Properties

Label 17.10.d.a.2.13
Level $17$
Weight $10$
Character 17.2
Analytic conductor $8.756$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 2.13
Character \(\chi\) \(=\) 17.2
Dual form 17.10.d.a.9.13

$q$-expansion

\(f(q)\) \(=\) \(q+(31.2113 + 31.2113i) q^{2} +(-114.097 + 47.2607i) q^{3} +1436.29i q^{4} +(205.870 + 497.013i) q^{5} +(-5036.20 - 2086.06i) q^{6} +(3921.77 - 9467.99i) q^{7} +(-28848.3 + 28848.3i) q^{8} +(-3133.33 + 3133.33i) q^{9} +O(q^{10})\) \(q+(31.2113 + 31.2113i) q^{2} +(-114.097 + 47.2607i) q^{3} +1436.29i q^{4} +(205.870 + 497.013i) q^{5} +(-5036.20 - 2086.06i) q^{6} +(3921.77 - 9467.99i) q^{7} +(-28848.3 + 28848.3i) q^{8} +(-3133.33 + 3133.33i) q^{9} +(-9086.97 + 21937.9i) q^{10} +(5430.59 + 2249.42i) q^{11} +(-67880.1 - 163877. i) q^{12} +73109.4i q^{13} +(417912. - 173105. i) q^{14} +(-46978.4 - 46978.4i) q^{15} -1.06541e6 q^{16} +(252672. + 233976. i) q^{17} -195591. q^{18} +(421726. + 421726. i) q^{19} +(-713856. + 295689. i) q^{20} +1.26562e6i q^{21} +(99288.4 + 239703. i) q^{22} +(-449080. - 186015. i) q^{23} +(1.92813e6 - 4.65491e6i) q^{24} +(1.17643e6 - 1.17643e6i) q^{25} +(-2.28184e6 + 2.28184e6i) q^{26} +(1.13965e6 - 2.75137e6i) q^{27} +(1.35988e7 + 5.63280e6i) q^{28} +(1.80019e6 + 4.34603e6i) q^{29} -2.93251e6i q^{30} +(-2.69479e6 + 1.11622e6i) q^{31} +(-1.84824e7 - 1.84824e7i) q^{32} -725926. q^{33} +(583497. + 1.51889e7i) q^{34} +5.51309e6 q^{35} +(-4.50038e6 - 4.50038e6i) q^{36} +(3.68495e6 - 1.52636e6i) q^{37} +2.63252e7i q^{38} +(-3.45520e6 - 8.34160e6i) q^{39} +(-2.02770e7 - 8.39901e6i) q^{40} +(-1.25691e6 + 3.03445e6i) q^{41} +(-3.95016e7 + 3.95016e7i) q^{42} +(2.61942e7 - 2.61942e7i) q^{43} +(-3.23083e6 + 7.79991e6i) q^{44} +(-2.20237e6 - 912250. i) q^{45} +(-8.21060e6 - 1.98222e7i) q^{46} +873124. i q^{47} +(1.21560e8 - 5.03519e7i) q^{48} +(-4.57282e7 - 4.57282e7i) q^{49} +7.34357e7 q^{50} +(-3.98871e7 - 1.47547e7i) q^{51} -1.05006e8 q^{52} +(-3.48677e7 - 3.48677e7i) q^{53} +(1.21444e8 - 5.03037e7i) q^{54} +3.16216e6i q^{55} +(1.59999e8 + 3.86272e8i) q^{56} +(-6.80489e7 - 2.81868e7i) q^{57} +(-7.94592e7 + 1.91832e8i) q^{58} +(-1.51858e7 + 1.51858e7i) q^{59} +(6.74747e7 - 6.74747e7i) q^{60} +(3.49262e7 - 8.43192e7i) q^{61} +(-1.18947e8 - 4.92693e7i) q^{62} +(1.73782e7 + 4.19546e7i) q^{63} -6.08232e8i q^{64} +(-3.63364e7 + 1.50510e7i) q^{65} +(-2.26571e7 - 2.26571e7i) q^{66} +1.62674e8 q^{67} +(-3.36058e8 + 3.62910e8i) q^{68} +6.00301e7 q^{69} +(1.72071e8 + 1.72071e8i) q^{70} +(1.77698e8 - 7.36048e7i) q^{71} -1.80783e8i q^{72} +(-1.27907e8 - 3.08794e8i) q^{73} +(1.62652e8 + 6.73726e7i) q^{74} +(-7.86286e7 + 1.89826e8i) q^{75} +(-6.05721e8 + 6.05721e8i) q^{76} +(4.25950e7 - 4.25950e7i) q^{77} +(1.52511e8 - 3.68194e8i) q^{78} +(4.03780e8 + 1.67251e8i) q^{79} +(-2.19335e8 - 5.29522e8i) q^{80} +2.80566e8i q^{81} +(-1.33939e8 + 5.54794e7i) q^{82} +(-4.66100e7 - 4.66100e7i) q^{83} -1.81780e9 q^{84} +(-6.42720e7 + 1.73750e8i) q^{85} +1.63511e9 q^{86} +(-4.10793e8 - 4.10793e8i) q^{87} +(-2.21556e8 + 9.17714e7i) q^{88} +9.76056e8i q^{89} +(-4.02662e7 - 9.72113e7i) q^{90} +(6.92199e8 + 2.86718e8i) q^{91} +(2.67172e8 - 6.45010e8i) q^{92} +(2.54715e8 - 2.54715e8i) q^{93} +(-2.72514e7 + 2.72514e7i) q^{94} +(-1.22783e8 + 2.96424e8i) q^{95} +(2.98229e9 + 1.23530e9i) q^{96} +(6.66031e7 + 1.60794e8i) q^{97} -2.85448e9i q^{98} +(-2.40641e7 + 9.96766e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.2113 + 31.2113i 1.37936 + 1.37936i 0.845701 + 0.533657i \(0.179183\pi\)
0.533657 + 0.845701i \(0.320817\pi\)
\(3\) −114.097 + 47.2607i −0.813261 + 0.336864i −0.750254 0.661149i \(-0.770069\pi\)
−0.0630070 + 0.998013i \(0.520069\pi\)
\(4\) 1436.29i 2.80526i
\(5\) 205.870 + 497.013i 0.147308 + 0.355634i 0.980260 0.197712i \(-0.0633510\pi\)
−0.832952 + 0.553345i \(0.813351\pi\)
\(6\) −5036.20 2086.06i −1.58643 0.657123i
\(7\) 3921.77 9467.99i 0.617363 1.49045i −0.237391 0.971414i \(-0.576292\pi\)
0.854754 0.519033i \(-0.173708\pi\)
\(8\) −28848.3 + 28848.3i −2.49010 + 2.49010i
\(9\) −3133.33 + 3133.33i −0.159190 + 0.159190i
\(10\) −9086.97 + 21937.9i −0.287355 + 0.693737i
\(11\) 5430.59 + 2249.42i 0.111836 + 0.0463238i 0.437900 0.899024i \(-0.355723\pi\)
−0.326064 + 0.945348i \(0.605723\pi\)
\(12\) −67880.1 163877.i −0.944990 2.28141i
\(13\) 73109.4i 0.709951i 0.934876 + 0.354975i \(0.115511\pi\)
−0.934876 + 0.354975i \(0.884489\pi\)
\(14\) 417912. 173105.i 2.90743 1.20429i
\(15\) −46978.4 46978.4i −0.239600 0.239600i
\(16\) −1.06541e6 −4.06421
\(17\) 252672. + 233976.i 0.733730 + 0.679441i
\(18\) −195591. −0.439160
\(19\) 421726. + 421726.i 0.742402 + 0.742402i 0.973040 0.230638i \(-0.0740813\pi\)
−0.230638 + 0.973040i \(0.574081\pi\)
\(20\) −713856. + 295689.i −0.997644 + 0.413238i
\(21\) 1.26562e6i 1.42009i
\(22\) 99288.4 + 239703.i 0.0903642 + 0.218158i
\(23\) −449080. 186015.i −0.334617 0.138603i 0.209047 0.977906i \(-0.432964\pi\)
−0.543665 + 0.839302i \(0.682964\pi\)
\(24\) 1.92813e6 4.65491e6i 1.18628 2.86392i
\(25\) 1.17643e6 1.17643e6i 0.602331 0.602331i
\(26\) −2.28184e6 + 2.28184e6i −0.979276 + 0.979276i
\(27\) 1.13965e6 2.75137e6i 0.412702 0.996350i
\(28\) 1.35988e7 + 5.63280e6i 4.18109 + 1.73186i
\(29\) 1.80019e6 + 4.34603e6i 0.472636 + 1.14104i 0.962994 + 0.269523i \(0.0868659\pi\)
−0.490358 + 0.871521i \(0.663134\pi\)
\(30\) 2.93251e6i 0.660989i
\(31\) −2.69479e6 + 1.11622e6i −0.524080 + 0.217081i −0.629008 0.777399i \(-0.716539\pi\)
0.104928 + 0.994480i \(0.466539\pi\)
\(32\) −1.84824e7 1.84824e7i −3.11590 3.11590i
\(33\) −725926. −0.106556
\(34\) 583497. + 1.51889e7i 0.0748831 + 1.94927i
\(35\) 5.51309e6 0.620996
\(36\) −4.50038e6 4.50038e6i −0.446568 0.446568i
\(37\) 3.68495e6 1.52636e6i 0.323239 0.133890i −0.215163 0.976578i \(-0.569028\pi\)
0.538402 + 0.842688i \(0.319028\pi\)
\(38\) 2.63252e7i 2.04808i
\(39\) −3.45520e6 8.34160e6i −0.239157 0.577376i
\(40\) −2.02770e7 8.39901e6i −1.25237 0.518750i
\(41\) −1.25691e6 + 3.03445e6i −0.0694669 + 0.167708i −0.954800 0.297250i \(-0.903931\pi\)
0.885333 + 0.464958i \(0.153931\pi\)
\(42\) −3.95016e7 + 3.95016e7i −1.95881 + 1.95881i
