Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.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: | \(75.1232582216\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-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 | ||||||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46410 | −0.441443 | −0.220722 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46410 | −0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.535898 | −0.129974 | −0.0649872 | − | 0.997886i | \(-0.520701\pi\) | ||||
−0.0649872 | + | 0.997886i | \(0.520701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.92820 | −1.58944 | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46410 | 0.305286 | 0.152643 | − | 0.988281i | \(-0.451221\pi\) | ||||
0.152643 | + | 0.988281i | \(0.451221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.92820 | 0.915144 | 0.457572 | − | 0.889172i | \(-0.348719\pi\) | ||||
0.457572 | + | 0.889172i | \(0.348719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.9282 | −1.96276 | −0.981382 | − | 0.192068i | \(-0.938481\pi\) | ||||
−0.981382 | + | 0.192068i | \(0.938481\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.46410 | 0.254867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4641 | −1.79039 | −0.895196 | − | 0.445673i | \(-0.852964\pi\) | ||||
−0.895196 | + | 0.445673i | \(0.852964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410 | 0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9282 | 1.59404 | 0.797021 | − | 0.603951i | \(-0.206408\pi\) | ||||
0.797021 | + | 0.603951i | \(0.206408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.535898 | 0.0750408 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.07180 | −0.683881 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.92820 | 0.917663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.07180 | 0.139536 | 0.0697680 | − | 0.997563i | \(-0.477774\pi\) | ||||
0.0697680 | + | 0.997563i | \(0.477774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92820 | 0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.92820 | −0.357737 | −0.178868 | − | 0.983873i | \(-0.557244\pi\) | ||||
−0.178868 | + | 0.983873i | \(0.557244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.46410 | −0.176257 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9282 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00000 | −0.808290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9282 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85641 | −0.201356 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.92820 | −0.528359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9282 | 1.13320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.0000 | −2.46235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92820 | 0.906522 | 0.453261 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453261 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.46410 | −0.147148 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4641 | −1.53874 | −0.769368 | − | 0.638806i | \(-0.779429\pi\) | ||||
−0.769368 | + | 0.638806i | \(0.779429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9282 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3923 | 1.19801 | 0.599005 | − | 0.800746i | \(-0.295563\pi\) | ||||
0.599005 | + | 0.800746i | \(0.295563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.8564 | −1.86793 | −0.933967 | − | 0.357360i | \(-0.883677\pi\) | ||||
−0.933967 | + | 0.357360i | \(0.883677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.07180 | 0.472947 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4641 | 1.03368 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.92820 | −0.259836 | −0.129918 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129918 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.46410 | −0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.92820 | −0.762788 | −0.381394 | − | 0.924413i | \(-0.624556\pi\) | ||||
−0.381394 | + | 0.924413i | \(0.624556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8564 | 1.51456 | 0.757280 | − | 0.653090i | \(-0.226528\pi\) | ||||
0.757280 | + | 0.653090i | \(0.226528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9282 | −0.920321 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.92820 | −0.244869 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.0718 | 1.41774 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8564 | −1.77865 | −0.889325 | − | 0.457277i | \(-0.848825\pi\) | ||||
−0.889325 | + | 0.457277i | \(0.848825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.535898 | −0.0433248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.8564 | −3.04070 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.928203 | −0.0740787 | −0.0370393 | − | 0.999314i | \(-0.511793\pi\) | ||||
−0.0370393 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9282 | 0.855963 | 0.427981 | − | 0.903788i | \(-0.359225\pi\) | ||||
0.427981 | + | 0.903788i | \(0.359225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.07180 | 0.394839 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.9282 | −0.845650 | −0.422825 | − | 0.906211i | \(-0.638961\pi\) | ||||
−0.422825 | + | 0.906211i | \(0.638961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.92820 | −0.529813 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.3923 | 1.70246 | 0.851228 | − | 0.524797i | \(-0.175859\pi\) | ||||
