Properties

Label 8.14.b.b.5.3
Level 8
Weight 14
Character 8.5
Analytic conductor 8.578
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(8.57847431615\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.3
Root \(-17.5296 - 43.4857i\)
Character \(\chi\) = 8.5
Dual form 8.14.b.b.5.4

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-25.0592 - 86.9715i) q^{2}\) \(-1746.24i q^{3}\) \(+(-6936.08 + 4358.86i) q^{4}\) \(-64905.5i q^{5}\) \(+(-151873. + 43759.4i) q^{6}\) \(+201238. q^{7}\) \(+(552909. + 494011. i) q^{8}\) \(-1.45504e6 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-25.0592 - 86.9715i) q^{2}\) \(-1746.24i q^{3}\) \(+(-6936.08 + 4358.86i) q^{4}\) \(-64905.5i q^{5}\) \(+(-151873. + 43759.4i) q^{6}\) \(+201238. q^{7}\) \(+(552909. + 494011. i) q^{8}\) \(-1.45504e6 q^{9}\) \(+(-5.64492e6 + 1.62648e6i) q^{10}\) \(+1.75974e6i q^{11}\) \(+(7.61163e6 + 1.21121e7i) q^{12}\) \(+1.36072e7i q^{13}\) \(+(-5.04285e6 - 1.75019e7i) q^{14}\) \(-1.13341e8 q^{15}\) \(+(2.91095e7 - 6.04668e7i) q^{16}\) \(+1.14077e8 q^{17}\) \(+(3.64621e7 + 1.26547e8i) q^{18}\) \(-2.75583e8i q^{19}\) \(+(2.82914e8 + 4.50189e8i) q^{20}\) \(-3.51410e8i q^{21}\) \(+(1.53048e8 - 4.40977e7i) q^{22}\) \(+1.08842e8 q^{23}\) \(+(8.62664e8 - 9.65513e8i) q^{24}\) \(-2.99201e9 q^{25}\) \(+(1.18344e9 - 3.40985e8i) q^{26}\) \(-2.43222e8i q^{27}\) \(+(-1.39580e9 + 8.77168e8i) q^{28}\) \(+1.20078e9i q^{29}\) \(+(2.84022e9 + 9.85741e9i) q^{30}\) \(-1.80300e9 q^{31}\) \(+(-5.98835e9 - 1.01645e9i) q^{32}\) \(+3.07294e9 q^{33}\) \(+(-2.85867e9 - 9.92145e9i) q^{34}\) \(-1.30614e10i q^{35}\) \(+(1.00923e10 - 6.34232e9i) q^{36}\) \(+1.90075e10i q^{37}\) \(+(-2.39679e10 + 6.90588e9i) q^{38}\) \(+2.37615e10 q^{39}\) \(+(3.20640e10 - 3.58868e10i) q^{40}\) \(+2.47690e10 q^{41}\) \(+(-3.05626e10 + 8.80604e9i) q^{42}\) \(-1.71033e10i q^{43}\) \(+(-7.67048e9 - 1.22057e10i) q^{44}\) \(+9.44400e10i q^{45}\) \(+(-2.72749e9 - 9.46614e9i) q^{46}\) \(+1.08638e10 q^{47}\) \(+(-1.05590e11 - 5.08322e10i) q^{48}\) \(-5.63924e10 q^{49}\) \(+(7.49774e10 + 2.60220e11i) q^{50}\) \(-1.99206e11i q^{51}\) \(+(-5.93120e10 - 9.43806e10i) q^{52}\) \(+8.06286e10i q^{53}\) \(+(-2.11534e10 + 6.09493e9i) q^{54}\) \(+1.14217e11 q^{55}\) \(+(1.11266e11 + 9.94137e10i) q^{56}\) \(-4.81235e11 q^{57}\) \(+(1.04434e11 - 3.00906e10i) q^{58}\) \(+4.80718e10i q^{59}\) \(+(7.86140e11 - 4.94037e11i) q^{60}\) \(-5.26856e10i q^{61}\) \(+(4.51816e10 + 1.56809e11i) q^{62}\) \(-2.92809e11 q^{63}\) \(+(6.16612e10 + 5.46287e11i) q^{64}\) \(+8.83182e11 q^{65}\) \(+(-7.70053e10 - 2.67258e11i) q^{66}\) \(-1.29726e12i q^{67}\) \(+(-7.91247e11 + 4.97246e11i) q^{68}\) \(-1.90064e11i q^{69}\) \(+(-1.13597e12 + 3.27308e11i) q^{70}\) \(-1.26160e12 q^{71}\) \(+(-8.04505e11 - 7.18806e11i) q^{72}\) \(+6.89487e11 q^{73}\) \(+(1.65311e12 - 4.76311e11i) q^{74}\) \(+5.22478e12i q^{75}\) \(+(1.20123e12 + 1.91147e12i) q^{76}\) \(+3.54127e11i q^{77}\) \(+(-5.95443e11 - 2.06657e12i) q^{78}\) \(+3.83954e12 q^{79}\) \(+(-3.92463e12 - 1.88936e12i) q^{80}\) \(-2.74453e12 q^{81}\) \(+(-6.20691e11 - 2.15420e12i) q^{82}\) \(-9.29026e11i q^{83}\) \(+(1.53175e12 + 2.43741e12i) q^{84}\) \(-7.40422e12i q^{85}\) \(+(-1.48750e12 + 4.28595e11i) q^{86}\) \(+2.09686e12 q^{87}\) \(+(-8.69334e11 + 9.72978e11i) q^{88}\) \(+6.60666e12 q^{89}\) \(+(8.21359e12 - 2.36659e12i) q^{90}\) \(+2.73828e12i q^{91}\) \(+(-7.54936e11 + 4.74427e11i) q^{92}\) \(+3.14847e12i q^{93}\) \(+(-2.72238e11 - 9.44840e11i) q^{94}\) \(-1.78869e13 q^{95}\) \(+(-1.77496e12 + 1.04571e13i) q^{96}\) \(+8.12199e11 q^{97}\) \(+(1.41315e12 + 4.90453e12i) q^{98}\) \(-2.56050e12i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut -\mathstrut 4542088q^{10} \) \(\mathstrut +\mathstrut 27987880q^{12} \) \(\mathstrut +\mathstrut 1408688q^{14} \) \(\mathstrut -\mathstrut 145914416q^{15} \) \(\mathstrut +\mathstrut 56624912q^{16} \) \(\mathstrut +\mathstrut 217326004q^{17} \) \(\mathstrut -\mathstrut 147615262q^{18} \) \(\mathstrut +\mathstrut 21655184q^{20} \) \(\mathstrut -\mathstrut 177987876q^{22} \) \(\mathstrut -\mathstrut 78679952q^{23} \) \(\mathstrut +\mathstrut 320199056q^{24} \) \(\mathstrut -\mathstrut 3076402574q^{25} \) \(\mathstrut +\mathstrut 3734872040q^{26} \) \(\mathstrut -\mathstrut 1653812448q^{28} \) \(\mathstrut +\mathstrut 6338232752q^{30} \) \(\mathstrut +\mathstrut 648233792q^{31} \) \(\mathstrut -\mathstrut 11298380000q^{32} \) \(\mathstrut +\mathstrut 15484079688q^{33} \) \(\mathstrut -\mathstrut 6096822724q^{34} \) \(\mathstrut +\mathstrut 4004708940q^{36} \) \(\mathstrut -\mathstrut 18764968628q^{38} \) \(\mathstrut -\mathstrut 63497510288q^{39} \) \(\mathstrut +\mathstrut 7466802592q^{40} \) \(\mathstrut +\mathstrut 59324640356q^{41} \) \(\mathstrut +\mathstrut 53897620960q^{42} \) \(\mathstrut +\mathstrut 13325704392q^{44} \) \(\mathstrut -\mathstrut 55046867440q^{46} \) \(\mathstrut -\mathstrut 10176534816q^{47} \) \(\mathstrut -\mathstrut 301841943264q^{48} \) \(\mathstrut +\mathstrut 182708552058q^{49} \) \(\mathstrut +\mathstrut 326454435302q^{50} \) \(\mathstrut -\mathstrut 53296499536q^{52} \) \(\mathstrut +\mathstrut 35449773752q^{54} \) \(\mathstrut -\mathstrut 123010753008q^{55} \) \(\mathstrut -\mathstrut 462152447680q^{56} \) \(\mathstrut -\mathstrut 511372324504q^{57} \) \(\mathstrut +\mathstrut 766482705096q^{58} \) \(\mathstrut +\mathstrut 1813082440992q^{60} \) \(\mathstrut -\mathstrut 1665308528960q^{62} \) \(\mathstrut -\mathstrut 898991123792q^{63} \) \(\mathstrut -\mathstrut 2180548996032q^{64} \) \(\mathstrut +\mathstrut 1577231990240q^{65} \) \(\mathstrut +\mathstrut 2269525079448q^{66} \) \(\mathstrut +\mathstrut 2338280915304q^{68} \) \(\mathstrut -\mathstrut 6070110714688q^{70} \) \(\mathstrut +\mathstrut 726361179984q^{71} \) \(\mathstrut -\mathstrut 3600753685960q^{72} \) \(\mathstrut -\mathstrut 633240365532q^{73} \) \(\mathstrut +\mathstrut 7528513982264q^{74} \) \(\mathstrut +\mathstrut 10338420845032q^{76} \) \(\mathstrut -\mathstrut 8252024440816q^{78} \) \(\mathstrut +\mathstrut 5445103565344q^{79} \) \(\mathstrut -\mathstrut 15406871881920q^{80} \) \(\mathstrut -\mathstrut 9674575380574q^{81} \) \(\mathstrut +\mathstrut 12273334206796q^{82} \) \(\mathstrut +\mathstrut 20362643366464q^{84} \) \(\mathstrut -\mathstrut 26794541719396q^{86} \) \(\mathstrut +\mathstrut 7632221772720q^{87} \) \(\mathstrut -\mathstrut 27677491769136q^{88} \) \(\mathstrut +\mathstrut 5506344808004q^{89} \) \(\mathstrut +\mathstrut 31454099524040q^{90} \) \(\mathstrut +\mathstrut 33971694298464q^{92} \) \(\mathstrut -\mathstrut 45356008560096q^{94} \) \(\mathstrut -\mathstrut 14214732035504q^{95} \) \(\mathstrut -\mathstrut 35398666935232q^{96} \) \(\mathstrut +\mathstrut 1361133320788q^{97} \) \(\mathstrut +\mathstrut 54325451514942q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −25.0592 86.9715i −0.276867 0.960908i
