Properties

Label 16.12.e.a.5.3
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.2934908890\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-42.3872 + 15.8533i) q^{2} +(-435.014 + 435.014i) q^{3} +(1545.35 - 1343.95i) q^{4} +(-1517.34 - 1517.34i) q^{5} +(11542.6 - 25335.4i) q^{6} -59722.7i q^{7} +(-44197.0 + 81465.1i) q^{8} -201326. i q^{9} +O(q^{10})\) \(q+(-42.3872 + 15.8533i) q^{2} +(-435.014 + 435.014i) q^{3} +(1545.35 - 1343.95i) q^{4} +(-1517.34 - 1517.34i) q^{5} +(11542.6 - 25335.4i) q^{6} -59722.7i q^{7} +(-44197.0 + 81465.1i) q^{8} -201326. i q^{9} +(88370.6 + 40261.0i) q^{10} +(56196.6 + 56196.6i) q^{11} +(-87611.4 + 1.25688e6i) q^{12} +(-315796. + 315796. i) q^{13} +(946798. + 2.53148e6i) q^{14} +1.32013e6 q^{15} +(581902. - 4.15374e6i) q^{16} +8.11170e6 q^{17} +(3.19168e6 + 8.53367e6i) q^{18} +(-1.33811e7 + 1.33811e7i) q^{19} +(-4.38405e6 - 305591. i) q^{20} +(2.59802e7 + 2.59802e7i) q^{21} +(-3.27292e6 - 1.49112e6i) q^{22} +2.84613e7i q^{23} +(-1.62121e7 - 5.46647e7i) q^{24} -4.42235e7i q^{25} +(8.37932e6 - 1.83921e7i) q^{26} +(1.05184e7 + 1.05184e7i) q^{27} +(-8.02643e7 - 9.22924e7i) q^{28} +(7.59695e7 - 7.59695e7i) q^{29} +(-5.59565e7 + 2.09283e7i) q^{30} +5.67278e7 q^{31} +(4.11851e7 + 1.85291e8i) q^{32} -4.88926e7 q^{33} +(-3.43832e8 + 1.28597e8i) q^{34} +(-9.06196e7 + 9.06196e7i) q^{35} +(-2.70573e8 - 3.11120e8i) q^{36} +(3.75680e8 + 3.75680e8i) q^{37} +(3.55053e8 - 7.79319e8i) q^{38} -2.74751e8i q^{39} +(1.90672e8 - 5.65483e7i) q^{40} -1.51696e7i q^{41} +(-1.51310e9 - 6.89356e8i) q^{42} +(1.08339e9 + 1.08339e9i) q^{43} +(1.62369e8 + 1.13180e7i) q^{44} +(-3.05481e8 + 3.05481e8i) q^{45} +(-4.51204e8 - 1.20639e9i) q^{46} +2.79798e9 q^{47} +(1.55380e9 + 2.06007e9i) q^{48} -1.58947e9 q^{49} +(7.01086e8 + 1.87451e9i) q^{50} +(-3.52870e9 + 3.52870e9i) q^{51} +(-6.36011e7 + 9.12430e8i) q^{52} +(2.03657e9 + 2.03657e9i) q^{53} +(-6.12597e8 - 2.79095e8i) q^{54} -1.70539e8i q^{55} +(4.86531e9 + 2.63956e9i) q^{56} -1.16419e10i q^{57} +(-2.01577e9 + 4.42450e9i) q^{58} +(-4.23123e9 - 4.23123e9i) q^{59} +(2.04006e9 - 1.77418e9i) q^{60} +(6.54407e9 - 6.54407e9i) q^{61} +(-2.40453e9 + 8.99320e8i) q^{62} -1.20238e10 q^{63} +(-4.68318e9 - 7.20103e9i) q^{64} +9.58341e8 q^{65} +(2.07242e9 - 7.75106e8i) q^{66} +(-8.01903e9 + 8.01903e9i) q^{67} +(1.25354e10 - 1.09017e10i) q^{68} +(-1.23810e10 - 1.23810e10i) q^{69} +(2.40450e9 - 5.27773e9i) q^{70} +1.40718e10i q^{71} +(1.64011e10 + 8.89803e9i) q^{72} -6.29343e9i q^{73} +(-2.18798e10 - 9.96828e9i) q^{74} +(1.92378e10 + 1.92378e10i) q^{75} +(-2.69494e9 + 3.86619e10i) q^{76} +(3.35621e9 - 3.35621e9i) q^{77} +(4.35570e9 + 1.16459e10i) q^{78} -3.46459e10 q^{79} +(-7.18558e9 + 5.41970e9i) q^{80} +2.65131e10 q^{81} +(2.40488e8 + 6.42997e8i) q^{82} +(4.29998e10 - 4.29998e10i) q^{83} +(7.50645e10 + 5.23238e9i) q^{84} +(-1.23082e10 - 1.23082e10i) q^{85} +(-6.30969e10 - 2.87465e10i) q^{86} +6.60955e10i q^{87} +(-7.06179e9 + 2.09434e9i) q^{88} -3.39308e9i q^{89} +(8.10561e9 - 1.77913e10i) q^{90} +(1.88602e10 + 1.88602e10i) q^{91} +(3.82505e10 + 4.39826e10i) q^{92} +(-2.46773e10 + 2.46773e10i) q^{93} +(-1.18599e11 + 4.43571e10i) q^{94} +4.06073e10 q^{95} +(-9.85200e10 - 6.26878e10i) q^{96} +1.55551e10 q^{97} +(6.73732e10 - 2.51983e10i) q^{98} +(1.13139e10 - 1.13139e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.3872 + 15.8533i −0.936634 + 0.350311i
\(3\) −435.014 + 435.014i −1.03356 + 1.03356i −0.0341434 + 0.999417i \(0.510870\pi\)
−0.999417 + 0.0341434i \(0.989130\pi\)
\(4\) 1545.35 1343.95i 0.754565 0.656225i
\(5\) −1517.34 1517.34i −0.217144 0.217144i 0.590150 0.807294i \(-0.299069\pi\)
−0.807294 + 0.590150i \(0.799069\pi\)
\(6\) 11542.6 25335.4i 0.606000 1.33013i
\(7\) 59722.7i 1.34307i −0.740971 0.671537i \(-0.765634\pi\)
0.740971 0.671537i \(-0.234366\pi\)
\(8\) −44197.0 + 81465.1i −0.476868 + 0.878975i
\(9\) 201326.i 1.13649i
\(10\) 88370.6 + 40261.0i 0.279452 + 0.127317i
\(11\) 56196.6 + 56196.6i 0.105208 + 0.105208i 0.757752 0.652543i \(-0.226298\pi\)
−0.652543 + 0.757752i \(0.726298\pi\)
\(12\) −87611.4 + 1.25688e6i −0.101640 + 1.45814i
\(13\) −315796. + 315796.i −0.235895 + 0.235895i −0.815148 0.579253i \(-0.803344\pi\)
0.579253 + 0.815148i \(0.303344\pi\)
\(14\) 946798. + 2.53148e6i 0.470493 + 1.25797i
\(15\) 1.32013e6 0.448863
\(16\) 581902. 4.15374e6i 0.138736 0.990329i
\(17\) 8.11170e6 1.38562 0.692808 0.721122i \(-0.256373\pi\)
0.692808 + 0.721122i \(0.256373\pi\)
\(18\) 3.19168e6 + 8.53367e6i 0.398126 + 1.06448i
\(19\) −1.33811e7 + 1.33811e7i −1.23978 + 1.23978i −0.279695 + 0.960089i \(0.590233\pi\)
−0.960089 + 0.279695i \(0.909767\pi\)
\(20\) −4.38405e6 305591.i −0.306345 0.0213538i
\(21\) 2.59802e7 + 2.59802e7i 1.38815 + 1.38815i
\(22\) −3.27292e6 1.49112e6i −0.135397 0.0616861i
\(23\) 2.84613e7i 0.922043i 0.887389 + 0.461022i \(0.152517\pi\)
−0.887389 + 0.461022i \(0.847483\pi\)
\(24\) −1.62121e7 5.46647e7i −0.415602 1.40135i
\(25\) 4.42235e7i 0.905697i
\(26\) 8.37932e6 1.83921e7i 0.138311 0.303584i
\(27\) 1.05184e7 + 1.05184e7i 0.141075 + 0.141075i
\(28\) −8.02643e7 9.22924e7i −0.881359 1.01344i
\(29\) 7.59695e7 7.59695e7i 0.687781 0.687781i −0.273960 0.961741i \(-0.588334\pi\)
0.961741 + 0.273960i \(0.0883335\pi\)
\(30\) −5.59565e7 + 2.09283e7i −0.420420 + 0.157241i
\(31\) 5.67278e7 0.355882 0.177941 0.984041i \(-0.443056\pi\)
0.177941 + 0.984041i \(0.443056\pi\)
\(32\) 4.11851e7 + 1.85291e8i 0.216978 + 0.976177i
\(33\) −4.88926e7 −0.217479
\(34\) −3.43832e8 + 1.28597e8i −1.29782 + 0.485396i
\(35\) −9.06196e7 + 9.06196e7i −0.291641 + 0.291641i
\(36\) −2.70573e8 3.11120e8i −0.745796 0.857558i
\(37\) 3.75680e8 + 3.75680e8i 0.890654 + 0.890654i 0.994585 0.103931i \(-0.0331421\pi\)
−0.103931 + 0.994585i \(0.533142\pi\)
\(38\) 3.55053e8 7.79319e8i 0.726914 1.59553i
\(39\) 2.74751e8i 0.487623i
\(40\) 1.90672e8 5.65483e7i 0.294413 0.0873151i
\(41\) 1.51696e7i 0.0204486i −0.999948 0.0102243i \(-0.996745\pi\)
0.999948 0.0102243i \(-0.00325455\pi\)
\(42\) −1.51310e9 6.89356e8i −1.78647 0.813903i
\(43\) 1.08339e9 + 1.08339e9i 1.12385 + 1.12385i 0.991158 + 0.132689i \(0.0423610\pi\)
0.132689 + 0.991158i \(0.457639\pi\)
