Properties

Label 177.7.c.a.58.1
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 58.1
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.60

$q$-expansion

\(f(q)\) \(=\) \(q-15.3575i q^{2} +15.5885 q^{3} -171.853 q^{4} -142.367 q^{5} -239.400i q^{6} +584.638 q^{7} +1656.35i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-15.3575i q^{2} +15.5885 q^{3} -171.853 q^{4} -142.367 q^{5} -239.400i q^{6} +584.638 q^{7} +1656.35i q^{8} +243.000 q^{9} +2186.40i q^{10} +1773.45i q^{11} -2678.92 q^{12} -2047.24i q^{13} -8978.57i q^{14} -2219.28 q^{15} +14438.8 q^{16} +3646.36 q^{17} -3731.87i q^{18} +562.351 q^{19} +24466.2 q^{20} +9113.60 q^{21} +27235.7 q^{22} -12118.1i q^{23} +25819.9i q^{24} +4643.38 q^{25} -31440.5 q^{26} +3788.00 q^{27} -100472. q^{28} +29947.3 q^{29} +34082.6i q^{30} -4051.38i q^{31} -115738. i q^{32} +27645.3i q^{33} -55998.9i q^{34} -83233.1 q^{35} -41760.2 q^{36} +43754.1i q^{37} -8636.31i q^{38} -31913.4i q^{39} -235810. i q^{40} +99607.1 q^{41} -139962. i q^{42} -20260.9i q^{43} -304772. i q^{44} -34595.2 q^{45} -186104. q^{46} +114033. i q^{47} +225079. q^{48} +224152. q^{49} -71310.6i q^{50} +56841.1 q^{51} +351825. i q^{52} -220188. q^{53} -58174.1i q^{54} -252480. i q^{55} +968364. i q^{56} +8766.19 q^{57} -459916. i q^{58} +(-168079. + 118025. i) q^{59} +381390. q^{60} -443485. i q^{61} -62219.1 q^{62} +142067. q^{63} -853356. q^{64} +291460. i q^{65} +424562. q^{66} -249807. i q^{67} -626637. q^{68} -188903. i q^{69} +1.27825e6i q^{70} +605052. q^{71} +402493. i q^{72} -199631. i q^{73} +671954. q^{74} +72383.1 q^{75} -96641.7 q^{76} +1.03682e6i q^{77} -490110. q^{78} +541051. q^{79} -2.05561e6 q^{80} +59049.0 q^{81} -1.52972e6i q^{82} -742610. i q^{83} -1.56620e6 q^{84} -519121. q^{85} -311157. q^{86} +466832. q^{87} -2.93745e6 q^{88} +827595. i q^{89} +531296. i q^{90} -1.19690e6i q^{91} +2.08253e6i q^{92} -63154.8i q^{93} +1.75126e6 q^{94} -80060.3 q^{95} -1.80417e6i q^{96} -497661. i q^{97} -3.44242e6i q^{98} +430947. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.3575i 1.91969i −0.280535 0.959844i \(-0.590512\pi\)
0.280535 0.959844i \(-0.409488\pi\)
\(3\) 15.5885 0.577350
\(4\) −171.853 −2.68520
\(5\) −142.367 −1.13894 −0.569468 0.822013i \(-0.692851\pi\)
−0.569468 + 0.822013i \(0.692851\pi\)
\(6\) 239.400i 1.10833i
\(7\) 584.638 1.70448 0.852242 0.523149i \(-0.175243\pi\)
0.852242 + 0.523149i \(0.175243\pi\)
\(8\) 1656.35i 3.23506i
\(9\) 243.000 0.333333
\(10\) 2186.40i 2.18640i
\(11\) 1773.45i 1.33242i 0.745766 + 0.666208i \(0.232084\pi\)
−0.745766 + 0.666208i \(0.767916\pi\)
\(12\) −2678.92 −1.55030
\(13\) 2047.24i 0.931836i −0.884828 0.465918i \(-0.845724\pi\)
0.884828 0.465918i \(-0.154276\pi\)
\(14\) 8978.57i 3.27207i
\(15\) −2219.28 −0.657565
\(16\) 14438.8 3.52510
\(17\) 3646.36 0.742185 0.371093 0.928596i \(-0.378983\pi\)
0.371093 + 0.928596i \(0.378983\pi\)
\(18\) 3731.87i 0.639896i
\(19\) 562.351 0.0819874 0.0409937 0.999159i \(-0.486948\pi\)
0.0409937 + 0.999159i \(0.486948\pi\)
\(20\) 24466.2 3.05827
\(21\) 9113.60 0.984084
\(22\) 27235.7 2.55782
\(23\) 12118.1i 0.995982i −0.867182 0.497991i \(-0.834071\pi\)
0.867182 0.497991i \(-0.165929\pi\)
\(24\) 25819.9i 1.86776i
\(25\) 4643.38 0.297176
\(26\) −31440.5 −1.78883
\(27\) 3788.00 0.192450
\(28\) −100472. −4.57688
\(29\) 29947.3 1.22790 0.613951 0.789344i \(-0.289579\pi\)
0.613951 + 0.789344i \(0.289579\pi\)
\(30\) 34082.6i 1.26232i
\(31\) 4051.38i 0.135993i −0.997686 0.0679967i \(-0.978339\pi\)
0.997686 0.0679967i \(-0.0216608\pi\)
\(32\) 115738.i 3.53203i
\(33\) 27645.3i 0.769271i
\(34\) 55998.9i 1.42476i
\(35\) −83233.1 −1.94130
\(36\) −41760.2 −0.895067
\(37\) 43754.1i 0.863802i 0.901921 + 0.431901i \(0.142157\pi\)
−0.901921 + 0.431901i \(0.857843\pi\)
\(38\) 8636.31i 0.157390i
\(39\) 31913.4i 0.537996i
\(40\) 235810.i 3.68452i
\(41\) 99607.1 1.44524 0.722618 0.691248i \(-0.242939\pi\)
0.722618 + 0.691248i \(0.242939\pi\)
\(42\) 139962.i 1.88913i
\(43\) 20260.9i 0.254832i −0.991849 0.127416i \(-0.959332\pi\)
0.991849 0.127416i \(-0.0406683\pi\)
\(44\) 304772.i 3.57780i
\(45\) −34595.2 −0.379645
\(46\) −186104. −1.91197
\(47\) 114033.i 1.09834i 0.835710 + 0.549171i \(0.185056\pi\)
−0.835710 + 0.549171i \(0.814944\pi\)
\(48\) 225079. 2.03522
\(49\) 224152. 1.90526
