Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6724,2,Mod(1,6724)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6724, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6724.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6724 = 2^{2} \cdot 41^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6724.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: | \(53.6914103191\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 164) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.46810\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6724.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.21551 | −1.27913 | −0.639563 | − | 0.768739i | \(-0.720885\pi\) | ||||
−0.639563 | + | 0.768739i | \(0.720885\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.59669 | 1.60849 | 0.804245 | − | 0.594298i | \(-0.202570\pi\) | ||||
0.804245 | + | 0.594298i | \(0.202570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.06479 | 1.91431 | 0.957156 | − | 0.289574i | \(-0.0935135\pi\) | ||||
0.957156 | + | 0.289574i | \(0.0935135\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.90849 | 0.636162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.55961 | 0.771753 | 0.385876 | − | 0.922551i | \(-0.373899\pi\) | ||||
0.385876 | + | 0.922551i | \(0.373899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.93620 | 1.36906 | 0.684528 | − | 0.728987i | \(-0.260009\pi\) | ||||
0.684528 | + | 0.728987i | \(0.260009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.96851 | −2.05746 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.68821 | −0.651986 | −0.325993 | − | 0.945372i | \(-0.605699\pi\) | ||||
−0.325993 | + | 0.945372i | \(0.605699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.72069 | −1.08300 | −0.541500 | − | 0.840701i | \(-0.682143\pi\) | ||||
−0.541500 | + | 0.840701i | \(0.682143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.2211 | −2.44864 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.49482 | −0.311692 | −0.155846 | − | 0.987781i | \(-0.549810\pi\) | ||||
−0.155846 | + | 0.987781i | \(0.549810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.93620 | 1.58724 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41826 | 0.465395 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.43102 | −0.451429 | −0.225715 | − | 0.974193i | \(-0.572472\pi\) | ||||
−0.225715 | + | 0.974193i | \(0.572472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.19339 | 0.573549 | 0.286774 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286774 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.67085 | −0.987168 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.2165 | 3.07915 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.90849 | 0.478152 | 0.239076 | − | 0.971001i | \(-0.423155\pi\) | ||||
0.239076 | + | 0.971001i | \(0.423155\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9362 | −1.75119 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.62441 | −1.16271 | −0.581356 | − | 0.813650i | \(-0.697477\pi\) | ||||
−0.581356 | + | 0.813650i | \(0.697477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.86424 | 1.02326 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.15171 | −0.751454 | −0.375727 | − | 0.926730i | \(-0.622607\pi\) | ||||
−0.375727 | + | 0.926730i | \(0.622607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.6521 | 2.66459 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.95575 | 0.833972 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1192 | 1.52734 | 0.763672 | − | 0.645605i | \(-0.223395\pi\) | ||||
0.763672 | + | 0.645605i | \(0.223395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.20614 | 1.24136 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4587 | 1.38529 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.49482 | 0.194609 | 0.0973046 | − | 0.995255i | \(-0.468978\pi\) | ||||
0.0973046 | + | 0.995255i | \(0.468978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.06380 | 0.136206 | 0.0681029 | − | 0.997678i | \(-0.478305\pi\) | ||||
0.0681029 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.66608 | 1.21781 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.7540 | 2.20211 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5596 | −1.29006 | −0.645031 | − | 0.764156i | \(-0.723156\pi\) | ||||
−0.645031 | + | 0.764156i | \(0.723156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.31179 | 0.398693 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6023 | 1.49562 | 0.747808 | − | 0.663915i | \(-0.231106\pi\) | ||||
0.747808 | + | 0.663915i | \(0.231106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.28490 | 0.969674 | 0.484837 | − | 0.874604i | \(-0.338879\pi\) | ||||
0.484837 | + | 0.874604i | \(0.338879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.5827 | −2.03028 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9639 | 1.47737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.28967 | 0.482625 | 0.241313 | − | 0.970447i | \(-0.422422\pi\) | ||||
0.241313 | + | 0.970447i | \(0.422422\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0831 | −1.23146 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5606 | 1.15918 | 0.579588 | − | 0.814909i | \(-0.303213\pi\) | ||||
0.579588 | + | 0.814909i | \(0.303213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.66866 | −1.04871 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.38595 | 0.577435 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.36722 | −0.992923 | −0.496462 | − | 0.868059i | \(-0.665368\pi\) | ||||
−0.496462 | + | 0.868059i | \(0.665368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.0008 | 2.62080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.07498 | −0.733641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.9789 | −1.74199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.37641 | 0.342823 | 0.171411 | − | 0.985200i | \(-0.445167\pi\) | ||||
0.171411 | + | 0.985200i | \(0.445167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.88499 | 0.490960 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24799 | 0.422691 | 0.211345 | − | 0.977411i | \(-0.432215\pi\) | ||||
0.211345 | + | 0.977411i | \(0.432215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.11923 | 0.110281 | 0.0551404 | − | 0.998479i | \(-0.482439\pi\) | ||||
