Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(100,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.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: | \(5.53363286007\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.100 |
Dual form | 693.2.i.f.298.2 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.207107 | − | 0.358719i | 0.146447 | − | 0.253653i | −0.783465 | − | 0.621436i | \(-0.786550\pi\) |
0.929912 | + | 0.367783i | \(0.119883\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.914214 | + | 1.58346i | 0.457107 | + | 0.791732i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.414214 | + | 0.717439i | 0.130986 | + | 0.226874i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | −0.671573 | − | 0.866025i | −0.179485 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | −0.792893 | − | 1.37333i | −0.192305 | − | 0.333082i | 0.753709 | − | 0.657209i | \(-0.228263\pi\) |
−0.946014 | + | 0.324127i | \(0.894930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.621320 | − | 1.07616i | 0.142541 | − | 0.246888i | −0.785912 | − | 0.618338i | \(-0.787806\pi\) |
0.928453 | + | 0.371451i | \(0.121139\pi\) | |||||||
\(20\) | −3.65685 | −0.817697 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.414214 | 0.0883106 | ||||||||
\(23\) | −3.50000 | + | 6.06218i | −0.729800 | + | 1.26405i | 0.227167 | + | 0.973856i | \(0.427054\pi\) |
−0.956967 | + | 0.290196i | \(0.906280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.79289 | − | 0.655892i | 0.905772 | − | 0.123952i | ||||
\(29\) | 5.24264 | 0.973534 | 0.486767 | − | 0.873532i | \(-0.338176\pi\) | ||||
0.486767 | + | 0.873532i | \(0.338176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | + | 4.89898i | 0.508001 | + | 0.879883i | 0.999957 | + | 0.00926296i | \(0.00294853\pi\) |
−0.491957 | + | 0.870620i | \(0.663718\pi\) | |||||||
\(32\) | 2.20711 | + | 3.82282i | 0.390165 | + | 0.675786i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.656854 | −0.112650 | ||||||||
\(35\) | 3.24264 | + | 4.18154i | 0.548106 | + | 0.706809i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74264 | + | 6.48244i | −0.615286 | + | 1.06571i | 0.375048 | + | 0.927005i | \(0.377626\pi\) |
−0.990334 | + | 0.138702i | \(0.955707\pi\) | |||||||
\(38\) | −0.257359 | − | 0.445759i | −0.0417492 | − | 0.0723117i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.58579 | + | 2.74666i | −0.250735 | + | 0.434286i | ||||
\(41\) | 6.82843 | 1.06642 | 0.533211 | − | 0.845983i | \(-0.320985\pi\) | ||||
0.533211 | + | 0.845983i | \(0.320985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2426 | −1.71449 | −0.857243 | − | 0.514912i | \(-0.827825\pi\) | ||||
−0.857243 | + | 0.514912i | \(0.827825\pi\) | |||||||
\(44\) | −0.914214 | + | 1.58346i | −0.137823 | + | 0.238716i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.44975 | + | 2.51104i | 0.213754 | + | 0.370232i | ||||
\(47\) | 2.08579 | − | 3.61269i | 0.304243 | − | 0.526965i | −0.672849 | − | 0.739780i | \(-0.734930\pi\) |
0.977093 | + | 0.212815i | \(0.0682631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0.414214 | 0.0585786 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.41421 | + | 7.64564i | 0.612141 | + | 1.06026i | ||||
\(53\) | −6.41421 | − | 11.1097i | −0.881060 | − | 1.52604i | −0.850164 | − | 0.526518i | \(-0.823497\pi\) |
−0.0308961 | − | 0.999523i | \(-0.509836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 1.58579 | − | 3.88437i | 0.211910 | − | 0.519070i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.08579 | − | 1.88064i | 0.142571 | − | 0.246940i | ||||
\(59\) | 1.32843 | + | 2.30090i | 0.172946 | + | 0.299552i | 0.939449 | − | 0.342690i | \(-0.111338\pi\) |
−0.766502 | + | 0.642242i | \(0.778005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | 2.34315 | 0.297580 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −4.82843 | + | 8.36308i | −0.598893 | + | 1.03731i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.41421 | + | 7.64564i | 0.539282 | + | 0.934064i | 0.998943 | + | 0.0459693i | \(0.0146376\pi\) |
−0.459661 | + | 0.888095i | \(0.652029\pi\) | |||||||
\(68\) | 1.44975 | − | 2.51104i | 0.175808 | − | 0.304508i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.17157 | − | 0.297173i | 0.259553 | − | 0.0355190i | ||||
\(71\) | 9.82843 | 1.16642 | 0.583210 | − | 0.812322i | \(-0.301797\pi\) | ||||
0.583210 | + | 0.812322i | \(0.301797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.82843 | − | 10.0951i | −0.682166 | − | 1.18155i | −0.974319 | − | 0.225174i | \(-0.927705\pi\) |
0.292153 | − | 0.956372i | \(-0.405628\pi\) | |||||||
\(74\) | 1.55025 | + | 2.68512i | 0.180213 | + | 0.312138i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27208 | 0.260625 | ||||||||
\(77\) | 2.62132 | − | 0.358719i | 0.298727 | − | 0.0408799i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.65685 | − | 8.06591i | 0.523937 | − | 0.907486i | −0.475675 | − | 0.879621i | \(-0.657796\pi\) |
0.999612 | − | 0.0278643i | \(-0.00887063\pi\) | |||||||
\(80\) | −3.00000 | − | 5.19615i | −0.335410 | − | 0.580948i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.41421 | − | 2.44949i | 0.156174 | − | 0.270501i | ||||
\(83\) | −2.82843 | −0.310460 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17157 | 0.344005 | ||||||||
\(86\) | −2.32843 | + | 4.03295i | −0.251081 | + | 0.434885i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.792893 | + | 1.37333i | 0.0845227 | + | 0.146398i | ||||
\(89\) | 7.07107 | − | 12.2474i | 0.749532 | − | 1.29823i | −0.198516 | − | 0.980098i | \(-0.563612\pi\) |
0.948047 | − | 0.318129i | \(-0.103055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82843 | − | 11.8272i | 0.506157 | − | 1.23983i | ||||
\(92\) | −12.7990 | −1.33439 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.863961 | − | 1.49642i | −0.0891108 | − | 0.154344i | ||||
\(95\) | 1.24264 | + | 2.15232i | 0.127492 | + | 0.220823i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.48528 | 0.556946 | 0.278473 | − | 0.960444i | \(-0.410172\pi\) | ||||
0.278473 | + | 0.960444i | \(0.410172\pi\) | |||||||
\(98\) | −2.79289 | + | 0.778985i | −0.282125 | + | 0.0786894i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.914214 | + | 1.58346i | −0.0914214 | + | 0.158346i | ||||
\(101\) | −7.44975 | − | 12.9033i | −0.741278 | − | 1.28393i | −0.951914 | − | 0.306366i | \(-0.900887\pi\) |
0.210636 | − | 0.977565i | \(-0.432446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24264 | − | 3.88437i | 0.220974 | − | 0.382738i | −0.734130 | − | 0.679009i | \(-0.762410\pi\) |
0.955104 | + | 0.296271i | \(0.0957431\pi\) | |||||||
\(104\) | 7.65685 | 0.750816 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.31371 | −0.516113 | ||||||||
\(107\) | −0.828427 | + | 1.43488i | −0.0800871 | + | 0.138715i | −0.903287 | − | 0.429036i | \(-0.858853\pi\) |
0.823200 | + | 0.567751i | \(0.192187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.585786 | + | 1.01461i | 0.0561082 | + | 0.0971822i | 0.892715 | − | 0.450621i | \(-0.148797\pi\) |
−0.836607 | + | 0.547803i | \(0.815464\pi\) | |||||||
\(110\) | −0.414214 | + | 0.717439i | −0.0394937 | + | 0.0684051i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.86396 | + | 6.27231i | 0.459601 | + | 0.592678i | ||||
\(113\) | −3.65685 | −0.344008 | −0.172004 | − | 0.985096i | \(-0.555024\pi\) | ||||
−0.172004 | + | 0.985096i | \(0.555024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.00000 | − | 12.1244i | −0.652753 | − | 1.13060i | ||||
\(116\) | 4.79289 | + | 8.30153i | 0.445009 | + | 0.770778i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.10051 | 0.101310 | ||||||||
\(119\) | −4.15685 | + | 0.568852i | −0.381058 | + | 0.0521466i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −0.828427 | − | 1.43488i | −0.0750023 | − | 0.129908i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.17157 | + | 8.95743i | −0.464421 | + | 0.804401i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.92893 | −0.171165 | −0.0855825 | − | 0.996331i | \(-0.527275\pi\) | ||||
