Properties

Label 177.7.c.a.58.11
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 58.11
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.50

$q$-expansion

\(f(q)\) \(=\) \(q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +1905.18i q^{10} -2167.83i q^{11} -996.058 q^{12} -1020.13i q^{13} -1050.96i q^{14} -2626.08 q^{15} -4102.57 q^{16} -2220.60 q^{17} -2748.13i q^{18} -5813.42 q^{19} +10764.3 q^{20} +1448.63 q^{21} -24516.3 q^{22} +10077.3i q^{23} -18.1326i q^{24} +12754.9 q^{25} -11536.9 q^{26} +3788.00 q^{27} -5937.96 q^{28} +45564.7 q^{29} +29698.8i q^{30} +32140.9i q^{31} +46322.2i q^{32} -33793.1i q^{33} +25113.1i q^{34} -15655.3 q^{35} -15527.0 q^{36} +30843.3i q^{37} +65745.0i q^{38} -15902.3i q^{39} +195.958i q^{40} -118262. q^{41} -16382.8i q^{42} +58251.0i q^{43} +138518. i q^{44} -40936.6 q^{45} +113966. q^{46} +88089.1i q^{47} -63952.8 q^{48} -109013. q^{49} -144247. i q^{50} -34615.8 q^{51} +65183.7i q^{52} -11175.7 q^{53} -42839.1i q^{54} +365199. i q^{55} -108.097i q^{56} -90622.3 q^{57} -515299. i q^{58} +(98432.3 - 180254. i) q^{59} +167799. q^{60} -318000. i q^{61} +363487. q^{62} +22582.0 q^{63} +261301. q^{64} +171855. i q^{65} -382171. q^{66} +231159. i q^{67} +141890. q^{68} +157090. i q^{69} +177048. i q^{70} +217430. q^{71} -282.659i q^{72} +494177. i q^{73} +348812. q^{74} +198829. q^{75} +371461. q^{76} -201456. i q^{77} -179842. q^{78} -939691. q^{79} +691133. q^{80} +59049.0 q^{81} +1.33745e6i q^{82} -512932. i q^{83} -92563.6 q^{84} +374090. q^{85} +658769. q^{86} +710284. q^{87} -2521.63 q^{88} -336771. i q^{89} +462958. i q^{90} -94801.0i q^{91} -643913. i q^{92} +501028. i q^{93} +996214. q^{94} +979349. q^{95} +722092. i q^{96} +1.00179e6i q^{97} +1.23285e6i q^{98} -526782. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.3092i 1.41365i −0.707391 0.706823i \(-0.750128\pi\)
0.707391 0.706823i \(-0.249872\pi\)
\(3\) 15.5885 0.577350
\(4\) −63.8971 −0.998393
\(5\) −168.463 −1.34771 −0.673853 0.738865i \(-0.735362\pi\)
−0.673853 + 0.738865i \(0.735362\pi\)
\(6\) 176.292i 0.816168i
\(7\) 92.9299 0.270933 0.135466 0.990782i \(-0.456747\pi\)
0.135466 + 0.990782i \(0.456747\pi\)
\(8\) 1.16321i 0.00227189i
\(9\) 243.000 0.333333
\(10\) 1905.18i 1.90518i
\(11\) 2167.83i 1.62872i −0.580360 0.814360i \(-0.697088\pi\)
0.580360 0.814360i \(-0.302912\pi\)
\(12\) −996.058 −0.576422
\(13\) 1020.13i 0.464331i −0.972676 0.232165i \(-0.925419\pi\)
0.972676 0.232165i \(-0.0745810\pi\)
\(14\) 1050.96i 0.383003i
\(15\) −2626.08 −0.778099
\(16\) −4102.57 −1.00160
\(17\) −2220.60 −0.451985 −0.225992 0.974129i \(-0.572562\pi\)
−0.225992 + 0.974129i \(0.572562\pi\)
\(18\) 2748.13i 0.471215i
\(19\) −5813.42 −0.847561 −0.423781 0.905765i \(-0.639297\pi\)
−0.423781 + 0.905765i \(0.639297\pi\)
\(20\) 10764.3 1.34554
\(21\) 1448.63 0.156423
\(22\) −24516.3 −2.30243
\(23\) 10077.3i 0.828252i 0.910220 + 0.414126i \(0.135913\pi\)
−0.910220 + 0.414126i \(0.864087\pi\)
\(24\) 18.1326i 0.00131168i
\(25\) 12754.9 0.816313
\(26\) −11536.9 −0.656399
\(27\) 3788.00 0.192450
\(28\) −5937.96 −0.270497
\(29\) 45564.7 1.86825 0.934124 0.356948i \(-0.116183\pi\)
0.934124 + 0.356948i \(0.116183\pi\)
\(30\) 29698.8i 1.09996i
\(31\) 32140.9i 1.07888i 0.842024 + 0.539440i \(0.181364\pi\)
−0.842024 + 0.539440i \(0.818636\pi\)
\(32\) 46322.2i 1.41364i
\(33\) 33793.1i 0.940342i
\(34\) 25113.1i 0.638946i
\(35\) −15655.3 −0.365138
\(36\) −15527.0 −0.332798
\(37\) 30843.3i 0.608913i 0.952526 + 0.304457i \(0.0984749\pi\)
−0.952526 + 0.304457i \(0.901525\pi\)
\(38\) 65745.0i 1.19815i
\(39\) 15902.3i 0.268081i
\(40\) 195.958i 0.00306184i
\(41\) −118262. −1.71591 −0.857954 0.513726i \(-0.828265\pi\)
−0.857954 + 0.513726i \(0.828265\pi\)
\(42\) 16382.8i 0.221127i
\(43\) 58251.0i 0.732652i 0.930487 + 0.366326i \(0.119384\pi\)
−0.930487 + 0.366326i \(0.880616\pi\)
\(44\) 138518.i 1.62610i
\(45\) −40936.6 −0.449236
\(46\) 113966. 1.17085
\(47\) 88089.1i 0.848455i 0.905556 + 0.424227i \(0.139454\pi\)
−0.905556 + 0.424227i \(0.860546\pi\)
\(48\) −63952.8 −0.578277
\(49\) −109013. −0.926595
\(50\) 144247.i 1.15398i
\(51\) −34615.8 −0.260954
\(52\) 65183.7i 0.463584i
\(53\) −11175.7 −0.0750667 −0.0375334 0.999295i \(-0.511950\pi\)
−0.0375334 + 0.999295i \(0.511950\pi\)
