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 | 569.8 | ||
Root | \(0.500000 + 1.08454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.f.569.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | \(0.113562\pi\) | ||||
−0.937032 | + | 0.349244i | \(0.886438\pi\) | |||||||
\(12\) | −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 | ||||||||
\(15\) | 3.87143 | − | 0.109805i | 0.999598 | − | 0.0283516i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.86140 | 1.17906 | 0.589532 | − | 0.807745i | \(-0.299312\pi\) | ||||
0.589532 | + | 0.807745i | \(0.299312\pi\) | |||||||
\(18\) | −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 | \(-0.283579\pi\) | ||||
0.628722 | + | 0.777631i | \(0.283579\pi\) | |||||||
\(24\) | 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 | \(-0.459872\pi\) | ||||
0.125731 | + | 0.992064i | \(0.459872\pi\) | |||||||
\(30\) | 0.109805 | + | 3.87143i | 0.0200476 | + | 0.706823i | ||||
\(31\) | − | 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 | \(-0.411696\pi\) | ||||
0.273870 | + | 0.961767i | \(0.411696\pi\) | |||||||
\(42\) | 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 | ||||||
\(45\) | 2.11780 | + | 6.36513i | 0.315704 | + | 0.948858i | ||||
\(46\) | 6.03049i | 0.889147i | ||||||||
\(47\) | −5.04648 | −0.736105 | −0.368053 | − | 0.929805i | \(-0.619975\pi\) | ||||
−0.368053 | + | 0.929805i | \(0.619975\pi\) | |||||||
\(48\) | 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 | \(0.0218788\pi\) | ||||
−0.997639 | + | 0.0686803i | \(0.978121\pi\) | |||||||
\(54\) | 3.31662 | − | 4.00000i | 0.451335 | − | 0.544331i | ||||
\(55\) | 5.00000 | + | 1.35416i | 0.674200 | + | 0.182595i | ||||
\(56\) | −4.86140 | −0.649632 | ||||||||
\(57\) | −4.96471 | + | 5.68785i | −0.657592 | + | 0.753374i | ||||
\(58\) | 1.35416i | 0.177810i | ||||||||
\(59\) | −9.90789 | −1.28990 | −0.644949 | − | 0.764226i | \(-0.723121\pi\) | ||||
−0.644949 | + | 0.764226i | \(0.723121\pi\) | |||||||
\(60\) | −3.87143 | + | 0.109805i | −0.499799 | + | 0.0141758i | ||||
\(61\) | 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 | \(-0.723691\pi\) | ||||
−0.646315 | + | 0.763071i | \(0.723691\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 2.02601 | − | 8.41993i | 0.233944 | − | 0.972250i | ||||
\(76\) | −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 | \(-0.679164\pi\) | ||||
−0.533608 | + | 0.845732i | \(0.679164\pi\) | |||||||
\(84\) | −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 | \(-0.649770\pi\) | ||||
−0.453347 | + | 0.891334i | \(0.649770\pi\) | |||||||
\(90\) | −6.36513 | + | 2.11780i | −0.670944 | + | 0.223236i | ||||
\(91\) | − | 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 | \(0.124855\pi\) | ||||
−0.924054 | + | 0.382262i | \(0.875145\pi\) | |||||||
\(102\) | −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 | ||||||
\(105\) | −0.533809 | − | 18.8206i | −0.0520944 | − | 1.83670i | ||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 19.9499i | 1.92863i | 0.264763 | + | 0.964314i | \(0.414706\pi\) | ||||
−0.264763 | + | 0.964314i | \(0.585294\pi\) | |||||||
\(108\) | 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 | \(0.127933\pi\) | ||||
−0.920314 | + | 0.391181i | \(0.872067\pi\) | |||||||
\(114\) | −5.68785 | − | 4.96471i | −0.532716 | − | 0.464988i | ||||
\(115\) | 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 | ||||||
\(120\) | −0.109805 | − | 3.87143i | −0.0100238 | − | 0.353411i | ||||
\(121\) | 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 | \(0.143907\pi\) | ||||