\(50\) 71310.6i 0.570485i
\(51\) 56841.1 0.428501
\(52\) 351825.i 2.50217i
\(53\) −220188. −1.47899 −0.739495 0.673162i \(-0.764936\pi\)
−0.739495 + 0.673162i \(0.764936\pi\)
\(54\) 58174.1i 0.369444i
\(55\) 252480.i 1.51754i
\(56\) 968364.i 5.51410i
\(57\) 8766.19 0.0473354
\(58\) 459916.i 2.35719i
\(59\) −168079. + 118025.i −0.818385 + 0.574671i
\(60\) 381390. 1.76569
\(61\) 443485.i 1.95384i −0.213597 0.976922i \(-0.568518\pi\)
0.213597 0.976922i \(-0.431482\pi\)
\(62\) −62219.1 −0.261065
\(63\) 142067. 0.568161
\(64\) −853356. −3.25529
\(65\) 291460.i 1.06130i
\(66\) 424562. 1.47676
\(67\) 249807.i 0.830577i −0.909690 0.415288i \(-0.863681\pi\)
0.909690 0.415288i \(-0.136319\pi\)
\(68\) −626637. −1.99292
\(69\) 188903.i 0.575031i
\(70\) 1.27825e6i 3.72668i
\(71\) 605052. 1.69051 0.845255 0.534363i \(-0.179448\pi\)
0.845255 + 0.534363i \(0.179448\pi\)
\(72\) 402493.i 1.07835i
\(73\) 199631.i 0.513169i −0.966522 0.256584i \(-0.917403\pi\)
0.966522 0.256584i \(-0.0825971\pi\)
\(74\) 671954. 1.65823
\(75\) 72383.1 0.171575
\(76\) −96641.7 −0.220152
\(77\) 1.03682e6i 2.27108i
\(78\) −490110. −1.03278
\(79\) 541051. 1.09738 0.548690 0.836026i \(-0.315127\pi\)
0.548690 + 0.836026i \(0.315127\pi\)
\(80\) −2.05561e6 −4.01486
\(81\) 59049.0 0.111111
\(82\) 1.52972e6i 2.77440i
\(83\) 742610.i 1.29875i −0.760467 0.649377i \(-0.775030\pi\)
0.760467 0.649377i \(-0.224970\pi\)
\(84\) −1.56620e6 −2.64246
\(85\) −519121. −0.845302
\(86\) −311157. −0.489197
\(87\) 466832. 0.708930
\(88\) −2.93745e6 −4.31044
\(89\) 827595.i 1.17395i 0.809607 + 0.586973i \(0.199680\pi\)
−0.809607 + 0.586973i \(0.800320\pi\)
\(90\) 531296.i 0.728801i
\(91\) 1.19690e6i 1.58830i
\(92\) 2.08253e6i 2.67441i
\(93\) 63154.8i 0.0785159i
\(94\) 1.75126e6 2.10847
\(95\) −80060.3 −0.0933784
\(96\) 1.80417e6i 2.03922i
\(97\) 497661.i 0.545279i −0.962116 0.272640i \(-0.912103\pi\)
0.962116 0.272640i \(-0.0878966\pi\)
\(98\) 3.44242e6i 3.65751i
\(99\) 430947.i 0.444139i
\(100\) −797977. −0.797977
\(101\) 1.36463e6i 1.32450i −0.749285 0.662248i \(-0.769603\pi\)
0.749285 0.662248i \(-0.230397\pi\)
\(102\) 872937.i 0.822588i
\(103\) 149108.i 0.136455i 0.997670 + 0.0682274i \(0.0217343\pi\)
−0.997670 + 0.0682274i \(0.978266\pi\)
\(104\) 3.39095e6 3.01454
\(105\) −1.29748e6 −1.12081
\(106\) 3.38153e6i 2.83920i
\(107\) −1.17390e6 −0.958254 −0.479127 0.877746i \(-0.659047\pi\)
−0.479127 + 0.877746i \(0.659047\pi\)
\(108\) −650978. −0.516767
\(109\) 535435.i 0.413454i −0.978399 0.206727i \(-0.933719\pi\)
0.978399 0.206727i \(-0.0662812\pi\)
\(110\) −3.87747e6 −2.91320
\(111\) 682060.i 0.498716i
\(112\) 8.44147e6 6.00847
\(113\) 1.93878e6i 1.34367i 0.740701 + 0.671835i \(0.234494\pi\)
−0.740701 + 0.671835i \(0.765506\pi\)
\(114\) 134627.i 0.0908692i
\(115\) 1.72522e6i 1.13436i
\(116\) −5.14653e6 −3.29716
\(117\) 497480.i 0.310612i
\(118\) 1.81257e6 + 2.58127e6i 1.10319 + 1.57104i
\(119\) 2.13180e6 1.26504
\(120\) 3.67591e6i 2.12726i
\(121\) −1.37355e6 −0.775333
\(122\) −6.81083e6 −3.75077
\(123\) 1.55272e6 0.834407
\(124\) 696241.i 0.365170i
\(125\) 1.56342e6 0.800472
\(126\) 2.18179e6i 1.09069i
\(127\) 1.74558e6 0.852173 0.426087 0.904682i \(-0.359892\pi\)
0.426087 + 0.904682i \(0.359892\pi\)
\(128\) 5.69821e6i 2.71712i
\(129\) 315836.i 0.147127i
\(130\) 4.47610e6 2.03737
\(131\) 1.26031e6i 0.560612i −0.959911 0.280306i \(-0.909564\pi\)
0.959911 0.280306i \(-0.0904360\pi\)
\(132\) 4.75092e6i 2.06565i
\(133\) 328772. 0.139746
\(134\) −3.83641e6 −1.59445
\(135\) −539286. −0.219188
\(136\) 6.03964e6i 2.40101i
\(137\) 3.60282e6 1.40114 0.700569 0.713585i \(-0.252930\pi\)
0.700569 + 0.713585i \(0.252930\pi\)
\(138\) −2.90107e6 −1.10388
\(139\) 4.34147e6 1.61656 0.808281 0.588797i \(-0.200398\pi\)
0.808281 + 0.588797i \(0.200398\pi\)
\(140\) 1.43038e7 5.21277
\(141\) 1.77760e6i 0.634128i
\(142\) 9.29209e6i 3.24525i
\(143\) 3.63068e6 1.24159
\(144\) 3.50863e6 1.17503
\(145\) −4.26351e6 −1.39850
\(146\) −3.06584e6 −0.985123
\(147\) 3.49419e6 1.10000
\(148\) 7.51927e6i 2.31948i
\(149\) 1.18051e6i 0.356871i 0.983952 + 0.178435i \(0.0571036\pi\)
−0.983952 + 0.178435i \(0.942896\pi\)
\(150\) 1.11162e6i 0.329370i
\(151\) 1.80511e6i 0.524292i −0.965028 0.262146i \(-0.915570\pi\)
0.965028 0.262146i \(-0.0844301\pi\)
