Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,2,Mod(43,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.f (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: | \(1.00611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 85.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.85 |
Dual form | 126.2.f.b.43.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | 3.00000 | − | 5.19615i | 0.832050 | − | 1.44115i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
0.896410 | − | 0.443227i | \(-0.146166\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 3.46410i | 0.894427i | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 1.50000 | + | 0.866025i | 0.327327 | + | 0.188982i | ||||
\(22\) | 0.500000 | − | 0.866025i | 0.106600 | − | 0.184637i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.00000 | + | 3.46410i | 0.371391 | + | 0.643268i | 0.989780 | − | 0.142605i | \(-0.0455477\pi\) |
−0.618389 | + | 0.785872i | \(0.712214\pi\) | |||||||
\(30\) | −3.00000 | + | 1.73205i | −0.547723 | + | 0.316228i | ||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | − | 0.866025i | −0.261116 | − | 0.150756i | ||||
\(34\) | −2.50000 | − | 4.33013i | −0.428746 | − | 0.742611i | ||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −3.50000 | − | 6.06218i | −0.567775 | − | 0.983415i | ||||
\(39\) | − | 10.3923i | − | 1.66410i | ||||||
\(40\) | 1.00000 | − | 1.73205i | 0.158114 | − | 0.273861i | ||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 1.73205i | 0.267261i | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 3.00000 | + | 5.19615i | 0.447214 | + | 0.774597i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −1.50000 | − | 0.866025i | −0.216506 | − | 0.125000i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −7.50000 | + | 4.33013i | −1.05021 | + | 0.606339i | ||||
\(52\) | 3.00000 | + | 5.19615i | 0.416025 | + | 0.720577i | ||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | −10.5000 | + | 6.06218i | −1.39076 | + | 0.802955i | ||||
\(58\) | −2.00000 | + | 3.46410i | −0.262613 | + | 0.454859i | ||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | −3.00000 | − | 1.73205i | −0.387298 | − | 0.223607i | ||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 3.00000 | 0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | − | 1.73205i | − | 0.213201i | ||||||
\(67\) | −6.50000 | + | 11.2583i | −0.794101 | + | 1.37542i | 0.129307 | + | 0.991605i | \(0.458725\pi\) |
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(68\) | 2.50000 | − | 4.33013i | 0.303170 | − | 0.525105i | ||||
\(69\) | 6.92820i | 0.834058i | ||||||||
\(70\) | −1.00000 | − | 1.73205i | −0.119523 | − | 0.207020i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.50000 | + | 2.59808i | −0.176777 | + | 0.306186i | ||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 1.50000 | + | 0.866025i | 0.173205 | + | 0.100000i | ||||
\(76\) | 3.50000 | − | 6.06218i | 0.401478 | − | 0.695379i | ||||
\(77\) | 0.500000 | − | 0.866025i | 0.0569803 | − | 0.0986928i | ||||
\(78\) | 9.00000 | − | 5.19615i | 1.01905 | − | 0.588348i | ||||
\(79\) | 3.00000 | + | 5.19615i | 0.337526 | + | 0.584613i | 0.983967 | − | 0.178352i | \(-0.0570765\pi\) |
−0.646440 | + | 0.762964i | \(0.723743\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | −8.00000 | − | 13.8564i | −0.878114 | − | 1.52094i | −0.853408 | − | 0.521243i | \(-0.825468\pi\) |
−0.0247060 | − | 0.999695i | \(-0.507865\pi\) | |||||||
\(84\) | −1.50000 | + | 0.866025i | −0.163663 | + | 0.0944911i | ||||
\(85\) | 5.00000 | − | 8.66025i | 0.542326 | − | 0.939336i | ||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 6.00000 | + | 3.46410i | 0.643268 | + | 0.371391i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −3.00000 | + | 5.19615i | −0.316228 | + | 0.547723i | ||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | −2.00000 | − | 3.46410i | −0.208514 | − | 0.361158i | ||||
\(93\) | − | 10.3923i | − | 1.07763i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.00000 | − | 12.1244i | 0.718185 | − | 1.24393i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 2.00000 | + | 3.46410i | 0.199007 | + | 0.344691i | 0.948207 | − | 0.317653i | \(-0.102895\pi\) |
−0.749199 | + | 0.662344i | \(0.769562\pi\) | |||||||
\(102\) | −7.50000 | − | 4.33013i | −0.742611 | − | 0.428746i | ||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | −3.00000 | + | 5.19615i | −0.294174 | + | 0.509525i | ||||
\(105\) | −3.00000 | + | 1.73205i | −0.292770 | + | 0.169031i | ||||
\(106\) | 6.00000 | + | 10.3923i | 0.582772 | + | 1.00939i | ||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 4.50000 | + | 2.59808i | 0.433013 | + | 0.250000i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | 3.00000 | − | 1.73205i | 0.284747 | − | 0.164399i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 5.00000 | − | 8.66025i | 0.470360 | − | 0.814688i | −0.529065 | − | 0.848581i | \(-0.677457\pi\) |
0.999425 | + | 0.0338931i | \(0.0107906\pi\) | |||||||
\(114\) | −10.5000 | − | 6.06218i | −0.983415 | − | 0.567775i | ||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | −9.00000 | − | 15.5885i | −0.832050 | − | 1.44115i | ||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | −2.50000 | − | 4.33013i | −0.229175 | − | 0.396942i | ||||
\(120\) | − | 3.46410i | − | 0.316228i | ||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | −6.00000 | + | 10.3923i | −0.543214 | + | 0.940875i | ||||
\(123\) | 5.19615i | 0.468521i | ||||||||
\(124\) | 3.00000 | + | 5.19615i | 0.269408 | + | 0.466628i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 1.50000 | + | 2.59808i | 0.133631 | + | 0.231455i | ||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | −6.00000 | + | 10.3923i | −0.526235 | + | 0.911465i | ||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 1.50000 | − | 0.866025i | 0.130558 | − | 0.0753778i | ||||
\(133\) | −3.50000 | − | 6.06218i | −0.303488 | − | 0.525657i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 9.00000 | + | 5.19615i | 0.774597 | + | 0.447214i | ||||
\(136\) | 5.00000 | 0.428746 | ||||||||
\(137\) | 9.50000 | + | 16.4545i | 0.811640 | + | 1.40580i | 0.911716 | + | 0.410822i | \(0.134758\pi\) |
−0.100076 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(138\) | −6.00000 | + | 3.46410i | −0.510754 | + | 0.294884i | ||||
\(139\) | 2.50000 | − | 4.33013i | 0.212047 | − | 0.367277i | −0.740308 | − | 0.672268i | \(-0.765320\pi\) |
0.952355 | + | 0.304991i | \(0.0986536\pi\) | |||||||
\(140\) | 1.00000 | − | 1.73205i | 0.0845154 | − | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 6.92820i | −0.335673 | − | 0.581402i | ||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0.500000 | + | 0.866025i | 0.0413803 | + | 0.0716728i | ||||
\(147\) | 1.73205i | 0.142857i | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 12.0000 | − | 20.7846i | 0.983078 | − | 1.70274i | 0.332896 | − | 0.942964i | \(-0.391974\pi\) |
0.650183 | − | 0.759778i | \(-0.274692\pi\) | |||||||
\(150\) | 1.73205i | 0.141421i | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | −7.50000 | + | 12.9904i | −0.606339 | + | 1.05021i | ||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 6.00000 | + | 10.3923i | 0.481932 | + | 0.834730i | ||||
\(156\) | 9.00000 | + | 5.19615i | 0.720577 | + | 0.416025i | ||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | −3.00000 | + | 5.19615i | −0.238667 | + | 0.413384i | ||||
