Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3135,2,Mod(1,3135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3135, 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("3135.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3135 = 3 \cdot 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3135.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: | \(25.0331010337\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 10x^{8} + 55x^{7} + 5x^{6} - 232x^{5} + 166x^{4} + 276x^{3} - 337x^{2} + 63x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.69746\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69746 | 1.90739 | 0.953697 | − | 0.300769i | \(-0.0972432\pi\) | ||||
0.953697 | + | 0.300769i | \(0.0972432\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.27631 | 2.63815 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.69746 | 1.10123 | ||||||||
\(7\) | −1.40612 | −0.531463 | −0.265731 | − | 0.964047i | \(-0.585613\pi\) | ||||
−0.265731 | + | 0.964047i | \(0.585613\pi\) | |||||||
\(8\) | 8.83771 | 3.12460 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.69746 | −0.853013 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.27631 | 1.52314 | ||||||||
\(13\) | 5.01699 | 1.39146 | 0.695731 | − | 0.718302i | \(-0.255081\pi\) | ||||
0.695731 | + | 0.718302i | \(0.255081\pi\) | |||||||
\(14\) | −3.79295 | −1.01371 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 13.2868 | 3.32170 | ||||||||
\(17\) | −4.66205 | −1.13071 | −0.565356 | − | 0.824847i | \(-0.691261\pi\) | ||||
−0.565356 | + | 0.824847i | \(0.691261\pi\) | |||||||
\(18\) | 2.69746 | 0.635798 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −5.27631 | −1.17982 | ||||||||
\(21\) | −1.40612 | −0.306840 | ||||||||
\(22\) | 2.69746 | 0.575101 | ||||||||
\(23\) | 1.13206 | 0.236050 | 0.118025 | − | 0.993011i | \(-0.462344\pi\) | ||||
0.118025 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(24\) | 8.83771 | 1.80399 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 13.5331 | 2.65407 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −7.41911 | −1.40208 | ||||||||
\(29\) | −0.808221 | −0.150083 | −0.0750415 | − | 0.997180i | \(-0.523909\pi\) | ||||
−0.0750415 | + | 0.997180i | \(0.523909\pi\) | |||||||
\(30\) | −2.69746 | −0.492487 | ||||||||
\(31\) | 5.01699 | 0.901077 | 0.450539 | − | 0.892757i | \(-0.351232\pi\) | ||||
0.450539 | + | 0.892757i | \(0.351232\pi\) | |||||||
\(32\) | 18.1652 | 3.21118 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −12.5757 | −2.15672 | ||||||||
\(35\) | 1.40612 | 0.237677 | ||||||||
\(36\) | 5.27631 | 0.879384 | ||||||||
\(37\) | −0.673156 | −0.110666 | −0.0553331 | − | 0.998468i | \(-0.517622\pi\) | ||||
−0.0553331 | + | 0.998468i | \(0.517622\pi\) | |||||||
\(38\) | 2.69746 | 0.437586 | ||||||||
\(39\) | 5.01699 | 0.803361 | ||||||||
\(40\) | −8.83771 | −1.39737 | ||||||||
\(41\) | 1.91557 | 0.299161 | 0.149581 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149581 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(42\) | −3.79295 | −0.585265 | ||||||||
\(43\) | 9.74641 | 1.48631 | 0.743157 | − | 0.669117i | \(-0.233328\pi\) | ||||
0.743157 | + | 0.669117i | \(0.233328\pi\) | |||||||
\(44\) | 5.27631 | 0.795433 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 3.05368 | 0.450241 | ||||||||
\(47\) | −11.6882 | −1.70490 | −0.852451 | − | 0.522807i | \(-0.824885\pi\) | ||||
−0.852451 | + | 0.522807i | \(0.824885\pi\) | |||||||
\(48\) | 13.2868 | 1.91778 | ||||||||
\(49\) | −5.02283 | −0.717548 | ||||||||
\(50\) | 2.69746 | 0.381479 | ||||||||
\(51\) | −4.66205 | −0.652817 | ||||||||
\(52\) | 26.4712 | 3.67089 | ||||||||
\(53\) | −2.09021 | −0.287112 | −0.143556 | − | 0.989642i | \(-0.545854\pi\) | ||||
−0.143556 | + | 0.989642i | \(0.545854\pi\) | |||||||
\(54\) | 2.69746 | 0.367078 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −12.4269 | −1.66061 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −2.18015 | −0.286267 | ||||||||
\(59\) | −2.94694 | −0.383659 | −0.191830 | − | 0.981428i | \(-0.561442\pi\) | ||||
−0.191830 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(60\) | −5.27631 | −0.681168 | ||||||||
\(61\) | −2.16107 | −0.276697 | −0.138348 | − | 0.990384i | \(-0.544179\pi\) | ||||
−0.138348 | + | 0.990384i | \(0.544179\pi\) | |||||||
\(62\) | 13.5331 | 1.71871 | ||||||||
\(63\) | −1.40612 | −0.177154 | ||||||||
\(64\) | 22.4264 | 2.80330 | ||||||||
\(65\) | −5.01699 | −0.622281 | ||||||||
\(66\) | 2.69746 | 0.332035 | ||||||||
\(67\) | 12.0264 | 1.46926 | 0.734628 | − | 0.678470i | \(-0.237356\pi\) | ||||
0.734628 | + | 0.678470i | \(0.237356\pi\) | |||||||
\(68\) | −24.5984 | −2.98299 | ||||||||
\(69\) | 1.13206 | 0.136284 | ||||||||
\(70\) | 3.79295 | 0.453344 | ||||||||
\(71\) | 7.24526 | 0.859855 | 0.429927 | − | 0.902863i | \(-0.358539\pi\) | ||||
0.429927 | + | 0.902863i | \(0.358539\pi\) | |||||||
\(72\) | 8.83771 | 1.04153 | ||||||||
\(73\) | 0.115071 | 0.0134680 | 0.00673400 | − | 0.999977i | \(-0.497856\pi\) | ||||
0.00673400 | + | 0.999977i | \(0.497856\pi\) | |||||||
\(74\) | −1.81581 | −0.211084 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 5.27631 | 0.605234 | ||||||||
\(77\) | −1.40612 | −0.160242 | ||||||||
\(78\) | 13.5331 | 1.53233 | ||||||||
\(79\) | −11.2787 | −1.26895 | −0.634475 | − | 0.772944i | \(-0.718784\pi\) | ||||
−0.634475 | + | 0.772944i | \(0.718784\pi\) | |||||||
\(80\) | −13.2868 | −1.48551 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.16717 | 0.570619 | ||||||||
\(83\) | −10.0518 | −1.10333 | −0.551663 | − | 0.834067i | \(-0.686006\pi\) | ||||
−0.551663 | + | 0.834067i | \(0.686006\pi\) | |||||||
\(84\) | −7.41911 | −0.809491 | ||||||||
\(85\) | 4.66205 | 0.505670 | ||||||||
\(86\) | 26.2906 | 2.83499 | ||||||||
\(87\) | −0.808221 | −0.0866504 | ||||||||
\(88\) | 8.83771 | 0.942103 | ||||||||
\(89\) | −12.3812 | −1.31240 | −0.656201 | − | 0.754586i | \(-0.727838\pi\) | ||||
−0.656201 | + | 0.754586i | \(0.727838\pi\) | |||||||
\(90\) | −2.69746 | −0.284338 | ||||||||
\(91\) | −7.05447 | −0.739510 | ||||||||
\(92\) | 5.97308 | 0.622737 | ||||||||
\(93\) | 5.01699 | 0.520237 | ||||||||
\(94\) | −31.5285 | −3.25192 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 18.1652 | 1.85398 | ||||||||
\(97\) | 2.28517 | 0.232024 | 0.116012 | − | 0.993248i | \(-0.462989\pi\) | ||||
0.116012 | + | 0.993248i | \(0.462989\pi\) | |||||||
\(98\) | −13.5489 | −1.36865 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 5.27631 | 0.527631 | ||||||||
\(101\) | 1.59838 | 0.159045 | 0.0795225 | − | 0.996833i | \(-0.474660\pi\) | ||||
0.0795225 | + | 0.996833i | \(0.474660\pi\) | |||||||
\(102\) | −12.5757 | −1.24518 | ||||||||
\(103\) | −0.0308290 | −0.00303767 | −0.00151884 | − | 0.999999i | \(-0.500483\pi\) | ||||
−0.00151884 | + | 0.999999i | \(0.500483\pi\) | |||||||
\(104\) | 44.3387 | 4.34777 | ||||||||
\(105\) | 1.40612 | 0.137223 | ||||||||
\(106\) | −5.63826 | −0.547636 | ||||||||
\(107\) | −3.58927 | −0.346988 | −0.173494 | − | 0.984835i | \(-0.555506\pi\) | ||||
−0.173494 | + | 0.984835i | \(0.555506\pi\) | |||||||
\(108\) | 5.27631 | 0.507713 | ||||||||