\(152\) 931450.i 0.265234i
\(153\) 886065. 0.247395
\(154\) 1.59230e7 4.35977
\(155\) 576783.i 0.154888i
\(156\) 5.48440e6i 1.44463i
\(157\) 6.24085e6i 1.61267i −0.591462 0.806333i \(-0.701449\pi\)
0.591462 0.806333i \(-0.298551\pi\)
\(158\) 8.30919e6i 2.10663i
\(159\) −3.43238e6 −0.853895
\(160\) 1.64772e7i 4.02276i
\(161\) 7.08471e6i 1.69764i
\(162\) 906845.i 0.213299i
\(163\) 3.89198e6 0.898686 0.449343 0.893359i \(-0.351658\pi\)
0.449343 + 0.893359i \(0.351658\pi\)
\(164\) −1.71178e7 −3.88075
\(165\) 3.93578e6i 0.876151i
\(166\) −1.14046e7 −2.49320
\(167\) 3.76388e6 0.808140 0.404070 0.914728i \(-0.367595\pi\)
0.404070 + 0.914728i \(0.367595\pi\)
\(168\) 1.50953e7i 3.18357i
\(169\) 635601. 0.131681
\(170\) 7.97240e6i 1.62272i
\(171\) 136651. 0.0273291
\(172\) 3.48189e6i 0.684274i
\(173\) 6.13706e6i 1.18528i −0.805467 0.592641i \(-0.798085\pi\)
0.805467 0.592641i \(-0.201915\pi\)
\(174\) 7.16938e6i 1.36092i
\(175\) 2.71469e6 0.506532
\(176\) 2.56064e7i 4.69690i
\(177\) −2.62009e6 + 1.83983e6i −0.472495 + 0.331786i
\(178\) 1.27098e7 2.25361
\(179\) 4.36255e6i 0.760643i 0.924854 + 0.380322i \(0.124187\pi\)
−0.924854 + 0.380322i \(0.875813\pi\)
\(180\) 5.94528e6 1.01942
\(181\) −6.52017e6 −1.09957 −0.549785 0.835306i \(-0.685290\pi\)
−0.549785 + 0.835306i \(0.685290\pi\)
\(182\) −1.83813e7 −3.04904
\(183\) 6.91325e6i 1.12805i
\(184\) 2.00718e7 3.22206
\(185\) 6.22915e6i 0.983815i
\(186\) −969900. −0.150726
\(187\) 6.46662e6i 0.988900i
\(188\) 1.95969e7i 2.94927i
\(189\) 2.21460e6 0.328028
\(190\) 1.22953e6i 0.179257i
\(191\) 7.81540e6i 1.12163i 0.827940 + 0.560817i \(0.189513\pi\)
−0.827940 + 0.560817i \(0.810487\pi\)
\(192\) −1.33025e7 −1.87945
\(193\) −3.91093e6 −0.544012 −0.272006 0.962296i \(-0.587687\pi\)
−0.272006 + 0.962296i \(0.587687\pi\)
\(194\) −7.64284e6 −1.04677
\(195\) 4.54341e6i 0.612743i
\(196\) −3.85212e7 −5.11601
\(197\) 4.95293e6 0.647833 0.323917 0.946086i \(-0.395000\pi\)
0.323917 + 0.946086i \(0.395000\pi\)
\(198\) 6.61827e6 0.852608
\(199\) −1.11977e6 −0.142091 −0.0710457 0.997473i \(-0.522634\pi\)
−0.0710457 + 0.997473i \(0.522634\pi\)
\(200\) 7.69105e6i 0.961382i
\(201\) 3.89410e6i 0.479534i
\(202\) −2.09573e7 −2.54262
\(203\) 1.75083e7 2.09294
\(204\) −9.76830e6 −1.15061
\(205\) −1.41808e7 −1.64603
\(206\) 2.28992e6 0.261951
\(207\) 2.94470e6i 0.331994i
\(208\) 2.95598e7i 3.28481i
\(209\) 997300.i 0.109241i
\(210\) 1.99260e7i 2.15160i
\(211\) 1.81512e6i 0.193223i −0.995322 0.0966115i \(-0.969200\pi\)
0.995322 0.0966115i \(-0.0308004\pi\)
\(212\) 3.78398e7 3.97138
\(213\) 9.43183e6 0.976017
\(214\) 1.80282e7i 1.83955i
\(215\) 2.88449e6i 0.290237i
\(216\) 6.27424e6i 0.622587i
\(217\) 2.36859e6i 0.231799i
\(218\) −8.22295e6 −0.793703
\(219\) 3.11194e6i 0.296278i
\(220\) 4.33894e7i 4.07489i
\(221\) 7.46498e6i 0.691595i
\(222\) 1.04747e7 0.957379
\(223\) −7.76823e6 −0.700499 −0.350249 0.936657i \(-0.613903\pi\)
−0.350249 + 0.936657i \(0.613903\pi\)
\(224\) 6.76645e7i 6.02028i
\(225\) 1.12834e6 0.0990587
\(226\) 2.97748e7 2.57943
\(227\) 1.84475e7i 1.57710i 0.614971 + 0.788550i \(0.289168\pi\)
−0.614971 + 0.788550i \(0.710832\pi\)
\(228\) −1.50649e6 −0.127105
\(229\) 1.23698e7i 1.03005i −0.857176 0.515024i \(-0.827783\pi\)
0.857176 0.515024i \(-0.172217\pi\)
\(230\) 2.64951e7 2.17762
\(231\) 1.61625e7i 1.31121i
\(232\) 4.96032e7i 3.97233i
\(233\) 1.92702e7i 1.52342i 0.647919 + 0.761709i \(0.275639\pi\)
−0.647919 + 0.761709i \(0.724361\pi\)
\(234\) −7.64005e6 −0.596278
\(235\) 1.62346e7i 1.25094i
\(236\) 2.88849e7 2.02830e7i 2.19753 1.54311i
\(237\) 8.43415e6 0.633572
\(238\) 3.27391e7i 2.42849i
\(239\) −9.18556e6 −0.672840 −0.336420 0.941712i \(-0.609216\pi\)
−0.336420 + 0.941712i \(0.609216\pi\)
\(240\) −3.20438e7 −2.31798
\(241\) −3.82811e6 −0.273485 −0.136743 0.990607i \(-0.543663\pi\)
−0.136743 + 0.990607i \(0.543663\pi\)
\(242\) 2.10943e7i 1.48840i
\(243\) 920483. 0.0641500
\(244\) 7.62142e7i 5.24646i
\(245\) −3.19119e7 −2.16997
\(246\) 2.38459e7i 1.60180i
\(247\) 1.15127e6i 0.0763988i
\(248\) 6.71050e6 0.439947
\(249\) 1.15761e7i 0.749835i
\(250\) 2.40102e7i 1.53666i
\(251\) −7.67636e6 −0.485438 −0.242719 0.970097i \(-0.578039\pi\)
−0.242719 + 0.970097i \(0.578039\pi\)
\(252\) −2.44146e7 −1.52563
\(253\) 2.14908e7 1.32706
\(254\) 2.68077e7i 1.63591i
