Properties

Label 177.7.c.a.58.8
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 58.8
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.53

$q$-expansion

\(f(q)\) \(=\) \(q-13.2493i q^{2} -15.5885 q^{3} -111.544 q^{4} -224.166 q^{5} +206.536i q^{6} +460.347 q^{7} +629.930i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-13.2493i q^{2} -15.5885 q^{3} -111.544 q^{4} -224.166 q^{5} +206.536i q^{6} +460.347 q^{7} +629.930i q^{8} +243.000 q^{9} +2970.05i q^{10} -1566.88i q^{11} +1738.80 q^{12} +3966.82i q^{13} -6099.29i q^{14} +3494.40 q^{15} +1207.30 q^{16} +6700.13 q^{17} -3219.58i q^{18} +8706.20 q^{19} +25004.5 q^{20} -7176.11 q^{21} -20760.0 q^{22} -7021.62i q^{23} -9819.63i q^{24} +34625.4 q^{25} +52557.7 q^{26} -3788.00 q^{27} -51349.1 q^{28} -38321.7 q^{29} -46298.5i q^{30} +35296.6i q^{31} +24319.6i q^{32} +24425.2i q^{33} -88772.1i q^{34} -103194. q^{35} -27105.3 q^{36} -59583.7i q^{37} -115351. i q^{38} -61836.6i q^{39} -141209. i q^{40} -7065.43 q^{41} +95078.5i q^{42} -9877.97i q^{43} +174776. i q^{44} -54472.4 q^{45} -93031.6 q^{46} +87041.4i q^{47} -18820.0 q^{48} +94270.7 q^{49} -458763. i q^{50} -104445. q^{51} -442477. i q^{52} -2972.73 q^{53} +50188.3i q^{54} +351241. i q^{55} +289987. i q^{56} -135716. q^{57} +507736. i q^{58} +(193592. - 68575.8i) q^{59} -389781. q^{60} +75860.0i q^{61} +467655. q^{62} +111864. q^{63} +399485. q^{64} -889227. i q^{65} +323617. q^{66} -305808. i q^{67} -747361. q^{68} +109456. i q^{69} +1.36725e6i q^{70} +351118. q^{71} +153073. i q^{72} -146464. i q^{73} -789443. q^{74} -539757. q^{75} -971128. q^{76} -721307. i q^{77} -819293. q^{78} +188502. q^{79} -270636. q^{80} +59049.0 q^{81} +93612.1i q^{82} -371074. i q^{83} +800454. q^{84} -1.50194e6 q^{85} -130876. q^{86} +597376. q^{87} +987022. q^{88} +609230. i q^{89} +721722. i q^{90} +1.82612e6i q^{91} +783222. i q^{92} -550219. i q^{93} +1.15324e6 q^{94} -1.95164e6 q^{95} -379105. i q^{96} -998439. i q^{97} -1.24902e6i q^{98} -380751. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.2493i 1.65616i −0.560607 0.828082i \(-0.689432\pi\)
0.560607 0.828082i \(-0.310568\pi\)
\(3\) −15.5885 −0.577350
\(4\) −111.544 −1.74288
\(5\) −224.166 −1.79333 −0.896664 0.442711i \(-0.854017\pi\)
−0.896664 + 0.442711i \(0.854017\pi\)
\(6\) 206.536i 0.956187i
\(7\) 460.347 1.34212 0.671060 0.741403i \(-0.265839\pi\)
0.671060 + 0.741403i \(0.265839\pi\)
\(8\) 629.930i 1.23033i
\(9\) 243.000 0.333333
\(10\) 2970.05i 2.97005i
\(11\) 1566.88i 1.17722i −0.808418 0.588609i \(-0.799676\pi\)
0.808418 0.588609i \(-0.200324\pi\)
\(12\) 1738.80 1.00625
\(13\) 3966.82i 1.80556i 0.430099 + 0.902782i \(0.358479\pi\)
−0.430099 + 0.902782i \(0.641521\pi\)
\(14\) 6099.29i 2.22277i
\(15\) 3494.40 1.03538
\(16\) 1207.30 0.294751
\(17\) 6700.13 1.36375 0.681877 0.731466i \(-0.261164\pi\)
0.681877 + 0.731466i \(0.261164\pi\)
\(18\) 3219.58i 0.552055i
\(19\) 8706.20 1.26931 0.634656 0.772795i \(-0.281142\pi\)
0.634656 + 0.772795i \(0.281142\pi\)
\(20\) 25004.5 3.12556
\(21\) −7176.11 −0.774874
\(22\) −20760.0 −1.94967
\(23\) 7021.62i 0.577104i −0.957464 0.288552i \(-0.906826\pi\)
0.957464 0.288552i \(-0.0931737\pi\)
\(24\) 9819.63i 0.710332i
\(25\) 34625.4 2.21603
\(26\) 52557.7 2.99031
\(27\) −3788.00 −0.192450
\(28\) −51349.1 −2.33916
\(29\) −38321.7 −1.57127 −0.785634 0.618691i \(-0.787663\pi\)
−0.785634 + 0.618691i \(0.787663\pi\)
\(30\) 46298.5i 1.71476i
\(31\) 35296.6i 1.18481i 0.805642 + 0.592403i \(0.201821\pi\)
−0.805642 + 0.592403i \(0.798179\pi\)
\(32\) 24319.6i 0.742175i
\(33\) 24425.2i 0.679667i
\(34\) 88772.1i 2.25860i
\(35\) −103194. −2.40686
\(36\) −27105.3 −0.580960
\(37\) 59583.7i 1.17631i −0.808748 0.588156i \(-0.799854\pi\)
0.808748 0.588156i \(-0.200146\pi\)
\(38\) 115351.i 2.10219i
\(39\) 61836.6i 1.04244i
\(40\) 141209.i 2.20639i
\(41\) −7065.43 −0.102515 −0.0512575 0.998685i \(-0.516323\pi\)
−0.0512575 + 0.998685i \(0.516323\pi\)
\(42\) 95078.5i 1.28332i
\(43\) 9877.97i 0.124240i −0.998069 0.0621201i \(-0.980214\pi\)
0.998069 0.0621201i \(-0.0197862\pi\)
\(44\) 174776.i 2.05175i
\(45\) −54472.4 −0.597776
\(46\) −93031.6 −0.955778
\(47\) 87041.4i 0.838363i 0.907902 + 0.419181i \(0.137683\pi\)
−0.907902 + 0.419181i \(0.862317\pi\)
\(48\) −18820.0 −0.170175
\(49\) 94270.7 0.801288
