Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.a (trivial) |
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: | yes |
Analytic conductor: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.57500224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 12x^{3} + 11x^{2} - 18x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.67361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 2.67361 | 1.54361 | 0.771805 | − | 0.635859i | \(-0.219354\pi\) | ||||
0.771805 | + | 0.635859i | \(0.219354\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.02460 | 1.35264 | 0.676321 | − | 0.736607i | \(-0.263573\pi\) | ||||
0.676321 | + | 0.736607i | \(0.263573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.969288 | 0.366356 | 0.183178 | − | 0.983080i | \(-0.441361\pi\) | ||||
0.183178 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.14820 | 1.38273 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.84959 | −0.512985 | −0.256493 | − | 0.966546i | \(-0.582567\pi\) | ||||
−0.256493 | + | 0.966546i | \(0.582567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.08661 | 2.08795 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.65727 | −1.12955 | −0.564777 | − | 0.825244i | \(-0.691038\pi\) | ||||
−0.564777 | + | 0.825244i | \(0.691038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.59150 | 0.565512 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.83619 | 1.84247 | 0.921236 | − | 0.389004i | \(-0.127181\pi\) | ||||
0.921236 | + | 0.389004i | \(0.127181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.14820 | 0.829641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.06985 | 0.590794 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.08776 | 0.759077 | 0.379539 | − | 0.925176i | \(-0.376083\pi\) | ||||
0.379539 | + | 0.925176i | \(0.376083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.58577 | −1.00323 | −0.501617 | − | 0.865090i | \(-0.667261\pi\) | ||||
−0.501617 | + | 0.865090i | \(0.667261\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.67361 | −0.465416 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.93171 | 0.495549 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04199 | 0.171303 | 0.0856514 | − | 0.996325i | \(-0.472703\pi\) | ||||
0.0856514 | + | 0.996325i | \(0.472703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.94510 | −0.791850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.65296 | 1.19519 | 0.597596 | − | 0.801798i | \(-0.296123\pi\) | ||||
0.597596 | + | 0.801798i | \(0.296123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.53564 | 0.844177 | 0.422088 | − | 0.906555i | \(-0.361297\pi\) | ||||
0.422088 | + | 0.906555i | \(0.361297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.5467 | 1.87035 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.35475 | 0.489340 | 0.244670 | − | 0.969606i | \(-0.421320\pi\) | ||||
0.244670 | + | 0.969606i | \(0.421320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.06048 | −0.865783 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.4517 | −1.74359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65116 | 0.776246 | 0.388123 | − | 0.921608i | \(-0.373124\pi\) | ||||
0.388123 | + | 0.921608i | \(0.373124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.02460 | −0.407837 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.67361 | 0.354129 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.98839 | 0.909811 | 0.454906 | − | 0.890540i | \(-0.349673\pi\) | ||||
0.454906 | + | 0.890540i | \(0.349673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2254 | −1.69334 | −0.846670 | − | 0.532119i | \(-0.821396\pi\) | ||||
−0.846670 | + | 0.532119i | \(0.821396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.02080 | 0.506574 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.59428 | −0.693886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0252 | 1.95779 | 0.978894 | − | 0.204369i | \(-0.0655143\pi\) | ||||
0.978894 | + | 0.204369i | \(0.0655143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.6245 | 2.84406 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.66300 | 0.197362 | 0.0986812 | − | 0.995119i | \(-0.468538\pi\) | ||||
0.0986812 | + | 0.995119i | \(0.468538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4425 | 1.57333 | 0.786663 | − | 0.617383i | \(-0.211807\pi\) | ||||
0.786663 | + | 0.617383i | \(0.211807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.0907 | 1.28064 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.969288 | −0.110461 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.63914 | −0.634453 | −0.317226 | − | 0.948350i | \(-0.602751\pi\) | ||||
−0.317226 | + | 0.948350i | \(0.602751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.23701 | −0.470779 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.89958 | 0.976856 | 0.488428 | − | 0.872604i | \(-0.337570\pi\) | ||||
0.488428 | + | 0.872604i | \(0.337570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.0864 | −1.52788 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.9291 | 1.17172 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.27111 | −0.346737 | −0.173368 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173368 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.79279 | −0.187935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.9342 | −1.54860 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.02460 | 0.310317 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00721 | −0.508405 | −0.254202 | − | 0.967151i | \(-0.581813\pi\) | ||||
−0.254202 | + | 0.967151i | \(0.581813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.14820 | −0.416910 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6207 | −1.25580 | −0.627901 | − | 0.778293i | \(-0.716086\pi\) | ||||
−0.627901 | + | 0.778293i | \(0.716086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.61871 | 0.849227 | 0.424614 | − | 0.905375i | \(-0.360410\pi\) | ||||
0.424614 | + | 0.905375i | \(0.360410\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.83825 | 0.764935 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.7496 | −1.52257 | −0.761284 | − | 0.648419i | \(-0.775430\pi\) | ||||
−0.761284 | + | 0.648419i | \(0.775430\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2609 | −1.07860 | −0.539301 | − | 0.842113i | \(-0.681312\pi\) | ||||