\(3\) 1746.24i 1.38298i −0.722385 0.691491i \(-0.756954\pi\)
0.722385 0.691491i \(-0.243046\pi\)
\(4\) −6936.08 + 4358.86i −0.846689 + 0.532088i
\(5\) 64905.5i 1.85770i −0.370453 0.928851i \(-0.620798\pi\)
0.370453 0.928851i \(-0.379202\pi\)
\(6\) −151873. + 43759.4i −1.32892 + 0.382902i
\(7\) 201238. 0.646505 0.323253 0.946313i \(-0.395224\pi\)
0.323253 + 0.946313i \(0.395224\pi\)
\(8\) 552909. + 494011.i 0.745708 + 0.666273i
\(9\) −1.45504e6 −0.912638
\(10\) −5.64492e6 + 1.62648e6i −1.78508 + 0.514337i
\(11\) 1.75974e6i 0.299500i 0.988724 + 0.149750i \(0.0478469\pi\)
−0.988724 + 0.149750i \(0.952153\pi\)
\(12\) 7.61163e6 + 1.21121e7i 0.735868 + 1.17096i
\(13\) 1.36072e7i 0.781875i 0.920417 + 0.390937i \(0.127849\pi\)
−0.920417 + 0.390937i \(0.872151\pi\)
\(14\) −5.04285e6 1.75019e7i −0.178996 0.621232i
\(15\) −1.13341e8 −2.56917
\(16\) 2.91095e7 6.04668e7i 0.433765 0.901026i
\(17\) 1.14077e8 1.14625 0.573126 0.819467i \(-0.305731\pi\)
0.573126 + 0.819467i \(0.305731\pi\)
\(18\) 3.64621e7 + 1.26547e8i 0.252680 + 0.876962i
\(19\) 2.75583e8i 1.34386i −0.740614 0.671931i \(-0.765465\pi\)
0.740614 0.671931i \(-0.234535\pi\)
\(20\) 2.82914e8 + 4.50189e8i 0.988461 + 1.57290i
\(21\) 3.51410e8i 0.894105i
\(22\) 1.53048e8 4.40977e7i 0.287792 0.0829218i
\(23\) 1.08842e8 0.153308 0.0766541 0.997058i \(-0.475576\pi\)
0.0766541 + 0.997058i \(0.475576\pi\)
\(24\) 8.62664e8 9.65513e8i 0.921443 1.03130i
\(25\) −2.99201e9 −2.45106
\(26\) 1.18344e9 3.40985e8i 0.751310 0.216475i
\(27\) 2.43222e8i 0.120820i
\(28\) −1.39580e9 + 8.77168e8i −0.547389 + 0.343998i
\(29\) 1.20078e9i 0.374867i 0.982277 + 0.187433i \(0.0600169\pi\)
−0.982277 + 0.187433i \(0.939983\pi\)
\(30\) 2.84022e9 + 9.85741e9i 0.711318 + 2.46873i
\(31\) −1.80300e9 −0.364875 −0.182437 0.983217i \(-0.558399\pi\)
−0.182437 + 0.983217i \(0.558399\pi\)
\(32\) −5.98835e9 1.01645e9i −0.985899 0.167344i
\(33\) 3.07294e9 0.414203
\(34\) −2.85867e9 9.92145e9i −0.317360 1.10144i
\(35\) 1.30614e10i 1.20101i
\(36\) 1.00923e10 6.34232e9i 0.772721 0.485604i
\(37\) 1.90075e10i 1.21790i 0.793207 + 0.608952i \(0.208410\pi\)
−0.793207 + 0.608952i \(0.791590\pi\)
\(38\) −2.39679e10 + 6.90588e9i −1.29133 + 0.372071i
\(39\) 2.37615e10 1.08132
\(40\) 3.20640e10 3.58868e10i 1.23774 1.38530i
\(41\) 2.47690e10 0.814355 0.407177 0.913349i \(-0.366513\pi\)
0.407177 + 0.913349i \(0.366513\pi\)
\(42\) −3.05626e10 + 8.80604e9i −0.859153 + 0.247548i
\(43\) 1.71033e10i 0.412606i −0.978488 0.206303i \(-0.933857\pi\)
0.978488 0.206303i \(-0.0661432\pi\)
\(44\) −7.67048e9 1.22057e10i −0.159360 0.253583i
\(45\) 9.44400e10i 1.69541i
\(46\) −2.72749e9 9.46614e9i −0.0424460 0.147315i
\(47\) 1.08638e10 0.147010 0.0735048 0.997295i \(-0.476582\pi\)
0.0735048 + 0.997295i \(0.476582\pi\)
\(48\) −1.05590e11 5.08322e10i −1.24610 0.599889i
\(49\) −5.63924e10 −0.582031
\(50\) 7.49774e10 + 2.60220e11i 0.678618 + 2.35524i
\(51\) 1.99206e11i 1.58525i
\(52\) −5.93120e10 9.43806e10i −0.416026 0.662005i
\(53\) 8.06286e10i 0.499684i 0.968287 + 0.249842i \(0.0803787\pi\)
−0.968287 + 0.249842i \(0.919621\pi\)
\(54\) −2.11534e10 + 6.09493e9i −0.116097 + 0.0334510i
\(55\) 1.14217e11 0.556382
\(56\) 1.11266e11 + 9.94137e10i 0.482104 + 0.430749i
\(57\) −4.81235e11 −1.85854
\(58\) 1.04434e11 3.00906e10i 0.360213 0.103788i
\(59\) 4.80718e10i 0.148372i 0.997244 + 0.0741861i \(0.0236359\pi\)
−0.997244 + 0.0741861i \(0.976364\pi\)
\(60\) 7.86140e11 4.94037e11i 2.17529 1.36702i
\(61\) 5.26856e10i 0.130933i −0.997855 0.0654663i \(-0.979147\pi\)
0.997855 0.0654663i \(-0.0208535\pi\)
\(62\) 4.51816e10 + 1.56809e11i 0.101022 + 0.350611i
\(63\) −2.92809e11 −0.590025
\(64\) 6.16612e10 + 5.46287e11i 0.112161 + 0.993690i
\(65\) 8.83182e11 1.45249
\(66\) −7.70053e10 2.67258e11i −0.114679 0.398011i
\(67\) 1.29726e12i 1.75202i −0.482293 0.876010i \(-0.660196\pi\)
0.482293 0.876010i \(-0.339804\pi\)
\(68\) −7.91247e11 + 4.97246e11i −0.970519 + 0.609907i
\(69\) 1.90064e11i 0.212022i
\(70\) −1.13597e12 + 3.27308e11i −1.15406 + 0.332522i
\(71\) −1.26160e12 −1.16881 −0.584404 0.811463i \(-0.698672\pi\)
−0.584404 + 0.811463i \(0.698672\pi\)
\(72\) −8.04505e11 7.18806e11i −0.680562 0.608066i
\(73\) 6.89487e11 0.533246 0.266623 0.963801i \(-0.414092\pi\)
0.266623 + 0.963801i \(0.414092\pi\)
\(74\) 1.65311e12 4.76311e11i 1.17029 0.337198i
\(75\) 5.22478e12i 3.38977i
\(76\) 1.20123e12 + 1.91147e12i 0.715052 + 1.13783i
\(77\) 3.54127e11i 0.193628i
\(78\) −5.95443e11 2.06657e12i −0.299382 1.03905i
\(79\) 3.83954e12 1.77706 0.888531 0.458816i \(-0.151726\pi\)
0.888531 + 0.458816i \(0.151726\pi\)
\(80\) −3.92463e12 1.88936e12i −1.67384 0.805806i
\(81\) −2.74453e12 −1.07973
\(82\) −6.20691e11 2.15420e12i −0.225468 0.782520i
\(83\) 9.29026e11i 0.311903i −0.987765 0.155952i \(-0.950156\pi\)
0.987765 0.155952i \(-0.0498444\pi\)
\(84\) 1.53175e12 + 2.43741e12i 0.475742 + 0.757029i
\(85\) 7.40422e12i 2.12940i
\(86\) −1.48750e12 + 4.28595e11i −0.396476 + 0.114237i
\(87\) 2.09686e12 0.518434
\(88\) −8.69334e11 + 9.72978e11i −0.199549 + 0.223340i
\(89\) 6.60666e12 1.40912 0.704558 0.709647i \(-0.251145\pi\)
0.704558 + 0.709647i \(0.251145\pi\)
\(90\) 8.21359e12 2.36659e12i 1.62913 0.469403i
\(91\) 2.73828e12i 0.505486i
\(92\) −7.54936e11 + 4.74427e11i −0.129804 + 0.0815734i