\(255\) −8.09230e6 −0.488035
\(256\) 3.28955e7 1.96072
\(257\) −2.93455e7 −1.72879 −0.864393 0.502816i \(-0.832297\pi\)
−0.864393 + 0.502816i \(0.832297\pi\)
\(258\) −4.85046e6 −0.282438
\(259\) 2.55803e7i 1.47234i
\(260\) 5.00882e7i 2.84981i
\(261\) 7.27720e6 0.409301
\(262\) −1.93552e7 −1.07620
\(263\) −1.49416e6 −0.0821351 −0.0410675 0.999156i \(-0.513076\pi\)
−0.0410675 + 0.999156i \(0.513076\pi\)
\(264\) −4.57902e7 −2.48864
\(265\) 3.13475e7 1.68448
\(266\) 5.04911e6i 0.268269i
\(267\) 1.29009e7i 0.677778i
\(268\) 4.29300e7i 2.23026i
\(269\) 1.42313e7i 0.731116i 0.930789 + 0.365558i \(0.119122\pi\)
−0.930789 + 0.365558i \(0.880878\pi\)
\(270\) 8.28208e6i 0.420773i
\(271\) 8.71158e6 0.437713 0.218856 0.975757i \(-0.429767\pi\)
0.218856 + 0.975757i \(0.429767\pi\)
\(272\) 5.26490e7 2.61628
\(273\) 1.86578e7i 0.917005i
\(274\) 5.53303e7i 2.68975i
\(275\) 8.23478e6i 0.395962i
\(276\) 3.24635e7i 1.54407i
\(277\) 4.17642e6 0.196501 0.0982505 0.995162i \(-0.468675\pi\)
0.0982505 + 0.995162i \(0.468675\pi\)
\(278\) 6.66741e7i 3.10329i
\(279\) 984486.i 0.0453312i
\(280\) 1.37863e8i 6.28021i
\(281\) −1.72008e7 −0.775228 −0.387614 0.921822i \(-0.626701\pi\)
−0.387614 + 0.921822i \(0.626701\pi\)
\(282\) 2.72995e7 1.21733
\(283\) 2.70788e7i 1.19473i 0.801968 + 0.597366i \(0.203786\pi\)
−0.801968 + 0.597366i \(0.796214\pi\)
\(284\) −1.03980e8 −4.53936
\(285\) −1.24802e6 −0.0539120
\(286\) 5.57581e7i 2.38347i
\(287\) 5.82341e7 2.46338
\(288\) 2.81242e7i 1.17734i
\(289\) −1.08416e7 −0.449161
\(290\) 6.54769e7i 2.68469i
\(291\) 7.75777e6i 0.314817i
\(292\) 3.43072e7i 1.37796i
\(293\) 4.01420e7 1.59586 0.797932 0.602747i \(-0.205927\pi\)
0.797932 + 0.602747i \(0.205927\pi\)
\(294\) 5.36620e7i 2.11166i
\(295\) 2.39289e7 1.68029e7i 0.932088 0.654513i
\(296\) −7.24721e7 −2.79445
\(297\) 6.71781e6i 0.256424i
\(298\) 1.81297e7 0.685081
\(299\) −2.48087e7 −0.928092
\(300\) −1.24392e7 −0.460712
\(301\) 1.18453e7i 0.434356i
\(302\) −2.77220e7 −1.00648
\(303\) 2.12725e7i 0.764698i
\(304\) 8.11968e6 0.289014
\(305\) 6.31377e7i 2.22530i
\(306\) 1.36077e7i 0.474921i
\(307\) 2.64835e7 0.915295 0.457647 0.889134i \(-0.348692\pi\)
0.457647 + 0.889134i \(0.348692\pi\)
\(308\) 1.78181e8i 6.09831i
\(309\) 2.32436e6i 0.0787822i
\(310\) 8.85795e6 0.297336
\(311\) −8.46832e6 −0.281524 −0.140762 0.990043i \(-0.544955\pi\)
−0.140762 + 0.990043i \(0.544955\pi\)
\(312\) 5.28597e7 1.74045
\(313\) 1.51004e7i 0.492443i 0.969214 + 0.246222i \(0.0791891\pi\)
−0.969214 + 0.246222i \(0.920811\pi\)
\(314\) −9.58438e7 −3.09581
\(315\) −2.02257e7 −0.647099
\(316\) −9.29811e7 −2.94668
\(317\) −8.85633e6 −0.278020 −0.139010 0.990291i \(-0.544392\pi\)
−0.139010 + 0.990291i \(0.544392\pi\)
\(318\) 5.27128e7i 1.63921i
\(319\) 5.31099e7i 1.63608i
\(320\) 1.21490e8 3.70757
\(321\) −1.82993e7 −0.553248
\(322\) −1.08803e8 −3.25893
\(323\) 2.05053e6 0.0608498
\(324\) −1.01477e7 −0.298356
\(325\) 9.50612e6i 0.276919i
\(326\) 5.97711e7i 1.72520i
\(327\) 8.34661e6i 0.238708i
\(328\) 1.64984e8i 4.67542i
\(329\) 6.66681e7i 1.87210i
\(330\) −6.04437e7 −1.68194
\(331\) 5.61297e7 1.54778 0.773889 0.633322i \(-0.218309\pi\)
0.773889 + 0.633322i \(0.218309\pi\)
\(332\) 1.27620e8i 3.48741i
\(333\) 1.06323e7i 0.287934i
\(334\) 5.78038e7i 1.55138i
\(335\) 3.55643e7i 0.945974i
\(336\) 1.31589e8 3.46899
\(337\) 3.64613e7i 0.952670i 0.879264 + 0.476335i \(0.158035\pi\)
−0.879264 + 0.476335i \(0.841965\pi\)
\(338\) 9.76124e6i 0.252787i
\(339\) 3.02226e7i 0.775768i
\(340\) 8.92124e7 2.26980
\(341\) 7.18491e6 0.181200
\(342\) 2.09862e6i 0.0524634i
\(343\) 6.22658e7 1.54300
\(344\) 3.35591e7 0.824395
\(345\) 2.68935e7i 0.654923i
\(346\) −9.42498e7 −2.27537
\(347\) 2.81353e7i 0.673385i −0.941615 0.336693i \(-0.890692\pi\)
0.941615 0.336693i \(-0.109308\pi\)
\(348\) −8.02265e7 −1.90362
\(349\) 2.03122e7i 0.477837i 0.971040 + 0.238919i \(0.0767929\pi\)
−0.971040 + 0.238919i \(0.923207\pi\)
\(350\) 4.16909e7i 0.972382i
\(351\) 7.75495e6i 0.179332i
\(352\) 2.05254e8 4.70613
\(353\) 5.37321e6i 0.122155i −0.998133 0.0610773i \(-0.980546\pi\)
0.998133 0.0610773i \(-0.0194536\pi\)
\(354\) 2.82552e7 + 4.02381e7i 0.636926 + 0.907042i
\(355\) −8.61395e7 −1.92538
\(356\) 1.42225e8i 3.15228i
\(357\) 3.32314e7 0.730373
\(358\) 6.69978e7 1.46020
