Properties

Label 5.18.b.a.4.5
Level 5
Weight 18
Character 5.4
Analytic conductor 9.161
Analytic rank 0
Dimension 8
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.16110436723\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.5
Root \(98.5951i\)
Character \(\chi\) = 5.4
Dual form 5.18.b.a.4.4

$q$-expansion

\(f(q)\) \(=\) \(q+197.190i q^{2} +12817.1i q^{3} +92188.0 q^{4} +(620811. + 614437. i) q^{5} -2.52741e6 q^{6} -4.49140e6i q^{7} +4.40247e7i q^{8} -3.51381e7 q^{9} +O(q^{10})\) \(q+197.190i q^{2} +12817.1i q^{3} +92188.0 q^{4} +(620811. + 614437. i) q^{5} -2.52741e6 q^{6} -4.49140e6i q^{7} +4.40247e7i q^{8} -3.51381e7 q^{9} +(-1.21161e8 + 1.22418e8i) q^{10} -1.08959e9 q^{11} +1.18158e9i q^{12} +2.20399e9i q^{13} +8.85659e8 q^{14} +(-7.87531e9 + 7.95700e9i) q^{15} +3.40203e9 q^{16} -4.96836e10i q^{17} -6.92889e9i q^{18} +6.53775e10 q^{19} +(5.72314e10 + 5.66438e10i) q^{20} +5.75667e10 q^{21} -2.14857e11i q^{22} -6.03064e10i q^{23} -5.64269e11 q^{24} +(7.87347e9 + 7.62899e11i) q^{25} -4.34604e11 q^{26} +1.20483e12i q^{27} -4.14053e11i q^{28} -2.63186e10 q^{29} +(-1.56904e12 - 1.55293e12i) q^{30} +3.03326e12 q^{31} +6.44125e12i q^{32} -1.39654e13i q^{33} +9.79712e12 q^{34} +(2.75968e12 - 2.78831e12i) q^{35} -3.23931e12 q^{36} -8.44655e12i q^{37} +1.28918e13i q^{38} -2.82487e13 q^{39} +(-2.70504e13 + 2.73310e13i) q^{40} +5.70631e13 q^{41} +1.13516e13i q^{42} +6.40476e13i q^{43} -1.00447e14 q^{44} +(-2.18141e13 - 2.15901e13i) q^{45} +1.18918e13 q^{46} -2.44975e14i q^{47} +4.36042e13i q^{48} +2.12458e14 q^{49} +(-1.50436e14 + 1.55257e12i) q^{50} +6.36800e14 q^{51} +2.03181e14i q^{52} -1.01305e14i q^{53} -2.37582e14 q^{54} +(-6.76432e14 - 6.69487e14i) q^{55} +1.97732e14 q^{56} +8.37950e14i q^{57} -5.18977e12i q^{58} -1.41965e15 q^{59} +(-7.26009e14 + 7.33540e14i) q^{60} +2.31838e15 q^{61} +5.98128e14i q^{62} +1.57819e14i q^{63} -8.24240e14 q^{64} +(-1.35421e15 + 1.36826e15i) q^{65} +2.75385e15 q^{66} -4.06306e15i q^{67} -4.58023e15i q^{68} +7.72954e14 q^{69} +(5.49827e14 + 5.44182e14i) q^{70} +2.68034e15 q^{71} -1.54694e15i q^{72} +6.95024e15i q^{73} +1.66558e15 q^{74} +(-9.77816e15 + 1.00915e14i) q^{75} +6.02702e15 q^{76} +4.89380e15i q^{77} -5.57037e15i q^{78} -8.28477e15 q^{79} +(2.11202e15 + 2.09034e15i) q^{80} -1.99802e16 q^{81} +1.12523e16i q^{82} +2.66711e16i q^{83} +5.30696e15 q^{84} +(3.05275e16 - 3.08441e16i) q^{85} -1.26296e16 q^{86} -3.37328e14i q^{87} -4.79690e16i q^{88} +6.55891e15 q^{89} +(4.25736e15 - 4.30153e15i) q^{90} +9.89897e15 q^{91} -5.55953e15i q^{92} +3.88776e16i q^{93} +4.83067e16 q^{94} +(4.05871e16 + 4.01704e16i) q^{95} -8.25582e16 q^{96} -1.11864e17i q^{97} +4.18946e16i q^{98} +3.82862e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + O(q^{10}) \) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + 329570200q^{10} + 463296576q^{11} - 29937907992q^{14} + 30646226400q^{15} + 30848001568q^{16} - 20615713280q^{19} - 47558579400q^{20} - 75039699024q^{21} + 1768741136160q^{24} - 1789249435000q^{25} - 838901194224q^{26} - 4079017824720q^{29} + 2416984007400q^{30} + 11329328658496q^{31} - 36406243632832q^{34} + 4019663899200q^{35} + 59729752432728q^{36} + 40318460422272q^{39} - 209747532172000q^{40} + 97217252847456q^{41} - 116357853210912q^{44} - 366841998003600q^{45} + 1081224261700136q^{46} - 856574357621656q^{49} - 1283266301910000q^{50} + 2468309514424896q^{51} - 3408409774777680q^{54} - 2042713226757600q^{55} + 8363016326678880q^{56} - 1091409512240640q^{59} - 11479379108104800q^{60} + 8064731010774976q^{61} - 3616160324265856q^{64} - 11989509557901600q^{65} + 27318846906958752q^{66} - 12078989597365008q^{69} - 13190931213697800q^{70} + 25241492058140736q^{71} - 29902523510328912q^{74} + 3839235716880000q^{75} + 20767634734678560q^{76} + 3229852337730880q^{79} + 1263407265391200q^{80} - 49353541005202632q^{81} + 101439947332382688q^{84} + 25693702369787200q^{85} - 165112838769552744q^{86} + 92963987535626640q^{89} + 206315814421823400q^{90} - 225591670236809664q^{91} + 162612564681867848q^{94} + 204319715505252000q^{95} - 654303222993538944q^{96} - 56327331239952768q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 197.190i 0.544666i 0.962203 + 0.272333i \(0.0877952\pi\)
−0.962203 + 0.272333i \(0.912205\pi\)
\(3\) 12817.1i 1.12787i 0.825819 + 0.563935i \(0.190713\pi\)
−0.825819 + 0.563935i \(0.809287\pi\)
\(4\) 92188.0 0.703339
\(5\) 620811. + 614437.i 0.710746 + 0.703449i
\(6\) −2.52741e6 −0.614313
\(7\) 4.49140e6i 0.294475i −0.989101 0.147237i \(-0.952962\pi\)
0.989101 0.147237i \(-0.0470381\pi\)
\(8\) 4.40247e7i 0.927751i
\(9\) −3.51381e7 −0.272093
\(10\) −1.21161e8 + 1.22418e8i −0.383145 + 0.387119i
\(11\) −1.08959e9 −1.53259 −0.766296 0.642487i \(-0.777903\pi\)
−0.766296 + 0.642487i \(0.777903\pi\)
\(12\) 1.18158e9i 0.793275i
\(13\) 2.20399e9i 0.749359i 0.927154 + 0.374680i \(0.122247\pi\)
−0.927154 + 0.374680i \(0.877753\pi\)
\(14\) 8.85659e8 0.160390
\(15\) −7.87531e9 + 7.95700e9i −0.793399 + 0.801630i
\(16\) 3.40203e9 0.198024
\(17\) 4.96836e10i 1.72742i −0.503991 0.863709i \(-0.668136\pi\)
0.503991 0.863709i \(-0.331864\pi\)
