Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.330805\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34984 | 0.888157 | 0.444078 | − | 0.895988i | \(-0.353531\pi\) | ||||
0.444078 | + | 0.895988i | \(0.353531\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.333733 | −0.100624 | −0.0503122 | − | 0.998734i | \(-0.516022\pi\) | ||||
−0.0503122 | + | 0.998734i | \(0.516022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37929 | 0.937247 | 0.468624 | − | 0.883398i | \(-0.344750\pi\) | ||||
0.468624 | + | 0.883398i | \(0.344750\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.81531 | −1.89549 | −0.947746 | − | 0.319026i | \(-0.896644\pi\) | ||||
−0.947746 | + | 0.319026i | \(0.896644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.20992 | 0.277575 | 0.138788 | − | 0.990322i | \(-0.455679\pi\) | ||||
0.138788 | + | 0.990322i | \(0.455679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35450 | −0.251524 | −0.125762 | − | 0.992060i | \(-0.540138\pi\) | ||||
−0.125762 | + | 0.992060i | \(0.540138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2907 | −1.84827 | −0.924134 | − | 0.382070i | \(-0.875211\pi\) | ||||
−0.924134 | + | 0.382070i | \(0.875211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.34984 | 0.397196 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.83910 | 0.466745 | 0.233372 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233372 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.94371 | −1.24060 | −0.620300 | − | 0.784365i | \(-0.712989\pi\) | ||||
−0.620300 | + | 0.784365i | \(0.712989\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.92175 | −1.20806 | −0.604028 | − | 0.796963i | \(-0.706438\pi\) | ||||
−0.604028 | + | 0.796963i | \(0.706438\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7314 | −1.71120 | −0.855600 | − | 0.517638i | \(-0.826811\pi\) | ||||
−0.855600 | + | 0.517638i | \(0.826811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.47824 | −0.211178 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.92062 | −1.08798 | −0.543990 | − | 0.839092i | \(-0.683087\pi\) | ||||
−0.543990 | + | 0.839092i | \(0.683087\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.333733 | −0.0450006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2728 | −1.72797 | −0.863985 | − | 0.503517i | \(-0.832039\pi\) | ||||
−0.863985 | + | 0.503517i | \(0.832039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.88487 | 0.369370 | 0.184685 | − | 0.982798i | \(-0.440873\pi\) | ||||
0.184685 | + | 0.982798i | \(0.440873\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.37929 | 0.419150 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.70597 | 0.941434 | 0.470717 | − | 0.882284i | \(-0.343995\pi\) | ||||
0.470717 | + | 0.882284i | \(0.343995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1945 | 1.80326 | 0.901630 | − | 0.432508i | \(-0.142371\pi\) | ||||
0.901630 | + | 0.432508i | \(0.142371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.02239 | −0.821909 | −0.410955 | − | 0.911656i | \(-0.634805\pi\) | ||||
−0.410955 | + | 0.911656i | \(0.634805\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.784221 | −0.0893703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.325047 | 0.0365707 | 0.0182853 | − | 0.999833i | \(-0.494179\pi\) | ||||
0.0182853 | + | 0.999833i | \(0.494179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4828 | −1.15063 | −0.575317 | − | 0.817930i | \(-0.695121\pi\) | ||||
−0.575317 | + | 0.817930i | \(0.695121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.81531 | −0.847690 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.05475 | −0.853802 | −0.426901 | − | 0.904298i | \(-0.640395\pi\) | ||||
−0.426901 | + | 0.904298i | \(0.640395\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.94081 | 0.832423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.20992 | 0.124135 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00919 | −0.102468 | −0.0512341 | − | 0.998687i | \(-0.516315\pi\) | ||||
−0.0512341 | + | 0.998687i | \(0.516315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6145 | 1.15569 | 0.577844 | − | 0.816147i | \(-0.303894\pi\) | ||||
0.577844 | + | 0.816147i | \(0.303894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8961 | 1.27069 | 0.635346 | − | 0.772228i | \(-0.280858\pi\) | ||||
0.635346 | + | 0.772228i | \(0.280858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2078 | 1.47019 | 0.735097 | − | 0.677962i | \(-0.237137\pi\) | ||||
0.735097 | + | 0.677962i | \(0.237137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0680 | −1.15590 | −0.577950 | − | 0.816072i | \(-0.696147\pi\) | ||||
−0.577950 | + | 0.816072i | \(0.696147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15370 | 0.108531 | 0.0542657 | − | 0.998527i | \(-0.482718\pi\) | ||||
