Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(67,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.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: | \(1.84454428669\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.67 |
Dual form | 231.2.i.d.100.2 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | + | 2.09077i | 0.853553 | + | 1.47840i | 0.877981 | + | 0.478696i | \(0.158890\pi\) |
−0.0244272 | + | 0.999702i | \(0.507776\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.91421 | + | 3.31552i | −0.957107 | + | 1.65776i | ||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −2.41421 | + | 4.18154i | −0.763441 | + | 1.32232i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −1.91421 | − | 3.31552i | −0.552586 | − | 0.957107i | ||||
\(13\) | −0.828427 | −0.229764 | −0.114882 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114882 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(14\) | 6.32843 | − | 0.866025i | 1.69134 | − | 0.231455i | ||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 2.20711 | − | 3.82282i | 0.535302 | − | 0.927170i | −0.463847 | − | 0.885916i | \(-0.653531\pi\) |
0.999149 | − | 0.0412548i | \(-0.0131355\pi\) | |||||||
\(18\) | 1.20711 | − | 2.09077i | 0.284518 | − | 0.492799i | ||||
\(19\) | −3.62132 | − | 6.27231i | −0.830788 | − | 1.43897i | −0.897414 | − | 0.441189i | \(-0.854557\pi\) |
0.0666264 | − | 0.997778i | \(-0.478776\pi\) | |||||||
\(20\) | −7.65685 | −1.71212 | ||||||||
\(21\) | 1.62132 | + | 2.09077i | 0.353801 | + | 0.456243i | ||||
\(22\) | −2.41421 | −0.514712 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 2.20711 | − | 3.82282i | 0.450524 | − | 0.780330i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 6.20711 | + | 8.00436i | 1.17303 | + | 1.51268i | ||||
\(29\) | 3.24264 | 0.602143 | 0.301072 | − | 0.953602i | \(-0.402656\pi\) | ||||
0.301072 | + | 0.953602i | \(0.402656\pi\) | |||||||
\(30\) | −2.41421 | − | 4.18154i | −0.440773 | − | 0.763441i | ||||
\(31\) | −2.82843 | + | 4.89898i | −0.508001 | + | 0.879883i | 0.491957 | + | 0.870620i | \(0.336282\pi\) |
−0.999957 | + | 0.00926296i | \(0.997051\pi\) | |||||||
\(32\) | −0.792893 | + | 1.37333i | −0.140165 | + | 0.242773i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 10.6569 | 1.82764 | ||||||||
\(35\) | 5.24264 | − | 0.717439i | 0.886168 | − | 0.121269i | ||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 4.74264 | + | 8.21449i | 0.779685 | + | 1.35045i | 0.932123 | + | 0.362142i | \(0.117954\pi\) |
−0.152438 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(38\) | 8.74264 | − | 15.1427i | 1.41824 | − | 2.45647i | ||||
\(39\) | 0.414214 | − | 0.717439i | 0.0663273 | − | 0.114882i | ||||
\(40\) | −4.41421 | − | 7.64564i | −0.697948 | − | 1.20888i | ||||
\(41\) | −1.17157 | −0.182969 | −0.0914845 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914845 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(42\) | −2.41421 | + | 5.91359i | −0.372521 | + | 0.912487i | ||||
\(43\) | −2.75736 | −0.420493 | −0.210247 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210247 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(44\) | −1.91421 | − | 3.31552i | −0.288579 | − | 0.499833i | ||||
\(45\) | 1.00000 | − | 1.73205i | 0.149071 | − | 0.258199i | ||||
\(46\) | −8.44975 | + | 14.6354i | −1.24585 | + | 2.15787i | ||||
\(47\) | −4.91421 | − | 8.51167i | −0.716812 | − | 1.24155i | −0.962257 | − | 0.272144i | \(-0.912267\pi\) |
0.245445 | − | 0.969411i | \(-0.421066\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | 2.20711 | + | 3.82282i | 0.309057 | + | 0.535302i | ||||
\(52\) | 1.58579 | − | 2.74666i | 0.219909 | − | 0.380894i | ||||
\(53\) | 3.58579 | − | 6.21076i | 0.492546 | − | 0.853114i | −0.507417 | − | 0.861700i | \(-0.669400\pi\) |
0.999963 | + | 0.00858626i | \(0.00273313\pi\) | |||||||
\(54\) | 1.20711 | + | 2.09077i | 0.164266 | + | 0.284518i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −4.41421 | + | 10.8126i | −0.589874 | + | 1.44489i | ||||
\(57\) | 7.24264 | 0.959311 | ||||||||
\(58\) | 3.91421 | + | 6.77962i | 0.513961 | + | 0.890207i | ||||
\(59\) | 4.32843 | − | 7.49706i | 0.563513 | − | 0.976034i | −0.433673 | − | 0.901070i | \(-0.642783\pi\) |
0.997186 | − | 0.0749632i | \(-0.0238839\pi\) | |||||||
\(60\) | 3.82843 | − | 6.63103i | 0.494248 | − | 0.856062i | ||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | −13.6569 | −1.73442 | ||||||||
\(63\) | −2.62132 | + | 0.358719i | −0.330255 | + | 0.0451944i | ||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −0.828427 | − | 1.43488i | −0.102754 | − | 0.177975i | ||||
\(66\) | 1.20711 | − | 2.09077i | 0.148585 | − | 0.257356i | ||||
\(67\) | 1.58579 | − | 2.74666i | 0.193735 | − | 0.335558i | −0.752750 | − | 0.658306i | \(-0.771273\pi\) |
0.946485 | + | 0.322748i | \(0.104607\pi\) | |||||||
\(68\) | 8.44975 | + | 14.6354i | 1.02468 | + | 1.77480i | ||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | 7.82843 | + | 10.0951i | 0.935676 | + | 1.20660i | ||||
\(71\) | −4.17157 | −0.495075 | −0.247537 | − | 0.968878i | \(-0.579621\pi\) | ||||
−0.247537 | + | 0.968878i | \(0.579621\pi\) | |||||||
\(72\) | 2.20711 | + | 3.82282i | 0.260110 | + | 0.450524i | ||||
\(73\) | −0.171573 | + | 0.297173i | −0.0200811 | + | 0.0347815i | −0.875891 | − | 0.482508i | \(-0.839726\pi\) |
0.855810 | + | 0.517290i | \(0.173059\pi\) | |||||||
\(74\) | −11.4497 | + | 19.8315i | −1.33101 | + | 2.30537i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 27.7279 | 3.18061 | ||||||||
\(77\) | 1.62132 | + | 2.09077i | 0.184767 | + | 0.238265i | ||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −6.65685 | − | 11.5300i | −0.748955 | − | 1.29723i | −0.948324 | − | 0.317303i | \(-0.897223\pi\) |
0.199370 | − | 0.979924i | \(-0.436111\pi\) | |||||||
\(80\) | 3.00000 | − | 5.19615i | 0.335410 | − | 0.580948i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.41421 | − | 2.44949i | −0.156174 | − | 0.270501i | ||||
\(83\) | −2.82843 | −0.310460 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | −10.0355 | + | 1.37333i | −1.09497 | + | 0.149843i | ||||
\(85\) | 8.82843 | 0.957577 | ||||||||
\(86\) | −3.32843 | − | 5.76500i | −0.358914 | − | 0.621656i | ||||
\(87\) | −1.62132 | + | 2.80821i | −0.173824 | + | 0.301072i | ||||
\(88\) | 2.20711 | − | 3.82282i | 0.235278 | − | 0.407514i | ||||
\(89\) | 7.07107 | + | 12.2474i | 0.749532 | + | 1.29823i | 0.948047 | + | 0.318129i | \(0.103055\pi\) |
−0.198516 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(90\) | 4.82843 | 0.508961 | ||||||||
\(91\) | −0.828427 | + | 2.02922i | −0.0868428 | + | 0.212720i | ||||
\(92\) | −26.7990 | −2.79399 | ||||||||
\(93\) | −2.82843 | − | 4.89898i | −0.293294 | − | 0.508001i | ||||
\(94\) | 11.8640 | − | 20.5490i | 1.22367 | − | 2.11947i | ||||
\(95\) | 7.24264 | − | 12.5446i | 0.743079 | − | 1.28705i | ||||
\(96\) | −0.792893 | − | 1.37333i | −0.0809243 | − | 0.140165i | ||||
\(97\) | −11.4853 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(98\) | 4.20711 | − | 16.3674i | 0.424982 | − | 1.65336i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.91421 | + | 3.31552i | 0.191421 | + | 0.331552i | ||||
\(101\) | −2.44975 | + | 4.24309i | −0.243759 | + | 0.422203i | −0.961782 | − | 0.273816i | \(-0.911714\pi\) |
0.718023 | + | 0.696019i | \(0.245047\pi\) | |||||||
\(102\) | −5.32843 | + | 9.22911i | −0.527593 | + | 0.913818i | ||||
\(103\) | −6.24264 | − | 10.8126i | −0.615106 | − | 1.06539i | −0.990366 | − | 0.138475i | \(-0.955780\pi\) |
0.375260 | − | 0.926919i | \(-0.377553\pi\) | |||||||
\(104\) | 3.65685 | 0.358584 | ||||||||
\(105\) | −2.00000 | + | 4.89898i | −0.195180 | + | 0.478091i | ||||
\(106\) | 17.3137 | 1.68166 | ||||||||
\(107\) | −4.82843 | − | 8.36308i | −0.466782 | − | 0.808490i | 0.532498 | − | 0.846431i | \(-0.321253\pi\) |
−0.999280 | + | 0.0379415i | \(0.987920\pi\) | |||||||
\(108\) | −1.91421 | + | 3.31552i | −0.184195 | + | 0.319036i | ||||
\(109\) | 3.41421 | − | 5.91359i | 0.327022 | − | 0.566419i | −0.654897 | − | 0.755718i | \(-0.727288\pi\) |
0.981920 | + | 0.189299i | \(0.0606214\pi\) | |||||||
\(110\) | −2.41421 | − | 4.18154i | −0.230186 | − | 0.398694i | ||||
\(111\) | −9.48528 | −0.900303 | ||||||||
\(112\) | −7.86396 | + | 1.07616i | −0.743074 | + | 0.101687i | ||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | 8.74264 | + | 15.1427i | 0.818823 | + | 1.41824i | ||||
\(115\) | −7.00000 | + | 12.1244i | −0.652753 | + | 1.13060i | ||||
\(116\) | −6.20711 | + | 10.7510i | −0.576315 | + | 0.998208i | ||||
\(117\) | 0.414214 | + | 0.717439i | 0.0382941 | + | 0.0663273i | ||||
\(118\) | 20.8995 | 1.92395 | ||||||||
\(119\) | −7.15685 | − | 9.22911i | −0.656068 | − | 0.846031i | ||||
\(120\) | 8.82843 | 0.805921 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −4.82843 | + | 8.36308i | −0.437145 | + | 0.757158i | ||||
\(123\) | 0.585786 | − | 1.01461i | 0.0528186 | − | 0.0914845i | ||||
\(124\) | −10.8284 | − | 18.7554i | −0.972421 | − | 1.68428i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −3.91421 | − | 5.04757i | −0.348706 | − | 0.449673i | ||||
\(127\) | −16.0711 | −1.42608 | −0.713038 | − | 0.701125i | \(-0.752681\pi\) | ||||
−0.713038 | + | 0.701125i | \(0.752681\pi\) | |||||||
\(128\) | −10.2782 | − | 17.8023i | −0.908471 | − | 1.57352i | ||||
