Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (of order \(4\), degree \(2\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 757.4 | ||
Root | \(-3.48873 + 3.48873i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.757 |
Dual form | 1050.3.l.h.43.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.267261 | + | 0.267261i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.1276 | 1.37524 | 0.687620 | − | 0.726071i | \(-0.258655\pi\) | ||||
0.687620 | + | 0.726071i | \(0.258655\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | −14.6465 | + | 14.6465i | −1.12665 | + | 1.12665i | −0.135932 | + | 0.990718i | \(0.543403\pi\) |
−0.990718 | + | 0.135932i | \(0.956597\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −15.9948 | − | 15.9948i | −0.940872 | − | 0.940872i | 0.0574751 | − | 0.998347i | \(-0.481695\pi\) |
−0.998347 | + | 0.0574751i | \(0.981695\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 2.05015i | 0.107903i | 0.998544 | + | 0.0539513i | \(0.0171816\pi\) | ||||
−0.998544 | + | 0.0539513i | \(0.982818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 15.1276 | + | 15.1276i | 0.687620 | + | 0.687620i | ||||
\(23\) | −19.4933 | + | 19.4933i | −0.847536 | + | 0.847536i | −0.989825 | − | 0.142289i | \(-0.954554\pi\) |
0.142289 | + | 0.989825i | \(0.454554\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −29.2929 | −1.12665 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −3.74166 | + | 3.74166i | −0.133631 | + | 0.133631i | ||||
\(29\) | 33.1037i | 1.14151i | 0.821122 | + | 0.570753i | \(0.193349\pi\) | ||||
−0.821122 | + | 0.570753i | \(0.806651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27.8179 | 0.897352 | 0.448676 | − | 0.893694i | \(-0.351896\pi\) | ||||
0.448676 | + | 0.893694i | \(0.351896\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −18.5275 | + | 18.5275i | −0.561440 | + | 0.561440i | ||||
\(34\) | − | 31.9896i | − | 0.940872i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 30.4627 | + | 30.4627i | 0.823315 | + | 0.823315i | 0.986582 | − | 0.163267i | \(-0.0522031\pi\) |
−0.163267 | + | 0.986582i | \(0.552203\pi\) | |||||||
\(38\) | −2.05015 | + | 2.05015i | −0.0539513 | + | 0.0539513i | ||||
\(39\) | − | 35.8763i | − | 0.919906i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.6233 | −0.649348 | −0.324674 | − | 0.945826i | \(-0.605255\pi\) | ||||
−0.324674 | + | 0.945826i | \(0.605255\pi\) | |||||||
\(42\) | −4.58258 | − | 4.58258i | −0.109109 | − | 0.109109i | ||||
\(43\) | −7.89901 | + | 7.89901i | −0.183698 | + | 0.183698i | −0.792965 | − | 0.609267i | \(-0.791464\pi\) |
0.609267 | + | 0.792965i | \(0.291464\pi\) | |||||||
\(44\) | 30.2553i | 0.687620i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −38.9867 | −0.847536 | ||||||||
\(47\) | −33.8904 | − | 33.8904i | −0.721072 | − | 0.721072i | 0.247752 | − | 0.968824i | \(-0.420308\pi\) |
−0.968824 | + | 0.247752i | \(0.920308\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 39.1791 | 0.768219 | ||||||||
\(52\) | −29.2929 | − | 29.2929i | −0.563325 | − | 0.563325i | ||||
\(53\) | −5.60358 | + | 5.60358i | −0.105728 | + | 0.105728i | −0.757992 | − | 0.652264i | \(-0.773819\pi\) |
0.652264 | + | 0.757992i | \(0.273819\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.48331 | −0.133631 | ||||||||
\(57\) | −2.51091 | − | 2.51091i | −0.0440511 | − | 0.0440511i | ||||
\(58\) | −33.1037 | + | 33.1037i | −0.570753 | + | 0.570753i | ||||
\(59\) | 5.80696i | 0.0984231i | 0.998788 | + | 0.0492115i | \(0.0156709\pi\) | ||||
−0.998788 | + | 0.0492115i | \(0.984329\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −98.2160 | −1.61010 | −0.805049 | − | 0.593208i | \(-0.797861\pi\) | ||||
−0.805049 | + | 0.593208i | \(0.797861\pi\) | |||||||
\(62\) | 27.8179 | + | 27.8179i | 0.448676 | + | 0.448676i | ||||
\(63\) | 5.61249 | − | 5.61249i | 0.0890871 | − | 0.0890871i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −37.0550 | −0.561440 | ||||||||
\(67\) | −51.6510 | − | 51.6510i | −0.770910 | − | 0.770910i | 0.207356 | − | 0.978266i | \(-0.433514\pi\) |
−0.978266 | + | 0.207356i | \(0.933514\pi\) | |||||||
\(68\) | 31.9896 | − | 31.9896i | 0.470436 | − | 0.470436i | ||||
\(69\) | − | 47.7487i | − | 0.692010i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.447 | −1.69643 | −0.848216 | − | 0.529651i | \(-0.822323\pi\) | ||||
−0.848216 | + | 0.529651i | \(0.822323\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −81.9558 | + | 81.9558i | −1.12268 | + | 1.12268i | −0.131346 | + | 0.991337i | \(0.541930\pi\) |
−0.991337 | + | 0.131346i | \(0.958070\pi\) | |||||||
\(74\) | 60.9253i | 0.823315i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.10030 | −0.0539513 | ||||||||
\(77\) | 28.3012 | + | 28.3012i | 0.367548 | + | 0.367548i | ||||
\(78\) | 35.8763 | − | 35.8763i | 0.459953 | − | 0.459953i | ||||
\(79\) | 33.0831i | 0.418774i | 0.977833 | + | 0.209387i | \(0.0671468\pi\) | ||||
−0.977833 | + | 0.209387i | \(0.932853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −26.6233 | − | 26.6233i | −0.324674 | − | 0.324674i | ||||
\(83\) | 97.0860 | − | 97.0860i | 1.16971 | − | 1.16971i | 0.187433 | − | 0.982277i | \(-0.439983\pi\) |
0.982277 | − | 0.187433i | \(-0.0600167\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.7980 | −0.183698 | ||||||||
\(87\) | −40.5435 | − | 40.5435i | −0.466018 | − | 0.466018i | ||||
\(88\) | −30.2553 | + | 30.2553i | −0.343810 | + | 0.343810i | ||||
\(89\) | − | 34.2132i | − | 0.384418i | −0.981354 | − | 0.192209i | \(-0.938435\pi\) | ||
0.981354 | − | 0.192209i | \(-0.0615652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −54.8020 | −0.602220 | ||||||||
\(92\) | −38.9867 | − | 38.9867i | −0.423768 | − | 0.423768i | ||||
\(93\) | −34.0699 | + | 34.0699i | −0.366343 | + | 0.366343i | ||||
\(94\) | − | 67.7807i | − | 0.721072i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −104.393 | − | 104.393i | −1.07622 | − | 1.07622i | −0.996845 | − | 0.0793705i | \(-0.974709\pi\) |
−0.0793705 | − | 0.996845i | \(-0.525291\pi\) | |||||||
\(98\) | −7.00000 | + | 7.00000i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | − | 45.3829i | − | 0.458413i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.2854 | 0.497876 | 0.248938 | − | 0.968519i | \(-0.419919\pi\) | ||||
0.248938 | + | 0.968519i | \(0.419919\pi\) | |||||||
\(102\) | 39.1791 | + | 39.1791i | 0.384109 | + | 0.384109i | ||||
\(103\) | −7.11461 | + | 7.11461i | −0.0690739 | + | 0.0690739i | −0.740800 | − | 0.671726i | \(-0.765553\pi\) |
0.671726 | + | 0.740800i | \(0.265553\pi\) | |||||||
\(104\) | − | 58.5858i | − | 0.563325i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2072 | −0.105728 | ||||||||
\(107\) | 4.56425 | + | 4.56425i | 0.0426566 | + | 0.0426566i | 0.728113 | − | 0.685457i | \(-0.240397\pi\) |
−0.685457 | + | 0.728113i | \(0.740397\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 58.0783i | − | 0.532829i | −0.963859 | − | 0.266414i | \(-0.914161\pi\) | ||
0.963859 | − | 0.266414i | \(-0.0858389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74.6180 | −0.672234 | ||||||||
\(112\) | −7.48331 | − | 7.48331i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | −9.58688 | + | 9.58688i | −0.0848396 | + | 0.0848396i | −0.748253 | − | 0.663413i | \(-0.769107\pi\) |
0.663413 | + | 0.748253i | \(0.269107\pi\) | |||||||
\(114\) | − | 5.02182i | − | 0.0440511i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −66.2073 | −0.570753 | ||||||||
\(117\) | 43.9394 | + | 43.9394i | 0.375550 | + | 0.375550i | ||||
\(118\) | −5.80696 | + | 5.80696i | −0.0492115 | + | 0.0492115i | ||||
\(119\) | − | 59.8471i | − | 0.502917i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 107.846 | 0.891286 | ||||||||
\(122\) | −98.2160 | − | 98.2160i | −0.805049 | − | 0.805049i | ||||
\(123\) | 32.6067 | − | 32.6067i | 0.265095 | − | 0.265095i | ||||
\(124\) | 55.6358i | 0.448676i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.2250 | 0.0890871 | ||||||||
\(127\) | 140.998 | + | 140.998i | 1.11022 | + | 1.11022i | 0.993120 | + | 0.117097i | \(0.0373590\pi\) |
