Properties

Label 8.14.b.b.5.5
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 5.5
Root \(1.33949 - 44.8086i\)
Character \(\chi\) = 8.5
Dual form 8.14.b.b.5.6

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(12.6790 - 89.6172i) q^{2}\) \(+86.8898i q^{3}\) \(+(-7870.49 - 2272.51i) q^{4}\) \(+45531.7i q^{5}\) \(+(7786.82 + 1101.67i) q^{6}\) \(-249036. q^{7}\) \(+(-303446. + 676518. i) q^{8}\) \(+1.58677e6 q^{9}\) \(+O(q^{10})\) \(q\)\(+(12.6790 - 89.6172i) q^{2}\) \(+86.8898i q^{3}\) \(+(-7870.49 - 2272.51i) q^{4}\) \(+45531.7i q^{5}\) \(+(7786.82 + 1101.67i) q^{6}\) \(-249036. q^{7}\) \(+(-303446. + 676518. i) q^{8}\) \(+1.58677e6 q^{9}\) \(+(4.08042e6 + 577295. i) q^{10}\) \(+5.28836e6i q^{11}\) \(+(197458. - 683865. i) q^{12}\) \(+1.17535e7i q^{13}\) \(+(-3.15752e6 + 2.23179e7i) q^{14}\) \(-3.95624e6 q^{15}\) \(+(5.67803e7 + 3.57715e7i) q^{16}\) \(-1.22707e8 q^{17}\) \(+(2.01187e7 - 1.42202e8i) q^{18}\) \(-5.19560e7i q^{19}\) \(+(1.03471e8 - 3.58356e8i) q^{20}\) \(-2.16387e7i q^{21}\) \(+(4.73928e8 + 6.70510e7i) q^{22}\) \(-1.22082e9 q^{23}\) \(+(-5.87825e7 - 2.63663e7i) q^{24}\) \(-8.52431e8 q^{25}\) \(+(1.05331e9 + 1.49022e8i) q^{26}\) \(+2.76405e8i q^{27}\) \(+(1.96003e9 + 5.65936e8i) q^{28}\) \(+4.04054e9i q^{29}\) \(+(-5.01611e7 + 3.54547e8i) q^{30}\) \(+1.61058e9 q^{31}\) \(+(3.92566e9 - 4.63494e9i) q^{32}\) \(-4.59505e8 q^{33}\) \(+(-1.55580e9 + 1.09967e10i) q^{34}\) \(-1.13390e10i q^{35}\) \(+(-1.24887e10 - 3.60596e9i) q^{36}\) \(+4.09023e9i q^{37}\) \(+(-4.65615e9 - 6.58749e8i) q^{38}\) \(-1.02126e9 q^{39}\) \(+(-3.08030e10 - 1.38164e10i) q^{40}\) \(+4.23280e10 q^{41}\) \(+(-1.93920e9 - 2.74356e8i) q^{42}\) \(-7.66300e10i q^{43}\) \(+(1.20178e10 - 4.16220e10i) q^{44}\) \(+7.22484e10i q^{45}\) \(+(-1.54787e10 + 1.09406e11i) q^{46}\) \(+6.09947e10 q^{47}\) \(+(-3.10818e9 + 4.93363e9i) q^{48}\) \(-3.48703e10 q^{49}\) \(+(-1.08079e10 + 7.63924e10i) q^{50}\) \(-1.06620e10i q^{51}\) \(+(2.67098e10 - 9.25055e10i) q^{52}\) \(+2.24645e11i q^{53}\) \(+(2.47706e10 + 3.50453e9i) q^{54}\) \(-2.40788e11 q^{55}\) \(+(7.55688e10 - 1.68477e11i) q^{56}\) \(+4.51445e9 q^{57}\) \(+(3.62102e11 + 5.12299e10i) q^{58}\) \(-4.64215e11i q^{59}\) \(+(3.11375e10 + 8.99059e9i) q^{60}\) \(-4.58331e10i q^{61}\) \(+(2.04205e10 - 1.44336e11i) q^{62}\) \(-3.95163e11 q^{63}\) \(+(-3.65597e11 - 4.10573e11i) q^{64}\) \(-5.35155e11 q^{65}\) \(+(-5.82605e9 + 4.11795e10i) q^{66}\) \(+8.92905e11i q^{67}\) \(+(9.65764e11 + 2.78853e11i) q^{68}\) \(-1.06076e11i q^{69}\) \(+(-1.01617e12 - 1.43767e11i) q^{70}\) \(+1.53438e12 q^{71}\) \(+(-4.81499e11 + 1.07348e12i) q^{72}\) \(+8.01210e11 q^{73}\) \(+(3.66555e11 + 5.18599e10i) q^{74}\) \(-7.40675e10i q^{75}\) \(+(-1.18070e11 + 4.08919e11i) q^{76}\) \(-1.31699e12i q^{77}\) \(+(-1.29485e10 + 9.15221e10i) q^{78}\) \(+5.92669e10 q^{79}\) \(+(-1.62874e12 + 2.58530e12i) q^{80}\) \(+2.50581e12 q^{81}\) \(+(5.36676e11 - 3.79332e12i) q^{82}\) \(+4.57014e12i q^{83}\) \(+(-4.91741e10 + 1.70307e11i) q^{84}\) \(-5.58705e12i q^{85}\) \(+(-6.86736e12 - 9.71590e11i) q^{86}\) \(-3.51082e11 q^{87}\) \(+(-3.57767e12 - 1.60473e12i) q^{88}\) \(-5.17348e12 q^{89}\) \(+(6.47470e12 + 9.16036e11i) q^{90}\) \(-2.92703e12i q^{91}\) \(+(9.60841e12 + 2.77431e12i) q^{92}\) \(+1.39943e11i q^{93}\) \(+(7.73351e11 - 5.46618e12i) q^{94}\) \(+2.36564e12 q^{95}\) \(+(4.02729e11 + 3.41100e11i) q^{96}\) \(-3.32642e12 q^{97}\) \(+(-4.42119e11 + 3.12498e12i) q^{98}\) \(+8.39143e12i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut -\mathstrut 4542088q^{10} \) \(\mathstrut +\mathstrut 27987880q^{12} \) \(\mathstrut +\mathstrut 1408688q^{14} \) \(\mathstrut -\mathstrut 145914416q^{15} \) \(\mathstrut +\mathstrut 56624912q^{16} \) \(\mathstrut +\mathstrut 217326004q^{17} \) \(\mathstrut -\mathstrut 147615262q^{18} \) \(\mathstrut +\mathstrut 21655184q^{20} \) \(\mathstrut -\mathstrut 177987876q^{22} \) \(\mathstrut -\mathstrut 78679952q^{23} \) \(\mathstrut +\mathstrut 320199056q^{24} \) \(\mathstrut -\mathstrut 3076402574q^{25} \) \(\mathstrut +\mathstrut 3734872040q^{26} \) \(\mathstrut -\mathstrut 1653812448q^{28} \) \(\mathstrut +\mathstrut 6338232752q^{30} \) \(\mathstrut +\mathstrut 648233792q^{31} \) \(\mathstrut -\mathstrut 11298380000q^{32} \) \(\mathstrut +\mathstrut 15484079688q^{33} \) \(\mathstrut -\mathstrut 6096822724q^{34} \) \(\mathstrut +\mathstrut 4004708940q^{36} \) \(\mathstrut -\mathstrut 18764968628q^{38} \) \(\mathstrut -\mathstrut 63497510288q^{39} \) \(\mathstrut +\mathstrut 7466802592q^{40} \) \(\mathstrut +\mathstrut 59324640356q^{41} \) \(\mathstrut +\mathstrut 53897620960q^{42} \) \(\mathstrut +\mathstrut 13325704392q^{44} \) \(\mathstrut -\mathstrut 55046867440q^{46} \) \(\mathstrut -\mathstrut 10176534816q^{47} \) \(\mathstrut -\mathstrut 301841943264q^{48} \) \(\mathstrut +\mathstrut 182708552058q^{49} \) \(\mathstrut +\mathstrut 326454435302q^{50} \) \(\mathstrut -\mathstrut 53296499536q^{52} \) \(\mathstrut +\mathstrut 35449773752q^{54} \) \(\mathstrut -\mathstrut 123010753008q^{55} \) \(\mathstrut -\mathstrut 462152447680q^{56} \) \(\mathstrut -\mathstrut 511372324504q^{57} \) \(\mathstrut +\mathstrut 766482705096q^{58} \) \(\mathstrut +\mathstrut 1813082440992q^{60} \) \(\mathstrut -\mathstrut 1665308528960q^{62} \) \(\mathstrut -\mathstrut 898991123792q^{63} \) \(\mathstrut -\mathstrut 2180548996032q^{64} \) \(\mathstrut +\mathstrut 1577231990240q^{65} \) \(\mathstrut +\mathstrut 2269525079448q^{66} \) \(\mathstrut +\mathstrut 2338280915304q^{68} \) \(\mathstrut -\mathstrut 6070110714688q^{70} \) \(\mathstrut +\mathstrut 726361179984q^{71} \) \(\mathstrut -\mathstrut 3600753685960q^{72} \) \(\mathstrut -\mathstrut 633240365532q^{73} \) \(\mathstrut +\mathstrut 7528513982264q^{74} \) \(\mathstrut +\mathstrut 10338420845032q^{76} \) \(\mathstrut -\mathstrut 8252024440816q^{78} \) \(\mathstrut +\mathstrut 5445103565344q^{79} \) \(\mathstrut -\mathstrut 15406871881920q^{80} \) \(\mathstrut -\mathstrut 9674575380574q^{81} \) \(\mathstrut +\mathstrut 12273334206796q^{82} \) \(\mathstrut +\mathstrut 20362643366464q^{84} \) \(\mathstrut -\mathstrut 26794541719396q^{86} \) \(\mathstrut +\mathstrut 7632221772720q^{87} \) \(\mathstrut -\mathstrut 27677491769136q^{88} \) \(\mathstrut +\mathstrut 5506344808004q^{89} \) \(\mathstrut +\mathstrut 31454099524040q^{90} \) \(\mathstrut +\mathstrut 33971694298464q^{92} \) \(\mathstrut -\mathstrut 45356008560096q^{94} \) \(\mathstrut -\mathstrut 14214732035504q^{95} \) \(\mathstrut -\mathstrut 35398666935232q^{96} \) \(\mathstrut +\mathstrut 1361133320788q^{97} \) \(\mathstrut +\mathstrut 54325451514942q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 12.6790 89.6172i 0.140084 0.990140i
