Properties

Label 17.10.d.a.2.2
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 2.2
Character \(\chi\) \(=\) 17.2
Dual form 17.10.d.a.9.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-24.8024 - 24.8024i) q^{2} +(109.545 - 45.3751i) q^{3} +718.321i q^{4} +(-625.855 - 1510.95i) q^{5} +(-3842.40 - 1591.57i) q^{6} +(4127.23 - 9964.00i) q^{7} +(5117.27 - 5117.27i) q^{8} +(-3976.74 + 3976.74i) q^{9} +O(q^{10})\) \(q+(-24.8024 - 24.8024i) q^{2} +(109.545 - 45.3751i) q^{3} +718.321i q^{4} +(-625.855 - 1510.95i) q^{5} +(-3842.40 - 1591.57i) q^{6} +(4127.23 - 9964.00i) q^{7} +(5117.27 - 5117.27i) q^{8} +(-3976.74 + 3976.74i) q^{9} +(-21952.5 + 52997.9i) q^{10} +(-19583.8 - 8111.87i) q^{11} +(32593.9 + 78688.6i) q^{12} +71034.1i q^{13} +(-349497. + 144766. i) q^{14} +(-137119. - 137119. i) q^{15} +113939. q^{16} +(44144.3 + 341525. i) q^{17} +197266. q^{18} +(-169075. - 169075. i) q^{19} +(1.08535e6 - 449565. i) q^{20} -1.27878e6i q^{21} +(284531. + 686920. i) q^{22} +(-2.18834e6 - 906442. i) q^{23} +(328376. - 792769. i) q^{24} +(-510200. + 510200. i) q^{25} +(1.76182e6 - 1.76182e6i) q^{26} +(-1.14831e6 + 2.77225e6i) q^{27} +(7.15736e6 + 2.96467e6i) q^{28} +(-527782. - 1.27418e6i) q^{29} +6.80176e6i q^{30} +(4.36823e6 - 1.80938e6i) q^{31} +(-5.44601e6 - 5.44601e6i) q^{32} -2.51339e6 q^{33} +(7.37576e6 - 9.56553e6i) q^{34} -1.76381e7 q^{35} +(-2.85658e6 - 2.85658e6i) q^{36} +(9.68365e6 - 4.01110e6i) q^{37} +8.38694e6i q^{38} +(3.22318e6 + 7.78144e6i) q^{39} +(-1.09346e7 - 4.52926e6i) q^{40} +(2.76380e6 - 6.67241e6i) q^{41} +(-3.17169e7 + 3.17169e7i) q^{42} +(-7.19816e6 + 7.19816e6i) q^{43} +(5.82693e6 - 1.40675e7i) q^{44} +(8.49751e6 + 3.51978e6i) q^{45} +(3.17943e7 + 7.67582e7i) q^{46} -4.00577e7i q^{47} +(1.24815e7 - 5.16999e6i) q^{48} +(-5.37131e7 - 5.37131e7i) q^{49} +2.53084e7 q^{50} +(2.03325e7 + 3.54093e7i) q^{51} -5.10253e7 q^{52} +(1.56564e7 + 1.56564e7i) q^{53} +(9.72394e7 - 4.02779e7i) q^{54} +3.46669e7i q^{55} +(-2.98684e7 - 7.21087e7i) q^{56} +(-2.61931e7 - 1.08496e7i) q^{57} +(-1.85124e7 + 4.46930e7i) q^{58} +(6.99342e7 - 6.99342e7i) q^{59} +(9.84954e7 - 9.84954e7i) q^{60} +(8.20876e7 - 1.98177e8i) q^{61} +(-1.53220e8 - 6.34657e7i) q^{62} +(2.32113e7 + 5.60371e7i) q^{63} +2.11812e8i q^{64} +(1.07329e8 - 4.44571e7i) q^{65} +(6.23381e7 + 6.23381e7i) q^{66} -1.65755e8 q^{67} +(-2.45325e8 + 3.17098e7i) q^{68} -2.80852e8 q^{69} +(4.37469e8 + 4.37469e8i) q^{70} +(-2.39377e7 + 9.91532e6i) q^{71} +4.07001e7i q^{72} +(1.39914e8 + 3.37781e8i) q^{73} +(-3.39663e8 - 1.40693e8i) q^{74} +(-3.27396e7 + 7.90404e7i) q^{75} +(1.21450e8 - 1.21450e8i) q^{76} +(-1.61653e8 + 1.61653e8i) q^{77} +(1.13056e8 - 2.72941e8i) q^{78} +(-5.05614e8 - 2.09432e8i) q^{79} +(-7.13092e7 - 1.72156e8i) q^{80} +2.45095e8i q^{81} +(-2.34041e8 + 9.69430e7i) q^{82} +(-4.08040e8 - 4.08040e8i) q^{83} +9.18576e8 q^{84} +(4.88398e8 - 2.80445e8i) q^{85} +3.57064e8 q^{86} +(-1.15632e8 - 1.15632e8i) q^{87} +(-1.41726e8 + 5.87049e7i) q^{88} +3.72848e7i q^{89} +(-1.23460e8 - 2.98058e8i) q^{90} +(7.07784e8 + 2.93174e8i) q^{91} +(6.51116e8 - 1.57193e9i) q^{92} +(3.96418e8 - 3.96418e8i) q^{93} +(-9.93530e8 + 9.93530e8i) q^{94} +(-1.49647e8 + 3.61280e8i) q^{95} +(-8.43697e8 - 3.49471e8i) q^{96} +(3.40284e8 + 8.21518e8i) q^{97} +2.66443e9i q^{98} +(1.10138e8 - 4.56208e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} + O(q^{10}) \) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} - 117636q^{10} - 115768q^{11} - 145528q^{12} + 463660q^{14} + 288244q^{15} - 3407880q^{16} - 271932q^{17} + 2193336q^{18} - 406700q^{19} + 493564q^{20} + 800964q^{22} - 4172180q^{23} + 15078440q^{24} + 11946576q^{25} - 14209012q^{26} - 7973656q^{27} + 13540804q^{28} + 7833752q^{29} + 5936252q^{31} - 26730116q^{32} - 1635208q^{33} - 53493988q^{34} + 46992776q^{35} - 12761764q^{36} + 74606796q^{37} + 74096776q^{39} - 69317672q^{40} - 71362288q^{41} - 308117664q^{42} - 3765712q^{43} + 163659820q^{44} + 14167408q^{45} + 72135428q^{46} + 164621412q^{48} - 284548508q^{49} + 226223888q^{50} - 406733132q^{51} + 103553016q^{52} - 244724728q^{53} + 971226260q^{54} + 470691652q^{56} - 440646580q^{57} - 308561768q^{58} - 481734984q^{59} + 379626176q^{60} + 507966228q^{61} + 358867236q^{62} + 1070586456q^{63} + 366263684q^{65} - 2244715148q^{66} - 311910088q^{67} - 1839196668q^{68} + 533688136q^{69} + 34867672q^{70} + 186006812q^{71} + 487115192q^{73} - 214149412q^{74} + 533015920q^{75} + 1104236912q^{76} - 237869092q^{77} - 2081523384q^{78} - 136338052q^{79} - 922534152q^{80} + 1951892384q^{82} + 1843663888q^{83} - 2630025952q^{84} - 395061976q^{85} + 1538547296q^{86} - 369395636q^{87} - 3388839640q^{88} + 874363684q^{90} + 2087197720q^{91} + 1061427500q^{92} + 576415420q^{93} + 6899365112q^{94} + 5031766876q^{95} + 490811364q^{96} - 3419996368q^{97} - 5630536112q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −24.8024 24.8024i −1.09612 1.09612i −0.994860 0.101263i \(-0.967712\pi\)
−0.101263 0.994860i \(-0.532288\pi\)
\(3\) 109.545 45.3751i 0.780814 0.323424i 0.0435700 0.999050i \(-0.486127\pi\)
0.737244 + 0.675627i \(0.236127\pi\)
\(4\) 718.321i 1.40297i
\(5\) −625.855 1510.95i −0.447825 1.08115i −0.973135 0.230235i \(-0.926051\pi\)
0.525310 0.850911i \(-0.323949\pi\)
\(6\) −3842.40 1591.57i −1.21038 0.501356i
\(7\) 4127.23 9964.00i 0.649706 1.56853i −0.163493 0.986544i \(-0.552276\pi\)
0.813199 0.581985i \(-0.197724\pi\)
\(8\) 5117.27 5117.27i 0.441706 0.441706i
\(9\) −3976.74 + 3976.74i −0.202039 + 0.202039i
\(10\) −21952.5 + 52997.9i −0.694197 + 1.67594i
\(11\) −19583.8 8111.87i −0.403301 0.167053i 0.171806 0.985131i \(-0.445040\pi\)
−0.575107 + 0.818078i \(0.695040\pi\)
\(12\) 32593.9 + 78688.6i 0.453754 + 1.09546i
\(13\) 71034.1i 0.689798i 0.938640 + 0.344899i \(0.112087\pi\)
−0.938640 + 0.344899i \(0.887913\pi\)
\(14\) −349497. + 144766.i −2.43146 + 1.00714i
\(15\) −137119. 137119.i −0.699337 0.699337i
\(16\) 113939. 0.434642
\(17\) 44144.3 + 341525.i 0.128190 + 0.991750i
\(18\) 197266. 0.442920
\(19\) −169075. 169075.i −0.297638 0.297638i 0.542450 0.840088i \(-0.317497\pi\)
−0.840088 + 0.542450i \(0.817497\pi\)
\(20\) 1.08535e6 449565.i 1.51682 0.628286i
\(21\) 1.27878e6i 1.43486i
\(22\) 284531. + 686920.i 0.258957 + 0.625178i
\(23\) −2.18834e6 906442.i −1.63057 0.675405i −0.635277 0.772285i \(-0.719114\pi\)
