Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(127,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.w (of order \(4\), 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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1663.3 | ||
Root | \(2.27943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1920.1663 |
Dual form | 1920.2.w.i.127.3 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.92741 | − | 1.13362i | 0.861964 | − | 0.506970i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.497835 | − | 0.497835i | −0.188164 | − | 0.188164i | 0.606738 | − | 0.794902i | \(-0.292478\pi\) |
−0.794902 | + | 0.606738i | \(0.792478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.29595i | 0.390745i | 0.980729 | + | 0.195373i | \(0.0625916\pi\) | ||||
−0.980729 | + | 0.195373i | \(0.937408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.60318 | − | 2.60318i | −0.721992 | − | 0.721992i | 0.247019 | − | 0.969011i | \(-0.420549\pi\) |
−0.969011 | + | 0.247019i | \(0.920549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.561294 | + | 2.16447i | −0.144926 | + | 0.558865i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0443160 | + | 0.0443160i | −0.0107482 | + | 0.0107482i | −0.712460 | − | 0.701712i | \(-0.752419\pi\) |
0.701712 | + | 0.712460i | \(0.252419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.31802 | −0.302374 | −0.151187 | − | 0.988505i | \(-0.548310\pi\) | ||||
−0.151187 | + | 0.988505i | \(0.548310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.704045 | 0.153635 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.631215 | − | 0.631215i | 0.131617 | − | 0.131617i | −0.638229 | − | 0.769847i | \(-0.720333\pi\) |
0.769847 | + | 0.638229i | \(0.220333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42981 | − | 4.36990i | 0.485963 | − | 0.873980i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 10.3020i | − | 1.91304i | −0.291670 | − | 0.956519i | \(-0.594211\pi\) | ||
0.291670 | − | 0.956519i | \(-0.405789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.02439i | − | 0.363590i | −0.983336 | − | 0.181795i | \(-0.941809\pi\) | ||
0.983336 | − | 0.181795i | \(-0.0581908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.916378 | − | 0.916378i | −0.159521 | − | 0.159521i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52389 | − | 0.395177i | −0.257584 | − | 0.0667970i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.03999 | + | 1.03999i | −0.170973 | + | 0.170973i | −0.787407 | − | 0.616434i | \(-0.788577\pi\) |
0.616434 | + | 0.787407i | \(0.288577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.68145 | 0.589504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.24951 | 0.195140 | 0.0975701 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975701 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.55886 | + | 2.55886i | −0.390223 | + | 0.390223i | −0.874767 | − | 0.484544i | \(-0.838986\pi\) |
0.484544 | + | 0.874767i | \(0.338986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.13362 | − | 1.92741i | −0.168990 | − | 0.287321i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.03931 | + | 4.03931i | 0.589193 | + | 0.589193i | 0.937413 | − | 0.348220i | \(-0.113214\pi\) |
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.50432i | − | 0.929189i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 0.0626722i | − | 0.00877587i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.557751 | + | 0.557751i | 0.0766130 | + | 0.0766130i | 0.744375 | − | 0.667762i | \(-0.232748\pi\) |
−0.667762 | + | 0.744375i | \(0.732748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46912 | + | 2.49784i | 0.198096 | + | 0.336808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.931979 | − | 0.931979i | 0.123444 | − | 0.123444i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2776 | −1.59841 | −0.799206 | − | 0.601057i | \(-0.794747\pi\) | ||||
−0.799206 | + | 0.601057i | \(0.794747\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87187 | −0.879853 | −0.439927 | − | 0.898034i | \(-0.644996\pi\) | ||||
−0.439927 | + | 0.898034i | \(0.644996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.497835 | + | 0.497835i | −0.0627213 | + | 0.0627213i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.96841 | − | 2.06638i | −0.988360 | − | 0.256303i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.36291 | − | 9.36291i | −1.14386 | − | 1.14386i | −0.987738 | − | 0.156123i | \(-0.950100\pi\) |
−0.156123 | − | 0.987738i | \(-0.549900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.892673i | 0.107465i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.62237i | − | 1.14196i | −0.820962 | − | 0.570982i | \(-0.806562\pi\) | ||
0.820962 | − | 0.570982i | \(-0.193438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.88834 | + | 2.88834i | 0.338055 | + | 0.338055i | 0.855635 | − | 0.517580i | \(-0.173167\pi\) |
−0.517580 | + | 0.855635i | \(0.673167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.37185 | + | 4.80812i | 0.158407 | + | 0.555194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.645172 | − | 0.645172i | 0.0735242 | − | 0.0735242i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9340 | 1.56770 | 0.783850 | − | 0.620951i | \(-0.213253\pi\) | ||||
0.783850 | + | 0.620951i | \(0.213253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.29163 | + | 4.29163i | −0.471067 | + | 0.471067i | −0.902260 | − | 0.431193i | \(-0.858093\pi\) |
0.431193 | + | 0.902260i | \(0.358093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0351776 | + | 0.135652i | −0.00381554 | + | 0.0147136i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.28463 | + | 7.28463i | 0.780995 | + | 0.780995i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.94393i | 0.206056i | 0.994678 | + | 0.103028i | \(0.0328532\pi\) | ||||
−0.994678 | + | 0.103028i | \(0.967147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59191i | 0.271706i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.43146 | + | 1.43146i | 0.148435 | + | 0.148435i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.54036 | + | 1.49413i | −0.260635 | + | 0.153294i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.03479 | − | 3.03479i | 0.308136 | − | 0.308136i | −0.536050 | − | 0.844186i | \(-0.680084\pi\) |
0.844186 | + | 0.536050i | \(0.180084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.29595 | 0.130248 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1703 | 1.31050 | 0.655248 | − | 0.755414i | \(-0.272564\pi\) | ||||
0.655248 | + | 0.755414i | \(0.272564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.39051 | − | 7.39051i | 0.728208 | − | 0.728208i | −0.242054 | − | 0.970263i | \(-0.577821\pi\) |
0.970263 | + | 0.242054i | \(0.0778212\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35698 | − | 0.798119i | 0.132428 | − | 0.0778885i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6589 | − | 12.6589i | −1.22378 | − | 1.22378i | −0.966278 | − | 0.257500i | \(-0.917101\pi\) |
−0.257500 | − | 0.966278i | \(-0.582899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.3665i | − | 1.08871i | −0.838854 | − | 0.544356i | \(-0.816774\pi\) | ||
0.838854 | − | 0.544356i | \(-0.183226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.47076i | − | 0.139599i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.78874 | − | 9.78874i | −0.920847 | − | 0.920847i | 0.0762421 | − | 0.997089i | \(-0.475708\pi\) |