0.117097 | + | 0.993120i | \(0.462641\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 19.3485i | − | 0.149989i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 184.764 | 1.41041 | 0.705205 | − | 0.709004i | \(-0.250855\pi\) | ||||
0.705205 | + | 0.709004i | \(0.250855\pi\) | |||||||
\(132\) | −37.0550 | − | 37.0550i | −0.280720 | − | 0.280720i | ||||
\(133\) | −3.83548 | + | 3.83548i | −0.0288382 | + | 0.0288382i | ||||
\(134\) | − | 103.302i | − | 0.770910i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 63.9793 | 0.470436 | ||||||||
\(137\) | 170.364 | + | 170.364i | 1.24353 | + | 1.24353i | 0.958527 | + | 0.285002i | \(0.0919944\pi\) |
0.285002 | + | 0.958527i | \(0.408006\pi\) | |||||||
\(138\) | 47.7487 | − | 47.7487i | 0.346005 | − | 0.346005i | ||||
\(139\) | 110.608i | 0.795741i | 0.917442 | + | 0.397870i | \(0.130251\pi\) | ||||
−0.917442 | + | 0.397870i | \(0.869749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 83.0141 | 0.588753 | ||||||||
\(142\) | −120.447 | − | 120.447i | −0.848216 | − | 0.848216i | ||||
\(143\) | −221.566 | + | 221.566i | −1.54941 | + | 1.54941i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −163.912 | −1.12268 | ||||||||
\(147\) | −8.57321 | − | 8.57321i | −0.0583212 | − | 0.0583212i | ||||
\(148\) | −60.9253 | + | 60.9253i | −0.411658 | + | 0.411658i | ||||
\(149\) | − | 150.705i | − | 1.01144i | −0.862697 | − | 0.505721i | \(-0.831227\pi\) | ||
0.862697 | − | 0.505721i | \(-0.168773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −190.444 | −1.26122 | −0.630610 | − | 0.776100i | \(-0.717195\pi\) | ||||
−0.630610 | + | 0.776100i | \(0.717195\pi\) | |||||||
\(152\) | −4.10030 | − | 4.10030i | −0.0269756 | − | 0.0269756i | ||||
\(153\) | −47.9845 | + | 47.9845i | −0.313624 | + | 0.313624i | ||||
\(154\) | 56.6025i | 0.367548i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 71.7527 | 0.459953 | ||||||||
\(157\) | 28.5711 | + | 28.5711i | 0.181981 | + | 0.181981i | 0.792219 | − | 0.610237i | \(-0.208926\pi\) |
−0.610237 | + | 0.792219i | \(0.708926\pi\) | |||||||
\(158\) | −33.0831 | + | 33.0831i | −0.209387 | + | 0.209387i | ||||
\(159\) | − | 13.7259i | − | 0.0863265i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −72.9374 | −0.453027 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 37.2908 | − | 37.2908i | 0.228778 | − | 0.228778i | −0.583404 | − | 0.812182i | \(-0.698280\pi\) |
0.812182 | + | 0.583404i | \(0.198280\pi\) | |||||||
\(164\) | − | 53.2466i | − | 0.324674i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 194.172 | 1.16971 | ||||||||
\(167\) | 70.7467 | + | 70.7467i | 0.423633 | + | 0.423633i | 0.886453 | − | 0.462820i | \(-0.153162\pi\) |
−0.462820 | + | 0.886453i | \(0.653162\pi\) | |||||||
\(168\) | 9.16515 | − | 9.16515i | 0.0545545 | − | 0.0545545i | ||||
\(169\) | − | 260.037i | − | 1.53868i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.15045 | 0.0359675 | ||||||||
\(172\) | −15.7980 | − | 15.7980i | −0.0918489 | − | 0.0918489i | ||||
\(173\) | −73.9048 | + | 73.9048i | −0.427196 | + | 0.427196i | −0.887672 | − | 0.460476i | \(-0.847679\pi\) |
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(174\) | − | 81.0871i | − | 0.466018i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −60.5106 | −0.343810 | ||||||||
\(177\) | −7.11205 | − | 7.11205i | −0.0401811 | − | 0.0401811i | ||||
\(178\) | 34.2132 | − | 34.2132i | 0.192209 | − | 0.192209i | ||||
\(179\) | 280.292i | 1.56588i | 0.622100 | + | 0.782938i | \(0.286280\pi\) | ||||
−0.622100 | + | 0.782938i | \(0.713720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −139.086 | −0.768430 | −0.384215 | − | 0.923244i | \(-0.625528\pi\) | ||||
−0.384215 | + | 0.923244i | \(0.625528\pi\) | |||||||
\(182\) | −54.8020 | − | 54.8020i | −0.301110 | − | 0.301110i | ||||
\(183\) | 120.290 | − | 120.290i | 0.657320 | − | 0.657320i | ||||
\(184\) | − | 77.9733i | − | 0.423768i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −68.1397 | −0.366343 | ||||||||
\(187\) | −241.964 | − | 241.964i | −1.29392 | − | 1.29392i | ||||
\(188\) | 67.7807 | − | 67.7807i | 0.360536 | − | 0.360536i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −231.713 | −1.21316 | −0.606580 | − | 0.795023i | \(-0.707459\pi\) | ||||
−0.606580 | + | 0.795023i | \(0.707459\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 148.989 | − | 148.989i | 0.771962 | − | 0.771962i | −0.206488 | − | 0.978449i | \(-0.566203\pi\) |
0.978449 | + | 0.206488i | \(0.0662033\pi\) | |||||||
\(194\) | − | 208.786i | − | 1.07622i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 255.090 | + | 255.090i | 1.29487 | + | 1.29487i | 0.931736 | + | 0.363135i | \(0.118294\pi\) |
0.363135 | + | 0.931736i | \(0.381706\pi\) | |||||||
\(198\) | 45.3829 | − | 45.3829i | 0.229207 | − | 0.229207i | ||||
\(199\) | 321.154i | 1.61384i | 0.590660 | + | 0.806920i | \(0.298867\pi\) | ||||
−0.590660 | + | 0.806920i | \(0.701133\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 126.518 | 0.629445 | ||||||||
\(202\) | 50.2854 | + | 50.2854i | 0.248938 | + | 0.248938i | ||||
\(203\) | −61.9313 | + | 61.9313i | −0.305080 | + | 0.305080i | ||||
\(204\) | 78.3583i | 0.384109i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.2292 | −0.0690739 | ||||||||
\(207\) | 58.4800 | + | 58.4800i | 0.282512 | + | 0.282512i | ||||
\(208\) | 58.5858 | − | 58.5858i | 0.281663 | − | 0.281663i | ||||
\(209\) | 31.0139i | 0.148392i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7166 | 0.107662 | 0.0538308 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538308 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(212\) | −11.2072 | − | 11.2072i | −0.0528640 | − | 0.0528640i | ||||
\(213\) | 147.516 | − | 147.516i | 0.692565 | − | 0.692565i | ||||
\(214\) | 9.12850i | 0.0426566i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 52.0426 | + | 52.0426i | 0.239828 | + | 0.239828i | ||||
\(218\) | 58.0783 | − | 58.0783i | 0.266414 | − | 0.266414i | ||||
\(219\) | − | 200.750i | − | 0.916667i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 468.535 | 2.12007 | ||||||||
\(222\) | −74.6180 | − | 74.6180i | −0.336117 | − | 0.336117i | ||||
\(223\) | −158.968 | + | 158.968i | −0.712863 | + | 0.712863i | −0.967133 | − | 0.254270i | \(-0.918165\pi\) |
0.254270 | + | 0.967133i | \(0.418165\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.1738 | −0.0848396 | ||||||||
\(227\) | 52.1650 | + | 52.1650i | 0.229802 | + | 0.229802i | 0.812610 | − | 0.582808i | \(-0.198046\pi\) |
−0.582808 | + | 0.812610i | \(0.698046\pi\) | |||||||
\(228\) | 5.02182 | − | 5.02182i | 0.0220255 | − | 0.0220255i | ||||
\(229\) | 115.486i | 0.504305i | 0.967688 | + | 0.252152i | \(0.0811384\pi\) | ||||
−0.967688 | + | 0.252152i | \(0.918862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −69.3236 | −0.300102 | ||||||||
\(232\) | −66.2073 | − | 66.2073i | −0.285376 | − | 0.285376i | ||||
\(233\) | 297.575 | − | 297.575i | 1.27714 | − | 1.27714i | 0.334885 | − | 0.942259i | \(-0.391302\pi\) |
0.942259 | − | 0.334885i | \(-0.108698\pi\) | |||||||
\(234\) | 87.8787i | 0.375550i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.6139 | −0.0492115 | ||||||||
\(237\) | −40.5184 | − | 40.5184i | −0.170964 | − | 0.170964i | ||||
\(238\) | 59.8471 | − | 59.8471i | 0.251459 | − | 0.251459i | ||||
\(239\) | 136.556i | 0.571362i | 0.958325 | + | 0.285681i | \(0.0922198\pi\) | ||||
−0.958325 | + | 0.285681i | \(0.907780\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 61.0110 | 0.253157 | 0.126579 | − | 0.991957i | \(-0.459600\pi\) | ||||
0.126579 | + | 0.991957i | \(0.459600\pi\) | |||||||
\(242\) | 107.846 | + | 107.846i | 0.445643 | + | 0.445643i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 196.432i | − | 0.805049i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 65.2134 | 0.265095 | ||||||||
\(247\) | −30.0274 | − | 30.0274i | −0.121568 | − | 0.121568i | ||||
\(248\) | −55.6358 | + | 55.6358i | −0.224338 | + | 0.224338i | ||||
\(249\) | 237.811i | 0.955064i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 215.934 | 0.860295 | 0.430147 | − | 0.902759i | \(-0.358462\pi\) | ||||
0.430147 | + | 0.902759i | \(0.358462\pi\) | |||||||
\(252\) | 11.2250 | + | 11.2250i | 0.0445435 | + | 0.0445435i | ||||