−0.995296 + 0.0968792i \(0.969114\pi\)
\(24\) 328376. 792769.i 0.202032 0.487749i
\(25\) −510200. + 510200.i −0.261223 + 0.261223i
\(26\) 1.76182e6 1.76182e6i 0.756103 0.756103i
\(27\) −1.14831e6 + 2.77225e6i −0.415835 + 1.00391i
\(28\) 7.15736e6 + 2.96467e6i 2.20060 + 0.911519i
\(29\) −527782. 1.27418e6i −0.138568 0.334533i 0.839328 0.543626i \(-0.182949\pi\)
−0.977896 + 0.209093i \(0.932949\pi\)
\(30\) 6.80176e6i 1.53312i
\(31\) 4.36823e6 1.80938e6i 0.849528 0.351886i 0.0849250 0.996387i \(-0.472935\pi\)
0.764603 + 0.644501i \(0.222935\pi\)
\(32\) −5.44601e6 5.44601e6i −0.918128 0.918128i
\(33\) −2.51339e6 −0.368932
\(34\) 7.37576e6 9.56553e6i 0.946568 1.22759i
\(35\) −1.76381e7 −1.98676
\(36\) −2.85658e6 2.85658e6i −0.283455 0.283455i
\(37\) 9.68365e6 4.01110e6i 0.849437 0.351848i 0.0848697 0.996392i \(-0.472953\pi\)
0.764567 + 0.644544i \(0.222953\pi\)
\(38\) 8.38694e6i 0.652495i
\(39\) 3.22318e6 + 7.78144e6i 0.223097 + 0.538604i
\(40\) −1.09346e7 4.52926e6i −0.675357 0.279742i
\(41\) 2.76380e6 6.67241e6i 0.152749 0.368770i −0.828918 0.559370i \(-0.811043\pi\)
0.981668 + 0.190600i \(0.0610433\pi\)
\(42\) −3.17169e7 + 3.17169e7i −1.57278 + 1.57278i
\(43\) −7.19816e6 + 7.19816e6i −0.321080 + 0.321080i −0.849181 0.528101i \(-0.822904\pi\)
0.528101 + 0.849181i \(0.322904\pi\)
\(44\) 5.82693e6 1.40675e7i 0.234370 0.565820i
\(45\) 8.49751e6 + 3.51978e6i 0.308912 + 0.127956i
\(46\) 3.17943e7 + 7.67582e7i 1.04698 + 2.52764i
\(47\) 4.00577e7i 1.19742i −0.800966 0.598709i \(-0.795680\pi\)
0.800966 0.598709i \(-0.204320\pi\)
\(48\) 1.24815e7 5.16999e6i 0.339375 0.140574i
\(49\) −5.37131e7 5.37131e7i −1.33106 1.33106i
\(50\) 2.53084e7 0.572664
\(51\) 2.03325e7 + 3.54093e7i 0.420848 + 0.732912i
\(52\) −5.10253e7 −0.967767
\(53\) 1.56564e7 + 1.56564e7i 0.272552 + 0.272552i 0.830127 0.557575i \(-0.188268\pi\)
−0.557575 + 0.830127i \(0.688268\pi\)
\(54\) 9.72394e7 4.02779e7i 1.55622 0.644607i
\(55\) 3.46669e7i 0.510838i
\(56\) −2.98684e7 7.21087e7i −0.405850 0.979809i
\(57\) −2.61931e7 1.08496e7i −0.328663 0.136137i
\(58\) −1.85124e7 + 4.46930e7i −0.214802 + 0.518577i
\(59\) 6.99342e7 6.99342e7i 0.751373 0.751373i −0.223362 0.974735i \(-0.571703\pi\)
0.974735 + 0.223362i \(0.0717033\pi\)
\(60\) 9.84954e7 9.84954e7i 0.981149 0.981149i
\(61\) 8.20876e7 1.98177e8i 0.759090 1.83260i 0.261462 0.965214i \(-0.415796\pi\)
0.497628 0.867391i \(-0.334204\pi\)
\(62\) −1.53220e8 6.34657e7i −1.31690 0.545477i
\(63\) 2.32113e7 + 5.60371e7i 0.185638 + 0.448171i
\(64\) 2.11812e8i 1.57812i
\(65\) 1.07329e8 4.44571e7i 0.745772 0.308909i
\(66\) 6.23381e7 + 6.23381e7i 0.404395 + 0.404395i
\(67\) −1.65755e8 −1.00492 −0.502458 0.864602i \(-0.667571\pi\)
−0.502458 + 0.864602i \(0.667571\pi\)
\(68\) −2.45325e8 + 3.17098e7i −1.39140 + 0.179847i
\(69\) −2.80852e8 −1.49162
\(70\) 4.37469e8 + 4.37469e8i 2.17774 + 2.17774i
\(71\) −2.39377e7 + 9.91532e6i −0.111794 + 0.0463067i −0.437880 0.899034i \(-0.644270\pi\)
0.326085 + 0.945340i \(0.394270\pi\)
\(72\) 4.07001e7i 0.178484i
\(73\) 1.39914e8 + 3.37781e8i 0.576643 + 1.39214i 0.895808 + 0.444441i \(0.146598\pi\)
−0.319165 + 0.947699i \(0.603402\pi\)
\(74\) −3.39663e8 1.40693e8i −1.31676 0.545419i
\(75\) −3.27396e7 + 7.90404e7i −0.119481 + 0.288452i
\(76\) 1.21450e8 1.21450e8i 0.417577 0.417577i
\(77\) −1.61653e8 + 1.61653e8i −0.524055 + 0.524055i
\(78\) 1.13056e8 2.72941e8i 0.345834 0.834918i
\(79\) −5.05614e8 2.09432e8i −1.46049 0.604953i −0.495819 0.868426i \(-0.665132\pi\)
−0.964667 + 0.263473i \(0.915132\pi\)
\(80\) −7.13092e7 1.72156e8i −0.194644 0.469912i
\(81\) 2.45095e8i 0.632634i
\(82\) −2.34041e8 + 9.69430e7i −0.571649 + 0.236785i
\(83\) −4.08040e8 4.08040e8i −0.943737 0.943737i 0.0547622 0.998499i \(-0.482560\pi\)
−0.998499 + 0.0547622i \(0.982560\pi\)
\(84\) 9.18576e8 2.01307
\(85\) 4.88398e8 2.80445e8i 1.01482 0.582723i
\(86\) 3.57064e8 0.703887
\(87\) −1.15632e8 1.15632e8i −0.216392 0.216392i
\(88\) −1.41726e8 + 5.87049e7i −0.251929 + 0.104352i
\(89\) 3.72848e7i 0.0629908i 0.999504 + 0.0314954i \(0.0100270\pi\)
−0.999504 + 0.0314954i \(0.989973\pi\)
\(90\) −1.23460e8 2.98058e8i −0.198351 0.478861i
\(91\) 7.07784e8 + 2.93174e8i 1.08197 + 0.448166i
\(92\) 6.51116e8 1.57193e9i 0.947575 2.28765i
\(93\) 3.96418e8 3.96418e8i 0.549515 0.549515i
\(94\) −9.93530e8 + 9.93530e8i −1.31252 + 1.31252i
\(95\) −1.49647e8 + 3.61280e8i −0.188500 + 0.455080i
\(96\) −8.43697e8 3.49471e8i −1.01383 0.419943i
\(97\) 3.40284e8 + 8.21518e8i 0.390273 + 0.942202i 0.989880 + 0.141908i \(0.0453236\pi\)
−0.599607 + 0.800295i \(0.704676\pi\)
\(98\) 2.66443e9i 2.91801i
\(99\) 1.10138e8 4.56208e7i 0.115234 0.0477315i
\(100\) −3.66488e8 3.66488e8i −0.366488 0.366488i
\(101\) 1.51590e9 1.44952 0.724760 0.689002i \(-0.241951\pi\)
0.724760 + 0.689002i \(0.241951\pi\)
\(102\) 3.73942e8 1.38253e9i 0.342061 1.26466i
\(103\) 4.65778e8 0.407766 0.203883 0.978995i \(-0.434644\pi\)
0.203883 + 0.978995i \(0.434644\pi\)
\(104\) 3.63501e8 + 3.63501e8i 0.304688 + 0.304688i
\(105\) −1.93217e9 + 8.00332e8i −1.55129 + 0.642567i
\(106\) 7.76632e8i 0.597501i
\(107\) −7.21884e8 1.74278e9i −0.532403 1.28533i −0.929928 0.367742i \(-0.880131\pi\)
0.397525 0.917591i \(-0.369869\pi\)
\(108\) −1.99137e9 8.24853e8i −1.40846 0.583404i
\(109\) −2.25360e8 + 5.44066e8i −0.152917 + 0.369175i −0.981711 0.190380i \(-0.939028\pi\)
0.828793 + 0.559555i \(0.189028\pi\)
\(110\) 8.59824e8 8.59824e8i 0.559941 0.559941i
\(111\) 8.78793e8 8.78793e8i 0.549456 0.549456i
\(112\) 4.70251e8 1.13529e9i 0.282390 0.681749i
\(113\) 1.35371e9 + 5.60727e8i 0.781041 + 0.323518i 0.737336 0.675527i \(-0.236084\pi\)
0.0437055 + 0.999044i \(0.486084\pi\)
\(114\) 3.80558e8 + 9.18749e8i 0.211032 + 0.509477i
\(115\) 3.87377e9i 2.06535i
\(116\) 9.15269e8 3.79117e8i 0.469340 0.194407i
\(117\) −2.82484e8 2.82484e8i −0.139366 0.139366i
\(118\) −3.46908e9 −1.64720
\(119\) 3.58515e9 + 9.69696e8i 1.63887 + 0.443276i
\(120\) −1.40335e9 −0.617803
\(121\) −1.34960e9 1.34960e9i −0.572362 0.572362i
\(122\) −6.95124e9 + 2.87930e9i −2.84082 + 1.17670i
\(123\) 8.56338e8i 0.337343i
\(124\) 1.29972e9 + 3.13779e9i 0.493686 + 1.19186i
\(125\) −1.86087e9 7.70799e8i −0.681744 0.282388i
\(126\) 8.14160e8 1.96556e9i 0.287768 0.694733i
\(127\) 2.03480e9 2.03480e9i 0.694072 0.694072i −0.269053 0.963125i \(-0.586711\pi\)