\(3\) 86.8898i 0.0688146i 0.999408 + 0.0344073i \(0.0109544\pi\)
−0.999408 + 0.0344073i \(0.989046\pi\)
\(4\) −7870.49 2272.51i −0.960753 0.277406i
\(5\) 45531.7i 1.30319i 0.758566 + 0.651596i \(0.225900\pi\)
−0.758566 + 0.651596i \(0.774100\pi\)
\(6\) 7786.82 + 1101.67i 0.0681361 + 0.00963984i
\(7\) −249036. −0.800063 −0.400032 0.916501i \(-0.631001\pi\)
−0.400032 + 0.916501i \(0.631001\pi\)
\(8\) −303446. + 676518.i −0.409257 + 0.912419i
\(9\) 1.58677e6 0.995265
\(10\) 4.08042e6 + 577295.i 1.29034 + 0.182557i
\(11\) 5.28836e6i 0.900054i 0.893015 + 0.450027i \(0.148586\pi\)
−0.893015 + 0.450027i \(0.851414\pi\)
\(12\) 197458. 683865.i 0.0190896 0.0661139i
\(13\) 1.17535e7i 0.675358i 0.941261 + 0.337679i \(0.109642\pi\)
−0.941261 + 0.337679i \(0.890358\pi\)
\(14\) −3.15752e6 + 2.23179e7i −0.112076 + 0.792174i
\(15\) −3.95624e6 −0.0896787
\(16\) 5.67803e7 + 3.57715e7i 0.846092 + 0.533037i
\(17\) −1.22707e8 −1.23297 −0.616483 0.787368i \(-0.711443\pi\)
−0.616483 + 0.787368i \(0.711443\pi\)
\(18\) 2.01187e7 1.42202e8i 0.139421 0.985451i
\(19\) 5.19560e7i 0.253359i −0.991944 0.126680i \(-0.959568\pi\)
0.991944 0.126680i \(-0.0404320\pi\)
\(20\) 1.03471e8 3.58356e8i 0.361513 1.25205i
\(21\) 2.16387e7i 0.0550560i
\(22\) 4.73928e8 + 6.70510e7i 0.891179 + 0.126083i
\(23\) −1.22082e9 −1.71957 −0.859784 0.510659i \(-0.829402\pi\)
−0.859784 + 0.510659i \(0.829402\pi\)
\(24\) −5.87825e7 2.63663e7i −0.0627878 0.0281629i
\(25\) −8.52431e8 −0.698311
\(26\) 1.05331e9 + 1.49022e8i 0.668699 + 0.0946070i
\(27\) 2.76405e8i 0.137303i
\(28\) 1.96003e9 + 5.65936e8i 0.768663 + 0.221942i
\(29\) 4.04054e9i 1.26140i 0.776027 + 0.630699i \(0.217232\pi\)
−0.776027 + 0.630699i \(0.782768\pi\)
\(30\) −5.01611e7 + 3.54547e8i −0.0125626 + 0.0887945i
\(31\) 1.61058e9 0.325935 0.162967 0.986631i \(-0.447893\pi\)
0.162967 + 0.986631i \(0.447893\pi\)
\(32\) 3.92566e9 4.63494e9i 0.646305 0.763079i
\(33\) −4.59505e8 −0.0619369
\(34\) −1.55580e9 + 1.09967e10i −0.172719 + 1.22081i
\(35\) 1.13390e10i 1.04264i
\(36\) −1.24887e10 3.60596e9i −0.956203 0.276092i
\(37\) 4.09023e9i 0.262081i 0.991377 + 0.131041i \(0.0418318\pi\)
−0.991377 + 0.131041i \(0.958168\pi\)
\(38\) −4.65615e9 6.58749e8i −0.250861 0.0354917i
\(39\) −1.02126e9 −0.0464745
\(40\) −3.08030e10 1.38164e10i −1.18906 0.533341i
\(41\) 4.23280e10 1.39166 0.695830 0.718207i \(-0.255037\pi\)
0.695830 + 0.718207i \(0.255037\pi\)
\(42\) −1.93920e9 2.74356e8i −0.0545132 0.00771248i
\(43\) 7.66300e10i 1.84865i −0.381611 0.924323i \(-0.624631\pi\)
0.381611 0.924323i \(-0.375369\pi\)
\(44\) 1.20178e10 4.16220e10i 0.249680 0.864729i
\(45\) 7.22484e10i 1.29702i
\(46\) −1.54787e10 + 1.09406e11i −0.240884 + 1.70261i
\(47\) 6.09947e10 0.825384 0.412692 0.910871i \(-0.364589\pi\)
0.412692 + 0.910871i \(0.364589\pi\)
\(48\) −3.10818e9 + 4.93363e9i −0.0366807 + 0.0582235i
\(49\) −3.48703e10 −0.359899
\(50\) −1.08079e10 + 7.63924e10i −0.0978224 + 0.691426i
\(51\) 1.06620e10i 0.0848461i
\(52\) 2.67098e10 9.25055e10i 0.187348 0.648852i
\(53\) 2.24645e11i 1.39220i 0.717943 + 0.696102i \(0.245084\pi\)
−0.717943 + 0.696102i \(0.754916\pi\)
\(54\) 2.47706e10 + 3.50453e9i 0.135950 + 0.0192340i
\(55\) −2.40788e11 −1.17294
\(56\) 7.55688e10 1.68477e11i 0.327431 0.729993i
\(57\) 4.51445e9 0.0174348
\(58\) 3.62102e11 + 5.12299e10i 1.24896 + 0.176702i
\(59\) 4.64215e11i 1.43279i −0.697697 0.716393i \(-0.745792\pi\)
0.697697 0.716393i \(-0.254208\pi\)
\(60\) 3.11375e10 + 8.99059e9i 0.0861591 + 0.0248774i
\(61\) 4.58331e10i 0.113903i −0.998377 0.0569515i \(-0.981862\pi\)
0.998377 0.0569515i \(-0.0181381\pi\)
\(62\) 2.04205e10 1.44336e11i 0.0456583 0.322721i
\(63\) −3.95163e11 −0.796274
\(64\) −3.65597e11 4.10573e11i −0.665018 0.746828i
\(65\) −5.35155e11 −0.880121
\(66\) −5.82605e9 + 4.11795e10i −0.00867638 + 0.0613262i
\(67\) 8.92905e11i 1.20592i 0.797771 + 0.602961i \(0.206012\pi\)
−0.797771 + 0.602961i \(0.793988\pi\)
\(68\) 9.65764e11 + 2.78853e11i 1.18458 + 0.342032i
\(69\) 1.06076e11i 0.118331i
\(70\) −1.01617e12 1.43767e11i −1.03236 0.146057i
\(71\) 1.53438e12 1.42152 0.710762 0.703432i \(-0.248350\pi\)
0.710762 + 0.703432i \(0.248350\pi\)
\(72\) −4.81499e11 + 1.07348e12i −0.407319 + 0.908098i
\(73\) 8.01210e11 0.619652 0.309826 0.950793i \(-0.399729\pi\)
0.309826 + 0.950793i \(0.399729\pi\)
\(74\) 3.66555e11 + 5.18599e10i 0.259497 + 0.0367135i
\(75\) 7.40675e10i 0.0480540i
\(76\) −1.18070e11 + 4.08919e11i −0.0702834 + 0.243416i
\(77\) 1.31699e12i 0.720100i
\(78\) −1.29485e10 + 9.15221e10i −0.00651034 + 0.0460162i
\(79\) 5.92669e10 0.0274306 0.0137153 0.999906i \(-0.495634\pi\)
0.0137153 + 0.999906i \(0.495634\pi\)
\(80\) −1.62874e12 + 2.58530e12i −0.694650 + 1.10262i
\(81\) 2.50581e12 0.985816
\(82\) 5.36676e11 3.79332e12i 0.194950 1.37794i
\(83\) 4.57014e12i 1.53434i 0.641444 + 0.767170i \(0.278336\pi\)
−0.641444 + 0.767170i \(0.721664\pi\)
\(84\) −4.91741e10 + 1.70307e11i −0.0152729 + 0.0528953i
\(85\) 5.58705e12i 1.60679i
\(86\) −6.86736e12 9.71590e11i −1.83042 0.258966i
\(87\) −3.51082e11 −0.0868026
\(88\) −3.57767e12 1.60473e12i −0.821227 0.368353i
\(89\) −5.17348e12 −1.10344 −0.551719 0.834030i \(-0.686028\pi\)
−0.551719 + 0.834030i \(0.686028\pi\)
\(90\) 6.47470e12 + 9.16036e11i 1.28423 + 0.181692i
\(91\) 2.92703e12i 0.540329i
\(92\) 9.60841e12 + 2.77431e12i 1.65208 + 0.477018i
\(93\) 1.39943e11i 0.0224291i
\(94\) 7.73351e11 5.46618e12i 0.115623 0.817246i
\(95\) 2.36564e12 0.330176
