Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-1.38255 + 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.109 |
Dual form | 144.2.k.c.37.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38255 | + | 0.297594i | −0.977609 | + | 0.210431i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82288 | − | 0.822876i | 0.911438 | − | 0.411438i | ||||
\(5\) | 0.595188 | − | 0.595188i | 0.266176 | − | 0.266176i | −0.561381 | − | 0.827557i | \(-0.689730\pi\) |
0.827557 | + | 0.561381i | \(0.189730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.64575i | − | 0.622036i | −0.950404 | − | 0.311018i | \(-0.899330\pi\) | ||
0.950404 | − | 0.311018i | \(-0.100670\pi\) | |||||||
\(8\) | −2.27533 | + | 1.68014i | −0.804450 | + | 0.594020i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.645751 | + | 1.00000i | −0.204204 | + | 0.316228i | ||||
\(11\) | 3.36028 | − | 3.36028i | 1.01316 | − | 1.01316i | 0.0132513 | − | 0.999912i | \(-0.495782\pi\) |
0.999912 | − | 0.0132513i | \(-0.00421814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575 | + | 2.64575i | 0.733799 | + | 0.733799i | 0.971370 | − | 0.237571i | \(-0.0763512\pi\) |
−0.237571 | + | 0.971370i | \(0.576351\pi\) | |||||||
\(14\) | 0.489766 | + | 2.27533i | 0.130895 | + | 0.608107i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.64575 | − | 3.00000i | 0.661438 | − | 0.750000i | ||||
\(17\) | 5.53019 | 1.34127 | 0.670634 | − | 0.741788i | \(-0.266022\pi\) | ||||
0.670634 | + | 0.741788i | \(0.266022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.64575 | − | 3.64575i | −0.836393 | − | 0.836393i | 0.151989 | − | 0.988382i | \(-0.451432\pi\) |
−0.988382 | + | 0.151989i | \(0.951432\pi\) | |||||||
\(20\) | 0.595188 | − | 1.57472i | 0.133088 | − | 0.352118i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.64575 | + | 5.64575i | −0.777277 | + | 1.20368i | ||||
\(23\) | 4.33981i | 0.904914i | 0.891786 | + | 0.452457i | \(0.149452\pi\) | ||||
−0.891786 | + | 0.452457i | \(0.850548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29150i | 0.858301i | ||||||||
\(26\) | −4.44524 | − | 2.87052i | −0.871783 | − | 0.562955i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.35425 | − | 3.00000i | −0.255929 | − | 0.566947i | ||||
\(29\) | −6.12538 | − | 6.12538i | −1.13745 | − | 1.13745i | −0.988905 | − | 0.148549i | \(-0.952540\pi\) |
−0.148549 | − | 0.988905i | \(-0.547460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.64575 | −1.01401 | −0.507003 | − | 0.861944i | \(-0.669247\pi\) | ||||
−0.507003 | + | 0.861944i | \(0.669247\pi\) | |||||||
\(32\) | −2.76510 | + | 4.93500i | −0.488804 | + | 0.872393i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.64575 | + | 1.64575i | −1.31124 | + | 0.282244i | ||||
\(35\) | −0.979531 | − | 0.979531i | −0.165571 | − | 0.165571i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.645751 | + | 0.645751i | −0.106161 | + | 0.106161i | −0.758192 | − | 0.652031i | \(-0.773917\pi\) |
0.652031 | + | 0.758192i | \(0.273917\pi\) | |||||||
\(38\) | 6.12538 | + | 3.95547i | 0.993668 | + | 0.641662i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.354249 | + | 2.35425i | −0.0560116 | + | 0.372239i | ||||
\(41\) | 7.91094i | 1.23548i | 0.786382 | + | 0.617741i | \(0.211952\pi\) | ||||
−0.786382 | + | 0.617741i | \(0.788048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.354249 | + | 0.354249i | −0.0540224 | + | 0.0540224i | −0.733602 | − | 0.679579i | \(-0.762162\pi\) |
0.679579 | + | 0.733602i | \(0.262162\pi\) | |||||||
\(44\) | 3.36028 | − | 8.89047i | 0.506582 | − | 1.34029i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.29150 | − | 6.00000i | −0.190422 | − | 0.884652i | ||||
\(47\) | −9.10132 | −1.32756 | −0.663782 | − | 0.747926i | \(-0.731050\pi\) | ||||
−0.663782 | + | 0.747926i | \(0.731050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29150 | 0.613072 | ||||||||
\(50\) | −1.27713 | − | 5.93321i | −0.180613 | − | 0.839082i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.00000 | + | 2.64575i | 0.970725 | + | 0.366900i | ||||
\(53\) | −4.93500 | + | 4.93500i | −0.677875 | + | 0.677875i | −0.959519 | − | 0.281644i | \(-0.909120\pi\) |
0.281644 | + | 0.959519i | \(0.409120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 2.76510 | + | 3.74463i | 0.369501 | + | 0.500397i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2915 | + | 6.64575i | 1.35134 | + | 0.872630i | ||||
\(59\) | 4.33981 | − | 4.33981i | 0.564996 | − | 0.564996i | −0.365727 | − | 0.930722i | \(-0.619179\pi\) |
0.930722 | + | 0.365727i | \(0.119179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.645751 | − | 0.645751i | −0.0826800 | − | 0.0826800i | 0.664557 | − | 0.747237i | \(-0.268620\pi\) |
−0.747237 | + | 0.664557i | \(0.768620\pi\) | |||||||
\(62\) | 7.80552 | − | 1.68014i | 0.991302 | − | 0.213378i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.35425 | − | 7.64575i | 0.294281 | − | 0.955719i | ||||
\(65\) | 3.14944 | 0.390640 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | + | 4.00000i | 0.488678 | + | 0.488678i | 0.907889 | − | 0.419211i | \(-0.137693\pi\) |
−0.419211 | + | 0.907889i | \(0.637693\pi\) | |||||||
\(68\) | 10.0808 | − | 4.55066i | 1.22248 | − | 0.551848i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.64575 | + | 1.06275i | 0.196705 | + | 0.127022i | ||||
\(71\) | 13.4411i | 1.59517i | 0.603207 | + | 0.797584i | \(0.293889\pi\) | ||||
−0.603207 | + | 0.797584i | \(0.706111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.29150i | − | 0.385241i | −0.981273 | − | 0.192621i | \(-0.938301\pi\) | ||
0.981273 | − | 0.192621i | \(-0.0616987\pi\) | |||||||
\(74\) | 0.700610 | − | 1.08495i | 0.0814443 | − | 0.126123i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.64575 | − | 3.64575i | −1.10644 | − | 0.418196i | ||||
\(77\) | −5.53019 | − | 5.53019i | −0.630224 | − | 0.630224i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64575 | 1.08523 | 0.542616 | − | 0.839981i | \(-0.317434\pi\) | ||||
0.542616 | + | 0.839981i | \(0.317434\pi\) | |||||||
\(80\) | −0.210845 | − | 3.36028i | −0.0235731 | − | 0.375691i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.35425 | − | 10.9373i | −0.259983 | − | 1.20782i | ||||
\(83\) | −3.36028 | − | 3.36028i | −0.368839 | − | 0.368839i | 0.498215 | − | 0.867054i | \(-0.333989\pi\) |
−0.867054 | + | 0.498215i | \(0.833989\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.29150 | − | 3.29150i | 0.357014 | − | 0.357014i | ||||
\(86\) | 0.384343 | − | 0.595188i | 0.0414448 | − | 0.0641808i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 13.2915i | −0.213201 | + | 1.41688i | ||||
\(89\) | 2.38075i | 0.252359i | 0.992007 | + | 0.126180i | \(0.0402716\pi\) | ||||
−0.992007 | + | 0.126180i | \(0.959728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.35425 | − | 4.35425i | 0.456449 | − | 0.456449i | ||||
\(92\) | 3.57113 | + | 7.91094i | 0.372316 | + | 0.824773i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.5830 | − | 2.70850i | 1.29784 | − | 0.279360i | ||||
\(95\) | −4.33981 | −0.445256 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5830 | −1.07454 | −0.537271 | − | 0.843410i | \(-0.680545\pi\) | ||||
−0.537271 | + | 0.843410i | \(0.680545\pi\) | |||||||
\(98\) | −5.93321 | + | 1.27713i | −0.599344 | + | 0.129009i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.53137 | + | 7.82288i | 0.353137 | + | 0.782288i | ||||
\(101\) | 0.595188 | − | 0.595188i | 0.0592234 | − | 0.0592234i | −0.676875 | − | 0.736098i | \(-0.736666\pi\) |
0.736098 | + | 0.676875i | \(0.236666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9373i | 1.66888i | 0.551101 | + | 0.834439i | \(0.314208\pi\) | ||||
−0.551101 | + | 0.834439i | \(0.685792\pi\) | |||||||
\(104\) | −10.4652 | − | 1.57472i | −1.02620 | − | 0.154414i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.35425 | − | 8.29150i | 0.520051 | − | 0.805342i | ||||
\(107\) | 2.38075 | − | 2.38075i | 0.230156 | − | 0.230156i | −0.582602 | − | 0.812758i | \(-0.697965\pi\) |
0.812758 | + | 0.582602i | \(0.197965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.64575 | − | 6.64575i | −0.636548 | − | 0.636548i | 0.313155 | − | 0.949702i | \(-0.398614\pi\) |
−0.949702 | + | 0.313155i | \(0.898614\pi\) | |||||||
\(110\) | 1.19038 | + | 5.53019i | 0.113498 | + | 0.527283i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.93725 | − | 4.35425i | −0.466527 | − | 0.411438i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.58301 | + | 2.58301i | 0.240866 | + | 0.240866i | ||||