−0.899533 | + | 0.436852i | \(0.856093\pi\) | |||||||
\(132\) | 3.84169 | − | 1.15831i | 0.334376 | − | 0.100818i | ||||
\(133\) | 17.9499 | − | 11.2620i | 1.55645 | − | 0.976544i | ||||
\(134\) | 7.00000i | 0.604708i | ||||||||
\(135\) | −9.49647 | + | 6.69455i | −0.817326 | + | 0.576175i | ||||
\(136\) | − | 4.86140i | − | 0.416862i | ||||||
\(137\) | 4.86140 | 0.415338 | 0.207669 | − | 0.978199i | \(-0.433412\pi\) | ||||
0.207669 | + | 0.978199i | \(0.433412\pi\) | |||||||
\(138\) | −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 | \(-0.947610\pi\) | ||
0.986486 | − | 0.163846i | \(-0.0523901\pi\) | |||||||
\(150\) | 8.41993 | + | 2.02601i | 0.687485 | + | 0.165423i | ||||
\(151\) | − | 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 | ||||||||
\(165\) | 0.254378 | + | 8.96864i | 0.0198033 | + | 0.698208i | ||||
\(166\) | − | 9.72281i | − | 0.754636i | ||||||
\(167\) | − | 5.05013i | − | 0.390790i | −0.980725 | − | 0.195395i | \(-0.937401\pi\) | ||
0.980725 | − | 0.195395i | \(-0.0625990\pi\) | |||||||
\(168\) | −2.43070 | − | 8.06173i | −0.187533 | − | 0.621976i | ||||
\(169\) | −2.00000 | −0.153846 | ||||||||
\(170\) | 10.4924 | + | 2.84169i | 0.804733 | + | 0.217947i | ||||
\(171\) | −11.9146 | − | 5.38912i | −0.911131 | − | 0.412116i | ||||
\(172\) | 1.16908i | 0.0891416i | ||||||||
\(173\) | − | 13.2665i | − | 1.00863i | −0.863519 | − | 0.504317i | \(-0.831744\pi\) | ||
0.863519 | − | 0.504317i | \(-0.168256\pi\) | |||||||
\(174\) | −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 | \(-0.532273\pi\) | ||||
−0.101215 | + | 0.994865i | \(0.532273\pi\) | |||||||
\(180\) | −2.11780 | − | 6.36513i | −0.157852 | − | 0.474429i | ||||
\(181\) | 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 | \(0.0578990\pi\) | ||||
−0.983503 | + | 0.180894i | \(0.942101\pi\) | |||||||
\(192\) | −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 | ||||||||
\(195\) | 12.8401 | − | 0.364183i | 0.919496 | − | 0.0260797i | ||||
\(196\) | 16.6332 | 1.18809 | ||||||||
\(197\) | 6.21557 | 0.442841 | 0.221420 | − | 0.975178i | \(-0.428931\pi\) | ||||
0.221420 | + | 0.975178i | \(0.428931\pi\) | |||||||
\(198\) | 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 | ||||
\(210\) | 18.8206 | − | 0.533809i | 1.29874 | − | 0.0368363i | ||||
\(211\) | 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 | ||||||||
\(225\) | 14.9759 | − | 0.850207i | 0.998392 | − | 0.0566805i | ||||
\(226\) | −8.31662 | −0.553214 | ||||||||
\(227\) | − | 0.0501256i | − | 0.00332695i | −0.999999 | − | 0.00166348i | \(-0.999470\pi\) | ||
0.999999 | − | 0.00166348i | \(-0.000529502\pi\) | |||||||
\(228\) | 4.96471 | − | 5.68785i | 0.328796 | − | 0.376687i | ||||
\(229\) | 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 | \(-0.665165\pi\) | ||||
−0.495909 | + | 0.868374i | \(0.665165\pi\) | |||||||
\(234\) | −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 | \(0.0660172\pi\) | ||||
−0.978570 | + | 0.205915i | \(0.933983\pi\) | |||||||
\(240\) | 3.87143 | − | 0.109805i | 0.249900 | − | 0.00708791i | ||||
\(241\) | − | 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 | \(0.0159103\pi\) | ||||
−0.998751 | + | 0.0499629i | \(0.984090\pi\) | |||||||
\(252\) | −8.06173 | − | 12.1535i | −0.507841 | − | 0.765599i | ||||
\(253\) | 13.9704i | 0.878310i | ||||||||
\(254\) | − | 3.36675i | − | 0.211249i | ||||||
\(255\) | 18.8206 | − | 0.533809i | 1.17859 | − | 0.0334284i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.9499i | 0.932548i | 0.884640 | + | 0.466274i | \(0.154404\pi\) | ||||