\(43\) 2.61942e7 2.61942e7i 1.16842 1.16842i 0.185835 0.982581i \(-0.440501\pi\)
0.982581 0.185835i \(-0.0594989\pi\)
\(44\) −3.23083e6 + 7.79991e6i −0.129950 + 0.313727i
\(45\) −2.20237e6 912250.i −0.0800633 0.0331633i
\(46\) −8.21060e6 1.98222e7i −0.270374 0.652741i
\(47\) 873124.i 0.0260997i 0.999915 + 0.0130499i \(0.00415402\pi\)
−0.999915 + 0.0130499i \(0.995846\pi\)
\(48\) 1.21560e8 5.03519e7i 3.30526 1.36909i
\(49\) −4.57282e7 4.57282e7i −1.13319 1.13319i
\(50\) 7.34357e7 1.66166
\(51\) −3.98871e7 1.47547e7i −0.825593 0.305396i
\(52\) −1.05006e8 −1.99159
\(53\) −3.48677e7 3.48677e7i −0.606991 0.606991i 0.335168 0.942159i \(-0.391207\pi\)
−0.942159 + 0.335168i \(0.891207\pi\)
\(54\) 1.21444e8 5.03037e7i 1.94359 0.805060i
\(55\) 3.16216e6i 0.0465964i
\(56\) 1.59999e8 + 3.86272e8i 2.17406 + 5.24865i
\(57\) −6.80489e7 2.81868e7i −0.853855 0.353678i
\(58\) −7.94592e7 + 1.91832e8i −0.921974 + 2.22584i
\(59\) −1.51858e7 + 1.51858e7i −0.163157 + 0.163157i −0.783964 0.620807i \(-0.786805\pi\)
0.620807 + 0.783964i \(0.286805\pi\)
\(60\) 6.74747e7 6.74747e7i 0.672141 0.672141i
\(61\) 3.49262e7 8.43192e7i 0.322973 0.779727i −0.676105 0.736805i \(-0.736333\pi\)
0.999078 0.0429216i \(-0.0136666\pi\)
\(62\) −1.18947e8 4.92693e7i −1.02233 0.423461i
\(63\) 1.73782e7 + 4.19546e7i 0.138986 + 0.335542i
\(64\) 6.08232e8i 4.53168i
\(65\) −3.63364e7 + 1.50510e7i −0.252482 + 0.104582i
\(66\) −2.26571e7 2.26571e7i −0.146979 0.146979i
\(67\) 1.62674e8 0.986237 0.493119 0.869962i \(-0.335857\pi\)
0.493119 + 0.869962i \(0.335857\pi\)
\(68\) −3.36058e8 + 3.62910e8i −1.90601 + 2.05830i
\(69\) 6.00301e7 0.318822
\(70\) 1.72071e8 + 1.72071e8i 0.856576 + 0.856576i
\(71\) 1.77698e8 7.36048e7i 0.829887 0.343750i 0.0730290 0.997330i \(-0.476733\pi\)
0.756858 + 0.653579i \(0.226733\pi\)
\(72\) 1.80783e8i 0.792796i
\(73\) −1.27907e8 3.08794e8i −0.527158 1.27267i −0.933377 0.358897i \(-0.883153\pi\)
0.406219 0.913776i \(-0.366847\pi\)
\(74\) 1.62652e8 + 6.73726e7i 0.630545 + 0.261180i
\(75\) −7.86286e7 + 1.89826e8i −0.286949 + 0.692756i
\(76\) −6.05721e8 + 6.05721e8i −2.08263 + 2.08263i
\(77\) 4.25950e7 4.25950e7i 0.138086 0.138086i
\(78\) 1.52511e8 3.68194e8i 0.466525 1.12629i
\(79\) 4.03780e8 + 1.67251e8i 1.16633 + 0.483112i 0.879979 0.475012i \(-0.157556\pi\)
0.286355 + 0.958124i \(0.407556\pi\)
\(80\) −2.19335e8 5.29522e8i −0.598692 1.44537i
\(81\) 2.80566e8i 0.724189i
\(82\) −1.33939e8 + 5.54794e7i −0.327149 + 0.135509i
\(83\) −4.66100e7 4.66100e7i −0.107802 0.107802i 0.651148 0.758951i \(-0.274288\pi\)
−0.758951 + 0.651148i \(0.774288\pi\)
\(84\) −1.81780e9 −3.98372
\(85\) −6.42720e7 + 1.73750e8i −0.133548 + 0.361026i
\(86\) 1.63511e9 3.22333
\(87\) −4.10793e8 4.10793e8i −0.768753 0.768753i
\(88\) −2.21556e8 + 9.17714e7i −0.393832 + 0.163131i
\(89\) 9.76056e8i 1.64900i 0.565864 + 0.824498i \(0.308543\pi\)
−0.565864 + 0.824498i \(0.691457\pi\)
\(90\) −4.02662e7 9.72113e7i −0.0646919 0.156180i
\(91\) 6.92199e8 + 2.86718e8i 1.05814 + 0.438298i
\(92\) 2.67172e8 6.45010e8i 0.388817 0.938688i
\(93\) 2.54715e8 2.54715e8i 0.353087 0.353087i
\(94\) −2.72514e7 + 2.72514e7i −0.0360009 + 0.0360009i
\(95\) −1.22783e8 + 2.96424e8i −0.154661 + 0.373385i
\(96\) 2.98229e9 + 1.23530e9i 3.58368 + 1.48441i
\(97\) 6.66031e7 + 1.60794e8i 0.0763874 + 0.184416i 0.957460 0.288565i \(-0.0931781\pi\)
−0.881073 + 0.472980i \(0.843178\pi\)
\(98\) 2.85448e9i 3.12614i
\(99\) −2.40641e7 + 9.96766e6i −0.0251774 + 0.0104288i
\(100\) 1.68969e9 + 1.68969e9i 1.68969 + 1.68969i
\(101\) −3.00464e8 −0.287307 −0.143653 0.989628i \(-0.545885\pi\)
−0.143653 + 0.989628i \(0.545885\pi\)
\(102\) −7.84415e8 1.70544e9i −0.717538 1.56004i
\(103\) −1.18093e9 −1.03385 −0.516926 0.856030i \(-0.672924\pi\)
−0.516926 + 0.856030i \(0.672924\pi\)
\(104\) −2.10909e9 2.10909e9i −1.76785 1.76785i
\(105\) −6.29029e8 + 2.60552e8i −0.505032 + 0.209191i
\(106\) 2.17653e9i 1.67452i
\(107\) 2.44748e8 + 5.90873e8i 0.180506 + 0.435780i 0.988071 0.153998i \(-0.0492151\pi\)
−0.807565 + 0.589778i \(0.799215\pi\)
\(108\) 3.95177e9 + 1.63688e9i 2.79502 + 1.15773i
\(109\) 1.46439e8 3.53536e8i 0.0993662 0.239891i −0.866377 0.499390i \(-0.833557\pi\)
0.965743 + 0.259499i \(0.0835574\pi\)
\(110\) −9.86953e7 + 9.86953e7i −0.0642731 + 0.0642731i
\(111\) −3.48307e8 + 3.48307e8i −0.217775 + 0.217775i
\(112\) −4.17828e9 + 1.00873e10i −2.50909 + 6.05749i
\(113\) −1.52424e9 6.31361e8i −0.879429 0.364271i −0.103153 0.994665i \(-0.532893\pi\)
−0.776275 + 0.630394i \(0.782893\pi\)
\(114\) −1.24415e9 3.00364e9i −0.689923 1.66562i
\(115\) 2.61494e8i 0.139419i
\(116\) −6.24217e9 + 2.58559e9i −3.20092 + 1.32586i
\(117\) −2.29076e8 2.29076e8i −0.113017 0.113017i
\(118\) −9.47940e8 −0.450103
\(119\) 3.20621e9 1.47469e9i 1.46565 0.674123i
\(120\) 2.71050e9 1.19326
\(121\) −1.64289e9 1.64289e9i −0.696745 0.696745i
\(122\) 3.72181e9 1.54162e9i 1.52102 0.630026i
\(123\) 4.05626e8i 0.159791i
\(124\) −1.60322e9 3.87051e9i −0.608968 1.47018i
\(125\) 1.79762e9 + 7.44599e8i 0.658571 + 0.272789i
\(126\) −7.67062e8 + 1.85185e9i −0.271121 + 0.654544i
\(127\) −1.26647e9 + 1.26647e9i −0.431996 + 0.431996i −0.889307 0.457311i \(-0.848813\pi\)
0.457311 + 0.889307i \(0.348813\pi\)
\(128\) 9.52072e9 9.52072e9i 3.13491 3.13491i
\(129\) −1.75074e9 + 4.22665e9i −0.556630 + 1.34382i
\(130\) −1.60387e9 6.64343e8i −0.492519 0.204008i
\(131\) −3.87878e8 9.36420e8i −0.115073 0.277811i 0.855841 0.517239i \(-0.173040\pi\)
−0.970914 + 0.239428i \(0.923040\pi\)
\(132\) 1.04264e9i 0.298918i
\(133\) 5.64681e9 2.33898e9i 1.56484 0.648179i
\(134\) 5.07727e9 + 5.07727e9i 1.36037 + 1.36037i
\(135\) 1.60209e9 0.415130
\(136\) −1.40390e10 + 5.39322e8i −3.51893 + 0.135183i
\(137\) −1.85032e9 −0.448750 −0.224375 0.974503i \(-0.572034\pi\)
−0.224375 + 0.974503i \(0.572034\pi\)
\(138\) 1.87362e9 + 1.87362e9i 0.439769 + 0.439769i
\(139\) −3.23012e9 + 1.33796e9i −0.733927 + 0.304002i −0.718165 0.695873i \(-0.755017\pi\)
−0.0157622 + 0.999876i \(0.505017\pi\)
\(140\) 7.91840e9i 1.74205i
\(141\) −4.12645e7 9.96213e7i −0.00879205 0.0212259i
\(142\) 7.84347e9 + 3.24887e9i 1.61887 + 0.670556i
\(143\) −1.64454e8 + 3.97027e8i −0.0328876 + 0.0793978i
