Properties

Label 8.14.b.b.5.2
Level 8
Weight 14
Character 8.5
Analytic conductor 8.578
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(8.57847431615\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(-46.7129 + 17.5509i\)
Character \(\chi\) = 8.5
Dual form 8.14.b.b.5.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-83.4258 + 35.1018i) q^{2}\) \(+622.159i q^{3}\) \(+(5727.73 - 5856.79i) q^{4}\) \(-26675.4i q^{5}\) \(+(-21838.9 - 51904.1i) q^{6}\) \(+50480.5 q^{7}\) \(+(-272257. + 689661. i) q^{8}\) \(+1.20724e6 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-83.4258 + 35.1018i) q^{2}\) \(+622.159i q^{3}\) \(+(5727.73 - 5856.79i) q^{4}\) \(-26675.4i q^{5}\) \(+(-21838.9 - 51904.1i) q^{6}\) \(+50480.5 q^{7}\) \(+(-272257. + 689661. i) q^{8}\) \(+1.20724e6 q^{9}\) \(+(936352. + 2.22541e6i) q^{10}\) \(+9.06102e6i q^{11}\) \(+(3.64385e6 + 3.56356e6i) q^{12}\) \(+8.06792e6i q^{13}\) \(+(-4.21138e6 + 1.77195e6i) q^{14}\) \(+1.65963e7 q^{15}\) \(+(-1.49501e6 - 6.70922e7i) q^{16}\) \(+5.68106e7 q^{17}\) \(+(-1.00715e8 + 4.23763e7i) q^{18}\) \(+1.06435e8i q^{19}\) \(+(-1.56232e8 - 1.52789e8i) q^{20}\) \(+3.14069e7i q^{21}\) \(+(-3.18058e8 - 7.55923e8i) q^{22}\) \(+6.31214e8 q^{23}\) \(+(-4.29078e8 - 1.69387e8i) q^{24}\) \(+5.09128e8 q^{25}\) \(+(-2.83198e8 - 6.73073e8i) q^{26}\) \(+1.74302e9i q^{27}\) \(+(2.89139e8 - 2.95653e8i) q^{28}\) \(+4.06467e9i q^{29}\) \(+(-1.38456e9 + 5.82560e8i) q^{30}\) \(+5.86986e9 q^{31}\) \(+(2.47978e9 + 5.54474e9i) q^{32}\) \(-5.63739e9 q^{33}\) \(+(-4.73947e9 + 1.99415e9i) q^{34}\) \(-1.34659e9i q^{35}\) \(+(6.91476e9 - 7.07055e9i) q^{36}\) \(-2.97403e10i q^{37}\) \(+(-3.73605e9 - 8.87941e9i) q^{38}\) \(-5.01953e9 q^{39}\) \(+(1.83969e10 + 7.26256e9i) q^{40}\) \(-5.32006e10 q^{41}\) \(+(-1.10244e9 - 2.62015e9i) q^{42}\) \(+8.32576e9i q^{43}\) \(+(5.30684e10 + 5.18991e10i) q^{44}\) \(-3.22036e10i q^{45}\) \(+(-5.26595e10 + 2.21567e10i) q^{46}\) \(+1.06617e11 q^{47}\) \(+(4.17420e10 - 9.30131e8i) q^{48}\) \(-9.43407e10 q^{49}\) \(+(-4.24744e10 + 1.78713e10i) q^{50}\) \(+3.53452e10i q^{51}\) \(+(4.72521e10 + 4.62109e10i) q^{52}\) \(+1.04708e11i q^{53}\) \(+(-6.11830e10 - 1.45413e11i) q^{54}\) \(+2.41706e11 q^{55}\) \(+(-1.37437e10 + 3.48144e10i) q^{56}\) \(-6.62194e10 q^{57}\) \(+(-1.42677e11 - 3.39098e11i) q^{58}\) \(+3.49274e11i q^{59}\) \(+(9.50593e10 - 9.72010e10i) q^{60}\) \(-2.73155e11i q^{61}\) \(+(-4.89698e11 + 2.06042e11i) q^{62}\) \(+6.09422e10 q^{63}\) \(+(-4.01508e11 - 3.75530e11i) q^{64}\) \(+2.15215e11 q^{65}\) \(+(4.70304e11 - 1.97882e11i) q^{66}\) \(-4.69722e11i q^{67}\) \(+(3.25396e11 - 3.32727e11i) q^{68}\) \(+3.92715e11i q^{69}\) \(+(4.72675e10 + 1.12340e11i) q^{70}\) \(-4.62545e11 q^{71}\) \(+(-3.28680e11 + 8.32587e11i) q^{72}\) \(+4.02036e11 q^{73}\) \(+(1.04394e12 + 2.48111e12i) q^{74}\) \(+3.16758e11i q^{75}\) \(+(6.23366e11 + 6.09630e11i) q^{76}\) \(+4.57405e11i q^{77}\) \(+(4.18758e11 - 1.76194e11i) q^{78}\) \(-3.34144e12 q^{79}\) \(+(-1.78971e12 + 3.98798e10i) q^{80}\) \(+8.40299e11 q^{81}\) \(+(4.43831e12 - 1.86744e12i) q^{82}\) \(-4.78169e12i q^{83}\) \(+(1.83943e11 + 1.79890e11i) q^{84}\) \(-1.51544e12i q^{85}\) \(+(-2.92249e11 - 6.94583e11i) q^{86}\) \(-2.52887e12 q^{87}\) \(+(-6.24903e12 - 2.46693e12i) q^{88}\) \(+3.03971e12 q^{89}\) \(+(1.13040e12 + 2.68661e12i) q^{90}\) \(+4.07273e11i q^{91}\) \(+(3.61543e12 - 3.69689e12i) q^{92}\) \(+3.65199e12i q^{93}\) \(+(-8.89459e12 + 3.74243e12i) q^{94}\) \(+2.83919e12 q^{95}\) \(+(-3.44971e12 + 1.54281e12i) q^{96}\) \(+4.70760e12 q^{97}\) \(+(7.87045e12 - 3.31153e12i) q^{98}\) \(+1.09388e13i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut -\mathstrut 4542088q^{10} \) \(\mathstrut +\mathstrut 27987880q^{12} \) \(\mathstrut +\mathstrut 1408688q^{14} \) \(\mathstrut -\mathstrut 145914416q^{15} \) \(\mathstrut +\mathstrut 56624912q^{16} \) \(\mathstrut +\mathstrut 217326004q^{17} \) \(\mathstrut -\mathstrut 147615262q^{18} \) \(\mathstrut +\mathstrut 21655184q^{20} \) \(\mathstrut -\mathstrut 177987876q^{22} \) \(\mathstrut -\mathstrut 78679952q^{23} \) \(\mathstrut +\mathstrut 320199056q^{24} \) \(\mathstrut -\mathstrut 3076402574q^{25} \) \(\mathstrut +\mathstrut 3734872040q^{26} \) \(\mathstrut -\mathstrut 1653812448q^{28} \) \(\mathstrut +\mathstrut 6338232752q^{30} \) \(\mathstrut +\mathstrut 648233792q^{31} \) \(\mathstrut -\mathstrut 11298380000q^{32} \) \(\mathstrut +\mathstrut 15484079688q^{33} \) \(\mathstrut -\mathstrut 6096822724q^{34} \) \(\mathstrut +\mathstrut 4004708940q^{36} \) \(\mathstrut -\mathstrut 18764968628q^{38} \) \(\mathstrut -\mathstrut 63497510288q^{39} \) \(\mathstrut +\mathstrut 7466802592q^{40} \) \(\mathstrut +\mathstrut 59324640356q^{41} \) \(\mathstrut +\mathstrut 53897620960q^{42} \) \(\mathstrut +\mathstrut 13325704392q^{44} \) \(\mathstrut -\mathstrut 55046867440q^{46} \) \(\mathstrut -\mathstrut 10176534816q^{47} \) \(\mathstrut -\mathstrut 301841943264q^{48} \) \(\mathstrut +\mathstrut 182708552058q^{49} \) \(\mathstrut +\mathstrut 326454435302q^{50} \) \(\mathstrut -\mathstrut 53296499536q^{52} \) \(\mathstrut +\mathstrut 35449773752q^{54} \) \(\mathstrut -\mathstrut 123010753008q^{55} \) \(\mathstrut -\mathstrut 462152447680q^{56} \) \(\mathstrut -\mathstrut 511372324504q^{57} \) \(\mathstrut +\mathstrut 766482705096q^{58} \) \(\mathstrut +\mathstrut 1813082440992q^{60} \) \(\mathstrut -\mathstrut 1665308528960q^{62} \) \(\mathstrut -\mathstrut 898991123792q^{63} \) \(\mathstrut -\mathstrut 2180548996032q^{64} \) \(\mathstrut +\mathstrut 1577231990240q^{65} \) \(\mathstrut +\mathstrut 2269525079448q^{66} \) \(\mathstrut +\mathstrut 2338280915304q^{68} \) \(\mathstrut -\mathstrut 6070110714688q^{70} \) \(\mathstrut +\mathstrut 726361179984q^{71} \) \(\mathstrut -\mathstrut 3600753685960q^{72} \) \(\mathstrut -\mathstrut 633240365532q^{73} \) \(\mathstrut +\mathstrut 7528513982264q^{74} \) \(\mathstrut +\mathstrut 10338420845032q^{76} \) \(\mathstrut -\mathstrut 8252024440816q^{78} \) \(\mathstrut +\mathstrut 5445103565344q^{79} \) \(\mathstrut -\mathstrut 15406871881920q^{80} \) \(\mathstrut -\mathstrut 9674575380574q^{81} \) \(\mathstrut +\mathstrut 12273334206796q^{82} \) \(\mathstrut +\mathstrut 20362643366464q^{84} \) \(\mathstrut -\mathstrut 26794541719396q^{86} \) \(\mathstrut +\mathstrut 7632221772720q^{87} \) \(\mathstrut -\mathstrut 27677491769136q^{88} \) \(\mathstrut +\mathstrut 5506344808004q^{89} \) \(\mathstrut +\mathstrut 31454099524040q^{90} \) \(\mathstrut +\mathstrut 33971694298464q^{92} \) \(\mathstrut -\mathstrut 45356008560096q^{94} \) \(\mathstrut -\mathstrut 14214732035504q^{95} \) \(\mathstrut -\mathstrut 35398666935232q^{96} \) \(\mathstrut +\mathstrut 1361133320788q^{97} \) \(\mathstrut +\mathstrut 54325451514942q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −83.4258 + 35.1018i −0.921734 + 0.387823i
