Properties

Label 177.7.c.a.58.3
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 58.3
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.58

$q$-expansion

\(f(q)\) \(=\) \(q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} -3548.48i q^{10} +416.675i q^{11} +2473.49 q^{12} +2776.81i q^{13} +8483.18i q^{14} -3706.89 q^{15} +10926.5 q^{16} +1573.64 q^{17} -3626.12i q^{18} +5373.33 q^{19} -37732.4 q^{20} +8861.90 q^{21} +6217.74 q^{22} -17579.4i q^{23} -22022.8i q^{24} +40922.4 q^{25} +41436.4 q^{26} -3788.00 q^{27} +90205.1 q^{28} -7605.19 q^{29} +55315.3i q^{30} -36501.6i q^{31} -72631.3i q^{32} -6495.31i q^{33} -23482.3i q^{34} -135185. q^{35} -38558.0 q^{36} +29052.8i q^{37} -80182.4i q^{38} -43286.2i q^{39} +335951. i q^{40} +99324.2 q^{41} -132240. i q^{42} -81683.7i q^{43} -66115.7i q^{44} +57784.7 q^{45} -262324. q^{46} +194198. i q^{47} -170327. q^{48} +205533. q^{49} -610657. i q^{50} -24530.6 q^{51} -440610. i q^{52} -48367.5 q^{53} +56525.6i q^{54} +99084.0i q^{55} -803143. i q^{56} -83762.0 q^{57} +113487. i q^{58} +(142452. - 147946. i) q^{59} +588190. q^{60} -148057. i q^{61} -544688. q^{62} -138143. q^{63} -384530. q^{64} +660318. i q^{65} -96925.0 q^{66} +288192. i q^{67} -249697. q^{68} +274035. i q^{69} +2.01728e6i q^{70} -195515. q^{71} +343302. i q^{72} -231637. i q^{73} +433534. q^{74} -637918. q^{75} -852612. q^{76} -236876. i q^{77} -645929. q^{78} +411213. q^{79} +2.59829e6 q^{80} +59049.0 q^{81} -1.48214e6i q^{82} +585218. i q^{83} -1.40616e6 q^{84} +374207. q^{85} -1.21891e6 q^{86} +118553. q^{87} -588663. q^{88} +251099. i q^{89} -862280. i q^{90} -1.57859e6i q^{91} +2.78940e6i q^{92} +569004. i q^{93} +2.89787e6 q^{94} +1.27776e6 q^{95} +1.13221e6i q^{96} -522437. i q^{97} -3.06702e6i q^{98} +101252. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.9223i 1.86529i −0.360800 0.932643i \(-0.617496\pi\)
0.360800 0.932643i \(-0.382504\pi\)
\(3\) −15.5885 −0.577350
\(4\) −158.675 −2.47929
\(5\) 237.797 1.90238 0.951188 0.308611i \(-0.0998642\pi\)
0.951188 + 0.308611i \(0.0998642\pi\)
\(6\) 232.615i 1.07692i
\(7\) −568.491 −1.65741 −0.828704 0.559687i \(-0.810921\pi\)
−0.828704 + 0.559687i \(0.810921\pi\)
\(8\) 1412.76i 2.75930i
\(9\) 243.000 0.333333
\(10\) 3548.48i 3.54848i
\(11\) 416.675i 0.313054i 0.987674 + 0.156527i \(0.0500298\pi\)
−0.987674 + 0.156527i \(0.949970\pi\)
\(12\) 2473.49 1.43142
\(13\) 2776.81i 1.26391i 0.775005 + 0.631955i \(0.217747\pi\)
−0.775005 + 0.631955i \(0.782253\pi\)
\(14\) 8483.18i 3.09154i
\(15\) −3706.89 −1.09834
\(16\) 10926.5 2.66760
\(17\) 1573.64 0.320301 0.160150 0.987093i \(-0.448802\pi\)
0.160150 + 0.987093i \(0.448802\pi\)
\(18\) 3626.12i 0.621762i
\(19\) 5373.33 0.783399 0.391699 0.920093i \(-0.371887\pi\)
0.391699 + 0.920093i \(0.371887\pi\)
\(20\) −37732.4 −4.71655
\(21\) 8861.90 0.956905
\(22\) 6217.74 0.583935
\(23\) 17579.4i 1.44484i −0.691455 0.722419i \(-0.743030\pi\)
0.691455 0.722419i \(-0.256970\pi\)
\(24\) 22022.8i 1.59308i
\(25\) 40922.4 2.61904
\(26\) 41436.4 2.35755
\(27\) −3788.00 −0.192450
\(28\) 90205.1 4.10920
\(29\) −7605.19 −0.311828 −0.155914 0.987771i \(-0.549832\pi\)
−0.155914 + 0.987771i \(0.549832\pi\)
\(30\) 55315.3i 2.04871i
\(31\) 36501.6i 1.22526i −0.790371 0.612628i \(-0.790112\pi\)
0.790371 0.612628i \(-0.209888\pi\)
\(32\) 72631.3i 2.21653i
\(33\) 6495.31i 0.180742i
\(34\) 23482.3i 0.597453i
\(35\) −135185. −3.15301
\(36\) −38558.0 −0.826431
\(37\) 29052.8i 0.573565i 0.957996 + 0.286782i \(0.0925857\pi\)
−0.957996 + 0.286782i \(0.907414\pi\)
\(38\) 80182.4i 1.46126i
\(39\) 43286.2i 0.729719i
\(40\) 335951.i 5.24923i
\(41\) 99324.2 1.44113 0.720566 0.693387i \(-0.243882\pi\)
0.720566 + 0.693387i \(0.243882\pi\)
\(42\) 132240.i 1.78490i
\(43\) 81683.7i 1.02738i −0.857977 0.513688i \(-0.828279\pi\)
0.857977 0.513688i \(-0.171721\pi\)
\(44\) 66115.7i 0.776152i
\(45\) 57784.7 0.634125
\(46\) −262324. −2.69504
\(47\) 194198.i 1.87047i 0.354028 + 0.935235i \(0.384812\pi\)
−0.354028 + 0.935235i \(0.615188\pi\)
\(48\) −170327. −1.54014
\(49\) 205533. 1.74700
\(50\) 610657.i 4.88525i
\(51\) −24530.6 −0.184926
\(52\) 440610.i 3.13360i
\(53\) −48367.5 −0.324882 −0.162441 0.986718i \(-0.551937\pi\)
−0.162441 + 0.986718i \(0.551937\pi\)
\(54\) 56525.6i 0.358974i
