Properties

Label 16.12.e.a.5.15
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM no
Inner twists 2

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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 5.15
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.15

$q$-expansion

\(f(q)\) \(=\) \(q+(26.1391 + 36.9425i) q^{2} +(255.917 - 255.917i) q^{3} +(-681.491 + 1931.29i) q^{4} +(-4214.49 - 4214.49i) q^{5} +(16143.6 + 2764.75i) q^{6} +80345.3i q^{7} +(-89160.1 + 25306.2i) q^{8} +46160.2i q^{9} +O(q^{10})\) \(q+(26.1391 + 36.9425i) q^{2} +(255.917 - 255.917i) q^{3} +(-681.491 + 1931.29i) q^{4} +(-4214.49 - 4214.49i) q^{5} +(16143.6 + 2764.75i) q^{6} +80345.3i q^{7} +(-89160.1 + 25306.2i) q^{8} +46160.2i q^{9} +(45530.5 - 265857. i) q^{10} +(611105. + 611105. i) q^{11} +(319844. + 668654. i) q^{12} +(370364. - 370364. i) q^{13} +(-2.96815e6 + 2.10016e6i) q^{14} -2.15712e6 q^{15} +(-3.26544e6 - 2.63231e6i) q^{16} -725142. q^{17} +(-1.70527e6 + 1.20659e6i) q^{18} +(-1.13100e7 + 1.13100e7i) q^{19} +(1.10115e7 - 5.26725e6i) q^{20} +(2.05617e7 + 2.05617e7i) q^{21} +(-6.60196e6 + 3.85495e7i) q^{22} -4.89011e7i q^{23} +(-1.63413e7 + 2.92939e7i) q^{24} -1.33043e7i q^{25} +(2.33632e7 + 4.00116e6i) q^{26} +(5.71481e7 + 5.71481e7i) q^{27} +(-1.55170e8 - 5.47546e7i) q^{28} +(4.98291e7 - 4.98291e7i) q^{29} +(-5.63852e7 - 7.96892e7i) q^{30} +4.20747e7 q^{31} +(1.18882e7 - 1.89440e8i) q^{32} +3.12784e8 q^{33} +(-1.89546e7 - 2.67885e7i) q^{34} +(3.38614e8 - 3.38614e8i) q^{35} +(-8.91486e7 - 3.14578e7i) q^{36} +(-1.05666e8 - 1.05666e8i) q^{37} +(-7.13450e8 - 1.22185e8i) q^{38} -1.89565e8i q^{39} +(4.82417e8 + 2.69111e8i) q^{40} +4.49063e8i q^{41} +(-2.22135e8 + 1.29706e9i) q^{42} +(7.89791e8 + 7.89791e8i) q^{43} +(-1.59668e9 + 7.63757e8i) q^{44} +(1.94542e8 - 1.94542e8i) q^{45} +(1.80653e9 - 1.27823e9i) q^{46} +1.32368e9 q^{47} +(-1.50933e9 + 1.62029e8i) q^{48} -4.47803e9 q^{49} +(4.91494e8 - 3.47763e8i) q^{50} +(-1.85576e8 + 1.85576e8i) q^{51} +(4.62880e8 + 9.67680e8i) q^{52} +(1.74345e9 + 1.74345e9i) q^{53} +(-6.17389e8 + 3.60499e9i) q^{54} -5.15099e9i q^{55} +(-2.03324e9 - 7.16359e9i) q^{56} +5.78882e9i q^{57} +(3.14330e9 + 5.38320e8i) q^{58} +(-6.71604e8 - 6.71604e8i) q^{59} +(1.47006e9 - 4.16601e9i) q^{60} +(-8.30682e8 + 8.30682e8i) q^{61} +(1.09980e9 + 1.55434e9i) q^{62} -3.70875e9 q^{63} +(7.30912e9 - 4.51262e9i) q^{64} -3.12179e9 q^{65} +(8.17590e9 + 1.15550e10i) q^{66} +(3.88275e9 - 3.88275e9i) q^{67} +(4.94178e8 - 1.40046e9i) q^{68} +(-1.25146e10 - 1.25146e10i) q^{69} +(2.13603e10 + 3.65816e9i) q^{70} -5.14233e9i q^{71} +(-1.16814e9 - 4.11565e9i) q^{72} -4.42543e9i q^{73} +(1.14154e9 - 6.66558e9i) q^{74} +(-3.40480e9 - 3.40480e9i) q^{75} +(-1.41352e10 - 2.95504e10i) q^{76} +(-4.90994e10 + 4.90994e10i) q^{77} +(7.00299e9 - 4.95506e9i) q^{78} +2.71827e10 q^{79} +(2.66833e9 + 2.48560e10i) q^{80} +2.10732e10 q^{81} +(-1.65895e10 + 1.17381e10i) q^{82} +(1.81378e10 - 1.81378e10i) q^{83} +(-5.37232e10 + 2.56979e10i) q^{84} +(3.05610e9 + 3.05610e9i) q^{85} +(-8.53237e9 + 4.98213e10i) q^{86} -2.55042e10i q^{87} +(-6.99509e10 - 3.90214e10i) q^{88} +5.56593e10i q^{89} +(1.22720e10 + 2.10170e9i) q^{90} +(2.97570e10 + 2.97570e10i) q^{91} +(9.44421e10 + 3.33257e10i) q^{92} +(1.07676e10 - 1.07676e10i) q^{93} +(3.45999e10 + 4.89000e10i) q^{94} +9.53314e10 q^{95} +(-4.54385e10 - 5.15232e10i) q^{96} +2.61297e10 q^{97} +(-1.17052e11 - 1.65430e11i) q^{98} +(-2.82087e10 + 2.82087e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.1391 + 36.9425i 0.577599 + 0.816321i
\(3\) 255.917 255.917i 0.608040 0.608040i −0.334394 0.942433i \(-0.608532\pi\)
0.942433 + 0.334394i \(0.108532\pi\)
\(4\) −681.491 + 1931.29i −0.332759 + 0.943012i
\(5\) −4214.49 4214.49i −0.603128 0.603128i 0.338013 0.941141i \(-0.390245\pi\)
−0.941141 + 0.338013i \(0.890245\pi\)
\(6\) 16143.6 + 2764.75i 0.847558 + 0.145152i
\(7\) 80345.3i 1.80685i 0.428751 + 0.903423i \(0.358954\pi\)
−0.428751 + 0.903423i \(0.641046\pi\)
\(8\) −89160.1 + 25306.2i −0.962002 + 0.273044i
\(9\) 46160.2i 0.260576i
\(10\) 45530.5 265857.i 0.143980 0.840712i
\(11\) 611105. + 611105.i 1.14408 + 1.14408i 0.987697 + 0.156382i \(0.0499831\pi\)
0.156382 + 0.987697i \(0.450017\pi\)
\(12\) 319844. + 668654.i 0.371058 + 0.775719i
\(13\) 370364. 370364.i 0.276656 0.276656i −0.555116 0.831773i \(-0.687326\pi\)
0.831773 + 0.555116i \(0.187326\pi\)
\(14\) −2.96815e6 + 2.10016e6i −1.47497 + 1.04363i
\(15\) −2.15712e6 −0.733452
\(16\) −3.26544e6 2.63231e6i −0.778542 0.627592i
\(17\) −725142. −0.123867 −0.0619333 0.998080i \(-0.519727\pi\)
−0.0619333 + 0.998080i \(0.519727\pi\)
\(18\) −1.70527e6 + 1.20659e6i −0.212713 + 0.150508i
\(19\) −1.13100e7 + 1.13100e7i −1.04789 + 1.04789i −0.0490973 + 0.998794i \(0.515634\pi\)
−0.998794 + 0.0490973i \(0.984366\pi\)
\(20\) 1.10115e7 5.26725e6i 0.769454 0.368061i
\(21\) 2.05617e7 + 2.05617e7i 1.09863 + 1.09863i
\(22\) −6.60196e6 + 3.85495e7i −0.273117 + 1.59475i
\(23\) 4.89011e7i 1.58422i −0.610378 0.792110i \(-0.708982\pi\)
0.610378 0.792110i \(-0.291018\pi\)
\(24\) −1.63413e7 + 2.92939e7i −0.418913 + 0.750957i
\(25\) 1.33043e7i 0.272472i
\(26\) 2.33632e7 + 4.00116e6i 0.385636 + 0.0660439i
\(27\) 5.71481e7 + 5.71481e7i 0.766480 + 0.766480i
\(28\) −1.55170e8 5.47546e7i −1.70388 0.601245i
\(29\) 4.98291e7 4.98291e7i 0.451122 0.451122i −0.444605 0.895727i \(-0.646656\pi\)
0.895727 + 0.444605i \(0.146656\pi\)
\(30\) −5.63852e7 7.96892e7i −0.423641 0.598732i
\(31\) 4.20747e7 0.263956 0.131978 0.991253i \(-0.457867\pi\)
0.131978 + 0.991253i \(0.457867\pi\)
\(32\) 1.18882e7 1.89440e8i 0.0626312 0.998037i
\(33\) 3.12784e8 1.39129
\(34\) −1.89546e7 2.67885e7i −0.0715452 0.101115i
\(35\) 3.38614e8 3.38614e8i 1.08976 1.08976i
\(36\) −8.91486e7 3.14578e7i −0.245726 0.0867090i
\(37\) −1.05666e8 1.05666e8i −0.250510 0.250510i 0.570670 0.821180i \(-0.306684\pi\)
−0.821180 + 0.570670i \(0.806684\pi\)
\(38\) −7.13450e8 1.22185e8i −1.46068 0.250155i
\(39\) 1.89565e8i 0.336436i
\(40\) 4.82417e8 + 2.69111e8i 0.744891 + 0.415530i
\(41\) 4.49063e8i 0.605335i 0.953096 + 0.302668i \(0.0978772\pi\)
−0.953096 + 0.302668i \(0.902123\pi\)