\(129\) | 1.37868 | − | 2.38794i | 0.121386 | − | 0.210247i | ||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 2.58579 | + | 4.47871i | 0.225921 | + | 0.391307i | 0.956595 | − | 0.291419i | \(-0.0941275\pi\) |
−0.730674 | + | 0.682726i | \(0.760794\pi\) | |||||||
\(132\) | 3.82843 | 0.333222 | ||||||||
\(133\) | −18.9853 | + | 2.59808i | −1.64623 | + | 0.225282i | ||||
\(134\) | 7.65685 | 0.661451 | ||||||||
\(135\) | 1.00000 | + | 1.73205i | 0.0860663 | + | 0.149071i | ||||
\(136\) | −9.74264 | + | 16.8747i | −0.835425 | + | 1.44700i | ||||
\(137\) | −0.242641 | + | 0.420266i | −0.0207302 | + | 0.0359057i | −0.876204 | − | 0.481940i | \(-0.839932\pi\) |
0.855474 | + | 0.517845i | \(0.173266\pi\) | |||||||
\(138\) | −8.44975 | − | 14.6354i | −0.719290 | − | 1.24585i | ||||
\(139\) | 8.41421 | 0.713684 | 0.356842 | − | 0.934165i | \(-0.383853\pi\) | ||||
0.356842 | + | 0.934165i | \(0.383853\pi\) | |||||||
\(140\) | −7.65685 | + | 18.7554i | −0.647122 | + | 1.58512i | ||||
\(141\) | 9.82843 | 0.827703 | ||||||||
\(142\) | −5.03553 | − | 8.72180i | −0.422573 | − | 0.731917i | ||||
\(143\) | 0.414214 | − | 0.717439i | 0.0346383 | − | 0.0599953i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | 3.24264 | + | 5.61642i | 0.269287 | + | 0.466418i | ||||
\(146\) | −0.828427 | −0.0685611 | ||||||||
\(147\) | 6.74264 | − | 1.88064i | 0.556124 | − | 0.155112i | ||||
\(148\) | −36.3137 | −2.98497 | ||||||||
\(149\) | 11.1066 | + | 19.2372i | 0.909888 | + | 1.57597i | 0.814218 | + | 0.580560i | \(0.197166\pi\) |
0.0956705 | + | 0.995413i | \(0.469500\pi\) | |||||||
\(150\) | −1.20711 | + | 2.09077i | −0.0985599 | + | 0.170711i | ||||
\(151\) | 9.44975 | − | 16.3674i | 0.769010 | − | 1.33196i | −0.169091 | − | 0.985600i | \(-0.554083\pi\) |
0.938101 | − | 0.346363i | \(-0.112583\pi\) | |||||||
\(152\) | 15.9853 | + | 27.6873i | 1.29658 | + | 2.24574i | ||||
\(153\) | −4.41421 | −0.356868 | ||||||||
\(154\) | −2.41421 | + | 5.91359i | −0.194543 | + | 0.476531i | ||||
\(155\) | −11.3137 | −0.908739 | ||||||||
\(156\) | 1.58579 | + | 2.74666i | 0.126965 | + | 0.219909i | ||||
\(157\) | −3.50000 | + | 6.06218i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | 16.0711 | − | 27.8359i | 1.27855 | − | 2.21451i | ||||
\(159\) | 3.58579 | + | 6.21076i | 0.284371 | + | 0.492546i | ||||
\(160\) | −3.17157 | −0.250735 | ||||||||
\(161\) | 18.3492 | − | 2.51104i | 1.44612 | − | 0.197897i | ||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | 10.4853 | + | 18.1610i | 0.821271 | + | 1.42248i | 0.904736 | + | 0.425972i | \(0.140068\pi\) |
−0.0834658 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(164\) | 2.24264 | − | 3.88437i | 0.175121 | − | 0.303318i | ||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | −3.41421 | − | 5.91359i | −0.264994 | − | 0.458984i | ||||
\(167\) | 5.17157 | 0.400188 | 0.200094 | − | 0.979777i | \(-0.435875\pi\) | ||||
0.200094 | + | 0.979777i | \(0.435875\pi\) | |||||||
\(168\) | −7.15685 | − | 9.22911i | −0.552163 | − | 0.712041i | ||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | 10.6569 | + | 18.4582i | 0.817343 | + | 1.41568i | ||||
\(171\) | −3.62132 | + | 6.27231i | −0.276929 | + | 0.479656i | ||||
\(172\) | 5.27817 | − | 9.14207i | 0.402457 | − | 0.697076i | ||||
\(173\) | 7.41421 | + | 12.8418i | 0.563692 | + | 0.976344i | 0.997170 | + | 0.0751793i | \(0.0239529\pi\) |
−0.433478 | + | 0.901164i | \(0.642714\pi\) | |||||||
\(174\) | −7.82843 | −0.593472 | ||||||||
\(175\) | −1.62132 | − | 2.09077i | −0.122560 | − | 0.158047i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 4.32843 | + | 7.49706i | 0.325345 | + | 0.563513i | ||||
\(178\) | −17.0711 | + | 29.5680i | −1.27953 | + | 2.21621i | ||||
\(179\) | −8.91421 | + | 15.4399i | −0.666280 | + | 1.15403i | 0.312657 | + | 0.949866i | \(0.398781\pi\) |
−0.978937 | + | 0.204164i | \(0.934552\pi\) | |||||||
\(180\) | 3.82843 | + | 6.63103i | 0.285354 | + | 0.494248i | ||||
\(181\) | −11.6569 | −0.866447 | −0.433224 | − | 0.901286i | \(-0.642624\pi\) | ||||
−0.433224 | + | 0.901286i | \(0.642624\pi\) | |||||||
\(182\) | −5.24264 | + | 0.717439i | −0.388610 | + | 0.0531801i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −15.4497 | − | 26.7597i | −1.13897 | − | 1.97275i | ||||
\(185\) | −9.48528 | + | 16.4290i | −0.697372 | + | 1.20788i | ||||
\(186\) | 6.82843 | − | 11.8272i | 0.500685 | − | 0.867211i | ||||
\(187\) | 2.20711 | + | 3.82282i | 0.161400 | + | 0.279552i | ||||
\(188\) | 37.6274 | 2.74426 | ||||||||
\(189\) | 1.00000 | − | 2.44949i | 0.0727393 | − | 0.178174i | ||||
\(190\) | 34.9706 | 2.53703 | ||||||||
\(191\) | 10.8284 | + | 18.7554i | 0.783517 | + | 1.35709i | 0.929881 | + | 0.367861i | \(0.119910\pi\) |
−0.146363 | + | 0.989231i | \(0.546757\pi\) | |||||||
\(192\) | 4.91421 | − | 8.51167i | 0.354653 | − | 0.614277i | ||||
\(193\) | 6.07107 | − | 10.5154i | 0.437005 | − | 0.756915i | −0.560452 | − | 0.828187i | \(-0.689373\pi\) |
0.997457 | + | 0.0712721i | \(0.0227059\pi\) | |||||||
\(194\) | −13.8640 | − | 24.0131i | −0.995374 | − | 1.72404i | ||||
\(195\) | 1.65685 | 0.118650 | ||||||||
\(196\) | 25.8137 | − | 7.19988i | 1.84384 | − | 0.514277i | ||||
\(197\) | −16.4142 | −1.16946 | −0.584732 | − | 0.811226i | \(-0.698800\pi\) | ||||
−0.584732 | + | 0.811226i | \(0.698800\pi\) | |||||||
\(198\) | 1.20711 | + | 2.09077i | 0.0857853 | + | 0.148585i | ||||
\(199\) | 9.89949 | − | 17.1464i | 0.701757 | − | 1.21548i | −0.266093 | − | 0.963947i | \(-0.585733\pi\) |
0.967849 | − | 0.251531i | \(-0.0809339\pi\) | |||||||
\(200\) | −2.20711 | + | 3.82282i | −0.156066 | + | 0.270314i | ||||
\(201\) | 1.58579 | + | 2.74666i | 0.111853 | + | 0.193735i | ||||
\(202\) | −11.8284 | −0.832245 | ||||||||
\(203\) | 3.24264 | − | 7.94282i | 0.227589 | − | 0.557476i | ||||
\(204\) | −16.8995 | −1.18320 | ||||||||
\(205\) | −1.17157 | − | 2.02922i | −0.0818262 | − | 0.141727i | ||||
\(206\) | 15.0711 | − | 26.1039i | 1.05005 | − | 1.81874i | ||||
\(207\) | 3.50000 | − | 6.06218i | 0.243267 | − | 0.421350i | ||||
\(208\) | 1.24264 | + | 2.15232i | 0.0861616 | + | 0.149236i | ||||
\(209\) | 7.24264 | 0.500984 | ||||||||
\(210\) | −12.6569 | + | 1.73205i | −0.873406 | + | 0.119523i | ||||
\(211\) | 14.9706 | 1.03062 | 0.515308 | − | 0.857005i | \(-0.327678\pi\) | ||||
0.515308 | + | 0.857005i | \(0.327678\pi\) | |||||||
\(212\) | 13.7279 | + | 23.7775i | 0.942838 | + | 1.63304i | ||||
\(213\) | 2.08579 | − | 3.61269i | 0.142916 | − | 0.247537i | ||||
\(214\) | 11.6569 | − | 20.1903i | 0.796846 | − | 1.38018i | ||||
\(215\) | −2.75736 | − | 4.77589i | −0.188050 | − | 0.325713i | ||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | 9.17157 | + | 11.8272i | 0.622607 | + | 0.802881i | ||||
\(218\) | 16.4853 | 1.11652 | ||||||||
\(219\) | −0.171573 | − | 0.297173i | −0.0115938 | − | 0.0200811i | ||||
\(220\) | 3.82843 | − | 6.63103i | 0.258113 | − | 0.447064i | ||||
\(221\) | −1.82843 | + | 3.16693i | −0.122993 | + | 0.213031i | ||||
\(222\) | −11.4497 | − | 19.8315i | −0.768457 | − | 1.33101i | ||||
\(223\) | −22.9706 | −1.53822 | −0.769111 | − | 0.639115i | \(-0.779301\pi\) | ||||
−0.769111 | + | 0.639115i | \(0.779301\pi\) | |||||||
\(224\) | 2.57107 | + | 3.31552i | 0.171787 | + | 0.221527i | ||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −9.24264 | − | 16.0087i | −0.614811 | − | 1.06488i | ||||
\(227\) | −7.48528 | + | 12.9649i | −0.496816 | + | 0.860510i | −0.999993 | − | 0.00367316i | \(-0.998831\pi\) |
0.503178 | + | 0.864183i | \(0.332164\pi\) | |||||||
\(228\) | −13.8640 | + | 24.0131i | −0.918163 | + | 1.59031i | ||||
\(229\) | 7.82843 | + | 13.5592i | 0.517317 | + | 0.896019i | 0.999798 | + | 0.0201128i | \(0.00640252\pi\) |
−0.482481 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(230\) | −33.7990 | −2.22864 | ||||||||
\(231\) | −2.62132 | + | 0.358719i | −0.172470 | + | 0.0236020i | ||||
\(232\) | −14.3137 | −0.939741 | ||||||||
\(233\) | −5.20711 | − | 9.01897i | −0.341129 | − | 0.590853i | 0.643514 | − | 0.765435i | \(-0.277476\pi\) |
−0.984643 | + | 0.174582i | \(0.944143\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | 9.82843 | − | 17.0233i | 0.641136 | − | 1.11048i | ||||
\(236\) | 16.5711 | + | 28.7019i | 1.07868 | + | 1.86834i | ||||
\(237\) | 13.3137 | 0.864818 | ||||||||
\(238\) | 10.6569 | − | 26.1039i | 0.690781 | − | 1.69206i | ||||
\(239\) | −6.48528 | −0.419498 | −0.209749 | − | 0.977755i | \(-0.567265\pi\) | ||||
−0.209749 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | −3.65685 | + | 6.33386i | −0.235559 | + | 0.408000i | −0.959435 | − | 0.281930i | \(-0.909025\pi\) |
0.723876 | + | 0.689930i | \(0.242359\pi\) | |||||||
\(242\) | 1.20711 | − | 2.09077i | 0.0775958 | − | 0.134400i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −15.3137 | −0.980360 | ||||||||
\(245\) | 3.48528 | − | 13.5592i | 0.222666 | − | 0.866268i | ||||
\(246\) | 2.82843 | 0.180334 | ||||||||
\(247\) | 3.00000 | + | 5.19615i | 0.190885 | + | 0.330623i | ||||
\(248\) | 12.4853 | − | 21.6251i | 0.792816 | − | 1.37320i | ||||
\(249\) | 1.41421 | − | 2.44949i | 0.0896221 | − | 0.155230i | ||||
\(250\) | 14.4853 | + | 25.0892i | 0.916130 | + | 1.58678i | ||||
\(251\) | −2.51472 | −0.158728 | −0.0793638 | − | 0.996846i | \(-0.525289\pi\) | ||||
−0.0793638 | + | 0.996846i | \(0.525289\pi\) | |||||||