0.963125 + 0.269053i \(0.0867107\pi\)
\(128\) 2.46509e9 2.46509e9i 0.811686 0.811686i
\(129\) −4.61906e8 + 1.11514e9i −0.146859 + 0.354549i
\(130\) −3.76466e9 1.55937e9i −1.15606 0.478856i
\(131\) 2.18755e9 + 5.28122e9i 0.648989 + 1.56680i 0.814228 + 0.580545i \(0.197161\pi\)
−0.165238 + 0.986254i \(0.552839\pi\)
\(132\) 1.80542e9i 0.517601i
\(133\) −2.38247e9 + 9.86853e8i −0.660231 + 0.273477i
\(134\) 4.11113e9 + 4.11113e9i 1.10151 + 1.10151i
\(135\) 4.90740e9 1.27160
\(136\) 1.97357e9 + 1.52178e9i 0.494685 + 0.381440i
\(137\) −2.50282e9 −0.606997 −0.303499 0.952832i \(-0.598155\pi\)
−0.303499 + 0.952832i \(0.598155\pi\)
\(138\) 6.96582e9 + 6.96582e9i 1.63499 + 1.63499i
\(139\) 7.47729e8 3.09720e8i 0.169894 0.0703724i −0.296115 0.955152i \(-0.595691\pi\)
0.466009 + 0.884780i \(0.345691\pi\)
\(140\) 1.26699e10i 2.78737i
\(141\) −1.81762e9 4.38813e9i −0.387274 0.934961i
\(142\) 8.39637e8 + 3.47789e8i 0.173298 + 0.0717825i
\(143\) 5.76219e8 1.39112e9i 0.115233 0.278196i
\(144\) −4.53105e8 + 4.53105e8i −0.0878148 + 0.0878148i
\(145\) −1.59490e9 + 1.59490e9i −0.299625 + 0.299625i
\(146\) 4.90760e9 1.18480e10i 0.893885 2.15803i
\(147\) −8.32125e9 3.44677e9i −1.46981 0.608814i
\(148\) 2.88126e9 + 6.95597e9i 0.493633 + 1.19174i
\(149\) 4.26492e9i 0.708880i −0.935079 0.354440i \(-0.884672\pi\)
0.935079 0.354440i \(-0.115328\pi\)
\(150\) 2.77241e9 1.14837e9i 0.447144 0.185213i
\(151\) −5.94802e9 5.94802e9i −0.931057 0.931057i 0.0667151 0.997772i \(-0.478748\pi\)
−0.997772 + 0.0667151i \(0.978748\pi\)
\(152\) −1.73041e9 −0.262937
\(153\) −1.53371e9 1.18260e9i −0.226272 0.174473i
\(154\) 8.01880e9 1.14886
\(155\) −5.46776e9 5.46776e9i −0.760881 0.760881i
\(156\) −5.58958e9 + 2.31528e9i −0.755646 + 0.312999i
\(157\) 1.40154e9i 0.184101i 0.995754 + 0.0920504i \(0.0293421\pi\)
−0.995754 + 0.0920504i \(0.970658\pi\)
\(158\) 7.34603e9 + 1.77349e10i 0.937769 + 2.26398i
\(159\) 2.42549e9 + 1.00467e9i 0.300962 + 0.124663i
\(160\) −4.82022e9 + 1.16370e10i −0.581469 + 1.40379i
\(161\) −1.80636e10 + 1.80636e10i −2.11879 + 2.11879i
\(162\) 6.07896e9 6.07896e9i 0.693444 0.693444i
\(163\) 3.54778e9 8.56510e9i 0.393652 0.950360i −0.595485 0.803366i \(-0.703040\pi\)
0.989137 0.146994i \(-0.0469598\pi\)
\(164\) 4.79294e9 + 1.98530e9i 0.517374 + 0.214303i
\(165\) 1.57302e9 + 3.79759e9i 0.165217 + 0.398870i
\(166\) 2.02408e10i 2.06890i
\(167\) 1.25459e10 5.19667e9i 1.24818 0.517012i 0.341917 0.939730i \(-0.388924\pi\)
0.906261 + 0.422718i \(0.138924\pi\)
\(168\) −6.54388e9 6.54388e9i −0.633787 0.633787i
\(169\) 5.55865e9 0.524179
\(170\) −1.90692e10 5.15775e9i −1.75110 0.473631i
\(171\) 1.34473e9 0.120269
\(172\) −5.17059e9 5.17059e9i −0.450466 0.450466i
\(173\) −6.12568e9 + 2.53734e9i −0.519933 + 0.215363i −0.627187 0.778868i \(-0.715794\pi\)
0.107255 + 0.994232i \(0.465794\pi\)
\(174\) 5.73590e9i 0.474384i
\(175\) 2.97793e9 + 7.18935e9i 0.240017 + 0.579453i
\(176\) −2.23135e9 9.24257e8i −0.175292 0.0726082i
\(177\) 4.48768e9 1.08342e10i 0.343671 0.829695i
\(178\) 9.24754e8 9.24754e8i 0.0690457 0.0690457i
\(179\) −3.07298e9 + 3.07298e9i −0.223728 + 0.223728i −0.810066 0.586338i \(-0.800569\pi\)
0.586338 + 0.810066i \(0.300569\pi\)
\(180\) −2.52833e9 + 6.10394e9i −0.179518 + 0.433395i
\(181\) 1.22430e10 + 5.07121e9i 0.847879 + 0.351203i 0.763955 0.645269i \(-0.223255\pi\)
0.0839235 + 0.996472i \(0.473255\pi\)
\(182\) −1.02833e10 2.48262e10i −0.694726 1.67722i
\(183\) 2.54340e10i 1.67643i
\(184\) −1.58369e10 + 6.55984e9i −1.01857 + 0.421904i
\(185\) −1.21211e10 1.21211e10i −0.760799 0.760799i
\(186\) −1.96642e10 −1.20467
\(187\) 1.90589e9 7.04644e9i 0.113975 0.421388i
\(188\) 2.87743e10 1.67994
\(189\) 2.28834e10 + 2.28834e10i 1.30450 + 1.30450i
\(190\) 1.26722e10 5.24901e9i 0.705443 0.292204i
\(191\) 4.77283e8i 0.0259493i 0.999916 + 0.0129746i \(0.00413007\pi\)
−0.999916 + 0.0129746i \(0.995870\pi\)
\(192\) 9.61098e9 + 2.32029e10i 0.510401 + 1.23222i
\(193\) 1.28054e10 + 5.30418e9i 0.664334 + 0.275176i 0.689261 0.724513i \(-0.257935\pi\)
−0.0249272 + 0.999689i \(0.507935\pi\)
\(194\) 1.19358e10 2.88155e10i 0.604982 1.46056i
\(195\) 9.74011e9 9.74011e9i 0.482401 0.482401i
\(196\) 3.85833e10 3.85833e10i 1.86744 1.86744i
\(197\) −1.08300e10 + 2.61460e10i −0.512309 + 1.23682i 0.430227 + 0.902721i \(0.358433\pi\)
−0.942537 + 0.334103i \(0.891567\pi\)
\(198\) −3.86321e9 1.60019e9i −0.178630 0.0739910i
\(199\) 9.56462e9 + 2.30910e10i 0.432343 + 1.04377i 0.978530 + 0.206105i \(0.0660790\pi\)
−0.546187 + 0.837664i \(0.683921\pi\)
\(200\) 5.22167e9i 0.230767i
\(201\) −1.81577e10 + 7.52115e9i −0.784653 + 0.325014i
\(202\) −3.75980e10 3.75980e10i −1.58885 1.58885i
\(203\) −1.48742e10 −0.614753
\(204\) −2.54353e10 + 1.46053e10i −1.02826 + 0.590438i
\(205\) −1.18114e10 −0.467099
\(206\) −1.15524e10 1.15524e10i −0.446962 0.446962i
\(207\) 1.23072e10 5.09779e9i 0.465898 0.192981i
\(208\) 8.09355e9i 0.299815i
\(209\) 1.93961e9 + 4.68264e9i 0.0703165 + 0.169759i
\(210\) 6.77728e10 + 2.80724e10i 2.40474 + 0.996076i
\(211\) 6.90025e9 1.66587e10i 0.239659 0.578588i −0.757588 0.652733i \(-0.773623\pi\)
0.997248 + 0.0741442i \(0.0236225\pi\)
\(212\) −1.12463e10 + 1.12463e10i −0.382383 + 0.382383i
\(213\) −2.17235e9 + 2.17235e9i −0.0723139 + 0.0723139i
\(214\) −2.53207e10 + 6.11297e10i −0.825305 + 1.99246i
\(215\) 1.53810e10 + 6.37104e9i 0.490922 + 0.203347i
\(216\) 8.31019e9 + 2.00626e10i 0.259758 + 0.627112i
\(217\) 5.09928e10i 1.56113i
\(218\) 1.90836e10 7.90470e9i 0.572278 0.237045i
\(219\) 3.06537e10 + 3.06537e10i 0.900502 + 0.900502i
\(220\) −2.49020e10 −0.716691
\(221\) −2.42599e10 + 3.13575e9i −0.684107 + 0.0884253i
\(222\) −4.35924e10 −1.20454
\(223\) −2.33519e10 2.33519e10i −0.632339 0.632339i 0.316315 0.948654i \(-0.397554\pi\)
−0.948654 + 0.316315i \(0.897554\pi\)
\(224\) −7.67409e10 + 3.17871e10i −2.03662 + 0.843597i
\(225\) 4.05787e9i 0.105554i
\(226\) −1.96680e10 4.74828e10i −0.501502 1.21073i
\(227\) 3.38615e10 + 1.40259e10i 0.846427 + 0.350602i 0.763385 0.645944i \(-0.223536\pi\)
0.0830428 + 0.996546i \(0.473536\pi\)
\(228\) 7.79347e9 1.88151e10i 0.190996 0.461105i
\(229\) −4.09750e9 + 4.09750e9i −0.0984599 + 0.0984599i −0.754621 0.656161i \(-0.772179\pi\)
0.656161 + 0.754621i \(0.272179\pi\)
\(230\) 9.60790e10 9.60790e10i 2.26388 2.26388i
\(231\) −1.03733e10 + 2.50434e10i −0.239698 + 0.578681i
