Properties

Label 17.10.d.a.2.3
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 2.3
Character \(\chi\) \(=\) 17.2
Dual form 17.10.d.a.9.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +O(q^{10})\) \(q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +(17077.8 - 41229.6i) q^{10} +(46761.8 + 19369.4i) q^{11} +(30962.2 + 74749.3i) q^{12} +76005.9i q^{13} +(294348. - 121923. i) q^{14} +(157446. + 157446. i) q^{15} +264282. q^{16} +(-324117. - 116345. i) q^{17} -182163. q^{18} +(-460062. - 460062. i) q^{19} +(-655597. + 271557. i) q^{20} +1.58964e6i q^{21} +(-618544. - 1.49330e6i) q^{22} +(547050. + 226596. i) q^{23} +(-8199.84 + 19796.2i) q^{24} +(169.290 - 169.290i) q^{25} +(1.71628e6 - 1.71628e6i) q^{26} +(-852342. + 2.05773e6i) q^{27} +(-4.68046e6 - 1.93871e6i) q^{28} +(1.35186e6 + 3.26369e6i) q^{29} -7.11053e6i q^{30} +(3.15043e6 - 1.30495e6i) q^{31} +(-5.91903e6 - 5.91903e6i) q^{32} +8.06462e6 q^{33} +(4.69168e6 + 9.94599e6i) q^{34} -1.39421e7 q^{35} +(2.04821e6 + 2.04821e6i) q^{36} +(-5.75330e6 + 2.38309e6i) q^{37} +2.07772e7i q^{38} +(4.63442e6 + 1.11885e7i) q^{39} +(-173625. - 71917.6i) q^{40} +(-6432.62 + 15529.7i) q^{41} +(3.58954e7 - 3.58954e7i) q^{42} +(2.30025e7 - 2.30025e7i) q^{43} +(-9.83554e6 + 2.37451e7i) q^{44} +(7.36477e6 + 3.05059e6i) q^{45} +(-7.23613e6 - 1.74696e7i) q^{46} +5.02215e7i q^{47} +(3.89038e7 - 1.61145e7i) q^{48} +(-4.18484e7 - 4.18484e7i) q^{49} -7645.44 q^{50} +(-5.48058e7 + 2.63632e6i) q^{51} -3.85949e7 q^{52} +(1.10317e7 + 1.10317e7i) q^{53} +(6.57120e7 - 2.72188e7i) q^{54} +7.07317e7i q^{55} +(-513437. - 1.23955e6i) q^{56} +(-9.57757e7 - 3.96716e7i) q^{57} +(4.31706e7 - 1.04223e8i) q^{58} +(-1.14670e8 + 1.14670e8i) q^{59} +(-7.99494e7 + 7.99494e7i) q^{60} +(5.96668e7 - 1.44048e8i) q^{61} +(-1.00606e8 - 4.16725e7i) q^{62} +(2.17789e7 + 5.25789e7i) q^{63} +1.32001e8i q^{64} +(-9.81298e7 + 4.06467e7i) q^{65} +(-1.82106e8 - 1.82106e8i) q^{66} +2.74298e8 q^{67} +(5.90785e7 - 1.64583e8i) q^{68} +9.43453e7 q^{69} +(3.14825e8 + 3.14825e8i) q^{70} +(2.51521e8 - 1.04183e8i) q^{71} +767119. i q^{72} +(3.28100e6 + 7.92104e6i) q^{73} +(1.83727e8 + 7.61020e7i) q^{74} +(14598.1 - 35242.9i) q^{75} +(2.33614e8 - 2.33614e8i) q^{76} +(-3.57068e8 + 3.57068e8i) q^{77} +(1.47996e8 - 3.57295e8i) q^{78} +(-2.65406e8 - 1.09935e8i) q^{79} +(1.41334e8 + 3.41210e8i) q^{80} +4.67160e8i q^{81} +(495928. - 205420. i) q^{82} +(2.62900e8 + 2.62900e8i) q^{83} -8.07202e8 q^{84} +(-2.31221e7 - 4.80681e8i) q^{85} -1.03883e9 q^{86} +(3.98003e8 + 3.98003e8i) q^{87} +(-6.28852e6 + 2.60479e6i) q^{88} -4.29631e8i q^{89} +(-9.74179e7 - 2.35188e8i) q^{90} +(-7.00572e8 - 2.90187e8i) q^{91} +(-1.15063e8 + 2.77786e8i) q^{92} +(3.84192e8 - 3.84192e8i) q^{93} +(1.13404e9 - 1.13404e9i) q^{94} +(3.47944e8 - 8.40011e8i) q^{95} +(-1.23222e9 - 5.10404e8i) q^{96} +(3.90001e8 + 9.41546e8i) q^{97} +1.88994e9i q^{98} +(2.66745e8 - 1.10489e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.5808 22.5808i −0.997942 0.997942i 0.00205624 0.999998i \(-0.499345\pi\)
−0.999998 + 0.00205624i \(0.999345\pi\)
\(3\) 147.205 60.9745i 1.04925 0.434613i 0.209625 0.977782i \(-0.432776\pi\)
0.839623 + 0.543169i \(0.182776\pi\)
\(4\) 507.789i 0.991775i
\(5\) 534.784 + 1291.08i 0.382660 + 0.923823i 0.991449 + 0.130491i \(0.0416554\pi\)
−0.608790 + 0.793332i \(0.708345\pi\)
\(6\) −4700.88 1947.17i −1.48081 0.613370i
\(7\) −3817.95 + 9217.34i −0.601020 + 1.45099i 0.271513 + 0.962435i \(0.412476\pi\)
−0.872533 + 0.488556i \(0.837524\pi\)
\(8\) −95.0916 + 95.0916i −0.00820800 + 0.00820800i
\(9\) 4033.58 4033.58i 0.204927 0.204927i
\(10\) 17077.8 41229.6i 0.540049 1.30379i
\(11\) 46761.8 + 19369.4i 0.962994 + 0.398885i 0.808100 0.589046i \(-0.200496\pi\)
0.154895 + 0.987931i \(0.450496\pi\)
\(12\) 30962.2 + 74749.3i 0.431038 + 1.04062i
\(13\) 76005.9i 0.738078i 0.929414 + 0.369039i \(0.120313\pi\)
−0.929414 + 0.369039i \(0.879687\pi\)
\(14\) 294348. 121923.i 2.04779 0.848221i
\(15\) 157446. + 157446.i 0.803011 + 0.803011i
\(16\) 264282. 1.00816
\(17\) −324117. 116345.i −0.941199 0.337852i
\(18\) −182163. −0.409011
\(19\) −460062. 460062.i −0.809888 0.809888i 0.174728 0.984617i \(-0.444095\pi\)
−0.984617 + 0.174728i \(0.944095\pi\)
\(20\) −655597. + 271557.i −0.916225 + 0.379513i
\(21\) 1.58964e6i 1.78366i
\(22\) −618544. 1.49330e6i −0.562948 1.35908i
\(23\) 547050. + 226596.i 0.407617 + 0.168840i 0.577064 0.816699i \(-0.304198\pi\)
−0.169447 + 0.985539i \(0.554198\pi\)
\(24\) −8199.84 + 19796.2i −0.00504493 + 0.0121795i
\(25\) 169.290 169.290i 8.66767e−5 8.66767e-5i
\(26\) 1.71628e6 1.71628e6i 0.736559 0.736559i
\(27\) −852342. + 2.05773e6i −0.308657 + 0.745165i
\(28\) −4.68046e6 1.93871e6i −1.43906 0.596077i
\(29\) 1.35186e6 + 3.26369e6i 0.354929 + 0.856875i 0.995997 + 0.0893904i \(0.0284919\pi\)
−0.641067 + 0.767485i \(0.721508\pi\)
\(30\) 7.11053e6i 1.60272i
\(31\) 3.15043e6 1.30495e6i 0.612692 0.253786i −0.0546868 0.998504i \(-0.517416\pi\)
0.667379 + 0.744718i \(0.267416\pi\)
\(32\) −5.91903e6 5.91903e6i −0.997874 0.997874i
\(33\) 8.06462e6 1.18378
\(34\) 4.69168e6 + 9.94599e6i 0.602106 + 1.27642i
\(35\) −1.39421e7 −1.57044
\(36\) 2.04821e6 + 2.04821e6i 0.203242 + 0.203242i
\(37\) −5.75330e6 + 2.38309e6i −0.504672 + 0.209042i −0.620469 0.784231i \(-0.713058\pi\)
0.115797 + 0.993273i \(0.463058\pi\)
\(38\) 2.07772e7i 1.61644i
\(39\) 4.63442e6 + 1.11885e7i 0.320778 + 0.774427i
\(40\) −173625. 71917.6i −0.0107236 0.00444187i
\(41\) −6432.62 + 15529.7i −0.000355517 + 0.000858294i −0.924057 0.382254i \(-0.875148\pi\)
0.923702 + 0.383113i \(0.125148\pi\)
\(42\) 3.58954e7 3.58954e7i 1.77999 1.77999i
\(43\) 2.30025e7 2.30025e7i 1.02605 1.02605i 0.0263957 0.999652i \(-0.491597\pi\)
0.999652 0.0263957i \(-0.00840299\pi\)
\(44\) −9.83554e6 + 2.37451e7i −0.395605 + 0.955074i
\(45\) 7.36477e6 + 3.05059e6i 0.267734 + 0.110899i
\(46\) −7.23613e6 1.74696e7i −0.238285 0.575270i
\(47\) 5.02215e7i 1.50124i 0.660736 + 0.750619i \(0.270244\pi\)
−0.660736 + 0.750619i \(0.729756\pi\)
\(48\) 3.89038e7 1.61145e7i 1.05781 0.438158i
\(49\) −4.18484e7 4.18484e7i −1.03704 1.03704i
