Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.l.811.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −0.118034 | − | 0.204441i | −0.0446127 | − | 0.0772714i | 0.842857 | − | 0.538138i | \(-0.180872\pi\) |
−0.887469 | + | 0.460866i | \(0.847539\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 2.11803 | − | 3.66854i | 0.638611 | − | 1.10611i | −0.347126 | − | 0.937818i | \(-0.612843\pi\) |
0.985738 | − | 0.168289i | \(-0.0538241\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(14\) | −0.118034 | − | 0.204441i | −0.0315459 | − | 0.0546391i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.85410 | − | 4.94345i | −0.692221 | − | 1.19896i | −0.971108 | − | 0.238639i | \(-0.923299\pi\) |
0.278887 | − | 0.960324i | \(-0.410035\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.61803 | + | 2.80252i | 0.371202 | + | 0.642942i | 0.989751 | − | 0.142805i | \(-0.0456123\pi\) |
−0.618548 | + | 0.785747i | \(0.712279\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | −0.118034 | + | 0.204441i | −0.0257571 | + | 0.0446127i | ||||
\(22\) | 2.11803 | − | 3.66854i | 0.451566 | − | 0.782136i | ||||
\(23\) | −1.23607 | −0.257738 | −0.128869 | − | 0.991662i | \(-0.541135\pi\) | ||||
−0.128869 | + | 0.991662i | \(0.541135\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.118034 | − | 0.204441i | −0.0223063 | − | 0.0386357i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.35410 | − | 5.40059i | 0.243204 | − | 0.969975i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.23607 | −0.737405 | ||||||||
\(34\) | −2.85410 | − | 4.94345i | −0.489474 | − | 0.847795i | ||||
\(35\) | −0.236068 | −0.0399028 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 0.618034 | + | 1.07047i | 0.101604 | + | 0.175984i | 0.912346 | − | 0.409421i | \(-0.134269\pi\) |
−0.810742 | + | 0.585404i | \(0.800936\pi\) | |||||||
\(38\) | 1.61803 | + | 2.80252i | 0.262480 | + | 0.454628i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −0.618034 | + | 1.07047i | −0.0965207 | + | 0.167179i | −0.910242 | − | 0.414076i | \(-0.864105\pi\) |
0.813722 | + | 0.581255i | \(0.197438\pi\) | |||||||
\(42\) | −0.118034 | + | 0.204441i | −0.0182130 | + | 0.0315459i | ||||
\(43\) | −0.763932 | − | 1.32317i | −0.116499 | − | 0.201781i | 0.801879 | − | 0.597486i | \(-0.203834\pi\) |
−0.918378 | + | 0.395705i | \(0.870500\pi\) | |||||||
\(44\) | 2.11803 | − | 3.66854i | 0.319306 | − | 0.553054i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −1.23607 | −0.182248 | ||||||||
\(47\) | 0.763932 | 0.111431 | 0.0557155 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557155 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 3.47214 | − | 6.01392i | 0.496019 | − | 0.859131i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | −2.85410 | + | 4.94345i | −0.399654 | + | 0.692221i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.73607 | − | 6.47106i | 0.513188 | − | 0.888868i | −0.486695 | − | 0.873572i | \(-0.661798\pi\) |
0.999883 | − | 0.0152962i | \(-0.00486912\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.11803 | − | 3.66854i | −0.285596 | − | 0.494666i | ||||
\(56\) | −0.118034 | − | 0.204441i | −0.0157730 | − | 0.0273196i | ||||
\(57\) | 1.61803 | − | 2.80252i | 0.214314 | − | 0.371202i | ||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | 3.11803 | + | 5.40059i | 0.405933 | + | 0.703097i | 0.994430 | − | 0.105403i | \(-0.0336131\pi\) |
−0.588496 | + | 0.808500i | \(0.700280\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −14.1803 | −1.81561 | −0.907803 | − | 0.419396i | \(-0.862242\pi\) | ||||
−0.907803 | + | 0.419396i | \(0.862242\pi\) | |||||||
\(62\) | 1.35410 | − | 5.40059i | 0.171971 | − | 0.685876i | ||||
\(63\) | 0.236068 | 0.0297418 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.23607 | −0.521424 | ||||||||
\(67\) | −2.61803 | + | 4.53457i | −0.319844 | + | 0.553986i | −0.980455 | − | 0.196742i | \(-0.936964\pi\) |
0.660611 | + | 0.750728i | \(0.270297\pi\) | |||||||
\(68\) | −2.85410 | − | 4.94345i | −0.346111 | − | 0.599481i | ||||
\(69\) | 0.618034 | + | 1.07047i | 0.0744025 | + | 0.128869i | ||||
\(70\) | −0.236068 | −0.0282155 | ||||||||
\(71\) | 1.23607 | − | 2.14093i | 0.146694 | − | 0.254082i | −0.783309 | − | 0.621632i | \(-0.786470\pi\) |
0.930004 | + | 0.367550i | \(0.119803\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −1.47214 | + | 2.54981i | −0.172300 | + | 0.298433i | −0.939224 | − | 0.343306i | \(-0.888453\pi\) |
0.766923 | + | 0.641739i | \(0.221787\pi\) | |||||||
\(74\) | 0.618034 | + | 1.07047i | 0.0718450 | + | 0.124439i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 1.61803 | + | 2.80252i | 0.185601 | + | 0.321471i | ||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.23607 | + | 9.06914i | 0.589104 | + | 1.02036i | 0.994350 | + | 0.106150i | \(0.0338524\pi\) |
−0.405246 | + | 0.914207i | \(0.632814\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.618034 | + | 1.07047i | −0.0682504 | + | 0.118213i | ||||
\(83\) | −2.35410 | + | 4.07742i | −0.258396 | + | 0.447555i | −0.965812 | − | 0.259242i | \(-0.916527\pi\) |
0.707416 | + | 0.706797i | \(0.249861\pi\) | |||||||
\(84\) | −0.118034 | + | 0.204441i | −0.0128786 | + | 0.0223063i | ||||
\(85\) | −5.70820 | −0.619142 | ||||||||
\(86\) | −0.763932 | − | 1.32317i | −0.0823769 | − | 0.142681i | ||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 2.11803 | − | 3.66854i | 0.225783 | − | 0.391068i | ||||
\(89\) | 10.9443 | 1.16009 | 0.580045 | − | 0.814584i | \(-0.303035\pi\) | ||||
0.580045 | + | 0.814584i | \(0.303035\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.23607 | −0.128869 | ||||||||
\(93\) | −5.35410 | + | 1.52761i | −0.555195 | + | 0.158406i | ||||
\(94\) | 0.763932 | 0.0787936 | ||||||||
\(95\) | 3.23607 | 0.332014 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 1.47214 | 0.149473 | 0.0747364 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747364 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(98\) | 3.47214 | − | 6.01392i | 0.350739 | − | 0.607497i | ||||
\(99\) | 2.11803 | + | 3.66854i | 0.212870 | + | 0.368702i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | −2.85410 | + | 4.94345i | −0.282598 | + | 0.489474i | ||||
\(103\) | −9.35410 | + | 16.2018i | −0.921687 | + | 1.59641i | −0.124883 | + | 0.992172i | \(0.539855\pi\) |
−0.796804 | + | 0.604237i | \(0.793478\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.118034 | + | 0.204441i | 0.0115189 | + | 0.0199514i | ||||
\(106\) | 3.73607 | − | 6.47106i | 0.362879 | − | 0.628525i | ||||
\(107\) | 5.35410 | + | 9.27358i | 0.517601 | + | 0.896510i | 0.999791 | + | 0.0204441i | \(0.00650800\pi\) |
−0.482190 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 3.23607 | 0.309959 | 0.154980 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154980 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(110\) | −2.11803 | − | 3.66854i | −0.201947 | − | 0.349782i | ||||
\(111\) | 0.618034 | − | 1.07047i | 0.0586612 | − | 0.101604i | ||||
\(112\) | −0.118034 | − | 0.204441i | −0.0111532 | − | 0.0193178i | ||||
\(113\) | 3.70820 | − | 6.42280i | 0.348838 | − | 0.604206i | −0.637205 | − | 0.770694i | \(-0.719910\pi\) |
0.986043 | + | 0.166488i | \(0.0532428\pi\) | |||||||
\(114\) | 1.61803 | − | 2.80252i | 0.151543 | − | 0.262480i | ||||
\(115\) | −0.618034 | + | 1.07047i | −0.0576320 | + | 0.0998215i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.11803 | + | 5.40059i | 0.287038 | + | 0.497165i | ||||
\(119\) | −0.673762 | + | 1.16699i | −0.0617637 | + | 0.106978i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −3.47214 | − | 6.01392i | −0.315649 | − | 0.546720i | ||||
\(122\) | −14.1803 | −1.28383 | ||||||||
\(123\) | 1.23607 | 0.111452 | ||||||||
\(124\) | 1.35410 | − | 5.40059i | 0.121602 | − | 0.484988i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.236068 | 0.0210306 | ||||||||
\(127\) | 4.59017 | + | 7.95041i | 0.407312 | + | 0.705485i | 0.994588 | − | 0.103902i | \(-0.0331329\pi\) |
−0.587276 | + | 0.809387i | \(0.699800\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.763932 | + | 1.32317i | −0.0672605 | + | 0.116499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.47214 | + | 11.2101i | 0.565473 | + | 0.979428i | 0.997005 | + | 0.0773308i | \(0.0246397\pi\) |
−0.431532 | + | 0.902097i | \(0.642027\pi\) | |||||||
\(132\) | −4.23607 | −0.368702 | ||||||||
\(133\) | 0.381966 | − | 0.661585i | 0.0331207 | − | 0.0573667i | ||||
\(134\) | −2.61803 | + | 4.53457i | −0.226164 | + | 0.391727i | ||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | −2.85410 | − | 4.94345i | −0.244737 | − | 0.423897i | ||||
\(137\) | 0.381966 | − | 0.661585i | 0.0326336 | − | 0.0565230i | −0.849247 | − | 0.527995i | \(-0.822944\pi\) |
0.881881 | + | 0.471472i | \(0.156277\pi\) | |||||||