\(109\) | −13.9057 | −1.33193 | −0.665963 | − | 0.745985i | \(-0.731979\pi\) | ||||
−0.665963 | + | 0.745985i | \(0.731979\pi\) | |||||||
\(110\) | −2.69746 | −0.257193 | ||||||||
\(111\) | −0.673156 | −0.0638931 | ||||||||
\(112\) | −18.6828 | −1.76536 | ||||||||
\(113\) | −2.29670 | −0.216055 | −0.108028 | − | 0.994148i | \(-0.534454\pi\) | ||||
−0.108028 | + | 0.994148i | \(0.534454\pi\) | |||||||
\(114\) | 2.69746 | 0.252641 | ||||||||
\(115\) | −1.13206 | −0.105565 | ||||||||
\(116\) | −4.26442 | −0.395942 | ||||||||
\(117\) | 5.01699 | 0.463821 | ||||||||
\(118\) | −7.94927 | −0.731790 | ||||||||
\(119\) | 6.55539 | 0.600932 | ||||||||
\(120\) | −8.83771 | −0.806769 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.82940 | −0.527769 | ||||||||
\(123\) | 1.91557 | 0.172721 | ||||||||
\(124\) | 26.4712 | 2.37718 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.79295 | −0.337903 | ||||||||
\(127\) | −8.62068 | −0.764962 | −0.382481 | − | 0.923963i | \(-0.624930\pi\) | ||||
−0.382481 | + | 0.923963i | \(0.624930\pi\) | |||||||
\(128\) | 24.1639 | 2.13581 | ||||||||
\(129\) | 9.74641 | 0.858124 | ||||||||
\(130\) | −13.5331 | −1.18693 | ||||||||
\(131\) | 1.78441 | 0.155905 | 0.0779525 | − | 0.996957i | \(-0.475162\pi\) | ||||
0.0779525 | + | 0.996957i | \(0.475162\pi\) | |||||||
\(132\) | 5.27631 | 0.459243 | ||||||||
\(133\) | −1.40612 | −0.121926 | ||||||||
\(134\) | 32.4407 | 2.80245 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −41.2018 | −3.53303 | ||||||||
\(137\) | −14.1021 | −1.20482 | −0.602410 | − | 0.798187i | \(-0.705793\pi\) | ||||
−0.602410 | + | 0.798187i | \(0.705793\pi\) | |||||||
\(138\) | 3.05368 | 0.259947 | ||||||||
\(139\) | −8.41218 | −0.713512 | −0.356756 | − | 0.934198i | \(-0.616117\pi\) | ||||
−0.356756 | + | 0.934198i | \(0.616117\pi\) | |||||||
\(140\) | 7.41911 | 0.627029 | ||||||||
\(141\) | −11.6882 | −0.984326 | ||||||||
\(142\) | 19.5438 | 1.64008 | ||||||||
\(143\) | 5.01699 | 0.419542 | ||||||||
\(144\) | 13.2868 | 1.10723 | ||||||||
\(145\) | 0.808221 | 0.0671191 | ||||||||
\(146\) | 0.310399 | 0.0256888 | ||||||||
\(147\) | −5.02283 | −0.414276 | ||||||||
\(148\) | −3.55178 | −0.291954 | ||||||||
\(149\) | 9.99865 | 0.819121 | 0.409561 | − | 0.912283i | \(-0.365682\pi\) | ||||
0.409561 | + | 0.912283i | \(0.365682\pi\) | |||||||
\(150\) | 2.69746 | 0.220247 | ||||||||
\(151\) | −10.3224 | −0.840023 | −0.420011 | − | 0.907519i | \(-0.637974\pi\) | ||||
−0.420011 | + | 0.907519i | \(0.637974\pi\) | |||||||
\(152\) | 8.83771 | 0.716833 | ||||||||
\(153\) | −4.66205 | −0.376904 | ||||||||
\(154\) | −3.79295 | −0.305645 | ||||||||
\(155\) | −5.01699 | −0.402974 | ||||||||
\(156\) | 26.4712 | 2.11939 | ||||||||
\(157\) | −23.8910 | −1.90671 | −0.953353 | − | 0.301857i | \(-0.902393\pi\) | ||||
−0.953353 | + | 0.301857i | \(0.902393\pi\) | |||||||
\(158\) | −30.4238 | −2.42039 | ||||||||
\(159\) | −2.09021 | −0.165764 | ||||||||
\(160\) | −18.1652 | −1.43608 | ||||||||
\(161\) | −1.59181 | −0.125452 | ||||||||
\(162\) | 2.69746 | 0.211933 | ||||||||
\(163\) | 22.4639 | 1.75951 | 0.879755 | − | 0.475427i | \(-0.157706\pi\) | ||||
0.879755 | + | 0.475427i | \(0.157706\pi\) | |||||||
\(164\) | 10.1071 | 0.789234 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −27.1143 | −2.10448 | ||||||||
\(167\) | 19.0243 | 1.47214 | 0.736071 | − | 0.676905i | \(-0.236679\pi\) | ||||
0.736071 | + | 0.676905i | \(0.236679\pi\) | |||||||
\(168\) | −12.4269 | −0.958753 | ||||||||
\(169\) | 12.1702 | 0.936166 | ||||||||
\(170\) | 12.5757 | 0.964512 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 51.4250 | 3.92112 | ||||||||
\(173\) | 10.0883 | 0.766997 | 0.383498 | − | 0.923542i | \(-0.374719\pi\) | ||||
0.383498 | + | 0.923542i | \(0.374719\pi\) | |||||||
\(174\) | −2.18015 | −0.165276 | ||||||||
\(175\) | −1.40612 | −0.106293 | ||||||||
\(176\) | 13.2868 | 1.00153 | ||||||||
\(177\) | −2.94694 | −0.221506 | ||||||||
\(178\) | −33.3977 | −2.50327 | ||||||||
\(179\) | 9.64997 | 0.721272 | 0.360636 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360636 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(180\) | −5.27631 | −0.393273 | ||||||||
\(181\) | 8.35091 | 0.620718 | 0.310359 | − | 0.950619i | \(-0.399551\pi\) | ||||
0.310359 | + | 0.950619i | \(0.399551\pi\) | |||||||
\(182\) | −19.0292 | −1.41054 | ||||||||
\(183\) | −2.16107 | −0.159751 | ||||||||
\(184\) | 10.0048 | 0.737564 | ||||||||
\(185\) | 0.673156 | 0.0494914 | ||||||||
\(186\) | 13.5331 | 0.992298 | ||||||||
\(187\) | −4.66205 | −0.340923 | ||||||||
\(188\) | −61.6706 | −4.49779 | ||||||||
\(189\) | −1.40612 | −0.102280 | ||||||||
\(190\) | −2.69746 | −0.195695 | ||||||||
\(191\) | −26.2081 | −1.89635 | −0.948175 | − | 0.317750i | \(-0.897073\pi\) | ||||
−0.948175 | + | 0.317750i | \(0.897073\pi\) | |||||||
\(192\) | 22.4264 | 1.61848 | ||||||||
\(193\) | −13.9918 | −1.00715 | −0.503576 | − | 0.863951i | \(-0.667982\pi\) | ||||
−0.503576 | + | 0.863951i | \(0.667982\pi\) | |||||||
\(194\) | 6.16415 | 0.442560 | ||||||||
\(195\) | −5.01699 | −0.359274 | ||||||||
\(196\) | −26.5020 | −1.89300 | ||||||||
\(197\) | 23.7263 | 1.69043 | 0.845215 | − | 0.534427i | \(-0.179472\pi\) | ||||
0.845215 | + | 0.534427i | \(0.179472\pi\) | |||||||
\(198\) | 2.69746 | 0.191700 | ||||||||
\(199\) | 15.6795 | 1.11149 | 0.555746 | − | 0.831352i | \(-0.312433\pi\) | ||||
0.555746 | + | 0.831352i | \(0.312433\pi\) | |||||||
\(200\) | 8.83771 | 0.624921 | ||||||||
\(201\) | 12.0264 | 0.848276 | ||||||||
\(202\) | 4.31158 | 0.303361 | ||||||||
\(203\) | 1.13645 | 0.0797634 | ||||||||
\(204\) | −24.5984 | −1.72223 | ||||||||
\(205\) | −1.91557 | −0.133789 | ||||||||
\(206\) | −0.0831601 | −0.00579404 | ||||||||
\(207\) | 1.13206 | 0.0786834 | ||||||||
\(208\) | 66.6597 | 4.62202 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 3.79295 | 0.261738 | ||||||||
\(211\) | 19.1010 | 1.31497 | 0.657485 | − | 0.753468i | \(-0.271620\pi\) | ||||
0.657485 | + | 0.753468i | \(0.271620\pi\) | |||||||
\(212\) | −11.0286 | −0.757445 | ||||||||
\(213\) | 7.24526 | 0.496437 | ||||||||
\(214\) | −9.68192 | −0.661843 | ||||||||
\(215\) | −9.74641 | −0.664700 | ||||||||
\(216\) | 8.83771 | 0.601330 | ||||||||
\(217\) | −7.05447 | −0.478889 | ||||||||
\(218\) | −37.5101 | −2.54051 | ||||||||
\(219\) | 0.115071 | 0.00777575 | ||||||||
\(220\) | −5.27631 | −0.355728 | ||||||||
\(221\) | −23.3894 | −1.57334 | ||||||||
\(222\) | −1.81581 | −0.121869 | ||||||||
\(223\) | −9.15846 | −0.613296 | −0.306648 | − | 0.951823i | \(-0.599207\pi\) | ||||
−0.306648 | + | 0.951823i | \(0.599207\pi\) | |||||||
\(224\) | −25.5424 | −1.70662 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.19526 | −0.412103 | ||||||||
\(227\) | −27.2511 | −1.80872 | −0.904359 | − | 0.426772i | \(-0.859651\pi\) | ||||
−0.904359 | + | 0.426772i | \(0.859651\pi\) | |||||||
\(228\) | 5.27631 | 0.349432 | ||||||||
\(229\) | 15.1334 | 1.00004 | 0.500021 | − | 0.866013i | \(-0.333326\pi\) | ||||
0.500021 | + | 0.866013i | \(0.333326\pi\) | |||||||
\(230\) | −3.05368 | −0.201354 | ||||||||
\(231\) | −1.40612 | −0.0925158 | ||||||||
\(232\) | −7.14283 | −0.468950 | ||||||||