\(159\) | 18.0000 | − | 10.3923i | 1.42749 | − | 0.824163i | ||||
\(160\) | 1.00000 | + | 1.73205i | 0.0790569 | + | 0.136931i | ||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | 3.00000 | − | 1.73205i | 0.233550 | − | 0.134840i | ||||
\(166\) | 8.00000 | − | 13.8564i | 0.620920 | − | 1.07547i | ||||
\(167\) | −10.0000 | + | 17.3205i | −0.773823 | + | 1.34030i | 0.161630 | + | 0.986851i | \(0.448325\pi\) |
−0.935454 | + | 0.353450i | \(0.885009\pi\) | |||||||
\(168\) | −1.50000 | − | 0.866025i | −0.115728 | − | 0.0668153i | ||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 10.0000 | 0.766965 | ||||||||
\(171\) | −10.5000 | + | 18.1865i | −0.802955 | + | 1.39076i | ||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −1.00000 | − | 1.73205i | −0.0760286 | − | 0.131685i | 0.825505 | − | 0.564396i | \(-0.190891\pi\) |
−0.901533 | + | 0.432710i | \(0.857557\pi\) | |||||||
\(174\) | 6.92820i | 0.525226i | ||||||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | − | 12.1244i | − | 0.911322i | ||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | 24.0000 | 1.79384 | 0.896922 | − | 0.442189i | \(-0.145798\pi\) | ||||
0.896922 | + | 0.442189i | \(0.145798\pi\) | |||||||
\(180\) | −6.00000 | −0.447214 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 3.00000 | + | 5.19615i | 0.222375 | + | 0.385164i | ||||
\(183\) | 18.0000 | + | 10.3923i | 1.33060 | + | 0.768221i | ||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | 9.00000 | − | 5.19615i | 0.659912 | − | 0.381000i | ||||
\(187\) | 2.50000 | + | 4.33013i | 0.182818 | + | 0.316650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | − | 2.59808i | 0.327327 | − | 0.188982i | ||||
\(190\) | 14.0000 | 1.01567 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 1.50000 | − | 0.866025i | 0.108253 | − | 0.0625000i | ||||
\(193\) | −8.50000 | + | 14.7224i | −0.611843 | + | 1.05974i | 0.379086 | + | 0.925361i | \(0.376238\pi\) |
−0.990930 | + | 0.134382i | \(0.957095\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 18.0000 | + | 10.3923i | 1.28901 | + | 0.744208i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 22.5167i | 1.58820i | ||||||||
\(202\) | −2.00000 | + | 3.46410i | −0.140720 | + | 0.243733i | ||||
\(203\) | −2.00000 | + | 3.46410i | −0.140372 | + | 0.243132i | ||||
\(204\) | − | 8.66025i | − | 0.606339i | ||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −14.0000 | −0.975426 | ||||||||
\(207\) | 6.00000 | + | 10.3923i | 0.417029 | + | 0.722315i | ||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | 3.50000 | + | 6.06218i | 0.242100 | + | 0.419330i | ||||
\(210\) | −3.00000 | − | 1.73205i | −0.207020 | − | 0.119523i | ||||
\(211\) | 8.00000 | − | 13.8564i | 0.550743 | − | 0.953914i | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | |||||||
\(212\) | −6.00000 | + | 10.3923i | −0.412082 | + | 0.713746i | ||||
\(213\) | −12.0000 | + | 6.92820i | −0.822226 | + | 0.474713i | ||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | 1.50000 | − | 0.866025i | 0.101361 | − | 0.0585206i | ||||
\(220\) | −1.00000 | + | 1.73205i | −0.0674200 | + | 0.116775i | ||||
\(221\) | −15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | ||||
\(222\) | 3.00000 | + | 1.73205i | 0.201347 | + | 0.116248i | ||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | − | 12.1244i | − | 0.802955i | ||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 4.00000 | − | 6.92820i | 0.263752 | − | 0.456832i | ||||
\(231\) | − | 1.73205i | − | 0.113961i | ||||||
\(232\) | −2.00000 | − | 3.46410i | −0.131306 | − | 0.227429i | ||||
\(233\) | −29.0000 | −1.89985 | −0.949927 | − | 0.312473i | \(-0.898843\pi\) | ||||
−0.949927 | + | 0.312473i | \(0.898843\pi\) | |||||||
\(234\) | 9.00000 | − | 15.5885i | 0.588348 | − | 1.01905i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.50000 | + | 6.06218i | 0.227831 | + | 0.394614i | ||||
\(237\) | 9.00000 | + | 5.19615i | 0.584613 | + | 0.337526i | ||||
\(238\) | 2.50000 | − | 4.33013i | 0.162051 | − | 0.280680i | ||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 3.00000 | − | 1.73205i | 0.193649 | − | 0.111803i | ||||
\(241\) | −11.5000 | − | 19.9186i | −0.740780 | − | 1.28307i | −0.952141 | − | 0.305661i | \(-0.901123\pi\) |
0.211360 | − | 0.977408i | \(-0.432211\pi\) | |||||||
\(242\) | 10.0000 | 0.642824 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | −1.00000 | − | 1.73205i | −0.0638877 | − | 0.110657i | ||||
\(246\) | −4.50000 | + | 2.59808i | −0.286910 | + | 0.165647i | ||||
\(247\) | −21.0000 | + | 36.3731i | −1.33620 | + | 2.31436i | ||||
\(248\) | −3.00000 | + | 5.19615i | −0.190500 | + | 0.329956i | ||||
\(249\) | −24.0000 | − | 13.8564i | −1.52094 | − | 0.878114i | ||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | −1.50000 | + | 2.59808i | −0.0944911 | + | 0.163663i | ||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −6.00000 | − | 10.3923i | −0.376473 | − | 0.652071i | ||||
\(255\) | − | 17.3205i | − | 1.08465i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.50000 | − | 12.9904i | 0.467837 | − | 0.810318i | −0.531487 | − | 0.847066i | \(-0.678367\pi\) |
0.999325 | + | 0.0367485i | \(0.0117000\pi\) | |||||||
\(258\) | 1.73205i | 0.107833i | ||||||||
\(259\) | 1.00000 | + | 1.73205i | 0.0621370 | + | 0.107624i | ||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | −9.00000 | − | 15.5885i | −0.554964 | − | 0.961225i | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | 1.50000 | + | 0.866025i | 0.0923186 | + | 0.0533002i | ||||
\(265\) | −12.0000 | + | 20.7846i | −0.737154 | + | 1.27679i | ||||
\(266\) | 3.50000 | − | 6.06218i | 0.214599 | − | 0.371696i | ||||
\(267\) | −9.00000 | + | 5.19615i | −0.550791 | + | 0.317999i | ||||
\(268\) | −6.50000 | − | 11.2583i | −0.397051 | − | 0.687712i | ||||
\(269\) | 20.0000 | 1.21942 | 0.609711 | − | 0.792624i | \(-0.291286\pi\) | ||||
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | 10.3923i | 0.632456i | ||||||||
\(271\) | −6.00000 | −0.364474 | −0.182237 | − | 0.983255i | \(-0.558334\pi\) | ||||
−0.182237 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(272\) | 2.50000 | + | 4.33013i | 0.151585 | + | 0.262553i | ||||
\(273\) | 9.00000 | − | 5.19615i | 0.544705 | − | 0.314485i | ||||
\(274\) | −9.50000 | + | 16.4545i | −0.573916 | + | 0.994052i | ||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | −6.00000 | − | 3.46410i | −0.361158 | − | 0.208514i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 5.00000 | 0.299880 | ||||||||
\(279\) | −9.00000 | − | 15.5885i | −0.538816 | − | 0.933257i | ||||
\(280\) | 2.00000 | 0.119523 | ||||||||
\(281\) | −11.0000 | − | 19.0526i | −0.656205 | − | 1.13658i | −0.981590 | − | 0.190999i | \(-0.938827\pi\) |
0.325385 | − | 0.945582i | \(-0.394506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | − | 24.2487i | − | 1.43637i | ||||||
\(286\) | −3.00000 | − | 5.19615i | −0.177394 | − | 0.307255i | ||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | −4.00000 | − | 6.92820i | −0.234888 | − | 0.406838i | ||||
\(291\) | 7.50000 | + | 4.33013i | 0.439658 | + | 0.253837i | ||||
\(292\) | −0.500000 | + | 0.866025i | −0.0292603 | + | 0.0506803i | ||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | −1.50000 | + | 0.866025i | −0.0874818 | + | 0.0505076i | ||||
\(295\) | 7.00000 | + | 12.1244i | 0.407556 | + | 0.705907i | ||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | −4.50000 | + | 2.59808i | −0.261116 | + | 0.150756i | ||||