−0.997089 | + | 0.0762421i | \(0.975708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.501052 | − | 1.93217i | 0.0467234 | − | 0.180176i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.60318 | + | 2.60318i | −0.240664 | + | 0.240664i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0441241 | 0.00404485 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.32050 | 0.847318 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.883534 | + | 0.883534i | −0.0796656 | + | 0.0796656i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.270555 | − | 11.1771i | −0.0241992 | − | 0.999707i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.85138 | + | 6.85138i | 0.607962 | + | 0.607962i | 0.942413 | − | 0.334451i | \(-0.108551\pi\) |
−0.334451 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.61878i | − | 0.318616i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.1559i | − | 0.887324i | −0.896194 | − | 0.443662i | \(-0.853679\pi\) | ||
0.896194 | − | 0.443662i | \(-0.146321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.656155 | + | 0.656155i | 0.0568959 | + | 0.0568959i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.16447 | + | 0.561294i | 0.186288 | + | 0.0483085i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.08343 | + | 7.08343i | −0.605178 | + | 0.605178i | −0.941682 | − | 0.336504i | \(-0.890756\pi\) |
0.336504 | + | 0.941682i | \(0.390756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2860 | 1.63582 | 0.817910 | − | 0.575346i | \(-0.195133\pi\) | ||||
0.817910 | + | 0.575346i | \(0.195133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.71244 | −0.481074 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.37360 | − | 3.37360i | 0.282115 | − | 0.282115i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6786 | − | 19.8562i | −0.969853 | − | 1.64897i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.59925 | + | 4.59925i | 0.379340 | + | 0.379340i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.31039i | − | 0.353121i | −0.984290 | − | 0.176560i | \(-0.943503\pi\) | ||
0.984290 | − | 0.176560i | \(-0.0564970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.92313i | 0.807533i | 0.914862 | + | 0.403766i | \(0.132299\pi\) | ||||
−0.914862 | + | 0.403766i | \(0.867701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0443160 | + | 0.0443160i | 0.00358273 | + | 0.00358273i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29488 | − | 3.90182i | −0.184329 | − | 0.313402i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.11359 | + | 8.11359i | −0.647535 | + | 0.647535i | −0.952397 | − | 0.304862i | \(-0.901390\pi\) |
0.304862 | + | 0.952397i | \(0.401390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.788780 | −0.0625543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.628482 | −0.0495313 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.5589 | + | 12.5589i | −0.983686 | + | 0.983686i | −0.999869 | − | 0.0161829i | \(-0.994849\pi\) |
0.0161829 | + | 0.999869i | \(0.494849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.80506 | − | 0.727412i | −0.218374 | − | 0.0566289i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.40357 | − | 7.40357i | −0.572906 | − | 0.572906i | 0.360034 | − | 0.932939i | \(-0.382765\pi\) |
−0.932939 | + | 0.360034i | \(0.882765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.553093i | 0.0425456i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.31802i | 0.100791i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.337923 | + | 0.337923i | 0.0256918 | + | 0.0256918i | 0.719836 | − | 0.694144i | \(-0.244217\pi\) |
−0.694144 | + | 0.719836i | \(0.744217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.38514 | + | 0.965842i | −0.255892 | + | 0.0730108i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.68160 | − | 8.68160i | 0.652549 | − | 0.652549i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.3264 | 1.22029 | 0.610147 | − | 0.792288i | \(-0.291111\pi\) | ||||
0.610147 | + | 0.792288i | \(0.291111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7305 | 1.54088 | 0.770441 | − | 0.637511i | \(-0.220036\pi\) | ||||
0.770441 | + | 0.637511i | \(0.220036\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85915 | − | 4.85915i | 0.359199 | − | 0.359199i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.825531 | + | 3.18343i | −0.0606942 | + | 0.234050i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0574315 | − | 0.0574315i | −0.00419981 | − | 0.00419981i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.704045i | − | 0.0512118i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.9680i | − | 1.58955i | −0.606904 | − | 0.794775i | \(-0.707589\pi\) | ||
0.606904 | − | 0.794775i | \(-0.292411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.74797 | − | 5.74797i | −0.413748 | − | 0.413748i | 0.469294 | − | 0.883042i | \(-0.344508\pi\) |
−0.883042 | + | 0.469294i | \(0.844508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.09567 | − | 4.17337i | 0.508131 | − | 0.298861i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.07856 | − | 8.07856i | 0.575574 | − | 0.575574i | −0.358107 | − | 0.933681i | \(-0.616578\pi\) |
0.933681 | + | 0.358107i | \(0.116578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.95046 | −0.563593 | −0.281797 | − | 0.959474i | \(-0.590930\pi\) | ||||
−0.281797 | + | 0.959474i | \(0.590930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2411 | 0.933959 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.12871 | + | 5.12871i | −0.359965 | + | 0.359965i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.40831 | − | 1.41646i | 0.168204 | − | 0.0989302i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.631215 | − | 0.631215i | −0.0438725 | − | 0.0438725i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.70809i | − | 0.118151i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9708i | 1.51254i | 0.654262 | + | 0.756268i | \(0.272979\pi\) | ||||
−0.654262 | + | 0.756268i | \(0.727021\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.80404 | + | 6.80404i | 0.466205 | + | 0.466205i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.03120 | + | 7.83276i | −0.138527 | + | 0.534190i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00781 | + | 1.00781i | −0.0684146 | + | 0.0684146i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.08473 | −0.276021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.230725 | 0.0155202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.34929 | − | 5.34929i | 0.358215 | − | 0.358215i | −0.504940 | − | 0.863155i | \(-0.668485\pi\) |
0.863155 | + | 0.504940i | \(0.168485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.36990 | − | 2.42981i | −0.291327 | − | 0.161988i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1937 | − | 15.1937i | −1.00844 | − | 1.00844i | −0.999964 | − | 0.00847965i | \(-0.997301\pi\) |
−0.00847965 | − | 0.999964i | \(-0.502699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.51752i | 0.496772i | 0.968661 | + | 0.248386i | \(0.0799001\pi\) | ||||
−0.968661 | + | 0.248386i | \(0.920100\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.912411i | 0.0600322i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0217 | + | 18.0217i | 1.18064 | + | 1.18064i | 0.979579 | + | 0.201060i | \(0.0644386\pi\) |
0.201060 | + | 0.979579i | \(0.435561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3644 | + | 3.20636i | 0.806567 | + | 0.209160i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.85284 | + | 9.85284i | −0.640011 | + | 0.640011i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9950 | −1.42274 | −0.711368 | − | 0.702819i | \(-0.751924\pi\) | ||||
