Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, 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("3744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.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: | \(29.8959905168\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.80423 | −1.43786 | −0.718931 | − | 0.695081i | \(-0.755368\pi\) | ||||
−0.718931 | + | 0.695081i | \(0.755368\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45309 | −0.438122 | −0.219061 | − | 0.975711i | \(-0.570299\pi\) | ||||
−0.219061 | + | 0.975711i | \(0.570299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.50651 | 1.95153 | 0.975763 | − | 0.218828i | \(-0.0702234\pi\) | ||||
0.975763 | + | 0.218828i | \(0.0702234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.80423 | −0.683259 | −0.341630 | − | 0.939835i | \(-0.610979\pi\) | ||||
−0.341630 | + | 0.939835i | \(0.610979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.3107 | −2.08089 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.763932 | 0.119306 | 0.0596531 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596531 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70228 | −0.717091 | −0.358546 | − | 0.933512i | \(-0.616727\pi\) | ||||
−0.358546 | + | 0.933512i | \(0.616727\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8576 | −1.58375 | −0.791875 | − | 0.610683i | \(-0.790895\pi\) | ||||
−0.791875 | + | 0.610683i | \(0.790895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.47214 | 1.06745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.9443 | 1.77803 | 0.889016 | − | 0.457876i | \(-0.151390\pi\) | ||||
0.889016 | + | 0.457876i | \(0.151390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.70228 | −0.634056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8576 | 1.41355 | 0.706773 | − | 0.707441i | \(-0.250150\pi\) | ||||
0.706773 | + | 0.707441i | \(0.250150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47214 | −0.572598 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.71040 | 0.819805 | 0.409903 | − | 0.912129i | \(-0.365563\pi\) | ||||
0.409903 | + | 0.912129i | \(0.365563\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45309 | −0.172449 | −0.0862247 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862247 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.52786 | 0.629959 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40456 | 1.05810 | 0.529048 | − | 0.848592i | \(-0.322549\pi\) | ||||
0.529048 | + | 0.848592i | \(0.322549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7638 | 1.51078 | 0.755388 | − | 0.655278i | \(-0.227449\pi\) | ||||
0.755388 | + | 0.655278i | \(0.227449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.29180 | 0.242930 | 0.121465 | − | 0.992596i | \(-0.461241\pi\) | ||||
0.121465 | + | 0.992596i | \(0.461241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.80423 | −0.398791 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.5276 | 2.82428 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.94427 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4721 | 1.44003 | 0.720016 | − | 0.693958i | \(-0.244135\pi\) | ||||
0.720016 | + | 0.693958i | \(0.244135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5146 | 1.03604 | 0.518018 | − | 0.855370i | \(-0.326670\pi\) | ||||
0.518018 | + | 0.855370i | \(0.326670\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.40456 | −0.909174 | −0.454587 | − | 0.890702i | \(-0.650213\pi\) | ||||
−0.454587 | + | 0.890702i | \(0.650213\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.40456 | 0.862115 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.88854 | −0.808049 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.60845 | −0.675141 | −0.337570 | − | 0.941300i | \(-0.609605\pi\) | ||||
−0.337570 | + | 0.941300i | \(0.609605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2169 | 1.32951 | 0.664754 | − | 0.747063i | \(-0.268537\pi\) | ||||
0.664754 | + | 0.747063i | \(0.268537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32.3607 | −2.80603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7082 | 1.17117 | 0.585585 | − | 0.810611i | \(-0.300865\pi\) | ||||
0.585585 | + | 0.810611i | \(0.300865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3107 | −1.04418 | −0.522091 | − | 0.852890i | \(-0.674848\pi\) | ||||
−0.522091 | + | 0.852890i | \(0.674848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.45309 | −0.121513 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.9443 | 1.07496 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7639 | 1.04566 | 0.522831 | − | 0.852436i | \(-0.324876\pi\) | ||||
0.522831 | + | 0.852436i | \(0.324876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00811 | −0.163418 | −0.0817090 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817090 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3107 | −0.988822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4164 | −1.70922 | −0.854608 | − | 0.519274i | \(-0.826202\pi\) | ||||
