Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.7 | ||
Root | \(1.71739 + 0.224843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.d.881.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.67271 | − | 0.449490i | 0.965740 | − | 0.259513i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.449490 | − | 1.67271i | −0.183504 | − | 0.682881i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.59592 | − | 1.50373i | 0.865306 | − | 0.501245i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 2.37874i | − | 0.717217i | −0.933488 | − | 0.358609i | \(-0.883251\pi\) | ||
0.933488 | − | 0.358609i | \(-0.116749\pi\) | |||||||
\(12\) | −1.67271 | + | 0.449490i | −0.482870 | + | 0.129757i | ||||
\(13\) | − | 3.07531i | − | 0.852938i | −0.904502 | − | 0.426469i | \(-0.859757\pi\) | ||
0.904502 | − | 0.426469i | \(-0.140243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.67271 | − | 0.449490i | 0.431892 | − | 0.116058i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.70529 | 1.14120 | 0.570600 | − | 0.821228i | \(-0.306711\pi\) | ||||
0.570600 | + | 0.821228i | \(0.306711\pi\) | |||||||
\(18\) | −1.50373 | − | 2.59592i | −0.354434 | − | 0.611863i | ||||
\(19\) | 0.527004i | 0.120903i | 0.998171 | + | 0.0604515i | \(0.0192540\pi\) | ||||
−0.998171 | + | 0.0604515i | \(0.980746\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.37874 | −0.507149 | ||||||||
\(23\) | 4.62269i | 0.963898i | 0.876199 | + | 0.481949i | \(0.160071\pi\) | ||||
−0.876199 | + | 0.481949i | \(0.839929\pi\) | |||||||
\(24\) | 0.449490 | + | 1.67271i | 0.0917518 | + | 0.341440i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.07531 | −0.603119 | ||||||||
\(27\) | 3.66630 | − | 3.68215i | 0.705580 | − | 0.708630i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.405050i | − | 0.0752159i | −0.999293 | − | 0.0376080i | \(-0.988026\pi\) | ||
0.999293 | − | 0.0376080i | \(-0.0119738\pi\) | |||||||
\(30\) | −0.449490 | − | 1.67271i | −0.0820653 | − | 0.305394i | ||||
\(31\) | − | 1.02895i | − | 0.184805i | −0.995722 | − | 0.0924024i | \(-0.970545\pi\) | ||
0.995722 | − | 0.0924024i | \(-0.0294546\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −1.06922 | − | 3.97894i | −0.186127 | − | 0.692645i | ||||
\(34\) | − | 4.70529i | − | 0.806950i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.59592 | + | 1.50373i | −0.432653 | + | 0.250622i | ||||
\(37\) | −5.54367 | −0.911374 | −0.455687 | − | 0.890140i | \(-0.650606\pi\) | ||||
−0.455687 | + | 0.890140i | \(0.650606\pi\) | |||||||
\(38\) | 0.527004 | 0.0854913 | ||||||||
\(39\) | −1.38232 | − | 5.14411i | −0.221349 | − | 0.823716i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −8.61981 | −1.34619 | −0.673094 | − | 0.739557i | \(-0.735035\pi\) | ||||
−0.673094 | + | 0.739557i | \(0.735035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5117 | 1.75552 | 0.877762 | − | 0.479097i | \(-0.159036\pi\) | ||||
0.877762 | + | 0.479097i | \(0.159036\pi\) | |||||||
\(44\) | 2.37874i | 0.358609i | ||||||||
\(45\) | 2.59592 | − | 1.50373i | 0.386976 | − | 0.224163i | ||||
\(46\) | 4.62269 | 0.681579 | ||||||||
\(47\) | −8.82018 | −1.28655 | −0.643277 | − | 0.765633i | \(-0.722426\pi\) | ||||
−0.643277 | + | 0.765633i | \(0.722426\pi\) | |||||||
\(48\) | 1.67271 | − | 0.449490i | 0.241435 | − | 0.0648783i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 7.87058 | − | 2.11498i | 1.10210 | − | 0.296157i | ||||
\(52\) | 3.07531i | 0.426469i | ||||||||
\(53\) | − | 12.2241i | − | 1.67910i | −0.543279 | − | 0.839552i | \(-0.682818\pi\) | ||
0.543279 | − | 0.839552i | \(-0.317182\pi\) | |||||||
\(54\) | −3.68215 | − | 3.66630i | −0.501077 | − | 0.498920i | ||||
\(55\) | − | 2.37874i | − | 0.320749i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.236883 | + | 0.881524i | 0.0313759 | + | 0.116761i | ||||
\(58\) | −0.405050 | −0.0531857 | ||||||||
\(59\) | 8.52051 | 1.10928 | 0.554638 | − | 0.832092i | \(-0.312857\pi\) | ||||
0.554638 | + | 0.832092i | \(0.312857\pi\) | |||||||
\(60\) | −1.67271 | + | 0.449490i | −0.215946 | + | 0.0580290i | ||||
\(61\) | 7.51223i | 0.961843i | 0.876764 | + | 0.480921i | \(0.159698\pi\) | ||||
−0.876764 | + | 0.480921i | \(0.840302\pi\) | |||||||
\(62\) | −1.02895 | −0.130677 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 3.07531i | − | 0.381446i | ||||||
\(66\) | −3.97894 | + | 1.06922i | −0.489774 | + | 0.131612i | ||||
\(67\) | 13.4124 | 1.63858 | 0.819291 | − | 0.573377i | \(-0.194367\pi\) | ||||
0.819291 | + | 0.573377i | \(0.194367\pi\) | |||||||
\(68\) | −4.70529 | −0.570600 | ||||||||
\(69\) | 2.07786 | + | 7.73243i | 0.250145 | + | 0.930875i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.7698i | − | 1.39682i | −0.715700 | − | 0.698408i | \(-0.753892\pi\) | ||
0.715700 | − | 0.698408i | \(-0.246108\pi\) | |||||||
\(72\) | 1.50373 | + | 2.59592i | 0.177217 | + | 0.305932i | ||||
\(73\) | − | 8.65046i | − | 1.01246i | −0.862398 | − | 0.506230i | \(-0.831039\pi\) | ||
0.862398 | − | 0.506230i | \(-0.168961\pi\) | |||||||
\(74\) | 5.54367i | 0.644439i | ||||||||
\(75\) | 1.67271 | − | 0.449490i | 0.193148 | − | 0.0519027i | ||||
\(76\) | − | 0.527004i | − | 0.0604515i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.14411 | + | 1.38232i | −0.582455 | + | 0.156517i | ||||
\(79\) | 1.91407 | 0.215350 | 0.107675 | − | 0.994186i | \(-0.465659\pi\) | ||||
0.107675 | + | 0.994186i | \(0.465659\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.47757 | − | 7.80714i | 0.497508 | − | 0.867460i | ||||
\(82\) | 8.61981i | 0.951899i | ||||||||
\(83\) | −12.9078 | −1.41682 | −0.708410 | − | 0.705801i | \(-0.750587\pi\) | ||||
−0.708410 | + | 0.705801i | \(0.750587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.70529 | 0.510360 | ||||||||
\(86\) | − | 11.5117i | − | 1.24134i | ||||||
\(87\) | −0.182066 | − | 0.677531i | −0.0195195 | − | 0.0726390i | ||||
\(88\) | 2.37874 | 0.253575 | ||||||||
\(89\) | −6.18780 | −0.655906 | −0.327953 | − | 0.944694i | \(-0.606359\pi\) | ||||
−0.327953 | + | 0.944694i | \(0.606359\pi\) | |||||||
\(90\) | −1.50373 | − | 2.59592i | −0.158507 | − | 0.273634i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 4.62269i | − | 0.481949i | ||||||
\(93\) | −0.462503 | − | 1.72113i | −0.0479593 | − | 0.178473i | ||||
\(94\) | 8.82018i | 0.909732i | ||||||||
\(95\) | 0.527004i | 0.0540694i | ||||||||
\(96\) | −0.449490 | − | 1.67271i | −0.0458759 | − | 0.170720i | ||||
\(97\) | 19.6433i | 1.99447i | 0.0742863 | + | 0.997237i | \(0.476332\pi\) | ||||
−0.0742863 | + | 0.997237i | \(0.523668\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.57699 | − | 6.17501i | −0.359501 | − | 0.620612i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −7.09724 | −0.706202 | −0.353101 | − | 0.935585i | \(-0.614873\pi\) | ||||
−0.353101 | + | 0.935585i | \(0.614873\pi\) | |||||||
\(102\) | −2.11498 | − | 7.87058i | −0.209414 | − | 0.779303i | ||||
\(103\) | − | 6.82964i | − | 0.672944i | −0.941693 | − | 0.336472i | \(-0.890766\pi\) | ||
0.941693 | − | 0.336472i | \(-0.109234\pi\) | |||||||
\(104\) | 3.07531 | 0.301559 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.2241 | −1.18731 | ||||||||
\(107\) | 13.1216i | 1.26851i | 0.773124 | + | 0.634255i | \(0.218693\pi\) | ||||
−0.773124 | + | 0.634255i | \(0.781307\pi\) | |||||||
\(108\) | −3.66630 | + | 3.68215i | −0.352790 | + | 0.354315i | ||||
\(109\) | 0.228271 | 0.0218644 | 0.0109322 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109322 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(110\) | −2.37874 | −0.226804 | ||||||||
\(111\) | −9.27295 | + | 2.49183i | −0.880150 | + | 0.236514i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.86352i | 0.551594i | 0.961216 | + | 0.275797i | \(0.0889417\pi\) | ||||
−0.961216 | + | 0.275797i | \(0.911058\pi\) | |||||||
\(114\) | 0.881524 | − | 0.236883i | 0.0825623 | − | 0.0221861i | ||||
\(115\) | 4.62269i | 0.431068i | ||||||||
\(116\) | 0.405050i | 0.0376080i | ||||||||
\(117\) | −4.62445 | − | 7.98326i | −0.427531 | − | 0.738052i | ||||