−0.711368 | + | 0.702819i | \(0.751924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.37342 | − | 12.5365i | −0.471071 | − | 0.800927i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.43103 | + | 3.43103i | 0.218312 | + | 0.218312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.06927i | − | 0.384625i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.90001i | − | 0.372405i | −0.982511 | − | 0.186203i | \(-0.940382\pi\) | ||
0.982511 | − | 0.186203i | \(-0.0596181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.818026 | + | 0.818026i | 0.0514289 | + | 0.0514289i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0710465 | − | 0.120795i | −0.00444910 | − | 0.00756448i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1089 | + | 14.1089i | −0.880092 | + | 0.880092i | −0.993543 | − | 0.113452i | \(-0.963809\pi\) |
0.113452 | + | 0.993543i | \(0.463809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.03548 | 0.0643418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.3020 | −0.637679 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.117239 | + | 0.117239i | −0.00722928 | + | 0.00722928i | −0.710712 | − | 0.703483i | \(-0.751627\pi\) |
0.703483 | + | 0.710712i | \(0.251627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.70729 | + | 0.442737i | 0.104878 | + | 0.0271971i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.37457 | − | 1.37457i | −0.0841221 | − | 0.0841221i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.2054i | − | 1.23195i | −0.787767 | − | 0.615973i | \(-0.788763\pi\) | ||
0.787767 | − | 0.615973i | \(-0.211237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.27633i | 0.502751i | 0.967890 | + | 0.251376i | \(0.0808830\pi\) | ||||
−0.967890 | + | 0.251376i | \(0.919117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.83276 | − | 1.83276i | −0.110923 | − | 0.110923i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.66319 | + | 3.14893i | 0.341503 | + | 0.189888i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1707 | + | 13.1707i | −0.791351 | + | 0.791351i | −0.981714 | − | 0.190363i | \(-0.939034\pi\) |
0.190363 | + | 0.981714i | \(0.439034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.02439 | −0.121197 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.324088 | −0.0193335 | −0.00966674 | − | 0.999953i | \(-0.503077\pi\) | ||||
−0.00966674 | + | 0.999953i | \(0.503077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2477 | − | 16.2477i | 0.965826 | − | 0.965826i | −0.0336094 | − | 0.999435i | \(-0.510700\pi\) |
0.999435 | + | 0.0336094i | \(0.0107002\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.739795 | − | 2.85281i | 0.0438217 | − | 0.168986i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.622048 | − | 0.622048i | −0.0367184 | − | 0.0367184i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9961i | 0.999769i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.29184i | 0.251592i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9985 | + | 16.9985i | 0.993064 | + | 0.993064i | 0.999976 | − | 0.00691168i | \(-0.00220007\pi\) |
−0.00691168 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.6640 | + | 13.9182i | −1.37777 | + | 0.810347i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.916378 | + | 0.916378i | −0.0531737 | + | 0.0531737i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.28633 | −0.190054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54779 | 0.146852 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.31282 | + | 9.31282i | −0.535007 | + | 0.535007i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.2449 | + | 7.79009i | −0.758402 | + | 0.446059i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.16935 | + | 9.16935i | 0.523322 | + | 0.523322i | 0.918573 | − | 0.395251i | \(-0.129342\pi\) |
−0.395251 | + | 0.918573i | \(0.629342\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4518i | 0.594580i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.4077i | − | 0.646872i | −0.946250 | − | 0.323436i | \(-0.895162\pi\) | ||
0.946250 | − | 0.323436i | \(-0.104838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9731 | + | 19.9731i | 1.12895 | + | 1.12895i | 0.990348 | + | 0.138600i | \(0.0442601\pi\) |
0.138600 | + | 0.990348i | \(0.455740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.395177 | + | 1.52389i | −0.0222657 | + | 0.0858614i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.1176 | + | 11.1176i | −0.624425 | + | 0.624425i | −0.946660 | − | 0.322234i | \(-0.895566\pi\) |
0.322234 | + | 0.946660i | \(0.395566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3510 | 0.747510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.9023 | 0.999211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0584092 | − | 0.0584092i | 0.00324997 | − | 0.00324997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.7009 | + | 5.05039i | −0.981868 | + | 0.280145i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.03732 | + | 8.03732i | 0.444465 | + | 0.444465i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.02182i | − | 0.221730i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.2957i | 1.39037i | 0.718829 | + | 0.695187i | \(0.244679\pi\) | ||||
−0.718829 | + | 0.695187i | \(0.755321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.03999 | + | 1.03999i | 0.0569909 | + | 0.0569909i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.6601 | − | 7.43218i | −1.56587 | − | 0.406063i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.49825 | + | 7.49825i | −0.408456 | + | 0.408456i | −0.881200 | − | 0.472744i | \(-0.843263\pi\) |
0.472744 | + | 0.881200i | \(0.343263\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8434 | 0.751869 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.62351 | 0.142071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.72293 | + | 6.72293i | −0.363004 | + | 0.363004i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.01195 | + | 1.72055i | 0.0544816 | + | 0.0926311i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1546 | − | 18.1546i | −0.974591 | − | 0.974591i | 0.0250941 | − | 0.999685i | \(-0.492011\pi\) |
−0.999685 | + | 0.0250941i | \(0.992011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.5709i | − | 0.619378i | −0.950838 | − | 0.309689i | \(-0.899775\pi\) | ||
0.950838 | − | 0.309689i | \(-0.100225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.68145i | − | 0.196501i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.93419 | + | 6.93419i | 0.369069 | + | 0.369069i | 0.867138 | − | 0.498068i | \(-0.165957\pi\) |
−0.498068 | + | 0.867138i | \(0.665957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.9081 | − | 18.5462i | −0.578942 | − | 0.984332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0312005 | + | 0.0312005i | −0.00165130 | + | 0.00165130i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.207103 | −0.0109305 | −0.00546524 | − | 0.999985i | \(-0.501740\pi\) | ||||
−0.00546524 | + | 0.999985i | \(0.501740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2628 | −0.908570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.59059 | + | 6.59059i | −0.345916 | + | 0.345916i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.84130 | + | 2.29274i | 0.462775 | + | 0.120007i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.25495 | + | 9.25495i | 0.483104 | + | 0.483104i | 0.906122 | − | 0.423017i | \(-0.139029\pi\) |