−0.854608 | + | 0.519274i | \(0.826202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.898056 | 0.0703412 | 0.0351706 | − | 0.999381i | \(-0.488803\pi\) | ||||
0.0351706 | + | 0.999381i | \(0.488803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8576 | −0.840190 | −0.420095 | − | 0.907480i | \(-0.638003\pi\) | ||||
−0.420095 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.52786 | 0.116161 | 0.0580807 | − | 0.998312i | \(-0.481502\pi\) | ||||
0.0580807 | + | 0.998312i | \(0.481502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.8172 | −1.57364 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.1231 | 1.35458 | 0.677291 | − | 0.735715i | \(-0.263154\pi\) | ||||
0.677291 | + | 0.735715i | \(0.263154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.52786 | −0.559542 | −0.279771 | − | 0.960067i | \(-0.590258\pi\) | ||||
−0.279771 | + | 0.960067i | \(0.590258\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.4721 | 1.65218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.59222 | 0.262689 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.5276 | −1.99183 | −0.995915 | − | 0.0902956i | \(-0.971219\pi\) | ||||
−0.995915 | + | 0.0902956i | \(0.971219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9443 | 1.07571 | 0.537856 | − | 0.843037i | \(-0.319234\pi\) | ||||
0.537856 | + | 0.843037i | \(0.319234\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.18034 | 0.582825 | 0.291413 | − | 0.956597i | \(-0.405875\pi\) | ||||
0.291413 | + | 0.956597i | \(0.405875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8254 | 1.61805 | 0.809023 | − | 0.587777i | \(-0.199997\pi\) | ||||
0.809023 | + | 0.587777i | \(0.199997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2169 | −1.06802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47214 | 0.172661 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.3607 | −0.855006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.6215 | 1.69501 | 0.847506 | − | 0.530786i | \(-0.178103\pi\) | ||||
0.847506 | + | 0.530786i | \(0.178103\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.2169 | −1.03778 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4721 | 0.982433 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00811 | 0.134473 | 0.0672366 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672366 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.5762 | −1.29932 | −0.649658 | − | 0.760227i | \(-0.725088\pi\) | ||||
−0.649658 | + | 0.760227i | \(0.725088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4164 | 1.27201 | 0.636006 | − | 0.771684i | \(-0.280586\pi\) | ||||
0.636006 | + | 0.771684i | \(0.280586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.1361 | −2.29203 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5762 | 1.26628 | 0.633138 | − | 0.774039i | \(-0.281766\pi\) | ||||
0.633138 | + | 0.774039i | \(0.281766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.8885 | −1.79646 | −0.898230 | − | 0.439527i | \(-0.855146\pi\) | ||||
−0.898230 | + | 0.439527i | \(0.855146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.1803 | 1.54483 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.50651 | 0.541256 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7153 | 1.37066 | 0.685329 | − | 0.728234i | \(-0.259659\pi\) | ||||
0.685329 | + | 0.728234i | \(0.259659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.4721 | 1.40177 | 0.700887 | − | 0.713273i | \(-0.252788\pi\) | ||||
0.700887 | + | 0.713273i | \(0.252788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.4176 | −1.64151 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.90617 | −0.179202 | −0.0896011 | − | 0.995978i | \(-0.528559\pi\) | ||||
−0.0896011 | + | 0.995978i | \(0.528559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.8885 | 2.57319 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.0000 | −1.21942 | −0.609711 | − | 0.792624i | \(-0.708714\pi\) | ||||
−0.609711 | + | 0.792624i | \(0.708714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.80423 | −0.231090 | −0.115545 | − | 0.993302i | \(-0.536861\pi\) | ||||
−0.115545 | + | 0.993302i | \(0.536861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.95148 | −0.479492 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7082 | 0.817763 | 0.408881 | − | 0.912588i | \(-0.365919\pi\) | ||||
0.408881 | + | 0.912588i | \(0.365919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.8254 | 1.35683 | 0.678413 | − | 0.734680i | \(-0.262668\pi\) | ||||
0.678413 | + | 0.734680i | \(0.262668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.90617 | −0.171546 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.1246 | −1.23411 | −0.617056 | − | 0.786919i | \(-0.711675\pi\) | ||||
