Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.2.c.a.383.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.23607i | − | 0.552786i | −0.961045 | − | 0.276393i | \(-0.910861\pi\) | ||
0.961045 | − | 0.276393i | \(-0.0891392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607i | 1.22312i | 0.791199 | + | 0.611559i | \(0.209457\pi\) | ||||
−0.791199 | + | 0.611559i | \(0.790543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.763932 | 0.230334 | 0.115167 | − | 0.993346i | \(-0.463260\pi\) | ||||
0.115167 | + | 0.993346i | \(0.463260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.763932 | + | 2.00000i | −0.197246 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.47214i | − | 1.56972i | −0.619671 | − | 0.784862i | \(-0.712734\pi\) | ||
0.619671 | − | 0.784862i | \(-0.287266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.23607i | − | 1.20124i | −0.799536 | − | 0.600618i | \(-0.794921\pi\) | ||
0.799536 | − | 0.600618i | \(-0.205079\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 5.23607i | 0.436436 | − | 1.14260i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.47214 | 1.34953 | 0.674767 | − | 0.738031i | \(-0.264244\pi\) | ||||
0.674767 | + | 0.738031i | \(0.264244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.47214 | 0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.23607i | 1.71509i | 0.514405 | + | 0.857547i | \(0.328013\pi\) | ||||
−0.514405 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.763932i | − | 0.137206i | −0.997644 | − | 0.0686031i | \(-0.978146\pi\) | ||
0.997644 | − | 0.0686031i | \(-0.0218542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23607 | − | 0.472136i | −0.215172 | − | 0.0821883i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.472136 | −0.0776187 | −0.0388093 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388093 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.23607 | − | 2.76393i | −1.15870 | − | 0.442583i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.47214i | 0.386083i | 0.981191 | + | 0.193041i | \(0.0618352\pi\) | ||||
−0.981191 | + | 0.193041i | \(0.938165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76393i | 0.421496i | 0.977540 | + | 0.210748i | \(0.0675899\pi\) | ||||
−0.977540 | + | 0.210748i | \(0.932410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.47214 | − | 2.76393i | 0.368524 | − | 0.412023i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.47214 | −0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | + | 10.4721i | −0.560112 | + | 1.46639i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.23607i | − | 0.169787i | −0.996390 | − | 0.0848935i | \(-0.972945\pi\) | ||
0.996390 | − | 0.0848935i | \(-0.0270550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.944272i | − | 0.127326i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.23607 | + | 8.47214i | −0.428628 | + | 1.12216i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23607 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.47214 | −1.08475 | −0.542373 | − | 0.840138i | \(-0.682474\pi\) | ||||
−0.542373 | + | 0.840138i | \(0.682474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.47214 | + | 7.23607i | −0.815412 | + | 0.911659i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.52786i | − | 0.685647i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70820i | 0.453029i | 0.974008 | + | 0.226515i | \(0.0727331\pi\) | ||||
−0.974008 | + | 0.226515i | \(0.927267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.4721 | − | 4.00000i | −1.26070 | − | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4164 | −1.35488 | −0.677439 | − | 0.735579i | \(-0.736910\pi\) | ||||
−0.677439 | + | 0.735579i | \(0.736910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.61803 | − | 2.14590i | −0.648715 | − | 0.247787i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.47214i | 0.281726i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.7082i | − | 1.54229i | −0.636657 | − | 0.771147i | \(-0.719683\pi\) | ||
0.636657 | − | 0.771147i | \(-0.280317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.23607 | 0.794262 | 0.397131 | − | 0.917762i | \(-0.370006\pi\) | ||||
0.397131 | + | 0.917762i | \(0.370006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.70820 | − | 14.9443i | 0.611984 | − | 1.60219i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.00000i | − | 0.423999i | −0.977270 | − | 0.212000i | \(-0.932002\pi\) | ||
0.977270 | − | 0.212000i | \(-0.0679975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4721i | 1.51709i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.472136 | + | 1.23607i | −0.0489582 | + | 0.128174i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.47214 | −0.664027 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.70820 | + | 1.52786i | 0.171681 | + | 0.153556i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7082i | 1.16501i | 0.812827 | + | 0.582505i | \(0.197927\pi\) | ||||
−0.812827 | + | 0.582505i | \(0.802073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.18034i | 0.806033i | 0.915193 | + | 0.403016i | \(0.132038\pi\) | ||||
