Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(151,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.i (of order \(3\), degree \(2\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.151 |
Dual form | 525.2.i.g.226.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.292893 | + | 0.507306i | −0.0883106 | + | 0.152958i | −0.906797 | − | 0.421567i | \(-0.861480\pi\) |
0.818487 | + | 0.574526i | \(0.194813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41421 | 1.22428 | 0.612141 | − | 0.790748i | \(-0.290308\pi\) | ||||
0.612141 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(14\) | −2.29289 | − | 2.95680i | −0.612801 | − | 0.790237i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 1.12132 | − | 1.94218i | 0.271960 | − | 0.471049i | −0.697404 | − | 0.716679i | \(-0.745661\pi\) |
0.969364 | + | 0.245630i | \(0.0789948\pi\) | |||||||
\(18\) | −0.707107 | + | 1.22474i | −0.166667 | + | 0.288675i | ||||
\(19\) | −2.32843 | − | 4.03295i | −0.534178 | − | 0.925223i | −0.999203 | − | 0.0399255i | \(-0.987288\pi\) |
0.465025 | − | 0.885298i | \(-0.346045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 2.44949i | −0.218218 | + | 0.534522i | ||||
\(22\) | 0.828427 | 0.176621 | ||||||||
\(23\) | 1.12132 | + | 1.94218i | 0.233811 | + | 0.404973i | 0.958927 | − | 0.283654i | \(-0.0915468\pi\) |
−0.725115 | + | 0.688628i | \(0.758213\pi\) | |||||||
\(24\) | 1.41421 | − | 2.44949i | 0.288675 | − | 0.500000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.12132 | − | 5.40629i | −0.612141 | − | 1.06026i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24264 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.91421 | − | 5.04757i | 0.523408 | − | 0.906570i | −0.476221 | − | 0.879326i | \(-0.657994\pi\) |
0.999629 | − | 0.0272438i | \(-0.00867303\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.292893 | − | 0.507306i | −0.0509862 | − | 0.0883106i | ||||
\(34\) | −3.17157 | −0.543920 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.20711 | − | 7.28692i | −0.691644 | − | 1.19796i | −0.971299 | − | 0.237862i | \(-0.923553\pi\) |
0.279655 | − | 0.960101i | \(-0.409780\pi\) | |||||||
\(38\) | −3.29289 | + | 5.70346i | −0.534178 | + | 0.925223i | ||||
\(39\) | −2.20711 | + | 3.82282i | −0.353420 | + | 0.612141i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 3.70711 | − | 0.507306i | 0.572019 | − | 0.0782790i | ||||
\(43\) | 7.58579 | 1.15682 | 0.578411 | − | 0.815746i | \(-0.303673\pi\) | ||||
0.578411 | + | 0.815746i | \(0.303673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.58579 | − | 2.74666i | 0.233811 | − | 0.404973i | ||||
\(47\) | −6.65685 | − | 11.5300i | −0.971002 | − | 1.68182i | −0.692543 | − | 0.721377i | \(-0.743510\pi\) |
−0.278459 | − | 0.960448i | \(-0.589824\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.12132 | + | 1.94218i | 0.157016 | + | 0.271960i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.41421 | − | 5.91359i | 0.468978 | − | 0.812294i | −0.530393 | − | 0.847752i | \(-0.677956\pi\) |
0.999371 | + | 0.0354577i | \(0.0112889\pi\) | |||||||
\(54\) | −0.707107 | − | 1.22474i | −0.0962250 | − | 0.166667i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.41421 | + | 1.01461i | −0.990766 | + | 0.135583i | ||||
\(57\) | 4.65685 | 0.616815 | ||||||||
\(58\) | −5.82843 | − | 10.0951i | −0.765310 | − | 1.32556i | ||||
\(59\) | 0.707107 | − | 1.22474i | 0.0920575 | − | 0.159448i | −0.816319 | − | 0.577601i | \(-0.803989\pi\) |
0.908377 | + | 0.418153i | \(0.137322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24264 | + | 3.88437i | 0.287141 | + | 0.497342i | 0.973126 | − | 0.230273i | \(-0.0739619\pi\) |
−0.685985 | + | 0.727615i | \(0.740629\pi\) | |||||||
\(62\) | −8.24264 | −1.04682 | ||||||||
\(63\) | −1.62132 | − | 2.09077i | −0.204267 | − | 0.263412i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.414214 | + | 0.717439i | −0.0509862 | + | 0.0883106i | ||||
\(67\) | −6.86396 | + | 11.8887i | −0.838566 | + | 1.45244i | 0.0525271 | + | 0.998619i | \(0.483272\pi\) |
−0.891093 | + | 0.453820i | \(0.850061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.24264 | −0.269982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.585786 | −0.0695201 | −0.0347600 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347600 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(72\) | 1.41421 | + | 2.44949i | 0.166667 | + | 0.288675i | ||||
\(73\) | −6.03553 | + | 10.4539i | −0.706406 | + | 1.22353i | 0.259776 | + | 0.965669i | \(0.416351\pi\) |
−0.966182 | + | 0.257862i | \(0.916982\pi\) | |||||||
\(74\) | −5.94975 | + | 10.3053i | −0.691644 | + | 1.19796i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.585786 | + | 1.43488i | −0.0667566 | + | 0.163520i | ||||
\(78\) | 6.24264 | 0.706840 | ||||||||
\(79\) | −3.32843 | − | 5.76500i | −0.374477 | − | 0.648614i | 0.615771 | − | 0.787925i | \(-0.288845\pi\) |
−0.990249 | + | 0.139311i | \(0.955511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.41421 | + | 7.64564i | 0.487468 | + | 0.844320i | ||||
\(83\) | −2.58579 | −0.283827 | −0.141913 | − | 0.989879i | \(-0.545325\pi\) | ||||
−0.141913 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.36396 | − | 9.29065i | −0.578411 | − | 1.00184i | ||||
\(87\) | −4.12132 | + | 7.13834i | −0.441852 | + | 0.765310i | ||||
\(88\) | 0.828427 | − | 1.43488i | 0.0883106 | − | 0.152958i | ||||
\(89\) | 6.12132 | + | 10.6024i | 0.648859 | + | 1.12386i | 0.983396 | + | 0.181474i | \(0.0580867\pi\) |
−0.334537 | + | 0.942383i | \(0.608580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.5711 | − | 1.58346i | 1.21298 | − | 0.165992i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.91421 | + | 5.04757i | 0.302190 | + | 0.523408i | ||||
\(94\) | −9.41421 | + | 16.3059i | −0.971002 | + | 1.68182i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17157 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(98\) | −7.07107 | − | 6.92820i | −0.714286 | − | 0.699854i | ||||
\(99\) | 0.585786 | 0.0588738 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.12132 | + | 1.94218i | −0.111576 | + | 0.193255i | −0.916406 | − | 0.400251i | \(-0.868923\pi\) |
0.804830 | + | 0.593505i | \(0.202256\pi\) | |||||||
\(102\) | 1.58579 | − | 2.74666i | 0.157016 | − | 0.271960i | ||||
\(103\) | 3.62132 | + | 6.27231i | 0.356819 | + | 0.618029i | 0.987428 | − | 0.158072i | \(-0.0505279\pi\) |
−0.630608 | + | 0.776101i | \(0.717195\pi\) | |||||||
\(104\) | −12.4853 | −1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.65685 | −0.937957 | ||||||||
\(107\) | 6.29289 | + | 10.8996i | 0.608357 | + | 1.05371i | 0.991511 | + | 0.130021i | \(0.0415044\pi\) |
−0.383154 | + | 0.923684i | \(0.625162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.74264 | + | 3.01834i | −0.166915 | + | 0.289105i | −0.937334 | − | 0.348433i | \(-0.886714\pi\) |
0.770419 | + | 0.637538i | \(0.220047\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.41421 | 0.798642 | ||||||||
\(112\) | 6.48528 | + | 8.36308i | 0.612801 | + | 0.790237i | ||||
\(113\) | 15.6569 | 1.47287 | 0.736436 | − | 0.676507i | \(-0.236507\pi\) | ||||
0.736436 | + | 0.676507i | \(0.236507\pi\) | |||||||
\(114\) | −3.29289 | − | 5.70346i | −0.308408 | − | 0.534178i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.20711 | − | 3.82282i | −0.204047 | − | 0.353420i | ||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | 2.24264 | − | 5.49333i | 0.205583 | − | 0.503572i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32843 | + | 9.22911i | 0.484402 | + | 0.839010i | ||||
\(122\) | 3.17157 | − | 5.49333i | 0.287141 | − | 0.497342i | ||||
\(123\) | 3.12132 | − | 5.40629i | 0.281440 | − | 0.487468i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.41421 | + | 3.46410i | −0.125988 | + | 0.308607i | ||||
\(127\) | 3.92893 | 0.348636 | 0.174318 | − | 0.984689i | \(-0.444228\pi\) | ||||
0.174318 | + | 0.984689i | \(0.444228\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.500000 | − | 0.866025i | ||||
\(129\) | −3.79289 | + | 6.56948i | −0.333946 | + | 0.578411i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.24264 | − | 5.61642i | −0.283311 | − | 0.490709i | 0.688887 | − | 0.724868i | \(-0.258099\pi\) |