\(359\) 5.22643e7 1.12959 0.564796 0.825231i \(-0.308955\pi\)
0.564796 + 0.825231i \(0.308955\pi\)
\(360\) 5.73017e7i 1.22817i
\(361\) −4.67296e7 −0.993278
\(362\) 1.00133e8i 2.11083i
\(363\) −2.14115e7 −0.447639
\(364\) 2.05690e8i 4.26490i
\(365\) 2.84209e7i 0.584466i
\(366\) −1.06170e8 −2.16551
\(367\) 1.30899e6i 0.0264812i 0.999912 + 0.0132406i \(0.00421474\pi\)
−0.999912 + 0.0132406i \(0.995785\pi\)
\(368\) 1.74971e8i 3.51094i
\(369\) 2.42045e7 0.481745
\(370\) −9.56641e7 −1.88862
\(371\) −1.28730e8 −2.52091
\(372\) 1.08533e7i 0.210831i
\(373\) −2.14407e7 −0.413154 −0.206577 0.978430i \(-0.566232\pi\)
−0.206577 + 0.978430i \(0.566232\pi\)
\(374\) 9.93111e7 1.89838
\(375\) 2.43713e7 0.462153
\(376\) −1.88879e8 −3.55320
\(377\) 6.13095e7i 1.14420i
\(378\) 3.40108e7i 0.629711i
\(379\) 4.05156e7 0.744227 0.372113 0.928187i \(-0.378633\pi\)
0.372113 + 0.928187i \(0.378633\pi\)
\(380\) 1.37586e7 0.250740
\(381\) 2.72109e7 0.492002
\(382\) 1.20025e8 2.15319
\(383\) 7.37761e7 1.31317 0.656583 0.754254i \(-0.272001\pi\)
0.656583 + 0.754254i \(0.272001\pi\)
\(384\) 8.88263e7i 1.56873i
\(385\) 1.47609e8i 2.58662i
\(386\) 6.00621e7i 1.04433i
\(387\) 4.92340e6i 0.0849439i
\(388\) 8.55245e7i 1.46418i
\(389\) 2.38734e7 0.405570 0.202785 0.979223i \(-0.435001\pi\)
0.202785 + 0.979223i \(0.435001\pi\)
\(390\) 6.97755e7 1.17628
\(391\) 4.41870e7i 0.739204i
\(392\) 3.71274e8i 6.16363i
\(393\) 1.96463e7i 0.323670i
\(394\) 7.60646e7i 1.24364i
\(395\) −7.70278e7 −1.24985
\(396\) 7.40595e7i 1.19260i
\(397\) 1.10820e8i 1.77111i 0.464533 + 0.885556i \(0.346222\pi\)
−0.464533 + 0.885556i \(0.653778\pi\)
\(398\) 1.71968e7i 0.272771i
\(399\) 5.12505e6 0.0806824
\(400\) 6.70448e7 1.04757
\(401\) 9.67278e7i 1.50009i 0.661385 + 0.750047i \(0.269969\pi\)
−0.661385 + 0.750047i \(0.730031\pi\)
\(402\) −5.98037e7 −0.920555
\(403\) −8.29417e6 −0.126724
\(404\) 2.34515e8i 3.55653i
\(405\) −8.40663e6 −0.126548
\(406\) 2.68884e8i 4.01779i
\(407\) −7.75956e7 −1.15094
\(408\) 9.41487e7i 1.38623i
\(409\) 3.32272e7i 0.485651i 0.970070 + 0.242825i \(0.0780742\pi\)
−0.970070 + 0.242825i \(0.921926\pi\)
\(410\) 2.17781e8i 3.15987i
\(411\) 5.61624e7 0.808947
\(412\) 2.56246e7i 0.366409i
\(413\) −9.82653e7 + 6.90020e7i −1.39492 + 0.979516i
\(414\) −4.52233e7 −0.637325
\(415\) 1.05723e8i 1.47920i
\(416\) −2.36943e8 −3.29127
\(417\) 6.76768e7 0.933322
\(418\) 1.53160e7 0.209709
\(419\) 5.48195e7i 0.745234i −0.927985 0.372617i \(-0.878461\pi\)
0.927985 0.372617i \(-0.121539\pi\)
\(420\) 2.22975e8 3.00960
\(421\) 8.66580e7i 1.16135i −0.814136 0.580674i \(-0.802789\pi\)
0.814136 0.580674i \(-0.197211\pi\)
\(422\) −2.78758e7 −0.370928
\(423\) 2.77100e7i 0.366114i
\(424\) 3.64707e8i 4.78462i
\(425\) 1.69314e7 0.220560
\(426\) 1.44849e8i 1.87365i
\(427\) 2.59278e8i 3.33029i
\(428\) 2.01738e8 2.57310
\(429\) 5.65967e7 0.716834
\(430\) 4.42985e7 0.557165
\(431\) 7.11138e7i 0.888223i 0.895972 + 0.444111i \(0.146481\pi\)
−0.895972 + 0.444111i \(0.853519\pi\)
\(432\) 5.46941e7 0.678405
\(433\) −4.47048e7 −0.550669 −0.275335 0.961348i \(-0.588789\pi\)
−0.275335 + 0.961348i \(0.588789\pi\)
\(434\) −3.63756e7 −0.444981
\(435\) −6.64616e7 −0.807426
\(436\) 9.20160e7i 1.11021i
\(437\) 6.81464e6i 0.0816580i
\(438\) −4.77917e7 −0.568761
\(439\) −9.88814e7 −1.16875 −0.584374 0.811484i \(-0.698660\pi\)
−0.584374 + 0.811484i \(0.698660\pi\)
\(440\) 4.18195e8 4.90932
\(441\) 5.44690e7 0.635088
\(442\) −1.14643e8 −1.32765
\(443\) 1.34618e8i 1.54844i −0.632919 0.774218i \(-0.718143\pi\)
0.632919 0.774218i \(-0.281857\pi\)
\(444\) 1.17214e8i 1.33915i
\(445\) 1.17822e8i 1.33705i
\(446\) 1.19301e8i 1.34474i
\(447\) 1.84023e7i 0.206040i
\(448\) −4.98904e8 −5.54860
\(449\) −9.71018e6 −0.107272 −0.0536362 0.998561i \(-0.517081\pi\)
−0.0536362 + 0.998561i \(0.517081\pi\)
\(450\) 1.73285e7i 0.190162i
\(451\) 1.76648e8i 1.92566i
\(452\) 3.33184e8i 3.60802i
\(453\) 2.81389e7i 0.302700i
\(454\) 2.83307e8 3.02754
\(455\) 1.70399e8i 1.80897i
\(456\) 1.45199e7i 0.153133i
\(457\) 1.07666e8i 1.12805i 0.825756 + 0.564027i \(0.190749\pi\)
−0.825756 + 0.564027i \(0.809251\pi\)
\(458\) −1.89970e8 −1.97737
\(459\) 1.38124e7 0.142834
\(460\) 2.96484e8i 3.04598i
\(461\) −1.61768e8 −1.65117 −0.825583 0.564281i \(-0.809153\pi\)
−0.825583 + 0.564281i \(0.809153\pi\)