−0.915193 | + | 0.403016i | \(0.867962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.47214 | − | 2.47214i | −0.631616 | − | 0.241256i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.18034 | 0.790823 | 0.395412 | − | 0.918504i | \(-0.370602\pi\) | ||||
0.395412 | + | 0.918504i | \(0.370602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.472136 | −0.0452224 | −0.0226112 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226112 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.763932 | + | 0.291796i | 0.0725092 | + | 0.0276961i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000i | 0.752577i | 0.926503 | + | 0.376288i | \(0.122800\pi\) | ||||
−0.926503 | + | 0.376288i | \(0.877200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.00000i | − | 0.746004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.0000 | + | 8.94427i | 0.924500 | + | 0.826898i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.9443 | 1.91996 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.52786 | − | 4.00000i | 0.137763 | − | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.4721i | − | 0.936656i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.76393i | − | 0.777673i | −0.921307 | − | 0.388837i | \(-0.872877\pi\) | ||
0.921307 | − | 0.388837i | \(-0.127123\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.70820 | − | 4.47214i | 0.150399 | − | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2361 | −0.981700 | −0.490850 | − | 0.871244i | \(-0.663314\pi\) | ||||
−0.490850 | + | 0.871244i | \(0.663314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.9443 | 1.46925 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.70820 | + | 2.94427i | −0.491284 | + | 0.253403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.4721i | − | 0.894695i | −0.894360 | − | 0.447347i | \(-0.852369\pi\) | ||
0.894360 | − | 0.447347i | \(-0.147631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.70820i | 0.314526i | 0.987557 | + | 0.157263i | \(0.0502670\pi\) | ||||
−0.987557 | + | 0.157263i | \(0.949733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9443 | − | 4.94427i | −1.09010 | − | 0.416383i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.41641 | 0.285694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4164 | 0.948081 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.61803 | + | 2.14590i | 0.463368 | + | 0.176991i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.70820i | 0.303788i | 0.988397 | + | 0.151894i | \(0.0485372\pi\) | ||||
−0.988397 | + | 0.151894i | \(0.951463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.29180i | 0.512019i | 0.966674 | + | 0.256010i | \(0.0824079\pi\) | ||||
−0.966674 | + | 0.256010i | \(0.917592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.9443 | − | 14.4721i | 1.04648 | − | 1.17000i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.944272 | −0.0758457 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47214 | 0.356915 | 0.178458 | − | 0.983948i | \(-0.442889\pi\) | ||||
0.178458 | + | 0.983948i | \(0.442889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.763932 | + | 2.00000i | −0.0605838 | + | 0.158610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.9443i | 1.65064i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.1803i | − | 1.42399i | −0.702182 | − | 0.711997i | \(-0.747791\pi\) | ||
0.702182 | − | 0.711997i | \(-0.252209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.583592 | + | 1.52786i | −0.0454326 | + | 0.118944i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.4721 | −1.73895 | −0.869473 | − | 0.493980i | \(-0.835541\pi\) | ||||
−0.869473 | + | 0.493980i | \(0.835541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.4721 | − | 11.7082i | 0.800824 | − | 0.895349i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.65248i | − | 0.657836i | −0.944359 | − | 0.328918i | \(-0.893316\pi\) | ||
0.944359 | − | 0.328918i | \(-0.106684\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2361i | 0.849367i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.23607 | − | 2.00000i | −0.393567 | − | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.1803 | −1.20938 | −0.604688 | − | 0.796463i | \(-0.706702\pi\) | ||||
−0.604688 | + | 0.796463i | \(0.706702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5279 | −0.856859 | −0.428430 | − | 0.903575i | \(-0.640933\pi\) | ||||
−0.428430 | + | 0.903575i | \(0.640933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.7082 | + | 5.23607i | 1.01334 | + | 0.387061i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.583592i | 0.0429065i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.94427i | − | 0.361561i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.9443 | − | 7.70820i | 1.08704 | − | 0.560689i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.94427 | −0.357755 | −0.178877 | − | 0.983871i | \(-0.557247\pi\) | ||||
−0.178877 | + | 0.983871i | \(0.557247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.8885 | 1.71954 | 0.859768 | − | 0.510686i | \(-0.170608\pi\) | ||||
0.859768 | + | 0.510686i | \(0.170608\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.41641 | + | 8.94427i | −0.244654 | + | 0.640513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.23607i | − | 0.658043i | −0.944323 | − | 0.329021i | \(-0.893281\pi\) | ||
