Properties

Label 177.11.c.a.58.9
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.9
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.92

$q$-expansion

\(f(q)\) \(=\) \(q-55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} -7808.09i q^{6} -6427.48 q^{7} +58404.0i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} -7808.09i q^{6} -6427.48 q^{7} +58404.0i q^{8} +19683.0 q^{9} +91929.7i q^{10} -42364.0i q^{11} -290891. q^{12} -179652. i q^{13} +357717. i q^{14} -231741. q^{15} +1.12727e6 q^{16} -2.44515e6 q^{17} -1.09544e6i q^{18} -2.94996e6 q^{19} +3.42485e6 q^{20} -901750. q^{21} -2.35774e6 q^{22} +4.47755e6i q^{23} +8.19385e6i q^{24} -7.03719e6 q^{25} -9.99843e6 q^{26} +2.76145e6 q^{27} +1.33268e7 q^{28} +3.67308e7 q^{29} +1.28974e7i q^{30} +595402. i q^{31} -2.93168e6i q^{32} -5.94350e6i q^{33} +1.36083e8i q^{34} +1.06169e7 q^{35} -4.08108e7 q^{36} -1.07486e7i q^{37} +1.64178e8i q^{38} -2.52045e7i q^{39} -9.64716e7i q^{40} +1.47249e8 q^{41} +5.01863e7i q^{42} +2.36868e8i q^{43} +8.78377e7i q^{44} -3.25123e7 q^{45} +2.49195e8 q^{46} -3.78784e8i q^{47} +1.58151e8 q^{48} -2.41163e8 q^{49} +3.91650e8i q^{50} -3.43046e8 q^{51} +3.72492e8i q^{52} -2.09357e8 q^{53} -1.53687e8i q^{54} +6.99767e7i q^{55} -3.75390e8i q^{56} -4.13868e8 q^{57} -2.04423e9i q^{58} +(2.07411e8 + 6.84177e8i) q^{59} +4.80493e8 q^{60} -3.23023e8i q^{61} +3.31367e7 q^{62} -1.26512e8 q^{63} +9.91162e8 q^{64} +2.96749e8i q^{65} -3.30782e8 q^{66} -1.67595e9i q^{67} +5.06980e9 q^{68} +6.28183e8i q^{69} -5.90876e8i q^{70} +1.42921e9 q^{71} +1.14957e9i q^{72} +2.75324e9i q^{73} -5.98206e8 q^{74} -9.87291e8 q^{75} +6.11647e9 q^{76} +2.72293e8i q^{77} -1.40274e9 q^{78} +4.89865e9 q^{79} -1.86202e9 q^{80} +3.87420e8 q^{81} -8.19506e9i q^{82} -4.90223e8i q^{83} +1.86969e9 q^{84} +4.03890e9 q^{85} +1.31827e10 q^{86} +5.15318e9 q^{87} +2.47422e9 q^{88} -6.61963e9i q^{89} +1.80945e9i q^{90} +1.15471e9i q^{91} -9.28378e9i q^{92} +8.35325e7i q^{93} -2.10810e10 q^{94} +4.87274e9 q^{95} -4.11304e8i q^{96} -1.12096e9i q^{97} +1.34218e10i q^{98} -8.33850e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 55.6543i 1.73920i −0.493758 0.869599i \(-0.664377\pi\)
0.493758 0.869599i \(-0.335623\pi\)
\(3\) 140.296 0.577350
\(4\) −2073.41 −2.02481
\(5\) −1651.80 −0.528575 −0.264288 0.964444i \(-0.585137\pi\)
−0.264288 + 0.964444i \(0.585137\pi\)
\(6\) 7808.09i 1.00413i
\(7\) −6427.48 −0.382429 −0.191214 0.981548i \(-0.561243\pi\)
−0.191214 + 0.981548i \(0.561243\pi\)
\(8\) 58404.0i 1.78235i
\(9\) 19683.0 0.333333
\(10\) 91929.7i 0.919297i
\(11\) 42364.0i 0.263047i −0.991313 0.131523i \(-0.958013\pi\)
0.991313 0.131523i \(-0.0419869\pi\)
\(12\) −290891. −1.16902
\(13\) 179652.i 0.483856i −0.970294 0.241928i \(-0.922220\pi\)
0.970294 0.241928i \(-0.0777798\pi\)
\(14\) 357717.i 0.665119i
\(15\) −231741. −0.305173
\(16\) 1.12727e6 1.07505
\(17\) −2.44515e6 −1.72211 −0.861056 0.508509i \(-0.830197\pi\)
−0.861056 + 0.508509i \(0.830197\pi\)
\(18\) 1.09544e6i 0.579733i
\(19\) −2.94996e6 −1.19137 −0.595687 0.803216i \(-0.703120\pi\)
−0.595687 + 0.803216i \(0.703120\pi\)
\(20\) 3.42485e6 1.07026
\(21\) −901750. −0.220795
\(22\) −2.35774e6 −0.457491
\(23\) 4.47755e6i 0.695667i 0.937556 + 0.347834i \(0.113083\pi\)
−0.937556 + 0.347834i \(0.886917\pi\)
\(24\) 8.19385e6i 1.02904i
\(25\) −7.03719e6 −0.720608
\(26\) −9.99843e6 −0.841521
\(27\) 2.76145e6 0.192450
\(28\) 1.33268e7 0.774345
\(29\) 3.67308e7 1.79077 0.895385 0.445292i \(-0.146900\pi\)
0.895385 + 0.445292i \(0.146900\pi\)
\(30\) 1.28974e7i 0.530756i
\(31\) 595402.i 0.0207970i 0.999946 + 0.0103985i \(0.00331001\pi\)
−0.999946 + 0.0103985i \(0.996690\pi\)
\(32\) 2.93168e6i 0.0873710i
\(33\) 5.94350e6i 0.151870i
\(34\) 1.36083e8i 2.99510i
\(35\) 1.06169e7 0.202142
\(36\) −4.08108e7 −0.674937
\(37\) 1.07486e7i 0.155004i −0.996992 0.0775021i \(-0.975306\pi\)
0.996992 0.0775021i \(-0.0246944\pi\)
\(38\) 1.64178e8i 2.07204i
\(39\) 2.52045e7i 0.279354i
\(40\) 9.64716e7i 0.942105i
\(41\) 1.47249e8 1.27097 0.635483 0.772115i \(-0.280801\pi\)
0.635483 + 0.772115i \(0.280801\pi\)
\(42\) 5.01863e7i 0.384007i
\(43\) 2.36868e8i 1.61126i 0.592422 + 0.805628i \(0.298172\pi\)
−0.592422 + 0.805628i \(0.701828\pi\)
\(44\) 8.78377e7i 0.532620i
\(45\) −3.25123e7 −0.176192
\(46\) 2.49195e8 1.20990
\(47\) 3.78784e8i 1.65159i −0.563969 0.825796i \(-0.690726\pi\)
0.563969 0.825796i \(-0.309274\pi\)
\(48\) 1.58151e8 0.620679