−0.539301 | + | 0.842113i | \(0.681312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.78589 | 0.264425 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3356 | −1.34858 | −0.674291 | − | 0.738466i | \(-0.735551\pi\) | ||||
−0.674291 | + | 0.738466i | \(0.735551\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.7259 | 2.49221 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.67250 | −0.709323 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.51424 | −0.413819 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.4610 | 1.84491 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.57634 | −0.230435 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.975074 | 0.0865239 | 0.0432619 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432619 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.8002 | 1.30308 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9828 | −1.30905 | −0.654526 | − | 0.756040i | \(-0.727132\pi\) | ||||
−0.654526 | + | 0.756040i | \(0.727132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.969288 | 0.0840479 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.28508 | 0.799132 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.85656 | 0.414924 | 0.207462 | − | 0.978243i | \(-0.433480\pi\) | ||||
0.207462 | + | 0.978243i | \(0.433480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.56887 | −0.641984 | −0.320992 | − | 0.947082i | \(-0.604016\pi\) | ||||
−0.320992 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.96930 | 0.755351 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.84959 | 0.154671 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.3638 | 1.02676 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.2034 | −1.33643 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.99722 | −0.409388 | −0.204694 | − | 0.978826i | \(-0.565620\pi\) | ||||
−0.204694 | + | 0.978826i | \(0.565620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.90781 | −0.399392 | −0.199696 | − | 0.979858i | \(-0.563995\pi\) | ||||
−0.199696 | + | 0.979858i | \(0.563995\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.3193 | −1.56187 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.8947 | −1.35702 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6033 | −1.32509 | −0.662546 | − | 0.749022i | \(-0.730524\pi\) | ||||
−0.662546 | + | 0.749022i | \(0.730524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.1090 | 1.19822 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.56481 | 0.675001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5034 | 1.52763 | 0.763814 | − | 0.645436i | \(-0.223324\pi\) | ||||
0.763814 | + | 0.645436i | \(0.223324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.08661 | −0.629542 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.6679 | −0.902888 | −0.451444 | − | 0.892300i | \(-0.649091\pi\) | ||||
−0.451444 | + | 0.892300i | \(0.649091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.57900 | −0.736846 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.14820 | 0.317221 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.5637 | −0.879172 | −0.439586 | − | 0.898201i | \(-0.644875\pi\) | ||||
−0.439586 | + | 0.898201i | \(0.644875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.02080 | 0.303944 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.6843 | 1.40439 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.90831 | 0.516351 | 0.258176 | − | 0.966098i | \(-0.416879\pi\) | ||||
0.258176 | + | 0.966098i | \(0.416879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2025 | −1.20432 | −0.602161 | − | 0.798375i | \(-0.705694\pi\) | ||||
−0.602161 | + | 0.798375i | \(0.705694\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.3596 | −2.61386 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.15161 | 0.231711 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.65727 | 0.340573 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.97557 | 0.216441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.32642 | −0.457764 | −0.228882 | − | 0.973454i | \(-0.573507\pi\) | ||||
−0.228882 | + | 0.973454i | \(0.573507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.82970 | −0.563594 | −0.281797 | − | 0.959474i | \(-0.590930\pi\) | ||||
−0.281797 | + | 0.959474i | \(0.590930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.9569 | −1.07109 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2294 | −0.728814 | −0.364407 | − | 0.931240i | \(-0.618728\pi\) | ||||
−0.364407 | + | 0.931240i | \(0.618728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2673 | −1.15316 | −0.576580 | − | 0.817041i | \(-0.695613\pi\) | ||||
−0.576580 | + | 0.817041i | \(0.695613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.8451 | 3.02206 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.96221 | 0.278093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.1471 | 1.61667 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.6543 | 2.54765 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8310 | −0.883320 | −0.441660 | − | 0.897182i | \(-0.645610\pi\) | ||||
−0.441660 | + | 0.897182i | \(0.645610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.44623 | 0.304651 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.7431 | 1.14187 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.41421 | −0.367541 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 35.9400 | 2.42860 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.61406 | 0.579445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.651776 | −0.0436461 | −0.0218231 | − | 0.999762i | \(-0.506947\pi\) | ||||
−0.0218231 | + | 0.999762i | \(0.506947\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.2076 | 1.14717 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.63048 | −0.440081 | −0.220040 | − | 0.975491i | \(-0.570619\pi\) | ||||
−0.220040 | + | 0.975491i | \(0.570619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0694 | −0.665405 | −0.332702 | − | 0.943032i | \(-0.607960\pi\) | ||||
−0.332702 | + | 0.943032i | \(0.607960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.59150 | −0.170508 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.23993 | −0.0812304 | −0.0406152 | − | 0.999175i | \(-0.512932\pi\) | ||||