\(96\) 4.02729e11 + 3.41100e11i 0.0525110 + 0.0444752i
\(97\) −3.32642e12 −0.405472 −0.202736 0.979233i \(-0.564983\pi\)
−0.202736 + 0.979233i \(0.564983\pi\)
\(98\) −4.42119e11 + 3.12498e12i −0.0504162 + 0.356350i
\(99\) 8.39143e12i 0.895792i
\(100\) 6.70904e12 + 1.93716e12i 0.670904 + 0.193716i
\(101\) 1.04951e13i 0.983783i 0.870657 + 0.491891i \(0.163694\pi\)
−0.870657 + 0.491891i \(0.836306\pi\)
\(102\) −9.55498e11 1.35183e11i −0.0840095 0.0118856i
\(103\) −1.41996e13 −1.17175 −0.585873 0.810403i \(-0.699248\pi\)
−0.585873 + 0.810403i \(0.699248\pi\)
\(104\) −7.95143e12 3.56654e12i −0.616210 0.276395i
\(105\) 9.85245e11 0.0717486
\(106\) 2.01320e13 + 2.84826e12i 1.37848 + 0.195026i
\(107\) 1.68471e12i 0.108525i −0.998527 0.0542625i \(-0.982719\pi\)
0.998527 0.0542625i \(-0.0172808\pi\)
\(108\) 6.28133e11 2.17544e12i 0.0380888 0.131915i
\(109\) 1.19613e12i 0.0683133i 0.999416 + 0.0341566i \(0.0108745\pi\)
−0.999416 + 0.0341566i \(0.989125\pi\)
\(110\) −3.05294e12 + 2.15787e13i −0.164311 + 1.16138i
\(111\) −3.55399e11 −0.0180350
\(112\) −1.41403e13 8.90838e12i −0.676927 0.426463i
\(113\) 1.04130e13 0.470506 0.235253 0.971934i \(-0.424408\pi\)
0.235253 + 0.971934i \(0.424408\pi\)
\(114\) 5.72386e10 4.04572e11i 0.00244235 0.0172629i
\(115\) 5.55858e13i 2.24093i
\(116\) 9.18216e12 3.18010e13i 0.349919 1.21189i
\(117\) 1.86501e13i 0.672160i
\(118\) −4.16017e13 5.88578e12i −1.41866 0.200711i
\(119\) 3.05584e13 0.986451
\(120\) 1.20050e12 2.67647e12i 0.0367016 0.0818246i
\(121\) 6.55596e12 0.189903
\(122\) −4.10744e12 5.81117e11i −0.112780 0.0159560i
\(123\) 3.67788e12i 0.0957666i
\(124\) −1.26760e13 3.66005e12i −0.313143 0.0904162i
\(125\) 1.67681e13i 0.393159i
\(126\) −5.01026e12 + 3.54134e13i −0.111545 + 0.788423i
\(127\) 2.30936e12 0.0488391 0.0244195 0.999702i \(-0.492226\pi\)
0.0244195 + 0.999702i \(0.492226\pi\)
\(128\) −4.14298e13 + 2.75582e13i −0.832622 + 0.553842i
\(129\) 6.65837e12 0.127214
\(130\) −6.78522e12 + 4.79591e13i −0.123291 + 0.871443i
\(131\) 2.94834e13i 0.509699i −0.966981 0.254850i \(-0.917974\pi\)
0.966981 0.254850i \(-0.0820259\pi\)
\(132\) 3.61653e12 + 1.04423e12i 0.0595060 + 0.0171817i
\(133\) 1.29389e13i 0.202704i
\(134\) 8.00196e13 + 1.13211e13i 1.19403 + 0.168931i
\(135\) −1.25852e13 −0.178933
\(136\) 3.72349e13 8.30135e13i 0.504600 1.12498i
\(137\) 7.84391e13 1.01356 0.506779 0.862076i \(-0.330836\pi\)
0.506779 + 0.862076i \(0.330836\pi\)
\(138\) −9.50628e12 1.34494e12i −0.117165 0.0165764i
\(139\) 9.83230e13i 1.15627i 0.815941 + 0.578135i \(0.196219\pi\)
−0.815941 + 0.578135i \(0.803781\pi\)
\(140\) −2.57680e13 + 8.92435e13i −0.289233 + 1.00172i
\(141\) 5.29982e12i 0.0567985i
\(142\) 1.94544e13 1.37507e14i 0.199133 1.40751i
\(143\) −6.21565e13 −0.607859
\(144\) 9.00974e13 + 5.67613e13i 0.842085 + 0.530513i
\(145\) −1.83972e14 −1.64384
\(146\) 1.01585e13 7.18022e13i 0.0868034 0.613542i
\(147\) 3.02987e12i 0.0247663i
\(148\) 9.29507e12 3.21921e13i 0.0727029 0.251795i
\(149\) 1.46382e14i 1.09591i −0.836507 0.547957i \(-0.815406\pi\)
0.836507 0.547957i \(-0.184594\pi\)
\(150\) −6.63773e12 9.39101e11i −0.0475802 0.00673161i
\(151\) 5.37629e12 0.0369090 0.0184545 0.999830i \(-0.494125\pi\)
0.0184545 + 0.999830i \(0.494125\pi\)
\(152\) 3.51492e13 + 1.57658e13i 0.231170 + 0.103689i
\(153\) −1.94708e14 −1.22713
\(154\) −1.18025e14 1.66981e13i −0.713000 0.100875i
\(155\) 7.33323e13i 0.424756i
\(156\) 8.03778e12 + 2.32081e12i 0.0446505 + 0.0128923i
\(157\) 1.49568e14i 0.797060i −0.917155 0.398530i \(-0.869521\pi\)
0.917155 0.398530i \(-0.130479\pi\)
\(158\) 7.51444e11 5.31133e12i 0.00384260 0.0271602i
\(159\) −1.95193e13 −0.0958040
\(160\) 2.11037e14 + 1.78742e14i 0.994439 + 0.842260i
\(161\) 3.04027e14 1.37576
\(162\) 3.17711e13 2.24564e14i 0.138097 0.976096i
\(163\) 3.22488e14i 1.34677i 0.739291 + 0.673386i \(0.235161\pi\)
−0.739291 + 0.673386i \(0.764839\pi\)
\(164\) −3.33142e14 9.61909e13i −1.33704 0.386055i
\(165\) 2.09220e13i 0.0807157i
\(166\) 4.09563e14 + 5.79447e13i 1.51921 + 0.214937i
\(167\) 1.29327e14 0.461351 0.230675 0.973031i \(-0.425906\pi\)
0.230675 + 0.973031i \(0.425906\pi\)
\(168\) 1.46389e13 + 6.56616e12i 0.0502342 + 0.0225321i
\(169\) 1.64731e14 0.543892
\(170\) −5.00696e14 7.08381e13i −1.59095 0.225086i
\(171\) 8.24424e13i 0.252160i
\(172\) −1.74142e14 + 6.03115e14i −0.512825 + 1.77609i
\(173\) 4.84488e13i 0.137399i −0.997637 0.0686995i \(-0.978115\pi\)
0.997637 0.0686995i \(-0.0218850\pi\)
\(174\) −4.45136e12 + 3.14630e13i −0.0121597 + 0.0859467i
\(175\) 2.12286e14 0.558693
\(176\) −1.89173e14 + 3.00275e14i −0.479762 + 0.761528i
\(177\) 4.03356e13 0.0985967
\(178\) −6.55945e13 + 4.63633e14i −0.154574 + 1.09256i
\(179\) 1.35115e14i 0.307014i −0.988148 0.153507i \(-0.950943\pi\)
0.988148 0.153507i \(-0.0490567\pi\)
\(180\) 1.64185e14 5.68630e14i 0.359801 1.24612i
\(181\) 2.37822e14i 0.502738i 0.967891 + 0.251369i \(0.0808808\pi\)
−0.967891 + 0.251369i \(0.919119\pi\)
\(182\) −2.62312e14 3.71118e13i −0.535001 0.0756916i
\(183\) 3.98243e12 0.00783820
\(184\) 3.70451e14 8.25904e14i 0.703745 1.56897i
\(185\) −1.86235e14 −0.341542
\(186\) 1.25413e13 + 1.77433e12i 0.0222079 + 0.00314196i
\(187\) 6.48919e14i 1.10974i
\(188\) −4.80058e14 1.38611e14i −0.792990 0.228966i
\(189\) 6.88347e13i 0.109851i
\(190\) 2.99939e13 2.12002e14i 0.0462525 0.326921i
\(191\) 2.46109e14 0.366784 0.183392 0.983040i \(-0.441292\pi\)
0.183392 + 0.983040i \(0.441292\pi\)
\(192\) 3.56746e13 3.17667e13i 0.0513927 0.0457629i
\(193\) −1.27091e14 −0.177008 −0.0885039 0.996076i \(-0.528209\pi\)
−0.0885039 + 0.996076i \(0.528209\pi\)
\(194\) −4.21756e13 + 2.98104e14i −0.0568002 + 0.401473i
\(195\) 4.64995e13i 0.0605652i
\(196\) 2.74446e14 + 7.92430e13i 0.345774 + 0.0998381i
\(197\) 4.31897e14i 0.526442i 0.964736 + 0.263221i \(0.0847848\pi\)
−0.964736 + 0.263221i \(0.915215\pi\)
\(198\) 7.52016e14 + 1.06395e14i 0.886959 + 0.125486i
\(199\) −1.16464e15 −1.32937 −0.664687 0.747122i \(-0.731435\pi\)
−0.664687 + 0.747122i \(0.731435\pi\)
\(200\) 2.58666e14 5.76685e14i 0.285789 0.637153i
\(201\) −7.75843e13 −0.0829850
\(202\) 9.40545e14 + 1.33068e14i 0.974082 + 0.137812i