\(44\) 1.62369e8 + 1.13180e7i 0.148427 + 0.0103461i
\(45\) −3.05481e8 + 3.05481e8i −0.246783 + 0.246783i
\(46\) −4.51204e8 1.20639e9i −0.323002 0.863617i
\(47\) 2.79798e9 1.77954 0.889768 0.456414i \(-0.150866\pi\)
0.889768 + 0.456414i \(0.150866\pi\)
\(48\) 1.55380e9 + 2.06007e9i 0.880173 + 1.16696i
\(49\) −1.58947e9 −0.803848
\(50\) 7.01086e8 + 1.87451e9i 0.317275 + 0.848306i
\(51\) −3.52870e9 + 3.52870e9i −1.43212 + 1.43212i
\(52\) −6.36011e7 + 9.12430e8i −0.0231978 + 0.332798i
\(53\) 2.03657e9 + 2.03657e9i 0.668932 + 0.668932i 0.957469 0.288537i \(-0.0931688\pi\)
−0.288537 + 0.957469i \(0.593169\pi\)
\(54\) −6.12597e8 2.79095e8i −0.181555 0.0827153i
\(55\) 1.70539e8i 0.0456908i
\(56\) 4.86531e9 + 2.63956e9i 1.18053 + 0.640469i
\(57\) 1.16419e10i 2.56278i
\(58\) −2.01577e9 + 4.42450e9i −0.403262 + 0.885136i
\(59\) −4.23123e9 4.23123e9i −0.770513 0.770513i 0.207683 0.978196i \(-0.433408\pi\)
−0.978196 + 0.207683i \(0.933408\pi\)
\(60\) 2.04006e9 1.77418e9i 0.338696 0.294555i
\(61\) 6.54407e9 6.54407e9i 0.992051 0.992051i −0.00791726 0.999969i \(-0.502520\pi\)
0.999969 + 0.00791726i \(0.00252017\pi\)
\(62\) −2.40453e9 + 8.99320e8i −0.333331 + 0.124669i
\(63\) −1.20238e10 −1.52640
\(64\) −4.68318e9 7.20103e9i −0.545194 0.838310i
\(65\) 9.58341e8 0.102446
\(66\) 2.07242e9 7.75106e8i 0.203698 0.0761850i
\(67\) −8.01903e9 + 8.01903e9i −0.725622 + 0.725622i −0.969744 0.244122i \(-0.921500\pi\)
0.244122 + 0.969744i \(0.421500\pi\)
\(68\) 1.25354e10 1.09017e10i 1.04554 0.909277i
\(69\) −1.23810e10 1.23810e10i −0.952987 0.952987i
\(70\) 2.40450e9 5.27773e9i 0.170996 0.375325i
\(71\) 1.40718e10i 0.925608i 0.886461 + 0.462804i \(0.153157\pi\)
−0.886461 + 0.462804i \(0.846843\pi\)
\(72\) 1.64011e10 + 8.89803e9i 0.998950 + 0.541958i
\(73\) 6.29343e9i 0.355314i −0.984093 0.177657i \(-0.943148\pi\)
0.984093 0.177657i \(-0.0568517\pi\)
\(74\) −2.18798e10 9.96828e9i −1.14622 0.522211i
\(75\) 1.92378e10 + 1.92378e10i 0.936092 + 0.936092i
\(76\) −2.69494e9 + 3.86619e10i −0.121920 + 1.74908i
\(77\) 3.35621e9 3.35621e9i 0.141303 0.141303i
\(78\) 4.35570e9 + 1.16459e10i 0.170820 + 0.456724i
\(79\) −3.46459e10 −1.26678 −0.633392 0.773831i \(-0.718338\pi\)
−0.633392 + 0.773831i \(0.718338\pi\)
\(80\) −7.18558e9 + 5.41970e9i −0.245170 + 0.184918i
\(81\) 2.65131e10 0.844875
\(82\) 2.40488e8 + 6.42997e8i 0.00716336 + 0.0191528i
\(83\) 4.29998e10 4.29998e10i 1.19822 1.19822i 0.223521 0.974699i \(-0.428245\pi\)
0.974699 0.223521i \(-0.0717553\pi\)
\(84\) 7.50645e10 + 5.23238e9i 1.95839 + 0.136510i
\(85\) −1.23082e10 1.23082e10i −0.300878 0.300878i
\(86\) −6.30969e10 2.87465e10i −1.44633 0.658937i
\(87\) 6.60955e10i 1.42173i
\(88\) −7.06179e9 + 2.09434e9i −0.142646 + 0.0423050i
\(89\) 3.39308e9i 0.0644093i −0.999481 0.0322047i \(-0.989747\pi\)
0.999481 0.0322047i \(-0.0102528\pi\)
\(90\) 8.10561e9 1.77913e10i 0.144694 0.317596i
\(91\) 1.88602e10 + 1.88602e10i 0.316824 + 0.316824i
\(92\) 3.82505e10 + 4.39826e10i 0.605068 + 0.695742i
\(93\) −2.46773e10 + 2.46773e10i −0.367826 + 0.367826i
\(94\) −1.18599e11 + 4.43571e10i −1.66677 + 0.623390i
\(95\) 4.06073e10 0.538423
\(96\) −9.85200e10 6.26878e10i −1.23320 0.784678i
\(97\) 1.55551e10 0.183920 0.0919601 0.995763i \(-0.470687\pi\)
0.0919601 + 0.995763i \(0.470687\pi\)
\(98\) 6.73732e10 2.51983e10i 0.752911 0.281596i
\(99\) 1.13139e10 1.13139e10i 0.119569 0.119569i
\(100\) −5.94341e10 6.83407e10i −0.594341 0.683407i
\(101\) 8.04221e10 + 8.04221e10i 0.761391 + 0.761391i 0.976574 0.215183i \(-0.0690347\pi\)
−0.215183 + 0.976574i \(0.569035\pi\)
\(102\) 9.36304e10 2.05513e11i 0.839684 1.84306i
\(103\) 2.48411e10i 0.211138i 0.994412 + 0.105569i \(0.0336663\pi\)
−0.994412 + 0.105569i \(0.966334\pi\)
\(104\) −1.17691e10 3.96836e10i −0.0948550 0.319837i
\(105\) 7.88415e10i 0.602856i
\(106\) −1.18611e11 5.40382e10i −0.860878 0.392210i
\(107\) 5.76499e10 + 5.76499e10i 0.397363 + 0.397363i 0.877302 0.479939i \(-0.159341\pi\)
−0.479939 + 0.877302i \(0.659341\pi\)
\(108\) 3.03908e10 + 2.11840e9i 0.199027 + 0.0138732i
\(109\) −5.69123e10 + 5.69123e10i −0.354291 + 0.354291i −0.861704 0.507412i \(-0.830602\pi\)
0.507412 + 0.861704i \(0.330602\pi\)
\(110\) 2.70359e9 + 7.22866e9i 0.0160060 + 0.0427955i
\(111\) −3.26852e11 −1.84109
\(112\) −2.48073e11 3.47528e10i −1.33009 0.186333i
\(113\) 1.29979e11 0.663653 0.331826 0.943340i \(-0.392335\pi\)
0.331826 + 0.943340i \(0.392335\pi\)
\(114\) 1.84562e11 + 4.93467e11i 0.897770 + 2.40039i
\(115\) 4.31854e10 4.31854e10i 0.200216 0.200216i
\(116\) 1.53002e10 2.19499e11i 0.0676360 0.970315i
\(117\) 6.35782e10 + 6.35782e10i 0.268093 + 0.268093i
\(118\) 2.46429e11 + 1.12271e11i 0.991608 + 0.451770i
\(119\) 4.84453e11i 1.86099i
\(120\) −5.83457e10 + 1.07544e11i −0.214048 + 0.394539i
\(121\) 2.78996e11i 0.977862i
\(122\) −1.73640e11 + 3.81130e11i −0.581662 + 1.27671i
\(123\) 6.59899e9 + 6.59899e9i 0.0211348 + 0.0211348i
\(124\) 8.76642e10 7.62393e10i 0.268536 0.233539i
\(125\) −1.41191e11 + 1.41191e11i −0.413811 + 0.413811i
\(126\) 5.09653e11 1.90616e11i 1.42967 0.534713i
\(127\) −9.81625e9 −0.0263648 −0.0131824 0.999913i \(-0.504196\pi\)
−0.0131824 + 0.999913i \(0.504196\pi\)
\(128\) 3.12667e11 + 2.30988e11i 0.804316 + 0.594202i
\(129\) −9.42576e11 −2.32313
\(130\) −4.06214e10 + 1.51928e10i −0.0959547 + 0.0358881i
\(131\) 3.01725e11 3.01725e11i 0.683312 0.683312i −0.277433 0.960745i \(-0.589484\pi\)
0.960745 + 0.277433i \(0.0894836\pi\)
\(132\) −7.55561e10 + 6.57092e10i −0.164102 + 0.142715i
\(133\) 7.99153e11 + 7.99153e11i 1.66512 + 1.66512i
\(134\) 2.12777e11 4.67032e11i 0.425449 0.933835i
\(135\) 3.19200e10i 0.0612671i
\(136\) −3.58513e11 + 6.60821e11i −0.660756 + 1.21792i
\(137\) 2.21227e11i 0.391629i −0.980641 0.195814i \(-0.937265\pi\)
0.980641 0.195814i \(-0.0627350\pi\)
\(138\) 7.21077e11 + 3.28518e11i 1.22644 + 0.558758i
\(139\) 1.76441e11 + 1.76441e11i 0.288415 + 0.288415i 0.836453 0.548038i \(-0.184625\pi\)
−0.548038 + 0.836453i \(0.684625\pi\)
\(140\) −1.82507e10 + 2.61827e11i −0.0286798 + 0.411444i
\(141\) −1.21716e12 + 1.21716e12i −1.83926 + 1.83926i
\(142\) −2.23083e11 5.96462e11i −0.324250 0.866956i
\(143\) −3.54934e10 −0.0496363