0.944323 | − | 0.329021i | \(-0.106719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.1803i | 1.14699i | 0.819208 | + | 0.573497i | \(0.194414\pi\) | ||||
−0.819208 | + | 0.573497i | \(0.805586\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29180 | − | 6.00000i | 0.161651 | − | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.8885 | −2.09776 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.05573 | 0.213421 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.4721 | + | 12.9443i | 1.00588 | + | 0.899689i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.00000i | − | 0.276686i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.76393i | 0.465648i | 0.972519 | + | 0.232824i | \(0.0747967\pi\) | ||||
−0.972519 | + | 0.232824i | \(0.925203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.4721 | + | 7.05573i | 1.26569 | + | 0.483451i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.41641 | 0.232997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47214 | 0.167820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.23607 | + | 1.23607i | 0.218673 | + | 0.0835257i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.9443i | − | 1.94700i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1803i | 0.815656i | 0.913059 | + | 0.407828i | \(0.133714\pi\) | ||||
−0.913059 | + | 0.407828i | \(0.866286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.76393 | + | 6.94427i | 0.517595 | + | 0.462951i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.1803 | 1.33942 | 0.669708 | − | 0.742624i | \(-0.266419\pi\) | ||||
0.669708 | + | 0.742624i | \(0.266419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4721 | 1.35284 | 0.676418 | − | 0.736518i | \(-0.263531\pi\) | ||||
0.676418 | + | 0.736518i | \(0.263531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.52786 | − | 4.00000i | 0.100526 | − | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.05573i | 0.462236i | 0.972926 | + | 0.231118i | \(0.0742384\pi\) | ||||
−0.972926 | + | 0.231118i | \(0.925762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.88854i | − | 0.645057i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.47214 | + | 22.1803i | −0.550324 | + | 1.44077i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29180i | 0.274193i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 23.4164i | − | 1.48995i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.7082 | − | 4.47214i | −0.741977 | − | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2918 | −0.649612 | −0.324806 | − | 0.945781i | \(-0.605299\pi\) | ||||
−0.324806 | + | 0.945781i | \(0.605299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.94427 | 0.310844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9443 | + | 4.94427i | 0.810602 | + | 0.309622i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.05573i | 0.190611i | 0.995448 | + | 0.0953055i | \(0.0303828\pi\) | ||||
−0.995448 | + | 0.0953055i | \(0.969617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.52786i | − | 0.0949369i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.4721 | + | 20.6525i | −1.14340 | + | 1.27836i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.52786 | −0.0942121 | −0.0471061 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471061 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.52786 | −0.0938559 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.47214 | + | 6.47214i | −0.151292 | + | 0.396088i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.18034i | 0.376822i | 0.982090 | + | 0.188411i | \(0.0603337\pi\) | ||||
−0.982090 | + | 0.188411i | \(0.939666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.7082i | − | 0.832714i | −0.909201 | − | 0.416357i | \(-0.863307\pi\) | ||
0.909201 | − | 0.416357i | \(-0.136693\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.94427 | − | 23.4164i | 0.541332 | − | 1.41723i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.65248 | 0.159950 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.4721 | −0.989715 | −0.494857 | − | 0.868974i | \(-0.664780\pi\) | ||||
−0.494857 | + | 0.868974i | \(0.664780\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.52786 | − | 1.70820i | 0.0914708 | − | 0.102267i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.05573i | − | 0.420909i | −0.977604 | − | 0.210455i | \(-0.932506\pi\) | ||
0.977604 | − | 0.210455i | \(-0.0674945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 25.2361i | − | 1.50013i | −0.661365 | − | 0.750064i | \(-0.730023\pi\) | ||
0.661365 | − | 0.750064i | \(-0.269977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4721 | + | 4.00000i | 0.620316 | + | 0.236940i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7082 | + | 5.23607i | 0.803589 | + | 0.306944i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 25.2361i | − | 1.47431i | −0.675725 | − | 0.737153i | \(-0.736169\pi\) | ||
0.675725 | − | 0.737153i | \(-0.263831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.00000i | − | 0.232889i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.81966 | − | 3.52786i | −0.105587 | − | 0.204707i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.9443 | 1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.23607 | − | 18.9443i | 0.415701 | − | 1.08832i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4721i | 0.599633i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.5967i | 1.23259i | 0.787515 | + | 0.616296i | \(0.211367\pi\) | ||||