\(116\) | −16.2062 | − | 6.12538i | −1.50471 | − | 0.568727i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.70850 | + | 7.29150i | −0.433452 | + | 0.671237i | ||||
\(119\) | − | 9.10132i | − | 0.834316i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.5830i | − | 1.05300i | ||||||
\(122\) | 1.08495 | + | 0.700610i | 0.0982271 | + | 0.0634303i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.2915 | + | 4.64575i | −0.924204 | + | 0.417201i | ||||
\(125\) | 5.53019 | + | 5.53019i | 0.494635 | + | 0.494635i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.937254 | 0.0831678 | 0.0415839 | − | 0.999135i | \(-0.486760\pi\) | ||||
0.0415839 | + | 0.999135i | \(0.486760\pi\) | |||||||
\(128\) | −0.979531 | + | 11.2712i | −0.0865792 | + | 0.996245i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.35425 | + | 0.937254i | −0.381893 | + | 0.0822026i | ||||
\(131\) | 6.72057 | + | 6.72057i | 0.587179 | + | 0.587179i | 0.936866 | − | 0.349688i | \(-0.113712\pi\) |
−0.349688 | + | 0.936866i | \(0.613712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | −6.72057 | − | 4.33981i | −0.580568 | − | 0.374903i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.5830 | + | 9.29150i | −1.07898 | + | 0.796740i | ||||
\(137\) | − | 10.2917i | − | 0.879279i | −0.898174 | − | 0.439639i | \(-0.855106\pi\) | ||
0.898174 | − | 0.439639i | \(-0.144894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5830 | + | 14.5830i | −1.23691 | + | 1.23691i | −0.275659 | + | 0.961256i | \(0.588896\pi\) |
−0.961256 | + | 0.275659i | \(0.911104\pi\) | |||||||
\(140\) | −2.59160 | − | 0.979531i | −0.219030 | − | 0.0827855i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 18.5830i | −0.335673 | − | 1.55945i | ||||
\(143\) | 17.7809 | 1.48692 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.29150 | −0.605526 | ||||||||
\(146\) | 0.979531 | + | 4.55066i | 0.0810666 | + | 0.376615i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.645751 | + | 1.70850i | −0.0530804 | + | 0.140438i | ||||
\(149\) | 11.6556 | − | 11.6556i | 0.954861 | − | 0.954861i | −0.0441630 | − | 0.999024i | \(-0.514062\pi\) |
0.999024 | + | 0.0441630i | \(0.0140621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.3542i | − | 0.842617i | −0.906917 | − | 0.421308i | \(-0.861571\pi\) | ||
0.906917 | − | 0.421308i | \(-0.138429\pi\) | |||||||
\(152\) | 14.4207 | + | 2.16991i | 1.16967 | + | 0.176003i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.29150 | + | 6.00000i | 0.748731 | + | 0.483494i | ||||
\(155\) | −3.36028 | + | 3.36028i | −0.269904 | + | 0.269904i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.64575 | − | 6.64575i | −0.530389 | − | 0.530389i | 0.390299 | − | 0.920688i | \(-0.372372\pi\) |
−0.920688 | + | 0.390299i | \(0.872372\pi\) | |||||||
\(158\) | −13.3357 | + | 2.87052i | −1.06093 | + | 0.228366i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.29150 | + | 4.58301i | 0.102102 | + | 0.362318i | ||||
\(161\) | 7.14226 | 0.562889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6458 | + | 11.6458i | 0.912166 | + | 0.912166i | 0.996442 | − | 0.0842767i | \(-0.0268580\pi\) |
−0.0842767 | + | 0.996442i | \(0.526858\pi\) | |||||||
\(164\) | 6.50972 | + | 14.4207i | 0.508324 | + | 1.12606i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.64575 | + | 3.64575i | 0.438195 | + | 0.282965i | ||||
\(167\) | − | 17.7809i | − | 1.37593i | −0.725743 | − | 0.687965i | \(-0.758504\pi\) | ||
0.725743 | − | 0.687965i | \(-0.241496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | −3.57113 | + | 5.53019i | −0.273893 | + | 0.424146i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.354249 | + | 0.937254i | −0.0270112 | + | 0.0714649i | ||||
\(173\) | 4.93500 | + | 4.93500i | 0.375201 | + | 0.375201i | 0.869367 | − | 0.494166i | \(-0.164527\pi\) |
−0.494166 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.06275 | 0.533893 | ||||||||
\(176\) | −1.19038 | − | 18.9713i | −0.0897280 | − | 1.43002i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.708497 | − | 3.29150i | −0.0531041 | − | 0.246709i | ||||
\(179\) | −2.38075 | − | 2.38075i | −0.177946 | − | 0.177946i | 0.612514 | − | 0.790460i | \(-0.290158\pi\) |
−0.790460 | + | 0.612514i | \(0.790158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.645751 | + | 0.645751i | −0.0479983 | + | 0.0479983i | −0.730699 | − | 0.682700i | \(-0.760805\pi\) |
0.682700 | + | 0.730699i | \(0.260805\pi\) | |||||||
\(182\) | −4.72416 | + | 7.31575i | −0.350178 | + | 0.542280i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.29150 | − | 9.87451i | −0.537537 | − | 0.727958i | ||||
\(185\) | 0.768687i | 0.0565150i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5830 | − | 18.5830i | 1.35892 | − | 1.35892i | ||||
\(188\) | −16.5906 | + | 7.48925i | −1.20999 | + | 0.546210i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 1.29150i | 0.435286 | − | 0.0936954i | ||||
\(191\) | 9.10132 | 0.658548 | 0.329274 | − | 0.944234i | \(-0.393196\pi\) | ||||
0.329274 | + | 0.944234i | \(0.393196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8745 | 0.854746 | 0.427373 | − | 0.904075i | \(-0.359439\pi\) | ||||
0.427373 | + | 0.904075i | \(0.359439\pi\) | |||||||
\(194\) | 14.6315 | − | 3.14944i | 1.05048 | − | 0.226117i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.82288 | − | 3.53137i | 0.558777 | − | 0.252241i | ||||
\(197\) | −8.50613 | + | 8.50613i | −0.606037 | + | 0.606037i | −0.941908 | − | 0.335871i | \(-0.890969\pi\) |
0.335871 | + | 0.941908i | \(0.390969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6458i | 0.967322i | 0.875256 | + | 0.483661i | \(0.160693\pi\) | ||||
−0.875256 | + | 0.483661i | \(0.839307\pi\) | |||||||
\(200\) | −7.21033 | − | 9.76458i | −0.509847 | − | 0.690460i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.645751 | + | 1.00000i | −0.0454349 | + | 0.0703598i | ||||
\(203\) | −10.0808 | + | 10.0808i | −0.707537 | + | 0.707537i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.70850 | + | 4.70850i | 0.328856 | + | 0.328856i | ||||
\(206\) | −5.04042 | − | 23.4166i | −0.351183 | − | 1.63151i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.9373 | − | 0.937254i | 1.03571 | − | 0.0649869i | ||||
\(209\) | −24.5015 | −1.69481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5830 | − | 14.5830i | −1.00394 | − | 1.00394i | −0.999992 | − | 0.00394326i | \(-0.998745\pi\) |
−0.00394326 | − | 0.999992i | \(-0.501255\pi\) | |||||||
\(212\) | −4.93500 | + | 13.0568i | −0.338937 | + | 0.896744i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.58301 | + | 4.00000i | −0.176571 | + | 0.273434i | ||||
\(215\) | 0.421689i | 0.0287590i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.29150i | 0.630748i | ||||||||
\(218\) | 11.1658 | + | 7.21033i | 0.756244 | + | 0.488345i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.29150 | − | 7.29150i | −0.221913 | − | 0.491593i | ||||
\(221\) | 14.6315 | + | 14.6315i | 0.984222 | + | 0.984222i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3542 | −0.961232 | −0.480616 | − | 0.876931i | \(-0.659587\pi\) | ||||
−0.480616 | + | 0.876931i | \(0.659587\pi\) | |||||||
\(224\) | 8.12179 | + | 4.55066i | 0.542660 | + | 0.304054i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.40122 | − | 1.40122i | −0.0930023 | − | 0.0930023i | 0.659075 | − | 0.752077i | \(-0.270948\pi\) |
−0.752077 | + | 0.659075i | \(0.770948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.9373 | − | 17.9373i | 1.18533 | − | 1.18533i | 0.206982 | − | 0.978345i | \(-0.433636\pi\) |
0.978345 | − | 0.206982i | \(-0.0663643\pi\) | |||||||
\(230\) | −4.33981 | − | 2.80244i | −0.286159 | − | 0.184787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.2288 | + | 3.64575i | 1.59070 | + | 0.239355i | ||||
\(233\) | − | 19.7400i | − | 1.29321i | −0.762825 | − | 0.646606i | \(-0.776188\pi\) | ||
0.762825 | − | 0.646606i | \(-0.223812\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.41699 | + | 5.41699i | −0.353366 | + | 0.353366i | ||||
\(236\) | 4.33981 | − | 11.4821i | 0.282498 | − | 0.747419i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.70850 | + | 12.5830i | 0.175566 | + | 0.815635i | ||||
\(239\) | −13.0194 | −0.842158 | −0.421079 | − | 0.907024i | \(-0.638348\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29150 | −0.0831930 | −0.0415965 | − | 0.999134i | \(-0.513244\pi\) | ||||
−0.0415965 | + | 0.999134i | \(0.513244\pi\) | |||||||
\(242\) | 3.44703 | + | 16.0141i | 0.221584 | + | 1.02942i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.70850 | − | 0.645751i | −0.109375 | − | 0.0413400i | ||||
