Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (of order \(6\), degree \(2\), not 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.g.424.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | −0.358719 | + | 2.62132i | −0.135583 | + | 0.990766i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.292893 | − | 0.507306i | −0.0883106 | − | 0.152958i | 0.818487 | − | 0.574526i | \(-0.194813\pi\) |
−0.906797 | + | 0.421567i | \(0.861480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.41421i | − | 1.22428i | −0.790748 | − | 0.612141i | \(-0.790308\pi\) | ||
0.790748 | − | 0.612141i | \(-0.209692\pi\) | |||||||
\(14\) | 2.29289 | − | 2.95680i | 0.612801 | − | 0.790237i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.94218 | + | 1.12132i | −0.471049 | + | 0.271960i | −0.716679 | − | 0.697404i | \(-0.754339\pi\) |
0.245630 | + | 0.969364i | \(0.421005\pi\) | |||||||
\(18\) | −1.22474 | + | 0.707107i | −0.288675 | + | 0.166667i | ||||
\(19\) | 2.32843 | − | 4.03295i | 0.534178 | − | 0.925223i | −0.465025 | − | 0.885298i | \(-0.653955\pi\) |
0.999203 | − | 0.0399255i | \(-0.0127121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 2.44949i | −0.218218 | − | 0.534522i | ||||
\(22\) | 0.828427i | 0.176621i | ||||||||
\(23\) | −1.94218 | − | 1.12132i | −0.404973 | − | 0.233811i | 0.283654 | − | 0.958927i | \(-0.408453\pi\) |
−0.688628 | + | 0.725115i | \(0.741787\pi\) | |||||||
\(24\) | −1.41421 | − | 2.44949i | −0.288675 | − | 0.500000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.12132 | + | 5.40629i | −0.612141 | + | 1.06026i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24264 | −1.53062 | −0.765310 | − | 0.643662i | \(-0.777414\pi\) | ||||
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.91421 | + | 5.04757i | 0.523408 | + | 0.906570i | 0.999629 | + | 0.0272438i | \(0.00867303\pi\) |
−0.476221 | + | 0.879326i | \(0.657994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.507306 | + | 0.292893i | 0.0883106 | + | 0.0509862i | ||||
\(34\) | 3.17157 | 0.543920 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.28692 | − | 4.20711i | −1.19796 | − | 0.691644i | −0.237862 | − | 0.971299i | \(-0.576447\pi\) |
−0.960101 | + | 0.279655i | \(0.909780\pi\) | |||||||
\(38\) | −5.70346 | + | 3.29289i | −0.925223 | + | 0.534178i | ||||
\(39\) | 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 | \(0.662080\pi\) | |||||||
\(42\) | −0.507306 | + | 3.70711i | −0.0782790 | + | 0.572019i | ||||
\(43\) | − | 7.58579i | − | 1.15682i | −0.815746 | − | 0.578411i | \(-0.803673\pi\) | ||
0.815746 | − | 0.578411i | \(-0.196327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.58579 | + | 2.74666i | 0.233811 | + | 0.404973i | ||||
\(47\) | −11.5300 | − | 6.65685i | −1.68182 | − | 0.971002i | −0.960448 | − | 0.278459i | \(-0.910176\pi\) |
−0.721377 | − | 0.692543i | \(-0.756490\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | −6.74264 | − | 1.88064i | −0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.12132 | − | 1.94218i | 0.157016 | − | 0.271960i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.91359 | − | 3.41421i | 0.812294 | − | 0.468978i | −0.0354577 | − | 0.999371i | \(-0.511289\pi\) |
0.847752 | + | 0.530393i | \(0.177956\pi\) | |||||||
\(54\) | 0.707107 | − | 1.22474i | 0.0962250 | − | 0.166667i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.41421 | − | 1.01461i | −0.990766 | − | 0.135583i | ||||
\(57\) | 4.65685i | 0.616815i | ||||||||
\(58\) | 10.0951 | + | 5.82843i | 1.32556 | + | 0.765310i | ||||
\(59\) | −0.707107 | − | 1.22474i | −0.0920575 | − | 0.159448i | 0.816319 | − | 0.577601i | \(-0.196011\pi\) |
−0.908377 | + | 0.418153i | \(0.862678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24264 | − | 3.88437i | 0.287141 | − | 0.497342i | −0.685985 | − | 0.727615i | \(-0.740629\pi\) |
0.973126 | + | 0.230273i | \(0.0739619\pi\) | |||||||
\(62\) | − | 8.24264i | − | 1.04682i | ||||||
\(63\) | 2.09077 | + | 1.62132i | 0.263412 | + | 0.204267i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.414214 | − | 0.717439i | −0.0509862 | − | 0.0883106i | ||||
\(67\) | 11.8887 | − | 6.86396i | 1.45244 | − | 0.838566i | 0.453820 | − | 0.891093i | \(-0.350061\pi\) |
0.998619 | + | 0.0525271i | \(0.0167276\pi\) | |||||||
\(68\) | 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 | \(0.511067\pi\) | |||||||
\(72\) | 2.44949 | + | 1.41421i | 0.288675 | + | 0.166667i | ||||
\(73\) | −10.4539 | + | 6.03553i | −1.22353 | + | 0.706406i | −0.965669 | − | 0.259776i | \(-0.916351\pi\) |
−0.257862 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(74\) | 5.94975 | + | 10.3053i | 0.691644 | + | 1.19796i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.43488 | − | 0.585786i | 0.163520 | − | 0.0667566i | ||||
\(78\) | − | 6.24264i | − | 0.706840i | ||||||
\(79\) | 3.32843 | − | 5.76500i | 0.374477 | − | 0.648614i | −0.615771 | − | 0.787925i | \(-0.711155\pi\) |
0.990249 | + | 0.139311i | \(0.0444888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.64564 | + | 4.41421i | 0.844320 | + | 0.487468i | ||||
\(83\) | 2.58579i | 0.283827i | 0.989879 | + | 0.141913i | \(0.0453255\pi\) | ||||
−0.989879 | + | 0.141913i | \(0.954675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.36396 | + | 9.29065i | −0.578411 | + | 1.00184i | ||||
\(87\) | 7.13834 | − | 4.12132i | 0.765310 | − | 0.441852i | ||||
\(88\) | 1.43488 | − | 0.828427i | 0.152958 | − | 0.0883106i | ||||
\(89\) | −6.12132 | + | 10.6024i | −0.648859 | + | 1.12386i | 0.334537 | + | 0.942383i | \(0.391420\pi\) |
−0.983396 | + | 0.181474i | \(0.941913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.5711 | + | 1.58346i | 1.21298 | + | 0.165992i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.04757 | − | 2.91421i | −0.523408 | − | 0.302190i | ||||
\(94\) | 9.41421 | + | 16.3059i | 0.971002 | + | 1.68182i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17157i | 0.525094i | 0.964919 | + | 0.262547i | \(0.0845624\pi\) | ||||
−0.964919 | + | 0.262547i | \(0.915438\pi\) | |||||||
\(98\) | 6.92820 | + | 7.07107i | 0.699854 | + | 0.714286i | ||||
\(99\) | −0.585786 | −0.0588738 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.12132 | − | 1.94218i | −0.111576 | − | 0.193255i | 0.804830 | − | 0.593505i | \(-0.202256\pi\) |
−0.916406 | + | 0.400251i | \(0.868923\pi\) | |||||||
\(102\) | −2.74666 | + | 1.58579i | −0.271960 | + | 0.157016i | ||||
\(103\) | −6.27231 | − | 3.62132i | −0.618029 | − | 0.356819i | 0.158072 | − | 0.987428i | \(-0.449472\pi\) |
−0.776101 | + | 0.630608i | \(0.782805\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.65685 | −0.937957 | ||||||||
\(107\) | 10.8996 | + | 6.29289i | 1.05371 | + | 0.608357i | 0.923684 | − | 0.383154i | \(-0.125162\pi\) |
0.130021 | + | 0.991511i | \(0.458496\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.74264 | + | 3.01834i | 0.166915 | + | 0.289105i | 0.937334 | − | 0.348433i | \(-0.113286\pi\) |
−0.770419 | + | 0.637538i | \(0.779953\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.41421 | 0.798642 | ||||||||
\(112\) | 8.36308 | + | 6.48528i | 0.790237 | + | 0.612801i | ||||
\(113\) | − | 15.6569i | − | 1.47287i | −0.676507 | − | 0.736436i | \(-0.736507\pi\) | ||
0.676507 | − | 0.736436i | \(-0.263493\pi\) | |||||||
\(114\) | 3.29289 | − | 5.70346i | 0.308408 | − | 0.534178i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.82282 | − | 2.20711i | −0.353420 | − | 0.204047i | ||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | −2.24264 | − | 5.49333i | −0.205583 | − | 0.503572i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32843 | − | 9.22911i | 0.484402 | − | 0.839010i | ||||
\(122\) | −5.49333 | + | 3.17157i | −0.497342 | + | 0.287141i | ||||
\(123\) | 5.40629 | − | 3.12132i | 0.487468 | − | 0.281440i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.41421 | − | 3.46410i | −0.125988 | − | 0.308607i | ||||
\(127\) | 3.92893i | 0.348636i | 0.984689 | + | 0.174318i | \(0.0557721\pi\) | ||||