−0.0855825 | + | 0.996331i | \(0.527275\pi\) | |||||||
\(128\) | −5.27817 | + | 9.14207i | −0.466529 | + | 0.808052i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | −5.41421 | + | 9.37769i | −0.473042 | + | 0.819333i | −0.999524 | − | 0.0308535i | \(-0.990177\pi\) |
0.526482 | + | 0.850186i | \(0.323511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.01472 | − | 2.59808i | −0.174698 | − | 0.225282i | ||||
\(134\) | 3.65685 | 0.315904 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.25736 | − | 2.17781i | −0.107818 | − | 0.186746i | ||||
\(137\) | −8.24264 | − | 14.2767i | −0.704216 | − | 1.21974i | −0.966974 | − | 0.254876i | \(-0.917965\pi\) |
0.262757 | − | 0.964862i | \(-0.415368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.58579 | 0.473780 | 0.236890 | − | 0.971536i | \(-0.423872\pi\) | ||||
0.236890 | + | 0.971536i | \(0.423872\pi\) | |||||||
\(140\) | −3.65685 | + | 8.95743i | −0.309061 | + | 0.757041i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.03553 | − | 3.52565i | 0.170818 | − | 0.295866i | ||||
\(143\) | 2.41421 | + | 4.18154i | 0.201887 | + | 0.349678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.24264 | + | 9.08052i | −0.435378 | + | 0.754096i | ||||
\(146\) | −4.82843 | −0.399603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.6863 | −1.12501 | ||||||||
\(149\) | 10.1066 | − | 17.5051i | 0.827965 | − | 1.43408i | −0.0716669 | − | 0.997429i | \(-0.522832\pi\) |
0.899632 | − | 0.436649i | \(-0.143835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.449747 | − | 0.778985i | −0.0365999 | − | 0.0633929i | 0.847145 | − | 0.531361i | \(-0.178319\pi\) |
−0.883745 | + | 0.467969i | \(0.844986\pi\) | |||||||
\(152\) | 0.985281 | − | 1.70656i | 0.0799169 | − | 0.138420i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.414214 | − | 1.01461i | 0.0333783 | − | 0.0817598i | ||||
\(155\) | −11.3137 | −0.908739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | −1.92893 | − | 3.34101i | −0.153458 | − | 0.265796i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.82843 | −0.697948 | ||||||||
\(161\) | 11.3492 | + | 14.6354i | 0.894446 | + | 1.15343i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.48528 | + | 11.2328i | −0.507966 | + | 0.879824i | 0.491991 | + | 0.870600i | \(0.336269\pi\) |
−0.999957 | + | 0.00922341i | \(0.997064\pi\) | |||||||
\(164\) | 6.24264 | + | 10.8126i | 0.487468 | + | 0.844320i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.585786 | + | 1.01461i | −0.0454658 | + | 0.0787492i | ||||
\(167\) | −10.8284 | −0.837929 | −0.418964 | − | 0.908003i | \(-0.637607\pi\) | ||||
−0.418964 | + | 0.908003i | \(0.637607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0.656854 | − | 1.13770i | 0.0503784 | − | 0.0872580i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2782 | − | 17.8023i | −0.783703 | − | 1.35741i | ||||
\(173\) | −4.58579 | + | 7.94282i | −0.348651 | + | 0.603881i | −0.986010 | − | 0.166686i | \(-0.946693\pi\) |
0.637359 | + | 0.770567i | \(0.280027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62132 | − | 0.358719i | 0.198153 | − | 0.0271166i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.92893 | − | 5.07306i | −0.219533 | − | 0.380242i | ||||
\(179\) | 6.08579 | + | 10.5409i | 0.454873 | + | 0.787863i | 0.998681 | − | 0.0513465i | \(-0.0163513\pi\) |
−0.543808 | + | 0.839210i | \(0.683018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.343146 | −0.0255058 | −0.0127529 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127529 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(182\) | −3.24264 | − | 4.18154i | −0.240361 | − | 0.309956i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.55025 | + | 9.61332i | −0.409170 | + | 0.708703i | ||||
\(185\) | −7.48528 | − | 12.9649i | −0.550329 | − | 0.953197i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.792893 | − | 1.37333i | 0.0579821 | − | 0.100428i | ||||
\(188\) | 7.62742 | 0.556287 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.02944 | 0.0746832 | ||||||||
\(191\) | −5.17157 | + | 8.95743i | −0.374202 | + | 0.648137i | −0.990207 | − | 0.139605i | \(-0.955417\pi\) |
0.616005 | + | 0.787742i | \(0.288750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.07107 | − | 13.9795i | −0.580968 | − | 1.00627i | −0.995365 | − | 0.0961701i | \(-0.969341\pi\) |
0.414397 | − | 0.910096i | \(-0.363993\pi\) | |||||||
\(194\) | 1.13604 | − | 1.96768i | 0.0815628 | − | 0.141271i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.18629 | − | 12.3960i | 0.227592 | − | 0.885431i | ||||
\(197\) | 13.5858 | 0.967947 | 0.483974 | − | 0.875083i | \(-0.339193\pi\) | ||||
0.483974 | + | 0.875083i | \(0.339193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.89949 | − | 17.1464i | −0.701757 | − | 1.21548i | −0.967849 | − | 0.251531i | \(-0.919066\pi\) |
0.266093 | − | 0.963947i | \(-0.414267\pi\) | |||||||
\(200\) | 0.792893 | + | 1.37333i | 0.0560660 | + | 0.0971092i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.17157 | −0.434230 | ||||||||
\(203\) | 5.24264 | − | 12.8418i | 0.367961 | − | 0.901317i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.82843 | + | 11.8272i | −0.476918 | + | 0.826046i | ||||
\(206\) | −0.928932 | − | 1.60896i | −0.0647218 | − | 0.112101i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.24264 | + | 12.5446i | −0.502187 | + | 0.869813i | ||||
\(209\) | 1.24264 | 0.0859553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.9706 | −1.30599 | −0.652994 | − | 0.757363i | \(-0.726487\pi\) | ||||
−0.652994 | + | 0.757363i | \(0.726487\pi\) | |||||||
\(212\) | 11.7279 | − | 20.3134i | 0.805477 | − | 1.39513i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.343146 | + | 0.594346i | 0.0234570 | + | 0.0406286i | ||||
\(215\) | 11.2426 | − | 19.4728i | 0.766742 | − | 1.32804i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.8284 | − | 2.02922i | 1.00662 | − | 0.137753i | ||||
\(218\) | 0.485281 | 0.0328674 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.82843 | − | 3.16693i | −0.123273 | − | 0.213514i | ||||
\(221\) | −3.82843 | − | 6.63103i | −0.257528 | − | 0.446051i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9706 | 0.734643 | 0.367322 | − | 0.930094i | \(-0.380275\pi\) | ||||
0.367322 | + | 0.930094i | \(0.380275\pi\) | |||||||
\(224\) | 11.5711 | − | 1.58346i | 0.773124 | − | 0.105800i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.757359 | + | 1.31178i | −0.0503788 | + | 0.0872586i | ||||
\(227\) | −9.48528 | − | 16.4290i | −0.629560 | − | 1.09043i | −0.987640 | − | 0.156739i | \(-0.949902\pi\) |
0.358080 | − | 0.933691i | \(-0.383432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.17157 | − | 3.76127i | 0.143502 | − | 0.248552i | −0.785311 | − | 0.619101i | \(-0.787497\pi\) |
0.928813 | + | 0.370549i | \(0.120830\pi\) | |||||||
\(230\) | −5.79899 | −0.382374 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.31371 | 0.545822 | ||||||||
\(233\) | 3.79289 | − | 6.56948i | 0.248481 | − | 0.430381i | −0.714624 | − | 0.699509i | \(-0.753402\pi\) |
0.963104 | + | 0.269128i | \(0.0867354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.17157 | + | 7.22538i | 0.272123 | + | 0.471332i | ||||
\(236\) | −2.42893 | + | 4.20703i | −0.158110 | + | 0.273855i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.656854 | + | 1.60896i | −0.0425775 | + | 0.104293i | ||||
\(239\) | −10.4853 | −0.678236 | −0.339118 | − | 0.940744i | \(-0.610129\pi\) | ||||
−0.339118 | + | 0.940744i | \(0.610129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.65685 | + | 13.2621i | 0.493221 | + | 0.854284i | 0.999970 | − | 0.00780972i | \(-0.00248593\pi\) |
−0.506748 | + | 0.862094i | \(0.669153\pi\) | |||||||
\(242\) | 0.207107 | + | 0.358719i | 0.0133133 | + | 0.0230594i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.31371 | 0.468212 | ||||||||
\(245\) | 13.4853 | − | 3.76127i | 0.861543 | − | 0.240299i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 4.48528 | + | 7.76874i | 0.284816 | + | 0.493315i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.48528 | + | 4.30463i | −0.157183 | + | 0.272249i | ||||
