Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(80,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.80");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.k (of order \(12\), degree \(4\), not 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 89.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.89 |
Dual form | 507.2.k.i.188.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | 0.583609 | − | 0.812035i | \(-0.301640\pi\) |
0.0994033 | + | 0.995047i | \(0.468307\pi\) | |||||||
\(3\) | −0.724745 | + | 1.57313i | −0.418432 | + | 0.908248i | ||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 1.41421 | − | 1.41421i | 0.632456 | − | 0.632456i | −0.316228 | − | 0.948683i | \(-0.602416\pi\) |
0.948683 | + | 0.316228i | \(0.102416\pi\) | |||||||
\(6\) | −1.10721 | + | 1.33195i | −0.452015 | + | 0.543767i | ||||
\(7\) | −0.366025 | − | 1.36603i | −0.138345 | − | 0.516309i | −0.999962 | − | 0.00875026i | \(-0.997215\pi\) |
0.861617 | − | 0.507559i | \(-0.169452\pi\) | |||||||
\(8\) | −2.12132 | − | 2.12132i | −0.750000 | − | 0.750000i | ||||
\(9\) | −1.94949 | − | 2.28024i | −0.649830 | − | 0.760080i | ||||
\(10\) | 1.73205 | − | 1.00000i | 0.547723 | − | 0.316228i | ||||
\(11\) | 1.03528 | − | 3.86370i | 0.312148 | − | 1.16495i | −0.614468 | − | 0.788941i | \(-0.710630\pi\) |
0.926616 | − | 0.376009i | \(-0.122704\pi\) | |||||||
\(12\) | 1.41421 | − | 1.00000i | 0.408248 | − | 0.288675i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 1.41421i | − | 0.377964i | ||||||
\(15\) | 1.19980 | + | 3.24969i | 0.309787 | + | 0.839066i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −1.29289 | − | 2.70711i | −0.304738 | − | 0.638071i | ||||
\(19\) | 1.36603 | − | 0.366025i | 0.313388 | − | 0.0839720i | −0.0986970 | − | 0.995118i | \(-0.531467\pi\) |
0.412085 | + | 0.911146i | \(0.364801\pi\) | |||||||
\(20\) | −1.93185 | + | 0.517638i | −0.431975 | + | 0.115747i | ||||
\(21\) | 2.41421 | + | 0.414214i | 0.526825 | + | 0.0903888i | ||||
\(22\) | 2.00000 | − | 3.46410i | 0.426401 | − | 0.738549i | ||||
\(23\) | −4.24264 | − | 7.34847i | −0.884652 | − | 1.53226i | −0.846112 | − | 0.533005i | \(-0.821063\pi\) |
−0.0385394 | − | 0.999257i | \(-0.512271\pi\) | |||||||
\(24\) | 4.87453 | − | 1.79970i | 0.995010 | − | 0.367362i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | −0.366025 | + | 1.36603i | −0.0691723 | + | 0.258155i | ||||
\(29\) | 2.44949 | − | 1.41421i | 0.454859 | − | 0.262613i | −0.255021 | − | 0.966935i | \(-0.582082\pi\) |
0.709880 | + | 0.704323i | \(0.248749\pi\) | |||||||
\(30\) | 0.317837 | + | 3.44949i | 0.0580289 | + | 0.629788i | ||||
\(31\) | 5.00000 | + | 5.00000i | 0.898027 | + | 0.898027i | 0.995261 | − | 0.0972349i | \(-0.0309998\pi\) |
−0.0972349 | + | 0.995261i | \(0.531000\pi\) | |||||||
\(32\) | 1.29410 | + | 4.82963i | 0.228766 | + | 0.853766i | ||||
\(33\) | 5.32780 | + | 4.42883i | 0.927452 | + | 0.770960i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.44949 | − | 1.41421i | −0.414039 | − | 0.239046i | ||||
\(36\) | 0.548188 | + | 2.94949i | 0.0913647 | + | 0.491582i | ||||
\(37\) | 1.36603 | + | 0.366025i | 0.224573 | + | 0.0601742i | 0.369351 | − | 0.929290i | \(-0.379580\pi\) |
−0.144778 | + | 0.989464i | \(0.546247\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | −0.948683 | ||||||||
\(41\) | −1.93185 | − | 0.517638i | −0.301705 | − | 0.0808415i | 0.104791 | − | 0.994494i | \(-0.466583\pi\) |
−0.406496 | + | 0.913653i | \(0.633249\pi\) | |||||||
\(42\) | 2.22474 | + | 1.02494i | 0.343286 | + | 0.158152i | ||||
\(43\) | −5.19615 | − | 3.00000i | −0.792406 | − | 0.457496i | 0.0484030 | − | 0.998828i | \(-0.484587\pi\) |
−0.840809 | + | 0.541332i | \(0.817920\pi\) | |||||||
\(44\) | −2.82843 | + | 2.82843i | −0.426401 | + | 0.426401i | ||||
\(45\) | −5.98174 | − | 0.467750i | −0.891705 | − | 0.0697281i | ||||
\(46\) | −2.19615 | − | 8.19615i | −0.323805 | − | 1.20846i | ||||
\(47\) | 2.82843 | + | 2.82843i | 0.412568 | + | 0.412568i | 0.882632 | − | 0.470064i | \(-0.155769\pi\) |
−0.470064 | + | 0.882632i | \(0.655769\pi\) | |||||||
\(48\) | 1.72474 | − | 0.158919i | 0.248945 | − | 0.0229379i | ||||
\(49\) | 4.33013 | − | 2.50000i | 0.618590 | − | 0.357143i | ||||
\(50\) | −0.258819 | + | 0.965926i | −0.0366025 | + | 0.136603i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 5.19565 | − | 0.0719302i | 0.707039 | − | 0.00978846i | ||||
\(55\) | −4.00000 | − | 6.92820i | −0.539360 | − | 0.934199i | ||||
\(56\) | −2.12132 | + | 3.67423i | −0.283473 | + | 0.490990i | ||||
\(57\) | −0.414214 | + | 2.41421i | −0.0548639 | + | 0.319770i | ||||
\(58\) | 2.73205 | − | 0.732051i | 0.358736 | − | 0.0961230i | ||||
\(59\) | −3.86370 | + | 1.03528i | −0.503011 | + | 0.134781i | −0.501397 | − | 0.865217i | \(-0.667180\pi\) |
−0.00161411 | + | 0.999999i | \(0.500514\pi\) | |||||||
\(60\) | 0.585786 | − | 3.41421i | 0.0756247 | − | 0.440773i | ||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 3.53553 | + | 6.12372i | 0.449013 | + | 0.777714i | ||||
\(63\) | −2.40130 | + | 3.49768i | −0.302536 | + | 0.440666i | ||||
\(64\) | 7.00000i | 0.875000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | + | 5.65685i | 0.492366 | + | 0.696311i | ||||
\(67\) | 1.83013 | − | 6.83013i | 0.223586 | − | 0.834433i | −0.759381 | − | 0.650647i | \(-0.774498\pi\) |
0.982966 | − | 0.183786i | \(-0.0588354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.6349 | − | 1.34847i | 1.76184 | − | 0.162337i | ||||
\(70\) | −2.00000 | − | 2.00000i | −0.239046 | − | 0.239046i | ||||
\(71\) | −1.03528 | − | 3.86370i | −0.122865 | − | 0.458537i | 0.876890 | − | 0.480691i | \(-0.159614\pi\) |
−0.999755 | + | 0.0221541i | \(0.992948\pi\) | |||||||
\(72\) | −0.701625 | + | 8.97261i | −0.0826873 | + | 1.05743i | ||||
\(73\) | −1.00000 | + | 1.00000i | −0.117041 | + | 0.117041i | −0.763202 | − | 0.646160i | \(-0.776374\pi\) |
0.646160 | + | 0.763202i | \(0.276374\pi\) | |||||||
\(74\) | 1.22474 | + | 0.707107i | 0.142374 | + | 0.0821995i | ||||
\(75\) | −1.57313 | − | 0.724745i | −0.181650 | − | 0.0836863i | ||||
\(76\) | −1.36603 | − | 0.366025i | −0.156694 | − | 0.0419860i | ||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | −1.93185 | − | 0.517638i | −0.215988 | − | 0.0578737i | ||||
\(81\) | −1.39898 | + | 8.89060i | −0.155442 | + | 0.987845i | ||||
\(82\) | −1.73205 | − | 1.00000i | −0.191273 | − | 0.110432i | ||||
\(83\) | 5.65685 | − | 5.65685i | 0.620920 | − | 0.620920i | −0.324846 | − | 0.945767i | \(-0.605313\pi\) |
0.945767 | + | 0.324846i | \(0.105313\pi\) | |||||||
\(84\) | −1.88366 | − | 1.56583i | −0.205525 | − | 0.170846i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.24264 | − | 4.24264i | −0.457496 | − | 0.457496i | ||||
\(87\) | 0.449490 | + | 4.87832i | 0.0481904 | + | 0.523010i | ||||
\(88\) | −10.3923 | + | 6.00000i | −1.10782 | + | 0.639602i | ||||
\(89\) | −3.62347 | + | 13.5230i | −0.384087 | + | 1.43343i | 0.455515 | + | 0.890228i | \(0.349455\pi\) |
−0.839601 | + | 0.543203i | \(0.817211\pi\) | |||||||
\(90\) | −5.65685 | − | 2.00000i | −0.596285 | − | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.48528i | 0.884652i | ||||||||
\(93\) | −11.4894 | + | 4.24194i | −1.19139 | + | 0.439868i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 1.41421 | − | 2.44949i | 0.145095 | − | 0.251312i | ||||
\(96\) | −8.53553 | − | 1.46447i | −0.871154 | − | 0.149466i | ||||
\(97\) | 9.56218 | − | 2.56218i | 0.970892 | − | 0.260150i | 0.261688 | − | 0.965153i | \(-0.415721\pi\) |
0.709204 | + | 0.705003i | \(0.249054\pi\) | |||||||
\(98\) | 4.82963 | − | 1.29410i | 0.487866 | − | 0.130723i | ||||
\(99\) | −10.8284 | + | 5.17157i | −1.08830 | + | 0.519763i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.24264 | + | 7.34847i | 0.422159 | + | 0.731200i | 0.996150 | − | 0.0876610i | \(-0.0279392\pi\) |
−0.573992 | + | 0.818861i | \(0.694606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.00000i | − | 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | − | 2.82843i | 0.390360 | − | 0.276026i | ||||
\(106\) | 1.46410 | − | 5.46410i | 0.142206 | − | 0.530720i | ||||
\(107\) | −4.89898 | + | 2.82843i | −0.473602 | + | 0.273434i | −0.717746 | − | 0.696305i | \(-0.754826\pi\) |
0.244144 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(108\) | −5.03723 | − | 1.27526i | −0.484708 | − | 0.122711i | ||||
\(109\) | −1.00000 | − | 1.00000i | −0.0957826 | − | 0.0957826i | 0.657592 | − | 0.753374i | \(-0.271575\pi\) |
−0.753374 | + | 0.657592i | \(0.771575\pi\) | |||||||
\(110\) | −2.07055 | − | 7.72741i | −0.197419 | − | 0.736779i | ||||
\(111\) | −1.56583 | + | 1.88366i | −0.148622 | + | 0.178789i | ||||
\(112\) | −1.00000 | + | 1.00000i | −0.0944911 | + | 0.0944911i | ||||
\(113\) | 12.2474 | + | 7.07107i | 1.15214 | + | 0.665190i | 0.949409 | − | 0.314044i | \(-0.101684\pi\) |
0.202735 | + | 0.979234i | \(0.435017\pi\) | |||||||
\(114\) | −1.02494 | + | 2.22474i | −0.0959948 | + | 0.208366i | ||||
\(115\) | −16.3923 | − | 4.39230i | −1.52859 | − | 0.409585i | ||||
\(116\) | −2.82843 | −0.262613 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.34847 | − | 9.43879i | 0.396959 | − | 0.861640i | ||||