\(50\) −7645.44 −0.000172997
\(51\) −5.48058e7 + 2.63632e6i −1.13439 + 0.0545672i
\(52\) −3.85949e7 −0.732007
\(53\) 1.10317e7 + 1.10317e7i 0.192045 + 0.192045i 0.796579 0.604534i \(-0.206641\pi\)
−0.604534 + 0.796579i \(0.706641\pi\)
\(54\) 6.57120e7 2.72188e7i 1.05165 0.435609i
\(55\) 7.07317e7i 1.04227i
\(56\) −513437. 1.23955e6i −0.00697656 0.0168429i
\(57\) −9.57757e7 3.96716e7i −1.20176 0.497786i
\(58\) 4.31706e7 1.04223e8i 0.500912 1.20931i
\(59\) −1.14670e8 + 1.14670e8i −1.23201 + 1.23201i −0.268824 + 0.963189i \(0.586635\pi\)
−0.963189 + 0.268824i \(0.913365\pi\)
\(60\) −7.99494e7 + 7.99494e7i −0.796406 + 0.796406i
\(61\) 5.96668e7 1.44048e8i 0.551758 1.33206i −0.364400 0.931243i \(-0.618726\pi\)
0.916157 0.400818i \(-0.131274\pi\)
\(62\) −1.00606e8 4.16725e7i −0.864694 0.358168i
\(63\) 2.17789e7 + 5.25789e7i 0.174182 + 0.420513i
\(64\) 1.32001e8i 0.983483i
\(65\) −9.81298e7 + 4.06467e7i −0.681853 + 0.282433i
\(66\) −1.82106e8 1.82106e8i −1.18134 1.18134i
\(67\) 2.74298e8 1.66298 0.831488 0.555542i \(-0.187489\pi\)
0.831488 + 0.555542i \(0.187489\pi\)
\(68\) 5.90785e7 1.64583e8i 0.335073 0.933458i
\(69\) 9.43453e7 0.501071
\(70\) 3.14825e8 + 3.14825e8i 1.56721 + 1.56721i
\(71\) 2.51521e8 1.04183e8i 1.17466 0.486560i 0.291929 0.956440i \(-0.405703\pi\)
0.882730 + 0.469880i \(0.155703\pi\)
\(72\) 767119.i 0.00336408i
\(73\) 3.28100e6 + 7.92104e6i 0.0135224 + 0.0326459i 0.930497 0.366301i \(-0.119376\pi\)
−0.916974 + 0.398947i \(0.869376\pi\)
\(74\) 1.83727e8 + 7.61020e7i 0.712245 + 0.295021i
\(75\) 14598.1 35242.9i 5.32746e−5 0.000128616i
\(76\) 2.33614e8 2.33614e8i 0.803227 0.803227i
\(77\) −3.57068e8 + 3.57068e8i −1.15756 + 1.15756i
\(78\) 1.47996e8 3.57295e8i 0.452715 1.09295i
\(79\) −2.65406e8 1.09935e8i −0.766634 0.317550i −0.0351260 0.999383i \(-0.511183\pi\)
−0.731508 + 0.681833i \(0.761183\pi\)
\(80\) 1.41334e8 + 3.41210e8i 0.385781 + 0.931359i
\(81\) 4.67160e8i 1.20582i
\(82\) 495928. 205420.i 0.00121131 0.000501742i
\(83\) 2.62900e8 + 2.62900e8i 0.608050 + 0.608050i 0.942436 0.334386i \(-0.108529\pi\)
−0.334386 + 0.942436i \(0.608529\pi\)
\(84\) −8.07202e8 −1.76899
\(85\) −2.31221e7 4.80681e8i −0.0480443 0.998784i
\(86\) −1.03883e9 −2.04787
\(87\) 3.98003e8 + 3.98003e8i 0.744818 + 0.744818i
\(88\) −6.28852e6 + 2.60479e6i −0.0111783 + 0.00463021i
\(89\) 4.29631e8i 0.725839i −0.931821 0.362919i \(-0.881780\pi\)
0.931821 0.362919i \(-0.118220\pi\)
\(90\) −9.74179e7 2.35188e8i −0.156512 0.377853i
\(91\) −7.00572e8 2.90187e8i −1.07094 0.443600i
\(92\) −1.15063e8 + 2.77786e8i −0.167452 + 0.404264i
\(93\) 3.84192e8 3.84192e8i 0.532568 0.532568i
\(94\) 1.13404e9 1.13404e9i 1.49815 1.49815i
\(95\) 3.47944e8 8.40011e8i 0.438282 1.05811i
\(96\) −1.23222e9 5.10404e8i −1.48071 0.613329i
\(97\) 3.90001e8 + 9.41546e8i 0.447294 + 1.07986i 0.973332 + 0.229402i \(0.0736770\pi\)
−0.526038 + 0.850461i \(0.676323\pi\)
\(98\) 1.88994e9i 2.06981i
\(99\) 2.66745e8 1.10489e8i 0.279086 0.115601i
\(100\) 85963.8 + 85963.8i 8.59638e−5 + 8.59638e-5i
\(101\) 5.60377e8 0.535838 0.267919 0.963441i \(-0.413664\pi\)
0.267919 + 0.963441i \(0.413664\pi\)
\(102\) 1.29709e9 + 1.17803e9i 1.18651 + 1.07760i
\(103\) −1.44725e8 −0.126699 −0.0633497 0.997991i \(-0.520178\pi\)
−0.0633497 + 0.997991i \(0.520178\pi\)
\(104\) −7.22753e6 7.22753e6i −0.00605814 0.00605814i
\(105\) −2.05236e9 + 8.50114e8i −1.64779 + 0.682535i
\(106\) 4.98212e8i 0.383299i
\(107\) −7.31531e8 1.76607e9i −0.539518 1.30251i −0.925060 0.379821i \(-0.875986\pi\)
0.385542 0.922690i \(-0.374014\pi\)
\(108\) −1.04489e9 4.32810e8i −0.739036 0.306119i
\(109\) 9.27654e8 2.23955e9i 0.629458 1.51965i −0.210840 0.977521i \(-0.567620\pi\)
0.840298 0.542125i \(-0.182380\pi\)
\(110\) 1.59718e9 1.59718e9i 1.04013 1.04013i
\(111\) −7.01609e8 + 7.01609e8i −0.438674 + 0.438674i
\(112\) −1.00902e9 + 2.43598e9i −0.605923 + 1.46283i
\(113\) −1.05934e9 4.38792e8i −0.611197 0.253166i 0.0555433 0.998456i \(-0.482311\pi\)
−0.666740 + 0.745290i \(0.732311\pi\)
\(114\) 1.26688e9 + 3.05851e9i 0.702527 + 1.69605i
\(115\) 8.27466e8i 0.441174i
\(116\) −1.65726e9 + 6.86461e8i −0.849827 + 0.352010i
\(117\) 3.06576e8 + 3.06576e8i 0.151252 + 0.151252i
\(118\) 5.17869e9 2.45895
\(119\) 2.30985e9 2.54330e9i 1.05590 1.16262i
\(120\) −2.99436e7 −0.0131822
\(121\) 1.44169e8 + 1.44169e8i 0.0611419 + 0.0611419i
\(122\) −4.60006e9 + 1.90541e9i −1.87994 + 0.778697i
\(123\) 2.67828e6i 0.00105508i
\(124\) 6.62640e8 + 1.59975e9i 0.251698 + 0.607653i
\(125\) 2.52195e9 + 1.04463e9i 0.923936 + 0.382707i
\(126\) 6.95490e8 1.67906e9i 0.245824 0.593470i
\(127\) −1.75016e9 + 1.75016e9i −0.596982 + 0.596982i −0.939508 0.342526i \(-0.888717\pi\)
0.342526 + 0.939508i \(0.388717\pi\)
\(128\) −4.98537e7 + 4.98537e7i −0.0164154 + 0.0164154i
\(129\) 1.98353e9 4.78866e9i 0.630645 1.52251i
\(130\) 3.13369e9 + 1.29802e9i 0.962301 + 0.398598i
\(131\) −7.70757e8 1.86077e9i −0.228663 0.552042i 0.767352 0.641226i \(-0.221574\pi\)
−0.996015 + 0.0891841i \(0.971574\pi\)
\(132\) 4.09513e9i 1.17404i
\(133\) 5.99704e9 2.48406e9i 1.66190 0.688381i
\(134\) −6.19388e9 6.19388e9i −1.65955 1.65955i
\(135\) −3.11252e9 −0.806511
\(136\) 4.18842e7 1.97574e7i 0.0104985 0.00495228i
\(137\) 2.91545e9 0.707070 0.353535 0.935421i \(-0.384979\pi\)
0.353535 + 0.935421i \(0.384979\pi\)
\(138\) −2.13040e9 2.13040e9i −0.500040 0.500040i
\(139\) −6.95579e9 + 2.88118e9i −1.58045 + 0.654642i −0.988484 0.151323i \(-0.951647\pi\)
−0.591962 + 0.805966i \(0.701647\pi\)
\(140\) 7.07965e9i 1.55753i
\(141\) 3.06223e9 + 7.39288e9i 0.652457 + 1.57517i
\(142\) −8.03211e9 3.32701e9i −1.65780 0.686683i
\(143\) −1.47219e9 + 3.55417e9i −0.294408 + 0.710765i
\(144\) 1.06600e9 1.06600e9i 0.206599 0.206599i
\(145\) −3.49073e9 + 3.49073e9i −0.655783 + 0.655783i
\(146\) 1.04776e8 2.52951e8i 0.0190842 0.0460733i
\(147\) −8.71199e9 3.60863e9i −1.53883 0.637403i
\(148\) −1.21011e9 2.92146e9i −0.207323 0.500521i
\(149\) 8.08087e9i 1.34314i 0.740943 + 0.671568i \(0.234379\pi\)
−0.740943 + 0.671568i \(0.765621\pi\)
\(150\) −1.12545e6 + 466177.i −0.000181516 + 7.51865e-5i
