Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(569,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1499238400.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 59x^{4} - 66x^{3} + 54x^{2} - 26x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 569.1 | ||
Root | \(0.500000 + 0.0845405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.f.569.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.500000 | − | 1.65831i | 0.288675 | − | 0.957427i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.584541 | + | 2.15831i | −0.261414 | + | 0.965227i | ||||
\(6\) | −1.65831 | − | 0.500000i | −0.677003 | − | 0.204124i | ||||
\(7\) | − | 4.86140i | − | 1.83744i | −0.394912 | − | 0.918719i | \(-0.629225\pi\) | ||
0.394912 | − | 0.918719i | \(-0.370775\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.50000 | − | 1.65831i | −0.833333 | − | 0.552771i | ||||
\(10\) | 2.15831 | + | 0.584541i | 0.682518 | + | 0.184848i | ||||
\(11\) | − | 2.31662i | − | 0.698489i | −0.937032 | − | 0.349244i | \(-0.886438\pi\) | ||
0.937032 | − | 0.349244i | \(-0.113562\pi\) | |||||||
\(12\) | −0.500000 | + | 1.65831i | −0.144338 | + | 0.478714i | ||||
\(13\) | 3.31662 | 0.919866 | 0.459933 | − | 0.887954i | \(-0.347873\pi\) | ||||
0.459933 | + | 0.887954i | \(0.347873\pi\) | |||||||
\(14\) | −4.86140 | −1.29926 | ||||||||
\(15\) | 3.28689 | + | 2.04851i | 0.848670 | + | 0.528922i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.86140 | −1.17906 | −0.589532 | − | 0.807745i | \(-0.700688\pi\) | ||||
−0.589532 | + | 0.807745i | \(0.700688\pi\) | |||||||
\(18\) | −1.65831 | + | 2.50000i | −0.390868 | + | 0.589256i | ||||
\(19\) | 2.31662 | + | 3.69232i | 0.531470 | + | 0.847077i | ||||
\(20\) | 0.584541 | − | 2.15831i | 0.130707 | − | 0.482613i | ||||
\(21\) | −8.06173 | − | 2.43070i | −1.75921 | − | 0.530423i | ||||
\(22\) | −2.31662 | −0.493906 | ||||||||
\(23\) | −6.03049 | −1.25744 | −0.628722 | − | 0.777631i | \(-0.716421\pi\) | ||||
−0.628722 | + | 0.777631i | \(0.716421\pi\) | |||||||
\(24\) | 1.65831 | + | 0.500000i | 0.338502 | + | 0.102062i | ||||
\(25\) | −4.31662 | − | 2.52324i | −0.863325 | − | 0.504648i | ||||
\(26\) | − | 3.31662i | − | 0.650444i | ||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 4.86140i | 0.918719i | ||||||||
\(29\) | −1.35416 | −0.251461 | −0.125731 | − | 0.992064i | \(-0.540128\pi\) | ||||
−0.125731 | + | 0.992064i | \(0.540128\pi\) | |||||||
\(30\) | 2.04851 | − | 3.28689i | 0.374004 | − | 0.600101i | ||||
\(31\) | − | 8.55373i | − | 1.53629i | −0.640273 | − | 0.768147i | \(-0.721179\pi\) | ||
0.640273 | − | 0.768147i | \(-0.278821\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −3.84169 | − | 1.15831i | −0.668752 | − | 0.201636i | ||||
\(34\) | 4.86140i | 0.833724i | ||||||||
\(35\) | 10.4924 | + | 2.84169i | 1.77354 | + | 0.480333i | ||||
\(36\) | 2.50000 | + | 1.65831i | 0.416667 | + | 0.276385i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 3.69232 | − | 2.31662i | 0.598974 | − | 0.375806i | ||||
\(39\) | 1.65831 | − | 5.50000i | 0.265543 | − | 0.880705i | ||||
\(40\) | −2.15831 | − | 0.584541i | −0.341259 | − | 0.0924240i | ||||
\(41\) | −3.50724 | −0.547739 | −0.273870 | − | 0.961767i | \(-0.588304\pi\) | ||||
−0.273870 | + | 0.961767i | \(0.588304\pi\) | |||||||
\(42\) | −2.43070 | + | 8.06173i | −0.375065 | + | 1.24395i | ||||
\(43\) | − | 1.16908i | − | 0.178283i | −0.996019 | − | 0.0891416i | \(-0.971588\pi\) | ||
0.996019 | − | 0.0891416i | \(-0.0284124\pi\) | |||||||
\(44\) | 2.31662i | 0.349244i | ||||||||
\(45\) | 5.04051 | − | 4.42643i | 0.751394 | − | 0.659853i | ||||
\(46\) | 6.03049i | 0.889147i | ||||||||
\(47\) | 5.04648 | 0.736105 | 0.368053 | − | 0.929805i | \(-0.380025\pi\) | ||||
0.368053 | + | 0.929805i | \(0.380025\pi\) | |||||||
\(48\) | 0.500000 | − | 1.65831i | 0.0721688 | − | 0.239357i | ||||
\(49\) | −16.6332 | −2.37618 | ||||||||
\(50\) | −2.52324 | + | 4.31662i | −0.356840 | + | 0.610463i | ||||
\(51\) | −2.43070 | + | 8.06173i | −0.340366 | + | 1.12887i | ||||
\(52\) | −3.31662 | −0.459933 | ||||||||
\(53\) | − | 1.00000i | − | 0.137361i | −0.997639 | − | 0.0686803i | \(-0.978121\pi\) | ||
0.997639 | − | 0.0686803i | \(-0.0218788\pi\) | |||||||
\(54\) | 3.31662 | + | 4.00000i | 0.451335 | + | 0.544331i | ||||
\(55\) | 5.00000 | + | 1.35416i | 0.674200 | + | 0.182595i | ||||
\(56\) | 4.86140 | 0.649632 | ||||||||
\(57\) | 7.28134 | − | 1.99553i | 0.964437 | − | 0.264314i | ||||
\(58\) | 1.35416i | 0.177810i | ||||||||
\(59\) | 9.90789 | 1.28990 | 0.644949 | − | 0.764226i | \(-0.276879\pi\) | ||||
0.644949 | + | 0.764226i | \(0.276879\pi\) | |||||||
\(60\) | −3.28689 | − | 2.04851i | −0.424335 | − | 0.264461i | ||||
\(61\) | 4.31662 | 0.552687 | 0.276344 | − | 0.961059i | \(-0.410877\pi\) | ||||
0.276344 | + | 0.961059i | \(0.410877\pi\) | |||||||
\(62\) | −8.55373 | −1.08632 | ||||||||
\(63\) | −8.06173 | + | 12.1535i | −1.01568 | + | 1.53120i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.93870 | + | 7.15831i | −0.240466 | + | 0.887879i | ||||
\(66\) | −1.15831 | + | 3.84169i | −0.142578 | + | 0.472879i | ||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | 4.86140 | 0.589532 | ||||||||
\(69\) | −3.01524 | + | 10.0004i | −0.362993 | + | 1.20391i | ||||
\(70\) | 2.84169 | − | 10.4924i | 0.339647 | − | 1.25409i | ||||
\(71\) | 10.8919 | 1.29263 | 0.646315 | − | 0.763071i | \(-0.276309\pi\) | ||||
0.646315 | + | 0.763071i | \(0.276309\pi\) | |||||||
\(72\) | 1.65831 | − | 2.50000i | 0.195434 | − | 0.294628i | ||||
\(73\) | − | 11.0770i | − | 1.29646i | −0.761444 | − | 0.648231i | \(-0.775509\pi\) | ||
0.761444 | − | 0.648231i | \(-0.224491\pi\) | |||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | −6.34264 | + | 5.89669i | −0.732385 | + | 0.680891i | ||||
\(76\) | −2.31662 | − | 3.69232i | −0.265735 | − | 0.423539i | ||||
\(77\) | −11.2620 | −1.28343 | ||||||||
\(78\) | −5.50000 | − | 1.65831i | −0.622752 | − | 0.187767i | ||||
\(79\) | 4.67632i | 0.526128i | 0.964778 | + | 0.263064i | \(0.0847330\pi\) | ||||
−0.964778 | + | 0.263064i | \(0.915267\pi\) | |||||||
\(80\) | −0.584541 | + | 2.15831i | −0.0653536 | + | 0.241307i | ||||
\(81\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(82\) | 3.50724i | 0.387310i | ||||||||
\(83\) | 9.72281 | 1.06722 | 0.533608 | − | 0.845732i | \(-0.320836\pi\) | ||||
0.533608 | + | 0.845732i | \(0.320836\pi\) | |||||||
\(84\) | 8.06173 | + | 2.43070i | 0.879606 | + | 0.265211i | ||||
\(85\) | 2.84169 | − | 10.4924i | 0.308224 | − | 1.13806i | ||||
\(86\) | −1.16908 | −0.126065 | ||||||||
\(87\) | −0.677081 | + | 2.24562i | −0.0725907 | + | 0.240756i | ||||
\(88\) | 2.31662 | 0.246953 | ||||||||
\(89\) | 8.55373 | 0.906693 | 0.453347 | − | 0.891334i | \(-0.350230\pi\) | ||||
0.453347 | + | 0.891334i | \(0.350230\pi\) | |||||||
\(90\) | −4.42643 | − | 5.04051i | −0.466587 | − | 0.531316i | ||||
\(91\) | − | 16.1235i | − | 1.69020i | ||||||
\(92\) | 6.03049 | 0.628722 | ||||||||
\(93\) | −14.1848 | − | 4.27686i | −1.47089 | − | 0.443490i | ||||
\(94\) | − | 5.04648i | − | 0.520505i | ||||||
\(95\) | −9.32335 | + | 2.84169i | −0.956555 | + | 0.291551i | ||||
\(96\) | −1.65831 | − | 0.500000i | −0.169251 | − | 0.0510310i | ||||
\(97\) | 16.6332 | 1.68885 | 0.844425 | − | 0.535673i | \(-0.179942\pi\) | ||||
0.844425 | + | 0.535673i | \(0.179942\pi\) | |||||||
\(98\) | 16.6332i | 1.68021i | ||||||||
\(99\) | −3.84169 | + | 5.79156i | −0.386104 | + | 0.582074i | ||||
\(100\) | 4.31662 | + | 2.52324i | 0.431662 | + | 0.252324i | ||||
\(101\) | − | 7.68338i | − | 0.764524i | −0.924054 | − | 0.382262i | \(-0.875145\pi\) | ||
0.924054 | − | 0.382262i | \(-0.124855\pi\) | |||||||
\(102\) | 8.06173 | + | 2.43070i | 0.798230 | + | 0.240675i | ||||
\(103\) | −15.5831 | −1.53545 | −0.767725 | − | 0.640779i | \(-0.778612\pi\) | ||||
−0.767725 | + | 0.640779i | \(0.778612\pi\) | |||||||
\(104\) | 3.31662i | 0.325222i | ||||||||
\(105\) | 9.95862 | − | 15.9789i | 0.971862 | − | 1.55938i | ||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | − | 19.9499i | − | 1.92863i | −0.264763 | − | 0.964314i | \(-0.585294\pi\) | ||
0.264763 | − | 0.964314i | \(-0.414706\pi\) | |||||||
\(108\) | 4.00000 | − | 3.31662i | 0.384900 | − | 0.319142i | ||||
\(109\) | 17.2925i | 1.65632i | 0.560489 | + | 0.828162i | \(0.310613\pi\) | ||||
−0.560489 | + | 0.828162i | \(0.689387\pi\) | |||||||
\(110\) | 1.35416 | − | 5.00000i | 0.129114 | − | 0.476731i | ||||
\(111\) | 1.00000 | − | 3.31662i | 0.0949158 | − | 0.314800i | ||||
\(112\) | − | 4.86140i | − | 0.459360i | ||||||
\(113\) | − | 8.31662i | − | 0.782362i | −0.920314 | − | 0.391181i | \(-0.872067\pi\) | ||
0.920314 | − | 0.391181i | \(-0.127933\pi\) | |||||||
\(114\) | −1.99553 | − | 7.28134i | −0.186898 | − | 0.681960i | ||||
\(115\) | 3.52506 | − | 13.0157i | 0.328714 | − | 1.21372i | ||||
\(116\) | 1.35416 | 0.125731 | ||||||||
\(117\) | −8.29156 | − | 5.50000i | −0.766555 | − | 0.508475i | ||||
