Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,2,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.82670423155\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.41542366334681088.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.9 | ||
Root | \(-1.64288 - 0.548592i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.2.c.a.353.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.64288 | − | 0.548592i | 0.948516 | − | 0.316730i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.54852i | 1.13973i | 0.821738 | + | 0.569865i | \(0.193005\pi\) | ||||
−0.821738 | + | 0.569865i | \(0.806995\pi\) | |||||||
\(6\) | −1.64288 | + | 0.548592i | −0.670702 | + | 0.223962i | ||||
\(7\) | −0.0900537 | −0.0340371 | −0.0170186 | − | 0.999855i | \(-0.505417\pi\) | ||||
−0.0170186 | + | 0.999855i | \(0.505417\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.39809 | − | 1.80254i | 0.799365 | − | 0.600846i | ||||
\(10\) | − | 2.54852i | − | 0.805911i | ||||||
\(11\) | 2.40488 | 0.725098 | 0.362549 | − | 0.931965i | \(-0.381907\pi\) | ||||
0.362549 | + | 0.931965i | \(0.381907\pi\) | |||||||
\(12\) | 1.64288 | − | 0.548592i | 0.474258 | − | 0.158365i | ||||
\(13\) | 2.81820i | 0.781628i | 0.920470 | + | 0.390814i | \(0.127806\pi\) | ||||
−0.920470 | + | 0.390814i | \(0.872194\pi\) | |||||||
\(14\) | 0.0900537 | 0.0240679 | ||||||||
\(15\) | 1.39809 | + | 4.18690i | 0.360986 | + | 1.08105i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.17124i | 0.769138i | 0.923096 | + | 0.384569i | \(0.125650\pi\) | ||||
−0.923096 | + | 0.384569i | \(0.874350\pi\) | |||||||
\(18\) | −2.39809 | + | 1.80254i | −0.565236 | + | 0.424862i | ||||
\(19\) | −2.49493 | −0.572376 | −0.286188 | − | 0.958173i | \(-0.592388\pi\) | ||||
−0.286188 | + | 0.958173i | \(0.592388\pi\) | |||||||
\(20\) | 2.54852i | 0.569865i | ||||||||
\(21\) | −0.147947 | + | 0.0494027i | −0.0322847 | + | 0.0107806i | ||||
\(22\) | −2.40488 | −0.512721 | ||||||||
\(23\) | 3.09208 | 0.644744 | 0.322372 | − | 0.946613i | \(-0.395520\pi\) | ||||
0.322372 | + | 0.946613i | \(0.395520\pi\) | |||||||
\(24\) | −1.64288 | + | 0.548592i | −0.335351 | + | 0.111981i | ||||
\(25\) | −1.49493 | −0.298986 | ||||||||
\(26\) | − | 2.81820i | − | 0.552695i | ||||||
\(27\) | 2.95092 | − | 4.27692i | 0.567904 | − | 0.823094i | ||||
\(28\) | −0.0900537 | −0.0170186 | ||||||||
\(29\) | − | 6.21894i | − | 1.15483i | −0.816451 | − | 0.577414i | \(-0.804062\pi\) | ||
0.816451 | − | 0.577414i | \(-0.195938\pi\) | |||||||
\(30\) | −1.39809 | − | 4.18690i | −0.255256 | − | 0.764420i | ||||
\(31\) | − | 2.16964i | − | 0.389679i | −0.980835 | − | 0.194839i | \(-0.937581\pi\) | ||
0.980835 | − | 0.194839i | \(-0.0624186\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.95092 | − | 1.31930i | 0.687767 | − | 0.229660i | ||||
\(34\) | − | 3.17124i | − | 0.543863i | ||||||
\(35\) | − | 0.229503i | − | 0.0387931i | ||||||
\(36\) | 2.39809 | − | 1.80254i | 0.399682 | − | 0.300423i | ||||
\(37\) | 11.5857i | 1.90467i | 0.305054 | + | 0.952335i | \(0.401326\pi\) | ||||
−0.305054 | + | 0.952335i | \(0.598674\pi\) | |||||||
\(38\) | 2.49493 | 0.404731 | ||||||||
\(39\) | 1.54604 | + | 4.62996i | 0.247565 | + | 0.741387i | ||||
\(40\) | − | 2.54852i | − | 0.402956i | ||||||
\(41\) | − | 0.762149i | − | 0.119028i | −0.998227 | − | 0.0595138i | \(-0.981045\pi\) | ||
0.998227 | − | 0.0595138i | \(-0.0189550\pi\) | |||||||
\(42\) | 0.147947 | − | 0.0494027i | 0.0228288 | − | 0.00762301i | ||||
\(43\) | − | 7.62643i | − | 1.16302i | −0.813539 | − | 0.581510i | \(-0.802462\pi\) | ||
0.813539 | − | 0.581510i | \(-0.197538\pi\) | |||||||
\(44\) | 2.40488 | 0.362549 | ||||||||
\(45\) | 4.59380 | + | 6.11158i | 0.684803 | + | 0.911061i | ||||
\(46\) | −3.09208 | −0.455903 | ||||||||
\(47\) | 7.90184 | 1.15260 | 0.576301 | − | 0.817238i | \(-0.304496\pi\) | ||||
0.576301 | + | 0.817238i | \(0.304496\pi\) | |||||||
\(48\) | 1.64288 | − | 0.548592i | 0.237129 | − | 0.0791824i | ||||
\(49\) | −6.99189 | −0.998841 | ||||||||
\(50\) | 1.49493 | 0.211415 | ||||||||
\(51\) | 1.73971 | + | 5.20995i | 0.243609 | + | 0.729539i | ||||
\(52\) | 2.81820i | 0.390814i | ||||||||
\(53\) | − | 3.58035i | − | 0.491799i | −0.969295 | − | 0.245899i | \(-0.920917\pi\) | ||
0.969295 | − | 0.245899i | \(-0.0790833\pi\) | |||||||
\(54\) | −2.95092 | + | 4.27692i | −0.401569 | + | 0.582016i | ||||
\(55\) | 6.12887i | 0.826416i | ||||||||
\(56\) | 0.0900537 | 0.0120339 | ||||||||
\(57\) | −4.09887 | + | 1.36870i | −0.542908 | + | 0.181288i | ||||
\(58\) | 6.21894i | 0.816587i | ||||||||
\(59\) | −7.57687 | + | 1.26134i | −0.986425 | + | 0.164212i | ||||
\(60\) | 1.39809 | + | 4.18690i | 0.180493 | + | 0.540526i | ||||
\(61\) | − | 3.56445i | − | 0.456382i | −0.973616 | − | 0.228191i | \(-0.926719\pi\) | ||
0.973616 | − | 0.228191i | \(-0.0732810\pi\) | |||||||
\(62\) | 2.16964i | 0.275545i | ||||||||
\(63\) | −0.215957 | + | 0.162325i | −0.0272081 | + | 0.0204511i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.18223 | −0.890846 | ||||||||
\(66\) | −3.95092 | + | 1.31930i | −0.486324 | + | 0.162394i | ||||
\(67\) | − | 14.5015i | − | 1.77165i | −0.464023 | − | 0.885823i | \(-0.653595\pi\) | ||
0.464023 | − | 0.885823i | \(-0.346405\pi\) | |||||||
\(68\) | 3.17124i | 0.384569i | ||||||||
\(69\) | 5.07991 | − | 1.69629i | 0.611550 | − | 0.204209i | ||||
\(70\) | 0.229503i | 0.0274309i | ||||||||
\(71\) | 4.84841i | 0.575401i | 0.957720 | + | 0.287700i | \(0.0928907\pi\) | ||||
−0.957720 | + | 0.287700i | \(0.907109\pi\) | |||||||
\(72\) | −2.39809 | + | 1.80254i | −0.282618 | + | 0.212431i | ||||
\(73\) | − | 6.03117i | − | 0.705895i | −0.935643 | − | 0.352948i | \(-0.885179\pi\) | ||
0.935643 | − | 0.352948i | \(-0.114821\pi\) | |||||||
\(74\) | − | 11.5857i | − | 1.34681i | ||||||
\(75\) | −2.45599 | + | 0.820106i | −0.283593 | + | 0.0946977i | ||||
\(76\) | −2.49493 | −0.286188 | ||||||||
\(77\) | −0.216568 | −0.0246802 | ||||||||
\(78\) | −1.54604 | − | 4.62996i | −0.175055 | − | 0.524240i | ||||
\(79\) | −11.0840 | −1.24704 | −0.623522 | − | 0.781806i | \(-0.714299\pi\) | ||||
−0.623522 | + | 0.781806i | \(0.714299\pi\) | |||||||
\(80\) | 2.54852i | 0.284933i | ||||||||
\(81\) | 2.50171 | − | 8.64531i | 0.277968 | − | 0.960590i | ||||
\(82\) | 0.762149i | 0.0841653i | ||||||||
\(83\) | −1.68527 | −0.184982 | −0.0924911 | − | 0.995714i | \(-0.529483\pi\) | ||||
−0.0924911 | + | 0.995714i | \(0.529483\pi\) | |||||||
\(84\) | −0.147947 | + | 0.0494027i | −0.0161424 | + | 0.00539028i | ||||
\(85\) | −8.08194 | −0.876610 | ||||||||
\(86\) | 7.62643i | 0.822379i | ||||||||
\(87\) | −3.41166 | − | 10.2170i | −0.365768 | − | 1.09537i | ||||
\(88\) | −2.40488 | −0.256361 | ||||||||
\(89\) | −8.62144 | −0.913871 | −0.456936 | − | 0.889500i | \(-0.651053\pi\) | ||||
−0.456936 | + | 0.889500i | \(0.651053\pi\) | |||||||
\(90\) | −4.59380 | − | 6.11158i | −0.484229 | − | 0.644217i | ||||
\(91\) | − | 0.253790i | − | 0.0266044i | ||||||
\(92\) | 3.09208 | 0.322372 | ||||||||
\(93\) | −1.19025 | − | 3.56445i | −0.123423 | − | 0.369617i | ||||
\(94\) | −7.90184 | −0.815012 | ||||||||
\(95\) | − | 6.35837i | − | 0.652355i | ||||||
\(96\) | −1.64288 | + | 0.548592i | −0.167676 | + | 0.0559904i | ||||
\(97\) | − | 0.394771i | − | 0.0400829i | −0.999799 | − | 0.0200415i | \(-0.993620\pi\) | ||
0.999799 | − | 0.0200415i | \(-0.00637982\pi\) | |||||||
\(98\) | 6.99189 | 0.706288 | ||||||||
\(99\) | 5.76712 | − | 4.33488i | 0.579617 | − | 0.435672i | ||||
\(100\) | −1.49493 | −0.149493 | ||||||||
\(101\) | −6.21657 | −0.618572 | −0.309286 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309286 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(102\) | −1.73971 | − | 5.20995i | −0.172257 | − | 0.515862i | ||||
\(103\) | 9.59563i | 0.945485i | 0.881201 | + | 0.472743i | \(0.156736\pi\) | ||||
−0.881201 | + | 0.472743i | \(0.843264\pi\) | |||||||
\(104\) | − | 2.81820i | − | 0.276347i | ||||||
\(105\) | −0.125904 | − | 0.377046i | −0.0122869 | − | 0.0367959i | ||||
\(106\) | 3.58035i | 0.347754i | ||||||||
\(107\) | − | 7.04711i | − | 0.681270i | −0.940196 | − | 0.340635i | \(-0.889358\pi\) | ||
0.940196 | − | 0.340635i | \(-0.110642\pi\) | |||||||
\(108\) | 2.95092 | − | 4.27692i | 0.283952 | − | 0.411547i | ||||
\(109\) | − | 10.0881i | − | 0.966264i | −0.875548 | − | 0.483132i | \(-0.839499\pi\) | ||
0.875548 | − | 0.483132i | \(-0.160501\pi\) | |||||||
\(110\) | − | 6.12887i | − | 0.584364i | ||||||
\(111\) | 6.35579 | + | 19.0338i | 0.603265 | + | 1.80661i | ||||
\(112\) | −0.0900537 | −0.00850928 | ||||||||