\(138\) | 0.618034 | + | 1.07047i | 0.0526105 | + | 0.0911241i | ||||
\(139\) | 17.1246 | 1.45249 | 0.726245 | − | 0.687436i | \(-0.241264\pi\) | ||||
0.726245 | + | 0.687436i | \(0.241264\pi\) | |||||||
\(140\) | −0.236068 | −0.0199514 | ||||||||
\(141\) | −0.381966 | − | 0.661585i | −0.0321673 | − | 0.0557155i | ||||
\(142\) | 1.23607 | − | 2.14093i | 0.103729 | − | 0.179663i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 1.50000 | − | 2.59808i | 0.124568 | − | 0.215758i | ||||
\(146\) | −1.47214 | + | 2.54981i | −0.121835 | + | 0.211024i | ||||
\(147\) | −6.94427 | −0.572754 | ||||||||
\(148\) | 0.618034 | + | 1.07047i | 0.0508021 | + | 0.0879918i | ||||
\(149\) | 8.73607 | + | 15.1313i | 0.715687 | + | 1.23961i | 0.962694 | + | 0.270592i | \(0.0872194\pi\) |
−0.247008 | + | 0.969014i | \(0.579447\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 9.18034 | 0.747085 | 0.373543 | − | 0.927613i | \(-0.378143\pi\) | ||||
0.373543 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(152\) | 1.61803 | + | 2.80252i | 0.131240 | + | 0.227314i | ||||
\(153\) | 5.70820 | 0.461481 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −4.00000 | − | 3.87298i | −0.321288 | − | 0.311086i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.1803 | −1.77018 | −0.885092 | − | 0.465416i | \(-0.845905\pi\) | ||||
−0.885092 | + | 0.465416i | \(0.845905\pi\) | |||||||
\(158\) | 5.23607 | + | 9.06914i | 0.416559 | + | 0.721502i | ||||
\(159\) | −7.47214 | −0.592579 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 0.145898 | + | 0.252703i | 0.0114984 | + | 0.0199158i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −18.7639 | −1.46970 | −0.734852 | − | 0.678227i | \(-0.762749\pi\) | ||||
−0.734852 | + | 0.678227i | \(0.762749\pi\) | |||||||
\(164\) | −0.618034 | + | 1.07047i | −0.0482603 | + | 0.0835894i | ||||
\(165\) | −2.11803 | + | 3.66854i | −0.164889 | + | 0.285596i | ||||
\(166\) | −2.35410 | + | 4.07742i | −0.182714 | + | 0.316469i | ||||
\(167\) | −2.14590 | − | 3.71680i | −0.166055 | − | 0.287615i | 0.770975 | − | 0.636866i | \(-0.219769\pi\) |
−0.937029 | + | 0.349251i | \(0.886436\pi\) | |||||||
\(168\) | −0.118034 | + | 0.204441i | −0.00910652 | + | 0.0157730i | ||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | −5.70820 | −0.437799 | ||||||||
\(171\) | −3.23607 | −0.247468 | ||||||||
\(172\) | −0.763932 | − | 1.32317i | −0.0582493 | − | 0.100891i | ||||
\(173\) | 3.50000 | − | 6.06218i | 0.266100 | − | 0.460899i | −0.701751 | − | 0.712422i | \(-0.747598\pi\) |
0.967851 | + | 0.251523i | \(0.0809315\pi\) | |||||||
\(174\) | −1.50000 | − | 2.59808i | −0.113715 | − | 0.196960i | ||||
\(175\) | −0.118034 | + | 0.204441i | −0.00892253 | + | 0.0154543i | ||||
\(176\) | 2.11803 | − | 3.66854i | 0.159653 | − | 0.276527i | ||||
\(177\) | 3.11803 | − | 5.40059i | 0.234366 | − | 0.405933i | ||||
\(178\) | 10.9443 | 0.820308 | ||||||||
\(179\) | 3.11803 | + | 5.40059i | 0.233053 | + | 0.403659i | 0.958705 | − | 0.284402i | \(-0.0917952\pi\) |
−0.725652 | + | 0.688062i | \(0.758462\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −2.70820 | + | 4.69075i | −0.201299 | + | 0.348660i | −0.948947 | − | 0.315435i | \(-0.897850\pi\) |
0.747648 | + | 0.664095i | \(0.231183\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.09017 | + | 12.2805i | 0.524120 | + | 0.907803i | ||||
\(184\) | −1.23607 | −0.0911241 | ||||||||
\(185\) | 1.23607 | 0.0908775 | ||||||||
\(186\) | −5.35410 | + | 1.52761i | −0.392582 | + | 0.112010i | ||||
\(187\) | −24.1803 | −1.76824 | ||||||||
\(188\) | 0.763932 | 0.0557155 | ||||||||
\(189\) | −0.118034 | − | 0.204441i | −0.00858571 | − | 0.0148709i | ||||
\(190\) | 3.23607 | 0.234769 | ||||||||
\(191\) | −9.85410 | + | 17.0678i | −0.713018 | + | 1.23498i | 0.250701 | + | 0.968064i | \(0.419339\pi\) |
−0.963719 | + | 0.266919i | \(0.913995\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 7.20820 | + | 12.4850i | 0.518858 | + | 0.898688i | 0.999760 | + | 0.0219138i | \(0.00697595\pi\) |
−0.480902 | + | 0.876774i | \(0.659691\pi\) | |||||||
\(194\) | 1.47214 | 0.105693 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.47214 | − | 6.01392i | 0.248010 | − | 0.429565i | ||||
\(197\) | 9.00000 | − | 15.5885i | 0.641223 | − | 1.11063i | −0.343937 | − | 0.938993i | \(-0.611761\pi\) |
0.985160 | − | 0.171639i | \(-0.0549062\pi\) | |||||||
\(198\) | 2.11803 | + | 3.66854i | 0.150522 | + | 0.260712i | ||||
\(199\) | −13.8262 | + | 23.9477i | −0.980116 | + | 1.69761i | −0.318217 | + | 0.948018i | \(0.603084\pi\) |
−0.661899 | + | 0.749593i | \(0.730249\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 5.23607 | 0.369324 | ||||||||
\(202\) | 1.47214 | 0.103579 | ||||||||
\(203\) | −0.354102 | − | 0.613323i | −0.0248531 | − | 0.0430468i | ||||
\(204\) | −2.85410 | + | 4.94345i | −0.199827 | + | 0.346111i | ||||
\(205\) | 0.618034 | + | 1.07047i | 0.0431654 | + | 0.0747646i | ||||
\(206\) | −9.35410 | + | 16.2018i | −0.651731 | + | 1.12883i | ||||
\(207\) | 0.618034 | − | 1.07047i | 0.0429563 | − | 0.0744025i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.7082 | 0.948216 | ||||||||
\(210\) | 0.118034 | + | 0.204441i | 0.00814512 | + | 0.0141078i | ||||
\(211\) | −8.56231 | − | 14.8303i | −0.589453 | − | 1.02096i | −0.994304 | − | 0.106580i | \(-0.966010\pi\) |
0.404851 | − | 0.914383i | \(-0.367324\pi\) | |||||||
\(212\) | 3.73607 | − | 6.47106i | 0.256594 | − | 0.444434i | ||||
\(213\) | −2.47214 | −0.169388 | ||||||||
\(214\) | 5.35410 | + | 9.27358i | 0.365999 | + | 0.633929i | ||||
\(215\) | −1.52786 | −0.104199 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.26393 | + | 0.360620i | −0.0858013 | + | 0.0244805i | ||||
\(218\) | 3.23607 | 0.219174 | ||||||||
\(219\) | 2.94427 | 0.198955 | ||||||||
\(220\) | −2.11803 | − | 3.66854i | −0.142798 | − | 0.247333i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.618034 | − | 1.07047i | 0.0414797 | − | 0.0718450i | ||||
\(223\) | 8.35410 | + | 14.4697i | 0.559432 | + | 0.968965i | 0.997544 | + | 0.0700443i | \(0.0223141\pi\) |
−0.438112 | + | 0.898920i | \(0.644353\pi\) | |||||||
\(224\) | −0.118034 | − | 0.204441i | −0.00788648 | − | 0.0136598i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.70820 | − | 6.42280i | 0.246666 | − | 0.427238i | ||||
\(227\) | 4.59017 | − | 7.95041i | 0.304660 | − | 0.527687i | −0.672525 | − | 0.740074i | \(-0.734790\pi\) |
0.977186 | + | 0.212387i | \(0.0681237\pi\) | |||||||
\(228\) | 1.61803 | − | 2.80252i | 0.107157 | − | 0.185601i | ||||
\(229\) | −2.14590 | − | 3.71680i | −0.141805 | − | 0.245613i | 0.786371 | − | 0.617754i | \(-0.211957\pi\) |
−0.928176 | + | 0.372141i | \(0.878624\pi\) | |||||||
\(230\) | −0.618034 | + | 1.07047i | −0.0407520 | + | 0.0705845i | ||||
\(231\) | 0.500000 | + | 0.866025i | 0.0328976 | + | 0.0569803i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 1.81966 | 0.119210 | 0.0596049 | − | 0.998222i | \(-0.481016\pi\) | ||||
0.0596049 | + | 0.998222i | \(0.481016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.381966 | − | 0.661585i | 0.0249167 | − | 0.0431570i | ||||
\(236\) | 3.11803 | + | 5.40059i | 0.202967 | + | 0.351549i | ||||
\(237\) | 5.23607 | − | 9.06914i | 0.340119 | − | 0.589104i | ||||
\(238\) | −0.673762 | + | 1.16699i | −0.0436735 | + | 0.0756447i | ||||
\(239\) | 1.70820 | − | 2.95870i | 0.110495 | − | 0.191382i | −0.805475 | − | 0.592629i | \(-0.798090\pi\) |
0.915970 | + | 0.401247i | \(0.131423\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −5.50000 | − | 9.52628i | −0.354286 | − | 0.613642i | 0.632709 | − | 0.774389i | \(-0.281943\pi\) |
−0.986996 | + | 0.160748i | \(0.948609\pi\) | |||||||
\(242\) | −3.47214 | − | 6.01392i | −0.223197 | − | 0.386589i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −14.1803 | −0.907803 | ||||||||
\(245\) | −3.47214 | − | 6.01392i | −0.221827 | − | 0.384215i | ||||
\(246\) | 1.23607 | 0.0788088 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.35410 | − | 5.40059i | 0.0859856 | − | 0.342938i | ||||
\(249\) | 4.70820 | 0.298370 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 3.23607 | + | 5.60503i | 0.204259 | + | 0.353787i | 0.949896 | − | 0.312565i | \(-0.101188\pi\) |
−0.745638 | + | 0.666352i | \(0.767855\pi\) | |||||||
\(252\) | 0.236068 | 0.0148709 | ||||||||
\(253\) | −2.61803 | + | 4.53457i | −0.164594 | + | 0.285086i | ||||
\(254\) | 4.59017 | + | 7.95041i | 0.288013 | + | 0.498853i | ||||
\(255\) | 2.85410 | + | 4.94345i | 0.178731 | + | 0.309571i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.32624 | + | 10.9574i | −0.394620 | + | 0.683502i | −0.993053 | − | 0.117671i | \(-0.962457\pi\) |
0.598433 | + | 0.801173i | \(0.295790\pi\) | |||||||
\(258\) | −0.763932 | + | 1.32317i | −0.0475603 | + | 0.0823769i | ||||