0.851228 | + | 0.524797i | \(0.175859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.07180 | −0.0805612 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.46410 | 0.707380 | 0.353690 | − | 0.935363i | \(-0.384927\pi\) | ||||
0.353690 | + | 0.935363i | \(0.384927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.92820 | 0.659992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.92820 | 0.509372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.784610 | 0.0573763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.46410 | −0.684798 | −0.342399 | − | 0.939555i | \(-0.611240\pi\) | ||||
−0.342399 | + | 0.939555i | \(0.611240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8564 | 1.14137 | 0.570685 | − | 0.821169i | \(-0.306678\pi\) | ||||
0.570685 | + | 0.821169i | \(0.306678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.92820 | −0.496139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.85641 | 0.559746 | 0.279873 | − | 0.960037i | \(-0.409708\pi\) | ||||
0.279873 | + | 0.960037i | \(0.409708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85641 | 0.415150 | 0.207575 | − | 0.978219i | \(-0.433443\pi\) | ||||
0.207575 | + | 0.978219i | \(0.433443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.92820 | 0.206540 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −39.7128 | −2.77366 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.46410 | 0.101762 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.1436 | 0.701647 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.46410 | 0.648470 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.7128 | −1.89000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9282 | 0.873607 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.07180 | −0.0720969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.9282 | 1.52180 | 0.760899 | − | 0.648870i | \(-0.224758\pi\) | ||||
0.760899 | + | 0.648870i | \(0.224758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8564 | −1.84080 | −0.920402 | − | 0.390974i | \(-0.872138\pi\) | ||||
−0.920402 | + | 0.390974i | \(0.872138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9282 | 0.846955 | 0.423477 | − | 0.905907i | \(-0.360809\pi\) | ||||
0.423477 | + | 0.905907i | \(0.360809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.8564 | 2.46948 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9282 | −0.709863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5359 | −0.940249 | −0.470125 | − | 0.882600i | \(-0.655791\pi\) | ||||
−0.470125 | + | 0.882600i | \(0.655791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.07180 | 0.197872 | 0.0989359 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989359 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8564 | −0.881662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.07180 | 0.572607 | 0.286303 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286303 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14359 | −0.134767 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.85641 | 0.116253 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4641 | −0.715111 | −0.357556 | − | 0.933892i | \(-0.616390\pi\) | ||||
−0.357556 | + | 0.933892i | \(0.616390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.92820 | 0.305048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.3923 | −0.764142 | −0.382071 | − | 0.924133i | \(-0.624789\pi\) | ||||
−0.382071 | + | 0.924133i | \(0.624789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820 | 0.425596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.46410 | 0.212000 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46410 | 0.211210 | 0.105605 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105605 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.92820 | 0.177876 | 0.0889378 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889378 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2487 | −0.618021 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.143594 | −0.00862770 | −0.00431385 | − | 0.999991i | \(-0.501373\pi\) | ||||
−0.00431385 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.9282 | −0.654254 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9282 | 0.887390 | 0.443695 | − | 0.896178i | \(-0.353667\pi\) | ||||
0.443695 | + | 0.896178i | \(0.353667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | 1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7128 | −0.983107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.92820 | −0.523381 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.5359 | 0.966037 | 0.483019 | − | 0.875610i | \(-0.339540\pi\) | ||||
0.483019 | + | 0.875610i | \(0.339540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.71281 | 0.216168 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.46410 | 0.0849558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.92820 | 0.169342 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.4641 | 0.888389 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.9282 | −1.77094 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9282 | −1.30858 | −0.654291 | − | 0.756243i | \(-0.727033\pi\) | ||||
−0.654291 | + | 0.756243i | \(0.727033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.9282 | 0.621684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9282 | 1.07332 | 0.536660 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.143594 | −0.00806502 | −0.00403251 | − | 0.999992i | \(-0.501284\pi\) | ||||