\(18\) 6.92889e9i 0.148200i
\(19\) 6.53775e10 0.883126 0.441563 0.897230i \(-0.354424\pi\)
0.441563 + 0.897230i \(0.354424\pi\)
\(20\) 5.72314e10 + 5.66438e10i 0.499895 + 0.494763i
\(21\) 5.75667e10 0.332129
\(22\) 2.14857e11i 0.834751i
\(23\) 6.03064e10i 0.160575i −0.996772 0.0802873i \(-0.974416\pi\)
0.996772 0.0802873i \(-0.0255838\pi\)
\(24\) −5.64269e11 −1.04638
\(25\) 7.87347e9 + 7.62899e11i 0.0103199 + 0.999947i
\(26\) −4.34604e11 −0.408151
\(27\) 1.20483e12i 0.820986i
\(28\) 4.14053e11i 0.207115i
\(29\) −2.63186e10 −0.00976967 −0.00488483 0.999988i \(-0.501555\pi\)
−0.00488483 + 0.999988i \(0.501555\pi\)
\(30\) −1.56904e12 1.55293e12i −0.436621 0.432138i
\(31\) 3.03326e12 0.638756 0.319378 0.947627i \(-0.396526\pi\)
0.319378 + 0.947627i \(0.396526\pi\)
\(32\) 6.44125e12i 1.03561i
\(33\) 1.39654e13i 1.72857i
\(34\) 9.79712e12 0.940866
\(35\) 2.75968e12 2.78831e12i 0.207148 0.209297i
\(36\) −3.23931e12 −0.191373
\(37\) 8.44655e12i 0.395334i −0.980269 0.197667i \(-0.936663\pi\)
0.980269 0.197667i \(-0.0633365\pi\)
\(38\) 1.28918e13i 0.481009i
\(39\) −2.82487e13 −0.845181
\(40\) −2.70504e13 + 2.73310e13i −0.652625 + 0.659395i
\(41\) 5.70631e13 1.11607 0.558036 0.829817i \(-0.311555\pi\)
0.558036 + 0.829817i \(0.311555\pi\)
\(42\) 1.13516e13i 0.180900i
\(43\) 6.40476e13i 0.835644i 0.908529 + 0.417822i \(0.137206\pi\)
−0.908529 + 0.417822i \(0.862794\pi\)
\(44\) −1.00447e14 −1.07793
\(45\) −2.18141e13 2.15901e13i −0.193389 0.191403i
\(46\) 1.18918e13 0.0874596
\(47\) 2.44975e14i 1.50069i −0.661048 0.750344i \(-0.729888\pi\)
0.661048 0.750344i \(-0.270112\pi\)
\(48\) 4.36042e13i 0.223346i
\(49\) 2.12458e14 0.913285
\(50\) −1.50436e14 + 1.55257e12i −0.544637 + 0.00562090i
\(51\) 6.36800e14 1.94830
\(52\) 2.03181e14i 0.527054i
\(53\) 1.01305e14i 0.223504i −0.993736 0.111752i \(-0.964354\pi\)
0.993736 0.111752i \(-0.0356463\pi\)
\(54\) −2.37582e14 −0.447163
\(55\) −6.76432e14 6.69487e14i −1.08928 1.07810i
\(56\) 1.97732e14 0.273199
\(57\) 8.37950e14i 0.996052i
\(58\) 5.18977e12i 0.00532121i
\(59\) −1.41965e15 −1.25875 −0.629373 0.777103i \(-0.716688\pi\)
−0.629373 + 0.777103i \(0.716688\pi\)
\(60\) −7.26009e14 + 7.33540e14i −0.558029 + 0.563817i
\(61\) 2.31838e15 1.54839 0.774195 0.632947i \(-0.218155\pi\)
0.774195 + 0.632947i \(0.218155\pi\)
\(62\) 5.98128e14i 0.347908i
\(63\) 1.57819e14i 0.0801244i
\(64\) −8.24240e14 −0.366036
\(65\) −1.35421e15 + 1.36826e15i −0.527136 + 0.532604i
\(66\) 2.75385e15 0.941492
\(67\) 4.06306e15i 1.22241i −0.791472 0.611206i \(-0.790685\pi\)
0.791472 0.611206i \(-0.209315\pi\)
\(68\) 4.58023e15i 1.21496i
\(69\) 7.72954e14 0.181107
\(70\) 5.49827e14 + 5.44182e14i 0.113997 + 0.112826i
\(71\) 2.68034e15 0.492599 0.246299 0.969194i \(-0.420785\pi\)
0.246299 + 0.969194i \(0.420785\pi\)
\(72\) 1.54694e15i 0.252434i
\(73\) 6.95024e15i 1.00869i 0.863504 + 0.504343i \(0.168265\pi\)
−0.863504 + 0.504343i \(0.831735\pi\)
\(74\) 1.66558e15 0.215325
\(75\) −9.77816e15 + 1.00915e14i −1.12781 + 0.0116395i
\(76\) 6.02702e15 0.621137
\(77\) 4.89380e15i 0.451310i
\(78\) 5.57037e15i 0.460341i
\(79\) −8.28477e15 −0.614399 −0.307199 0.951645i \(-0.599392\pi\)
−0.307199 + 0.951645i \(0.599392\pi\)
\(80\) 2.11202e15 + 2.09034e15i 0.140745 + 0.139300i
\(81\) −1.99802e16 −1.19806
\(82\) 1.12523e16i 0.607887i
\(83\) 2.66711e16i 1.29980i 0.760018 + 0.649902i \(0.225190\pi\)
−0.760018 + 0.649902i \(0.774810\pi\)
\(84\) 5.30696e15 0.233600
\(85\) 3.05275e16 3.08441e16i 1.21515 1.22776i
\(86\) −1.26296e16 −0.455147
\(87\) 3.37328e14i 0.0110189i
\(88\) 4.79690e16i 1.42186i
\(89\) 6.55891e15 0.176611 0.0883053 0.996093i \(-0.471855\pi\)
0.0883053 + 0.996093i \(0.471855\pi\)
\(90\) 4.25736e15 4.30153e15i 0.104251 0.105332i
\(91\) 9.89897e15 0.220667
\(92\) 5.55953e15i 0.112938i
\(93\) 3.88776e16i 0.720434i
\(94\) 4.83067e16 0.817373
\(95\) 4.05871e16 + 4.01704e16i 0.627678 + 0.621234i
\(96\) −8.25582e16 −1.16803
\(97\) 1.11864e17i 1.44920i −0.689169 0.724601i \(-0.742024\pi\)
0.689169 0.724601i \(-0.257976\pi\)
\(98\) 4.18946e16i 0.497435i
\(99\) 3.82862e16 0.417007
\(100\) 7.25839e14 + 7.03301e16i 0.00725839 + 0.703301i
\(101\) −1.99528e17 −1.83346 −0.916732 0.399503i \(-0.869183\pi\)
−0.916732 + 0.399503i \(0.869183\pi\)
\(102\) 1.25571e17i 1.06117i
\(103\) 1.36484e17i 1.06161i −0.847495 0.530804i \(-0.821890\pi\)
0.847495 0.530804i \(-0.178110\pi\)
\(104\) −9.70298e16 −0.695219
\(105\) 3.57380e16 + 3.53711e16i 0.236060 + 0.233636i
\(106\) 1.99764e16 0.121735
\(107\) 4.55554e16i 0.256317i 0.991754 + 0.128158i \(0.0409066\pi\)
−0.991754 + 0.128158i \(0.959093\pi\)
\(108\) 1.11071e17i 0.577431i
\(109\) 2.16082e17 1.03871 0.519355 0.854559i \(-0.326172\pi\)
0.519355 + 0.854559i \(0.326172\pi\)
\(110\) 1.32016e17 1.33386e17i 0.587205 0.593296i
\(111\) 1.08260e17 0.445886
\(112\) 1.52799e16i 0.0583132i
\(113\) 2.03188e17i 0.719005i −0.933144 0.359502i \(-0.882946\pi\)
0.933144 0.359502i \(-0.117054\pi\)
\(114\) −1.65236e17 −0.542516
\(115\) 3.70545e16 3.74389e16i 0.112956 0.114128i
\(116\) −2.42626e15 −0.00687139
\(117\) 7.74438e16i 0.203895i
\(118\) 2.79941e17i 0.685597i