0.0542657 | + | 0.998527i | \(0.482718\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.3648 | −1.68349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8886 | −0.989875 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.77157 | −0.689615 | −0.344808 | − | 0.938673i | \(-0.612056\pi\) | ||||
−0.344808 | + | 0.938673i | \(0.612056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.59841 | 0.139654 | 0.0698268 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698268 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.84312 | 0.246530 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.98666 | −0.426039 | −0.213019 | − | 0.977048i | \(-0.568330\pi\) | ||||
−0.213019 | + | 0.977048i | \(0.568330\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3677 | −0.964192 | −0.482096 | − | 0.876118i | \(-0.660124\pi\) | ||||
−0.482096 | + | 0.876118i | \(0.660124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.12778 | −0.0943100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.35450 | −0.112485 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.4841 | 1.51428 | 0.757139 | − | 0.653254i | \(-0.226596\pi\) | ||||
0.757139 | + | 0.653254i | \(0.226596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6892 | −1.19539 | −0.597694 | − | 0.801724i | \(-0.703916\pi\) | ||||
−0.597694 | + | 0.801724i | \(0.703916\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2907 | −0.826570 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.70994 | 0.615320 | 0.307660 | − | 0.951496i | \(-0.400454\pi\) | ||||
0.307660 | + | 0.951496i | \(0.400454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.34984 | 0.185193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2704 | −1.27440 | −0.637198 | − | 0.770700i | \(-0.719907\pi\) | ||||
−0.637198 | + | 0.770700i | \(0.719907\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.6828 | −1.21357 | −0.606786 | − | 0.794865i | \(-0.707542\pi\) | ||||
−0.606786 | + | 0.794865i | \(0.707542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.58037 | −0.121567 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.7815 | 1.12382 | 0.561908 | − | 0.827200i | \(-0.310068\pi\) | ||||
0.561908 | + | 0.827200i | \(0.310068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34984 | 0.177631 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.66161 | −0.647399 | −0.323700 | − | 0.946160i | \(-0.604927\pi\) | ||||
−0.323700 | + | 0.946160i | \(0.604927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.53481 | 0.411400 | 0.205700 | − | 0.978615i | \(-0.434053\pi\) | ||||
0.205700 | + | 0.978615i | \(0.434053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.83910 | 0.208734 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.60823 | 0.190733 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.81157 | −0.131081 | −0.0655403 | − | 0.997850i | \(-0.520877\pi\) | ||||
−0.0655403 | + | 0.997850i | \(0.520877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.9261 | 1.93819 | 0.969093 | − | 0.246695i | \(-0.0793447\pi\) | ||||
0.969093 | + | 0.246695i | \(0.0793447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.60772 | −0.542028 | −0.271014 | − | 0.962575i | \(-0.587359\pi\) | ||||
−0.271014 | + | 0.962575i | \(0.587359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.99167 | −0.566515 | −0.283257 | − | 0.959044i | \(-0.591415\pi\) | ||||
−0.283257 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.18286 | −0.223393 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.94371 | −0.554813 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.403791 | −0.0279308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.70950 | 0.324215 | 0.162108 | − | 0.986773i | \(-0.448171\pi\) | ||||
0.162108 | + | 0.986773i | \(0.448171\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.92175 | −0.540259 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.1816 | −1.64155 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.4102 | −1.77654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.3766 | 1.69934 | 0.849670 | − | 0.527315i | \(-0.176801\pi\) | ||||
0.849670 | + | 0.527315i | \(0.176801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4820 | 0.695714 | 0.347857 | − | 0.937548i | \(-0.386909\pi\) | ||||
0.347857 | + | 0.937548i | \(0.386909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.3540 | 1.93977 | 0.969884 | − | 0.243566i | \(-0.0783173\pi\) | ||||
0.969884 | + | 0.243566i | \(0.0783173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9472 | −1.37229 | −0.686147 | − | 0.727463i | \(-0.740700\pi\) | ||||
