Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.24197.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 6x^{2} - x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.509552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.41546 | 1.97465 | 0.987327 | − | 0.158699i | \(-0.0507301\pi\) | ||||
0.987327 | + | 0.158699i | \(0.0507301\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67510 | 0.505063 | 0.252531 | − | 0.967589i | \(-0.418737\pi\) | ||||
0.252531 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.66537 | −1.29394 | −0.646970 | − | 0.762515i | \(-0.723964\pi\) | ||||
−0.646970 | + | 0.762515i | \(0.723964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.41546 | 1.14007 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.24991 | 1.51583 | 0.757913 | − | 0.652356i | \(-0.226219\pi\) | ||||
0.757913 | + | 0.652356i | \(0.226219\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.694209 | 0.159262 | 0.0796312 | − | 0.996824i | \(-0.474626\pi\) | ||||
0.0796312 | + | 0.996824i | \(0.474626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.4963 | 2.89926 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.60012 | 1.03992 | 0.519958 | − | 0.854192i | \(-0.325948\pi\) | ||||
0.519958 | + | 0.854192i | \(0.325948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24991 | −0.763306 | −0.381653 | − | 0.924306i | \(-0.624645\pi\) | ||||
−0.381653 | + | 0.924306i | \(0.624645\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.67510 | 0.291598 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.41546 | −0.746349 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.26901 | 1.52382 | 0.761908 | − | 0.647685i | \(-0.224263\pi\) | ||||
0.761908 | + | 0.647685i | \(0.224263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.66537 | −0.747057 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.15582 | −0.805203 | −0.402602 | − | 0.915375i | \(-0.631894\pi\) | ||||
−0.402602 | + | 0.915375i | \(0.631894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.20376 | −0.641068 | −0.320534 | − | 0.947237i | \(-0.603862\pi\) | ||||
−0.320534 | + | 0.947237i | \(0.603862\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.41546 | 0.658218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.92501 | 0.280792 | 0.140396 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140396 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.24991 | 0.875162 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.84066 | −0.252833 | −0.126417 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126417 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39636 | 0.997324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.694209 | 0.0919502 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.39779 | −1.22349 | −0.611744 | − | 0.791056i | \(-0.709532\pi\) | ||||
−0.611744 | + | 0.791056i | \(0.709532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.72125 | 0.988605 | 0.494302 | − | 0.869290i | \(-0.335424\pi\) | ||||
0.494302 | + | 0.869290i | \(0.335424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.5998 | −2.55508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.22728 | 1.00512 | 0.502561 | − | 0.864542i | \(-0.332391\pi\) | ||||
0.502561 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6654 | 1.26575 | 0.632873 | − | 0.774255i | \(-0.281875\pi\) | ||||
0.632873 | + | 0.774255i | \(0.281875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9117 | −1.39416 | −0.697082 | − | 0.716991i | \(-0.745519\pi\) | ||||
−0.697082 | + | 0.716991i | \(0.745519\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.4963 | 1.67389 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.67510 | −0.190896 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.581012 | −0.0653689 | −0.0326845 | − | 0.999466i | \(-0.510406\pi\) | ||||
−0.0326845 | + | 0.999466i | \(0.510406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.95032 | −0.762897 | −0.381449 | − | 0.924390i | \(-0.624575\pi\) | ||||
−0.381449 | + | 0.924390i | \(0.624575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.5962 | 2.99323 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.60012 | 0.600396 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.4963 | −1.43060 | −0.715302 | − | 0.698816i | \(-0.753711\pi\) | ||||
−0.715302 | + | 0.698816i | \(0.753711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.66537 | 0.489064 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.24991 | −0.440695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.06525 | 0.314488 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0999 | 1.02549 | 0.512746 | − | 0.858540i | \(-0.328628\pi\) | ||||
0.512746 | + | 0.858540i | \(0.328628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.67510 | 0.168354 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.7830 | −1.37146 | −0.685729 | − | 0.727857i | \(-0.740516\pi\) | ||||
−0.685729 | + | 0.727857i | \(0.740516\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5553 | −1.63125 | −0.815623 | − | 0.578584i | \(-0.803605\pi\) | ||||
−0.815623 | + | 0.578584i | \(0.803605\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.41546 | −0.430905 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.33463 | 0.129024 | 0.0645118 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645118 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00794 | 0.383891 | 0.191945 | − | 0.981406i | \(-0.438520\pi\) | ||||
0.191945 | + | 0.981406i | \(0.438520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.26901 | 0.879776 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.06525 | −0.852787 | −0.426394 | − | 0.904538i | \(-0.640216\pi\) | ||||
−0.426394 | + | 0.904538i | \(0.640216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.41546 | 0.411744 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.66537 | −0.431314 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.24991 | −0.572928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.19403 | −0.744911 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.15582 | −0.464884 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.9305 | 3.75038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4977 | 1.90761 | 0.953807 | − | 0.300419i | \(-0.0971267\pi\) | ||||