\(118\) | − | 9.90789i | − | 0.912095i | ||||||
\(119\) | 23.6332i | 2.16646i | ||||||||
\(120\) | −2.04851 | + | 3.28689i | −0.187002 | + | 0.300050i | ||||
\(121\) | 5.63325 | 0.512114 | ||||||||
\(122\) | − | 4.31662i | − | 0.390809i | ||||||
\(123\) | −1.75362 | + | 5.81610i | −0.158119 | + | 0.524420i | ||||
\(124\) | 8.55373i | 0.768147i | ||||||||
\(125\) | 7.96919 | − | 7.84169i | 0.712786 | − | 0.701382i | ||||
\(126\) | 12.1535 | + | 8.06173i | 1.08272 | + | 0.718196i | ||||
\(127\) | −3.36675 | −0.298751 | −0.149375 | − | 0.988781i | \(-0.547726\pi\) | ||||
−0.149375 | + | 0.988781i | \(0.547726\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.93870 | − | 0.584541i | −0.170693 | − | 0.0514659i | ||||
\(130\) | 7.15831 | + | 1.93870i | 0.627826 | + | 0.170035i | ||||
\(131\) | − | 10.0000i | − | 0.873704i | −0.899533 | − | 0.436852i | \(-0.856093\pi\) | ||
0.899533 | − | 0.436852i | \(-0.143907\pi\) | |||||||
\(132\) | 3.84169 | + | 1.15831i | 0.334376 | + | 0.100818i | ||||
\(133\) | 17.9499 | − | 11.2620i | 1.55645 | − | 0.976544i | ||||
\(134\) | − | 7.00000i | − | 0.604708i | ||||||
\(135\) | −4.82015 | − | 10.5720i | −0.414852 | − | 0.909889i | ||||
\(136\) | − | 4.86140i | − | 0.416862i | ||||||
\(137\) | −4.86140 | −0.415338 | −0.207669 | − | 0.978199i | \(-0.566588\pi\) | ||||
−0.207669 | + | 0.978199i | \(0.566588\pi\) | |||||||
\(138\) | 10.0004 | + | 3.01524i | 0.851293 | + | 0.256674i | ||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | −10.4924 | − | 2.84169i | −0.886772 | − | 0.240166i | ||||
\(141\) | 2.52324 | − | 8.36865i | 0.212495 | − | 0.704767i | ||||
\(142\) | − | 10.8919i | − | 0.914027i | ||||||
\(143\) | − | 7.68338i | − | 0.642516i | ||||||
\(144\) | −2.50000 | − | 1.65831i | −0.208333 | − | 0.138193i | ||||
\(145\) | 0.791562 | − | 2.92270i | 0.0657356 | − | 0.242717i | ||||
\(146\) | −11.0770 | −0.916736 | ||||||||
\(147\) | −8.31662 | + | 27.5831i | −0.685944 | + | 2.27502i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 4.00000i | 0.327693i | 0.986486 | + | 0.163846i | \(0.0523901\pi\) | ||||
−0.986486 | + | 0.163846i | \(0.947610\pi\) | |||||||
\(150\) | 5.89669 | + | 6.34264i | 0.481463 | + | 0.517874i | ||||
\(151\) | − | 2.70832i | − | 0.220400i | −0.993909 | − | 0.110200i | \(-0.964851\pi\) | ||
0.993909 | − | 0.110200i | \(-0.0351492\pi\) | |||||||
\(152\) | −3.69232 | + | 2.31662i | −0.299487 | + | 0.187903i | ||||
\(153\) | 12.1535 | + | 8.06173i | 0.982553 | + | 0.651752i | ||||
\(154\) | 11.2620i | 0.907522i | ||||||||
\(155\) | 18.4616 | + | 5.00000i | 1.48287 | + | 0.401610i | ||||
\(156\) | −1.65831 | + | 5.50000i | −0.132771 | + | 0.440352i | ||||
\(157\) | 2.33816i | 0.186606i | 0.995638 | + | 0.0933028i | \(0.0297425\pi\) | ||||
−0.995638 | + | 0.0933028i | \(0.970258\pi\) | |||||||
\(158\) | 4.67632 | 0.372028 | ||||||||
\(159\) | −1.65831 | − | 0.500000i | −0.131513 | − | 0.0396526i | ||||
\(160\) | 2.15831 | + | 0.584541i | 0.170630 | + | 0.0462120i | ||||
\(161\) | 29.3166i | 2.31047i | ||||||||
\(162\) | 8.29156 | − | 3.50000i | 0.651447 | − | 0.274986i | ||||
\(163\) | 15.9384i | 1.24839i | 0.781269 | + | 0.624195i | \(0.214573\pi\) | ||||
−0.781269 | + | 0.624195i | \(0.785427\pi\) | |||||||
\(164\) | 3.50724 | 0.273870 | ||||||||
\(165\) | 4.74562 | − | 7.61448i | 0.369446 | − | 0.592787i | ||||
\(166\) | − | 9.72281i | − | 0.754636i | ||||||
\(167\) | 5.05013i | 0.390790i | 0.980725 | + | 0.195395i | \(0.0625990\pi\) | ||||
−0.980725 | + | 0.195395i | \(0.937401\pi\) | |||||||
\(168\) | 2.43070 | − | 8.06173i | 0.187533 | − | 0.621976i | ||||
\(169\) | −2.00000 | −0.153846 | ||||||||
\(170\) | −10.4924 | − | 2.84169i | −0.804733 | − | 0.217947i | ||||
\(171\) | 0.331463 | − | 13.0725i | 0.0253476 | − | 0.999679i | ||||
\(172\) | 1.16908i | 0.0891416i | ||||||||
\(173\) | 13.2665i | 1.00863i | 0.863519 | + | 0.504317i | \(0.168256\pi\) | ||||
−0.863519 | + | 0.504317i | \(0.831744\pi\) | |||||||
\(174\) | 2.24562 | + | 0.677081i | 0.170240 | + | 0.0513293i | ||||
\(175\) | −12.2665 | + | 20.9849i | −0.927260 | + | 1.58631i | ||||
\(176\) | − | 2.31662i | − | 0.174622i | ||||||
\(177\) | 4.95394 | − | 16.4304i | 0.372361 | − | 1.23498i | ||||
\(178\) | − | 8.55373i | − | 0.641129i | ||||||
\(179\) | 2.70832 | 0.202429 | 0.101215 | − | 0.994865i | \(-0.467727\pi\) | ||||
0.101215 | + | 0.994865i | \(0.467727\pi\) | |||||||
\(180\) | −5.04051 | + | 4.42643i | −0.375697 | + | 0.329927i | ||||
\(181\) | 2.70832i | 0.201308i | 0.994921 | + | 0.100654i | \(0.0320935\pi\) | ||||
−0.994921 | + | 0.100654i | \(0.967906\pi\) | |||||||
\(182\) | −16.1235 | −1.19515 | ||||||||
\(183\) | 2.15831 | − | 7.15831i | 0.159547 | − | 0.529158i | ||||
\(184\) | − | 6.03049i | − | 0.444573i | ||||||
\(185\) | −1.16908 | + | 4.31662i | −0.0859525 | + | 0.317365i | ||||
\(186\) | −4.27686 | + | 14.1848i | −0.313595 | + | 1.04008i | ||||
\(187\) | 11.2620i | 0.823563i | ||||||||
\(188\) | −5.04648 | −0.368053 | ||||||||
\(189\) | 16.1235 | + | 19.4456i | 1.17281 | + | 1.41446i | ||||
\(190\) | 2.84169 | + | 9.32335i | 0.206158 | + | 0.676387i | ||||
\(191\) | − | 5.00000i | − | 0.361787i | −0.983503 | − | 0.180894i | \(-0.942101\pi\) | ||
0.983503 | − | 0.180894i | \(-0.0578990\pi\) | |||||||
\(192\) | −0.500000 | + | 1.65831i | −0.0360844 | + | 0.119678i | ||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | − | 16.6332i | − | 1.19420i | ||||||
\(195\) | 10.9014 | + | 6.79413i | 0.780663 | + | 0.486538i | ||||
\(196\) | 16.6332 | 1.18809 | ||||||||
\(197\) | −6.21557 | −0.442841 | −0.221420 | − | 0.975178i | \(-0.571069\pi\) | ||||
−0.221420 | + | 0.975178i | \(0.571069\pi\) | |||||||
\(198\) | 5.79156 | + | 3.84169i | 0.411588 | + | 0.273017i | ||||
\(199\) | 21.2164 | 1.50399 | 0.751994 | − | 0.659169i | \(-0.229092\pi\) | ||||
0.751994 | + | 0.659169i | \(0.229092\pi\) | |||||||
\(200\) | 2.52324 | − | 4.31662i | 0.178420 | − | 0.305231i | ||||
\(201\) | 3.50000 | − | 11.6082i | 0.246871 | − | 0.818778i | ||||
\(202\) | −7.68338 | −0.540600 | ||||||||
\(203\) | 6.58312i | 0.462045i | ||||||||
\(204\) | 2.43070 | − | 8.06173i | 0.170183 | − | 0.564434i | ||||
\(205\) | 2.05013 | − | 7.56973i | 0.143187 | − | 0.528693i | ||||
\(206\) | 15.5831i | 1.08573i | ||||||||
\(207\) | 15.0762 | + | 10.0004i | 1.04787 | + | 0.695078i | ||||
\(208\) | 3.31662 | 0.229967 | ||||||||
\(209\) | 8.55373 | − | 5.36675i | 0.591674 | − | 0.371226i | ||||
\(210\) | −15.9789 | − | 9.95862i | −1.10265 | − | 0.687210i | ||||
\(211\) | 18.4616i | 1.27095i | 0.772121 | + | 0.635475i | \(0.219196\pi\) | ||||
−0.772121 | + | 0.635475i | \(0.780804\pi\) | |||||||
\(212\) | 1.00000i | 0.0686803i | ||||||||
\(213\) | 5.44594 | − | 18.0622i | 0.373150 | − | 1.23760i | ||||
\(214\) | −19.9499 | −1.36375 | ||||||||
\(215\) | 2.52324 | + | 0.683375i | 0.172084 | + | 0.0466058i | ||||
\(216\) | −3.31662 | − | 4.00000i | −0.225668 | − | 0.272166i | ||||
\(217\) | −41.5831 | −2.82285 | ||||||||
\(218\) | 17.2925 | 1.17120 | ||||||||
\(219\) | −18.3691 | − | 5.53848i | −1.24127 | − | 0.374256i | ||||
\(220\) | −5.00000 | − | 1.35416i | −0.337100 | − | 0.0912975i | ||||
\(221\) | −16.1235 | −1.08458 | ||||||||
\(222\) | −3.31662 | − | 1.00000i | −0.222597 | − | 0.0671156i | ||||
\(223\) | −23.2665 | −1.55804 | −0.779020 | − | 0.626999i | \(-0.784283\pi\) | ||||
−0.779020 | + | 0.626999i | \(0.784283\pi\) | |||||||
\(224\) | −4.86140 | −0.324816 | ||||||||
\(225\) | 6.60724 | + | 13.4664i | 0.440483 | + | 0.897761i | ||||
\(226\) | −8.31662 | −0.553214 | ||||||||
\(227\) | 0.0501256i | 0.00332695i | 0.999999 | + | 0.00166348i | \(0.000529502\pi\) | ||||
−0.999999 | + | 0.00166348i | \(0.999470\pi\) | |||||||
\(228\) | −7.28134 | + | 1.99553i | −0.482218 | + | 0.132157i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | −13.0157 | − | 3.52506i | −0.858228 | − | 0.232436i | ||||
\(231\) | −5.63102 | + | 18.6760i | −0.370494 | + | 1.22879i | ||||
\(232\) | − | 1.35416i | − | 0.0889050i | ||||||
\(233\) | 15.1395 | 0.991818 | 0.495909 | − | 0.868374i | \(-0.334835\pi\) | ||||
0.495909 | + | 0.868374i | \(0.334835\pi\) | |||||||
\(234\) | −5.50000 | + | 8.29156i | −0.359546 | + | 0.542036i | ||||
\(235\) | −2.94987 | + | 10.8919i | −0.192429 | + | 0.710509i | ||||
\(236\) | −9.90789 | −0.644949 | ||||||||
\(237\) | 7.75481 | + | 2.33816i | 0.503729 | + | 0.151880i | ||||
\(238\) | 23.6332 | 1.53192 | ||||||||
\(239\) | − | 6.36675i | − | 0.411831i | −0.978570 | − | 0.205915i | \(-0.933983\pi\) | ||
0.978570 | − | 0.205915i | \(-0.0660172\pi\) | |||||||
\(240\) | 3.28689 | + | 2.04851i | 0.212168 | + | 0.132231i | ||||
\(241\) | − | 17.1075i | − | 1.10199i | −0.834509 | − | 0.550994i | \(-0.814249\pi\) | ||
0.834509 | − | 0.550994i | \(-0.185751\pi\) | |||||||
\(242\) | − | 5.63325i | − | 0.362119i | ||||||
\(243\) | 15.5000 | − | 1.65831i | 0.994325 | − | 0.106381i | ||||
\(244\) | −4.31662 | −0.276344 | ||||||||