−0.0406152 | + | 0.999175i | \(0.512932\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.1468 | 0.661903 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.0769 | −0.979348 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3466 | 1.05737 | 0.528686 | − | 0.848817i | \(-0.322685\pi\) | ||||
0.528686 | + | 0.848817i | \(0.322685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.17786 | 0.204704 | 0.102352 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102352 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.5377 | −1.31749 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.3305 | −1.17109 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.84959 | −0.117687 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.7940 | 1.50789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.1261 | 1.71218 | 0.856091 | − | 0.516825i | \(-0.172886\pi\) | ||||
0.856091 | + | 0.516825i | \(0.172886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.83619 | −0.555526 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −37.6615 | −2.35846 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5115 | 0.718065 | 0.359032 | − | 0.933325i | \(-0.383107\pi\) | ||||
0.359032 | + | 0.933325i | \(0.383107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00999 | 0.0627578 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.9569 | 1.04960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.62648 | 0.408606 | 0.204303 | − | 0.978908i | \(-0.434507\pi\) | ||||
0.204303 | + | 0.978908i | \(0.434507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.0925 | 1.04998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.74568 | −0.535227 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.79395 | −0.292292 | −0.146146 | − | 0.989263i | \(-0.546687\pi\) | ||||
−0.146146 | + | 0.989263i | \(0.546687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5511 | −0.762423 | −0.381211 | − | 0.924488i | \(-0.624493\pi\) | ||||
−0.381211 | + | 0.924488i | \(0.624493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.79323 | −0.290099 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.14820 | −0.250146 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.27079 | −0.256607 | −0.128303 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128303 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.1709 | −1.38721 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92584 | −0.114886 | −0.0574430 | − | 0.998349i | \(-0.518295\pi\) | ||||
−0.0574430 | + | 0.998349i | \(0.518295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.2590 | −1.50149 | −0.750746 | − | 0.660591i | \(-0.770306\pi\) | ||||
−0.750746 | + | 0.660591i | \(0.770306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.08661 | 0.479009 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.41792 | 0.437866 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.69017 | 0.275892 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3873 | −0.784779 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.91449 | −0.462369 | −0.231185 | − | 0.972910i | \(-0.574260\pi\) | ||||
−0.231185 | + | 0.972910i | \(0.574260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.1371 | 1.23065 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.06985 | −0.178131 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.3434 | −0.945161 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.36563 | 0.309270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.7428 | −1.93847 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.0016 | −2.29048 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9862 | −1.42604 | −0.713018 | − | 0.701145i | \(-0.752672\pi\) | ||||
−0.713018 | + | 0.701145i | \(0.752672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.0431 | 1.31088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0956 | −0.912696 | −0.456348 | − | 0.889801i | \(-0.650843\pi\) | ||||
−0.456348 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 35.2383 | 1.99178 | 0.995892 | − | 0.0905486i | \(-0.0288621\pi\) | ||||
0.995892 | + | 0.0905486i | \(0.0288621\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.1613 | 0.685213 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.75601 | 0.210959 | 0.105479 | − | 0.994421i | \(-0.466362\pi\) | ||||
0.105479 | + | 0.994421i | \(0.466362\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.08776 | −0.228870 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.1082 | −2.35025 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.65727 | −0.259137 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.67250 | −0.425594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.1074 | −1.66494 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.25172 | 0.179273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.0695 | −1.04816 | −0.524078 | − | 0.851670i | \(-0.675590\pi\) | ||||
−0.524078 | + | 0.851670i | \(0.675590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.32240 | 0.236866 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 48.4698 | 2.64819 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.7795 | 1.07746 | 0.538730 | − | 0.842478i | \(-0.318904\pi\) | ||||
0.538730 | + | 0.842478i | \(0.318904\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −38.3279 | −2.08169 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.58577 | 0.302486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6594 | −0.683541 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 71.4548 | 3.84700 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.8434 | 0.743152 | 0.371576 | − | 0.928402i | \(-0.378817\pi\) | ||||
0.371576 | + | 0.928402i | \(0.378817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.1062 | 1.50449 | 0.752245 | − | 0.658883i | \(-0.228971\pi\) | ||||
0.752245 | + | 0.658883i | \(0.228971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.67799 | −0.303068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.43671 | 0.395816 | 0.197908 | − | 0.980221i | \(-0.436585\pi\) | ||||
0.197908 | + | 0.980221i | \(0.436585\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.02992 | 0.266961 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0693 | −0.638776 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2344 | 0.540152 | 0.270076 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270076 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.67361 | 0.140328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.6582 | 2.12815 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.82204 | −0.460507 | −0.230253 | − | 0.973131i | \(-0.573955\pi\) | ||||