\(3\) 622.159i 0.492735i 0.969177 + 0.246367i \(0.0792370\pi\)
−0.969177 + 0.246367i \(0.920763\pi\)
\(4\) 5727.73 5856.79i 0.699186 0.714940i
\(5\) 26675.4i 0.763494i −0.924267 0.381747i \(-0.875323\pi\)
0.924267 0.381747i \(-0.124677\pi\)
\(6\) −21838.9 51904.1i −0.191094 0.454170i
\(7\) 50480.5 0.162176 0.0810880 0.996707i \(-0.474161\pi\)
0.0810880 + 0.996707i \(0.474161\pi\)
\(8\) −272257. + 689661.i −0.367193 + 0.930145i
\(9\) 1.20724e6 0.757213
\(10\) 936352. + 2.22541e6i 0.296101 + 0.703738i
\(11\) 9.06102e6i 1.54214i 0.636749 + 0.771071i \(0.280279\pi\)
−0.636749 + 0.771071i \(0.719721\pi\)
\(12\) 3.64385e6 + 3.56356e6i 0.352276 + 0.344513i
\(13\) 8.06792e6i 0.463586i 0.972765 + 0.231793i \(0.0744592\pi\)
−0.972765 + 0.231793i \(0.925541\pi\)
\(14\) −4.21138e6 + 1.77195e6i −0.149483 + 0.0628956i
\(15\) 1.65963e7 0.376200
\(16\) −1.49501e6 6.70922e7i −0.0222773 0.999752i
\(17\) 5.68106e7 0.570836 0.285418 0.958403i \(-0.407868\pi\)
0.285418 + 0.958403i \(0.407868\pi\)
\(18\) −1.00715e8 + 4.23763e7i −0.697948 + 0.293665i
\(19\) 1.06435e8i 0.519022i 0.965740 + 0.259511i \(0.0835613\pi\)
−0.965740 + 0.259511i \(0.916439\pi\)
\(20\) −1.56232e8 1.52789e8i −0.545852 0.533824i
\(21\) 3.14069e7i 0.0799097i
\(22\) −3.18058e8 7.55923e8i −0.598079 1.42145i
\(23\) 6.31214e8 0.889090 0.444545 0.895757i \(-0.353365\pi\)
0.444545 + 0.895757i \(0.353365\pi\)
\(24\) −4.29078e8 1.69387e8i −0.458314 0.180929i
\(25\) 5.09128e8 0.417078
\(26\) −2.83198e8 6.73073e8i −0.179789 0.427303i
\(27\) 1.74302e9i 0.865839i
\(28\) 2.89139e8 2.95653e8i 0.113391 0.115946i
\(29\) 4.06467e9i 1.26893i 0.772951 + 0.634465i \(0.218780\pi\)
−0.772951 + 0.634465i \(0.781220\pi\)
\(30\) −1.38456e9 + 5.82560e8i −0.346756 + 0.145899i
\(31\) 5.86986e9 1.18789 0.593946 0.804505i \(-0.297569\pi\)
0.593946 + 0.804505i \(0.297569\pi\)
\(32\) 2.47978e9 + 5.54474e9i 0.408261 + 0.912865i
\(33\) −5.63739e9 −0.759867
\(34\) −4.73947e9 + 1.99415e9i −0.526158 + 0.221383i
\(35\) 1.34659e9i 0.123820i
\(36\) 6.91476e9 7.07055e9i 0.529433 0.541361i
\(37\) 2.97403e10i 1.90561i −0.303581 0.952806i \(-0.598182\pi\)
0.303581 0.952806i \(-0.401818\pi\)
\(38\) −3.73605e9 8.87941e9i −0.201289 0.478400i
\(39\) −5.01953e9 −0.228425
\(40\) 1.83969e10 + 7.26256e9i 0.710159 + 0.280350i
\(41\) −5.32006e10 −1.74913 −0.874564 0.484910i \(-0.838852\pi\)
−0.874564 + 0.484910i \(0.838852\pi\)
\(42\) −1.10244e9 2.62015e9i −0.0309908 0.0736555i
\(43\) 8.32576e9i 0.200853i 0.994944 + 0.100427i \(0.0320208\pi\)
−0.994944 + 0.100427i \(0.967979\pi\)
\(44\) 5.30684e10 + 5.18991e10i 1.10254 + 1.07824i
\(45\) 3.22036e10i 0.578127i
\(46\) −5.26595e10 + 2.21567e10i −0.819504 + 0.344810i
\(47\) 1.06617e11 1.44274 0.721372 0.692548i \(-0.243512\pi\)
0.721372 + 0.692548i \(0.243512\pi\)
\(48\) 4.17420e10 9.30131e8i 0.492612 0.0109768i
\(49\) −9.43407e10 −0.973699
\(50\) −4.24744e10 + 1.78713e10i −0.384435 + 0.161752i
\(51\) 3.53452e10i 0.281270i
\(52\) 4.72521e10 + 4.62109e10i 0.331436 + 0.324133i
\(53\) 1.04708e11i 0.648913i 0.945901 + 0.324457i \(0.105181\pi\)
−0.945901 + 0.324457i \(0.894819\pi\)
\(54\) −6.11830e10 1.45413e11i −0.335793 0.798073i
\(55\) 2.41706e11 1.17742
\(56\) −1.37437e10 + 3.48144e10i −0.0595499 + 0.150847i
\(57\) −6.62194e10 −0.255740
\(58\) −1.42677e11 3.39098e11i −0.492121 1.16962i
\(59\) 3.49274e11i 1.07802i 0.842298 + 0.539011i \(0.181202\pi\)
−0.842298 + 0.539011i \(0.818798\pi\)
\(60\) 9.50593e10 9.72010e10i 0.263034 0.268960i
\(61\) 2.73155e11i 0.678836i −0.940636 0.339418i \(-0.889770\pi\)
0.940636 0.339418i \(-0.110230\pi\)
\(62\) −4.89698e11 + 2.06042e11i −1.09492 + 0.460692i
\(63\) 6.09422e10 0.122802
\(64\) −4.01508e11 3.75530e11i −0.730338 0.683086i
\(65\) 2.15215e11 0.353945
\(66\) 4.70304e11 1.97882e11i 0.700395 0.294694i
\(67\) 4.69722e11i 0.634387i −0.948361 0.317193i \(-0.897260\pi\)
0.948361 0.317193i \(-0.102740\pi\)
\(68\) 3.25396e11 3.32727e11i 0.399120 0.408113i
\(69\) 3.92715e11i 0.438085i
\(70\) 4.72675e10 + 1.12340e11i 0.0480204 + 0.114129i
\(71\) −4.62545e11 −0.428524 −0.214262 0.976776i \(-0.568735\pi\)
−0.214262 + 0.976776i \(0.568735\pi\)
\(72\) −3.28680e11 + 8.32587e11i −0.278043 + 0.704317i
\(73\) 4.02036e11 0.310933 0.155466 0.987841i \(-0.450312\pi\)
0.155466 + 0.987841i \(0.450312\pi\)
\(74\) 1.04394e12 + 2.48111e12i 0.739041 + 1.75647i
\(75\) 3.16758e11i 0.205509i
\(76\) 6.23366e11 + 6.09630e11i 0.371069 + 0.362893i
\(77\) 4.57405e11i 0.250098i
\(78\) 4.18758e11 1.76194e11i 0.210547 0.0885884i
\(79\) −3.34144e12 −1.54653 −0.773264 0.634084i \(-0.781377\pi\)
−0.773264 + 0.634084i \(0.781377\pi\)
\(80\) −1.78971e12 + 3.98798e10i −0.763304 + 0.0170086i
\(81\) 8.40299e11 0.330583
\(82\) 4.43831e12 1.86744e12i 1.61223 0.678353i
\(83\) 4.78169e12i 1.60537i −0.596406 0.802683i \(-0.703405\pi\)
0.596406 0.802683i \(-0.296595\pi\)
\(84\) 1.83943e11 + 1.79890e11i 0.0571306 + 0.0558718i
\(85\) 1.51544e12i 0.435829i
\(86\) −2.92249e11 6.94583e11i −0.0778956 0.185133i
\(87\) −2.52887e12 −0.625246
\(88\) −6.24903e12 2.46693e12i −1.43442 0.566264i
\(89\) 3.03971e12 0.648331 0.324166 0.946000i \(-0.394917\pi\)
0.324166 + 0.946000i \(0.394917\pi\)
\(90\) 1.13040e12 + 2.68661e12i 0.224211 + 0.532879i
\(91\) 4.07273e11i 0.0751824i
\(92\) 3.61543e12 3.69689e12i 0.621639 0.635646i
\(93\) 3.65199e12i 0.585315i