\(233\) | 16.3510 | 1.07119 | 0.535595 | − | 0.844475i | \(-0.320087\pi\) | ||||
0.535595 | + | 0.844475i | \(0.320087\pi\) | |||||||
\(234\) | 13.5331 | 0.884689 | ||||||||
\(235\) | 11.6882 | 0.762456 | ||||||||
\(236\) | −15.5490 | −1.01215 | ||||||||
\(237\) | −11.2787 | −0.732628 | ||||||||
\(238\) | 17.6829 | 1.14621 | ||||||||
\(239\) | −19.6404 | −1.27043 | −0.635216 | − | 0.772335i | \(-0.719089\pi\) | ||||
−0.635216 | + | 0.772335i | \(0.719089\pi\) | |||||||
\(240\) | −13.2868 | −0.857659 | ||||||||
\(241\) | 5.71386 | 0.368062 | 0.184031 | − | 0.982920i | \(-0.441085\pi\) | ||||
0.184031 | + | 0.982920i | \(0.441085\pi\) | |||||||
\(242\) | 2.69746 | 0.173399 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.4025 | −0.729968 | ||||||||
\(245\) | 5.02283 | 0.320897 | ||||||||
\(246\) | 5.16717 | 0.329447 | ||||||||
\(247\) | 5.01699 | 0.319223 | ||||||||
\(248\) | 44.3387 | 2.81551 | ||||||||
\(249\) | −10.0518 | −0.637005 | ||||||||
\(250\) | −2.69746 | −0.170603 | ||||||||
\(251\) | −15.9340 | −1.00575 | −0.502874 | − | 0.864360i | \(-0.667724\pi\) | ||||
−0.502874 | + | 0.864360i | \(0.667724\pi\) | |||||||
\(252\) | −7.41911 | −0.467360 | ||||||||
\(253\) | 1.13206 | 0.0711719 | ||||||||
\(254\) | −23.2540 | −1.45908 | ||||||||
\(255\) | 4.66205 | 0.291949 | ||||||||
\(256\) | 20.3285 | 1.27053 | ||||||||
\(257\) | −16.6133 | −1.03631 | −0.518155 | − | 0.855287i | \(-0.673381\pi\) | ||||
−0.518155 | + | 0.855287i | \(0.673381\pi\) | |||||||
\(258\) | 26.2906 | 1.63678 | ||||||||
\(259\) | 0.946536 | 0.0588149 | ||||||||
\(260\) | −26.4712 | −1.64167 | ||||||||
\(261\) | −0.808221 | −0.0500276 | ||||||||
\(262\) | 4.81339 | 0.297372 | ||||||||
\(263\) | −8.26598 | −0.509702 | −0.254851 | − | 0.966980i | \(-0.582026\pi\) | ||||
−0.254851 | + | 0.966980i | \(0.582026\pi\) | |||||||
\(264\) | 8.83771 | 0.543924 | ||||||||
\(265\) | 2.09021 | 0.128400 | ||||||||
\(266\) | −3.79295 | −0.232561 | ||||||||
\(267\) | −12.3812 | −0.757715 | ||||||||
\(268\) | 63.4549 | 3.87612 | ||||||||
\(269\) | −23.7962 | −1.45088 | −0.725439 | − | 0.688287i | \(-0.758363\pi\) | ||||
−0.725439 | + | 0.688287i | \(0.758363\pi\) | |||||||
\(270\) | −2.69746 | −0.164162 | ||||||||
\(271\) | −27.3012 | −1.65843 | −0.829215 | − | 0.558930i | \(-0.811212\pi\) | ||||
−0.829215 | + | 0.558930i | \(0.811212\pi\) | |||||||
\(272\) | −61.9437 | −3.75589 | ||||||||
\(273\) | −7.05447 | −0.426956 | ||||||||
\(274\) | −38.0398 | −2.29807 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 5.97308 | 0.359537 | ||||||||
\(277\) | 7.43984 | 0.447017 | 0.223508 | − | 0.974702i | \(-0.428249\pi\) | ||||
0.223508 | + | 0.974702i | \(0.428249\pi\) | |||||||
\(278\) | −22.6915 | −1.36095 | ||||||||
\(279\) | 5.01699 | 0.300359 | ||||||||
\(280\) | 12.4269 | 0.742647 | ||||||||
\(281\) | −0.966594 | −0.0576622 | −0.0288311 | − | 0.999584i | \(-0.509178\pi\) | ||||
−0.0288311 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(282\) | −31.5285 | −1.87750 | ||||||||
\(283\) | −8.91259 | −0.529799 | −0.264899 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264899 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(284\) | 38.2282 | 2.26843 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 13.5331 | 0.800231 | ||||||||
\(287\) | −2.69351 | −0.158993 | ||||||||
\(288\) | 18.1652 | 1.07039 | ||||||||
\(289\) | 4.73470 | 0.278512 | ||||||||
\(290\) | 2.18015 | 0.128023 | ||||||||
\(291\) | 2.28517 | 0.133959 | ||||||||
\(292\) | 0.607148 | 0.0355306 | ||||||||
\(293\) | 12.3764 | 0.723039 | 0.361519 | − | 0.932365i | \(-0.382258\pi\) | ||||
0.361519 | + | 0.932365i | \(0.382258\pi\) | |||||||
\(294\) | −13.5489 | −0.790188 | ||||||||
\(295\) | 2.94694 | 0.171578 | ||||||||
\(296\) | −5.94916 | −0.345788 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 26.9710 | 1.56239 | ||||||||
\(299\) | 5.67952 | 0.328455 | ||||||||
\(300\) | 5.27631 | 0.304628 | ||||||||
\(301\) | −13.7046 | −0.789920 | ||||||||
\(302\) | −27.8442 | −1.60225 | ||||||||
\(303\) | 1.59838 | 0.0918246 | ||||||||
\(304\) | 13.2868 | 0.762050 | ||||||||
\(305\) | 2.16107 | 0.123742 | ||||||||
\(306\) | −12.5757 | −0.718905 | ||||||||
\(307\) | 1.81161 | 0.103394 | 0.0516971 | − | 0.998663i | \(-0.483537\pi\) | ||||
0.0516971 | + | 0.998663i | \(0.483537\pi\) | |||||||
\(308\) | −7.41911 | −0.422743 | ||||||||
\(309\) | −0.0308290 | −0.00175380 | ||||||||
\(310\) | −13.5331 | −0.768630 | ||||||||
\(311\) | 15.5874 | 0.883880 | 0.441940 | − | 0.897045i | \(-0.354290\pi\) | ||||
0.441940 | + | 0.897045i | \(0.354290\pi\) | |||||||
\(312\) | 44.3387 | 2.51018 | ||||||||
\(313\) | 22.4976 | 1.27164 | 0.635821 | − | 0.771837i | \(-0.280662\pi\) | ||||
0.635821 | + | 0.771837i | \(0.280662\pi\) | |||||||
\(314\) | −64.4450 | −3.63684 | ||||||||
\(315\) | 1.40612 | 0.0792258 | ||||||||
\(316\) | −59.5097 | −3.34768 | ||||||||
\(317\) | 28.1537 | 1.58127 | 0.790635 | − | 0.612287i | \(-0.209750\pi\) | ||||
0.790635 | + | 0.612287i | \(0.209750\pi\) | |||||||
\(318\) | −5.63826 | −0.316178 | ||||||||
\(319\) | −0.808221 | −0.0452517 | ||||||||
\(320\) | −22.4264 | −1.25367 | ||||||||
\(321\) | −3.58927 | −0.200334 | ||||||||
\(322\) | −4.29384 | −0.239286 | ||||||||
\(323\) | −4.66205 | −0.259403 | ||||||||
\(324\) | 5.27631 | 0.293128 | ||||||||
\(325\) | 5.01699 | 0.278292 | ||||||||
\(326\) | 60.5956 | 3.35608 | ||||||||
\(327\) | −13.9057 | −0.768987 | ||||||||
\(328\) | 16.9292 | 0.934761 | ||||||||
\(329\) | 16.4350 | 0.906092 | ||||||||
\(330\) | −2.69746 | −0.148490 | ||||||||
\(331\) | −18.7770 | −1.03208 | −0.516039 | − | 0.856565i | \(-0.672594\pi\) | ||||
−0.516039 | + | 0.856565i | \(0.672594\pi\) | |||||||
\(332\) | −53.0362 | −2.91074 | ||||||||
\(333\) | −0.673156 | −0.0368887 | ||||||||
\(334\) | 51.3172 | 2.80795 | ||||||||
\(335\) | −12.0264 | −0.657072 | ||||||||
\(336\) | −18.6828 | −1.01923 | ||||||||
\(337\) | −5.42312 | −0.295416 | −0.147708 | − | 0.989031i | \(-0.547190\pi\) | ||||
−0.147708 | + | 0.989031i | \(0.547190\pi\) | |||||||
\(338\) | 32.8286 | 1.78564 | ||||||||
\(339\) | −2.29670 | −0.124740 | ||||||||
\(340\) | 24.5984 | 1.33404 | ||||||||
\(341\) | 5.01699 | 0.271685 | ||||||||
\(342\) | 2.69746 | 0.145862 | ||||||||
\(343\) | 16.9055 | 0.912812 | ||||||||
\(344\) | 86.1360 | 4.64414 | ||||||||
\(345\) | −1.13206 | −0.0609479 | ||||||||
\(346\) | 27.2127 | 1.46296 | ||||||||
\(347\) | 19.6791 | 1.05643 | 0.528214 | − | 0.849111i | \(-0.322862\pi\) | ||||
0.528214 | + | 0.849111i | \(0.322862\pi\) | |||||||
\(348\) | −4.26442 | −0.228597 | ||||||||
\(349\) | 22.4859 | 1.20364 | 0.601822 | − | 0.798630i | \(-0.294442\pi\) | ||||
0.601822 | + | 0.798630i | \(0.294442\pi\) | |||||||
\(350\) | −3.79295 | −0.202742 | ||||||||
\(351\) | 5.01699 | 0.267787 | ||||||||
\(352\) | 18.1652 | 0.968208 | ||||||||
\(353\) | −32.7869 | −1.74507 | −0.872537 | − | 0.488549i | \(-0.837526\pi\) | ||||
−0.872537 | + | 0.488549i | \(0.837526\pi\) | |||||||
\(354\) | −7.94927 | −0.422499 | ||||||||
\(355\) | −7.24526 | −0.384539 | ||||||||
\(356\) | −65.3268 | −3.46232 | ||||||||
\(357\) | 6.55539 | 0.346948 | ||||||||
\(358\) | 26.0304 | 1.37575 | ||||||||