\(144\) −8.36258e11 1.17152e11i −1.12550 0.157673i
\(145\) −2.30543e11 −0.298695
\(146\) 9.97714e10 + 2.66761e11i 0.124470 + 0.332799i
\(147\) 6.91441e11 6.91441e11i 0.830825 0.830825i
\(148\) 1.08545e12 + 7.56617e10i 1.25653 + 0.0875864i
\(149\) 1.96547e10 + 1.96547e10i 0.0219251 + 0.0219251i 0.717984 0.696059i \(-0.245065\pi\)
−0.696059 + 0.717984i \(0.745065\pi\)
\(150\) −1.12042e12 5.10455e11i −1.20470 0.548852i
\(151\) 1.18330e12i 1.22666i −0.789828 0.613329i \(-0.789830\pi\)
0.789828 0.613329i \(-0.210170\pi\)
\(152\) −4.98686e11 1.68149e12i −0.498526 1.68095i
\(153\) 1.63310e12i 1.57474i
\(154\) −8.90536e10 + 1.95467e11i −0.0828490 + 0.181849i
\(155\) −8.60753e10 8.60753e10i −0.0772777 0.0772777i
\(156\) −3.69252e11 4.24587e11i −0.319991 0.367943i
\(157\) 4.40152e11 4.40152e11i 0.368260 0.368260i −0.498582 0.866842i \(-0.666146\pi\)
0.866842 + 0.498582i \(0.166146\pi\)
\(158\) 1.46854e12 5.49250e11i 1.18651 0.443768i
\(159\) −1.77187e12 −1.38276
\(160\) 2.18657e11 3.43641e11i 0.164855 0.259086i
\(161\) 1.69978e12 1.23837
\(162\) −1.12382e12 + 4.20319e11i −0.791339 + 0.295969i
\(163\) 1.90450e11 1.90450e11i 0.129643 0.129643i −0.639308 0.768951i \(-0.720779\pi\)
0.768951 + 0.639308i \(0.220779\pi\)
\(164\) −2.03872e10 2.34423e10i −0.0134189 0.0154298i
\(165\) 7.41867e10 + 7.41867e10i 0.0472242 + 0.0472242i
\(166\) −1.14095e12 + 2.50433e12i −0.702544 + 1.54204i
\(167\) 2.80229e12i 1.66945i 0.550669 + 0.834723i \(0.314372\pi\)
−0.550669 + 0.834723i \(0.685628\pi\)
\(168\) −3.26472e12 + 9.68230e11i −1.88211 + 0.558184i
\(169\) 1.59271e12i 0.888707i
\(170\) 7.16836e11 + 3.26586e11i 0.387214 + 0.176412i
\(171\) 2.69396e12 + 2.69396e12i 1.40901 + 1.40901i
\(172\) 3.13023e12 + 2.18193e11i 1.58551 + 0.110518i
\(173\) 4.15917e11 4.15917e11i 0.204058 0.204058i −0.597678 0.801736i \(-0.703910\pi\)
0.801736 + 0.597678i \(0.203910\pi\)
\(174\) −1.04783e12 2.80160e12i −0.498046 1.33164i
\(175\) −2.64114e12 −1.21642
\(176\) 2.66127e11 2.00725e11i 0.118787 0.0895948i
\(177\) 3.68128e12 1.59274
\(178\) 5.37913e10 + 1.43823e11i 0.0225633 + 0.0603279i
\(179\) 1.25777e12 1.25777e12i 0.511575 0.511575i −0.403434 0.915009i \(-0.632183\pi\)
0.915009 + 0.403434i \(0.132183\pi\)
\(180\) −6.15236e10 + 8.82625e11i −0.0242685 + 0.348159i
\(181\) −7.02645e11 7.02645e11i −0.268846 0.268846i 0.559789 0.828635i \(-0.310882\pi\)
−0.828635 + 0.559789i \(0.810882\pi\)
\(182\) −1.09843e12 5.00436e11i −0.407735 0.185761i
\(183\) 5.69352e12i 2.05069i
\(184\) −2.31860e12 1.25790e12i −0.810453 0.439693i
\(185\) 1.14007e12i 0.386800i
\(186\) 6.54787e11 1.43722e12i 0.215665 0.473371i
\(187\) 4.55850e11 + 4.55850e11i 0.145779 + 0.145779i
\(188\) 4.32386e12 3.76035e12i 1.34277 1.16778i
\(189\) 6.28187e11 6.28187e11i 0.189474 0.189474i
\(190\) −1.72123e12 + 6.43757e11i −0.504305 + 0.188615i
\(191\) −1.55093e12 −0.441478 −0.220739 0.975333i \(-0.570847\pi\)
−0.220739 + 0.975333i \(0.570847\pi\)
\(192\) 5.16979e12 + 1.09530e12i 1.42993 + 0.302953i
\(193\) −4.58114e12 −1.23143 −0.615713 0.787971i \(-0.711132\pi\)
−0.615713 + 0.787971i \(0.711132\pi\)
\(194\) −6.59339e11 + 2.46600e11i −0.172266 + 0.0644292i
\(195\) −4.16891e11 + 4.16891e11i −0.105885 + 0.105885i
\(196\) −2.45629e12 + 2.13617e12i −0.606555 + 0.527505i
\(197\) 8.42541e11 + 8.42541e11i 0.202315 + 0.202315i 0.800991 0.598676i \(-0.204306\pi\)
−0.598676 + 0.800991i \(0.704306\pi\)
\(198\) −3.00202e11 + 6.58925e11i −0.0701059 + 0.153878i
\(199\) 6.45938e12i 1.46723i −0.679564 0.733616i \(-0.737831\pi\)
0.679564 0.733616i \(-0.262169\pi\)
\(200\) 3.60267e12 + 1.95455e12i 0.796085 + 0.431898i
\(201\) 6.97677e12i 1.49995i
\(202\) −4.68382e12 2.13392e12i −0.979868 0.446421i
\(203\) −4.53710e12 4.53710e12i −0.923741 0.923741i
\(204\) −7.10677e11 + 1.01955e13i −0.140834 + 2.02042i
\(205\) −2.30175e10 + 2.30175e10i −0.00444029 + 0.00444029i
\(206\) −3.93812e11 1.05294e12i −0.0739638 0.197759i
\(207\) 5.73001e12 1.04790
\(208\) 1.12797e12 + 1.49550e12i 0.200887 + 0.266341i
\(209\) −1.50394e12 −0.260871
\(210\) 1.24989e12 + 3.34187e12i 0.211187 + 0.564655i
\(211\) −5.66233e12 + 5.66233e12i −0.932055 + 0.932055i −0.997834 0.0657787i \(-0.979047\pi\)
0.0657787 + 0.997834i \(0.479047\pi\)
\(212\) 5.88426e12 + 4.10163e11i 0.943723 + 0.0657824i
\(213\) −6.12140e12 6.12140e12i −0.956672 0.956672i
\(214\) −3.35755e12 1.52968e12i −0.511384 0.232983i
\(215\) 3.28773e12i 0.488073i
\(216\) −1.32176e12 + 3.92000e11i −0.191275 + 0.0567271i
\(217\) 3.38793e12i 0.477976i
\(218\) 1.51011e12 3.31460e12i 0.207729 0.455953i
\(219\) 2.73773e12 + 2.73773e12i 0.367238 + 0.367238i
\(220\) −2.29196e11 2.63542e11i −0.0299834 0.0344766i
\(221\) −2.56165e12 + 2.56165e12i −0.326860 + 0.326860i
\(222\) 1.38543e13 5.18167e12i 1.72443 0.644953i
\(223\) 2.46919e12 0.299832 0.149916 0.988699i \(-0.452100\pi\)
0.149916 + 0.988699i \(0.452100\pi\)
\(224\) 1.10660e13 2.45968e12i 1.31108 0.291417i
\(225\) −8.90336e12 −1.02932
\(226\) −5.50943e12 + 2.06059e12i −0.621599 + 0.232485i
\(227\) −2.54818e12 + 2.54818e12i −0.280600 + 0.280600i −0.833348 0.552748i \(-0.813579\pi\)
0.552748 + 0.833348i \(0.313579\pi\)
\(228\) −1.56461e13 1.79908e13i −1.68176 1.93379i
\(229\) 8.81027e12 + 8.81027e12i 0.924473 + 0.924473i 0.997342 0.0728690i \(-0.0232155\pi\)
−0.0728690 + 0.997342i \(0.523215\pi\)
\(230\) −1.14588e12 + 2.51514e12i −0.117391 + 0.257667i
\(231\) 2.92000e12i 0.292090i
\(232\) 2.83123e12 + 9.54649e12i 0.276562 + 0.932524i
\(233\) 1.10524e13i 1.05438i 0.849747 + 0.527191i \(0.176755\pi\)
−0.849747 + 0.527191i \(0.823245\pi\)
\(234\) −3.70282e12 1.68698e12i −0.345021 0.157189i
\(235\) −4.24549e12 4.24549e12i −0.386415 0.386415i
\(236\) −1.22253e13 8.52166e11i −1.08703 0.0757719i
\(237\) 1.50714e13 1.50714e13i 1.30930 1.30930i
\(238\) 7.68015e12 + 2.05346e13i 0.651923 + 1.74306i
\(239\) 8.37084e12 0.694353 0.347177 0.937800i \(-0.387140\pi\)
0.347177 + 0.937800i \(0.387140\pi\)
\(240\) 7.68185e11 5.48347e12i 0.0622736 0.444522i
\(241\) 1.48928e13 1.18000 0.590002 0.807402i \(-0.299127\pi\)
0.590002 + 0.807402i \(0.299127\pi\)
\(242\) 4.42299e12 + 1.18258e13i 0.342556 + 0.915899i