0.0551404 | + | 0.998479i | \(0.482439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −40.3588 | −3.93862 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.322149 | −0.0311434 | −0.0155717 | − | 0.999879i | \(-0.504957\pi\) | ||||
−0.0155717 | + | 0.999879i | \(0.504957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.23763 | −0.310109 | −0.155055 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155055 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.44378 | −0.611616 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.10187 | 0.197727 | 0.0988637 | − | 0.995101i | \(-0.468479\pi\) | ||||
0.0988637 | + | 0.995101i | \(0.468479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.37641 | −0.501353 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.42066 | 0.870941 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6152 | −1.24810 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.44838 | −0.404398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5606 | 0.944569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0658 | −1.15940 | −0.579700 | − | 0.814830i | \(-0.696830\pi\) | ||||
−0.579700 | + | 0.814830i | \(0.696830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.8919 | 1.48725 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.43102 | 0.736622 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.9093 | −2.07320 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.69774 | 0.748583 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.5606 | 1.41487 | 0.707434 | − | 0.706779i | \(-0.249853\pi\) | ||||
0.707434 | + | 0.706779i | \(0.249853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.18303 | −0.185162 | −0.0925810 | − | 0.995705i | \(-0.529512\pi\) | ||||
−0.0925810 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.4137 | 0.961204 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.6348 | 1.05657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.74363 | −0.726119 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41.3240 | −3.40834 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.43102 | −0.199157 | −0.0995785 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995785 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.343113 | 0.0279221 | 0.0139611 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139611 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.13040 | −0.414769 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4856 | 0.922548 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6348 | 0.848746 | 0.424373 | − | 0.905487i | \(-0.360494\pi\) | ||||
0.424373 | + | 0.905487i | \(0.360494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.6348 | −1.95366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.57096 | −0.596675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.173834 | −0.0136157 | −0.00680785 | − | 0.999977i | \(-0.502167\pi\) | ||||
−0.00680785 | + | 0.999977i | \(0.502167\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.3963 | −1.58785 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.5596 | −1.12666 | −0.563328 | − | 0.826233i | \(-0.690479\pi\) | ||||
−0.563328 | + | 0.826233i | \(0.690479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3661 | 0.874312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.00937 | −0.688963 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.2592 | −1.69233 | −0.846167 | − | 0.532918i | \(-0.821095\pi\) | ||||
−0.846167 | + | 0.532918i | \(0.821095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.1952 | 3.03847 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.31179 | −0.248930 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.9268 | 1.33991 | 0.669957 | − | 0.742400i | \(-0.266312\pi\) | ||||
0.669957 | + | 0.742400i | \(0.266312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9916 | −1.56030 | −0.780148 | − | 0.625595i | \(-0.784856\pi\) | ||||
−0.780148 | + | 0.625595i | \(0.784856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.35686 | −0.174224 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.4609 | 0.769103 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.88077 | −0.503172 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.2480 | 0.890910 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.45074 | −0.466759 | −0.233380 | − | 0.972386i | \(-0.574978\pi\) | ||||
−0.233380 | + | 0.972386i | \(0.574978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.20374 | −0.446555 | −0.223278 | − | 0.974755i | \(-0.571676\pi\) | ||||
−0.223278 | + | 0.974755i | \(0.571676\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −39.3341 | −2.81678 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1850 | 1.01064 | 0.505320 | − | 0.862932i | \(-0.331374\pi\) | ||||
0.505320 | + | 0.862932i | \(0.331374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7099 | −1.32631 | −0.663155 | − | 0.748482i | \(-0.730783\pi\) | ||||
−0.663155 | + | 0.748482i | \(0.730783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.3949 | 1.65015 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3126 | −0.864176 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.85285 | −0.198286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0831 | −0.835808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6984 | −1.01188 | −0.505940 | − | 0.862569i | \(-0.668854\pi\) | ||||
−0.505940 | + | 0.862569i | \(0.668854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.9205 | −1.91308 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.4226 | −1.87021 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1738 | 1.09795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.3553 | −1.24033 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2695 | −0.892605 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1109 | 1.34672 | 0.673361 | − | 0.739314i | \(-0.264850\pi\) | ||||
0.673361 | + | 0.739314i | \(0.264850\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.1461 | 1.00974 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.71149 | 0.445457 | 0.222729 | − | 0.974880i | \(-0.428504\pi\) | ||||
0.222729 | + | 0.974880i | \(0.428504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7624 | −0.843361 | −0.421680 | − | 0.906745i | \(-0.638560\pi\) | ||||