\(55\) 99084.0i 0.595546i
\(56\) 803143.i 4.57329i
\(57\) −83762.0 −0.452296
\(58\) 113487.i 0.581649i
\(59\) 142452. 147946.i 0.693605 0.720355i
\(60\) 588190. 2.72310
\(61\) 148057.i 0.652288i −0.945320 0.326144i \(-0.894250\pi\)
0.945320 0.326144i \(-0.105750\pi\)
\(62\) −544688. −2.28545
\(63\) −138143. −0.552469
\(64\) −384530. −1.46687
\(65\) 660318.i 2.40443i
\(66\) −96925.0 −0.337135
\(67\) 288192.i 0.958204i 0.877759 + 0.479102i \(0.159038\pi\)
−0.877759 + 0.479102i \(0.840962\pi\)
\(68\) −249697. −0.794120
\(69\) 274035.i 0.834178i
\(70\) 2.01728e6i 5.88127i
\(71\) −195515. −0.546266 −0.273133 0.961976i \(-0.588060\pi\)
−0.273133 + 0.961976i \(0.588060\pi\)
\(72\) 343302.i 0.919768i
\(73\) 231637.i 0.595442i −0.954653 0.297721i \(-0.903773\pi\)
0.954653 0.297721i \(-0.0962266\pi\)
\(74\) 433534. 1.06986
\(75\) −637918. −1.51210
\(76\) −852612. −1.94227
\(77\) 236876.i 0.518858i
\(78\) −645929. −1.36113
\(79\) 411213. 0.834038 0.417019 0.908898i \(-0.363075\pi\)
0.417019 + 0.908898i \(0.363075\pi\)
\(80\) 2.59829e6 5.07478
\(81\) 59049.0 0.111111
\(82\) 1.48214e6i 2.68812i
\(83\) 585218.i 1.02349i 0.859138 + 0.511745i \(0.171001\pi\)
−0.859138 + 0.511745i \(0.828999\pi\)
\(84\) −1.40616e6 −2.37245
\(85\) 374207. 0.609333
\(86\) −1.21891e6 −1.91635
\(87\) 118553. 0.180034
\(88\) −588663. −0.863811
\(89\) 251099.i 0.356185i 0.984014 + 0.178092i \(0.0569926\pi\)
−0.984014 + 0.178092i \(0.943007\pi\)
\(90\) 862280.i 1.18283i
\(91\) 1.57859e6i 2.09481i
\(92\) 2.78940e6i 3.58218i
\(93\) 569004.i 0.707402i
\(94\) 2.89787e6 3.48896
\(95\) 1.27776e6 1.49032
\(96\) 1.13221e6i 1.27971i
\(97\) 522437.i 0.572425i −0.958166 0.286213i \(-0.907604\pi\)
0.958166 0.286213i \(-0.0923963\pi\)
\(98\) 3.06702e6i 3.25866i
\(99\) 101252.i 0.104351i
\(100\) −6.49336e6 −6.49336
\(101\) 1.18118e6i 1.14644i −0.819401 0.573220i \(-0.805694\pi\)
0.819401 0.573220i \(-0.194306\pi\)
\(102\) 366053.i 0.344940i
\(103\) 910974.i 0.833670i −0.908982 0.416835i \(-0.863139\pi\)
0.908982 0.416835i \(-0.136861\pi\)
\(104\) −3.92298e6 −3.48751
\(105\) 2.10733e6 1.82039
\(106\) 721753.i 0.605998i
\(107\) 115592. 0.0943578 0.0471789 0.998886i \(-0.484977\pi\)
0.0471789 + 0.998886i \(0.484977\pi\)
\(108\) 601059. 0.477140
\(109\) 980508.i 0.757132i 0.925574 + 0.378566i \(0.123583\pi\)
−0.925574 + 0.378566i \(0.876417\pi\)
\(110\) 1.47856e6 1.11086
\(111\) 452888.i 0.331148i
\(112\) −6.21161e6 −4.42130
\(113\) 821694.i 0.569475i −0.958606 0.284737i \(-0.908094\pi\)
0.958606 0.284737i \(-0.0919064\pi\)
\(114\) 1.24992e6i 0.843661i
\(115\) 4.18032e6i 2.74863i
\(116\) 1.20675e6 0.773114
\(117\) 674765.i 0.421303i
\(118\) −2.20769e6 2.12571e6i −1.34367 1.29377i
\(119\) −894599. −0.530869
\(120\) 5.23696e6i 3.03065i
\(121\) 1.59794e6 0.901997
\(122\) −2.20935e6 −1.21670
\(123\) −1.54831e6 −0.832038
\(124\) 5.79188e6i 3.03777i
\(125\) 6.01566e6 3.08002
\(126\) 2.06141e6i 1.03051i
\(127\) 1.80210e6 0.879766 0.439883 0.898055i \(-0.355020\pi\)
0.439883 + 0.898055i \(0.355020\pi\)
\(128\) 1.08967e6i 0.519594i
\(129\) 1.27332e6i 0.593156i
\(130\) 9.85345e6 4.48496
\(131\) 1.05222e6i 0.468048i −0.972231 0.234024i \(-0.924810\pi\)
0.972231 0.234024i \(-0.0751895\pi\)
\(132\) 1.03064e6i 0.448112i
\(133\) −3.05469e6 −1.29841
\(134\) 4.30049e6 1.78732
\(135\) −900774. −0.366113
\(136\) 2.22318e6i 0.883808i
\(137\) 2.66845e6 1.03776 0.518880 0.854847i \(-0.326349\pi\)
0.518880 + 0.854847i \(0.326349\pi\)
\(138\) 4.08923e6 1.55598
\(139\) −1.59715e6 −0.594705 −0.297353 0.954768i \(-0.596104\pi\)
−0.297353 + 0.954768i \(0.596104\pi\)
\(140\) 2.14505e7 7.81724
\(141\) 3.02724e6i 1.07992i
\(142\) 2.91753e6i 1.01894i
\(143\) −1.15703e6 −0.395672
\(144\) 2.65514e6 0.889200
\(145\) −1.80849e6 −0.593215
\(146\) −3.45656e6 −1.11067
\(147\) −3.20394e6 −1.00863
\(148\) 4.60994e6i 1.42204i
\(149\) 6.57201e6i 1.98673i −0.114995 0.993366i \(-0.536685\pi\)
0.114995 0.993366i \(-0.463315\pi\)
\(150\) 9.51919e6i 2.82050i
\(151\) 1.47674e6i 0.428918i 0.976733 + 0.214459i \(0.0687988\pi\)
−0.976733 + 0.214459i \(0.931201\pi\)
\(152\) 7.59125e6i 2.16164i
\(153\) 382394. 0.106767
\(154\) −3.53473e6 −0.967818
\(155\) 8.67998e6i 2.33090i
\(156\) 6.86843e6i 1.80919i
\(157\) 2.33787e6i 0.604117i 0.953289 + 0.302058i \(0.0976738\pi\)