\(259\) | 0.145898 | − | 0.252703i | 0.00906566 | − | 0.0157022i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 6.47214 | + | 11.2101i | 0.399850 | + | 0.692560i | ||||
\(263\) | 4.47214 | 0.275764 | 0.137882 | − | 0.990449i | \(-0.455971\pi\) | ||||
0.137882 | + | 0.990449i | \(0.455971\pi\) | |||||||
\(264\) | −4.23607 | −0.260712 | ||||||||
\(265\) | −3.73607 | − | 6.47106i | −0.229505 | − | 0.397514i | ||||
\(266\) | 0.381966 | − | 0.661585i | 0.0234198 | − | 0.0405644i | ||||
\(267\) | −5.47214 | − | 9.47802i | −0.334889 | − | 0.580045i | ||||
\(268\) | −2.61803 | + | 4.53457i | −0.159922 | + | 0.276993i | ||||
\(269\) | 11.0000 | − | 19.0526i | 0.670682 | − | 1.16166i | −0.307029 | − | 0.951700i | \(-0.599335\pi\) |
0.977711 | − | 0.209955i | \(-0.0673317\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 1.76393 | 0.107151 | 0.0535756 | − | 0.998564i | \(-0.482938\pi\) | ||||
0.0535756 | + | 0.998564i | \(0.482938\pi\) | |||||||
\(272\) | −2.85410 | − | 4.94345i | −0.173055 | − | 0.299741i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.381966 | − | 0.661585i | 0.0230754 | − | 0.0399678i | ||||
\(275\) | −4.23607 | −0.255445 | ||||||||
\(276\) | 0.618034 | + | 1.07047i | 0.0372013 | + | 0.0644345i | ||||
\(277\) | −10.6525 | −0.640045 | −0.320023 | − | 0.947410i | \(-0.603691\pi\) | ||||
−0.320023 | + | 0.947410i | \(0.603691\pi\) | |||||||
\(278\) | 17.1246 | 1.02707 | ||||||||
\(279\) | 4.00000 | + | 3.87298i | 0.239474 | + | 0.231869i | ||||
\(280\) | −0.236068 | −0.0141078 | ||||||||
\(281\) | −0.472136 | −0.0281653 | −0.0140826 | − | 0.999901i | \(-0.504483\pi\) | ||||
−0.0140826 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(282\) | −0.381966 | − | 0.661585i | −0.0227457 | − | 0.0393968i | ||||
\(283\) | 7.41641 | 0.440860 | 0.220430 | − | 0.975403i | \(-0.429254\pi\) | ||||
0.220430 | + | 0.975403i | \(0.429254\pi\) | |||||||
\(284\) | 1.23607 | − | 2.14093i | 0.0733471 | − | 0.127041i | ||||
\(285\) | −1.61803 | − | 2.80252i | −0.0958441 | − | 0.166007i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.291796 | 0.0172242 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −7.79180 | + | 13.4958i | −0.458341 | + | 0.793870i | ||||
\(290\) | 1.50000 | − | 2.59808i | 0.0880830 | − | 0.152564i | ||||
\(291\) | −0.736068 | − | 1.27491i | −0.0431491 | − | 0.0747364i | ||||
\(292\) | −1.47214 | + | 2.54981i | −0.0861502 | + | 0.149217i | ||||
\(293\) | −1.20820 | − | 2.09267i | −0.0705840 | − | 0.122255i | 0.828573 | − | 0.559880i | \(-0.189153\pi\) |
−0.899157 | + | 0.437625i | \(0.855820\pi\) | |||||||
\(294\) | −6.94427 | −0.404998 | ||||||||
\(295\) | 6.23607 | 0.363078 | ||||||||
\(296\) | 0.618034 | + | 1.07047i | 0.0359225 | + | 0.0622196i | ||||
\(297\) | 2.11803 | − | 3.66854i | 0.122901 | − | 0.212870i | ||||
\(298\) | 8.73607 | + | 15.1313i | 0.506067 | + | 0.876533i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.500000 | + | 0.866025i | −0.0288675 | + | 0.0500000i | ||||
\(301\) | −0.180340 | + | 0.312358i | −0.0103946 | + | 0.0180040i | ||||
\(302\) | 9.18034 | 0.528269 | ||||||||
\(303\) | −0.736068 | − | 1.27491i | −0.0422860 | − | 0.0732415i | ||||
\(304\) | 1.61803 | + | 2.80252i | 0.0928006 | + | 0.160735i | ||||
\(305\) | −7.09017 | + | 12.2805i | −0.405982 | + | 0.703181i | ||||
\(306\) | 5.70820 | 0.326316 | ||||||||
\(307\) | −7.61803 | − | 13.1948i | −0.434784 | − | 0.753068i | 0.562494 | − | 0.826801i | \(-0.309842\pi\) |
−0.997278 | + | 0.0737332i | \(0.976509\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 18.7082 | 1.06427 | ||||||||
\(310\) | −4.00000 | − | 3.87298i | −0.227185 | − | 0.219971i | ||||
\(311\) | −0.583592 | −0.0330925 | −0.0165462 | − | 0.999863i | \(-0.505267\pi\) | ||||
−0.0165462 | + | 0.999863i | \(0.505267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.44427 | − | 16.3580i | −0.533822 | − | 0.924606i | −0.999219 | − | 0.0395048i | \(-0.987422\pi\) |
0.465398 | − | 0.885102i | \(-0.345911\pi\) | |||||||
\(314\) | −22.1803 | −1.25171 | ||||||||
\(315\) | 0.118034 | − | 0.204441i | 0.00665046 | − | 0.0115189i | ||||
\(316\) | 5.23607 | + | 9.06914i | 0.294552 | + | 0.510179i | ||||
\(317\) | −10.4443 | − | 18.0900i | −0.586609 | − | 1.01604i | −0.994673 | − | 0.103083i | \(-0.967129\pi\) |
0.408064 | − | 0.912953i | \(-0.366204\pi\) | |||||||
\(318\) | −7.47214 | −0.419017 | ||||||||
\(319\) | 6.35410 | − | 11.0056i | 0.355761 | − | 0.616197i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 5.35410 | − | 9.27358i | 0.298837 | − | 0.517601i | ||||
\(322\) | 0.145898 | + | 0.252703i | 0.00813058 | + | 0.0140826i | ||||
\(323\) | 9.23607 | − | 15.9973i | 0.513909 | − | 0.890116i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.7639 | −1.03924 | ||||||||
\(327\) | −1.61803 | − | 2.80252i | −0.0894775 | − | 0.154980i | ||||
\(328\) | −0.618034 | + | 1.07047i | −0.0341252 | + | 0.0591066i | ||||
\(329\) | −0.0901699 | − | 0.156179i | −0.00497123 | − | 0.00861042i | ||||
\(330\) | −2.11803 | + | 3.66854i | −0.116594 | + | 0.201947i | ||||
\(331\) | 8.61803 | − | 14.9269i | 0.473690 | − | 0.820455i | −0.525856 | − | 0.850573i | \(-0.676255\pi\) |
0.999546 | + | 0.0301183i | \(0.00958839\pi\) | |||||||
\(332\) | −2.35410 | + | 4.07742i | −0.129198 | + | 0.223778i | ||||
\(333\) | −1.23607 | −0.0677361 | ||||||||
\(334\) | −2.14590 | − | 3.71680i | −0.117418 | − | 0.203374i | ||||
\(335\) | 2.61803 | + | 4.53457i | 0.143038 | + | 0.247750i | ||||
\(336\) | −0.118034 | + | 0.204441i | −0.00643928 | + | 0.0111532i | ||||
\(337\) | −26.4164 | −1.43899 | −0.719497 | − | 0.694496i | \(-0.755627\pi\) | ||||
−0.719497 | + | 0.694496i | \(0.755627\pi\) | |||||||
\(338\) | 6.50000 | + | 11.2583i | 0.353553 | + | 0.612372i | ||||
\(339\) | −7.41641 | −0.402804 | ||||||||
\(340\) | −5.70820 | −0.309571 | ||||||||
\(341\) | −16.9443 | − | 16.4062i | −0.917584 | − | 0.888447i | ||||
\(342\) | −3.23607 | −0.174987 | ||||||||
\(343\) | −3.29180 | −0.177740 | ||||||||
\(344\) | −0.763932 | − | 1.32317i | −0.0411885 | − | 0.0713405i | ||||
\(345\) | 1.23607 | 0.0665477 | ||||||||
\(346\) | 3.50000 | − | 6.06218i | 0.188161 | − | 0.325905i | ||||
\(347\) | 7.11803 | + | 12.3288i | 0.382116 | + | 0.661844i | 0.991365 | − | 0.131135i | \(-0.0418621\pi\) |
−0.609248 | + | 0.792979i | \(0.708529\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −27.2361 | −1.45791 | −0.728957 | − | 0.684560i | \(-0.759994\pi\) | ||||
−0.728957 | + | 0.684560i | \(0.759994\pi\) | |||||||
\(350\) | −0.118034 | + | 0.204441i | −0.00630918 | + | 0.0109278i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.11803 | − | 3.66854i | 0.112892 | − | 0.195534i | ||||
\(353\) | −11.1803 | − | 19.3649i | −0.595069 | − | 1.03069i | −0.993537 | − | 0.113508i | \(-0.963791\pi\) |
0.398468 | − | 0.917182i | \(-0.369542\pi\) | |||||||
\(354\) | 3.11803 | − | 5.40059i | 0.165722 | − | 0.287038i | ||||
\(355\) | −1.23607 | − | 2.14093i | −0.0656037 | − | 0.113629i | ||||
\(356\) | 10.9443 | 0.580045 | ||||||||
\(357\) | 1.34752 | 0.0713185 | ||||||||
\(358\) | 3.11803 | + | 5.40059i | 0.164793 | + | 0.285430i | ||||
\(359\) | 3.38197 | − | 5.85774i | 0.178493 | − | 0.309160i | −0.762871 | − | 0.646550i | \(-0.776211\pi\) |
0.941365 | + | 0.337391i | \(0.109544\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 4.26393 | − | 7.38535i | 0.224417 | − | 0.388702i | ||||
\(362\) | −2.70820 | + | 4.69075i | −0.142340 | + | 0.246540i | ||||
\(363\) | −3.47214 | + | 6.01392i | −0.182240 | + | 0.315649i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.47214 | + | 2.54981i | 0.0770551 | + | 0.133463i | ||||
\(366\) | 7.09017 | + | 12.2805i | 0.370609 | + | 0.641914i | ||||
\(367\) | 8.00000 | − | 13.8564i | 0.417597 | − | 0.723299i | −0.578101 | − | 0.815966i | \(-0.696206\pi\) |
0.995697 | + | 0.0926670i | \(0.0295392\pi\) | |||||||
\(368\) | −1.23607 | −0.0644345 | ||||||||
\(369\) | −0.618034 | − | 1.07047i | −0.0321736 | − | 0.0557262i | ||||
\(370\) | 1.23607 | 0.0642601 | ||||||||
\(371\) | −1.76393 | −0.0915788 | ||||||||
\(372\) | −5.35410 | + | 1.52761i | −0.277597 | + | 0.0792029i | ||||
\(373\) | 7.23607 | 0.374669 | 0.187335 | − | 0.982296i | \(-0.440015\pi\) | ||||
0.187335 | + | 0.982296i | \(0.440015\pi\) | |||||||
\(374\) | −24.1803 | −1.25034 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0.763932 | 0.0393968 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.118034 | − | 0.204441i | −0.00607101 | − | 0.0105153i | ||||
\(379\) | 5.00000 | + | 8.66025i | 0.256833 | + | 0.444847i | 0.965392 | − | 0.260804i | \(-0.0839877\pi\) |
−0.708559 | + | 0.705652i | \(0.750654\pi\) | |||||||
\(380\) | 3.23607 | 0.166007 | ||||||||
\(381\) | 4.59017 | − | 7.95041i | 0.235162 | − | 0.407312i | ||||
\(382\) | −9.85410 | + | 17.0678i | −0.504180 | + | 0.873265i | ||||