−0.787515 | + | 0.616296i | \(0.788633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.05573 | − | 13.2361i | 0.287610 | − | 0.752974i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.4721 | −0.820640 | −0.410320 | − | 0.911942i | \(-0.634583\pi\) | ||||
−0.410320 | + | 0.911942i | \(0.634583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.47214 | 0.478873 | 0.239437 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239437 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.94427 | + | 8.00000i | 0.503953 | + | 0.450749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.1246i | 1.52347i | 0.647889 | + | 0.761735i | \(0.275652\pi\) | ||||
−0.647889 | + | 0.761735i | \(0.724348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.05573i | 0.395045i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.2361 | − | 5.05573i | −0.738765 | − | 0.282183i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8885 | −1.88561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.5279 | 0.861331 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.763932 | + | 0.291796i | 0.0422455 | + | 0.0161364i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.8885i | 1.42728i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.5410i | 1.89855i | 0.314453 | + | 0.949273i | \(0.398179\pi\) | ||||
−0.314453 | + | 0.949273i | \(0.601821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.05573 | − | 0.944272i | −0.0578535 | − | 0.0517458i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.58359 | 0.250428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3607 | −1.21806 | −0.609032 | − | 0.793146i | \(-0.708442\pi\) | ||||
−0.609032 | + | 0.793146i | \(0.708442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.94427 | − | 12.9443i | 0.268536 | − | 0.703036i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.583592i | − | 0.0316033i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164i | 0.616428i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.94427 | + | 12.9443i | −0.266191 | + | 0.696896i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2918 | −0.552493 | −0.276246 | − | 0.961087i | \(-0.589091\pi\) | ||||
−0.276246 | + | 0.961087i | \(0.589091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5279 | −1.04530 | −0.522651 | − | 0.852547i | \(-0.675057\pi\) | ||||
−0.522651 | + | 0.852547i | \(0.675057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6525 | − | 20.6525i | −0.568587 | − | 1.10235i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 25.8885i | − | 1.37791i | −0.724805 | − | 0.688954i | \(-0.758070\pi\) | ||
0.724805 | − | 0.688954i | \(-0.241930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.1115i | 0.748958i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.8885 | − | 12.9443i | −1.79357 | − | 0.685084i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.58359 | 0.241913 | 0.120956 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120956 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.41641 | −0.442969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.8541 | + | 6.43769i | 0.884611 | + | 0.337891i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.47214i | 0.129398i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.763932i | − | 0.0398769i | −0.999801 | − | 0.0199385i | \(-0.993653\pi\) | ||
0.999801 | − | 0.0199385i | \(-0.00634703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.94427 | + | 5.52786i | −0.257389 | + | 0.287769i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4164 | −1.52312 | −0.761562 | − | 0.648092i | \(-0.775567\pi\) | ||||
−0.761562 | + | 0.648092i | \(0.775567\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.47214 | + | 16.9443i | −0.334220 | + | 0.874998i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.3050i | 2.12731i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.6525i | 1.06085i | 0.847733 | + | 0.530423i | \(0.177967\pi\) | ||||
−0.847733 | + | 0.530423i | \(0.822033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.41641 | + | 14.1803i | −0.277491 | + | 0.726481i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0557 | −0.564921 | −0.282461 | − | 0.959279i | \(-0.591151\pi\) | ||||
−0.282461 | + | 0.959279i | \(0.591151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.05573 | 0.155734 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.52786 | + | 6.18034i | −0.280997 | + | 0.314164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.81966i | 0.497877i | 0.968519 | + | 0.248938i | \(0.0800816\pi\) | ||||
−0.968519 | + | 0.248938i | \(0.919918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 41.8885i | − | 2.11839i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.1803 | + | 6.94427i | 0.917077 | + | 0.350292i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.9443 | −0.852559 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.41641 | 0.472596 | 0.236298 | − | 0.971681i | \(-0.424066\pi\) | ||||
