Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(1.17421 + 0.0566033i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.181 |
Dual form | 450.2.h.e.271.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −2.15743 | + | 0.587785i | −0.964832 | + | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.83337 | 0.692947 | 0.346474 | − | 0.938060i | \(-0.387379\pi\) | ||||
0.346474 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.22570 | + | 1.87020i | 0.387600 | + | 0.591410i | ||||
\(11\) | 0.566541 | + | 1.74363i | 0.170819 | + | 0.525726i | 0.999418 | − | 0.0341166i | \(-0.0108618\pi\) |
−0.828599 | + | 0.559842i | \(0.810862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.747156 | + | 2.29951i | −0.207224 | + | 0.637769i | 0.792391 | + | 0.610014i | \(0.208836\pi\) |
−0.999615 | + | 0.0277557i | \(0.991164\pi\) | |||||||
\(14\) | −0.566541 | − | 1.74363i | −0.151414 | − | 0.466006i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 2.25284 | + | 1.63679i | 0.546395 | + | 0.396979i | 0.826455 | − | 0.563003i | \(-0.190354\pi\) |
−0.280060 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35294 | + | 0.982966i | 0.310385 | + | 0.225508i | 0.732062 | − | 0.681238i | \(-0.238558\pi\) |
−0.421677 | + | 0.906746i | \(0.638558\pi\) | |||||||
\(20\) | 1.39991 | − | 1.74363i | 0.313029 | − | 0.389889i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.48322 | − | 1.07763i | 0.316224 | − | 0.229750i | ||||
\(23\) | 2.39991 | + | 7.38615i | 0.500415 | + | 1.54012i | 0.808344 | + | 0.588710i | \(0.200364\pi\) |
−0.307929 | + | 0.951409i | \(0.599636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.30902 | − | 2.53621i | 0.861803 | − | 0.507242i | ||||
\(26\) | 2.41785 | 0.474179 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.48322 | + | 1.07763i | −0.280303 | + | 0.203652i | ||||
\(29\) | 6.13597 | − | 4.45805i | 1.13942 | − | 0.827838i | 0.152383 | − | 0.988321i | \(-0.451305\pi\) |
0.987039 | + | 0.160483i | \(0.0513052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.28304 | + | 3.11181i | 0.769256 | + | 0.558897i | 0.901735 | − | 0.432288i | \(-0.142294\pi\) |
−0.132479 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.860510 | − | 2.64838i | 0.147576 | − | 0.454193i | ||||
\(35\) | −3.95536 | + | 1.07763i | −0.668578 | + | 0.182152i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.406315 | + | 1.25051i | −0.0667977 | + | 0.205582i | −0.978884 | − | 0.204416i | \(-0.934471\pi\) |
0.912086 | + | 0.409998i | \(0.134471\pi\) | |||||||
\(38\) | 0.516776 | − | 1.59047i | 0.0838321 | − | 0.258009i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.09089 | − | 0.792578i | −0.330599 | − | 0.125318i | ||||
\(41\) | −1.08621 | + | 3.34301i | −0.169637 | + | 0.522090i | −0.999348 | − | 0.0361034i | \(-0.988505\pi\) |
0.829711 | + | 0.558194i | \(0.188505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.30550 | −0.656583 | −0.328291 | − | 0.944576i | \(-0.606473\pi\) | ||||
−0.328291 | + | 0.944576i | \(0.606473\pi\) | |||||||
\(44\) | −1.48322 | − | 1.07763i | −0.223604 | − | 0.162458i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.28304 | − | 4.56489i | 0.926383 | − | 0.673057i | ||||
\(47\) | 1.48322 | − | 1.07763i | 0.216350 | − | 0.157188i | −0.474332 | − | 0.880346i | \(-0.657310\pi\) |
0.690682 | + | 0.723158i | \(0.257310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.63877 | −0.519824 | ||||||||
\(50\) | −3.74364 | − | 3.31439i | −0.529431 | − | 0.468725i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.747156 | − | 2.29951i | −0.103612 | − | 0.318885i | ||||
\(53\) | −5.27267 | + | 3.83082i | −0.724257 | + | 0.526203i | −0.887741 | − | 0.460342i | \(-0.847727\pi\) |
0.163485 | + | 0.986546i | \(0.447727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.24716 | − | 3.42877i | −0.303006 | − | 0.462335i | ||||
\(56\) | 1.48322 | + | 1.07763i | 0.198204 | + | 0.144004i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.13597 | − | 4.45805i | −0.805693 | − | 0.585370i | ||||
\(59\) | 2.79981 | − | 8.61694i | 0.364505 | − | 1.12183i | −0.585786 | − | 0.810466i | \(-0.699214\pi\) |
0.950291 | − | 0.311364i | \(-0.100786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.799717 | + | 2.46127i | 0.102393 | + | 0.315134i | 0.989110 | − | 0.147180i | \(-0.0470195\pi\) |
−0.886717 | + | 0.462313i | \(0.847019\pi\) | |||||||
\(62\) | 1.63597 | − | 5.03501i | 0.207769 | − | 0.639447i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0.260320 | − | 5.40020i | 0.0322887 | − | 0.669812i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.68574 | − | 5.58402i | −0.938963 | − | 0.682196i | 0.00920814 | − | 0.999958i | \(-0.497069\pi\) |
−0.948171 | + | 0.317761i | \(0.897069\pi\) | |||||||
\(68\) | −2.78467 | −0.337691 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.24716 | + | 3.42877i | 0.268587 | + | 0.409816i | ||||
\(71\) | 0.247156 | − | 0.179569i | 0.0293320 | − | 0.0213110i | −0.573023 | − | 0.819540i | \(-0.694229\pi\) |
0.602355 | + | 0.798229i | \(0.294229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.61920 | + | 14.2164i | 0.540636 | + | 1.66391i | 0.731145 | + | 0.682222i | \(0.238986\pi\) |
−0.190509 | + | 0.981685i | \(0.561014\pi\) | |||||||
\(74\) | 1.31486 | 0.152850 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.67232 | −0.191829 | ||||||||
\(77\) | 1.03868 | + | 3.19672i | 0.118368 | + | 0.364300i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.79981 | − | 2.03418i | 0.315004 | − | 0.228864i | −0.419037 | − | 0.907969i | \(-0.637632\pi\) |
0.734041 | + | 0.679106i | \(0.237632\pi\) | |||||||
\(80\) | −0.107666 | + | 2.23347i | −0.0120374 | + | 0.249710i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.51505 | 0.388172 | ||||||||
\(83\) | −5.15555 | − | 3.74572i | −0.565895 | − | 0.411147i | 0.267717 | − | 0.963498i | \(-0.413731\pi\) |
−0.833612 | + | 0.552351i | \(0.813731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.82243 | − | 2.20707i | −0.631532 | − | 0.239390i | ||||
\(86\) | 1.33047 | + | 4.09478i | 0.143469 | + | 0.441551i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.566541 | + | 1.74363i | −0.0603935 | + | 0.185872i | ||||
\(89\) | 1.02608 | + | 3.15794i | 0.108764 | + | 0.334741i | 0.990595 | − | 0.136824i | \(-0.0436894\pi\) |
−0.881832 | + | 0.471565i | \(0.843689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.36981 | + | 4.21584i | −0.143595 | + | 0.441940i | ||||
\(92\) | −6.28304 | − | 4.56489i | −0.655052 | − | 0.475923i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.48322 | − | 1.07763i | −0.152983 | − | 0.111149i | ||||
\(95\) | −3.49664 | − | 1.32545i | −0.358748 | − | 0.135988i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.97214 | + | 6.51864i | −0.910982 | + | 0.661867i | −0.941263 | − | 0.337674i | \(-0.890360\pi\) |
0.0302807 | + | 0.999541i | \(0.490360\pi\) | |||||||
\(98\) | 1.12444 | + | 3.46068i | 0.113586 | + | 0.349581i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.99532 | + | 4.58462i | −0.199532 | + | 0.458462i | ||||
\(101\) | 13.1807 | 1.31152 | 0.655762 | − | 0.754968i | \(-0.272347\pi\) | ||||
0.655762 | + | 0.754968i | \(0.272347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.13029 | − | 1.54774i | 0.209903 | − | 0.152504i | −0.477867 | − | 0.878432i | \(-0.658590\pi\) |
0.687770 | + | 0.725929i | \(0.258590\pi\) | |||||||
\(104\) | −1.95608 | + | 1.42118i | −0.191809 | + | 0.139358i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.27267 | + | 3.83082i | 0.512127 | + | 0.372082i | ||||
\(107\) | −18.8045 | −1.81790 | −0.908949 | − | 0.416908i | \(-0.863114\pi\) | ||||
−0.908949 | + | 0.416908i | \(0.863114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.18574 | − | 9.80470i | 0.305139 | − | 0.939120i | −0.674487 | − | 0.738287i | \(-0.735635\pi\) |
0.979625 | − | 0.200833i | \(-0.0643649\pi\) | |||||||
\(110\) | −2.56654 | + | 3.19672i | −0.244710 | + | 0.304795i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.566541 | − | 1.74363i | 0.0535331 | − | 0.164758i | ||||
\(113\) | −1.87160 | + | 5.76019i | −0.176065 | + | 0.541873i | −0.999681 | − | 0.0252760i | \(-0.991954\pi\) |
0.823615 | + | 0.567149i | \(0.191954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.51911 | − | 14.5245i | −0.887661 | − | 1.35442i | ||||
\(116\) | −2.34373 | + | 7.21327i | −0.217610 | + | 0.669735i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.06039 | −0.834076 | ||||||||
\(119\) | 4.13029 | + | 3.00083i | 0.378623 | + | 0.275086i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.17989 | − | 4.48996i | 0.561809 | − | 0.408178i | ||||
\(122\) | 2.09369 | − | 1.52115i | 0.189553 | − | 0.137719i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.29413 | −0.475427 | ||||||||