\(298\) | 24.0000 | 1.39028 | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | −1.50000 | + | 0.866025i | −0.0866025 | + | 0.0500000i | ||||
\(301\) | −0.500000 | + | 0.866025i | −0.0288195 | + | 0.0499169i | ||||
\(302\) | 5.00000 | − | 8.66025i | 0.287718 | − | 0.498342i | ||||
\(303\) | 6.00000 | + | 3.46410i | 0.344691 | + | 0.199007i | ||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | −15.0000 | −0.857493 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0.500000 | + | 0.866025i | 0.0284901 | + | 0.0493464i | ||||
\(309\) | 24.2487i | 1.37946i | ||||||||
\(310\) | −6.00000 | + | 10.3923i | −0.340777 | + | 0.590243i | ||||
\(311\) | −1.00000 | + | 1.73205i | −0.0567048 | + | 0.0982156i | −0.892984 | − | 0.450088i | \(-0.851393\pi\) |
0.836280 | + | 0.548303i | \(0.184726\pi\) | |||||||
\(312\) | 10.3923i | 0.588348i | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | −3.00000 | + | 5.19615i | −0.169031 | + | 0.292770i | ||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 18.0000 | + | 10.3923i | 1.00939 | + | 0.582772i | ||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | −1.00000 | + | 1.73205i | −0.0559017 | + | 0.0968246i | ||||
\(321\) | 4.50000 | − | 2.59808i | 0.251166 | − | 0.145010i | ||||
\(322\) | −2.00000 | − | 3.46410i | −0.111456 | − | 0.193047i | ||||
\(323\) | 35.0000 | 1.94745 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | −2.00000 | − | 3.46410i | −0.110770 | − | 0.191859i | ||||
\(327\) | −3.00000 | + | 1.73205i | −0.165900 | + | 0.0957826i | ||||
\(328\) | 1.50000 | − | 2.59808i | 0.0828236 | − | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.00000 | + | 1.73205i | 0.165145 | + | 0.0953463i | ||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 16.0000 | 0.878114 | ||||||||
\(333\) | 3.00000 | − | 5.19615i | 0.164399 | − | 0.284747i | ||||
\(334\) | −20.0000 | −1.09435 | ||||||||
\(335\) | −13.0000 | − | 22.5167i | −0.710266 | − | 1.23022i | ||||
\(336\) | − | 1.73205i | − | 0.0944911i | ||||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | − | 17.3205i | − | 0.940721i | ||||||
\(340\) | 5.00000 | + | 8.66025i | 0.271163 | + | 0.469668i | ||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | −21.0000 | −1.13555 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −0.500000 | − | 0.866025i | −0.0269582 | − | 0.0466930i | ||||
\(345\) | −12.0000 | − | 6.92820i | −0.646058 | − | 0.373002i | ||||
\(346\) | 1.00000 | − | 1.73205i | 0.0537603 | − | 0.0931156i | ||||
\(347\) | 1.50000 | − | 2.59808i | 0.0805242 | − | 0.139472i | −0.822951 | − | 0.568112i | \(-0.807674\pi\) |
0.903475 | + | 0.428640i | \(0.141007\pi\) | |||||||
\(348\) | −6.00000 | + | 3.46410i | −0.321634 | + | 0.185695i | ||||
\(349\) | 7.00000 | + | 12.1244i | 0.374701 | + | 0.649002i | 0.990282 | − | 0.139072i | \(-0.0444119\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −27.0000 | − | 15.5885i | −1.44115 | − | 0.832050i | ||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 7.50000 | + | 12.9904i | 0.399185 | + | 0.691408i | 0.993626 | − | 0.112731i | \(-0.0359599\pi\) |
−0.594441 | + | 0.804139i | \(0.702627\pi\) | |||||||
\(354\) | 10.5000 | − | 6.06218i | 0.558069 | − | 0.322201i | ||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | 3.00000 | − | 5.19615i | 0.159000 | − | 0.275396i | ||||
\(357\) | −7.50000 | − | 4.33013i | −0.396942 | − | 0.229175i | ||||
\(358\) | 12.0000 | + | 20.7846i | 0.634220 | + | 1.09850i | ||||
\(359\) | 2.00000 | 0.105556 | 0.0527780 | − | 0.998606i | \(-0.483192\pi\) | ||||
0.0527780 | + | 0.998606i | \(0.483192\pi\) | |||||||
\(360\) | −3.00000 | − | 5.19615i | −0.158114 | − | 0.273861i | ||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.3205i | − | 0.909091i | ||||||
\(364\) | −3.00000 | + | 5.19615i | −0.157243 | + | 0.272352i | ||||
\(365\) | −1.00000 | + | 1.73205i | −0.0523424 | + | 0.0906597i | ||||
\(366\) | 20.7846i | 1.08643i | ||||||||
\(367\) | 11.0000 | + | 19.0526i | 0.574195 | + | 0.994535i | 0.996129 | + | 0.0879086i | \(0.0280183\pi\) |
−0.421933 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 4.50000 | + | 7.79423i | 0.234261 | + | 0.405751i | ||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | 9.00000 | + | 5.19615i | 0.466628 | + | 0.269408i | ||||
\(373\) | −11.0000 | + | 19.0526i | −0.569558 | + | 0.986504i | 0.427051 | + | 0.904227i | \(0.359552\pi\) |
−0.996610 | + | 0.0822766i | \(0.973781\pi\) | |||||||
\(374\) | −2.50000 | + | 4.33013i | −0.129272 | + | 0.223906i | ||||
\(375\) | −18.0000 | + | 10.3923i | −0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 4.50000 | + | 2.59808i | 0.231455 | + | 0.133631i | ||||
\(379\) | −17.0000 | −0.873231 | −0.436616 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436616 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(380\) | 7.00000 | + | 12.1244i | 0.359092 | + | 0.621966i | ||||
\(381\) | −18.0000 | + | 10.3923i | −0.922168 | + | 0.532414i | ||||
\(382\) | 6.00000 | − | 10.3923i | 0.306987 | − | 0.531717i | ||||
\(383\) | −2.00000 | + | 3.46410i | −0.102195 | + | 0.177007i | −0.912589 | − | 0.408879i | \(-0.865920\pi\) |
0.810394 | + | 0.585886i | \(0.199253\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 1.00000 | + | 1.73205i | 0.0509647 | + | 0.0882735i | ||||
\(386\) | −17.0000 | −0.865277 | ||||||||
\(387\) | 3.00000 | 0.152499 | ||||||||
\(388\) | −5.00000 | −0.253837 | ||||||||
\(389\) | −4.00000 | − | 6.92820i | −0.202808 | − | 0.351274i | 0.746624 | − | 0.665246i | \(-0.231673\pi\) |
−0.949432 | + | 0.313972i | \(0.898340\pi\) | |||||||
\(390\) | 20.7846i | 1.05247i | ||||||||
\(391\) | 10.0000 | − | 17.3205i | 0.505722 | − | 0.875936i | ||||
\(392\) | 0.500000 | − | 0.866025i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | − | 6.92820i | − | 0.349482i | ||||||
\(394\) | 5.00000 | + | 8.66025i | 0.251896 | + | 0.436297i | ||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 1.50000 | − | 2.59808i | 0.0753778 | − | 0.130558i | ||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 7.00000 | + | 12.1244i | 0.350878 | + | 0.607739i | ||||
\(399\) | −10.5000 | − | 6.06218i | −0.525657 | − | 0.303488i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −4.50000 | + | 7.79423i | −0.224719 | + | 0.389225i | −0.956235 | − | 0.292599i | \(-0.905480\pi\) |
0.731516 | + | 0.681824i | \(0.238813\pi\) | |||||||
\(402\) | −19.5000 | + | 11.2583i | −0.972572 | + | 0.561514i | ||||
\(403\) | −18.0000 | − | 31.1769i | −0.896644 | − | 1.55303i | ||||
\(404\) | −4.00000 | −0.199007 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | −4.00000 | −0.198517 | ||||||||
\(407\) | −1.00000 | − | 1.73205i | −0.0495682 | − | 0.0858546i | ||||
\(408\) | 7.50000 | − | 4.33013i | 0.371305 | − | 0.214373i | ||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | 3.00000 | − | 5.19615i | 0.148159 | − | 0.256620i | ||||
\(411\) | 28.5000 | + | 16.4545i | 1.40580 | + | 0.811640i | ||||
\(412\) | −7.00000 | − | 12.1244i | −0.344865 | − | 0.597324i | ||||
\(413\) | 7.00000 | 0.344447 | ||||||||
\(414\) | −6.00000 | + | 10.3923i | −0.294884 | + | 0.510754i | ||||
\(415\) | 32.0000 | 1.57082 | ||||||||
\(416\) | −3.00000 | − | 5.19615i | −0.147087 | − | 0.254762i | ||||
\(417\) | − | 8.66025i | − | 0.424094i | ||||||