\(243\) −1.33969e13 + 1.33969e13i −1.01430 + 1.01430i
\(244\) 1.31797e12 1.89078e13i 0.0975578 1.39958i
\(245\) 2.41177e12 + 2.41177e12i 0.174551 + 0.174551i
\(246\) −3.84328e11 1.75097e11i −0.0271994 0.0123918i
\(247\) 8.45139e12i 0.584918i
\(248\) −2.50720e12 + 4.62133e12i −0.169709 + 0.312812i
\(249\) 3.74110e13i 2.47687i
\(250\) 3.74635e12 8.22302e12i 0.242627 0.532551i
\(251\) −7.98403e12 7.98403e12i −0.505844 0.505844i 0.407404 0.913248i \(-0.366434\pi\)
−0.913248 + 0.407404i \(0.866434\pi\)
\(252\) −1.85809e13 + 1.61593e13i −1.15176 + 1.00166i
\(253\) −1.59943e12 + 1.59943e12i −0.0970067 + 0.0970067i
\(254\) 4.16083e11 1.55619e11i 0.0246942 0.00923588i
\(255\) 1.07085e13 0.621952
\(256\) −1.69150e13 4.83414e12i −0.961504 0.274789i
\(257\) 2.70752e12 0.150640 0.0753200 0.997159i \(-0.476002\pi\)
0.0753200 + 0.997159i \(0.476002\pi\)
\(258\) 3.99531e13 1.49429e13i 2.17592 0.813816i
\(259\) 2.24366e13 2.24366e13i 1.19621 1.19621i
\(260\) 1.48097e12 1.28796e12i 0.0773024 0.0672279i
\(261\) −1.52947e13 1.52947e13i −0.781659 0.781659i
\(262\) −8.00595e12 + 1.75726e13i −0.400641 + 0.879384i
\(263\) 9.34160e11i 0.0457788i 0.999738 + 0.0228894i \(0.00728656\pi\)
−0.999738 + 0.0228894i \(0.992713\pi\)
\(264\) 2.16091e12 3.98304e12i 0.103709 0.191158i
\(265\) 6.18034e12i 0.290509i
\(266\) −4.65430e13 2.12047e13i −2.14292 0.976299i
\(267\) 1.47603e12 + 1.47603e12i 0.0665709 + 0.0665709i
\(268\) −1.61503e12 + 2.31694e13i −0.0713573 + 1.02370i
\(269\) −1.46911e13 + 1.46911e13i −0.635942 + 0.635942i −0.949552 0.313610i \(-0.898462\pi\)
0.313610 + 0.949552i \(0.398462\pi\)
\(270\) 5.06036e11 + 1.35300e12i 0.0214625 + 0.0573848i
\(271\) 3.98105e13 1.65450 0.827249 0.561835i \(-0.189905\pi\)
0.827249 + 0.561835i \(0.189905\pi\)
\(272\) 4.72022e12 3.36939e13i 0.192235 1.37222i
\(273\) −1.64089e13 −0.654914
\(274\) 3.50716e12 + 9.37718e12i 0.137192 + 0.366813i
\(275\) 2.48521e12 2.48521e12i 0.0952869 0.0952869i
\(276\) −3.57725e13 2.49353e12i −1.34447 0.0937162i
\(277\) −1.57182e13 1.57182e13i −0.579114 0.579114i 0.355545 0.934659i \(-0.384295\pi\)
−0.934659 + 0.355545i \(0.884295\pi\)
\(278\) −1.02760e13 4.68167e12i −0.371174 0.169104i
\(279\) 1.14208e13i 0.404458i
\(280\) −3.37721e12 1.13874e13i −0.117271 0.395419i
\(281\) 5.65668e13i 1.92609i 0.269339 + 0.963045i \(0.413195\pi\)
−0.269339 + 0.963045i \(0.586805\pi\)
\(282\) 3.22960e13 7.08879e13i 1.07840 2.36702i
\(283\) −2.30718e13 2.30718e13i −0.755538 0.755538i 0.219969 0.975507i \(-0.429404\pi\)
−0.975507 + 0.219969i \(0.929404\pi\)
\(284\) 1.89117e13 + 2.17458e13i 0.607408 + 0.698432i
\(285\) −1.76647e13 + 1.76647e13i −0.556493 + 0.556493i
\(286\) 1.50446e12 5.62685e11i 0.0464910 0.0173881i
\(287\) −9.05970e11 −0.0274640
\(288\) 3.73039e13 8.29165e12i 1.10942 0.246594i
\(289\) 3.15279e13 0.919933
\(290\) 9.77208e12 3.65486e12i 0.279768 0.104636i
\(291\) −6.76670e12 + 6.76670e12i −0.190093 + 0.190093i
\(292\) −8.45806e12 9.72555e12i −0.233166 0.268107i
\(293\) −1.47734e13 1.47734e13i −0.399675 0.399675i 0.478443 0.878118i \(-0.341201\pi\)
−0.878118 + 0.478443i \(0.841201\pi\)
\(294\) −1.83467e13 + 4.02698e13i −0.487132 + 1.06923i
\(295\) 1.28404e13i 0.334625i
\(296\) −4.72088e13 + 1.40009e13i −1.20759 + 0.358138i
\(297\) 1.18220e12i 0.0296845i
\(298\) −1.14470e12 5.21517e11i −0.0282164 0.0128552i
\(299\) −8.98797e12 8.98797e12i −0.217505 0.217505i
\(300\) 5.55838e13 + 3.87448e12i 1.32063 + 0.0920548i
\(301\) 6.47027e13 6.47027e13i 1.50941 1.50941i
\(302\) 1.87592e13 + 5.01570e13i 0.429711 + 1.14893i
\(303\) −6.99694e13 −1.57389
\(304\) 4.77950e13 + 6.33680e13i 1.05579 + 1.39980i
\(305\) −1.98592e13 −0.430836
\(306\) 2.58900e13 + 6.92226e13i 0.551650 + 1.47496i
\(307\) 3.74033e13 3.74033e13i 0.782796 0.782796i −0.197506 0.980302i \(-0.563284\pi\)
0.980302 + 0.197506i \(0.0632842\pi\)
\(308\) 6.75938e11 9.69710e12i 0.0138956 0.199348i
\(309\) −1.08062e13 1.08062e13i −0.218223 0.218223i
\(310\) 5.01306e12 + 2.28392e12i 0.0994521 + 0.0453097i
\(311\) 5.07867e13i 0.989847i 0.868937 + 0.494924i \(0.164804\pi\)
−0.868937 + 0.494924i \(0.835196\pi\)
\(312\) 2.23826e13 + 1.21432e13i 0.428609 + 0.232532i
\(313\) 1.06893e13i 0.201120i −0.994931 0.100560i \(-0.967937\pi\)
0.994931 0.100560i \(-0.0320634\pi\)
\(314\) −1.16790e13 + 2.56347e13i −0.215919 + 0.473930i
\(315\) 1.82441e13 + 1.82441e13i 0.331448 + 0.331448i
\(316\) −5.35400e13 + 4.65623e13i −0.955871 + 0.831296i
\(317\) −1.50024e13 + 1.50024e13i −0.263229 + 0.263229i −0.826365 0.563135i \(-0.809595\pi\)
0.563135 + 0.826365i \(0.309595\pi\)
\(318\) 7.51046e13 2.80899e13i 1.29514 0.484397i
\(319\) 8.53846e12 0.144721
\(320\) −3.82043e12 + 1.80324e13i −0.0636485 + 0.300420i
\(321\) −5.01569e13 −0.821398
\(322\) −7.20491e13 + 2.69471e13i −1.15990 + 0.433815i
\(323\) −1.08543e14 + 1.08543e14i −1.71787 + 1.71787i
\(324\) 4.09720e13 3.56323e13i 0.637513 0.554429i
\(325\) 1.39656e13 + 1.39656e13i 0.213649 + 0.213649i
\(326\) −5.05338e12 + 1.10919e13i −0.0760125 + 0.166843i
\(327\) 4.95153e13i 0.732363i
\(328\) 1.23579e12 + 6.70452e11i 0.0179738 + 0.00975128i
\(329\) 1.67103e14i 2.39005i
\(330\) −4.32067e12 1.96847e12i −0.0607749 0.0276886i
\(331\) 1.15849e12 + 1.15849e12i 0.0160265 + 0.0160265i 0.715075 0.699048i \(-0.246393\pi\)
−0.699048 + 0.715075i \(0.746393\pi\)
\(332\) 8.66012e12 1.24239e14i 0.117832 1.69044i
\(333\) 7.56344e13 7.56344e13i 1.01222 1.01222i
\(334\) −4.44254e13 1.18781e14i −0.584825 1.56366i
\(335\) 2.43352e13 0.315129
\(336\) 1.23033e14 9.27970e13i 1.56731 1.18214i
\(337\) 1.54894e14 1.94120 0.970602 0.240691i \(-0.0773741\pi\)
0.970602 + 0.240691i \(0.0773741\pi\)
\(338\) −2.52496e13 6.75103e13i −0.311324 0.832393i
\(339\) −5.65425e13 + 5.65425e13i −0.685925 + 0.685925i
\(340\) −3.55621e13 2.47886e12i −0.424476 0.0295882i
\(341\) 3.18791e12 + 3.18791e12i 0.0374418 + 0.0374418i
\(342\) −1.56898e14 7.14815e13i −1.81331 0.826133i
\(343\) 2.31639e13i 0.263447i
\(344\) −1.36141e14 + 4.03757e13i −1.52376 + 0.451906i
\(345\) 3.75725e13i 0.413871i
\(346\) −1.10359e13 + 2.42232e13i −0.119644 + 0.262611i
\(347\) 4.18262e13 + 4.18262e13i 0.446309 + 0.446309i 0.894126 0.447816i \(-0.147798\pi\)