−0.00403251 | + | 0.999992i | \(0.501284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.21539 | −0.403984 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3923 | −0.691671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.71281 | 0.206586 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000 | 0.776580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0000 | 1.31916 | 0.659580 | − | 0.751635i | \(-0.270734\pi\) | ||||
0.659580 | + | 0.751635i | \(0.270734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.1436 | −0.554204 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85641 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.8564 | 1.07845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.07180 | −0.273056 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.3205 | 1.25191 | 0.625955 | − | 0.779859i | \(-0.284709\pi\) | ||||
0.625955 | + | 0.779859i | \(0.284709\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7846 | 0.577287 | 0.288643 | − | 0.957437i | \(-0.406796\pi\) | ||||
0.288643 | + | 0.957437i | \(0.406796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.53590 | −0.454320 | −0.227160 | − | 0.973857i | \(-0.572944\pi\) | ||||
−0.227160 | + | 0.973857i | \(0.572944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.7846 | −1.74003 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.32051 | −0.386362 | −0.193181 | − | 0.981163i | \(-0.561880\pi\) | ||||
−0.193181 | + | 0.981163i | \(0.561880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.85641 | 0.464841 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −44.7846 | −2.34413 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4641 | −0.596797 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.0000 | −1.55334 | −0.776671 | − | 0.629907i | \(-0.783093\pi\) | ||||
−0.776671 | + | 0.629907i | \(0.783093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.85641 | 0.507631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.92820 | 0.150016 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.7128 | 1.82484 | 0.912420 | − | 0.409256i | \(-0.134212\pi\) | ||||
0.912420 | + | 0.409256i | \(0.134212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.7846 | −0.749609 | −0.374805 | − | 0.927104i | \(-0.622290\pi\) | ||||
−0.374805 | + | 0.927104i | \(0.622290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.784610 | −0.0396794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.8564 | 1.90476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7846 | 0.541264 | 0.270632 | − | 0.962683i | \(-0.412767\pi\) | ||||
0.270632 | + | 0.962683i | \(0.412767\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.92820 | 0.246103 | 0.123051 | − | 0.992400i | \(-0.460732\pi\) | ||||
0.123051 | + | 0.992400i | \(0.460732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8564 | −1.08875 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.46410 | 0.172133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.92820 | −0.145146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.92820 | −0.243684 | −0.121842 | − | 0.992550i | \(-0.538880\pi\) | ||||
−0.121842 | + | 0.992550i | \(0.538880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.92820 | 0.440396 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8564 | 0.680184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.8564 | −0.874432 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0718 | −0.834012 | −0.417006 | − | 0.908904i | \(-0.636921\pi\) | ||||
−0.417006 | + | 0.908904i | \(0.636921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.14359 | 0.201946 | 0.100973 | − | 0.994889i | \(-0.467804\pi\) | ||||
0.100973 | + | 0.994889i | \(0.467804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9282 | 0.531347 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.75129 | −0.181964 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.92820 | 0.141375 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2487 | 0.493663 | 0.246832 | − | 0.969058i | \(-0.420611\pi\) | ||||
0.246832 | + | 0.969058i | \(0.420611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.8564 | 1.33869 | 0.669347 | − | 0.742950i | \(-0.266574\pi\) | ||||
0.669347 | + | 0.742950i | \(0.266574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.0718 | −0.818530 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.1436 | −0.485234 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | 0.661330 | 0.330665 | − | 0.943748i | \(-0.392727\pi\) | ||||
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3923 | −1.34896 | −0.674480 | − | 0.738294i | \(-0.735632\pi\) | ||||
−0.674480 | + | 0.738294i | \(0.735632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.85641 | 0.370767 | 0.185383 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185383 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7846 | 0.790356 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.8564 | 1.02690 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.7128 | 1.76413 | 0.882065 | − | 0.471127i | \(-0.156153\pi\) | ||||
0.882065 | + | 0.471127i | \(0.156153\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.535898 | 0.0250136 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.1769 | −1.26576 | −0.632878 | − | 0.774252i | \(-0.718126\pi\) | ||||
−0.632878 | + | 0.774252i | \(0.718126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.7846 | −1.52363 | −0.761815 | − | 0.647795i | \(-0.775691\pi\) | ||||