\(118\) | − | 8.52051i | − | 0.784377i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.449490 | + | 1.67271i | 0.0410327 | + | 0.152697i | ||||
\(121\) | 5.34159 | 0.485599 | ||||||||
\(122\) | 7.51223 | 0.680125 | ||||||||
\(123\) | −14.4184 | + | 3.87452i | −1.30007 | + | 0.349354i | ||||
\(124\) | 1.02895i | 0.0924024i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.49742 | 0.665288 | 0.332644 | − | 0.943052i | \(-0.392059\pi\) | ||||
0.332644 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 19.2558 | − | 5.17442i | 1.69538 | − | 0.455582i | ||||
\(130\) | −3.07531 | −0.269723 | ||||||||
\(131\) | 6.52049 | 0.569698 | 0.284849 | − | 0.958572i | \(-0.408057\pi\) | ||||
0.284849 | + | 0.958572i | \(0.408057\pi\) | |||||||
\(132\) | 1.06922 | + | 3.97894i | 0.0930637 | + | 0.346322i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 13.4124i | − | 1.15865i | ||||||
\(135\) | 3.66630 | − | 3.68215i | 0.315545 | − | 0.316909i | ||||
\(136\) | 4.70529i | 0.403475i | ||||||||
\(137\) | 7.24223i | 0.618746i | 0.950941 | + | 0.309373i | \(0.100119\pi\) | ||||
−0.950941 | + | 0.309373i | \(0.899881\pi\) | |||||||
\(138\) | 7.73243 | − | 2.07786i | 0.658228 | − | 0.176879i | ||||
\(139\) | 8.99820i | 0.763218i | 0.924324 | + | 0.381609i | \(0.124630\pi\) | ||||
−0.924324 | + | 0.381609i | \(0.875370\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.7536 | + | 3.96458i | −1.24248 | + | 0.333878i | ||||
\(142\) | −11.7698 | −0.987698 | ||||||||
\(143\) | −7.31537 | −0.611742 | ||||||||
\(144\) | 2.59592 | − | 1.50373i | 0.216326 | − | 0.125311i | ||||
\(145\) | − | 0.405050i | − | 0.0336376i | ||||||
\(146\) | −8.65046 | −0.715917 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.54367 | 0.455687 | ||||||||
\(149\) | − | 7.43451i | − | 0.609059i | −0.952503 | − | 0.304529i | \(-0.901501\pi\) | ||
0.952503 | − | 0.304529i | \(-0.0984992\pi\) | |||||||
\(150\) | −0.449490 | − | 1.67271i | −0.0367007 | − | 0.136576i | ||||
\(151\) | 19.4341 | 1.58152 | 0.790761 | − | 0.612125i | \(-0.209685\pi\) | ||||
0.790761 | + | 0.612125i | \(0.209685\pi\) | |||||||
\(152\) | −0.527004 | −0.0427456 | ||||||||
\(153\) | 12.2145 | − | 7.07550i | 0.987486 | − | 0.572020i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1.02895i | − | 0.0826473i | ||||||
\(156\) | 1.38232 | + | 5.14411i | 0.110674 | + | 0.411858i | ||||
\(157\) | 15.2417i | 1.21642i | 0.793777 | + | 0.608209i | \(0.208112\pi\) | ||||
−0.793777 | + | 0.608209i | \(0.791888\pi\) | |||||||
\(158\) | − | 1.91407i | − | 0.152275i | ||||||
\(159\) | −5.49460 | − | 20.4473i | −0.435750 | − | 1.62158i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.80714 | − | 4.47757i | −0.613387 | − | 0.351791i | ||||
\(163\) | −23.0876 | −1.80836 | −0.904179 | − | 0.427155i | \(-0.859516\pi\) | ||||
−0.904179 | + | 0.427155i | \(0.859516\pi\) | |||||||
\(164\) | 8.61981 | 0.673094 | ||||||||
\(165\) | −1.06922 | − | 3.97894i | −0.0832387 | − | 0.309760i | ||||
\(166\) | 12.9078i | 1.00184i | ||||||||
\(167\) | −6.03310 | −0.466856 | −0.233428 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233428 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.54245 | 0.272496 | ||||||||
\(170\) | − | 4.70529i | − | 0.360879i | ||||||
\(171\) | 0.792473 | + | 1.36806i | 0.0606019 | + | 0.104618i | ||||
\(172\) | −11.5117 | −0.877762 | ||||||||
\(173\) | −11.3332 | −0.861650 | −0.430825 | − | 0.902435i | \(-0.641777\pi\) | ||||
−0.430825 | + | 0.902435i | \(0.641777\pi\) | |||||||
\(174\) | −0.677531 | + | 0.182066i | −0.0513635 | + | 0.0138024i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.37874i | − | 0.179304i | ||||||
\(177\) | 14.2523 | − | 3.82989i | 1.07127 | − | 0.287872i | ||||
\(178\) | 6.18780i | 0.463795i | ||||||||
\(179\) | 19.1994i | 1.43503i | 0.696544 | + | 0.717514i | \(0.254720\pi\) | ||||
−0.696544 | + | 0.717514i | \(0.745280\pi\) | |||||||
\(180\) | −2.59592 | + | 1.50373i | −0.193488 | + | 0.112082i | ||||
\(181\) | 23.8389i | 1.77193i | 0.463753 | + | 0.885964i | \(0.346502\pi\) | ||||
−0.463753 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.37668 | + | 12.5658i | 0.249611 | + | 0.928889i | ||||
\(184\) | −4.62269 | −0.340789 | ||||||||
\(185\) | −5.54367 | −0.407579 | ||||||||
\(186\) | −1.72113 | + | 0.462503i | −0.126200 | + | 0.0339124i | ||||
\(187\) | − | 11.1927i | − | 0.818488i | ||||||
\(188\) | 8.82018 | 0.643277 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.527004 | 0.0382329 | ||||||||
\(191\) | 10.4546i | 0.756466i | 0.925710 | + | 0.378233i | \(0.123468\pi\) | ||||
−0.925710 | + | 0.378233i | \(0.876532\pi\) | |||||||
\(192\) | −1.67271 | + | 0.449490i | −0.120717 | + | 0.0324392i | ||||
\(193\) | −20.1184 | −1.44816 | −0.724079 | − | 0.689717i | \(-0.757735\pi\) | ||||
−0.724079 | + | 0.689717i | \(0.757735\pi\) | |||||||
\(194\) | 19.6433 | 1.41031 | ||||||||
\(195\) | −1.38232 | − | 5.14411i | −0.0989903 | − | 0.368377i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.5601i | 1.46485i | 0.680849 | + | 0.732424i | \(0.261611\pi\) | ||||
−0.680849 | + | 0.732424i | \(0.738389\pi\) | |||||||
\(198\) | −6.17501 | + | 3.57699i | −0.438839 | + | 0.254206i | ||||
\(199\) | − | 5.70991i | − | 0.404765i | −0.979307 | − | 0.202382i | \(-0.935132\pi\) | ||
0.979307 | − | 0.202382i | \(-0.0648684\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 22.4350 | − | 6.02874i | 1.58244 | − | 0.425234i | ||||
\(202\) | 7.09724i | 0.499360i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.87058 | + | 2.11498i | −0.551051 | + | 0.148078i | ||||
\(205\) | −8.61981 | −0.602034 | ||||||||
\(206\) | −6.82964 | −0.475843 | ||||||||
\(207\) | 6.95130 | + | 12.0001i | 0.483149 | + | 0.834067i | ||||
\(208\) | − | 3.07531i | − | 0.213235i | ||||||
\(209\) | 1.25360 | 0.0867136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3767 | 0.920891 | 0.460446 | − | 0.887688i | \(-0.347690\pi\) | ||||
0.460446 | + | 0.887688i | \(0.347690\pi\) | |||||||
\(212\) | 12.2241i | 0.839552i | ||||||||
\(213\) | −5.29040 | − | 19.6874i | −0.362492 | − | 1.34896i | ||||
\(214\) | 13.1216 | 0.896972 | ||||||||
\(215\) | 11.5117 | 0.785094 | ||||||||
\(216\) | 3.68215 | + | 3.66630i | 0.250539 | + | 0.249460i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 0.228271i | − | 0.0154604i | ||||||
\(219\) | −3.88830 | − | 14.4697i | −0.262747 | − | 0.977773i | ||||
\(220\) | 2.37874i | 0.160375i | ||||||||
\(221\) | − | 14.4702i | − | 0.973373i | ||||||
\(222\) | 2.49183 | + | 9.27295i | 0.167240 | + | 0.622360i | ||||
\(223\) | − | 24.5364i | − | 1.64308i | −0.570153 | − | 0.821539i | \(-0.693116\pi\) | ||
0.570153 | − | 0.821539i | \(-0.306884\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.59592 | − | 1.50373i | 0.173061 | − | 0.100249i | ||||
\(226\) | 5.86352 | 0.390036 | ||||||||
\(227\) | −20.2310 | −1.34278 | −0.671390 | − | 0.741104i | \(-0.734302\pi\) | ||||
−0.671390 | + | 0.741104i | \(0.734302\pi\) | |||||||
\(228\) | −0.236883 | − | 0.881524i | −0.0156880 | − | 0.0583804i | ||||
\(229\) | 25.1923i | 1.66475i | 0.554209 | + | 0.832377i | \(0.313021\pi\) | ||||
−0.554209 | + | 0.832377i | \(0.686979\pi\) | |||||||
\(230\) | 4.62269 | 0.304811 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.405050 | 0.0265928 | ||||||||
\(233\) | 2.40100i | 0.157295i | 0.996902 | + | 0.0786474i | \(0.0250601\pi\) | ||||
−0.996902 | + | 0.0786474i | \(0.974940\pi\) | |||||||
\(234\) | −7.98326 | + | 4.62445i | −0.521882 | + | 0.302310i | ||||
\(235\) | −8.82018 | −0.575365 | ||||||||
\(236\) | −8.52051 | −0.554638 | ||||||||
\(237\) | 3.20169 | − | 0.860357i | 0.207972 | − | 0.0558862i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6579i | 0.754086i | 0.926196 | + | 0.377043i | \(0.123059\pi\) | ||||
−0.926196 | + | 0.377043i | \(0.876941\pi\) | |||||||
\(240\) | 1.67271 | − | 0.449490i | 0.107973 | − | 0.0290145i | ||||
\(241\) | − | 14.9969i | − | 0.966038i | −0.875610 | − | 0.483019i | \(-0.839540\pi\) | ||
0.875610 | − | 0.483019i | \(-0.160460\pi\) | |||||||
\(242\) | − | 5.34159i | − | 0.343371i | ||||||
\(243\) | 3.98044 | − | 15.0717i | 0.255345 | − | 0.966850i | ||||