−0.884640 | + | 0.466274i | \(0.845596\pi\) | |||||||
\(258\) | 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 | \(-0.265598\pi\) | ||||
0.671623 | + | 0.740893i | \(0.265598\pi\) | |||||||
\(264\) | 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 | \(-0.355345\pi\) | ||||
0.438965 | + | 0.898504i | \(0.355345\pi\) | |||||||
\(270\) | −6.69455 | − | 9.49647i | −0.407417 | − | 0.577937i | ||||
\(271\) | 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 | \(-0.632958\pi\) | ||||
−0.405660 | + | 0.914024i | \(0.632958\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 9.37408 | + | 14.0402i | 0.555273 | + | 0.831668i | ||||
\(286\) | −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 | \(-0.922371\pi\) | ||
0.970409 | − | 0.241467i | \(-0.0776286\pi\) | |||||||
\(294\) | 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 | ||||||||
\(300\) | −2.02601 | + | 8.41993i | −0.116972 | + | 0.486125i | ||||
\(301\) | −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 | \(-0.819990\pi\) | ||
0.844311 | − | 0.535853i | \(-0.180010\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 30.9435 | − | 10.2955i | 1.74347 | − | 0.580086i | ||||
\(316\) | − | 4.67632i | − | 0.263064i | ||||||
\(317\) | − | 17.0000i | − | 0.954815i | −0.878682 | − | 0.477408i | \(-0.841577\pi\) | ||
0.878682 | − | 0.477408i | \(-0.158423\pi\) | |||||||
\(318\) | −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 | ||||||||
\(330\) | −8.96864 | + | 0.254378i | −0.493708 | + | 0.0140030i | ||||
\(331\) | 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 | ||||||||
\(342\) | 5.38912 | − | 11.9146i | 0.291410 | − | 0.644267i | ||||
\(343\) | 46.8311i | 2.52864i | ||||||||
\(344\) | −1.16908 | −0.0630326 | ||||||||
\(345\) | 23.3466 | − | 0.662180i | 1.25694 | − | 0.0356506i | ||||
\(346\) | 13.2665 | 0.713211 | ||||||||
\(347\) | −24.8623 | −1.33468 | −0.667338 | − | 0.744755i | \(-0.732566\pi\) | ||||
−0.667338 | + | 0.744755i | \(0.732566\pi\) | |||||||
\(348\) | −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 | \(-0.321339\pi\) | ||||
0.532269 | + | 0.846575i | \(0.321339\pi\) | |||||||
\(354\) | 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 | \(0.372601\pi\) | ||||
−0.389636 | + | 0.920969i | \(0.627399\pi\) | |||||||
\(360\) | 6.36513 | − | 2.11780i | 0.335472 | − | 0.111618i | ||||
\(361\) | −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 | ||||||||
\(375\) | −16.9886 | − | 9.29456i | −0.877286 | − | 0.479969i | ||||
\(376\) | 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 | \(-0.773250\pi\) | ||
0.756824 | − | 0.653618i | \(-0.226750\pi\) | |||||||
\(384\) | 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 | \(-0.722237\pi\) | ||
0.642822 | − | 0.766015i | \(-0.277763\pi\) | |||||||
\(390\) | 0.364183 | + | 12.8401i | 0.0184411 | + | 0.650182i | ||||
\(391\) | 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 | ||||||||
\(399\) | 27.6509 | + | 24.1355i | 1.38428 | + | 1.20829i | ||||
\(400\) | −4.31662 | − | 2.52324i | −0.215831 | − | 0.126162i | ||||
\(401\) | 8.92389 | 0.445638 | 0.222819 | − | 0.974860i | \(-0.428474\pi\) | ||||
0.222819 | + | 0.974860i | \(0.428474\pi\) | |||||||
\(402\) | −11.6082 | + | 3.50000i | −0.578964 | + | 0.174564i | ||||
\(403\) | − | 28.3695i | − | 1.41319i | ||||||
\(404\) | − | 7.68338i | − | 0.382262i | ||||||
\(405\) | −15.8499 | − | 12.4008i | −0.787587 | − | 0.616203i | ||||
\(406\) | 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 | \(0.189425\pi\) | ||||