\(144\) 3.33828e9 3.33828e9i 0.646981 0.646981i
\(145\) −1.78943e9 + 1.78943e9i −0.336170 + 0.336170i
\(146\) 5.64574e9 1.36300e10i 1.02833 2.48261i
\(147\) 7.37862e9 + 3.05633e9i 1.30331 + 0.539848i
\(148\) 2.19229e9 + 5.29267e9i 0.375596 + 0.906769i
\(149\) 8.01790e9i 1.33267i −0.745653 0.666334i \(-0.767862\pi\)
0.745653 0.666334i \(-0.232138\pi\)
\(150\) −8.37883e9 + 3.47062e9i −1.35136 + 0.559753i
\(151\) −2.60025e9 2.60025e9i −0.407023 0.407023i 0.473676 0.880699i \(-0.342927\pi\)
−0.880699 + 0.473676i \(0.842927\pi\)
\(152\) −2.43322e10 −3.69730
\(153\) −1.52483e9 + 5.85779e7i −0.224963 + 0.00864216i
\(154\) 2.65889e9 0.380941
\(155\) −1.10955e9 1.10955e9i −0.154403 0.154403i
\(156\) 1.19810e10 4.96268e9i 1.61969 0.670896i
\(157\) 1.15703e10i 1.51983i 0.650020 + 0.759917i \(0.274760\pi\)
−0.650020 + 0.759917i \(0.725240\pi\)
\(158\) 7.38238e9 + 1.78226e10i 0.942409 + 2.27518i
\(159\) 5.62619e9 + 2.33044e9i 0.698116 + 0.289169i
\(160\) 5.38104e9 1.29910e10i 0.649122 1.56712i
\(161\) −3.52238e9 + 3.52238e9i −0.413161 + 0.413161i
\(162\) −8.75682e9 + 8.75682e9i −0.998915 + 0.998915i
\(163\) 4.17592e9 1.00816e10i 0.463349 1.11862i −0.503665 0.863899i \(-0.668015\pi\)
0.967014 0.254724i \(-0.0819845\pi\)
\(164\) −4.35836e9 1.80529e9i −0.470464 0.194872i
\(165\) −1.49446e8 3.60795e8i −0.0156966 0.0378950i
\(166\) 2.90952e9i 0.297396i
\(167\) 7.14405e9 2.95916e9i 0.710756 0.294405i 0.00213868 0.999998i \(-0.499319\pi\)
0.708617 + 0.705593i \(0.249319\pi\)
\(168\) −3.65110e10 3.65110e10i −3.53616 3.53616i
\(169\) 5.25951e9 0.495970
\(170\) −7.42897e9 + 3.41694e9i −0.682195 + 0.313774i
\(171\) −2.64282e9 −0.236366
\(172\) 3.76225e10 + 3.76225e10i 3.27771 + 3.27771i
\(173\) 3.38175e9 1.40077e9i 0.287035 0.118894i −0.234521 0.972111i \(-0.575352\pi\)
0.521555 + 0.853218i \(0.325352\pi\)
\(174\) 2.56428e10i 2.12077i
\(175\) −6.52473e9 1.57521e10i −0.525886 1.26960i
\(176\) −5.78579e9 2.39655e9i −0.454523 0.188270i
\(177\) 1.01497e9 2.45036e9i 0.0777274 0.187651i
\(178\) −3.04640e10 + 3.04640e10i −2.27456 + 2.27456i
\(179\) 2.36815e9 2.36815e9i 0.172413 0.172413i −0.615626 0.788039i \(-0.711097\pi\)
0.788039 + 0.615626i \(0.211097\pi\)
\(180\) 1.31026e9 3.16324e9i 0.0930316 0.224598i
\(181\) −1.61839e10 6.70360e9i −1.12081 0.464253i −0.256160 0.966634i \(-0.582457\pi\)
−0.864646 + 0.502382i \(0.832457\pi\)
\(182\) 1.26556e10 + 3.05533e10i 0.854990 + 2.06413i
\(183\) 1.12712e10i 0.742920i
\(184\) 1.83214e10 7.58899e9i 1.17836 0.488094i
\(185\) 1.51724e9 + 1.51724e9i 0.0952317 + 0.0952317i
\(186\) 1.59000e10 0.974067
\(187\) 8.45843e8 + 1.83900e9i 0.0505828 + 0.109975i
\(188\) −1.25406e9 −0.0732164
\(189\) −2.15805e10 2.15805e10i −1.23022 1.23022i
\(190\) −1.30840e10 + 5.41956e9i −0.728365 + 0.301699i
\(191\) 1.53102e10i 0.832398i 0.909273 + 0.416199i \(0.136638\pi\)
−0.909273 + 0.416199i \(0.863362\pi\)
\(192\) 2.87455e10 + 6.93977e10i 1.52656 + 3.68544i
\(193\) −2.65058e10 1.09791e10i −1.37510 0.569583i −0.431930 0.901907i \(-0.642167\pi\)
−0.943165 + 0.332324i \(0.892167\pi\)
\(194\) −2.93983e9 + 7.09737e9i −0.149009 + 0.359741i
\(195\) 3.43456e9 3.43456e9i 0.170104 0.170104i
\(196\) 6.56791e10 6.56791e10i 3.17888 3.17888i
\(197\) 5.18010e9 1.25059e10i 0.245042 0.591583i −0.752728 0.658332i \(-0.771263\pi\)
0.997770 + 0.0667485i \(0.0212625\pi\)
\(198\) −1.06217e9 4.39967e8i −0.0491137 0.0203435i
\(199\) −6.64683e9 1.60469e10i −0.300453 0.725357i −0.999943 0.0107143i \(-0.996589\pi\)
0.699490 0.714642i \(-0.253411\pi\)
\(200\) 6.78760e10i 2.99972i
\(201\) −1.85607e10 + 7.68809e9i −0.802069 + 0.332228i
\(202\) −9.37787e9 9.37787e9i −0.396299 0.396299i
\(203\) 4.82081e10 1.99245
\(204\) 2.11920e10 5.72894e10i 0.856715 2.31600i
\(205\) −1.76692e9 −0.0698756
\(206\) −3.68585e10 3.68585e10i −1.42605 1.42605i
\(207\) 1.98997e9 8.24271e8i 0.0753319 0.0312035i
\(208\) 7.78914e10i 2.88539i
\(209\) 1.34158e9 + 3.23886e9i 0.0486360 + 0.117418i
\(210\) −2.77650e10 1.15006e10i −0.985170 0.408071i
\(211\) −4.43916e9 + 1.07171e10i −0.154181 + 0.372225i −0.982030 0.188726i \(-0.939564\pi\)
0.827849 + 0.560951i \(0.189564\pi\)
\(212\) 5.00802e10 5.00802e10i 1.70277 1.70277i
\(213\) −1.67962e10 + 1.67962e10i −0.559118 + 0.559118i
\(214\) −1.08030e10 + 2.60808e10i −0.352114 + 0.850079i
\(215\) 1.84115e10 + 7.62628e9i 0.587645 + 0.243411i
\(216\) 4.64953e10 + 1.12250e11i 1.45334 + 3.50867i
\(217\) 2.98918e10i 0.915131i
\(218\) 1.56049e10 6.46376e9i 0.467958 0.193834i
\(219\) 2.91877e10 + 2.91877e10i 0.857435 + 0.857435i
\(220\) −4.54179e9 −0.130715
\(221\) −1.71059e10 + 1.84727e10i −0.482370 + 0.520912i
\(222\) −2.17422e10 −0.600780
\(223\) 2.46815e10 + 2.46815e10i 0.668344 + 0.668344i 0.957333 0.288988i \(-0.0933189\pi\)
−0.288988 + 0.957333i \(0.593319\pi\)
\(224\) −2.47475e11 + 1.02508e11i −6.56773 + 2.72044i
\(225\) 7.37228e9i 0.191770i
\(226\) −2.78679e10 6.72792e10i −0.710586 1.71551i
\(227\) 5.30638e10 + 2.19797e10i 1.32642 + 0.549422i 0.929633 0.368487i \(-0.120124\pi\)
0.396790 + 0.917909i \(0.370124\pi\)
\(228\) 4.04844e10 9.77380e10i 0.992158 2.39528i
\(229\) −1.06593e10 + 1.06593e10i −0.256134 + 0.256134i −0.823480 0.567346i \(-0.807970\pi\)
0.567346 + 0.823480i \(0.307970\pi\)
\(230\) 8.16156e9 8.16156e9i 0.192308 0.192308i
\(231\) −2.84691e9 + 6.87306e9i −0.0657840 + 0.158817i
\(232\) −1.77308e11 7.34435e10i −4.01821 1.66440i
\(233\) −7.69625e9 1.85804e10i −0.171071 0.413003i 0.814970 0.579503i \(-0.196753\pi\)
−0.986041 + 0.166500i \(0.946753\pi\)
\(234\) 1.42995e10i 0.311782i
\(235\) −4.33954e8 + 1.79750e8i −0.00928194 + 0.00384471i
\(236\) −2.18113e10 2.18113e10i −0.457696 0.457696i
\(237\) −5.39747e10 −1.11128
\(238\) 1.46097e11 + 5.40429e10i 2.95151 + 1.09180i
\(239\) 2.91857e10 0.578602 0.289301 0.957238i \(-0.406577\pi\)
0.289301 + 0.957238i \(0.406577\pi\)
\(240\) 5.00511e10 + 5.00511e10i 0.973786 + 0.973786i
\(241\) −8.81475e9 + 3.65119e9i −0.168319 + 0.0697200i −0.465252 0.885178i \(-0.654036\pi\)
0.296933 + 0.954898i \(0.404036\pi\)
\(242\) 1.02553e11i 1.92212i
\(243\) 9.17209e9 + 2.21434e10i 0.168749 + 0.407395i
\(244\) 1.21107e11 + 5.01642e10i 2.18733 + 0.906023i