−0.617056 | + | 0.786919i | \(0.711675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.1361 | 2.04570 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8885 | 1.03108 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4721 | −0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.898056 | −0.0512548 | −0.0256274 | − | 0.999672i | \(-0.508158\pi\) | ||||
−0.0256274 | + | 0.999672i | \(0.508158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8885 | −0.671980 | −0.335990 | − | 0.941866i | \(-0.609071\pi\) | ||||
−0.335990 | + | 0.941866i | \(0.609071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.5967 | −1.54999 | −0.774994 | − | 0.631969i | \(-0.782247\pi\) | ||||
−0.774994 | + | 0.631969i | \(0.782247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.81234 | −0.325429 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.0292 | −1.17010 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.47214 | 0.303539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.3050 | 2.27722 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50651 | −0.467560 | −0.233780 | − | 0.972290i | \(-0.575110\pi\) | ||||
−0.233780 | + | 0.972290i | \(0.575110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.7153 | 1.18643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.52786 | 0.299351 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.79611 | −0.0969809 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.81234 | −0.312023 | −0.156011 | − | 0.987755i | \(-0.549864\pi\) | ||||
−0.156011 | + | 0.987755i | \(0.549864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.8885 | 1.49284 | 0.746420 | − | 0.665475i | \(-0.231771\pi\) | ||||
0.746420 | + | 0.665475i | \(0.231771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2361 | −1.23673 | −0.618366 | − | 0.785891i | \(-0.712205\pi\) | ||||
−0.618366 | + | 0.785891i | \(0.712205\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.70228 | −0.249571 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.9807 | 1.52954 | 0.764772 | − | 0.644301i | \(-0.222852\pi\) | ||||
0.764772 | + | 0.644301i | \(0.222852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.3607 | 2.80846 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.4164 | 1.01630 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7153 | −1.13353 | −0.566765 | − | 0.823880i | \(-0.691805\pi\) | ||||
−0.566765 | + | 0.823880i | \(0.691805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −49.2429 | −2.55657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.898056 | −0.0461300 | −0.0230650 | − | 0.999734i | \(-0.507342\pi\) | ||||
−0.0230650 | + | 0.999734i | \(0.507342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.1684 | −1.18385 | −0.591925 | − | 0.805993i | \(-0.701632\pi\) | ||||
−0.591925 | + | 0.805993i | \(0.701632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.8885 | 0.911685 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.52786 | 0.280274 | 0.140137 | − | 0.990132i | \(-0.455246\pi\) | ||||
0.140137 | + | 0.990132i | \(0.455246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.4338 | 1.53129 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8328 | −1.44708 | −0.723539 | − | 0.690284i | \(-0.757486\pi\) | ||||
−0.723539 | + | 0.690284i | \(0.757486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2918 | 0.913449 | 0.456724 | − | 0.889608i | \(-0.349023\pi\) | ||||
0.456724 | + | 0.889608i | \(0.349023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.80423 | −0.189502 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0906 | −0.500173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8885 | 1.18121 | 0.590606 | − | 0.806960i | \(-0.298889\pi\) | ||||
0.590606 | + | 0.806960i | \(0.298889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.3050 | −2.03248 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.5407 | 2.18641 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.0260 | 1.66228 | 0.831140 | − | 0.556063i | \(-0.187689\pi\) | ||||
0.831140 | + | 0.556063i | \(0.187689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.5279 | −0.656198 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0130 | 0.823318 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.9807 | −1.39595 | −0.697976 | − | 0.716121i | \(-0.745916\pi\) | ||||
−0.697976 | + | 0.716121i | \(0.745916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4164 | 0.836979 | 0.418490 | − | 0.908222i | \(-0.362560\pi\) | ||||
0.418490 | + | 0.908222i | \(0.362560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.7315 | −1.22810 | −0.614049 | − | 0.789268i | \(-0.710460\pi\) | ||||
−0.614049 | + | 0.789268i | \(0.710460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.40456 | −0.446824 | −0.223412 | − | 0.974724i | \(-0.571720\pi\) | ||||