\(113\) | −13.2519 | −1.24664 | −0.623318 | − | 0.781969i | \(-0.714216\pi\) | ||||
−0.623318 | + | 0.781969i | \(0.714216\pi\) | |||||||
\(114\) | 4.09887 | − | 1.36870i | 0.383894 | − | 0.128190i | ||||
\(115\) | 7.88022i | 0.734834i | ||||||||
\(116\) | − | 6.21894i | − | 0.577414i | ||||||
\(117\) | 5.07991 | + | 6.75831i | 0.469638 | + | 0.624806i | ||||
\(118\) | 7.57687 | − | 1.26134i | 0.697508 | − | 0.116116i | ||||
\(119\) | − | 0.285582i | − | 0.0261792i | ||||||
\(120\) | −1.39809 | − | 4.18690i | −0.127628 | − | 0.382210i | ||||
\(121\) | −5.21657 | −0.474233 | ||||||||
\(122\) | 3.56445i | 0.322710i | ||||||||
\(123\) | −0.418109 | − | 1.25212i | −0.0376996 | − | 0.112900i | ||||
\(124\) | − | 2.16964i | − | 0.194839i | ||||||
\(125\) | 8.93272i | 0.798967i | ||||||||
\(126\) | 0.215957 | − | 0.162325i | 0.0192390 | − | 0.0144611i | ||||
\(127\) | −2.96557 | −0.263152 | −0.131576 | − | 0.991306i | \(-0.542004\pi\) | ||||
−0.131576 | + | 0.991306i | \(0.542004\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.18380 | − | 12.5293i | −0.368363 | − | 1.10314i | ||||
\(130\) | 7.18223 | 0.629923 | ||||||||
\(131\) | 5.28039 | 0.461350 | 0.230675 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230675 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(132\) | 3.95092 | − | 1.31930i | 0.343883 | − | 0.114830i | ||||
\(133\) | 0.224678 | 0.0194820 | ||||||||
\(134\) | 14.5015i | 1.25274i | ||||||||
\(135\) | 10.8998 | + | 7.52046i | 0.938106 | + | 0.647258i | ||||
\(136\) | − | 3.17124i | − | 0.271931i | ||||||
\(137\) | − | 8.64237i | − | 0.738368i | −0.929356 | − | 0.369184i | \(-0.879637\pi\) | ||
0.929356 | − | 0.369184i | \(-0.120363\pi\) | |||||||
\(138\) | −5.07991 | + | 1.69629i | −0.432431 | + | 0.144398i | ||||
\(139\) | 1.00194 | 0.0849833 | 0.0424916 | − | 0.999097i | \(-0.486470\pi\) | ||||
0.0424916 | + | 0.999097i | \(0.486470\pi\) | |||||||
\(140\) | − | 0.229503i | − | 0.0193966i | ||||||
\(141\) | 12.9818 | − | 4.33488i | 1.09326 | − | 0.365063i | ||||
\(142\) | − | 4.84841i | − | 0.406870i | ||||||
\(143\) | 6.77743i | 0.566757i | ||||||||
\(144\) | 2.39809 | − | 1.80254i | 0.199841 | − | 0.150212i | ||||
\(145\) | 15.8491 | 1.31619 | ||||||||
\(146\) | 6.03117i | 0.499143i | ||||||||
\(147\) | −11.4868 | + | 3.83569i | −0.947417 | + | 0.316363i | ||||
\(148\) | 11.5857i | 0.952335i | ||||||||
\(149\) | −21.1213 | −1.73033 | −0.865164 | − | 0.501489i | \(-0.832786\pi\) | ||||
−0.865164 | + | 0.501489i | \(0.832786\pi\) | |||||||
\(150\) | 2.45599 | − | 0.820106i | 0.200531 | − | 0.0669614i | ||||
\(151\) | 18.8555i | 1.53444i | 0.641383 | + | 0.767221i | \(0.278361\pi\) | ||||
−0.641383 | + | 0.767221i | \(0.721639\pi\) | |||||||
\(152\) | 2.49493 | 0.202366 | ||||||||
\(153\) | 5.71627 | + | 7.60492i | 0.462133 | + | 0.614822i | ||||
\(154\) | 0.216568 | 0.0174516 | ||||||||
\(155\) | 5.52936 | 0.444129 | ||||||||
\(156\) | 1.54604 | + | 4.62996i | 0.123782 | + | 0.370693i | ||||
\(157\) | − | 15.3653i | − | 1.22628i | −0.789973 | − | 0.613141i | \(-0.789906\pi\) | ||
0.789973 | − | 0.613141i | \(-0.210094\pi\) | |||||||
\(158\) | 11.0840 | 0.881794 | ||||||||
\(159\) | −1.96415 | − | 5.88208i | −0.155767 | − | 0.466479i | ||||
\(160\) | − | 2.54852i | − | 0.201478i | ||||||
\(161\) | −0.278454 | −0.0219452 | ||||||||
\(162\) | −2.50171 | + | 8.64531i | −0.196553 | + | 0.679240i | ||||
\(163\) | 22.4341 | 1.75718 | 0.878589 | − | 0.477579i | \(-0.158486\pi\) | ||||
0.878589 | + | 0.477579i | \(0.158486\pi\) | |||||||
\(164\) | − | 0.762149i | − | 0.0595138i | ||||||
\(165\) | 3.36224 | + | 10.0690i | 0.261750 | + | 0.783869i | ||||
\(166\) | 1.68527 | 0.130802 | ||||||||
\(167\) | 14.3138i | 1.10763i | 0.832639 | + | 0.553817i | \(0.186829\pi\) | ||||
−0.832639 | + | 0.553817i | \(0.813171\pi\) | |||||||
\(168\) | 0.147947 | − | 0.0494027i | 0.0114144 | − | 0.00381150i | ||||
\(169\) | 5.05774 | 0.389057 | ||||||||
\(170\) | 8.08194 | 0.619857 | ||||||||
\(171\) | −5.98308 | + | 4.49721i | −0.457537 | + | 0.343910i | ||||
\(172\) | − | 7.62643i | − | 0.581510i | ||||||
\(173\) | 4.77735 | 0.363215 | 0.181608 | − | 0.983371i | \(-0.441870\pi\) | ||||
0.181608 | + | 0.983371i | \(0.441870\pi\) | |||||||
\(174\) | 3.41166 | + | 10.2170i | 0.258637 | + | 0.774546i | ||||
\(175\) | 0.134624 | 0.0101766 | ||||||||
\(176\) | 2.40488 | 0.181274 | ||||||||
\(177\) | −11.7559 | + | 6.22883i | −0.883629 | + | 0.468188i | ||||
\(178\) | 8.62144 | 0.646205 | ||||||||
\(179\) | 0.495022 | 0.0369997 | 0.0184998 | − | 0.999829i | \(-0.494111\pi\) | ||||
0.0184998 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(180\) | 4.59380 | + | 6.11158i | 0.342401 | + | 0.455530i | ||||
\(181\) | 19.6569 | 1.46108 | 0.730542 | − | 0.682868i | \(-0.239267\pi\) | ||||
0.730542 | + | 0.682868i | \(0.239267\pi\) | |||||||
\(182\) | 0.253790i | 0.0188121i | ||||||||
\(183\) | −1.95543 | − | 5.85596i | −0.144550 | − | 0.432885i | ||||
\(184\) | −3.09208 | −0.227951 | ||||||||
\(185\) | −29.5262 | −2.17081 | ||||||||
\(186\) | 1.19025 | + | 3.56445i | 0.0872731 | + | 0.261358i | ||||
\(187\) | 7.62643i | 0.557700i | ||||||||
\(188\) | 7.90184 | 0.576301 | ||||||||
\(189\) | −0.265741 | + | 0.385153i | −0.0193298 | + | 0.0280158i | ||||
\(190\) | 6.35837i | 0.461285i | ||||||||
\(191\) | 24.2458 | 1.75437 | 0.877183 | − | 0.480155i | \(-0.159420\pi\) | ||||
0.877183 | + | 0.480155i | \(0.159420\pi\) | |||||||
\(192\) | 1.64288 | − | 0.548592i | 0.118564 | − | 0.0395912i | ||||
\(193\) | 7.81178 | 0.562304 | 0.281152 | − | 0.959663i | \(-0.409283\pi\) | ||||
0.281152 | + | 0.959663i | \(0.409283\pi\) | |||||||
\(194\) | 0.394771i | 0.0283429i | ||||||||
\(195\) | −11.7995 | + | 3.94011i | −0.844981 | + | 0.282157i | ||||
\(196\) | −6.99189 | −0.499421 | ||||||||
\(197\) | − | 14.1485i | − | 1.00804i | −0.863692 | − | 0.504020i | \(-0.831854\pi\) | ||
0.863692 | − | 0.504020i | \(-0.168146\pi\) | |||||||
\(198\) | −5.76712 | + | 4.33488i | −0.409851 | + | 0.308067i | ||||
\(199\) | 7.12946 | 0.505394 | 0.252697 | − | 0.967545i | \(-0.418682\pi\) | ||||
0.252697 | + | 0.967545i | \(0.418682\pi\) | |||||||
\(200\) | 1.49493 | 0.105708 | ||||||||
\(201\) | −7.95543 | − | 23.8243i | −0.561133 | − | 1.68043i | ||||
\(202\) | 6.21657 | 0.437396 | ||||||||
\(203\) | 0.560039i | 0.0393070i | ||||||||
\(204\) | 1.73971 | + | 5.20995i | 0.121804 | + | 0.364770i | ||||
\(205\) | 1.94235 | 0.135659 | ||||||||
\(206\) | − | 9.59563i | − | 0.668559i | ||||||
\(207\) | 7.41511 | − | 5.57360i | 0.515386 | − | 0.387392i | ||||
\(208\) | 2.81820i | 0.195407i | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0.125904 | + | 0.377046i | 0.00868818 | + | 0.0260186i | ||||
\(211\) | − | 18.1479i | − | 1.24935i | −0.780883 | − | 0.624677i | \(-0.785231\pi\) | ||
0.780883 | − | 0.624677i | \(-0.214769\pi\) | |||||||
\(212\) | − | 3.58035i | − | 0.245899i | ||||||
\(213\) | 2.65980 | + | 7.96535i | 0.182246 | + | 0.545777i | ||||
\(214\) | 7.04711i | 0.481731i | ||||||||
\(215\) | 19.4361 | 1.32553 | ||||||||
\(216\) | −2.95092 | + | 4.27692i | −0.200785 | + | 0.291008i | ||||
\(217\) | 0.195384i | 0.0132635i | ||||||||
\(218\) | 10.0881i | 0.683252i | ||||||||
\(219\) | −3.30865 | − | 9.90848i | −0.223578 | − | 0.669553i | ||||
\(220\) | 6.12887i | 0.413208i | ||||||||
\(221\) | −8.93718 | −0.601180 | ||||||||
\(222\) | −6.35579 | − | 19.0338i | −0.426573 | − | 1.27747i | ||||
\(223\) | 19.4889 | 1.30508 | 0.652538 | − | 0.757756i | \(-0.273704\pi\) | ||||
0.652538 | + | 0.757756i | \(0.273704\pi\) | |||||||
\(224\) | 0.0900537 | 0.00601697 | ||||||||
\(225\) | −3.58498 | + | 2.69467i | −0.238999 | + | 0.179645i | ||||
\(226\) | 13.2519 | 0.881504 | ||||||||
\(227\) | 1.03534 | 0.0687182 | 0.0343591 | − | 0.999410i | \(-0.489061\pi\) | ||||
0.0343591 | + | 0.999410i | \(0.489061\pi\) | |||||||
\(228\) | −4.09887 | + | 1.36870i | −0.271454 | + | 0.0906442i | ||||
\(229\) | 10.7961i | 0.713427i | 0.934214 | + | 0.356714i | \(0.116103\pi\) | ||||
−0.934214 | + | 0.356714i | \(0.883897\pi\) | |||||||
\(230\) | − | 7.88022i | − | 0.519606i | ||||||
\(231\) | −0.355795 | + | 0.118807i | −0.0234096 | + | 0.00781696i | ||||
\(232\) | 6.21894i | 0.408293i | ||||||||
\(233\) | 9.44022 | 0.618449 | 0.309225 | − | 0.950989i | \(-0.399930\pi\) | ||||
0.309225 | + | 0.950989i | \(0.399930\pi\) | |||||||
\(234\) | −5.07991 | − | 6.75831i | −0.332084 | − | 0.441805i | ||||
\(235\) | 20.1380i | 1.31366i | ||||||||
\(236\) | −7.57687 | + | 1.26134i | −0.493213 | + | 0.0821061i | ||||
\(237\) | −18.2096 | + | 6.08058i | −1.18284 | + | 0.394976i | ||||