−0.953289 + 0.302058i \(0.902326\pi\)
\(158\) 6.13624e6i 1.55572i
\(159\) 753974. 0.187571
\(160\) 1.72715e7i 4.21668i
\(161\) 9.99370e6i 2.39469i
\(162\) 881146.i 0.207254i
\(163\) 1.65292e6 0.381670 0.190835 0.981622i \(-0.438880\pi\)
0.190835 + 0.981622i \(0.438880\pi\)
\(164\) −1.57602e7 −3.57299
\(165\) 1.54457e6i 0.343839i
\(166\) 8.73279e6 1.90910
\(167\) 7.33918e6 1.57579 0.787895 0.615810i \(-0.211171\pi\)
0.787895 + 0.615810i \(0.211171\pi\)
\(168\) 1.25198e7i 2.64039i
\(169\) −2.88387e6 −0.597470
\(170\) 5.58402e6i 1.13658i
\(171\) 1.30572e6 0.261133
\(172\) 1.29611e7i 2.54717i
\(173\) 9.58118e6i 1.85046i 0.379401 + 0.925232i \(0.376130\pi\)
−0.379401 + 0.925232i \(0.623870\pi\)
\(174\) 1.76908e6i 0.335815i
\(175\) −2.32640e7 −4.34081
\(176\) 4.55279e6i 0.835102i
\(177\) −2.22061e6 + 2.30625e6i −0.400453 + 0.415897i
\(178\) 3.74698e6 0.664387
\(179\) 5.21840e6i 0.909867i −0.890525 0.454934i \(-0.849663\pi\)
0.890525 0.454934i \(-0.150337\pi\)
\(180\) −9.16897e6 −1.57218
\(181\) 937112. 0.158036 0.0790179 0.996873i \(-0.474822\pi\)
0.0790179 + 0.996873i \(0.474822\pi\)
\(182\) −2.35562e7 −3.90743
\(183\) 2.30798e6i 0.376599i
\(184\) 2.48355e7 3.98675
\(185\) 6.90867e6i 1.09114i
\(186\) 8.49084e6 1.31951
\(187\) 655695.i 0.100271i
\(188\) 3.08143e7i 4.63744i
\(189\) 2.15344e6 0.318968
\(190\) 1.90671e7i 2.77987i
\(191\) 4.78038e6i 0.686061i 0.939324 + 0.343031i \(0.111453\pi\)
−0.939324 + 0.343031i \(0.888547\pi\)
\(192\) 5.99423e6 0.846895
\(193\) 7.50133e6 1.04344 0.521719 0.853118i \(-0.325291\pi\)
0.521719 + 0.853118i \(0.325291\pi\)
\(194\) −7.79595e6 −1.06774
\(195\) 1.02933e7i 1.38820i
\(196\) −3.26129e7 −4.33132
\(197\) 1.17472e7 1.53651 0.768254 0.640146i \(-0.221126\pi\)
0.768254 + 0.640146i \(0.221126\pi\)
\(198\) 1.51091e6 0.194645
\(199\) 1.30642e7 1.65777 0.828883 0.559422i \(-0.188977\pi\)
0.828883 + 0.559422i \(0.188977\pi\)
\(200\) 5.78137e7i 7.22672i
\(201\) 4.49247e6i 0.553219i
\(202\) −1.76259e7 −2.13844
\(203\) 4.32348e6 0.516827
\(204\) 3.89239e6 0.458485
\(205\) 2.36190e7 2.74157
\(206\) −1.35938e7 −1.55503
\(207\) 4.27178e6i 0.481613i
\(208\) 3.03408e7i 3.37161i
\(209\) 2.23893e6i 0.245246i
\(210\) 3.14462e7i 3.39555i
\(211\) 1.79409e7i 1.90984i −0.296868 0.954919i \(-0.595942\pi\)
0.296868 0.954919i \(-0.404058\pi\)
\(212\) 7.67469e6 0.805477
\(213\) 3.04777e6 0.315387
\(214\) 1.72490e6i 0.176004i
\(215\) 1.94241e7i 1.95446i
\(216\) 5.35154e6i 0.531028i
\(217\) 2.07508e7i 2.03075i
\(218\) 1.46314e7 1.41227
\(219\) 3.61087e6i 0.343779i
\(220\) 1.57221e7i 1.47653i
\(221\) 4.36970e6i 0.404832i
\(222\) −6.75813e6 −0.617685
\(223\) 4.56125e6 0.411310 0.205655 0.978625i \(-0.434068\pi\)
0.205655 + 0.978625i \(0.434068\pi\)
\(224\) 4.12902e7i 3.67370i
\(225\) 9.94415e6 0.873012
\(226\) −1.22615e7 −1.06223
\(227\) 5.19345e6i 0.443995i 0.975047 + 0.221998i \(0.0712578\pi\)
−0.975047 + 0.221998i \(0.928742\pi\)
\(228\) 1.32909e7 1.12137
\(229\) 1.07784e7i 0.897525i 0.893651 + 0.448762i \(0.148135\pi\)
−0.893651 + 0.448762i \(0.851865\pi\)
\(230\) −6.23799e7 −5.12698
\(231\) 3.69253e6i 0.299563i
\(232\) 1.07443e7i 0.860429i
\(233\) 6.65739e6i 0.526303i 0.964754 + 0.263152i \(0.0847620\pi\)
−0.964754 + 0.263152i \(0.915238\pi\)
\(234\) 1.00690e7 0.785852
\(235\) 4.61797e7i 3.55834i
\(236\) −2.26035e7 + 2.34753e7i −1.71965 + 1.78597i
\(237\) −6.41018e6 −0.481532
\(238\) 1.33495e7i 0.990223i
\(239\) −1.00785e7 −0.738247 −0.369123 0.929380i \(-0.620342\pi\)
−0.369123 + 0.929380i \(0.620342\pi\)
\(240\) −4.05033e7 −2.92992
\(241\) −5.64758e6 −0.403470 −0.201735 0.979440i \(-0.564658\pi\)
−0.201735 + 0.979440i \(0.564658\pi\)
\(242\) 2.38450e7i 1.68248i
\(243\) −920483. −0.0641500
\(244\) 2.34929e7i 1.61721i
\(245\) 4.88751e7 3.32345
\(246\) 2.31044e7i 1.55199i
\(247\) 1.49207e7i 0.990146i
\(248\) 5.15681e7 3.38085
\(249\) 9.12264e6i 0.590912i
\(250\) 8.97674e7i 5.74511i
\(251\) −1.14392e7 −0.723393 −0.361697 0.932296i \(-0.617802\pi\)
−0.361697 + 0.932296i \(0.617802\pi\)
\(252\) 2.19198e7 1.36973
\(253\) 7.32487e6 0.452312
\(254\) 2.68914e7i 1.64102i
\(255\) −5.83330e6 −0.351799
\(256\) −8.34960e6 −0.497675
\(257\) −7.49665e6 −0.441639 −0.220820 0.975315i \(-0.570873\pi\)
−0.220820 + 0.975315i \(0.570873\pi\)