\(50\) 458763.i 3.67011i
\(51\) −104445. −0.787364
\(52\) 442477.i 3.14688i
\(53\) −2972.73 −0.0199677 −0.00998384 0.999950i \(-0.503178\pi\)
−0.00998384 + 0.999950i \(0.503178\pi\)
\(54\) 50188.3i 0.318729i
\(55\) 351241.i 2.11114i
\(56\) 289987.i 1.65125i
\(57\) −135716. −0.732837
\(58\) 507736.i 2.60228i
\(59\) 193592. 68575.8i 0.942609 0.333899i
\(60\) −389781. −1.80454
\(61\) 75860.0i 0.334213i 0.985939 + 0.167107i \(0.0534424\pi\)
−0.985939 + 0.167107i \(0.946558\pi\)
\(62\) 467655. 1.96223
\(63\) 111864. 0.447374
\(64\) 399485. 1.52392
\(65\) 889227.i 3.23797i
\(66\) 323617. 1.12564
\(67\) 305808.i 1.01678i −0.861128 0.508388i \(-0.830242\pi\)
0.861128 0.508388i \(-0.169758\pi\)
\(68\) −747361. −2.37686
\(69\) 109456.i 0.333191i
\(70\) 1.36725e6i 3.98616i
\(71\) 351118. 0.981021 0.490510 0.871435i \(-0.336810\pi\)
0.490510 + 0.871435i \(0.336810\pi\)
\(72\) 153073.i 0.410111i
\(73\) 146464.i 0.376499i −0.982121 0.188249i \(-0.939719\pi\)
0.982121 0.188249i \(-0.0602813\pi\)
\(74\) −789443. −1.94817
\(75\) −539757. −1.27942
\(76\) −971128. −2.21226
\(77\) 721307.i 1.57997i
\(78\) −819293. −1.72646
\(79\) 188502. 0.382326 0.191163 0.981558i \(-0.438774\pi\)
0.191163 + 0.981558i \(0.438774\pi\)
\(80\) −270636. −0.528586
\(81\) 59049.0 0.111111
\(82\) 93612.1i 0.169782i
\(83\) 371074.i 0.648972i −0.945890 0.324486i \(-0.894809\pi\)
0.945890 0.324486i \(-0.105191\pi\)
\(84\) 800454. 1.35051
\(85\) −1.50194e6 −2.44566
\(86\) −130876. −0.205762
\(87\) 597376. 0.907172
\(88\) 987022. 1.44837
\(89\) 609230.i 0.864194i 0.901827 + 0.432097i \(0.142226\pi\)
−0.901827 + 0.432097i \(0.857774\pi\)
\(90\) 721722.i 0.990016i
\(91\) 1.82612e6i 2.42328i
\(92\) 783222.i 1.00582i
\(93\) 550219.i 0.684048i
\(94\) 1.15324e6 1.38847
\(95\) −1.95164e6 −2.27629
\(96\) 379105.i 0.428495i
\(97\) 998439.i 1.09397i −0.837142 0.546986i \(-0.815775\pi\)
0.837142 0.546986i \(-0.184225\pi\)
\(98\) 1.24902e6i 1.32706i
\(99\) 380751.i 0.392406i
\(100\) −3.86227e6 −3.86227
\(101\) 1.19215e6i 1.15709i 0.815651 + 0.578544i \(0.196379\pi\)
−0.815651 + 0.578544i \(0.803621\pi\)
\(102\) 1.38382e6i 1.30400i
\(103\) 9419.64i 0.00862031i 0.999991 + 0.00431015i \(0.00137197\pi\)
−0.999991 + 0.00431015i \(0.998628\pi\)
\(104\) −2.49882e6 −2.22144
\(105\) 1.60864e6 1.38960
\(106\) 39386.6i 0.0330698i
\(107\) −413246. −0.337332 −0.168666 0.985673i \(-0.553946\pi\)
−0.168666 + 0.985673i \(0.553946\pi\)
\(108\) 422529. 0.335417
\(109\) 1.77849e6i 1.37332i −0.726978 0.686661i \(-0.759076\pi\)
0.726978 0.686661i \(-0.240924\pi\)
\(110\) 4.65370e6 3.49639
\(111\) 928818.i 0.679144i
\(112\) 555778. 0.395592
\(113\) 2.68112e6i 1.85815i −0.369888 0.929076i \(-0.620604\pi\)
0.369888 0.929076i \(-0.379396\pi\)
\(114\) 1.79815e6i 1.21370i
\(115\) 1.57401e6i 1.03494i
\(116\) 4.27456e6 2.73853
\(117\) 963938.i 0.601854i
\(118\) −908582. 2.56496e6i −0.552991 1.56112i
\(119\) 3.08439e6 1.83032
\(120\) 2.20123e6i 1.27386i
\(121\) −683541. −0.385841
\(122\) 1.00509e6 0.553512
\(123\) 110139. 0.0591870
\(124\) 3.93713e6i 2.06498i
\(125\) −4.25926e6 −2.18074
\(126\) 1.48213e6i 0.740924i
\(127\) 3.22453e6 1.57418 0.787092 0.616835i \(-0.211586\pi\)
0.787092 + 0.616835i \(0.211586\pi\)
\(128\) 3.73645e6i 1.78168i
\(129\) 153982.i 0.0717301i
\(130\) −1.17816e7 −5.36261
\(131\) 2.07176e6i 0.921562i −0.887514 0.460781i \(-0.847569\pi\)
0.887514 0.460781i \(-0.152431\pi\)
\(132\) 2.72449e6i 1.18458i
\(133\) 4.00788e6 1.70357
\(134\) −4.05175e6 −1.68395
\(135\) 849140. 0.345126
\(136\) 4.22061e6i 1.67787i
\(137\) −280882. −0.109235 −0.0546176 0.998507i \(-0.517394\pi\)
−0.0546176 + 0.998507i \(0.517394\pi\)
\(138\) 1.45022e6 0.551819
\(139\) −2.20910e6 −0.822568 −0.411284 0.911507i \(-0.634920\pi\)
−0.411284 + 0.911507i \(0.634920\pi\)
\(140\) 1.15107e7 4.19488
\(141\) 1.35684e6i 0.484029i
\(142\) 4.65207e6i 1.62473i
\(143\) 6.21552e6 2.12554
\(144\) 293374. 0.0982504
\(145\) 8.59042e6 2.81780
\(146\) −1.94055e6 −0.623544
\(147\) −1.46954e6 −0.462624
\(148\) 6.64622e6i 2.05017i
\(149\) 1.69318e6i 0.511851i −0.966697 0.255925i \(-0.917620\pi\)
0.966697 0.255925i \(-0.0823801\pi\)
\(150\) 7.15141e6i 2.11894i
\(151\) 958302.i 0.278337i −0.990269 0.139169i \(-0.955557\pi\)
0.990269 0.139169i \(-0.0444430\pi\)
\(152\) 5.48430e6i 1.56167i