−0.686147 | + | 0.727463i | \(0.740700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.7314 | −0.765272 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.00679442 | 0.000439494 0 | 0.000219747 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000219747 | 1.00000i | \(0.499930\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2482 | 1.81963 | 0.909814 | − | 0.415017i | \(-0.136224\pi\) | ||||
0.909814 | + | 0.415017i | \(0.136224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.47824 | −0.0944415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.08868 | 0.260156 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.85470 | −0.622023 | −0.311011 | − | 0.950406i | \(-0.600668\pi\) | ||||
−0.311011 | + | 0.950406i | \(0.600668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.333733 | −0.0209816 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.06873 | −0.440935 | −0.220467 | − | 0.975394i | \(-0.570758\pi\) | ||||
−0.220467 | + | 0.975394i | \(0.570758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.67143 | 0.414542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.9113 | −0.734482 | −0.367241 | − | 0.930126i | \(-0.619698\pi\) | ||||
−0.367241 | + | 0.930126i | \(0.619698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.92062 | −0.486560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.5465 | 1.86245 | 0.931227 | − | 0.364440i | \(-0.118739\pi\) | ||||
0.931227 | + | 0.364440i | \(0.118739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1356 | 0.737183 | 0.368591 | − | 0.929592i | \(-0.379840\pi\) | ||||
0.368591 | + | 0.929592i | \(0.379840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.333733 | −0.0201249 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7470 | 0.825974 | 0.412987 | − | 0.910737i | \(-0.364485\pi\) | ||||
0.412987 | + | 0.910737i | \(0.364485\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.3351 | −1.27275 | −0.636374 | − | 0.771381i | \(-0.719566\pi\) | ||||
−0.636374 | + | 0.771381i | \(0.719566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1882 | 0.962287 | 0.481144 | − | 0.876642i | \(-0.340222\pi\) | ||||
0.481144 | + | 0.876642i | \(0.340222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.6665 | −1.10185 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.0791 | 2.59289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.4006 | 1.48392 | 0.741959 | − | 0.670445i | \(-0.233897\pi\) | ||||
0.741959 | + | 0.670445i | \(0.233897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.2728 | −0.772772 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.37929 | 0.195430 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6149 | −1.07294 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.88487 | 0.165187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8342 | −1.01785 | −0.508927 | − | 0.860810i | \(-0.669958\pi\) | ||||
−0.508927 | + | 0.860810i | \(0.669958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.21196 | 0.465658 | 0.232829 | − | 0.972518i | \(-0.425202\pi\) | ||||
0.232829 | + | 0.972518i | \(0.425202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.6902 | 1.50862 | 0.754308 | − | 0.656520i | \(-0.227972\pi\) | ||||
0.754308 | + | 0.656520i | \(0.227972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.2587 | −1.02551 | −0.512756 | − | 0.858534i | \(-0.671375\pi\) | ||||
−0.512756 | + | 0.858534i | \(0.671375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.452042 | 0.0253095 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.45592 | −0.526141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.37929 | 0.187449 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.5669 | −1.51981 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.2539 | −0.948359 | −0.474179 | − | 0.880428i | \(-0.657255\pi\) | ||||
−0.474179 | + | 0.880428i | \(0.657255\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.70597 | 0.421022 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.1028 | −1.85770 | −0.928848 | − | 0.370460i | \(-0.879200\pi\) | ||||
−0.928848 | + | 0.370460i | \(0.879200\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.43436 | 0.185981 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9225 | −1.07572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.63528 | 0.409883 | 0.204942 | − | 0.978774i | \(-0.434300\pi\) | ||||
0.204942 | + | 0.978774i | \(0.434300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.9799 | 1.65832 | 0.829158 | − | 0.559015i | \(-0.188820\pi\) | ||||
0.829158 | + | 0.559015i | \(0.188820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.93004 | −0.368849 | −0.184424 | − | 0.982847i | \(-0.559042\pi\) | ||||
−0.184424 | + | 0.982847i | \(0.559042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1945 | 0.806442 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.20979 | 0.486074 | 0.243037 | − | 0.970017i | \(-0.421856\pi\) | ||||