\(54\) 42839.1i 0.272056i
\(55\) 365199.i 2.19504i
\(56\) 108.097i 0.000615529i
\(57\) −90622.3 −0.489340
\(58\) 515299.i 2.64104i
\(59\) 98432.3 180254.i 0.479271 0.877667i
\(60\) 167799. 0.776848
\(61\) 318000.i 1.40100i −0.713653 0.700499i \(-0.752961\pi\)
0.713653 0.700499i \(-0.247039\pi\)
\(62\) 363487. 1.52515
\(63\) 22582.0 0.0903109
\(64\) 261301. 0.996783
\(65\) 171855.i 0.625781i
\(66\) −382171. −1.32931
\(67\) 231159.i 0.768577i 0.923213 + 0.384288i \(0.125553\pi\)
−0.923213 + 0.384288i \(0.874447\pi\)
\(68\) 141890. 0.451259
\(69\) 157090.i 0.478191i
\(70\) 177048.i 0.516175i
\(71\) 217430. 0.607499 0.303749 0.952752i \(-0.401761\pi\)
0.303749 + 0.952752i \(0.401761\pi\)
\(72\) 282.659i 0.000757296i
\(73\) 494177.i 1.27032i 0.772379 + 0.635162i \(0.219067\pi\)
−0.772379 + 0.635162i \(0.780933\pi\)
\(74\) 348812. 0.860787
\(75\) 198829. 0.471298
\(76\) 371461. 0.846199
\(77\) 201456.i 0.441274i
\(78\) −179842. −0.378972
\(79\) −939691. −1.90592 −0.952958 0.303101i \(-0.901978\pi\)
−0.952958 + 0.303101i \(0.901978\pi\)
\(80\) 691133. 1.34987
\(81\) 59049.0 0.111111
\(82\) 1.33745e6i 2.42569i
\(83\) 512932.i 0.897068i −0.893766 0.448534i \(-0.851946\pi\)
0.893766 0.448534i \(-0.148054\pi\)
\(84\) −92563.6 −0.156172
\(85\) 374090. 0.609143
\(86\) 658769. 1.03571
\(87\) 710284. 1.07863
\(88\) −2521.63 −0.00370027
\(89\) 336771.i 0.477710i −0.971055 0.238855i \(-0.923228\pi\)
0.971055 0.238855i \(-0.0767721\pi\)
\(90\) 462958.i 0.635060i
\(91\) 94801.0i 0.125802i
\(92\) 643913.i 0.826921i
\(93\) 501028.i 0.622892i
\(94\) 996214. 1.19941
\(95\) 979349. 1.14226
\(96\) 722092.i 0.816166i
\(97\) 1.00179e6i 1.09764i 0.835939 + 0.548822i \(0.184923\pi\)
−0.835939 + 0.548822i \(0.815077\pi\)
\(98\) 1.23285e6i 1.30988i
\(99\) 526782.i 0.542907i
\(100\) −815001. −0.815001
\(101\) 455641.i 0.442240i 0.975247 + 0.221120i \(0.0709713\pi\)
−0.975247 + 0.221120i \(0.929029\pi\)
\(102\) 391475.i 0.368896i
\(103\) 1.35184e6i 1.23712i −0.785737 0.618561i \(-0.787716\pi\)
0.785737 0.618561i \(-0.212284\pi\)
\(104\) −1186.63 −0.00105491
\(105\) −244042. −0.210812
\(106\) 126388.i 0.106118i
\(107\) −420968. −0.343635 −0.171818 0.985129i \(-0.554964\pi\)
−0.171818 + 0.985129i \(0.554964\pi\)
\(108\) −242042. −0.192141
\(109\) 342130.i 0.264187i −0.991237 0.132093i \(-0.957830\pi\)
0.991237 0.132093i \(-0.0421699\pi\)
\(110\) 4.13010e6 3.10300
\(111\) 480799.i 0.351556i
\(112\) −381252. −0.271367
\(113\) 350125.i 0.242654i −0.992613 0.121327i \(-0.961285\pi\)
0.992613 0.121327i \(-0.0387150\pi\)
\(114\) 1.02486e6i 0.691753i
\(115\) 1.69766e6i 1.11624i
\(116\) −2.91146e6 −1.86525
\(117\) 247893.i 0.154777i
\(118\) −2.03853e6 1.11319e6i −1.24071 0.677520i
\(119\) −206360. −0.122458
\(120\) 3054.68i 0.00176775i
\(121\) −2.92791e6 −1.65273
\(122\) −3.59631e6 −1.98052
\(123\) −1.84352e6 −0.990680
\(124\) 2.05371e6i 1.07715i
\(125\) 483509. 0.247556
\(126\) 255383.i 0.127668i
\(127\) 2.73008e6 1.33280 0.666399 0.745596i \(-0.267835\pi\)
0.666399 + 0.745596i \(0.267835\pi\)
\(128\) 9528.98i 0.00454377i
\(129\) 908042.i 0.422997i
\(130\) 1.94354e6 0.884633
\(131\) 1.24107e6i 0.552055i −0.961150 0.276028i \(-0.910982\pi\)
0.961150 0.276028i \(-0.0890181\pi\)
\(132\) 2.15928e6i 0.938830i
\(133\) −540241. −0.229632
\(134\) 2.61422e6 1.08649
\(135\) −638138. −0.259366
\(136\) 2583.02i 0.00102686i
\(137\) −935575. −0.363846 −0.181923 0.983313i \(-0.558232\pi\)
−0.181923 + 0.983313i \(0.558232\pi\)
\(138\) 1.77656e6 0.675993
\(139\) −4.06182e6 −1.51243 −0.756217 0.654321i \(-0.772954\pi\)
−0.756217 + 0.654321i \(0.772954\pi\)
\(140\) 1.00033e6 0.364551
\(141\) 1.37317e6i 0.489856i
\(142\) 2.45896e6i 0.858788i
\(143\) −2.21147e6 −0.756264
\(144\) −996925. −0.333868
\(145\) −7.67598e6 −2.51785
\(146\) 5.58873e6 1.79579
\(147\) −1.69934e6 −0.534970
\(148\) 1.97080e6i 0.607935i
\(149\) 2.93990e6i 0.888738i −0.895844 0.444369i \(-0.853428\pi\)
0.895844 0.444369i \(-0.146572\pi\)
\(150\) 2.24859e6i 0.666249i
\(151\) 4.14191e6i 1.20301i 0.798869 + 0.601506i \(0.205432\pi\)
−0.798869 + 0.601506i \(0.794568\pi\)
\(152\) 6762.21i 0.00192556i
\(153\) −539606. −0.150662
\(154\) −2.27830e6 −0.623804
\(155\) 5.41457e6i 1.45401i
\(156\) 1.01611e6i 0.267651i
\(157\) 2.10154e6i 0.543050i −0.962431 0.271525i \(-0.912472\pi\)