\(42\) −2.22135e8 + 1.29706e9i −0.262268 + 1.53141i
\(43\) 7.89791e8 + 7.89791e8i 0.819286 + 0.819286i 0.986005 0.166718i \(-0.0533170\pi\)
−0.166718 + 0.986005i \(0.553317\pi\)
\(44\) −1.59668e9 + 7.63757e8i −1.45958 + 0.698177i
\(45\) 1.94542e8 1.94542e8i 0.157161 0.157161i
\(46\) 1.80653e9 1.27823e9i 1.29323 0.915044i
\(47\) 1.32368e9 0.841870 0.420935 0.907091i \(-0.361702\pi\)
0.420935 + 0.907091i \(0.361702\pi\)
\(48\) −1.50933e9 + 1.62029e8i −0.854985 + 0.0917839i
\(49\) −4.47803e9 −2.26469
\(50\) 4.91494e8 3.47763e8i 0.222425 0.157380i
\(51\) −1.85576e8 + 1.85576e8i −0.0753158 + 0.0753158i
\(52\) 4.62880e8 + 9.67680e8i 0.168830 + 0.352950i
\(53\) 1.74345e9 + 1.74345e9i 0.572655 + 0.572655i 0.932870 0.360214i \(-0.117296\pi\)
−0.360214 + 0.932870i \(0.617296\pi\)
\(54\) −6.17389e8 + 3.60499e9i −0.182976 + 1.06841i
\(55\) 5.15099e9i 1.38005i
\(56\) −2.03324e9 7.16359e9i −0.493348 1.73819i
\(57\) 5.78882e9i 1.27432i
\(58\) 3.14330e9 + 5.38320e8i 0.628828 + 0.107693i
\(59\) −6.71604e8 6.71604e8i −0.122300 0.122300i 0.643308 0.765608i \(-0.277562\pi\)
−0.765608 + 0.643308i \(0.777562\pi\)
\(60\) 1.47006e9 4.16601e9i 0.244063 0.691654i
\(61\) −8.30682e8 + 8.30682e8i −0.125928 + 0.125928i −0.767262 0.641334i \(-0.778381\pi\)
0.641334 + 0.767262i \(0.278381\pi\)
\(62\) 1.09980e9 + 1.55434e9i 0.152461 + 0.215473i
\(63\) −3.70875e9 −0.470820
\(64\) 7.30912e9 4.51262e9i 0.850894 0.525338i
\(65\) −3.12179e9 −0.333718
\(66\) 8.17590e9 + 1.15550e10i 0.803608 + 1.13574i
\(67\) 3.88275e9 3.88275e9i 0.351340 0.351340i −0.509268 0.860608i \(-0.670084\pi\)
0.860608 + 0.509268i \(0.170084\pi\)
\(68\) 4.94178e8 1.40046e9i 0.0412178 0.116808i
\(69\) −1.25146e10 1.25146e10i −0.963269 0.963269i
\(70\) 2.13603e10 + 3.65816e9i 1.51904 + 0.260150i
\(71\) 5.14233e9i 0.338251i −0.985595 0.169125i \(-0.945906\pi\)
0.985595 0.169125i \(-0.0540943\pi\)
\(72\) −1.16814e9 4.11565e9i −0.0711486 0.250674i
\(73\) 4.42543e9i 0.249850i −0.992166 0.124925i \(-0.960131\pi\)
0.992166 0.124925i \(-0.0398690\pi\)
\(74\) 1.14154e9 6.66558e9i 0.0598023 0.349191i
\(75\) −3.40480e9 3.40480e9i −0.165674 0.165674i
\(76\) −1.41352e10 2.95504e10i −0.639478 1.33687i
\(77\) −4.90994e10 + 4.90994e10i −2.06717 + 2.06717i
\(78\) 7.00299e9 4.95506e9i 0.274640 0.194325i
\(79\) 2.71827e10 0.993902 0.496951 0.867779i \(-0.334453\pi\)
0.496951 + 0.867779i \(0.334453\pi\)
\(80\) 2.66833e9 + 2.48560e10i 0.0910425 + 0.848080i
\(81\) 2.10732e10 0.671525
\(82\) −1.65895e10 + 1.17381e10i −0.494148 + 0.349641i
\(83\) 1.81378e10 1.81378e10i 0.505423 0.505423i −0.407695 0.913118i \(-0.633667\pi\)
0.913118 + 0.407695i \(0.133667\pi\)
\(84\) −5.37232e10 + 2.56979e10i −1.40160 + 0.670444i
\(85\) 3.05610e9 + 3.05610e9i 0.0747075 + 0.0747075i
\(86\) −8.53237e9 + 4.98213e10i −0.195582 + 1.14202i
\(87\) 2.55042e10i 0.548600i
\(88\) −6.99509e10 3.90214e10i −1.41299 0.788221i
\(89\) 5.56593e10i 1.05656i 0.849071 + 0.528278i \(0.177162\pi\)
−0.849071 + 0.528278i \(0.822838\pi\)
\(90\) 1.22720e10 + 2.10170e9i 0.219069 + 0.0375177i
\(91\) 2.97570e10 + 2.97570e10i 0.499875 + 0.499875i
\(92\) 9.44421e10 + 3.33257e10i 1.49394 + 0.527164i
\(93\) 1.07676e10 1.07676e10i 0.160496 0.160496i
\(94\) 3.45999e10 + 4.89000e10i 0.486263 + 0.687236i
\(95\) 9.53314e10 1.26403
\(96\) −4.54385e10 5.15232e10i −0.568764 0.644928i
\(97\) 2.61297e10 0.308951 0.154476 0.987997i \(-0.450631\pi\)
0.154476 + 0.987997i \(0.450631\pi\)
\(98\) −1.17052e11 1.65430e11i −1.30808 1.84871i
\(99\) −2.82087e10 + 2.82087e10i −0.298119 + 0.298119i
\(100\) 2.56945e10 + 9.06677e9i 0.256945 + 0.0906677i
\(101\) −4.83525e10 4.83525e10i −0.457774 0.457774i 0.440150 0.897924i \(-0.354925\pi\)
−0.897924 + 0.440150i \(0.854925\pi\)
\(102\) −1.17064e10 2.00484e9i −0.104984 0.0179795i
\(103\) 8.13751e10i 0.691651i −0.938299 0.345825i \(-0.887599\pi\)
0.938299 0.345825i \(-0.112401\pi\)
\(104\) −2.36492e10 + 4.23942e10i −0.190604 + 0.341683i
\(105\) 1.73314e11i 1.32523i
\(106\) −1.88351e10 + 1.09980e11i −0.136705 + 0.798235i
\(107\) −1.97606e10 1.97606e10i −0.136204 0.136204i 0.635718 0.771922i \(-0.280704\pi\)
−0.771922 + 0.635718i \(0.780704\pi\)
\(108\) −1.49315e11 + 7.14235e10i −0.977853 + 0.467746i
\(109\) 1.02515e11 1.02515e11i 0.638175 0.638175i −0.311930 0.950105i \(-0.600975\pi\)
0.950105 + 0.311930i \(0.100975\pi\)
\(110\) 1.90290e11 1.34642e11i 1.12657 0.797117i
\(111\) −5.40834e10 −0.304640
\(112\) 2.11494e11 2.62363e11i 1.13396 1.40671i
\(113\) 2.99733e11 1.53039 0.765196 0.643798i \(-0.222642\pi\)
0.765196 + 0.643798i \(0.222642\pi\)
\(114\) −2.13853e11 + 1.51315e11i −1.04025 + 0.736045i
\(115\) −2.06093e11 + 2.06093e11i −0.955488 + 0.955488i
\(116\) 6.22763e10 + 1.30192e11i 0.275298 + 0.575529i
\(117\) 1.70961e10 + 1.70961e10i 0.0720899 + 0.0720899i
\(118\) 7.25556e9 4.23659e10i 0.0291958 0.170477i
\(119\) 5.82617e10i 0.223808i
\(120\) 1.92329e11 5.45885e10i 0.705582 0.200265i
\(121\) 4.61586e11i 1.61783i
\(122\) −5.24008e10 8.97413e9i −0.175533 0.0300617i
\(123\) 1.14923e11 + 1.14923e11i 0.368068 + 0.368068i
\(124\) −2.86736e10 + 8.12584e10i −0.0878339 + 0.248914i
\(125\) −2.61856e11 + 2.61856e11i −0.767464 + 0.767464i
\(126\) −9.69436e10 1.37010e11i −0.271945 0.384340i
\(127\) −6.80100e11 −1.82664 −0.913319 0.407245i \(-0.866490\pi\)
−0.913319 + 0.407245i \(0.866490\pi\)
\(128\) 3.57761e11 + 1.52061e11i 0.920319 + 0.391168i
\(129\) 4.04242e11 0.996317
\(130\) −8.16009e10 1.15327e11i −0.192755 0.272421i
\(131\) −4.89403e11 + 4.89403e11i −1.10834 + 1.10834i −0.114976 + 0.993368i \(0.536679\pi\)
−0.993368 + 0.114976i \(0.963321\pi\)
\(132\) −2.13159e11 + 6.04076e11i −0.462965 + 1.31200i
\(133\) −9.08702e11 9.08702e11i −1.89338 1.89338i
\(134\) 2.44930e11 + 4.19466e10i 0.489740 + 0.0838726i
\(135\) 4.81700e11i 0.924572i
\(136\) 6.46538e10 1.83506e10i 0.119160 0.0338210i
\(137\) 6.45344e11i 1.14243i −0.820802 0.571213i \(-0.806473\pi\)
0.820802 0.571213i \(-0.193527\pi\)
\(138\) 1.35199e11 7.89442e11i 0.229954 1.34272i
\(139\) 7.22257e11 + 7.22257e11i 1.18062 + 1.18062i 0.979584 + 0.201036i \(0.0644310\pi\)
0.201036 + 0.979584i \(0.435569\pi\)
\(140\) 4.23199e11 + 8.84724e11i 0.665029 + 1.39028i