−0.423017 | + | 0.906122i | \(0.639029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.24951i | − | 0.0650467i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.555337i | − | 0.0288316i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6272 | + | 13.6272i | 0.705592 | + | 0.705592i | 0.965605 | − | 0.260013i | \(-0.0837268\pi\) |
−0.260013 | + | 0.965605i | \(0.583727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.09469 | + | 7.71207i | 0.418008 | + | 0.398249i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.8180 | + | 26.8180i | −1.38120 | + | 1.38120i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0342 | 0.926355 | 0.463178 | − | 0.886266i | \(-0.346709\pi\) | ||||
0.463178 | + | 0.886266i | \(0.346709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.68932 | −0.496399 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.4015 | + | 12.4015i | −0.633685 | + | 0.633685i | −0.948990 | − | 0.315305i | \(-0.897893\pi\) |
0.315305 | + | 0.948990i | \(0.397893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.512131 | − | 1.97489i | 0.0261006 | − | 0.100650i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.55886 | + | 2.55886i | 0.130074 | + | 0.130074i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7012i | 1.30310i | 0.758604 | + | 0.651552i | \(0.225882\pi\) | ||||
−0.758604 | + | 0.651552i | \(0.774118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0559458i | 0.00282930i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.18129 | + | 7.18129i | 0.362248 | + | 0.362248i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.8566 | − | 15.7959i | 1.35130 | − | 0.794777i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7752 | + | 22.7752i | −1.14305 | + | 1.14305i | −0.155163 | + | 0.987889i | \(0.549590\pi\) |
−0.987889 | + | 0.155163i | \(0.950410\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.927944 | −0.0464553 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.9756 | 1.09741 | 0.548704 | − | 0.836017i | \(-0.315121\pi\) | ||||
0.548704 | + | 0.836017i | \(0.315121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.26984 | + | 5.26984i | −0.262510 | + | 0.262510i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.92741 | + | 1.13362i | −0.0957737 | + | 0.0563300i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.34778 | − | 1.34778i | −0.0668067 | − | 0.0668067i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.9242i | − | 0.737956i | −0.929438 | − | 0.368978i | \(-0.879708\pi\) | ||
0.929438 | − | 0.368978i | \(-0.120292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 10.0175i | − | 0.494126i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.11224 | + | 6.11224i | 0.300764 | + | 0.300764i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.40665 | + | 13.1368i | −0.167226 | + | 0.644860i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.6373 | + | 13.6373i | −0.667821 | + | 0.667821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.8701 | −0.970720 | −0.485360 | − | 0.874314i | \(-0.661312\pi\) | ||||
−0.485360 | + | 0.874314i | \(0.661312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6819 | 0.520606 | 0.260303 | − | 0.965527i | \(-0.416178\pi\) | ||||
0.260303 | + | 0.965527i | \(0.416178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.03931 | − | 4.03931i | 0.196398 | − | 0.196398i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0859767 | + | 0.301336i | 0.00417048 | + | 0.0146169i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.42106 | + | 3.42106i | 0.165557 | + | 0.165557i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.77100i | 0.230346i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.0578i | − | 0.628972i | −0.949262 | − | 0.314486i | \(-0.898168\pi\) | ||
0.949262 | − | 0.314486i | \(-0.101832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1148 | + | 15.1148i | 0.726369 | + | 0.726369i | 0.969894 | − | 0.243525i | \(-0.0783040\pi\) |
−0.243525 | + | 0.969894i | \(0.578304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.2985 | + | 5.78247i | 1.06913 | + | 0.277248i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.831952 | + | 0.831952i | −0.0397977 | + | 0.0397977i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.2133 | −1.44200 | −0.721001 | − | 0.692934i | \(-0.756318\pi\) | ||||
−0.721001 | + | 0.692934i | \(0.756318\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50432 | −0.309730 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.36619 | + | 9.36619i | −0.445001 | + | 0.445001i | −0.893689 | − | 0.448688i | \(-0.851892\pi\) |
0.448688 | + | 0.893689i | \(0.351892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.20368 | + | 3.74675i | 0.104464 | + | 0.177613i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.04790 | + | 3.04790i | 0.144161 | + | 0.144161i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.9264i | 1.50670i | 0.657619 | + | 0.753350i | \(0.271564\pi\) | ||||
−0.657619 | + | 0.753350i | \(0.728436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.61930i | 0.0762500i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.01671 | − | 7.01671i | −0.329674 | − | 0.329674i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.93824 | + | 4.99567i | 0.137747 | + | 0.234201i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1817 | + | 13.1817i | −0.616615 | + | 0.616615i | −0.944661 | − | 0.328047i | \(-0.893610\pi\) |
0.328047 | + | 0.944661i | \(0.393610\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0626722 | −0.00292529 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.04893 | 0.235152 | 0.117576 | − | 0.993064i | \(-0.462488\pi\) | ||||
0.117576 | + | 0.993064i | \(0.462488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7581 | − | 26.7581i | 1.24355 | − | 1.24355i | 0.285036 | − | 0.958517i | \(-0.407994\pi\) |
0.958517 | − | 0.285036i | \(-0.0920055\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.38173 | + | 1.13628i | 0.203198 | + | 0.0526936i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.3602 | + | 23.3602i | 1.08098 | + | 1.08098i | 0.996418 | + | 0.0845632i | \(0.0269495\pi\) |
0.0845632 | + | 0.996418i | \(0.473051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.32237i | 0.430467i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.4743i | − | 0.528710i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.31617 | − | 3.31617i | −0.152478 | − | 0.152478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.20254 | + | 5.75960i | −0.146942 | + | 0.264268i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.557751 | − | 0.557751i | 0.0255377 | − | 0.0255377i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.4867 | −1.84989 | −0.924943 | − | 0.380106i | \(-0.875887\pi\) | ||||
−0.924943 | + | 0.380106i | \(0.875887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.41454 | 0.246882 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.444404 | − | 0.444404i | 0.0202211 | − | 0.0202211i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.40898 | − | 9.28957i | 0.109386 | − | 0.421818i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.51912 | − | 4.51912i | −0.204781 | − | 0.204781i | 0.597264 | − | 0.802045i | \(-0.296255\pi\) |
−0.802045 | + | 0.597264i | \(0.796255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 17.7609i | − | 0.803176i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5364i | 1.19757i | 0.800909 | + | 0.598786i | \(0.204350\pi\) | ||||