0.962431 0.271525i \(-0.0875279\pi\)
\(158\) 1.06271e7i 2.69429i
\(159\) −174212. −0.0433398
\(160\) 7.80359e6i 1.90517i
\(161\) 936487.i 0.224401i
\(162\) 667795.i 0.157072i
\(163\) −6.16709e6 −1.42403 −0.712013 0.702167i \(-0.752216\pi\)
−0.712013 + 0.702167i \(0.752216\pi\)
\(164\) 7.55661e6 1.71315
\(165\) 5.69289e6i 1.26730i
\(166\) −5.80083e6 −1.26814
\(167\) −4.27307e6 −0.917466 −0.458733 0.888574i \(-0.651697\pi\)
−0.458733 + 0.888574i \(0.651697\pi\)
\(168\) 1685.06i 0.000355376i
\(169\) 3.78614e6 0.784397
\(170\) 4.23064e6i 0.861112i
\(171\) −1.41266e6 −0.282520
\(172\) 3.72207e6i 0.731474i
\(173\) 3.88594e6i 0.750512i 0.926921 + 0.375256i \(0.122445\pi\)
−0.926921 + 0.375256i \(0.877555\pi\)
\(174\) 8.03271e6i 1.52481i
\(175\) 1.18531e6 0.221166
\(176\) 8.89366e6i 1.63133i
\(177\) 1.53441e6 2.80989e6i 0.276707 0.506721i
\(178\) −3.80860e6 −0.675313
\(179\) 5.75429e6i 1.00330i 0.865070 + 0.501652i \(0.167274\pi\)
−0.865070 + 0.501652i \(0.832726\pi\)
\(180\) 2.61573e6 0.448514
\(181\) −4.25879e6 −0.718209 −0.359105 0.933297i \(-0.616918\pi\)
−0.359105 + 0.933297i \(0.616918\pi\)
\(182\) −1.07212e6 −0.177840
\(183\) 4.95713e6i 0.808867i
\(184\) 11722.0 0.00188170
\(185\) 5.19596e6i 0.820636i
\(186\) 5.66620e6 0.880549
\(187\) 4.81388e6i 0.736157i
\(188\) 5.62864e6i 0.847091i
\(189\) 352018. 0.0521410
\(190\) 1.10756e7i 1.61476i
\(191\) 1.21863e7i 1.74893i −0.485090 0.874464i \(-0.661213\pi\)
0.485090 0.874464i \(-0.338787\pi\)
\(192\) 4.07328e6 0.575493
\(193\) 9.12282e6 1.26899 0.634494 0.772928i \(-0.281209\pi\)
0.634494 + 0.772928i \(0.281209\pi\)
\(194\) 1.13294e7 1.55168
\(195\) 2.67896e6i 0.361295i
\(196\) 6.96562e6 0.925106
\(197\) −6.85796e6 −0.897008 −0.448504 0.893781i \(-0.648043\pi\)
−0.448504 + 0.893781i \(0.648043\pi\)
\(198\) −5.95746e6 −0.767477
\(199\) 8.47472e6 1.07539 0.537695 0.843139i \(-0.319295\pi\)
0.537695 + 0.843139i \(0.319295\pi\)
\(200\) 14836.6i 0.00185457i
\(201\) 3.60342e6i 0.443738i
\(202\) 5.15291e6 0.625171
\(203\) 4.23433e6 0.506170
\(204\) 2.21185e6 0.260534
\(205\) 1.99228e7 2.31254
\(206\) −1.52881e7 −1.74885
\(207\) 2.44879e6i 0.276084i
\(208\) 4.18517e6i 0.465076i
\(209\) 1.26025e7i 1.38044i
\(210\) 2.75991e6i 0.298014i
\(211\) 1.57833e7i 1.68016i −0.542459 0.840082i \(-0.682507\pi\)
0.542459 0.840082i \(-0.317493\pi\)
\(212\) 714096. 0.0749461
\(213\) 3.38941e6 0.350740
\(214\) 4.76079e6i 0.485778i
\(215\) 9.81315e6i 0.987400i
\(216\) 4406.22i 0.000437225i
\(217\) 2.98686e6i 0.292304i
\(218\) −3.86920e6 −0.373467
\(219\) 7.70346e6i 0.733422i
\(220\) 2.33352e7i 2.19151i
\(221\) 2.26531e6i 0.209870i
\(222\) 5.43744e6 0.496976
\(223\) −1.74562e7 −1.57411 −0.787055 0.616882i \(-0.788395\pi\)
−0.787055 + 0.616882i \(0.788395\pi\)
\(224\) 4.30472e6i 0.383002i
\(225\) 3.09944e6 0.272104
\(226\) −3.95962e6 −0.343027
\(227\) 6.98819e6i 0.597430i −0.954342 0.298715i \(-0.903442\pi\)
0.954342 0.298715i \(-0.0965581\pi\)
\(228\) 5.79051e6 0.488553
\(229\) 4.63019e6i 0.385560i −0.981242 0.192780i \(-0.938250\pi\)
0.981242 0.192780i \(-0.0617504\pi\)
\(230\) −1.91991e7 −1.57797
\(231\) 3.14039e6i 0.254769i
\(232\) 53001.2i 0.00424445i
\(233\) 2.02015e7i 1.59704i 0.601968 + 0.798520i \(0.294383\pi\)
−0.601968 + 0.798520i \(0.705617\pi\)
\(234\) −2.80346e6 −0.218800
\(235\) 1.48398e7i 1.14347i
\(236\) −6.28954e6 + 1.15177e7i −0.478501 + 0.876256i
\(237\) −1.46483e7 −1.10038
\(238\) 2.33376e6i 0.173112i
\(239\) −2.80006e6 −0.205104 −0.102552 0.994728i \(-0.532701\pi\)
−0.102552 + 0.994728i \(0.532701\pi\)
\(240\) 1.07737e7 0.779347
\(241\) −9.86332e6 −0.704648 −0.352324 0.935878i \(-0.614608\pi\)
−0.352324 + 0.935878i \(0.614608\pi\)
\(242\) 3.31122e7i 2.33637i
\(243\) 920483. 0.0641500
\(244\) 2.03193e7i 1.39875i
\(245\) 1.83647e7 1.24878
\(246\) 2.08487e7i 1.40047i
\(247\) 5.93047e6i 0.393549i
\(248\) 37386.6 0.00245110
\(249\) 7.99582e6i 0.517923i
\(250\) 5.46808e6i 0.349957i
\(251\) 1.88216e6 0.119024 0.0595121 0.998228i \(-0.481046\pi\)
0.0595121 + 0.998228i \(0.481046\pi\)
\(252\) −1.44292e6 −0.0901658
\(253\) 2.18459e7 1.34899
\(254\) 3.08749e7i 1.88410i
\(255\) 5.83149e6 0.351689
\(256\) 1.68310e7 1.00321
\(257\) −1.37476e7 −0.809891 −0.404945 0.914341i \(-0.632709\pi\)
−0.404945 + 0.914341i \(0.632709\pi\)
\(258\) 1.02692e7 0.597967