\(251\) | 19.4853 | 1.22990 | 0.614950 | − | 0.788566i | \(-0.289176\pi\) | ||||
0.614950 | + | 0.788566i | \(0.289176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | −0.399495 | + | 0.691946i | −0.0250665 | + | 0.0434165i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.98528 | − | 3.43861i | −0.124080 | − | 0.214913i | ||||
\(257\) | −14.7279 | + | 25.5095i | −0.918703 | + | 1.59124i | −0.117314 | + | 0.993095i | \(0.537429\pi\) |
−0.801388 | + | 0.598145i | \(0.795905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.1360 | + | 15.6500i | 0.754097 | + | 0.972444i | ||||
\(260\) | −17.6569 | −1.09503 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.24264 | + | 3.88437i | 0.138551 | + | 0.239977i | ||||
\(263\) | 9.00000 | + | 15.5885i | 0.554964 | + | 0.961225i | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.6569 | 1.57609 | ||||||||
\(266\) | −1.34924 | + | 0.184640i | −0.0827274 | + | 0.0113210i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.07107 | + | 13.9795i | −0.493019 | + | 0.853934i | ||||
\(269\) | 5.89949 | + | 10.2182i | 0.359699 | + | 0.623016i | 0.987910 | − | 0.155026i | \(-0.0495462\pi\) |
−0.628212 | + | 0.778042i | \(0.716213\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.48528 | + | 9.50079i | −0.333207 | + | 0.577132i | −0.983139 | − | 0.182861i | \(-0.941464\pi\) |
0.649932 | + | 0.759993i | \(0.274798\pi\) | |||||||
\(272\) | 4.75736 | 0.288457 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.82843 | −0.412520 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.17157 | + | 12.4215i | 0.430898 | + | 0.746337i | 0.996951 | − | 0.0780316i | \(-0.0248635\pi\) |
−0.566053 | + | 0.824369i | \(0.691530\pi\) | |||||||
\(278\) | 1.15685 | − | 2.00373i | 0.0693835 | − | 0.120176i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.14214 | + | 6.63103i | 0.307301 | + | 0.396280i | ||||
\(281\) | −11.5858 | −0.691150 | −0.345575 | − | 0.938391i | \(-0.612316\pi\) | ||||
−0.345575 | + | 0.938391i | \(0.612316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8284 | − | 27.4156i | −0.940902 | − | 1.62969i | −0.763755 | − | 0.645506i | \(-0.776646\pi\) |
−0.177147 | − | 0.984184i | \(-0.556687\pi\) | |||||||
\(284\) | 8.98528 | + | 15.5630i | 0.533178 | + | 0.923492i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 6.82843 | − | 16.7262i | 0.403069 | − | 0.987314i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24264 | − | 12.5446i | 0.426038 | − | 0.737919i | ||||
\(290\) | 2.17157 | + | 3.76127i | 0.127519 | + | 0.220870i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.6569 | − | 18.4582i | 0.623645 | − | 1.08019i | ||||
\(293\) | 19.7279 | 1.15252 | 0.576259 | − | 0.817267i | \(-0.304512\pi\) | ||||
0.576259 | + | 0.817267i | \(0.304512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.31371 | −0.309376 | ||||||||
\(296\) | −5.93503 | + | 10.2798i | −0.344967 | + | 0.597500i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.18629 | − | 7.25087i | −0.242505 | − | 0.420032i | ||||
\(299\) | −16.8995 | + | 29.2708i | −0.977323 | + | 1.69277i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2426 | + | 27.5387i | −0.648015 | + | 1.58731i | ||||
\(302\) | −0.372583 | −0.0214397 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.86396 | + | 3.22848i | 0.106905 | + | 0.185166i | ||||
\(305\) | 4.00000 | + | 6.92820i | 0.229039 | + | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.31371 | 0.303269 | 0.151635 | − | 0.988437i | \(-0.451546\pi\) | ||||
0.151635 | + | 0.988437i | \(0.451546\pi\) | |||||||
\(308\) | 2.96447 | + | 3.82282i | 0.168916 | + | 0.217825i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.34315 | + | 4.05845i | −0.133082 | + | 0.230504i | ||||
\(311\) | −7.81371 | − | 13.5337i | −0.443075 | − | 0.767428i | 0.554841 | − | 0.831956i | \(-0.312779\pi\) |
−0.997916 | + | 0.0645283i | \(0.979446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.3995 | − | 30.1368i | 0.983478 | − | 1.70343i | 0.334962 | − | 0.942232i | \(-0.391276\pi\) |
0.648515 | − | 0.761202i | \(-0.275390\pi\) | |||||||
\(314\) | −2.89949 | −0.163628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.0294 | 0.957981 | ||||||||
\(317\) | −1.34315 | + | 2.32640i | −0.0754386 | + | 0.130663i | −0.901277 | − | 0.433243i | \(-0.857369\pi\) |
0.825838 | + | 0.563907i | \(0.190702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.62132 | + | 4.54026i | 0.146766 | + | 0.254206i | ||||
\(320\) | 4.17157 | − | 7.22538i | 0.233198 | − | 0.403911i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.60051 | − | 1.04011i | 0.423560 | − | 0.0579628i | ||||
\(323\) | −1.97056 | −0.109645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41421 | + | 4.18154i | 0.133916 | + | 0.231950i | ||||
\(326\) | 2.68629 | + | 4.65279i | 0.148780 | + | 0.257694i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.8284 | 0.597900 | ||||||||
\(329\) | −6.76346 | − | 8.72180i | −0.372881 | − | 0.480848i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.75736 | + | 4.77589i | −0.151558 | + | 0.262506i | −0.931800 | − | 0.362971i | \(-0.881762\pi\) |
0.780242 | + | 0.625477i | \(0.215096\pi\) | |||||||
\(332\) | −2.58579 | − | 4.47871i | −0.141913 | − | 0.245801i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.24264 | + | 3.88437i | −0.122712 | + | 0.212543i | ||||
\(335\) | −17.6569 | −0.964697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1421 | 1.75089 | 0.875447 | − | 0.483314i | \(-0.160567\pi\) | ||||
0.875447 | + | 0.483314i | \(0.160567\pi\) | |||||||
\(338\) | 2.13604 | − | 3.69973i | 0.116185 | − | 0.201239i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.89949 | + | 5.02207i | 0.157247 | + | 0.272360i | ||||
\(341\) | −2.82843 | + | 4.89898i | −0.153168 | + | 0.265295i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | −17.8284 | −0.961244 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.89949 | + | 3.29002i | 0.102117 | + | 0.176873i | ||||
\(347\) | −9.48528 | − | 16.4290i | −0.509197 | − | 0.881954i | −0.999943 | − | 0.0106521i | \(-0.996609\pi\) |
0.490747 | − | 0.871302i | \(-0.336724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9706 | −1.22959 | −0.614793 | − | 0.788688i | \(-0.710760\pi\) | ||||
−0.614793 | + | 0.788688i | \(0.710760\pi\) | |||||||
\(350\) | 0.414214 | − | 1.01461i | 0.0221406 | − | 0.0542333i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.20711 | + | 3.82282i | −0.117639 | + | 0.203757i | ||||
\(353\) | −4.65685 | − | 8.06591i | −0.247859 | − | 0.429305i | 0.715072 | − | 0.699051i | \(-0.246394\pi\) |
−0.962932 | + | 0.269746i | \(0.913060\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.82843 | + | 17.0233i | −0.521639 | + | 0.903505i | ||||
\(356\) | 25.8579 | 1.37046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.04163 | 0.266458 | ||||||||
\(359\) | −4.00000 | + | 6.92820i | −0.211112 | + | 0.365657i | −0.952063 | − | 0.305903i | \(-0.901042\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72792 | + | 15.1172i | 0.459364 | + | 0.795642i | ||||
\(362\) | −0.0710678 | + | 0.123093i | −0.00373524 | + | 0.00646963i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.1421 | − | 3.16693i | 1.21298 | − | 0.165992i | ||||
\(365\) | 23.3137 | 1.22030 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.0711 | − | 20.9077i | −0.630105 | − | 1.09137i | −0.987530 | − | 0.157431i | \(-0.949679\pi\) |
0.357425 | − | 0.933942i | \(-0.383655\pi\) | |||||||
\(368\) | −10.5000 | − | 18.1865i | −0.547350 | − | 0.948039i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.20101 | −0.322375 | ||||||||
\(371\) | −33.6274 | + | 4.60181i | −1.74585 | + | 0.238914i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.82843 | + | 8.36308i | −0.250006 | + | 0.433024i | −0.963527 | − | 0.267610i | \(-0.913766\pi\) |
0.713521 | + | 0.700634i | \(0.247099\pi\) | |||||||
\(374\) | −0.328427 | − | 0.568852i | −0.0169826 | − | 0.0294147i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.30761 | − | 5.72895i | 0.170577 | − | 0.295448i | ||||