\(119\) −2.23149e17 −0.508681
\(120\) −3.50305e17 3.46708e17i −0.743713 0.736077i
\(121\) 6.81767e17 1.34884
\(122\) 4.57161e17i 0.843355i
\(123\) 7.31384e17i 1.25879i
\(124\) 2.79630e17 0.449262
\(125\) −4.63865e17 + 4.78454e17i −0.696076 + 0.717968i
\(126\) −3.11204e16 −0.0436410
\(127\) 1.49219e17i 0.195655i −0.995203 0.0978277i \(-0.968811\pi\)
0.995203 0.0978277i \(-0.0311894\pi\)
\(128\) 6.81736e17i 0.836241i
\(129\) −8.20905e17 −0.942498
\(130\) −2.69807e17 2.67037e17i −0.290091 0.287113i
\(131\) −4.10281e17 −0.413309 −0.206655 0.978414i \(-0.566258\pi\)
−0.206655 + 0.978414i \(0.566258\pi\)
\(132\) 1.28745e18i 1.21577i
\(133\) 2.93636e17i 0.260058i
\(134\) 8.01196e17 0.665806
\(135\) −7.40295e17 + 7.47975e17i −0.577521 + 0.583512i
\(136\) 2.18731e18 1.60261
\(137\) 6.17653e17i 0.425226i −0.977137 0.212613i \(-0.931803\pi\)
0.977137 0.212613i \(-0.0681973\pi\)
\(138\) 1.52419e17i 0.0986431i
\(139\) −1.59873e18 −0.973080 −0.486540 0.873658i \(-0.661741\pi\)
−0.486540 + 0.873658i \(0.661741\pi\)
\(140\) 2.54409e17 2.57049e17i 0.145695 0.147207i
\(141\) 3.13987e18 1.69258
\(142\) 5.28536e17i 0.268302i
\(143\) 2.40145e18i 1.14846i
\(144\) −1.19541e17 −0.0538810
\(145\) −1.63389e16 1.61711e16i −0.00694375 0.00687246i
\(146\) −1.37052e18 −0.549397
\(147\) 2.72310e18i 1.03007i
\(148\) 7.78671e17i 0.278054i
\(149\) 1.08941e18 0.367373 0.183687 0.982985i \(-0.441197\pi\)
0.183687 + 0.982985i \(0.441197\pi\)
\(150\) −1.98995e16 1.92816e18i −0.00633965 0.614280i
\(151\) −4.15139e18 −1.24994 −0.624970 0.780649i \(-0.714889\pi\)
−0.624970 + 0.780649i \(0.714889\pi\)
\(152\) 2.87822e18i 0.819321i
\(153\) 1.74579e18i 0.470018i
\(154\) −9.65009e17 −0.245813
\(155\) 1.88308e18 + 1.86375e18i 0.453993 + 0.449332i
\(156\) −2.60419e18 −0.594448
\(157\) 8.05540e16i 0.0174157i −0.999962 0.00870783i \(-0.997228\pi\)
0.999962 0.00870783i \(-0.00277182\pi\)
\(158\) 1.63368e18i 0.334642i
\(159\) 1.29844e18 0.252084
\(160\) −3.95774e18 + 3.99880e18i −0.728497 + 0.736054i
\(161\) −2.70860e17 −0.0472852
\(162\) 3.93991e18i 0.652542i
\(163\) 2.71154e18i 0.426207i 0.977030 + 0.213104i \(0.0683572\pi\)
−0.977030 + 0.213104i \(0.931643\pi\)
\(164\) 5.26053e18 0.784977
\(165\) 8.58088e18 8.66990e18i 1.21596 1.22857i
\(166\) −5.25929e18 −0.707959
\(167\) 7.86788e18i 1.00639i −0.864172 0.503197i \(-0.832157\pi\)
0.864172 0.503197i \(-0.167843\pi\)
\(168\) 2.53436e18i 0.308133i
\(169\) 3.79286e18 0.438460
\(170\) 6.08216e18 + 6.01971e18i 0.668717 + 0.661851i
\(171\) −2.29724e18 −0.240292
\(172\) 5.90443e18i 0.587741i
\(173\) 3.01075e18i 0.285288i −0.989774 0.142644i \(-0.954440\pi\)
0.989774 0.142644i \(-0.0455604\pi\)
\(174\) 6.65178e16 0.00600163
\(175\) 3.42648e18 3.53628e16i 0.294459 0.00303895i
\(176\) −3.70683e18 −0.303491
\(177\) 1.81958e19i 1.41970i
\(178\) 1.29335e18i 0.0961938i
\(179\) −1.11507e19 −0.790774 −0.395387 0.918515i \(-0.629390\pi\)
−0.395387 + 0.918515i \(0.629390\pi\)
\(180\) −2.01100e18 1.99035e18i −0.136018 0.134621i
\(181\) −1.16284e19 −0.750332 −0.375166 0.926958i \(-0.622414\pi\)
−0.375166 + 0.926958i \(0.622414\pi\)
\(182\) 1.95198e18i 0.120190i
\(183\) 2.97149e19i 1.74638i
\(184\) 2.65497e18 0.148973
\(185\) 5.18987e18 5.24371e18i 0.278097 0.280982i
\(186\) −7.66627e18 −0.392396
\(187\) 5.41349e19i 2.64743i
\(188\) 2.25838e19i 1.05549i
\(189\) 5.41139e18 0.241759
\(190\) −7.92120e18 + 8.00337e18i −0.338365 + 0.341875i
\(191\) 1.23347e19 0.503901 0.251951 0.967740i \(-0.418928\pi\)
0.251951 + 0.967740i \(0.418928\pi\)
\(192\) 1.05644e19i 0.412842i
\(193\) 4.31622e19i 1.61386i −0.590645 0.806931i \(-0.701127\pi\)
0.590645 0.806931i \(-0.298873\pi\)
\(194\) 2.20584e19 0.789331
\(195\) −1.75371e19 1.73571e19i −0.600709 0.594541i
\(196\) 1.95861e19 0.642349
\(197\) 2.74515e18i 0.0862191i −0.999070 0.0431096i \(-0.986274\pi\)
0.999070 0.0431096i \(-0.0137265\pi\)
\(198\) 7.54967e18i 0.227130i
\(199\) −5.45248e19 −1.57160 −0.785802 0.618478i \(-0.787750\pi\)
−0.785802 + 0.618478i \(0.787750\pi\)
\(200\) −3.35864e19 + 3.46627e17i −0.927701 + 0.00957430i
\(201\) 5.20767e19 1.37872
\(202\) 3.93450e19i 0.998625i
\(203\) 1.18207e17i 0.00287692i
\(204\) 5.87053e19 1.37032
\(205\) 3.54254e19 + 3.50617e19i 0.793244 + 0.785100i
\(206\) 2.69132e19 0.578222
\(207\) 2.11905e18i 0.0436912i
\(208\) 7.49803e18i 0.148391i
\(209\) −7.12349e19 −1.35347
\(210\) −6.97484e18 + 7.04719e18i −0.127254 + 0.128574i
\(211\) 8.75529e18 0.153416 0.0767078 0.997054i \(-0.475559\pi\)
0.0767078 + 0.997054i \(0.475559\pi\)
\(212\) 9.33911e18i 0.157199i
\(213\) 3.43541e19i 0.555588i
\(214\) −8.98307e18 −0.139607
\(215\) −3.93532e19 + 3.97615e19i −0.587833 + 0.593931i
\(216\) −5.30425e19 −0.761670
\(217\) 1.36236e19i 0.188097i
\(218\) 4.26093e19i 0.565750i
\(219\) −8.90820e19 −1.13767
\(220\) −6.23589e19 6.17187e19i −0.766136 0.758270i
\(221\) 1.09502e20 1.29446
\(222\) 2.13479e19i 0.242859i
\(223\) 4.58536e19i 0.502091i −0.967975 0.251045i \(-0.919226\pi\)
0.967975 0.251045i \(-0.0807743\pi\)
\(224\) 2.89302e19 0.304960
\(225\) −2.76659e17 2.68068e19i −0.00280797 0.272078i
\(226\) 4.00667e19 0.391617
