Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.508203 | 0.192083 | 0.0960414 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960414 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.36266 | −1.61690 | −0.808452 | − | 0.588563i | \(-0.799694\pi\) | ||||
−0.808452 | + | 0.588563i | \(0.799694\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.87086 | 1.90897 | 0.954483 | − | 0.298267i | \(-0.0964085\pi\) | ||||
0.954483 | + | 0.298267i | \(0.0964085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.508203 | 0.116590 | 0.0582949 | − | 0.998299i | \(-0.481434\pi\) | ||||
0.0582949 | + | 0.998299i | \(0.481434\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.508203 | −0.110899 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.87086 | −0.390102 | −0.195051 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195051 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87086 | 0.718802 | 0.359401 | − | 0.933183i | \(-0.382981\pi\) | ||||
0.359401 | + | 0.933183i | \(0.382981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.37907 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.36266 | 0.933520 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.508203 | −0.0859020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.74173 | −1.60153 | −0.800765 | − | 0.598978i | \(-0.795574\pi\) | ||||
−0.800765 | + | 0.598978i | \(0.795574\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.983593 | −0.153611 | −0.0768057 | − | 0.997046i | \(-0.524472\pi\) | ||||
−0.0768057 | + | 0.997046i | \(0.524472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.34625 | −0.633966 | −0.316983 | − | 0.948431i | \(-0.602670\pi\) | ||||
−0.316983 | + | 0.948431i | \(0.602670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74173 | −0.963104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.87086 | −1.10214 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.01641 | 0.414335 | 0.207168 | − | 0.978305i | \(-0.433575\pi\) | ||||
0.207168 | + | 0.978305i | \(0.433575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.36266 | 0.723101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.508203 | −0.0673132 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.3627 | −1.73967 | −0.869835 | − | 0.493342i | \(-0.835775\pi\) | ||||
−0.869835 | + | 0.493342i | \(0.835775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.508203 | 0.0640276 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.37907 | 0.290649 | 0.145325 | − | 0.989384i | \(-0.453577\pi\) | ||||
0.145325 | + | 0.989384i | \(0.453577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.87086 | 0.225226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1044 | 1.55521 | 0.777603 | − | 0.628756i | \(-0.216436\pi\) | ||||
0.777603 | + | 0.628756i | \(0.216436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.87086 | −0.921215 | −0.460608 | − | 0.887604i | \(-0.652368\pi\) | ||||
−0.460608 | + | 0.887604i | \(0.652368\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.72532 | −0.310579 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7581 | −1.43540 | −0.717701 | − | 0.696351i | \(-0.754806\pi\) | ||||
−0.717701 | + | 0.696351i | \(0.754806\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.1044 | 1.87745 | 0.938725 | − | 0.344666i | \(-0.112008\pi\) | ||||
0.938725 | + | 0.344666i | \(0.112008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.87086 | −0.853715 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.87086 | −0.415000 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.508203 | −0.0532742 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.37907 | −0.661479 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.508203 | −0.0521406 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6126 | 1.58522 | 0.792609 | − | 0.609730i | \(-0.208722\pi\) | ||||
0.792609 | + | 0.609730i | \(0.208722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.36266 | −0.538968 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.85446 | 0.284029 | 0.142015 | − | 0.989865i | \(-0.454642\pi\) | ||||
0.142015 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.75814 | −0.862965 | −0.431482 | − | 0.902121i | \(-0.642009\pi\) | ||||
−0.431482 | + | 0.902121i | \(0.642009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.508203 | 0.0495956 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.14554 | −0.109723 | −0.0548615 | − | 0.998494i | \(-0.517472\pi\) | ||||
−0.0548615 | + | 0.998494i | \(0.517472\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.74173 | 0.924644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.87086 | −0.364140 | −0.182070 | − | 0.983286i | \(-0.558280\pi\) | ||||
−0.182070 | + | 0.983286i | \(0.558280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.87086 | 0.174459 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.7581 | 1.61438 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.983593 | 0.0886876 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.72532 | 0.596776 | 0.298388 | − | 0.954445i | \(-0.403551\pi\) | ||||
0.298388 | + | 0.954445i | \(0.403551\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5962 | 1.10053 | 0.550267 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550267 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.258271 | 0.0223949 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9836 | 1.10926 | 0.554632 | − | 0.832096i | \(-0.312859\pi\) | ||||
0.554632 | + | 0.832096i | \(0.312859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.74173 | 0.656645 | 0.328322 | − | 0.944566i | \(-0.393517\pi\) | ||||