−0.800909 | + | 0.598786i | \(0.795650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.456544 | + | 0.456544i | 0.0205617 | + | 0.0205617i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.49784 | − | 1.46912i | 0.112269 | − | 0.0660320i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.79035 | + | 4.79035i | −0.214877 | + | 0.214877i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.4486 | 1.31830 | 0.659151 | − | 0.752011i | \(-0.270916\pi\) | ||||
0.659151 | + | 0.752011i | \(0.270916\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4702 | 0.467775 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.1983 | − | 11.1983i | 0.499306 | − | 0.499306i | −0.411916 | − | 0.911222i | \(-0.635140\pi\) |
0.911222 | + | 0.411916i | \(0.135140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.3846 | − | 14.9301i | 1.12960 | − | 0.664382i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.391095 | − | 0.391095i | −0.0173692 | − | 0.0173692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.20339i | − | 0.0533394i | −0.999644 | − | 0.0266697i | \(-0.991510\pi\) | ||
0.999644 | − | 0.0266697i | \(-0.00849024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.87584i | − | 0.127220i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.931979 | − | 0.931979i | −0.0411479 | − | 0.0411479i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.86651 | − | 22.6226i | 0.258509 | − | 0.996869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.23476 | + | 5.23476i | −0.230224 | + | 0.230224i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.477896 | −0.0209773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.34008 | 0.146332 | 0.0731658 | − | 0.997320i | \(-0.476690\pi\) | ||||
0.0731658 | + | 0.997320i | \(0.476690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8561 | − | 24.8561i | 1.08688 | − | 1.08688i | 0.0910337 | − | 0.995848i | \(-0.470983\pi\) |
0.995848 | − | 0.0910337i | \(-0.0290171\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.71070 | − | 3.07661i | 0.0746610 | − | 0.134274i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0897126 | + | 0.0897126i | 0.00390794 | + | 0.00390794i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2031i | 0.965354i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.2776i | 0.532804i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.25269 | − | 3.25269i | −0.140890 | − | 0.140890i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.7491 | − | 10.0485i | −1.67527 | − | 0.434433i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.5445 | + | 11.5445i | −0.498183 | + | 0.498183i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.42930 | 0.363076 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.8547 | 1.15458 | 0.577288 | − | 0.816541i | \(-0.304111\pi\) | ||||
0.577288 | + | 0.816541i | \(0.304111\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.6586 | + | 14.6586i | −0.629063 | + | 0.629063i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8853 | − | 21.9079i | −0.551945 | − | 0.938431i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5864 | − | 28.5864i | −1.22227 | − | 1.22227i | −0.966824 | − | 0.255442i | \(-0.917779\pi\) |
−0.255442 | − | 0.966824i | \(-0.582221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.87187i | 0.293284i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5782i | 0.578453i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.93684 | − | 6.93684i | −0.294985 | − | 0.294985i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.66729 | − | 2.83476i | −0.0707723 | − | 0.120329i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.23619 | + | 2.23619i | −0.0947503 | + | 0.0947503i | −0.752893 | − | 0.658143i | \(-0.771342\pi\) |
0.658143 | + | 0.752893i | \(0.271342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.3224 | 0.563476 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0812204 | 0.00342913 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.69968 | − | 8.69968i | 0.366648 | − | 0.366648i | −0.499605 | − | 0.866253i | \(-0.666522\pi\) |
0.866253 | + | 0.499605i | \(0.166522\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.9636 | − | 7.77020i | −1.26058 | − | 0.326895i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.497835 | + | 0.497835i | 0.0209071 | + | 0.0209071i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.8686i | − | 0.958703i | −0.877623 | − | 0.479351i | \(-0.840872\pi\) | ||
0.877623 | − | 0.479351i | \(-0.159128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.03649i | − | 0.168922i | −0.996427 | − | 0.0844610i | \(-0.973083\pi\) | ||
0.996427 | − | 0.0844610i | \(-0.0269168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.5337 | + | 15.5337i | 0.648931 | + | 0.648931i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.22461 | − | 4.29208i | −0.0510698 | − | 0.178992i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0370 | − | 20.0370i | 0.834153 | − | 0.834153i | −0.153929 | − | 0.988082i | \(-0.549193\pi\) |
0.988082 | + | 0.153929i | \(0.0491928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.12886 | 0.337824 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.27304 | 0.177276 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.722821 | + | 0.722821i | −0.0299362 | + | 0.0299362i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.06638 | + | 7.96841i | −0.0854342 | + | 0.329453i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.2589 | + | 11.2589i | 0.464705 | + | 0.464705i | 0.900194 | − | 0.435489i | \(-0.143425\pi\) |
−0.435489 | + | 0.900194i | \(0.643425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.66817i | 0.109940i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4248i | 0.469954i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.63591 | + | 1.63591i | 0.0671786 | + | 0.0671786i | 0.739898 | − | 0.672719i | \(-0.234874\pi\) |
−0.672719 | + | 0.739898i | \(0.734874\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0850452 | − | 0.0500199i | 0.00348651 | − | 0.00205062i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.62183 | − | 5.62183i | 0.230086 | − | 0.230086i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8538 | −0.729487 | −0.364743 | − | 0.931108i | \(-0.618843\pi\) | ||||
−0.364743 | + | 0.931108i | \(0.618843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.53165 | 0.0624774 | 0.0312387 | − | 0.999512i | \(-0.490055\pi\) | ||||
0.0312387 | + | 0.999512i | \(0.490055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.36291 | + | 9.36291i | −0.381287 | + | 0.381287i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.9644 | − | 10.5659i | 0.730358 | − | 0.429565i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.73762 | + | 9.73762i | 0.395238 | + | 0.395238i | 0.876550 | − | 0.481312i | \(-0.159839\pi\) |
−0.481312 | + | 0.876550i | \(0.659839\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 7.25309i | − | 0.293910i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 21.0301i | − | 0.850786i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9908 | − | 28.9908i | −1.17093 | − | 1.17093i | −0.981989 | − | 0.188938i | \(-0.939495\pi\) |
−0.188938 | − | 0.981989i | \(-0.560505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.701341 | + | 2.70452i | −0.0282808 | + | 0.109057i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7163 | + | 13.7163i | −0.552197 | + | 0.552197i | −0.927075 | − | 0.374877i | \(-0.877685\pi\) |
0.374877 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.99970 | 0.321535 | 0.160768 | − | 0.986992i | \(-0.448603\pi\) | ||||