\(227\) 4.24431e19i 0.399565i 0.979840 + 0.199782i \(0.0640235\pi\)
−0.979840 + 0.199782i \(0.935977\pi\)
\(228\) 7.72490e19i 0.700562i
\(229\) 1.66894e20 1.45828 0.729138 0.684367i \(-0.239921\pi\)
0.729138 + 0.684367i \(0.239921\pi\)
\(230\) 7.38258e18 + 7.30679e18i 0.0621615 + 0.0615233i
\(231\) −6.27243e19 −0.509019
\(232\) 1.15867e18i 0.00906382i
\(233\) 6.95294e19i 0.524377i −0.965017 0.262188i \(-0.915556\pi\)
0.965017 0.262188i \(-0.0844442\pi\)
\(234\) 1.52712e19 0.111055
\(235\) 1.50522e20 1.52083e20i 1.05566 1.06661i
\(236\) −1.30875e20 −0.885326
\(237\) 1.06187e20i 0.692962i
\(238\) 4.40027e19i 0.277061i
\(239\) −4.98454e19 −0.302861 −0.151430 0.988468i \(-0.548388\pi\)
−0.151430 + 0.988468i \(0.548388\pi\)
\(240\) −2.67921e19 + 2.70700e19i −0.157112 + 0.158742i
\(241\) −2.34973e19 −0.133007 −0.0665033 0.997786i \(-0.521184\pi\)
−0.0665033 + 0.997786i \(0.521184\pi\)
\(242\) 1.34438e20i 0.734668i
\(243\) 1.00496e20i 0.530269i
\(244\) 2.13727e20 1.08904
\(245\) 1.31896e20 + 1.30542e20i 0.649113 + 0.642449i
\(246\) −1.44222e20 −0.685618
\(247\) 1.44091e20i 0.661779i
\(248\) 1.33538e20i 0.592606i
\(249\) −3.41847e20 −1.46601
\(250\) −9.43464e19 9.14697e19i −0.391053 0.379129i
\(251\) −1.73046e20 −0.693322 −0.346661 0.937990i \(-0.612685\pi\)
−0.346661 + 0.937990i \(0.612685\pi\)
\(252\) 1.45490e19i 0.0563546i
\(253\) 6.57095e19i 0.246096i
\(254\) 2.94245e19 0.106567
\(255\) 3.95333e20 + 3.91274e20i 1.38475 + 1.37053i
\(256\) −2.42466e20 −0.821508
\(257\) 4.12299e20i 1.35139i −0.737181 0.675695i \(-0.763844\pi\)
0.737181 0.675695i \(-0.236156\pi\)
\(258\) 1.61875e20i 0.513347i
\(259\) −3.79368e19 −0.116416
\(260\) −1.24842e20 + 1.26137e20i −0.370755 + 0.374601i
\(261\) 9.24785e17 0.00265825
\(262\) 8.09033e19i 0.225116i
\(263\) 2.09492e20i 0.564343i 0.959364 + 0.282171i \(0.0910546\pi\)
−0.959364 + 0.282171i \(0.908945\pi\)
\(264\) 6.14824e20 1.60368
\(265\) 6.22456e19 6.28913e19i 0.157224 0.158855i
\(266\) 5.79022e19 0.141645
\(267\) 8.40663e19i 0.199194i
\(268\) 3.74566e20i 0.859770i
\(269\) −1.23146e20 −0.273859 −0.136930 0.990581i \(-0.543723\pi\)
−0.136930 + 0.990581i \(0.543723\pi\)
\(270\) −1.47493e20 1.45979e20i −0.317819 0.314556i
\(271\) 1.71222e20 0.357536 0.178768 0.983891i \(-0.442789\pi\)
0.178768 + 0.983891i \(0.442789\pi\)
\(272\) 1.69025e20i 0.342071i
\(273\) 1.26876e20i 0.248884i
\(274\) 1.21795e20 0.231606
\(275\) −8.57888e18 8.31250e20i −0.0158162 1.53251i
\(276\) 7.12571e19 0.127380
\(277\) 4.23825e20i 0.734698i 0.930083 + 0.367349i \(0.119734\pi\)
−0.930083 + 0.367349i \(0.880266\pi\)
\(278\) 3.15253e20i 0.530004i
\(279\) −1.06583e20 −0.173801
\(280\) 1.22754e20 + 1.21494e20i 0.194175 + 0.192182i
\(281\) −3.64626e20 −0.559556 −0.279778 0.960065i \(-0.590261\pi\)
−0.279778 + 0.960065i \(0.590261\pi\)
\(282\) 6.19152e20i 0.921892i
\(283\) 5.68589e20i 0.821511i 0.911745 + 0.410756i \(0.134735\pi\)
−0.911745 + 0.410756i \(0.865265\pi\)
\(284\) 2.47095e20 0.346464
\(285\) −5.14868e20 + 5.20209e20i −0.700671 + 0.707940i
\(286\) 4.73542e20 0.625529
\(287\) 2.56293e20i 0.328655i
\(288\) 2.26333e20i 0.281781i
\(289\) −1.64122e21 −1.98397
\(290\) 3.18879e18 3.22187e18i 0.00374320 0.00378203i
\(291\) 1.43377e21 1.63451
\(292\) 6.40729e20i 0.709448i
\(293\) 1.46631e21i 1.57707i 0.614991 + 0.788534i \(0.289159\pi\)
−0.614991 + 0.788534i \(0.710841\pi\)
\(294\) −5.36968e20 −0.561043
\(295\) −8.81333e20 8.72284e20i −0.894649 0.885464i
\(296\) 3.71857e20 0.366772
\(297\) 1.31278e21i 1.25824i
\(298\) 2.14821e20i 0.200096i
\(299\) 1.32914e20 0.120328
\(300\) −9.01429e20 + 9.30316e18i −0.793233 + 0.00818653i
\(301\) 2.87663e20 0.246076
\(302\) 8.18613e20i 0.680800i
\(303\) 2.55737e21i 2.06791i
\(304\) 2.22416e20 0.174880
\(305\) 1.43927e21 + 1.42450e21i 1.10051 + 1.08921i
\(306\) −3.44252e20 −0.256003
\(307\) 1.00902e21i 0.729833i 0.931040 + 0.364916i \(0.118902\pi\)
−0.931040 + 0.364916i \(0.881098\pi\)
\(308\) 4.51149e20i 0.317424i
\(309\) 1.74933e21 1.19736
\(310\) −3.67512e20 + 3.71325e20i −0.244736 + 0.247275i
\(311\) 1.79361e21 1.16216 0.581078 0.813848i \(-0.302631\pi\)
0.581078 + 0.813848i \(0.302631\pi\)
\(312\) 1.24364e21i 0.784117i
\(313\) 6.24766e20i 0.383345i 0.981459 + 0.191673i \(0.0613912\pi\)
−0.981459 + 0.191673i \(0.938609\pi\)
\(314\) 1.58845e19 0.00948572
\(315\) −9.69699e19 + 9.79758e19i −0.0563634 + 0.0569481i
\(316\) −7.63757e20 −0.432130
\(317\) 3.52085e20i 0.193930i −0.995288 0.0969648i \(-0.969087\pi\)
0.995288 0.0969648i \(-0.0309134\pi\)
\(318\) 2.56039e20i 0.137302i
\(319\) 2.86766e19 0.0149729
\(320\) −5.11697e20 5.06444e20i −0.260159 0.257488i
\(321\) −5.83888e20 −0.289092
\(322\) 5.34109e19i 0.0257546i
\(323\) 3.24819e21i 1.52553i
\(324\) −1.84194e21 −0.842641
\(325\) −1.68142e21 + 1.73530e19i −0.749320 + 0.00773332i
\(326\) −5.34689e20 −0.232141
\(327\) 2.76955e21i 1.17153i
\(328\) 2.51218e21i 1.03544i
\(329\) −1.10028e21 −0.441914
\(330\) 1.70962e21 + 1.69207e21i 0.669161 + 0.662291i
\(331\) −2.87953e21 −1.09846 −0.549229 0.835672i \(-0.685079\pi\)
−0.549229 + 0.835672i \(0.685079\pi\)
\(332\) 2.45876e21i 0.914202i
\(333\) 2.96795e20i 0.107568i