\(258\) 1.90009e7 1.10641
\(259\) 1.65162e7i 0.950631i
\(260\) 1.04776e8i 5.96129i
\(261\) −1.84806e6 −0.103943
\(262\) −1.57015e7 −0.873044
\(263\) 5.41778e6 0.297820 0.148910 0.988851i \(-0.452424\pi\)
0.148910 + 0.988851i \(0.452424\pi\)
\(264\) 9.17634e6 0.498721
\(265\) −1.15016e7 −0.618048
\(266\) 4.55830e7i 2.42191i
\(267\) 3.91425e6i 0.205643i
\(268\) 4.57288e7i 2.37567i
\(269\) 2.76710e7i 1.42157i 0.703409 + 0.710785i \(0.251660\pi\)
−0.703409 + 0.710785i \(0.748340\pi\)
\(270\) 1.34416e7i 0.682905i
\(271\) 2.37766e7 1.19465 0.597327 0.801998i \(-0.296230\pi\)
0.597327 + 0.801998i \(0.296230\pi\)
\(272\) 1.71943e7 0.854434
\(273\) 2.46078e7i 1.20944i
\(274\) 3.98193e7i 1.93572i
\(275\) 1.70513e7i 0.819899i
\(276\) 4.34824e7i 2.06817i
\(277\) 1.81769e7 0.855226 0.427613 0.903962i \(-0.359355\pi\)
0.427613 + 0.903962i \(0.359355\pi\)
\(278\) 2.38332e7i 1.10930i
\(279\) 8.86989e6i 0.408419i
\(280\) 1.90985e8i 8.70012i
\(281\) −2.61915e7 −1.18043 −0.590217 0.807245i \(-0.700958\pi\)
−0.590217 + 0.807245i \(0.700958\pi\)
\(282\) −4.51734e7 −2.01435
\(283\) 3.33164e7i 1.46994i −0.678101 0.734969i \(-0.737197\pi\)
0.678101 0.734969i \(-0.262803\pi\)
\(284\) 3.10232e7 1.35435
\(285\) −1.99183e7 −0.860436
\(286\) 1.72655e7i 0.738041i
\(287\) −5.64649e7 −2.38854
\(288\) 1.76494e7i 0.738844i
\(289\) −2.16612e7 −0.897407
\(290\) 2.69868e7i 1.10652i
\(291\) 8.14398e6i 0.330490i
\(292\) 3.67550e7i 1.47628i
\(293\) 1.78407e7 0.709267 0.354633 0.935005i \(-0.384606\pi\)
0.354633 + 0.935005i \(0.384606\pi\)
\(294\) 4.78101e7i 1.88139i
\(295\) 3.38746e7 3.51811e7i 1.31950 1.37039i
\(296\) −4.10447e7 −1.58264
\(297\) 1.57836e6i 0.0602472i
\(298\) −9.80694e7 −3.70582
\(299\) 4.88145e7 1.82615
\(300\) 1.01221e8 3.74894
\(301\) 4.64364e7i 1.70278i
\(302\) 2.20364e7 0.800055
\(303\) 1.84128e7i 0.661898i
\(304\) 5.87116e7 2.08979
\(305\) 3.52075e7i 1.24090i
\(306\) 5.70620e6i 0.199151i
\(307\) −2.29419e7 −0.792892 −0.396446 0.918058i \(-0.629757\pi\)
−0.396446 + 0.918058i \(0.629757\pi\)
\(308\) 3.75862e7i 1.28640i
\(309\) 1.42007e7i 0.481320i
\(310\) −1.29525e8 −4.34779
\(311\) −5.79269e7 −1.92575 −0.962874 0.269951i \(-0.912992\pi\)
−0.962874 + 0.269951i \(0.912992\pi\)
\(312\) 6.11532e7 2.01352
\(313\) 1.90759e7i 0.622087i −0.950396 0.311043i \(-0.899322\pi\)
0.950396 0.311043i \(-0.100678\pi\)
\(314\) 3.48863e7 1.12685
\(315\) −3.28501e7 −1.05100
\(316\) −6.52491e7 −2.06782
\(317\) 3.26544e6 0.102509 0.0512547 0.998686i \(-0.483678\pi\)
0.0512547 + 0.998686i \(0.483678\pi\)
\(318\) 1.12510e7i 0.349873i
\(319\) 3.16889e6i 0.0976191i
\(320\) −9.14401e7 −2.79053
\(321\) −1.80191e6 −0.0544775
\(322\) 1.49129e8 4.46678
\(323\) 8.45568e6 0.250923
\(324\) −9.36958e6 −0.275477
\(325\) 1.13634e8i 3.31023i
\(326\) 2.46653e7i 0.711924i
\(327\) 1.52846e7i 0.437131i
\(328\) 1.40322e8i 3.97652i
\(329\) 1.10400e8i 3.10013i
\(330\) −2.30485e7 −0.641358
\(331\) 8.69953e6 0.239890 0.119945 0.992781i \(-0.461728\pi\)
0.119945 + 0.992781i \(0.461728\pi\)
\(332\) 9.28593e7i 2.53753i
\(333\) 7.05983e6i 0.191188i
\(334\) 1.09517e8i 2.93930i
\(335\) 6.85313e7i 1.82286i
\(336\) 9.68293e7 2.55264
\(337\) 4.16849e7i 1.08915i −0.838711 0.544576i \(-0.816691\pi\)
0.838711 0.544576i \(-0.183309\pi\)
\(338\) 4.30340e7i 1.11445i
\(339\) 1.28089e7i 0.328786i
\(340\) −5.93771e7 −1.51071
\(341\) 1.52093e7 0.383571
\(342\) 1.94843e7i 0.487088i
\(343\) −4.99611e7 −1.23808
\(344\) 1.15400e8 2.83484
\(345\) 6.51647e7i 1.58692i
\(346\) 1.42973e8 3.45165
\(347\) 6.07357e6i 0.145364i 0.997355 + 0.0726818i \(0.0231558\pi\)
−0.997355 + 0.0726818i \(0.976844\pi\)
\(348\) −1.88114e7 −0.446358
\(349\) 2.69330e7i 0.633591i 0.948494 + 0.316795i \(0.102607\pi\)
−0.948494 + 0.316795i \(0.897393\pi\)
\(350\) 3.47153e8i 8.09685i
\(351\) 1.05185e7i 0.243240i
\(352\) 3.02636e7 0.693893
\(353\) 2.66019e7i 0.604768i −0.953186 0.302384i \(-0.902217\pi\)
0.953186 0.302384i \(-0.0977826\pi\)
\(354\) 3.44145e7 + 3.31365e7i 0.775768 + 0.746960i
\(355\) −4.64928e7 −1.03920
\(356\) 3.98431e7i 0.883087i
\(357\) 1.39454e7 0.306498
\(358\) −7.78704e7 −1.69716
\(359\) 3.78830e7 0.818768 0.409384 0.912362i \(-0.365744\pi\)
0.409384 + 0.912362i \(0.365744\pi\)
\(360\) 8.16361e7i 1.74974i
\(361\) −1.81732e7 −0.386286
\(362\) 1.39838e7i 0.294782i
