Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(113,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.113");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.15533688251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.65856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 14x^{2} + 21 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(1.30710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.113 |
Dual form | 336.3.d.c.113.3 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.82288 | + | 2.38267i | 0.607625 | + | 0.794224i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.37953i | 1.47591i | 0.674852 | + | 0.737953i | \(0.264208\pi\) | ||||
−0.674852 | + | 0.737953i | \(0.735792\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.35425 | + | 8.68663i | −0.261583 | + | 0.965181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.61419i | 0.237654i | 0.992915 | + | 0.118827i | \(0.0379133\pi\) | ||||
−0.992915 | + | 0.118827i | \(0.962087\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.35425 | −0.488788 | −0.244394 | − | 0.969676i | \(-0.578589\pi\) | ||||
−0.244394 | + | 0.969676i | \(0.578589\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −17.5830 | + | 13.4520i | −1.17220 | + | 0.896798i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 12.1449i | − | 0.714405i | −0.934027 | − | 0.357202i | \(-0.883731\pi\) | ||
0.934027 | − | 0.357202i | \(-0.116269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.2288 | 0.538356 | 0.269178 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269178 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82288 | + | 6.30396i | 0.229661 | + | 0.300188i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.30231i | − | 0.187057i | −0.995617 | − | 0.0935284i | \(-0.970185\pi\) | ||
0.995617 | − | 0.0935284i | \(-0.0298146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −29.4575 | −1.17830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −24.9889 | + | 10.2252i | −0.925514 | + | 0.378713i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.3733i | 0.599078i | 0.954084 | + | 0.299539i | \(0.0968328\pi\) | ||||
−0.954084 | + | 0.299539i | \(0.903167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.2915 | −1.26747 | −0.633734 | − | 0.773551i | \(-0.718479\pi\) | ||||
−0.633734 | + | 0.773551i | \(0.718479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.22876 | + | 4.76534i | −0.188750 | + | 0.144404i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.5244i | 0.557840i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.0405 | 1.10920 | 0.554602 | − | 0.832116i | \(-0.312871\pi\) | ||||
0.554602 | + | 0.832116i | \(0.312871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.5830 | − | 15.1401i | −0.297000 | − | 0.388207i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 30.2802i | − | 0.738541i | −0.929322 | − | 0.369270i | \(-0.879608\pi\) | ||
0.929322 | − | 0.369270i | \(-0.120392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 55.8745 | 1.29941 | 0.649704 | − | 0.760188i | \(-0.274893\pi\) | ||||
0.649704 | + | 0.760188i | \(0.274893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −64.1033 | − | 17.3733i | −1.42452 | − | 0.386072i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.9749i | 0.850530i | 0.905069 | + | 0.425265i | \(0.139819\pi\) | ||||
−0.905069 | + | 0.425265i | \(0.860181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.9373 | − | 22.1386i | 0.567397 | − | 0.434090i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 105.002i | 1.98116i | 0.136928 | + | 0.990581i | \(0.456277\pi\) | ||||
−0.136928 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.2915 | −0.350755 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.6458 | + | 24.3718i | 0.327118 | + | 0.427575i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 41.3640i | − | 0.701085i | −0.936547 | − | 0.350542i | \(-0.885997\pi\) | ||
0.936547 | − | 0.350542i | \(-0.114003\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.4797 | −0.335733 | −0.167867 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167867 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.22876 | + | 22.9827i | −0.0988692 | + | 0.364804i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 46.8914i | − | 0.721406i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 27.1660 | 0.405463 | 0.202731 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.2510 | − | 7.84257i | 0.148565 | − | 0.113660i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 67.8049i | 0.954999i | 0.878632 | + | 0.477499i | \(0.158457\pi\) | ||||
−0.878632 | + | 0.477499i | \(0.841543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60.7895 | 0.832733 | 0.416367 | − | 0.909197i | \(-0.363303\pi\) | ||||
0.416367 | + | 0.909197i | \(0.363303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −53.6974 | − | 70.1876i | −0.715965 | − | 0.935834i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.91650i | 0.0898246i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.2470 | 0.800596 | 0.400298 | − | 0.916385i | \(-0.368907\pi\) | ||||
0.400298 | + | 0.916385i | \(0.368907\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −69.9150 | − | 40.9010i | −0.863148 | − | 0.504950i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 89.9435i | − | 1.08366i | −0.840489 | − | 0.541828i | \(-0.817732\pi\) | ||
0.840489 | − | 0.541828i | \(-0.182268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 89.6235 | 1.05439 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −41.3948 | + | 31.6693i | −0.475802 | + | 0.364015i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 63.1745i | 0.709826i | 0.934899 | + | 0.354913i | \(0.115490\pi\) | ||||
−0.934899 | + | 0.354913i | \(0.884510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.8118 | −0.184745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −71.6235 | − | 93.6188i | −0.770145 | − | 1.00665i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 75.4835i | 0.794563i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.1660 | 0.197588 | 0.0987939 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987939 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.7085 | − | 6.15445i | −0.229379 | − | 0.0621662i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 98.7122i | − | 0.977348i | −0.872466 | − | 0.488674i | \(-0.837481\pi\) | ||
0.872466 | − | 0.488674i | \(-0.162519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.2510 | 0.546126 | 0.273063 | − | 0.961996i | \(-0.411963\pi\) | ||||
0.273063 | + | 0.961996i | \(0.411963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46.5203 | + | 35.5906i | −0.443050 | + | 0.338958i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 123.137i | − | 1.15081i | −0.817868 | − | 0.575406i | \(-0.804844\pi\) | ||
0.817868 | − | 0.575406i | \(-0.195156\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 164.539 | 1.50953 | 0.754764 | − | 0.655996i | \(-0.227751\pi\) | ||||
0.754764 | + | 0.655996i | \(0.227751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 74.8118 | + | 97.7861i | 0.673980 | + | 0.880956i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 144.050i | − | 1.27478i | −0.770540 | − | 0.637391i | \(-0.780014\pi\) | ||