\(418\) | −3.50000 | + | 6.06218i | −0.171191 | + | 0.296511i | ||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | − | 3.46410i | − | 0.169031i | ||||||
\(421\) | 6.00000 | + | 10.3923i | 0.292422 | + | 0.506490i | 0.974382 | − | 0.224900i | \(-0.0722054\pi\) |
−0.681960 | + | 0.731390i | \(0.738872\pi\) | |||||||
\(422\) | 16.0000 | 0.778868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | −2.50000 | − | 4.33013i | −0.121268 | − | 0.210042i | ||||
\(426\) | −12.0000 | − | 6.92820i | −0.581402 | − | 0.335673i | ||||
\(427\) | −6.00000 | + | 10.3923i | −0.290360 | + | 0.502919i | ||||
\(428\) | −1.50000 | + | 2.59808i | −0.0725052 | + | 0.125583i | ||||
\(429\) | −9.00000 | + | 5.19615i | −0.434524 | + | 0.250873i | ||||
\(430\) | −1.00000 | − | 1.73205i | −0.0482243 | − | 0.0835269i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 3.00000 | + | 5.19615i | 0.144005 | + | 0.249423i | ||||
\(435\) | −12.0000 | + | 6.92820i | −0.575356 | + | 0.332182i | ||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 14.0000 | − | 24.2487i | 0.669711 | − | 1.15997i | ||||
\(438\) | 1.50000 | + | 0.866025i | 0.0716728 | + | 0.0413803i | ||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | −3.50000 | − | 6.06218i | −0.166290 | − | 0.288023i | 0.770823 | − | 0.637050i | \(-0.219845\pi\) |
−0.937113 | + | 0.349027i | \(0.886512\pi\) | |||||||
\(444\) | 3.46410i | 0.164399i | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | −2.00000 | + | 3.46410i | −0.0947027 | + | 0.164030i | ||||
\(447\) | − | 41.5692i | − | 1.96616i | ||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | 17.0000 | 0.802280 | 0.401140 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401140 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(450\) | 1.50000 | + | 2.59808i | 0.0707107 | + | 0.122474i | ||||
\(451\) | 3.00000 | 0.141264 | ||||||||
\(452\) | 5.00000 | + | 8.66025i | 0.235180 | + | 0.407344i | ||||
\(453\) | −15.0000 | − | 8.66025i | −0.704761 | − | 0.406894i | ||||
\(454\) | 1.50000 | − | 2.59808i | 0.0703985 | − | 0.121934i | ||||
\(455\) | −6.00000 | + | 10.3923i | −0.281284 | + | 0.487199i | ||||
\(456\) | 10.5000 | − | 6.06218i | 0.491708 | − | 0.283887i | ||||
\(457\) | −0.500000 | − | 0.866025i | −0.0233890 | − | 0.0405110i | 0.854094 | − | 0.520119i | \(-0.174112\pi\) |
−0.877483 | + | 0.479608i | \(0.840779\pi\) | |||||||
\(458\) | 26.0000 | 1.21490 | ||||||||
\(459\) | 25.9808i | 1.21268i | ||||||||
\(460\) | 8.00000 | 0.373002 | ||||||||
\(461\) | −7.00000 | − | 12.1244i | −0.326023 | − | 0.564688i | 0.655696 | − | 0.755025i | \(-0.272375\pi\) |
−0.981719 | + | 0.190337i | \(0.939042\pi\) | |||||||
\(462\) | 1.50000 | − | 0.866025i | 0.0697863 | − | 0.0402911i | ||||
\(463\) | 4.00000 | − | 6.92820i | 0.185896 | − | 0.321981i | −0.757982 | − | 0.652275i | \(-0.773815\pi\) |
0.943878 | + | 0.330294i | \(0.107148\pi\) | |||||||
\(464\) | 2.00000 | − | 3.46410i | 0.0928477 | − | 0.160817i | ||||
\(465\) | 18.0000 | + | 10.3923i | 0.834730 | + | 0.481932i | ||||
\(466\) | −14.5000 | − | 25.1147i | −0.671700 | − | 1.16342i | ||||
\(467\) | −13.0000 | −0.601568 | −0.300784 | − | 0.953692i | \(-0.597248\pi\) | ||||
−0.300784 | + | 0.953692i | \(0.597248\pi\) | |||||||
\(468\) | 18.0000 | 0.832050 | ||||||||
\(469\) | −13.0000 | −0.600284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.46410i | 0.159617i | ||||||||
\(472\) | −3.50000 | + | 6.06218i | −0.161101 | + | 0.279034i | ||||
\(473\) | 0.500000 | − | 0.866025i | 0.0229900 | − | 0.0398199i | ||||
\(474\) | 10.3923i | 0.477334i | ||||||||
\(475\) | −3.50000 | − | 6.06218i | −0.160591 | − | 0.278152i | ||||
\(476\) | 5.00000 | 0.229175 | ||||||||
\(477\) | 18.0000 | − | 31.1769i | 0.824163 | − | 1.42749i | ||||
\(478\) | −6.00000 | −0.274434 | ||||||||
\(479\) | 10.0000 | + | 17.3205i | 0.456912 | + | 0.791394i | 0.998796 | − | 0.0490589i | \(-0.0156222\pi\) |
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(480\) | 3.00000 | + | 1.73205i | 0.136931 | + | 0.0790569i | ||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 11.5000 | − | 19.9186i | 0.523811 | − | 0.907267i | ||||
\(483\) | −6.00000 | + | 3.46410i | −0.273009 | + | 0.157622i | ||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | −10.0000 | −0.453143 | −0.226572 | − | 0.973995i | \(-0.572752\pi\) | ||||
−0.226572 | + | 0.973995i | \(0.572752\pi\) | |||||||
\(488\) | −6.00000 | − | 10.3923i | −0.271607 | − | 0.470438i | ||||
\(489\) | −6.00000 | + | 3.46410i | −0.271329 | + | 0.156652i | ||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | −16.5000 | + | 28.5788i | −0.744635 | + | 1.28974i | 0.205731 | + | 0.978609i | \(0.434043\pi\) |
−0.950365 | + | 0.311136i | \(0.899290\pi\) | |||||||
\(492\) | −4.50000 | − | 2.59808i | −0.202876 | − | 0.117130i | ||||
\(493\) | −10.0000 | − | 17.3205i | −0.450377 | − | 0.780076i | ||||
\(494\) | −42.0000 | −1.88967 | ||||||||
\(495\) | 3.00000 | − | 5.19615i | 0.134840 | − | 0.233550i | ||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | −4.00000 | − | 6.92820i | −0.179425 | − | 0.310772i | ||||
\(498\) | − | 27.7128i | − | 1.24184i | ||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | 34.6410i | 1.54765i | ||||||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 2.00000 | + | 3.46410i | 0.0889108 | + | 0.153998i | ||||
\(507\) | −34.5000 | − | 19.9186i | −1.53220 | − | 0.884615i | ||||
\(508\) | 6.00000 | − | 10.3923i | 0.266207 | − | 0.461084i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 15.0000 | − | 8.66025i | 0.664211 | − | 0.383482i | ||||
\(511\) | 0.500000 | + | 0.866025i | 0.0221187 | + | 0.0383107i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | 15.0000 | 0.661622 | ||||||||
\(515\) | −14.0000 | − | 24.2487i | −0.616914 | − | 1.06853i | ||||
\(516\) | −1.50000 | + | 0.866025i | −0.0660338 | + | 0.0381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.00000 | + | 1.73205i | −0.0439375 | + | 0.0761019i | ||||
\(519\) | −3.00000 | − | 1.73205i | −0.131685 | − | 0.0760286i | ||||
\(520\) | −6.00000 | − | 10.3923i | −0.263117 | − | 0.455733i | ||||
\(521\) | −9.00000 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(522\) | 6.00000 | + | 10.3923i | 0.262613 | + | 0.454859i | ||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 2.00000 | + | 3.46410i | 0.0873704 | + | 0.151330i | ||||
\(525\) | 1.73205i | 0.0755929i | ||||||||
\(526\) | 9.00000 | − | 15.5885i | 0.392419 | − | 0.679689i | ||||
\(527\) | −15.0000 | + | 25.9808i | −0.653410 | + | 1.13174i | ||||
\(528\) | 1.73205i | 0.0753778i | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | −24.0000 | −1.04249 | ||||||||
\(531\) | −10.5000 | − | 18.1865i | −0.455661 | − | 0.789228i | ||||
\(532\) | 7.00000 | 0.303488 | ||||||||
\(533\) | 9.00000 | + | 15.5885i | 0.389833 | + | 0.675211i | ||||
\(534\) | −9.00000 | − | 5.19615i | −0.389468 | − | 0.224860i | ||||
\(535\) | −3.00000 | + | 5.19615i | −0.129701 | + | 0.224649i | ||||
\(536\) | 6.50000 | − | 11.2583i | 0.280757 | − | 0.486286i | ||||
\(537\) | 36.0000 | − | 20.7846i | 1.55351 | − | 0.896922i | ||||
\(538\) | 10.0000 | + | 17.3205i | 0.431131 | + | 0.746740i | ||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −9.00000 | + | 5.19615i | −0.387298 | + | 0.223607i | ||||
\(541\) | −24.0000 | −1.03184 | −0.515920 | − | 0.856637i | \(-0.672550\pi\) | ||||
−0.515920 | + | 0.856637i | \(0.672550\pi\) | |||||||