\(359\) | −23.9266 | −1.26280 | −0.631399 | − | 0.775458i | \(-0.717519\pi\) | ||||
−0.631399 | + | 0.775458i | \(0.717519\pi\) | |||||||
\(360\) | −8.83771 | −0.465788 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 22.5263 | 1.18395 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −37.2216 | −1.95094 | ||||||||
\(365\) | −0.115071 | −0.00602307 | ||||||||
\(366\) | −5.82940 | −0.304708 | ||||||||
\(367\) | −12.9529 | −0.676137 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(368\) | 15.0414 | 0.784088 | ||||||||
\(369\) | 1.91557 | 0.0997205 | ||||||||
\(370\) | 1.81581 | 0.0943996 | ||||||||
\(371\) | 2.93908 | 0.152589 | ||||||||
\(372\) | 26.4712 | 1.37247 | ||||||||
\(373\) | −4.89069 | −0.253231 | −0.126615 | − | 0.991952i | \(-0.540411\pi\) | ||||
−0.126615 | + | 0.991952i | \(0.540411\pi\) | |||||||
\(374\) | −12.5757 | −0.650274 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −103.297 | −5.32714 | ||||||||
\(377\) | −4.05484 | −0.208835 | ||||||||
\(378\) | −3.79295 | −0.195088 | ||||||||
\(379\) | −33.5136 | −1.72148 | −0.860738 | − | 0.509049i | \(-0.829997\pi\) | ||||
−0.860738 | + | 0.509049i | \(0.829997\pi\) | |||||||
\(380\) | −5.27631 | −0.270669 | ||||||||
\(381\) | −8.62068 | −0.441651 | ||||||||
\(382\) | −70.6953 | −3.61709 | ||||||||
\(383\) | 7.19995 | 0.367900 | 0.183950 | − | 0.982936i | \(-0.441112\pi\) | ||||
0.183950 | + | 0.982936i | \(0.441112\pi\) | |||||||
\(384\) | 24.1639 | 1.23311 | ||||||||
\(385\) | 1.40612 | 0.0716624 | ||||||||
\(386\) | −37.7423 | −1.92103 | ||||||||
\(387\) | 9.74641 | 0.495438 | ||||||||
\(388\) | 12.0572 | 0.612114 | ||||||||
\(389\) | 4.71089 | 0.238851 | 0.119426 | − | 0.992843i | \(-0.461895\pi\) | ||||
0.119426 | + | 0.992843i | \(0.461895\pi\) | |||||||
\(390\) | −13.5331 | −0.685277 | ||||||||
\(391\) | −5.27771 | −0.266905 | ||||||||
\(392\) | −44.3904 | −2.24205 | ||||||||
\(393\) | 1.78441 | 0.0900118 | ||||||||
\(394\) | 64.0008 | 3.22432 | ||||||||
\(395\) | 11.2787 | 0.567491 | ||||||||
\(396\) | 5.27631 | 0.265144 | ||||||||
\(397\) | −9.32680 | −0.468098 | −0.234049 | − | 0.972225i | \(-0.575198\pi\) | ||||
−0.234049 | + | 0.972225i | \(0.575198\pi\) | |||||||
\(398\) | 42.2950 | 2.12006 | ||||||||
\(399\) | −1.40612 | −0.0703939 | ||||||||
\(400\) | 13.2868 | 0.664340 | ||||||||
\(401\) | −0.176644 | −0.00882117 | −0.00441058 | − | 0.999990i | \(-0.501404\pi\) | ||||
−0.00441058 | + | 0.999990i | \(0.501404\pi\) | |||||||
\(402\) | 32.4407 | 1.61800 | ||||||||
\(403\) | 25.1702 | 1.25381 | ||||||||
\(404\) | 8.43355 | 0.419585 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 3.06554 | 0.152140 | ||||||||
\(407\) | −0.673156 | −0.0333671 | ||||||||
\(408\) | −41.2018 | −2.03980 | ||||||||
\(409\) | −7.01295 | −0.346768 | −0.173384 | − | 0.984854i | \(-0.555470\pi\) | ||||
−0.173384 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(410\) | −5.16717 | −0.255189 | ||||||||
\(411\) | −14.1021 | −0.695603 | ||||||||
\(412\) | −0.162663 | −0.00801384 | ||||||||
\(413\) | 4.14375 | 0.203901 | ||||||||
\(414\) | 3.05368 | 0.150080 | ||||||||
\(415\) | 10.0518 | 0.493422 | ||||||||
\(416\) | 91.1346 | 4.46824 | ||||||||
\(417\) | −8.41218 | −0.411946 | ||||||||
\(418\) | 2.69746 | 0.131937 | ||||||||
\(419\) | 23.5858 | 1.15224 | 0.576121 | − | 0.817365i | \(-0.304566\pi\) | ||||
0.576121 | + | 0.817365i | \(0.304566\pi\) | |||||||
\(420\) | 7.41911 | 0.362015 | ||||||||
\(421\) | −21.9892 | −1.07169 | −0.535844 | − | 0.844317i | \(-0.680006\pi\) | ||||
−0.535844 | + | 0.844317i | \(0.680006\pi\) | |||||||
\(422\) | 51.5243 | 2.50817 | ||||||||
\(423\) | −11.6882 | −0.568301 | ||||||||
\(424\) | −18.4726 | −0.897111 | ||||||||
\(425\) | −4.66205 | −0.226143 | ||||||||
\(426\) | 19.5438 | 0.946902 | ||||||||
\(427\) | 3.03872 | 0.147054 | ||||||||
\(428\) | −18.9381 | −0.915407 | ||||||||
\(429\) | 5.01699 | 0.242222 | ||||||||
\(430\) | −26.2906 | −1.26784 | ||||||||
\(431\) | −6.65872 | −0.320739 | −0.160370 | − | 0.987057i | \(-0.551269\pi\) | ||||
−0.160370 | + | 0.987057i | \(0.551269\pi\) | |||||||
\(432\) | 13.2868 | 0.639261 | ||||||||
\(433\) | 27.7058 | 1.33146 | 0.665728 | − | 0.746195i | \(-0.268121\pi\) | ||||
0.665728 | + | 0.746195i | \(0.268121\pi\) | |||||||
\(434\) | −19.0292 | −0.913430 | ||||||||
\(435\) | 0.808221 | 0.0387512 | ||||||||
\(436\) | −73.3708 | −3.51382 | ||||||||
\(437\) | 1.13206 | 0.0541537 | ||||||||
\(438\) | 0.310399 | 0.0148314 | ||||||||
\(439\) | −7.10884 | −0.339286 | −0.169643 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169643 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(440\) | −8.83771 | −0.421321 | ||||||||
\(441\) | −5.02283 | −0.239183 | ||||||||
\(442\) | −63.0921 | −3.00099 | ||||||||
\(443\) | −19.5733 | −0.929954 | −0.464977 | − | 0.885323i | \(-0.653937\pi\) | ||||
−0.464977 | + | 0.885323i | \(0.653937\pi\) | |||||||
\(444\) | −3.55178 | −0.168560 | ||||||||
\(445\) | 12.3812 | 0.586924 | ||||||||
\(446\) | −24.7046 | −1.16980 | ||||||||
\(447\) | 9.99865 | 0.472920 | ||||||||
\(448\) | −31.5341 | −1.48985 | ||||||||
\(449\) | 15.8026 | 0.745773 | 0.372886 | − | 0.927877i | \(-0.378368\pi\) | ||||
0.372886 | + | 0.927877i | \(0.378368\pi\) | |||||||
\(450\) | 2.69746 | 0.127160 | ||||||||
\(451\) | 1.91557 | 0.0902006 | ||||||||
\(452\) | −12.1181 | −0.569987 | ||||||||
\(453\) | −10.3224 | −0.484987 | ||||||||
\(454\) | −73.5088 | −3.44994 | ||||||||
\(455\) | 7.05447 | 0.330719 | ||||||||
\(456\) | 8.83771 | 0.413864 | ||||||||
\(457\) | 17.2740 | 0.808045 | 0.404022 | − | 0.914749i | \(-0.367612\pi\) | ||||
0.404022 | + | 0.914749i | \(0.367612\pi\) | |||||||
\(458\) | 40.8218 | 1.90748 | ||||||||
\(459\) | −4.66205 | −0.217606 | ||||||||
\(460\) | −5.97308 | −0.278496 | ||||||||
\(461\) | 6.91319 | 0.321979 | 0.160990 | − | 0.986956i | \(-0.448531\pi\) | ||||
0.160990 | + | 0.986956i | \(0.448531\pi\) | |||||||
\(462\) | −3.79295 | −0.176464 | ||||||||
\(463\) | 33.5631 | 1.55981 | 0.779906 | − | 0.625897i | \(-0.215267\pi\) | ||||
0.779906 | + | 0.625897i | \(0.215267\pi\) | |||||||
\(464\) | −10.7387 | −0.498530 | ||||||||
\(465\) | −5.01699 | −0.232657 | ||||||||
\(466\) | 44.1063 | 2.04318 | ||||||||
\(467\) | 0.0247568 | 0.00114561 | 0.000572805 | − | 1.00000i | \(-0.499818\pi\) | ||||
0.000572805 | 1.00000i | \(0.499818\pi\) | ||||||||
\(468\) | 26.4712 | 1.22363 | ||||||||
\(469\) | −16.9105 | −0.780855 | ||||||||
\(470\) | 31.5285 | 1.45430 | ||||||||
\(471\) | −23.8910 | −1.10084 | ||||||||
\(472\) | −26.0442 | −1.19878 | ||||||||
\(473\) | 9.74641 | 0.448140 | ||||||||
\(474\) | −30.4238 | −1.39741 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 34.5882 | 1.58535 | ||||||||
\(477\) | −2.09021 | −0.0957040 | ||||||||
\(478\) | −52.9793 | −2.42321 | ||||||||
\(479\) | 11.7875 | 0.538585 | 0.269293 | − | 0.963058i | \(-0.413210\pi\) | ||||
0.269293 | + | 0.963058i | \(0.413210\pi\) | |||||||
\(480\) | −18.1652 | −0.829124 | ||||||||
\(481\) | −3.37721 | −0.153988 | ||||||||
\(482\) | 15.4129 | 0.702039 | ||||||||
\(483\) | −1.59181 | −0.0724297 | ||||||||
\(484\) | 5.27631 | 0.239832 | ||||||||
\(485\) | −2.28517 | −0.103764 | ||||||||