\(151\) 2.25623e9 + 2.25623e9i 0.353172 + 0.353172i 0.861288 0.508116i \(-0.169658\pi\)
−0.508116 + 0.861288i \(0.669658\pi\)
\(152\) 8.74961e7 0.0132951
\(153\) −1.77664e9 + 8.38067e8i −0.262112 + 0.123642i
\(154\) 1.61258e10 2.31035
\(155\) 3.36960e9 + 3.36960e9i 0.468906 + 0.468906i
\(156\) −5.68139e9 + 2.35331e9i −0.768058 + 0.318140i
\(157\) 2.16958e9i 0.284988i −0.989796 0.142494i \(-0.954488\pi\)
0.989796 0.142494i \(-0.0455122\pi\)
\(158\) 3.51067e9 + 8.47550e9i 0.448160 + 1.08195i
\(159\) 2.29659e9 + 9.51278e8i 0.284968 + 0.118038i
\(160\) 4.47655e9 1.08074e10i 0.540012 1.30371i
\(161\) −4.17722e9 + 4.17722e9i −0.489971 + 0.489971i
\(162\) 1.05489e10 1.05489e10i 1.20334 1.20334i
\(163\) 6.17014e9 1.48960e10i 0.684622 1.65282i −0.0707222 0.997496i \(-0.522530\pi\)
0.755344 0.655328i \(-0.227470\pi\)
\(164\) −7.88581e6 3.26641e6i −0.000851234 0.000352593i
\(165\) 4.31283e9 + 1.04121e10i 0.452986 + 1.09360i
\(166\) 1.18730e10i 1.21360i
\(167\) −1.02730e10 + 4.25523e9i −1.02206 + 0.423350i −0.829839 0.558003i \(-0.811568\pi\)
−0.192218 + 0.981352i \(0.561568\pi\)
\(168\) −1.51162e8 1.51162e8i −0.0146403 0.0146403i
\(169\) 4.82760e9 0.455241
\(170\) −1.03321e10 + 1.13763e10i −0.948783 + 1.04467i
\(171\) −3.71139e9 −0.331936
\(172\) 1.16804e10 + 1.16804e10i 1.01761 + 1.01761i
\(173\) 1.37526e10 5.69650e9i 1.16728 0.483504i 0.286989 0.957934i \(-0.407346\pi\)
0.880294 + 0.474429i \(0.157346\pi\)
\(174\) 1.79745e10i 1.48657i
\(175\) 914066. + 2.20675e6i 7.36726e−5 + 0.000177861i
\(176\) 1.23583e10 + 5.11898e9i 0.970850 + 0.402139i
\(177\) −9.88810e9 + 2.38720e10i −0.757239 + 1.82814i
\(178\) −9.70142e9 + 9.70142e9i −0.724345 + 0.724345i
\(179\) 1.03071e10 1.03071e10i 0.750408 0.750408i −0.224147 0.974555i \(-0.571960\pi\)
0.974555 + 0.224147i \(0.0719597\pi\)
\(180\) −1.54906e9 + 3.73975e9i −0.109987 + 0.265532i
\(181\) 2.68335e9 + 1.11148e9i 0.185833 + 0.0769747i 0.473660 0.880708i \(-0.342933\pi\)
−0.287826 + 0.957683i \(0.592933\pi\)
\(182\) 9.26686e9 + 2.23722e10i 0.626053 + 1.51143i
\(183\) 2.48429e10i 1.63746i
\(184\) −7.35672e7 + 3.04725e7i −0.00473156 + 0.00195988i
\(185\) −6.15354e9 6.15354e9i −0.386235 0.386235i
\(186\) −1.73508e10 −1.06294
\(187\) −1.29028e10 1.17184e10i −0.771606 0.700780i
\(188\) −2.55019e10 −1.48889
\(189\) −1.57127e10 1.57127e10i −0.895718 0.895718i
\(190\) −2.68250e10 + 1.11113e10i −1.49331 + 0.618548i
\(191\) 1.67129e10i 0.908658i 0.890834 + 0.454329i \(0.150121\pi\)
−0.890834 + 0.454329i \(0.849879\pi\)
\(192\) 8.04869e9 + 1.94312e10i 0.427434 + 1.03192i
\(193\) 9.28945e9 + 3.84782e9i 0.481928 + 0.199621i 0.610402 0.792092i \(-0.291008\pi\)
−0.128474 + 0.991713i \(0.541008\pi\)
\(194\) 1.24543e10 3.00674e10i 0.631267 1.52401i
\(195\) −1.19668e10 + 1.19668e10i −0.592685 + 0.592685i
\(196\) 2.12501e10 2.12501e10i 1.02851 1.02851i
\(197\) −2.48261e9 + 5.99355e9i −0.117439 + 0.283522i −0.971658 0.236391i \(-0.924035\pi\)
0.854220 + 0.519912i \(0.174035\pi\)
\(198\) −8.51827e9 3.52838e9i −0.393875 0.163148i
\(199\) −1.78596e8 4.31168e8i −0.00807295 0.0194898i 0.919792 0.392407i \(-0.128358\pi\)
−0.927865 + 0.372917i \(0.878358\pi\)
\(200\) 32196.2i 1.42288e-6i
\(201\) 4.03782e10 1.67252e10i 1.74488 0.722751i
\(202\) −1.26538e10 1.26538e10i −0.534735 0.534735i
\(203\) −3.52439e10 −1.45664
\(204\) −1.33869e9 2.78298e10i −0.0541184 1.12506i
\(205\) −2.34902e7 −0.000928954
\(206\) 3.26800e9 + 3.26800e9i 0.126439 + 0.126439i
\(207\) 3.12056e9 1.29258e9i 0.118132 0.0489317i
\(208\) 2.00870e10i 0.744099i
\(209\) −1.26022e10 3.04244e10i −0.456865 1.10297i
\(210\) 6.55402e10 + 2.71476e10i 2.32553 + 0.963264i
\(211\) 4.06743e8 9.81965e8i 0.0141270 0.0341055i −0.916659 0.399671i \(-0.869124\pi\)
0.930786 + 0.365565i \(0.119124\pi\)
\(212\) −5.60179e9 + 5.60179e9i −0.190465 + 0.190465i
\(213\) 3.06728e10 3.06728e10i 1.02104 1.02104i
\(214\) −2.33608e10 + 5.63980e10i −0.761423 + 1.83824i
\(215\) 4.19995e10 + 1.73968e10i 1.34051 + 0.555259i
\(216\) −1.14623e8 2.76724e8i −0.00358285 0.00864978i
\(217\) 3.40208e10i 1.04154i
\(218\) −7.15182e10 + 2.96238e10i −2.14468 + 0.888356i
\(219\) 9.65963e8 + 9.65963e8i 0.0283767 + 0.0283767i
\(220\) −3.59167e10 −1.03370
\(221\) 8.84287e9 2.46348e10i 0.249361 0.694679i
\(222\) 3.16858e10 0.875542
\(223\) −3.39091e10 3.39091e10i −0.918214 0.918214i 0.0786853 0.996900i \(-0.474928\pi\)
−0.996900 + 0.0786853i \(0.974928\pi\)
\(224\) 7.71563e10 3.19592e10i 2.04765 0.848164i
\(225\) 1.36569e6i 3.55248e-5i
\(226\) 1.40124e10 + 3.38290e10i 0.357294 + 0.862584i
\(227\) 1.94473e10 + 8.05532e9i 0.486118 + 0.201357i 0.612262 0.790655i \(-0.290260\pi\)
−0.126143 + 0.992012i \(0.540260\pi\)
\(228\) 2.01448e10 4.86338e10i 0.493692 1.19188i
\(229\) 1.13634e10 1.13634e10i 0.273054 0.273054i −0.557275 0.830328i \(-0.688153\pi\)
0.830328 + 0.557275i \(0.188153\pi\)
\(230\) 1.86849e10 1.86849e10i 0.440266 0.440266i
\(231\) −3.07903e10 + 7.43344e10i −0.711476 + 1.71765i
\(232\) −4.38900e8 1.81798e8i −0.00994649 0.00411997i
\(233\) 2.32763e10 + 5.61939e10i 0.517382 + 1.24907i 0.939506 + 0.342533i \(0.111285\pi\)
−0.422124 + 0.906538i \(0.638715\pi\)
\(234\) 1.38455e10i 0.301882i
\(235\) −6.48401e10 + 2.68576e10i −1.38688 + 0.574463i
\(236\) −5.82281e10 5.82281e10i −1.22188 1.22188i
\(237\) −4.57724e10 −0.942401
\(238\) −1.09588e11 + 5.27150e9i −2.21395 + 0.106497i
\(239\) 4.66769e10 0.925362 0.462681 0.886525i \(-0.346887\pi\)
0.462681 + 0.886525i \(0.346887\pi\)
\(240\) 4.16102e10 + 4.16102e10i 0.809561 + 0.809561i
\(241\) −9.08976e9 + 3.76510e9i −0.173570 + 0.0718952i −0.467777 0.883847i \(-0.654945\pi\)
0.294206 + 0.955742i \(0.404945\pi\)
\(242\) 6.51093e9i 0.122032i
\(243\) 1.17082e10 + 2.82661e10i 0.215408 + 0.520040i
\(244\) 7.31462e10 + 3.02981e10i 1.32111 + 0.547220i
\(245\) 3.16498e10 7.64095e10i 0.561208 1.35488i
\(246\) 6.04779e7 6.04779e7i 0.00105290 0.00105290i
\(247\) 3.49674e10 3.49674e10i 0.597761 0.597761i
\(248\) −1.75490e8 + 4.23670e8i −0.00294591 + 0.00711205i
\(249\) 5.47305e10 + 2.26701e10i 0.902262 + 0.373729i
\(250\) −3.33593e10 8.05364e10i −0.540115 1.30395i