\(253\) | −294.888 | + | 294.888i | −1.16557 | + | 1.16557i | ||||
\(254\) | 281.995i | 1.11022i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 144.579 | + | 144.579i | 0.562564 | + | 0.562564i | 0.930035 | − | 0.367471i | \(-0.119776\pi\) |
−0.367471 | + | 0.930035i | \(0.619776\pi\) | |||||||
\(258\) | 19.3485 | − | 19.3485i | 0.0749944 | − | 0.0749944i | ||||
\(259\) | 113.981i | 0.440081i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 99.3110 | 0.380502 | ||||||||
\(262\) | 184.764 | + | 184.764i | 0.705205 | + | 0.705205i | ||||
\(263\) | 0.389678 | − | 0.389678i | 0.00148167 | − | 0.00148167i | −0.706366 | − | 0.707847i | \(-0.749667\pi\) |
0.707847 | + | 0.706366i | \(0.249667\pi\) | |||||||
\(264\) | − | 74.1100i | − | 0.280720i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.67096 | −0.0288382 | ||||||||
\(267\) | 41.9025 | + | 41.9025i | 0.156938 | + | 0.156938i | ||||
\(268\) | 103.302 | − | 103.302i | 0.385455 | − | 0.385455i | ||||
\(269\) | 272.956i | 1.01471i | 0.861738 | + | 0.507353i | \(0.169376\pi\) | ||||
−0.861738 | + | 0.507353i | \(0.830624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −176.708 | −0.652058 | −0.326029 | − | 0.945360i | \(-0.605711\pi\) | ||||
−0.326029 | + | 0.945360i | \(0.605711\pi\) | |||||||
\(272\) | 63.9793 | + | 63.9793i | 0.235218 | + | 0.235218i | ||||
\(273\) | 67.1185 | − | 67.1185i | 0.245855 | − | 0.245855i | ||||
\(274\) | 340.727i | 1.24353i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 95.4974 | 0.346005 | ||||||||
\(277\) | 203.152 | + | 203.152i | 0.733402 | + | 0.733402i | 0.971292 | − | 0.237890i | \(-0.0764559\pi\) |
−0.237890 | + | 0.971292i | \(0.576456\pi\) | |||||||
\(278\) | −110.608 | + | 110.608i | −0.397870 | + | 0.397870i | ||||
\(279\) | − | 83.4538i | − | 0.299117i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 368.543 | 1.31154 | 0.655770 | − | 0.754961i | \(-0.272344\pi\) | ||||
0.655770 | + | 0.754961i | \(0.272344\pi\) | |||||||
\(282\) | 83.0141 | + | 83.0141i | 0.294376 | + | 0.294376i | ||||
\(283\) | −385.601 | + | 385.601i | −1.36255 | + | 1.36255i | −0.491888 | + | 0.870659i | \(0.663693\pi\) |
−0.870659 | + | 0.491888i | \(0.836307\pi\) | |||||||
\(284\) | − | 240.893i | − | 0.848216i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −443.133 | −1.54941 | ||||||||
\(287\) | −49.8076 | − | 49.8076i | −0.173546 | − | 0.173546i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 222.669i | 0.770480i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 255.709 | 0.878726 | ||||||||
\(292\) | −163.912 | − | 163.912i | −0.561341 | − | 0.561341i | ||||
\(293\) | 241.653 | − | 241.653i | 0.824754 | − | 0.824754i | −0.162032 | − | 0.986786i | \(-0.551805\pi\) |
0.986786 | + | 0.162032i | \(0.0518048\pi\) | |||||||
\(294\) | − | 17.1464i | − | 0.0583212i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −121.851 | −0.411658 | ||||||||
\(297\) | 55.5825 | + | 55.5825i | 0.187147 | + | 0.187147i | ||||
\(298\) | 150.705 | − | 150.705i | 0.505721 | − | 0.505721i | ||||
\(299\) | − | 571.016i | − | 1.90975i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.5554 | −0.0981907 | ||||||||
\(302\) | −190.444 | − | 190.444i | −0.630610 | − | 0.630610i | ||||
\(303\) | −61.5868 | + | 61.5868i | −0.203257 | + | 0.203257i | ||||
\(304\) | − | 8.20060i | − | 0.0269756i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −95.9689 | −0.313624 | ||||||||
\(307\) | −315.513 | − | 315.513i | −1.02773 | − | 1.02773i | −0.999604 | − | 0.0281252i | \(-0.991046\pi\) |
−0.0281252 | − | 0.999604i | \(-0.508954\pi\) | |||||||
\(308\) | −56.6025 | + | 56.6025i | −0.183774 | + | 0.183774i | ||||
\(309\) | − | 17.4272i | − | 0.0563986i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 84.6545 | 0.272201 | 0.136101 | − | 0.990695i | \(-0.456543\pi\) | ||||
0.136101 | + | 0.990695i | \(0.456543\pi\) | |||||||
\(312\) | 71.7527 | + | 71.7527i | 0.229976 | + | 0.229976i | ||||
\(313\) | 189.513 | − | 189.513i | 0.605474 | − | 0.605474i | −0.336286 | − | 0.941760i | \(-0.609171\pi\) |
0.941760 | + | 0.336286i | \(0.109171\pi\) | |||||||
\(314\) | 57.1422i | 0.181981i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −66.1663 | −0.209387 | ||||||||
\(317\) | 21.9357 | + | 21.9357i | 0.0691977 | + | 0.0691977i | 0.740859 | − | 0.671661i | \(-0.234419\pi\) |
−0.671661 | + | 0.740859i | \(0.734419\pi\) | |||||||
\(318\) | 13.7259 | − | 13.7259i | 0.0431633 | − | 0.0431633i | ||||
\(319\) | 500.780i | 1.56984i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1801 | −0.0348289 | ||||||||
\(322\) | −72.9374 | − | 72.9374i | −0.226514 | − | 0.226514i | ||||
\(323\) | 32.7918 | − | 32.7918i | 0.101523 | − | 0.101523i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 74.5817 | 0.228778 | ||||||||
\(327\) | 71.1311 | + | 71.1311i | 0.217526 | + | 0.217526i | ||||
\(328\) | 53.2466 | − | 53.2466i | 0.162337 | − | 0.162337i | ||||
\(329\) | − | 126.806i | − | 0.385429i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 165.937 | 0.501320 | 0.250660 | − | 0.968075i | \(-0.419352\pi\) | ||||
0.250660 | + | 0.968075i | \(0.419352\pi\) | |||||||
\(332\) | 194.172 | + | 194.172i | 0.584855 | + | 0.584855i | ||||
\(333\) | 91.3880 | − | 91.3880i | 0.274438 | − | 0.274438i | ||||
\(334\) | 141.493i | 0.423633i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | −73.8705 | − | 73.8705i | −0.219200 | − | 0.219200i | 0.588961 | − | 0.808161i | \(-0.299537\pi\) |
−0.808161 | + | 0.588961i | \(0.799537\pi\) | |||||||
\(338\) | 260.037 | − | 260.037i | 0.769340 | − | 0.769340i | ||||
\(339\) | − | 23.4830i | − | 0.0692713i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 420.820 | 1.23408 | ||||||||
\(342\) | 6.15045 | + | 6.15045i | 0.0179838 | + | 0.0179838i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 31.5960i | − | 0.0918489i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −147.810 | −0.427196 | ||||||||
\(347\) | −31.2699 | − | 31.2699i | −0.0901149 | − | 0.0901149i | 0.660612 | − | 0.750727i | \(-0.270297\pi\) |
−0.750727 | + | 0.660612i | \(0.770297\pi\) | |||||||
\(348\) | 81.0871 | − | 81.0871i | 0.233009 | − | 0.233009i | ||||
\(349\) | − | 546.387i | − | 1.56558i | −0.622287 | − | 0.782789i | \(-0.713796\pi\) | ||
0.622287 | − | 0.782789i | \(-0.286204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −107.629 | −0.306635 | ||||||||
\(352\) | −60.5106 | − | 60.5106i | −0.171905 | − | 0.171905i | ||||
\(353\) | 184.331 | − | 184.331i | 0.522184 | − | 0.522184i | −0.396046 | − | 0.918231i | \(-0.629618\pi\) |
0.918231 | + | 0.396046i | \(0.129618\pi\) | |||||||
\(354\) | − | 14.2241i | − | 0.0401811i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 68.4265 | 0.192209 | ||||||||
\(357\) | 73.2975 | + | 73.2975i | 0.205315 | + | 0.205315i | ||||
\(358\) | −280.292 | + | 280.292i | −0.782938 | + | 0.782938i | ||||
\(359\) | 319.232i | 0.889226i | 0.895723 | + | 0.444613i | \(0.146659\pi\) | ||||
−0.895723 | + | 0.444613i | \(0.853341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 356.797 | 0.988357 | ||||||||
\(362\) | −139.086 | − | 139.086i | −0.384215 | − | 0.384215i | ||||
\(363\) | −132.083 | + | 132.083i | −0.363866 | + | 0.363866i | ||||
\(364\) | − | 109.604i | − | 0.301110i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 240.579 | 0.657320 | ||||||||
\(367\) | −116.440 | − | 116.440i | −0.317276 | − | 0.317276i | 0.530444 | − | 0.847720i | \(-0.322025\pi\) |
−0.847720 | + | 0.530444i | \(0.822025\pi\) | |||||||
\(368\) | 77.9733 | − | 77.9733i | 0.211884 | − | 0.211884i | ||||
\(369\) | 79.8698i | 0.216449i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.9667 | −0.0565140 | ||||||||
\(372\) | −68.1397 | − | 68.1397i | −0.183171 | − | 0.183171i | ||||
\(373\) | −380.962 | + | 380.962i | −1.02135 | + | 1.02135i | −0.0215784 | + | 0.999767i | \(0.506869\pi\) |
−0.999767 | + | 0.0215784i | \(0.993131\pi\) | |||||||
\(374\) | − | 483.928i | − | 1.29392i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 135.561 | 0.360536 | ||||||||
\(377\) | −484.851 | − | 484.851i | −1.28608 | − | 1.28608i | ||||
\(378\) | −13.7477 | + | 13.7477i | −0.0363696 | + | 0.0363696i | ||||