\(232\) −9.22112e9 3.81951e9i −0.208972 0.0865590i
\(233\) −2.79641e7 6.75113e7i −0.000621583 0.00150063i 0.923568 0.383434i \(-0.125259\pi\)
−0.924190 + 0.381933i \(0.875259\pi\)
\(234\) 1.40126e10i 0.305525i
\(235\) −6.05252e10 + 2.50703e10i −1.29458 + 0.536235i
\(236\) 5.02353e10 + 5.02353e10i 1.05416 + 1.05416i
\(237\) −6.48906e10 −1.33602
\(238\) −6.48696e10 1.12971e11i −1.31052 2.28229i
\(239\) 6.99325e10 1.38640 0.693200 0.720745i \(-0.256200\pi\)
0.693200 + 0.720745i \(0.256200\pi\)
\(240\) −1.56232e10 1.56232e10i −0.303961 0.303961i
\(241\) 5.42130e10 2.24558e10i 1.03521 0.428796i 0.200617 0.979670i \(-0.435705\pi\)
0.834589 + 0.550873i \(0.185705\pi\)
\(242\) 6.69467e10i 1.25476i
\(243\) −1.14809e10 2.77173e10i −0.211226 0.509944i
\(244\) 1.42355e11 + 5.89652e10i 2.57109 + 1.06498i
\(245\) −4.75411e10 + 1.14774e11i −0.842988 + 2.03515i
\(246\) −2.12393e10 + 2.12393e10i −0.369770 + 0.369770i
\(247\) 1.20101e10 1.20101e10i 0.205310 0.205310i
\(248\) 1.30943e10 3.16125e10i 0.219812 0.530673i
\(249\) −6.32136e10 2.61839e10i −1.04211 0.431656i
\(250\) 2.70365e10 + 6.52718e10i 0.437744 + 1.05681i
\(251\) 3.69311e10i 0.587300i 0.955913 + 0.293650i \(0.0948701\pi\)
−0.955913 + 0.293650i \(0.905130\pi\)
\(252\) −4.02527e10 + 1.66732e10i −0.628771 + 0.260445i
\(253\) 3.55031e10 + 3.55031e10i 0.544784 + 0.544784i
\(254\) −1.00936e11 −1.52158
\(255\) 4.07764e10 5.28825e10i 0.603919 0.783215i
\(256\) −1.38329e10 −0.201295
\(257\) 2.17662e10 + 2.17662e10i 0.311232 + 0.311232i 0.845387 0.534155i \(-0.179370\pi\)
−0.534155 + 0.845387i \(0.679370\pi\)
\(258\) 3.91146e10 1.62018e10i 0.549604 0.227654i
\(259\) 1.13043e11i 1.56097i
\(260\) 3.19345e10 + 7.70966e10i 0.433391 + 1.04630i
\(261\) 7.16592e9 + 2.96822e9i 0.0955850 + 0.0395926i
\(262\) 7.67305e10 1.85244e11i 1.00603 2.42878i
\(263\) −1.56867e10 + 1.56867e10i −0.202176 + 0.202176i −0.800932 0.598756i \(-0.795662\pi\)
0.598756 + 0.800932i \(0.295662\pi\)
\(264\) −1.28617e10 + 1.28617e10i −0.162960 + 0.162960i
\(265\) 1.38573e10 3.34546e10i 0.172613 0.416724i
\(266\) 8.35675e10 + 3.46148e10i 1.02346 + 0.423930i
\(267\) 1.69180e9 + 4.08437e9i 0.0203727 + 0.0491841i
\(268\) 1.19065e11i 1.40987i
\(269\) −5.27329e10 + 2.18427e10i −0.614039 + 0.254343i −0.667954 0.744202i \(-0.732830\pi\)
0.0539153 + 0.998546i \(0.482830\pi\)
\(270\) −1.21716e11 1.21716e11i −1.39383 1.39383i
\(271\) 3.32663e10 0.374664 0.187332 0.982297i \(-0.440016\pi\)
0.187332 + 0.982297i \(0.440016\pi\)
\(272\) 5.02975e9 + 3.89129e10i 0.0557168 + 0.431056i
\(273\) 9.08371e10 0.989764
\(274\) 6.20760e10 + 6.20760e10i 0.665343 + 0.665343i
\(275\) 1.41303e10 5.85298e9i 0.148989 0.0617134i
\(276\) 2.01742e11i 2.09270i
\(277\) 1.30958e10 + 3.16161e10i 0.133651 + 0.322663i 0.976510 0.215472i \(-0.0691290\pi\)
−0.842859 + 0.538135i \(0.819129\pi\)
\(278\) −2.62273e10 1.08637e10i −0.263361 0.109088i
\(279\) −1.01759e10 + 2.45667e10i −0.100543 + 0.242733i
\(280\) −9.02592e10 + 9.02592e10i −0.877567 + 0.877567i
\(281\) 4.73681e10 4.73681e10i 0.453218 0.453218i −0.443203 0.896421i \(-0.646158\pi\)
0.896421 + 0.443203i \(0.146158\pi\)
\(282\) −6.37549e10 + 1.53918e11i −0.600333 + 1.44933i
\(283\) 1.94262e10 + 8.04662e9i 0.180032 + 0.0745717i 0.470879 0.882198i \(-0.343937\pi\)
−0.290847 + 0.956770i \(0.593937\pi\)
\(284\) −7.12239e9 1.71950e10i −0.0649670 0.156844i
\(285\) 4.63667e10i 0.416298i
\(286\) −4.87947e10 + 2.02114e10i −0.431247 + 0.178628i
\(287\) −5.50771e10 5.50771e10i −0.479184 0.479184i
\(288\) 4.33147e10 0.370996
\(289\) −1.14690e11 + 3.01527e10i −0.967135 + 0.254265i
\(290\) 7.91148e10 0.656851
\(291\) 7.45529e10 + 7.45529e10i 0.609461 + 0.609461i
\(292\) −2.42636e11 + 1.00503e11i −1.95313 + 0.809014i
\(293\) 3.54172e10i 0.280743i −0.990099 0.140372i \(-0.955170\pi\)
0.990099 0.140372i \(-0.0448297\pi\)
\(294\) 1.20899e11 + 2.91875e11i 0.943754 + 2.27842i
\(295\) −1.49436e11 6.18983e10i −1.14883 0.475860i
\(296\) 2.90280e10 7.00798e10i 0.219788 0.530616i
\(297\) 4.49763e10 4.49763e10i 0.335413 0.335413i
\(298\) −1.05780e11 + 1.05780e11i −0.777019 + 0.777019i
\(299\) 6.43883e10 1.55447e11i 0.465893 1.12477i
\(300\) −5.67764e10 2.35176e10i −0.404690 0.167628i
\(301\) 4.20141e10 + 1.01431e11i 0.295016 + 0.712231i
\(302\) 2.95051e11i 2.04111i
\(303\) 1.66059e11 6.87840e10i 1.13180 0.468809i
\(304\) −1.92642e10 1.92642e10i −0.129366 0.129366i
\(305\) −3.50810e11 −2.32125
\(306\) 8.70815e9 + 6.73711e10i 0.0567779 + 0.439266i
\(307\) −9.48586e9 −0.0609472 −0.0304736 0.999536i \(-0.509702\pi\)
−0.0304736 + 0.999536i \(0.509702\pi\)
\(308\) −1.16119e11 1.16119e11i −0.735234 0.735234i
\(309\) 5.10237e10 2.11347e10i 0.318390 0.131881i
\(310\) 2.71227e11i 1.66804i
\(311\) −5.98731e10 1.44547e11i −0.362919 0.876165i −0.994870 0.101157i \(-0.967746\pi\)
0.631951 0.775008i \(-0.282254\pi\)
\(312\) 5.63137e10 + 2.33259e10i 0.336448 + 0.139361i
\(313\) −3.03614e10 + 7.32989e10i −0.178802 + 0.431666i −0.987716 0.156261i \(-0.950056\pi\)
0.808914 + 0.587927i \(0.200056\pi\)
\(314\) 3.47615e10 3.47615e10i 0.201797 0.201797i
\(315\) 7.01422e10 7.01422e10i 0.401404 0.401404i
\(316\) 1.50440e11 3.63194e11i 0.848732 2.04902i
\(317\) 1.16509e11 + 4.82595e10i 0.648025 + 0.268421i 0.682390 0.730989i \(-0.260941\pi\)
−0.0343645 + 0.999409i \(0.510941\pi\)
\(318\) −3.52397e10 8.50763e10i −0.193246 0.466537i
\(319\) 2.92345e10i 0.158066i
\(320\) 3.20036e11 1.32563e11i 1.70618 0.706722i
\(321\) −1.58158e11 1.58158e11i −0.831415 0.831415i
\(322\) 8.96041e11 4.64490
\(323\) 5.02796e10 6.52070e10i 0.257028 0.333336i
\(324\) −1.76057e11 −0.887567
\(325\) −3.62416e10 3.62416e10i −0.180191 0.180191i
\(326\) −3.00429e11 + 1.24442e11i −1.47320 + 0.610221i
\(327\) 6.98256e10i 0.337714i
\(328\) −2.00014e10 4.82877e10i −0.0954176 0.230358i
\(329\) −3.99136e11 1.65327e11i −1.87819 0.777971i
\(330\) 5.51750e10 1.33204e11i 0.256112 0.618308i
\(331\) −7.63569e10 + 7.63569e10i −0.349641 + 0.349641i −0.859976 0.510335i \(-0.829522\pi\)
0.510335 + 0.859976i \(0.329522\pi\)
\(332\) 2.93104e11 2.93104e11i 1.32404 1.32404i
\(333\) −2.25582e10 + 5.44604e10i −0.100532 + 0.242707i
\(334\) −4.40058e11 1.82278e11i −1.93487 0.801448i
\(335\) 1.03739e11 + 2.50447e11i 0.450027 + 1.08646i
\(336\) 1.45703e11i 0.623651i
\(337\) 2.21020e11 9.15493e10i 0.933461 0.386652i 0.136471 0.990644i \(-0.456424\pi\)