\(49\) −2.41163e8 −0.853748
\(50\) 3.91650e8i 1.25328i
\(51\) −3.43046e8 −0.994262
\(52\) 3.72492e8i 0.979717i
\(53\) −2.09357e8 −0.500620 −0.250310 0.968166i \(-0.580532\pi\)
−0.250310 + 0.968166i \(0.580532\pi\)
\(54\) 1.53687e8i 0.334709i
\(55\) 6.99767e7i 0.139040i
\(56\) 3.75390e8i 0.681621i
\(57\) −4.13868e8 −0.687840
\(58\) 2.04423e9i 3.11451i
\(59\) 2.07411e8 + 6.84177e8i 0.290116 + 0.956992i
\(60\) 4.80493e8 0.617917
\(61\) 3.23023e8i 0.382458i −0.981545 0.191229i \(-0.938753\pi\)
0.981545 0.191229i \(-0.0612473\pi\)
\(62\) 3.31367e7 0.0361702
\(63\) −1.26512e8 −0.127476
\(64\) 9.91162e8 0.923091
\(65\) 2.96749e8i 0.255754i
\(66\) −3.30782e8 −0.264132
\(67\) 1.67595e9i 1.24133i −0.784075 0.620666i \(-0.786862\pi\)
0.784075 0.620666i \(-0.213138\pi\)
\(68\) 5.06980e9 3.48695
\(69\) 6.28183e8i 0.401644i
\(70\) 5.90876e8i 0.351565i
\(71\) 1.42921e9 0.792143 0.396071 0.918220i \(-0.370373\pi\)
0.396071 + 0.918220i \(0.370373\pi\)
\(72\) 1.14957e9i 0.594116i
\(73\) 2.75324e9i 1.32810i 0.747689 + 0.664049i \(0.231164\pi\)
−0.747689 + 0.664049i \(0.768836\pi\)
\(74\) −5.98206e8 −0.269583
\(75\) −9.87291e8 −0.416043
\(76\) 6.11647e9 2.41231
\(77\) 2.72293e8i 0.100597i
\(78\) −1.40274e9 −0.485853
\(79\) 4.89865e9 1.59199 0.795996 0.605301i \(-0.206947\pi\)
0.795996 + 0.605301i \(0.206947\pi\)
\(80\) −1.86202e9 −0.568243
\(81\) 3.87420e8 0.111111
\(82\) 8.19506e9i 2.21046i
\(83\) 4.90223e8i 0.124452i −0.998062 0.0622261i \(-0.980180\pi\)
0.998062 0.0622261i \(-0.0198200\pi\)
\(84\) 1.86969e9 0.447068
\(85\) 4.03890e9 0.910266
\(86\) 1.31827e10 2.80229
\(87\) 5.15318e9 1.03390
\(88\) 2.47422e9 0.468841
\(89\) 6.61963e9i 1.18545i −0.805405 0.592725i \(-0.798052\pi\)
0.805405 0.592725i \(-0.201948\pi\)
\(90\) 1.80945e9i 0.306432i
\(91\) 1.15471e9i 0.185040i
\(92\) 9.28378e9i 1.40859i
\(93\) 8.35325e7i 0.0120072i
\(94\) −2.10810e10 −2.87245
\(95\) 4.87274e9 0.629731
\(96\) 4.11304e8i 0.0504437i
\(97\) 1.12096e9i 0.130537i −0.997868 0.0652683i \(-0.979210\pi\)
0.997868 0.0652683i \(-0.0207903\pi\)
\(98\) 1.34218e10i 1.48484i
\(99\) 8.33850e8i 0.0876823i
\(100\) 1.45910e10 1.45910
\(101\) 4.89302e9i 0.465554i 0.972530 + 0.232777i \(0.0747813\pi\)
−0.972530 + 0.232777i \(0.925219\pi\)
\(102\) 1.90920e10i 1.72922i
\(103\) 6.05488e8i 0.0522300i 0.999659 + 0.0261150i \(0.00831360\pi\)
−0.999659 + 0.0261150i \(0.991686\pi\)
\(104\) 1.04924e10 0.862400
\(105\) 1.48951e9 0.116707
\(106\) 1.16516e10i 0.870677i
\(107\) −1.34731e10 −0.960612 −0.480306 0.877101i \(-0.659474\pi\)
−0.480306 + 0.877101i \(0.659474\pi\)
\(108\) −5.72560e9 −0.389675
\(109\) 2.45190e10i 1.59357i −0.604265 0.796783i \(-0.706533\pi\)
0.604265 0.796783i \(-0.293467\pi\)
\(110\) 3.89451e9 0.241818
\(111\) 1.50799e9i 0.0894917i
\(112\) −7.24549e9 −0.411129
\(113\) 3.11336e10i 1.68981i 0.534917 + 0.844904i \(0.320343\pi\)
−0.534917 + 0.844904i \(0.679657\pi\)
\(114\) 2.30336e10i 1.19629i
\(115\) 7.39601e9i 0.367712i
\(116\) −7.61578e10 −3.62597
\(117\) 3.53610e9i 0.161285i
\(118\) 3.80774e10 1.15433e10i 1.66440 0.504569i
\(119\) 1.57162e10 0.658585
\(120\) 1.35346e10i 0.543925i
\(121\) 2.41427e10 0.930806
\(122\) −1.79776e10 −0.665171
\(123\) 2.06585e10 0.733792
\(124\) 1.23451e9i 0.0421101i
\(125\) 2.77548e10 0.909471
\(126\) 7.04094e9i 0.221706i
\(127\) −2.06395e10 −0.624713 −0.312356 0.949965i \(-0.601118\pi\)
−0.312356 + 0.949965i \(0.601118\pi\)
\(128\) 5.81645e10i 1.69281i
\(129\) 3.32317e10i 0.930259i
\(130\) 1.65154e10 0.444807
\(131\) 5.93554e10i 1.53852i 0.638934 + 0.769261i \(0.279376\pi\)
−0.638934 + 0.769261i \(0.720624\pi\)
\(132\) 1.23233e10i 0.307508i
\(133\) 1.89608e10 0.455616
\(134\) −9.32741e10 −2.15892
\(135\) −4.56135e9 −0.101724
\(136\) 1.42807e11i 3.06941i
\(137\) −6.49128e10 −1.34502 −0.672508 0.740090i \(-0.734783\pi\)
−0.672508 + 0.740090i \(0.734783\pi\)
\(138\) 3.49611e10 0.698538
\(139\) 8.69158e10 1.67504 0.837519 0.546408i \(-0.184005\pi\)
0.837519 + 0.546408i \(0.184005\pi\)
\(140\) −2.20131e10 −0.409300
\(141\) 5.31420e10i 0.953547i
\(142\) 7.95416e10i 1.37769i
\(143\) −7.61078e9 −0.127277
\(144\) 2.21880e10 0.358349
\(145\) −6.06718e10 −0.946557
\(146\) 1.53230e11 2.30983
\(147\) −3.38342e10 −0.492912
\(148\) 2.22862e10i 0.313854i
\(149\) 7.01159e10i 0.954741i −0.878702 0.477370i \(-0.841590\pi\)
0.878702 0.477370i \(-0.158410\pi\)
\(150\) 5.49470e10i 0.723582i
\(151\) 3.25291e10i 0.414369i 0.978302 + 0.207184i \(0.0664300\pi\)