\(244\) | − | 7.51223i | − | 0.480921i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.87452 | + | 14.4184i | 0.247031 | + | 0.919287i | ||||
\(247\) | 1.62070 | 0.103123 | ||||||||
\(248\) | 1.02895 | 0.0653384 | ||||||||
\(249\) | −21.5911 | + | 5.80195i | −1.36828 | + | 0.367684i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 5.21694 | 0.329290 | 0.164645 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164645 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9962 | 0.691324 | ||||||||
\(254\) | − | 7.49742i | − | 0.470430i | ||||||
\(255\) | 7.87058 | − | 2.11498i | 0.492875 | − | 0.132445i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.41292 | 0.275270 | 0.137635 | − | 0.990483i | \(-0.456050\pi\) | ||||
0.137635 | + | 0.990483i | \(0.456050\pi\) | |||||||
\(258\) | −5.17442 | − | 19.2558i | −0.322145 | − | 1.19881i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.07531i | 0.190723i | ||||||||
\(261\) | −0.609088 | − | 1.05148i | −0.0377016 | − | 0.0650848i | ||||
\(262\) | − | 6.52049i | − | 0.402837i | ||||||
\(263\) | − | 14.8146i | − | 0.913509i | −0.889593 | − | 0.456754i | \(-0.849012\pi\) | ||
0.889593 | − | 0.456754i | \(-0.150988\pi\) | |||||||
\(264\) | 3.97894 | − | 1.06922i | 0.244887 | − | 0.0658060i | ||||
\(265\) | − | 12.2241i | − | 0.750918i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3504 | + | 2.78136i | −0.633434 | + | 0.170216i | ||||
\(268\) | −13.4124 | −0.819291 | ||||||||
\(269\) | −12.8575 | −0.783934 | −0.391967 | − | 0.919979i | \(-0.628205\pi\) | ||||
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(270\) | −3.68215 | − | 3.66630i | −0.224089 | − | 0.223124i | ||||
\(271\) | 10.7220i | 0.651317i | 0.945487 | + | 0.325659i | \(0.105586\pi\) | ||||
−0.945487 | + | 0.325659i | \(0.894414\pi\) | |||||||
\(272\) | 4.70529 | 0.285300 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.24223 | 0.437519 | ||||||||
\(275\) | − | 2.37874i | − | 0.143443i | ||||||
\(276\) | −2.07786 | − | 7.73243i | −0.125072 | − | 0.465437i | ||||
\(277\) | −4.06144 | −0.244028 | −0.122014 | − | 0.992528i | \(-0.538935\pi\) | ||||
−0.122014 | + | 0.992528i | \(0.538935\pi\) | |||||||
\(278\) | 8.99820 | 0.539676 | ||||||||
\(279\) | −1.54727 | − | 2.67107i | −0.0926325 | − | 0.159913i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80282i | 0.107547i | 0.998553 | + | 0.0537736i | \(0.0171249\pi\) | ||||
−0.998553 | + | 0.0537736i | \(0.982875\pi\) | |||||||
\(282\) | 3.96458 | + | 14.7536i | 0.236088 | + | 0.878564i | ||||
\(283\) | 10.4139i | 0.619044i | 0.950892 | + | 0.309522i | \(0.100169\pi\) | ||||
−0.950892 | + | 0.309522i | \(0.899831\pi\) | |||||||
\(284\) | 11.7698i | 0.698408i | ||||||||
\(285\) | 0.236883 | + | 0.881524i | 0.0140317 | + | 0.0522170i | ||||
\(286\) | 7.31537i | 0.432567i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.50373 | − | 2.59592i | −0.0886084 | − | 0.152966i | ||||
\(289\) | 5.13971 | 0.302336 | ||||||||
\(290\) | −0.405050 | −0.0237854 | ||||||||
\(291\) | 8.82947 | + | 32.8575i | 0.517593 | + | 1.92614i | ||||
\(292\) | 8.65046i | 0.506230i | ||||||||
\(293\) | 21.0309 | 1.22864 | 0.614319 | − | 0.789058i | \(-0.289431\pi\) | ||||
0.614319 | + | 0.789058i | \(0.289431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.52051 | 0.496083 | ||||||||
\(296\) | − | 5.54367i | − | 0.322219i | ||||||
\(297\) | −8.75888 | − | 8.72118i | −0.508242 | − | 0.506054i | ||||
\(298\) | −7.43451 | −0.430670 | ||||||||
\(299\) | 14.2162 | 0.822146 | ||||||||
\(300\) | −1.67271 | + | 0.449490i | −0.0965740 | + | 0.0259513i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 19.4341i | − | 1.11831i | ||||||
\(303\) | −11.8716 | + | 3.19014i | −0.682007 | + | 0.183269i | ||||
\(304\) | 0.527004i | 0.0302257i | ||||||||
\(305\) | 7.51223i | 0.430149i | ||||||||
\(306\) | −7.07550 | − | 12.2145i | −0.404479 | − | 0.698258i | ||||
\(307\) | − | 3.52243i | − | 0.201036i | −0.994935 | − | 0.100518i | \(-0.967950\pi\) | ||
0.994935 | − | 0.100518i | \(-0.0320500\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.06986 | − | 11.4240i | −0.174638 | − | 0.649889i | ||||
\(310\) | −1.02895 | −0.0584404 | ||||||||
\(311\) | −3.17187 | −0.179860 | −0.0899302 | − | 0.995948i | \(-0.528664\pi\) | ||||
−0.0899302 | + | 0.995948i | \(0.528664\pi\) | |||||||
\(312\) | 5.14411 | − | 1.38232i | 0.291228 | − | 0.0782587i | ||||
\(313\) | 29.9466i | 1.69268i | 0.532640 | + | 0.846342i | \(0.321200\pi\) | ||||
−0.532640 | + | 0.846342i | \(0.678800\pi\) | |||||||
\(314\) | 15.2417 | 0.860138 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.91407 | −0.107675 | ||||||||
\(317\) | − | 16.3905i | − | 0.920585i | −0.887767 | − | 0.460292i | \(-0.847745\pi\) | ||
0.887767 | − | 0.460292i | \(-0.152255\pi\) | |||||||
\(318\) | −20.4473 | + | 5.49460i | −1.14663 | + | 0.308122i | ||||
\(319\) | −0.963509 | −0.0539462 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 5.89802 | + | 21.9486i | 0.329195 | + | 1.22505i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.47970i | 0.137974i | ||||||||
\(324\) | −4.47757 | + | 7.80714i | −0.248754 | + | 0.433730i | ||||
\(325\) | − | 3.07531i | − | 0.170588i | ||||||
\(326\) | 23.0876i | 1.27870i | ||||||||
\(327\) | 0.381830 | − | 0.102605i | 0.0211153 | − | 0.00567409i | ||||
\(328\) | − | 8.61981i | − | 0.475950i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.97894 | + | 1.06922i | −0.219034 | + | 0.0588587i | ||||
\(331\) | 15.5958 | 0.857224 | 0.428612 | − | 0.903489i | \(-0.359003\pi\) | ||||
0.428612 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(332\) | 12.9078 | 0.708410 | ||||||||
\(333\) | −14.3909 | + | 8.33621i | −0.788617 | + | 0.456821i | ||||
\(334\) | 6.03310i | 0.330117i | ||||||||
\(335\) | 13.4124 | 0.732797 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.26228 | −0.504548 | −0.252274 | − | 0.967656i | \(-0.581178\pi\) | ||||
−0.252274 | + | 0.967656i | \(0.581178\pi\) | |||||||
\(338\) | − | 3.54245i | − | 0.192684i | ||||||
\(339\) | 2.63560 | + | 9.80797i | 0.143146 | + | 0.532696i | ||||
\(340\) | −4.70529 | −0.255180 | ||||||||
\(341\) | −2.44760 | −0.132545 | ||||||||
\(342\) | 1.36806 | − | 0.792473i | 0.0739761 | − | 0.0428520i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.5117i | 0.620671i | ||||||||
\(345\) | 2.07786 | + | 7.73243i | 0.111868 | + | 0.416300i | ||||
\(346\) | 11.3332i | 0.609279i | ||||||||
\(347\) | 17.1376i | 0.919994i | 0.887920 | + | 0.459997i | \(0.152150\pi\) | ||||
−0.887920 | + | 0.459997i | \(0.847850\pi\) | |||||||
\(348\) | 0.182066 | + | 0.677531i | 0.00975977 | + | 0.0363195i | ||||
\(349\) | 4.28660i | 0.229457i | 0.993397 | + | 0.114728i | \(0.0365998\pi\) | ||||
−0.993397 | + | 0.114728i | \(0.963400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3238 | − | 11.2750i | −0.604418 | − | 0.601816i | ||||
\(352\) | −2.37874 | −0.126787 | ||||||||
\(353\) | 4.02994 | 0.214492 | 0.107246 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107246 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(354\) | −3.82989 | − | 14.2523i | −0.203556 | − | 0.757503i | ||||
\(355\) | − | 11.7698i | − | 0.624675i | ||||||
\(356\) | 6.18780 | 0.327953 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.1994 | 1.01472 | ||||||||
\(359\) | 15.3930i | 0.812412i | 0.913782 | + | 0.406206i | \(0.133148\pi\) | ||||
−0.913782 | + | 0.406206i | \(0.866852\pi\) | |||||||
\(360\) | 1.50373 | + | 2.59592i | 0.0792537 | + | 0.136817i | ||||
\(361\) | 18.7223 | 0.985382 | ||||||||
\(362\) | 23.8389 | 1.25294 | ||||||||
\(363\) | 8.93494 | − | 2.40100i | 0.468963 | − | 0.126020i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.65046i | − | 0.452786i | ||||||
\(366\) | 12.5658 | − | 3.37668i | 0.656824 | − | 0.176502i | ||||
\(367\) | − | 2.00965i | − | 0.104903i | −0.998623 | − | 0.0524514i | \(-0.983297\pi\) | ||
0.998623 | − | 0.0524514i | \(-0.0167035\pi\) | |||||||
\(368\) | 4.62269i | 0.240975i | ||||||||
\(369\) | −22.3763 | + | 12.9619i | −1.16486 | + | 0.674770i | ||||