\(245\) | 2.55425 | − | 2.55425i | 0.163185 | − | 0.163185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.2915i | − | 1.22749i | ||||||
\(248\) | 12.8459 | − | 9.48566i | 0.815718 | − | 0.602340i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.29150 | − | 6.00000i | −0.587646 | − | 0.379473i | ||||
\(251\) | −18.7605 | + | 18.7605i | −1.18415 | + | 1.18415i | −0.205492 | + | 0.978659i | \(0.565879\pi\) |
−0.978659 | + | 0.205492i | \(0.934121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.5830 | + | 14.5830i | 0.916826 | + | 0.916826i | ||||
\(254\) | −1.29580 | + | 0.278921i | −0.0813056 | + | 0.0175011i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.00000 | − | 15.8745i | −0.125000 | − | 0.992157i | ||||
\(257\) | −29.2630 | −1.82538 | −0.912688 | − | 0.408656i | \(-0.865998\pi\) | ||||
−0.912688 | + | 0.408656i | \(0.865998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.06275 | + | 1.06275i | 0.0660358 | + | 0.0660358i | ||||
\(260\) | 5.74103 | − | 2.59160i | 0.356044 | − | 0.160724i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.2915 | − | 7.29150i | −0.697591 | − | 0.450471i | ||||
\(263\) | − | 8.67963i | − | 0.535209i | −0.963529 | − | 0.267604i | \(-0.913768\pi\) | ||
0.963529 | − | 0.267604i | \(-0.0862320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.87451i | 0.360868i | ||||||||
\(266\) | 6.50972 | − | 10.0808i | 0.399137 | − | 0.618097i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.5830 | + | 4.00000i | 0.646460 | + | 0.244339i | ||||
\(269\) | 10.4652 | + | 10.4652i | 0.638074 | + | 0.638074i | 0.950080 | − | 0.312006i | \(-0.101001\pi\) |
−0.312006 | + | 0.950080i | \(0.601001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.35425 | 0.385993 | 0.192997 | − | 0.981199i | \(-0.438179\pi\) | ||||
0.192997 | + | 0.981199i | \(0.438179\pi\) | |||||||
\(272\) | 14.6315 | − | 16.5906i | 0.887166 | − | 1.00595i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.06275 | + | 14.2288i | 0.185027 | + | 0.859591i | ||||
\(275\) | 14.4207 | + | 14.4207i | 0.869599 | + | 0.869599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5203 | + | 16.5203i | −0.992606 | + | 0.992606i | −0.999973 | − | 0.00736669i | \(-0.997655\pi\) |
0.00736669 | + | 0.999973i | \(0.497655\pi\) | |||||||
\(278\) | 15.8219 | − | 24.5015i | 0.948934 | − | 1.46950i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.87451 | + | 0.583005i | 0.231546 | + | 0.0348412i | ||||
\(281\) | 2.38075i | 0.142024i | 0.997475 | + | 0.0710119i | \(0.0226228\pi\) | ||||
−0.997475 | + | 0.0710119i | \(0.977377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.58301 | + | 2.58301i | −0.153544 | + | 0.153544i | −0.779699 | − | 0.626155i | \(-0.784628\pi\) |
0.626155 | + | 0.779699i | \(0.284628\pi\) | |||||||
\(284\) | 11.0604 | + | 24.5015i | 0.656313 | + | 1.45390i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.5830 | + | 5.29150i | −1.45362 | + | 0.312893i | ||||
\(287\) | 13.0194 | 0.768513 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5830 | 0.799000 | ||||||||
\(290\) | 10.0808 | − | 2.16991i | 0.591968 | − | 0.127421i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.70850 | − | 6.00000i | −0.158503 | − | 0.351123i | ||||
\(293\) | 2.55425 | − | 2.55425i | 0.149221 | − | 0.149221i | −0.628549 | − | 0.777770i | \(-0.716351\pi\) |
0.777770 | + | 0.628549i | \(0.216351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.16601i | − | 0.300777i | ||||||
\(296\) | 0.384343 | − | 2.55425i | 0.0223395 | − | 0.148463i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.6458 | + | 19.5830i | −0.732549 | + | 1.13441i | ||||
\(299\) | −11.4821 | + | 11.4821i | −0.664025 | + | 0.664025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.583005 | + | 0.583005i | 0.0336039 | + | 0.0336039i | ||||
\(302\) | 3.08136 | + | 14.3152i | 0.177312 | + | 0.823750i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.5830 | + | 1.29150i | −1.18052 | + | 0.0740728i | ||||
\(305\) | −0.768687 | −0.0440149 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | − | 20.0000i | −1.14146 | − | 1.14146i | −0.988183 | − | 0.153277i | \(-0.951017\pi\) |
−0.153277 | − | 0.988183i | \(-0.548983\pi\) | |||||||
\(308\) | −14.6315 | − | 5.53019i | −0.833708 | − | 0.315112i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.64575 | − | 5.64575i | 0.207065 | − | 0.320657i | ||||
\(311\) | − | 8.67963i | − | 0.492177i | −0.969247 | − | 0.246088i | \(-0.920855\pi\) | ||
0.969247 | − | 0.246088i | \(-0.0791453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.29150i | 0.525187i | 0.964907 | + | 0.262593i | \(0.0845778\pi\) | ||||
−0.964907 | + | 0.262593i | \(0.915422\pi\) | |||||||
\(314\) | 11.1658 | + | 7.21033i | 0.630123 | + | 0.406903i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.5830 | − | 7.93725i | 0.989121 | − | 0.446505i | ||||
\(317\) | −0.595188 | − | 0.595188i | −0.0334291 | − | 0.0334291i | 0.690195 | − | 0.723624i | \(-0.257525\pi\) |
−0.723624 | + | 0.690195i | \(0.757525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.1660 | −2.30485 | ||||||||
\(320\) | −3.14944 | − | 5.95188i | −0.176059 | − | 0.332720i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.87451 | + | 2.12549i | −0.550285 | + | 0.118449i | ||||
\(323\) | −20.1617 | − | 20.1617i | −1.12183 | − | 1.12183i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3542 | + | 11.3542i | −0.629820 | + | 0.629820i | ||||
\(326\) | −19.5665 | − | 12.6351i | −1.08369 | − | 0.699793i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.2915 | − | 18.0000i | −0.733900 | − | 0.993884i | ||||
\(329\) | 14.9785i | 0.825792i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | + | 8.00000i | −0.439720 | + | 0.439720i | −0.891918 | − | 0.452198i | \(-0.850640\pi\) |
0.452198 | + | 0.891918i | \(0.350640\pi\) | |||||||
\(332\) | −8.89047 | − | 3.36028i | −0.487928 | − | 0.184419i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.29150 | + | 24.5830i | 0.289538 | + | 1.34512i | ||||
\(335\) | 4.76150 | 0.260149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70850 | 0.256488 | 0.128244 | − | 0.991743i | \(-0.459066\pi\) | ||||
0.128244 | + | 0.991743i | \(0.459066\pi\) | |||||||
\(338\) | −0.297594 | − | 1.38255i | −0.0161870 | − | 0.0752007i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.29150 | − | 8.70850i | 0.178507 | − | 0.472285i | ||||
\(341\) | −18.9713 | + | 18.9713i | −1.02735 | + | 1.02735i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5830i | − | 1.00339i | ||||||
\(344\) | 0.210845 | − | 1.40122i | 0.0113680 | − | 0.0755487i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.29150 | − | 5.35425i | −0.445754 | − | 0.287846i | ||||
\(347\) | 3.36028 | − | 3.36028i | 0.180389 | − | 0.180389i | −0.611136 | − | 0.791526i | \(-0.709287\pi\) |
0.791526 | + | 0.611136i | \(0.209287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.22876 | + | 3.22876i | 0.172831 | + | 0.172831i | 0.788222 | − | 0.615391i | \(-0.211002\pi\) |
−0.615391 | + | 0.788222i | \(0.711002\pi\) | |||||||
\(350\) | −9.76458 | + | 2.10183i | −0.521939 | + | 0.112348i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.29150 | + | 25.8745i | 0.388638 | + | 1.37912i | ||||
\(353\) | 7.14226 | 0.380144 | 0.190072 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190072 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 8.00000i | 0.424596 | + | 0.424596i | ||||
\(356\) | 1.95906 | + | 4.33981i | 0.103830 | + | 0.230010i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | + | 2.58301i | 0.211407 | + | 0.136516i | ||||
\(359\) | − | 4.76150i | − | 0.251303i | −0.992074 | − | 0.125651i | \(-0.959898\pi\) | ||
0.992074 | − | 0.125651i | \(-0.0401020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.58301i | 0.399106i | ||||||||
\(362\) | 0.700610 | − | 1.08495i | 0.0368233 | − | 0.0570239i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.35425 | − | 11.5203i | 0.228225 | − | 0.603826i | ||||
\(365\) | −1.95906 | − | 1.95906i | −0.102542 | − | 0.102542i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.8118 | 1.81716 | 0.908580 | − | 0.417712i | \(-0.137168\pi\) | ||||
0.908580 | + | 0.417712i | \(0.137168\pi\) | |||||||
\(368\) | 13.0194 | + | 11.4821i | 0.678685 | + | 0.598544i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.228757 | − | 1.06275i | −0.0118925 | − | 0.0552495i | ||||
\(371\) | 8.12179 | + | 8.12179i | 0.421662 | + | 0.421662i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9373 | − | 11.9373i | 0.618088 | − | 0.618088i | −0.326953 | − | 0.945041i | \(-0.606022\pi\) |