−0.972198 | + | 0.234160i | \(0.924766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.55025 | − | 9.73641i | −0.654690 | − | 0.844254i | ||||
\(134\) | 19.4142 | 1.67713 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.17157 | + | 5.49333i | −0.271960 | + | 0.471049i | ||||
\(137\) | −8.53553 | + | 14.7840i | −0.729240 | + | 1.26308i | 0.227965 | + | 0.973669i | \(0.426793\pi\) |
−0.957205 | + | 0.289411i | \(0.906541\pi\) | |||||||
\(138\) | 1.58579 | + | 2.74666i | 0.134991 | + | 0.233811i | ||||
\(139\) | −5.48528 | −0.465255 | −0.232628 | − | 0.972566i | \(-0.574732\pi\) | ||||
−0.232628 | + | 0.972566i | \(0.574732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3137 | 1.12122 | ||||||||
\(142\) | 0.414214 | + | 0.717439i | 0.0347600 | + | 0.0602061i | ||||
\(143\) | −1.29289 | + | 2.23936i | −0.108117 | + | 0.187264i | ||||
\(144\) | 2.00000 | − | 3.46410i | 0.166667 | − | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.0711 | 1.41281 | ||||||||
\(147\) | −1.74264 | + | 6.77962i | −0.143731 | + | 0.559173i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.17157 | − | 5.49333i | −0.259825 | − | 0.450031i | 0.706370 | − | 0.707843i | \(-0.250332\pi\) |
−0.966195 | + | 0.257812i | \(0.916998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.24264 | + | 9.08052i | −0.426640 | + | 0.738962i | −0.996572 | − | 0.0827296i | \(-0.973636\pi\) |
0.569932 | + | 0.821692i | \(0.306970\pi\) | |||||||
\(152\) | 6.58579 | + | 11.4069i | 0.534178 | + | 0.925223i | ||||
\(153\) | −2.24264 | −0.181307 | ||||||||
\(154\) | 2.17157 | − | 0.297173i | 0.174990 | − | 0.0239469i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.07107 | − | 10.5154i | 0.484524 | − | 0.839220i | −0.515318 | − | 0.856999i | \(-0.672326\pi\) |
0.999842 | + | 0.0177789i | \(0.00565951\pi\) | |||||||
\(158\) | −4.70711 | + | 8.15295i | −0.374477 | + | 0.648614i | ||||
\(159\) | 3.41421 | + | 5.91359i | 0.270765 | + | 0.468978i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.63604 | + | 4.68885i | 0.286560 | + | 0.369533i | ||||
\(162\) | 1.41421 | 0.111111 | ||||||||
\(163\) | 1.65685 | + | 2.86976i | 0.129775 | + | 0.224777i | 0.923589 | − | 0.383383i | \(-0.125241\pi\) |
−0.793814 | + | 0.608160i | \(0.791908\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.82843 | + | 3.16693i | 0.141913 | + | 0.245801i | ||||
\(167\) | −20.2426 | −1.56642 | −0.783211 | − | 0.621756i | \(-0.786420\pi\) | ||||
−0.783211 | + | 0.621756i | \(0.786420\pi\) | |||||||
\(168\) | 2.82843 | − | 6.92820i | 0.218218 | − | 0.534522i | ||||
\(169\) | 6.48528 | 0.498868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.32843 | + | 4.03295i | −0.178059 | + | 0.308408i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41421 | + | 2.44949i | 0.107521 | + | 0.186231i | 0.914765 | − | 0.403986i | \(-0.132375\pi\) |
−0.807245 | + | 0.590217i | \(0.799042\pi\) | |||||||
\(174\) | 11.6569 | 0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.34315 | −0.176621 | ||||||||
\(177\) | 0.707107 | + | 1.22474i | 0.0531494 | + | 0.0920575i | ||||
\(178\) | 8.65685 | − | 14.9941i | 0.648859 | − | 1.12386i | ||||
\(179\) | −4.17157 | + | 7.22538i | −0.311798 | + | 0.540050i | −0.978752 | − | 0.205049i | \(-0.934265\pi\) |
0.666954 | + | 0.745099i | \(0.267598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6569 | −0.792118 | −0.396059 | − | 0.918225i | \(-0.629622\pi\) | ||||
−0.396059 | + | 0.918225i | \(0.629622\pi\) | |||||||
\(182\) | −10.1213 | − | 13.0519i | −0.750242 | − | 0.967473i | ||||
\(183\) | −4.48528 | −0.331562 | ||||||||
\(184\) | −3.17157 | − | 5.49333i | −0.233811 | − | 0.404973i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.12132 | − | 7.13834i | 0.302190 | − | 0.523408i | ||||
\(187\) | 0.656854 | + | 1.13770i | 0.0480339 | + | 0.0831972i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.62132 | − | 0.358719i | 0.190673 | − | 0.0260930i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.48528 | + | 12.9649i | 0.541616 | + | 0.938106i | 0.998811 | + | 0.0487401i | \(0.0155206\pi\) |
−0.457196 | + | 0.889366i | \(0.651146\pi\) | |||||||
\(192\) | −4.00000 | + | 6.92820i | −0.288675 | + | 0.500000i | ||||
\(193\) | −7.62132 | + | 13.2005i | −0.548595 | + | 0.950194i | 0.449777 | + | 0.893141i | \(0.351504\pi\) |
−0.998371 | + | 0.0570527i | \(0.981830\pi\) | |||||||
\(194\) | −3.65685 | − | 6.33386i | −0.262547 | − | 0.454744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5563 | 1.82081 | 0.910407 | − | 0.413713i | \(-0.135768\pi\) | ||||
0.910407 | + | 0.413713i | \(0.135768\pi\) | |||||||
\(198\) | −0.414214 | − | 0.717439i | −0.0294369 | − | 0.0509862i | ||||
\(199\) | −11.2426 | + | 19.4728i | −0.796970 | + | 1.38039i | 0.124611 | + | 0.992206i | \(0.460232\pi\) |
−0.921581 | + | 0.388186i | \(0.873102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.86396 | − | 11.8887i | −0.484146 | − | 0.838566i | ||||
\(202\) | 3.17157 | 0.223151 | ||||||||
\(203\) | 21.6066 | − | 2.95680i | 1.51649 | − | 0.207526i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.12132 | − | 8.87039i | 0.356819 | − | 0.618029i | ||||
\(207\) | 1.12132 | − | 1.94218i | 0.0779372 | − | 0.134991i | ||||
\(208\) | 8.82843 | + | 15.2913i | 0.612141 | + | 1.06026i | ||||
\(209\) | 2.72792 | 0.188694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.1421 | −1.93738 | −0.968692 | − | 0.248265i | \(-0.920140\pi\) | ||||
−0.968692 | + | 0.248265i | \(0.920140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.292893 | − | 0.507306i | 0.0200687 | − | 0.0347600i | ||||
\(214\) | 8.89949 | − | 15.4144i | 0.608357 | − | 1.05371i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.82843 | −0.192450 | ||||||||
\(217\) | 5.82843 | − | 14.2767i | 0.395659 | − | 0.969164i | ||||
\(218\) | 4.92893 | 0.333829 | ||||||||
\(219\) | −6.03553 | − | 10.4539i | −0.407844 | − | 0.706406i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.94975 | − | 8.57321i | 0.332956 | − | 0.576697i | ||||
\(222\) | −5.94975 | − | 10.3053i | −0.399321 | − | 0.691644i | ||||
\(223\) | −22.8284 | −1.52870 | −0.764352 | − | 0.644799i | \(-0.776941\pi\) | ||||
−0.764352 | + | 0.644799i | \(0.776941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0711 | − | 19.1757i | −0.736436 | − | 1.27555i | ||||
\(227\) | 4.46447 | − | 7.73268i | 0.296317 | − | 0.513236i | −0.678973 | − | 0.734163i | \(-0.737575\pi\) |
0.975290 | + | 0.220927i | \(0.0709082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.15685 | − | 7.19988i | −0.274693 | − | 0.475782i | 0.695365 | − | 0.718657i | \(-0.255243\pi\) |
−0.970058 | + | 0.242875i | \(0.921909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.949747 | − | 1.22474i | −0.0624888 | − | 0.0805823i | ||||
\(232\) | −23.3137 | −1.53062 | ||||||||
\(233\) | −2.75736 | − | 4.77589i | −0.180641 | − | 0.312879i | 0.761458 | − | 0.648214i | \(-0.224484\pi\) |
−0.942099 | + | 0.335335i | \(0.891150\pi\) | |||||||
\(234\) | −3.12132 | + | 5.40629i | −0.204047 | + | 0.353420i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.65685 | 0.432409 | ||||||||
\(238\) | −8.31371 | + | 1.13770i | −0.538898 | + | 0.0737465i | ||||
\(239\) | −5.31371 | −0.343715 | −0.171858 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171858 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8284 | − | 18.7554i | 0.697520 | − | 1.20814i | −0.271803 | − | 0.962353i | \(-0.587620\pi\) |
0.969324 | − | 0.245788i | \(-0.0790466\pi\) | |||||||
\(242\) | 7.53553 | − | 13.0519i | 0.484402 | − | 0.839010i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.82843 | −0.562880 | ||||||||
\(247\) | −10.2782 | − | 17.8023i | −0.653985 | − | 1.13273i | ||||
\(248\) | −8.24264 | + | 14.2767i | −0.523408 | + | 0.906570i | ||||
\(249\) | 1.29289 | − | 2.23936i | 0.0819338 | − | 0.141913i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.58579 | −0.163213 | −0.0816067 | − | 0.996665i | \(-0.526005\pi\) | ||||
−0.0816067 | + | 0.996665i | \(0.526005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31371 | −0.0825921 | ||||||||