0.328322 | + | 0.944566i | \(0.393517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.34625 | 0.366021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.36266 | 0.448448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.87086 | −0.321458 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.74173 | 0.556048 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.74173 | −0.142688 | −0.0713440 | − | 0.997452i | \(-0.522729\pi\) | ||||
−0.0713440 | + | 0.997452i | \(0.522729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62093 | 0.131910 | 0.0659548 | − | 0.997823i | \(-0.478991\pi\) | ||||
0.0659548 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.87086 | 0.636322 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.37907 | −0.512379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4671 | 1.63345 | 0.816724 | − | 0.577028i | \(-0.195788\pi\) | ||||
0.816724 | + | 0.577028i | \(0.195788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.01641 | −0.239217 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.950780 | −0.0749319 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0880 | −1.57341 | −0.786706 | − | 0.617328i | \(-0.788215\pi\) | ||||
−0.786706 | + | 0.617328i | \(0.788215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.36266 | −0.417483 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.08798 | −0.625867 | −0.312933 | − | 0.949775i | \(-0.601312\pi\) | ||||
−0.312933 | + | 0.949775i | \(0.601312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.508203 | 0.0388633 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4342 | 1.70564 | 0.852822 | − | 0.522202i | \(-0.174889\pi\) | ||||
0.852822 | + | 0.522202i | \(0.174889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.508203 | 0.0384166 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3627 | 1.00440 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.90368 | −0.291775 | −0.145887 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145887 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.983593 | −0.0731099 | −0.0365550 | − | 0.999332i | \(-0.511638\pi\) | ||||
−0.0365550 | + | 0.999332i | \(0.511638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.74173 | 0.716226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.2088 | −3.08661 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.508203 | −0.0369664 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.27468 | 0.381662 | 0.190831 | − | 0.981623i | \(-0.438882\pi\) | ||||
0.190831 | + | 0.981623i | \(0.438882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.5798 | −1.26542 | −0.632710 | − | 0.774389i | \(-0.718058\pi\) | ||||
−0.632710 | + | 0.774389i | \(0.718058\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0164 | 1.06987 | 0.534937 | − | 0.844892i | \(-0.320335\pi\) | ||||
0.534937 | + | 0.844892i | \(0.320335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4835 | 1.09759 | 0.548797 | − | 0.835956i | \(-0.315086\pi\) | ||||
0.548797 | + | 0.835956i | \(0.315086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.37907 | −0.167807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.96719 | 0.138069 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.983593 | 0.0686971 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.87086 | −0.130034 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.72532 | −0.188515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.1044 | −0.897898 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.24186 | 0.220072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.87086 | 0.531864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.87086 | −0.529452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5410 | −0.705879 | −0.352939 | − | 0.935646i | \(-0.614818\pi\) | ||||
−0.352939 | + | 0.935646i | \(0.614818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3463 | 1.08494 | 0.542470 | − | 0.840075i | \(-0.317489\pi\) | ||||
0.542470 | + | 0.840075i | \(0.317489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8873 | 1.11594 | 0.557971 | − | 0.829860i | \(-0.311580\pi\) | ||||
0.557971 | + | 0.829860i | \(0.311580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.72532 | 0.179313 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.11273 | 0.203922 | 0.101961 | − | 0.994788i | \(-0.467488\pi\) | ||||
0.101961 | + | 0.994788i | \(0.467488\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.34625 | 0.283518 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7581 | 0.828730 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0716 | −0.974899 | −0.487450 | − | 0.873151i | \(-0.662073\pi\) | ||||
−0.487450 | + | 0.873151i | \(0.662073\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.74173 | 0.430713 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.508203 | −0.0323362 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.1044 | −1.08395 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6454 | 0.987529 | 0.493765 | − | 0.869596i | \(-0.335620\pi\) | ||||
0.493765 | + | 0.869596i | \(0.335620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0328 | 0.630758 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.87086 | 0.492893 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5962 | −0.910485 | −0.455243 | − | 0.890367i | \(-0.650447\pi\) | ||||
−0.455243 | + | 0.890367i | \(0.650447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.95078 | −0.307626 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.87086 | 0.239601 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.5634 | 1.14467 | 0.572333 | − | 0.820021i | \(-0.306038\pi\) | ||||
0.572333 | + | 0.820021i | \(0.306038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.01641 | −0.185296 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.61259 | 0.464148 | 0.232074 | − | 0.972698i | \(-0.425449\pi\) | ||||