\(121\) | −4.33013 | − | 2.50000i | −0.393648 | − | 0.227273i | ||||
\(122\) | −5.65685 | + | 5.65685i | −0.512148 | + | 0.512148i | ||||
\(123\) | 2.21441 | − | 2.66390i | 0.199667 | − | 0.240196i | ||||
\(124\) | −1.83013 | − | 6.83013i | −0.164350 | − | 0.613364i | ||||
\(125\) | 8.48528 | + | 8.48528i | 0.758947 | + | 0.758947i | ||||
\(126\) | −3.22474 | + | 2.75699i | −0.287283 | + | 0.245613i | ||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0.776457 | − | 2.89778i | 0.0686298 | − | 0.256130i | ||||
\(129\) | 8.48528 | − | 6.00000i | 0.747087 | − | 0.528271i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3137i | 0.988483i | 0.869325 | + | 0.494242i | \(0.164554\pi\) | ||||
−0.869325 | + | 0.494242i | \(0.835446\pi\) | |||||||
\(132\) | −2.39960 | − | 6.49938i | −0.208859 | − | 0.565698i | ||||
\(133\) | −1.00000 | − | 1.73205i | −0.0867110 | − | 0.150188i | ||||
\(134\) | 3.53553 | − | 6.12372i | 0.305424 | − | 0.529009i | ||||
\(135\) | 5.07107 | − | 9.07107i | 0.436448 | − | 0.780713i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5230 | − | 3.62347i | 1.15534 | − | 0.309574i | 0.370240 | − | 0.928936i | \(-0.379276\pi\) |
0.785105 | + | 0.619363i | \(0.212609\pi\) | |||||||
\(138\) | 14.4853 | + | 2.48528i | 1.23307 | + | 0.211561i | ||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 1.41421 | + | 2.44949i | 0.119523 | + | 0.207020i | ||||
\(141\) | −6.49938 | + | 2.39960i | −0.547346 | + | 0.202083i | ||||
\(142\) | − | 4.00000i | − | 0.335673i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | 1.46410 | − | 5.46410i | 0.121587 | − | 0.453769i | ||||
\(146\) | −1.22474 | + | 0.707107i | −0.101361 | + | 0.0585206i | ||||
\(147\) | 0.794593 | + | 8.62372i | 0.0655369 | + | 0.711273i | ||||
\(148\) | −1.00000 | − | 1.00000i | −0.0821995 | − | 0.0821995i | ||||
\(149\) | 0.517638 | + | 1.93185i | 0.0424066 | + | 0.158263i | 0.983882 | − | 0.178817i | \(-0.0572271\pi\) |
−0.941476 | + | 0.337081i | \(0.890560\pi\) | |||||||
\(150\) | −1.33195 | − | 1.10721i | −0.108753 | − | 0.0904030i | ||||
\(151\) | −1.00000 | + | 1.00000i | −0.0813788 | + | 0.0813788i | −0.746625 | − | 0.665246i | \(-0.768327\pi\) |
0.665246 | + | 0.746625i | \(0.268327\pi\) | |||||||
\(152\) | −3.67423 | − | 2.12132i | −0.298020 | − | 0.172062i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.46410 | − | 1.46410i | −0.440310 | − | 0.117981i | ||||
\(155\) | 14.1421 | 1.13592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −9.65926 | − | 2.58819i | −0.768449 | − | 0.205905i | ||||
\(159\) | 8.89898 | + | 4.09978i | 0.705735 | + | 0.325133i | ||||
\(160\) | 8.66025 | + | 5.00000i | 0.684653 | + | 0.395285i | ||||
\(161\) | −8.48528 | + | 8.48528i | −0.668734 | + | 0.668734i | ||||
\(162\) | −3.65237 | + | 8.22558i | −0.286957 | + | 0.646263i | ||||
\(163\) | −0.366025 | − | 1.36603i | −0.0286693 | − | 0.106995i | 0.950109 | − | 0.311919i | \(-0.100972\pi\) |
−0.978778 | + | 0.204924i | \(0.934305\pi\) | |||||||
\(164\) | 1.41421 | + | 1.41421i | 0.110432 | + | 0.110432i | ||||
\(165\) | 13.7980 | − | 1.27135i | 1.07417 | − | 0.0989744i | ||||
\(166\) | 6.92820 | − | 4.00000i | 0.537733 | − | 0.310460i | ||||
\(167\) | 1.03528 | − | 3.86370i | 0.0801121 | − | 0.298982i | −0.914232 | − | 0.405192i | \(-0.867205\pi\) |
0.994344 | + | 0.106209i | \(0.0338714\pi\) | |||||||
\(168\) | −4.24264 | − | 6.00000i | −0.327327 | − | 0.462910i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.49768 | − | 2.40130i | −0.267474 | − | 0.183632i | ||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | 4.24264 | − | 7.34847i | 0.322562 | − | 0.558694i | −0.658454 | − | 0.752621i | \(-0.728789\pi\) |
0.981016 | + | 0.193927i | \(0.0621226\pi\) | |||||||
\(174\) | −0.828427 | + | 4.82843i | −0.0628029 | + | 0.366042i | ||||
\(175\) | 1.36603 | − | 0.366025i | 0.103262 | − | 0.0276689i | ||||
\(176\) | −3.86370 | + | 1.03528i | −0.291238 | + | 0.0780369i | ||||
\(177\) | 1.17157 | − | 6.82843i | 0.0880608 | − | 0.513256i | ||||
\(178\) | −7.00000 | + | 12.1244i | −0.524672 | + | 0.908759i | ||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 4.94646 | + | 3.39595i | 0.368688 | + | 0.253119i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | − | 11.3137i | −0.591377 | − | 0.836333i | ||||
\(184\) | −6.58846 | + | 24.5885i | −0.485708 | + | 1.81269i | ||||
\(185\) | 2.44949 | − | 1.41421i | 0.180090 | − | 0.103975i | ||||
\(186\) | −12.1958 | + | 1.12372i | −0.894239 | + | 0.0823955i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.03528 | − | 3.86370i | −0.0755053 | − | 0.281790i | ||||
\(189\) | −3.76198 | − | 6.31249i | −0.273644 | − | 0.459166i | ||||
\(190\) | 2.00000 | − | 2.00000i | 0.145095 | − | 0.145095i | ||||
\(191\) | −2.44949 | − | 1.41421i | −0.177239 | − | 0.102329i | 0.408756 | − | 0.912644i | \(-0.365963\pi\) |
−0.585995 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(192\) | −11.0119 | − | 5.07321i | −0.794717 | − | 0.366128i | ||||
\(193\) | 25.9545 | + | 6.95448i | 1.86824 | + | 0.500595i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
0.868255 | + | 0.496119i | \(0.165242\pi\) | |||||||
\(194\) | 9.89949 | 0.710742 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | 21.2504 | + | 5.69402i | 1.51403 | + | 0.405682i | 0.917770 | − | 0.397112i | \(-0.129988\pi\) |
0.596256 | + | 0.802794i | \(0.296654\pi\) | |||||||
\(198\) | −11.7980 | + | 2.19275i | −0.838444 | + | 0.155832i | ||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 2.12132 | − | 2.12132i | 0.150000 | − | 0.150000i | ||||
\(201\) | 9.41832 | + | 7.82913i | 0.664317 | + | 0.552224i | ||||
\(202\) | 2.19615 | + | 8.19615i | 0.154521 | + | 0.576679i | ||||
\(203\) | −2.82843 | − | 2.82843i | −0.198517 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.46410 | + | 2.00000i | −0.241943 | + | 0.139686i | ||||
\(206\) | 1.55291 | − | 5.79555i | 0.108197 | − | 0.403795i | ||||
\(207\) | −8.48528 | + | 24.0000i | −0.589768 | + | 1.66812i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.65685i | − | 0.391293i | ||||||
\(210\) | 4.59575 | − | 1.69677i | 0.317137 | − | 0.117089i | ||||
\(211\) | −7.00000 | − | 12.1244i | −0.481900 | − | 0.834675i | 0.517884 | − | 0.855451i | \(-0.326720\pi\) |
−0.999784 | + | 0.0207756i | \(0.993386\pi\) | |||||||
\(212\) | −2.82843 | + | 4.89898i | −0.194257 | + | 0.336463i | ||||
\(213\) | 6.82843 | + | 1.17157i | 0.467876 | + | 0.0802749i | ||||
\(214\) | −5.46410 | + | 1.46410i | −0.373518 | + | 0.100084i | ||||
\(215\) | −11.5911 | + | 3.10583i | −0.790507 | + | 0.211816i | ||||
\(216\) | −13.6066 | − | 7.60660i | −0.925812 | − | 0.517564i | ||||
\(217\) | 5.00000 | − | 8.66025i | 0.339422 | − | 0.587896i | ||||
\(218\) | −0.707107 | − | 1.22474i | −0.0478913 | − | 0.0829502i | ||||
\(219\) | −0.848387 | − | 2.29788i | −0.0573287 | − | 0.155276i | ||||
\(220\) | 8.00000i | 0.539360i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.00000 | + | 1.41421i | −0.134231 | + | 0.0949158i | ||||
\(223\) | 4.02628 | − | 15.0263i | 0.269620 | − | 1.00623i | −0.689742 | − | 0.724055i | \(-0.742276\pi\) |
0.959362 | − | 0.282179i | \(-0.0910572\pi\) | |||||||
\(224\) | 6.12372 | − | 3.53553i | 0.409159 | − | 0.236228i | ||||
\(225\) | 2.28024 | − | 1.94949i | 0.152016 | − | 0.129966i | ||||
\(226\) | 10.0000 | + | 10.0000i | 0.665190 | + | 0.665190i | ||||
\(227\) | 2.07055 | + | 7.72741i | 0.137427 | + | 0.512886i | 0.999976 | + | 0.00691198i | \(0.00220017\pi\) |
−0.862549 | + | 0.505974i | \(0.831133\pi\) | |||||||
\(228\) | 1.56583 | − | 1.88366i | 0.103699 | − | 0.124749i | ||||
\(229\) | −1.00000 | + | 1.00000i | −0.0660819 | + | 0.0660819i | −0.739375 | − | 0.673293i | \(-0.764879\pi\) |
0.673293 | + | 0.739375i | \(0.264879\pi\) | |||||||
\(230\) | −14.6969 | − | 8.48528i | −0.969087 | − | 0.559503i | ||||
\(231\) | 4.09978 | − | 8.89898i | 0.269745 | − | 0.585510i | ||||
\(232\) | −8.19615 | − | 2.19615i | −0.538104 | − | 0.144184i | ||||
\(233\) | −25.4558 | −1.66767 | −0.833834 | − | 0.552015i | \(-0.813859\pi\) | ||||
−0.833834 | + | 0.552015i | \(0.813859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 3.86370 | + | 1.03528i | 0.251506 | + | 0.0673907i | ||||
\(237\) | 7.24745 | − | 15.7313i | 0.470772 | − | 1.02186i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1421 | − | 14.1421i | 0.914779 | − | 0.914779i | −0.0818647 | − | 0.996643i | \(-0.526088\pi\) |
0.996643 | + | 0.0818647i | \(0.0260876\pi\) | |||||||
\(240\) | 2.21441 | − | 2.66390i | 0.142940 | − | 0.171954i | ||||
\(241\) | 6.22243 | + | 23.2224i | 0.400822 | + | 1.49589i | 0.811633 | + | 0.584168i | \(0.198579\pi\) |
−0.410811 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(242\) | −3.53553 | − | 3.53553i | −0.227273 | − | 0.227273i | ||||
\(243\) | −12.9722 | − | 8.64420i | −0.832167 | − | 0.554526i | ||||
\(244\) | 6.92820 | − | 4.00000i | 0.443533 | − | 0.256074i | ||||
\(245\) | 2.58819 | − | 9.65926i | 0.165353 | − | 0.617107i | ||||
\(246\) | 2.82843 | − | 2.00000i | 0.180334 | − | 0.127515i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 21.2132i | − | 1.34704i | ||||||