\(245\) | 9.72281 | − | 35.8997i | 0.621167 | − | 2.29355i | ||||
\(246\) | 5.81610 | + | 1.75362i | 0.370821 | + | 0.111807i | ||||
\(247\) | 7.68338 | + | 12.2461i | 0.488881 | + | 0.779198i | ||||
\(248\) | 8.55373 | 0.543162 | ||||||||
\(249\) | 4.86140 | − | 16.1235i | 0.308079 | − | 1.02178i | ||||
\(250\) | −7.84169 | − | 7.96919i | −0.495952 | − | 0.504016i | ||||
\(251\) | − | 1.58312i | − | 0.0999259i | −0.998751 | − | 0.0499629i | \(-0.984090\pi\) | ||
0.998751 | − | 0.0499629i | \(-0.0159103\pi\) | |||||||
\(252\) | 8.06173 | − | 12.1535i | 0.507841 | − | 0.765599i | ||||
\(253\) | 13.9704i | 0.878310i | ||||||||
\(254\) | 3.36675i | 0.211249i | ||||||||
\(255\) | −15.9789 | − | 9.95862i | −1.00064 | − | 0.623633i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.9499i | − | 0.932548i | −0.884640 | − | 0.466274i | \(-0.845596\pi\) | ||
0.884640 | − | 0.466274i | \(-0.154404\pi\) | |||||||
\(258\) | −0.584541 | + | 1.93870i | −0.0363919 | + | 0.120698i | ||||
\(259\) | − | 9.72281i | − | 0.604146i | ||||||
\(260\) | 1.93870 | − | 7.15831i | 0.120233 | − | 0.443940i | ||||
\(261\) | 3.38540 | + | 2.24562i | 0.209551 | + | 0.139001i | ||||
\(262\) | −10.0000 | −0.617802 | ||||||||
\(263\) | −21.7838 | −1.34325 | −0.671623 | − | 0.740893i | \(-0.734402\pi\) | ||||
−0.671623 | + | 0.740893i | \(0.734402\pi\) | |||||||
\(264\) | 1.15831 | − | 3.84169i | 0.0712892 | − | 0.236440i | ||||
\(265\) | 2.15831 | + | 0.584541i | 0.132584 | + | 0.0359080i | ||||
\(266\) | −11.2620 | − | 17.9499i | −0.690521 | − | 1.10058i | ||||
\(267\) | 4.27686 | − | 14.1848i | 0.261740 | − | 0.868093i | ||||
\(268\) | −7.00000 | −0.427593 | ||||||||
\(269\) | −14.3991 | −0.877931 | −0.438965 | − | 0.898504i | \(-0.644655\pi\) | ||||
−0.438965 | + | 0.898504i | \(0.644655\pi\) | |||||||
\(270\) | −10.5720 | + | 4.82015i | −0.643388 | + | 0.293345i | ||||
\(271\) | 9.31662 | 0.565945 | 0.282972 | − | 0.959128i | \(-0.408680\pi\) | ||||
0.282972 | + | 0.959128i | \(0.408680\pi\) | |||||||
\(272\) | −4.86140 | −0.294766 | ||||||||
\(273\) | −26.7377 | − | 8.06173i | −1.61824 | − | 0.487918i | ||||
\(274\) | 4.86140i | 0.293688i | ||||||||
\(275\) | −5.84541 | + | 10.0000i | −0.352491 | + | 0.603023i | ||||
\(276\) | 3.01524 | − | 10.0004i | 0.181496 | − | 0.601955i | ||||
\(277\) | − | 12.0610i | − | 0.724673i | −0.932047 | − | 0.362337i | \(-0.881979\pi\) | ||
0.932047 | − | 0.362337i | \(-0.118021\pi\) | |||||||
\(278\) | 10.0000i | 0.599760i | ||||||||
\(279\) | −14.1848 | + | 21.3843i | −0.849219 | + | 1.28025i | ||||
\(280\) | −2.84169 | + | 10.4924i | −0.169823 | + | 0.627043i | ||||
\(281\) | 13.6002 | 0.811321 | 0.405660 | − | 0.914024i | \(-0.367042\pi\) | ||||
0.405660 | + | 0.914024i | \(0.367042\pi\) | |||||||
\(282\) | −8.36865 | − | 2.52324i | −0.498346 | − | 0.150257i | ||||
\(283\) | − | 15.1395i | − | 0.899947i | −0.893042 | − | 0.449974i | \(-0.851433\pi\) | ||
0.893042 | − | 0.449974i | \(-0.148567\pi\) | |||||||
\(284\) | −10.8919 | −0.646315 | ||||||||
\(285\) | 0.0507319 | + | 16.8819i | 0.00300510 | + | 0.999995i | ||||
\(286\) | −7.68338 | −0.454328 | ||||||||
\(287\) | 17.0501i | 1.00644i | ||||||||
\(288\) | −1.65831 | + | 2.50000i | −0.0977170 | + | 0.147314i | ||||
\(289\) | 6.63325 | 0.390191 | ||||||||
\(290\) | −2.92270 | − | 0.791562i | −0.171627 | − | 0.0464821i | ||||
\(291\) | 8.31662 | − | 27.5831i | 0.487529 | − | 1.61695i | ||||
\(292\) | 11.0770i | 0.648231i | ||||||||
\(293\) | 8.26650i | 0.482934i | 0.970409 | + | 0.241467i | \(0.0776286\pi\) | ||||
−0.970409 | + | 0.241467i | \(0.922371\pi\) | |||||||
\(294\) | 27.5831 | + | 8.31662i | 1.60868 | + | 0.485035i | ||||
\(295\) | −5.79156 | + | 21.3843i | −0.337198 | + | 1.24504i | ||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 7.68338 | + | 9.26650i | 0.445835 | + | 0.537697i | ||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | −20.0009 | −1.15668 | ||||||||
\(300\) | 6.34264 | − | 5.89669i | 0.366192 | − | 0.340446i | ||||
\(301\) | −5.68338 | −0.327584 | ||||||||
\(302\) | −2.70832 | −0.155846 | ||||||||
\(303\) | −12.7414 | − | 3.84169i | −0.731976 | − | 0.220699i | ||||
\(304\) | 2.31662 | + | 3.69232i | 0.132868 | + | 0.211769i | ||||
\(305\) | −2.52324 | + | 9.31662i | −0.144480 | + | 0.533468i | ||||
\(306\) | 8.06173 | − | 12.1535i | 0.460858 | − | 0.694770i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 11.2620 | 0.641715 | ||||||||
\(309\) | −7.79156 | + | 25.8417i | −0.443246 | + | 1.47008i | ||||
\(310\) | 5.00000 | − | 18.4616i | 0.283981 | − | 1.04855i | ||||
\(311\) | 18.8997i | 1.07171i | 0.844311 | + | 0.535853i | \(0.180010\pi\) | ||||
−0.844311 | + | 0.535853i | \(0.819990\pi\) | |||||||
\(312\) | 5.50000 | + | 1.65831i | 0.311376 | + | 0.0938835i | ||||
\(313\) | 28.5546i | 1.61400i | 0.590551 | + | 0.807000i | \(0.298910\pi\) | ||||
−0.590551 | + | 0.807000i | \(0.701090\pi\) | |||||||
\(314\) | 2.33816 | 0.131950 | ||||||||
\(315\) | −21.5187 | − | 24.5039i | −1.21244 | − | 1.38064i | ||||
\(316\) | − | 4.67632i | − | 0.263064i | ||||||
\(317\) | 17.0000i | 0.954815i | 0.878682 | + | 0.477408i | \(0.158423\pi\) | ||||
−0.878682 | + | 0.477408i | \(0.841577\pi\) | |||||||
\(318\) | −0.500000 | + | 1.65831i | −0.0280386 | + | 0.0929935i | ||||
\(319\) | 3.13708i | 0.175643i | ||||||||
\(320\) | 0.584541 | − | 2.15831i | 0.0326768 | − | 0.120653i | ||||
\(321\) | −33.0831 | − | 9.97494i | −1.84652 | − | 0.556747i | ||||
\(322\) | 29.3166 | 1.63375 | ||||||||
\(323\) | −11.2620 | − | 17.9499i | −0.626637 | − | 0.998758i | ||||
\(324\) | −3.50000 | − | 8.29156i | −0.194444 | − | 0.460642i | ||||
\(325\) | −14.3166 | − | 8.36865i | −0.794143 | − | 0.464209i | ||||
\(326\) | 15.9384 | 0.882745 | ||||||||
\(327\) | 28.6764 | + | 8.64627i | 1.58581 | + | 0.478140i | ||||
\(328\) | − | 3.50724i | − | 0.193655i | ||||||
\(329\) | − | 24.5330i | − | 1.35255i | ||||||
\(330\) | −7.61448 | − | 4.74562i | −0.419163 | − | 0.261238i | ||||
\(331\) | 15.7533i | 0.865879i | 0.901423 | + | 0.432940i | \(0.142524\pi\) | ||||
−0.901423 | + | 0.432940i | \(0.857476\pi\) | |||||||
\(332\) | −9.72281 | −0.533608 | ||||||||
\(333\) | −5.00000 | − | 3.31662i | −0.273998 | − | 0.181750i | ||||
\(334\) | 5.05013 | 0.276331 | ||||||||
\(335\) | −4.09178 | + | 15.1082i | −0.223558 | + | 0.825448i | ||||
\(336\) | −8.06173 | − | 2.43070i | −0.439803 | − | 0.132606i | ||||
\(337\) | 18.2164 | 0.992309 | 0.496155 | − | 0.868234i | \(-0.334745\pi\) | ||||
0.496155 | + | 0.868234i | \(0.334745\pi\) | |||||||
\(338\) | 2.00000i | 0.108786i | ||||||||
\(339\) | −13.7916 | − | 4.15831i | −0.749055 | − | 0.225849i | ||||
\(340\) | −2.84169 | + | 10.4924i | −0.154112 | + | 0.569032i | ||||
\(341\) | −19.8158 | −1.07308 | ||||||||
\(342\) | −13.0725 | − | 0.331463i | −0.706880 | − | 0.0179235i | ||||
\(343\) | 46.8311i | 2.52864i | ||||||||
\(344\) | 1.16908 | 0.0630326 | ||||||||
\(345\) | −19.8215 | − | 12.3535i | −1.06715 | − | 0.665090i | ||||
\(346\) | 13.2665 | 0.713211 | ||||||||
\(347\) | 24.8623 | 1.33468 | 0.667338 | − | 0.744755i | \(-0.267434\pi\) | ||||
0.667338 | + | 0.744755i | \(0.267434\pi\) | |||||||
\(348\) | 0.677081 | − | 2.24562i | 0.0362953 | − | 0.120378i | ||||
\(349\) | −4.63325 | −0.248012 | −0.124006 | − | 0.992281i | \(-0.539574\pi\) | ||||
−0.124006 | + | 0.992281i | \(0.539574\pi\) | |||||||
\(350\) | 20.9849 | + | 12.2665i | 1.12169 | + | 0.655672i | ||||
\(351\) | −13.2665 | + | 11.0000i | −0.708113 | + | 0.587137i | ||||
\(352\) | −2.31662 | −0.123477 | ||||||||
\(353\) | −20.0009 | −1.06454 | −0.532269 | − | 0.846575i | \(-0.678661\pi\) | ||||
−0.532269 | + | 0.846575i | \(0.678661\pi\) | |||||||
\(354\) | −16.4304 | − | 4.95394i | −0.873265 | − | 0.263299i | ||||
\(355\) | −6.36675 | + | 23.5081i | −0.337912 | + | 1.24768i | ||||
\(356\) | −8.55373 | −0.453347 | ||||||||
\(357\) | 39.1913 | + | 11.8166i | 2.07422 | + | 0.625402i | ||||
\(358\) | − | 2.70832i | − | 0.143139i | ||||||
\(359\) | − | 34.8997i | − | 1.84194i | −0.389636 | − | 0.920969i | \(-0.627399\pi\) | ||
0.389636 | − | 0.920969i | \(-0.372601\pi\) | |||||||
\(360\) | 4.42643 | + | 5.04051i | 0.233293 | + | 0.265658i | ||||
\(361\) | −8.26650 | + | 17.1075i | −0.435079 | + | 0.900392i | ||||
\(362\) | 2.70832 | 0.142346 | ||||||||
\(363\) | 2.81662 | − | 9.34169i | 0.147834 | − | 0.490311i | ||||
\(364\) | 16.1235i | 0.845099i | ||||||||
\(365\) | 23.9076 | + | 6.47494i | 1.25138 | + | 0.338914i | ||||
\(366\) | −7.15831 | − | 2.15831i | −0.374171 | − | 0.112817i | ||||
\(367\) | 2.33816i | 0.122051i | 0.998136 | + | 0.0610255i | \(0.0194371\pi\) | ||||
−0.998136 | + | 0.0610255i | \(0.980563\pi\) | |||||||
\(368\) | −6.03049 | −0.314361 | ||||||||
\(369\) | 8.76811 | + | 5.81610i | 0.456449 | + | 0.302774i | ||||
\(370\) | 4.31662 | + | 1.16908i | 0.224411 | + | 0.0607776i | ||||
\(371\) | −4.86140 | −0.252392 | ||||||||
\(372\) | 14.1848 | + | 4.27686i | 0.735445 | + | 0.221745i | ||||