0.232074 | + | 0.972698i | \(0.425449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.34625 | −0.264016 | −0.132008 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132008 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.508203 | 0.0307579 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.36266 | −0.323381 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.25827 | 0.135686 | 0.0678432 | − | 0.997696i | \(-0.478388\pi\) | ||||
0.0678432 | + | 0.997696i | \(0.478388\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.37907 | 0.381905 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0328135 | −0.00195749 | −0.000978745 | − | 1.00000i | \(-0.500312\pi\) | ||||
−0.000978745 | 1.00000i | \(0.500312\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0328 | −1.07194 | −0.535970 | − | 0.844237i | \(-0.680054\pi\) | ||||
−0.535970 | + | 0.844237i | \(0.680054\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.508203 | 0.0301034 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.499865 | −0.0295061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.9505 | 2.64415 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.6126 | −0.915226 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.4999 | 1.78182 | 0.890911 | − | 0.454179i | \(-0.150067\pi\) | ||||
0.890911 | + | 0.454179i | \(0.150067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.3627 | 0.778004 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.36266 | 0.311173 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.87086 | 0.108195 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.06563 | −0.234339 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.85446 | −0.163984 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.65375 | 0.436822 | 0.218411 | − | 0.975857i | \(-0.429913\pi\) | ||||
0.218411 | + | 0.975857i | \(0.429913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.75814 | 0.498233 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.03281 | 0.115270 | 0.0576351 | − | 0.998338i | \(-0.481644\pi\) | ||||
0.0576351 | + | 0.998338i | \(0.481644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9836 | 0.959969 | 0.479985 | − | 0.877277i | \(-0.340642\pi\) | ||||
0.479985 | + | 0.877277i | \(0.340642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.508203 | −0.0286340 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4506 | −1.09246 | −0.546229 | − | 0.837636i | \(-0.683937\pi\) | ||||
−0.546229 | + | 0.837636i | \(0.683937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7581 | −1.16223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14554 | 0.0633486 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.20878 | −0.121774 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.9917 | 0.878981 | 0.439491 | − | 0.898247i | \(-0.355159\pi\) | ||||
0.439491 | + | 0.898247i | \(0.355159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.74173 | −0.533843 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.37907 | −0.129982 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.4342 | 1.65786 | 0.828929 | − | 0.559353i | \(-0.188951\pi\) | ||||
0.828929 | + | 0.559353i | \(0.188951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.87086 | 0.210237 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.2088 | −1.85251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.98359 | −0.377079 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.87086 | −0.100724 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.258271 | −0.0138647 | −0.00693235 | − | 0.999976i | \(-0.502207\pi\) | ||||
−0.00693235 | + | 0.999976i | \(0.502207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8545 | 0.795141 | 0.397570 | − | 0.917572i | \(-0.369853\pi\) | ||||
0.397570 | + | 0.917572i | \(0.369853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.4671 | 1.94095 | 0.970473 | − | 0.241211i | \(-0.0775446\pi\) | ||||
0.970473 | + | 0.241211i | \(0.0775446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.1044 | −0.695509 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | −0.211702 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.0716 | −0.584335 | −0.292168 | − | 0.956367i | \(-0.594377\pi\) | ||||
−0.292168 | + | 0.956367i | \(0.594377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7417 | −0.986407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.7581 | −0.932060 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.87086 | 0.411980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0000 | 1.46159 | 0.730794 | − | 0.682598i | \(-0.239150\pi\) | ||||
0.730794 | + | 0.682598i | \(0.239150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.983593 | −0.0512038 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.53295 | 0.0795867 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.5327 | 1.68448 | 0.842239 | − | 0.539104i | \(-0.181237\pi\) | ||||
0.842239 | + | 0.539104i | \(0.181237\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.87086 | −0.199360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2663 | −1.09238 | −0.546189 | − | 0.837662i | \(-0.683922\pi\) | ||||
−0.546189 | + | 0.837662i | \(0.683922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.72532 | −0.344549 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6373 | 0.543543 | 0.271771 | − | 0.962362i | \(-0.412391\pi\) | ||||
0.271771 | + | 0.962362i | \(0.412391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.72532 | 0.138895 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6454 | 1.30027 | 0.650137 | − | 0.759817i | \(-0.274712\pi\) | ||||