\(249\) | 4.79920 | + | 12.9988i | 0.304137 | + | 0.823763i | ||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | −12.7279 | + | 22.0454i | −0.803379 | + | 1.39149i | 0.114000 | + | 0.993481i | \(0.463633\pi\) |
−0.917380 | + | 0.398013i | \(0.869700\pi\) | |||||||
\(252\) | 3.82843 | − | 1.82843i | 0.241168 | − | 0.115180i | ||||
\(253\) | −32.7846 | + | 8.78461i | −2.06115 | + | 0.552284i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | −4.24264 | − | 7.34847i | −0.264649 | − | 0.458385i | 0.702823 | − | 0.711365i | \(-0.251923\pi\) |
−0.967472 | + | 0.252980i | \(0.918589\pi\) | |||||||
\(258\) | 9.74907 | − | 3.59940i | 0.606950 | − | 0.224089i | ||||
\(259\) | − | 2.00000i | − | 0.124274i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.00000 | − | 2.82843i | −0.495188 | − | 0.175075i | ||||
\(262\) | −2.92820 | + | 10.9282i | −0.180905 | + | 0.675147i | ||||
\(263\) | −19.5959 | + | 11.3137i | −1.20834 | + | 0.697633i | −0.962396 | − | 0.271652i | \(-0.912430\pi\) |
−0.245940 | + | 0.969285i | \(0.579097\pi\) | |||||||
\(264\) | −1.90702 | − | 20.6969i | −0.117369 | − | 1.27381i | ||||
\(265\) | −8.00000 | − | 8.00000i | −0.491436 | − | 0.491436i | ||||
\(266\) | −0.517638 | − | 1.93185i | −0.0317384 | − | 0.118449i | ||||
\(267\) | −18.6473 | − | 15.5009i | −1.14120 | − | 0.948639i | ||||
\(268\) | −5.00000 | + | 5.00000i | −0.305424 | + | 0.305424i | ||||
\(269\) | −17.1464 | − | 9.89949i | −1.04544 | − | 0.603583i | −0.124068 | − | 0.992274i | \(-0.539594\pi\) |
−0.921368 | + | 0.388691i | \(0.872927\pi\) | |||||||
\(270\) | 7.24604 | − | 7.44949i | 0.440980 | − | 0.453362i | ||||
\(271\) | 25.9545 | + | 6.95448i | 1.57662 | + | 0.422455i | 0.937878 | − | 0.346964i | \(-0.112788\pi\) |
0.638744 | + | 0.769419i | \(0.279454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | 0.845771 | ||||||||
\(275\) | 3.86370 | + | 1.03528i | 0.232990 | + | 0.0624295i | ||||
\(276\) | −13.3485 | − | 6.14966i | −0.803483 | − | 0.370166i | ||||
\(277\) | 10.3923 | + | 6.00000i | 0.624413 | + | 0.360505i | 0.778585 | − | 0.627539i | \(-0.215938\pi\) |
−0.154172 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(278\) | 2.82843 | − | 2.82843i | 0.169638 | − | 0.169638i | ||||
\(279\) | 1.65375 | − | 21.1486i | 0.0990072 | − | 1.26614i | ||||
\(280\) | 2.19615 | + | 8.19615i | 0.131245 | + | 0.489814i | ||||
\(281\) | −9.89949 | − | 9.89949i | −0.590554 | − | 0.590554i | 0.347227 | − | 0.937781i | \(-0.387123\pi\) |
−0.937781 | + | 0.347227i | \(0.887123\pi\) | |||||||
\(282\) | −6.89898 | + | 0.635674i | −0.410828 | + | 0.0378539i | ||||
\(283\) | 10.3923 | − | 6.00000i | 0.617758 | − | 0.356663i | −0.158237 | − | 0.987401i | \(-0.550581\pi\) |
0.775996 | + | 0.630738i | \(0.217248\pi\) | |||||||
\(284\) | −1.03528 | + | 3.86370i | −0.0614323 | + | 0.229269i | ||||
\(285\) | 2.82843 | + | 4.00000i | 0.167542 | + | 0.236940i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.82843i | 0.166957i | ||||||||
\(288\) | 8.48988 | − | 12.3662i | 0.500271 | − | 0.728683i | ||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 2.82843 | − | 4.89898i | 0.166091 | − | 0.287678i | ||||
\(291\) | −2.89949 | + | 16.8995i | −0.169971 | + | 0.990666i | ||||
\(292\) | 1.36603 | − | 0.366025i | 0.0799406 | − | 0.0214200i | ||||
\(293\) | 13.5230 | − | 3.62347i | 0.790020 | − | 0.211685i | 0.158822 | − | 0.987307i | \(-0.449230\pi\) |
0.631198 | + | 0.775622i | \(0.282564\pi\) | |||||||
\(294\) | −1.46447 | + | 8.53553i | −0.0854094 | + | 0.497802i | ||||
\(295\) | −4.00000 | + | 6.92820i | −0.232889 | + | 0.403376i | ||||
\(296\) | −2.12132 | − | 3.67423i | −0.123299 | − | 0.213561i | ||||
\(297\) | −0.287721 | − | 20.7826i | −0.0166952 | − | 1.20593i | ||||
\(298\) | 2.00000i | 0.115857i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | + | 1.41421i | 0.0577350 | + | 0.0816497i | ||||
\(301\) | −2.19615 | + | 8.19615i | −0.126584 | + | 0.472418i | ||||
\(302\) | −1.22474 | + | 0.707107i | −0.0704761 | + | 0.0406894i | ||||
\(303\) | −14.6349 | + | 1.34847i | −0.840756 | + | 0.0774675i | ||||
\(304\) | −1.00000 | − | 1.00000i | −0.0573539 | − | 0.0573539i | ||||
\(305\) | 4.14110 | + | 15.4548i | 0.237119 | + | 0.884940i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.0000 | − | 17.0000i | 0.970241 | − | 0.970241i | −0.0293286 | − | 0.999570i | \(-0.509337\pi\) |
0.999570 | + | 0.0293286i | \(0.00933691\pi\) | |||||||
\(308\) | 4.89898 | + | 2.82843i | 0.279145 | + | 0.161165i | ||||
\(309\) | 9.43879 | + | 4.34847i | 0.536954 | + | 0.247376i | ||||
\(310\) | 13.6603 | + | 3.66025i | 0.775850 | + | 0.207888i | ||||
\(311\) | 8.48528 | 0.481156 | 0.240578 | − | 0.970630i | \(-0.422663\pi\) | ||||
0.240578 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000 | 0.452187 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(314\) | 13.5230 | + | 3.62347i | 0.763145 | + | 0.204484i | ||||
\(315\) | 1.55051 | + | 8.34242i | 0.0873614 | + | 0.470042i | ||||
\(316\) | 8.66025 | + | 5.00000i | 0.487177 | + | 0.281272i | ||||
\(317\) | −7.07107 | + | 7.07107i | −0.397151 | + | 0.397151i | −0.877227 | − | 0.480076i | \(-0.840609\pi\) |
0.480076 | + | 0.877227i | \(0.340609\pi\) | |||||||
\(318\) | 7.53465 | + | 6.26330i | 0.422522 | + | 0.351229i | ||||
\(319\) | −2.92820 | − | 10.9282i | −0.163948 | − | 0.611862i | ||||
\(320\) | 9.89949 | + | 9.89949i | 0.553399 | + | 0.553399i | ||||
\(321\) | −0.898979 | − | 9.75663i | −0.0501761 | − | 0.544562i | ||||
\(322\) | −10.3923 | + | 6.00000i | −0.579141 | + | 0.334367i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.65685 | − | 7.00000i | 0.314270 | − | 0.388889i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.41421i | − | 0.0783260i | ||||||
\(327\) | 2.29788 | − | 0.848387i | 0.127073 | − | 0.0469159i | ||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | 2.82843 | − | 4.89898i | 0.155936 | − | 0.270089i | ||||
\(330\) | 13.6569 | + | 2.34315i | 0.751785 | + | 0.128986i | ||||
\(331\) | 9.56218 | − | 2.56218i | 0.525585 | − | 0.140830i | 0.0137361 | − | 0.999906i | \(-0.495628\pi\) |
0.511849 | + | 0.859076i | \(0.328961\pi\) | |||||||
\(332\) | −7.72741 | + | 2.07055i | −0.424097 | + | 0.113636i | ||||
\(333\) | −1.82843 | − | 3.82843i | −0.100197 | − | 0.209797i | ||||
\(334\) | 2.00000 | − | 3.46410i | 0.109435 | − | 0.189547i | ||||
\(335\) | −7.07107 | − | 12.2474i | −0.386334 | − | 0.669150i | ||||
\(336\) | −0.848387 | − | 2.29788i | −0.0462833 | − | 0.125359i | ||||
\(337\) | − | 6.00000i | − | 0.326841i | −0.986557 | − | 0.163420i | \(-0.947747\pi\) | ||
0.986557 | − | 0.163420i | \(-0.0522527\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.0000 | + | 14.1421i | −1.08625 | + | 0.768095i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.4949 | − | 14.1421i | 1.32647 | − | 0.765840i | ||||
\(342\) | −2.75699 | − | 3.22474i | −0.149081 | − | 0.174374i | ||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 4.65874 | + | 17.3867i | 0.251183 | + | 0.937426i | ||||
\(345\) | 18.7899 | − | 22.6040i | 1.01162 | − | 1.21696i | ||||
\(346\) | 6.00000 | − | 6.00000i | 0.322562 | − | 0.322562i | ||||
\(347\) | 12.2474 | + | 7.07107i | 0.657477 | + | 0.379595i | 0.791315 | − | 0.611408i | \(-0.209397\pi\) |
−0.133838 | + | 0.991003i | \(0.542730\pi\) | |||||||
\(348\) | 2.04989 | − | 4.44949i | 0.109886 | − | 0.238518i | ||||
\(349\) | −23.2224 | − | 6.22243i | −1.24307 | − | 0.333079i | −0.423413 | − | 0.905937i | \(-0.639168\pi\) |
−0.819655 | + | 0.572857i | \(0.805835\pi\) | |||||||
\(350\) | 1.41421 | 0.0755929 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.0000 | 1.06600 | ||||||||
\(353\) | −25.1141 | − | 6.72930i | −1.33669 | − | 0.358164i | −0.481483 | − | 0.876455i | \(-0.659902\pi\) |
−0.855204 | + | 0.518291i | \(0.826568\pi\) | |||||||
\(354\) | 2.89898 | − | 6.29253i | 0.154079 | − | 0.334444i | ||||
\(355\) | −6.92820 | − | 4.00000i | −0.367711 | − | 0.212298i | ||||
\(356\) | 9.89949 | − | 9.89949i | 0.524672 | − | 0.524672i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.82843 | + | 2.82843i | 0.149279 | + | 0.149279i | 0.777796 | − | 0.628517i | \(-0.216338\pi\) |
−0.628517 | + | 0.777796i | \(0.716338\pi\) | |||||||
\(360\) | 11.6969 | + | 13.6814i | 0.616483 | + | 0.721075i | ||||
\(361\) | −14.7224 | + | 8.50000i | −0.774865 | + | 0.447368i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.07107 | − | 5.00000i | 0.371135 | − | 0.262432i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.82843i | 0.148047i | ||||||||
\(366\) | −4.79920 | − | 12.9988i | −0.250858 | − | 0.679456i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | −4.24264 | + | 7.34847i | −0.221163 | + | 0.383065i | ||||
\(369\) | 2.58579 | + | 5.41421i | 0.134611 | + | 0.281853i | ||||
\(370\) | 2.73205 | − | 0.732051i | 0.142033 | − | 0.0380575i | ||||
\(371\) | −7.72741 | + | 2.07055i | −0.401187 | + | 0.107498i | ||||
\(372\) | 12.0711 | + | 2.07107i | 0.625856 | + | 0.107380i | ||||
\(373\) | 2.00000 | − | 3.46410i | 0.103556 | − | 0.179364i | −0.809591 | − | 0.586994i | \(-0.800311\pi\) |