\(542\) | −3.00000 | − | 5.19615i | −0.128861 | − | 0.223194i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | 2.00000 | − | 3.46410i | 0.0856706 | − | 0.148386i | ||||
\(546\) | 9.00000 | + | 5.19615i | 0.385164 | + | 0.222375i | ||||
\(547\) | 10.5000 | + | 18.1865i | 0.448948 | + | 0.777600i | 0.998318 | − | 0.0579790i | \(-0.0184657\pi\) |
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(548\) | −19.0000 | −0.811640 | ||||||||
\(549\) | 36.0000 | 1.53644 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −14.0000 | − | 24.2487i | −0.596420 | − | 1.03303i | ||||
\(552\) | − | 6.92820i | − | 0.294884i | ||||||
\(553\) | −3.00000 | + | 5.19615i | −0.127573 | + | 0.220963i | ||||
\(554\) | 1.00000 | − | 1.73205i | 0.0424859 | − | 0.0735878i | ||||
\(555\) | 6.92820i | 0.294086i | ||||||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | −28.0000 | −1.18640 | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||||
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(558\) | 9.00000 | − | 15.5885i | 0.381000 | − | 0.659912i | ||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 1.00000 | + | 1.73205i | 0.0422577 | + | 0.0731925i | ||||
\(561\) | 7.50000 | + | 4.33013i | 0.316650 | + | 0.182818i | ||||
\(562\) | 11.0000 | − | 19.0526i | 0.464007 | − | 0.803684i | ||||
\(563\) | −15.5000 | + | 26.8468i | −0.653247 | + | 1.13146i | 0.329083 | + | 0.944301i | \(0.393260\pi\) |
−0.982330 | + | 0.187156i | \(0.940073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | + | 17.3205i | 0.420703 | + | 0.728679i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 4.50000 | − | 7.79423i | 0.188982 | − | 0.327327i | ||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 21.0000 | − | 12.1244i | 0.879593 | − | 0.507833i | ||||
\(571\) | 16.5000 | − | 28.5788i | 0.690504 | − | 1.19599i | −0.281170 | − | 0.959658i | \(-0.590722\pi\) |
0.971673 | − | 0.236329i | \(-0.0759443\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | −18.0000 | − | 10.3923i | −0.751961 | − | 0.434145i | ||||
\(574\) | −1.50000 | − | 2.59808i | −0.0626088 | − | 0.108442i | ||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −35.0000 | −1.45707 | −0.728535 | − | 0.685009i | \(-0.759798\pi\) | ||||
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 29.4449i | 1.22369i | ||||||||
\(580\) | 4.00000 | − | 6.92820i | 0.166091 | − | 0.287678i | ||||
\(581\) | 8.00000 | − | 13.8564i | 0.331896 | − | 0.574861i | ||||
\(582\) | 8.66025i | 0.358979i | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 36.0000 | 1.48842 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.5000 | + | 40.7032i | 0.969949 | + | 1.68000i | 0.695686 | + | 0.718346i | \(0.255100\pi\) |
0.274263 | + | 0.961655i | \(0.411566\pi\) | |||||||
\(588\) | −1.50000 | − | 0.866025i | −0.0618590 | − | 0.0357143i | ||||
\(589\) | −21.0000 | + | 36.3731i | −0.865290 | + | 1.49873i | ||||
\(590\) | −7.00000 | + | 12.1244i | −0.288185 | + | 0.499152i | ||||
\(591\) | 15.0000 | − | 8.66025i | 0.617018 | − | 0.356235i | ||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | −4.50000 | − | 2.59808i | −0.184637 | − | 0.106600i | ||||
\(595\) | 10.0000 | 0.409960 | ||||||||
\(596\) | 12.0000 | + | 20.7846i | 0.491539 | + | 0.851371i | ||||
\(597\) | 21.0000 | − | 12.1244i | 0.859473 | − | 0.496217i | ||||
\(598\) | −12.0000 | + | 20.7846i | −0.490716 | + | 0.849946i | ||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | −1.50000 | − | 0.866025i | −0.0612372 | − | 0.0353553i | ||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | −1.00000 | −0.0407570 | ||||||||
\(603\) | 19.5000 | + | 33.7750i | 0.794101 | + | 1.37542i | ||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 10.0000 | + | 17.3205i | 0.406558 | + | 0.704179i | ||||
\(606\) | 6.92820i | 0.281439i | ||||||||
\(607\) | 12.0000 | − | 20.7846i | 0.487065 | − | 0.843621i | −0.512824 | − | 0.858494i | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | −3.50000 | + | 6.06218i | −0.141944 | + | 0.245854i | ||||
\(609\) | 6.92820i | 0.280745i | ||||||||
\(610\) | −12.0000 | − | 20.7846i | −0.485866 | − | 0.841544i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.50000 | − | 12.9904i | −0.303170 | − | 0.525105i | ||||
\(613\) | 42.0000 | 1.69636 | 0.848182 | − | 0.529705i | \(-0.177697\pi\) | ||||
0.848182 | + | 0.529705i | \(0.177697\pi\) | |||||||
\(614\) | 3.50000 | + | 6.06218i | 0.141249 | + | 0.244650i | ||||
\(615\) | −9.00000 | − | 5.19615i | −0.362915 | − | 0.209529i | ||||
\(616\) | −0.500000 | + | 0.866025i | −0.0201456 | + | 0.0348932i | ||||
\(617\) | 8.50000 | − | 14.7224i | 0.342197 | − | 0.592703i | −0.642643 | − | 0.766165i | \(-0.722162\pi\) |
0.984840 | + | 0.173463i | \(0.0554956\pi\) | |||||||
\(618\) | −21.0000 | + | 12.1244i | −0.844744 | + | 0.487713i | ||||
\(619\) | −18.5000 | − | 32.0429i | −0.743578 | − | 1.28791i | −0.950856 | − | 0.309633i | \(-0.899794\pi\) |
0.207279 | − | 0.978282i | \(-0.433539\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | 18.0000 | + | 10.3923i | 0.722315 | + | 0.417029i | ||||
\(622\) | −2.00000 | −0.0801927 | ||||||||
\(623\) | −3.00000 | − | 5.19615i | −0.120192 | − | 0.208179i | ||||
\(624\) | −9.00000 | + | 5.19615i | −0.360288 | + | 0.208013i | ||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −8.50000 | + | 14.7224i | −0.339728 | + | 0.588427i | ||||
\(627\) | 10.5000 | + | 6.06218i | 0.419330 | + | 0.242100i | ||||
\(628\) | −1.00000 | − | 1.73205i | −0.0399043 | − | 0.0691164i | ||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | −6.00000 | −0.239046 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | −3.00000 | − | 5.19615i | −0.119334 | − | 0.206692i | ||||
\(633\) | − | 27.7128i | − | 1.10149i | ||||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 20.7846i | 0.824163i | ||||||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | 4.00000 | 0.158362 | ||||||||
\(639\) | −12.0000 | + | 20.7846i | −0.474713 | + | 0.822226i | ||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | −0.500000 | − | 0.866025i | −0.0197488 | − | 0.0342059i | 0.855982 | − | 0.517005i | \(-0.172953\pi\) |
−0.875731 | + | 0.482800i | \(0.839620\pi\) | |||||||
\(642\) | 4.50000 | + | 2.59808i | 0.177601 | + | 0.102538i | ||||
\(643\) | 3.50000 | − | 6.06218i | 0.138027 | − | 0.239069i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.926750 | + | 0.375680i | \(0.122591\pi\) | |||||||
\(644\) | 2.00000 | − | 3.46410i | 0.0788110 | − | 0.136505i | ||||
\(645\) | −3.00000 | + | 1.73205i | −0.118125 | + | 0.0681994i | ||||
\(646\) | 17.5000 | + | 30.3109i | 0.688528 | + | 1.19257i | ||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | −7.00000 | −0.274774 | ||||||||
\(650\) | 3.00000 | + | 5.19615i | 0.117670 | + | 0.203810i | ||||
\(651\) | 9.00000 | − | 5.19615i | 0.352738 | − | 0.203653i | ||||
\(652\) | 2.00000 | − | 3.46410i | 0.0783260 | − | 0.135665i | ||||
\(653\) | 3.00000 | − | 5.19615i | 0.117399 | − | 0.203341i | −0.801337 | − | 0.598213i | \(-0.795878\pi\) |
0.918736 | + | 0.394872i | \(0.129211\pi\) | |||||||
\(654\) | −3.00000 | − | 1.73205i | −0.117309 | − | 0.0677285i | ||||
\(655\) | 4.00000 | + | 6.92820i | 0.156293 | + | 0.270707i | ||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 1.50000 | − | 2.59808i | 0.0585206 | − | 0.101361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.00000 | − | 13.8564i | −0.311636 | − | 0.539769i | 0.667081 | − | 0.744985i | \(-0.267544\pi\) |