\(93\) 3.14847e12i 0.504615i
\(94\) −2.72238e11 9.44840e11i −0.0407021 0.141263i
\(95\) −1.78869e13 −2.49649
\(96\) −1.77496e12 + 1.04571e13i −0.231433 + 1.36348i
\(97\) 8.12199e11 0.0990025 0.0495013 0.998774i \(-0.484237\pi\)
0.0495013 + 0.998774i \(0.484237\pi\)
\(98\) 1.41315e12 + 4.90453e12i 0.161145 + 0.559278i
\(99\) 2.56050e12i 0.273335i
\(100\) 2.07528e13 1.30418e13i 2.07528 1.30418i
\(101\) 2.94586e12i 0.276136i −0.990423 0.138068i \(-0.955911\pi\)
0.990423 0.138068i \(-0.0440893\pi\)
\(102\) −1.73252e13 + 4.99194e12i −1.52328 + 0.438902i
\(103\) −2.42353e12 −0.199989 −0.0999946 0.994988i \(-0.531883\pi\)
−0.0999946 + 0.994988i \(0.531883\pi\)
\(104\) −6.72212e12 + 7.52355e12i −0.520942 + 0.583050i
\(105\) −2.28084e13 −1.66098
\(106\) 7.01238e12 2.02048e12i 0.480151 0.138346i
\(107\) 1.12502e13i 0.724715i −0.932039 0.362358i \(-0.881972\pi\)
0.932039 0.362358i \(-0.118028\pi\)
\(108\) 1.06017e12 + 1.68701e12i 0.0642867 + 0.102297i
\(109\) 2.03236e13i 1.16072i 0.814359 + 0.580361i \(0.197089\pi\)
−0.814359 + 0.580361i \(0.802911\pi\)
\(110\) −2.86218e12 9.93362e12i −0.154044 0.534632i
\(111\) 3.31917e13 1.68434
\(112\) 5.85792e12 1.21682e13i 0.280431 0.582518i
\(113\) 5.93927e12 0.268363 0.134182 0.990957i \(-0.457159\pi\)
0.134182 + 0.990957i \(0.457159\pi\)
\(114\) 1.20593e13 + 4.18537e13i 0.514567 + 1.78588i
\(115\) 7.06443e12i 0.284801i
\(116\) −5.23404e12 8.32871e12i −0.199462 0.317396i
\(117\) 1.97990e13i 0.713569i
\(118\) 4.18088e12 1.20464e12i 0.142572 0.0410794i
\(119\) 2.29566e13 0.741058
\(120\) −6.26671e13 5.59916e13i −1.91585 1.71177i
\(121\) 3.14260e13 0.910300
\(122\) −4.58214e12 + 1.32026e12i −0.125814 + 0.0362509i
\(123\) 4.32527e13i 1.12624i
\(124\) 1.25057e13 7.85902e12i 0.308936 0.194145i
\(125\) 1.14968e14i 2.69564i
\(126\) 7.33755e12 + 2.54660e13i 0.163359 + 0.566960i
\(127\) −2.04322e13 −0.432106 −0.216053 0.976382i \(-0.569318\pi\)
−0.216053 + 0.976382i \(0.569318\pi\)
\(128\) 4.59662e13 1.90523e13i 0.923791 0.382897i
\(129\) −2.98665e13 −0.570626
\(130\) −2.21318e13 7.68116e13i −0.402147 1.39571i
\(131\) 8.08054e13i 1.39694i 0.715641 + 0.698469i \(0.246135\pi\)
−0.715641 + 0.698469i \(0.753865\pi\)
\(132\) −2.13141e13 + 1.33945e13i −0.350701 + 0.220392i
\(133\) 5.54577e13i 0.868813i
\(134\) −1.12824e14 + 3.25081e13i −1.68353 + 0.485077i
\(135\) −1.57864e13 −0.224447
\(136\) 6.30742e13 + 5.63553e13i 0.854769 + 0.763717i
\(137\) −3.37588e12 −0.0436218 −0.0218109 0.999762i \(-0.506943\pi\)
−0.0218109 + 0.999762i \(0.506943\pi\)
\(138\) −1.65302e13 + 4.76285e12i −0.203734 + 0.0587020i
\(139\) 1.16370e14i 1.36850i −0.729249 0.684249i \(-0.760130\pi\)
0.729249 0.684249i \(-0.239870\pi\)
\(140\) 5.69330e13 + 9.05951e13i 0.639045 + 1.01689i
\(141\) 1.89708e13i 0.203311i
\(142\) 3.16147e13 + 1.09723e14i 0.323604 + 1.12312i
\(143\) −2.39452e13 −0.234172
\(144\) −4.23554e13 + 8.79817e13i −0.395870 + 0.822311i
\(145\) 7.79373e13 0.696391
\(146\) −1.72780e13 5.99657e13i −0.147638 0.512400i
\(147\) 9.84748e13i 0.804938i
\(148\) −8.28510e13 1.31837e14i −0.648032 1.03119i
\(149\) 2.16755e14i 1.62277i −0.584509 0.811387i \(-0.698713\pi\)
0.584509 0.811387i \(-0.301287\pi\)
\(150\) 4.54407e14 1.30929e14i 3.25726 0.938516i
\(151\) −1.68669e14 −1.15793 −0.578967 0.815351i \(-0.696544\pi\)
−0.578967 + 0.815351i \(0.696544\pi\)
\(152\) 1.36141e14 1.52372e14i 0.895378 1.00213i
\(153\) −1.65987e14 −1.04611
\(154\) 3.07989e13 8.87412e12i 0.186059 0.0536094i
\(155\) 1.17024e14i 0.677829i
\(156\) −1.64811e14 + 1.03573e14i −0.915541 + 0.575356i
\(157\) 2.89792e12i 0.0154433i −0.999970 0.00772163i \(-0.997542\pi\)
0.999970 0.00772163i \(-0.00245789\pi\)
\(158\) −9.62156e13 3.33930e14i −0.492010 1.70759i
\(159\) 1.40797e14 0.691054
\(160\) −6.59729e13 + 3.88677e14i −0.310875 + 1.83151i
\(161\) 2.19031e13 0.0991145
\(162\) 6.87756e13 + 2.38696e14i 0.298942 + 1.03752i
\(163\) 1.11885e14i 0.467252i 0.972327 + 0.233626i \(0.0750592\pi\)
−0.972327 + 0.233626i \(0.924941\pi\)
\(164\) −1.71800e14 + 1.07965e14i −0.689505 + 0.433308i
\(165\) 1.99451e14i 0.769466i
\(166\) −8.07988e13 + 2.32806e13i −0.299711 + 0.0863558i
\(167\) 3.97953e14 1.41963 0.709814 0.704389i \(-0.248779\pi\)
0.709814 + 0.704389i \(0.248779\pi\)
\(168\) 1.73600e14 1.94298e14i 0.595718 0.666741i
\(169\) 1.17719e14 0.388672
\(170\) −6.43956e14 + 1.85543e14i −2.04615 + 0.589560i
\(171\) 4.00985e14i 1.22646i
\(172\) 7.45510e13 + 1.18630e14i 0.219543 + 0.349349i
\(173\) 1.14455e14i 0.324589i 0.986742 + 0.162294i \(0.0518894\pi\)
−0.986742 + 0.162294i \(0.948111\pi\)
\(174\) −5.25454e13 1.82367e14i −0.143537 0.498167i
\(175\) −6.02106e14 −1.58462
\(176\) 1.06406e14 + 5.12252e13i 0.269857 + 0.129913i
\(177\) 8.39451e13 0.205196
\(178\) −1.65557e14 5.74591e14i −0.390138 1.35403i
\(179\) 5.75190e14i 1.30697i −0.756938 0.653487i \(-0.773306\pi\)
0.756938 0.653487i \(-0.226694\pi\)
\(180\) −4.11651e14 6.55043e14i −0.902107 1.43549i
\(181\) 6.03188e14i 1.27509i 0.770412 + 0.637546i \(0.220051\pi\)
−0.770412 + 0.637546i \(0.779949\pi\)
\(182\) 2.38153e14 6.86191e13i 0.485726 0.139953i
\(183\) −9.20018e13 −0.181077
\(184\) 6.01797e13 + 5.37691e13i 0.114323 + 0.102145i
\(185\) 1.23369e15 2.26250
\(186\) 2.73827e14 7.88980e13i 0.484889 0.139711i
\(187\) 2.00746e14i 0.343303i
\(188\) −7.53521e13 + 4.73538e13i −0.124471 + 0.0782220i
\(189\) 4.89454e13i 0.0781106i
\(190\) 4.48230e14 + 1.55565e15i 0.691197 + 2.39890i
\(191\) 4.64876e14 0.692820 0.346410 0.938083i \(-0.387401\pi\)
0.346410 + 0.938083i \(0.387401\pi\)
\(192\) 9.53949e14 1.07675e14i 1.37426 0.155117i
\(193\) −1.24010e15 −1.72717 −0.863583 0.504206i \(-0.831785\pi\)
−0.863583 + 0.504206i \(0.831785\pi\)
\(194\) −2.03530e13 7.06382e13i −0.0274106 0.0951323i
\(195\) 1.54225e15i 2.00877i
\(196\) 3.91142e14 2.45807e14i 0.492799 0.309692i
\(197\) 6.14978e14i 0.749599i 0.927106 + 0.374799i \(0.122288\pi\)
−0.927106 + 0.374799i \(0.877712\pi\)
\(198\) −2.22690e14 + 6.41639e13i −0.262650 + 0.0756776i
\(199\) 7.60323e14 0.867867 0.433933 0.900945i \(-0.357125\pi\)
0.433933 + 0.900945i \(0.357125\pi\)