\(363\) −2.49095e7 −0.520768
\(364\) 2.50483e8i 5.19366i
\(365\) 5.50826e7i 1.13276i
\(366\) 3.44404e7 0.702465
\(367\) 4.23690e7i 0.857137i 0.903509 + 0.428569i \(0.140982\pi\)
−0.903509 + 0.428569i \(0.859018\pi\)
\(368\) 1.92080e8i 3.85425i
\(369\) 2.41358e7 0.480377
\(370\) 1.03093e8 2.03528
\(371\) 2.74965e7 0.538462
\(372\) 9.02865e7i 1.75386i
\(373\) 2.26006e7 0.435505 0.217753 0.976004i \(-0.430127\pi\)
0.217753 + 0.976004i \(0.430127\pi\)
\(374\) 9.78448e6 0.187035
\(375\) −9.37748e7 −1.77825
\(376\) −2.74355e8 −5.16119
\(377\) 2.11182e7i 0.394123i
\(378\) 3.21343e7i 0.594967i
\(379\) −3.95902e7 −0.727227 −0.363613 0.931550i \(-0.618457\pi\)
−0.363613 + 0.931550i \(0.618457\pi\)
\(380\) −2.02749e8 −3.69494
\(381\) −2.80919e7 −0.507933
\(382\) 7.13343e7 1.27970
\(383\) −1.05831e7 −0.188372 −0.0941858 0.995555i \(-0.530025\pi\)
−0.0941858 + 0.995555i \(0.530025\pi\)
\(384\) 1.69862e7i 0.299988i
\(385\) 5.63283e7i 0.987063i
\(386\) 1.11937e8i 1.94631i
\(387\) 1.98491e7i 0.342459i
\(388\) 8.28975e7i 1.41921i
\(389\) −3.28357e7 −0.557824 −0.278912 0.960317i \(-0.589974\pi\)
−0.278912 + 0.960317i \(0.589974\pi\)
\(390\) −1.53600e8 −2.58939
\(391\) 2.76635e7i 0.462783i
\(392\) 2.90369e8i 4.82050i
\(393\) 1.64024e7i 0.270228i
\(394\) 1.75295e8i 2.86603i
\(395\) 9.77853e7 1.58665
\(396\) 1.60661e7i 0.258717i
\(397\) 4.64196e7i 0.741874i 0.928658 + 0.370937i \(0.120963\pi\)
−0.928658 + 0.370937i \(0.879037\pi\)
\(398\) 1.94948e8i 3.09221i
\(399\) 4.76179e7 0.749638
\(400\) 4.47138e8 6.98654
\(401\) 3.20229e7i 0.496624i 0.968680 + 0.248312i \(0.0798758\pi\)
−0.968680 + 0.248312i \(0.920124\pi\)
\(402\) −6.70380e7 −1.03191
\(403\) 1.01358e8 1.54861
\(404\) 1.87423e8i 2.84236i
\(405\) 1.40417e7 0.211375
\(406\) 6.45162e7i 0.964030i
\(407\) −1.21056e7 −0.179557
\(408\) 3.46559e7i 0.510267i
\(409\) 6.55020e7i 0.957380i 0.877984 + 0.478690i \(0.158888\pi\)
−0.877984 + 0.478690i \(0.841112\pi\)
\(410\) 3.52450e8i 5.11382i
\(411\) −4.15970e7 −0.599151
\(412\) 1.44548e8i 2.06691i
\(413\) −8.09826e7 + 8.41059e7i −1.14959 + 1.19392i
\(414\) −6.37448e7 −0.898346
\(415\) 1.39163e8i 1.94706i
\(416\) 2.01683e8 2.80150
\(417\) 2.48971e7 0.343353
\(418\) 3.34100e7 0.457454
\(419\) 1.79347e7i 0.243810i −0.992542 0.121905i \(-0.961100\pi\)
0.992542 0.121905i \(-0.0389003\pi\)
\(420\) −3.34380e8 −4.51329
\(421\) 1.27320e7i 0.170629i 0.996354 + 0.0853143i \(0.0271894\pi\)
−0.996354 + 0.0853143i \(0.972811\pi\)
\(422\) −2.67719e8 −3.56239
\(423\) 4.71901e7i 0.623490i
\(424\) 6.83318e7i 0.896448i
\(425\) 6.43971e7 0.838880
\(426\) 4.54797e7i 0.588287i
\(427\) 8.41691e7i 1.08111i
\(428\) −1.83416e7 −0.233941
\(429\) 1.80363e7 0.228441
\(430\) −2.89853e8 −3.64562
\(431\) 5.74355e7i 0.717379i −0.933457 0.358689i \(-0.883224\pi\)
0.933457 0.358689i \(-0.116776\pi\)
\(432\) −4.13895e7 −0.513380
\(433\) −9.16313e7 −1.12870 −0.564352 0.825534i \(-0.690874\pi\)
−0.564352 + 0.825534i \(0.690874\pi\)
\(434\) 3.09650e8 3.78793
\(435\) 2.81916e7 0.342493
\(436\) 1.55582e8i 1.87715i
\(437\) 9.44597e7i 1.13188i
\(438\) 5.38824e7 0.641246
\(439\) 2.60876e7 0.308348 0.154174 0.988044i \(-0.450728\pi\)
0.154174 + 0.988044i \(0.450728\pi\)
\(440\) −1.39982e8 −1.64329
\(441\) 4.99445e7 0.582333
\(442\) 6.52059e7 0.755127
\(443\) 1.18657e7i 0.136484i 0.997669 + 0.0682422i \(0.0217391\pi\)
−0.997669 + 0.0682422i \(0.978261\pi\)
\(444\) 7.18619e7i 0.821012i
\(445\) 5.97107e7i 0.677598i
\(446\) 6.80643e7i 0.767211i
\(447\) 1.02447e8i 1.14704i
\(448\) 2.18602e8 2.43119
\(449\) 4.68237e7 0.517282 0.258641 0.965974i \(-0.416725\pi\)
0.258641 + 0.965974i \(0.416725\pi\)
\(450\) 1.48390e8i 1.62842i
\(451\) 4.13859e7i 0.451152i
\(452\) 1.30382e8i 1.41189i
\(453\) 2.30202e7i 0.247636i
\(454\) 7.74982e7 0.828179
\(455\) 3.75384e8i 3.98513i
\(456\) 1.18336e8i 1.24802i
\(457\) 3.74987e7i 0.392887i −0.980515 0.196443i \(-0.937061\pi\)
0.980515 0.196443i \(-0.0629392\pi\)
\(458\) 1.60838e8 1.67414
\(459\) −5.96094e6 −0.0616420
\(460\) 6.63311e8i 6.81465i
\(461\) −3.39765e7 −0.346797 −0.173399 0.984852i \(-0.555475\pi\)
−0.173399 + 0.984852i \(0.555475\pi\)
\(462\) 5.51010e7 0.558770
\(463\) 1.00232e8i 1.00987i 0.863159 + 0.504933i \(0.168483\pi\)
−0.863159 + 0.504933i \(0.831517\pi\)