\(245\) 1.33135e10 3.21416e10i 0.236072 0.569928i
\(246\) 1.26601e10 1.26601e10i 0.220409 0.220409i
\(247\) −3.08321e10 + 3.08321e10i −0.527069 + 0.527069i
\(248\) 4.55392e10 1.09941e11i 0.764456 1.84556i
\(249\) 7.52090e9 + 3.11526e9i 0.123986 + 0.0513567i
\(250\) 3.28662e10 + 7.93460e10i 0.532132 + 1.28468i
\(251\) 1.75778e10i 0.279533i 0.990185 + 0.139766i \(0.0446351\pi\)
−0.990185 + 0.139766i \(0.955365\pi\)
\(252\) −6.02590e10 + 2.49601e10i −0.941282 + 0.389892i
\(253\) −2.02034e9 2.02034e9i −0.0310015 0.0310015i
\(254\) −7.90566e10 −1.19175
\(255\) −8.78264e8 2.28619e10i −0.0130075 0.338596i
\(256\) 2.82893e11 4.11664
\(257\) 4.14195e10 + 4.14195e10i 0.592251 + 0.592251i 0.938239 0.345988i \(-0.112456\pi\)
−0.345988 + 0.938239i \(0.612456\pi\)
\(258\) −1.86562e11 + 7.72765e10i −2.62141 + 1.08582i
\(259\) 4.08751e10i 0.564430i
\(260\) −2.16176e10 5.21896e10i −0.293378 0.708278i
\(261\) −1.92582e10 7.97699e9i −0.256881 0.106404i
\(262\) 1.71207e10 4.13331e10i 0.224474 0.541928i
\(263\) 8.99350e10 8.99350e10i 1.15912 1.15912i 0.174453 0.984665i \(-0.444184\pi\)
0.984665 0.174453i \(-0.0558157\pi\)
\(264\) 2.09418e10 2.09418e10i 0.265336 0.265336i
\(265\) 1.01515e10 2.45079e10i 0.126452 0.305281i
\(266\) 2.49247e11 + 1.03241e11i 3.05255 + 1.26441i
\(267\) −4.61291e10 1.11366e11i −0.555488 1.34107i
\(268\) 2.33647e11i 2.76665i
\(269\) −4.43476e10 + 1.83694e10i −0.516398 + 0.213899i −0.625634 0.780117i \(-0.715160\pi\)
0.109236 + 0.994016i \(0.465160\pi\)
\(270\) 5.00032e10 + 5.00032e10i 0.572613 + 0.572613i
\(271\) 6.84715e9 0.0771166 0.0385583 0.999256i \(-0.487723\pi\)
0.0385583 + 0.999256i \(0.487723\pi\)
\(272\) −2.69198e11 2.49280e11i −2.98203 2.76139i
\(273\) −9.25287e10 −1.00819
\(274\) −5.77509e10 5.77509e10i −0.618987 0.618987i
\(275\) 9.03498e9 3.74241e9i 0.0952643 0.0394598i
\(276\) 8.62207e10i 0.894377i
\(277\) 3.12373e10 + 7.54135e10i 0.318797 + 0.769644i 0.999318 + 0.0369159i \(0.0117534\pi\)
−0.680521 + 0.732728i \(0.738247\pi\)
\(278\) −1.42576e11 5.90569e10i −1.43168 0.593020i
\(279\) 4.94619e9 1.19412e10i 0.0488711 0.117985i
\(280\) −1.59044e11 + 1.59044e11i −1.54634 + 1.54634i
\(281\) −3.24884e9 + 3.24884e9i −0.0310850 + 0.0310850i −0.722478 0.691393i \(-0.756997\pi\)
0.691393 + 0.722478i \(0.256997\pi\)
\(282\) 1.82139e9 4.39723e9i 0.0171507 0.0414055i
\(283\) −1.70234e11 7.05132e10i −1.57764 0.653479i −0.589601 0.807695i \(-0.700715\pi\)
−0.988037 + 0.154216i \(0.950715\pi\)
\(284\) 1.05718e11 + 2.55226e11i 0.964308 + 2.32805i
\(285\) 3.96240e10i 0.355759i
\(286\) −1.75246e10 + 7.25891e9i −0.154882 + 0.0641541i
\(287\) 2.38009e10 + 2.38009e10i 0.207073 + 0.207073i
\(288\) 1.15823e11 0.992040
\(289\) 9.09792e9 + 1.18238e11i 0.0767188 + 0.997053i
\(290\) −1.11701e11 −0.927399
\(291\) −1.51985e10 1.51985e10i −0.124246 0.124246i
\(292\) 4.43519e11 1.83712e11i 3.57017 1.47881i
\(293\) 7.48477e10i 0.593300i −0.954986 0.296650i \(-0.904131\pi\)
0.954986 0.296650i \(-0.0958694\pi\)
\(294\) 1.34905e11 + 3.25688e11i 1.05309 + 2.54237i
\(295\) −1.06739e10 4.42126e9i −0.0820583 0.0339897i
\(296\) −6.22719e10 + 1.50338e11i −0.471497 + 1.13830i
\(297\) 1.23780e10 1.23780e10i 0.0923094 0.0923094i
\(298\) 2.50249e11 2.50249e11i 1.83823 1.83823i
\(299\) 1.35995e10 3.28320e10i 0.0984014 0.237562i
\(300\) −2.72646e11 1.12934e11i −1.94336 0.804966i
\(301\) −1.45279e11 3.50734e11i −1.02012 2.46280i
\(302\) 1.62314e11i 1.12286i
\(303\) 3.42822e10 1.42001e10i 0.233656 0.0967833i
\(304\) −4.49310e11 4.49310e11i −3.01728 3.01728i
\(305\) 4.90980e10 0.324874
\(306\) −4.94202e10 4.57637e10i −0.322224 0.298383i
\(307\) −5.33972e10 −0.343081 −0.171540 0.985177i \(-0.554874\pi\)
−0.171540 + 0.985177i \(0.554874\pi\)
\(308\) 6.11789e10 + 6.11789e10i 0.387368 + 0.387368i
\(309\) 1.34742e11 5.58118e10i 0.840792 0.348267i
\(310\) 6.92611e10i 0.425953i
\(311\) 3.19664e10 + 7.71737e10i 0.193763 + 0.467786i 0.990664 0.136324i \(-0.0435288\pi\)
−0.796901 + 0.604110i \(0.793529\pi\)
\(312\) 3.40318e11 + 1.40964e11i 2.03324 + 0.842197i
\(313\) −2.36488e9 + 5.70932e9i −0.0139270 + 0.0336229i −0.930690 0.365809i \(-0.880792\pi\)
0.916763 + 0.399432i \(0.130792\pi\)
\(314\) −3.61124e11 + 3.61124e11i −2.09639 + 2.09639i
\(315\) −1.72744e10 + 1.72744e10i −0.0988563 + 0.0988563i
\(316\) −2.40221e11 + 5.79946e11i −1.35525 + 3.27187i
\(317\) 2.26196e11 + 9.36934e10i 1.25811 + 0.521126i 0.909328 0.416079i \(-0.136596\pi\)
0.348780 + 0.937205i \(0.386596\pi\)
\(318\) 1.02865e11 + 2.48337e11i 0.564084 + 1.36182i
\(319\) 2.76509e10i 0.149504i
\(320\) 3.02299e11 1.25217e11i 1.61162 0.667555i
\(321\) −5.58502e10 5.58502e10i −0.293597 0.293597i
\(322\) −2.19876e11 −1.13979
\(323\) 7.88419e9 + 2.05232e11i 0.0403038 + 1.04914i
\(324\) −4.02974e11 −2.03154
\(325\) 8.60080e10 + 8.60080e10i 0.427626 + 0.427626i
\(326\) 4.44995e11 1.84323e11i 2.18210 0.903857i
\(327\) 4.72584e10i 0.228567i
\(328\) −5.12792e10 1.23799e11i −0.244629 0.590588i
\(329\) 8.26673e9 + 3.42419e9i 0.0389002 + 0.0161130i
\(330\) 6.59647e9 1.59253e10i 0.0306195 0.0739221i
\(331\) −1.18152e11 + 1.18152e11i −0.541024 + 0.541024i −0.923829 0.382805i \(-0.874958\pi\)
0.382805 + 0.923829i \(0.374958\pi\)
\(332\) 6.69455e10 6.69455e10i 0.302413 0.302413i
\(333\) −6.76360e9 + 1.63288e10i −0.0301425 + 0.0727704i
\(334\) 3.15335e11 + 1.30616e11i 1.38648 + 0.574297i
\(335\) 3.34896e10 + 8.08511e10i 0.145281 + 0.350739i
\(336\) 1.34840e12i 5.77154i
\(337\) −1.62022e11 + 6.71116e10i −0.684288 + 0.283441i −0.697618 0.716470i \(-0.745757\pi\)
0.0133302 + 0.999911i \(0.495757\pi\)
\(338\) 1.64156e11 + 1.64156e11i 0.684120 + 0.684120i
\(339\) 2.03751e11 0.837915
\(340\) −2.49555e11 9.23133e10i −1.01277 0.374636i
\(341\) −1.71452e10 −0.0686668
\(342\) −8.24857e10 8.24857e10i −0.326033 0.326033i
\(343\) −2.30222e11 + 9.53613e10i −0.898099 + 0.372005i
\(344\) 1.51132e12i 5.81893i
\(345\) 1.23584e10 + 2.98358e10i 0.0469651 + 0.113384i
\(346\) 1.49269e11 + 6.18291e10i 0.559920 + 0.231927i
\(347\) 1.84496e11 4.45412e11i 0.683130 1.64922i −0.0750528 0.997180i \(-0.523913\pi\)
0.758183 0.652042i \(-0.226087\pi\)
\(348\) 5.90019e11 5.90019e11i 2.15655 2.15655i