0.770540 | − | 0.637391i | \(-0.219986\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.7490 | 0.276078 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.9595 | − | 55.1970i | 0.127859 | − | 0.471769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 32.1323i | − | 0.270020i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.166 | 0.943521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 72.1477 | − | 55.1970i | 0.586567 | − | 0.448756i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 32.8944i | − | 0.263155i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.5830 | 0.288055 | 0.144028 | − | 0.989574i | \(-0.453995\pi\) | ||||
0.144028 | + | 0.989574i | \(0.453995\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 101.852 | + | 133.131i | 0.789553 | + | 1.03202i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 33.6855i | − | 0.257141i | −0.991700 | − | 0.128570i | \(-0.958961\pi\) | ||
0.991700 | − | 0.128570i | \(-0.0410389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.0627 | 0.203479 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −75.4575 | − | 184.406i | −0.558945 | − | 1.36597i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 39.9749i | 0.291788i | 0.989300 | + | 0.145894i | \(0.0466058\pi\) | ||||
−0.989300 | + | 0.145894i | \(0.953394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 194.642 | 1.40030 | 0.700150 | − | 0.713995i | \(-0.253116\pi\) | ||||
0.700150 | + | 0.713995i | \(0.253116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −95.2470 | + | 72.8693i | −0.675511 | + | 0.516803i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 16.6112i | − | 0.116162i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −128.207 | −0.884183 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7601 | + | 16.6787i | 0.0868036 | + | 0.113461i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 203.685i | − | 1.36701i | −0.729945 | − | 0.683506i | \(-0.760454\pi\) | ||
0.729945 | − | 0.683506i | \(-0.239546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −165.749 | −1.09768 | −0.548838 | − | 0.835929i | \(-0.684930\pi\) | ||||
−0.548838 | + | 0.835929i | \(0.684930\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 105.498 | + | 28.5921i | 0.689530 | + | 0.186876i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 289.953i | − | 1.87066i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −302.723 | −1.92817 | −0.964086 | − | 0.265592i | \(-0.914433\pi\) | ||||
−0.964086 | + | 0.265592i | \(0.914433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −250.184 | + | 191.405i | −1.57349 | + | 1.20380i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.3828i | − | 0.0707008i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 145.041 | 0.889819 | 0.444910 | − | 0.895576i | \(-0.353236\pi\) | ||||
0.444910 | + | 0.895576i | \(0.353236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −35.1660 | − | 45.9653i | −0.213127 | − | 0.278578i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.6594i | − | 0.117721i | −0.998266 | − | 0.0588604i | \(-0.981253\pi\) | ||
0.998266 | − | 0.0588604i | \(-0.0187467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −128.624 | −0.761086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.0810 | + | 88.8534i | −0.140825 | + | 0.519611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.6884i | 0.113806i | 0.998380 | + | 0.0569030i | \(0.0181226\pi\) | ||||
−0.998380 | + | 0.0569030i | \(0.981877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −77.9373 | −0.445356 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 98.5568 | − | 75.4014i | 0.556818 | − | 0.425997i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 341.745i | 1.90919i | 0.297910 | + | 0.954594i | \(0.403711\pi\) | ||||
−0.297910 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 215.889 | 1.19276 | 0.596378 | − | 0.802704i | \(-0.296606\pi\) | ||||
0.596378 | + | 0.802704i | \(0.296606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −37.3320 | − | 48.7965i | −0.204000 | − | 0.266648i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 302.860i | 1.63708i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.7490 | 0.169781 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −66.1144 | + | 27.0534i | −0.349812 | + | 0.143140i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 44.7112i | − | 0.234090i | −0.993127 | − | 0.117045i | \(-0.962658\pi\) | ||
0.993127 | − | 0.117045i | \(-0.0373422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −145.122 | −0.751925 | −0.375963 | − | 0.926635i | \(-0.622688\pi\) | ||||
−0.375963 | + | 0.926635i | \(0.622688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 111.727 | − | 85.4772i | 0.572958 | − | 0.438344i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 87.4643i | 0.443981i | 0.975049 | + | 0.221991i | \(0.0712554\pi\) | ||||
−0.975049 | + | 0.221991i | \(0.928745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −65.4170 | −0.328729 | −0.164364 | − | 0.986400i | \(-0.552557\pi\) | ||||
−0.164364 | + | 0.986400i | \(0.552557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.5203 | + | 64.7277i | 0.246369 | + | 0.322028i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 45.9653i | 0.226430i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 223.454 | 1.09002 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37.3725 | + | 10.1287i | 0.180544 | + | 0.0489309i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.7399i | 0.127942i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −40.5830 | −0.192337 | −0.0961683 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961683 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −161.557 | + | 123.600i | −0.758483 | + | 0.580281i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 412.328i | 1.91780i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −103.956 | −0.479058 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 110.812 | + | 144.842i | 0.505990 | + | 0.661377i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 77.1716i | 0.349193i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −100.959 | −0.452733 | −0.226367 | − | 0.974042i | \(-0.572685\pi\) | ||||
−0.226367 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 69.3503 | − | 255.886i | 0.308224 | − | 1.13727i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 391.279i | 1.72370i | 0.507166 | + | 0.861849i | \(0.330693\pi\) | ||||
−0.507166 | + | 0.861849i | \(0.669307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.81176 | −0.0297457 | −0.0148728 | − | 0.999889i | \(-0.504734\pi\) | ||||
−0.0148728 | + | 0.999889i | \(0.504734\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.4797 | + | 12.6079i | −0.0713409 | + | 0.0545797i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 116.877i | 0.501616i | 0.968037 | + | 0.250808i | \(0.0806963\pi\) | ||||
−0.968037 | + | 0.250808i | \(0.919304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −294.996 | −1.25530 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 115.292 | + | 150.697i | 0.486462 | + | 0.635852i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 59.9623i | 0.250888i | 0.992101 | + | 0.125444i | \(0.0400356\pi\) | ||||
−0.992101 | + | 0.125444i | \(0.959964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.753 | 0.559141 | 0.279570 | − | 0.960125i | \(-0.409808\pi\) | ||||