0.236298 | + | 0.971681i | \(0.424066\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.4164 | − | 10.4721i | −1.37254 | − | 0.524263i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3607i | 0.817013i | 0.912755 | + | 0.408507i | \(0.133950\pi\) | ||||
−0.912755 | + | 0.408507i | \(0.866050\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.41641i | − | 0.170183i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0557 | − | 1.23607i | 0.549364 | − | 0.0614207i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.360680 | −0.0178782 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.88854 | 0.192276 | 0.0961381 | − | 0.995368i | \(-0.469351\pi\) | ||||
0.0961381 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.47214 | + | 16.9443i | −0.319247 | + | 0.835799i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.4721i | 0.515300i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.94427i | − | 0.439057i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.29180 | − | 6.00000i | 0.112230 | − | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1803 | 0.595049 | 0.297524 | − | 0.954714i | \(-0.403839\pi\) | ||||
0.297524 | + | 0.954714i | \(0.403839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.41641 | −0.263980 | −0.131990 | − | 0.991251i | \(-0.542137\pi\) | ||||
−0.131990 | + | 0.991251i | \(0.542137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.8885 | + | 16.0000i | 0.869771 | + | 0.777947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 22.4721i | − | 1.09006i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 27.4164i | − | 1.32677i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.52786 | − | 2.11146i | −0.266888 | − | 0.101942i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.52786 | 0.361766 | 0.180883 | − | 0.983505i | \(-0.442104\pi\) | ||||
0.180883 | + | 0.983505i | \(0.442104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.4721 | − | 7.05573i | −0.885671 | − | 0.338296i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 33.8885i | − | 1.62111i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.180340i | 0.00860715i | 0.999991 | + | 0.00430358i | \(0.00136988\pi\) | ||||
−0.999991 | + | 0.00430358i | \(0.998630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.76393 | − | 6.94427i | −0.369711 | − | 0.330680i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7082 | 1.41148 | 0.705740 | − | 0.708471i | \(-0.250615\pi\) | ||||
0.705740 | + | 0.708471i | \(0.250615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.94427 | −0.234381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.29180 | − | 6.00000i | 0.108398 | − | 0.283790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.4164i | − | 1.29386i | −0.762549 | − | 0.646930i | \(-0.776053\pi\) | ||
0.762549 | − | 0.646930i | \(-0.223947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.88854i | 0.0889281i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.88854 | − | 10.1803i | 0.182700 | − | 0.478314i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8885 | 0.838628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.8885 | + | 15.4164i | −1.39508 | + | 0.719576i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1803i | 0.660444i | 0.943903 | + | 0.330222i | \(0.107124\pi\) | ||||
−0.943903 | + | 0.330222i | \(0.892876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.2361i | 1.82345i | 0.410796 | + | 0.911727i | \(0.365251\pi\) | ||||
−0.410796 | + | 0.911727i | \(0.634749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.52786 | + | 0.583592i | 0.0708530 | + | 0.0270634i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2361 | 0.705041 | 0.352521 | − | 0.935804i | \(-0.385325\pi\) | ||||
0.352521 | + | 0.935804i | \(0.385325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | −0.554109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.23607 | − | 2.76393i | −0.333420 | − | 0.127355i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.11146i | 0.0970849i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 18.1803i | − | 0.834171i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.47214 | − | 2.76393i | 0.113191 | − | 0.126552i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.8885 | 1.91394 | 0.956968 | − | 0.290193i | \(-0.0937194\pi\) | ||||
0.956968 | + | 0.290193i | \(0.0937194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.11146 | −0.0962741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.9443 | − | 33.8885i | 0.588985 | − | 1.54198i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4721i | 0.475515i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.34752i | 0.0610621i | 0.999534 | + | 0.0305311i | \(0.00971985\pi\) | ||||
−0.999534 | + | 0.0305311i | \(0.990280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2361 | + | 29.4164i | −0.508113 | + | 1.33026i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.0689 | 1.17647 | 0.588236 | − | 0.808689i | \(-0.299823\pi\) | ||||
0.588236 | + | 0.808689i | \(0.299823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 59.7771 | 2.69222 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.88854 | − | 2.11146i | 0.0848837 | − | 0.0949029i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 36.9443i | − | 1.65718i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7639i | 1.01905i | 0.860455 | + | 0.509527i | \(0.170180\pi\) | ||||