\(486\) | 2.69746 | 0.122359 | ||||||||
\(487\) | −10.4020 | −0.471362 | −0.235681 | − | 0.971831i | \(-0.575732\pi\) | ||||
−0.235681 | + | 0.971831i | \(0.575732\pi\) | |||||||
\(488\) | −19.0989 | −0.864567 | ||||||||
\(489\) | 22.4639 | 1.01585 | ||||||||
\(490\) | 13.5489 | 0.612077 | ||||||||
\(491\) | 24.9081 | 1.12409 | 0.562043 | − | 0.827108i | \(-0.310015\pi\) | ||||
0.562043 | + | 0.827108i | \(0.310015\pi\) | |||||||
\(492\) | 10.1071 | 0.455664 | ||||||||
\(493\) | 3.76797 | 0.169701 | ||||||||
\(494\) | 13.5331 | 0.608885 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 66.6597 | 2.99311 | ||||||||
\(497\) | −10.1877 | −0.456981 | ||||||||
\(498\) | −27.1143 | −1.21502 | ||||||||
\(499\) | 14.4290 | 0.645931 | 0.322965 | − | 0.946411i | \(-0.395320\pi\) | ||||
0.322965 | + | 0.946411i | \(0.395320\pi\) | |||||||
\(500\) | −5.27631 | −0.235964 | ||||||||
\(501\) | 19.0243 | 0.849941 | ||||||||
\(502\) | −42.9815 | −1.91836 | ||||||||
\(503\) | 7.09937 | 0.316545 | 0.158273 | − | 0.987395i | \(-0.449408\pi\) | ||||
0.158273 | + | 0.987395i | \(0.449408\pi\) | |||||||
\(504\) | −12.4269 | −0.553537 | ||||||||
\(505\) | −1.59838 | −0.0711271 | ||||||||
\(506\) | 3.05368 | 0.135753 | ||||||||
\(507\) | 12.1702 | 0.540496 | ||||||||
\(508\) | −45.4853 | −2.01809 | ||||||||
\(509\) | 24.1458 | 1.07025 | 0.535123 | − | 0.844774i | \(-0.320265\pi\) | ||||
0.535123 | + | 0.844774i | \(0.320265\pi\) | |||||||
\(510\) | 12.5757 | 0.556861 | ||||||||
\(511\) | −0.161803 | −0.00715774 | ||||||||
\(512\) | 6.50750 | 0.287594 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −44.8138 | −1.97665 | ||||||||
\(515\) | 0.0308290 | 0.00135849 | ||||||||
\(516\) | 51.4250 | 2.26386 | ||||||||
\(517\) | −11.6882 | −0.514047 | ||||||||
\(518\) | 2.55325 | 0.112183 | ||||||||
\(519\) | 10.0883 | 0.442826 | ||||||||
\(520\) | −44.3387 | −1.94438 | ||||||||
\(521\) | 25.1347 | 1.10117 | 0.550586 | − | 0.834778i | \(-0.314404\pi\) | ||||
0.550586 | + | 0.834778i | \(0.314404\pi\) | |||||||
\(522\) | −2.18015 | −0.0954224 | ||||||||
\(523\) | 33.5952 | 1.46901 | 0.734507 | − | 0.678601i | \(-0.237413\pi\) | ||||
0.734507 | + | 0.678601i | \(0.237413\pi\) | |||||||
\(524\) | 9.41511 | 0.411301 | ||||||||
\(525\) | −1.40612 | −0.0613680 | ||||||||
\(526\) | −22.2972 | −0.972203 | ||||||||
\(527\) | −23.3894 | −1.01886 | ||||||||
\(528\) | 13.2868 | 0.578233 | ||||||||
\(529\) | −21.7184 | −0.944280 | ||||||||
\(530\) | 5.63826 | 0.244910 | ||||||||
\(531\) | −2.94694 | −0.127886 | ||||||||
\(532\) | −7.41911 | −0.321659 | ||||||||
\(533\) | 9.61038 | 0.416272 | ||||||||
\(534\) | −33.3977 | −1.44526 | ||||||||
\(535\) | 3.58927 | 0.155178 | ||||||||
\(536\) | 106.286 | 4.59085 | ||||||||
\(537\) | 9.64997 | 0.416427 | ||||||||
\(538\) | −64.1893 | −2.76740 | ||||||||
\(539\) | −5.02283 | −0.216349 | ||||||||
\(540\) | −5.27631 | −0.227056 | ||||||||
\(541\) | 21.3488 | 0.917855 | 0.458928 | − | 0.888474i | \(-0.348234\pi\) | ||||
0.458928 | + | 0.888474i | \(0.348234\pi\) | |||||||
\(542\) | −73.6440 | −3.16328 | ||||||||
\(543\) | 8.35091 | 0.358372 | ||||||||
\(544\) | −84.6870 | −3.63093 | ||||||||
\(545\) | 13.9057 | 0.595655 | ||||||||
\(546\) | −19.0292 | −0.814374 | ||||||||
\(547\) | 45.7018 | 1.95407 | 0.977033 | − | 0.213088i | \(-0.0683521\pi\) | ||||
0.977033 | + | 0.213088i | \(0.0683521\pi\) | |||||||
\(548\) | −74.4068 | −3.17850 | ||||||||
\(549\) | −2.16107 | −0.0922322 | ||||||||
\(550\) | 2.69746 | 0.115020 | ||||||||
\(551\) | −0.808221 | −0.0344314 | ||||||||
\(552\) | 10.0048 | 0.425833 | ||||||||
\(553\) | 15.8591 | 0.674399 | ||||||||
\(554\) | 20.0687 | 0.852638 | ||||||||
\(555\) | 0.673156 | 0.0285739 | ||||||||
\(556\) | −44.3852 | −1.88235 | ||||||||
\(557\) | 31.8893 | 1.35119 | 0.675597 | − | 0.737271i | \(-0.263886\pi\) | ||||
0.675597 | + | 0.737271i | \(0.263886\pi\) | |||||||
\(558\) | 13.5331 | 0.572903 | ||||||||
\(559\) | 48.8976 | 2.06815 | ||||||||
\(560\) | 18.6828 | 0.789492 | ||||||||
\(561\) | −4.66205 | −0.196832 | ||||||||
\(562\) | −2.60735 | −0.109985 | ||||||||
\(563\) | −0.348296 | −0.0146789 | −0.00733947 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733947 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(564\) | −61.6706 | −2.59680 | ||||||||
\(565\) | 2.29670 | 0.0966229 | ||||||||
\(566\) | −24.0414 | −1.01054 | ||||||||
\(567\) | −1.40612 | −0.0590514 | ||||||||
\(568\) | 64.0316 | 2.68671 | ||||||||
\(569\) | 21.3120 | 0.893448 | 0.446724 | − | 0.894672i | \(-0.352591\pi\) | ||||
0.446724 | + | 0.894672i | \(0.352591\pi\) | |||||||
\(570\) | −2.69746 | −0.112984 | ||||||||
\(571\) | 38.1340 | 1.59586 | 0.797929 | − | 0.602752i | \(-0.205929\pi\) | ||||
0.797929 | + | 0.602752i | \(0.205929\pi\) | |||||||
\(572\) | 26.4712 | 1.10681 | ||||||||
\(573\) | −26.2081 | −1.09486 | ||||||||
\(574\) | −7.26565 | −0.303263 | ||||||||
\(575\) | 1.13206 | 0.0472101 | ||||||||
\(576\) | 22.4264 | 0.934432 | ||||||||
\(577\) | −17.3041 | −0.720379 | −0.360189 | − | 0.932879i | \(-0.617288\pi\) | ||||
−0.360189 | + | 0.932879i | \(0.617288\pi\) | |||||||
\(578\) | 12.7717 | 0.531232 | ||||||||
\(579\) | −13.9918 | −0.581479 | ||||||||
\(580\) | 4.26442 | 0.177070 | ||||||||
\(581\) | 14.1340 | 0.586376 | ||||||||
\(582\) | 6.16415 | 0.255512 | ||||||||
\(583\) | −2.09021 | −0.0865675 | ||||||||
\(584\) | 1.01696 | 0.0420822 | ||||||||
\(585\) | −5.01699 | −0.207427 | ||||||||
\(586\) | 33.3850 | 1.37912 | ||||||||
\(587\) | 12.9968 | 0.536436 | 0.268218 | − | 0.963358i | \(-0.413565\pi\) | ||||
0.268218 | + | 0.963358i | \(0.413565\pi\) | |||||||
\(588\) | −26.5020 | −1.09292 | ||||||||
\(589\) | 5.01699 | 0.206721 | ||||||||
\(590\) | 7.94927 | 0.327266 | ||||||||
\(591\) | 23.7263 | 0.975970 | ||||||||
\(592\) | −8.94408 | −0.367599 | ||||||||
\(593\) | 2.38938 | 0.0981200 | 0.0490600 | − | 0.998796i | \(-0.484377\pi\) | ||||
0.0490600 | + | 0.998796i | \(0.484377\pi\) | |||||||
\(594\) | 2.69746 | 0.110678 | ||||||||
\(595\) | −6.55539 | −0.268745 | ||||||||
\(596\) | 52.7559 | 2.16097 | ||||||||
\(597\) | 15.6795 | 0.641721 | ||||||||
\(598\) | 15.3203 | 0.626493 | ||||||||
\(599\) | 7.18538 | 0.293587 | 0.146793 | − | 0.989167i | \(-0.453105\pi\) | ||||
0.146793 | + | 0.989167i | \(0.453105\pi\) | |||||||
\(600\) | 8.83771 | 0.360798 | ||||||||
\(601\) | −5.32419 | −0.217178 | −0.108589 | − | 0.994087i | \(-0.534633\pi\) | ||||
−0.108589 | + | 0.994087i | \(0.534633\pi\) | |||||||
\(602\) | −36.9676 | −1.50669 | ||||||||
\(603\) | 12.0264 | 0.489752 | ||||||||
\(604\) | −54.4640 | −2.21611 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 4.31158 | 0.175146 | ||||||||
\(607\) | −27.9968 | −1.13635 | −0.568177 | − | 0.822906i | \(-0.692351\pi\) | ||||
−0.568177 | + | 0.822906i | \(0.692351\pi\) | |||||||
\(608\) | 18.1652 | 0.736696 | ||||||||
\(609\) | 1.13645 | 0.0460514 | ||||||||
\(610\) | 5.82940 | 0.236026 | ||||||||
\(611\) | −58.6397 | −2.37231 | ||||||||
\(612\) | −24.5984 | −0.994331 | ||||||||
\(613\) | 15.9169 | 0.642877 | 0.321439 | − | 0.946930i | \(-0.395834\pi\) | ||||
0.321439 | + | 0.946930i | \(0.395834\pi\) | |||||||
\(614\) | 4.88676 | 0.197214 | ||||||||