\(141\) 3.38752e11 3.38752e11i 0.511890 0.511890i
\(142\) 1.89970e11 1.34416e11i 0.276121 0.195373i
\(143\) 4.52662e11 0.633033
\(144\) 1.21508e11 1.50734e11i 0.163535 0.202869i
\(145\) −4.20008e11 −0.544169
\(146\) 1.63486e11 1.15677e11i 0.203958 0.144313i
\(147\) −1.14600e12 + 1.14600e12i −1.37702 + 1.37702i
\(148\) 2.76082e11 1.32061e11i 0.319594 0.152875i
\(149\) 7.59849e11 + 7.59849e11i 0.847623 + 0.847623i 0.989836 0.142213i \(-0.0454219\pi\)
−0.142213 + 0.989836i \(0.545422\pi\)
\(150\) 3.67831e10 2.14780e11i 0.0395500 0.230936i
\(151\) 1.60628e12i 1.66513i −0.553925 0.832566i \(-0.686871\pi\)
0.553925 0.832566i \(-0.313129\pi\)
\(152\) 7.22185e11 1.29461e12i 0.721953 1.29419i
\(153\) 3.34727e10i 0.0322766i
\(154\) −3.09727e12 5.30436e11i −2.88147 0.493480i
\(155\) −1.77323e11 1.77323e11i −0.159200 0.159200i
\(156\) 3.66104e11 + 1.29187e11i 0.317263 + 0.111952i
\(157\) −4.80944e11 + 4.80944e11i −0.402389 + 0.402389i −0.879074 0.476685i \(-0.841838\pi\)
0.476685 + 0.879074i \(0.341838\pi\)
\(158\) 7.10532e11 + 1.00420e12i 0.574077 + 0.811343i
\(159\) 8.92358e11 0.696394
\(160\) −8.48495e11 + 7.48289e11i −0.639719 + 0.564170i
\(161\) 3.92897e12 2.86244
\(162\) 5.50834e11 + 7.78494e11i 0.387872 + 0.548180i
\(163\) 1.15153e12 1.15153e12i 0.783872 0.783872i −0.196610 0.980482i \(-0.562993\pi\)
0.980482 + 0.196610i \(0.0629933\pi\)
\(164\) −8.67270e11 3.06032e11i −0.570838 0.201431i
\(165\) −1.31822e12 1.31822e12i −0.839127 0.839127i
\(166\) 1.14416e12 + 1.95948e11i 0.704518 + 0.120656i
\(167\) 1.12515e12i 0.670301i 0.942165 + 0.335150i \(0.108787\pi\)
−0.942165 + 0.335150i \(0.891213\pi\)
\(168\) −2.35362e12 1.31294e12i −1.35686 0.756912i
\(169\) 1.51782e12i 0.846923i
\(170\) −3.30161e10 + 1.92784e11i −0.0178343 + 0.104136i
\(171\) −5.22070e11 5.22070e11i −0.273055 0.273055i
\(172\) −2.06355e12 + 9.87079e11i −1.04522 + 0.499972i
\(173\) −3.94285e11 + 3.94285e11i −0.193445 + 0.193445i −0.797183 0.603738i \(-0.793677\pi\)
0.603738 + 0.797183i \(0.293677\pi\)
\(174\) 9.42188e11 6.66658e11i 0.447834 0.316871i
\(175\) 1.06894e12 0.492315
\(176\) −3.86910e11 3.60415e12i −0.172699 1.60873i
\(177\) −3.43750e11 −0.148727
\(178\) −2.05619e12 + 1.45489e12i −0.862489 + 0.610266i
\(179\) 4.94035e11 4.94035e11i 0.200940 0.200940i −0.599463 0.800403i \(-0.704619\pi\)
0.800403 + 0.599463i \(0.204619\pi\)
\(180\) 2.43137e11 + 5.08294e11i 0.0959076 + 0.200501i
\(181\) −1.41767e12 1.41767e12i −0.542430 0.542430i 0.381811 0.924240i \(-0.375301\pi\)
−0.924240 + 0.381811i \(0.875301\pi\)
\(182\) −3.21475e11 + 1.87712e12i −0.119331 + 0.696785i
\(183\) 4.25171e11i 0.153138i
\(184\) 1.23750e12 + 4.36003e12i 0.432562 + 1.52402i
\(185\) 8.90656e11i 0.302180i
\(186\) 6.79239e11 + 1.16326e11i 0.223718 + 0.0383139i
\(187\) −4.43138e11 4.43138e11i −0.141713 0.141713i
\(188\) −9.02077e11 + 2.55641e12i −0.280140 + 0.793893i
\(189\) −4.59158e12 + 4.59158e12i −1.38491 + 1.38491i
\(190\) 2.49188e12 + 3.52178e12i 0.730100 + 1.03185i
\(191\) 1.48907e12 0.423868 0.211934 0.977284i \(-0.432024\pi\)
0.211934 + 0.977284i \(0.432024\pi\)
\(192\) 7.15673e11 3.02538e12i 0.197951 0.836803i
\(193\) 4.59604e11 0.123543 0.0617716 0.998090i \(-0.480325\pi\)
0.0617716 + 0.998090i \(0.480325\pi\)
\(194\) 6.83008e11 + 9.65295e11i 0.178450 + 0.252203i
\(195\) −7.98918e11 + 7.98918e11i −0.202914 + 0.202914i
\(196\) 3.05174e12 8.64837e12i 0.753597 2.13563i
\(197\) 2.16767e12 + 2.16767e12i 0.520509 + 0.520509i 0.917725 0.397216i \(-0.130024\pi\)
−0.397216 + 0.917725i \(0.630024\pi\)
\(198\) −1.77945e12 3.04748e11i −0.415554 0.0711676i
\(199\) 6.81559e12i 1.54814i −0.633097 0.774072i \(-0.718217\pi\)
0.633097 0.774072i \(-0.281783\pi\)
\(200\) 3.36682e11 + 1.18621e12i 0.0743969 + 0.262119i
\(201\) 1.98732e12i 0.427257i
\(202\) 5.22368e11 3.05015e12i 0.109281 0.638100i
\(203\) 4.00353e12 + 4.00353e12i 0.815108 + 0.815108i
\(204\) −2.31932e11 4.84869e11i −0.0459617 0.0960857i
\(205\) 1.89257e12 1.89257e12i 0.365095 0.365095i
\(206\) 3.00620e12 2.12708e12i 0.564609 0.399497i
\(207\) 2.25728e12 0.412809
\(208\) −2.18432e12 + 2.34489e11i −0.389016 + 0.0417614i
\(209\) −1.38231e13 −2.39774
\(210\) 6.40265e12 4.53028e12i 1.08182 0.765454i
\(211\) 9.06969e11 9.06969e11i 0.149293 0.149293i −0.628509 0.777802i \(-0.716335\pi\)
0.777802 + 0.628509i \(0.216335\pi\)
\(212\) −4.55526e12 + 2.17896e12i −0.730577 + 0.349464i
\(213\) −1.31601e12 1.31601e12i −0.205670 0.205670i
\(214\) 2.13480e11 1.24653e12i 0.0325149 0.189857i
\(215\) 6.65713e12i 0.988270i
\(216\) −6.54153e12 3.64913e12i −0.946638 0.528072i
\(217\) 3.38051e12i 0.476928i
\(218\) 6.46678e12 + 1.10750e12i 0.889564 + 0.152346i
\(219\) −1.13254e12 1.13254e12i −0.151919 0.151919i
\(220\) 9.94804e12 + 3.51035e12i 1.30141 + 0.459225i
\(221\) −2.68567e11 + 2.68567e11i −0.0342685 + 0.0342685i
\(222\) −1.41369e12 1.99797e12i −0.175960 0.248684i
\(223\) −1.21567e13 −1.47618 −0.738090 0.674702i \(-0.764272\pi\)
−0.738090 + 0.674702i \(0.764272\pi\)
\(224\) 1.52206e13 + 9.55160e11i 1.80330 + 0.113165i
\(225\) 6.14129e11 0.0709996
\(226\) 7.83475e12 + 1.10729e13i 0.883952 + 1.24929i
\(227\) 5.41697e12 5.41697e12i 0.596506 0.596506i −0.342875 0.939381i \(-0.611401\pi\)
0.939381 + 0.342875i \(0.111401\pi\)
\(228\) −1.11799e13 3.94503e12i −1.20170 0.424042i
\(229\) −6.76215e11 6.76215e11i −0.0709561 0.0709561i 0.670738 0.741694i \(-0.265977\pi\)
−0.741694 + 0.670738i \(0.765977\pi\)
\(230\) −1.30007e13 2.22649e12i −1.33187 0.228096i
\(231\) 2.51307e13i 2.51385i
\(232\) −3.18178e12 + 5.70376e12i −0.310804 + 0.557156i
\(233\) 2.89696e12i 0.276366i 0.990407 + 0.138183i \(0.0441262\pi\)
−0.990407 + 0.138183i \(0.955874\pi\)
\(234\) −1.84695e11 + 1.07845e12i −0.0172094 + 0.100487i
\(235\) −5.57864e12 5.57864e12i −0.507756 0.507756i
\(236\) 1.75475e12 8.39369e11i 0.156027 0.0746340i
\(237\) 6.95651e12 6.95651e12i 0.604332 0.604332i
\(238\) 2.15233e12 1.52291e12i 0.182699 0.129271i
\(239\) −2.40938e12 −0.199856 −0.0999278 0.994995i \(-0.531861\pi\)
−0.0999278 + 0.994995i \(0.531861\pi\)
\(240\) 7.04394e12 + 5.67820e12i 0.571023 + 0.460309i
\(241\) 6.75923e12 0.535555 0.267777 0.963481i \(-0.413711\pi\)
0.267777 + 0.963481i \(0.413711\pi\)