0.913147 | + | 0.407630i | \(0.133645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.4981 | + | 7.19881i | −1.00688 | + | 0.371745i | ||||
\(376\) | − | 12.0000i | − | 0.618853i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | − | 7.07107i | −0.102869 | − | 0.363696i | ||||
\(379\) | −6.95448 | + | 25.9545i | −0.357228 | + | 1.33319i | 0.520430 | + | 0.853904i | \(0.325772\pi\) |
−0.877658 | + | 0.479288i | \(0.840895\pi\) | |||||||
\(380\) | −2.44949 | + | 1.41421i | −0.125656 | + | 0.0725476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.00000 | − | 2.00000i | −0.102329 | − | 0.102329i | ||||
\(383\) | −4.14110 | − | 15.4548i | −0.211601 | − | 0.789704i | −0.987336 | − | 0.158645i | \(-0.949287\pi\) |
0.775735 | − | 0.631059i | \(-0.217379\pi\) | |||||||
\(384\) | 3.99585 | + | 3.32162i | 0.203913 | + | 0.169506i | ||||
\(385\) | −8.00000 | + | 8.00000i | −0.407718 | + | 0.407718i | ||||
\(386\) | 23.2702 | + | 13.4350i | 1.18442 | + | 0.683825i | ||||
\(387\) | 3.28913 | + | 17.6969i | 0.167196 | + | 0.899586i | ||||
\(388\) | −9.56218 | − | 2.56218i | −0.485446 | − | 0.130075i | ||||
\(389\) | 16.9706 | 0.860442 | 0.430221 | − | 0.902724i | \(-0.358436\pi\) | ||||
0.430221 | + | 0.902724i | \(0.358436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −14.4889 | − | 3.88229i | −0.731799 | − | 0.196085i | ||||
\(393\) | −17.7980 | − | 8.19955i | −0.897788 | − | 0.413613i | ||||
\(394\) | 19.0526 | + | 11.0000i | 0.959854 | + | 0.554172i | ||||
\(395\) | −14.1421 | + | 14.1421i | −0.711568 | + | 0.711568i | ||||
\(396\) | 11.9635 | + | 0.935500i | 0.601187 | + | 0.0470106i | ||||
\(397\) | 6.22243 | + | 23.2224i | 0.312295 | + | 1.16550i | 0.926482 | + | 0.376340i | \(0.122817\pi\) |
−0.614187 | + | 0.789161i | \(0.710516\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.44949 | − | 0.317837i | 0.172690 | − | 0.0159118i | ||||
\(400\) | 0.866025 | − | 0.500000i | 0.0433013 | − | 0.0250000i | ||||
\(401\) | 5.69402 | − | 21.2504i | 0.284346 | − | 1.06119i | −0.664970 | − | 0.746870i | \(-0.731556\pi\) |
0.949316 | − | 0.314323i | \(-0.101777\pi\) | |||||||
\(402\) | 7.07107 | + | 10.0000i | 0.352673 | + | 0.498755i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 8.48528i | − | 0.422159i | ||||||
\(405\) | 10.5948 | + | 14.5517i | 0.526458 | + | 0.723078i | ||||
\(406\) | −2.00000 | − | 3.46410i | −0.0992583 | − | 0.171920i | ||||
\(407\) | 2.82843 | − | 4.89898i | 0.140200 | − | 0.242833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4186 | + | 8.41858i | −1.55355 | + | 0.416272i | −0.930614 | − | 0.366002i | \(-0.880726\pi\) |
−0.622935 | + | 0.782274i | \(0.714060\pi\) | |||||||
\(410\) | −3.86370 | + | 1.03528i | −0.190815 | + | 0.0511286i | ||||
\(411\) | −4.10051 | + | 23.8995i | −0.202263 | + | 1.17888i | ||||
\(412\) | −3.00000 | + | 5.19615i | −0.147799 | + | 0.255996i | ||||
\(413\) | 2.82843 | + | 4.89898i | 0.139178 | + | 0.241063i | ||||
\(414\) | −14.4078 | + | 20.9861i | −0.708105 | + | 1.03141i | ||||
\(415\) | − | 16.0000i | − | 0.785409i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | + | 5.65685i | 0.195881 | + | 0.277017i | ||||
\(418\) | 1.46410 | − | 5.46410i | 0.0716116 | − | 0.267258i | ||||
\(419\) | 9.79796 | − | 5.65685i | 0.478662 | − | 0.276355i | −0.241197 | − | 0.970476i | \(-0.577540\pi\) |
0.719859 | + | 0.694121i | \(0.244207\pi\) | |||||||
\(420\) | −4.87832 | + | 0.449490i | −0.238037 | + | 0.0219329i | ||||
\(421\) | −25.0000 | − | 25.0000i | −1.21843 | − | 1.21843i | −0.968183 | − | 0.250242i | \(-0.919490\pi\) |
−0.250242 | − | 0.968183i | \(-0.580510\pi\) | |||||||
\(422\) | −3.62347 | − | 13.5230i | −0.176388 | − | 0.658287i | ||||
\(423\) | 0.935500 | − | 11.9635i | 0.0454856 | − | 0.581684i | ||||
\(424\) | −12.0000 | + | 12.0000i | −0.582772 | + | 0.582772i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.29253 | + | 2.89898i | 0.304874 | + | 0.140456i | ||||
\(427\) | 10.9282 | + | 2.92820i | 0.528853 | + | 0.141706i | ||||
\(428\) | 5.65685 | 0.273434 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | −0.578691 | ||||||||
\(431\) | −30.9096 | − | 8.28221i | −1.48886 | − | 0.398940i | −0.579511 | − | 0.814964i | \(-0.696756\pi\) |
−0.909353 | + | 0.416024i | \(0.863423\pi\) | |||||||
\(432\) | −3.72474 | − | 3.62302i | −0.179207 | − | 0.174313i | ||||
\(433\) | −15.5885 | − | 9.00000i | −0.749133 | − | 0.432512i | 0.0762473 | − | 0.997089i | \(-0.475706\pi\) |
−0.825381 | + | 0.564577i | \(0.809039\pi\) | |||||||
\(434\) | 7.07107 | − | 7.07107i | 0.339422 | − | 0.339422i | ||||
\(435\) | 7.53465 | + | 6.26330i | 0.361259 | + | 0.300302i | ||||
\(436\) | 0.366025 | + | 1.36603i | 0.0175294 | + | 0.0654208i | ||||
\(437\) | −8.48528 | − | 8.48528i | −0.405906 | − | 0.405906i | ||||
\(438\) | −0.224745 | − | 2.43916i | −0.0107387 | − | 0.116547i | ||||
\(439\) | −25.9808 | + | 15.0000i | −1.23999 | + | 0.715911i | −0.969093 | − | 0.246696i | \(-0.920655\pi\) |
−0.270901 | + | 0.962607i | \(0.587322\pi\) | |||||||
\(440\) | −6.21166 | + | 23.1822i | −0.296129 | + | 1.10517i | ||||
\(441\) | −14.1421 | − | 5.00000i | −0.673435 | − | 0.238095i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.2843i | 1.34383i | 0.740630 | + | 0.671913i | \(0.234527\pi\) | ||||
−0.740630 | + | 0.671913i | \(0.765473\pi\) | |||||||
\(444\) | 2.29788 | − | 0.848387i | 0.109052 | − | 0.0402627i | ||||
\(445\) | 14.0000 | + | 24.2487i | 0.663664 | + | 1.14950i | ||||
\(446\) | 7.77817 | − | 13.4722i | 0.368307 | − | 0.637927i | ||||
\(447\) | −3.41421 | − | 0.585786i | −0.161487 | − | 0.0277067i | ||||
\(448\) | 9.56218 | − | 2.56218i | 0.451770 | − | 0.121052i | ||||
\(449\) | −21.2504 | + | 5.69402i | −1.00287 | + | 0.268717i | −0.722646 | − | 0.691218i | \(-0.757074\pi\) |
−0.280221 | + | 0.959936i | \(0.590408\pi\) | |||||||
\(450\) | 2.70711 | − | 1.29289i | 0.127614 | − | 0.0609476i | ||||
\(451\) | −4.00000 | + | 6.92820i | −0.188353 | + | 0.326236i | ||||
\(452\) | −7.07107 | − | 12.2474i | −0.332595 | − | 0.576072i | ||||
\(453\) | −0.848387 | − | 2.29788i | −0.0398607 | − | 0.107964i | ||||
\(454\) | 8.00000i | 0.375459i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | − | 4.24264i | 0.280976 | − | 0.198680i | ||||
\(457\) | 10.6147 | − | 39.6147i | 0.496536 | − | 1.85310i | −0.0247126 | − | 0.999695i | \(-0.507867\pi\) |
0.521249 | − | 0.853405i | \(-0.325466\pi\) | |||||||
\(458\) | −1.22474 | + | 0.707107i | −0.0572286 | + | 0.0330409i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | + | 12.0000i | 0.559503 | + | 0.559503i | ||||
\(461\) | −2.58819 | − | 9.65926i | −0.120544 | − | 0.449877i | 0.879098 | − | 0.476642i | \(-0.158146\pi\) |
−0.999642 | + | 0.0267651i | \(0.991479\pi\) | |||||||
\(462\) | 6.26330 | − | 7.53465i | 0.291395 | − | 0.350544i | ||||
\(463\) | 17.0000 | − | 17.0000i | 0.790057 | − | 0.790057i | −0.191446 | − | 0.981503i | \(-0.561318\pi\) |
0.981503 | + | 0.191446i | \(0.0613177\pi\) | |||||||
\(464\) | −2.44949 | − | 1.41421i | −0.113715 | − | 0.0656532i | ||||
\(465\) | −10.2494 | + | 22.2474i | −0.475306 | + | 1.03170i | ||||
\(466\) | −24.5885 | − | 6.58846i | −1.13904 | − | 0.305204i | ||||
\(467\) | −25.4558 | −1.17796 | −0.588978 | − | 0.808149i | \(-0.700470\pi\) | ||||
−0.588978 | + | 0.808149i | \(0.700470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | 7.72741 | + | 2.07055i | 0.356439 | + | 0.0955075i | ||||
\(471\) | −10.1464 | + | 22.0239i | −0.467523 | + | 1.01481i | ||||
\(472\) | 10.3923 | + | 6.00000i | 0.478345 | + | 0.276172i | ||||
\(473\) | −16.9706 | + | 16.9706i | −0.780307 | + | 0.780307i | ||||
\(474\) | 11.0721 | − | 13.3195i | 0.508557 | − | 0.611785i | ||||
\(475\) | 0.366025 | + | 1.36603i | 0.0167944 | + | 0.0626775i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8990 | + | 11.0280i | −0.590604 | + | 0.504936i | ||||
\(478\) | 17.3205 | − | 10.0000i | 0.792222 | − | 0.457389i | ||||
\(479\) | −8.28221 | + | 30.9096i | −0.378424 | + | 1.41230i | 0.469853 | + | 0.882744i | \(0.344307\pi\) |
−0.848277 | + | 0.529552i | \(0.822360\pi\) | |||||||
\(480\) | −14.1421 | + | 10.0000i | −0.645497 | + | 0.456435i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.0416i | 1.09507i | ||||||||
\(483\) | −7.19881 | − | 19.4981i | −0.327557 | − | 0.887196i | ||||
\(484\) | 2.50000 | + | 4.33013i | 0.113636 | + | 0.196824i | ||||
\(485\) | 9.89949 | − | 17.1464i | 0.449513 | − | 0.778579i | ||||
\(486\) | −10.2929 | − | 11.7071i | −0.466895 | − | 0.531045i | ||||
\(487\) | 25.9545 | − | 6.95448i | 1.17611 | − | 0.315138i | 0.382727 | − | 0.923861i | \(-0.374985\pi\) |
0.793382 | + | 0.608724i | \(0.208318\pi\) | |||||||
\(488\) | 23.1822 | − | 6.21166i | 1.04941 | − | 0.281189i | ||||
\(489\) | 2.41421 | + | 0.414214i | 0.109175 | + | 0.0187314i | ||||
\(490\) | 5.00000 | − | 8.66025i | 0.225877 | − | 0.391230i | ||||
\(491\) | 21.2132 | + | 36.7423i | 0.957338 | + | 1.65816i | 0.728924 | + | 0.684595i | \(0.240021\pi\) |
0.228415 | + | 0.973564i | \(0.426646\pi\) | |||||||