\(94\) −8.89459e12 + 3.74243e12i −1.32983 + 0.559530i
\(95\) 2.83919e12 0.396270
\(96\) −3.44971e12 + 1.54281e12i −0.449800 + 0.201164i
\(97\) 4.70760e12 0.573830 0.286915 0.957956i \(-0.407370\pi\)
0.286915 + 0.957956i \(0.407370\pi\)
\(98\) 7.87045e12 3.31153e12i 0.897491 0.377623i
\(99\) 1.09388e13i 1.16773i
\(100\) 2.91615e12 2.98185e12i 0.291615 0.298185i
\(101\) 1.03295e13i 0.968260i 0.874996 + 0.484130i \(0.160864\pi\)
−0.874996 + 0.484130i \(0.839136\pi\)
\(102\) −1.24068e12 2.94870e12i −0.109083 0.259256i
\(103\) 3.92826e12 0.324159 0.162079 0.986778i \(-0.448180\pi\)
0.162079 + 0.986778i \(0.448180\pi\)
\(104\) −5.56413e12 2.19655e12i −0.431202 0.170226i
\(105\) 8.37790e11 0.0610105
\(106\) −3.67543e12 8.73535e12i −0.251664 0.598125i
\(107\) 7.39245e12i 0.476205i 0.971240 + 0.238102i \(0.0765254\pi\)
−0.971240 + 0.238102i \(0.923475\pi\)
\(108\) 1.02085e13 + 9.98354e12i 0.619023 + 0.605383i
\(109\) 2.46418e13i 1.40734i −0.710525 0.703672i \(-0.751542\pi\)
0.710525 0.703672i \(-0.248458\pi\)
\(110\) −2.01645e13 + 8.48431e12i −1.08526 + 0.456629i
\(111\) 1.85032e13 0.938961
\(112\) −7.54687e10 3.38685e12i −0.00361285 0.162136i
\(113\) −2.74600e13 −1.24077 −0.620384 0.784298i \(-0.713023\pi\)
−0.620384 + 0.784298i \(0.713023\pi\)
\(114\) 5.52440e12 2.32442e12i 0.235724 0.0991819i
\(115\) 1.68379e13i 0.678814i
\(116\) 2.38059e13 + 2.32813e13i 0.907209 + 0.887219i
\(117\) 9.73993e12i 0.351033i
\(118\) −1.22601e13 2.91385e13i −0.418082 0.993650i
\(119\) 2.86783e12 0.0925758
\(120\) −4.51847e12 + 1.14458e13i −0.138138 + 0.349920i
\(121\) −4.75794e13 −1.37820
\(122\) 9.58821e12 + 2.27881e13i 0.263268 + 0.625706i
\(123\) 3.30992e13i 0.861856i
\(124\) 3.36210e13 3.43785e13i 0.830558 0.849271i
\(125\) 4.61439e13i 1.08193i
\(126\) −5.08415e12 + 2.13918e12i −0.113190 + 0.0476253i
\(127\) −5.26162e12 −0.111274 −0.0556372 0.998451i \(-0.517719\pi\)
−0.0556372 + 0.998451i \(0.517719\pi\)
\(128\) 4.66779e13 + 1.72353e13i 0.938094 + 0.346381i
\(129\) −5.17994e12 −0.0989673
\(130\) −1.79545e13 + 7.55442e12i −0.326243 + 0.137268i
\(131\) 8.17887e13i 1.41394i 0.707246 + 0.706968i \(0.249937\pi\)
−0.707246 + 0.706968i \(0.750063\pi\)
\(132\) −3.22895e13 + 3.30170e13i −0.531289 + 0.543259i
\(133\) 5.37288e12i 0.0841728i
\(134\) 1.64881e13 + 3.91869e13i 0.246030 + 0.584736i
\(135\) 4.64956e13 0.661063
\(136\) −1.54671e13 + 3.91800e13i −0.209607 + 0.530960i
\(137\) 4.43802e13 0.573464 0.286732 0.958011i \(-0.407431\pi\)
0.286732 + 0.958011i \(0.407431\pi\)
\(138\) −1.37850e13 3.27626e13i −0.169900 0.403798i
\(139\) 2.15053e13i 0.252901i 0.991973 + 0.126450i \(0.0403584\pi\)
−0.991973 + 0.126450i \(0.959642\pi\)
\(140\) −7.88666e12 7.71288e12i −0.0885240 0.0865734i
\(141\) 6.63325e13i 0.710890i
\(142\) 3.85882e13 1.62361e13i 0.394985 0.166191i
\(143\) −7.31036e13 −0.714915
\(144\) −1.80483e12 8.09965e13i −0.0168687 0.757025i
\(145\) 1.08426e14 0.968820
\(146\) −3.35402e13 + 1.41122e13i −0.286597 + 0.120587i
\(147\) 5.86949e13i 0.479775i
\(148\) −1.74183e14 1.70345e14i −1.36240 1.33238i
\(149\) 1.27918e13i 0.0957679i 0.998853 + 0.0478839i \(0.0152478\pi\)
−0.998853 + 0.0478839i \(0.984752\pi\)
\(150\) −1.11188e13 2.64258e13i −0.0797010 0.189424i
\(151\) −1.69973e13 −0.116689 −0.0583444 0.998297i \(-0.518582\pi\)
−0.0583444 + 0.998297i \(0.518582\pi\)
\(152\) −7.34039e13 2.89777e13i −0.482765 0.190581i
\(153\) 6.85841e13 0.432244
\(154\) −1.60557e13 3.81594e13i −0.0969940 0.230524i
\(155\) 1.56581e14i 0.906948i
\(156\) −2.87505e13 + 2.93983e13i −0.159711 + 0.163310i
\(157\) 1.27151e14i 0.677599i 0.940859 + 0.338799i \(0.110021\pi\)
−0.940859 + 0.338799i \(0.889979\pi\)
\(158\) 2.78763e14 1.17291e14i 1.42549 0.599780i
\(159\) −6.51450e13 −0.319742
\(160\) 1.47908e14 6.61489e13i 0.696967 0.311704i
\(161\) 3.18640e13 0.144189
\(162\) −7.01026e13 + 2.94960e13i −0.304710 + 0.128208i
\(163\) 8.50516e13i 0.355192i 0.984103 + 0.177596i \(0.0568320\pi\)
−0.984103 + 0.177596i \(0.943168\pi\)
\(164\) −3.04719e14 + 3.11585e14i −1.22297 + 1.25052i
\(165\) 1.50380e14i 0.580154i
\(166\) 1.67846e14 + 3.98917e14i 0.622598 + 1.47972i
\(167\) −3.22006e14 −1.14870 −0.574351 0.818609i \(-0.694745\pi\)
−0.574351 + 0.818609i \(0.694745\pi\)
\(168\) −2.16601e13 8.55076e12i −0.0743276 0.0293423i
\(169\) 2.37784e14 0.785088
\(170\) 5.31947e13 + 1.26427e14i 0.169025 + 0.401719i
\(171\) 1.28493e14i 0.393010i
\(172\) 4.87622e13 + 4.76877e13i 0.143598 + 0.140434i
\(173\) 5.68385e14i 1.61192i −0.591971 0.805959i \(-0.701650\pi\)
0.591971 0.805959i \(-0.298350\pi\)
\(174\) 2.10973e14 8.87677e13i 0.576310 0.242485i
\(175\) 2.57010e13 0.0676400
\(176\) 6.07924e14 1.35463e13i 1.54176 0.0343548i
\(177\) −2.17304e14 −0.531179
\(178\) −2.53590e14 + 1.06699e14i −0.597589 + 0.251438i
\(179\) 5.79456e14i 1.31667i −0.752726 0.658334i \(-0.771262\pi\)
0.752726 0.658334i \(-0.228738\pi\)
\(180\) −1.88610e14 1.84454e14i −0.413326 0.404218i
\(181\) 1.23355e14i 0.260763i 0.991464 + 0.130381i \(0.0416202\pi\)
−0.991464 + 0.130381i \(0.958380\pi\)
\(182\) −1.42960e13 3.39771e13i −0.0291575 0.0692982i
\(183\) 1.69946e14 0.334486
\(184\) −1.71853e14 + 4.35323e14i −0.326468 + 0.826982i
\(185\) −7.93334e14 −1.45492
\(186\) −1.28191e14 3.04670e14i −0.226999 0.539505i
\(187\) 5.14762e14i 0.880310i
\(188\) 6.10672e14 6.24431e14i 1.00875 1.03147i
\(189\) 8.79884e13i 0.140418i
\(190\) −2.36862e14 + 9.96605e13i −0.365255 + 0.153683i
\(191\) 7.14579e13 0.106496 0.0532480 0.998581i \(-0.483043\pi\)
0.0532480 + 0.998581i \(0.483043\pi\)
\(192\) 2.33640e14 2.49802e14i 0.336580 0.359863i
\(193\) 1.08856e14 0.151611 0.0758054 0.997123i \(-0.475847\pi\)
0.0758054 + 0.997123i \(0.475847\pi\)
\(194\) −3.92735e14 + 1.65245e14i −0.528918 + 0.222545i
\(195\) 1.33898e14i 0.174401i
\(196\) −5.40359e14 + 5.52533e14i −0.680797 + 0.696136i
\(197\) 7.97270e14i 0.971796i −0.874015 0.485898i \(-0.838493\pi\)
0.874015 0.485898i \(-0.161507\pi\)
\(198\) −3.83972e14 9.12581e14i −0.452873 1.07634i
\(199\) 1.45222e15 1.65763 0.828817 0.559520i \(-0.189015\pi\)
0.828817 + 0.559520i \(0.189015\pi\)