−0.421680 | + | 0.906745i | \(0.638560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.7217 | −1.88975 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.0750 | 1.90477 | 0.952383 | − | 0.304906i | \(-0.0986249\pi\) | ||||
0.952383 | + | 0.304906i | \(0.0986249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5291 | −1.20871 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.50380 | −0.617338 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0971 | −1.68808 | −0.844041 | − | 0.536279i | \(-0.819829\pi\) | ||||
−0.844041 | + | 0.536279i | \(0.819829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.06380 | 0.0685255 | 0.0342627 | − | 0.999413i | \(-0.489092\pi\) | ||||
0.0342627 | + | 0.999413i | \(0.489092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.3000 | 1.10980 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 67.0859 | 4.28596 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.3023 | −1.48269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.3971 | −1.48273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.82815 | −0.494108 | −0.247054 | − | 0.969002i | \(-0.579463\pi\) | ||||
−0.247054 | + | 0.969002i | \(0.579463\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.82617 | −0.240549 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.4210 | 1.34144 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.49482 | −0.467514 | −0.233757 | − | 0.972295i | \(-0.575102\pi\) | ||||
−0.233757 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7309 | 0.915332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.63957 | −0.287182 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.5919 | −0.961439 | −0.480720 | − | 0.876874i | \(-0.659625\pi\) | ||||
−0.480720 | + | 0.876874i | \(0.659625\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.9924 | 2.45672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.7532 | 1.27007 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.80860 | 0.537070 | 0.268535 | − | 0.963270i | \(-0.413461\pi\) | ||||
0.268535 | + | 0.963270i | \(0.413461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8816 | −1.20772 | −0.603860 | − | 0.797090i | \(-0.706372\pi\) | ||||
−0.603860 | + | 0.797090i | \(0.706372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55.3896 | −3.35233 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.3136 | 1.22496 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.08232 | −0.425535 | −0.212768 | − | 0.977103i | \(-0.568248\pi\) | ||||
−0.212768 | + | 0.977103i | \(0.568248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.09453 | 0.364870 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.2695 | 1.86538 | 0.932692 | − | 0.360675i | \(-0.117453\pi\) | ||||
0.932692 | + | 0.360675i | \(0.117453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.18303 | −0.129768 | −0.0648838 | − | 0.997893i | \(-0.520668\pi\) | ||||
−0.0648838 | + | 0.997893i | \(0.520668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 37.6169 | 2.22823 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.77354 | −0.574914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.48048 | −0.438514 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.6798 | 1.96760 | 0.983798 | − | 0.179278i | \(-0.0573762\pi\) | ||||
0.983798 | + | 0.179278i | \(0.0573762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.37641 | 0.313027 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.18982 | 0.359170 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.37874 | −0.426723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.6160 | −2.22579 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.41147 | −0.540675 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.82617 | 0.219086 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7532 | −0.727862 | −0.363931 | − | 0.931426i | \(-0.618566\pi\) | ||||
−0.363931 | + | 0.931426i | \(0.618566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.47966 | −0.141063 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.18204 | −0.123732 | −0.0618660 | − | 0.998084i | \(-0.519705\pi\) | ||||
−0.0618660 | + | 0.998084i | \(0.519705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.3042 | 1.65637 | 0.828187 | − | 0.560452i | \(-0.189373\pi\) | ||||
0.828187 | + | 0.560452i | \(0.189373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 34.7659 | 1.95884 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.5511 | 1.60359 | 0.801794 | − | 0.597601i | \(-0.203879\pi\) | ||||
0.801794 | + | 0.597601i | \(0.203879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.22247 | −0.348392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.713725 | 0.0398363 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.6902 | 0.706101 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 39.1747 | 2.17302 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.17301 | 0.396669 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.0923 | −1.43852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.80761 | 0.264250 | 0.132125 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132125 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.55080 | 0.304182 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.9797 | −2.07505 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3148 | 0.888724 | 0.444362 | − | 0.895847i | \(-0.353430\pi\) | ||||
0.444362 | + | 0.895847i | \(0.353430\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.65672 | −0.252918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.17383 | 0.442638 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 59.0156 | 3.18654 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.9115 | 0.641294 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.6034 | −1.69656 | −0.848281 | − | 0.529547i | \(-0.822362\pi\) | ||||
−0.848281 | + | 0.529547i | \(0.822362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.97311 | 0.266204 | 0.133102 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133102 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9370 | 0.637151 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.72430 | 0.0917750 | 0.0458875 | − | 0.998947i | \(-0.485388\pi\) | ||||
0.0458875 | + | 0.998947i | \(0.485388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 45.3265 | 2.40568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.1646 | 1.59648 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.13796 | −0.376727 | −0.188364 | − | 0.982099i | \(-0.560318\pi\) | ||||