\(373\) | −16.6834 | −0.863832 | −0.431916 | − | 0.901914i | \(-0.642162\pi\) | ||||
−0.431916 | + | 0.901914i | \(0.642162\pi\) | |||||||
\(374\) | 11.2620 | 0.582347 | ||||||||
\(375\) | −9.01937 | − | 17.1362i | −0.465758 | − | 0.884912i | ||||
\(376\) | 5.04648i | 0.260253i | ||||||||
\(377\) | −4.49124 | −0.231311 | ||||||||
\(378\) | 19.4456 | − | 16.1235i | 1.00017 | − | 0.829301i | ||||
\(379\) | − | 22.7678i | − | 1.16950i | −0.811213 | − | 0.584751i | \(-0.801192\pi\) | ||
0.811213 | − | 0.584751i | \(-0.198808\pi\) | |||||||
\(380\) | 9.32335 | − | 2.84169i | 0.478278 | − | 0.145775i | ||||
\(381\) | −1.68338 | + | 5.58312i | −0.0862419 | + | 0.286032i | ||||
\(382\) | −5.00000 | −0.255822 | ||||||||
\(383\) | 25.5831i | 1.30724i | 0.756824 | + | 0.653618i | \(0.226750\pi\) | ||||
−0.756824 | + | 0.653618i | \(0.773250\pi\) | |||||||
\(384\) | 1.65831 | + | 0.500000i | 0.0846254 | + | 0.0255155i | ||||
\(385\) | 6.58312 | − | 24.3070i | 0.335507 | − | 1.23880i | ||||
\(386\) | − | 6.00000i | − | 0.305392i | ||||||
\(387\) | −1.93870 | + | 2.92270i | −0.0985497 | + | 0.148569i | ||||
\(388\) | −16.6332 | −0.844425 | ||||||||
\(389\) | 30.2164i | 1.53203i | 0.642822 | + | 0.766015i | \(0.277763\pi\) | ||||
−0.642822 | + | 0.766015i | \(0.722237\pi\) | |||||||
\(390\) | 6.79413 | − | 10.9014i | 0.344034 | − | 0.552012i | ||||
\(391\) | 29.3166 | 1.48261 | ||||||||
\(392\) | − | 16.6332i | − | 0.840106i | ||||||
\(393\) | −16.5831 | − | 5.00000i | −0.836508 | − | 0.252217i | ||||
\(394\) | 6.21557i | 0.313136i | ||||||||
\(395\) | −10.0930 | − | 2.73350i | −0.507832 | − | 0.137537i | ||||
\(396\) | 3.84169 | − | 5.79156i | 0.193052 | − | 0.291037i | ||||
\(397\) | 16.7373i | 0.840021i | 0.907519 | + | 0.420010i | \(0.137974\pi\) | ||||
−0.907519 | + | 0.420010i | \(0.862026\pi\) | |||||||
\(398\) | − | 21.2164i | − | 1.06348i | ||||||
\(399\) | −9.70106 | − | 35.3975i | −0.485660 | − | 1.77209i | ||||
\(400\) | −4.31662 | − | 2.52324i | −0.215831 | − | 0.126162i | ||||
\(401\) | −8.92389 | −0.445638 | −0.222819 | − | 0.974860i | \(-0.571526\pi\) | ||||
−0.222819 | + | 0.974860i | \(0.571526\pi\) | |||||||
\(402\) | −11.6082 | − | 3.50000i | −0.578964 | − | 0.174564i | ||||
\(403\) | − | 28.3695i | − | 1.41319i | ||||||
\(404\) | 7.68338i | 0.382262i | ||||||||
\(405\) | −19.9417 | + | 2.70734i | −0.990910 | + | 0.134529i | ||||
\(406\) | 6.58312 | 0.326715 | ||||||||
\(407\) | − | 4.63325i | − | 0.229662i | ||||||
\(408\) | −8.06173 | − | 2.43070i | −0.399115 | − | 0.120338i | ||||
\(409\) | − | 1.16908i | − | 0.0578073i | −0.999582 | − | 0.0289037i | \(-0.990798\pi\) | ||
0.999582 | − | 0.0289037i | \(-0.00920160\pi\) | |||||||
\(410\) | −7.56973 | − | 2.05013i | −0.373842 | − | 0.101248i | ||||
\(411\) | −2.43070 | + | 8.06173i | −0.119898 | + | 0.397656i | ||||
\(412\) | 15.5831 | 0.767725 | ||||||||
\(413\) | − | 48.1662i | − | 2.37011i | ||||||
\(414\) | 10.0004 | − | 15.0762i | 0.491494 | − | 0.740955i | ||||
\(415\) | −5.68338 | + | 20.9849i | −0.278986 | + | 1.03011i | ||||
\(416\) | − | 3.31662i | − | 0.162611i | ||||||
\(417\) | −5.00000 | + | 16.5831i | −0.244851 | + | 0.812079i | ||||
\(418\) | −5.36675 | − | 8.55373i | −0.262496 | − | 0.418376i | ||||
\(419\) | − | 22.9499i | − | 1.12117i | −0.828095 | − | 0.560587i | \(-0.810575\pi\) | ||
0.828095 | − | 0.560587i | \(-0.189425\pi\) | |||||||
\(420\) | −9.95862 | + | 15.9789i | −0.485931 | + | 0.779690i | ||||
\(421\) | − | 24.3070i | − | 1.18465i | −0.805699 | − | 0.592326i | \(-0.798210\pi\) | ||
0.805699 | − | 0.592326i | \(-0.201790\pi\) | |||||||
\(422\) | 18.4616 | 0.898697 | ||||||||
\(423\) | −12.6162 | − | 8.36865i | −0.613421 | − | 0.406898i | ||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 20.9849 | + | 12.2665i | 1.01792 | + | 0.595013i | ||||
\(426\) | −18.0622 | − | 5.44594i | −0.875114 | − | 0.263857i | ||||
\(427\) | − | 20.9849i | − | 1.01553i | ||||||
\(428\) | 19.9499i | 0.964314i | ||||||||
\(429\) | −12.7414 | − | 3.84169i | −0.615162 | − | 0.185478i | ||||
\(430\) | 0.683375 | − | 2.52324i | 0.0329553 | − | 0.121682i | ||||
\(431\) | 33.4160 | 1.60959 | 0.804796 | − | 0.593552i | \(-0.202275\pi\) | ||||
0.804796 | + | 0.593552i | \(0.202275\pi\) | |||||||
\(432\) | −4.00000 | + | 3.31662i | −0.192450 | + | 0.159571i | ||||
\(433\) | 8.31662 | 0.399671 | 0.199836 | − | 0.979829i | \(-0.435959\pi\) | ||||
0.199836 | + | 0.979829i | \(0.435959\pi\) | |||||||
\(434\) | 41.5831i | 1.99605i | ||||||||
\(435\) | −4.45097 | − | 2.77401i | −0.213408 | − | 0.133004i | ||||
\(436\) | − | 17.2925i | − | 0.828162i | ||||||
\(437\) | −13.9704 | − | 22.2665i | −0.668293 | − | 1.06515i | ||||
\(438\) | −5.53848 | + | 18.3691i | −0.264639 | + | 0.877708i | ||||
\(439\) | − | 1.16908i | − | 0.0557972i | −0.999611 | − | 0.0278986i | \(-0.991118\pi\) | ||
0.999611 | − | 0.0278986i | \(-0.00888155\pi\) | |||||||
\(440\) | −1.35416 | + | 5.00000i | −0.0645571 | + | 0.238366i | ||||
\(441\) | 41.5831 | + | 27.5831i | 1.98015 | + | 1.31348i | ||||
\(442\) | 16.1235i | 0.766914i | ||||||||
\(443\) | 3.87740 | 0.184221 | 0.0921105 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921105 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(444\) | −1.00000 | + | 3.31662i | −0.0474579 | + | 0.157400i | ||||
\(445\) | −5.00000 | + | 18.4616i | −0.237023 | + | 0.875164i | ||||
\(446\) | 23.2665i | 1.10170i | ||||||||
\(447\) | 6.63325 | + | 2.00000i | 0.313742 | + | 0.0945968i | ||||
\(448\) | 4.86140i | 0.229680i | ||||||||
\(449\) | 31.5066 | 1.48689 | 0.743444 | − | 0.668798i | \(-0.233191\pi\) | ||||
0.743444 | + | 0.668798i | \(0.233191\pi\) | |||||||
\(450\) | 13.4664 | − | 6.60724i | 0.634813 | − | 0.311468i | ||||
\(451\) | 8.12497i | 0.382590i | ||||||||
\(452\) | 8.31662i | 0.391181i | ||||||||
\(453\) | −4.49124 | − | 1.35416i | −0.211017 | − | 0.0636240i | ||||
\(454\) | 0.0501256 | 0.00235251 | ||||||||
\(455\) | 34.7994 | + | 9.42481i | 1.63142 | + | 0.441842i | ||||
\(456\) | 1.99553 | + | 7.28134i | 0.0934491 | + | 0.340980i | ||||
\(457\) | − | 18.8318i | − | 0.880913i | −0.897774 | − | 0.440457i | \(-0.854817\pi\) | ||
0.897774 | − | 0.440457i | \(-0.145183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.4456 | − | 16.1235i | 0.907644 | − | 0.752578i | ||||
\(460\) | −3.52506 | + | 13.0157i | −0.164357 | + | 0.606859i | ||||
\(461\) | − | 11.5831i | − | 0.539480i | −0.962933 | − | 0.269740i | \(-0.913062\pi\) | ||
0.962933 | − | 0.269740i | \(-0.0869377\pi\) | |||||||
\(462\) | 18.6760 | + | 5.63102i | 0.868886 | + | 0.261979i | ||||
\(463\) | 4.67632i | 0.217327i | 0.994079 | + | 0.108664i | \(0.0346571\pi\) | ||||
−0.994079 | + | 0.108664i | \(0.965343\pi\) | |||||||
\(464\) | −1.35416 | −0.0628653 | ||||||||
\(465\) | 17.5224 | − | 28.1151i | 0.812580 | − | 1.30381i | ||||
\(466\) | − | 15.1395i | − | 0.701322i | ||||||
\(467\) | 8.18357 | 0.378690 | 0.189345 | − | 0.981911i | \(-0.439363\pi\) | ||||
0.189345 | + | 0.981911i | \(0.439363\pi\) | |||||||
\(468\) | 8.29156 | + | 5.50000i | 0.383278 | + | 0.254238i | ||||
\(469\) | − | 34.0298i | − | 1.57135i | ||||||
\(470\) | 10.8919 | + | 2.94987i | 0.502405 | + | 0.136068i | ||||
\(471\) | 3.87740 | + | 1.16908i | 0.178661 | + | 0.0538684i | ||||
\(472\) | 9.90789i | 0.456048i | ||||||||
\(473\) | −2.70832 | −0.124529 | ||||||||
\(474\) | 2.33816 | − | 7.75481i | 0.107395 | − | 0.356190i | ||||
\(475\) | −0.683375 | − | 21.7838i | −0.0313554 | − | 0.999508i | ||||
\(476\) | − | 23.6332i | − | 1.08323i | ||||||
\(477\) | −1.65831 | + | 2.50000i | −0.0759289 | + | 0.114467i | ||||
\(478\) | −6.36675 | −0.291208 | ||||||||
\(479\) | 14.0000i | 0.639676i | 0.947472 | + | 0.319838i | \(0.103629\pi\) | ||||
−0.947472 | + | 0.319838i | \(0.896371\pi\) | |||||||
\(480\) | 2.04851 | − | 3.28689i | 0.0935011 | − | 0.150025i | ||||
\(481\) | 6.63325 | 0.302450 | ||||||||
\(482\) | −17.1075 | −0.779223 | ||||||||
\(483\) | 48.6161 | + | 14.6583i | 2.21211 | + | 0.666976i | ||||
\(484\) | −5.63325 | −0.256057 | ||||||||
\(485\) | −9.72281 | + | 35.8997i | −0.441490 | + | 1.63012i | ||||
\(486\) | −1.65831 | − | 15.5000i | −0.0752226 | − | 0.703094i | ||||
\(487\) | −16.5330 | −0.749182 | −0.374591 | − | 0.927190i | \(-0.622217\pi\) | ||||
−0.374591 | + | 0.927190i | \(0.622217\pi\) | |||||||
\(488\) | 4.31662i | 0.195404i | ||||||||
\(489\) | 26.4308 | + | 7.96919i | 1.19524 | + | 0.360379i | ||||
\(490\) | −35.8997 | − | 9.72281i | −1.62179 | − | 0.439232i | ||||
\(491\) | 41.5831i | 1.87662i | 0.345795 | + | 0.938310i | \(0.387609\pi\) | ||||
−0.345795 | + | 0.938310i | \(0.612391\pi\) | |||||||
\(492\) | 1.75362 | − | 5.81610i | 0.0790594 | − | 0.262210i | ||||
\(493\) | 6.58312 | 0.296489 | ||||||||
\(494\) | 12.2461 | − | 7.68338i | 0.550976 | − | 0.345691i | ||||
\(495\) | −10.2544 | − | 11.6770i | −0.460900 | − | 0.524841i | ||||
\(496\) | − | 8.55373i | − | 0.384074i | ||||||