−0.978302 + 0.207184i \(0.933570\pi\)
\(152\) 1.72290e11i 2.12344i
\(153\) −4.81280e10 −0.574038
\(154\) 1.51543e10 0.174958
\(155\) 9.83483e8i 0.0109928i
\(156\) 5.22592e10i 0.565640i
\(157\) 1.35643e11i 1.42200i −0.703194 0.710998i \(-0.748244\pi\)
0.703194 0.710998i \(-0.251756\pi\)
\(158\) 2.72631e11i 2.76879i
\(159\) −2.93720e10 −0.289033
\(160\) 4.84255e9i 0.0461821i
\(161\) 2.87794e10i 0.266043i
\(162\) 2.15616e10i 0.193244i
\(163\) −2.53362e10 −0.220193 −0.110097 0.993921i \(-0.535116\pi\)
−0.110097 + 0.993921i \(0.535116\pi\)
\(164\) −3.05307e11 −2.57346
\(165\) 9.81746e9i 0.0802748i
\(166\) −2.72830e10 −0.216447
\(167\) −8.34235e10 −0.642253 −0.321126 0.947036i \(-0.604061\pi\)
−0.321126 + 0.947036i \(0.604061\pi\)
\(168\) 5.26658e10i 0.393534i
\(169\) 1.05584e11 0.765883
\(170\) 2.24782e11i 1.58313i
\(171\) −5.80641e10 −0.397125
\(172\) 4.91124e11i 3.26249i
\(173\) 2.37750e11i 1.53423i 0.641509 + 0.767115i \(0.278309\pi\)
−0.641509 + 0.767115i \(0.721691\pi\)
\(174\) 2.86797e11i 1.79816i
\(175\) 4.52314e10 0.275581
\(176\) 4.77556e10i 0.282788i
\(177\) 2.90989e10 + 9.59873e10i 0.167498 + 0.552519i
\(178\) −3.68411e11 −2.06173
\(179\) 2.07663e11i 1.13004i −0.825077 0.565020i \(-0.808868\pi\)
0.825077 0.565020i \(-0.191132\pi\)
\(180\) 6.74112e10 0.356755
\(181\) 8.92034e10 0.459186 0.229593 0.973287i \(-0.426260\pi\)
0.229593 + 0.973287i \(0.426260\pi\)
\(182\) 6.42647e10 0.321822
\(183\) 4.53188e10i 0.220812i
\(184\) −2.61507e11 −1.23992
\(185\) 1.77545e10i 0.0819313i
\(186\) 4.64895e9 0.0208829
\(187\) 1.03586e11i 0.452996i
\(188\) 7.85374e11i 3.34416i
\(189\) −1.77491e10 −0.0735984
\(190\) 2.71189e11i 1.09523i
\(191\) 8.84099e10i 0.347804i 0.984763 + 0.173902i \(0.0556375\pi\)
−0.984763 + 0.173902i \(0.944362\pi\)
\(192\) 1.39056e11 0.532947
\(193\) −2.58894e11 −0.966796 −0.483398 0.875401i \(-0.660598\pi\)
−0.483398 + 0.875401i \(0.660598\pi\)
\(194\) −6.23864e10 −0.227029
\(195\) 4.16328e10i 0.147660i
\(196\) 5.00028e11 1.72868
\(197\) 2.60482e11 0.877904 0.438952 0.898510i \(-0.355350\pi\)
0.438952 + 0.898510i \(0.355350\pi\)
\(198\) −4.64074e10 −0.152497
\(199\) 1.43116e11 0.458589 0.229294 0.973357i \(-0.426358\pi\)
0.229294 + 0.973357i \(0.426358\pi\)
\(200\) 4.11000e11i 1.28438i
\(201\) 2.35130e11i 0.716683i
\(202\) 2.72318e11 0.809692
\(203\) −2.36086e11 −0.684842
\(204\) 7.11273e11 2.01319
\(205\) −2.43226e11 −0.671801
\(206\) 3.36981e10 0.0908383
\(207\) 8.81317e10i 0.231889i
\(208\) 2.02516e11i 0.520168i
\(209\) 1.24972e11i 0.313387i
\(210\) 8.28976e10i 0.202976i
\(211\) 5.72585e11i 1.36908i 0.728977 + 0.684538i \(0.239996\pi\)
−0.728977 + 0.684538i \(0.760004\pi\)
\(212\) 4.34082e11 1.01366
\(213\) 2.00512e11 0.457344
\(214\) 7.49835e11i 1.67069i
\(215\) 3.91258e11i 0.851670i
\(216\) 1.61280e11i 0.343013i
\(217\) 3.82693e9i 0.00795338i
\(218\) −1.36459e12 −2.77153
\(219\) 3.86269e11i 0.766778i
\(220\) 1.45090e11i 0.281530i
\(221\) 4.39278e11i 0.833255i
\(222\) −8.39260e10 −0.155644
\(223\) 1.04640e12 1.89746 0.948731 0.316085i \(-0.102368\pi\)
0.948731 + 0.316085i \(0.102368\pi\)
\(224\) 1.88433e10i 0.0334132i
\(225\) −1.38513e11 −0.240203
\(226\) 1.73272e12 2.93891
\(227\) 7.11857e11i 1.18104i −0.807024 0.590519i \(-0.798923\pi\)
0.807024 0.590519i \(-0.201077\pi\)
\(228\) 8.58117e11 1.39275
\(229\) 1.23805e12i 1.96589i 0.183900 + 0.982945i \(0.441128\pi\)
−0.183900 + 0.982945i \(0.558872\pi\)
\(230\) −4.11620e11 −0.639525
\(231\) 3.82017e10i 0.0580795i
\(232\) 2.14522e12i 3.19178i
\(233\) 4.46825e11i 0.650666i −0.945599 0.325333i \(-0.894524\pi\)
0.945599 0.325333i \(-0.105476\pi\)
\(234\) −1.96799e11 −0.280507
\(235\) 6.25675e11i 0.872991i
\(236\) −4.30047e11 1.41858e12i −0.587429 1.93773i
\(237\) 6.87262e11 0.919138
\(238\) 8.74673e11i 1.14541i
\(239\) −8.29032e11 −1.06312 −0.531559 0.847021i \(-0.678394\pi\)
−0.531559 + 0.847021i \(0.678394\pi\)
\(240\) −2.61234e11 −0.328075
\(241\) −4.35002e11 −0.535065 −0.267532 0.963549i \(-0.586208\pi\)
−0.267532 + 0.963549i \(0.586208\pi\)
\(242\) 1.34365e12i 1.61886i
\(243\) 5.43536e10 0.0641500
\(244\) 6.69757e11i 0.774405i
\(245\) 3.98352e11 0.451270
\(246\) 1.14973e12i 1.27621i
\(247\) 5.29967e11i 0.576454i
\(248\) −3.47738e10 −0.0370676
\(249\) 6.87763e10i 0.0718526i
\(250\) 1.54468e12i 1.58175i
\(251\) 6.03262e11 0.605532 0.302766 0.953065i \(-0.402090\pi\)
0.302766 + 0.953065i \(0.402090\pi\)