\(379\) | 189.542i | 0.500111i | 0.968231 | + | 0.250056i | \(0.0804489\pi\) | ||||
−0.968231 | + | 0.250056i | \(0.919551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −345.372 | −0.906489 | ||||||||
\(382\) | −231.713 | − | 231.713i | −0.606580 | − | 0.606580i | ||||
\(383\) | 306.102 | − | 306.102i | 0.799222 | − | 0.799222i | −0.183751 | − | 0.982973i | \(-0.558824\pi\) |
0.982973 | + | 0.183751i | \(0.0588239\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 297.977 | 0.771962 | ||||||||
\(387\) | 23.6970 | + | 23.6970i | 0.0612326 | + | 0.0612326i | ||||
\(388\) | 208.786 | − | 208.786i | 0.538108 | − | 0.538108i | ||||
\(389\) | 316.187i | 0.812819i | 0.913691 | + | 0.406410i | \(0.133219\pi\) | ||||
−0.913691 | + | 0.406410i | \(0.866781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 623.585 | 1.59485 | ||||||||
\(392\) | −14.0000 | − | 14.0000i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | −226.288 | + | 226.288i | −0.575797 | + | 0.575797i | ||||
\(394\) | 510.179i | 1.29487i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 90.7659 | 0.229207 | ||||||||
\(397\) | 134.126 | + | 134.126i | 0.337849 | + | 0.337849i | 0.855557 | − | 0.517709i | \(-0.173215\pi\) |
−0.517709 | + | 0.855557i | \(0.673215\pi\) | |||||||
\(398\) | −321.154 | + | 321.154i | −0.806920 | + | 0.806920i | ||||
\(399\) | − | 9.39496i | − | 0.0235463i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −504.024 | −1.25692 | −0.628459 | − | 0.777842i | \(-0.716314\pi\) | ||||
−0.628459 | + | 0.777842i | \(0.716314\pi\) | |||||||
\(402\) | 126.518 | + | 126.518i | 0.314723 | + | 0.314723i | ||||
\(403\) | −407.434 | + | 407.434i | −1.01100 | + | 1.01100i | ||||
\(404\) | 100.571i | 0.248938i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −123.863 | −0.305080 | ||||||||
\(407\) | 460.828 | + | 460.828i | 1.13226 | + | 1.13226i | ||||
\(408\) | −78.3583 | + | 78.3583i | −0.192055 | + | 0.192055i | ||||
\(409\) | 112.495i | 0.275048i | 0.990498 | + | 0.137524i | \(0.0439145\pi\) | ||||
−0.990498 | + | 0.137524i | \(0.956086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −417.304 | −1.01534 | ||||||||
\(412\) | −14.2292 | − | 14.2292i | −0.0345370 | − | 0.0345370i | ||||
\(413\) | −10.8638 | + | 10.8638i | −0.0263047 | + | 0.0263047i | ||||
\(414\) | 116.960i | 0.282512i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 117.172 | 0.281663 | ||||||||
\(417\) | −135.466 | − | 135.466i | −0.324860 | − | 0.324860i | ||||
\(418\) | −31.0139 | + | 31.0139i | −0.0741960 | + | 0.0741960i | ||||
\(419\) | 224.563i | 0.535950i | 0.963426 | + | 0.267975i | \(0.0863545\pi\) | ||||
−0.963426 | + | 0.267975i | \(0.913645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 474.635 | 1.12740 | 0.563699 | − | 0.825980i | \(-0.309378\pi\) | ||||
0.563699 | + | 0.825980i | \(0.309378\pi\) | |||||||
\(422\) | 22.7166 | + | 22.7166i | 0.0538308 | + | 0.0538308i | ||||
\(423\) | −101.671 | + | 101.671i | −0.240357 | + | 0.240357i | ||||
\(424\) | − | 22.4143i | − | 0.0528640i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 295.033 | 0.692565 | ||||||||
\(427\) | −183.745 | − | 183.745i | −0.430317 | − | 0.430317i | ||||
\(428\) | −9.12850 | + | 9.12850i | −0.0213283 | + | 0.0213283i | ||||
\(429\) | − | 542.724i | − | 1.26509i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 142.798 | 0.331317 | 0.165659 | − | 0.986183i | \(-0.447025\pi\) | ||||
0.165659 | + | 0.986183i | \(0.447025\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 226.490 | − | 226.490i | 0.523072 | − | 0.523072i | −0.395426 | − | 0.918498i | \(-0.629403\pi\) |
0.918498 | + | 0.395426i | \(0.129403\pi\) | |||||||
\(434\) | 104.085i | 0.239828i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 116.157 | 0.266414 | ||||||||
\(437\) | −39.9642 | − | 39.9642i | −0.0914514 | − | 0.0914514i | ||||
\(438\) | 200.750 | − | 200.750i | 0.458333 | − | 0.458333i | ||||
\(439\) | 231.354i | 0.527003i | 0.964659 | + | 0.263502i | \(0.0848774\pi\) | ||||
−0.964659 | + | 0.263502i | \(0.915123\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | 468.535 | + | 468.535i | 1.06003 | + | 1.06003i | ||||
\(443\) | 291.498 | − | 291.498i | 0.658008 | − | 0.658008i | −0.296900 | − | 0.954909i | \(-0.595953\pi\) |
0.954909 | + | 0.296900i | \(0.0959529\pi\) | |||||||
\(444\) | − | 149.236i | − | 0.336117i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −317.937 | −0.712863 | ||||||||
\(447\) | 184.575 | + | 184.575i | 0.412919 | + | 0.412919i | ||||
\(448\) | 14.9666 | − | 14.9666i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 186.920i | 0.416303i | 0.978097 | + | 0.208152i | \(0.0667448\pi\) | ||||
−0.978097 | + | 0.208152i | \(0.933255\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −402.747 | −0.893010 | ||||||||
\(452\) | −19.1738 | − | 19.1738i | −0.0424198 | − | 0.0424198i | ||||
\(453\) | 233.245 | − | 233.245i | 0.514891 | − | 0.514891i | ||||
\(454\) | 104.330i | 0.229802i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.0436 | 0.0220255 | ||||||||
\(457\) | 358.683 | + | 358.683i | 0.784865 | + | 0.784865i | 0.980647 | − | 0.195782i | \(-0.0627246\pi\) |
−0.195782 | + | 0.980647i | \(0.562725\pi\) | |||||||
\(458\) | −115.486 | + | 115.486i | −0.252152 | + | 0.252152i | ||||
\(459\) | − | 117.537i | − | 0.256073i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −178.973 | −0.388227 | −0.194113 | − | 0.980979i | \(-0.562183\pi\) | ||||
−0.194113 | + | 0.980979i | \(0.562183\pi\) | |||||||
\(462\) | −69.3236 | − | 69.3236i | −0.150051 | − | 0.150051i | ||||
\(463\) | −244.313 | + | 244.313i | −0.527675 | + | 0.527675i | −0.919878 | − | 0.392204i | \(-0.871713\pi\) |
0.392204 | + | 0.919878i | \(0.371713\pi\) | |||||||
\(464\) | − | 132.415i | − | 0.285376i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 595.149 | 1.27714 | ||||||||
\(467\) | −165.494 | − | 165.494i | −0.354377 | − | 0.354377i | 0.507358 | − | 0.861735i | \(-0.330622\pi\) |
−0.861735 | + | 0.507358i | \(0.830622\pi\) | |||||||
\(468\) | −87.8787 | + | 87.8787i | −0.187775 | + | 0.187775i | ||||
\(469\) | − | 193.260i | − | 0.412069i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −69.9846 | −0.148587 | ||||||||
\(472\) | −11.6139 | − | 11.6139i | −0.0246058 | − | 0.0246058i | ||||
\(473\) | −119.493 | + | 119.493i | −0.252629 | + | 0.252629i | ||||
\(474\) | − | 81.0368i | − | 0.170964i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 119.694 | 0.251459 | ||||||||
\(477\) | 16.8107 | + | 16.8107i | 0.0352427 | + | 0.0352427i | ||||
\(478\) | −136.556 | + | 136.556i | −0.285681 | + | 0.285681i | ||||
\(479\) | − | 326.343i | − | 0.681300i | −0.940190 | − | 0.340650i | \(-0.889353\pi\) | ||
0.940190 | − | 0.340650i | \(-0.110647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −892.340 | −1.85518 | ||||||||
\(482\) | 61.0110 | + | 61.0110i | 0.126579 | + | 0.126579i | ||||
\(483\) | 89.3297 | − | 89.3297i | 0.184948 | − | 0.184948i | ||||
\(484\) | 215.691i | 0.445643i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 373.708 | + | 373.708i | 0.767367 | + | 0.767367i | 0.977642 | − | 0.210275i | \(-0.0674360\pi\) |
−0.210275 | + | 0.977642i | \(0.567436\pi\) | |||||||
\(488\) | 196.432 | − | 196.432i | 0.402525 | − | 0.402525i | ||||
\(489\) | 91.3435i | 0.186797i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 418.263 | 0.851859 | 0.425930 | − | 0.904756i | \(-0.359947\pi\) | ||||
0.425930 | + | 0.904756i | \(0.359947\pi\) | |||||||
\(492\) | 65.2134 | + | 65.2134i | 0.132548 | + | 0.132548i | ||||
\(493\) | 529.487 | − | 529.487i | 1.07401 | − | 1.07401i | ||||
\(494\) | − | 60.0548i | − | 0.121568i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −111.272 | −0.224338 | ||||||||
\(497\) | −225.335 | − | 225.335i | −0.453390 | − | 0.453390i | ||||
\(498\) | −237.811 | + | 237.811i | −0.477532 | + | 0.477532i | ||||
\(499\) | − | 541.732i | − | 1.08563i | −0.839851 | − | 0.542817i | \(-0.817358\pi\) | ||
0.839851 | − | 0.542817i | \(-0.182642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −173.293 | −0.345895 | ||||||||
\(502\) | 215.934 | + | 215.934i | 0.430147 | + | 0.430147i | ||||