0.953807 | + | 0.300419i | \(0.0971267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.20376 | −0.370121 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.17529 | −0.102685 | −0.0513426 | − | 0.998681i | \(-0.516350\pi\) | ||||
−0.0513426 | + | 0.998681i | \(0.516350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.694209 | −0.0601956 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.41546 | 0.380022 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8562 | 1.35469 | 0.677345 | − | 0.735666i | \(-0.263131\pi\) | ||||
0.677345 | + | 0.735666i | \(0.263131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.93438 | 0.164072 | 0.0820361 | − | 0.996629i | \(-0.473858\pi\) | ||||
0.0820361 | + | 0.996629i | \(0.473858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.92501 | 0.162115 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.81498 | −0.653521 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.7271 | 2.05347 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.61301 | 0.214067 | 0.107033 | − | 0.994255i | \(-0.465865\pi\) | ||||
0.107033 | + | 0.994255i | \(0.465865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.26281 | 0.753797 | 0.376898 | − | 0.926255i | \(-0.376991\pi\) | ||||
0.376898 | + | 0.926255i | \(0.376991\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.24991 | 0.505275 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.7653 | −1.50727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.77504 | −0.620516 | −0.310258 | − | 0.950652i | \(-0.600415\pi\) | ||||
−0.310258 | + | 0.950652i | \(0.600415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.84066 | −0.145973 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.12077 | 0.557742 | 0.278871 | − | 0.960329i | \(-0.410040\pi\) | ||||
0.278871 | + | 0.960329i | \(0.410040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.39636 | 0.575805 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.9867 | 0.927562 | 0.463781 | − | 0.885950i | \(-0.346493\pi\) | ||||
0.463781 | + | 0.885950i | \(0.346493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.76567 | 0.674282 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.694209 | 0.0530875 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.09993 | −0.159655 | −0.0798275 | − | 0.996809i | \(-0.525437\pi\) | ||||
−0.0798275 | + | 0.996809i | \(0.525437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.4963 | −1.09582 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.39779 | −0.706381 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9726 | 1.19385 | 0.596924 | − | 0.802298i | \(-0.296389\pi\) | ||||
0.596924 | + | 0.802298i | \(0.296389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.89970 | −0.215533 | −0.107767 | − | 0.994176i | \(-0.534370\pi\) | ||||
−0.107767 | + | 0.994176i | \(0.534370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.72125 | 0.570771 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 40.9270 | 3.00901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4692 | 0.765587 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5486 | 1.55921 | 0.779603 | − | 0.626275i | \(-0.215421\pi\) | ||||
0.779603 | + | 0.626275i | \(0.215421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.58722 | 0.330195 | 0.165098 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165098 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.5998 | −1.47518 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.8656 | −0.845389 | −0.422695 | − | 0.906272i | \(-0.638916\pi\) | ||||
−0.422695 | + | 0.906272i | \(0.638916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.52866 | 0.179252 | 0.0896259 | − | 0.995976i | \(-0.471433\pi\) | ||||
0.0896259 | + | 0.995976i | \(0.471433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.22728 | 0.580307 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.60012 | −0.393051 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.7653 | −1.59000 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.16287 | 0.0804376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9797 | 1.51314 | 0.756572 | − | 0.653911i | \(-0.226873\pi\) | ||||
0.756572 | + | 0.653911i | \(0.226873\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.6654 | 0.730779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.5615 | −1.26589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.24991 | 0.288503 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.9117 | −0.804921 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.1581 | −1.96139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0302726 | −0.00202720 | −0.00101360 | − | 0.999999i | \(-0.500323\pi\) | ||||
−0.00101360 | + | 0.999999i | \(0.500323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.4963 | 0.966419 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2393 | −1.40970 | −0.704852 | − | 0.709355i | \(-0.748986\pi\) | ||||
−0.704852 | + | 0.709355i | \(0.748986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4360 | 1.15220 | 0.576102 | − | 0.817378i | \(-0.304573\pi\) | ||||
0.576102 | + | 0.817378i | \(0.304573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.67510 | −0.110214 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2082 | −0.734272 | −0.367136 | − | 0.930167i | \(-0.619662\pi\) | ||||
−0.367136 | + | 0.930167i | \(0.619662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.49982 | 0.554467 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.581012 | −0.0377408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.5654 | 1.20090 | 0.600449 | − | 0.799663i | \(-0.294989\pi\) | ||||
0.600449 | + | 0.799663i | \(0.294989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6556 | −0.879637 | −0.439818 | − | 0.898087i | \(-0.644957\pi\) | ||||
−0.439818 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.41546 | 0.282093 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.23874 | −0.206076 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.95032 | −0.440459 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.604526 | −0.0381574 | −0.0190787 | − | 0.999818i | \(-0.506073\pi\) | ||||