\(252\) | 3.82843 | − | 9.37769i | 0.241168 | − | 0.590739i | ||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | −19.3995 | − | 33.6009i | −1.21723 | − | 2.10831i | ||||
\(255\) | −4.41421 | + | 7.64564i | −0.276429 | + | 0.478789i | ||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | −10.7279 | − | 18.5813i | −0.669189 | − | 1.15907i | −0.978131 | − | 0.207989i | \(-0.933308\pi\) |
0.308942 | − | 0.951081i | \(-0.400025\pi\) | |||||||
\(258\) | 6.65685 | 0.414438 | ||||||||
\(259\) | 24.8640 | − | 3.40256i | 1.54497 | − | 0.211424i | ||||
\(260\) | 6.34315 | 0.393385 | ||||||||
\(261\) | −1.62132 | − | 2.80821i | −0.100357 | − | 0.173824i | ||||
\(262\) | −6.24264 | + | 10.8126i | −0.385672 | + | 0.668003i | ||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 2.20711 | + | 3.82282i | 0.135838 | + | 0.235278i | ||||
\(265\) | 14.3431 | 0.881092 | ||||||||
\(266\) | −28.3492 | − | 36.5577i | −1.73820 | − | 2.24150i | ||||
\(267\) | −14.1421 | −0.865485 | ||||||||
\(268\) | 6.07107 | + | 10.5154i | 0.370849 | + | 0.642330i | ||||
\(269\) | 13.8995 | − | 24.0746i | 0.847467 | − | 1.46786i | −0.0359941 | − | 0.999352i | \(-0.511460\pi\) |
0.883461 | − | 0.468504i | \(-0.155207\pi\) | |||||||
\(270\) | −2.41421 | + | 4.18154i | −0.146924 | + | 0.254480i | ||||
\(271\) | 11.4853 | + | 19.8931i | 0.697681 | + | 1.20842i | 0.969268 | + | 0.246005i | \(0.0791181\pi\) |
−0.271587 | + | 0.962414i | \(0.587549\pi\) | |||||||
\(272\) | −13.2426 | −0.802953 | ||||||||
\(273\) | −1.34315 | − | 1.73205i | −0.0812909 | − | 0.104828i | ||||
\(274\) | −1.17157 | −0.0707773 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | 13.3995 | − | 23.2086i | 0.806555 | − | 1.39699i | ||||
\(277\) | 12.8284 | − | 22.2195i | 0.770785 | − | 1.33504i | −0.166348 | − | 0.986067i | \(-0.553197\pi\) |
0.937133 | − | 0.348972i | \(-0.113469\pi\) | |||||||
\(278\) | 10.1569 | + | 17.5922i | 0.609168 | + | 1.05511i | ||||
\(279\) | 5.65685 | 0.338667 | ||||||||
\(280\) | −23.1421 | + | 3.16693i | −1.38301 | + | 0.189260i | ||||
\(281\) | 14.4142 | 0.859880 | 0.429940 | − | 0.902857i | \(-0.358535\pi\) | ||||
0.429940 | + | 0.902857i | \(0.358535\pi\) | |||||||
\(282\) | 11.8640 | + | 20.5490i | 0.706489 | + | 1.22367i | ||||
\(283\) | −10.1716 | + | 17.6177i | −0.604637 | + | 1.04726i | 0.387471 | + | 0.921882i | \(0.373349\pi\) |
−0.992109 | + | 0.125381i | \(0.959985\pi\) | |||||||
\(284\) | 7.98528 | − | 13.8309i | 0.473839 | − | 0.820714i | ||||
\(285\) | 7.24264 | + | 12.5446i | 0.429017 | + | 0.743079i | ||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | −1.17157 | + | 2.86976i | −0.0691558 | + | 0.169396i | ||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −1.24264 | − | 2.15232i | −0.0730965 | − | 0.126607i | ||||
\(290\) | −7.82843 | + | 13.5592i | −0.459701 | + | 0.796226i | ||||
\(291\) | 5.74264 | − | 9.94655i | 0.336640 | − | 0.583077i | ||||
\(292\) | −0.656854 | − | 1.13770i | −0.0384395 | − | 0.0665791i | ||||
\(293\) | 5.72792 | 0.334629 | 0.167314 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167314 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(294\) | 12.0711 | + | 11.8272i | 0.703999 | + | 0.689775i | ||||
\(295\) | 17.3137 | 1.00804 | ||||||||
\(296\) | −20.9350 | − | 36.2605i | −1.21682 | − | 2.10760i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | −26.8137 | + | 46.4427i | −1.55328 | + | 2.69035i | ||||
\(299\) | −2.89949 | − | 5.02207i | −0.167682 | − | 0.290434i | ||||
\(300\) | −3.82843 | −0.221034 | ||||||||
\(301\) | −2.75736 | + | 6.75412i | −0.158932 | + | 0.389301i | ||||
\(302\) | 45.6274 | 2.62556 | ||||||||
\(303\) | −2.44975 | − | 4.24309i | −0.140734 | − | 0.243759i | ||||
\(304\) | −10.8640 | + | 18.8169i | −0.623091 | + | 1.07923i | ||||
\(305\) | −4.00000 | + | 6.92820i | −0.229039 | + | 0.396708i | ||||
\(306\) | −5.32843 | − | 9.22911i | −0.304606 | − | 0.527593i | ||||
\(307\) | −17.3137 | −0.988146 | −0.494073 | − | 0.869421i | \(-0.664492\pi\) | ||||
−0.494073 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(308\) | −10.0355 | + | 1.37333i | −0.571828 | + | 0.0782528i | ||||
\(309\) | 12.4853 | 0.710263 | ||||||||
\(310\) | −13.6569 | − | 23.6544i | −0.775657 | − | 1.34348i | ||||
\(311\) | −14.8137 | + | 25.6581i | −0.840008 | + | 1.45494i | 0.0498782 | + | 0.998755i | \(0.484117\pi\) |
−0.889887 | + | 0.456182i | \(0.849217\pi\) | |||||||
\(312\) | −1.82843 | + | 3.16693i | −0.103514 | + | 0.179292i | ||||
\(313\) | −2.39949 | − | 4.15605i | −0.135627 | − | 0.234914i | 0.790210 | − | 0.612837i | \(-0.209972\pi\) |
−0.925837 | + | 0.377923i | \(0.876638\pi\) | |||||||
\(314\) | −16.8995 | −0.953694 | ||||||||
\(315\) | −3.24264 | − | 4.18154i | −0.182702 | − | 0.235603i | ||||
\(316\) | 50.9706 | 2.86732 | ||||||||
\(317\) | 12.6569 | + | 21.9223i | 0.710880 | + | 1.23128i | 0.964527 | + | 0.263983i | \(0.0850363\pi\) |
−0.253648 | + | 0.967297i | \(0.581630\pi\) | |||||||
\(318\) | −8.65685 | + | 14.9941i | −0.485452 | + | 0.840828i | ||||
\(319\) | −1.62132 | + | 2.80821i | −0.0907765 | + | 0.157230i | ||||
\(320\) | −9.82843 | − | 17.0233i | −0.549426 | − | 0.951633i | ||||
\(321\) | 9.65685 | 0.538993 | ||||||||
\(322\) | 27.3995 | + | 35.3330i | 1.52691 | + | 1.96903i | ||||
\(323\) | −31.9706 | −1.77889 | ||||||||
\(324\) | −1.91421 | − | 3.31552i | −0.106345 | − | 0.184195i | ||||
\(325\) | −0.414214 | + | 0.717439i | −0.0229764 | + | 0.0397964i | ||||
\(326\) | −25.3137 | + | 43.8446i | −1.40200 | + | 2.42833i | ||||
\(327\) | 3.41421 | + | 5.91359i | 0.188806 | + | 0.327022i | ||||
\(328\) | 5.17157 | 0.285552 | ||||||||
\(329\) | −25.7635 | + | 3.52565i | −1.42039 | + | 0.194375i | ||||
\(330\) | 4.82843 | 0.265796 | ||||||||
\(331\) | −11.2426 | − | 19.4728i | −0.617951 | − | 1.07032i | −0.989859 | − | 0.142053i | \(-0.954629\pi\) |
0.371908 | − | 0.928270i | \(-0.378704\pi\) | |||||||
\(332\) | 5.41421 | − | 9.37769i | 0.297144 | − | 0.514668i | ||||
\(333\) | 4.74264 | − | 8.21449i | 0.259895 | − | 0.450152i | ||||
\(334\) | 6.24264 | + | 10.8126i | 0.341582 | + | 0.591638i | ||||
\(335\) | 6.34315 | 0.346563 | ||||||||
\(336\) | 3.00000 | − | 7.34847i | 0.163663 | − | 0.400892i | ||||
\(337\) | 3.85786 | 0.210151 | 0.105076 | − | 0.994464i | \(-0.466492\pi\) | ||||
0.105076 | + | 0.994464i | \(0.466492\pi\) | |||||||
\(338\) | −14.8640 | − | 25.7451i | −0.808493 | − | 1.40035i | ||||
\(339\) | 3.82843 | − | 6.63103i | 0.207932 | − | 0.360148i | ||||
\(340\) | −16.8995 | + | 29.2708i | −0.916504 | + | 1.58743i | ||||
\(341\) | −2.82843 | − | 4.89898i | −0.153168 | − | 0.265295i | ||||
\(342\) | −17.4853 | −0.945496 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 12.1716 | 0.656247 | ||||||||
\(345\) | −7.00000 | − | 12.1244i | −0.376867 | − | 0.652753i | ||||
\(346\) | −17.8995 | + | 31.0028i | −0.962283 | + | 1.66672i | ||||
\(347\) | −7.48528 | + | 12.9649i | −0.401831 | + | 0.695992i | −0.993947 | − | 0.109861i | \(-0.964959\pi\) |
0.592116 | + | 0.805853i | \(0.298293\pi\) | |||||||
\(348\) | −6.20711 | − | 10.7510i | −0.332736 | − | 0.576315i | ||||
\(349\) | 10.9706 | 0.587241 | 0.293620 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293620 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(350\) | 2.41421 | − | 5.91359i | 0.129045 | − | 0.316095i | ||||
\(351\) | −0.828427 | −0.0442182 | ||||||||
\(352\) | −0.792893 | − | 1.37333i | −0.0422614 | − | 0.0731988i | ||||
\(353\) | −6.65685 | + | 11.5300i | −0.354309 | + | 0.613680i | −0.986999 | − | 0.160724i | \(-0.948617\pi\) |
0.632691 | + | 0.774405i | \(0.281950\pi\) | |||||||
\(354\) | −10.4497 | + | 18.0995i | −0.555398 | + | 0.961977i | ||||
\(355\) | −4.17157 | − | 7.22538i | −0.221404 | − | 0.383483i | ||||
\(356\) | −54.1421 | −2.86953 | ||||||||
\(357\) | 11.5711 | − | 1.58346i | 0.612406 | − | 0.0838058i | ||||
\(358\) | −43.0416 | −2.27482 | ||||||||
\(359\) | 4.00000 | + | 6.92820i | 0.211112 | + | 0.365657i | 0.952063 | − | 0.305903i | \(-0.0989582\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(360\) | −4.41421 | + | 7.64564i | −0.232649 | + | 0.402961i | ||||
\(361\) | −16.7279 | + | 28.9736i | −0.880417 | + | 1.52493i | ||||
\(362\) | −14.0711 | − | 24.3718i | −0.739559 | − | 1.28095i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −5.14214 | − | 6.63103i | −0.269521 | − | 0.347560i | ||||
\(365\) | −0.686292 | −0.0359221 | ||||||||
\(366\) | −4.82843 | − | 8.36308i | −0.252386 | − | 0.437145i | ||||
\(367\) | 2.07107 | − | 3.58719i | 0.108109 | − | 0.187250i | −0.806895 | − | 0.590695i | \(-0.798854\pi\) |
0.915004 | + | 0.403445i | \(0.132187\pi\) | |||||||
\(368\) | 10.5000 | − | 18.1865i | 0.547350 | − | 0.948039i | ||||
\(369\) | 0.585786 | + | 1.01461i | 0.0304948 | + | 0.0528186i | ||||
\(370\) | −45.7990 | −2.38098 | ||||||||
\(371\) | −11.6274 | − | 14.9941i | −0.603665 | − | 0.778455i | ||||
\(372\) | 21.6569 | 1.12286 | ||||||||
\(373\) | 0.828427 | + | 1.43488i | 0.0428943 | + | 0.0742952i | 0.886675 | − | 0.462392i | \(-0.153009\pi\) |
−0.843781 | + | 0.536687i | \(0.819675\pi\) | |||||||
\(374\) | −5.32843 | + | 9.22911i | −0.275526 | + | 0.477226i | ||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | 21.6924 | + | 37.5723i | 1.11870 | + | 1.93764i | ||||
\(377\) | −2.68629 | −0.138351 | ||||||||
\(378\) | 6.32843 | − | 0.866025i | 0.325499 | − | 0.0445435i | ||||