\(615\) | −1.91557 | −0.0772432 | ||||||||
\(616\) | −12.4269 | −0.500693 | ||||||||
\(617\) | −3.91208 | −0.157494 | −0.0787471 | − | 0.996895i | \(-0.525092\pi\) | ||||
−0.0787471 | + | 0.996895i | \(0.525092\pi\) | |||||||
\(618\) | −0.0831601 | −0.00334519 | ||||||||
\(619\) | 46.2645 | 1.85953 | 0.929764 | − | 0.368157i | \(-0.120011\pi\) | ||||
0.929764 | + | 0.368157i | \(0.120011\pi\) | |||||||
\(620\) | −26.4712 | −1.06311 | ||||||||
\(621\) | 1.13206 | 0.0454279 | ||||||||
\(622\) | 42.0464 | 1.68591 | ||||||||
\(623\) | 17.4094 | 0.697492 | ||||||||
\(624\) | 66.6597 | 2.66852 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 60.6865 | 2.42552 | ||||||||
\(627\) | 1.00000 | 0.0399362 | ||||||||
\(628\) | −126.056 | −5.03018 | ||||||||
\(629\) | 3.13829 | 0.125132 | ||||||||
\(630\) | 3.79295 | 0.151115 | ||||||||
\(631\) | 41.9303 | 1.66922 | 0.834610 | − | 0.550841i | \(-0.185693\pi\) | ||||
0.834610 | + | 0.550841i | \(0.185693\pi\) | |||||||
\(632\) | −99.6776 | −3.96496 | ||||||||
\(633\) | 19.1010 | 0.759198 | ||||||||
\(634\) | 75.9436 | 3.01611 | ||||||||
\(635\) | 8.62068 | 0.342101 | ||||||||
\(636\) | −11.0286 | −0.437311 | ||||||||
\(637\) | −25.1995 | −0.998440 | ||||||||
\(638\) | −2.18015 | −0.0863128 | ||||||||
\(639\) | 7.24526 | 0.286618 | ||||||||
\(640\) | −24.1639 | −0.955162 | ||||||||
\(641\) | 22.3702 | 0.883568 | 0.441784 | − | 0.897121i | \(-0.354346\pi\) | ||||
0.441784 | + | 0.897121i | \(0.354346\pi\) | |||||||
\(642\) | −9.68192 | −0.382115 | ||||||||
\(643\) | 24.1399 | 0.951986 | 0.475993 | − | 0.879449i | \(-0.342089\pi\) | ||||
0.475993 | + | 0.879449i | \(0.342089\pi\) | |||||||
\(644\) | −8.39886 | −0.330961 | ||||||||
\(645\) | −9.74641 | −0.383765 | ||||||||
\(646\) | −12.5757 | −0.494784 | ||||||||
\(647\) | −40.1149 | −1.57708 | −0.788540 | − | 0.614984i | \(-0.789162\pi\) | ||||
−0.788540 | + | 0.614984i | \(0.789162\pi\) | |||||||
\(648\) | 8.83771 | 0.347178 | ||||||||
\(649\) | −2.94694 | −0.115678 | ||||||||
\(650\) | 13.5331 | 0.530813 | ||||||||
\(651\) | −7.05447 | −0.276487 | ||||||||
\(652\) | 118.527 | 4.64186 | ||||||||
\(653\) | 28.1355 | 1.10103 | 0.550514 | − | 0.834826i | \(-0.314432\pi\) | ||||
0.550514 | + | 0.834826i | \(0.314432\pi\) | |||||||
\(654\) | −37.5101 | −1.46676 | ||||||||
\(655\) | −1.78441 | −0.0697228 | ||||||||
\(656\) | 25.4518 | 0.993724 | ||||||||
\(657\) | 0.115071 | 0.00448933 | ||||||||
\(658\) | 44.3328 | 1.72827 | ||||||||
\(659\) | −30.0783 | −1.17169 | −0.585843 | − | 0.810425i | \(-0.699236\pi\) | ||||
−0.585843 | + | 0.810425i | \(0.699236\pi\) | |||||||
\(660\) | −5.27631 | −0.205380 | ||||||||
\(661\) | −39.0094 | −1.51729 | −0.758645 | − | 0.651505i | \(-0.774138\pi\) | ||||
−0.758645 | + | 0.651505i | \(0.774138\pi\) | |||||||
\(662\) | −50.6503 | −1.96858 | ||||||||
\(663\) | −23.3894 | −0.908370 | ||||||||
\(664\) | −88.8347 | −3.44745 | ||||||||
\(665\) | 1.40612 | 0.0545269 | ||||||||
\(666\) | −1.81581 | −0.0703613 | ||||||||
\(667\) | −0.914953 | −0.0354271 | ||||||||
\(668\) | 100.378 | 3.88373 | ||||||||
\(669\) | −9.15846 | −0.354086 | ||||||||
\(670\) | −32.4407 | −1.25329 | ||||||||
\(671\) | −2.16107 | −0.0834272 | ||||||||
\(672\) | −25.5424 | −0.985320 | ||||||||
\(673\) | 11.8069 | 0.455124 | 0.227562 | − | 0.973764i | \(-0.426925\pi\) | ||||
0.227562 | + | 0.973764i | \(0.426925\pi\) | |||||||
\(674\) | −14.6287 | −0.563476 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 64.2135 | 2.46975 | ||||||||
\(677\) | −2.23798 | −0.0860126 | −0.0430063 | − | 0.999075i | \(-0.513694\pi\) | ||||
−0.0430063 | + | 0.999075i | \(0.513694\pi\) | |||||||
\(678\) | −6.19526 | −0.237928 | ||||||||
\(679\) | −3.21321 | −0.123312 | ||||||||
\(680\) | 41.2018 | 1.58002 | ||||||||
\(681\) | −27.2511 | −1.04426 | ||||||||
\(682\) | 13.5331 | 0.518211 | ||||||||
\(683\) | 1.35333 | 0.0517836 | 0.0258918 | − | 0.999665i | \(-0.491757\pi\) | ||||
0.0258918 | + | 0.999665i | \(0.491757\pi\) | |||||||
\(684\) | 5.27631 | 0.201745 | ||||||||
\(685\) | 14.1021 | 0.538812 | ||||||||
\(686\) | 45.6020 | 1.74109 | ||||||||
\(687\) | 15.1334 | 0.577375 | ||||||||
\(688\) | 129.499 | 4.93708 | ||||||||
\(689\) | −10.4865 | −0.399505 | ||||||||
\(690\) | −3.05368 | −0.116252 | ||||||||
\(691\) | −46.8171 | −1.78100 | −0.890502 | − | 0.454979i | \(-0.849647\pi\) | ||||
−0.890502 | + | 0.454979i | \(0.849647\pi\) | |||||||
\(692\) | 53.2288 | 2.02345 | ||||||||
\(693\) | −1.40612 | −0.0534140 | ||||||||
\(694\) | 53.0835 | 2.01502 | ||||||||
\(695\) | 8.41218 | 0.319092 | ||||||||
\(696\) | −7.14283 | −0.270748 | ||||||||
\(697\) | −8.93047 | −0.338266 | ||||||||
\(698\) | 60.6550 | 2.29582 | ||||||||
\(699\) | 16.3510 | 0.618452 | ||||||||
\(700\) | −7.41911 | −0.280416 | ||||||||
\(701\) | 11.1371 | 0.420641 | 0.210321 | − | 0.977632i | \(-0.432549\pi\) | ||||
0.210321 | + | 0.977632i | \(0.432549\pi\) | |||||||
\(702\) | 13.5331 | 0.510775 | ||||||||
\(703\) | −0.673156 | −0.0253886 | ||||||||
\(704\) | 22.4264 | 0.845225 | ||||||||
\(705\) | 11.6882 | 0.440204 | ||||||||
\(706\) | −88.4416 | −3.32854 | ||||||||
\(707\) | −2.24751 | −0.0845264 | ||||||||
\(708\) | −15.5490 | −0.584366 | ||||||||
\(709\) | 4.94349 | 0.185657 | 0.0928284 | − | 0.995682i | \(-0.470409\pi\) | ||||
0.0928284 | + | 0.995682i | \(0.470409\pi\) | |||||||
\(710\) | −19.5438 | −0.733467 | ||||||||
\(711\) | −11.2787 | −0.422983 | ||||||||
\(712\) | −109.421 | −4.10073 | ||||||||
\(713\) | 5.67952 | 0.212700 | ||||||||
\(714\) | 17.6829 | 0.661767 | ||||||||
\(715\) | −5.01699 | −0.187625 | ||||||||
\(716\) | 50.9162 | 1.90283 | ||||||||
\(717\) | −19.6404 | −0.733484 | ||||||||
\(718\) | −64.5411 | −2.40865 | ||||||||
\(719\) | −35.5266 | −1.32492 | −0.662459 | − | 0.749098i | \(-0.730487\pi\) | ||||
−0.662459 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(720\) | −13.2868 | −0.495169 | ||||||||
\(721\) | 0.0433492 | 0.00161441 | ||||||||
\(722\) | 2.69746 | 0.100389 | ||||||||
\(723\) | 5.71386 | 0.212501 | ||||||||
\(724\) | 44.0620 | 1.63755 | ||||||||
\(725\) | −0.808221 | −0.0300166 | ||||||||
\(726\) | 2.69746 | 0.100112 | ||||||||
\(727\) | −4.88967 | −0.181348 | −0.0906739 | − | 0.995881i | \(-0.528902\pi\) | ||||
−0.0906739 | + | 0.995881i | \(0.528902\pi\) | |||||||
\(728\) | −62.3454 | −2.31067 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.310399 | −0.0114884 | ||||||||
\(731\) | −45.4382 | −1.68059 | ||||||||
\(732\) | −11.4025 | −0.421447 | ||||||||
\(733\) | 7.10138 | 0.262295 | 0.131148 | − | 0.991363i | \(-0.458134\pi\) | ||||
0.131148 | + | 0.991363i | \(0.458134\pi\) | |||||||
\(734\) | −34.9400 | −1.28966 | ||||||||
\(735\) | 5.02283 | 0.185270 | ||||||||
\(736\) | 20.5641 | 0.758001 | ||||||||
\(737\) | 12.0264 | 0.442998 | ||||||||
\(738\) | 5.16717 | 0.190206 | ||||||||
\(739\) | 28.3115 | 1.04145 | 0.520727 | − | 0.853723i | \(-0.325661\pi\) | ||||
0.520727 | + | 0.853723i | \(0.325661\pi\) | |||||||
\(740\) | 3.55178 | 0.130566 | ||||||||
\(741\) | 5.01699 | 0.184304 | ||||||||
\(742\) | 7.92805 | 0.291048 | ||||||||
\(743\) | −34.7657 | −1.27543 | −0.637714 | − | 0.770273i | \(-0.720120\pi\) | ||||