−0.984689 | + | 0.174318i | \(0.944228\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 3.79289 | + | 6.56948i | 0.333946 | + | 0.578411i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.24264 | + | 5.61642i | −0.283311 | + | 0.490709i | −0.972198 | − | 0.234160i | \(-0.924766\pi\) |
0.688887 | + | 0.724868i | \(0.258099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.73641 | + | 7.55025i | 0.844254 | + | 0.654690i | ||||
\(134\) | −19.4142 | −1.67713 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.17157 | − | 5.49333i | −0.271960 | − | 0.471049i | ||||
\(137\) | 14.7840 | − | 8.53553i | 1.26308 | − | 0.729240i | 0.289411 | − | 0.957205i | \(-0.406541\pi\) |
0.973669 | + | 0.227965i | \(0.0732072\pi\) | |||||||
\(138\) | −2.74666 | − | 1.58579i | −0.233811 | − | 0.134991i | ||||
\(139\) | 5.48528 | 0.465255 | 0.232628 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232628 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3137 | 1.12122 | ||||||||
\(142\) | 0.717439 | + | 0.414214i | 0.0602061 | + | 0.0347600i | ||||
\(143\) | −2.23936 | + | 1.29289i | −0.187264 | + | 0.108117i | ||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.0711 | 1.41281 | ||||||||
\(147\) | 6.77962 | − | 1.74264i | 0.559173 | − | 0.143731i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.17157 | − | 5.49333i | 0.259825 | − | 0.450031i | −0.706370 | − | 0.707843i | \(-0.749668\pi\) |
0.966195 | + | 0.257812i | \(0.0830017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.24264 | − | 9.08052i | −0.426640 | − | 0.738962i | 0.569932 | − | 0.821692i | \(-0.306970\pi\) |
−0.996572 | + | 0.0827296i | \(0.973636\pi\) | |||||||
\(152\) | 11.4069 | + | 6.58579i | 0.925223 | + | 0.534178i | ||||
\(153\) | 2.24264i | 0.181307i | ||||||||
\(154\) | −2.17157 | − | 0.297173i | −0.174990 | − | 0.0239469i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5154 | + | 6.07107i | −0.839220 | + | 0.484524i | −0.856999 | − | 0.515318i | \(-0.827674\pi\) |
0.0177789 | + | 0.999842i | \(0.494340\pi\) | |||||||
\(158\) | −8.15295 | + | 4.70711i | −0.648614 | + | 0.374477i | ||||
\(159\) | −3.41421 | + | 5.91359i | −0.270765 | + | 0.468978i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.63604 | − | 4.68885i | 0.286560 | − | 0.369533i | ||||
\(162\) | 1.41421i | 0.111111i | ||||||||
\(163\) | −2.86976 | − | 1.65685i | −0.224777 | − | 0.129775i | 0.383383 | − | 0.923589i | \(-0.374759\pi\) |
−0.608160 | + | 0.793814i | \(0.708092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.82843 | − | 3.16693i | 0.141913 | − | 0.245801i | ||||
\(167\) | − | 20.2426i | − | 1.56642i | −0.621756 | − | 0.783211i | \(-0.713580\pi\) | ||
0.621756 | − | 0.783211i | \(-0.286420\pi\) | |||||||
\(168\) | 6.92820 | − | 2.82843i | 0.534522 | − | 0.218218i | ||||
\(169\) | −6.48528 | −0.498868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.32843 | − | 4.03295i | −0.178059 | − | 0.308408i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.44949 | − | 1.41421i | −0.186231 | − | 0.107521i | 0.403986 | − | 0.914765i | \(-0.367625\pi\) |
−0.590217 | + | 0.807245i | \(0.700958\pi\) | |||||||
\(174\) | −11.6569 | −0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.34315 | −0.176621 | ||||||||
\(177\) | 1.22474 | + | 0.707107i | 0.0920575 | + | 0.0531494i | ||||
\(178\) | 14.9941 | − | 8.65685i | 1.12386 | − | 0.648859i | ||||
\(179\) | 4.17157 | + | 7.22538i | 0.311798 | + | 0.540050i | 0.978752 | − | 0.205049i | \(-0.0657354\pi\) |
−0.666954 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6569 | −0.792118 | −0.396059 | − | 0.918225i | \(-0.629622\pi\) | ||||
−0.396059 | + | 0.918225i | \(0.629622\pi\) | |||||||
\(182\) | −13.0519 | − | 10.1213i | −0.967473 | − | 0.750242i | ||||
\(183\) | 4.48528i | 0.331562i | ||||||||
\(184\) | 3.17157 | − | 5.49333i | 0.233811 | − | 0.404973i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.12132 | + | 7.13834i | 0.302190 | + | 0.523408i | ||||
\(187\) | 1.13770 | + | 0.656854i | 0.0831972 | + | 0.0480339i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.62132 | − | 0.358719i | −0.190673 | − | 0.0260930i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.48528 | − | 12.9649i | 0.541616 | − | 0.938106i | −0.457196 | − | 0.889366i | \(-0.651146\pi\) |
0.998811 | − | 0.0487401i | \(-0.0155206\pi\) | |||||||
\(192\) | 6.92820 | − | 4.00000i | 0.500000 | − | 0.288675i | ||||
\(193\) | −13.2005 | + | 7.62132i | −0.950194 | + | 0.548595i | −0.893141 | − | 0.449777i | \(-0.851504\pi\) |
−0.0570527 | + | 0.998371i | \(0.518170\pi\) | |||||||
\(194\) | 3.65685 | − | 6.33386i | 0.262547 | − | 0.454744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5563i | 1.82081i | 0.413713 | + | 0.910407i | \(0.364232\pi\) | ||||
−0.413713 | + | 0.910407i | \(0.635768\pi\) | |||||||
\(198\) | 0.717439 | + | 0.414214i | 0.0509862 | + | 0.0294369i | ||||
\(199\) | 11.2426 | + | 19.4728i | 0.796970 | + | 1.38039i | 0.921581 | + | 0.388186i | \(0.126898\pi\) |
−0.124611 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.86396 | + | 11.8887i | −0.484146 | + | 0.838566i | ||||
\(202\) | 3.17157i | 0.223151i | ||||||||
\(203\) | 2.95680 | − | 21.6066i | 0.207526 | − | 1.51649i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.12132 | + | 8.87039i | 0.356819 | + | 0.618029i | ||||
\(207\) | −1.94218 | + | 1.12132i | −0.134991 | + | 0.0779372i | ||||
\(208\) | −15.2913 | − | 8.82843i | −1.06026 | − | 0.612141i | ||||
\(209\) | −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 | ||||||||
\(213\) | 0.507306 | − | 0.292893i | 0.0347600 | − | 0.0200687i | ||||
\(214\) | −8.89949 | − | 15.4144i | −0.608357 | − | 1.05371i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.82843 | −0.192450 | ||||||||
\(217\) | −14.2767 | + | 5.82843i | −0.969164 | + | 0.395659i | ||||
\(218\) | − | 4.92893i | − | 0.333829i | ||||||
\(219\) | 6.03553 | − | 10.4539i | 0.407844 | − | 0.706406i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.94975 | + | 8.57321i | 0.332956 | + | 0.576697i | ||||
\(222\) | −10.3053 | − | 5.94975i | −0.691644 | − | 0.399321i | ||||
\(223\) | 22.8284i | 1.52870i | 0.644799 | + | 0.764352i | \(0.276941\pi\) | ||||
−0.644799 | + | 0.764352i | \(0.723059\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0711 | + | 19.1757i | −0.736436 | + | 1.27555i | ||||
\(227\) | −7.73268 | + | 4.46447i | −0.513236 | + | 0.296317i | −0.734163 | − | 0.678973i | \(-0.762425\pi\) |
0.220927 | + | 0.975290i | \(0.429092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.15685 | − | 7.19988i | 0.274693 | − | 0.475782i | −0.695365 | − | 0.718657i | \(-0.744757\pi\) |
0.970058 | + | 0.242875i | \(0.0780906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.949747 | + | 1.22474i | −0.0624888 | + | 0.0805823i | ||||
\(232\) | − | 23.3137i | − | 1.53062i | ||||||
\(233\) | 4.77589 | + | 2.75736i | 0.312879 | + | 0.180641i | 0.648214 | − | 0.761458i | \(-0.275516\pi\) |
−0.335335 | + | 0.942099i | \(0.608850\pi\) | |||||||
\(234\) | 3.12132 | + | 5.40629i | 0.204047 | + | 0.353420i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.65685i | 0.432409i | ||||||||
\(238\) | −1.13770 | + | 8.31371i | −0.0737465 | + | 0.538898i | ||||
\(239\) | 5.31371 | 0.343715 | 0.171858 | − | 0.985122i | \(-0.445023\pi\) | ||||
0.171858 | + | 0.985122i | \(0.445023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8284 | + | 18.7554i | 0.697520 | + | 1.20814i | 0.969324 | + | 0.245788i | \(0.0790466\pi\) |
−0.271803 | + | 0.962353i | \(0.587620\pi\) | |||||||
\(242\) | −13.0519 | + | 7.53553i | −0.839010 | + | 0.484402i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.82843 | −0.562880 | ||||||||
\(247\) | −17.8023 | − | 10.2782i | −1.13273 | − | 0.653985i | ||||
\(248\) | −14.2767 | + | 8.24264i | −0.906570 | + | 0.523408i | ||||
\(249\) | −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 | ||||||||
\(253\) | 1.31371i | 0.0825921i | ||||||||
\(254\) | 2.77817 | − | 4.81194i | 0.174318 | − | 0.301928i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.74729 | − | 5.05025i | −0.545641 | − | 0.315026i | 0.201721 | − | 0.979443i | \(-0.435347\pi\) |