0.945041 | + | 0.326953i | \(0.106022\pi\) | |||||||
\(374\) | −20.1617 | + | 31.2221i | −1.04254 | + | 1.61446i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.7085 | − | 15.2915i | 1.06796 | − | 0.788599i | ||||
\(377\) | − | 32.4125i | − | 1.66933i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.35425 | − | 8.35425i | 0.429129 | − | 0.429129i | −0.459203 | − | 0.888332i | \(-0.651865\pi\) |
0.888332 | + | 0.459203i | \(0.151865\pi\) | |||||||
\(380\) | −7.91094 | + | 3.57113i | −0.405823 | + | 0.183195i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.5830 | + | 2.70850i | −0.643803 | + | 0.138579i | ||||
\(383\) | −9.10132 | −0.465056 | −0.232528 | − | 0.972590i | \(-0.574700\pi\) | ||||
−0.232528 | + | 0.972590i | \(0.574700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.58301 | −0.335501 | ||||||||
\(386\) | −16.4171 | + | 3.53378i | −0.835607 | + | 0.179865i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.2915 | + | 8.70850i | −0.979378 | + | 0.442107i | ||||
\(389\) | 20.7569 | − | 20.7569i | 1.05242 | − | 1.05242i | 0.0538679 | − | 0.998548i | \(-0.482845\pi\) |
0.998548 | − | 0.0538679i | \(-0.0171550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | −9.76458 | + | 7.21033i | −0.493186 | + | 0.364177i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.22876 | − | 14.2915i | 0.464938 | − | 0.719996i | ||||
\(395\) | 5.74103 | − | 5.74103i | 0.288863 | − | 0.288863i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.06275 | + | 8.06275i | 0.404658 | + | 0.404658i | 0.879871 | − | 0.475213i | \(-0.157629\pi\) |
−0.475213 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(398\) | −4.06089 | − | 18.8659i | −0.203554 | − | 0.945662i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.8745 | + | 11.3542i | 0.643725 | + | 0.567712i | ||||
\(401\) | 16.5906 | 0.828494 | 0.414247 | − | 0.910165i | \(-0.364045\pi\) | ||||
0.414247 | + | 0.910165i | \(0.364045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.9373 | − | 14.9373i | −0.744078 | − | 0.744078i | ||||
\(404\) | 0.595188 | − | 1.57472i | 0.0296117 | − | 0.0783452i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.9373 | − | 16.9373i | 0.542807 | − | 0.840582i | ||||
\(407\) | 4.33981i | 0.215117i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.1660i | − | 1.24438i | −0.782867 | − | 0.622190i | \(-0.786243\pi\) | ||
0.782867 | − | 0.622190i | \(-0.213757\pi\) | |||||||
\(410\) | −7.91094 | − | 5.10850i | −0.390694 | − | 0.252291i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.9373 | + | 30.8745i | 0.686639 | + | 1.52108i | ||||
\(413\) | −7.14226 | − | 7.14226i | −0.351447 | − | 0.351447i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | −20.3725 | + | 5.74103i | −0.998846 | + | 0.281477i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.8745 | − | 7.29150i | 1.65686 | − | 0.356639i | ||||
\(419\) | 18.7605 | + | 18.7605i | 0.916509 | + | 0.916509i | 0.996774 | − | 0.0802643i | \(-0.0255764\pi\) |
−0.0802643 | + | 0.996774i | \(0.525576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3542 | − | 11.3542i | 0.553372 | − | 0.553372i | −0.374040 | − | 0.927412i | \(-0.622028\pi\) |
0.927412 | + | 0.374040i | \(0.122028\pi\) | |||||||
\(422\) | 24.5015 | + | 15.8219i | 1.19271 | + | 0.770197i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.93725 | − | 19.5203i | 0.142646 | − | 0.947988i | ||||
\(425\) | 23.7328i | 1.15121i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.06275 | + | 1.06275i | −0.0514299 | + | 0.0514299i | ||||
\(428\) | 2.38075 | − | 6.29888i | 0.115078 | − | 0.304468i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.125492 | − | 0.583005i | −0.00605177 | − | 0.0281150i | ||||
\(431\) | 31.2221 | 1.50391 | 0.751957 | − | 0.659212i | \(-0.229110\pi\) | ||||
0.751957 | + | 0.659212i | \(0.229110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | −2.76510 | − | 12.8459i | −0.132729 | − | 0.616625i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.5830 | − | 6.64575i | −0.842073 | − | 0.318274i | ||||
\(437\) | 15.8219 | − | 15.8219i | 0.756863 | − | 0.756863i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.479741i | − | 0.0228968i | −0.999934 | − | 0.0114484i | \(-0.996356\pi\) | ||
0.999934 | − | 0.0114484i | \(-0.00364422\pi\) | |||||||
\(440\) | 6.72057 | + | 9.10132i | 0.320390 | + | 0.433888i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.5830 | − | 15.8745i | −1.16929 | − | 0.755073i | ||||
\(443\) | 21.5629 | − | 21.5629i | 1.02449 | − | 1.02449i | 0.0247926 | − | 0.999693i | \(-0.492107\pi\) |
0.999693 | − | 0.0247926i | \(-0.00789253\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.41699 | + | 1.41699i | 0.0671720 | + | 0.0671720i | ||||
\(446\) | 19.8454 | − | 4.27174i | 0.939708 | − | 0.202273i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.5830 | − | 3.87451i | −0.594491 | − | 0.183053i | ||||
\(449\) | 9.44832 | 0.445894 | 0.222947 | − | 0.974831i | \(-0.428432\pi\) | ||||
0.222947 | + | 0.974831i | \(0.428432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.5830 | + | 26.5830i | 1.25174 | + | 1.25174i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.35425 | + | 1.52026i | 0.110490 | + | 0.0713493i | ||||
\(455\) | − | 5.18319i | − | 0.242992i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41699i | 0.253396i | 0.991941 | + | 0.126698i | \(0.0404380\pi\) | ||||
−0.991941 | + | 0.126698i | \(0.959562\pi\) | |||||||
\(458\) | −19.4611 | + | 30.1371i | −0.909357 | + | 1.40822i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.83399 | + | 2.58301i | 0.318636 | + | 0.120433i | ||||
\(461\) | 8.50613 | + | 8.50613i | 0.396170 | + | 0.396170i | 0.876880 | − | 0.480710i | \(-0.159621\pi\) |
−0.480710 | + | 0.876880i | \(0.659621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0627 | 0.700025 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(464\) | −34.5824 | + | 2.16991i | −1.60545 | + | 0.100735i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.87451 | + | 27.2915i | 0.272131 | + | 1.26425i | ||||
\(467\) | −25.4810 | − | 25.4810i | −1.17912 | − | 1.17912i | −0.979968 | − | 0.199154i | \(-0.936181\pi\) |
−0.199154 | − | 0.979968i | \(-0.563819\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.58301 | − | 6.58301i | 0.303975 | − | 0.303975i | ||||
\(470\) | 5.87719 | − | 9.10132i | 0.271094 | − | 0.419812i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.58301 | + | 17.1660i | −0.118892 | + | 0.790130i | ||||
\(473\) | 2.38075i | 0.109467i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6458 | − | 15.6458i | 0.717876 | − | 0.717876i | ||||
\(476\) | −7.48925 | − | 16.5906i | −0.343269 | − | 0.760428i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | − | 3.87451i | 0.823301 | − | 0.177216i | ||||
\(479\) | −22.1208 | −1.01072 | −0.505362 | − | 0.862908i | \(-0.668641\pi\) | ||||
−0.505362 | + | 0.862908i | \(0.668641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.41699 | −0.155802 | ||||||||
\(482\) | 1.78556 | − | 0.384343i | 0.0813302 | − | 0.0175064i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.53137 | − | 21.1144i | −0.433244 | − | 0.959744i | ||||
\(485\) | −6.29888 | + | 6.29888i | −0.286017 | + | 0.286017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.22876i | 0.372881i | 0.982466 | + | 0.186440i | \(0.0596951\pi\) | ||||
−0.982466 | + | 0.186440i | \(0.940305\pi\) | |||||||
\(488\) | 2.55425 | + | 0.384343i | 0.115625 | + | 0.0173984i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.77124 | + | 4.29150i | −0.125192 | + | 0.193870i | ||||
\(491\) | 15.4002 | − | 15.4002i | 0.695001 | − | 0.695001i | −0.268327 | − | 0.963328i | \(-0.586471\pi\) |
0.963328 | + | 0.268327i | \(0.0864707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.8745 | − | 33.8745i | −1.52563 | − | 1.52563i | ||||
\(494\) | 5.74103 | + | 26.6714i | 0.258301 | + | 1.20000i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9373 | + | 16.9373i | −0.670703 | + | 0.760505i | ||||
\(497\) | 22.1208 | 0.992252 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5830 | + | 10.5830i | 0.473760 | + | 0.473760i | 0.903129 | − | 0.429369i | \(-0.141264\pi\) |
−0.429369 | + | 0.903129i | \(0.641264\pi\) | |||||||
\(500\) | 14.6315 | + | 5.53019i | 0.654341 | + | 0.247318i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.3542 | − | 31.5203i | 0.908455 | − | 1.40682i | ||||
\(503\) | 31.6438i | 1.41093i | 0.708747 | + | 0.705463i | \(0.249261\pi\) | ||||
−0.708747 | + | 0.705463i | \(0.750739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.708497i | − | 0.0315277i | ||||||