−0.978717 | + | 0.205216i | \(0.934210\pi\) | |||||||
\(660\) | 3.46410i | 0.134840i | ||||||||
\(661\) | −14.0000 | + | 24.2487i | −0.544537 | + | 0.943166i | 0.454099 | + | 0.890951i | \(0.349961\pi\) |
−0.998636 | + | 0.0522143i | \(0.983372\pi\) | |||||||
\(662\) | 4.00000 | − | 6.92820i | 0.155464 | − | 0.269272i | ||||
\(663\) | 51.9615i | 2.01802i | ||||||||
\(664\) | 8.00000 | + | 13.8564i | 0.310460 | + | 0.537733i | ||||
\(665\) | 14.0000 | 0.542897 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | −16.0000 | −0.619522 | ||||||||
\(668\) | −10.0000 | − | 17.3205i | −0.386912 | − | 0.670151i | ||||
\(669\) | 6.00000 | + | 3.46410i | 0.231973 | + | 0.133930i | ||||
\(670\) | 13.0000 | − | 22.5167i | 0.502234 | − | 0.869894i | ||||
\(671\) | 6.00000 | − | 10.3923i | 0.231627 | − | 0.401190i | ||||
\(672\) | 1.50000 | − | 0.866025i | 0.0578638 | − | 0.0334077i | ||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | 9.00000 | 0.346667 | ||||||||
\(675\) | 4.50000 | − | 2.59808i | 0.173205 | − | 0.100000i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | −15.0000 | − | 25.9808i | −0.576497 | − | 0.998522i | −0.995877 | − | 0.0907112i | \(-0.971086\pi\) |
0.419380 | − | 0.907811i | \(-0.362247\pi\) | |||||||
\(678\) | 15.0000 | − | 8.66025i | 0.576072 | − | 0.332595i | ||||
\(679\) | −2.50000 | + | 4.33013i | −0.0959412 | + | 0.166175i | ||||
\(680\) | −5.00000 | + | 8.66025i | −0.191741 | + | 0.332106i | ||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | −3.00000 | − | 5.19615i | −0.114876 | − | 0.198971i | ||||
\(683\) | 39.0000 | 1.49229 | 0.746147 | − | 0.665782i | \(-0.231902\pi\) | ||||
0.746147 | + | 0.665782i | \(0.231902\pi\) | |||||||
\(684\) | −10.5000 | − | 18.1865i | −0.401478 | − | 0.695379i | ||||
\(685\) | −38.0000 | −1.45191 | ||||||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | − | 45.0333i | − | 1.71813i | ||||||
\(688\) | 0.500000 | − | 0.866025i | 0.0190623 | − | 0.0330169i | ||||
\(689\) | 36.0000 | − | 62.3538i | 1.37149 | − | 2.37549i | ||||
\(690\) | − | 13.8564i | − | 0.527504i | ||||||
\(691\) | −16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) |
0.382791 | − | 0.923835i | \(-0.374963\pi\) | |||||||
\(692\) | 2.00000 | 0.0760286 | ||||||||
\(693\) | −1.50000 | − | 2.59808i | −0.0569803 | − | 0.0986928i | ||||
\(694\) | 3.00000 | 0.113878 | ||||||||
\(695\) | 5.00000 | + | 8.66025i | 0.189661 | + | 0.328502i | ||||
\(696\) | −6.00000 | − | 3.46410i | −0.227429 | − | 0.131306i | ||||
\(697\) | 7.50000 | − | 12.9904i | 0.284083 | − | 0.492046i | ||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | −43.5000 | + | 25.1147i | −1.64532 | + | 0.949927i | ||||
\(700\) | −0.500000 | − | 0.866025i | −0.0188982 | − | 0.0327327i | ||||
\(701\) | 8.00000 | 0.302156 | 0.151078 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(702\) | − | 31.1769i | − | 1.17670i | ||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.50000 | + | 12.9904i | −0.282266 | + | 0.488899i | ||||
\(707\) | −2.00000 | + | 3.46410i | −0.0752177 | + | 0.130281i | ||||
\(708\) | 10.5000 | + | 6.06218i | 0.394614 | + | 0.227831i | ||||
\(709\) | 2.00000 | + | 3.46410i | 0.0751116 | + | 0.130097i | 0.901135 | − | 0.433539i | \(-0.142735\pi\) |
−0.826023 | + | 0.563636i | \(0.809402\pi\) | |||||||
\(710\) | 16.0000 | 0.600469 | ||||||||
\(711\) | 18.0000 | 0.675053 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 12.0000 | + | 20.7846i | 0.449404 | + | 0.778390i | ||||
\(714\) | − | 8.66025i | − | 0.324102i | ||||||
\(715\) | 6.00000 | − | 10.3923i | 0.224387 | − | 0.388650i | ||||
\(716\) | −12.0000 | + | 20.7846i | −0.448461 | + | 0.776757i | ||||
\(717\) | 10.3923i | 0.388108i | ||||||||
\(718\) | 1.00000 | + | 1.73205i | 0.0373197 | + | 0.0646396i | ||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 3.00000 | − | 5.19615i | 0.111803 | − | 0.193649i | ||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 15.0000 | + | 25.9808i | 0.558242 | + | 0.966904i | ||||
\(723\) | −34.5000 | − | 19.9186i | −1.28307 | − | 0.740780i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | + | 3.46410i | −0.0742781 | + | 0.128654i | ||||
\(726\) | 15.0000 | − | 8.66025i | 0.556702 | − | 0.321412i | ||||
\(727\) | 7.00000 | + | 12.1244i | 0.259616 | + | 0.449667i | 0.966139 | − | 0.258022i | \(-0.0830708\pi\) |
−0.706523 | + | 0.707690i | \(0.749737\pi\) | |||||||
\(728\) | −6.00000 | −0.222375 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −2.00000 | −0.0740233 | ||||||||
\(731\) | −2.50000 | − | 4.33013i | −0.0924658 | − | 0.160156i | ||||
\(732\) | −18.0000 | + | 10.3923i | −0.665299 | + | 0.384111i | ||||
\(733\) | 9.00000 | − | 15.5885i | 0.332423 | − | 0.575773i | −0.650564 | − | 0.759452i | \(-0.725467\pi\) |
0.982986 | + | 0.183679i | \(0.0588007\pi\) | |||||||
\(734\) | −11.0000 | + | 19.0526i | −0.406017 | + | 0.703243i | ||||
\(735\) | −3.00000 | − | 1.73205i | −0.110657 | − | 0.0638877i | ||||
\(736\) | 2.00000 | + | 3.46410i | 0.0737210 | + | 0.127688i | ||||
\(737\) | 13.0000 | 0.478861 | ||||||||
\(738\) | −4.50000 | + | 7.79423i | −0.165647 | + | 0.286910i | ||||
\(739\) | −33.0000 | −1.21392 | −0.606962 | − | 0.794731i | \(-0.707612\pi\) | ||||
−0.606962 | + | 0.794731i | \(0.707612\pi\) | |||||||
\(740\) | −2.00000 | − | 3.46410i | −0.0735215 | − | 0.127343i | ||||
\(741\) | 72.7461i | 2.67240i | ||||||||
\(742\) | −6.00000 | + | 10.3923i | −0.220267 | + | 0.381514i | ||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 10.3923i | 0.381000i | ||||||||
\(745\) | 24.0000 | + | 41.5692i | 0.879292 | + | 1.52298i | ||||
\(746\) | −22.0000 | −0.805477 | ||||||||
\(747\) | −48.0000 | −1.75623 | ||||||||
\(748\) | −5.00000 | −0.182818 | ||||||||
\(749\) | 1.50000 | + | 2.59808i | 0.0548088 | + | 0.0949316i | ||||
\(750\) | −18.0000 | − | 10.3923i | −0.657267 | − | 0.379473i | ||||
\(751\) | 9.00000 | − | 15.5885i | 0.328415 | − | 0.568831i | −0.653783 | − | 0.756682i | \(-0.726819\pi\) |
0.982197 | + | 0.187851i | \(0.0601523\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.50000 | − | 2.59808i | 0.163989 | − | 0.0946792i | ||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 5.19615i | 0.188982i | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | −8.50000 | − | 14.7224i | −0.308734 | − | 0.534743i | ||||
\(759\) | 6.00000 | − | 3.46410i | 0.217786 | − | 0.125739i | ||||
\(760\) | −7.00000 | + | 12.1244i | −0.253917 | + | 0.439797i | ||||
\(761\) | −5.00000 | + | 8.66025i | −0.181250 | + | 0.313934i | −0.942306 | − | 0.334752i | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | −18.0000 | − | 10.3923i | −0.652071 | − | 0.376473i | ||||
\(763\) | −1.00000 | − | 1.73205i | −0.0362024 | − | 0.0627044i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | −15.0000 | − | 25.9808i | −0.542326 | − | 0.939336i | ||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | −21.0000 | − | 36.3731i | −0.758266 | − | 1.31336i | ||||
\(768\) | 1.73205i | 0.0625000i | ||||||||
\(769\) | −11.0000 | + | 19.0526i | −0.396670 | + | 0.687053i | −0.993313 | − | 0.115454i | \(-0.963168\pi\) |
0.596643 | + | 0.802507i | \(0.296501\pi\) | |||||||
\(770\) | −1.00000 | + | 1.73205i | −0.0360375 | + | 0.0624188i | ||||
\(771\) | − | 25.9808i | − | 0.935674i | ||||||
\(772\) | −8.50000 | − | 14.7224i | −0.305922 | − | 0.529872i | ||||
\(773\) | −52.0000 | −1.87031 | −0.935155 | − | 0.354239i | \(-0.884740\pi\) | ||||