−0.860455 | + | 0.509527i | \(0.829820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 36.3607 | + | 13.8885i | 1.62448 | + | 0.620494i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.4721 | −1.35869 | −0.679343 | − | 0.733821i | \(-0.737735\pi\) | ||||
−0.679343 | + | 0.733821i | \(0.737735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4721 | 0.644002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.3262 | − | 4.32624i | −0.503016 | − | 0.192135i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2918i | 0.544824i | 0.962181 | + | 0.272412i | \(0.0878214\pi\) | ||||
−0.962181 | + | 0.272412i | \(0.912179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.47214i | − | 0.286310i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.1803 | + | 12.4721i | −1.06759 | + | 0.550658i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.1115 | 0.445564 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.11146 | 0.268782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.34752 | + | 14.0000i | −0.234730 | + | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.3607i | − | 0.892018i | −0.895029 | − | 0.446009i | \(-0.852845\pi\) | ||
0.895029 | − | 0.446009i | \(-0.147155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.1803i | − | 1.49460i | −0.664486 | − | 0.747301i | \(-0.731349\pi\) | ||
0.664486 | − | 0.747301i | \(-0.268651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.94427 | − | 18.1803i | 0.303073 | − | 0.793455i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.94427 | −0.215376 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.23607 | + | 6.47214i | 0.314019 | + | 0.280867i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0557i | 0.478877i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.1115i | − | 0.437156i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.1803 | + | 10.0000i | 1.12977 | + | 0.431532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.65248 | −0.114250 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3607 | −0.789387 | −0.394694 | − | 0.918813i | \(-0.629149\pi\) | ||||
−0.394694 | + | 0.918813i | \(0.629149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.6525 | + | 7.12461i | 0.800454 | + | 0.305746i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.583592i | 0.0249983i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.76393i | 0.118177i | 0.998253 | + | 0.0590886i | \(0.0188194\pi\) | ||||
−0.998253 | + | 0.0590886i | \(0.981181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.9443 | − | 16.9443i | −0.808522 | − | 0.723164i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.3607 | 2.06023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.3607 | 1.88641 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.360680 | − | 0.944272i | 0.0153100 | − | 0.0400821i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.6525i | − | 0.705588i | −0.935701 | − | 0.352794i | \(-0.885232\pi\) | ||
0.935701 | − | 0.352794i | \(-0.114768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3607i | 0.522801i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.05573 | + | 8.00000i | −0.129013 | + | 0.337760i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.5410 | −1.54002 | −0.770010 | − | 0.638032i | \(-0.779749\pi\) | ||||
−0.770010 | + | 0.638032i | \(0.779749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.88854 | 0.416014 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28.9443 | + | 3.23607i | −1.21555 | + | 0.135902i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 37.5279i | − | 1.57325i | −0.617431 | − | 0.786625i | \(-0.711827\pi\) | ||
0.617431 | − | 0.786625i | \(-0.288173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.1246i | − | 1.46992i | −0.678111 | − | 0.734960i | \(-0.737201\pi\) | ||
0.678111 | − | 0.734960i | \(-0.262799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | + | 3.05573i | 0.334205 | + | 0.127655i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4721 | 0.937153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5279 | 0.812956 | 0.406478 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406478 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.6525 | − | 14.7639i | −1.60634 | − | 0.613568i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.4164i | 0.971476i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.944272i | − | 0.0391077i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.0557 | − | 12.3607i | 0.457098 | − | 0.511051i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.5967 | −1.13904 | −0.569520 | − | 0.821978i | \(-0.692871\pi\) | ||||
−0.569520 | + | 0.821978i | \(0.692871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.70820 | + | 14.9443i | −0.234804 | + | 0.614725i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0557i | 0.454004i | 0.973894 | + | 0.227002i | \(0.0728924\pi\) | ||||
−0.973894 | + | 0.227002i | \(0.927108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 25.8885i | − | 1.06133i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.0000 | − | 26.1803i | 0.409273 | − | 1.07149i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.4164 | −0.793333 | −0.396666 | − | 0.917963i | \(-0.629833\pi\) | ||||