\(506\) | −24.5015 | − | 15.8219i | −1.08923 | − | 0.703369i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.70850 | − | 0.771243i | 0.0758023 | − | 0.0342184i | ||||
\(509\) | −24.6750 | − | 24.6750i | −1.09370 | − | 1.09370i | −0.995130 | − | 0.0985706i | \(-0.968573\pi\) |
−0.0985706 | − | 0.995130i | \(-0.531427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.41699 | −0.239634 | ||||||||
\(512\) | 7.48925 | + | 21.3521i | 0.330981 | + | 0.943637i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 40.4575 | − | 8.70850i | 1.78450 | − | 0.384115i | ||||
\(515\) | 10.0808 | + | 10.0808i | 0.444215 | + | 0.444215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.5830 | + | 30.5830i | −1.34504 | + | 1.34504i | ||||
\(518\) | −1.78556 | − | 1.15303i | −0.0784532 | − | 0.0506612i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.16601 | + | 5.29150i | −0.314250 | + | 0.232048i | ||||
\(521\) | − | 14.2098i | − | 0.622543i | −0.950321 | − | 0.311272i | \(-0.899245\pi\) | ||
0.950321 | − | 0.311272i | \(-0.100755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9373 | + | 18.9373i | −0.828068 | + | 0.828068i | −0.987249 | − | 0.159181i | \(-0.949115\pi\) |
0.159181 | + | 0.987249i | \(0.449115\pi\) | |||||||
\(524\) | 17.7809 | + | 6.72057i | 0.776764 | + | 0.293589i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.58301 | + | 12.0000i | 0.112624 | + | 0.523225i | ||||
\(527\) | −31.2221 | −1.36006 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.16601 | 0.181131 | ||||||||
\(530\) | −1.74822 | − | 8.12179i | −0.0759377 | − | 0.352788i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | + | 15.8745i | −0.260133 | + | 0.688247i | ||||
\(533\) | −20.9304 | + | 20.9304i | −0.906596 | + | 0.906596i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.83399i | − | 0.122524i | ||||||
\(536\) | −15.8219 | − | 2.38075i | −0.683401 | − | 0.102833i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.5830 | − | 11.3542i | −0.758057 | − | 0.489516i | ||||
\(539\) | 14.4207 | − | 14.4207i | 0.621142 | − | 0.621142i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.5203 | − | 28.5203i | −1.22618 | − | 1.22618i | −0.965397 | − | 0.260785i | \(-0.916019\pi\) |
−0.260785 | − | 0.965397i | \(-0.583981\pi\) | |||||||
\(542\) | −8.78505 | + | 1.89099i | −0.377350 | + | 0.0812248i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.2915 | + | 27.2915i | −0.655618 | + | 1.17011i | ||||
\(545\) | −7.91094 | −0.338868 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9373 | + | 14.9373i | 0.638671 | + | 0.638671i | 0.950228 | − | 0.311557i | \(-0.100850\pi\) |
−0.311557 | + | 0.950228i | \(0.600850\pi\) | |||||||
\(548\) | −8.46878 | − | 18.7605i | −0.361769 | − | 0.801408i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.2288 | − | 15.6458i | −1.03312 | − | 0.667137i | ||||
\(551\) | 44.6632i | 1.90272i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.8745i | − | 0.675053i | ||||||
\(554\) | 17.9237 | − | 27.7564i | 0.761506 | − | 1.17926i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.5830 | + | 38.5830i | −0.618457 | + | 1.63628i | ||||
\(557\) | −18.7978 | − | 18.7978i | −0.796489 | − | 0.796489i | 0.186051 | − | 0.982540i | \(-0.440431\pi\) |
−0.982540 | + | 0.186051i | \(0.940431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.87451 | −0.0792832 | ||||||||
\(560\) | −5.53019 | + | 0.346998i | −0.233693 | + | 0.0146633i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.708497 | − | 3.29150i | −0.0298862 | − | 0.138844i | ||||
\(563\) | −5.31935 | − | 5.31935i | −0.224184 | − | 0.224184i | 0.586074 | − | 0.810258i | \(-0.300673\pi\) |
−0.810258 | + | 0.586074i | \(0.800673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.80244 | − | 4.33981i | 0.117795 | − | 0.182416i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.5830 | − | 30.5830i | −0.947562 | − | 1.28323i | ||||
\(569\) | 41.0921i | 1.72267i | 0.508038 | + | 0.861335i | \(0.330371\pi\) | ||||
−0.508038 | + | 0.861335i | \(0.669629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | − | 4.00000i | 0.167395 | − | 0.167395i | −0.618438 | − | 0.785833i | \(-0.712234\pi\) |
0.785833 | + | 0.618438i | \(0.212234\pi\) | |||||||
\(572\) | 32.4125 | − | 14.6315i | 1.35523 | − | 0.611774i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.0000 | + | 3.87451i | −0.751305 | + | 0.161719i | ||||
\(575\) | −18.6243 | −0.776688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0405 | −1.62528 | −0.812639 | − | 0.582767i | \(-0.801970\pi\) | ||||
−0.812639 | + | 0.582767i | \(0.801970\pi\) | |||||||
\(578\) | −18.7792 | + | 4.04222i | −0.781110 | + | 0.168134i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.2915 | + | 6.00000i | −0.551900 | + | 0.249136i | ||||
\(581\) | −5.53019 | + | 5.53019i | −0.229431 | + | 0.229431i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.1660i | 1.37360i | ||||||||
\(584\) | 5.53019 | + | 7.48925i | 0.228841 | + | 0.309907i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.77124 | + | 4.29150i | −0.114479 | + | 0.177280i | ||||
\(587\) | −4.76150 | + | 4.76150i | −0.196528 | + | 0.196528i | −0.798510 | − | 0.601982i | \(-0.794378\pi\) |
0.601982 | + | 0.798510i | \(0.294378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5830 | + | 20.5830i | 0.848108 | + | 0.848108i | ||||
\(590\) | 1.53737 | + | 7.14226i | 0.0632927 | + | 0.294042i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.228757 | + | 3.64575i | 0.00940184 | + | 0.149839i | ||||
\(593\) | 22.1208 | 0.908391 | 0.454195 | − | 0.890902i | \(-0.349927\pi\) | ||||
0.454195 | + | 0.890902i | \(0.349927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.41699 | − | 5.41699i | −0.222075 | − | 0.222075i | ||||
\(596\) | 11.6556 | − | 30.8377i | 0.477431 | − | 1.26316i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.4575 | − | 19.2915i | 0.509426 | − | 0.788888i | ||||
\(599\) | − | 13.8628i | − | 0.566420i | −0.959058 | − | 0.283210i | \(-0.908601\pi\) | ||
0.959058 | − | 0.283210i | \(-0.0913993\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.29150i | − | 0.134263i | −0.997744 | − | 0.0671316i | \(-0.978615\pi\) | ||
0.997744 | − | 0.0671316i | \(-0.0213847\pi\) | |||||||
\(602\) | −0.979531 | − | 0.632534i | −0.0399227 | − | 0.0257801i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.52026 | − | 18.8745i | −0.346684 | − | 0.767993i | ||||
\(605\) | −6.89407 | − | 6.89407i | −0.280284 | − | 0.280284i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1033 | 0.572434 | 0.286217 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286217 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(608\) | 28.0726 | − | 7.91094i | 1.13850 | − | 0.320831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.06275 | − | 0.228757i | 0.0430293 | − | 0.00926208i | ||||
\(611\) | −24.0798 | − | 24.0798i | −0.974165 | − | 0.974165i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6458 | − | 26.6458i | 1.07621 | − | 1.07621i | 0.0793662 | − | 0.996846i | \(-0.474710\pi\) |
0.996846 | − | 0.0793662i | \(-0.0252897\pi\) | |||||||
\(614\) | 33.6028 | + | 21.6991i | 1.35610 | + | 0.875703i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.8745 | + | 3.29150i | 0.881349 | + | 0.132618i | ||||
\(617\) | 31.6438i | 1.27393i | 0.770893 | + | 0.636965i | \(0.219810\pi\) | ||||
−0.770893 | + | 0.636965i | \(0.780190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.1660 | + | 21.1660i | −0.850734 | + | 0.850734i | −0.990224 | − | 0.139490i | \(-0.955454\pi\) |
0.139490 | + | 0.990224i | \(0.455454\pi\) | |||||||
\(620\) | −3.36028 | + | 8.89047i | −0.134952 | + | 0.357050i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.58301 | + | 12.0000i | 0.103569 | + | 0.481156i | ||||
\(623\) | 3.91813 | 0.156976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8745 | −0.594980 | ||||||||
\(626\) | −2.76510 | − | 12.8459i | −0.110515 | − | 0.513427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.5830 | − | 6.64575i | −0.701638 | − | 0.265194i | ||||
\(629\) | −3.57113 | + | 3.57113i | −0.142390 | + | 0.142390i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.22876i | − | 0.327582i | −0.986495 | − | 0.163791i | \(-0.947628\pi\) | ||
0.986495 | − | 0.163791i | \(-0.0523722\pi\) | |||||||
\(632\) | −21.9473 | + | 16.2062i | −0.873015 | + | 0.644649i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.00000 | + | 0.645751i | 0.0397151 | + | 0.0256461i | ||||