\(503\) | 419.289 | − | 419.289i | 0.833578 | − | 0.833578i | −0.154427 | − | 0.988004i | \(-0.549353\pi\) |
0.988004 | + | 0.154427i | \(0.0493531\pi\) | |||||||
\(504\) | 22.4499i | 0.0445435i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −589.776 | −1.16557 | ||||||||
\(507\) | 318.479 | + | 318.479i | 0.628164 | + | 0.628164i | ||||
\(508\) | −281.995 | + | 281.995i | −0.555109 | + | 0.555109i | ||||
\(509\) | 340.522i | 0.669002i | 0.942395 | + | 0.334501i | \(0.108568\pi\) | ||||
−0.942395 | + | 0.334501i | \(0.891432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −306.651 | −0.600099 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −7.53273 | + | 7.53273i | −0.0146837 | + | 0.0146837i | ||||
\(514\) | 289.158i | 0.562564i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 38.6971 | 0.0749944 | ||||||||
\(517\) | −512.681 | − | 512.681i | −0.991647 | − | 0.991647i | ||||
\(518\) | −113.981 | + | 113.981i | −0.220040 | + | 0.220040i | ||||
\(519\) | − | 181.029i | − | 0.348804i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −507.014 | −0.973155 | −0.486578 | − | 0.873637i | \(-0.661755\pi\) | ||||
−0.486578 | + | 0.873637i | \(0.661755\pi\) | |||||||
\(522\) | 99.3110 | + | 99.3110i | 0.190251 | + | 0.190251i | ||||
\(523\) | 286.897 | − | 286.897i | 0.548561 | − | 0.548561i | −0.377464 | − | 0.926024i | \(-0.623204\pi\) |
0.926024 | + | 0.377464i | \(0.123204\pi\) | |||||||
\(524\) | 369.527i | 0.705205i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.779357 | 0.00148167 | ||||||||
\(527\) | −444.943 | − | 444.943i | −0.844294 | − | 0.844294i | ||||
\(528\) | 74.1100 | − | 74.1100i | 0.140360 | − | 0.140360i | ||||
\(529\) | − | 230.980i | − | 0.436635i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.4209 | 0.0328077 | ||||||||
\(532\) | −7.67096 | − | 7.67096i | −0.0144191 | − | 0.0144191i | ||||
\(533\) | 389.937 | − | 389.937i | 0.731588 | − | 0.731588i | ||||
\(534\) | 83.8050i | 0.156938i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 206.604 | 0.385455 | ||||||||
\(537\) | −343.286 | − | 343.286i | −0.639266 | − | 0.639266i | ||||
\(538\) | −272.956 | + | 272.956i | −0.507353 | + | 0.507353i | ||||
\(539\) | 105.894i | 0.196463i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −604.754 | −1.11784 | −0.558922 | − | 0.829220i | \(-0.688785\pi\) | ||||
−0.558922 | + | 0.829220i | \(0.688785\pi\) | |||||||
\(542\) | −176.708 | − | 176.708i | −0.326029 | − | 0.326029i | ||||
\(543\) | 170.345 | − | 170.345i | 0.313710 | − | 0.313710i | ||||
\(544\) | 127.959i | 0.235218i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 134.237 | 0.245855 | ||||||||
\(547\) | −298.464 | − | 298.464i | −0.545637 | − | 0.545637i | 0.379539 | − | 0.925176i | \(-0.376083\pi\) |
−0.925176 | + | 0.379539i | \(0.876083\pi\) | |||||||
\(548\) | −340.727 | + | 340.727i | −0.621765 | + | 0.621765i | ||||
\(549\) | 294.648i | 0.536699i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −67.8675 | −0.123171 | ||||||||
\(552\) | 95.4974 | + | 95.4974i | 0.173003 | + | 0.173003i | ||||
\(553\) | −61.8929 | + | 61.8929i | −0.111922 | + | 0.111922i | ||||
\(554\) | 406.304i | 0.733402i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −221.216 | −0.397870 | ||||||||
\(557\) | −392.034 | − | 392.034i | −0.703831 | − | 0.703831i | 0.261400 | − | 0.965231i | \(-0.415816\pi\) |
−0.965231 | + | 0.261400i | \(0.915816\pi\) | |||||||
\(558\) | 83.4538 | − | 83.4538i | 0.149559 | − | 0.149559i | ||||
\(559\) | − | 231.385i | − | 0.413926i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 592.688 | 1.05649 | ||||||||
\(562\) | 368.543 | + | 368.543i | 0.655770 | + | 0.655770i | ||||
\(563\) | −575.129 | + | 575.129i | −1.02154 | + | 1.02154i | −0.0217803 | + | 0.999763i | \(0.506933\pi\) |
−0.999763 | + | 0.0217803i | \(0.993067\pi\) | |||||||
\(564\) | 166.028i | 0.294376i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −771.201 | −1.36255 | ||||||||
\(567\) | −16.8375 | − | 16.8375i | −0.0296957 | − | 0.0296957i | ||||
\(568\) | 240.893 | − | 240.893i | 0.424108 | − | 0.424108i | ||||
\(569\) | 193.452i | 0.339986i | 0.985445 | + | 0.169993i | \(0.0543745\pi\) | ||||
−0.985445 | + | 0.169993i | \(0.945625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 117.456 | 0.205703 | 0.102851 | − | 0.994697i | \(-0.467203\pi\) | ||||
0.102851 | + | 0.994697i | \(0.467203\pi\) | |||||||
\(572\) | −443.133 | − | 443.133i | −0.774707 | − | 0.774707i | ||||
\(573\) | 283.790 | − | 283.790i | 0.495270 | − | 0.495270i | ||||
\(574\) | − | 99.6152i | − | 0.173546i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 703.423 | + | 703.423i | 1.21910 | + | 1.21910i | 0.967946 | + | 0.251157i | \(0.0808111\pi\) |
0.251157 | + | 0.967946i | \(0.419189\pi\) | |||||||
\(578\) | −222.669 | + | 222.669i | −0.385240 | + | 0.385240i | ||||
\(579\) | 364.946i | 0.630304i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 363.262 | 0.625236 | ||||||||
\(582\) | 255.709 | + | 255.709i | 0.439363 | + | 0.439363i | ||||
\(583\) | −84.7690 | + | 84.7690i | −0.145401 | + | 0.145401i | ||||
\(584\) | − | 327.823i | − | 0.561341i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 483.306 | 0.824754 | ||||||||
\(587\) | 180.492 | + | 180.492i | 0.307483 | + | 0.307483i | 0.843932 | − | 0.536450i | \(-0.180235\pi\) |
−0.536450 | + | 0.843932i | \(0.680235\pi\) | |||||||
\(588\) | 17.1464 | − | 17.1464i | 0.0291606 | − | 0.0291606i | ||||
\(589\) | 57.0309i | 0.0968267i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −624.840 | −1.05726 | ||||||||
\(592\) | −121.851 | − | 121.851i | −0.205829 | − | 0.205829i | ||||
\(593\) | 701.554 | − | 701.554i | 1.18306 | − | 1.18306i | 0.204111 | − | 0.978948i | \(-0.434570\pi\) |
0.978948 | − | 0.204111i | \(-0.0654304\pi\) | |||||||
\(594\) | 111.165i | 0.187147i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 301.410 | 0.505721 | ||||||||
\(597\) | −393.332 | − | 393.332i | −0.658848 | − | 0.658848i | ||||
\(598\) | 571.016 | − | 571.016i | 0.954877 | − | 0.954877i | ||||
\(599\) | − | 349.739i | − | 0.583871i | −0.956438 | − | 0.291935i | \(-0.905701\pi\) | ||
0.956438 | − | 0.291935i | \(-0.0942992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −227.029 | −0.377752 | −0.188876 | − | 0.982001i | \(-0.560484\pi\) | ||||
−0.188876 | + | 0.982001i | \(0.560484\pi\) | |||||||
\(602\) | −29.5554 | − | 29.5554i | −0.0490953 | − | 0.0490953i | ||||
\(603\) | −154.953 | + | 154.953i | −0.256970 | + | 0.256970i | ||||
\(604\) | − | 380.888i | − | 0.630610i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −123.174 | −0.203257 | ||||||||
\(607\) | −13.0530 | − | 13.0530i | −0.0215042 | − | 0.0215042i | 0.696273 | − | 0.717777i | \(-0.254840\pi\) |
−0.717777 | + | 0.696273i | \(0.754840\pi\) | |||||||
\(608\) | 8.20060 | − | 8.20060i | 0.0134878 | − | 0.0134878i | ||||
\(609\) | − | 151.700i | − | 0.249097i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 992.747 | 1.62479 | ||||||||
\(612\) | −95.9689 | − | 95.9689i | −0.156812 | − | 0.156812i | ||||
\(613\) | 301.420 | − | 301.420i | 0.491713 | − | 0.491713i | −0.417133 | − | 0.908846i | \(-0.636965\pi\) |
0.908846 | + | 0.417133i | \(0.136965\pi\) | |||||||
\(614\) | − | 631.026i | − | 1.02773i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −113.205 | −0.183774 | ||||||||
\(617\) | 676.069 | + | 676.069i | 1.09574 | + | 1.09574i | 0.994904 | + | 0.100832i | \(0.0321503\pi\) |
0.100832 | + | 0.994904i | \(0.467850\pi\) | |||||||
\(618\) | 17.4272 | − | 17.4272i | 0.0281993 | − | 0.0281993i | ||||
\(619\) | − | 180.575i | − | 0.291721i | −0.989305 | − | 0.145860i | \(-0.953405\pi\) | ||
0.989305 | − | 0.145860i | \(-0.0465950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −143.246 | −0.230670 | ||||||||
\(622\) | 84.6545 | + | 84.6545i | 0.136101 | + | 0.136101i | ||||
\(623\) | 64.0071 | − | 64.0071i | 0.102740 | − | 0.102740i | ||||
\(624\) | 143.505i | 0.229976i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 379.027 | 0.605474 | ||||||||
\(627\) | −37.9842 | − | 37.9842i | −0.0605808 | − | 0.0605808i | ||||
\(628\) | −57.1422 | + | 57.1422i | −0.0909907 | + | 0.0909907i | ||||