\(497\) | − | 52.9499i | − | 2.37513i | ||||||
\(498\) | −16.1235 | − | 4.86140i | −0.722509 | − | 0.217845i | ||||
\(499\) | 41.5831 | 1.86152 | 0.930758 | − | 0.365635i | \(-0.119148\pi\) | ||||
0.930758 | + | 0.365635i | \(0.119148\pi\) | |||||||
\(500\) | −7.96919 | + | 7.84169i | −0.356393 | + | 0.350691i | ||||
\(501\) | 8.37469 | + | 2.52506i | 0.374153 | + | 0.112811i | ||||
\(502\) | −1.58312 | −0.0706583 | ||||||||
\(503\) | 13.7853 | 0.614656 | 0.307328 | − | 0.951604i | \(-0.400565\pi\) | ||||
0.307328 | + | 0.951604i | \(0.400565\pi\) | |||||||
\(504\) | −12.1535 | − | 8.06173i | −0.541360 | − | 0.359098i | ||||
\(505\) | 16.5831 | + | 4.49124i | 0.737939 | + | 0.199858i | ||||
\(506\) | 13.9704 | 0.621059 | ||||||||
\(507\) | −1.00000 | + | 3.31662i | −0.0444116 | + | 0.147296i | ||||
\(508\) | 3.36675 | 0.149375 | ||||||||
\(509\) | −17.1075 | −0.758275 | −0.379137 | − | 0.925340i | \(-0.623779\pi\) | ||||
−0.379137 | + | 0.925340i | \(0.623779\pi\) | |||||||
\(510\) | −9.95862 | + | 15.9789i | −0.440975 | + | 0.707557i | ||||
\(511\) | −53.8496 | −2.38217 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −21.5125 | − | 7.08592i | −0.949802 | − | 0.312851i | ||||
\(514\) | −14.9499 | −0.659411 | ||||||||
\(515\) | 9.10897 | − | 33.6332i | 0.401389 | − | 1.48206i | ||||
\(516\) | 1.93870 | + | 0.584541i | 0.0853466 | + | 0.0257330i | ||||
\(517\) | − | 11.6908i | − | 0.514161i | ||||||
\(518\) | −9.72281 | −0.427196 | ||||||||
\(519\) | 22.0000 | + | 6.63325i | 0.965693 | + | 0.291167i | ||||
\(520\) | −7.15831 | − | 1.93870i | −0.313913 | − | 0.0850177i | ||||
\(521\) | 41.9697 | 1.83873 | 0.919363 | − | 0.393410i | \(-0.128705\pi\) | ||||
0.919363 | + | 0.393410i | \(0.128705\pi\) | |||||||
\(522\) | 2.24562 | − | 3.38540i | 0.0982882 | − | 0.148175i | ||||
\(523\) | −29.0000 | −1.26808 | −0.634041 | − | 0.773300i | \(-0.718605\pi\) | ||||
−0.634041 | + | 0.773300i | \(0.718605\pi\) | |||||||
\(524\) | 10.0000i | 0.436852i | ||||||||
\(525\) | 28.6662 | + | 30.8341i | 1.25110 | + | 1.34571i | ||||
\(526\) | 21.7838i | 0.949818i | ||||||||
\(527\) | 41.5831i | 1.81139i | ||||||||
\(528\) | −3.84169 | − | 1.15831i | −0.167188 | − | 0.0504091i | ||||
\(529\) | 13.3668 | 0.581163 | ||||||||
\(530\) | 0.584541 | − | 2.15831i | 0.0253908 | − | 0.0937511i | ||||
\(531\) | −24.7697 | − | 16.4304i | −1.07491 | − | 0.713017i | ||||
\(532\) | −17.9499 | + | 11.2620i | −0.778226 | + | 0.488272i | ||||
\(533\) | −11.6322 | −0.503847 | ||||||||
\(534\) | −14.1848 | − | 4.27686i | −0.613834 | − | 0.185078i | ||||
\(535\) | 43.0581 | + | 11.6615i | 1.86156 | + | 0.504171i | ||||
\(536\) | 7.00000i | 0.302354i | ||||||||
\(537\) | 1.35416 | − | 4.49124i | 0.0584364 | − | 0.193811i | ||||
\(538\) | 14.3991i | 0.620791i | ||||||||
\(539\) | 38.5330i | 1.65973i | ||||||||
\(540\) | 4.82015 | + | 10.5720i | 0.207426 | + | 0.454944i | ||||
\(541\) | −28.8496 | −1.24034 | −0.620171 | − | 0.784467i | \(-0.712937\pi\) | ||||
−0.620171 | + | 0.784467i | \(0.712937\pi\) | |||||||
\(542\) | − | 9.31662i | − | 0.400183i | ||||||
\(543\) | 4.49124 | + | 1.35416i | 0.192738 | + | 0.0581126i | ||||
\(544\) | 4.86140i | 0.208431i | ||||||||
\(545\) | −37.3227 | − | 10.1082i | −1.59873 | − | 0.432987i | ||||
\(546\) | −8.06173 | + | 26.7377i | −0.345010 | + | 1.14427i | ||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 4.86140 | 0.207669 | ||||||||
\(549\) | −10.7916 | − | 7.15831i | −0.460573 | − | 0.305509i | ||||
\(550\) | 10.0000 | + | 5.84541i | 0.426401 | + | 0.249249i | ||||
\(551\) | −3.13708 | − | 5.00000i | −0.133644 | − | 0.213007i | ||||
\(552\) | −10.0004 | − | 3.01524i | −0.425646 | − | 0.128337i | ||||
\(553\) | 22.7335 | 0.966727 | ||||||||
\(554\) | −12.0610 | −0.512422 | ||||||||
\(555\) | 6.57377 | + | 4.09701i | 0.279041 | + | 0.173909i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | −34.5851 | −1.46542 | −0.732708 | − | 0.680543i | \(-0.761744\pi\) | ||||
−0.732708 | + | 0.680543i | \(0.761744\pi\) | |||||||
\(558\) | 21.3843 | + | 14.1848i | 0.905270 | + | 0.600488i | ||||
\(559\) | − | 3.87740i | − | 0.163997i | ||||||
\(560\) | 10.4924 | + | 2.84169i | 0.443386 | + | 0.120083i | ||||
\(561\) | 18.6760 | + | 5.63102i | 0.788501 | + | 0.237742i | ||||
\(562\) | − | 13.6002i | − | 0.573690i | ||||||
\(563\) | − | 9.89975i | − | 0.417225i | −0.977998 | − | 0.208612i | \(-0.933105\pi\) | ||
0.977998 | − | 0.208612i | \(-0.0668947\pi\) | |||||||
\(564\) | −2.52324 | + | 8.36865i | −0.106248 | + | 0.352384i | ||||
\(565\) | 17.9499 | + | 4.86140i | 0.755157 | + | 0.204521i | ||||
\(566\) | −15.1395 | −0.636359 | ||||||||
\(567\) | 40.3086 | − | 17.0149i | 1.69280 | − | 0.714559i | ||||
\(568\) | 10.8919i | 0.457014i | ||||||||
\(569\) | −17.1075 | −0.717182 | −0.358591 | − | 0.933495i | \(-0.616743\pi\) | ||||
−0.358591 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(570\) | 16.8819 | − | 0.0507319i | 0.707104 | − | 0.00212493i | ||||
\(571\) | −25.6834 | −1.07482 | −0.537408 | − | 0.843322i | \(-0.680596\pi\) | ||||
−0.537408 | + | 0.843322i | \(0.680596\pi\) | |||||||
\(572\) | 7.68338i | 0.321258i | ||||||||
\(573\) | −8.29156 | − | 2.50000i | −0.346385 | − | 0.104439i | ||||
\(574\) | 17.0501 | 0.711658 | ||||||||
\(575\) | 26.0313 | + | 15.2164i | 1.08558 | + | 0.634567i | ||||
\(576\) | 2.50000 | + | 1.65831i | 0.104167 | + | 0.0690963i | ||||
\(577\) | 6.40065i | 0.266462i | 0.991085 | + | 0.133231i | \(0.0425353\pi\) | ||||
−0.991085 | + | 0.133231i | \(0.957465\pi\) | |||||||
\(578\) | − | 6.63325i | − | 0.275907i | ||||||
\(579\) | 3.00000 | − | 9.94987i | 0.124676 | − | 0.413503i | ||||
\(580\) | −0.791562 | + | 2.92270i | −0.0328678 | + | 0.121359i | ||||
\(581\) | − | 47.2665i | − | 1.96094i | ||||||
\(582\) | −27.5831 | − | 8.31662i | −1.14336 | − | 0.344735i | ||||
\(583\) | −2.31662 | −0.0959448 | ||||||||
\(584\) | 11.0770 | 0.458368 | ||||||||
\(585\) | 16.7175 | − | 14.6808i | 0.691182 | − | 0.606977i | ||||
\(586\) | 8.26650 | 0.341486 | ||||||||
\(587\) | −26.0313 | −1.07443 | −0.537214 | − | 0.843446i | \(-0.680523\pi\) | ||||
−0.537214 | + | 0.843446i | \(0.680523\pi\) | |||||||
\(588\) | 8.31662 | − | 27.5831i | 0.342972 | − | 1.13751i | ||||
\(589\) | 31.5831 | − | 19.8158i | 1.30136 | − | 0.816495i | ||||
\(590\) | 21.3843 | + | 5.79156i | 0.880378 | + | 0.238435i | ||||
\(591\) | −3.10778 | + | 10.3073i | −0.127837 | + | 0.423988i | ||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −21.7838 | −0.894553 | −0.447276 | − | 0.894396i | \(-0.647606\pi\) | ||||
−0.447276 | + | 0.894396i | \(0.647606\pi\) | |||||||
\(594\) | 9.26650 | − | 7.68338i | 0.380209 | − | 0.315253i | ||||
\(595\) | −51.0079 | − | 13.8146i | −2.09112 | − | 0.566343i | ||||
\(596\) | − | 4.00000i | − | 0.163846i | ||||||
\(597\) | 10.6082 | − | 35.1834i | 0.434164 | − | 1.43996i | ||||
\(598\) | 20.0009i | 0.817896i | ||||||||
\(599\) | 48.1853 | 1.96880 | 0.984399 | − | 0.175953i | \(-0.0563007\pi\) | ||||
0.984399 | + | 0.175953i | \(0.0563007\pi\) | |||||||
\(600\) | −5.89669 | − | 6.34264i | −0.240731 | − | 0.258937i | ||||
\(601\) | 22.9529i | 0.936267i | 0.883658 | + | 0.468133i | \(0.155073\pi\) | ||||
−0.883658 | + | 0.468133i | \(0.844927\pi\) | |||||||
\(602\) | 5.68338i | 0.231637i | ||||||||
\(603\) | −17.5000 | − | 11.6082i | −0.712655 | − | 0.472722i | ||||
\(604\) | 2.70832i | 0.110200i | ||||||||
\(605\) | −3.29286 | + | 12.1583i | −0.133874 | + | 0.494306i | ||||
\(606\) | −3.84169 | + | 12.7414i | −0.156058 | + | 0.517585i | ||||
\(607\) | −23.3668 | −0.948427 | −0.474214 | − | 0.880410i | \(-0.657268\pi\) | ||||
−0.474214 | + | 0.880410i | \(0.657268\pi\) | |||||||
\(608\) | 3.69232 | − | 2.31662i | 0.149743 | − | 0.0939515i | ||||
\(609\) | 10.9169 | + | 3.29156i | 0.442374 | + | 0.133381i | ||||
\(610\) | 9.31662 | + | 2.52324i | 0.377219 | + | 0.102163i | ||||
\(611\) | 16.7373 | 0.677118 | ||||||||
\(612\) | −12.1535 | − | 8.06173i | −0.491277 | − | 0.325876i | ||||
\(613\) | 13.2301i | 0.534357i | 0.963647 | + | 0.267178i | \(0.0860913\pi\) | ||||
−0.963647 | + | 0.267178i | \(0.913909\pi\) | |||||||
\(614\) | − | 2.00000i | − | 0.0807134i | ||||||
\(615\) | −11.5279 | − | 7.18461i | −0.464850 | − | 0.289712i | ||||
\(616\) | − | 11.2620i | − | 0.453761i | ||||||
\(617\) | −17.4776 | −0.703622 | −0.351811 | − | 0.936071i | \(-0.614434\pi\) | ||||
−0.351811 | + | 0.936071i | \(0.614434\pi\) | |||||||
\(618\) | 25.8417 | + | 7.79156i | 1.03951 | + | 0.313423i | ||||
\(619\) | −31.5831 | −1.26943 | −0.634716 | − | 0.772745i | \(-0.718883\pi\) | ||||
−0.634716 | + | 0.772745i | \(0.718883\pi\) | |||||||
\(620\) | −18.4616 | − | 5.00000i | −0.741436 | − | 0.200805i | ||||
\(621\) | 24.1219 | − | 20.0009i | 0.967980 | − | 0.802607i | ||||
\(622\) | 18.8997 | 0.757811 | ||||||||
\(623\) | − | 41.5831i | − | 1.66599i | ||||||
\(624\) | 1.65831 | − | 5.50000i | 0.0663856 | − | 0.220176i | ||||
