Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{73})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 19x^{2} + 18x + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.1 | ||
Root | \(2.38600 + 4.13267i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.2.i.g.121.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −4.77200 | −1.43881 | −0.719406 | − | 0.694589i | \(-0.755586\pi\) | ||||
−0.719406 | + | 0.694589i | \(0.755586\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.88600 | − | 3.26665i | −0.523083 | − | 0.906006i | −0.999639 | − | 0.0268618i | \(-0.991449\pi\) |
0.476557 | − | 0.879144i | \(-0.341885\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.38600 | − | 4.13267i | −0.317970 | − | 0.948101i | ||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.500000 | − | 0.866025i | 0.109109 | − | 0.188982i | ||||
\(22\) | −2.38600 | + | 4.13267i | −0.508697 | + | 0.881089i | ||||
\(23\) | −2.38600 | − | 4.13267i | −0.497516 | − | 0.861722i | 0.502480 | − | 0.864589i | \(-0.332421\pi\) |
−0.999996 | + | 0.00286638i | \(0.999088\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −3.77200 | −0.739750 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −5.77200 | −1.03668 | −0.518341 | − | 0.855174i | \(-0.673450\pi\) | ||||
−0.518341 | + | 0.855174i | \(0.673450\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.38600 | − | 4.13267i | 0.415349 | − | 0.719406i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 0.866025i | 0.0845154 | − | 0.146385i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | −4.27200 | − | 0.866025i | −0.693010 | − | 0.140488i | ||||
\(39\) | 3.77200 | 0.604004 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −2.38600 | + | 4.13267i | −0.372631 | + | 0.645415i | −0.989969 | − | 0.141282i | \(-0.954878\pi\) |
0.617339 | + | 0.786698i | \(0.288211\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −0.113999 | + | 0.197452i | −0.0173847 | + | 0.0301112i | −0.874587 | − | 0.484869i | \(-0.838867\pi\) |
0.857202 | + | 0.514980i | \(0.172201\pi\) | |||||||
\(44\) | 2.38600 | + | 4.13267i | 0.359703 | + | 0.623024i | ||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −4.77200 | −0.703593 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.88600 | + | 3.26665i | −0.261541 | + | 0.453003i | ||||
\(53\) | −0.613999 | − | 1.06348i | −0.0843393 | − | 0.146080i | 0.820770 | − | 0.571258i | \(-0.193545\pi\) |
−0.905109 | + | 0.425179i | \(0.860211\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 2.38600 | − | 4.13267i | 0.321728 | − | 0.557250i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 4.27200 | + | 0.866025i | 0.565840 | + | 0.114708i | ||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −1.77200 | + | 3.06920i | −0.230695 | + | 0.399575i | −0.958013 | − | 0.286725i | \(-0.907433\pi\) |
0.727318 | + | 0.686301i | \(0.240767\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 2.88600 | + | 4.99870i | 0.369515 | + | 0.640018i | 0.989490 | − | 0.144603i | \(-0.0461907\pi\) |
−0.619975 | + | 0.784621i | \(0.712857\pi\) | |||||||
\(62\) | −2.88600 | + | 4.99870i | −0.366522 | + | 0.634836i | ||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.77200 | 0.467859 | ||||||||
\(66\) | −2.38600 | − | 4.13267i | −0.293696 | − | 0.508697i | ||||
\(67\) | 1.11400 | + | 1.92950i | 0.136097 | + | 0.235726i | 0.926016 | − | 0.377485i | \(-0.123211\pi\) |
−0.789919 | + | 0.613211i | \(0.789878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.77200 | 0.574482 | ||||||||
\(70\) | −0.500000 | − | 0.866025i | −0.0597614 | − | 0.103510i | ||||
\(71\) | −4.77200 | + | 8.26535i | −0.566332 | + | 0.980917i | 0.430592 | + | 0.902547i | \(0.358305\pi\) |
−0.996924 | + | 0.0783698i | \(0.975029\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 5.88600 | − | 10.1949i | 0.688904 | − | 1.19322i | −0.283288 | − | 0.959035i | \(-0.591425\pi\) |
0.972193 | − | 0.234182i | \(-0.0752413\pi\) | |||||||
\(74\) | −0.500000 | + | 0.866025i | −0.0581238 | + | 0.100673i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.88600 | + | 3.26665i | −0.331047 | + | 0.374710i | ||||
\(77\) | 4.77200 | 0.543820 | ||||||||
\(78\) | 1.88600 | − | 3.26665i | 0.213548 | − | 0.369875i | ||||
\(79\) | 7.65800 | − | 13.2640i | 0.861593 | − | 1.49232i | −0.00879850 | − | 0.999961i | \(-0.502801\pi\) |
0.870391 | − | 0.492361i | \(-0.163866\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.38600 | + | 4.13267i | 0.263490 | + | 0.456378i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.113999 | + | 0.197452i | 0.0122928 | + | 0.0212918i | ||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 4.77200 | 0.508697 | ||||||||
\(89\) | 4.15800 | + | 7.20187i | 0.440747 | + | 0.763397i | 0.997745 | − | 0.0671171i | \(-0.0213801\pi\) |
−0.556998 | + | 0.830514i | \(0.688047\pi\) | |||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | 1.88600 | + | 3.26665i | 0.197707 | + | 0.342438i | ||||
\(92\) | −2.38600 | + | 4.13267i | −0.248758 | + | 0.430861i | ||||
\(93\) | 2.88600 | − | 4.99870i | 0.299264 | − | 0.518341i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.27200 | + | 0.866025i | 0.438298 | + | 0.0888523i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.00000 | − | 8.66025i | 0.507673 | − | 0.879316i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
0.999961 | − | 0.00888289i | \(-0.00282755\pi\) | |||||||
\(98\) | −3.00000 | + | 5.19615i | −0.303046 | + | 0.524891i | ||||
\(99\) | 2.38600 | + | 4.13267i | 0.239802 | + | 0.415349i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0000 | −1.28093 | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||||
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 1.88600 | + | 3.26665i | 0.184938 | + | 0.320321i | ||||
\(105\) | 0.500000 | + | 0.866025i | 0.0487950 | + | 0.0845154i | ||||
\(106\) | −1.22800 | −0.119274 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 3.77200 | − | 6.53330i | 0.361292 | − | 0.625777i | −0.626882 | − | 0.779115i | \(-0.715669\pi\) |
0.988174 | + | 0.153338i | \(0.0490023\pi\) | |||||||
\(110\) | −2.38600 | − | 4.13267i | −0.227496 | − | 0.394035i | ||||
\(111\) | 0.500000 | − | 0.866025i | 0.0474579 | − | 0.0821995i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 3.54400 | 0.333392 | 0.166696 | − | 0.986008i | \(-0.446690\pi\) | ||||
0.166696 | + | 0.986008i | \(0.446690\pi\) | |||||||
\(114\) | 2.88600 | − | 3.26665i | 0.270299 | − | 0.305950i | ||||
\(115\) | 4.77200 | 0.444991 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | −1.88600 | + | 3.26665i | −0.174361 | + | 0.302002i | ||||
\(118\) | 1.77200 | + | 3.06920i | 0.163126 | + | 0.282543i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | 11.7720 | 1.07018 | ||||||||
\(122\) | 5.77200 | 0.522572 | ||||||||
\(123\) | −2.38600 | − | 4.13267i | −0.215138 | − | 0.372631i | ||||
\(124\) | 2.88600 | + | 4.99870i | 0.259171 | + | 0.448897i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −8.15800 | − | 14.1301i | −0.723906 | − | 1.25384i | −0.959423 | − | 0.281971i | \(-0.909012\pi\) |
0.235517 | − | 0.971870i | \(-0.424322\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.113999 | − | 0.197452i | −0.0100371 | − | 0.0173847i | ||||
\(130\) | 1.88600 | − | 3.26665i | 0.165413 | − | 0.286504i | ||||
\(131\) | −7.15800 | + | 12.3980i | −0.625398 | + | 1.08322i | 0.363066 | + | 0.931763i | \(0.381730\pi\) |
−0.988464 | + | 0.151457i | \(0.951603\pi\) | |||||||
\(132\) | −4.77200 | −0.415349 | ||||||||
\(133\) | 1.38600 | + | 4.13267i | 0.120182 | + | 0.358348i | ||||
\(134\) | 2.22800 | 0.192470 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.77200 | − | 13.4615i | −0.664007 | − | 1.15009i | −0.979554 | − | 0.201184i | \(-0.935521\pi\) |
0.315547 | − | 0.948910i | \(-0.397812\pi\) | |||||||
\(138\) | 2.38600 | − | 4.13267i | 0.203110 | − | 0.351797i | ||||
\(139\) | 1.11400 | + | 1.92950i | 0.0944882 | + | 0.163658i | 0.909395 | − | 0.415934i | \(-0.136545\pi\) |
−0.814907 | + | 0.579592i | \(0.803212\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.77200 | + | 8.26535i | 0.400458 | + | 0.693613i | ||||
\(143\) | 9.00000 | + | 15.5885i | 0.752618 | + | 1.30357i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | −5.88600 | − | 10.1949i | −0.487129 | − | 0.843732i | ||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 0.500000 | + | 0.866025i | 0.0410997 | + | 0.0711868i | ||||