\(125\) | −7.80566 | + | 8.00448i | −0.698159 | + | 0.715942i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.102986 | + | 0.316957i | 0.00913850 | + | 0.0281254i | 0.955522 | − | 0.294921i | \(-0.0952932\pi\) |
−0.946383 | + | 0.323046i | \(0.895293\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.21634 | + | 1.42118i | −0.457503 | + | 0.124645i | ||||
\(131\) | −4.18910 | − | 3.04356i | −0.366003 | − | 0.265917i | 0.389548 | − | 0.921006i | \(-0.372631\pi\) |
−0.755552 | + | 0.655089i | \(0.772631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.48043 | + | 1.80214i | 0.215080 | + | 0.156265i | ||||
\(134\) | −2.93569 | + | 9.03513i | −0.253605 | + | 0.780516i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.860510 | + | 2.64838i | 0.0737881 | + | 0.227096i | ||||
\(137\) | 6.03299 | − | 18.5676i | 0.515433 | − | 1.58634i | −0.267060 | − | 0.963680i | \(-0.586052\pi\) |
0.782493 | − | 0.622660i | \(-0.213948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.45825 | − | 7.56572i | −0.208506 | − | 0.641716i | −0.999551 | − | 0.0299582i | \(-0.990463\pi\) |
0.791045 | − | 0.611758i | \(-0.209537\pi\) | |||||||
\(140\) | 2.56654 | − | 3.19672i | 0.216912 | − | 0.270172i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.247156 | − | 0.179569i | −0.0207409 | − | 0.0150691i | ||||
\(143\) | −4.43280 | −0.370689 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6176 | + | 13.2246i | −0.881741 | + | 1.09824i | ||||
\(146\) | 12.0932 | − | 8.78624i | 1.00084 | − | 0.727154i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.406315 | − | 1.25051i | −0.0333989 | − | 0.102791i | ||||
\(149\) | 1.67955 | 0.137594 | 0.0687969 | − | 0.997631i | \(-0.478084\pi\) | ||||
0.0687969 | + | 0.997631i | \(0.478084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2664 | −1.73063 | −0.865316 | − | 0.501227i | \(-0.832882\pi\) | ||||
−0.865316 | + | 0.501227i | \(0.832882\pi\) | |||||||
\(152\) | 0.516776 | + | 1.59047i | 0.0419161 | + | 0.129004i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.71929 | − | 1.97568i | 0.219127 | − | 0.159205i | ||||
\(155\) | −11.0694 | − | 4.19601i | −0.889118 | − | 0.337031i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4514 | 0.834113 | 0.417056 | − | 0.908881i | \(-0.363062\pi\) | ||||
0.417056 | + | 0.908881i | \(0.363062\pi\) | |||||||
\(158\) | −2.79981 | − | 2.03418i | −0.222741 | − | 0.161831i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.15743 | − | 0.587785i | 0.170560 | − | 0.0464685i | ||||
\(161\) | 4.39991 | + | 13.5415i | 0.346761 | + | 1.06722i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.21706 | − | 9.90109i | 0.251980 | − | 0.775513i | −0.742430 | − | 0.669923i | \(-0.766327\pi\) |
0.994410 | − | 0.105590i | \(-0.0336731\pi\) | |||||||
\(164\) | −1.08621 | − | 3.34301i | −0.0848187 | − | 0.261045i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.96924 | + | 6.06071i | −0.152843 | + | 0.470402i | ||||
\(167\) | 1.71650 | + | 1.24711i | 0.132826 | + | 0.0965041i | 0.652215 | − | 0.758034i | \(-0.273840\pi\) |
−0.519388 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.78772 | + | 4.20502i | 0.445209 | + | 0.323463i | ||||
\(170\) | −0.299814 | + | 6.21949i | −0.0229947 | + | 0.477013i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.48322 | − | 2.53071i | 0.265593 | − | 0.192965i | ||||
\(173\) | 5.59774 | + | 17.2281i | 0.425588 | + | 1.30983i | 0.902430 | + | 0.430837i | \(0.141782\pi\) |
−0.476841 | + | 0.878989i | \(0.658218\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.90000 | − | 4.64980i | 0.597184 | − | 0.351492i | ||||
\(176\) | 1.83337 | 0.138195 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.68630 | − | 1.95171i | 0.201347 | − | 0.146287i | ||||
\(179\) | 8.54361 | − | 6.20730i | 0.638579 | − | 0.463955i | −0.220782 | − | 0.975323i | \(-0.570861\pi\) |
0.859362 | + | 0.511368i | \(0.170861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6886 | − | 10.6719i | −1.09180 | − | 0.793237i | −0.112096 | − | 0.993697i | \(-0.535756\pi\) |
−0.979702 | + | 0.200460i | \(0.935756\pi\) | |||||||
\(182\) | 4.43280 | 0.328581 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.39991 | + | 7.38615i | −0.176923 | + | 0.544514i | ||||
\(185\) | 0.141566 | − | 2.93671i | 0.0104081 | − | 0.215911i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.57763 | + | 4.85544i | −0.115368 | + | 0.355065i | ||||
\(188\) | −0.566541 | + | 1.74363i | −0.0413193 | + | 0.127168i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.180052 | + | 3.73509i | −0.0130623 | + | 0.270972i | ||||
\(191\) | 6.76906 | − | 20.8330i | 0.489792 | − | 1.50742i | −0.335127 | − | 0.942173i | \(-0.608779\pi\) |
0.824919 | − | 0.565251i | \(-0.191221\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.4248 | 1.97408 | 0.987041 | − | 0.160465i | \(-0.0512995\pi\) | ||||
0.987041 | + | 0.160465i | \(0.0512995\pi\) | |||||||
\(194\) | 8.97214 | + | 6.51864i | 0.644162 | + | 0.468011i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.94383 | − | 2.13882i | 0.210273 | − | 0.152773i | ||||
\(197\) | −0.909110 | + | 0.660507i | −0.0647714 | + | 0.0470592i | −0.619700 | − | 0.784839i | \(-0.712746\pi\) |
0.554928 | + | 0.831898i | \(0.312746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4992 | 1.80759 | 0.903794 | − | 0.427968i | \(-0.140770\pi\) | ||||
0.903794 | + | 0.427968i | \(0.140770\pi\) | |||||||
\(200\) | 4.97682 | + | 0.480938i | 0.351914 | + | 0.0340074i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.07305 | − | 12.5355i | −0.286579 | − | 0.881998i | ||||
\(203\) | 11.2495 | − | 8.17323i | 0.789559 | − | 0.573648i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.378451 | − | 7.85077i | 0.0264321 | − | 0.548322i | ||||
\(206\) | −2.13029 | − | 1.54774i | −0.148424 | − | 0.107836i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.95608 | + | 1.42118i | 0.135630 | + | 0.0985408i | ||||
\(209\) | −0.947439 | + | 2.91592i | −0.0655358 | + | 0.201698i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58341 | + | 20.2617i | 0.453221 | + | 1.39487i | 0.873211 | + | 0.487342i | \(0.162033\pi\) |
−0.419990 | + | 0.907529i | \(0.637967\pi\) | |||||||
\(212\) | 2.01398 | − | 6.19839i | 0.138321 | − | 0.425708i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.81090 | + | 17.8841i | 0.397225 | + | 1.22253i | ||||
\(215\) | 9.28882 | − | 2.53071i | 0.633492 | − | 0.172593i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.85237 | + | 5.70508i | 0.533054 | + | 0.387286i | ||||
\(218\) | −10.3093 | −0.698232 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.83337 | + | 1.45309i | 0.258445 | + | 0.0979670i | ||||
\(221\) | −5.44703 | + | 3.95750i | −0.366407 | + | 0.266210i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00280 | + | 3.08629i | 0.0671522 | + | 0.206673i | 0.979002 | − | 0.203851i | \(-0.0653458\pi\) |
−0.911850 | + | 0.410524i | \(0.865346\pi\) | |||||||
\(224\) | −1.83337 | −0.122497 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.05662 | 0.402880 | ||||||||
\(227\) | −5.06085 | − | 15.5757i | −0.335901 | − | 1.03380i | −0.966277 | − | 0.257506i | \(-0.917099\pi\) |
0.630376 | − | 0.776290i | \(-0.282901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.11788 | − | 2.99181i | 0.272117 | − | 0.197705i | −0.443355 | − | 0.896346i | \(-0.646212\pi\) |
0.715472 | + | 0.698642i | \(0.246212\pi\) | |||||||
\(230\) | −10.8720 | + | 13.5415i | −0.716881 | + | 0.892901i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.58448 | 0.497946 | ||||||||
\(233\) | −1.34536 | − | 0.977464i | −0.0881378 | − | 0.0640358i | 0.542844 | − | 0.839834i | \(-0.317348\pi\) |
−0.630981 | + | 0.775798i | \(0.717348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.56654 | + | 3.19672i | −0.167423 | + | 0.208531i | ||||
\(236\) | 2.79981 | + | 8.61694i | 0.182252 | + | 0.560915i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.57763 | − | 4.85544i | 0.102263 | − | 0.314732i | ||||
\(239\) | −3.95536 | − | 12.1733i | −0.255851 | − | 0.787428i | −0.993661 | − | 0.112420i | \(-0.964140\pi\) |
0.737810 | − | 0.675009i | \(-0.235860\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.122209 | − | 0.376121i | 0.00787219 | − | 0.0242281i | −0.947043 | − | 0.321106i | \(-0.895945\pi\) |
0.954915 | + | 0.296878i | \(0.0959454\pi\) | |||||||
\(242\) | −6.17989 | − | 4.48996i | −0.397259 | − | 0.288625i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.09369 | − | 1.52115i | −0.134034 | − | 0.0973817i | ||||
\(245\) | 7.85040 | − | 2.13882i | 0.501543 | − | 0.136644i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.27120 | + | 2.37666i | −0.208141 | + | 0.151223i | ||||