\(252\) 2.62311e11 0.258115
\(253\) 1.89687e11 0.182993
\(254\) 1.14868e12i 1.08650i
\(255\) 5.66642e11 0.525542
\(256\) −2.22216e12 −2.02104
\(257\) −1.71456e12 −1.52928 −0.764640 0.644458i \(-0.777083\pi\)
−0.764640 + 0.644458i \(0.777083\pi\)
\(258\) 1.84949e12 1.61790
\(259\) 6.90864e10i 0.0592780i
\(260\) 6.15282e11i 0.517854i
\(261\) 7.22972e11 0.596924
\(262\) 3.30339e12 2.67580
\(263\) 1.07745e12 0.856288 0.428144 0.903710i \(-0.359168\pi\)
0.428144 + 0.903710i \(0.359168\pi\)
\(264\) 3.47124e11 0.270686
\(265\) 3.45815e11 0.264615
\(266\) 1.05525e12i 0.792406i
\(267\) 9.28708e11i 0.684420i
\(268\) 3.47493e12i 2.51346i
\(269\) 1.28198e12i 0.910165i 0.890449 + 0.455083i \(0.150390\pi\)
−0.890449 + 0.455083i \(0.849610\pi\)
\(270\) 2.53859e11i 0.176919i
\(271\) 4.50951e11 0.308520 0.154260 0.988030i \(-0.450701\pi\)
0.154260 + 0.988030i \(0.450701\pi\)
\(272\) −2.75634e12 −1.85135
\(273\) 1.62001e11i 0.106833i
\(274\) 3.61268e12i 2.33925i
\(275\) 2.98123e11i 0.189554i
\(276\) 1.30248e12i 0.813252i
\(277\) 1.91181e12 1.17232 0.586160 0.810195i \(-0.300639\pi\)
0.586160 + 0.810195i \(0.300639\pi\)
\(278\) 4.83724e12i 2.91322i
\(279\) 1.17193e10i 0.00693235i
\(280\) 6.20069e11i 0.360288i
\(281\) −4.01203e11 −0.228998 −0.114499 0.993423i \(-0.536526\pi\)
−0.114499 + 0.993423i \(0.536526\pi\)
\(282\) −2.95758e12 −1.65841
\(283\) 3.77846e11i 0.208153i −0.994569 0.104077i \(-0.966811\pi\)
0.994569 0.104077i \(-0.0331887\pi\)
\(284\) −2.96333e12 −1.60394
\(285\) 6.83626e11 0.363575
\(286\) 4.23573e11i 0.221360i
\(287\) −9.46441e11 −0.486053
\(288\) 5.77043e10i 0.0291237i
\(289\) 3.96278e12 1.96567
\(290\) 3.37665e12i 1.64625i
\(291\) 1.57267e11i 0.0753653i
\(292\) 5.70859e12i 2.68915i
\(293\) 1.67521e12 0.775767 0.387883 0.921708i \(-0.373206\pi\)
0.387883 + 0.921708i \(0.373206\pi\)
\(294\) 1.88302e12i 0.857271i
\(295\) −3.42601e11 1.13012e12i −0.153348 0.505842i
\(296\) 6.27761e11 0.276271
\(297\) 1.16986e11i 0.0506234i
\(298\) −3.90226e12 −1.66048
\(299\) 8.04403e11 0.336603
\(300\) 2.04705e12 0.842409
\(301\) 1.52246e12i 0.616190i
\(302\) 1.81038e12 0.720669
\(303\) 6.86472e11i 0.268788i
\(304\) −3.32540e12 −1.28078
\(305\) 5.33568e11i 0.202158i
\(306\) 2.67853e12i 0.998365i
\(307\) −1.64568e12 −0.603466 −0.301733 0.953392i \(-0.597565\pi\)
−0.301733 + 0.953392i \(0.597565\pi\)
\(308\) 5.64575e11i 0.203689i
\(309\) 8.49477e10i 0.0301550i
\(310\) −5.47351e10 −0.0191187
\(311\) 4.42075e11 0.151948 0.0759739 0.997110i \(-0.475793\pi\)
0.0759739 + 0.997110i \(0.475793\pi\)
\(312\) 1.47204e12 0.497907
\(313\) 4.05890e12i 1.35110i 0.737316 + 0.675548i \(0.236093\pi\)
−0.737316 + 0.675548i \(0.763907\pi\)
\(314\) −7.54911e12 −2.47313
\(315\) 2.08972e11 0.0673807
\(316\) −1.01569e13 −3.22348
\(317\) −4.01843e12 −1.25534 −0.627669 0.778481i \(-0.715991\pi\)
−0.627669 + 0.778481i \(0.715991\pi\)
\(318\) 1.63468e12i 0.502686i
\(319\) 1.55606e12i 0.471057i
\(320\) −1.63720e12 −0.487923
\(321\) −1.89022e12 −0.554610
\(322\) −1.60170e12 −0.462702
\(323\) 7.21311e12 2.05168
\(324\) −8.03280e11 −0.224979
\(325\) 1.26425e12i 0.348671i
\(326\) 1.41007e12i 0.382960i
\(327\) 3.43992e12i 0.920046i
\(328\) 8.59994e12i 2.26530i
\(329\) 2.43463e12i 0.631616i
\(330\) 5.46384e11 0.139614
\(331\) 4.62890e11 0.116503 0.0582516 0.998302i \(-0.481447\pi\)
0.0582516 + 0.998302i \(0.481447\pi\)
\(332\) 1.01643e12i 0.251992i
\(333\) 2.11565e11i 0.0516680i
\(334\) 4.64288e12i 1.11700i
\(335\) 2.76833e12i 0.656137i
\(336\) −1.01651e12 −0.237365
\(337\) 2.91225e11i 0.0670007i 0.999439 + 0.0335003i \(0.0106655\pi\)
−0.999439 + 0.0335003i \(0.989335\pi\)
\(338\) 5.87618e12i 1.33202i
\(339\) 4.36793e12i 0.975612i
\(340\) −8.37428e12 −1.84312
\(341\) 2.52236e10 0.00547060
\(342\) 3.23152e12i 0.690679i
\(343\) 3.36567e12 0.708926
\(344\) −1.38340e13 −2.87182
\(345\) 1.03763e12i 0.212299i
\(346\) 1.32318e13 2.66833
\(347\) 9.42217e12i 1.87285i 0.350864 + 0.936427i \(0.385888\pi\)
−0.350864 + 0.936427i \(0.614112\pi\)
\(348\) −1.06846e13 −2.09346
\(349\) 2.22714e12i 0.430150i 0.976598 + 0.215075i \(0.0689996\pi\)
−0.976598 + 0.215075i \(0.931000\pi\)
\(350\) 2.51732e12i 0.479290i
\(351\) 4.96101e11i 0.0931181i
\(352\) −1.24198e11 −0.0229827
\(353\) 1.90174e11i 0.0346959i −0.999850 0.0173479i \(-0.994478\pi\)
0.999850 0.0173479i \(-0.00552230\pi\)
\(354\) 5.34211e12 1.61948e12i 0.960941 0.291313i
\(355\) −2.36076e12 −0.418707
\(356\) 1.37252e13i 2.40031i