\(153\) 1.62813e6 0.454585
\(154\) −9.55683e6 −2.61669
\(155\) 7.91230e6i 2.12475i
\(156\) 6.89753e6i 1.81685i
\(157\) 3.40122e6i 0.878894i 0.898269 + 0.439447i \(0.144826\pi\)
−0.898269 + 0.439447i \(0.855174\pi\)
\(158\) 2.49752e6i 0.633195i
\(159\) 46340.3 0.0115283
\(160\) 5.45163e6i 1.33096i
\(161\) 3.23238e6i 0.774543i
\(162\) 782359.i 0.184018i
\(163\) −182298. −0.0420938 −0.0210469 0.999778i \(-0.506700\pi\)
−0.0210469 + 0.999778i \(0.506700\pi\)
\(164\) 788109. 0.178671
\(165\) 5.47530e6i 1.21887i
\(166\) −4.91648e6 −1.07481
\(167\) 4.78402e6 1.02717 0.513587 0.858038i \(-0.328316\pi\)
0.513587 + 0.858038i \(0.328316\pi\)
\(168\) 4.52044e6i 0.953352i
\(169\) −1.09089e7 −2.26006
\(170\) 1.98997e7i 4.05042i
\(171\) 2.11561e6 0.423104
\(172\) 1.10183e6i 0.216536i
\(173\) 8.66796e6i 1.67409i −0.547135 0.837044i \(-0.684282\pi\)
0.547135 0.837044i \(-0.315718\pi\)
\(174\) 7.91482e6i 1.50243i
\(175\) 1.59397e7 2.97418
\(176\) 1.89169e6i 0.346986i
\(177\) −3.01780e6 + 1.06899e6i −0.544216 + 0.192777i
\(178\) 8.07188e6 1.43125
\(179\) 5.24760e6i 0.914960i 0.889220 + 0.457480i \(0.151248\pi\)
−0.889220 + 0.457480i \(0.848752\pi\)
\(180\) 6.07608e6 1.04185
\(181\) 3.23180e6 0.545015 0.272507 0.962154i \(-0.412147\pi\)
0.272507 + 0.962154i \(0.412147\pi\)
\(182\) 2.41948e7 4.01336
\(183\) 1.18254e6i 0.192958i
\(184\) 4.42313e6 0.710029
\(185\) 1.33566e7i 2.10951i
\(186\) −7.29003e6 −1.13290
\(187\) 1.04983e7i 1.60544i
\(188\) 9.70897e6i 1.46117i
\(189\) −1.74379e6 −0.258291
\(190\) 2.58578e7i 3.76991i
\(191\) 1.90730e6i 0.273728i 0.990590 + 0.136864i \(0.0437023\pi\)
−0.990590 + 0.136864i \(0.956298\pi\)
\(192\) −6.22736e6 −0.879833
\(193\) −1.15832e7 −1.61122 −0.805612 0.592443i \(-0.798163\pi\)
−0.805612 + 0.592443i \(0.798163\pi\)
\(194\) −1.32286e7 −1.81180
\(195\) 1.38617e7i 1.86944i
\(196\) −1.05154e7 −1.39655
\(197\) −2.50665e6 −0.327864 −0.163932 0.986472i \(-0.552418\pi\)
−0.163932 + 0.986472i \(0.552418\pi\)
\(198\) −5.04469e6 −0.649888
\(199\) 1.30088e6 0.165074 0.0825371 0.996588i \(-0.473698\pi\)
0.0825371 + 0.996588i \(0.473698\pi\)
\(200\) 2.18116e7i 2.72645i
\(201\) 4.76708e6i 0.587036i
\(202\) 1.57952e7 1.91633
\(203\) −1.76413e7 −2.10883
\(204\) 1.16502e7 1.37228
\(205\) 1.58383e6 0.183843
\(206\) 124804. 0.0142766
\(207\) 1.70625e6i 0.192368i
\(208\) 4.78915e6i 0.532192i
\(209\) 1.36415e7i 1.49426i
\(210\) 2.13134e7i 2.30141i
\(211\) 5.44641e6i 0.579779i −0.957060 0.289890i \(-0.906381\pi\)
0.957060 0.289890i \(-0.0936186\pi\)
\(212\) 331591. 0.0348013
\(213\) −5.47339e6 −0.566393
\(214\) 5.47523e6i 0.558677i
\(215\) 2.21431e6i 0.222804i
\(216\) 2.38617e6i 0.236777i
\(217\) 1.62487e7i 1.59015i
\(218\) −2.35638e7 −2.27445
\(219\) 2.28316e6i 0.217372i
\(220\) 3.91789e7i 3.67946i
\(221\) 2.65782e7i 2.46235i
\(222\) 1.23062e7 1.12477
\(223\) 1.43801e7 1.29672 0.648360 0.761334i \(-0.275455\pi\)
0.648360 + 0.761334i \(0.275455\pi\)
\(224\) 1.11955e7i 0.996089i
\(225\) 8.41398e6 0.738676
\(226\) −3.55230e7 −3.07741
\(227\) 1.47692e7i 1.26264i 0.775521 + 0.631321i \(0.217487\pi\)
−0.775521 + 0.631321i \(0.782513\pi\)
\(228\) 1.51384e7 1.27725
\(229\) 160746.i 0.0133855i −0.999978 0.00669275i \(-0.997870\pi\)
0.999978 0.00669275i \(-0.00213038\pi\)
\(230\) 2.08545e7 1.71402
\(231\) 1.12441e7i 0.912195i
\(232\) 2.41400e7i 1.93318i
\(233\) 1.32519e7i 1.04764i −0.851829 0.523819i \(-0.824507\pi\)
0.851829 0.523819i \(-0.175493\pi\)
\(234\) 1.27715e7 0.996770
\(235\) 1.95117e7i 1.50346i
\(236\) −2.15941e7 + 7.64924e6i −1.64285 + 0.581946i
\(237\) −2.93845e6 −0.220736
\(238\) 4.08660e7i 3.03132i
\(239\) 1.99713e7 1.46289 0.731446 0.681899i \(-0.238846\pi\)
0.731446 + 0.681899i \(0.238846\pi\)
\(240\) 4.21880e6 0.305179
\(241\) 3.58286e6 0.255964 0.127982 0.991777i \(-0.459150\pi\)
0.127982 + 0.991777i \(0.459150\pi\)
\(242\) 9.05644e6i 0.639016i
\(243\) −920483. −0.0641500
\(244\) 8.46175e6i 0.582493i
\(245\) −2.11323e7 −1.43697
\(246\) 1.45927e6i 0.0980234i
\(247\) 3.45360e7i 2.29182i
\(248\) −2.22344e7 −1.45770
\(249\) 5.78447e6i 0.374684i
\(250\) 5.64322e7i 3.61166i
\(251\) 2.20964e7 1.39734 0.698668 0.715446i \(-0.253776\pi\)
0.698668 + 0.715446i \(0.253776\pi\)
\(252\) −1.24778e7 −0.779719
\(253\) −1.10020e7 −0.679376
\(254\) 4.27228e7i 2.60711i
\(255\) 2.34130e7 1.41200