−0.747362 | + | 0.664417i | \(0.768680\pi\) | |||||||
\(258\) | − | 10.7279i | − | 0.667891i | ||||||
\(259\) | 13.6421 | − | 17.5922i | 0.847681 | − | 1.09313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.12132 | + | 7.13834i | −0.255103 | + | 0.441852i | ||||
\(262\) | 7.94282 | − | 4.58579i | 0.490709 | − | 0.283311i | ||||
\(263\) | 5.91359 | − | 3.41421i | 0.364648 | − | 0.210529i | −0.306470 | − | 0.951880i | \(-0.599148\pi\) |
0.671118 | + | 0.741351i | \(0.265815\pi\) | |||||||
\(264\) | −0.828427 | + | 1.43488i | −0.0509862 | + | 0.0883106i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.58579 | − | 16.1318i | −0.403800 | − | 0.989105i | ||||
\(267\) | − | 12.2426i | − | 0.749237i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0711 | − | 17.4436i | −0.614044 | − | 1.06356i | −0.990551 | − | 0.137142i | \(-0.956208\pi\) |
0.376508 | − | 0.926414i | \(-0.377125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.07107 | − | 7.05130i | 0.247300 | − | 0.428336i | −0.715476 | − | 0.698637i | \(-0.753790\pi\) |
0.962776 | + | 0.270302i | \(0.0871234\pi\) | |||||||
\(272\) | 8.97056i | 0.543920i | ||||||||
\(273\) | −10.8126 | + | 4.41421i | −0.654407 | + | 0.267160i | ||||
\(274\) | −24.1421 | −1.45848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5916 | + | 6.69239i | −0.696469 | + | 0.402107i | −0.806031 | − | 0.591873i | \(-0.798389\pi\) |
0.109562 | + | 0.993980i | \(0.465055\pi\) | |||||||
\(278\) | −6.71807 | − | 3.87868i | −0.402923 | − | 0.232628i | ||||
\(279\) | 5.82843 | 0.348939 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65685 | −0.0988396 | −0.0494198 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494198 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(282\) | −16.3059 | − | 9.41421i | −0.971002 | − | 0.560608i | ||||
\(283\) | −4.11999 | + | 2.37868i | −0.244908 | + | 0.141398i | −0.617431 | − | 0.786625i | \(-0.711826\pi\) |
0.372522 | + | 0.928023i | \(0.378493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.65685 | 0.216234 | ||||||||
\(287\) | 2.23936 | − | 16.3640i | 0.132185 | − | 0.965934i | ||||
\(288\) | 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 | ||||||||
\(293\) | 7.31371i | 0.427271i | 0.976913 | + | 0.213636i | \(0.0685306\pi\) | ||||
−0.976913 | + | 0.213636i | \(0.931469\pi\) | |||||||
\(294\) | −9.53553 | − | 2.65962i | −0.556124 | − | 0.155112i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.8995 | − | 20.6105i | 0.691644 | − | 1.19796i | ||||
\(297\) | 0.507306 | − | 0.292893i | 0.0294369 | − | 0.0169954i | ||||
\(298\) | −7.76874 | + | 4.48528i | −0.450031 | + | 0.259825i | ||||
\(299\) | −4.94975 | + | 8.57321i | −0.286251 | + | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.8848 | + | 2.72117i | 1.14614 | + | 0.156846i | ||||
\(302\) | 14.8284i | 0.853280i | ||||||||
\(303\) | 1.94218 | + | 1.12132i | 0.111576 | + | 0.0644182i | ||||
\(304\) | −9.31371 | − | 16.1318i | −0.534178 | − | 0.925223i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.58579 | − | 2.74666i | 0.0906534 | − | 0.157016i | ||||
\(307\) | − | 4.41421i | − | 0.251932i | −0.992035 | − | 0.125966i | \(-0.959797\pi\) | ||
0.992035 | − | 0.125966i | \(-0.0402031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.24264 | 0.412019 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.46447 | + | 2.53653i | 0.0830423 | + | 0.143833i | 0.904555 | − | 0.426356i | \(-0.140203\pi\) |
−0.821513 | + | 0.570190i | \(0.806870\pi\) | |||||||
\(312\) | −10.8126 | + | 6.24264i | −0.612141 | + | 0.353420i | ||||
\(313\) | 14.0410 | + | 8.10660i | 0.793647 | + | 0.458212i | 0.841245 | − | 0.540654i | \(-0.181823\pi\) |
−0.0475980 | + | 0.998867i | \(0.515157\pi\) | |||||||
\(314\) | 17.1716 | 0.969048 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.2335 | + | 9.94975i | 0.967928 | + | 0.558833i | 0.898604 | − | 0.438761i | \(-0.144582\pi\) |
0.0693241 | + | 0.997594i | \(0.477916\pi\) | |||||||
\(318\) | 8.36308 | − | 4.82843i | 0.468978 | − | 0.270765i | ||||
\(319\) | 2.41421 | + | 4.18154i | 0.135170 | + | 0.234121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.5858 | −0.702470 | ||||||||
\(322\) | −7.76874 | + | 3.17157i | −0.432935 | + | 0.176745i | ||||
\(323\) | 10.4437i | 0.581100i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.34315 | + | 4.05845i | 0.129775 | + | 0.224777i | ||||
\(327\) | −3.01834 | − | 1.74264i | −0.166915 | − | 0.0963683i | ||||
\(328\) | − | 17.6569i | − | 0.974937i | ||||||
\(329\) | 21.5858 | − | 27.8359i | 1.19006 | − | 1.53464i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.81371 | + | 15.2658i | −0.484445 | + | 0.839084i | −0.999840 | − | 0.0178689i | \(-0.994312\pi\) |
0.515395 | + | 0.856953i | \(0.327645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.28692 | + | 4.20711i | −0.399321 | + | 0.230548i | ||||
\(334\) | −14.3137 | + | 24.7921i | −0.783211 | + | 1.35656i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.4853 | − | 1.43488i | −0.572019 | − | 0.0782790i | ||||
\(337\) | − | 18.8995i | − | 1.02952i | −0.857334 | − | 0.514761i | \(-0.827881\pi\) | ||
0.857334 | − | 0.514761i | \(-0.172119\pi\) | |||||||
\(338\) | 7.94282 | + | 4.58579i | 0.432032 | + | 0.249434i | ||||
\(339\) | 7.82843 | + | 13.5592i | 0.425182 | + | 0.736436i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70711 | − | 2.95680i | 0.0924450 | − | 0.160119i | ||||
\(342\) | 6.58579i | 0.356119i | ||||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | 21.4558 | 1.15682 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | −7.76874 | + | 4.48528i | −0.417048 | + | 0.240783i | −0.693813 | − | 0.720155i | \(-0.744071\pi\) |
0.276766 | + | 0.960937i | \(0.410737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6274 | −1.53239 | −0.766195 | − | 0.642608i | \(-0.777852\pi\) | ||||
−0.766195 | + | 0.642608i | \(0.777852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.41421 | 0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0373 | + | 6.94975i | −0.640682 | + | 0.369898i | −0.784877 | − | 0.619651i | \(-0.787274\pi\) |
0.144195 | + | 0.989549i | \(0.453941\pi\) | |||||||
\(354\) | −1.00000 | − | 1.73205i | −0.0531494 | − | 0.0920575i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.68885 | + | 3.63604i | 0.248160 | + | 0.192440i | ||||
\(358\) | − | 11.7990i | − | 0.623596i | ||||||
\(359\) | −14.7071 | + | 25.4735i | −0.776211 | + | 1.34444i | 0.157900 | + | 0.987455i | \(0.449528\pi\) |
−0.934111 | + | 0.356982i | \(0.883806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.34315 | − | 2.32640i | −0.0706919 | − | 0.122442i | ||||
\(362\) | 13.0519 | + | 7.53553i | 0.685994 | + | 0.396059i | ||||
\(363\) | 10.6569i | 0.559340i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.17157 | − | 5.49333i | 0.165781 | − | 0.287141i | ||||
\(367\) | 19.4113 | − | 11.2071i | 1.01326 | − | 0.585006i | 0.101116 | − | 0.994875i | \(-0.467759\pi\) |
0.912145 | + | 0.409868i | \(0.134425\pi\) | |||||||
\(368\) | −7.76874 | + | 4.48528i | −0.404973 | + | 0.233811i | ||||
\(369\) | −3.12132 | + | 5.40629i | −0.162489 | + | 0.281440i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.82843 | + | 16.7262i | 0.354514 | + | 0.868379i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.31615 | − | 5.37868i | −0.482372 | − | 0.278497i | 0.239033 | − | 0.971012i | \(-0.423170\pi\) |
−0.721404 | + | 0.692514i | \(0.756503\pi\) | |||||||
\(374\) | −0.928932 | − | 1.60896i | −0.0480339 | − | 0.0831972i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.8284 | − | 32.6118i | 0.971002 | − | 1.68182i | ||||
\(377\) | 36.3848i | 1.87391i | ||||||||
\(378\) | 2.95680 | + | 2.29289i | 0.152081 | + | 0.117934i | ||||
\(379\) | 24.7990 | 1.27384 | 0.636919 | − | 0.770931i | \(-0.280208\pi\) | ||||
0.636919 | + | 0.770931i | \(0.280208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.96447 | − | 3.40256i | −0.100643 | − | 0.174318i | ||||
\(382\) | −18.3351 | + | 10.5858i | −0.938106 | + | 0.541616i | ||||