−0.828095 | + | 0.560587i | \(0.810575\pi\) | |||||||
\(420\) | 0.533809 | + | 18.8206i | 0.0260472 | + | 0.918350i | ||||
\(421\) | − | 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 | \(-0.797725\pi\) | ||||
−0.804796 | + | 0.593552i | \(0.797725\pi\) | |||||||
\(432\) | −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 | ||||||
\(435\) | 5.24253 | − | 0.148694i | 0.251360 | − | 0.00712934i | ||||
\(436\) | − | 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 | \(-0.529361\pi\) | ||||
−0.0921105 | + | 0.995749i | \(0.529361\pi\) | |||||||
\(444\) | −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 | \(-0.766809\pi\) | ||||
−0.743444 | + | 0.668798i | \(0.766809\pi\) | |||||||
\(450\) | 0.850207 | + | 14.9759i | 0.0400792 | + | 0.705970i | ||||
\(451\) | 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 | ||||
\(456\) | 5.68785 | + | 4.96471i | 0.266358 | + | 0.232494i | ||||
\(457\) | − | 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 | \(0.0869377\pi\) | ||||
−0.962933 | + | 0.269740i | \(0.913062\pi\) | |||||||
\(462\) | −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 | ||||||||
\(465\) | −0.939246 | − | 33.1151i | −0.0435565 | − | 1.53568i | ||||
\(466\) | − | 15.1395i | − | 0.701322i | ||||||
\(467\) | −8.18357 | −0.378690 | −0.189345 | − | 0.981911i | \(-0.560637\pi\) | ||||
−0.189345 | + | 0.981911i | \(0.560637\pi\) | |||||||
\(468\) | 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 | \(-0.896371\pi\) | ||
0.947472 | − | 0.319838i | \(-0.103629\pi\) | |||||||
\(480\) | 0.109805 | + | 3.87143i | 0.00501191 | + | 0.176706i | ||||
\(481\) | 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 | \(-0.612391\pi\) | ||
0.345795 | − | 0.938310i | \(-0.387609\pi\) | |||||||
\(492\) | −1.75362 | − | 5.81610i | −0.0790594 | − | 0.262210i | ||||
\(493\) | 6.58312 | 0.296489 | ||||||||
\(494\) | −12.2461 | + | 7.68338i | −0.550976 | + | 0.345691i | ||||
\(495\) | −14.7456 | + | 4.90616i | −0.662766 | + | 0.220515i | ||||
\(496\) | − | 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 | \(-0.599435\pi\) | ||||
−0.307328 | + | 0.951604i | \(0.599435\pi\) | |||||||
\(504\) | 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 | \(-0.376221\pi\) | ||||
0.379137 | + | 0.925340i | \(0.376221\pi\) | |||||||
\(510\) | 0.533809 | + | 18.8206i | 0.0236374 | + | 0.833389i | ||||
\(511\) | −53.8496 | −2.38217 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.97955 | − | 22.4527i | 0.131550 | − | 0.991309i | ||||
\(514\) | −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 | \(-0.871295\pi\) | ||||
−0.919363 | + | 0.393410i | \(0.871295\pi\) | |||||||
\(522\) | −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 | ||||||
\(525\) | −40.9327 | − | 9.84926i | −1.78645 | − | 0.429857i | ||||
\(526\) | 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 | ||||||
\(540\) | 9.49647 | − | 6.69455i | 0.408663 | − | 0.288087i | ||||
\(541\) | −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 | ||||||||
\(555\) | 7.74285 | − | 0.219611i | 0.328666 | − | 0.00932196i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | 34.5851 | 1.46542 | 0.732708 | − | 0.680543i | \(-0.238256\pi\) | ||||
0.732708 | + | 0.680543i | \(0.238256\pi\) | |||||||
\(558\) | −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 | \(0.0668947\pi\) | ||||
−0.977998 | + | 0.208612i | \(0.933105\pi\) | |||||||
\(564\) | 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 | \(-0.383257\pi\) | ||||
0.358591 | + | 0.933495i | \(0.383257\pi\) | |||||||