\(492\) | −3.24969 | + | 1.19980i | −0.146507 | + | 0.0540912i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00000 | + | 22.6274i | −0.359573 | + | 1.01703i | ||||
\(496\) | 1.83013 | − | 6.83013i | 0.0821751 | − | 0.306682i | ||||
\(497\) | −4.89898 | + | 2.82843i | −0.219749 | + | 0.126872i | ||||
\(498\) | 1.27135 | + | 13.7980i | 0.0569705 | + | 0.618301i | ||||
\(499\) | 23.0000 | + | 23.0000i | 1.02962 | + | 1.02962i | 0.999548 | + | 0.0300737i | \(0.00957421\pi\) |
0.0300737 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(500\) | −3.10583 | − | 11.5911i | −0.138897 | − | 0.518370i | ||||
\(501\) | 5.32780 | + | 4.42883i | 0.238029 | + | 0.197865i | ||||
\(502\) | −18.0000 | + | 18.0000i | −0.803379 | + | 0.803379i | ||||
\(503\) | 4.89898 | + | 2.82843i | 0.218435 | + | 0.126113i | 0.605225 | − | 0.796054i | \(-0.293083\pi\) |
−0.386791 | + | 0.922168i | \(0.626416\pi\) | |||||||
\(504\) | 12.5136 | − | 2.32577i | 0.557401 | − | 0.103598i | ||||
\(505\) | 16.3923 | + | 4.39230i | 0.729448 | + | 0.195455i | ||||
\(506\) | −33.9411 | −1.50887 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.8415 | + | 8.79985i | 1.45567 | + | 0.390046i | 0.897993 | − | 0.440010i | \(-0.145025\pi\) |
0.557680 | + | 0.830056i | \(0.311692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.73205 | + | 1.00000i | 0.0766214 | + | 0.0442374i | ||||
\(512\) | 7.77817 | − | 7.77817i | 0.343750 | − | 0.343750i | ||||
\(513\) | 6.31249 | − | 3.76198i | 0.278703 | − | 0.166095i | ||||
\(514\) | −2.19615 | − | 8.19615i | −0.0968681 | − | 0.361517i | ||||
\(515\) | −8.48528 | − | 8.48528i | −0.373906 | − | 0.373906i | ||||
\(516\) | −10.3485 | + | 0.953512i | −0.455566 | + | 0.0419760i | ||||
\(517\) | 13.8564 | − | 8.00000i | 0.609404 | − | 0.351840i | ||||
\(518\) | 0.517638 | − | 1.93185i | 0.0227437 | − | 0.0848807i | ||||
\(519\) | 8.48528 | + | 12.0000i | 0.372463 | + | 0.526742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.1127i | − | 1.36307i | −0.731785 | − | 0.681536i | \(-0.761312\pi\) | ||
0.731785 | − | 0.681536i | \(-0.238688\pi\) | |||||||
\(522\) | −6.99536 | − | 4.80260i | −0.306178 | − | 0.210204i | ||||
\(523\) | −10.0000 | − | 17.3205i | −0.437269 | − | 0.757373i | 0.560208 | − | 0.828352i | \(-0.310721\pi\) |
−0.997478 | + | 0.0709788i | \(0.977388\pi\) | |||||||
\(524\) | 5.65685 | − | 9.79796i | 0.247121 | − | 0.428026i | ||||
\(525\) | −0.414214 | + | 2.41421i | −0.0180778 | + | 0.105365i | ||||
\(526\) | −21.8564 | + | 5.85641i | −0.952985 | + | 0.255351i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.17157 | − | 6.82843i | 0.0509862 | − | 0.297169i | ||||
\(529\) | −24.5000 | + | 42.4352i | −1.06522 | + | 1.84501i | ||||
\(530\) | −5.65685 | − | 9.79796i | −0.245718 | − | 0.425596i | ||||
\(531\) | 9.89293 | + | 6.79191i | 0.429316 | + | 0.294744i | ||||
\(532\) | 2.00000i | 0.0867110i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −14.0000 | − | 19.7990i | −0.605839 | − | 0.856786i | ||||
\(535\) | −2.92820 | + | 10.9282i | −0.126597 | + | 0.472467i | ||||
\(536\) | −18.3712 | + | 10.6066i | −0.793514 | + | 0.458135i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.0000 | − | 14.0000i | −0.603583 | − | 0.603583i | ||||
\(539\) | −5.17638 | − | 19.3185i | −0.222963 | − | 0.832107i | ||||
\(540\) | −8.92721 | + | 5.32024i | −0.384166 | + | 0.228947i | ||||
\(541\) | −1.00000 | + | 1.00000i | −0.0429934 | + | 0.0429934i | −0.728277 | − | 0.685283i | \(-0.759678\pi\) |
0.685283 | + | 0.728277i | \(0.259678\pi\) | |||||||
\(542\) | 23.2702 | + | 13.4350i | 0.999539 | + | 0.577084i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.82843 | −0.121157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −13.5230 | − | 3.62347i | −0.577672 | − | 0.154787i | ||||
\(549\) | 23.5959 | − | 4.38551i | 1.00705 | − | 0.187169i | ||||
\(550\) | 3.46410 | + | 2.00000i | 0.147710 | + | 0.0852803i | ||||
\(551\) | 2.82843 | − | 2.82843i | 0.120495 | − | 0.120495i | ||||
\(552\) | −33.9059 | − | 28.1849i | −1.44313 | − | 1.19963i | ||||
\(553\) | 3.66025 | + | 13.6603i | 0.155650 | + | 0.580893i | ||||
\(554\) | 8.48528 | + | 8.48528i | 0.360505 | + | 0.360505i | ||||
\(555\) | 0.449490 | + | 4.87832i | 0.0190798 | + | 0.207073i | ||||
\(556\) | −3.46410 | + | 2.00000i | −0.146911 | + | 0.0848189i | ||||
\(557\) | −3.62347 | + | 13.5230i | −0.153531 | + | 0.572986i | 0.845695 | + | 0.533666i | \(0.179186\pi\) |
−0.999227 | + | 0.0393204i | \(0.987481\pi\) | |||||||
\(558\) | 7.07107 | − | 20.0000i | 0.299342 | − | 0.846668i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.82843i | 0.119523i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.00000 | − | 12.1244i | −0.295277 | − | 0.511435i | ||||
\(563\) | −16.9706 | + | 29.3939i | −0.715224 | + | 1.23880i | 0.247649 | + | 0.968850i | \(0.420342\pi\) |
−0.962873 | + | 0.269954i | \(0.912991\pi\) | |||||||
\(564\) | 6.82843 | + | 1.17157i | 0.287529 | + | 0.0493321i | ||||
\(565\) | 27.3205 | − | 7.32051i | 1.14938 | − | 0.307976i | ||||
\(566\) | 11.5911 | − | 3.10583i | 0.487211 | − | 0.130548i | ||||
\(567\) | 12.6569 | − | 1.34315i | 0.531538 | − | 0.0564068i | ||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | 4.24264 | + | 7.34847i | 0.177861 | + | 0.308064i | 0.941148 | − | 0.337996i | \(-0.109749\pi\) |
−0.763287 | + | 0.646060i | \(0.776416\pi\) | |||||||
\(570\) | 1.69677 | + | 4.59575i | 0.0710701 | + | 0.192495i | ||||
\(571\) | 12.0000i | 0.502184i | 0.967963 | + | 0.251092i | \(0.0807897\pi\) | ||||
−0.967963 | + | 0.251092i | \(0.919210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000 | − | 2.82843i | 0.167102 | − | 0.118159i | ||||
\(574\) | −0.732051 | + | 2.73205i | −0.0305552 | + | 0.114034i | ||||
\(575\) | 7.34847 | − | 4.24264i | 0.306452 | − | 0.176930i | ||||
\(576\) | 15.9617 | − | 13.6464i | 0.665070 | − | 0.568601i | ||||
\(577\) | −1.00000 | − | 1.00000i | −0.0416305 | − | 0.0416305i | 0.685985 | − | 0.727616i | \(-0.259372\pi\) |
−0.727616 | + | 0.685985i | \(0.759372\pi\) | |||||||
\(578\) | 4.39992 | + | 16.4207i | 0.183013 | + | 0.683013i | ||||
\(579\) | −29.7507 | + | 35.7896i | −1.23640 | + | 1.48737i | ||||
\(580\) | −4.00000 | + | 4.00000i | −0.166091 | + | 0.166091i | ||||
\(581\) | −9.79796 | − | 5.65685i | −0.406488 | − | 0.234686i | ||||
\(582\) | −7.17461 | + | 15.5732i | −0.297397 | + | 0.645530i | ||||
\(583\) | −21.8564 | − | 5.85641i | −0.905200 | − | 0.242548i | ||||
\(584\) | 4.24264 | 0.175562 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0000 | 0.578335 | ||||||||
\(587\) | −7.72741 | − | 2.07055i | −0.318944 | − | 0.0854608i | 0.0957952 | − | 0.995401i | \(-0.469461\pi\) |
−0.414739 | + | 0.909940i | \(0.636127\pi\) | |||||||
\(588\) | 3.62372 | − | 7.86566i | 0.149440 | − | 0.324374i | ||||
\(589\) | 8.66025 | + | 5.00000i | 0.356840 | + | 0.206021i | ||||
\(590\) | −5.65685 | + | 5.65685i | −0.232889 | + | 0.232889i | ||||
\(591\) | −24.3585 | + | 29.3029i | −1.00198 | + | 1.20536i | ||||
\(592\) | −0.366025 | − | 1.36603i | −0.0150436 | − | 0.0561433i | ||||
\(593\) | −9.89949 | − | 9.89949i | −0.406524 | − | 0.406524i | 0.474001 | − | 0.880524i | \(-0.342809\pi\) |
−0.880524 | + | 0.474001i | \(0.842809\pi\) | |||||||
\(594\) | 5.10102 | − | 20.1489i | 0.209297 | − | 0.826721i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.517638 | − | 1.93185i | 0.0212033 | − | 0.0791317i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3137i | 0.462266i | 0.972922 | + | 0.231133i | \(0.0742432\pi\) | ||||
−0.972922 | + | 0.231133i | \(0.925757\pi\) | |||||||
\(600\) | 1.79970 | + | 4.87453i | 0.0734725 | + | 0.199002i | ||||
\(601\) | −4.00000 | − | 6.92820i | −0.163163 | − | 0.282607i | 0.772838 | − | 0.634603i | \(-0.218836\pi\) |
−0.936002 | + | 0.351996i | \(0.885503\pi\) | |||||||
\(602\) | −4.24264 | + | 7.34847i | −0.172917 | + | 0.299501i | ||||
\(603\) | −19.1421 | + | 9.14214i | −0.779528 | + | 0.372297i | ||||
\(604\) | 1.36603 | − | 0.366025i | 0.0555828 | − | 0.0148934i | ||||
\(605\) | −9.65926 | + | 2.58819i | −0.392705 | + | 0.105225i | ||||
\(606\) | −14.4853 | − | 2.48528i | −0.588424 | − | 0.100958i | ||||
\(607\) | 20.0000 | − | 34.6410i | 0.811775 | − | 1.40604i | −0.0998457 | − | 0.995003i | \(-0.531835\pi\) |
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(608\) | 3.53553 | + | 6.12372i | 0.143385 | + | 0.248350i | ||||
\(609\) | 6.49938 | − | 2.39960i | 0.263368 | − | 0.0972368i | ||||
\(610\) | 16.0000i | 0.647821i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.366025 | + | 1.36603i | −0.0147836 | + | 0.0551732i | −0.972924 | − | 0.231127i | \(-0.925759\pi\) |
0.958140 | + | 0.286300i | \(0.0924254\pi\) | |||||||
\(614\) | 20.8207 | − | 12.0208i | 0.840254 | − | 0.485121i | ||||
\(615\) | −0.635674 | − | 6.89898i | −0.0256329 | − | 0.278194i | ||||
\(616\) | 12.0000 | + | 12.0000i | 0.483494 | + | 0.483494i | ||||
\(617\) | 9.83512 | + | 36.7052i | 0.395947 | + | 1.47769i | 0.820161 | + | 0.572133i | \(0.193884\pi\) |
−0.424214 | + | 0.905562i | \(0.639449\pi\) | |||||||
\(618\) | 7.99171 | + | 6.64324i | 0.321474 | + | 0.267230i | ||||