\(238\) | 0.285582i | 0.0185115i | ||||||||
\(239\) | − | 10.1040i | − | 0.653573i | −0.945098 | − | 0.326786i | \(-0.894034\pi\) | ||
0.945098 | − | 0.326786i | \(-0.105966\pi\) | |||||||
\(240\) | 1.39809 | + | 4.18690i | 0.0902466 | + | 0.270263i | ||||
\(241\) | −16.8918 | −1.08810 | −0.544048 | − | 0.839054i | \(-0.683109\pi\) | ||||
−0.544048 | + | 0.839054i | \(0.683109\pi\) | |||||||
\(242\) | 5.21657 | 0.335334 | ||||||||
\(243\) | −0.632739 | − | 15.5756i | −0.0405902 | − | 0.999176i | ||||
\(244\) | − | 3.56445i | − | 0.228191i | ||||||
\(245\) | − | 17.8189i | − | 1.13841i | ||||||
\(246\) | 0.418109 | + | 1.25212i | 0.0266576 | + | 0.0798321i | ||||
\(247\) | − | 7.03122i | − | 0.447386i | ||||||
\(248\) | 2.16964i | 0.137772i | ||||||||
\(249\) | −2.76869 | + | 0.924524i | −0.175459 | + | 0.0585893i | ||||
\(250\) | − | 8.93272i | − | 0.564955i | ||||||
\(251\) | 23.6479i | 1.49264i | 0.665587 | + | 0.746320i | \(0.268181\pi\) | ||||
−0.665587 | + | 0.746320i | \(0.731819\pi\) | |||||||
\(252\) | −0.215957 | + | 0.162325i | −0.0136040 | + | 0.0102255i | ||||
\(253\) | 7.43608 | 0.467502 | ||||||||
\(254\) | 2.96557 | 0.186076 | ||||||||
\(255\) | −13.2776 | + | 4.43369i | −0.831478 | + | 0.277648i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 22.4410i | − | 1.39983i | −0.714227 | − | 0.699914i | \(-0.753222\pi\) | ||
0.714227 | − | 0.699914i | \(-0.246778\pi\) | |||||||
\(258\) | 4.18380 | + | 12.5293i | 0.260472 | + | 0.780040i | ||||
\(259\) | − | 1.04333i | − | 0.0648295i | ||||||
\(260\) | −7.18223 | −0.445423 | ||||||||
\(261\) | −11.2099 | − | 14.9136i | −0.693874 | − | 0.923129i | ||||
\(262\) | −5.28039 | −0.326224 | ||||||||
\(263\) | 1.14864i | 0.0708282i | 0.999373 | + | 0.0354141i | \(0.0112750\pi\) | ||||
−0.999373 | + | 0.0354141i | \(0.988725\pi\) | |||||||
\(264\) | −3.95092 | + | 1.31930i | −0.243162 | + | 0.0811970i | ||||
\(265\) | 9.12458 | 0.560518 | ||||||||
\(266\) | −0.224678 | −0.0137759 | ||||||||
\(267\) | −14.1640 | + | 4.72965i | −0.866821 | + | 0.289450i | ||||
\(268\) | − | 14.5015i | − | 0.885823i | ||||||
\(269\) | −9.58711 | −0.584536 | −0.292268 | − | 0.956336i | \(-0.594410\pi\) | ||||
−0.292268 | + | 0.956336i | \(0.594410\pi\) | |||||||
\(270\) | −10.8998 | − | 7.52046i | −0.663341 | − | 0.457681i | ||||
\(271\) | −10.6508 | −0.646992 | −0.323496 | − | 0.946229i | \(-0.604858\pi\) | ||||
−0.323496 | + | 0.946229i | \(0.604858\pi\) | |||||||
\(272\) | 3.17124i | 0.192284i | ||||||||
\(273\) | −0.139227 | − | 0.416945i | −0.00842639 | − | 0.0252347i | ||||
\(274\) | 8.64237i | 0.522105i | ||||||||
\(275\) | −3.59512 | −0.216794 | ||||||||
\(276\) | 5.07991 | − | 1.69629i | 0.305775 | − | 0.102105i | ||||
\(277\) | −22.3887 | −1.34521 | −0.672605 | − | 0.740002i | \(-0.734825\pi\) | ||||
−0.672605 | + | 0.740002i | \(0.734825\pi\) | |||||||
\(278\) | −1.00194 | −0.0600923 | ||||||||
\(279\) | −3.91086 | − | 5.20300i | −0.234137 | − | 0.311496i | ||||
\(280\) | 0.229503i | 0.0137154i | ||||||||
\(281\) | 31.5953i | 1.88482i | 0.334463 | + | 0.942409i | \(0.391445\pi\) | ||||
−0.334463 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(282\) | −12.9818 | + | 4.33488i | −0.773052 | + | 0.258138i | ||||
\(283\) | 9.11894i | 0.542065i | 0.962570 | + | 0.271032i | \(0.0873650\pi\) | ||||
−0.962570 | + | 0.271032i | \(0.912635\pi\) | |||||||
\(284\) | 4.84841i | 0.287700i | ||||||||
\(285\) | −3.48815 | − | 10.4460i | −0.206620 | − | 0.618769i | ||||
\(286\) | − | 6.77743i | − | 0.400758i | ||||||
\(287\) | 0.0686344i | 0.00405136i | ||||||||
\(288\) | −2.39809 | + | 1.80254i | −0.141309 | + | 0.106216i | ||||
\(289\) | 6.94326 | 0.408427 | ||||||||
\(290\) | −15.8491 | −0.930689 | ||||||||
\(291\) | −0.216568 | − | 0.648561i | −0.0126954 | − | 0.0380193i | ||||
\(292\) | − | 6.03117i | − | 0.352948i | ||||||
\(293\) | 24.3784i | 1.42420i | 0.702079 | + | 0.712099i | \(0.252256\pi\) | ||||
−0.702079 | + | 0.712099i | \(0.747744\pi\) | |||||||
\(294\) | 11.4868 | − | 3.83569i | 0.669925 | − | 0.223702i | ||||
\(295\) | −3.21454 | − | 19.3098i | −0.187158 | − | 1.12426i | ||||
\(296\) | − | 11.5857i | − | 0.673403i | ||||||
\(297\) | 7.09659 | − | 10.2855i | 0.411786 | − | 0.596824i | ||||
\(298\) | 21.1213 | 1.22353 | ||||||||
\(299\) | 8.71411i | 0.503950i | ||||||||
\(300\) | −2.45599 | + | 0.820106i | −0.141797 | + | 0.0473489i | ||||
\(301\) | 0.686789i | 0.0395858i | ||||||||
\(302\) | − | 18.8555i | − | 1.08501i | ||||||
\(303\) | −10.2131 | + | 3.41036i | −0.586725 | + | 0.195920i | ||||
\(304\) | −2.49493 | −0.143094 | ||||||||
\(305\) | 9.08406 | 0.520152 | ||||||||
\(306\) | −5.71627 | − | 7.60492i | −0.326778 | − | 0.434745i | ||||
\(307\) | 8.37649 | 0.478071 | 0.239036 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239036 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(308\) | −0.216568 | −0.0123401 | ||||||||
\(309\) | 5.26408 | + | 15.7644i | 0.299463 | + | 0.896808i | ||||
\(310\) | −5.52936 | −0.314047 | ||||||||
\(311\) | − | 27.9904i | − | 1.58719i | −0.608447 | − | 0.793594i | \(-0.708207\pi\) | ||
0.608447 | − | 0.793594i | \(-0.291793\pi\) | |||||||
\(312\) | −1.54604 | − | 4.62996i | −0.0875274 | − | 0.262120i | ||||
\(313\) | 13.0090i | 0.735315i | 0.929961 | + | 0.367657i | \(0.119840\pi\) | ||||
−0.929961 | + | 0.367657i | \(0.880160\pi\) | |||||||
\(314\) | 15.3653i | 0.867112i | ||||||||
\(315\) | −0.413689 | − | 0.550371i | −0.0233087 | − | 0.0310099i | ||||
\(316\) | −11.0840 | −0.623522 | ||||||||
\(317\) | 14.2111i | 0.798174i | 0.916913 | + | 0.399087i | \(0.130673\pi\) | ||||
−0.916913 | + | 0.399087i | \(0.869327\pi\) | |||||||
\(318\) | 1.96415 | + | 5.88208i | 0.110144 | + | 0.329850i | ||||
\(319\) | − | 14.9558i | − | 0.837363i | ||||||
\(320\) | 2.54852i | 0.142466i | ||||||||
\(321\) | −3.86599 | − | 11.5775i | −0.215778 | − | 0.646195i | ||||
\(322\) | 0.278454 | 0.0155176 | ||||||||
\(323\) | − | 7.91201i | − | 0.440236i | ||||||
\(324\) | 2.50171 | − | 8.64531i | 0.138984 | − | 0.480295i | ||||
\(325\) | − | 4.21301i | − | 0.233696i | ||||||
\(326\) | −22.4341 | −1.24251 | ||||||||
\(327\) | −5.53424 | − | 16.5735i | −0.306044 | − | 0.916517i | ||||
\(328\) | 0.762149i | 0.0420826i | ||||||||
\(329\) | −0.711590 | −0.0392312 | ||||||||
\(330\) | −3.36224 | − | 10.0690i | −0.185085 | − | 0.554279i | ||||
\(331\) | −22.8299 | −1.25484 | −0.627422 | − | 0.778679i | \(-0.715890\pi\) | ||||
−0.627422 | + | 0.778679i | \(0.715890\pi\) | |||||||
\(332\) | −1.68527 | −0.0924911 | ||||||||
\(333\) | 20.8836 | + | 27.7835i | 1.14441 | + | 1.52253i | ||||
\(334\) | − | 14.3138i | − | 0.783215i | ||||||
\(335\) | 36.9574 | 2.01920 | ||||||||
\(336\) | −0.147947 | + | 0.0494027i | −0.00807119 | + | 0.00269514i | ||||
\(337\) | 24.9076i | 1.35680i | 0.734692 | + | 0.678400i | \(0.237327\pi\) | ||||
−0.734692 | + | 0.678400i | \(0.762673\pi\) | |||||||
\(338\) | −5.05774 | −0.275105 | ||||||||
\(339\) | −21.7713 | + | 7.26989i | −1.18245 | + | 0.394846i | ||||
\(340\) | −8.08194 | −0.438305 | ||||||||
\(341\) | − | 5.21772i | − | 0.282555i | ||||||
\(342\) | 5.98308 | − | 4.49721i | 0.323528 | − | 0.243181i | ||||
\(343\) | 1.26002 | 0.0680348 | ||||||||
\(344\) | 7.62643i | 0.411190i | ||||||||
\(345\) | 4.32302 | + | 12.9462i | 0.232744 | + | 0.697002i | ||||
\(346\) | −4.77735 | −0.256832 | ||||||||
\(347\) | 26.9745 | 1.44807 | 0.724033 | − | 0.689766i | \(-0.242287\pi\) | ||||
0.724033 | + | 0.689766i | \(0.242287\pi\) | |||||||
\(348\) | −3.41166 | − | 10.2170i | −0.182884 | − | 0.547686i | ||||
\(349\) | − | 24.7901i | − | 1.32698i | −0.748184 | − | 0.663491i | \(-0.769074\pi\) | ||
0.748184 | − | 0.663491i | \(-0.230926\pi\) | |||||||
\(350\) | −0.134624 | −0.00719596 | ||||||||
\(351\) | 12.0532 | + | 8.31628i | 0.643354 | + | 0.443890i | ||||
\(352\) | −2.40488 | −0.128180 | ||||||||
\(353\) | 18.8958 | 1.00572 | 0.502860 | − | 0.864368i | \(-0.332281\pi\) | ||||
0.502860 | + | 0.864368i | \(0.332281\pi\) | |||||||
\(354\) | 11.7559 | − | 6.22883i | 0.624820 | − | 0.331059i | ||||
\(355\) | −12.3563 | −0.655802 | ||||||||
\(356\) | −8.62144 | −0.456936 | ||||||||
\(357\) | −0.156668 | − | 0.469176i | −0.00829174 | − | 0.0248314i | ||||
\(358\) | −0.495022 | −0.0261627 | ||||||||
\(359\) | − | 24.5978i | − | 1.29822i | −0.760694 | − | 0.649111i | \(-0.775141\pi\) | ||
0.760694 | − | 0.649111i | \(-0.224859\pi\) | |||||||
\(360\) | −4.59380 | − | 6.11158i | −0.242114 | − | 0.322109i | ||||
\(361\) | −12.7753 | −0.672385 | ||||||||
\(362\) | −19.6569 | −1.03314 | ||||||||
\(363\) | −8.57018 | + | 2.86177i | −0.449818 | + | 0.150204i | ||||