\(242\) −1.70521e13 + 1.20655e13i −1.32067 + 0.934458i
\(243\) −4.73063e12 + 4.73063e12i −0.358166 + 0.358166i
\(244\) −1.03818e12 2.17039e12i −0.0768476 0.160655i
\(245\) 1.88726e13 + 1.88726e13i 1.36590 + 1.36590i
\(246\) −1.24155e12 + 7.24951e12i −0.0878659 + 0.513057i
\(247\) 8.37761e12i 0.579811i
\(248\) −3.75139e12 + 1.06475e12i −0.253926 + 0.0720717i
\(249\) 9.28353e12i 0.614634i
\(250\) −1.65183e13 2.82892e12i −1.06978 0.183211i
\(251\) −1.02005e13 1.02005e13i −0.646273 0.646273i 0.305817 0.952090i \(-0.401070\pi\)
−0.952090 + 0.305817i \(0.901070\pi\)
\(252\) 2.52748e12 7.16267e12i 0.156670 0.443989i
\(253\) 2.98837e13 2.98837e13i 1.81247 1.81247i
\(254\) −1.77772e13 2.51246e13i −1.05506 1.49112i
\(255\) 1.56422e12 0.0908502
\(256\) 3.73406e12 + 1.71913e13i 0.212257 + 0.977214i
\(257\) −1.59010e13 −0.884695 −0.442347 0.896844i \(-0.645854\pi\)
−0.442347 + 0.896844i \(0.645854\pi\)
\(258\) 1.05665e13 + 1.49337e13i 0.575472 + 0.813314i
\(259\) 8.48976e12 8.48976e12i 0.452633 0.452633i
\(260\) 2.12747e12 6.02908e12i 0.111048 0.314700i
\(261\) 2.30012e12 + 2.30012e12i 0.117551 + 0.117551i
\(262\) −3.08723e13 5.28718e12i −1.54494 0.264586i
\(263\) 2.14522e13i 1.05127i 0.850710 + 0.525636i \(0.176173\pi\)
−0.850710 + 0.525636i \(0.823827\pi\)
\(264\) −2.78879e13 + 7.91539e12i −1.33842 + 0.379884i
\(265\) 1.46955e13i 0.690769i
\(266\) 9.81700e12 5.73223e13i 0.451991 2.63922i
\(267\) 1.42441e13 + 1.42441e13i 0.642428 + 0.642428i
\(268\) 4.85265e12 + 1.01448e13i 0.214406 + 0.448229i
\(269\) −1.79297e13 + 1.79297e13i −0.776130 + 0.776130i −0.979170 0.203040i \(-0.934918\pi\)
0.203040 + 0.979170i \(0.434918\pi\)
\(270\) 1.77952e13 1.25912e13i 0.754747 0.534031i
\(271\) 1.69476e13 0.704330 0.352165 0.935938i \(-0.385446\pi\)
0.352165 + 0.935938i \(0.385446\pi\)
\(272\) 2.36791e12 + 1.90880e12i 0.0964354 + 0.0777377i
\(273\) 1.52306e13 0.607888
\(274\) 2.38406e13 1.68687e13i 0.932586 0.659864i
\(275\) 8.13033e12 8.13033e12i 0.311730 0.311730i
\(276\) 3.26979e13 1.56407e13i 1.22891 0.587837i
\(277\) 6.82782e12 + 6.82782e12i 0.251561 + 0.251561i 0.821610 0.570050i \(-0.193076\pi\)
−0.570050 + 0.821610i \(0.693076\pi\)
\(278\) −7.80278e12 + 4.55611e13i −0.281840 + 1.64569i
\(279\) 1.94218e12i 0.0687806i
\(280\) −2.16218e13 + 3.87599e13i −0.750798 + 1.34590i
\(281\) 4.34594e13i 1.47979i −0.672724 0.739893i \(-0.734876\pi\)
0.672724 0.739893i \(-0.265124\pi\)
\(282\) 2.13690e13 + 3.65965e12i 0.713534 + 0.122200i
\(283\) −2.07572e13 2.07572e13i −0.679739 0.679739i 0.280202 0.959941i \(-0.409599\pi\)
−0.959941 + 0.280202i \(0.909599\pi\)
\(284\) 9.93131e12 + 3.50445e12i 0.318974 + 0.112556i
\(285\) 2.43969e13 2.43969e13i 0.768578 0.768578i
\(286\) 1.18322e13 + 1.67225e13i 0.365639 + 0.516758i
\(287\) −3.60801e13 −1.09375
\(288\) 8.74458e12 + 5.48761e11i 0.260064 + 0.0163202i
\(289\) −3.37461e13 −0.984657
\(290\) −1.09787e13 1.55161e13i −0.314311 0.444217i
\(291\) 6.68703e12 6.68703e12i 0.187855 0.187855i
\(292\) 8.54678e12 + 3.01589e12i 0.235612 + 0.0831400i
\(293\) 4.66490e12 + 4.66490e12i 0.126203 + 0.126203i 0.767387 0.641184i \(-0.221556\pi\)
−0.641184 + 0.767387i \(0.721556\pi\)
\(294\) −7.22917e13 1.23807e13i −1.91946 0.328725i
\(295\) 5.66093e12i 0.147525i
\(296\) 1.20952e13 + 6.74718e12i 0.309392 + 0.172591i
\(297\) 6.98469e13i 1.75383i
\(298\) −8.20889e12 + 4.79325e13i −0.202346 + 1.18152i
\(299\) −1.81112e13 1.81112e13i −0.438284 0.438284i
\(300\) 8.89598e12 4.25530e12i 0.211362 0.101103i
\(301\) −6.34560e13 + 6.34560e13i −1.48032 + 1.48032i
\(302\) 5.93401e13 4.19869e13i 1.35928 0.961779i
\(303\) −2.47484e13 −0.556690
\(304\) 6.67034e13 7.16070e12i 1.47348 0.158180i
\(305\) 7.00180e12 0.151901
\(306\) 1.23656e12 8.74948e11i 0.0263481 0.0186429i
\(307\) −2.07573e13 + 2.07573e13i −0.434421 + 0.434421i −0.890129 0.455708i \(-0.849386\pi\)
0.455708 + 0.890129i \(0.349386\pi\)
\(308\) −6.13642e13 1.28286e14i −1.26150 2.63724i
\(309\) −2.08253e13 2.08253e13i −0.420551 0.420551i
\(310\) 1.91568e12 1.11858e13i 0.0380044 0.221911i
\(311\) 6.82615e13i 1.33043i 0.746650 + 0.665217i \(0.231661\pi\)
−0.746650 + 0.665217i \(0.768339\pi\)
\(312\) 4.79717e12 + 1.69016e13i 0.0918618 + 0.323652i
\(313\) 6.58243e13i 1.23849i −0.785198 0.619245i \(-0.787439\pi\)
0.785198 0.619245i \(-0.212561\pi\)
\(314\) −3.03387e13 5.19579e12i −0.560898 0.0960592i
\(315\) 1.56305e13 + 1.56305e13i 0.283965 + 0.283965i
\(316\) −1.85248e13 + 5.24976e13i −0.330730 + 0.937261i
\(317\) 1.67518e13 1.67518e13i 0.293924 0.293924i −0.544704 0.838628i \(-0.683358\pi\)
0.838628 + 0.544704i \(0.183358\pi\)
\(318\) 2.33255e13 + 3.29659e13i 0.402236 + 0.568481i
\(319\) 6.09016e13 1.03224
\(320\) −4.98226e13 1.17858e13i −0.830044 0.196352i
\(321\) −1.01141e13 −0.165635
\(322\) 1.02700e14 + 1.45146e14i 1.65334 + 2.33667i
\(323\) 8.20133e12 8.20133e12i 0.129799 0.129799i
\(324\) −1.43612e13 + 4.06983e13i −0.223456 + 0.633256i
\(325\) −4.92744e12 4.92744e12i −0.0753811 0.0753811i
\(326\) 7.26406e13 + 1.24404e13i 1.09265 + 0.187127i
\(327\) 5.24704e13i 0.776071i
\(328\) −1.13641e13 4.00385e13i −0.165283 0.582334i
\(329\) 1.06351e14i 1.52113i
\(330\) 1.42412e13 8.31557e13i 0.200318 1.16968i
\(331\) −2.92920e13 2.92920e13i −0.405224 0.405224i 0.474845 0.880069i \(-0.342504\pi\)
−0.880069 + 0.474845i \(0.842504\pi\)
\(332\) 2.26685e13 + 4.73900e13i 0.308435 + 0.644804i
\(333\) 4.87756e12 4.87756e12i 0.0652769 0.0652769i
\(334\) −4.15658e13 + 2.94104e13i −0.547180 + 0.387165i
\(335\) −3.27276e13 −0.423806
\(336\) −1.30183e13 1.21268e14i −0.165839 1.54483i
\(337\) −8.08695e13 −1.01349 −0.506746 0.862095i \(-0.669152\pi\)
−0.506746 + 0.862095i \(0.669152\pi\)
\(338\) −5.60721e13 + 3.96745e13i −0.691361 + 0.489182i
\(339\) 7.67066e13 7.67066e13i 0.930539 0.930539i
\(340\) −7.98492e12 + 3.81951e12i −0.0953096 + 0.0455904i
\(341\) 2.57121e13 + 2.57121e13i 0.301987 + 0.301987i
\(342\) 5.64009e12 3.29330e13i 0.0651842 0.380617i
\(343\) 2.00920e14i 2.28510i
\(344\) −9.04045e13 5.04312e13i −1.01186 0.564454i
\(345\) 1.05485e14i 1.16195i
\(346\) −2.48722e13 4.25959e12i −0.269647 0.0461796i
\(347\) 7.33385e13 + 7.33385e13i 0.782564 + 0.782564i 0.980263 0.197698i \(-0.0633467\pi\)