0.243037 | + | 0.970017i | \(0.421856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5361 | −0.922952 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.02239 | −0.367569 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8092 | 0.929631 | 0.464816 | − | 0.885408i | \(-0.346121\pi\) | ||||
0.464816 | + | 0.885408i | \(0.346121\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.6122 | −0.966297 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.0055 | −1.39829 | −0.699145 | − | 0.714980i | \(-0.746436\pi\) | ||||
−0.699145 | + | 0.714980i | \(0.746436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.57725 | −0.235740 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.9380 | −1.53781 | −0.768907 | − | 0.639361i | \(-0.779199\pi\) | ||||
−0.768907 | + | 0.639361i | \(0.779199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.61303 | 0.0824221 | 0.0412110 | − | 0.999150i | \(-0.486878\pi\) | ||||
0.0412110 | + | 0.999150i | \(0.486878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.784221 | −0.0399676 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.1507 | −0.768172 | −0.384086 | − | 0.923297i | \(-0.625483\pi\) | ||||
−0.384086 | + | 0.923297i | \(0.625483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.81531 | −0.395237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.325047 | 0.0163549 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.69395 | −0.285771 | −0.142885 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142885 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.72660 | 0.435786 | 0.217893 | − | 0.975973i | \(-0.430082\pi\) | ||||
0.217893 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.7754 | −1.73228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.947501 | −0.0469659 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0768 | 0.992733 | 0.496367 | − | 0.868113i | \(-0.334667\pi\) | ||||
0.496367 | + | 0.868113i | \(0.334667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.1890 | −1.53471 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4828 | −0.514579 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.8662 | −0.970527 | −0.485263 | − | 0.874368i | \(-0.661276\pi\) | ||||
−0.485263 | + | 0.874368i | \(0.661276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3892 | −0.993708 | −0.496854 | − | 0.867834i | \(-0.665512\pi\) | ||||
−0.496854 | + | 0.867834i | \(0.665512\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.81531 | −0.379098 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.77900 | 0.328059 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.44768 | 0.117901 | 0.0589503 | − | 0.998261i | \(-0.481225\pi\) | ||||
0.0589503 | + | 0.998261i | \(0.481225\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6576 | 1.28108 | 0.640542 | − | 0.767923i | \(-0.278710\pi\) | ||||
0.640542 | + | 0.767923i | \(0.278710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.20992 | 0.0578784 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2544 | 0.680324 | 0.340162 | − | 0.940367i | \(-0.389518\pi\) | ||||
0.340162 | + | 0.940367i | \(0.389518\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.350414 | −0.0166487 | −0.00832433 | − | 0.999965i | \(-0.502650\pi\) | ||||
−0.00832433 | + | 0.999965i | \(0.502650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.05475 | −0.381832 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.04679 | 0.190980 | 0.0954900 | − | 0.995430i | \(-0.469558\pi\) | ||||
0.0954900 | + | 0.995430i | \(0.469558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.65108 | 0.124835 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.94081 | 0.372271 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.60780 | −0.262322 | −0.131161 | − | 0.991361i | \(-0.541870\pi\) | ||||
−0.131161 | + | 0.991361i | \(0.541870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0088 | 0.605880 | 0.302940 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302940 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6108 | 0.864918 | 0.432459 | − | 0.901654i | \(-0.357646\pi\) | ||||
0.432459 | + | 0.901654i | \(0.357646\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4676 | −1.03968 | −0.519838 | − | 0.854265i | \(-0.674008\pi\) | ||||
−0.519838 | + | 0.854265i | \(0.674008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.1078 | 0.836141 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.64375 | 0.121560 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.20992 | 0.0555150 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.60035 | −0.301578 | −0.150789 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150789 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.59414 | 0.437455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00919 | −0.0458252 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.00974374 | 0.000441531 0 | 0.000220765 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000220765 | 1.00000i | \(0.499930\pi\) | ||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1282 | −1.72070 | −0.860351 | − | 0.509702i | \(-0.829756\pi\) | ||||