\(357\) 2.20492e12 0.380234
\(358\) −1.15573e13 −1.96536
\(359\) −5.83565e12 −0.978627 −0.489314 0.872108i \(-0.662753\pi\)
−0.489314 + 0.872108i \(0.662753\pi\)
\(360\) 1.89885e12i 0.314035i
\(361\) 2.57121e12 0.419373
\(362\) 4.96456e12i 0.798616i
\(363\) 3.38713e12 0.537401
\(364\) 2.39418e12i 0.374672i
\(365\) 4.54780e12i 0.702000i
\(366\) −2.52219e12 −0.384036
\(367\) 4.45054e12i 0.668471i −0.942490 0.334236i \(-0.891522\pi\)
0.942490 0.334236i \(-0.108478\pi\)
\(368\) 5.04740e12i 0.747875i
\(369\) 2.89831e12 0.423655
\(370\) 9.88115e11 0.142495
\(371\) 1.34564e12 0.191451
\(372\) 1.73197e11i 0.0243123i
\(373\) −6.13757e12 −0.850066 −0.425033 0.905178i \(-0.639737\pi\)
−0.425033 + 0.905178i \(0.639737\pi\)
\(374\) 5.76503e12 0.787851
\(375\) 3.89390e12 0.525083
\(376\) 2.21225e13 2.94371
\(377\) 6.59877e12i 0.866475i
\(378\) 9.87817e11i 0.128002i
\(379\) 2.88638e12 0.369111 0.184555 0.982822i \(-0.440915\pi\)
0.184555 + 0.982822i \(0.440915\pi\)
\(380\) −1.01032e13 −1.27509
\(381\) −2.89564e12 −0.360678
\(382\) 4.92039e12 0.604899
\(383\) 9.06675e12 1.10017 0.550083 0.835110i \(-0.314596\pi\)
0.550083 + 0.835110i \(0.314596\pi\)
\(384\) 8.16025e12i 0.977344i
\(385\) 4.49774e11i 0.0531729i
\(386\) 1.44086e13i 1.68145i
\(387\) 4.66228e12i 0.537085i
\(388\) 2.32421e12i 0.264312i
\(389\) 1.21502e13 1.36406 0.682030 0.731324i \(-0.261097\pi\)
0.682030 + 0.731324i \(0.261097\pi\)
\(390\) 2.31704e12 0.256810
\(391\) 1.09483e13i 1.19802i
\(392\) 1.40849e13i 1.52168i
\(393\) 8.32733e12i 0.888266i
\(394\) 1.44970e13i 1.52685i
\(395\) −8.09158e12 −0.841488
\(396\) 1.72891e12i 0.177540i
\(397\) 3.53287e12i 0.358241i −0.983827 0.179121i \(-0.942675\pi\)
0.983827 0.179121i \(-0.0573252\pi\)
\(398\) 7.96504e12i 0.797577i
\(399\) 2.66013e12 0.263050
\(400\) −7.93280e12 −0.774688
\(401\) 8.52789e12i 0.822469i 0.911530 + 0.411234i \(0.134902\pi\)
−0.911530 + 0.411234i \(0.865098\pi\)
\(402\) −1.30860e13 −1.24645
\(403\) 1.06965e11 0.0100628
\(404\) 1.01452e13i 0.942660i
\(405\) −6.39940e11 −0.0587306
\(406\) 1.31392e13i 1.19108i
\(407\) −4.55353e11 −0.0407734
\(408\) 2.00352e13i 1.77212i
\(409\) 6.06947e12i 0.530316i −0.964205 0.265158i \(-0.914576\pi\)
0.964205 0.265158i \(-0.0854241\pi\)
\(410\) 1.35366e13i 1.16839i
\(411\) −9.10701e12 −0.776545
\(412\) 1.25542e12i 0.105756i
\(413\) −1.33313e12 4.39753e12i −0.110949 0.365981i
\(414\) 4.90491e12 0.403301
\(415\) 8.09748e11i 0.0657824i
\(416\) −5.26684e11 −0.0422750
\(417\) 1.21939e13 0.967084
\(418\) 6.95524e12 0.545043
\(419\) 8.83996e12i 0.684511i 0.939607 + 0.342255i \(0.111191\pi\)
−0.939607 + 0.342255i \(0.888809\pi\)
\(420\) −3.08836e12 −0.236309
\(421\) 1.43920e12i 0.108820i 0.998519 + 0.0544102i \(0.0173279\pi\)
−0.998519 + 0.0544102i \(0.982672\pi\)
\(422\) 3.18668e13 2.38109
\(423\) 7.45561e12i 0.550531i
\(424\) 1.22273e13i 0.892279i
\(425\) 1.72070e13 1.24097
\(426\) 1.11594e13i 0.795412i
\(427\) 2.07622e12i 0.146263i
\(428\) 2.79352e13 1.94506
\(429\) −1.06776e12 −0.0734833
\(430\) −2.17752e13 −1.48122
\(431\) 4.30204e12i 0.289260i −0.989486 0.144630i \(-0.953801\pi\)
0.989486 0.144630i \(-0.0461991\pi\)
\(432\) 3.11289e12 0.206893
\(433\) 2.66770e13 1.75266 0.876330 0.481712i \(-0.159985\pi\)
0.876330 + 0.481712i \(0.159985\pi\)
\(434\) −2.12985e11 −0.0138325
\(435\) −8.51201e12 −0.546495
\(436\) 5.08378e13i 3.22667i
\(437\) 1.32086e13i 0.828800i
\(438\) 2.14976e13 1.33358
\(439\) 1.51588e13 0.929701 0.464850 0.885389i \(-0.346108\pi\)
0.464850 + 0.885389i \(0.346108\pi\)
\(440\) −4.08692e12 −0.247818
\(441\) −4.74681e12 −0.284583
\(442\) 2.44477e13 1.44919
\(443\) 1.75776e13i 1.03024i 0.857117 + 0.515122i \(0.172253\pi\)
−0.857117 + 0.515122i \(0.827747\pi\)
\(444\) 3.12667e12i 0.181204i
\(445\) 1.09343e13i 0.626600i
\(446\) 5.82367e13i 3.30006i
\(447\) 9.83699e12i 0.551220i
\(448\) −6.37067e12 −0.353016
\(449\) 3.46668e11 0.0189968 0.00949842 0.999955i \(-0.496977\pi\)
0.00949842 + 0.999955i \(0.496977\pi\)
\(450\) 7.70885e12i 0.417760i
\(451\) 6.23806e12i 0.334323i
\(452\) 6.45527e13i 3.42154i
\(453\) 4.56370e12i 0.239236i
\(454\) −3.96179e13 −2.05406
\(455\) 1.90735e12i 0.0978077i
\(456\) 2.41716e13i 1.22597i
\(457\) 2.42767e13i 1.21789i 0.793212 + 0.608945i \(0.208407\pi\)
−0.793212 + 0.608945i \(0.791593\pi\)
\(458\) 6.89026e13 3.41907
\(459\) −6.75217e12 −0.331421
\(460\) 1.53349e13i 0.744548i
\(461\) −3.10274e12 −0.149019 −0.0745093 0.997220i \(-0.523739\pi\)