\(203\) 1.00624e15i 1.00920i
\(204\) −2.42295e13 + 8.39150e13i −0.0235368 + 0.0815162i
\(205\) 1.92727e15i 1.81360i
\(206\) −1.80036e14 + 1.27253e15i −0.164143 + 1.16019i
\(207\) −1.93716e15 −1.71142
\(208\) −4.20439e14 + 6.67365e14i −0.359991 + 0.571415i
\(209\) 2.74762e14 0.228037
\(210\) 1.24919e13 8.82949e13i 0.0100509 0.0710412i
\(211\) 1.10642e15i 0.863146i 0.902078 + 0.431573i \(0.142041\pi\)
−0.902078 + 0.431573i \(0.857959\pi\)
\(212\) 5.10507e14 1.76806e15i 0.386205 1.33756i
\(213\) 1.33322e14i 0.0978217i
\(214\) −1.50979e14 2.13604e13i −0.107455 0.0152026i
\(215\) 3.48909e15 2.40914
\(216\) −1.86993e14 8.38739e13i −0.125278 0.0561924i
\(217\) −4.01091e14 −0.260768
\(218\) 1.07194e14 + 1.51657e13i 0.0676397 + 0.00956962i
\(219\) 6.96170e13i 0.0426411i
\(220\) 1.89512e15 + 5.47193e14i 1.12691 + 0.325381i
\(221\) 1.44223e15i 0.832694i
\(222\) −4.50610e12 + 3.18499e13i −0.00252642 + 0.0178572i
\(223\) −6.47353e14 −0.352500 −0.176250 0.984345i \(-0.556397\pi\)
−0.176250 + 0.984345i \(0.556397\pi\)
\(224\) −9.77629e14 + 1.15427e15i −0.517085 + 0.610511i
\(225\) −1.35261e15 −0.695004
\(226\) 1.32026e14 9.33183e14i 0.0659105 0.465867i
\(227\) 2.07784e15i 1.00796i −0.863715 0.503981i \(-0.831868\pi\)
0.863715 0.503981i \(-0.168132\pi\)
\(228\) −3.55309e13 1.02591e13i −0.0167506 0.00483653i
\(229\) 2.11802e15i 0.970509i −0.874373 0.485254i \(-0.838727\pi\)
0.874373 0.485254i \(-0.161273\pi\)
\(230\) −4.98144e15 7.04771e14i −2.21883 0.313919i
\(231\) 1.14433e14 0.0495534
\(232\) −2.73350e15 1.22608e15i −1.15092 0.516236i
\(233\) 3.45947e15 1.41643 0.708217 0.705995i \(-0.249500\pi\)
0.708217 + 0.705995i \(0.249500\pi\)
\(234\) 1.67137e15 + 2.36464e14i 0.665532 + 0.0941590i
\(235\) 2.77719e15i 1.07563i
\(236\) −1.05493e15 + 3.65360e15i −0.397463 + 1.37655i
\(237\) 5.14969e12i 0.00188763i
\(238\) 3.87449e14 2.73856e15i 0.138186 0.976724i
\(239\) 7.67582e14 0.266402 0.133201 0.991089i \(-0.457474\pi\)
0.133201 + 0.991089i \(0.457474\pi\)
\(240\) −2.24636e14 1.41521e14i −0.0758764 0.0478021i
\(241\) 3.34399e14 0.109940 0.0549698 0.998488i \(-0.482494\pi\)
0.0549698 + 0.998488i \(0.482494\pi\)
\(242\) 8.31229e13 5.87527e14i 0.0266024 0.188030i
\(243\) 6.58408e14i 0.205142i
\(244\) −1.04156e14 + 3.60729e14i −0.0315974 + 0.109433i
\(245\) 1.58770e15i 0.469018i
\(246\) 3.29601e14 + 4.66317e13i 0.0948223 + 0.0134154i
\(247\) 6.10663e14 0.171108
\(248\) −4.88723e14 + 1.08959e15i −0.133391 + 0.297389i
\(249\) −3.97098e14 −0.105585
\(250\) 1.50271e15 + 2.12602e14i 0.389282 + 0.0550753i
\(251\) 6.50564e15i 1.64214i 0.570825 + 0.821071i \(0.306623\pi\)
−0.570825 + 0.821071i \(0.693377\pi\)
\(252\) 3.11013e15 + 8.98012e14i 0.765023 + 0.220891i
\(253\) 6.45611e15i 1.54770i
\(254\) 2.92803e13 2.06958e14i 0.00684158 0.0483575i
\(255\) 4.85458e14 0.110571
\(256\) 1.94440e15 + 4.06223e15i 0.431743 + 0.901997i
\(257\) 1.04460e14 0.0226143 0.0113072 0.999936i \(-0.496401\pi\)
0.0113072 + 0.999936i \(0.496401\pi\)
\(258\) 8.44213e13 5.96704e14i 0.0178207 0.125960i
\(259\) 1.01861e15i 0.209682i
\(260\) 4.21193e15 + 1.21614e15i 0.845579 + 0.244151i
\(261\) 6.41142e15i 1.25542i
\(262\) −2.64222e15 3.73819e14i −0.504673 0.0714008i
\(263\) −4.31849e14 −0.0804673 −0.0402337 0.999190i \(-0.512810\pi\)
−0.0402337 + 0.999190i \(0.512810\pi\)
\(264\) 1.39435e14 3.10863e14i 0.0253481 0.0565124i
\(265\) −1.02284e16 −1.81431
\(266\) 1.15955e15 + 1.64052e14i 0.200705 + 0.0283956i
\(267\) 4.49523e14i 0.0759327i
\(268\) 2.02913e15 7.02760e15i 0.334530 1.15859i
\(269\) 6.51041e15i 1.04765i 0.851824 + 0.523827i \(0.175496\pi\)
−0.851824 + 0.523827i \(0.824504\pi\)
\(270\) −1.59567e14 + 1.12785e15i −0.0250657 + 0.177168i
\(271\) −7.50666e15 −1.15119 −0.575594 0.817735i \(-0.695229\pi\)
−0.575594 + 0.817735i \(0.695229\pi\)
\(272\) −6.96734e15 4.38941e15i −1.04320 0.657217i
\(273\) 2.54329e14 0.0371825
\(274\) 9.94527e14 7.02949e15i 0.141984 1.00356i
\(275\) 4.50796e15i 0.628518i
\(276\) −2.41060e14 + 8.34873e14i −0.0328258 + 0.113687i
\(277\) 9.31932e15i 1.23955i −0.784778 0.619777i \(-0.787223\pi\)
0.784778 0.619777i \(-0.212777\pi\)
\(278\) 8.81143e15 + 1.24663e15i 1.14487 + 0.161975i
\(279\) 2.55562e15 0.324391
\(280\) 7.67104e15 + 3.44077e15i 0.951321 + 0.426706i
\(281\) 7.70003e15 0.933042 0.466521 0.884510i \(-0.345507\pi\)
0.466521 + 0.884510i \(0.345507\pi\)
\(282\) 4.74955e14 + 6.71963e13i 0.0562385 + 0.00795658i
\(283\) 5.78501e15i 0.669410i −0.942323 0.334705i \(-0.891363\pi\)
0.942323 0.334705i \(-0.108637\pi\)
\(284\) −1.20763e16 3.48690e15i −1.36573 0.394339i
\(285\) 2.05550e14i 0.0227210i
\(286\) −7.88081e14 + 5.57029e15i −0.0851514 + 0.601865i
\(287\) −1.05412e16 −1.11342
\(288\) 6.22913e15 7.35460e15i 0.643245 0.759466i
\(289\) 5.15243e15 0.520206
\(290\) −2.33258e15 + 1.64871e16i −0.230277 + 1.62764i
\(291\) 2.89032e14i 0.0279024i
\(292\) −6.30591e15 1.82076e15i −0.595332 0.171895i
\(293\) 1.41861e16i 1.30985i 0.755693 + 0.654926i \(0.227300\pi\)
−0.755693 + 0.654926i \(0.772700\pi\)
\(294\) −2.71529e14 3.84157e13i −0.0245221 0.00346937i
\(295\) 2.11365e16 1.86720
\(296\) −2.76711e15 1.24116e15i −0.239128 0.107259i
\(297\) −1.46173e15 −0.123580
\(298\) −1.31183e16 1.85597e15i −1.08511 0.153520i
\(299\) 1.43488e16i 1.16132i
\(300\) −1.68319e14 + 5.82948e14i −0.0133305 + 0.0461680i
\(301\) 1.90836e16i 1.47903i
\(302\) 6.81658e13 4.81808e14i 0.00517037 0.0365451i
\(303\) −9.11921e14 −0.0676987
\(304\) 1.85854e15 2.95007e15i 0.135050 0.214365i
\(305\) 2.08686e15 0.148438
\(306\) −2.46870e15 + 1.74492e16i −0.171901 + 1.21503i
\(307\) 9.07714e15i 0.618799i 0.950932 + 0.309400i \(0.100128\pi\)
−0.950932 + 0.309400i \(0.899872\pi\)
\(308\) −2.99287e15 + 1.03654e16i −0.199760 + 0.691838i
\(309\) 1.23380e15i 0.0806333i
\(310\) 6.57184e15 + 9.29779e14i 0.420568 + 0.0595016i
\(311\) 1.48689e16 0.931827 0.465914 0.884830i \(-0.345726\pi\)
0.465914 + 0.884830i \(0.345726\pi\)
\(312\) 3.09896e14 6.90898e14i 0.0190200 0.0424042i
\(313\) 9.98994e15 0.600516 0.300258 0.953858i \(-0.402927\pi\)
0.300258 + 0.953858i \(0.402927\pi\)