0.650137 | + | 0.759817i | \(0.274712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7253 | −0.744692 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.5962 | −0.635394 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7581 | 0.641931 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.291084 | 0.0146091 | 0.00730455 | − | 0.999973i | \(-0.497675\pi\) | ||||
0.00730455 | + | 0.999973i | \(0.497675\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.258271 | −0.0129297 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.4999 | −1.32334 | −0.661670 | − | 0.749795i | \(-0.730152\pi\) | ||||
−0.661670 | + | 0.749795i | \(0.730152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.37907 | −0.317764 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.2416 | 2.58952 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.2580 | −1.74340 | −0.871698 | − | 0.490043i | \(-0.836981\pi\) | ||||
−0.871698 | + | 0.490043i | \(0.836981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.9836 | −0.640433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.79095 | −0.334161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1044 | −0.839622 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.74173 | −0.379114 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.9201 | −0.631187 | −0.315594 | − | 0.948894i | \(-0.602204\pi\) | ||||
−0.315594 | + | 0.948894i | \(0.602204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.59619 | 0.126530 | 0.0632652 | − | 0.997997i | \(-0.479849\pi\) | ||||
0.0632652 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.34625 | −0.211322 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.87086 | 0.381793 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.04922 | 0.147562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.36266 | −0.258912 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3463 | 0.980045 | 0.490022 | − | 0.871710i | \(-0.336989\pi\) | ||||
0.490022 | + | 0.871710i | \(0.336989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.70892 | −0.370467 | −0.185233 | − | 0.982695i | \(-0.559304\pi\) | ||||
−0.185233 | + | 0.982695i | \(0.559304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.87086 | 0.185594 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.950780 | −0.0454820 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7581 | 0.799822 | 0.399911 | − | 0.916554i | \(-0.369041\pi\) | ||||
0.399911 | + | 0.916554i | \(0.369041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.74173 | −0.321035 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.67610 | −0.174657 | −0.0873284 | − | 0.996180i | \(-0.527833\pi\) | ||||
−0.0873284 | + | 0.996180i | \(0.527833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.74173 | 0.0823810 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5163 | 0.921030 | 0.460515 | − | 0.887652i | \(-0.347665\pi\) | ||||
0.460515 | + | 0.887652i | \(0.347665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.27468 | 0.248375 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.62093 | −0.0761580 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.508203 | 0.0238249 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.129135 | 0.00604070 | 0.00302035 | − | 0.999995i | \(-0.499039\pi\) | ||||
0.00302035 | + | 0.999995i | \(0.499039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.87086 | −0.367381 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.0328135 | −0.00152828 | −0.000764139 | − | 1.00000i | \(-0.500243\pi\) | ||||
−0.000764139 | 1.00000i | \(0.500243\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.1840 | 1.91398 | 0.956992 | − | 0.290113i | \(-0.0936931\pi\) | ||||
0.956992 | + | 0.290113i | \(0.0936931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.37907 | 0.295822 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.27468 | 0.0589850 | 0.0294925 | − | 0.999565i | \(-0.490611\pi\) | ||||
0.0294925 | + | 0.999565i | \(0.490611\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.20905 | 0.0558288 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4671 | −0.943072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.9013 | 1.97260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.508203 | 0.0233180 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.01641 | 0.138112 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1372 | 0.874401 | 0.437201 | − | 0.899364i | \(-0.355970\pi\) | ||||
0.437201 | + | 0.899364i | \(0.355970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.74173 | 0.444185 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.950780 | 0.0432620 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.6126 | −0.708931 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.71725 | 0.0778162 | 0.0389081 | − | 0.999243i | \(-0.487612\pi\) | ||||
0.0389081 | + | 0.999243i | \(0.487612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0880 | 0.908410 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.6454 | −1.42814 | −0.714069 | − | 0.700076i | \(-0.753150\pi\) | ||||
−0.714069 | + | 0.700076i | \(0.753150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.4671 | 1.37217 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.36266 | 0.241034 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.65970 | 0.298728 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75007 | −0.167876 | −0.0839380 | − | 0.996471i | \(-0.526750\pi\) | ||||
−0.0839380 | + | 0.996471i | \(0.526750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.08798 | 0.361344 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.5962 | 1.63174 | 0.815872 | − | 0.578233i | \(-0.196258\pi\) | ||||
0.815872 | + | 0.578233i | \(0.196258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.85446 | −0.127022 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.4835 | −0.597644 | −0.298822 | − | 0.954309i | \(-0.596594\pi\) | ||||