\(254\) | −2.77817 | − | 4.81194i | −0.174318 | − | 0.301928i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.05025 | − | 8.74729i | −0.315026 | − | 0.545641i | 0.664417 | − | 0.747362i | \(-0.268680\pi\) |
−0.979443 | + | 0.201721i | \(0.935347\pi\) | |||||||
\(258\) | 10.7279 | 0.667891 | ||||||||
\(259\) | −13.6421 | − | 17.5922i | −0.847681 | − | 1.09313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.12132 | − | 7.13834i | −0.255103 | − | 0.441852i | ||||
\(262\) | −4.58579 | + | 7.94282i | −0.283311 | + | 0.490709i | ||||
\(263\) | 3.41421 | − | 5.91359i | 0.210529 | − | 0.364648i | −0.741351 | − | 0.671118i | \(-0.765815\pi\) |
0.951880 | + | 0.306470i | \(0.0991479\pi\) | |||||||
\(264\) | 0.828427 | + | 1.43488i | 0.0509862 | + | 0.0883106i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.58579 | + | 16.1318i | −0.403800 | + | 0.989105i | ||||
\(267\) | −12.2426 | −0.749237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0711 | − | 17.4436i | 0.614044 | − | 1.06356i | −0.376508 | − | 0.926414i | \(-0.622875\pi\) |
0.990551 | − | 0.137142i | \(-0.0437915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.07107 | + | 7.05130i | 0.247300 | + | 0.428336i | 0.962776 | − | 0.270302i | \(-0.0871234\pi\) |
−0.715476 | + | 0.698637i | \(0.753790\pi\) | |||||||
\(272\) | 8.97056 | 0.543920 | ||||||||
\(273\) | −4.41421 | + | 10.8126i | −0.267160 | + | 0.654407i | ||||
\(274\) | 24.1421 | 1.45848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.69239 | − | 11.5916i | 0.402107 | − | 0.696469i | −0.591873 | − | 0.806031i | \(-0.701611\pi\) |
0.993980 | + | 0.109562i | \(0.0349448\pi\) | |||||||
\(278\) | 3.87868 | + | 6.71807i | 0.232628 | + | 0.402923i | ||||
\(279\) | −5.82843 | −0.348939 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65685 | −0.0988396 | −0.0494198 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494198 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(282\) | −9.41421 | − | 16.3059i | −0.560608 | − | 0.971002i | ||||
\(283\) | −2.37868 | + | 4.11999i | −0.141398 | + | 0.244908i | −0.928023 | − | 0.372522i | \(-0.878493\pi\) |
0.786625 | + | 0.617431i | \(0.211826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.65685 | 0.216234 | ||||||||
\(287\) | −16.3640 | + | 2.23936i | −0.965934 | + | 0.132185i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.98528 | + | 10.3668i | 0.352075 | + | 0.609812i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.58579 | + | 4.47871i | −0.151581 | + | 0.262547i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.31371 | −0.427271 | −0.213636 | − | 0.976913i | \(-0.568531\pi\) | ||||
−0.213636 | + | 0.976913i | \(0.568531\pi\) | |||||||
\(294\) | 9.53553 | − | 2.65962i | 0.556124 | − | 0.155112i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.8995 | + | 20.6105i | 0.691644 | + | 1.19796i | ||||
\(297\) | −0.292893 | + | 0.507306i | −0.0169954 | + | 0.0294369i | ||||
\(298\) | −4.48528 | + | 7.76874i | −0.259825 | + | 0.450031i | ||||
\(299\) | 4.94975 | + | 8.57321i | 0.286251 | + | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.8848 | − | 2.72117i | 1.14614 | − | 0.156846i | ||||
\(302\) | 14.8284 | 0.853280 | ||||||||
\(303\) | −1.12132 | − | 1.94218i | −0.0644182 | − | 0.111576i | ||||
\(304\) | 9.31371 | − | 16.1318i | 0.534178 | − | 0.925223i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.58579 | + | 2.74666i | 0.0906534 | + | 0.157016i | ||||
\(307\) | −4.41421 | −0.251932 | −0.125966 | − | 0.992035i | \(-0.540203\pi\) | ||||
−0.125966 | + | 0.992035i | \(0.540203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.24264 | −0.412019 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.46447 | − | 2.53653i | 0.0830423 | − | 0.143833i | −0.821513 | − | 0.570190i | \(-0.806870\pi\) |
0.904555 | + | 0.426356i | \(0.140203\pi\) | |||||||
\(312\) | 6.24264 | − | 10.8126i | 0.353420 | − | 0.612141i | ||||
\(313\) | −8.10660 | − | 14.0410i | −0.458212 | − | 0.793647i | 0.540654 | − | 0.841245i | \(-0.318177\pi\) |
−0.998867 | + | 0.0475980i | \(0.984843\pi\) | |||||||
\(314\) | −17.1716 | −0.969048 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.94975 | + | 17.2335i | 0.558833 | + | 0.967928i | 0.997594 | + | 0.0693241i | \(0.0220842\pi\) |
−0.438761 | + | 0.898604i | \(0.644582\pi\) | |||||||
\(318\) | 4.82843 | − | 8.36308i | 0.270765 | − | 0.468978i | ||||
\(319\) | −2.41421 | + | 4.18154i | −0.135170 | + | 0.234121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.5858 | −0.702470 | ||||||||
\(322\) | 3.17157 | − | 7.76874i | 0.176745 | − | 0.432935i | ||||
\(323\) | −10.4437 | −0.581100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.34315 | − | 4.05845i | 0.129775 | − | 0.224777i | ||||
\(327\) | −1.74264 | − | 3.01834i | −0.0963683 | − | 0.166915i | ||||
\(328\) | 17.6569 | 0.974937 | ||||||||
\(329\) | −21.5858 | − | 27.8359i | −1.19006 | − | 1.53464i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.81371 | − | 15.2658i | −0.484445 | − | 0.839084i | 0.515395 | − | 0.856953i | \(-0.327645\pi\) |
−0.999840 | + | 0.0178689i | \(0.994312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.20711 | + | 7.28692i | −0.230548 | + | 0.399321i | ||||
\(334\) | 14.3137 | + | 24.7921i | 0.783211 | + | 1.35656i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.4853 | + | 1.43488i | −0.572019 | + | 0.0782790i | ||||
\(337\) | −18.8995 | −1.02952 | −0.514761 | − | 0.857334i | \(-0.672119\pi\) | ||||
−0.514761 | + | 0.857334i | \(0.672119\pi\) | |||||||
\(338\) | −4.58579 | − | 7.94282i | −0.249434 | − | 0.432032i | ||||
\(339\) | −7.82843 | + | 13.5592i | −0.425182 | + | 0.736436i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70711 | + | 2.95680i | 0.0924450 | + | 0.160119i | ||||
\(342\) | 6.58579 | 0.356119 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | −21.4558 | −1.15682 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | − | 3.46410i | 0.107521 | − | 0.186231i | ||||
\(347\) | 4.48528 | − | 7.76874i | 0.240783 | − | 0.417048i | −0.720155 | − | 0.693813i | \(-0.755929\pi\) |
0.960937 | + | 0.276766i | \(0.0892626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6274 | 1.53239 | 0.766195 | − | 0.642608i | \(-0.222148\pi\) | ||||
0.766195 | + | 0.642608i | \(0.222148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.41421 | 0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.94975 | + | 12.0373i | −0.369898 | + | 0.640682i | −0.989549 | − | 0.144195i | \(-0.953941\pi\) |
0.619651 | + | 0.784877i | \(0.287274\pi\) | |||||||
\(354\) | 1.00000 | − | 1.73205i | 0.0531494 | − | 0.0920575i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.63604 | + | 4.68885i | 0.192440 | + | 0.248160i | ||||
\(358\) | 11.7990 | 0.623596 | ||||||||
\(359\) | 14.7071 | + | 25.4735i | 0.776211 | + | 1.34444i | 0.934111 | + | 0.356982i | \(0.116194\pi\) |
−0.157900 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.34315 | + | 2.32640i | −0.0706919 | + | 0.122442i | ||||
\(362\) | 7.53553 | + | 13.0519i | 0.396059 | + | 0.685994i | ||||
\(363\) | −10.6569 | −0.559340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.17157 | + | 5.49333i | 0.165781 | + | 0.287141i | ||||
\(367\) | −11.2071 | + | 19.4113i | −0.585006 | + | 1.01326i | 0.409868 | + | 0.912145i | \(0.365575\pi\) |
−0.994875 | + | 0.101116i | \(0.967759\pi\) | |||||||
\(368\) | −4.48528 | + | 7.76874i | −0.233811 | + | 0.404973i | ||||
\(369\) | 3.12132 | + | 5.40629i | 0.162489 | + | 0.281440i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.82843 | − | 16.7262i | 0.354514 | − | 0.868379i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.37868 | + | 9.31615i | 0.278497 | + | 0.482372i | 0.971012 | − | 0.239033i | \(-0.0768303\pi\) |
−0.692514 | + | 0.721404i | \(0.743497\pi\) | |||||||
\(374\) | 0.928932 | − | 1.60896i | 0.0480339 | − | 0.0831972i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.8284 | + | 32.6118i | 0.971002 | + | 1.68182i | ||||
\(377\) | 36.3848 | 1.87391 | ||||||||
\(378\) | −2.29289 | − | 2.95680i | −0.117934 | − | 0.152081i | ||||
\(379\) | −24.7990 | −1.27384 | −0.636919 | − | 0.770931i | \(-0.719792\pi\) | ||||