\(635\) | 0.557842 | − | 0.557842i | 0.0221373 | − | 0.0221373i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3542 | + | 11.3542i | 0.449872 | + | 0.449872i | ||||
\(638\) | 56.9140 | − | 12.2508i | 2.25325 | − | 0.485012i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.12549 | + | 7.29150i | 0.242131 | + | 0.288222i | ||||
\(641\) | 16.5906 | 0.655288 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.64575 | − | 3.64575i | −0.143774 | − | 0.143774i | 0.631556 | − | 0.775330i | \(-0.282417\pi\) |
−0.775330 | + | 0.631556i | \(0.782417\pi\) | |||||||
\(644\) | 13.0194 | − | 5.87719i | 0.513038 | − | 0.231594i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33.8745 | + | 21.8745i | 1.33277 | + | 0.860641i | ||||
\(647\) | 4.33981i | 0.170616i | 0.996355 | + | 0.0853079i | \(0.0271874\pi\) | ||||
−0.996355 | + | 0.0853079i | \(0.972813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.1660i | − | 1.14487i | ||||||
\(650\) | 12.3188 | − | 19.0767i | 0.483184 | − | 0.748252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.8118 | + | 11.6458i | 1.20668 | + | 0.456083i | ||||
\(653\) | −20.7569 | − | 20.7569i | −0.812280 | − | 0.812280i | 0.172696 | − | 0.984975i | \(-0.444752\pi\) |
−0.984975 | + | 0.172696i | \(0.944752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 23.7328 | + | 20.9304i | 0.926611 | + | 0.817194i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.45751 | − | 20.7085i | −0.173772 | − | 0.807301i | ||||
\(659\) | 24.9232 | + | 24.9232i | 0.970870 | + | 0.970870i | 0.999588 | − | 0.0287175i | \(-0.00914231\pi\) |
−0.0287175 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.77124 | + | 2.77124i | −0.107789 | + | 0.107789i | −0.758944 | − | 0.651155i | \(-0.774285\pi\) |
0.651155 | + | 0.758944i | \(0.274285\pi\) | |||||||
\(662\) | 8.67963 | − | 13.4411i | 0.337343 | − | 0.522404i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2915 | + | 2.00000i | 0.515810 | + | 0.0776151i | ||||
\(665\) | 7.14226i | 0.276965i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.5830 | − | 26.5830i | 1.02930 | − | 1.02930i | ||||
\(668\) | −14.6315 | − | 32.4125i | −0.566110 | − | 1.25408i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.58301 | + | 1.41699i | −0.254324 | + | 0.0547433i | ||||
\(671\) | −4.33981 | −0.167537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | −6.50972 | + | 1.40122i | −0.250745 | + | 0.0539730i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.822876 | + | 1.82288i | 0.0316491 | + | 0.0701106i | ||||
\(677\) | −14.0363 | + | 14.0363i | −0.539460 | + | 0.539460i | −0.923370 | − | 0.383911i | \(-0.874577\pi\) |
0.383911 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4170i | 0.668403i | ||||||||
\(680\) | −1.95906 | + | 13.0194i | −0.0751266 | + | 0.499273i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.5830 | − | 31.8745i | 0.788164 | − | 1.22054i | ||||
\(683\) | −0.557842 | + | 0.557842i | −0.0213452 | + | 0.0213452i | −0.717699 | − | 0.696354i | \(-0.754805\pi\) |
0.696354 | + | 0.717699i | \(0.254805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.12549 | − | 6.12549i | −0.234043 | − | 0.234043i | ||||
\(686\) | 5.53019 | + | 25.6919i | 0.211144 | + | 0.980921i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.125492 | + | 2.00000i | 0.00478434 | + | 0.0762493i | ||||
\(689\) | −26.1136 | −0.994848 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.64575 | − | 3.64575i | −0.138691 | − | 0.138691i | 0.634353 | − | 0.773044i | \(-0.281267\pi\) |
−0.773044 | + | 0.634353i | \(0.781267\pi\) | |||||||
\(692\) | 13.0568 | + | 4.93500i | 0.496345 | + | 0.187601i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.64575 | + | 5.64575i | −0.138391 | + | 0.214310i | ||||
\(695\) | 17.3593i | 0.658474i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.7490i | 1.65711i | ||||||||
\(698\) | −5.42477 | − | 3.50305i | −0.205330 | − | 0.132592i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.8745 | − | 5.81176i | 0.486611 | − | 0.219664i | ||||
\(701\) | −4.16632 | − | 4.16632i | −0.157360 | − | 0.157360i | 0.624036 | − | 0.781396i | \(-0.285492\pi\) |
−0.781396 | + | 0.624036i | \(0.785492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.70850 | 0.177584 | ||||||||
\(704\) | −17.7809 | − | 33.6028i | −0.670145 | − | 1.26645i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.87451 | + | 2.12549i | −0.371632 | + | 0.0799940i | ||||
\(707\) | −0.979531 | − | 0.979531i | −0.0368391 | − | 0.0368391i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.77124 | + | 8.77124i | −0.329411 | + | 0.329411i | −0.852362 | − | 0.522951i | \(-0.824831\pi\) |
0.522951 | + | 0.852362i | \(0.324831\pi\) | |||||||
\(710\) | −13.4411 | − | 8.67963i | −0.504437 | − | 0.325741i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00000 | − | 5.41699i | −0.149906 | − | 0.203010i | ||||
\(713\) | − | 24.5015i | − | 0.917589i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5830 | − | 10.5830i | 0.395782 | − | 0.395782i | ||||
\(716\) | −6.29888 | − | 2.38075i | −0.235400 | − | 0.0889729i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.41699 | + | 6.58301i | 0.0528818 | + | 0.245676i | ||||
\(719\) | −40.3234 | −1.50381 | −0.751904 | − | 0.659272i | \(-0.770865\pi\) | ||||
−0.751904 | + | 0.659272i | \(0.770865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.8745 | 1.03810 | ||||||||
\(722\) | −2.25666 | − | 10.4839i | −0.0839841 | − | 0.390169i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.645751 | + | 1.70850i | −0.0239992 | + | 0.0634958i | ||||
\(725\) | 26.2871 | − | 26.2871i | 0.976278 | − | 0.976278i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.3948i | − | 1.23854i | −0.785177 | − | 0.619272i | \(-0.787428\pi\) | ||
0.785177 | − | 0.619272i | \(-0.212572\pi\) | |||||||
\(728\) | −2.59160 | + | 17.2231i | −0.0960510 | + | 0.638331i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.29150 | + | 2.12549i | 0.121824 | + | 0.0786680i | ||||
\(731\) | −1.95906 | + | 1.95906i | −0.0724586 | + | 0.0724586i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6458 | − | 12.6458i | −0.467081 | − | 0.467081i | 0.433886 | − | 0.900968i | \(-0.357142\pi\) |
−0.900968 | + | 0.433886i | \(0.857142\pi\) | |||||||
\(734\) | −48.1289 | + | 10.3598i | −1.77647 | + | 0.382386i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.4170 | − | 12.0000i | −0.789441 | − | 0.442326i | ||||
\(737\) | 26.8823 | 0.990221 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.16601 | − | 9.16601i | −0.337177 | − | 0.337177i | 0.518127 | − | 0.855304i | \(-0.326630\pi\) |
−0.855304 | + | 0.518127i | \(0.826630\pi\) | |||||||
\(740\) | 0.632534 | + | 1.40122i | 0.0232524 | + | 0.0515099i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.6458 | − | 8.81176i | −0.500951 | − | 0.323490i | ||||
\(743\) | 22.5425i | 0.827002i | 0.910504 | + | 0.413501i | \(0.135694\pi\) | ||||
−0.910504 | + | 0.413501i | \(0.864306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.8745i | − | 0.508323i | ||||||
\(746\) | −12.9514 | + | 20.0563i | −0.474183 | + | 0.734312i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.5830 | − | 49.1660i | 0.679462 | − | 1.79769i | ||||
\(749\) | −3.91813 | − | 3.91813i | −0.143165 | − | 0.143165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.9373 | 0.472087 | 0.236044 | − | 0.971742i | \(-0.424149\pi\) | ||||
0.236044 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(752\) | −24.0798 | + | 27.3040i | −0.878101 | + | 0.995673i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.64575 | + | 44.8118i | 0.351278 | + | 1.63195i | ||||
\(755\) | −6.16272 | − | 6.16272i | −0.224284 | − | 0.224284i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.22876 | + | 7.22876i | −0.262734 | + | 0.262734i | −0.826164 | − | 0.563430i | \(-0.809481\pi\) |
0.563430 | + | 0.826164i | \(0.309481\pi\) | |||||||
\(758\) | −9.06397 | + | 14.0363i | −0.329218 | + | 0.509822i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.87451 | − | 7.29150i | 0.358186 | − | 0.264491i | ||||
\(761\) | 7.91094i | 0.286771i | 0.989667 | + | 0.143386i | \(0.0457989\pi\) | ||||
−0.989667 | + | 0.143386i | \(0.954201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9373 | + | 10.9373i | −0.395955 | + | 0.395955i | ||||
\(764\) | 16.5906 | − | 7.48925i | 0.600226 | − | 0.270952i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.5830 | − | 2.70850i | 0.454642 | − | 0.0978620i | ||||