0.796990 + 0.603992i \(0.206424\pi\)
\(338\) −1.37868e11 1.37868e11i −0.574565 0.574565i
\(339\) 1.73736e11 0.714481
\(340\) 2.01449e11 + 3.50827e11i 0.817544 + 1.42376i
\(341\) −1.00224e11 −0.401399
\(342\) −3.33527e10 3.33527e10i −0.131830 0.131830i
\(343\) −3.54800e11 + 1.46963e11i −1.38408 + 0.573303i
\(344\) 7.36699e10i 0.283646i
\(345\) 1.75773e11 + 4.24353e11i 0.667984 + 1.61266i
\(346\) 2.14864e11 + 8.89996e10i 0.805975 + 0.333846i
\(347\) −5.10121e10 + 1.23154e11i −0.188882 + 0.456002i −0.989745 0.142846i \(-0.954375\pi\)
0.800863 + 0.598848i \(0.204375\pi\)
\(348\) 8.30608e10 8.30608e10i 0.303592 0.303592i
\(349\) −7.11623e10 + 7.11623e10i −0.256765 + 0.256765i −0.823737 0.566972i \(-0.808115\pi\)
0.566972 + 0.823737i \(0.308115\pi\)
\(350\) 1.04454e11 2.52173e11i 0.372063 0.898241i
\(351\) −1.96925e11 8.15689e10i −0.692497 0.286842i
\(352\) 6.24761e10 + 1.50831e11i 0.216906 + 0.523658i
\(353\) 9.24641e10i 0.316947i −0.987363 0.158474i \(-0.949343\pi\)
0.987363 0.158474i \(-0.0506573\pi\)
\(354\) −3.80021e11 + 1.57410e11i −1.28615 + 0.532742i
\(355\) 2.99631e10 + 2.99631e10i 0.100129 + 0.100129i
\(356\) −2.67825e10 −0.0883743
\(357\) 4.36736e11 5.64509e10i 1.42302 0.183935i
\(358\) 1.52435e11 0.490467
\(359\) 2.85847e11 + 2.85847e11i 0.908256 + 0.908256i 0.996131 0.0878754i \(-0.0280077\pi\)
−0.0878754 + 0.996131i \(0.528008\pi\)
\(360\) 6.14958e10 2.54724e10i 0.192967 0.0799297i
\(361\) 2.65515e11i 0.822824i
\(362\) −1.77877e11 4.29434e11i −0.544418 1.31434i
\(363\) −2.09080e11 8.66038e10i −0.632023 0.261793i
\(364\) −2.10593e11 + 5.08417e11i −0.628764 + 1.51797i
\(365\) 4.22804e11 4.22804e11i 1.24687 1.24687i
\(366\) −6.30826e11 + 6.30826e11i −1.83757 + 1.83757i
\(367\) −2.07857e11 + 5.01812e11i −0.598092 + 1.44392i 0.277432 + 0.960745i \(0.410517\pi\)
−0.875523 + 0.483176i \(0.839483\pi\)
\(368\) −2.49337e11 1.03279e11i −0.708716 0.293560i
\(369\) 1.55435e10 + 3.75254e10i 0.0436446 + 0.105367i
\(370\) 6.01267e11i 1.66786i
\(371\) 2.20617e11 9.13827e10i 0.604585 0.250427i
\(372\) 2.84755e11 + 2.84755e11i 0.770954 + 0.770954i
\(373\) −7.02135e10 −0.187815 −0.0939077 0.995581i \(-0.529936\pi\)
−0.0939077 + 0.995581i \(0.529936\pi\)
\(374\) −2.22040e11 + 1.27498e11i −0.586825 + 0.336962i
\(375\) −2.38825e11 −0.623646
\(376\) −2.04986e11 2.04986e11i −0.528908 0.528908i
\(377\) 9.05101e10 3.74905e10i 0.230760 0.0955840i
\(378\) 1.13513e12i 2.85978i
\(379\) −1.28989e11 3.11408e11i −0.321127 0.775269i −0.999189 0.0402646i \(-0.987180\pi\)
0.678062 0.735005i \(-0.262820\pi\)
\(380\) −2.59515e11 1.07495e11i −0.638464 0.264460i
\(381\) 1.30573e11 3.15232e11i 0.317462 0.766421i
\(382\) 1.18378e10 1.18378e10i 0.0284436 0.0284436i
\(383\) −1.90740e11 + 1.90740e11i −0.452946 + 0.452946i −0.896331 0.443385i \(-0.853777\pi\)
0.443385 + 0.896331i \(0.353777\pi\)
\(384\) 1.58185e11 3.81892e11i 0.371257 0.896294i
\(385\) 3.45421e11 + 1.43078e11i 0.801265 + 0.331895i
\(386\) −1.86049e11 4.49162e11i −0.426565 1.02982i
\(387\) 5.72504e10i 0.129742i
\(388\) −5.90114e11 + 2.44433e11i −1.32188 + 0.547542i
\(389\) 4.94082e11 + 4.94082e11i 1.09402 + 1.09402i 0.995095 + 0.0989263i \(0.0315408\pi\)
0.0989263 + 0.995095i \(0.468459\pi\)
\(390\) −4.83157e11 −1.05754
\(391\) 2.12969e11 7.87388e11i 0.460810 1.70370i
\(392\) −5.49729e11 −1.17588
\(393\) 4.79272e11 + 4.79272e11i 1.01348 + 1.01348i
\(394\) 9.17097e11 3.79874e11i 1.91726 0.794157i
\(395\) 8.95031e11i 1.84991i
\(396\) 3.27704e10 + 7.91148e10i 0.0669659 + 0.161670i
\(397\) −4.97087e11 2.05900e11i −1.00433 0.416006i −0.180945 0.983493i \(-0.557916\pi\)
−0.823382 + 0.567487i \(0.807916\pi\)
\(398\) 3.35488e11 8.09939e11i 0.670198 1.61800i
\(399\) −2.16210e11 + 2.16210e11i −0.427069 + 0.427069i
\(400\) −5.81316e10 + 5.81316e10i −0.113538 + 0.113538i
\(401\) 3.74179e10 9.03347e10i 0.0722652 0.174464i −0.883620 0.468206i \(-0.844901\pi\)
0.955885 + 0.293742i \(0.0949007\pi\)
\(402\) 6.36897e11 + 2.63811e11i 1.21633 + 0.503821i
\(403\) 1.28528e11 + 3.10293e11i 0.242730 + 0.586003i
\(404\) 1.08890e12i 2.03363i
\(405\) 3.70326e11 1.53394e11i 0.683969 0.283309i
\(406\) 3.68916e11 + 3.68916e11i 0.673845 + 0.673845i
\(407\) −2.22180e11 −0.401356
\(408\) 2.85246e11 + 7.71522e10i 0.509623 + 0.137841i
\(409\) 8.67529e11 1.53295 0.766477 0.642271i \(-0.222008\pi\)
0.766477 + 0.642271i \(0.222008\pi\)
\(410\) 2.92952e11 + 2.92952e11i 0.511998 + 0.511998i
\(411\) −2.74172e11 + 1.13566e11i −0.473952 + 0.196317i
\(412\) 3.34578e11i 0.572085i
\(413\) −4.08191e11 9.85459e11i −0.690379 1.66672i
\(414\) −4.31685e11 1.78810e11i −0.722213 0.299150i
\(415\) −3.61153e11 + 8.71900e11i −0.597688 + 1.44295i
\(416\) 3.86852e11 3.86852e11i 0.633323 0.633323i
\(417\) 6.78566e10 6.78566e10i 0.109895 0.109895i
\(418\) 6.80338e10 1.64248e11i 0.109001 0.263152i
\(419\) 5.15318e11 + 2.13452e11i 0.816793 + 0.338327i 0.751661 0.659550i \(-0.229253\pi\)
0.0651324 + 0.997877i \(0.479253\pi\)
\(420\) −5.74896e11 1.38792e12i −0.901503 2.17642i
\(421\) 2.55514e11i 0.396411i −0.980160 0.198206i \(-0.936489\pi\)
0.980160 0.198206i \(-0.0635114\pi\)
\(422\) −5.84319e11 + 2.42033e11i −0.896900 + 0.371508i
\(423\) 1.59299e11 + 1.59299e11i 0.241926 + 0.241926i
\(424\) 1.60236e11 0.240776
\(425\) −1.96768e11 1.51724e11i −0.292554 0.225581i
\(426\) 1.07759e11 0.158530
\(427\) −1.63584e12 1.63584e12i −2.38131 2.38131i
\(428\) 1.25188e12 5.18545e11i 1.80329 0.746946i
\(429\) 1.78536e11i 0.254489i
\(430\) −2.23470e11 5.39505e11i −0.315218 0.761004i
\(431\) 8.02446e11 + 3.32384e11i 1.12013 + 0.463973i 0.864415 0.502779i \(-0.167689\pi\)
0.255715 + 0.966752i \(0.417689\pi\)
\(432\) −1.30837e11 + 3.15868e11i −0.180739 + 0.436343i
\(433\) −2.97003e11 + 2.97003e11i −0.406037 + 0.406037i −0.880354 0.474317i \(-0.842695\pi\)
0.474317 + 0.880354i \(0.342695\pi\)
\(434\) −1.26475e12 + 1.26475e12i −1.71119 + 1.71119i
\(435\) −1.02345e11 + 2.47082e11i −0.137045 + 0.330857i
\(436\) −3.90815e11 1.61881e11i −0.517943 0.214539i
\(437\) 2.16737e11 + 5.23251e11i 0.284294 + 0.686346i
\(438\) 1.52057e12i 1.97412i
\(439\) −2.64967e11 + 1.09753e11i −0.340487 + 0.141034i −0.546374 0.837541i \(-0.683992\pi\)
0.205887 + 0.978576i \(0.433992\pi\)
\(440\) 1.77400e11 + 1.77400e11i 0.225640 + 0.225640i
\(441\) 4.27206e11 0.537853
\(442\) 6.79479e11 + 5.23931e11i 0.846790 + 0.652940i
