Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, 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("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23607 | −0.784862 | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392431 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.70820 | 1.43138 | 0.715689 | − | 0.698419i | \(-0.246113\pi\) | ||||
0.715689 | + | 0.698419i | \(0.246113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4721 | −1.88085 | −0.940426 | − | 0.340000i | \(-0.889573\pi\) | ||||
−0.940426 | + | 0.340000i | \(0.889573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.472136 | −0.0776187 | −0.0388093 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388093 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.472136 | −0.0737352 | −0.0368676 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368676 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7082 | 1.70782 | 0.853909 | − | 0.520423i | \(-0.174226\pi\) | ||||
0.853909 | + | 0.520423i | \(0.174226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.76393 | −0.929098 | −0.464549 | − | 0.885548i | \(-0.653783\pi\) | ||||
−0.464549 | + | 0.885548i | \(0.653783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.47214 | 0.872703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4164 | 1.71780 | 0.858898 | − | 0.512148i | \(-0.171150\pi\) | ||||
0.858898 | + | 0.512148i | \(0.171150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4721 | −1.27938 | −0.639688 | − | 0.768635i | \(-0.720936\pi\) | ||||
−0.639688 | + | 0.768635i | \(0.720936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.70820 | 0.677439 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.52786 | 0.412905 | 0.206453 | − | 0.978457i | \(-0.433808\pi\) | ||||
0.206453 | + | 0.978457i | \(0.433808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.291796 | 0.0320288 | 0.0160144 | − | 0.999872i | \(-0.494902\pi\) | ||||
0.0160144 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4721 | −1.13586 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.47214 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.23607 | −0.332014 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.41641 | 0.956091 | 0.478046 | − | 0.878335i | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.2361 | 1.51605 | 0.758023 | − | 0.652228i | \(-0.226166\pi\) | ||||
0.758023 | + | 0.652228i | \(0.226166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.18034 | −0.404129 | −0.202064 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202064 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.76393 | 0.260009 | 0.130004 | − | 0.991513i | \(-0.458501\pi\) | ||||
0.130004 | + | 0.991513i | \(0.458501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.47214 | −0.603530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.23607 | −0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4164 | 1.01304 | 0.506521 | − | 0.862228i | \(-0.330931\pi\) | ||||
0.506521 | + | 0.862228i | \(0.330931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7639 | 0.940449 | 0.470225 | − | 0.882547i | \(-0.344173\pi\) | ||||
0.470225 | + | 0.882547i | \(0.344173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4721 | 1.56679 | 0.783393 | − | 0.621527i | \(-0.213487\pi\) | ||||
0.783393 | + | 0.621527i | \(0.213487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427 | 0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.9443 | 2.07151 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.4721 | −1.84099 | −0.920495 | − | 0.390755i | \(-0.872214\pi\) | ||||
−0.920495 | + | 0.390755i | \(0.872214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.8885 | −2.72199 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4721 | −0.995385 | −0.497692 | − | 0.867354i | \(-0.665819\pi\) | ||||
−0.497692 | + | 0.867354i | \(0.665819\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.41641 | −0.264370 | −0.132185 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132185 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5279 | 0.876447 | 0.438224 | − | 0.898866i | \(-0.355608\pi\) | ||||
0.438224 | + | 0.898866i | \(0.355608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.47214 | 0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.70820 | −0.426651 | −0.213326 | − | 0.976981i | \(-0.568430\pi\) | ||||
−0.213326 | + | 0.976981i | \(0.568430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4721 | −0.927047 | −0.463523 | − | 0.886085i | \(-0.653415\pi\) | ||||
−0.463523 | + | 0.886085i | \(0.653415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.52786 | −0.112331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.47214 | −0.473289 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0000 | 0.723575 | 0.361787 | − | 0.932261i | \(-0.382167\pi\) | ||||
0.361787 | + | 0.932261i | \(0.382167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.472136 | 0.0339851 | 0.0169925 | − | 0.999856i | \(-0.494591\pi\) | ||||
0.0169925 | + | 0.999856i | \(0.494591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.05573 | −0.216615 | −0.108307 | − | 0.994117i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994117i | \(0.534543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.70820 | 0.541010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.52786 | −0.106711 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.47214 | 0.170189 | 0.0850944 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850944 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.8885 | 1.76558 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4721 | −0.710895 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4721 | −1.50485 | −0.752423 | − | 0.658680i | \(-0.771115\pi\) | ||||