0.279570 | + | 0.960125i | \(0.409808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29.9928 | − | 241.142i | −0.123427 | − | 0.992354i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 51.6567i | 0.210844i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −64.9961 | −0.263142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 214.306 | − | 163.956i | 0.860666 | − | 0.658457i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 268.248i | − | 1.06872i | −0.845257 | − | 0.534359i | \(-0.820553\pi\) | ||
0.845257 | − | 0.534359i | \(-0.179447\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2470 | 0.0444547 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 163.373 | + | 213.543i | 0.640677 | + | 0.837425i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 234.129i | 0.911007i | 0.890234 | + | 0.455504i | \(0.150541\pi\) | ||||
−0.890234 | + | 0.455504i | \(0.849459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108.583 | 0.419239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −150.915 | − | 40.9010i | −0.578218 | − | 0.156709i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 250.142i | − | 0.951111i | −0.879686 | − | 0.475555i | \(-0.842247\pi\) | ||
0.879686 | − | 0.475555i | \(-0.157753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −774.863 | −2.92401 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −150.524 | + | 115.159i | −0.563761 | + | 0.431308i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 340.684i | 1.26648i | 0.773955 | + | 0.633241i | \(0.218276\pi\) | ||||
−0.773955 | + | 0.633241i | \(0.781724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2994 | 0.0785955 | 0.0392977 | − | 0.999228i | \(-0.487488\pi\) | ||||
0.0392977 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.6458 | − | 40.0569i | −0.112255 | − | 0.146729i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 77.0075i | − | 0.280027i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −226.915 | −0.819188 | −0.409594 | − | 0.912268i | \(-0.634330\pi\) | ||||
−0.409594 | + | 0.912268i | \(0.634330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 92.5020 | − | 341.311i | 0.331548 | − | 1.22334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 235.489i | − | 0.838039i | −0.907977 | − | 0.419019i | \(-0.862374\pi\) | ||
0.907977 | − | 0.419019i | \(-0.137626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −368.634 | −1.30259 | −0.651297 | − | 0.758823i | \(-0.725775\pi\) | ||||
−0.651297 | + | 0.758823i | \(0.725775\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −179.852 | + | 137.597i | −0.631061 | + | 0.482796i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 80.1138i | − | 0.279142i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 141.502 | 0.489626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.9373 | + | 45.6663i | 0.120059 | + | 0.156929i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 531.625i | − | 1.81442i | −0.420677 | − | 0.907211i | \(-0.638207\pi\) | ||
0.420677 | − | 0.907211i | \(-0.361793\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 305.247 | 1.03474 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.7307 | − | 65.3257i | −0.0900024 | − | 0.219952i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.3379i | 0.0914312i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 147.830 | 0.491130 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 235.199 | − | 179.940i | 0.776233 | − | 0.593861i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 151.131i | − | 0.495511i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −567.763 | −1.84939 | −0.924696 | − | 0.380706i | \(-0.875681\pi\) | ||||
−0.924696 | + | 0.380706i | \(0.875681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 102.539 | + | 134.028i | 0.331840 | + | 0.433746i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 42.7531i | − | 0.137470i | −0.997635 | − | 0.0687349i | \(-0.978104\pi\) | ||
0.997635 | − | 0.0687349i | \(-0.0218963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.118 | −0.505168 | −0.252584 | − | 0.967575i | \(-0.581280\pi\) | ||||
−0.252584 | + | 0.967575i | \(0.581280\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −169.601 | − | 45.9653i | −0.538417 | − | 0.145922i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 140.944i | − | 0.444619i | −0.974976 | − | 0.222309i | \(-0.928641\pi\) | ||
0.974976 | − | 0.222309i | \(-0.0713595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.4170 | −0.142373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 293.395 | − | 224.463i | 0.914002 | − | 0.699262i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 124.227i | − | 0.384604i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 187.180 | 0.575940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 299.933 | + | 392.041i | 0.917227 | + | 1.19890i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 105.764i | 0.321470i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 258.369 | 0.780570 | 0.390285 | − | 0.920694i | \(-0.372377\pi\) | ||||
0.390285 | + | 0.920694i | \(0.372377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −96.6196 | + | 356.504i | −0.290149 | + | 1.07058i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 200.472i | 0.598425i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 328.959 | 0.976141 | 0.488070 | − | 0.872804i | \(-0.337701\pi\) | ||||
0.488070 | + | 0.872804i | \(0.337701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 343.225 | − | 262.586i | 1.01246 | − | 0.774590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 102.715i | − | 0.301218i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 57.8745 | + | 75.6475i | 0.167752 | + | 0.219268i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 128.635i | − | 0.370707i | −0.982672 | − | 0.185353i | \(-0.940657\pi\) | ||
0.982672 | − | 0.185353i | \(-0.0593430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −73.4837 | −0.210555 | −0.105277 | − | 0.994443i | \(-0.533573\pi\) | ||||
−0.105277 | + | 0.994443i | \(0.533573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 158.786 | − | 64.9737i | 0.452381 | − | 0.185110i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 239.685i | − | 0.678995i | −0.940607 | − | 0.339498i | \(-0.889743\pi\) | ||
0.940607 | − | 0.339498i | \(-0.110257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −500.369 | −1.40949 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 76.5608 | − | 58.5732i | 0.214456 | − | 0.164071i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 180.215i | − | 0.501992i | −0.967988 | − | 0.250996i | \(-0.919242\pi\) | ||
0.967988 | − | 0.250996i | \(-0.0807581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −256.373 | −0.710173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 208.110 | + | 272.020i | 0.573307 | + | 0.749367i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 448.598i | 1.22904i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −229.786 | −0.626119 | −0.313059 | − | 0.949734i | \(-0.601354\pi\) | ||||
−0.313059 | + | 0.949734i | \(0.601354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 263.033 | + | 71.2871i | 0.712826 | + | 0.193190i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 277.808i | 0.748809i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 441.749 | 1.18431 | 0.592157 | − | 0.805823i | \(-0.298277\pi\) | ||||
0.592157 | + | 0.805823i | \(0.298277\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 78.3765 | − | 59.9623i | 0.209004 | − | 0.159900i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 110.394i | − | 0.292822i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 421.203 | 1.11135 | 0.555676 | − | 0.831399i | \(-0.312459\pi\) | ||||