−0.197698 + 0.980263i \(0.563347\pi\)
\(348\) 4.92560e13 + 1.73809e13i 0.517337 + 0.182552i
\(349\) 2.93654e13 2.93654e13i 0.303596 0.303596i −0.538823 0.842419i \(-0.681131\pi\)
0.842419 + 0.538823i \(0.181131\pi\)
\(350\) 2.79411e13 + 3.94892e13i 0.284361 + 0.401887i
\(351\) 4.23312e13 0.424103
\(352\) 1.23033e14 1.08503e14i 1.21349 1.07018i
\(353\) 5.76163e13 0.559480 0.279740 0.960076i \(-0.409752\pi\)
0.279740 + 0.960076i \(0.409752\pi\)
\(354\) −8.98532e12 1.26990e13i −0.0859044 0.121409i
\(355\) −2.16723e13 + 2.16723e13i −0.204009 + 0.204009i
\(356\) −1.07494e14 3.79313e13i −0.996345 0.351579i
\(357\) −1.49102e13 1.49102e13i −0.136084 0.136084i
\(358\) 3.11645e13 + 5.33722e12i 0.280094 + 0.0479687i
\(359\) 1.50109e14i 1.32858i −0.747475 0.664290i \(-0.768734\pi\)
0.747475 0.664290i \(-0.231266\pi\)
\(360\) −1.24222e13 + 2.22685e13i −0.108277 + 0.194100i
\(361\) 1.39340e14i 1.19615i
\(362\) 1.53156e13 8.94290e13i 0.129490 0.756103i
\(363\) 1.18128e14 + 1.18128e14i 0.983706 + 0.983706i
\(364\) −7.77485e13 + 3.71902e13i −0.637726 + 0.305050i
\(365\) −1.86509e13 + 1.86509e13i −0.150692 + 0.150692i
\(366\) −1.57069e13 + 1.11136e13i −0.125010 + 0.0884523i
\(367\) 2.30917e14 1.81047 0.905237 0.424908i \(-0.139693\pi\)
0.905237 + 0.424908i \(0.139693\pi\)
\(368\) −1.28723e14 + 1.59684e14i −0.994244 + 1.23338i
\(369\) −2.07288e13 −0.157736
\(370\) −3.29030e13 + 2.32810e13i −0.246676 + 0.174539i
\(371\) −1.40078e14 + 1.40078e14i −1.03470 + 1.03470i
\(372\) 1.34574e13 + 2.81334e13i 0.0979430 + 0.204756i
\(373\) −7.43352e13 7.43352e13i −0.533084 0.533084i 0.388405 0.921489i \(-0.373026\pi\)
−0.921489 + 0.388405i \(0.873026\pi\)
\(374\) 4.78736e12 2.79538e13i 0.0338300 0.197537i
\(375\) 1.34027e14i 0.933297i
\(376\) −1.18020e14 + 3.34974e13i −0.809880 + 0.229868i
\(377\) 3.69098e13i 0.249611i
\(378\) −2.89644e14 4.96043e13i −1.93045 0.330609i
\(379\) 5.39364e13 + 5.39364e13i 0.354296 + 0.354296i 0.861705 0.507409i \(-0.169397\pi\)
−0.507409 + 0.861705i \(0.669397\pi\)
\(380\) −6.49675e13 + 1.84112e14i −0.420616 + 1.19199i
\(381\) −1.74049e14 + 1.74049e14i −1.11067 + 1.11067i
\(382\) 3.89229e13 + 5.50098e13i 0.244826 + 0.346012i
\(383\) 1.62840e13 0.100965 0.0504823 0.998725i \(-0.483924\pi\)
0.0504823 + 0.998725i \(0.483924\pi\)
\(384\) 1.30472e14 5.26421e13i 0.797436 0.321745i
\(385\) 4.13857e14 2.49354
\(386\) 1.20136e13 + 1.69789e13i 0.0713583 + 0.100851i
\(387\) −3.64569e13 + 3.64569e13i −0.213486 + 0.213486i
\(388\) −1.78072e13 + 5.04640e13i −0.102806 + 0.291345i
\(389\) −1.00553e14 1.00553e14i −0.572361 0.572361i 0.360426 0.932788i \(-0.382631\pi\)
−0.932788 + 0.360426i \(0.882631\pi\)
\(390\) −5.03970e13 8.63098e12i −0.282846 0.0484401i
\(391\) 3.54603e13i 0.196232i
\(392\) 3.99262e14 1.13322e14i 2.17864 0.618360i
\(393\) 2.50493e14i 1.34783i
\(394\) −2.34180e13 + 1.36740e14i −0.124257 + 0.725548i
\(395\) −1.14561e14 1.14561e14i −0.599451 0.599451i
\(396\) −3.52552e13 7.37031e13i −0.181928 0.380332i
\(397\) −5.36644e13 + 5.36644e13i −0.273110 + 0.273110i −0.830351 0.557241i \(-0.811860\pi\)
0.557241 + 0.830351i \(0.311860\pi\)
\(398\) 2.51785e14 1.78154e14i 1.26378 0.894206i
\(399\) −4.65104e14 −2.30250
\(400\) −3.50211e13 + 4.34445e13i −0.171001 + 0.212131i
\(401\) 1.33118e14 0.641127 0.320563 0.947227i \(-0.396128\pi\)
0.320563 + 0.947227i \(0.396128\pi\)
\(402\) 7.34165e13 5.19468e13i 0.348779 0.246783i
\(403\) 1.55830e13 1.55830e13i 0.0730252 0.0730252i
\(404\) 1.26334e14 6.04308e13i 0.584015 0.279358i
\(405\) −8.88126e13 8.88126e13i −0.405016 0.405016i
\(406\) −4.32515e13 + 2.52549e14i −0.194584 + 1.13620i
\(407\) 1.29146e14i 0.573207i
\(408\) 1.18498e13 2.12422e13i 0.0518894 0.0930184i
\(409\) 3.22329e14i 1.39259i −0.717758 0.696293i \(-0.754832\pi\)
0.717758 0.696293i \(-0.245168\pi\)
\(410\) 1.19386e14 + 2.04461e13i 0.508913 + 0.0871562i
\(411\) −1.65154e14 1.65154e14i −0.694640 0.694640i
\(412\) 1.57159e14 + 5.54564e13i 0.652235 + 0.230153i
\(413\) 5.39602e13 5.39602e13i 0.220978 0.220978i
\(414\) 5.90035e13 + 8.33897e13i 0.238438 + 0.336985i
\(415\) −1.52883e14 −0.609669
\(416\) −6.57588e13 7.45647e13i −0.258786 0.293440i
\(417\) 3.69675e14 1.43573
\(418\) −3.61325e14 5.10661e14i −1.38493 1.95733i
\(419\) −2.82378e14 + 2.82378e14i −1.06820 + 1.06820i −0.0707064 + 0.997497i \(0.522525\pi\)
−0.997497 + 0.0707064i \(0.977475\pi\)
\(420\) 3.34719e14 + 1.18112e14i 1.24971 + 0.440984i
\(421\) −1.97312e14 1.97312e14i −0.727112 0.727112i 0.242931 0.970044i \(-0.421891\pi\)
−0.970044 + 0.242931i \(0.921891\pi\)
\(422\) 5.72131e13 + 9.79829e12i 0.208102 + 0.0356395i
\(423\) 6.11014e13i 0.219371i
\(424\) −1.99567e14 1.11326e14i −0.707255 0.394535i
\(425\) 9.64752e12i 0.0337502i
\(426\) 1.42173e13 8.30159e13i 0.0490979 0.286687i
\(427\) −6.67414e13 6.67414e13i −0.227532 0.227532i
\(428\) 5.16301e13 2.46968e13i 0.173765 0.0831188i
\(429\) 1.15844e14 1.15844e14i 0.384909 0.384909i
\(430\) 2.45931e14 1.74012e14i 0.806745 0.570823i
\(431\) 3.78445e14 1.22568 0.612840 0.790207i \(-0.290027\pi\)
0.612840 + 0.790207i \(0.290027\pi\)
\(432\) −3.61823e13 3.37045e14i −0.115701 1.07777i
\(433\) −5.87357e14 −1.85447 −0.927233 0.374485i \(-0.877820\pi\)
−0.927233 + 0.374485i \(0.877820\pi\)
\(434\) −1.24884e14 + 8.83635e13i −0.389327 + 0.275473i
\(435\) −1.07487e14 + 1.07487e14i −0.330876 + 0.330876i
\(436\) 1.28122e14 + 2.67848e14i 0.389448 + 0.814165i
\(437\) 5.53070e14 + 5.53070e14i 1.66009 + 1.66009i
\(438\) 1.22352e13 7.14425e13i 0.0362664 0.211763i
\(439\) 1.95351e14i 0.571821i 0.958256 + 0.285910i \(0.0922960\pi\)
−0.958256 + 0.285910i \(0.907704\pi\)
\(440\) 1.30352e14 + 4.59263e14i 0.376815 + 1.32761i
\(441\) 2.06707e14i 0.590123i
\(442\) −1.69416e13 2.90141e12i −0.0477675 0.00818064i
\(443\) 3.24637e14 + 3.24637e14i 0.904018 + 0.904018i 0.995781 0.0917627i \(-0.0292501\pi\)
−0.0917627 + 0.995781i \(0.529250\pi\)
\(444\) 3.68573e13 1.04451e14i 0.101372 0.287279i
\(445\) 2.34575e14 2.34575e14i 0.637239 0.637239i
\(446\) −3.17766e14 4.49099e14i −0.852640 1.20504i
\(447\) 3.88916e14 1.03078
\(448\) 3.62567e14 + 5.87253e14i 0.949204 + 1.53743i