\(462\) 2.48215e8 2.51711
\(463\) 6.83555e7i 0.688701i −0.938841 0.344350i \(-0.888099\pi\)
0.938841 0.344350i \(-0.111901\pi\)
\(464\) 4.32403e8 4.32848
\(465\) 8.99116e6i 0.0894246i
\(466\) 2.95942e8 2.92449
\(467\) 3.74836e7i 0.368037i −0.982923 0.184018i \(-0.941089\pi\)
0.982923 0.184018i \(-0.0589106\pi\)
\(468\) 8.54934e7i 0.834055i
\(469\) 1.46046e8i 1.41570i
\(470\) −2.49322e8 −2.40142
\(471\) 9.72852e7i 0.931073i
\(472\) −1.95491e8 2.78398e8i −1.85909 2.64752i
\(473\) 3.59316e7 0.339542
\(474\) 1.29527e8i 1.21626i
\(475\) 2.61121e6 0.0243647
\(476\) −3.66355e8 −3.39689
\(477\) −5.35056e7 −0.492997
\(478\) 1.41067e8i 1.29164i
\(479\) −9.43319e7 −0.858326 −0.429163 0.903227i \(-0.641191\pi\)
−0.429163 + 0.903227i \(0.641191\pi\)
\(480\) 2.56854e8i 2.32254i
\(481\) 8.95754e7 0.804921
\(482\) 5.87902e7i 0.525006i
\(483\) 1.10440e8i 0.980130i
\(484\) 2.36048e8 2.08192
\(485\) 7.08506e7i 0.621038i
\(486\) 1.41363e7i 0.123148i
\(487\) 7.84183e7 0.678938 0.339469 0.940617i \(-0.389753\pi\)
0.339469 + 0.940617i \(0.389753\pi\)
\(488\) 7.34567e8 6.32080
\(489\) 6.06700e7 0.518856
\(490\) 4.90087e8i 4.16567i
\(491\) 1.69057e8 1.42820 0.714100 0.700044i \(-0.246836\pi\)
0.714100 + 0.700044i \(0.246836\pi\)
\(492\) −2.66839e8 −2.24055
\(493\) 1.09199e8 0.911331
\(494\) −1.76806e7 −0.146662
\(495\) 6.13527e7i 0.505846i
\(496\) 5.84971e7i 0.479390i
\(497\) 3.53736e8 2.88145
\(498\) −1.77781e8 −1.43945
\(499\) −1.51272e8 −1.21747 −0.608734 0.793375i \(-0.708322\pi\)
−0.608734 + 0.793375i \(0.708322\pi\)
\(500\) −2.68678e8 −2.14943
\(501\) 5.86731e7 0.466580
\(502\) 1.17890e8i 0.931890i
\(503\) 1.39770e8i 1.09827i −0.835732 0.549137i \(-0.814957\pi\)
0.835732 0.549137i \(-0.185043\pi\)
\(504\) 2.35312e8i 1.83803i
\(505\) 1.94278e8i 1.50852i
\(506\) 3.30045e8i 2.54755i
\(507\) 9.90804e6 0.0760263
\(508\) −2.99982e8 −2.28826
\(509\) 1.39563e8i 1.05832i 0.848521 + 0.529161i \(0.177493\pi\)
−0.848521 + 0.529161i \(0.822507\pi\)
\(510\) 1.24277e8i 0.936875i
\(511\) 1.16712e8i 0.874687i
\(512\) 1.40507e8i 1.04686i
\(513\) 2.13018e6 0.0157785
\(514\) 4.50673e8i 3.31873i
\(515\) 2.12280e7i 0.155413i
\(516\) 5.42773e7i 0.395066i
\(517\) −2.02232e8 −1.46345
\(518\) 3.92850e8 2.82642
\(519\) 9.56672e7i 0.684323i
\(520\) −4.82760e8 −3.43337
\(521\) −2.47764e8 −1.75196 −0.875980 0.482347i \(-0.839785\pi\)
−0.875980 + 0.482347i \(0.839785\pi\)
\(522\) 1.11760e8i 0.785730i
\(523\) −1.38810e8 −0.970324 −0.485162 0.874424i \(-0.661239\pi\)
−0.485162 + 0.874424i \(0.661239\pi\)
\(524\) 2.16587e8i 1.50536i
\(525\) 4.23179e7 0.292446
\(526\) 2.29465e7i 0.157674i
\(527\) 1.47728e7i 0.100932i
\(528\) 3.99165e8i 2.71176i
\(529\) 1.18712e6 0.00801915
\(530\) 4.81418e8i 3.23367i
\(531\) −4.08432e7 + 2.86801e7i −0.272795 + 0.191557i
\(532\) −5.65004e7 −0.375246
\(533\) 2.03920e8i 1.34672i
\(534\) 1.98126e8 1.30112
\(535\) 1.67125e8 1.09139
\(536\) 4.13767e8 2.68696
\(537\) 6.80054e7i 0.439158i
\(538\) 2.18556e8 1.40351
\(539\) 3.97522e8i 2.53860i
\(540\) 9.26777e7 0.588565
\(541\) 2.45184e8i 1.54846i −0.632902 0.774232i \(-0.718136\pi\)
0.632902 0.774232i \(-0.281864\pi\)
\(542\) 1.33788e8i 0.840271i
\(543\) −1.01639e8 −0.634837
\(544\) 4.22020e8i 2.62142i
\(545\) 7.62283e7i 0.470898i
\(546\) −2.86537e8 −1.76036
\(547\) 1.41249e8 0.863025 0.431513 0.902107i \(-0.357980\pi\)
0.431513 + 0.902107i \(0.357980\pi\)
\(548\) −6.19155e8 −3.76233
\(549\) 1.07767e8i 0.651281i
\(550\) 1.26466e8 0.760124
\(551\) 1.68409e7 0.100672
\(552\) 3.12889e8 1.86026
\(553\) 3.16319e8 1.87046
\(554\) 6.41393e7i 0.377220i
\(555\) 9.71028e7i 0.568006i
\(556\) −7.46093e8 −4.34079
\(557\) −4.71404e7 −0.272790 −0.136395 0.990655i \(-0.543552\pi\)
−0.136395 + 0.990655i \(0.543552\pi\)
\(558\) −1.51192e7 −0.0870217
\(559\) −4.14790e7 −0.237461
\(560\) −1.20179e9 −6.84327
\(561\) 1.00805e8i 0.570942i
\(562\) 2.64161e8i 1.48820i
\(563\) 7.33285e7i 0.410911i −0.978666 0.205455i \(-0.934132\pi\)
0.978666 0.205455i \(-0.0658676\pi\)
\(564\) 3.05486e8i 1.70276i
\(565\) 2.76018e8i 1.53036i
\(566\) 4.15863e8 2.29351
\(567\) 3.45223e7 0.189387
\(568\) 1.00218e9i 5.46890i
\(569\) 1.74218e8i 0.945708i −0.881141 0.472854i \(-0.843224\pi\)
0.881141 0.472854i \(-0.156776\pi\)
\(570\) 1.91664e7i 0.103494i
\(571\) 1.41847e8i 0.761925i 0.924590 + 0.380963i \(0.124407\pi\)