\(383\) | 6.90983 | − | 11.9682i | 0.353076 | − | 0.611545i | −0.633711 | − | 0.773570i | \(-0.718469\pi\) |
0.986787 | + | 0.162025i | \(0.0518024\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −0.500000 | + | 0.866025i | −0.0254824 | + | 0.0441367i | ||||
\(386\) | 7.20820 | + | 12.4850i | 0.366888 | + | 0.635469i | ||||
\(387\) | 1.52786 | 0.0776657 | ||||||||
\(388\) | 1.47214 | 0.0747364 | ||||||||
\(389\) | 1.76393 | + | 3.05522i | 0.0894349 | + | 0.154906i | 0.907272 | − | 0.420543i | \(-0.138161\pi\) |
−0.817838 | + | 0.575449i | \(0.804827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.52786 | + | 6.11044i | 0.178412 | + | 0.309018i | ||||
\(392\) | 3.47214 | − | 6.01392i | 0.175369 | − | 0.303749i | ||||
\(393\) | 6.47214 | − | 11.2101i | 0.326476 | − | 0.565473i | ||||
\(394\) | 9.00000 | − | 15.5885i | 0.453413 | − | 0.785335i | ||||
\(395\) | 10.4721 | 0.526910 | ||||||||
\(396\) | 2.11803 | + | 3.66854i | 0.106435 | + | 0.184351i | ||||
\(397\) | 7.18034 | + | 12.4367i | 0.360371 | + | 0.624181i | 0.988022 | − | 0.154314i | \(-0.0493168\pi\) |
−0.627651 | + | 0.778495i | \(0.715983\pi\) | |||||||
\(398\) | −13.8262 | + | 23.9477i | −0.693047 | + | 1.20039i | ||||
\(399\) | −0.763932 | −0.0382444 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 29.3050 | 1.46342 | 0.731710 | − | 0.681616i | \(-0.238723\pi\) | ||||
0.731710 | + | 0.681616i | \(0.238723\pi\) | |||||||
\(402\) | 5.23607 | 0.261151 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.47214 | 0.0732415 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −0.354102 | − | 0.613323i | −0.0175738 | − | 0.0304387i | ||||
\(407\) | 5.23607 | 0.259542 | ||||||||
\(408\) | −2.85410 | + | 4.94345i | −0.141299 | + | 0.244737i | ||||
\(409\) | 5.73607 | + | 9.93516i | 0.283630 | + | 0.491262i | 0.972276 | − | 0.233836i | \(-0.0751278\pi\) |
−0.688646 | + | 0.725098i | \(0.741794\pi\) | |||||||
\(410\) | 0.618034 | + | 1.07047i | 0.0305225 | + | 0.0528666i | ||||
\(411\) | −0.763932 | −0.0376820 | ||||||||
\(412\) | −9.35410 | + | 16.2018i | −0.460844 | + | 0.798204i | ||||
\(413\) | 0.736068 | − | 1.27491i | 0.0362195 | − | 0.0627341i | ||||
\(414\) | 0.618034 | − | 1.07047i | 0.0303747 | − | 0.0526105i | ||||
\(415\) | 2.35410 | + | 4.07742i | 0.115558 | + | 0.200153i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.56231 | − | 14.8303i | −0.419298 | − | 0.726245i | ||||
\(418\) | 13.7082 | 0.670490 | ||||||||
\(419\) | 0.708204 | 0.0345980 | 0.0172990 | − | 0.999850i | \(-0.494493\pi\) | ||||
0.0172990 | + | 0.999850i | \(0.494493\pi\) | |||||||
\(420\) | 0.118034 | + | 0.204441i | 0.00575947 | + | 0.00997569i | ||||
\(421\) | 14.6180 | − | 25.3192i | 0.712439 | − | 1.23398i | −0.251499 | − | 0.967857i | \(-0.580924\pi\) |
0.963939 | − | 0.266124i | \(-0.0857430\pi\) | |||||||
\(422\) | −8.56231 | − | 14.8303i | −0.416807 | − | 0.721930i | ||||
\(423\) | −0.381966 | + | 0.661585i | −0.0185718 | + | 0.0321673i | ||||
\(424\) | 3.73607 | − | 6.47106i | 0.181440 | − | 0.314262i | ||||
\(425\) | −2.85410 | + | 4.94345i | −0.138444 | + | 0.239793i | ||||
\(426\) | −2.47214 | −0.119775 | ||||||||
\(427\) | 1.67376 | + | 2.89904i | 0.0809990 | + | 0.140294i | ||||
\(428\) | 5.35410 | + | 9.27358i | 0.258800 | + | 0.448255i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.52786 | −0.0736801 | ||||||||
\(431\) | 10.8541 | + | 18.7999i | 0.522824 | + | 0.905557i | 0.999647 | + | 0.0265582i | \(0.00845473\pi\) |
−0.476824 | + | 0.878999i | \(0.658212\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 6.00000 | 0.288342 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(434\) | −1.26393 | + | 0.360620i | −0.0606707 | + | 0.0173103i | ||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | 3.23607 | 0.154980 | ||||||||
\(437\) | −2.00000 | − | 3.46410i | −0.0956730 | − | 0.165710i | ||||
\(438\) | 2.94427 | 0.140683 | ||||||||
\(439\) | −10.5902 | + | 18.3427i | −0.505441 | + | 0.875450i | 0.494539 | + | 0.869155i | \(0.335337\pi\) |
−0.999980 | + | 0.00629443i | \(0.997996\pi\) | |||||||
\(440\) | −2.11803 | − | 3.66854i | −0.100973 | − | 0.174891i | ||||
\(441\) | 3.47214 | + | 6.01392i | 0.165340 | + | 0.286377i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0000 | − | 27.7128i | 0.760183 | − | 1.31668i | −0.182573 | − | 0.983192i | \(-0.558443\pi\) |
0.942756 | − | 0.333483i | \(-0.108224\pi\) | |||||||
\(444\) | 0.618034 | − | 1.07047i | 0.0293306 | − | 0.0508021i | ||||
\(445\) | 5.47214 | − | 9.47802i | 0.259404 | − | 0.449301i | ||||
\(446\) | 8.35410 | + | 14.4697i | 0.395578 | + | 0.685162i | ||||
\(447\) | 8.73607 | − | 15.1313i | 0.413202 | − | 0.715687i | ||||
\(448\) | −0.118034 | − | 0.204441i | −0.00557658 | − | 0.00965892i | ||||
\(449\) | 0.111456 | 0.00525994 | 0.00262997 | − | 0.999997i | \(-0.499163\pi\) | ||||
0.00262997 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 2.61803 | + | 4.53457i | 0.123278 | + | 0.213524i | ||||
\(452\) | 3.70820 | − | 6.42280i | 0.174419 | − | 0.302103i | ||||
\(453\) | −4.59017 | − | 7.95041i | −0.215665 | − | 0.373543i | ||||
\(454\) | 4.59017 | − | 7.95041i | 0.215427 | − | 0.373131i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.61803 | − | 2.80252i | 0.0757714 | − | 0.131240i | ||||
\(457\) | 19.8885 | 0.930347 | 0.465173 | − | 0.885220i | \(-0.345992\pi\) | ||||
0.465173 | + | 0.885220i | \(0.345992\pi\) | |||||||
\(458\) | −2.14590 | − | 3.71680i | −0.100271 | − | 0.173675i | ||||
\(459\) | −2.85410 | − | 4.94345i | −0.133218 | − | 0.230740i | ||||
\(460\) | −0.618034 | + | 1.07047i | −0.0288160 | + | 0.0499107i | ||||
\(461\) | −27.0000 | −1.25752 | −0.628758 | − | 0.777601i | \(-0.716436\pi\) | ||||
−0.628758 | + | 0.777601i | \(0.716436\pi\) | |||||||
\(462\) | 0.500000 | + | 0.866025i | 0.0232621 | + | 0.0402911i | ||||
\(463\) | −14.7082 | −0.683548 | −0.341774 | − | 0.939782i | \(-0.611028\pi\) | ||||
−0.341774 | + | 0.939782i | \(0.611028\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | −1.35410 | + | 5.40059i | −0.0627950 | + | 0.250447i | ||||
\(466\) | 1.81966 | 0.0842941 | ||||||||
\(467\) | −36.5967 | −1.69350 | −0.846748 | − | 0.531995i | \(-0.821443\pi\) | ||||
−0.846748 | + | 0.531995i | \(0.821443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23607 | 0.0570763 | ||||||||
\(470\) | 0.381966 | − | 0.661585i | 0.0176188 | − | 0.0305166i | ||||
\(471\) | 11.0902 | + | 19.2087i | 0.511008 | + | 0.885092i | ||||
\(472\) | 3.11803 | + | 5.40059i | 0.143519 | + | 0.248582i | ||||
\(473\) | −6.47214 | −0.297589 | ||||||||
\(474\) | 5.23607 | − | 9.06914i | 0.240501 | − | 0.416559i | ||||
\(475\) | 1.61803 | − | 2.80252i | 0.0742405 | − | 0.128588i | ||||
\(476\) | −0.673762 | + | 1.16699i | −0.0308818 | + | 0.0534889i | ||||
\(477\) | 3.73607 | + | 6.47106i | 0.171063 | + | 0.296289i | ||||
\(478\) | 1.70820 | − | 2.95870i | 0.0781314 | − | 0.135328i | ||||
\(479\) | 5.32624 | + | 9.22531i | 0.243362 | + | 0.421515i | 0.961670 | − | 0.274210i | \(-0.0884164\pi\) |
−0.718308 | + | 0.695725i | \(0.755083\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.50000 | − | 9.52628i | −0.250518 | − | 0.433910i | ||||
\(483\) | 0.145898 | − | 0.252703i | 0.00663859 | − | 0.0114984i | ||||
\(484\) | −3.47214 | − | 6.01392i | −0.157824 | − | 0.273360i | ||||
\(485\) | 0.736068 | − | 1.27491i | 0.0334231 | − | 0.0578906i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −0.409830 | + | 0.709846i | −0.0185712 | + | 0.0321662i | −0.875162 | − | 0.483831i | \(-0.839245\pi\) |
0.856590 | + | 0.515997i | \(0.172578\pi\) | |||||||
\(488\) | −14.1803 | −0.641914 | ||||||||
\(489\) | 9.38197 | + | 16.2500i | 0.424267 | + | 0.734852i | ||||
\(490\) | −3.47214 | − | 6.01392i | −0.156855 | − | 0.271681i | ||||
\(491\) | −14.6459 | + | 25.3674i | −0.660960 | + | 1.14482i | 0.319404 | + | 0.947619i | \(0.396517\pi\) |
−0.980364 | + | 0.197198i | \(0.936816\pi\) | |||||||
\(492\) | 1.23607 | 0.0557262 | ||||||||
\(493\) | −8.56231 | − | 14.8303i | −0.385627 | − | 0.667925i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.23607 | 0.190397 | ||||||||
\(496\) | 1.35410 | − | 5.40059i | 0.0608010 | − | 0.242494i | ||||
\(497\) | −0.583592 | −0.0261777 | ||||||||
\(498\) | 4.70820 | 0.210980 | ||||||||
\(499\) | 4.32624 | + | 7.49326i | 0.193669 | + | 0.335445i | 0.946463 | − | 0.322811i | \(-0.104628\pi\) |
−0.752794 | + | 0.658256i | \(0.771295\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −2.14590 | + | 3.71680i | −0.0958717 | + | 0.166055i | ||||
\(502\) | 3.23607 | + | 5.60503i | 0.144433 | + | 0.250165i | ||||
\(503\) | −3.85410 | − | 6.67550i | −0.171846 | − | 0.297646i | 0.767219 | − | 0.641385i | \(-0.221640\pi\) |
−0.939065 | + | 0.343739i | \(0.888306\pi\) | |||||||
\(504\) | 0.236068 | 0.0105153 | ||||||||
\(505\) | 0.736068 | − | 1.27491i | 0.0327546 | − | 0.0567326i | ||||