\(200\) −1.65431e15 1.47809e15i −1.82777 1.63307i
\(201\) −2.26532e15 −2.42301
\(202\) −2.56206e14 + 7.38209e13i −0.265342 + 0.0764531i
\(203\) 2.41643e14i 0.242353i
\(204\) 8.68312e14 + 1.38171e15i 0.843490 + 1.34221i
\(205\) 1.60764e15i 1.51283i
\(206\) 6.07316e13 + 2.10778e14i 0.0553704 + 0.192171i
\(207\) −1.58369e14 −0.139915
\(208\) 8.22785e14 + 3.96099e14i 0.704490 + 0.339150i
\(209\) 4.84956e14 0.402487
\(210\) 5.71560e14 + 1.98368e15i 0.459871 + 1.59605i
\(211\) 4.95425e13i 0.0386493i 0.999813 + 0.0193247i \(0.00615161\pi\)
−0.999813 + 0.0193247i \(0.993848\pi\)
\(212\) −3.51449e14 5.59246e14i −0.265876 0.423077i
\(213\) 2.20306e15i 1.61644i
\(214\) −9.78450e14 + 2.81922e14i −0.696385 + 0.200650i
\(215\) −1.11010e15 −0.766499
\(216\) 1.20154e14 1.34480e14i 0.0804989 0.0900963i
\(217\) −3.62831e14 −0.235893
\(218\) 1.76757e15 5.09292e14i 1.11535 0.321366i
\(219\) 1.20401e15i 0.737469i
\(220\) −7.92218e14 + 4.97856e14i −0.471083 + 0.296044i
\(221\) 1.55227e15i 0.896225i
\(222\) −8.31755e14 2.88673e15i −0.466338 1.61850i
\(223\) −1.52553e15 −0.830691 −0.415346 0.909664i \(-0.636339\pi\)
−0.415346 + 0.909664i \(0.636339\pi\)
\(224\) −1.20508e15 2.04547e14i −0.637389 0.108189i
\(225\) 4.35350e15 2.23693
\(226\) −1.48833e14 5.16547e14i −0.0743010 0.257872i
\(227\) 2.28161e15i 1.10681i 0.832912 + 0.553406i \(0.186672\pi\)
−0.832912 + 0.553406i \(0.813328\pi\)
\(228\) 3.33788e15 2.09764e15i 1.57360 0.988904i
\(229\) 1.55903e15i 0.714371i −0.934033 0.357185i \(-0.883736\pi\)
0.934033 0.357185i \(-0.116264\pi\)
\(230\) −6.14404e14 + 1.77029e14i −0.273667 + 0.0788520i
\(231\) 6.18391e14 0.267785
\(232\) −5.93200e14 + 6.63923e14i −0.249764 + 0.279541i
\(233\) 2.57854e15 1.05575 0.527874 0.849323i \(-0.322989\pi\)
0.527874 + 0.849323i \(0.322989\pi\)
\(234\) −1.72195e15 + 4.96147e14i −0.685674 + 0.197564i
\(235\) 7.05119e14i 0.273100i
\(236\) −2.09539e14 3.33430e14i −0.0789471 0.125625i
\(237\) 6.70476e15i 2.45765i
\(238\) −5.75273e14 1.99657e15i −0.205175 0.712089i
\(239\) 4.22444e15 1.46616 0.733082 0.680140i \(-0.238081\pi\)
0.733082 + 0.680140i \(0.238081\pi\)
\(240\) −3.29929e15 + 6.85335e15i −1.11442 + 2.31489i
\(241\) −3.67088e15 −1.20687 −0.603433 0.797414i \(-0.706201\pi\)
−0.603433 + 0.797414i \(0.706201\pi\)
\(242\) −7.87509e14 2.73317e15i −0.252032 0.874714i
\(243\) 4.40484e15i 1.37243i
\(244\) 2.29649e14 + 3.65431e14i 0.0696677 + 0.110859i
\(245\) 3.66017e15i 1.08124i
\(246\) −3.76175e15 + 1.08388e15i −1.08221 + 0.311818i
\(247\) 3.74992e15 1.05073
\(248\) −9.96893e14 8.90701e14i −0.272090 0.243106i
\(249\) −1.62230e15 −0.431357
\(250\) 9.99892e15 2.88100e15i 2.59026 0.746333i
\(251\) 3.43128e15i 0.866119i 0.901365 + 0.433059i \(0.142566\pi\)
−0.901365 + 0.433059i \(0.857434\pi\)
\(252\) 2.03095e15 1.27631e15i 0.499568 0.313945i
\(253\) 1.91534e14i 0.0459158i
\(254\) 5.12012e14 + 1.77701e15i 0.119636 + 0.415214i
\(255\) −1.29296e16 −2.94491
\(256\) −2.80888e15 3.52032e15i −0.623696 0.781667i
\(257\) −4.41136e15 −0.955009 −0.477504 0.878629i \(-0.658459\pi\)
−0.477504 + 0.878629i \(0.658459\pi\)
\(258\) 7.48430e14 + 2.59754e15i 0.157988 + 0.548320i
\(259\) 3.82502e15i 0.787381i
\(260\) −6.12582e15 + 3.84967e15i −1.22981 + 0.772853i
\(261\) 1.74719e15i 0.342118i
\(262\) 7.02776e15 2.02491e15i 1.34233 0.386766i
\(263\) 4.10604e15 0.765086 0.382543 0.923938i \(-0.375048\pi\)
0.382543 + 0.923938i \(0.375048\pi\)
\(264\) 1.69906e15 + 1.51807e15i 0.308875 + 0.275972i
\(265\) 5.23323e15 0.928265
\(266\) −4.82324e15 + 1.38972e15i −0.834850 + 0.240546i
\(267\) 1.15368e16i 1.94878i
\(268\) 5.65456e15 + 8.99786e15i 0.932229 + 1.48342i
\(269\) 7.35764e15i 1.18399i −0.805941 0.591996i \(-0.798340\pi\)
0.805941 0.591996i \(-0.201660\pi\)
\(270\) 3.95594e14 + 1.37297e15i 0.0621421 + 0.215673i
\(271\) −4.40071e15 −0.674874 −0.337437 0.941348i \(-0.609560\pi\)
−0.337437 + 0.941348i \(0.609560\pi\)
\(272\) 3.32072e15 6.89787e15i 0.497204 1.03280i
\(273\) 4.78171e15 0.699078
\(274\) 8.45968e13 + 2.93606e14i 0.0120775 + 0.0419166i
\(275\) 5.26518e15i 0.734092i
\(276\) 8.28465e14 + 1.31830e15i 0.112814 + 0.179517i
\(277\) 5.52444e15i 0.734801i −0.930063 0.367400i \(-0.880248\pi\)
0.930063 0.367400i \(-0.119752\pi\)
\(278\) −1.01209e16 + 2.91613e15i −1.31500 + 0.378892i
\(279\) 2.62343e15 0.332999
\(280\) 6.45249e15 7.22178e15i 0.800203 0.895606i
\(281\) −9.11467e15 −1.10446 −0.552230 0.833692i \(-0.686223\pi\)
−0.552230 + 0.833692i \(0.686223\pi\)
\(282\) −1.64992e15 + 4.75393e14i −0.195364 + 0.0562903i
\(283\) 6.59039e14i 0.0762604i 0.999273 + 0.0381302i \(0.0121402\pi\)
−0.999273 + 0.0381302i \(0.987860\pi\)
\(284\) 8.75057e15 5.49915e15i 0.989617 0.621908i
\(285\) 3.12348e16i 3.45261i
\(286\) 6.00046e14 + 2.08255e15i 0.0648344 + 0.225017i
\(287\) 4.98446e15 0.526485
\(288\) 8.71329e15 + 1.47897e15i 0.899769 + 0.152724i
\(289\) 3.10898e15 0.313894
\(290\) −1.95304e15 6.77832e15i −0.192808 0.669168i
\(291\) 1.41830e15i 0.136919i
\(292\) −4.78233e15 + 3.00538e15i −0.451493 + 0.283734i
\(293\) 1.53744e14i 0.0141958i 0.999975 + 0.00709789i \(0.00225935\pi\)
−0.999975 + 0.00709789i \(0.997741\pi\)
\(294\) 8.56450e15 2.46770e15i 0.773471 0.222861i
\(295\) 3.12012e15 0.275631
\(296\) −9.38991e15 + 1.05094e16i −0.811456 + 0.908201i
\(297\) 4.28008e14 0.0361855
\(298\) −1.88515e16 + 5.43170e15i −1.55934 + 0.449293i
\(299\) 1.48103e15i 0.119868i
\(300\) −2.27741e16 3.62395e16i −1.80366 2.87008i
\(301\) 3.44183e15i 0.266752i
\(302\) 4.22669e15 + 1.46694e16i 0.320594 + 1.11267i
\(303\) −5.14419e15 −0.381892
\(304\) −1.66636e16 8.02208e15i −1.21085 0.582920i
\(305\) −3.41958e15 −0.243234
\(306\) 4.15948e15 + 1.44361e16i 0.289634 + 1.00522i
\(307\) 1.20014e16i 0.818148i −0.912501 0.409074i \(-0.865852\pi\)
0.912501 0.409074i \(-0.134148\pi\)
\(308\) −1.54359e15 2.45625e15i −0.103027 0.163943i
\(309\) 4.23207e15i 0.276581i
\(310\) 1.01778e16 2.93253e15i 0.651331 0.187669i
\(311\) 2.06212e16 1.29232 0.646162 0.763200i \(-0.276373\pi\)
0.646162 + 0.763200i \(0.276373\pi\)
\(312\) 1.31379e16 + 1.17384e16i 0.806348 + 0.720453i