0.160768 | + | 0.986992i | \(0.448603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.892673 | 0.0358217 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.967757 | − | 0.967757i | 0.0387724 | − | 0.0387724i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.1920 | − | 21.2361i | −0.527680 | − | 0.849443i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.20780 | + | 1.20780i | 0.0482350 | + | 0.0482350i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.0921760i | − | 0.00367530i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 36.4507i | − | 1.45108i | −0.688180 | − | 0.725540i | \(-0.741590\pi\) | ||
0.688180 | − | 0.725540i | \(-0.258410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.5357 | − | 15.5357i | −0.617490 | − | 0.617490i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.9723 | + | 5.43856i | 0.832259 | + | 0.215823i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.9319 | + | 16.9319i | −0.670867 | + | 0.670867i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.62237 | −0.380655 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.24546 | 0.246681 | 0.123340 | − | 0.992364i | \(-0.460639\pi\) | ||||
0.123340 | + | 0.992364i | \(0.460639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.02997 | − | 9.02997i | 0.356107 | − | 0.356107i | −0.506268 | − | 0.862376i | \(-0.668976\pi\) |
0.862376 | + | 0.506268i | \(0.168976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.10232 | − | 6.97487i | −0.161529 | − | 0.274635i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5611 | + | 21.5611i | 0.847654 | + | 0.847654i | 0.989840 | − | 0.142186i | \(-0.0454131\pi\) |
−0.142186 | + | 0.989840i | \(0.545413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.9113i | − | 0.624572i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.42526i | − | 0.0558603i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.2913 | + | 32.2913i | 1.26366 | + | 1.26366i | 0.949308 | + | 0.314347i | \(0.101786\pi\) |
0.314347 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.5129 | − | 19.5745i | −0.449846 | − | 0.764841i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.88834 | − | 2.88834i | 0.112685 | − | 0.112685i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.28376 | 0.283735 | 0.141867 | − | 0.989886i | \(-0.454689\pi\) | ||||
0.141867 | + | 0.989886i | \(0.454689\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.8338 | 1.31598 | 0.657991 | − | 0.753026i | \(-0.271407\pi\) | ||||
0.657991 | + | 0.753026i | \(0.271407\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.163147 | + | 0.163147i | −0.00633611 | + | 0.00633611i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00851 | + | 0.520849i | 0.0778867 | + | 0.0201977i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.50279 | − | 6.50279i | −0.251789 | − | 0.251789i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.56503i | 0.292481i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.90564i | − | 0.343798i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0728 | + | 20.0728i | 0.773750 | + | 0.773750i | 0.978760 | − | 0.205010i | \(-0.0657225\pi\) |
−0.205010 | + | 0.978760i | \(0.565723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.80812 | − | 1.37185i | 0.185065 | − | 0.0528024i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6171 | − | 11.6171i | 0.446483 | − | 0.446483i | −0.447700 | − | 0.894184i | \(-0.647757\pi\) |
0.894184 | + | 0.447700i | \(0.147757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.02165 | −0.115960 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.4872 | 0.823391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.7302 | + | 16.7302i | −0.640162 | + | 0.640162i | −0.950595 | − | 0.310433i | \(-0.899526\pi\) |
0.310433 | + | 0.950595i | \(0.399526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.62276 | + | 21.6826i | −0.214835 | + | 0.828449i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.31569 | − | 5.31569i | −0.202806 | − | 0.202806i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.90385i | − | 0.110628i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3660i | 1.11714i | 0.829459 | + | 0.558568i | \(0.188649\pi\) | ||||
−0.829459 | + | 0.558568i | \(0.811351\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.645172 | − | 0.645172i | −0.0245081 | − | 0.0245081i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.1721 | − | 21.8630i | 1.41002 | − | 0.829312i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0553731 | + | 0.0553731i | −0.00209741 | + | 0.00209741i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4865 | −0.963988 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.17508 | −0.308769 | −0.154384 | − | 0.988011i | \(-0.549339\pi\) | ||||
−0.154384 | + | 0.988011i | \(0.549339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37072 | − | 1.37072i | 0.0516977 | − | 0.0516977i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0102 | + | 6.47573i | −0.414669 | + | 0.243890i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.55665 | − | 6.55665i | −0.246588 | − | 0.246588i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.4019i | − | 0.465762i | −0.972505 | − | 0.232881i | \(-0.925185\pi\) | ||
0.972505 | − | 0.232881i | \(-0.0748153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 13.9340i | − | 0.522566i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.27782 | − | 1.27782i | −0.0478548 | − | 0.0478548i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.67793 | − | 10.3267i | 0.100149 | − | 0.386197i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.5528 | − | 15.5528i | 0.580830 | − | 0.580830i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.5828 | 0.655729 | 0.327865 | − | 0.944725i | \(-0.393671\pi\) | ||||
0.327865 | + | 0.944725i | \(0.393671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.35851 | −0.274045 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.82843 | + | 2.82843i | −0.105190 | + | 0.105190i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −45.0188 | − | 25.0320i | −1.67196 | − | 0.929665i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.46814 | + | 5.46814i | 0.202802 | + | 0.202802i | 0.801199 | − | 0.598397i | \(-0.204196\pi\) |
−0.598397 | + | 0.801199i | \(0.704196\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.226797i | − | 0.00838839i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.3113 | + | 27.3113i | 1.00877 | + | 1.00877i | 0.999961 | + | 0.00880605i | \(0.00280309\pi\) |
0.00880605 | + | 0.999961i | \(0.497197\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.0784 | + | 3.65084i | 0.519291 | + | 0.134663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.1339 | − | 12.1339i | 0.446958 | − | 0.446958i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.1910 | −1.58881 | −0.794404 | − | 0.607390i | \(-0.792216\pi\) | ||||
−0.794404 | + | 0.607390i | \(0.792216\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.85222 | −0.178251 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.43997 | − | 6.43997i | 0.236259 | − | 0.236259i | −0.579040 | − | 0.815299i | \(-0.696572\pi\) |
0.815299 | + | 0.579040i | \(0.196572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.88634 | − | 8.30788i | −0.179022 | − | 0.304377i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.29163 | + | 4.29163i | 0.157022 | + | 0.157022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.6041i | 0.460542i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.9736i | 1.13024i | 0.825008 | + | 0.565120i | \(0.191170\pi\) | ||||