−0.188364 | + | 0.982099i | \(0.560318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.28490 | 0.172889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.85542 | 0.517276 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.7982 | 1.55971 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.38595 | −0.489943 | −0.244971 | − | 0.969530i | \(-0.578779\pi\) | ||||
−0.244971 | + | 0.969530i | \(0.578779\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 56.3166 | 2.92381 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.1212 | 1.19717 | 0.598585 | − | 0.801059i | \(-0.295730\pi\) | ||||
0.598585 | + | 0.801059i | \(0.295730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.3971 | −1.20822 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.99080 | 0.307727 | 0.153863 | − | 0.988092i | \(-0.450828\pi\) | ||||
0.153863 | + | 0.988092i | \(0.450828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.9474 | 1.48302 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.5811 | 1.51153 | 0.755763 | − | 0.654845i | \(-0.227266\pi\) | ||||
0.755763 | + | 0.654845i | \(0.227266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.6272 | 2.37634 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.5511 | −0.739672 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8620 | 1.15915 | 0.579576 | − | 0.814918i | \(-0.303218\pi\) | ||||
0.579576 | + | 0.814918i | \(0.303218\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.01839 | 0.203219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.6790 | −0.942232 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.4286 | 0.776298 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.588531 | 0.0295375 | 0.0147688 | − | 0.999891i | \(-0.495299\pi\) | ||||
0.0147688 | + | 0.999891i | \(0.495299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 52.9713 | 2.65188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0926758 | −0.00462801 | −0.00231400 | − | 0.999997i | \(-0.500737\pi\) | ||||
−0.00231400 | + | 0.999997i | \(0.500737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.7632 | 0.785220 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −39.8626 | −1.98079 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.44460 | 0.369015 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.29526 | −0.0640463 | −0.0320232 | − | 0.999487i | \(-0.510195\pi\) | ||||
−0.0320232 | + | 0.999487i | \(0.510195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.6902 | −1.80979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.57096 | 0.372543 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.9833 | 1.86452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.83652 | 0.236846 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.75201 | 0.0855912 | 0.0427956 | − | 0.999084i | \(-0.486374\pi\) | ||||
0.0427956 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.7364 | −1.79042 | −0.895212 | − | 0.445641i | \(-0.852976\pi\) | ||||
−0.895212 | + | 0.445641i | \(0.852976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.83196 | −0.478046 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.3341 | −1.03486 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.38793 | 0.260740 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.9924 | −1.35149 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3126 | 0.593078 | 0.296539 | − | 0.955021i | \(-0.404168\pi\) | ||||
0.296539 | + | 0.955021i | \(0.404168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.7632 | −0.853644 | −0.426822 | − | 0.904336i | \(-0.640367\pi\) | ||||
−0.426822 | + | 0.904336i | \(0.640367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.3716 | 0.928798 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.05659 | 0.337562 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.22230 | −0.153792 | −0.0768961 | − | 0.997039i | \(-0.524501\pi\) | ||||
−0.0768961 | + | 0.997039i | \(0.524501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 35.5973 | 1.69511 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.8537 | −1.70346 | −0.851730 | − | 0.523982i | \(-0.824446\pi\) | ||||
−0.851730 | + | 0.523982i | \(0.824446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.6910 | −1.59711 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.38595 | 0.254747 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.3437 | −0.724113 | −0.362057 | − | 0.932156i | \(-0.617925\pi\) | ||||
−0.362057 | + | 0.932156i | \(0.617925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.760170 | −0.0357159 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 89.9203 | 4.21553 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.5917 | −1.29068 | −0.645342 | − | 0.763894i | \(-0.723285\pi\) | ||||
−0.645342 | + | 0.763894i | \(0.723285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.50079 | −0.303431 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.08116 | −0.376377 | −0.188189 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188189 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.23622 | 0.382770 | 0.191385 | − | 0.981515i | \(-0.438702\pi\) | ||||
0.191385 | + | 0.981515i | \(0.438702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.4465 | −1.18005 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.7333 | −1.09825 | −0.549123 | − | 0.835742i | \(-0.685038\pi\) | ||||
−0.549123 | + | 0.835742i | \(0.685038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.4822 | −2.46958 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5614 | −1.08565 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.5155 | −0.897325 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.4643 | −1.71898 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.2209 | 0.971638 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6987 | 0.762985 | 0.381492 | − | 0.924372i | \(-0.375410\pi\) | ||||
0.381492 | + | 0.924372i | \(0.375410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3569 | 0.654617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.7735 | 0.763223 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.1439 | 0.551427 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.927003 | 0.0420065 | 0.0210033 | − | 0.999779i | \(-0.493314\pi\) | ||||