\(379\) | 18.8284 | 0.967151 | 0.483576 | − | 0.875303i | \(-0.339338\pi\) | ||||
0.483576 | + | 0.875303i | \(0.339338\pi\) | |||||||
\(380\) | 27.7279 | + | 48.0262i | 1.42241 | + | 2.46369i | ||||
\(381\) | 8.03553 | − | 13.9180i | 0.411673 | − | 0.713038i | ||||
\(382\) | −26.1421 | + | 45.2795i | −1.33755 | + | 2.31670i | ||||
\(383\) | −1.15685 | − | 2.00373i | −0.0591125 | − | 0.102386i | 0.834955 | − | 0.550319i | \(-0.185494\pi\) |
−0.894067 | + | 0.447933i | \(0.852160\pi\) | |||||||
\(384\) | 20.5563 | 1.04901 | ||||||||
\(385\) | −2.00000 | + | 4.89898i | −0.101929 | + | 0.249675i | ||||
\(386\) | 29.3137 | 1.49203 | ||||||||
\(387\) | 1.37868 | + | 2.38794i | 0.0700822 | + | 0.121386i | ||||
\(388\) | 21.9853 | − | 38.0796i | 1.11613 | − | 1.93320i | ||||
\(389\) | 5.89949 | − | 10.2182i | 0.299116 | − | 0.518085i | −0.676818 | − | 0.736151i | \(-0.736641\pi\) |
0.975934 | + | 0.218066i | \(0.0699748\pi\) | |||||||
\(390\) | 2.00000 | + | 3.46410i | 0.101274 | + | 0.175412i | ||||
\(391\) | 30.8995 | 1.56265 | ||||||||
\(392\) | 22.0711 | + | 21.6251i | 1.11476 | + | 1.09223i | ||||
\(393\) | −5.17157 | −0.260871 | ||||||||
\(394\) | −19.8137 | − | 34.3183i | −0.998200 | − | 1.72893i | ||||
\(395\) | 13.3137 | − | 23.0600i | 0.669885 | − | 1.16028i | ||||
\(396\) | −1.91421 | + | 3.31552i | −0.0961929 | + | 0.166611i | ||||
\(397\) | −8.74264 | − | 15.1427i | −0.438781 | − | 0.759990i | 0.558815 | − | 0.829292i | \(-0.311256\pi\) |
−0.997596 | + | 0.0693020i | \(0.977923\pi\) | |||||||
\(398\) | 47.7990 | 2.39595 | ||||||||
\(399\) | 7.24264 | − | 17.7408i | 0.362586 | − | 0.888150i | ||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −3.75736 | − | 6.50794i | −0.187634 | − | 0.324991i | 0.756827 | − | 0.653615i | \(-0.226748\pi\) |
−0.944461 | + | 0.328624i | \(0.893415\pi\) | |||||||
\(402\) | −3.82843 | + | 6.63103i | −0.190945 | + | 0.330726i | ||||
\(403\) | 2.34315 | − | 4.05845i | 0.116720 | − | 0.202166i | ||||
\(404\) | −9.37868 | − | 16.2443i | −0.466607 | − | 0.808187i | ||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 20.5208 | − | 2.80821i | 1.01843 | − | 0.139369i | ||||
\(407\) | −9.48528 | −0.470168 | ||||||||
\(408\) | −9.74264 | − | 16.8747i | −0.482333 | − | 0.835425i | ||||
\(409\) | 3.89949 | − | 6.75412i | 0.192818 | − | 0.333970i | −0.753365 | − | 0.657602i | \(-0.771571\pi\) |
0.946183 | + | 0.323632i | \(0.104904\pi\) | |||||||
\(410\) | 2.82843 | − | 4.89898i | 0.139686 | − | 0.241943i | ||||
\(411\) | −0.242641 | − | 0.420266i | −0.0119686 | − | 0.0207302i | ||||
\(412\) | 47.7990 | 2.35489 | ||||||||
\(413\) | −14.0355 | − | 18.0995i | −0.690643 | − | 0.890618i | ||||
\(414\) | 16.8995 | 0.830565 | ||||||||
\(415\) | −2.82843 | − | 4.89898i | −0.138842 | − | 0.240481i | ||||
\(416\) | 0.656854 | − | 1.13770i | 0.0322049 | − | 0.0557806i | ||||
\(417\) | −4.20711 | + | 7.28692i | −0.206023 | + | 0.356842i | ||||
\(418\) | 8.74264 | + | 15.1427i | 0.427617 | + | 0.740654i | ||||
\(419\) | 14.7990 | 0.722978 | 0.361489 | − | 0.932376i | \(-0.382269\pi\) | ||||
0.361489 | + | 0.932376i | \(0.382269\pi\) | |||||||
\(420\) | −12.4142 | − | 16.0087i | −0.605752 | − | 0.781146i | ||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | 18.0711 | + | 31.3000i | 0.879686 | + | 1.52366i | ||||
\(423\) | −4.91421 | + | 8.51167i | −0.238937 | + | 0.413851i | ||||
\(424\) | −15.8284 | + | 27.4156i | −0.768696 | + | 1.33142i | ||||
\(425\) | −2.20711 | − | 3.82282i | −0.107060 | − | 0.185434i | ||||
\(426\) | 10.0711 | 0.487945 | ||||||||
\(427\) | 10.4853 | − | 1.43488i | 0.507418 | − | 0.0694386i | ||||
\(428\) | 36.9706 | 1.78704 | ||||||||
\(429\) | 0.414214 | + | 0.717439i | 0.0199984 | + | 0.0346383i | ||||
\(430\) | 6.65685 | − | 11.5300i | 0.321022 | − | 0.556026i | ||||
\(431\) | −3.48528 | + | 6.03668i | −0.167880 | + | 0.290777i | −0.937674 | − | 0.347515i | \(-0.887025\pi\) |
0.769794 | + | 0.638292i | \(0.220359\pi\) | |||||||
\(432\) | −1.50000 | − | 2.59808i | −0.0721688 | − | 0.125000i | ||||
\(433\) | 0.857864 | 0.0412263 | 0.0206132 | − | 0.999788i | \(-0.493438\pi\) | ||||
0.0206132 | + | 0.999788i | \(0.493438\pi\) | |||||||
\(434\) | −13.6569 | + | 33.4523i | −0.655550 | + | 1.60576i | ||||
\(435\) | −6.48528 | −0.310945 | ||||||||
\(436\) | 13.0711 | + | 22.6398i | 0.625991 | + | 1.08425i | ||||
\(437\) | 25.3492 | − | 43.9062i | 1.21262 | − | 2.10032i | ||||
\(438\) | 0.414214 | − | 0.717439i | 0.0197919 | − | 0.0342806i | ||||
\(439\) | −15.4497 | − | 26.7597i | −0.737376 | − | 1.27717i | −0.953673 | − | 0.300845i | \(-0.902731\pi\) |
0.216297 | − | 0.976328i | \(-0.430602\pi\) | |||||||
\(440\) | 8.82843 | 0.420879 | ||||||||
\(441\) | −1.74264 | + | 6.77962i | −0.0829829 | + | 0.322839i | ||||
\(442\) | −8.82843 | −0.419925 | ||||||||
\(443\) | −16.8137 | − | 29.1222i | −0.798843 | − | 1.38364i | −0.920370 | − | 0.391049i | \(-0.872112\pi\) |
0.121526 | − | 0.992588i | \(-0.461221\pi\) | |||||||
\(444\) | 18.1569 | − | 31.4486i | 0.861686 | − | 1.49248i | ||||
\(445\) | −14.1421 | + | 24.4949i | −0.670402 | + | 1.16117i | ||||
\(446\) | −27.7279 | − | 48.0262i | −1.31296 | − | 2.27411i | ||||
\(447\) | −22.2132 | −1.05065 | ||||||||
\(448\) | −9.82843 | + | 24.0746i | −0.464350 | + | 1.13742i | ||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | −1.20711 | − | 2.09077i | −0.0569036 | − | 0.0985599i | ||||
\(451\) | 0.585786 | − | 1.01461i | 0.0275836 | − | 0.0477762i | ||||
\(452\) | 14.6569 | − | 25.3864i | 0.689400 | − | 1.19408i | ||||
\(453\) | 9.44975 | + | 16.3674i | 0.443988 | + | 0.769010i | ||||
\(454\) | −36.1421 | −1.69623 | ||||||||
\(455\) | −4.34315 | + | 0.594346i | −0.203610 | + | 0.0278634i | ||||
\(456\) | −31.9706 | −1.49716 | ||||||||
\(457\) | −9.41421 | − | 16.3059i | −0.440378 | − | 0.762758i | 0.557339 | − | 0.830285i | \(-0.311822\pi\) |
−0.997717 | + | 0.0675273i | \(0.978489\pi\) | |||||||
\(458\) | −18.8995 | + | 32.7349i | −0.883115 | + | 1.52960i | ||||
\(459\) | 2.20711 | − | 3.82282i | 0.103019 | − | 0.178434i | ||||
\(460\) | −26.7990 | − | 46.4172i | −1.24951 | − | 2.16421i | ||||
\(461\) | 6.75736 | 0.314722 | 0.157361 | − | 0.987541i | \(-0.449701\pi\) | ||||
0.157361 | + | 0.987541i | \(0.449701\pi\) | |||||||
\(462\) | −3.91421 | − | 5.04757i | −0.182106 | − | 0.234834i | ||||
\(463\) | 18.6274 | 0.865689 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(464\) | −4.86396 | − | 8.42463i | −0.225804 | − | 0.391104i | ||||
\(465\) | 5.65685 | − | 9.79796i | 0.262330 | − | 0.454369i | ||||
\(466\) | 12.5711 | − | 21.7737i | 0.582343 | − | 1.00865i | ||||
\(467\) | 4.15685 | + | 7.19988i | 0.192356 | + | 0.333171i | 0.946031 | − | 0.324077i | \(-0.105054\pi\) |
−0.753674 | + | 0.657248i | \(0.771720\pi\) | |||||||
\(468\) | −3.17157 | −0.146606 | ||||||||
\(469\) | −5.14214 | − | 6.63103i | −0.237442 | − | 0.306193i | ||||
\(470\) | 47.4558 | 2.18897 | ||||||||
\(471\) | −3.50000 | − | 6.06218i | −0.161271 | − | 0.279330i | ||||
\(472\) | −19.1066 | + | 33.0936i | −0.879453 | + | 1.52326i | ||||
\(473\) | 1.37868 | − | 2.38794i | 0.0633918 | − | 0.109798i | ||||
\(474\) | 16.0711 | + | 27.8359i | 0.738169 | + | 1.27855i | ||||
\(475\) | −7.24264 | −0.332315 | ||||||||
\(476\) | 44.2990 | − | 6.06218i | 2.03044 | − | 0.277859i | ||||
\(477\) | −7.17157 | −0.328364 | ||||||||
\(478\) | −7.82843 | − | 13.5592i | −0.358064 | − | 0.620185i | ||||
\(479\) | −7.00000 | + | 12.1244i | −0.319838 | + | 0.553976i | −0.980454 | − | 0.196748i | \(-0.936962\pi\) |
0.660616 | + | 0.750724i | \(0.270295\pi\) | |||||||
\(480\) | 1.58579 | − | 2.74666i | 0.0723809 | − | 0.125367i | ||||
\(481\) | −3.92893 | − | 6.80511i | −0.179144 | − | 0.310286i | ||||
\(482\) | −17.6569 | −0.804248 | ||||||||
\(483\) | −7.00000 | + | 17.1464i | −0.318511 | + | 0.780189i | ||||
\(484\) | 3.82843 | 0.174019 | ||||||||
\(485\) | −11.4853 | − | 19.8931i | −0.521520 | − | 0.903299i | ||||
\(486\) | 1.20711 | − | 2.09077i | 0.0547555 | − | 0.0948393i | ||||
\(487\) | 16.3137 | − | 28.2562i | 0.739245 | − | 1.28041i | −0.213591 | − | 0.976923i | \(-0.568516\pi\) |
0.952836 | − | 0.303486i | \(-0.0981506\pi\) | |||||||
\(488\) | −8.82843 | − | 15.2913i | −0.399644 | − | 0.692204i | ||||
\(489\) | −20.9706 | −0.948322 | ||||||||
\(490\) | 32.5563 | − | 9.08052i | 1.47075 | − | 0.410216i | ||||
\(491\) | −1.51472 | −0.0683583 | −0.0341791 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341791 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(492\) | 2.24264 | + | 3.88437i | 0.101106 | + | 0.175121i | ||||
\(493\) | 7.15685 | − | 12.3960i | 0.322329 | − | 0.558289i | ||||
\(494\) | −7.24264 | + | 12.5446i | −0.325862 | + | 0.564409i | ||||
\(495\) | 1.00000 | + | 1.73205i | 0.0449467 | + | 0.0778499i | ||||
\(496\) | 16.9706 | 0.762001 | ||||||||
\(497\) | −4.17157 | + | 10.2182i | −0.187121 | + | 0.458350i | ||||
\(498\) | 6.82843 | 0.305989 | ||||||||
\(499\) | 15.8995 | + | 27.5387i | 0.711759 | + | 1.23280i | 0.964196 | + | 0.265190i | \(0.0854346\pi\) |
−0.252437 | + | 0.967613i | \(0.581232\pi\) | |||||||
\(500\) | −22.9706 | + | 39.7862i | −1.02727 | + | 1.77929i | ||||
\(501\) | −2.58579 | + | 4.47871i | −0.115524 | + | 0.200094i | ||||
\(502\) | −3.03553 | − | 5.25770i | −0.135483 | − | 0.234663i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 11.5711 | − | 1.58346i | 0.515416 | − | 0.0705331i | ||||