\(349\) 3.62958e11 3.62958e11i 1.30961 1.30961i 0.387915 0.921695i \(-0.373195\pi\)
0.921695 0.387915i \(-0.126805\pi\)
\(350\) 2.87998e11 6.95289e11i 1.02585 2.47662i
\(351\) 2.01151e11 + 8.33195e10i 0.707359 + 0.292998i
\(352\) −5.87956e10 1.41945e11i −0.204128 0.492809i
\(353\) 4.72291e11i 1.61891i 0.587180 + 0.809456i \(0.300238\pi\)
−0.587180 + 0.809456i \(0.699762\pi\)
\(354\) 1.08157e11 4.48003e10i 0.366051 0.151623i
\(355\) 7.31651e10 + 7.31651e10i 0.244499 + 0.244499i
\(356\) −1.40190e12 −4.62586
\(357\) −2.96125e11 + 3.19786e11i −0.964868 + 1.04196i
\(358\) 1.47826e11 0.475639
\(359\) −3.24175e11 3.24175e11i −1.03004 1.03004i −0.999535 0.0305074i \(-0.990288\pi\)
−0.0305074 0.999535i \(-0.509712\pi\)
\(360\) 8.98515e10 3.72177e10i 0.281945 0.116785i
\(361\) 3.30176e10i 0.102320i
\(362\) −2.95893e11 7.14350e11i −0.905621 2.18636i
\(363\) 2.65094e11 + 1.09805e11i 0.801345 + 0.331928i
\(364\) −4.11811e11 + 9.94200e11i −1.22954 + 2.96837i
\(365\) 1.27143e11 1.27143e11i 0.374951 0.374951i
\(366\) −3.51790e11 + 3.51790e11i −1.02475 + 1.02475i
\(367\) 4.26747e10 1.03026e11i 0.122793 0.296448i −0.850515 0.525950i \(-0.823710\pi\)
0.973308 + 0.229502i \(0.0737097\pi\)
\(368\) 4.78454e11 + 1.98182e11i 1.35996 + 0.563312i
\(369\) −5.56963e9 1.34463e10i −0.0156390 0.0377558i
\(370\) 9.47101e10i 0.262717i
\(371\) −4.66870e11 + 1.93384e11i −1.27942 + 0.529954i
\(372\) 3.65846e11 + 3.65846e11i 0.990500 + 0.990500i
\(373\) 4.62799e11 1.23795 0.618974 0.785411i \(-0.287549\pi\)
0.618974 + 0.785411i \(0.287549\pi\)
\(374\) −3.09976e10 + 8.37973e10i −0.0819230 + 0.221466i
\(375\) −2.40294e11 −0.627484
\(376\) −2.51882e10 2.51882e10i −0.0649908 0.0649908i
\(377\) −3.17736e11 + 1.31611e11i −0.810085 + 0.335548i
\(378\) 1.34711e12i 3.39383i
\(379\) −1.25460e11 3.02888e11i −0.312341 0.754058i −0.999617 0.0276621i \(-0.991194\pi\)
0.687276 0.726396i \(-0.258806\pi\)
\(380\) −4.25751e11 1.76352e11i −1.04744 0.433864i
\(381\) 8.46469e10 2.04356e11i 0.205802 0.496849i
\(382\) −4.77852e11 + 4.77852e11i −1.14818 + 1.14818i
\(383\) −7.49320e10 + 7.49320e10i −0.177940 + 0.177940i −0.790457 0.612517i \(-0.790157\pi\)
0.612517 + 0.790457i \(0.290157\pi\)
\(384\) −6.36334e11 + 1.53625e12i −1.49346 + 3.60554i
\(385\) 2.99393e10 + 1.24013e10i 0.0694495 + 0.0287669i
\(386\) −4.84610e11 1.16995e12i −1.11109 2.68241i
\(387\) 1.64150e11i 0.372000i
\(388\) −2.30947e11 + 9.56615e10i −0.517333 + 0.214286i
\(389\) −3.97425e10 3.97425e10i −0.0879998 0.0879998i 0.661737 0.749736i \(-0.269820\pi\)
−0.749736 + 0.661737i \(0.769820\pi\)
\(390\) 2.14394e11 0.469270
\(391\) −6.99466e10 1.52075e11i −0.151346 0.329050i
\(392\) 2.63837e12 5.64349
\(393\) 8.85117e10 + 8.85117e10i 0.187169 + 0.187169i
\(394\) 5.52002e11 2.28647e11i 1.15401 0.478005i
\(395\) 2.35116e11i 0.485954i
\(396\) −1.43165e10 3.45630e10i −0.0292555 0.0706290i
\(397\) 3.56605e11 + 1.47711e11i 0.720493 + 0.298438i 0.712639 0.701531i \(-0.247500\pi\)
0.00785435 + 0.999969i \(0.497500\pi\)
\(398\) 2.93388e11 7.08300e11i 0.586095 1.41496i
\(399\) −5.33744e11 + 5.33744e11i −1.05428 + 1.05428i
\(400\) −1.25338e12 + 1.25338e12i −2.44800 + 2.44800i
\(401\) −1.01576e11 + 2.45227e11i −0.196175 + 0.473607i −0.991103 0.133096i \(-0.957508\pi\)
0.794929 + 0.606703i \(0.207508\pi\)
\(402\) −8.19258e11 3.39348e11i −1.56460 0.648079i
\(403\) −8.16061e10 1.97015e11i −0.154117 0.372071i
\(404\) 4.31554e11i 0.805970i
\(405\) −1.39445e11 + 5.77599e10i −0.257546 + 0.106679i
\(406\) 1.50464e12 + 1.50464e12i 2.74831 + 2.74831i
\(407\) 2.34449e10 0.0423519
\(408\) 1.57632e12 7.25028e11i 2.81627 1.29534i
\(409\) −8.76403e11 −1.54863 −0.774317 0.632798i \(-0.781907\pi\)
−0.774317 + 0.632798i \(0.781907\pi\)
\(410\) −5.51480e10 5.51480e10i −0.0963835 0.0963835i
\(411\) 2.11117e11 8.74474e10i 0.364951 0.151168i
\(412\) 1.69617e12i 2.90022i
\(413\) 8.42240e10 + 2.03335e11i 0.142449 + 0.343903i
\(414\) 8.78360e10 + 3.63829e10i 0.146950 + 0.0608689i
\(415\) 1.35702e10 3.27614e10i 0.0224579 0.0542183i
\(416\) 1.35124e12 1.35124e12i 2.21214 2.21214i
\(417\) 3.05316e11 3.05316e11i 0.494467 0.494467i
\(418\) −5.92166e10 + 1.42962e11i −0.0948747 + 0.229048i
\(419\) −3.15142e11 1.30536e11i −0.499509 0.206904i 0.118680 0.992933i \(-0.462134\pi\)
−0.618190 + 0.786029i \(0.712134\pi\)
\(420\) −3.74229e11 9.03469e11i −0.586835 1.41674i
\(421\) 3.20568e11i 0.497337i −0.968589 0.248668i \(-0.920007\pi\)
0.968589 0.248668i \(-0.0799930\pi\)
\(422\) −4.73046e11 + 1.95942e11i −0.726102 + 0.300761i
\(423\) −2.73579e9 2.73579e9i −0.00415481 0.00415481i
\(424\) 2.01175e12 3.02293
\(425\) 5.72506e11 2.19934e10i 0.851197 0.0326996i
\(426\) −1.04846e12 −1.54245
\(427\) −6.61361e11 6.61361e11i −0.962750 0.962750i
\(428\) −8.48666e11 + 3.51529e11i −1.22247 + 0.506366i
\(429\) 5.30720e10i 0.0756498i
\(430\) 3.36620e11 + 8.12672e11i 0.474823 + 1.14632i
\(431\) 1.26388e12 + 5.23514e11i 1.76423 + 0.730770i 0.995873 + 0.0907541i \(0.0289277\pi\)
0.768362 + 0.640016i \(0.221072\pi\)
\(432\) −1.21420e12 + 2.93133e12i −1.67731 + 4.04937i
\(433\) 5.13051e11 5.13051e11i 0.701398 0.701398i −0.263312 0.964711i \(-0.584815\pi\)
0.964711 + 0.263312i \(0.0848150\pi\)
\(434\) −9.32962e11 + 9.32962e11i −1.26229 + 1.26229i
\(435\) 1.19600e11 2.88740e11i 0.160151 0.386638i
\(436\) 5.07781e11 + 2.10330e11i 0.672957 + 0.278748i
\(437\) −1.10941e11 2.67836e11i −0.145521 0.351320i
\(438\) 1.82197e12i 2.36542i
\(439\) 9.53551e9 3.94974e9i 0.0122533 0.00507549i −0.376548 0.926397i \(-0.622889\pi\)
0.388802 + 0.921321i \(0.372889\pi\)
\(440\) −9.12232e10 9.12232e10i −0.116029 0.116029i
\(441\) 2.86564e11 0.360784
\(442\) −1.11045e12 + 4.26592e10i −1.38389 + 0.0531633i
\(443\) −1.08663e12 −1.34049 −0.670244 0.742141i \(-0.733811\pi\)
−0.670244 + 0.742141i \(0.733811\pi\)
\(444\) −5.00270e11 5.00270e11i −0.610916 0.610916i
\(445\) −4.85113e11 + 2.00940e11i −0.586439 + 0.242911i
\(446\) 1.54069e12i 1.84377i
\(447\) 3.78931e11 + 9.14821e11i 0.448928 + 1.08381i
\(448\) −5.75873e12 2.38535e12i −6.75423 2.79769i
\(449\) 5.25129e11 1.26777e12i 0.609758 1.47209i −0.253506 0.967334i \(-0.581584\pi\)