−0.637714 | + | 0.770273i | \(0.720120\pi\) | |||||||
\(744\) | 44.3387 | 1.62554 | ||||||||
\(745\) | −9.99865 | −0.366322 | ||||||||
\(746\) | −13.1925 | −0.483010 | ||||||||
\(747\) | −10.0518 | −0.367775 | ||||||||
\(748\) | −24.5984 | −0.899406 | ||||||||
\(749\) | 5.04694 | 0.184411 | ||||||||
\(750\) | −2.69746 | −0.0984974 | ||||||||
\(751\) | 30.9171 | 1.12818 | 0.564091 | − | 0.825713i | \(-0.309227\pi\) | ||||
0.564091 | + | 0.825713i | \(0.309227\pi\) | |||||||
\(752\) | −155.299 | −5.66317 | ||||||||
\(753\) | −15.9340 | −0.580668 | ||||||||
\(754\) | −10.9378 | −0.398330 | ||||||||
\(755\) | 10.3224 | 0.375670 | ||||||||
\(756\) | −7.41911 | −0.269830 | ||||||||
\(757\) | −7.25068 | −0.263530 | −0.131765 | − | 0.991281i | \(-0.542064\pi\) | ||||
−0.131765 | + | 0.991281i | \(0.542064\pi\) | |||||||
\(758\) | −90.4016 | −3.28353 | ||||||||
\(759\) | 1.13206 | 0.0410911 | ||||||||
\(760\) | −8.83771 | −0.320578 | ||||||||
\(761\) | −31.0893 | −1.12699 | −0.563494 | − | 0.826120i | \(-0.690543\pi\) | ||||
−0.563494 | + | 0.826120i | \(0.690543\pi\) | |||||||
\(762\) | −23.2540 | −0.842402 | ||||||||
\(763\) | 19.5531 | 0.707868 | ||||||||
\(764\) | −138.282 | −5.00286 | ||||||||
\(765\) | 4.66205 | 0.168557 | ||||||||
\(766\) | 19.4216 | 0.701731 | ||||||||
\(767\) | −14.7848 | −0.533847 | ||||||||
\(768\) | 20.3285 | 0.733540 | ||||||||
\(769\) | −4.18138 | −0.150784 | −0.0753922 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753922 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(770\) | 3.79295 | 0.136688 | ||||||||
\(771\) | −16.6133 | −0.598313 | ||||||||
\(772\) | −73.8250 | −2.65702 | ||||||||
\(773\) | −29.7300 | −1.06931 | −0.534656 | − | 0.845070i | \(-0.679559\pi\) | ||||
−0.534656 | + | 0.845070i | \(0.679559\pi\) | |||||||
\(774\) | 26.2906 | 0.944995 | ||||||||
\(775\) | 5.01699 | 0.180215 | ||||||||
\(776\) | 20.1957 | 0.724982 | ||||||||
\(777\) | 0.946536 | 0.0339568 | ||||||||
\(778\) | 12.7074 | 0.455584 | ||||||||
\(779\) | 1.91557 | 0.0686323 | ||||||||
\(780\) | −26.4712 | −0.947819 | ||||||||
\(781\) | 7.24526 | 0.259256 | ||||||||
\(782\) | −14.2364 | −0.509093 | ||||||||
\(783\) | −0.808221 | −0.0288835 | ||||||||
\(784\) | −66.7373 | −2.38348 | ||||||||
\(785\) | 23.8910 | 0.852705 | ||||||||
\(786\) | 4.81339 | 0.171688 | ||||||||
\(787\) | −30.6245 | −1.09164 | −0.545822 | − | 0.837901i | \(-0.683783\pi\) | ||||
−0.545822 | + | 0.837901i | \(0.683783\pi\) | |||||||
\(788\) | 125.187 | 4.45961 | ||||||||
\(789\) | −8.26598 | −0.294277 | ||||||||
\(790\) | 30.4238 | 1.08243 | ||||||||
\(791\) | 3.22943 | 0.114825 | ||||||||
\(792\) | 8.83771 | 0.314034 | ||||||||
\(793\) | −10.8421 | −0.385013 | ||||||||
\(794\) | −25.1587 | −0.892848 | ||||||||
\(795\) | 2.09021 | 0.0741320 | ||||||||
\(796\) | 82.7300 | 2.93229 | ||||||||
\(797\) | 9.33845 | 0.330785 | 0.165392 | − | 0.986228i | \(-0.447111\pi\) | ||||
0.165392 | + | 0.986228i | \(0.447111\pi\) | |||||||
\(798\) | −3.79295 | −0.134269 | ||||||||
\(799\) | 54.4911 | 1.92776 | ||||||||
\(800\) | 18.1652 | 0.642237 | ||||||||
\(801\) | −12.3812 | −0.437467 | ||||||||
\(802\) | −0.476490 | −0.0168254 | ||||||||
\(803\) | 0.115071 | 0.00406075 | ||||||||
\(804\) | 63.4549 | 2.23788 | ||||||||
\(805\) | 1.59181 | 0.0561038 | ||||||||
\(806\) | 67.8956 | 2.39152 | ||||||||
\(807\) | −23.7962 | −0.837665 | ||||||||
\(808\) | 14.1260 | 0.496952 | ||||||||
\(809\) | 13.3621 | 0.469787 | 0.234894 | − | 0.972021i | \(-0.424526\pi\) | ||||
0.234894 | + | 0.972021i | \(0.424526\pi\) | |||||||
\(810\) | −2.69746 | −0.0947792 | ||||||||
\(811\) | −15.2884 | −0.536849 | −0.268425 | − | 0.963301i | \(-0.586503\pi\) | ||||
−0.268425 | + | 0.963301i | \(0.586503\pi\) | |||||||
\(812\) | 5.99628 | 0.210428 | ||||||||
\(813\) | −27.3012 | −0.957495 | ||||||||
\(814\) | −1.81581 | −0.0636442 | ||||||||
\(815\) | −22.4639 | −0.786877 | ||||||||
\(816\) | −61.9437 | −2.16846 | ||||||||
\(817\) | 9.74641 | 0.340984 | ||||||||
\(818\) | −18.9172 | −0.661424 | ||||||||
\(819\) | −7.05447 | −0.246503 | ||||||||
\(820\) | −10.1071 | −0.352956 | ||||||||
\(821\) | −50.8035 | −1.77306 | −0.886528 | − | 0.462676i | \(-0.846889\pi\) | ||||
−0.886528 | + | 0.462676i | \(0.846889\pi\) | |||||||
\(822\) | −38.0398 | −1.32679 | ||||||||
\(823\) | −41.1037 | −1.43279 | −0.716393 | − | 0.697697i | \(-0.754208\pi\) | ||||
−0.716393 | + | 0.697697i | \(0.754208\pi\) | |||||||
\(824\) | −0.272458 | −0.00949152 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 11.1776 | 0.388919 | ||||||||
\(827\) | 15.3631 | 0.534228 | 0.267114 | − | 0.963665i | \(-0.413930\pi\) | ||||
0.267114 | + | 0.963665i | \(0.413930\pi\) | |||||||
\(828\) | 5.97308 | 0.207579 | ||||||||
\(829\) | 24.3478 | 0.845635 | 0.422818 | − | 0.906215i | \(-0.361041\pi\) | ||||
0.422818 | + | 0.906215i | \(0.361041\pi\) | |||||||
\(830\) | 27.1143 | 0.941151 | ||||||||
\(831\) | 7.43984 | 0.258085 | ||||||||
\(832\) | 112.513 | 3.90068 | ||||||||
\(833\) | 23.4167 | 0.811340 | ||||||||
\(834\) | −22.6915 | −0.785744 | ||||||||
\(835\) | −19.0243 | −0.658362 | ||||||||
\(836\) | 5.27631 | 0.182485 | ||||||||
\(837\) | 5.01699 | 0.173412 | ||||||||
\(838\) | 63.6218 | 2.19778 | ||||||||
\(839\) | −41.3971 | −1.42919 | −0.714593 | − | 0.699541i | \(-0.753388\pi\) | ||||
−0.714593 | + | 0.699541i | \(0.753388\pi\) | |||||||
\(840\) | 12.4269 | 0.428768 | ||||||||
\(841\) | −28.3468 | −0.977475 | ||||||||
\(842\) | −59.3150 | −2.04413 | ||||||||
\(843\) | −0.966594 | −0.0332913 | ||||||||
\(844\) | 100.783 | 3.46909 | ||||||||
\(845\) | −12.1702 | −0.418666 | ||||||||
\(846\) | −31.5285 | −1.08397 | ||||||||
\(847\) | −1.40612 | −0.0483148 | ||||||||
\(848\) | −27.7721 | −0.953699 | ||||||||
\(849\) | −8.91259 | −0.305879 | ||||||||
\(850\) | −12.5757 | −0.431343 | ||||||||
\(851\) | −0.762051 | −0.0261228 | ||||||||
\(852\) | 38.2282 | 1.30968 | ||||||||
\(853\) | −5.51540 | −0.188844 | −0.0944218 | − | 0.995532i | \(-0.530100\pi\) | ||||
−0.0944218 | + | 0.995532i | \(0.530100\pi\) | |||||||
\(854\) | 8.19683 | 0.280490 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | −31.7209 | −1.08420 | ||||||||
\(857\) | 15.1585 | 0.517804 | 0.258902 | − | 0.965904i | \(-0.416639\pi\) | ||||
0.258902 | + | 0.965904i | \(0.416639\pi\) | |||||||
\(858\) | 13.5331 | 0.462014 | ||||||||
\(859\) | −7.51823 | −0.256519 | −0.128259 | − | 0.991741i | \(-0.540939\pi\) | ||||
−0.128259 | + | 0.991741i | \(0.540939\pi\) | |||||||
\(860\) | −51.4250 | −1.75358 | ||||||||
\(861\) | −2.69351 | −0.0917947 | ||||||||
\(862\) | −17.9616 | −0.611776 | ||||||||
\(863\) | −25.2622 | −0.859936 | −0.429968 | − | 0.902844i | \(-0.641475\pi\) | ||||
−0.429968 | + | 0.902844i | \(0.641475\pi\) | |||||||
\(864\) | 18.1652 | 0.617993 | ||||||||
\(865\) | −10.0883 | −0.343011 | ||||||||
\(866\) | 74.7353 | 2.53961 | ||||||||
\(867\) | 4.73470 | 0.160799 | ||||||||
\(868\) | −37.2216 | −1.26338 | ||||||||
\(869\) | −11.2787 | −0.382603 | ||||||||
\(870\) | 2.18015 | 0.0739139 | ||||||||
\(871\) | 60.3362 | 2.04442 | ||||||||
\(872\) | −122.895 | −4.16174 | ||||||||
\(873\) | 2.28517 | 0.0773412 | ||||||||