0.555676 | + | 0.831399i | \(0.312459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.6863 | + | 87.1653i | 0.175030 | + | 0.228780i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 595.591i | − | 1.55507i | −0.628841 | − | 0.777534i | \(-0.716470\pi\) | ||
0.628841 | − | 0.777534i | \(-0.283530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −51.0405 | −0.132573 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −131.542 | + | 485.361i | −0.339903 | + | 1.25416i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 367.347i | − | 0.944336i | −0.881509 | − | 0.472168i | \(-0.843472\pi\) | ||
0.881509 | − | 0.472168i | \(-0.156528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.2510 | −0.133634 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 80.2614 | − | 61.4044i | 0.204227 | − | 0.156245i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 466.734i | 1.18160i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 408.346 | 1.02858 | 0.514290 | − | 0.857616i | \(-0.328055\pi\) | ||||
0.514290 | + | 0.857616i | \(0.328055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 49.3320 | + | 64.4816i | 0.123639 | + | 0.161608i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 238.817i | − | 0.595555i | −0.954635 | − | 0.297777i | \(-0.903755\pi\) | ||
0.954635 | − | 0.297777i | \(-0.0962453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 249.668 | 0.619524 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 301.830 | − | 515.940i | 0.745259 | − | 1.27393i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 107.288i | 0.263606i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −649.365 | −1.58769 | −0.793844 | − | 0.608121i | \(-0.791924\pi\) | ||||
−0.793844 | + | 0.608121i | \(0.791924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −95.2470 | + | 72.8693i | −0.231745 | + | 0.177297i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 109.439i | − | 0.264985i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 663.741 | 1.59938 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 354.808 | + | 463.768i | 0.850858 | + | 1.11215i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5178i | 0.0274888i | 0.999906 | + | 0.0137444i | \(0.00437512\pi\) | ||||
−0.999906 | + | 0.0137444i | \(0.995625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.9921 | −0.199506 | −0.0997531 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997531 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −347.247 | − | 94.1108i | −0.820915 | − | 0.222484i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 357.758i | 0.841783i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.1843 | −0.126895 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 39.5791 | − | 30.2802i | 0.0922589 | − | 0.0705832i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 694.004i | − | 1.61022i | −0.593127 | − | 0.805109i | \(-0.702107\pi\) | ||
0.593127 | − | 0.805109i | \(-0.297893\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 116.834 | 0.269824 | 0.134912 | − | 0.990858i | \(-0.456925\pi\) | ||||
0.134912 | + | 0.990858i | \(0.456925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −233.705 | − | 305.474i | −0.537252 | − | 0.702239i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 44.0072i | − | 0.100703i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 528.073 | 1.20290 | 0.601450 | − | 0.798910i | \(-0.294590\pi\) | ||||
0.601450 | + | 0.798910i | \(0.294590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.4797 | + | 60.8064i | −0.0373690 | + | 0.137883i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 272.252i | − | 0.614564i | −0.951619 | − | 0.307282i | \(-0.900581\pi\) | ||
0.951619 | − | 0.307282i | \(-0.0994194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −466.199 | −1.04764 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 485.314 | − | 371.292i | 1.08571 | − | 0.830631i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 525.770i | − | 1.17098i | −0.810680 | − | 0.585490i | \(-0.800902\pi\) | ||
0.810680 | − | 0.585490i | \(-0.199098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 79.1581 | 0.175517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −302.140 | − | 394.925i | −0.666975 | − | 0.871800i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 124.063i | − | 0.272666i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −513.786 | −1.12426 | −0.562129 | − | 0.827050i | \(-0.690017\pi\) | ||||
−0.562129 | + | 0.827050i | \(0.690017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 124.184 | + | 303.487i | 0.270554 | + | 0.661192i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 687.879i | 1.49214i | 0.665865 | + | 0.746072i | \(0.268063\pi\) | ||||
−0.665865 | + | 0.746072i | \(0.731937\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −781.061 | −1.68696 | −0.843479 | − | 0.537162i | \(-0.819496\pi\) | ||||
−0.843479 | + | 0.537162i | \(0.819496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 690.863 | − | 528.548i | 1.48573 | − | 1.13666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 163.353i | − | 0.349792i | −0.984587 | − | 0.174896i | \(-0.944041\pi\) | ||
0.984587 | − | 0.174896i | \(-0.0559589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 71.8745 | 0.153251 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −551.826 | − | 721.289i | −1.17161 | − | 1.53140i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 146.067i | 0.308809i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −301.314 | −0.634345 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −912.110 | − | 247.200i | −1.91218 | − | 0.518239i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 700.159i | − | 1.46171i | −0.682533 | − | 0.730855i | \(-0.739122\pi\) | ||
0.682533 | − | 0.730855i | \(-0.260878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −260.782 | −0.542166 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.1216 | − | 20.7495i | 0.0561523 | − | 0.0429596i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 141.436i | 0.291621i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −86.5909 | −0.177805 | −0.0889023 | − | 0.996040i | \(-0.528336\pi\) | ||||
−0.0889023 | + | 0.996040i | \(0.528336\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 264.391 | + | 345.584i | 0.540677 | + | 0.706716i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 741.494i | 1.51017i | 0.655627 | + | 0.755085i | \(0.272404\pi\) | ||||
−0.655627 | + | 0.755085i | \(0.727596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 210.996 | 0.427984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.4170 | − | 167.578i | 0.0917515 | − | 0.338542i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 179.395i | 0.360956i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −379.814 | −0.761151 | −0.380575 | − | 0.924750i | \(-0.624274\pi\) | ||||
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.8419 | − | 35.8366i | 0.0934967 | − | 0.0715302i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 465.808i | 0.926059i | 0.886343 | + | 0.463029i | \(0.153238\pi\) | ||||
−0.886343 | + | 0.463029i | \(0.846762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 728.450 | 1.44247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −234.465 | − | 306.468i | −0.462455 | − | 0.604473i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 750.503i | − | 1.47447i | −0.675639 | − | 0.737233i | \(-0.736132\pi\) | ||