\(570\) | −14.0402 | + | 9.37408i | −0.588078 | + | 0.392637i | ||||
\(571\) | −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 | ||||||||
\(585\) | 7.02396 | + | 21.1108i | 0.290405 | + | 0.872822i | ||||
\(586\) | 8.26650 | 0.341486 | ||||||||
\(587\) | 26.0313 | 1.07443 | 0.537214 | − | 0.843446i | \(-0.319477\pi\) | ||||
0.537214 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(588\) | 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 | \(-0.352394\pi\) | ||||
0.447276 | + | 0.894396i | \(0.352394\pi\) | |||||||
\(594\) | 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 | \(-0.943699\pi\) | ||||
−0.984399 | + | 0.175953i | \(0.943699\pi\) | |||||||
\(600\) | −8.41993 | − | 2.02601i | −0.343742 | − | 0.0827116i | ||||
\(601\) | 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 | ||||||||
\(615\) | 13.5780 | − | 0.385114i | 0.547519 | − | 0.0155293i | ||||
\(616\) | − | 11.2620i | − | 0.453761i | ||||||
\(617\) | 17.4776 | 0.703622 | 0.351811 | − | 0.936071i | \(-0.385566\pi\) | ||||
0.351811 | + | 0.936071i | \(0.385566\pi\) | |||||||
\(618\) | 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 | ||||||||
\(627\) | −13.1766 | − | 11.5014i | −0.526223 | − | 0.459321i | ||||
\(628\) | − | 2.33816i | − | 0.0933028i | ||||||
\(629\) | 9.72281 | 0.387674 | ||||||||
\(630\) | 10.2955 | + | 30.9435i | 0.410183 | + | 1.23282i | ||||
\(631\) | 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 | \(-0.347634\pi\) | ||||
0.460602 | + | 0.887607i | \(0.347634\pi\) | |||||||
\(642\) | −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 | ||||||||
\(645\) | −0.128371 | − | 4.52601i | −0.00505462 | − | 0.178212i | ||||
\(646\) | −17.9499 | + | 11.2620i | −0.706228 | + | 0.443099i | ||||
\(647\) | −3.69232 | −0.145160 | −0.0725801 | − | 0.997363i | \(-0.523123\pi\) | ||||
−0.0725801 | + | 0.997363i | \(0.523123\pi\) | |||||||
\(648\) | −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 | \(-0.675925\pi\) | ||||
−0.524975 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(654\) | −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 | \(-0.420973\pi\) | ||||
0.245729 | + | 0.969339i | \(0.420973\pi\) | |||||||
\(660\) | −0.254378 | − | 8.96864i | −0.00990165 | − | 0.349104i | ||||
\(661\) | 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 | ||||||||
\(675\) | 8.89785 | + | 24.4096i | 0.342478 | + | 0.939526i | ||||
\(676\) | 2.00000 | 0.0769231 | ||||||||
\(677\) | − | 20.1662i | − | 0.775052i | −0.921859 | − | 0.387526i | \(-0.873330\pi\) | ||
0.921859 | − | 0.387526i | \(-0.126670\pi\) | |||||||
\(678\) | −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 | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 11.9146 | + | 5.38912i | 0.455566 | + | 0.206058i | ||||
\(685\) | 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 | ||||||||
\(690\) | 0.662180 | + | 23.3466i | 0.0252088 | + | 0.888789i | ||||
\(691\) | 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 | \(0.0649714\pi\) | ||||
−0.979241 | + | 0.202699i | \(0.935029\pi\) | |||||||
\(702\) | 11.0000 | − | 13.2665i | 0.415168 | − | 0.500712i | ||||
\(703\) | 4.63325 | + | 7.38465i | 0.174746 | + | 0.278517i | ||||
\(704\) | − | 2.31662i | − | 0.0873111i | ||||||
\(705\) | −19.5371 | + | 0.554131i | −0.735809 | + | 0.0208698i | ||||
\(706\) | 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 | \(0.0291230\pi\) | ||||
−0.995817 | + | 0.0913649i | \(0.970877\pi\) | |||||||
\(720\) | 2.11780 | + | 6.36513i | 0.0789259 | + | 0.237214i | ||||
\(721\) | 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 | ||||||||