\(149\) | −1.77200 | + | 3.06920i | −0.145168 | + | 0.251438i | −0.929436 | − | 0.368984i | \(-0.879706\pi\) |
0.784268 | + | 0.620423i | \(0.213039\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 1.38600 | + | 4.13267i | 0.112420 | + | 0.335204i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.38600 | − | 4.13267i | 0.192269 | − | 0.333020i | ||||
\(155\) | 2.88600 | − | 4.99870i | 0.231809 | − | 0.401505i | ||||
\(156\) | −1.88600 | − | 3.26665i | −0.151001 | − | 0.261541i | ||||
\(157\) | −10.2720 | + | 17.7916i | −0.819795 | + | 1.41993i | 0.0860381 | + | 0.996292i | \(0.472579\pi\) |
−0.905833 | + | 0.423635i | \(0.860754\pi\) | |||||||
\(158\) | −7.65800 | − | 13.2640i | −0.609238 | − | 1.05523i | ||||
\(159\) | 1.22800 | 0.0973866 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 2.38600 | + | 4.13267i | 0.188043 | + | 0.325700i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 7.31601 | 0.573034 | 0.286517 | − | 0.958075i | \(-0.407503\pi\) | ||||
0.286517 | + | 0.958075i | \(0.407503\pi\) | |||||||
\(164\) | 4.77200 | 0.372631 | ||||||||
\(165\) | 2.38600 | + | 4.13267i | 0.185750 | + | 0.321728i | ||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | −7.15800 | − | 12.3980i | −0.553903 | − | 0.959388i | −0.997988 | − | 0.0634033i | \(-0.979805\pi\) |
0.444085 | − | 0.895985i | \(-0.353529\pi\) | |||||||
\(168\) | −0.500000 | + | 0.866025i | −0.0385758 | + | 0.0668153i | ||||
\(169\) | −0.613999 | + | 1.06348i | −0.0472307 | + | 0.0818060i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.88600 | + | 3.26665i | −0.220698 | + | 0.249807i | ||||
\(172\) | 0.227998 | 0.0173847 | ||||||||
\(173\) | 7.15800 | − | 12.3980i | 0.544213 | − | 0.942604i | −0.454443 | − | 0.890776i | \(-0.650162\pi\) |
0.998656 | − | 0.0518286i | \(-0.0165049\pi\) | |||||||
\(174\) | −3.00000 | + | 5.19615i | −0.227429 | + | 0.393919i | ||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 2.38600 | − | 4.13267i | 0.179852 | − | 0.311512i | ||||
\(177\) | −1.77200 | − | 3.06920i | −0.133192 | − | 0.230695i | ||||
\(178\) | 8.31601 | 0.623311 | ||||||||
\(179\) | −26.3160 | −1.96695 | −0.983475 | − | 0.181042i | \(-0.942053\pi\) | ||||
−0.983475 | + | 0.181042i | \(0.942053\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 8.54400 | + | 14.7986i | 0.635071 | + | 1.09997i | 0.986500 | + | 0.163760i | \(0.0523624\pi\) |
−0.351429 | + | 0.936214i | \(0.614304\pi\) | |||||||
\(182\) | 3.77200 | 0.279599 | ||||||||
\(183\) | −5.77200 | −0.426679 | ||||||||
\(184\) | 2.38600 | + | 4.13267i | 0.175898 | + | 0.304665i | ||||
\(185\) | 0.500000 | − | 0.866025i | 0.0367607 | − | 0.0636715i | ||||
\(186\) | −2.88600 | − | 4.99870i | −0.211612 | − | 0.366522i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 2.88600 | − | 3.26665i | 0.209373 | − | 0.236988i | ||||
\(191\) | −9.54400 | −0.690580 | −0.345290 | − | 0.938496i | \(-0.612219\pi\) | ||||
−0.345290 | + | 0.938496i | \(0.612219\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 2.88600 | − | 4.99870i | 0.207739 | − | 0.359814i | −0.743263 | − | 0.668999i | \(-0.766723\pi\) |
0.951002 | + | 0.309185i | \(0.100056\pi\) | |||||||
\(194\) | −5.00000 | − | 8.66025i | −0.358979 | − | 0.621770i | ||||
\(195\) | −1.88600 | + | 3.26665i | −0.135059 | + | 0.233930i | ||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | 14.3160 | 1.01997 | 0.509987 | − | 0.860182i | \(-0.329650\pi\) | ||||
0.509987 | + | 0.860182i | \(0.329650\pi\) | |||||||
\(198\) | 4.77200 | 0.339131 | ||||||||
\(199\) | −12.6580 | − | 21.9243i | −0.897302 | − | 1.55417i | −0.830929 | − | 0.556378i | \(-0.812191\pi\) |
−0.0663726 | − | 0.997795i | \(-0.521143\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −2.22800 | −0.157151 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.38600 | − | 4.13267i | −0.166646 | − | 0.288639i | ||||
\(206\) | −6.50000 | + | 11.2583i | −0.452876 | + | 0.784405i | ||||
\(207\) | −2.38600 | + | 4.13267i | −0.165839 | + | 0.287241i | ||||
\(208\) | 3.77200 | 0.261541 | ||||||||
\(209\) | 6.61400 | + | 19.7211i | 0.457500 | + | 1.36414i | ||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 1.72800 | − | 2.99298i | 0.118960 | − | 0.206045i | −0.800396 | − | 0.599472i | \(-0.795377\pi\) |
0.919356 | + | 0.393427i | \(0.128711\pi\) | |||||||
\(212\) | −0.613999 | + | 1.06348i | −0.0421696 | + | 0.0730399i | ||||
\(213\) | −4.77200 | − | 8.26535i | −0.326972 | − | 0.566332i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.113999 | − | 0.197452i | −0.00777467 | − | 0.0134661i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.77200 | 0.391829 | ||||||||
\(218\) | −3.77200 | − | 6.53330i | −0.255472 | − | 0.442491i | ||||
\(219\) | 5.88600 | + | 10.1949i | 0.397739 | + | 0.688904i | ||||
\(220\) | −4.77200 | −0.321728 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.500000 | − | 0.866025i | −0.0335578 | − | 0.0581238i | ||||
\(223\) | 12.5000 | − | 21.6506i | 0.837062 | − | 1.44983i | −0.0552786 | − | 0.998471i | \(-0.517605\pi\) |
0.892341 | − | 0.451363i | \(-0.149062\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 1.77200 | − | 3.06920i | 0.117872 | − | 0.204160i | ||||
\(227\) | −25.0880 | −1.66515 | −0.832575 | − | 0.553913i | \(-0.813134\pi\) | ||||
−0.832575 | + | 0.553913i | \(0.813134\pi\) | |||||||
\(228\) | −1.38600 | − | 4.13267i | −0.0917902 | − | 0.273693i | ||||
\(229\) | −18.8600 | −1.24630 | −0.623152 | − | 0.782101i | \(-0.714148\pi\) | ||||
−0.623152 | + | 0.782101i | \(0.714148\pi\) | |||||||
\(230\) | 2.38600 | − | 4.13267i | 0.157328 | − | 0.272501i | ||||
\(231\) | −2.38600 | + | 4.13267i | −0.156987 | + | 0.271910i | ||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | 10.7720 | − | 18.6577i | 0.705697 | − | 1.22230i | −0.260742 | − | 0.965409i | \(-0.583967\pi\) |
0.966439 | − | 0.256895i | \(-0.0826995\pi\) | |||||||
\(234\) | 1.88600 | + | 3.26665i | 0.123292 | + | 0.213548i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.54400 | 0.230695 | ||||||||
\(237\) | 7.65800 | + | 13.2640i | 0.497441 | + | 0.861593i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.54400 | −0.229243 | −0.114621 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114621 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 1.65800 | + | 2.87175i | 0.106801 | + | 0.184985i | 0.914473 | − | 0.404648i | \(-0.132606\pi\) |
−0.807671 | + | 0.589633i | \(0.799272\pi\) | |||||||
\(242\) | 5.88600 | − | 10.1949i | 0.378366 | − | 0.655350i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.88600 | − | 4.99870i | 0.184757 | − | 0.320009i | ||||
\(245\) | 3.00000 | − | 5.19615i | 0.191663 | − | 0.331970i | ||||
\(246\) | −4.77200 | −0.304252 | ||||||||
\(247\) | −10.8860 | + | 12.3218i | −0.692660 | + | 0.784018i | ||||
\(248\) | 5.77200 | 0.366522 | ||||||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 7.77200 | + | 13.4615i | 0.490564 | + | 0.849682i | 0.999941 | − | 0.0108612i | \(-0.00345730\pi\) |
−0.509377 | + | 0.860544i | \(0.670124\pi\) | |||||||
\(252\) | 0.500000 | − | 0.866025i | 0.0314970 | − | 0.0545545i | ||||
\(253\) | 11.3860 | + | 19.7211i | 0.715832 | + | 1.23986i | ||||
\(254\) | −16.3160 | −1.02376 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.0000 | + | 25.9808i | 0.935674 | + | 1.62064i | 0.773427 | + | 0.633885i | \(0.218541\pi\) |
0.162247 | + | 0.986750i | \(0.448126\pi\) | |||||||
\(258\) | −0.227998 | −0.0141945 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | −1.88600 | − | 3.26665i | −0.116965 | − | 0.202589i | ||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 7.15800 | + | 12.3980i | 0.442223 | + | 0.765953i | ||||
\(263\) | −3.61400 | + | 6.25963i | −0.222849 | + | 0.385985i | −0.955672 | − | 0.294434i | \(-0.904869\pi\) |
0.732823 | + | 0.680419i | \(0.238202\pi\) | |||||||
\(264\) | −2.38600 | + | 4.13267i | −0.146848 | + | 0.254349i | ||||
\(265\) | 1.22800 | 0.0754353 | ||||||||
\(266\) | 4.27200 | + | 0.866025i | 0.261933 | + | 0.0530994i | ||||
\(267\) | −8.31601 | −0.508931 | ||||||||
\(268\) | 1.11400 | − | 1.92950i | 0.0680483 | − | 0.117863i | ||||
\(269\) | 4.22800 | − | 7.32311i | 0.257786 | − | 0.446498i | −0.707863 | − | 0.706350i | \(-0.750341\pi\) |
0.965648 | + | 0.259852i | \(0.0836738\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | −14.7720 | + | 25.5859i | −0.897335 | + | 1.55423i | −0.0664476 | + | 0.997790i | \(0.521167\pi\) |