−0.752423 | + | 0.658680i | \(0.771115\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4721 | −0.960549 | −0.480275 | − | 0.877118i | \(-0.659463\pi\) | ||||
−0.480275 | + | 0.877118i | \(0.659463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.94427 | −0.194563 | −0.0972815 | − | 0.995257i | \(-0.531015\pi\) | ||||
−0.0972815 | + | 0.995257i | \(0.531015\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 37.8885 | 2.47158 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4164 | 0.867835 | 0.433918 | − | 0.900953i | \(-0.357131\pi\) | ||||
0.433918 | + | 0.900953i | \(0.357131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.41641 | −0.348902 | −0.174451 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174451 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.23607 | 0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.47214 | −0.284555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2361 | −1.08793 | −0.543965 | − | 0.839108i | \(-0.683078\pi\) | ||||
−0.543965 | + | 0.839108i | \(0.683078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9443 | 0.932198 | 0.466099 | − | 0.884733i | \(-0.345659\pi\) | ||||
0.466099 | + | 0.884733i | \(0.345659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.472136 | −0.0293371 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5279 | 0.710839 | 0.355419 | − | 0.934707i | \(-0.384338\pi\) | ||||
0.355419 | + | 0.934707i | \(0.384338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8885 | −1.34460 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4164 | −1.17946 | −0.589731 | − | 0.807599i | \(-0.700766\pi\) | ||||
−0.589731 | + | 0.807599i | \(0.700766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.9443 | 0.659964 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.41641 | −0.325440 | −0.162720 | − | 0.986672i | \(-0.552027\pi\) | ||||
−0.162720 | + | 0.986672i | \(0.552027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76393 | 0.403502 | 0.201751 | − | 0.979437i | \(-0.435337\pi\) | ||||
0.201751 | + | 0.979437i | \(0.435337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9443 | −1.00723 | −0.503616 | − | 0.863927i | \(-0.667997\pi\) | ||||
−0.503616 | + | 0.863927i | \(0.667997\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.472136 | −0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4721 | 0.962312 | 0.481156 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481156 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.9443 | −1.68520 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.94427 | −0.517261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.4164 | 2.48602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.4721 | −1.51084 | −0.755422 | − | 0.655238i | \(-0.772568\pi\) | ||||
−0.755422 | + | 0.655238i | \(0.772568\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.6525 | 1.85155 | 0.925776 | − | 0.378072i | \(-0.123413\pi\) | ||||
0.925776 | + | 0.378072i | \(0.123413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.4164 | −1.21053 | −0.605263 | − | 0.796025i | \(-0.706932\pi\) | ||||
−0.605263 | + | 0.796025i | \(0.706932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.6525 | 0.935296 | 0.467648 | − | 0.883915i | \(-0.345101\pi\) | ||||
0.467648 | + | 0.883915i | \(0.345101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4164 | 0.863153 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.23607 | 0.180060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.4721 | 1.35747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7082 | 0.645494 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9443 | −1.59092 | −0.795461 | − | 0.606005i | \(-0.792771\pi\) | ||||
−0.795461 | + | 0.606005i | \(0.792771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.8885 | −1.85153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9443 | 0.596172 | 0.298086 | − | 0.954539i | \(-0.403652\pi\) | ||||
0.298086 | + | 0.954539i | \(0.403652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.9443 | −1.13420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3607 | −0.770922 | −0.385461 | − | 0.922724i | \(-0.625958\pi\) | ||||
−0.385461 | + | 0.922724i | \(0.625958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0557 | 0.912972 | 0.456486 | − | 0.889731i | \(-0.349108\pi\) | ||||
0.456486 | + | 0.889731i | \(0.349108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.81966 | 0.416199 | 0.208099 | − | 0.978108i | \(-0.433272\pi\) | ||||
0.208099 | + | 0.978108i | \(0.433272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.4721 | 0.980399 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.94427 | −0.155393 | −0.0776964 | − | 0.996977i | \(-0.524756\pi\) | ||||
−0.0776964 | + | 0.996977i | \(0.524756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4164 | 0.597562 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.05573 | 0.159508 | 0.0797539 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797539 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.76393 | −0.351166 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.88854 | −0.201341 | −0.100671 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100671 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.4721 | 1.77541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4721 | 0.535101 | 0.267551 | − | 0.963544i | \(-0.413786\pi\) | ||||