\(443\) 2.71905e11 0.335428 0.167714 0.985836i \(-0.446361\pi\)
0.167714 + 0.985836i \(0.446361\pi\)
\(444\) 6.31256e11 + 6.31256e11i 0.770872 + 0.770872i
\(445\) 5.63354e10 2.33349e10i 0.0681022 0.0282089i
\(446\) 1.15837e12i 1.38624i
\(447\) −1.93521e11 4.67201e11i −0.229268 0.553503i
\(448\) 2.11049e12 + 8.74195e11i 2.47533 + 1.02531i
\(449\) 8.25598e9 1.99317e10i 0.00958650 0.0231439i −0.919014 0.394225i \(-0.871013\pi\)
0.928600 + 0.371081i \(0.121013\pi\)
\(450\) −1.00645e11 + 1.00645e11i −0.115701 + 0.115701i
\(451\) −1.08251e11 + 1.08251e11i −0.123208 + 0.123208i
\(452\) −4.02782e11 + 9.72402e11i −0.453886 + 1.09578i
\(453\) −9.21469e11 3.81685e11i −1.02811 0.425856i
\(454\) −4.91971e11 1.18772e12i −0.543486 1.31209i
\(455\) 1.25291e12i 1.37047i
\(456\) −1.89558e11 + 7.85173e10i −0.205305 + 0.0850401i
\(457\) −1.11135e12 1.11135e12i −1.19186 1.19186i −0.976544 0.215320i \(-0.930921\pi\)
−0.215320 0.976544i \(-0.569079\pi\)
\(458\) 2.03256e11 0.215848
\(459\) −9.97485e11 2.69796e11i −1.04894 0.283712i
\(460\) −2.78261e12 −2.89763
\(461\) 6.74059e11 + 6.74059e11i 0.695094 + 0.695094i 0.963348 0.268254i \(-0.0864466\pi\)
−0.268254 + 0.963348i \(0.586447\pi\)
\(462\) 8.78420e11 3.63854e11i 0.897044 0.371568i
\(463\) 1.32544e12i 1.34044i 0.742164 + 0.670219i \(0.233800\pi\)
−0.742164 + 0.670219i \(0.766200\pi\)
\(464\) −6.01348e10 1.45178e11i −0.0602276 0.145402i
\(465\) −8.47066e11 3.50866e11i −0.840193 0.348019i
\(466\) −9.80867e8 + 2.36802e9i −0.000963549 + 0.00232621i
\(467\) 1.54807e11 1.54807e11i 0.150614 0.150614i −0.627778 0.778392i \(-0.716035\pi\)
0.778392 + 0.627778i \(0.216035\pi\)
\(468\) 2.02914e11 2.02914e11i 0.195527 0.195527i
\(469\) −6.84108e11 + 1.65158e12i −0.652900 + 1.57624i
\(470\) 2.12298e12 + 8.79366e11i 2.00680 + 0.831245i
\(471\) 6.35948e10 + 1.53532e11i 0.0595426 + 0.143749i
\(472\) 7.15745e11i 0.663773i
\(473\) 1.99358e11 8.25767e10i 0.183129 0.0758547i
\(474\) 1.60944e12 + 1.60944e12i 1.46445 + 1.46445i
\(475\) 1.72524e11 0.155499
\(476\) −6.96553e11 + 2.57529e12i −0.621904 + 2.29929i
\(477\) −1.24523e11 −0.110132
\(478\) −1.73450e12 1.73450e12i −1.51967 1.51967i
\(479\) 1.31223e12 5.43542e11i 1.13893 0.471762i 0.268126 0.963384i \(-0.413596\pi\)
0.870809 + 0.491622i \(0.163596\pi\)
\(480\) 1.49350e12i 1.28416i
\(481\) 2.84925e11 + 6.87869e11i 0.242704 + 0.585940i
\(482\) −1.90157e12 7.87657e11i −1.60473 0.664700i
\(483\) −1.15914e12 + 2.79841e12i −0.969112 + 2.33964i
\(484\) 9.69446e11 9.69446e11i 0.803007 0.803007i
\(485\) 1.02830e12 1.02830e12i 0.843884 0.843884i
\(486\) −4.02703e11 + 9.72210e11i −0.327432 + 0.790491i
\(487\) −6.84513e11 2.83534e11i −0.551444 0.228415i 0.0895223 0.995985i \(-0.471466\pi\)
−0.640966 + 0.767569i \(0.721466\pi\)
\(488\) −5.94061e11 1.43419e12i −0.474178 1.14477i
\(489\) 1.09925e12i 0.869371i
\(490\) 4.02582e12 1.66755e12i 3.15480 1.30676i
\(491\) −1.61010e12 1.61010e12i −1.25022 1.25022i −0.955623 0.294593i \(-0.904816\pi\)
−0.294593 0.955623i \(-0.595184\pi\)
\(492\) 6.15126e11 0.473283
\(493\) 4.11865e11 2.36498e11i 0.314010 0.180309i
\(494\) −5.95759e11 −0.450090
\(495\) −1.37861e11 1.37861e11i −0.103209 0.103209i
\(496\) 4.97711e11 2.06159e11i 0.369241 0.152945i
\(497\) 2.79438e11i 0.205439i
\(498\) 9.18426e11 + 2.21728e12i 0.669133 + 1.61543i
\(499\) −1.30535e11 5.40696e10i −0.0942489 0.0390392i 0.335061 0.942196i \(-0.391243\pi\)
−0.429310 + 0.903157i \(0.641243\pi\)
\(500\) 5.53681e11 1.33670e12i 0.396182 0.956468i
\(501\) 1.13854e12 1.13854e12i 0.807381 0.807381i
\(502\) 9.15981e11 9.15981e11i 0.643753 0.643753i
\(503\) 6.47964e11 1.56432e12i 0.451331 1.08961i −0.520486 0.853870i \(-0.674249\pi\)
0.971817 0.235739i \(-0.0757509\pi\)
\(504\) 4.05536e11 + 1.67979e11i 0.279958 + 0.115962i
\(505\) −9.48733e11 2.29044e12i −0.649131 1.56714i
\(506\) 1.76113e12i 1.19430i
\(507\) 6.08924e11 2.52224e11i 0.409286 0.169532i
\(508\) 1.46164e12 + 1.46164e12i 0.973764 + 0.973764i
\(509\) −1.99900e12 −1.32003 −0.660015 0.751253i \(-0.729450\pi\)
−0.660015 + 0.751253i \(0.729450\pi\)
\(510\) −2.32297e12 + 3.00259e11i −1.52047 + 0.196531i
\(511\) 3.94311e12 2.55826
\(512\) −9.19037e11 9.19037e11i −0.591042 0.591042i
\(513\) 6.62869e11 2.74569e11i 0.422571 0.175034i
\(514\) 1.07971e12i 0.682297i
\(515\) −2.91509e11 7.03766e11i −0.182608 0.440855i
\(516\) −8.01029e11 3.31797e11i −0.497422 0.206039i
\(517\) −3.24943e11 + 7.84482e11i −0.200032 + 0.482921i
\(518\) −2.80373e12 + 2.80373e12i −1.71101 + 1.71101i
\(519\) −5.55907e11 + 5.55907e11i −0.336317 + 0.336317i
\(520\) 3.21732e11 7.76730e11i 0.192965 0.465860i
\(521\) 1.92119e12 + 7.95783e11i 1.14235 + 0.473179i 0.871963 0.489572i \(-0.162847\pi\)
0.270391 + 0.962751i \(0.412847\pi\)
\(522\) −1.04113e11 2.51351e11i −0.0613746 0.148171i
\(523\) 9.71740e11i 0.567927i −0.958835 0.283963i \(-0.908351\pi\)
0.958835 0.283963i \(-0.0916495\pi\)
\(524\) −3.79361e12 + 1.57137e12i −2.19817 + 0.910514i
\(525\) 6.52435e11 + 6.52435e11i 0.374818 + 0.374818i
\(526\) 7.78134e11 0.443219
\(527\) 8.10781e11 + 1.41198e12i 0.457884 + 0.797411i
\(528\) −2.86372e11 −0.160353
\(529\) 2.69360e12 + 2.69360e12i 1.49549 + 1.49549i
\(530\) −1.17345e12 + 4.86059e11i −0.645986 + 0.267576i
\(531\) 5.56220e11i 0.303614i
\(532\) −7.08878e11 1.71138e12i −0.383680 0.926285i
\(533\) 4.73969e11 + 1.96324e11i 0.254377 + 0.105366i
\(534\) 5.93415e10 1.43263e11i 0.0315808 0.0762428i
\(535\) −2.18146e12 + 2.18146e12i −1.15121 + 1.15121i
\(536\) −8.48214e11 + 8.48214e11i −0.443878 + 0.443878i
\(537\) −1.97193e11 + 4.76066e11i −0.102331 + 0.247049i
\(538\) 1.84965e12 + 7.66152e11i 0.951854 + 0.394271i
\(539\) 6.16192e11 + 1.48762e12i 0.314461 + 0.759176i
\(540\) 3.52509e12i 1.78402i
\(541\) −2.39530e12 + 9.92167e11i −1.20219 + 0.497963i −0.891706 0.452616i \(-0.850491\pi\)
−0.310484 + 0.950579i \(0.600491\pi\)
\(542\) −8.25085e11 8.25085e11i −0.410678 0.410678i
\(543\) 1.57127e12 0.775623
\(544\) 1.61954e12 2.10036e12i 0.792858 1.02825i
\(545\) 9.63098e11 0.467613
\(546\) −2.25298e12 2.25298e12i −1.08490 1.08490i
\(547\) 5.16273e11 2.13847e11i 0.246568 0.102132i −0.255977 0.966683i \(-0.582397\pi\)
0.502545 + 0.864551i \(0.332397\pi\)
\(548\) 1.79783e12i 0.851600i
\(549\) 4.61657e11 + 1.11454e12i 0.216892 + 0.523624i
\(550\) −4.95635e11 2.05299e11i −0.230956 0.0956652i