\(370\) | 5.54367i | 0.288202i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.462503 | + | 1.72113i | 0.0239797 | + | 0.0892367i | ||||
\(373\) | 8.85050 | 0.458262 | 0.229131 | − | 0.973396i | \(-0.426412\pi\) | ||||
0.229131 | + | 0.973396i | \(0.426412\pi\) | |||||||
\(374\) | −11.1927 | −0.578758 | ||||||||
\(375\) | 1.67271 | − | 0.449490i | 0.0863784 | − | 0.0232116i | ||||
\(376\) | − | 8.82018i | − | 0.454866i | ||||||
\(377\) | −1.24566 | −0.0641546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4030 | 0.585731 | 0.292865 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292865 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(380\) | − | 0.527004i | − | 0.0270347i | ||||||
\(381\) | 12.5410 | − | 3.37002i | 0.642495 | − | 0.172651i | ||||
\(382\) | 10.4546 | 0.534902 | ||||||||
\(383\) | 8.73221 | 0.446195 | 0.223098 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223098 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(384\) | 0.449490 | + | 1.67271i | 0.0229380 | + | 0.0853601i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.1184i | 1.02400i | ||||||||
\(387\) | 29.8835 | − | 17.3106i | 1.51906 | − | 0.879947i | ||||
\(388\) | − | 19.6433i | − | 0.997237i | ||||||
\(389\) | 27.3884i | 1.38865i | 0.719663 | + | 0.694324i | \(0.244296\pi\) | ||||
−0.719663 | + | 0.694324i | \(0.755704\pi\) | |||||||
\(390\) | −5.14411 | + | 1.38232i | −0.260482 | + | 0.0699967i | ||||
\(391\) | 21.7511i | 1.10000i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9069 | − | 2.93090i | 0.550179 | − | 0.147844i | ||||
\(394\) | 20.5601 | 1.03580 | ||||||||
\(395\) | 1.91407 | 0.0963074 | ||||||||
\(396\) | 3.57699 | + | 6.17501i | 0.179751 | + | 0.310306i | ||||
\(397\) | − | 1.55639i | − | 0.0781127i | −0.999237 | − | 0.0390564i | \(-0.987565\pi\) | ||
0.999237 | − | 0.0390564i | \(-0.0124352\pi\) | |||||||
\(398\) | −5.70991 | −0.286212 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 34.6328i | 1.72948i | 0.502218 | + | 0.864741i | \(0.332517\pi\) | ||||
−0.502218 | + | 0.864741i | \(0.667483\pi\) | |||||||
\(402\) | −6.02874 | − | 22.4350i | −0.300686 | − | 1.11896i | ||||
\(403\) | −3.16434 | −0.157627 | ||||||||
\(404\) | 7.09724 | 0.353101 | ||||||||
\(405\) | 4.47757 | − | 7.80714i | 0.222492 | − | 0.387940i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1870i | 0.653653i | ||||||||
\(408\) | 2.11498 | + | 7.87058i | 0.104707 | + | 0.389652i | ||||
\(409\) | − | 13.5926i | − | 0.672111i | −0.941842 | − | 0.336056i | \(-0.890907\pi\) | ||
0.941842 | − | 0.336056i | \(-0.109093\pi\) | |||||||
\(410\) | 8.61981i | 0.425702i | ||||||||
\(411\) | 3.25531 | + | 12.1142i | 0.160573 | + | 0.597547i | ||||
\(412\) | 6.82964i | 0.336472i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.0001 | − | 6.95130i | 0.589774 | − | 0.341638i | ||||
\(415\) | −12.9078 | −0.633621 | ||||||||
\(416\) | −3.07531 | −0.150780 | ||||||||
\(417\) | 4.04461 | + | 15.0514i | 0.198065 | + | 0.737069i | ||||
\(418\) | − | 1.25360i | − | 0.0613158i | ||||||
\(419\) | 17.5962 | 0.859631 | 0.429815 | − | 0.902917i | \(-0.358579\pi\) | ||||
0.429815 | + | 0.902917i | \(0.358579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.7006 | −1.54499 | −0.772497 | − | 0.635019i | \(-0.780992\pi\) | ||||
−0.772497 | + | 0.635019i | \(0.780992\pi\) | |||||||
\(422\) | − | 13.3767i | − | 0.651169i | ||||||
\(423\) | −22.8964 | + | 13.2632i | −1.11326 | + | 0.644879i | ||||
\(424\) | 12.2241 | 0.593653 | ||||||||
\(425\) | 4.70529 | 0.228240 | ||||||||
\(426\) | −19.6874 | + | 5.29040i | −0.953859 | + | 0.256321i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 13.1216i | − | 0.634255i | ||||||
\(429\) | −12.2365 | + | 3.28819i | −0.590784 | + | 0.158755i | ||||
\(430\) | − | 11.5117i | − | 0.555145i | ||||||
\(431\) | − | 10.3717i | − | 0.499587i | −0.968299 | − | 0.249793i | \(-0.919637\pi\) | ||
0.968299 | − | 0.249793i | \(-0.0803627\pi\) | |||||||
\(432\) | 3.66630 | − | 3.68215i | 0.176395 | − | 0.177158i | ||||
\(433\) | − | 41.0608i | − | 1.97326i | −0.162987 | − | 0.986628i | \(-0.552113\pi\) | ||
0.162987 | − | 0.986628i | \(-0.447887\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.182066 | − | 0.677531i | −0.00872940 | − | 0.0324851i | ||||
\(436\) | −0.228271 | −0.0109322 | ||||||||
\(437\) | −2.43618 | −0.116538 | ||||||||
\(438\) | −14.4697 | + | 3.88830i | −0.691390 | + | 0.185790i | ||||
\(439\) | 10.6387i | 0.507756i | 0.967236 | + | 0.253878i | \(0.0817062\pi\) | ||||
−0.967236 | + | 0.253878i | \(0.918294\pi\) | |||||||
\(440\) | 2.37874 | 0.113402 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.4702 | −0.688279 | ||||||||
\(443\) | − | 20.3371i | − | 0.966247i | −0.875552 | − | 0.483123i | \(-0.839502\pi\) | ||
0.875552 | − | 0.483123i | \(-0.160498\pi\) | |||||||
\(444\) | 9.27295 | − | 2.49183i | 0.440075 | − | 0.118257i | ||||
\(445\) | −6.18780 | −0.293330 | ||||||||
\(446\) | −24.5364 | −1.16183 | ||||||||
\(447\) | −3.34174 | − | 12.4358i | −0.158059 | − | 0.588192i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6792i | 0.503983i | 0.967730 | + | 0.251991i | \(0.0810854\pi\) | ||||
−0.967730 | + | 0.251991i | \(0.918915\pi\) | |||||||
\(450\) | −1.50373 | − | 2.59592i | −0.0708867 | − | 0.122373i | ||||
\(451\) | 20.5043i | 0.965510i | ||||||||
\(452\) | − | 5.86352i | − | 0.275797i | ||||||
\(453\) | 32.5076 | − | 8.73543i | 1.52734 | − | 0.410426i | ||||
\(454\) | 20.2310i | 0.949489i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.881524 | + | 0.236883i | −0.0412811 | + | 0.0110931i | ||||
\(457\) | 1.04759 | 0.0490044 | 0.0245022 | − | 0.999700i | \(-0.492200\pi\) | ||||
0.0245022 | + | 0.999700i | \(0.492200\pi\) | |||||||
\(458\) | 25.1923 | 1.17716 | ||||||||
\(459\) | 17.2510 | − | 17.3256i | 0.805208 | − | 0.808688i | ||||
\(460\) | − | 4.62269i | − | 0.215534i | ||||||
\(461\) | 0.442723 | 0.0206197 | 0.0103098 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103098 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.83270 | 0.0851730 | 0.0425865 | − | 0.999093i | \(-0.486440\pi\) | ||||
0.0425865 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(464\) | − | 0.405050i | − | 0.0188040i | ||||||
\(465\) | −0.462503 | − | 1.72113i | −0.0214481 | − | 0.0798157i | ||||
\(466\) | 2.40100 | 0.111224 | ||||||||
\(467\) | 3.33622 | 0.154382 | 0.0771909 | − | 0.997016i | \(-0.475405\pi\) | ||||
0.0771909 | + | 0.997016i | \(0.475405\pi\) | |||||||
\(468\) | 4.62445 | + | 7.98326i | 0.213765 | + | 0.369026i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.82018i | 0.406844i | ||||||||
\(471\) | 6.85099 | + | 25.4949i | 0.315677 | + | 1.17474i | ||||
\(472\) | 8.52051i | 0.392188i | ||||||||
\(473\) | − | 27.3834i | − | 1.25909i | ||||||
\(474\) | −0.860357 | − | 3.20169i | −0.0395175 | − | 0.147058i | ||||
\(475\) | 0.527004i | 0.0241806i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.3817 | − | 31.7326i | −0.841642 | − | 1.45294i | ||||
\(478\) | 11.6579 | 0.533219 | ||||||||
\(479\) | −39.9415 | −1.82497 | −0.912487 | − | 0.409105i | \(-0.865841\pi\) | ||||
−0.912487 | + | 0.409105i | \(0.865841\pi\) | |||||||
\(480\) | −0.449490 | − | 1.67271i | −0.0205163 | − | 0.0763484i | ||||
\(481\) | 17.0485i | 0.777346i | ||||||||
\(482\) | −14.9969 | −0.683092 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.34159 | −0.242800 | ||||||||
\(485\) | 19.6433i | 0.891956i | ||||||||
\(486\) | −15.0717 | − | 3.98044i | −0.683666 | − | 0.180556i | ||||
\(487\) | 25.7832 | 1.16835 | 0.584175 | − | 0.811628i | \(-0.301418\pi\) | ||||
0.584175 | + | 0.811628i | \(0.301418\pi\) | |||||||
\(488\) | −7.51223 | −0.340063 | ||||||||
\(489\) | −38.6188 | + | 10.3776i | −1.74640 | + | 0.469293i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.6154i | − | 1.11088i | −0.831557 | − | 0.555439i | \(-0.812550\pi\) | ||
0.831557 | − | 0.555439i | \(-0.187450\pi\) | |||||||
\(492\) | 14.4184 | − | 3.87452i | 0.650034 | − | 0.174677i | ||||
\(493\) | − | 1.90588i | − | 0.0858364i | ||||||
\(494\) | − | 1.62070i | − | 0.0729188i | ||||||