\(248\) | 1.63597 | + | 5.03501i | 0.103885 | + | 0.319724i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.0248 | + | 4.95010i | 0.634024 | + | 0.313072i | ||||
\(251\) | −9.36589 | −0.591170 | −0.295585 | − | 0.955316i | \(-0.595515\pi\) | ||||
−0.295585 | + | 0.955316i | \(0.595515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5191 | + | 8.36912i | −0.724200 | + | 0.526162i | ||||
\(254\) | 0.269620 | − | 0.195890i | 0.0169175 | − | 0.0122913i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 4.97926 | 0.310598 | 0.155299 | − | 0.987868i | \(-0.450366\pi\) | ||||
0.155299 | + | 0.987868i | \(0.450366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.744923 | + | 2.29264i | −0.0462873 | + | 0.142458i | ||||
\(260\) | 2.96356 | + | 4.52187i | 0.183792 | + | 0.280434i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.60009 | + | 4.92458i | −0.0988541 | + | 0.304242i | ||||
\(263\) | 6.12199 | − | 18.8416i | 0.377498 | − | 1.16182i | −0.564279 | − | 0.825584i | \(-0.690846\pi\) |
0.941778 | − | 0.336236i | \(-0.109154\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.12372 | − | 11.3639i | 0.560466 | − | 0.698080i | ||||
\(266\) | 0.947439 | − | 2.91592i | 0.0580912 | − | 0.178786i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.50010 | 0.580311 | ||||||||
\(269\) | 11.9685 | + | 8.69564i | 0.729734 | + | 0.530183i | 0.889479 | − | 0.456976i | \(-0.151067\pi\) |
−0.159745 | + | 0.987158i | \(0.551067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1583 | − | 7.38047i | 0.617075 | − | 0.448331i | −0.234823 | − | 0.972038i | \(-0.575451\pi\) |
0.851899 | + | 0.523707i | \(0.175451\pi\) | |||||||
\(272\) | 2.25284 | − | 1.63679i | 0.136599 | − | 0.0992448i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.5232 | −1.17944 | ||||||||
\(275\) | 6.86346 | + | 6.07648i | 0.413882 | + | 0.366426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.95664 | − | 6.02193i | −0.117563 | − | 0.361823i | 0.874910 | − | 0.484286i | \(-0.160921\pi\) |
−0.992473 | + | 0.122463i | \(0.960921\pi\) | |||||||
\(278\) | −6.43579 | + | 4.67587i | −0.385993 | + | 0.280440i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.83337 | − | 1.45309i | −0.229087 | − | 0.0868384i | ||||
\(281\) | −16.2525 | − | 11.8082i | −0.969545 | − | 0.704416i | −0.0141971 | − | 0.999899i | \(-0.504519\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.46981 | − | 1.06788i | −0.0873709 | − | 0.0634787i | 0.543242 | − | 0.839576i | \(-0.317197\pi\) |
−0.630613 | + | 0.776097i | \(0.717197\pi\) | |||||||
\(284\) | −0.0944052 | + | 0.290549i | −0.00560192 | + | 0.0172409i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.36981 | + | 4.21584i | 0.0809986 | + | 0.249288i | ||||
\(287\) | −1.99142 | + | 6.12896i | −0.117550 | + | 0.361781i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.85705 | − | 8.79311i | −0.168062 | − | 0.517242i | ||||
\(290\) | 15.8583 | + | 6.01129i | 0.931232 | + | 0.352995i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.0932 | − | 8.78624i | −0.707702 | − | 0.514176i | ||||
\(293\) | 6.85931 | 0.400725 | 0.200363 | − | 0.979722i | \(-0.435788\pi\) | ||||
0.200363 | + | 0.979722i | \(0.435788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.975494 | + | 20.2361i | −0.0567955 | + | 1.17819i | ||||
\(296\) | −1.06375 | + | 0.772856i | −0.0618290 | + | 0.0449214i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.519009 | − | 1.59734i | −0.0300654 | − | 0.0925317i | ||||
\(299\) | −18.7776 | −1.08594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.89356 | −0.454977 | ||||||||
\(302\) | 6.57167 | + | 20.2255i | 0.378157 | + | 1.16385i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.35294 | − | 0.982966i | 0.0775963 | − | 0.0563770i | ||||
\(305\) | −3.17203 | − | 4.83997i | −0.181630 | − | 0.277136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.89526 | −0.165241 | −0.0826206 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826206 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(308\) | −2.71929 | − | 1.97568i | −0.154946 | − | 0.112575i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.569997 | + | 11.8243i | −0.0323736 | + | 0.671575i | ||||
\(311\) | 6.38090 | + | 19.6384i | 0.361828 | + | 1.11359i | 0.951944 | + | 0.306272i | \(0.0990819\pi\) |
−0.590116 | + | 0.807318i | \(0.700918\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.07629 | − | 15.6232i | 0.286929 | − | 0.883076i | −0.698885 | − | 0.715234i | \(-0.746320\pi\) |
0.985814 | − | 0.167842i | \(-0.0536798\pi\) | |||||||
\(314\) | −3.22966 | − | 9.93987i | −0.182260 | − | 0.560939i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.06943 | + | 3.29138i | −0.0601603 | + | 0.185154i | ||||
\(317\) | 13.3535 | + | 9.70191i | 0.750009 | + | 0.544914i | 0.895830 | − | 0.444397i | \(-0.146582\pi\) |
−0.145820 | + | 0.989311i | \(0.546582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2495 | + | 8.17323i | 0.629850 | + | 0.457613i | ||||
\(320\) | −1.22570 | − | 1.87020i | −0.0685187 | − | 0.104548i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.5191 | − | 8.36912i | 0.641935 | − | 0.466393i | ||||
\(323\) | 1.43905 | + | 4.42894i | 0.0800709 | + | 0.246433i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.61254 | + | 11.8036i | 0.144917 | + | 0.654744i | ||||
\(326\) | −10.4106 | −0.576591 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.84373 | + | 2.06609i | −0.157019 | + | 0.114081i | ||||
\(329\) | 2.71929 | − | 1.97568i | 0.149919 | − | 0.108923i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2245 | − | 16.1471i | −1.22157 | − | 0.887522i | −0.225340 | − | 0.974280i | \(-0.572349\pi\) |
−0.996229 | + | 0.0867577i | \(0.972349\pi\) | |||||||
\(332\) | 6.37261 | 0.349742 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.655643 | − | 2.01786i | 0.0358752 | − | 0.110413i | ||||
\(335\) | 19.8637 | + | 7.52957i | 1.08527 | + | 0.411384i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.848317 | + | 2.61085i | −0.0462108 | + | 0.142222i | −0.971500 | − | 0.237041i | \(-0.923822\pi\) |
0.925289 | + | 0.379263i | \(0.123822\pi\) | |||||||
\(338\) | 2.21071 | − | 6.80387i | 0.120247 | − | 0.370082i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00773 | − | 1.63679i | 0.325815 | − | 0.0887672i | ||||
\(341\) | −2.99934 | + | 9.23102i | −0.162423 | + | 0.499888i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5048 | −1.05316 | ||||||||
\(344\) | −3.48322 | − | 2.53071i | −0.187803 | − | 0.136447i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.6551 | − | 10.6475i | 0.787862 | − | 0.572415i | ||||
\(347\) | −17.2637 | + | 12.5428i | −0.926762 | + | 0.673332i | −0.945198 | − | 0.326498i | \(-0.894131\pi\) |
0.0184361 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7650 | −0.897411 | −0.448705 | − | 0.893680i | \(-0.648115\pi\) | ||||
−0.448705 | + | 0.893680i | \(0.648115\pi\) | |||||||
\(350\) | −6.86346 | − | 6.07648i | −0.366867 | − | 0.324802i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.566541 | − | 1.74363i | −0.0301967 | − | 0.0929360i | ||||
\(353\) | 2.41785 | − | 1.75667i | 0.128689 | − | 0.0934981i | −0.521579 | − | 0.853203i | \(-0.674657\pi\) |
0.650268 | + | 0.759705i | \(0.274657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.427674 | + | 0.532683i | −0.0226986 | + | 0.0282719i | ||||
\(356\) | −2.68630 | − | 1.95171i | −0.142374 | − | 0.103441i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.54361 | − | 6.20730i | −0.451544 | − | 0.328066i | ||||
\(359\) | −2.07194 | + | 6.37678i | −0.109353 | + | 0.336554i | −0.990727 | − | 0.135865i | \(-0.956619\pi\) |
0.881375 | + | 0.472418i | \(0.156619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00711 | − | 15.4103i | −0.263532 | − | 0.811068i | ||||
\(362\) | −5.61056 | + | 17.2675i | −0.294884 | + | 0.907561i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.36981 | − | 4.21584i | −0.0717976 | − | 0.220970i | ||||
\(365\) | −18.3218 | − | 27.9559i | −0.959007 | − | 1.46328i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.24949 | − | 2.36089i | −0.169622 | − | 0.123237i | 0.499736 | − | 0.866178i | \(-0.333430\pi\) |
−0.669357 | + | 0.742941i | \(0.733430\pi\) | |||||||
\(368\) | 7.76626 | 0.404844 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.83672 | + | 0.772856i | −0.147474 | + | 0.0401789i | ||||
\(371\) | −9.66673 | + | 7.02329i | −0.501872 | + | 0.364631i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.21467 | + | 25.2822i | 0.425340 | + | 1.30906i | 0.902669 | + | 0.430336i | \(0.141605\pi\) |
−0.477329 | + | 0.878725i | \(0.658395\pi\) | |||||||
\(374\) | 5.10532 | 0.263990 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.83337 | 0.0945486 | ||||||||