\(259\) 2.86626e6i 0.164975i
\(260\) 1.09811e7i 0.624776i
\(261\) 1.10722e7 0.622750
\(262\) −1.40355e7 −0.780410
\(263\) −1.68338e7 −0.925370 −0.462685 0.886523i \(-0.653114\pi\)
−0.462685 + 0.886523i \(0.653114\pi\)
\(264\) −39308.3 −0.00213635
\(265\) 1.88270e6 0.101168
\(266\) 6.10967e6i 0.324618i
\(267\) 5.24974e6i 0.275806i
\(268\) 1.47704e7i 0.767342i
\(269\) 1.72737e7i 0.887418i −0.896171 0.443709i \(-0.853662\pi\)
0.896171 0.443709i \(-0.146338\pi\)
\(270\) 7.21681e6i 0.366652i
\(271\) −3.26972e7 −1.64287 −0.821435 0.570302i \(-0.806826\pi\)
−0.821435 + 0.570302i \(0.806826\pi\)
\(272\) 9.11018e6 0.452710
\(273\) 1.47780e6i 0.0726320i
\(274\) 1.05806e7i 0.514349i
\(275\) 2.76504e7i 1.32954i
\(276\) 1.00376e7i 0.477423i
\(277\) −533431. −0.0250980 −0.0125490 0.999921i \(-0.503995\pi\)
−0.0125490 + 0.999921i \(0.503995\pi\)
\(278\) 4.59358e7i 2.13804i
\(279\) 7.81025e6i 0.359627i
\(280\) 18210.3i 0.000829552i
\(281\) 2.06979e7 0.932839 0.466419 0.884564i \(-0.345544\pi\)
0.466419 + 0.884564i \(0.345544\pi\)
\(282\) 1.55294e7 0.692482
\(283\) 1.73488e7i 0.765437i 0.923865 + 0.382718i \(0.125012\pi\)
−0.923865 + 0.382718i \(0.874988\pi\)
\(284\) −1.38932e7 −0.606522
\(285\) 1.52665e7 0.659486
\(286\) 2.50099e7i 1.06909i
\(287\) −1.09901e7 −0.464896
\(288\) 1.12563e7i 0.471214i
\(289\) −1.92065e7 −0.795710
\(290\) 8.68089e7i 3.55935i
\(291\) 1.56164e7i 0.633725i
\(292\) 3.15765e7i 1.26828i
\(293\) −3.04473e7 −1.21045 −0.605224 0.796055i \(-0.706917\pi\)
−0.605224 + 0.796055i \(0.706917\pi\)
\(294\) 1.92182e7i 0.756258i
\(295\) −1.65822e7 + 3.03662e7i −0.645917 + 1.18284i
\(296\) 35877.1 0.00138338
\(297\) 8.21171e6i 0.313447i
\(298\) −3.32478e7 −1.25636
\(299\) 1.02802e7 0.384583
\(300\) −1.27046e7 −0.470541
\(301\) 5.41326e6i 0.198499i
\(302\) 4.68415e7 1.70063
\(303\) 7.10273e6i 0.255328i
\(304\) 2.38500e7 0.848921
\(305\) 5.35713e7i 1.88814i
\(306\) 6.10249e6i 0.212982i
\(307\) 2.60536e7 0.900434 0.450217 0.892919i \(-0.351347\pi\)
0.450217 + 0.892919i \(0.351347\pi\)
\(308\) 1.28725e7i 0.440564i
\(309\) 2.10731e7i 0.714253i
\(310\) −6.12342e7 −2.05546
\(311\) 2.88151e6 0.0957943 0.0478971 0.998852i \(-0.484748\pi\)
0.0478971 + 0.998852i \(0.484748\pi\)
\(312\) −18497.7 −0.000609051
\(313\) 2.54062e7i 0.828527i −0.910157 0.414263i \(-0.864039\pi\)
0.910157 0.414263i \(-0.135961\pi\)
\(314\) −2.37667e7 −0.767680
\(315\) −3.80423e6 −0.121713
\(316\) 6.00436e7 1.90285
\(317\) 1.01318e7 0.318061 0.159031 0.987274i \(-0.449163\pi\)
0.159031 + 0.987274i \(0.449163\pi\)
\(318\) 1.97019e6i 0.0612671i
\(319\) 9.87764e7i 3.04285i
\(320\) −4.40196e7 −1.34337
\(321\) −6.56224e6 −0.198398
\(322\) 1.05909e7 0.317223
\(323\) 1.29093e7 0.383085
\(324\) −3.77306e6 −0.110933
\(325\) 1.30117e7i 0.379039i
\(326\) 6.97447e7i 2.01307i
\(327\) 5.33328e6i 0.152528i
\(328\) 137563.i 0.00389835i
\(329\) 8.18612e6i 0.229874i
\(330\) 6.43818e7 1.79152
\(331\) 1.79208e7 0.494165 0.247083 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(332\) 3.27749e7i 0.895627i
\(333\) 7.49492e6i 0.202971i
\(334\) 4.83248e7i 1.29697i
\(335\) 3.89419e7i 1.03582i
\(336\) −5.94313e6 −0.156674
\(337\) 4.02550e7i 1.05179i −0.850549 0.525896i \(-0.823730\pi\)
0.850549 0.525896i \(-0.176270\pi\)
\(338\) 4.28180e7i 1.10886i
\(339\) 5.45791e6i 0.140096i
\(340\) −2.39033e7 −0.608164
\(341\) 6.96760e7 1.75719
\(342\) 1.59760e7i 0.399384i
\(343\) −2.10637e7 −0.521978
\(344\) 67757.9 0.00166450
\(345\) 2.64639e7i 0.644462i
\(346\) 4.39467e7 1.06096
\(347\) 7.99654e7i 1.91388i −0.290293 0.956938i \(-0.593753\pi\)
0.290293 0.956938i \(-0.406247\pi\)
\(348\) −4.53851e7 −1.07690
\(349\) 2.89196e7i 0.680324i 0.940367 + 0.340162i \(0.110482\pi\)
−0.940367 + 0.340162i \(0.889518\pi\)
\(350\) 1.34049e7i 0.312650i
\(351\) 3.86426e6i 0.0893605i
\(352\) 1.00418e8 2.30243
\(353\) 5.02325e6i 0.114199i 0.998369 + 0.0570993i \(0.0181852\pi\)
−0.998369 + 0.0570993i \(0.981815\pi\)
\(354\) −3.17775e7 1.73529e7i −0.716324 0.391166i
\(355\) −3.66291e7 −0.818730
\(356\) 2.15187e7i 0.476943i
\(357\) −3.21684e6 −0.0707009
\(358\) 6.50762e7 1.41832
\(359\) 6.63944e7 1.43499 0.717494 0.696565i \(-0.245289\pi\)
0.717494 + 0.696565i \(0.245289\pi\)
\(360\) 47617.7i 0.00102061i
\(361\) −1.32500e7 −0.281640
\(362\) 4.81634e7i 1.01529i