−0.0190787 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.67510 | 0.105313 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.5962 | 1.72814 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1602 | 0.883291 | 0.441645 | − | 0.897190i | \(-0.354395\pi\) | ||||
0.441645 | + | 0.897190i | \(0.354395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.26901 | −0.575948 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.60012 | 0.346639 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.5788 | −1.26895 | −0.634473 | − | 0.772945i | \(-0.718783\pi\) | ||||
−0.634473 | + | 0.772945i | \(0.718783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.12734 | −0.499259 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4963 | −0.825960 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.496655 | −0.0302816 | −0.0151408 | − | 0.999885i | \(-0.504820\pi\) | ||||
−0.0151408 | + | 0.999885i | \(0.504820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0547 | −1.46122 | −0.730609 | − | 0.682797i | \(-0.760764\pi\) | ||||
−0.730609 | + | 0.682797i | \(0.760764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.66537 | 0.282361 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.2828 | 1.46431 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2402 | 1.39637 | 0.698183 | − | 0.715919i | \(-0.253992\pi\) | ||||
0.698183 | + | 0.715919i | \(0.253992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.24991 | −0.254435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0697 | −0.898985 | −0.449492 | − | 0.893284i | \(-0.648395\pi\) | ||||
−0.449492 | + | 0.893284i | \(0.648395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.22691 | −0.548483 | −0.274241 | − | 0.961661i | \(-0.588427\pi\) | ||||
−0.274241 | + | 0.961661i | \(0.588427\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.06525 | 0.181570 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.15582 | 0.304338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.0614 | 1.29773 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0999 | 0.592069 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.3881 | −0.723718 | −0.361859 | − | 0.932233i | \(-0.617858\pi\) | ||||
−0.361859 | + | 0.932233i | \(0.617858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.4956 | −2.41596 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.67510 | 0.0971994 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.66537 | −0.269805 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.20376 | 0.242301 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.7830 | −0.791811 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.0929 | 1.95215 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.823281 | −0.0469871 | −0.0234936 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234936 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5553 | −0.941800 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6632 | 1.73875 | 0.869375 | − | 0.494152i | \(-0.164521\pi\) | ||||
0.869375 | + | 0.494152i | \(0.164521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1323 | 0.742282 | 0.371141 | − | 0.928577i | \(-0.378967\pi\) | ||||
0.371141 | + | 0.928577i | \(0.378967\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.41546 | −0.248783 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.2269 | −0.855229 | −0.427614 | − | 0.903961i | \(-0.640646\pi\) | ||||
−0.427614 | + | 0.903961i | \(0.640646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.38078 | 0.525223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.33463 | 0.0744918 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.33874 | 0.241414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −67.6305 | −3.75147 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.00794 | 0.221639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.92501 | −0.106129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.5674 | −1.40531 | −0.702655 | − | 0.711530i | \(-0.748002\pi\) | ||||
−0.702655 | + | 0.711530i | \(0.748002\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.26901 | 0.507939 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.3272 | 1.98477 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.2890 | 0.887318 | 0.443659 | − | 0.896196i | \(-0.353680\pi\) | ||||
0.443659 | + | 0.896196i | \(0.353680\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.06525 | −0.492357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.11904 | −0.385518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.41546 | 0.237720 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6729 | −1.16346 | −0.581732 | − | 0.813380i | \(-0.697625\pi\) | ||||
−0.581732 | + | 0.813380i | \(0.697625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.5198 | −1.15193 | −0.575964 | − | 0.817475i | \(-0.695373\pi\) | ||||
−0.575964 | + | 0.817475i | \(0.695373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.66537 | −0.249019 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.1852 | −1.07435 | −0.537174 | − | 0.843471i | \(-0.680508\pi\) | ||||
−0.537174 | + | 0.843471i | \(0.680508\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 47.0925 | 2.49941 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.24991 | −0.330780 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.2492 | −1.22705 | −0.613524 | − | 0.789676i | \(-0.710249\pi\) | ||||
−0.613524 | + | 0.789676i | \(0.710249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5181 | −0.974635 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.19403 | −0.430075 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −52.5959 | −2.75299 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7171 | −1.44682 | −0.723409 | − | 0.690419i | \(-0.757426\pi\) | ||||
−0.723409 | + | 0.690419i | \(0.757426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.15582 | −0.268401 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.84066 | 0.0955621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.7303 | −1.28048 | −0.640242 | − | 0.768173i | \(-0.721166\pi\) | ||||