\(200\) −1.38614e14 + 3.51126e14i −0.153148 + 0.387943i
\(201\) 2.92241e14 0.312584
\(202\) −3.62585e14 8.61750e14i −0.375514 0.892478i
\(203\) 2.05186e14i 0.205790i
\(204\) 2.07009e14 + 2.02448e14i 0.201091 + 0.196660i
\(205\) 1.41915e15i 1.33545i
\(206\) −3.27718e14 + 1.37889e14i −0.298788 + 0.125716i
\(207\) 7.62028e14 0.673230
\(208\) 5.41295e14 1.20616e13i 0.463471 0.0103275i
\(209\) −9.64408e14 −0.800405
\(210\) −6.98933e13 + 2.94079e13i −0.0562355 + 0.0236613i
\(211\) 1.42871e15i 1.11457i 0.830320 + 0.557287i \(0.188158\pi\)
−0.830320 + 0.557287i \(0.811842\pi\)
\(212\) 6.13252e14 + 5.99739e14i 0.463934 + 0.453711i
\(213\) 2.87776e14i 0.211148i
\(214\) −2.59488e14 6.16721e14i −0.184683 0.438934i
\(215\) 2.22093e14 0.153350
\(216\) −1.20209e15 4.74549e14i −0.805356 0.317930i
\(217\) 2.96314e14 0.192647
\(218\) 8.64971e14 + 2.05576e15i 0.545801 + 1.29720i
\(219\) 2.50130e14i 0.153207i
\(220\) 1.38443e15 1.41562e15i 0.823233 0.841781i
\(221\) 4.58343e14i 0.264631i
\(222\) −1.54364e15 + 6.49495e14i −0.865472 + 0.364151i
\(223\) −2.08322e15 −1.13437 −0.567183 0.823591i \(-0.691967\pi\)
−0.567183 + 0.823591i \(0.691967\pi\)
\(224\) 1.25180e14 + 2.79902e14i 0.0662101 + 0.148045i
\(225\) 6.14640e14 0.315816
\(226\) 2.29087e15 9.63895e14i 1.14366 0.481199i
\(227\) 2.90336e15i 1.40842i −0.709990 0.704212i \(-0.751301\pi\)
0.709990 0.704212i \(-0.248699\pi\)
\(228\) −3.79287e14 + 3.87833e14i −0.178810 + 0.182839i
\(229\) 2.20366e15i 1.00975i −0.863192 0.504875i \(-0.831539\pi\)
0.863192 0.504875i \(-0.168461\pi\)
\(230\) 5.91039e14 + 1.40471e15i 0.263260 + 0.625686i
\(231\) −2.84578e14 −0.123232
\(232\) −2.80324e15 1.10664e15i −1.18029 0.465943i
\(233\) −1.29391e15 −0.529772 −0.264886 0.964280i \(-0.585334\pi\)
−0.264886 + 0.964280i \(0.585334\pi\)
\(234\) −3.41889e14 8.12562e14i −0.136139 0.323559i
\(235\) 2.84404e15i 1.10153i
\(236\) 2.04562e15 + 2.00055e15i 0.770721 + 0.753739i
\(237\) 2.07891e15i 0.762028i
\(238\) −2.39251e14 + 1.00666e14i −0.0853302 + 0.0359030i
\(239\) −4.34770e15 −1.50895 −0.754473 0.656332i \(-0.772107\pi\)
−0.754473 + 0.656332i \(0.772107\pi\)
\(240\) −2.48116e13 1.11348e15i −0.00838072 0.376106i
\(241\) 2.63820e15 0.867355 0.433677 0.901068i \(-0.357216\pi\)
0.433677 + 0.901068i \(0.357216\pi\)
\(242\) 3.96935e15 1.67012e15i 1.27034 0.534500i
\(243\) 3.30173e15i 1.02873i
\(244\) −1.59981e15 1.56456e15i −0.485326 0.474632i
\(245\) 2.51657e15i 0.743413i
\(246\) 1.16184e15 + 2.76133e15i 0.334248 + 0.794402i
\(247\) −8.58708e14 −0.240611
\(248\) −1.59811e15 + 4.04821e15i −0.436186 + 1.10491i
\(249\) 2.97497e15 0.791020
\(250\) 1.61973e15 + 3.84959e15i 0.419597 + 0.997251i
\(251\) 1.18733e15i 0.299704i −0.988708 0.149852i \(-0.952120\pi\)
0.988708 0.149852i \(-0.0478797\pi\)
\(252\) 3.49060e14 3.56925e14i 0.0858612 0.0877958i
\(253\) 5.71944e15i 1.37110i
\(254\) 4.38955e14 1.84692e14i 0.102565 0.0431548i
\(255\) 9.42846e14 0.214748
\(256\) −4.49913e15 + 2.00607e14i −0.999007 + 0.0445436i
\(257\) −8.62360e13 −0.0186691 −0.00933455 0.999956i \(-0.502971\pi\)
−0.00933455 + 0.999956i \(0.502971\pi\)
\(258\) 4.32141e14 1.81825e14i 0.0912215 0.0383818i
\(259\) 1.50131e15i 0.309044i
\(260\) 1.23269e15 1.26047e15i 0.247473 0.253049i
\(261\) 4.90703e15i 0.960850i
\(262\) −2.87093e15 6.82328e15i −0.548357 1.30327i
\(263\) 3.35128e15 0.624452 0.312226 0.950008i \(-0.398925\pi\)
0.312226 + 0.950008i \(0.398925\pi\)
\(264\) 1.53482e15 3.88789e15i 0.279018 0.706786i
\(265\) 2.79312e15 0.495441
\(266\) −1.88598e14 4.48237e14i −0.0326442 0.0775849i
\(267\) 1.89118e15i 0.319455i
\(268\) −2.75106e15 2.69044e15i −0.453548 0.443555i
\(269\) 7.67954e15i 1.23579i −0.786260 0.617896i \(-0.787985\pi\)
0.786260 0.617896i \(-0.212015\pi\)
\(270\) −3.87894e15 + 1.63208e15i −0.609324 + 0.256376i
\(271\) −2.08567e15 −0.319849 −0.159925 0.987129i \(-0.551125\pi\)
−0.159925 + 0.987129i \(0.551125\pi\)
\(272\) −8.49321e13 3.81155e15i −0.0127167 0.570694i
\(273\) −2.53388e14 −0.0370450
\(274\) −3.70246e15 + 1.55782e15i −0.528581 + 0.222403i
\(275\) 4.61322e15i 0.643193i
\(276\) 2.30005e15 + 2.24937e15i 0.313205 + 0.306303i
\(277\) 4.24355e15i 0.564431i −0.959351 0.282215i \(-0.908931\pi\)
0.959351 0.282215i \(-0.0910692\pi\)
\(278\) −7.54875e14 1.79410e15i −0.0980807 0.233107i
\(279\) 7.08634e15 0.899487
\(280\) 9.28687e14 + 3.66618e14i 0.115171 + 0.0454660i
\(281\) −2.75085e15 −0.333331 −0.166666 0.986013i \(-0.553300\pi\)
−0.166666 + 0.986013i \(0.553300\pi\)
\(282\) −2.32839e15 5.53384e15i −0.275700 0.655251i
\(283\) 8.54209e14i 0.0988445i −0.998778 0.0494223i \(-0.984262\pi\)
0.998778 0.0494223i \(-0.0157380\pi\)
\(284\) −2.64933e15 + 2.70903e15i −0.299618 + 0.306369i
\(285\) 1.76643e15i 0.195256i
\(286\) 6.09873e15 2.56607e15i 0.658962 0.277261i
\(287\) −2.68559e15 −0.283666
\(288\) 2.99369e15 + 6.69385e15i 0.309140 + 0.691233i
\(289\) −6.67714e15 −0.674147
\(290\) −9.04556e15 + 3.80596e15i −0.892994 + 0.375731i
\(291\) 2.92887e15i 0.282746i
\(292\) 2.30275e15 2.35464e15i 0.217400 0.222298i
\(293\) 7.18596e15i 0.663507i −0.943366 0.331753i \(-0.892360\pi\)
0.943366 0.331753i \(-0.107640\pi\)
\(294\) 2.06029e15 + 4.89667e15i 0.186068 + 0.442225i
\(295\) 9.31701e15 0.823064
\(296\) 2.05107e16 + 8.09702e15i 1.77249 + 0.699728i
\(297\) −1.57935e16 −1.33525
\(298\) −4.49013e14 1.06716e15i −0.0371410 0.0882725i
\(299\) 5.09259e15i 0.412169i
\(300\) 1.85519e15 + 1.81431e15i 0.146926 + 0.143689i
\(301\) 4.20288e14i 0.0325736i
\(302\) 1.41801e15 5.96634e14i 0.107556 0.0452546i
\(303\) −6.42661e15 −0.477095
\(304\) 7.14095e15 1.59121e14i 0.518893 0.0115624i
\(305\) −7.28650e15 −0.518287
\(306\) −5.72168e15 + 2.40742e15i −0.398414 + 0.167634i
\(307\) 1.79040e16i 1.22054i −0.792195 0.610268i \(-0.791062\pi\)
0.792195 0.610268i \(-0.208938\pi\)
\(308\) 2.67892e15 + 2.61989e15i 0.178805 + 0.174865i
\(309\) 2.44400e15i 0.159724i
\(310\) 5.49626e15 + 1.30629e16i 0.351735 + 0.835964i
\(311\) 2.77510e16 1.73915 0.869575 0.493802i \(-0.164393\pi\)
0.869575 + 0.493802i \(0.164393\pi\)
\(312\) 1.36660e15 3.46177e15i 0.0838760 0.212468i