0.0210033 | + | 0.999779i | \(0.493314\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.385130 | 0.0174162 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.8752 | −1.21286 | −0.606430 | − | 0.795137i | \(-0.707399\pi\) | ||||
−0.606430 | + | 0.795137i | \(0.707399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53509 | 0.294326 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.5698 | 0.789703 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 63.8279 | 2.86307 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2155 | −0.815438 | −0.407719 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407719 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.2570 | 1.44114 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9591 | −0.845346 | −0.422673 | − | 0.906282i | \(-0.638908\pi\) | ||||
−0.422673 | + | 0.906282i | \(0.638908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2787 | 0.679894 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.1816 | −1.11835 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.4218 | −0.550588 | −0.275294 | − | 0.961360i | \(-0.588775\pi\) | ||||
−0.275294 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.9613 | 1.85626 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.4159 | −0.504022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.02552 | 0.177386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1864 | −0.579937 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.3154 | 2.16471 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.17267 | 0.314240 | 0.157120 | − | 0.987579i | \(-0.449779\pi\) | ||||
0.157120 | + | 0.987579i | \(0.449779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.6563 | 1.55914 | 0.779570 | − | 0.626315i | \(-0.215437\pi\) | ||||
0.779570 | + | 0.626315i | \(0.215437\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −89.0529 | −3.88659 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.58448 | −0.373946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7655 | −0.902848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.85285 | 0.123803 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.15867 | −0.0500938 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.7171 | −1.71392 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 47.7422 | 2.05640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.9731 | 1.24565 | 0.622826 | − | 0.782361i | \(-0.285985\pi\) | ||||
0.622826 | + | 0.782361i | \(0.285985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.5072 | 1.99581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.6448 | −0.498807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1178 | −0.689148 | −0.344574 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344574 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.03025 | 0.0866489 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4761 | 0.488898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.7263 | 0.923895 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.1763 | −0.983779 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2675 | 1.15536 | 0.577681 | − | 0.816262i | \(-0.303958\pi\) | ||||
0.577681 | + | 0.816262i | \(0.303958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.6356 | −1.59182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.2444 | 0.643620 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.9173 | −1.76660 | −0.883302 | − | 0.468805i | \(-0.844685\pi\) | ||||
−0.883302 | + | 0.468805i | \(0.844685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.55978 | 0.318043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −56.1338 | −2.35740 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.3762 | 1.56689 | 0.783446 | − | 0.621460i | \(-0.213460\pi\) | ||||
0.783446 | + | 0.621460i | \(0.213460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.3228 | 1.10157 | 0.550787 | − | 0.834646i | \(-0.314327\pi\) | ||||
0.550787 | + | 0.834646i | \(0.314327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.2917 | 0.597044 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.8632 | −0.494730 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8262 | 0.575591 | 0.287795 | − | 0.957692i | \(-0.407078\pi\) | ||||
0.287795 | + | 0.957692i | \(0.407078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.7445 | 0.571200 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 53.4873 | 2.21903 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4609 | 1.17873 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.8832 | 1.40090 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.7004 | −0.936945 | −0.468472 | − | 0.883478i | \(-0.655195\pi\) | ||||
−0.468472 | + | 0.883478i | \(0.655195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.0750 | −0.621154 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.4270 | −1.29274 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.4167 | −0.674152 | −0.337076 | − | 0.941477i | \(-0.609438\pi\) | ||||
−0.337076 | + | 0.941477i | \(0.609438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.9697 | −2.00756 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.4520 | 1.69652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.54909 | −0.267588 | −0.133794 | − | 0.991009i | \(-0.542716\pi\) | ||||
−0.133794 | + | 0.991009i | \(0.542716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7783 | 1.01073 | 0.505365 | − | 0.862906i | \(-0.331358\pi\) | ||||
0.505365 | + | 0.862906i | \(0.331358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.1529 | −0.820688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9994 | −0.650470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7982 | −0.641231 | −0.320615 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320615 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.2787 | 1.10539 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.4299 | −1.02878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3415 | 1.58899 | 0.794494 | − | 0.607272i | \(-0.207736\pi\) | ||||
0.794494 | + | 0.607272i | \(0.207736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.4075 | −1.06313 | −0.531563 | − | 0.847019i | \(-0.678395\pi\) | ||||
−0.531563 | + | 0.847019i | \(0.678395\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9278 | 1.36367 | 0.681837 | − | 0.731504i | \(-0.261181\pi\) | ||||