0.267551 | + | 0.963544i | \(0.413786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.47214 | 0.329851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.3607 | −1.03233 | −0.516164 | − | 0.856490i | \(-0.672640\pi\) | ||||
−0.516164 | + | 0.856490i | \(0.672640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.47214 | 0.327310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9443 | 0.651297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8885 | 0.797423 | 0.398712 | − | 0.917076i | \(-0.369457\pi\) | ||||
0.398712 | + | 0.917076i | \(0.369457\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.23607 | 0.461227 | 0.230614 | − | 0.973045i | \(-0.425927\pi\) | ||||
0.230614 | + | 0.973045i | \(0.425927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46.8328 | −2.33291 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.944272 | −0.0468058 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3050 | −1.35014 | −0.675071 | − | 0.737752i | \(-0.735887\pi\) | ||||
−0.675071 | + | 0.737752i | \(0.735887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.94427 | −0.440119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.944272 | 0.0463525 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.5967 | −1.05507 | −0.527535 | − | 0.849533i | \(-0.676884\pi\) | ||||
−0.527535 | + | 0.849533i | \(0.676884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4721 | 1.19270 | 0.596349 | − | 0.802725i | \(-0.296617\pi\) | ||||
0.596349 | + | 0.802725i | \(0.296617\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.7082 | −0.858974 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4164 | 0.649265 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.65248 | 0.127765 | 0.0638826 | − | 0.997957i | \(-0.479652\pi\) | ||||
0.0638826 | + | 0.997957i | \(0.479652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4164 | 1.79812 | 0.899059 | − | 0.437828i | \(-0.144252\pi\) | ||||
0.899059 | + | 0.437828i | \(0.144252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3607 | −1.54449 | −0.772245 | − | 0.635324i | \(-0.780866\pi\) | ||||
−0.772245 | + | 0.635324i | \(0.780866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.4164 | 0.637433 | 0.318716 | − | 0.947850i | \(-0.396748\pi\) | ||||
0.318716 | + | 0.947850i | \(0.396748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4721 | 0.686045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.7639 | −0.885525 | −0.442762 | − | 0.896639i | \(-0.646001\pi\) | ||||
−0.442762 | + | 0.896639i | \(0.646001\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.944272 | −0.0444640 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.4721 | 0.678464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.41641 | −0.253369 | −0.126684 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0689 | 1.40045 | 0.700224 | − | 0.713923i | \(-0.253084\pi\) | ||||
0.700224 | + | 0.713923i | \(0.253084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.11146 | −0.284023 | −0.142012 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142012 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.2361 | −1.16779 | −0.583893 | − | 0.811831i | \(-0.698471\pi\) | ||||
−0.583893 | + | 0.811831i | \(0.698471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4721 | −0.483558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.0000 | 0.735681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.47214 | −0.251079 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.2918 | 0.561626 | 0.280813 | − | 0.959762i | \(-0.409396\pi\) | ||||
0.280813 | + | 0.959762i | \(0.409396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.11146 | −0.0962741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.4721 | 1.38367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5836 | −0.570217 | −0.285108 | − | 0.958495i | \(-0.592030\pi\) | ||||
−0.285108 | + | 0.958495i | \(0.592030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.3050 | 1.41277 | 0.706386 | − | 0.707826i | \(-0.250324\pi\) | ||||
0.706386 | + | 0.707826i | \(0.250324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.9443 | −1.12343 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.70820 | 0.256048 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.8885 | −1.33799 | −0.668997 | − | 0.743265i | \(-0.733276\pi\) | ||||
−0.668997 | + | 0.743265i | \(0.733276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.7082 | 0.700394 | 0.350197 | − | 0.936676i | \(-0.386115\pi\) | ||||
0.350197 | + | 0.936676i | \(0.386115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.3050 | 2.19404 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.88854 | −0.349654 | −0.174827 | − | 0.984599i | \(-0.555937\pi\) | ||||
−0.174827 | + | 0.984599i | \(0.555937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52786 | 0.156064 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.9443 | 0.570393 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.4164 | 1.02985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.8885 | −1.92279 | −0.961396 | − | 0.275169i | \(-0.911266\pi\) | ||||