\(625\) | 12.2665 | + | 21.7838i | 0.490660 | + | 0.871351i | ||||
\(626\) | 28.5546 | 1.14127 | ||||||||
\(627\) | −4.62289 | − | 16.8681i | −0.184620 | − | 0.673648i | ||||
\(628\) | − | 2.33816i | − | 0.0933028i | ||||||
\(629\) | −9.72281 | −0.387674 | ||||||||
\(630\) | −24.5039 | + | 21.5187i | −0.976260 | + | 0.857324i | ||||
\(631\) | 15.8997 | 0.632959 | 0.316480 | − | 0.948599i | \(-0.397499\pi\) | ||||
0.316480 | + | 0.948599i | \(0.397499\pi\) | |||||||
\(632\) | −4.67632 | −0.186014 | ||||||||
\(633\) | 30.6151 | + | 9.23081i | 1.21684 | + | 0.366892i | ||||
\(634\) | 17.0000 | 0.675156 | ||||||||
\(635\) | 1.96800 | − | 7.26650i | 0.0780978 | − | 0.288362i | ||||
\(636\) | 1.65831 | + | 0.500000i | 0.0657564 | + | 0.0198263i | ||||
\(637\) | −55.1662 | −2.18577 | ||||||||
\(638\) | 3.13708 | 0.124198 | ||||||||
\(639\) | −27.2297 | − | 18.0622i | −1.07719 | − | 0.714528i | ||||
\(640\) | −2.15831 | − | 0.584541i | −0.0853148 | − | 0.0231060i | ||||
\(641\) | −23.3230 | −0.921204 | −0.460602 | − | 0.887607i | \(-0.652366\pi\) | ||||
−0.460602 | + | 0.887607i | \(0.652366\pi\) | |||||||
\(642\) | −9.97494 | + | 33.0831i | −0.393679 | + | 1.30569i | ||||
\(643\) | − | 46.6460i | − | 1.83954i | −0.392458 | − | 0.919770i | \(-0.628375\pi\) | ||
0.392458 | − | 0.919770i | \(-0.371625\pi\) | |||||||
\(644\) | − | 29.3166i | − | 1.15524i | ||||||
\(645\) | 2.39487 | − | 3.84264i | 0.0942979 | − | 0.151304i | ||||
\(646\) | −17.9499 | + | 11.2620i | −0.706228 | + | 0.443099i | ||||
\(647\) | 3.69232 | 0.145160 | 0.0725801 | − | 0.997363i | \(-0.476877\pi\) | ||||
0.0725801 | + | 0.997363i | \(0.476877\pi\) | |||||||
\(648\) | −8.29156 | + | 3.50000i | −0.325723 | + | 0.137493i | ||||
\(649\) | − | 22.9529i | − | 0.900979i | ||||||
\(650\) | −8.36865 | + | 14.3166i | −0.328245 | + | 0.561544i | ||||
\(651\) | −20.7916 | + | 68.9578i | −0.814886 | + | 2.70267i | ||||
\(652\) | − | 15.9384i | − | 0.624195i | ||||||
\(653\) | 26.8303 | 1.04995 | 0.524975 | − | 0.851118i | \(-0.324075\pi\) | ||||
0.524975 | + | 0.851118i | \(0.324075\pi\) | |||||||
\(654\) | 8.64627 | − | 28.6764i | 0.338096 | − | 1.12134i | ||||
\(655\) | 21.5831 | + | 5.84541i | 0.843322 | + | 0.228399i | ||||
\(656\) | −3.50724 | −0.136935 | ||||||||
\(657\) | −18.3691 | + | 27.6924i | −0.716646 | + | 1.08038i | ||||
\(658\) | −24.5330 | −0.956396 | ||||||||
\(659\) | −12.6162 | −0.491458 | −0.245729 | − | 0.969339i | \(-0.579027\pi\) | ||||
−0.245729 | + | 0.969339i | \(0.579027\pi\) | |||||||
\(660\) | −4.74562 | + | 7.61448i | −0.184723 | + | 0.296393i | ||||
\(661\) | 21.5987i | 0.840092i | 0.907503 | + | 0.420046i | \(0.137986\pi\) | ||||
−0.907503 | + | 0.420046i | \(0.862014\pi\) | |||||||
\(662\) | 15.7533 | 0.612269 | ||||||||
\(663\) | −8.06173 | + | 26.7377i | −0.313092 | + | 1.03841i | ||||
\(664\) | 9.72281i | 0.377318i | ||||||||
\(665\) | 13.8146 | + | 45.3246i | 0.535707 | + | 1.75761i | ||||
\(666\) | −3.31662 | + | 5.00000i | −0.128517 | + | 0.193746i | ||||
\(667\) | 8.16625 | 0.316198 | ||||||||
\(668\) | − | 5.05013i | − | 0.195395i | ||||||
\(669\) | −11.6332 | + | 38.5831i | −0.449767 | + | 1.49171i | ||||
\(670\) | 15.1082 | + | 4.09178i | 0.583680 | + | 0.158079i | ||||
\(671\) | − | 10.0000i | − | 0.386046i | ||||||
\(672\) | −2.43070 | + | 8.06173i | −0.0937664 | + | 0.310988i | ||||
\(673\) | −13.2665 | −0.511386 | −0.255693 | − | 0.966758i | \(-0.582304\pi\) | ||||
−0.255693 | + | 0.966758i | \(0.582304\pi\) | |||||||
\(674\) | − | 18.2164i | − | 0.701668i | ||||||
\(675\) | 25.6351 | − | 4.22366i | 0.986697 | − | 0.162569i | ||||
\(676\) | 2.00000 | 0.0769231 | ||||||||
\(677\) | 20.1662i | 0.775052i | 0.921859 | + | 0.387526i | \(0.126670\pi\) | ||||
−0.921859 | + | 0.387526i | \(0.873330\pi\) | |||||||
\(678\) | −4.15831 | + | 13.7916i | −0.159699 | + | 0.529662i | ||||
\(679\) | − | 80.8609i | − | 3.10316i | ||||||
\(680\) | 10.4924 | + | 2.84169i | 0.402366 | + | 0.108974i | ||||
\(681\) | 0.0831240 | + | 0.0250628i | 0.00318532 | + | 0.000960409i | ||||
\(682\) | 19.8158i | 0.758785i | ||||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | −0.331463 | + | 13.0725i | −0.0126738 | + | 0.499839i | ||||
\(685\) | 2.84169 | − | 10.4924i | 0.108575 | − | 0.400895i | ||||
\(686\) | 46.8311 | 1.78802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.16908i | − | 0.0445708i | ||||||
\(689\) | − | 3.31662i | − | 0.126353i | ||||||
\(690\) | −12.3535 | + | 19.8215i | −0.470289 | + | 0.754592i | ||||
\(691\) | 25.8997 | 0.985273 | 0.492636 | − | 0.870235i | \(-0.336033\pi\) | ||||
0.492636 | + | 0.870235i | \(0.336033\pi\) | |||||||
\(692\) | − | 13.2665i | − | 0.504317i | ||||||
\(693\) | 28.1551 | + | 18.6760i | 1.06952 | + | 0.709442i | ||||
\(694\) | − | 24.8623i | − | 0.943758i | ||||||
\(695\) | 5.84541 | − | 21.5831i | 0.221729 | − | 0.818695i | ||||
\(696\) | −2.24562 | − | 0.677081i | −0.0851201 | − | 0.0256647i | ||||
\(697\) | 17.0501 | 0.645820 | ||||||||
\(698\) | 4.63325i | 0.175371i | ||||||||
\(699\) | 7.56973 | − | 25.1059i | 0.286313 | − | 0.949594i | ||||
\(700\) | 12.2665 | − | 20.9849i | 0.463630 | − | 0.793153i | ||||
\(701\) | − | 10.7335i | − | 0.405399i | −0.979241 | − | 0.202699i | \(-0.935029\pi\) | ||
0.979241 | − | 0.202699i | \(-0.0649714\pi\) | |||||||
\(702\) | 11.0000 | + | 13.2665i | 0.415168 | + | 0.500712i | ||||
\(703\) | 4.63325 | + | 7.38465i | 0.174746 | + | 0.278517i | ||||
\(704\) | 2.31662i | 0.0873111i | ||||||||
\(705\) | 16.5872 | + | 10.3378i | 0.624711 | + | 0.389342i | ||||
\(706\) | 20.0009i | 0.752742i | ||||||||
\(707\) | −37.3520 | −1.40477 | ||||||||
\(708\) | −4.95394 | + | 16.4304i | −0.186181 | + | 0.617491i | ||||
\(709\) | 15.3668 | 0.577110 | 0.288555 | − | 0.957463i | \(-0.406825\pi\) | ||||
0.288555 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(710\) | 23.5081 | + | 6.36675i | 0.882243 | + | 0.238940i | ||||
\(711\) | 7.75481 | − | 11.6908i | 0.290828 | − | 0.438440i | ||||
\(712\) | 8.55373i | 0.320564i | ||||||||
\(713\) | 51.5831i | 1.93180i | ||||||||
\(714\) | 11.8166 | − | 39.1913i | 0.442226 | − | 1.46670i | ||||
\(715\) | 16.5831 | + | 4.49124i | 0.620174 | + | 0.167963i | ||||
\(716\) | −2.70832 | −0.101215 | ||||||||
\(717\) | −10.5581 | − | 3.18338i | −0.394298 | − | 0.118885i | ||||
\(718\) | −34.8997 | −1.30245 | ||||||||
\(719\) | − | 4.89975i | − | 0.182730i | −0.995817 | − | 0.0913649i | \(-0.970877\pi\) | ||
0.995817 | − | 0.0913649i | \(-0.0291230\pi\) | |||||||
\(720\) | 5.04051 | − | 4.42643i | 0.187849 | − | 0.164963i | ||||
\(721\) | 75.7559i | 2.82130i | ||||||||
\(722\) | 17.1075 | + | 8.26650i | 0.636674 | + | 0.307647i | ||||
\(723\) | −28.3695 | − | 8.55373i | −1.05507 | − | 0.318117i | ||||
\(724\) | − | 2.70832i | − | 0.100654i | ||||||
\(725\) | 5.84541 | + | 3.41688i | 0.217093 | + | 0.126900i | ||||
\(726\) | −9.34169 | − | 2.81662i | −0.346703 | − | 0.104535i | ||||
\(727\) | − | 7.56973i | − | 0.280746i | −0.990099 | − | 0.140373i | \(-0.955170\pi\) | ||
0.990099 | − | 0.140373i | \(-0.0448301\pi\) | |||||||
\(728\) | 16.1235 | 0.597575 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 6.47494 | − | 23.9076i | 0.239648 | − | 0.884858i | ||||
\(731\) | 5.68338i | 0.210207i | ||||||||
\(732\) | −2.15831 | + | 7.15831i | −0.0797735 | + | 0.264579i | ||||
\(733\) | − | 9.72281i | − | 0.359120i | −0.983747 | − | 0.179560i | \(-0.942533\pi\) | ||
0.983747 | − | 0.179560i | \(-0.0574674\pi\) | |||||||
\(734\) | 2.33816 | 0.0863031 | ||||||||
\(735\) | −54.6716 | − | 34.0733i | −2.01659 | − | 1.25681i | ||||
\(736\) | 6.03049i | 0.222287i | ||||||||
\(737\) | − | 16.2164i | − | 0.597338i | ||||||
\(738\) | 5.81610 | − | 8.76811i | 0.214094 | − | 0.322759i | ||||
\(739\) | 36.2164 | 1.33224 | 0.666120 | − | 0.745844i | \(-0.267954\pi\) | ||||
0.666120 | + | 0.745844i | \(0.267954\pi\) | |||||||
\(740\) | 1.16908 | − | 4.31662i | 0.0429763 | − | 0.158682i | ||||
\(741\) | 24.1495 | − | 6.61841i | 0.887153 | − | 0.243133i | ||||
\(742\) | 4.86140i | 0.178468i | ||||||||
\(743\) | 14.8496i | 0.544780i | 0.962187 | + | 0.272390i | \(0.0878141\pi\) | ||||
−0.962187 | + | 0.272390i | \(0.912186\pi\) | |||||||
\(744\) | 4.27686 | − | 14.1848i | 0.156797 | − | 0.520038i | ||||
\(745\) | −8.63325 | − | 2.33816i | −0.316298 | − | 0.0856636i | ||||
\(746\) | 16.6834i | 0.610822i | ||||||||
\(747\) | −24.3070 | − | 16.1235i | −0.889347 | − | 0.589926i | ||||
\(748\) | − | 11.2620i | − | 0.411781i | ||||||
\(749\) | −96.9844 | −3.54373 | ||||||||
\(750\) | −17.1362 | + | 9.01937i | −0.625727 | + | 0.329341i | ||||
\(751\) | 22.9529i | 0.837562i | 0.908087 | + | 0.418781i | \(0.137542\pi\) | ||||
−0.908087 | + | 0.418781i | \(0.862458\pi\) | |||||||
\(752\) | 5.04648 | 0.184026 | ||||||||
\(753\) | −2.62531 | − | 0.791562i | −0.0956718 | − | 0.0288461i | ||||
\(754\) | 4.49124i | 0.163561i | ||||||||
\(755\) | 5.84541 | + | 1.58312i | 0.212736 | + | 0.0576158i | ||||