\(314\) −1.34039e16 1.89637e15i −0.789200 0.111656i
\(315\) 1.79924e16i 1.03770i
\(316\) −4.66459e14 1.34685e14i −0.0263541 0.00760942i
\(317\) 2.22336e16i 1.23062i −0.788284 0.615311i \(-0.789030\pi\)
0.788284 0.615311i \(-0.210970\pi\)
\(318\) −2.47485e14 + 1.74927e15i −0.0134206 + 0.0948593i
\(319\) −2.13678e16 −1.13533
\(320\) 1.86941e16 1.66463e16i 0.973260 0.866646i
\(321\) 1.46384e14 0.00746811
\(322\) 3.85475e15 2.72460e16i 0.192723 1.36220i
\(323\) 6.37536e15i 0.312384i
\(324\) −1.97220e16 5.69448e15i −0.947126 0.273471i
\(325\) 1.00190e16i 0.471610i
\(326\) 2.89005e16 + 4.08881e15i 1.33349 + 0.188661i
\(327\) −1.03931e14 −0.00470095
\(328\) −1.28443e16 + 2.86357e16i −0.569546 + 1.26978i
\(329\) −1.51899e16 −0.660360
\(330\) −1.87497e15 2.65270e14i −0.0799198 0.0113070i
\(331\) 2.73268e16i 1.14211i 0.820913 + 0.571053i \(0.193465\pi\)
−0.820913 + 0.571053i \(0.806535\pi\)
\(332\) 1.03857e16 3.59692e16i 0.425635 1.47412i
\(333\) 6.49026e15i 0.260840i
\(334\) 1.63973e15 1.15899e16i 0.0646280 0.456802i
\(335\) −4.06555e16 −1.57155
\(336\) 7.74048e14 1.22865e15i 0.0293469 0.0465825i
\(337\) −1.93018e16 −0.717801 −0.358900 0.933376i \(-0.616848\pi\)
−0.358900 + 0.933376i \(0.616848\pi\)
\(338\) 2.08862e15 1.47628e16i 0.0761906 0.538529i
\(339\) 9.04782e14i 0.0323777i
\(340\) −1.26966e16 + 4.39728e16i −0.445734 + 1.54373i
\(341\) 8.51732e15i 0.293359i
\(342\) −7.38825e15 1.04528e15i −0.249673 0.0353236i
\(343\) 3.28128e16 1.08801
\(344\) 5.18416e16 + 2.32530e16i 1.68674 + 0.756571i
\(345\) 4.82984e15 0.154209
\(346\) −4.34185e15 6.14281e14i −0.136044 0.0192474i
\(347\) 7.29553e15i 0.224344i 0.993689 + 0.112172i \(0.0357808\pi\)
−0.993689 + 0.112172i \(0.964219\pi\)
\(348\) 2.76318e15 + 7.97836e14i 0.0833959 + 0.0240796i
\(349\) 5.37690e16i 1.59282i −0.604758 0.796409i \(-0.706730\pi\)
0.604758 0.796409i \(-0.293270\pi\)
\(350\) 2.69156e15 1.90244e16i 0.0782641 0.553184i
\(351\) −3.24871e15 −0.0927289
\(352\) 2.45112e16 + 2.07603e16i 0.686812 + 0.581710i
\(353\) −4.64817e16 −1.27863 −0.639317 0.768943i \(-0.720783\pi\)
−0.639317 + 0.768943i \(0.720783\pi\)
\(354\) 5.11414e14 3.61476e15i 0.0138118 0.0976245i
\(355\) 6.98630e16i 1.85252i
\(356\) 4.07178e16 + 1.17568e16i 1.06013 + 0.306100i
\(357\) 2.65522e15i 0.0678823i
\(358\) −1.21086e16 1.71311e15i −0.303986 0.0430077i
\(359\) 4.50239e16 1.11002 0.555008 0.831845i \(-0.312715\pi\)
0.555008 + 0.831845i \(0.312715\pi\)
\(360\) −4.88774e16 2.19235e16i −1.18343 0.530815i
\(361\) 3.93536e16 0.935809
\(362\) 2.13130e16 + 3.01534e15i 0.497781 + 0.0704257i
\(363\) 5.69646e14i 0.0130681i
\(364\) −6.65170e15 + 2.30372e16i −0.149890 + 0.519123i
\(365\) 3.64804e16i 0.807526i
\(366\) 5.04932e13 3.56894e14i 0.00109801 0.00776091i
\(367\) −1.88578e16 −0.402868 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(368\) −6.93182e16 4.36704e16i −1.45491 0.916593i
\(369\) 6.71650e16 1.38507
\(370\) −2.36127e15 + 1.66898e16i −0.0478447 + 0.338175i
\(371\) 5.59445e16i 1.11385i
\(372\) 3.18021e14 1.10142e15i 0.00622196 0.0215488i
\(373\) 7.72158e16i 1.48456i −0.670088 0.742282i \(-0.733744\pi\)
0.670088 0.742282i \(-0.266256\pi\)
\(374\) −5.81543e16 8.22763e15i −1.09879 0.155457i
\(375\) −1.45697e15 −0.0270551
\(376\) −1.85086e16 + 4.12640e16i −0.337794 + 0.753097i
\(377\) −4.74903e16 −0.851895
\(378\) −6.16877e15 8.72753e14i −0.108768 0.0153884i
\(379\) 2.71019e16i 0.469726i 0.972028 + 0.234863i \(0.0754642\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(380\) −1.86188e16 5.37594e15i −0.317218 0.0915928i
\(381\) 2.00660e14i 0.00336084i
\(382\) 3.12041e15 2.20556e16i 0.0513806 0.363167i
\(383\) −7.57350e16 −1.22604 −0.613020 0.790067i \(-0.710045\pi\)
−0.613020 + 0.790067i \(0.710045\pi\)
\(384\) −2.39452e15 3.59983e15i −0.0381124 0.0572966i
\(385\) 5.99648e16 0.938429
\(386\) −1.61138e15 + 1.13895e16i −0.0247960 + 0.175262i
\(387\) 1.21594e17i 1.83989i
\(388\) 2.61805e16 + 7.55931e15i 0.389558 + 0.112480i
\(389\) 4.92786e16i 0.721085i 0.932743 + 0.360542i \(0.117408\pi\)
−0.932743 + 0.360542i \(0.882592\pi\)
\(390\) −4.16716e15 5.89566e14i −0.0599680 0.00848423i
\(391\) 1.49803e17 2.12017
\(392\) 1.05812e16 2.35904e16i 0.147291 0.328379i
\(393\) 2.56181e15 0.0350748
\(394\) 3.87054e16 + 5.47602e15i 0.521251 + 0.0737462i
\(395\) 2.69852e15i 0.0357474i
\(396\) 1.90696e16 6.60446e16i 0.248498 0.860635i
\(397\) 3.19333e16i 0.409361i 0.978829 + 0.204680i \(0.0656155\pi\)
−0.978829 + 0.204680i \(0.934385\pi\)
\(398\) −1.47665e16 + 1.04372e17i −0.186224 + 1.31627i
\(399\) −1.12426e15 −0.0139490
\(400\) −4.84012e16 3.04927e16i −0.590835 0.372226i
\(401\) −4.73693e16 −0.568930 −0.284465 0.958686i \(-0.591816\pi\)
−0.284465 + 0.958686i \(0.591816\pi\)
\(402\) −9.83690e14 + 6.95289e15i −0.0116249 + 0.0821668i
\(403\) 1.89299e16i 0.220123i
\(404\) 2.38503e16 8.26019e16i 0.272907 0.945172i
\(405\) 1.14094e17i 1.28471i
\(406\) −9.01762e16 1.27581e16i −0.999247 0.141373i
\(407\) −2.16306e16 −0.235887
\(408\) 7.21303e15 + 3.23533e15i 0.0774152 + 0.0347239i
\(409\) −6.85823e16 −0.724453 −0.362227 0.932090i \(-0.617983\pi\)
−0.362227 + 0.932090i \(0.617983\pi\)
\(410\) 1.72716e17 + 2.44358e16i 1.79572 + 0.254057i
\(411\) 6.81556e15i 0.0697477i
\(412\) 1.11758e17 + 3.22687e16i 1.12576 + 0.325049i
\(413\) 1.15606e17i 1.14632i
\(414\) −2.45612e16 + 1.73603e17i −0.239744 + 1.69455i
\(415\) −2.08086e17 −1.99954
\(416\) 5.44766e16 + 4.61401e16i 0.515351 + 0.436487i
\(417\) −8.54327e15 −0.0795682
\(418\) 3.48370e15 2.46234e16i 0.0319444 0.225789i
\(419\) 8.53203e16i 0.770302i −0.922853 0.385151i \(-0.874149\pi\)
0.922853 0.385151i \(-0.125851\pi\)
\(420\) −7.75436e15 2.23898e15i −0.0689327 0.0199035i
\(421\) 8.55909e16i 0.749193i −0.927188 0.374597i \(-0.877781\pi\)
0.927188 0.374597i \(-0.122219\pi\)
\(422\) 9.91543e16 + 1.40283e16i 0.854635 + 0.120913i
\(423\) 9.67848e16 0.821476
\(424\) −1.51976e17 6.81674e16i −1.27027 0.569769i
\(425\) 1.04599e17 0.860994
\(426\) 1.19480e16 + 1.69039e15i 0.0968571 + 0.0137033i
\(427\) 1.14141e16i 0.0911297i
\(428\) −3.82851e15 + 1.32595e16i −0.0301055 + 0.104266i
\(429\) 5.40077e15i 0.0418296i