\(629\) | − | 974.490i | − | 1.54927i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −778.962 | −1.23449 | −0.617244 | − | 0.786771i | \(-0.711751\pi\) | ||||
−0.617244 | + | 0.786771i | \(0.711751\pi\) | |||||||
\(632\) | −66.1663 | − | 66.1663i | −0.104693 | − | 0.104693i | ||||
\(633\) | −27.8220 | + | 27.8220i | −0.0439527 | + | 0.0439527i | ||||
\(634\) | 43.8713i | 0.0691977i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 27.4518 | 0.0431633 | ||||||||
\(637\) | −102.525 | − | 102.525i | −0.160950 | − | 0.160950i | ||||
\(638\) | −500.780 | + | 500.780i | −0.784922 | + | 0.784922i | ||||
\(639\) | 361.340i | 0.565477i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 773.498 | 1.20671 | 0.603353 | − | 0.797475i | \(-0.293831\pi\) | ||||
0.603353 | + | 0.797475i | \(0.293831\pi\) | |||||||
\(642\) | −11.1801 | − | 11.1801i | −0.0174145 | − | 0.0174145i | ||||
\(643\) | −544.963 | + | 544.963i | −0.847532 | + | 0.847532i | −0.989825 | − | 0.142292i | \(-0.954553\pi\) |
0.142292 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(644\) | − | 145.875i | − | 0.226514i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 65.5835 | 0.101523 | ||||||||
\(647\) | 654.936 | + | 654.936i | 1.01227 | + | 1.01227i | 0.999924 | + | 0.0123424i | \(0.00392881\pi\) |
0.0123424 | + | 0.999924i | \(0.496071\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 87.8457i | 0.135355i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −127.478 | −0.195818 | ||||||||
\(652\) | 74.5817 | + | 74.5817i | 0.114389 | + | 0.114389i | ||||
\(653\) | 504.090 | − | 504.090i | 0.771960 | − | 0.771960i | −0.206489 | − | 0.978449i | \(-0.566204\pi\) |
0.978449 | + | 0.206489i | \(0.0662038\pi\) | |||||||
\(654\) | 142.262i | 0.217526i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 106.493 | 0.162337 | ||||||||
\(657\) | 245.868 | + | 245.868i | 0.374228 | + | 0.374228i | ||||
\(658\) | 126.806 | − | 126.806i | 0.192715 | − | 0.192715i | ||||
\(659\) | − | 726.533i | − | 1.10248i | −0.834347 | − | 0.551239i | \(-0.814155\pi\) | ||
0.834347 | − | 0.551239i | \(-0.185845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1149.24 | 1.73865 | 0.869323 | − | 0.494245i | \(-0.164555\pi\) | ||||
0.869323 | + | 0.494245i | \(0.164555\pi\) | |||||||
\(662\) | 165.937 | + | 165.937i | 0.250660 | + | 0.250660i | ||||
\(663\) | −573.835 | + | 573.835i | −0.865514 | + | 0.865514i | ||||
\(664\) | 388.344i | 0.584855i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 182.776 | 0.274438 | ||||||||
\(667\) | −645.301 | − | 645.301i | −0.967467 | − | 0.967467i | ||||
\(668\) | −141.493 | + | 141.493i | −0.211816 | + | 0.211816i | ||||
\(669\) | − | 389.391i | − | 0.582050i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1485.78 | −2.21427 | ||||||||
\(672\) | 18.3303 | + | 18.3303i | 0.0272772 | + | 0.0272772i | ||||
\(673\) | −743.671 | + | 743.671i | −1.10501 | + | 1.10501i | −0.111212 | + | 0.993797i | \(0.535473\pi\) |
−0.993797 | + | 0.111212i | \(0.964527\pi\) | |||||||
\(674\) | − | 147.741i | − | 0.219200i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 520.074 | 0.769340 | ||||||||
\(677\) | 182.111 | + | 182.111i | 0.268997 | + | 0.268997i | 0.828696 | − | 0.559699i | \(-0.189083\pi\) |
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(678\) | 23.4830 | − | 23.4830i | 0.0346356 | − | 0.0346356i | ||||
\(679\) | − | 390.603i | − | 0.575261i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −127.778 | −0.187632 | ||||||||
\(682\) | 420.820 | + | 420.820i | 0.617038 | + | 0.617038i | ||||
\(683\) | −309.149 | + | 309.149i | −0.452634 | + | 0.452634i | −0.896228 | − | 0.443594i | \(-0.853703\pi\) |
0.443594 | + | 0.896228i | \(0.353703\pi\) | |||||||
\(684\) | 12.3009i | 0.0179838i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.1916 | −0.0381802 | ||||||||
\(687\) | −141.441 | − | 141.441i | −0.205882 | − | 0.205882i | ||||
\(688\) | 31.5960 | − | 31.5960i | 0.0459245 | − | 0.0459245i | ||||
\(689\) | − | 164.145i | − | 0.238237i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −634.866 | −0.918764 | −0.459382 | − | 0.888239i | \(-0.651929\pi\) | ||||
−0.459382 | + | 0.888239i | \(0.651929\pi\) | |||||||
\(692\) | −147.810 | − | 147.810i | −0.213598 | − | 0.213598i | ||||
\(693\) | 84.9037 | − | 84.9037i | 0.122516 | − | 0.122516i | ||||
\(694\) | − | 62.5397i | − | 0.0901149i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 162.174 | 0.233009 | ||||||||
\(697\) | 425.835 | + | 425.835i | 0.610953 | + | 0.610953i | ||||
\(698\) | 546.387 | − | 546.387i | 0.782789 | − | 0.782789i | ||||
\(699\) | 728.906i | 1.04278i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 863.013 | 1.23112 | 0.615559 | − | 0.788091i | \(-0.288930\pi\) | ||||
0.615559 | + | 0.788091i | \(0.288930\pi\) | |||||||
\(702\) | −107.629 | − | 107.629i | −0.153318 | − | 0.153318i | ||||
\(703\) | −62.4530 | + | 62.4530i | −0.0888379 | + | 0.0888379i | ||||
\(704\) | − | 121.021i | − | 0.171905i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 368.662 | 0.522184 | ||||||||
\(707\) | 94.0754 | + | 94.0754i | 0.133063 | + | 0.133063i | ||||
\(708\) | 14.2241 | − | 14.2241i | 0.0200905 | − | 0.0200905i | ||||
\(709\) | − | 653.419i | − | 0.921607i | −0.887502 | − | 0.460803i | \(-0.847561\pi\) | ||
0.887502 | − | 0.460803i | \(-0.152439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 99.2494 | 0.139591 | ||||||||
\(712\) | 68.4265 | + | 68.4265i | 0.0961046 | + | 0.0961046i | ||||
\(713\) | −542.264 | + | 542.264i | −0.760539 | + | 0.760539i | ||||
\(714\) | 146.595i | 0.205315i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −560.583 | −0.782938 | ||||||||
\(717\) | −167.246 | − | 167.246i | −0.233258 | − | 0.233258i | ||||
\(718\) | −319.232 | + | 319.232i | −0.444613 | + | 0.444613i | ||||
\(719\) | − | 961.796i | − | 1.33769i | −0.743404 | − | 0.668843i | \(-0.766790\pi\) | ||
0.743404 | − | 0.668843i | \(-0.233210\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.6204 | −0.0369216 | ||||||||
\(722\) | 356.797 | + | 356.797i | 0.494179 | + | 0.494179i | ||||
\(723\) | −74.7229 | + | 74.7229i | −0.103351 | + | 0.103351i | ||||
\(724\) | − | 278.172i | − | 0.384215i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −264.167 | −0.363866 | ||||||||
\(727\) | −948.990 | − | 948.990i | −1.30535 | − | 1.30535i | −0.924733 | − | 0.380618i | \(-0.875711\pi\) |
−0.380618 | − | 0.924733i | \(-0.624289\pi\) | |||||||
\(728\) | 109.604 | − | 109.604i | 0.150555 | − | 0.150555i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 252.686 | 0.345672 | ||||||||
\(732\) | 240.579 | + | 240.579i | 0.328660 | + | 0.328660i | ||||
\(733\) | −731.489 | + | 731.489i | −0.997938 | + | 0.997938i | −0.999998 | − | 0.00205981i | \(-0.999344\pi\) |
0.00205981 | + | 0.999998i | \(0.499344\pi\) | |||||||
\(734\) | − | 232.880i | − | 0.317276i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 155.947 | 0.211884 | ||||||||
\(737\) | −781.357 | − | 781.357i | −1.06019 | − | 1.06019i | ||||
\(738\) | −79.8698 | + | 79.8698i | −0.108225 | + | 0.108225i | ||||
\(739\) | 33.8430i | 0.0457956i | 0.999738 | + | 0.0228978i | \(0.00728924\pi\) | ||||
−0.999738 | + | 0.0228978i | \(0.992711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 73.5518 | 0.0992602 | ||||||||
\(742\) | −20.9667 | − | 20.9667i | −0.0282570 | − | 0.0282570i | ||||
\(743\) | −39.7475 | + | 39.7475i | −0.0534959 | + | 0.0534959i | −0.733349 | − | 0.679853i | \(-0.762044\pi\) |
0.679853 | + | 0.733349i | \(0.262044\pi\) | |||||||
\(744\) | − | 136.279i | − | 0.183171i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −761.924 | −1.02135 | ||||||||
\(747\) | −291.258 | − | 291.258i | −0.389903 | − | 0.389903i | ||||
\(748\) | 483.928 | − | 483.928i | 0.646962 | − | 0.646962i | ||||
\(749\) | 17.0779i | 0.0228009i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 578.927 | 0.770874 | 0.385437 | − | 0.922734i | \(-0.374051\pi\) | ||||
0.385437 | + | 0.922734i | \(0.374051\pi\) | |||||||
\(752\) | 135.561 | + | 135.561i | 0.180268 | + | 0.180268i | ||||
\(753\) | −264.464 | + | 264.464i | −0.351214 | + | 0.351214i | ||||