\(251\) 5.71571e10i 0.908947i −0.890760 0.454473i \(-0.849827\pi\)
0.890760 0.454473i \(-0.150173\pi\)
\(252\) −2.66990e10 + 1.10591e10i −0.417054 + 0.172749i
\(253\) 2.11920e10 + 2.11920e10i 0.325185 + 0.325185i
\(254\) 7.90402e10 1.19151
\(255\) −3.27130e10 6.93490e10i −0.484495 1.02709i
\(256\) 6.98359e10 1.01625
\(257\) 6.08016e10 + 6.08016e10i 0.869392 + 0.869392i 0.992405 0.123013i \(-0.0392556\pi\)
−0.123013 + 0.992405i \(0.539256\pi\)
\(258\) −1.52922e11 + 6.33423e10i −2.14873 + 0.890031i
\(259\) 6.21286e10i 0.857912i
\(260\) −2.06399e10 4.98292e10i −0.280110 0.676245i
\(261\) 1.86172e10 + 7.71149e9i 0.248331 + 0.102862i
\(262\) −2.46135e10 + 5.94221e10i −0.322713 + 0.779099i
\(263\) −1.84881e10 + 1.84881e10i −0.238282 + 0.238282i −0.816138 0.577856i \(-0.803889\pi\)
0.577856 + 0.816138i \(0.303889\pi\)
\(264\) −7.66878e8 + 7.66878e8i −0.00971648 + 0.00971648i
\(265\) −8.34328e9 + 2.01425e10i −0.103928 + 0.250903i
\(266\) −1.91510e11 7.93262e10i −2.34544 0.971514i
\(267\) −2.61965e10 6.32440e10i −0.315459 0.761585i
\(268\) 1.39285e11i 1.64930i
\(269\) 1.98411e10 8.21845e9i 0.231036 0.0956983i −0.264162 0.964478i \(-0.585095\pi\)
0.495198 + 0.868780i \(0.335095\pi\)
\(270\) 7.02834e10 + 7.02834e10i 0.804851 + 0.804851i
\(271\) −1.61241e11 −1.81599 −0.907997 0.418976i \(-0.862389\pi\)
−0.907997 + 0.418976i \(0.862389\pi\)
\(272\) −8.56584e10 3.07478e10i −0.948877 0.340608i
\(273\) −1.20822e11 −1.31648
\(274\) −6.58332e10 6.58332e10i −0.705615 0.705615i
\(275\) 1.11954e7 4.63727e6i 0.000118043 4.88951e-5i
\(276\) 4.79075e10i 0.496950i
\(277\) 1.81719e10 + 4.38710e10i 0.185457 + 0.447732i 0.989075 0.147413i \(-0.0470946\pi\)
−0.803618 + 0.595145i \(0.797095\pi\)
\(278\) 2.22127e11 + 9.20081e10i 2.23049 + 0.923898i
\(279\) 7.44389e9 1.79711e10i 0.0735498 0.177565i
\(280\) 1.32578e9 1.32578e9i 0.0128902 0.0128902i
\(281\) 1.92745e9 1.92745e9i 0.0184419 0.0184419i −0.697826 0.716268i \(-0.745849\pi\)
0.716268 + 0.697826i \(0.245849\pi\)
\(282\) 9.77897e10 2.36085e11i 0.920815 2.22304i
\(283\) −3.92533e10 1.62592e10i −0.363778 0.150682i 0.193304 0.981139i \(-0.438079\pi\)
−0.557083 + 0.830457i \(0.688079\pi\)
\(284\) 5.29032e10 + 1.27720e11i 0.482558 + 1.16500i
\(285\) 1.44870e11i 1.30070i
\(286\) 1.13499e11 4.70130e10i 1.00310 0.415499i
\(287\) −1.18583e8 1.18583e8i −0.00103170 0.00103170i
\(288\) −4.77498e10 −0.408983
\(289\) 9.15158e10 + 7.54185e10i 0.771713 + 0.635971i
\(290\) 1.57647e11 1.30887
\(291\) 1.14821e11 + 1.14821e11i 0.938645 + 0.938645i
\(292\) −4.02221e9 + 1.66606e9i −0.0323774 + 0.0134112i
\(293\) 6.93631e9i 0.0549825i 0.999622 + 0.0274912i \(0.00875183\pi\)
−0.999622 + 0.0274912i \(0.991248\pi\)
\(294\) 1.15238e11 + 2.78210e11i 0.899568 + 2.17175i
\(295\) −2.09372e11 8.67246e10i −1.60960 0.666720i
\(296\) 3.20478e8 7.73703e8i 0.00242653 0.00585816i
\(297\) −7.97140e10 + 7.97140e10i −0.594471 + 0.594471i
\(298\) 1.82473e11 1.82473e11i 1.34037 1.34037i
\(299\) −1.72226e10 + 4.15790e10i −0.124617 + 0.300853i
\(300\) 1.78959e7 + 7.41274e6i 0.000127558 + 5.28364e-5i
\(301\) 1.24200e11 + 2.99845e11i 0.872110 + 2.10546i
\(302\) 1.01895e11i 0.704891i
\(303\) 8.24905e10 3.41687e10i 0.562228 0.232882i
\(304\) −1.21586e11 1.21586e11i −0.816495 0.816495i
\(305\) 2.17887e11 1.44172
\(306\) 5.90422e10 + 2.11937e10i 0.384961 + 0.138185i
\(307\) 1.64410e10 0.105635 0.0528173 0.998604i \(-0.483180\pi\)
0.0528173 + 0.998604i \(0.483180\pi\)
\(308\) −1.81315e11 1.81315e11i −1.14804 1.14804i
\(309\) −2.13042e10 + 8.82451e9i −0.132939 + 0.0550652i
\(310\) 1.52177e11i 0.935881i
\(311\) −4.68694e10 1.13153e11i −0.284098 0.685872i 0.715826 0.698279i \(-0.246051\pi\)
−0.999923 + 0.0124071i \(0.996051\pi\)
\(312\) −1.50463e9 6.23237e8i −0.00898945 0.00372355i
\(313\) −9.05020e10 + 2.18491e11i −0.532977 + 1.28672i 0.396565 + 0.918006i \(0.370202\pi\)
−0.929543 + 0.368715i \(0.879798\pi\)
\(314\) −4.89909e10 + 4.89909e10i −0.284402 + 0.284402i
\(315\) −5.62367e10 + 5.62367e10i −0.321827 + 0.321827i
\(316\) 5.58236e10 1.34770e11i 0.314938 0.760329i
\(317\) 4.00600e10 + 1.65934e10i 0.222815 + 0.0922930i 0.491298 0.870991i \(-0.336522\pi\)
−0.268483 + 0.963284i \(0.586522\pi\)
\(318\) −3.03782e10 7.33395e10i −0.166587 0.402176i
\(319\) 1.78800e11i 0.966742i
\(320\) −1.70424e11 + 7.05919e10i −0.908564 + 0.376340i
\(321\) −2.15371e11 2.15371e11i −1.13218 1.13218i
\(322\) 1.88650e11 0.977926
\(323\) 9.55882e10 + 2.02640e11i 0.488644 + 1.03589i
\(324\) −2.37218e11 −1.19590
\(325\) 1.28671e7 + 1.28671e7i 6.39741e−5 + 6.39741e-5i
\(326\) −4.75692e11 + 1.97038e11i −2.33263 + 0.966209i
\(327\) 3.86238e11i 1.86806i
\(328\) −865057. 2.08843e6i −4.12679e−6 9.96296e-6i
\(329\) −4.62909e11 1.91743e11i −2.17828 0.902274i
\(330\) 1.37726e11 3.32501e11i 0.639300 1.54341i
\(331\) 1.20201e11 1.20201e11i 0.550406 0.550406i −0.376152 0.926558i \(-0.622753\pi\)
0.926558 + 0.376152i \(0.122753\pi\)
\(332\) −1.33498e11 + 1.33498e11i −0.603049 + 0.603049i
\(333\) −1.35940e10 + 3.28188e10i −0.0605826 + 0.146259i
\(334\) 3.28061e11 + 1.35887e11i 1.44243 + 0.597475i
\(335\) 1.46690e11 + 3.54141e11i 0.636355 + 1.53630i
\(336\) 4.20114e11i 1.79821i
\(337\) −9.48238e9 + 3.92773e9i −0.0400482 + 0.0165885i −0.402618 0.915368i \(-0.631900\pi\)
0.362569 + 0.931957i \(0.381900\pi\)
\(338\) −1.09011e11 1.09011e11i −0.454304 0.454304i
\(339\) −1.82695e11 −0.751327
\(340\) 2.44084e11 1.17411e10i 0.990569 0.0476492i
\(341\) 1.72596e11 0.691251
\(342\) 8.38064e10 + 8.38064e10i 0.331253 + 0.331253i
\(343\) 1.73553e11 7.18878e10i 0.677029 0.280435i
\(344\) 4.37469e9i 0.0168436i
\(345\) 5.04543e10 + 1.21808e11i 0.191740 + 0.462901i
\(346\) −4.39176e11 1.81913e11i −1.64739 0.682371i
\(347\) −5.75630e10 + 1.38969e11i −0.213138 + 0.514561i −0.993902 0.110265i \(-0.964830\pi\)
0.780764 + 0.624826i \(0.214830\pi\)
\(348\) −2.02102e11 + 2.02102e11i −0.738692 + 0.738692i
\(349\) 3.10027e11 3.10027e11i 1.11862 1.11862i 0.126681 0.991943i \(-0.459567\pi\)
0.991943 0.126681i \(-0.0404326\pi\)
\(350\) 2.91899e7 7.04706e7i 0.000103974 0.000251016i
\(351\) −1.56400e11 6.47830e10i −0.549990 0.227813i