\(551\) −1.26197e11 + 3.04666e11i −0.0583266 + 0.140813i
\(552\) −1.43720e12 + 1.43720e12i −0.658857 + 0.658857i
\(553\) −4.17357e12 + 4.17357e12i −1.89777 + 1.89777i
\(554\) 4.59348e11 1.10896e12i 0.207180 0.500177i
\(555\) −1.87781e12 7.77813e11i −0.840103 0.347982i
\(556\) 2.22478e11 + 5.37110e11i 0.0987304 + 0.238356i
\(557\) 3.73545e12i 1.64435i −0.569235 0.822175i \(-0.692761\pi\)
0.569235 0.822175i \(-0.307239\pi\)
\(558\) 8.61701e11 3.56928e11i 0.376273 0.155857i
\(559\) −5.11315e11 5.11315e11i −0.221480 0.221480i
\(560\) −2.00967e12 −0.863532
\(561\) −1.10952e11 8.58384e11i −0.0472934 0.365888i
\(562\) −2.34969e12 −0.993566
\(563\) 3.38714e11 + 3.38714e11i 0.142084 + 0.142084i 0.774571 0.632487i \(-0.217966\pi\)
−0.632487 + 0.774571i \(0.717966\pi\)
\(564\) 3.15209e12 1.30564e12i 1.31172 0.543334i
\(565\) 2.39632e12i 0.989299i
\(566\) −2.82243e11 6.81394e11i −0.115598 0.279077i
\(567\) 2.44213e12 + 1.01156e12i 0.992305 + 0.411026i
\(568\) −7.17564e10 + 1.73235e11i −0.0289263 + 0.0698343i
\(569\) 3.32872e12 3.32872e12i 1.33129 1.33129i 0.427070 0.904219i \(-0.359546\pi\)
0.904219 0.427070i \(-0.140454\pi\)
\(570\) 1.15001e12 1.15001e12i 0.456314 0.456314i
\(571\) 1.77861e11 4.29395e11i 0.0700195 0.169042i −0.884995 0.465600i \(-0.845839\pi\)
0.955015 + 0.296558i \(0.0958387\pi\)
\(572\) 9.99269e11 + 4.13911e11i 0.390302 + 0.161668i
\(573\) 2.16567e10 + 5.22840e10i 0.00839262 + 0.0202616i
\(574\) 2.73209e12i 1.05049i
\(575\) 1.57896e12 6.54027e11i 0.602374 0.249511i
\(576\) −8.42320e11 8.42320e11i −0.318842 0.318842i
\(577\) −1.23582e11 −0.0464158 −0.0232079 0.999731i \(-0.507388\pi\)
−0.0232079 + 0.999731i \(0.507388\pi\)
\(578\) 3.59246e12 + 2.09674e12i 1.33880 + 0.781393i
\(579\) 1.64345e12 0.607719
\(580\) −1.14565e12 1.14565e12i −0.420365 0.420365i
\(581\) −5.74978e12 + 2.38164e12i −2.09343 + 0.867128i
\(582\) 3.69819e12i 1.33609i
\(583\) −1.79609e11 4.33613e11i −0.0643900 0.155451i
\(584\) 2.44450e12 + 1.01254e12i 0.869624 + 0.360210i
\(585\) −2.50025e11 + 6.03613e11i −0.0882635 + 0.213087i
\(586\) −8.78432e11 + 8.78432e11i −0.307729 + 0.307729i
\(587\) −2.01954e12 + 2.01954e12i −0.702071 + 0.702071i −0.964855 0.262784i \(-0.915359\pi\)
0.262784 + 0.964855i \(0.415359\pi\)
\(588\) 2.47589e12 5.97733e12i 0.854149 2.06210i
\(589\) −1.04448e12 4.32637e11i −0.357586 0.148117i
\(590\) 2.17114e12 + 5.24160e12i 0.737656 + 1.78086i
\(591\) 3.35559e12i 1.13142i
\(592\) 1.10334e12 4.57020e11i 0.369201 0.152928i
\(593\) 4.71365e11 + 4.71365e11i 0.156535 + 0.156535i 0.781029 0.624494i \(-0.214695\pi\)
−0.624494 + 0.781029i \(0.714695\pi\)
\(594\) −2.23105e12 −0.735308
\(595\) −7.78623e11 6.02386e12i −0.254684 1.97037i
\(596\) 3.06358e12 0.994538
\(597\) 2.09551e12 + 2.09551e12i 0.675159 + 0.675159i
\(598\) −5.45245e12 + 2.25848e12i −1.74356 + 0.722205i
\(599\) 2.92151e11i 0.0927230i −0.998925 0.0463615i \(-0.985237\pi\)
0.998925 0.0463615i \(-0.0147626\pi\)
\(600\) 2.36934e11 + 5.72009e11i 0.0746356 + 0.180186i
\(601\) −3.53766e12 1.46535e12i −1.10607 0.458147i −0.246484 0.969147i \(-0.579275\pi\)
−0.859581 + 0.511000i \(0.829275\pi\)
\(602\) 1.47368e12 3.55778e12i 0.457320 1.10407i
\(603\) 6.59164e11 6.59164e11i 0.203033 0.203033i
\(604\) 4.27259e12 4.27259e12i 1.30625 1.30625i
\(605\) −1.19452e12 + 2.88383e12i −0.362488 + 0.875124i
\(606\) −5.82469e12 2.41266e12i −1.75447 0.726725i
\(607\) −6.36037e11 1.53553e12i −0.190166 0.459102i 0.799825 0.600234i \(-0.204926\pi\)
−0.989991 + 0.141132i \(0.954926\pi\)
\(608\) 1.84157e12i 0.546539i
\(609\) −1.62940e12 + 6.74918e11i −0.480008 + 0.198826i
\(610\) 8.70094e12 + 8.70094e12i 2.54438 + 2.54438i
\(611\) 2.84547e12 0.825977
\(612\) 8.49490e11 1.10169e12i 0.244781 0.317453i
\(613\) −3.34407e12 −0.956540 −0.478270 0.878213i \(-0.658736\pi\)
−0.478270 + 0.878213i \(0.658736\pi\)
\(614\) 2.35272e11 + 2.35272e11i 0.0668056 + 0.0668056i
\(615\) −1.29388e12 + 5.35944e11i −0.364718 + 0.151071i
\(616\) 1.65445e12i 0.462957i
\(617\) 1.15640e12 + 2.79180e12i 0.321236 + 0.775533i 0.999183 + 0.0404218i \(0.0128702\pi\)
−0.677946 + 0.735111i \(0.737130\pi\)
\(618\) −1.78970e12 7.41320e11i −0.493552 0.204436i
\(619\) 1.68883e12 4.07720e12i 0.462357 1.11623i −0.505069 0.863079i \(-0.668533\pi\)
0.967427 0.253151i \(-0.0814669\pi\)
\(620\) 3.92761e12 3.92761e12i 1.06749 1.06749i
\(621\) 5.02577e12 5.02577e12i 1.35610 1.35610i
\(622\) −2.10011e12 + 5.07011e12i −0.562580 + 1.35819i
\(623\) 3.71506e11 + 1.53883e11i 0.0988029 + 0.0409255i
\(624\) 3.67245e11 + 8.86609e11i 0.0969674 + 0.234100i
\(625\) 4.70333e12i 1.23295i
\(626\) 2.57103e12 1.06495e12i 0.669148 0.277170i
\(627\) 4.24951e11 + 4.24951e11i 0.109808 + 0.109808i
\(628\) −1.00675e12 −0.258288
\(629\) 1.79737e12 + 3.13014e12i 0.457835 + 0.797325i
\(630\) −3.47940e12 −0.879977
\(631\) 1.83030e12 + 1.83030e12i 0.459610 + 0.459610i 0.898527 0.438918i \(-0.144638\pi\)
−0.438918 + 0.898527i \(0.644638\pi\)
\(632\) −3.65909e12 + 1.51564e12i −0.912318 + 0.377894i
\(633\) 2.13798e12i 0.529281i
\(634\) −1.69275e12 4.08665e12i −0.416093 1.00454i
\(635\) −4.34796e12 1.80099e12i −1.06122 0.439570i
\(636\) −7.21676e11 + 1.74228e12i −0.174898 + 0.422242i
\(637\) 3.81546e12 3.81546e12i 0.918163 0.918163i
\(638\) 7.25087e11 7.25087e11i 0.173260 0.173260i
\(639\) 5.57634e10 1.34625e11i 0.0132311 0.0319426i
\(640\) −5.26741e12 2.18183e12i −1.24104 0.514058i
\(641\) 8.55967e11 + 2.06649e12i 0.200261 + 0.483472i 0.991824 0.127615i \(-0.0407323\pi\)
−0.791563 + 0.611088i \(0.790732\pi\)
\(642\) 7.84539e12i 1.82267i
\(643\) −3.93067e12 + 1.62814e12i −0.906813 + 0.375614i −0.786836 0.617162i \(-0.788282\pi\)
−0.119977 + 0.992777i \(0.538282\pi\)
\(644\) −1.29755e13 1.29755e13i −2.97260 2.97260i
\(645\) 1.97401e12 0.449086
\(646\) −2.86435e12 + 3.70236e11i −0.647112 + 0.0836434i
\(647\) 3.30319e11 0.0741079 0.0370539 0.999313i \(-0.488203\pi\)
0.0370539 + 0.999313i \(0.488203\pi\)
\(648\) 1.25422e12 + 1.25422e12i 0.279438 + 0.279438i
\(649\) −1.93687e12 + 8.02280e11i −0.428549 + 0.177511i
\(650\) 1.79776e12i 0.395023i
\(651\) −2.31380e12 5.58601e12i −0.504907 1.21895i
\(652\) 6.15249e12 + 2.54845e12i 1.33333 + 0.552283i
\(653\) −5.17745e11 + 1.24995e12i −0.111431 + 0.269019i −0.969751 0.244097i \(-0.921509\pi\)
0.858320 + 0.513115i \(0.171509\pi\)
\(654\) 1.73184e12 1.73184e12i 0.370177 0.370177i