\(313\) 8.26927e15 0.497083 0.248542 0.968621i \(-0.420049\pi\)
0.248542 + 0.968621i \(0.420049\pi\)
\(314\) −4.46323e15 1.06077e16i −0.262789 0.624566i
\(315\) 1.62565e15i 0.0937583i
\(316\) −1.91389e16 + 1.95701e16i −1.08131 + 1.10567i
\(317\) 1.49970e15i 0.0830079i −0.999138 0.0415040i \(-0.986785\pi\)
0.999138 0.0415040i \(-0.0132149\pi\)
\(318\) 5.43477e15 2.28670e15i 0.294717 0.124003i
\(319\) −3.68300e16 −1.95687
\(320\) −1.00174e16 + 1.07104e16i −0.521532 + 0.557608i
\(321\) −4.59928e15 −0.234643
\(322\) −2.65828e15 + 1.11848e15i −0.132904 + 0.0559199i
\(323\) 6.04662e15i 0.296276i
\(324\) 4.81301e15 4.92145e15i 0.231139 0.236347i
\(325\) 4.10761e15i 0.193351i
\(326\) −2.98546e15 7.09550e15i −0.137752 0.327392i
\(327\) 1.53311e16 0.693447
\(328\) 1.44843e16 3.66904e16i 0.642268 1.62694i
\(329\) 5.38206e15 0.233978
\(330\) −5.27859e15 1.25455e16i −0.224997 0.534747i
\(331\) 2.14800e16i 0.897742i 0.893597 + 0.448871i \(0.148174\pi\)
−0.893597 + 0.448871i \(0.851826\pi\)
\(332\) −2.80054e16 2.73883e16i −1.14774 1.12245i
\(333\) 3.59037e16i 1.44295i
\(334\) 2.68636e16 1.13030e16i 1.05880 0.445493i
\(335\) −1.25300e16 −0.484350
\(336\) 2.10716e15 4.69535e13i 0.0798899 0.00178017i
\(337\) 4.34776e16 1.61686 0.808428 0.588596i \(-0.200319\pi\)
0.808428 + 0.588596i \(0.200319\pi\)
\(338\) −1.98373e16 + 8.34663e15i −0.723642 + 0.304476i
\(339\) 1.70845e16i 0.611370i
\(340\) −8.87562e15 8.68005e15i −0.311592 0.304726i
\(341\) 5.31869e16i 1.83190i
\(342\) −4.51031e15 1.07196e16i −0.152418 0.362250i
\(343\) −9.65337e15 −0.320086
\(344\) −5.74195e15 2.26675e15i −0.186823 0.0737520i
\(345\) 1.04758e16 0.334475
\(346\) 1.99513e16 + 4.74180e16i 0.625139 + 1.48576i
\(347\) 1.66277e15i 0.0511317i 0.999673 + 0.0255658i \(0.00813874\pi\)
−0.999673 + 0.0255658i \(0.991861\pi\)
\(348\) −1.44847e16 + 1.48110e16i −0.437163 + 0.447013i
\(349\) 3.69674e16i 1.09510i 0.836773 + 0.547549i \(0.184439\pi\)
−0.836773 + 0.547549i \(0.815561\pi\)
\(350\) −2.14413e15 + 9.02152e14i −0.0623460 + 0.0262324i
\(351\) −1.40625e16 −0.401391
\(352\) −5.02410e16 + 2.24693e16i −1.40777 + 0.629596i
\(353\) 2.09201e16 0.575478 0.287739 0.957709i \(-0.407096\pi\)
0.287739 + 0.957709i \(0.407096\pi\)
\(354\) 1.81287e16 7.62775e15i 0.489606 0.206004i
\(355\) 1.23386e16i 0.327175i
\(356\) 1.74106e16 1.78029e16i 0.453304 0.463518i
\(357\) 1.78424e15i 0.0456153i
\(358\) 2.03399e16 + 4.83416e16i 0.510634 + 1.21362i
\(359\) 3.51028e16 0.865423 0.432711 0.901533i \(-0.357557\pi\)
0.432711 + 0.901533i \(0.357557\pi\)
\(360\) 2.22096e16 + 8.76767e15i 0.537742 + 0.212284i
\(361\) 3.07246e16 0.730617
\(362\) −4.32998e15 1.02910e16i −0.101130 0.240354i
\(363\) 2.96019e16i 0.679089i
\(364\) 2.38531e15 + 2.33275e15i 0.0537509 + 0.0525665i
\(365\) 1.07245e16i 0.237395i
\(366\) −1.41778e16 + 5.96539e15i −0.308307 + 0.129721i
\(367\) −9.02016e16 −1.92701 −0.963507 0.267683i \(-0.913742\pi\)
−0.963507 + 0.267683i \(0.913742\pi\)
\(368\) −9.43669e14 4.23495e16i −0.0198066 0.888869i
\(369\) −6.42260e16 −1.32446
\(370\) 6.61845e16 2.78474e16i 1.34105 0.564253i
\(371\) 5.28571e15i 0.105238i
\(372\) 2.13889e16 + 2.09176e16i 0.418465 + 0.409244i
\(373\) 5.62933e16i 1.08230i −0.840925 0.541152i \(-0.817988\pi\)
0.840925 0.541152i \(-0.182012\pi\)
\(374\) −1.80690e16 4.29444e16i −0.341405 0.811411i
\(375\) 2.87088e16 0.533104
\(376\) −2.90272e16 + 7.35293e16i −0.529766 + 1.34196i
\(377\) −3.27934e16 −0.588258
\(378\) −3.08855e15 7.34051e15i −0.0544575 0.129428i
\(379\) 8.75626e16i 1.51762i −0.651310 0.758811i \(-0.725780\pi\)
0.651310 0.758811i \(-0.274220\pi\)
\(380\) 1.62621e16 1.66285e16i 0.277066 0.283309i
\(381\) 3.27356e15i 0.0548288i
\(382\) −5.96144e15 + 2.50830e15i −0.0981610 + 0.0413017i
\(383\) −2.39043e16 −0.386975 −0.193488 0.981103i \(-0.561980\pi\)
−0.193488 + 0.981103i \(0.561980\pi\)
\(384\) −1.07231e16 + 2.90411e16i −0.170674 + 0.462231i
\(385\) 1.22014e16 0.190949
\(386\) −9.08140e15 + 3.82104e15i −0.139745 + 0.0587982i
\(387\) 1.00512e16i 0.152089i
\(388\) 2.69639e16 2.75714e16i 0.401214 0.410254i
\(389\) 6.79906e16i 0.994893i −0.867495 0.497447i \(-0.834271\pi\)
0.867495 0.497447i \(-0.165729\pi\)
\(390\) −4.70005e15 1.11705e16i −0.0676367 0.160751i
\(391\) 3.58596e16 0.507524
\(392\) 2.56850e16 6.50631e16i 0.357536 0.905681i
\(393\) −5.08855e16 −0.696695
\(394\) 2.79856e16 + 6.65129e16i 0.376885 + 0.895737i
\(395\) 8.91342e16i 1.18076i
\(396\) 6.40664e16 + 6.26547e16i 0.834856 + 0.816461i
\(397\) 7.25697e16i 0.930287i 0.885235 + 0.465144i \(0.153997\pi\)
−0.885235 + 0.465144i \(0.846003\pi\)
\(398\) −1.21153e17 + 5.09756e16i −1.52790 + 0.642869i
\(399\) −3.34279e15 −0.0414749
\(400\) −7.61150e14 3.41585e16i −0.00929138 0.416974i
\(401\) −3.28988e16 −0.395132 −0.197566 0.980290i \(-0.563304\pi\)
−0.197566 + 0.980290i \(0.563304\pi\)
\(402\) −2.43805e16 + 1.02582e16i −0.288120 + 0.121228i
\(403\) 4.73576e16i 0.550690i
\(404\) 6.04979e16 + 5.91648e16i 0.692247 + 0.676994i
\(405\) 2.24153e16i 0.252398i
\(406\) −7.20240e15 1.71178e16i −0.0798101 0.189684i
\(407\) 2.69478e17 2.93873
\(408\) −2.43762e16 9.62299e15i −0.261622 0.103281i
\(409\) 8.11813e15 0.0857540 0.0428770 0.999080i \(-0.486348\pi\)
0.0428770 + 0.999080i \(0.486348\pi\)
\(410\) −4.98145e16 1.18393e17i −0.517918 1.23093i
\(411\) 2.76115e16i 0.282565i
\(412\) 2.25000e16 2.30070e16i 0.226647 0.231754i
\(413\) 1.76315e16i 0.174829i
\(414\) −6.35728e16 + 2.67485e16i −0.620539 + 0.261094i
\(415\) −1.27553e17 −1.22569
\(416\) −4.47346e16 + 2.00067e16i −0.423191 + 0.189264i
\(417\) −1.33797e16 −0.124613
\(418\) 8.04565e16 3.38524e16i 0.737761 0.310416i
\(419\) 5.76432e16i 0.520424i 0.965552 + 0.260212i \(0.0837924\pi\)
−0.965552 + 0.260212i \(0.916208\pi\)
\(420\) 4.79864e15 4.90676e15i 0.0426577 0.0436189i
\(421\) 3.89380e16i 0.340832i 0.985372 + 0.170416i \(0.0545112\pi\)
−0.985372 + 0.170416i \(0.945489\pi\)
\(422\) −5.01503e16 1.19191e17i −0.432257 1.02734i
\(423\) 1.28712e17 1.09246
\(424\) −7.22130e16 2.85075e16i −0.603583 0.238277i
\(425\) 2.89238e16 0.238083
\(426\) 1.01015e16 + 2.40080e16i 0.0818883 + 0.194623i
\(427\) 1.37890e16i 0.110091i