−0.0745093 + 0.997220i \(0.523739\pi\)
\(462\) 2.12609e12 0.101012
\(463\) 2.46401e13i 1.15808i 0.815300 + 0.579038i \(0.196572\pi\)
−0.815300 + 0.579038i \(0.803428\pi\)
\(464\) 4.14054e13 1.92516
\(465\) 1.37979e11i 0.00634670i
\(466\) −2.48678e13 −1.13164
\(467\) 3.96954e13i 1.78713i 0.448937 + 0.893564i \(0.351803\pi\)
−0.448937 + 0.893564i \(0.648197\pi\)
\(468\) 7.33176e12i 0.326572i
\(469\) 1.07722e13i 0.474721i
\(470\) 3.48215e13 1.51830
\(471\) 1.90301e13i 0.820989i
\(472\) −3.99586e13 + 1.21136e13i −1.70569 + 0.517087i
\(473\) 1.00347e13 0.423836
\(474\) 3.82491e13i 1.59856i
\(475\) 2.07594e13 0.858514
\(476\) −3.25860e13 −1.33351
\(477\) −4.12077e12 −0.166873
\(478\) 4.61392e13i 1.84897i
\(479\) 2.53641e13 1.00587 0.502934 0.864325i \(-0.332254\pi\)
0.502934 + 0.864325i \(0.332254\pi\)
\(480\) 6.79391e11i 0.0266633i
\(481\) −1.93101e12 −0.0749997
\(482\) 2.42098e13i 0.930584i
\(483\) 4.03763e12i 0.153600i
\(484\) −5.00577e13 −1.88471
\(485\) 1.85160e12i 0.0689984i
\(486\) 3.02501e12i 0.111570i
\(487\) −1.22072e13 −0.445628 −0.222814 0.974861i \(-0.571524\pi\)
−0.222814 + 0.974861i \(0.571524\pi\)
\(488\) 1.88658e13 0.681674
\(489\) −3.55457e12 −0.127129
\(490\) 2.21700e13i 0.784848i
\(491\) −4.37652e13 −1.53363 −0.766817 0.641866i \(-0.778160\pi\)
−0.766817 + 0.641866i \(0.778160\pi\)
\(492\) −4.28334e13 −1.48579
\(493\) −8.98124e13 −3.08391
\(494\) 2.94950e13 1.00257
\(495\) 1.37735e12i 0.0463467i
\(496\) 6.71177e11i 0.0223578i
\(497\) −9.18620e12 −0.302938
\(498\) −3.82770e12 −0.124966
\(499\) −3.80257e13 −1.22906 −0.614531 0.788893i \(-0.710655\pi\)
−0.614531 + 0.788893i \(0.710655\pi\)
\(500\) −5.75471e13 −1.84151
\(501\) −1.17040e13 −0.370805
\(502\) 3.35741e13i 1.05314i
\(503\) 7.64477e12i 0.237424i 0.992929 + 0.118712i \(0.0378765\pi\)
−0.992929 + 0.118712i \(0.962124\pi\)
\(504\) 7.38881e12i 0.227207i
\(505\) 8.08228e12i 0.246081i
\(506\) 1.05569e13i 0.318261i
\(507\) 1.48130e13 0.442183
\(508\) 4.27940e13 1.26493
\(509\) 6.27268e13i 1.83596i −0.396621 0.917982i \(-0.629817\pi\)
0.396621 0.917982i \(-0.370183\pi\)
\(510\) 3.15361e13i 0.914022i
\(511\) 1.76964e13i 0.507903i
\(512\) 6.41123e13i 1.82218i
\(513\) −8.14617e12 −0.229280
\(514\) 9.54227e13i 2.65972i
\(515\) 1.00014e12i 0.0276075i
\(516\) 6.89028e13i 1.88360i
\(517\) −1.60468e13 −0.434446
\(518\) 3.84496e12 0.103096
\(519\) 3.33555e13i 0.885788i
\(520\) −1.73313e13 −0.455843
\(521\) 6.93620e12 0.180690 0.0903448 0.995911i \(-0.471203\pi\)
0.0903448 + 0.995911i \(0.471203\pi\)
\(522\) 4.02365e13i 1.03817i
\(523\) 3.19441e13 0.816360 0.408180 0.912901i \(-0.366164\pi\)
0.408180 + 0.912901i \(0.366164\pi\)
\(524\) 1.23068e14i 3.11522i
\(525\) 6.34579e12 0.159107
\(526\) 5.99650e13i 1.48926i
\(527\) 1.45585e12i 0.0358149i
\(528\) 6.69992e12i 0.163268i
\(529\) 2.13780e13 0.516047
\(530\) 1.92461e13i 0.460218i
\(531\) 4.08247e12 + 1.34666e13i 0.0967052 + 0.318997i
\(532\) −3.93135e13 −0.922535
\(533\) 2.64537e13i 0.614964i
\(534\) −5.16866e13 −1.19034
\(535\) 2.22548e13 0.507756
\(536\) 9.78824e13 2.21249
\(537\) 2.91343e13i 0.652429i
\(538\) 7.13478e13 1.58296
\(539\) 1.02166e13i 0.224576i
\(540\) 9.45754e12 0.205972
\(541\) 2.47793e13i 0.534691i 0.963601 + 0.267345i \(0.0861464\pi\)
−0.963601 + 0.267345i \(0.913854\pi\)
\(542\) 2.50974e13i 0.536577i
\(543\) 1.25149e13 0.265111
\(544\) 7.16842e12i 0.150463i
\(545\) 4.05004e13i 0.842319i
\(546\) 9.01609e12 0.185804
\(547\) −3.88238e13 −0.792797 −0.396398 0.918079i \(-0.629740\pi\)
−0.396398 + 0.918079i \(0.629740\pi\)
\(548\) 1.34591e14 2.72340
\(549\) 6.35806e12i 0.127486i
\(550\) 1.65919e13 0.329672
\(551\) −1.08354e14 −2.13348
\(552\) −3.66884e13 −0.715869
\(553\) −3.14860e13 −0.608824
\(554\) 1.06401e14i 2.03890i
\(555\) 2.49089e12i 0.0473031i
\(556\) −1.80212e14 −3.39163
\(557\) 7.83101e13 1.46064 0.730318 0.683107i \(-0.239372\pi\)
0.730318 + 0.683107i \(0.239372\pi\)
\(558\) 6.52229e11 0.0120567
\(559\) 4.25539e13 0.779616
\(560\) 1.19681e13 0.217312
\(561\) 1.45328e13i 0.261538i
\(562\) 2.23287e13i 0.398274i
\(563\) 6.47119e13i 1.14404i 0.820239 + 0.572021i \(0.193840\pi\)
−0.820239 + 0.572021i \(0.806160\pi\)
\(564\) 1.10185e14i 1.93075i
\(565\) 5.14264e13i 0.893191i
\(566\) −2.10288e13 −0.362020
\(567\) −2.49014e12 −0.0424921
\(568\) 8.34714e13i 1.41187i
\(569\) 3.52782e13i 0.591487i −0.955267 0.295743i \(-0.904433\pi\)
0.955267 0.295743i \(-0.0955673\pi\)