−0.636919 | + | 0.770931i | \(0.719792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.96447 | + | 3.40256i | −0.100643 | + | 0.174318i | ||||
\(382\) | 10.5858 | − | 18.3351i | 0.541616 | − | 0.938106i | ||||
\(383\) | −2.24264 | − | 3.88437i | −0.114594 | − | 0.198482i | 0.803024 | − | 0.595947i | \(-0.203223\pi\) |
−0.917617 | + | 0.397465i | \(0.869890\pi\) | |||||||
\(384\) | 11.3137 | 0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.5563 | 1.09719 | ||||||||
\(387\) | −3.79289 | − | 6.56948i | −0.192804 | − | 0.333946i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4350 | − | 31.9304i | 0.934693 | − | 1.61894i | 0.159513 | − | 0.987196i | \(-0.449008\pi\) |
0.775180 | − | 0.631740i | \(-0.217659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.02944 | 0.254350 | ||||||||
\(392\) | −19.0711 | + | 5.31925i | −0.963234 | + | 0.268662i | ||||
\(393\) | 6.48528 | 0.327139 | ||||||||
\(394\) | −18.0711 | − | 31.3000i | −0.910407 | − | 1.57687i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.10660 | + | 15.7731i | 0.457047 | + | 0.791629i | 0.998803 | − | 0.0489067i | \(-0.0155737\pi\) |
−0.541756 | + | 0.840536i | \(0.682240\pi\) | |||||||
\(398\) | 31.7990 | 1.59394 | ||||||||
\(399\) | 12.2071 | − | 1.67050i | 0.611120 | − | 0.0836298i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.24264 | + | 14.2767i | 0.411618 | + | 0.712943i | 0.995067 | − | 0.0992068i | \(-0.0316305\pi\) |
−0.583449 | + | 0.812150i | \(0.698297\pi\) | |||||||
\(402\) | −9.70711 | + | 16.8132i | −0.484146 | + | 0.838566i | ||||
\(403\) | 12.8640 | − | 22.2810i | 0.640800 | − | 1.10990i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.8995 | − | 24.3718i | −0.937966 | − | 1.20955i | ||||
\(407\) | 4.92893 | 0.244318 | ||||||||
\(408\) | −3.17157 | − | 5.49333i | −0.157016 | − | 0.271960i | ||||
\(409\) | 1.84315 | − | 3.19242i | 0.0911377 | − | 0.157855i | −0.816852 | − | 0.576847i | \(-0.804283\pi\) |
0.907990 | + | 0.418992i | \(0.137616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.53553 | − | 14.7840i | −0.421027 | − | 0.729240i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41421 | − | 3.46410i | 0.0695889 | − | 0.170457i | ||||
\(414\) | −3.17157 | −0.155874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.74264 | − | 4.75039i | 0.134308 | − | 0.232628i | ||||
\(418\) | −1.92893 | − | 3.34101i | −0.0943472 | − | 0.163414i | ||||
\(419\) | −8.82843 | −0.431297 | −0.215648 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215648 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5147 | 0.512456 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(422\) | 19.8995 | + | 34.4669i | 0.968692 | + | 1.67782i | ||||
\(423\) | −6.65685 | + | 11.5300i | −0.323667 | + | 0.560608i | ||||
\(424\) | −9.65685 | + | 16.7262i | −0.468978 | + | 0.812294i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.828427 | −0.0401374 | ||||||||
\(427\) | 7.27208 | + | 9.37769i | 0.351921 | + | 0.453818i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.29289 | − | 2.23936i | −0.0624215 | − | 0.108117i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5858 | + | 26.9954i | −0.750741 | + | 1.30032i | 0.196723 | + | 0.980459i | \(0.436970\pi\) |
−0.947464 | + | 0.319862i | \(0.896363\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | −6.55635 | −0.315078 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(434\) | −21.6066 | + | 2.95680i | −1.03715 | + | 0.141931i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.22183 | − | 9.04447i | 0.249794 | − | 0.432656i | ||||
\(438\) | −8.53553 | + | 14.7840i | −0.407844 | + | 0.706406i | ||||
\(439\) | −5.82843 | − | 10.0951i | −0.278176 | − | 0.481814i | 0.692756 | − | 0.721172i | \(-0.256396\pi\) |
−0.970931 | + | 0.239358i | \(0.923063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | −8.24264 | − | 14.2767i | −0.391620 | − | 0.678305i | 0.601044 | − | 0.799216i | \(-0.294752\pi\) |
−0.992663 | + | 0.120911i | \(0.961418\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1421 | + | 27.9590i | 0.764352 | + | 1.32390i | ||||
\(447\) | 6.34315 | 0.300020 | ||||||||
\(448\) | 20.9706 | − | 2.86976i | 0.990766 | − | 0.135583i | ||||
\(449\) | 26.9706 | 1.27282 | 0.636410 | − | 0.771351i | \(-0.280419\pi\) | ||||
0.636410 | + | 0.771351i | \(0.280419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82843 | − | 3.16693i | 0.0860973 | − | 0.149125i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.24264 | − | 9.08052i | −0.246321 | − | 0.426640i | ||||
\(454\) | −12.6274 | −0.592634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.1716 | −0.616815 | ||||||||
\(457\) | −0.550253 | − | 0.953065i | −0.0257397 | − | 0.0445825i | 0.852869 | − | 0.522126i | \(-0.174861\pi\) |
−0.878608 | + | 0.477543i | \(0.841527\pi\) | |||||||
\(458\) | −5.87868 | + | 10.1822i | −0.274693 | + | 0.475782i | ||||
\(459\) | 1.12132 | − | 1.94218i | 0.0523388 | − | 0.0906534i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9289 | −0.602160 | −0.301080 | − | 0.953599i | \(-0.597347\pi\) | ||||
−0.301080 | + | 0.953599i | \(0.597347\pi\) | |||||||
\(462\) | −0.828427 | + | 2.02922i | −0.0385419 | + | 0.0944080i | ||||
\(463\) | 7.58579 | 0.352541 | 0.176271 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176271 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(464\) | 16.4853 | + | 28.5533i | 0.765310 | + | 1.32556i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.89949 | + | 6.75412i | −0.180641 | + | 0.312879i | ||||
\(467\) | 14.6569 | + | 25.3864i | 0.678238 | + | 1.17474i | 0.975511 | + | 0.219951i | \(0.0705896\pi\) |
−0.297273 | + | 0.954793i | \(0.596077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7279 | + | 33.6264i | −0.633897 | + | 1.55272i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.07107 | + | 10.5154i | 0.279740 | + | 0.484524i | ||||
\(472\) | −2.00000 | + | 3.46410i | −0.0920575 | + | 0.159448i | ||||
\(473\) | −2.22183 | + | 3.84831i | −0.102160 | + | 0.176946i | ||||
\(474\) | −4.70711 | − | 8.15295i | −0.216205 | − | 0.374477i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.82843 | −0.312652 | ||||||||
\(478\) | 3.75736 | + | 6.50794i | 0.171858 | + | 0.297666i | ||||
\(479\) | −5.31371 | + | 9.20361i | −0.242790 | + | 0.420524i | −0.961508 | − | 0.274778i | \(-0.911396\pi\) |
0.718718 | + | 0.695301i | \(0.244729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5711 | − | 32.1660i | −0.846768 | − | 1.46664i | ||||
\(482\) | −30.6274 | −1.39504 | ||||||||
\(483\) | −5.87868 | + | 0.804479i | −0.267489 | + | 0.0366051i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.707107 | + | 1.22474i | −0.0320750 | + | 0.0555556i | ||||
\(487\) | −9.44975 | + | 16.3674i | −0.428209 | + | 0.741680i | −0.996714 | − | 0.0810001i | \(-0.974189\pi\) |
0.568505 | + | 0.822680i | \(0.307522\pi\) | |||||||
\(488\) | −6.34315 | − | 10.9867i | −0.287141 | − | 0.497342i | ||||
\(489\) | −3.31371 | −0.149851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1421 | 0.818743 | 0.409372 | − | 0.912368i | \(-0.365748\pi\) | ||||
0.409372 | + | 0.912368i | \(0.365748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.24264 | − | 16.0087i | 0.416268 | − | 0.720997i | ||||
\(494\) | −14.5355 | + | 25.1763i | −0.653985 | + | 1.13273i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.3137 | 1.04682 | ||||||||
\(497\) | −1.53553 | + | 0.210133i | −0.0688781 | + | 0.00942575i | ||||
\(498\) | −3.65685 | −0.163868 | ||||||||
\(499\) | 15.3995 | + | 26.6727i | 0.689376 | + | 1.19403i | 0.972040 | + | 0.234815i | \(0.0754486\pi\) |
−0.282664 | + | 0.959219i | \(0.591218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1213 | − | 17.5306i | 0.452187 | − | 0.783211i | ||||
\(502\) | 1.82843 | + | 3.16693i | 0.0816067 | + | 0.141347i | ||||
\(503\) | 1.51472 | 0.0675380 | 0.0337690 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337690 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(504\) | 4.58579 | + | 5.91359i | 0.204267 | + | 0.263412i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.928932 | + | 1.60896i | 0.0412961 | + | 0.0715269i | ||||