−0.961396 | + | 0.275169i | \(0.911266\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.3050 | −0.931600 | −0.465800 | − | 0.884890i | \(-0.654233\pi\) | ||||
−0.465800 | + | 0.884890i | \(0.654233\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.8885 | 1.47621 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.11146 | −0.0914573 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.5279 | −0.584861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.3607 | 1.38618 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.70820 | −0.328381 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3050 | 1.24169 | 0.620845 | − | 0.783933i | \(-0.286789\pi\) | ||||
0.620845 | + | 0.783933i | \(0.286789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.7771 | 1.51321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.52786 | −0.401552 | −0.200776 | − | 0.979637i | \(-0.564346\pi\) | ||||
−0.200776 | + | 0.979637i | \(0.564346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.94427 | 0.376288 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.87539 | 0.204387 | 0.102193 | − | 0.994765i | \(-0.467414\pi\) | ||||
0.102193 | + | 0.994765i | \(0.467414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.8885 | 0.916007 | 0.458004 | − | 0.888950i | \(-0.348565\pi\) | ||||
0.458004 | + | 0.888950i | \(0.348565\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.9443 | −0.456408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4721 | −1.35183 | −0.675916 | − | 0.736978i | \(-0.736252\pi\) | ||||
−0.675916 | + | 0.736978i | \(0.736252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.291796 | 0.0121057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5279 | −0.560267 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.87539 | 0.201229 | 0.100614 | − | 0.994925i | \(-0.467919\pi\) | ||||
0.100614 | + | 0.994925i | \(0.467919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.4721 | 0.431497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5410 | −0.843519 | −0.421759 | − | 0.906708i | \(-0.638587\pi\) | ||||
−0.421759 | + | 0.906708i | \(0.638587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4721 | −0.429316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5967 | −0.473830 | −0.236915 | − | 0.971530i | \(-0.576136\pi\) | ||||
−0.236915 | + | 0.971530i | \(0.576136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3050 | −1.44012 | −0.720060 | − | 0.693912i | \(-0.755886\pi\) | ||||
−0.720060 | + | 0.693912i | \(0.755886\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.6525 | −0.920954 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9443 | −1.17481 | −0.587406 | − | 0.809292i | \(-0.699851\pi\) | ||||
−0.587406 | + | 0.809292i | \(0.699851\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.3607 | 2.11829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.36068 | −0.0953470 | −0.0476735 | − | 0.998863i | \(-0.515181\pi\) | ||||
−0.0476735 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.8885 | −1.20327 | −0.601634 | − | 0.798772i | \(-0.705483\pi\) | ||||
−0.601634 | + | 0.798772i | \(0.705483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.58359 | 0.345004 | 0.172502 | − | 0.985009i | \(-0.444815\pi\) | ||||
0.172502 | + | 0.985009i | \(0.444815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.47214 | 0.179172 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.52786 | 0.0609199 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.94427 | −0.356066 | −0.178033 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178033 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.9443 | 1.46609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.7639 | −0.899121 | −0.449561 | − | 0.893250i | \(-0.648419\pi\) | ||||
−0.449561 | + | 0.893250i | \(0.648419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.9443 | −1.29920 | −0.649598 | − | 0.760278i | \(-0.725063\pi\) | ||||
−0.649598 | + | 0.760278i | \(0.725063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.29180 | −0.168728 | −0.0843640 | − | 0.996435i | \(-0.526886\pi\) | ||||
−0.0843640 | + | 0.996435i | \(0.526886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8885 | −0.702187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.7214 | −1.59355 | −0.796775 | − | 0.604276i | \(-0.793462\pi\) | ||||
−0.796775 | + | 0.604276i | \(0.793462\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.8328 | 1.36103 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.2361 | 1.37260 | 0.686301 | − | 0.727317i | \(-0.259233\pi\) | ||||
0.686301 | + | 0.727317i | \(0.259233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.2492 | 1.72110 | 0.860548 | − | 0.509370i | \(-0.170121\pi\) | ||||
0.860548 | + | 0.509370i | \(0.170121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.23607 | −0.125489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.4164 | −0.596926 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8328 | 1.03587 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3607 | 1.01613 | 0.508065 | − | 0.861319i | \(-0.330361\pi\) | ||||
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0000 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.41641 | 0.361369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.2361 | 0.889103 | 0.444552 | − | 0.895753i | \(-0.353363\pi\) | ||||
0.444552 | + | 0.895753i | \(0.353363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9443 | 0.494575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.2492 | −1.15240 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3607 | 0.774557 | 0.387278 | − | 0.921963i | \(-0.373415\pi\) | ||||