\(619\) | −1.00000 | + | 1.00000i | −0.0401934 | + | 0.0401934i | −0.726918 | − | 0.686724i | \(-0.759048\pi\) |
0.686724 | + | 0.726918i | \(0.259048\pi\) | |||||||
\(620\) | −12.2474 | − | 7.07107i | −0.491869 | − | 0.283981i | ||||
\(621\) | −31.6055 | − | 30.7423i | −1.26829 | − | 1.23365i | ||||
\(622\) | 8.19615 | + | 2.19615i | 0.328636 | + | 0.0880577i | ||||
\(623\) | 19.7990 | 0.793230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 7.72741 | + | 2.07055i | 0.308849 | + | 0.0827559i | ||||
\(627\) | 8.89898 | + | 4.09978i | 0.355391 | + | 0.163729i | ||||
\(628\) | −12.1244 | − | 7.00000i | −0.483814 | − | 0.279330i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.661498 | + | 8.45946i | −0.0263547 | + | 0.337033i | ||||
\(631\) | −6.95448 | − | 25.9545i | −0.276854 | − | 1.03323i | −0.954589 | − | 0.297926i | \(-0.903705\pi\) |
0.677735 | − | 0.735306i | \(-0.262961\pi\) | |||||||
\(632\) | 21.2132 | + | 21.2132i | 0.843816 | + | 0.843816i | ||||
\(633\) | 24.1464 | − | 2.22486i | 0.959734 | − | 0.0884303i | ||||
\(634\) | −8.66025 | + | 5.00000i | −0.343943 | + | 0.198575i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.65685 | − | 8.00000i | −0.224309 | − | 0.317221i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 11.3137i | − | 0.447914i | ||||||
\(639\) | −6.79191 | + | 9.89293i | −0.268684 | + | 0.391358i | ||||
\(640\) | −3.00000 | − | 5.19615i | −0.118585 | − | 0.205396i | ||||
\(641\) | −8.48528 | + | 14.6969i | −0.335148 | + | 0.580494i | −0.983513 | − | 0.180836i | \(-0.942120\pi\) |
0.648365 | + | 0.761330i | \(0.275453\pi\) | |||||||
\(642\) | 1.65685 | − | 9.65685i | 0.0653908 | − | 0.381126i | ||||
\(643\) | −6.83013 | + | 1.83013i | −0.269354 | + | 0.0721732i | −0.390968 | − | 0.920404i | \(-0.627860\pi\) |
0.121614 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(644\) | 11.5911 | − | 3.10583i | 0.456754 | − | 0.122387i | ||||
\(645\) | 3.51472 | − | 20.4853i | 0.138392 | − | 0.806607i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 21.8275 | − | 15.8921i | 0.857465 | − | 0.624302i | ||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | + | 14.1421i | 0.391931 | + | 0.554274i | ||||
\(652\) | −0.366025 | + | 1.36603i | −0.0143347 | + | 0.0534977i | ||||
\(653\) | −12.2474 | + | 7.07107i | −0.479280 | + | 0.276712i | −0.720116 | − | 0.693853i | \(-0.755912\pi\) |
0.240837 | + | 0.970566i | \(0.422578\pi\) | |||||||
\(654\) | 2.43916 | − | 0.224745i | 0.0953786 | − | 0.00878822i | ||||
\(655\) | 16.0000 | + | 16.0000i | 0.625172 | + | 0.625172i | ||||
\(656\) | 0.517638 | + | 1.93185i | 0.0202104 | + | 0.0754261i | ||||
\(657\) | 4.22973 | + | 0.330749i | 0.165017 | + | 0.0129038i | ||||
\(658\) | 4.00000 | − | 4.00000i | 0.155936 | − | 0.155936i | ||||
\(659\) | −2.44949 | − | 1.41421i | −0.0954186 | − | 0.0550899i | 0.451531 | − | 0.892255i | \(-0.350878\pi\) |
−0.546950 | + | 0.837165i | \(0.684211\pi\) | |||||||
\(660\) | −12.5851 | − | 5.79796i | −0.489873 | − | 0.225685i | ||||
\(661\) | 1.36603 | + | 0.366025i | 0.0531322 | + | 0.0142367i | 0.285287 | − | 0.958442i | \(-0.407911\pi\) |
−0.232155 | + | 0.972679i | \(0.574578\pi\) | |||||||
\(662\) | 9.89949 | 0.384755 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0000 | −0.931381 | ||||||||
\(665\) | −3.86370 | − | 1.03528i | −0.149828 | − | 0.0401463i | ||||
\(666\) | −0.775255 | − | 4.17121i | −0.0300405 | − | 0.161631i | ||||
\(667\) | −20.7846 | − | 12.0000i | −0.804783 | − | 0.464642i | ||||
\(668\) | −2.82843 | + | 2.82843i | −0.109435 | + | 0.109435i | ||||
\(669\) | 20.7203 | + | 17.2241i | 0.801093 | + | 0.665922i | ||||
\(670\) | −3.66025 | − | 13.6603i | −0.141408 | − | 0.527742i | ||||
\(671\) | 22.6274 | + | 22.6274i | 0.873522 | + | 0.873522i | ||||
\(672\) | 1.12372 | + | 12.1958i | 0.0433486 | + | 0.470463i | ||||
\(673\) | −10.3923 | + | 6.00000i | −0.400594 | + | 0.231283i | −0.686740 | − | 0.726903i | \(-0.740959\pi\) |
0.286146 | + | 0.958186i | \(0.407626\pi\) | |||||||
\(674\) | 1.55291 | − | 5.79555i | 0.0598160 | − | 0.223236i | ||||
\(675\) | 1.41421 | + | 5.00000i | 0.0544331 | + | 0.192450i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 22.6274i | − | 0.869642i | −0.900517 | − | 0.434821i | \(-0.856812\pi\) | ||
0.900517 | − | 0.434821i | \(-0.143188\pi\) | |||||||
\(678\) | −22.9788 | + | 8.48387i | −0.882494 | + | 0.325821i | ||||
\(679\) | −7.00000 | − | 12.1244i | −0.268635 | − | 0.465290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6569 | − | 2.34315i | −0.523332 | − | 0.0897895i | ||||
\(682\) | 27.3205 | − | 7.32051i | 1.04616 | − | 0.280317i | ||||
\(683\) | −3.86370 | + | 1.03528i | −0.147840 | + | 0.0396137i | −0.331980 | − | 0.943286i | \(-0.607717\pi\) |
0.184140 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(684\) | 1.82843 | + | 3.82843i | 0.0699117 | + | 0.146384i | ||||
\(685\) | 14.0000 | − | 24.2487i | 0.534913 | − | 0.926496i | ||||
\(686\) | −8.48528 | − | 14.6969i | −0.323970 | − | 0.561132i | ||||
\(687\) | −0.848387 | − | 2.29788i | −0.0323680 | − | 0.0876695i | ||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 24.0000 | − | 16.9706i | 0.913664 | − | 0.646058i | ||||
\(691\) | 4.02628 | − | 15.0263i | 0.153167 | − | 0.571627i | −0.846088 | − | 0.533042i | \(-0.821049\pi\) |
0.999255 | − | 0.0385841i | \(-0.0122848\pi\) | |||||||
\(692\) | −7.34847 | + | 4.24264i | −0.279347 | + | 0.161281i | ||||
\(693\) | 11.0280 | + | 12.8990i | 0.418918 | + | 0.489992i | ||||
\(694\) | 10.0000 | + | 10.0000i | 0.379595 | + | 0.379595i | ||||
\(695\) | −2.07055 | − | 7.72741i | −0.0785405 | − | 0.293117i | ||||
\(696\) | 9.39496 | − | 11.3020i | 0.356115 | − | 0.428400i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −20.8207 | − | 12.0208i | −0.788074 | − | 0.454995i | ||||
\(699\) | 18.4490 | − | 40.0454i | 0.697805 | − | 1.51466i | ||||
\(700\) | −1.36603 | − | 0.366025i | −0.0516309 | − | 0.0138345i | ||||
\(701\) | 50.9117 | 1.92291 | 0.961454 | − | 0.274966i | \(-0.0886666\pi\) | ||||
0.961454 | + | 0.274966i | \(0.0886666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 27.0459 | + | 7.24693i | 1.01933 | + | 0.273129i | ||||
\(705\) | −5.79796 | + | 12.5851i | −0.218364 | + | 0.473981i | ||||
\(706\) | −22.5167 | − | 13.0000i | −0.847426 | − | 0.489261i | ||||
\(707\) | 8.48528 | − | 8.48528i | 0.319122 | − | 0.319122i | ||||
\(708\) | −4.42883 | + | 5.32780i | −0.166445 | + | 0.200231i | ||||
\(709\) | −6.95448 | − | 25.9545i | −0.261181 | − | 0.974741i | −0.964547 | − | 0.263913i | \(-0.914987\pi\) |
0.703365 | − | 0.710828i | \(-0.251680\pi\) | |||||||
\(710\) | −5.65685 | − | 5.65685i | −0.212298 | − | 0.212298i | ||||
\(711\) | 19.4949 | + | 22.8024i | 0.731116 | + | 0.855156i | ||||
\(712\) | 36.3731 | − | 21.0000i | 1.36314 | − | 0.787008i | ||||
\(713\) | 15.5291 | − | 57.9555i | 0.581571 | − | 2.17045i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.9980 | + | 32.4969i | 0.448074 | + | 1.21362i | ||||
\(718\) | 2.00000 | + | 3.46410i | 0.0746393 | + | 0.129279i | ||||
\(719\) | 12.7279 | − | 22.0454i | 0.474671 | − | 0.822155i | −0.524908 | − | 0.851159i | \(-0.675900\pi\) |
0.999579 | + | 0.0290041i | \(0.00923357\pi\) | |||||||
\(720\) | 2.58579 | + | 5.41421i | 0.0963666 | + | 0.201776i | ||||
\(721\) | −8.19615 | + | 2.19615i | −0.305241 | + | 0.0817890i | ||||
\(722\) | −16.4207 | + | 4.39992i | −0.611117 | + | 0.163748i | ||||
\(723\) | −41.0416 | − | 7.04163i | −1.52635 | − | 0.261881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.41421 | + | 2.44949i | 0.0525226 | + | 0.0909718i | ||||
\(726\) | 8.12422 | − | 2.99950i | 0.301518 | − | 0.111322i | ||||
\(727\) | − | 48.0000i | − | 1.78022i | −0.455744 | − | 0.890111i | \(-0.650627\pi\) | ||
0.455744 | − | 0.890111i | \(-0.349373\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | −0.732051 | + | 2.73205i | −0.0270944 | + | 0.101118i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.27135 | + | 13.7980i | 0.0469904 | + | 0.509987i | ||||
\(733\) | 5.00000 | + | 5.00000i | 0.184679 | + | 0.184679i | 0.793391 | − | 0.608712i | \(-0.208314\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(734\) | −2.07055 | − | 7.72741i | −0.0764255 | − | 0.285224i | ||||
\(735\) | 13.3195 | + | 11.0721i | 0.491298 | + | 0.408399i | ||||
\(736\) | 30.0000 | − | 30.0000i | 1.10581 | − | 1.10581i | ||||
\(737\) | −24.4949 | − | 14.1421i | −0.902281 | − | 0.520932i | ||||
\(738\) | 1.09638 | + | 5.89898i | 0.0403582 | + | 0.217144i | ||||
\(739\) | 1.36603 | + | 0.366025i | 0.0502501 | + | 0.0134645i | 0.283857 | − | 0.958867i | \(-0.408386\pi\) |
−0.233606 | + | 0.972331i | \(0.575053\pi\) | |||||||
\(740\) | −2.82843 | −0.103975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | −0.293689 | ||||||||
\(743\) | 15.4548 | + | 4.14110i | 0.566982 | + | 0.151922i | 0.530912 | − | 0.847427i | \(-0.321849\pi\) |
0.0360700 | + | 0.999349i | \(0.488516\pi\) | |||||||
\(744\) | 33.3712 | + | 15.3742i | 1.22345 | + | 0.563644i | ||||
\(745\) | 3.46410 | + | 2.00000i | 0.126915 | + | 0.0732743i | ||||
\(746\) | 2.82843 | − | 2.82843i | 0.103556 | − | 0.103556i | ||||