0.675639 | − | 0.737233i | \(-0.263868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 160.834 | 0.314744 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −255.605 | + | 104.592i | −0.498256 | + | 0.203882i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 415.106i | 0.806031i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −104.502 | −0.202131 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.9111 | + | 35.8896i | −0.0903875 | + | 0.0691514i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 726.946i | − | 1.39529i | −0.716443 | − | 0.697645i | \(-0.754231\pi\) | ||
0.716443 | − | 0.697645i | \(-0.245769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 624.707 | 1.19447 | 0.597234 | − | 0.802067i | \(-0.296266\pi\) | ||||
0.597234 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −142.070 | − | 185.699i | −0.270609 | − | 0.353712i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 477.190i | 0.905485i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 510.490 | 0.965010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 359.314 | + | 97.3812i | 0.676674 | + | 0.183392i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 192.408i | 0.360990i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 908.693 | 1.69849 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −814.265 | + | 622.958i | −1.51632 | + | 1.16007i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.2993i | 0.0339505i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −291.757 | −0.539292 | −0.269646 | − | 0.962960i | \(-0.586907\pi\) | ||||
−0.269646 | + | 0.962960i | \(0.586907\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 393.539 | + | 514.392i | 0.724749 | + | 0.947315i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1214.22i | 2.22792i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −204.952 | −0.374683 | −0.187342 | − | 0.982295i | \(-0.559987\pi\) | ||||
−0.187342 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 48.2144 | − | 177.900i | 0.0878222 | − | 0.324044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 177.707i | 0.322517i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 167.336 | 0.302597 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −721.616 | + | 552.076i | −1.30021 | + | 0.994731i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 503.883i | 0.904637i | 0.891857 | + | 0.452318i | \(0.149403\pi\) | ||||
−0.891857 | + | 0.452318i | \(0.850597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −355.041 | −0.635135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.8745 | + | 75.6475i | 0.103163 | + | 0.134844i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 108.735i | 0.193135i | 0.995326 | + | 0.0965674i | \(0.0307863\pi\) | ||||
−0.995326 | + | 0.0965674i | \(0.969214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1063.02 | 1.88146 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −184.978 | − | 108.214i | −0.326239 | − | 0.190853i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 434.871i | 0.764273i | 0.924106 | + | 0.382136i | \(0.124812\pi\) | ||||
−0.924106 | + | 0.382136i | \(0.875188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −119.122 | −0.208619 | −0.104310 | − | 0.994545i | \(-0.533263\pi\) | ||||
−0.104310 | + | 0.994545i | \(0.533263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 106.532 | − | 81.5029i | 0.185920 | − | 0.142239i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 126.735i | 0.220409i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −655.417 | −1.13590 | −0.567952 | − | 0.823061i | \(-0.692264\pi\) | ||||
−0.567952 | + | 0.823061i | \(0.692264\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −264.539 | − | 345.777i | −0.456889 | − | 0.597197i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 237.968i | − | 0.409584i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −274.494 | −0.470830 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 407.328 | + | 110.394i | 0.696287 | + | 0.188708i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 736.236i | 1.25424i | 0.778925 | + | 0.627118i | \(0.215765\pi\) | ||||
−0.778925 | + | 0.627118i | \(0.784235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −401.903 | −0.682348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −208.399 | + | 159.437i | −0.352620 | + | 0.269774i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 832.884i | − | 1.40453i | −0.711917 | − | 0.702263i | \(-0.752173\pi\) | ||
0.711917 | − | 0.702263i | \(-0.247827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 237.122 | 0.398524 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −119.247 | − | 155.867i | −0.199744 | − | 0.261084i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 69.3290i | 0.115741i | 0.998324 | + | 0.0578706i | \(0.0184311\pi\) | ||||
−0.998324 | + | 0.0578706i | \(0.981569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −161.720 | −0.269085 | −0.134543 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134543 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −63.9555 | + | 235.981i | −0.106062 | + | 0.391345i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 842.492i | 1.39255i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −929.608 | −1.53148 | −0.765740 | − | 0.643151i | \(-0.777627\pi\) | ||||
−0.765740 | + | 0.643151i | \(0.777627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −109.520 | + | 83.7891i | −0.179836 | + | 0.137585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 254.010i | − | 0.415729i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 297.940 | 0.486036 | 0.243018 | − | 0.970022i | \(-0.421863\pi\) | ||||
0.243018 | + | 0.970022i | \(0.421863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 407.328 | + | 532.417i | 0.662322 | + | 0.865718i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 975.575i | 1.58116i | 0.612360 | + | 0.790579i | \(0.290220\pi\) | ||||
−0.612360 | + | 0.790579i | \(0.709780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −357.034 | −0.576792 | −0.288396 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288396 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.9921 | + | 107.510i | 0.0708408 | + | 0.173124i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 167.144i | 0.268289i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −493.693 | −0.789908 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −63.7124 | + | 48.7435i | −0.101615 | + | 0.0777409i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 498.432i | − | 0.792420i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 813.223 | 1.28879 | 0.644393 | − | 0.764695i | \(-0.277110\pi\) | ||||
0.644393 | + | 0.764695i | \(0.277110\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −73.9778 | − | 96.6960i | −0.116869 | − | 0.152758i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 269.966i | 0.425143i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.4797 | −0.0698269 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −588.996 | − | 159.630i | −0.921747 | − | 0.249812i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 646.727i | − | 1.00893i | −0.863431 | − | 0.504467i | \(-0.831689\pi\) | ||