−0.761815 | + | 0.647795i | \(0.775691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.8564 | 1.75555 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7846 | −0.961797 | −0.480899 | − | 0.876776i | \(-0.659689\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.928203 | 0.0427693 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7128 | 0.538556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −48.4974 | −2.22521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.07180 | −0.231736 | −0.115868 | − | 0.993265i | \(-0.536965\pi\) | ||||
−0.115868 | + | 0.993265i | \(0.536965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.9282 | 1.40438 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7128 | 1.25579 | 0.627894 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627894 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.9282 | −0.494190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.53590 | −0.294961 | −0.147480 | − | 0.989065i | \(-0.547116\pi\) | ||||
−0.147480 | + | 0.989065i | \(0.547116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64102 | −0.118945 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.07180 | −0.227960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.8564 | −0.978427 | −0.489214 | − | 0.872164i | \(-0.662716\pi\) | ||||
−0.489214 | + | 0.872164i | \(0.662716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.9282 | 0.488236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.5692 | −2.38380 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.2487 | −1.78399 | −0.891996 | − | 0.452043i | \(-0.850696\pi\) | ||||
−0.891996 | + | 0.452043i | \(0.850696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.92820 | 0.305888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.8564 | −1.66815 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.3923 | −0.982913 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3923 | −1.33151 | −0.665756 | − | 0.746170i | \(-0.731891\pi\) | ||||
−0.665756 | + | 0.746170i | \(0.731891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.85641 | 0.255109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8564 | −0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.07180 | 0.0465120 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9282 | −0.993131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 42.9282 | 1.85595 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.46410 | −0.408406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.85641 | 0.337773 | 0.168887 | − | 0.985635i | \(-0.445983\pi\) | ||||
0.168887 | + | 0.985635i | \(0.445983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | 0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820 | 0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9282 | 0.467256 | 0.233628 | − | 0.972326i | \(-0.424940\pi\) | ||||
0.233628 | + | 0.972326i | \(0.424940\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.92820 | −0.381046 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.1436 | −1.45457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.92820 | −0.294086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.14359 | 0.175570 | 0.0877848 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877848 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.784610 | −0.0331262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.0718 | −1.39381 | −0.696905 | − | 0.717163i | \(-0.745440\pi\) | ||||
−0.696905 | + | 0.717163i | \(0.745440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −68.7846 | −2.89379 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.9282 | −1.04504 | −0.522522 | − | 0.852626i | \(-0.675009\pi\) | ||||
−0.522522 | + | 0.852626i | \(0.675009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7846 | 0.702414 | 0.351207 | − | 0.936298i | \(-0.385771\pi\) | ||||
0.351207 | + | 0.936298i | \(0.385771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.46410 | 0.395369 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2487 | 0.427401 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8564 | −0.993155 | −0.496578 | − | 0.867992i | \(-0.665410\pi\) | ||||
−0.496578 | + | 0.867992i | \(0.665410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.8564 | −0.658970 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.92820 | −0.121274 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.92820 | 0.286446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7846 | 0.857873 | 0.428936 | − | 0.903335i | \(-0.358888\pi\) | ||||
0.428936 | + | 0.903335i | \(0.358888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 75.7128 | 3.11969 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.85641 | −0.323169 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.53590 | −0.350527 | −0.175264 | − | 0.984522i | \(-0.556078\pi\) | ||||
−0.175264 | + | 0.984522i | \(0.556078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.85641 | −0.239687 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.3923 | 1.16008 | 0.580039 | − | 0.814589i | \(-0.303037\pi\) | ||||
0.580039 | + | 0.814589i | \(0.303037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.5692 | −1.77723 | −0.888613 | − | 0.458658i | \(-0.848330\pi\) | ||||
−0.888613 | + | 0.458658i | \(0.848330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.92820 | −0.119246 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.6795 | −1.24730 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8564 | 0.562414 | 0.281207 | − | 0.959647i | \(-0.409265\pi\) | ||||
0.281207 | + | 0.959647i | \(0.409265\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.8564 | 0.884216 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.8564 | −1.12511 | −0.562555 | − | 0.826760i | \(-0.690181\pi\) | ||||