\(506\) | −2.61803 | + | 4.53457i | −0.116386 | + | 0.201586i | ||||
\(507\) | 6.50000 | − | 11.2583i | 0.288675 | − | 0.500000i | ||||
\(508\) | 4.59017 | + | 7.95041i | 0.203656 | + | 0.352742i | ||||
\(509\) | 10.6803 | − | 18.4989i | 0.473398 | − | 0.819949i | −0.526139 | − | 0.850399i | \(-0.676361\pi\) |
0.999536 | + | 0.0304499i | \(0.00969401\pi\) | |||||||
\(510\) | 2.85410 | + | 4.94345i | 0.126382 | + | 0.218900i | ||||
\(511\) | 0.695048 | 0.0307471 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.61803 | + | 2.80252i | 0.0714379 | + | 0.123734i | ||||
\(514\) | −6.32624 | + | 10.9574i | −0.279038 | + | 0.483309i | ||||
\(515\) | 9.35410 | + | 16.2018i | 0.412191 | + | 0.713936i | ||||
\(516\) | −0.763932 | + | 1.32317i | −0.0336302 | + | 0.0582493i | ||||
\(517\) | 1.61803 | − | 2.80252i | 0.0711611 | − | 0.123255i | ||||
\(518\) | 0.145898 | − | 0.252703i | 0.00641039 | − | 0.0111031i | ||||
\(519\) | −7.00000 | −0.307266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.47214 | − | 11.2101i | −0.283549 | − | 0.491122i | 0.688707 | − | 0.725040i | \(-0.258179\pi\) |
−0.972256 | + | 0.233918i | \(0.924845\pi\) | |||||||
\(522\) | −1.50000 | + | 2.59808i | −0.0656532 | + | 0.113715i | ||||
\(523\) | −23.4164 | −1.02393 | −0.511964 | − | 0.859007i | \(-0.671082\pi\) | ||||
−0.511964 | + | 0.859007i | \(0.671082\pi\) | |||||||
\(524\) | 6.47214 | + | 11.2101i | 0.282737 | + | 0.489714i | ||||
\(525\) | 0.236068 | 0.0103029 | ||||||||
\(526\) | 4.47214 | 0.194994 | ||||||||
\(527\) | −30.5623 | + | 8.71991i | −1.33131 | + | 0.379845i | ||||
\(528\) | −4.23607 | −0.184351 | ||||||||
\(529\) | −21.4721 | −0.933571 | ||||||||
\(530\) | −3.73607 | − | 6.47106i | −0.162284 | − | 0.281085i | ||||
\(531\) | −6.23607 | −0.270622 | ||||||||
\(532\) | 0.381966 | − | 0.661585i | 0.0165603 | − | 0.0286833i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.47214 | − | 9.47802i | −0.236802 | − | 0.410154i | ||||
\(535\) | 10.7082 | 0.462956 | ||||||||
\(536\) | −2.61803 | + | 4.53457i | −0.113082 | + | 0.195864i | ||||
\(537\) | 3.11803 | − | 5.40059i | 0.134553 | − | 0.233053i | ||||
\(538\) | 11.0000 | − | 19.0526i | 0.474244 | − | 0.821414i | ||||
\(539\) | −14.7082 | − | 25.4754i | −0.633527 | − | 1.09730i | ||||
\(540\) | 0.500000 | − | 0.866025i | 0.0215166 | − | 0.0372678i | ||||
\(541\) | −0.326238 | − | 0.565061i | −0.0140261 | − | 0.0242939i | 0.858927 | − | 0.512098i | \(-0.171131\pi\) |
−0.872953 | + | 0.487804i | \(0.837798\pi\) | |||||||
\(542\) | 1.76393 | 0.0757674 | ||||||||
\(543\) | 5.41641 | 0.232440 | ||||||||
\(544\) | −2.85410 | − | 4.94345i | −0.122369 | − | 0.211949i | ||||
\(545\) | 1.61803 | − | 2.80252i | 0.0693090 | − | 0.120047i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.70820 | − | 15.0831i | 0.372336 | − | 0.644905i | −0.617589 | − | 0.786501i | \(-0.711890\pi\) |
0.989924 | + | 0.141597i | \(0.0452236\pi\) | |||||||
\(548\) | 0.381966 | − | 0.661585i | 0.0163168 | − | 0.0282615i | ||||
\(549\) | 7.09017 | − | 12.2805i | 0.302601 | − | 0.524120i | ||||
\(550\) | −4.23607 | −0.180627 | ||||||||
\(551\) | 4.85410 | + | 8.40755i | 0.206792 | + | 0.358174i | ||||
\(552\) | 0.618034 | + | 1.07047i | 0.0263053 | + | 0.0455621i | ||||
\(553\) | 1.23607 | − | 2.14093i | 0.0525630 | − | 0.0910417i | ||||
\(554\) | −10.6525 | −0.452580 | ||||||||
\(555\) | −0.618034 | − | 1.07047i | −0.0262341 | − | 0.0454388i | ||||
\(556\) | 17.1246 | 0.726245 | ||||||||
\(557\) | 24.4164 | 1.03456 | 0.517278 | − | 0.855817i | \(-0.326945\pi\) | ||||
0.517278 | + | 0.855817i | \(0.326945\pi\) | |||||||
\(558\) | 4.00000 | + | 3.87298i | 0.169334 | + | 0.163956i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.236068 | −0.00997569 | ||||||||
\(561\) | 12.0902 | + | 20.9408i | 0.510447 | + | 0.884121i | ||||
\(562\) | −0.472136 | −0.0199159 | ||||||||
\(563\) | 0.937694 | − | 1.62413i | 0.0395191 | − | 0.0684491i | −0.845589 | − | 0.533834i | \(-0.820751\pi\) |
0.885108 | + | 0.465385i | \(0.154084\pi\) | |||||||
\(564\) | −0.381966 | − | 0.661585i | −0.0160837 | − | 0.0278577i | ||||
\(565\) | −3.70820 | − | 6.42280i | −0.156005 | − | 0.270209i | ||||
\(566\) | 7.41641 | 0.311735 | ||||||||
\(567\) | −0.118034 | + | 0.204441i | −0.00495696 | + | 0.00858571i | ||||
\(568\) | 1.23607 | − | 2.14093i | 0.0518643 | − | 0.0898315i | ||||
\(569\) | −4.47214 | + | 7.74597i | −0.187482 | + | 0.324728i | −0.944410 | − | 0.328770i | \(-0.893366\pi\) |
0.756928 | + | 0.653498i | \(0.226699\pi\) | |||||||
\(570\) | −1.61803 | − | 2.80252i | −0.0677720 | − | 0.117385i | ||||
\(571\) | 19.1803 | − | 33.2213i | 0.802672 | − | 1.39027i | −0.115179 | − | 0.993345i | \(-0.536744\pi\) |
0.917851 | − | 0.396924i | \(-0.129922\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.7082 | 0.823322 | ||||||||
\(574\) | 0.291796 | 0.0121793 | ||||||||
\(575\) | 0.618034 | + | 1.07047i | 0.0257738 | + | 0.0446415i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 14.4164 | + | 24.9700i | 0.600163 | + | 1.03951i | 0.992796 | + | 0.119817i | \(0.0382309\pi\) |
−0.392633 | + | 0.919695i | \(0.628436\pi\) | |||||||
\(578\) | −7.79180 | + | 13.4958i | −0.324096 | + | 0.561351i | ||||
\(579\) | 7.20820 | − | 12.4850i | 0.299563 | − | 0.518858i | ||||
\(580\) | 1.50000 | − | 2.59808i | 0.0622841 | − | 0.107879i | ||||
\(581\) | 1.11146 | 0.0461110 | ||||||||
\(582\) | −0.736068 | − | 1.27491i | −0.0305110 | − | 0.0528466i | ||||
\(583\) | −15.8262 | − | 27.4118i | −0.655456 | − | 1.13528i | ||||
\(584\) | −1.47214 | + | 2.54981i | −0.0609174 | + | 0.105512i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.20820 | − | 2.09267i | −0.0499104 | − | 0.0864474i | ||||
\(587\) | −9.65248 | −0.398400 | −0.199200 | − | 0.979959i | \(-0.563834\pi\) | ||||
−0.199200 | + | 0.979959i | \(0.563834\pi\) | |||||||
\(588\) | −6.94427 | −0.286377 | ||||||||
\(589\) | 17.3262 | − | 4.94345i | 0.713915 | − | 0.203691i | ||||
\(590\) | 6.23607 | 0.256735 | ||||||||
\(591\) | −18.0000 | −0.740421 | ||||||||
\(592\) | 0.618034 | + | 1.07047i | 0.0254010 | + | 0.0439959i | ||||
\(593\) | −20.5410 | −0.843519 | −0.421759 | − | 0.906708i | \(-0.638587\pi\) | ||||
−0.421759 | + | 0.906708i | \(0.638587\pi\) | |||||||
\(594\) | 2.11803 | − | 3.66854i | 0.0869040 | − | 0.150522i | ||||
\(595\) | 0.673762 | + | 1.16699i | 0.0276216 | + | 0.0478419i | ||||
\(596\) | 8.73607 | + | 15.1313i | 0.357843 | + | 0.619803i | ||||
\(597\) | 27.6525 | 1.13174 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4164 | + | 23.2379i | −0.548180 | + | 0.949475i | 0.450220 | + | 0.892918i | \(0.351346\pi\) |
−0.998399 | + | 0.0565571i | \(0.981988\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −20.1246 | − | 34.8569i | −0.820900 | − | 1.42184i | −0.905013 | − | 0.425384i | \(-0.860139\pi\) |
0.0841128 | − | 0.996456i | \(-0.473194\pi\) | |||||||
\(602\) | −0.180340 | + | 0.312358i | −0.00735011 | + | 0.0127308i | ||||
\(603\) | −2.61803 | − | 4.53457i | −0.106615 | − | 0.184662i | ||||
\(604\) | 9.18034 | 0.373543 | ||||||||
\(605\) | −6.94427 | −0.282325 | ||||||||
\(606\) | −0.736068 | − | 1.27491i | −0.0299007 | − | 0.0517896i | ||||
\(607\) | 20.0000 | − | 34.6410i | 0.811775 | − | 1.40604i | −0.0998457 | − | 0.995003i | \(-0.531835\pi\) |
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(608\) | 1.61803 | + | 2.80252i | 0.0656199 | + | 0.113657i | ||||
\(609\) | −0.354102 | + | 0.613323i | −0.0143489 | + | 0.0248531i | ||||
\(610\) | −7.09017 | + | 12.2805i | −0.287073 | + | 0.497224i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 5.70820 | 0.230740 | ||||||||
\(613\) | 3.70820 | + | 6.42280i | 0.149773 | + | 0.259414i | 0.931143 | − | 0.364653i | \(-0.118812\pi\) |
−0.781371 | + | 0.624067i | \(0.785479\pi\) | |||||||
\(614\) | −7.61803 | − | 13.1948i | −0.307439 | − | 0.532500i | ||||
\(615\) | 0.618034 | − | 1.07047i | 0.0249215 | − | 0.0431654i | ||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | −0.145898 | − | 0.252703i | −0.00587363 | − | 0.0101734i | 0.863074 | − | 0.505078i | \(-0.168536\pi\) |
−0.868947 | + | 0.494905i | \(0.835203\pi\) | |||||||
\(618\) | 18.7082 | 0.752554 | ||||||||
\(619\) | 26.0000 | 1.04503 | 0.522514 | − | 0.852631i | \(-0.324994\pi\) | ||||
0.522514 | + | 0.852631i | \(0.324994\pi\) | |||||||
\(620\) | −4.00000 | − | 3.87298i | −0.160644 | − | 0.155543i | ||||
\(621\) | −1.23607 | −0.0496017 | ||||||||
\(622\) | −0.583592 | −0.0233999 | ||||||||
\(623\) | −1.29180 | − | 2.23746i | −0.0517547 | − | 0.0896418i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −9.44427 | − | 16.3580i | −0.377469 | − | 0.653796i | ||||
\(627\) | −6.85410 | − | 11.8717i | −0.273726 | − | 0.474108i | ||||
\(628\) | −22.1803 | −0.885092 | ||||||||