−0.230253 | + | 0.973131i | \(0.573955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.7460 | 1.65263 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.47760 | 0.284383 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6493 | 1.17273 | 0.586367 | − | 0.810045i | \(-0.300558\pi\) | ||||
0.586367 | + | 0.810045i | \(0.300558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.88814 | −0.355702 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.56070 | −0.389396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1676 | 0.984575 | 0.492288 | − | 0.870433i | \(-0.336161\pi\) | ||||
0.492288 | + | 0.870433i | \(0.336161\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.60697 | 0.133559 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.4177 | −1.55427 | −0.777137 | − | 0.629332i | \(-0.783329\pi\) | ||||
−0.777137 | + | 0.629332i | \(0.783329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.93171 | −0.149414 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.9630 | 1.16727 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.5570 | −0.636664 | −0.318332 | − | 0.947979i | \(-0.603123\pi\) | ||||
−0.318332 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.1525 | −2.08117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40.0581 | −2.02067 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.0561 | −0.858187 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.8655 | 1.34834 | 0.674170 | − | 0.738576i | \(-0.264502\pi\) | ||||
0.674170 | + | 0.738576i | \(0.264502\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.59150 | 0.129737 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2412 | 0.910920 | 0.455460 | − | 0.890256i | \(-0.349475\pi\) | ||||
0.455460 | + | 0.890256i | \(0.349475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3314 | 0.514644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.8153 | −0.636796 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.04199 | −0.0516497 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.3976 | −1.60196 | −0.800980 | − | 0.598691i | \(-0.795688\pi\) | ||||
−0.800980 | + | 0.598691i | \(0.795688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9846 | 0.640482 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.77376 | 0.333315 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.9177 | 1.32134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.2362 | −0.990973 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.0152 | 1.61290 | 0.806449 | − | 0.591304i | \(-0.201387\pi\) | ||||
0.806449 | + | 0.591304i | \(0.201387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0812 | 0.637539 | 0.318769 | − | 0.947832i | \(-0.396730\pi\) | ||||
0.318769 | + | 0.947832i | \(0.396730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.9162 | 0.676628 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.3193 | −0.937124 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8192 | −0.620366 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.94510 | 0.238752 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8903 | 1.24709 | 0.623546 | − | 0.781786i | \(-0.285691\pi\) | ||||
0.623546 | + | 0.781786i | \(0.285691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.1103 | −1.44701 | −0.723505 | − | 0.690319i | \(-0.757470\pi\) | ||||
−0.723505 | + | 0.690319i | \(0.757470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.0561 | 1.58492 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.83619 | 0.422692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1810 | 0.629094 | 0.314547 | − | 0.949242i | \(-0.398147\pi\) | ||||
0.314547 | + | 0.949242i | \(0.398147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.1401 | −1.19715 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.24227 | 0.0590223 | 0.0295111 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295111 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.89380 | −0.469011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.3606 | −0.631936 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.2083 | −0.528954 | −0.264477 | − | 0.964392i | \(-0.585199\pi\) | ||||
−0.264477 | + | 0.964392i | \(0.585199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.65296 | −0.360364 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.1216 | −0.616505 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.42247 | −0.254209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6855 | 1.15474 | 0.577370 | − | 0.816483i | \(-0.304079\pi\) | ||||
0.577370 | + | 0.816483i | \(0.304079\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2971 | −0.667333 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.47546 | 0.348167 | 0.174084 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174084 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9185 | 1.25101 | 0.625505 | − | 0.780220i | \(-0.284893\pi\) | ||||
0.625505 | + | 0.780220i | \(0.284893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −45.1699 | −2.09470 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.1476 | −1.07114 | −0.535572 | − | 0.844489i | \(-0.679904\pi\) | ||||
−0.535572 | + | 0.844489i | \(0.679904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5330 | 0.717248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.3909 | −2.04543 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.53564 | −0.254529 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.14820 | 0.190333 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.4422 | 1.07334 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.76571 | −0.217751 | −0.108875 | − | 0.994055i | \(-0.534725\pi\) | ||||
−0.108875 | + | 0.994055i | \(0.534725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.92727 | −0.0878758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.8990 | 1.04194 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.1448 | −0.687690 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.1889 | −0.597645 | −0.298822 | − | 0.954309i | \(-0.596594\pi\) | ||||