−0.640242 | + | 0.768173i | \(0.721166\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 41.9305 | 2.16528 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.1266 | −1.34559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.11140 | 0.159822 | 0.0799109 | − | 0.996802i | \(-0.474536\pi\) | ||||
0.0799109 | + | 0.996802i | \(0.474536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.4977 | 1.10136 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9503 | 0.968316 | 0.484158 | − | 0.874980i | \(-0.339126\pi\) | ||||
0.484158 | + | 0.874980i | \(0.339126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.39636 | −0.376953 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.20376 | −0.213689 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.1693 | −1.02262 | −0.511312 | − | 0.859395i | \(-0.670840\pi\) | ||||
−0.511312 | + | 0.859395i | \(0.670840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.24991 | 0.316071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.17529 | −0.0592854 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.56543 | −0.129081 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.41634 | 0.422404 | 0.211202 | − | 0.977442i | \(-0.432262\pi\) | ||||
0.211202 | + | 0.977442i | \(0.432262\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.694209 | −0.0347539 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.86329 | −0.292799 | −0.146399 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146399 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8274 | 0.987673 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.41546 | 0.219406 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.5266 | 0.769623 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.2686 | −1.29890 | −0.649451 | − | 0.760404i | \(-0.725001\pi\) | ||||
−0.649451 | + | 0.760404i | \(0.725001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.8562 | 0.782130 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.39779 | 0.462435 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.6889 | −1.50646 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.93438 | 0.0947271 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.800648 | 0.0391142 | 0.0195571 | − | 0.999809i | \(-0.493774\pi\) | ||||
0.0195571 | + | 0.999809i | \(0.493774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3845 | 1.13969 | 0.569846 | − | 0.821751i | \(-0.307003\pi\) | ||||
0.569846 | + | 0.821751i | \(0.307003\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.92501 | 0.0935973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 90.6005 | 4.39477 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.72125 | −0.373658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.81498 | −0.377311 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4853 | 1.61293 | 0.806465 | − | 0.591281i | \(-0.201378\pi\) | ||||
0.806465 | + | 0.591281i | \(0.201378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1373 | 1.15996 | 0.579982 | − | 0.814629i | \(-0.303059\pi\) | ||||
0.579982 | + | 0.814629i | \(0.303059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.7271 | 1.18557 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.694209 | 0.0332085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4469 | 0.784968 | 0.392484 | − | 0.919759i | \(-0.371616\pi\) | ||||
0.392484 | + | 0.919759i | \(0.371616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.58542 | −0.455417 | −0.227709 | − | 0.973729i | \(-0.573123\pi\) | ||||
−0.227709 | + | 0.973729i | \(0.573123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −59.5923 | −2.82495 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.61301 | 0.123591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.17319 | 0.196945 | 0.0984725 | − | 0.995140i | \(-0.468604\pi\) | ||||
0.0984725 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.63653 | −0.406678 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.26281 | 0.435205 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.5998 | 0.965731 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.02668 | 0.375472 | 0.187736 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187736 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.24991 | 0.291721 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6192 | 0.541158 | 0.270579 | − | 0.962698i | \(-0.412785\pi\) | ||||
0.270579 | + | 0.962698i | \(0.412785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8714 | 1.66708 | 0.833542 | − | 0.552456i | \(-0.186309\pi\) | ||||
0.833542 | + | 0.552456i | \(0.186309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.7653 | −0.870220 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1731 | 0.609579 | 0.304790 | − | 0.952420i | \(-0.401414\pi\) | ||||
0.304790 | + | 0.952420i | \(0.401414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.22728 | −0.379900 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.77504 | −0.358255 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.04174 | −0.323779 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0635 | 0.461743 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.84066 | −0.0842778 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.23080 | −0.239002 | −0.119501 | − | 0.992834i | \(-0.538129\pi\) | ||||
−0.119501 | + | 0.992834i | \(0.538129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.2434 | −1.97173 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.5959 | 2.02499 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.9779 | −1.31311 | −0.656557 | − | 0.754277i | \(-0.727988\pi\) | ||||
−0.656557 | + | 0.754277i | \(0.727988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.12077 | 0.322012 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6912 | 0.753262 | 0.376631 | − | 0.926363i | \(-0.377083\pi\) | ||||