\(756\) | −16.1235 | − | 19.4456i | −0.586404 | − | 0.707230i | ||||
\(757\) | 19.4456i | 0.706763i | 0.935479 | + | 0.353381i | \(0.114968\pi\) | ||||
−0.935479 | + | 0.353381i | \(0.885032\pi\) | |||||||
\(758\) | −22.7678 | −0.826963 | ||||||||
\(759\) | 23.1672 | + | 6.98519i | 0.840918 | + | 0.253546i | ||||
\(760\) | −2.84169 | − | 9.32335i | −0.103079 | − | 0.338193i | ||||
\(761\) | − | 17.3166i | − | 0.627727i | −0.949468 | − | 0.313864i | \(-0.898377\pi\) | ||
0.949468 | − | 0.313864i | \(-0.101623\pi\) | |||||||
\(762\) | 5.58312 | + | 1.68338i | 0.202255 | + | 0.0609822i | ||||
\(763\) | 84.0660 | 3.04339 | ||||||||
\(764\) | 5.00000i | 0.180894i | ||||||||
\(765\) | −24.5039 | + | 21.5187i | −0.885942 | + | 0.778009i | ||||
\(766\) | 25.5831 | 0.924356 | ||||||||
\(767\) | 32.8607 | 1.18653 | ||||||||
\(768\) | 0.500000 | − | 1.65831i | 0.0180422 | − | 0.0598392i | ||||
\(769\) | 18.1662 | 0.655092 | 0.327546 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327546 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(770\) | −24.3070 | − | 6.58312i | −0.875964 | − | 0.237239i | ||||
\(771\) | −24.7916 | − | 7.47494i | −0.892846 | − | 0.269203i | ||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | 42.1662i | 1.51661i | 0.651897 | + | 0.758307i | \(0.273973\pi\) | ||||
−0.651897 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(774\) | 2.92270 | + | 1.93870i | 0.105054 | + | 0.0696852i | ||||
\(775\) | −21.5831 | + | 36.9232i | −0.775289 | + | 1.32632i | ||||
\(776\) | 16.6332i | 0.597099i | ||||||||
\(777\) | −16.1235 | − | 4.86140i | −0.578426 | − | 0.174402i | ||||
\(778\) | 30.2164 | 1.08331 | ||||||||
\(779\) | −8.12497 | − | 12.9499i | −0.291107 | − | 0.463977i | ||||
\(780\) | −10.9014 | − | 6.79413i | −0.390332 | − | 0.243269i | ||||
\(781\) | − | 25.2324i | − | 0.902887i | ||||||
\(782\) | − | 29.3166i | − | 1.04836i | ||||||
\(783\) | 5.41664 | − | 4.49124i | 0.193575 | − | 0.160504i | ||||
\(784\) | −16.6332 | −0.594045 | ||||||||
\(785\) | −5.04648 | − | 1.36675i | −0.180117 | − | 0.0487814i | ||||
\(786\) | −5.00000 | + | 16.5831i | −0.178344 | + | 0.591500i | ||||
\(787\) | 21.6332 | 0.771142 | 0.385571 | − | 0.922678i | \(-0.374004\pi\) | ||||
0.385571 | + | 0.922678i | \(0.374004\pi\) | |||||||
\(788\) | 6.21557 | 0.221420 | ||||||||
\(789\) | −10.8919 | + | 36.1243i | −0.387762 | + | 1.28606i | ||||
\(790\) | −2.73350 | + | 10.0930i | −0.0972536 | + | 0.359092i | ||||
\(791\) | −40.4305 | −1.43754 | ||||||||
\(792\) | −5.79156 | − | 3.84169i | −0.205794 | − | 0.136508i | ||||
\(793\) | 14.3166 | 0.508398 | ||||||||
\(794\) | 16.7373 | 0.593984 | ||||||||
\(795\) | 2.04851 | − | 3.28689i | 0.0726531 | − | 0.116574i | ||||
\(796\) | −21.2164 | −0.751994 | ||||||||
\(797\) | − | 18.3668i | − | 0.650584i | −0.945614 | − | 0.325292i | \(-0.894537\pi\) | ||
0.945614 | − | 0.325292i | \(-0.105463\pi\) | |||||||
\(798\) | −35.3975 | + | 9.70106i | −1.25306 | + | 0.343414i | ||||
\(799\) | −24.5330 | −0.867915 | ||||||||
\(800\) | −2.52324 | + | 4.31662i | −0.0892101 | + | 0.152616i | ||||
\(801\) | −21.3843 | − | 14.1848i | −0.755578 | − | 0.501194i | ||||
\(802\) | 8.92389i | 0.315113i | ||||||||
\(803\) | −25.6612 | −0.905563 | ||||||||
\(804\) | −3.50000 | + | 11.6082i | −0.123435 | + | 0.409389i | ||||
\(805\) | −63.2744 | − | 17.1368i | −2.23013 | − | 0.603991i | ||||
\(806\) | −28.3695 | −0.999273 | ||||||||
\(807\) | −7.19957 | + | 23.8783i | −0.253437 | + | 0.840555i | ||||
\(808\) | 7.68338 | 0.270300 | ||||||||
\(809\) | − | 17.9499i | − | 0.631084i | −0.948912 | − | 0.315542i | \(-0.897814\pi\) | ||
0.948912 | − | 0.315542i | \(-0.102186\pi\) | |||||||
\(810\) | 2.70734 | + | 19.9417i | 0.0951262 | + | 0.700679i | ||||
\(811\) | 6.77081i | 0.237755i | 0.992909 | + | 0.118878i | \(0.0379296\pi\) | ||||
−0.992909 | + | 0.118878i | \(0.962070\pi\) | |||||||
\(812\) | − | 6.58312i | − | 0.231022i | ||||||
\(813\) | 4.65831 | − | 15.4499i | 0.163374 | − | 0.541851i | ||||
\(814\) | −4.63325 | −0.162395 | ||||||||
\(815\) | −34.4000 | − | 9.31662i | −1.20498 | − | 0.326347i | ||||
\(816\) | −2.43070 | + | 8.06173i | −0.0850916 | + | 0.282217i | ||||
\(817\) | 4.31662 | − | 2.70832i | 0.151020 | − | 0.0947522i | ||||
\(818\) | −1.16908 | −0.0408760 | ||||||||
\(819\) | −26.7377 | + | 40.3086i | −0.934292 | + | 1.40850i | ||||
\(820\) | −2.05013 | + | 7.56973i | −0.0715935 | + | 0.264346i | ||||
\(821\) | − | 30.0000i | − | 1.04701i | −0.852023 | − | 0.523504i | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | 8.06173 | + | 2.43070i | 0.281185 | + | 0.0847805i | ||||
\(823\) | − | 16.9224i | − | 0.589877i | −0.955516 | − | 0.294938i | \(-0.904701\pi\) | ||
0.955516 | − | 0.294938i | \(-0.0952991\pi\) | |||||||
\(824\) | − | 15.5831i | − | 0.542864i | ||||||
\(825\) | 13.6604 | + | 14.6935i | 0.475595 | + | 0.511562i | ||||
\(826\) | −48.1662 | −1.67592 | ||||||||
\(827\) | − | 24.5831i | − | 0.854839i | −0.904053 | − | 0.427419i | \(-0.859423\pi\) | ||
0.904053 | − | 0.427419i | \(-0.140577\pi\) | |||||||
\(828\) | −15.0762 | − | 10.0004i | −0.523935 | − | 0.347539i | ||||
\(829\) | 28.9833i | 1.00663i | 0.864102 | + | 0.503317i | \(0.167887\pi\) | ||||
−0.864102 | + | 0.503317i | \(0.832113\pi\) | |||||||
\(830\) | 20.9849 | + | 5.68338i | 0.728395 | + | 0.197273i | ||||
\(831\) | −20.0009 | − | 6.03049i | −0.693822 | − | 0.209195i | ||||
\(832\) | −3.31662 | −0.114983 | ||||||||
\(833\) | 80.8609 | 2.80167 | ||||||||
\(834\) | 16.5831 | + | 5.00000i | 0.574227 | + | 0.173136i | ||||
\(835\) | −10.8997 | − | 2.95200i | −0.377201 | − | 0.102158i | ||||
\(836\) | −8.55373 | + | 5.36675i | −0.295837 | + | 0.185613i | ||||
\(837\) | 28.3695 | + | 34.2149i | 0.980593 | + | 1.18264i | ||||
\(838\) | −22.9499 | −0.792790 | ||||||||
\(839\) | −36.9232 | −1.27473 | −0.637366 | − | 0.770561i | \(-0.719976\pi\) | ||||
−0.637366 | + | 0.770561i | \(0.719976\pi\) | |||||||
\(840\) | 15.9789 | + | 9.95862i | 0.551324 | + | 0.343605i | ||||
\(841\) | −27.1662 | −0.936767 | ||||||||
\(842\) | −24.3070 | −0.837675 | ||||||||
\(843\) | 6.80011 | − | 22.5534i | 0.234208 | − | 0.776780i | ||||
\(844\) | − | 18.4616i | − | 0.635475i | ||||||
\(845\) | 1.16908 | − | 4.31662i | 0.0402176 | − | 0.148496i | ||||
\(846\) | −8.36865 | + | 12.6162i | −0.287720 | + | 0.433754i | ||||
\(847\) | − | 27.3855i | − | 0.940977i | ||||||
\(848\) | − | 1.00000i | − | 0.0343401i | ||||||
\(849\) | −25.1059 | − | 7.56973i | −0.861634 | − | 0.259792i | ||||
\(850\) | 12.2665 | − | 20.9849i | 0.420737 | − | 0.719775i | ||||
\(851\) | −12.0610 | −0.413445 | ||||||||
\(852\) | −5.44594 | + | 18.0622i | −0.186575 | + | 0.618799i | ||||
\(853\) | − | 38.5211i | − | 1.31894i | −0.751732 | − | 0.659468i | \(-0.770782\pi\) | ||
0.751732 | − | 0.659468i | \(-0.229218\pi\) | |||||||
\(854\) | −20.9849 | −0.718087 | ||||||||
\(855\) | 28.0208 | + | 8.35680i | 0.958290 | + | 0.285797i | ||||
\(856\) | 19.9499 | 0.681873 | ||||||||
\(857\) | 12.0000i | 0.409912i | 0.978771 | + | 0.204956i | \(0.0657052\pi\) | ||||
−0.978771 | + | 0.204956i | \(0.934295\pi\) | |||||||
\(858\) | −3.84169 | + | 12.7414i | −0.131153 | + | 0.434985i | ||||
\(859\) | −16.9499 | −0.578322 | −0.289161 | − | 0.957280i | \(-0.593376\pi\) | ||||
−0.289161 | + | 0.957280i | \(0.593376\pi\) | |||||||
\(860\) | −2.52324 | − | 0.683375i | −0.0860418 | − | 0.0233029i | ||||
\(861\) | 28.2744 | + | 8.52506i | 0.963590 | + | 0.290533i | ||||
\(862\) | − | 33.4160i | − | 1.13815i | ||||||
\(863\) | − | 18.3166i | − | 0.623505i | −0.950163 | − | 0.311753i | \(-0.899084\pi\) | ||
0.950163 | − | 0.311753i | \(-0.100916\pi\) | |||||||
\(864\) | 3.31662 | + | 4.00000i | 0.112834 | + | 0.136083i | ||||
\(865\) | −28.6332 | − | 7.75481i | −0.973560 | − | 0.263671i | ||||
\(866\) | − | 8.31662i | − | 0.282610i | ||||||
\(867\) | 3.31662 | − | 11.0000i | 0.112638 | − | 0.373580i | ||||
\(868\) | 41.5831 | 1.41142 | ||||||||
\(869\) | 10.8333 | 0.367494 | ||||||||
\(870\) | −2.77401 | + | 4.45097i | −0.0940477 | + | 0.150902i | ||||
\(871\) | 23.2164 | 0.786657 | ||||||||
\(872\) | −17.2925 | −0.585599 | ||||||||
\(873\) | −41.5831 | − | 27.5831i | −1.40738 | − | 0.933547i | ||||
\(874\) | −22.2665 | + | 13.9704i | −0.753176 | + | 0.472555i | ||||
\(875\) | −38.1216 | − | 38.7414i | −1.28875 | − | 1.30970i | ||||
\(876\) | 18.3691 | + | 5.53848i | 0.620634 | + | 0.187128i | ||||
\(877\) | 0.0501256 | 0.00169262 | 0.000846311 | − | 1.00000i | \(-0.499731\pi\) | ||||
0.000846311 | 1.00000i | \(0.499731\pi\) | ||||||||
\(878\) | −1.16908 | −0.0394546 | ||||||||
\(879\) | 13.7084 | + | 4.13325i | 0.462374 | + | 0.139411i | ||||
\(880\) | 5.00000 | + | 1.35416i | 0.168550 | + | 0.0456488i | ||||
\(881\) | − | 23.8997i | − | 0.805203i | −0.915375 | − | 0.402601i | \(-0.868106\pi\) | ||
0.915375 | − | 0.402601i | \(-0.131894\pi\) | |||||||
\(882\) | 27.5831 | − | 41.5831i | 0.928772 | − | 1.40018i | ||||