−0.298822 | + | 0.954309i | \(0.596594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | −0.176950 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.508203 | −0.0224377 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.75814 | 0.385930 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.3075 | 1.02506 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.4342 | −0.984754 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9508 | −0.479762 | −0.239881 | − | 0.970802i | \(-0.577108\pi\) | ||||
−0.239881 | + | 0.970802i | \(0.577108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.9341 | 1.44011 | 0.720054 | − | 0.693918i | \(-0.244117\pi\) | ||||
0.720054 | + | 0.693918i | \(0.244117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.508203 | −0.0221798 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 50.2088 | 2.18713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.4999 | −0.847820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.3627 | −0.579890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.983593 | 0.0426042 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.90368 | 0.168456 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.1536 | 1.55725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.2723 | −1.64545 | −0.822727 | − | 0.568437i | \(-0.807548\pi\) | ||||
−0.822727 | + | 0.568437i | \(0.807548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.983593 | 0.0422100 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.14554 | 0.0490696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4506 | 1.08819 | 0.544096 | − | 0.839023i | \(-0.316873\pi\) | ||||
0.544096 | + | 0.839023i | \(0.316873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.96719 | 0.0838050 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.48373 | −0.275716 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.74173 | −0.413513 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.4506 | −0.824150 | −0.412075 | − | 0.911150i | \(-0.635196\pi\) | ||||
−0.412075 | + | 0.911150i | \(0.635196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.2088 | 1.78206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4342 | −0.692621 | −0.346310 | − | 0.938120i | \(-0.612566\pi\) | ||||
−0.346310 | + | 0.938120i | \(0.612566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.87086 | 0.162849 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.508203 | 0.0213425 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.1924 | 1.81072 | 0.905359 | − | 0.424646i | \(-0.139602\pi\) | ||||
0.905359 | + | 0.424646i | \(0.139602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0164 | 0.544720 | 0.272360 | − | 0.962195i | \(-0.412196\pi\) | ||||
0.272360 | + | 0.962195i | \(0.412196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.27468 | −0.220353 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.87086 | −0.0780204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.12914 | −0.171898 | −0.0859491 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859491 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.5798 | 0.730591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.69251 | 0.360626 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.1760 | −0.669940 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.68656 | −0.399807 | −0.199904 | − | 0.979816i | \(-0.564063\pi\) | ||||
−0.199904 | + | 0.979816i | \(0.564063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.24186 | 0.133579 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.0164 | −0.617692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.65970 | 0.191351 | 0.0956754 | − | 0.995413i | \(-0.469499\pi\) | ||||
0.0956754 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | −0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.4835 | −0.633696 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.1432 | 1.23162 | 0.615808 | − | 0.787896i | \(-0.288830\pi\) | ||||
0.615808 | + | 0.787896i | \(0.288830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.7089 | −1.45660 | −0.728299 | − | 0.685260i | \(-0.759689\pi\) | ||||
−0.728299 | + | 0.685260i | \(0.759689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.37907 | 0.0968831 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.7581 | −0.721971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.9669 | 1.41926 | 0.709632 | − | 0.704573i | \(-0.248861\pi\) | ||||
0.709632 | + | 0.704573i | \(0.248861\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.96719 | −0.0797144 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.34625 | 0.175831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8074 | 1.36547 | 0.682733 | − | 0.730668i | \(-0.260791\pi\) | ||||
0.682733 | + | 0.730668i | \(0.260791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.983593 | −0.0396623 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.4671 | 1.79018 | 0.895088 | − | 0.445889i | \(-0.147113\pi\) | ||||
0.895088 | + | 0.445889i | \(0.147113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0081 | 1.00516 | 0.502580 | − | 0.864531i | \(-0.332384\pi\) | ||||
0.502580 | + | 0.864531i | \(0.332384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.87086 | 0.0750752 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.01641 | 0.0407215 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.72532 | 0.108839 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −76.6758 | −3.05727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6043 | −1.01929 | −0.509645 | − | 0.860385i | \(-0.670223\pi\) | ||||