\(377\) | 5.66679 | + | 17.4406i | 0.291855 | + | 0.898236i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6431 | − | 9.18578i | 0.649435 | − | 0.471842i | −0.213644 | − | 0.976912i | \(-0.568533\pi\) |
0.863079 | + | 0.505070i | \(0.168533\pi\) | |||||||
\(380\) | 3.60792 | − | 0.982966i | 0.185082 | − | 0.0504251i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.9051 | −1.12076 | ||||||||
\(383\) | 10.8776 | + | 7.90306i | 0.555821 | + | 0.403828i | 0.829927 | − | 0.557872i | \(-0.188382\pi\) |
−0.274106 | + | 0.961699i | \(0.588382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.11986 | − | 6.28618i | −0.209967 | − | 0.320374i | ||||
\(386\) | −8.47474 | − | 26.0826i | −0.431353 | − | 1.32757i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.42705 | − | 10.5474i | 0.173982 | − | 0.535462i | ||||
\(389\) | 7.75991 | + | 23.8826i | 0.393443 | + | 1.21089i | 0.930167 | + | 0.367136i | \(0.119662\pi\) |
−0.536724 | + | 0.843758i | \(0.680338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.68294 | + | 20.5680i | −0.337971 | + | 1.04017i | ||||
\(392\) | −2.94383 | − | 2.13882i | −0.148686 | − | 0.108026i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.909110 | + | 0.660507i | 0.0458003 | + | 0.0332759i | ||||
\(395\) | −4.84474 | + | 6.03430i | −0.243765 | + | 0.303619i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.84628 | + | 2.06794i | −0.142850 | + | 0.103787i | −0.656915 | − | 0.753964i | \(-0.728139\pi\) |
0.514065 | + | 0.857751i | \(0.328139\pi\) | |||||||
\(398\) | −7.87968 | − | 24.2511i | −0.394972 | − | 1.21560i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.08052 | − | 4.88185i | −0.0540261 | − | 0.244093i | ||||
\(401\) | −29.8696 | −1.49161 | −0.745807 | − | 0.666162i | \(-0.767936\pi\) | ||||
−0.745807 | + | 0.666162i | \(0.767936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3557 | + | 7.52388i | −0.515856 | + | 0.374791i | ||||
\(404\) | −10.6634 | + | 7.74739i | −0.530523 | + | 0.385447i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2495 | − | 8.17323i | −0.558303 | − | 0.405631i | ||||
\(407\) | −2.41062 | −0.119490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9784 | + | 36.8656i | −0.592291 | + | 1.82289i | −0.0245200 | + | 0.999699i | \(0.507806\pi\) |
−0.567771 | + | 0.823186i | \(0.692194\pi\) | |||||||
\(410\) | −7.58347 | + | 2.06609i | −0.374521 | + | 0.102037i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.813697 | + | 2.50430i | −0.0400880 | + | 0.123378i | ||||
\(413\) | 5.13308 | − | 15.7980i | 0.252582 | − | 0.777369i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3244 | + | 5.05079i | 0.654070 | + | 0.247933i | ||||
\(416\) | 0.747156 | − | 2.29951i | 0.0366323 | − | 0.112743i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.06598 | 0.149962 | ||||||||
\(419\) | −15.2988 | − | 11.1152i | −0.747395 | − | 0.543014i | 0.147624 | − | 0.989044i | \(-0.452838\pi\) |
−0.895018 | + | 0.446030i | \(0.852838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8414 | − | 12.9625i | 0.869536 | − | 0.631755i | −0.0609265 | − | 0.998142i | \(-0.519406\pi\) |
0.930462 | + | 0.366388i | \(0.119406\pi\) | |||||||
\(422\) | 17.2356 | − | 12.5224i | 0.839016 | − | 0.609581i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.51738 | −0.316512 | ||||||||
\(425\) | 13.8588 | + | 1.33925i | 0.672250 | + | 0.0649633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46617 | + | 4.51242i | 0.0709531 | + | 0.218371i | ||||
\(428\) | 15.2131 | − | 11.0530i | 0.735355 | − | 0.534267i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.27725 | − | 8.05216i | −0.254492 | − | 0.388310i | ||||
\(431\) | −7.44763 | − | 5.41102i | −0.358740 | − | 0.260640i | 0.393787 | − | 0.919202i | \(-0.371165\pi\) |
−0.752526 | + | 0.658562i | \(0.771165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.1516 | − | 20.4533i | −1.35288 | − | 0.982923i | −0.998862 | − | 0.0476837i | \(-0.984816\pi\) |
−0.354015 | − | 0.935240i | \(-0.615184\pi\) | |||||||
\(434\) | 2.99934 | − | 9.23102i | 0.143973 | − | 0.443103i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.18574 | + | 9.80470i | 0.152569 | + | 0.469560i | ||||
\(437\) | −4.01342 | + | 12.3520i | −0.191988 | + | 0.590878i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.58025 | − | 7.94118i | −0.123148 | − | 0.379012i | 0.870411 | − | 0.492326i | \(-0.163853\pi\) |
−0.993559 | + | 0.113314i | \(0.963853\pi\) | |||||||
\(440\) | 0.197391 | − | 4.09478i | 0.00941024 | − | 0.195211i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.44703 | + | 3.95750i | 0.259089 | + | 0.188239i | ||||
\(443\) | 1.19887 | 0.0569599 | 0.0284799 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284799 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.06988 | − | 6.20992i | −0.192931 | − | 0.294379i | ||||
\(446\) | 2.62535 | − | 1.90743i | 0.124314 | − | 0.0903194i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.566541 | + | 1.74363i | 0.0267666 | + | 0.0823790i | ||||
\(449\) | −32.7953 | −1.54771 | −0.773853 | − | 0.633365i | \(-0.781673\pi\) | ||||
−0.773853 | + | 0.633365i | \(0.781673\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.44437 | −0.303453 | ||||||||
\(452\) | −1.87160 | − | 5.76019i | −0.0880326 | − | 0.270936i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.2495 | + | 9.62631i | −0.621829 | + | 0.451785i | ||||
\(455\) | 0.477261 | − | 9.90054i | 0.0223743 | − | 0.464145i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7884 | 0.925664 | 0.462832 | − | 0.886446i | \(-0.346833\pi\) | ||||
0.462832 | + | 0.886446i | \(0.346833\pi\) | |||||||
\(458\) | −4.11788 | − | 2.99181i | −0.192416 | − | 0.139798i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.2384 | + | 6.15537i | 0.757119 | + | 0.286995i | ||||
\(461\) | −2.90468 | − | 8.93970i | −0.135285 | − | 0.416363i | 0.860350 | − | 0.509704i | \(-0.170245\pi\) |
−0.995634 | + | 0.0933412i | \(0.970245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.47977 | − | 16.8650i | 0.254666 | − | 0.783783i | −0.739229 | − | 0.673454i | \(-0.764810\pi\) |
0.993895 | − | 0.110328i | \(-0.0351902\pi\) | |||||||
\(464\) | −2.34373 | − | 7.21327i | −0.108805 | − | 0.334868i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.513883 | + | 1.58157i | −0.0238052 | + | 0.0732649i | ||||
\(467\) | 17.6857 | + | 12.8494i | 0.818398 | + | 0.594601i | 0.916253 | − | 0.400599i | \(-0.131198\pi\) |
−0.0978549 | + | 0.995201i | \(0.531198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0908 | − | 10.2375i | −0.650651 | − | 0.472726i | ||||
\(470\) | 3.83337 | + | 1.45309i | 0.176820 | + | 0.0670258i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.33001 | − | 5.32556i | 0.337391 | − | 0.245129i | ||||
\(473\) | −2.43924 | − | 7.50722i | −0.112157 | − | 0.345182i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.32284 | + | 0.804283i | 0.381878 | + | 0.0369030i | ||||
\(476\) | −5.10532 | −0.234002 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.3553 | + | 7.52354i | −0.473639 | + | 0.344119i | ||||
\(479\) | −4.94352 | + | 3.59168i | −0.225875 | + | 0.164108i | −0.694967 | − | 0.719041i | \(-0.744581\pi\) |
0.469092 | + | 0.883149i | \(0.344581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.57198 | − | 1.86865i | −0.117272 | − | 0.0852031i | ||||
\(482\) | −0.395477 | −0.0180135 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.36051 | + | 7.26490i | −0.107296 | + | 0.330223i | ||||
\(485\) | 15.5252 | − | 19.3372i | 0.704963 | − | 0.878057i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.56421 | − | 4.81415i | 0.0708812 | − | 0.218150i | −0.909340 | − | 0.416053i | \(-0.863413\pi\) |
0.980222 | + | 0.197903i | \(0.0634131\pi\) | |||||||
\(488\) | −0.799717 | + | 2.46127i | −0.0362015 | + | 0.111417i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.46004 | − | 6.80524i | −0.201484 | − | 0.307429i | ||||
\(491\) | −0.736165 | + | 2.26568i | −0.0332227 | + | 0.102249i | −0.966293 | − | 0.257446i | \(-0.917119\pi\) |
0.933070 | + | 0.359695i | \(0.117119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.1203 | 0.951209 | ||||||||
\(494\) | 3.27120 | + | 2.37666i | 0.147178 | + | 0.106931i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.28304 | − | 3.11181i | 0.192314 | − | 0.139724i | ||||
\(497\) | 0.453127 | − | 0.329216i | 0.0203255 | − | 0.0147674i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0503313 | −0.00225314 | −0.00112657 | − | 0.999999i | \(-0.500359\pi\) | ||||
−0.00112657 | + | 0.999999i | \(0.500359\pi\) | |||||||
\(500\) | 1.61000 | − | 11.0638i | 0.0720012 | − | 0.494789i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.89422 | + | 8.90749i | 0.129175 | + | 0.397561i | ||||
\(503\) | −4.37744 | + | 3.18040i | −0.195181 | + | 0.141807i | −0.681083 | − | 0.732206i | \(-0.738491\pi\) |