−0.860351 | + | 0.509702i | \(0.829756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.5858 | 0.476762 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 35.7048 | 1.60158 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1894 | 0.769505 | 0.384753 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384753 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.7526 | −0.524022 | −0.262011 | − | 0.965065i | \(-0.584386\pi\) | ||||
−0.262011 | + | 0.965065i | \(0.584386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6145 | 0.516839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2543 | −0.764783 | −0.382391 | − | 0.924000i | \(-0.624899\pi\) | ||||
−0.382391 | + | 0.924000i | \(0.624899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5015 | −0.729984 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.8961 | 0.568270 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.91516 | 0.172188 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.6710 | −1.60658 | −0.803292 | − | 0.595585i | \(-0.796920\pi\) | ||||
−0.803292 | + | 0.595585i | \(0.796920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3419 | −1.10813 | −0.554063 | − | 0.832475i | \(-0.686923\pi\) | ||||
−0.554063 | + | 0.832475i | \(0.686923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 80.4252 | 3.50338 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.8441 | −1.16275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2078 | 0.657491 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.493339 | 0.0212496 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.2913 | 1.34532 | 0.672658 | − | 0.739953i | \(-0.265152\pi\) | ||||
0.672658 | + | 0.739953i | \(0.265152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0680 | −0.516934 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8281 | −1.70293 | −0.851464 | − | 0.524412i | \(-0.824285\pi\) | ||||
−0.851464 | + | 0.524412i | \(0.824285\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.63884 | −0.0698168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.763810 | 0.0324805 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.5055 | −1.20782 | −0.603908 | − | 0.797054i | \(-0.706390\pi\) | ||||
−0.603908 | + | 0.797054i | \(0.706390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.7699 | −1.13225 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.7082 | 0.451296 | 0.225648 | − | 0.974209i | \(-0.427550\pi\) | ||||
0.225648 | + | 0.974209i | \(0.427550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.15370 | 0.0485367 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.8053 | 1.66873 | 0.834363 | − | 0.551216i | \(-0.185836\pi\) | ||||
0.834363 | + | 0.551216i | \(0.185836\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6536 | −1.24097 | −0.620483 | − | 0.784220i | \(-0.713063\pi\) | ||||
−0.620483 | + | 0.784220i | \(0.713063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6699 | 0.485824 | 0.242912 | − | 0.970048i | \(-0.421897\pi\) | ||||
0.242912 | + | 0.970048i | \(0.421897\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.6329 | −1.02194 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.64338 | 0.109477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.01134 | 0.330663 | 0.165332 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165332 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4510 | −0.513033 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.83280 | 0.280590 | 0.140295 | − | 0.990110i | \(-0.455195\pi\) | ||||
0.140295 | + | 0.990110i | \(0.455195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.3648 | −0.752881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.5228 | −1.24713 | −0.623563 | − | 0.781773i | \(-0.714316\pi\) | ||||
−0.623563 | + | 0.781773i | \(0.714316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2373 | −0.907080 | −0.453540 | − | 0.891236i | \(-0.649839\pi\) | ||||
−0.453540 | + | 0.891236i | \(0.649839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8886 | −0.442685 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.5255 | −1.84782 | −0.923912 | − | 0.382605i | \(-0.875027\pi\) | ||||
−0.923912 | + | 0.382605i | \(0.875027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.6438 | −1.60382 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.297344 | 0.0120096 | 0.00600481 | − | 0.999982i | \(-0.498089\pi\) | ||||