\(313\) 1.11034e16 0.667448 0.333724 0.942671i \(-0.391695\pi\)
0.333724 + 0.942671i \(0.391695\pi\)
\(314\) −2.52036e14 + 7.26194e13i −0.0148395 + 0.00427573i
\(315\) 1.90049e16i 1.09609i
\(316\) −2.66313e16 + 1.67360e16i −1.50462 + 0.945554i
\(317\) 2.68332e16i 1.48521i 0.669732 + 0.742603i \(0.266409\pi\)
−0.669732 + 0.742603i \(0.733591\pi\)
\(318\) −3.52825e15 1.22453e16i −0.191330 0.664040i
\(319\) −2.11307e15 −0.112273
\(320\) 3.54570e16 4.00215e15i 1.84598 0.208362i
\(321\) −1.96457e16 −1.00227
\(322\) −5.48873e14 1.90494e15i −0.0274416 0.0952399i
\(323\) 3.14377e16i 1.54040i
\(324\) 1.90363e16 1.19630e16i 0.914195 0.574511i
\(325\) 4.07130e16i 1.91642i
\(326\) 9.73078e15 2.80374e15i 0.448986 0.129367i
\(327\) 3.54899e16 1.60526
\(328\) 1.36950e16 + 1.22362e16i 0.607271 + 0.542583i
\(329\) 2.18621e15 0.0950424
\(330\) −1.73465e16 + 4.99806e15i −0.739386 + 0.213040i
\(331\) 3.59991e16i 1.50456i 0.658844 + 0.752280i \(0.271046\pi\)
−0.658844 + 0.752280i \(0.728954\pi\)
\(332\) 4.04950e15 + 6.44380e15i 0.165960 + 0.264085i
\(333\) 2.76566e16i 1.11151i
\(334\) −9.97236e15 3.46105e16i −0.393048 1.36413i
\(335\) −8.41989e16 −3.25473
\(336\) −2.12486e16 1.02294e16i −0.805612 0.387831i
\(337\) 1.47079e16 0.546961 0.273480 0.961878i \(-0.411825\pi\)
0.273480 + 0.961878i \(0.411825\pi\)
\(338\) −2.94994e15 1.02382e16i −0.107610 0.373478i
\(339\) 1.03714e16i 0.371141i
\(340\) 3.22740e16 + 5.13562e16i 1.13303 + 1.80294i
\(341\) 3.17281e15i 0.109280i
\(342\) 3.48742e16 1.00483e16i 1.17851 0.339566i
\(343\) −3.08460e16 −1.02279
\(344\) 8.44924e15 9.45658e15i 0.274908 0.307684i
\(345\) −1.23362e16 −0.393874
\(346\) 9.95428e15 2.86813e15i 0.311900 0.0898679i
\(347\) 3.17052e15i 0.0974964i −0.998811 0.0487482i \(-0.984477\pi\)
0.998811 0.0487482i \(-0.0155232\pi\)
\(348\) −1.45440e16 + 9.13991e15i −0.438952 + 0.275852i
\(349\) 2.58614e16i 0.766101i 0.923727 + 0.383051i \(0.125127\pi\)
−0.923727 + 0.383051i \(0.874873\pi\)
\(350\) 1.50883e16 + 5.23661e16i 0.438730 + 1.52268i
\(351\) 3.30957e15 0.0944659
\(352\) 1.78868e15 1.05380e16i 0.0501195 0.295277i
\(353\) 5.29307e16 1.45603 0.728017 0.685559i \(-0.240442\pi\)
0.728017 + 0.685559i \(0.240442\pi\)
\(354\) −2.10359e15 7.30083e15i −0.0568121 0.197175i
\(355\) 8.18848e16i 2.17130i
\(356\) −4.58243e16 + 2.87975e16i −1.19308 + 0.749773i
\(357\) 4.00878e16i 1.02487i
\(358\) −5.00251e16 + 1.44138e16i −1.25588 + 0.361858i
\(359\) 1.99812e16 0.492614 0.246307 0.969192i \(-0.420783\pi\)
0.246307 + 0.969192i \(0.420783\pi\)
\(360\) −4.66545e16 + 5.22168e16i −1.12961 + 1.26428i
\(361\) −3.38931e16 −0.805963
\(362\) 5.24601e16 1.51154e16i 1.22525 0.353031i
\(363\) 5.48774e16i 1.25893i
\(364\) −1.19358e16 1.89929e16i −0.268963 0.427990i
\(365\) 4.47514e16i 0.990612i
\(366\) 2.30549e15 + 8.00153e15i 0.0501344 + 0.173999i
\(367\) −6.18176e15 −0.132063 −0.0660317 0.997818i \(-0.521034\pi\)
−0.0660317 + 0.997818i \(0.521034\pi\)
\(368\) 3.16833e15 6.58132e15i 0.0664997 0.138135i
\(369\) −3.60399e16 −0.743211
\(370\) −3.09152e16 1.07296e17i −0.626413 2.17406i
\(371\) 1.62255e16i 0.323049i
\(372\) −1.37237e16 2.18380e16i −0.268500 0.427252i
\(373\) 2.71930e16i 0.522817i 0.965228 + 0.261408i \(0.0841870\pi\)
−0.965228 + 0.261408i \(0.915813\pi\)
\(374\) 1.74592e16 5.03053e15i 0.329882 0.0950492i
\(375\) 2.00762e17 3.72801
\(376\) 6.00669e15 + 5.36684e15i 0.109626 + 0.0979484i
\(377\) −1.63393e16 −0.293099
\(378\) −4.25685e15 + 1.22653e15i −0.0750571 + 0.0216263i
\(379\) 7.60971e16i 1.31890i 0.751747 + 0.659452i \(0.229212\pi\)
−0.751747 + 0.659452i \(0.770788\pi\)
\(380\) 1.24065e17 7.79664e16i 2.11375 1.32835i
\(381\) 3.56795e16i 0.597594i
\(382\) −1.16494e16 4.04310e16i −0.191819 0.665737i
\(383\) −1.01040e17 −1.63568 −0.817842 0.575443i \(-0.804830\pi\)
−0.817842 + 0.575443i \(0.804830\pi\)
\(384\) −3.32699e16 8.02681e16i −0.529539 1.27759i
\(385\) 2.29848e16 0.359704
\(386\) 3.10759e16 + 1.07853e17i 0.478196 + 1.65965i
\(387\) 2.48860e16i 0.376560i
\(388\) −5.63348e15 + 3.54027e15i −0.0838244 + 0.0526780i
\(389\) 8.29495e16i 1.21378i 0.794784 + 0.606892i \(0.207584\pi\)
−0.794784 + 0.606892i \(0.792416\pi\)
\(390\) −1.34132e17 + 3.86475e16i −1.93024 + 0.556162i
\(391\) 1.24164e16 0.175730
\(392\) −3.11799e16 2.78585e16i −0.434025 0.387791i
\(393\) 1.41106e17 1.93194
\(394\) 5.34855e16 1.54108e16i 0.720296 0.207539i
\(395\) 2.49207e17i 3.30125i
\(396\) 1.11609e16 + 1.77598e16i 0.145438 + 0.231430i
\(397\) 8.74976e16i 1.12165i −0.827934 0.560826i \(-0.810484\pi\)
0.827934 0.560826i \(-0.189516\pi\)
\(398\) −1.90531e16 6.61264e16i −0.240284 0.833940i
\(399\) −9.68427e16 −1.20155
\(400\) −8.70960e16 + 1.80918e17i −1.06318 + 2.20847i
\(401\) −6.49955e16 −0.780629 −0.390315 0.920682i \(-0.627634\pi\)
−0.390315 + 0.920682i \(0.627634\pi\)
\(402\) 5.67671e16 + 1.97018e17i 0.670853 + 2.32829i
\(403\) 2.45337e16i 0.285286i
\(404\) 1.28406e16 + 2.04327e16i 0.146929 + 0.233802i
\(405\) 1.78135e17i 2.00582i
\(406\) 2.10160e16 6.05536e15i 0.232879 0.0670997i
\(407\) −3.34483e16 −0.364762
\(408\) 9.84101e16 1.10143e17i 1.05621 1.18213i
\(409\) 9.07398e16 0.958509 0.479255 0.877676i \(-0.340907\pi\)
0.479255 + 0.877676i \(0.340907\pi\)
\(410\) −1.39819e17 + 4.02862e16i −1.45369 + 0.418853i
\(411\) 5.89511e15i 0.0603282i
\(412\) 1.68098e16 1.05638e16i 0.169329 0.106412i
\(413\) 9.67387e15i 0.0959235i
\(414\) 3.96860e15 + 1.37736e16i 0.0387378 + 0.134445i
\(415\) −6.02988e16 −0.579424
\(416\) 1.38310e16 8.14847e16i 0.130842 0.770849i
\(417\) −2.03210e17 −1.89261
\(418\) −1.21526e16 4.21773e16i −0.111435 0.386753i
\(419\) 2.71651e16i 0.245257i 0.992453 + 0.122628i \(0.0391323\pi\)
−0.992453 + 0.122628i \(0.960868\pi\)
\(420\) 1.58201e17 9.94188e16i 1.40633 0.883788i
\(421\) 5.61455e16i 0.491452i −0.969339 0.245726i \(-0.920974\pi\)
0.969339 0.245726i \(-0.0790264\pi\)
\(422\) 4.30878e15 1.24149e15i 0.0371384 0.0107007i
\(423\) −1.58073e16 −0.134166
\(424\) −3.98314e16 + 4.45803e16i −0.332926 + 0.372619i
\(425\) −3.41320e17 −2.80953
\(426\) 1.91604e17 5.52069e16i 1.55325 0.447539i
\(427\) 1.06023e16i 0.0846486i