\(377\) | 25.3137 | 1.30372 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1716 | 0.676578 | 0.338289 | − | 0.941042i | \(-0.390152\pi\) | ||||
0.338289 | + | 0.941042i | \(0.390152\pi\) | |||||||
\(380\) | −2.27208 | + | 3.93535i | −0.116555 | + | 0.201879i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.14214 | + | 3.71029i | 0.109601 | + | 0.189835i | ||||
\(383\) | −10.1569 | + | 17.5922i | −0.518991 | + | 0.898919i | 0.480765 | + | 0.876849i | \(0.340359\pi\) |
−0.999756 | + | 0.0220695i | \(0.992974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | + | 4.89898i | −0.101929 | + | 0.249675i | ||||
\(386\) | −6.68629 | −0.340323 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.01472 | + | 8.68575i | 0.254584 | + | 0.440952i | ||||
\(389\) | 13.8995 | + | 24.0746i | 0.704732 | + | 1.22063i | 0.966788 | + | 0.255580i | \(0.0822663\pi\) |
−0.262056 | + | 0.965053i | \(0.584400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1005 | 0.561377 | ||||||||
\(392\) | −7.92893 | − | 7.76874i | −0.400472 | − | 0.392380i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.81371 | − | 4.87349i | 0.141753 | − | 0.245523i | ||||
\(395\) | 9.31371 | + | 16.1318i | 0.468624 | + | 0.811680i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.257359 | + | 0.445759i | −0.0129165 | + | 0.0223720i | −0.872411 | − | 0.488772i | \(-0.837445\pi\) |
0.859495 | + | 0.511144i | \(0.170778\pi\) | |||||||
\(398\) | −8.20101 | −0.411079 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 12.2426 | − | 21.2049i | 0.611368 | − | 1.05892i | −0.379642 | − | 0.925134i | \(-0.623953\pi\) |
0.991010 | − | 0.133787i | \(-0.0427139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6569 | + | 23.6544i | 0.680296 | + | 1.17831i | ||||
\(404\) | 13.6213 | − | 23.5928i | 0.677686 | − | 1.17379i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.52082 | − | 4.54026i | −0.174735 | − | 0.225329i | ||||
\(407\) | −7.48528 | −0.371032 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8995 | − | 27.5387i | −0.786179 | − | 1.36170i | −0.928292 | − | 0.371852i | \(-0.878723\pi\) |
0.142113 | − | 0.989851i | \(-0.454611\pi\) | |||||||
\(410\) | 2.82843 | + | 4.89898i | 0.139686 | + | 0.241943i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.20101 | 0.404035 | ||||||||
\(413\) | 6.96447 | − | 0.953065i | 0.342699 | − | 0.0468973i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.82843 | − | 4.89898i | 0.138842 | − | 0.240481i | ||||
\(416\) | 10.6569 | + | 18.4582i | 0.522495 | + | 0.904988i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.257359 | − | 0.445759i | 0.0125879 | − | 0.0218028i | ||||
\(419\) | 24.7990 | 1.21151 | 0.605755 | − | 0.795651i | \(-0.292871\pi\) | ||||
0.605755 | + | 0.795651i | \(0.292871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | −3.92893 | + | 6.80511i | −0.191257 | + | 0.331268i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.1716 | − | 17.6177i | −0.493975 | − | 0.855590i | ||||
\(425\) | 0.792893 | − | 1.37333i | 0.0384610 | − | 0.0666164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.48528 | − | 8.36308i | −0.313845 | − | 0.404718i | ||||
\(428\) | −3.02944 | −0.146433 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.65685 | − | 8.06591i | −0.224573 | − | 0.388973i | ||||
\(431\) | −13.4853 | − | 23.3572i | −0.649563 | − | 1.12508i | −0.983227 | − | 0.182384i | \(-0.941618\pi\) |
0.333664 | − | 0.942692i | \(-0.391715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1421 | 1.40048 | 0.700241 | − | 0.713907i | \(-0.253076\pi\) | ||||
0.700241 | + | 0.713907i | \(0.253076\pi\) | |||||||
\(434\) | 2.34315 | − | 5.73951i | 0.112475 | − | 0.275505i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.07107 | + | 1.85514i | −0.0512948 | + | 0.0888453i | ||||
\(437\) | 4.34924 | + | 7.53311i | 0.208052 | + | 0.360357i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.55025 | + | 9.61332i | −0.264899 | + | 0.458819i | −0.967537 | − | 0.252729i | \(-0.918672\pi\) |
0.702638 | + | 0.711547i | \(0.252005\pi\) | |||||||
\(440\) | −3.17157 | −0.151199 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.17157 | −0.150856 | ||||||||
\(443\) | −5.81371 | + | 10.0696i | −0.276218 | + | 0.478423i | −0.970442 | − | 0.241336i | \(-0.922414\pi\) |
0.694224 | + | 0.719759i | \(0.255748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1421 | + | 24.4949i | 0.670402 | + | 1.16117i | ||||
\(446\) | 2.27208 | − | 3.93535i | 0.107586 | − | 0.186344i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.17157 | + | 10.2182i | −0.197088 | + | 0.482766i | ||||
\(449\) | 4.00000 | 0.188772 | 0.0943858 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943858 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.41421 | + | 5.91359i | 0.160769 | + | 0.278460i | ||||
\(452\) | −3.34315 | − | 5.79050i | −0.157248 | − | 0.272362i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.85786 | −0.368788 | ||||||||
\(455\) | 15.6569 | + | 20.1903i | 0.734005 | + | 0.946534i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.58579 | + | 11.4069i | −0.308070 | + | 0.533593i | −0.977940 | − | 0.208885i | \(-0.933016\pi\) |
0.669870 | + | 0.742478i | \(0.266350\pi\) | |||||||
\(458\) | −0.899495 | − | 1.55797i | −0.0420306 | − | 0.0727992i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.7990 | − | 22.1685i | 0.596756 | − | 1.03361i | ||||
\(461\) | −15.2426 | −0.709921 | −0.354960 | − | 0.934881i | \(-0.615506\pi\) | ||||
−0.354960 | + | 0.934881i | \(0.615506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6274 | −1.23748 | −0.618741 | − | 0.785595i | \(-0.712357\pi\) | ||||
−0.618741 | + | 0.785595i | \(0.712357\pi\) | |||||||
\(464\) | −7.86396 | + | 13.6208i | −0.365075 | + | 0.632329i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.57107 | − | 2.72117i | −0.0727783 | − | 0.126056i | ||||
\(467\) | 7.15685 | − | 12.3960i | 0.331180 | − | 0.573620i | −0.651564 | − | 0.758594i | \(-0.725887\pi\) |
0.982743 | + | 0.184974i | \(0.0592200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1421 | − | 3.16693i | 1.06860 | − | 0.146235i | ||||
\(470\) | 3.45584 | 0.159406 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.10660 | + | 3.64874i | 0.0969642 | + | 0.167947i | ||||
\(473\) | −5.62132 | − | 9.73641i | −0.258469 | − | 0.447681i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.24264 | 0.0570163 | ||||||||
\(476\) | −4.70101 | − | 6.06218i | −0.215470 | − | 0.277859i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.17157 | + | 3.76127i | −0.0993254 | + | 0.172037i | ||||
\(479\) | 7.00000 | + | 12.1244i | 0.319838 | + | 0.553976i | 0.980454 | − | 0.196748i | \(-0.0630381\pi\) |
−0.660616 | + | 0.750724i | \(0.729705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0711 | + | 31.3000i | −0.823970 | + | 1.42716i | ||||
\(482\) | 6.34315 | 0.288922 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.82843 | −0.0831103 | ||||||||
\(485\) | −5.48528 | + | 9.50079i | −0.249074 | + | 0.431408i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.31371 | − | 10.9357i | −0.286101 | − | 0.495542i | 0.686774 | − | 0.726871i | \(-0.259026\pi\) |
−0.972876 | + | 0.231329i | \(0.925693\pi\) | |||||||
\(488\) | 3.17157 | − | 5.49333i | 0.143570 | − | 0.248671i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.44365 | − | 5.61642i | 0.0652175 | − | 0.253724i | ||||
\(491\) | 18.4853 | 0.834229 | 0.417115 | − | 0.908854i | \(-0.363041\pi\) | ||||
0.417115 | + | 0.908854i | \(0.363041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.15685 | − | 7.19988i | −0.187215 | − | 0.324266i | ||||
\(494\) | −1.24264 | − | 2.15232i | −0.0559090 | − | 0.0968373i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.9706 | −0.762001 | ||||||||
\(497\) | 9.82843 | − | 24.0746i | 0.440865 | − | 1.07989i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.89949 | + | 6.75412i | −0.174565 | + | 0.302356i | −0.940011 | − | 0.341145i | \(-0.889185\pi\) |
0.765445 | + | 0.643501i | \(0.222519\pi\) | |||||||