\(428\) 4.32960e16 + 4.23420e16i 0.340458 + 0.332956i
\(429\) 4.54821e16i 0.352264i
\(430\) −1.85283e16 + 7.79584e15i −0.141348 + 0.0594728i
\(431\) −5.38838e16 −0.404908 −0.202454 0.979292i \(-0.564892\pi\)
−0.202454 + 0.979292i \(0.564892\pi\)
\(432\) 1.16943e17 2.60582e15i 0.865625 0.0192886i
\(433\) 5.06818e16 0.369557 0.184778 0.982780i \(-0.440843\pi\)
0.184778 + 0.982780i \(0.440843\pi\)
\(434\) −2.47202e16 + 1.04011e16i −0.177570 + 0.0747132i
\(435\) 6.74585e16i 0.477371i
\(436\) −1.44322e17 1.41142e17i −1.00617 0.983996i
\(437\) 6.71832e16i 0.461457i
\(438\) −8.78001e15 2.08673e16i −0.0594173 0.141216i
\(439\) −8.26240e16 −0.550918 −0.275459 0.961313i \(-0.588830\pi\)
−0.275459 + 0.961313i \(0.588830\pi\)
\(440\) −6.58062e16 + 1.66695e17i −0.432339 + 1.09517i
\(441\) −1.13892e17 −0.737297
\(442\) −1.60887e16 3.82377e16i −0.102630 0.243920i
\(443\) 7.44258e16i 0.467842i −0.972256 0.233921i \(-0.924844\pi\)
0.972256 0.233921i \(-0.0751557\pi\)
\(444\) 1.05981e17 1.08369e17i 0.656508 0.671300i
\(445\) 8.10853e16i 0.494997i
\(446\) 1.73794e17 7.31247e16i 1.04558 0.439934i
\(447\) −7.95851e15 −0.0471881
\(448\) −2.02683e16 1.89570e16i −0.118443 0.110780i
\(449\) −7.45593e16 −0.429438 −0.214719 0.976676i \(-0.568884\pi\)
−0.214719 + 0.976676i \(0.568884\pi\)
\(450\) −5.12769e16 + 2.15750e16i −0.291099 + 0.122481i
\(451\) 4.82052e17i 2.69741i
\(452\) −1.57284e17 + 1.60827e17i −0.867528 + 0.887075i
\(453\) 1.05750e16i 0.0574966i
\(454\) 1.01913e17 + 2.42215e17i 0.546219 + 1.29819i
\(455\) 1.08642e16 0.0574013
\(456\) 1.80287e16 4.56689e16i 0.0939060 0.237875i
\(457\) 2.69972e17 1.38632 0.693159 0.720785i \(-0.256218\pi\)
0.693159 + 0.720785i \(0.256218\pi\)
\(458\) 7.73523e16 + 1.83842e17i 0.391605 + 0.930721i
\(459\) 9.90218e16i 0.494252i
\(460\) −9.86158e16 9.64428e16i −0.485311 0.474618i
\(461\) 4.89036e16i 0.237293i 0.992937 + 0.118646i \(0.0378555\pi\)
−0.992937 + 0.118646i \(0.962145\pi\)
\(462\) 2.37412e16 9.98920e15i 0.113587 0.0477923i
\(463\) −4.05876e17 −1.91477 −0.957386 0.288813i \(-0.906739\pi\)
−0.957386 + 0.288813i \(0.906739\pi\)
\(464\) 2.72707e17 6.07670e15i 1.26862 0.0282684i
\(465\) 9.74181e16 0.446885
\(466\) 1.07945e17 4.54184e16i 0.488309 0.205458i
\(467\) 2.47217e17i 1.10286i 0.834223 + 0.551428i \(0.185917\pi\)
−0.834223 + 0.551428i \(0.814083\pi\)
\(468\) 5.70447e16 + 5.57877e16i 0.250967 + 0.245437i
\(469\) 2.37118e16i 0.102882i
\(470\) 9.98308e16 + 2.37266e17i 0.427197 + 1.01531i
\(471\) −7.91082e16 −0.333876
\(472\) −2.40880e17 9.50924e16i −1.00272 0.395843i
\(473\) −7.54399e16 −0.309744
\(474\) 7.29733e16 + 1.73435e17i 0.295532 + 0.702387i
\(475\) 5.41890e16i 0.216472i
\(476\) 1.64261e16 1.67962e16i 0.0647277 0.0661861i
\(477\) 1.26408e17i 0.491365i
\(478\) 3.62711e17 1.52612e17i 1.39085 0.585204i
\(479\) −1.68600e17 −0.637788 −0.318894 0.947790i \(-0.603311\pi\)
−0.318894 + 0.947790i \(0.603311\pi\)
\(480\) 4.11551e16 + 9.20223e16i 0.153588 + 0.343420i
\(481\) 2.39943e17 0.883414
\(482\) −2.20094e17 + 9.26054e16i −0.799470 + 0.336380i
\(483\) 1.98245e16i 0.0710469i
\(484\) −2.72522e17 + 2.78662e17i −0.963622 + 0.985333i
\(485\) 1.25577e17i 0.438115i
\(486\) −1.15897e17 2.75450e17i −0.398965 0.948215i
\(487\) 7.90235e16 0.268422 0.134211 0.990953i \(-0.457150\pi\)
0.134211 + 0.990953i \(0.457150\pi\)
\(488\) 1.88384e17 + 7.43683e16i 0.631415 + 0.249264i
\(489\) −5.29156e16 −0.175015
\(490\) −8.83362e16 2.09947e17i −0.288313 0.685229i
\(491\) 1.92491e17i 0.619984i −0.950739 0.309992i \(-0.899674\pi\)
0.950739 0.309992i \(-0.100326\pi\)
\(492\) −1.93855e17 1.89584e17i −0.616175 0.602598i
\(493\) 2.30916e17i 0.724351i
\(494\) 7.16384e16 3.01422e16i 0.221779 0.0933145i
\(495\) 2.91798e17 0.891554
\(496\) −8.77548e15 3.93822e17i −0.0264631 1.18760i
\(497\) −2.33495e16 −0.0694962
\(498\) −2.48190e17 + 1.04427e17i −0.729109 + 0.306776i
\(499\) 2.23025e17i 0.646697i −0.946280 0.323349i \(-0.895191\pi\)
0.946280 0.323349i \(-0.104809\pi\)
\(500\) −2.70255e17 2.64300e17i −0.773514 0.756470i
\(501\) 2.00339e17i 0.566005i
\(502\) 4.16774e16 + 9.90539e16i 0.116232 + 0.276247i
\(503\) 9.72300e16 0.267675 0.133838 0.991003i \(-0.457270\pi\)
0.133838 + 0.991003i \(0.457270\pi\)
\(504\) −1.65920e16 + 4.20294e16i −0.0450919 + 0.114223i
\(505\) 2.75544e17 0.739260
\(506\) −2.00762e17 4.77149e17i −0.531746 1.26379i
\(507\) 1.47939e17i 0.386840i
\(508\) −3.01372e16 + 3.08162e16i −0.0778016 + 0.0795545i
\(509\) 2.69652e17i 0.687287i −0.939100 0.343643i \(-0.888339\pi\)
0.939100 0.343643i \(-0.111661\pi\)
\(510\) −7.86577e16 + 3.30955e16i −0.197941 + 0.0832843i
\(511\) 2.02950e16 0.0504258
\(512\) 3.68302e17 1.74663e17i 0.903544 0.428496i
\(513\) −1.85518e17 −0.449389
\(514\) 7.19431e15 3.02704e15i 0.0172079 0.00724031i
\(515\) 1.04788e17i 0.247493i
\(516\) −2.96693e16 + 3.03378e16i −0.0691966 + 0.0707557i
\(517\) 9.66056e17i 2.22492i
\(518\) 5.26985e16 + 1.25248e17i 0.119855 + 0.284857i
\(519\) 3.53626e17 0.794248
\(520\) −5.85938e16 + 1.48425e17i −0.129966 + 0.329220i
\(521\) −6.40373e17 −1.40277 −0.701387 0.712781i \(-0.747436\pi\)
−0.701387 + 0.712781i \(0.747436\pi\)
\(522\) −1.72245e17 4.09373e17i −0.372640 0.885648i
\(523\) 8.02434e17i 1.71454i 0.514864 + 0.857272i \(0.327842\pi\)
−0.514864 + 0.857272i \(0.672158\pi\)
\(524\) 4.79019e17 + 4.68464e17i 1.01088 + 0.988604i
\(525\) 1.59901e16i 0.0333285i
\(526\) −2.79584e17 + 1.17636e17i −0.575578 + 0.242177i
\(527\) 3.33470e17 0.678091
\(528\) 8.42794e15 + 3.78225e17i 0.0169278 + 0.759679i
\(529\) −1.05605e17 −0.209519
\(530\) −2.33019e17 + 9.80436e16i −0.456665 + 0.192144i
\(531\) 4.21658e17i 0.816293i
\(532\) 3.14678e16 + 3.07744e16i 0.0601785 + 0.0588525i
\(533\) 4.29219e17i 0.810871i
\(534\) −6.63838e16 1.57773e17i −0.123892 0.294453i
\(535\) 1.97196e17 0.363579
\(536\) 3.23948e17 + 1.27885e17i 0.590072 + 0.232943i
\(537\) 3.60514e17 0.648768
\(538\) 2.69565e17 + 6.40672e17i 0.479269 + 1.13907i
\(539\) 8.54823e17i 1.50158i
\(540\) 2.66315e17 2.72315e17i 0.462206 0.472620i
\(541\) 1.00333e18i 1.72053i −0.509848 0.860265i \(-0.670298\pi\)