0.387278 | + | 0.921963i | \(0.373415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59.7771 | 2.26747 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.52786 | 0.0578720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.7771 | −1.65344 | −0.826719 | − | 0.562615i | \(-0.809795\pi\) | ||||
−0.826719 | + | 0.562615i | \(0.809795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.472136 | 0.0178069 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.2361 | 0.573011 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.3050 | −1.02546 | −0.512729 | − | 0.858550i | \(-0.671366\pi\) | ||||
−0.512729 | + | 0.858550i | \(0.671366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.9443 | 0.784369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.9443 | 1.08245 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.2361 | 1.38867 | 0.694336 | − | 0.719651i | \(-0.255698\pi\) | ||||
0.694336 | + | 0.719651i | \(0.255698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.1803 | 1.56654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.41641 | −0.126708 | −0.0633538 | − | 0.997991i | \(-0.520180\pi\) | ||||
−0.0633538 | + | 0.997991i | \(0.520180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5836 | 0.390914 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.9443 | −0.771492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0000 | 0.882854 | 0.441427 | − | 0.897297i | \(-0.354472\pi\) | ||||
0.441427 | + | 0.897297i | \(0.354472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.403252 | −0.0147939 | −0.00739695 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739695 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −72.7214 | −2.66430 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.18034 | −0.152746 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0557 | −0.549391 | −0.274696 | − | 0.961531i | \(-0.588577\pi\) | ||||
−0.274696 | + | 0.961531i | \(0.588577\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.9443 | 0.471090 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8885 | 0.722861 | 0.361431 | − | 0.932399i | \(-0.382288\pi\) | ||||
0.361431 | + | 0.932399i | \(0.382288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.7639 | −0.752692 | −0.376346 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376346 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | 0.362024 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.0000 | −1.44432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.4721 | 1.02673 | 0.513366 | − | 0.858170i | \(-0.328398\pi\) | ||||
0.513366 | + | 0.858170i | \(0.328398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.2492 | 1.30379 | 0.651897 | − | 0.758308i | \(-0.273973\pi\) | ||||
0.651897 | + | 0.758308i | \(0.273973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −57.3050 | −2.05845 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.472136 | 0.0169160 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4164 | 0.408511 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.3607 | −1.44053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.4721 | −1.08621 | −0.543107 | − | 0.839663i | \(-0.682752\pi\) | ||||
−0.543107 | + | 0.839663i | \(0.682752\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.76393 | 0.0982741 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.0000 | 2.13066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.41641 | 0.191859 | 0.0959295 | − | 0.995388i | \(-0.469418\pi\) | ||||
0.0959295 | + | 0.995388i | \(0.469418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.8885 | −1.34040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.05573 | 0.248991 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.47214 | −0.228113 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.8885 | −1.19146 | −0.595729 | − | 0.803186i | \(-0.703137\pi\) | ||||
−0.595729 | + | 0.803186i | \(0.703137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9443 | −0.735453 | −0.367726 | − | 0.929934i | \(-0.619864\pi\) | ||||
−0.367726 | + | 0.929934i | \(0.619864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.7771 | −1.81367 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.2492 | −1.75371 | −0.876855 | − | 0.480755i | \(-0.840363\pi\) | ||||
−0.876855 | + | 0.480755i | \(0.840363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8328 | 0.377608 | 0.188804 | − | 0.982015i | \(-0.439539\pi\) | ||||
0.188804 | + | 0.982015i | \(0.439539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.2361 | −1.08618 | −0.543092 | − | 0.839673i | \(-0.682747\pi\) | ||||
−0.543092 | + | 0.839673i | \(0.682747\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.4164 | −0.882748 | −0.441374 | − | 0.897323i | \(-0.645509\pi\) | ||||
−0.441374 | + | 0.897323i | \(0.645509\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.23607 | −0.112123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0557 | −0.382599 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.94427 | −0.308791 | −0.154395 | − | 0.988009i | \(-0.549343\pi\) | ||||
−0.154395 | + | 0.988009i | \(0.549343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.4164 | 1.04884 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.6525 | 0.779269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.944272 | 0.0323692 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.7771 | 1.43042 | 0.715210 | − | 0.698909i | \(-0.246331\pi\) | ||||