−0.447816 + 0.894126i \(0.647798\pi\)
\(348\) 8.88291e13 + 1.02141e14i 0.932974 + 1.07279i
\(349\) −1.30512e14 + 1.30512e14i −1.34931 + 1.34931i −0.462897 + 0.886412i \(0.653190\pi\)
−0.886412 + 0.462897i \(0.846810\pi\)
\(350\) 1.11951e14 4.18707e13i 1.13934 0.426124i
\(351\) −6.64335e12 −0.0665576
\(352\) −8.09824e12 + 1.27272e13i −0.0798741 + 0.125530i
\(353\) −1.77057e14 −1.71930 −0.859652 0.510880i \(-0.829320\pi\)
−0.859652 + 0.510880i \(0.829320\pi\)
\(354\) −1.56039e14 + 5.83603e13i −1.49182 + 0.557955i
\(355\) 2.13516e13 2.13516e13i 0.200990 0.200990i
\(356\) −4.56012e12 5.24349e12i −0.0422670 0.0486010i
\(357\) 2.10743e14 + 2.10743e14i 1.92344 + 1.92344i
\(358\) −3.33736e13 + 7.32531e13i −0.299948 + 0.658369i
\(359\) 1.06853e14i 0.945727i 0.881136 + 0.472863i \(0.156780\pi\)
−0.881136 + 0.472863i \(0.843220\pi\)
\(360\) −1.13847e13 3.83874e13i −0.0992331 0.334599i
\(361\) 2.41616e14i 2.07413i
\(362\) 4.09224e13 + 1.86439e13i 0.345990 + 0.157631i
\(363\) 1.21367e14 + 1.21367e14i 1.01068 + 1.01068i
\(364\) 5.44927e13 + 3.79843e12i 0.446973 + 0.0311563i
\(365\) −9.54928e12 + 9.54928e12i −0.0771542 + 0.0771542i
\(366\) −9.02608e13 2.41332e14i −0.718379 1.92075i
\(367\) 4.42951e13 0.347290 0.173645 0.984808i \(-0.444446\pi\)
0.173645 + 0.984808i \(0.444446\pi\)
\(368\) 1.18221e14 + 1.65617e13i 0.913127 + 0.127921i
\(369\) −3.05404e12 −0.0232397
\(370\) 1.80738e13 + 4.83243e13i 0.135500 + 0.362290i
\(371\) 1.21629e14 1.21629e14i 0.898425 0.898425i
\(372\) −4.97000e12 + 7.13002e13i −0.0361718 + 0.518925i
\(373\) −9.20225e13 9.20225e13i −0.659926 0.659926i 0.295436 0.955362i \(-0.404535\pi\)
−0.955362 + 0.295436i \(0.904535\pi\)
\(374\) −2.65489e13 1.20955e13i −0.187609 0.0854733i
\(375\) 1.22840e14i 0.855397i
\(376\) −1.23662e14 + 2.27938e14i −0.848604 + 1.56417i
\(377\) 4.79818e13i 0.324488i
\(378\) −1.66683e13 + 3.65859e13i −0.111093 + 0.243842i
\(379\) −4.11973e13 4.11973e13i −0.270616 0.270616i 0.558732 0.829348i \(-0.311288\pi\)
−0.829348 + 0.558732i \(0.811288\pi\)
\(380\) 6.27524e13 5.45741e13i 0.406275 0.353327i
\(381\) 4.27020e12 4.27020e12i 0.0272496 0.0272496i
\(382\) 6.57396e13 2.45873e13i 0.413503 0.154654i
\(383\) −2.44621e13 −0.151670 −0.0758351 0.997120i \(-0.524162\pi\)
−0.0758351 + 0.997120i \(0.524162\pi\)
\(384\) −2.36497e14 + 3.55313e13i −1.44545 + 0.217165i
\(385\) −1.01850e13 −0.0613661
\(386\) 1.94182e14 7.26259e13i 1.15339 0.431382i
\(387\) 2.18114e14 2.18114e14i 1.27724 1.27724i
\(388\) 2.40381e13 2.09053e13i 0.138780 0.120693i
\(389\) 4.33424e13 + 4.33424e13i 0.246712 + 0.246712i 0.819620 0.572908i \(-0.194185\pi\)
−0.572908 + 0.819620i \(0.694185\pi\)
\(390\) 1.10618e13 2.42799e13i 0.0620825 0.136267i
\(391\) 2.30870e14i 1.27760i
\(392\) 7.02498e13 1.29486e14i 0.383329 0.706562i
\(393\) 2.62509e14i 1.41249i
\(394\) −4.90700e13 2.23559e13i −0.260367 0.118622i
\(395\) 5.25696e13 + 5.25696e13i 0.275075 + 0.275075i
\(396\) 2.27860e12 3.26891e13i 0.0117583 0.168686i
\(397\) −2.24044e13 + 2.24044e13i −0.114021 + 0.114021i −0.761815 0.647794i \(-0.775692\pi\)
0.647794 + 0.761815i \(0.275692\pi\)
\(398\) 1.02402e14 + 2.73795e14i 0.513987 + 1.37426i
\(399\) −6.95285e14 −3.44201
\(400\) −1.83693e14 2.57337e13i −0.896938 0.125653i
\(401\) 3.28823e14 1.58368 0.791842 0.610727i \(-0.209123\pi\)
0.791842 + 0.610727i \(0.209123\pi\)
\(402\) 1.10605e14 + 2.95726e14i 0.525448 + 1.40490i
\(403\) −1.79144e13 + 1.79144e13i −0.0839508 + 0.0839508i
\(404\) 2.32363e14 + 1.61969e13i 1.07416 + 0.0748748i
\(405\) −4.02294e13 4.02294e13i −0.183460 0.183460i
\(406\) 2.64243e14 + 1.20387e14i 1.18880 + 0.541611i
\(407\) 4.22239e13i 0.187409i
\(408\) −1.31508e14 4.43424e14i −0.575865 1.94173i
\(409\) 1.11279e14i 0.480767i −0.970678 0.240384i \(-0.922727\pi\)
0.970678 0.240384i \(-0.0772732\pi\)
\(410\) 6.10744e11 1.34055e12i 0.00260344 0.00571440i
\(411\) 9.62366e13 + 9.62366e13i 0.404772 + 0.404772i
\(412\) 3.33852e13 + 3.83881e13i 0.138554 + 0.159317i
\(413\) −2.52700e14 + 2.52700e14i −1.03486 + 1.03486i
\(414\) −2.42879e14 + 9.08393e13i −0.981495 + 0.367089i
\(415\) −1.30491e14 −0.520373
\(416\) −7.15202e13 4.55080e13i −0.281459 0.179091i
\(417\) −1.53508e14 −0.596188
\(418\) 6.37479e13 2.38424e13i 0.244341 0.0913860i
\(419\) 1.31929e14 1.31929e14i 0.499072 0.499072i −0.412077 0.911149i \(-0.635197\pi\)
0.911149 + 0.412077i \(0.135197\pi\)
\(420\) −1.05959e14 1.21838e14i −0.395610 0.454894i
\(421\) 1.11228e13 + 1.11228e13i 0.0409887 + 0.0409887i 0.727304 0.686315i \(-0.240773\pi\)
−0.686315 + 0.727304i \(0.740773\pi\)
\(422\) 1.50244e14 3.29777e14i 0.546485 1.19950i
\(423\) 5.63308e14i 2.02243i
\(424\) −2.55920e14 + 7.58989e13i −0.906967 + 0.268982i
\(425\) 3.58728e14i 1.25495i
\(426\) 3.56513e14 + 1.62425e14i 1.23118 + 0.560919i
\(427\) −3.90830e14 3.90830e14i −1.33240 1.33240i
\(428\) 1.66568e14 + 1.16106e13i 0.560596 + 0.0390765i
\(429\) 1.54401e13 1.54401e13i 0.0513021 0.0513021i
\(430\) 5.21212e13 + 1.39358e14i 0.170977 + 0.457146i
\(431\) 4.45018e14 1.44129 0.720647 0.693302i \(-0.243845\pi\)
0.720647 + 0.693302i \(0.243845\pi\)
\(432\) 4.98114e13 3.75701e13i 0.159283 0.120138i
\(433\) −1.12463e13 −0.0355080 −0.0177540 0.999842i \(-0.505652\pi\)
−0.0177540 + 0.999842i \(0.505652\pi\)
\(434\) 5.37098e13 + 1.43605e14i 0.167440 + 0.447689i
\(435\) 1.00289e14 1.00289e14i 0.308720 0.308720i
\(436\) −1.14621e13 + 1.64437e14i −0.0348408 + 0.499831i
\(437\) −3.80842e14 3.80842e14i −1.14313 1.14313i
\(438\) −1.59447e14 7.26427e13i −0.472615 0.215320i
\(439\) 5.67001e13i 0.165970i 0.996551 + 0.0829849i \(0.0264453\pi\)
−0.996551 + 0.0829849i \(0.973555\pi\)
\(440\) 1.38930e13 + 7.53731e12i 0.0401610 + 0.0217885i
\(441\) 3.20002e14i 0.913568i
\(442\) 6.79706e13 1.49191e14i 0.191646 0.420651i
\(443\) −2.60481e13 2.60481e13i −0.0725362 0.0725362i 0.669908 0.742444i \(-0.266334\pi\)
−0.742444 + 0.669908i \(0.766334\pi\)
\(444\) −5.05100e14 + 4.39273e14i −1.38922 + 1.20817i
\(445\) −5.14845e12 + 5.14845e12i −0.0139861 + 0.0139861i
\(446\) −1.04662e14 + 3.91447e13i −0.280833 + 0.105034i
\(447\) −1.71001e13 −0.0453219
\(448\) −4.30065e14 + 2.79692e14i −1.12591 + 0.732236i