\(449\) −4.80220e13 −0.124190 −0.0620949 0.998070i \(-0.519778\pi\)
−0.0620949 + 0.998070i \(0.519778\pi\)
\(450\) 1.60528e13 + 2.26875e13i 0.0410093 + 0.0579585i
\(451\) −2.74425e14 + 2.74425e14i −0.692551 + 0.692551i
\(452\) −2.04265e14 + 5.78870e14i −0.509252 + 1.44318i
\(453\) −4.11075e14 4.11075e14i −1.01247 1.01247i
\(454\) 3.41711e14 + 5.85213e13i 0.831481 + 0.142399i
\(455\) 2.50821e14i 0.602978i
\(456\) −1.46493e14 5.16132e14i −0.347945 1.22590i
\(457\) 5.54781e13i 0.130192i −0.997879 0.0650958i \(-0.979265\pi\)
0.997879 0.0650958i \(-0.0207353\pi\)
\(458\) 7.30537e12 4.26567e13i 0.0169388 0.0989070i
\(459\) −4.14405e13 4.14405e13i −0.0949413 0.0949413i
\(460\) −2.57575e14 5.38476e14i −0.583089 1.21898i
\(461\) −2.39250e13 + 2.39250e13i −0.0535177 + 0.0535177i −0.733359 0.679841i \(-0.762049\pi\)
0.679841 + 0.733359i \(0.262049\pi\)
\(462\) −9.28390e14 + 6.56895e14i −2.05211 + 1.45199i
\(463\) −7.76509e14 −1.69610 −0.848049 0.529918i \(-0.822223\pi\)
−0.848049 + 0.529918i \(0.822223\pi\)
\(464\) −2.93880e14 + 3.15484e13i −0.634338 + 0.0680971i
\(465\) −9.07601e13 −0.193599
\(466\) −1.07021e14 + 7.57240e13i −0.225603 + 0.159629i
\(467\) 4.52807e14 4.52807e14i 0.943344 0.943344i −0.0551351 0.998479i \(-0.517559\pi\)
0.998479 + 0.0551351i \(0.0175589\pi\)
\(468\) −4.46683e13 + 2.13666e13i −0.0919702 + 0.0439930i
\(469\) 3.11960e14 + 3.11960e14i 0.634817 + 0.634817i
\(470\) 6.02678e13 3.51909e14i 0.121213 0.707771i
\(471\) 2.46163e14i 0.489337i
\(472\) 7.68761e13 + 4.28845e13i 0.151046 + 0.0842597i
\(473\) 9.65290e14i 1.87466i
\(474\) 4.38828e14 + 7.51534e13i 0.842390 + 0.144267i
\(475\) 1.50471e14 + 1.50471e14i 0.285521 + 0.285521i
\(476\) 1.12520e14 + 3.97049e13i 0.211053 + 0.0744741i
\(477\) −8.04782e13 + 8.04782e13i −0.149220 + 0.149220i
\(478\) −6.29790e13 8.90083e13i −0.115436 0.163146i
\(479\) 1.36724e14 0.247742 0.123871 0.992298i \(-0.460469\pi\)
0.123871 + 0.992298i \(0.460469\pi\)
\(480\) −2.56442e13 + 4.08644e14i −0.0459370 + 0.732012i
\(481\) −7.82697e13 −0.138610
\(482\) 1.76681e14 + 2.49703e14i 0.309336 + 0.437184i
\(483\) 1.00549e15 1.00549e15i 1.74048 1.74048i
\(484\) −8.91456e14 3.14567e14i −1.52563 0.538349i
\(485\) −1.10123e14 1.10123e14i −0.186337 0.186337i
\(486\) −2.98416e14 5.11066e13i −0.499255 0.0855022i
\(487\) 1.79388e14i 0.296746i 0.988931 + 0.148373i \(0.0474037\pi\)
−0.988931 + 0.148373i \(0.952596\pi\)
\(488\) 5.30423e13 9.50852e13i 0.0867587 0.155526i
\(489\) 5.89394e14i 0.953250i
\(490\) −2.03887e14 + 1.19051e15i −0.326070 + 1.90395i
\(491\) −3.42827e14 3.42827e14i −0.542159 0.542159i 0.382002 0.924161i \(-0.375235\pi\)
−0.924161 + 0.382002i \(0.875235\pi\)
\(492\) −3.00268e14 + 1.43630e14i −0.469570 + 0.224614i
\(493\) −3.61332e13 + 3.61332e13i −0.0558790 + 0.0558790i
\(494\) −3.09489e14 + 2.18983e14i −0.473312 + 0.334898i
\(495\) 2.37771e14 0.359608
\(496\) −1.37393e14 1.10754e14i −0.205501 0.165657i
\(497\) 4.13162e14 0.611167
\(498\) 3.42956e14 2.42663e14i 0.501738 0.355012i
\(499\) 1.85485e14 1.85485e14i 0.268383 0.268383i −0.560065 0.828448i \(-0.689224\pi\)
0.828448 + 0.560065i \(0.189224\pi\)
\(500\) −3.27267e14 6.84173e14i −0.468347 0.979109i
\(501\) 2.87945e14 + 2.87945e14i 0.407569 + 0.407569i
\(502\) 1.10199e14 6.43464e14i 0.154280 0.900852i
\(503\) 3.66232e14i 0.507145i −0.967316 0.253572i \(-0.918394\pi\)
0.967316 0.253572i \(-0.0816056\pi\)
\(504\) 3.30673e14 9.38546e13i 0.452929 0.128555i
\(505\) 4.07562e14i 0.552193i
\(506\) 1.88511e15 + 3.22843e14i 2.52644 + 0.432677i
\(507\) 3.88436e14 + 3.88436e14i 0.514963 + 0.514963i
\(508\) 4.63482e14 1.31347e15i 0.607831 1.72254i
\(509\) 7.50462e13 7.50462e13i 0.0973600 0.0973600i −0.656749 0.754109i \(-0.728069\pi\)
0.754109 + 0.656749i \(0.228069\pi\)
\(510\) 4.08873e13 + 5.77860e13i 0.0524750 + 0.0741629i
\(511\) 3.55562e14 0.451441
\(512\) −5.37485e14 + 5.87312e14i −0.675121 + 0.737707i
\(513\) −1.29268e15 −1.60638
\(514\) −4.15640e14 5.87424e14i −0.510999 0.722195i
\(515\) −3.42954e14 + 3.42954e14i −0.417154 + 0.417154i
\(516\) −2.75487e14 + 7.80707e14i −0.331534 + 0.939539i
\(517\) 8.08908e14 + 8.08908e14i 0.963166 + 0.963166i
\(518\) 5.35547e14 + 9.17176e13i 0.630935 + 0.108054i
\(519\) 2.01809e14i 0.235244i
\(520\) 2.78339e14 7.90008e13i 0.321038 0.0911198i
\(521\) 8.52126e14i 0.972516i −0.873815 0.486258i \(-0.838362\pi\)
0.873815 0.486258i \(-0.161638\pi\)
\(522\) −2.48490e13 + 1.45095e14i −0.0280621 + 0.163857i
\(523\) 3.84070e14 + 3.84070e14i 0.429192 + 0.429192i 0.888353 0.459161i \(-0.151850\pi\)
−0.459161 + 0.888353i \(0.651850\pi\)
\(524\) −6.11654e14 1.27870e15i −0.676370 1.41399i
\(525\) 2.73559e14 2.73559e14i 0.299347 0.299347i
\(526\) −7.92497e14 + 5.60742e14i −0.858175 + 0.607213i
\(527\) −3.05102e13 −0.0326954
\(528\) −1.02138e15 8.23345e14i −1.08318 0.873163i
\(529\) −1.43851e15 −1.50975
\(530\) 5.42889e14 3.84128e14i 0.563889 0.398987i
\(531\) 3.10014e13 3.10014e13i 0.0318685 0.0318685i
\(532\) 2.37424e15 1.13569e15i 2.41552 1.15544i
\(533\) 1.66317e14 + 1.66317e14i 0.167470 + 0.167470i
\(534\) −1.53884e14 + 8.98544e14i −0.153362 + 0.895493i
\(535\) 1.66562e14i 0.164297i
\(536\) −2.47928e14 + 4.44444e14i −0.242058 + 0.433921i
\(537\) 2.52864e14i 0.244359i
\(538\) −1.13103e15 1.93700e14i −1.08186 0.185279i
\(539\) −2.73655e15 2.73655e15i −2.59098 2.59098i
\(540\) 9.30301e14 + 3.28274e14i 0.871882 + 0.307660i
\(541\) 1.73890e13 1.73890e13i 0.0161320 0.0161320i −0.698995 0.715127i \(-0.746369\pi\)
0.715127 + 0.698995i \(0.246369\pi\)
\(542\) 4.42994e14 + 6.26084e14i 0.406820 + 0.574959i
\(543\) −7.25612e14 −0.659637
\(544\) −8.62063e12 + 1.37371e14i −0.00775792 + 0.123623i
\(545\) −8.64092e14 −0.769803
\(546\) 3.98115e14 + 5.62657e14i 0.351115 + 0.496231i
\(547\) 1.23494e15 1.23494e15i 1.07824 1.07824i 0.0815740 0.996667i \(-0.474005\pi\)
0.996667 0.0815740i \(-0.0259947\pi\)
\(548\) 1.24634e15 + 4.39796e14i 1.07732 + 0.380153i
\(549\) −3.83445e13 3.83445e13i −0.0328137 0.0328137i
\(550\) 5.12874e14 + 8.78346e13i 0.434526 + 0.0744167i
\(551\) 1.12713e15i 0.945454i
\(552\) 1.43250e15 + 7.99107e14i 1.18968 + 0.663651i
\(553\) 2.18400e15i 1.79583i
\(554\) −7.37631e13 + 4.30710e14i −0.0600531 + 0.350656i