0.863264 0.504753i \(-0.168416\pi\)
\(450\) −2.30099e11 + 2.30099e11i −0.264520 + 0.264520i
\(451\) −1.36516e10 + 1.36516e10i −0.0155377 + 0.0155377i
\(452\) 9.06819e11 2.18925e12i 1.02187 2.46702i
\(453\) 4.19571e11 + 1.73792e11i 0.468127 + 0.193905i
\(454\) 9.70174e11 + 2.34221e12i 1.07176 + 2.58746i
\(455\) 4.03059e11i 0.440877i
\(456\) 2.77624e12 1.14996e12i 3.00687 1.24549i
\(457\) 4.30302e11 + 4.30302e11i 0.461477 + 0.461477i 0.899139 0.437662i \(-0.144193\pi\)
−0.437662 + 0.899139i \(0.644193\pi\)
\(458\) −6.65379e11 −0.706601
\(459\) 9.31714e11 4.28540e11i 0.979773 0.450645i
\(460\) 3.75581e11 0.391105
\(461\) 6.30625e11 + 6.30625e11i 0.650305 + 0.650305i 0.953066 0.302762i \(-0.0979086\pi\)
−0.302762 + 0.953066i \(0.597909\pi\)
\(462\) −3.03373e11 + 1.25661e11i −0.309805 + 0.128325i
\(463\) 7.18298e11i 0.726424i 0.931706 + 0.363212i \(0.118320\pi\)
−0.931706 + 0.363212i \(0.881680\pi\)
\(464\) −1.91793e12 4.63030e12i −1.92089 4.63744i
\(465\) 1.79035e11 + 7.41588e10i 0.177582 + 0.0735570i
\(466\) 3.39708e11 8.20128e11i 0.333710 0.805647i
\(467\) −1.42957e12 + 1.42957e12i −1.39084 + 1.39084i −0.567403 + 0.823440i \(0.692052\pi\)
−0.823440 + 0.567403i \(0.807948\pi\)
\(468\) 3.29020e11 3.29020e11i 0.317042 0.317042i
\(469\) 6.37970e11 1.54020e12i 0.608867 1.46993i
\(470\) −1.91545e10 7.93406e9i −0.0181063 0.00749989i
\(471\) −5.46820e11 1.32014e12i −0.511977 1.23602i
\(472\) 8.76172e11i 0.812551i
\(473\) 2.01172e11 8.33282e10i 0.184796 0.0765450i
\(474\) −1.68462e12 1.68462e12i −1.53285 1.53285i
\(475\) 9.92260e11 0.894343
\(476\) 2.11808e12 + 4.60505e12i 1.89109 + 4.11152i
\(477\) 2.18504e11 0.193254
\(478\) 9.10925e11 + 9.10925e11i 0.798099 + 0.798099i
\(479\) −1.02116e12 + 4.22980e11i −0.886309 + 0.367121i −0.778940 0.627098i \(-0.784243\pi\)
−0.107369 + 0.994219i \(0.534243\pi\)
\(480\) 1.73655e12i 1.49314i
\(481\) 1.11591e11 + 2.69405e11i 0.0950554 + 0.229484i
\(482\) −3.89078e11 1.61161e11i −0.328341 0.136003i
\(483\) 2.35424e11 5.68364e11i 0.196829 0.475187i
\(484\) 2.35967e12 2.35967e12i 1.95455 1.95455i
\(485\) −6.62053e10 + 6.62053e10i −0.0543319 + 0.0543319i
\(486\) −4.04851e11 + 9.77397e11i −0.329179 + 0.794708i
\(487\) −9.50225e11 3.93596e11i −0.765502 0.317081i −0.0344529 0.999406i \(-0.510969\pi\)
−0.731049 + 0.682325i \(0.760969\pi\)
\(488\) 1.42491e12 + 3.44003e12i 1.13736 + 2.74583i
\(489\) 1.34764e12i 1.06582i
\(490\) 1.41871e12 5.87650e11i 1.11176 0.460507i
\(491\) −1.40035e12 1.40035e12i −1.08735 1.08735i −0.995801 0.0915488i \(-0.970818\pi\)
−0.0915488 0.995801i \(-0.529182\pi\)
\(492\) 5.82597e11 0.448255
\(493\) −5.62014e11 + 1.51932e12i −0.428485 + 1.15835i
\(494\) −1.92462e12 −1.45403
\(495\) −9.90812e9 9.90812e9i −0.00741767 0.00741767i
\(496\) 2.87105e12 1.18923e12i 2.12997 0.882262i
\(497\) 1.97110e12i 1.44912i
\(498\) 1.37506e11 + 3.31969e11i 0.100182 + 0.241860i
\(499\) 2.00026e12 + 8.28534e11i 1.44422 + 0.598216i 0.960817 0.277182i \(-0.0894005\pi\)
0.483403 + 0.875398i \(0.339401\pi\)
\(500\) −1.06946e12 + 2.58191e12i −0.765244 + 1.84746i
\(501\) −6.75266e11 + 6.75266e11i −0.478856 + 0.478856i
\(502\) −5.48626e11 + 5.48626e11i −0.385576 + 0.385576i
\(503\) 1.08462e12 2.61851e12i 0.755479 1.82389i 0.229714 0.973258i \(-0.426221\pi\)
0.525765 0.850630i \(-0.323779\pi\)
\(504\) −1.71165e12 7.08989e11i −1.18162 0.489443i
\(505\) −6.18564e10 1.49335e11i −0.0423227 0.102176i
\(506\) 1.26115e11i 0.0855244i
\(507\) −6.00097e11 + 2.48568e11i −0.403353 + 0.167074i
\(508\) −1.81903e12 1.81903e12i −1.21186 1.21186i
\(509\) −2.07781e12 −1.37207 −0.686034 0.727570i \(-0.740650\pi\)
−0.686034 + 0.727570i \(0.740650\pi\)
\(510\) 6.86139e11 7.40963e11i 0.449104 0.484988i
\(511\) −3.42528e12 −2.22230
\(512\) 3.95487e12 + 3.95487e12i 2.54341 + 2.54341i
\(513\) 1.64094e12 6.79701e11i 1.04608 0.433301i
\(514\) 2.58551e12i 1.63385i
\(515\) −2.43119e11 5.86940e11i −0.152295 0.367673i
\(516\) −6.07070e12 2.51457e12i −3.76977 1.56149i
\(517\) −1.96403e9 + 4.74158e9i −0.00120904 + 0.00291888i
\(518\) 1.27577e12 1.27577e12i 0.778551 0.778551i
\(519\) −3.19648e11 + 3.19648e11i −0.193383 + 0.193383i
\(520\) 6.14047e11 1.48244e12i 0.368287 0.889124i
\(521\) 1.98793e12 + 8.23428e11i 1.18204 + 0.489617i 0.885155 0.465297i \(-0.154052\pi\)
0.296884 + 0.954913i \(0.404052\pi\)
\(522\) −3.52100e11 8.50045e11i −0.207562 0.501100i
\(523\) 1.61870e12i 0.946036i −0.881053 0.473018i \(-0.843165\pi\)
0.881053 0.473018i \(-0.156835\pi\)
\(524\) 1.34497e12 5.57106e11i 0.779332 0.322810i
\(525\) 1.48891e12 + 1.48891e12i 0.855365 + 0.855365i
\(526\) 5.61398e12 3.19768
\(527\) −9.42066e11 3.48481e11i −0.532027 0.196803i
\(528\) 7.73407e11 0.433067
\(529\) −1.10654e12 1.10654e12i −0.614349 0.614349i
\(530\) 1.08177e12 4.48082e11i 0.595514 0.246670i
\(531\) 9.51646e10i 0.0519458i
\(532\) 3.35946e12 + 8.11046e12i 1.81831 + 4.38978i
\(533\) −2.21847e11 9.18921e10i −0.119064 0.0493181i
\(534\) 2.03611e12 4.91561e12i 1.08359 2.61603i
\(535\) −2.43286e11 + 2.43286e11i −0.128388 + 0.128388i
\(536\) −4.69287e12 + 4.69287e12i −2.45582 + 2.45582i
\(537\) −1.58279e11 + 3.82120e11i −0.0821371 + 0.198297i
\(538\) −1.95748e12 8.10814e11i −1.00734 0.417254i
\(539\) −1.45469e11 3.51193e11i −0.0742372 0.179224i
\(540\) 2.30106e12i 1.16455i
\(541\) −2.83506e12 + 1.17432e12i −1.42290 + 0.589386i −0.955588 0.294705i \(-0.904779\pi\)
−0.467315 + 0.884091i \(0.654779\pi\)
\(542\) 2.13708e11 + 2.13708e11i 0.106371 + 0.106371i
\(543\) 2.16336e12 1.06790
\(544\) −3.45530e11 8.99443e12i −0.169157 4.40330i
\(545\) 2.05860e11 0.0999509
\(546\) −2.88794e12 2.88794e12i −1.39066 1.39066i
\(547\) −4.20030e11 + 1.73982e11i −0.200603 + 0.0830926i −0.480723 0.876872i \(-0.659626\pi\)
0.280120 + 0.959965i \(0.409626\pi\)
\(548\) 2.65760e12i 1.25886i
\(549\) 1.54765e11 + 3.73636e11i 0.0727105 + 0.175539i
\(550\) 3.98799e11 + 1.65188e11i 0.185833 + 0.0769744i
\(551\) −1.07365e12 + 2.59202e12i −0.496227 + 1.19800i
\(552\) −1.73177e12 + 1.73177e12i −0.793897 + 0.793897i
\(553\) 3.16707e12 3.16707e12i 1.44010 1.44010i
\(554\) −1.37880e12 + 3.32871e12i −0.621880 + 1.50135i
\(555\) −2.44819e11 1.01407e11i −0.109528 0.0453681i