−0.830888 | + | 0.556440i | \(0.812167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.77200 | −0.228292 | ||||||||
\(274\) | −15.5440 | −0.939048 | ||||||||
\(275\) | 2.38600 | + | 4.13267i | 0.143881 | + | 0.249210i | ||||
\(276\) | −2.38600 | − | 4.13267i | −0.143620 | − | 0.248758i | ||||
\(277\) | −29.0880 | −1.74773 | −0.873864 | − | 0.486170i | \(-0.838394\pi\) | ||||
−0.873864 | + | 0.486170i | \(0.838394\pi\) | |||||||
\(278\) | 2.22800 | 0.133626 | ||||||||
\(279\) | 2.88600 | + | 4.99870i | 0.172780 | + | 0.299264i | ||||
\(280\) | −0.500000 | + | 0.866025i | −0.0298807 | + | 0.0517549i | ||||
\(281\) | −9.61400 | − | 16.6519i | −0.573523 | − | 0.993371i | −0.996200 | − | 0.0870909i | \(-0.972243\pi\) |
0.422677 | − | 0.906280i | \(-0.361090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.3160 | + | 21.3319i | −0.732111 | + | 1.26805i | 0.223869 | + | 0.974619i | \(0.428131\pi\) |
−0.955980 | + | 0.293433i | \(0.905202\pi\) | |||||||
\(284\) | 9.54400 | 0.566332 | ||||||||
\(285\) | −2.88600 | + | 3.26665i | −0.170952 | + | 0.193500i | ||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 2.38600 | − | 4.13267i | 0.140841 | − | 0.243944i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | −3.00000 | + | 5.19615i | −0.176166 | + | 0.305129i | ||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | −11.7720 | −0.688904 | ||||||||
\(293\) | −28.7720 | −1.68088 | −0.840439 | − | 0.541906i | \(-0.817703\pi\) | ||||
−0.840439 | + | 0.541906i | \(0.817703\pi\) | |||||||
\(294\) | −3.00000 | − | 5.19615i | −0.174964 | − | 0.303046i | ||||
\(295\) | −1.77200 | − | 3.06920i | −0.103170 | − | 0.178696i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | −4.77200 | −0.276900 | ||||||||
\(298\) | 1.77200 | + | 3.06920i | 0.102649 | + | 0.177794i | ||||
\(299\) | −9.00000 | + | 15.5885i | −0.520483 | + | 0.901504i | ||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | 0.113999 | − | 0.197452i | 0.00657080 | − | 0.0113810i | ||||
\(302\) | 4.00000 | − | 6.92820i | 0.230174 | − | 0.398673i | ||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 4.27200 | + | 0.866025i | 0.245016 | + | 0.0496700i | ||||
\(305\) | −5.77200 | −0.330504 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.22800 | − | 5.59106i | 0.184232 | − | 0.319098i | −0.759086 | − | 0.650991i | \(-0.774354\pi\) |
0.943317 | + | 0.331892i | \(0.107687\pi\) | |||||||
\(308\) | −2.38600 | − | 4.13267i | −0.135955 | − | 0.235481i | ||||
\(309\) | 6.50000 | − | 11.2583i | 0.369772 | − | 0.640464i | ||||
\(310\) | −2.88600 | − | 4.99870i | −0.163914 | − | 0.283907i | ||||
\(311\) | 8.45600 | 0.479496 | 0.239748 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239748 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(312\) | −3.77200 | −0.213548 | ||||||||
\(313\) | 9.77200 | + | 16.9256i | 0.552346 | + | 0.956692i | 0.998105 | + | 0.0615384i | \(0.0196007\pi\) |
−0.445759 | + | 0.895153i | \(0.647066\pi\) | |||||||
\(314\) | 10.2720 | + | 17.7916i | 0.579683 | + | 1.00404i | ||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −15.3160 | −0.861593 | ||||||||
\(317\) | −14.3860 | − | 24.9173i | −0.807998 | − | 1.39949i | −0.914248 | − | 0.405155i | \(-0.867218\pi\) |
0.106250 | − | 0.994339i | \(-0.466116\pi\) | |||||||
\(318\) | 0.613999 | − | 1.06348i | 0.0344314 | − | 0.0596369i | ||||
\(319\) | −14.3160 | − | 24.7960i | −0.801542 | − | 1.38831i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.77200 | 0.265933 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.88600 | + | 3.26665i | −0.104617 | + | 0.181201i | ||||
\(326\) | 3.65800 | − | 6.33585i | 0.202598 | − | 0.350910i | ||||
\(327\) | 3.77200 | + | 6.53330i | 0.208592 | + | 0.361292i | ||||
\(328\) | 2.38600 | − | 4.13267i | 0.131745 | − | 0.228189i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.77200 | 0.262690 | ||||||||
\(331\) | −9.45600 | −0.519749 | −0.259874 | − | 0.965642i | \(-0.583681\pi\) | ||||
−0.259874 | + | 0.965642i | \(0.583681\pi\) | |||||||
\(332\) | −3.00000 | − | 5.19615i | −0.164646 | − | 0.285176i | ||||
\(333\) | 0.500000 | + | 0.866025i | 0.0273998 | + | 0.0474579i | ||||
\(334\) | −14.3160 | −0.783337 | ||||||||
\(335\) | −2.22800 | −0.121729 | ||||||||
\(336\) | 0.500000 | + | 0.866025i | 0.0272772 | + | 0.0472456i | ||||
\(337\) | 2.34200 | − | 4.05646i | 0.127577 | − | 0.220969i | −0.795160 | − | 0.606399i | \(-0.792613\pi\) |
0.922737 | + | 0.385430i | \(0.125947\pi\) | |||||||
\(338\) | 0.613999 | + | 1.06348i | 0.0333971 | + | 0.0578456i | ||||
\(339\) | −1.77200 | + | 3.06920i | −0.0962419 | + | 0.166696i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.5440 | 1.49159 | ||||||||
\(342\) | 1.38600 | + | 4.13267i | 0.0749463 | + | 0.223469i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0.113999 | − | 0.197452i | 0.00614642 | − | 0.0106459i | ||||
\(345\) | −2.38600 | + | 4.13267i | −0.128458 | + | 0.222496i | ||||
\(346\) | −7.15800 | − | 12.3980i | −0.384817 | − | 0.666522i | ||||
\(347\) | −4.77200 | + | 8.26535i | −0.256174 | + | 0.443707i | −0.965214 | − | 0.261462i | \(-0.915795\pi\) |
0.709039 | + | 0.705169i | \(0.249129\pi\) | |||||||
\(348\) | 3.00000 | + | 5.19615i | 0.160817 | + | 0.278543i | ||||
\(349\) | −17.7720 | −0.951313 | −0.475657 | − | 0.879631i | \(-0.657790\pi\) | ||||
−0.475657 | + | 0.879631i | \(0.657790\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −1.88600 | − | 3.26665i | −0.100667 | − | 0.174361i | ||||
\(352\) | −2.38600 | − | 4.13267i | −0.127174 | − | 0.220272i | ||||
\(353\) | 3.54400 | 0.188628 | 0.0943141 | − | 0.995542i | \(-0.469934\pi\) | ||||
0.0943141 | + | 0.995542i | \(0.469934\pi\) | |||||||
\(354\) | −3.54400 | −0.188362 | ||||||||
\(355\) | −4.77200 | − | 8.26535i | −0.253272 | − | 0.438679i | ||||
\(356\) | 4.15800 | − | 7.20187i | 0.220374 | − | 0.381698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.1580 | + | 22.7903i | −0.695422 | + | 1.20451i | ||||
\(359\) | 6.54400 | − | 11.3345i | 0.345379 | − | 0.598215i | −0.640043 | − | 0.768339i | \(-0.721084\pi\) |
0.985423 | + | 0.170124i | \(0.0544169\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −15.1580 | + | 11.4558i | −0.797790 | + | 0.602936i | ||||
\(362\) | 17.0880 | 0.898126 | ||||||||
\(363\) | −5.88600 | + | 10.1949i | −0.308935 | + | 0.535091i | ||||
\(364\) | 1.88600 | − | 3.26665i | 0.0988533 | − | 0.171219i | ||||
\(365\) | 5.88600 | + | 10.1949i | 0.308087 | + | 0.533623i | ||||
\(366\) | −2.88600 | + | 4.99870i | −0.150854 | + | 0.261286i | ||||
\(367\) | 8.88600 | + | 15.3910i | 0.463845 | + | 0.803404i | 0.999149 | − | 0.0412561i | \(-0.0131360\pi\) |
−0.535303 | + | 0.844660i | \(0.679803\pi\) | |||||||
\(368\) | 4.77200 | 0.248758 | ||||||||
\(369\) | 4.77200 | 0.248420 | ||||||||
\(370\) | −0.500000 | − | 0.866025i | −0.0259938 | − | 0.0450225i | ||||
\(371\) | 0.613999 | + | 1.06348i | 0.0318772 | + | 0.0552130i | ||||
\(372\) | −5.77200 | −0.299264 | ||||||||
\(373\) | −8.77200 | −0.454197 | −0.227099 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227099 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3160 | − | 19.5999i | 0.582804 | − | 1.00945i | ||||
\(378\) | −0.500000 | + | 0.866025i | −0.0257172 | + | 0.0445435i | ||||
\(379\) | −17.7720 | −0.912886 | −0.456443 | − | 0.889753i | \(-0.650877\pi\) | ||||
−0.456443 | + | 0.889753i | \(0.650877\pi\) | |||||||
\(380\) | −1.38600 | − | 4.13267i | −0.0711003 | − | 0.212002i | ||||
\(381\) | 16.3160 | 0.835894 | ||||||||
\(382\) | −4.77200 | + | 8.26535i | −0.244157 | + | 0.422892i | ||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −2.38600 | + | 4.13267i | −0.121602 | + | 0.210621i | ||||
\(386\) | −2.88600 | − | 4.99870i | −0.146894 | − | 0.254427i | ||||
\(387\) | 0.227998 | 0.0115898 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −12.5440 | − | 21.7269i | −0.636006 | − | 1.10160i | −0.986301 | − | 0.164956i | \(-0.947252\pi\) |
0.350295 | − | 0.936640i | \(-0.386081\pi\) | |||||||
\(390\) | 1.88600 | + | 3.26665i | 0.0955014 | + | 0.165413i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | −7.15800 | − | 12.3980i | −0.361073 | − | 0.625398i | ||||
\(394\) | 7.15800 | − | 12.3980i | 0.360615 | − | 0.624603i | ||||
\(395\) | 7.65800 | + | 13.2640i | 0.385316 | + | 0.667387i | ||||
\(396\) | 2.38600 | − | 4.13267i | 0.119901 | − | 0.207675i | ||||