\(352\) −1.62137e11 3.91432e11i −0.562910 1.35898i
\(353\) 3.32465e10i 0.113962i −0.998375 0.0569810i \(-0.981853\pi\)
0.998375 0.0569810i \(-0.0181475\pi\)
\(354\) 7.62331e11 3.15768e11i 2.58005 1.06869i
\(355\) 2.69019e11 + 2.69019e11i 0.898990 + 0.898990i
\(356\) 2.18162e11 0.719869
\(357\) 1.84946e11 5.15230e11i 0.602612 1.67878i
\(358\) −4.65485e11 −1.49773
\(359\) 1.44809e11 + 1.44809e11i 0.460119 + 0.460119i 0.898695 0.438575i \(-0.144517\pi\)
−0.438575 + 0.898695i \(0.644517\pi\)
\(360\) −9.90414e8 + 4.10243e8i −0.00310782 + 0.00128730i
\(361\) 1.00627e11i 0.311839i
\(362\) −3.54941e10 8.56905e10i −0.108635 0.262267i
\(363\) 3.00132e10 + 1.24319e10i 0.0907260 + 0.0375800i
\(364\) 1.47354e11 3.55743e11i 0.439951 1.06214i
\(365\) −8.47208e9 + 8.47208e9i −0.0249846 + 0.0249846i
\(366\) −5.60973e11 + 5.60973e11i −1.63409 + 1.63409i
\(367\) 1.22419e11 2.95545e11i 0.352249 0.850405i −0.644092 0.764948i \(-0.722765\pi\)
0.996342 0.0854576i \(-0.0272352\pi\)
\(368\) 1.44576e11 + 5.98852e10i 0.410942 + 0.170218i
\(369\) 3.66939e7 + 8.85868e7i 0.000103033 + 0.000248743i
\(370\) 2.77904e11i 0.770881i
\(371\) −1.43802e11 + 5.95647e10i −0.394078 + 0.163232i
\(372\) 1.95088e11 + 1.95088e11i 0.528188 + 0.528188i
\(373\) 1.73495e11 0.464084 0.232042 0.972706i \(-0.425459\pi\)
0.232042 + 0.972706i \(0.425459\pi\)
\(374\) 2.67436e10 + 5.55967e11i 0.0706801 + 1.46935i
\(375\) 4.34941e11 1.13577
\(376\) −4.77565e9 4.77565e9i −0.0123222 0.0123222i
\(377\) −2.48059e11 + 1.02750e11i −0.632440 + 0.261965i
\(378\) 7.09610e11i 1.78775i
\(379\) −5.13111e10 1.23876e11i −0.127742 0.308397i 0.847049 0.531514i \(-0.178377\pi\)
−0.974792 + 0.223117i \(0.928377\pi\)
\(380\) 4.26548e11 + 1.76682e11i 1.04940 + 0.434677i
\(381\) −1.50918e11 + 3.64348e11i −0.366926 + 0.885838i
\(382\) 3.77390e11 3.77390e11i 0.906788 0.906788i
\(383\) −4.09179e11 + 4.09179e11i −0.971669 + 0.971669i −0.999610 0.0279404i \(-0.991105\pi\)
0.0279404 + 0.999610i \(0.491105\pi\)
\(384\) −4.29893e9 + 1.03785e10i −0.0100895 + 0.0243582i
\(385\) −6.51958e11 2.70050e11i −1.51233 0.626427i
\(386\) −1.22877e11 2.96651e11i −0.281726 0.680146i
\(387\) 1.85565e11i 0.420530i
\(388\) −4.78106e11 + 1.98038e11i −1.07098 + 0.443615i
\(389\) −2.40690e11 2.40690e11i −0.532948 0.532948i 0.388500 0.921449i \(-0.372993\pi\)
−0.921449 + 0.388500i \(0.872993\pi\)
\(390\) 5.40442e11 1.18293
\(391\) −1.50945e11 1.37090e11i −0.326605 0.296626i
\(392\) 7.95886e9 0.0170241
\(393\) −2.26919e11 2.26919e11i −0.479849 0.479849i
\(394\) 1.91399e11 7.92800e10i 0.400135 0.165741i
\(395\) 4.01452e11i 0.829748i
\(396\) 5.61053e10 + 1.35450e11i 0.114650 + 0.276791i
\(397\) 3.12258e11 + 1.29341e11i 0.630893 + 0.261324i 0.675132 0.737697i \(-0.264086\pi\)
−0.0442395 + 0.999021i \(0.514086\pi\)
\(398\) −5.70330e9 + 1.37690e10i −0.0113934 + 0.0275060i
\(399\) 7.31333e11 7.31333e11i 1.44457 1.44457i
\(400\) 4.47405e7 4.47405e7i 8.73837e−5 8.73837e-5i
\(401\) 2.59597e11 6.26723e11i 0.501361 1.21039i −0.447382 0.894343i \(-0.647643\pi\)
0.948743 0.316049i \(-0.102357\pi\)
\(402\) −1.28944e12 5.34104e11i −2.46255 1.02002i
\(403\) 9.91840e10 + 2.39451e11i 0.187313 + 0.452215i
\(404\) 2.84553e11i 0.531431i
\(405\) −6.03141e11 + 2.49829e11i −1.11396 + 0.461419i
\(406\) 7.95836e11 + 7.95836e11i 1.45364 + 1.45364i
\(407\) −3.15193e11 −0.569380
\(408\) 4.96089e9 5.46227e9i 0.00886316 0.00975893i
\(409\) 3.79922e11 0.671336 0.335668 0.941980i \(-0.391038\pi\)
0.335668 + 0.941980i \(0.391038\pi\)
\(410\) 5.30428e8 + 5.30428e8i 0.000927042 + 0.000927042i
\(411\) 4.29170e11 1.77768e11i 0.741892 0.307302i
\(412\) 7.34895e10i 0.125657i
\(413\) −6.19148e11 1.49476e12i −1.04717 2.52810i
\(414\) −9.96524e10 4.12774e10i −0.166719 0.0690575i
\(415\) −1.98831e11 + 4.80020e11i −0.329054 + 0.794407i
\(416\) 4.49881e11 4.49881e11i 0.736509 0.736509i
\(417\) −8.48252e11 + 8.48252e11i −1.37376 + 1.37376i
\(418\) −4.02441e11 + 9.71577e11i −0.644775 + 1.55663i
\(419\) 5.82365e11 + 2.41224e11i 0.923065 + 0.382346i 0.793043 0.609165i \(-0.208495\pi\)
0.130022 + 0.991511i \(0.458495\pi\)
\(420\) −4.31678e11 1.04216e12i −0.676922 1.63423i
\(421\) 3.36779e11i 0.522488i −0.965273 0.261244i \(-0.915867\pi\)
0.965273 0.261244i \(-0.0841327\pi\)
\(422\) −3.13582e10 + 1.29890e10i −0.0481332 + 0.0199374i
\(423\) 2.02572e11 + 2.02572e11i 0.307644 + 0.307644i
\(424\) −2.09805e9 −0.00315261
\(425\) −7.45659e7 + 3.51739e7i −0.000110864 + 5.22962e-5i
\(426\) −1.38523e12 −2.03788
\(427\) 1.09994e12 + 1.09994e12i 1.60119 + 1.60119i
\(428\) 8.96792e11 3.71463e11i 1.29180 0.535080i
\(429\) 6.12959e11i 0.873723i
\(430\) −5.55551e11 1.34122e12i −0.783638 1.89187i
\(431\) −1.91658e11 7.93872e10i −0.267534 0.110816i 0.244884 0.969552i \(-0.421250\pi\)
−0.512418 + 0.858736i \(0.671250\pi\)
\(432\) −2.25259e11 + 5.43823e11i −0.311175 + 0.751244i
\(433\) −4.61492e11 + 4.61492e11i −0.630911 + 0.630911i −0.948297 0.317385i \(-0.897195\pi\)
0.317385 + 0.948297i \(0.397195\pi\)
\(434\) 7.68219e11 7.68219e11i 1.03940 1.03940i
\(435\) −3.01009e11 + 7.26700e11i −0.403068 + 0.973092i
\(436\) 1.13722e12 + 4.71052e11i 1.50715 + 0.624281i
\(437\) −1.47429e11 3.55925e11i −0.193382 0.466866i
\(438\) 4.36245e10i 0.0566366i
\(439\) 5.53757e11 2.29374e11i 0.711589 0.294750i 0.00262700 0.999997i \(-0.499164\pi\)
0.708962 + 0.705247i \(0.249164\pi\)
\(440\) −6.72599e9 6.72599e9i −0.00855498 0.00855498i
\(441\) −3.37597e11 −0.425036
\(442\) −7.55954e11 + 3.56595e11i −0.942096 + 0.444401i
\(443\) 1.38710e11 0.171117 0.0855583 0.996333i \(-0.472733\pi\)
0.0855583 + 0.996333i \(0.472733\pi\)
\(444\) −3.56269e11 3.56269e11i −0.435066 0.435066i
\(445\) 5.54688e11 2.29759e11i 0.670546 0.277749i
\(446\) 1.53139e12i 1.83265i
\(447\) 4.92727e11 + 1.18955e12i 0.583745 + 1.40928i
\(448\) −1.21670e12 5.03972e11i −1.42702 0.591093i
\(449\) −6.81450e10 + 1.64517e11i −0.0791271 + 0.191030i −0.958492 0.285118i \(-0.907967\pi\)
0.879365 + 0.476148i \(0.157967\pi\)
\(450\) −3.08385e7 + 3.08385e7i −3.54517e−5 + 3.54517e-5i
\(451\) −6.01601e8 + 6.01601e8i −0.000684722 + 0.000684722i
\(452\) 2.22814e11 5.37919e11i 0.251084 0.606170i