\(505\) | −9.79899 | −0.436049 | ||||||||
\(506\) | −8.44975 | − | 14.6354i | −0.375637 | − | 0.650623i | ||||
\(507\) | 6.15685 | − | 10.6640i | 0.273435 | − | 0.473604i | ||||
\(508\) | 30.7635 | − | 53.2839i | 1.36491 | − | 2.36409i | ||||
\(509\) | 6.00000 | + | 10.3923i | 0.265945 | + | 0.460631i | 0.967811 | − | 0.251679i | \(-0.0809826\pi\) |
−0.701866 | + | 0.712309i | \(0.747649\pi\) | |||||||
\(510\) | −21.3137 | −0.943787 | ||||||||
\(511\) | 0.556349 | + | 0.717439i | 0.0246114 | + | 0.0317376i | ||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −3.62132 | − | 6.27231i | −0.159885 | − | 0.276929i | ||||
\(514\) | 25.8995 | − | 44.8592i | 1.14238 | − | 1.97866i | ||||
\(515\) | 12.4853 | − | 21.6251i | 0.550167 | − | 0.952918i | ||||
\(516\) | 5.27817 | + | 9.14207i | 0.232359 | + | 0.402457i | ||||
\(517\) | 9.82843 | 0.432254 | ||||||||
\(518\) | 37.1274 | + | 47.8776i | 1.63129 | + | 2.10362i | ||||
\(519\) | −14.8284 | −0.650896 | ||||||||
\(520\) | 3.65685 | + | 6.33386i | 0.160364 | + | 0.277758i | ||||
\(521\) | −15.5858 | + | 26.9954i | −0.682826 | + | 1.18269i | 0.291289 | + | 0.956635i | \(0.405916\pi\) |
−0.974115 | + | 0.226054i | \(0.927418\pi\) | |||||||
\(522\) | 3.91421 | − | 6.77962i | 0.171320 | − | 0.296736i | ||||
\(523\) | 11.1421 | + | 19.2987i | 0.487212 | + | 0.843875i | 0.999892 | − | 0.0147044i | \(-0.00468072\pi\) |
−0.512680 | + | 0.858580i | \(0.671347\pi\) | |||||||
\(524\) | −19.7990 | −0.864923 | ||||||||
\(525\) | 2.62132 | − | 0.358719i | 0.114404 | − | 0.0156558i | ||||
\(526\) | −43.4558 | −1.89476 | ||||||||
\(527\) | 12.4853 | + | 21.6251i | 0.543867 | + | 0.942006i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 17.3137 | + | 29.9882i | 0.752059 | + | 1.30261i | ||||
\(531\) | −8.65685 | −0.375675 | ||||||||
\(532\) | 27.7279 | − | 67.9193i | 1.20216 | − | 2.94467i | ||||
\(533\) | 0.970563 | 0.0420397 | ||||||||
\(534\) | −17.0711 | − | 29.5680i | −0.738737 | − | 1.27953i | ||||
\(535\) | 9.65685 | − | 16.7262i | 0.417502 | − | 0.723135i | ||||
\(536\) | −7.00000 | + | 12.1244i | −0.302354 | + | 0.523692i | ||||
\(537\) | −8.91421 | − | 15.4399i | −0.384677 | − | 0.666280i | ||||
\(538\) | 67.1127 | 2.89343 | ||||||||
\(539\) | 6.74264 | − | 1.88064i | 0.290426 | − | 0.0810048i | ||||
\(540\) | −7.65685 | −0.329499 | ||||||||
\(541\) | −9.82843 | − | 17.0233i | −0.422557 | − | 0.731890i | 0.573632 | − | 0.819113i | \(-0.305534\pi\) |
−0.996189 | + | 0.0872230i | \(0.972201\pi\) | |||||||
\(542\) | −27.7279 | + | 48.0262i | −1.19102 | + | 2.06290i | ||||
\(543\) | 5.82843 | − | 10.0951i | 0.250122 | − | 0.433224i | ||||
\(544\) | 3.50000 | + | 6.06218i | 0.150061 | + | 0.259914i | ||||
\(545\) | 13.6569 | 0.584995 | ||||||||
\(546\) | 2.00000 | − | 4.89898i | 0.0855921 | − | 0.209657i | ||||
\(547\) | −24.2132 | −1.03528 | −0.517641 | − | 0.855598i | \(-0.673190\pi\) | ||||
−0.517641 | + | 0.855598i | \(0.673190\pi\) | |||||||
\(548\) | −0.928932 | − | 1.60896i | −0.0396820 | − | 0.0687313i | ||||
\(549\) | 2.00000 | − | 3.46410i | 0.0853579 | − | 0.147844i | ||||
\(550\) | −1.20711 | + | 2.09077i | −0.0514712 | + | 0.0891507i | ||||
\(551\) | −11.7426 | − | 20.3389i | −0.500253 | − | 0.866464i | ||||
\(552\) | 30.8995 | 1.31517 | ||||||||
\(553\) | −34.8995 | + | 4.77589i | −1.48408 | + | 0.203091i | ||||
\(554\) | 61.9411 | 2.63163 | ||||||||
\(555\) | −9.48528 | − | 16.4290i | −0.402628 | − | 0.697372i | ||||
\(556\) | −16.1066 | + | 27.8975i | −0.683072 | + | 1.18312i | ||||
\(557\) | 4.27817 | − | 7.41002i | 0.181272 | − | 0.313972i | −0.761042 | − | 0.648703i | \(-0.775312\pi\) |
0.942314 | + | 0.334730i | \(0.108645\pi\) | |||||||
\(558\) | 6.82843 | + | 11.8272i | 0.289070 | + | 0.500685i | ||||
\(559\) | 2.28427 | 0.0966144 | ||||||||
\(560\) | −9.72792 | − | 12.5446i | −0.411080 | − | 0.530107i | ||||
\(561\) | −4.41421 | −0.186368 | ||||||||
\(562\) | 17.3995 | + | 30.1368i | 0.733953 | + | 1.27124i | ||||
\(563\) | −12.4142 | + | 21.5020i | −0.523197 | + | 0.906203i | 0.476439 | + | 0.879208i | \(0.341927\pi\) |
−0.999636 | + | 0.0269957i | \(0.991406\pi\) | |||||||
\(564\) | −18.8137 | + | 32.5863i | −0.792200 | + | 1.37213i | ||||
\(565\) | −7.65685 | − | 13.2621i | −0.322126 | − | 0.557939i | ||||
\(566\) | −49.1127 | −2.06436 | ||||||||
\(567\) | 1.62132 | + | 2.09077i | 0.0680891 | + | 0.0878041i | ||||
\(568\) | 18.4142 | 0.772643 | ||||||||
\(569\) | −0.621320 | − | 1.07616i | −0.0260471 | − | 0.0451149i | 0.852708 | − | 0.522388i | \(-0.174959\pi\) |
−0.878755 | + | 0.477273i | \(0.841625\pi\) | |||||||
\(570\) | −17.4853 | + | 30.2854i | −0.732378 | + | 1.26852i | ||||
\(571\) | 1.96447 | − | 3.40256i | 0.0822103 | − | 0.142392i | −0.821989 | − | 0.569504i | \(-0.807135\pi\) |
0.904199 | + | 0.427111i | \(0.140469\pi\) | |||||||
\(572\) | 1.58579 | + | 2.74666i | 0.0663051 | + | 0.114844i | ||||
\(573\) | −21.6569 | −0.904728 | ||||||||
\(574\) | −7.41421 | + | 1.01461i | −0.309463 | + | 0.0423491i | ||||
\(575\) | 7.00000 | 0.291920 | ||||||||
\(576\) | 4.91421 | + | 8.51167i | 0.204759 | + | 0.354653i | ||||
\(577\) | −3.82843 | + | 6.63103i | −0.159380 | + | 0.276053i | −0.934645 | − | 0.355582i | \(-0.884283\pi\) |
0.775266 | + | 0.631635i | \(0.217616\pi\) | |||||||
\(578\) | 3.00000 | − | 5.19615i | 0.124784 | − | 0.216131i | ||||
\(579\) | 6.07107 | + | 10.5154i | 0.252305 | + | 0.437005i | ||||
\(580\) | −24.8284 | −1.03094 | ||||||||
\(581\) | −2.82843 | + | 6.92820i | −0.117343 | + | 0.287430i | ||||
\(582\) | 27.7279 | 1.14936 | ||||||||
\(583\) | 3.58579 | + | 6.21076i | 0.148508 | + | 0.257224i | ||||
\(584\) | 0.757359 | − | 1.31178i | 0.0313398 | − | 0.0542820i | ||||
\(585\) | −0.828427 | + | 1.43488i | −0.0342512 | + | 0.0593249i | ||||
\(586\) | 6.91421 | + | 11.9758i | 0.285624 | + | 0.494714i | ||||
\(587\) | 8.68629 | 0.358522 | 0.179261 | − | 0.983802i | \(-0.442629\pi\) | ||||
0.179261 | + | 0.983802i | \(0.442629\pi\) | |||||||
\(588\) | −6.67157 | + | 25.9553i | −0.275131 | + | 1.07038i | ||||
\(589\) | 40.9706 | 1.68816 | ||||||||
\(590\) | 20.8995 | + | 36.1990i | 0.860419 | + | 1.49029i | ||||
\(591\) | 8.20711 | − | 14.2151i | 0.337595 | − | 0.584732i | ||||
\(592\) | 14.2279 | − | 24.6435i | 0.584764 | − | 1.01284i | ||||
\(593\) | 11.1360 | + | 19.2882i | 0.457302 | + | 0.792071i | 0.998817 | − | 0.0486202i | \(-0.0154824\pi\) |
−0.541515 | + | 0.840691i | \(0.682149\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | 8.82843 | − | 21.6251i | 0.361930 | − | 0.886544i | ||||
\(596\) | −85.0416 | −3.48344 | ||||||||
\(597\) | 9.89949 | + | 17.1464i | 0.405159 | + | 0.701757i | ||||
\(598\) | 7.00000 | − | 12.1244i | 0.286251 | − | 0.495802i | ||||
\(599\) | 0.686292 | − | 1.18869i | 0.0280411 | − | 0.0485686i | −0.851664 | − | 0.524088i | \(-0.824406\pi\) |
0.879705 | + | 0.475519i | \(0.157740\pi\) | |||||||
\(600\) | −2.20711 | − | 3.82282i | −0.0901048 | − | 0.156066i | ||||
\(601\) | −14.4853 | −0.590867 | −0.295433 | − | 0.955363i | \(-0.595464\pi\) | ||||
−0.295433 | + | 0.955363i | \(0.595464\pi\) | |||||||
\(602\) | −17.4497 | + | 2.38794i | −0.711199 | + | 0.0973253i | ||||
\(603\) | −3.17157 | −0.129156 | ||||||||
\(604\) | 36.1777 | + | 62.6616i | 1.47205 | + | 2.54966i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 5.91421 | − | 10.2437i | 0.240249 | − | 0.416123i | ||||
\(607\) | 9.34315 | + | 16.1828i | 0.379227 | + | 0.656840i | 0.990950 | − | 0.134232i | \(-0.0428568\pi\) |
−0.611723 | + | 0.791072i | \(0.709523\pi\) | |||||||
\(608\) | 11.4853 | 0.465790 | ||||||||
\(609\) | 5.25736 | + | 6.77962i | 0.213039 | + | 0.274724i | ||||
\(610\) | −19.3137 | −0.781989 | ||||||||
\(611\) | 4.07107 | + | 7.05130i | 0.164698 | + | 0.285265i | ||||
\(612\) | 8.44975 | − | 14.6354i | 0.341561 | − | 0.591601i | ||||
\(613\) | −12.5858 | + | 21.7992i | −0.508335 | + | 0.880462i | 0.491618 | + | 0.870811i | \(0.336406\pi\) |
−0.999953 | + | 0.00965147i | \(0.996928\pi\) | |||||||
\(614\) | −20.8995 | − | 36.1990i | −0.843435 | − | 1.46087i | ||||
\(615\) | 2.34315 | 0.0944848 | ||||||||
\(616\) | −7.15685 | − | 9.22911i | −0.288358 | − | 0.371851i | ||||
\(617\) | 13.1716 | 0.530268 | 0.265134 | − | 0.964212i | \(-0.414584\pi\) | ||||
0.265134 | + | 0.964212i | \(0.414584\pi\) | |||||||
\(618\) | 15.0711 | + | 26.1039i | 0.606247 | + | 1.05005i | ||||
\(619\) | −17.3137 | + | 29.9882i | −0.695897 | + | 1.20533i | 0.273981 | + | 0.961735i | \(0.411660\pi\) |
−0.969877 | + | 0.243593i | \(0.921674\pi\) | |||||||
\(620\) | 21.6569 | − | 37.5108i | 0.869760 | − | 1.50647i | ||||
\(621\) | 3.50000 | + | 6.06218i | 0.140450 | + | 0.243267i | ||||
\(622\) | −71.5269 | −2.86797 | ||||||||
\(623\) | 37.0711 | − | 5.07306i | 1.48522 | − | 0.203248i | ||||
\(624\) | −2.48528 | −0.0994909 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 5.79289 | − | 10.0336i | 0.231531 | − | 0.401023i | ||||
\(627\) | −3.62132 | + | 6.27231i | −0.144622 | + | 0.250492i | ||||
\(628\) | −13.3995 | − | 23.2086i | −0.534698 | − | 0.926124i | ||||
\(629\) | 41.8701 | 1.66947 | ||||||||
\(630\) | 4.82843 | − | 11.8272i | 0.192369 | − | 0.471206i | ||||
\(631\) | 26.2843 | 1.04636 | 0.523180 | − | 0.852222i | \(-0.324745\pi\) | ||||
0.523180 | + | 0.852222i | \(0.324745\pi\) | |||||||