−0.396666 | + | 0.917963i | \(0.629833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7771 | −1.54096 | −0.770480 | − | 0.637464i | \(-0.779983\pi\) | ||||
−0.770480 | + | 0.637464i | \(0.779983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.41641 | + | 8.29180i | −0.302019 | + | 0.337668i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.8754i | 0.523459i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2361i | 1.59254i | 0.604940 | + | 0.796271i | \(0.293197\pi\) | ||||
−0.604940 | + | 0.796271i | \(0.706803\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 48.3607 | + | 18.4721i | 1.95967 | + | 0.748529i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7771 | 1.44739 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.3050 | 1.74907 | 0.874535 | − | 0.484962i | \(-0.161167\pi\) | ||||
0.874535 | + | 0.484962i | \(0.161167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.94427 | − | 1.88854i | −0.199372 | − | 0.0761534i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8885i | 0.559132i | 0.960127 | + | 0.279566i | \(0.0901905\pi\) | ||||
−0.960127 | + | 0.279566i | \(0.909809\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.1246i | − | 0.447136i | −0.974688 | − | 0.223568i | \(-0.928230\pi\) | ||
0.974688 | − | 0.223568i | \(-0.0717705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.4164 | − | 29.8885i | −0.618639 | − | 1.19939i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9443 | 0.518601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.47214 | + | 6.47214i | −0.0987276 | + | 0.258472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.05573i | 0.121840i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.1246i | 0.840958i | 0.907302 | + | 0.420479i | \(0.138138\pi\) | ||||
−0.907302 | + | 0.420479i | \(0.861862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.18034 | − | 10.9443i | 0.166154 | − | 0.434996i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.8328 | −0.429887 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5279 | −0.615236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.5279 | − | 22.8328i | −1.00987 | − | 0.903252i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.3050i | 1.47346i | 0.676189 | + | 0.736729i | \(0.263630\pi\) | ||||
−0.676189 | + | 0.736729i | \(0.736370\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.6525i | 1.76092i | 0.474119 | + | 0.880461i | \(0.342767\pi\) | ||||
−0.474119 | + | 0.880461i | \(0.657233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.52786 | − | 2.11146i | −0.217659 | − | 0.0831385i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3050 | 1.15210 | 0.576048 | − | 0.817416i | \(-0.304594\pi\) | ||||
0.576048 | + | 0.817416i | \(0.304594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.47214 | 0.0970398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | − | 1.52786i | −0.156772 | − | 0.0598817i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.7082i | − | 1.08431i | −0.840280 | − | 0.542153i | \(-0.817609\pi\) | ||
0.840280 | − | 0.542153i | \(-0.182391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8885i | 0.542670i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.47214 | − | 4.00000i | −0.174475 | − | 0.156055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.7082 | 1.62472 | 0.812360 | − | 0.583156i | \(-0.198182\pi\) | ||||
0.812360 | + | 0.583156i | \(0.198182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3050 | 0.439712 | 0.219856 | − | 0.975532i | \(-0.429441\pi\) | ||||
0.219856 | + | 0.975532i | \(0.429441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8885 | + | 46.8328i | −0.694733 | + | 1.81884i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 20.9443i | − | 0.812184i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.7771i | 2.31458i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.52786 | − | 19.7082i | 0.291044 | − | 0.761963i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.47214 | −0.249854 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41641 | 0.0545985 | 0.0272993 | − | 0.999627i | \(-0.491309\pi\) | ||||
0.0272993 | + | 0.999627i | \(0.491309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.27051 | − | 16.0344i | −0.318332 | − | 0.617166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.7082i | 1.06491i | 0.846457 | + | 0.532456i | \(0.178731\pi\) | ||||
−0.846457 | + | 0.532456i | \(0.821269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.4164i | − | 1.05215i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.6525 | − | 12.4721i | −1.25125 | − | 0.477933i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.76393 | 0.335343 | 0.167671 | − | 0.985843i | \(-0.446375\pi\) | ||||
0.167671 | + | 0.985843i | \(0.446375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.9443 | −0.494575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.1246 | − | 12.6525i | −1.26378 | − | 0.482722i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.52786i | − | 0.210595i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.2918i | − | 0.619769i | −0.950774 | − | 0.309885i | \(-0.899710\pi\) | ||