\(397\) | 16.0440 | − | 27.7890i | 0.805225 | − | 1.39469i | −0.110913 | − | 0.993830i | \(-0.535378\pi\) |
0.916139 | − | 0.400861i | \(-0.131289\pi\) | |||||||
\(398\) | −25.3160 | −1.26898 | ||||||||
\(399\) | −4.27200 | − | 0.866025i | −0.213868 | − | 0.0433555i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 12.5440 | − | 21.7269i | 0.626418 | − | 1.08499i | −0.361847 | − | 0.932237i | \(-0.617854\pi\) |
0.988265 | − | 0.152750i | \(-0.0488129\pi\) | |||||||
\(402\) | −1.11400 | + | 1.92950i | −0.0555612 | + | 0.0962349i | ||||
\(403\) | 10.8860 | + | 18.8551i | 0.542270 | + | 0.939240i | ||||
\(404\) | 3.00000 | − | 5.19615i | 0.149256 | − | 0.258518i | ||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 4.77200 | 0.236539 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7020 | − | 25.4646i | −0.726967 | − | 1.25914i | −0.958159 | − | 0.286236i | \(-0.907596\pi\) |
0.231192 | − | 0.972908i | \(-0.425738\pi\) | |||||||
\(410\) | −4.77200 | −0.235672 | ||||||||
\(411\) | 15.5440 | 0.766729 | ||||||||
\(412\) | 6.50000 | + | 11.2583i | 0.320232 | + | 0.554658i | ||||
\(413\) | 1.77200 | − | 3.06920i | 0.0871945 | − | 0.151025i | ||||
\(414\) | 2.38600 | + | 4.13267i | 0.117266 | + | 0.203110i | ||||
\(415\) | −3.00000 | + | 5.19615i | −0.147264 | + | 0.255069i | ||||
\(416\) | 1.88600 | − | 3.26665i | 0.0924688 | − | 0.160161i | ||||
\(417\) | −2.22800 | −0.109106 | ||||||||
\(418\) | 20.3860 | + | 4.13267i | 0.997112 | + | 0.202136i | ||||
\(419\) | 17.8600 | 0.872519 | 0.436259 | − | 0.899821i | \(-0.356303\pi\) | ||||
0.436259 | + | 0.899821i | \(0.356303\pi\) | |||||||
\(420\) | 0.500000 | − | 0.866025i | 0.0243975 | − | 0.0422577i | ||||
\(421\) | 0.227998 | − | 0.394904i | 0.0111119 | − | 0.0192465i | −0.860416 | − | 0.509592i | \(-0.829796\pi\) |
0.871528 | + | 0.490346i | \(0.163130\pi\) | |||||||
\(422\) | −1.72800 | − | 2.99298i | −0.0841176 | − | 0.145696i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.613999 | + | 1.06348i | 0.0298184 | + | 0.0516470i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.54400 | −0.462408 | ||||||||
\(427\) | −2.88600 | − | 4.99870i | −0.139663 | − | 0.241904i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | −0.869048 | ||||||||
\(430\) | −0.227998 | −0.0109950 | ||||||||
\(431\) | −15.5440 | − | 26.9230i | −0.748728 | − | 1.29684i | −0.948432 | − | 0.316979i | \(-0.897331\pi\) |
0.199704 | − | 0.979856i | \(-0.436002\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 7.65800 | + | 13.2640i | 0.368020 | + | 0.637430i | 0.989256 | − | 0.146194i | \(-0.0467024\pi\) |
−0.621236 | + | 0.783624i | \(0.713369\pi\) | |||||||
\(434\) | 2.88600 | − | 4.99870i | 0.138532 | − | 0.239945i | ||||
\(435\) | 3.00000 | − | 5.19615i | 0.143839 | − | 0.249136i | ||||
\(436\) | −7.54400 | −0.361292 | ||||||||
\(437\) | −13.7720 | + | 15.5885i | −0.658804 | + | 0.745697i | ||||
\(438\) | 11.7720 | 0.562488 | ||||||||
\(439\) | 10.6580 | − | 18.4602i | 0.508679 | − | 0.881057i | −0.491271 | − | 0.871007i | \(-0.663467\pi\) |
0.999949 | − | 0.0100505i | \(-0.00319922\pi\) | |||||||
\(440\) | −2.38600 | + | 4.13267i | −0.113748 | + | 0.197018i | ||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.45600 | − | 4.25391i | −0.116688 | − | 0.202109i | 0.801765 | − | 0.597639i | \(-0.203894\pi\) |
−0.918453 | + | 0.395530i | \(0.870561\pi\) | |||||||
\(444\) | −1.00000 | −0.0474579 | ||||||||
\(445\) | −8.31601 | −0.394216 | ||||||||
\(446\) | −12.5000 | − | 21.6506i | −0.591892 | − | 1.02519i | ||||
\(447\) | −1.77200 | − | 3.06920i | −0.0838128 | − | 0.145168i | ||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 10.7720 | 0.508362 | 0.254181 | − | 0.967157i | \(-0.418194\pi\) | ||||
0.254181 | + | 0.967157i | \(0.418194\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | 11.3860 | − | 19.7211i | 0.536146 | − | 0.928632i | ||||
\(452\) | −1.77200 | − | 3.06920i | −0.0833480 | − | 0.144363i | ||||
\(453\) | −4.00000 | + | 6.92820i | −0.187936 | + | 0.325515i | ||||
\(454\) | −12.5440 | + | 21.7269i | −0.588719 | + | 1.01969i | ||||
\(455\) | −3.77200 | −0.176834 | ||||||||
\(456\) | −4.27200 | − | 0.866025i | −0.200055 | − | 0.0405554i | ||||
\(457\) | 16.8600 | 0.788678 | 0.394339 | − | 0.918965i | \(-0.370974\pi\) | ||||
0.394339 | + | 0.918965i | \(0.370974\pi\) | |||||||
\(458\) | −9.43000 | + | 16.3332i | −0.440635 | + | 0.763203i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.38600 | − | 4.13267i | −0.111248 | − | 0.192687i | ||||
\(461\) | 8.31601 | − | 14.4037i | 0.387315 | − | 0.670849i | −0.604772 | − | 0.796398i | \(-0.706736\pi\) |
0.992087 | + | 0.125549i | \(0.0400693\pi\) | |||||||
\(462\) | 2.38600 | + | 4.13267i | 0.111007 | + | 0.192269i | ||||
\(463\) | −23.6320 | −1.09827 | −0.549136 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549136 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 2.88600 | + | 4.99870i | 0.133835 | + | 0.231809i | ||||
\(466\) | −10.7720 | − | 18.6577i | −0.499003 | − | 0.864299i | ||||
\(467\) | 25.0880 | 1.16093 | 0.580467 | − | 0.814284i | \(-0.302870\pi\) | ||||
0.580467 | + | 0.814284i | \(0.302870\pi\) | |||||||
\(468\) | 3.77200 | 0.174361 | ||||||||
\(469\) | −1.11400 | − | 1.92950i | −0.0514397 | − | 0.0890962i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.2720 | − | 17.7916i | −0.473309 | − | 0.819795i | ||||
\(472\) | 1.77200 | − | 3.06920i | 0.0815630 | − | 0.141271i | ||||
\(473\) | 0.544004 | − | 0.942242i | 0.0250133 | − | 0.0433243i | ||||
\(474\) | 15.3160 | 0.703487 | ||||||||
\(475\) | −2.88600 | + | 3.26665i | −0.132419 | + | 0.149884i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.613999 | + | 1.06348i | −0.0281131 | + | 0.0486933i | ||||
\(478\) | −1.77200 | + | 3.06920i | −0.0810495 | + | 0.140382i | ||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 1.88600 | + | 3.26665i | 0.0859942 | + | 0.148946i | ||||
\(482\) | 3.31601 | 0.151040 | ||||||||
\(483\) | −4.77200 | −0.217134 | ||||||||
\(484\) | −5.88600 | − | 10.1949i | −0.267545 | − | 0.463402i | ||||
\(485\) | 5.00000 | + | 8.66025i | 0.227038 | + | 0.393242i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 16.3160 | 0.739349 | 0.369674 | − | 0.929161i | \(-0.379469\pi\) | ||||
0.369674 | + | 0.929161i | \(0.379469\pi\) | |||||||
\(488\) | −2.88600 | − | 4.99870i | −0.130643 | − | 0.226281i | ||||
\(489\) | −3.65800 | + | 6.33585i | −0.165421 | + | 0.286517i | ||||
\(490\) | −3.00000 | − | 5.19615i | −0.135526 | − | 0.234738i | ||||
\(491\) | −16.1580 | + | 27.9865i | −0.729200 | + | 1.26301i | 0.228021 | + | 0.973656i | \(0.426774\pi\) |
−0.957222 | + | 0.289356i | \(0.906559\pi\) | |||||||
\(492\) | −2.38600 | + | 4.13267i | −0.107569 | + | 0.186315i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 5.22800 | + | 15.5885i | 0.235219 | + | 0.701358i | ||||
\(495\) | −4.77200 | −0.214486 | ||||||||
\(496\) | 2.88600 | − | 4.99870i | 0.129585 | − | 0.224448i | ||||
\(497\) | 4.77200 | − | 8.26535i | 0.214054 | − | 0.370752i | ||||
\(498\) | 3.00000 | + | 5.19615i | 0.134433 | + | 0.232845i | ||||
\(499\) | 14.8160 | − | 25.6621i | 0.663256 | − | 1.14879i | −0.316500 | − | 0.948593i | \(-0.602508\pi\) |
0.979755 | − | 0.200200i | \(-0.0641591\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 14.3160 | 0.639592 | ||||||||
\(502\) | 15.5440 | 0.693763 | ||||||||
\(503\) | 4.15800 | + | 7.20187i | 0.185396 | + | 0.321116i | 0.943710 | − | 0.330774i | \(-0.107310\pi\) |
−0.758314 | + | 0.651890i | \(0.773976\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 22.7720 | 1.01234 | ||||||||
\(507\) | −0.613999 | − | 1.06348i | −0.0272687 | − | 0.0472307i | ||||
\(508\) | −8.15800 | + | 14.1301i | −0.361953 | + | 0.626921i | ||||
\(509\) | 8.31601 | + | 14.4037i | 0.368600 | + | 0.638435i | 0.989347 | − | 0.145577i | \(-0.0465037\pi\) |
−0.620747 | + | 0.784011i | \(0.713170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.88600 | + | 10.1949i | −0.260381 | + | 0.450994i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.38600 | − | 4.13267i | −0.0611934 | − | 0.182462i | ||||
\(514\) | 30.0000 | 1.32324 | ||||||||
\(515\) | 6.50000 | − | 11.2583i | 0.286424 | − | 0.496101i | ||||
\(516\) | −0.113999 | + | 0.197452i | −0.00501853 | + | 0.00869235i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.500000 | − | 0.866025i | 0.0219687 | − | 0.0380510i | ||||