\(453\) 4.69701e11 + 1.94557e11i 0.524059 + 0.217072i
\(454\) −2.57240e11 6.21031e11i −0.284175 0.686060i
\(455\) 1.05968e12i 1.15911i
\(456\) 1.28799e10 5.33503e9i 0.0139499 0.00577824i
\(457\) 1.15093e11 + 1.15093e11i 0.123431 + 0.123431i 0.766124 0.642693i \(-0.222183\pi\)
−0.642693 + 0.766124i \(0.722183\pi\)
\(458\) −5.13189e11 −0.544983
\(459\) 5.15665e11 5.67781e11i 0.542263 0.597068i
\(460\) −4.20178e11 −0.437545
\(461\) −1.01437e12 1.01437e12i −1.04602 1.04602i −0.998889 0.0471320i \(-0.984992\pi\)
−0.0471320 0.998889i \(-0.515008\pi\)
\(462\) 2.37380e12 9.83262e11i 2.42413 1.00411i
\(463\) 8.05823e11i 0.814939i 0.913219 + 0.407470i \(0.133589\pi\)
−0.913219 + 0.407470i \(0.866411\pi\)
\(464\) 3.57274e11 + 8.62535e11i 0.357824 + 0.863865i
\(465\) 7.01483e11 + 2.90564e11i 0.695791 + 0.288206i
\(466\) 7.43307e11 1.79450e12i 0.730183 1.76282i
\(467\) −6.52494e11 + 6.52494e11i −0.634820 + 0.634820i −0.949273 0.314453i \(-0.898179\pi\)
0.314453 + 0.949273i \(0.398179\pi\)
\(468\) −1.55676e11 + 1.55676e11i −0.150008 + 0.150008i
\(469\) −1.04726e12 + 2.52830e12i −0.999482 + 2.41296i
\(470\) 2.07061e12 + 8.57675e11i 1.95730 + 0.810742i
\(471\) −1.32289e11 3.19374e11i −0.123860 0.299023i
\(472\) 2.18083e10i 0.0202247i
\(473\) 1.52118e12 6.30094e11i 1.39735 0.578803i
\(474\) 1.03358e12 + 1.03358e12i 0.940461 + 0.940461i
\(475\) −1.55768e8 −0.000140397
\(476\) 1.29146e12 + 1.17292e12i 1.15305 + 1.04721i
\(477\) 8.89948e10 0.0787104
\(478\) −1.05400e12 1.05400e12i −0.923458 0.923458i
\(479\) −3.79472e11 + 1.57182e11i −0.329359 + 0.136425i −0.541235 0.840872i \(-0.682043\pi\)
0.211875 + 0.977297i \(0.432043\pi\)
\(480\) 1.86386e12i 1.60261i
\(481\) −1.81129e11 4.37285e11i −0.154289 0.372487i
\(482\) 2.90274e11 + 1.20235e11i 0.244960 + 0.101466i
\(483\) −3.60206e11 + 8.69613e11i −0.301154 + 0.727050i
\(484\) −7.32076e10 + 7.32076e10i −0.0606390 + 0.0606390i
\(485\) −1.00705e12 + 1.00705e12i −0.826441 + 0.826441i
\(486\) 3.73891e11 9.02652e11i 0.304005 0.733934i
\(487\) 6.74522e11 + 2.79396e11i 0.543395 + 0.225082i 0.637459 0.770484i \(-0.279986\pi\)
−0.0940634 + 0.995566i \(0.529986\pi\)
\(488\) 8.02398e9 + 1.93716e10i 0.00640473 + 0.0154624i
\(489\) 2.56900e12i 2.03177i
\(490\) −2.44007e12 + 1.01071e12i −1.91214 + 0.792035i
\(491\) −1.55074e12 1.55074e12i −1.20413 1.20413i −0.972900 0.231227i \(-0.925726\pi\)
−0.231227 0.972900i \(-0.574274\pi\)
\(492\) −1.36000e9 −0.00104640
\(493\) −5.84496e10 1.21510e12i −0.0445626 0.926404i
\(494\) −1.57919e12 −1.19306
\(495\) 2.85302e11 + 2.85302e11i 0.213590 + 0.213590i
\(496\) 8.32604e11 3.44876e11i 0.617690 0.255856i
\(497\) 2.71612e12i 1.99685i
\(498\) −7.23951e11 1.74777e12i −0.527445 1.27336i
\(499\) −1.94673e12 8.06362e11i −1.40557 0.582207i −0.454381 0.890807i \(-0.650140\pi\)
−0.951192 + 0.308600i \(0.900140\pi\)
\(500\) −5.30450e11 + 1.28062e12i −0.379559 + 0.916337i
\(501\) −1.25279e12 + 1.25279e12i −0.888398 + 0.888398i
\(502\) −1.29066e12 + 1.29066e12i −0.907076 + 0.907076i
\(503\) 1.11753e11 2.69795e11i 0.0778400 0.187922i −0.880169 0.474660i \(-0.842571\pi\)
0.958009 + 0.286738i \(0.0925709\pi\)
\(504\) −7.07080e9 2.92882e9i −0.00488125 0.00202188i
\(505\) 2.99680e11 + 7.23492e11i 0.205044 + 0.495020i
\(506\) 9.57067e11i 0.649030i
\(507\) 7.10650e11 2.94361e11i 0.477661 0.197854i
\(508\) −8.88712e11 8.88712e11i −0.592072 0.592072i
\(509\) 3.27240e11 0.216091 0.108045 0.994146i \(-0.465541\pi\)
0.108045 + 0.994146i \(0.465541\pi\)
\(510\) −8.27272e11 + 2.30464e12i −0.541480 + 1.50848i
\(511\) −8.55376e10 −0.0554962
\(512\) −1.55143e12 1.55143e12i −0.997739 0.997739i
\(513\) 1.33882e12 5.54556e11i 0.853479 0.353522i
\(514\) 2.74590e12i 1.73521i
\(515\) −7.73963e10 1.86851e11i −0.0484828 0.117048i
\(516\) 2.43163e12 + 1.00721e12i 1.50999 + 0.625458i
\(517\) −9.72758e11 + 2.34845e12i −0.598822 + 1.44568i
\(518\) −1.40292e12 + 1.40292e12i −0.856147 + 0.856147i
\(519\) 1.67711e12 1.67711e12i 1.01463 1.01463i
\(520\) 5.46616e9 1.31965e10i 0.00327844 0.00791486i
\(521\) 4.23798e11 + 1.75543e11i 0.251994 + 0.104379i 0.505105 0.863058i \(-0.331454\pi\)
−0.253111 + 0.967437i \(0.581454\pi\)
\(522\) −2.46260e11 5.94524e11i −0.145170 0.350471i
\(523\) 2.19925e11i 0.128534i −0.997933 0.0642669i \(-0.979529\pi\)
0.997933 0.0642669i \(-0.0204709\pi\)
\(524\) 9.44879e11 3.91382e11i 0.547502 0.226783i
\(525\) 2.69111e8 + 2.69111e8i 0.000154602 + 0.000154602i
\(526\) 8.34954e11 0.475583
\(527\) −1.17293e12 + 5.64214e10i −0.662408 + 0.0318637i
\(528\) 2.13134e12 1.19344
\(529\) −1.02569e12 1.02569e12i −0.569463 0.569463i
\(530\) 6.43232e11 2.66436e11i 0.354100 0.146673i
\(531\) 9.25060e11i 0.504946i
\(532\) 1.26138e12 + 3.04523e12i 0.682719 + 1.64823i
\(533\) −1.18035e9 4.88917e8i −0.000633488 0.000262399i
\(534\) −8.36563e11 + 2.01964e12i −0.445208 + 1.07483i
\(535\) 1.88893e12 1.88893e12i 0.996838 0.996838i
\(536\) −2.60834e10 + 2.60834e10i −0.0136497 + 0.0136497i
\(537\) 8.88790e11 2.14573e12i 0.461227 1.11350i
\(538\) −6.33608e11 2.62449e11i −0.326062 0.135059i
\(539\) −1.14633e12 2.76748e12i −0.585004 1.41233i
\(540\) 1.58050e12i 0.799878i
\(541\) 1.46492e12 6.06791e11i 0.735237 0.304545i 0.0165348 0.999863i \(-0.494737\pi\)
0.718702 + 0.695318i \(0.244737\pi\)
\(542\) 3.64096e12 + 3.64096e12i 1.81226 + 1.81226i
\(543\) 4.62776e11 0.228440
\(544\) 1.22981e12 + 2.60711e12i 0.602065 + 1.27633i
\(545\) 3.38754e12 1.64475
\(546\) 2.72826e12 + 2.72826e12i 1.31377 + 1.31377i
\(547\) −3.38579e12 + 1.40244e12i −1.61702 + 0.669793i −0.993690 0.112163i \(-0.964222\pi\)
−0.623334 + 0.781956i \(0.714222\pi\)
\(548\) 1.48043e12i 0.701255i
\(549\) −3.40360e11 8.21702e11i −0.159905 0.386046i
\(550\) −3.57514e8 1.48087e8i −0.000166595 6.90058e-5i
\(551\) 8.79557e11 2.12344e12i 0.406520 0.981426i
\(552\) −8.97145e9 + 8.97145e9i −0.00411279 + 0.00411279i
\(553\) 2.02661e12 2.02661e12i 0.921525 0.921525i
\(554\) 5.80305e11 1.40098e12i 0.261736 0.631885i
\(555\) −1.28104e12 5.30626e11i −0.573120 0.237394i
\(556\) −1.46303e12 3.53207e12i −0.649258 1.56745i
\(557\) 1.44850e12i 0.637632i 0.947817 + 0.318816i \(0.103285\pi\)