\(256\) −2.39384e7 −1.42684
\(257\) −1.57000e7 −0.924911 −0.462456 0.886642i \(-0.653032\pi\)
−0.462456 + 0.886642i \(0.653032\pi\)
\(258\) 2.04016e6 0.118797
\(259\) 2.74292e7i 1.57875i
\(260\) 9.91882e7i 5.64339i
\(261\) −9.31216e6 −0.523756
\(262\) −2.74493e7 −1.52626
\(263\) 9.82007e6 0.539818 0.269909 0.962886i \(-0.413006\pi\)
0.269909 + 0.962886i \(0.413006\pi\)
\(264\) −1.53862e7 −0.836216
\(265\) 666385. 0.0358086
\(266\) 5.31016e7i 2.82139i
\(267\) 9.49696e6i 0.498943i
\(268\) 3.41112e7i 1.77212i
\(269\) 8.38467e6i 0.430754i −0.976531 0.215377i \(-0.930902\pi\)
0.976531 0.215377i \(-0.0690980\pi\)
\(270\) 1.12505e7i 0.571586i
\(271\) −4.37105e6 −0.219623 −0.109812 0.993952i \(-0.535025\pi\)
−0.109812 + 0.993952i \(0.535025\pi\)
\(272\) 8.08907e6 0.401968
\(273\) 2.84663e7i 1.39908i
\(274\) 3.72150e6i 0.180911i
\(275\) 5.42538e7i 2.60875i
\(276\) 1.22092e7i 0.580712i
\(277\) 2.03885e7 0.959280 0.479640 0.877465i \(-0.340767\pi\)
0.479640 + 0.877465i \(0.340767\pi\)
\(278\) 2.92691e7i 1.36231i
\(279\) 8.57707e6i 0.394936i
\(280\) 6.50052e7i 2.96124i
\(281\) 1.58550e7 0.714575 0.357288 0.933994i \(-0.383702\pi\)
0.357288 + 0.933994i \(0.383702\pi\)
\(282\) −1.79772e7 −0.801632
\(283\) 2.80181e7i 1.23618i −0.786109 0.618088i \(-0.787908\pi\)
0.786109 0.618088i \(-0.212092\pi\)
\(284\) −3.91652e7 −1.70980
\(285\) 3.04230e7 1.31422
\(286\) 8.23514e7i 3.52024i
\(287\) −3.25255e6 −0.137587
\(288\) 5.90966e6i 0.247392i
\(289\) 2.07541e7 0.859827
\(290\) 1.13817e8i 4.66674i
\(291\) 1.55641e7i 0.631605i
\(292\) 1.63373e7i 0.656192i
\(293\) −3.79082e7 −1.50706 −0.753530 0.657414i \(-0.771650\pi\)
−0.753530 + 0.657414i \(0.771650\pi\)
\(294\) 1.94703e7i 0.766181i
\(295\) −4.33968e7 + 1.53724e7i −1.69041 + 0.598790i
\(296\) 3.75336e7 1.44725
\(297\) 5.93532e6i 0.226556i
\(298\) −2.24334e7 −0.847709
\(299\) 2.78535e7 1.04200
\(300\) 6.02069e7 2.22988
\(301\) 4.54730e6i 0.166745i
\(302\) −1.26968e7 −0.460972
\(303\) 1.85838e7i 0.668046i
\(304\) 1.05110e7 0.374131
\(305\) 1.70052e7i 0.599354i
\(306\) 2.15716e7i 0.752867i
\(307\) −7.94326e6 −0.274526 −0.137263 0.990535i \(-0.543831\pi\)
−0.137263 + 0.990535i \(0.543831\pi\)
\(308\) 8.04578e7i 2.75369i
\(309\) 146838.i 0.00497694i
\(310\) −1.04832e8 −3.51893
\(311\) 1.84910e6 0.0614722 0.0307361 0.999528i \(-0.490215\pi\)
0.0307361 + 0.999528i \(0.490215\pi\)
\(312\) 3.89527e7 1.28255
\(313\) 1.39026e7i 0.453382i −0.973967 0.226691i \(-0.927209\pi\)
0.973967 0.226691i \(-0.0727907\pi\)
\(314\) 4.50639e7 1.45559
\(315\) −2.50762e7 −0.802288
\(316\) −2.10263e7 −0.666349
\(317\) 5.90330e7 1.85318 0.926589 0.376077i \(-0.122727\pi\)
0.926589 + 0.376077i \(0.122727\pi\)
\(318\) 613977.i 0.0190928i
\(319\) 6.00453e7i 1.84972i
\(320\) −8.95511e7 −2.73288
\(321\) 6.44187e6 0.194759
\(322\) −4.28269e7 −1.28277
\(323\) 5.83327e7 1.73103
\(324\) −6.58658e6 −0.193653
\(325\) 1.37353e8i 4.00118i
\(326\) 2.41532e6i 0.0697142i
\(327\) 2.77239e7i 0.792888i
\(328\) 4.45073e6i 0.126127i
\(329\) 4.00693e7i 1.12518i
\(330\) −7.25440e7 −2.01864
\(331\) 3.69169e7 1.01798 0.508992 0.860771i \(-0.330018\pi\)
0.508992 + 0.860771i \(0.330018\pi\)
\(332\) 4.13912e7i 1.13108i
\(333\) 1.44788e7i 0.392104i
\(334\) 6.33850e7i 1.70117i
\(335\) 6.85519e7i 1.82341i
\(336\) −8.66372e6 −0.228395
\(337\) 3.10257e7i 0.810647i −0.914173 0.405324i \(-0.867159\pi\)
0.914173 0.405324i \(-0.132841\pi\)
\(338\) 1.44535e8i 3.74303i
\(339\) 4.17946e7i 1.07281i
\(340\) 1.67533e8 4.26249
\(341\) 5.53054e7 1.39477
\(342\) 2.80304e7i 0.700729i
\(343\) −1.07621e7 −0.266695
\(344\) 6.22243e6 0.152857
\(345\) 2.45364e7i 0.597521i
\(346\) −1.14844e8 −2.77257
\(347\) 7.35778e7i 1.76100i 0.474049 + 0.880498i \(0.342792\pi\)
−0.474049 + 0.880498i \(0.657208\pi\)
\(348\) −6.66339e7 −1.58109
\(349\) 3.00755e7i 0.707516i −0.935337 0.353758i \(-0.884904\pi\)
0.935337 0.353758i \(-0.115096\pi\)
\(350\) 2.11191e8i 4.92573i
\(351\) 1.50263e7i 0.347481i
\(352\) 3.81058e7 0.873702
\(353\) 7.81394e7i 1.77642i 0.459437 + 0.888210i \(0.348051\pi\)
−0.459437 + 0.888210i \(0.651949\pi\)
\(354\) 1.41634e7 + 3.99838e7i 0.319270 + 0.901310i
\(355\) −7.87088e7 −1.75929
\(356\) 6.79562e7i 1.50619i
\(357\) −4.80808e7 −1.05674
\(358\) 6.95271e7 1.51532
\(359\) −2.92202e7 −0.631538 −0.315769 0.948836i \(-0.602263\pi\)