\(430\) 4.42381e16 3.12683e17i 0.337483 2.38539i
\(431\) −2.15111e17 −1.61644 −0.808220 0.588880i \(-0.799569\pi\)
−0.808220 + 0.588880i \(0.799569\pi\)
\(432\) −9.88742e15 + 1.56943e16i −0.0731878 + 0.116171i
\(433\) −6.08494e16 −0.443696 −0.221848 0.975081i \(-0.571209\pi\)
−0.221848 + 0.975081i \(0.571209\pi\)
\(434\) −5.08543e15 + 3.59447e16i −0.0365295 + 0.258197i
\(435\) 1.59853e16i 0.113121i
\(436\) 2.71821e15 9.41411e15i 0.0189505 0.0656322i
\(437\) 6.34287e16i 0.435669i
\(438\) 6.23888e15 + 8.82672e14i 0.0422206 + 0.00597335i
\(439\) 2.01095e17 1.34086 0.670428 0.741975i \(-0.266111\pi\)
0.670428 + 0.741975i \(0.266111\pi\)
\(440\) 7.30660e16 1.62897e17i 0.480035 1.07022i
\(441\) −5.53312e16 −0.358195
\(442\) −1.29249e17 1.82860e16i −0.824483 0.116647i
\(443\) 7.60262e16i 0.477902i −0.971032 0.238951i \(-0.923196\pi\)
0.971032 0.238951i \(-0.0768036\pi\)
\(444\) 2.79716e15 + 8.07647e14i 0.0173272 + 0.00500302i
\(445\) 2.35557e17i 1.43799i
\(446\) −8.20777e15 + 5.80139e16i −0.0493797 + 0.349024i
\(447\) 1.27191e16 0.0754149
\(448\) 9.10468e16 + 1.02247e17i 0.532056 + 0.597509i
\(449\) 8.77575e16 0.505455 0.252728 0.967537i \(-0.418672\pi\)
0.252728 + 0.967537i \(0.418672\pi\)
\(450\) −1.71498e16 + 1.21217e17i −0.0973591 + 0.688151i
\(451\) 2.23846e17i 1.25257i
\(452\) −8.19553e16 2.36636e16i −0.452040 0.130521i
\(453\) 4.67145e14i 0.00253988i
\(454\) −1.86210e17 2.63449e16i −0.998023 0.141200i
\(455\) 1.33273e17 0.704153
\(456\) −1.36989e15 + 3.05410e15i −0.00713533 + 0.0159079i
\(457\) −8.19691e16 −0.420916 −0.210458 0.977603i \(-0.567495\pi\)
−0.210458 + 0.977603i \(0.567495\pi\)
\(458\) −1.89811e17 2.68543e16i −0.960939 0.135953i
\(459\) 3.39168e16i 0.169290i
\(460\) −1.26319e17 + 4.37487e17i −0.621646 + 2.15298i
\(461\) 1.34599e17i 0.653110i −0.945178 0.326555i \(-0.894112\pi\)
0.945178 0.326555i \(-0.105888\pi\)
\(462\) 1.45089e15 1.02552e16i 0.00694165 0.0490648i
\(463\) 1.44197e17 0.680269 0.340135 0.940377i \(-0.389527\pi\)
0.340135 + 0.940377i \(0.389527\pi\)
\(464\) −1.44536e17 + 2.29423e17i −0.672372 + 1.06726i
\(465\) −6.37183e15 −0.0292294
\(466\) 4.38626e16 3.10028e17i 0.198420 1.40247i
\(467\) 3.32854e17i 1.48489i 0.669908 + 0.742444i \(0.266333\pi\)
−0.669908 + 0.742444i \(0.733667\pi\)
\(468\) 4.23825e16 1.46785e17i 0.186461 0.645779i
\(469\) 2.22365e17i 0.964813i
\(470\) 2.48884e17 + 3.52120e16i 1.06503 + 0.150679i
\(471\) 1.29959e16 0.0548494
\(472\) 3.14050e17 + 1.40864e17i 1.30730 + 0.586378i
\(473\) 4.05247e17 1.66388
\(474\) 4.61501e14 + 6.52928e13i 0.00186902 + 0.000264427i
\(475\) 4.42889e16i 0.176924i
\(476\) −2.40510e17 6.94443e16i −0.947736 0.273647i
\(477\) 3.56460e17i 1.38561i
\(478\) 9.73215e15 6.87885e16i 0.0373188 0.263776i
\(479\) 1.65749e17 0.627004 0.313502 0.949588i \(-0.398498\pi\)
0.313502 + 0.949588i \(0.398498\pi\)
\(480\) −1.55308e16 + 1.83369e16i −0.0579598 + 0.0684320i
\(481\) −4.80743e16 −0.176999
\(482\) 4.23984e15 2.99679e16i 0.0154008 0.108856i
\(483\) 2.64168e16i 0.0946726i
\(484\) −5.15986e16 1.48985e16i −0.182450 0.0526802i
\(485\) 1.51457e17i 0.528408i
\(486\) 5.90047e16 + 8.34794e15i 0.203119 + 0.0287372i
\(487\) −4.13371e17 −1.40411 −0.702056 0.712122i \(-0.747734\pi\)
−0.702056 + 0.712122i \(0.747734\pi\)
\(488\) 3.10069e16 + 1.39079e16i 0.103927 + 0.0466156i
\(489\) −2.80209e16 −0.0926776
\(490\) −1.42285e17 2.01304e16i −0.464393 0.0657020i
\(491\) 2.41125e17i 0.776626i −0.921527 0.388313i \(-0.873058\pi\)
0.921527 0.388313i \(-0.126942\pi\)
\(492\) 8.35801e15 2.89467e16i 0.0265662 0.0920080i
\(493\) 4.95802e17i 1.55526i
\(494\) 7.74258e15 5.47259e16i 0.0239696 0.169421i
\(495\) −3.82076e17 −1.16739
\(496\) 9.14491e16 + 5.76128e16i 0.275771 + 0.173735i
\(497\) −3.82116e17 −1.13731
\(498\) −5.03480e15 + 3.55869e16i −0.0147908 + 0.104544i
\(499\) 2.61865e17i 0.759319i 0.925126 + 0.379660i \(0.123959\pi\)
−0.925126 + 0.379660i \(0.876041\pi\)
\(500\) 3.81056e16 1.31973e17i 0.109065 0.377728i
\(501\) 1.12372e16i 0.0317477i
\(502\) 5.83017e17 + 8.24849e16i 1.62595 + 0.230038i
\(503\) 4.41721e17 1.21606 0.608031 0.793913i \(-0.291960\pi\)
0.608031 + 0.793913i \(0.291960\pi\)
\(504\) 1.19911e17 2.67335e17i 0.325881 0.726536i
\(505\) −4.77861e17 −1.28206
\(506\) −5.78579e17 8.18569e16i −1.53244 0.216809i
\(507\) 1.43135e16i 0.0374277i
\(508\) −1.81758e16 5.24804e15i −0.0469223 0.0135482i
\(509\) 6.01276e17i 1.53253i 0.642527 + 0.766263i \(0.277886\pi\)
−0.642527 + 0.766263i \(0.722114\pi\)
\(510\) 6.15511e15 4.35054e16i 0.0154892 0.109481i
\(511\) −1.99530e17 −0.495761
\(512\) 3.88699e17 1.22747e17i 0.953583 0.301131i
\(513\) 1.43609e16 0.0347871
\(514\) 1.32444e15 9.36139e15i 0.00316791 0.0223913i
\(515\) 6.46531e17i 1.52701i
\(516\) −5.24046e16 1.51312e16i −0.122221 0.0352899i
\(517\) 3.22562e17i 0.742890i
\(518\) −9.12852e16 1.29150e16i −0.207614 0.0293731i
\(519\) 4.20971e15 0.00945506
\(520\) 1.62390e17 3.62042e17i 0.360196 0.803040i
\(521\) −1.78457e16 −0.0390921 −0.0195460 0.999809i \(-0.506222\pi\)
−0.0195460 + 0.999809i \(0.506222\pi\)
\(522\) 5.74573e17 + 8.12902e16i 1.24305 + 0.175865i
\(523\) 3.35491e17i 0.716836i 0.933561 + 0.358418i \(0.116684\pi\)
−0.933561 + 0.358418i \(0.883316\pi\)
\(524\) −6.70012e16 + 2.32049e17i −0.141394 + 0.489695i
\(525\) 1.84455e16i 0.0384463i
\(526\) −5.47540e15 + 3.87011e16i −0.0112722 + 0.0796739i
\(527\) −1.97629e17 −0.401867
\(528\) −2.60908e16 1.64372e16i −0.0524043 0.0330146i
\(529\) 9.86354e17 1.95691
\(530\) −1.29686e17 + 9.16644e17i −0.254156 + 1.79642i
\(531\) 7.36605e17i 1.42600i
\(532\) 2.94037e16 1.01835e17i 0.0562312 0.194748i
\(533\) 4.97501e17i 0.939869i
\(534\) −4.02850e16 5.69949e15i −0.0751840 0.0106370i
\(535\) 7.67075e16 0.141429
\(536\) −6.04066e17 2.70948e17i −1.10031 0.493531i
\(537\) 1.17401e16 0.0211270
\(538\) 5.83444e17 + 8.25453e16i 1.03732 + 0.146760i
\(539\) 1.84406e17i 0.323929i
\(540\) 9.90515e16 + 2.85999e16i 0.171910 + 0.0496370i
\(541\) 2.18609e17i 0.374874i 0.982277 + 0.187437i \(0.0600181\pi\)
−0.982277 + 0.187437i \(0.939982\pi\)
\(542\) −9.51768e16 + 6.72726e17i −0.161263 + 1.13984i