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.61487 | −0.145060 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −47.4430 | −1.90076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.69774 | −0.0679097 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.7703 | 1.06910 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.81861 | −0.311748 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.68017 | −0.226124 | −0.113062 | − | 0.993588i | \(-0.536066\pi\) | ||||
−0.113062 | + | 0.993588i | \(0.536066\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.5644 | 1.29432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.9936 | −1.86488 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 92.0706 | 3.64797 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0513 | 0.951454 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5802 | −0.615379 | −0.307690 | − | 0.951487i | \(-0.599556\pi\) | ||||
−0.307690 | + | 0.951487i | \(0.599556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9372 | −0.904554 | −0.452277 | − | 0.891877i | \(-0.649388\pi\) | ||||
−0.452277 | + | 0.891877i | \(0.649388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 60.7552 | 2.39223 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0546 | 0.591858 | 0.295929 | − | 0.955210i | \(-0.404371\pi\) | ||||
0.295929 | + | 0.955210i | \(0.404371\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.82617 | 0.150190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.8333 | −1.40442 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.8652 | 1.79484 | 0.897422 | − | 0.441174i | \(-0.145438\pi\) | ||||
0.897422 | + | 0.441174i | \(0.145438\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.3238 | 1.18485 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.8116 | 0.616870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.37302 | 0.170349 | 0.0851744 | − | 0.996366i | \(-0.472855\pi\) | ||||
0.0851744 | + | 0.996366i | \(0.472855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4946 | −0.991625 | −0.495813 | − | 0.868430i | \(-0.665130\pi\) | ||||
−0.495813 | + | 0.868430i | \(0.665130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.3988 | 1.14175 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −85.9944 | −3.33472 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.63394 | 0.140707 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −44.5558 | −1.72263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.72292 | 0.105117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7540 | −1.22403 | −0.612013 | − | 0.790848i | \(-0.709640\pi\) | ||||
−0.612013 | + | 0.790848i | \(0.709640\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.1918 | 0.738693 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8998 | −1.07228 | −0.536138 | − | 0.844131i | \(-0.680117\pi\) | ||||
−0.536138 | + | 0.844131i | \(0.680117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.1008 | 0.656270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8694 | −0.569796 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.11782 | −0.310620 | −0.155310 | − | 0.987866i | \(-0.549638\pi\) | ||||
−0.155310 | + | 0.987866i | \(0.549638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.5634 | 2.27580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.2752 | 1.07876 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.8867 | 2.09102 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.6390 | 1.01339 | 0.506697 | − | 0.862124i | \(-0.330866\pi\) | ||||
0.506697 | + | 0.862124i | \(0.330866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.7414 | 0.939850 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.85168 | −0.297831 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −64.4159 | −2.43643 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.1302 | 1.62900 | 0.814502 | − | 0.580160i | \(-0.197010\pi\) | ||||
0.814502 | + | 0.580160i | \(0.197010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.7301 | −0.517839 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 41.0514 | 1.54609 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.5152 | 0.809162 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.5175 | −1.85967 | −0.929835 | − | 0.367978i | \(-0.880050\pi\) | ||||
−0.929835 | + | 0.367978i | \(0.880050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.18677 | 0.307028 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.77354 | −0.178771 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.4434 | 1.69949 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 57.8184 | 2.15927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4839 | 0.614745 | 0.307372 | − | 0.951589i | \(-0.400550\pi\) | ||||
0.307372 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.66866 | 0.211112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.35686 | −0.0876527 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.2931 | −0.716526 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.5947 | −1.80228 | −0.901139 | − | 0.433530i | \(-0.857268\pi\) | ||||
−0.901139 | + | 0.433530i | \(0.857268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.07896 | −0.188110 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.4960 | 0.758071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8166 | 0.436457 | 0.218229 | − | 0.975898i | \(-0.429972\pi\) | ||||
0.218229 | + | 0.975898i | \(0.429972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −148.630 | −5.48228 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.0285 | −0.995609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.68017 | −0.208949 | −0.104474 | − | 0.994528i | \(-0.533316\pi\) | ||||
−0.104474 | + | 0.994528i | \(0.533316\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.6264 | 1.89654 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4980 | −0.898743 | −0.449372 | − | 0.893345i | \(-0.648352\pi\) | ||||
−0.449372 | + | 0.893345i | \(0.648352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.74363 | −0.320342 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.1548 | 0.737424 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.63162 | −0.0596181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7897 | 1.30598 | 0.652992 | − | 0.757365i | \(-0.273513\pi\) | ||||