−0.947817 + 0.318816i \(0.896715\pi\)
\(558\) −5.73893e11 + 2.37714e11i −0.250598 + 0.103801i
\(559\) 1.74833e12 + 1.74833e12i 0.757303 + 0.757303i
\(560\) −3.68466e12 −1.58326
\(561\) −2.61388e12 9.38275e11i −1.11417 0.399942i
\(562\) −8.70470e10 −0.0368079
\(563\) 2.43763e12 + 2.43763e12i 1.02254 + 1.02254i 0.999740 + 0.0228010i \(0.00725841\pi\)
0.0228010 + 0.999740i \(0.492742\pi\)
\(564\) −3.75402e12 + 1.55497e12i −1.56222 + 0.647091i
\(565\) 1.60235e12i 0.661514i
\(566\) 5.19225e11 + 1.25352e12i 0.212658 + 0.513402i
\(567\) −4.30597e12 1.78359e12i −1.74963 0.724722i
\(568\) −1.40106e10 + 3.38245e10i −0.00564792 + 0.0136353i
\(569\) 2.07409e12 2.07409e12i 0.829513 0.829513i −0.157936 0.987449i \(-0.550484\pi\)
0.987449 + 0.157936i \(0.0504841\pi\)
\(570\) −3.27129e12 + 3.27129e12i −1.29802 + 1.29802i
\(571\) −1.85799e12 + 4.48559e12i −0.731444 + 1.76586i −0.0937195 + 0.995599i \(0.529876\pi\)
−0.637725 + 0.770264i \(0.720124\pi\)
\(572\) −1.80477e12 7.47559e11i −0.704919 0.291987i
\(573\) 1.01906e12 + 2.46022e12i 0.394915 + 0.953408i
\(574\) 5.35542e9i 0.00205916i
\(575\) 1.30971e8 5.42499e7i 4.99654e−5 2.06963e-5i
\(576\) 5.32436e11 + 5.32436e11i 0.201542 + 0.201542i
\(577\) 3.14368e12 1.18072 0.590360 0.807140i \(-0.298986\pi\)
0.590360 + 0.807140i \(0.298986\pi\)
\(578\) −3.63490e11 3.76952e12i −0.135462 1.40479i
\(579\) 1.60208e12 0.592420
\(580\) −1.77255e12 1.77255e12i −0.650390 0.650390i
\(581\) −3.42698e12 + 1.41950e12i −1.24773 + 0.516825i
\(582\) 5.18549e12i 1.87343i
\(583\) 3.02186e11 + 7.29541e11i 0.108334 + 0.261542i
\(584\) −1.06522e9 4.41229e8i −0.000378950 0.000156966i
\(585\) −2.31863e11 + 5.59766e11i −0.0818521 + 0.197608i
\(586\) 1.56628e11 1.56628e11i 0.0548693 0.0548693i
\(587\) 3.74660e11 3.74660e11i 0.130246 0.130246i −0.638978 0.769225i \(-0.720643\pi\)
0.769225 + 0.638978i \(0.220643\pi\)
\(588\) 1.83242e12 4.42385e12i 0.632160 1.52617i
\(589\) −2.04975e12 8.49036e11i −0.701750 0.290675i
\(590\) 2.76948e12 + 6.68611e12i 0.940943 + 2.27164i
\(591\) 1.03366e12i 0.348525i
\(592\) −1.52050e12 + 6.29810e11i −0.508789 + 0.210747i
\(593\) −1.30887e12 1.30887e12i −0.434660 0.434660i 0.455550 0.890210i \(-0.349443\pi\)
−0.890210 + 0.455550i \(0.849443\pi\)
\(594\) 3.60002e12 1.18649
\(595\) 4.51888e12 + 1.62209e12i 1.47810 + 0.530577i
\(596\) −4.10338e12 −1.33209
\(597\) −5.25806e10 5.25806e10i −0.0169411 0.0169411i
\(598\) 1.32779e12 5.49989e11i 0.424594 0.175873i
\(599\) 9.54735e11i 0.303014i 0.988456 + 0.151507i \(0.0484126\pi\)
−0.988456 + 0.151507i \(0.951587\pi\)
\(600\) 1.96315e6 + 4.73946e6i 6.18404e−7 + 1.49296e-6i
\(601\) 4.89651e12 + 2.02820e12i 1.53092 + 0.634126i 0.979742 0.200264i \(-0.0641800\pi\)
0.551174 + 0.834390i \(0.314180\pi\)
\(602\) 3.96621e12 9.57528e12i 1.23081 2.97144i
\(603\) 1.10640e12 1.10640e12i 0.340789 0.340789i
\(604\) −1.14569e12 + 1.14569e12i −0.350267 + 0.350267i
\(605\) −1.09035e11 + 2.63234e11i −0.0330877 + 0.0798808i
\(606\) −2.63426e12 1.09115e12i −0.793473 0.328667i
\(607\) −1.05947e12 2.55778e12i −0.316765 0.764739i −0.999422 0.0339997i \(-0.989175\pi\)
0.682657 0.730739i \(-0.260825\pi\)
\(608\) 5.44624e12i 1.61633i
\(609\) −5.18809e12 + 2.14898e12i −1.52837 + 0.633073i
\(610\) −4.92007e12 4.92007e12i −1.43876 1.43876i
\(611\) −3.81713e12 −1.10803
\(612\) −4.25561e11 9.02156e11i −0.122625 0.259956i
\(613\) 6.26290e11 0.179144 0.0895722 0.995980i \(-0.471450\pi\)
0.0895722 + 0.995980i \(0.471450\pi\)
\(614\) −3.71252e11 3.71252e11i −0.105417 0.105417i
\(615\) −3.45788e9 + 1.43230e9i −0.000974703 + 0.000403735i
\(616\) 6.79083e10i 0.0190025i
\(617\) −1.44420e12 3.48661e12i −0.401184 0.968545i −0.987379 0.158375i \(-0.949375\pi\)
0.586195 0.810170i \(-0.300625\pi\)
\(618\) 6.80332e11 + 2.81803e11i 0.187617 + 0.0777137i
\(619\) −5.69735e11 + 1.37546e12i −0.155979 + 0.376566i −0.982480 0.186369i \(-0.940328\pi\)
0.826501 + 0.562935i \(0.190328\pi\)
\(620\) −1.71104e12 + 1.71104e12i −0.465049 + 0.465049i
\(621\) −9.32547e11 + 9.32547e11i −0.251628 + 0.251628i
\(622\) −1.49673e12 + 3.61343e12i −0.400948 + 0.967973i
\(623\) 3.96005e12 + 1.64031e12i 1.05318 + 0.436244i
\(624\) 1.22480e12 + 2.95692e12i 0.323395 + 0.780744i
\(625\) 3.81423e12i 0.999877i
\(626\) 6.97733e12 2.89010e12i 1.81595 0.752192i
\(627\) −3.71023e12 3.71023e12i −0.958731 0.958731i
\(628\) 1.10169e12 0.282644
\(629\) 2.14200e12 1.03036e11i 0.545622 0.0262460i
\(630\) 2.53974e12 0.642328
\(631\) −5.79226e10 5.79226e10i −0.0145451 0.0145451i 0.699797 0.714342i \(-0.253274\pi\)
−0.714342 + 0.699797i \(0.753274\pi\)
\(632\) 3.56917e10 1.47840e10i 0.00889899 0.00368608i
\(633\) 1.69352e11i 0.0419249i
\(634\) −5.29896e11 1.27928e12i −0.130253 0.314459i
\(635\) −3.19556e12 1.32364e12i −0.779946 0.323064i
\(636\) −4.83048e11 + 1.16618e12i −0.117067 + 0.282624i
\(637\) 3.18072e12 3.18072e12i 0.765417 0.765417i
\(638\) 4.03746e12 4.03746e12i 0.964752 0.964752i
\(639\) 5.94298e11 1.43476e12i 0.141010 0.340429i
\(640\) −9.10262e10 3.77043e10i −0.0214465 0.00888343i
\(641\) −3.33558e11 8.05280e11i −0.0780387 0.188402i 0.880045 0.474890i \(-0.157512\pi\)
−0.958084 + 0.286488i \(0.907512\pi\)
\(642\) 9.72650e12i 2.25969i
\(643\) 6.48078e11 2.68443e11i 0.149513 0.0619302i −0.306672 0.951815i \(-0.599216\pi\)
0.456185 + 0.889885i \(0.349216\pi\)
\(644\) −2.12114e12 2.12114e12i −0.485941 0.485941i
\(645\) 7.24332e12 1.64785
\(646\) 2.41731e12 6.73424e12i 0.546118 1.52140i
\(647\) −6.30742e12 −1.41509 −0.707543 0.706671i \(-0.750196\pi\)
−0.707543 + 0.706671i \(0.750196\pi\)
\(648\) −4.44230e10 4.44230e10i −0.00989737 0.00989737i
\(649\) −7.58325e12 + 3.14108e12i −1.67785 + 0.694990i
\(650\) 5.81098e8i 0.000127685i
\(651\) 2.07440e12 + 5.00806e12i 0.452667 + 1.09284i
\(652\) 7.56404e12 + 3.13313e12i 1.63923 + 0.678991i
\(653\) −7.96043e11 + 1.92182e12i −0.171328 + 0.413622i −0.986099 0.166161i \(-0.946863\pi\)
0.814771 + 0.579783i \(0.196863\pi\)
\(654\) −8.72158e12 + 8.72158e12i −1.86421 + 1.86421i
\(655\) 1.99022e12 1.99022e12i 0.422489 0.422489i
\(656\) −1.70003e9 + 4.10423e9i −0.000358417 + 0.000865295i