\(464\) −8.30979e7 −0.831833
\(465\) 1.35307e8i 1.34574i
\(466\) 9.93435e7 0.981706
\(467\) 1.69289e8i 1.66218i 0.556140 + 0.831089i \(0.312282\pi\)
−0.556140 + 0.831089i \(0.687718\pi\)
\(468\) 1.07068e8i 1.04453i
\(469\) 1.63835e8i 1.58813i
\(470\) 6.89106e8 6.63732
\(471\) 3.64438e7i 0.348787i
\(472\) 2.09013e8 + 2.01251e8i 1.98768 + 1.91387i
\(473\) 3.40355e7 0.321624
\(474\) 9.56545e7i 0.898195i
\(475\) 2.19890e8 2.05175
\(476\) 1.41950e8 1.31618
\(477\) −1.17533e7 −0.108294
\(478\) 1.50394e8i 1.37704i
\(479\) −1.74885e6 −0.0159127 −0.00795637 0.999968i \(-0.502533\pi\)
−0.00795637 + 0.999968i \(0.502533\pi\)
\(480\) 2.69236e8i 2.43450i
\(481\) −8.06741e7 −0.724935
\(482\) 8.42748e7i 0.752587i
\(483\) 1.55786e8i 1.38257i
\(484\) −2.53553e8 −2.23632
\(485\) 1.24234e8i 1.08897i
\(486\) 1.37357e7i 0.119658i
\(487\) −8.62647e7 −0.746872 −0.373436 0.927656i \(-0.621821\pi\)
−0.373436 + 0.927656i \(0.621821\pi\)
\(488\) 2.09170e8 1.79986
\(489\) −2.57664e7 −0.220357
\(490\) 7.29328e8i 6.19919i
\(491\) 2.23878e8 1.89132 0.945662 0.325150i \(-0.105415\pi\)
0.945662 + 0.325150i \(0.105415\pi\)
\(492\) 2.45678e8 2.06286
\(493\) −1.19678e7 −0.0998790
\(494\) 2.22651e8 1.84691
\(495\) 2.40774e7i 0.198515i
\(496\) 3.98834e8i 3.26849i
\(497\) 1.11148e8 0.905385
\(498\) −1.36131e8 −1.10222
\(499\) 2.25336e8 1.81355 0.906774 0.421616i \(-0.138537\pi\)
0.906774 + 0.421616i \(0.138537\pi\)
\(500\) −9.54533e8 −7.63626
\(501\) −1.14407e8 −0.909783
\(502\) 1.70699e8i 1.34934i
\(503\) 1.53443e8i 1.20571i 0.797851 + 0.602854i \(0.205970\pi\)
−0.797851 + 0.602854i \(0.794030\pi\)
\(504\) 1.95164e8i 1.52443i
\(505\) 2.80881e8i 2.18096i
\(506\) 1.09304e8i 0.843692i
\(507\) 4.49551e7 0.344949
\(508\) −2.85947e8 −2.18120
\(509\) 1.46180e7i 0.110849i −0.998463 0.0554247i \(-0.982349\pi\)
0.998463 0.0554247i \(-0.0176513\pi\)
\(510\) 8.70463e7i 0.656205i
\(511\) 1.31684e8i 0.986891i
\(512\) 1.94334e8i 1.44790i
\(513\) −2.03542e7 −0.150765
\(514\) 1.11867e8i 0.823784i
\(515\) 2.16627e8i 1.58595i
\(516\) 2.02044e8i 1.47061i
\(517\) −8.09173e7 −0.585558
\(518\) −2.46460e8 −1.77320
\(519\) 1.49356e8i 1.06837i
\(520\) −9.32873e8 −6.63456
\(521\) −2.03766e8 −1.44085 −0.720423 0.693535i \(-0.756052\pi\)
−0.720423 + 0.693535i \(0.756052\pi\)
\(522\) 2.75773e7i 0.193883i
\(523\) −1.03055e8 −0.720385 −0.360193 0.932878i \(-0.617289\pi\)
−0.360193 + 0.932878i \(0.617289\pi\)
\(524\) 1.66960e8i 1.16043i
\(525\) 3.62650e8 2.50617
\(526\) 8.08457e7i 0.555520i
\(527\) 5.74403e7i 0.392451i
\(528\) 7.09709e7i 0.482146i
\(529\) −1.60998e8 −1.08756
\(530\) 1.71631e8i 1.15284i
\(531\) 3.46158e7 3.59508e7i 0.231202 0.240118i
\(532\) 4.84702e8 3.21914
\(533\) 2.75805e8i 1.82146i
\(534\) −5.84096e7 −0.383584
\(535\) 2.74875e7 0.179504
\(536\) −4.07148e8 −2.64398
\(537\) 8.13467e7i 0.525312i
\(538\) 4.12915e8 2.65164
\(539\) 8.56403e7i 0.546905i
\(540\) 1.42930e8 0.907700
\(541\) 8.57244e7i 0.541393i −0.962665 0.270697i \(-0.912746\pi\)
0.962665 0.270697i \(-0.0872540\pi\)
\(542\) 3.54801e8i 2.22837i
\(543\) −1.46081e7 −0.0912420
\(544\) 1.14295e8i 0.709957i
\(545\) 2.33162e8i 1.44035i
\(546\) 3.67205e8 2.25596
\(547\) −2.50356e8 −1.52966 −0.764832 0.644230i \(-0.777178\pi\)
−0.764832 + 0.644230i \(0.777178\pi\)
\(548\) −4.23415e8 −2.57291
\(549\) 3.59779e7i 0.217429i
\(550\) 2.54445e8 1.52935
\(551\) −4.08652e7 −0.244286
\(552\) −3.87147e8 −2.30175
\(553\) −2.33771e8 −1.38234
\(554\) 2.71241e8i 1.59524i
\(555\) 1.07695e8i 0.629968i
\(556\) 2.53427e8 1.47445
\(557\) 2.40770e8 1.39328 0.696638 0.717423i \(-0.254679\pi\)
0.696638 + 0.717423i \(0.254679\pi\)
\(558\) −1.32359e8 −0.761818
\(559\) 2.26820e8 1.29851
\(560\) −1.47710e9 −8.41097
\(561\) 1.02213e7i 0.0578917i
\(562\) 3.90837e8i 2.20185i
\(563\) 2.33540e8i 1.30869i 0.756198 + 0.654343i \(0.227055\pi\)
−0.756198 + 0.654343i \(0.772945\pi\)
\(564\) 4.80347e8i 2.67743i
\(565\) 1.95396e8i 1.08336i
\(566\) −4.97157e8 −2.74186
\(567\) −3.35688e7 −0.184156
\(568\) 2.76216e8i 1.50731i
\(569\) 2.43872e8i 1.32381i −0.749589 0.661904i \(-0.769749\pi\)
0.749589 0.661904i \(-0.230251\pi\)
\(570\) 2.97227e8i 1.60496i
\(571\) 3.01057e8i 1.61712i −0.588417 0.808558i \(-0.700249\pi\)
0.588417 0.808558i \(-0.299751\pi\)
\(572\) 1.83591e8 0.980987
\(573\) 7.45188e7i 0.396098i