−0.924590 + 0.380963i \(0.875593\pi\)
\(572\) −6.23942e8 −3.33393
\(573\) 1.21830e8i 0.647575i
\(574\) 8.94329e8i 4.72892i
\(575\) 5.62690e7i 0.295982i
\(576\) −2.07366e8 −1.08510
\(577\) 1.44952e8 0.754563 0.377282 0.926099i \(-0.376859\pi\)
0.377282 + 0.926099i \(0.376859\pi\)
\(578\) 1.66501e8i 0.862248i
\(579\) −6.09654e7 −0.314085
\(580\) 7.32696e8 3.75526
\(581\) 4.34158e8i 2.21370i
\(582\) −1.19140e8 −0.604350
\(583\) 3.90491e8i 1.97063i
\(584\) 3.30659e8 1.66013
\(585\) 7.08248e7i 0.353767i
\(586\) 6.16480e8i 3.06356i
\(587\) 3.09187e8i 1.52865i 0.644834 + 0.764323i \(0.276927\pi\)
−0.644834 + 0.764323i \(0.723073\pi\)
\(588\) −6.00486e8 −2.95373
\(589\) 2.27830e6i 0.0111497i
\(590\) −2.58051e8 3.67488e8i −1.25646 1.78932i
\(591\) 7.72085e7 0.374027
\(592\) 6.31757e8i 3.04499i
\(593\) −2.12830e8 −1.02063 −0.510316 0.859987i \(-0.670472\pi\)
−0.510316 + 0.859987i \(0.670472\pi\)
\(594\) 1.03169e8 0.492253
\(595\) −3.03498e8 −1.44080
\(596\) 2.02874e8i 0.958270i
\(597\) −1.74554e7 −0.0820365
\(598\) 3.81000e8i 1.78165i
\(599\) −1.53295e8 −0.713260 −0.356630 0.934246i \(-0.616074\pi\)
−0.356630 + 0.934246i \(0.616074\pi\)
\(600\) 1.19892e8i 0.555054i
\(601\) 1.13259e8i 0.521735i 0.965375 + 0.260867i \(0.0840086\pi\)
−0.965375 + 0.260867i \(0.915991\pi\)
\(602\) −1.81914e8 −0.833828
\(603\) 6.07031e7i 0.276859i
\(604\) 3.10213e8i 1.40783i
\(605\) 1.95548e8 0.883055
\(606\) −3.26692e8 −1.46798
\(607\) −3.65896e7 −0.163603 −0.0818016 0.996649i \(-0.526067\pi\)
−0.0818016 + 0.996649i \(0.526067\pi\)
\(608\) 6.50852e7i 0.289582i
\(609\) 2.72928e8 1.20836
\(610\) 9.69637e8 4.27189
\(611\) 2.33454e8 1.02347
\(612\) −1.52273e8 −0.664305
\(613\) 4.36665e8i 1.89569i 0.318735 + 0.947844i \(0.396742\pi\)
−0.318735 + 0.947844i \(0.603258\pi\)
\(614\) 4.06721e8i 1.75708i
\(615\) −2.21056e8 −0.950337
\(616\) −1.71734e9 −7.34708
\(617\) 2.76981e8 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(618\) 3.56964e7 0.151237
\(619\) 1.28857e8 0.543296 0.271648 0.962397i \(-0.412431\pi\)
0.271648 + 0.962397i \(0.412431\pi\)
\(620\) 9.91218e7i 0.415905i
\(621\) 4.59034e7i 0.191677i
\(622\) 1.30052e8i 0.540439i
\(623\) 4.83843e8i 2.00097i
\(624\) 4.60791e8i 1.89649i
\(625\) −2.95132e8 −1.20886
\(626\) 2.31905e8 0.945337
\(627\) 1.55464e7i 0.0630705i
\(628\) 1.07251e9i 4.33033i
\(629\) 1.59543e8i 0.641101i
\(630\) 3.10615e8i 1.24223i
\(631\) 6.88588e7 0.274076 0.137038 0.990566i \(-0.456242\pi\)
0.137038 + 0.990566i \(0.456242\pi\)
\(632\) 8.96169e8i 3.55009i
\(633\) 2.82950e7i 0.111557i
\(634\) 1.36011e8i 0.533712i
\(635\) −2.48513e8 −0.970571
\(636\) 5.89865e8 2.29288
\(637\) 4.58894e8i 1.77539i
\(638\) 8.15636e8 3.14076
\(639\) 1.47028e8 0.563503
\(640\) 8.11238e8i 3.09463i
\(641\) −2.85061e8 −1.08234 −0.541170 0.840913i \(-0.682018\pi\)
−0.541170 + 0.840913i \(0.682018\pi\)
\(642\) 2.81032e8i 1.06206i
\(643\) −1.78023e8 −0.669642 −0.334821 0.942282i \(-0.608676\pi\)
−0.334821 + 0.942282i \(0.608676\pi\)
\(644\) 1.21753e9i 4.55849i
\(645\) 4.49647e7i 0.167568i
\(646\) 3.14911e7i 0.116813i
\(647\) −1.25538e8 −0.463514 −0.231757 0.972774i \(-0.574447\pi\)
−0.231757 + 0.972774i \(0.574447\pi\)
\(648\) 9.78058e7i 0.359451i
\(649\) −2.09311e8 2.98079e8i −0.765701 1.09043i
\(650\) −1.45990e8 −0.531599
\(651\) 3.69227e7i 0.133829i
\(652\) −6.68848e8 −2.41315
\(653\) 1.87020e8 0.671659 0.335830 0.941923i \(-0.390983\pi\)
0.335830 + 0.941923i \(0.390983\pi\)
\(654\) −1.28183e8 −0.458245
\(655\) 1.79426e8i 0.638502i
\(656\) 1.43821e9 5.09460
\(657\) 4.85104e7i 0.171056i
\(658\) 1.02385e9 3.59386
\(659\) 4.16762e8i 1.45623i −0.685453 0.728117i \(-0.740396\pi\)
0.685453 0.728117i \(-0.259604\pi\)
\(660\) 6.76374e8i 2.35264i
\(661\) 9.85540e7 0.341248 0.170624 0.985336i \(-0.445422\pi\)
0.170624 + 0.985336i \(0.445422\pi\)
\(662\) 8.62011e8i 2.97125i
\(663\) 1.16368e8i 0.399293i
\(664\) 1.23002e9 4.20154
\(665\) −4.68063e7 −0.159162
\(666\) 1.63285e8 0.552743
\(667\) 3.62905e8i 1.22297i
\(668\) −6.46833e8 −2.17002
\(669\) −1.21095e8 −0.404433
\(670\) 5.46178e8 1.81597
\(671\) 7.86497e8 2.60333
\(672\) 1.05479e9i 3.47581i
\(673\) 1.98818e8i 0.652244i −0.945328 0.326122i \(-0.894258\pi\)
0.945328 0.326122i \(-0.105742\pi\)
\(674\) 5.59955e8 1.82883
\(675\) 1.75891e7 0.0571916