0.652992 | + | 0.757365i | \(0.273513\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3433 | 0.632027 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.23407 | 0.0449124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.7169 | −1.37084 | −0.685421 | − | 0.728147i | \(-0.740382\pi\) | ||||
−0.685421 | + | 0.728147i | \(0.740382\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.47691 | 0.307692 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.6533 | −0.821181 | −0.410590 | − | 0.911820i | \(-0.634677\pi\) | ||||
−0.410590 | + | 0.911820i | \(0.634677\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.3979 | −0.593646 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.4525 | −0.667151 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.37874 | 0.266431 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.6292 | −1.53725 | −0.768624 | − | 0.639701i | \(-0.779058\pi\) | ||||
−0.768624 | + | 0.639701i | \(0.779058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6049 | 0.598009 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.7635 | −0.423105 | −0.211552 | − | 0.977367i | \(-0.567852\pi\) | ||||
−0.211552 | + | 0.977367i | \(0.567852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.3433 | 0.910360 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.6364 | −1.17082 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.2570 | 1.15425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.87884 | −0.210093 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.2500 | 1.36520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.4517 | 1.22807 | 0.614036 | − | 0.789278i | \(-0.289545\pi\) | ||||
0.614036 | + | 0.789278i | \(0.289545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 34.5441 | 1.22980 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.6455 | 0.378512 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.25113 | 0.186473 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −88.6037 | −3.14245 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.2161 | 1.45995 | 0.729974 | − | 0.683475i | \(-0.239532\pi\) | ||||
0.729974 | + | 0.683475i | \(0.239532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8489 | 0.489937 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.8772 | −0.631660 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.2061 | 0.748349 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.2304 | −0.959746 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5155 | −0.686979 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.4123 | −0.436393 | −0.218196 | − | 0.975905i | \(-0.570017\pi\) | ||||
−0.218196 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.91665 | 0.137532 | 0.0687660 | − | 0.997633i | \(-0.478094\pi\) | ||||
0.0687660 | + | 0.997633i | \(0.478094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.0479 | 1.54483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.625226 | −0.0219007 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.9924 | 1.25922 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 47.7137 | 1.66725 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6326 | 0.999283 | 0.499642 | − | 0.866232i | \(-0.333465\pi\) | ||||
0.499642 | + | 0.866232i | \(0.333465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.8212 | −1.52751 | −0.763755 | − | 0.645506i | \(-0.776647\pi\) | ||||
−0.763755 | + | 0.645506i | \(0.776647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −45.0050 | −1.56687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1924 | −0.389198 | −0.194599 | − | 0.980883i | \(-0.562341\pi\) | ||||
−0.194599 | + | 0.980883i | \(0.562341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6278 | 0.924820 | 0.462410 | − | 0.886666i | \(-0.346985\pi\) | ||||
0.462410 | + | 0.886666i | \(0.346985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.6910 | 0.544313 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −50.1408 | −1.73727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.3665 | −1.81222 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.72244 | 0.266927 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.43085 | −0.325589 | −0.162795 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162795 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0901 | −0.796212 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −69.2780 | −2.38606 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.8802 | 1.40632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5301 | −0.774144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.83652 | 0.165989 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.34767 | −0.149036 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.6045 | 1.11636 | 0.558179 | − | 0.829721i | \(-0.311500\pi\) | ||||
0.558179 | + | 0.829721i | \(0.311500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.4039 | −1.10819 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.25499 | −0.145348 | −0.0726739 | − | 0.997356i | \(-0.523153\pi\) | ||||
−0.0726739 | + | 0.997356i | \(0.523153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5164 | 0.836487 | 0.418244 | − | 0.908335i | \(-0.362646\pi\) | ||||
0.418244 | + | 0.908335i | \(0.362646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.11643 | −0.140125 | −0.0700624 | − | 0.997543i | \(-0.522320\pi\) | ||||
−0.0700624 | + | 0.997543i | \(0.522320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.0594 | −2.72210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.6534 | 0.735387 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9799 | 0.372467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.1244 | −1.76617 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.44384 | 0.218091 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 53.4873 | 1.80820 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.17301 | −0.107145 | −0.0535725 | − | 0.998564i | \(-0.517061\pi\) | ||||
−0.0535725 | + | 0.998564i | \(0.517061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −74.6180 | −2.51680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0391 | 0.540371 | 0.270186 | − | 0.962808i | \(-0.412915\pi\) | ||||
0.270186 | + | 0.962808i | \(0.412915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5648 | 1.23050 | 0.615252 | − | 0.788330i | \(-0.289054\pi\) | ||||
0.615252 | + | 0.788330i | \(0.289054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.9115 | −0.400401 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.6498 | 1.49919 | 0.749596 | − | 0.661896i | \(-0.230248\pi\) | ||||