\(383\) | 3.88437 | + | 2.24264i | 0.198482 | + | 0.114594i | 0.595947 | − | 0.803024i | \(-0.296777\pi\) |
−0.397465 | + | 0.917617i | \(0.630110\pi\) | |||||||
\(384\) | −11.3137 | −0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.5563 | 1.09719 | ||||||||
\(387\) | −6.56948 | − | 3.79289i | −0.333946 | − | 0.192804i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4350 | − | 31.9304i | −0.934693 | − | 1.61894i | −0.775180 | − | 0.631740i | \(-0.782341\pi\) |
−0.159513 | − | 0.987196i | \(-0.550992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.02944 | 0.254350 | ||||||||
\(392\) | 5.31925 | − | 19.0711i | 0.268662 | − | 0.963234i | ||||
\(393\) | − | 6.48528i | − | 0.327139i | ||||||
\(394\) | 18.0711 | − | 31.3000i | 0.910407 | − | 1.57687i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7731 | + | 9.10660i | 0.791629 | + | 0.457047i | 0.840536 | − | 0.541756i | \(-0.182240\pi\) |
−0.0489067 | + | 0.998803i | \(0.515574\pi\) | |||||||
\(398\) | − | 31.7990i | − | 1.59394i | ||||||
\(399\) | −12.2071 | − | 1.67050i | −0.611120 | − | 0.0836298i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.24264 | − | 14.2767i | 0.411618 | − | 0.712943i | −0.583449 | − | 0.812150i | \(-0.698297\pi\) |
0.995067 | + | 0.0992068i | \(0.0316305\pi\) | |||||||
\(402\) | 16.8132 | − | 9.70711i | 0.838566 | − | 0.484146i | ||||
\(403\) | 22.2810 | − | 12.8640i | 1.10990 | − | 0.640800i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.8995 | + | 24.3718i | −0.937966 | + | 1.20955i | ||||
\(407\) | 4.92893i | 0.244318i | ||||||||
\(408\) | 5.49333 | + | 3.17157i | 0.271960 | + | 0.157016i | ||||
\(409\) | −1.84315 | − | 3.19242i | −0.0911377 | − | 0.157855i | 0.816852 | − | 0.576847i | \(-0.195717\pi\) |
−0.907990 | + | 0.418992i | \(0.862384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.53553 | + | 14.7840i | −0.421027 | + | 0.729240i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.46410 | − | 1.41421i | 0.170457 | − | 0.0695889i | ||||
\(414\) | 3.17157 | 0.155874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.75039 | + | 2.74264i | −0.232628 | + | 0.134308i | ||||
\(418\) | 3.34101 | + | 1.92893i | 0.163414 | + | 0.0943472i | ||||
\(419\) | 8.82843 | 0.431297 | 0.215648 | − | 0.976471i | \(-0.430813\pi\) | ||||
0.215648 | + | 0.976471i | \(0.430813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5147 | 0.512456 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(422\) | 34.4669 | + | 19.8995i | 1.67782 | + | 0.968692i | ||||
\(423\) | −11.5300 | + | 6.65685i | −0.560608 | + | 0.323667i | ||||
\(424\) | 9.65685 | + | 16.7262i | 0.468978 | + | 0.812294i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.828427 | −0.0401374 | ||||||||
\(427\) | 9.37769 | + | 7.27208i | 0.453818 | + | 0.351921i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.29289 | − | 2.23936i | 0.0624215 | − | 0.108117i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5858 | − | 26.9954i | −0.750741 | − | 1.30032i | −0.947464 | − | 0.319862i | \(-0.896363\pi\) |
0.196723 | − | 0.980459i | \(-0.436970\pi\) | |||||||
\(432\) | 3.46410 | + | 2.00000i | 0.166667 | + | 0.0962250i | ||||
\(433\) | 6.55635i | 0.315078i | 0.987513 | + | 0.157539i | \(0.0503560\pi\) | ||||
−0.987513 | + | 0.157539i | \(0.949644\pi\) | |||||||
\(434\) | 21.6066 | + | 2.95680i | 1.03715 | + | 0.141931i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.04447 | + | 5.22183i | −0.432656 | + | 0.249794i | ||||
\(438\) | −14.7840 | + | 8.53553i | −0.706406 | + | 0.407844i | ||||
\(439\) | 5.82843 | − | 10.0951i | 0.278176 | − | 0.481814i | −0.692756 | − | 0.721172i | \(-0.743604\pi\) |
0.970931 | + | 0.239358i | \(0.0769369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | − | 14.0000i | − | 0.665912i | ||||||
\(443\) | 14.2767 | + | 8.24264i | 0.678305 | + | 0.391620i | 0.799216 | − | 0.601044i | \(-0.205248\pi\) |
−0.120911 | + | 0.992663i | \(0.538582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1421 | − | 27.9590i | 0.764352 | − | 1.32390i | ||||
\(447\) | 6.34315i | 0.300020i | ||||||||
\(448\) | 2.86976 | − | 20.9706i | 0.135583 | − | 0.990766i | ||||
\(449\) | −26.9706 | −1.27282 | −0.636410 | − | 0.771351i | \(-0.719581\pi\) | ||||
−0.636410 | + | 0.771351i | \(0.719581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82843 | + | 3.16693i | 0.0860973 | + | 0.149125i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.08052 | + | 5.24264i | 0.426640 | + | 0.246321i | ||||
\(454\) | 12.6274 | 0.592634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.1716 | −0.616815 | ||||||||
\(457\) | −0.953065 | − | 0.550253i | −0.0445825 | − | 0.0257397i | 0.477543 | − | 0.878608i | \(-0.341527\pi\) |
−0.522126 | + | 0.852869i | \(0.674861\pi\) | |||||||
\(458\) | −10.1822 | + | 5.87868i | −0.475782 | + | 0.274693i | ||||
\(459\) | −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 | \(0.597347\pi\) | |||||||
\(462\) | 2.02922 | − | 0.828427i | 0.0944080 | − | 0.0385419i | ||||
\(463\) | − | 7.58579i | − | 0.352541i | −0.984342 | − | 0.176271i | \(-0.943597\pi\) | ||
0.984342 | − | 0.176271i | \(-0.0564034\pi\) | |||||||
\(464\) | −16.4853 | + | 28.5533i | −0.765310 | + | 1.32556i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.89949 | − | 6.75412i | −0.180641 | − | 0.312879i | ||||
\(467\) | 25.3864 | + | 14.6569i | 1.17474 | + | 0.678238i | 0.954793 | − | 0.297273i | \(-0.0960770\pi\) |
0.219951 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7279 | + | 33.6264i | 0.633897 | + | 1.55272i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.07107 | − | 10.5154i | 0.279740 | − | 0.484524i | ||||
\(472\) | 3.46410 | − | 2.00000i | 0.159448 | − | 0.0920575i | ||||
\(473\) | −3.84831 | + | 2.22183i | −0.176946 | + | 0.102160i | ||||
\(474\) | 4.70711 | − | 8.15295i | 0.216205 | − | 0.374477i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.82843i | − | 0.312652i | ||||||
\(478\) | −6.50794 | − | 3.75736i | −0.297666 | − | 0.171858i | ||||
\(479\) | 5.31371 | + | 9.20361i | 0.242790 | + | 0.420524i | 0.961508 | − | 0.274778i | \(-0.0886042\pi\) |
−0.718718 | + | 0.695301i | \(0.755271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5711 | + | 32.1660i | −0.846768 | + | 1.46664i | ||||
\(482\) | − | 30.6274i | − | 1.39504i | ||||||
\(483\) | −0.804479 | + | 5.87868i | −0.0366051 | + | 0.267489i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.707107 | − | 1.22474i | −0.0320750 | − | 0.0555556i | ||||
\(487\) | 16.3674 | − | 9.44975i | 0.741680 | − | 0.428209i | −0.0810001 | − | 0.996714i | \(-0.525811\pi\) |
0.822680 | + | 0.568505i | \(0.192478\pi\) | |||||||
\(488\) | 10.9867 | + | 6.34315i | 0.497342 | + | 0.287141i | ||||
\(489\) | 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 | ||||||||
\(493\) | 16.0087 | − | 9.24264i | 0.720997 | − | 0.416268i | ||||
\(494\) | 14.5355 | + | 25.1763i | 0.653985 | + | 1.13273i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.3137 | 1.04682 | ||||||||
\(497\) | 0.210133 | − | 1.53553i | 0.00942575 | − | 0.0688781i | ||||
\(498\) | 3.65685i | 0.163868i | ||||||||
\(499\) | −15.3995 | + | 26.6727i | −0.689376 | + | 1.19403i | 0.282664 | + | 0.959219i | \(0.408782\pi\) |
−0.972040 | + | 0.234815i | \(0.924551\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1213 | + | 17.5306i | 0.452187 | + | 0.783211i | ||||
\(502\) | 3.16693 | + | 1.82843i | 0.141347 | + | 0.0816067i | ||||
\(503\) | − | 1.51472i | − | 0.0675380i | −0.999430 | − | 0.0337690i | \(-0.989249\pi\) | ||
0.999430 | − | 0.0337690i | \(-0.0107510\pi\) | |||||||
\(504\) | −4.58579 | + | 5.91359i | −0.204267 | + | 0.263412i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.928932 | − | 1.60896i | 0.0412961 | − | 0.0715269i | ||||
\(507\) | 5.61642 | − | 3.24264i | 0.249434 | − | 0.144011i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8995 | + | 22.3426i | −0.571760 | + | 0.990317i | 0.424625 | + | 0.905369i | \(0.360406\pi\) |
−0.996385 | + | 0.0849483i | \(0.972927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0711 | − | 29.5680i | −0.533993 | − | 1.30801i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 4.03295 | + | 2.32843i | 0.178059 | + | 0.102803i | ||||