\(495\) | −3.57699 | − | 6.17501i | −0.160774 | − | 0.277546i | ||||
\(496\) | − | 1.02895i | − | 0.0462012i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.80195 | + | 21.5911i | 0.259992 | + | 0.967520i | ||||
\(499\) | 32.2260 | 1.44263 | 0.721316 | − | 0.692606i | \(-0.243538\pi\) | ||||
0.721316 | + | 0.692606i | \(0.243538\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −10.0916 | + | 2.71182i | −0.450861 | + | 0.121155i | ||||
\(502\) | − | 5.21694i | − | 0.232843i | ||||||
\(503\) | −19.8072 | −0.883160 | −0.441580 | − | 0.897222i | \(-0.645582\pi\) | ||||
−0.441580 | + | 0.897222i | \(0.645582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.09724 | −0.315823 | ||||||||
\(506\) | − | 10.9962i | − | 0.488840i | ||||||
\(507\) | 5.92549 | − | 1.59230i | 0.263160 | − | 0.0707163i | ||||
\(508\) | −7.49742 | −0.332644 | ||||||||
\(509\) | 23.3685 | 1.03579 | 0.517895 | − | 0.855444i | \(-0.326716\pi\) | ||||
0.517895 | + | 0.855444i | \(0.326716\pi\) | |||||||
\(510\) | −2.11498 | − | 7.87058i | −0.0936529 | − | 0.348515i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.94051 | + | 1.93215i | 0.0856755 | + | 0.0853067i | ||||
\(514\) | − | 4.41292i | − | 0.194646i | ||||||
\(515\) | − | 6.82964i | − | 0.300950i | ||||||
\(516\) | −19.2558 | + | 5.17442i | −0.847689 | + | 0.227791i | ||||
\(517\) | 20.9809i | 0.922739i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.9572 | + | 5.09418i | −0.832130 | + | 0.223610i | ||||
\(520\) | 3.07531 | 0.134861 | ||||||||
\(521\) | 7.16731 | 0.314006 | 0.157003 | − | 0.987598i | \(-0.449817\pi\) | ||||
0.157003 | + | 0.987598i | \(0.449817\pi\) | |||||||
\(522\) | −1.05148 | + | 0.609088i | −0.0460219 | + | 0.0266590i | ||||
\(523\) | − | 3.00258i | − | 0.131294i | −0.997843 | − | 0.0656469i | \(-0.979089\pi\) | ||
0.997843 | − | 0.0656469i | \(-0.0209111\pi\) | |||||||
\(524\) | −6.52049 | −0.284849 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8146 | −0.645948 | ||||||||
\(527\) | − | 4.84150i | − | 0.210899i | ||||||
\(528\) | −1.06922 | − | 3.97894i | −0.0465319 | − | 0.173161i | ||||
\(529\) | 1.63070 | 0.0709002 | ||||||||
\(530\) | −12.2241 | −0.530979 | ||||||||
\(531\) | 22.1185 | − | 12.8126i | 0.959863 | − | 0.556019i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.5086i | 1.14822i | ||||||||
\(534\) | 2.78136 | + | 10.3504i | 0.120361 | + | 0.447906i | ||||
\(535\) | 13.1216i | 0.567295i | ||||||||
\(536\) | 13.4124i | 0.579327i | ||||||||
\(537\) | 8.62993 | + | 32.1150i | 0.372409 | + | 1.38586i | ||||
\(538\) | 12.8575i | 0.554325i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.66630 | + | 3.68215i | −0.157773 | + | 0.158455i | ||||
\(541\) | −40.5334 | −1.74267 | −0.871334 | − | 0.490691i | \(-0.836744\pi\) | ||||
−0.871334 | + | 0.490691i | \(0.836744\pi\) | |||||||
\(542\) | 10.7220 | 0.460551 | ||||||||
\(543\) | 10.7153 | + | 39.8755i | 0.459839 | + | 1.71122i | ||||
\(544\) | − | 4.70529i | − | 0.201737i | ||||||
\(545\) | 0.228271 | 0.00977804 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2050 | −0.949415 | −0.474708 | − | 0.880144i | \(-0.657446\pi\) | ||||
−0.474708 | + | 0.880144i | \(0.657446\pi\) | |||||||
\(548\) | − | 7.24223i | − | 0.309373i | ||||||
\(549\) | 11.2964 | + | 19.5011i | 0.482119 | + | 0.832288i | ||||
\(550\) | −2.37874 | −0.101430 | ||||||||
\(551\) | 0.213463 | 0.00909383 | ||||||||
\(552\) | −7.73243 | + | 2.07786i | −0.329114 | + | 0.0884394i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.06144i | 0.172554i | ||||||||
\(555\) | −9.27295 | + | 2.49183i | −0.393615 | + | 0.105772i | ||||
\(556\) | − | 8.99820i | − | 0.381609i | ||||||
\(557\) | − | 22.3893i | − | 0.948663i | −0.880346 | − | 0.474332i | \(-0.842690\pi\) | ||
0.880346 | − | 0.474332i | \(-0.157310\pi\) | |||||||
\(558\) | −2.67107 | + | 1.54727i | −0.113075 | + | 0.0655010i | ||||
\(559\) | − | 35.4022i | − | 1.49735i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.03099 | − | 18.7221i | −0.212409 | − | 0.790446i | ||||
\(562\) | 1.80282 | 0.0760473 | ||||||||
\(563\) | 19.5160 | 0.822499 | 0.411250 | − | 0.911523i | \(-0.365092\pi\) | ||||
0.411250 | + | 0.911523i | \(0.365092\pi\) | |||||||
\(564\) | 14.7536 | − | 3.96458i | 0.621238 | − | 0.166939i | ||||
\(565\) | 5.86352i | 0.246680i | ||||||||
\(566\) | 10.4139 | 0.437730 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.7698 | 0.493849 | ||||||||
\(569\) | − | 5.99419i | − | 0.251290i | −0.992075 | − | 0.125645i | \(-0.959900\pi\) | ||
0.992075 | − | 0.125645i | \(-0.0401000\pi\) | |||||||
\(570\) | 0.881524 | − | 0.236883i | 0.0369230 | − | 0.00992194i | ||||
\(571\) | 11.2819 | 0.472131 | 0.236065 | − | 0.971737i | \(-0.424142\pi\) | ||||
0.236065 | + | 0.971737i | \(0.424142\pi\) | |||||||
\(572\) | 7.31537 | 0.305871 | ||||||||
\(573\) | 4.69923 | + | 17.4875i | 0.196313 | + | 0.730549i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.62269i | 0.192780i | ||||||||
\(576\) | −2.59592 | + | 1.50373i | −0.108163 | + | 0.0626556i | ||||
\(577\) | − | 17.8477i | − | 0.743008i | −0.928431 | − | 0.371504i | \(-0.878842\pi\) | ||
0.928431 | − | 0.371504i | \(-0.121158\pi\) | |||||||
\(578\) | − | 5.13971i | − | 0.213784i | ||||||
\(579\) | −33.6523 | + | 9.04305i | −1.39854 | + | 0.375816i | ||||
\(580\) | 0.405050i | 0.0168188i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 32.8575 | − | 8.82947i | 1.36199 | − | 0.365993i | ||||
\(583\) | −29.0779 | −1.20428 | ||||||||
\(584\) | 8.65046 | 0.357959 | ||||||||
\(585\) | −4.62445 | − | 7.98326i | −0.191198 | − | 0.330067i | ||||
\(586\) | − | 21.0309i | − | 0.868779i | ||||||
\(587\) | −7.42282 | −0.306373 | −0.153186 | − | 0.988197i | \(-0.548953\pi\) | ||||
−0.153186 | + | 0.988197i | \(0.548953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.542260 | 0.0223434 | ||||||||
\(590\) | − | 8.52051i | − | 0.350784i | ||||||
\(591\) | 9.24158 | + | 34.3911i | 0.380148 | + | 1.41466i | ||||
\(592\) | −5.54367 | −0.227843 | ||||||||
\(593\) | −36.9646 | −1.51796 | −0.758978 | − | 0.651116i | \(-0.774301\pi\) | ||||
−0.758978 | + | 0.651116i | \(0.774301\pi\) | |||||||
\(594\) | −8.72118 | + | 8.75888i | −0.357834 | + | 0.359381i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.43451i | 0.304529i | ||||||||
\(597\) | −2.56655 | − | 9.55102i | −0.105042 | − | 0.390897i | ||||
\(598\) | − | 14.2162i | − | 0.581345i | ||||||
\(599\) | − | 34.1065i | − | 1.39355i | −0.717288 | − | 0.696777i | \(-0.754617\pi\) | ||
0.717288 | − | 0.696777i | \(-0.245383\pi\) | |||||||
\(600\) | 0.449490 | + | 1.67271i | 0.0183504 | + | 0.0682881i | ||||
\(601\) | 19.2247i | 0.784192i | 0.919924 | + | 0.392096i | \(0.128250\pi\) | ||||
−0.919924 | + | 0.392096i | \(0.871750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.8174 | − | 20.1687i | 1.41787 | − | 0.821331i | ||||
\(604\) | −19.4341 | −0.790761 | ||||||||
\(605\) | 5.34159 | 0.217167 | ||||||||
\(606\) | 3.19014 | + | 11.8716i | 0.129591 | + | 0.482252i | ||||
\(607\) | − | 23.6482i | − | 0.959849i | −0.877310 | − | 0.479925i | \(-0.840664\pi\) | ||
0.877310 | − | 0.479925i | \(-0.159336\pi\) | |||||||
\(608\) | 0.527004 | 0.0213728 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.51223 | 0.304161 | ||||||||
\(611\) | 27.1248i | 1.09735i | ||||||||
\(612\) | −12.2145 | + | 7.07550i | −0.493743 | + | 0.286010i | ||||
\(613\) | −29.9776 | −1.21078 | −0.605392 | − | 0.795928i | \(-0.706984\pi\) | ||||
−0.605392 | + | 0.795928i | \(0.706984\pi\) | |||||||
\(614\) | −3.52243 | −0.142154 | ||||||||
\(615\) | −14.4184 | + | 3.87452i | −0.581408 | + | 0.156236i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.68803i | 0.390026i | 0.980801 | + | 0.195013i | \(0.0624748\pi\) | ||||
−0.980801 | + | 0.195013i | \(0.937525\pi\) | |||||||
\(618\) | −11.4240 | + | 3.06986i | −0.459541 | + | 0.123488i | ||||
\(619\) | 6.19797i | 0.249118i | 0.992212 | + | 0.124559i | \(0.0397515\pi\) | ||||
−0.992212 | + | 0.124559i | \(0.960248\pi\) | |||||||
\(620\) | 1.02895i | 0.0413236i | ||||||||
\(621\) | 17.0215 | + | 16.9482i | 0.683047 | + | 0.680107i | ||||