0.863431 | − | 0.504467i | \(-0.168311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −144.561 | −0.224822 | −0.112411 | − | 0.993662i | \(-0.535857\pi\) | ||||
−0.112411 | + | 0.993662i | \(0.535857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −982.442 | + | 751.622i | −1.52317 | + | 1.16531i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 716.654i | − | 1.10766i | −0.832631 | − | 0.553828i | \(-0.813166\pi\) | ||
0.832631 | − | 0.553828i | \(-0.186834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 108.133 | 0.166615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −189.498 | − | 247.692i | −0.291088 | − | 0.380479i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 378.999i | − | 0.580397i | −0.956966 | − | 0.290199i | \(-0.906279\pi\) | ||
0.956966 | − | 0.290199i | \(-0.0937214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 248.583 | 0.379516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −143.114 | + | 528.056i | −0.217829 | + | 0.803738i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 710.721i | − | 1.07848i | −0.842151 | − | 0.539242i | \(-0.818711\pi\) | ||
0.842151 | − | 0.539242i | \(-0.181289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 91.5045 | 0.138433 | 0.0692167 | − | 0.997602i | \(-0.477950\pi\) | ||||
0.0692167 | + | 0.997602i | \(0.477950\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −183.875 | + | 140.674i | −0.277337 | + | 0.212178i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 199.710i | 0.300316i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 74.7451 | 0.112062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −184.037 | − | 240.553i | −0.275092 | − | 0.359571i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 53.5379i | − | 0.0797883i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 645.806 | 0.959594 | 0.479797 | − | 0.877380i | \(-0.340710\pi\) | ||||
0.479797 | + | 0.877380i | \(0.340710\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 736.110 | − | 301.210i | 1.09053 | − | 0.446237i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 335.571i | 0.495674i | 0.968802 | + | 0.247837i | \(0.0797198\pi\) | ||||
−0.968802 | + | 0.247837i | \(0.920280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.7085 | 0.0746811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −932.290 | + | 713.254i | −1.36900 | + | 1.04736i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 113.336i | − | 0.165939i | −0.996552 | − | 0.0829694i | \(-0.973560\pi\) | ||
0.996552 | − | 0.0829694i | \(-0.0264404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −294.996 | −0.430651 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.4170 | − | 16.2302i | −0.0180742 | − | 0.0236247i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 667.206i | − | 0.968369i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −565.667 | −0.818620 | −0.409310 | − | 0.912395i | \(-0.634231\pi\) | ||||
−0.409310 | + | 0.912395i | \(0.634231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −60.0810 | − | 16.2832i | −0.0866970 | − | 0.0234966i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1436.37i | 2.06671i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −367.749 | −0.527617 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −278.478 | + | 213.051i | −0.398395 | + | 0.304794i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 872.955i | 1.24530i | 0.782501 | + | 0.622650i | \(0.213944\pi\) | ||||
−0.782501 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 419.793 | 0.597146 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −537.741 | − | 702.879i | −0.762753 | − | 0.996991i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 261.168i | − | 0.369403i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1092.04 | 1.54025 | 0.770125 | − | 0.637894i | \(-0.220194\pi\) | ||||
0.770125 | + | 0.637894i | \(0.220194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −148.899 | + | 549.404i | −0.209422 | + | 0.772720i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 169.044i | 0.237088i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 122.583 | 0.171445 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −142.871 | + | 109.304i | −0.199262 | + | 0.152446i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 901.769i | − | 1.25420i | −0.778939 | − | 0.627099i | \(-0.784242\pi\) | ||
0.778939 | − | 0.627099i | \(-0.215758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 148.826 | 0.206416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 245.638 | + | 321.072i | 0.339748 | + | 0.444083i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 511.773i | − | 0.705894i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −297.506 | −0.409224 | −0.204612 | − | 0.978843i | \(-0.565593\pi\) | ||||
−0.204612 | + | 0.978843i | \(0.565593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 519.889 | − | 511.035i | 0.713153 | − | 0.701008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 678.589i | − | 0.928302i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 456.966 | 0.623419 | 0.311709 | − | 0.950177i | \(-0.399098\pi\) | ||||
0.311709 | + | 0.950177i | \(0.399098\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −123.081 | + | 94.1638i | −0.167457 | + | 0.128114i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 71.0171i | 0.0963597i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 332.199 | 0.449525 | 0.224762 | − | 0.974414i | \(-0.427839\pi\) | ||||
0.224762 | + | 0.974414i | \(0.427839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −118.480 | − | 154.864i | −0.159892 | − | 0.208994i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 64.5346i | 0.0868568i | 0.999057 | + | 0.0434284i | \(0.0138280\pi\) | ||||
−0.999057 | + | 0.0434284i | \(0.986172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1503.10 | 2.01758 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 781.306 | + | 211.749i | 1.04592 | + | 0.283466i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 325.790i | − | 0.434966i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 611.668 | 0.814471 | 0.407236 | − | 0.913323i | \(-0.366493\pi\) | ||||
0.407236 | + | 0.913323i | \(0.366493\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 639.148 | − | 488.983i | 0.848802 | − | 0.649380i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1223.15i | − | 1.62007i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −207.357 | −0.273919 | −0.136960 | − | 0.990577i | \(-0.543733\pi\) | ||||
−0.136960 | + | 0.990577i | \(0.543733\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.5020 | + | 26.7980i | 0.0270118 | + | 0.0353070i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 337.770i | 0.443851i | 0.975064 | + | 0.221925i | \(0.0712341\pi\) | ||||
−0.975064 | + | 0.221925i | \(0.928766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 435.328 | 0.570548 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −210.996 | + | 778.526i | −0.275812 | + | 1.01768i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 262.837i | 0.342682i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1042.22 | −1.35529 | −0.677646 | − | 0.735388i | \(-0.737000\pi\) | ||||
−0.677646 | + | 0.735388i | \(0.737000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −557.852 | + | 426.788i | −0.723544 | + | 0.553551i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 291.448i | 0.377035i | 0.982070 | + | 0.188517i | \(0.0603682\pi\) | ||||