\(735\) | −64.3944 | + | 1.82642i | −2.37522 | + | 0.0673686i | ||||
\(736\) | 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 | ||||
\(741\) | −16.4661 | + | 18.8645i | −0.604897 | + | 0.693003i | ||||
\(742\) | 4.86140i | 0.178468i | ||||||||
\(743\) | − | 14.8496i | − | 0.544780i | −0.962187 | − | 0.272390i | \(-0.912186\pi\) | ||
0.962187 | − | 0.272390i | \(-0.0878141\pi\) | |||||||
\(744\) | −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 | ||||||||
\(750\) | 9.29456 | − | 16.9886i | 0.339389 | − | 0.620335i | ||||
\(751\) | 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 | \(0.101623\pi\) | ||||
−0.949468 | + | 0.313864i | \(0.898377\pi\) | |||||||
\(762\) | 5.58312 | − | 1.68338i | 0.202255 | − | 0.0609822i | ||||
\(763\) | 84.0660 | 3.04339 | ||||||||
\(764\) | − | 5.00000i | − | 0.180894i | ||||||
\(765\) | 10.2955 | + | 30.9435i | 0.372235 | + | 1.11876i | ||||
\(766\) | 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 | \(-0.726027\pi\) | ||
0.651897 | − | 0.758307i | \(-0.273973\pi\) | |||||||
\(774\) | −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 | ||||
\(780\) | −12.8401 | + | 0.364183i | −0.459748 | + | 0.0130399i | ||||
\(781\) | − | 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 | ||||||||
\(795\) | 0.109805 | + | 3.87143i | 0.00389440 | + | 0.137305i | ||||
\(796\) | −21.2164 | −0.751994 | ||||||||
\(797\) | 18.3668i | 0.650584i | 0.945614 | + | 0.325292i | \(0.105463\pi\) | ||||
−0.945614 | + | 0.325292i | \(0.894537\pi\) | |||||||
\(798\) | −24.1355 | + | 27.6509i | −0.854387 | + | 0.978832i | ||||
\(799\) | −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 | \(0.102186\pi\) | ||||
−0.948912 | + | 0.315542i | \(0.897814\pi\) | |||||||
\(810\) | 12.4008 | − | 15.8499i | 0.435721 | − | 0.556908i | ||||
\(811\) | 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 | \(0.175375\pi\) | ||||
−0.852023 | + | 0.523504i | \(0.824625\pi\) | |||||||
\(822\) | −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 | ||||||||
\(825\) | 19.5058 | + | 4.69351i | 0.679106 | + | 0.163407i | ||||
\(826\) | −48.1662 | −1.67592 | ||||||||
\(827\) | 24.5831i | 0.854839i | 0.904053 | + | 0.427419i | \(0.140577\pi\) | ||||
−0.904053 | + | 0.427419i | \(0.859423\pi\) | |||||||
\(828\) | 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 | \(-0.280024\pi\) | ||||
0.637366 | + | 0.770561i | \(0.280024\pi\) | |||||||
\(840\) | −18.8206 | + | 0.533809i | −0.649371 | + | 0.0184181i | ||||
\(841\) | −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 | ||||||||
\(855\) | −18.5960 | + | 22.5652i | −0.635969 | + | 0.771715i | ||||
\(856\) | 19.9499 | 0.681873 | ||||||||
\(857\) | − | 12.0000i | − | 0.409912i | −0.978771 | − | 0.204956i | \(-0.934295\pi\) | ||
0.978771 | − | 0.204956i | \(-0.0657052\pi\) | |||||||
\(858\) | −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 | \(0.100916\pi\) | ||||
−0.950163 | + | 0.311753i | \(0.899084\pi\) | |||||||
\(864\) | 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 | ||||||||
\(870\) | 0.148694 | + | 5.24253i | 0.00504121 | + | 0.177739i | ||||
\(871\) | 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 | \(0.131894\pi\) | ||||
−0.915375 | + | 0.402601i | \(0.868106\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | −38.3577 | + | 1.08794i | −1.28938 | + | 0.0365707i | ||||
\(886\) | − | 3.87740i | − | 0.130264i | ||||||
\(887\) | − | 0.416876i | − | 0.0139973i | −0.999976 | − | 0.00699866i | \(-0.997772\pi\) | ||
0.999976 | − | 0.00699866i | \(-0.00222776\pi\) | |||||||