\(622\) | 3.17187i | 0.127180i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.38232 | − | 5.14411i | −0.0553372 | − | 0.205929i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.9466 | 1.19691 | ||||||||
\(627\) | 2.09692 | − | 0.563483i | 0.0837428 | − | 0.0225034i | ||||
\(628\) | − | 15.2417i | − | 0.608209i | ||||||
\(629\) | −26.0846 | −1.04006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.86885 | −0.313254 | −0.156627 | − | 0.987658i | \(-0.550062\pi\) | ||||
−0.156627 | + | 0.987658i | \(0.550062\pi\) | |||||||
\(632\) | 1.91407i | 0.0761377i | ||||||||
\(633\) | 22.3754 | − | 6.01271i | 0.889341 | − | 0.238984i | ||||
\(634\) | −16.3905 | −0.650952 | ||||||||
\(635\) | 7.49742 | 0.297526 | ||||||||
\(636\) | 5.49460 | + | 20.4473i | 0.217875 | + | 0.810789i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.963509i | 0.0381457i | ||||||||
\(639\) | −17.6986 | − | 30.5534i | −0.700146 | − | 1.20867i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − | 23.4908i | − | 0.927832i | −0.885879 | − | 0.463916i | \(-0.846444\pi\) | ||
0.885879 | − | 0.463916i | \(-0.153556\pi\) | |||||||
\(642\) | 21.9486 | − | 5.89802i | 0.866241 | − | 0.232776i | ||||
\(643\) | − | 13.9315i | − | 0.549405i | −0.961529 | − | 0.274702i | \(-0.911421\pi\) | ||
0.961529 | − | 0.274702i | \(-0.0885793\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.2558 | − | 5.17442i | 0.758196 | − | 0.203742i | ||||
\(646\) | 2.47970 | 0.0975626 | ||||||||
\(647\) | −10.7038 | −0.420810 | −0.210405 | − | 0.977614i | \(-0.567478\pi\) | ||||
−0.210405 | + | 0.977614i | \(0.567478\pi\) | |||||||
\(648\) | 7.80714 | + | 4.47757i | 0.306693 | + | 0.175895i | ||||
\(649\) | − | 20.2681i | − | 0.795592i | ||||||
\(650\) | −3.07531 | −0.120624 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.0876 | 0.904179 | ||||||||
\(653\) | − | 19.0444i | − | 0.745264i | −0.927979 | − | 0.372632i | \(-0.878455\pi\) | ||
0.927979 | − | 0.372632i | \(-0.121545\pi\) | |||||||
\(654\) | −0.102605 | − | 0.381830i | −0.00401219 | − | 0.0149308i | ||||
\(655\) | 6.52049 | 0.254776 | ||||||||
\(656\) | −8.61981 | −0.336547 | ||||||||
\(657\) | −13.0080 | − | 22.4559i | −0.507490 | − | 0.876087i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.3453i | 0.948359i | 0.880428 | + | 0.474179i | \(0.157255\pi\) | ||||
−0.880428 | + | 0.474179i | \(0.842745\pi\) | |||||||
\(660\) | 1.06922 | + | 3.97894i | 0.0416194 | + | 0.154880i | ||||
\(661\) | 38.7658i | 1.50782i | 0.656980 | + | 0.753908i | \(0.271834\pi\) | ||||
−0.656980 | + | 0.753908i | \(0.728166\pi\) | |||||||
\(662\) | − | 15.5958i | − | 0.606149i | ||||||
\(663\) | −6.50423 | − | 24.2045i | −0.252603 | − | 0.940025i | ||||
\(664\) | − | 12.9078i | − | 0.500922i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.33621 | + | 14.3909i | 0.323021 | + | 0.557636i | ||||
\(667\) | 1.87242 | 0.0725005 | ||||||||
\(668\) | 6.03310 | 0.233428 | ||||||||
\(669\) | −11.0289 | − | 41.0423i | −0.426401 | − | 1.58679i | ||||
\(670\) | − | 13.4124i | − | 0.518165i | ||||||
\(671\) | 17.8696 | 0.689850 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2944 | −0.628102 | −0.314051 | − | 0.949406i | \(-0.601686\pi\) | ||||
−0.314051 | + | 0.949406i | \(0.601686\pi\) | |||||||
\(674\) | 9.26228i | 0.356770i | ||||||||
\(675\) | 3.66630 | − | 3.68215i | 0.141116 | − | 0.141726i | ||||
\(676\) | −3.54245 | −0.136248 | ||||||||
\(677\) | −49.6659 | −1.90881 | −0.954407 | − | 0.298507i | \(-0.903511\pi\) | ||||
−0.954407 | + | 0.298507i | \(0.903511\pi\) | |||||||
\(678\) | 9.80797 | − | 2.63560i | 0.376673 | − | 0.101219i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.70529i | 0.180439i | ||||||||
\(681\) | −33.8406 | + | 9.09365i | −1.29678 | + | 0.348469i | ||||
\(682\) | 2.44760i | 0.0937236i | ||||||||
\(683\) | − | 8.27581i | − | 0.316665i | −0.987386 | − | 0.158332i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158332i | \(-0.0506118\pi\) | |||||||
\(684\) | −0.792473 | − | 1.36806i | −0.0303010 | − | 0.0523090i | ||||
\(685\) | 7.24223i | 0.276712i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3237 | + | 42.1394i | 0.432026 | + | 1.60772i | ||||
\(688\) | 11.5117 | 0.438881 | ||||||||
\(689\) | −37.5928 | −1.43217 | ||||||||
\(690\) | 7.73243 | − | 2.07786i | 0.294368 | − | 0.0791026i | ||||
\(691\) | − | 15.8177i | − | 0.601733i | −0.953666 | − | 0.300867i | \(-0.902724\pi\) | ||
0.953666 | − | 0.300867i | \(-0.0972759\pi\) | |||||||
\(692\) | 11.3332 | 0.430825 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.1376 | 0.650534 | ||||||||
\(695\) | 8.99820i | 0.341321i | ||||||||
\(696\) | 0.677531 | − | 0.182066i | 0.0256818 | − | 0.00690120i | ||||
\(697\) | −40.5587 | −1.53627 | ||||||||
\(698\) | 4.28660 | 0.162250 | ||||||||
\(699\) | 1.07923 | + | 4.01618i | 0.0408201 | + | 0.151906i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.6281i | − | 1.68558i | −0.538243 | − | 0.842790i | \(-0.680912\pi\) | ||
0.538243 | − | 0.842790i | \(-0.319088\pi\) | |||||||
\(702\) | −11.2750 | + | 11.3238i | −0.425548 | + | 0.427388i | ||||
\(703\) | − | 2.92153i | − | 0.110188i | ||||||
\(704\) | 2.37874i | 0.0896521i | ||||||||
\(705\) | −14.7536 | + | 3.96458i | −0.555653 | + | 0.149315i | ||||
\(706\) | − | 4.02994i | − | 0.151669i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.2523 | + | 3.82989i | −0.535636 | + | 0.143936i | ||||
\(709\) | −33.8584 | −1.27158 | −0.635790 | − | 0.771862i | \(-0.719325\pi\) | ||||
−0.635790 | + | 0.771862i | \(0.719325\pi\) | |||||||
\(710\) | −11.7698 | −0.441712 | ||||||||
\(711\) | 4.96877 | − | 2.87825i | 0.186343 | − | 0.107943i | ||||
\(712\) | − | 6.18780i | − | 0.231898i | ||||||
\(713\) | 4.75652 | 0.178133 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.31537 | −0.273579 | ||||||||
\(716\) | − | 19.1994i | − | 0.717514i | ||||||
\(717\) | 5.24011 | + | 19.5003i | 0.195695 | + | 0.728251i | ||||
\(718\) | 15.3930 | 0.574462 | ||||||||
\(719\) | 18.9821 | 0.707913 | 0.353956 | − | 0.935262i | \(-0.384836\pi\) | ||||
0.353956 | + | 0.935262i | \(0.384836\pi\) | |||||||
\(720\) | 2.59592 | − | 1.50373i | 0.0967441 | − | 0.0560409i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.7223i | − | 0.696771i | ||||||
\(723\) | −6.74098 | − | 25.0855i | −0.250700 | − | 0.932942i | ||||
\(724\) | − | 23.8389i | − | 0.885964i | ||||||
\(725\) | − | 0.405050i | − | 0.0150432i | ||||||
\(726\) | −2.40100 | − | 8.93494i | −0.0891093 | − | 0.331607i | ||||
\(727\) | 3.67665i | 0.136360i | 0.997673 | + | 0.0681798i | \(0.0217191\pi\) | ||||
−0.997673 | + | 0.0681798i | \(0.978281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.116463 | − | 26.9997i | −0.00431345 | − | 0.999991i | ||||
\(730\) | −8.65046 | −0.320168 | ||||||||
\(731\) | 54.1660 | 2.00340 | ||||||||
\(732\) | −3.37668 | − | 12.5658i | −0.124806 | − | 0.464445i | ||||
\(733\) | − | 8.19545i | − | 0.302706i | −0.988480 | − | 0.151353i | \(-0.951637\pi\) | ||
0.988480 | − | 0.151353i | \(-0.0483630\pi\) | |||||||
\(734\) | −2.00965 | −0.0741776 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.62269 | 0.170395 | ||||||||
\(737\) | − | 31.9046i | − | 1.17522i | ||||||
\(738\) | 12.9619 | + | 22.3763i | 0.477134 | + | 0.823684i | ||||
\(739\) | 32.3413 | 1.18969 | 0.594847 | − | 0.803839i | \(-0.297212\pi\) | ||||
0.594847 | + | 0.803839i | \(0.297212\pi\) | |||||||
\(740\) | 5.54367 | 0.203789 | ||||||||
\(741\) | 2.71096 | − | 0.728490i | 0.0995897 | − | 0.0267617i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.1355i | − | 1.25231i | −0.779698 | − | 0.626155i | \(-0.784628\pi\) | ||
0.779698 | − | 0.626155i | \(-0.215372\pi\) | |||||||
\(744\) | 1.72113 | − | 0.462503i | 0.0630999 | − | 0.0169562i | ||||
\(745\) | − | 7.43451i | − | 0.272379i | ||||||
\(746\) | − | 8.85050i | − | 0.324040i | ||||||
\(747\) | −33.5077 | + | 19.4100i | −1.22598 | + | 0.710174i | ||||
\(748\) | 11.1927i | 0.409244i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.449490 | − | 1.67271i | −0.0164131 | − | 0.0610787i | ||||