\(754\) | − | 969.702i | − | 1.28608i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | −114.632 | − | 114.632i | −0.151429 | − | 0.151429i | 0.627327 | − | 0.778756i | \(-0.284149\pi\) |
−0.778756 | + | 0.627327i | \(0.784149\pi\) | |||||||
\(758\) | −189.542 | + | 189.542i | −0.250056 | + | 0.250056i | ||||
\(759\) | − | 722.326i | − | 0.951681i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −87.5262 | −0.115015 | −0.0575073 | − | 0.998345i | \(-0.518315\pi\) | ||||
−0.0575073 | + | 0.998345i | \(0.518315\pi\) | |||||||
\(762\) | −345.372 | − | 345.372i | −0.453245 | − | 0.453245i | ||||
\(763\) | 108.655 | − | 108.655i | 0.142404 | − | 0.142404i | ||||
\(764\) | − | 463.427i | − | 0.606580i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 612.204 | 0.799222 | ||||||||
\(767\) | −85.0514 | − | 85.0514i | −0.110888 | − | 0.110888i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 780.679i | − | 1.01519i | −0.861596 | − | 0.507594i | \(-0.830535\pi\) | ||
0.861596 | − | 0.507594i | \(-0.169465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −354.144 | −0.459331 | ||||||||
\(772\) | 297.977 | + | 297.977i | 0.385981 | + | 0.385981i | ||||
\(773\) | −692.751 | + | 692.751i | −0.896186 | + | 0.896186i | −0.995096 | − | 0.0989107i | \(-0.968464\pi\) |
0.0989107 | + | 0.995096i | \(0.468464\pi\) | |||||||
\(774\) | 47.3941i | 0.0612326i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 417.572 | 0.538108 | ||||||||
\(777\) | −139.597 | − | 139.597i | −0.179662 | − | 0.179662i | ||||
\(778\) | −316.187 | + | 316.187i | −0.406410 | + | 0.406410i | ||||
\(779\) | − | 54.5817i | − | 0.0700664i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1822.07 | −2.33300 | ||||||||
\(782\) | 623.585 | + | 623.585i | 0.797423 | + | 0.797423i | ||||
\(783\) | −121.631 | + | 121.631i | −0.155339 | + | 0.155339i | ||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −452.577 | −0.575797 | ||||||||
\(787\) | −505.691 | − | 505.691i | −0.642556 | − | 0.642556i | 0.308627 | − | 0.951183i | \(-0.400130\pi\) |
−0.951183 | + | 0.308627i | \(0.900130\pi\) | |||||||
\(788\) | −510.179 | + | 510.179i | −0.647436 | + | 0.647436i | ||||
\(789\) | 0.954513i | 0.00120978i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.8708 | −0.0453487 | ||||||||
\(792\) | 90.7659 | + | 90.7659i | 0.114603 | + | 0.114603i | ||||
\(793\) | 1438.52 | − | 1438.52i | 1.81402 | − | 1.81402i | ||||
\(794\) | 268.252i | 0.337849i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −642.309 | −0.806920 | ||||||||
\(797\) | −221.290 | − | 221.290i | −0.277654 | − | 0.277654i | 0.554518 | − | 0.832172i | \(-0.312903\pi\) |
−0.832172 | + | 0.554518i | \(0.812903\pi\) | |||||||
\(798\) | 9.39496 | − | 9.39496i | 0.0117731 | − | 0.0117731i | ||||
\(799\) | 1084.14i | 1.35687i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −102.640 | −0.128139 | ||||||||
\(802\) | −504.024 | − | 504.024i | −0.628459 | − | 0.628459i | ||||
\(803\) | −1239.80 | + | 1239.80i | −1.54396 | + | 1.54396i | ||||
\(804\) | 253.037i | 0.314723i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −814.868 | −1.01100 | ||||||||
\(807\) | −334.301 | − | 334.301i | −0.414252 | − | 0.414252i | ||||
\(808\) | −100.571 | + | 100.571i | −0.124469 | + | 0.124469i | ||||
\(809\) | 322.881i | 0.399112i | 0.979886 | + | 0.199556i | \(0.0639500\pi\) | ||||
−0.979886 | + | 0.199556i | \(0.936050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1239.53 | −1.52840 | −0.764199 | − | 0.644981i | \(-0.776865\pi\) | ||||
−0.764199 | + | 0.644981i | \(0.776865\pi\) | |||||||
\(812\) | −123.863 | − | 123.863i | −0.152540 | − | 0.152540i | ||||
\(813\) | 216.422 | − | 216.422i | 0.266202 | − | 0.266202i | ||||
\(814\) | 921.657i | 1.13226i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −156.717 | −0.192055 | ||||||||
\(817\) | −16.1941 | − | 16.1941i | −0.0198215 | − | 0.0198215i | ||||
\(818\) | −112.495 | + | 112.495i | −0.137524 | + | 0.137524i | ||||
\(819\) | 164.406i | 0.200740i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −887.758 | −1.08131 | −0.540657 | − | 0.841243i | \(-0.681824\pi\) | ||||
−0.540657 | + | 0.841243i | \(0.681824\pi\) | |||||||
\(822\) | −417.304 | − | 417.304i | −0.507669 | − | 0.507669i | ||||
\(823\) | 905.171 | − | 905.171i | 1.09984 | − | 1.09984i | 0.105414 | − | 0.994428i | \(-0.466383\pi\) |
0.994428 | − | 0.105414i | \(-0.0336169\pi\) | |||||||
\(824\) | − | 28.4585i | − | 0.0345370i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.7277 | −0.0263047 | ||||||||
\(827\) | −752.036 | − | 752.036i | −0.909354 | − | 0.909354i | 0.0868659 | − | 0.996220i | \(-0.472315\pi\) |
−0.996220 | + | 0.0868659i | \(0.972315\pi\) | |||||||
\(828\) | −116.960 | + | 116.960i | −0.141256 | + | 0.141256i | ||||
\(829\) | 1043.36i | 1.25858i | 0.777172 | + | 0.629288i | \(0.216653\pi\) | ||||
−0.777172 | + | 0.629288i | \(0.783347\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −497.619 | −0.598820 | ||||||||
\(832\) | 117.172 | + | 117.172i | 0.140831 | + | 0.140831i | ||||
\(833\) | 111.964 | − | 111.964i | 0.134410 | − | 0.134410i | ||||
\(834\) | − | 270.933i | − | 0.324860i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −62.0279 | −0.0741960 | ||||||||
\(837\) | 102.210 | + | 102.210i | 0.122114 | + | 0.122114i | ||||
\(838\) | −224.563 | + | 224.563i | −0.267975 | + | 0.267975i | ||||
\(839\) | 28.1225i | 0.0335190i | 0.999860 | + | 0.0167595i | \(0.00533497\pi\) | ||||
−0.999860 | + | 0.0167595i | \(0.994665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −254.852 | −0.303035 | ||||||||
\(842\) | 474.635 | + | 474.635i | 0.563699 | + | 0.563699i | ||||
\(843\) | −451.371 | + | 451.371i | −0.535434 | + | 0.535434i | ||||
\(844\) | 45.4332i | 0.0538308i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −203.342 | −0.240357 | ||||||||
\(847\) | 201.761 | + | 201.761i | 0.238206 | + | 0.238206i | ||||
\(848\) | 22.4143 | − | 22.4143i | 0.0264320 | − | 0.0264320i | ||||
\(849\) | − | 944.525i | − | 1.11251i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1187.64 | −1.39558 | ||||||||
\(852\) | 295.033 | + | 295.033i | 0.346283 | + | 0.346283i | ||||
\(853\) | 285.266 | − | 285.266i | 0.334427 | − | 0.334427i | −0.519838 | − | 0.854265i | \(-0.674008\pi\) |
0.854265 | + | 0.519838i | \(0.174008\pi\) | |||||||
\(854\) | − | 367.491i | − | 0.430317i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.2570 | −0.0213283 | ||||||||
\(857\) | 307.011 | + | 307.011i | 0.358239 | + | 0.358239i | 0.863164 | − | 0.504924i | \(-0.168480\pi\) |
−0.504924 | + | 0.863164i | \(0.668480\pi\) | |||||||
\(858\) | 542.724 | − | 542.724i | 0.632546 | − | 0.632546i | ||||
\(859\) | 875.499i | 1.01921i | 0.860409 | + | 0.509604i | \(0.170208\pi\) | ||||
−0.860409 | + | 0.509604i | \(0.829792\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.003 | 0.141699 | ||||||||
\(862\) | 142.798 | + | 142.798i | 0.165659 | + | 0.165659i | ||||
\(863\) | −642.774 | + | 642.774i | −0.744814 | + | 0.744814i | −0.973500 | − | 0.228686i | \(-0.926557\pi\) |
0.228686 | + | 0.973500i | \(0.426557\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 452.980 | 0.523072 | ||||||||
\(867\) | −272.712 | − | 272.712i | −0.314547 | − | 0.314547i | ||||
\(868\) | −104.085 | + | 104.085i | −0.119914 | + | 0.119914i | ||||
\(869\) | 500.470i | 0.575915i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1513.01 | 1.73709 | ||||||||
\(872\) | 116.157 | + | 116.157i | 0.133207 | + | 0.133207i | ||||
\(873\) | −313.179 | + | 313.179i | −0.358739 | + | 0.358739i | ||||
\(874\) | − | 79.9285i | − | 0.0914514i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 401.500 | 0.458333 | ||||||||
\(877\) | −943.109 | − | 943.109i | −1.07538 | − | 1.07538i | −0.996917 | − | 0.0784638i | \(-0.974999\pi\) |
−0.0784638 | − | 0.996917i | \(-0.525001\pi\) | |||||||
\(878\) | −231.354 | + | 231.354i | −0.263502 | + | 0.263502i | ||||
\(879\) | 591.926i | 0.673408i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −422.894 | −0.480016 | −0.240008 | − | 0.970771i | \(-0.577150\pi\) | ||||