\(363\) −4.56416e7 −0.954203
\(364\) 6.05751e6i 0.125600i
\(365\) 8.32508e7i 1.71202i
\(366\) −5.60610e7 −1.14345
\(367\) 5.35677e7i 1.08369i −0.840479 0.541845i \(-0.817726\pi\)
0.840479 0.541845i \(-0.182274\pi\)
\(368\) 4.13430e7i 0.829581i
\(369\) −2.87377e7 −0.571969
\(370\) −5.87620e7 −1.16009
\(371\) −1.03856e6 −0.0203380
\(372\) 3.20142e7i 0.621891i
\(373\) −1.04211e7 −0.200811 −0.100406 0.994947i \(-0.532014\pi\)
−0.100406 + 0.994947i \(0.532014\pi\)
\(374\) 5.44409e7 1.04066
\(375\) 7.53715e6 0.142927
\(376\) 102466. 0.00192759
\(377\) 4.64821e7i 0.867485i
\(378\) 3.98103e6i 0.0737089i
\(379\) −2.74387e6 −0.0504017 −0.0252009 0.999682i \(-0.508023\pi\)
−0.0252009 + 0.999682i \(0.508023\pi\)
\(380\) −6.25776e7 −1.14043
\(381\) 4.25577e7 0.769491
\(382\) −1.37817e8 −2.47236
\(383\) −1.28382e7 −0.228511 −0.114256 0.993451i \(-0.536448\pi\)
−0.114256 + 0.993451i \(0.536448\pi\)
\(384\) 148542.i 0.00262335i
\(385\) 3.39379e7i 0.594707i
\(386\) 1.03171e8i 1.79390i
\(387\) 1.41550e7i 0.244217i
\(388\) 6.40115e7i 1.09588i
\(389\) −2.90971e7 −0.494312 −0.247156 0.968976i \(-0.579496\pi\)
−0.247156 + 0.968976i \(0.579496\pi\)
\(390\) 3.02968e7 0.510743
\(391\) 2.23778e7i 0.374357i
\(392\) 126805.i 0.00210512i
\(393\) 1.93464e7i 0.318729i
\(394\) 7.75578e7i 1.26805i
\(395\) 1.58304e8 2.56862
\(396\) 3.36598e7i 0.542034i
\(397\) 7.44147e7i 1.18929i −0.803989 0.594645i \(-0.797293\pi\)
0.803989 0.594645i \(-0.202707\pi\)
\(398\) 9.58420e7i 1.52022i
\(399\) −8.42153e6 −0.132578
\(400\) −5.23278e7 −0.817623
\(401\) 9.10030e7i 1.41131i 0.708555 + 0.705656i \(0.249347\pi\)
−0.708555 + 0.705656i \(0.750653\pi\)
\(402\) 4.07516e7 0.627288
\(403\) 3.27881e7 0.500957
\(404\) 2.91141e7i 0.441530i
\(405\) −9.94759e6 −0.149745
\(406\) 4.78867e7i 0.715545i
\(407\) 6.68629e7 0.991749
\(408\) 40265.3i 0.000592857i
\(409\) 3.42520e7i 0.500629i 0.968165 + 0.250315i \(0.0805341\pi\)
−0.968165 + 0.250315i \(0.919466\pi\)
\(410\) 2.25311e8i 3.26911i
\(411\) −1.45842e7 −0.210066
\(412\) 8.63785e7i 1.23513i
\(413\) 9.14730e6 1.67510e7i 0.129850 0.237789i
\(414\) 2.76938e7 0.390285
\(415\) 8.64102e7i 1.20899i
\(416\) 4.72549e7 0.656397
\(417\) −6.33175e7 −0.873204
\(418\) 1.42524e8 1.95145
\(419\) 5.34154e7i 0.726147i −0.931761 0.363073i \(-0.881727\pi\)
0.931761 0.363073i \(-0.118273\pi\)
\(420\) 1.55936e7 0.210474
\(421\) 1.18306e8i 1.58549i 0.609557 + 0.792743i \(0.291348\pi\)
−0.609557 + 0.792743i \(0.708652\pi\)
\(422\) −1.78496e8 −2.37516
\(423\) 2.14057e7i 0.282818i
\(424\) 12999.7i 0.000170543i
\(425\) −2.83235e7 −0.368961
\(426\) 3.83313e7i 0.495821i
\(427\) 2.95517e7i 0.379576i
\(428\) 2.68986e7 0.343083
\(429\) −3.44735e7 −0.436629
\(430\) −1.10978e8 −1.39583
\(431\) 5.76869e6i 0.0720519i −0.999351 0.0360260i \(-0.988530\pi\)
0.999351 0.0360260i \(-0.0114699\pi\)
\(432\) −1.55405e7 −0.192759
\(433\) 2.45928e7 0.302931 0.151465 0.988463i \(-0.451601\pi\)
0.151465 + 0.988463i \(0.451601\pi\)
\(434\) 3.37788e7 0.413214
\(435\) −1.19657e8 −1.45368
\(436\) 2.18611e7i 0.263762i
\(437\) 5.85839e7i 0.701994i
\(438\) 8.71197e7 1.03680
\(439\) −1.40058e8 −1.65545 −0.827725 0.561134i \(-0.810365\pi\)
−0.827725 + 0.561134i \(0.810365\pi\)
\(440\) 424802. 0.00498688
\(441\) −2.64902e7 −0.308865
\(442\) 2.56188e7 0.296682
\(443\) 4.00366e7i 0.460517i −0.973129 0.230259i \(-0.926043\pi\)
0.973129 0.230259i \(-0.0739572\pi\)
\(444\) 3.07217e7i 0.350991i
\(445\) 5.67336e7i 0.643813i
\(446\) 1.97415e8i 2.22523i
\(447\) 4.58285e7i 0.513113i
\(448\) 2.42827e7 0.270061
\(449\) −3.40721e7 −0.376409 −0.188205 0.982130i \(-0.560267\pi\)
−0.188205 + 0.982130i \(0.560267\pi\)
\(450\) 3.50520e7i 0.384659i
\(451\) 2.56372e8i 2.79473i
\(452\) 2.23720e7i 0.242264i
\(453\) 6.45660e7i 0.694559i
\(454\) −7.90306e7 −0.844555
\(455\) 1.59705e7i 0.169545i
\(456\) 105412.i 0.00111173i
\(457\) 1.04927e6i 0.0109936i −0.999985 0.00549681i \(-0.998250\pi\)
0.999985 0.00549681i \(-0.00174970\pi\)
\(458\) −5.23636e7 −0.545045
\(459\) −8.41163e6 −0.0869845
\(460\) 1.08476e8i 1.11445i
\(461\) −1.56607e8 −1.59848 −0.799242 0.601009i \(-0.794765\pi\)
−0.799242 + 0.601009i \(0.794765\pi\)
\(462\) −3.55151e7 −0.360154
\(463\) 6.06662e7i 0.611228i 0.952155 + 0.305614i \(0.0988618\pi\)
−0.952155 + 0.305614i \(0.901138\pi\)