\(519\) | 7.15800 | + | 12.3980i | 0.314201 | + | 0.544213i | ||||
\(520\) | −3.77200 | −0.165413 | ||||||||
\(521\) | −33.5440 | −1.46959 | −0.734795 | − | 0.678290i | \(-0.762722\pi\) | ||||
−0.734795 | + | 0.678290i | \(0.762722\pi\) | |||||||
\(522\) | −3.00000 | − | 5.19615i | −0.131306 | − | 0.227429i | ||||
\(523\) | 1.65800 | + | 2.87175i | 0.0724994 | + | 0.125573i | 0.899996 | − | 0.435898i | \(-0.143569\pi\) |
−0.827497 | + | 0.561471i | \(0.810236\pi\) | |||||||
\(524\) | 14.3160 | 0.625398 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 3.61400 | + | 6.25963i | 0.157578 | + | 0.272933i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.38600 | + | 4.13267i | 0.103837 | + | 0.179852i | ||||
\(529\) | 0.113999 | − | 0.197452i | 0.00495648 | − | 0.00858488i | ||||
\(530\) | 0.613999 | − | 1.06348i | 0.0266704 | − | 0.0461945i | ||||
\(531\) | 3.54400 | 0.153797 | ||||||||
\(532\) | 2.88600 | − | 3.26665i | 0.125124 | − | 0.141627i | ||||
\(533\) | 18.0000 | 0.779667 | ||||||||
\(534\) | −4.15800 | + | 7.20187i | −0.179934 | + | 0.311655i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.11400 | − | 1.92950i | −0.0481174 | − | 0.0833418i | ||||
\(537\) | 13.1580 | − | 22.7903i | 0.567810 | − | 0.983475i | ||||
\(538\) | −4.22800 | − | 7.32311i | −0.182282 | − | 0.315722i | ||||
\(539\) | 28.6320 | 1.23327 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 4.65800 | + | 8.06790i | 0.200263 | + | 0.346866i | 0.948613 | − | 0.316438i | \(-0.102487\pi\) |
−0.748350 | + | 0.663304i | \(0.769154\pi\) | |||||||
\(542\) | 14.7720 | + | 25.5859i | 0.634512 | + | 1.09901i | ||||
\(543\) | −17.0880 | −0.733317 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.77200 | + | 6.53330i | 0.161575 | + | 0.279856i | ||||
\(546\) | −1.88600 | + | 3.26665i | −0.0807134 | + | 0.139800i | ||||
\(547\) | 15.4300 | + | 26.7256i | 0.659739 | + | 1.14270i | 0.980683 | + | 0.195604i | \(0.0626667\pi\) |
−0.320944 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(548\) | −7.77200 | + | 13.4615i | −0.332003 | + | 0.575047i | ||||
\(549\) | 2.88600 | − | 4.99870i | 0.123172 | − | 0.213339i | ||||
\(550\) | 4.77200 | 0.203479 | ||||||||
\(551\) | 17.3160 | − | 19.5999i | 0.737687 | − | 0.834984i | ||||
\(552\) | −4.77200 | −0.203110 | ||||||||
\(553\) | −7.65800 | + | 13.2640i | −0.325651 | + | 0.564045i | ||||
\(554\) | −14.5440 | + | 25.1910i | −0.617916 | + | 1.07026i | ||||
\(555\) | 0.500000 | + | 0.866025i | 0.0212238 | + | 0.0367607i | ||||
\(556\) | 1.11400 | − | 1.92950i | 0.0472441 | − | 0.0818292i | ||||
\(557\) | −5.38600 | − | 9.32883i | −0.228212 | − | 0.395275i | 0.729066 | − | 0.684443i | \(-0.239955\pi\) |
−0.957278 | + | 0.289168i | \(0.906621\pi\) | |||||||
\(558\) | 5.77200 | 0.244348 | ||||||||
\(559\) | 0.860009 | 0.0363745 | ||||||||
\(560\) | 0.500000 | + | 0.866025i | 0.0211289 | + | 0.0365963i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.2280 | −0.811084 | ||||||||
\(563\) | 20.4560 | 0.862117 | 0.431059 | − | 0.902324i | \(-0.358140\pi\) | ||||
0.431059 | + | 0.902324i | \(0.358140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.77200 | + | 3.06920i | −0.0745487 | + | 0.129122i | ||||
\(566\) | 12.3160 | + | 21.3319i | 0.517680 | + | 0.896649i | ||||
\(567\) | 0.500000 | − | 0.866025i | 0.0209980 | − | 0.0363696i | ||||
\(568\) | 4.77200 | − | 8.26535i | 0.200229 | − | 0.346806i | ||||
\(569\) | 10.7720 | 0.451586 | 0.225793 | − | 0.974175i | \(-0.427503\pi\) | ||||
0.225793 | + | 0.974175i | \(0.427503\pi\) | |||||||
\(570\) | 1.38600 | + | 4.13267i | 0.0580532 | + | 0.173099i | ||||
\(571\) | 40.8600 | 1.70994 | 0.854969 | − | 0.518679i | \(-0.173576\pi\) | ||||
0.854969 | + | 0.518679i | \(0.173576\pi\) | |||||||
\(572\) | 9.00000 | − | 15.5885i | 0.376309 | − | 0.651786i | ||||
\(573\) | 4.77200 | − | 8.26535i | 0.199353 | − | 0.345290i | ||||
\(574\) | −2.38600 | − | 4.13267i | −0.0995898 | − | 0.172495i | ||||
\(575\) | −2.38600 | + | 4.13267i | −0.0995031 | + | 0.172344i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −7.54400 | −0.314061 | −0.157030 | − | 0.987594i | \(-0.550192\pi\) | ||||
−0.157030 | + | 0.987594i | \(0.550192\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | 2.88600 | + | 4.99870i | 0.119938 | + | 0.207739i | ||||
\(580\) | 3.00000 | + | 5.19615i | 0.124568 | + | 0.215758i | ||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 10.0000 | 0.414513 | ||||||||
\(583\) | 2.93000 | + | 5.07492i | 0.121348 | + | 0.210182i | ||||
\(584\) | −5.88600 | + | 10.1949i | −0.243564 | + | 0.421866i | ||||
\(585\) | −1.88600 | − | 3.26665i | −0.0779765 | − | 0.135059i | ||||
\(586\) | −14.3860 | + | 24.9173i | −0.594280 | + | 1.02932i | ||||
\(587\) | 4.22800 | − | 7.32311i | 0.174508 | − | 0.302257i | −0.765483 | − | 0.643456i | \(-0.777500\pi\) |
0.939991 | + | 0.341199i | \(0.110833\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 8.00000 | + | 23.8538i | 0.329634 | + | 0.982879i | ||||
\(590\) | −3.54400 | −0.145904 | ||||||||
\(591\) | −7.15800 | + | 12.3980i | −0.294441 | + | 0.509987i | ||||
\(592\) | 0.500000 | − | 0.866025i | 0.0205499 | − | 0.0355934i | ||||
\(593\) | 4.77200 | + | 8.26535i | 0.195963 | + | 0.339417i | 0.947216 | − | 0.320597i | \(-0.103884\pi\) |
−0.751253 | + | 0.660014i | \(0.770550\pi\) | |||||||
\(594\) | −2.38600 | + | 4.13267i | −0.0978988 | + | 0.169566i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.54400 | 0.145168 | ||||||||
\(597\) | 25.3160 | 1.03612 | ||||||||
\(598\) | 9.00000 | + | 15.5885i | 0.368037 | + | 0.637459i | ||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 15.6320 | 0.637643 | 0.318822 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318822 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(602\) | −0.113999 | − | 0.197452i | −0.00464625 | − | 0.00804755i | ||||
\(603\) | 1.11400 | − | 1.92950i | 0.0453655 | − | 0.0785754i | ||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | −5.88600 | + | 10.1949i | −0.239300 | + | 0.414480i | ||||
\(606\) | −3.00000 | + | 5.19615i | −0.121867 | + | 0.211079i | ||||
\(607\) | −5.91199 | −0.239960 | −0.119980 | − | 0.992776i | \(-0.538283\pi\) | ||||
−0.119980 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(608\) | 2.88600 | − | 3.26665i | 0.117043 | − | 0.132480i | ||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | −2.88600 | + | 4.99870i | −0.116851 | + | 0.202391i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.93000 | + | 6.80697i | −0.158731 | + | 0.274931i | −0.934411 | − | 0.356195i | \(-0.884074\pi\) |
0.775680 | + | 0.631126i | \(0.217407\pi\) | |||||||
\(614\) | −3.22800 | − | 5.59106i | −0.130271 | − | 0.225637i | ||||
\(615\) | 4.77200 | 0.192426 | ||||||||
\(616\) | −4.77200 | −0.192269 | ||||||||
\(617\) | −15.5440 | − | 26.9230i | −0.625778 | − | 1.08388i | −0.988390 | − | 0.151939i | \(-0.951448\pi\) |
0.362612 | − | 0.931940i | \(-0.381885\pi\) | |||||||
\(618\) | −6.50000 | − | 11.2583i | −0.261468 | − | 0.452876i | ||||
\(619\) | 37.1760 | 1.49423 | 0.747115 | − | 0.664695i | \(-0.231438\pi\) | ||||
0.747115 | + | 0.664695i | \(0.231438\pi\) | |||||||
\(620\) | −5.77200 | −0.231809 | ||||||||
\(621\) | −2.38600 | − | 4.13267i | −0.0957469 | − | 0.165839i | ||||
\(622\) | 4.22800 | − | 7.32311i | 0.169527 | − | 0.293630i | ||||
\(623\) | −4.15800 | − | 7.20187i | −0.166587 | − | 0.288537i | ||||
\(624\) | −1.88600 | + | 3.26665i | −0.0755005 | + | 0.130771i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 19.5440 | 0.781135 | ||||||||
\(627\) | −20.3860 | − | 4.13267i | −0.814138 | − | 0.165043i | ||||
\(628\) | 20.5440 | 0.819795 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.500000 | + | 0.866025i | −0.0199205 | + | 0.0345033i | ||||
\(631\) | 0.569995 | + | 0.987261i | 0.0226912 | + | 0.0393022i | 0.877148 | − | 0.480220i | \(-0.159443\pi\) |
−0.854457 | + | 0.519522i | \(0.826110\pi\) | |||||||
\(632\) | −7.65800 | + | 13.2640i | −0.304619 | + | 0.527616i | ||||
\(633\) | 1.72800 | + | 2.99298i | 0.0686818 | + | 0.118960i | ||||
\(634\) | −28.7720 | −1.14268 | ||||||||
\(635\) | 16.3160 | 0.647481 | ||||||||
\(636\) | −0.613999 | − | 1.06348i | −0.0243466 | − | 0.0421696i | ||||
\(637\) | 11.3160 | + | 19.5999i | 0.448356 | + | 0.776576i | ||||
\(638\) | −28.6320 | −1.13355 | ||||||||