\(874\) | 3.05368 | 0.103292 | ||||||||
\(875\) | 1.40612 | 0.0475355 | ||||||||
\(876\) | 0.607148 | 0.0205136 | ||||||||
\(877\) | −14.0647 | −0.474932 | −0.237466 | − | 0.971396i | \(-0.576317\pi\) | ||||
−0.237466 | + | 0.971396i | \(0.576317\pi\) | |||||||
\(878\) | −19.1758 | −0.647153 | ||||||||
\(879\) | 12.3764 | 0.417447 | ||||||||
\(880\) | −13.2868 | −0.447898 | ||||||||
\(881\) | 41.7826 | 1.40769 | 0.703846 | − | 0.710352i | \(-0.251464\pi\) | ||||
0.703846 | + | 0.710352i | \(0.251464\pi\) | |||||||
\(882\) | −13.5489 | −0.456215 | ||||||||
\(883\) | 34.7074 | 1.16800 | 0.583999 | − | 0.811754i | \(-0.301487\pi\) | ||||
0.583999 | + | 0.811754i | \(0.301487\pi\) | |||||||
\(884\) | −123.410 | −4.15072 | ||||||||
\(885\) | 2.94694 | 0.0990604 | ||||||||
\(886\) | −52.7982 | −1.77379 | ||||||||
\(887\) | 0.659136 | 0.0221316 | 0.0110658 | − | 0.999939i | \(-0.496478\pi\) | ||||
0.0110658 | + | 0.999939i | \(0.496478\pi\) | |||||||
\(888\) | −5.94916 | −0.199641 | ||||||||
\(889\) | 12.1217 | 0.406548 | ||||||||
\(890\) | 33.3977 | 1.11949 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −48.3228 | −1.61797 | ||||||||
\(893\) | −11.6882 | −0.391131 | ||||||||
\(894\) | 26.9710 | 0.902044 | ||||||||
\(895\) | −9.64997 | −0.322563 | ||||||||
\(896\) | −33.9773 | −1.13510 | ||||||||
\(897\) | 5.67952 | 0.189634 | ||||||||
\(898\) | 42.6271 | 1.42248 | ||||||||
\(899\) | −4.05484 | −0.135236 | ||||||||
\(900\) | 5.27631 | 0.175877 | ||||||||
\(901\) | 9.74465 | 0.324641 | ||||||||
\(902\) | 5.16717 | 0.172048 | ||||||||
\(903\) | −13.7046 | −0.456061 | ||||||||
\(904\) | −20.2976 | −0.675087 | ||||||||
\(905\) | −8.35091 | −0.277594 | ||||||||
\(906\) | −27.8442 | −0.925062 | ||||||||
\(907\) | 12.6324 | 0.419451 | 0.209726 | − | 0.977760i | \(-0.432743\pi\) | ||||
0.209726 | + | 0.977760i | \(0.432743\pi\) | |||||||
\(908\) | −143.785 | −4.77167 | ||||||||
\(909\) | 1.59838 | 0.0530150 | ||||||||
\(910\) | 19.0292 | 0.630811 | ||||||||
\(911\) | 38.3845 | 1.27174 | 0.635868 | − | 0.771798i | \(-0.280642\pi\) | ||||
0.635868 | + | 0.771798i | \(0.280642\pi\) | |||||||
\(912\) | 13.2868 | 0.439970 | ||||||||
\(913\) | −10.0518 | −0.332665 | ||||||||
\(914\) | 46.5960 | 1.54126 | ||||||||
\(915\) | 2.16107 | 0.0714427 | ||||||||
\(916\) | 79.8484 | 2.63827 | ||||||||
\(917\) | −2.50910 | −0.0828577 | ||||||||
\(918\) | −12.5757 | −0.415060 | ||||||||
\(919\) | 28.5593 | 0.942084 | 0.471042 | − | 0.882111i | \(-0.343878\pi\) | ||||
0.471042 | + | 0.882111i | \(0.343878\pi\) | |||||||
\(920\) | −10.0048 | −0.329849 | ||||||||
\(921\) | 1.81161 | 0.0596947 | ||||||||
\(922\) | 18.6481 | 0.614142 | ||||||||
\(923\) | 36.3494 | 1.19646 | ||||||||
\(924\) | −7.41911 | −0.244071 | ||||||||
\(925\) | −0.673156 | −0.0221332 | ||||||||
\(926\) | 90.5353 | 2.97518 | ||||||||
\(927\) | −0.0308290 | −0.00101256 | ||||||||
\(928\) | −14.6815 | −0.481944 | ||||||||
\(929\) | −14.6340 | −0.480125 | −0.240063 | − | 0.970757i | \(-0.577168\pi\) | ||||
−0.240063 | + | 0.970757i | \(0.577168\pi\) | |||||||
\(930\) | −13.5331 | −0.443769 | ||||||||
\(931\) | −5.02283 | −0.164617 | ||||||||
\(932\) | 86.2730 | 2.82597 | ||||||||
\(933\) | 15.5874 | 0.510308 | ||||||||
\(934\) | 0.0667807 | 0.00218513 | ||||||||
\(935\) | 4.66205 | 0.152465 | ||||||||
\(936\) | 44.3387 | 1.44926 | ||||||||
\(937\) | 1.73736 | 0.0567570 | 0.0283785 | − | 0.999597i | \(-0.490966\pi\) | ||||
0.0283785 | + | 0.999597i | \(0.490966\pi\) | |||||||
\(938\) | −45.6155 | −1.48940 | ||||||||
\(939\) | 22.4976 | 0.734182 | ||||||||
\(940\) | 61.6706 | 2.01147 | ||||||||
\(941\) | 4.73828 | 0.154463 | 0.0772317 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772317 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(942\) | −64.4450 | −2.09973 | ||||||||
\(943\) | 2.16853 | 0.0706172 | ||||||||
\(944\) | −39.1554 | −1.27440 | ||||||||
\(945\) | 1.40612 | 0.0457410 | ||||||||
\(946\) | 26.2906 | 0.854780 | ||||||||
\(947\) | −49.0444 | −1.59373 | −0.796864 | − | 0.604159i | \(-0.793509\pi\) | ||||
−0.796864 | + | 0.604159i | \(0.793509\pi\) | |||||||
\(948\) | −59.5097 | −1.93279 | ||||||||
\(949\) | 0.577308 | 0.0187402 | ||||||||
\(950\) | 2.69746 | 0.0875173 | ||||||||
\(951\) | 28.1537 | 0.912947 | ||||||||
\(952\) | 57.9346 | 1.87767 | ||||||||
\(953\) | −30.5961 | −0.991104 | −0.495552 | − | 0.868578i | \(-0.665034\pi\) | ||||
−0.495552 | + | 0.868578i | \(0.665034\pi\) | |||||||
\(954\) | −5.63826 | −0.182545 | ||||||||
\(955\) | 26.2081 | 0.848073 | ||||||||
\(956\) | −103.629 | −3.35159 | ||||||||
\(957\) | −0.808221 | −0.0261261 | ||||||||
\(958\) | 31.7964 | 1.02729 | ||||||||
\(959\) | 19.8291 | 0.640317 | ||||||||
\(960\) | −22.4264 | −0.723808 | ||||||||
\(961\) | −5.82984 | −0.188059 | ||||||||
\(962\) | −9.10991 | −0.293715 | ||||||||
\(963\) | −3.58927 | −0.115663 | ||||||||
\(964\) | 30.1481 | 0.971004 | ||||||||
\(965\) | 13.9918 | 0.450412 | ||||||||
\(966\) | −4.29384 | −0.138152 | ||||||||
\(967\) | 50.1971 | 1.61423 | 0.807115 | − | 0.590395i | \(-0.201028\pi\) | ||||
0.807115 | + | 0.590395i | \(0.201028\pi\) | |||||||
\(968\) | 8.83771 | 0.284055 | ||||||||
\(969\) | −4.66205 | −0.149767 | ||||||||
\(970\) | −6.16415 | −0.197919 | ||||||||
\(971\) | 27.0879 | 0.869294 | 0.434647 | − | 0.900601i | \(-0.356873\pi\) | ||||
0.434647 | + | 0.900601i | \(0.356873\pi\) | |||||||
\(972\) | 5.27631 | 0.169238 | ||||||||
\(973\) | 11.8285 | 0.379205 | ||||||||
\(974\) | −28.0591 | −0.899072 | ||||||||
\(975\) | 5.01699 | 0.160672 | ||||||||
\(976\) | −28.7137 | −0.919102 | ||||||||
\(977\) | −10.3603 | −0.331455 | −0.165728 | − | 0.986172i | \(-0.552997\pi\) | ||||
−0.165728 | + | 0.986172i | \(0.552997\pi\) | |||||||
\(978\) | 60.5956 | 1.93763 | ||||||||
\(979\) | −12.3812 | −0.395704 | ||||||||
\(980\) | 26.5020 | 0.846575 | ||||||||
\(981\) | −13.9057 | −0.443975 | ||||||||
\(982\) | 67.1887 | 2.14408 | ||||||||
\(983\) | −23.8319 | −0.760119 | −0.380059 | − | 0.924962i | \(-0.624096\pi\) | ||||
−0.380059 | + | 0.924962i | \(0.624096\pi\) | |||||||
\(984\) | 16.9292 | 0.539684 | ||||||||
\(985\) | −23.7263 | −0.755983 | ||||||||
\(986\) | 10.1639 | 0.323686 | ||||||||
\(987\) | 16.4350 | 0.523132 | ||||||||
\(988\) | 26.4712 | 0.842160 | ||||||||
\(989\) | 11.0335 | 0.350845 | ||||||||
\(990\) | −2.69746 | −0.0857310 | ||||||||
\(991\) | 3.72047 | 0.118185 | 0.0590923 | − | 0.998253i | \(-0.481179\pi\) | ||||
0.0590923 | + | 0.998253i | \(0.481179\pi\) | |||||||
\(992\) | 91.1346 | 2.89353 | ||||||||
\(993\) | −18.7770 | −0.595871 | ||||||||
\(994\) | −27.4809 | −0.871642 | ||||||||
\(995\) | −15.6795 | −0.497075 | ||||||||
\(996\) | −53.0362 | −1.68052 | ||||||||
\(997\) | 53.3247 | 1.68881 | 0.844406 | − | 0.535704i | \(-0.179954\pi\) | ||||
0.844406 | + | 0.535704i | \(0.179954\pi\) | |||||||
\(998\) | 38.9217 | 1.23204 | ||||||||
\(999\) | −0.673156 | −0.0212977 |
(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 | 3135.2.a.x.1.10 | ✓ | 10 | |
3.2 | odd | 2 | 9405.2.a.bm.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3135.2.a.x.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial | |
9405.2.a.bm.1.1 | 10 | 3.2 | odd | 2 |