−0.298822 | + | 0.954309i | \(0.596594\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.1447 | 2.35806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9640 | 0.855831 | 0.427916 | − | 0.903819i | \(-0.359248\pi\) | ||||
0.427916 | + | 0.903819i | \(0.359248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.0378 | −0.857419 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.5467 | −0.563930 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.61193 | 0.0723049 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.8350 | −1.11177 | −0.555883 | − | 0.831260i | \(-0.687620\pi\) | ||||
−0.555883 | + | 0.831260i | \(0.687620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.1954 | −1.39371 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.7702 | 1.72868 | 0.864338 | − | 0.502911i | \(-0.167738\pi\) | ||||
0.864338 | + | 0.502911i | \(0.167738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.1725 | −1.69865 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.6105 | −1.13740 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0143 | −1.15306 | −0.576531 | − | 0.817075i | \(-0.695594\pi\) | ||||
−0.576531 | + | 0.817075i | \(0.695594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.0297 | 0.576398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.06985 | 0.135537 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.0682 | 1.14870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.35475 | −0.147542 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9169 | −1.35710 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.59103 | −0.420191 | −0.210095 | − | 0.977681i | \(-0.567377\pi\) | ||||
−0.210095 | + | 0.977681i | \(0.567377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.4599 | 1.76919 | 0.884594 | − | 0.466362i | \(-0.154436\pi\) | ||||
0.884594 | + | 0.466362i | \(0.154436\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.7501 | 0.469172 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.0144 | 1.13321 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.0782 | 2.39470 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.9893 | 1.25803 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.1549 | −0.613116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.6361 | −2.05949 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.4701 | 0.797045 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.06048 | 0.261043 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.04034 | 0.302688 | 0.151344 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151344 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −43.3192 | −1.85901 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.0598 | −1.45896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.8725 | 1.74758 | 0.873790 | − | 0.486303i | \(-0.161655\pi\) | ||||
0.873790 | + | 0.486303i | \(0.161655\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −54.8617 | −2.34144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.08776 | 0.174144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.46595 | −0.232436 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.42620 | 0.357672 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.2633 | −0.816211 | −0.408106 | − | 0.912935i | \(-0.633810\pi\) | ||||
−0.408106 | + | 0.912935i | \(0.633810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2387 | −0.433050 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.4517 | 0.525713 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.67190 | −0.196897 | −0.0984485 | − | 0.995142i | \(-0.531388\pi\) | ||||
−0.0984485 | + | 0.995142i | \(0.531388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −43.3595 | −1.82415 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.10689 | −0.172473 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9661 | 1.13048 | 0.565239 | − | 0.824927i | \(-0.308784\pi\) | ||||
0.565239 | + | 0.824927i | \(0.308784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.5199 | 1.40276 | 0.701382 | − | 0.712785i | \(-0.252567\pi\) | ||||
0.701382 | + | 0.712785i | \(0.252567\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9144 | −0.706609 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.6543 | 1.52859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.6163 | 0.691747 | 0.345873 | − | 0.938281i | \(-0.387583\pi\) | ||||
0.345873 | + | 0.938281i | \(0.387583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.9336 | −0.869970 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.62626 | 0.357877 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.65116 | −0.234047 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23.2062 | −0.959460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.4649 | −0.679580 | −0.339790 | − | 0.940501i | \(-0.610356\pi\) | ||||
−0.339790 | + | 0.940501i | \(0.610356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.58577 | −0.230157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.3494 | −1.12500 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0948 | 0.578802 | 0.289401 | − | 0.957208i | \(-0.406544\pi\) | ||||
0.289401 | + | 0.957208i | \(0.406544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6538 | −0.559749 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.4925 | −1.78003 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5656 | 0.513416 | 0.256708 | − | 0.966489i | \(-0.417362\pi\) | ||||
0.256708 | + | 0.966489i | \(0.417362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5612 | 1.12425 | 0.562123 | − | 0.827053i | \(-0.309985\pi\) | ||||
0.562123 | + | 0.827053i | \(0.309985\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.4757 | 2.70710 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.02460 | 0.122967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.9679 | −1.21636 | −0.608180 | − | 0.793800i | \(-0.708100\pi\) | ||||
−0.608180 | + | 0.793800i | \(0.708100\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5934 | 0.429267 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.20493 | −0.251024 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.1855 | 1.38074 | 0.690370 | − | 0.723456i | \(-0.257448\pi\) | ||||
0.690370 | + | 0.723456i | \(0.257448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 61.8865 | 2.49550 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.3758 | −1.30340 | −0.651700 | − | 0.758477i | \(-0.725944\pi\) | ||||