\(639\) | 9.54400 | 0.377555 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −1.22800 | + | 2.12696i | −0.0485030 | + | 0.0840097i | −0.889258 | − | 0.457407i | \(-0.848778\pi\) |
0.840755 | + | 0.541416i | \(0.182112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6580 | + | 21.9243i | −0.499183 | + | 0.864610i | −1.00000 | 0.000943247i | \(-0.999700\pi\) | |
0.500817 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(644\) | 2.38600 | − | 4.13267i | 0.0940216 | − | 0.162850i | ||||
\(645\) | 0.227998 | 0.00897742 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.3160 | −1.50636 | −0.753179 | − | 0.657816i | \(-0.771481\pi\) | ||||
−0.753179 | + | 0.657816i | \(0.771481\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 8.45600 | − | 14.6462i | 0.331927 | − | 0.574914i | ||||
\(650\) | 1.88600 | + | 3.26665i | 0.0739750 | + | 0.128129i | ||||
\(651\) | −2.88600 | + | 4.99870i | −0.113111 | + | 0.195915i | ||||
\(652\) | −3.65800 | − | 6.33585i | −0.143258 | − | 0.248131i | ||||
\(653\) | 3.68399 | 0.144166 | 0.0720829 | − | 0.997399i | \(-0.477035\pi\) | ||||
0.0720829 | + | 0.997399i | \(0.477035\pi\) | |||||||
\(654\) | 7.54400 | 0.294994 | ||||||||
\(655\) | −7.15800 | − | 12.3980i | −0.279686 | − | 0.484431i | ||||
\(656\) | −2.38600 | − | 4.13267i | −0.0931577 | − | 0.161354i | ||||
\(657\) | −11.7720 | −0.459270 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1580 | − | 33.1826i | −0.746290 | − | 1.29261i | −0.949590 | − | 0.313495i | \(-0.898500\pi\) |
0.203300 | − | 0.979117i | \(-0.434833\pi\) | |||||||
\(660\) | 2.38600 | − | 4.13267i | 0.0928750 | − | 0.160864i | ||||
\(661\) | −3.31601 | − | 5.74349i | −0.128978 | − | 0.223396i | 0.794303 | − | 0.607522i | \(-0.207836\pi\) |
−0.923281 | + | 0.384126i | \(0.874503\pi\) | |||||||
\(662\) | −4.72800 | + | 8.18913i | −0.183759 | + | 0.318280i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −4.27200 | − | 0.866025i | −0.165661 | − | 0.0335830i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 14.3160 | − | 24.7960i | 0.554318 | − | 0.960107i | ||||
\(668\) | −7.15800 | + | 12.3980i | −0.276951 | + | 0.479694i | ||||
\(669\) | 12.5000 | + | 21.6506i | 0.483278 | + | 0.837062i | ||||
\(670\) | −1.11400 | + | 1.92950i | −0.0430375 | + | 0.0745432i | ||||
\(671\) | −13.7720 | − | 23.8538i | −0.531662 | − | 0.920866i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −29.7720 | −1.14763 | −0.573813 | − | 0.818986i | \(-0.694536\pi\) | ||||
−0.573813 | + | 0.818986i | \(0.694536\pi\) | |||||||
\(674\) | −2.34200 | − | 4.05646i | −0.0902104 | − | 0.156249i | ||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 1.22800 | 0.0472307 | ||||||||
\(677\) | −8.31601 | −0.319610 | −0.159805 | − | 0.987149i | \(-0.551087\pi\) | ||||
−0.159805 | + | 0.987149i | \(0.551087\pi\) | |||||||
\(678\) | 1.77200 | + | 3.06920i | 0.0680533 | + | 0.117872i | ||||
\(679\) | −5.00000 | + | 8.66025i | −0.191882 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5440 | − | 21.7269i | 0.480687 | − | 0.832575i | ||||
\(682\) | 13.7720 | − | 23.8538i | 0.527357 | − | 0.913409i | ||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 4.27200 | + | 0.866025i | 0.163344 | + | 0.0331133i | ||||
\(685\) | 15.5440 | 0.593906 | ||||||||
\(686\) | 6.50000 | − | 11.2583i | 0.248171 | − | 0.429845i | ||||
\(687\) | 9.43000 | − | 16.3332i | 0.359777 | − | 0.623152i | ||||
\(688\) | −0.113999 | − | 0.197452i | −0.00434617 | − | 0.00752779i | ||||
\(689\) | −2.31601 | + | 4.01144i | −0.0882328 | + | 0.152824i | ||||
\(690\) | 2.38600 | + | 4.13267i | 0.0908335 | + | 0.157328i | ||||
\(691\) | 49.8600 | 1.89676 | 0.948382 | − | 0.317130i | \(-0.102719\pi\) | ||||
0.948382 | + | 0.317130i | \(0.102719\pi\) | |||||||
\(692\) | −14.3160 | −0.544213 | ||||||||
\(693\) | −2.38600 | − | 4.13267i | −0.0906367 | − | 0.156987i | ||||
\(694\) | 4.77200 | + | 8.26535i | 0.181143 | + | 0.313748i | ||||
\(695\) | −2.22800 | −0.0845128 | ||||||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8.88600 | + | 15.3910i | −0.336340 | + | 0.582558i | ||||
\(699\) | 10.7720 | + | 18.6577i | 0.407435 | + | 0.705697i | ||||
\(700\) | 0.500000 | − | 0.866025i | 0.0188982 | − | 0.0327327i | ||||
\(701\) | 8.31601 | − | 14.4037i | 0.314091 | − | 0.544022i | −0.665153 | − | 0.746707i | \(-0.731634\pi\) |
0.979244 | + | 0.202685i | \(0.0649669\pi\) | |||||||
\(702\) | −3.77200 | −0.142365 | ||||||||
\(703\) | 1.38600 | + | 4.13267i | 0.0522740 | + | 0.155867i | ||||
\(704\) | −4.77200 | −0.179852 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.77200 | − | 3.06920i | 0.0666902 | − | 0.115511i | ||||
\(707\) | −3.00000 | − | 5.19615i | −0.112827 | − | 0.195421i | ||||
\(708\) | −1.77200 | + | 3.06920i | −0.0665959 | + | 0.115347i | ||||
\(709\) | 13.1140 | + | 22.7141i | 0.492507 | + | 0.853046i | 0.999963 | − | 0.00863116i | \(-0.00274742\pi\) |
−0.507456 | + | 0.861678i | \(0.669414\pi\) | |||||||
\(710\) | −9.54400 | −0.358180 | ||||||||
\(711\) | −15.3160 | −0.574395 | ||||||||
\(712\) | −4.15800 | − | 7.20187i | −0.155828 | − | 0.269902i | ||||
\(713\) | 13.7720 | + | 23.8538i | 0.515766 | + | 0.893332i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 13.1580 | + | 22.7903i | 0.491738 | + | 0.851715i | ||||
\(717\) | 1.77200 | − | 3.06920i | 0.0661766 | − | 0.114621i | ||||
\(718\) | −6.54400 | − | 11.3345i | −0.244220 | − | 0.423002i | ||||
\(719\) | 11.3160 | − | 19.5999i | 0.422016 | − | 0.730953i | −0.574121 | − | 0.818771i | \(-0.694656\pi\) |
0.996137 | + | 0.0878178i | \(0.0279893\pi\) | |||||||
\(720\) | −0.500000 | + | 0.866025i | −0.0186339 | + | 0.0322749i | ||||
\(721\) | 13.0000 | 0.484145 | ||||||||
\(722\) | 2.34200 | + | 18.8551i | 0.0871601 | + | 0.701714i | ||||
\(723\) | −3.31601 | −0.123324 | ||||||||
\(724\) | 8.54400 | − | 14.7986i | 0.317535 | − | 0.549987i | ||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 5.88600 | + | 10.1949i | 0.218450 | + | 0.378366i | ||||
\(727\) | 8.20201 | − | 14.2063i | 0.304196 | − | 0.526882i | −0.672886 | − | 0.739746i | \(-0.734946\pi\) |
0.977082 | + | 0.212864i | \(0.0682790\pi\) | |||||||
\(728\) | −1.88600 | − | 3.26665i | −0.0698998 | − | 0.121070i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.7720 | 0.435701 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.88600 | + | 4.99870i | 0.106670 | + | 0.184757i | ||||
\(733\) | −37.4040 | −1.38155 | −0.690774 | − | 0.723070i | \(-0.742730\pi\) | ||||
−0.690774 | + | 0.723070i | \(0.742730\pi\) | |||||||
\(734\) | 17.7720 | 0.655977 | ||||||||
\(735\) | 3.00000 | + | 5.19615i | 0.110657 | + | 0.191663i | ||||
\(736\) | 2.38600 | − | 4.13267i | 0.0879492 | − | 0.152332i | ||||
\(737\) | −5.31601 | − | 9.20759i | −0.195818 | − | 0.339166i | ||||
\(738\) | 2.38600 | − | 4.13267i | 0.0878299 | − | 0.152126i | ||||
\(739\) | −2.50000 | + | 4.33013i | −0.0919640 | + | 0.159286i | −0.908337 | − | 0.418238i | \(-0.862648\pi\) |
0.816373 | + | 0.577524i | \(0.195981\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | −5.22800 | − | 15.5885i | −0.192055 | − | 0.572656i | ||||
\(742\) | 1.22800 | 0.0450812 | ||||||||
\(743\) | −14.3860 | + | 24.9173i | −0.527771 | + | 0.914127i | 0.471705 | + | 0.881757i | \(0.343639\pi\) |
−0.999476 | + | 0.0323700i | \(0.989695\pi\) | |||||||
\(744\) | −2.88600 | + | 4.99870i | −0.105806 | + | 0.183261i | ||||
\(745\) | −1.77200 | − | 3.06920i | −0.0649211 | − | 0.112447i | ||||
\(746\) | −4.38600 | + | 7.59678i | −0.160583 | + | 0.278138i | ||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −21.1140 | − | 36.5705i | −0.770461 | − | 1.33448i | −0.937311 | − | 0.348495i | \(-0.886693\pi\) |
0.166850 | − | 0.985982i | \(-0.446640\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.5440 | −0.566455 | ||||||||
\(754\) | −11.3160 | − | 19.5999i | −0.412105 | − | 0.713786i | ||||
\(755\) | −4.00000 | + | 6.92820i | −0.145575 | + | 0.252143i | ||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | −10.8160 | + | 18.7339i | −0.393114 | + | 0.680894i | −0.992859 | − | 0.119298i | \(-0.961936\pi\) |
0.599744 | + | 0.800192i | \(0.295269\pi\) | |||||||
\(758\) | −8.88600 | + | 15.3910i | −0.322754 | + | 0.559026i | ||||
\(759\) | −22.7720 | −0.826571 | ||||||||
\(760\) | −4.27200 | − | 0.866025i | −0.154962 | − | 0.0314140i | ||||
\(761\) | −54.9480 | −1.99186 | −0.995932 | − | 0.0901077i | \(-0.971279\pi\) | ||||
−0.995932 | + | 0.0901077i | \(0.971279\pi\) | |||||||