\(556\) −1.92170e12 4.63940e12i −0.852805 2.05885i
\(557\) 4.10026e12i 1.80494i 0.430751 + 0.902471i \(0.358249\pi\)
−0.430751 + 0.902471i \(0.641751\pi\)
\(558\) 5.27077e11 2.18322e11i 0.230155 0.0953332i
\(559\) 1.91504e12 + 1.91504e12i 0.829518 + 0.829518i
\(560\) −5.87369e12 −2.52386
\(561\) −1.83421e11 1.69850e11i −0.0781836 0.0723988i
\(562\) −2.02801e11 −0.0857545
\(563\) 1.30039e12 + 1.30039e12i 0.545490 + 0.545490i 0.925133 0.379643i \(-0.123953\pi\)
−0.379643 + 0.925133i \(0.623953\pi\)
\(564\) 1.43085e11 5.92678e10i 0.0595441 0.0246640i
\(565\) 8.87546e11i 0.366415i
\(566\) −3.11242e12 7.51403e12i −1.27475 3.07751i
\(567\) 2.65639e12 + 1.10031e12i 1.07936 + 0.447088i
\(568\) −3.00291e12 + 7.24966e12i −1.21053 + 2.92247i
\(569\) −1.49588e12 + 1.49588e12i −0.598262 + 0.598262i −0.939850 0.341588i \(-0.889035\pi\)
0.341588 + 0.939850i \(0.389035\pi\)
\(570\) 1.23672e12 1.23672e12i 0.490720 0.490720i
\(571\) 9.01742e11 2.17700e12i 0.354993 0.857029i −0.640995 0.767545i \(-0.721478\pi\)
0.995988 0.0894842i \(-0.0285219\pi\)
\(572\) −5.70247e11 2.36204e11i −0.222731 0.0922582i
\(573\) −7.23572e11 1.74686e12i −0.280405 0.676958i
\(574\) 1.48571e12i 0.571257i
\(575\) −7.47144e11 + 3.09477e11i −0.285035 + 0.118066i
\(576\) 1.90579e12 + 1.90579e12i 0.721398 + 0.721398i
\(577\) −4.33825e11 −0.162939 −0.0814693 0.996676i \(-0.525961\pi\)
−0.0814693 + 0.996676i \(0.525961\pi\)
\(578\) −3.40642e12 + 3.97433e12i −1.26947 + 1.48112i
\(579\) 3.54312e12 1.31018
\(580\) −2.57015e12 2.57015e12i −0.943044 0.943044i
\(581\) −6.24097e11 + 2.58509e11i −0.227227 + 0.0941204i
\(582\) 9.48729e11i 0.342759i
\(583\) −1.10920e11 2.67785e11i −0.0397650 0.0960013i
\(584\) 1.25981e13 + 5.21831e12i 4.48175 + 1.85640i
\(585\) 6.66941e10 1.61014e11i 0.0235443 0.0568410i
\(586\) 2.33609e12 2.33609e12i 0.818373 0.818373i
\(587\) −9.98493e10 + 9.98493e10i −0.0347115 + 0.0347115i −0.724250 0.689538i \(-0.757814\pi\)
0.689538 + 0.724250i \(0.257814\pi\)
\(588\) −4.38977e12 + 1.05979e13i −1.51441 + 3.65611i
\(589\) −1.60720e12 6.65725e11i −0.550239 0.227916i
\(590\) −1.95152e11 4.71139e11i −0.0663039 0.160072i
\(591\) 1.67170e12i 0.563657i
\(592\) −3.92598e12 + 1.62619e12i −1.31371 + 0.544157i
\(593\) 1.87759e12 + 1.87759e12i 0.623524 + 0.623524i 0.946431 0.322906i \(-0.104660\pi\)
−0.322906 + 0.946431i \(0.604660\pi\)
\(594\) 7.72667e11 0.254656
\(595\) 1.39300e12 + 1.28993e12i 0.455643 + 0.421930i
\(596\) 1.15160e13 3.73848
\(597\) 1.51677e12 + 1.51677e12i 0.488693 + 0.488693i
\(598\) 1.44919e12 6.00273e11i 0.463414 0.191952i
\(599\) 4.05378e11i 0.128659i 0.997929 + 0.0643294i \(0.0204908\pi\)
−0.997929 + 0.0643294i \(0.979509\pi\)
\(600\) −3.20787e12 7.74448e12i −1.01050 2.43956i
\(601\) −5.37771e12 2.22752e12i −1.68136 0.696444i −0.681975 0.731375i \(-0.738879\pi\)
−0.999390 + 0.0349314i \(0.988879\pi\)
\(602\) 6.41253e12 1.54812e13i 1.98996 4.80420i
\(603\) −5.09712e11 + 5.09712e11i −0.156999 + 0.156999i
\(604\) 3.73471e12 3.73471e12i 1.14180 1.14180i
\(605\) 4.78317e11 1.15476e12i 0.145150 0.350423i
\(606\) 1.51320e12 + 6.26786e11i 0.455794 + 0.188796i
\(607\) 1.23341e12 + 2.97773e12i 0.368774 + 0.890298i 0.993952 + 0.109816i \(0.0350262\pi\)
−0.625178 + 0.780482i \(0.714974\pi\)
\(608\) 1.55890e13i 4.62650i
\(609\) −5.50042e12 + 2.27835e12i −1.62039 + 0.671185i
\(610\) 1.53241e12 + 1.53241e12i 0.448117 + 0.448117i
\(611\) −6.38336e10 −0.0185295
\(612\) −8.41349e10 2.19010e12i −0.0242435 0.631078i
\(613\) −3.39350e12 −0.970680 −0.485340 0.874326i \(-0.661304\pi\)
−0.485340 + 0.874326i \(0.661304\pi\)
\(614\) −1.66660e12 1.66660e12i −0.473231 0.473231i
\(615\) 2.01602e11 8.35061e10i 0.0568271 0.0235386i
\(616\) 2.45759e12i 0.687696i
\(617\) −4.47557e10 1.08050e11i −0.0124327 0.0300151i 0.917541 0.397641i \(-0.130171\pi\)
−0.929974 + 0.367625i \(0.880171\pi\)
\(618\) 5.94742e12 + 2.46350e12i 1.64014 + 0.679367i
\(619\) 5.85925e10 1.41455e11i 0.0160411 0.0387266i −0.915656 0.401963i \(-0.868328\pi\)
0.931697 + 0.363236i \(0.118328\pi\)
\(620\) 1.59364e12 1.59364e12i 0.433139 0.433139i
\(621\) −1.02359e12 + 1.02359e12i −0.276194 + 0.276194i
\(622\) −1.41098e12 + 3.40640e12i −0.377975 + 0.912514i
\(623\) 9.24129e12 + 3.82787e12i 2.45774 + 1.01803i
\(624\) 3.68120e12 + 8.88720e12i 0.971983 + 2.34657i
\(625\) 2.20272e12i 0.577431i
\(626\) −2.52006e11 + 1.04384e11i −0.0655883 + 0.0271676i
\(627\) −3.06142e11 3.06142e11i −0.0791076 0.0791076i
\(628\) −1.66183e13 −4.26352
\(629\) 1.28821e12 + 4.76525e11i 0.328141 + 0.121383i
\(630\) −1.07831e12 −0.272716
\(631\) 7.31569e11 + 7.31569e11i 0.183706 + 0.183706i 0.792968 0.609263i \(-0.208534\pi\)
−0.609263 + 0.792968i \(0.708534\pi\)
\(632\) −1.64733e13 + 6.82347e12i −4.10728 + 1.70129i
\(633\) 1.43259e12i 0.354654i
\(634\) 4.13558e12 + 9.98416e12i 1.01656 + 2.45420i
\(635\) −8.90183e11 3.68726e11i −0.217269 0.0899957i
\(636\) −3.34720e12 + 8.08085e12i −0.811193 + 1.95839i
\(637\) 3.34316e12 3.34316e12i 0.804508 0.804508i
\(638\) −8.63021e11 + 8.63021e11i −0.206219 + 0.206219i
\(639\) −3.26158e11 + 7.87414e11i −0.0773880 + 0.186831i
\(640\) 6.69195e12 + 2.77190e12i 1.57668 + 0.653081i
\(641\) −2.59923e12 6.27510e12i −0.608112 1.46811i −0.865050 0.501685i \(-0.832714\pi\)
0.256938 0.966428i \(-0.417286\pi\)
\(642\) 3.48631e12i 0.809951i
\(643\) 3.79475e12 1.57184e12i 0.875454 0.362625i 0.100722 0.994915i \(-0.467885\pi\)
0.774732 + 0.632290i \(0.217885\pi\)
\(644\) −5.05916e12 5.05916e12i −1.15902 1.15902i
\(645\) −2.46112e12 −0.559906
\(646\) −6.15948e12 + 6.65163e12i −1.39155 + 1.50273i
\(647\) −6.38861e12 −1.43330 −0.716651 0.697432i \(-0.754326\pi\)
−0.716651 + 0.697432i \(0.754326\pi\)
\(648\) −8.09385e12 8.09385e12i −1.80330 1.80330i
\(649\) −1.16627e11 + 4.83087e10i −0.0258047 + 0.0106887i
\(650\) 5.36884e12i 1.17970i
\(651\) −1.41271e12 3.41058e12i −0.308275 0.744241i
\(652\) 1.44801e13 + 5.99784e12i 3.13802 + 1.29981i
\(653\) 8.34683e11 2.01510e12i 0.179644 0.433699i −0.808248 0.588842i \(-0.799584\pi\)
0.987892 + 0.155143i \(0.0495840\pi\)
\(654\) −1.47500e12 + 1.47500e12i −0.315276 + 0.315276i
\(655\) 3.85561e11 3.85561e11i 0.0818478 0.0818478i