\(334\) 1.55147e21 0.548148
\(335\) 2.49650e21 2.52239e21i 0.859904 0.868824i
\(336\) 1.95844e20 0.0657697
\(337\) 6.69424e20i 0.219203i 0.993976 + 0.109602i \(0.0349575\pi\)
−0.993976 + 0.109602i \(0.965042\pi\)
\(338\) 7.47916e20i 0.238814i
\(339\) 2.60428e21 0.810944
\(340\) 2.81427e21 2.84346e21i 0.854662 0.863528i
\(341\) −3.30502e21 −0.978952
\(342\) 4.52993e20i 0.130879i
\(343\) 1.99907e21i 0.563414i
\(344\) −2.81968e21 −0.775269
\(345\) 4.79858e20 + 4.74932e20i 0.128721 + 0.127400i
\(346\) 5.93691e20 0.155387
\(347\) 8.92234e20i 0.227865i −0.993488 0.113933i \(-0.963655\pi\)
0.993488 0.113933i \(-0.0363448\pi\)
\(348\) 3.10976e19i 0.00775004i
\(349\) 2.36533e21 0.575274 0.287637 0.957739i \(-0.407130\pi\)
0.287637 + 0.957739i \(0.407130\pi\)
\(350\) 6.97321e18 + 6.75668e20i 0.00165521 + 0.160382i
\(351\) −2.65544e21 −0.615213
\(352\) 7.01835e21i 1.58717i
\(353\) 2.51330e21i 0.554829i 0.960750 + 0.277414i \(0.0894774\pi\)
−0.960750 + 0.277414i \(0.910523\pi\)
\(354\) 3.58803e21 0.773265
\(355\) 1.66398e21 + 1.64690e21i 0.350113 + 0.346518i
\(356\) 6.04653e20 0.124217
\(357\) 2.86012e21i 0.573726i
\(358\) 2.19881e21i 0.430708i
\(359\) 2.10167e21 0.402033 0.201017 0.979588i \(-0.435576\pi\)
0.201017 + 0.979588i \(0.435576\pi\)
\(360\) 9.50499e20 9.60360e20i 0.177574 0.179417i
\(361\) −1.20617e21 −0.220089
\(362\) 2.29301e21i 0.408680i
\(363\) 8.73829e21i 1.52132i
\(364\) 9.12566e20 0.155204
\(365\) −4.27049e21 + 4.31479e21i −0.709558 + 0.716919i
\(366\) −5.85948e21 −0.951196
\(367\) 7.00996e21i 1.11187i 0.831226 + 0.555935i \(0.187640\pi\)
−0.831226 + 0.555935i \(0.812360\pi\)
\(368\) 2.05165e20i 0.0317977i
\(369\) −2.00509e21 −0.303675
\(370\) 1.03401e21 + 1.02339e21i 0.153042 + 0.151470i
\(371\) −4.55001e20 −0.0658164
\(372\) 3.58405e21i 0.506709i
\(373\) 5.69623e21i 0.787158i −0.919291 0.393579i \(-0.871237\pi\)
0.919291 0.393579i \(-0.128763\pi\)
\(374\) −1.06749e22 −1.44196
\(375\) −6.13239e21 5.94541e21i −0.809775 0.785084i
\(376\) 1.07850e22 1.39226
\(377\) 5.80058e19i 0.00732099i
\(378\) 1.06707e21i 0.131678i
\(379\) 4.63351e21 0.559083 0.279542 0.960134i \(-0.409817\pi\)
0.279542 + 0.960134i \(0.409817\pi\)
\(380\) 3.74164e21 + 3.70323e21i 0.441470 + 0.436938i
\(381\) 1.91255e21 0.220674
\(382\) 2.43228e21i 0.274458i
\(383\) 8.22870e20i 0.0908117i −0.998969 0.0454058i \(-0.985542\pi\)
0.998969 0.0454058i \(-0.0144581\pi\)
\(384\) −8.73788e21 −0.943171
\(385\) −3.00693e21 + 3.03812e21i −0.317473 + 0.320767i
\(386\) 8.51117e21 0.879016
\(387\) 2.25051e21i 0.227373i
\(388\) 1.03125e22i 1.01928i
\(389\) 6.11949e21 0.591757 0.295879 0.955226i \(-0.404388\pi\)
0.295879 + 0.955226i \(0.404388\pi\)
\(390\) 3.42264e21 3.45815e21i 0.323826 0.327186i
\(391\) −2.99624e21 −0.277379
\(392\) 9.35339e21i 0.847301i
\(393\) 5.25861e21i 0.466159i
\(394\) 5.41317e20 0.0469606
\(395\) −5.14328e21 5.09047e21i −0.436681 0.432198i
\(396\) 3.52953e21 0.293297
\(397\) 1.23524e22i 1.00469i −0.864668 0.502344i \(-0.832471\pi\)
0.864668 0.502344i \(-0.167529\pi\)
\(398\) 1.07518e22i 0.855999i
\(399\) 3.76357e21 0.293312
\(400\) 2.67858e19 + 2.59541e21i 0.00204359 + 0.198014i
\(401\) 2.56078e22 1.91269 0.956346 0.292237i \(-0.0943996\pi\)
0.956346 + 0.292237i \(0.0943996\pi\)
\(402\) 1.02690e22i 0.750943i
\(403\) 6.68525e21i 0.478657i
\(404\) −1.83941e22 −1.28955
\(405\) −1.24040e22 1.22766e22i −0.851515 0.842772i
\(406\) −2.33093e19 −0.00156696
\(407\) 9.20330e21i 0.605887i
\(408\) 2.80349e22i 1.80754i
\(409\) 1.54083e22 0.972986 0.486493 0.873684i \(-0.338276\pi\)
0.486493 + 0.873684i \(0.338276\pi\)
\(410\) −6.91382e21 + 6.98554e21i −0.427617 + 0.432053i
\(411\) 7.91652e21 0.479600
\(412\) 1.25822e22i 0.746670i
\(413\) 6.37620e21i 0.370669i
\(414\) −4.17856e20 −0.0237971
\(415\) −1.63877e22 + 1.65577e22i −0.914345 + 0.923830i
\(416\) −1.41964e22 −0.776043
\(417\) 2.04911e22i 1.09751i
\(418\) 1.40468e22i 0.737190i
\(419\) −2.60959e22 −1.34200 −0.671001 0.741456i \(-0.734136\pi\)
−0.671001 + 0.741456i \(0.734136\pi\)
\(420\) 3.29462e21 + 3.26079e21i 0.166030 + 0.164325i
\(421\) −2.31572e22 −1.14364 −0.571818 0.820380i \(-0.693762\pi\)
−0.571818 + 0.820380i \(0.693762\pi\)
\(422\) 1.72646e21i 0.0835603i
\(423\) 8.60796e21i 0.408326i
\(424\) 4.45992e21 0.207356
\(425\) 3.79036e22 3.91182e20i 1.72733 0.0178268i
\(426\) −6.77430e21 −0.302610
\(427\) 1.04127e22i 0.455962i
\(428\) 4.19966e21i 0.180278i
\(429\) 3.07796e22 1.29532
\(430\) −7.84057e21 7.76007e21i −0.323494 0.320172i
\(431\) 6.11457e20 0.0247348 0.0123674 0.999924i \(-0.496063\pi\)
0.0123674 + 0.999924i \(0.496063\pi\)
\(432\) 4.09889e21i 0.162575i
\(433\) 3.10026e22i 1.20573i 0.797842 + 0.602867i \(0.205975\pi\)
−0.797842 + 0.602867i \(0.794025\pi\)
\(434\) 2.68643e21 0.102450
\(435\) 2.07267e20 2.09417e20i 0.00775125 0.00783166i
\(436\) 1.99202e22 0.730565
\(437\) 3.94268e21i 0.141808i
\(438\) 1.75661e22i 0.619649i
\(439\) −1.11795e22 −0.386787 −0.193394 0.981121i \(-0.561949\pi\)
−0.193394 + 0.981121i \(0.561949\pi\)
\(440\) 2.94739e22 2.97797e22i 1.00021 1.01058i
\(441\) −7.46536e21 −0.248498
\(442\) 2.15927e22i 0.705047i