\(500\) | −10.9706 | − | 19.0016i | −0.490618 | − | 0.849776i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.03553 | − | 6.98975i | 0.180115 | − | 0.311968i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.7990 | 1.32604 | ||||||||
\(506\) | −1.44975 | + | 2.51104i | −0.0644491 | + | 0.111629i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.76346 | − | 3.05440i | −0.0782407 | − | 0.135517i | ||||
\(509\) | −6.00000 | + | 10.3923i | −0.265945 | + | 0.460631i | −0.967811 | − | 0.251679i | \(-0.919017\pi\) |
0.701866 | + | 0.712309i | \(0.252351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.5563 | + | 4.18154i | −1.35173 | + | 0.184980i | ||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.10051 | + | 10.5664i | 0.269082 | + | 0.466063i | ||||
\(515\) | 4.48528 | + | 7.76874i | 0.197645 | + | 0.342331i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.17157 | 0.183466 | ||||||||
\(518\) | 8.12742 | − | 1.11221i | 0.357098 | − | 0.0488678i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.65685 | + | 13.2621i | −0.335775 | + | 0.581580i | ||||
\(521\) | 18.4142 | + | 31.8944i | 0.806741 | + | 1.39732i | 0.915109 | + | 0.403206i | \(0.132104\pi\) |
−0.108368 | + | 0.994111i | \(0.534562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.1421 | + | 29.6910i | −0.749573 | + | 1.29830i | 0.198454 | + | 0.980110i | \(0.436408\pi\) |
−0.948027 | + | 0.318189i | \(0.896925\pi\) | |||||||
\(524\) | −19.7990 | −0.864923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.45584 | 0.325090 | ||||||||
\(527\) | 4.48528 | − | 7.76874i | 0.195382 | − | 0.338411i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | − | 22.5167i | −0.565217 | − | 0.978985i | ||||
\(530\) | 5.31371 | − | 9.20361i | 0.230813 | − | 0.399779i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.27208 | − | 5.56543i | 0.0985071 | − | 0.241292i | ||||
\(533\) | 32.9706 | 1.42811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.65685 | − | 2.86976i | −0.0716321 | − | 0.124070i | ||||
\(536\) | 7.00000 | + | 12.1244i | 0.302354 | + | 0.523692i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.88730 | 0.210707 | ||||||||
\(539\) | 1.74264 | − | 6.77962i | 0.0750608 | − | 0.292019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.17157 | + | 7.22538i | −0.179350 | + | 0.310643i | −0.941658 | − | 0.336571i | \(-0.890733\pi\) |
0.762308 | + | 0.647214i | \(0.224066\pi\) | |||||||
\(542\) | 2.27208 | + | 3.93535i | 0.0975941 | + | 0.169038i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.50000 | − | 6.06218i | 0.150061 | − | 0.259914i | ||||
\(545\) | −2.34315 | −0.100369 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2132 | 0.778740 | 0.389370 | − | 0.921081i | \(-0.372693\pi\) | ||||
0.389370 | + | 0.921081i | \(0.372693\pi\) | |||||||
\(548\) | 15.0711 | − | 26.1039i | 0.643804 | − | 1.11510i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.207107 | + | 0.358719i | 0.00883106 | + | 0.0152958i | ||||
\(551\) | 3.25736 | − | 5.64191i | 0.138768 | − | 0.240354i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1005 | − | 19.4728i | −0.642139 | − | 0.828069i | ||||
\(554\) | 5.94113 | 0.252414 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.10660 | + | 8.84489i | 0.216568 | + | 0.375107i | ||||
\(557\) | 11.2782 | + | 19.5344i | 0.477872 | + | 0.827698i | 0.999678 | − | 0.0253659i | \(-0.00807509\pi\) |
−0.521807 | + | 0.853064i | \(0.674742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −54.2843 | −2.29598 | ||||||||
\(560\) | −15.7279 | + | 2.15232i | −0.664626 | + | 0.0909520i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.39949 | + | 4.15605i | −0.101217 | + | 0.175312i | ||||
\(563\) | 9.58579 | + | 16.6031i | 0.403993 | + | 0.699736i | 0.994204 | − | 0.107513i | \(-0.0342888\pi\) |
−0.590211 | + | 0.807249i | \(0.700955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.65685 | − | 6.33386i | 0.153845 | − | 0.266467i | ||||
\(566\) | −13.1127 | −0.551168 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.5858 | 0.653965 | ||||||||
\(569\) | −3.62132 | + | 6.27231i | −0.151814 | + | 0.262949i | −0.931894 | − | 0.362730i | \(-0.881845\pi\) |
0.780081 | + | 0.625679i | \(0.215178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.03553 | + | 15.6500i | 0.378125 | + | 0.654932i | 0.990790 | − | 0.135411i | \(-0.0432355\pi\) |
−0.612664 | + | 0.790343i | \(0.709902\pi\) | |||||||
\(572\) | −4.41421 | + | 7.64564i | −0.184568 | + | 0.319680i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.58579 | − | 5.91359i | −0.191407 | − | 0.246829i | ||||
\(575\) | −7.00000 | −0.291920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.82843 | + | 3.16693i | 0.0761184 | + | 0.131841i | 0.901572 | − | 0.432629i | \(-0.142414\pi\) |
−0.825454 | + | 0.564470i | \(0.809081\pi\) | |||||||
\(578\) | −3.00000 | − | 5.19615i | −0.124784 | − | 0.216131i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.1716 | −0.796056 | ||||||||
\(581\) | −2.82843 | + | 6.92820i | −0.117343 | + | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.41421 | − | 11.1097i | 0.265650 | − | 0.460119i | ||||
\(584\) | −9.24264 | − | 16.0087i | −0.382463 | − | 0.662446i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.08579 | − | 7.07679i | 0.168782 | − | 0.292339i | ||||
\(587\) | −31.3137 | −1.29246 | −0.646228 | − | 0.763145i | \(-0.723654\pi\) | ||||
−0.646228 | + | 0.763145i | \(0.723654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.02944 | 0.289643 | ||||||||
\(590\) | −1.10051 | + | 1.90613i | −0.0453071 | + | 0.0784742i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.2279 | − | 19.4473i | −0.461465 | − | 0.799280i | ||||
\(593\) | −23.8640 | + | 41.3336i | −0.979975 | + | 1.69737i | −0.317546 | + | 0.948243i | \(0.602859\pi\) |
−0.662429 | + | 0.749124i | \(0.730475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.17157 | − | 7.76874i | 0.130022 | − | 0.318487i | ||||
\(596\) | 36.9584 | 1.51387 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.00000 | + | 12.1244i | 0.286251 | + | 0.495802i | ||||
\(599\) | −23.3137 | − | 40.3805i | −0.952572 | − | 1.64990i | −0.739828 | − | 0.672796i | \(-0.765093\pi\) |
−0.212744 | − | 0.977108i | \(-0.568240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.48528 | 0.101377 | 0.0506884 | − | 0.998715i | \(-0.483858\pi\) | ||||
0.0506884 | + | 0.998715i | \(0.483858\pi\) | |||||||
\(602\) | 7.55025 | + | 9.73641i | 0.307725 | + | 0.396827i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.822330 | − | 1.42432i | 0.0334602 | − | 0.0579547i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.6569 | − | 35.7787i | 0.838436 | − | 1.45221i | −0.0527662 | − | 0.998607i | \(-0.516804\pi\) |
0.891202 | − | 0.453607i | \(-0.149863\pi\) | |||||||
\(608\) | 5.48528 | 0.222458 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.31371 | 0.134168 | ||||||||
\(611\) | 10.0711 | − | 17.4436i | 0.407432 | − | 0.705693i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.4142 | − | 26.6982i | −0.622574 | − | 1.07833i | −0.989005 | − | 0.147885i | \(-0.952754\pi\) |
0.366430 | − | 0.930445i | \(-0.380580\pi\) | |||||||
\(614\) | 1.10051 | − | 1.90613i | 0.0444128 | − | 0.0769252i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.15685 | − | 0.568852i | 0.167484 | − | 0.0229197i | ||||
\(617\) | −18.8284 | −0.758004 | −0.379002 | − | 0.925396i | \(-0.623733\pi\) | ||||
−0.379002 | + | 0.925396i | \(0.623733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.31371 | + | 9.20361i | 0.213576 | + | 0.369924i | 0.952831 | − | 0.303501i | \(-0.0981556\pi\) |
−0.739255 | + | 0.673425i | \(0.764822\pi\) | |||||||
\(620\) | −10.3431 | − | 17.9149i | −0.415391 | − | 0.719478i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.47309 | −0.259547 | ||||||||
\(623\) | −22.9289 | − | 29.5680i | −0.918628 | − | 1.18462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −7.20711 | − | 12.4831i | −0.288054 | − | 0.498924i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.39949 | − | 11.0843i | 0.255368 | − | 0.442310i | ||||
\(629\) | 11.8701 | 0.473290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.2843 | −1.20560 | −0.602799 | − | 0.797893i | \(-0.705948\pi\) | ||||