\(514\) | 7.14214 | + | 12.3705i | 0.315026 | + | 0.545641i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.79899i | 0.342999i | ||||||||
\(518\) | −29.1477 | + | 11.8995i | −1.28068 | + | 0.522834i | ||||
\(519\) | 2.82843 | 0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5563 | − | 20.0162i | −0.506293 | − | 0.876925i | −0.999973 | − | 0.00728166i | \(-0.997682\pi\) |
0.493681 | − | 0.869643i | \(-0.335651\pi\) | |||||||
\(522\) | 10.0951 | − | 5.82843i | 0.441852 | − | 0.255103i | ||||
\(523\) | 9.01897 | + | 5.20711i | 0.394372 | + | 0.227691i | 0.684053 | − | 0.729432i | \(-0.260216\pi\) |
−0.289681 | + | 0.957123i | \(0.593549\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.65685 | −0.421059 | ||||||||
\(527\) | −11.3199 | − | 6.53553i | −0.493102 | − | 0.284692i | ||||
\(528\) | 2.02922 | − | 1.17157i | 0.0883106 | − | 0.0509862i | ||||
\(529\) | −8.98528 | − | 15.5630i | −0.390664 | − | 0.676651i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.41421 | −0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.5563i | 1.19360i | ||||||||
\(534\) | −8.65685 | + | 14.9941i | −0.374619 | + | 0.648859i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.4142 | + | 33.6264i | 0.838566 | + | 1.45244i | ||||
\(537\) | −7.22538 | − | 4.17157i | −0.311798 | − | 0.180017i | ||||
\(538\) | 28.4853i | 1.22809i | ||||||||
\(539\) | 1.02082 | + | 3.97141i | 0.0439696 | + | 0.171061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.84315 | + | 8.38857i | −0.208223 | + | 0.360653i | −0.951155 | − | 0.308714i | \(-0.900101\pi\) |
0.742932 | + | 0.669367i | \(0.233435\pi\) | |||||||
\(542\) | −9.97204 | + | 5.75736i | −0.428336 | + | 0.247300i | ||||
\(543\) | 9.22911 | − | 5.32843i | 0.396059 | − | 0.228665i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.3640 | + | 2.23936i | 0.700313 | + | 0.0958356i | ||||
\(547\) | − | 7.79899i | − | 0.333461i | −0.986003 | − | 0.166730i | \(-0.946679\pi\) | ||
0.986003 | − | 0.166730i | \(-0.0533209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.24264 | − | 3.88437i | −0.0957136 | − | 0.165781i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.1924 | + | 33.2422i | −0.817623 | + | 1.41616i | ||||
\(552\) | 6.34315i | 0.269982i | ||||||||
\(553\) | 13.9180 | + | 10.7929i | 0.591852 | + | 0.458961i | ||||
\(554\) | 18.9289 | 0.804213 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0233 | − | 9.82843i | 0.721302 | − | 0.416444i | −0.0939298 | − | 0.995579i | \(-0.529943\pi\) |
0.815232 | + | 0.579135i | \(0.196610\pi\) | |||||||
\(558\) | −7.13834 | − | 4.12132i | −0.302190 | − | 0.174469i | ||||
\(559\) | −33.4853 | −1.41628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31371 | −0.0554648 | ||||||||
\(562\) | 2.02922 | + | 1.17157i | 0.0855976 | + | 0.0494198i | ||||
\(563\) | 36.6193 | − | 21.1421i | 1.54332 | − | 0.891035i | 0.544691 | − | 0.838637i | \(-0.316647\pi\) |
0.998626 | − | 0.0523981i | \(-0.0166865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.72792 | 0.282796 | ||||||||
\(567\) | 2.44949 | − | 1.00000i | 0.102869 | − | 0.0419961i | ||||
\(568\) | − | 1.65685i | − | 0.0695201i | ||||||
\(569\) | 8.43503 | − | 14.6099i | 0.353615 | − | 0.612479i | −0.633265 | − | 0.773935i | \(-0.718286\pi\) |
0.986880 | + | 0.161456i | \(0.0516190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.98528 | + | 5.17066i | 0.124930 | + | 0.216385i | 0.921706 | − | 0.387890i | \(-0.126796\pi\) |
−0.796775 | + | 0.604275i | \(0.793463\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9706i | 0.625404i | ||||||||
\(574\) | −14.3137 | + | 18.4582i | −0.597443 | + | 0.770431i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.00000 | + | 6.92820i | −0.166667 | + | 0.288675i | ||||
\(577\) | 21.2664 | − | 12.2782i | 0.885333 | − | 0.511147i | 0.0129197 | − | 0.999917i | \(-0.495887\pi\) |
0.872413 | + | 0.488769i | \(0.162554\pi\) | |||||||
\(578\) | 14.6609 | − | 8.46447i | 0.609812 | − | 0.352075i | ||||
\(579\) | 7.62132 | − | 13.2005i | 0.316731 | − | 0.548595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.77817 | − | 0.927572i | −0.281206 | − | 0.0384822i | ||||
\(582\) | 7.31371i | 0.303163i | ||||||||
\(583\) | −3.46410 | − | 2.00000i | −0.143468 | − | 0.0828315i | ||||
\(584\) | −17.0711 | − | 29.5680i | −0.706406 | − | 1.22353i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.17157 | − | 8.95743i | 0.213636 | − | 0.370028i | ||||
\(587\) | − | 21.7574i | − | 0.898022i | −0.893526 | − | 0.449011i | \(-0.851776\pi\) | ||
0.893526 | − | 0.449011i | \(-0.148224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.1421 | 1.11837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7782 | − | 22.1324i | −0.525624 | − | 0.910407i | ||||
\(592\) | −29.1477 | + | 16.8284i | −1.19796 | + | 0.691644i | ||||
\(593\) | −9.16756 | − | 5.29289i | −0.376467 | − | 0.217353i | 0.299813 | − | 0.953998i | \(-0.403076\pi\) |
−0.676280 | + | 0.736645i | \(0.736409\pi\) | |||||||
\(594\) | −0.828427 | −0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.4728 | − | 11.2426i | −0.796970 | − | 0.460131i | ||||
\(598\) | 12.1244 | − | 7.00000i | 0.495802 | − | 0.286251i | ||||
\(599\) | −6.92893 | − | 12.0013i | −0.283108 | − | 0.490358i | 0.689040 | − | 0.724723i | \(-0.258032\pi\) |
−0.972149 | + | 0.234365i | \(0.924699\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8284 | −1.21673 | −0.608363 | − | 0.793659i | \(-0.708174\pi\) | ||||
−0.608363 | + | 0.793659i | \(0.708174\pi\) | |||||||
\(602\) | −22.4296 | − | 17.3934i | −0.914163 | − | 0.708902i | ||||
\(603\) | − | 13.7279i | − | 0.559044i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.58579 | − | 2.74666i | −0.0644182 | − | 0.111576i | ||||
\(607\) | 6.27231 | + | 3.62132i | 0.254585 | + | 0.146985i | 0.621862 | − | 0.783127i | \(-0.286376\pi\) |
−0.367277 | + | 0.930112i | \(0.619710\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −15.7116 | + | 9.07107i | −0.634584 | + | 0.366377i | −0.782525 | − | 0.622619i | \(-0.786069\pi\) |
0.147941 | + | 0.988996i | \(0.452735\pi\) | |||||||
\(614\) | −3.12132 | + | 5.40629i | −0.125966 | + | 0.218180i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.65685 | + | 4.05845i | 0.0667566 | + | 0.163520i | ||||
\(617\) | 3.17157i | 0.127683i | 0.997960 | + | 0.0638414i | \(0.0203352\pi\) | ||||
−0.997960 | + | 0.0638414i | \(0.979665\pi\) | |||||||
\(618\) | −8.87039 | − | 5.12132i | −0.356819 | − | 0.206010i | ||||
\(619\) | 3.01472 | + | 5.22165i | 0.121172 | + | 0.209876i | 0.920230 | − | 0.391378i | \(-0.128001\pi\) |
−0.799058 | + | 0.601254i | \(0.794668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12132 | − | 1.94218i | 0.0449970 | − | 0.0779372i | ||||
\(622\) | − | 4.14214i | − | 0.166085i | ||||||
\(623\) | −25.5965 | − | 19.8492i | −1.02550 | − | 0.795243i | ||||
\(624\) | 17.6569 | 0.706840 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.4645 | − | 19.8570i | −0.458212 | − | 0.793647i | ||||
\(627\) | 2.36245 | − | 1.36396i | 0.0943472 | − | 0.0544714i | ||||
\(628\) | 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 | \(0.396829\pi\) | |||||||
\(632\) | 16.3059 | + | 9.41421i | 0.648614 | + | 0.374477i | ||||
\(633\) | 24.3718 | − | 14.0711i | 0.968692 | − | 0.559275i | ||||
\(634\) | −14.0711 | − | 24.3718i | −0.558833 | − | 0.967928i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.30153 | + | 29.7635i | −0.328919 | + | 1.17927i | ||||
\(638\) | − | 6.82843i | − | 0.270340i | ||||||
\(639\) | −0.292893 | + | 0.507306i | −0.0115867 | + | 0.0200687i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.6066 | − | 25.2994i | −0.576926 | − | 0.999265i | −0.995829 | − | 0.0912345i | \(-0.970919\pi\) |
0.418903 | − | 0.908031i | \(-0.362415\pi\) | |||||||
\(642\) | 15.4144 | + | 8.89949i | 0.608357 | + | 0.351235i | ||||
\(643\) | − | 6.55635i | − | 0.258557i | −0.991608 | − | 0.129279i | \(-0.958734\pi\) | ||