0.00600481 | + | 0.999982i | \(0.498089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4980 | −1.18755 | −0.593773 | − | 0.804633i | \(-0.702362\pi\) | ||||
−0.593773 | + | 0.804633i | \(0.702362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.774004 | 0.0311098 | 0.0155549 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155549 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9274 | −0.758310 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.1884 | −0.884710 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4887 | 1.05450 | 0.527249 | − | 0.849711i | \(-0.323224\pi\) | ||||
0.527249 | + | 0.849711i | \(0.323224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.77157 | −0.308405 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.99542 | −0.197926 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.5092 | −1.40253 | −0.701264 | − | 0.712901i | \(-0.747381\pi\) | ||||
−0.701264 | + | 0.712901i | \(0.747381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.28511 | −0.129552 | −0.0647761 | − | 0.997900i | \(-0.520633\pi\) | ||||
−0.0647761 | + | 0.997900i | \(0.520633\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1929 | 0.479352 | 0.239676 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239676 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.42957 | 0.173876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.9398 | 0.741171 | 0.370585 | − | 0.928798i | \(-0.379157\pi\) | ||||
0.370585 | + | 0.928798i | \(0.379157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.59841 | 0.0624550 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.9980 | −0.623192 | −0.311596 | − | 0.950215i | \(-0.600864\pi\) | ||||
−0.311596 | + | 0.950215i | \(0.600864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2112 | 1.44735 | 0.723675 | − | 0.690141i | \(-0.242452\pi\) | ||||
0.723675 | + | 0.690141i | \(0.242452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.84312 | 0.110252 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.35450 | −0.0524464 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.962779 | −0.0371677 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8952 | 1.22947 | 0.614736 | − | 0.788733i | \(-0.289263\pi\) | ||||
0.614736 | + | 0.788733i | \(0.289263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.4331 | −0.823743 | −0.411871 | − | 0.911242i | \(-0.635125\pi\) | ||||
−0.411871 | + | 0.911242i | \(0.635125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.37145 | −0.0910078 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5938 | 1.17064 | 0.585320 | − | 0.810802i | \(-0.300969\pi\) | ||||
0.585320 | + | 0.810802i | \(0.300969\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.98666 | −0.190530 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.7661 | −1.01971 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.45708 | −0.283681 | −0.141840 | − | 0.989890i | \(-0.545302\pi\) | ||||
−0.141840 | + | 0.989890i | \(0.545302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3677 | −0.431200 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 62.0826 | 2.35155 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.1300 | 1.66677 | 0.833383 | − | 0.552696i | \(-0.186401\pi\) | ||||
0.833383 | + | 0.552696i | \(0.186401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.43508 | 0.129557 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2923 | 1.02643 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.5296 | 0.733451 | 0.366726 | − | 0.930329i | \(-0.380479\pi\) | ||||
0.366726 | + | 0.930329i | \(0.380479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.2907 | −0.385390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.12778 | −0.0421767 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.4663 | 0.800557 | 0.400278 | − | 0.916394i | \(-0.368913\pi\) | ||||
0.400278 | + | 0.916394i | \(0.368913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.3038 | 1.12857 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.35450 | −0.0503048 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.33502 | 0.197865 | 0.0989325 | − | 0.995094i | \(-0.468457\pi\) | ||||
0.0989325 | + | 0.995094i | \(0.468457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.9109 | 2.28986 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.2267 | −0.599349 | −0.299674 | − | 0.954042i | \(-0.596878\pi\) | ||||
−0.299674 | + | 0.954042i | \(0.596878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.57174 | −0.0947313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.0855 | 1.73207 | 0.866034 | − | 0.499985i | \(-0.166661\pi\) | ||||
0.866034 | + | 0.499985i | \(0.166661\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.2973 | −1.62511 | −0.812555 | − | 0.582885i | \(-0.801924\pi\) | ||||