\(464\) −1.86933e8 −1.87125
\(465\) 8.44048e7i 0.839476i
\(466\) 2.28462e8 2.25765
\(467\) 3.79040e7i 0.372164i 0.982534 + 0.186082i \(0.0595790\pi\)
−0.982534 + 0.186082i \(0.940421\pi\)
\(468\) 1.58396e7i 0.154528i
\(469\) 2.14816e7i 0.208233i
\(470\) −1.67826e8 −1.61646
\(471\) 3.27598e7i 0.313530i
\(472\) −209673. 114497.i −0.00199396 0.00108885i
\(473\) 1.26278e8 1.19328
\(474\) 1.65660e8i 1.55555i
\(475\) −7.41496e7 −0.691875
\(476\) 1.31858e7 0.122261
\(477\) −2.71570e6 −0.0250222
\(478\) 3.16664e7i 0.289944i
\(479\) 9.92174e7 0.902779 0.451389 0.892327i \(-0.350929\pi\)
0.451389 + 0.892327i \(0.350929\pi\)
\(480\) 1.21646e8i 1.09995i
\(481\) 3.14643e7 0.282737
\(482\) 1.11546e8i 0.996122i
\(483\) 1.45984e7i 0.129558i
\(484\) 1.87085e8 1.65007
\(485\) 1.68765e8i 1.47930i
\(486\) 1.04099e7i 0.0906854i
\(487\) 6.99901e7 0.605968 0.302984 0.952996i \(-0.402017\pi\)
0.302984 + 0.952996i \(0.402017\pi\)
\(488\) −369900. −0.00318291
\(489\) −9.61355e7 −0.822161
\(490\) 2.07689e8i 1.76533i
\(491\) 3.01568e7 0.254766 0.127383 0.991854i \(-0.459342\pi\)
0.127383 + 0.991854i \(0.459342\pi\)
\(492\) 1.17796e8 0.989088
\(493\) −1.01181e8 −0.844420
\(494\) 6.70687e7 0.556338
\(495\) 8.87434e7i 0.731679i
\(496\) 1.31861e8i 1.08061i
\(497\) 2.02058e7 0.164591
\(498\) −9.04260e7 −0.732159
\(499\) 1.43575e7 0.115552 0.0577759 0.998330i \(-0.481599\pi\)
0.0577759 + 0.998330i \(0.481599\pi\)
\(500\) −3.08948e7 −0.247159
\(501\) −6.66105e7 −0.529699
\(502\) 2.12856e7i 0.168258i
\(503\) 1.00141e8i 0.786883i −0.919350 0.393441i \(-0.871284\pi\)
0.919350 0.393441i \(-0.128716\pi\)
\(504\) 26267.5i 0.000205176i
\(505\) 7.67587e7i 0.596010i
\(506\) 2.47059e8i 1.90699i
\(507\) 5.90200e7 0.452872
\(508\) −1.74444e8 −1.33066
\(509\) 1.08822e8i 0.825211i −0.910910 0.412606i \(-0.864619\pi\)
0.910910 0.412606i \(-0.135381\pi\)
\(510\) 6.59492e7i 0.497163i
\(511\) 4.59239e7i 0.344172i
\(512\) 1.89735e8i 1.41363i
\(513\) −2.20212e7 −0.163113
\(514\) 1.55473e8i 1.14490i
\(515\) 2.27735e8i 1.66728i
\(516\) 5.80213e7i 0.422317i
\(517\) 1.90962e8 1.38189
\(518\) 3.24151e7 0.233216
\(519\) 6.05758e7i 0.433308i
\(520\) 199903. 0.00142171
\(521\) 7.68972e7 0.543748 0.271874 0.962333i \(-0.412357\pi\)
0.271874 + 0.962333i \(0.412357\pi\)
\(522\) 1.25218e8i 0.880347i
\(523\) −1.09922e7 −0.0768389 −0.0384194 0.999262i \(-0.512232\pi\)
−0.0384194 + 0.999262i \(0.512232\pi\)
\(524\) 7.93008e7i 0.551168i
\(525\) 1.84772e7 0.127690
\(526\) 1.90376e8i 1.30815i
\(527\) 7.13722e7i 0.487638i
\(528\) 1.38638e8i 0.941850i
\(529\) 4.64831e7 0.313999
\(530\) 2.12917e7i 0.143016i
\(531\) 2.39190e7 4.38018e7i 0.159757 0.292556i
\(532\) 3.45199e7 0.229263
\(533\) 1.20643e8i 0.796749i
\(534\) −5.93702e7 −0.389892
\(535\) 7.09176e7 0.463119
\(536\) 268886. 0.00174612
\(537\) 8.97005e7i 0.579258i
\(538\) −1.95351e8 −1.25449
\(539\) 2.36321e8i 1.50916i
\(540\) 4.07752e7 0.258949
\(541\) 8.42068e7i 0.531808i 0.963999 + 0.265904i \(0.0856705\pi\)
−0.963999 + 0.265904i \(0.914330\pi\)
\(542\) 3.69778e8i 2.32244i
\(543\) −6.63880e7 −0.414658
\(544\) 1.02863e8i 0.638945i
\(545\) 5.76363e7i 0.356046i
\(546\) −1.67127e7 −0.102676
\(547\) 2.79154e8 1.70562 0.852808 0.522225i \(-0.174898\pi\)
0.852808 + 0.522225i \(0.174898\pi\)
\(548\) 5.97806e7 0.363261
\(549\) 7.72740e7i 0.467000i
\(550\) −3.12703e8 −1.87950
\(551\) −2.64887e8 −1.58346
\(552\) 182728. 0.00108640
\(553\) −8.73255e7 −0.516375
\(554\) 6.03266e6i 0.0354797i
\(555\) 8.09970e7i 0.473795i
\(556\) 2.59539e8 1.51000
\(557\) −1.47415e7 −0.0853055 −0.0426528 0.999090i \(-0.513581\pi\)
−0.0426528 + 0.999090i \(0.513581\pi\)
\(558\) 8.83274e7 0.508385
\(559\) 5.94238e7 0.340193
\(560\) 6.42269e7 0.365724
\(561\) 7.50409e7i 0.425020i
\(562\) 2.34075e8i 1.31870i
\(563\) 6.53827e7i 0.366385i −0.983077 0.183192i \(-0.941357\pi\)
0.983077 0.183192i \(-0.0586432\pi\)
\(564\) 8.77419e7i 0.489068i
\(565\) 5.89832e7i 0.327027i
\(566\) 1.96200e8 1.08206
\(567\) 5.48742e6 0.0301036
\(568\) 252917.i 0.00138017i
\(569\) 1.66059e8i 0.901415i 0.892672 + 0.450707i \(0.148828\pi\)
−0.892672 + 0.450707i \(0.851172\pi\)
\(570\) 1.72652e8i 0.932280i
\(571\) 2.76472e8i 1.48506i 0.669815 + 0.742528i \(0.266374\pi\)
−0.669815 + 0.742528i \(0.733626\pi\)
\(572\) 1.41307e8 0.755049