−0.223412 | + | 0.974724i | \(0.571720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41641 | 0.351571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.81966 | −0.180261 | −0.0901305 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901305 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.11006 | −0.0522706 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.3107 | −0.577136 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.05573 | 0.423609 | 0.211805 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211805 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.0689 | 1.58675 | 0.793373 | − | 0.608736i | \(-0.208323\pi\) | ||||
0.793373 | + | 0.608736i | \(0.208323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0211 | −0.883987 | −0.441993 | − | 0.897018i | \(-0.645729\pi\) | ||||
−0.441993 | + | 0.897018i | \(0.645729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5276 | 1.27383 | 0.636914 | − | 0.770935i | \(-0.280211\pi\) | ||||
0.636914 | + | 0.770935i | \(0.280211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.5279 | −1.17877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.83282 | 0.314173 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 46.5488 | 2.13580 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6700 | 0.761671 | 0.380836 | − | 0.924643i | \(-0.375636\pi\) | ||||
0.380836 | + | 0.924643i | \(0.375636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.94427 | 0.316632 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.4721 | −1.02041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0049 | 0.679937 | 0.339969 | − | 0.940437i | \(-0.389584\pi\) | ||||
0.339969 | + | 0.940437i | \(0.389584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.71851 | 0.393461 | 0.196730 | − | 0.980458i | \(-0.436968\pi\) | ||||
0.196730 | + | 0.980458i | \(0.436968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.88854 | −0.445358 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.52786 | 0.247959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.1280 | −1.48301 | −0.741506 | − | 0.670946i | \(-0.765888\pi\) | ||||
−0.741506 | + | 0.670946i | \(0.765888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7153 | 0.968237 | 0.484119 | − | 0.875002i | \(-0.339140\pi\) | ||||
0.484119 | + | 0.875002i | \(0.339140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.8328 | 2.08403 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7082 | −1.13950 | −0.569748 | − | 0.821819i | \(-0.692959\pi\) | ||||
−0.569748 | + | 0.821819i | \(0.692959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.8254 | −1.00973 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.0260 | 1.49937 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7771 | 0.693876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.8885 | −1.65993 | −0.829964 | − | 0.557818i | \(-0.811639\pi\) | ||||
−0.829964 | + | 0.557818i | \(0.811639\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.3107 | −0.538311 | −0.269155 | − | 0.963097i | \(-0.586745\pi\) | ||||
−0.269155 | + | 0.963097i | \(0.586745\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.40456 | 0.409669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.763932 | 0.0330896 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.4338 | −1.31577 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.8576 | −0.467672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.94427 | −0.298558 | −0.149279 | − | 0.988795i | \(-0.547695\pi\) | ||||
−0.149279 | + | 0.988795i | \(0.547695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.52786 | 0.408129 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3107 | 0.526369 | 0.263184 | − | 0.964746i | \(-0.415227\pi\) | ||||
0.263184 | + | 0.964746i | \(0.415227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.0260 | 1.44956 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.7771 | −1.52140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5967 | 1.16931 | 0.584656 | − | 0.811281i | \(-0.301230\pi\) | ||||
0.584656 | + | 0.811281i | \(0.301230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.70228 | −0.198885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.3107 | −0.518836 | −0.259418 | − | 0.965765i | \(-0.583531\pi\) | ||||
−0.259418 | + | 0.965765i | \(0.583531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9443 | 0.544570 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.4721 | 0.606704 | 0.303352 | − | 0.952879i | \(-0.401894\pi\) | ||||
0.303352 | + | 0.952879i | \(0.401894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.01623 | −0.168074 | −0.0840370 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840370 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0557 | 0.543517 | 0.271759 | − | 0.962365i | \(-0.412395\pi\) | ||||
0.271759 | + | 0.962365i | \(0.412395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −52.3607 | −2.17229 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8091 | −0.778994 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9807 | 1.19616 | 0.598081 | − | 0.801435i | \(-0.295930\pi\) | ||||
0.598081 | + | 0.801435i | \(0.295930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.3607 | −1.33340 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.7082 | −1.87701 | −0.938505 | − | 0.345264i | \(-0.887789\pi\) | ||||