\(428\) 4.90383e16 + 7.80326e16i 0.385612 + 0.613608i
\(429\) 4.18141e16i 0.323855i
\(430\) 2.78181e16 + 9.65469e16i 0.212218 + 0.736535i
\(431\) 2.41184e17 1.81237 0.906183 0.422886i \(-0.138983\pi\)
0.906183 + 0.422886i \(0.138983\pi\)
\(432\) −1.47069e16 7.08006e15i −0.108862 0.0524074i
\(433\) 1.95363e17 1.42452 0.712262 0.701913i \(-0.247671\pi\)
0.712262 + 0.701913i \(0.247671\pi\)
\(434\) 9.09224e15 + 3.15559e16i 0.0653112 + 0.226672i
\(435\) 1.36097e17i 0.963096i
\(436\) −8.85878e16 1.40966e17i −0.617607 0.982771i
\(437\) 2.99950e16i 0.206025i
\(438\) −1.04715e17 + 3.01715e16i −0.708640 + 0.204181i
\(439\) 2.53786e17 1.69219 0.846093 0.533035i \(-0.178948\pi\)
0.846093 + 0.533035i \(0.178948\pi\)
\(440\) 6.31516e16 + 5.64245e16i 0.414899 + 0.370702i
\(441\) 8.20532e16 0.531184
\(442\) 1.35003e17 3.88986e16i 0.861190 0.248135i
\(443\) 2.11073e17i 1.32681i 0.748260 + 0.663406i \(0.230890\pi\)
−0.748260 + 0.663406i \(0.769110\pi\)
\(444\) −2.30220e17 + 1.44678e17i −1.42611 + 0.896216i
\(445\) 4.28808e17i 2.61772i
\(446\) 3.82285e16 + 1.32678e17i 0.229991 + 0.798218i
\(447\) −3.78507e17 −2.24427
\(448\) 1.24086e16 + 1.09934e17i 0.0725127 + 0.642426i
\(449\) 1.85856e17 1.07047 0.535236 0.844703i \(-0.320223\pi\)
0.535236 + 0.844703i \(0.320223\pi\)
\(450\) −1.09095e17 3.78630e17i −0.619332 2.14948i
\(451\) 4.35871e16i 0.243899i
\(452\) −4.11952e16 + 2.58885e16i −0.227220 + 0.142793i
\(453\) 2.94536e17i 1.60140i
\(454\) 1.98435e17 5.71753e16i 1.06354 0.306440i
\(455\) 1.77730e17 0.939043
\(456\) −2.66079e17 2.37736e17i −1.38592 1.23829i
\(457\) 3.69775e16 0.189882 0.0949408 0.995483i \(-0.469734\pi\)
0.0949408 + 0.995483i \(0.469734\pi\)
\(458\) −1.35591e17 + 3.90680e16i −0.686445 + 0.197786i
\(459\) 2.77460e16i 0.138490i
\(460\) 3.07929e16 + 4.89994e16i 0.151539 + 0.241138i
\(461\) 2.06980e17i 1.00432i 0.864774 + 0.502161i \(0.167462\pi\)
−0.864774 + 0.502161i \(0.832538\pi\)
\(462\) −1.54964e16 5.37824e16i −0.0741408 0.257316i
\(463\) −3.70448e17 −1.74764 −0.873819 0.486252i \(-0.838364\pi\)
−0.873819 + 0.486252i \(0.838364\pi\)
\(464\) 7.26075e16 + 3.49541e16i 0.337765 + 0.162604i
\(465\) 2.04353e17 0.937425
\(466\) −6.46160e16 2.24259e17i −0.292302 1.01448i
\(467\) 2.35711e16i 0.105153i 0.998617 + 0.0525763i \(0.0167433\pi\)
−0.998617 + 0.0525763i \(0.983257\pi\)
\(468\) 8.63013e16 + 1.37328e17i 0.379681 + 0.604171i
\(469\) 2.61057e17i 1.13269i
\(470\) −6.13253e16 + 1.76697e16i −0.262424 + 0.0756124i
\(471\) −5.06047e15 −0.0213577
\(472\) −2.37480e16 + 2.65794e16i −0.0988564 + 0.110642i
\(473\) 3.00975e16 0.123576
\(474\) −5.83123e17 + 1.68016e17i −2.36157 + 0.680441i
\(475\) 8.24549e17i 3.29388i
\(476\) −1.59229e17 + 1.00065e17i −0.627446 + 0.394308i
\(477\) 1.17318e17i 0.456031i
\(478\) −1.05861e17 3.67406e17i −0.405933 1.40885i
\(479\) 1.66653e17 0.630424 0.315212 0.949021i \(-0.397924\pi\)
0.315212 + 0.949021i \(0.397924\pi\)
\(480\) 6.78723e17 + 1.15205e17i 2.53294 + 0.429934i
\(481\) −2.58639e17 −0.952248
\(482\) 9.19890e16 + 3.19261e17i 0.334141 + 1.15969i
\(483\) 3.82481e16i 0.137074i
\(484\) −2.17973e17 + 1.36982e17i −0.770741 + 0.484359i
\(485\) 5.27162e16i 0.183917i
\(486\) 3.83095e17 1.10382e17i 1.31878 0.379980i
\(487\) 1.46517e17 0.497681 0.248841 0.968544i \(-0.419950\pi\)
0.248841 + 0.968544i \(0.419950\pi\)
\(488\) 2.60273e16 2.91303e16i 0.0872369 0.0976375i
\(489\) 1.95378e17 0.646201
\(490\) 3.18331e17 9.17209e16i 1.03897 0.299360i
\(491\) 4.34559e17i 1.39965i −0.714315 0.699825i \(-0.753261\pi\)
0.714315 0.699825i \(-0.246739\pi\)
\(492\) 1.88533e17 + 3.00004e17i 0.599258 + 0.953573i
\(493\) 1.36982e17i 0.429692i
\(494\) −9.39698e16 3.26136e17i −0.290913 1.00966i
\(495\) −1.66190e17 −0.507776
\(496\) −5.24843e16 + 1.09021e17i −0.158270 + 0.328762i
\(497\) −2.53882e17 −0.755640
\(498\) 4.06536e16 + 1.41094e17i 0.119429 + 0.414494i
\(499\) 4.52968e17i 1.31345i −0.754129 0.656726i \(-0.771941\pi\)
0.754129 0.656726i \(-0.228059\pi\)
\(500\) −5.01129e17 7.97425e17i −1.43431 2.28236i
\(501\) 6.94922e17i 1.96332i
\(502\) 2.98424e17 8.59851e16i 0.832261 0.239800i
\(503\) −1.03763e17 −0.285662 −0.142831 0.989747i \(-0.545620\pi\)
−0.142831 + 0.989747i \(0.545620\pi\)
\(504\) −1.61897e17 1.44651e17i −0.439987 0.393118i
\(505\) −1.91203e17 −0.512979
\(506\) 1.66580e16 4.79968e15i 0.0441209 0.0127126i
\(507\) 2.05566e17i 0.537526i
\(508\) 1.41719e17 8.90610e16i 0.365859 0.229918i
\(509\) 2.43253e17i 0.620000i 0.950737 + 0.310000i \(0.100329\pi\)
−0.950737 + 0.310000i \(0.899671\pi\)
\(510\) 3.24004e17 + 1.12450e18i 0.815350 + 2.82979i
\(511\) 1.38751e17 0.344746
\(512\) −2.35779e17 + 3.32508e17i −0.578429 + 0.815733i
\(513\) −6.70279e16 −0.162365
\(514\) 1.10545e17 + 3.83663e17i 0.264411 + 0.917676i
\(515\) 1.57300e17i 0.371520i
\(516\) 2.07157e17 1.30184e17i 0.483143 0.303623i
\(517\) 1.91175e16i 0.0440294i
\(518\) 3.32668e17 9.58518e16i 0.756601 0.218000i
\(519\) 1.99865e17 0.448900
\(520\) 4.88319e17 + 4.36302e17i 1.08313 + 0.967755i
\(521\) 2.48301e17 0.543917 0.271959 0.962309i \(-0.412329\pi\)
0.271959 + 0.962309i \(0.412329\pi\)
\(522\) −1.51955e17 + 4.37830e16i −0.328744 + 0.0947212i
\(523\) 6.94419e16i 0.148375i 0.997244 + 0.0741875i \(0.0236363\pi\)
−0.997244 + 0.0741875i \(0.976364\pi\)
\(524\) −3.52220e17 5.60472e17i −0.743293 1.18277i
\(525\) 1.05142e18i 2.19150i
\(526\) −1.02894e17 3.57108e17i −0.211827 0.735178i
\(527\) −2.05680e17 −0.418238
\(528\) 8.94516e16 1.85811e17i 0.179667 0.373208i
\(529\) −4.92190e17 −0.976497
\(530\) −1.31140e17 4.55142e17i −0.257006 0.891977i
\(531\) 6.99465e16i 0.135410i
\(532\) 2.41733e17 + 3.84659e17i 0.462285 + 0.735615i
\(533\) 3.37037e17i 0.636724i
\(534\) −1.00337e18 + 2.89103e17i −1.87260 + 0.539553i
\(535\) −7.30202e17 −1.34631
\(536\) 6.40859e17 7.17264e17i 1.16732 1.30650i
\(537\) −1.00442e18 −1.80752
\(538\) −6.39904e17 + 1.84376e17i −1.13771 + 0.327808i
\(539\) 9.92362e16i 0.174318i
\(540\) 1.09496e17 6.88109e16i 0.190037 0.119426i
\(541\) 1.98249e17i 0.339961i −0.985447 0.169981i \(-0.945629\pi\)
0.985447 0.169981i \(-0.0543705\pi\)