\(573\) 1.89966e8i 1.00974i
\(574\) 1.24289e8i 0.657198i
\(575\) 1.28535e8i 0.676113i
\(576\) 6.34961e7 0.332261
\(577\) −3.22502e8 −1.67883 −0.839413 0.543494i \(-0.817101\pi\)
−0.839413 + 0.543494i \(0.817101\pi\)
\(578\) 2.17209e8i 1.12485i
\(579\) 1.42211e8 0.732650
\(580\) 4.90473e8 2.51380
\(581\) 4.76667e7i 0.243045i
\(582\) 1.76608e8 0.895862
\(583\) 2.42270e7i 0.122263i
\(584\) 574831. 0.00288603
\(585\) 4.17608e7i 0.208594i
\(586\) 3.44334e8i 1.71114i
\(587\) 1.21510e7i 0.0600754i −0.999549 0.0300377i \(-0.990437\pi\)
0.999549 0.0300377i \(-0.00956274\pi\)
\(588\) 1.08583e8 0.534110
\(589\) 1.86849e8i 0.914418i
\(590\) 3.43417e8 + 1.87531e8i 1.67211 + 0.913098i
\(591\) −1.06905e8 −0.517888
\(592\) 1.26537e8i 0.609890i
\(593\) 4.17858e6 0.0200385 0.0100192 0.999950i \(-0.496811\pi\)
0.0100192 + 0.999950i \(0.496811\pi\)
\(594\) −9.28676e7 −0.443103
\(595\) 3.47642e7 0.165037
\(596\) 1.87851e8i 0.887310i
\(597\) 1.32108e8 0.620877
\(598\) 1.16261e8i 0.543663i
\(599\) −2.48158e8 −1.15464 −0.577322 0.816517i \(-0.695902\pi\)
−0.577322 + 0.816517i \(0.695902\pi\)
\(600\) 231279.i 0.00107074i
\(601\) 1.92847e8i 0.888361i −0.895937 0.444180i \(-0.853495\pi\)
0.895937 0.444180i \(-0.146505\pi\)
\(602\) 6.12194e7 0.280608
\(603\) 5.61717e7i 0.256192i
\(604\) 2.64656e8i 1.20108i
\(605\) 4.93245e8 2.22739
\(606\) 8.03260e7 0.360943
\(607\) 3.24748e8 1.45205 0.726023 0.687671i \(-0.241367\pi\)
0.726023 + 0.687671i \(0.241367\pi\)
\(608\) 2.69291e8i 1.19815i
\(609\) 6.60066e7 0.292237
\(610\) 6.05847e8 2.66915
\(611\) 8.98627e7 0.393963
\(612\) 3.44793e7 0.150420
\(613\) 1.14218e8i 0.495851i 0.968779 + 0.247926i \(0.0797489\pi\)
−0.968779 + 0.247926i \(0.920251\pi\)
\(614\) 2.94644e8i 1.27289i
\(615\) 3.10566e8 1.33515
\(616\) −234335. −0.00100252
\(617\) −1.75757e8 −0.748266 −0.374133 0.927375i \(-0.622060\pi\)
−0.374133 + 0.927375i \(0.622060\pi\)
\(618\) −2.38319e8 −1.00970
\(619\) −3.06354e8 −1.29167 −0.645835 0.763477i \(-0.723491\pi\)
−0.645835 + 0.763477i \(0.723491\pi\)
\(620\) 3.45976e8i 1.45168i
\(621\) 3.81729e7i 0.159397i
\(622\) 3.25875e7i 0.135419i
\(623\) 3.12961e7i 0.129427i
\(624\) 6.52404e7i 0.268512i
\(625\) −2.80749e8 −1.14995
\(626\) −2.87323e8 −1.17124
\(627\) 1.96453e8i 0.796997i
\(628\) 1.34283e8i 0.542177i
\(629\) 6.84907e7i 0.275220i
\(630\) 4.30227e7i 0.172058i
\(631\) 8.45835e7 0.336665 0.168332 0.985730i \(-0.446162\pi\)
0.168332 + 0.985730i \(0.446162\pi\)
\(632\) 1.09306e6i 0.00433003i
\(633\) 2.46038e8i 0.970043i
\(634\) 1.14583e8i 0.449625i
\(635\) −4.59918e8 −1.79622
\(636\) 1.11317e7 0.0432701
\(637\) 1.11208e8i 0.430247i
\(638\) −1.11708e9 −4.30152
\(639\) 5.28356e7 0.202500
\(640\) 1.60528e6i 0.00612367i
\(641\) 2.62531e8 0.996796 0.498398 0.866948i \(-0.333922\pi\)
0.498398 + 0.866948i \(0.333922\pi\)
\(642\) 7.42134e7i 0.280464i
\(643\) 2.91322e8 1.09582 0.547911 0.836537i \(-0.315423\pi\)
0.547911 + 0.836537i \(0.315423\pi\)
\(644\) 5.98388e7i 0.224040i
\(645\) 1.52972e8i 0.570075i
\(646\) 1.45993e8i 0.541546i
\(647\) −5.24571e8 −1.93683 −0.968415 0.249345i \(-0.919785\pi\)
−0.968415 + 0.249345i \(0.919785\pi\)
\(648\) 68686.2i 0.000252432i
\(649\) −3.90760e8 2.13384e8i −1.42947 0.780599i
\(650\) −1.47151e8 −0.535827
\(651\) 4.65605e7i 0.168762i
\(652\) 3.94060e8 1.42174
\(653\) −4.08780e8 −1.46808 −0.734040 0.679106i \(-0.762368\pi\)
−0.734040 + 0.679106i \(0.762368\pi\)
\(654\) −6.03149e7 −0.215621
\(655\) 2.09075e8i 0.744008i
\(656\) 4.85179e8 1.71866
\(657\) 1.20085e8i 0.423441i
\(658\) 9.25781e7 0.324961
\(659\) 3.23254e8i 1.12950i −0.825261 0.564751i \(-0.808972\pi\)
0.825261 0.564751i \(-0.191028\pi\)
\(660\) 3.63759e8i 1.26527i
\(661\) 1.67484e8 0.579922 0.289961 0.957039i \(-0.406358\pi\)
0.289961 + 0.957039i \(0.406358\pi\)
\(662\) 2.02669e8i 0.698574i
\(663\) 3.53127e7i 0.121169i
\(664\) −596646. −0.00203804
\(665\) 9.10108e7 0.309477
\(666\) 8.47612e7 0.286929
\(667\) 4.59171e8i 1.54738i
\(668\) 2.73037e8 0.915992
\(669\) −2.72115e8 −0.908813
\(670\) −4.40400e8 −1.46428
\(671\) −6.89369e8 −2.28183
\(672\) 6.71039e7i 0.221126i
\(673\) 4.37433e8i 1.43505i 0.696534 + 0.717523i \(0.254724\pi\)
−0.696534 + 0.717523i \(0.745276\pi\)
\(674\) −4.55250e8 −1.48686
\(675\) 4.83155e7 0.157099
\(676\) −2.41923e8 −0.783137