−0.562555 | + | 0.826760i | \(0.690181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.7128 | 1.60138 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7846 | 0.756240 | 0.378120 | − | 0.925757i | \(-0.376571\pi\) | ||||
0.378120 | + | 0.925757i | \(0.376571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.46410 | −0.0587524 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.1436 | −0.405096 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.07180 | −0.0427353 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9282 | −1.07199 | −0.535997 | − | 0.844220i | \(-0.680064\pi\) | ||||
−0.535997 | + | 0.844220i | \(0.680064\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1436 | −0.402536 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.46410 | −0.374394 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.78461 | −0.267976 | −0.133988 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133988 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7846 | 0.504176 | 0.252088 | − | 0.967704i | \(-0.418883\pi\) | ||||
0.252088 | + | 0.967704i | \(0.418883\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.7128 | 1.09119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.07180 | −0.199393 | −0.0996965 | − | 0.995018i | \(-0.531787\pi\) | ||||
−0.0996965 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.56922 | −0.0615972 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.9282 | 0.818984 | 0.409492 | − | 0.912314i | \(-0.365706\pi\) | ||||
0.409492 | + | 0.912314i | \(0.365706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.5692 | −1.62424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.9282 | −0.504377 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5359 | 0.566238 | 0.283119 | − | 0.959085i | \(-0.408631\pi\) | ||||
0.283119 | + | 0.959085i | \(0.408631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7846 | 1.04180 | 0.520900 | − | 0.853618i | \(-0.325596\pi\) | ||||
0.520900 | + | 0.853618i | \(0.325596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.07180 | 0.0416251 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.21539 | 0.279381 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | 0.927894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0718 | 0.504631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8564 | 1.22797 | 0.613987 | − | 0.789316i | \(-0.289565\pi\) | ||||
0.613987 | + | 0.789316i | \(0.289565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.60770 | −0.0617887 | −0.0308944 | − | 0.999523i | \(-0.509836\pi\) | ||||
−0.0308944 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.9282 | −0.878611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.2487 | −0.698268 | −0.349134 | − | 0.937073i | \(-0.613524\pi\) | ||||
−0.349134 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.9282 | −1.18171 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.8564 | 1.06279 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.8564 | 1.59229 | 0.796146 | − | 0.605104i | \(-0.206869\pi\) | ||||
0.796146 | + | 0.605104i | \(0.206869\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 61.8564 | 2.34635 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.14359 | 0.232705 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.9282 | −0.488990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6410 | −1.08176 | −0.540878 | − | 0.841101i | \(-0.681908\pi\) | ||||
−0.540878 | + | 0.841101i | \(0.681908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8564 | −0.522604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.8564 | −1.42575 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7128 | −0.665219 | −0.332609 | − | 0.943065i | \(-0.607929\pi\) | ||||
−0.332609 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.9282 | 0.409840 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.1436 | −0.379349 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.5359 | 0.542853 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8564 | −0.516757 | −0.258378 | − | 0.966044i | \(-0.583188\pi\) | ||||
−0.258378 | + | 0.966044i | \(0.583188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.07180 | −0.114241 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.4974 | 1.28120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0718 | 0.781510 | 0.390755 | − | 0.920495i | \(-0.372214\pi\) | ||||
0.390755 | + | 0.920495i | \(0.372214\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.28719 | 0.158567 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.71281 | 0.211008 | 0.105504 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105504 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.28719 | 0.157921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.0718 | −1.36371 | −0.681854 | − | 0.731488i | \(-0.738826\pi\) | ||||
−0.681854 | + | 0.731488i | \(0.738826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564 | 0.509028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.6077 | −0.425845 | −0.212923 | − | 0.977069i | \(-0.568298\pi\) | ||||
−0.212923 | + | 0.977069i | \(0.568298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.3538 | 2.28447 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.7128 | −1.01125 | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||||