0.376631 | + | 0.926363i | \(0.377083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.0002 | 1.57633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39636 | 0.332441 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6654 | −0.478407 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.57213 | −0.428507 | −0.214254 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214254 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9867 | 0.535528 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.6348 | 0.920060 | 0.460030 | − | 0.887903i | \(-0.347839\pi\) | ||||
0.460030 | + | 0.887903i | \(0.347839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −60.8582 | −2.70815 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.76567 | 0.389297 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.23665 | 0.276434 | 0.138217 | − | 0.990402i | \(-0.455863\pi\) | ||||
0.138217 | + | 0.990402i | \(0.455863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9117 | 0.526945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.694209 | 0.0306501 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −73.0994 | −3.22115 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.22460 | 0.141818 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.09993 | −0.0921769 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6615 | 0.554709 | 0.277355 | − | 0.960768i | \(-0.410542\pi\) | ||||
0.277355 | + | 0.960768i | \(0.410542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.3446 | −1.89533 | −0.947663 | − | 0.319272i | \(-0.896562\pi\) | ||||
−0.947663 | + | 0.319272i | \(0.896562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.4963 | −0.632670 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.5615 | −1.15704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.39779 | −0.407829 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0538 | 1.04189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.89301 | 0.254777 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.9726 | 0.689268 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.67510 | 0.0721518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.87439 | 0.252560 | 0.126280 | − | 0.991995i | \(-0.459696\pi\) | ||||
0.126280 | + | 0.991995i | \(0.459696\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.89970 | −0.124438 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.6969 | 0.758051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8580 | −0.592524 | −0.296262 | − | 0.955107i | \(-0.595740\pi\) | ||||
−0.296262 | + | 0.955107i | \(0.595740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.72125 | 0.329535 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.88765 | 0.165620 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.581012 | 0.0247071 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 40.9270 | 1.73725 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.5921 | −0.787773 | −0.393887 | − | 0.919159i | \(-0.628870\pi\) | ||||
−0.393887 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.6121 | 0.829503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.4692 | 0.442012 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.09582 | −0.214763 | −0.107382 | − | 0.994218i | \(-0.534247\pi\) | ||||
−0.107382 | + | 0.994218i | \(0.534247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.0273 | −1.68396 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.3028 | −1.22844 | −0.614218 | − | 0.789136i | \(-0.710529\pi\) | ||||
−0.614218 | + | 0.789136i | \(0.710529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.10736 | 0.213736 | 0.106868 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106868 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.5486 | 0.900208 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4963 | 0.604537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7379 | 1.02985 | 0.514926 | − | 0.857235i | \(-0.327819\pi\) | ||||
0.514926 | + | 0.857235i | \(0.327819\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.58722 | 0.190638 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.95032 | 0.288348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.08329 | −0.127697 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.5998 | −0.851695 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.8319 | −1.60276 | −0.801382 | − | 0.598152i | \(-0.795902\pi\) | ||||
−0.801382 | + | 0.598152i | \(0.795902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.95032 | −0.121566 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8656 | −0.488086 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.9162 | 1.51596 | 0.757982 | − | 0.652275i | \(-0.226185\pi\) | ||||
0.757982 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.5962 | −1.13133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.52866 | 0.103491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.4224 | −1.65161 | −0.825807 | − | 0.563953i | \(-0.809280\pi\) | ||||
−0.825807 | + | 0.563953i | \(0.809280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98464 | 0.121746 | 0.0608730 | − | 0.998146i | \(-0.480612\pi\) | ||||
0.0608730 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.22728 | 0.335041 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.1804 | −1.47094 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.1893 | 1.18476 | 0.592378 | − | 0.805660i | \(-0.298189\pi\) | ||||
0.592378 | + | 0.805660i | \(0.298189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.60012 | −0.226928 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.98090 | −0.363328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.88595 | −0.237731 | −0.118866 | − | 0.992910i | \(-0.537926\pi\) | ||||
−0.118866 | + | 0.992910i | \(0.537926\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.7653 | −0.917986 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.07326 | −0.325017 | −0.162509 | − | 0.986707i | \(-0.551959\pi\) | ||||
−0.162509 | + | 0.986707i | \(0.551959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8589 | −0.436457 | −0.218228 | − | 0.975898i | \(-0.570028\pi\) | ||||
−0.218228 | + | 0.975898i | \(0.570028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.4963 | 0.540717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 112.661 | 4.50644 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.16287 | 0.0464406 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 57.9305 | 2.30984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1891 | −0.923145 | −0.461572 | − | 0.887103i | \(-0.652715\pi\) | ||||