\(629\) | 3.52786 | − | 6.11044i | 0.140665 | − | 0.243639i | ||||
\(630\) | 0.118034 | − | 0.204441i | 0.00470259 | − | 0.00814512i | ||||
\(631\) | 3.29837 | − | 5.71295i | 0.131306 | − | 0.227429i | −0.792874 | − | 0.609385i | \(-0.791416\pi\) |
0.924180 | + | 0.381956i | \(0.124750\pi\) | |||||||
\(632\) | 5.23607 | + | 9.06914i | 0.208280 | + | 0.360751i | ||||
\(633\) | −8.56231 | + | 14.8303i | −0.340321 | + | 0.589453i | ||||
\(634\) | −10.4443 | − | 18.0900i | −0.414795 | − | 0.718446i | ||||
\(635\) | 9.18034 | 0.364311 | ||||||||
\(636\) | −7.47214 | −0.296289 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.35410 | − | 11.0056i | 0.251561 | − | 0.435717i | ||||
\(639\) | 1.23607 | + | 2.14093i | 0.0488981 | + | 0.0846940i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 12.1459 | − | 21.0373i | 0.479734 | − | 0.830924i | −0.519996 | − | 0.854169i | \(-0.674066\pi\) |
0.999730 | + | 0.0232450i | \(0.00739978\pi\) | |||||||
\(642\) | 5.35410 | − | 9.27358i | 0.211310 | − | 0.365999i | ||||
\(643\) | 16.2918 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(644\) | 0.145898 | + | 0.252703i | 0.00574919 | + | 0.00995789i | ||||
\(645\) | 0.763932 | + | 1.32317i | 0.0300798 | + | 0.0520997i | ||||
\(646\) | 9.23607 | − | 15.9973i | 0.363388 | − | 0.629407i | ||||
\(647\) | −36.1803 | −1.42240 | −0.711198 | − | 0.702992i | \(-0.751847\pi\) | ||||
−0.711198 | + | 0.702992i | \(0.751847\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 26.4164 | 1.03693 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.944272 | + | 0.914287i | 0.0370089 | + | 0.0358337i | ||||
\(652\) | −18.7639 | −0.734852 | ||||||||
\(653\) | 13.3607 | 0.522844 | 0.261422 | − | 0.965225i | \(-0.415809\pi\) | ||||
0.261422 | + | 0.965225i | \(0.415809\pi\) | |||||||
\(654\) | −1.61803 | − | 2.80252i | −0.0632701 | − | 0.109587i | ||||
\(655\) | 12.9443 | 0.505775 | ||||||||
\(656\) | −0.618034 | + | 1.07047i | −0.0241302 | + | 0.0417947i | ||||
\(657\) | −1.47214 | − | 2.54981i | −0.0574335 | − | 0.0994777i | ||||
\(658\) | −0.0901699 | − | 0.156179i | −0.00351519 | − | 0.00608849i | ||||
\(659\) | −16.1246 | −0.628126 | −0.314063 | − | 0.949402i | \(-0.601690\pi\) | ||||
−0.314063 | + | 0.949402i | \(0.601690\pi\) | |||||||
\(660\) | −2.11803 | + | 3.66854i | −0.0824444 | + | 0.142798i | ||||
\(661\) | 0.145898 | − | 0.252703i | 0.00567478 | − | 0.00982900i | −0.863174 | − | 0.504906i | \(-0.831527\pi\) |
0.868849 | + | 0.495077i | \(0.164860\pi\) | |||||||
\(662\) | 8.61803 | − | 14.9269i | 0.334949 | − | 0.580149i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.35410 | + | 4.07742i | −0.0913569 | + | 0.158235i | ||||
\(665\) | −0.381966 | − | 0.661585i | −0.0148120 | − | 0.0256551i | ||||
\(666\) | −1.23607 | −0.0478967 | ||||||||
\(667\) | −3.70820 | −0.143582 | ||||||||
\(668\) | −2.14590 | − | 3.71680i | −0.0830273 | − | 0.143807i | ||||
\(669\) | 8.35410 | − | 14.4697i | 0.322988 | − | 0.559432i | ||||
\(670\) | 2.61803 | + | 4.53457i | 0.101143 | + | 0.175186i | ||||
\(671\) | −30.0344 | + | 52.0212i | −1.15947 | + | 2.00826i | ||||
\(672\) | −0.118034 | + | 0.204441i | −0.00455326 | + | 0.00788648i | ||||
\(673\) | 17.6803 | − | 30.6232i | 0.681527 | − | 1.18044i | −0.292988 | − | 0.956116i | \(-0.594650\pi\) |
0.974515 | − | 0.224323i | \(-0.0720171\pi\) | |||||||
\(674\) | −26.4164 | −1.01752 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | −4.79180 | + | 8.29963i | −0.184164 | + | 0.318981i | −0.943294 | − | 0.331957i | \(-0.892291\pi\) |
0.759131 | + | 0.650938i | \(0.225624\pi\) | |||||||
\(678\) | −7.41641 | −0.284825 | ||||||||
\(679\) | −0.173762 | − | 0.300965i | −0.00666838 | − | 0.0115500i | ||||
\(680\) | −5.70820 | −0.218900 | ||||||||
\(681\) | −9.18034 | −0.351791 | ||||||||
\(682\) | −16.9443 | − | 16.4062i | −0.648830 | − | 0.628227i | ||||
\(683\) | −38.5967 | −1.47686 | −0.738432 | − | 0.674328i | \(-0.764433\pi\) | ||||
−0.738432 | + | 0.674328i | \(0.764433\pi\) | |||||||
\(684\) | −3.23607 | −0.123734 | ||||||||
\(685\) | −0.381966 | − | 0.661585i | −0.0145942 | − | 0.0252778i | ||||
\(686\) | −3.29180 | −0.125681 | ||||||||
\(687\) | −2.14590 | + | 3.71680i | −0.0818711 | + | 0.141805i | ||||
\(688\) | −0.763932 | − | 1.32317i | −0.0291246 | − | 0.0504453i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.23607 | 0.0470563 | ||||||||
\(691\) | 9.61803 | − | 16.6589i | 0.365887 | − | 0.633735i | −0.623031 | − | 0.782197i | \(-0.714099\pi\) |
0.988918 | + | 0.148462i | \(0.0474322\pi\) | |||||||
\(692\) | 3.50000 | − | 6.06218i | 0.133050 | − | 0.230449i | ||||
\(693\) | 0.500000 | − | 0.866025i | 0.0189934 | − | 0.0328976i | ||||
\(694\) | 7.11803 | + | 12.3288i | 0.270197 | + | 0.467995i | ||||
\(695\) | 8.56231 | − | 14.8303i | 0.324787 | − | 0.562547i | ||||
\(696\) | −1.50000 | − | 2.59808i | −0.0568574 | − | 0.0984798i | ||||
\(697\) | 7.05573 | 0.267255 | ||||||||
\(698\) | −27.2361 | −1.03090 | ||||||||
\(699\) | −0.909830 | − | 1.57587i | −0.0344129 | − | 0.0596049i | ||||
\(700\) | −0.118034 | + | 0.204441i | −0.00446127 | + | 0.00772714i | ||||
\(701\) | 14.6803 | + | 25.4271i | 0.554469 | + | 0.960368i | 0.997945 | + | 0.0640818i | \(0.0204119\pi\) |
−0.443476 | + | 0.896286i | \(0.646255\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | + | 3.46410i | −0.0754314 | + | 0.130651i | ||||
\(704\) | 2.11803 | − | 3.66854i | 0.0798264 | − | 0.138263i | ||||
\(705\) | −0.763932 | −0.0287713 | ||||||||
\(706\) | −11.1803 | − | 19.3649i | −0.420778 | − | 0.728808i | ||||
\(707\) | −0.173762 | − | 0.300965i | −0.00653500 | − | 0.0113189i | ||||
\(708\) | 3.11803 | − | 5.40059i | 0.117183 | − | 0.202967i | ||||
\(709\) | 11.1246 | 0.417794 | 0.208897 | − | 0.977938i | \(-0.433013\pi\) | ||||
0.208897 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(710\) | −1.23607 | − | 2.14093i | −0.0463888 | − | 0.0803478i | ||||
\(711\) | −10.4721 | −0.392736 | ||||||||
\(712\) | 10.9443 | 0.410154 | ||||||||
\(713\) | −1.67376 | + | 6.67550i | −0.0626829 | + | 0.249999i | ||||
\(714\) | 1.34752 | 0.0504298 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.11803 | + | 5.40059i | 0.116526 | + | 0.201830i | ||||
\(717\) | −3.41641 | −0.127588 | ||||||||
\(718\) | 3.38197 | − | 5.85774i | 0.126214 | − | 0.218609i | ||||
\(719\) | −20.5623 | − | 35.6150i | −0.766845 | − | 1.32821i | −0.939266 | − | 0.343191i | \(-0.888492\pi\) |
0.172421 | − | 0.985023i | \(-0.444841\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | 4.41641 | 0.164476 | ||||||||
\(722\) | 4.26393 | − | 7.38535i | 0.158687 | − | 0.274854i | ||||
\(723\) | −5.50000 | + | 9.52628i | −0.204547 | + | 0.354286i | ||||
\(724\) | −2.70820 | + | 4.69075i | −0.100650 | + | 0.174330i | ||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | −3.47214 | + | 6.01392i | −0.128863 | + | 0.223197i | ||||
\(727\) | 20.8820 | + | 36.1686i | 0.774469 | + | 1.34142i | 0.935092 | + | 0.354404i | \(0.115316\pi\) |
−0.160623 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.47214 | + | 2.54981i | 0.0544862 | + | 0.0943729i | ||||
\(731\) | −4.36068 | + | 7.55292i | −0.161286 | + | 0.279355i | ||||
\(732\) | 7.09017 | + | 12.2805i | 0.262060 | + | 0.453902i | ||||
\(733\) | −14.8885 | + | 25.7877i | −0.549921 | + | 0.952491i | 0.448358 | + | 0.893854i | \(0.352009\pi\) |
−0.998279 | + | 0.0586371i | \(0.981325\pi\) | |||||||
\(734\) | 8.00000 | − | 13.8564i | 0.295285 | − | 0.511449i | ||||
\(735\) | −3.47214 | + | 6.01392i | −0.128072 | + | 0.221827i | ||||
\(736\) | −1.23607 | −0.0455621 | ||||||||
\(737\) | 11.0902 | + | 19.2087i | 0.408512 | + | 0.707563i | ||||
\(738\) | −0.618034 | − | 1.07047i | −0.0227501 | − | 0.0394044i | ||||
\(739\) | −13.1459 | + | 22.7694i | −0.483580 | + | 0.837585i | −0.999822 | − | 0.0188579i | \(-0.993997\pi\) |
0.516242 | + | 0.856442i | \(0.327330\pi\) | |||||||
\(740\) | 1.23607 | 0.0454388 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.76393 | −0.0647560 | ||||||||
\(743\) | −38.3607 | −1.40732 | −0.703658 | − | 0.710538i | \(-0.748451\pi\) | ||||
−0.703658 | + | 0.710538i | \(0.748451\pi\) | |||||||
\(744\) | −5.35410 | + | 1.52761i | −0.196291 | + | 0.0560049i | ||||
\(745\) | 17.4721 | 0.640130 | ||||||||
\(746\) | 7.23607 | 0.264931 | ||||||||
\(747\) | −2.35410 | − | 4.07742i | −0.0861321 | − | 0.149185i | ||||
\(748\) | −24.1803 | −0.884121 | ||||||||
\(749\) | 1.26393 | − | 2.18919i | 0.0461831 | − | 0.0799914i | ||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | 22.8262 | + | 39.5362i | 0.832941 | + | 1.44270i | 0.895696 | + | 0.444668i | \(0.146678\pi\) |
−0.0627544 | + | 0.998029i | \(0.519988\pi\) | |||||||
\(752\) | 0.763932 | 0.0278577 | ||||||||
\(753\) | 3.23607 | − | 5.60503i | 0.117929 | − | 0.204259i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.59017 | − | 7.95041i | 0.167053 | − | 0.289345i | ||||