\(655\) 6.61055e12 6.61055e12i 1.40330 1.40330i
\(656\) 3.14905e11 7.60247e11i 0.0663914 0.160283i
\(657\) −1.89967e12 7.86868e11i −0.397771 0.164762i
\(658\) 5.79901e12 + 1.40001e13i 1.20597 + 2.91148i
\(659\) 3.08677e12i 0.637558i −0.947829 0.318779i \(-0.896727\pi\)
0.947829 0.318779i \(-0.103273\pi\)
\(660\) −2.72789e12 + 1.12993e12i −0.559603 + 0.231795i
\(661\) −4.35438e12 4.35438e12i −0.887197 0.887197i 0.107056 0.994253i \(-0.465858\pi\)
−0.994253 + 0.107056i \(0.965858\pi\)
\(662\) 3.78768e12 0.766500
\(663\) −2.51527e12 + 1.44430e12i −0.505561 + 0.290300i
\(664\) −4.17610e12 −0.833710
\(665\) 2.98217e12 + 2.98217e12i 0.591336 + 0.591336i
\(666\) 1.91025e12 7.91252e11i 0.376233 0.155841i
\(667\) 3.26674e12i 0.639070i
\(668\) 3.73288e12 + 9.01197e12i 0.725354 + 1.75116i
\(669\) −3.61768e12 1.49849e12i −0.698252 0.289226i
\(670\) 3.63873e12 8.78466e12i 0.697610 1.68418i
\(671\) −3.21517e12 + 3.21517e12i −0.612284 + 0.612284i
\(672\) −6.96425e12 + 6.96425e12i −1.31739 + 1.31739i
\(673\) −3.03457e12 + 7.32610e12i −0.570202 + 1.37659i 0.331180 + 0.943567i \(0.392553\pi\)
−0.901383 + 0.433023i \(0.857447\pi\)
\(674\) −7.75247e12 3.21118e12i −1.44701 0.599370i
\(675\) −8.28539e11 2.00027e12i −0.153619 0.370870i
\(676\) 3.99290e12i 0.735408i
\(677\) 2.27590e12 9.42708e11i 0.416393 0.172476i −0.164643 0.986353i \(-0.552647\pi\)
0.581037 + 0.813877i \(0.302647\pi\)
\(678\) −4.30907e12 4.30907e12i −0.783159 0.783159i
\(679\) 9.59003e12 1.73143
\(680\) 1.06415e12 3.93438e12i 0.190860 0.705645i
\(681\) 4.34579e12 0.774295
\(682\) 2.48580e12 + 2.48580e12i 0.439983 + 0.439983i
\(683\) −5.24772e12 + 2.17368e12i −0.922736 + 0.382210i −0.792918 0.609328i \(-0.791439\pi\)
−0.129818 + 0.991538i \(0.541439\pi\)
\(684\) 9.65951e11i 0.168734i
\(685\) 1.56640e12 + 3.78163e12i 0.271829 + 0.656252i
\(686\) 1.24449e13 + 5.15486e12i 2.14553 + 0.888707i
\(687\) −2.62937e11 + 6.34786e11i −0.0450346 + 0.108723i
\(688\) −8.20150e11 + 8.20150e11i −0.139555 + 0.139555i
\(689\) −1.11214e12 + 1.11214e12i −0.188006 + 0.188006i
\(690\) 6.16540e12 1.48846e13i 1.03548 2.49986i
\(691\) 5.02719e12 + 2.08233e12i 0.838830 + 0.347455i 0.760392 0.649464i \(-0.225007\pi\)
0.0784376 + 0.996919i \(0.475007\pi\)
\(692\) −1.82263e12 4.40021e12i −0.302148 0.729451i
\(693\) 1.28571e12i 0.211759i
\(694\) 4.31975e12 1.78930e12i 0.706872 0.292796i
\(695\) −9.35940e11 9.35940e11i −0.152166 0.152166i
\(696\) −1.18344e12 −0.191163
\(697\) 2.40080e12 + 6.49358e11i 0.385308 + 0.104217i
\(698\) 3.53000e12 0.562892
\(699\) −6.12667e9 6.12667e9i −0.000970682 0.000970682i
\(700\) −5.16426e12 + 2.13911e12i −0.812956 + 0.336738i
\(701\) 7.42727e11i 0.116171i 0.998312 + 0.0580856i \(0.0184996\pi\)
−0.998312 + 0.0580856i \(0.981500\pi\)
\(702\) 2.86110e12 + 6.90732e12i 0.444648 + 1.07348i
\(703\) −2.31544e12 9.59086e11i −0.357548 0.148101i
\(704\) 1.71819e12 4.14807e12i 0.263629 0.636458i
\(705\) −5.49267e12 + 5.49267e12i −0.837399 + 0.837399i
\(706\) −2.29333e12 + 2.29333e12i −0.347413 + 0.347413i
\(707\) 6.25646e12 1.51044e13i 0.941762 2.27361i
\(708\) 7.78246e12 + 3.22360e12i 1.16404 + 0.482160i
\(709\) −2.18949e12 5.28591e12i −0.325414 0.785618i −0.998921 0.0464375i \(-0.985213\pi\)
0.673508 0.739180i \(-0.264787\pi\)
\(710\) 1.48631e12i 0.219507i
\(711\) 2.84355e12 1.17784e12i 0.417300 0.172851i
\(712\) 1.90797e11 + 1.90797e11i 0.0278234 + 0.0278234i
\(713\) −1.11993e13 −1.62288
\(714\) −1.22322e13 9.43199e12i −1.76142 1.35819i
\(715\) −2.46253e12 −0.352375
\(716\) −2.20738e12 2.20738e12i −0.313884 0.313884i
\(717\) 7.66077e12 3.17320e12i 1.08252 0.448395i
\(718\) 1.41794e13i 1.99112i
\(719\) −1.84267e12 4.44860e12i −0.257139 0.620788i 0.741608 0.670833i \(-0.234063\pi\)
−0.998747 + 0.0500453i \(0.984063\pi\)
\(720\) 9.68196e11 + 4.01040e11i 0.134266 + 0.0556149i
\(721\) 1.92237e12 4.64101e12i 0.264928 0.639594i
\(722\) −6.58542e12 + 6.58542e12i −0.901916 + 0.901916i
\(723\) 4.91984e12 4.91984e12i 0.669621 0.669621i
\(724\) −3.64276e12 + 8.79440e12i −0.492728 + 1.18955i
\(725\) 9.19360e11 + 3.80811e11i 0.123585 + 0.0511905i
\(726\) 3.03771e12 + 7.33368e12i 0.405818 + 0.979732i
\(727\) 1.09017e13i 1.44740i 0.690114 + 0.723700i \(0.257560\pi\)
−0.690114 + 0.723700i \(0.742440\pi\)
\(728\) 5.12218e12 2.12168e12i 0.675870 0.279955i
\(729\) −5.92658e12 5.92658e12i −0.777196 0.777196i
\(730\) −2.09732e13 −2.73345
\(731\) −2.77611e12 2.14059e12i −0.359590 0.277272i
\(732\) 1.82698e13 2.35198
\(733\) −3.75785e12 3.75785e12i −0.480808 0.480808i 0.424581 0.905390i \(-0.360421\pi\)
−0.905390 + 0.424581i \(0.860421\pi\)
\(734\) 1.76015e13 7.29079e12i 2.23830 0.927133i
\(735\) 1.47301e13i 1.86172i
\(736\) 6.98124e12 + 1.68542e13i 0.876966 + 2.11718i
\(737\) 3.24611e12 + 1.34458e12i 0.405284 + 0.167874i
\(738\) 5.45203e11 1.31624e12i 0.0676558 0.163335i
\(739\) 6.89708e12 6.89708e12i 0.850678 0.850678i −0.139538 0.990217i \(-0.544562\pi\)
0.990217 + 0.139538i \(0.0445619\pi\)
\(740\) 8.70686e12 8.70686e12i 1.06738 1.06738i
\(741\) 7.70688e11 1.86061e12i 0.0939068 0.226711i
\(742\) −7.73836e12 3.20534e12i −0.937198 0.388200i
\(743\) 1.41379e12 + 3.41319e12i 0.170191 + 0.410876i 0.985844 0.167664i \(-0.0536225\pi\)
−0.815654 + 0.578541i \(0.803622\pi\)
\(744\) 4.05716e12i 0.485449i
\(745\) −6.44407e12 + 2.66922e12i −0.766402 + 0.317454i
\(746\) 1.74147e12 + 1.74147e12i 0.205869 + 0.205869i
\(747\) 3.24534e12 0.381344
\(748\) 5.06161e12 + 1.36904e12i 0.591196 + 0.159904i
\(749\) −2.03445e13 −2.36199
\(750\) 5.92343e12 + 5.92343e12i 0.683593 + 0.683593i
\(751\) −9.05554e12 + 3.75093e12i −1.03881 + 0.430288i −0.835883 0.548907i \(-0.815044\pi\)
−0.202923 + 0.979195i \(0.565044\pi\)
\(752\) 4.56413e12i 0.520449i
\(753\) 1.67575e12 + 4.04562e12i 0.189947 + 0.458572i
\(754\) −3.17473e12 1.31501e12i −0.357713 0.148170i
\(755\) −5.26455e12 + 1.27097e13i −0.589658 + 1.42356i
\(756\) −1.64377e13 + 1.64377e13i −1.83017 + 1.83017i
\(757\) 2.24931e11 2.24931e11i 0.0248953 0.0248953i −0.694550 0.719445i \(-0.744396\pi\)
0.719445 + 0.694550i \(0.244396\pi\)
\(758\) −4.52442e12 + 1.09229e13i −0.497796 + 1.20179i
\(759\) 5.50015e12 + 2.27824e12i 0.601571 + 0.249179i
\(760\) 1.08298e12 + 2.61455e12i 0.117750 + 0.284273i
\(761\) 1.17912e13i 1.27446i −0.770674 0.637230i \(-0.780080\pi\)
0.770674 0.637230i \(-0.219920\pi\)
\(762\) −1.10570e13 +