\(364\) | − | 0.253790i | − | 0.0133022i | ||||||
\(365\) | 15.3705 | 0.804531 | ||||||||
\(366\) | 1.95543 | + | 5.85596i | 0.102212 | + | 0.306096i | ||||
\(367\) | 19.6069i | 1.02347i | 0.859143 | + | 0.511735i | \(0.170997\pi\) | ||||
−0.859143 | + | 0.511735i | \(0.829003\pi\) | |||||||
\(368\) | 3.09208 | 0.161186 | ||||||||
\(369\) | −1.37380 | − | 1.82770i | −0.0715173 | − | 0.0951465i | ||||
\(370\) | 29.5262 | 1.53500 | ||||||||
\(371\) | 0.322424i | 0.0167394i | ||||||||
\(372\) | −1.19025 | − | 3.56445i | −0.0617114 | − | 0.184808i | ||||
\(373\) | −5.00294 | −0.259043 | −0.129521 | − | 0.991577i | \(-0.541344\pi\) | ||||
−0.129521 | + | 0.991577i | \(0.541344\pi\) | |||||||
\(374\) | − | 7.62643i | − | 0.394353i | ||||||
\(375\) | 4.90042 | + | 14.6754i | 0.253056 | + | 0.757833i | ||||
\(376\) | −7.90184 | −0.407506 | ||||||||
\(377\) | 17.5262 | 0.902646 | ||||||||
\(378\) | 0.265741 | − | 0.385153i | 0.0136683 | − | 0.0198101i | ||||
\(379\) | 1.41105 | 0.0724807 | 0.0362403 | − | 0.999343i | \(-0.488462\pi\) | ||||
0.0362403 | + | 0.999343i | \(0.488462\pi\) | |||||||
\(380\) | − | 6.35837i | − | 0.326177i | ||||||
\(381\) | −4.87207 | + | 1.62689i | −0.249604 | + | 0.0833479i | ||||
\(382\) | −24.2458 | −1.24052 | ||||||||
\(383\) | 32.4479i | 1.65801i | 0.559241 | + | 0.829005i | \(0.311093\pi\) | ||||
−0.559241 | + | 0.829005i | \(0.688907\pi\) | |||||||
\(384\) | −1.64288 | + | 0.548592i | −0.0838378 | + | 0.0279952i | ||||
\(385\) | − | 0.551927i | − | 0.0281288i | ||||||
\(386\) | −7.81178 | −0.397609 | ||||||||
\(387\) | −13.7469 | − | 18.2889i | −0.698796 | − | 0.929677i | ||||
\(388\) | − | 0.394771i | − | 0.0200415i | ||||||
\(389\) | 2.14262i | 0.108635i | 0.998524 | + | 0.0543176i | \(0.0172983\pi\) | ||||
−0.998524 | + | 0.0543176i | \(0.982702\pi\) | |||||||
\(390\) | 11.7995 | − | 3.94011i | 0.597492 | − | 0.199515i | ||||
\(391\) | 9.80573i | 0.495897i | ||||||||
\(392\) | 6.99189 | 0.353144 | ||||||||
\(393\) | 8.67504 | − | 2.89678i | 0.437598 | − | 0.146123i | ||||
\(394\) | 14.1485i | 0.712792i | ||||||||
\(395\) | − | 28.2477i | − | 1.42129i | ||||||
\(396\) | 5.76712 | − | 4.33488i | 0.289809 | − | 0.217836i | ||||
\(397\) | 24.1710i | 1.21311i | 0.795043 | + | 0.606553i | \(0.207448\pi\) | ||||
−0.795043 | + | 0.606553i | \(0.792552\pi\) | |||||||
\(398\) | −7.12946 | −0.357367 | ||||||||
\(399\) | 0.369118 | − | 0.123256i | 0.0184790 | − | 0.00617054i | ||||
\(400\) | −1.49493 | −0.0747465 | ||||||||
\(401\) | 13.4312 | 0.670722 | 0.335361 | − | 0.942090i | \(-0.391142\pi\) | ||||
0.335361 | + | 0.942090i | \(0.391142\pi\) | |||||||
\(402\) | 7.95543 | + | 23.8243i | 0.396781 | + | 1.18825i | ||||
\(403\) | 6.11448 | 0.304584 | ||||||||
\(404\) | −6.21657 | −0.309286 | ||||||||
\(405\) | 22.0327 | + | 6.37565i | 1.09481 | + | 0.316809i | ||||
\(406\) | − | 0.560039i | − | 0.0277943i | ||||||
\(407\) | 27.8621i | 1.38107i | ||||||||
\(408\) | −1.73971 | − | 5.20995i | −0.0861287 | − | 0.257931i | ||||
\(409\) | − | 0.0382281i | − | 0.00189026i | −1.00000 | 0.000945129i | \(-0.999699\pi\) | |||
1.00000 | 0.000945129i | \(-0.000300844\pi\) | ||||||||
\(410\) | −1.94235 | −0.0959257 | ||||||||
\(411\) | −4.74113 | − | 14.1984i | −0.233863 | − | 0.700353i | ||||
\(412\) | 9.59563i | 0.472743i | ||||||||
\(413\) | 0.682326 | − | 0.113588i | 0.0335751 | − | 0.00558931i | ||||
\(414\) | −7.41511 | + | 5.57360i | −0.364433 | + | 0.273927i | ||||
\(415\) | − | 4.29493i | − | 0.210830i | ||||||
\(416\) | − | 2.81820i | − | 0.138174i | ||||||
\(417\) | 1.64606 | − | 0.549655i | 0.0806080 | − | 0.0269167i | ||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −16.4059 | −0.801480 | −0.400740 | − | 0.916192i | \(-0.631247\pi\) | ||||
−0.400740 | + | 0.916192i | \(0.631247\pi\) | |||||||
\(420\) | −0.125904 | − | 0.377046i | −0.00614347 | − | 0.0183980i | ||||
\(421\) | − | 18.1688i | − | 0.885491i | −0.896647 | − | 0.442746i | \(-0.854005\pi\) | ||
0.896647 | − | 0.442746i | \(-0.145995\pi\) | |||||||
\(422\) | 18.1479i | 0.883427i | ||||||||
\(423\) | 18.9493 | − | 14.2434i | 0.921349 | − | 0.692536i | ||||
\(424\) | 3.58035i | 0.173877i | ||||||||
\(425\) | − | 4.74078i | − | 0.229961i | ||||||
\(426\) | −2.65980 | − | 7.96535i | −0.128868 | − | 0.385922i | ||||
\(427\) | 0.320992i | 0.0155339i | ||||||||
\(428\) | − | 7.04711i | − | 0.340635i | ||||||
\(429\) | 3.71804 | + | 11.1345i | 0.179509 | + | 0.537578i | ||||
\(430\) | −19.4361 | −0.937291 | ||||||||
\(431\) | 33.4322 | 1.61037 | 0.805186 | − | 0.593022i | \(-0.202065\pi\) | ||||
0.805186 | + | 0.593022i | \(0.202065\pi\) | |||||||
\(432\) | 2.95092 | − | 4.27692i | 0.141976 | − | 0.205774i | ||||
\(433\) | 13.7095 | 0.658835 | 0.329418 | − | 0.944184i | \(-0.393148\pi\) | ||||
0.329418 | + | 0.944184i | \(0.393148\pi\) | |||||||
\(434\) | − | 0.195384i | − | 0.00937874i | ||||||
\(435\) | 26.0381 | − | 8.69467i | 1.24843 | − | 0.416877i | ||||
\(436\) | − | 10.0881i | − | 0.483132i | ||||||
\(437\) | −7.71453 | −0.369036 | ||||||||
\(438\) | 3.30865 | + | 9.90848i | 0.158093 | + | 0.473445i | ||||
\(439\) | −35.8086 | −1.70905 | −0.854526 | − | 0.519409i | \(-0.826152\pi\) | ||||
−0.854526 | + | 0.519409i | \(0.826152\pi\) | |||||||
\(440\) | − | 6.12887i | − | 0.292182i | ||||||
\(441\) | −16.7672 | + | 12.6031i | −0.798439 | + | 0.600150i | ||||
\(442\) | 8.93718 | 0.425098 | ||||||||
\(443\) | −9.77441 | −0.464396 | −0.232198 | − | 0.972669i | \(-0.574592\pi\) | ||||
−0.232198 | + | 0.972669i | \(0.574592\pi\) | |||||||
\(444\) | 6.35579 | + | 19.0338i | 0.301633 | + | 0.903305i | ||||
\(445\) | − | 21.9719i | − | 1.04157i | ||||||
\(446\) | −19.4889 | −0.922828 | ||||||||
\(447\) | −34.6998 | + | 11.5870i | −1.64124 | + | 0.548046i | ||||
\(448\) | −0.0900537 | −0.00425464 | ||||||||
\(449\) | 21.4713i | 1.01329i | 0.862154 | + | 0.506646i | \(0.169115\pi\) | ||||
−0.862154 | + | 0.506646i | \(0.830885\pi\) | |||||||
\(450\) | 3.58498 | − | 2.69467i | 0.168998 | − | 0.127028i | ||||
\(451\) | − | 1.83287i | − | 0.0863067i | ||||||
\(452\) | −13.2519 | −0.623318 | ||||||||
\(453\) | 10.3440 | + | 30.9774i | 0.486003 | + | 1.45544i | ||||
\(454\) | −1.03534 | −0.0485911 | ||||||||
\(455\) | 0.646787 | 0.0303218 | ||||||||
\(456\) | 4.09887 | − | 1.36870i | 0.191947 | − | 0.0640952i | ||||
\(457\) | − | 19.2356i | − | 0.899803i | −0.893078 | − | 0.449902i | \(-0.851459\pi\) | ||
0.893078 | − | 0.449902i | \(-0.148541\pi\) | |||||||
\(458\) | − | 10.7961i | − | 0.504469i | ||||||
\(459\) | 13.5631 | + | 9.35806i | 0.633073 | + | 0.436797i | ||||
\(460\) | 7.88022i | 0.367417i | ||||||||
\(461\) | − | 24.1597i | − | 1.12523i | −0.826718 | − | 0.562616i | \(-0.809795\pi\) | ||
0.826718 | − | 0.562616i | \(-0.190205\pi\) | |||||||
\(462\) | 0.355795 | − | 0.118807i | 0.0165531 | − | 0.00552742i | ||||
\(463\) | − | 3.60000i | − | 0.167306i | −0.996495 | − | 0.0836532i | \(-0.973341\pi\) | ||
0.996495 | − | 0.0836532i | \(-0.0266588\pi\) | |||||||
\(464\) | − | 6.21894i | − | 0.288707i | ||||||
\(465\) | 9.08406 | − | 3.03336i | 0.421263 | − | 0.140669i | ||||
\(466\) | −9.44022 | −0.437310 | ||||||||
\(467\) | −35.4938 | −1.64246 | −0.821229 | − | 0.570599i | \(-0.806711\pi\) | ||||
−0.821229 | + | 0.570599i | \(0.806711\pi\) | |||||||
\(468\) | 5.07991 | + | 6.75831i | 0.234819 | + | 0.312403i | ||||
\(469\) | 1.30592i | 0.0603017i | ||||||||
\(470\) | − | 20.1380i | − | 0.928894i | ||||||
\(471\) | −8.42926 | − | 25.2433i | −0.388400 | − | 1.16315i | ||||
\(472\) | 7.57687 | − | 1.26134i | 0.348754 | − | 0.0580578i | ||||
\(473\) | − | 18.3406i | − | 0.843303i | ||||||
\(474\) | 18.2096 | − | 6.08058i | 0.836395 | − | 0.279290i | ||||
\(475\) | 3.72975 | 0.171133 | ||||||||
\(476\) | − | 0.285582i | − | 0.0130896i | ||||||
\(477\) | −6.45372 | − | 8.58602i | −0.295495 | − | 0.393127i | ||||
\(478\) | 10.1040i | 0.462146i | ||||||||
\(479\) | 20.5292i | 0.938004i | 0.883197 | + | 0.469002i | \(0.155386\pi\) | ||||
−0.883197 | + | 0.469002i | \(0.844614\pi\) | |||||||
\(480\) | −1.39809 | − | 4.18690i | −0.0638140 | − | 0.191105i | ||||
\(481\) | −32.6507 | −1.48874 | ||||||||
\(482\) | 16.8918 | 0.769400 | ||||||||
\(483\) | −0.457465 | + | 0.152757i | −0.0208154 | + | 0.00695070i | ||||
\(484\) | −5.21657 | −0.237117 | ||||||||
\(485\) | 1.00608 | 0.0456837 | ||||||||
\(486\) | 0.632739 | + | 15.5756i | 0.0287016 | + | 0.706524i | ||||
\(487\) | 11.9099 | 0.539691 | 0.269846 | − | 0.962904i | \(-0.413027\pi\) | ||||
0.269846 | + | 0.962904i | \(0.413027\pi\) | |||||||
\(488\) | 3.56445i | 0.161355i | ||||||||