0.509848 0.860265i \(-0.329702\pi\)
\(542\) 1.73999e17 7.32107e16i 0.294816 0.124045i
\(543\) −7.67464e16 −0.128487
\(544\) 1.40877e17 + 3.15000e17i 0.233050 + 0.521096i
\(545\) −6.57329e17 −1.07450
\(546\) 2.11391e16 8.89438e15i 0.0341456 0.0143669i
\(547\) 8.57926e17i 1.36941i 0.728822 + 0.684703i \(0.240068\pi\)
−0.728822 + 0.684703i \(0.759932\pi\)
\(548\) 2.54198e17 2.59925e17i 0.400958 0.409992i
\(549\) 3.29764e17i 0.514023i
\(550\) −1.61932e17 3.84862e17i −0.249445 0.592853i
\(551\) −4.32622e17 −0.658602
\(552\) −2.70840e17 1.06920e17i −0.407483 0.160862i
\(553\) −1.68678e17 −0.250810
\(554\) 1.48956e17 + 3.54021e17i 0.218899 + 0.520255i
\(555\) 4.93580e17i 0.716890i
\(556\) 1.25952e17 + 1.23177e17i 0.180809 + 0.176825i
\(557\) 1.46708e17i 0.208160i −0.994569 0.104080i \(-0.966810\pi\)
0.994569 0.104080i \(-0.0331897\pi\)
\(558\) −5.91184e17 + 2.48743e17i −0.829087 + 0.348842i
\(559\) −6.71716e16 −0.0931127
\(560\) −9.03454e16 + 2.01315e15i −0.123790 + 0.00275839i
\(561\) −3.20263e17 −0.433759
\(562\) 2.29492e17 9.65597e16i 0.307242 0.129274i
\(563\) 7.50214e17i 0.992843i −0.868082 0.496422i \(-0.834647\pi\)
0.868082 0.496422i \(-0.165353\pi\)
\(564\) 3.88495e17 + 3.79935e17i 0.508243 + 0.497044i
\(565\) 7.32506e17i 0.947319i
\(566\) 2.99843e16 + 7.12631e16i 0.0383342 + 0.0911083i
\(567\) 4.24187e16 0.0536127
\(568\) 1.25931e17 3.18999e17i 0.157351 0.398589i
\(569\) −5.82283e17 −0.719291 −0.359645 0.933089i \(-0.617102\pi\)
−0.359645 + 0.933089i \(0.617102\pi\)
\(570\) −6.20047e16 1.47366e17i −0.0757247 0.179974i
\(571\) 6.73020e17i 0.812630i −0.913733 0.406315i \(-0.866814\pi\)
0.913733 0.406315i \(-0.133186\pi\)
\(572\) −4.18718e17 + 4.28152e17i −0.499859 + 0.511121i
\(573\) 4.44582e16i 0.0524743i
\(574\) 2.24048e17 9.42691e16i 0.261465 0.110012i
\(575\) 3.21369e17 0.370820
\(576\) −4.84717e17 4.53356e17i −0.553021 0.517241i
\(577\) 9.35938e17 1.05585 0.527927 0.849290i \(-0.322969\pi\)
0.527927 + 0.849290i \(0.322969\pi\)
\(578\) 5.57046e17 2.34379e17i 0.621384 0.261450i
\(579\) 6.77257e16i 0.0747039i
\(580\) 6.21038e17 6.35030e17i 0.677386 0.692648i
\(581\) 2.41382e17i 0.260352i
\(582\) −1.02809e17 2.44344e17i −0.109655 0.260616i
\(583\) −9.48761e17 −1.00072
\(584\) −1.09457e17 + 2.77268e17i −0.114172 + 0.289212i
\(585\) 2.59816e17 0.268011
\(586\) 2.52240e17 + 5.99495e17i 0.257323 + 0.611576i
\(587\) 1.30002e18i 1.31160i 0.754935 + 0.655799i \(0.227668\pi\)
−0.754935 + 0.655799i \(0.772332\pi\)
\(588\) −3.43764e17 3.36189e17i −0.343010 0.335452i
\(589\) 6.24758e17i 0.616541i
\(590\) −7.77279e17 + 3.27043e17i −0.758645 + 0.319203i
\(591\) 4.96029e17 0.478838
\(592\) −1.99534e18 + 4.44620e16i −1.90514 + 0.0424519i
\(593\) 1.33010e18 1.25611 0.628057 0.778168i \(-0.283851\pi\)
0.628057 + 0.778168i \(0.283851\pi\)
\(594\) 1.31759e18 5.54380e17i 1.23074 0.517840i
\(595\) 7.65003e16i 0.0706810i
\(596\) 7.49186e16 + 7.32678e16i 0.0684682 + 0.0669596i
\(597\) 9.03514e17i 0.816773i
\(598\) −1.78759e17 4.24853e17i −0.159849 0.379910i
\(599\) −1.69219e18 −1.49684 −0.748418 0.663227i \(-0.769186\pi\)
−0.748418 + 0.663227i \(0.769186\pi\)
\(600\) −2.18456e17 8.62398e16i −0.191153 0.0754614i
\(601\) 1.09369e18 0.946695 0.473347 0.880876i \(-0.343046\pi\)
0.473347 + 0.880876i \(0.343046\pi\)
\(602\) −1.47529e16 3.50629e16i −0.0126328 0.0300241i
\(603\) 5.67067e17i 0.480366i
\(604\) −9.73558e16 + 9.95493e16i −0.0815871 + 0.0834254i
\(605\) 1.26920e18i 1.05225i
\(606\) 5.36145e17 2.25585e17i 0.439755 0.185029i
\(607\) 1.88846e18 1.53243 0.766214 0.642585i \(-0.222138\pi\)
0.766214 + 0.642585i \(0.222138\pi\)
\(608\) −5.90154e17 + 2.63935e17i −0.473797 + 0.211896i
\(609\) −1.27658e17 −0.101400
\(610\) 6.07882e17 2.55769e17i 0.477722 0.201004i
\(611\) 8.60176e17i 0.668835i
\(612\) 3.92831e17 4.01682e17i 0.302219 0.309028i
\(613\) 9.88263e17i 0.752280i −0.926563 0.376140i \(-0.877251\pi\)
0.926563 0.376140i \(-0.122749\pi\)
\(614\) 6.28462e17 + 1.49366e18i 0.473353 + 1.12501i
\(615\) −8.82934e17 −0.658021
\(616\) −3.15454e17 1.24532e17i −0.232628 0.0918345i
\(617\) 1.64690e18 1.20175 0.600873 0.799345i \(-0.294820\pi\)
0.600873 + 0.799345i \(0.294820\pi\)
\(618\) −8.57887e16 2.03893e17i −0.0619448 0.147223i
\(619\) 2.50056e17i 0.178669i 0.996002 + 0.0893343i \(0.0284740\pi\)
−0.996002 + 0.0893343i \(0.971526\pi\)
\(620\) −9.17060e17 8.96853e17i −0.648413 0.634125i
\(621\) 1.10022e18i 0.769809i
\(622\) −2.31515e18 + 9.74111e17i −1.60303 + 0.674483i
\(623\) 1.53446e17 0.105144
\(624\) 7.50423e15 + 3.36771e17i 0.00508869 + 0.228368i
\(625\) −6.09411e17 −0.408969
\(626\) −6.89871e17 + 2.90266e17i −0.458178 + 0.192780i
\(627\) 6.00015e17i 0.394387i
\(628\) 7.44697e17 + 7.28288e17i 0.484442 + 0.473768i
\(629\) 1.68956e18i 1.08779i
\(630\) 5.70633e16 + 1.35622e17i 0.0363616 + 0.0864202i
\(631\) −1.79473e18 −1.13190 −0.565949 0.824440i \(-0.691490\pi\)
−0.565949 + 0.824440i \(0.691490\pi\)
\(632\) 9.09733e17 2.30446e18i 0.567875 1.43850i
\(633\) −8.88885e17 −0.549189
\(634\) 5.26421e16 + 1.25114e17i 0.0321924 + 0.0765112i
\(635\) 1.40356e17i 0.0849573i
\(636\) −3.73133e17 + 3.81540e17i −0.223559 + 0.228596i
\(637\) 7.61134e17i 0.451393i
\(638\) 3.07257e18 1.29280e18i 1.80371 0.758920i
\(639\) −5.58404e17 −0.324484
\(640\) 4.59758e17 1.24515e18i 0.264460 0.716229i
\(641\) −8.87296e16 −0.0505233 −0.0252616 0.999681i \(-0.508042\pi\)
−0.0252616 + 0.999681i \(0.508042\pi\)
\(642\) 3.83698e17 1.61443e17i 0.216278 0.0909999i
\(643\) 3.35822e18i 1.87386i −0.349511 0.936932i \(-0.613652\pi\)
0.349511 0.936932i \(-0.386348\pi\)
\(644\) 1.82509e17 1.86621e17i 0.100815 0.103086i
\(645\) 1.38177e17i 0.0755609i
\(646\) −2.12247e17 5.04444e17i −0.114903 0.273088i
\(647\) −4.29076e16 −0.0229962 −0.0114981 0.999934i \(-0.503660\pi\)
−0.0114981 + 0.999934i \(0.503660\pi\)
\(648\) −2.28778e17 + 5.79521e17i −0.121388 + 0.307490i
\(649\) −3.16478e18 −1.66247
\(650\) −1.44184e17 3.42680e17i −0.0749861 0.178218i
\(651\) 1.84354e17i 0.0949241i
\(652\) 4.98129e17 + 4.87153e17i 0.253941 + 0.248345i
\(653\) 6.77971e17i 0.342197i −0.985254 0.171098i \(-0.945268\pi\)