−0.505627 | + | 0.862752i | \(0.668739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.07180 | −0.330595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −75.7128 | −2.75547 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.14359 | 0.0778075 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.4641 | −0.995573 | −0.497786 | − | 0.867300i | \(-0.665854\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.85641 | −0.0671185 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.14359 | 0.0774007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.14359 | −0.149422 | −0.0747109 | − | 0.997205i | \(-0.523803\pi\) | ||||
−0.0747109 | + | 0.997205i | \(0.523803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4641 | 0.412870 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.32051 | −0.191365 | −0.0956827 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956827 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −76.4974 | −2.74787 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 79.4256 | 2.84572 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564 | 0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.92820 | −0.176120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.21539 | −0.114762 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.7128 | −0.845270 | −0.422635 | − | 0.906300i | \(-0.638895\pi\) | ||||
−0.422635 | + | 0.906300i | \(0.638895\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3923 | 0.441178 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.8564 | −0.634100 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.92820 | −0.245718 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.39230 | 0.226427 | 0.113214 | − | 0.993571i | \(-0.463886\pi\) | ||||
0.113214 | + | 0.993571i | \(0.463886\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.85641 | −0.207185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.46410 | −0.122398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.9282 | 0.667962 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.46410 | −0.121942 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.0000 | −1.33601 | −0.668004 | − | 0.744157i | \(-0.732851\pi\) | ||||
−0.668004 | + | 0.744157i | \(0.732851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5692 | 1.31923 | 0.659617 | − | 0.751602i | \(-0.270719\pi\) | ||||
0.659617 | + | 0.751602i | \(0.270719\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.92820 | −0.102697 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.8564 | 1.32605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.4256 | 1.93910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1436 | 0.423814 | 0.211907 | − | 0.977290i | \(-0.432033\pi\) | ||||
0.211907 | + | 0.977290i | \(0.432033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0718 | 0.734517 | 0.367258 | − | 0.930119i | \(-0.380296\pi\) | ||||
0.367258 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.2487 | 0.356814 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.1769 | −1.29277 | −0.646384 | − | 0.763012i | \(-0.723720\pi\) | ||||
−0.646384 | + | 0.763012i | \(0.723720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7128 | 0.754117 | 0.377059 | − | 0.926189i | \(-0.376936\pi\) | ||||
0.377059 | + | 0.926189i | \(0.376936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.143594 | 0.00498120 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.8564 | −1.31007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.9282 | 0.377734 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.9282 | −0.377283 | −0.188642 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188642 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71281 | −0.162511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.9282 | −0.445271 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.1769 | −1.07252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9282 | −0.512335 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.92820 | 0.100378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0718 | 0.789963 | 0.394982 | − | 0.918689i | \(-0.370751\pi\) | ||||
0.394982 | + | 0.918689i | \(0.370751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0000 | −0.820783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.1769 | −1.88481 | −0.942404 | − | 0.334477i | \(-0.891440\pi\) | ||||
−0.942404 | + | 0.334477i | \(0.891440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.9282 | 1.32821 | 0.664107 | − | 0.747638i | \(-0.268812\pi\) | ||||
0.664107 | + | 0.747638i | \(0.268812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.46410 | 0.322162 | 0.161081 | − | 0.986941i | \(-0.448502\pi\) | ||||
0.161081 | + | 0.986941i | \(0.448502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 77.5692 | 2.63743 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.7128 | 0.567597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.85641 | −0.198437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.92820 | 0.302174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.14359 | −0.274990 | −0.137495 | − | 0.990502i | \(-0.543905\pi\) | ||||
−0.137495 | + | 0.990502i | \(0.543905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.5359 | −0.557742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.3205 | 0.448779 | 0.224390 | − | 0.974500i | \(-0.427961\pi\) | ||||
0.224390 | + | 0.974500i | \(0.427961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5692 | −1.12969 | −0.564847 | − | 0.825196i | \(-0.691065\pi\) | ||||