−0.461572 | + | 0.887103i | \(0.652715\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.9797 | 0.873614 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 94.9223 | 3.76688 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.66537 | −0.184849 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.6654 | 0.421915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.7138 | −1.84509 | −0.922543 | − | 0.385895i | \(-0.873893\pi\) | ||||
−0.922543 | + | 0.385895i | \(0.873893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.7524 | −1.33106 | −0.665532 | − | 0.746369i | \(-0.731795\pi\) | ||||
−0.665532 | + | 0.746369i | \(0.731795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.5615 | −0.730860 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9277 | −0.744124 | −0.372062 | − | 0.928208i | \(-0.621349\pi\) | ||||
−0.372062 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7423 | −0.617938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.24991 | 0.166567 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.1696 | −0.397967 | −0.198984 | − | 0.980003i | \(-0.563764\pi\) | ||||
−0.198984 | + | 0.980003i | \(0.563764\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.18943 | −0.202768 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.9117 | −0.464722 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.60754 | 0.179484 | 0.0897421 | − | 0.995965i | \(-0.471396\pi\) | ||||
0.0897421 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1205 | −1.21045 | −0.605223 | − | 0.796056i | \(-0.706916\pi\) | ||||
−0.605223 | + | 0.796056i | \(0.706916\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.1581 | −1.13241 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.06525 | −0.118865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.60012 | 0.216837 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0302726 | −0.00117041 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.9339 | 0.499308 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.9447 | −1.42411 | −0.712057 | − | 0.702122i | \(-0.752236\pi\) | ||||
−0.712057 | + | 0.702122i | \(0.752236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.4963 | 0.557962 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.331401 | 0.0127368 | 0.00636838 | − | 0.999980i | \(-0.497973\pi\) | ||||
0.00636838 | + | 0.999980i | \(0.497973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0999 | −0.387600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.2393 | −0.813893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.8856 | 0.646109 | 0.323055 | − | 0.946380i | \(-0.395290\pi\) | ||||
0.323055 | + | 0.946380i | \(0.395290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.0126 | 2.67504 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.4360 | 0.665225 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.58734 | 0.327152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1963 | 0.425929 | 0.212964 | − | 0.977060i | \(-0.431688\pi\) | ||||
0.212964 | + | 0.977060i | \(0.431688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.67510 | −0.0636319 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.54119 | 0.323986 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.2234 | −1.22055 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.2082 | −0.423932 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.50609 | 0.359040 | 0.179520 | − | 0.983754i | \(-0.442546\pi\) | ||||
0.179520 | + | 0.983754i | \(0.442546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.43463 | 0.242687 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.49982 | 0.320122 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7830 | 0.518362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2890 | 1.36286 | 0.681431 | − | 0.731882i | \(-0.261358\pi\) | ||||
0.681431 | + | 0.731882i | \(0.261358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.581012 | −0.0217896 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.24991 | −0.159160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.5067 | −1.29048 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.5654 | 0.693339 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.5772 | 1.25222 | 0.626109 | − | 0.779736i | \(-0.284647\pi\) | ||||
0.626109 | + | 0.779736i | \(0.284647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.5553 | 0.616553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.6556 | −0.507858 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 81.1809 | 3.01498 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.5410 | −1.39232 | −0.696159 | − | 0.717887i | \(-0.745109\pi\) | ||||
−0.696159 | + | 0.717887i | \(0.745109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.2731 | −0.971747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2222 | 0.894668 | 0.447334 | − | 0.894367i | \(-0.352374\pi\) | ||||
0.447334 | + | 0.894367i | \(0.352374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.41546 | 0.162867 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.7815 | 0.507650 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.4377 | 0.715028 | 0.357514 | − | 0.933908i | \(-0.383624\pi\) | ||||
0.357514 | + | 0.933908i | \(0.383624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.23874 | −0.118978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.7282 | −1.31074 | −0.655370 | − | 0.755308i | \(-0.727487\pi\) | ||||
−0.655370 | + | 0.755308i | \(0.727487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5377 | 0.422707 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.95032 | −0.254299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.33463 | −0.0487664 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4795 | −0.528363 | −0.264182 | − | 0.964473i | \(-0.585102\pi\) | ||||
−0.264182 | + | 0.964473i | \(0.585102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.604526 | −0.0220302 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.8996 | 1.48849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8034 | 0.792460 | 0.396230 | − | 0.918151i | \(-0.370318\pi\) | ||||