\(888\) | 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 | ||||||
\(900\) | −14.9759 | + | 0.850207i | −0.499196 | + | 0.0283402i | ||||
\(901\) | 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 | \(-0.498048\pi\) | ||||
0.00613197 | + | 0.999981i | \(0.498048\pi\) | |||||||
\(912\) | −4.96471 | + | 5.68785i | −0.164398 | + | 0.188344i | ||||
\(913\) | − | 22.5241i | − | 0.745439i | ||||||
\(914\) | 18.8318 | 0.622900 | ||||||||
\(915\) | 16.7115 | − | 0.473989i | 0.552465 | − | 0.0156696i | ||||
\(916\) | 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 | \(0.213902\pi\) | ||||
−0.782582 | + | 0.622547i | \(0.786098\pi\) | |||||||
\(930\) | 33.1151 | − | 0.939246i | 1.08589 | − | 0.0307991i | ||||
\(931\) | −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 | \(-0.429831\pi\) | ||||
0.218660 | + | 0.975801i | \(0.429831\pi\) | |||||||
\(942\) | −1.16908 | − | 3.87740i | −0.0380907 | − | 0.126333i | ||||
\(943\) | 21.1504 | 0.688751 | ||||||||
\(944\) | −9.90789 | −0.322474 | ||||||||
\(945\) | 32.5449 | + | 46.1662i | 1.05869 | + | 1.50179i | ||||
\(946\) | 2.70832i | 0.0880551i | ||||||||
\(947\) | 17.4776 | 0.567946 | 0.283973 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283973 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(948\) | 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 | \(-0.804486\pi\) | ||
0.817220 | − | 0.576325i | \(-0.195514\pi\) | |||||||
\(954\) | 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 | ||||||
\(960\) | −3.87143 | + | 0.109805i | −0.124950 | + | 0.00354395i | ||||
\(961\) | −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 | ||||||
\(969\) | −24.1355 | + | 27.6509i | −0.775343 | + | 0.888276i | ||||
\(970\) | 35.8997 | + | 9.72281i | 1.15267 | + | 0.312181i | ||||
\(971\) | 48.9842 | 1.57198 | 0.785989 | − | 0.618241i | \(-0.212154\pi\) | ||||
0.785989 | + | 0.618241i | \(0.212154\pi\) | |||||||
\(972\) | −15.5000 | − | 1.65831i | −0.497163 | − | 0.0531904i | ||||
\(973\) | 48.6140i | 1.55849i | ||||||||
\(974\) | − | 16.5330i | − | 0.529751i | ||||||
\(975\) | 6.71952 | − | 27.9258i | 0.215197 | − | 0.894340i | ||||
\(976\) | 4.31662 | 0.138172 | ||||||||
\(977\) | − | 3.58312i | − | 0.114634i | −0.998356 | − | 0.0573171i | \(-0.981745\pi\) | ||
0.998356 | − | 0.0573171i | \(-0.0182546\pi\) | |||||||
\(978\) | −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 | \(0.214740\pi\) | ||||
−0.780941 | + | 0.624605i | \(0.785260\pi\) | |||||||
\(984\) | 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 | ||||||
\(990\) | −4.90616 | − | 14.7456i | −0.155928 | − | 0.468647i | ||||
\(991\) | − | 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.569.8 | yes | 8 | |
3.2 | odd | 2 | inner | 570.2.c.f.569.1 | yes | 8 | |
5.4 | even | 2 | 570.2.c.c.569.1 | ✓ | 8 | ||
15.14 | odd | 2 | 570.2.c.c.569.8 | yes | 8 | ||
19.18 | odd | 2 | 570.2.c.c.569.2 | yes | 8 | ||
57.56 | even | 2 | 570.2.c.c.569.7 | yes | 8 | ||
95.94 | odd | 2 | inner | 570.2.c.f.569.7 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.f.569.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.c.569.1 | ✓ | 8 | 5.4 | even | 2 | ||
570.2.c.c.569.2 | yes | 8 | 19.18 | odd | 2 | ||
570.2.c.c.569.7 | yes | 8 | 57.56 | even | 2 | ||
570.2.c.c.569.8 | yes | 8 | 15.14 | odd | 2 | ||
570.2.c.f.569.1 | yes | 8 | 3.2 | odd | 2 | inner | |
570.2.c.f.569.2 | yes | 8 | 285.284 | even | 2 | inner | |
570.2.c.f.569.7 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.f.569.8 | yes | 8 | 1.1 | even | 1 | trivial |