\(443\) 4.87194e22i 1.56052i −0.625454 0.780261i \(-0.715086\pi\)
0.625454 0.780261i \(-0.284914\pi\)
\(444\) 9.98030e21 0.313609
\(445\) 4.07185e21 + 4.03004e21i 0.125525 + 0.124237i
\(446\) 9.04188e21 0.273472
\(447\) 1.39631e22i 0.414349i
\(448\) 3.70199e21i 0.107788i
\(449\) −8.32387e21 −0.237811 −0.118905 0.992906i \(-0.537938\pi\)
−0.118905 + 0.992906i \(0.537938\pi\)
\(450\) 5.28604e21 5.45543e19i 0.148192 0.00152941i
\(451\) −6.21756e22 −1.71048
\(452\) 1.87315e22i 0.505704i
\(453\) 5.32088e22i 1.40977i
\(454\) −8.36936e21 −0.217629
\(455\) 6.14539e21 + 6.08229e21i 0.156838 + 0.155228i
\(456\) −3.68905e22 −0.924088
\(457\) 6.51348e22i 1.60149i 0.599002 + 0.800747i \(0.295564\pi\)
−0.599002 + 0.800747i \(0.704436\pi\)
\(458\) 3.29099e22i 0.794273i
\(459\) 5.98605e22 1.41818
\(460\) 3.41598e21 3.45142e21i 0.0794464 0.0802705i
\(461\) −3.15500e22 −0.720346 −0.360173 0.932886i \(-0.617282\pi\)
−0.360173 + 0.932886i \(0.617282\pi\)
\(462\) 1.23686e22i 0.277245i
\(463\) 7.28815e22i 1.60391i 0.597388 + 0.801953i \(0.296205\pi\)
−0.597388 + 0.801953i \(0.703795\pi\)
\(464\) −8.95368e19 −0.00193463
\(465\) −2.38878e22 + 2.41356e22i −0.506788 + 0.512045i
\(466\) 1.37105e22 0.285610
\(467\) 2.24397e22i 0.459011i 0.973307 + 0.229506i \(0.0737109\pi\)
−0.973307 + 0.229506i \(0.926289\pi\)
\(468\) 7.13939e21i 0.143407i
\(469\) −1.82488e22 −0.359969
\(470\) 2.99893e22 + 2.96814e22i 0.580945 + 0.574980i
\(471\) 1.03247e21 0.0196426
\(472\) 6.24995e22i 1.16780i
\(473\) 6.97859e22i 1.28070i
\(474\) 2.09390e22 0.377433
\(475\) 5.14747e20 + 4.98764e22i 0.00911378 + 0.883079i
\(476\) −2.05716e22 −0.357775
\(477\) 3.55966e21i 0.0608139i
\(478\) 9.82902e21i 0.164958i
\(479\) −6.47401e22 −1.06739 −0.533693 0.845678i \(-0.679196\pi\)
−0.533693 + 0.845678i \(0.679196\pi\)
\(480\) −5.12531e22 5.07268e22i −0.830174 0.821651i
\(481\) 1.86161e22 0.296248
\(482\) 4.63344e21i 0.0724442i
\(483\) 3.47164e21i 0.0533316i
\(484\) 6.28508e22 0.948692
\(485\) 6.87331e22 6.94461e22i 1.01944 1.03001i
\(486\) 1.98169e22 0.288820
\(487\) 1.32206e23i 1.89346i −0.322030 0.946730i \(-0.604365\pi\)
0.322030 0.946730i \(-0.395635\pi\)
\(488\) 1.02066e23i 1.43652i
\(489\) −3.47541e22 −0.480707
\(490\) −2.57416e22 + 2.60086e22i −0.349920 + 0.353550i
\(491\) 1.24365e23 1.66151 0.830757 0.556636i \(-0.187908\pi\)
0.830757 + 0.556636i \(0.187908\pi\)
\(492\) 6.74248e22i 0.885353i
\(493\) 1.30760e21i 0.0168763i
\(494\) −2.84133e22 −0.360448
\(495\) 2.37685e22 + 2.35245e22i 0.296386 + 0.293343i
\(496\) 1.03192e22 0.126489
\(497\) 1.20384e22i 0.145058i
\(498\) 6.74088e22i 0.798486i
\(499\) 1.71668e22 0.199910 0.0999550 0.994992i \(-0.468130\pi\)
0.0999550 + 0.994992i \(0.468130\pi\)
\(500\) −4.27628e22 + 4.41077e22i −0.489578 + 0.504975i
\(501\) 1.00844e23 1.13508
\(502\) 3.41230e22i 0.377629i
\(503\) 6.39694e22i 0.696057i 0.937484 + 0.348028i \(0.113149\pi\)
−0.937484 + 0.348028i \(0.886851\pi\)
\(504\) −6.94793e21 −0.0743355
\(505\) −1.23869e23 1.22597e23i −1.30313 1.28975i
\(506\) −1.29573e22 −0.134040
\(507\) 4.86136e22i 0.494527i
\(508\) 1.37562e22i 0.137612i
\(509\) −1.87713e23 −1.84669 −0.923346 0.383970i \(-0.874557\pi\)
−0.923346 + 0.383970i \(0.874557\pi\)
\(510\) −7.71553e22 + 7.79557e22i −0.746482 + 0.754226i
\(511\) 3.12163e22 0.297032
\(512\) 4.15445e22i 0.388793i
\(513\) 7.87691e22i 0.725034i
\(514\) 8.13013e22 0.736057
\(515\) 8.38606e22 8.47306e22i 0.746787 0.754534i
\(516\) −7.56777e22 −0.662896
\(517\) 2.66923e23i 2.29994i
\(518\) 7.48076e21i 0.0634078i
\(519\) 3.85891e22 0.321768
\(520\) −6.02372e22 5.96187e22i −0.494124 0.489051i
\(521\) 2.51826e22 0.203226 0.101613 0.994824i \(-0.467600\pi\)
0.101613 + 0.994824i \(0.467600\pi\)
\(522\) 1.82359e20i 0.00144786i
\(523\) 1.41643e23i 1.10645i −0.833033 0.553223i \(-0.813398\pi\)
0.833033 0.553223i \(-0.186602\pi\)
\(524\) −3.78230e22 −0.290696
\(525\) 4.53249e20 + 4.39176e22i 0.00342754 + 0.332112i
\(526\) −4.13097e22 −0.307378
\(527\) 1.50703e23i 1.10340i
\(528\) 4.75109e22i 0.342298i
\(529\) 1.37413e23 0.974216
\(530\) 1.24015e22 + 1.22742e22i 0.0865229 + 0.0856345i
\(531\) 4.98837e22 0.342496
\(532\) 2.70697e22i 0.182909i
\(533\) 1.25766e23i 0.836340i
\(534\) −1.65771e22 −0.108494
\(535\) −2.79909e22 + 2.82813e22i −0.180306 + 0.182176i
\(536\) 1.78875e23 1.13409
\(537\) 1.42920e23i 0.891891i
\(538\) 2.42833e22i 0.149162i
\(539\) −2.31493e23 −1.39969
\(540\) −6.82464e22 + 6.89543e22i −0.406193 + 0.410407i
\(541\) 4.04123e22 0.236776 0.118388 0.992967i \(-0.462227\pi\)
0.118388 + 0.992967i \(0.462227\pi\)
\(542\) 3.37632e22i 0.194738i
\(543\) 1.49043e23i 0.846278i
\(544\) 3.20025e23 1.78893
\(545\) 1.34146e23 + 1.32769e23i 0.738259 + 0.730679i
\(546\) −2.50187e22 −0.135559
\(547\) 2.57609e23i 1.37426i −0.726535 0.687130i \(-0.758870\pi\)
0.726535 0.687130i \(-0.241130\pi\)
\(548\) 5.69402e22i 0.299078i
\(549\) −8.14633e22 −0.421305
\(550\) 1.63914e23 1.69167e21i 0.834707 0.00861456i
\(551\) −1.72064e21 −0.00862785
\(552\) 3.40291e22i 0.168023i
\(553\) 3.72102e22i 0.180925i
\(554\) −8.35742e22 −0.400165
\(555\) 6.72092e22 + 6.65191e22i 0.316912 + 0.313658i