\(574\) 8.42586e8i 4.45532i
\(575\) 7.19390e8i 3.78408i
\(576\) −9.34408e7 −0.488955
\(577\) 7.05247e7 0.367125 0.183563 0.983008i \(-0.441237\pi\)
0.183563 + 0.983008i \(0.441237\pi\)
\(578\) 3.23235e8i 1.67392i
\(579\) −1.16934e8 −0.602429
\(580\) 2.86962e8 1.47075
\(581\) 3.32691e8i 1.69634i
\(582\) 1.21527e8 0.616458
\(583\) 2.01535e7i 0.101706i
\(584\) 3.27249e8 1.64301
\(585\) 1.60457e8i 0.801478i
\(586\) 2.66224e8i 1.32299i
\(587\) 1.98624e8i 0.982014i 0.871156 + 0.491007i \(0.163371\pi\)
−0.871156 + 0.491007i \(0.836629\pi\)
\(588\) 5.08384e8 2.50069
\(589\) 1.96135e8i 0.959864i
\(590\) −5.24982e8 5.05487e8i −2.55616 2.46124i
\(591\) −1.83120e8 −0.887103
\(592\) 3.17445e8i 1.53004i
\(593\) 2.54012e8 1.21812 0.609060 0.793124i \(-0.291547\pi\)
0.609060 + 0.793124i \(0.291547\pi\)
\(594\) −2.35528e7 −0.112378
\(595\) −2.12733e8 −1.00991
\(596\) 1.04281e9i 4.92569i
\(597\) −2.03651e8 −0.957112
\(598\) 7.28425e8i 3.40629i
\(599\) 2.12333e8 0.987955 0.493978 0.869475i \(-0.335542\pi\)
0.493978 + 0.869475i \(0.335542\pi\)
\(600\) 9.01227e8i 4.17235i
\(601\) 5.30450e7i 0.244355i −0.992508 0.122178i \(-0.961012\pi\)
0.992508 0.122178i \(-0.0389877\pi\)
\(602\) 6.92937e8 3.17618
\(603\) 7.00307e7i 0.319401i
\(604\) 2.34322e8i 1.06341i
\(605\) 3.79986e8 1.71594
\(606\) 2.74761e8 1.23463
\(607\) 1.69882e7 0.0759594 0.0379797 0.999279i \(-0.487908\pi\)
0.0379797 + 0.999279i \(0.487908\pi\)
\(608\) 3.90272e8i 1.73643i
\(609\) −6.73964e7 −0.298390
\(610\) −5.25377e8 −2.31463
\(611\) −5.39250e8 −2.36411
\(612\) −6.06763e7 −0.264707
\(613\) 3.39053e8i 1.47192i 0.677022 + 0.735962i \(0.263270\pi\)
−0.677022 + 0.735962i \(0.736730\pi\)
\(614\) 3.42346e8i 1.47897i
\(615\) −3.68184e8 −1.58285
\(616\) 3.34649e8 1.43169
\(617\) 4.28788e7 0.182552 0.0912760 0.995826i \(-0.470905\pi\)
0.0912760 + 0.995826i \(0.470905\pi\)
\(618\) 2.11907e8 0.897799
\(619\) −2.18000e7 −0.0919148 −0.0459574 0.998943i \(-0.514634\pi\)
−0.0459574 + 0.998943i \(0.514634\pi\)
\(620\) 1.37729e9i 5.77898i
\(621\) 6.65905e7i 0.278059i
\(622\) 8.64403e8i 3.59207i
\(623\) 1.42748e8i 0.590344i
\(624\) 4.72966e8i 1.94660i
\(625\) 7.91092e8 3.24031
\(626\) −2.84655e8 −1.16037
\(627\) 3.49015e7i 0.141593i
\(628\) 3.70961e8i 1.49778i
\(629\) 4.57186e7i 0.183713i
\(630\) 4.90198e8i 1.96042i
\(631\) −3.17528e8 −1.26385 −0.631924 0.775031i \(-0.717734\pi\)
−0.631924 + 0.775031i \(0.717734\pi\)
\(632\) 5.80947e8i 2.30136i
\(633\) 2.79671e8i 1.10265i
\(634\) 4.87278e7i 0.191209i
\(635\) 4.28533e8 1.67365
\(636\) −1.19637e8 −0.465043
\(637\) 5.70726e8i 2.20805i
\(638\) −4.72871e7 −0.182088
\(639\) −4.75100e7 −0.182089
\(640\) 2.59120e8i 0.988463i
\(641\) −1.98433e7 −0.0753425 −0.0376712 0.999290i \(-0.511994\pi\)
−0.0376712 + 0.999290i \(0.511994\pi\)
\(642\) 2.68886e7i 0.101616i
\(643\) −1.33186e8 −0.500985 −0.250493 0.968119i \(-0.580593\pi\)
−0.250493 + 0.968119i \(0.580593\pi\)
\(644\) 1.58575e9i 5.93713i
\(645\) 3.02792e8i 1.12841i
\(646\) 1.26178e8i 0.468044i
\(647\) 8.23746e7 0.304145 0.152072 0.988369i \(-0.451405\pi\)
0.152072 + 0.988369i \(0.451405\pi\)
\(648\) 8.34223e7i 0.306589i
\(649\) 6.16453e7 + 5.93561e7i 0.225510 + 0.217136i
\(650\) 1.69568e9 6.17452
\(651\) 3.23473e8i 1.17245i
\(652\) −2.62276e8 −0.946272
\(653\) 7.86537e7 0.282475 0.141237 0.989976i \(-0.454892\pi\)
0.141237 + 0.989976i \(0.454892\pi\)
\(654\) −2.28081e8 −0.815373
\(655\) 2.50214e8i 0.890404i
\(656\) 1.08526e9 3.84436
\(657\) 5.62878e7i 0.198481i
\(658\) −1.64742e9 −5.78263
\(659\) 4.32893e8i 1.51260i −0.654224 0.756301i \(-0.727004\pi\)
0.654224 0.756301i \(-0.272996\pi\)
\(660\) 2.45084e8i 0.852477i
\(661\) 2.67269e8 0.925430 0.462715 0.886507i \(-0.346875\pi\)
0.462715 + 0.886507i \(0.346875\pi\)
\(662\) 1.29817e8i 0.447463i
\(663\) 6.81168e7i 0.233730i
\(664\) −8.26774e8 −2.82412
\(665\) −7.26396e8 −2.47007
\(666\) 1.05349e8 0.356621
\(667\) 1.33694e8i 0.450542i
\(668\) −1.16454e9 −3.90684
\(669\) −7.11029e7 −0.237470
\(670\) 1.02264e9 3.40016
\(671\) 6.16916e7 0.204201
\(672\) 6.43651e8i 2.12101i
\(673\) 9.44890e7i 0.309982i 0.987916 + 0.154991i \(0.0495348\pi\)
−0.987916 + 0.154991i \(0.950465\pi\)
\(674\) −6.22034e8 −2.03158
\(675\) −1.55014e8 −0.504034
\(676\) 4.57598e8 1.48130