\(751\) | 43.8356 | 1.59958 | 0.799791 | − | 0.600278i | \(-0.204944\pi\) | ||||
0.799791 | + | 0.600278i | \(0.204944\pi\) | |||||||
\(752\) | −8.82018 | −0.321639 | ||||||||
\(753\) | 8.72642 | − | 2.34496i | 0.318008 | − | 0.0854552i | ||||
\(754\) | 1.24566i | 0.0453641i | ||||||||
\(755\) | 19.4341 | 0.707278 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2063 | −0.879792 | −0.439896 | − | 0.898049i | \(-0.644985\pi\) | ||||
−0.439896 | + | 0.898049i | \(0.644985\pi\) | |||||||
\(758\) | − | 11.4030i | − | 0.414174i | ||||||
\(759\) | 18.3934 | − | 4.94268i | 0.667639 | − | 0.179408i | ||||
\(760\) | −0.527004 | −0.0191164 | ||||||||
\(761\) | −9.24874 | −0.335267 | −0.167633 | − | 0.985849i | \(-0.553612\pi\) | ||||
−0.167633 | + | 0.985849i | \(0.553612\pi\) | |||||||
\(762\) | −3.37002 | − | 12.5410i | −0.122083 | − | 0.454313i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 10.4546i | − | 0.378233i | ||||||
\(765\) | 12.2145 | − | 7.07550i | 0.441617 | − | 0.255815i | ||||
\(766\) | − | 8.73221i | − | 0.315508i | ||||||
\(767\) | − | 26.2032i | − | 0.946144i | ||||||
\(768\) | 1.67271 | − | 0.449490i | 0.0603587 | − | 0.0162196i | ||||
\(769\) | − | 28.3177i | − | 1.02116i | −0.859830 | − | 0.510580i | \(-0.829431\pi\) | ||
0.859830 | − | 0.510580i | \(-0.170569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.38153 | − | 1.98356i | 0.265839 | − | 0.0714363i | ||||
\(772\) | 20.1184 | 0.724079 | ||||||||
\(773\) | 36.4274 | 1.31020 | 0.655101 | − | 0.755541i | \(-0.272626\pi\) | ||||
0.655101 | + | 0.755541i | \(0.272626\pi\) | |||||||
\(774\) | −17.3106 | − | 29.8835i | −0.622217 | − | 1.07414i | ||||
\(775\) | − | 1.02895i | − | 0.0369610i | ||||||
\(776\) | −19.6433 | −0.705153 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.3884 | 0.981922 | ||||||||
\(779\) | − | 4.54267i | − | 0.162758i | ||||||
\(780\) | 1.38232 | + | 5.14411i | 0.0494951 | + | 0.184189i | ||||
\(781\) | −27.9972 | −1.00182 | ||||||||
\(782\) | 21.7511 | 0.777818 | ||||||||
\(783\) | −1.49146 | − | 1.48504i | −0.0533003 | − | 0.0530709i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.2417i | 0.543999i | ||||||||
\(786\) | −2.93090 | − | 10.9069i | −0.104542 | − | 0.389036i | ||||
\(787\) | 53.8639i | 1.92004i | 0.279930 | + | 0.960021i | \(0.409689\pi\) | ||||
−0.279930 | + | 0.960021i | \(0.590311\pi\) | |||||||
\(788\) | − | 20.5601i | − | 0.732424i | ||||||
\(789\) | −6.65903 | − | 24.7806i | −0.237068 | − | 0.882211i | ||||
\(790\) | − | 1.91407i | − | 0.0680996i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.17501 | − | 3.57699i | 0.219419 | − | 0.127103i | ||||
\(793\) | 23.1025 | 0.820393 | ||||||||
\(794\) | −1.55639 | −0.0552340 | ||||||||
\(795\) | −5.49460 | − | 20.4473i | −0.194873 | − | 0.725191i | ||||
\(796\) | 5.70991i | 0.202382i | ||||||||
\(797\) | −36.1305 | −1.27981 | −0.639905 | − | 0.768454i | \(-0.721026\pi\) | ||||
−0.639905 | + | 0.768454i | \(0.721026\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.5014 | −1.46822 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −16.0630 | + | 9.30481i | −0.567559 | + | 0.328769i | ||||
\(802\) | 34.6328 | 1.22293 | ||||||||
\(803\) | −20.5772 | −0.726154 | ||||||||
\(804\) | −22.4350 | + | 6.02874i | −0.791222 | + | 0.212617i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.16434i | 0.111459i | ||||||||
\(807\) | −21.5068 | + | 5.77931i | −0.757076 | + | 0.203441i | ||||
\(808\) | − | 7.09724i | − | 0.249680i | ||||||
\(809\) | 32.5143i | 1.14314i | 0.820552 | + | 0.571572i | \(0.193666\pi\) | ||||
−0.820552 | + | 0.571572i | \(0.806334\pi\) | |||||||
\(810\) | −7.80714 | − | 4.47757i | −0.274315 | − | 0.157326i | ||||
\(811\) | − | 34.2613i | − | 1.20308i | −0.798844 | − | 0.601538i | \(-0.794555\pi\) | ||
0.798844 | − | 0.601538i | \(-0.205445\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.81945 | + | 17.9349i | 0.169026 | + | 0.629003i | ||||
\(814\) | 13.1870 | 0.462202 | ||||||||
\(815\) | −23.0876 | −0.808722 | ||||||||
\(816\) | 7.87058 | − | 2.11498i | 0.275525 | − | 0.0740391i | ||||
\(817\) | 6.06673i | 0.212248i | ||||||||
\(818\) | −13.5926 | −0.475254 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.61981 | 0.301017 | ||||||||
\(821\) | − | 47.6242i | − | 1.66209i | −0.556202 | − | 0.831047i | \(-0.687742\pi\) | ||
0.556202 | − | 0.831047i | \(-0.312258\pi\) | |||||||
\(822\) | 12.1142 | − | 3.25531i | 0.422530 | − | 0.113542i | ||||
\(823\) | −22.6266 | −0.788712 | −0.394356 | − | 0.918958i | \(-0.629032\pi\) | ||||
−0.394356 | + | 0.918958i | \(0.629032\pi\) | |||||||
\(824\) | 6.82964 | 0.237922 | ||||||||
\(825\) | −1.06922 | − | 3.97894i | −0.0372255 | − | 0.138529i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.2958i | − | 1.40122i | −0.713543 | − | 0.700612i | \(-0.752911\pi\) | ||
0.713543 | − | 0.700612i | \(-0.247089\pi\) | |||||||
\(828\) | −6.95130 | − | 12.0001i | −0.241574 | − | 0.417033i | ||||
\(829\) | − | 23.5997i | − | 0.819652i | −0.912164 | − | 0.409826i | \(-0.865589\pi\) | ||
0.912164 | − | 0.409826i | \(-0.134411\pi\) | |||||||
\(830\) | 12.9078i | 0.448038i | ||||||||
\(831\) | −6.79361 | + | 1.82558i | −0.235668 | + | 0.0633286i | ||||
\(832\) | 3.07531i | 0.106617i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.0514 | − | 4.04461i | 0.521187 | − | 0.140053i | ||||
\(835\) | −6.03310 | −0.208784 | ||||||||
\(836\) | −1.25360 | −0.0433568 | ||||||||
\(837\) | −3.78875 | − | 3.77244i | −0.130958 | − | 0.130395i | ||||
\(838\) | − | 17.5962i | − | 0.607851i | ||||||
\(839\) | 53.9263 | 1.86174 | 0.930871 | − | 0.365349i | \(-0.119050\pi\) | ||||
0.930871 | + | 0.365349i | \(0.119050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8359 | 0.994343 | ||||||||
\(842\) | 31.7006i | 1.09248i | ||||||||
\(843\) | 0.810350 | + | 3.01559i | 0.0279099 | + | 0.103863i | ||||
\(844\) | −13.3767 | −0.460446 | ||||||||
\(845\) | 3.54245 | 0.121864 | ||||||||
\(846\) | 13.2632 | + | 22.8964i | 0.455998 | + | 0.787196i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 12.2241i | − | 0.419776i | ||||||
\(849\) | 4.68096 | + | 17.4195i | 0.160650 | + | 0.597836i | ||||
\(850\) | − | 4.70529i | − | 0.161390i | ||||||
\(851\) | − | 25.6267i | − | 0.878472i | ||||||
\(852\) | 5.29040 | + | 19.6874i | 0.181246 | + | 0.674480i | ||||
\(853\) | − | 7.89413i | − | 0.270290i | −0.990826 | − | 0.135145i | \(-0.956850\pi\) | ||
0.990826 | − | 0.135145i | \(-0.0431500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.792473 | + | 1.36806i | 0.0271020 | + | 0.0467866i | ||||
\(856\) | −13.1216 | −0.448486 | ||||||||
\(857\) | −4.65257 | −0.158929 | −0.0794643 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794643 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(858\) | 3.28819 | + | 12.2365i | 0.112257 | + | 0.417747i | ||||
\(859\) | − | 21.4003i | − | 0.730167i | −0.930975 | − | 0.365084i | \(-0.881040\pi\) | ||
0.930975 | − | 0.365084i | \(-0.118960\pi\) | |||||||
\(860\) | −11.5117 | −0.392547 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.3717 | −0.353261 | ||||||||
\(863\) | 6.53711i | 0.222526i | 0.993791 | + | 0.111263i | \(0.0354896\pi\) | ||||
−0.993791 | + | 0.111263i | \(0.964510\pi\) | |||||||
\(864\) | −3.68215 | − | 3.66630i | −0.125269 | − | 0.124730i | ||||
\(865\) | −11.3332 | −0.385342 | ||||||||
\(866\) | −41.0608 | −1.39530 | ||||||||
\(867\) | 8.59725 | − | 2.31025i | 0.291978 | − | 0.0784602i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.55308i | − | 0.154453i | ||||||
\(870\) | −0.677531 | + | 0.182066i | −0.0229705 | + | 0.00617262i | ||||
\(871\) | − | 41.2473i | − | 1.39761i | ||||||
\(872\) | 0.228271i | 0.00773022i | ||||||||
\(873\) | 29.5383 | + | 50.9923i | 0.999719 | + | 1.72583i | ||||
\(874\) | 2.43618i | 0.0824049i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.88830 | + | 14.4697i | 0.131373 | + | 0.488886i | ||||
\(877\) | −12.1401 | −0.409943 | −0.204971 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204971 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(878\) | 10.6387 | 0.359038 | ||||||||