−0.315769 + 0.948836i \(0.602263\pi\)
\(360\) 3.43138e7i 0.735463i
\(361\) 2.87521e7 0.611150
\(362\) 4.28191e7i 0.902634i
\(363\) 1.06553e7 0.222765
\(364\) 2.03693e8i 4.22349i
\(365\) 3.28324e7i 0.675186i
\(366\) −1.56679e7 −0.319570
\(367\) 7.33923e7i 1.48475i 0.669987 + 0.742373i \(0.266300\pi\)
−0.669987 + 0.742373i \(0.733700\pi\)
\(368\) 8.47720e6i 0.170102i
\(369\) −1.71690e6 −0.0341716
\(370\) 1.76966e8 3.49370
\(371\) −1.36849e6 −0.0267990
\(372\) 6.13738e7i 1.19221i
\(373\) 4.77308e7 0.919754 0.459877 0.887983i \(-0.347893\pi\)
0.459877 + 0.887983i \(0.347893\pi\)
\(374\) −1.39095e8 −2.65887
\(375\) 6.63952e7 1.25905
\(376\) −5.48299e7 −1.03146
\(377\) 1.52015e8i 2.83702i
\(378\) 2.31041e7i 0.427773i
\(379\) −2.31283e7 −0.424841 −0.212421 0.977178i \(-0.568135\pi\)
−0.212421 + 0.977178i \(0.568135\pi\)
\(380\) 2.17694e8 3.96730
\(381\) −5.02655e7 −0.908856
\(382\) 2.52704e7 0.453338
\(383\) −7.21705e7 −1.28459 −0.642293 0.766459i \(-0.722017\pi\)
−0.642293 + 0.766459i \(0.722017\pi\)
\(384\) 5.82455e7i 1.02865i
\(385\) 1.61693e8i 2.83340i
\(386\) 1.53469e8i 2.66845i
\(387\) 2.40035e6i 0.0414134i
\(388\) 1.11370e8i 1.90666i
\(389\) 6.16152e7 1.04674 0.523370 0.852105i \(-0.324674\pi\)
0.523370 + 0.852105i \(0.324674\pi\)
\(390\) 1.83658e8 3.09610
\(391\) 4.70457e7i 0.787028i
\(392\) 5.93839e7i 0.985850i
\(393\) 3.22955e7i 0.532064i
\(394\) 3.32113e7i 0.542997i
\(395\) −4.22557e7 −0.685637
\(396\) 4.24706e7i 0.683916i
\(397\) 2.31569e7i 0.370091i 0.982730 + 0.185046i \(0.0592433\pi\)
−0.982730 + 0.185046i \(0.940757\pi\)
\(398\) 1.72358e7i 0.273390i
\(399\) −6.24766e7 −0.983556
\(400\) 4.18033e7 0.653177
\(401\) 7.13538e7i 1.10658i −0.832988 0.553291i \(-0.813372\pi\)
0.832988 0.553291i \(-0.186628\pi\)
\(402\) 6.31606e7 0.972228
\(403\) −1.40015e8 −2.13924
\(404\) 1.32978e8i 2.01667i
\(405\) −1.32368e7 −0.199259
\(406\) 2.33735e8i 3.49257i
\(407\) −9.33603e7 −1.38477
\(408\) 6.57928e7i 0.968719i
\(409\) 2.42489e7i 0.354423i −0.984173 0.177212i \(-0.943292\pi\)
0.984173 0.177212i \(-0.0567077\pi\)
\(410\) 2.09847e7i 0.304474i
\(411\) 4.37852e6 0.0630670
\(412\) 1.05071e6i 0.0150242i
\(413\) 8.91196e7 3.15687e7i 1.26509 0.448133i
\(414\) −2.26067e7 −0.318593
\(415\) 8.31822e7i 1.16382i
\(416\) −9.64715e7 −1.34004
\(417\) 3.44365e7 0.474910
\(418\) −1.80741e8 −2.47473
\(419\) 1.33284e8i 1.81191i −0.423377 0.905954i \(-0.639155\pi\)
0.423377 0.905954i \(-0.360845\pi\)
\(420\) −1.79435e8 −2.42191
\(421\) 9.90160e6i 0.132696i 0.997797 + 0.0663482i \(0.0211348\pi\)
−0.997797 + 0.0663482i \(0.978865\pi\)
\(422\) −7.21612e7 −0.960210
\(423\) 2.11511e7i 0.279454i
\(424\) 1.87261e6i 0.0245669i
\(425\) 2.31995e8 3.02212
\(426\) 7.25187e7i 0.938039i
\(427\) 3.49220e7i 0.448554i
\(428\) 4.60952e7 0.587929
\(429\) −9.68904e7 −1.22718
\(430\) 2.93380e7 0.368999
\(431\) 1.02767e8i 1.28357i −0.766884 0.641786i \(-0.778194\pi\)
0.766884 0.641786i \(-0.221806\pi\)
\(432\) −4.57325e6 −0.0567249
\(433\) 6.29630e7 0.775571 0.387786 0.921750i \(-0.373240\pi\)
0.387786 + 0.921750i \(0.373240\pi\)
\(434\) 2.15284e8 2.63356
\(435\) −1.33911e8 −1.62686
\(436\) 1.98381e8i 2.39354i
\(437\) 6.11316e7i 0.732524i
\(438\) 3.02502e7 0.360003
\(439\) 5.99040e7 0.708047 0.354023 0.935237i \(-0.384813\pi\)
0.354023 + 0.935237i \(0.384813\pi\)
\(440\) −2.21257e8 −2.59740
\(441\) 2.29078e7 0.267096
\(442\) 3.52143e8 4.07805
\(443\) 2.24838e6i 0.0258617i −0.999916 0.0129309i \(-0.995884\pi\)
0.999916 0.0129309i \(-0.00411614\pi\)
\(444\) 1.03604e8i 1.18367i
\(445\) 1.36569e8i 1.54978i
\(446\) 1.90526e8i 2.14758i
\(447\) 2.63940e7i 0.295517i
\(448\) 1.83902e8 2.04528
\(449\) 1.02985e7 0.113772 0.0568861 0.998381i \(-0.481883\pi\)
0.0568861 + 0.998381i \(0.481883\pi\)
\(450\) 1.11480e8i 1.22337i
\(451\) 1.10707e7i 0.120682i
\(452\) 2.99064e8i 3.23854i
\(453\) 1.49384e7i 0.160698i
\(454\) 1.95682e8 2.09114
\(455\) 4.09353e8i 4.34574i
\(456\) 8.54917e7i 0.901633i
\(457\) 1.32085e8i 1.38390i 0.721945 + 0.691950i \(0.243248\pi\)
−0.721945 + 0.691950i \(0.756752\pi\)
\(458\) −2.12978e6 −0.0221686
\(459\) −2.53800e7 −0.262455
\(460\) 1.75572e8i 1.80377i
\(461\) −1.68560e8 −1.72049 −0.860245 0.509881i \(-0.829689\pi\)
−0.860245 + 0.509881i \(0.829689\pi\)
\(462\) 1.48976e8 1.51074