\(677\) 1.68879e8 0.544263 0.272131 0.962260i \(-0.412271\pi\)
0.272131 + 0.962260i \(0.412271\pi\)
\(678\) −6.17244e7 −0.198047
\(679\) 9.30963e7i 0.297388i
\(680\) 435144.i 0.00138390i
\(681\) 1.08935e8i 0.344927i
\(682\) 7.87977e8i 2.48405i
\(683\) 3.53781e8i 1.11038i 0.831723 + 0.555191i \(0.187355\pi\)
−0.831723 + 0.555191i \(0.812645\pi\)
\(684\) 9.02651e7 0.282066
\(685\) 1.57610e8 0.490357
\(686\) 2.38213e8i 0.737892i
\(687\) 7.21775e7i 0.222603i
\(688\) 2.38979e8i 0.733827i
\(689\) 1.14007e7i 0.0348558i
\(690\) −2.99285e8 −0.911040
\(691\) 4.68094e8i 1.41873i 0.704843 + 0.709364i \(0.251018\pi\)
−0.704843 + 0.709364i \(0.748982\pi\)
\(692\) 2.48300e8i 0.749305i
\(693\) 4.89538e7i 0.147091i
\(694\) −9.04342e8 −2.70554
\(695\) 6.84268e8 2.03832
\(696\) 826207.i 0.00245054i
\(697\) 2.62613e8 0.775565
\(698\) 3.27056e8 0.961737
\(699\) 3.14910e8i 0.922052i
\(700\) −7.57380e7 −0.220810
\(701\) 1.00783e8i 0.292572i 0.989242 + 0.146286i \(0.0467319\pi\)
−0.989242 + 0.146286i \(0.953268\pi\)
\(702\) −4.37016e7 −0.126324
\(703\) 1.79305e8i 0.516091i
\(704\) 5.66454e8i 1.62348i
\(705\) 2.31329e8i 0.660182i
\(706\) 5.68087e7 0.161436
\(707\) 4.23427e7i 0.119817i
\(708\) −9.80442e7 + 1.79544e8i −0.276263 + 0.505907i
\(709\) −5.94810e7 −0.166893 −0.0834467 0.996512i \(-0.526593\pi\)
−0.0834467 + 0.996512i \(0.526593\pi\)
\(710\) 4.14244e8i 1.15739i
\(711\) −2.28345e8 −0.635306
\(712\) −391734. −0.00108530
\(713\) −3.23895e8 −0.893585
\(714\) 3.63798e7i 0.0999460i
\(715\) 3.72552e8 1.01922
\(716\) 3.67683e8i 1.00169i
\(717\) −4.36487e7 −0.118417
\(718\) 7.50865e8i 2.02856i
\(719\) 5.99700e8i 1.61342i −0.590948 0.806709i \(-0.701246\pi\)
0.590948 0.806709i \(-0.298754\pi\)
\(720\) 1.67945e8 0.449956
\(721\) 1.25626e8i 0.335177i
\(722\) 1.49846e8i 0.398138i
\(723\) −1.53754e8 −0.406828
\(724\) 2.72125e8 0.717055
\(725\) 5.81173e8 1.52508
\(726\) 5.16168e8i 1.34890i
\(727\) 7.48401e7 0.194774 0.0973870 0.995247i \(-0.468952\pi\)
0.0973870 + 0.995247i \(0.468952\pi\)
\(728\) −110273. −0.000285809
\(729\) 1.43489e7 0.0370370
\(730\) −9.41496e8 −2.42019
\(731\) 1.29352e8i 0.331148i
\(732\) 3.16746e8i 0.807567i
\(733\) 4.96276e8 1.26012 0.630059 0.776547i \(-0.283031\pi\)
0.630059 + 0.776547i \(0.283031\pi\)
\(734\) −6.05806e8 −1.53195
\(735\) 2.86277e8 0.720983
\(736\) −4.66805e8 −1.17085
\(737\) 5.01113e8 1.25180
\(738\) 3.24999e8i 0.808562i
\(739\) 7.85026e8i 1.94514i 0.232613 + 0.972569i \(0.425273\pi\)
−0.232613 + 0.972569i \(0.574727\pi\)
\(740\) 3.32007e8i 0.819318i
\(741\) 9.24469e7i 0.227215i
\(742\) 1.17452e7i 0.0287508i
\(743\) −3.78436e8 −0.922626 −0.461313 0.887237i \(-0.652621\pi\)
−0.461313 + 0.887237i \(0.652621\pi\)
\(744\) 582799. 0.00141514
\(745\) 4.95265e8i 1.19776i
\(746\) 1.17854e8i 0.283876i
\(747\) 1.24642e8i 0.299023i
\(748\) 3.07593e8i 0.734974i
\(749\) −3.91205e7 −0.0931020
\(750\) 8.52389e7i 0.202048i
\(751\) 1.08582e8i 0.256354i −0.991751 0.128177i \(-0.959087\pi\)
0.991751 0.128177i \(-0.0409125\pi\)
\(752\) 3.61392e8i 0.849816i
\(753\) 2.93400e7 0.0687187
\(754\) −5.25674e8 −1.22632
\(755\) 6.97760e8i 1.62131i
\(756\) −2.24930e7 −0.0520572
\(757\) −2.72312e8 −0.627739 −0.313870 0.949466i \(-0.601625\pi\)
−0.313870 + 0.949466i \(0.601625\pi\)
\(758\) 3.10308e7i 0.0712501i
\(759\) 3.40544e8 0.778840
\(760\) 1.13919e6i 0.00259510i
\(761\) −3.11053e8 −0.705798 −0.352899 0.935661i \(-0.614804\pi\)
−0.352899 + 0.935661i \(0.614804\pi\)
\(762\) 4.81292e8i 1.08779i
\(763\) 3.17941e7i 0.0715769i
\(764\) 7.78670e8i 1.74612i
\(765\) 9.09039e7 0.203048
\(766\) 1.45189e8i 0.323034i
\(767\) −1.83884e8 1.00414e8i −0.407528 0.222540i
\(768\) 2.62370e8 0.579202
\(769\) 2.21410e8i 0.486876i −0.969916 0.243438i \(-0.921725\pi\)
0.969916 0.243438i \(-0.0782753\pi\)
\(770\) 3.83810e8 0.840705
\(771\) −2.14303e8 −0.467591
\(772\) −5.82922e8 −1.26695
\(773\) 1.59034e8i 0.344311i −0.985070 0.172155i \(-0.944927\pi\)
0.985070 0.172155i \(-0.0550731\pi\)
\(774\) 1.60081e8 0.345237
\(775\) 4.09954e8i 0.880704i
\(776\) 1.16529e6 0.00249372
\(777\) 4.46806e7i 0.0952481i
\(778\) 3.29064e8i 0.698782i
\(779\) 6.87508e8 1.45434
\(780\) 1.71178e8i 0.360714i
\(781\) 4.71351e8i 0.989445i
\(782\) −2.53074e8 −0.529208
\(783\) 1.72599e8 0.359545
\(784\) 4.47234e8 0.928082
\(785\) 3.54033e8i 0.731872i