\(632\) | 29.3848 | + | 50.8959i | 1.16886 | + | 2.02453i | ||||
\(633\) | −7.48528 | + | 12.9649i | −0.297513 | + | 0.515308i | ||||
\(634\) | −30.5563 | + | 52.9251i | −1.21355 | + | 2.10193i | ||||
\(635\) | −16.0711 | − | 27.8359i | −0.637761 | − | 1.10463i | ||||
\(636\) | −27.4558 | −1.08870 | ||||||||
\(637\) | 4.14214 | + | 4.05845i | 0.164117 | + | 0.160802i | ||||
\(638\) | −7.82843 | −0.309930 | ||||||||
\(639\) | 2.08579 | + | 3.61269i | 0.0825124 | + | 0.142916i | ||||
\(640\) | 20.5563 | − | 35.6046i | 0.812561 | − | 1.40740i | ||||
\(641\) | 6.24264 | − | 10.8126i | 0.246569 | − | 0.427071i | −0.716002 | − | 0.698098i | \(-0.754030\pi\) |
0.962572 | + | 0.271027i | \(0.0873633\pi\) | |||||||
\(642\) | 11.6569 | + | 20.1903i | 0.460059 | + | 0.796846i | ||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | −26.7990 | + | 65.6439i | −1.05603 | + | 2.58673i | ||||
\(645\) | 5.51472 | 0.217142 | ||||||||
\(646\) | −38.5919 | − | 66.8431i | −1.51838 | − | 2.62991i | ||||
\(647\) | 9.65685 | − | 16.7262i | 0.379650 | − | 0.657573i | −0.611361 | − | 0.791352i | \(-0.709378\pi\) |
0.991011 | + | 0.133778i | \(0.0427110\pi\) | |||||||
\(648\) | 2.20711 | − | 3.82282i | 0.0867033 | − | 0.150175i | ||||
\(649\) | 4.32843 | + | 7.49706i | 0.169906 | + | 0.294285i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | −14.8284 | + | 2.02922i | −0.581172 | + | 0.0795315i | ||||
\(652\) | −80.2843 | −3.14417 | ||||||||
\(653\) | −15.5563 | − | 26.9444i | −0.608767 | − | 1.05442i | −0.991444 | − | 0.130533i | \(-0.958331\pi\) |
0.382677 | − | 0.923882i | \(-0.375002\pi\) | |||||||
\(654\) | −8.24264 | + | 14.2767i | −0.322313 | + | 0.558262i | ||||
\(655\) | −5.17157 | + | 8.95743i | −0.202070 | + | 0.349996i | ||||
\(656\) | 1.75736 | + | 3.04384i | 0.0686134 | + | 0.118842i | ||||
\(657\) | 0.343146 | 0.0133874 | ||||||||
\(658\) | −38.4706 | − | 49.6096i | −1.49974 | − | 1.93398i | ||||
\(659\) | 34.4853 | 1.34336 | 0.671678 | − | 0.740843i | \(-0.265574\pi\) | ||||
0.671678 | + | 0.740843i | \(0.265574\pi\) | |||||||
\(660\) | 3.82843 | + | 6.63103i | 0.149021 | + | 0.258113i | ||||
\(661\) | −5.98528 | + | 10.3668i | −0.232800 | + | 0.403222i | −0.958631 | − | 0.284651i | \(-0.908122\pi\) |
0.725831 | + | 0.687873i | \(0.241456\pi\) | |||||||
\(662\) | 27.1421 | − | 47.0116i | 1.05491 | − | 1.82716i | ||||
\(663\) | −1.82843 | − | 3.16693i | −0.0710102 | − | 0.122993i | ||||
\(664\) | 12.4853 | 0.484523 | ||||||||
\(665\) | −23.4853 | − | 30.2854i | −0.910720 | − | 1.17442i | ||||
\(666\) | 22.8995 | 0.887337 | ||||||||
\(667\) | 11.3492 | + | 19.6575i | 0.439444 | + | 0.761140i | ||||
\(668\) | −9.89949 | + | 17.1464i | −0.383023 | + | 0.663415i | ||||
\(669\) | 11.4853 | − | 19.8931i | 0.444047 | − | 0.769111i | ||||
\(670\) | 7.65685 | + | 13.2621i | 0.295810 | + | 0.512358i | ||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | −4.15685 | + | 0.568852i | −0.160354 | + | 0.0219440i | ||||
\(673\) | 27.1716 | 1.04739 | 0.523694 | − | 0.851907i | \(-0.324554\pi\) | ||||
0.523694 | + | 0.851907i | \(0.324554\pi\) | |||||||
\(674\) | 4.65685 | + | 8.06591i | 0.179375 | + | 0.310687i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 23.5711 | − | 40.8263i | 0.906580 | − | 1.57024i | ||||
\(677\) | 16.0061 | + | 27.7234i | 0.615164 | + | 1.06550i | 0.990356 | + | 0.138548i | \(0.0442437\pi\) |
−0.375191 | + | 0.926947i | \(0.622423\pi\) | |||||||
\(678\) | 18.4853 | 0.709923 | ||||||||
\(679\) | −11.4853 | + | 28.1331i | −0.440765 | + | 1.07965i | ||||
\(680\) | −38.9706 | −1.49445 | ||||||||
\(681\) | −7.48528 | − | 12.9649i | −0.286837 | − | 0.496816i | ||||
\(682\) | 6.82843 | − | 11.8272i | 0.261474 | − | 0.452886i | ||||
\(683\) | −1.60051 | + | 2.77216i | −0.0612416 | + | 0.106074i | −0.895021 | − | 0.446025i | \(-0.852839\pi\) |
0.833779 | + | 0.552098i | \(0.186173\pi\) | |||||||
\(684\) | −13.8640 | − | 24.0131i | −0.530102 | − | 0.918163i | ||||
\(685\) | −0.970563 | −0.0370833 | ||||||||
\(686\) | −35.8848 | − | 26.6727i | −1.37009 | − | 1.01837i | ||||
\(687\) | −15.6569 | −0.597346 | ||||||||
\(688\) | 4.13604 | + | 7.16383i | 0.157685 | + | 0.273118i | ||||
\(689\) | −2.97056 | + | 5.14517i | −0.113169 | + | 0.196015i | ||||
\(690\) | 16.8995 | − | 29.2708i | 0.643353 | − | 1.11432i | ||||
\(691\) | 5.72792 | + | 9.92105i | 0.217900 | + | 0.377415i | 0.954166 | − | 0.299278i | \(-0.0967459\pi\) |
−0.736265 | + | 0.676693i | \(0.763413\pi\) | |||||||
\(692\) | −56.7696 | −2.15805 | ||||||||
\(693\) | 1.00000 | − | 2.44949i | 0.0379869 | − | 0.0930484i | ||||
\(694\) | −36.1421 | −1.37194 | ||||||||
\(695\) | 8.41421 | + | 14.5738i | 0.319169 | + | 0.552817i | ||||
\(696\) | 7.15685 | − | 12.3960i | 0.271280 | − | 0.469871i | ||||
\(697\) | −2.58579 | + | 4.47871i | −0.0979436 | + | 0.169643i | ||||
\(698\) | 13.2426 | + | 22.9369i | 0.501241 | + | 0.868175i | ||||
\(699\) | 10.4142 | 0.393902 | ||||||||
\(700\) | 10.0355 | − | 1.37333i | 0.379308 | − | 0.0519070i | ||||
\(701\) | −2.89949 | −0.109512 | −0.0547562 | − | 0.998500i | \(-0.517438\pi\) | ||||
−0.0547562 | + | 0.998500i | \(0.517438\pi\) | |||||||
\(702\) | −1.00000 | − | 1.73205i | −0.0377426 | − | 0.0653720i | ||||
\(703\) | 34.3492 | − | 59.4946i | 1.29551 | − | 2.24388i | ||||
\(704\) | 4.91421 | − | 8.51167i | 0.185211 | − | 0.320796i | ||||
\(705\) | 9.82843 | + | 17.0233i | 0.370160 | + | 0.641136i | ||||
\(706\) | −32.1421 | −1.20969 | ||||||||
\(707\) | 7.94365 | + | 10.2437i | 0.298752 | + | 0.385255i | ||||
\(708\) | −33.1421 | −1.24556 | ||||||||
\(709\) | −12.8848 | − | 22.3171i | −0.483898 | − | 0.838136i | 0.515931 | − | 0.856630i | \(-0.327446\pi\) |
−0.999829 | + | 0.0184943i | \(0.994113\pi\) | |||||||
\(710\) | 10.0711 | − | 17.4436i | 0.377960 | − | 0.654647i | ||||
\(711\) | −6.65685 | + | 11.5300i | −0.249652 | + | 0.432409i | ||||
\(712\) | −31.2132 | − | 54.0629i | −1.16976 | − | 2.02609i | ||||
\(713\) | −39.5980 | −1.48296 | ||||||||
\(714\) | 17.2782 | + | 22.2810i | 0.646619 | + | 0.833847i | ||||
\(715\) | 1.65685 | 0.0619628 | ||||||||
\(716\) | −34.1274 | − | 59.1104i | −1.27540 | − | 2.20906i | ||||
\(717\) | 3.24264 | − | 5.61642i | 0.121099 | − | 0.209749i | ||||
\(718\) | −9.65685 | + | 16.7262i | −0.360391 | + | 0.624215i | ||||
\(719\) | −5.60051 | − | 9.70036i | −0.208864 | − | 0.361762i | 0.742493 | − | 0.669854i | \(-0.233643\pi\) |
−0.951357 | + | 0.308091i | \(0.900310\pi\) | |||||||
\(720\) | −6.00000 | −0.223607 | ||||||||
\(721\) | −32.7279 | + | 4.47871i | −1.21885 | + | 0.166796i | ||||
\(722\) | −80.7696 | −3.00593 | ||||||||
\(723\) | −3.65685 | − | 6.33386i | −0.136000 | − | 0.235559i | ||||
\(724\) | 22.3137 | − | 38.6485i | 0.829282 | − | 1.43636i | ||||
\(725\) | 1.62132 | − | 2.80821i | 0.0602143 | − | 0.104294i | ||||
\(726\) | 1.20711 | + | 2.09077i | 0.0447999 | + | 0.0775958i | ||||
\(727\) | 46.0833 | 1.70913 | 0.854567 | − | 0.519342i | \(-0.173823\pi\) | ||||
0.854567 | + | 0.519342i | \(0.173823\pi\) | |||||||
\(728\) | 3.65685 | − | 8.95743i | 0.135532 | − | 0.331984i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.828427 | − | 1.43488i | −0.0306615 | − | 0.0531072i | ||||
\(731\) | −6.08579 | + | 10.5409i | −0.225091 | + | 0.389869i | ||||
\(732\) | 7.65685 | − | 13.2621i | 0.283005 | − | 0.490180i | ||||
\(733\) | −4.82843 | − | 8.36308i | −0.178342 | − | 0.308897i | 0.762971 | − | 0.646433i | \(-0.223740\pi\) |
−0.941313 | + | 0.337536i | \(0.890407\pi\) | |||||||
\(734\) | 10.0000 | 0.369107 | ||||||||
\(735\) | 10.0000 | + | 9.79796i | 0.368856 | + | 0.361403i | ||||
\(736\) | −11.1005 | −0.409170 | ||||||||
\(737\) | 1.58579 | + | 2.74666i | 0.0584132 | + | 0.101175i | ||||
\(738\) | −1.41421 | + | 2.44949i | −0.0520579 | + | 0.0901670i | ||||
\(739\) | 19.8284 | − | 34.3438i | 0.729400 | − | 1.26336i | −0.227736 | − | 0.973723i | \(-0.573132\pi\) |
0.957137 | − | 0.289636i | \(-0.0935342\pi\) | |||||||
\(740\) | −36.3137 | − | 62.8972i | −1.33492 | − | 2.31215i | ||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 17.3137 | − | 42.4098i | 0.635606 | − | 1.55691i | ||||
\(743\) | 33.7990 | 1.23996 | 0.619982 | − | 0.784616i | \(-0.287140\pi\) | ||||
0.619982 | + | 0.784616i | \(0.287140\pi\) | |||||||
\(744\) | 12.4853 | + | 21.6251i | 0.457733 | + | 0.792816i | ||||
\(745\) | −22.2132 | + | 38.4744i | −0.813829 | + | 1.40959i | ||||
\(746\) | −2.00000 | + | 3.46410i | −0.0732252 | + | 0.126830i | ||||
\(747\) | 1.41421 | + | 2.44949i | 0.0517434 | + | 0.0896221i | ||||
\(748\) | −16.8995 | −0.617907 | ||||||||
\(749\) | −25.3137 | + | 3.46410i | −0.924943 | + | 0.126576i | ||||
\(750\) | −28.9706 | −1.05786 | ||||||||
\(751\) | 14.6569 | + | 25.3864i | 0.534836 | + | 0.926363i | 0.999171 | + | 0.0407039i | \(0.0129600\pi\) |
−0.464335 | + | 0.885660i | \(0.653707\pi\) | |||||||
\(752\) | −14.7426 | + | 25.5350i | −0.537609 | + | 0.931166i | ||||
\(753\) | 1.25736 | − | 2.17781i | 0.0458207 | − | 0.0793638i | ||||
\(754\) | −3.24264 | − | 5.61642i | −0.118090 | − | 0.204538i | ||||
\(755\) | 37.7990 | 1.37565 | ||||||||
\(756\) | 6.20711 | + | 8.00436i | 0.225750 | + | 0.291116i | ||||
\(757\) | −7.68629 | −0.279363 | −0.139682 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139682 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(758\) | 22.7279 | + | 39.3659i | 0.825515 | + | 1.42983i | ||||