0.396230 | + | 0.918151i | \(0.370318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.67510 | 0.0608024 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.98196 | −0.216846 | −0.108423 | − | 0.994105i | \(-0.534580\pi\) | ||||
−0.108423 | + | 0.994105i | \(0.534580\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00794 | −0.145097 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.5962 | 0.997744 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.8441 | 1.58312 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0694 | −0.579476 | −0.289738 | − | 0.957106i | \(-0.593568\pi\) | ||||
−0.289738 | + | 0.957106i | \(0.593568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1602 | 0.509968 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.5039 | 1.31295 | 0.656476 | − | 0.754347i | \(-0.272046\pi\) | ||||
0.656476 | + | 0.754347i | \(0.272046\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −61.6079 | −2.21302 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.26901 | −0.332524 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.57921 | −0.128239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8656 | 0.639282 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.60012 | 0.200132 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.3304 | −1.22530 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.7402 | 1.59482 | 0.797408 | − | 0.603440i | \(-0.206204\pi\) | ||||
0.797408 | + | 0.603440i | \(0.206204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.5788 | −0.732626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.06525 | 0.322323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0225 | −1.27920 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.12734 | −0.288247 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3919 | −0.403521 | −0.201761 | − | 0.979435i | \(-0.564666\pi\) | ||||
−0.201761 | + | 0.979435i | \(0.564666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0312 | 0.425632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.4963 | −0.476868 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.9534 | −0.704141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.41546 | −0.155625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.496655 | −0.0174831 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4803 | −0.825523 | −0.412761 | − | 0.910839i | \(-0.635436\pi\) | ||||
−0.412761 | + | 0.910839i | \(0.635436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.320003 | 0.0112368 | 0.00561841 | − | 0.999984i | \(-0.498212\pi\) | ||||
0.00561841 | + | 0.999984i | \(0.498212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0547 | −0.843634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.4415 | 1.10135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.91829 | −0.102098 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.66537 | 0.163021 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.4892 | 1.76208 | 0.881042 | − | 0.473038i | \(-0.156843\pi\) | ||||
0.881042 | + | 0.473038i | \(0.156843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6259 | 1.03270 | 0.516348 | − | 0.856379i | \(-0.327291\pi\) | ||||
0.516348 | + | 0.856379i | \(0.327291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.2828 | 0.845418 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.13318 | 0.108951 | 0.0544757 | − | 0.998515i | \(-0.482651\pi\) | ||||
0.0544757 | + | 0.998515i | \(0.482651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1070 | −0.698345 | −0.349172 | − | 0.937059i | \(-0.613537\pi\) | ||||
−0.349172 | + | 0.937059i | \(0.613537\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.2402 | 0.806193 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.24991 | 0.216547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.9270 | 1.83161 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.24991 | −0.146898 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.63075 | 0.228919 | 0.114460 | − | 0.993428i | \(-0.463486\pi\) | ||||
0.114460 | + | 0.993428i | \(0.463486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.36131 | 0.0814244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.0697 | −0.519029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.7045 | 1.33147 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.19403 | 0.281550 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.22691 | −0.316667 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.26901 | 0.317738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.1804 | −1.23879 | −0.619397 | − | 0.785078i | \(-0.712623\pi\) | ||||
−0.619397 | + | 0.785078i | \(0.712623\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.06525 | 0.104829 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.6983 | 0.433764 | 0.216882 | − | 0.976198i | \(-0.430411\pi\) | ||||
0.216882 | + | 0.976198i | \(0.430411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.2759 | −1.68127 | −0.840636 | − | 0.541600i | \(-0.817819\pi\) | ||||
−0.840636 | + | 0.541600i | \(0.817819\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.15582 | 0.175710 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.28011 | 0.111656 | 0.0558282 | − | 0.998440i | \(-0.482220\pi\) | ||||
0.0558282 | + | 0.998440i | \(0.482220\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.27218 | −0.315263 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.0614 | 0.749243 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.973255 | −0.0330154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.3833 | −1.30057 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0999 | 0.341831 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.9305 | −1.41751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.64380 | 0.258113 | 0.129056 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129056 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.3881 | −0.417839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.21611 | 0.175735 | 0.0878676 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878676 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.2052 | 1.52127 | 0.760637 | − | 0.649177i | \(-0.224887\pi\) | ||||