−0.812555 | + | 0.582885i | \(0.801924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.4841 | 0.677206 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.7359 | 1.30576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.6518 | −1.33744 | −0.668721 | − | 0.743513i | \(-0.733158\pi\) | ||||
−0.668721 | + | 0.743513i | \(0.733158\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.6892 | −0.534594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.88129 | 0.141068 | 0.0705339 | − | 0.997509i | \(-0.477530\pi\) | ||||
0.0705339 | + | 0.997509i | \(0.477530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.935040 | 0.0338952 | 0.0169476 | − | 0.999856i | \(-0.494605\pi\) | ||||
0.0169476 | + | 0.999856i | \(0.494605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.3578 | −1.02662 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.8527 | −1.61954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.23198 | −0.152609 | −0.0763046 | − | 0.997085i | \(-0.524312\pi\) | ||||
−0.0763046 | + | 0.997085i | \(0.524312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.17222 | −0.0781293 | −0.0390646 | − | 0.999237i | \(-0.512438\pi\) | ||||
−0.0390646 | + | 0.999237i | \(0.512438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.2907 | −0.369653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.61127 | −0.344360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.07093 | −0.181452 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.70994 | 0.275180 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.4188 | −1.40513 | −0.702564 | − | 0.711621i | \(-0.747961\pi\) | ||||
−0.702564 | + | 0.711621i | \(0.747961\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.71102 | 0.0963928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.74884 | 0.346191 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.30785 | −0.188014 | −0.0940068 | − | 0.995572i | \(-0.529968\pi\) | ||||
−0.0940068 | + | 0.995572i | \(0.529968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 91.6845 | 3.24356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.34361 | 0.0827041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34984 | 0.0828210 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.9515 | 1.86168 | 0.930838 | − | 0.365431i | \(-0.119079\pi\) | ||||
0.930838 | + | 0.365431i | \(0.119079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.8333 | −1.46897 | −0.734483 | − | 0.678627i | \(-0.762575\pi\) | ||||
−0.734483 | + | 0.678627i | \(0.762575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.2704 | −0.569927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.58469 | −0.335326 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.5303 | −1.69372 | −0.846860 | − | 0.531816i | \(-0.821510\pi\) | ||||
−0.846860 | + | 0.531816i | \(0.821510\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.4844 | −1.13233 | −0.566167 | − | 0.824291i | \(-0.691574\pi\) | ||||
−0.566167 | + | 0.824291i | \(0.691574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.9416 | 1.56277 | 0.781385 | − | 0.624049i | \(-0.214513\pi\) | ||||
0.781385 | + | 0.624049i | \(0.214513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.782855 | 0.0271897 | 0.0135948 | − | 0.999908i | \(-0.495672\pi\) | ||||
0.0135948 | + | 0.999908i | \(0.495672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5529 | 0.400285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6828 | −0.542726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.55402 | −0.226270 | −0.113135 | − | 0.993580i | \(-0.536089\pi\) | ||||
−0.113135 | + | 0.993580i | \(0.536089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1653 | −0.936736 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.58037 | −0.0543665 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.5865 | −0.879164 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83910 | 0.0973230 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.8079 | −1.15756 | −0.578780 | − | 0.815484i | \(-0.696471\pi\) | ||||
−0.578780 | + | 0.815484i | \(0.696471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.8990 | 1.67036 | 0.835180 | − | 0.549977i | \(-0.185364\pi\) | ||||
0.835180 | + | 0.549977i | \(0.185364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.46428 | −0.288797 | −0.144399 | − | 0.989520i | \(-0.546125\pi\) | ||||
−0.144399 | + | 0.989520i | \(0.546125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.62307 | 0.123331 | 0.0616654 | − | 0.998097i | \(-0.480359\pi\) | ||||
0.0616654 | + | 0.998097i | \(0.480359\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7815 | 0.502586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.108479 | −0.00367990 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.0407 | 0.882357 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.34984 | 0.0794392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.9308 | −0.369108 | −0.184554 | − | 0.982822i | \(-0.559084\pi\) | ||||