\(489\) | 36.8565 | − | 12.3072i | 1.66671 | − | 0.556550i | ||||
\(490\) | 17.8189i | 0.804978i | ||||||||
\(491\) | − | 22.3000i | − | 1.00638i | −0.864175 | − | 0.503192i | \(-0.832159\pi\) | ||
0.864175 | − | 0.503192i | \(-0.167841\pi\) | |||||||
\(492\) | −0.418109 | − | 1.25212i | −0.0188498 | − | 0.0564498i | ||||
\(493\) | 19.7217 | 0.888222 | ||||||||
\(494\) | 7.03122i | 0.316349i | ||||||||
\(495\) | 11.0475 | + | 14.6976i | 0.496549 | + | 0.660608i | ||||
\(496\) | − | 2.16964i | − | 0.0974197i | ||||||
\(497\) | − | 0.436618i | − | 0.0195850i | ||||||
\(498\) | 2.76869 | − | 0.924524i | 0.124068 | − | 0.0414289i | ||||
\(499\) | −7.29667 | −0.326644 | −0.163322 | − | 0.986573i | \(-0.552221\pi\) | ||||
−0.163322 | + | 0.986573i | \(0.552221\pi\) | |||||||
\(500\) | 8.93272i | 0.399484i | ||||||||
\(501\) | 7.85242 | + | 23.5158i | 0.350820 | + | 1.05061i | ||||
\(502\) | − | 23.6479i | − | 1.05546i | ||||||
\(503\) | −26.0707 | −1.16243 | −0.581217 | − | 0.813748i | \(-0.697423\pi\) | ||||
−0.581217 | + | 0.813748i | \(0.697423\pi\) | |||||||
\(504\) | 0.215957 | − | 0.162325i | 0.00961951 | − | 0.00723054i | ||||
\(505\) | − | 15.8430i | − | 0.705005i | ||||||
\(506\) | −7.43608 | −0.330574 | ||||||||
\(507\) | 8.30925 | − | 2.77464i | 0.369027 | − | 0.123226i | ||||
\(508\) | −2.96557 | −0.131576 | ||||||||
\(509\) | −12.3401 | −0.546966 | −0.273483 | − | 0.961877i | \(-0.588176\pi\) | ||||
−0.273483 | + | 0.961877i | \(0.588176\pi\) | |||||||
\(510\) | 13.2776 | − | 4.43369i | 0.587944 | − | 0.196327i | ||||
\(511\) | 0.543130i | 0.0240266i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.36234 | + | 10.6706i | −0.325055 | + | 0.471120i | ||||
\(514\) | 22.4410i | 0.989828i | ||||||||
\(515\) | −24.4546 | −1.07760 | ||||||||
\(516\) | −4.18380 | − | 12.5293i | −0.184181 | − | 0.551571i | ||||
\(517\) | 19.0029 | 0.835748 | ||||||||
\(518\) | 1.04333i | 0.0458414i | ||||||||
\(519\) | 7.84860 | − | 2.62082i | 0.344516 | − | 0.115041i | ||||
\(520\) | 7.18223 | 0.314962 | ||||||||
\(521\) | − | 34.2123i | − | 1.49887i | −0.662079 | − | 0.749434i | \(-0.730326\pi\) | ||
0.662079 | − | 0.749434i | \(-0.269674\pi\) | |||||||
\(522\) | 11.2099 | + | 14.9136i | 0.490643 | + | 0.652751i | ||||
\(523\) | 25.1911 | 1.10153 | 0.550765 | − | 0.834660i | \(-0.314336\pi\) | ||||
0.550765 | + | 0.834660i | \(0.314336\pi\) | |||||||
\(524\) | 5.28039 | 0.230675 | ||||||||
\(525\) | 0.221171 | − | 0.0738536i | 0.00965269 | − | 0.00322324i | ||||
\(526\) | − | 1.14864i | − | 0.0500831i | ||||||
\(527\) | 6.88044 | 0.299717 | ||||||||
\(528\) | 3.95092 | − | 1.31930i | 0.171942 | − | 0.0574150i | ||||
\(529\) | −13.4390 | −0.584305 | ||||||||
\(530\) | −9.12458 | −0.396346 | ||||||||
\(531\) | −15.8965 | + | 16.6824i | −0.689847 | + | 0.723955i | ||||
\(532\) | 0.224678 | 0.00974102 | ||||||||
\(533\) | 2.14789 | 0.0930354 | ||||||||
\(534\) | 14.1640 | − | 4.72965i | 0.612935 | − | 0.204672i | ||||
\(535\) | 17.9597 | 0.776464 | ||||||||
\(536\) | 14.5015i | 0.626372i | ||||||||
\(537\) | 0.813260 | − | 0.271565i | 0.0350948 | − | 0.0117189i | ||||
\(538\) | 9.58711 | 0.413329 | ||||||||
\(539\) | −16.8146 | −0.724258 | ||||||||
\(540\) | 10.8998 | + | 7.52046i | 0.469053 | + | 0.323629i | ||||
\(541\) | 31.3137i | 1.34628i | 0.739514 | + | 0.673141i | \(0.235055\pi\) | ||||
−0.739514 | + | 0.673141i | \(0.764945\pi\) | |||||||
\(542\) | 10.6508 | 0.457493 | ||||||||
\(543\) | 32.2939 | − | 10.7836i | 1.38586 | − | 0.462769i | ||||
\(544\) | − | 3.17124i | − | 0.135966i | ||||||
\(545\) | 25.7097 | 1.10128 | ||||||||
\(546\) | 0.139227 | + | 0.416945i | 0.00595836 | + | 0.0178436i | ||||
\(547\) | −41.1416 | −1.75909 | −0.879544 | − | 0.475818i | \(-0.842152\pi\) | ||||
−0.879544 | + | 0.475818i | \(0.842152\pi\) | |||||||
\(548\) | − | 8.64237i | − | 0.369184i | ||||||
\(549\) | −6.42506 | − | 8.54790i | −0.274215 | − | 0.364815i | ||||
\(550\) | 3.59512 | 0.153297 | ||||||||
\(551\) | 15.5158i | 0.660996i | ||||||||
\(552\) | −5.07991 | + | 1.69629i | −0.216216 | + | 0.0721989i | ||||
\(553\) | 0.998153 | 0.0424458 | ||||||||
\(554\) | 22.3887 | 0.951207 | ||||||||
\(555\) | −48.5080 | + | 16.1978i | −2.05905 | + | 0.687560i | ||||
\(556\) | 1.00194 | 0.0424916 | ||||||||
\(557\) | 28.9042i | 1.22471i | 0.790582 | + | 0.612356i | \(0.209778\pi\) | ||||
−0.790582 | + | 0.612356i | \(0.790222\pi\) | |||||||
\(558\) | 3.91086 | + | 5.20300i | 0.165560 | + | 0.220261i | ||||
\(559\) | 21.4928 | 0.909049 | ||||||||
\(560\) | − | 0.229503i | − | 0.00969829i | ||||||
\(561\) | 4.18380 | + | 12.5293i | 0.176640 | + | 0.528987i | ||||
\(562\) | − | 31.5953i | − | 1.33277i | ||||||
\(563\) | −46.5072 | −1.96005 | −0.980023 | − | 0.198883i | \(-0.936269\pi\) | ||||
−0.980023 | + | 0.198883i | \(0.936269\pi\) | |||||||
\(564\) | 12.9818 | − | 4.33488i | 0.546630 | − | 0.182531i | ||||
\(565\) | − | 33.7727i | − | 1.42083i | ||||||
\(566\) | − | 9.11894i | − | 0.383298i | ||||||
\(567\) | −0.225289 | + | 0.778543i | −0.00946123 | + | 0.0326957i | ||||
\(568\) | − | 4.84841i | − | 0.203435i | ||||||
\(569\) | 26.9664 | 1.13049 | 0.565246 | − | 0.824922i | \(-0.308781\pi\) | ||||
0.565246 | + | 0.824922i | \(0.308781\pi\) | |||||||
\(570\) | 3.48815 | + | 10.4460i | 0.146102 | + | 0.437536i | ||||
\(571\) | 14.2679i | 0.597095i | 0.954395 | + | 0.298547i | \(0.0965021\pi\) | ||||
−0.954395 | + | 0.298547i | \(0.903498\pi\) | |||||||
\(572\) | 6.77743i | 0.283378i | ||||||||
\(573\) | 39.8329 | − | 13.3011i | 1.66404 | − | 0.555660i | ||||
\(574\) | − | 0.0686344i | − | 0.00286474i | ||||||
\(575\) | −4.62245 | −0.192769 | ||||||||
\(576\) | 2.39809 | − | 1.80254i | 0.0999206 | − | 0.0751058i | ||||
\(577\) | 35.9765 | 1.49772 | 0.748860 | − | 0.662728i | \(-0.230601\pi\) | ||||
0.748860 | + | 0.662728i | \(0.230601\pi\) | |||||||
\(578\) | −6.94326 | −0.288802 | ||||||||
\(579\) | 12.8338 | − | 4.28548i | 0.533355 | − | 0.178098i | ||||
\(580\) | 15.8491 | 0.658097 | ||||||||
\(581\) | 0.151765 | 0.00629626 | ||||||||
\(582\) | 0.216568 | + | 0.648561i | 0.00897704 | + | 0.0268837i | ||||
\(583\) | − | 8.61030i | − | 0.356602i | ||||||
\(584\) | 6.03117i | 0.249572i | ||||||||
\(585\) | −17.2237 | + | 12.9462i | −0.712111 | + | 0.535261i | ||||
\(586\) | − | 24.3784i | − | 1.00706i | ||||||
\(587\) | 21.6537 | 0.893742 | 0.446871 | − | 0.894598i | \(-0.352538\pi\) | ||||
0.446871 | + | 0.894598i | \(0.352538\pi\) | |||||||
\(588\) | −11.4868 | + | 3.83569i | −0.473709 | + | 0.158181i | ||||
\(589\) | 5.41310i | 0.223043i | ||||||||
\(590\) | 3.21454 | + | 19.3098i | 0.132340 | + | 0.794971i | ||||
\(591\) | −7.76176 | − | 23.2443i | −0.319276 | − | 0.956142i | ||||
\(592\) | 11.5857i | 0.476168i | ||||||||
\(593\) | 39.6547i | 1.62842i | 0.580567 | + | 0.814212i | \(0.302831\pi\) | ||||
−0.580567 | + | 0.814212i | \(0.697169\pi\) | |||||||
\(594\) | −7.09659 | + | 10.2855i | −0.291177 | + | 0.422018i | ||||
\(595\) | 0.727809 | 0.0298373 | ||||||||
\(596\) | −21.1213 | −0.865164 | ||||||||
\(597\) | 11.7128 | − | 3.91116i | 0.479374 | − | 0.160073i | ||||
\(598\) | − | 8.71411i | − | 0.356347i | ||||||
\(599\) | − | 8.17342i | − | 0.333957i | −0.985961 | − | 0.166978i | \(-0.946599\pi\) | ||
0.985961 | − | 0.166978i | \(-0.0534010\pi\) | |||||||
\(600\) | 2.45599 | − | 0.820106i | 0.100265 | − | 0.0334807i | ||||
\(601\) | 32.7522i | 1.33599i | 0.744165 | + | 0.667996i | \(0.232847\pi\) | ||||
−0.744165 | + | 0.667996i | \(0.767153\pi\) | |||||||
\(602\) | − | 0.686789i | − | 0.0279914i | ||||||
\(603\) | −26.1396 | − | 34.7761i | −1.06449 | − | 1.41619i | ||||
\(604\) | 18.8555i | 0.767221i | ||||||||
\(605\) | − | 13.2945i | − | 0.540498i | ||||||
\(606\) | 10.2131 | − | 3.41036i | 0.414877 | − | 0.138536i | ||||
\(607\) | −12.9889 | −0.527205 | −0.263603 | − | 0.964631i | \(-0.584911\pi\) | ||||
−0.263603 | + | 0.964631i | \(0.584911\pi\) | |||||||
\(608\) | 2.49493 | 0.101183 | ||||||||
\(609\) | 0.307233 | + | 0.920075i | 0.0124497 | + | 0.0372833i | ||||
\(610\) | −9.08406 | −0.367803 | ||||||||
\(611\) | 22.2690i | 0.900906i | ||||||||
\(612\) | 5.71627 | + | 7.60492i | 0.231067 | + | 0.307411i | ||||
\(613\) | 26.0490i | 1.05211i | 0.850451 | + | 0.526054i | \(0.176329\pi\) | ||||
−0.850451 | + | 0.526054i | \(0.823671\pi\) | |||||||
\(614\) | −8.37649 | −0.338048 | ||||||||
\(615\) | 3.19104 | − | 1.06556i | 0.128675 | − | 0.0429674i | ||||
\(616\) | 0.216568 | 0.00872578 | ||||||||
\(617\) | 29.7818i | 1.19897i | 0.800386 | + | 0.599485i | \(0.204628\pi\) | ||||