\(883\) | − | 46.6460i | − | 1.56976i | −0.619645 | − | 0.784882i | \(-0.712723\pi\) | ||
0.619645 | − | 0.784882i | \(-0.287277\pi\) | |||||||
\(884\) | 16.1235 | 0.542290 | ||||||||
\(885\) | 32.5661 | + | 20.2964i | 1.09470 | + | 0.682255i | ||||
\(886\) | − | 3.87740i | − | 0.130264i | ||||||
\(887\) | 0.416876i | 0.0139973i | 0.999976 | + | 0.00699866i | \(0.00222776\pi\) | ||||
−0.999976 | + | 0.00699866i | \(0.997772\pi\) | |||||||
\(888\) | 3.31662 | + | 1.00000i | 0.111299 | + | 0.0335578i | ||||
\(889\) | 16.3671i | 0.548936i | ||||||||
\(890\) | 18.4616 | + | 5.00000i | 0.618835 | + | 0.167600i | ||||
\(891\) | 19.2084 | − | 8.10819i | 0.643507 | − | 0.271634i | ||||
\(892\) | 23.2665 | 0.779020 | ||||||||
\(893\) | 11.6908 | + | 18.6332i | 0.391218 | + | 0.623538i | ||||
\(894\) | 2.00000 | − | 6.63325i | 0.0668900 | − | 0.221849i | ||||
\(895\) | −1.58312 | + | 5.84541i | −0.0529180 | + | 0.195390i | ||||
\(896\) | 4.86140 | 0.162408 | ||||||||
\(897\) | −10.0004 | + | 33.1677i | −0.333905 | + | 1.10744i | ||||
\(898\) | − | 31.5066i | − | 1.05139i | ||||||
\(899\) | 11.5831i | 0.386319i | ||||||||
\(900\) | −6.60724 | − | 13.4664i | −0.220241 | − | 0.448881i | ||||
\(901\) | 4.86140i | 0.161957i | ||||||||
\(902\) | 8.12497 | 0.270532 | ||||||||
\(903\) | −2.84169 | + | 9.42481i | −0.0945654 | + | 0.313638i | ||||
\(904\) | 8.31662 | 0.276607 | ||||||||
\(905\) | −5.84541 | − | 1.58312i | −0.194308 | − | 0.0526248i | ||||
\(906\) | −1.35416 | + | 4.49124i | −0.0449890 | + | 0.149212i | ||||
\(907\) | 60.1662 | 1.99779 | 0.998894 | − | 0.0470245i | \(-0.0149739\pi\) | ||||
0.998894 | + | 0.0470245i | \(0.0149739\pi\) | |||||||
\(908\) | − | 0.0501256i | − | 0.00166348i | ||||||
\(909\) | −12.7414 | + | 19.2084i | −0.422607 | + | 0.637104i | ||||
\(910\) | 9.42481 | − | 34.7994i | 0.312429 | − | 1.15359i | ||||
\(911\) | −0.370160 | −0.0122639 | −0.00613197 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613197 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(912\) | 7.28134 | − | 1.99553i | 0.241109 | − | 0.0660785i | ||||
\(913\) | − | 22.5241i | − | 0.745439i | ||||||
\(914\) | −18.8318 | −0.622900 | ||||||||
\(915\) | 14.1883 | + | 8.84264i | 0.469049 | + | 0.292329i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.6140 | −1.60538 | ||||||||
\(918\) | −16.1235 | − | 19.4456i | −0.532153 | − | 0.641801i | ||||
\(919\) | 1.94987 | 0.0643204 | 0.0321602 | − | 0.999483i | \(-0.489761\pi\) | ||||
0.0321602 | + | 0.999483i | \(0.489761\pi\) | |||||||
\(920\) | 13.0157 | + | 3.52506i | 0.429114 | + | 0.116218i | ||||
\(921\) | 1.00000 | − | 3.31662i | 0.0329511 | − | 0.109287i | ||||
\(922\) | −11.5831 | −0.381470 | ||||||||
\(923\) | 36.1243 | 1.18905 | ||||||||
\(924\) | 5.63102 | − | 18.6760i | 0.185247 | − | 0.614395i | ||||
\(925\) | −8.63325 | − | 5.04648i | −0.283859 | − | 0.165927i | ||||
\(926\) | 4.67632 | 0.153674 | ||||||||
\(927\) | 38.9578 | + | 25.8417i | 1.27954 | + | 0.848752i | ||||
\(928\) | 1.35416i | 0.0444525i | ||||||||
\(929\) | − | 37.9499i | − | 1.24509i | −0.782582 | − | 0.622547i | \(-0.786098\pi\) | ||
0.782582 | − | 0.622547i | \(-0.213902\pi\) | |||||||
\(930\) | −28.1151 | − | 17.5224i | −0.921931 | − | 0.574581i | ||||
\(931\) | −38.5330 | − | 61.4153i | −1.26287 | − | 2.01281i | ||||
\(932\) | −15.1395 | −0.495909 | ||||||||
\(933\) | 31.3417 | + | 9.44987i | 1.02608 | + | 0.309375i | ||||
\(934\) | − | 8.18357i | − | 0.267774i | ||||||
\(935\) | −24.3070 | − | 6.58312i | −0.794925 | − | 0.215291i | ||||
\(936\) | 5.50000 | − | 8.29156i | 0.179773 | − | 0.271018i | ||||
\(937\) | 55.0147i | 1.79725i | 0.438716 | + | 0.898626i | \(0.355433\pi\) | ||||
−0.438716 | + | 0.898626i | \(0.644567\pi\) | |||||||
\(938\) | −34.0298 | −1.11111 | ||||||||
\(939\) | 47.3524 | + | 14.2773i | 1.54529 | + | 0.465922i | ||||
\(940\) | 2.94987 | − | 10.8919i | 0.0962143 | − | 0.355254i | ||||
\(941\) | −13.4151 | −0.437321 | −0.218660 | − | 0.975801i | \(-0.570169\pi\) | ||||
−0.218660 | + | 0.975801i | \(0.570169\pi\) | |||||||
\(942\) | 1.16908 | − | 3.87740i | 0.0380907 | − | 0.126333i | ||||
\(943\) | 21.1504 | 0.688751 | ||||||||
\(944\) | 9.90789 | 0.322474 | ||||||||
\(945\) | −51.3945 | + | 23.4327i | −1.67186 | + | 0.762266i | ||||
\(946\) | 2.70832i | 0.0880551i | ||||||||
\(947\) | −17.4776 | −0.567946 | −0.283973 | − | 0.958832i | \(-0.591653\pi\) | ||||
−0.283973 | + | 0.958832i | \(0.591653\pi\) | |||||||
\(948\) | −7.75481 | − | 2.33816i | −0.251864 | − | 0.0759400i | ||||
\(949\) | − | 36.7382i | − | 1.19257i | ||||||
\(950\) | −21.7838 | + | 0.683375i | −0.706759 | + | 0.0221716i | ||||
\(951\) | 28.1913 | + | 8.50000i | 0.914166 | + | 0.275631i | ||||
\(952\) | −23.6332 | −0.765958 | ||||||||
\(953\) | 35.5831i | 1.15265i | 0.817220 | + | 0.576325i | \(0.195514\pi\) | ||||
−0.817220 | + | 0.576325i | \(0.804486\pi\) | |||||||
\(954\) | 2.50000 | + | 1.65831i | 0.0809405 | + | 0.0536898i | ||||
\(955\) | 10.7916 | + | 2.92270i | 0.349207 | + | 0.0945764i | ||||
\(956\) | 6.36675i | 0.205915i | ||||||||
\(957\) | 5.20226 | + | 1.56854i | 0.168165 | + | 0.0507037i | ||||
\(958\) | 14.0000 | 0.452319 | ||||||||
\(959\) | 23.6332i | 0.763157i | ||||||||
\(960\) | −3.28689 | − | 2.04851i | −0.106084 | − | 0.0661153i | ||||
\(961\) | −42.1662 | −1.36020 | ||||||||
\(962\) | − | 6.63325i | − | 0.213865i | ||||||
\(963\) | −33.0831 | + | 49.8747i | −1.06609 | + | 1.60719i | ||||
\(964\) | 17.1075i | 0.550994i | ||||||||
\(965\) | −3.50724 | + | 12.9499i | −0.112902 | + | 0.416871i | ||||
\(966\) | 14.6583 | − | 48.6161i | 0.471623 | − | 1.56420i | ||||
\(967\) | − | 26.4601i | − | 0.850900i | −0.904982 | − | 0.425450i | \(-0.860116\pi\) | ||
0.904982 | − | 0.425450i | \(-0.139884\pi\) | |||||||
\(968\) | 5.63325i | 0.181059i | ||||||||
\(969\) | −35.3975 | + | 9.70106i | −1.13713 | + | 0.311643i | ||||
\(970\) | 35.8997 | + | 9.72281i | 1.15267 | + | 0.312181i | ||||
\(971\) | −48.9842 | −1.57198 | −0.785989 | − | 0.618241i | \(-0.787846\pi\) | ||||
−0.785989 | + | 0.618241i | \(0.787846\pi\) | |||||||
\(972\) | −15.5000 | + | 1.65831i | −0.497163 | + | 0.0531904i | ||||
\(973\) | 48.6140i | 1.55849i | ||||||||
\(974\) | 16.5330i | 0.529751i | ||||||||
\(975\) | −21.0361 | + | 19.5571i | −0.673696 | + | 0.626329i | ||||
\(976\) | 4.31662 | 0.138172 | ||||||||
\(977\) | 3.58312i | 0.114634i | 0.998356 | + | 0.0573171i | \(0.0182546\pi\) | ||||
−0.998356 | + | 0.0573171i | \(0.981745\pi\) | |||||||
\(978\) | 7.96919 | − | 26.4308i | 0.254826 | − | 0.845164i | ||||
\(979\) | − | 19.8158i | − | 0.633315i | ||||||
\(980\) | −9.72281 | + | 35.8997i | −0.310584 | + | 1.14678i | ||||
\(981\) | 28.6764 | − | 43.2313i | 0.915568 | − | 1.38027i | ||||
\(982\) | 41.5831 | 1.32697 | ||||||||
\(983\) | − | 39.1662i | − | 1.24921i | −0.780941 | − | 0.624605i | \(-0.785260\pi\) | ||
0.780941 | − | 0.624605i | \(-0.214740\pi\) | |||||||
\(984\) | −5.81610 | − | 1.75362i | −0.185411 | − | 0.0559034i | ||||
\(985\) | 3.63325 | − | 13.4151i | 0.115765 | − | 0.427442i | ||||
\(986\) | − | 6.58312i | − | 0.209649i | ||||||
\(987\) | −40.6834 | − | 12.2665i | −1.29497 | − | 0.390447i | ||||
\(988\) | −7.68338 | − | 12.2461i | −0.244441 | − | 0.389599i | ||||
\(989\) | 7.05013i | 0.224181i | ||||||||
\(990\) | −11.6770 | + | 10.2544i | −0.371118 | + | 0.325906i | ||||
\(991\) | − | 13.9704i | − | 0.443783i | −0.975071 | − | 0.221892i | \(-0.928777\pi\) | ||
0.975071 | − | 0.221892i | \(-0.0712232\pi\) | |||||||
\(992\) | −8.55373 | −0.271581 | ||||||||
\(993\) | 26.1239 | + | 7.87665i | 0.829016 | + | 0.249958i | ||||
\(994\) | −52.9499 | −1.67947 | ||||||||
\(995\) | −12.4018 | + | 45.7916i | −0.393164 | + | 1.45169i | ||||
\(996\) | −4.86140 | + | 16.1235i | −0.154039 | + | 0.510891i | ||||
\(997\) | − | 17.9064i | − | 0.567101i | −0.958957 | − | 0.283550i | \(-0.908488\pi\) | ||
0.958957 | − | 0.283550i | \(-0.0915123\pi\) | |||||||
\(998\) | − | 41.5831i | − | 1.31629i | ||||||
\(999\) | −8.00000 | + | 6.63325i | −0.253109 | + | 0.209867i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.2.c.f.569.1 | yes | 8 | |
3.2 | odd | 2 | inner | 570.2.c.f.569.8 | yes | 8 | |
5.4 | even | 2 | 570.2.c.c.569.8 | yes | 8 | ||
15.14 | odd | 2 | 570.2.c.c.569.1 | ✓ | 8 | ||
19.18 | odd | 2 | 570.2.c.c.569.7 | yes | 8 | ||
57.56 | even | 2 | 570.2.c.c.569.2 | yes | 8 | ||
95.94 | odd | 2 | inner | 570.2.c.f.569.2 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.f.569.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.c.569.1 | ✓ | 8 | 15.14 | odd | 2 | ||
570.2.c.c.569.2 | yes | 8 | 57.56 | even | 2 | ||
570.2.c.c.569.7 | yes | 8 | 19.18 | odd | 2 | ||
570.2.c.c.569.8 | yes | 8 | 5.4 | even | 2 | ||
570.2.c.f.569.1 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.c.f.569.2 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.f.569.7 | yes | 8 | 285.284 | even | 2 | inner | |
570.2.c.f.569.8 | yes | 8 | 3.2 | odd | 2 | inner |