\(556\) −1.47383e23 −0.684405
\(557\) 2.94142e23i 1.34520i 0.740004 + 0.672602i \(0.234824\pi\)
−0.740004 + 0.672602i \(0.765176\pi\)
\(558\) 2.10171e22i 0.0946633i
\(559\) −1.41160e23 −0.626198
\(560\) 9.38852e21 9.48592e21i 0.0410203 0.0414459i
\(561\) −6.93853e23 −2.98596
\(562\) 7.19007e22i 0.304771i
\(563\) 2.02557e23i 0.845719i 0.906195 + 0.422859i \(0.138974\pi\)
−0.906195 + 0.422859i \(0.861026\pi\)
\(564\) 2.89459e23 1.19046
\(565\) 1.24846e23 1.26141e23i 0.505783 0.511030i
\(566\) −1.12120e23 −0.447449
\(567\) 8.97391e22i 0.352798i
\(568\) 1.18001e23i 0.457009i
\(569\) −1.65130e23 −0.630045 −0.315022 0.949084i \(-0.602012\pi\)
−0.315022 + 0.949084i \(0.602012\pi\)
\(570\) −1.02580e23 1.01527e23i −0.385591 0.381632i
\(571\) 9.39406e22 0.347894 0.173947 0.984755i \(-0.444348\pi\)
0.173947 + 0.984755i \(0.444348\pi\)
\(572\) 2.21385e23i 0.807759i
\(573\) 1.58095e23i 0.568336i
\(574\) 5.05384e22 0.179007
\(575\) 4.60077e22 4.74821e20i 0.160566 0.00165712i
\(576\) 2.89622e22 0.0995957
\(577\) 3.22752e23i 1.09364i 0.837250 + 0.546820i \(0.184162\pi\)
−0.837250 + 0.546820i \(0.815838\pi\)
\(578\) 3.23633e23i 1.08060i
\(579\) 5.53215e23 1.82023
\(580\) −1.50625e21 1.49078e21i −0.00488381 0.00483367i
\(581\) 1.19791e23 0.382759
\(582\) 2.82725e23i 0.890263i
\(583\) 1.10381e23i 0.342541i
\(584\) −3.05982e23 −0.935809
\(585\) 4.75844e22 4.80780e22i 0.143430 0.144918i
\(586\) −2.89141e23 −0.858975
\(587\) 1.54906e23i 0.453570i −0.973945 0.226785i \(-0.927178\pi\)
0.973945 0.226785i \(-0.0728215\pi\)
\(588\) 2.51037e23i 0.724486i
\(589\) 1.98307e23 0.564102
\(590\) 1.72006e23 1.73790e23i 0.482282 0.487285i
\(591\) 3.51849e22 0.0972440
\(592\) 2.87354e22i 0.0782859i
\(593\) 6.15543e23i 1.65308i −0.562879 0.826539i \(-0.690306\pi\)
0.562879 0.826539i \(-0.309694\pi\)
\(594\) 2.58867e23 0.685319
\(595\) −1.38533e23 1.37111e23i −0.361543 0.357831i
\(596\) 1.00430e23 0.258388
\(597\) 6.98851e23i 1.77257i
\(598\) 2.62094e22i 0.0655387i
\(599\) −2.44389e23 −0.602496 −0.301248 0.953546i \(-0.597403\pi\)
−0.301248 + 0.953546i \(0.597403\pi\)
\(600\) −4.44275e21 4.30480e23i −0.0107986 1.04633i
\(601\) −2.29017e23 −0.548825 −0.274413 0.961612i \(-0.588483\pi\)
−0.274413 + 0.961612i \(0.588483\pi\)
\(602\) 5.67244e22i 0.134029i
\(603\) 1.42768e23i 0.332609i
\(604\) −3.82708e23 −0.879131
\(605\) 4.23249e23 + 4.18903e23i 0.958683 + 0.948840i
\(606\) 5.04289e23 1.12632
\(607\) 5.08927e23i 1.12086i 0.828202 + 0.560430i \(0.189364\pi\)
−0.828202 + 0.560430i \(0.810636\pi\)
\(608\) 4.21113e23i 0.914572i
\(609\) −1.51507e21 −0.00324479
\(610\) −2.80897e23 + 2.83811e23i −0.593257 + 0.599412i
\(611\) 5.39922e23 1.12455
\(612\) 1.60941e23i 0.330582i
\(613\) 3.80505e23i 0.770808i −0.922748 0.385404i \(-0.874062\pi\)
0.922748 0.385404i \(-0.125938\pi\)
\(614\) −1.98969e23 −0.397515
\(615\) −4.49389e23 + 4.54051e23i −0.885491 + 0.894677i
\(616\) −2.15448e23 −0.418703
\(617\) 3.08703e23i 0.591721i −0.955231 0.295860i \(-0.904394\pi\)
0.955231 0.295860i \(-0.0956063\pi\)
\(618\) 3.44950e23i 0.652160i
\(619\) −2.71878e22 −0.0506995 −0.0253497 0.999679i \(-0.508070\pi\)
−0.0253497 + 0.999679i \(0.508070\pi\)
\(620\) 1.73597e23 + 1.71815e23i 0.319311 + 0.316032i
\(621\) 7.26593e22 0.131829
\(622\) 3.53682e23i 0.632987i
\(623\) 2.94587e22i 0.0520074i
\(624\) −9.61031e22 −0.167366
\(625\) −5.81953e23 + 1.20133e22i −0.999787 + 0.0206387i
\(626\) −1.23198e23 −0.208795
\(627\) 9.13025e23i 1.52654i
\(628\) 7.42611e21i 0.0122491i
\(629\) −4.19655e23 −0.682907
\(630\) −1.93199e22 1.91215e22i −0.0310177 0.0306992i
\(631\) 1.08541e22 0.0171927 0.00859636 0.999963i \(-0.497264\pi\)
0.00859636 + 0.999963i \(0.497264\pi\)
\(632\) 3.64734e23i 0.570009i
\(633\) 1.12217e23i 0.173033i
\(634\) 6.94278e22 0.105627
\(635\) 9.16855e22 9.26367e22i 0.137634 0.139061i
\(636\) 1.19700e23 0.177301
\(637\) 4.68254e23i 0.684379i
\(638\) 5.65474e21i 0.00815524i
\(639\) −9.41819e22 −0.134032
\(640\) −4.18884e23 + 4.23229e23i −0.588252 + 0.594355i
\(641\) 1.29824e24 1.79913 0.899563 0.436792i \(-0.143885\pi\)
0.899563 + 0.436792i \(0.143885\pi\)
\(642\) 1.15137e23i 0.157459i
\(643\) 9.64078e23i 1.30113i −0.759453 0.650563i \(-0.774533\pi\)
0.759453 0.650563i \(-0.225467\pi\)
\(644\) −2.49701e22 −0.0332575
\(645\) −5.09627e23 5.04395e23i −0.669877 0.662999i
\(646\) 6.40511e23 0.830903
\(647\) 1.43576e24i 1.83821i 0.394017 + 0.919103i \(0.371085\pi\)
−0.394017 + 0.919103i \(0.628915\pi\)
\(648\) 8.79624e23i 1.11150i
\(649\) 1.54684e24 1.92915
\(650\) −3.42184e21 3.31559e23i −0.00421208 0.408129i
\(651\) 1.74615e23 0.212149
\(652\) 2.49971e23i 0.299768i
\(653\) 4.34101e23i 0.513841i 0.966433 + 0.256920i \(0.0827078\pi\)
−0.966433 + 0.256920i \(0.917292\pi\)
\(654\) −5.46128e23 −0.638093
\(655\) −2.54707e23 2.52092e23i −0.293758 0.290742i
\(656\) 1.94131e23 0.221010
\(657\) 2.44218e23i 0.274456i
\(658\) 2.16964e23i 0.240696i
\(659\) −2.96685e22 −0.0324915 −0.0162457 0.999868i \(-0.505171\pi\)
−0.0162457 + 0.999868i \(0.505171\pi\)
\(660\) 7.91055e23 7.99261e23i 0.855230 0.864102i
\(661\) −3.46155e23 −0.369453 −0.184726 0.982790i \(-0.559140\pi\)