\(543\) −2.06643e16 −0.0345958
\(544\) −4.81706e17 + 5.68740e17i −0.796873 + 0.940851i
\(545\) −5.44617e16 −0.0890254
\(546\) 3.22463e15 2.27923e16i 0.00520869 0.0368159i
\(547\) 5.87423e17i 0.937633i 0.883296 + 0.468817i \(0.155319\pi\)
−0.883296 + 0.468817i \(0.844681\pi\)
\(548\) −6.17354e17 1.78254e17i −0.973779 0.281167i
\(549\) 7.27268e16i 0.113364i
\(550\) −4.03991e17 5.71563e16i −0.622320 0.0880454i
\(551\) 2.09930e17 0.319587
\(552\) 7.17626e16 + 3.21884e16i 0.107968 + 0.0484279i
\(553\) −1.47596e16 −0.0219462
\(554\) −8.35171e17 1.18159e17i −1.22733 0.173642i
\(555\) 1.61819e16i 0.0235031i
\(556\) 2.23440e17 7.73850e17i 0.320756 1.11089i
\(557\) 6.63373e17i 0.941237i −0.882337 0.470619i \(-0.844031\pi\)
0.882337 0.470619i \(-0.155969\pi\)
\(558\) 3.24027e16 2.29028e17i 0.0454421 0.321193i
\(559\) 9.00667e17 1.24850
\(560\) 4.05613e17 6.43832e17i 0.555764 0.882166i
\(561\) 5.63844e16 0.0763661
\(562\) 9.76285e16 6.90055e17i 0.130705 0.923842i
\(563\) 1.15064e18i 1.52277i −0.648298 0.761387i \(-0.724519\pi\)
0.648298 0.761387i \(-0.275481\pi\)
\(564\) 1.20439e16 4.17122e16i 0.0157562 0.0545693i
\(565\) 4.74121e17i 0.613160i
\(566\) −5.18436e17 7.33480e16i −0.662809 0.0937737i
\(567\) −6.24037e17 −0.788715
\(568\) −4.65602e17 + 1.03804e18i −0.581769 + 1.29703i
\(569\) 8.26006e17 1.02036 0.510180 0.860068i \(-0.329579\pi\)
0.510180 + 0.860068i \(0.329579\pi\)
\(570\) 1.84208e16 + 2.60617e15i 0.0224969 + 0.00318285i
\(571\) 3.74515e17i 0.452204i −0.974104 0.226102i \(-0.927402\pi\)
0.974104 0.226102i \(-0.0725983\pi\)
\(572\) 4.89202e17 + 1.41251e17i 0.584002 + 0.168624i
\(573\) 2.13843e16i 0.0252401i
\(574\) −1.33652e17 + 9.44672e17i −0.155972 + 1.10244i
\(575\) 1.04066e18 1.20079
\(576\) −5.80120e17 6.51486e17i −0.661868 0.743291i
\(577\) −1.13319e18 −1.27838 −0.639189 0.769050i \(-0.720730\pi\)
−0.639189 + 0.769050i \(0.720730\pi\)
\(578\) 6.53275e16 4.61746e17i 0.0728727 0.515077i
\(579\) 1.10429e16i 0.0121807i
\(580\) 1.44795e18 + 4.18079e17i 1.57933 + 0.456012i
\(581\) 1.13813e18i 1.22757i
\(582\) −2.59022e16 3.66463e15i −0.0276272 0.00390868i
\(583\) −1.18800e18 −1.25306
\(584\) −2.43124e17 + 5.42033e17i −0.253597 + 0.565382i
\(585\) −8.49169e17 −0.875954
\(586\) 1.27132e18 + 1.79865e17i 1.29694 + 0.183490i
\(587\) 1.80779e18i 1.82390i 0.410301 + 0.911950i \(0.365424\pi\)
−0.410301 + 0.911950i \(0.634576\pi\)
\(588\) −6.88541e15 + 2.38466e16i −0.00687032 + 0.0237943i
\(589\) 8.36792e16i 0.0825787i
\(590\) 2.67989e17 1.89419e18i 0.261565 1.84879i
\(591\) −3.75275e16 −0.0362269
\(592\) −1.46314e17 + 2.32244e17i −0.139699 + 0.221745i
\(593\) 4.84457e17 0.457509 0.228755 0.973484i \(-0.426535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(594\) −1.85332e16 + 1.30996e17i −0.0173117 + 0.122362i
\(595\) 1.39138e18i 1.28554i
\(596\) −3.32654e17 + 1.15210e18i −0.304013 + 1.05290i
\(597\) 1.01195e17i 0.0914803i
\(598\) −1.28590e18 1.81928e17i −1.14987 0.162683i
\(599\) −1.07468e18 −0.950620 −0.475310 0.879818i \(-0.657664\pi\)
−0.475310 + 0.879818i \(0.657664\pi\)
\(600\) 5.01080e16 + 2.24755e16i 0.0438454 + 0.0196664i
\(601\) 3.25263e17 0.281547 0.140774 0.990042i \(-0.455041\pi\)
0.140774 + 0.990042i \(0.455041\pi\)
\(602\) 1.71022e18 + 2.41960e17i 1.46445 + 0.207189i
\(603\) 1.41684e18i 1.20021i
\(604\) −4.23140e16 1.22177e16i −0.0354604 0.0102388i
\(605\) 2.98504e17i 0.247480i
\(606\) −1.15622e16 + 8.17238e16i −0.00948351 + 0.0670311i
\(607\) −4.02710e16 −0.0326788 −0.0163394 0.999867i \(-0.505201\pi\)
−0.0163394 + 0.999867i \(0.505201\pi\)
\(608\) −2.40813e17 2.03961e17i −0.193333 0.163748i
\(609\) 8.74318e16 0.0694476
\(610\) 2.64592e16 1.87018e17i 0.0207938 0.146974i
\(611\) 7.16899e17i 0.557430i
\(612\) 1.53245e18 + 4.42476e17i 1.17897 + 0.340412i
\(613\) 8.13502e17i 0.619250i −0.950859 0.309625i \(-0.899797\pi\)
0.950859 0.309625i \(-0.100203\pi\)
\(614\) 8.13468e17 + 1.15089e17i 0.612698 + 0.0866840i
\(615\) −1.67460e17 −0.124802
\(616\) 8.90968e17 + 3.99635e17i 0.657033 + 0.294706i
\(617\) −4.37374e17 −0.319153 −0.159577 0.987186i \(-0.551013\pi\)
−0.159577 + 0.987186i \(0.551013\pi\)
\(618\) −1.10570e17 1.56433e16i −0.0798382 0.0112955i
\(619\) 2.59586e18i 1.85478i −0.374099 0.927389i \(-0.622048\pi\)
0.374099 0.927389i \(-0.377952\pi\)
\(620\) 1.66648e17 5.77161e17i 0.117830 0.408085i
\(621\) 3.37439e17i 0.236102i
\(622\) 1.88522e17 1.33251e18i 0.130534 0.922639i
\(623\) 1.28838e18 0.882820
\(624\) −5.79872e16 3.65319e16i −0.0393217 0.0247726i
\(625\) −1.80404e18 −1.21067
\(626\) 1.26662e17 8.95270e17i 0.0841228 0.594595i
\(627\) 2.38740e16i 0.0156923i
\(628\) −3.39895e17 + 1.17717e18i −0.221109 + 0.765777i
\(629\) 5.01899e17i 0.323137i
\(630\) −1.61243e18 2.28126e17i −1.02747 0.145365i
\(631\) 2.52029e16 0.0158950 0.00794748 0.999968i \(-0.497470\pi\)
0.00794748 + 0.999968i \(0.497470\pi\)
\(632\) −1.79843e16 + 4.00951e16i −0.0112262 + 0.0250283i
\(633\) −9.61366e16 −0.0593970
\(634\) −1.99251e18 2.81899e17i −1.21849 0.172391i
\(635\) 1.05149e17i 0.0636467i
\(636\) 1.53627e17 + 4.43578e16i 0.0920439 + 0.0265766i
\(637\) 4.09846e17i 0.243061i
\(638\) −2.70922e17 + 1.91492e18i −0.159041 + 1.12413i
\(639\) 2.43472e18 1.41479
\(640\) −1.25477e18 1.88637e18i −0.721762 1.08507i
\(641\) 5.97617e17 0.340287 0.170144 0.985419i \(-0.445577\pi\)
0.170144 + 0.985419i \(0.445577\pi\)
\(642\) 1.85600e15 1.31185e16i 0.00104616 0.00739447i
\(643\) 2.19754e17i 0.122621i 0.998119 + 0.0613106i \(0.0195280\pi\)
−0.998119 + 0.0613106i \(0.980472\pi\)
\(644\) −2.39284e18 6.90903e17i −1.32177 0.381645i
\(645\) 3.03167e17i 0.165784i
\(646\) 5.71342e17 + 8.08331e16i 0.309304 + 0.0437600i
\(647\) −3.20518e18 −1.71781 −0.858905 0.512135i \(-0.828855\pi\)
−0.858905 + 0.512135i \(0.828855\pi\)
\(648\) −7.60378e17 + 1.69523e18i −0.403452 + 0.899478i
\(649\) 2.45494e18 1.28959
\(650\) −8.97876e17 1.27031e17i −0.466960 0.0660651i
\(651\) 3.48508e16i 0.0179447i
\(652\) 7.32856e17 2.53814e18i 0.373602 1.29391i
\(653\) 2.61177e17i 0.131826i 0.997825 + 0.0659128i \(0.0209959\pi\)
−0.997825 + 0.0659128i \(0.979004\pi\)