0.760637 | + | 0.649177i | \(0.224887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41.4956 | −1.39486 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.59600 | 0.288626 | 0.144313 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144313 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4977 | −0.721010 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.67510 | 0.0561181 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.33636 | 0.0447196 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 70.5263 | 2.35744 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.66537 | −0.155772 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.8000 | −0.793774 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.5039 | −0.383251 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.20376 | 0.139892 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8035 | −0.425603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.50429 | −0.0831537 | −0.0415769 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415769 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7830 | −0.457152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.5776 | −0.979951 | −0.489975 | − | 0.871736i | \(-0.662994\pi\) | ||||
−0.489975 | + | 0.871736i | \(0.662994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6425 | −0.385311 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.0929 | 1.12708 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.17529 | 0.0388114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5583 | −0.777117 | −0.388558 | − | 0.921424i | \(-0.627027\pi\) | ||||
−0.388558 | + | 0.921424i | \(0.627027\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.823281 | −0.0271280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.7579 | −1.63780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 134.366 | 4.41794 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.5553 | −0.543749 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.9337 | −1.24456 | −0.622281 | − | 0.782794i | \(-0.713794\pi\) | ||||
−0.622281 | + | 0.782794i | \(0.713794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.694209 | 0.0227518 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.6632 | 1.00387 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.2265 | 1.51177 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.3490 | −1.38348 | −0.691741 | − | 0.722146i | \(-0.743156\pi\) | ||||
−0.691741 | + | 0.722146i | \(0.743156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1323 | 0.428556 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.9735 | −1.10750 | −0.553752 | − | 0.832682i | \(-0.686804\pi\) | ||||
−0.553752 | + | 0.832682i | \(0.686804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.15582 | −0.167896 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.41546 | −0.143635 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.7471 | 0.901659 | 0.450829 | − | 0.892610i | \(-0.351128\pi\) | ||||
0.450829 | + | 0.892610i | \(0.351128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.5727 | 1.80397 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.2269 | −0.493766 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.25582 | −0.202646 | −0.101323 | − | 0.994854i | \(-0.532308\pi\) | ||||
−0.101323 | + | 0.994854i | \(0.532308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 95.1472 | 3.07889 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.38078 | 0.303237 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8562 | −0.512024 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9383 | −0.417364 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.33463 | 0.0430079 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.2547 | 0.652021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.1613 | −1.38797 | −0.693987 | − | 0.719988i | \(-0.744147\pi\) | ||||
−0.693987 | + | 0.719988i | \(0.744147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.33874 | 0.139381 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.69189 | −0.214753 | −0.107377 | − | 0.994218i | \(-0.534245\pi\) | ||||
−0.107377 | + | 0.994218i | \(0.534245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.93438 | −0.0620135 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −67.6305 | −2.16591 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.1871 | −1.50965 | −0.754825 | − | 0.655926i | \(-0.772278\pi\) | ||||
−0.754825 | + | 0.655926i | \(0.772278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6077 | −0.722545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00794 | 0.127964 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.4505 | −0.588480 | −0.294240 | − | 0.955732i | \(-0.595066\pi\) | ||||
−0.294240 | + | 0.955732i | \(0.595066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.3921 | −1.66935 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.92501 | −0.0612738 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.20376 | −0.133672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.3764 | 0.774342 | 0.387171 | − | 0.922008i | \(-0.373452\pi\) | ||||
0.387171 | + | 0.922008i | \(0.373452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5674 | −0.811356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1652 | 0.353960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.5570 | 1.88619 | 0.943094 | − | 0.332525i | \(-0.107901\pi\) | ||||
0.943094 | + | 0.332525i | \(0.107901\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.26901 | 0.293259 |
(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 | 7728.2.a.cd.1.4 | 4 | ||
4.3 | odd | 2 | 483.2.a.i.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 1449.2.a.p.1.3 | 4 | |||
28.27 | even | 2 | 3381.2.a.w.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.i.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
1449.2.a.p.1.3 | 4 | 12.11 | even | 2 | |||
3381.2.a.w.1.2 | 4 | 28.27 | even | 2 | |||
7728.2.a.cd.1.4 | 4 | 1.1 | even | 1 | trivial |