0.991608 | − | 0.129279i | \(-0.0412661\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.38478 | − | 12.7908i | 0.290550 | − | 0.503248i | ||||
\(647\) | −40.1704 | + | 23.1924i | −1.57926 | + | 0.911787i | −0.584299 | + | 0.811539i | \(0.698630\pi\) |
−0.994962 | + | 0.100248i | \(0.968036\pi\) | |||||||
\(648\) | 2.44949 | − | 1.41421i | 0.0962250 | − | 0.0555556i | ||||
\(649\) | −0.414214 | + | 0.717439i | −0.0162593 | + | 0.0281619i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.44975 | − | 12.1859i | 0.370365 | − | 0.477603i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0665 | − | 8.12132i | −0.550466 | − | 0.317812i | 0.198844 | − | 0.980031i | \(-0.436281\pi\) |
−0.749310 | + | 0.662219i | \(0.769615\pi\) | |||||||
\(654\) | 2.46447 | + | 4.26858i | 0.0963683 | + | 0.166915i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.4853 | + | 21.6251i | −0.487468 | + | 0.844320i | ||||
\(657\) | 12.0711i | 0.470937i | ||||||||
\(658\) | −46.1200 | + | 18.8284i | −1.79795 | + | 0.734009i | ||||
\(659\) | 4.68629 | 0.182552 | 0.0912760 | − | 0.995826i | \(-0.470905\pi\) | ||||
0.0912760 | + | 0.995826i | \(0.470905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.84315 | − | 8.38857i | −0.188377 | − | 0.326278i | 0.756333 | − | 0.654187i | \(-0.226989\pi\) |
−0.944709 | + | 0.327910i | \(0.893656\pi\) | |||||||
\(662\) | 21.5891 | − | 12.4645i | 0.839084 | − | 0.484445i | ||||
\(663\) | −8.57321 | − | 4.94975i | −0.332956 | − | 0.192232i | ||||
\(664\) | −7.31371 | −0.283827 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.8995 | 0.461096 | ||||||||
\(667\) | 16.0087 | + | 9.24264i | 0.619860 | + | 0.357876i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4142 | − | 19.7700i | −0.441299 | − | 0.764352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.62742 | −0.101430 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.7279i | 1.06883i | 0.845221 | + | 0.534416i | \(0.179469\pi\) | ||||
−0.845221 | + | 0.534416i | \(0.820531\pi\) | |||||||
\(674\) | −13.3640 | + | 23.1471i | −0.514761 | + | 0.891591i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.7694 | − | 7.94975i | −0.529200 | − | 0.305534i | 0.211491 | − | 0.977380i | \(-0.432168\pi\) |
−0.740691 | + | 0.671846i | \(0.765502\pi\) | |||||||
\(678\) | − | 22.1421i | − | 0.850364i | ||||||
\(679\) | −13.5563 | − | 1.85514i | −0.520245 | − | 0.0711939i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.46447 | − | 7.73268i | 0.171079 | − | 0.296317i | ||||
\(682\) | −4.18154 | + | 2.41421i | −0.160119 | + | 0.0924450i | ||||
\(683\) | 20.2773 | − | 11.7071i | 0.775889 | − | 0.447960i | −0.0590821 | − | 0.998253i | \(-0.518817\pi\) |
0.834972 | + | 0.550293i | \(0.185484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.0208 | + | 15.6245i | −0.802578 | + | 0.596547i | ||||
\(687\) | 8.31371i | 0.317188i | ||||||||
\(688\) | −26.2779 | − | 15.1716i | −1.00184 | − | 0.578411i | ||||
\(689\) | −15.0711 | − | 26.1039i | −0.574162 | − | 0.994478i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.84315 | + | 6.65652i | −0.146200 | + | 0.253226i | −0.929820 | − | 0.368014i | \(-0.880038\pi\) |
0.783620 | + | 0.621241i | \(0.213371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.210133 | − | 1.53553i | 0.00798229 | − | 0.0583301i | ||||
\(694\) | 12.6863 | 0.481565 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.6569 | + | 20.1903i | 0.441852 | + | 0.765310i | ||||
\(697\) | 12.1244 | − | 7.00000i | 0.459243 | − | 0.265144i | ||||
\(698\) | 35.0613 | + | 20.2426i | 1.32709 | + | 0.766195i | ||||
\(699\) | −5.51472 | −0.208586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21320 | −0.0458221 | −0.0229110 | − | 0.999738i | \(-0.507293\pi\) | ||||
−0.0229110 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(702\) | −5.40629 | − | 3.12132i | −0.204047 | − | 0.117807i | ||||
\(703\) | −33.9341 | + | 19.5919i | −1.27985 | + | 0.738922i | ||||
\(704\) | 2.34315 | + | 4.05845i | 0.0883106 | + | 0.152958i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.6569 | 0.739795 | ||||||||
\(707\) | 5.49333 | − | 2.24264i | 0.206598 | − | 0.0843432i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.5563 | − | 44.2649i | 0.959789 | − | 1.66240i | 0.236781 | − | 0.971563i | \(-0.423908\pi\) |
0.723008 | − | 0.690840i | \(-0.242759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.32843 | − | 5.76500i | −0.124826 | − | 0.216205i | ||||
\(712\) | −29.9882 | − | 17.3137i | −1.12386 | − | 0.648859i | ||||
\(713\) | − | 13.0711i | − | 0.489515i | ||||||
\(714\) | −3.17157 | − | 7.76874i | −0.118693 | − | 0.290738i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.60181 | + | 2.65685i | −0.171858 | + | 0.0992220i | ||||
\(718\) | 36.0249 | − | 20.7990i | 1.34444 | − | 0.776211i | ||||
\(719\) | 17.2426 | − | 29.8651i | 0.643042 | − | 1.11378i | −0.341708 | − | 0.939806i | \(-0.611005\pi\) |
0.984750 | − | 0.173975i | \(-0.0556613\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7426 | − | 15.1427i | 0.437319 | − | 0.563944i | ||||
\(722\) | 3.79899i | 0.141384i | ||||||||
\(723\) | −18.7554 | − | 10.8284i | −0.697520 | − | 0.402714i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.53553 | − | 13.0519i | 0.279670 | − | 0.484402i | ||||
\(727\) | − | 13.2426i | − | 0.491142i | −0.969379 | − | 0.245571i | \(-0.921024\pi\) | ||
0.969379 | − | 0.245571i | \(-0.0789755\pi\) | |||||||
\(728\) | −4.47871 | + | 32.7279i | −0.165992 | + | 1.21298i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.50610 | + | 14.7330i | 0.314609 | + | 0.544919i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6646 | + | 9.62132i | 0.615522 | + | 0.355372i | 0.775123 | − | 0.631810i | \(-0.217688\pi\) |
−0.159602 | + | 0.987181i | \(0.551021\pi\) | |||||||
\(734\) | −31.6985 | −1.17001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.96426 | − | 4.02082i | −0.256532 | − | 0.148109i | ||||
\(738\) | 7.64564 | − | 4.41421i | 0.281440 | − | 0.162489i | ||||
\(739\) | −3.42893 | − | 5.93908i | −0.126135 | − | 0.218473i | 0.796041 | − | 0.605243i | \(-0.206924\pi\) |
−0.922176 | + | 0.386770i | \(0.873591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.5563 | 0.755156 | ||||||||
\(742\) | 3.46410 | − | 25.3137i | 0.127171 | − | 0.929295i | ||||
\(743\) | 20.7279i | 0.760434i | 0.924897 | + | 0.380217i | \(0.124151\pi\) | ||||
−0.924897 | + | 0.380217i | \(0.875849\pi\) | |||||||
\(744\) | 8.24264 | − | 14.2767i | 0.302190 | − | 0.523408i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.60660 | + | 13.1750i | 0.278497 | + | 0.482372i | ||||
\(747\) | 2.23936 | + | 1.29289i | 0.0819338 | + | 0.0473045i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.4056 | + | 26.3140i | −0.745604 | + | 0.961492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8137 | − | 22.1940i | 0.467579 | − | 0.809870i | −0.531735 | − | 0.846911i | \(-0.678460\pi\) |
0.999314 | + | 0.0370405i | \(0.0117931\pi\) | |||||||
\(752\) | −46.1200 | + | 26.6274i | −1.68182 | + | 0.971002i | ||||
\(753\) | 2.23936 | − | 1.29289i | 0.0816067 | − | 0.0471156i | ||||
\(754\) | 25.7279 | − | 44.5621i | 0.936956 | − | 1.62285i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.5980i | 1.36652i | 0.730174 | + | 0.683261i | \(0.239439\pi\) | ||||
−0.730174 | + | 0.683261i | \(0.760561\pi\) | |||||||
\(758\) | −30.3724 | − | 17.5355i | −1.10318 | − | 0.636919i | ||||
\(759\) | −0.656854 | − | 1.13770i | −0.0238423 | − | 0.0412961i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.5355 | − | 30.3724i | 0.635663 | − | 1.10100i | −0.350712 | − | 0.936483i | \(-0.614060\pi\) |
0.986374 | − | 0.164516i | \(-0.0526064\pi\) | |||||||
\(762\) | 5.55635i | 0.201285i | ||||||||
\(763\) | −8.53716 | + | 3.48528i | −0.309066 | + | 0.126176i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.17157 | − | 5.49333i | −0.114594 | − | 0.198482i | ||||
\(767\) | −5.40629 | + | 3.12132i | −0.195210 | + | 0.112704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.9706 | −0.648035 | −0.324018 | − | 0.946051i | \(-0.605034\pi\) | ||||