−0.509645 | + | 0.860385i | \(0.670223\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.72532 | −0.266886 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.74173 | 0.267117 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1044 | 0.518402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.7581 | −1.37286 | −0.686432 | − | 0.727194i | \(-0.740824\pi\) | ||||
−0.686432 | + | 0.727194i | \(0.740824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0716 | −0.752110 | −0.376055 | − | 0.926597i | \(-0.622720\pi\) | ||||
−0.376055 | + | 0.926597i | \(0.622720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8381 | 0.622658 | 0.311329 | − | 0.950302i | \(-0.399226\pi\) | ||||
0.311329 | + | 0.950302i | \(0.399226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 71.6594 | 2.81288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.24186 | −0.127059 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.0328 | −0.940477 | −0.470238 | − | 0.882539i | \(-0.655832\pi\) | ||||
−0.470238 | + | 0.882539i | \(0.655832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5962 | −0.492174 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.87086 | −0.307072 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.11273 | 0.199164 | 0.0995818 | − | 0.995029i | \(-0.468249\pi\) | ||||
0.0995818 | + | 0.995029i | \(0.468249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0796 | 1.32554 | 0.662772 | − | 0.748821i | \(-0.269380\pi\) | ||||
0.662772 | + | 0.748821i | \(0.269380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.87086 | 0.305679 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.258271 | −0.0100153 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.24186 | −0.280406 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.5410 | 0.407539 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.1760 | −1.24214 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1432 | −1.70159 | −0.850797 | − | 0.525495i | \(-0.823880\pi\) | ||||
−0.850797 | + | 0.525495i | \(0.823880\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.1760 | 1.00602 | 0.503012 | − | 0.864279i | \(-0.332225\pi\) | ||||
0.503012 | + | 0.864279i | \(0.332225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.93437 | 0.304493 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.3463 | −0.626390 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.03876 | −0.192803 | −0.0964015 | − | 0.995343i | \(-0.530733\pi\) | ||||
−0.0964015 | + | 0.995343i | \(0.530733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.9836 | −0.496078 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8873 | −0.644290 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.01641 | −0.114916 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.4423 | 1.72871 | 0.864353 | − | 0.502885i | \(-0.167728\pi\) | ||||
0.864353 | + | 0.502885i | \(0.167728\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.72532 | −0.103526 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.74173 | −0.293661 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.74173 | −0.293239 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.11273 | −0.117734 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.19476 | 0.158434 | 0.0792170 | − | 0.996857i | \(-0.474758\pi\) | ||||
0.0792170 | + | 0.996857i | \(0.474758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.95078 | −0.186722 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.34625 | −0.163689 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.45065 | 0.0545571 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6946 | −1.07765 | −0.538825 | − | 0.842418i | \(-0.681131\pi\) | ||||
−0.538825 | + | 0.842418i | \(0.681131\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.7581 | −0.478467 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.9344 | −0.446946 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.36266 | −0.200552 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.0716 | 0.562858 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7745 | −0.812053 | −0.406027 | − | 0.913861i | \(-0.633086\pi\) | ||||
−0.406027 | + | 0.913861i | \(0.633086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.45091 | −0.165761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.87086 | 0.143760 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4342 | 0.609512 | 0.304756 | − | 0.952430i | \(-0.401425\pi\) | ||||
0.304756 | + | 0.952430i | \(0.401425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.9669 | −2.32892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7089 | 0.432479 | 0.216239 | − | 0.976340i | \(-0.430621\pi\) | ||||
0.216239 | + | 0.976340i | \(0.430621\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.74173 | −0.248672 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7581 | −0.469952 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.4423 | −1.08305 | −0.541526 | − | 0.840684i | \(-0.682153\pi\) | ||||
−0.541526 | + | 0.840684i | \(0.682153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.508203 | 0.0186693 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.3296 | −1.03931 | −0.519656 | − | 0.854376i | \(-0.673940\pi\) | ||||
−0.519656 | + | 0.854376i | \(0.673940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.74173 | 0.0638120 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1044 | 0.625817 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.03281 | 0.0742774 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.24186 | 0.264259 | 0.132130 | − | 0.991232i | \(-0.457818\pi\) | ||||
0.132130 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.6454 | −0.570150 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.62093 | −0.0589918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7909 | 1.19181 | 0.595904 | − | 0.803056i | \(-0.296794\pi\) | ||||