0.985254 0.171098i \(-0.0547316\pi\)
\(654\) −1.27901e18 + 5.38149e17i −0.639174 + 0.268935i
\(655\) 2.18174e18 1.07953
\(656\) 7.95353e16 + 3.56935e18i 0.0389659 + 1.74869i
\(657\) 4.85354e17 0.235442
\(658\) −4.49003e17 + 1.88920e17i −0.215666 + 0.0907422i
\(659\) 1.20273e18i 0.572021i 0.958227 + 0.286010i \(0.0923292\pi\)
−0.958227 + 0.286010i \(0.907671\pi\)
\(660\) 8.80741e17 + 8.61334e17i 0.414775 + 0.405635i
\(661\) 1.00191e18i 0.467217i −0.972331 0.233608i \(-0.924947\pi\)
0.972331 0.233608i \(-0.0750534\pi\)
\(662\) −7.53985e17 1.79198e18i −0.348165 0.827479i
\(663\) −2.85162e17 −0.130393
\(664\) 3.29775e18 + 1.30185e18i 1.49322 + 0.589480i
\(665\) 1.43324e17 0.0642654
\(666\) 1.26028e18 + 2.99530e18i 0.559611 + 1.33002i
\(667\) 2.56567e18i 1.12819i
\(668\) −1.84437e18 + 1.88592e18i −0.803156 + 0.821252i
\(669\) 1.29609e18i 0.558942i
\(670\) 1.04532e18 4.39825e17i 0.446442 0.187842i
\(671\) 2.47506e18 1.04686
\(672\) −1.74143e17 + 7.78821e16i −0.0729468 + 0.0326240i
\(673\) −3.10962e18 −1.29006 −0.645029 0.764158i \(-0.723155\pi\)
−0.645029 + 0.764158i \(0.723155\pi\)
\(674\) −3.62715e18 + 1.52614e18i −1.49031 + 0.627054i
\(675\) 8.87419e17i 0.361122i
\(676\) 1.36196e18 1.39265e18i 0.548923 0.561291i
\(677\) 3.32505e18i 1.32731i 0.748040 + 0.663653i \(0.230995\pi\)
−0.748040 + 0.663653i \(0.769005\pi\)
\(678\) 5.99695e17 + 1.42529e18i 0.237103 + 0.563520i
\(679\) 2.37642e17 0.0930614
\(680\) 1.04514e18 + 4.12590e17i 0.405384 + 0.160034i
\(681\) 1.80635e18 0.693979
\(682\) −1.86695e18 4.43716e18i −0.710453 1.68852i
\(683\) 1.67034e18i 0.629607i −0.949157 0.314804i \(-0.898061\pi\)
0.949157 0.314804i \(-0.101939\pi\)
\(684\) 7.52553e17 + 7.35971e17i 0.280978 + 0.274787i
\(685\) 1.18386e18i 0.437836i
\(686\) 8.05341e17 3.38850e17i 0.295035 0.124137i
\(687\) 1.37103e18 0.497539
\(688\) 5.58593e17 1.24471e16i 0.200803 0.00447447i
\(689\) −8.44776e17 −0.300827
\(690\) −8.73954e17 + 3.67720e17i −0.308297 + 0.129717i
\(691\) 1.34749e18i 0.470890i 0.971888 + 0.235445i \(0.0756547\pi\)
−0.971888 + 0.235445i \(0.924345\pi\)
\(692\) −3.32891e18 3.25556e18i −1.15242 1.12703i
\(693\) 5.52198e17i 0.189378i
\(694\) −5.83661e16 1.38718e17i −0.0198301 0.0471298i
\(695\) 5.73662e17 0.193088
\(696\) 6.88503e17 1.74406e18i 0.229586 0.581569i
\(697\) −3.02236e18 −0.998465
\(698\) −1.29762e18 3.08403e18i −0.424705 1.00939i
\(699\) 8.05015e17i 0.261037i
\(700\) 1.47209e17 1.50525e17i 0.0472929 0.0483585i
\(701\) 3.66094e18i 1.16527i 0.812735 + 0.582634i \(0.197978\pi\)
−0.812735 + 0.582634i \(0.802022\pi\)
\(702\) 1.17318e18 4.93620e17i 0.369975 0.155669i
\(703\) 3.16541e18 0.989053
\(704\) 3.40269e18 3.63807e18i 1.05342 1.12629i
\(705\) 1.76944e18 0.542760
\(706\) −1.74528e18 + 7.34334e17i −0.530438 + 0.223184i
\(707\) 5.21440e17i 0.157028i
\(708\) −1.24466e18 + 1.27270e18i −0.371393 + 0.379761i
\(709\) 5.56977e18i 1.64678i −0.567473 0.823392i \(-0.692079\pi\)
0.567473 0.823392i \(-0.307921\pi\)
\(710\) −4.33105e17 1.02935e18i −0.126886 0.301568i
\(711\) −4.03393e18 −1.17105
\(712\) −8.27583e17 + 2.09637e18i −0.238063 + 0.603042i
\(713\) 3.70514e18 1.05614
\(714\) −6.26301e16 1.48852e17i −0.0176907 0.0420452i
\(715\) 1.95007e18i 0.545833i
\(716\) −3.39375e18 3.31897e18i −0.941338 0.920596i
\(717\) 2.70496e18i 0.743510i
\(718\) −2.92848e18 + 1.23217e18i −0.797689 + 0.335631i
\(719\) 2.56260e18 0.691740 0.345870 0.938282i \(-0.387584\pi\)
0.345870 + 0.938282i \(0.387584\pi\)
\(720\) −2.16061e18 + 4.81446e16i −0.577983 + 0.0128791i
\(721\) 1.98300e17 0.0525708
\(722\) −2.56323e18 + 1.07849e18i −0.673434 + 0.283350i
\(723\) 1.64138e18i 0.427376i
\(724\) 7.22464e17 + 7.06544e17i 0.186430 + 0.182322i
\(725\) 2.06943e18i 0.529242i
\(726\) 1.03908e18 + 2.46956e18i 0.263367 + 0.625939i
\(727\) −1.47166e18 −0.369688 −0.184844 0.982768i \(-0.559178\pi\)
−0.184844 + 0.982768i \(0.559178\pi\)
\(728\) −2.80880e17 1.10883e17i −0.0699306 0.0276065i
\(729\) −7.14494e17 −0.176307
\(730\) 3.76447e17 + 8.94696e17i 0.0920673 + 0.218815i
\(731\) 4.72991e17i 0.114654i
\(732\) 9.73403e17 9.95334e17i 0.233868 0.239137i
\(733\) 5.45589e18i 1.29924i 0.760259 + 0.649620i \(0.225072\pi\)
−0.760259 + 0.649620i \(0.774928\pi\)
\(734\) 7.52514e18 3.16623e18i 1.77619 0.747341i
\(735\) −1.56571e18 −0.366305
\(736\) 1.56527e18 + 3.49992e18i 0.362981 + 0.811619i
\(737\) 4.25616e18 0.978315
\(738\) 5.35811e18 2.25445e18i 1.22080 0.513657i
\(739\) 3.33360e18i 0.752878i −0.926441 0.376439i \(-0.877148\pi\)
0.926441 0.376439i \(-0.122852\pi\)
\(740\) −4.54400e18 + 4.64639e18i −1.01726 + 1.04018i
\(741\) 5.34253e17i 0.118557i
\(742\) −1.85538e17 4.40965e17i −0.0408138 0.0970015i
\(743\) −7.19594e18 −1.56913 −0.784567 0.620044i \(-0.787115\pi\)
−0.784567 + 0.620044i \(0.787115\pi\)
\(744\) −2.51863e18 9.94280e17i −0.544428 0.214924i
\(745\) 3.41225e17 0.0731181
\(746\) 1.97599e18 + 4.69631e18i 0.419743 + 0.997596i
\(747\) 5.77266e18i 1.21560i
\(748\) 3.01485e18 + 2.94842e18i 0.629369 + 0.615501i
\(749\) 3.73175e17i 0.0772290i
\(750\) −2.39506e18 + 1.00773e18i −0.491380 + 0.206750i
\(751\) 1.83541e18 0.373313 0.186656 0.982425i \(-0.440235\pi\)
0.186656 + 0.982425i \(0.440235\pi\)
\(752\) −1.59393e17 7.15315e18i −0.0321405 1.44239i
\(753\) 7.38708e17 0.147674
\(754\) 2.73582e18 1.15111e18i 0.542217 0.228140i
\(755\) 4.53408e17i 0.0890911i
\(756\) 5.15329e17 + 5.03974e17i 0.100391 + 0.0981786i
\(757\) 5.20889e17i 0.100605i 0.998734 + 0.0503027i \(0.0160186\pi\)
−0.998734 + 0.0503027i \(0.983981\pi\)
\(758\) 3.07360e18 + 7.30498e18i 0.588570 + 1.39884i
\(759\) −3.55840e18 −0.675590
\(760\) −7.72990e17 + 1.95808e18i −0.145508 + 0.368588i
\(761\) 1.39388e18 0.260150 0.130075 0.991504i \(-0.458478\pi\)
0.130075 + 0.991504i \(0.458478\pi\)
\(762\) 1.14908e17 + 2.73100e17i 0.0212639 + 0.0505375i
\(763\) 1.24393e18i 0.228237i
\(764\) 4.09292e17 4.18514e17i 0.0744606 0.0761383i
\(765\) 1.82950e18i 0.330015i
\(766\) 1.99423e18 8.39081e17i 0.356688 0.150078i
\(767\) −2.81792e18 −0.499756
\(768\) −1.24809e17 2.79917e18i −0.0219482 0.492246i
\(769\) −5.95951e18 −1.03918 −0.519589 0.854417i