−0.800386 | + | 0.599485i | \(0.795372\pi\) | |||||||
\(618\) | −5.26408 | − | 15.7644i | −0.211752 | − | 0.634139i | ||||
\(619\) | −17.1132 | −0.687839 | −0.343920 | − | 0.938999i | \(-0.611755\pi\) | ||||
−0.343920 | + | 0.938999i | \(0.611755\pi\) | |||||||
\(620\) | 5.52936 | 0.222065 | ||||||||
\(621\) | 9.12448 | − | 13.2246i | 0.366153 | − | 0.530685i | ||||
\(622\) | 27.9904i | 1.12231i | ||||||||
\(623\) | 0.776393 | 0.0311055 | ||||||||
\(624\) | 1.54604 | + | 4.62996i | 0.0618912 | + | 0.185347i | ||||
\(625\) | −30.2398 | −1.20959 | ||||||||
\(626\) | − | 13.0090i | − | 0.519946i | ||||||
\(627\) | −9.85727 | + | 3.29155i | −0.393661 | + | 0.131452i | ||||
\(628\) | − | 15.3653i | − | 0.613141i | ||||||
\(629\) | −36.7409 | −1.46495 | ||||||||
\(630\) | 0.413689 | + | 0.550371i | 0.0164817 | + | 0.0219273i | ||||
\(631\) | −13.0597 | −0.519898 | −0.259949 | − | 0.965622i | \(-0.583706\pi\) | ||||
−0.259949 | + | 0.965622i | \(0.583706\pi\) | |||||||
\(632\) | 11.0840 | 0.440897 | ||||||||
\(633\) | −9.95580 | − | 29.8148i | −0.395707 | − | 1.18503i | ||||
\(634\) | − | 14.2111i | − | 0.564394i | ||||||
\(635\) | − | 7.55780i | − | 0.299922i | ||||||
\(636\) | −1.96415 | − | 5.88208i | −0.0778836 | − | 0.233240i | ||||
\(637\) | − | 19.7046i | − | 0.780723i | ||||||
\(638\) | 14.9558i | 0.592105i | ||||||||
\(639\) | 8.73945 | + | 11.6270i | 0.345727 | + | 0.459955i | ||||
\(640\) | − | 2.54852i | − | 0.100739i | ||||||
\(641\) | 16.0393i | 0.633514i | 0.948507 | + | 0.316757i | \(0.102594\pi\) | ||||
−0.948507 | + | 0.316757i | \(0.897406\pi\) | |||||||
\(642\) | 3.86599 | + | 11.5775i | 0.152578 | + | 0.456929i | ||||
\(643\) | 39.0313 | 1.53924 | 0.769622 | − | 0.638500i | \(-0.220445\pi\) | ||||
0.769622 | + | 0.638500i | \(0.220445\pi\) | |||||||
\(644\) | −0.278454 | −0.0109726 | ||||||||
\(645\) | 31.9311 | − | 10.6625i | 1.25729 | − | 0.419834i | ||||
\(646\) | 7.91201i | 0.311294i | ||||||||
\(647\) | − | 10.0658i | − | 0.395726i | −0.980230 | − | 0.197863i | \(-0.936600\pi\) | ||
0.980230 | − | 0.197863i | \(-0.0634001\pi\) | |||||||
\(648\) | −2.50171 | + | 8.64531i | −0.0982766 | + | 0.339620i | ||||
\(649\) | −18.2214 | + | 3.03336i | −0.715254 | + | 0.119070i | ||||
\(650\) | 4.21301i | 0.165248i | ||||||||
\(651\) | 0.107186 | + | 0.320992i | 0.00420096 | + | 0.0125807i | ||||
\(652\) | 22.4341 | 0.878589 | ||||||||
\(653\) | − | 17.2684i | − | 0.675766i | −0.941188 | − | 0.337883i | \(-0.890289\pi\) | ||
0.941188 | − | 0.337883i | \(-0.109711\pi\) | |||||||
\(654\) | 5.53424 | + | 16.5735i | 0.216406 | + | 0.648075i | ||||
\(655\) | 13.4572i | 0.525815i | ||||||||
\(656\) | − | 0.762149i | − | 0.0297569i | ||||||
\(657\) | −10.8714 | − | 14.4633i | −0.424134 | − | 0.564268i | ||||
\(658\) | 0.711590 | 0.0277407 | ||||||||
\(659\) | 8.90478 | 0.346881 | 0.173440 | − | 0.984844i | \(-0.444512\pi\) | ||||
0.173440 | + | 0.984844i | \(0.444512\pi\) | |||||||
\(660\) | 3.36224 | + | 10.0690i | 0.130875 | + | 0.391934i | ||||
\(661\) | −23.3948 | −0.909953 | −0.454977 | − | 0.890503i | \(-0.650352\pi\) | ||||
−0.454977 | + | 0.890503i | \(0.650352\pi\) | |||||||
\(662\) | 22.8299 | 0.887309 | ||||||||
\(663\) | −14.6827 | + | 4.90286i | −0.570229 | + | 0.190411i | ||||
\(664\) | 1.68527 | 0.0654011 | ||||||||
\(665\) | 0.572595i | 0.0222043i | ||||||||
\(666\) | −20.8836 | − | 27.7835i | −0.809223 | − | 1.07659i | ||||
\(667\) | − | 19.2295i | − | 0.744568i | ||||||
\(668\) | 14.3138i | 0.553817i | ||||||||
\(669\) | 32.0179 | − | 10.6915i | 1.23789 | − | 0.413356i | ||||
\(670\) | −36.9574 | −1.42779 | ||||||||
\(671\) | − | 8.57207i | − | 0.330921i | ||||||
\(672\) | 0.147947 | − | 0.0494027i | 0.00570719 | − | 0.00190575i | ||||
\(673\) | 46.3809i | 1.78785i | 0.448216 | + | 0.893925i | \(0.352060\pi\) | ||||
−0.448216 | + | 0.893925i | \(0.647940\pi\) | |||||||
\(674\) | − | 24.9076i | − | 0.959403i | ||||||
\(675\) | −4.41142 | + | 6.39370i | −0.169796 | + | 0.246094i | ||||
\(676\) | 5.05774 | 0.194529 | ||||||||
\(677\) | 1.46357i | 0.0562496i | 0.999604 | + | 0.0281248i | \(0.00895358\pi\) | ||||
−0.999604 | + | 0.0281248i | \(0.991046\pi\) | |||||||
\(678\) | 21.7713 | − | 7.26989i | 0.836121 | − | 0.279198i | ||||
\(679\) | 0.0355506i | 0.00136431i | ||||||||
\(680\) | 8.08194 | 0.309928 | ||||||||
\(681\) | 1.70094 | − | 0.567981i | 0.0651803 | − | 0.0217651i | ||||
\(682\) | 5.21772i | 0.199797i | ||||||||
\(683\) | −5.74279 | −0.219742 | −0.109871 | − | 0.993946i | \(-0.535044\pi\) | ||||
−0.109871 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(684\) | −5.98308 | + | 4.49721i | −0.228769 | + | 0.171955i | ||||
\(685\) | 22.0252 | 0.841540 | ||||||||
\(686\) | −1.26002 | −0.0481079 | ||||||||
\(687\) | 5.92266 | + | 17.7367i | 0.225964 | + | 0.676697i | ||||
\(688\) | − | 7.62643i | − | 0.290755i | ||||||
\(689\) | 10.0901 | 0.384404 | ||||||||
\(690\) | −4.32302 | − | 12.9462i | −0.164575 | − | 0.492855i | ||||
\(691\) | − | 13.4494i | − | 0.511640i | −0.966724 | − | 0.255820i | \(-0.917655\pi\) | ||
0.966724 | − | 0.255820i | \(-0.0823455\pi\) | |||||||
\(692\) | 4.77735 | 0.181608 | ||||||||
\(693\) | −0.519351 | + | 0.390372i | −0.0197285 | + | 0.0148290i | ||||
\(694\) | −26.9745 | −1.02394 | ||||||||
\(695\) | 2.55345i | 0.0968581i | ||||||||
\(696\) | 3.41166 | + | 10.2170i | 0.129319 | + | 0.387273i | ||||
\(697\) | 2.41695 | 0.0915487 | ||||||||
\(698\) | 24.7901i | 0.938319i | ||||||||
\(699\) | 15.5091 | − | 5.17883i | 0.586609 | − | 0.195881i | ||||
\(700\) | 0.134624 | 0.00508831 | ||||||||
\(701\) | 43.2164 | 1.63226 | 0.816130 | − | 0.577868i | \(-0.196115\pi\) | ||||
0.816130 | + | 0.577868i | \(0.196115\pi\) | |||||||
\(702\) | −12.0532 | − | 8.31628i | −0.454920 | − | 0.313878i | ||||
\(703\) | − | 28.9054i | − | 1.09019i | ||||||
\(704\) | 2.40488 | 0.0906372 | ||||||||
\(705\) | 11.0475 | + | 33.0842i | 0.416073 | + | 1.24602i | ||||
\(706\) | −18.8958 | −0.711151 | ||||||||
\(707\) | 0.559825 | 0.0210544 | ||||||||
\(708\) | −11.7559 | + | 6.22883i | −0.441814 | + | 0.234094i | ||||
\(709\) | −48.6141 | −1.82574 | −0.912871 | − | 0.408249i | \(-0.866140\pi\) | ||||
−0.912871 | + | 0.408249i | \(0.866140\pi\) | |||||||
\(710\) | 12.3563 | 0.463722 | ||||||||
\(711\) | −26.5804 | + | 19.9793i | −0.996843 | + | 0.749282i | ||||
\(712\) | 8.62144 | 0.323102 | ||||||||
\(713\) | − | 6.70871i | − | 0.251243i | ||||||
\(714\) | 0.156668 | + | 0.469176i | 0.00586314 | + | 0.0175585i | ||||
\(715\) | −17.2724 | −0.645950 | ||||||||
\(716\) | 0.495022 | 0.0184998 | ||||||||
\(717\) | −5.54296 | − | 16.5996i | −0.207006 | − | 0.619924i | ||||
\(718\) | 24.5978i | 0.917982i | ||||||||
\(719\) | 45.3674 | 1.69192 | 0.845959 | − | 0.533248i | \(-0.179029\pi\) | ||||
0.845959 | + | 0.533248i | \(0.179029\pi\) | |||||||
\(720\) | 4.59380 | + | 6.11158i | 0.171201 | + | 0.227765i | ||||
\(721\) | − | 0.864122i | − | 0.0321816i | ||||||
\(722\) | 12.7753 | 0.475448 | ||||||||
\(723\) | −27.7511 | + | 9.26669i | −1.03208 | + | 0.344632i | ||||
\(724\) | 19.6569 | 0.730542 | ||||||||
\(725\) | 9.29688i | 0.345278i | ||||||||
\(726\) | 8.57018 | − | 2.86177i | 0.318069 | − | 0.106210i | ||||
\(727\) | −3.48894 | −0.129398 | −0.0646988 | − | 0.997905i | \(-0.520609\pi\) | ||||
−0.0646988 | + | 0.997905i | \(0.520609\pi\) | |||||||
\(728\) | 0.253790i | 0.00940607i | ||||||||
\(729\) | −9.58416 | − | 25.2417i | −0.354969 | − | 0.934878i | ||||
\(730\) | −15.3705 | −0.568889 | ||||||||
\(731\) | 24.1852 | 0.894523 | ||||||||
\(732\) | −1.95543 | − | 5.85596i | −0.0722748 | − | 0.216443i | ||||
\(733\) | −10.4331 | −0.385357 | −0.192678 | − | 0.981262i | \(-0.561717\pi\) | ||||
−0.192678 | + | 0.981262i | \(0.561717\pi\) | |||||||
\(734\) | − | 19.6069i | − | 0.723702i | ||||||
\(735\) | −9.77532 | − | 29.2743i | −0.360568 | − | 1.07980i | ||||
\(736\) | −3.09208 | −0.113976 | ||||||||
\(737\) | − | 34.8744i | − | 1.28462i | ||||||
\(738\) | 1.37380 | + | 1.82770i | 0.0505704 | + | 0.0672787i | ||||
\(739\) | − | 51.5614i | − | 1.89672i | −0.317201 | − | 0.948358i | \(-0.602743\pi\) | ||
0.317201 | − | 0.948358i | \(-0.397257\pi\) | |||||||
\(740\) | −29.5262 | −1.08541 | ||||||||
\(741\) | −3.85727 | − | 11.5514i | −0.141700 | − | 0.424352i | ||||
\(742\) | − | 0.322424i | − | 0.0118366i | ||||||
\(743\) | − | 30.2886i | − | 1.11118i | −0.831456 | − | 0.555591i | \(-0.812492\pi\) | ||
0.831456 | − | 0.555591i | \(-0.187508\pi\) | |||||||
\(744\) | 1.19025 | + | 3.56445i | 0.0436366 | + | 0.130679i | ||||
\(745\) | − | 53.8281i | − | 1.97211i | ||||||
\(746\) | 5.00294 | 0.183171 | ||||||||