\(570\) 3.80468e13i 0.632330i
\(571\) 9.85801e13i 1.62409i 0.583598 + 0.812043i \(0.301644\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(572\) 1.57802e13 0.257711
\(573\) 1.24036e13i 0.200804i
\(574\) 5.26735e13i 0.845343i
\(575\) 3.15094e13i 0.501304i
\(576\) 1.95090e13 0.307697
\(577\) −2.85789e13 −0.446855 −0.223427 0.974721i \(-0.571725\pi\)
−0.223427 + 0.974721i \(0.571725\pi\)
\(578\) 2.20546e14i 3.41869i
\(579\) −3.63218e13 −0.558180
\(580\) 1.25797e14 1.91660
\(581\) 3.15089e12i 0.0475941i
\(582\) −8.75257e12 −0.131075
\(583\) 8.86919e12i 0.131686i
\(584\) −1.60800e14 −2.36713
\(585\) 5.84091e12i 0.0852514i
\(586\) 9.32327e13i 1.34921i
\(587\) 1.17700e14i 1.68883i 0.535692 + 0.844413i \(0.320051\pi\)
−0.535692 + 0.844413i \(0.679949\pi\)
\(588\) 7.01520e13 0.998053
\(589\) 1.75641e12i 0.0247771i
\(590\) −6.28961e13 + 1.90672e13i −0.879759 + 0.266702i
\(591\) 3.65447e13 0.506858
\(592\) 1.21166e13i 0.166637i
\(593\) −5.84651e13 −0.797302 −0.398651 0.917103i \(-0.630522\pi\)
−0.398651 + 0.917103i \(0.630522\pi\)
\(594\) −6.51077e12 −0.0880441
\(595\) −2.59599e13 −0.348112
\(596\) 1.45379e14i 1.93317i
\(597\) 2.00786e13 0.264766
\(598\) 4.47685e13i 0.585419i
\(599\) −1.34740e14 −1.74728 −0.873639 0.486575i \(-0.838246\pi\)
−0.873639 + 0.486575i \(0.838246\pi\)
\(600\) 5.76617e13i 0.741534i
\(601\) 1.67071e13i 0.213073i 0.994309 + 0.106536i \(0.0339761\pi\)
−0.994309 + 0.106536i \(0.966024\pi\)
\(602\) −8.47318e13 −1.07168
\(603\) 3.29878e13i 0.413777i
\(604\) 6.74459e13i 0.839018i
\(605\) −3.98789e13 −0.492001
\(606\) 3.82052e13 0.467476
\(607\) 2.65267e13 0.321914 0.160957 0.986961i \(-0.448542\pi\)
0.160957 + 0.986961i \(0.448542\pi\)
\(608\) 8.64836e12i 0.104092i
\(609\) −3.31220e13 −0.395394
\(610\) 2.96954e13 0.351593
\(611\) −6.80495e13 −0.799133
\(612\) 9.97888e13 1.16232
\(613\) 2.40505e13i 0.277857i 0.990302 + 0.138928i \(0.0443658\pi\)
−0.990302 + 0.138928i \(0.955634\pi\)
\(614\) 9.15892e13i 1.04955i
\(615\) −3.41236e13 −0.387864
\(616\) −1.59030e13 −0.179298
\(617\) −5.25545e13 −0.587738 −0.293869 0.955846i \(-0.594943\pi\)
−0.293869 + 0.955846i \(0.594943\pi\)
\(618\) 4.72771e12 0.0524455
\(619\) 3.62492e13 0.398882 0.199441 0.979910i \(-0.436087\pi\)
0.199441 + 0.979910i \(0.436087\pi\)
\(620\) 2.03916e12i 0.0222583i
\(621\) 1.23645e13i 0.133881i
\(622\) 2.46034e13i 0.264267i
\(623\) 4.25475e13i 0.453350i
\(624\) 2.84123e13i 0.300319i
\(625\) 2.28772e13 0.239885
\(626\) 2.25895e14 2.34982
\(627\) 1.75331e13i 0.180934i
\(628\) 2.81242e14i 2.87927i
\(629\) 2.62820e13i 0.266935i
\(630\) 1.16302e13i 0.117188i
\(631\) −2.24031e13 −0.223956 −0.111978 0.993711i \(-0.535719\pi\)
−0.111978 + 0.993711i \(0.535719\pi\)
\(632\) 2.86101e14i 2.83749i
\(633\) 8.03314e13i 0.790436i
\(634\) 2.23643e14i 2.18328i
\(635\) 3.40923e13 0.330208
\(636\) 6.09000e13 0.585237
\(637\) 4.33255e13i 0.413091i
\(638\) −8.66015e13 −0.819261
\(639\) 2.81311e13 0.264048
\(640\) 9.60760e13i 0.894777i
\(641\) −2.86399e13 −0.264656 −0.132328 0.991206i \(-0.542245\pi\)
−0.132328 + 0.991206i \(0.542245\pi\)
\(642\) 1.05199e14i 0.964576i
\(643\) −1.20323e13 −0.109470 −0.0547350 0.998501i \(-0.517431\pi\)
−0.0547350 + 0.998501i \(0.517431\pi\)
\(644\) 5.96713e13i 0.538687i
\(645\) 5.48920e13i 0.491712i
\(646\) 4.01441e14i 3.56828i
\(647\) 3.55855e13 0.313871 0.156936 0.987609i \(-0.449838\pi\)
0.156936 + 0.987609i \(0.449838\pi\)
\(648\) 2.26269e13i 0.198039i
\(649\) 2.89844e13 8.78674e12i 0.251734 0.0763140i
\(650\) 7.03609e13 0.606407
\(651\) 5.36903e11i 0.00459189i
\(652\) 5.25323e13 0.445849
\(653\) −6.82597e13 −0.574908 −0.287454 0.957794i \(-0.592809\pi\)
−0.287454 + 0.957794i \(0.592809\pi\)
\(654\) −1.91446e14 −1.60014
\(655\) 9.80431e13i 0.813225i
\(656\) 1.65989e14 1.36635
\(657\) 5.41921e13i 0.442700i
\(658\) 1.35498e14 1.09851
\(659\) 1.49491e14i 1.20278i 0.798954 + 0.601392i \(0.205387\pi\)
−0.798954 + 0.601392i \(0.794613\pi\)
\(660\) 2.03556e13i 0.162541i
\(661\) 1.75015e14 1.38697 0.693487 0.720469i \(-0.256073\pi\)
0.693487 + 0.720469i \(0.256073\pi\)
\(662\) 2.57618e13i 0.202622i
\(663\) 6.16289e13i 0.481080i
\(664\) 2.86310e13 0.221817
\(665\) −3.13194e13 −0.240827
\(666\) −1.17745e13 −0.0898610
\(667\) 1.64464e14i 1.24578i
\(668\) 1.72971e14 1.30044
\(669\) 1.46806e14 1.09550
\(670\) 1.54070e14 1.14115
\(671\) −1.36845e13 −0.100604
\(672\) 2.64365e12i 0.0192911i