−0.935155 | + | 0.354239i | \(0.884740\pi\) | |||||||
\(774\) | 1.50000 | + | 2.59808i | 0.0539164 | + | 0.0933859i | ||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | −2.50000 | − | 4.33013i | −0.0897448 | − | 0.155443i | ||||
\(777\) | 3.00000 | + | 1.73205i | 0.107624 | + | 0.0621370i | ||||
\(778\) | 4.00000 | − | 6.92820i | 0.143407 | − | 0.248388i | ||||
\(779\) | 10.5000 | − | 18.1865i | 0.376202 | − | 0.651600i | ||||
\(780\) | −18.0000 | + | 10.3923i | −0.644503 | + | 0.372104i | ||||
\(781\) | 4.00000 | + | 6.92820i | 0.143131 | + | 0.247911i | ||||
\(782\) | 20.0000 | 0.715199 | ||||||||
\(783\) | 18.0000 | − | 10.3923i | 0.643268 | − | 0.371391i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −2.00000 | − | 3.46410i | −0.0713831 | − | 0.123639i | ||||
\(786\) | 6.00000 | − | 3.46410i | 0.214013 | − | 0.123560i | ||||
\(787\) | 6.00000 | − | 10.3923i | 0.213877 | − | 0.370446i | −0.739048 | − | 0.673653i | \(-0.764724\pi\) |
0.952925 | + | 0.303207i | \(0.0980575\pi\) | |||||||
\(788\) | −5.00000 | + | 8.66025i | −0.178118 | + | 0.308509i | ||||
\(789\) | −27.0000 | − | 15.5885i | −0.961225 | − | 0.554964i | ||||
\(790\) | −6.00000 | − | 10.3923i | −0.213470 | − | 0.369742i | ||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | 72.0000 | 2.55679 | ||||||||
\(794\) | 9.00000 | + | 15.5885i | 0.319398 | + | 0.553214i | ||||
\(795\) | 41.5692i | 1.47431i | ||||||||
\(796\) | −7.00000 | + | 12.1244i | −0.248108 | + | 0.429736i | ||||
\(797\) | 6.00000 | − | 10.3923i | 0.212531 | − | 0.368114i | −0.739975 | − | 0.672634i | \(-0.765163\pi\) |
0.952506 | + | 0.304520i | \(0.0984960\pi\) | |||||||
\(798\) | − | 12.1244i | − | 0.429198i | ||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −9.00000 | + | 15.5885i | −0.317999 | + | 0.550791i | ||||
\(802\) | −9.00000 | −0.317801 | ||||||||
\(803\) | −0.500000 | − | 0.866025i | −0.0176446 | − | 0.0305614i | ||||
\(804\) | −19.5000 | − | 11.2583i | −0.687712 | − | 0.397051i | ||||
\(805\) | 4.00000 | − | 6.92820i | 0.140981 | − | 0.244187i | ||||
\(806\) | 18.0000 | − | 31.1769i | 0.634023 | − | 1.09816i | ||||
\(807\) | 30.0000 | − | 17.3205i | 1.05605 | − | 0.609711i | ||||
\(808\) | −2.00000 | − | 3.46410i | −0.0703598 | − | 0.121867i | ||||
\(809\) | −43.0000 | −1.51180 | −0.755900 | − | 0.654687i | \(-0.772800\pi\) | ||||
−0.755900 | + | 0.654687i | \(0.772800\pi\) | |||||||
\(810\) | 9.00000 | + | 15.5885i | 0.316228 | + | 0.547723i | ||||
\(811\) | 31.0000 | 1.08856 | 0.544279 | − | 0.838905i | \(-0.316803\pi\) | ||||
0.544279 | + | 0.838905i | \(0.316803\pi\) | |||||||
\(812\) | −2.00000 | − | 3.46410i | −0.0701862 | − | 0.121566i | ||||
\(813\) | −9.00000 | + | 5.19615i | −0.315644 | + | 0.182237i | ||||
\(814\) | 1.00000 | − | 1.73205i | 0.0350500 | − | 0.0607083i | ||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 7.50000 | + | 4.33013i | 0.262553 | + | 0.151585i | ||||
\(817\) | −3.50000 | − | 6.06218i | −0.122449 | − | 0.212089i | ||||
\(818\) | −11.0000 | −0.384606 | ||||||||
\(819\) | 9.00000 | − | 15.5885i | 0.314485 | − | 0.544705i | ||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −23.0000 | − | 39.8372i | −0.802706 | − | 1.39033i | −0.917829 | − | 0.396976i | \(-0.870060\pi\) |
0.115124 | − | 0.993351i | \(-0.463274\pi\) | |||||||
\(822\) | 32.9090i | 1.14783i | ||||||||
\(823\) | −17.0000 | + | 29.4449i | −0.592583 | + | 1.02638i | 0.401300 | + | 0.915947i | \(0.368558\pi\) |
−0.993883 | + | 0.110437i | \(0.964775\pi\) | |||||||
\(824\) | 7.00000 | − | 12.1244i | 0.243857 | − | 0.422372i | ||||
\(825\) | − | 1.73205i | − | 0.0603023i | ||||||
\(826\) | 3.50000 | + | 6.06218i | 0.121781 | + | 0.210930i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | −12.0000 | −0.417029 | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | 16.0000 | + | 27.7128i | 0.555368 | + | 0.961926i | ||||
\(831\) | −3.00000 | − | 1.73205i | −0.104069 | − | 0.0600842i | ||||
\(832\) | 3.00000 | − | 5.19615i | 0.104006 | − | 0.180144i | ||||
\(833\) | 2.50000 | − | 4.33013i | 0.0866199 | − | 0.150030i | ||||
\(834\) | 7.50000 | − | 4.33013i | 0.259704 | − | 0.149940i | ||||
\(835\) | −20.0000 | − | 34.6410i | −0.692129 | − | 1.19880i | ||||
\(836\) | −7.00000 | −0.242100 | ||||||||
\(837\) | −27.0000 | − | 15.5885i | −0.933257 | − | 0.538816i | ||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | 10.0000 | + | 17.3205i | 0.345238 | + | 0.597970i | 0.985397 | − | 0.170272i | \(-0.0544647\pi\) |
−0.640159 | + | 0.768243i | \(0.721131\pi\) | |||||||
\(840\) | 3.00000 | − | 1.73205i | 0.103510 | − | 0.0597614i | ||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | −6.00000 | + | 10.3923i | −0.206774 | + | 0.358142i | ||||
\(843\) | −33.0000 | − | 19.0526i | −1.13658 | − | 0.656205i | ||||
\(844\) | 8.00000 | + | 13.8564i | 0.275371 | + | 0.476957i | ||||
\(845\) | 46.0000 | 1.58245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | −6.00000 | − | 10.3923i | −0.206041 | − | 0.356873i | ||||
\(849\) | 6.92820i | 0.237775i | ||||||||
\(850\) | 2.50000 | − | 4.33013i | 0.0857493 | − | 0.148522i | ||||
\(851\) | −4.00000 | + | 6.92820i | −0.137118 | + | 0.237496i | ||||
\(852\) | − | 13.8564i | − | 0.474713i | ||||||
\(853\) | −22.0000 | − | 38.1051i | −0.753266 | − | 1.30469i | −0.946232 | − | 0.323489i | \(-0.895144\pi\) |
0.192966 | − | 0.981205i | \(-0.438189\pi\) | |||||||
\(854\) | −12.0000 | −0.410632 | ||||||||
\(855\) | −21.0000 | − | 36.3731i | −0.718185 | − | 1.24393i | ||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −15.0000 | − | 25.9808i | −0.512390 | − | 0.887486i | −0.999897 | − | 0.0143666i | \(-0.995427\pi\) |
0.487507 | − | 0.873119i | \(-0.337907\pi\) | |||||||
\(858\) | −9.00000 | − | 5.19615i | −0.307255 | − | 0.177394i | ||||
\(859\) | −14.5000 | + | 25.1147i | −0.494734 | + | 0.856904i | −0.999982 | − | 0.00607046i | \(-0.998068\pi\) |
0.505248 | + | 0.862974i | \(0.331401\pi\) | |||||||
\(860\) | 1.00000 | − | 1.73205i | 0.0340997 | − | 0.0590624i | ||||
\(861\) | −4.50000 | + | 2.59808i | −0.153360 | + | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.0000 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 4.00000 | 0.136004 | ||||||||
\(866\) | −12.5000 | − | 21.6506i | −0.424767 | − | 0.735719i | ||||
\(867\) | 12.0000 | − | 6.92820i | 0.407541 | − | 0.235294i | ||||
\(868\) | −3.00000 | + | 5.19615i | −0.101827 | + | 0.176369i | ||||
\(869\) | 3.00000 | − | 5.19615i | 0.101768 | − | 0.176267i | ||||
\(870\) | −12.0000 | − | 6.92820i | −0.406838 | − | 0.234888i | ||||
\(871\) | 39.0000 | + | 67.5500i | 1.32146 | + | 2.28884i | ||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | 15.0000 | 0.507673 | ||||||||
\(874\) | 28.0000 | 0.947114 | ||||||||
\(875\) | −6.00000 | − | 10.3923i | −0.202837 | − | 0.351324i | ||||
\(876\) | 1.73205i | 0.0585206i | ||||||||
\(877\) | −8.00000 | + | 13.8564i | −0.270141 | + | 0.467898i | −0.968898 | − | 0.247462i | \(-0.920404\pi\) |
0.698757 | + | 0.715359i | \(0.253737\pi\) | |||||||
\(878\) | −12.0000 | + | 20.7846i | −0.404980 | + | 0.701447i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | −1.50000 | + | 2.59808i | −0.0505076 | + | 0.0874818i | ||||
\(883\) | 53.0000 | 1.78359 | 0.891796 | − | 0.452438i | \(-0.149446\pi\) | ||||
0.891796 | + | 0.452438i | \(0.149446\pi\) | |||||||
\(884\) | −15.0000 | − | 25.9808i | −0.504505 | − | 0.873828i | ||||