−0.825008 | + | 0.565120i | \(0.808830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.17193 | + | 4.17193i | 0.152034 | + | 0.152034i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.2491 | + | 19.1259i | 0.409395 | + | 0.696064i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.745659 | − | 0.745659i | 0.0271014 | − | 0.0271014i | −0.693426 | − | 0.720528i | \(-0.743900\pi\) |
0.720528 | + | 0.693426i | \(0.243900\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.15686 | −0.0419915 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.8010 | −0.609036 | −0.304518 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304518 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.65864 | + | 5.65864i | −0.204857 | + | 0.204857i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.135652 | + | 0.0351776i | 0.00490453 | + | 0.00127185i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.9609 | + | 31.9609i | 1.15404 | + | 1.15404i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.86682i | 0.0673192i | 0.999433 | + | 0.0336596i | \(0.0107162\pi\) | ||||
−0.999433 | + | 0.0336596i | \(0.989284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 19.9531i | − | 0.718592i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.1527 | − | 27.1527i | −0.976613 | − | 0.976613i | 0.0231192 | − | 0.999733i | \(-0.492640\pi\) |
−0.999733 | + | 0.0231192i | \(0.992640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.84636 | − | 4.91888i | −0.317771 | − | 0.176691i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.732198 | + | 0.732198i | −0.0262674 | + | 0.0262674i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.64687 | −0.0590053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4702 | 0.446217 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.28463 | − | 7.28463i | 0.260332 | − | 0.260332i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.44049 | + | 24.8359i | −0.229871 | + | 0.886433i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6728 | − | 17.6728i | −0.629968 | − | 0.629968i | 0.318092 | − | 0.948060i | \(-0.396958\pi\) |
−0.948060 | + | 0.318092i | \(0.896958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 0.165801i | − | 0.00590268i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.74636i | 0.346541i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8887 | + | 17.8887i | 0.635247 | + | 0.635247i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.52030 | + | 0.894176i | −0.0539195 | + | 0.0317132i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.2811 | + | 13.2811i | −0.470441 | + | 0.470441i | −0.902057 | − | 0.431616i | \(-0.857943\pi\) |
0.431616 | + | 0.902057i | \(0.357943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.358012 | −0.0126655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.94393 | 0.0686854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.74316 | + | 3.74316i | −0.132093 | + | 0.132093i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.21134 | + | 0.712460i | −0.0426942 | + | 0.0251109i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.2874 | + | 14.2874i | 0.502940 | + | 0.502940i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.1968i | − | 1.27261i | −0.771437 | − | 0.636305i | \(-0.780462\pi\) | ||
0.771437 | − | 0.636305i | \(-0.219538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7922i | 0.624769i | 0.949956 | + | 0.312385i | \(0.101128\pi\) | ||||
−0.949956 | + | 0.312385i | \(0.898872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.85225 | − | 5.85225i | −0.205247 | − | 0.205247i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.96910 | + | 38.4430i | −0.349202 | + | 1.34660i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.37263 | − | 3.37263i | 0.117993 | − | 0.117993i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.59191 | 0.0905686 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.81859 | 0.0983693 | 0.0491847 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491847 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.3448 | − | 29.3448i | 1.02290 | − | 1.02290i | 0.0231652 | − | 0.999732i | \(-0.492626\pi\) |
0.999732 | − | 0.0231652i | \(-0.00737438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.23111 | + | 1.77785i | −0.216939 | + | 0.0618968i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.5161 | − | 34.5161i | −1.20024 | − | 1.20024i | −0.974093 | − | 0.226150i | \(-0.927386\pi\) |
−0.226150 | − | 0.974093i | \(-0.572614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.5050i | − | 1.51099i | −0.655153 | − | 0.755496i | \(-0.727396\pi\) | ||
0.655153 | − | 0.755496i | \(-0.272604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.6262i | − | 0.646135i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.288245 | + | 0.288245i | 0.00998711 | + | 0.00998711i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6625 | − | 5.87688i | −0.784270 | − | 0.203378i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.43146 | − | 1.43146i | 0.0494784 | − | 0.0494784i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.7040 | 0.921924 | 0.460962 | − | 0.887420i | \(-0.347504\pi\) | ||||
0.460962 | + | 0.887420i | \(0.347504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.1317 | −2.65972 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.229165 | − | 0.229165i | 0.00789286 | − | 0.00789286i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.626996 | + | 1.06604i | 0.0215693 | + | 0.0366727i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.64007 | − | 4.64007i | −0.159435 | − | 0.159435i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.9777i | 0.788593i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31291i | 0.0450060i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.0644 | − | 39.0644i | −1.33754 | − | 1.33754i | −0.898438 | − | 0.439101i | \(-0.855297\pi\) |
−0.439101 | − | 0.898438i | \(-0.644703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.49413 | + | 2.54036i | 0.0510981 | + | 0.0868784i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.48615 | + | 2.48615i | −0.0849253 | + | 0.0849253i | −0.748293 | − | 0.663368i | \(-0.769126\pi\) |
0.663368 | + | 0.748293i | \(0.269126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.23229 | 0.178524 | 0.0892618 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892618 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.879709 | 0.0299804 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.69832 | − | 3.69832i | 0.125892 | − | 0.125892i | −0.641353 | − | 0.767246i | \(-0.721627\pi\) |
0.767246 | + | 0.641353i | \(0.221627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.03439 | + | 0.268240i | 0.0351704 | + | 0.00912044i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0180 | − | 12.0180i | −0.408154 | − | 0.408154i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0579i | 0.612571i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.7467i | 1.65172i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.03479 | − | 3.03479i | −0.102712 | − | 0.102712i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.42965 | + | 5.69903i | −0.183556 | + | 0.192662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.11469 | − | 6.11469i | 0.206478 | − | 0.206478i | −0.596290 | − | 0.802769i | \(-0.703359\pi\) |
0.802769 | + | 0.596290i | \(0.203359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0395 | −0.810834 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.1700 | 1.69027 | 0.845135 | − | 0.534553i | \(-0.179520\pi\) | ||||
0.845135 | + | 0.534553i | \(0.179520\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9781 | + | 15.9781i | −0.537707 | + | 0.537707i | −0.922855 | − | 0.385148i | \(-0.874150\pi\) |