−0.938505 | + | 0.345264i | \(0.887789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.4338 | 1.24766 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5276 | 1.12475 | 0.562374 | − | 0.826883i | \(-0.309888\pi\) | ||||
0.562374 | + | 0.826883i | \(0.309888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.8885 | −1.13760 | −0.568799 | − | 0.822477i | \(-0.692592\pi\) | ||||
−0.568799 | + | 0.822477i | \(0.692592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.7639 | −1.16942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.9322 | −1.49903 | −0.749516 | − | 0.661986i | \(-0.769714\pi\) | ||||
−0.749516 | + | 0.661986i | \(0.769714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8576 | −0.439253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0689 | −0.888460 | −0.444230 | − | 0.895913i | \(-0.646523\pi\) | ||||
−0.444230 | + | 0.895913i | \(0.646523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5358 | 1.18714 | 0.593571 | − | 0.804782i | \(-0.297718\pi\) | ||||
0.593571 | + | 0.804782i | \(0.297718\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.71851 | −0.349300 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.1672 | −0.684500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.4387 | −1.80889 | −0.904443 | − | 0.426594i | \(-0.859713\pi\) | ||||
−0.904443 | + | 0.426594i | \(0.859713\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.6215 | −0.977073 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.47214 | 0.296057 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3607 | −0.804199 | −0.402099 | − | 0.915596i | \(-0.631719\pi\) | ||||
−0.402099 | + | 0.915596i | \(0.631719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.7364 | 1.60649 | 0.803244 | − | 0.595650i | \(-0.203106\pi\) | ||||
0.803244 | + | 0.595650i | \(0.203106\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7771 | −0.619305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0557 | 0.589176 | 0.294588 | − | 0.955624i | \(-0.404818\pi\) | ||||
0.294588 | + | 0.955624i | \(0.404818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.2429 | 1.92408 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6215 | 0.959116 | 0.479558 | − | 0.877510i | \(-0.340797\pi\) | ||||
0.479558 | + | 0.877510i | \(0.340797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.7771 | −1.00261 | −0.501306 | − | 0.865270i | \(-0.667147\pi\) | ||||
−0.501306 | + | 0.865270i | \(0.667147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −104.721 | −4.06092 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.49839 | 0.250868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.41641 | −0.362976 | −0.181488 | − | 0.983393i | \(-0.558091\pi\) | ||||
−0.181488 | + | 0.983393i | \(0.558091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.7771 | 1.68249 | 0.841245 | − | 0.540654i | \(-0.181823\pi\) | ||||
0.841245 | + | 0.540654i | \(0.181823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.4176 | 1.01381 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8576 | −0.415456 | −0.207728 | − | 0.978187i | \(-0.566607\pi\) | ||||
−0.207728 | + | 0.978187i | \(0.566607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.3607 | 1.69493 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9443 | 0.493137 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5195 | 0.970808 | 0.485404 | − | 0.874290i | \(-0.338672\pi\) | ||||
0.485404 | + | 0.874290i | \(0.338672\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.8384 | −1.51116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.88854 | −0.0715337 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.47214 | −0.0933713 | −0.0466856 | − | 0.998910i | \(-0.514866\pi\) | ||||
−0.0466856 | + | 0.998910i | \(0.514866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.0715 | 2.22792 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55.0553 | −2.07057 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.7771 | −1.71919 | −0.859597 | − | 0.510972i | \(-0.829286\pi\) | ||||
−0.859597 | + | 0.510972i | \(0.829286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.70228 | −0.175855 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.6215 | −0.918226 | −0.459113 | − | 0.888378i | \(-0.651833\pi\) | ||||
−0.459113 | + | 0.888378i | \(0.651833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0000 | −1.48968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.8885 | 0.812920 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.2299 | −1.19534 | −0.597671 | − | 0.801742i | \(-0.703907\pi\) | ||||
−0.597671 | + | 0.801742i | \(0.703907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6247 | 0.429954 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.05573 | −0.186738 | −0.0933688 | − | 0.995632i | \(-0.529764\pi\) | ||||