0.595904 | + | 0.803056i | \(0.296794\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0328 | −0.364168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.4342 | −1.97324 | −0.986620 | − | 0.163038i | \(-0.947871\pi\) | ||||
−0.986620 | + | 0.163038i | \(0.947871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.582168 | −0.0210759 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.87086 | −0.284572 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.3627 | 0.482498 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9341 | −1.25976 | −0.629878 | − | 0.776694i | \(-0.716895\pi\) | ||||
−0.629878 | + | 0.776694i | \(0.716895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5962 | 0.525669 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.5327 | −1.60173 | −0.800865 | − | 0.598846i | \(-0.795626\pi\) | ||||
−0.800865 | + | 0.598846i | \(0.795626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.37907 | 0.229143 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.95078 | 0.177608 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.499865 | −0.0179095 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.2744 | −2.51462 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.87086 | −0.138333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4671 | −0.730500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.1536 | −1.43132 | −0.715661 | − | 0.698448i | \(-0.753874\pi\) | ||||
−0.715661 | + | 0.698448i | \(0.753874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.5634 | −0.660874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.96719 | −0.0699451 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | −0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.01641 | 0.106981 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.1267 | 1.66932 | 0.834658 | − | 0.550769i | \(-0.185666\pi\) | ||||
0.834658 | + | 0.550769i | \(0.185666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.2088 | −1.21022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.2088 | 1.48952 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.950780 | 0.0335106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.61259 | −0.267976 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.2416 | −0.360075 | −0.180038 | − | 0.983660i | \(-0.557622\pi\) | ||||
−0.180038 | + | 0.983660i | \(0.557622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.0409 | −1.23045 | −0.615226 | − | 0.788351i | \(-0.710935\pi\) | ||||
−0.615226 | + | 0.788351i | \(0.710935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.34625 | 0.152430 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.0880 | 0.703651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.06563 | −0.142238 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.508203 | −0.0177581 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7417 | 0.479590 | 0.239795 | − | 0.970824i | \(-0.422920\pi\) | ||||
0.239795 | + | 0.970824i | \(0.422920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.1432 | −1.74788 | −0.873940 | − | 0.486033i | \(-0.838443\pi\) | ||||
−0.873940 | + | 0.486033i | \(0.838443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.36266 | 0.186704 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.62093 | −0.334553 | −0.167276 | − | 0.985910i | \(-0.553497\pi\) | ||||
−0.167276 | + | 0.985910i | \(0.553497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06563 | 0.0717422 | 0.0358711 | − | 0.999356i | \(-0.488579\pi\) | ||||
0.0358711 | + | 0.999356i | \(0.488579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.25827 | −0.0783385 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.0632 | −1.83853 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.08798 | 0.279896 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.37907 | −0.220493 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.58812 | 0.261971 | 0.130985 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130985 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0164 | −0.483324 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0328135 | 0.00113016 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.02474 | 0.310094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.0328 | 0.618885 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.2255 | 0.624761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.6430 | −1.52855 | −0.764274 | − | 0.644892i | \(-0.776902\pi\) | ||||
−0.764274 | + | 0.644892i | \(0.776902\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.508203 | −0.0173802 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.43663 | 0.117393 | 0.0586965 | − | 0.998276i | \(-0.481306\pi\) | ||||
0.0586965 | + | 0.998276i | \(0.481306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.5819 | −1.41876 | −0.709378 | − | 0.704828i | \(-0.751024\pi\) | ||||
−0.709378 | + | 0.704828i | \(0.751024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.499865 | 0.0170354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9117 | −1.12033 | −0.560164 | − | 0.828381i | \(-0.689262\pi\) | ||||
−0.560164 | + | 0.828381i | \(0.689262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.4342 | −0.762787 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.9505 | −1.52660 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.4176 | 2.32091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.37907 | −0.0806116 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.6126 | 0.528406 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.508203 | −0.0171804 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.4506 | −1.19708 | −0.598542 | − | 0.801092i | \(-0.704253\pi\) | ||||