−0.982070 | + | 0.188517i | \(0.939632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1157.43 | 1.49346 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 197.933 | + | 258.718i | 0.254740 | + | 0.332970i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 309.729i | − | 0.397598i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −177.255 | −0.226959 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −177.646 | − | 434.138i | −0.226878 | − | 0.554455i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2233.95i | − | 2.84580i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −293.889 | −0.373429 | −0.186715 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186715 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 596.006 | − | 455.978i | 0.755395 | − | 0.577919i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 381.122i | − | 0.481822i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 130.133 | 0.164103 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1412.48 | − | 1846.24i | −1.77670 | − | 2.32232i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 568.764i | − | 0.713631i | −0.934175 | − | 0.356816i | \(-0.883862\pi\) | ||
0.934175 | − | 0.356816i | \(-0.116138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 485.490 | 0.607622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −548.774 | − | 148.729i | −0.685111 | − | 0.185679i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 158.915i | 0.197902i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 84.0000 | 0.104348 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −811.737 | + | 621.024i | −1.00587 | + | 0.769546i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 183.697i | − | 0.227067i | −0.993534 | − | 0.113534i | \(-0.963783\pi\) | ||
0.993534 | − | 0.113534i | \(-0.0362169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 544.663 | 0.671594 | 0.335797 | − | 0.941934i | \(-0.390994\pi\) | ||||
0.335797 | + | 0.941934i | \(0.390994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.8261 | + | 50.7494i | 0.0477566 | + | 0.0624224i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1070.33i | 1.31329i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 571.527 | 0.699543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 39.5791 | − | 146.038i | 0.0483261 | − | 0.178312i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1188.78i | 1.44797i | 0.689818 | + | 0.723983i | \(0.257691\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1265.15 | −1.53724 | −0.768621 | − | 0.639704i | \(-0.779057\pi\) | ||||
−0.768621 | + | 0.639704i | \(0.779057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 183.484 | − | 140.375i | 0.222404 | − | 0.170152i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 790.941i | 0.956398i | 0.878252 | + | 0.478199i | \(0.158710\pi\) | ||||
−0.878252 | + | 0.478199i | \(0.841290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 99.1961 | 0.119658 | 0.0598288 | − | 0.998209i | \(-0.480945\pi\) | ||||
0.0598288 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −413.638 | − | 540.664i | −0.497759 | − | 0.650619i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 85.0141i | − | 0.102058i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 145.077 | 0.173745 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 981.851 | − | 401.765i | 1.17306 | − | 0.480006i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 243.824i | − | 0.290612i | −0.989387 | − | 0.145306i | \(-0.953583\pi\) | ||
0.989387 | − | 0.145306i | \(-0.0464167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 539.170 | 0.641106 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 561.093 | − | 429.267i | 0.665591 | − | 0.509214i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 949.182i | − | 1.12329i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 302.055 | 0.356617 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −671.974 | − | 878.334i | −0.791489 | − | 1.03455i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 176.569i | − | 0.207484i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1122.06 | −1.31543 | −0.657713 | − | 0.753268i | \(-0.728476\pi\) | ||||
−0.657713 | + | 0.753268i | \(0.728476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −655.697 | − | 177.707i | −0.766897 | − | 0.207844i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 871.489i | − | 1.01691i | −0.861090 | − | 0.508453i | \(-0.830217\pi\) | ||
0.861090 | − | 0.508453i | \(-0.169783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1674.92 | 1.94985 | 0.974925 | − | 0.222533i | \(-0.0714324\pi\) | ||||
0.974925 | + | 0.222533i | \(0.0714324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 190.885 | − | 146.038i | 0.221701 | − | 0.169614i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1320.74i | 1.53041i | 0.643787 | + | 0.765205i | \(0.277362\pi\) | ||||
−0.643787 | + | 0.765205i | \(0.722638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −145.292 | −0.167967 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 257.940 | + | 337.153i | 0.297509 | + | 0.388873i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 165.340i | 0.190264i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −172.620 | −0.198186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −45.1216 | + | 166.488i | −0.0516856 | + | 0.190708i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 87.0303i | − | 0.0994632i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −344.790 | −0.393147 | −0.196573 | − | 0.980489i | \(-0.562981\pi\) | ||||
−0.196573 | + | 0.980489i | \(0.562981\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1266.69 | − | 969.087i | 1.44106 | − | 1.10249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 518.737i | 0.588805i | 0.955682 | + | 0.294403i | \(0.0951206\pi\) | ||||
−0.955682 | + | 0.294403i | \(0.904879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 584.008 | 0.661391 | 0.330695 | − | 0.943738i | \(-0.392717\pi\) | ||||
0.330695 | + | 0.943738i | \(0.392717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 556.427 | + | 727.303i | 0.628732 | + | 0.821812i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 263.213i | − | 0.296745i | −0.988932 | − | 0.148373i | \(-0.952597\pi\) | ||
0.988932 | − | 0.148373i | \(-0.0474035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 96.7895 | 0.108875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 106.923 | − | 182.771i | 0.120003 | − | 0.205130i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 408.893i | 0.457887i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2521.92 | −2.81778 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −65.1373 | + | 49.8336i | −0.0726168 | + | 0.0555559i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 682.621i | − | 0.759312i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1275.23 | 1.41535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 269.476 | + | 352.230i | 0.298423 | + | 0.390067i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1593.16i | 1.76040i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1501.72 | 1.65570 | 0.827849 | − | 0.560951i | \(-0.189565\pi\) | ||||
0.827849 | + | 0.560951i | \(0.189565\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 857.476 | + | 232.393i | 0.943318 | + | 0.255658i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 879.178i | − | 0.965069i | −0.875877 | − | 0.482534i | \(-0.839716\pi\) | ||