\(767\) | 22.9641 | 0.829187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.2915 | 0.623548 | 0.311774 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311774 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(770\) | 9.10132 | − | 1.95906i | 0.327989 | − | 0.0705997i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.6458 | − | 9.77124i | 0.779048 | − | 0.351675i | ||||
\(773\) | −21.5256 | + | 21.5256i | −0.774221 | + | 0.774221i | −0.978841 | − | 0.204620i | \(-0.934404\pi\) |
0.204620 | + | 0.978841i | \(0.434404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 24.2288i | − | 0.870323i | ||||||
\(776\) | 24.0798 | − | 17.7809i | 0.864415 | − | 0.638299i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.5203 | + | 34.8745i | −0.807390 | + | 1.25031i | ||||
\(779\) | 28.8413 | − | 28.8413i | 1.03335 | − | 1.03335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.1660 | + | 45.1660i | 1.61617 | + | 1.61617i | ||||
\(782\) | −7.14226 | − | 33.1811i | −0.255407 | − | 1.18656i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.3542 | − | 12.8745i | 0.405509 | − | 0.459804i | ||||
\(785\) | −7.91094 | −0.282354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.22876 | + | 6.22876i | 0.222031 | + | 0.222031i | 0.809353 | − | 0.587322i | \(-0.199818\pi\) |
−0.587322 | + | 0.809353i | \(0.699818\pi\) | |||||||
\(788\) | −8.50613 | + | 22.5051i | −0.303018 | + | 0.801711i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.22876 | + | 9.64575i | −0.221609 | + | 0.343180i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.41699i | − | 0.121341i | ||||||
\(794\) | −13.5466 | − | 8.74771i | −0.480749 | − | 0.310444i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.2288 | + | 24.8745i | 0.397993 | + | 0.881654i | ||||
\(797\) | 21.5256 | + | 21.5256i | 0.762475 | + | 0.762475i | 0.976769 | − | 0.214294i | \(-0.0687451\pi\) |
−0.214294 | + | 0.976769i | \(0.568745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.3320 | −1.78062 | ||||||||
\(800\) | −21.1786 | − | 11.8664i | −0.748776 | − | 0.419541i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.9373 | + | 4.93725i | −0.809943 | + | 0.174340i | ||||
\(803\) | −11.0604 | − | 11.0604i | −0.390312 | − | 0.390312i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.25098 | − | 4.25098i | 0.149828 | − | 0.149828i | ||||
\(806\) | 25.0967 | + | 16.2062i | 0.883994 | + | 0.570840i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.354249 | + | 2.35425i | −0.0124624 | + | 0.0828222i | ||||
\(809\) | − | 17.4339i | − | 0.612945i | −0.951880 | − | 0.306473i | \(-0.900851\pi\) | ||
0.951880 | − | 0.306473i | \(-0.0991488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6458 | + | 15.6458i | −0.549397 | + | 0.549397i | −0.926266 | − | 0.376870i | \(-0.877000\pi\) |
0.376870 | + | 0.926266i | \(0.377000\pi\) | |||||||
\(812\) | −10.0808 | + | 26.6714i | −0.353768 | + | 0.935983i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.29150 | − | 6.00000i | −0.0452671 | − | 0.210300i | ||||
\(815\) | 13.8628 | 0.485593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.58301 | 0.0903679 | ||||||||
\(818\) | 7.48925 | + | 34.7932i | 0.261856 | + | 1.21652i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.4575 | + | 4.70850i | 0.435035 | + | 0.164428i | ||||
\(821\) | 7.73744 | − | 7.73744i | 0.270039 | − | 0.270039i | −0.559077 | − | 0.829116i | \(-0.688844\pi\) |
0.829116 | + | 0.559077i | \(0.188844\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.2288i | − | 1.12342i | −0.827333 | − | 0.561712i | \(-0.810143\pi\) | ||
0.827333 | − | 0.561712i | \(-0.189857\pi\) | |||||||
\(824\) | −28.4570 | − | 38.5378i | −0.991346 | − | 1.34253i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | + | 7.74902i | 0.417533 | + | 0.269623i | ||||
\(827\) | 4.33981 | − | 4.33981i | 0.150910 | − | 0.150910i | −0.627614 | − | 0.778524i | \(-0.715968\pi\) |
0.778524 | + | 0.627614i | \(0.215968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6458 | + | 14.6458i | 0.508668 | + | 0.508668i | 0.914117 | − | 0.405449i | \(-0.132885\pi\) |
−0.405449 | + | 0.914117i | \(0.632885\pi\) | |||||||
\(830\) | 5.53019 | − | 1.19038i | 0.191956 | − | 0.0413186i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.4575 | − | 14.0000i | 0.917249 | − | 0.485363i | ||||
\(833\) | 23.7328 | 0.822294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5830 | − | 10.5830i | −0.366240 | − | 0.366240i | ||||
\(836\) | −44.6632 | + | 20.1617i | −1.54471 | + | 0.697307i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.5203 | − | 20.3542i | −1.08885 | − | 0.703126i | ||||
\(839\) | − | 52.9212i | − | 1.82704i | −0.406793 | − | 0.913521i | \(-0.633353\pi\) | ||
0.406793 | − | 0.913521i | \(-0.366647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.0405i | 1.58760i | ||||||||
\(842\) | −12.3188 | + | 19.0767i | −0.424535 | + | 0.657428i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −38.5830 | − | 14.5830i | −1.32808 | − | 0.501968i | ||||
\(845\) | 0.595188 | + | 0.595188i | 0.0204751 | + | 0.0204751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0627 | −0.655004 | ||||||||
\(848\) | 1.74822 | + | 27.8618i | 0.0600341 | + | 0.956778i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.06275 | − | 32.8118i | −0.242250 | − | 1.12543i | ||||
\(851\) | −2.80244 | − | 2.80244i | −0.0960664 | − | 0.0960664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9373 | − | 11.9373i | 0.408724 | − | 0.408724i | −0.472570 | − | 0.881293i | \(-0.656673\pi\) |
0.881293 | + | 0.472570i | \(0.156673\pi\) | |||||||
\(854\) | 1.15303 | − | 1.78556i | 0.0394559 | − | 0.0611007i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.41699 | + | 9.41699i | −0.0484319 | + | 0.321866i | ||||
\(857\) | − | 10.2917i | − | 0.351558i | −0.984430 | − | 0.175779i | \(-0.943756\pi\) | ||
0.984430 | − | 0.175779i | \(-0.0562443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.77124 | + | 5.77124i | −0.196912 | + | 0.196912i | −0.798675 | − | 0.601763i | \(-0.794465\pi\) |
0.601763 | + | 0.798675i | \(0.294465\pi\) | |||||||
\(860\) | 0.346998 | + | 0.768687i | 0.0118325 | + | 0.0262120i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.1660 | + | 9.29150i | −1.47024 | + | 0.316470i | ||||
\(863\) | 53.3428 | 1.81581 | 0.907906 | − | 0.419174i | \(-0.137680\pi\) | ||||
0.907906 | + | 0.419174i | \(0.137680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.87451 | 0.199739 | ||||||||
\(866\) | 5.53019 | − | 1.19038i | 0.187924 | − | 0.0404506i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.64575 | + | 16.9373i | 0.259514 | + | 0.574888i | ||||
\(869\) | 32.4125 | − | 32.4125i | 1.09952 | − | 1.09952i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1660i | 0.717183i | ||||||||
\(872\) | 26.2871 | + | 3.95547i | 0.890193 | + | 0.133949i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.1660 | + | 26.5830i | −0.580649 | + | 0.899184i | ||||
\(875\) | 9.10132 | − | 9.10132i | 0.307681 | − | 0.307681i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.9373 | − | 21.9373i | −0.740768 | − | 0.740768i | 0.231957 | − | 0.972726i | \(-0.425487\pi\) |
−0.972726 | + | 0.231957i | \(0.925487\pi\) | |||||||
\(878\) | 0.142768 | + | 0.663265i | 0.00481819 | + | 0.0223841i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0000 | − | 10.5830i | −0.404520 | − | 0.356753i | ||||
\(881\) | −14.9785 | −0.504639 | −0.252319 | − | 0.967644i | \(-0.581193\pi\) | ||||
−0.252319 | + | 0.967644i | \(0.581193\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3948 | − | 35.3948i | −1.19113 | − | 1.19113i | −0.976751 | − | 0.214378i | \(-0.931228\pi\) |
−0.214378 | − | 0.976751i | \(-0.568772\pi\) | |||||||
\(884\) | 38.7113 | + | 14.6315i | 1.30200 | + | 0.492111i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.3948 | + | 36.2288i | −0.785963 | + | 1.21713i | ||||
\(887\) | − | 4.76150i | − | 0.159876i | −0.996800 | − | 0.0799378i | \(-0.974528\pi\) | ||
0.996800 | − | 0.0799378i | \(-0.0254722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.54249i | − | 0.0517333i | ||||||
\(890\) | −2.38075 | − | 1.53737i | −0.0798030 | − | 0.0515329i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.1660 | + | 11.8118i | −0.876103 | + | 0.395487i | ||||
\(893\) | 33.1811 | + | 33.1811i | 1.11036 | + | 1.11036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.83399 | −0.0947298 | ||||||||
\(896\) | 18.5496 | + | 1.61206i | 0.619700 | + | 0.0538553i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.0627 | + | 2.81176i | −0.435909 | + | 0.0938297i | ||||
\(899\) | 34.5824 | + | 34.5824i | 1.15339 | + | 1.15339i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.2915 | + | 27.2915i | −0.909212 | + | 0.909212i | ||||