\(762\) | 8.15800 | − | 14.1301i | 0.295533 | − | 0.511879i | ||||
\(763\) | −3.77200 | + | 6.53330i | −0.136556 | + | 0.236521i | ||||
\(764\) | 4.77200 | + | 8.26535i | 0.172645 | + | 0.299030i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | − | 20.7846i | −0.433578 | − | 0.750978i | ||||
\(767\) | 13.3680 | 0.482690 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 3.43000 | + | 5.94094i | 0.123689 | + | 0.214236i | 0.921220 | − | 0.389043i | \(-0.127194\pi\) |
−0.797531 | + | 0.603278i | \(0.793861\pi\) | |||||||
\(770\) | 2.38600 | + | 4.13267i | 0.0859855 | + | 0.148931i | ||||
\(771\) | −30.0000 | −1.08042 | ||||||||
\(772\) | −5.77200 | −0.207739 | ||||||||
\(773\) | −2.38600 | − | 4.13267i | −0.0858185 | − | 0.148642i | 0.819921 | − | 0.572476i | \(-0.194017\pi\) |
−0.905740 | + | 0.423834i | \(0.860684\pi\) | |||||||
\(774\) | 0.113999 | − | 0.197452i | 0.00409761 | − | 0.00709727i | ||||
\(775\) | 2.88600 | + | 4.99870i | 0.103668 | + | 0.179559i | ||||
\(776\) | −5.00000 | + | 8.66025i | −0.179490 | + | 0.310885i | ||||
\(777\) | −0.500000 | + | 0.866025i | −0.0179374 | + | 0.0310685i | ||||
\(778\) | −25.0880 | −0.899449 | ||||||||
\(779\) | 20.3860 | + | 4.13267i | 0.730404 | + | 0.148068i | ||||
\(780\) | 3.77200 | 0.135059 | ||||||||
\(781\) | 22.7720 | − | 39.4423i | 0.814846 | − | 1.41136i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | + | 5.19615i | 0.107211 | + | 0.185695i | ||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | −10.2720 | − | 17.7916i | −0.366623 | − | 0.635010i | ||||
\(786\) | −14.3160 | −0.510635 | ||||||||
\(787\) | 8.68399 | 0.309551 | 0.154775 | − | 0.987950i | \(-0.450535\pi\) | ||||
0.154775 | + | 0.987950i | \(0.450535\pi\) | |||||||
\(788\) | −7.15800 | − | 12.3980i | −0.254993 | − | 0.441661i | ||||
\(789\) | −3.61400 | − | 6.25963i | −0.128662 | − | 0.222849i | ||||
\(790\) | 15.3160 | 0.544919 | ||||||||
\(791\) | −3.54400 | −0.126010 | ||||||||
\(792\) | −2.38600 | − | 4.13267i | −0.0847829 | − | 0.146848i | ||||
\(793\) | 10.8860 | − | 18.8551i | 0.386573 | − | 0.669564i | ||||
\(794\) | −16.0440 | − | 27.7890i | −0.569380 | − | 0.986196i | ||||
\(795\) | −0.613999 | + | 1.06348i | −0.0217763 | + | 0.0377177i | ||||
\(796\) | −12.6580 | + | 21.9243i | −0.448651 | + | 0.777086i | ||||
\(797\) | −7.22800 | −0.256029 | −0.128014 | − | 0.991772i | \(-0.540860\pi\) | ||||
−0.128014 | + | 0.991772i | \(0.540860\pi\) | |||||||
\(798\) | −2.88600 | + | 3.26665i | −0.102163 | + | 0.115638i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 4.15800 | − | 7.20187i | 0.146916 | − | 0.254466i | ||||
\(802\) | −12.5440 | − | 21.7269i | −0.442944 | − | 0.767202i | ||||
\(803\) | −28.0880 | + | 48.6499i | −0.991204 | + | 1.71682i | ||||
\(804\) | 1.11400 | + | 1.92950i | 0.0392877 | + | 0.0680483i | ||||
\(805\) | −4.77200 | −0.168191 | ||||||||
\(806\) | 21.7720 | 0.766886 | ||||||||
\(807\) | 4.22800 | + | 7.32311i | 0.148833 | + | 0.257786i | ||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −16.6140 | − | 28.7763i | −0.583396 | − | 1.01047i | −0.995073 | − | 0.0991423i | \(-0.968390\pi\) |
0.411677 | − | 0.911330i | \(-0.364943\pi\) | |||||||
\(812\) | −3.00000 | + | 5.19615i | −0.105279 | + | 0.182349i | ||||
\(813\) | −14.7720 | − | 25.5859i | −0.518077 | − | 0.897335i | ||||
\(814\) | 2.38600 | − | 4.13267i | 0.0836293 | − | 0.144850i | ||||
\(815\) | −3.65800 | + | 6.33585i | −0.128134 | + | 0.221935i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.974008 | + | 0.197452i | 0.0340762 | + | 0.00690798i | ||||
\(818\) | −29.4040 | −1.02809 | ||||||||
\(819\) | 1.88600 | − | 3.26665i | 0.0659022 | − | 0.114146i | ||||
\(820\) | −2.38600 | + | 4.13267i | −0.0833228 | + | 0.144319i | ||||
\(821\) | 15.0000 | + | 25.9808i | 0.523504 | + | 0.906735i | 0.999626 | + | 0.0273557i | \(0.00870868\pi\) |
−0.476122 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(822\) | 7.77200 | − | 13.4615i | 0.271080 | − | 0.469524i | ||||
\(823\) | −0.930005 | − | 1.61082i | −0.0324179 | − | 0.0561495i | 0.849361 | − | 0.527812i | \(-0.176987\pi\) |
−0.881779 | + | 0.471662i | \(0.843654\pi\) | |||||||
\(824\) | 13.0000 | 0.452876 | ||||||||
\(825\) | −4.77200 | −0.166140 | ||||||||
\(826\) | −1.77200 | − | 3.06920i | −0.0616558 | − | 0.106791i | ||||
\(827\) | 21.0000 | + | 36.3731i | 0.730242 | + | 1.26482i | 0.956780 | + | 0.290813i | \(0.0939258\pi\) |
−0.226538 | + | 0.974002i | \(0.572741\pi\) | |||||||
\(828\) | 4.77200 | 0.165839 | ||||||||
\(829\) | −28.4040 | −0.986512 | −0.493256 | − | 0.869884i | \(-0.664193\pi\) | ||||
−0.493256 | + | 0.869884i | \(0.664193\pi\) | |||||||
\(830\) | 3.00000 | + | 5.19615i | 0.104132 | + | 0.180361i | ||||
\(831\) | 14.5440 | − | 25.1910i | 0.504526 | − | 0.873864i | ||||
\(832\) | −1.88600 | − | 3.26665i | −0.0653853 | − | 0.113251i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.11400 | + | 1.92950i | −0.0385746 | + | 0.0668132i | ||||
\(835\) | 14.3160 | 0.495426 | ||||||||
\(836\) | 13.7720 | − | 15.5885i | 0.476315 | − | 0.539138i | ||||
\(837\) | −5.77200 | −0.199510 | ||||||||
\(838\) | 8.93000 | − | 15.4672i | 0.308482 | − | 0.534306i | ||||
\(839\) | 26.3160 | − | 45.5807i | 0.908529 | − | 1.57362i | 0.0924212 | − | 0.995720i | \(-0.470539\pi\) |
0.816108 | − | 0.577899i | \(-0.196127\pi\) | |||||||
\(840\) | −0.500000 | − | 0.866025i | −0.0172516 | − | 0.0298807i | ||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −0.227998 | − | 0.394904i | −0.00785733 | − | 0.0136093i | ||||
\(843\) | 19.2280 | 0.662247 | ||||||||
\(844\) | −3.45600 | −0.118960 | ||||||||
\(845\) | −0.613999 | − | 1.06348i | −0.0211222 | − | 0.0365847i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.7720 | −0.404491 | ||||||||
\(848\) | 1.22800 | 0.0421696 | ||||||||
\(849\) | −12.3160 | − | 21.3319i | −0.422684 | − | 0.732111i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.38600 | + | 4.13267i | 0.0817911 | + | 0.141666i | ||||
\(852\) | −4.77200 | + | 8.26535i | −0.163486 | + | 0.283166i | ||||
\(853\) | −9.65800 | + | 16.7282i | −0.330684 | + | 0.572761i | −0.982646 | − | 0.185490i | \(-0.940613\pi\) |
0.651962 | + | 0.758251i | \(0.273946\pi\) | |||||||
\(854\) | −5.77200 | −0.197514 | ||||||||
\(855\) | −1.38600 | − | 4.13267i | −0.0474002 | − | 0.141334i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.6320 | + | 49.5921i | −0.978051 | + | 1.69403i | −0.308575 | + | 0.951200i | \(0.599852\pi\) |
−0.669476 | + | 0.742834i | \(0.733481\pi\) | |||||||
\(858\) | −9.00000 | + | 15.5885i | −0.307255 | + | 0.532181i | ||||
\(859\) | 16.7280 | + | 28.9737i | 0.570752 | + | 0.988571i | 0.996489 | + | 0.0837244i | \(0.0266815\pi\) |
−0.425737 | + | 0.904847i | \(0.639985\pi\) | |||||||
\(860\) | −0.113999 | + | 0.197452i | −0.00388734 | + | 0.00673306i | ||||
\(861\) | 2.38600 | + | 4.13267i | 0.0813147 | + | 0.140841i | ||||
\(862\) | −31.0880 | −1.05886 | ||||||||
\(863\) | −50.3160 | −1.71278 | −0.856388 | − | 0.516332i | \(-0.827297\pi\) | ||||
−0.856388 | + | 0.516332i | \(0.827297\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 7.15800 | + | 12.3980i | 0.243379 | + | 0.421545i | ||||
\(866\) | 15.3160 | 0.520459 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | −2.88600 | − | 4.99870i | −0.0979573 | − | 0.169667i | ||||
\(869\) | −36.5440 | + | 63.2961i | −1.23967 | + | 2.14717i | ||||
\(870\) | −3.00000 | − | 5.19615i | −0.101710 | − | 0.176166i | ||||
\(871\) | 4.20201 | − | 7.27809i | 0.142380 | − | 0.246609i | ||||
\(872\) | −3.77200 | + | 6.53330i | −0.127736 | + | 0.221245i | ||||
\(873\) | −10.0000 | −0.338449 | ||||||||
\(874\) | 6.61400 | + | 19.7211i | 0.223722 | + | 0.667077i | ||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 5.88600 | − | 10.1949i | 0.198870 | − | 0.344452i | ||||
\(877\) | 5.27200 | − | 9.13138i | 0.178023 | − | 0.308345i | −0.763180 | − | 0.646185i | \(-0.776363\pi\) |
0.941203 | + | 0.337841i | \(0.109697\pi\) | |||||||
\(878\) | −10.6580 | − | 18.4602i | −0.359690 | − | 0.623002i | ||||
\(879\) | 14.3860 | − | 24.9173i | 0.485228 | − | 0.840439i | ||||
\(880\) | 2.38600 | + | 4.13267i | 0.0804321 | + | 0.139312i | ||||
\(881\) | 0.139991 | 0.00471640 | 0.00235820 | − | 0.999997i | \(-0.499249\pi\) | ||||
0.00235820 | + | 0.999997i | \(0.499249\pi\) | |||||||
\(882\) | 6.00000 | 0.202031 | ||||||||