0.875877 | − | 0.482534i | \(-0.160284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 235.129 | 0.257535 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 360.095 | − | 275.493i | 0.393547 | − | 0.301085i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 89.1234i | − | 0.0971901i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −76.9882 | −0.0837739 | −0.0418869 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418869 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1034.96 | − | 1352.79i | −1.12374 | − | 1.46883i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 430.849i | − | 0.466792i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1208.95 | −1.30697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −132.429 | + | 488.631i | −0.142857 | + | 0.527110i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1629.76i | 1.75431i | 0.480204 | + | 0.877157i | \(0.340563\pi\) | ||||
−0.480204 | + | 0.877157i | \(0.659437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 71.6013 | 0.0769079 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 101.867 | − | 77.9336i | 0.109182 | − | 0.0835301i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 234.293i | 0.250581i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −497.720 | −0.531185 | −0.265592 | − | 0.964085i | \(-0.585568\pi\) | ||||
−0.265592 | + | 0.964085i | \(0.585568\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −288.229 | − | 376.742i | −0.306953 | − | 0.401217i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 238.894i | − | 0.253873i | −0.991911 | − | 0.126936i | \(-0.959486\pi\) | ||
0.991911 | − | 0.126936i | \(-0.0405144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −130.275 | −0.138149 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −199.642 | − | 487.893i | −0.211261 | − | 0.516289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 667.910i | 0.705291i | 0.935757 | + | 0.352645i | \(0.114718\pi\) | ||||
−0.935757 | + | 0.352645i | \(0.885282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −386.272 | −0.407030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 335.824 | − | 256.924i | 0.353127 | − | 0.270162i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.3247i | − | 0.0118832i | −0.999982 | − | 0.00594162i | \(-0.998109\pi\) | ||
0.999982 | − | 0.00594162i | \(-0.00189129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 329.948 | 0.345495 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −82.7895 | − | 108.214i | −0.0865094 | − | 0.113076i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 105.764i | 0.110285i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 582.822 | 0.606475 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1069.64 | + | 289.895i | 1.11074 | + | 0.301033i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1070.93i | − | 1.10977i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −830.324 | −0.858660 | −0.429330 | − | 0.903148i | \(-0.641250\pi\) | ||||
−0.429330 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 295.992 | − | 226.450i | 0.305461 | − | 0.233695i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1217.58i | 1.25394i | 0.779044 | + | 0.626970i | \(0.215705\pi\) | ||||
−0.779044 | + | 0.626970i | \(0.784295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 514.974 | 0.529264 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 341.207 | + | 445.989i | 0.349955 | + | 0.457425i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 424.579i | 0.434574i | 0.976108 | + | 0.217287i | \(0.0697207\pi\) | ||||
−0.976108 | + | 0.217287i | \(0.930279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −165.150 | −0.168693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −387.365 | + | 1429.29i | −0.394867 | + | 1.45697i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 76.7273i | − | 0.0780542i | −0.999238 | − | 0.0390271i | \(-0.987574\pi\) | ||
0.999238 | − | 0.0390271i | \(-0.0124259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −645.446 | −0.655275 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −252.000 | + | 192.794i | −0.255319 | + | 0.195333i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 240.389i | − | 0.243063i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −181.271 | −0.182917 | −0.0914585 | − | 0.995809i | \(-0.529153\pi\) | ||||
−0.0914585 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 470.974 | + | 615.608i | 0.474294 | + | 0.619947i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 482.747i | − | 0.485173i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1184.43 | −1.18800 | −0.593998 | − | 0.804466i | \(-0.702451\pi\) | ||||
−0.593998 | + | 0.804466i | \(0.702451\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1025.56 | + | 419.649i | −1.02658 | + | 0.420069i |
(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 | 336.3.d.c.113.4 | 4 | ||
3.2 | odd | 2 | inner | 336.3.d.c.113.3 | 4 | ||
4.3 | odd | 2 | 21.3.b.a.8.2 | ✓ | 4 | ||
8.3 | odd | 2 | 1344.3.d.f.449.4 | 4 | |||
8.5 | even | 2 | 1344.3.d.b.449.1 | 4 | |||
12.11 | even | 2 | 21.3.b.a.8.3 | yes | 4 | ||
20.3 | even | 4 | 525.3.f.a.449.3 | 8 | |||
20.7 | even | 4 | 525.3.f.a.449.6 | 8 | |||
20.19 | odd | 2 | 525.3.c.a.176.3 | 4 | |||
24.5 | odd | 2 | 1344.3.d.b.449.2 | 4 | |||
24.11 | even | 2 | 1344.3.d.f.449.3 | 4 | |||
28.3 | even | 6 | 147.3.h.c.128.3 | 8 | |||
28.11 | odd | 6 | 147.3.h.e.128.3 | 8 | |||
28.19 | even | 6 | 147.3.h.c.116.2 | 8 | |||
28.23 | odd | 6 | 147.3.h.e.116.2 | 8 | |||
28.27 | even | 2 | 147.3.b.f.50.2 | 4 | |||
36.7 | odd | 6 | 567.3.r.c.134.2 | 8 | |||
36.11 | even | 6 | 567.3.r.c.134.3 | 8 | |||
36.23 | even | 6 | 567.3.r.c.512.2 | 8 | |||
36.31 | odd | 6 | 567.3.r.c.512.3 | 8 | |||
60.23 | odd | 4 | 525.3.f.a.449.5 | 8 | |||
60.47 | odd | 4 | 525.3.f.a.449.4 | 8 | |||
60.59 | even | 2 | 525.3.c.a.176.2 | 4 | |||
84.11 | even | 6 | 147.3.h.e.128.2 | 8 | |||
84.23 | even | 6 | 147.3.h.e.116.3 | 8 | |||
84.47 | odd | 6 | 147.3.h.c.116.3 | 8 | |||
84.59 | odd | 6 | 147.3.h.c.128.2 | 8 | |||
84.83 | odd | 2 | 147.3.b.f.50.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.2 | ✓ | 4 | 4.3 | odd | 2 | ||
21.3.b.a.8.3 | yes | 4 | 12.11 | even | 2 | ||
147.3.b.f.50.2 | 4 | 28.27 | even | 2 | |||
147.3.b.f.50.3 | 4 | 84.83 | odd | 2 | |||
147.3.h.c.116.2 | 8 | 28.19 | even | 6 | |||
147.3.h.c.116.3 | 8 | 84.47 | odd | 6 | |||
147.3.h.c.128.2 | 8 | 84.59 | odd | 6 | |||
147.3.h.c.128.3 | 8 | 28.3 | even | 6 | |||
147.3.h.e.116.2 | 8 | 28.23 | odd | 6 | |||
147.3.h.e.116.3 | 8 | 84.23 | even | 6 | |||
147.3.h.e.128.2 | 8 | 84.11 | even | 6 | |||
147.3.h.e.128.3 | 8 | 28.11 | odd | 6 | |||
336.3.d.c.113.3 | 4 | 3.2 | odd | 2 | inner | ||
336.3.d.c.113.4 | 4 | 1.1 | even | 1 | trivial | ||
525.3.c.a.176.2 | 4 | 60.59 | even | 2 | |||
525.3.c.a.176.3 | 4 | 20.19 | odd | 2 | |||
525.3.f.a.449.3 | 8 | 20.3 | even | 4 | |||
525.3.f.a.449.4 | 8 | 60.47 | odd | 4 | |||
525.3.f.a.449.5 | 8 | 60.23 | odd | 4 | |||
525.3.f.a.449.6 | 8 | 20.7 | even | 4 | |||
567.3.r.c.134.2 | 8 | 36.7 | odd | 6 | |||
567.3.r.c.134.3 | 8 | 36.11 | even | 6 | |||
567.3.r.c.512.2 | 8 | 36.23 | even | 6 | |||
567.3.r.c.512.3 | 8 | 36.31 | odd | 6 | |||
1344.3.d.b.449.1 | 4 | 8.5 | even | 2 | |||
1344.3.d.b.449.2 | 4 | 24.5 | odd | 2 | |||
1344.3.d.f.449.3 | 4 | 24.11 | even | 2 | |||
1344.3.d.f.449.4 | 4 | 8.3 | odd | 2 |