\(463\) 5.21499e7i 0.525425i −0.964874 0.262713i \(-0.915383\pi\)
0.964874 0.262713i \(-0.0846171\pi\)
\(464\) −4.62658e7 −0.463133
\(465\) 1.23340e8i 1.22672i
\(466\) −1.75579e8 −1.73506
\(467\) 8.72860e7i 0.857026i −0.903536 0.428513i \(-0.859038\pi\)
0.903536 0.428513i \(-0.140962\pi\)
\(468\) 1.07522e8i 1.04896i
\(469\) 1.40778e8i 1.36464i
\(470\) −2.58517e8 −2.48998
\(471\) 5.30198e7i 0.507430i
\(472\) 4.31979e7 + 1.21949e8i 0.410806 + 1.15972i
\(473\) −1.54776e7 −0.146258
\(474\) 3.89325e7i 0.365575i
\(475\) 3.01456e8 2.81283
\(476\) −3.44046e8 −3.19003
\(477\) −722373. −0.00665589
\(478\) 2.64606e8i 2.42279i
\(479\) −1.18080e8 −1.07441 −0.537204 0.843452i \(-0.680519\pi\)
−0.537204 + 0.843452i \(0.680519\pi\)
\(480\) 8.49825e7i 0.768433i
\(481\) 2.36358e8 2.12390
\(482\) 4.74704e7i 0.423918i
\(483\) 5.03879e7i 0.447182i
\(484\) 7.62451e7 0.672474
\(485\) 2.23816e8i 1.96185i
\(486\) 1.21958e7i 0.106243i
\(487\) −1.31294e6 −0.0113673 −0.00568365 0.999984i \(-0.501809\pi\)
−0.00568365 + 0.999984i \(0.501809\pi\)
\(488\) −4.77865e7 −0.411193
\(489\) 2.84174e6 0.0243029
\(490\) 2.79989e8i 2.37986i
\(491\) −9.85100e7 −0.832216 −0.416108 0.909315i \(-0.636606\pi\)
−0.416108 + 0.909315i \(0.636606\pi\)
\(492\) −1.22854e7 −0.103156
\(493\) −2.56760e8 −2.14282
\(494\) 4.57578e8 3.79563
\(495\) 8.53515e7i 0.703713i
\(496\) 4.26136e7i 0.349223i
\(497\) 1.61636e8 1.31665
\(498\) 7.66403e7 0.620539
\(499\) −8.98227e7 −0.722911 −0.361455 0.932389i \(-0.617720\pi\)
−0.361455 + 0.932389i \(0.617720\pi\)
\(500\) 4.75096e8 3.80077
\(501\) −7.45755e7 −0.593039
\(502\) 2.92763e8i 2.31422i
\(503\) 2.20691e7i 0.173412i −0.996234 0.0867062i \(-0.972366\pi\)
0.996234 0.0867062i \(-0.0276341\pi\)
\(504\) 7.04667e7i 0.550418i
\(505\) 2.67240e8i 2.07504i
\(506\) 1.45769e8i 1.12516i
\(507\) 1.70052e8 1.30485
\(508\) −3.59678e8 −2.74361
\(509\) 1.05035e8i 0.796488i 0.917280 + 0.398244i \(0.130380\pi\)
−0.917280 + 0.398244i \(0.869620\pi\)
\(510\) 3.10206e8i 2.33851i
\(511\) 6.74245e7i 0.505307i
\(512\) 7.80340e7i 0.581399i
\(513\) −3.29791e7 −0.244279
\(514\) 2.08014e8i 1.53181i
\(515\) 2.11156e6i 0.0154590i
\(516\) 1.71759e7i 0.125017i
\(517\) 1.36383e8 0.986936
\(518\) −3.63418e8 −2.61467
\(519\) 1.35120e8i 0.966536i
\(520\) 5.60151e8 3.98377
\(521\) 1.73155e8 1.22440 0.612198 0.790704i \(-0.290285\pi\)
0.612198 + 0.790704i \(0.290285\pi\)
\(522\) 1.23380e8i 0.867426i
\(523\) −1.42119e7 −0.0993456 −0.0496728 0.998766i \(-0.515818\pi\)
−0.0496728 + 0.998766i \(0.515818\pi\)
\(524\) 2.31093e8i 1.60617i
\(525\) −2.48476e8 −1.71714
\(526\) 1.30109e8i 0.894027i
\(527\) 2.36492e8i 1.61579i
\(528\) 2.94885e7i 0.200333i
\(529\) 9.87328e7 0.666952
\(530\) 8.82914e6i 0.0593050i
\(531\) 4.70429e7 1.66639e7i 0.314203 0.111300i
\(532\) −4.47056e8 −2.96912
\(533\) 2.80273e7i 0.185097i
\(534\) −1.25828e8 −0.826331
\(535\) 9.26358e7 0.604947
\(536\) 1.92638e8 1.25097
\(537\) 8.18020e7i 0.528252i
\(538\) −1.11091e8 −0.713399
\(539\) 1.47711e8i 0.943290i
\(540\) −9.47168e7 −0.601514
\(541\) 2.54744e8i 1.60884i −0.594062 0.804420i \(-0.702476\pi\)
0.594062 0.804420i \(-0.297524\pi\)
\(542\) 5.79135e7i 0.363732i
\(543\) −5.03787e7 −0.314664
\(544\) 1.62944e8i 1.01215i
\(545\) 3.98678e8i 2.46282i
\(546\) −3.77159e8 −2.31711
\(547\) −7.57754e7 −0.462985 −0.231492 0.972837i \(-0.574361\pi\)
−0.231492 + 0.972837i \(0.574361\pi\)
\(548\) 3.13308e7 0.190384
\(549\) 1.84340e7i 0.111404i
\(550\) −7.18826e8 −4.32051
\(551\) −3.33636e8 −1.99443
\(552\) −6.89497e7 −0.409935
\(553\) 8.67763e7 0.513128
\(554\) 2.70133e8i 1.58873i
\(555\) 2.08210e8i 1.21793i
\(556\) 2.46413e8 1.43364
\(557\) 2.79672e8 1.61839 0.809197 0.587538i \(-0.199903\pi\)
0.809197 + 0.587538i \(0.199903\pi\)
\(558\) 1.13640e8 0.654078
\(559\) 3.91841e7 0.224324
\(560\) −1.24587e8 −0.709426
\(561\) 1.63652e8i 0.926899i
\(562\) 2.10068e8i 1.18345i
\(563\) 2.66407e8i 1.49287i −0.665460 0.746433i \(-0.731765\pi\)
0.665460 0.746433i \(-0.268235\pi\)
\(564\) 1.51348e8i 0.843605i
\(565\) 6.01017e8i 3.33228i
\(566\) −3.71221e8 −2.04731
\(567\) 2.71831e7 0.149125
\(568\) 2.21180e8i 1.20698i
\(569\) 7.39562e7i 0.401456i −0.979647 0.200728i \(-0.935669\pi\)
0.979647 0.200728i \(-0.0643307\pi\)
\(570\) 4.03084e8i 2.17656i
\(571\) 2.66103e8i 1.42936i −0.699451 0.714680i \(-0.746572\pi\)