0.485903 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.4364 | + | 7.74739i | −1.26540 | + | 0.344755i | ||||
\(506\) | 11.5191 | + | 8.36912i | 0.512087 | + | 0.372053i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.269620 | − | 0.195890i | −0.0119625 | − | 0.00869123i | ||||
\(509\) | −5.85472 | + | 18.0190i | −0.259506 | + | 0.798678i | 0.733402 | + | 0.679795i | \(0.237931\pi\) |
−0.992908 | + | 0.118883i | \(0.962069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.46868 | + | 26.0639i | 0.374632 | + | 1.15300i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.53868 | − | 4.73556i | −0.0678681 | − | 0.208877i | ||||
\(515\) | −3.68621 | + | 4.59130i | −0.162434 | + | 0.202317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.71929 | + | 1.97568i | 0.119594 | + | 0.0868904i | ||||
\(518\) | 2.41062 | 0.105917 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.38476 | − | 4.21584i | 0.148432 | − | 0.184877i | ||||
\(521\) | 31.0817 | − | 22.5822i | 1.36171 | − | 0.989342i | 0.363379 | − | 0.931642i | \(-0.381623\pi\) |
0.998334 | − | 0.0577005i | \(-0.0183768\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.79057 | − | 11.6662i | −0.165750 | − | 0.510127i | 0.833341 | − | 0.552760i | \(-0.186425\pi\) |
−0.999091 | + | 0.0426332i | \(0.986425\pi\) | |||||||
\(524\) | 5.17801 | 0.226202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.8112 | −0.863809 | ||||||||
\(527\) | 4.55565 | + | 14.0208i | 0.198447 | + | 0.610757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −30.1883 | + | 21.9331i | −1.31254 | + | 0.953613i | ||||
\(530\) | −13.6271 | − | 5.16553i | −0.591924 | − | 0.224376i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.06598 | −0.132927 | ||||||||
\(533\) | −6.87572 | − | 4.99550i | −0.297820 | − | 0.216379i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.5694 | − | 11.0530i | 1.75397 | − | 0.477863i | ||||
\(536\) | −2.93569 | − | 9.03513i | −0.126803 | − | 0.390258i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.57157 | − | 14.0698i | 0.197094 | − | 0.606594i | ||||
\(539\) | −2.06151 | − | 6.34468i | −0.0887957 | − | 0.273285i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9872 | − | 39.9704i | 0.558362 | − | 1.71846i | −0.128534 | − | 0.991705i | \(-0.541027\pi\) |
0.686896 | − | 0.726756i | \(-0.258973\pi\) | |||||||
\(542\) | −10.1583 | − | 7.38047i | −0.436338 | − | 0.317018i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.25284 | − | 1.63679i | −0.0965899 | − | 0.0701767i | ||||
\(545\) | −1.10996 | + | 23.0255i | −0.0475453 | + | 0.986304i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6719 | + | 11.3863i | −0.670080 | + | 0.486842i | −0.870052 | − | 0.492960i | \(-0.835915\pi\) |
0.199972 | + | 0.979802i | \(0.435915\pi\) | |||||||
\(548\) | 6.03299 | + | 18.5676i | 0.257717 | + | 0.793170i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.65815 | − | 8.40528i | 0.155984 | − | 0.358402i | ||||
\(551\) | 12.6837 | 0.540344 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.13308 | − | 3.72940i | 0.218281 | − | 0.158590i | ||||
\(554\) | −5.12256 | + | 3.72176i | −0.217637 | + | 0.158122i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.43579 | + | 4.67587i | 0.272938 | + | 0.198301i | ||||
\(557\) | −8.54685 | −0.362142 | −0.181071 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181071 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.21688 | − | 9.90054i | 0.136060 | − | 0.418748i | ||||
\(560\) | −0.197391 | + | 4.09478i | −0.00834129 | + | 0.173036i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.20792 | + | 19.1060i | −0.261865 | + | 0.805938i | ||||
\(563\) | 7.24949 | − | 22.3116i | 0.305529 | − | 0.940323i | −0.673950 | − | 0.738777i | \(-0.735404\pi\) |
0.979479 | − | 0.201546i | \(-0.0645964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.652091 | − | 13.5273i | 0.0274337 | − | 0.569098i | ||||
\(566\) | −0.561416 | + | 1.72786i | −0.0235981 | + | 0.0726274i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.305502 | 0.0128186 | ||||||||
\(569\) | −5.74445 | − | 4.17359i | −0.240820 | − | 0.174966i | 0.460829 | − | 0.887489i | \(-0.347552\pi\) |
−0.701649 | + | 0.712523i | \(0.747552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.67745 | − | 7.03108i | 0.404989 | − | 0.294241i | −0.366581 | − | 0.930386i | \(-0.619472\pi\) |
0.771570 | + | 0.636145i | \(0.219472\pi\) | |||||||
\(572\) | 3.58621 | − | 2.60553i | 0.149947 | − | 0.108943i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.44437 | 0.268983 | ||||||||
\(575\) | 29.0741 | + | 25.7404i | 1.21247 | + | 1.07345i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8457 | + | 39.5350i | 0.534774 | + | 1.64587i | 0.744137 | + | 0.668027i | \(0.232861\pi\) |
−0.209362 | + | 0.977838i | \(0.567139\pi\) | |||||||
\(578\) | −7.47987 | + | 5.43444i | −0.311121 | + | 0.226043i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.816590 | − | 16.9397i | 0.0339070 | − | 0.703385i | ||||
\(581\) | −9.45200 | − | 6.86728i | −0.392135 | − | 0.284903i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.66673 | − | 7.02329i | −0.400355 | − | 0.290875i | ||||
\(584\) | −4.61920 | + | 14.2164i | −0.191144 | + | 0.588280i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.11964 | − | 6.52359i | −0.0875617 | − | 0.269487i | ||||
\(587\) | −5.91072 | + | 18.1913i | −0.243962 | + | 0.750836i | 0.751844 | + | 0.659341i | \(0.229165\pi\) |
−0.995806 | + | 0.0914953i | \(0.970835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.73588 | + | 8.42016i | 0.112730 | + | 0.346947i | ||||
\(590\) | 19.5472 | − | 5.32556i | 0.804744 | − | 0.219250i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.06375 | + | 0.772856i | 0.0437197 | + | 0.0317642i | ||||
\(593\) | −0.538428 | −0.0221106 | −0.0110553 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110553 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.6747 | − | 4.04636i | −0.437618 | − | 0.165885i | ||||
\(596\) | −1.35878 | + | 0.987213i | −0.0556579 | + | 0.0404378i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.80261 | + | 17.8586i | 0.237286 | + | 0.730292i | ||||
\(599\) | 38.4209 | 1.56983 | 0.784917 | − | 0.619601i | \(-0.212705\pi\) | ||||
0.784917 | + | 0.619601i | \(0.212705\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6034 | 0.799639 | 0.399820 | − | 0.916594i | \(-0.369073\pi\) | ||||
0.399820 | + | 0.916594i | \(0.369073\pi\) | |||||||
\(602\) | 2.43924 | + | 7.50722i | 0.0994162 | + | 0.305971i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.2048 | − | 12.5001i | 0.700055 | − | 0.508620i | ||||
\(605\) | −10.6936 | + | 13.3192i | −0.434755 | + | 0.541503i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.4415 | −1.31676 | −0.658381 | − | 0.752685i | \(-0.728758\pi\) | ||||
−0.658381 | + | 0.752685i | \(0.728758\pi\) | |||||||
\(608\) | −1.35294 | − | 0.982966i | −0.0548688 | − | 0.0398646i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.62287 | + | 4.51242i | −0.146686 | + | 0.182702i | ||||
\(611\) | 1.36981 | + | 4.21584i | 0.0554166 | + | 0.170555i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.25273 | + | 22.3216i | −0.292935 | + | 0.901561i | 0.690972 | + | 0.722881i | \(0.257183\pi\) |
−0.983907 | + | 0.178680i | \(0.942817\pi\) | |||||||
\(614\) | 0.894685 | + | 2.75356i | 0.0361065 | + | 0.111124i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.03868 | + | 3.19672i | −0.0418495 | + | 0.128799i | ||||
\(617\) | 14.0876 | + | 10.2353i | 0.567147 | + | 0.412056i | 0.834068 | − | 0.551662i | \(-0.186006\pi\) |
−0.266921 | + | 0.963718i | \(0.586006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.1801 | − | 7.39624i | −0.409171 | − | 0.297280i | 0.364095 | − | 0.931362i | \(-0.381378\pi\) |
−0.773266 | + | 0.634082i | \(0.781378\pi\) | |||||||
\(620\) | 11.4217 | − | 3.11181i | 0.458707 | − | 0.124973i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.7054 | − | 12.1372i | 0.669826 | − | 0.486657i | ||||
\(623\) | 1.88117 | + | 5.78966i | 0.0753676 | + | 0.231958i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1353 | − | 21.8572i | 0.485410 | − | 0.874287i | ||||
\(626\) | −16.4272 | −0.656563 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.45536 | + | 6.14318i | −0.337406 | + | 0.245140i | ||||
\(629\) | −2.96218 | + | 2.15215i | −0.118110 | + | 0.0858118i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.7653 | − | 24.5319i | −1.34418 | − | 0.976601i | −0.999279 | − | 0.0379610i | \(-0.987914\pi\) |
−0.344897 | − | 0.938640i | \(-0.612086\pi\) | |||||||
\(632\) | 3.46076 | 0.137662 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.10060 | − | 15.6980i | 0.202571 | − | 0.623448i | ||||