\(677\) −5.98234e8 −1.92799 −0.963995 0.265920i \(-0.914324\pi\)
−0.963995 + 0.265920i \(0.914324\pi\)
\(678\) 1.91139e8 0.613281
\(679\) 2.97001e8i 0.948742i
\(680\) 5.28666e8i 1.68133i
\(681\) 8.09579e7i 0.256341i
\(682\) 2.26957e8i 0.715470i
\(683\) 1.94951e8i 0.611876i 0.952051 + 0.305938i \(0.0989700\pi\)
−0.952051 + 0.305938i \(0.901030\pi\)
\(684\) −2.07185e8 −0.647425
\(685\) 6.34549e8 1.97421
\(686\) 7.45535e8i 2.30938i
\(687\) 1.68018e8i 0.518186i
\(688\) 8.92515e8i 2.74063i
\(689\) 1.34307e8i 0.410622i
\(690\) 9.72407e8 2.96006
\(691\) 3.82858e8i 1.16039i 0.814478 + 0.580195i \(0.197024\pi\)
−0.814478 + 0.580195i \(0.802976\pi\)
\(692\) 1.52029e9i 4.58784i
\(693\) 5.75608e7i 0.172953i
\(694\) 9.06316e7 0.271145
\(695\) −3.79798e8 −1.13135
\(696\) 1.67487e8i 0.496769i
\(697\) 1.56300e8 0.461596
\(698\) 4.01902e8 1.18183
\(699\) 1.03778e8i 0.303861i
\(700\) 3.69141e9 10.7621
\(701\) 2.40447e8i 0.698016i −0.937120 0.349008i \(-0.886519\pi\)
0.937120 0.349008i \(-0.113481\pi\)
\(702\) −1.56961e8 −0.453712
\(703\) 1.56110e8i 0.449330i
\(704\) 1.60224e8i 0.459208i
\(705\) 7.19870e8i 2.05441i
\(706\) −3.96962e8 −1.12807
\(707\) 6.71490e8i 1.90012i
\(708\) 3.52354e8 3.65943e8i 0.992840 1.03113i
\(709\) 3.37545e8 0.947093 0.473546 0.880769i \(-0.342974\pi\)
0.473546 + 0.880769i \(0.342974\pi\)
\(710\) 6.93779e8i 1.93841i
\(711\) 9.99248e7 0.278013
\(712\) −3.54744e8 −0.982822
\(713\) −6.41675e8 −1.77030
\(714\) 2.08098e8i 0.571706i
\(715\) −2.75138e8 −0.752717
\(716\) 8.28028e8i 2.25583i
\(717\) 1.57108e8 0.426227
\(718\) 5.65301e8i 1.52724i
\(719\) 1.76060e8i 0.473667i 0.971550 + 0.236834i \(0.0761097\pi\)
−0.971550 + 0.236834i \(0.923890\pi\)
\(720\) 6.31383e8 1.69159
\(721\) 5.17880e8i 1.38173i
\(722\) 2.71185e8i 0.720534i
\(723\) 8.80370e7 0.232943
\(724\) −1.48696e8 −0.391817
\(725\) −3.11223e8 −0.816690
\(726\) 3.71706e8i 0.971382i
\(727\) −2.54718e7 −0.0662914 −0.0331457 0.999451i \(-0.510553\pi\)
−0.0331457 + 0.999451i \(0.510553\pi\)
\(728\) 2.23018e9 5.78023
\(729\) 1.43489e7 0.0370370
\(730\) −8.21959e8 −2.11291
\(731\) 1.28541e8i 0.329070i
\(732\) 3.66218e8i 0.933699i
\(733\) −5.53773e7 −0.140611 −0.0703056 0.997525i \(-0.522397\pi\)
−0.0703056 + 0.997525i \(0.522397\pi\)
\(734\) 6.32243e8 1.59881
\(735\) −7.61887e8 −1.91880
\(736\) −1.27681e9 −3.20253
\(737\) −1.20082e8 −0.299969
\(738\) 3.60161e8i 0.896041i
\(739\) 1.60876e8i 0.398618i −0.979937 0.199309i \(-0.936130\pi\)
0.979937 0.199309i \(-0.0638698\pi\)
\(740\) 1.09623e9i 2.70525i
\(741\) 2.32591e8i 0.571661i
\(742\) 4.10310e8i 1.00439i
\(743\) 2.88499e8 0.703359 0.351680 0.936120i \(-0.385611\pi\)
0.351680 + 0.936120i \(0.385611\pi\)
\(744\) −8.03868e8 −1.95194
\(745\) 1.56280e9i 3.77951i
\(746\) 3.37253e8i 0.812342i
\(747\) 1.42208e8i 0.341163i
\(748\) 1.04042e8i 0.248602i
\(749\) −6.57132e7 −0.156389
\(750\) 1.39933e9i 3.31694i
\(751\) 7.51038e7i 0.177314i −0.996062 0.0886568i \(-0.971743\pi\)
0.996062 0.0886568i \(-0.0282574\pi\)
\(752\) 2.12190e9i 4.98966i
\(753\) 1.78319e8 0.417651
\(754\) −3.15131e8 −0.735153
\(755\) 3.51165e8i 0.815964i
\(756\) −3.41697e8 −0.790816
\(757\) −3.66017e8 −0.843749 −0.421874 0.906654i \(-0.638628\pi\)
−0.421874 + 0.906654i \(0.638628\pi\)
\(758\) 5.90776e8i 1.35649i
\(759\) −1.14183e8 −0.261143
\(760\) 1.80518e9i 4.11224i
\(761\) −1.74119e8 −0.395088 −0.197544 0.980294i \(-0.563296\pi\)
−0.197544 + 0.980294i \(0.563296\pi\)
\(762\) 4.19196e8i 0.947441i
\(763\) 5.57410e8i 1.25488i
\(764\) 7.58526e8i 1.70095i
\(765\) 9.09322e7 0.203111
\(766\) 1.57924e8i 0.351367i
\(767\) 4.10818e8 + 3.95562e8i 0.910465 + 0.876655i
\(768\) 1.30157e8 0.287333
\(769\) 4.02756e8i 0.885653i 0.896607 + 0.442826i \(0.146024\pi\)
−0.896607 + 0.442826i \(0.853976\pi\)
\(770\) −8.40548e8 −1.84115
\(771\) 1.16861e8 0.254981
\(772\) −1.19027e9 −2.58699
\(773\) 2.63971e8i 0.571502i 0.958304 + 0.285751i \(0.0922429\pi\)
−0.958304 + 0.285751i \(0.907757\pi\)
\(774\) −2.96194e8 −0.638784
\(775\) 1.49373e9i 3.20899i
\(776\) 7.38080e8 1.57949
\(777\) 2.57463e8i 0.548847i
\(778\) 4.89983e8i 1.04050i
\(779\) 5.33702e8 1.12898
\(780\) 1.63329e9i 3.44175i
\(781\) 8.14660e7i 0.171011i
\(782\) −4.12803e8 −0.863223
\(783\) 2.88084e7 0.0600114
\(784\) 2.24575e9 4.66030
\(785\) 5.55938e8i 1.14926i
\(786\) 2.44762e8