−0.651700 | + | 0.758477i | \(0.725944\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.6473 | 0.669113 | 0.334557 | − | 0.942376i | \(-0.391413\pi\) | ||||
0.334557 | + | 0.942376i | \(0.391413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.1258 | 1.08852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.17065 | −0.127029 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5334 | −1.14134 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.67361 | −0.106774 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.85285 | −0.193496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8558 | −1.14873 | −0.574366 | − | 0.818599i | \(-0.694751\pi\) | ||||
−0.574366 | + | 0.818599i | \(0.694751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −34.3050 | −1.36350 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.94921 | 0.117036 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.2094 | 0.444134 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.89848 | 0.272900 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.96322 | −0.0775427 | −0.0387713 | − | 0.999248i | \(-0.512344\pi\) | ||||
−0.0387713 | + | 0.999248i | \(0.512344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0709 | 1.50137 | 0.750685 | − | 0.660660i | \(-0.229724\pi\) | ||||
0.750685 | + | 0.660660i | \(0.229724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.7645 | 1.76260 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.4128 | −1.47085 | −0.735425 | − | 0.677606i | \(-0.763018\pi\) | ||||
−0.735425 | + | 0.677606i | \(0.763018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.98839 | −0.274318 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.4755 | −0.567340 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.0792 | 1.72495 | 0.862476 | − | 0.506098i | \(-0.168913\pi\) | ||||
0.862476 | + | 0.506098i | \(0.168913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.3169 | −1.77068 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 55.7622 | 2.17549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.82050 | 0.109871 | 0.0549356 | − | 0.998490i | \(-0.482505\pi\) | ||||
0.0549356 | + | 0.998490i | \(0.482505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.28117 | −0.166518 | −0.0832591 | − | 0.996528i | \(-0.526533\pi\) | ||||
−0.0832591 | + | 0.996528i | \(0.526533\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.0307 | 0.894437 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.93171 | 0.113687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.1202 | 1.39858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.74260 | −0.0673726 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2254 | 0.510561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.6368 | −1.56643 | −0.783216 | − | 0.621750i | \(-0.786422\pi\) | ||||
−0.783216 | + | 0.621750i | \(0.786422\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.7344 | 0.490147 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.97819 | 0.191327 | 0.0956637 | − | 0.995414i | \(-0.469503\pi\) | ||||
0.0956637 | + | 0.995414i | \(0.469503\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.85342 | −0.186257 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7273 | −0.679313 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.348085 | −0.0133191 | −0.00665956 | − | 0.999978i | \(-0.502120\pi\) | ||||
−0.00665956 | + | 0.999978i | \(0.502120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6892 | 0.561244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9217 | −1.02713 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.4524 | −0.398203 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.02411 | 0.191126 | 0.0955630 | − | 0.995423i | \(-0.469535\pi\) | ||||
0.0955630 | + | 0.995423i | \(0.469535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.02080 | −0.152738 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8928 | −0.868374 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.6419 | −1.35003 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.31509 | −0.125388 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.6906 | −1.38578 | −0.692892 | − | 0.721041i | \(-0.743664\pi\) | ||||
−0.692892 | + | 0.721041i | \(0.743664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.04199 | 0.0392995 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.1285 | 1.02172 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.2331 | −0.460071 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.9102 | 1.98708 | 0.993542 | − | 0.113461i | \(-0.0361936\pi\) | ||||
0.993542 | + | 0.113461i | \(0.0361936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.3923 | −0.877280 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −49.3569 | −1.84843 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.59428 | 0.209214 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.7044 | 1.63217 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.3648 | −1.28159 | −0.640795 | − | 0.767712i | \(-0.721395\pi\) | ||||
−0.640795 | + | 0.767712i | \(0.721395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.35401 | 0.311120 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.49636 | 0.315983 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.9569 | 0.629762 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.01822 | 0.334467 | 0.167234 | − | 0.985917i | \(-0.446517\pi\) | ||||
0.167234 | + | 0.985917i | \(0.446517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.1988 | −1.56292 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.7810 | −0.953543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4550 | 0.423100 | 0.211550 | − | 0.977367i | \(-0.432149\pi\) | ||||
0.211550 | + | 0.977367i | \(0.432149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −49.0087 | −1.80771 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0252 | −0.590295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.02492 | 0.0744878 | 0.0372439 | − | 0.999306i | \(-0.488142\pi\) | ||||
0.0372439 | + | 0.999306i | \(0.488142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.94510 | −0.181663 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.4042 | −0.565126 | −0.282563 | − | 0.959249i | \(-0.591185\pi\) | ||||