\(656\) 1.33912e12 3.23293e12i 0.282328 0.681600i
\(657\) 1.36833e12 + 5.66781e11i 0.286515 + 0.118678i
\(658\) 1.51142e11 + 3.64889e11i 0.0314318 + 0.0758830i
\(659\) 8.86604e12i 1.83124i −0.402045 0.915620i \(-0.631700\pi\)
0.402045 0.915620i \(-0.368300\pi\)
\(660\) 5.18206e11 2.14648e11i 0.106305 0.0440331i
\(661\) −7.07032e10 7.07032e10i −0.0144056 0.0144056i 0.699867 0.714273i \(-0.253242\pi\)
−0.714273 + 0.699867i \(0.753242\pi\)
\(662\) −7.37538e12 −1.49253
\(663\) 1.07871e12 2.91612e12i 0.216816 0.586131i
\(664\) 2.68924e12 0.536876
\(665\) 2.32501e12 + 2.32501e12i 0.461029 + 0.461029i
\(666\) −7.20743e11 + 2.98542e11i −0.141954 + 0.0587991i
\(667\) 2.28658e12i 0.447322i
\(668\) 4.25022e12 + 1.02609e13i 0.825881 + 1.99385i
\(669\) −3.98257e12 1.64963e12i −0.768680 0.318398i
\(670\) −1.47821e12 + 3.56872e12i −0.283401 + 0.684189i
\(671\) 3.79340e11 3.79340e11i 0.0722398 0.0722398i
\(672\) 2.33917e13 2.33917e13i 4.42486 4.42486i
\(673\) −2.50686e12 + 6.05210e12i −0.471045 + 1.13720i 0.492657 + 0.870224i \(0.336026\pi\)
−0.963702 + 0.266980i \(0.913974\pi\)
\(674\) −7.15155e12 2.96227e12i −1.33485 0.552911i
\(675\) −1.89607e12 4.57751e12i −0.351549 0.848716i
\(676\) 7.55419e12i 1.39132i
\(677\) −6.79952e11 + 2.81645e11i −0.124403 + 0.0515292i −0.444016 0.896019i \(-0.646447\pi\)
0.319614 + 0.947548i \(0.396447\pi\)
\(678\) 6.35932e12 + 6.35932e12i 1.15579 + 1.15579i
\(679\) 1.78360e12 0.322020
\(680\) −3.15825e12 6.86653e12i −0.566444 1.23154i
\(681\) −7.09322e12 −1.26381
\(682\) −5.35123e11 5.35123e11i −0.0947161 0.0947161i
\(683\) 6.37198e12 2.63936e12i 1.12042 0.464093i 0.255906 0.966702i \(-0.417626\pi\)
0.864514 + 0.502608i \(0.167626\pi\)
\(684\) 3.79585e12i 0.663066i
\(685\) −3.80925e11 9.19633e11i −0.0661046 0.159591i
\(686\) −1.01619e13 4.20919e12i −1.75193 0.725672i
\(687\) 7.12430e11 1.71996e12i 0.122022 0.294586i
\(688\) −2.79075e13 + 2.79075e13i −4.74868 + 4.74868i
\(689\) 2.54916e12 2.54916e12i 0.430934 0.430934i
\(690\) −5.45492e11 + 1.31693e12i −0.0916152 + 0.221179i
\(691\) −7.42149e12 3.07408e12i −1.23834 0.512937i −0.335144 0.942167i \(-0.608785\pi\)
−0.903195 + 0.429230i \(0.858785\pi\)
\(692\) 2.01191e12 + 4.85718e12i 0.333527 + 0.805206i
\(693\) 2.66929e11i 0.0439639i
\(694\) 1.96602e13 8.14353e12i 3.21715 1.33259i
\(695\) −1.32997e12 1.32997e12i −0.216227 0.216227i
\(696\) 2.37014e13 3.82853
\(697\) −1.02758e12 + 4.72632e11i −0.164918 + 0.0758536i
\(698\) 2.26568e13 3.61284
\(699\) 1.75624e12 + 1.75624e12i 0.278252 + 0.278252i
\(700\) 2.26246e13 9.37141e12i 3.56155 1.47524i
\(701\) 2.02365e12i 0.316522i 0.987397 + 0.158261i \(0.0505887\pi\)
−0.987397 + 0.158261i \(0.949411\pi\)
\(702\) 3.67768e12 + 8.87869e12i 0.571553 + 1.37985i
\(703\) 2.19774e12 + 9.10335e11i 0.339374 + 0.140573i
\(704\) 1.36817e12 3.30306e12i 0.209925 0.506803i
\(705\) 4.10180e10 4.10180e10i 0.00625350 0.00625350i
\(706\) −1.47408e13 + 1.47408e13i −2.23306 + 2.23306i
\(707\) −1.17835e12 + 2.84479e12i −0.177373 + 0.428216i
\(708\) 3.51943e12 + 1.45780e12i 0.526408 + 0.218045i
\(709\) −6.98393e11 1.68607e12i −0.103799 0.250592i 0.863444 0.504444i \(-0.168302\pi\)
−0.967243 + 0.253852i \(0.918302\pi\)
\(710\) 4.56716e12i 0.674502i
\(711\) −1.78923e12 + 7.41124e11i −0.262575 + 0.108762i
\(712\) −2.81576e13 2.81576e13i −4.10616 4.10616i
\(713\) 1.41781e12 0.205454
\(714\) −1.92234e13 + 7.38485e11i −2.76814 + 0.106341i
\(715\) −2.31184e11 −0.0330811
\(716\) 3.40135e12 + 3.40135e12i 0.483663 + 0.483663i
\(717\) −3.33002e12 + 1.37934e12i −0.470555 + 0.194910i
\(718\) 2.02359e13i 2.84159i
\(719\) 4.11483e12 + 9.93408e12i 0.574211 + 1.38627i 0.897939 + 0.440119i \(0.145064\pi\)
−0.323728 + 0.946150i \(0.604936\pi\)
\(720\) 2.34642e12 + 9.71919e11i 0.325394 + 0.134783i
\(721\) −4.63135e12 + 1.11811e13i −0.638262 + 1.54090i
\(722\) −1.03052e12 + 1.03052e12i −0.141137 + 0.141137i
\(723\) 8.33182e11 8.33182e11i 0.113401 0.113401i
\(724\) 9.62833e12 2.32448e13i 1.30235 3.14415i
\(725\) 7.23059e12 + 2.99501e12i 0.971969 + 0.402603i
\(726\) 4.84675e12 + 1.17011e13i 0.647494 + 1.56319i
\(727\) 3.46261e10i 0.00459726i 0.999997 + 0.00229863i \(0.000731677\pi\)
−0.999997 + 0.00229863i \(0.999268\pi\)
\(728\) −2.82401e13 + 1.16975e13i −3.72628 + 1.54348i
\(729\) −5.99793e12 5.99793e12i −0.786552 0.786552i
\(730\) 7.93659e12 1.03438
\(731\) 1.27474e13 4.89703e11i 1.65117 0.0634314i
\(732\) −1.61888e13 −2.08408
\(733\) 5.45453e12 + 5.45453e12i 0.697894 + 0.697894i 0.963956 0.266062i \(-0.0857225\pi\)
−0.266062 + 0.963956i \(0.585723\pi\)
\(734\) 4.54751e12 1.88364e12i 0.578284 0.239533i
\(735\) 4.29648e12i 0.543025i
\(736\) 4.86208e12 + 1.17381e13i 0.610762 + 1.47451i
\(737\) 8.83416e11 + 3.65923e11i 0.110296 + 0.0456863i
\(738\) 2.45841e11 5.93512e11i 0.0305070 0.0736505i
\(739\) −3.67021e12 + 3.67021e12i −0.452680 + 0.452680i −0.896243 0.443563i \(-0.853714\pi\)
0.443563 + 0.896243i \(0.353714\pi\)
\(740\) −2.17920e12 + 2.17920e12i −0.267149 + 0.267149i
\(741\) 2.06072e12 4.97501e12i 0.251094 0.606195i
\(742\) −2.06074e13 8.53587e12i −2.49578 1.03378i
\(743\) 5.06436e12 + 1.22264e13i 0.609642 + 1.47180i 0.863391 + 0.504535i \(0.168336\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(744\) 1.46962e13i 1.75844i
\(745\) 3.98500e12 1.65064e12i 0.473942 0.196313i
\(746\) 1.44446e13 + 1.44446e13i 1.70757 + 1.70757i
\(747\) 2.92089e11 0.0343220
\(748\) −2.64133e12 + 1.21488e12i −0.308508 + 0.141898i
\(749\) 6.55422e12 0.760945
\(750\) −7.49989e12 7.49989e12i −0.865525 0.865525i
\(751\) −7.67079e12 + 3.17735e12i −0.879955 + 0.364489i −0.776479 0.630143i \(-0.782996\pi\)
−0.103476 + 0.994632i \(0.532996\pi\)
\(752\) 9.30234e11i 0.106075i
\(753\) −8.30739e11 2.00558e12i −0.0941645 0.227333i
\(754\) −1.40247e13 5.80922e12i −1.58024 0.654556i
\(755\) 7.57046e11 1.82767e12i 0.0847931 0.204709i
\(756\) 3.09958e13 3.09958e13i 3.45108 3.45108i
\(757\) 7.21628e12 7.21628e12i 0.798697 0.798697i −0.184193 0.982890i \(-0.558967\pi\)
0.982890 + 0.184193i \(0.0589672\pi\)
\(758\) 5.53774e12 1.33693e13i 0.609286 1.47095i
\(759\) 3.25999e11 + 1.35033e11i 0.0356556 + 0.0147690i
\(760\) &min