\(507\) | −3.24264 | + | 5.61642i | −0.144011 | + | 0.249434i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8995 | + | 22.3426i | 0.571760 | + | 0.990317i | 0.996385 | + | 0.0849483i | \(0.0270725\pi\) |
−0.424625 | + | 0.905369i | \(0.639594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0711 | + | 29.5680i | −0.533993 | + | 1.30801i | ||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −2.32843 | − | 4.03295i | −0.102803 | − | 0.178059i | ||||
\(514\) | −7.14214 | + | 12.3705i | −0.315026 | + | 0.545641i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.79899 | 0.342999 | ||||||||
\(518\) | −11.8995 | + | 29.1477i | −0.522834 | + | 1.28068i | ||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5563 | + | 20.0162i | −0.506293 | + | 0.876925i | 0.493681 | + | 0.869643i | \(0.335651\pi\) |
−0.999973 | + | 0.00728166i | \(0.997682\pi\) | |||||||
\(522\) | −5.82843 | + | 10.0951i | −0.255103 | + | 0.441852i | ||||
\(523\) | −5.20711 | − | 9.01897i | −0.227691 | − | 0.394372i | 0.729432 | − | 0.684053i | \(-0.239784\pi\) |
−0.957123 | + | 0.289681i | \(0.906451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.65685 | −0.421059 | ||||||||
\(527\) | −6.53553 | − | 11.3199i | −0.284692 | − | 0.493102i | ||||
\(528\) | 1.17157 | − | 2.02922i | 0.0509862 | − | 0.0883106i | ||||
\(529\) | 8.98528 | − | 15.5630i | 0.390664 | − | 0.676651i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.41421 | −0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.5563 | −1.19360 | ||||||||
\(534\) | 8.65685 | + | 14.9941i | 0.374619 | + | 0.648859i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.4142 | − | 33.6264i | 0.838566 | − | 1.45244i | ||||
\(537\) | −4.17157 | − | 7.22538i | −0.180017 | − | 0.311798i | ||||
\(538\) | −28.4853 | −1.22809 | ||||||||
\(539\) | −1.02082 | + | 3.97141i | −0.0439696 | + | 0.171061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.84315 | − | 8.38857i | −0.208223 | − | 0.360653i | 0.742932 | − | 0.669367i | \(-0.233435\pi\) |
−0.951155 | + | 0.308714i | \(0.900101\pi\) | |||||||
\(542\) | 5.75736 | − | 9.97204i | 0.247300 | − | 0.428336i | ||||
\(543\) | 5.32843 | − | 9.22911i | 0.228665 | − | 0.396059i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.3640 | − | 2.23936i | 0.700313 | − | 0.0958356i | ||||
\(547\) | −7.79899 | −0.333461 | −0.166730 | − | 0.986003i | \(-0.553321\pi\) | ||||
−0.166730 | + | 0.986003i | \(0.553321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.24264 | − | 3.88437i | 0.0957136 | − | 0.165781i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.1924 | − | 33.2422i | −0.817623 | − | 1.41616i | ||||
\(552\) | 6.34315 | 0.269982 | ||||||||
\(553\) | −10.7929 | − | 13.9180i | −0.458961 | − | 0.591852i | ||||
\(554\) | −18.9289 | −0.804213 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.82843 | + | 17.0233i | −0.416444 | + | 0.721302i | −0.995579 | − | 0.0939298i | \(-0.970057\pi\) |
0.579135 | + | 0.815232i | \(0.303390\pi\) | |||||||
\(558\) | 4.12132 | + | 7.13834i | 0.174469 | + | 0.302190i | ||||
\(559\) | 33.4853 | 1.41628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31371 | −0.0554648 | ||||||||
\(562\) | 1.17157 | + | 2.02922i | 0.0494198 | + | 0.0855976i | ||||
\(563\) | 21.1421 | − | 36.6193i | 0.891035 | − | 1.54332i | 0.0523981 | − | 0.998626i | \(-0.483314\pi\) |
0.838637 | − | 0.544691i | \(-0.183353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.72792 | 0.282796 | ||||||||
\(567\) | −1.00000 | + | 2.44949i | −0.0419961 | + | 0.102869i | ||||
\(568\) | 1.65685 | 0.0695201 | ||||||||
\(569\) | −8.43503 | − | 14.6099i | −0.353615 | − | 0.612479i | 0.633265 | − | 0.773935i | \(-0.281714\pi\) |
−0.986880 | + | 0.161456i | \(0.948381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.98528 | − | 5.17066i | 0.124930 | − | 0.216385i | −0.796775 | − | 0.604275i | \(-0.793463\pi\) |
0.921706 | + | 0.387890i | \(0.126796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.9706 | −0.625404 | ||||||||
\(574\) | 14.3137 | + | 18.4582i | 0.597443 | + | 0.770431i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | ||||
\(577\) | −12.2782 | + | 21.2664i | −0.511147 | + | 0.885333i | 0.488769 | + | 0.872413i | \(0.337446\pi\) |
−0.999917 | + | 0.0129197i | \(0.995887\pi\) | |||||||
\(578\) | 8.46447 | − | 14.6609i | 0.352075 | − | 0.609812i | ||||
\(579\) | −7.62132 | − | 13.2005i | −0.316731 | − | 0.548595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.77817 | + | 0.927572i | −0.281206 | + | 0.0384822i | ||||
\(582\) | 7.31371 | 0.303163 | ||||||||
\(583\) | 2.00000 | + | 3.46410i | 0.0828315 | + | 0.143468i | ||||
\(584\) | 17.0711 | − | 29.5680i | 0.706406 | − | 1.22353i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.17157 | + | 8.95743i | 0.213636 | + | 0.370028i | ||||
\(587\) | −21.7574 | −0.898022 | −0.449011 | − | 0.893526i | \(-0.648224\pi\) | ||||
−0.449011 | + | 0.893526i | \(0.648224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.1421 | −1.11837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7782 | + | 22.1324i | −0.525624 | + | 0.910407i | ||||
\(592\) | 16.8284 | − | 29.1477i | 0.691644 | − | 1.19796i | ||||
\(593\) | 5.29289 | + | 9.16756i | 0.217353 | + | 0.376467i | 0.953998 | − | 0.299813i | \(-0.0969244\pi\) |
−0.736645 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2426 | − | 19.4728i | −0.460131 | − | 0.796970i | ||||
\(598\) | 7.00000 | − | 12.1244i | 0.286251 | − | 0.495802i | ||||
\(599\) | 6.92893 | − | 12.0013i | 0.283108 | − | 0.490358i | −0.689040 | − | 0.724723i | \(-0.741968\pi\) |
0.972149 | + | 0.234365i | \(0.0753010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8284 | −1.21673 | −0.608363 | − | 0.793659i | \(-0.708174\pi\) | ||||
−0.608363 | + | 0.793659i | \(0.708174\pi\) | |||||||
\(602\) | −17.3934 | − | 22.4296i | −0.708902 | − | 0.914163i | ||||
\(603\) | 13.7279 | 0.559044 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.58579 | + | 2.74666i | −0.0644182 | + | 0.111576i | ||||
\(607\) | 3.62132 | + | 6.27231i | 0.146985 | + | 0.254585i | 0.930112 | − | 0.367277i | \(-0.119710\pi\) |
−0.783127 | + | 0.621862i | \(0.786376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.24264 | + | 20.1903i | −0.334009 | + | 0.818151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.3848 | − | 50.8959i | −1.18878 | − | 2.05903i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.07107 | + | 15.7116i | −0.366377 | + | 0.634584i | −0.988996 | − | 0.147941i | \(-0.952735\pi\) |
0.622619 | + | 0.782525i | \(0.286069\pi\) | |||||||
\(614\) | 3.12132 | + | 5.40629i | 0.125966 | + | 0.218180i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.65685 | − | 4.05845i | 0.0667566 | − | 0.163520i | ||||
\(617\) | 3.17157 | 0.127683 | 0.0638414 | − | 0.997960i | \(-0.479665\pi\) | ||||
0.0638414 | + | 0.997960i | \(0.479665\pi\) | |||||||
\(618\) | 5.12132 | + | 8.87039i | 0.206010 | + | 0.356819i | ||||
\(619\) | −3.01472 | + | 5.22165i | −0.121172 | + | 0.209876i | −0.920230 | − | 0.391378i | \(-0.871999\pi\) |
0.799058 | + | 0.601254i | \(0.205332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12132 | + | 1.94218i | 0.0449970 | + | 0.0779372i | ||||
\(622\) | −4.14214 | −0.166085 | ||||||||
\(623\) | 19.8492 | + | 25.5965i | 0.795243 | + | 1.02550i | ||||
\(624\) | −17.6569 | −0.706840 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.4645 | + | 19.8570i | −0.458212 | + | 0.793647i | ||||
\(627\) | −1.36396 | + | 2.36245i | −0.0544714 | + | 0.0943472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.8701 | −0.752398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 9.41421 | + | 16.3059i | 0.374477 | + | 0.648614i | ||||
\(633\) | 14.0711 | − | 24.3718i | 0.559275 | − | 0.968692i | ||||
\(634\) | 14.0711 | − | 24.3718i | 0.558833 | − | 0.967928i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.7635 | − | 8.30153i | 1.17927 | − | 0.328919i | ||||
\(638\) | 6.82843 | 0.270340 | ||||||||
\(639\) | 0.292893 | + | 0.507306i | 0.0115867 | + | 0.0200687i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.6066 | + | 25.2994i | −0.576926 | + | 0.999265i | 0.418903 | + | 0.908031i | \(0.362415\pi\) |