0.699451 0.714680i \(-0.253428\pi\)
\(572\) −6.93306e8 −3.70456
\(573\) 2.97319e7i 0.158037i
\(574\) 4.30941e7i 0.227867i
\(575\) 2.43127e8i 1.27888i
\(576\) 9.70749e7 0.507972
\(577\) −1.28656e8 −0.669733 −0.334866 0.942266i \(-0.608691\pi\)
−0.334866 + 0.942266i \(0.608691\pi\)
\(578\) 2.74978e8i 1.42401i
\(579\) 1.80564e8 0.930241
\(580\) −9.58212e8 −4.91109
\(581\) 1.70823e8i 0.870999i
\(582\) 2.06214e8 1.04604
\(583\) 4.65790e6i 0.0235063i
\(584\) 9.22623e7 0.463218
\(585\) 2.16082e8i 1.07932i
\(586\) 5.02258e8i 2.49594i
\(587\) 1.86641e8i 0.922769i 0.887200 + 0.461384i \(0.152647\pi\)
−0.887200 + 0.461384i \(0.847353\pi\)
\(588\) 1.63918e8 0.806298
\(589\) 3.07299e8i 1.50389i
\(590\) 2.03673e8 + 5.74978e8i 0.991695 + 2.79959i
\(591\) 3.90747e7 0.189293
\(592\) 7.19354e7i 0.346719i
\(593\) 4.19768e7 0.201300 0.100650 0.994922i \(-0.467908\pi\)
0.100650 + 0.994922i \(0.467908\pi\)
\(594\) 7.86389e7 0.375213
\(595\) −6.91415e8 −3.28237
\(596\) 1.88864e8i 0.892094i
\(597\) −2.02788e7 −0.0953056
\(598\) 3.69040e8i 1.72572i
\(599\) −5.23574e7 −0.243611 −0.121806 0.992554i \(-0.538868\pi\)
−0.121806 + 0.992554i \(0.538868\pi\)
\(600\) 3.40009e8i 1.57412i
\(601\) 1.99557e8i 0.919269i −0.888108 0.459635i \(-0.847980\pi\)
0.888108 0.459635i \(-0.152020\pi\)
\(602\) −6.02486e7 −0.276158
\(603\) 7.43115e7i 0.338925i
\(604\) 1.06893e8i 0.485109i
\(605\) 1.53227e8 0.691940
\(606\) −2.46222e8 −1.10639
\(607\) −1.17781e6 −0.00526633 −0.00263317 0.999997i \(-0.500838\pi\)
−0.00263317 + 0.999997i \(0.500838\pi\)
\(608\) 2.11731e8i 0.942051i
\(609\) 2.75000e8 1.21753
\(610\) −2.25308e8 −0.992628
\(611\) −3.45278e8 −1.51372
\(612\) −1.81609e8 −0.792287
\(613\) 7.99912e7i 0.347265i −0.984811 0.173632i \(-0.944450\pi\)
0.984811 0.173632i \(-0.0555505\pi\)
\(614\) 1.05243e8i 0.454660i
\(615\) −2.46895e7 −0.106142
\(616\) 4.54373e8 1.94388
\(617\) 8.34368e7 0.355224 0.177612 0.984101i \(-0.443163\pi\)
0.177612 + 0.984101i \(0.443163\pi\)
\(618\) −1.94550e6 −0.00824262
\(619\) 1.44257e8 0.608225 0.304113 0.952636i \(-0.401640\pi\)
0.304113 + 0.952636i \(0.401640\pi\)
\(620\) 8.82572e8i 3.70318i
\(621\) 2.65979e7i 0.111064i
\(622\) 2.44993e7i 0.101808i
\(623\) 2.80457e8i 1.15985i
\(624\) 7.46554e7i 0.307261i
\(625\) 4.13758e8 1.69475
\(626\) −1.84200e8 −0.750874
\(627\) 2.12651e8i 0.862709i
\(628\) 3.79387e8i 1.53181i
\(629\) 3.99218e8i 1.60420i
\(630\) 3.32243e8i 1.32872i
\(631\) 2.82421e8 1.12411 0.562055 0.827100i \(-0.310011\pi\)
0.562055 + 0.827100i \(0.310011\pi\)
\(632\) 1.18743e8i 0.470388i
\(633\) 8.49011e7i 0.334736i
\(634\) 7.82147e8i 3.06917i
\(635\) −7.22831e8 −2.82303
\(636\) −5.16899e6 −0.0200925
\(637\) 3.73955e8i 1.44678i
\(638\) 7.95559e8 3.06345
\(639\) 8.53217e7 0.327007
\(640\) 8.37586e8i 3.19514i
\(641\) 1.25319e8 0.475819 0.237910 0.971287i \(-0.423538\pi\)
0.237910 + 0.971287i \(0.423538\pi\)
\(642\) 8.53503e7i 0.322552i
\(643\) 4.06213e8 1.52799 0.763996 0.645221i \(-0.223235\pi\)
0.763996 + 0.645221i \(0.223235\pi\)
\(644\) 3.60554e8i 1.34993i
\(645\) 3.45176e7i 0.128636i
\(646\) 7.72868e8i 2.86687i
\(647\) −5.97655e7 −0.220667 −0.110334 0.993895i \(-0.535192\pi\)
−0.110334 + 0.993895i \(0.535192\pi\)
\(648\) 3.71967e7i 0.136704i
\(649\) −1.07450e8 3.03335e8i −0.393071 1.10966i
\(650\) 1.81983e9 6.62661
\(651\) 2.53292e8i 0.918075i
\(652\) 2.03343e7 0.0733644
\(653\) 2.07427e8 0.744947 0.372474 0.928043i \(-0.378510\pi\)
0.372474 + 0.928043i \(0.378510\pi\)
\(654\) 3.67323e8 1.31315
\(655\) 4.64418e8i 1.65266i
\(656\) −8.53010e6 −0.0302164
\(657\) 3.55909e7i 0.125500i
\(658\) 5.30890e8 1.86349
\(659\) 1.87199e8i 0.654106i −0.945006 0.327053i \(-0.893944\pi\)
0.945006 0.327053i \(-0.106056\pi\)
\(660\) 6.10739e8i 2.12434i
\(661\) −2.21184e7 −0.0765860 −0.0382930 0.999267i \(-0.512192\pi\)
−0.0382930 + 0.999267i \(0.512192\pi\)
\(662\) 4.89123e8i 1.68595i
\(663\) 4.14313e8i 1.42164i
\(664\) 2.33751e8 0.798451
\(665\) −8.98431e8 −3.05506
\(666\) −1.91835e8 −0.649388
\(667\) 2.69080e8i 0.906784i
\(668\) −5.33631e8 −1.79024
\(669\) −2.24163e8 −0.748662
\(670\) 9.08266e8 3.01987
\(671\) 1.18863e8 0.393441
\(672\) 1.74520e8i 0.575092i
\(673\) 8.70516e7i 0.285582i −0.989753 0.142791i \(-0.954392\pi\)
0.989753 0.142791i \(-0.0456077\pi\)
\(674\) −4.11069e8 −1.34256
\(675\) −1.31161e8 −0.426475