−0.184554 | + | 0.982822i | \(0.559084\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0740 | 0.541545 | 0.270773 | − | 0.962643i | \(-0.412721\pi\) | ||||
0.270773 | + | 0.962643i | \(0.412721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7421 | 0.832639 | 0.416319 | − | 0.909218i | \(-0.363320\pi\) | ||||
0.416319 | + | 0.909218i | \(0.363320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.8153 | −1.26971 | −0.634856 | − | 0.772630i | \(-0.718941\pi\) | ||||
−0.634856 | + | 0.772630i | \(0.718941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.2620 | −0.612487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.1941 | −0.474986 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.66161 | −0.289526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9388 | 0.464884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.9021 | 2.06226 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.53481 | 0.183983 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.9550 | −1.79155 | −0.895774 | − | 0.444510i | \(-0.853378\pi\) | ||||
−0.895774 | + | 0.444510i | \(0.853378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.8570 | −1.05547 | −0.527735 | − | 0.849409i | \(-0.676959\pi\) | ||||
−0.527735 | + | 0.849409i | \(0.676959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.49845 | 0.115782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.75601 | 0.124034 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8032 | −0.884157 | −0.442078 | − | 0.896976i | \(-0.645759\pi\) | ||||
−0.442078 | + | 0.896976i | \(0.645759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.3468 | 1.69010 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.83910 | 0.0933489 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.25414 | 0.139574 | 0.0697870 | − | 0.997562i | \(-0.477768\pi\) | ||||
0.0697870 | + | 0.997562i | \(0.477768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.78856 | −0.0586176 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.60823 | 0.0852983 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6296 | 1.09863 | 0.549316 | − | 0.835615i | \(-0.314888\pi\) | ||||
0.549316 | + | 0.835615i | \(0.314888\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.3525 | 1.21766 | 0.608829 | − | 0.793302i | \(-0.291640\pi\) | ||||
0.608829 | + | 0.793302i | \(0.291640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.94371 | −0.258683 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.4779 | −1.70530 | −0.852652 | − | 0.522479i | \(-0.825007\pi\) | ||||
−0.852652 | + | 0.522479i | \(0.825007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.7307 | −0.770332 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.95962 | 0.128265 | 0.0641323 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641323 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.81157 | −0.0586210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.7179 | −0.378389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.8988 | 2.41609 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.9261 | 0.866783 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.7487 | −0.795864 | −0.397932 | − | 0.917415i | \(-0.630272\pi\) | ||||
−0.397932 | + | 0.917415i | \(0.630272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3608 | −0.653408 | −0.326704 | − | 0.945127i | \(-0.605938\pi\) | ||||
−0.326704 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.7122 | −0.856354 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.2849 | −1.57676 | −0.788381 | − | 0.615187i | \(-0.789081\pi\) | ||||
−0.788381 | + | 0.615187i | \(0.789081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.68814 | 0.0859134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.9279 | −0.508022 | −0.254011 | − | 0.967201i | \(-0.581750\pi\) | ||||
−0.254011 | + | 0.967201i | \(0.581750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.60772 | −0.242402 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.92175 | −0.251897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8100 | 0.438688 | 0.219344 | − | 0.975648i | \(-0.429608\pi\) | ||||
0.219344 | + | 0.975648i | \(0.429608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.99167 | −0.253353 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.7356 | −1.41679 | −0.708396 | − | 0.705815i | \(-0.750581\pi\) | ||||
−0.708396 | + | 0.705815i | \(0.750581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.a.bw.1.6 | yes | 7 | |
3.2 | odd | 2 | 8280.2.a.bv.1.6 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bv.1.6 | ✓ | 7 | 3.2 | odd | 2 | ||
8280.2.a.bw.1.6 | yes | 7 | 1.1 | even | 1 | trivial |