\(635\) | −0.408487 | − | 0.623280i | −0.0162103 | − | 0.0247341i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.71873 | − | 8.36739i | 0.107720 | − | 0.331528i | ||||
\(638\) | 4.29692 | − | 13.2246i | 0.170117 | − | 0.523565i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.39991 | + | 1.74363i | −0.0553362 | + | 0.0689232i | ||||
\(641\) | 4.44926 | − | 13.6934i | 0.175735 | − | 0.540858i | −0.823931 | − | 0.566690i | \(-0.808224\pi\) |
0.999666 | + | 0.0258324i | \(0.00822362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1666 | 1.18966 | 0.594828 | − | 0.803853i | \(-0.297220\pi\) | ||||
0.594828 | + | 0.803853i | \(0.297220\pi\) | |||||||
\(644\) | −11.5191 | − | 8.36912i | −0.453916 | − | 0.329790i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.76748 | − | 2.73724i | 0.148230 | − | 0.107695i | ||||
\(647\) | −8.64660 | + | 6.28212i | −0.339933 | + | 0.246976i | −0.744633 | − | 0.667474i | \(-0.767376\pi\) |
0.404701 | + | 0.914449i | \(0.367376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6110 | 0.652039 | ||||||||
\(650\) | 10.4185 | − | 6.13217i | 0.408649 | − | 0.240524i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.21706 | + | 9.90109i | 0.125990 | + | 0.387757i | ||||
\(653\) | 8.22432 | − | 5.97532i | 0.321843 | − | 0.233832i | −0.415119 | − | 0.909767i | \(-0.636260\pi\) |
0.736961 | + | 0.675935i | \(0.236260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8266 | + | 4.10398i | 0.423032 | + | 0.160356i | ||||
\(656\) | 2.84373 | + | 2.06609i | 0.111029 | + | 0.0806674i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.71929 | − | 1.97568i | −0.106009 | − | 0.0770201i | ||||
\(659\) | −9.61668 | + | 29.5971i | −0.374613 | + | 1.15294i | 0.569127 | + | 0.822250i | \(0.307281\pi\) |
−0.943740 | + | 0.330689i | \(0.892719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8131 | + | 39.4347i | 0.498372 | + | 1.53383i | 0.811635 | + | 0.584165i | \(0.198578\pi\) |
−0.313262 | + | 0.949667i | \(0.601422\pi\) | |||||||
\(662\) | −8.48901 | + | 26.1265i | −0.329935 | + | 1.01543i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.96924 | − | 6.06071i | −0.0764215 | − | 0.235201i | ||||
\(665\) | −6.41062 | − | 2.43003i | −0.248593 | − | 0.0942324i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.6536 | + | 34.6224i | 1.84515 | + | 1.34058i | ||||
\(668\) | −2.12171 | −0.0820913 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.02284 | − | 21.2182i | 0.0395156 | − | 0.819732i | ||||
\(671\) | −3.83849 | + | 2.78883i | −0.148183 | + | 0.107661i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.662831 | + | 2.03998i | 0.0255503 | + | 0.0786356i | 0.963019 | − | 0.269435i | \(-0.0868369\pi\) |
−0.937468 | + | 0.348071i | \(0.886837\pi\) | |||||||
\(674\) | 2.74521 | 0.105742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.15401 | −0.275154 | ||||||||
\(677\) | −12.8391 | − | 39.5147i | −0.493446 | − | 1.51867i | −0.819364 | − | 0.573274i | \(-0.805673\pi\) |
0.325918 | − | 0.945398i | \(-0.394327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.4492 | + | 11.9510i | −0.631263 | + | 0.458639i | ||||
\(680\) | −3.41317 | − | 5.20790i | −0.130889 | − | 0.199714i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.70607 | 0.371665 | ||||||||
\(683\) | −23.3247 | − | 16.9464i | −0.892495 | − | 0.648436i | 0.0440323 | − | 0.999030i | \(-0.485980\pi\) |
−0.936527 | + | 0.350595i | \(0.885980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.10198 | + | 43.6045i | −0.0803124 | + | 1.66604i | ||||
\(686\) | 6.02730 | + | 18.5501i | 0.230123 | + | 0.708247i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.33047 | + | 4.09478i | −0.0507238 | + | 0.156112i | ||||
\(689\) | −4.86950 | − | 14.9868i | −0.185513 | − | 0.570951i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2050 | + | 46.7963i | −0.578426 | + | 1.78021i | 0.0457774 | + | 0.998952i | \(0.485424\pi\) |
−0.624204 | + | 0.781262i | \(0.714576\pi\) | |||||||
\(692\) | −14.6551 | − | 10.6475i | −0.557103 | − | 0.404759i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.2637 | + | 12.5428i | 0.655319 | + | 0.476117i | ||||
\(695\) | 9.75053 | + | 14.8776i | 0.369859 | + | 0.564340i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.91886 | + | 5.75339i | −0.299948 | + | 0.217925i | ||||
\(698\) | 5.18067 | + | 15.9445i | 0.196091 | + | 0.603507i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.65815 | + | 8.40528i | −0.138265 | + | 0.317690i | ||||
\(701\) | 24.9783 | 0.943419 | 0.471709 | − | 0.881754i | \(-0.343637\pi\) | ||||
0.471709 | + | 0.881754i | \(0.343637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.77893 | + | 1.29247i | −0.0670935 | + | 0.0487462i | ||||
\(704\) | −1.48322 | + | 1.07763i | −0.0559011 | + | 0.0406145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.41785 | − | 1.75667i | −0.0909969 | − | 0.0661131i | ||||
\(707\) | 24.1650 | 0.908817 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.02602 | − | 9.31312i | 0.113644 | − | 0.349762i | −0.878017 | − | 0.478629i | \(-0.841134\pi\) |
0.991662 | + | 0.128867i | \(0.0411340\pi\) | |||||||
\(710\) | 0.638770 | + | 0.242134i | 0.0239726 | + | 0.00908712i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.02608 | + | 3.15794i | −0.0384538 | + | 0.118349i | ||||
\(713\) | −12.7054 | + | 39.1032i | −0.475821 | + | 1.46443i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.56346 | − | 2.60553i | 0.357653 | − | 0.0974414i | ||||
\(716\) | −3.26337 | + | 10.0436i | −0.121958 | + | 0.375348i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.70494 | 0.250226 | ||||||||
\(719\) | −6.94474 | − | 5.04565i | −0.258995 | − | 0.188171i | 0.450709 | − | 0.892671i | \(-0.351171\pi\) |
−0.709704 | + | 0.704500i | \(0.751171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.90559 | − | 2.83758i | 0.145452 | − | 0.105677i | ||||
\(722\) | −13.1088 | + | 9.52408i | −0.487858 | + | 0.354450i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.1561 | 0.674768 | ||||||||
\(725\) | 15.1335 | − | 34.7719i | 0.562043 | − | 1.29140i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.42142 | − | 22.8408i | −0.275245 | − | 0.847118i | −0.989154 | − | 0.146880i | \(-0.953077\pi\) |
0.713909 | − | 0.700238i | \(-0.246923\pi\) | |||||||
\(728\) | −3.58621 | + | 2.60553i | −0.132914 | + | 0.0965675i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.9259 | + | 26.0639i | −0.774501 | + | 0.964669i | ||||
\(731\) | −9.69962 | − | 7.04719i | −0.358754 | − | 0.260650i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3787 | + | 11.1733i | 0.568025 | + | 0.412695i | 0.834387 | − | 0.551178i | \(-0.185822\pi\) |
−0.266362 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(734\) | −1.24119 | + | 3.82000i | −0.0458133 | + | 0.140999i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39991 | − | 7.38615i | −0.0884617 | − | 0.272257i | ||||
\(737\) | 5.38220 | − | 16.5647i | 0.198256 | − | 0.610168i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.42507 | − | 19.7743i | −0.236350 | − | 0.727411i | −0.996939 | − | 0.0781776i | \(-0.975090\pi\) |
0.760589 | − | 0.649233i | \(-0.224910\pi\) | |||||||
\(740\) | 1.61163 | + | 2.45906i | 0.0592446 | + | 0.0903968i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.66673 | + | 7.02329i | 0.354877 | + | 0.257833i | ||||
\(743\) | −6.53365 | −0.239696 | −0.119848 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119848 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.62351 | + | 0.987213i | −0.132755 | + | 0.0361687i | ||||
\(746\) | 21.5063 | − | 15.6252i | 0.787401 | − | 0.572080i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.57763 | − | 4.85544i | −0.0576838 | − | 0.177533i | ||||
\(749\) | −34.4755 | −1.25971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9879 | 1.02129 | 0.510646 | − | 0.859791i | \(-0.329406\pi\) | ||||
0.510646 | + | 0.859791i | \(0.329406\pi\) | |||||||
\(752\) | −0.566541 | − | 1.74363i | −0.0206596 | − | 0.0635838i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.8359 | − | 10.7789i | 0.540290 | − | 0.392544i | ||||
\(755\) | 45.8807 | − | 12.5001i | 1.66977 | − | 0.454923i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.48558 | 0.163031 | 0.0815156 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815156 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(758\) | −12.6431 | − | 9.18578i | −0.459220 | − | 0.333643i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.04977 | − | 3.12758i | −0.0743528 | − | 0.113449i | ||||
\(761\) | −0.138770 | − | 0.427091i | −0.00503042 | − | 0.0154820i | 0.948510 | − | 0.316748i | \(-0.102591\pi\) |
−0.953540 | + | 0.301266i | \(0.902591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.84063 | − | 17.9756i | 0.211445 | − | 0.650760i | ||||