−0.282563 | + | 0.959249i | \(0.591185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1146 | −0.553755 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.9173 | 1.35073 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.2659 | −0.557802 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.2986 | −0.777196 | −0.388598 | − | 0.921407i | \(-0.627040\pi\) | ||||
−0.388598 | + | 0.921407i | \(0.627040\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 72.5246 | 2.64294 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.8442 | −0.540234 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.6493 | 1.62281 | 0.811403 | − | 0.584487i | \(-0.198704\pi\) | ||||
0.811403 | + | 0.584487i | \(0.198704\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.6245 | −0.857517 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.8034 | 1.22537 | 0.612687 | − | 0.790326i | \(-0.290089\pi\) | ||||
0.612687 | + | 0.790326i | \(0.290089\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9151 | −0.395153 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −58.4332 | −2.11266 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9257 | −0.466720 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3344 | 0.733279 | 0.366639 | − | 0.930363i | \(-0.380508\pi\) | ||||
0.366639 | + | 0.930363i | \(0.380508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.7772 | 1.10841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.8998 | −1.36316 | −0.681581 | − | 0.731743i | \(-0.738707\pi\) | ||||
−0.681581 | + | 0.731743i | \(0.738707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.1709 | −0.832323 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.70033 | 0.0968737 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.65296 | 0.274196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.66300 | −0.0595070 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.5488 | 0.448458 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.2185 | −1.79237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1646 | −0.861375 | −0.430687 | − | 0.902501i | \(-0.641729\pi\) | ||||
−0.430687 | + | 0.902501i | \(0.641729\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.7167 | 0.630729 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8953 | −0.494061 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.4616 | 0.868658 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.6987 | 1.62077 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.3914 | −1.07652 | −0.538260 | − | 0.842779i | \(-0.680918\pi\) | ||||
−0.538260 | + | 0.842779i | \(0.680918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6240 | −0.552736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5692 | −0.479445 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.4425 | −0.474376 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.9051 | 0.913035 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8172 | −0.451186 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.39736 | −0.119445 | −0.0597224 | − | 0.998215i | \(-0.519022\pi\) | ||||
−0.0597224 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.5382 | −1.45860 | −0.729301 | − | 0.684193i | \(-0.760155\pi\) | ||||
−0.729301 | + | 0.684193i | \(0.760155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.5567 | −1.17688 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58.9901 | 2.06633 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.53564 | 0.193667 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.43686 | −0.259865 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.87958 | 0.274999 | 0.137500 | − | 0.990502i | \(-0.456093\pi\) | ||||
0.137500 | + | 0.990502i | \(0.456093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9346 | 0.729734 | 0.364867 | − | 0.931060i | \(-0.381114\pi\) | ||||
0.364867 | + | 0.931060i | \(0.381114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0907 | −0.386128 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6684 | −0.370975 | −0.185488 | − | 0.982647i | \(-0.559386\pi\) | ||||
−0.185488 | + | 0.982647i | \(0.559386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.4722 | 1.61405 | 0.807024 | − | 0.590519i | \(-0.201077\pi\) | ||||
0.807024 | + | 0.590519i | \(0.201077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4184 | −0.396101 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.2253 | 0.977949 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.2907 | −1.22128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.1475 | −0.592704 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.8909 | −1.30814 | −0.654070 | − | 0.756434i | \(-0.726940\pi\) | ||||
−0.654070 | + | 0.756434i | \(0.726940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2902 | −0.423801 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.14895 | −0.177339 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.9726 | −0.996689 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.969288 | 0.0333051 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −67.5328 | −2.31772 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.20725 | 0.315621 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.9291 | −1.12747 | −0.563735 | − | 0.825956i | \(-0.690636\pi\) | ||||
−0.563735 | + | 0.825956i | \(0.690636\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.5467 | 0.429087 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.84255 | 0.199578 | 0.0997888 | − | 0.995009i | \(-0.468183\pi\) | ||||
0.0997888 | + | 0.995009i | \(0.468183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.6377 | 1.11358 | 0.556792 | − | 0.830652i | \(-0.312032\pi\) | ||||
0.556792 | + | 0.830652i | \(0.312032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.8326 | 0.675895 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.74557 | 0.0594199 | 0.0297099 | − | 0.999559i | \(-0.490542\pi\) | ||||
0.0297099 | + | 0.999559i | \(0.490542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.9756 | −1.18920 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.5397 | 0.425870 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.63914 | 0.191295 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.6401 | −1.00432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.7709 | −0.702989 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.49722 | −0.0844213 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.3270 | 0.787696 | 0.393848 | − | 0.919176i | \(-0.371144\pi\) | ||||