\(747\) | −4.04143 | + | 3.03776i | −0.147868 | + | 0.111146i | ||||
\(748\) | 7.62643i | 0.278850i | ||||||||
\(749\) | 0.634619i | 0.0231885i | ||||||||
\(750\) | −4.90042 | − | 14.6754i | −0.178938 | − | 0.535869i | ||||
\(751\) | 15.9239i | 0.581071i | 0.956864 | + | 0.290535i | \(0.0938334\pi\) | ||||
−0.956864 | + | 0.290535i | \(0.906167\pi\) | |||||||
\(752\) | 7.90184 | 0.288150 | ||||||||
\(753\) | 12.9730 | + | 38.8506i | 0.472764 | + | 1.41579i | ||||
\(754\) | −17.5262 | −0.638267 | ||||||||
\(755\) | −48.0536 | −1.74885 | ||||||||
\(756\) | −0.265741 | + | 0.385153i | −0.00966492 | + | 0.0140079i | ||||
\(757\) | −34.0455 | −1.23740 | −0.618702 | − | 0.785626i | \(-0.712341\pi\) | ||||
−0.618702 | + | 0.785626i | \(0.712341\pi\) | |||||||
\(758\) | −1.41105 | −0.0512516 | ||||||||
\(759\) | 12.2166 | − | 4.07937i | 0.443433 | − | 0.148072i | ||||
\(760\) | 6.35837i | 0.230642i | ||||||||
\(761\) | − | 37.6293i | − | 1.36406i | −0.731324 | − | 0.682030i | \(-0.761097\pi\) | ||
0.731324 | − | 0.682030i | \(-0.238903\pi\) | |||||||
\(762\) | 4.87207 | − | 1.62689i | 0.176496 | − | 0.0589359i | ||||
\(763\) | 0.908470i | 0.0328888i | ||||||||
\(764\) | 24.2458 | 0.877183 | ||||||||
\(765\) | −19.3813 | + | 14.5680i | −0.700731 | + | 0.526708i | ||||
\(766\) | − | 32.4479i | − | 1.17239i | ||||||
\(767\) | −3.55470 | − | 21.3532i | −0.128353 | − | 0.771018i | ||||
\(768\) | 1.64288 | − | 0.548592i | 0.0592822 | − | 0.0197956i | ||||
\(769\) | 47.2538i | 1.70401i | 0.523530 | + | 0.852007i | \(0.324615\pi\) | ||||
−0.523530 | + | 0.852007i | \(0.675385\pi\) | |||||||
\(770\) | 0.551927i | 0.0198901i | ||||||||
\(771\) | −12.3109 | − | 36.8677i | −0.443367 | − | 1.32776i | ||||
\(772\) | 7.81178 | 0.281152 | ||||||||
\(773\) | −51.6780 | −1.85873 | −0.929365 | − | 0.369163i | \(-0.879645\pi\) | ||||
−0.929365 | + | 0.369163i | \(0.879645\pi\) | |||||||
\(774\) | 13.7469 | + | 18.2889i | 0.494123 | + | 0.657381i | ||||
\(775\) | 3.24346i | 0.116509i | ||||||||
\(776\) | 0.394771i | 0.0141715i | ||||||||
\(777\) | −0.572363 | − | 1.71407i | −0.0205334 | − | 0.0614918i | ||||
\(778\) | − | 2.14262i | − | 0.0768166i | ||||||
\(779\) | 1.90151i | 0.0681286i | ||||||||
\(780\) | −11.7995 | + | 3.94011i | −0.422491 | + | 0.141079i | ||||
\(781\) | 11.6598i | 0.417222i | ||||||||
\(782\) | − | 9.80573i | − | 0.350652i | ||||||
\(783\) | −26.5979 | − | 18.3516i | −0.950533 | − | 0.655832i | ||||
\(784\) | −6.99189 | −0.249710 | ||||||||
\(785\) | 39.1586 | 1.39763 | ||||||||
\(786\) | −8.67504 | + | 2.89678i | −0.309428 | + | 0.103325i | ||||
\(787\) | −9.00194 | −0.320884 | −0.160442 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160442 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(788\) | − | 14.1485i | − | 0.504020i | ||||||
\(789\) | 0.630135 | + | 1.88708i | 0.0224334 | + | 0.0671817i | ||||
\(790\) | 28.2477i | 1.00501i | ||||||||
\(791\) | 1.19338 | 0.0424319 | ||||||||
\(792\) | −5.76712 | + | 4.33488i | −0.204926 | + | 0.154033i | ||||
\(793\) | 10.0453 | 0.356721 | ||||||||
\(794\) | − | 24.1710i | − | 0.857795i | ||||||
\(795\) | 14.9906 | − | 5.00567i | 0.531660 | − | 0.177533i | ||||
\(796\) | 7.12946 | 0.252697 | ||||||||
\(797\) | −11.9676 | −0.423914 | −0.211957 | − | 0.977279i | \(-0.567984\pi\) | ||||
−0.211957 | + | 0.977279i | \(0.567984\pi\) | |||||||
\(798\) | −0.369118 | + | 0.123256i | −0.0130666 | + | 0.00436323i | ||||
\(799\) | 25.0586i | 0.886509i | ||||||||
\(800\) | 1.49493 | 0.0528538 | ||||||||
\(801\) | −20.6750 | + | 15.5405i | −0.730517 | + | 0.549096i | ||||
\(802\) | −13.4312 | −0.474272 | ||||||||
\(803\) | − | 14.5042i | − | 0.511843i | ||||||
\(804\) | −7.95543 | − | 23.8243i | −0.280566 | − | 0.840217i | ||||
\(805\) | − | 0.709643i | − | 0.0250116i | ||||||
\(806\) | −6.11448 | −0.215373 | ||||||||
\(807\) | −15.7504 | + | 5.25941i | −0.554442 | + | 0.185140i | ||||
\(808\) | 6.21657 | 0.218698 | ||||||||
\(809\) | 14.9616 | 0.526021 | 0.263010 | − | 0.964793i | \(-0.415285\pi\) | ||||
0.263010 | + | 0.964793i | \(0.415285\pi\) | |||||||
\(810\) | −22.0327 | − | 6.37565i | −0.774151 | − | 0.224018i | ||||
\(811\) | − | 38.6780i | − | 1.35817i | −0.734061 | − | 0.679084i | \(-0.762377\pi\) | ||
0.734061 | − | 0.679084i | \(-0.237623\pi\) | |||||||
\(812\) | 0.560039i | 0.0196535i | ||||||||
\(813\) | −17.4980 | + | 5.84296i | −0.613682 | + | 0.204922i | ||||
\(814\) | − | 27.8621i | − | 0.976565i | ||||||
\(815\) | 57.1738i | 2.00271i | ||||||||
\(816\) | 1.73971 | + | 5.20995i | 0.0609022 | + | 0.182385i | ||||
\(817\) | 19.0274i | 0.665685i | ||||||||
\(818\) | 0.0382281i | 0.00133661i | ||||||||
\(819\) | −0.457465 | − | 0.608611i | −0.0159851 | − | 0.0212666i | ||||
\(820\) | 1.94235 | 0.0678297 | ||||||||
\(821\) | −35.1175 | −1.22561 | −0.612804 | − | 0.790235i | \(-0.709959\pi\) | ||||
−0.612804 | + | 0.790235i | \(0.709959\pi\) | |||||||
\(822\) | 4.74113 | + | 14.1984i | 0.165366 | + | 0.495225i | ||||
\(823\) | − | 32.7075i | − | 1.14011i | −0.821606 | − | 0.570055i | \(-0.806922\pi\) | ||
0.821606 | − | 0.570055i | \(-0.193078\pi\) | |||||||
\(824\) | − | 9.59563i | − | 0.334279i | ||||||
\(825\) | −5.90635 | + | 1.97225i | −0.205633 | + | 0.0686651i | ||||
\(826\) | −0.682326 | + | 0.113588i | −0.0237412 | + | 0.00395224i | ||||
\(827\) | 0.276178i | 0.00960367i | 0.999988 | + | 0.00480183i | \(0.00152848\pi\) | ||||
−0.999988 | + | 0.00480183i | \(0.998472\pi\) | |||||||
\(828\) | 7.41511 | − | 5.57360i | 0.257693 | − | 0.193696i | ||||
\(829\) | 14.4293 | 0.501150 | 0.250575 | − | 0.968097i | \(-0.419380\pi\) | ||||
0.250575 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(830\) | 4.29493i | 0.149079i | ||||||||
\(831\) | −36.7820 | + | 12.2823i | −1.27595 | + | 0.426068i | ||||
\(832\) | 2.81820i | 0.0977035i | ||||||||
\(833\) | − | 22.1729i | − | 0.768247i | ||||||
\(834\) | −1.64606 | + | 0.549655i | −0.0569985 | + | 0.0190330i | ||||
\(835\) | −36.4789 | −1.26240 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | −9.27939 | − | 6.40243i | −0.320743 | − | 0.221300i | ||||
\(838\) | 16.4059 | 0.566732 | ||||||||
\(839\) | 35.9674 | 1.24173 | 0.620866 | − | 0.783917i | \(-0.286781\pi\) | ||||
0.620866 | + | 0.783917i | \(0.286781\pi\) | |||||||
\(840\) | 0.125904 | + | 0.377046i | 0.00434409 | + | 0.0130093i | ||||
\(841\) | −9.67522 | −0.333628 | ||||||||
\(842\) | 18.1688i | 0.626137i | ||||||||
\(843\) | 17.3329 | + | 51.9072i | 0.596978 | + | 1.78778i | ||||
\(844\) | − | 18.1479i | − | 0.624677i | ||||||
\(845\) | 12.8897i | 0.443420i | ||||||||
\(846\) | −18.9493 | + | 14.2434i | −0.651492 | + | 0.489697i | ||||
\(847\) | 0.469771 | 0.0161415 | ||||||||
\(848\) | − | 3.58035i | − | 0.122950i | ||||||
\(849\) | 5.00257 | + | 14.9813i | 0.171688 | + | 0.514157i | ||||
\(850\) | 4.74078i | 0.162607i | ||||||||
\(851\) | 35.8238i | 1.22802i | ||||||||
\(852\) | 2.65980 | + | 7.96535i | 0.0911232 | + | 0.272888i | ||||
\(853\) | 35.5254 | 1.21637 | 0.608183 | − | 0.793797i | \(-0.291899\pi\) | ||||
0.608183 | + | 0.793797i | \(0.291899\pi\) | |||||||
\(854\) | − | 0.320992i | − | 0.0109841i | ||||||
\(855\) | −11.4612 | − | 15.2480i | −0.391965 | − | 0.521469i | ||||
\(856\) | 7.04711i | 0.240865i | ||||||||
\(857\) | −35.2644 | −1.20461 | −0.602304 | − | 0.798267i | \(-0.705750\pi\) | ||||
−0.602304 | + | 0.798267i | \(0.705750\pi\) | |||||||
\(858\) | −3.71804 | − | 11.1345i | −0.126932 | − | 0.380125i | ||||
\(859\) | 3.82290i | 0.130436i | 0.997871 | + | 0.0652179i | \(0.0207742\pi\) | ||||
−0.997871 | + | 0.0652179i | \(0.979226\pi\) | |||||||
\(860\) | 19.4361 | 0.662765 | ||||||||
\(861\) | 0.0376522 | + | 0.112758i | 0.00128318 | + | 0.00384278i | ||||
\(862\) | −33.4322 | −1.13871 | ||||||||
\(863\) | −37.2359 | −1.26752 | −0.633762 | − | 0.773528i | \(-0.718490\pi\) | ||||
−0.633762 | + | 0.773528i | \(0.718490\pi\) | |||||||
\(864\) | −2.95092 | + | 4.27692i | −0.100392 | + | 0.145504i | ||||
\(865\) | 12.1752i | 0.413968i | ||||||||
\(866\) | −13.7095 | −0.465867 | ||||||||
\(867\) | 11.4069 | − | 3.80902i | 0.387400 | − | 0.129361i | ||||
\(868\) | 0.195384i | 0.00663177i | ||||||||
\(869\) | −26.6556 | −0.904229 | ||||||||
\(870\) | −26.0381 | + | 8.69467i | −0.882773 | + | 0.294777i | ||||
\(871\) | 40.8683 | 1.38477 | ||||||||
\(872\) | 10.0881i | 0.341626i | ||||||||
\(873\) | −0.711590 | − | 0.946698i | −0.0240837 | − | 0.0320409i | ||||
\(874\) | 7.71453 | 0.260948 | ||||||||
\(875\) | − | 0.804425i | − | 0.0271945i | ||||||
\(876\) | −3.30865 | − | 9.90848i | −0.111789 | − | 0.334777i | ||||