\(747\) | −23.9270 | − | 1.87100i | −0.875442 | − | 0.0684563i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | + | 5.65685i | 0.206697 | + | 0.206697i | ||||
\(750\) | −20.6969 | + | 1.90702i | −0.755745 | + | 0.0696347i | ||||
\(751\) | 25.9808 | − | 15.0000i | 0.948051 | − | 0.547358i | 0.0555764 | − | 0.998454i | \(-0.482300\pi\) |
0.892475 | + | 0.451097i | \(0.148967\pi\) | |||||||
\(752\) | 1.03528 | − | 3.86370i | 0.0377526 | − | 0.140895i | ||||
\(753\) | −25.4558 | − | 36.0000i | −0.927663 | − | 1.31191i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.82843i | 0.102937i | ||||||||
\(756\) | 0.101725 | + | 7.34777i | 0.00369969 | + | 0.267236i | ||||
\(757\) | 8.00000 | + | 13.8564i | 0.290765 | + | 0.503620i | 0.973991 | − | 0.226587i | \(-0.0727569\pi\) |
−0.683226 | + | 0.730207i | \(0.739424\pi\) | |||||||
\(758\) | −13.4350 | + | 23.2702i | −0.487982 | + | 0.845210i | ||||
\(759\) | 9.94113 | − | 57.9411i | 0.360840 | − | 2.10313i | ||||
\(760\) | −8.19615 | + | 2.19615i | −0.297306 | + | 0.0796628i | ||||
\(761\) | 48.2963 | − | 12.9410i | 1.75074 | − | 0.469109i | 0.765955 | − | 0.642894i | \(-0.222266\pi\) |
0.984784 | + | 0.173784i | \(0.0555996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | + | 1.73205i | −0.0362024 | + | 0.0627044i | ||||
\(764\) | 1.41421 | + | 2.44949i | 0.0511645 | + | 0.0886194i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 16.0000i | − | 0.578103i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.0000 | + | 24.0416i | 0.613435 | + | 0.867528i | ||||
\(769\) | −4.75833 | + | 17.7583i | −0.171590 | + | 0.640382i | 0.825518 | + | 0.564376i | \(0.190883\pi\) |
−0.997107 | + | 0.0760054i | \(0.975783\pi\) | |||||||
\(770\) | −9.79796 | + | 5.65685i | −0.353094 | + | 0.203859i | ||||
\(771\) | 14.6349 | − | 1.34847i | 0.527065 | − | 0.0485639i | ||||
\(772\) | −19.0000 | − | 19.0000i | −0.683825 | − | 0.683825i | ||||
\(773\) | 3.62347 | + | 13.5230i | 0.130327 | + | 0.486387i | 0.999973 | − | 0.00728800i | \(-0.00231986\pi\) |
−0.869646 | + | 0.493675i | \(0.835653\pi\) | |||||||
\(774\) | −1.40325 | + | 17.9452i | −0.0504388 | + | 0.645028i | ||||
\(775\) | −5.00000 | + | 5.00000i | −0.179605 | + | 0.179605i | ||||
\(776\) | −25.7196 | − | 14.8492i | −0.923281 | − | 0.533057i | ||||
\(777\) | 3.14626 | + | 1.44949i | 0.112872 | + | 0.0520002i | ||||
\(778\) | 16.3923 | + | 4.39230i | 0.587693 | + | 0.157472i | ||||
\(779\) | −2.82843 | −0.101339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2474 | − | 10.5352i | 0.366214 | − | 0.376496i | ||||
\(784\) | −4.33013 | − | 2.50000i | −0.154647 | − | 0.0892857i | ||||
\(785\) | 19.7990 | − | 19.7990i | 0.706656 | − | 0.706656i | ||||
\(786\) | −15.0693 | − | 12.5266i | −0.537504 | − | 0.446809i | ||||
\(787\) | −6.95448 | − | 25.9545i | −0.247901 | − | 0.925177i | −0.971903 | − | 0.235380i | \(-0.924366\pi\) |
0.724003 | − | 0.689797i | \(-0.242300\pi\) | |||||||
\(788\) | −15.5563 | − | 15.5563i | −0.554172 | − | 0.554172i | ||||
\(789\) | −3.59592 | − | 39.0265i | −0.128018 | − | 1.38938i | ||||
\(790\) | −17.3205 | + | 10.0000i | −0.616236 | + | 0.355784i | ||||
\(791\) | 5.17638 | − | 19.3185i | 0.184051 | − | 0.686887i | ||||
\(792\) | 33.9411 | + | 12.0000i | 1.20605 | + | 0.426401i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 24.0416i | 0.853206i | ||||||||
\(795\) | 18.3830 | − | 6.78710i | 0.651978 | − | 0.240714i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.48528 | − | 14.6969i | 0.300564 | − | 0.520592i | −0.675700 | − | 0.737177i | \(-0.736158\pi\) |
0.976264 | + | 0.216585i | \(0.0694917\pi\) | |||||||
\(798\) | 3.41421 | + | 0.585786i | 0.120862 | + | 0.0207366i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.82963 | + | 1.29410i | −0.170753 | + | 0.0457532i | ||||
\(801\) | 37.8995 | − | 18.1005i | 1.33911 | − | 0.639550i | ||||
\(802\) | 11.0000 | − | 19.0526i | 0.388424 | − | 0.672769i | ||||
\(803\) | 2.82843 | + | 4.89898i | 0.0998130 | + | 0.172881i | ||||
\(804\) | −4.24194 | − | 11.4894i | −0.149602 | − | 0.405199i | ||||
\(805\) | 24.0000i | 0.845889i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0000 | − | 19.7990i | 0.985647 | − | 0.696957i | ||||
\(808\) | 6.58846 | − | 24.5885i | 0.231781 | − | 0.865019i | ||||
\(809\) | −26.9444 | + | 15.5563i | −0.947314 | + | 0.546932i | −0.892246 | − | 0.451550i | \(-0.850871\pi\) |
−0.0550686 | + | 0.998483i | \(0.517538\pi\) | |||||||
\(810\) | 6.46750 | + | 16.7980i | 0.227245 | + | 0.590220i | ||||
\(811\) | −1.00000 | − | 1.00000i | −0.0351147 | − | 0.0351147i | 0.689331 | − | 0.724446i | \(-0.257904\pi\) |
−0.724446 | + | 0.689331i | \(0.757904\pi\) | |||||||
\(812\) | 1.03528 | + | 3.86370i | 0.0363311 | + | 0.135589i | ||||
\(813\) | −29.7507 | + | 35.7896i | −1.04340 | + | 1.25520i | ||||
\(814\) | 4.00000 | − | 4.00000i | 0.140200 | − | 0.140200i | ||||
\(815\) | −2.44949 | − | 1.41421i | −0.0858019 | − | 0.0495377i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.19615 | − | 2.19615i | −0.286747 | − | 0.0768336i | ||||
\(818\) | −32.5269 | −1.13728 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 9.65926 | + | 2.58819i | 0.337110 | + | 0.0903285i | 0.423403 | − | 0.905941i | \(-0.360835\pi\) |
−0.0862928 | + | 0.996270i | \(0.527502\pi\) | |||||||
\(822\) | −10.1464 | + | 22.0239i | −0.353897 | + | 0.768170i | ||||
\(823\) | −25.9808 | − | 15.0000i | −0.905632 | − | 0.522867i | −0.0266091 | − | 0.999646i | \(-0.508471\pi\) |
−0.879023 | + | 0.476779i | \(0.841804\pi\) | |||||||
\(824\) | −12.7279 | + | 12.7279i | −0.443398 | + | 0.443398i | ||||
\(825\) | −4.42883 | + | 5.32780i | −0.154192 | + | 0.185490i | ||||
\(826\) | 1.46410 | + | 5.46410i | 0.0509426 | + | 0.190120i | ||||
\(827\) | −22.6274 | − | 22.6274i | −0.786832 | − | 0.786832i | 0.194141 | − | 0.980974i | \(-0.437808\pi\) |
−0.980974 | + | 0.194141i | \(0.937808\pi\) | |||||||
\(828\) | 19.3485 | − | 16.5420i | 0.672406 | − | 0.574873i | ||||
\(829\) | 15.5885 | − | 9.00000i | 0.541409 | − | 0.312583i | −0.204240 | − | 0.978921i | \(-0.565472\pi\) |
0.745650 | + | 0.666338i | \(0.232139\pi\) | |||||||
\(830\) | 4.14110 | − | 15.4548i | 0.143740 | − | 0.536444i | ||||
\(831\) | −16.9706 | + | 12.0000i | −0.588702 | + | 0.416275i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.39960 | + | 6.49938i | 0.0830914 | + | 0.225055i | ||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | −2.82843 | + | 4.89898i | −0.0978232 | + | 0.169435i | ||||
\(837\) | 32.0711 | + | 17.9289i | 1.10854 | + | 0.619715i | ||||
\(838\) | 10.9282 | − | 2.92820i | 0.377509 | − | 0.101153i | ||||
\(839\) | −3.86370 | + | 1.03528i | −0.133390 | + | 0.0357417i | −0.324896 | − | 0.945750i | \(-0.605329\pi\) |
0.191506 | + | 0.981491i | \(0.438663\pi\) | |||||||
\(840\) | −14.4853 | − | 2.48528i | −0.499790 | − | 0.0857504i | ||||
\(841\) | −10.5000 | + | 18.1865i | −0.362069 | + | 0.627122i | ||||
\(842\) | −17.6777 | − | 30.6186i | −0.609213 | − | 1.05519i | ||||
\(843\) | 22.7478 | − | 8.39861i | 0.783477 | − | 0.289263i | ||||
\(844\) | 14.0000i | 0.481900i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | − | 11.3137i | 0.137523 | − | 0.388973i | ||||
\(847\) | −1.83013 | + | 6.83013i | −0.0628839 | + | 0.234686i | ||||
\(848\) | −4.89898 | + | 2.82843i | −0.168232 | + | 0.0971286i | ||||
\(849\) | 1.90702 | + | 20.6969i | 0.0654489 | + | 0.710317i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.10583 | − | 11.5911i | −0.106466 | − | 0.397338i | ||||
\(852\) | −5.32780 | − | 4.42883i | −0.182528 | − | 0.151729i | ||||
\(853\) | −37.0000 | + | 37.0000i | −1.26686 | + | 1.26686i | −0.319152 | + | 0.947703i | \(0.603398\pi\) |
−0.947703 | + | 0.319152i | \(0.896602\pi\) | |||||||
\(854\) | 9.79796 | + | 5.65685i | 0.335279 | + | 0.193574i | ||||
\(855\) | −8.34242 | + | 1.55051i | −0.285305 | + | 0.0530263i | ||||
\(856\) | 16.3923 | + | 4.39230i | 0.560277 | + | 0.150126i | ||||
\(857\) | −8.48528 | −0.289852 | −0.144926 | − | 0.989443i | \(-0.546294\pi\) | ||||
−0.144926 | + | 0.989443i | \(0.546294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | 11.5911 | + | 3.10583i | 0.395254 | + | 0.105908i | ||||
\(861\) | −4.44949 | − | 2.04989i | −0.151638 | − | 0.0698600i | ||||
\(862\) | −27.7128 | − | 16.0000i | −0.943902 | − | 0.544962i | ||||
\(863\) | −2.82843 | + | 2.82843i | −0.0962808 | + | 0.0962808i | −0.753607 | − | 0.657326i | \(-0.771688\pi\) |
0.657326 | + | 0.753607i | \(0.271688\pi\) | |||||||
\(864\) | 13.3006 | + | 22.3180i | 0.452496 | + | 0.759274i | ||||
\(865\) | −4.39230 | − | 16.3923i | −0.149343 | − | 0.557355i | ||||
\(866\) | −12.7279 | − | 12.7279i | −0.432512 | − | 0.432512i | ||||
\(867\) | −29.3207 | + | 2.70162i | −0.995782 | + | 0.0917517i | ||||
\(868\) | −8.66025 | + | 5.00000i | −0.293948 | + | 0.169711i | ||||
\(869\) | −10.3528 | + | 38.6370i | −0.351193 | + | 1.31067i | ||||
\(870\) | 5.65685 | + | 8.00000i | 0.191785 | + | 0.271225i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.24264i | 0.143674i | ||||||||
\(873\) | −24.4837 | − | 16.8091i | −0.828649 | − | 0.568902i | ||||