\(879\) | 35.1786 | − | 9.45319i | 1.18654 | − | 0.318848i | ||||
\(880\) | − | 2.37874i | − | 0.0801873i | ||||||
\(881\) | −22.1583 | −0.746533 | −0.373266 | − | 0.927724i | \(-0.621762\pi\) | ||||
−0.373266 | + | 0.927724i | \(0.621762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.8759 | −1.40924 | −0.704618 | − | 0.709587i | \(-0.748881\pi\) | ||||
−0.704618 | + | 0.709587i | \(0.748881\pi\) | |||||||
\(884\) | 14.4702i | 0.486686i | ||||||||
\(885\) | 14.2523 | − | 3.82989i | 0.479087 | − | 0.128740i | ||||
\(886\) | −20.3371 | −0.683240 | ||||||||
\(887\) | −15.7929 | −0.530274 | −0.265137 | − | 0.964211i | \(-0.585417\pi\) | ||||
−0.265137 | + | 0.964211i | \(0.585417\pi\) | |||||||
\(888\) | −2.49183 | − | 9.27295i | −0.0836202 | − | 0.311180i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.18780i | 0.207416i | ||||||||
\(891\) | −18.5712 | − | 10.6510i | −0.622157 | − | 0.356821i | ||||
\(892\) | 24.5364i | 0.821539i | ||||||||
\(893\) | − | 4.64826i | − | 0.155548i | ||||||
\(894\) | −12.4358 | + | 3.34174i | −0.415915 | + | 0.111765i | ||||
\(895\) | 19.1994i | 0.641764i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.7796 | − | 6.39006i | 0.793979 | − | 0.213358i | ||||
\(898\) | 10.6792 | 0.356369 | ||||||||
\(899\) | −0.416776 | −0.0139003 | ||||||||
\(900\) | −2.59592 | + | 1.50373i | −0.0865306 | + | 0.0501245i | ||||
\(901\) | − | 57.5177i | − | 1.91619i | ||||||
\(902\) | 20.5043 | 0.682719 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.86352 | −0.195018 | ||||||||
\(905\) | 23.8389i | 0.792431i | ||||||||
\(906\) | −8.73543 | − | 32.5076i | −0.290215 | − | 1.07999i | ||||
\(907\) | −12.7671 | −0.423926 | −0.211963 | − | 0.977278i | \(-0.567986\pi\) | ||||
−0.211963 | + | 0.977278i | \(0.567986\pi\) | |||||||
\(908\) | 20.2310 | 0.671390 | ||||||||
\(909\) | −18.4238 | + | 10.6724i | −0.611080 | + | 0.353980i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7485i | 0.853086i | 0.904467 | + | 0.426543i | \(0.140269\pi\) | ||||
−0.904467 | + | 0.426543i | \(0.859731\pi\) | |||||||
\(912\) | 0.236883 | + | 0.881524i | 0.00784398 | + | 0.0291902i | ||||
\(913\) | 30.7044i | 1.01617i | ||||||||
\(914\) | − | 1.04759i | − | 0.0346513i | ||||||
\(915\) | 3.37668 | + | 12.5658i | 0.111629 | + | 0.415412i | ||||
\(916\) | − | 25.1923i | − | 0.832377i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −17.3256 | − | 17.2510i | −0.571829 | − | 0.569368i | ||||
\(919\) | 28.0971 | 0.926837 | 0.463418 | − | 0.886140i | \(-0.346623\pi\) | ||||
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(920\) | −4.62269 | −0.152406 | ||||||||
\(921\) | −1.58330 | − | 5.89201i | −0.0521715 | − | 0.194148i | ||||
\(922\) | − | 0.442723i | − | 0.0145803i | ||||||
\(923\) | −36.1958 | −1.19140 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.54367 | −0.182275 | ||||||||
\(926\) | − | 1.83270i | − | 0.0602264i | ||||||
\(927\) | −10.2700 | − | 17.7292i | −0.337310 | − | 0.582302i | ||||
\(928\) | −0.405050 | −0.0132964 | ||||||||
\(929\) | −52.5107 | −1.72282 | −0.861409 | − | 0.507911i | \(-0.830418\pi\) | ||||
−0.861409 | + | 0.507911i | \(0.830418\pi\) | |||||||
\(930\) | −1.72113 | + | 0.462503i | −0.0564382 | + | 0.0151661i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 2.40100i | − | 0.0786474i | ||||||
\(933\) | −5.30562 | + | 1.42573i | −0.173698 | + | 0.0466762i | ||||
\(934\) | − | 3.33622i | − | 0.109164i | ||||||
\(935\) | − | 11.1927i | − | 0.366039i | ||||||
\(936\) | 7.98326 | − | 4.62445i | 0.260941 | − | 0.151155i | ||||
\(937\) | − | 18.1141i | − | 0.591762i | −0.955225 | − | 0.295881i | \(-0.904387\pi\) | ||
0.955225 | − | 0.295881i | \(-0.0956131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.4607 | + | 50.0920i | 0.439274 | + | 1.63469i | ||||
\(940\) | 8.82018 | 0.287682 | ||||||||
\(941\) | 2.94549 | 0.0960201 | 0.0480101 | − | 0.998847i | \(-0.484712\pi\) | ||||
0.0480101 | + | 0.998847i | \(0.484712\pi\) | |||||||
\(942\) | 25.4949 | − | 6.85099i | 0.830669 | − | 0.223217i | ||||
\(943\) | − | 39.8468i | − | 1.29759i | ||||||
\(944\) | 8.52051 | 0.277319 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.3834 | −0.890312 | ||||||||
\(947\) | − | 27.5386i | − | 0.894885i | −0.894313 | − | 0.447442i | \(-0.852335\pi\) | ||
0.894313 | − | 0.447442i | \(-0.147665\pi\) | |||||||
\(948\) | −3.20169 | + | 0.860357i | −0.103986 | + | 0.0279431i | ||||
\(949\) | −26.6029 | −0.863566 | ||||||||
\(950\) | 0.527004 | 0.0170983 | ||||||||
\(951\) | −7.36739 | − | 27.4166i | −0.238904 | − | 0.889045i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.2980i | − | 1.17581i | −0.808931 | − | 0.587904i | \(-0.799953\pi\) | ||
0.808931 | − | 0.587904i | \(-0.200047\pi\) | |||||||
\(954\) | −31.7326 | + | 18.3817i | −1.02738 | + | 0.595131i | ||||
\(955\) | 10.4546i | 0.338302i | ||||||||
\(956\) | − | 11.6579i | − | 0.377043i | ||||||
\(957\) | −1.61167 | + | 0.433088i | −0.0520979 | + | 0.0139998i | ||||
\(958\) | 39.9415i | 1.29045i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.67271 | + | 0.449490i | −0.0539865 | + | 0.0145072i | ||||
\(961\) | 29.9413 | 0.965847 | ||||||||
\(962\) | 17.0485 | 0.549666 | ||||||||
\(963\) | 19.7313 | + | 34.0625i | 0.635834 | + | 1.09765i | ||||
\(964\) | 14.9969i | 0.483019i | ||||||||
\(965\) | −20.1184 | −0.647636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.5718 | 0.854493 | 0.427247 | − | 0.904135i | \(-0.359484\pi\) | ||||
0.427247 | + | 0.904135i | \(0.359484\pi\) | |||||||
\(968\) | 5.34159i | 0.171685i | ||||||||
\(969\) | 1.11460 | + | 4.14782i | 0.0358062 | + | 0.133247i | ||||
\(970\) | 19.6433 | 0.630708 | ||||||||
\(971\) | 28.6200 | 0.918461 | 0.459230 | − | 0.888317i | \(-0.348125\pi\) | ||||
0.459230 | + | 0.888317i | \(0.348125\pi\) | |||||||
\(972\) | −3.98044 | + | 15.0717i | −0.127673 | + | 0.483425i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 25.7832i | − | 0.826149i | ||||||
\(975\) | −1.38232 | − | 5.14411i | −0.0442698 | − | 0.164743i | ||||
\(976\) | 7.51223i | 0.240461i | ||||||||
\(977\) | 30.2325i | 0.967223i | 0.875283 | + | 0.483611i | \(0.160675\pi\) | ||||
−0.875283 | + | 0.483611i | \(0.839325\pi\) | |||||||
\(978\) | 10.3776 | + | 38.6188i | 0.331840 | + | 1.23489i | ||||
\(979\) | 14.7192i | 0.470427i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.592571 | − | 0.343258i | 0.0189193 | − | 0.0109594i | ||||
\(982\) | −24.6154 | −0.785510 | ||||||||
\(983\) | 7.02239 | 0.223980 | 0.111990 | − | 0.993709i | \(-0.464278\pi\) | ||||
0.111990 | + | 0.993709i | \(0.464278\pi\) | |||||||
\(984\) | −3.87452 | − | 14.4184i | −0.123515 | − | 0.459643i | ||||
\(985\) | 20.5601i | 0.655100i | ||||||||
\(986\) | −1.90588 | −0.0606955 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.62070 | −0.0515614 | ||||||||
\(989\) | 53.2152i | 1.69215i | ||||||||
\(990\) | −6.17501 | + | 3.57699i | −0.196255 | + | 0.113684i | ||||
\(991\) | 33.0169 | 1.04882 | 0.524408 | − | 0.851467i | \(-0.324287\pi\) | ||||
0.524408 | + | 0.851467i | \(0.324287\pi\) | |||||||
\(992\) | −1.02895 | −0.0326692 | ||||||||
\(993\) | 26.0873 | − | 7.01017i | 0.827855 | − | 0.222461i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.70991i | − | 0.181016i | ||||||
\(996\) | 21.5911 | − | 5.80195i | 0.684140 | − | 0.183842i | ||||
\(997\) | − | 49.4552i | − | 1.56626i | −0.621857 | − | 0.783131i | \(-0.713622\pi\) | ||
0.621857 | − | 0.783131i | \(-0.286378\pi\) | |||||||
\(998\) | − | 32.2260i | − | 1.02009i | ||||||
\(999\) | −20.3248 | + | 20.4126i | −0.643047 | + | 0.645827i |
(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 | 1470.2.b.d.881.7 | yes | 16 | |
3.2 | odd | 2 | 1470.2.b.c.881.10 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.b.c.881.2 | ✓ | 16 | ||
21.20 | even | 2 | inner | 1470.2.b.d.881.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.b.c.881.2 | ✓ | 16 | 7.6 | odd | 2 | ||
1470.2.b.c.881.10 | yes | 16 | 3.2 | odd | 2 | ||
1470.2.b.d.881.7 | yes | 16 | 1.1 | even | 1 | trivial | |
1470.2.b.d.881.15 | yes | 16 | 21.20 | even | 2 | inner |