\(877\) | −1.68417 | −0.0568705 | −0.0284352 | − | 0.999596i | \(-0.509052\pi\) | ||||
−0.0284352 | + | 0.999596i | \(0.509052\pi\) | |||||||
\(878\) | 35.8086 | 1.20848 | ||||||||
\(879\) | 13.3738 | + | 40.0507i | 0.451086 | + | 1.35088i | ||||
\(880\) | 6.12887i | 0.206604i | ||||||||
\(881\) | 47.0444 | 1.58497 | 0.792484 | − | 0.609893i | \(-0.208788\pi\) | ||||
0.792484 | + | 0.609893i | \(0.208788\pi\) | |||||||
\(882\) | 16.7672 | − | 12.6031i | 0.564581 | − | 0.424370i | ||||
\(883\) | 24.2011 | 0.814431 | 0.407216 | − | 0.913332i | \(-0.366500\pi\) | ||||
0.407216 | + | 0.913332i | \(0.366500\pi\) | |||||||
\(884\) | −8.93718 | −0.300590 | ||||||||
\(885\) | −15.8743 | − | 29.9601i | −0.533608 | − | 1.00710i | ||||
\(886\) | 9.77441 | 0.328378 | ||||||||
\(887\) | 39.4291 | 1.32390 | 0.661949 | − | 0.749549i | \(-0.269729\pi\) | ||||
0.661949 | + | 0.749549i | \(0.269729\pi\) | |||||||
\(888\) | −6.35579 | − | 19.0338i | −0.213287 | − | 0.638733i | ||||
\(889\) | 0.267061 | 0.00895692 | ||||||||
\(890\) | 21.9719i | 0.736499i | ||||||||
\(891\) | 6.01631 | − | 20.7909i | 0.201554 | − | 0.696522i | ||||
\(892\) | 19.4889 | 0.652538 | ||||||||
\(893\) | −19.7145 | −0.659722 | ||||||||
\(894\) | 34.6998 | − | 11.5870i | 1.16053 | − | 0.387527i | ||||
\(895\) | 1.26157i | 0.0421697i | ||||||||
\(896\) | 0.0900537 | 0.00300848 | ||||||||
\(897\) | 4.78049 | + | 14.3162i | 0.159616 | + | 0.478005i | ||||
\(898\) | − | 21.4713i | − | 0.716505i | ||||||
\(899\) | −13.4929 | −0.450012 | ||||||||
\(900\) | −3.58498 | + | 2.69467i | −0.119499 | + | 0.0898223i | ||||
\(901\) | 11.3541 | 0.378261 | ||||||||
\(902\) | 1.83287i | 0.0610280i | ||||||||
\(903\) | 0.376767 | + | 1.12831i | 0.0125380 | + | 0.0375478i | ||||
\(904\) | 13.2519 | 0.440752 | ||||||||
\(905\) | 50.0959i | 1.66524i | ||||||||
\(906\) | −10.3440 | − | 30.9774i | −0.343656 | − | 1.02915i | ||||
\(907\) | 29.9312 | 0.993849 | 0.496924 | − | 0.867794i | \(-0.334463\pi\) | ||||
0.496924 | + | 0.867794i | \(0.334463\pi\) | |||||||
\(908\) | 1.03534 | 0.0343591 | ||||||||
\(909\) | −14.9079 | + | 11.2056i | −0.494464 | + | 0.371666i | ||||
\(910\) | −0.646787 | −0.0214408 | ||||||||
\(911\) | − | 18.3864i | − | 0.609167i | −0.952486 | − | 0.304584i | \(-0.901483\pi\) | ||
0.952486 | − | 0.304584i | \(-0.0985173\pi\) | |||||||
\(912\) | −4.09887 | + | 1.36870i | −0.135727 | + | 0.0453221i | ||||
\(913\) | −4.05286 | −0.134130 | ||||||||
\(914\) | 19.2356i | 0.636257i | ||||||||
\(915\) | 14.9240 | − | 4.98344i | 0.493372 | − | 0.164748i | ||||
\(916\) | 10.7961i | 0.356714i | ||||||||
\(917\) | −0.475519 | −0.0157030 | ||||||||
\(918\) | −13.5631 | − | 9.35806i | −0.447650 | − | 0.308862i | ||||
\(919\) | 29.3770i | 0.969059i | 0.874775 | + | 0.484529i | \(0.161009\pi\) | ||||
−0.874775 | + | 0.484529i | \(0.838991\pi\) | |||||||
\(920\) | − | 7.88022i | − | 0.259803i | ||||||
\(921\) | 13.7615 | − | 4.59527i | 0.453458 | − | 0.151419i | ||||
\(922\) | 24.1597i | 0.795659i | ||||||||
\(923\) | −13.6638 | −0.449750 | ||||||||
\(924\) | −0.355795 | + | 0.118807i | −0.0117048 | + | 0.00390848i | ||||
\(925\) | − | 17.3198i | − | 0.569470i | ||||||
\(926\) | 3.60000i | 0.118303i | ||||||||
\(927\) | 17.2965 | + | 23.0112i | 0.568091 | + | 0.755788i | ||||
\(928\) | 6.21894i | 0.204147i | ||||||||
\(929\) | 13.6185 | 0.446809 | 0.223404 | − | 0.974726i | \(-0.428283\pi\) | ||||
0.223404 | + | 0.974726i | \(0.428283\pi\) | |||||||
\(930\) | −9.08406 | + | 3.03336i | −0.297878 | + | 0.0994679i | ||||
\(931\) | 17.4443 | 0.571713 | ||||||||
\(932\) | 9.44022 | 0.309225 | ||||||||
\(933\) | −15.3553 | − | 45.9848i | −0.502710 | − | 1.50547i | ||||
\(934\) | 35.4938 | 1.16139 | ||||||||
\(935\) | −19.4361 | −0.635628 | ||||||||
\(936\) | −5.07991 | − | 6.75831i | −0.166042 | − | 0.220902i | ||||
\(937\) | − | 32.0303i | − | 1.04639i | −0.852214 | − | 0.523193i | \(-0.824741\pi\) | ||
0.852214 | − | 0.523193i | \(-0.175259\pi\) | |||||||
\(938\) | − | 1.30592i | − | 0.0426398i | ||||||
\(939\) | 7.13665 | + | 21.3723i | 0.232896 | + | 0.697458i | ||||
\(940\) | 20.1380i | 0.656828i | ||||||||
\(941\) | 24.1681 | 0.787859 | 0.393929 | − | 0.919141i | \(-0.371115\pi\) | ||||
0.393929 | + | 0.919141i | \(0.371115\pi\) | |||||||
\(942\) | 8.42926 | + | 25.2433i | 0.274640 | + | 0.822470i | ||||
\(943\) | − | 2.35663i | − | 0.0767424i | ||||||
\(944\) | −7.57687 | + | 1.26134i | −0.246606 | + | 0.0410530i | ||||
\(945\) | −0.981568 | − | 0.677246i | −0.0319304 | − | 0.0220308i | ||||
\(946\) | 18.3406i | 0.596305i | ||||||||
\(947\) | − | 52.4492i | − | 1.70437i | −0.523242 | − | 0.852184i | \(-0.675277\pi\) | ||
0.523242 | − | 0.852184i | \(-0.324723\pi\) | |||||||
\(948\) | −18.2096 | + | 6.08058i | −0.591421 | + | 0.197488i | ||||
\(949\) | 16.9971 | 0.551748 | ||||||||
\(950\) | −3.72975 | −0.121009 | ||||||||
\(951\) | 7.79608 | + | 23.3471i | 0.252805 | + | 0.757081i | ||||
\(952\) | 0.285582i | 0.00925576i | ||||||||
\(953\) | − | 28.1139i | − | 0.910699i | −0.890313 | − | 0.455349i | \(-0.849514\pi\) | ||
0.890313 | − | 0.455349i | \(-0.150486\pi\) | |||||||
\(954\) | 6.45372 | + | 8.58602i | 0.208947 | + | 0.277983i | ||||
\(955\) | 61.7909i | 1.99951i | ||||||||
\(956\) | − | 10.1040i | − | 0.326786i | ||||||
\(957\) | −8.20462 | − | 24.5705i | −0.265218 | − | 0.794252i | ||||
\(958\) | − | 20.5292i | − | 0.663269i | ||||||
\(959\) | 0.778278i | 0.0251319i | ||||||||
\(960\) | 1.39809 | + | 4.18690i | 0.0451233 | + | 0.135132i | ||||
\(961\) | 26.2927 | 0.848150 | ||||||||
\(962\) | 32.6507 | 1.05270 | ||||||||
\(963\) | −12.7027 | − | 16.8996i | −0.409338 | − | 0.544583i | ||||
\(964\) | −16.8918 | −0.544048 | ||||||||
\(965\) | 19.9084i | 0.640876i | ||||||||
\(966\) | 0.457465 | − | 0.152757i | 0.0147187 | − | 0.00491489i | ||||
\(967\) | 11.7506i | 0.377872i | 0.981989 | + | 0.188936i | \(0.0605039\pi\) | ||||
−0.981989 | + | 0.188936i | \(0.939496\pi\) | |||||||
\(968\) | 5.21657 | 0.167667 | ||||||||
\(969\) | −4.34046 | − | 12.9985i | −0.139436 | − | 0.417571i | ||||
\(970\) | −1.00608 | −0.0323033 | ||||||||
\(971\) | − | 12.3331i | − | 0.395788i | −0.980223 | − | 0.197894i | \(-0.936590\pi\) | ||
0.980223 | − | 0.197894i | \(-0.0634101\pi\) | |||||||
\(972\) | −0.632739 | − | 15.5756i | −0.0202951 | − | 0.499588i | ||||
\(973\) | −0.0902283 | −0.00289259 | ||||||||
\(974\) | −11.9099 | −0.381619 | ||||||||
\(975\) | −2.31122 | − | 6.92147i | −0.0740184 | − | 0.221664i | ||||
\(976\) | − | 3.56445i | − | 0.114095i | ||||||
\(977\) | −41.1499 | −1.31650 | −0.658251 | − | 0.752799i | \(-0.728703\pi\) | ||||
−0.658251 | + | 0.752799i | \(0.728703\pi\) | |||||||
\(978\) | −36.8565 | + | 12.3072i | −1.17854 | + | 0.393540i | ||||
\(979\) | −20.7335 | −0.662646 | ||||||||
\(980\) | − | 17.8189i | − | 0.569205i | ||||||
\(981\) | −18.1842 | − | 24.1922i | −0.580576 | − | 0.772397i | ||||
\(982\) | 22.3000i | 0.711621i | ||||||||
\(983\) | −9.26094 | −0.295378 | −0.147689 | − | 0.989034i | \(-0.547183\pi\) | ||||
−0.147689 | + | 0.989034i | \(0.547183\pi\) | |||||||
\(984\) | 0.418109 | + | 1.25212i | 0.0133288 | + | 0.0399160i | ||||
\(985\) | 36.0577 | 1.14889 | ||||||||
\(986\) | −19.7217 | −0.628068 | ||||||||
\(987\) | −1.16906 | + | 0.390372i | −0.0372114 | + | 0.0124257i | ||||
\(988\) | − | 7.03122i | − | 0.223693i | ||||||
\(989\) | − | 23.5816i | − | 0.749850i | ||||||
\(990\) | −11.0475 | − | 14.6976i | −0.351113 | − | 0.467120i | ||||
\(991\) | 0.617671i | 0.0196210i | 0.999952 | + | 0.00981048i | \(0.00312282\pi\) | ||||
−0.999952 | + | 0.00981048i | \(0.996877\pi\) | |||||||
\(992\) | 2.16964i | 0.0688861i | ||||||||
\(993\) | −37.5067 | + | 12.5243i | −1.19024 | + | 0.397446i | ||||
\(994\) | 0.436618i | 0.0138487i | ||||||||
\(995\) | 18.1695i | 0.576013i | ||||||||
\(996\) | −2.76869 | + | 0.924524i | −0.0877293 | + | 0.0292947i | ||||
\(997\) | 35.1173 | 1.11218 | 0.556088 | − | 0.831123i | \(-0.312302\pi\) | ||||
0.556088 | + | 0.831123i | \(0.312302\pi\) | |||||||
\(998\) | 7.29667 | 0.230972 | ||||||||
\(999\) | 49.5510 | + | 34.1883i | 1.56772 | + | 1.08167i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 354.2.c.a.353.9 | ✓ | 10 | |
3.2 | odd | 2 | 354.2.c.b.353.10 | yes | 10 | ||
59.58 | odd | 2 | 354.2.c.b.353.9 | yes | 10 | ||
177.176 | even | 2 | inner | 354.2.c.a.353.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.2.c.a.353.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
354.2.c.a.353.10 | yes | 10 | 177.176 | even | 2 | inner | |
354.2.c.b.353.9 | yes | 10 | 59.58 | odd | 2 | ||
354.2.c.b.353.10 | yes | 10 | 3.2 | odd | 2 |