0.385148 | + | 0.922855i | \(0.374150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.89137 | − | 26.5746i | 0.231651 | − | 0.893297i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.977167 | + | 0.977167i | 0.0328100 | + | 0.0328100i | 0.723321 | − | 0.690511i | \(-0.242614\pi\) |
−0.690511 | + | 0.723321i | \(0.742614\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.82172i | − | 0.228793i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.29595i | − | 0.0434161i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.32387 | − | 5.32387i | −0.178157 | − | 0.178157i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.4677 | − | 18.5079i | 1.05185 | − | 0.618652i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.32379 | − | 2.32379i | 0.0775890 | − | 0.0775890i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.8553 | −0.695563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0494346 | −0.00164691 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.80156 | + | 1.80156i | −0.0599520 | + | 0.0599520i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.9561 | − | 23.5005i | 1.32819 | − | 0.781181i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4983 | + | 15.4983i | 0.514612 | + | 0.514612i | 0.915936 | − | 0.401324i | \(-0.131450\pi\) |
−0.401324 | + | 0.915936i | \(0.631450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 13.1703i | − | 0.436832i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.09146i | − | 0.168688i | −0.996437 | − | 0.0843438i | \(-0.973121\pi\) | ||
0.996437 | − | 0.0843438i | \(-0.0268794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.56175 | − | 5.56175i | −0.184067 | − | 0.184067i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.85714 | − | 14.8740i | 0.127513 | − | 0.491719i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.05596 | + | 5.05596i | −0.166962 | + | 0.166962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.20340 | 0.171644 | 0.0858221 | − | 0.996310i | \(-0.472648\pi\) | ||||
0.0858221 | + | 0.996310i | \(0.472648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.9674 | −0.427291 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0488 | + | 25.0488i | −0.824490 | + | 0.824490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.01766 | + | 7.07161i | 0.0663403 | + | 0.232513i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.39051 | − | 7.39051i | −0.242736 | − | 0.242736i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 31.5196i | − | 1.03413i | −0.855947 | − | 0.517063i | \(-0.827025\pi\) | ||
0.855947 | − | 0.517063i | \(-0.172975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.57280i | 0.280962i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.06647 | + | 8.06647i | 0.264084 | + | 0.264084i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.175799 | − | 0.0455885i | −0.00574926 | − | 0.00149090i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8065 | + | 21.8065i | −0.712387 | + | 0.712387i | −0.967034 | − | 0.254647i | \(-0.918041\pi\) |
0.254647 | + | 0.967034i | \(0.418041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.2463 | −0.921782 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.8633 | −0.614925 | −0.307463 | − | 0.951560i | \(-0.599480\pi\) | ||||
−0.307463 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.788707 | − | 0.788707i | 0.0256838 | − | 0.0256838i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.798119 | − | 1.35698i | −0.0259628 | − | 0.0441427i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.9995 | + | 35.9995i | 1.16983 | + | 1.16983i | 0.982250 | + | 0.187577i | \(0.0600635\pi\) |
0.187577 | + | 0.982250i | \(0.439936\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.0378i | − | 0.488146i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 15.7226i | − | 0.509841i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.8455 | − | 26.8455i | −0.869609 | − | 0.869609i | 0.122820 | − | 0.992429i | \(-0.460806\pi\) |
−0.992429 | + | 0.122820i | \(0.960806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.9034 | − | 42.3414i | −0.805854 | − | 1.37013i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.44055 | + | 9.44055i | −0.305170 | + | 0.305170i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.05276 | 0.227746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.9019 | 0.867802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6589 | + | 12.6589i | −0.407926 | + | 0.407926i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.5947 | − | 4.56268i | −0.566394 | − | 0.146878i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.09081 | − | 9.09081i | −0.292341 | − | 0.292341i | 0.545664 | − | 0.838004i | \(-0.316278\pi\) |
−0.838004 | + | 0.545664i | \(0.816278\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0826031i | 0.00265359i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.336247i | 0.0107907i | 0.999985 | + | 0.00539534i | \(0.00171740\pi\) | ||||
−0.999985 | + | 0.00539534i | \(0.998283\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.60127 | − | 9.60127i | −0.307803 | − | 0.307803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.94524 | − | 16.0876i | 0.286477 | − | 0.515215i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.3570 | − | 14.3570i | 0.459322 | − | 0.459322i | −0.439111 | − | 0.898433i | \(-0.644706\pi\) |
0.898433 | + | 0.439111i | \(0.144706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.51925 | −0.0805154 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3665 | −0.362904 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.3583 | + | 33.3583i | −1.06396 | + | 1.06396i | −0.0661546 | + | 0.997809i | \(0.521073\pi\) |
−0.997809 | + | 0.0661546i | \(0.978927\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.41268 | − | 24.7287i | 0.204325 | − | 0.787922i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.84385 | + | 2.84385i | 0.0905209 | + | 0.0905209i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.23039i | 0.102720i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9160i | 0.569119i | 0.958658 | + | 0.284560i | \(0.0918474\pi\) | ||||
−0.958658 | + | 0.284560i | \(0.908153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.8867 | − | 17.8867i | −0.567618 | − | 0.567618i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.3238 | + | 9.01280i | −0.485797 | + | 0.285725i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7719 | − | 36.7719i | 1.16458 | − | 1.16458i | 0.181116 | − | 0.983462i | \(-0.442029\pi\) |
0.983462 | − | 0.181116i | \(-0.0579708\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.47076 | −0.0465329 |
(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 | 1920.2.w.i.1663.3 | yes | 12 | |
4.3 | odd | 2 | 1920.2.w.j.1663.6 | yes | 12 | ||
5.2 | odd | 4 | 1920.2.w.j.127.6 | yes | 12 | ||
8.3 | odd | 2 | 1920.2.w.l.1663.1 | yes | 12 | ||
8.5 | even | 2 | 1920.2.w.k.1663.4 | yes | 12 | ||
20.7 | even | 4 | inner | 1920.2.w.i.127.3 | ✓ | 12 | |
40.27 | even | 4 | 1920.2.w.k.127.4 | yes | 12 | ||
40.37 | odd | 4 | 1920.2.w.l.127.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1920.2.w.i.127.3 | ✓ | 12 | 20.7 | even | 4 | inner | |
1920.2.w.i.1663.3 | yes | 12 | 1.1 | even | 1 | trivial | |
1920.2.w.j.127.6 | yes | 12 | 5.2 | odd | 4 | ||
1920.2.w.j.1663.6 | yes | 12 | 4.3 | odd | 2 | ||
1920.2.w.k.127.4 | yes | 12 | 40.27 | even | 4 | ||
1920.2.w.k.1663.4 | yes | 12 | 8.5 | even | 2 | ||
1920.2.w.l.127.1 | yes | 12 | 40.37 | odd | 4 | ||
1920.2.w.l.1663.1 | yes | 12 | 8.3 | odd | 2 |