\(759\) | 3.50000 | − | 6.06218i | 0.127042 | − | 0.220043i | ||||
\(760\) | −31.9706 | + | 55.3746i | −1.15969 | + | 2.00865i | ||||
\(761\) | 0.100505 | + | 0.174080i | 0.00364331 | + | 0.00631039i | 0.867841 | − | 0.496841i | \(-0.165507\pi\) |
−0.864198 | + | 0.503152i | \(0.832174\pi\) | |||||||
\(762\) | 38.7990 | 1.40554 | ||||||||
\(763\) | −11.0711 | − | 14.2767i | −0.400800 | − | 0.516850i | ||||
\(764\) | −82.9117 | −2.99964 | ||||||||
\(765\) | −4.41421 | − | 7.64564i | −0.159596 | − | 0.276429i | ||||
\(766\) | 2.79289 | − | 4.83743i | 0.100911 | − | 0.174784i | ||||
\(767\) | −3.58579 | + | 6.21076i | −0.129475 | + | 0.224258i | ||||
\(768\) | 14.9853 | + | 25.9553i | 0.540735 | + | 0.936580i | ||||
\(769\) | 33.7990 | 1.21882 | 0.609411 | − | 0.792854i | \(-0.291406\pi\) | ||||
0.609411 | + | 0.792854i | \(0.291406\pi\) | |||||||
\(770\) | −12.6569 | + | 1.73205i | −0.456121 | + | 0.0624188i | ||||
\(771\) | 21.4558 | 0.772713 | ||||||||
\(772\) | 23.2426 | + | 40.2574i | 0.836521 | + | 1.44890i | ||||
\(773\) | 25.8284 | − | 44.7361i | 0.928984 | − | 1.60905i | 0.143959 | − | 0.989584i | \(-0.454017\pi\) |
0.785025 | − | 0.619464i | \(-0.212650\pi\) | |||||||
\(774\) | −3.32843 | + | 5.76500i | −0.119638 | + | 0.207219i | ||||
\(775\) | 2.82843 | + | 4.89898i | 0.101600 | + | 0.175977i | ||||
\(776\) | 50.6985 | 1.81997 | ||||||||
\(777\) | −9.48528 | + | 23.2341i | −0.340283 | + | 0.833519i | ||||
\(778\) | 28.4853 | 1.02125 | ||||||||
\(779\) | 4.24264 | + | 7.34847i | 0.152008 | + | 0.263286i | ||||
\(780\) | −3.17157 | + | 5.49333i | −0.113561 | + | 0.196693i | ||||
\(781\) | 2.08579 | − | 3.61269i | 0.0746353 | − | 0.129272i | ||||
\(782\) | 37.2990 | + | 64.6037i | 1.33381 | + | 2.31023i | ||||
\(783\) | 3.24264 | 0.115883 | ||||||||
\(784\) | −5.22792 | + | 20.3389i | −0.186712 | + | 0.726388i | ||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | −6.24264 | − | 10.8126i | −0.222668 | − | 0.385672i | ||||
\(787\) | −14.7635 | + | 25.5711i | −0.526260 | + | 0.911510i | 0.473272 | + | 0.880917i | \(0.343073\pi\) |
−0.999532 | + | 0.0305931i | \(0.990260\pi\) | |||||||
\(788\) | 31.4203 | − | 54.4216i | 1.11930 | − | 1.93869i | ||||
\(789\) | −9.00000 | − | 15.5885i | −0.320408 | − | 0.554964i | ||||
\(790\) | 64.2843 | 2.28713 | ||||||||
\(791\) | −7.65685 | + | 18.7554i | −0.272246 | + | 0.666865i | ||||
\(792\) | −4.41421 | −0.156852 | ||||||||
\(793\) | −1.65685 | − | 2.86976i | −0.0588366 | − | 0.101908i | ||||
\(794\) | 21.1066 | − | 36.5577i | 0.749045 | − | 1.29738i | ||||
\(795\) | −7.17157 | + | 12.4215i | −0.254349 | + | 0.440546i | ||||
\(796\) | 37.8995 | + | 65.6439i | 1.34331 | + | 2.32668i | ||||
\(797\) | 11.1716 | 0.395717 | 0.197859 | − | 0.980231i | \(-0.436601\pi\) | ||||
0.197859 | + | 0.980231i | \(0.436601\pi\) | |||||||
\(798\) | 45.8345 | − | 6.27231i | 1.62252 | − | 0.222037i | ||||
\(799\) | −43.3848 | −1.53484 | ||||||||
\(800\) | 0.792893 | + | 1.37333i | 0.0280330 | + | 0.0485546i | ||||
\(801\) | 7.07107 | − | 12.2474i | 0.249844 | − | 0.432742i | ||||
\(802\) | 9.07107 | − | 15.7116i | 0.320311 | − | 0.554794i | ||||
\(803\) | −0.171573 | − | 0.297173i | −0.00605468 | − | 0.0104870i | ||||
\(804\) | −12.1421 | −0.428220 | ||||||||
\(805\) | 22.6985 | + | 29.2708i | 0.800016 | + | 1.03166i | ||||
\(806\) | 11.3137 | 0.398508 | ||||||||
\(807\) | 13.8995 | + | 24.0746i | 0.489285 | + | 0.847467i | ||||
\(808\) | 10.8137 | − | 18.7299i | 0.380425 | − | 0.658915i | ||||
\(809\) | −5.41421 | + | 9.37769i | −0.190354 | + | 0.329702i | −0.945367 | − | 0.326007i | \(-0.894297\pi\) |
0.755014 | + | 0.655709i | \(0.227630\pi\) | |||||||
\(810\) | −2.41421 | − | 4.18154i | −0.0848268 | − | 0.146924i | ||||
\(811\) | 14.9706 | 0.525688 | 0.262844 | − | 0.964838i | \(-0.415340\pi\) | ||||
0.262844 | + | 0.964838i | \(0.415340\pi\) | |||||||
\(812\) | 20.1274 | + | 25.9553i | 0.706334 | + | 0.910851i | ||||
\(813\) | −22.9706 | −0.805613 | ||||||||
\(814\) | −11.4497 | − | 19.8315i | −0.401313 | − | 0.695095i | ||||
\(815\) | −20.9706 | + | 36.3221i | −0.734567 | + | 1.27231i | ||||
\(816\) | 6.62132 | − | 11.4685i | 0.231793 | − | 0.401477i | ||||
\(817\) | 9.98528 | + | 17.2950i | 0.349341 | + | 0.605076i | ||||
\(818\) | 18.8284 | 0.658321 | ||||||||
\(819\) | 2.17157 | − | 0.297173i | 0.0758809 | − | 0.0103841i | ||||
\(820\) | 8.97056 | 0.313266 | ||||||||
\(821\) | −19.4142 | − | 33.6264i | −0.677561 | − | 1.17357i | −0.975713 | − | 0.219051i | \(-0.929704\pi\) |
0.298153 | − | 0.954518i | \(-0.403630\pi\) | |||||||
\(822\) | 0.585786 | − | 1.01461i | 0.0204316 | − | 0.0353887i | ||||
\(823\) | 16.5858 | − | 28.7274i | 0.578144 | − | 1.00138i | −0.417548 | − | 0.908655i | \(-0.637110\pi\) |
0.995692 | − | 0.0927202i | \(-0.0295562\pi\) | |||||||
\(824\) | 27.5563 | + | 47.7290i | 0.959971 | + | 1.66272i | ||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 20.8995 | − | 51.1931i | 0.727186 | − | 1.78124i | ||||
\(827\) | −37.3137 | −1.29752 | −0.648762 | − | 0.760991i | \(-0.724713\pi\) | ||||
−0.648762 | + | 0.760991i | \(0.724713\pi\) | |||||||
\(828\) | 13.3995 | + | 23.2086i | 0.465665 | + | 0.806555i | ||||
\(829\) | 3.08579 | − | 5.34474i | 0.107174 | − | 0.185630i | −0.807450 | − | 0.589935i | \(-0.799153\pi\) |
0.914624 | + | 0.404305i | \(0.132487\pi\) | |||||||
\(830\) | 6.82843 | − | 11.8272i | 0.237018 | − | 0.410528i | ||||
\(831\) | 12.8284 | + | 22.2195i | 0.445013 | + | 0.770785i | ||||
\(832\) | 8.14214 | 0.282278 | ||||||||
\(833\) | −29.7635 | + | 8.30153i | −1.03124 | + | 0.287631i | ||||
\(834\) | −20.3137 | −0.703406 | ||||||||
\(835\) | 5.17157 | + | 8.95743i | 0.178970 | + | 0.309985i | ||||
\(836\) | −13.8640 | + | 24.0131i | −0.479495 | + | 0.830510i | ||||
\(837\) | −2.82843 | + | 4.89898i | −0.0977647 | + | 0.169334i | ||||
\(838\) | 17.8640 | + | 30.9413i | 0.617100 | + | 1.06885i | ||||
\(839\) | 8.97056 | 0.309698 | 0.154849 | − | 0.987938i | \(-0.450511\pi\) | ||||
0.154849 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(840\) | 8.82843 | − | 21.6251i | 0.304610 | − | 0.746138i | ||||
\(841\) | −18.4853 | −0.637423 | ||||||||
\(842\) | −8.44975 | − | 14.6354i | −0.291198 | − | 0.504369i | ||||
\(843\) | −7.20711 | + | 12.4831i | −0.248226 | + | 0.429940i | ||||
\(844\) | −28.6569 | + | 49.6351i | −0.986410 | + | 1.70851i | ||||
\(845\) | −12.3137 | − | 21.3280i | −0.423604 | − | 0.733704i | ||||
\(846\) | −23.7279 | −0.815783 | ||||||||
\(847\) | −2.62132 | + | 0.358719i | −0.0900696 | + | 0.0123257i | ||||
\(848\) | −21.5147 | −0.738818 | ||||||||
\(849\) | −10.1716 | − | 17.6177i | −0.349087 | − | 0.604637i | ||||
\(850\) | 5.32843 | − | 9.22911i | 0.182764 | − | 0.316556i | ||||
\(851\) | −33.1985 | + | 57.5015i | −1.13803 | + | 1.97112i | ||||
\(852\) | 7.98528 | + | 13.8309i | 0.273571 | + | 0.473839i | ||||
\(853\) | −12.4853 | −0.427488 | −0.213744 | − | 0.976890i | \(-0.568566\pi\) | ||||
−0.213744 | + | 0.976890i | \(0.568566\pi\) | |||||||
\(854\) | 15.6569 | + | 20.1903i | 0.535767 | + | 0.690897i | ||||
\(855\) | −14.4853 | −0.495386 | ||||||||
\(856\) | 21.3137 | + | 36.9164i | 0.728488 | + | 1.26178i | ||||
\(857\) | 22.1777 | − | 38.4129i | 0.757575 | − | 1.31216i | −0.186509 | − | 0.982453i | \(-0.559717\pi\) |
0.944084 | − | 0.329705i | \(-0.106949\pi\) | |||||||
\(858\) | −1.00000 | + | 1.73205i | −0.0341394 | + | 0.0591312i | ||||
\(859\) | 12.2426 | + | 21.2049i | 0.417714 | + | 0.723501i | 0.995709 | − | 0.0925389i | \(-0.0294982\pi\) |
−0.577996 | + | 0.816040i | \(0.696165\pi\) | |||||||
\(860\) | 21.1127 | 0.719937 | ||||||||
\(861\) | −1.89949 | − | 2.44949i | −0.0647346 | − | 0.0834784i | ||||
\(862\) | −16.8284 | −0.573179 | ||||||||
\(863\) | −1.31371 | − | 2.27541i | −0.0447192 | − | 0.0774559i | 0.842799 | − | 0.538228i | \(-0.180906\pi\) |
−0.887519 | + | 0.460772i | \(0.847573\pi\) | |||||||
\(864\) | −0.792893 | + | 1.37333i | −0.0269748 | + | 0.0467217i | ||||
\(865\) | −14.8284 | + | 25.6836i | −0.504182 | + | 0.873268i | ||||
\(866\) | 1.03553 | + | 1.79360i | 0.0351889 | + | 0.0609489i | ||||
\(867\) | 2.48528 | 0.0844046 | ||||||||
\(868\) | −56.7696 | + | 7.76874i | −1.92688 | + | 0.263688i | ||||
\(869\) | 13.3137 | 0.451637 | ||||||||
\(870\) | −7.82843 | − | 13.5592i | −0.265409 | − | 0.459701i | ||||
\(871\) | −1.31371 | + | 2.27541i | −0.0445133 | + | 0.0770993i | ||||
\(872\) | −15.0711 | + | 26.1039i | −0.510371 | + | 0.883988i | ||||
\(873\) | 5.74264 | + | 9.94655i | 0.194359 | + | 0.336640i | ||||
\(874\) | 122.397 | 4.14014 | ||||||||
\(875\) | 12.0000 | − | 29.3939i | 0.405674 | − | 0.993694i | ||||
\(876\) | 1.31371 | 0.0443861 | ||||||||
\(877\) | −1.24264 | − | 2.15232i | −0.0419610 | − | 0.0726786i | 0.844282 | − | 0.535899i | \(-0.180027\pi\) |
−0.886243 | + | 0.463220i | \(0.846694\pi\) | |||||||
\(878\) | 37.2990 | − | 64.6037i | 1.25878 | − | 2.18027i | ||||
\(879\) | −2.86396 | + | 4.96053i | −0.0965990 | + | 0.167314i | ||||
\(880\) | 3.00000 | + | 5.19615i | 0.101130 | + | 0.175162i | ||||
\(881\) | 16.6863 | 0.562175 | 0.281088 | − | 0.959682i | \(-0.409305\pi\) | ||||
0.281088 | + | 0.959682i | \(0.409305\pi\) | |||||||
\(882\) | −16.2782 | + | 4.54026i | −0.548115 | + | 0.152879i | ||||
\(883\) | 39.6569 | 1.33456 | 0.667280 | − | 0.744807i | \(-0.267459\pi\) | ||||