−0.995829 | + | 0.0912345i | \(0.970919\pi\) | |||||||
\(642\) | 8.89949 | + | 15.4144i | 0.351235 | + | 0.608357i | ||||
\(643\) | 6.55635 | 0.258557 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.38478 | + | 12.7908i | 0.290550 | + | 0.503248i | ||||
\(647\) | 23.1924 | − | 40.1704i | 0.911787 | − | 1.57926i | 0.100248 | − | 0.994962i | \(-0.468036\pi\) |
0.811539 | − | 0.584299i | \(-0.198630\pi\) | |||||||
\(648\) | 1.41421 | − | 2.44949i | 0.0555556 | − | 0.0962250i | ||||
\(649\) | 0.414214 | + | 0.717439i | 0.0162593 | + | 0.0281619i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.44975 | + | 12.1859i | 0.370365 | + | 0.477603i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.12132 | + | 14.0665i | 0.317812 | + | 0.550466i | 0.980031 | − | 0.198844i | \(-0.0637186\pi\) |
−0.662219 | + | 0.749310i | \(0.730385\pi\) | |||||||
\(654\) | −2.46447 | + | 4.26858i | −0.0963683 | + | 0.166915i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.4853 | − | 21.6251i | −0.487468 | − | 0.844320i | ||||
\(657\) | 12.0711 | 0.470937 | ||||||||
\(658\) | −18.8284 | + | 46.1200i | −0.734009 | + | 1.79795i | ||||
\(659\) | −4.68629 | −0.182552 | −0.0912760 | − | 0.995826i | \(-0.529095\pi\) | ||||
−0.0912760 | + | 0.995826i | \(0.529095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.84315 | + | 8.38857i | −0.188377 | + | 0.326278i | −0.944709 | − | 0.327910i | \(-0.893656\pi\) |
0.756333 | + | 0.654187i | \(0.226989\pi\) | |||||||
\(662\) | −12.4645 | + | 21.5891i | −0.484445 | + | 0.839084i | ||||
\(663\) | 4.94975 | + | 8.57321i | 0.192232 | + | 0.332956i | ||||
\(664\) | 7.31371 | 0.283827 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.8995 | 0.461096 | ||||||||
\(667\) | 9.24264 | + | 16.0087i | 0.357876 | + | 0.619860i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.4142 | − | 19.7700i | 0.441299 | − | 0.764352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.62742 | −0.101430 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.7279 | −1.06883 | −0.534416 | − | 0.845221i | \(-0.679469\pi\) | ||||
−0.534416 | + | 0.845221i | \(0.679469\pi\) | |||||||
\(674\) | 13.3640 | + | 23.1471i | 0.514761 | + | 0.891591i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.94975 | − | 13.7694i | −0.305534 | − | 0.529200i | 0.671846 | − | 0.740691i | \(-0.265502\pi\) |
−0.977380 | + | 0.211491i | \(0.932168\pi\) | |||||||
\(678\) | 22.1421 | 0.850364 | ||||||||
\(679\) | 13.5563 | − | 1.85514i | 0.520245 | − | 0.0711939i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.46447 | + | 7.73268i | 0.171079 | + | 0.296317i | ||||
\(682\) | 2.41421 | − | 4.18154i | 0.0924450 | − | 0.160119i | ||||
\(683\) | 11.7071 | − | 20.2773i | 0.447960 | − | 0.775889i | −0.550293 | − | 0.834972i | \(-0.685484\pi\) |
0.998253 | + | 0.0590821i | \(0.0188174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.0208 | − | 15.6245i | −0.802578 | − | 0.596547i | ||||
\(687\) | 8.31371 | 0.317188 | ||||||||
\(688\) | 15.1716 | + | 26.2779i | 0.578411 | + | 1.00184i | ||||
\(689\) | 15.0711 | − | 26.1039i | 0.574162 | − | 0.994478i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.84315 | − | 6.65652i | −0.146200 | − | 0.253226i | 0.783620 | − | 0.621241i | \(-0.213371\pi\) |
−0.929820 | + | 0.368014i | \(0.880038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.53553 | − | 0.210133i | 0.0583301 | − | 0.00798229i | ||||
\(694\) | −12.6863 | −0.481565 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.6569 | − | 20.1903i | 0.441852 | − | 0.765310i | ||||
\(697\) | −7.00000 | + | 12.1244i | −0.265144 | + | 0.459243i | ||||
\(698\) | −20.2426 | − | 35.0613i | −0.766195 | − | 1.32709i | ||||
\(699\) | 5.51472 | 0.208586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21320 | −0.0458221 | −0.0229110 | − | 0.999738i | \(-0.507293\pi\) | ||||
−0.0229110 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(702\) | −3.12132 | − | 5.40629i | −0.117807 | − | 0.204047i | ||||
\(703\) | −19.5919 | + | 33.9341i | −0.738922 | + | 1.27985i | ||||
\(704\) | −2.34315 | + | 4.05845i | −0.0883106 | + | 0.152958i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.6569 | 0.739795 | ||||||||
\(707\) | −2.24264 | + | 5.49333i | −0.0843432 | + | 0.206598i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.5563 | − | 44.2649i | −0.959789 | − | 1.66240i | −0.723008 | − | 0.690840i | \(-0.757241\pi\) |
−0.236781 | − | 0.971563i | \(-0.576092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.32843 | + | 5.76500i | −0.124826 | + | 0.216205i | ||||
\(712\) | −17.3137 | − | 29.9882i | −0.648859 | − | 1.12386i | ||||
\(713\) | 13.0711 | 0.489515 | ||||||||
\(714\) | 3.17157 | − | 7.76874i | 0.118693 | − | 0.290738i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.65685 | − | 4.60181i | 0.0992220 | − | 0.171858i | ||||
\(718\) | 20.7990 | − | 36.0249i | 0.776211 | − | 1.34444i | ||||
\(719\) | −17.2426 | − | 29.8651i | −0.643042 | − | 1.11378i | −0.984750 | − | 0.173975i | \(-0.944339\pi\) |
0.341708 | − | 0.939806i | \(-0.388995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7426 | + | 15.1427i | 0.437319 | + | 0.563944i | ||||
\(722\) | 3.79899 | 0.141384 | ||||||||
\(723\) | 10.8284 | + | 18.7554i | 0.402714 | + | 0.697520i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.53553 | + | 13.0519i | 0.279670 | + | 0.484402i | ||||
\(727\) | −13.2426 | −0.491142 | −0.245571 | − | 0.969379i | \(-0.578976\pi\) | ||||
−0.245571 | + | 0.969379i | \(0.578976\pi\) | |||||||
\(728\) | −32.7279 | + | 4.47871i | −1.21298 | + | 0.165992i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.50610 | − | 14.7330i | 0.314609 | − | 0.544919i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.62132 | − | 16.6646i | −0.355372 | − | 0.615522i | 0.631810 | − | 0.775123i | \(-0.282312\pi\) |
−0.987181 | + | 0.159602i | \(0.948979\pi\) | |||||||
\(734\) | 31.6985 | 1.17001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.02082 | − | 6.96426i | −0.148109 | − | 0.256532i | ||||
\(738\) | 4.41421 | − | 7.64564i | 0.162489 | − | 0.281440i | ||||
\(739\) | 3.42893 | − | 5.93908i | 0.126135 | − | 0.218473i | −0.796041 | − | 0.605243i | \(-0.793076\pi\) |
0.922176 | + | 0.386770i | \(0.126409\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.5563 | 0.755156 | ||||||||
\(742\) | −25.3137 | + | 3.46410i | −0.929295 | + | 0.127171i | ||||
\(743\) | −20.7279 | −0.760434 | −0.380217 | − | 0.924897i | \(-0.624151\pi\) | ||||
−0.380217 | + | 0.924897i | \(0.624151\pi\) | |||||||
\(744\) | −8.24264 | − | 14.2767i | −0.302190 | − | 0.523408i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.60660 | − | 13.1750i | 0.278497 | − | 0.482372i | ||||
\(747\) | 1.29289 | + | 2.23936i | 0.0473045 | + | 0.0819338i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.4056 | + | 26.3140i | 0.745604 | + | 0.961492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8137 | + | 22.1940i | 0.467579 | + | 0.809870i | 0.999314 | − | 0.0370405i | \(-0.0117931\pi\) |
−0.531735 | + | 0.846911i | \(0.678460\pi\) | |||||||
\(752\) | 26.6274 | − | 46.1200i | 0.971002 | − | 1.68182i | ||||
\(753\) | 1.29289 | − | 2.23936i | 0.0471156 | − | 0.0816067i | ||||
\(754\) | −25.7279 | − | 44.5621i | −0.936956 | − | 1.62285i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.5980 | 1.36652 | 0.683261 | − | 0.730174i | \(-0.260561\pi\) | ||||
0.683261 | + | 0.730174i | \(0.260561\pi\) | |||||||
\(758\) | 17.5355 | + | 30.3724i | 0.636919 | + | 1.10318i | ||||
\(759\) | 0.656854 | − | 1.13770i | 0.0238423 | − | 0.0412961i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.5355 | + | 30.3724i | 0.635663 | + | 1.10100i | 0.986374 | + | 0.164516i | \(0.0526064\pi\) |
−0.350712 | + | 0.936483i | \(0.614060\pi\) | |||||||
\(762\) | 5.55635 | 0.201285 | ||||||||
\(763\) | −3.48528 | + | 8.53716i | −0.126176 | + | 0.309066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.17157 | + | 5.49333i | −0.114594 | + | 0.198482i | ||||
\(767\) | 3.12132 | − | 5.40629i | 0.112704 | − | 0.195210i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9706 | 0.648035 | 0.324018 | − | 0.946051i | \(-0.394966\pi\) | ||||