0.715210 | + | 0.698909i | \(0.246331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.2492 | 1.64816 | 0.824081 | − | 0.566472i | \(-0.191692\pi\) | ||||
0.824081 | + | 0.566472i | \(0.191692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9443 | −0.851088 | −0.425544 | − | 0.904938i | \(-0.639917\pi\) | ||||
−0.425544 | + | 0.904938i | \(0.639917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.87539 | −0.234041 | −0.117020 | − | 0.993130i | \(-0.537334\pi\) | ||||
−0.117020 | + | 0.993130i | \(0.537334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.3050 | 1.26841 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.8328 | −1.58687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.52786 | 0.0516512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.8328 | −0.838545 | −0.419272 | − | 0.907861i | \(-0.637715\pi\) | ||||
−0.419272 | + | 0.907861i | \(0.637715\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8197 | 0.802505 | 0.401252 | − | 0.915968i | \(-0.368575\pi\) | ||||
0.401252 | + | 0.915968i | \(0.368575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.8885 | −1.00583 | −0.502915 | − | 0.864336i | \(-0.667739\pi\) | ||||
−0.502915 | + | 0.864336i | \(0.667739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.4164 | 1.72639 | 0.863197 | − | 0.504867i | \(-0.168459\pi\) | ||||
0.863197 | + | 0.504867i | \(0.168459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4164 | 0.382894 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.7082 | −0.391800 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.4721 | −0.617455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −80.7214 | −2.69221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8885 | 0.729213 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.3607 | −1.34163 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.4721 | −1.14463 | −0.572314 | − | 0.820034i | \(-0.693954\pi\) | ||||
−0.572314 | + | 0.820034i | \(0.693954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.5410 | −1.34318 | −0.671592 | − | 0.740921i | \(-0.734389\pi\) | ||||
−0.671592 | + | 0.740921i | \(0.734389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.583592 | 0.0193141 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7639 | 0.355456 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.7771 | 1.18018 | 0.590089 | − | 0.807338i | \(-0.299093\pi\) | ||||
0.590089 | + | 0.807338i | \(0.299093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.5279 | 0.840260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.58359 | −0.0849480 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.5967 | 1.82407 | 0.912035 | − | 0.410112i | \(-0.134510\pi\) | ||||
0.912035 | + | 0.410112i | \(0.134510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.9443 | −0.684951 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.8885 | 1.69512 | 0.847562 | − | 0.530696i | \(-0.178069\pi\) | ||||
0.847562 | + | 0.530696i | \(0.178069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.8328 | 1.33111 | 0.665556 | − | 0.746348i | \(-0.268195\pi\) | ||||
0.665556 | + | 0.746348i | \(0.268195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.944272 | 0.0307497 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.0000 | 0.844886 | 0.422443 | − | 0.906389i | \(-0.361173\pi\) | ||||
0.422443 | + | 0.906389i | \(0.361173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.7771 | 0.512146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.6525 | −1.44644 | −0.723218 | − | 0.690620i | \(-0.757338\pi\) | ||||
−0.723218 | + | 0.690620i | \(0.757338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.3607 | 1.04717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.52786 | 0.0491837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.8328 | −1.12015 | −0.560074 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560074 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.83282 | −0.219275 | −0.109638 | − | 0.993972i | \(-0.534969\pi\) | ||||
−0.109638 | + | 0.993972i | \(0.534969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4721 | 0.592189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.06888 | 0.258146 | 0.129073 | − | 0.991635i | \(-0.458800\pi\) | ||||
0.129073 | + | 0.991635i | \(0.458800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.94427 | 0.285860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.7214 | 1.29881 | 0.649405 | − | 0.760443i | \(-0.275018\pi\) | ||||
0.649405 | + | 0.760443i | \(0.275018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.8328 | 1.23732 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.63932 | 0.242671 | 0.121336 | − | 0.992612i | \(-0.461282\pi\) | ||||
0.121336 | + | 0.992612i | \(0.461282\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.88854 | −0.313488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.52786 | −0.238410 | −0.119205 | − | 0.992870i | \(-0.538035\pi\) | ||||
−0.119205 | + | 0.992870i | \(0.538035\pi\) | |||||||
\(998\) | 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 | 9576.2.a.bv.1.2 | yes | 2 | |
3.2 | odd | 2 | 9576.2.a.bi.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9576.2.a.bi.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
9576.2.a.bv.1.2 | yes | 2 | 1.1 | even | 1 | trivial |