−0.602799 | + | 0.797893i | \(0.705948\pi\) | |||||||
\(632\) | 7.38478 | − | 12.7908i | 0.293751 | − | 0.508791i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.556349 | + | 0.963625i | 0.0220954 | + | 0.0382704i | ||||
\(635\) | 1.92893 | − | 3.34101i | 0.0765473 | − | 0.132584i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1421 | − | 23.6544i | −0.956546 | − | 0.937220i | ||||
\(638\) | 2.17157 | 0.0859734 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.5563 | − | 18.2841i | −0.417276 | − | 0.722744i | ||||
\(641\) | 2.24264 | + | 3.88437i | 0.0885790 | + | 0.153423i | 0.906911 | − | 0.421323i | \(-0.138434\pi\) |
−0.818332 | + | 0.574746i | \(0.805101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | −12.7990 | + | 31.3510i | −0.504351 | + | 1.23540i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.408117 | + | 0.706879i | −0.0160571 | + | 0.0278118i | ||||
\(647\) | 1.65685 | + | 2.86976i | 0.0651377 | + | 0.112822i | 0.896755 | − | 0.442527i | \(-0.145918\pi\) |
−0.831617 | + | 0.555349i | \(0.812585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.32843 | + | 2.30090i | −0.0521453 | + | 0.0903184i | ||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.7157 | −0.928780 | ||||||||
\(653\) | −15.5563 | + | 26.9444i | −0.608767 | + | 1.05442i | 0.382677 | + | 0.923882i | \(0.375002\pi\) |
−0.991444 | + | 0.130533i | \(0.958331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8284 | − | 18.7554i | −0.423102 | − | 0.732834i | ||||
\(656\) | −10.2426 | + | 17.7408i | −0.399908 | + | 0.692661i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.52944 | + | 0.619839i | −0.176576 | + | 0.0241639i | ||||
\(659\) | −17.5147 | −0.682277 | −0.341138 | − | 0.940013i | \(-0.610812\pi\) | ||||
−0.341138 | + | 0.940013i | \(0.610812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9853 | + | 19.0271i | 0.427278 | + | 0.740067i | 0.996630 | − | 0.0820266i | \(-0.0261393\pi\) |
−0.569352 | + | 0.822094i | \(0.692806\pi\) | |||||||
\(662\) | 1.14214 | + | 1.97824i | 0.0443904 | + | 0.0768864i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.48528 | −0.174063 | ||||||||
\(665\) | 6.51472 | − | 0.891519i | 0.252630 | − | 0.0345716i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3492 | + | 31.7818i | −0.710486 | + | 1.23060i | ||||
\(668\) | −9.89949 | − | 17.1464i | −0.383023 | − | 0.663415i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.65685 | + | 6.33386i | −0.141277 | + | 0.244698i | ||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.8284 | 1.26544 | 0.632721 | − | 0.774379i | \(-0.281938\pi\) | ||||
0.632721 | + | 0.774379i | \(0.281938\pi\) | |||||||
\(674\) | 6.65685 | − | 11.5300i | 0.256412 | − | 0.444119i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.42893 | + | 16.3314i | 0.362651 | + | 0.628130i | ||||
\(677\) | 25.0061 | − | 43.3118i | 0.961062 | − | 1.66461i | 0.241221 | − | 0.970470i | \(-0.422452\pi\) |
0.719841 | − | 0.694139i | \(-0.244215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.48528 | − | 13.4361i | 0.210506 | − | 0.515632i | ||||
\(680\) | 5.02944 | 0.192870 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.17157 | + | 2.02922i | 0.0448618 | + | 0.0777030i | ||||
\(683\) | 21.3995 | + | 37.0650i | 0.818829 | + | 1.41825i | 0.906546 | + | 0.422108i | \(0.138710\pi\) |
−0.0877167 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.9706 | 1.25974 | ||||||||
\(686\) | −0.884776 | + | 7.62015i | −0.0337809 | + | 0.290939i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.8640 | − | 29.2092i | 0.642932 | − | 1.11359i | ||||
\(689\) | −30.9706 | − | 53.6426i | −1.17988 | − | 2.04362i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7279 | + | 34.1698i | −0.750486 | + | 1.29988i | 0.197102 | + | 0.980383i | \(0.436847\pi\) |
−0.947588 | + | 0.319496i | \(0.896486\pi\) | |||||||
\(692\) | −16.7696 | −0.637483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.85786 | −0.298280 | ||||||||
\(695\) | −5.58579 | + | 9.67487i | −0.211881 | + | 0.366989i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.41421 | − | 9.37769i | −0.205078 | − | 0.355205i | ||||
\(698\) | −4.75736 | + | 8.23999i | −0.180069 | + | 0.311888i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.96447 | + | 3.82282i | 0.112046 | + | 0.144489i | ||||
\(701\) | −16.8995 | −0.638285 | −0.319143 | − | 0.947707i | \(-0.603395\pi\) | ||||
−0.319143 | + | 0.947707i | \(0.603395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.65076 | + | 8.05535i | 0.175407 | + | 0.303813i | ||||
\(704\) | −2.08579 | − | 3.61269i | −0.0786110 | − | 0.136158i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.85786 | −0.145193 | ||||||||
\(707\) | −39.0563 | + | 5.34474i | −1.46887 | + | 0.201010i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8848 | − | 41.3696i | 0.897012 | − | 1.55367i | 0.0657165 | − | 0.997838i | \(-0.479067\pi\) |
0.831295 | − | 0.555831i | \(-0.187600\pi\) | |||||||
\(710\) | 4.07107 | + | 7.05130i | 0.152784 | + | 0.264630i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.2132 | − | 19.4218i | 0.420233 | − | 0.727864i | ||||
\(713\) | −39.5980 | −1.48296 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.65685 | −0.361146 | ||||||||
\(716\) | −11.1274 | + | 19.2733i | −0.415851 | + | 0.720275i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.65685 | + | 2.86976i | 0.0618333 | + | 0.107098i | ||||
\(719\) | 25.3995 | − | 43.9932i | 0.947241 | − | 1.64067i | 0.196041 | − | 0.980596i | \(-0.437191\pi\) |
0.751200 | − | 0.660074i | \(-0.229475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.27208 | − | 9.37769i | −0.270826 | − | 0.349244i | ||||
\(722\) | 7.23045 | 0.269089 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.313708 | − | 0.543359i | −0.0116589 | − | 0.0201938i | ||||
\(725\) | 2.62132 | + | 4.54026i | 0.0973534 | + | 0.168621i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.0833 | −1.85749 | −0.928743 | − | 0.370725i | \(-0.879109\pi\) | ||||
−0.928743 | + | 0.370725i | \(0.879109\pi\) | |||||||
\(728\) | 7.65685 | − | 18.7554i | 0.283782 | − | 0.695121i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.82843 | − | 8.36308i | 0.178708 | − | 0.309532i | ||||
\(731\) | 8.91421 | + | 15.4399i | 0.329704 | + | 0.571064i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.828427 | − | 1.43488i | 0.0305987 | − | 0.0529984i | −0.850321 | − | 0.526265i | \(-0.823592\pi\) |
0.880919 | + | 0.473267i | \(0.156925\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.8995 | −1.13897 | ||||||||
\(737\) | −4.41421 | + | 7.64564i | −0.162600 | + | 0.281631i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1716 | + | 24.5459i | 0.521310 | + | 0.902935i | 0.999693 | + | 0.0247837i | \(0.00788971\pi\) |
−0.478383 | + | 0.878151i | \(0.658777\pi\) | |||||||
\(740\) | 13.6863 | − | 23.7054i | 0.503118 | − | 0.871426i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.31371 | + | 13.0159i | −0.195072 | + | 0.477828i | ||||
\(743\) | 5.79899 | 0.212744 | 0.106372 | − | 0.994326i | \(-0.466077\pi\) | ||||
0.106372 | + | 0.994326i | \(0.466077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2132 | + | 35.0103i | 0.740554 | + | 1.28268i | ||||
\(746\) | 2.00000 | + | 3.46410i | 0.0732252 | + | 0.126830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.89949 | 0.106016 | ||||||||
\(749\) | 2.68629 | + | 3.46410i | 0.0981550 | + | 0.126576i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.34315 | − | 5.79050i | 0.121993 | − | 0.211298i | −0.798560 | − | 0.601915i | \(-0.794405\pi\) |
0.920554 | + | 0.390616i | \(0.127738\pi\) | |||||||
\(752\) | 6.25736 | + | 10.8381i | 0.228182 | + | 0.395224i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.24264 | − | 9.08052i | 0.190926 | − | 0.330693i | ||||
\(755\) | 1.79899 | 0.0654719 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.3137 | −1.10177 | −0.550885 | − | 0.834581i | \(-0.685710\pi\) | ||||
−0.550885 | + | 0.834581i | \(0.685710\pi\) | |||||||