0.667280 | + | 0.744807i | \(0.267459\pi\) | |||||||
\(884\) | −7.00000 | − | 12.1244i | −0.235435 | − | 0.407786i | ||||
\(885\) | −8.65685 | + | 14.9941i | −0.290997 | + | 0.504022i | ||||
\(886\) | 40.5919 | − | 70.3072i | 1.36371 | − | 2.36202i | ||||
\(887\) | 6.65685 | + | 11.5300i | 0.223515 | + | 0.387140i | 0.955873 | − | 0.293780i | \(-0.0949134\pi\) |
−0.732358 | + | 0.680920i | \(0.761580\pi\) | |||||||
\(888\) | 41.8701 | 1.40507 | ||||||||
\(889\) | −16.0711 | + | 39.3659i | −0.539006 | + | 1.32029i | ||||
\(890\) | −68.2843 | −2.28889 | ||||||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | 43.9706 | − | 76.1592i | 1.47224 | − | 2.55000i | ||||
\(893\) | −35.5919 | + | 61.6469i | −1.19104 | + | 2.06294i | ||||
\(894\) | −26.8137 | − | 46.4427i | −0.896785 | − | 1.55328i | ||||
\(895\) | −35.6569 | −1.19188 | ||||||||
\(896\) | −53.8848 | + | 7.37396i | −1.80016 | + | 0.246347i | ||||
\(897\) | 5.79899 | 0.193623 | ||||||||
\(898\) | −4.82843 | − | 8.36308i | −0.161127 | − | 0.279080i | ||||
\(899\) | −9.17157 | + | 15.8856i | −0.305889 | + | 0.529815i | ||||
\(900\) | 1.91421 | − | 3.31552i | 0.0638071 | − | 0.110517i | ||||
\(901\) | −15.8284 | − | 27.4156i | −0.527321 | − | 0.913347i | ||||
\(902\) | 2.82843 | 0.0941763 | ||||||||
\(903\) | −4.47056 | − | 5.76500i | −0.148771 | − | 0.191847i | ||||
\(904\) | 33.7990 | 1.12414 | ||||||||
\(905\) | −11.6569 | − | 20.1903i | −0.387487 | − | 0.671147i | ||||
\(906\) | −22.8137 | + | 39.5145i | −0.757935 | + | 1.31278i | ||||
\(907\) | 8.75736 | − | 15.1682i | 0.290783 | − | 0.503652i | −0.683212 | − | 0.730220i | \(-0.739417\pi\) |
0.973995 | + | 0.226569i | \(0.0727508\pi\) | |||||||
\(908\) | −28.6569 | − | 49.6351i | −0.951011 | − | 1.64720i | ||||
\(909\) | 4.89949 | 0.162506 | ||||||||
\(910\) | −6.48528 | − | 8.36308i | −0.214985 | − | 0.277233i | ||||
\(911\) | −4.51472 | −0.149579 | −0.0747897 | − | 0.997199i | \(-0.523829\pi\) | ||||
−0.0747897 | + | 0.997199i | \(0.523829\pi\) | |||||||
\(912\) | −10.8640 | − | 18.8169i | −0.359742 | − | 0.623091i | ||||
\(913\) | 1.41421 | − | 2.44949i | 0.0468036 | − | 0.0810663i | ||||
\(914\) | 22.7279 | − | 39.3659i | 0.751773 | − | 1.30211i | ||||
\(915\) | −4.00000 | − | 6.92820i | −0.132236 | − | 0.229039i | ||||
\(916\) | −59.9411 | −1.98051 | ||||||||
\(917\) | 13.5563 | − | 1.85514i | 0.447670 | − | 0.0612622i | ||||
\(918\) | 10.6569 | 0.351729 | ||||||||
\(919\) | −28.1777 | − | 48.8052i | −0.929496 | − | 1.60993i | −0.784167 | − | 0.620550i | \(-0.786909\pi\) |
−0.145329 | − | 0.989383i | \(-0.546424\pi\) | |||||||
\(920\) | 30.8995 | − | 53.5195i | 1.01873 | − | 1.76449i | ||||
\(921\) | 8.65685 | − | 14.9941i | 0.285253 | − | 0.494073i | ||||
\(922\) | 8.15685 | + | 14.1281i | 0.268632 | + | 0.465284i | ||||
\(923\) | 3.45584 | 0.113750 | ||||||||
\(924\) | 3.82843 | − | 9.37769i | 0.125946 | − | 0.308503i | ||||
\(925\) | 9.48528 | 0.311874 | ||||||||
\(926\) | 22.4853 | + | 38.9456i | 0.738912 | + | 1.27983i | ||||
\(927\) | −6.24264 | + | 10.8126i | −0.205035 | + | 0.355131i | ||||
\(928\) | −2.57107 | + | 4.45322i | −0.0843994 | + | 0.146184i | ||||
\(929\) | 11.4142 | + | 19.7700i | 0.374488 | + | 0.648633i | 0.990250 | − | 0.139300i | \(-0.0444851\pi\) |
−0.615762 | + | 0.787932i | \(0.711152\pi\) | |||||||
\(930\) | 27.3137 | 0.895652 | ||||||||
\(931\) | −12.6213 | + | 49.1023i | −0.413647 | + | 1.60926i | ||||
\(932\) | 39.8701 | 1.30599 | ||||||||
\(933\) | −14.8137 | − | 25.6581i | −0.484979 | − | 0.840008i | ||||
\(934\) | −10.0355 | + | 17.3821i | −0.328373 | + | 0.568758i | ||||
\(935\) | −4.41421 | + | 7.64564i | −0.144360 | + | 0.250039i | ||||
\(936\) | −1.82843 | − | 3.16693i | −0.0597640 | − | 0.103514i | ||||
\(937\) | 5.85786 | 0.191368 | 0.0956840 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956840 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(938\) | 7.65685 | − | 18.7554i | 0.250005 | − | 0.612385i | ||||
\(939\) | 4.79899 | 0.156609 | ||||||||
\(940\) | 37.6274 | + | 65.1726i | 1.22727 | + | 2.12570i | ||||
\(941\) | 6.03553 | − | 10.4539i | 0.196753 | − | 0.340786i | −0.750721 | − | 0.660619i | \(-0.770294\pi\) |
0.947474 | + | 0.319834i | \(0.103627\pi\) | |||||||
\(942\) | 8.44975 | − | 14.6354i | 0.275308 | − | 0.476847i | ||||
\(943\) | −4.10051 | − | 7.10228i | −0.133531 | − | 0.231282i | ||||
\(944\) | −25.9706 | −0.845270 | ||||||||
\(945\) | 5.24264 | − | 0.717439i | 0.170543 | − | 0.0233383i | ||||
\(946\) | 6.65685 | 0.216433 | ||||||||
\(947\) | −18.7426 | − | 32.4632i | −0.609054 | − | 1.05491i | −0.991397 | − | 0.130892i | \(-0.958216\pi\) |
0.382343 | − | 0.924021i | \(-0.375117\pi\) | |||||||
\(948\) | −25.4853 | + | 44.1418i | −0.827723 | + | 1.43366i | ||||
\(949\) | 0.142136 | − | 0.246186i | 0.00461392 | − | 0.00799154i | ||||
\(950\) | −8.74264 | − | 15.1427i | −0.283649 | − | 0.491294i | ||||
\(951\) | −25.3137 | −0.820853 | ||||||||
\(952\) | 31.5919 | + | 40.7392i | 1.02390 | + | 1.32037i | ||||
\(953\) | −14.1421 | −0.458109 | −0.229054 | − | 0.973414i | \(-0.573563\pi\) | ||||
−0.229054 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(954\) | −8.65685 | − | 14.9941i | −0.280276 | − | 0.485452i | ||||
\(955\) | −21.6569 | + | 37.5108i | −0.700799 | + | 1.21382i | ||||
\(956\) | 12.4142 | − | 21.5020i | 0.401504 | − | 0.695426i | ||||
\(957\) | −1.62132 | − | 2.80821i | −0.0524098 | − | 0.0907765i | ||||
\(958\) | −33.7990 | −1.09200 | ||||||||
\(959\) | 0.786797 | + | 1.01461i | 0.0254070 | + | 0.0327635i | ||||
\(960\) | 19.6569 | 0.634422 | ||||||||
\(961\) | −0.500000 | − | 0.866025i | −0.0161290 | − | 0.0279363i | ||||
\(962\) | 9.48528 | − | 16.4290i | 0.305818 | − | 0.529692i | ||||
\(963\) | −4.82843 | + | 8.36308i | −0.155594 | + | 0.269497i | ||||
\(964\) | −14.0000 | − | 24.2487i | −0.450910 | − | 0.780998i | ||||
\(965\) | 24.2843 | 0.781738 | ||||||||
\(966\) | −44.2990 | + | 6.06218i | −1.42530 | + | 0.195047i | ||||
\(967\) | −21.0416 | −0.676653 | −0.338327 | − | 0.941029i | \(-0.609861\pi\) | ||||
−0.338327 | + | 0.941029i | \(0.609861\pi\) | |||||||
\(968\) | 2.20711 | + | 3.82282i | 0.0709391 | + | 0.122870i | ||||
\(969\) | 15.9853 | − | 27.6873i | 0.513521 | − | 0.889445i | ||||
\(970\) | 27.7279 | − | 48.0262i | 0.890290 | − | 1.54203i | ||||
\(971\) | −2.48528 | − | 4.30463i | −0.0797565 | − | 0.138142i | 0.823388 | − | 0.567478i | \(-0.192081\pi\) |
−0.903145 | + | 0.429336i | \(0.858748\pi\) | |||||||
\(972\) | 3.82843 | 0.122797 | ||||||||
\(973\) | 8.41421 | − | 20.6105i | 0.269747 | − | 0.660743i | ||||
\(974\) | 78.7696 | 2.52394 | ||||||||
\(975\) | −0.414214 | − | 0.717439i | −0.0132655 | − | 0.0229764i | ||||
\(976\) | 6.00000 | − | 10.3923i | 0.192055 | − | 0.332650i | ||||
\(977\) | 6.41421 | − | 11.1097i | 0.205209 | − | 0.355432i | −0.744990 | − | 0.667075i | \(-0.767546\pi\) |
0.950199 | + | 0.311643i | \(0.100879\pi\) | |||||||
\(978\) | −25.3137 | − | 43.8446i | −0.809443 | − | 1.40200i | ||||
\(979\) | −14.1421 | −0.451985 | ||||||||
\(980\) | 38.2843 | + | 37.5108i | 1.22295 | + | 1.19824i | ||||
\(981\) | −6.82843 | −0.218015 | ||||||||
\(982\) | −1.82843 | − | 3.16693i | −0.0583475 | − | 0.101061i | ||||
\(983\) | 1.01472 | − | 1.75754i | 0.0323645 | − | 0.0560570i | −0.849389 | − | 0.527767i | \(-0.823030\pi\) |
0.881754 | + | 0.471710i | \(0.156363\pi\) | |||||||
\(984\) | −2.58579 | + | 4.47871i | −0.0824319 | + | 0.142776i | ||||
\(985\) | −16.4142 | − | 28.4303i | −0.523000 | − | 0.905863i | ||||
\(986\) | 34.5563 | 1.10050 | ||||||||
\(987\) | 9.82843 | − | 24.0746i | 0.312842 | − | 0.766304i | ||||
\(988\) | −22.9706 | −0.730791 | ||||||||
\(989\) | −9.65076 | − | 16.7156i | −0.306876 | − | 0.531525i | ||||
\(990\) | −2.41421 | + | 4.18154i | −0.0767287 | + | 0.132898i | ||||
\(991\) | 12.3431 | − | 21.3790i | 0.392093 | − | 0.679125i | −0.600632 | − | 0.799525i | \(-0.705084\pi\) |
0.992725 | + | 0.120400i | \(0.0384178\pi\) | |||||||
\(992\) | −4.48528 | − | 7.76874i | −0.142408 | − | 0.246658i | ||||
\(993\) | 22.4853 | 0.713549 | ||||||||
\(994\) | −26.3995 | + | 3.61269i | −0.837341 | + | 0.114588i | ||||
\(995\) | 39.5980 | 1.25534 | ||||||||
\(996\) | 5.41421 | + | 9.37769i | 0.171556 | + | 0.297144i | ||||
\(997\) | −4.92893 | + | 8.53716i | −0.156101 | + | 0.270375i | −0.933459 | − | 0.358683i | \(-0.883226\pi\) |
0.777358 | + | 0.629058i | \(0.216559\pi\) | |||||||
\(998\) | −38.3848 | + | 66.4844i | −1.21505 | + | 2.10453i | ||||
\(999\) | 4.74264 | + | 8.21449i | 0.150051 | + | 0.259895i |
(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 | 231.2.i.d.67.2 | ✓ | 4 | |
3.2 | odd | 2 | 693.2.i.f.298.1 | 4 | |||
7.2 | even | 3 | inner | 231.2.i.d.100.2 | yes | 4 | |
7.3 | odd | 6 | 1617.2.a.m.1.1 | 2 | |||
7.4 | even | 3 | 1617.2.a.n.1.1 | 2 | |||
21.2 | odd | 6 | 693.2.i.f.100.1 | 4 | |||
21.11 | odd | 6 | 4851.2.a.be.1.2 | 2 | |||
21.17 | even | 6 | 4851.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.d.67.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
231.2.i.d.100.2 | yes | 4 | 7.2 | even | 3 | inner | |
693.2.i.f.100.1 | 4 | 21.2 | odd | 6 | |||
693.2.i.f.298.1 | 4 | 3.2 | odd | 2 | |||
1617.2.a.m.1.1 | 2 | 7.3 | odd | 6 | |||
1617.2.a.n.1.1 | 2 | 7.4 | even | 3 | |||
4851.2.a.bd.1.2 | 2 | 21.17 | even | 6 | |||
4851.2.a.be.1.2 | 2 | 21.11 | odd | 6 |