−0.324018 | + | 0.946051i | \(0.605034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1005 | 0.363761 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.8365 | − | 19.5355i | 1.21702 | − | 0.702644i | 0.252737 | − | 0.967535i | \(-0.418669\pi\) |
0.964278 | + | 0.264891i | \(0.0853359\pi\) | |||||||
\(774\) | 5.36396 | + | 9.29065i | 0.192804 | + | 0.333946i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.6274 | −0.525094 | ||||||||
\(777\) | −3.01834 | + | 22.0563i | −0.108282 | + | 0.791267i | ||||
\(778\) | 52.1421i | 1.86939i | ||||||||
\(779\) | −14.5355 | + | 25.1763i | −0.520790 | + | 0.902034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.171573 | + | 0.297173i | 0.00613936 | + | 0.0106337i | ||||
\(782\) | −6.15978 | − | 3.55635i | −0.220273 | − | 0.127175i | ||||
\(783\) | − | 8.24264i | − | 0.294568i | ||||||
\(784\) | −20.0000 | + | 19.5959i | −0.714286 | + | 0.699854i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.58579 | + | 7.94282i | −0.163570 | + | 0.283311i | ||||
\(787\) | −16.3059 | + | 9.41421i | −0.581242 | + | 0.335580i | −0.761627 | − | 0.648016i | \(-0.775599\pi\) |
0.180385 | + | 0.983596i | \(0.442266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.41421 | + | 5.91359i | −0.121549 | + | 0.210529i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.0416 | + | 5.61642i | 1.45927 | + | 0.199697i | ||||
\(792\) | − | 1.65685i | − | 0.0588738i | ||||||
\(793\) | −17.1464 | − | 9.89949i | −0.608888 | − | 0.351541i | ||||
\(794\) | −12.8787 | − | 22.3065i | −0.457047 | − | 0.791629i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 41.5563i | − | 1.47200i | −0.676981 | − | 0.736001i | \(-0.736712\pi\) | ||
0.676981 | − | 0.736001i | \(-0.263288\pi\) | |||||||
\(798\) | 13.7694 | + | 10.6777i | 0.487430 | + | 0.377985i | ||||
\(799\) | 29.8579 | 1.05630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.12132 | + | 10.6024i | 0.216286 | + | 0.374619i | ||||
\(802\) | −20.1903 | + | 11.6569i | −0.712943 | + | 0.411618i | ||||
\(803\) | 6.12372 | + | 3.53553i | 0.216102 | + | 0.124766i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.3848 | −1.28160 | ||||||||
\(807\) | 17.4436 | + | 10.0711i | 0.614044 | + | 0.354518i | ||||
\(808\) | 5.49333 | − | 3.17157i | 0.193255 | − | 0.111576i | ||||
\(809\) | 20.3137 | + | 35.1844i | 0.714192 | + | 1.23702i | 0.963270 | + | 0.268533i | \(0.0865390\pi\) |
−0.249078 | + | 0.968483i | \(0.580128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.9706 | 0.385229 | 0.192614 | − | 0.981275i | \(-0.438303\pi\) | ||||
0.192614 | + | 0.981275i | \(0.438303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.14214i | 0.285557i | ||||||||
\(814\) | 3.48528 | − | 6.03668i | 0.122159 | − | 0.211586i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.48528 | − | 7.76874i | −0.157016 | − | 0.271960i | ||||
\(817\) | −30.5931 | − | 17.6630i | −1.07032 | − | 0.617948i | ||||
\(818\) | 5.21320i | 0.182275i | ||||||||
\(819\) | 7.15685 | − | 9.22911i | 0.250081 | − | 0.322491i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.77817 | − | 15.2042i | 0.306360 | − | 0.530632i | −0.671203 | − | 0.741274i | \(-0.734222\pi\) |
0.977563 | + | 0.210642i | \(0.0675554\pi\) | |||||||
\(822\) | 20.9077 | − | 12.0711i | 0.729240 | − | 0.421027i | ||||
\(823\) | −29.6910 | + | 17.1421i | −1.03496 | + | 0.597537i | −0.918403 | − | 0.395646i | \(-0.870521\pi\) |
−0.116562 | + | 0.993183i | \(0.537187\pi\) | |||||||
\(824\) | 10.2426 | − | 17.7408i | 0.356819 | − | 0.618029i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.24264 | − | 0.717439i | −0.182415 | − | 0.0249629i | ||||
\(827\) | − | 7.17157i | − | 0.249380i | −0.992196 | − | 0.124690i | \(-0.960206\pi\) | ||
0.992196 | − | 0.124690i | \(-0.0397936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.67157 | − | 6.35935i | −0.127519 | − | 0.220869i | 0.795196 | − | 0.606353i | \(-0.207368\pi\) |
−0.922715 | + | 0.385483i | \(0.874035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.69239 | − | 11.5916i | 0.232156 | − | 0.402107i | ||||
\(832\) | 35.3137i | 1.22428i | ||||||||
\(833\) | 15.2042 | − | 3.90812i | 0.526796 | − | 0.135408i | ||||
\(834\) | 7.75736 | 0.268615 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.04757 | + | 2.91421i | −0.174469 | + | 0.100730i | ||||
\(838\) | −10.8126 | − | 6.24264i | −0.373514 | − | 0.215648i | ||||
\(839\) | 32.7279 | 1.12989 | 0.564947 | − | 0.825127i | \(-0.308897\pi\) | ||||
0.564947 | + | 0.825127i | \(0.308897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | −12.8778 | − | 7.43503i | −0.443800 | − | 0.256228i | ||||
\(843\) | 1.43488 | − | 0.828427i | 0.0494198 | − | 0.0285325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.8284 | 0.647335 | ||||||||
\(847\) | 22.2810 | + | 17.2782i | 0.765585 | + | 0.593685i | ||||
\(848\) | − | 27.3137i | − | 0.937957i | ||||||
\(849\) | 2.37868 | − | 4.11999i | 0.0816361 | − | 0.141398i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.43503 | + | 16.3419i | 0.323429 | + | 0.560195i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.0122i | − | 1.50695i | −0.657477 | − | 0.753474i | \(-0.728376\pi\) | ||
0.657477 | − | 0.753474i | \(-0.271624\pi\) | |||||||
\(854\) | −6.34315 | − | 15.5375i | −0.217058 | − | 0.531681i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.7990 | + | 30.8288i | −0.608357 | + | 1.05371i | ||||
\(857\) | −1.94218 | + | 1.12132i | −0.0663437 | + | 0.0383036i | −0.532805 | − | 0.846238i | \(-0.678862\pi\) |
0.466461 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(858\) | −3.16693 | + | 1.82843i | −0.108117 | + | 0.0624215i | ||||
\(859\) | 2.17157 | − | 3.76127i | 0.0740931 | − | 0.128333i | −0.826598 | − | 0.562792i | \(-0.809727\pi\) |
0.900692 | + | 0.434459i | \(0.143060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.24264 | + | 15.2913i | 0.212749 | + | 0.521126i | ||||
\(862\) | 44.0833i | 1.50148i | ||||||||
\(863\) | −25.8067 | − | 14.8995i | −0.878470 | − | 0.507185i | −0.00831615 | − | 0.999965i | \(-0.502647\pi\) |
−0.870154 | + | 0.492781i | \(0.835980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.63604 | − | 8.02986i | 0.157539 | − | 0.272866i | ||||
\(867\) | − | 11.9706i | − | 0.406542i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.89949 | −0.132281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.2990 | − | 52.4794i | −1.02664 | − | 1.77820i | ||||
\(872\) | −8.53716 | + | 4.92893i | −0.289105 | + | 0.166915i | ||||
\(873\) | 4.47871 | + | 2.58579i | 0.151581 | + | 0.0875156i | ||||
\(874\) | 14.7696 | 0.499588 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5885 | − | 9.00000i | −0.526385 | − | 0.303908i | 0.213158 | − | 0.977018i | \(-0.431625\pi\) |
−0.739543 | + | 0.673109i | \(0.764958\pi\) | |||||||
\(878\) | −14.2767 | + | 8.24264i | −0.481814 | + | 0.278176i | ||||
\(879\) | −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 | \(0.555745\pi\) | |||||||
\(882\) | 9.58783 | − | 2.46447i | 0.322839 | − | 0.0829829i | ||||
\(883\) | − | 6.07107i | − | 0.204308i | −0.994769 | − | 0.102154i | \(-0.967427\pi\) | ||
0.994769 | − | 0.102154i | \(-0.0325734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.6569 | − | 20.1903i | −0.391620 | − | 0.678305i | ||||
\(887\) | −32.2276 | − | 18.6066i | −1.08210 | − | 0.624749i | −0.150635 | − | 0.988589i | \(-0.548132\pi\) |
−0.931461 | + | 0.363841i | \(0.881465\pi\) | |||||||
\(888\) | 23.7990i | 0.798642i | ||||||||
\(889\) | −10.2990 | − | 1.40938i | −0.345417 | − | 0.0472692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.292893 | + | 0.507306i | −0.00981229 | + | 0.0169954i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53.6936 | + | 31.0000i | −1.79679 | + | 1.03738i | ||||
\(894\) | 4.48528 | − | 7.76874i | 0.150010 | − | 0.259825i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.3431 | + | 23.6544i | −0.612801 | + | 0.790237i | ||||
\(897\) | − | 9.89949i | − | 0.330535i | ||||||
\(898\) | 33.0321 | + | 19.0711i | 1.10229 | + | 0.636410i | ||||