−0.564847 | + | 0.825196i | \(0.691065\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.71281 | −0.124805 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.9282 | −0.904161 | −0.452080 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452080 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.46410 | −0.0490492 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −75.7128 | −2.53363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.7846 | 1.09587 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.92820 | −0.0977699 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.8564 | −1.79621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.07180 | −0.0357067 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.7846 | −0.690904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.7128 | −1.45146 | −0.725730 | − | 0.687980i | \(-0.758498\pi\) | ||||
−0.725730 | + | 0.687980i | \(0.758498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.4641 | −0.512912 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1769 | −0.966674 | −0.483337 | − | 0.875434i | \(-0.660575\pi\) | ||||
−0.483337 | + | 0.875434i | \(0.660575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.85641 | −0.193819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.9282 | 1.02245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.9282 | 0.755510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.9282 | −0.623029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.9282 | −0.358929 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.6077 | −0.446454 | −0.223227 | − | 0.974766i | \(-0.571659\pi\) | ||||
−0.223227 | + | 0.974766i | \(0.571659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.9282 | −0.619682 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.71797 | 0.0888870 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.0000 | −0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.5359 | −1.19104 | −0.595518 | − | 0.803342i | \(-0.703053\pi\) | ||||
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7846 | −0.546582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2487 | 0.852969 | 0.426484 | − | 0.904495i | \(-0.359752\pi\) | ||||
0.426484 | + | 0.904495i | \(0.359752\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.8564 | −0.839334 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.143594 | 0.00465634 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.0000 | −0.712650 | −0.356325 | − | 0.934362i | \(-0.615970\pi\) | ||||
−0.356325 | + | 0.934362i | \(0.615970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.7846 | −1.06089 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.21539 | 0.233240 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.3923 | 0.399336 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.9282 | 1.76820 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.9282 | −1.12322 | −0.561608 | − | 0.827404i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827404i | \(0.689817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.71281 | −0.119273 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.85641 | −0.0595749 | −0.0297875 | − | 0.999556i | \(-0.509483\pi\) | ||||
−0.0297875 | + | 0.999556i | \(0.509483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.4974 | 1.23164 | 0.615821 | − | 0.787886i | \(-0.288825\pi\) | ||||
0.615821 | + | 0.787886i | \(0.288825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.07180 | 0.162095 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.71281 | −0.118420 | −0.0592102 | − | 0.998246i | \(-0.518858\pi\) | ||||
−0.0592102 | + | 0.998246i | \(0.518858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.2154 | 0.867154 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.7128 | −0.372446 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0000 | −0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.2872 | 0.643147 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.0718 | 0.984054 | 0.492027 | − | 0.870580i | \(-0.336256\pi\) | ||||
0.492027 | + | 0.870580i | \(0.336256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 9408.2.a.do.1.2 | 2 | ||
4.3 | odd | 2 | 9408.2.a.dx.1.2 | 2 | |||
7.6 | odd | 2 | 1344.2.a.v.1.1 | 2 | |||
8.3 | odd | 2 | 4704.2.a.bm.1.1 | 2 | |||
8.5 | even | 2 | 4704.2.a.bn.1.1 | 2 | |||
21.20 | even | 2 | 4032.2.a.bs.1.2 | 2 | |||
28.27 | even | 2 | 1344.2.a.u.1.1 | 2 | |||
56.13 | odd | 2 | 672.2.a.i.1.2 | ✓ | 2 | ||
56.27 | even | 2 | 672.2.a.j.1.2 | yes | 2 | ||
84.83 | odd | 2 | 4032.2.a.br.1.2 | 2 | |||
112.13 | odd | 4 | 5376.2.c.bh.2689.4 | 4 | |||
112.27 | even | 4 | 5376.2.c.bn.2689.3 | 4 | |||
112.69 | odd | 4 | 5376.2.c.bh.2689.1 | 4 | |||
112.83 | even | 4 | 5376.2.c.bn.2689.2 | 4 | |||
168.83 | odd | 2 | 2016.2.a.s.1.1 | 2 | |||
168.125 | even | 2 | 2016.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.a.i.1.2 | ✓ | 2 | 56.13 | odd | 2 | ||
672.2.a.j.1.2 | yes | 2 | 56.27 | even | 2 | ||
1344.2.a.u.1.1 | 2 | 28.27 | even | 2 | |||
1344.2.a.v.1.1 | 2 | 7.6 | odd | 2 | |||
2016.2.a.s.1.1 | 2 | 168.83 | odd | 2 | |||
2016.2.a.t.1.1 | 2 | 168.125 | even | 2 | |||
4032.2.a.br.1.2 | 2 | 84.83 | odd | 2 | |||
4032.2.a.bs.1.2 | 2 | 21.20 | even | 2 | |||
4704.2.a.bm.1.1 | 2 | 8.3 | odd | 2 | |||
4704.2.a.bn.1.1 | 2 | 8.5 | even | 2 | |||
5376.2.c.bh.2689.1 | 4 | 112.69 | odd | 4 | |||
5376.2.c.bh.2689.4 | 4 | 112.13 | odd | 4 | |||
5376.2.c.bn.2689.2 | 4 | 112.83 | even | 4 | |||
5376.2.c.bn.2689.3 | 4 | 112.27 | even | 4 | |||
9408.2.a.do.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9408.2.a.dx.1.2 | 2 | 4.3 | odd | 2 |