i
\(709\) −3.15831e7 −0.0886168 −0.0443084 0.999018i \(-0.514108\pi\)
−0.0443084 + 0.999018i \(0.514108\pi\)
\(710\) 2.08786e7i 0.0583346i
\(711\) −7.15737e7 −0.199134
\(712\) 1.92552e8 0.533469
\(713\) −1.37946e7 −0.0380575
\(714\) 6.85493e7i 0.188325i
\(715\) −1.00141e8 −0.273964
\(716\) 4.71359e7i 0.128414i
\(717\) −3.66095e6 −0.00993199
\(718\) 3.26137e8i 0.881103i
\(719\) 3.58858e8i 0.965463i 0.875768 + 0.482732i \(0.160355\pi\)
−0.875768 + 0.482732i \(0.839645\pi\)
\(720\) 8.49226e7 0.227523
\(721\) 1.93360e8i 0.515895i
\(722\) 1.46501e8i 0.389251i
\(723\) −1.90310e7 −0.0503554
\(724\) 2.99693e6 0.00789697
\(725\) 3.32781e8 0.873262
\(726\) 2.14775e8i 0.561273i
\(727\) −3.39579e8 −0.883766 −0.441883 0.897073i \(-0.645689\pi\)
−0.441883 + 0.897073i \(0.645689\pi\)
\(728\) −1.20663e8 −0.312738
\(729\) 1.43489e7 0.0370370
\(730\) 1.20841e7 0.0310632
\(731\) 2.27624e8i 0.582727i
\(732\) 9.17912e6i 0.0234028i
\(733\) −1.11024e8 −0.281906 −0.140953 0.990016i \(-0.545017\pi\)
−0.140953 + 0.990016i \(0.545017\pi\)
\(734\) −1.21042e8 −0.306089
\(735\) 1.21066e8 0.304903
\(736\) 2.30853e7 0.0579032
\(737\) 1.60563e8 0.401090
\(738\) 1.01801e8i 0.253269i
\(739\) 4.54492e8i 1.12614i −0.826408 0.563071i \(-0.809620\pi\)
0.826408 0.563071i \(-0.190380\pi\)
\(740\) 8.93113e7i 0.220400i
\(741\) 2.49857e8i 0.614098i
\(742\) 1.17407e8i 0.287398i
\(743\) 4.20852e8 1.02604 0.513019 0.858377i \(-0.328527\pi\)
0.513019 + 0.858377i \(0.328527\pi\)
\(744\) −6.44601e7 −0.156521
\(745\) 3.25065e8i 0.786142i
\(746\) 6.50557e8i 1.56700i
\(747\) 2.51911e8i 0.604345i
\(748\) 3.92449e7i 0.0937731i
\(749\) 9.15245e7 0.217817
\(750\) 2.61415e8i 0.619651i
\(751\) 5.84213e8i 1.37928i 0.724154 + 0.689639i \(0.242231\pi\)
−0.724154 + 0.689639i \(0.757769\pi\)
\(752\) 2.69016e8i 0.632592i
\(753\) −3.86413e8 −0.905039
\(754\) 8.23220e8 1.92045
\(755\) 2.05096e8i 0.476557i
\(756\) −5.94338e6 −0.0137552
\(757\) 8.50539e7 0.196068 0.0980340 0.995183i \(-0.468745\pi\)
0.0980340 + 0.995183i \(0.468745\pi\)
\(758\) 2.50099e8i 0.574254i
\(759\) 1.07422e7 0.0245679
\(760\) 1.70405e8i 0.388187i
\(761\) 5.25615e8 1.19265 0.596326 0.802743i \(-0.296627\pi\)
0.596326 + 0.802743i \(0.296627\pi\)
\(762\) 3.48574e8i 0.787827i
\(763\) 1.95070e7i 0.0439154i
\(764\) 4.59127e7i 0.102956i
\(765\) −8.80789e7 −0.196738
\(766\) 4.38343e8i 0.975276i
\(767\) 1.67160e7 + 5.94087e8i 0.0370464 + 1.31663i
\(768\) 1.86188e8 0.411025
\(769\) 8.09871e8i 1.78089i 0.455091 + 0.890445i \(0.349607\pi\)
−0.455091 + 0.890445i \(0.650393\pi\)
\(770\) −3.01403e7 −0.0660199
\(771\) 3.17573e8 0.692916
\(772\) 1.49726e8 0.325421
\(773\) 1.15979e8i 0.251096i 0.992088 + 0.125548i \(0.0400688\pi\)
−0.992088 + 0.125548i \(0.959931\pi\)
\(774\) −9.80641e7 −0.211489
\(775\) 1.01039e8i 0.217062i
\(776\) 2.54597e7 0.0544839
\(777\) 1.17018e8i 0.249454i
\(778\) 2.80086e8i 0.594774i
\(779\) −2.59228e8 −0.548365
\(780\) 5.22207e7i 0.110042i
\(781\) 1.56613e7i 0.0328757i
\(782\) −6.46094e7 −0.135106
\(783\) −1.20386e8 −0.250778
\(784\) 5.26627e8 1.09284
\(785\)