\(899\) | −24.0208 | − | 41.6053i | −0.801139 | − | 1.38761i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.65685 | + | 13.2621i | −0.255087 | + | 0.441823i | ||||
\(902\) | − | 5.17157i | − | 0.172195i | ||||||
\(903\) | −18.5813 | + | 7.58579i | −0.618347 | + | 0.252439i | ||||
\(904\) | 44.2843 | 1.47287 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.41421 | − | 12.8418i | −0.246321 | − | 0.426640i | ||||
\(907\) | 39.3044 | − | 22.6924i | 1.30508 | − | 0.753488i | 0.323809 | − | 0.946122i | \(-0.395036\pi\) |
0.981271 | + | 0.192634i | \(0.0617030\pi\) | |||||||
\(908\) | 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 | \(0.522390\pi\) | |||||||
\(912\) | 16.1318 | + | 9.31371i | 0.534178 | + | 0.308408i | ||||
\(913\) | 1.31178 | − | 0.757359i | 0.0434137 | − | 0.0250649i | ||||
\(914\) | 0.778175 | + | 1.34784i | 0.0257397 | + | 0.0445825i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5592 | − | 10.5147i | −0.447765 | − | 0.347227i | ||||
\(918\) | 3.17157i | 0.104678i | ||||||||
\(919\) | −17.6716 | + | 30.6081i | −0.582931 | + | 1.00967i | 0.412198 | + | 0.911094i | \(0.364761\pi\) |
−0.995130 | + | 0.0985727i | \(0.968572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.20711 | + | 3.82282i | 0.0727266 | + | 0.125966i | ||||
\(922\) | 15.8346 | + | 9.14214i | 0.521486 | + | 0.301080i | ||||
\(923\) | 2.58579i | 0.0851122i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.36396 | + | 9.29065i | −0.176271 | + | 0.305310i | ||||
\(927\) | −6.27231 | + | 3.62132i | −0.206010 | + | 0.118940i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5061 | − | 26.8573i | 0.508739 | − | 0.881161i | −0.491210 | − | 0.871041i | \(-0.663445\pi\) |
0.999949 | − | 0.0101199i | \(-0.00322133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.2843 | + | 22.8138i | −0.763111 | + | 0.747693i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.53653 | − | 1.46447i | −0.0830423 | − | 0.0479445i | ||||
\(934\) | −20.7279 | − | 35.9018i | −0.678238 | − | 1.17474i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.24264 | − | 10.8126i | 0.204047 | − | 0.353420i | ||||
\(937\) | 22.0711i | 0.721030i | 0.932753 | + | 0.360515i | \(0.117399\pi\) | ||||
−0.932753 | + | 0.360515i | \(0.882601\pi\) | |||||||
\(938\) | 6.96426 | − | 50.8909i | 0.227391 | − | 1.66165i | ||||
\(939\) | −16.2132 | −0.529098 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3640 | + | 31.8073i | 0.598648 | + | 1.03689i | 0.993021 | + | 0.117938i | \(0.0376285\pi\) |
−0.394373 | + | 0.918950i | \(0.629038\pi\) | |||||||
\(942\) | −14.8710 | + | 8.58579i | −0.484524 | + | 0.279740i | ||||
\(943\) | 12.1244 | + | 7.00000i | 0.394823 | + | 0.227951i | ||||
\(944\) | −5.65685 | −0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.28427 | 0.204319 | ||||||||
\(947\) | −16.5160 | − | 9.53553i | −0.536699 | − | 0.309863i | 0.207041 | − | 0.978332i | \(-0.433617\pi\) |
−0.743740 | + | 0.668469i | \(0.766950\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.6421 | + | 46.1455i | 0.864840 | + | 1.49795i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.8995 | −0.645285 | ||||||||
\(952\) | 15.5375 | − | 6.34315i | 0.503572 | − | 0.205583i | ||||
\(953\) | 31.5147i | 1.02086i | 0.859919 | + | 0.510431i | \(0.170514\pi\) | ||||
−0.859919 | + | 0.510431i | \(0.829486\pi\) | |||||||
\(954\) | −4.82843 | + | 8.36308i | −0.156326 | + | 0.270765i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.18154 | − | 2.41421i | −0.135170 | − | 0.0780404i | ||||
\(958\) | − | 15.0294i | − | 0.485579i | ||||||
\(959\) | 17.0711 | + | 41.8154i | 0.551254 | + | 1.35029i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.48528 | + | 2.57258i | −0.0479123 | + | 0.0829865i | ||||
\(962\) | 45.4896 | − | 26.2635i | 1.46664 | − | 0.846768i | ||||
\(963\) | 10.8996 | − | 6.29289i | 0.351235 | − | 0.202786i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.14214 | − | 6.63103i | 0.165446 | − | 0.213350i | ||||
\(967\) | 13.3848i | 0.430425i | 0.976567 | + | 0.215213i | \(0.0690445\pi\) | ||||
−0.976567 | + | 0.215213i | \(0.930956\pi\) | |||||||
\(968\) | 26.1039 | + | 15.0711i | 0.839010 | + | 0.484402i | ||||
\(969\) | −5.22183 | − | 9.04447i | −0.167749 | − | 0.290550i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8284 | + | 22.2195i | −0.411684 | + | 0.713057i | −0.995074 | − | 0.0991347i | \(-0.968393\pi\) |
0.583390 | + | 0.812192i | \(0.301726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.96768 | + | 14.3787i | −0.0630808 | + | 0.460959i | ||||
\(974\) | −26.7279 | −0.856418 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.97056 | − | 15.5375i | −0.287141 | − | 0.497342i | ||||
\(977\) | 39.5760 | − | 22.8492i | 1.26615 | − | 0.731012i | 0.291893 | − | 0.956451i | \(-0.405715\pi\) |
0.974257 | + | 0.225439i | \(0.0723816\pi\) | |||||||
\(978\) | −4.05845 | − | 2.34315i | −0.129775 | − | 0.0749255i | ||||
\(979\) | 7.17157 | 0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48528 | 0.111276 | ||||||||
\(982\) | −22.2195 | − | 12.8284i | −0.709052 | − | 0.409372i | ||||
\(983\) | −49.4971 | + | 28.5772i | −1.57871 | + | 0.911470i | −0.583673 | + | 0.811989i | \(0.698385\pi\) |
−0.995039 | + | 0.0994811i | \(0.968282\pi\) | |||||||
\(984\) | 8.82843 | + | 15.2913i | 0.281440 | + | 0.487468i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26.1421 | −0.832535 | ||||||||
\(987\) | −4.77589 | + | 34.8995i | −0.152018 | + | 1.11086i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.50610 | + | 14.7330i | −0.270478 | + | 0.468482i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.67157 | + | 16.7517i | 0.307228 | + | 0.532134i | 0.977755 | − | 0.209751i | \(-0.0672654\pi\) |
−0.670527 | + | 0.741885i | \(0.733932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 17.6274i | − | 0.559389i | ||||||
\(994\) | −1.34315 | + | 1.73205i | −0.0426020 | + | 0.0549373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.00436 | + | 4.62132i | −0.253501 | + | 0.146359i | −0.621366 | − | 0.783520i | \(-0.713422\pi\) |
0.367865 | + | 0.929879i | \(0.380089\pi\) | |||||||
\(998\) | 37.7209 | − | 21.7782i | 1.19403 | − | 0.689376i | ||||
\(999\) | 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.r.g.499.1 | 8 | ||
5.2 | odd | 4 | 105.2.i.c.16.2 | ✓ | 4 | ||
5.3 | odd | 4 | 525.2.i.g.226.1 | 4 | |||
5.4 | even | 2 | inner | 525.2.r.g.499.4 | 8 | ||
7.4 | even | 3 | inner | 525.2.r.g.424.4 | 8 | ||
15.2 | even | 4 | 315.2.j.d.226.1 | 4 | |||
20.7 | even | 4 | 1680.2.bg.p.961.2 | 4 | |||
35.2 | odd | 12 | 735.2.a.i.1.1 | 2 | |||
35.4 | even | 6 | inner | 525.2.r.g.424.1 | 8 | ||
35.12 | even | 12 | 735.2.a.j.1.1 | 2 | |||
35.17 | even | 12 | 735.2.i.j.361.2 | 4 | |||
35.18 | odd | 12 | 525.2.i.g.151.1 | 4 | |||
35.23 | odd | 12 | 3675.2.a.z.1.2 | 2 | |||
35.27 | even | 4 | 735.2.i.j.226.2 | 4 | |||
35.32 | odd | 12 | 105.2.i.c.46.2 | yes | 4 | ||
35.33 | even | 12 | 3675.2.a.x.1.2 | 2 | |||
105.2 | even | 12 | 2205.2.a.u.1.2 | 2 | |||
105.32 | even | 12 | 315.2.j.d.46.1 | 4 | |||
105.47 | odd | 12 | 2205.2.a.s.1.2 | 2 | |||
140.67 | even | 12 | 1680.2.bg.p.1201.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.2 | ✓ | 4 | 5.2 | odd | 4 | ||
105.2.i.c.46.2 | yes | 4 | 35.32 | odd | 12 | ||
315.2.j.d.46.1 | 4 | 105.32 | even | 12 | |||
315.2.j.d.226.1 | 4 | 15.2 | even | 4 | |||
525.2.i.g.151.1 | 4 | 35.18 | odd | 12 | |||
525.2.i.g.226.1 | 4 | 5.3 | odd | 4 | |||
525.2.r.g.424.1 | 8 | 35.4 | even | 6 | inner | ||
525.2.r.g.424.4 | 8 | 7.4 | even | 3 | inner | ||
525.2.r.g.499.1 | 8 | 1.1 | even | 1 | trivial | ||
525.2.r.g.499.4 | 8 | 5.4 | even | 2 | inner | ||
735.2.a.i.1.1 | 2 | 35.2 | odd | 12 | |||
735.2.a.j.1.1 | 2 | 35.12 | even | 12 | |||
735.2.i.j.226.2 | 4 | 35.27 | even | 4 | |||
735.2.i.j.361.2 | 4 | 35.17 | even | 12 | |||
1680.2.bg.p.961.2 | 4 | 20.7 | even | 4 | |||
1680.2.bg.p.1201.2 | 4 | 140.67 | even | 12 | |||
2205.2.a.s.1.2 | 2 | 105.47 | odd | 12 | |||
2205.2.a.u.1.2 | 2 | 105.2 | even | 12 | |||
3675.2.a.x.1.2 | 2 | 35.33 | even | 12 | |||
3675.2.a.z.1.2 | 2 | 35.23 | odd | 12 |