−0.0933688 | + | 0.995632i | \(0.529764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.75078 | −0.359174 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3319 | −1.15256 | −0.576281 | − | 0.817252i | \(-0.695496\pi\) | ||||
−0.576281 | + | 0.817252i | \(0.695496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.6960 | −1.85986 | −0.929928 | − | 0.367741i | \(-0.880131\pi\) | ||||
−0.929928 | + | 0.367741i | \(0.880131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.3050 | 1.51330 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.7771 | 1.30727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.1361 | −1.28213 | −0.641067 | − | 0.767485i | \(-0.721508\pi\) | ||||
−0.641067 | + | 0.767485i | \(0.721508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.49839 | −0.236501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.4164 | −1.65069 | −0.825344 | − | 0.564631i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564631i | \(0.809019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6525 | 0.386152 | 0.193076 | − | 0.981184i | \(-0.438154\pi\) | ||||
0.193076 | + | 0.981184i | \(0.438154\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2007 | −0.405492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.8576 | 0.392047 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8328 | 0.607007 | 0.303503 | − | 0.952830i | \(-0.401844\pi\) | ||||
0.303503 | + | 0.952830i | \(0.401844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.2918 | −0.801780 | −0.400890 | − | 0.916126i | \(-0.631299\pi\) | ||||
−0.400890 | + | 0.916126i | \(0.631299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.8172 | −0.747777 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.49839 | 0.232829 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.11146 | 0.0755538 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −69.3050 | −2.47360 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.3287 | −1.58015 | −0.790073 | − | 0.613013i | \(-0.789957\pi\) | ||||
−0.790073 | + | 0.613013i | \(0.789957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.2169 | −0.541051 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.47214 | −0.158810 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.4164 | −0.546077 | −0.273039 | − | 0.962003i | \(-0.588029\pi\) | ||||
−0.273039 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.8416 | 0.949587 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.71851 | −0.307670 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.00000 | −0.140633 | −0.0703163 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703163 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.49028 | −0.157675 | −0.0788375 | − | 0.996887i | \(-0.525121\pi\) | ||||
−0.0788375 | + | 0.996887i | \(0.525121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.90617 | 0.101799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.0000 | −1.39942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5967 | 0.404729 | 0.202365 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202365 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1068 | 0.491734 | 0.245867 | − | 0.969304i | \(-0.420927\pi\) | ||||
0.245867 | + | 0.969304i | \(0.420927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.4823 | −0.781787 | −0.390894 | − | 0.920436i | \(-0.627834\pi\) | ||||
−0.390894 | + | 0.920436i | \(0.627834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.47214 | −0.294249 | −0.147125 | − | 0.989118i | \(-0.547002\pi\) | ||||
−0.147125 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4721 | −0.640022 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.1361 | −1.21593 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.3560 | −0.599197 | −0.299599 | − | 0.954065i | \(-0.596853\pi\) | ||||
−0.299599 | + | 0.954065i | \(0.596853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.23607 | 0.111324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.8140 | 1.16186 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8328 | 1.12417 | 0.562087 | − | 0.827078i | \(-0.309999\pi\) | ||||
0.562087 | + | 0.827078i | \(0.309999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.3050 | −0.454488 | −0.227244 | − | 0.973838i | \(-0.572972\pi\) | ||||
−0.227244 | + | 0.973838i | \(0.572972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.40456 | 0.320880 | 0.160440 | − | 0.987046i | \(-0.448709\pi\) | ||||
0.160440 | + | 0.987046i | \(0.448709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1684 | −0.788661 | −0.394330 | − | 0.918969i | \(-0.629023\pi\) | ||||
−0.394330 | + | 0.918969i | \(0.629023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.94427 | 0.168110 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6656 | −0.463575 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.71040 | 0.227373 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.81234 | −0.196493 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0557 | 0.440861 | 0.220430 | − | 0.975403i | \(-0.429254\pi\) | ||||