\(885\) | 21.0000 | + | 12.1244i | 0.705907 | + | 0.407556i | ||||
\(886\) | 3.50000 | − | 6.06218i | 0.117585 | − | 0.203663i | ||||
\(887\) | 3.00000 | − | 5.19615i | 0.100730 | − | 0.174470i | −0.811256 | − | 0.584692i | \(-0.801215\pi\) |
0.911986 | + | 0.410222i | \(0.134549\pi\) | |||||||
\(888\) | −3.00000 | + | 1.73205i | −0.100673 | + | 0.0581238i | ||||
\(889\) | −6.00000 | − | 10.3923i | −0.201234 | − | 0.348547i | ||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | −4.50000 | + | 7.79423i | −0.150756 | + | 0.261116i | ||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 36.0000 | − | 20.7846i | 1.20402 | − | 0.695141i | ||||
\(895\) | −24.0000 | + | 41.5692i | −0.802232 | + | 1.38951i | ||||
\(896\) | −0.500000 | + | 0.866025i | −0.0167038 | + | 0.0289319i | ||||
\(897\) | 36.0000 | + | 20.7846i | 1.20201 | + | 0.693978i | ||||
\(898\) | 8.50000 | + | 14.7224i | 0.283649 | + | 0.491294i | ||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | −1.50000 | + | 2.59808i | −0.0500000 | + | 0.0866025i | ||||
\(901\) | −60.0000 | −1.99889 | ||||||||
\(902\) | 1.50000 | + | 2.59808i | 0.0499445 | + | 0.0865065i | ||||
\(903\) | 1.73205i | 0.0576390i | ||||||||
\(904\) | −5.00000 | + | 8.66025i | −0.166298 | + | 0.288036i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 17.3205i | − | 0.575435i | ||||||
\(907\) | 13.5000 | + | 23.3827i | 0.448260 | + | 0.776409i | 0.998273 | − | 0.0587469i | \(-0.0187105\pi\) |
−0.550013 | + | 0.835156i | \(0.685377\pi\) | |||||||
\(908\) | 3.00000 | 0.0995585 | ||||||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | −12.0000 | −0.397796 | ||||||||
\(911\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(912\) | 10.5000 | + | 6.06218i | 0.347690 | + | 0.200739i | ||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | −36.0000 | + | 20.7846i | −1.19012 | + | 0.687118i | ||||
\(916\) | 13.0000 | + | 22.5167i | 0.429532 | + | 0.743971i | ||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | −22.5000 | + | 12.9904i | −0.742611 | + | 0.428746i | ||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 4.00000 | + | 6.92820i | 0.131876 | + | 0.228416i | ||||
\(921\) | 10.5000 | − | 6.06218i | 0.345987 | − | 0.199756i | ||||
\(922\) | 7.00000 | − | 12.1244i | 0.230533 | − | 0.399294i | ||||
\(923\) | −24.0000 | + | 41.5692i | −0.789970 | + | 1.36827i | ||||
\(924\) | 1.50000 | + | 0.866025i | 0.0493464 | + | 0.0284901i | ||||
\(925\) | 1.00000 | + | 1.73205i | 0.0328798 | + | 0.0569495i | ||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | 21.0000 | + | 36.3731i | 0.689730 | + | 1.19465i | ||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 20.7846i | 0.681554i | ||||||||
\(931\) | 3.50000 | − | 6.06218i | 0.114708 | − | 0.198680i | ||||
\(932\) | 14.5000 | − | 25.1147i | 0.474963 | − | 0.822661i | ||||
\(933\) | 3.46410i | 0.113410i | ||||||||
\(934\) | −6.50000 | − | 11.2583i | −0.212686 | − | 0.368384i | ||||
\(935\) | −10.0000 | −0.327035 | ||||||||
\(936\) | 9.00000 | + | 15.5885i | 0.294174 | + | 0.509525i | ||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | −6.50000 | − | 11.2583i | −0.212233 | − | 0.367598i | ||||
\(939\) | 25.5000 | + | 14.7224i | 0.832161 | + | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0000 | + | 17.3205i | −0.325991 | + | 0.564632i | −0.981712 | − | 0.190370i | \(-0.939031\pi\) |
0.655722 | + | 0.755003i | \(0.272364\pi\) | |||||||
\(942\) | −3.00000 | + | 1.73205i | −0.0977453 | + | 0.0564333i | ||||
\(943\) | −6.00000 | − | 10.3923i | −0.195387 | − | 0.338420i | ||||
\(944\) | −7.00000 | −0.227831 | ||||||||
\(945\) | 10.3923i | 0.338062i | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 18.5000 | + | 32.0429i | 0.601169 | + | 1.04126i | 0.992644 | + | 0.121067i | \(0.0386316\pi\) |
−0.391475 | + | 0.920189i | \(0.628035\pi\) | |||||||
\(948\) | −9.00000 | + | 5.19615i | −0.292306 | + | 0.168763i | ||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | 3.50000 | − | 6.06218i | 0.113555 | − | 0.196683i | ||||
\(951\) | 9.00000 | + | 5.19615i | 0.291845 | + | 0.168497i | ||||
\(952\) | 2.50000 | + | 4.33013i | 0.0810255 | + | 0.140340i | ||||
\(953\) | −35.0000 | −1.13376 | −0.566881 | − | 0.823800i | \(-0.691850\pi\) | ||||
−0.566881 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(954\) | 36.0000 | 1.16554 | ||||||||
\(955\) | 24.0000 | 0.776622 | ||||||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | − | 6.92820i | − | 0.223957i | ||||||
\(958\) | −10.0000 | + | 17.3205i | −0.323085 | + | 0.559600i | ||||
\(959\) | −9.50000 | + | 16.4545i | −0.306771 | + | 0.531343i | ||||
\(960\) | 3.46410i | 0.111803i | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 12.0000 | 0.386896 | ||||||||
\(963\) | 4.50000 | − | 7.79423i | 0.145010 | − | 0.251166i | ||||
\(964\) | 23.0000 | 0.740780 | ||||||||
\(965\) | −17.0000 | − | 29.4449i | −0.547249 | − | 0.947864i | ||||
\(966\) | −6.00000 | − | 3.46410i | −0.193047 | − | 0.111456i | ||||
\(967\) | −7.00000 | + | 12.1244i | −0.225105 | + | 0.389893i | −0.956351 | − | 0.292221i | \(-0.905606\pi\) |
0.731246 | + | 0.682114i | \(0.238939\pi\) | |||||||
\(968\) | −5.00000 | + | 8.66025i | −0.160706 | + | 0.278351i | ||||
\(969\) | 52.5000 | − | 30.3109i | 1.68654 | − | 0.973726i | ||||
\(970\) | −5.00000 | − | 8.66025i | −0.160540 | − | 0.278064i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 13.5000 | − | 7.79423i | 0.433013 | − | 0.250000i | ||||
\(973\) | 5.00000 | 0.160293 | ||||||||
\(974\) | −5.00000 | − | 8.66025i | −0.160210 | − | 0.277492i | ||||
\(975\) | 9.00000 | − | 5.19615i | 0.288231 | − | 0.166410i | ||||
\(976\) | 6.00000 | − | 10.3923i | 0.192055 | − | 0.332650i | ||||
\(977\) | 7.50000 | − | 12.9904i | 0.239946 | − | 0.415599i | −0.720752 | − | 0.693193i | \(-0.756204\pi\) |
0.960699 | + | 0.277594i | \(0.0895368\pi\) | |||||||
\(978\) | −6.00000 | − | 3.46410i | −0.191859 | − | 0.110770i | ||||
\(979\) | 3.00000 | + | 5.19615i | 0.0958804 | + | 0.166070i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | −3.00000 | + | 5.19615i | −0.0957826 | + | 0.165900i | ||||
\(982\) | −33.0000 | −1.05307 | ||||||||
\(983\) | 30.0000 | + | 51.9615i | 0.956851 | + | 1.65732i | 0.730073 | + | 0.683369i | \(0.239486\pi\) |
0.226778 | + | 0.973946i | \(0.427181\pi\) | |||||||
\(984\) | − | 5.19615i | − | 0.165647i | ||||||
\(985\) | −10.0000 | + | 17.3205i | −0.318626 | + | 0.551877i | ||||
\(986\) | 10.0000 | − | 17.3205i | 0.318465 | − | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.0000 | − | 36.3731i | −0.668099 | − | 1.15718i | ||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 6.00000 | 0.190693 | ||||||||
\(991\) | −28.0000 | −0.889449 | −0.444725 | − | 0.895667i | \(-0.646698\pi\) | ||||
−0.444725 | + | 0.895667i | \(0.646698\pi\) | |||||||
\(992\) | −3.00000 | − | 5.19615i | −0.0952501 | − | 0.164978i | ||||
\(993\) | −12.0000 | − | 6.92820i | −0.380808 | − | 0.219860i | ||||
\(994\) | 4.00000 | − | 6.92820i | 0.126872 | − | 0.219749i | ||||
\(995\) | −14.0000 | + | 24.2487i | −0.443830 | + | 0.768736i | ||||
\(996\) | 24.0000 | − | 13.8564i | 0.760469 | − | 0.439057i | ||||
\(997\) | −1.00000 | − | 1.73205i | −0.0316703 | − | 0.0548546i | 0.849756 | − | 0.527176i | \(-0.176749\pi\) |
−0.881426 | + | 0.472322i | \(0.843416\pi\) | |||||||
\(998\) | 29.0000 | 0.917979 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))