\(902\) | −44.6632 | − | 28.8413i | −1.48712 | − | 0.960311i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.768687i | 0.0255520i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.1033 | − | 16.1033i | 0.534700 | − | 0.534700i | −0.387267 | − | 0.921967i | \(-0.626581\pi\) |
0.921967 | + | 0.387267i | \(0.126581\pi\) | |||||||
\(908\) | −3.70728 | − | 1.40122i | −0.123030 | − | 0.0465011i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.54249 | + | 7.16601i | 0.0511329 | + | 0.237551i | ||||
\(911\) | −5.18319 | −0.171727 | −0.0858634 | − | 0.996307i | \(-0.527365\pi\) | ||||
−0.0858634 | + | 0.996307i | \(0.527365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5830 | −0.747388 | ||||||||
\(914\) | −1.61206 | − | 7.48925i | −0.0533224 | − | 0.247722i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.9373 | − | 47.4575i | 0.592664 | − | 1.56804i | ||||
\(917\) | 11.0604 | − | 11.0604i | 0.365246 | − | 0.365246i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1033i | 1.38886i | 0.719561 | + | 0.694429i | \(0.244343\pi\) | ||||
−0.719561 | + | 0.694429i | \(0.755657\pi\) | |||||||
\(920\) | −10.2170 | − | 1.53737i | −0.336845 | − | 0.0506857i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.2915 | − | 9.22876i | −0.470666 | − | 0.303933i | ||||
\(923\) | −35.5619 | + | 35.5619i | −1.17053 | + | 1.17053i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.77124 | − | 2.77124i | −0.0911179 | − | 0.0911179i | ||||
\(926\) | −20.8250 | + | 4.48258i | −0.684351 | + | 0.147307i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 47.1660 | − | 13.2915i | 1.54830 | − | 0.436315i | ||||
\(929\) | −23.7328 | −0.778649 | −0.389324 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389324 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.6458 | − | 15.6458i | −0.512769 | − | 0.512769i | ||||
\(932\) | −16.2436 | − | 35.9836i | −0.532076 | − | 1.17868i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42.8118 | + | 27.6458i | 1.40084 | + | 0.904597i | ||||
\(935\) | − | 22.1208i | − | 0.723426i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.1660i | 1.01815i | 0.860722 | + | 0.509075i | \(0.170012\pi\) | ||||
−0.860722 | + | 0.509075i | \(0.829988\pi\) | |||||||
\(938\) | −7.14226 | + | 11.0604i | −0.233203 | + | 0.361134i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.41699 | + | 14.3320i | −0.176683 | + | 0.467459i | ||||
\(941\) | 12.4243 | + | 12.4243i | 0.405019 | + | 0.405019i | 0.879997 | − | 0.474978i | \(-0.157544\pi\) |
−0.474978 | + | 0.879997i | \(0.657544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3320 | −1.11800 | ||||||||
\(944\) | −1.53737 | − | 24.5015i | −0.0500372 | − | 0.797456i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.708497 | − | 3.29150i | −0.0230352 | − | 0.107016i | ||||
\(947\) | −2.38075 | − | 2.38075i | −0.0773640 | − | 0.0773640i | 0.667366 | − | 0.744730i | \(-0.267422\pi\) |
−0.744730 | + | 0.667366i | \(0.767422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.70850 | − | 8.70850i | 0.282690 | − | 0.282690i | ||||
\(950\) | −16.9749 | + | 26.2871i | −0.550739 | + | 0.852865i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.2915 | + | 20.7085i | 0.495600 | + | 0.671166i | ||||
\(953\) | − | 25.2702i | − | 0.818582i | −0.912404 | − | 0.409291i | \(-0.865776\pi\) | ||
0.912404 | − | 0.409291i | \(-0.134224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.41699 | − | 5.41699i | 0.175290 | − | 0.175290i | ||||
\(956\) | −23.7328 | + | 10.7134i | −0.767574 | + | 0.346496i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.5830 | − | 6.58301i | 0.988092 | − | 0.212687i | ||||
\(959\) | −16.9376 | −0.546943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.874508 | 0.0282099 | ||||||||
\(962\) | 4.72416 | − | 1.01688i | 0.152313 | − | 0.0327854i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.35425 | + | 1.06275i | −0.0758252 | + | 0.0342287i | ||||
\(965\) | 7.06756 | − | 7.06756i | 0.227513 | − | 0.227513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.3948i | − | 1.45980i | −0.683555 | − | 0.729899i | \(-0.739567\pi\) | ||
0.683555 | − | 0.729899i | \(-0.260433\pi\) | |||||||
\(968\) | 19.4611 | + | 26.3552i | 0.625503 | + | 0.847087i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.83399 | − | 10.5830i | 0.219426 | − | 0.339800i | ||||
\(971\) | −20.7195 | + | 20.7195i | −0.664922 | + | 0.664922i | −0.956536 | − | 0.291614i | \(-0.905808\pi\) |
0.291614 | + | 0.956536i | \(0.405808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000 | + | 24.0000i | 0.769405 | + | 0.769405i | ||||
\(974\) | −2.44883 | − | 11.3766i | −0.0784655 | − | 0.364531i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.64575 | + | 0.228757i | −0.116698 | + | 0.00732232i | ||||
\(977\) | −20.5087 | −0.656131 | −0.328066 | − | 0.944655i | \(-0.606397\pi\) | ||||
−0.328066 | + | 0.944655i | \(0.606397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | + | 8.00000i | 0.255681 | + | 0.255681i | ||||
\(980\) | 2.55425 | − | 6.75791i | 0.0815925 | − | 0.215874i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.7085 | + | 25.8745i | −0.533190 | + | 0.825689i | ||||
\(983\) | − | 26.8823i | − | 0.857411i | −0.903444 | − | 0.428706i | \(-0.858970\pi\) | ||
0.903444 | − | 0.428706i | \(-0.141030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1255i | 0.322625i | ||||||||
\(986\) | 56.9140 | + | 36.7523i | 1.81251 | + | 1.17043i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.8745 | − | 35.1660i | −0.505035 | − | 1.11878i | ||||
\(989\) | −1.53737 | − | 1.53737i | −0.0488856 | − | 0.0488856i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.06275 | 0.0972913 | 0.0486457 | − | 0.998816i | \(-0.484509\pi\) | ||||
0.0486457 | + | 0.998816i | \(0.484509\pi\) | |||||||
\(992\) | 15.6110 | − | 27.8618i | 0.495651 | − | 0.884613i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.5830 | + | 6.58301i | −0.970034 | + | 0.208800i | ||||
\(995\) | 8.12179 | + | 8.12179i | 0.257478 | + | 0.257478i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.5203 | − | 36.5203i | 1.15661 | − | 1.15661i | 0.171408 | − | 0.985200i | \(-0.445168\pi\) |
0.985200 | − | 0.171408i | \(-0.0548317\pi\) | |||||||
\(998\) | −17.7809 | − | 11.4821i | −0.562846 | − | 0.363459i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.k.c.109.1 | yes | 8 | |
3.2 | odd | 2 | inner | 144.2.k.c.109.4 | yes | 8 | |
4.3 | odd | 2 | 576.2.k.c.145.3 | 8 | |||
8.3 | odd | 2 | 1152.2.k.d.289.2 | 8 | |||
8.5 | even | 2 | 1152.2.k.e.289.2 | 8 | |||
12.11 | even | 2 | 576.2.k.c.145.2 | 8 | |||
16.3 | odd | 4 | 1152.2.k.d.865.2 | 8 | |||
16.5 | even | 4 | inner | 144.2.k.c.37.1 | ✓ | 8 | |
16.11 | odd | 4 | 576.2.k.c.433.3 | 8 | |||
16.13 | even | 4 | 1152.2.k.e.865.2 | 8 | |||
24.5 | odd | 2 | 1152.2.k.e.289.3 | 8 | |||
24.11 | even | 2 | 1152.2.k.d.289.3 | 8 | |||
32.5 | even | 8 | 9216.2.a.bq.1.6 | 8 | |||
32.11 | odd | 8 | 9216.2.a.bt.1.3 | 8 | |||
32.21 | even | 8 | 9216.2.a.bq.1.3 | 8 | |||
32.27 | odd | 8 | 9216.2.a.bt.1.6 | 8 | |||
48.5 | odd | 4 | inner | 144.2.k.c.37.4 | yes | 8 | |
48.11 | even | 4 | 576.2.k.c.433.2 | 8 | |||
48.29 | odd | 4 | 1152.2.k.e.865.3 | 8 | |||
48.35 | even | 4 | 1152.2.k.d.865.3 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bq.1.4 | 8 | |||
96.11 | even | 8 | 9216.2.a.bt.1.5 | 8 | |||
96.53 | odd | 8 | 9216.2.a.bq.1.5 | 8 | |||
96.59 | even | 8 | 9216.2.a.bt.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.1 | ✓ | 8 | 16.5 | even | 4 | inner | |
144.2.k.c.37.4 | yes | 8 | 48.5 | odd | 4 | inner | |
144.2.k.c.109.1 | yes | 8 | 1.1 | even | 1 | trivial | |
144.2.k.c.109.4 | yes | 8 | 3.2 | odd | 2 | inner | |
576.2.k.c.145.2 | 8 | 12.11 | even | 2 | |||
576.2.k.c.145.3 | 8 | 4.3 | odd | 2 | |||
576.2.k.c.433.2 | 8 | 48.11 | even | 4 | |||
576.2.k.c.433.3 | 8 | 16.11 | odd | 4 | |||
1152.2.k.d.289.2 | 8 | 8.3 | odd | 2 | |||
1152.2.k.d.289.3 | 8 | 24.11 | even | 2 | |||
1152.2.k.d.865.2 | 8 | 16.3 | odd | 4 | |||
1152.2.k.d.865.3 | 8 | 48.35 | even | 4 | |||
1152.2.k.e.289.2 | 8 | 8.5 | even | 2 | |||
1152.2.k.e.289.3 | 8 | 24.5 | odd | 2 | |||
1152.2.k.e.865.2 | 8 | 16.13 | even | 4 | |||
1152.2.k.e.865.3 | 8 | 48.29 | odd | 4 | |||
9216.2.a.bq.1.3 | 8 | 32.21 | even | 8 | |||
9216.2.a.bq.1.4 | 8 | 96.5 | odd | 8 | |||
9216.2.a.bq.1.5 | 8 | 96.53 | odd | 8 | |||
9216.2.a.bq.1.6 | 8 | 32.5 | even | 8 | |||
9216.2.a.bt.1.3 | 8 | 32.11 | odd | 8 | |||
9216.2.a.bt.1.4 | 8 | 96.59 | even | 8 | |||
9216.2.a.bt.1.5 | 8 | 96.11 | even | 8 | |||
9216.2.a.bt.1.6 | 8 | 32.27 | odd | 8 |