−0.240008 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(882\) | 21.0000 | + | 21.0000i | 0.0238095 | + | 0.0238095i | ||||
\(883\) | 104.376 | − | 104.376i | 0.118206 | − | 0.118206i | −0.645529 | − | 0.763736i | \(-0.723363\pi\) |
0.763736 | + | 0.645529i | \(0.223363\pi\) | |||||||
\(884\) | 937.069i | 1.06003i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 582.995 | 0.658008 | ||||||||
\(887\) | −530.292 | − | 530.292i | −0.597849 | − | 0.597849i | 0.341891 | − | 0.939740i | \(-0.388933\pi\) |
−0.939740 | + | 0.341891i | \(0.888933\pi\) | |||||||
\(888\) | 149.236 | − | 149.236i | 0.168059 | − | 0.168059i | ||||
\(889\) | 527.565i | 0.593436i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −136.149 | −0.152804 | ||||||||
\(892\) | −317.937 | − | 317.937i | −0.356431 | − | 0.356431i | ||||
\(893\) | 69.4803 | − | 69.4803i | 0.0778055 | − | 0.0778055i | ||||
\(894\) | 369.150i | 0.412919i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333 | 0.0334077 | ||||||||
\(897\) | 699.349 | + | 699.349i | 0.779654 | + | 0.779654i | ||||
\(898\) | −186.920 | + | 186.920i | −0.208152 | + | 0.208152i | ||||
\(899\) | 920.875i | 1.02433i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 179.257 | 0.198953 | ||||||||
\(902\) | −402.747 | − | 402.747i | −0.446505 | − | 0.446505i | ||||
\(903\) | 36.1978 | − | 36.1978i | 0.0400862 | − | 0.0400862i | ||||
\(904\) | − | 38.3475i | − | 0.0424198i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 466.491 | 0.514891 | ||||||||
\(907\) | 460.614 | + | 460.614i | 0.507844 | + | 0.507844i | 0.913864 | − | 0.406020i | \(-0.133084\pi\) |
−0.406020 | + | 0.913864i | \(0.633084\pi\) | |||||||
\(908\) | −104.330 | + | 104.330i | −0.114901 | + | 0.114901i | ||||
\(909\) | − | 150.856i | − | 0.165959i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1095.00 | 1.20198 | 0.600990 | − | 0.799257i | \(-0.294773\pi\) | ||||
0.600990 | + | 0.799257i | \(0.294773\pi\) | |||||||
\(912\) | 10.0436 | + | 10.0436i | 0.0110128 | + | 0.0110128i | ||||
\(913\) | 1468.68 | − | 1468.68i | 1.60863 | − | 1.60863i | ||||
\(914\) | 717.367i | 0.784865i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −230.972 | −0.252152 | ||||||||
\(917\) | 345.661 | + | 345.661i | 0.376948 | + | 0.376948i | ||||
\(918\) | 117.537 | − | 117.537i | 0.128036 | − | 0.128036i | ||||
\(919\) | − | 981.230i | − | 1.06772i | −0.845574 | − | 0.533858i | \(-0.820742\pi\) | ||
0.845574 | − | 0.533858i | \(-0.179258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 772.846 | 0.839138 | ||||||||
\(922\) | −178.973 | − | 178.973i | −0.194113 | − | 0.194113i | ||||
\(923\) | 1764.12 | − | 1764.12i | 1.91128 | − | 1.91128i | ||||
\(924\) | − | 138.647i | − | 0.150051i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −488.627 | −0.527675 | ||||||||
\(927\) | 21.3438 | + | 21.3438i | 0.0230246 | + | 0.0230246i | ||||
\(928\) | 132.415 | − | 132.415i | 0.142688 | − | 0.142688i | ||||
\(929\) | 907.859i | 0.977244i | 0.872496 | + | 0.488622i | \(0.162500\pi\) | ||||
−0.872496 | + | 0.488622i | \(0.837500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.3510 | −0.0154147 | ||||||||
\(932\) | 595.149 | + | 595.149i | 0.638572 | + | 0.638572i | ||||
\(933\) | −103.680 | + | 103.680i | −0.111126 | + | 0.111126i | ||||
\(934\) | − | 330.988i | − | 0.354377i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −175.757 | −0.187775 | ||||||||
\(937\) | 1133.74 | + | 1133.74i | 1.20997 | + | 1.20997i | 0.971035 | + | 0.238937i | \(0.0767990\pi\) |
0.238937 | + | 0.971035i | \(0.423201\pi\) | |||||||
\(938\) | 193.260 | − | 193.260i | 0.206034 | − | 0.206034i | ||||
\(939\) | 464.211i | 0.494367i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1246.83 | −1.32500 | −0.662501 | − | 0.749061i | \(-0.730505\pi\) | ||||
−0.662501 | + | 0.749061i | \(0.730505\pi\) | |||||||
\(942\) | −69.9846 | − | 69.9846i | −0.0742936 | − | 0.0742936i | ||||
\(943\) | 518.976 | − | 518.976i | 0.550346 | − | 0.550346i | ||||
\(944\) | − | 23.2278i | − | 0.0246058i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −238.987 | −0.252629 | ||||||||
\(947\) | −435.731 | − | 435.731i | −0.460117 | − | 0.460117i | 0.438577 | − | 0.898694i | \(-0.355483\pi\) |
−0.898694 | + | 0.438577i | \(0.855483\pi\) | |||||||
\(948\) | 81.0368 | − | 81.0368i | 0.0854819 | − | 0.0854819i | ||||
\(949\) | − | 2400.72i | − | 2.52974i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.7312 | −0.0564996 | ||||||||
\(952\) | 119.694 | + | 119.694i | 0.125729 | + | 0.125729i | ||||
\(953\) | −1133.89 | + | 1133.89i | −1.18981 | + | 1.18981i | −0.212687 | + | 0.977120i | \(0.568222\pi\) |
−0.977120 | + | 0.212687i | \(0.931778\pi\) | |||||||
\(954\) | 33.6215i | 0.0352427i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −273.111 | −0.285681 | ||||||||
\(957\) | −613.328 | − | 613.328i | −0.640886 | − | 0.640886i | ||||
\(958\) | 326.343 | − | 326.343i | 0.340650 | − | 0.340650i | ||||
\(959\) | 637.442i | 0.664694i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −187.163 | −0.194759 | ||||||||
\(962\) | −892.340 | − | 892.340i | −0.927588 | − | 0.927588i | ||||
\(963\) | 13.6928 | − | 13.6928i | 0.0142189 | − | 0.0142189i | ||||
\(964\) | 122.022i | 0.126579i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 178.659 | 0.184948 | ||||||||
\(967\) | 1229.34 | + | 1229.34i | 1.27129 | + | 1.27129i | 0.945411 | + | 0.325882i | \(0.105661\pi\) |
0.325882 | + | 0.945411i | \(0.394339\pi\) | |||||||
\(968\) | −215.691 | + | 215.691i | −0.222821 | + | 0.222821i | ||||
\(969\) | 80.3231i | 0.0828928i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −990.708 | −1.02030 | −0.510148 | − | 0.860086i | \(-0.670410\pi\) | ||||
−0.510148 | + | 0.860086i | \(0.670410\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −206.928 | + | 206.928i | −0.212671 | + | 0.212671i | ||||
\(974\) | 747.415i | 0.767367i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 392.864 | 0.402525 | ||||||||
\(977\) | −295.891 | − | 295.891i | −0.302857 | − | 0.302857i | 0.539273 | − | 0.842131i | \(-0.318699\pi\) |
−0.842131 | + | 0.539273i | \(0.818699\pi\) | |||||||
\(978\) | −91.3435 | + | 91.3435i | −0.0933983 | + | 0.0933983i | ||||
\(979\) | − | 517.566i | − | 0.528668i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −174.235 | −0.177610 | ||||||||
\(982\) | 418.263 | + | 418.263i | 0.425930 | + | 0.425930i | ||||
\(983\) | −859.585 | + | 859.585i | −0.874451 | + | 0.874451i | −0.992954 | − | 0.118503i | \(-0.962191\pi\) |
0.118503 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(984\) | 130.427i | 0.132548i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1058.97 | 1.07401 | ||||||||
\(987\) | 155.305 | + | 155.305i | 0.157351 | + | 0.157351i | ||||
\(988\) | 60.0548 | − | 60.0548i | 0.0607842 | − | 0.0607842i | ||||
\(989\) | − | 307.956i | − | 0.311381i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −866.595 | −0.874465 | −0.437233 | − | 0.899348i | \(-0.644041\pi\) | ||||
−0.437233 | + | 0.899348i | \(0.644041\pi\) | |||||||
\(992\) | −111.272 | − | 111.272i | −0.112169 | − | 0.112169i | ||||
\(993\) | −203.231 | + | 203.231i | −0.204663 | + | 0.204663i | ||||
\(994\) | − | 450.670i | − | 0.453390i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −475.622 | −0.477532 | ||||||||
\(997\) | 251.901 | + | 251.901i | 0.252659 | + | 0.252659i | 0.822060 | − | 0.569401i | \(-0.192825\pi\) |
−0.569401 | + | 0.822060i | \(0.692825\pi\) | |||||||
\(998\) | 541.732 | − | 541.732i | 0.542817 | − | 0.542817i | ||||
\(999\) | 223.854i | 0.224078i |
(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 | 1050.3.l.h.757.4 | 16 | ||
5.2 | odd | 4 | 210.3.l.b.43.6 | ✓ | 16 | ||
5.3 | odd | 4 | inner | 1050.3.l.h.43.4 | 16 | ||
5.4 | even | 2 | 210.3.l.b.127.6 | yes | 16 | ||
15.2 | even | 4 | 630.3.o.f.253.5 | 16 | |||
15.14 | odd | 2 | 630.3.o.f.127.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.6 | ✓ | 16 | 5.2 | odd | 4 | ||
210.3.l.b.127.6 | yes | 16 | 5.4 | even | 2 | ||
630.3.o.f.127.5 | 16 | 15.14 | odd | 2 | |||
630.3.o.f.253.5 | 16 | 15.2 | even | 4 | |||
1050.3.l.h.43.4 | 16 | 5.3 | odd | 4 | inner | ||
1050.3.l.h.757.4 | 16 | 1.1 | even | 1 | trivial |