0.393848 | + | 0.919176i | \(0.371144\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.1603 | −0.713718 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.0551 | 0.338764 | 0.169382 | − | 0.985551i | \(-0.445823\pi\) | ||||
0.169382 | + | 0.985551i | \(0.445823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8721 | −0.399528 | −0.199764 | − | 0.979844i | \(-0.564018\pi\) | ||||
−0.199764 | + | 0.979844i | \(0.564018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.5124 | 1.89964 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5554 | 0.690184 | 0.345092 | − | 0.938569i | \(-0.387848\pi\) | ||||
0.345092 | + | 0.938569i | \(0.387848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.945128 | 0.0316986 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.23701 | 0.141945 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.35475 | 0.112262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.8949 | 0.698439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.6958 | −1.45896 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.8333 | −0.761532 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3190 | −0.876812 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.3456 | 0.477392 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.0061 | −1.62902 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2269 | 1.60135 | 0.800674 | − | 0.599101i | \(-0.204475\pi\) | ||||
0.800674 | + | 0.599101i | \(0.204475\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −52.3531 | −1.73644 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.5598 | −1.90704 | −0.953521 | − | 0.301327i | \(-0.902571\pi\) | ||||
−0.953521 | + | 0.301327i | \(0.902571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.89958 | −0.294533 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −106.949 | −3.53561 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.5226 | −0.479579 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.8946 | −1.08509 | −0.542546 | − | 0.840026i | \(-0.682540\pi\) | ||||
−0.542546 | + | 0.840026i | \(0.682540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −66.8034 | −2.20125 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.07588 | −0.101244 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.32240 | 0.142120 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35.7522 | 1.17426 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.1170 | 1.21777 | 0.608884 | − | 0.793259i | \(-0.291617\pi\) | ||||
0.608884 | + | 0.793259i | \(0.291617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.06048 | −0.198624 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43.0333 | −1.40885 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.0864 | 0.460674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0894 | 0.917641 | 0.458820 | − | 0.888529i | \(-0.348272\pi\) | ||||
0.458820 | + | 0.888529i | \(0.348272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 94.2134 | 3.07454 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7448 | −0.643663 | −0.321831 | − | 0.946797i | \(-0.604298\pi\) | ||||
−0.321831 | + | 0.946797i | \(0.604298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.6230 | 2.20211 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.99991 | 0.292767 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.93635 | 0.322888 | 0.161444 | − | 0.986882i | \(-0.448385\pi\) | ||||
0.161444 | + | 0.986882i | \(0.448385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.8632 | −0.807093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0421 | 0.325638 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0494 | −1.29733 | −0.648663 | − | 0.761076i | \(-0.724672\pi\) | ||||
−0.648663 | + | 0.761076i | \(0.724672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.1349 | −0.619191 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9291 | −0.353287 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.70741 | 0.152010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.200781 | 0.00647680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −65.3324 | −2.10531 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.6817 | −0.762341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.2715 | −1.58446 | −0.792232 | − | 0.610220i | \(-0.791081\pi\) | ||||
−0.792232 | + | 0.610220i | \(0.791081\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.4517 | −0.400007 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.6709 | 1.78656 | 0.893281 | − | 0.449498i | \(-0.148397\pi\) | ||||
0.893281 | + | 0.449498i | \(0.148397\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.33642 | −0.235195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.5133 | −0.656951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.1309 | −0.548067 | −0.274034 | − | 0.961720i | \(-0.588358\pi\) | ||||
−0.274034 | + | 0.961720i | \(0.588358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.27111 | 0.104545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.7127 | −1.49142 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.1356 | 1.12065 | 0.560326 | − | 0.828272i | \(-0.310676\pi\) | ||||
0.560326 | + | 0.828272i | \(0.310676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.9398 | −0.985824 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.69383 | 0.276728 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.9139 | 1.55537 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91682 | 0.0926559 | 0.0463280 | − | 0.998926i | \(-0.485248\pi\) | ||||
0.0463280 | + | 0.998926i | \(0.485248\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.9845 | −1.61794 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.2022 | −1.55981 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.94047 | −0.219807 | −0.109903 | − | 0.993942i | \(-0.535054\pi\) | ||||
−0.109903 | + | 0.993942i | \(0.535054\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.19877 | 0.101205 |
(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 | 3344.2.a.y.1.5 | 6 | ||
4.3 | odd | 2 | 1672.2.a.h.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.h.1.2 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.y.1.5 | 6 | 1.1 | even | 1 | trivial |