0.950774 | − | 0.309885i | \(-0.100290\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.94427 | + | 5.52786i | −0.187817 | + | 0.209986i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.58359 | 0.173866 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | 0.606043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.36068 | − | 11.4164i | 0.164936 | − | 0.431808i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7082i | − | 1.04652i | −0.852172 | − | 0.523262i | \(-0.824715\pi\) | ||
0.852172 | − | 0.523262i | \(-0.175285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.47214i | 0.0932384i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.11146 | + | 16.0000i | −0.230171 | + | 0.602595i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.8885 | −1.42495 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4721 | −0.618624 | −0.309312 | − | 0.950961i | \(-0.600099\pi\) | ||||
−0.309312 | + | 0.950961i | \(0.600099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.4164 | − | 30.6525i | 1.02820 | − | 1.14956i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.94427i | − | 0.185164i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.22291i | − | 0.157928i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9443 | + | 4.94427i | 0.483413 | + | 0.184647i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8328 | −0.851520 | −0.425760 | − | 0.904836i | \(-0.639993\pi\) | ||||
−0.425760 | + | 0.904836i | \(0.639993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.4721 | −0.985874 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.23607 | + | 1.23607i | 0.120351 | + | 0.0459699i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.0689i | 1.19101i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.18034i | 0.303392i | 0.988427 | + | 0.151696i | \(0.0484735\pi\) | ||||
−0.988427 | + | 0.151696i | \(0.951527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.8885 | 0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.58359 | 0.0954272 | 0.0477136 | − | 0.998861i | \(-0.484807\pi\) | ||||
0.0477136 | + | 0.998861i | \(0.484807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.65248 | − | 6.94427i | 0.0978380 | − | 0.256143i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.83282i | 0.104348i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 27.1246i | − | 0.997795i | −0.866661 | − | 0.498897i | \(-0.833738\pi\) | ||
0.866661 | − | 0.498897i | \(-0.166262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4721 | + | 37.8885i | −0.531647 | + | 1.39187i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4164 | 0.712319 | 0.356159 | − | 0.934425i | \(-0.384086\pi\) | ||||
0.356159 | + | 0.934425i | \(0.384086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.58359 | 0.167930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.1803 | + | 14.4721i | 0.592008 | + | 0.529508i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.4721i | 0.967271i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.5967i | − | 1.15298i | −0.817104 | − | 0.576491i | \(-0.804422\pi\) | ||
0.817104 | − | 0.576491i | \(-0.195578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.6525 | + | 6.36068i | 0.606850 | + | 0.231796i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.77709 | 0.283037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4164 | −0.778393 | −0.389196 | − | 0.921155i | \(-0.627247\pi\) | ||||
−0.389196 | + | 0.921155i | \(0.627247\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | − | 3.05573i | −0.290382 | − | 0.110916i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 38.2492i | − | 1.38653i | −0.720681 | − | 0.693267i | \(-0.756171\pi\) | ||
0.720681 | − | 0.693267i | \(-0.243829\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.52786i | − | 0.0553124i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.8885 | − | 16.0000i | −0.646762 | − | 0.578481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4721 | 0.522559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.7771 | −0.785302 | −0.392651 | − | 0.919688i | \(-0.628442\pi\) | ||||
−0.392651 | + | 0.919688i | \(0.628442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.88854 | − | 4.94427i | 0.0680142 | − | 0.178064i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.1803i | − | 1.08551i | −0.839891 | − | 0.542756i | \(-0.817381\pi\) | ||
0.839891 | − | 0.542756i | \(-0.182619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.65248i | − | 0.0952797i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.944272 | + | 2.47214i | −0.0338756 | + | 0.0886874i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.9443 | 0.463777 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.72136 | −0.312075 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.6525 | − | 22.0000i | 1.52428 | − | 0.786216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.52786i | − | 0.197298i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.81966i | 0.207448i | 0.994606 | + | 0.103724i | \(0.0330759\pi\) | ||||
−0.994606 | + | 0.103724i | \(0.966924\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.47214 | + | 0.944272i | 0.0880104 | + | 0.0336170i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.8885 | −0.920491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.8885 | −1.34546 | ||||||||
\(794\) |