0.220430 | + | 0.975403i | \(0.429254\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3607 | 1.35979 | 0.679893 | − | 0.733311i | \(-0.262026\pi\) | ||||
0.679893 | + | 0.733311i | \(0.262026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.8546 | −1.47582 | −0.737912 | − | 0.674896i | \(-0.764188\pi\) | ||||
−0.737912 | + | 0.674896i | \(0.764188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.9030 | 0.533969 | 0.266985 | − | 0.963701i | \(-0.413973\pi\) | ||||
0.266985 | + | 0.963701i | \(0.413973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.9443 | 0.970760 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −92.3607 | −3.09073 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.6475 | 1.96037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.2169 | −0.507512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.0000 | −1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.3607 | −0.809776 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.60845 | 0.252635 | 0.126317 | − | 0.991990i | \(-0.459684\pi\) | ||||
0.126317 | + | 0.991990i | \(0.459684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.71851 | −0.288857 | −0.144429 | − | 0.989515i | \(-0.546134\pi\) | ||||
−0.144429 | + | 0.989515i | \(0.546134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0000 | −0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −57.8885 | −1.91165 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.40456 | 0.310228 | 0.155114 | − | 0.987897i | \(-0.450426\pi\) | ||||
0.155114 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.45309 | −0.0478289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.0000 | 1.24943 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.1803 | −1.18704 | −0.593519 | − | 0.804820i | \(-0.702262\pi\) | ||||
−0.593519 | + | 0.804820i | \(0.702262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 63.5618 | 2.08315 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.6247 | 0.380168 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.4721 | 1.19149 | 0.595746 | − | 0.803173i | \(-0.296856\pi\) | ||||
0.595746 | + | 0.803173i | \(0.296856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.70820 | 0.0556859 | 0.0278429 | − | 0.999612i | \(-0.491136\pi\) | ||||
0.0278429 | + | 0.999612i | \(0.491136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.6960 | 1.64740 | 0.823700 | − | 0.567026i | \(-0.191906\pi\) | ||||
0.823700 | + | 0.567026i | \(0.191906\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.5836 | −0.407623 | −0.203811 | − | 0.979010i | \(-0.565333\pi\) | ||||
−0.203811 | + | 0.979010i | \(0.565333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −89.0813 | −2.88260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.1491 | −1.68398 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5279 | −0.533157 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.3607 | 1.55679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4419 | 1.04326 | 0.521631 | − | 0.853171i | \(-0.325324\pi\) | ||||
0.521631 | + | 0.853171i | \(0.325324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8091 | −0.603614 | −0.301807 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301807 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.8328 | 1.50139 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.87539 | −0.219963 | −0.109982 | − | 0.993934i | \(-0.535079\pi\) | ||||
−0.109982 | + | 0.993934i | \(0.535079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.33017 | −0.106433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0778 | 0.417116 | 0.208558 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208558 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.4721 | 0.843472 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.1199 | 0.988555 | 0.494278 | − | 0.869304i | \(-0.335433\pi\) | ||||
0.494278 | + | 0.869304i | \(0.335433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73.8644 | 2.34166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8885 | 1.26328 | 0.631641 | − | 0.775261i | \(-0.282382\pi\) | ||||
0.631641 | + | 0.775261i | \(0.282382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3744.2.a.bf.1.3 | yes | 4 | |
3.2 | odd | 2 | 3744.2.a.bb.1.1 | ✓ | 4 | ||
4.3 | odd | 2 | inner | 3744.2.a.bf.1.4 | yes | 4 | |
8.3 | odd | 2 | 7488.2.a.cz.1.2 | 4 | |||
8.5 | even | 2 | 7488.2.a.cz.1.1 | 4 | |||
12.11 | even | 2 | 3744.2.a.bb.1.2 | yes | 4 | ||
24.5 | odd | 2 | 7488.2.a.dd.1.3 | 4 | |||
24.11 | even | 2 | 7488.2.a.dd.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3744.2.a.bb.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
3744.2.a.bb.1.2 | yes | 4 | 12.11 | even | 2 | ||
3744.2.a.bf.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
3744.2.a.bf.1.4 | yes | 4 | 4.3 | odd | 2 | inner | |
7488.2.a.cz.1.1 | 4 | 8.5 | even | 2 | |||
7488.2.a.cz.1.2 | 4 | 8.3 | odd | 2 | |||
7488.2.a.dd.1.3 | 4 | 24.5 | odd | 2 | |||
7488.2.a.dd.1.4 | 4 | 24.11 | even | 2 |