\(673\) 2.32901e13i 0.168693i −0.996437 0.0843463i \(-0.973120\pi\)
0.996437 0.0843463i \(-0.0268802\pi\)
\(674\) 1.62079e13 0.116527
\(675\) −1.94328e13 −0.138681
\(676\) −2.18918e14 −1.55077
\(677\) −9.46918e13 −0.665838 −0.332919 0.942955i \(-0.608034\pi\)
−0.332919 + 0.942955i \(0.608034\pi\)
\(678\) 2.43094e14 1.69678
\(679\) 7.20496e12i 0.0499209i
\(680\) 2.35888e14i 1.62241i
\(681\) 9.98708e13i 0.681872i
\(682\) 1.40380e12i 0.00951445i
\(683\) 2.43084e13i 0.163551i 0.996651 + 0.0817754i \(0.0260590\pi\)
−0.996651 + 0.0817754i \(0.973941\pi\)
\(684\) 1.20390e14 0.804103
\(685\) 1.07223e14 0.710942
\(686\) 1.87314e14i 1.23296i
\(687\) 1.73693e14i 1.13501i
\(688\) 2.67014e14i 1.73218i
\(689\) 3.76115e13i 0.242228i
\(690\) −5.77487e13 −0.369230
\(691\) 2.82671e14i 1.79428i −0.441745 0.897141i \(-0.645640\pi\)
0.441745 0.897141i \(-0.354360\pi\)
\(692\) 4.92953e14i 3.10653i
\(693\) 5.35955e12i 0.0335322i
\(694\) 5.24385e14 3.25726
\(695\) −1.43567e14 −0.885384
\(696\) 3.00966e14i 1.84277i
\(697\) −3.60047e14 −2.18875
\(698\) 1.23950e14 0.748116
\(699\) 6.26879e13i 0.375662i
\(700\) −9.37830e13 −0.558000
\(701\) 1.30823e14i 0.772850i −0.922321 0.386425i \(-0.873710\pi\)
0.922321 0.386425i \(-0.126290\pi\)
\(702\) −2.76102e13 −0.161951
\(703\) 3.17080e13i 0.184668i
\(704\) 4.19895e13i 0.242816i
\(705\) 8.77798e13i 0.504021i
\(706\) −1.05840e13 −0.0603430
\(707\) 3.14498e13i 0.178041i
\(708\) −6.03339e13 1.99021e14i −0.339152 1.11875i
\(709\) −2.90493e14 −1.62145 −0.810726 0.585425i \(-0.800928\pi\)
−0.810726 + 0.585425i \(0.800928\pi\)
\(710\) 1.31387e14i 0.728214i
\(711\) 9.64202e13 0.530664
\(712\) 3.86613e14 2.11289
\(713\) −2.66594e12 −0.0144678
\(714\) 1.22713e14i 0.661303i
\(715\) 1.25715e13 0.0672754
\(716\) 4.30569e14i 2.28812i
\(717\) −1.16310e14 −0.613792
\(718\) 3.24779e14i 1.70203i
\(719\) 2.13909e14i 1.11323i 0.830770 + 0.556616i \(0.187900\pi\)
−0.830770 + 0.556616i \(0.812100\pi\)
\(720\) −3.66501e13 −0.189414
\(721\) 3.89176e12i 0.0199742i
\(722\) 1.43099e14i 0.729374i
\(723\) −6.10291e13 −0.308920
\(724\) −1.84955e14 −0.929765
\(725\) −2.58481e14 −1.29044
\(726\) 1.88508e14i 0.934647i
\(727\) −2.68389e13 −0.132158 −0.0660789 0.997814i \(-0.521049\pi\)
−0.0660789 + 0.997814i \(0.521049\pi\)
\(728\) −6.74397e13 −0.329806
\(729\) 7.62560e12 0.0370370
\(730\) −2.53105e14 −1.22092
\(731\) 5.79179e14i 2.77476i
\(732\) 9.39644e13i 0.447103i
\(733\) 3.37680e14 1.59582 0.797912 0.602774i \(-0.205938\pi\)
0.797912 + 0.602774i \(0.205938\pi\)
\(734\) −2.47692e14 −1.16260
\(735\) 5.58872e13 0.260541
\(736\) 1.31268e13 0.0607811
\(737\) −7.10000e13 −0.326528
\(738\) 1.61303e14i 0.736820i
\(739\) 1.09944e14i 0.498828i −0.968397 0.249414i \(-0.919762\pi\)
0.968397 0.249414i \(-0.0802380\pi\)
\(740\) 3.68123e13i 0.165895i
\(741\) 7.43524e13i 0.332816i
\(742\) 7.48905e13i 0.332972i
\(743\) −3.17357e14 −1.40154 −0.700769 0.713389i \(-0.747159\pi\)
−0.700769 + 0.713389i \(0.747159\pi\)
\(744\) −4.87863e12 −0.0214010
\(745\) 1.15817e14i 0.504652i
\(746\) 3.41583e14i 1.47843i
\(747\) 9.64905e12i 0.0414841i
\(748\) 2.14777e14i 0.917232i
\(749\) 8.65979e13 0.367365
\(750\) 2.16712e14i 0.913224i
\(751\) 7.95007e13i 0.332791i 0.986059 + 0.166395i \(0.0532128\pi\)
−0.986059 + 0.166395i \(0.946787\pi\)
\(752\) 4.26992e14i 1.77554i
\(753\) 8.46353e13 0.349604
\(754\) −3.67250e14 −1.50697
\(755\) 5.37314e13i 0.219025i
\(756\) 3.68012e13 0.149023
\(757\) −2.85972e13 −0.115039 −0.0575193 0.998344i \(-0.518319\pi\)
−0.0575193 + 0.998344i \(0.518319\pi\)
\(758\) 1.60639e14i 0.641957i
\(759\) 2.66123e13 0.105651
\(760\) 2.84587e14i 1.12240i
\(761\) −6.02955e12 −0.0236245 −0.0118122 0.999930i \(-0.503760\pi\)
−0.0118122 + 0.999930i \(0.503760\pi\)
\(762\) 1.61155e14i 0.627291i
\(763\) 1.57595e14i 0.609425i
\(764\) 1.83310e14i 0.704236i
\(765\) 7.94976e13 0.303422
\(766\) 5.04604e14i 1.91341i
\(767\) 1.22914e14 3.72618e13i 0.463046 0.140374i
\(768\) −3.11760e14 −1.16685
\(769\) 2.20971e14i 0.821681i 0.911707 + 0.410841i \(0.134765\pi\)
−0.911707 + 0.410841i \(0.865235\pi\)
\(770\) −2.50318e13 −0.0924782
\(771\) −2.40546e14 −0.882930
\(772\) 5.36792e14 1.95758
\(773\) 4.20413e14i 1.52328i −0.648003 0.761638i \(-0.724395\pi\)
0.648003 0.761638i \(-0.275605\pi\)
\(774\) 2.59476e14 0.934098
\(775\) 4.18995e12i 0.0149865i
\(776\) 6.54687e13 0.232662
\(777\) 9.69255e12i 0.0342242i
\(778\) 6.76209e14i 2.37237i
\(779\) −4.34379e14 −1.51420