−0.598542 | + | 0.801092i | \(0.704253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.4999 | −1.02873 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1924 | 0.646608 | 0.323304 | − | 0.946295i | \(-0.395206\pi\) | ||||
0.323304 | + | 0.946295i | \(0.395206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.2088 | 1.01661 | 0.508303 | − | 0.861178i | \(-0.330273\pi\) | ||||
0.508303 | + | 0.861178i | \(0.330273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.3627 | −0.449181 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9201 | 0.433814 | 0.216907 | − | 0.976192i | \(-0.430403\pi\) | ||||
0.216907 | + | 0.976192i | \(0.430403\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.41783 | 0.114630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.36266 | −0.179656 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.20878 | −0.0739140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.90368 | 0.130486 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.87086 | −0.0624664 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.6925 | 0.823541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7417 | 0.790952 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.06563 | 0.135296 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.983593 | 0.0326957 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.5491 | −1.18039 | −0.590194 | − | 0.807261i | \(-0.700949\pi\) | ||||
−0.590194 | + | 0.807261i | \(0.700949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.85446 | 0.0946764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.53295 | −0.0507888 | −0.0253944 | − | 0.999678i | \(-0.508084\pi\) | ||||
−0.0253944 | + | 0.999678i | \(0.508084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −91.7251 | −3.03566 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.40142 | 0.211394 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.65375 | −0.252199 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1044 | −0.431336 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.74173 | −0.320306 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.75814 | −0.287655 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.9997 | 1.41078 | 0.705388 | − | 0.708822i | \(-0.250773\pi\) | ||||
0.705388 | + | 0.708822i | \(0.250773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.42617 | −0.112288 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.03281 | −0.0665513 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.2088 | 1.38037 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4178 | −0.830364 | −0.415182 | − | 0.909738i | \(-0.636282\pi\) | ||||
−0.415182 | + | 0.909738i | \(0.636282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.9836 | −0.554239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.2911 | −0.661470 | −0.330735 | − | 0.943724i | \(-0.607297\pi\) | ||||
−0.330735 | + | 0.943724i | \(0.607297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.84017 | 0.0599242 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.508203 | 0.0165319 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.4119 | 0.793280 | 0.396640 | − | 0.917974i | \(-0.370176\pi\) | ||||
0.396640 | + | 0.917974i | \(0.370176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.87086 | 0.255499 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.4506 | 0.630730 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.1455 | 0.944117 | 0.472058 | − | 0.881567i | \(-0.343511\pi\) | ||||
0.472058 | + | 0.881567i | \(0.343511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.27468 | −0.170685 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7581 | 0.671015 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.59831 | 0.213070 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.69251 | 0.312662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.5798 | 0.565913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2007 | 0.810400 | 0.405200 | − | 0.914228i | \(-0.367202\pi\) | ||||
0.405200 | + | 0.914228i | \(0.367202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5962 | −0.404231 | −0.202115 | − | 0.979362i | \(-0.564782\pi\) | ||||
−0.202115 | + | 0.979362i | \(0.564782\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.93437 | 0.126130 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.7909 | 0.921104 | 0.460552 | − | 0.887633i | \(-0.347651\pi\) | ||||
0.460552 | + | 0.887633i | \(0.347651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.7253 | −0.342783 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14554 | −0.0365743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.2968 | 1.60422 | 0.802109 | − | 0.597178i | \(-0.203711\pi\) | ||||
0.802109 | + | 0.597178i | \(0.203711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0164 | −0.478463 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.20878 | 0.0703063 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9669 | 0.475920 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.2744 | 1.21583 | 0.607913 | − | 0.794003i | \(-0.292007\pi\) | ||||
0.607913 | + | 0.794003i | \(0.292007\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.9917 | −0.507480 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.4835 | −0.490859 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1267 | 1.36584 | 0.682919 | − | 0.730494i | \(-0.260710\pi\) | ||||
0.682919 | + | 0.730494i | \(0.260710\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.74173 | 0.308215 |
(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 | 6240.2.a.bx.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 6240.2.a.ca.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.bx.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6240.2.a.ca.1.2 | yes | 3 | 4.3 | odd | 2 |