\(449\) −3.91719e14 −1.01302 −0.506512 0.862233i \(-0.669065\pi\)
−0.506512 + 0.862233i \(0.669065\pi\)
\(450\) 3.77388e14 1.41147e14i 0.964095 0.360581i
\(451\) 8.52481e11 8.52481e11i 0.00215136 0.00215136i
\(452\) 2.00862e14 1.74685e14i 0.500769 0.435506i
\(453\) 5.14753e14 + 5.14753e14i 1.26782 + 1.26782i
\(454\) 6.76132e13 1.48407e14i 0.164522 0.361117i
\(455\) 5.72347e13i 0.137593i
\(456\) 9.48407e14 + 5.14537e14i 2.25262 + 1.22211i
\(457\) 1.98305e14i 0.465365i 0.972553 + 0.232683i \(0.0747504\pi\)
−0.972553 + 0.232683i \(0.925250\pi\)
\(458\) −5.13114e14 2.33771e14i −1.18974 0.542039i
\(459\) 8.53222e13 + 8.53222e13i 0.195475 + 0.195475i
\(460\) 8.69751e12 1.24776e14i 0.0196891 0.282463i
\(461\) −2.94593e14 + 2.94593e14i −0.658972 + 0.658972i −0.955137 0.296165i \(-0.904292\pi\)
0.296165 + 0.955137i \(0.404292\pi\)
\(462\) −4.62914e13 1.23770e14i −0.102322 0.273581i
\(463\) 5.44141e14 1.18855 0.594273 0.804263i \(-0.297440\pi\)
0.594273 + 0.804263i \(0.297440\pi\)
\(464\) −2.71351e14 3.59765e14i −0.585710 0.776550i
\(465\) 7.48878e13 0.159742
\(466\) −1.75216e14 4.68479e14i −0.369361 0.987569i
\(467\) −6.92417e13 + 6.92417e13i −0.144253 + 0.144253i −0.775545 0.631292i \(-0.782525\pi\)
0.631292 + 0.775545i \(0.282525\pi\)
\(468\) 1.83696e14 + 1.28046e13i 0.378223 + 0.0263641i
\(469\) 4.78918e14 + 4.78918e14i 0.974564 + 0.974564i
\(470\) 2.47259e14 + 1.12650e14i 0.497295 + 0.226564i
\(471\) 3.82944e14i 0.761238i
\(472\) 5.31705e14 1.57689e14i 1.04470 0.309829i
\(473\) 1.21765e14i 0.236476i
\(474\) −3.99904e14 + 8.77767e14i −0.767671 + 1.68499i
\(475\) 5.91757e14 + 5.91757e14i 1.12287 + 1.12287i
\(476\) −6.51080e14 7.48648e14i −1.22123 1.40423i
\(477\) 4.10015e14 4.10015e14i 0.760237 0.760237i
\(478\) −3.54816e14 + 1.32705e14i −0.650354 + 0.243239i
\(479\) 5.45377e14 0.988216 0.494108 0.869401i \(-0.335495\pi\)
0.494108 + 0.869401i \(0.335495\pi\)
\(480\) 5.43696e13 + 2.44607e14i 0.0973933 + 0.438169i
\(481\) −2.37277e14 −0.420201
\(482\) −6.31265e14 + 2.36100e14i −1.10523 + 0.413368i
\(483\) −7.39429e14 + 7.39429e14i −1.27993 + 1.27993i
\(484\) −3.74956e14 4.31145e14i −0.641698 0.737861i
\(485\) −2.36025e13 2.36025e13i −0.0399372 0.0399372i
\(486\) 3.55471e14 7.80239e14i 0.594710 1.30535i
\(487\) 2.73024e14i 0.451640i −0.974169 0.225820i \(-0.927494\pi\)
0.974169 0.225820i \(-0.0725061\pi\)
\(488\) 2.43885e14 + 8.22342e14i 0.398911 + 1.34507i
\(489\) 1.65696e14i 0.267987i
\(490\) −1.40462e14 6.39937e13i −0.224637 0.102343i
\(491\) 2.44712e13 + 2.44712e13i 0.0386996 + 0.0386996i 0.726192 0.687492i \(-0.241288\pi\)
−0.687492 + 0.726192i \(0.741288\pi\)
\(492\) 1.90664e13 + 1.32903e12i 0.0298168 + 0.00207839i
\(493\) 6.16242e14 6.16242e14i 0.953001 0.953001i
\(494\) 1.33982e14 + 3.58231e14i 0.204903 + 0.547853i
\(495\) −3.43340e13 −0.0519273
\(496\) 3.30100e13 2.35633e14i 0.0493738 0.352441i
\(497\) 8.40402e14 1.24316
\(498\) −5.93085e14 1.58575e15i −0.867673 2.31992i
\(499\) −5.44937e14 + 5.44937e14i −0.788484 + 0.788484i −0.981246 0.192762i \(-0.938256\pi\)
0.192762 + 0.981246i \(0.438256\pi\)
\(500\) −2.84357e13 + 4.07943e14i −0.0406939 + 0.583800i
\(501\) −1.21903e15 1.21903e15i −1.72547 1.72547i
\(502\) 4.64994e14 + 2.11848e14i 0.650993 + 0.296588i
\(503\) 2.12390e14i 0.294110i 0.989128 + 0.147055i \(0.0469794\pi\)
−0.989128 + 0.147055i \(0.953021\pi\)
\(504\) 5.31414e14 9.79516e14i 0.727889 1.34166i
\(505\) 2.44055e14i 0.330663i
\(506\) 4.24391e13 9.31514e13i 0.0568773 0.124842i
\(507\) −6.92848e14 6.92848e14i −0.918532 0.918532i
\(508\) −1.51695e13 + 1.31925e13i −0.0198940 + 0.0173013i
\(509\) 2.91460e14 2.91460e14i 0.378121 0.378121i −0.492303 0.870424i \(-0.663845\pi\)
0.870424 + 0.492303i \(0.163845\pi\)
\(510\) −4.53902e14 + 1.69764e14i −0.582541 + 0.217876i
\(511\) −3.75861e14 −0.477212
\(512\) 7.93615e14 6.32513e13i 0.996839 0.0794484i
\(513\) −2.81495e14 −0.349804
\(514\) −1.14764e14 + 4.29231e13i −0.141094 + 0.0527708i
\(515\) 3.76924e13 3.76924e13i 0.0458473 0.0458473i
\(516\) −1.45661e15 + 1.26677e15i −1.75295 + 1.52449i
\(517\) 1.57237e14 + 1.57237e14i 0.187222 + 0.187222i
\(518\) −5.95332e14 + 1.30672e15i −0.701368 + 1.53946i
\(519\) 3.61859e14i 0.421812i
\(520\) −4.23558e13 + 7.80713e13i −0.0488534 + 0.0900478i
\(521\) 1.21124e15i 1.38236i −0.722681 0.691182i \(-0.757090\pi\)
0.722681 0.691182i \(-0.242910\pi\)
\(522\) 8.90769e14 + 4.05828e14i 1.00595 + 0.458305i
\(523\) −7.39703e14 7.39703e14i −0.826605 0.826605i 0.160440 0.987046i \(-0.448709\pi\)
−0.987046 + 0.160440i \(0.948709\pi\)
\(524\) 6.07671e13 8.71773e14i 0.0671965 0.964010i
\(525\) 1.14893e15 1.14893e15i 1.25724 1.25724i
\(526\) −1.48095e13 3.95964e13i −0.0160368 0.0428780i
\(527\) 4.60159e14 0.493116
\(528\) −2.84507e13 + 2.03087e14i −0.0301722 + 0.215375i
\(529\) 1.42765e14 0.149836
\(530\) 9.79784e13 + 2.61967e14i 0.101768 + 0.272101i
\(531\) −8.51858e14 + 8.51858e14i −0.875684 + 0.875684i
\(532\) 2.30899e15 + 1.60949e14i 2.34914 + 0.163747i
\(533\) 4.79051e12 + 4.79051e12i 0.00482372 + 0.00482372i
\(534\) −8.59649e13 3.91650e13i −0.0856730 0.0390320i
\(535\) 1.74949e14i 0.172570i
\(536\) −2.98854e14 1.00769e15i −0.291778 0.983830i
\(537\) 1.09429e15i 1.05749i
\(538\) 3.89813e14 8.55617e14i 0.372867 0.818422i
\(539\) −8.93228e13 8.93228e13i −0.0845716 0.0845716i
\(540\) −4.28989e13 4.93275e13i −0.0402050 0.0462300i
\(541\) −9.36873e14 + 9.36873e14i −0.869152 + 0.869152i −0.992379 0.123227i \(-0.960676\pi\)
0.123227 + 0.992379i \(0.460676\pi\)
\(542\) −1.68745e15 + 6.31126e14i −1.54966 + 0.579588i
\(543\) 6.11320e14 0.555737
\(544\) 3.34081e14 + 1.50302e15i 0.300648 + 1.35261i
\(545\) 1.72711e14 0.153865
\(546\) 6.95527e14 2.60134e14i 0.613415 0.229423i
\(547\) −7.01752e13 + 7.01752e13i −0.0612708 + 0.0612708i −0.737078 0.675807i \(-0.763795\pi\)
0.675807 + 0.737078i \(0.263795\pi\)
\(548\) −2.97318e14 3.41872e14i −0.256997 0.295509i
\(549\) −1.31750e15 1.31750e15i −1.12746 1.12746i
\(550\) −6.59424e13 + 1.44740e14i −0.0558689 + 0.122629i
\(551\) 2.03311e15i 1.70540i
\(552\) 1.55583e15 4.61417e14i 1.29210 0.383203i
\(553\) 2.06914e15i 1.70138i
\(554\) 9.15435e14 + 4.17066e14i 0.745288 + 0.339548i