\(676\) 1.21682e9 3.93901
\(677\) −8.24674e7 −0.265776 −0.132888 0.991131i \(-0.542425\pi\)
−0.132888 + 0.991131i \(0.542425\pi\)
\(678\) 5.53749e8 1.77674
\(679\) 4.59629e8i 1.46824i
\(680\) 9.46118e8i 3.00897i
\(681\) 2.30230e8i 0.728987i
\(682\) 7.32758e8i 2.30998i
\(683\) 1.62347e8i 0.509546i −0.967001 0.254773i \(-0.917999\pi\)
0.967001 0.254773i \(-0.0820007\pi\)
\(684\) −2.35984e8 −0.737419
\(685\) 6.29643e7 0.195895
\(686\) 1.42591e8i 0.441691i
\(687\) 2.50579e6i 0.00772812i
\(688\) 1.19257e7i 0.0366200i
\(689\) 1.17923e7i 0.0360529i
\(690\) −3.25090e8 −0.989593
\(691\) 3.43304e8i 1.04051i 0.854012 + 0.520253i \(0.174162\pi\)
−0.854012 + 0.520253i \(0.825838\pi\)
\(692\) 9.66862e8i 2.91774i
\(693\) 1.75278e8i 0.526656i
\(694\) 9.74856e8 2.91650
\(695\) 4.95206e8 1.47513
\(696\) 3.76305e8i 1.11612i
\(697\) −4.73393e7 −0.139805
\(698\) −3.98480e8 −1.17176
\(699\) 2.06577e8i 0.604855i
\(700\) −1.77799e9 −5.18364
\(701\) 3.99694e8i 1.16031i −0.814506 0.580155i \(-0.802992\pi\)
0.814506 0.580155i \(-0.197008\pi\)
\(702\) −1.99088e8 −0.575485
\(703\) 5.18748e8i 1.49311i
\(704\) 6.25944e8i 1.79398i
\(705\) 3.04158e8i 0.868023i
\(706\) 1.03529e9 2.94204
\(707\) 5.48803e8i 1.55295i
\(708\) 3.36619e8 1.19240e8i 0.948502 0.335986i
\(709\) −7.80876e7 −0.219101 −0.109550 0.993981i \(-0.534941\pi\)
−0.109550 + 0.993981i \(0.534941\pi\)
\(710\) 1.04284e9i 2.91368i
\(711\) 4.58059e7 0.127442
\(712\) −3.83772e8 −1.06325
\(713\) 2.47839e8 0.683756
\(714\) 6.37038e8i 1.75013i
\(715\) −1.39331e9 −3.81179
\(716\) 5.85340e8i 1.59466i
\(717\) −3.11322e8 −0.844601
\(718\) 3.87148e8i 1.04593i
\(719\) 1.51010e8i 0.406273i 0.979150 + 0.203137i \(0.0651136\pi\)
−0.979150 + 0.203137i \(0.934886\pi\)
\(720\) −6.57645e7 −0.176195
\(721\) 4.33631e6i 0.0115695i
\(722\) 3.80946e8i 1.01217i
\(723\) −5.58512e7 −0.147781
\(724\) −3.60488e8 −0.949895
\(725\) −1.32690e9 −3.48198
\(726\) 1.41176e8i 0.368936i
\(727\) 5.97563e8 1.55518 0.777589 0.628773i \(-0.216442\pi\)
0.777589 + 0.628773i \(0.216442\pi\)
\(728\) −1.15033e9 −2.98144
\(729\) 1.43489e7 0.0370370
\(730\) 4.35006e8 1.11822
\(731\) 6.61837e7i 0.169433i
\(732\) 1.31906e8i 0.336303i
\(733\) 4.51581e8 1.14663 0.573315 0.819335i \(-0.305657\pi\)
0.573315 + 0.819335i \(0.305657\pi\)
\(734\) 9.72397e8 2.45898
\(735\) 3.29420e8 0.829637
\(736\) 1.70763e8 0.428312
\(737\) −4.79164e8 −1.19697
\(738\) 2.27477e7i 0.0565939i
\(739\) 4.61246e8i 1.14288i 0.820645 + 0.571439i \(0.193614\pi\)
−0.820645 + 0.571439i \(0.806386\pi\)
\(740\) 1.48986e9i 3.67663i
\(741\) 5.38362e8i 1.32318i
\(742\) 1.81315e7i 0.0443836i
\(743\) 3.52308e8 0.858927 0.429464 0.903084i \(-0.358703\pi\)
0.429464 + 0.903084i \(0.358703\pi\)
\(744\) 3.46599e8 0.841606
\(745\) 3.79553e8i 0.917917i
\(746\) 6.32400e8i 1.52326i
\(747\) 9.01710e7i 0.216324i
\(748\) 1.17102e9i 2.79808i
\(749\) −1.90237e8 −0.452740
\(750\) 8.79691e8i 2.08519i
\(751\) 1.58247e8i 0.373609i 0.982397 + 0.186804i \(0.0598130\pi\)
−0.982397 + 0.186804i \(0.940187\pi\)
\(752\) 1.05085e8i 0.247108i
\(753\) −3.44449e8 −0.806753
\(754\) −2.01410e9 −4.69858
\(755\) 2.14819e8i 0.499150i
\(756\) 1.94510e8 0.450171
\(757\) −2.71720e8 −0.626375 −0.313187 0.949691i \(-0.601397\pi\)
−0.313187 + 0.949691i \(0.601397\pi\)
\(758\) 3.06434e8i 0.703607i
\(759\) 1.71504e8 0.392238
\(760\) 1.22939e9i 2.80059i
\(761\) −2.64372e8 −0.599876 −0.299938 0.953959i \(-0.596966\pi\)
−0.299938 + 0.953959i \(0.596966\pi\)
\(762\) 6.65983e8i 1.50521i
\(763\) 8.18724e8i 1.84316i
\(764\) 2.12749e8i 0.477075i
\(765\) −3.64972e8 −0.815220
\(766\) 9.56209e8i 2.12749i
\(767\) 2.72028e8 + 7.67945e8i 0.602875 + 1.70194i
\(768\) 3.73162e8 0.823785
\(769\) 6.69624e8i 1.47249i −0.676716 0.736244i \(-0.736597\pi\)
0.676716 0.736244i \(-0.263403\pi\)
\(770\) 2.14232e9 4.69258
\(771\) 2.44739e8 0.533998
\(772\) 1.29204e9 2.80817
\(773\) 6.33270e8i 1.37104i −0.728053 0.685521i \(-0.759575\pi\)
0.728053 0.685521i \(-0.240425\pi\)
\(774\) −3.18029e7 −0.0685874
\(775\) 1.22216e9i 2.62557i
\(776\) 6.28946e8 1.34595
\(777\) 4.27579e8i 0.911493i
\(778\) 8.16359e8i 1.73357i
\(779\) −6.15131e7 −0.130123
\(780\) 1.54619e9i 3.25821i
\(781\) 5.50159e8i 1.15487i
\(782\) −6.23324e8 −1.30345
\(783\) 1.45162e8 0.302391
\(784\) 1.13813e8 0.236181
\(785\) 7.62439e8i 1.57615i