0.324018 | + | 0.946051i | \(0.394966\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1005 | 0.363761 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5355 | − | 33.8365i | 0.702644 | − | 1.21702i | −0.264891 | − | 0.964278i | \(-0.585336\pi\) |
0.967535 | − | 0.252737i | \(-0.0813308\pi\) | |||||||
\(774\) | −5.36396 | + | 9.29065i | −0.192804 | + | 0.333946i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.6274 | −0.525094 | ||||||||
\(777\) | 22.0563 | − | 3.01834i | 0.791267 | − | 0.108282i | ||||
\(778\) | −52.1421 | −1.86939 | ||||||||
\(779\) | 14.5355 | + | 25.1763i | 0.520790 | + | 0.902034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.171573 | − | 0.297173i | 0.00613936 | − | 0.0106337i | ||||
\(782\) | −3.55635 | − | 6.15978i | −0.127175 | − | 0.220273i | ||||
\(783\) | 8.24264 | 0.294568 | ||||||||
\(784\) | 20.0000 | + | 19.5959i | 0.714286 | + | 0.699854i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.58579 | − | 7.94282i | −0.163570 | − | 0.283311i | ||||
\(787\) | 9.41421 | − | 16.3059i | 0.335580 | − | 0.581242i | −0.648016 | − | 0.761627i | \(-0.724401\pi\) |
0.983596 | + | 0.180385i | \(0.0577342\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.41421 | + | 5.91359i | 0.121549 | + | 0.210529i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.0416 | − | 5.61642i | 1.45927 | − | 0.199697i | ||||
\(792\) | −1.65685 | −0.0588738 | ||||||||
\(793\) | 9.89949 | + | 17.1464i | 0.351541 | + | 0.608888i | ||||
\(794\) | 12.8787 | − | 22.3065i | 0.457047 | − | 0.791629i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.5563 | −1.47200 | −0.736001 | − | 0.676981i | \(-0.763288\pi\) | ||||
−0.736001 | + | 0.676981i | \(0.763288\pi\) | |||||||
\(798\) | −10.6777 | − | 13.7694i | −0.377985 | − | 0.487430i | ||||
\(799\) | −29.8579 | −1.05630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.12132 | − | 10.6024i | 0.216286 | − | 0.374619i | ||||
\(802\) | 11.6569 | − | 20.1903i | 0.411618 | − | 0.712943i | ||||
\(803\) | −3.53553 | − | 6.12372i | −0.124766 | − | 0.216102i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.3848 | −1.28160 | ||||||||
\(807\) | 10.0711 | + | 17.4436i | 0.354518 | + | 0.614044i | ||||
\(808\) | 3.17157 | − | 5.49333i | 0.111576 | − | 0.193255i | ||||
\(809\) | −20.3137 | + | 35.1844i | −0.714192 | + | 1.23702i | 0.249078 | + | 0.968483i | \(0.419872\pi\) |
−0.963270 | + | 0.268533i | \(0.913461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.9706 | 0.385229 | 0.192614 | − | 0.981275i | \(-0.438303\pi\) | ||||
0.192614 | + | 0.981275i | \(0.438303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.14214 | −0.285557 | ||||||||
\(814\) | −3.48528 | − | 6.03668i | −0.122159 | − | 0.211586i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.48528 | + | 7.76874i | −0.157016 | + | 0.271960i | ||||
\(817\) | −17.6630 | − | 30.5931i | −0.617948 | − | 1.07032i | ||||
\(818\) | −5.21320 | −0.182275 | ||||||||
\(819\) | −7.15685 | − | 9.22911i | −0.250081 | − | 0.322491i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.77817 | + | 15.2042i | 0.306360 | + | 0.530632i | 0.977563 | − | 0.210642i | \(-0.0675554\pi\) |
−0.671203 | + | 0.741274i | \(0.734222\pi\) | |||||||
\(822\) | −12.0711 | + | 20.9077i | −0.421027 | + | 0.729240i | ||||
\(823\) | −17.1421 | + | 29.6910i | −0.597537 | + | 1.03496i | 0.395646 | + | 0.918403i | \(0.370521\pi\) |
−0.993183 | + | 0.116562i | \(0.962813\pi\) | |||||||
\(824\) | −10.2426 | − | 17.7408i | −0.356819 | − | 0.618029i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.24264 | + | 0.717439i | −0.182415 | + | 0.0249629i | ||||
\(827\) | −7.17157 | −0.249380 | −0.124690 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124690 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.67157 | − | 6.35935i | 0.127519 | − | 0.220869i | −0.795196 | − | 0.606353i | \(-0.792632\pi\) |
0.922715 | + | 0.385483i | \(0.125965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.69239 | + | 11.5916i | 0.232156 | + | 0.402107i | ||||
\(832\) | 35.3137 | 1.22428 | ||||||||
\(833\) | 3.90812 | − | 15.2042i | 0.135408 | − | 0.526796i | ||||
\(834\) | −7.75736 | −0.268615 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.91421 | − | 5.04757i | 0.100730 | − | 0.174469i | ||||
\(838\) | 6.24264 | + | 10.8126i | 0.215648 | + | 0.373514i | ||||
\(839\) | −32.7279 | −1.12989 | −0.564947 | − | 0.825127i | \(-0.691103\pi\) | ||||
−0.564947 | + | 0.825127i | \(0.691103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | −7.43503 | − | 12.8778i | −0.256228 | − | 0.443800i | ||||
\(843\) | 0.828427 | − | 1.43488i | 0.0285325 | − | 0.0494198i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.8284 | 0.647335 | ||||||||
\(847\) | 17.2782 | + | 22.2810i | 0.593685 | + | 0.765585i | ||||
\(848\) | 27.3137 | 0.937957 | ||||||||
\(849\) | −2.37868 | − | 4.11999i | −0.0816361 | − | 0.141398i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.43503 | − | 16.3419i | 0.323429 | − | 0.560195i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.0122 | 1.50695 | 0.753474 | − | 0.657477i | \(-0.228376\pi\) | ||||
0.753474 | + | 0.657477i | \(0.228376\pi\) | |||||||
\(854\) | 6.34315 | − | 15.5375i | 0.217058 | − | 0.531681i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.7990 | − | 30.8288i | −0.608357 | − | 1.05371i | ||||
\(857\) | 1.12132 | − | 1.94218i | 0.0383036 | − | 0.0663437i | −0.846238 | − | 0.532805i | \(-0.821138\pi\) |
0.884542 | + | 0.466461i | \(0.154471\pi\) | |||||||
\(858\) | −1.82843 | + | 3.16693i | −0.0624215 | + | 0.108117i | ||||
\(859\) | −2.17157 | − | 3.76127i | −0.0740931 | − | 0.128333i | 0.826598 | − | 0.562792i | \(-0.190273\pi\) |
−0.900692 | + | 0.434459i | \(0.856940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.24264 | − | 15.2913i | 0.212749 | − | 0.521126i | ||||
\(862\) | 44.0833 | 1.50148 | ||||||||
\(863\) | 14.8995 | + | 25.8067i | 0.507185 | + | 0.878470i | 0.999965 | + | 0.00831615i | \(0.00264714\pi\) |
−0.492781 | + | 0.870154i | \(0.664020\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.63604 | + | 8.02986i | 0.157539 | + | 0.272866i | ||||
\(867\) | −11.9706 | −0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.89949 | 0.132281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.2990 | + | 52.4794i | −1.02664 | + | 1.77820i | ||||
\(872\) | 4.92893 | − | 8.53716i | 0.166915 | − | 0.289105i | ||||
\(873\) | −2.58579 | − | 4.47871i | −0.0875156 | − | 0.151581i | ||||
\(874\) | −14.7696 | −0.499588 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.00000 | − | 15.5885i | −0.303908 | − | 0.526385i | 0.673109 | − | 0.739543i | \(-0.264958\pi\) |
−0.977018 | + | 0.213158i | \(0.931625\pi\) | |||||||
\(878\) | −8.24264 | + | 14.2767i | −0.278176 | + | 0.481814i | ||||
\(879\) | 3.65685 | − | 6.33386i | 0.123343 | − | 0.213636i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3431 | −0.348469 | −0.174235 | − | 0.984704i | \(-0.555745\pi\) | ||||
−0.174235 | + | 0.984704i | \(0.555745\pi\) | |||||||
\(882\) | −2.46447 | + | 9.58783i | −0.0829829 | + | 0.322839i | ||||
\(883\) | 6.07107 | 0.204308 | 0.102154 | − | 0.994769i | \(-0.467427\pi\) | ||||
0.102154 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.6569 | + | 20.1903i | −0.391620 | + | 0.678305i | ||||
\(887\) | −18.6066 | − | 32.2276i | −0.624749 | − | 1.08210i | −0.988589 | − | 0.150635i | \(-0.951868\pi\) |
0.363841 | − | 0.931461i | \(-0.381465\pi\) | |||||||
\(888\) | −23.7990 | −0.798642 | ||||||||
\(889\) | 10.2990 | − | 1.40938i | 0.345417 | − | 0.0472692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.292893 | − | 0.507306i | −0.00981229 | − | 0.0169954i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.0000 | + | 53.6936i | −1.03738 | + | 1.79679i | ||||
\(894\) | −4.48528 | − | 7.76874i | −0.150010 | − | 0.259825i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.3431 | − | 23.6544i | −0.612801 | − | 0.790237i | ||||
\(897\) | −9.89949 | −0.330535 | ||||||||
\(898\) | −19.0711 | − | 33.0321i | −0.636410 | − | 1.10229i | ||||