\(555\) 2.27934e14 + 2.27934e14i 0.183737 + 0.183737i
\(556\) −1.88710e15 + 9.02674e14i −1.50620 + 0.720476i
\(557\) −1.19349e15 + 1.19349e15i −0.943223 + 0.943223i −0.998473 0.0552494i \(-0.982405\pi\)
0.0552494 + 0.998473i \(0.482405\pi\)
\(558\) −7.17488e13 + 5.07669e13i −0.0561470 + 0.0397276i
\(559\) 5.85021e14 0.453321
\(560\) −1.99706e15 + 2.14387e14i −1.53235 + 0.164500i
\(561\) −2.26813e14 −0.172334
\(562\) 1.60550e15 1.13599e15i 1.20798 0.854723i
\(563\) −5.15004e14 + 5.15004e14i −0.383720 + 0.383720i −0.872440 0.488720i \(-0.837464\pi\)
0.488720 + 0.872440i \(0.337464\pi\)
\(564\) 4.23371e14 + 8.85085e14i 0.312382 + 0.653055i
\(565\) −1.26322e15 1.26322e15i −0.923023 0.923023i
\(566\) 2.24246e14 1.30939e15i 0.162269 0.947502i
\(567\) 1.69313e15i 1.21334i
\(568\) 1.30133e14 + 4.58490e14i 0.0923573 + 0.325398i
\(569\) 1.36483e15i 0.959315i −0.877456 0.479657i \(-0.840761\pi\)
0.877456 0.479657i \(-0.159239\pi\)
\(570\) 1.53900e15 + 2.63568e14i 1.07134 + 0.183477i
\(571\) 1.77410e15 + 1.77410e15i 1.22315 + 1.22315i 0.966507 + 0.256639i \(0.0826150\pi\)
0.256639 + 0.966507i \(0.417385\pi\)
\(572\) −3.08485e14 + 8.74222e14i −0.210648 + 0.596957i
\(573\) 3.81077e14 3.81077e14i 0.257729 0.257729i
\(574\) −9.43102e14 1.33289e15i −0.631747 0.892849i
\(575\) −6.50596e14 −0.431656
\(576\) 2.08303e14 + 3.37391e14i 0.136890 + 0.221722i
\(577\) 3.65991e14 0.238234 0.119117 0.992880i \(-0.461994\pi\)
0.119117 + 0.992880i \(0.461994\pi\)
\(578\) −8.82093e14 1.24666e15i −0.568737 0.803796i
\(579\) 1.17620e14 1.17620e14i 0.0751191 0.0751191i
\(580\) 2.86232e14 8.11157e14i 0.181077 0.513158i
\(581\) 1.45728e15 + 1.45728e15i 0.913220 + 0.913220i
\(582\) 4.21828e14 + 7.22421e13i 0.261854 + 0.0448450i
\(583\) 2.13087e15i 1.31032i
\(584\) 1.11991e14 + 3.94572e14i 0.0682201 + 0.240356i
\(585\) 1.44102e14i 0.0869589i
\(586\) −5.03964e13 + 2.94269e14i −0.0301275 + 0.175917i
\(587\) −1.82609e15 1.82609e15i −1.08146 1.08146i −0.996373 0.0850900i \(-0.972882\pi\)
−0.0850900 0.996373i \(-0.527118\pi\)
\(588\) −1.43227e15 2.99425e15i −0.840331 1.75676i
\(589\) −4.75864e14 + 4.75864e14i −0.276598 + 0.276598i
\(590\) −2.09129e14 + 1.47972e14i −0.120428 + 0.0852105i
\(591\) 1.10949e15 0.632981
\(592\) 6.69005e13 + 6.23192e14i 0.0378146 + 0.352251i
\(593\) 3.34557e15 1.87357 0.936784 0.349909i \(-0.113787\pi\)
0.936784 + 0.349909i \(0.113787\pi\)
\(594\) −2.58032e15 + 1.82574e15i −1.43169 + 1.01301i
\(595\) −2.45543e14 + 2.45543e14i −0.134985 + 0.134985i
\(596\) −1.98532e15 + 9.49657e14i −1.08137 + 0.517264i
\(597\) −1.74422e15 1.74422e15i −0.941333 0.941333i
\(598\) 1.95661e14 1.14248e15i 0.104628 0.610933i
\(599\) 3.39597e15i 1.79935i −0.436556 0.899677i \(-0.643802\pi\)
0.436556 0.899677i \(-0.356198\pi\)
\(600\) 3.89735e14 + 2.17409e14i 0.204615 + 0.114142i
\(601\) 3.43538e15i 1.78717i −0.448898 0.893583i \(-0.648183\pi\)
0.448898 0.893583i \(-0.351817\pi\)
\(602\) −4.00290e15 6.85536e14i −2.06345 0.353386i
\(603\) 1.79228e14 + 1.79228e14i 0.0915507 + 0.0915507i
\(604\) 3.10220e15 + 1.09467e15i 1.57024 + 0.554089i
\(605\) 1.94535e15 1.94535e15i 0.975760 0.975760i
\(606\) −6.46902e14 9.14268e14i −0.321543 0.454437i
\(607\) 1.96296e14 0.0966884 0.0483442 0.998831i \(-0.484606\pi\)
0.0483442 + 0.998831i \(0.484606\pi\)
\(608\) 2.00810e15 + 2.27701e15i 0.980203 + 1.11146i
\(609\) 2.04914e15 0.991236
\(610\) 1.83021e14 + 2.58664e14i 0.0877378 + 0.124000i
\(611\) 4.90244e14 4.90244e14i 0.232909 0.232909i
\(612\) 6.46455e13 + 2.28114e13i 0.0304372 + 0.0107403i
\(613\) 1.99692e15 + 1.99692e15i 0.931813 + 0.931813i 0.997819 0.0660064i \(-0.0210258\pi\)
−0.0660064 + 0.997819i \(0.521026\pi\)
\(614\) −1.30941e15 2.24248e14i −0.605547 0.103706i
\(615\) 9.68681e14i 0.443984i
\(616\) 3.13519e15 5.62023e15i 1.42419 2.55305i
\(617\) 2.13465e15i 0.961079i 0.876973 + 0.480539i \(0.159559\pi\)
−0.876973 + 0.480539i \(0.840441\pi\)
\(618\) 2.24982e14 1.31369e15i 0.100395 0.586214i
\(619\) 1.66182e15 + 1.66182e15i 0.734998 + 0.734998i 0.971605 0.236608i \(-0.0760356\pi\)
−0.236608 + 0.971605i \(0.576036\pi\)
\(620\) 4.63307e14 2.21618e14i 0.203102 0.0971519i
\(621\) 2.79460e15 2.79460e15i 1.21427 1.21427i
\(622\) −2.52175e15 + 1.78430e15i −1.08606 + 0.768457i
\(623\) −4.47196e15 −1.90903
\(624\) −4.98993e14 + 6.19013e14i −0.211144 + 0.261930i
\(625\) 1.55756e15 0.653287
\(626\) 2.43171e15 1.72059e15i 1.01100 0.715350i
\(627\) −3.53757e15 + 3.53757e15i −1.45792 + 1.45792i
\(628\) −6.01082e14 1.25660e15i −0.245559 0.513357i
\(629\) 7.66229e13 + 7.66229e13i 0.0310299 + 0.0310299i
\(630\) −1.68861e14 + 9.85996e14i −0.0677887 + 0.395824i
\(631\) 1.28852e15i 0.512778i −0.966574 0.256389i \(-0.917467\pi\)
0.966574 0.256389i \(-0.0825328\pi\)
\(632\) −2.42361e15 + 6.87892e14i −0.956135 + 0.271379i
\(633\) 4.64217e14i 0.181552i
\(634\) 1.05673e15 + 1.80975e14i 0.409707 + 0.0701662i
\(635\) 2.86627e15 + 2.86627e15i 1.10170 + 1.10170i
\(636\) −6.08134e14 + 1.72340e15i −0.231732 + 0.656708i
\(637\) −1.65850e15 + 1.65850e15i −0.626541 + 0.626541i
\(638\) 1.59192e15 + 2.24986e15i 0.596220 + 0.842638i
\(639\) 2.37371e14 0.0881399
\(640\) −8.66921e14 2.14864e15i −0.319146 0.790995i
\(641\) −2.37556e15 −0.867055 −0.433528 0.901140i \(-0.642731\pi\)
−0.433528 + 0.901140i \(0.642731\pi\)
\(642\) −2.64375e14 3.73641e14i −0.0956704 0.135211i
\(643\) −3.12329e15 + 3.12329e15i −1.12060 + 1.12060i −0.128951 + 0.991651i \(0.541161\pi\)
−0.991651 + 0.128951i \(0.958839\pi\)
\(644\) −2.67756e15 + 7.58798e15i −0.952504 + 2.69932i
\(645\) −1.70367e15 1.70367e15i −0.600907 0.600907i
\(646\) 5.17353e14 + 8.86017e13i 0.180929 + 0.0309858i
\(647\) 2.99929e15i 1.04003i −0.854158 0.520014i \(-0.825927\pi\)
0.854158 0.520014i \(-0.174073\pi\)
\(648\) −1.87889e15 + 5.33282e14i −0.646008 + 0.183356i
\(649\) 8.20841e14i 0.279842i
\(650\) 5.32327e13 3.10831e14i 0.0179951 0.105075i
\(651\) 8.65128e14 + 8.65128e14i 0.289991 + 0.289991i
\(652\) 1.43918e15 + 3.00870e15i 0.478360 + 1.00004i
\(653\) 1.19197e15 1.19197e15i 0.392866 0.392866i −0.482842 0.875708i \(-0.660395\pi\)
0.875708 + 0.482842i \(0.160395\pi\)
\(654\) 1.93839e15 1.37153e15i 0.633523 0.448258i