\(676\) −1.09230e8 −0.353591
\(677\) 1.57413e8 0.507313 0.253656 0.967294i \(-0.418367\pi\)
0.253656 + 0.967294i \(0.418367\pi\)
\(678\) 4.64143e8 1.48923
\(679\) 2.90952e8i 0.929419i
\(680\) 8.59846e8i 2.73460i
\(681\) 2.87567e8i 0.910539i
\(682\) 1.10342e8i 0.347847i
\(683\) 2.84746e8i 0.893707i −0.894607 0.446854i \(-0.852545\pi\)
0.894607 0.446854i \(-0.147455\pi\)
\(684\) −2.34839e7 −0.0733842
\(685\) −5.12923e8 −1.59581
\(686\) 9.56247e8i 2.96209i
\(687\) 1.92827e8i 0.594698i
\(688\) 2.92543e8i 0.898307i
\(689\) 4.50778e8i 1.37818i
\(690\) 4.13017e8 1.25725
\(691\) 9.90109e7i 0.300088i 0.988679 + 0.150044i \(0.0479416\pi\)
−0.988679 + 0.150044i \(0.952058\pi\)
\(692\) 1.05467e9i 3.18272i
\(693\) 2.51948e8i 0.757027i
\(694\) −4.32088e8 −1.29269
\(695\) −6.18082e8 −1.84116
\(696\) 7.73237e8i 2.29343i
\(697\) 3.63203e8 1.07263
\(698\) 3.11944e8 0.917298
\(699\) 3.00393e8i 0.879546i
\(700\) −4.66528e8 −1.36014
\(701\) 4.25678e8i 1.23574i −0.786280 0.617870i \(-0.787996\pi\)
0.786280 0.617870i \(-0.212004\pi\)
\(702\) −1.19097e8 −0.344261
\(703\) 2.46052e7i 0.0708208i
\(704\) 1.51338e9i 4.33741i
\(705\) 2.53072e8i 0.722231i
\(706\) −8.25190e7 −0.234499
\(707\) 7.97813e8i 2.25758i
\(708\) 4.50270e8 3.16180e8i 1.26874 0.890912i
\(709\) −3.64346e8 −1.02229 −0.511146 0.859494i \(-0.670779\pi\)
−0.511146 + 0.859494i \(0.670779\pi\)
\(710\) 1.32289e9i 3.69614i
\(711\) 1.31475e8 0.365793
\(712\) −1.37079e9 −3.79778
\(713\) −4.90951e7 −0.135447
\(714\) 5.10352e8i 1.40209i
\(715\) −5.16889e8 −1.41410
\(716\) 7.49716e8i 2.04248i
\(717\) −1.43189e8 −0.388464
\(718\) 8.02648e8i 2.16846i
\(719\) 1.67040e8i 0.449401i 0.974428 + 0.224700i \(0.0721403\pi\)
−0.974428 + 0.224700i \(0.927860\pi\)
\(720\) −4.99513e8 −1.33829
\(721\) 8.71741e7i 0.232585i
\(722\) 7.17650e8i 1.90678i
\(723\) −5.96744e7 −0.157897
\(724\) 1.12051e9 2.95257
\(725\) 1.39057e8 0.364903
\(726\) 3.28827e8i 0.859327i
\(727\) 3.16596e8 0.823953 0.411977 0.911194i \(-0.364839\pi\)
0.411977 + 0.911194i \(0.364839\pi\)
\(728\) 1.98248e9 5.13824
\(729\) 1.43489e7 0.0370370
\(730\) 4.36474e8 1.12199
\(731\) 7.38785e7i 0.189132i
\(732\) 1.18806e9i 3.02905i
\(733\) −2.05904e8 −0.522822 −0.261411 0.965228i \(-0.584188\pi\)
−0.261411 + 0.965228i \(0.584188\pi\)
\(734\) 2.01028e7 0.0508357
\(735\) −4.97457e8 −1.25283
\(736\) −1.40252e9 −3.51784
\(737\) 4.43019e8 1.10667
\(738\) 3.71721e8i 0.924800i
\(739\) 4.82162e7i 0.119470i 0.998214 + 0.0597351i \(0.0190256\pi\)
−0.998214 + 0.0597351i \(0.980974\pi\)
\(740\) 1.07050e9i 2.64174i
\(741\) 1.79465e7i 0.0441089i
\(742\) 1.97697e9i 4.83936i
\(743\) −5.06474e8 −1.23478 −0.617392 0.786656i \(-0.711811\pi\)
−0.617392 + 0.786656i \(0.711811\pi\)
\(744\) 1.04606e8 0.254003
\(745\) 1.68066e8i 0.406453i
\(746\) 3.29275e8i 0.793126i
\(747\) 1.80454e8i 0.432918i
\(748\) 1.11131e9i 2.65539i
\(749\) −6.86308e8 −1.63333
\(750\) 3.74283e8i 0.887188i
\(751\) 4.53729e8i 1.07122i 0.844467 + 0.535608i \(0.179918\pi\)
−0.844467 + 0.535608i \(0.820082\pi\)
\(752\) 1.64650e9i 3.87176i
\(753\) −1.19663e8 −0.280268
\(754\) −9.41560e8 −2.19651
\(755\) 2.56988e8i 0.597135i
\(756\) −3.80586e8 −0.880821
\(757\) 1.29246e8 0.297940 0.148970 0.988842i \(-0.452404\pi\)
0.148970 + 0.988842i \(0.452404\pi\)
\(758\) 6.22219e8i 1.42868i
\(759\) 3.35009e8 0.766180
\(760\) 1.32608e8i 0.302084i
\(761\) −1.51435e8 −0.343615 −0.171808 0.985131i \(-0.554961\pi\)
−0.171808 + 0.985131i \(0.554961\pi\)
\(762\) 4.17891e8i 0.944491i
\(763\) 3.13036e8i 0.704726i
\(764\) 1.34310e9i 3.01181i
\(765\) −1.26146e8 −0.281767
\(766\) 1.13302e9i 2.52087i
\(767\) 2.41627e8 + 3.44099e8i 0.535499 + 0.762600i
\(768\) 5.12790e8 1.13202
\(769\) 6.47028e8i 1.42280i −0.702787 0.711401i \(-0.748061\pi\)
0.702787 0.711401i \(-0.251939\pi\)
\(770\) −2.26691e9 −4.96550
\(771\) −4.57450e8 −0.998116
\(772\) 6.72104e8 1.46078
\(773\) 5.11737e8i 1.10792i −0.832544 0.553959i \(-0.813116\pi\)
0.832544 0.553959i \(-0.186884\pi\)
\(774\) −7.56111e7 −0.163066
\(775\) 1.88121e7i 0.0404140i
\(776\) 8.24301e8 1.76401
\(777\) 3.98758e8i 0.850053i
\(778\) 3.66636e8i 0.778567i
\(779\) 5.60142e7 0.118491
\(780\) 7.80798e8i 1.64534i
\(781\) 1.07303e9i 2.25246i
\(782\) −6.78602e8 −1.41904
\(783\) 1.13440e8 0.236310
\(784\) 3.23649e9 6.71624
\(785\) 8.88491e8i