\(899\) | 24.0208 | − | 41.6053i | 0.801139 | − | 1.38761i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.65685 | − | 13.2621i | −0.255087 | − | 0.441823i | ||||
\(902\) | −5.17157 | −0.172195 | ||||||||
\(903\) | −7.58579 | + | 18.5813i | −0.252439 | + | 0.618347i | ||||
\(904\) | −44.2843 | −1.47287 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.41421 | + | 12.8418i | −0.246321 | + | 0.426640i | ||||
\(907\) | −22.6924 | + | 39.3044i | −0.753488 | + | 1.30508i | 0.192634 | + | 0.981271i | \(0.438297\pi\) |
−0.946122 | + | 0.323809i | \(0.895036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.24264 | 0.0743837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.24264 | −0.140565 | −0.0702825 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702825 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(912\) | 9.31371 | + | 16.1318i | 0.308408 | + | 0.534178i | ||||
\(913\) | 0.757359 | − | 1.31178i | 0.0250649 | − | 0.0434137i | ||||
\(914\) | −0.778175 | + | 1.34784i | −0.0257397 | + | 0.0445825i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5147 | − | 13.5592i | −0.347227 | − | 0.447765i | ||||
\(918\) | −3.17157 | −0.104678 | ||||||||
\(919\) | 17.6716 | + | 30.6081i | 0.582931 | + | 1.00967i | 0.995130 | + | 0.0985727i | \(0.0314277\pi\) |
−0.412198 | + | 0.911094i | \(0.635239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.20711 | − | 3.82282i | 0.0727266 | − | 0.125966i | ||||
\(922\) | 9.14214 | + | 15.8346i | 0.301080 | + | 0.521486i | ||||
\(923\) | −2.58579 | −0.0851122 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.36396 | − | 9.29065i | −0.176271 | − | 0.305310i | ||||
\(927\) | 3.62132 | − | 6.27231i | 0.118940 | − | 0.206010i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.5061 | − | 26.8573i | −0.508739 | − | 0.881161i | −0.999949 | − | 0.0101199i | \(-0.996779\pi\) |
0.491210 | − | 0.871041i | \(-0.336555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.2843 | − | 22.8138i | −0.763111 | − | 0.747693i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.46447 | + | 2.53653i | 0.0479445 | + | 0.0830423i | ||||
\(934\) | 20.7279 | − | 35.9018i | 0.678238 | − | 1.17474i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.24264 | + | 10.8126i | 0.204047 | + | 0.353420i | ||||
\(937\) | 22.0711 | 0.721030 | 0.360515 | − | 0.932753i | \(-0.382601\pi\) | ||||
0.360515 | + | 0.932753i | \(0.382601\pi\) | |||||||
\(938\) | 50.8909 | − | 6.96426i | 1.66165 | − | 0.227391i | ||||
\(939\) | 16.2132 | 0.529098 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3640 | − | 31.8073i | 0.598648 | − | 1.03689i | −0.394373 | − | 0.918950i | \(-0.629038\pi\) |
0.993021 | − | 0.117938i | \(-0.0376285\pi\) | |||||||
\(942\) | 8.58579 | − | 14.8710i | 0.279740 | − | 0.484524i | ||||
\(943\) | −7.00000 | − | 12.1244i | −0.227951 | − | 0.394823i | ||||
\(944\) | 5.65685 | 0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.28427 | 0.204319 | ||||||||
\(947\) | −9.53553 | − | 16.5160i | −0.309863 | − | 0.536699i | 0.668469 | − | 0.743740i | \(-0.266950\pi\) |
−0.978332 | + | 0.207041i | \(0.933617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.6421 | + | 46.1455i | −0.864840 | + | 1.49795i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.8995 | −0.645285 | ||||||||
\(952\) | −6.34315 | + | 15.5375i | −0.205583 | + | 0.503572i | ||||
\(953\) | −31.5147 | −1.02086 | −0.510431 | − | 0.859919i | \(-0.670514\pi\) | ||||
−0.510431 | + | 0.859919i | \(0.670514\pi\) | |||||||
\(954\) | 4.82843 | + | 8.36308i | 0.156326 | + | 0.270765i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.41421 | − | 4.18154i | −0.0780404 | − | 0.135170i | ||||
\(958\) | 15.0294 | 0.485579 | ||||||||
\(959\) | −17.0711 | + | 41.8154i | −0.551254 | + | 1.35029i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.48528 | − | 2.57258i | −0.0479123 | − | 0.0829865i | ||||
\(962\) | −26.2635 | + | 45.4896i | −0.846768 | + | 1.46664i | ||||
\(963\) | 6.29289 | − | 10.8996i | 0.202786 | − | 0.351235i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.14214 | + | 6.63103i | 0.165446 | + | 0.213350i | ||||
\(967\) | 13.3848 | 0.430425 | 0.215213 | − | 0.976567i | \(-0.430956\pi\) | ||||
0.215213 | + | 0.976567i | \(0.430956\pi\) | |||||||
\(968\) | −15.0711 | − | 26.1039i | −0.484402 | − | 0.839010i | ||||
\(969\) | 5.22183 | − | 9.04447i | 0.167749 | − | 0.290550i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8284 | − | 22.2195i | −0.411684 | − | 0.713057i | 0.583390 | − | 0.812192i | \(-0.301726\pi\) |
−0.995074 | + | 0.0991347i | \(0.968393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3787 | + | 1.96768i | −0.460959 | + | 0.0630808i | ||||
\(974\) | 26.7279 | 0.856418 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.97056 | + | 15.5375i | −0.287141 | + | 0.497342i | ||||
\(977\) | −22.8492 | + | 39.5760i | −0.731012 | + | 1.26615i | 0.225439 | + | 0.974257i | \(0.427618\pi\) |
−0.956451 | + | 0.291893i | \(0.905715\pi\) | |||||||
\(978\) | 2.34315 | + | 4.05845i | 0.0749255 | + | 0.129775i | ||||
\(979\) | −7.17157 | −0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48528 | 0.111276 | ||||||||
\(982\) | −12.8284 | − | 22.2195i | −0.409372 | − | 0.709052i | ||||
\(983\) | −28.5772 | + | 49.4971i | −0.911470 | + | 1.57871i | −0.0994811 | + | 0.995039i | \(0.531718\pi\) |
−0.811989 | + | 0.583673i | \(0.801615\pi\) | |||||||
\(984\) | −8.82843 | + | 15.2913i | −0.281440 | + | 0.487468i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26.1421 | −0.832535 | ||||||||
\(987\) | 34.8995 | − | 4.77589i | 1.11086 | − | 0.152018i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.50610 | + | 14.7330i | 0.270478 | + | 0.468482i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.67157 | − | 16.7517i | 0.307228 | − | 0.532134i | −0.670527 | − | 0.741885i | \(-0.733932\pi\) |
0.977755 | + | 0.209751i | \(0.0672654\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6274 | 0.559389 | ||||||||
\(994\) | 1.34315 | + | 1.73205i | 0.0426020 | + | 0.0549373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.62132 | − | 8.00436i | 0.146359 | − | 0.253501i | −0.783520 | − | 0.621366i | \(-0.786578\pi\) |
0.929879 | + | 0.367865i | \(0.119911\pi\) | |||||||
\(998\) | 21.7782 | − | 37.7209i | 0.689376 | − | 1.19403i | ||||
\(999\) | −4.20711 | − | 7.28692i | −0.133107 | − | 0.230548i |
(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 | 525.2.i.g.151.1 | 4 | ||
5.2 | odd | 4 | 525.2.r.g.424.4 | 8 | |||
5.3 | odd | 4 | 525.2.r.g.424.1 | 8 | |||
5.4 | even | 2 | 105.2.i.c.46.2 | yes | 4 | ||
7.2 | even | 3 | inner | 525.2.i.g.226.1 | 4 | ||
7.3 | odd | 6 | 3675.2.a.x.1.2 | 2 | |||
7.4 | even | 3 | 3675.2.a.z.1.2 | 2 | |||
15.14 | odd | 2 | 315.2.j.d.46.1 | 4 | |||
20.19 | odd | 2 | 1680.2.bg.p.1201.2 | 4 | |||
35.2 | odd | 12 | 525.2.r.g.499.1 | 8 | |||
35.4 | even | 6 | 735.2.a.i.1.1 | 2 | |||
35.9 | even | 6 | 105.2.i.c.16.2 | ✓ | 4 | ||
35.19 | odd | 6 | 735.2.i.j.226.2 | 4 | |||
35.23 | odd | 12 | 525.2.r.g.499.4 | 8 | |||
35.24 | odd | 6 | 735.2.a.j.1.1 | 2 | |||
35.34 | odd | 2 | 735.2.i.j.361.2 | 4 | |||
105.44 | odd | 6 | 315.2.j.d.226.1 | 4 | |||
105.59 | even | 6 | 2205.2.a.s.1.2 | 2 | |||
105.74 | odd | 6 | 2205.2.a.u.1.2 | 2 | |||
140.79 | odd | 6 | 1680.2.bg.p.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.2 | ✓ | 4 | 35.9 | even | 6 | ||
105.2.i.c.46.2 | yes | 4 | 5.4 | even | 2 | ||
315.2.j.d.46.1 | 4 | 15.14 | odd | 2 | |||
315.2.j.d.226.1 | 4 | 105.44 | odd | 6 | |||
525.2.i.g.151.1 | 4 | 1.1 | even | 1 | trivial | ||
525.2.i.g.226.1 | 4 | 7.2 | even | 3 | inner | ||
525.2.r.g.424.1 | 8 | 5.3 | odd | 4 | |||
525.2.r.g.424.4 | 8 | 5.2 | odd | 4 | |||
525.2.r.g.499.1 | 8 | 35.2 | odd | 12 | |||
525.2.r.g.499.4 | 8 | 35.23 | odd | 12 | |||
735.2.a.i.1.1 | 2 | 35.4 | even | 6 | |||
735.2.a.j.1.1 | 2 | 35.24 | odd | 6 | |||
735.2.i.j.226.2 | 4 | 35.19 | odd | 6 | |||
735.2.i.j.361.2 | 4 | 35.34 | odd | 2 | |||
1680.2.bg.p.961.2 | 4 | 140.79 | odd | 6 | |||
1680.2.bg.p.1201.2 | 4 | 20.19 | odd | 2 | |||
2205.2.a.s.1.2 | 2 | 105.59 | even | 6 | |||
2205.2.a.u.1.2 | 2 | 105.74 | odd | 6 | |||
3675.2.a.x.1.2 | 2 | 7.3 | odd | 6 | |||
3675.2.a.z.1.2 | 2 | 7.4 | even | 3 |