\(756\) | −0.118034 | − | 0.204441i | −0.00429285 | − | 0.00743544i | ||||
\(757\) | −6.29180 | + | 10.8977i | −0.228679 | + | 0.396084i | −0.957417 | − | 0.288709i | \(-0.906774\pi\) |
0.728738 | + | 0.684793i | \(0.240107\pi\) | |||||||
\(758\) | 5.00000 | + | 8.66025i | 0.181608 | + | 0.314555i | ||||
\(759\) | 5.23607 | 0.190057 | ||||||||
\(760\) | 3.23607 | 0.117385 | ||||||||
\(761\) | −18.8541 | − | 32.6563i | −0.683461 | − | 1.18379i | −0.973918 | − | 0.226901i | \(-0.927141\pi\) |
0.290457 | − | 0.956888i | \(-0.406193\pi\) | |||||||
\(762\) | 4.59017 | − | 7.95041i | 0.166284 | − | 0.288013i | ||||
\(763\) | −0.381966 | − | 0.661585i | −0.0138281 | − | 0.0239510i | ||||
\(764\) | −9.85410 | + | 17.0678i | −0.356509 | + | 0.617492i | ||||
\(765\) | 2.85410 | − | 4.94345i | 0.103190 | − | 0.178731i | ||||
\(766\) | 6.90983 | − | 11.9682i | 0.249662 | − | 0.432428i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 17.2082 | + | 29.8055i | 0.620544 | + | 1.07481i | 0.989385 | + | 0.145321i | \(0.0464214\pi\) |
−0.368841 | + | 0.929493i | \(0.620245\pi\) | |||||||
\(770\) | −0.500000 | + | 0.866025i | −0.0180187 | + | 0.0312094i | ||||
\(771\) | 12.6525 | 0.455668 | ||||||||
\(772\) | 7.20820 | + | 12.4850i | 0.259429 | + | 0.449344i | ||||
\(773\) | −6.94427 | −0.249768 | −0.124884 | − | 0.992171i | \(-0.539856\pi\) | ||||
−0.124884 | + | 0.992171i | \(0.539856\pi\) | |||||||
\(774\) | 1.52786 | 0.0549179 | ||||||||
\(775\) | −5.35410 | + | 1.52761i | −0.192325 | + | 0.0548734i | ||||
\(776\) | 1.47214 | 0.0528466 | ||||||||
\(777\) | −0.291796 | −0.0104681 | ||||||||
\(778\) | 1.76393 | + | 3.05522i | 0.0632400 | + | 0.109535i | ||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.23607 | − | 9.06914i | −0.187361 | − | 0.324519i | ||||
\(782\) | 3.52786 | + | 6.11044i | 0.126156 | + | 0.218509i | ||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 3.47214 | − | 6.01392i | 0.124005 | − | 0.214783i | ||||
\(785\) | −11.0902 | + | 19.2087i | −0.395825 | + | 0.685589i | ||||
\(786\) | 6.47214 | − | 11.2101i | 0.230853 | − | 0.399850i | ||||
\(787\) | 10.5066 | + | 18.1979i | 0.374519 | + | 0.648686i | 0.990255 | − | 0.139267i | \(-0.0444745\pi\) |
−0.615736 | + | 0.787953i | \(0.711141\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | −2.23607 | − | 3.87298i | −0.0796061 | − | 0.137882i | ||||
\(790\) | 10.4721 | 0.372582 | ||||||||
\(791\) | −1.75078 | −0.0622504 | ||||||||
\(792\) | 2.11803 | + | 3.66854i | 0.0752611 | + | 0.130356i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.18034 | + | 12.4367i | 0.254821 | + | 0.441362i | ||||
\(795\) | −3.73607 | + | 6.47106i | −0.132505 | + | 0.229505i | ||||
\(796\) | −13.8262 | + | 23.9477i | −0.490058 | + | 0.848805i | ||||
\(797\) | −16.0279 | + | 27.7611i | −0.567736 | + | 0.983348i | 0.429053 | + | 0.903279i | \(0.358847\pi\) |
−0.996789 | + | 0.0800685i | \(0.974486\pi\) | |||||||
\(798\) | −0.763932 | −0.0270429 | ||||||||
\(799\) | −2.18034 | − | 3.77646i | −0.0771349 | − | 0.133602i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −5.47214 | + | 9.47802i | −0.193348 | + | 0.334889i | ||||
\(802\) | 29.3050 | 1.03479 | ||||||||
\(803\) | 6.23607 | + | 10.8012i | 0.220066 | + | 0.381166i | ||||
\(804\) | 5.23607 | 0.184662 | ||||||||
\(805\) | 0.291796 | 0.0102845 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0000 | −0.774437 | ||||||||
\(808\) | 1.47214 | 0.0517896 | ||||||||
\(809\) | −22.2705 | − | 38.5737i | −0.782989 | − | 1.35618i | −0.930193 | − | 0.367071i | \(-0.880361\pi\) |
0.147203 | − | 0.989106i | \(-0.452973\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 8.41641 | − | 14.5776i | 0.295540 | − | 0.511890i | −0.679570 | − | 0.733610i | \(-0.737834\pi\) |
0.975110 | + | 0.221720i | \(0.0711671\pi\) | |||||||
\(812\) | −0.354102 | − | 0.613323i | −0.0124265 | − | 0.0215234i | ||||
\(813\) | −0.881966 | − | 1.52761i | −0.0309319 | − | 0.0535756i | ||||
\(814\) | 5.23607 | 0.183524 | ||||||||
\(815\) | −9.38197 | + | 16.2500i | −0.328636 | + | 0.569214i | ||||
\(816\) | −2.85410 | + | 4.94345i | −0.0999136 | + | 0.173055i | ||||
\(817\) | 2.47214 | − | 4.28187i | 0.0864891 | − | 0.149803i | ||||
\(818\) | 5.73607 | + | 9.93516i | 0.200557 | + | 0.347375i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.618034 | + | 1.07047i | 0.0215827 | + | 0.0373823i | ||||
\(821\) | 40.8885 | 1.42702 | 0.713510 | − | 0.700645i | \(-0.247104\pi\) | ||||
0.713510 | + | 0.700645i | \(0.247104\pi\) | |||||||
\(822\) | −0.763932 | −0.0266452 | ||||||||
\(823\) | 12.4098 | + | 21.4945i | 0.432579 | + | 0.749250i | 0.997095 | − | 0.0761731i | \(-0.0242702\pi\) |
−0.564515 | + | 0.825423i | \(0.690937\pi\) | |||||||
\(824\) | −9.35410 | + | 16.2018i | −0.325866 | + | 0.564416i | ||||
\(825\) | 2.11803 | + | 3.66854i | 0.0737405 | + | 0.127722i | ||||
\(826\) | 0.736068 | − | 1.27491i | 0.0256111 | − | 0.0443597i | ||||
\(827\) | 9.41641 | − | 16.3097i | 0.327441 | − | 0.567144i | −0.654563 | − | 0.756008i | \(-0.727147\pi\) |
0.982003 | + | 0.188864i | \(0.0604805\pi\) | |||||||
\(828\) | 0.618034 | − | 1.07047i | 0.0214782 | − | 0.0372013i | ||||
\(829\) | −36.7639 | −1.27686 | −0.638432 | − | 0.769678i | \(-0.720417\pi\) | ||||
−0.638432 | + | 0.769678i | \(0.720417\pi\) | |||||||
\(830\) | 2.35410 | + | 4.07742i | 0.0817121 | + | 0.141529i | ||||
\(831\) | 5.32624 | + | 9.22531i | 0.184765 | + | 0.320023i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.6393 | −1.37342 | ||||||||
\(834\) | −8.56231 | − | 14.8303i | −0.296488 | − | 0.513533i | ||||
\(835\) | −4.29180 | −0.148524 | ||||||||
\(836\) | 13.7082 | 0.474108 | ||||||||
\(837\) | 1.35410 | − | 5.40059i | 0.0468046 | − | 0.186672i | ||||
\(838\) | 0.708204 | 0.0244645 | ||||||||
\(839\) | −17.3475 | −0.598903 | −0.299452 | − | 0.954112i | \(-0.596804\pi\) | ||||
−0.299452 | + | 0.954112i | \(0.596804\pi\) | |||||||
\(840\) | 0.118034 | + | 0.204441i | 0.00407256 | + | 0.00705388i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 14.6180 | − | 25.3192i | 0.503771 | − | 0.872556i | ||||
\(843\) | 0.236068 | + | 0.408882i | 0.00813061 | + | 0.0140826i | ||||
\(844\) | −8.56231 | − | 14.8303i | −0.294727 | − | 0.510482i | ||||
\(845\) | 13.0000 | 0.447214 | ||||||||
\(846\) | −0.381966 | + | 0.661585i | −0.0131323 | + | 0.0227457i | ||||
\(847\) | −0.819660 | + | 1.41969i | −0.0281639 | + | 0.0487812i | ||||
\(848\) | 3.73607 | − | 6.47106i | 0.128297 | − | 0.222217i | ||||
\(849\) | −3.70820 | − | 6.42280i | −0.127265 | − | 0.220430i | ||||
\(850\) | −2.85410 | + | 4.94345i | −0.0978949 | + | 0.169559i | ||||
\(851\) | −0.763932 | − | 1.32317i | −0.0261873 | − | 0.0453577i | ||||
\(852\) | −2.47214 | −0.0846940 | ||||||||
\(853\) | 14.4721 | 0.495516 | 0.247758 | − | 0.968822i | \(-0.420306\pi\) | ||||
0.247758 | + | 0.968822i | \(0.420306\pi\) | |||||||
\(854\) | 1.67376 | + | 2.89904i | 0.0572750 | + | 0.0992031i | ||||
\(855\) | −1.61803 | + | 2.80252i | −0.0553356 | + | 0.0958441i | ||||
\(856\) | 5.35410 | + | 9.27358i | 0.182999 | + | 0.316964i | ||||
\(857\) | −22.0000 | + | 38.1051i | −0.751506 | + | 1.30165i | 0.195587 | + | 0.980686i | \(0.437339\pi\) |
−0.947093 | + | 0.320960i | \(0.895995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.61803 | − | 14.9269i | 0.294044 | − | 0.509298i | −0.680718 | − | 0.732545i | \(-0.738332\pi\) |
0.974762 | + | 0.223247i | \(0.0716656\pi\) | |||||||
\(860\) | −1.52786 | −0.0520997 | ||||||||
\(861\) | −0.145898 | − | 0.252703i | −0.00497219 | − | 0.00861209i | ||||
\(862\) | 10.8541 | + | 18.7999i | 0.369692 | + | 0.640326i | ||||
\(863\) | −22.4721 | + | 38.9229i | −0.764960 | + | 1.32495i | 0.175307 | + | 0.984514i | \(0.443908\pi\) |
−0.940268 | + | 0.340436i | \(0.889425\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.50000 | − | 6.06218i | −0.119004 | − | 0.206120i | ||||
\(866\) | 6.00000 | 0.203888 | ||||||||
\(867\) | 15.5836 | 0.529247 | ||||||||
\(868\) | −1.26393 | + | 0.360620i | −0.0429006 | + | 0.0122402i | ||||
\(869\) | 44.3607 | 1.50483 | ||||||||
\(870\) | −3.00000 | −0.101710 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.23607 | 0.109587 | ||||||||
\(873\) | −0.736068 | + | 1.27491i | −0.0249121 | + | 0.0431491i | ||||
\(874\) | −2.00000 | − | 3.46410i | −0.0676510 | − | 0.117175i | ||||
\(875\) | 0.118034 | + | 0.204441i | 0.00399028 | + | 0.00691136i | ||||
\(876\) | 2.94427 | 0.0994777 | ||||||||
\(877\) | −28.6180 | + | 49.5679i | −0.966362 | + | 1.67379i | −0.260453 | + | 0.965487i | \(0.583872\pi\) |
−0.705909 | + | 0.708302i | \(0.749461\pi\) | |||||||
\(878\) | −10.5902 | + | 18.3427i | −0.357401 | + | 0.619037i | ||||
\(879\) | −1.20820 | + | 2.09267i | −0.0407517 | + | 0.0705840i | ||||