0.749596 | + | 0.661896i | \(0.230248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66.1755 | −2.21945 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.3686 | −0.950382 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3196 | 0.813825 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.4773 | 2.15524 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.3477 | 0.545833 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.76319 | −0.258917 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8908 | −0.995807 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 85.5542 | 2.84707 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −75.5004 | −2.50972 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.2692 | −1.43673 | −0.718365 | − | 0.695667i | \(-0.755109\pi\) | ||||
−0.718365 | + | 0.695667i | \(0.755109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.10723 | 0.268900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.64116 | −0.0543739 | −0.0271870 | − | 0.999630i | \(-0.508655\pi\) | ||||
−0.0271870 | + | 0.999630i | \(0.508655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0311 | 0.894598 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.47691 | −0.280238 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.7014 | 1.41012 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.67802 | −0.220288 | −0.110144 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110144 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.2548 | 0.931027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.2074 | 2.04758 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.0823 | 0.758942 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.13603 | 0.0701564 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3505 | 0.766104 | 0.383052 | − | 0.923727i | \(-0.374873\pi\) | ||||
0.383052 | + | 0.923727i | \(0.374873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −88.0508 | −2.88575 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.83433 | 0.158269 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.7480 | −0.809347 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.9295 | −1.50045 | −0.750225 | − | 0.661182i | \(-0.770055\pi\) | ||||
−0.750225 | + | 0.661182i | \(0.770055\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −64.9238 | −2.11871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2488 | −0.431899 | −0.215949 | − | 0.976405i | \(-0.569285\pi\) | ||||
−0.215949 | + | 0.976405i | \(0.569285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 44.0523 | 1.43302 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.1017 | −0.718207 | −0.359104 | − | 0.933298i | \(-0.616918\pi\) | ||||
−0.359104 | + | 0.933298i | \(0.616918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8959 | 1.32754 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.2552 | −2.05119 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.2642 | −0.591635 | −0.295818 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295818 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.2013 | −0.750778 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.7860 | 0.445637 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 83.8760 | 2.70850 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.8023 | −0.671042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.614817 | −0.0198122 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.3130 | −0.718279 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0843 | 0.903132 | 0.451566 | − | 0.892238i | \(-0.350866\pi\) | ||||
0.451566 | + | 0.892238i | \(0.350866\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.1152 | −0.903192 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.1505 | 1.09594 | 0.547972 | − | 0.836497i | \(-0.315400\pi\) | ||||
0.547972 | + | 0.836497i | \(0.315400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0566 | −0.354458 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −86.7918 | −2.77956 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.4597 | −1.32641 | −0.663206 | − | 0.748437i | \(-0.730805\pi\) | ||||
−0.663206 | + | 0.748437i | \(0.730805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9765 | −0.766291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.17898 | −0.197280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.1240 | −1.08839 | −0.544193 | − | 0.838960i | \(-0.683164\pi\) | ||||
−0.544193 | + | 0.838960i | \(0.683164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.0191 | 1.62560 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.8078 | 1.84004 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3971 | 0.362408 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3535 | 0.678315 | 0.339158 | − | 0.940730i | \(-0.389858\pi\) | ||||
0.339158 | + | 0.940730i | \(0.389858\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6513 | −0.338009 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.2938 | −2.13336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3560 | 0.613012 | 0.306506 | − | 0.951869i | \(-0.400840\pi\) | ||||
0.306506 | + | 0.951869i | \(0.400840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.03348 | 0.222529 |
(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 | 6724.2.a.c.1.2 | 4 | ||
41.40 | even | 2 | 164.2.a.a.1.3 | ✓ | 4 | ||
123.122 | odd | 2 | 1476.2.a.g.1.1 | 4 | |||
164.163 | odd | 2 | 656.2.a.i.1.2 | 4 | |||
205.122 | odd | 4 | 4100.2.d.c.1149.3 | 8 | |||
205.163 | odd | 4 | 4100.2.d.c.1149.6 | 8 | |||
205.204 | even | 2 | 4100.2.a.c.1.2 | 4 | |||
287.286 | odd | 2 | 8036.2.a.i.1.2 | 4 | |||
328.163 | odd | 2 | 2624.2.a.y.1.3 | 4 | |||
328.245 | even | 2 | 2624.2.a.v.1.2 | 4 | |||
492.491 | even | 2 | 5904.2.a.bp.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.3 | ✓ | 4 | 41.40 | even | 2 | ||
656.2.a.i.1.2 | 4 | 164.163 | odd | 2 | |||
1476.2.a.g.1.1 | 4 | 123.122 | odd | 2 | |||
2624.2.a.v.1.2 | 4 | 328.245 | even | 2 | |||
2624.2.a.y.1.3 | 4 | 328.163 | odd | 2 | |||
4100.2.a.c.1.2 | 4 | 205.204 | even | 2 | |||
4100.2.d.c.1149.3 | 8 | 205.122 | odd | 4 | |||
4100.2.d.c.1149.6 | 8 | 205.163 | odd | 4 | |||
5904.2.a.bp.1.1 | 4 | 492.491 | even | 2 | |||
6724.2.a.c.1.2 | 4 | 1.1 | even | 1 | trivial | ||
8036.2.a.i.1.2 | 4 | 287.286 | odd | 2 |