\(654\) −1.31774e15 + 9.31403e15i −0.000658530 + 0.00465460i
\(655\) 1.34243e18 0.664236
\(656\) 2.40340e18 + 1.51414e18i 1.17747 + 0.741806i
\(657\) 1.27134e18 0.616717
\(658\) −1.92592e17 + 1.36127e18i −0.0925060 + 0.653848i
\(659\) 2.06165e17i 0.0980529i 0.998797 + 0.0490265i \(0.0156119\pi\)
−0.998797 + 0.0490265i \(0.984388\pi\)
\(660\) −4.75455e16 + 1.64666e17i −0.0223910 + 0.0775478i
\(661\) 1.46618e18i 0.683718i 0.939751 + 0.341859i \(0.111057\pi\)
−0.939751 + 0.341859i \(0.888943\pi\)
\(662\) 2.44895e18 + 3.46475e17i 1.13084 + 0.159991i
\(663\) 1.25315e17 0.0573015
\(664\) −3.09178e18 1.38679e18i −1.39996 0.627939i
\(665\) −5.89129e17 −0.264162
\(666\) 5.81639e17 + 8.22899e16i 0.258268 + 0.0365396i
\(667\) 4.93275e18i 2.16906i
\(668\) −1.01786e18 2.93896e17i −0.443244 0.127981i
\(669\) 5.62484e16i 0.0242572i
\(670\) −5.15470e17 + 3.64343e18i −0.220149 + 1.55605i
\(671\) 2.42382e17 0.102519
\(672\) −1.00294e17 8.49460e16i −0.0420121 0.0355830i
\(673\) 2.71250e18 1.12531 0.562655 0.826692i \(-0.309780\pi\)
0.562655 + 0.826692i \(0.309780\pi\)
\(674\) −2.44727e17 + 1.72977e18i −0.100553 + 0.710723i
\(675\) 2.35616e17i 0.0958805i
\(676\) −1.29652e18 3.74353e17i −0.522546 0.150879i
\(677\) 3.72209e18i 1.48580i 0.669402 + 0.742901i \(0.266550\pi\)
−0.669402 + 0.742901i \(0.733450\pi\)
\(678\) 8.10841e16 + 1.14717e16i 0.0320585 + 0.00453561i
\(679\) 8.28396e17 0.324403
\(680\) 3.77974e18 + 1.69537e18i 1.46607 + 0.657591i
\(681\) 1.80543e17 0.0693626
\(682\) 7.63298e17 + 1.07991e17i 0.290466 + 0.0410950i
\(683\) 8.34945e17i 0.314719i 0.987541 + 0.157360i \(0.0502982\pi\)
−0.987541 + 0.157360i \(0.949702\pi\)
\(684\) −1.87351e17 + 6.48861e17i −0.0699506 + 0.242263i
\(685\) 3.57146e18i 1.32086i
\(686\) 4.16032e17 2.94059e18i 0.152412 1.07728i
\(687\) 1.84034e17 0.0667852
\(688\) 2.74117e18 4.35107e18i 0.985397 1.56412i
\(689\) −2.64035e18 −0.940235
\(690\) 6.12374e16 4.32837e17i 0.0216022 0.152688i
\(691\) 9.77059e17i 0.341439i 0.985320 + 0.170720i \(0.0546092\pi\)
−0.985320 + 0.170720i \(0.945391\pi\)
\(692\) −1.10100e17 + 3.81316e17i −0.0381153 + 0.132006i
\(693\) 2.08976e18i 0.716690i
\(694\) 6.53805e17 + 9.24999e16i 0.222132 + 0.0314271i
\(695\) −4.47681e18 −1.50684
\(696\) 1.06534e17 2.37513e17i 0.0355246 0.0792004i
\(697\) −5.19395e18 −1.71587
\(698\) −4.81862e18 6.81735e17i −1.57711 0.223129i
\(699\) 3.00593e17i 0.0974714i
\(700\) −1.67079e18 4.82421e17i −0.536766 0.154985i
\(701\) 1.70397e18i 0.542370i −0.962527 0.271185i \(-0.912584\pi\)
0.962527 0.271185i \(-0.0874156\pi\)
\(702\) −4.11904e16 + 2.91141e17i −0.0129899 + 0.0918146i
\(703\) 2.12512e17 0.0664008
\(704\) 2.17126e18 1.93341e18i 0.672185 0.598552i
\(705\) −2.41310e17 −0.0740194
\(706\) −5.89340e17 + 4.16556e18i −0.179116 + 1.26603i
\(707\) 2.61366e18i 0.787088i
\(708\) −3.17461e17 9.16630e16i −0.0947270 0.0273513i
\(709\) 5.77024e17i 0.170605i 0.996355 + 0.0853027i \(0.0271857\pi\)
−0.996355 + 0.0853027i \(0.972814\pi\)
\(710\) 6.26093e18 + 8.85792e17i 1.83425 + 0.259509i
\(711\) 9.40431e16 0.0273008
\(712\) 1.56987e18 3.49995e18i 0.451590 1.00680i
\(713\) −1.96622e18 −0.560467
\(714\) 2.37953e17 + 3.36654e16i 0.0672129 + 0.00950923i
\(715\) 2.83009e18i 0.792157i
\(716\) −3.07049e17 + 1.06342e18i −0.0851673 + 0.294964i
\(717\) 6.66950e16i 0.0183324i
\(718\) 5.70857e17 4.03491e18i 0.155496 1.09907i
\(719\) 2.65402e18 0.716417 0.358209 0.933642i \(-0.383388\pi\)
0.358209 + 0.933642i \(0.383388\pi\)
\(720\) −2.58444e18 + 4.10229e18i −0.691360 + 1.09740i
\(721\) 3.53620e18 0.937471
\(722\) 4.98963e17 3.52676e18i 0.131092 0.926582i
\(723\) 2.90559e16i 0.00756546i
\(724\) 5.40454e17 1.87178e18i 0.139463 0.483007i
\(725\) 3.44428e18i 0.880848i
\(726\) 5.10501e16 + 7.22253e15i 0.0129392 + 0.00183063i
\(727\) −6.78102e18 −1.70342 −0.851710 0.524014i \(-0.824434\pi\)
−0.851710 + 0.524014i \(0.824434\pi\)
\(728\) 1.98019e18 + 8.88195e17i 0.493007 + 0.221133i
\(729\) 3.93786e18 0.971699
\(730\) 3.26927e18 + 4.62534e17i 0.799563 + 0.113122i
\(731\) 9.40303e18i 2.27932i
\(732\) −3.13437e16 9.05011e15i −0.00753057 0.00217436i
\(733\) 3.94118e17i 0.0938535i −0.998898 0.0469267i \(-0.985057\pi\)
0.998898 0.0469267i \(-0.0149427\pi\)
\(734\) −2.39098e17 + 1.68999e18i −0.0564354 + 0.398895i
\(735\) 1.37955e17 0.0322753
\(736\) −4.79250e18 + 5.65841e18i −1.11137 + 1.31217i
\(737\) −4.72200e18 −1.08539
\(738\) 8.51584e17 6.01914e18i 0.194026 1.37141i
\(739\) 2.42319e18i 0.547266i −0.961834 0.273633i \(-0.911775\pi\)
0.961834 0.273633i \(-0.0882253\pi\)
\(740\) 1.46576e18 + 4.23220e17i 0.328138 + 0.0947459i
\(741\) 5.30604e16i 0.0117748i
\(742\) −5.01359e18 7.09319e17i −1.10287 0.156033i
\(743\) 2.76079e18 0.602013 0.301006 0.953622i \(-0.402677\pi\)
0.301006 + 0.953622i \(0.402677\pi\)
\(744\) −9.46739e16 4.24651e16i −0.0204647 0.00917926i
\(745\) 6.66501e18 1.42819
\(746\) −6.91986e18 9.79017e17i −1.46992 0.207964i
\(747\) 7.25177e18i 1.52707i
\(748\) −1.47467e18 + 5.10731e18i −0.307847 + 1.06618i
\(749\) 4.19552e17i 0.0868269i
\(750\) −1.84729e16 + 1.30570e17i −0.00378999 + 0.0267883i
\(751\) 7.34720e18 1.49438 0.747192 0.664608i \(-0.231402\pi\)
0.747192 + 0.664608i \(0.231402\pi\)
\(752\) 3.46330e18 + 2.18187e18i 0.698351 + 0.439960i
\(753\) −5.65274e17 −0.113003
\(754\) −6.02128e17 + 4.25595e18i −0.119337 + 0.843495i
\(755\) 2.44791e17i 0.0480995i
\(756\) −1.56427e17 + 5.41762e17i −0.0304734 + 0.105540i
\(757\) 1.26012e18i 0.243382i −0.992568 0.121691i \(-0.961168\pi\)
0.992568 0.121691i \(-0.0388317\pi\)
\(758\) 2.42880e18 + 3.43624e17i 0.465095 + 0.0658012i
\(759\) 5.60970e17 0.106505
\(760\) −7.17844e17 + 1.60040e18i −0.135127 + 0.301259i
\(761\) −3.58935e18 −0.669908 −0.334954 0.942235i \(-0.608721\pi\)
−0.334954 + 0.942235i \(0.608721\pi\)
\(762\) 1.79826e16 + 2.54416e15i 0.00332770 + 0.000470801i
\(763\) 2.97878e17i 0.0546550i
\(764\) −1.93700e18 5.59284e17i −0.352389 0.101748i
\(765\) 8.86539e18i 1.59918i
\(766\) −9.60242e17 + 6.78716e18i −0.171749 + 1.21395i
\(767\) 5.45614e18 0.967644
\(768\) −3.52967e17 + 1.68948e17i −0.0620706 + 0.0297103i
\(769\) −4.46415e17 −0.0778426 −0.0389213 0.999242i