\(880\) | −2.11803 | − | 3.66854i | −0.0713989 | − | 0.123667i | ||||
\(881\) | −4.32624 | + | 7.49326i | −0.145755 | + | 0.252454i | −0.929654 | − | 0.368433i | \(-0.879894\pi\) |
0.783900 | + | 0.620888i | \(0.213228\pi\) | |||||||
\(882\) | 3.47214 | + | 6.01392i | 0.116913 | + | 0.202499i | ||||
\(883\) | 33.2361 | 1.11848 | 0.559241 | − | 0.829005i | \(-0.311093\pi\) | ||||
0.559241 | + | 0.829005i | \(0.311093\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.11803 | − | 5.40059i | −0.104812 | − | 0.181539i | ||||
\(886\) | 16.0000 | − | 27.7128i | 0.537531 | − | 0.931030i | ||||
\(887\) | 22.1246 | + | 38.3210i | 0.742872 | + | 1.28669i | 0.951183 | + | 0.308629i | \(0.0998701\pi\) |
−0.208311 | + | 0.978063i | \(0.566797\pi\) | |||||||
\(888\) | 0.618034 | − | 1.07047i | 0.0207399 | − | 0.0359225i | ||||
\(889\) | 1.08359 | − | 1.87684i | 0.0363425 | − | 0.0629471i | ||||
\(890\) | 5.47214 | − | 9.47802i | 0.183426 | − | 0.317704i | ||||
\(891\) | −4.23607 | −0.141914 | ||||||||
\(892\) | 8.35410 | + | 14.4697i | 0.279716 | + | 0.484482i | ||||
\(893\) | 1.23607 | + | 2.14093i | 0.0413634 | + | 0.0716436i | ||||
\(894\) | 8.73607 | − | 15.1313i | 0.292178 | − | 0.506067i | ||||
\(895\) | 6.23607 | 0.208449 | ||||||||
\(896\) | −0.118034 | − | 0.204441i | −0.00394324 | − | 0.00682989i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.111456 | 0.00371934 | ||||||||
\(899\) | 4.06231 | − | 16.2018i | 0.135485 | − | 0.540360i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −42.6525 | −1.42096 | ||||||||
\(902\) | 2.61803 | + | 4.53457i | 0.0871710 | + | 0.150985i | ||||
\(903\) | 0.360680 | 0.0120027 | ||||||||
\(904\) | 3.70820 | − | 6.42280i | 0.123333 | − | 0.213619i | ||||
\(905\) | 2.70820 | + | 4.69075i | 0.0900237 | + | 0.155926i | ||||
\(906\) | −4.59017 | − | 7.95041i | −0.152498 | − | 0.264135i | ||||
\(907\) | 1.52786 | 0.0507319 | 0.0253659 | − | 0.999678i | \(-0.491925\pi\) | ||||
0.0253659 | + | 0.999678i | \(0.491925\pi\) | |||||||
\(908\) | 4.59017 | − | 7.95041i | 0.152330 | − | 0.263844i | ||||
\(909\) | −0.736068 | + | 1.27491i | −0.0244138 | + | 0.0422860i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.27051 | + | 14.3249i | 0.274014 | + | 0.474607i | 0.969886 | − | 0.243560i | \(-0.0783151\pi\) |
−0.695872 | + | 0.718166i | \(0.744982\pi\) | |||||||
\(912\) | 1.61803 | − | 2.80252i | 0.0535785 | − | 0.0928006i | ||||
\(913\) | 9.97214 | + | 17.2722i | 0.330030 | + | 0.571628i | ||||
\(914\) | 19.8885 | 0.657855 | ||||||||
\(915\) | 14.1803 | 0.468788 | ||||||||
\(916\) | −2.14590 | − | 3.71680i | −0.0709025 | − | 0.122807i | ||||
\(917\) | 1.52786 | − | 2.64634i | 0.0504545 | − | 0.0873898i | ||||
\(918\) | −2.85410 | − | 4.94345i | −0.0941994 | − | 0.163158i | ||||
\(919\) | −1.59017 | + | 2.75426i | −0.0524549 | + | 0.0908545i | −0.891061 | − | 0.453884i | \(-0.850038\pi\) |
0.838606 | + | 0.544739i | \(0.183371\pi\) | |||||||
\(920\) | −0.618034 | + | 1.07047i | −0.0203760 | + | 0.0352922i | ||||
\(921\) | −7.61803 | + | 13.1948i | −0.251023 | + | 0.434784i | ||||
\(922\) | −27.0000 | −0.889198 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.500000 | + | 0.866025i | 0.0164488 | + | 0.0284901i | ||||
\(925\) | 0.618034 | − | 1.07047i | 0.0203208 | − | 0.0351967i | ||||
\(926\) | −14.7082 | −0.483342 | ||||||||
\(927\) | −9.35410 | − | 16.2018i | −0.307229 | − | 0.532136i | ||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | 12.7639 | 0.418771 | 0.209386 | − | 0.977833i | \(-0.432854\pi\) | ||||
0.209386 | + | 0.977833i | \(0.432854\pi\) | |||||||
\(930\) | −1.35410 | + | 5.40059i | −0.0444028 | + | 0.177092i | ||||
\(931\) | 22.4721 | 0.736495 | ||||||||
\(932\) | 1.81966 | 0.0596049 | ||||||||
\(933\) | 0.291796 | + | 0.505406i | 0.00955297 | + | 0.0165462i | ||||
\(934\) | −36.5967 | −1.19748 | ||||||||
\(935\) | −12.0902 | + | 20.9408i | −0.395391 | + | 0.684837i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9443 | + | 48.4009i | 0.912900 | + | 1.58119i | 0.809948 | + | 0.586502i | \(0.199495\pi\) |
0.102952 | + | 0.994686i | \(0.467171\pi\) | |||||||
\(938\) | 1.23607 | 0.0403591 | ||||||||
\(939\) | −9.44427 | + | 16.3580i | −0.308202 | + | 0.533822i | ||||
\(940\) | 0.381966 | − | 0.661585i | 0.0124584 | − | 0.0215785i | ||||
\(941\) | −30.3885 | + | 52.6345i | −0.990638 | + | 1.71584i | −0.377095 | + | 0.926175i | \(0.623077\pi\) |
−0.613543 | + | 0.789661i | \(0.710256\pi\) | |||||||
\(942\) | 11.0902 | + | 19.2087i | 0.361337 | + | 0.625854i | ||||
\(943\) | 0.763932 | − | 1.32317i | 0.0248770 | − | 0.0430883i | ||||
\(944\) | 3.11803 | + | 5.40059i | 0.101483 | + | 0.175774i | ||||
\(945\) | −0.236068 | −0.00767929 | ||||||||
\(946\) | −6.47214 | −0.210427 | ||||||||
\(947\) | 0.763932 | + | 1.32317i | 0.0248245 | + | 0.0429972i | 0.878171 | − | 0.478347i | \(-0.158764\pi\) |
−0.853346 | + | 0.521345i | \(0.825431\pi\) | |||||||
\(948\) | 5.23607 | − | 9.06914i | 0.170060 | − | 0.294552i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.61803 | − | 2.80252i | 0.0524960 | − | 0.0909257i | ||||
\(951\) | −10.4443 | + | 18.0900i | −0.338679 | + | 0.586609i | ||||
\(952\) | −0.673762 | + | 1.16699i | −0.0218368 | + | 0.0378224i | ||||
\(953\) | 47.4853 | 1.53820 | 0.769100 | − | 0.639129i | \(-0.220705\pi\) | ||||
0.769100 | + | 0.639129i | \(0.220705\pi\) | |||||||
\(954\) | 3.73607 | + | 6.47106i | 0.120960 | + | 0.209508i | ||||
\(955\) | 9.85410 | + | 17.0678i | 0.318871 | + | 0.552301i | ||||
\(956\) | 1.70820 | − | 2.95870i | 0.0552473 | − | 0.0956911i | ||||
\(957\) | −12.7082 | −0.410798 | ||||||||
\(958\) | 5.32624 | + | 9.22531i | 0.172083 | + | 0.298056i | ||||
\(959\) | −0.180340 | −0.00582348 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −27.3328 | − | 14.6259i | −0.881704 | − | 0.471803i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.7082 | −0.345067 | ||||||||
\(964\) | −5.50000 | − | 9.52628i | −0.177143 | − | 0.306821i | ||||
\(965\) | 14.4164 | 0.464081 | ||||||||
\(966\) | 0.145898 | − | 0.252703i | 0.00469419 | − | 0.00813058i | ||||
\(967\) | 14.9443 | + | 25.8842i | 0.480575 | + | 0.832381i | 0.999752 | − | 0.0222862i | \(-0.00709451\pi\) |
−0.519176 | + | 0.854667i | \(0.673761\pi\) | |||||||
\(968\) | −3.47214 | − | 6.01392i | −0.111599 | − | 0.193295i | ||||
\(969\) | −18.4721 | −0.593411 | ||||||||
\(970\) | 0.736068 | − | 1.27491i | 0.0236337 | − | 0.0409348i | ||||
\(971\) | −1.06231 | + | 1.83997i | −0.0340910 | + | 0.0590474i | −0.882568 | − | 0.470186i | \(-0.844187\pi\) |
0.848477 | + | 0.529233i | \(0.177520\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −2.02129 | − | 3.50097i | −0.0647995 | − | 0.112236i | ||||
\(974\) | −0.409830 | + | 0.709846i | −0.0131318 | + | 0.0227449i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.1803 | −0.453902 | ||||||||
\(977\) | 38.2492 | 1.22370 | 0.611851 | − | 0.790973i | \(-0.290425\pi\) | ||||
0.611851 | + | 0.790973i | \(0.290425\pi\) | |||||||
\(978\) | 9.38197 | + | 16.2500i | 0.300002 | + | 0.519619i | ||||
\(979\) | 23.1803 | − | 40.1495i | 0.740847 | − | 1.28318i | ||||
\(980\) | −3.47214 | − | 6.01392i | −0.110913 | − | 0.192107i | ||||
\(981\) | −1.61803 | + | 2.80252i | −0.0516598 | + | 0.0894775i | ||||
\(982\) | −14.6459 | + | 25.3674i | −0.467369 | + | 0.809508i | ||||
\(983\) | 17.1803 | − | 29.7572i | 0.547968 | − | 0.949108i | −0.450446 | − | 0.892804i | \(-0.648735\pi\) |
0.998414 | − | 0.0563043i | \(-0.0179317\pi\) | |||||||
\(984\) | 1.23607 | 0.0394044 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | −8.56231 | − | 14.8303i | −0.272679 | − | 0.472295i | ||||
\(987\) | −0.0901699 | + | 0.156179i | −0.00287014 | + | 0.00497123i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.944272 | + | 1.63553i | 0.0300261 | + | 0.0520067i | ||||
\(990\) | 4.23607 | 0.134631 | ||||||||
\(991\) | −7.63932 | −0.242671 | −0.121336 | − | 0.992612i | \(-0.538718\pi\) | ||||
−0.121336 | + | 0.992612i | \(0.538718\pi\) | |||||||
\(992\) | 1.35410 | − | 5.40059i | 0.0429928 | − | 0.171469i | ||||
\(993\) | −17.2361 | −0.546970 | ||||||||
\(994\) | −0.583592 | −0.0185104 | ||||||||
\(995\) | 13.8262 | + | 23.9477i | 0.438321 | + | 0.759195i | ||||
\(996\) | 4.70820 | 0.149185 | ||||||||
\(997\) | 4.03444 | − | 6.98786i | 0.127772 | − | 0.221308i | −0.795041 | − | 0.606556i | \(-0.792551\pi\) |
0.922813 | + | 0.385248i | \(0.125884\pi\) | |||||||
\(998\) | 4.32624 | + | 7.49326i | 0.136945 | + | 0.237195i | ||||
\(999\) | 0.618034 | + | 1.07047i | 0.0195537 | + | 0.0338681i |
(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 | 930.2.i.l.211.1 | ✓ | 4 | |
31.5 | even | 3 | inner | 930.2.i.l.811.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.l.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
930.2.i.l.811.1 | yes | 4 | 31.5 | even | 3 | inner |