\(883\) | 16.6580 | + | 28.8525i | 0.560586 | + | 0.970964i | 0.997445 | + | 0.0714341i | \(0.0227576\pi\) |
−0.436859 | + | 0.899530i | \(0.643909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.54400 | 0.119130 | ||||||||
\(886\) | −4.91199 | −0.165022 | ||||||||
\(887\) | 7.08801 | + | 12.2768i | 0.237992 | + | 0.412214i | 0.960138 | − | 0.279526i | \(-0.0901775\pi\) |
−0.722146 | + | 0.691741i | \(0.756844\pi\) | |||||||
\(888\) | −0.500000 | + | 0.866025i | −0.0167789 | + | 0.0290619i | ||||
\(889\) | 8.15800 | + | 14.1301i | 0.273611 | + | 0.473908i | ||||
\(890\) | −4.15800 | + | 7.20187i | −0.139377 | + | 0.241407i | ||||
\(891\) | 2.38600 | − | 4.13267i | 0.0799340 | − | 0.138450i | ||||
\(892\) | −25.0000 | −0.837062 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −3.54400 | −0.118529 | ||||||||
\(895\) | 13.1580 | − | 22.7903i | 0.439824 | − | 0.761797i | ||||
\(896\) | −0.500000 | + | 0.866025i | −0.0167038 | + | 0.0289319i | ||||
\(897\) | −9.00000 | − | 15.5885i | −0.300501 | − | 0.520483i | ||||
\(898\) | 5.38600 | − | 9.32883i | 0.179733 | − | 0.311307i | ||||
\(899\) | −17.3160 | − | 29.9922i | −0.577521 | − | 1.00030i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −11.3860 | − | 19.7211i | −0.379112 | − | 0.656642i | ||||
\(903\) | 0.113999 | + | 0.197452i | 0.00379365 | + | 0.00657080i | ||||
\(904\) | −3.54400 | −0.117872 | ||||||||
\(905\) | −17.0880 | −0.568025 | ||||||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 18.7720 | − | 32.5141i | 0.623314 | − | 1.07961i | −0.365550 | − | 0.930792i | \(-0.619119\pi\) |
0.988864 | − | 0.148820i | \(-0.0475475\pi\) | |||||||
\(908\) | 12.5440 | + | 21.7269i | 0.416287 | + | 0.721031i | ||||
\(909\) | 3.00000 | − | 5.19615i | 0.0995037 | − | 0.172345i | ||||
\(910\) | −1.88600 | + | 3.26665i | −0.0625203 | + | 0.108288i | ||||
\(911\) | −32.1760 | −1.06604 | −0.533019 | − | 0.846103i | \(-0.678943\pi\) | ||||
−0.533019 | + | 0.846103i | \(0.678943\pi\) | |||||||
\(912\) | −2.88600 | + | 3.26665i | −0.0955650 | + | 0.108170i | ||||
\(913\) | −28.6320 | −0.947581 | ||||||||
\(914\) | 8.43000 | − | 14.6012i | 0.278840 | − | 0.482965i | ||||
\(915\) | 2.88600 | − | 4.99870i | 0.0954082 | − | 0.165252i | ||||
\(916\) | 9.43000 | + | 16.3332i | 0.311576 | + | 0.539666i | ||||
\(917\) | 7.15800 | − | 12.3980i | 0.236378 | − | 0.409419i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4040 | 0.870988 | 0.435494 | − | 0.900192i | \(-0.356574\pi\) | ||||
0.435494 | + | 0.900192i | \(0.356574\pi\) | |||||||
\(920\) | −4.77200 | −0.157328 | ||||||||
\(921\) | 3.22800 | + | 5.59106i | 0.106366 | + | 0.184232i | ||||
\(922\) | −8.31601 | − | 14.4037i | −0.273873 | − | 0.474362i | ||||
\(923\) | 36.0000 | 1.18495 | ||||||||
\(924\) | 4.77200 | 0.156987 | ||||||||
\(925\) | 0.500000 | + | 0.866025i | 0.0164399 | + | 0.0284747i | ||||
\(926\) | −11.8160 | + | 20.4659i | −0.388298 | + | 0.672552i | ||||
\(927\) | 6.50000 | + | 11.2583i | 0.213488 | + | 0.369772i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | −28.0180 | + | 48.5286i | −0.919241 | + | 1.59217i | −0.118671 | + | 0.992934i | \(0.537863\pi\) |
−0.800570 | + | 0.599239i | \(0.795470\pi\) | |||||||
\(930\) | 5.77200 | 0.189271 | ||||||||
\(931\) | 8.31601 | + | 24.7960i | 0.272546 | + | 0.812658i | ||||
\(932\) | −21.5440 | −0.705697 | ||||||||
\(933\) | −4.22800 | + | 7.32311i | −0.138418 | + | 0.239748i | ||||
\(934\) | 12.5440 | − | 21.7269i | 0.410452 | − | 0.710924i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.88600 | − | 3.26665i | 0.0616459 | − | 0.106774i | ||||
\(937\) | 22.1140 | + | 38.3026i | 0.722433 | + | 1.25129i | 0.960022 | + | 0.279925i | \(0.0903095\pi\) |
−0.237589 | + | 0.971366i | \(0.576357\pi\) | |||||||
\(938\) | −2.22800 | −0.0727467 | ||||||||
\(939\) | −19.5440 | −0.637794 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5440 | − | 21.7269i | −0.408923 | − | 0.708275i | 0.585846 | − | 0.810422i | \(-0.300762\pi\) |
−0.994769 | + | 0.102147i | \(0.967429\pi\) | |||||||
\(942\) | −20.5440 | −0.669360 | ||||||||
\(943\) | 22.7720 | 0.741558 | ||||||||
\(944\) | −1.77200 | − | 3.06920i | −0.0576737 | − | 0.0998939i | ||||
\(945\) | 0.500000 | − | 0.866025i | 0.0162650 | − | 0.0281718i | ||||
\(946\) | −0.544004 | − | 0.942242i | −0.0176871 | − | 0.0306349i | ||||
\(947\) | −23.3160 | + | 40.3845i | −0.757668 | + | 1.31232i | 0.186368 | + | 0.982480i | \(0.440328\pi\) |
−0.944037 | + | 0.329840i | \(0.893005\pi\) | |||||||
\(948\) | 7.65800 | − | 13.2640i | 0.248720 | − | 0.430796i | ||||
\(949\) | −44.4040 | −1.44142 | ||||||||
\(950\) | 1.38600 | + | 4.13267i | 0.0449678 | + | 0.134082i | ||||
\(951\) | 28.7720 | 0.932996 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | − | 51.9615i | 0.971795 | − | 1.68320i | 0.281666 | − | 0.959512i | \(-0.409113\pi\) |
0.690129 | − | 0.723686i | \(-0.257554\pi\) | |||||||
\(954\) | 0.613999 | + | 1.06348i | 0.0198790 | + | 0.0344314i | ||||
\(955\) | 4.77200 | − | 8.26535i | 0.154418 | − | 0.267460i | ||||
\(956\) | 1.77200 | + | 3.06920i | 0.0573106 | + | 0.0992649i | ||||
\(957\) | 28.6320 | 0.925541 | ||||||||
\(958\) | 18.0000 | 0.581554 | ||||||||
\(959\) | 7.77200 | + | 13.4615i | 0.250971 | + | 0.434695i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | 2.31601 | 0.0747099 | ||||||||
\(962\) | 3.77200 | 0.121614 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.65800 | − | 2.87175i | 0.0534007 | − | 0.0924927i | ||||
\(965\) | 2.88600 | + | 4.99870i | 0.0929037 | + | 0.160914i | ||||
\(966\) | −2.38600 | + | 4.13267i | −0.0767683 | + | 0.132967i | ||||
\(967\) | 26.8860 | − | 46.5679i | 0.864596 | − | 1.49752i | −0.00285275 | − | 0.999996i | \(-0.500908\pi\) |
0.867448 | − | 0.497527i | \(-0.165759\pi\) | |||||||
\(968\) | −11.7720 | −0.378366 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | 2.45600 | − | 4.25391i | 0.0788167 | − | 0.136514i | −0.823923 | − | 0.566702i | \(-0.808219\pi\) |
0.902740 | + | 0.430187i | \(0.141552\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −1.11400 | − | 1.92950i | −0.0357132 | − | 0.0618570i | ||||
\(974\) | 8.15800 | − | 14.1301i | 0.261399 | − | 0.452757i | ||||
\(975\) | −1.88600 | − | 3.26665i | −0.0604004 | − | 0.104617i | ||||
\(976\) | −5.77200 | −0.184757 | ||||||||
\(977\) | −8.17601 | −0.261574 | −0.130787 | − | 0.991410i | \(-0.541750\pi\) | ||||
−0.130787 | + | 0.991410i | \(0.541750\pi\) | |||||||
\(978\) | 3.65800 | + | 6.33585i | 0.116970 | + | 0.202598i | ||||
\(979\) | −19.8420 | − | 34.3673i | −0.634153 | − | 1.09839i | ||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | −7.54400 | −0.240862 | ||||||||
\(982\) | 16.1580 | + | 27.9865i | 0.515623 | + | 0.893085i | ||||
\(983\) | −10.1580 | + | 17.5942i | −0.323990 | + | 0.561167i | −0.981307 | − | 0.192447i | \(-0.938358\pi\) |
0.657317 | + | 0.753614i | \(0.271691\pi\) | |||||||
\(984\) | 2.38600 | + | 4.13267i | 0.0760629 | + | 0.131745i | ||||
\(985\) | −7.15800 | + | 12.3980i | −0.228073 | + | 0.395034i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.1140 | + | 3.26665i | 0.512655 | + | 0.103926i | ||||
\(989\) | 1.08801 | 0.0345966 | ||||||||
\(990\) | −2.38600 | + | 4.13267i | −0.0758321 | + | 0.131345i | ||||
\(991\) | −12.1140 | + | 20.9821i | −0.384814 | + | 0.666517i | −0.991743 | − | 0.128239i | \(-0.959068\pi\) |
0.606929 | + | 0.794756i | \(0.292401\pi\) | |||||||
\(992\) | −2.88600 | − | 4.99870i | −0.0916306 | − | 0.158709i | ||||
\(993\) | 4.72800 | − | 8.18913i | 0.150038 | − | 0.259874i | ||||
\(994\) | −4.77200 | − | 8.26535i | −0.151359 | − | 0.262161i | ||||
\(995\) | 25.3160 | 0.802571 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 1.72800 | + | 2.99298i | 0.0547262 | + | 0.0947886i | 0.892091 | − | 0.451856i | \(-0.149238\pi\) |
−0.837364 | + | 0.546645i | \(0.815905\pi\) | |||||||
\(998\) | −14.8160 | − | 25.6621i | −0.468992 | − | 0.812319i | ||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 570.2.i.g.391.1 | yes | 4 | |
3.2 | odd | 2 | 1710.2.l.l.1531.2 | 4 | |||
19.7 | even | 3 | inner | 570.2.i.g.121.1 | ✓ | 4 | |
57.26 | odd | 6 | 1710.2.l.l.1261.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.g.121.1 | ✓ | 4 | 19.7 | even | 3 | inner | |
570.2.i.g.391.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1710.2.l.l.1261.2 | 4 | 57.26 | odd | 6 | |||
1710.2.l.l.1531.2 | 4 | 3.2 | odd | 2 |