\(542\) 1.10278e17 + 3.82737e17i 0.186850 + 0.648492i
\(543\) 1.05331e18 1.76343
\(544\) −6.83133e17 1.15953e17i −1.13009 0.191818i
\(545\) 1.31911e18 2.15628
\(546\) −1.19826e17 4.15872e17i −0.193552 0.671750i
\(547\) 1.76150e17i 0.281168i 0.990069 + 0.140584i \(0.0448980\pi\)
−0.990069 + 0.140584i \(0.955102\pi\)
\(548\) 2.34154e16 1.47150e16i 0.0369341 0.0232106i
\(549\) 7.66596e16i 0.119494i
\(550\) −4.57920e17 + 1.31941e17i −0.705395 + 0.203246i
\(551\) 3.30915e17 0.503769
\(552\) 9.38940e16 1.05088e17i 0.141265 0.158107i
\(553\) 7.72660e17 1.14888
\(554\) −4.80468e17 + 1.38438e17i −0.706076 + 0.203442i
\(555\) 2.15432e18i 3.12900i
\(556\) 5.07240e17 + 8.07150e17i 0.728161 + 1.15869i
\(557\) 8.23416e17i 1.16832i 0.811640 + 0.584158i \(0.198575\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(558\) −6.57410e16 2.28164e17i −0.0921964 0.319981i
\(559\) 2.32728e17 0.322606
\(560\) −7.89783e17 3.80211e17i −1.08215 0.520958i
\(561\) 3.50552e17 0.474781
\(562\) 2.28406e17 + 7.92716e17i 0.305788 + 1.06128i
\(563\) 6.70494e17i 0.887341i 0.896190 + 0.443670i \(0.146324\pi\)
−0.896190 + 0.443670i \(0.853676\pi\)
\(564\) 8.26912e16 + 1.31583e17i 0.108180 + 0.172142i
\(565\) 3.85491e17i 0.498539i
\(566\) 5.73176e16 1.65150e16i 0.0732792 0.0211140i
\(567\) −5.52303e17 −0.698051
\(568\) −6.97551e17 6.23246e17i −0.871589 0.778745i
\(569\) 1.03780e18 1.28198 0.640991 0.767548i \(-0.278524\pi\)
0.640991 + 0.767548i \(0.278524\pi\)
\(570\) 2.71654e18 7.82717e17i 3.31764 0.955913i
\(571\) 1.11651e18i 1.34812i 0.738676 + 0.674061i \(0.235451\pi\)
−0.738676 + 0.674061i \(0.764549\pi\)
\(572\) 1.66086e17 1.04374e17i 0.198271 0.124600i
\(573\) 8.11787e17i 0.958158i
\(574\) −1.24906e17 4.33506e17i −0.145766 0.505904i
\(575\) −3.25657e17 −0.375767
\(576\) −8.97195e16 7.94869e17i −0.102362 0.906879i
\(577\) −1.29130e18 −1.45675 −0.728373 0.685181i \(-0.759723\pi\)
−0.728373 + 0.685181i \(0.759723\pi\)
\(578\) −7.79085e16 2.70393e17i −0.0869068 0.301623i
\(579\) 2.16552e18i 2.38864i
\(580\) −5.40579e17 + 3.39718e17i −0.589627 + 0.370541i
\(581\) 1.86955e17i 0.201647i
\(582\) −1.23351e17 + 3.55413e16i −0.131566 + 0.0379083i
\(583\) −1.41886e17 −0.149656
\(584\) 3.81223e17 + 3.40614e17i 0.397646 + 0.355287i
\(585\) −1.28507e18 −1.32560
\(586\) 1.33714e16 3.85270e15i 0.0136408 0.00393034i
\(587\) 1.10482e18i 1.11466i −0.830291 0.557331i \(-0.811826\pi\)
0.830291 0.557331i \(-0.188174\pi\)
\(588\) −4.29238e17 6.83029e17i −0.428298 0.681532i
\(589\) 4.96876e17i 0.490341i
\(590\) −7.81877e16 2.71362e17i −0.0763133 0.264857i
\(591\) 1.07390e18 1.03668
\(592\) 1.14932e18 + 5.53297e17i 1.09736 + 0.528284i
\(593\) −1.43752e18 −1.35756 −0.678779 0.734342i \(-0.737491\pi\)
−0.678779 + 0.734342i \(0.737491\pi\)
\(594\) −1.07255e16 3.72245e16i −0.0100186 0.0347710i
\(595\) 1.49001e18i 1.37667i
\(596\) 9.44805e17 + 1.50343e18i 0.863459 + 1.37399i
\(597\) 1.32771e18i 1.20024i
\(598\) 1.28808e17 3.71135e16i 0.115182 0.0331874i
\(599\) 6.32077e17 0.559107 0.279554 0.960130i \(-0.409813\pi\)
0.279554 + 0.960130i \(0.409813\pi\)
\(600\) −2.58110e18 + 2.88883e18i −2.25851 + 2.52778i
\(601\) 3.05117e17 0.264109 0.132054 0.991242i \(-0.457843\pi\)
0.132054 + 0.991242i \(0.457843\pi\)
\(602\) −2.99341e17 + 8.62494e16i −0.256324 + 0.0738549i
\(603\) 1.88756e18i 1.59896i
\(604\) 1.16990e18 7.35203e17i 0.980410 0.616123i
\(605\) 2.03972e18i 1.69107i
\(606\) 1.28909e17 + 4.47398e17i 0.105733 + 0.366963i
\(607\) −1.57496e18 −1.27804 −0.639018 0.769192i \(-0.720659\pi\)
−0.639018 + 0.769192i \(0.720659\pi\)
\(608\) −2.80115e17 + 1.65029e18i −0.224887 + 1.32491i
\(609\) 4.21966e17 0.335170
\(610\) 8.56918e16 + 2.97406e17i 0.0673435 + 0.233725i
\(611\) 1.47826e17i 0.114943i
\(612\) 1.15130e18 7.23513e17i 0.885733 0.556624i
\(613\) 1.32874e17i 0.101146i −0.998720 0.0505728i \(-0.983895\pi\)
0.998720 0.0505728i \(-0.0161047\pi\)
\(614\) −1.04378e18 + 3.00744e17i −0.786165 + 0.226518i
\(615\) −2.80734e18 −2.09221
\(616\) −1.74943e17 + 1.95800e17i −0.129009 + 0.144390i
\(617\) −1.56261e17 −0.114024 −0.0570121 0.998373i \(-0.518157\pi\)
−0.0570121 + 0.998373i \(0.518157\pi\)
\(618\) 3.68070e17 1.06052e17i 0.265769 0.0765763i
\(619\) 9.31102e17i 0.665286i 0.943053 + 0.332643i \(0.107940\pi\)
−0.943053 + 0.332643i \(0.892060\pi\)
\(620\) −5.10093e17 8.11690e17i −0.360665 0.573910i
\(621\) 2.64727e16i 0.0185227i
\(622\) −5.16750e17 1.79346e18i −0.357802 1.24180i
\(623\) 1.32951e18 0.911001
\(624\) 6.91684e17 1.43678e18i 0.469038 0.974296i
\(625\) 3.80967e18 2.55663
\(626\) −2.78242e17 9.65678e17i −0.184794 0.641356i
\(627\) 8.46851e17i 0.556632i
\(628\) 1.26316e16 + 2.01002e16i 0.00821717 + 0.0130756i
\(629\) 2.16831e18i 1.39602i
\(630\) 1.65288e18 4.76247e17i 1.05324 0.303472i
\(631\) −1.97753e18 −1.24719 −0.623594 0.781748i \(-0.714328\pi\)
−0.623594 + 0.781748i \(0.714328\pi\)
\(632\) 2.12292e18 + 1.89678e18i 1.32517 + 1.18401i
\(633\) 8.65132e16 0.0534513
\(634\) 2.33372e18 6.72417e17i 1.42715 0.411205i
\(635\) 1.32616e18i 0.802724i
\(636\) −9.76579e17 + 6.13715e17i −0.585108 + 0.367702i
\(637\) 7.67343e17i 0.455075i
\(638\) 5.29517e16 + 1.83777e17i 0.0310846 + 0.107884i
\(639\) 1.83568e18 1.06670
\(640\) −1.23660e18 2.98346e18i −0.711308 1.71613i
\(641\) 3.46004e17 0.197017 0.0985084 0.995136i \(-0.468593\pi\)
0.0985084 + 0.995136i \(0.468593\pi\)
\(642\) 4.92304e17 + 1.70861e18i 0.277495 + 0.963087i
\(643\) 3.31505e18i 1.84977i −0.380241 0.924887i \(-0.624159\pi\)
0.380241 0.924887i \(-0.375841\pi\)
\(644\) −1.51922e17 + 9.54726e16i −0.0839192 + 0.0527376i
\(645\) 1.93850e18i 1.06005i
\(646\) −2.73418e18 + 7.87803e17i −1.48019 + 0.426487i
\(647\) −1.25070e18 −0.670309 −0.335155 0.942163i \(-0.608789\pi\)
−0.335155 + 0.942163i \(0.608789\pi\)
\(648\) −1.51747e18 1.35583e18i −0.805163 0.719395i
\(649\) −8.45941e16 −0.0444375
\(650\) −3.54087e18 + 1.02023e18i −1.84150 + 0.530594i
\(651\) 6.33591e17i 0.326236i
\(652\) −4.87690e17 7.76041e17i −0.248619 0.395617i
\(653\) 3.28489e18i 1.65800i −0.559248 0.829000i \(-0.688910\pi\)
0.559248 0.829000i \(-0.311090\pi\)