\(758\) | 2.72792 | − | 4.72490i | 0.0990826 | − | 0.171616i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.97056 | + | 3.41311i | 0.0714798 | + | 0.123807i | ||||
\(761\) | −19.8995 | + | 34.4669i | −0.721356 | + | 1.24943i | 0.239100 | + | 0.970995i | \(0.423148\pi\) |
−0.960456 | + | 0.278431i | \(0.910186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.07107 | − | 0.420266i | 0.111180 | − | 0.0152147i | ||||
\(764\) | −18.9117 | −0.684201 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.20711 | + | 7.28692i | 0.152009 | + | 0.263287i | ||||
\(767\) | 6.41421 | + | 11.1097i | 0.231604 | + | 0.401150i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.79899 | −0.209117 | −0.104558 | − | 0.994519i | \(-0.533343\pi\) | ||||
−0.104558 | + | 0.994519i | \(0.533343\pi\) | |||||||
\(770\) | 1.34315 | + | 1.73205i | 0.0484036 | + | 0.0624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.7574 | − | 25.5605i | 0.531129 | − | 0.919942i | ||||
\(773\) | −20.1716 | − | 34.9382i | −0.725521 | − | 1.25664i | −0.958759 | − | 0.284220i | \(-0.908265\pi\) |
0.233238 | − | 0.972420i | \(-0.425068\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.82843 | + | 4.89898i | −0.101600 | + | 0.175977i | ||||
\(776\) | 8.69848 | 0.312257 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.5147 | 0.412823 | ||||||||
\(779\) | 4.24264 | − | 7.34847i | 0.152008 | − | 0.263286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.91421 | + | 8.51167i | 0.175844 | + | 0.304571i | ||||
\(782\) | 2.29899 | − | 3.98197i | 0.0822117 | − | 0.142395i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.2279 | − | 5.64191i | 0.722426 | − | 0.201497i | ||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7635 | + | 30.7672i | 0.633199 | + | 1.09673i | 0.986894 | + | 0.161372i | \(0.0515918\pi\) |
−0.353695 | + | 0.935361i | \(0.615075\pi\) | |||||||
\(788\) | 12.4203 | + | 21.5126i | 0.442455 | + | 0.766355i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.71573 | 0.274513 | ||||||||
\(791\) | −3.65685 | + | 8.95743i | −0.130023 | + | 0.318489i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.65685 | − | 16.7262i | 0.342925 | − | 0.593963i | ||||
\(794\) | 0.106602 | + | 0.184640i | 0.00378315 | + | 0.00655261i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1005 | − | 31.3510i | 0.641555 | − | 1.11121i | ||||
\(797\) | −16.8284 | −0.596093 | −0.298047 | − | 0.954551i | \(-0.596335\pi\) | ||||
−0.298047 | + | 0.954551i | \(0.596335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61522 | −0.234030 | ||||||||
\(800\) | −2.20711 | + | 3.82282i | −0.0780330 | + | 0.135157i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.07107 | − | 8.78335i | −0.179066 | − | 0.310151i | ||||
\(803\) | 5.82843 | − | 10.0951i | 0.205681 | − | 0.356249i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.6985 | + | 5.02207i | −1.29345 | + | 0.177005i | ||||
\(806\) | 11.3137 | 0.398508 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.8137 | − | 20.4619i | −0.415605 | − | 0.719849i | ||||
\(809\) | 2.58579 | + | 4.47871i | 0.0909114 | + | 0.157463i | 0.907895 | − | 0.419198i | \(-0.137689\pi\) |
−0.816983 | + | 0.576661i | \(0.804355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.9706 | −0.666147 | −0.333073 | − | 0.942901i | \(-0.608086\pi\) | ||||
−0.333073 | + | 0.942901i | \(0.608086\pi\) | |||||||
\(812\) | 25.1274 | − | 3.43861i | 0.881799 | − | 0.120671i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.55025 | + | 2.68512i | −0.0543363 | + | 0.0941133i | ||||
\(815\) | −12.9706 | − | 22.4657i | −0.454339 | − | 0.786938i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.98528 | + | 12.0989i | −0.244384 | + | 0.423286i | ||||
\(818\) | −13.1716 | −0.460533 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.9706 | −0.872010 | ||||||||
\(821\) | 16.5858 | − | 28.7274i | 0.578848 | − | 1.00259i | −0.416764 | − | 0.909015i | \(-0.636836\pi\) |
0.995612 | − | 0.0935793i | \(-0.0298309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.4142 | + | 33.6264i | 0.676737 | + | 1.17214i | 0.975958 | + | 0.217959i | \(0.0699399\pi\) |
−0.299221 | + | 0.954184i | \(0.596727\pi\) | |||||||
\(824\) | 3.55635 | − | 6.15978i | 0.123891 | − | 0.214586i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.10051 | − | 2.69568i | 0.0382915 | − | 0.0937946i | ||||
\(827\) | 14.6863 | 0.510692 | 0.255346 | − | 0.966850i | \(-0.417811\pi\) | ||||
0.255346 | + | 0.966850i | \(0.417811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.91421 | + | 10.2437i | 0.205409 | + | 0.355779i | 0.950263 | − | 0.311449i | \(-0.100814\pi\) |
−0.744854 | + | 0.667228i | \(0.767481\pi\) | |||||||
\(830\) | −1.17157 | − | 2.02922i | −0.0406659 | − | 0.0704354i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.1421 | −0.698303 | ||||||||
\(833\) | −2.76346 | + | 10.7510i | −0.0957481 | + | 0.372501i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8284 | − | 18.7554i | 0.374733 | − | 0.649057i | ||||
\(836\) | 1.13604 | + | 1.96768i | 0.0392907 | + | 0.0680535i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.13604 | − | 8.89588i | 0.177422 | − | 0.307303i | ||||
\(839\) | 24.9706 | 0.862080 | 0.431040 | − | 0.902333i | \(-0.358147\pi\) | ||||
0.431040 | + | 0.902333i | \(0.358147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.51472 | −0.0522317 | ||||||||
\(842\) | −1.44975 | + | 2.51104i | −0.0499616 | + | 0.0865360i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.3431 | − | 30.0392i | −0.596976 | − | 1.03399i | ||||
\(845\) | −10.3137 | + | 17.8639i | −0.354802 | + | 0.614536i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.62132 | + | 2.09077i | 0.0557092 | + | 0.0718397i | ||||
\(848\) | 38.4853 | 1.32159 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.328427 | − | 0.568852i | −0.0112650 | − | 0.0195115i | ||||
\(851\) | −26.1985 | − | 45.3771i | −0.898072 | − | 1.55551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.48528 | 0.153573 | 0.0767866 | − | 0.997048i | \(-0.475534\pi\) | ||||
0.0767866 | + | 0.997048i | \(0.475534\pi\) | |||||||
\(854\) | −4.34315 | + | 0.594346i | −0.148619 | + | 0.0203381i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.31371 | + | 2.27541i | −0.0449016 | + | 0.0777719i | ||||
\(857\) | 13.1777 | + | 22.8244i | 0.450141 | + | 0.779666i | 0.998394 | − | 0.0566456i | \(-0.0180405\pi\) |
−0.548254 | + | 0.836312i | \(0.684707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.75736 | − | 6.50794i | 0.128199 | − | 0.222048i | −0.794780 | − | 0.606898i | \(-0.792414\pi\) |
0.922979 | + | 0.384850i | \(0.125747\pi\) | |||||||
\(860\) | 41.1127 | 1.40193 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1716 | −0.380505 | ||||||||
\(863\) | −21.3137 | + | 36.9164i | −0.725527 | + | 1.25665i | 0.233230 | + | 0.972422i | \(0.425071\pi\) |
−0.958757 | + | 0.284228i | \(0.908263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.17157 | − | 15.8856i | −0.311843 | − | 0.540128i | ||||
\(866\) | 6.03553 | − | 10.4539i | 0.205096 | − | 0.355236i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.7696 | + | 21.6251i | 0.569196 | + | 0.734005i | ||||
\(869\) | 9.31371 | 0.315946 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.3137 | + | 36.9164i | 0.722187 | + | 1.25087i | ||||
\(872\) | 0.928932 | + | 1.60896i | 0.0314576 | + | 0.0544862i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.60303 | 0.121874 | ||||||||
\(875\) | −12.0000 | + | 29.3939i | −0.405674 | + | 0.993694i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.24264 | − | 12.5446i | 0.244567 | − | 0.423602i | −0.717443 | − | 0.696617i | \(-0.754688\pi\) |
0.962010 | + | 0.273015i | \(0.0880210\pi\) | |||||||
\(878\) | 2.29899 | + | 3.98197i | 0.0775872 | + | 0.134385i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.00000 | − | 5.19615i | 0.101130 | − | 0.175162i | ||||
\(881\) | −39.3137 | −1.32451 | −0.662256 | − | 0.749277i | \(-0.730401\pi\) | ||||
−0.662256 | + | 0.749277i | \(0.730401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.3431 | 0.953823 | 0.476911 | − | 0.878951i | \(-0.341756\pi\) | ||||