\(764\) | 6.76906 | + | 20.8330i | 0.244896 | + | 0.753712i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.15489 | − | 12.7874i | 0.150122 | − | 0.462028i | ||||
\(767\) | 17.7228 | + | 12.8764i | 0.639935 | + | 0.464940i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9783 | − | 12.3355i | −0.612254 | − | 0.444829i | 0.237953 | − | 0.971277i | \(-0.423524\pi\) |
−0.850207 | + | 0.526448i | \(0.823524\pi\) | |||||||
\(770\) | −4.70541 | + | 5.86076i | −0.169571 | + | 0.211207i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.1872 | + | 16.1199i | −0.798533 | + | 0.580168i | ||||
\(773\) | −10.8283 | − | 33.3262i | −0.389468 | − | 1.19866i | −0.933187 | − | 0.359392i | \(-0.882984\pi\) |
0.543718 | − | 0.839268i | \(-0.317016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.3479 | + | 2.54615i | 0.946444 | + | 0.0914602i | ||||
\(776\) | −11.0902 | −0.398114 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.3157 | − | 14.7602i | 0.728354 | − | 0.529180i | ||||
\(779\) | −4.75564 | + | 3.45517i | −0.170388 | + | 0.123794i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.453127 | + | 0.329216i | 0.0162142 | + | 0.0117803i | ||||
\(782\) | 21.6265 | 0.773361 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.12444 | + | 3.46068i | −0.0401586 | + | 0.123596i | ||||
\(785\) | −22.5482 | + | 6.14318i | −0.804779 | + | 0.219259i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1132 | − | 37.2807i | 0.431790 | − | 1.32891i | −0.464550 | − | 0.885547i | \(-0.653784\pi\) |
0.896340 | − | 0.443367i | \(-0.146216\pi\) | |||||||
\(788\) | 0.347249 | − | 1.06872i | 0.0123702 | − | 0.0380717i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.23607 | + | 2.74292i | 0.257448 | + | 0.0975888i | ||||
\(791\) | −3.43132 | + | 10.5605i | −0.122004 | + | 0.375489i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.25724 | −0.222201 | ||||||||
\(794\) | 2.84628 | + | 2.06794i | 0.101011 | + | 0.0733884i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.6293 | + | 14.9880i | −0.731185 | + | 0.531237i | ||||
\(797\) | −6.98479 | + | 5.07475i | −0.247414 | + | 0.179757i | −0.704580 | − | 0.709625i | \(-0.748865\pi\) |
0.457166 | + | 0.889381i | \(0.348865\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.10532 | 0.180613 | ||||||||
\(800\) | −4.30902 | + | 2.53621i | −0.152347 | + | 0.0896686i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.23020 | + | 28.4076i | 0.325930 | + | 1.00311i | ||||
\(803\) | −22.1713 | + | 16.1084i | −0.782408 | + | 0.568453i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4520 | − | 26.6287i | −0.615102 | − | 0.938538i | ||||
\(806\) | 10.3557 | + | 7.52388i | 0.364765 | + | 0.265017i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.6634 | + | 7.74739i | 0.375136 | + | 0.272552i | ||||
\(809\) | 14.1830 | − | 43.6508i | 0.498648 | − | 1.53468i | −0.312546 | − | 0.949903i | \(-0.601182\pi\) |
0.811194 | − | 0.584778i | \(-0.198818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1734 | + | 37.4660i | 0.427467 | + | 1.31561i | 0.900612 | + | 0.434623i | \(0.143119\pi\) |
−0.473145 | + | 0.880984i | \(0.656881\pi\) | |||||||
\(812\) | −4.29692 | + | 13.2246i | −0.150792 | + | 0.464091i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.744923 | + | 2.29264i | 0.0261096 | + | 0.0803569i | ||||
\(815\) | −1.12087 | + | 23.2519i | −0.0392623 | + | 0.814477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82507 | − | 4.23216i | −0.203794 | − | 0.148065i | ||||
\(818\) | 38.7628 | 1.35531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.30839 | + | 6.57385i | 0.150456 | + | 0.229569i | ||||
\(821\) | 22.0672 | − | 16.0328i | 0.770152 | − | 0.559548i | −0.131855 | − | 0.991269i | \(-0.542093\pi\) |
0.902007 | + | 0.431721i | \(0.142093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.89701 | + | 5.83841i | 0.0661258 | + | 0.203514i | 0.978660 | − | 0.205486i | \(-0.0658775\pi\) |
−0.912534 | + | 0.409000i | \(0.865878\pi\) | |||||||
\(824\) | 2.63318 | 0.0917311 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.6110 | −0.577971 | ||||||||
\(827\) | −13.6170 | − | 41.9087i | −0.473508 | − | 1.45731i | −0.847959 | − | 0.530062i | \(-0.822169\pi\) |
0.374451 | − | 0.927247i | \(-0.377831\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.80236 | + | 2.76257i | −0.132061 | + | 0.0959481i | −0.651855 | − | 0.758344i | \(-0.726009\pi\) |
0.519794 | + | 0.854292i | \(0.326009\pi\) | |||||||
\(830\) | 0.686112 | − | 14.2331i | 0.0238153 | − | 0.494036i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.41785 | −0.0838238 | ||||||||
\(833\) | −8.19758 | − | 5.95589i | −0.284029 | − | 0.206359i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.43625 | − | 1.68162i | −0.153523 | − | 0.0581948i | ||||
\(836\) | −0.947439 | − | 2.91592i | −0.0327679 | − | 0.100849i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.84362 | + | 17.9848i | −0.201864 | + | 0.621275i | ||||
\(839\) | 14.2747 | + | 43.9331i | 0.492819 | + | 1.51674i | 0.820328 | + | 0.571893i | \(0.193791\pi\) |
−0.327509 | + | 0.944848i | \(0.606209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.81451 | − | 27.1283i | 0.303949 | − | 0.935458i | ||||
\(842\) | −17.8414 | − | 12.9625i | −0.614855 | − | 0.446718i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.2356 | − | 12.5224i | −0.593274 | − | 0.431039i | ||||
\(845\) | −14.9583 | − | 5.67011i | −0.514580 | − | 0.195058i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3300 | − | 8.23173i | 0.389304 | − | 0.282846i | ||||
\(848\) | 2.01398 | + | 6.19839i | 0.0691604 | + | 0.212854i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.00889 | − | 13.5943i | −0.103204 | − | 0.466282i | ||||
\(851\) | −10.2116 | −0.350048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.2282 | + | 7.43121i | −0.350206 | + | 0.254440i | −0.748956 | − | 0.662620i | \(-0.769444\pi\) |
0.398749 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(854\) | 3.83849 | − | 2.78883i | 0.131350 | − | 0.0954317i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.2131 | − | 11.0530i | −0.519974 | − | 0.377783i | ||||
\(857\) | 19.4162 | 0.663245 | 0.331623 | − | 0.943412i | \(-0.392404\pi\) | ||||
0.331623 | + | 0.943412i | \(0.392404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.88593 | − | 8.88197i | 0.0984665 | − | 0.303049i | −0.889675 | − | 0.456594i | \(-0.849069\pi\) |
0.988142 | + | 0.153545i | \(0.0490691\pi\) | |||||||
\(860\) | −6.02730 | + | 7.50722i | −0.205529 | + | 0.255994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.84474 | + | 8.75521i | −0.0968923 | + | 0.298204i | ||||
\(863\) | 5.05071 | − | 15.5445i | 0.171928 | − | 0.529141i | −0.827552 | − | 0.561390i | \(-0.810267\pi\) |
0.999480 | + | 0.0322489i | \(0.0102669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.2032 | − | 33.8781i | −0.754930 | − | 1.15189i | ||||
\(866\) | −10.7529 | + | 33.0941i | −0.365400 | + | 1.12458i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.70607 | −0.329445 | ||||||||
\(869\) | 5.13308 | + | 3.72940i | 0.174128 | + | 0.126511i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5829 | − | 13.5013i | 0.629659 | − | 0.457474i | ||||
\(872\) | 8.34038 | − | 6.05964i | 0.282441 | − | 0.205205i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.9877 | 0.439315 | ||||||||
\(875\) | −14.3106 | + | 14.6751i | −0.483787 | + | 0.496110i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.9717 | − | 33.7673i | −0.370487 | − | 1.14024i | −0.946473 | − | 0.322782i | \(-0.895382\pi\) |
0.575986 | − | 0.817459i | \(-0.304618\pi\) | |||||||
\(878\) | −6.75517 | + | 4.90792i | −0.227976 | + | 0.165634i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.95536 | + | 1.07763i | −0.133335 | + | 0.0363267i | ||||
\(881\) | −25.5378 | − | 18.5543i | −0.860390 | − | 0.625110i | 0.0676008 | − | 0.997712i | \(-0.478466\pi\) |
−0.927991 | + | 0.372602i | \(0.878466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.2592 | − | 20.5315i | −0.950997 | − | 0.690940i | 4.54670e−5 | − | 1.00000i | \(-0.499986\pi\) |
−0.951042 | + | 0.309060i | \(0.899986\pi\) | |||||||
\(884\) | 2.08058 | − | 6.40337i | 0.0699775 | − | 0.215369i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.370470 | − | 1.14019i | −0.0124462 | − | 0.0383054i | ||||
\(887\) | 13.2668 | − | 40.8311i | 0.445456 | − | 1.37097i | −0.436526 | − | 0.899692i | \(-0.643791\pi\) |
0.881982 | − | 0.471282i | \(-0.156209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.188810 | + | 0.581099i | 0.00633250 | + | 0.0194894i | ||||
\(890\) | −4.64832 | + | 5.78966i | −0.155812 | + | 0.194070i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.62535 | − | 1.90743i | −0.0879033 | − | 0.0638655i | ||||