\(654\) −8.89348e17 3.08661e18i −0.444443 1.54251i
\(655\) 5.24471e18 2.59509
\(656\) 7.21013e17 1.49770e18i 0.353239 0.733755i
\(657\) −1.00323e18 −0.486660
\(658\) −5.47845e16 1.90137e17i −0.0263141 0.0913271i
\(659\) 7.72337e17i 0.367326i 0.982989 + 0.183663i \(0.0587955\pi\)
−0.982989 + 0.183663i \(0.941204\pi\)
\(660\) 8.69378e17 + 1.38340e18i 0.409424 + 0.651499i
\(661\) 3.52021e18i 1.64157i 0.571238 + 0.820784i \(0.306463\pi\)
−0.571238 + 0.820784i \(0.693537\pi\)
\(662\) 3.13089e18 9.02107e17i 1.44574 0.416563i
\(663\) 2.71064e18 1.23946
\(664\) 4.58949e17 5.13667e17i 0.207813 0.232589i
\(665\) −3.59951e18 −1.61400
\(666\) −2.40534e18 + 6.93052e17i −1.06805 + 0.307739i
\(667\) 1.30695e17i 0.0574701i
\(668\) −2.76023e18 + 1.73462e18i −1.20198 + 0.755367i
\(669\) 2.66395e18i 1.14883i
\(670\) 2.10995e18 + 7.32291e18i 0.901129 + 3.12750i
\(671\) 9.27131e16 0.0392143
\(672\) −3.57189e17 + 2.10436e18i −0.149623 + 0.881497i
\(673\) −3.14223e18 −1.30359 −0.651793 0.758397i \(-0.725983\pi\)
−0.651793 + 0.758397i \(0.725983\pi\)
\(674\) −3.68568e17 1.27917e18i −0.151436 0.525579i
\(675\) 7.27723e17i 0.296136i
\(676\) −8.16508e17 + 5.13121e17i −0.329084 + 0.206808i
\(677\) 6.57394e17i 0.262421i −0.991354 0.131211i \(-0.958114\pi\)
0.991354 0.131211i \(-0.0418865\pi\)
\(678\) −9.02016e17 + 2.59899e17i −0.356633 + 0.102757i
\(679\) 1.63445e17 0.0640057
\(680\) 3.65777e18 4.09386e18i 1.41876 1.58791i
\(681\) 3.98425e18 1.53070
\(682\) −2.75944e17 + 7.95080e16i −0.105008 + 0.0302561i
\(683\) 8.10111e17i 0.305358i −0.988276 0.152679i \(-0.951210\pi\)
0.988276 0.152679i \(-0.0487901\pi\)
\(684\) −1.74784e18 2.78126e18i −0.652584 1.03843i
\(685\) 2.19113e17i 0.0810364i
\(686\) 7.72975e17 + 2.68272e18i 0.283177 + 0.982809i
\(687\) −2.72244e18 −0.987962
\(688\) −1.03418e18 4.97869e17i −0.371769 0.178974i
\(689\) −1.09713e18 −0.390691
\(690\) 3.09135e17 + 1.07290e18i 0.109051 + 0.378477i
\(691\) 4.18606e18i 1.46284i −0.681925 0.731422i \(-0.738857\pi\)
0.681925 0.731422i \(-0.261143\pi\)
\(692\) −4.98892e17 7.93865e17i −0.172710 0.274826i
\(693\) 5.15269e17i 0.176713i
\(694\) −2.75745e17 + 7.94505e16i −0.0936851 + 0.0269936i
\(695\) −7.55303e18 −2.54226
\(696\) 1.15937e18 + 1.03587e18i 0.386600 + 0.345418i
\(697\) 2.82558e18 0.933456
\(698\) 2.24920e18 6.48064e17i 0.736153 0.212108i
\(699\) 4.50275e18i 1.46008i
\(700\) 4.17626e18 2.62450e18i 1.34168 0.843158i
\(701\) 2.70632e18i 0.861414i 0.902492 + 0.430707i \(0.141736\pi\)
−0.902492 + 0.430707i \(0.858264\pi\)
\(702\) −8.29350e16 2.87838e17i −0.0261545 0.0907731i
\(703\) 5.23814e18 1.63669
\(704\) −9.61325e17 + 1.08508e17i −0.297610 + 0.0335922i
\(705\) −1.23131e18 −0.377692
\(706\) −1.32640e18 4.60346e18i −0.403128 1.39912i
\(707\) 5.92819e17i 0.178524i
\(708\) −5.82250e17 + 3.65905e17i −0.173737 + 0.109182i
\(709\) 3.11949e18i 0.922322i 0.887317 + 0.461161i \(0.152567\pi\)
−0.887317 + 0.461161i \(0.847433\pi\)
\(710\) 7.12165e18 2.05197e18i 2.08642 0.601161i
\(711\) −5.58668e18 −1.62182
\(712\) 3.65288e18 + 3.26376e18i 1.05079 + 0.938855i
\(713\) −1.96242e17 −0.0559383
\(714\) −3.48649e18 + 1.00457e18i −0.984806 + 0.283753i
\(715\) 1.55417e18i 0.435021i
\(716\) 2.50718e18 + 3.98956e18i 0.695425 + 1.10660i
\(717\) 7.37690e18i 2.02768i
\(718\) −5.00711e17 1.73779e18i −0.136389 0.473357i
\(719\) −3.38700e17 −0.0914276 −0.0457138 0.998955i \(-0.514556\pi\)
−0.0457138 + 0.998955i \(0.514556\pi\)
\(720\) 5.71049e18 + 2.74910e18i 1.52761 + 0.735410i
\(721\) −4.87706e17 −0.129294
\(722\) 8.49334e17 + 2.94774e18i 0.223145 + 0.774456i
\(723\) 6.41024e18i 1.66907i
\(724\) −2.62921e18 4.18376e18i −0.678461 1.07961i
\(725\) 3.59276e18i 0.918820i
\(726\) −4.77277e18 + 1.37518e18i −1.20971 + 0.348556i
\(727\) 3.24412e18 0.814936 0.407468 0.913219i \(-0.366412\pi\)
0.407468 + 0.913219i \(0.366412\pi\)
\(728\) −1.35274e18 + 1.51402e18i −0.336792 + 0.376945i
\(729\) 3.31625e18 0.818311
\(730\) −3.89210e18 + 1.12143e18i −0.951887 + 0.274268i
\(731\) 1.95110e18i 0.472950i
\(732\) 6.38132e17 4.01023e17i 0.153316 0.0963491i
\(733\) 3.91150e18i 0.931468i 0.884925 + 0.465734i \(0.154210\pi\)
−0.884925 + 0.465734i \(0.845790\pi\)
\(734\) 1.54910e17 + 5.37637e17i 0.0365640 + 0.126901i
\(735\) 6.39155e18 1.49534
\(736\) −6.51783e17 1.10632e17i −0.151146 0.0256551i
\(737\) 2.28284e18 0.524730
\(738\) 9.03130e17 + 3.13444e18i 0.205771 + 0.714158i
\(739\) 3.74151e17i 0.0845002i −0.999107 0.0422501i \(-0.986547\pi\)
0.999107 0.0422501i \(-0.0134526\pi\)
\(740\) −8.55696e18 + 5.37748e18i −1.91564 + 1.20385i
\(741\) 6.54827e18i 1.45314i
\(742\) 1.41116e18 4.06597e17i 0.310420 0.0894415i
\(743\) 1.22444e18 0.267000 0.133500 0.991049i \(-0.457378\pi\)
0.133500 + 0.991049i \(0.457378\pi\)
\(744\) −1.55538e18 + 1.74082e18i −0.336211 + 0.376296i
\(745\) −1.40686e19 −3.01463
\(746\) 2.36502e18 6.81434e17i 0.502379 0.144751i
\(747\) 1.35177e18i 0.284655i
\(748\) −8.75026e17 1.39239e18i −0.182667 0.290671i
\(749\) 2.26397e18i 0.468532i
\(750\) −5.03092e18 1.74605e19i −1.03216 3.58228i
\(751\) −7.11954e18 −1.44808 −0.724040 0.689758i \(-0.757717\pi\)
−0.724040 + 0.689758i \(0.757717\pi\)
\(752\) 3.16239e17 6.56899e17i 0.0637676 0.132459i
\(753\) 5.99185e18 1.19783
\(754\) 4.09449e17 + 1.42105e18i 0.0811495 + 0.281641i
\(755\) 1.09475e19i 2.15110i
\(756\) 2.13346e17 + 3.39489e17i 0.0415617 + 0.0661354i
\(757\) 3.29155e18i 0.635737i 0.948135 + 0.317868i \(0.102967\pi\)
−0.948135 + 0.317868i \(0.897033\pi\)
\(758\) 6.61828e18 1.90693e18i 1.26735 0.365161i
\(759\) 3.34465e17 0.0635007
\(760\) −9.88981e18 8.83631e18i −1.86166 1.66335i
\(761\) 1.97090e18 0.367844 0.183922 0.982941i \(-0.441121\pi\)
0.183922 + 0.982941i \(0.441121\pi\)
\(762\) 3.10310e18 8.94098e17i 0.574233 0.165454i
\(763\) 4.08988e18i 0.750413i
\(764\) −3.22442e18 + 2.02633e18i −0.586603 + 0.368641i
\(765\) 1.07734e19i 1.94337i
\(766\) 2.53197e18 + 8.78756e18i 0.452867 + 1.57174i
\(767\) −6.54123e17 −0.116009
\(768\) −6.14732e18 + 4.90498e18i −1.08103 + 0.862560i
\(769\) 5.34643e18 0.932272 0.466136 0.884713i \(-0.345646\pi\)
0.466