0.476911 | + | 0.878951i | \(0.341756\pi\) | |||||||
\(884\) | 7.00000 | − | 12.1244i | 0.235435 | − | 0.407786i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.40812 | + | 4.17098i | 0.0809023 | + | 0.140127i | ||||
\(887\) | 4.65685 | − | 8.06591i | 0.156362 | − | 0.270827i | −0.777192 | − | 0.629263i | \(-0.783357\pi\) |
0.933554 | + | 0.358437i | \(0.116690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.92893 | + | 4.72490i | −0.0646943 | + | 0.158468i | ||||
\(890\) | 11.7157 | 0.392712 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0294 | + | 17.3715i | 0.335810 | + | 0.581641i | ||||
\(893\) | −2.59188 | − | 4.48927i | −0.0867341 | − | 0.150228i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.3431 | −0.813702 | ||||||||
\(896\) | 17.1152 | + | 22.0709i | 0.571779 | + | 0.737337i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.828427 | − | 1.43488i | 0.0276450 | − | 0.0478825i | ||||
\(899\) | 14.8284 | + | 25.6836i | 0.494556 | + | 0.856596i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1716 | + | 17.6177i | −0.338864 | + | 0.586930i | ||||
\(902\) | 2.82843 | 0.0941763 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.79899 | −0.192872 | ||||||||
\(905\) | 0.343146 | − | 0.594346i | 0.0114066 | − | 0.0197567i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2426 | + | 29.8651i | 0.572532 | + | 0.991655i | 0.996305 | + | 0.0858867i | \(0.0273723\pi\) |
−0.423772 | + | 0.905769i | \(0.639294\pi\) | |||||||
\(908\) | 17.3431 | − | 30.0392i | 0.575553 | − | 0.996886i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.4853 | − | 1.43488i | 0.347584 | − | 0.0475657i | ||||
\(911\) | 21.4853 | 0.711839 | 0.355920 | − | 0.934517i | \(-0.384168\pi\) | ||||
0.355920 | + | 0.934517i | \(0.384168\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.41421 | − | 2.44949i | −0.0468036 | − | 0.0810663i | ||||
\(914\) | 2.72792 | + | 4.72490i | 0.0902316 | + | 0.156286i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.94113 | 0.262382 | ||||||||
\(917\) | 17.5563 | + | 22.6398i | 0.579762 | + | 0.747631i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.17767 | − | 12.4321i | 0.236769 | − | 0.410097i | −0.723016 | − | 0.690831i | \(-0.757245\pi\) |
0.959785 | + | 0.280735i | \(0.0905781\pi\) | |||||||
\(920\) | −11.1005 | − | 19.2266i | −0.365973 | − | 0.633884i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.15685 | + | 5.46783i | −0.103965 | + | 0.180073i | ||||
\(923\) | 47.4558 | 1.56203 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.48528 | −0.246115 | ||||||||
\(926\) | −5.51472 | + | 9.55177i | −0.181225 | + | 0.313891i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.5711 | + | 20.0417i | 0.379839 | + | 0.657900i | ||||
\(929\) | −8.58579 | + | 14.8710i | −0.281691 | + | 0.487902i | −0.971801 | − | 0.235802i | \(-0.924228\pi\) |
0.690111 | + | 0.723704i | \(0.257562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.37868 | + | 2.33696i | −0.274600 | + | 0.0765907i | ||||
\(932\) | 13.8701 | 0.454329 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.96447 | − | 5.13461i | −0.0970003 | − | 0.168009i | ||||
\(935\) | 1.58579 | + | 2.74666i | 0.0518608 | + | 0.0898255i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.1421 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(938\) | 3.65685 | − | 8.95743i | 0.119401 | − | 0.292470i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.62742 | + | 13.2111i | −0.248779 | + | 0.430898i | ||||
\(941\) | 1.03553 | + | 1.79360i | 0.0337574 | + | 0.0584696i | 0.882411 | − | 0.470480i | \(-0.155919\pi\) |
−0.848653 | + | 0.528950i | \(0.822586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.8995 | + | 41.3951i | −0.778275 | + | 1.34801i | ||||
\(944\) | −7.97056 | −0.259420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.65685 | −0.151407 | ||||||||
\(947\) | 10.2574 | − | 17.7663i | 0.333319 | − | 0.577326i | −0.649841 | − | 0.760070i | \(-0.725165\pi\) |
0.983161 | + | 0.182744i | \(0.0584979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.1421 | − | 48.7436i | −0.913532 | − | 1.58228i | ||||
\(950\) | 0.257359 | − | 0.445759i | 0.00834984 | − | 0.0144623i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.59188 | + | 0.902079i | −0.213644 | + | 0.0292365i | ||||
\(953\) | −14.1421 | −0.458109 | −0.229054 | − | 0.973414i | \(-0.573563\pi\) | ||||
−0.229054 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.3431 | − | 17.9149i | −0.334696 | − | 0.579711i | ||||
\(956\) | −9.58579 | − | 16.6031i | −0.310026 | − | 0.536982i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.79899 | 0.187357 | ||||||||
\(959\) | −43.2132 | + | 5.91359i | −1.39543 | + | 0.190960i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.0161290 | + | 0.0279363i | ||||
\(962\) | 7.48528 | + | 12.9649i | 0.241335 | + | 0.418005i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.0000 | + | 24.2487i | −0.450910 | + | 0.780998i | ||||
\(965\) | 32.2843 | 1.03927 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0416 | 0.869600 | 0.434800 | − | 0.900527i | \(-0.356819\pi\) | ||||
0.434800 | + | 0.900527i | \(0.356819\pi\) | |||||||
\(968\) | −0.792893 | + | 1.37333i | −0.0254846 | + | 0.0441405i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.27208 | + | 3.93535i | 0.0729520 | + | 0.126357i | ||||
\(971\) | −14.4853 | + | 25.0892i | −0.464855 | + | 0.805152i | −0.999195 | − | 0.0401174i | \(-0.987227\pi\) |
0.534340 | + | 0.845270i | \(0.320560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.58579 | − | 13.6823i | 0.179072 | − | 0.438635i | ||||
\(974\) | −5.23045 | −0.167594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | + | 10.3923i | 0.192055 | + | 0.332650i | ||||
\(977\) | −3.58579 | − | 6.21076i | −0.114719 | − | 0.198700i | 0.802948 | − | 0.596049i | \(-0.203264\pi\) |
−0.917668 | + | 0.397349i | \(0.869930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1421 | 0.451985 | ||||||||
\(980\) | 18.2843 | + | 17.9149i | 0.584070 | + | 0.572269i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.82843 | − | 6.63103i | 0.122170 | − | 0.211605i | ||||
\(983\) | −17.9853 | − | 31.1514i | −0.573641 | − | 0.993576i | −0.996188 | − | 0.0872347i | \(-0.972197\pi\) |
0.422546 | − | 0.906341i | \(-0.361136\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.5858 | + | 23.5313i | −0.432879 | + | 0.749769i | ||||
\(986\) | −3.44365 | −0.109668 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.9706 | 0.349020 | ||||||||
\(989\) | 39.3492 | − | 68.1549i | 1.25123 | − | 2.16720i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6569 | + | 40.9749i | 0.751485 | + | 1.30161i | 0.947103 | + | 0.320930i | \(0.103995\pi\) |
−0.195618 | + | 0.980680i | \(0.562671\pi\) | |||||||
\(992\) | −12.4853 | + | 21.6251i | −0.396408 | + | 0.686599i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.60051 | − | 8.51167i | −0.209355 | − | 0.269974i | ||||
\(995\) | 39.5980 | 1.25534 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0711 | − | 33.0321i | −0.603987 | − | 1.04614i | −0.992211 | − | 0.124571i | \(-0.960245\pi\) |
0.388224 | − | 0.921565i | \(-0.373089\pi\) | |||||||
\(998\) | 1.61522 | + | 2.79765i | 0.0511290 | + | 0.0885580i | ||||
\(999\) | 0 | 0 |
(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 | 693.2.i.f.100.2 | 4 | ||
3.2 | odd | 2 | 231.2.i.d.100.1 | yes | 4 | ||
7.2 | even | 3 | 4851.2.a.be.1.1 | 2 | |||
7.4 | even | 3 | inner | 693.2.i.f.298.2 | 4 | ||
7.5 | odd | 6 | 4851.2.a.bd.1.1 | 2 | |||
21.2 | odd | 6 | 1617.2.a.n.1.2 | 2 | |||
21.5 | even | 6 | 1617.2.a.m.1.2 | 2 | |||
21.11 | odd | 6 | 231.2.i.d.67.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.d.67.1 | ✓ | 4 | 21.11 | odd | 6 | ||
231.2.i.d.100.1 | yes | 4 | 3.2 | odd | 2 | ||
693.2.i.f.100.2 | 4 | 1.1 | even | 1 | trivial | ||
693.2.i.f.298.2 | 4 | 7.4 | even | 3 | inner | ||
1617.2.a.m.1.2 | 2 | 21.5 | even | 6 | |||
1617.2.a.n.1.2 | 2 | 21.2 | odd | 6 | |||
4851.2.a.bd.1.1 | 2 | 7.5 | odd | 6 | |||
4851.2.a.be.1.1 | 2 | 7.2 | even | 3 |