\(874\) | −6.00000 | − | 10.3923i | −0.202953 | − | 0.351525i | ||||
\(875\) | 8.48528 | − | 14.6969i | 0.286855 | − | 0.496847i | ||||
\(876\) | −0.414214 | + | 2.41421i | −0.0139950 | + | 0.0815687i | ||||
\(877\) | 17.7583 | − | 4.75833i | 0.599656 | − | 0.160677i | 0.0537936 | − | 0.998552i | \(-0.482869\pi\) |
0.545863 | + | 0.837875i | \(0.316202\pi\) | |||||||
\(878\) | −28.9778 | + | 7.76457i | −0.977953 | + | 0.262042i | ||||
\(879\) | −4.10051 | + | 23.8995i | −0.138307 | + | 0.806110i | ||||
\(880\) | −4.00000 | + | 6.92820i | −0.134840 | + | 0.233550i | ||||
\(881\) | −12.7279 | − | 22.0454i | −0.428815 | − | 0.742729i | 0.567954 | − | 0.823061i | \(-0.307735\pi\) |
−0.996768 | + | 0.0803319i | \(0.974402\pi\) | |||||||
\(882\) | −12.3662 | − | 8.48988i | −0.416390 | − | 0.285869i | ||||
\(883\) | 36.0000i | 1.21150i | 0.795656 | + | 0.605748i | \(0.207126\pi\) | ||||
−0.795656 | + | 0.605748i | \(0.792874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | − | 11.3137i | −0.268917 | − | 0.380306i | ||||
\(886\) | −7.32051 | + | 27.3205i | −0.245937 | + | 0.917850i | ||||
\(887\) | −12.2474 | + | 7.07107i | −0.411229 | + | 0.237423i | −0.691318 | − | 0.722551i | \(-0.742969\pi\) |
0.280089 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(888\) | 7.31747 | − | 0.674235i | 0.245558 | − | 0.0226258i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.24693 | + | 27.0459i | 0.242918 | + | 0.906581i | ||||
\(891\) | 32.9023 | + | 14.6095i | 1.10227 | + | 0.489436i | ||||
\(892\) | −11.0000 | + | 11.0000i | −0.368307 | + | 0.368307i | ||||
\(893\) | 4.89898 | + | 2.82843i | 0.163938 | + | 0.0946497i | ||||
\(894\) | −3.14626 | − | 1.44949i | −0.105227 | − | 0.0484782i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.24264 | −0.141737 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0000 | −0.734150 | ||||||||
\(899\) | 19.3185 | + | 5.17638i | 0.644309 | + | 0.172642i | ||||
\(900\) | −2.94949 | + | 0.548188i | −0.0983163 | + | 0.0182729i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −5.65685 | + | 5.65685i | −0.188353 | + | 0.188353i | ||||
\(903\) | −11.3020 | − | 9.39496i | −0.376106 | − | 0.312645i | ||||
\(904\) | −10.9808 | − | 40.9808i | −0.365215 | − | 1.36300i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.224745 | − | 2.43916i | −0.00746665 | − | 0.0810356i | ||||
\(907\) | −10.3923 | + | 6.00000i | −0.345071 | + | 0.199227i | −0.662512 | − | 0.749051i | \(-0.730510\pi\) |
0.317441 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(908\) | 2.07055 | − | 7.72741i | 0.0687137 | − | 0.256443i | ||||
\(909\) | 8.48528 | − | 24.0000i | 0.281439 | − | 0.796030i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.0833i | − | 1.59307i | −0.604593 | − | 0.796535i | \(-0.706664\pi\) | ||
0.604593 | − | 0.796535i | \(-0.293336\pi\) | |||||||
\(912\) | 2.29788 | − | 0.848387i | 0.0760903 | − | 0.0280929i | ||||
\(913\) | −16.0000 | − | 27.7128i | −0.529523 | − | 0.917160i | ||||
\(914\) | 20.5061 | − | 35.5176i | 0.678281 | − | 1.17482i | ||||
\(915\) | −27.3137 | − | 4.68629i | −0.902963 | − | 0.154924i | ||||
\(916\) | 1.36603 | − | 0.366025i | 0.0451347 | − | 0.0120938i | ||||
\(917\) | 15.4548 | − | 4.14110i | 0.510363 | − | 0.136751i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0000 | − | 29.4449i | 0.560778 | − | 0.971296i | −0.436650 | − | 0.899631i | \(-0.643835\pi\) |
0.997429 | − | 0.0716652i | \(-0.0228313\pi\) | |||||||
\(920\) | 25.4558 | + | 44.0908i | 0.839254 | + | 1.45363i | ||||
\(921\) | 14.4226 | + | 39.0639i | 0.475240 | + | 1.28720i | ||||
\(922\) | − | 10.0000i | − | 0.329332i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.00000 | + | 5.65685i | −0.263181 | + | 0.186097i | ||||
\(925\) | −0.366025 | + | 1.36603i | −0.0120348 | + | 0.0449146i | ||||
\(926\) | 20.8207 | − | 12.0208i | 0.684209 | − | 0.395029i | ||||
\(927\) | −13.6814 | + | 11.6969i | −0.449357 | + | 0.384178i | ||||
\(928\) | 10.0000 | + | 10.0000i | 0.328266 | + | 0.328266i | ||||
\(929\) | −11.9057 | − | 44.4326i | −0.390613 | − | 1.45779i | −0.829126 | − | 0.559061i | \(-0.811162\pi\) |
0.438514 | − | 0.898725i | \(-0.355505\pi\) | |||||||
\(930\) | −15.6583 | + | 18.8366i | −0.513455 | + | 0.617678i | ||||
\(931\) | 5.00000 | − | 5.00000i | 0.163868 | − | 0.163868i | ||||
\(932\) | 22.0454 | + | 12.7279i | 0.722121 | + | 0.416917i | ||||
\(933\) | −6.14966 | + | 13.3485i | −0.201331 | + | 0.437009i | ||||
\(934\) | −24.5885 | − | 6.58846i | −0.804559 | − | 0.215581i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | −9.65926 | − | 2.58819i | −0.315386 | − | 0.0845074i | ||||
\(939\) | −5.79796 | + | 12.5851i | −0.189209 | + | 0.410698i | ||||
\(940\) | −6.92820 | − | 4.00000i | −0.225973 | − | 0.130466i | ||||
\(941\) | 26.8701 | − | 26.8701i | 0.875939 | − | 0.875939i | −0.117173 | − | 0.993112i | \(-0.537383\pi\) |
0.993112 | + | 0.117173i | \(0.0373831\pi\) | |||||||
\(942\) | −15.5009 | + | 18.6473i | −0.505046 | + | 0.607562i | ||||
\(943\) | 4.39230 | + | 16.3923i | 0.143033 | + | 0.533807i | ||||
\(944\) | 2.82843 | + | 2.82843i | 0.0920575 | + | 0.0920575i | ||||
\(945\) | −14.2474 | − | 3.60697i | −0.463470 | − | 0.117335i | ||||
\(946\) | −20.7846 | + | 12.0000i | −0.675766 | + | 0.390154i | ||||
\(947\) | −8.28221 | + | 30.9096i | −0.269136 | + | 1.00443i | 0.690535 | + | 0.723299i | \(0.257375\pi\) |
−0.959670 | + | 0.281128i | \(0.909291\pi\) | |||||||
\(948\) | −14.1421 | + | 10.0000i | −0.459315 | + | 0.324785i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.41421i | 0.0458831i | ||||||||
\(951\) | −5.99900 | − | 16.2484i | −0.194531 | − | 0.526892i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.7279 | + | 22.0454i | −0.412298 | + | 0.714121i | −0.995141 | − | 0.0984642i | \(-0.968607\pi\) |
0.582843 | + | 0.812585i | \(0.301940\pi\) | |||||||
\(954\) | −15.3137 | + | 7.31371i | −0.495800 | + | 0.236790i | ||||
\(955\) | −5.46410 | + | 1.46410i | −0.176814 | + | 0.0473772i | ||||
\(956\) | −19.3185 | + | 5.17638i | −0.624805 | + | 0.167416i | ||||
\(957\) | 19.3137 | + | 3.31371i | 0.624324 | + | 0.107117i | ||||
\(958\) | −16.0000 | + | 27.7128i | −0.516937 | + | 0.895360i | ||||
\(959\) | −9.89949 | − | 17.1464i | −0.319671 | − | 0.553687i | ||||
\(960\) | −22.7478 | + | 8.39861i | −0.734183 | + | 0.271064i | ||||
\(961\) | 19.0000i | 0.612903i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0000 | + | 5.65685i | 0.515593 | + | 0.182290i | ||||
\(964\) | 6.22243 | − | 23.2224i | 0.200411 | − | 0.747944i | ||||
\(965\) | 46.5403 | − | 26.8701i | 1.49819 | − | 0.864978i | ||||
\(966\) | −1.90702 | − | 20.6969i | −0.0613575 | − | 0.665913i | ||||
\(967\) | 23.0000 | + | 23.0000i | 0.739630 | + | 0.739630i | 0.972506 | − | 0.232876i | \(-0.0748137\pi\) |
−0.232876 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(968\) | 3.88229 | + | 14.4889i | 0.124781 | + | 0.465690i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.0000 | − | 14.0000i | 0.449513 | − | 0.449513i | ||||
\(971\) | 26.9444 | + | 15.5563i | 0.864687 | + | 0.499227i | 0.865579 | − | 0.500773i | \(-0.166951\pi\) |
−0.000892350 | 1.00000i | \(0.500284\pi\) | ||||||||
\(972\) | 6.91215 | + | 13.9722i | 0.221707 | + | 0.448158i | ||||
\(973\) | −5.46410 | − | 1.46410i | −0.175171 | − | 0.0469369i | ||||
\(974\) | 26.8701 | 0.860972 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | −36.7052 | − | 9.83512i | −1.17430 | − | 0.314653i | −0.381638 | − | 0.924312i | \(-0.624640\pi\) |
−0.792664 | + | 0.609658i | \(0.791307\pi\) | |||||||
\(978\) | 2.22474 | + | 1.02494i | 0.0711395 | + | 0.0327741i | ||||
\(979\) | 48.4974 | + | 28.0000i | 1.54998 | + | 0.894884i | ||||
\(980\) | −7.07107 | + | 7.07107i | −0.225877 | + | 0.225877i | ||||
\(981\) | −0.330749 | + | 4.22973i | −0.0105600 | + | 0.135045i | ||||
\(982\) | 10.9808 | + | 40.9808i | 0.350410 | + | 1.30775i | ||||
\(983\) | 2.82843 | + | 2.82843i | 0.0902128 | + | 0.0902128i | 0.750773 | − | 0.660560i | \(-0.229681\pi\) |
−0.660560 | + | 0.750773i | \(0.729681\pi\) | |||||||
\(984\) | −10.3485 | + | 0.953512i | −0.329897 | + | 0.0303968i | ||||
\(985\) | 38.1051 | − | 22.0000i | 1.21413 | − | 0.700978i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.65685 | + | 8.00000i | 0.180060 | + | 0.254643i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.9117i | 1.61890i | ||||||||
\(990\) | −13.5838 | + | 19.7859i | −0.431722 | + | 0.628836i | ||||
\(991\) | 8.00000 | + | 13.8564i | 0.254128 | + | 0.440163i | 0.964658 | − | 0.263504i | \(-0.0848781\pi\) |
−0.710530 | + | 0.703667i | \(0.751545\pi\) | |||||||
\(992\) | −17.6777 | + | 30.6186i | −0.561267 | + | 0.972142i | ||||
\(993\) | −2.89949 | + | 16.8995i | −0.0920127 | + | 0.536289i | ||||
\(994\) | −5.46410 | + | 1.46410i | −0.173311 | + | 0.0464385i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.34315 | − | 13.6569i | 0.0742454 | − | 0.432734i | ||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | 16.2635 | + | 28.1691i | 0.514811 | + | 0.891678i | ||||
\(999\) | 7.34777 | − | 0.101725i | 0.232473 | − | 0.00321842i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))