\(555\) 4.95946e14 + 4.95946e14i 0.399781 + 0.399781i
\(556\) 5.09790e14 + 3.55350e13i 0.406893 + 0.0283625i
\(557\) −4.21492e14 + 4.21492e14i −0.333109 + 0.333109i −0.853766 0.520657i \(-0.825687\pi\)
0.520657 + 0.853766i \(0.325687\pi\)
\(558\) 1.81057e14 + 4.84096e14i 0.141686 + 0.378829i
\(559\) −6.84259e14 −0.530219
\(560\) 3.23679e14 + 4.29142e14i 0.248359 + 0.329281i
\(561\) −3.96602e14 −0.301342
\(562\) −8.96767e14 2.39771e15i −0.674730 1.80404i
\(563\) 1.18164e15 1.18164e15i 0.880416 0.880416i −0.113160 0.993577i \(-0.536097\pi\)
0.993577 + 0.113160i \(0.0360974\pi\)
\(564\) −2.45135e14 + 3.51674e15i −0.180872 + 2.59481i
\(565\) −1.97222e14 1.97222e14i −0.144108 0.144108i
\(566\) 1.34371e15 + 6.12186e14i 0.972335 + 0.442989i
\(567\) 1.58343e15i 1.13473i
\(568\) −1.14636e15 6.21930e14i −0.813586 0.441393i
\(569\) 9.73112e14i 0.683983i 0.939703 + 0.341992i \(0.111101\pi\)
−0.939703 + 0.341992i \(0.888899\pi\)
\(570\) 4.68714e14 1.02880e15i 0.326285 0.716175i
\(571\) −1.00987e15 1.00987e15i −0.696253 0.696253i 0.267347 0.963600i \(-0.413853\pi\)
−0.963600 + 0.267347i \(0.913853\pi\)
\(572\) −5.48497e13 + 4.77013e13i −0.0374538 + 0.0325726i
\(573\) 6.74676e14 6.74676e14i 0.456294 0.456294i
\(574\) 3.84015e13 1.43626e13i 0.0257237 0.00962092i
\(575\) 1.25866e15 0.835092
\(576\) −1.44976e15 + 9.42848e14i −0.952734 + 0.619609i
\(577\) 1.63029e15 1.06120 0.530602 0.847621i \(-0.321966\pi\)
0.530602 + 0.847621i \(0.321966\pi\)
\(578\) −1.33638e15 + 4.99819e14i −0.861640 + 0.322262i
\(579\) 1.99286e15 1.99286e15i 1.27275 1.27275i
\(580\) −3.56270e14 + 3.09838e14i −0.225385 + 0.196011i
\(581\) −2.56806e15 2.56806e15i −1.60930 1.60930i
\(582\) 1.79547e14 3.94096e14i 0.111456 0.244639i
\(583\) 2.28897e14i 0.140755i
\(584\) 5.12695e14 + 2.78151e14i 0.312312 + 0.169438i
\(585\) 1.92939e14i 0.116430i
\(586\) 8.60407e14 + 3.91995e14i 0.514360 + 0.234339i
\(587\) 7.41304e14 + 7.41304e14i 0.439022 + 0.439022i 0.891683 0.452661i \(-0.149525\pi\)
−0.452661 + 0.891683i \(0.649525\pi\)
\(588\) 1.39256e14 1.99778e15i 0.0817029 1.17212i
\(589\) −7.59078e14 + 7.59078e14i −0.441217 + 0.441217i
\(590\) −2.03562e14 5.44269e14i −0.117223 0.313421i
\(591\) −7.33034e14 −0.418209
\(592\) 1.77909e15 1.34187e15i 1.00561 0.758474i
\(593\) −3.32085e15 −1.85972 −0.929861 0.367910i \(-0.880073\pi\)
−0.929861 + 0.367910i \(0.880073\pi\)
\(594\) −1.87417e13 5.01101e13i −0.0103988 0.0278035i
\(595\) −7.35079e14 + 7.35079e14i −0.404102 + 0.404102i
\(596\) 5.67883e13 + 3.95844e12i 0.0309317 + 0.00215610i
\(597\) 2.80992e15 + 2.80992e15i 1.51647 + 1.51647i
\(598\) 5.23463e14 + 2.38486e14i 0.279917 + 0.127528i
\(599\) 2.87597e15i 1.52383i −0.647675 0.761916i \(-0.724259\pi\)
0.647675 0.761916i \(-0.275741\pi\)
\(600\) −2.41746e15 + 7.16955e14i −1.26919 + 0.376409i
\(601\) 3.01761e14i 0.156984i 0.996915 + 0.0784918i \(0.0250104\pi\)
−0.996915 + 0.0784918i \(0.974990\pi\)
\(602\) −1.71682e15 + 3.76832e15i −0.885001 + 1.94252i
\(603\) 1.61444e15 + 1.61444e15i 0.824665 + 0.824665i
\(604\) −1.59030e15 1.82862e15i −0.804964 0.925593i
\(605\) −4.23331e14 + 4.23331e14i −0.212337 + 0.212337i
\(606\) 2.96581e15 1.10924e15i 1.47416 0.551350i
\(607\) −1.10741e15 −0.545470 −0.272735 0.962089i \(-0.587928\pi\)
−0.272735 + 0.962089i \(0.587928\pi\)
\(608\) −3.03049e15 1.92828e15i −1.47925 0.941242i
\(609\) 3.94740e15 1.90948
\(610\) 8.41775e14 3.14832e14i 0.403536 0.150926i
\(611\) −8.83592e14 + 8.83592e14i −0.419783 + 0.419783i
\(612\) −2.19481e15 2.52371e15i −1.03339 1.18825i
\(613\) 2.34187e15 + 2.34187e15i 1.09277 + 1.09277i 0.995231 + 0.0975435i \(0.0310985\pi\)
0.0975435 + 0.995231i \(0.468902\pi\)
\(614\) −9.92456e14 + 2.17838e15i −0.458971 + 1.00741i
\(615\) 2.00258e13i 0.00917861i
\(616\) 1.25079e14 + 4.21749e14i 0.0568188 + 0.191584i
\(617\) 6.98011e14i 0.314264i 0.987578 + 0.157132i \(0.0502248\pi\)
−0.987578 + 0.157132i \(0.949775\pi\)
\(618\) 6.29358e14 + 2.86731e14i 0.280841 + 0.127949i
\(619\) −2.28130e15 2.28130e15i −1.00898 1.00898i −0.999959 0.00902486i \(-0.997127\pi\)
−0.00902486 0.999959i \(-0.502873\pi\)
\(620\) −2.48697e14 1.73355e13i −0.109023 0.00759945i
\(621\) −2.99367e14 + 2.99367e14i −0.130077 + 0.130077i
\(622\) −8.05135e14 2.15271e15i −0.346754 0.927124i
\(623\) −2.02644e14 −0.0865065
\(624\) −1.14125e15 1.59878e14i −0.482908 0.0676511i
\(625\) −1.73088e15 −0.725984
\(626\) 1.69460e14 + 4.53089e14i 0.0704545 + 0.188376i
\(627\) 6.54235e14 6.54235e14i 0.269626 0.269626i
\(628\) 8.86463e13 1.27173e15i 0.0362145 0.519538i
\(629\) 3.04741e15 + 3.04741e15i 1.23410 + 1.23410i
\(630\) −1.06255e15 4.84089e14i −0.426555 0.194335i
\(631\) 3.06944e15i 1.22151i 0.791819 + 0.610755i \(0.209134\pi\)
−0.791819 + 0.610755i \(0.790866\pi\)
\(632\) 1.53125e15 2.82243e15i 0.604089 1.11347i
\(633\) 4.92638e15i 1.92667i
\(634\) 3.98072e14 8.73745e14i 0.154337 0.338761i
\(635\) 1.48946e13 + 1.48946e13i 0.00572497 + 0.00572497i
\(636\) −2.73816e15 + 2.38130e15i −1.04338 + 0.907404i
\(637\) 5.01949e14 5.01949e14i 0.189624 0.189624i
\(638\) −3.61921e14 + 1.35362e14i −0.135550 + 0.0506972i
\(639\) 2.83302e15 1.05195
\(640\) −1.23934e14 8.24909e14i −0.0456249 0.303680i
\(641\) −2.26554e15 −0.826899 −0.413449 0.910527i \(-0.635676\pi\)
−0.413449 + 0.910527i \(0.635676\pi\)
\(642\) 2.12601e15 7.95151e14i 0.769349 0.287744i
\(643\) −4.93160e14 + 4.93160e14i −0.176941 + 0.176941i −0.790021 0.613080i \(-0.789930\pi\)
0.613080 + 0.790021i \(0.289930\pi\)
\(644\) 2.62676e15 2.28442e15i 0.934432 0.812652i
\(645\) 1.43021e15 + 1.43021e15i 0.504453 + 0.504453i
\(646\) 2.88008e15 6.32161e15i 1.00722 2.21080i
\(647\) 2.61317e15i 0.906139i −0.891475 0.453069i \(-0.850329\pi\)
0.891475 0.453069i \(-0.149671\pi\)
\(648\) −1.17180e15 + 2.15989e15i −0.402894 + 0.742624i
\(649\) 4.75561e14i 0.162129i
\(650\) −8.13364e14 3.70563e14i −0.274955 0.125268i
\(651\) 1.47380e15 + 1.47380e15i 0.494017 + 0.494017i
\(652\) 3.83564e13 5.50266e14i 0.0127490 0.182899i
\(653\) −3.24689e15 + 3.24689e15i −1.07015 + 1.07015i −0.0728038 + 0.997346i \(0.523195\pi\)
−0.997346 + 0.0728038i \(0.976805\pi\)
\(654\) 7.84978e14 + 2.09881e15i 0.256555 + 0.685956i
\(655\) −9.15639e14 −0.296754