\(655\) 4.12517e15 1.33695
\(656\) 1.18207e15 1.46639e15i 0.379904 0.471279i
\(657\) 2.04279e14 0.0651049
\(658\) −3.92889e15 + 2.77994e15i −1.24173 + 0.878602i
\(659\) 2.22810e15 2.22810e15i 0.698337 0.698337i −0.265715 0.964052i \(-0.585608\pi\)
0.964052 + 0.265715i \(0.0856079\pi\)
\(660\) 3.44423e15 1.64751e15i 1.07053 0.512079i
\(661\) −1.31704e15 1.31704e15i −0.405967 0.405967i 0.474362 0.880330i \(-0.342679\pi\)
−0.880330 + 0.474362i \(0.842679\pi\)
\(662\) 3.16451e14 1.84779e15i 0.0967360 0.564850i
\(663\) 1.37461e14i 0.0416732i
\(664\) −1.15817e15 + 2.07617e15i −0.348215 + 0.624220i
\(665\) 7.65942e15i 2.28390i
\(666\) 3.07684e14 + 5.26939e13i 0.0909907 + 0.0155830i
\(667\) −2.43670e15 2.43670e15i −0.714677 0.714677i
\(668\) −2.17299e15 7.66780e14i −0.632102 0.223049i
\(669\) −3.11111e15 + 3.11111e15i −0.897576 + 0.897576i
\(670\) −8.55471e14 1.20904e15i −0.244790 0.345962i
\(671\) −1.01527e15 −0.288142
\(672\) 4.13965e15 3.65076e15i 1.16529 1.02767i
\(673\) 1.44297e14 0.0402879 0.0201439 0.999797i \(-0.493588\pi\)
0.0201439 + 0.999797i \(0.493588\pi\)
\(674\) −2.11386e15 2.98752e15i −0.585392 0.827335i
\(675\) 7.60315e14 7.60315e14i 0.208845 0.208845i
\(676\) −2.93135e15 1.03438e15i −0.798658 0.281821i
\(677\) −1.26299e14 1.26299e14i −0.0341320 0.0341320i 0.689835 0.723967i \(-0.257683\pi\)
−0.723967 + 0.689835i \(0.757683\pi\)
\(678\) 4.83878e15 + 8.28687e14i 1.29710 + 0.222140i
\(679\) 2.09940e15i 0.558227i
\(680\) −3.49821e14 1.95144e14i −0.0922671 0.0514703i
\(681\) 2.77259e15i 0.725398i
\(682\) −2.77776e14 + 1.62196e15i −0.0720909 + 0.420945i
\(683\) −2.21846e14 2.21846e14i −0.0571133 0.0571133i 0.677973 0.735087i \(-0.262859\pi\)
−0.735087 + 0.677973i \(0.762859\pi\)
\(684\) 1.36405e15 6.52481e14i 0.348356 0.166632i
\(685\) −2.71979e15 + 2.71979e15i −0.689029 + 0.689029i
\(686\) 7.42247e15 5.25187e15i 1.86537 1.31987i
\(687\) −3.46109e14 −0.0862882
\(688\) −5.00042e14 4.65799e15i −0.123672 1.15203i
\(689\) 1.29143e15 0.316857
\(690\) −3.89689e15 + 2.75730e15i −0.948524 + 0.671141i
\(691\) −4.10228e15 + 4.10228e15i −0.990596 + 0.990596i −0.999956 0.00936034i \(-0.997020\pi\)
0.00936034 + 0.999956i \(0.497020\pi\)
\(692\) −4.92777e14 1.03018e15i −0.118050 0.246791i
\(693\) −2.26644e15 2.26644e15i −0.538655 0.538655i
\(694\) −7.92300e14 + 4.62631e15i −0.186815 + 1.09083i
\(695\) 6.08788e15i 1.42413i
\(696\) 6.45416e14 + 2.27396e15i 0.149792 + 0.527754i
\(697\) 3.25635e14i 0.0749808i
\(698\) 1.85242e15 + 3.17244e14i 0.423189 + 0.0724752i
\(699\) 7.41381e14 + 7.41381e14i 0.168042 + 0.168042i
\(700\) −7.28472e14 + 2.06443e15i −0.163822 + 0.464259i
\(701\) −3.04410e15 + 3.04410e15i −0.679218 + 0.679218i −0.959823 0.280605i \(-0.909465\pi\)
0.280605 + 0.959823i \(0.409465\pi\)
\(702\) 1.10650e15 + 1.56382e15i 0.244961 + 0.346204i
\(703\) 2.39016e15 0.525015
\(704\) 7.22432e15 + 1.70896e15i 1.57452 + 0.372462i
\(705\) −2.85533e15 −0.617471
\(706\) 1.50604e15 + 2.12849e15i 0.323155 + 0.456715i
\(707\) 3.88489e15 3.88489e15i 0.827127 0.827127i
\(708\) 2.34262e14 6.63879e14i 0.0494902 0.140251i
\(709\) −4.62095e15 4.62095e15i −0.968672 0.968672i 0.0308521 0.999524i \(-0.490178\pi\)
−0.999524 + 0.0308521i \(0.990178\pi\)
\(710\) −1.36712e15 2.34133e14i −0.284372 0.0487014i
\(711\) 1.25476e15i 0.258987i
\(712\) −1.40853e15 4.96259e15i −0.288486 1.01641i
\(713\) 2.05750e15i 0.418165i
\(714\) 1.61079e14 9.40557e14i 0.0324863 0.189690i
\(715\) −1.90774e15 1.90774e15i −0.381800 0.381800i
\(716\) 6.17443e14 + 1.29080e15i 0.122624 + 0.256353i
\(717\) −6.16600e14 + 6.16600e14i −0.121520 + 0.121520i
\(718\) 5.54540e15 3.92372e15i 1.08455 0.767386i
\(719\) −1.71684e12 −0.000333212 −0.000166606 1.00000i \(-0.500053\pi\)
−0.000166606 1.00000i \(0.500053\pi\)
\(720\) −1.14736e15 + 1.23171e14i −0.220989 + 0.0237235i
\(721\) 6.53810e15 1.24971
\(722\) 5.14757e15 3.64223e15i 0.976444 0.690896i
\(723\) 1.72980e15 1.72980e15i 0.325638 0.325638i
\(724\) 3.70406e15 1.77180e15i 0.692016 0.331019i
\(725\) −6.62942e14 6.62942e14i −0.122918 0.122918i
\(726\) −1.27617e15 + 7.45168e15i −0.234832 + 1.37121i
\(727\) 5.86270e14i 0.107068i 0.998566 + 0.0535339i \(0.0170485\pi\)
−0.998566 + 0.0535339i \(0.982951\pi\)
\(728\) −3.40618e15 1.90010e15i −0.617368 0.344393i
\(729\) 6.15434e15i 1.10708i
\(730\) −1.17653e15 2.01492e14i −0.210052 0.0359734i
\(731\) −5.72711e14 5.72711e14i −0.101482 0.101482i
\(732\) −8.21128e14 2.89750e14i −0.144411 0.0509581i
\(733\) −3.03937e15 + 3.03937e15i −0.530531 + 0.530531i −0.920731 0.390199i \(-0.872406\pi\)
0.390199 + 0.920731i \(0.372406\pi\)
\(734\) 6.03597e15 + 8.53064e15i 1.04573 + 1.47793i
\(735\) 9.65964e15 1.66104
\(736\) −9.26382e15 5.81346e14i −1.58111 0.0992217i
\(737\) 4.74553e15 0.803921
\(738\) −5.41834e14 7.65774e14i −0.0911079 0.128763i
\(739\) 3.93959e15 3.93959e15i 0.657516 0.657516i −0.297276 0.954792i \(-0.596078\pi\)
0.954792 + 0.297276i \(0.0960781\pi\)
\(740\) −1.72011e15 6.06974e14i −0.284959 0.100553i
\(741\) 2.14397e15 + 2.14397e15i 0.352548 + 0.352548i
\(742\) −8.83636e15 1.51331e15i −1.44229 0.247006i
\(743\) 1.16532e15i 0.188803i 0.995534 + 0.0944013i \(0.0300937\pi\)
−0.995534 + 0.0944013i \(0.969906\pi\)
\(744\) −6.87555e14 + 1.23253e15i −0.110575 + 0.198220i
\(745\) 6.40475e15i 1.02245i
\(746\) 8.03068e14 4.68918e15i 0.127259 0.743077i
\(747\) 8.37243e14 + 8.37243e14i 0.131701 + 0.131701i
\(748\) 1.15782e15 5.53832e14i 0.180794 0.0864808i
\(749\) 1.58767e15 1.58767e15i 0.246099 0.246099i
\(750\) −4.95128e15 + 3.50335e15i −0.761870 + 0.539071i
\(751\) −7.91358e15 −1.20880 −0.604399 0.796682i \(-0.706587\pi\)
−0.604399 + 0.796682i \(0.706587\pi\)
\(752\) −4.32241e15 3.48434e15i −0.655432 0.528351i
\(753\) −5.22096e15 −0.785919
\(754\) 1.36354e15 9.64791e14i 0.203763 0.144175i
\(755\) −6.76966e15 + 6.76966e15i −1.00429 + 1.00429i
\(756\) −5.73854e15 1.19968e16i −0.845145 1.76683i
\(757\) 4.02992e15 + 4.02992e15i 0.589209 + 0.589209i 0.937417 0.348208i \(-0.113210\pi\)
−0.348208 + 0.937417i \(0.613210\pi\)
\(758\) −5.82693e14 + 3.40240e15i −0.0845783 + 0.493861i
\(759\) 1.52955e16i 2.20411i
\(760\) −8.49976e15 + 2.41248e15i −1.21599 + 0.345135i
\(761\) 7.01563e15i