\(893\) | 3.06598 | 0.102599 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.7837 | + | 18.4136i | −0.494164 | + | 0.615500i | ||||
\(896\) | 1.48322 | − | 1.07763i | 0.0495510 | − | 0.0360009i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.1343 | + | 31.1902i | 0.338186 | + | 1.04083i | ||||
\(899\) | 40.1532 | 1.33918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1487 | −0.604622 | ||||||||
\(902\) | 1.99142 | + | 6.12896i | 0.0663070 | + | 0.204072i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.89991 | + | 3.55999i | −0.162968 | + | 0.118404i | ||||
\(905\) | 37.9625 | + | 14.3902i | 1.26192 | + | 0.478345i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.8259 | −1.32240 | −0.661199 | − | 0.750211i | \(-0.729952\pi\) | ||||
−0.661199 | + | 0.750211i | \(0.729952\pi\) | |||||||
\(908\) | 13.2495 | + | 9.62631i | 0.439700 | + | 0.319460i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.56346 | + | 2.60553i | −0.317026 | + | 0.0863726i | ||||
\(911\) | 0.522189 | + | 1.60713i | 0.0173009 | + | 0.0532467i | 0.959334 | − | 0.282273i | \(-0.0910882\pi\) |
−0.942033 | + | 0.335519i | \(0.891088\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.61034 | − | 11.1115i | 0.119485 | − | 0.367737i | ||||
\(914\) | −6.11496 | − | 18.8199i | −0.202265 | − | 0.622508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.57289 | + | 4.84085i | −0.0519697 | + | 0.159946i | ||||
\(917\) | −7.68015 | − | 5.57995i | −0.253621 | − | 0.184266i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.2013 | + | 17.5833i | 0.798327 | + | 0.580019i | 0.910423 | − | 0.413679i | \(-0.135756\pi\) |
−0.112096 | + | 0.993697i | \(0.535756\pi\) | |||||||
\(920\) | 0.836161 | − | 17.3457i | 0.0275674 | − | 0.571872i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.60456 | + | 5.52504i | −0.250443 | + | 0.181957i | ||||
\(923\) | 0.228257 | + | 0.702504i | 0.00751318 | + | 0.0231232i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.42074 | + | 6.41896i | 0.0467135 | + | 0.211054i | ||||
\(926\) | −17.7329 | −0.582739 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.13597 | + | 4.45805i | −0.201423 | + | 0.146343i | ||||
\(929\) | −12.8664 | + | 9.34795i | −0.422131 | + | 0.306696i | −0.778495 | − | 0.627651i | \(-0.784017\pi\) |
0.356363 | + | 0.934347i | \(0.384017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.92303 | − | 3.57679i | −0.161346 | − | 0.117225i | ||||
\(932\) | 1.66296 | 0.0544721 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.75535 | − | 20.7908i | 0.221042 | − | 0.680297i | ||||
\(935\) | 0.549668 | − | 11.4026i | 0.0179761 | − | 0.372905i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2973 | − | 44.0026i | 0.467073 | − | 1.43750i | −0.389284 | − | 0.921118i | \(-0.627278\pi\) |
0.856357 | − | 0.516384i | \(-0.172722\pi\) | |||||||
\(938\) | −5.38220 | + | 16.5647i | −0.175735 | + | 0.540856i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.197391 | − | 4.09478i | 0.00643818 | − | 0.133557i | ||||
\(941\) | 3.60650 | − | 11.0997i | 0.117569 | − | 0.361839i | −0.874906 | − | 0.484294i | \(-0.839077\pi\) |
0.992474 | + | 0.122455i | \(0.0390766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.2988 | −0.888971 | ||||||||
\(944\) | −7.33001 | − | 5.32556i | −0.238571 | − | 0.173332i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.38602 | + | 4.63972i | −0.207628 | + | 0.150850i | ||||
\(947\) | −2.37336 | + | 1.72435i | −0.0771238 | + | 0.0560337i | −0.625679 | − | 0.780081i | \(-0.715178\pi\) |
0.548555 | + | 0.836114i | \(0.315178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.1421 | −1.17322 | ||||||||
\(950\) | −1.80698 | − | 8.16403i | −0.0586262 | − | 0.264876i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.57763 | + | 4.85544i | 0.0511313 | + | 0.157366i | ||||
\(953\) | −8.03924 | + | 5.84085i | −0.260417 | + | 0.189204i | −0.710331 | − | 0.703868i | \(-0.751455\pi\) |
0.449914 | + | 0.893072i | \(0.351455\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.35843 | + | 48.9245i | −0.0763171 | + | 1.58316i | ||||
\(956\) | 10.3553 | + | 7.52354i | 0.334913 | + | 0.243329i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.94352 | + | 3.59168i | 0.159718 | + | 0.116042i | ||||
\(959\) | 11.0607 | − | 34.0413i | 0.357168 | − | 1.09925i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.918471 | − | 2.82676i | −0.0296281 | − | 0.0911859i | ||||
\(962\) | −0.982407 | + | 3.02354i | −0.0316741 | + | 0.0974828i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.122209 | + | 0.376121i | 0.00393610 | + | 0.0121141i | ||||
\(965\) | −59.1672 | + | 16.1199i | −1.90466 | + | 0.518918i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.7193 | − | 26.6781i | −1.18081 | − | 0.857910i | −0.188549 | − | 0.982064i | \(-0.560379\pi\) |
−0.992263 | + | 0.124153i | \(0.960379\pi\) | |||||||
\(968\) | 7.63877 | 0.245519 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.1883 | − | 8.78982i | −0.744532 | − | 0.282224i | ||||
\(971\) | −3.78844 | + | 2.75246i | −0.121577 | + | 0.0883307i | −0.646912 | − | 0.762565i | \(-0.723940\pi\) |
0.525335 | + | 0.850895i | \(0.323940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.50688 | − | 13.8707i | −0.144484 | − | 0.444675i | ||||
\(974\) | −5.06189 | −0.162194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.58794 | 0.0828379 | ||||||||
\(977\) | −0.991339 | − | 3.05103i | −0.0317157 | − | 0.0976110i | 0.933946 | − | 0.357415i | \(-0.116342\pi\) |
−0.965661 | + | 0.259804i | \(0.916342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.92498 | + | 3.57820i | −0.157403 | + | 0.114360i | ||||
\(980\) | −5.09394 | + | 6.34468i | −0.162720 | + | 0.202674i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.38228 | 0.0760216 | ||||||||
\(983\) | 15.8337 | + | 11.5038i | 0.505015 | + | 0.366915i | 0.810929 | − | 0.585144i | \(-0.198962\pi\) |
−0.305914 | + | 0.952059i | \(0.598962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.57311 | − | 1.95936i | 0.0501233 | − | 0.0624304i | ||||
\(986\) | −6.52652 | − | 20.0866i | −0.207847 | − | 0.639687i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.24949 | − | 3.84552i | 0.0397514 | − | 0.122342i | ||||
\(989\) | −10.3328 | − | 31.8011i | −0.328564 | − | 1.01122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9762 | − | 43.0144i | 0.443969 | − | 1.36640i | −0.439641 | − | 0.898173i | \(-0.644894\pi\) |
0.883610 | − | 0.468223i | \(-0.155106\pi\) | |||||||
\(992\) | −4.28304 | − | 3.11181i | −0.135987 | − | 0.0988000i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.453127 | − | 0.329216i | −0.0143723 | − | 0.0104421i | ||||
\(995\) | −55.0127 | + | 14.9880i | −1.74402 | + | 0.475153i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.9808 | − | 34.1335i | 1.48790 | − | 1.08102i | 0.512991 | − | 0.858394i | \(-0.328537\pi\) |
0.974904 | − | 0.222626i | \(-0.0714627\pi\) | |||||||
\(998\) | 0.0155532 | + | 0.0478679i | 0.000492329 | + | 0.00151523i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.h.e.181.1 | 8 | ||
3.2 | odd | 2 | 50.2.d.b.31.1 | yes | 8 | ||
12.11 | even | 2 | 400.2.u.d.81.2 | 8 | |||
15.2 | even | 4 | 250.2.e.c.99.2 | 16 | |||
15.8 | even | 4 | 250.2.e.c.99.3 | 16 | |||
15.14 | odd | 2 | 250.2.d.d.151.2 | 8 | |||
25.21 | even | 5 | inner | 450.2.h.e.271.1 | 8 | ||
75.2 | even | 20 | 1250.2.b.e.1249.5 | 8 | |||
75.11 | odd | 10 | 1250.2.a.l.1.4 | 4 | |||
75.14 | odd | 10 | 1250.2.a.f.1.1 | 4 | |||
75.23 | even | 20 | 1250.2.b.e.1249.4 | 8 | |||
75.29 | odd | 10 | 250.2.d.d.101.2 | 8 | |||
75.47 | even | 20 | 250.2.e.c.149.3 | 16 | |||
75.53 | even | 20 | 250.2.e.c.149.2 | 16 | |||
75.71 | odd | 10 | 50.2.d.b.21.1 | ✓ | 8 | ||
300.11 | even | 10 | 10000.2.a.t.1.1 | 4 | |||
300.71 | even | 10 | 400.2.u.d.321.2 | 8 | |||
300.239 | even | 10 | 10000.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.21.1 | ✓ | 8 | 75.71 | odd | 10 | ||
50.2.d.b.31.1 | yes | 8 | 3.2 | odd | 2 | ||
250.2.d.d.101.2 | 8 | 75.29 | odd | 10 | |||
250.2.d.d.151.2 | 8 | 15.14 | odd | 2 | |||
250.2.e.c.99.2 | 16 | 15.2 | even | 4 | |||
250.2.e.c.99.3 | 16 | 15.8 | even | 4 | |||
250.2.e.c.149.2 | 16 | 75.53 | even | 20 | |||
250.2.e.c.149.3 | 16 | 75.47 | even | 20 | |||
400.2.u.d.81.2 | 8 | 12.11 | even | 2 | |||
400.2.u.d.321.2 | 8 | 300.71 | even | 10 | |||
450.2.h.e.181.1 | 8 | 1.1 | even | 1 | trivial | ||
450.2.h.e.271.1 | 8 | 25.21 | even | 5 | inner | ||
1250.2.a.f.1.1 | 4 | 75.14 | odd | 10 | |||
1250.2.a.l.1.4 | 4 | 75.11 | odd | 10 | |||
1250.2.b.e.1249.4 | 8 | 75.23 | even | 20 | |||
1250.2.b.e.1249.5 | 8 | 75.2 | even | 20 | |||
10000.2.a.t.1.1 | 4 | 300.11 | even | 10 | |||
10000.2.a.x.1.4 | 4 | 300.239 | even | 10 |