−0.184726 + 0.982790i \(0.559140\pi\)
\(662\) 5.67815e23i 0.598293i
\(663\) 1.40350e24i 1.45998i
\(664\) −1.17419e24 −1.20589
\(665\) 1.80421e23 1.82293e23i 0.182938 0.184835i
\(666\) −5.85252e22 −0.0585884
\(667\) 1.58718e21i 0.00156876i
\(668\) 7.25325e23i 0.707836i
\(669\) 5.87711e23 0.566294
\(670\) 4.97391e23 + 4.92284e23i 0.473219 + 0.468360i
\(671\) −2.52609e24 −2.37305
\(672\) 3.70802e23i 0.343956i
\(673\) 1.41988e24i 1.30054i 0.759703 + 0.650270i \(0.225344\pi\)
−0.759703 + 0.650270i \(0.774656\pi\)
\(674\) −1.32004e23 −0.119393
\(675\) −9.19167e23 + 9.48622e21i −0.820942 + 0.00847250i
\(676\) 3.49657e23 0.308386
\(677\) 8.46838e23i 0.737559i −0.929517 0.368779i \(-0.879776\pi\)
0.929517 0.368779i \(-0.120224\pi\)
\(678\) 5.13539e23i 0.441694i
\(679\) −5.02423e23 −0.426753
\(680\) 1.35790e24 + 1.34396e24i 1.13905 + 1.12736i
\(681\) −5.43997e23 −0.450657
\(682\) 6.51717e23i 0.533202i
\(683\) 3.07314e23i 0.248317i −0.992262 0.124159i \(-0.960377\pi\)
0.992262 0.124159i \(-0.0396232\pi\)
\(684\) −2.11778e23 −0.169007
\(685\) 3.79509e23 3.83446e23i 0.299124 0.302227i
\(686\) 3.94197e23 0.306872
\(687\) 2.13910e24i 1.64475i
\(688\) 2.17892e23i 0.165478i
\(689\) 2.23275e23 0.167485
\(690\) −9.36519e22 + 9.46234e22i −0.0693904 + 0.0701102i
\(691\) 2.97612e23 0.217815 0.108907 0.994052i \(-0.465265\pi\)
0.108907 + 0.994052i \(0.465265\pi\)
\(692\) 2.77555e23i 0.200654i
\(693\) 1.71959e23i 0.122798i
\(694\) 1.75940e23 0.124111
\(695\) −9.92507e23 9.82317e23i −0.691613 0.684512i
\(696\) 1.48508e22 0.0102228
\(697\) 2.83510e24i 1.92792i
\(698\) 4.66419e23i 0.313332i
\(699\) 8.91166e23 0.591429
\(700\) 3.15880e23 3.26003e21i 0.207104 0.00213741i
\(701\) −2.35616e24 −1.52617 −0.763084 0.646299i \(-0.776316\pi\)
−0.763084 + 0.646299i \(0.776316\pi\)
\(702\) 5.23626e23i 0.335086i
\(703\) 5.52214e23i 0.349130i
\(704\) 8.98087e23 0.560984
\(705\) 1.94927e24 + 1.92925e24i 1.20300 + 1.19064i
\(706\) −4.95597e23 −0.302196
\(707\) 8.96159e23i 0.539909i
\(708\) 1.67743e24i 0.998533i
\(709\) 2.77907e24 1.63458 0.817289 0.576227i \(-0.195476\pi\)
0.817289 + 0.576227i \(0.195476\pi\)
\(710\) −3.24752e23 + 3.28121e23i −0.188737 + 0.190694i
\(711\) 2.91111e23 0.167173
\(712\) 2.88754e23i 0.163851i
\(713\) 1.82925e23i 0.102568i
\(714\) 5.63988e23 0.312489
\(715\) 1.47554e24 1.49085e24i 0.807885 0.816265i
\(716\) −1.02796e24 −0.556182
\(717\) 6.38874e23i 0.341588i
\(718\) 4.14429e23i 0.218974i
\(719\) −9.31893e23 −0.486598 −0.243299 0.969951i \(-0.578230\pi\)
−0.243299 + 0.969951i \(0.578230\pi\)
\(720\) −7.42124e22 7.34504e22i −0.0382957 0.0379025i
\(721\) −6.13002e23 −0.312617
\(722\) 2.37845e23i 0.119875i
\(723\) 3.01167e23i 0.150014i
\(724\) −1.07200e24 −0.527738
\(725\) −2.07219e20 2.00784e22i −0.000100822 0.00976915i
\(726\) −1.72310e24 −0.828610
\(727\) 7.77376e23i 0.369478i 0.982788 + 0.184739i \(0.0591440\pi\)
−0.982788 + 0.184739i \(0.940856\pi\)
\(728\) 4.35799e23i 0.204724i
\(729\) −1.29218e24 −0.599983
\(730\) −8.50834e23 8.42098e23i −0.390482 0.386472i
\(731\) 3.18212e24 1.44351
\(732\) 2.73936e24i 1.22830i
\(733\) 2.62599e24i 1.16388i −0.813230 0.581942i \(-0.802293\pi\)
0.813230 0.581942i \(-0.197707\pi\)
\(734\) −1.38230e24 −0.605598
\(735\) −1.67317e24 + 1.69053e24i −0.724599 + 0.732116i
\(736\) 3.88449e23 0.166292
\(737\) 4.42708e24i 1.87346i
\(738\) 3.95384e23i 0.165402i
\(739\) 5.55636e23 0.229780 0.114890 0.993378i \(-0.463348\pi\)
0.114890 + 0.993378i \(0.463348\pi\)
\(740\) 4.78444e23 4.83407e23i 0.195597 0.197626i
\(741\) −1.84683e24 −0.746401
\(742\) 8.97217e22i 0.0358479i
\(743\) 5.15655e23i 0.203683i 0.994801 + 0.101841i \(0.0324734\pi\)
−0.994801 + 0.101841i \(0.967527\pi\)
\(744\) −1.71157e24 −0.668383
\(745\) 6.76317e23 + 6.69373e23i 0.261109 + 0.258428i
\(746\) 1.12324e24 0.428739
\(747\) 9.37173e23i 0.353667i
\(748\) 4.99059e24i 1.86204i
\(749\) 2.04607e23 0.0754788
\(750\) 1.17238e24 1.20925e24i 0.427609 0.441057i
\(751\) 3.82210e24 1.37836 0.689180 0.724590i \(-0.257971\pi\)
0.689180 + 0.724590i \(0.257971\pi\)
\(752\) 8.33414e23i 0.297173i
\(753\) 2.21795e24i 0.781978i
\(754\) 1.14382e22 0.00398750
\(755\) −2.57723e24 2.55077e24i −0.888390 0.879269i
\(756\) 4.98865e23 0.170039
\(757\) 3.94460e24i 1.32950i −0.747067 0.664749i \(-0.768538\pi\)
0.747067 0.664749i \(-0.231462\pi\)
\(758\) 9.13682e23i 0.304514i
\(759\) −8.42206e23 −0.277564
\(760\) −1.76849e24 + 1.78683e24i −0.576350 + 0.582329i
\(761\) −3.70043e23 −0.119257 −0.0596284 0.998221i \(-0.518992\pi\)
−0.0596284 + 0.998221i \(0.518992\pi\)
\(762\) 3.77137e23i 0.120194i
\(763\) 9.70512e23i 0.305874i
\(764\) 1.13711e24 0.354413
\(765\) −1.07268e24 + 1.08380e24i −0.330633 + 0.334063i
\(766\) 1.62262e23 0.0494620
\(767\) 3.12888e24i 0.943254i
\(768\) 3.10772e24i 0.926555i
\(769\) −1.11643e24 −0.329197 −0.164599 0.986361i \(-0.552633\pi\)
−0.164599 + 0.986361i \(0.552633\pi\)
\(770\) −5.99088e23 5.92937e23i −0.174711 0.172917i
\(771\) 5.28448e24 1.52419
\(772\) 3.97904e24i 1.13509i
\(773\) 4.91642e24i 1.38715i 0.720385 + 0.693574i \(0.243965\pi\)
−0.720385 + 0.693574i \(0.756035\pi\)
\(774\) 4.43779e23 0.123842