\(656\) −6.30107e13 8.82723e12i −0.0202508 0.00283696i
\(657\) −1.26703e15 −0.403812
\(658\) 2.64912e15 + 7.08302e15i 0.837259 + 2.23860i
\(659\) −8.89857e13 + 8.89857e13i −0.0278901 + 0.0278901i −0.720914 0.693024i \(-0.756278\pi\)
0.693024 + 0.720914i \(0.256278\pi\)
\(660\) 2.14347e14 + 1.49411e13i 0.0666234 + 0.00464400i
\(661\) 2.37602e14 + 2.37602e14i 0.0732388 + 0.0732388i 0.742777 0.669539i \(-0.233508\pi\)
−0.669539 + 0.742777i \(0.733508\pi\)
\(662\) −6.74708e13 3.07393e13i −0.0206252 0.00939668i
\(663\) 2.22870e15i 0.675659i
\(664\) 1.60252e15 + 5.40344e15i 0.481813 + 1.62460i
\(665\) 2.42517e15i 0.723142i
\(666\) −2.00688e15 + 4.40498e15i −0.593489 + 1.30267i
\(667\) 2.16219e15 + 2.16219e15i 0.634164 + 0.634164i
\(668\) 3.76614e15 + 4.33052e15i 1.09553 + 1.25971i
\(669\) −1.07413e15 + 1.07413e15i −0.309894 + 0.309894i
\(670\) −1.03150e15 + 3.85792e14i −0.295160 + 0.110393i
\(671\) 7.35510e14 0.208744
\(672\) −3.74388e15 + 5.88387e15i −1.05388 + 1.65627i
\(673\) 4.98817e14 0.139270 0.0696352 0.997573i \(-0.477816\pi\)
0.0696352 + 0.997573i \(0.477816\pi\)
\(674\) −6.56554e15 + 2.45558e15i −1.81820 + 0.680024i
\(675\) 4.65160e14 4.65160e14i 0.127771 0.127771i
\(676\) 2.14052e15 + 2.46129e15i 0.583192 + 0.670587i
\(677\) −3.03419e15 3.03419e15i −0.819984 0.819984i 0.166121 0.986105i \(-0.446876\pi\)
−0.986105 + 0.166121i \(0.946876\pi\)
\(678\) 1.50030e15 3.29306e15i 0.402174 0.882747i
\(679\) 9.28995e14i 0.247019i
\(680\) 1.54668e15 4.58703e14i 0.407944 0.120985i
\(681\) 2.21698e15i 0.580034i
\(682\) −1.85665e14 8.45878e13i −0.0481855 0.0219530i
\(683\) 3.12787e15 + 3.12787e15i 0.805257 + 0.805257i 0.983912 0.178655i \(-0.0571745\pi\)
−0.178655 + 0.983912i \(0.557175\pi\)
\(684\) 7.78367e15 + 5.42562e14i 1.98781 + 0.138561i
\(685\) −3.35676e14 + 3.35676e14i −0.0850398 + 0.0850398i
\(686\) 3.67222e14 + 9.81851e14i 0.0922883 + 0.246753i
\(687\) −7.66517e15 −1.91100
\(688\) 5.13053e15 3.86968e15i 1.26890 0.957060i
\(689\) −1.28628e15 −0.315595
\(690\) −5.95646e14 1.59259e15i −0.144983 0.387646i
\(691\) 2.77334e15 2.77334e15i 0.669689 0.669689i −0.287955 0.957644i \(-0.592975\pi\)
0.957644 + 0.287955i \(0.0929752\pi\)
\(692\) 8.37653e13 1.20171e15i 0.0200669 0.287883i
\(693\) −6.75694e14 6.75694e14i −0.160590 0.160590i
\(694\) −2.43597e15 1.10981e15i −0.574375 0.261681i
\(695\) 5.35441e14i 0.125255i
\(696\) −5.38448e15 2.92123e15i −1.24966 0.677976i
\(697\) 1.23051e14i 0.0283339i
\(698\) 3.46300e15 7.60109e15i 0.791131 1.73649i
\(699\) −4.80793e15 4.80793e15i −1.08977 1.08977i
\(700\) −4.08149e15 + 3.54956e15i −0.917866 + 0.798244i
\(701\) 3.58804e15 3.58804e15i 0.800587 0.800587i −0.182600 0.983187i \(-0.558451\pi\)
0.983187 + 0.182600i \(0.0584514\pi\)
\(702\) 2.81593e14 1.05319e14i 0.0623401 0.0233158i
\(703\) −1.00540e16 −2.20844
\(704\) 1.41495e14 6.67852e14i 0.0308383 0.145556i
\(705\) 3.69369e15 0.798767
\(706\) 7.50496e15 2.80693e15i 1.61036 0.602291i
\(707\) 4.80302e15 4.80302e15i 1.02260 1.02260i
\(708\) 5.68886e15 4.94746e15i 1.20183 1.04520i
\(709\) −2.93575e15 2.93575e15i −0.615410 0.615410i 0.328940 0.944351i \(-0.393308\pi\)
−0.944351 + 0.328940i \(0.893308\pi\)
\(710\) −5.66543e14 + 1.24353e15i −0.117845 + 0.258663i
\(711\) 6.97513e15i 1.43969i
\(712\) 2.76417e14 + 1.49964e14i 0.0566142 + 0.0307147i
\(713\) 1.61454e15i 0.328139i
\(714\) −1.22738e16 5.59185e15i −2.47536 1.12776i
\(715\) 5.38555e13 + 5.38555e13i 0.0107782 + 0.0107782i
\(716\) 2.53314e14 3.63407e15i 0.0503080 0.721725i
\(717\) −3.64143e15 + 3.64143e15i −0.717656 + 0.717656i
\(718\) −1.69396e15 4.52918e15i −0.331298 0.885800i
\(719\) 4.19879e15 0.814920 0.407460 0.913223i \(-0.366415\pi\)
0.407460 + 0.913223i \(0.366415\pi\)
\(720\) 1.09113e15 + 1.44665e15i 0.210159 + 0.278634i
\(721\) 1.48357e15 0.283573
\(722\) 3.83040e15 + 1.02414e16i 0.726589 + 1.94270i
\(723\) −6.47858e15 + 6.47858e15i −1.21960 + 1.21960i
\(724\) −2.03015e15 1.41512e14i −0.379285 0.0264382i
\(725\) −3.35964e15 3.35964e15i −0.622922 0.622922i
\(726\) −7.06846e15 3.22034e15i −1.30069 0.592585i
\(727\) 4.12785e15i 0.753849i 0.926244 + 0.376925i \(0.123018\pi\)
−0.926244 + 0.376925i \(0.876982\pi\)
\(728\) −2.37001e15 + 7.02882e14i −0.429564 + 0.127397i
\(729\) 6.95891e15i 1.25181i
\(730\) 2.53380e14 5.56154e14i 0.0452373 0.0992932i
\(731\) 8.78811e15 + 8.78811e15i 1.55722 + 1.55722i
\(732\) 7.65181e15 + 8.79848e15i 1.34571 + 1.54738i
\(733\) 4.75984e15 4.75984e15i 0.830845 0.830845i −0.156787 0.987632i \(-0.550114\pi\)
0.987632 + 0.156787i \(0.0501136\pi\)
\(734\) −1.87754e15 + 7.02221e14i −0.325283 + 0.121659i
\(735\) −2.09830e15 −0.360817
\(736\) −5.27361e15 + 1.17218e15i −0.900077 + 0.200063i
\(737\) −9.01285e14 −0.152683
\(738\) 1.29452e14 4.84165e13i 0.0217671 0.00814111i
\(739\) 3.24543e15 3.24543e15i 0.541661 0.541661i −0.382355 0.924016i \(-0.624887\pi\)
0.924016 + 0.382355i \(0.124887\pi\)
\(740\) −1.53220e15 1.76180e15i −0.253828 0.291866i
\(741\) 3.67647e15 + 3.67647e15i 0.604548 + 0.604548i
\(742\) −3.22731e15 + 7.08375e15i −0.526767 + 1.15622i
\(743\) 9.92853e15i 1.60859i 0.594227 + 0.804297i \(0.297458\pi\)
−0.594227 + 0.804297i \(0.702542\pi\)
\(744\) −9.19676e14 3.10101e15i −0.147905 0.498714i
\(745\) 5.96457e13i 0.00952182i
\(746\) 5.35943e15 + 2.44172e15i 0.849288 + 0.386930i
\(747\) −8.65699e15 8.65699e15i −1.36177 1.36177i
\(748\) 1.31709e15 + 9.18079e13i 0.205663 + 0.0143358i
\(749\) 3.44300e15 3.44300e15i 0.533688 0.533688i
\(750\) 1.94741e15 + 5.20684e15i 0.299655 + 0.801193i
\(751\) 2.11436e14 0.0322969 0.0161484 0.999870i \(-0.494860\pi\)
0.0161484 + 0.999870i \(0.494860\pi\)
\(752\) 1.62815e15 1.16221e16i 0.246886 1.76233i
\(753\) 6.94632e15 1.04564
\(754\) −7.60668e14 2.03381e15i −0.113672 0.303927i
\(755\) −1.79548e15 + 1.79548e15i −0.266361 + 0.266361i
\(756\) 1.26516e14 1.81502e15i 0.0186327 0.267308i
\(757\) 7.13066e15 + 7.13066e15i 1.04256 + 1.04256i 0.999053 + 0.0435106i \(0.0138542\pi\)
0.0435106 + 0.999053i \(0.486146\pi\)
\(758\) 2.39935e15 + 1.09313e15i 0.348267 + 0.158668i
\(759\) 1.39155e15i 0.200525i
\(760\) −1.79472e15 + 3.30807e15i −0.256757 + 0.473261i
\(761\) 7.63959e15i