\(657\) 4.51843e10 + 1.87160e10i 0.00946114 + 0.00391893i
\(658\) 6.12315e12 + 1.47826e13i 1.27338 + 3.07421i
\(659\) 1.77225e12i 0.366051i 0.983108 + 0.183025i \(0.0585890\pi\)
−0.983108 + 0.183025i \(0.941411\pi\)
\(660\) −5.28714e12 + 2.19001e12i −1.08461 + 0.449260i
\(661\) 9.39346e11 + 9.39346e11i 0.191390 + 0.191390i 0.796296 0.604907i \(-0.206790\pi\)
−0.604907 + 0.796296i \(0.706790\pi\)
\(662\) −5.42849e12 −1.09855
\(663\) −2.00376e11 4.16557e12i −0.0402748 0.837266i
\(664\) −4.99992e10 −0.00998175
\(665\) 6.41424e12 + 6.41424e12i 1.27188 + 1.27188i
\(666\) 1.04804e12 4.34112e11i 0.206416 0.0855004i
\(667\) 2.09173e12i 0.409203i
\(668\) −2.16076e12 5.21654e12i −0.419868 1.01365i
\(669\) −7.05919e12 2.92401e12i −1.36250 0.564367i
\(670\) 4.68442e12 1.13092e13i 0.898089 2.16818i
\(671\) 5.58025e12 5.58025e12i 1.06268 1.06268i
\(672\) 9.40913e12 9.40913e12i 1.77987 1.77987i
\(673\) 2.71863e12 6.56336e12i 0.510838 1.23327i −0.432559 0.901605i \(-0.642389\pi\)
0.943397 0.331666i \(-0.107611\pi\)
\(674\) 3.02812e11 + 1.25429e11i 0.0565201 + 0.0234114i
\(675\) 2.04061e8 + 4.92648e8i 3.78350e−5 + 9.13418e-5i
\(676\) 2.45140e12i 0.451497i
\(677\) 1.04359e11 4.32271e10i 0.0190934 0.00790874i −0.373116 0.927785i \(-0.621711\pi\)
0.392210 + 0.919876i \(0.371711\pi\)
\(678\) 4.12541e12 + 4.12541e12i 0.749780 + 0.749780i
\(679\) −1.01676e13 −1.83570
\(680\) 4.79074e10 + 4.35100e10i 0.00859237 + 0.00780367i
\(681\) 3.35391e12 0.597571
\(682\) −3.89736e12 3.89736e12i −0.689828 0.689828i
\(683\) 3.09603e12 1.28242e12i 0.544392 0.225495i −0.0935014 0.995619i \(-0.529806\pi\)
0.637894 + 0.770125i \(0.279806\pi\)
\(684\) 1.88460e12i 0.329206i
\(685\) 1.55913e12 + 3.76408e12i 0.270567 + 0.653208i
\(686\) −5.54225e12 2.29568e12i −0.955493 0.395778i
\(687\) 9.79875e11 2.36563e12i 0.167828 0.405174i
\(688\) 6.07916e12 6.07916e12i 1.03442 1.03442i
\(689\) −8.38477e11 + 8.38477e11i −0.141744 + 0.141744i
\(690\) 1.61122e12 3.88982e12i 0.270603 0.653293i
\(691\) −6.97270e12 2.88819e12i −1.16346 0.481919i −0.284432 0.958696i \(-0.591805\pi\)
−0.879024 + 0.476777i \(0.841805\pi\)
\(692\) 2.89262e12 + 6.98340e12i 0.479528 + 1.15768i
\(693\) 2.88052e12i 0.474430i
\(694\) 4.43787e12 1.83823e12i 0.726201 0.300802i
\(695\) −7.43968e12 7.43968e12i −1.20955 1.20955i
\(696\) −7.56936e10 −0.0122269
\(697\) 3.89172e9 4.28504e9i 0.000624588 0.000687714i
\(698\) −1.40013e13 −2.23264
\(699\) 6.85278e12 + 6.85278e12i 1.08572 + 1.08572i
\(700\) −1.12056e9 + 4.64152e8i −0.000176399 + 7.30667e-5i
\(701\) 1.61959e12i 0.253323i 0.991946 + 0.126662i \(0.0404262\pi\)
−0.991946 + 0.126662i \(0.959574\pi\)
\(702\) 2.06879e12 + 4.99450e12i 0.321513 + 0.776202i
\(703\) 3.74325e12 + 1.55050e12i 0.578029 + 0.239427i
\(704\) −2.55677e12 + 6.17259e12i −0.392297 + 0.947089i
\(705\) −7.90718e12 + 7.90718e12i −1.20551 + 1.20551i
\(706\) −7.50735e11 + 7.50735e11i −0.113727 + 0.113727i
\(707\) −2.13949e12 + 5.16518e12i −0.322050 + 0.777496i
\(708\) −1.21219e13 5.02106e12i −1.81310 0.751011i
\(709\) −6.57643e11 1.58769e12i −0.0977422 0.235971i 0.867444 0.497535i \(-0.165761\pi\)
−0.965186 + 0.261565i \(0.915761\pi\)
\(710\) 1.21493e13i 1.79428i
\(711\) −1.51396e12 + 6.27105e11i −0.222179 + 0.0920295i
\(712\) 4.08543e10 + 4.08543e10i 0.00595768 + 0.00595768i
\(713\) 2.01914e12 0.292593
\(714\) −1.58106e13 + 7.45808e12i −2.27670 + 1.07395i
\(715\) −5.37602e12 −0.769279
\(716\) 5.23382e12 + 5.23382e12i 0.744236 + 0.744236i
\(717\) 6.87110e12 2.84610e12i 0.970935 0.402175i
\(718\) 6.53982e12i 0.918345i
\(719\) 5.14369e12 + 1.24180e13i 0.717786 + 1.73289i 0.679561 + 0.733619i \(0.262170\pi\)
0.0382249 + 0.999269i \(0.487830\pi\)
\(720\) 1.94638e12 + 8.06217e11i 0.269918 + 0.111804i
\(721\) 5.52551e11 1.33398e12i 0.0761489 0.183840i
\(722\) 2.27223e12 2.27223e12i 0.311197 0.311197i
\(723\) −1.10849e12 + 1.10849e12i −0.150872 + 0.150872i
\(724\) −5.64397e11 + 1.36258e12i −0.0763416 + 0.184305i
\(725\) 7.81368e8 + 3.23653e8i 0.000105035 + 4.35070e-5i
\(726\) −3.97001e11 9.58444e11i −0.0530367 0.128042i
\(727\) 1.27527e13i 1.69316i −0.532263 0.846579i \(-0.678658\pi\)
0.532263 0.846579i \(-0.321342\pi\)
\(728\) 9.42129e10 3.90243e10i 0.0124314 0.00514924i
\(729\) −3.05490e12 3.05490e12i −0.400611 0.400611i
\(730\) 3.82614e11 0.0498663
\(731\) −1.01317e13 + 4.77929e12i −1.31237 + 0.619063i
\(732\) 1.26149e13 1.62400
\(733\) 8.09689e12 + 8.09689e12i 1.03598 + 1.03598i 0.999328 + 0.0366492i \(0.0116684\pi\)
0.0366492 + 0.999328i \(0.488332\pi\)
\(734\) −9.43796e12 + 3.90933e12i −1.20018 + 0.497130i
\(735\) 1.31777e13i 1.66551i
\(736\) −1.89678e12 4.57923e12i −0.238269 0.575231i
\(737\) 1.28267e13 + 5.31298e12i 1.60144 + 0.663337i
\(738\) 1.17179e9 2.82894e9i 0.000145410 0.000351051i
\(739\) −9.02381e12 + 9.02381e12i −1.11299 + 1.11299i −0.120242 + 0.992745i \(0.538367\pi\)
−0.992745 + 0.120242i \(0.961633\pi\)
\(740\) 3.12470e12 3.12470e12i 0.383059 0.383059i
\(741\) 3.01528e12 7.27952e12i 0.367405 0.886994i
\(742\) 4.59219e12 + 1.90215e12i 0.556163 + 0.230370i
\(743\) −1.73861e12 4.19739e12i −0.209292 0.505277i 0.784020 0.620736i \(-0.213166\pi\)
−0.993312 + 0.115459i \(0.963166\pi\)
\(744\) 7.30669e10i 0.00874264i
\(745\) −1.04331e13 + 4.32152e12i −1.24082 + 0.513965i
\(746\) −3.91766e12 3.91766e12i −0.463129 0.463129i
\(747\) 2.12086e12 0.249212
\(748\) 5.95048e12 6.55188e12i 0.695016 0.765259i
\(749\) 1.90714e13 2.21419
\(750\) −9.82133e12 9.82133e12i −1.13343 1.13343i
\(751\) −8.21191e12 + 3.40149e12i −0.942030 + 0.390202i −0.800230 0.599694i \(-0.795289\pi\)
−0.141800 + 0.989895i \(0.545289\pi\)
\(752\) 1.32727e13i 1.51348i
\(753\) −3.48513e12 8.41384e12i −0.395040 0.953711i
\(754\) 7.92156e12 + 3.28122e12i 0.892565 + 0.369712i
\(755\) −1.70638e12 + 4.11957e12i −0.191124 + 0.461413i
\(756\) 7.97871e12 7.97871e12i 0.888351 0.888351i
\(757\) 4.45431e12 4.45431e12i 0.493003 0.493003i −0.416248 0.909251i \(-0.636655\pi\)
0.909251 + 0.416248i \(0.136655\pi\)
\(758\) −1.63858e12 + 3.95587e12i −0.180283 + 0.435242i
\(759\) 4.41175e12 + 1.82741e12i 0.482529 + 0.199870i
\(760\) 4.67915e10 +